LMFDB - Embedded newform 512.2.o.a.141.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

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("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			141.27
Character	$\chi$	$=$	512.141
Dual form			512.2.o.a.69.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.499741 - 1.32297i) q^{2} +(-0.688170 + 2.08312i) q^{3} +(-1.50052 + 1.32229i) q^{4} +(-0.920269 + 2.38571i) q^{5} +(3.09982 - 0.130590i) q^{6} +(0.865414 - 1.44386i) q^{7} +(2.49922 + 1.32434i) q^{8} +(-1.45619 - 1.07999i) q^{9} +O(q^{10})$	\(q+(-0.499741 - 1.32297i) q^{2} +(-0.688170 + 2.08312i) q^{3} +(-1.50052 + 1.32229i) q^{4} +(-0.920269 + 2.38571i) q^{5} +(3.09982 - 0.130590i) q^{6} +(0.865414 - 1.44386i) q^{7} +(2.49922 + 1.32434i) q^{8} +(-1.45619 - 1.07999i) q^{9} +(3.61612 + 0.0252554i) q^{10} +(0.412875 + 3.34750i) q^{11} +(-1.72188 - 4.03572i) q^{12} +(-0.0702522 + 2.86176i) q^{13} +(-2.34267 - 0.423366i) q^{14} +(-4.33642 - 3.55880i) q^{15} +(0.503107 - 3.96823i) q^{16} +(-4.44756 - 5.41937i) q^{17} +(-0.701075 + 2.46622i) q^{18} +(1.05324 + 0.741773i) q^{19} +(-1.77371 - 4.79666i) q^{20} +(2.41217 + 2.79638i) q^{21} +(4.22232 - 2.21911i) q^{22} +(-0.0809892 + 0.171237i) q^{23} +(-4.47866 + 4.29481i) q^{24} +(-1.13995 - 1.03319i) q^{25} +(3.82114 - 1.33720i) q^{26} +(-2.12912 + 1.49949i) q^{27} +(0.610625 + 3.31086i) q^{28} +(-8.54446 + 2.36457i) q^{29} +(-2.54112 + 7.51544i) q^{30} +(-4.46226 + 0.887600i) q^{31} +(-5.50129 + 1.31749i) q^{32} +(-7.25738 - 1.44358i) q^{33} +(-4.94706 + 8.59229i) q^{34} +(2.64820 + 3.39336i) q^{35} +(3.61310 - 0.304969i) q^{36} +(-1.95362 - 8.69985i) q^{37} +(0.455001 - 1.76410i) q^{38} +(-5.91304 - 2.11572i) q^{39} +(-5.45945 + 4.74366i) q^{40} +(-1.15808 + 1.04962i) q^{41} +(2.49407 - 4.58871i) q^{42} +(-0.749639 + 1.48928i) q^{43} +(-5.04589 - 4.47705i) q^{44} +(3.91662 - 2.48017i) q^{45} +(0.267016 + 0.0215723i) q^{46} +(7.25384 + 3.87726i) q^{47} +(7.92009 + 3.77885i) q^{48} +(1.96400 + 3.67438i) q^{49} +(-0.797201 + 2.02444i) q^{50} +(14.3499 - 5.53536i) q^{51} +(-3.67865 - 4.38701i) q^{52} +(-0.00441413 - 0.00122155i) q^{53} +(3.04780 + 2.06741i) q^{54} +(-8.36611 - 2.09560i) q^{55} +(4.07502 - 2.46241i) q^{56} +(-2.27001 + 1.68356i) q^{57} +(7.39828 + 10.1224i) q^{58} +(3.24920 - 0.0797633i) q^{59} +(11.2126 - 0.393943i) q^{60} +(-9.03309 - 7.79199i) q^{61} +(3.40425 + 5.45989i) q^{62} +(-2.81956 + 1.16790i) q^{63} +(4.49223 + 6.61966i) q^{64} +(-6.76266 - 2.80119i) q^{65} +(1.71699 + 10.3227i) q^{66} +(10.4913 - 0.773888i) q^{67} +(13.8396 + 2.25090i) q^{68} +(-0.300974 - 0.286551i) q^{69} +(3.16591 - 5.19930i) q^{70} +(-0.433135 + 2.91996i) q^{71} +(-2.20908 - 4.62763i) q^{72} +(-3.42024 - 5.70633i) q^{73} +(-10.5334 + 6.93225i) q^{74} +(2.93673 - 1.66364i) q^{75} +(-2.56124 + 0.279639i) q^{76} +(5.19062 + 2.30084i) q^{77} +(0.155948 + 8.88011i) q^{78} +(14.1948 + 4.30595i) q^{79} +(9.00405 + 4.85211i) q^{80} +(-3.23727 - 10.6718i) q^{81} +(1.96737 + 1.00757i) q^{82} +(-2.07044 + 9.22008i) q^{83} +(-7.31713 - 1.00643i) q^{84} +(17.0220 - 5.62330i) q^{85} +(2.34490 + 0.247500i) q^{86} +(0.954357 - 19.4264i) q^{87} +(-3.40138 + 8.91294i) q^{88} +(-0.747215 - 1.57985i) q^{89} +(-5.23850 - 3.94214i) q^{90} +(4.07117 + 2.57804i) q^{91} +(-0.104899 - 0.364036i) q^{92} +(1.22182 - 9.90626i) q^{93} +(1.50447 - 11.5343i) q^{94} +(-2.73892 + 1.83008i) q^{95} +(1.04133 - 12.3665i) q^{96} +(9.50261 + 6.34944i) q^{97} +(3.87962 - 4.43456i) q^{98} +(3.01403 - 5.32051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{79}{128}\right)$	$1$

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 $

$2$	−0.499741	−	1.32297i	−0.353370	−	0.935484i
$2$	−0.499741	−	1.32297i	−0.353370	−	0.935484i
$3$	−0.688170	+	2.08312i	−0.397315	+	1.20269i	0.536181	+	0.844103i	$0.319867\pi$
$3$	−0.688170	+	2.08312i	−0.397315	+	1.20269i	−0.933496	+	0.358588i	$0.883258\pi$
$4$	−1.50052	+	1.32229i	−0.750259	+	0.661144i
$5$	−0.920269	+	2.38571i	−0.411557	+	1.06692i	0.559660	+	0.828722i	$0.310932\pi$
$5$	−0.920269	+	2.38571i	−0.411557	+	1.06692i	−0.971217	+	0.238198i	$0.923443\pi$
$6$	3.09982	−	0.130590i	1.26550	−	0.0533132i
$7$	0.865414	−	1.44386i	0.327096	−	0.545726i	−0.649621	−	0.760258i	$-0.725073\pi$
$7$	0.865414	−	1.44386i	0.327096	−	0.545726i	0.976717	+	0.214532i	$0.0688226\pi$
$8$	2.49922	+	1.32434i	0.883609	+	0.468226i
$9$	−1.45619	−	1.07999i	−0.485398	−	0.359996i
$10$	3.61612	+	0.0252554i	1.14352	+	0.00798647i
$11$	0.412875	+	3.34750i	0.124486	+	1.00931i	0.916842	+	0.399250i	$0.130729\pi$
$11$	0.412875	+	3.34750i	0.124486	+	1.00931i	−0.792356	+	0.610060i	$0.791146\pi$
$12$	−1.72188	−	4.03572i	−0.497063	−	1.16501i
$13$	−0.0702522	+	2.86176i	−0.0194845	+	0.793709i	0.907811	+	0.419379i	$0.137752\pi$
$13$	−0.0702522	+	2.86176i	−0.0194845	+	0.793709i	−0.927296	+	0.374330i	$0.877873\pi$
$14$	−2.34267	−	0.423366i	−0.626104	−	0.113149i
$15$	−4.33642	−	3.55880i	−1.11966	−	0.918879i
$16$	0.503107	−	3.96823i	0.125777	−	0.992059i
$17$	−4.44756	−	5.41937i	−1.07869	−	1.31439i	−0.946335	−	0.323189i	$-0.895245\pi$
$17$	−4.44756	−	5.41937i	−1.07869	−	1.31439i	−0.132358	−	0.991202i	$-0.542255\pi$
$18$	−0.701075	+	2.46622i	−0.165245	+	0.581294i
$19$	1.05324	+	0.741773i	0.241629	+	0.170175i	0.690301	−	0.723522i	$-0.257478\pi$
$19$	1.05324	+	0.741773i	0.241629	+	0.170175i	−0.448672	+	0.893696i	$0.648103\pi$
$20$	−1.77371	−	4.79666i	−0.396614	−	1.07256i
$21$	2.41217	+	2.79638i	0.526380	+	0.610220i
$22$	4.22232	−	2.21911i	0.900203	−	0.473115i
$23$	−0.0809892	+	0.171237i	−0.0168874	+	0.0357054i	−0.912257	−	0.409619i	$-0.865662\pi$
$23$	−0.0809892	+	0.171237i	−0.0168874	+	0.0357054i	0.895369	+	0.445324i	$0.146912\pi$
$24$	−4.47866	+	4.29481i	−0.914203	+	0.876675i
$25$	−1.13995	−	1.03319i	−0.227989	−	0.206637i
$26$	3.82114	−	1.33720i	0.749387	−	0.262246i
$27$	−2.12912	+	1.49949i	−0.409749	+	0.288578i
$28$	0.610625	+	3.31086i	0.115397	+	0.625693i
$29$	−8.54446	+	2.36457i	−1.58667	+	0.439090i	−0.944779	−	0.327709i	$-0.893724\pi$
$29$	−8.54446	+	2.36457i	−1.58667	+	0.439090i	−0.641888	+	0.766798i	$0.721849\pi$
$30$	−2.54112	+	7.51544i	−0.463943	+	1.37213i
$31$	−4.46226	+	0.887600i	−0.801446	+	0.159418i	−0.578787	−	0.815479i	$-0.696474\pi$
$31$	−4.46226	+	0.887600i	−0.801446	+	0.159418i	−0.222659	+	0.974896i	$0.571474\pi$
$32$	−5.50129	+	1.31749i	−0.972500	+	0.232902i
$33$	−7.25738	−	1.44358i	−1.26335	−	0.251295i
$34$	−4.94706	+	8.59229i	−0.848413	+	1.47357i
$35$	2.64820	+	3.39336i	0.447628	+	0.573582i
$36$	3.61310	−	0.304969i	0.602183	−	0.0508281i
$37$	−1.95362	−	8.69985i	−0.321172	−	1.43025i	−0.824359	−	0.566068i	$-0.808464\pi$
$37$	−1.95362	−	8.69985i	−0.321172	−	1.43025i	0.503186	−	0.864178i	$-0.332161\pi$
$38$	0.455001	−	1.76410i	0.0738109	−	0.286175i
$39$	−5.91304	−	2.11572i	−0.946845	−	0.338786i
$40$	−5.45945	+	4.74366i	−0.863215	+	0.750039i
$41$	−1.15808	+	1.04962i	−0.180862	+	0.163924i	−0.756970	−	0.653450i	$-0.773321\pi$
$41$	−1.15808	+	1.04962i	−0.180862	+	0.163924i	0.576108	+	0.817374i	$0.304571\pi$
$42$	2.49407	−	4.58871i	0.384844	−	0.708053i
$43$	−0.749639	+	1.48928i	−0.114319	+	0.227112i	−0.943136	−	0.332407i	$-0.892139\pi$
$43$	−0.749639	+	1.48928i	−0.114319	+	0.227112i	0.828817	+	0.559519i	$0.189014\pi$
$44$	−5.04589	−	4.47705i	−0.760696	−	0.674940i
$45$	3.91662	−	2.48017i	0.583856	−	0.369723i
$46$	0.267016	+	0.0215723i	0.0393694	+	0.00318066i
$47$	7.25384	+	3.87726i	1.05808	+	0.565556i	0.906203	−	0.422843i	$-0.138968\pi$
$47$	7.25384	+	3.87726i	1.05808	+	0.565556i	0.151878	+	0.988399i	$0.451468\pi$
$48$	7.92009	+	3.77885i	1.14317	+	0.545431i
$49$	1.96400	+	3.67438i	0.280571	+	0.524912i
$50$	−0.797201	+	2.02444i	−0.112741	+	0.286300i
$51$	14.3499	−	5.53536i	2.00939	−	0.775106i
$52$	−3.67865	−	4.38701i	−0.510138	−	0.608369i
$53$	−0.00441413	−	0.00122155i	−0.000606327	−	0.000167793i	0.266410	−	0.963860i	$-0.414163\pi$
$53$	−0.00441413	−	0.00122155i	−0.000606327	−	0.000167793i	−0.267016	+	0.963692i	$0.586038\pi$
$54$	3.04780	+	2.06741i	0.414753	+	0.281339i
$55$	−8.36611	−	2.09560i	−1.12809	−	0.282571i
$56$	4.07502	−	2.46241i	0.544548	−	0.329054i
$57$	−2.27001	+	1.68356i	−0.300670	+	0.222992i
$58$	7.39828	+	10.1224i	0.971442	+	1.32914i
$59$	3.24920	−	0.0797633i	0.423010	−	0.0103843i	0.187519	−	0.982261i	$-0.439955\pi$
$59$	3.24920	−	0.0797633i	0.423010	−	0.0103843i	0.235490	+	0.971877i	$0.424330\pi$
$60$	11.2126	−	0.393943i	1.44754	−	0.0508578i
$61$	−9.03309	−	7.79199i	−1.15657	−	0.997663i	−0.999950	−	0.0100033i	$-0.996816\pi$
$61$	−9.03309	−	7.79199i	−1.15657	−	0.997663i	−0.156618	−	0.987659i	$-0.550059\pi$
$62$	3.40425	+	5.45989i	0.432340	+	0.693406i
$63$	−2.81956	+	1.16790i	−0.355231	+	0.147141i
$64$	4.49223	+	6.61966i	0.561529	+	0.827457i
$65$	−6.76266	−	2.80119i	−0.838805	−	0.347444i
$66$	1.71699	+	10.3227i	0.211347	+	1.27064i
$67$	10.4913	−	0.773888i	1.28172	−	0.0945455i	0.584496	−	0.811397i	$-0.301292\pi$
$67$	10.4913	−	0.773888i	1.28172	−	0.0945455i	0.697226	+	0.716851i	$0.254417\pi$
$68$	13.8396	+	2.25090i	1.67830	+	0.272962i
$69$	−0.300974	−	0.286551i	−0.0362330	−	0.0344967i
$70$	3.16591	−	5.19930i	0.378398	−	0.621435i
$71$	−0.433135	+	2.91996i	−0.0514036	+	0.346535i	0.948181	+	0.317729i	$0.102920\pi$
$71$	−0.433135	+	2.91996i	−0.0514036	+	0.346535i	−0.999585	+	0.0288056i	$0.990830\pi$
$72$	−2.20908	−	4.62763i	−0.260343	−	0.545372i
$73$	−3.42024	−	5.70633i	−0.400309	−	0.667876i	0.589898	−	0.807477i	$-0.299168\pi$
