LMFDB - Embedded newform 462.2.y.b.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			289.3
Character	$\chi$	$=$	462.289
Dual form			462.2.y.b.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.97343 - 0.878627i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.867452 + 2.49951i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.97343 - 0.878627i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.867452 + 2.49951i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.08009 - 1.87078i) q^{10} +(2.39384 - 2.29555i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.0379411 - 0.0275658i) q^{13} +(2.39514 - 1.12397i) q^{14} +(0.667534 - 2.05446i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.255923 - 2.43494i) q^{17} +(-0.978148 + 0.207912i) q^{18} +(3.96305 + 0.842372i) q^{19} +(-1.74763 + 1.26973i) q^{20} +(2.43793 + 1.02785i) q^{21} +(-2.53320 - 2.14078i) q^{22} +(-0.166857 + 0.289005i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-0.223220 + 0.247911i) q^{25} +(-0.0313807 - 0.0348518i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.36817 - 2.26453i) q^{28} +(-0.528046 + 1.62516i) q^{29} +(-2.11298 - 0.449128i) q^{30} +(-6.74262 - 3.00201i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.104132 - 3.31499i) q^{33} -2.44836 q^{34} +(3.90799 + 4.17043i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-7.02130 - 7.79795i) q^{37} +(0.423506 - 4.02939i) q^{38} +(0.00490215 - 0.0466409i) q^{39} +(1.44545 + 1.60533i) q^{40} +(1.71407 + 5.27536i) q^{41} +(0.767389 - 2.53202i) q^{42} +1.20405 q^{43} +(-1.86426 + 2.74309i) q^{44} +(-1.08009 - 1.87078i) q^{45} +(0.304863 + 0.135734i) q^{46} +(3.16170 + 0.672040i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-5.49505 + 4.33640i) q^{49} +(0.269886 + 0.196084i) q^{50} +(-1.63827 - 1.81948i) q^{51} +(-0.0313807 + 0.0348518i) q^{52} +(-1.04218 - 0.464009i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.70714 - 6.63339i) q^{55} +(-2.10911 + 1.59739i) q^{56} +(3.27780 - 2.38146i) q^{57} +(1.67145 + 0.355278i) q^{58} +(4.34164 - 0.922845i) q^{59} +(-0.225801 + 2.14835i) q^{60} +(-0.689815 + 0.307125i) q^{61} +(-2.28077 + 7.01948i) q^{62} +(2.39514 - 1.12397i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0506539 - 0.0877352i) q^{65} +(-3.28595 + 0.450072i) q^{66} +(5.85390 + 10.1393i) q^{67} +(0.255923 + 2.43494i) q^{68} +(0.103123 + 0.317381i) q^{69} +(3.73909 - 4.32251i) q^{70} +(-0.545177 - 0.396094i) q^{71} +(0.913545 - 0.406737i) q^{72} +(-9.02166 + 1.91761i) q^{73} +(-7.02130 + 7.79795i) q^{74} +(0.0348704 + 0.331770i) q^{75} -4.05159 q^{76} +(7.81427 + 