$73$	−3.42024	−	5.70633i	−0.400309	−	0.667876i	−0.990208	+	0.139602i	$0.955418\pi$
$74$	−10.5334	+	6.93225i	−1.22448	+	0.805858i
$75$	2.93673	−	1.66364i	0.339105	−	0.192100i
$76$	−2.56124	+	0.279639i	−0.293794	+	0.0320768i
$77$	5.19062	+	2.30084i	0.591526	+	0.262205i
$78$	0.155948	+	8.88011i	0.0176576	+	1.00547i
$79$	14.1948	+	4.30595i	1.59704	+	0.484458i	0.958491	−	0.285121i	$-0.0920339\pi$
$79$	14.1948	+	4.30595i	1.59704	+	0.484458i	0.638552	+	0.769579i	$0.279534\pi$
$80$	9.00405	+	4.85211i	1.00668	+	0.542482i
$81$	−3.23727	−	10.6718i	−0.359696	−	1.18576i
$82$	1.96737	+	1.00757i	0.217259	+	0.111268i
$83$	−2.07044	+	9.22008i	−0.227260	+	1.01204i	0.720601	+	0.693350i	$0.243866\pi$
$83$	−2.07044	+	9.22008i	−0.227260	+	1.01204i	−0.947861	+	0.318685i	$0.896759\pi$
$84$	−7.31713	−	1.00643i	−0.798365	−	0.109810i
$85$	17.0220	−	5.62330i	1.84629	−	0.609933i
$86$	2.34490	+	0.247500i	0.252857	+	0.0266886i
$87$	0.954357	−	19.4264i	0.102318	−	2.08273i
$88$	−3.40138	+	8.91294i	−0.362588	+	0.950123i
$89$	−0.747215	−	1.57985i	−0.0792046	−	0.167464i	0.860501	−	0.509449i	$-0.170151\pi$
$89$	−0.747215	−	1.57985i	−0.0792046	−	0.167464i	−0.939705	+	0.341985i	$0.888901\pi$
$90$	−5.23850	−	3.94214i	−0.552187	−	0.415538i
$91$	4.07117	+	2.57804i	0.426774	+	0.270252i
$92$	−0.104899	−	0.364036i	−0.0109365	−	0.0379533i
$93$	1.22182	−	9.90626i	0.126697	−	1.02723i
$94$	1.50447	−	11.5343i	0.155174	−	1.18967i
$95$	−2.73892	+	1.83008i	−0.281007	+	0.187763i
$96$	1.04133	−	12.3665i	0.106280	−	1.26215i
$97$	9.50261	+	6.34944i	0.964844	+	0.644688i	0.934918	−	0.354864i	$-0.115473\pi$
$97$	9.50261	+	6.34944i	0.964844	+	0.644688i	0.0299262	+	0.999552i	$0.490473\pi$
$98$	3.87962	−	4.43456i	0.391901	−	0.447958i
$99$	3.01403	−	5.32051i	0.302922	−	0.534732i
$100$	3.07668	+	0.0429779i	0.307668	+	0.00429779i
$101$	−12.8586	−	2.23117i	−1.27948	−	0.222010i	−0.509715	−	0.860343i	$-0.670249\pi$
$101$	−12.8586	−	2.23117i	−1.27948	−	0.222010i	−0.769760	+	0.638333i	$0.779624\pi$
$102$	−14.4944	−	16.2183i	−1.43516	−	1.60585i
$103$	−11.9207	+	0.585626i	−1.17458	+	0.0577035i	−0.626979	−	0.779036i	$-0.715709\pi$
$103$	−11.9207	+	0.585626i	−1.17458	+	0.0577035i	−0.547602	+	0.836739i	$0.684459\pi$
$104$	−3.96553	+	7.05913i	−0.388852	+	0.692205i
$105$	−8.89119	+	3.18132i	−0.867692	+	0.310465i
$106$	0.000589838		0.00645023i	5.72901e−5		0.000626502i
$107$	−3.99226	−	0.294487i	−0.385946	−	0.0284691i	−0.120799	−	0.992677i	$-0.538546\pi$
$107$	−3.99226	−	0.294487i	−0.385946	−	0.0284691i	−0.265147	+	0.964208i	$0.585421\pi$
$108$	1.21202	−	5.06533i	0.116626	−	0.487411i
$109$	0.457077	+	2.63420i	0.0437800	+	0.252311i	0.999058	−	0.0433994i	$-0.0138188\pi$
$109$	0.457077	+	2.63420i	0.0437800	+	0.252311i	−0.955278	+	0.295710i	$0.904444\pi$
$110$	1.40846	+	12.1154i	0.134292	+	1.15516i
$111$	19.4673	+	1.91736i	1.84775	+	0.181988i
$112$	−5.29416	−	4.16058i	−0.500251	−	0.393138i
$113$	1.59391	+	16.1833i	0.149943	+	1.52239i	0.716042	+	0.698057i	$0.245952\pi$
$113$	1.59391	+	16.1833i	0.149943	+	1.52239i	−0.566099	+	0.824337i	$0.691548\pi$
$114$	3.36172	+	2.16182i	0.314854	+	0.202473i
$115$	−0.333990	−	0.350801i	−0.0311447	−	0.0327123i
$116$	9.69447	−	14.8463i	0.900109	−	1.37845i
$117$	3.19296	−	4.09140i	0.295190	−	0.378250i
$118$	−1.72928	−	4.25874i	−0.159193	−	0.392049i
$119$	−11.6738	+	1.73164i	−1.07013	+	0.158739i
$120$	−6.12459	−	14.6371i	−0.559096	−	1.33618i
$121$	−0.364955	+	0.0914164i	−0.0331777	+	0.00831058i
$122$	−5.79440	+	15.8445i	−0.524600	+	1.43449i
$123$	−1.38954	−	3.13475i	−0.125290	−	0.282651i
$124$	5.52204	−	7.23226i	0.495894	−	0.649476i
$125$	−7.90615	+	3.97962i	−0.707147	+	0.355948i
$126$	2.95415	+	3.14655i	0.263176	+	0.280317i
$127$	2.85656	−	2.85656i	0.253479	−	0.253479i	−0.568917	−	0.822395i	$-0.692637\pi$
$127$	2.85656	−	2.85656i	0.253479	−	0.253479i	0.822395	+	0.568917i	$0.192637\pi$
$128$	6.51268	−	9.25121i	0.575645	−	0.817700i
$129$	−2.58646	−	2.58646i	−0.227725	−	0.227725i
$130$	−0.326316	+	10.3467i	−0.0286198	+	0.907465i
$131$	6.59215	+	13.0964i	0.575959	+	1.14423i	0.973933	+	0.226837i	$0.0728385\pi$
$131$	6.59215	+	13.0964i	0.575959	+	1.14423i	−0.397974	+	0.917397i	$0.630287\pi$
$132$	12.7987	−	7.43023i	1.11398	−	0.646718i
$133$	1.98250	−	0.878782i	0.171905	−	0.0762000i
$134$	−6.26679	−	13.4930i	−0.541368	−	1.16562i
$135$	−1.61799	−	6.45939i	−0.139255	−	0.555936i
$136$	−3.93834	−	19.4343i	−0.337710	−	1.66648i
$137$	2.03863	+	13.7433i	0.174172	+	1.17417i	0.883201	+	0.468994i	$0.155384\pi$
$137$	2.03863	+	13.7433i	0.174172	+	1.17417i	−0.709029	+	0.705179i	$0.750866\pi$
$138$	−0.228690	+	0.541381i	−0.0194674	+	0.0460854i
$139$	−3.03422	−	2.36793i	−0.257359	−	0.200845i	0.478301	−	0.878196i	$-0.341253\pi$
$139$	−3.03422	−	2.36793i	−0.257359	−	0.200845i	−0.735660	+	0.677351i	$0.763128\pi$
$140$	−8.46067	−	1.59011i	−0.715057	−	0.134389i
$141$	−13.0687	+	12.4424i	−1.10058	+	1.04784i
$142$	4.07948	−	0.886196i	0.342342	−	0.0743680i
$143$	−9.60874	+	0.946379i	−0.803523	+	0.0791401i
$144$	−5.01827	+	5.23517i	−0.418189	+	0.436264i
$145$	2.22203	−	22.5606i	0.184529	−	1.87356i
$146$	−5.84009	+	7.37658i	−0.483329	+	0.610490i
$147$	−9.00576	+	1.56265i	−0.742782	+	0.128885i
$148$	14.4351	+	10.4710i	1.18656	+	0.860713i
$149$	−0.925367	+	12.5449i	−0.0758090	+	1.02772i	0.816810	+	0.576906i	$0.195740\pi$
$149$	−0.925367	+	12.5449i	−0.0758090	+	1.02772i	−0.892619	+	0.450811i	$0.851135\pi$
$150$	−3.66855	−	3.05383i	−0.299536	−	0.249344i
$151$	0.0472423	+	0.132033i	0.00384452	+	0.0107447i	0.943451	−	0.331512i	$-0.107559\pi$
$151$	0.0472423	+	0.132033i	0.00384452	+	0.0107447i	−0.939606	+	0.342257i	$0.888809\pi$
$152$	1.64991	+	3.24871i	0.133826	+	0.263505i
$153$	0.623664	+	12.6950i	0.0504202	+	1.02633i
$154$	0.449989	−	8.01687i	0.0362611	−	0.646018i
$155$	1.98893	−	11.4625i	0.159755	−	0.920689i
$156$	11.6702	−	4.64407i	0.934365	−	0.371823i
$157$	−6.13509	−	3.47549i	−0.489633	−	0.277374i	0.228168	−	0.973622i	$-0.426726\pi$
$157$	−6.13509	−	3.47549i	−0.489633	−	0.277374i	−0.717801	+	0.696248i	$0.754851\pi$
$158$	−1.39708	−	20.9312i	−0.111145	−	1.66520i
$159$	0.00558232	−	0.00835453i	0.000442706	−	0.000662557i
$160$	1.91952	−	14.3369i	0.151751	−	1.13343i
$161$	0.177153	+	0.265128i	0.0139616	+	0.0208950i
$162$	−12.5008	+	9.61598i	−0.982153	+	0.755503i
$163$	19.7139	+	2.43148i	1.54411	+	0.190448i	0.848976	−	0.528431i	$-0.177220\pi$
$163$	19.7139	+	2.43148i	1.54411	+	0.190448i	0.695135	+	0.718879i	$0.255345\pi$
$164$	0.349817	−	3.10630i	0.0273161	−	0.242561i
$165$	10.1227	−	15.9855i	0.788051	−	1.24447i
$166$	13.2326	−	1.86852i	1.02705	−	0.145025i
$167$	6.27953	−	2.97000i	0.485925	−	0.229825i	−0.168861	−	0.985640i	$-0.554009\pi$
$167$	6.27953	−	2.97000i	0.485925	−	0.229825i	0.654786	+	0.755815i	$0.272759\pi$
$168$	2.32519	+	10.1833i	0.179393	+	0.785661i
$169$	4.79962	+	0.235790i	0.369201	+	0.0181377i
$170$	−15.9461	−	19.7094i	−1.22301	−	1.51164i
$171$	−0.732613	−	2.21765i	−0.0560243	−	0.169588i
$172$	−0.844406	−	3.22592i	−0.0643854	−	0.245974i
$173$	9.72247	+	2.18325i	0.739186	+	0.165990i	0.572367	−	0.819998i	$-0.306025\pi$
$173$	9.72247	+	2.18325i	0.739186	+	0.165990i	0.166819	+	0.985987i	$0.446650\pi$
$174$	−26.1775	+	8.44557i	−1.98451	+	0.640257i
$175$	−2.47830	+	0.751784i	−0.187342	+	0.0568295i
$176$	13.4914	+	0.0457674i	1.01695	+	0.00344984i
$177$	−2.06985	+	6.82336i	−0.155579	+	0.512875i
$178$	−1.71669	+	1.77806i	−0.128671	+	0.133271i
$179$	−6.44656	+	14.5432i	−0.481838	+	1.08701i	0.494187	+	0.869355i	$0.335466\pi$
$179$	−6.44656	+	14.5432i	−0.481838	+	1.08701i	−0.976026	+	0.217655i	$0.930159\pi$
$180$	−2.59746	+	8.90045i	−0.193603	+	0.663400i
$181$	6.01150	+	10.6118i	0.446831	+	0.788768i	0.998988	−	0.0449725i	$-0.0143200\pi$
$181$	6.01150	+	10.6118i	0.446831	+	0.788768i	−0.552157	+	0.833740i	$0.686195\pi$
$182$	1.37615	−	6.67440i	0.102007	−	0.494739i
$183$	22.4480	−	13.4548i	1.65940	−	0.994607i
$184$	−0.429187	+	0.320703i	−0.0316401	+	0.0236425i
$185$	22.5531	+	3.34544i	1.65814	+	0.245962i
$186$	−13.7163	+	3.33413i	−1.00573	+	0.244470i
$187$	16.3051	−	17.1257i	1.19234	−	1.25236i
$188$	−16.0114	+	3.77377i	−1.16775	+	0.275231i
$189$	0.322485	+	4.37182i	0.0234573	+	0.318003i
$190$	3.78990	+	2.70894i	0.274948	+	0.196527i
$191$	−4.58832	+	11.0772i	−0.331999	+	0.801517i	0.666434	+	0.745564i	$0.267820\pi$
$191$	−4.58832	+	11.0772i	−0.331999	+	0.801517i	−0.998433	+	0.0559532i	$0.982180\pi$
$192$	−16.8810	+	4.80241i	−1.21828	+	0.346584i
$193$	8.49591	+	20.5109i	0.611549	+	1.47641i	0.861298	+	0.508099i	$0.169652\pi$
$193$	8.49591	+	20.5109i	0.611549	+	1.47641i	−0.249749	+	0.968311i	$0.580348\pi$
$194$	3.65130	−	15.7448i	0.262148	−	1.13041i
$195$	10.4891	−	12.1598i	0.751138	−	0.870778i
$196$	−7.80561	−	2.91651i	−0.557544	−	0.208322i
$197$	−0.517526	−	21.0817i	−0.0368722	−	1.50201i	−0.678278	−	0.734805i	$-0.737274\pi$
$197$	−0.517526	−	21.0817i	−0.0368722	−	1.50201i	0.641406	−	0.767201i	$-0.278351\pi$
$198$	−8.54513	−	1.32861i	−0.607276	−	0.0944200i
$199$	−16.3421	−	22.0348i	−1.15846	−	1.56200i	−0.766791	−	0.641897i	$-0.778148\pi$
$199$	−16.3421	−	22.0348i	−1.15846	−	1.56200i	−0.391670	−	0.920106i	$-0.628102\pi$
$200$	−1.48069	−	4.09185i	−0.104700	−	0.289337i
$201$	−5.60773	+	22.3873i	−0.395539	+	1.57908i
$202$	3.47417	+	18.1266i	0.244442	+	1.27538i
$203$	−3.98040	+	14.3833i	−0.279369	+	1.00951i
$204$	−14.2129	+	27.2806i	−0.995103	+	1.91002i
$205$	−1.43835	−	3.72878i	−0.100459	−	0.260429i
$206$	6.73203	+	15.4781i	0.469043	+	1.07841i
$207$	0.302870	−	0.161887i	0.0210509	−	0.0112520i
$208$	11.3208	+	1.71855i	0.784955	+	0.119160i
$209$	−2.04823	+	3.83197i	−0.141679	+	0.265063i
$210$	8.65210	+	10.1730i	0.597051	+	0.702002i
$211$	−4.31730	−	6.81777i	−0.297215	−	0.469355i	0.662998	−	0.748621i	$-0.269284\pi$
$211$	−4.31730	−	6.81777i	−0.297215	−	0.469355i	−0.960214	+	0.279267i	$0.909909\pi$
$212$	0.00823872	−	0.00400379i	0.000565838	−	0.000274981i
$213$	−5.78455	−	2.91170i	−0.396351	−	0.199506i
$214$	1.60550	+	5.42882i	0.109750	+	0.371106i
$215$	−2.86311	−	3.15895i	−0.195262	−	0.215439i
$216$	−7.30699	+	0.927886i	−0.497177	+	0.0631347i
$217$	−2.58014	+	7.21101i	−0.175151	+	0.489515i
$218$	3.25656	−	1.92112i	0.220562	−	0.130115i
$219$	14.2407	−	3.19785i	0.962297	−	0.216091i
$220$	15.3245	−	7.91792i	1.03318	−	0.533826i
$221$	15.8214	−	12.3471i	1.06426	−	0.830558i
$222$	−7.19197	−	26.7128i	−0.482694	−	1.79285i
$223$	0.544705	−	2.73842i	0.0364761	−	0.183378i	−0.958252	−	0.285925i	$-0.907699\pi$
$223$	0.544705	−	2.73842i	0.0364761	−	0.183378i	0.994728	+	0.102547i	$0.0326992\pi$
$224$	−2.85863	+	9.08325i	−0.191000	+	0.606900i
$225$	0.544154	+	2.73565i	0.0362770	+	0.182377i
$226$	20.6135	−	10.1962i	1.37119	−	0.678238i
$227$	0.616709	+	2.22850i	0.0409324	+	0.147911i	0.981401	−	0.191971i	$-0.0614879\pi$
$227$	0.616709	+	2.22850i	0.0409324	+	0.147911i	−0.940468	+	0.339882i	$0.889613\pi$
$228$	1.18005	−	5.52781i	0.0781505	−	0.366088i
$229$	7.41364	+	10.5266i	0.489907	+	0.695615i	0.984869	−	0.173300i	$-0.0554429\pi$
$229$	7.41364	+	10.5266i	0.489907	+	0.695615i	−0.494962	+	0.868915i	$0.664818\pi$
$230$	−0.297191	+	0.617169i	−0.0195962	+	0.0406949i
$231$	−8.36496	+	9.22931i	−0.550374	+	0.607244i
$232$	−24.4860	−	5.40621i	−1.60759	−	0.354935i
$233$	−11.3917	−	5.38788i	−0.746297	−	0.352972i	0.0162821	−	0.999867i	$-0.494817\pi$
$233$	−11.3917	−	5.38788i	−0.746297	−	0.352972i	−0.762579	+	0.646895i	$0.776067\pi$
$234$	−7.00847	−	2.17956i	−0.458158	−	0.142483i
$235$	−15.9255	+	13.7374i	−1.03886	+	0.896130i
$236$	−4.77001	+	4.41606i	−0.310501	+	0.287461i
$237$	−18.7383	+	26.6063i	−1.21718	+	1.72827i
$238$	8.12478	+	14.5787i	0.526651	+	0.944998i
$239$	1.26246	−	1.03607i	0.0816617	−	0.0670180i	−0.592677	−	0.805440i	$-0.701929\pi$
$239$	1.26246	−	1.03607i	0.0816617	−	0.0670180i	0.674339	+	0.738422i	$0.264429\pi$
$240$	−16.3039	+	15.4175i	−1.05241	+	0.995192i
$241$	−13.7569	+	16.7628i	−0.886157	+	1.07979i	0.110149	+	0.993915i	$0.464867\pi$
$241$	−13.7569	+	16.7628i	−0.886157	+	1.07979i	−0.996306	+	0.0858706i	$0.972633\pi$
$242$	0.303324	+	0.437141i	0.0194984	+	0.0281005i
$243$	16.6484	+	0.408696i	1.06800	+	0.0262179i
$244$	23.8576	−	0.252320i	1.52732	−	0.0161531i
$245$	−10.5734	+	1.30411i	−0.675510	+	0.0833163i
$246$	−3.45278	+	3.40488i	−0.220141	+	0.217087i
$247$	−2.19677	+	2.96200i	−0.139777	+	0.188467i
$248$	−12.3277	−	3.69126i	−0.782808	−	0.234395i
$249$	−17.7817	−	10.6580i	−1.12687	−	0.675421i
$250$	9.21596	+	8.47084i	0.582868	+	0.535743i
$251$	−3.08834	−	1.19131i	−0.194935	−	0.0751946i	0.260459	−	0.965485i	$-0.416126\pi$
$251$	−3.08834	−	1.19131i	−0.194935	−	0.0751946i	−0.455393	+	0.890290i	$0.650501\pi$
$252$	2.68650	−	5.48072i	0.169233	−	0.345253i
$253$	−0.606655	−	0.200412i	−0.0381401	−	0.0125998i
$254$	−5.20669	−	2.35161i	−0.326697	−	0.147553i
$255$			39.3287i			2.46286i
$256$	−15.4938	−	3.99289i	−0.968360	−	0.249556i
$257$			2.98801i			0.186387i	0.995648	+	0.0931936i	$0.0297075\pi$
$257$			2.98801i			0.186387i	−0.995648	+	0.0931936i	$0.970292\pi$
$258$	−2.12926	+	4.71439i	−0.132562	+	0.293505i
$259$	−14.2520	−	4.70823i	−0.885577	−	0.292555i
$260$	13.8515	−	4.73896i	0.859032	−	0.293898i
$261$	14.9961	+	5.78464i	0.928236	+	0.358060i
$262$	14.0318	−	15.2660i	0.866885	−	0.943138i
$263$	17.8609	+	10.7054i	1.10135	+	0.660123i	0.944833	−	0.327552i	$-0.106224\pi$
$263$	17.8609	+	10.7054i	1.10135	+	0.660123i	0.156516	+	0.987675i	$0.449974\pi$
$264$	−16.2260	−	13.2191i	−0.998642	−	0.813579i
$265$	0.00697645	−	0.00940665i	0.000428560	−	0.000577846i
$266$	−2.15334	−	2.18363i	−0.132030	−	0.133887i
$267$	3.80524	−	0.469331i	0.232877	−	0.0287226i
$268$	−14.7191	+	15.0338i	−0.899115	+	0.918336i
$269$	3.45367	+	0.0847827i	0.210574	+	0.00516929i	0.129692	−	0.991554i	$-0.458601\pi$
$269$	3.45367	+	0.0847827i	0.210574	+	0.00516929i	0.0808821	+	0.996724i	$0.474226\pi$
$270$	−7.73702	+	5.36858i	−0.470860	+	0.326722i
$271$	−10.5451	+	12.8493i	−0.640570	+	0.780537i	−0.987545	−	0.157338i	$-0.949709\pi$
$271$	−10.5451	+	12.8493i	−0.640570	+	0.780537i	0.346975	+	0.937874i	$0.387209\pi$
$272$	−23.7429	+	14.9224i	−1.43963	+	0.904806i
$273$	−8.17202	+	6.70661i	−0.494593	+	0.405902i
$274$	17.1633	−	9.56517i	1.03687	−	0.577853i
$275$	2.98794	−	4.24255i	0.180180	−	0.255835i
$276$	0.830519	+	0.0320005i	0.0499914	+	0.00192621i
$277$	22.7778	−	19.6483i	1.36859	−	1.18055i	0.404633	−	0.914479i	$-0.367399\pi$
$277$	22.7778	−	19.6483i	1.36859	−	1.18055i	0.963953	−	0.266071i	$-0.0857257\pi$
$278$	−1.61638	+	5.19754i	−0.0969441	+	0.311728i
$279$	7.45652	+	3.52667i	0.446410	+	0.211136i
$280$	2.12448	+	11.9879i	0.126962	+	0.716413i
$281$	11.4583	−	12.6423i	0.683546	−	0.754177i	−0.296046	−	0.955174i	$-0.595668\pi$
$281$	11.4583	−	12.6423i	0.683546	−	0.754177i	0.979592	+	0.200997i	$0.0644181\pi$
$282$	22.9919	+	11.0715i	1.36915	+	0.659300i
$283$	−5.74262	−	8.15390i	−0.341363	−	0.484699i	0.610159	−	0.792279i	$-0.291106\pi$
$283$	−5.74262	−	8.15390i	−0.341363	−	0.484699i	−0.951522	+	0.307580i	$0.900481\pi$
$284$	−3.21110	−	4.95418i	−0.190544	−	0.293976i
$285$	−1.92745	−	6.96490i	−0.114172	−	0.412565i
$286$	6.05392	+	12.2392i	0.357976	+	0.723717i
$287$	0.513286	+	2.58046i	0.0302983	+	0.152320i
$288$	9.43383	+	4.02280i	0.555894	+	0.237046i
$289$	−6.27223	+	31.5326i	−0.368955	+	1.85486i
$290$	−30.9575	+	8.33479i	−1.81789	+	0.489435i
$291$	−19.7661	+	15.4256i	−1.15871	+	0.904265i
$292$	12.6776	+	4.03990i	0.741898	+	0.236417i
$293$	12.1515	−	2.72871i	0.709898	−	0.159413i	0.150860	−	0.988555i	$-0.451796\pi$
$293$	12.1515	−	2.72871i	0.709898	−	0.159413i	0.559038	+	0.829142i	$0.311171\pi$
$294$	6.56789	+	11.1335i	0.383047	+	0.649316i
$295$	−2.79984	+	7.82504i	−0.163013	+	0.455591i
$296$	6.63906	−	24.3301i	0.385888	−	1.41416i
$297$	−5.89862	−	6.50812i	−0.342272	−	0.377640i
$298$	17.0590	−	5.04496i	0.988202	−	0.292247i
$299$	−0.484350	−	0.243801i	−0.0280107	−	0.0140994i
$300$	−2.20681	+	6.37952i	−0.127410	+	0.368322i
$301$	1.50155	+	2.37121i	0.0865480	+	0.136674i
$302$	0.151068	−	0.128483i	0.00869296	−	0.00739335i
$303$	13.4967	−	25.2505i	0.775365	−	1.45061i
$304$	3.47342	−	3.80630i	0.199214	−	0.218306i
$305$	26.9023	−	14.3796i	1.54042	−	0.823372i
$306$	16.4834	−	7.16929i	0.942296	−	0.409841i
$307$	9.52960	+	24.7046i	0.543883	+	1.40996i	0.883069	+	0.469244i	$0.155474\pi$
$307$	9.52960	+	24.7046i	0.543883	+	1.40996i	−0.339186	+	0.940719i	$0.610151\pi$
$308$	−10.8310	+	3.41104i	−0.617153	+	0.194362i
$309$	6.98354	−	25.2353i	0.397280	−	1.43558i
$310$	−16.1585	+	3.09697i	−0.917742	+	0.175896i
$311$	−6.25809	+	24.9837i	−0.354863	+	1.41669i	0.485294	+	0.874351i	$0.338713\pi$
$311$	−6.25809	+	24.9837i	−0.354863	+	1.41669i	−0.840157	+	0.542343i	$0.817537\pi$
$312$	−11.9761	−	13.1186i	−0.678012	−	0.742692i
$313$	−0.641220	−	0.864585i	−0.0362439	−	0.0488692i	0.784714	−	0.619858i	$-0.212810\pi$
$313$	−0.641220	−	0.864585i	−0.0362439	−	0.0488692i	−0.820958	+	0.570989i	$0.806560\pi$
$314$	−1.53202	+	9.85340i	−0.0864568	+	0.556060i
$315$	−0.191514	−	7.80142i	−0.0107906	−	0.439560i
$316$	−26.9933	+	12.3085i	−1.51849	+	0.692407i
$317$	7.52831	−	8.72741i	0.422832	−	0.490180i	−0.505031	−	0.863101i	$-0.668519\pi$
$317$	7.52831	−	8.72741i	0.422832	−	0.490180i	0.927863	+	0.372921i	$0.121644\pi$
$318$	−0.0138425	−	0.00321016i	−0.000776250	−	0.000180017i
$319$	−11.4432	−	27.6263i	−0.640696	−	1.54678i
$320$	−19.9266	+	4.62528i	−1.11393	+	0.258561i
$321$	3.36081	−	8.11370i	0.187582	−	0.452863i
$322$	0.262227	−	0.366864i	0.0146133	−	0.0204445i
$323$	−0.664394	−	9.00697i	−0.0369679	−	0.501161i
$324$	18.9688	+	11.7327i	1.05382	+	0.651816i
$325$	3.03681	−	3.18967i	0.168452	−	0.176931i
$326$	−6.63506	−	27.2961i	−0.367482	−	1.51179i
$327$	−5.80190	−	0.860631i	−0.320846	−	0.0475930i
$328$	−4.28437	+	1.08955i	−0.236565	+	0.0601602i
$329$	11.8758	−	7.11807i	0.654733	−	0.392432i
$330$	−26.2071	−	5.40346i	−1.44265	−	0.297451i
$331$	13.1180	+	23.1565i	0.721030	+	1.27280i	0.953852	+	0.300276i	$0.0970789\pi$
$331$	13.1180	+	23.1565i	0.721030	+	1.27280i	−0.232822	+	0.972519i	$0.574796\pi$
$332$	−9.08487	−	16.5726i	−0.498597	−	0.909540i
$333$	−6.55088	+	14.7785i	−0.358986	+	0.809860i
$334$	−7.06737	−	6.82342i	−0.386709	−	0.373361i
$335$	−7.80859	+	25.7415i	−0.426629	+	1.40641i
$336$	12.3103	−	8.16519i	0.671581	−	0.445448i
$337$	30.2347	−	9.17158i	1.64699	−	0.499608i	0.675631	−	0.737240i	$-0.263871\pi$
$337$	30.2347	−	9.17158i	1.64699	−	0.499608i	0.971355	+	0.237632i	$0.0763711\pi$
$338$	−2.08662	−	6.46760i	−0.113497	−	0.351791i
$339$	−34.8086	−	7.81654i	−1.89054	−	0.424536i
$340$	−18.1062	+	30.9458i	−0.981944	+	1.67827i
$341$	−4.81360	−	14.5710i	−0.260671	−	0.789062i
$342$	−2.56778	+	2.07748i	−0.138849	+	0.112337i
$343$	18.7742	+	0.922317i	1.01371	+	0.0498004i
$344$	−3.84583	+	2.72925i	−0.207353	+	0.147151i
$345$	0.960603	−	0.454331i	0.0517171	−	0.0244604i
$346$	−1.97033	−	13.9536i	−0.105926	−	0.750152i