3.99214i) q^{77} -0.0468978 q^{78} +(-0.0104096 - 0.0990408i) q^{79} +(1.44545 - 1.60533i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(5.06729 - 2.25610i) q^{82} +(5.09453 + 3.70139i) q^{83} +(-2.59836 - 0.498517i) q^{84} +(-1.63436 - 5.03005i) q^{85} +(-0.125857 - 1.19745i) q^{86} +(0.854397 + 1.47986i) q^{87} +(2.92293 + 1.56731i) q^{88} +(-6.90533 + 11.9604i) q^{89} +(-1.74763 + 1.26973i) q^{90} +(0.101813 + 0.0709219i) q^{91} +(0.103123 - 0.317381i) q^{92} +(-6.74262 + 3.00201i) q^{93} +(0.337871 - 3.21463i) q^{94} +(8.56092 - 1.81968i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-5.16852 + 3.75515i) q^{97} +(4.88704 + 5.01167i) q^{98} +(-2.53320 - 2.14078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	1.97343	−	0.878627i	0.882544	−	0.392934i	0.0851322	−	0.996370i	$-0.472869\pi$
$5$	1.97343	−	0.878627i	0.882544	−	0.392934i	0.797412	+	0.603436i	$0.206202\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	0.867452	+	2.49951i	0.327866	+	0.944724i
$7$	0.867452	+	2.49951i	0.327866	+	0.944724i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−1.08009	−	1.87078i	−0.341555	−	0.591591i
$11$	2.39384	−	2.29555i	0.721770	−	0.692133i
$11$	2.39384	−	2.29555i	0.721770	−	0.692133i
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.0379411	−	0.0275658i	0.0105230	−	0.00764538i	−0.582511	−	0.812823i	$-0.697930\pi$
$13$	0.0379411	−	0.0275658i	0.0105230	−	0.00764538i	0.593034	+	0.805177i	$0.297930\pi$
$14$	2.39514	−	1.12397i	0.640128	−	0.300393i
$15$	0.667534	−	2.05446i	0.172357	−	0.530459i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.255923	−	2.43494i	0.0620704	−	0.590561i	−0.918640	−	0.395095i	$-0.870712\pi$
$17$	0.255923	−	2.43494i	0.0620704	−	0.590561i	0.980711	−	0.195465i	$-0.0626217\pi$
$18$	−0.978148	+	0.207912i	−0.230552	+	0.0490053i
$19$	3.96305	+	0.842372i	0.909186	+	0.193253i	0.638687	−	0.769467i	$-0.279478\pi$
$19$	3.96305	+	0.842372i	0.909186	+	0.193253i	0.270499	+	0.962720i	$0.412811\pi$
$20$	−1.74763	+	1.26973i	−0.390781	+	0.283919i
$21$	2.43793	+	1.02785i	0.532001	+	0.224296i
$22$	−2.53320	−	2.14078i	−0.540079	−	0.456415i
$23$	−0.166857	+	0.289005i	−0.0347921	+	0.0602617i	−0.882897	−	0.469566i	$-0.844410\pi$
$23$	−0.166857	+	0.289005i	−0.0347921	+	0.0602617i	0.848105	+	0.529828i	$0.177744\pi$
$24$	0.913545	+	0.406737i	0.186477	+	0.0830248i
$25$	−0.223220	+	0.247911i	−0.0446440	+	0.0495822i
$26$	−0.0313807	−	0.0348518i	−0.00615427	−	0.00683501i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.36817	−	2.26453i	−0.258560	−	0.427956i
$29$	−0.528046	+	1.62516i	−0.0980557	+	0.301784i	−0.988038	−	0.154211i	$-0.950717\pi$
$29$	−0.528046	+	1.62516i	−0.0980557	+	0.301784i	0.889982	+	0.455995i	$0.150717\pi$
$30$	−2.11298	−	0.449128i	−0.385776	−	0.0819992i
$31$	−6.74262	−	3.00201i	−1.21101	−	0.539177i	−0.300945	−	0.953641i	$-0.597302\pi$
$31$	−6.74262	−	3.00201i	−1.21101	−	0.539177i	−0.910065	+	0.414465i	$0.863969\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.104132	−	3.31499i	−0.0181270	−	0.577066i
$34$	−2.44836			−0.419890
$35$	3.90799	+	4.17043i	0.660570	+	0.704931i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−7.02130	−	7.79795i	−1.15430	−	1.28197i	−0.953179	−	0.302407i	$-0.902210\pi$
$37$	−7.02130	−	7.79795i	−1.15430	−	1.28197i	−0.201116	−	0.979567i	$-0.564457\pi$
$38$	0.423506	−	4.02939i	0.0687017	−	0.653653i
$39$	0.00490215	−	0.0466409i	0.000784972	−	0.00746851i
$40$	1.44545	+	1.60533i	0.228545	+	0.253825i
$41$	1.71407	+	5.27536i	0.267692	+	0.823872i	0.991061	+	0.133410i	$0.0425928\pi$
$41$	1.71407	+	5.27536i	0.267692	+	0.823872i	−0.723368	+	0.690462i	$0.757407\pi$
$42$	0.767389	−	2.53202i	0.118411	−	0.390699i
$43$	1.20405			0.183616			0.0918078	−	0.995777i	$-0.470735\pi$
$43$	1.20405			0.183616			0.0918078	+	0.995777i	$0.470735\pi$
$44$	−1.86426	+	2.74309i	−0.281047	+	0.413536i
$45$	−1.08009	−	1.87078i	−0.161011	−	0.278879i
$46$	0.304863	+	0.135734i	0.0449496	+	0.0200129i
$47$	3.16170	+	0.672040i	0.461181	+	0.0980271i	0.432642	−	0.901566i	$-0.357581\pi$
$47$	3.16170	+	0.672040i	0.461181	+	0.0980271i	0.0285388	+	0.999593i	$0.490915\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−5.49505	+	4.33640i	−0.785008	+	0.619486i
$50$	0.269886	+	0.196084i	0.0381676	+	0.0277304i
$51$	−1.63827	−	1.81948i	−0.229404	−	0.254779i
$52$	−0.0313807	+	0.0348518i	−0.00435172	+	0.00483308i
$53$	−1.04218	−	0.464009i	−0.143155	−	0.0637366i	0.333909	−	0.942605i	$-0.391632\pi$
$53$	−1.04218	−	0.464009i	−0.143155	−	0.0637366i	−0.477064	+	0.878869i	$0.658299\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.70714	−	6.63339i	0.365031	−	0.894446i
$56$	−2.10911	+	1.59739i	−0.281842	+	0.213460i
$57$	3.27780	−	2.38146i	0.434155	−	0.315432i
$58$	1.67145	+	0.355278i	0.219472	+	0.0466503i
$59$	4.34164	−	0.922845i	0.565234	−	0.120144i	0.0835727	−	0.996502i	$-0.473367\pi$
$59$	4.34164	−	0.922845i	0.565234	−	0.120144i	0.481661	+	0.876358i	$0.340034\pi$
$60$	−0.225801	+	2.14835i	−0.0291508	+	0.277351i
$61$	−0.689815	+	0.307125i	−0.0883217	+	0.0393234i	−0.450422	−	0.892816i	$-0.648726\pi$
$61$	−0.689815	+	0.307125i	−0.0883217	+	0.0393234i	0.362100	+	0.932139i	$0.382060\pi$
$62$	−2.28077	+	7.01948i	−0.289658	+	0.891475i
$63$	2.39514	−	1.12397i	0.301759	−	0.141607i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.0506539	−	0.0877352i	0.00628285	−	0.0108822i