$347$	−12.8280	+	20.2576i	−0.688642	+	1.08748i	0.302302	+	0.953212i	$0.402245\pi$
$347$	−12.8280	+	20.2576i	−0.688642	+	1.08748i	−0.990944	+	0.134273i	$0.957130\pi$
$348$	24.2552	+	30.4116i	1.30022	+	1.63023i
$349$	−16.1216	−	1.98840i	−0.862967	−	0.106437i	−0.321247	−	0.946996i	$-0.604102\pi$
$349$	−16.1216	−	1.98840i	−0.862967	−	0.106437i	−0.541721	+	0.840559i	$0.682227\pi$
$350$	2.23310	+	2.90303i	0.119364	+	0.155173i
$351$	−4.14161	−	6.19836i	−0.221063	−	0.330844i
$352$	−6.68165	−	17.8716i	−0.356133	−	0.952561i
$353$	−1.70374	+	2.54983i	−0.0906811	+	0.135714i	−0.874037	−	0.485860i	$-0.838506\pi$
$353$	−1.70374	+	2.54983i	−0.0906811	+	0.135714i	0.783356	+	0.621574i	$0.213506\pi$
$354$	10.0615	−	0.671565i	0.534764	−	0.0356933i
$355$	−6.56756	−	3.72048i	−0.348570	−	0.197462i
$356$	3.21023	+	1.38256i	0.170142	+	0.0732757i
$357$	4.42633	−	25.5096i	0.234266	−	1.35011i
$358$	22.4619	+	1.26079i	1.18715	+	0.0666349i
$359$	−0.0998042	−	2.03156i	−0.00526747	−	0.107222i	−0.999989	−	0.00461393i	$-0.998531\pi$
$359$	−0.0998042	−	2.03156i	−0.00526747	−	0.107222i	0.994722	−	0.102608i	$-0.0327187\pi$
$360$	13.0731	−	1.01155i	0.689014	−	0.0533136i
$361$	−5.84183	−	16.3268i	−0.307465	−	0.859306i
$362$	11.0349	−	13.2562i	0.579982	−	0.696731i
$363$	0.0607196	−	0.823155i	0.00318695	−	0.0432044i
$364$	−9.51777	+	1.51486i	−0.498867	+	0.0794005i
$365$	16.7612	−	2.90834i	0.877320	−	0.152229i
$366$	−29.0185	−	22.9742i	−1.51682	−	1.20088i
$367$	0.930332	−	9.44582i	0.0485629	−	0.493068i	−0.939883	−	0.341496i	$-0.889067\pi$
$367$	0.930332	−	9.44582i	0.0485629	−	0.493068i	0.988446	−	0.151572i	$-0.0484335\pi$
$368$	0.638763	+	0.407535i	0.0332978	+	0.0212442i
$369$	2.81998	−	0.277743i	0.146802	−	0.0144587i
$370$	−6.84480	−	31.5091i	−0.355844	−	1.63808i
$371$	−0.00558379	+	0.00531621i	−0.000289896	+	0.000276004i
$372$	11.2656	+	16.4801i	0.584092	+	0.854454i
$373$	−12.6802	−	9.89576i	−0.656558	−	0.512383i	0.231074	−	0.972936i	$-0.425776\pi$
$373$	−12.6802	−	9.89576i	−0.656558	−	0.512383i	−0.887632	+	0.460553i	$0.847651\pi$
$374$	−30.8052	−	13.0127i	−1.59290	−	0.672872i
$375$	−2.84926	−	19.2081i	−0.147135	−	0.991903i
$376$	12.9941	+	19.2967i	0.670122	+	0.995152i
$377$	−6.16656	−	24.6183i	−0.317594	−	1.26791i
$378$	5.62264	−	2.61142i	0.289198	−	0.134317i
$379$	12.0880	−	5.35823i	0.620917	−	0.275234i	−0.0707003	−	0.997498i	$-0.522523\pi$
$379$	12.0880	−	5.35823i	0.620917	−	0.275234i	0.691618	+	0.722264i	$0.256898\pi$
$380$	1.68989	−	6.36771i	0.0866896	−	0.326657i
$381$	3.98476	+	7.91636i	0.204145	+	0.405567i
$382$	16.9478	+	0.534502i	0.867125	+	0.0273475i
$383$	1.06921	+	1.06921i	0.0546338	+	0.0546338i	0.733896	−	0.679262i	$-0.237700\pi$
$383$	1.06921	+	1.06921i	0.0546338	+	0.0546338i	−0.679262	+	0.733896i	$0.737700\pi$
$384$	14.7896	+	19.9331i	0.754727	+	1.01721i
$385$	−10.2659	+	10.2659i	−0.523198	+	0.523198i
$386$	22.8897	−	21.4900i	1.16505	−	1.09381i
$387$	2.70002	−	1.35908i	0.137250	−	0.0690857i
$388$	−22.6546	+	3.03774i	−1.15011	+	0.154218i
$389$	−4.29772	−	9.69551i	−0.217903	−	0.491582i	0.771597	−	0.636111i	$-0.219458\pi$
$389$	−4.29772	−	9.69551i	−0.217903	−	0.491582i	−0.989500	+	0.144530i	$0.953833\pi$
$390$	−21.3289	−	7.80004i	−1.08003	−	0.394971i
$391$	1.28820	−	0.322678i	0.0651472	−	0.0163185i
$392$	0.0423249	+	11.7841i	0.00213773	+	0.595188i
$393$	−31.8178	+	4.71973i	−1.60500	+	0.238079i
$394$	−27.6319	+	11.2200i	−1.39207	+	0.565258i
$395$	−23.3358	+	29.9021i	−1.17415	+	1.50454i
$396$	2.51264	+	11.9689i	0.126265	+	0.601462i
$397$	12.0049	+	12.6092i	0.602510	+	0.632836i	0.952725	−	0.303833i	$-0.0982666\pi$
$397$	12.0049	+	12.6092i	0.602510	+	0.632836i	−0.350215	+	0.936669i	$0.613892\pi$
$398$	−20.9846	+	32.6318i	−1.05186	+	1.63569i
$399$	0.466311	+	4.73454i	0.0233448	+	0.237023i
$400$	−4.67344	+	4.00377i	−0.233672	+	0.200189i
$401$	−17.0247	−	1.67679i	−0.850175	−	0.0837349i	−0.336462	−	0.941697i	$-0.609230\pi$
$401$	−17.0247	−	1.67679i	−0.850175	−	0.0837349i	−0.513713	+	0.857962i	$0.671730\pi$
$402$	32.4202	−	3.76898i	1.61697	−	0.187980i
$403$	−2.22661	−	12.8323i	−0.110915	−	0.639221i
$404$	22.2448	−	13.6548i	1.10672	−	0.679353i
$405$	28.4390	+	2.09779i	1.41315	+	0.104240i
$406$	21.0179	−	1.92197i	1.04310	−	0.0953857i
$407$	28.3161	−	10.1317i	1.40358	−	0.502209i
$408$	43.1943	+	5.17008i	2.13844	+	0.255957i
$409$	−28.1670	+	1.38376i	−1.39277	+	0.0684223i	−0.731559	−	0.681779i	$-0.761207\pi$
$409$	−28.1670	+	1.38376i	−1.39277	+	0.0684223i	−0.661210	+	0.750201i	$0.729957\pi$
$410$	−4.21428	+	3.76632i	−0.208128	+	0.186006i
$411$	−30.0320	−	5.21105i	−1.48137	−	0.257042i
$412$	17.1128	−	16.6413i	0.843089	−	0.819860i
$413$	2.69673	−	4.76040i	0.132698	−	0.234244i
$414$	−0.365529	−	0.319787i	−0.0179648	−	0.0157167i
$415$	−20.0910	−	13.4244i	−0.986230	−	0.658978i
$416$	−3.38387	−	15.8359i	−0.165908	−	0.776420i
$417$	7.02074	−	4.69111i	0.343807	−	0.229724i
$418$	6.09318	+	0.794763i	0.298027	+	0.0388731i
$419$	1.86531	−	15.1235i	0.0911262	−	0.738831i	−0.875603	−	0.483031i	$-0.839536\pi$
$419$	1.86531	−	15.1235i	0.0911262	−	0.738831i	0.966730	−	0.255801i	$-0.0823391\pi$
$420$	9.13477	−	16.5303i	0.445731	−	0.806598i
$421$	−17.9056	−	11.3386i	−0.872665	−	0.552609i	0.0217923	−	0.999763i	$-0.493063\pi$
$421$	−17.9056	−	11.3386i	−0.872665	−	0.552609i	−0.894457	+	0.447154i	$0.852438\pi$
$422$	−6.86219	+	9.11880i	−0.334046	+	0.443896i
$423$	−6.37561	−	13.4801i	−0.309993	−	0.655425i
$424$	−0.00941413	−	0.00889875i	−0.000457191	−	0.000432162i
$425$	−0.529241	+	10.7730i	−0.0256720	+	0.522565i
$426$	−0.961322	+	9.10791i	−0.0465762	+	0.441280i
$427$	−19.0679	+	6.29917i	−0.922759	+	0.304838i
$428$	6.37985	−	4.83703i	0.308382	−	0.233807i
$429$	4.64103	−	20.6674i	0.224071	−	0.997834i
$430$	−2.74840	+	5.36647i	−0.132539	+	0.258794i
$431$	−10.9962	−	36.2496i	−0.529668	−	1.74608i	−0.656669	−	0.754179i	$-0.728035\pi$
$431$	−10.9962	−	36.2496i	−0.529668	−	1.74608i	0.127001	−	0.991903i	$-0.459465\pi$
$432$	4.87917	+	9.20324i	0.234749	+	0.442791i
$433$	31.4347	+	9.53560i	1.51065	+	0.458252i	0.933558	−	0.358425i	$-0.116686\pi$
$433$	31.4347	+	9.53560i	1.51065	+	0.458252i	0.577095	+	0.816677i	$0.304186\pi$
$434$	10.8294	−	0.190180i	0.519826	−	0.00912893i
$435$	45.4674	+	20.1543i	2.17999	+	0.966325i
$436$	−4.16902	−	3.34828i	−0.199660	−	0.160353i
$437$	−0.212320	+	0.120278i	−0.0101566	+	0.00575367i
$438$	−11.3473	−	17.2420i	−0.542197	−	0.823853i
$439$	3.73835	+	6.23706i	0.178422	+	0.297679i	0.933927	−	0.357464i	$-0.116358\pi$
$439$	3.73835	+	6.23706i	0.178422	+	0.297679i	−0.755505	+	0.655143i	$0.772608\pi$
$440$	−18.1335	−	16.3170i	−0.864480	−	0.777882i
$441$	1.10832	−	7.47171i	0.0527773	−	0.355796i
$442$	−24.2415	−	14.7609i	−1.15305	−	0.702104i
$443$	−26.4610	−	25.1930i	−1.25720	−	1.19696i	−0.971078	−	0.238764i	$-0.923258\pi$
$443$	−26.4610	−	25.1930i	−1.25720	−	1.19696i	−0.286124	−	0.958192i	$-0.592367\pi$
$444$	−31.7463	+	22.8643i	−1.50661	+	1.08509i
$445$	4.45670	−	0.328746i	0.211268	−	0.0155841i
$446$	−3.89506	+	0.647869i	−0.184437	+	0.0306775i
$447$	−25.4957	−	10.5607i	−1.20591	−	0.499503i
$448$	13.4455	−	0.757386i	0.635239	−	0.0357831i
$449$	−0.257840	+	0.106801i	−0.0121682	+	0.00504024i	−0.388759	−	0.921339i	$-0.627096\pi$
$449$	−0.257840	+	0.106801i	−0.0121682	+	0.00504024i	0.376591	+	0.926380i	$0.377096\pi$
$450$	3.34726	−	2.08702i	0.157791	−	0.0983830i
$451$	−3.99176	−	3.44332i	−0.187965	−	0.162140i
$452$	−23.7907	−	22.1757i	−1.11902	−	1.04306i
$453$	−0.307552	+	0.00754998i	−0.0144501	+	0.000354729i
$454$	2.64005	−	1.92956i	0.123904	−	0.0905589i
$455$	−9.89701	+	7.34012i	−0.463979	+	0.344110i
$456$	−7.90287	+	1.20130i	−0.370086	+	0.0562562i
$457$	−27.2575	−	6.82766i	−1.27505	−	0.319384i	−0.454394	−	0.890801i	$-0.650144\pi$
$457$	−27.2575	−	6.82766i	−1.27505	−	0.319384i	−0.820660	+	0.571417i	$0.806394\pi$
$458$	10.2215	−	15.0686i	0.477618	−	0.704110i
$459$	17.5957	+	4.86939i	0.821297	+	0.227283i
$460$	0.965018	+	0.0847516i	0.0449942	+	0.00395156i
$461$	−2.03606	+	0.785394i	−0.0948286	+	0.0365794i	−0.406844	−	0.913498i	$-0.633371\pi$
$461$	−2.03606	+	0.785394i	−0.0948286	+	0.0365794i	0.312016	+	0.950077i	$0.398996\pi$
$462$	16.3905	+	6.45436i	0.762553	+	0.300284i
$463$	14.1061	+	26.3906i	0.655564	+	1.22647i	0.961600	+	0.274454i	$0.0884970\pi$
$463$	14.1061	+	26.3906i	0.655564	+	1.22647i	−0.306036	+	0.952020i	$0.599003\pi$
$464$	5.08439	+	35.0961i	0.236037	+	1.62929i
$465$	22.5090	+	12.0313i	1.04383	+	0.557939i
$466$	−1.43512	+	17.7635i	−0.0664805	+	0.822878i
$467$	20.0614	−	12.7037i	0.928329	−	0.587858i	0.0171431	−	0.999853i	$-0.494543\pi$
$467$	20.0614	−	12.7037i	0.928329	−	0.587858i	0.911186	+	0.411995i	$0.135168\pi$
$468$	0.618918	+	10.3612i	0.0286095	+	0.478949i
$469$	7.96197	−	15.8177i	0.367650	−	0.730394i
$470$	26.1329	+	14.2038i	1.20542	+	0.655174i
$471$	11.4618	−	10.3884i	0.528134	−	0.478673i
$472$	8.22610	+	4.10371i	0.378637	+	0.188888i
$473$	−5.29486	−	1.89453i	−0.243458	−	0.0871106i
$474$	44.5638	+	11.4940i	2.04688	+	0.527936i
$475$	−0.434243	−	1.93377i	−0.0199245	−	0.0887276i
$476$	15.2270	−	18.0344i	0.697927	−	0.826608i
$477$	0.00510857	+	0.00654602i	0.000233905	+	0.000299722i
$478$	−2.00160	−	1.15243i	−0.0915511	−	0.0527110i
$479$	16.4887	+	3.27981i	0.753388	+	0.149858i	0.556822	−	0.830632i	$-0.312021\pi$
$479$	16.4887	+	3.27981i	0.753388	+	0.149858i	0.196567	+	0.980490i	$0.437021\pi$
$480$	28.5446	+	13.8648i	1.30288	+	0.632840i