$66$	−3.28595	+	0.450072i	−0.404472	+	0.0554000i
$67$	5.85390	+	10.1393i	0.715168	+	1.23871i	0.962895	+	0.269877i	$0.0869830\pi$
$67$	5.85390	+	10.1393i	0.715168	+	1.23871i	−0.247727	+	0.968830i	$0.579684\pi$
$68$	0.255923	+	2.43494i	0.0310352	+	0.295280i
$69$	0.103123	+	0.317381i	0.0124146	+	0.0382082i
$70$	3.73909	−	4.32251i	0.446906	−	0.516638i
$71$	−0.545177	−	0.396094i	−0.0647006	−	0.0470077i	0.554965	−	0.831874i	$-0.312732\pi$
$71$	−0.545177	−	0.396094i	−0.0647006	−	0.0470077i	−0.619665	+	0.784866i	$0.712732\pi$
$72$	0.913545	−	0.406737i	0.107662	−	0.0479344i
$73$	−9.02166	+	1.91761i	−1.05591	+	0.224440i	−0.702978	−	0.711211i	$-0.748147\pi$
$73$	−9.02166	+	1.91761i	−1.05591	+	0.224440i	−0.352927	+	0.935651i	$0.614814\pi$
$74$	−7.02130	+	7.79795i	−0.816210	+	0.906493i
$75$	0.0348704	+	0.331770i	0.00402649	+	0.0383095i
$76$	−4.05159			−0.464749
$77$	7.81427	+	3.99214i	0.890519	+	0.454947i
$78$	−0.0468978			−0.00531013
$79$	−0.0104096	−	0.0990408i	−0.00117117	−	0.0111430i	0.993921	−	0.110098i	$-0.0351166\pi$
$79$	−0.0104096	−	0.0990408i	−0.00117117	−	0.0111430i	−0.995092	+	0.0989553i	$0.968450\pi$
$80$	1.44545	−	1.60533i	0.161606	−	0.179481i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	5.06729	−	2.25610i	0.559589	−	0.249145i
$83$	5.09453	+	3.70139i	0.559197	+	0.406281i	0.831165	−	0.556026i	$-0.187674\pi$
$83$	5.09453	+	3.70139i	0.559197	+	0.406281i	−0.271968	+	0.962306i	$0.587674\pi$
$84$	−2.59836	−	0.498517i	−0.283504	−	0.0543927i
$85$	−1.63436	−	5.03005i	−0.177271	−	0.545585i
$86$	−0.125857	−	1.19745i	−0.0135715	−	0.129125i
$87$	0.854397	+	1.47986i	0.0916009	+	0.158657i
$88$	2.92293	+	1.56731i	0.311586	+	0.167076i
$89$	−6.90533	+	11.9604i	−0.731963	+	1.26780i	0.224080	+	0.974571i	$0.428062\pi$
$89$	−6.90533	+	11.9604i	−0.731963	+	1.26780i	−0.956043	+	0.293227i	$0.905271\pi$
$90$	−1.74763	+	1.26973i	−0.184216	+	0.133841i
$91$	0.101813	+	0.0709219i	0.0106729	+	0.00743464i
$92$	0.103123	−	0.317381i	0.0107514	−	0.0330893i
$93$	−6.74262	+	3.00201i	−0.699177	+	0.311294i
$94$	0.337871	−	3.21463i	0.0348487	−	0.331563i
$95$	8.56092	−	1.81968i	0.878332	−	0.186695i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	−5.16852	+	3.75515i	−0.524784	+	0.381278i	−0.818403	−	0.574645i	$-0.805140\pi$
$97$	−5.16852	+	3.75515i	−0.524784	+	0.381278i	0.293619	+	0.955923i	$0.405140\pi$
$98$	4.88704	+	5.01167i	0.493665	+	0.506256i
$99$	−2.53320	−	2.14078i	−0.254596	−	0.215156i
$100$	0.166799	−	0.288904i	0.0166799	−	0.0288904i
$101$	−0.433258	−	0.192899i	−0.0431108	−	0.0191942i	0.385068	−	0.922888i	$-0.374178\pi$
$101$	−0.433258	−	0.192899i	−0.0431108	−	0.0191942i	−0.428179	+	0.903694i	$0.640845\pi$
$102$	−1.63827	+	1.81948i	−0.162213	+	0.180156i
$103$	−10.2122	−	11.3418i	−1.00624	−	1.11754i	−0.993058	−	0.117625i	$-0.962472\pi$
$103$	−10.2122	−	11.3418i	−1.00624	−	1.11754i	−0.0131779	−	0.999913i	$-0.504195\pi$
$104$	0.0379411	+	0.0275658i	0.00372043	+	0.00270305i
$105$	5.71418	−	0.113639i	0.557647	−	0.0110900i
$106$	−0.352530	+	1.08498i	−0.0342407	+	0.105382i
$107$	2.74045	+	0.582500i	0.264929	+	0.0563124i	0.338461	−	0.940980i	$-0.390094\pi$
$107$	2.74045	+	0.582500i	0.264929	+	0.0563124i	−0.0735318	+	0.997293i	$0.523427\pi$
$108$	0.913545	+	0.406737i	0.0879060	+	0.0391383i
$109$	7.87586	+	13.6414i	0.754371	+	1.30661i	0.945687	+	0.325080i	$0.105391\pi$
$109$	7.87586	+	13.6414i	0.754371	+	1.30661i	−0.191316	+	0.981529i	$0.561275\pi$
$110$	−6.88002	−	1.99893i	−0.655984	−	0.190591i
$111$	−10.4932			−0.995968
$112$	1.80910	+	1.93059i	0.170944	+	0.182423i
$113$	4.13197	+	12.7169i	0.388703	+	1.19631i	0.933758	+	0.357905i	$0.116509\pi$
$113$	4.13197	+	12.7169i	0.388703	+	1.19631i	−0.545055	+	0.838401i	$0.683491\pi$
$114$	−2.71104	−	3.01091i	−0.253912	−	0.281998i
$115$	−0.0753530	+	0.716936i	−0.00702671	+	0.0668546i
$116$	0.178618	−	1.69943i	0.0165842	−	0.157788i
$117$	−0.0313807	−	0.0348518i	−0.00290115	−	0.00322205i
$118$	−1.37161	−	4.22140i	−0.126267	−	0.388611i
$119$	6.30816	−	1.47252i	0.578268	−	0.134985i
$120$	2.16019			0.197197
$121$	0.460937	−	10.9903i	0.0419034	−	0.999122i
$122$	0.377548	+	0.653932i	0.0341816	+	0.0592043i
$123$	5.06729	+	2.25610i	0.456902	+	0.203426i
$124$	7.21943	+	1.53454i	0.648324	+	0.137806i
$125$	−3.56036	+	10.9577i	−0.318448	+	0.980083i
$126$	−1.36817	−	2.26453i	−0.121886	−	0.201741i
$127$	10.2044	+	7.41391i	0.905492	+	0.657878i	0.939871	−	0.341530i	$-0.110945\pi$
$127$	10.2044	+	7.41391i	0.905492	+	0.657878i	−0.0343788	+	0.999409i	$0.510945\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	0.805665	−	0.894782i	0.0709348	−	0.0787811i
$130$	−0.0925494	−	0.0412056i	−0.00811712	−	0.00361397i
$131$	−0.809199	+	1.40157i	−0.0707001	+	0.122456i	−0.899208	−	0.437521i	$-0.855857\pi$
$131$	−0.809199	+	1.40157i	−0.0707001	+	0.122456i	0.828508	+	0.559977i	$0.189190\pi$
$132$	0.791081	+	3.22090i	0.0688548	+	0.280343i
$133$	1.33224	+	10.6364i	0.115520	+	0.922291i
$134$	9.47181	−	6.88167i	0.818240	−	0.594486i
$135$	−2.11298	−	0.449128i	−0.181856	−	0.0386548i
$136$	2.39485	−	0.509042i	0.205357	−	0.0436500i
$137$	1.86965	−	17.7885i	0.159735	−	1.51978i	−0.561726	−	0.827323i	$-0.689862\pi$
$137$	1.86965	−	17.7885i	0.159735	−	1.51978i	0.721461	−	0.692455i	$-0.243471\pi$