$481$	25.0341	−	4.97959i	1.14146	−	0.227050i
$482$	29.0516	+	9.82291i	1.32326	+	0.447421i
$483$	−0.674205	+	0.186578i	−0.0306774	+	0.00848957i
$484$	0.426742	−	0.619747i	0.0193974	−	0.0281703i
$485$	−23.8929	+	16.8273i	−1.08492	+	0.764086i
$486$	−7.77921	−	22.2297i	−0.352872	−	1.00836i
$487$	−30.9852	−	28.0834i	−1.40407	−	1.27258i	−0.916810	−	0.399325i	$-0.869245\pi$
$487$	−30.9852	−	28.0834i	−1.40407	−	1.27258i	−0.487265	−	0.873254i	$-0.662005\pi$
$488$	−12.2564	−	31.4368i	−0.554822	−	1.42308i
$489$	−18.6316	+	39.3932i	−0.842549	+	1.78142i
$490$	7.00926	+	13.3366i	0.316646	+	0.602487i
$491$	20.5924	+	23.8723i	0.929321	+	1.07734i	0.996825	+	0.0796223i	$0.0253714\pi$
$491$	20.5924	+	23.8723i	0.929321	+	1.07734i	−0.0675041	+	0.997719i	$0.521504\pi$
$492$	6.23007	+	2.86637i	0.280873	+	0.129226i
$493$	50.8165	+	35.7890i	2.28866	+	1.61186i
$494$	5.01646	+	1.42603i	0.225701	+	0.0641603i
$495$	9.91946	+	12.0869i	0.445847	+	0.543266i
$496$	1.27721	+	18.1539i	0.0573482	+	0.815133i
$497$	3.84115	+	3.15235i	0.172299	+	0.141402i
$498$	−5.21394	+	28.8510i	−0.233642	+	1.29284i
$499$	−0.214160	+	8.72392i	−0.00958712	+	0.390536i	0.975649	+	0.219337i	$0.0703893\pi$
$499$	−0.214160	+	8.72392i	−0.00958712	+	0.390536i	−0.985236	+	0.171200i	$0.945236\pi$
$500$	6.60111	−	16.4257i	0.295211	−	0.734579i
$501$	1.86548	+	15.1249i	0.0833434	+	0.675730i
$502$	−0.0326937	+	4.68114i	−0.00145919	+	0.208930i
$503$	−10.0438	−	7.44900i	−0.447831	−	0.332134i	0.348168	−	0.937432i	$-0.386804\pi$
$503$	−10.0438	−	7.44900i	−0.447831	−	0.332134i	−0.795999	+	0.605298i	$0.793054\pi$
$504$	−8.59340	−	0.815223i	−0.382780	−	0.0363129i
$505$	17.1563	−	28.6235i	0.763444	−	1.27373i
$506$	0.0380310	+	0.902743i	0.00169068	+	0.0401318i
$507$	−3.79414	+	9.83593i	−0.168503	+	0.436829i
$508$	−0.509123	+	8.06351i	−0.0225887	+	0.357760i
$509$	−8.36659	+	25.3260i	−0.370843	+	1.12256i	0.580458	+	0.814291i	$0.302874\pi$
$509$	−8.36659	+	25.3260i	−0.370843	+	1.12256i	−0.951300	+	0.308266i	$0.900251\pi$
$510$	52.0308	−	19.6541i	2.30396	−	0.870300i
$511$	−11.1990			−0.495417
$512$	2.46038	+	22.4933i	0.108734	+	0.994071i
$513$	−3.35475			−0.148116
$514$	3.95306	−	1.49323i	0.174362	−	0.0658637i
$515$	9.57311	−	28.9782i	0.421842	−	1.27693i
$516$	7.30109	+	0.460984i	0.321412	+	0.0202937i
$517$	−9.98420	+	25.8831i	−0.439105	+	1.13834i
$518$	0.893453	+	21.2079i	0.0392561	+	0.931823i
$519$	−11.2387	+	18.7506i	−0.493324	+	0.823062i
$520$	−13.1917	−	15.9569i	−0.578493	−	0.699755i
$521$	−5.35662	−	3.97274i	−0.234678	−	0.174049i	0.471969	−	0.881615i	$-0.343543\pi$
$521$	−5.35662	−	3.97274i	−0.234678	−	0.174049i	−0.706647	+	0.707566i	$0.749793\pi$
$522$	0.158751	−	22.7303i	0.00694834	−	0.994877i
$523$	−5.48907	−	44.5042i	−0.240020	−	1.94603i	−0.315594	−	0.948894i	$-0.602204\pi$
$523$	−5.48907	−	44.5042i	−0.240020	−	1.94603i	0.0755739	−	0.997140i	$-0.475921\pi$
$524$	−27.2088	−	10.9346i	−1.18862	−	0.477680i
$525$	0.139435	−	5.67995i	0.00608544	−	0.247893i
$526$	5.23714	−	28.9794i	0.228350	−	1.26356i
$527$	24.6564	+	20.2350i	1.07405	+	0.881451i
$528$	−9.37971	+	28.0727i	−0.408200	+	1.22171i
$529$	14.5683	+	17.7515i	0.633404	+	0.771805i
$530$	−0.0159312	−	0.00452877i	−0.000692006	−	0.000196717i
$531$	−4.81761	−	3.39294i	−0.209066	−	0.147241i
$532$	−1.81277	+	3.94006i	−0.0785937	+	0.170823i
$533$	−2.92241	−	3.38789i	−0.126584	−	0.146746i
$534$	−2.52255	−	4.79968i	−0.109161	−	0.207703i
$535$	4.37651	−	9.25335i	0.189213	−	0.400057i
$536$	27.2451	+	11.9600i	1.17681	+	0.516594i
$537$	−25.8589	−	23.4372i	−1.11590	−	1.01139i
$538$	−1.61377	−	4.61148i	−0.0695747	−	0.198815i
$539$	−11.4891	+	8.09155i	−0.494871	+	0.348528i
$540$	10.9690	+	7.55297i	0.472031	+	0.325028i
$541$	−14.0753	+	3.89515i	−0.605143	+	0.167466i	−0.555800	−	0.831316i	$-0.687588\pi$
$541$	−14.0753	+	3.89515i	−0.605143	+	0.167466i	−0.0493431	+	0.998782i	$0.515713\pi$
$542$	22.2690	+	7.52960i	0.956538	+	0.323424i
$543$	−26.2426	+	5.21997i	−1.12618	+	0.224011i
$544$	31.6073	+	23.9539i	1.35515	+	1.02702i
$545$	−6.70506	−	1.33372i	−0.287213	−	0.0571303i
$546$	12.9566	+	7.45980i	0.554490	+	0.319250i
$547$	9.49320	+	12.1644i	0.405900	+	0.520113i	0.947168	−	0.320737i	$-0.103931\pi$
$547$	9.49320	+	12.1644i	0.405900	+	0.520113i	−0.541268	+	0.840850i	$0.682056\pi$
$548$	−21.2317	−	17.9265i	−0.906972	−	0.765781i
$549$	4.73868	+	21.1023i	0.202242	+	0.900623i
$550$	−7.10598	−	1.83279i	−0.303000	−	0.0781504i
$551$	−10.7533	−	3.84760i	−0.458107	−	0.163913i
$552$	−0.372709	−	1.11475i	−0.0158635	−	0.0474468i
$553$	18.5016	−	16.7688i	0.786767	−	0.713084i
$554$	−37.3772	−	20.3154i	−1.58800	−	0.863118i
$555$	−22.4894	+	44.6787i	−0.954620	+	1.89650i
$556$	7.68398	−	0.458994i	0.325873	−	0.0194657i
$557$	27.1099	−	17.1672i	1.14868	−	0.727396i	0.181982	−	0.983302i	$-0.441749\pi$
$557$	27.1099	−	17.1672i	1.14868	−	0.727396i	0.966702	+	0.255906i	$0.0823738\pi$
$558$	0.939364	−	11.6272i	0.0397664	−	0.492219i
$559$	−4.20928	−	2.24991i	−0.178034	−	0.0951610i
$560$	14.7980	−	8.80147i	0.625328	−	0.371930i
$561$	24.4543	+	45.7509i	1.03246	+	1.93160i
$562$	−22.4516	−	8.84117i	−0.947065	−	0.372942i
$563$	26.6063	−	10.2632i	1.12132	−	0.432542i	0.272996	−	0.962015i	$-0.411985\pi$
$563$	26.6063	−	10.2632i	1.12132	−	0.432542i	0.848327	+	0.529473i	$0.177610\pi$
$564$	3.15732	−	35.9506i	0.132947	−	1.51379i
$565$	−40.0754	−	11.0903i	−1.68598	−	0.466575i
$566$	−7.91756	+	11.6722i	−0.332800	+	0.490618i
$567$	−18.2102	−	4.56141i	−0.764756	−	0.191561i
$568$	−4.94952	+	6.72400i	−0.207677	+	0.282133i
$569$	29.3049	−	21.7340i	1.22852	−	0.911135i	0.230444	−	0.973086i	$-0.425982\pi$
$569$	29.3049	−	21.7340i	1.22852	−	0.911135i	0.998079	+	0.0619505i	$0.0197321\pi$
$570$	−8.25116	+	6.03061i	−0.345603	+	0.252595i
$571$	−35.8441	+	0.879924i	−1.50003	+	0.0368237i	−0.766241	−	0.642553i	$-0.777875\pi$
$571$	−35.8441	+	0.879924i	−1.50003	+	0.0368237i	−0.733789	+	0.679377i	$0.762250\pi$
$572$	13.1667	−	14.1256i	0.550528	−	0.590620i
$573$	−19.9176	−	17.1810i	−0.832069	−	0.717748i
$574$	3.15737	−	1.96863i	0.131786	−	0.0821689i
$575$	0.269243	−	0.111524i	0.0112282	−	0.00465088i
$576$	0.607590	−	14.4911i	0.0253162	−	0.603794i
$577$	33.3417	+	13.8106i	1.38803	+	0.574942i	0.946617	−	0.322361i	$-0.104476\pi$
$577$	33.3417	+	13.8106i	1.38803	+	0.574942i	0.441416	+	0.897303i	$0.354476\pi$
$578$	44.8513	−	7.46016i	1.86557	−	0.310302i
$579$	−48.5734	+	3.58299i	−2.01864	+	0.148904i
$580$	26.4975	+	36.7908i	1.10025	+	1.52765i
$581$	11.5207	+	10.9686i	0.477958	+	0.455054i
$582$	30.2856	+	18.4412i	1.25538	+	0.764412i
$583$	0.00226667	−	0.0152806i	9.38759e−5	−	0.000632860i
$584$	−0.990807	−	18.7910i	−0.0409999	−	0.777576i
$585$	6.82251	+	11.3827i	0.282076	+	0.470615i
$586$	−9.68261	−	14.7125i	−0.399985	−	0.607766i
$587$	1.72105	−	0.974965i	0.0710355	−	0.0402411i	−0.456970	−	0.889482i	$-0.651065\pi$
$587$	1.72105	−	0.974965i	0.0710355	−	0.0402411i	0.528005	+	0.849241i	$0.322940\pi$
$588$	11.4470	−	14.2530i	0.472067	−	0.587783i
$589$	−5.35822	−	2.37514i	−0.220782	−	0.0978658i
$590$	11.7515	−	0.206374i	0.483802	−	0.00849629i
$591$	44.2718	+	13.4297i	1.82110	+	0.552424i
$592$	−35.5059	+	3.37545i	−1.45928	+	0.138730i
$593$	−4.48542	−	14.7864i	−0.184194	−	0.607206i	−0.999599	−	0.0283154i	$-0.990986\pi$
$593$	−4.48542	−	14.7864i	−0.184194	−	0.607206i	0.815405	−	0.578891i	$-0.196514\pi$
$594$	−5.66229	+	11.0561i	−0.232327	+	0.453637i
$595$	6.61182	−	29.4438i	0.271058	−	1.20708i
$596$	−15.1994	−	20.0474i	−0.622593	−	0.821175i
$597$	57.1472	−	18.8789i	2.33888	−	0.772662i
$598$	−0.0804931	+	0.762619i	−0.00329161	+	0.0311858i
$599$	0.443000	−	9.01747i	0.0181005	−	0.368444i	−0.972609	−	0.232448i	$-0.925327\pi$
$599$	0.443000	−	9.01747i	0.0181005	−	0.368444i	0.990709	−	0.135996i	$-0.0434234\pi$
$600$	9.54278	−	0.268560i	0.389582	−	0.0109639i
$601$	2.24207	+	4.74045i	0.0914558	+	0.193367i	0.944532	−	0.328419i	$-0.106516\pi$
$601$	2.24207	+	4.74045i	0.0914558	+	0.193367i	−0.853076	+	0.521786i	$0.825266\pi$
$602$	2.38666	−	3.17150i	0.0972730	−	0.129261i
$603$	−16.1132	−	10.2036i	−0.656181	−	0.415522i
$604$	−0.245474	−	0.135650i	−0.00998819	−	0.00551953i
$605$	0.117764	−	0.954802i	0.00478777	−	0.0388182i
$606$	−40.1507	−	5.23704i	−1.63101	−	0.212740i
$607$	−26.4781	+	17.6921i	−1.07471	+	0.718099i	−0.961315	−	0.275451i	$-0.911173\pi$
$607$	−26.4781	+	17.6921i	−1.07471	+	0.718099i	−0.113396	+	0.993550i	$0.536173\pi$
$608$	−6.77145	−	2.69308i	−0.274618	−	0.109219i
$609$	−27.2230	−	18.1898i	−1.10313	−	0.737088i
$610$	−32.4680	−	28.4049i	−1.31459	−	1.15008i
$611$	−11.6054	+	20.4864i	−0.469503	+	0.828789i
$612$	−17.7222	−	18.2244i	−0.716379	−	0.736676i
$613$	4.01180	+	0.696113i	0.162035	+	0.0281157i	0.251400	−	0.967883i	$-0.419109\pi$
$613$	4.01180	+	0.696113i	0.162035	+	0.0281157i	−0.0893654	+	0.995999i	$0.528484\pi$
$614$	27.9211	−	24.9533i	1.12681	−	1.00703i
$615$	8.75734	−	0.430220i	0.353130	−	0.0173482i
$616$	9.92540	+	12.6245i	0.399906	+	0.508655i
$617$	3.24057	−	1.15949i	0.130460	−	0.0466795i	−0.270850	−	0.962622i	$-0.587305\pi$
$617$	3.24057	−	1.15949i	0.130460	−	0.0466795i	0.401311	+	0.915942i	$0.368555\pi$
$618$	−36.8756	+	3.37206i	−1.48335	+	0.135644i
$619$	2.70511	+	0.199541i	0.108728	+	0.00802023i	0.127819	−	0.991798i	$-0.459202\pi$
$619$	2.70511	+	0.199541i	0.108728	+	0.00802023i	−0.0190914	+	0.999818i	$0.506077\pi$
$620$	12.1723	+	19.8296i	0.488851	+	0.796376i
$621$	−0.0843337	−	0.486027i	−0.00338419	−	0.0195036i