$138$	0.304863	−	0.135734i	0.0259517	−	0.0115544i
$139$	−4.89449	+	15.0637i	−0.415145	+	1.27769i	0.496975	+	0.867765i	$0.334444\pi$
$139$	−4.89449	+	15.0637i	−0.415145	+	1.27769i	−0.912121	+	0.409922i	$0.865556\pi$
$140$	−4.68967	−	3.26678i	−0.396349	−	0.276093i
$141$	2.61501	−	1.89992i	0.220224	−	0.160002i
$142$	−0.336938	+	0.583594i	−0.0282752	+	0.0489741i
$143$	0.0275463	−	0.153084i	0.00230354	−	0.0128015i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.385847	+	3.67109i	0.0320429	+	0.304867i
$146$	2.85013	+	8.77179i	0.235878	+	0.725959i
$147$	−0.454335	+	6.98524i	−0.0374729	+	0.576133i
$148$	8.48915	+	6.16773i	0.697804	+	0.506984i
$149$	14.7728	−	6.57728i	1.21024	−	0.538832i	0.300405	−	0.953812i	$-0.402878\pi$
$149$	14.7728	−	6.57728i	1.21024	−	0.538832i	0.909831	+	0.414980i	$0.136211\pi$
$150$	0.326307	−	0.0693588i	0.0266429	−	0.00566312i
$151$	14.8306	−	16.4711i	1.20690	−	1.34040i	0.282362	−	0.959308i	$-0.408882\pi$
$151$	14.8306	−	16.4711i	1.20690	−	1.34040i	0.924538	−	0.381090i	$-0.124451\pi$
$152$	0.423506	+	4.02939i	0.0343509	+	0.326827i
$153$	−2.44836			−0.197938
$154$	3.15346	−	8.18876i	0.254113	−	0.659869i
$155$	−15.9437			−1.28063
$156$	0.00490215	+	0.0466409i	0.000392486	+	0.00373426i
$157$	−14.1109	+	15.6718i	−1.12617	+	1.25074i	−0.161622	+	0.986853i	$0.551672\pi$
$157$	−14.1109	+	15.6718i	−1.12617	+	1.25074i	−0.964553	+	0.263890i	$0.914994\pi$
$158$	−0.0974102	+	0.0207052i	−0.00774954	+	0.00164721i
$159$	−1.04218	+	0.464009i	−0.0826504	+	0.0367983i
$160$	−1.74763	−	1.26973i	−0.138162	−	0.100381i
$161$	−0.867111	−	0.166362i	−0.0683379	−	0.0131112i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−0.200727	−	1.90979i	−0.0157221	−	0.149586i	0.983844	−	0.179026i	$-0.0572945\pi$
$163$	−0.200727	−	1.90979i	−0.0157221	−	0.149586i	−0.999567	+	0.0294393i	$0.990628\pi$
$164$	−2.77342	−	4.80370i	−0.216568	−	0.375106i
$165$	−3.11813	−	6.45040i	−0.242746	−	0.502163i
$166$	3.14859	−	5.45352i	0.244378	−	0.423276i
$167$	−12.0358	+	8.74453i	−0.931359	+	0.676672i	−0.946325	−	0.323216i	$-0.895236\pi$
$167$	−12.0358	+	8.74453i	−0.931359	+	0.676672i	0.0149663	+	0.999888i	$0.495236\pi$
$168$	−0.224184	+	2.63624i	−0.0172961	+	0.203390i
$169$	−4.01654	+	12.3616i	−0.308965	+	0.950896i
$170$	−4.83165	+	2.15119i	−0.370571	+	0.164989i
$171$	0.423506	−	4.02939i	0.0323863	−	0.308135i
$172$	−1.17774	+	0.250336i	−0.0898015	+	0.0190879i
$173$	−21.5331	−	4.57700i	−1.63713	−	0.347983i	−0.704749	−	0.709456i	$-0.748941\pi$
$173$	−21.5331	−	4.57700i	−1.63713	−	0.347983i	−0.932383	+	0.361473i	$0.882274\pi$
$174$	1.38244	−	1.00440i	0.104803	−	0.0761436i
$175$	−0.813288	−	0.342889i	−0.0614788	−	0.0259200i
$176$	1.25320	−	3.07075i	0.0944634	−	0.231466i
$177$	2.21932	−	3.84397i	0.166814	−	0.288931i
$178$	12.6167	+	5.61730i	0.945659	+	0.421034i
$179$	12.1356	−	13.4780i	0.907060	−	1.00739i	−0.0928711	−	0.995678i	$-0.529604\pi$
$179$	12.1356	−	13.4780i	0.907060	−	1.00739i	0.999931	−	0.0117144i	$-0.00372888\pi$
$180$	1.44545	+	1.60533i	0.107737	+	0.119654i
$181$	−11.4518	−	8.32024i	−0.851208	−	0.618439i	0.0742709	−	0.997238i	$-0.476337\pi$
$181$	−11.4518	−	8.32024i	−0.851208	−	0.618439i	−0.925479	+	0.378799i	$0.876337\pi$
$182$	0.0598911	−	0.108669i	0.00443942	−	0.00805505i
$183$	−0.233338	+	0.718139i	−0.0172488	+	0.0530864i
$184$	−0.326422	−	0.0693831i	−0.0240641	−	0.00511499i
$185$	−20.7075	−	9.21958i	−1.52245	−	0.677837i
$186$	3.69036	+	6.39189i	0.270590	+	0.468676i
$187$	−4.97689	−	6.41635i	−0.363946	−	0.469210i
$188$	−3.23233			−0.235742
$189$	0.767389	−	2.53202i	0.0558193	−	0.184177i
$190$	−2.70457	−	8.32382i	−0.196210	−	0.603873i
$191$	−16.7595	−	18.6133i	−1.21267	−	1.34681i	−0.920645	−	0.390400i	$-0.872337\pi$
$191$	−16.7595	−	18.6133i	−1.21267	−	1.34681i	−0.292028	−	0.956410i	$-0.594330\pi$
$192$	−0.104528	+	0.994522i	−0.00754369	+	0.0717734i
$193$	−0.330887	+	3.14818i	−0.0238178	+	0.226611i	0.976138	+	0.217153i	$0.0696772\pi$
$193$	−0.330887	+	3.14818i	−0.0238178	+	0.226611i	−0.999955	+	0.00945760i	$0.996990\pi$
$194$	4.27484	+	4.74769i	0.306916	+	0.340864i
$195$	−0.0313059	−	0.0963495i	−0.00224186	−	0.00689973i
$196$	4.47339	−	5.38413i	0.319528	−	0.384580i
$197$	−18.2995			−1.30379			−0.651893	−	0.758311i	$-0.726025\pi$
$197$	−18.2995			−1.30379			−0.651893	+	0.758311i	$0.726025\pi$
$198$	−1.86426	+	2.74309i	−0.132487	+	0.194943i
$199$	3.54957	+	6.14804i	0.251623	+	0.435823i	0.963973	−	0.266001i	$-0.0857025\pi$
$199$	3.54957	+	6.14804i	0.251623	+	0.435823i	−0.712350	+	0.701824i	$0.752369\pi$
$200$	−0.304756	−	0.135686i	−0.0215495	−	0.00959447i
$201$	11.4520	+	2.43419i	0.807759	+	0.171694i
$202$	−0.146554	+	0.451048i	−0.0103115	+	0.0317356i
$203$	−4.52015	+	0.0898931i	−0.317252	+	0.00630926i
$204$	1.98076	+	1.43911i	0.138681	+	0.100758i
$205$	8.01766	+	8.90451i	0.559978	+	0.621918i
$206$	−10.2122	+	11.3418i	−0.711516	+	0.790219i
$207$	0.304863	+	0.135734i	0.0211895	+	0.00943416i
$208$	0.0234489	−	0.0406147i	0.00162589	−	0.00281612i
$209$	11.4206	−	7.08086i	0.789980	−	0.489793i
$210$	−0.710311	−	5.67100i	−0.0490161	−	0.391336i
$211$	0.199281	−	0.144786i	0.0137190	−	0.00996747i	−0.580905	−	0.813972i	$-0.697301\pi$
$211$	0.199281	−	0.144786i	0.0137190	−	0.00996747i	0.594624	+	0.804004i	$0.297301\pi$