$622$	36.1802	−	4.20609i	1.45069	−	0.168649i
$623$	−2.92773	−	0.288356i	−0.117297	−	0.0115527i
$624$	−11.3706	+	22.3999i	−0.455187	+	0.896714i
$625$	−2.97242	−	30.1795i	−0.118897	−	1.20718i
$626$	−0.823379	+	1.28039i	−0.0329089	+	0.0511745i
$627$	−6.57293	−	6.90377i	−0.262498	−	0.275710i
$628$	13.8014	−	2.89733i	0.550736	−	0.115616i
$629$	−38.4589	+	49.2805i	−1.53346	+	1.96494i
$630$	−10.2254	+	4.15206i	−0.407388	+	0.165422i
$631$	−2.01805	+	0.299349i	−0.0803373	+	0.0119169i	−0.186778	−	0.982402i	$-0.559805\pi$
$631$	−2.01805	+	0.299349i	−0.0803373	+	0.0119169i	0.106441	+	0.994319i	$0.466055\pi$
$632$	29.7735	+	29.5604i	1.18433	+	1.17585i
$633$	17.1733	−	4.30168i	0.682577	−	0.170977i
$634$	−15.3083	−	5.59832i	−0.607972	−	0.222338i
$635$	4.18611	+	9.44371i	0.166121	+	0.374762i
$636$	0.00267073	+	0.0199175i	0.000105901	+	0.000789782i
$637$	−10.6532	+	5.36236i	−0.422094	+	0.212464i
$638$	−30.8303	+	28.9451i	−1.22058	+	1.14595i
$639$	3.78424	−	3.78424i	0.149702	−	0.149702i
$640$	16.0773	+	24.0510i	0.635510	+	0.950697i
$641$	−20.8769	−	20.8769i	−0.824588	−	0.824588i	0.162175	−	0.986762i	$-0.448149\pi$
$641$	−20.8769	−	20.8769i	−0.824588	−	0.824588i	−0.986762	+	0.162175i	$0.948149\pi$
$642$	−12.4137	−	0.391507i	−0.489931	−	0.0154515i
$643$	−8.62752	−	17.1399i	−0.340236	−	0.675933i	0.656700	−	0.754152i	$-0.271952\pi$
$643$	−8.62752	−	17.1399i	−0.340236	−	0.675933i	−0.996936	+	0.0782187i	$0.975077\pi$
$644$	−0.616396	−	0.163582i	−0.0242894	−	0.00644603i
$645$	8.55079	−	3.79030i	0.336687	−	0.149243i
$646$	−11.5840	+	5.38013i	−0.455765	+	0.211678i
$647$	1.13442	+	4.52886i	0.0445986	+	0.178048i	0.988237	−	0.152931i	$-0.0488712\pi$
$647$	1.13442	+	4.52886i	0.0445986	+	0.178048i	−0.943638	+	0.330979i	$0.892621\pi$
$648$	6.04253	−	30.9586i	0.237373	−	1.21617i
$649$	1.60852	+	10.8438i	0.0631399	+	0.425655i
$650$	−5.73747	−	2.42362i	−0.225042	−	0.0950621i
$651$	−13.2458	−	10.3371i	−0.519145	−	0.405145i
$652$	−32.7962	+	22.4190i	−1.28440	+	0.877995i
$653$	−30.0987	+	28.6563i	−1.17785	+	1.12141i	−0.187582	+	0.982249i	$0.560065\pi$
$653$	−30.0987	+	28.6563i	−1.17785	+	1.12141i	−0.990270	+	0.139159i	$0.955560\pi$
$654$	1.76086	+	8.10586i	0.0688550	+	0.316964i
$655$	−37.3106	+	3.67477i	−1.45785	+	0.143585i
$656$	3.58252	+	5.12362i	0.139874	+	0.200044i
$657$	−1.18223	+	12.0033i	−0.0461231	+	0.468295i
$658$	−15.3518	−	12.1541i	−0.598476	−	0.473818i
$659$	45.8816	−	7.96121i	1.78729	−	0.310125i	0.821649	−	0.569993i	$-0.193054\pi$
$659$	45.8816	−	7.96121i	1.78729	−	0.310125i	0.965644	+	0.259868i	$0.0836792\pi$
$660$	5.94814	+	37.3717i	0.231531	+	1.45469i
$661$	−3.06269	+	41.5199i	−0.119125	+	1.61494i	0.525742	+	0.850644i	$0.323788\pi$
$661$	−3.06269	+	41.5199i	−0.119125	+	1.61494i	−0.644867	+	0.764295i	$0.723087\pi$
$662$	24.0798	−	28.9270i	0.935889	−	1.12428i
$663$	14.8328	+	41.4548i	0.576057	+	1.60997i
$664$	−17.3850	+	20.3011i	−0.674670	+	0.787834i
$665$	0.272083	+	5.53838i	0.0105509	+	0.214769i
$666$	22.8254	+	1.28119i	0.884465	+	0.0496452i
$667$	0.287106	−	1.65463i	0.0111168	−	0.0640677i
$668$	−5.49535	+	12.7599i	−0.212622	+	0.493695i
$669$	5.32960	+	3.01918i	0.206054	+	0.116728i
$670$	37.9575	−	2.53351i	1.46643	−	0.0978781i
$671$	22.3542	−	33.4554i	0.862973	−	1.29153i
$672$	−16.9543	−	12.2057i	−0.654026	−	0.470845i
$673$	−7.21693	−	10.8009i	−0.278192	−	0.416344i	0.665892	−	0.746048i	$-0.268051\pi$
$673$	−7.21693	−	10.8009i	−0.278192	−	0.416344i	−0.944084	+	0.329704i	$0.893051\pi$
$674$	−27.2433	−	35.4162i	−1.04937	−	1.36418i
$675$	3.97634	+	0.490435i	0.153049	+	0.0188768i
$676$	−7.51370	+	5.99267i	−0.288988	+	0.230487i
$677$	−22.6915	+	35.8339i	−0.872107	+	1.37721i	0.0534386	+	0.998571i	$0.482982\pi$
$677$	−22.6915	+	35.8339i	−0.872107	+	1.37721i	−0.925546	+	0.378636i	$0.876393\pi$
$678$	7.05422	+	49.9571i	0.270916	+	1.91859i
$679$	17.3914	−	8.22551i	0.667420	−	0.315666i
$680$	49.9889	+	8.48906i	1.91699	+	0.325541i
$681$	−5.06664	−	0.248908i	−0.194154	−	0.00953818i
$682$	−16.8715	+	13.6500i	−0.646041	+	0.522684i
$683$	−14.9623	−	45.2916i	−0.572517	−	1.73303i	−0.674527	−	0.738250i	$-0.735652\pi$
$683$	−14.9623	−	45.2916i	−0.572517	−	1.73303i	0.102010	−	0.994783i	$-0.467473\pi$
$684$	4.03167	+	2.35890i	0.154155	+	0.0901947i
$685$	−34.6637	−	7.78399i	−1.32443	−	0.297411i
$686$	−8.16203	−	25.2987i	−0.311628	−	0.965908i
$687$	−27.0300	+	8.19945i	−1.03126	+	0.312829i
$688$	5.53265	+	3.72401i	0.210930	+	0.141976i
$689$	0.00380589	−	0.0125463i	0.000144993	−	0.000477978i
$690$	−1.08112	−	1.04380i	−0.0411576	−	0.0397369i
$691$	1.81191	−	4.08761i	0.0689283	−	0.155500i	−0.876433	−	0.481523i	$-0.840084\pi$
$691$	1.81191	−	4.08761i	0.0689283	−	0.155500i	0.945362	+	0.326023i	$0.105709\pi$
$692$	−17.4756	+	9.57990i	−0.664324	+	0.364173i
$693$	−5.07367	−	8.95627i	−0.192733	−	0.340221i
$694$	33.2109	+	6.84753i	1.26067	+	0.259929i
$695$	8.44147	−	5.05962i	0.320203	−	0.191922i
$696$	28.1124	−	47.2870i	1.06560	−	1.79241i
$697$	10.8390	+	1.60781i	0.410555	+	0.0609000i
$698$	5.42600	+	22.3221i	0.205377	+	0.844903i
$699$	19.0631	−	20.0226i	0.721031	−	0.757323i
$700$	2.72466	−	4.40509i	0.102982	−	0.166497i
$701$	1.11565	+	15.1245i	0.0421375	+	0.571244i	0.976583	+	0.215139i	$0.0690204\pi$
$701$	1.11565	+	15.1245i	0.0421375	+	0.571244i	−0.934446	+	0.356105i	$0.884105\pi$
$702$	−6.13053	+	8.57682i	−0.231382	+	0.323711i
$703$	4.39569	−	10.6121i	0.165787	−	0.400245i
$704$	−20.3046	+	17.7708i	−0.765258	+	0.669763i
$705$	−17.6573	−	42.6284i	−0.665011	−	1.60548i
$706$	4.22479	+	0.979751i	0.159002	+	0.0368734i
$707$	−14.3495	+	16.6350i	−0.539668	+	0.625625i
$708$	−5.91662	−	12.9755i	−0.222360	−	0.487650i
$709$	0.436423	+	17.7779i	0.0163902	+	0.667663i	0.950508	+	0.310699i	$0.100563\pi$
$709$	0.436423	+	17.7779i	0.0163902	+	0.667663i	−0.934118	+	0.356964i	$0.883812\pi$
$710$	−1.64001	+	10.5480i	−0.0615486	+	0.395859i
$711$	−16.0201	−	21.6005i	−0.600799	−	0.810084i
$712$	0.224812	−	4.93797i	0.00842517	−	0.185058i
$713$	0.209405	−	0.835992i	0.00784228	−	0.0313081i
$714$	−35.9605	+	6.89226i	−1.34579	+	0.257936i
$715$	6.58484	−	23.7946i	0.246259	−	0.889866i
$716$	−9.55713	−	30.3465i	−0.357167	−	1.13410i
$717$	1.28948	+	3.34285i	0.0481565	+	0.124841i
$718$	−2.63783	+	1.14729i	−0.0984428	+	0.0428166i
$719$	−16.8487	+	9.00584i	−0.628352	+	0.335861i	−0.754646	−	0.656132i	$-0.772192\pi$
$719$	−16.8487	+	9.00584i	−0.628352	+	0.335861i	0.126294	+	0.991993i	$0.459692\pi$
$720$	−7.87143	−	16.7899i	−0.293351	−	0.625722i
$721$	−9.47077	+	17.7186i	−0.352710	+	0.659874i
$722$	−18.6805	+	15.8878i	−0.695218	+	0.591281i
$723$	−25.4518	−	40.1929i	−0.946564	−	1.49479i
$724$	−23.0522	−	7.97423i	−0.856729	−	0.296360i
$725$	12.1833	+	6.13254i	0.452475	+	0.227757i
$726$	−1.11936	+	0.331034i	−0.0415432	+	0.0122858i
$727$	−6.70854	−	7.40174i	−0.248806	−	0.274515i	0.603724	−	0.797193i	$-0.293683\pi$
$727$	−6.70854	−	7.40174i	−0.248806	−	0.274515i	−0.852530	+	0.522678i	$0.824933\pi$
$728$	6.76055	+	11.8347i	0.250563	+	0.438624i
$729$	−1.03728	+	2.89902i	−0.0384179	+	0.107371i
$730$	−12.2239	−	20.7212i	−0.452427	−	0.766925i
$731$	11.4050	−	2.56108i	0.421829	−	0.0947250i
$732$	−15.8925	+	49.8719i	−0.587402	+	1.84332i
$733$	29.0563	−	22.6757i	1.07322	−	0.837547i	0.0858996	−	0.996304i	$-0.472624\pi$
$733$	29.0563	−	22.6757i	1.07322	−	0.837547i	0.987318	+	0.158757i	$0.0507486\pi$
$734$	−12.9615	+	3.48966i	−0.478417	+	0.128806i
$735$	4.55970	−	22.9231i	0.168187	−	0.845533i
$736$	0.219941	−	1.04873i	0.00810715	−	0.0386567i
$737$	6.92220	+	34.8003i	0.254983	+	1.28188i
$738$	−1.77670	−	3.59195i	−0.0654014	−	0.132222i
$739$	6.09087	+	22.0096i	0.224056	+	0.809636i	0.986663	+	0.162774i	$0.0520440\pi$
$739$	6.09087	+	22.0096i	0.224056	+	0.809636i	−0.762607	+	0.646862i	$0.776081\pi$
$740$	−38.2650	+	24.8019i	−1.40665	+	0.911734i
$741$	−4.65845	−	6.61450i	−0.171133	−	0.242990i
$742$	0.00982366	+	0.00473048i	0.000360638	+	0.000173661i
$743$	19.0054	−	20.9693i	0.697241	−	0.769287i	−0.284670	−	0.958625i	$-0.591884\pi$
$743$	19.0054	−	20.9693i	0.697241	−	0.769287i	0.981912	+	0.189338i	$0.0606342\pi$
$744$	16.1729	−	23.1398i	0.592927	−	0.848348i
$745$	−29.0769	−	13.7523i	−1.06529	−	0.503846i
$746$	−6.75499	+	21.7210i	−0.247318	+	0.795261i
$747$	12.9725	−	11.1902i	0.474640	−	0.409427i
$748$	−1.82087	+	47.2575i	−0.0665775	+	1.72790i
$749$	−3.88015	+	5.50939i	−0.141778	+	0.201309i
$750$	−23.9879	+	13.3686i	−0.875916	+	0.488151i
$751$	−1.09895	+	0.901882i	−0.0401011	+	0.0329101i	−0.654230	−	0.756295i	$-0.727007\pi$
$751$	−1.09895	+	0.901882i	−0.0401011	+	0.0329101i	0.614129	+	0.789205i	$0.289507\pi$
$752$	19.0353	−	26.8343i	0.694147	−	0.978545i
$753$	4.60694	−	5.61358i	0.167886	−	0.204570i
$754$	−29.4877	+	20.4610i	−1.07388	+	0.745145i
$755$	−0.358468	−	0.00879990i	−0.0130460	−	0.000320261i
$756$	−6.26470	−	6.13358i	−0.227845	−	0.223076i
$757$	15.4064	−	1.90020i	0.559955	−	0.0690639i	0.162539	−	0.986702i	$-0.448032\pi$
$757$	15.4064	−	1.90020i	0.559955	−	0.0690639i	0.397417	+	0.917638i	$0.369907\pi$
$758$	−13.1296	−	13.3143i	−0.476890	−	0.483598i
$759$	0.834964	−	1.12582i	0.0303073	−	0.0408646i
$760$	−9.26882	+	0.946525i	−0.336215	+	0.0343341i
$761$	10.2394	+	6.13726i	0.371178	+	0.222475i	0.687513	−	0.726172i	$-0.258702\pi$
$761$	10.2394	+	6.13726i	0.371178	+	0.222475i	−0.316335	+	0.948647i	$0.602452\pi$
$762$	8.48178	−	9.22786i	0.307263	−	0.334290i
$763$	4.19896	+	1.61972i	0.152013	+	0.0586378i
$764$	−7.76238	−	22.6886i	−0.280833	−	0.820845i
$765$	−30.8604	−	10.1949i	−1.11576	−	0.368598i
$766$	0.880205	−	1.94886i	0.0318031	−	0.0704150i
$767$			9.30402i			0.335949i
$768$	18.9800	−	29.5276i	0.684883	−	1.06549i
$769$		−	35.3311i		−	1.27407i	−0.770834	−	0.637036i	$-0.780160\pi$
$769$		−	35.3311i		−	1.27407i	0.770834	−	0.637036i	$-0.219840\pi$
$770$	18.7118	+	8.45122i	0.674326	+	0.304561i
$771$	−6.22439	−	2.05626i	−0.224166	−	0.0740545i
$772$	−39.8696	−	19.5430i	−1.43494	−	0.703368i
$773$	−27.5368	−	10.6221i	−0.990430	−	0.382051i	−0.190201	−	0.981745i	$-0.560914\pi$
$773$	−27.5368	−	10.6221i	−0.990430	−	0.382051i	−0.800229	+	0.599694i	$0.795289\pi$
$774$	−3.14733	−	2.89287i	−0.113128	−	0.103982i
$775$	6.00380	+	3.59854i	0.215663	+	0.129263i
$776$	15.3403	+	28.4534i	0.550685	+	1.02142i
$777$	19.6156	−	26.4486i	0.703706	−	0.948838i
$778$	−10.6791	+	10.5310i	−0.382866	+	0.377555i
$779$	−1.99832	+	0.246469i	−0.0715972	+	0.00883068i
$780$	0.339656	+	32.1155i	0.0121616	+	1.14992i
$781$	−9.95339	−	0.244342i	−0.356160	−	0.00874324i
$782$	−1.07066	−	1.54300i	−0.0382868	−	0.0551777i
$783$	14.6465	−	17.8468i	0.523423	−	0.637793i
$784$	15.5689	−	5.94500i	0.556033	−	0.212321i
$785$	13.9374	−	11.4381i	0.497448	−	0.408245i
$786$	22.1447	+	39.7355i	0.789877	+	1.41732i
$787$	10.6265	−	15.0885i	0.378794	−	0.537846i	−0.582695	−	0.812691i	$-0.698002\pi$
$787$	10.6265	−	15.0885i	0.378794	−	0.537846i	0.961488	+	0.274845i	$0.0886266\pi$
$788$	28.6526	+	30.9491i	1.02071	+	1.10252i
$789$	−34.5920	+	29.8392i	−1.23151	+	1.06231i
$790$	51.2215	+	15.9294i	1.82238	+	0.566741i
$791$	24.7457	+	11.7038i	0.879856	+	0.416141i
$792$	14.5789	−	9.30553i	0.518040	−	0.330658i
$793$	22.9334	−	25.3031i	0.814389	−	0.898539i
$794$	10.6822	−	22.1835i	0.379098	−	0.787263i
$795$	0.0147942	+	0.0210062i	0.000524697	+	0.000745012i
$796$	53.6579	+	11.4546i	1.90185	+	0.405997i
$797$	−0.216429	−	0.782076i	−0.00766633	−	0.0277025i	0.959843	−	0.280536i	$-0.0905124\pi$
$797$	−0.216429	−	0.782076i	−0.00766633	−	0.0277025i	−0.967510	+	0.252834i	$0.918637\pi$
$798$	6.03064	−	2.98296i	0.213482	−	0.105596i
$799$	−11.2496	−	56.5556i	−0.397983	−	2.00079i
$800$	7.63239	+	4.18199i	0.269846	+	0.147856i
$801$	−0.618131	+	3.10756i	−0.0218406	+	0.109800i
$802$	6.28961	+	23.3612i	0.222094	+	0.824914i
$803$	17.6898	−	13.8053i	0.624260	−	0.487177i
$804$	−21.1880	−	41.0076i	−0.747243	−	1.44623i
$805$	−0.795545	+	0.178646i	−0.0280393	+	0.00629643i
$806$	−15.8640	+	9.35856i	−0.558787	+	0.329641i
$807$	−2.55332	+	7.13606i	−0.0898812	+	0.251201i
$808$	−29.1816	−	22.6054i	−1.02661	−	0.795254i
$809$	26.6564	+	29.4108i	0.937189	+	1.03403i	0.999353	+	0.0359626i	$0.0114497\pi$
$809$	26.6564	+	29.4108i	0.937189	+	1.03403i	−0.0621643	+	0.998066i	$0.519800\pi$
$810$	−11.4368	−	38.6725i	−0.401850	−	1.35881i
$811$	15.0598	+	7.58044i	0.528820	+	0.266185i	0.693871	−	0.720100i	$-0.255904\pi$
$811$	15.0598	+	7.58044i	0.528820	+	0.266185i	−0.165051	+	0.986285i	$0.552779\pi$
$812$	−13.0462	−	26.8456i	−0.457832	−	0.942097i
$813$	−19.5097	−	30.8092i	−0.684236	−	1.08053i
$814$	−27.5547	−	32.3983i	−0.965791	−	1.13556i
$815$	−23.9429	+	44.7939i	−0.838682	+	1.56906i
$816$	−14.7461	−	59.7286i	−0.516216	−	2.09092i
$817$	−1.89425	+	1.01250i	−0.0662715	+	0.0354229i
$818$	15.9069	+	36.5727i	0.556171	+	1.27873i
$819$	−3.14416	−	8.15094i	−0.109866	−	0.284817i
$820$	7.08880	+	3.69319i	0.247551	+	0.128972i
$821$	11.9332	−	43.1212i	0.416473	−	1.50494i	−0.393970	−	0.919123i	$-0.628899\pi$
$821$	11.9332	−	43.1212i	0.416473	−	1.50494i	0.810443	−	0.585817i	$-0.199226\pi$
$822$	8.11415	+	42.3357i	0.283013	+	1.47663i
$823$	−5.34297	+	21.3303i	−0.186244	+	0.743529i	0.802842	+	0.596192i	$0.203320\pi$
$823$	−5.34297	+	21.3303i	−0.186244	+	0.743529i	−0.989086	+	0.147337i	$0.952930\pi$
$824$	−30.5680	−	14.3235i	−1.06489	−	0.498982i
$825$	6.78153	+	9.14384i	0.236103	+	0.318348i
$826$	−7.64555	−	1.18874i	−0.266023	−	0.0413615i
$827$	0.349993	+	14.2571i	0.0121705	+	0.495769i	0.974564	+	0.224110i	$0.0719474\pi$
$827$	0.349993	+	14.2571i	0.0121705	+	0.495769i	−0.962393	+	0.271659i	$0.912428\pi$
$828$	−0.240400	+	0.643397i	−0.00835448	+	0.0223596i
$829$	−11.3256	+	13.1295i	−0.393355	+	0.456008i	−0.918744	−	0.394855i	$-0.870795\pi$
$829$	−11.3256	+	13.1295i	−0.393355	+	0.456008i	0.525389	+	0.850862i	$0.323920\pi$
$830$	−7.71981	+	33.2886i	−0.267959	+	1.15547i
$831$	25.2547	+	60.9703i	0.876077	+	2.11504i
$832$	−19.2594	+	12.3906i	−0.667701	+	0.429568i
$833$	11.1778	−	26.9857i	0.387289	−	0.934999i
$834$	−9.71476	−	6.94391i	−0.336395	−	0.240448i
$835$	1.30669	+	17.7143i	0.0452197	+	0.613029i
$836$	−1.99356	−	8.45830i	−0.0689489	−	0.292536i
$837$	8.16974	−	8.58094i	0.282387	−	0.296601i
$838$	−20.9402	+	5.09008i	−0.723366	+	0.175834i
$839$	21.3585	+	3.16823i	0.737377	+	0.109380i	0.504846	−	0.863209i	$-0.331549\pi$
$839$	21.3585	+	3.16823i	0.737377	+	0.109380i	0.232531	+	0.972589i	$0.425299\pi$
$840$	−26.4342	−	3.82417i	−0.912068	−	0.131946i
$841$	42.5425	−	25.4990i	1.46698	−	0.879276i
$842$	−6.05249	+	29.3550i	−0.208583	+	1.01164i
$843$	18.4502	+	32.5691i	0.635458	+	1.12174i
$844$	15.4932	+	4.52146i	0.533300	+	0.155635i
$845$	−4.97947	+	11.2335i	−0.171299	+	0.386444i
$846$	−14.6477	+	15.1713i	−0.503597	+	0.521601i
$847$	−0.183845	+	0.606055i	−0.00631698	+	0.0208243i
$848$	−0.00706819	+	0.0169017i	−0.000242723	+	0.000580407i
$849$	20.9375	−	6.35131i	0.718572	−	0.217976i
$850$	14.5168	−	4.68352i	0.497923	−	0.160643i
$851$	1.64796	+	0.370062i	0.0564913	+	0.0126856i
$852$	12.5299	−	3.27979i	0.429268	−	0.112364i
$853$	11.6028	+	35.1221i	0.397271	+	1.20256i	0.933529	+	0.358503i	$0.116713\pi$
$853$	11.6028	+	35.1221i	0.397271	+	1.20256i	−0.536258	+	0.844054i	$0.680162\pi$
$854$	17.8626	+	22.0783i	0.611247	+	0.755505i
$855$	5.96486	+	0.293035i	0.203994	+	0.0100216i
$856$	−9.58754	−	6.02311i	−0.327695	−	0.205866i
$857$	23.7165	−	11.2171i	0.810140	−	0.383167i	0.0228408	−	0.999739i	$-0.492729\pi$
$857$	23.7165	−	11.2171i	0.810140	−	0.383167i	0.787299	+	0.616572i	$0.211479\pi$
$858$	−29.6618	+	4.18841i	−1.01264	+	0.142990i
$859$	−28.3492	+	44.7682i	−0.967261	+	1.52747i	−0.122403	+	0.992480i	$0.539060\pi$
$859$	−28.3492	+	44.7682i	−0.967261	+	1.52747i	−0.844858	+	0.534991i	$0.820315\pi$
$860$	8.47319	+	0.954210i	0.288933	+	0.0325383i
$861$	−5.72865	−	0.706561i	−0.195232	−	0.0240795i
$862$	−42.4620	+	32.6631i	−1.44626	+	1.11251i
$863$	15.4206	+	23.0786i	0.524925	+	0.785605i	0.995298	−	0.0968624i	$-0.0308807\pi$
$863$	15.4206	+	23.0786i	0.524925	+	0.785605i	−0.470373	+	0.882468i	$0.655881\pi$
$864$	9.73733	−	11.0543i	0.331271	−	0.376073i
$865$	−14.1559	+	21.1858i	−0.481315	+	0.720338i
$866$	−3.09384	−	46.3526i	−0.105133	−	1.57512i
$867$	−61.3700	−	34.7657i	−2.08423	−	1.18070i
$868$	−5.66348	−	14.2319i	−0.192231	−	0.483063i
$869$	−8.55350	+	49.2950i	−0.290158	+	1.67222i
$870$	3.94169	−	70.2241i	0.133636	−	2.38082i
$871$	1.47764	+	30.0781i	0.0500679	+	1.01916i
$872$	−2.34625	+	7.18878i	−0.0794540	+	0.243443i
$873$	−6.98034	−	19.5087i	−0.236249	−	0.660270i
$874$	0.265229	+	0.220786i	0.00897152	+	0.00746820i
$875$	−1.09609	+	14.8593i	−0.0370547	+	0.502338i
$876$	−17.1399	+	23.6287i	−0.579104	+	0.798341i
$877$	2.36549	−	0.410452i	0.0798770	−	0.0138600i	−0.130883	−	0.991398i	$-0.541781\pi$
$877$	2.36549	−	0.410452i	0.0798770	−	0.0138600i	0.210760	+	0.977538i	$0.432406\pi$
$878$	6.38326	−	8.06266i	0.215425	−	0.272102i
$879$	−2.67807	+	27.1909i	−0.0903289	+	0.917125i
$880$	−12.5249	+	32.1444i	−0.422214	+	1.08359i
$881$	1.54316	−	0.151988i	0.0519903	−	0.00512060i	−0.0719885	−	0.997405i	$-0.522934\pi$
$881$	1.54316	−	0.151988i	0.0519903	−	0.00512060i	0.123979	+	0.992285i	$0.460434\pi$
$882$	−10.4388	+	2.26764i	−0.351491	+	0.0763554i
$883$	32.5646	−	31.0040i	1.09588	−	1.04337i	0.0970418	−	0.995280i	$-0.469062\pi$
$883$	32.5646	−	31.0040i	1.09588	−	1.04337i	0.998843	−	0.0480888i	$-0.0153131\pi$
$884$	−7.41380	+	39.4475i	−0.249353	+	1.32676i
$885$	−14.3737	−	11.2174i	−0.483168	−	0.377068i
$886$	−20.1060	+	47.5972i	−0.675475	+	1.59906i
$887$	−2.08192	−	14.0352i	−0.0699042	−	0.471256i	−0.995655	−	0.0931210i	$-0.970316\pi$
$887$	−2.08192	−	14.0352i	−0.0699042	−	0.471256i	0.925751	−	0.378135i	$-0.123434\pi$
$888$	46.1138	+	30.5732i	1.54748	+	1.02597i
$889$	−1.65235	−	6.59656i	−0.0554181	−	0.221242i
$890$	−2.66212	−	5.73181i	−0.0892345	−	0.192131i
$891$	34.3874	−	15.2429i	1.15202	−	0.510656i
$892$	2.80364	+	4.82930i	0.0938727	+	0.161697i
$893$	4.76397	+	9.46438i	0.159420	+	0.316713i
$894$	−1.23023	+	39.0078i	−0.0411452	+	1.30462i
$895$	−28.7633	−	28.7633i	−0.961450	−	0.961450i
$896$	−7.72125	−	17.4095i	−0.257949	−	0.581611i
$897$	0.841183	−	0.841183i	0.0280863	−	0.0280863i
$898$	0.270148	+	0.287743i	0.00901495	+	0.00960210i
$899$	36.0289	−	18.1354i	1.20163	−	0.604849i
$900$	−4.43383	−	3.38536i	−0.147794	−	0.112845i
$901$	0.0130121	+	0.0293547i	0.000433494	+	0.000977948i
$902$	−2.56057	+	7.00177i	−0.0852577	+	0.233133i
$903$	−5.97284	+	1.49612i	−0.198764	+	0.0497877i
$904$	−17.4487	+	42.5565i	−0.580334	+	1.41541i
$905$	−30.8488	+	4.57599i	−1.02545	+	0.152111i
$906$	0.163685	+	0.403110i	0.00543806	+	0.0133924i
$907$	−27.6338	+	35.4095i	−0.917566	+	1.17575i	0.0664709	+	0.997788i	$0.478826\pi$
$907$	−27.6338	+	35.4095i	−0.917566	+	1.17575i	−0.984037	+	0.177964i	$0.943049\pi$
$908$	−3.87211	−	2.52844i	−0.128500	−	0.0839092i
$909$	16.3149	+	17.1361i	0.541133	+	0.568369i
$910$	14.6567	+	9.42532i	0.485866	+	0.312446i
$911$	3.35142	+	34.0275i	0.111037	+	1.12738i	0.875668	+	0.482913i	$0.160421\pi$
$911$	3.35142	+	34.0275i	0.111037	+	1.12738i	−0.764631	+	0.644469i	$0.777079\pi$
$912$	5.53868	+	9.85495i	0.183404	+	0.326330i
$913$	−31.7191	−	3.12405i	−1.04975	−	0.103391i
$914$	4.58890	+	39.4731i	0.151787	+	1.30565i
$915$	11.4410	+	65.9363i	0.378229	+	2.17979i
$916$	−25.0435	−	5.99232i	−0.827459	−	0.197992i
$917$	24.6142	+	1.81565i	0.812832	+	0.0599581i
$918$	−2.35123	−	25.7121i	−0.0776020	−	0.848625i
$919$	23.2392	−	8.31514i	0.766592	−	0.274291i	0.0755853	−	0.997139i	$-0.475917\pi$
$919$	23.2392	−	8.31514i	0.766592	−	0.274291i	0.691007	+	0.722848i	$0.257167\pi$
$920$	−0.370135	−	1.31905i	−0.0122030	−	0.0434877i
$921$	−58.0206	+	2.85037i	−1.91184	+	0.0939228i
$922$	2.05656	+	2.30115i	0.0677291	+	0.0757845i
$923$	−8.32578	−	1.44466i	−0.274046	−	0.0475515i
$924$	0.347961	−	24.9096i	0.0114471	−	0.819467i
$925$	−6.76155	+	11.9358i	−0.222318	+	0.392447i
$926$	27.8646	−	31.8504i	0.915689	−	1.04667i
$927$	17.9913	+	12.0214i	0.590912	+	0.394835i
$928$	43.8903	−	24.2655i	1.44077	−	0.796553i
$929$	45.0653	−	30.1117i	1.47854	−	0.987932i	0.484997	−	0.874516i	$-0.338821\pi$
$929$	45.0653	−	30.1117i	1.47854	−	0.987932i	0.993548	−	0.113416i	$-0.0361792\pi$
$930$	4.66844	−	35.7914i	0.153084	−	1.17365i
$931$	−0.657003	+	5.32684i	−0.0215324	+	0.174580i
$932$	24.2178	−	6.97853i	0.793281	−	0.228589i
$933$	−47.7374	−	30.2294i	−1.56285	−	0.989666i
$934$	−26.8322	−	20.1921i	−0.877975	−	0.660705i
$935$	25.8520	+	54.6594i	0.845450	+	1.78755i
$936$	13.3984	−	5.99675i	0.437939	−	0.196010i
$937$	−2.59533	+	52.8292i	−0.0847858	+	1.72586i	0.460546	+	0.887636i	$0.347653\pi$
$937$	−2.59533	+	52.8292i	−0.0847858	+	1.72586i	−0.545332	+	0.838220i	$0.683597\pi$
$938$	−24.9053	−	2.62871i	−0.813188	−	0.0858305i
$939$	2.24230	−	0.740757i	0.0731748	−	0.0241737i
$940$	5.73165	−	41.6713i	0.186946	−	1.35917i
$941$	1.45249	−	6.46822i	0.0473498	−	0.210858i	−0.946314	−	0.323247i	$-0.895225\pi$
$941$	1.45249	−	6.46822i	0.0473498	−	0.210858i	0.993664	+	0.112389i	$0.0358504\pi$
$942$	−19.4715	−	9.97220i	−0.634417	−	0.324912i
$943$	−0.0859427	−	0.283315i	−0.00279868	−	0.00922601i
$944$	1.31817	−	12.9337i	0.0429029	−	0.420956i
$945$	−10.7267	−	3.25390i	−0.348938	−	0.105849i
$946$	0.139644	+	7.95174i	0.00454023	+	0.258533i
$947$	−12.6572	−	5.61054i	−0.411303	−	0.182318i	0.189204	−	0.981938i	$-0.439409\pi$
$947$	−12.6572	−	5.61054i	−0.411303	−	0.182318i	−0.600506	+	0.799620i	$0.705034\pi$
$948$	−7.06410	−	64.7007i	−0.229431	−	2.10138i
$949$	16.5704	−	9.38703i	0.537899	−	0.304716i
$950$	−2.34132	+	1.54088i	−0.0759625	+	0.0499927i
$951$	12.9995	+	21.6883i	0.421537	+	0.703293i
$952$	−31.4686	−	11.1323i	−1.01990	−	0.360801i
$953$	4.83225	−	32.5764i	0.156532	−	1.05525i	−0.758443	−	0.651740i	$-0.774039\pi$
$953$	4.83225	−	32.5764i	0.156532	−	1.05525i	0.914974	−	0.403512i	$-0.132211\pi$
$954$	0.00610725	−	0.0100298i	0.000197730	−	0.000324727i
$955$	−22.2044	−	21.1404i	−0.718519	−	0.684087i
$956$	−0.524354	+	3.22398i	−0.0169588	+	0.104271i
$957$	65.4239	−	4.82595i	2.11485	−	0.156001i
$958$	−3.90099	−	23.4532i	−0.126035	−	0.757738i
$959$	21.6077	+	8.95019i	0.697748	+	0.289017i
$960$	4.07790	−	44.6926i	0.131614	−	1.44245i
$961$	−9.51630	+	3.94178i	−0.306977	+	0.127154i
$962$	−19.0984	−	30.6309i	−0.615758	−	0.987581i
$963$	5.49546	+	4.74042i	0.177089	+	0.152758i
$964$	−1.52282	−	43.3434i	−0.0490467	−	1.39600i
$965$	−56.7516	+	1.39317i	−1.82690	+	0.0448479i
$966$	0.583765	+	0.798714i	0.0187823	+	0.0256982i
$967$	−18.4502	+	13.6836i	−0.593318	+	0.440035i	−0.850238	−	0.526398i	$-0.823542\pi$
$967$	−18.4502	+	13.6836i	−0.593318	+	0.440035i	0.256920	+	0.966433i	$0.417292\pi$
$968$	−1.03317	−	0.254855i	−0.0332073	−	0.00819136i
$969$	19.2198	+	4.81432i	0.617430	+	0.154658i
$970$	34.2023	+	23.2004i	1.09817	+	0.744919i
$971$	35.7942	+	9.90560i	1.14869	+	0.317886i	0.788525	−	0.615003i	$-0.210845\pi$
$971$	35.7942	+	9.90560i	1.14869	+	0.317886i	0.360166	+	0.932888i	$0.382720\pi$
$972$	−25.5217	+	21.4008i	−0.818608	+	0.686430i
$973$	−6.04480	+	2.33173i	−0.193787	+	0.0747520i
$974$	−21.6690	+	55.0270i	−0.694318	+	1.76318i
$975$	4.55462	+	8.52109i	0.145864	+	0.272893i
$976$	−35.4651	+	31.9252i	−1.13521	+	1.02190i
$977$	−11.4356	−	6.11247i	−0.365858	−	0.195555i	0.278216	−	0.960519i	$-0.410257\pi$
$977$	−11.4356	−	6.11247i	−0.365858	−	0.195555i	−0.644074	+	0.764963i	$0.722757\pi$
$978$	61.4271	+	4.96270i	1.96422	+	0.158690i
$979$	4.98005	−	3.15358i	0.159163	−	0.100789i
$980$	14.1412	−	15.9379i	0.451724	−	0.509118i
$981$	2.17931	−	4.32954i	0.0695800	−	0.138232i
$982$	21.2915	−	39.1731i	0.679441	−	1.25006i
$983$	−8.28452	+	7.50865i	−0.264235	+	0.239489i	−0.792915	−	0.609333i	$-0.791437\pi$
$983$	−8.28452	+	7.50865i	−0.264235	+	0.239489i	0.528679	+	0.848822i	$0.322687\pi$
$984$	0.678717	−	9.67466i	0.0216367	−	0.308417i
$985$	50.7709	+	18.1661i	1.61770	+	0.578821i
$986$	21.9528	−	85.1142i	0.699121	−	2.71059i
$987$	6.65524	+	29.6371i	0.211839	+	0.943360i
$988$	−0.620327	−	7.34929i	−0.0197352	−	0.233812i
$989$	−0.194307	−	0.248981i	−0.00617860	−	0.00791714i
$990$	11.0335	−	19.1635i	0.350667	−	0.609056i
$991$	38.4256	+	7.64333i	1.22063	+	0.242798i	0.763032	−	0.646361i	$-0.223710\pi$
$991$	38.4256	+	7.64333i	1.22063	+	0.242798i	0.457598	+	0.889159i	$0.348710\pi$
$992$	23.3788	−	10.7619i	0.742278	−	0.341692i
$993$	−57.2652	+	11.3908i	−1.81726	+	0.361475i
$994$	2.25090	−	6.65711i	0.0713942	−	0.211151i
$995$	67.6076	−	18.7095i	2.14331	−	0.593132i
$996$	40.7747	−	7.52012i	1.29200	−	0.238284i
$997$	43.7269	−	30.7960i	1.38485	−	0.975319i	0.386248	−	0.922395i	$-0.373771\pi$
$997$	43.7269	−	30.7960i	1.38485	−	0.975319i	0.998599	−	0.0529236i	$-0.0168540\pi$
$998$	11.6485	−	4.07637i	0.368728	−	0.129035i
$999$	17.2048	+	15.5936i	0.544337	+	0.493359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.141.27	yes	4032
512.69	even	128	inner	512.2.o.a.69.27	✓	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.69.27	✓	4032	512.69	even	128	inner
512.2.o.a.141.27	yes	4032	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.499741 - 1.32297i) q^{2} +(-0.688170 + 2.08312i) q^{3} +(-1.50052 + 1.32229i) q^{4} +(-0.920269 + 2.38571i) q^{5} +(3.09982 - 0.130590i) q^{6} +(0.865414 - 1.44386i) q^{7} +(2.49922 + 1.32434i) q^{8} +(-1.45619 - 1.07999i) q^{9} +O(q^{10})\)	\(q+(-0.499741 - 1.32297i) q^{2} +(-0.688170 + 2.08312i) q^{3} +(-1.50052 + 1.32229i) q^{4} +(-0.920269 + 2.38571i) q^{5} +(3.09982 - 0.130590i) q^{6} +(0.865414 - 1.44386i) q^{7} +(2.49922 + 1.32434i) q^{8} +(-1.45619 - 1.07999i) q^{9} +(3.61612 + 0.0252554i) q^{10} +(0.412875 + 3.34750i) q^{11} +(-1.72188 - 4.03572i) q^{12} +(-0.0702522 + 2.86176i) q^{13} +(-2.34267 - 0.423366i) q^{14} +(-4.33642 - 3.55880i) q^{15} +(0.503107 - 3.96823i) q^{16} +(-4.44756 - 5.41937i) q^{17} +(-0.701075 + 2.46622i) q^{18} +(1.05324 + 0.741773i) q^{19} +(-1.77371 - 4.79666i) q^{20} +(2.41217 + 2.79638i) q^{21} +(4.22232 - 2.21911i) q^{22} +(-0.0809892 + 0.171237i) q^{23} +(-4.47866 + 4.29481i) q^{24} +(-1.13995 - 1.03319i) q^{25} +(3.82114 - 1.33720i) q^{26} +(-2.12912 + 1.49949i) q^{27} +(0.610625 + 3.31086i) q^{28} +(-8.54446 + 2.36457i) q^{29} +(-2.54112 + 7.51544i) q^{30} +(-4.46226 + 0.887600i) q^{31} +(-5.50129 + 1.31749i) q^{32} +(-7.25738 - 1.44358i) q^{33} +(-4.94706 + 8.59229i) q^{34} +(2.64820 + 3.39336i) q^{35} +(3.61310 - 0.304969i) q^{36} +(-1.95362 - 8.69985i) q^{37} +(0.455001 - 1.76410i) q^{38} +(-5.91304 - 2.11572i) q^{39} +(-5.45945 + 4.74366i) q^{40} +(-1.15808 + 1.04962i) q^{41} +(2.49407 - 4.58871i) q^{42} +(-0.749639 + 1.48928i) q^{43} +(-5.04589 - 4.47705i) q^{44} +(3.91662 - 2.48017i) q^{45} +(0.267016 + 0.0215723i) q^{46} +(7.25384 + 3.87726i) q^{47} +(7.92009 + 3.77885i) q^{48} +(1.96400 + 3.67438i) q^{49} +(-0.797201 + 2.02444i) q^{50} +(14.3499 - 5.53536i) q^{51} +(-3.67865 - 4.38701i) q^{52} +(-0.00441413 - 0.00122155i) q^{53} +(3.04780 + 2.06741i) q^{54} +(-8.36611 - 2.09560i) q^{55} +(4.07502 - 2.46241i) q^{56} +(-2.27001 + 1.68356i) q^{57} +(7.39828 + 10.1224i) q^{58} +(3.24920 - 0.0797633i) q^{59} +(11.2126 - 0.393943i) q^{60} +(-9.03309 - 7.79199i) q^{61} +(3.40425 + 5.45989i) q^{62} +(-2.81956 + 1.16790i) q^{63} +(4.49223 + 6.61966i) q^{64} +(-6.76266 - 2.80119i) q^{65} +(1.71699 + 10.3227i) q^{66} +(10.4913 - 0.773888i) q^{67} +(13.8396 + 2.25090i) q^{68} +(-0.300974 - 0.286551i) q^{69} +(3.16591 - 5.19930i) q^{70} +(-0.433135 + 2.91996i) q^{71} +(-2.20908 - 4.62763i) q^{72} +(-3.42024 - 5.70633i) q^{73} +(-10.5334 + 6.93225i) q^{74} +(2.93673 - 1.66364i) q^{75} +(-2.56124 + 0.279639i) q^{76} +(5.19062 + 2.30084i) q^{77} +(0.155948 + 8.88011i) q^{78} +(14.1948 + 4.30595i) q^{79} +(9.00405 + 4.85211i) q^{80} +(-3.23727 - 10.6718i) q^{81} +(1.96737 + 1.00757i) q^{82} +(-2.07044 + 9.22008i) q^{83} +(-7.31713 - 1.00643i) q^{84} +(17.0220 - 5.62330i) q^{85} +(2.34490 + 0.247500i) q^{86} +(0.954357 - 19.4264i) q^{87} +(-3.40138 + 8.91294i) q^{88} +(-0.747215 - 1.57985i) q^{89} +(-5.23850 - 3.94214i) q^{90} +(4.07117 + 2.57804i) q^{91} +(-0.104899 - 0.364036i) q^{92} +(1.22182 - 9.90626i) q^{93} +(1.50447 - 11.5343i) q^{94} +(-2.73892 + 1.83008i) q^{95} +(1.04133 - 12.3665i) q^{96} +(9.50261 + 6.34944i) q^{97} +(3.87962 - 4.43456i) q^{98} +(3.01403 - 5.32051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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