$212$	1.11588	+	0.237188i	0.0766390	+	0.0162901i
$213$	−0.659150	+	0.140107i	−0.0451642	+	0.00959995i
$214$	0.292854	−	2.78632i	0.0200191	−	0.190469i
$215$	2.37610	−	1.05791i	0.162049	−	0.0721487i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	1.65464	−	19.4573i	0.112324	−	1.32085i
$218$	12.7434	−	9.25863i	0.863093	−	0.627074i
$219$	−4.61160	+	7.98753i	−0.311623	+	0.539747i
$220$	−1.26883	+	7.05128i	−0.0855442	+	0.475397i
$221$	−0.0574112	−	0.0994392i	−0.00386190	−	0.00668900i
$222$	1.09684	+	10.4357i	0.0736148	+	0.700398i
$223$	−4.52581	−	13.9290i	−0.303071	−	0.932756i	−0.980390	−	0.197067i	$-0.936858\pi$
$223$	−4.52581	−	13.9290i	−0.303071	−	0.932756i	0.677319	−	0.735689i	$-0.263142\pi$
$224$	1.73091	−	2.00099i	0.115651	−	0.133697i
$225$	0.269886	+	0.196084i	0.0179924	+	0.0130722i
$226$	12.2153	−	5.43862i	0.812552	−	0.361771i
$227$	25.1175	−	5.33889i	1.66711	−	0.354355i	0.724763	−	0.688999i	$-0.241949\pi$
$227$	25.1175	−	5.33889i	1.66711	−	0.354355i	0.942345	+	0.334644i	$0.108616\pi$
$228$	−2.71104	+	3.01091i	−0.179543	+	0.199403i
$229$	0.824259	+	7.84230i	0.0544686	+	0.518234i	0.987407	+	0.158199i	$0.0505687\pi$
$229$	0.824259	+	7.84230i	0.0544686	+	0.518234i	−0.932939	+	0.360035i	$0.882765\pi$
$230$	0.720885			0.0475338
$231$	8.19551	−	3.13587i	0.539225	−	0.206325i
$232$	−1.70879			−0.112188
$233$	−1.54615	−	14.7106i	−0.101291	−	0.963723i	−0.920636	−	0.390422i	$-0.872329\pi$
$233$	−1.54615	−	14.7106i	−0.101291	−	0.963723i	0.819345	−	0.573301i	$-0.194337\pi$
$234$	−0.0313807	+	0.0348518i	−0.00205142	+	0.00227834i
$235$	6.82986	−	1.45173i	0.445531	−	0.0947005i
$236$	−4.05490	+	1.80536i	−0.263951	+	0.117519i
$237$	−0.0805671	−	0.0585354i	−0.00523339	−	0.00380228i
$238$	−2.12383	−	6.11968i	−0.137668	−	0.396680i
$239$	0.413456	+	1.27249i	0.0267442	+	0.0823103i	0.963538	−	0.267572i	$-0.0862215\pi$
$239$	0.413456	+	1.27249i	0.0267442	+	0.0823103i	−0.936794	+	0.349883i	$0.886221\pi$
$240$	−0.225801	−	2.14835i	−0.0145754	−	0.138676i
$241$	−11.0212	−	19.0893i	−0.709939	−	1.22965i	−0.964879	−	0.262694i	$-0.915389\pi$
$241$	−11.0212	−	19.0893i	−0.709939	−	1.22965i	0.254940	−	0.966957i	$-0.417944\pi$
$242$	−10.9783	+	0.690391i	−0.705713	+	0.0443800i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.610886	−	0.443834i	0.0391079	−	0.0284136i
$245$	−7.03402	+	13.3857i	−0.449387	+	0.855180i
$246$	1.71407	−	5.27536i	0.109285	−	0.336345i
$247$	0.173583	−	0.0772842i	0.0110448	−	0.00491747i
$248$	0.771495	−	7.34029i	0.0489900	−	0.466109i
$249$	6.15958	−	1.30926i	0.390347	−	0.0829709i
$250$	11.2698	+	2.39547i	0.712764	+	0.151503i
$251$	3.31877	−	2.41122i	0.209479	−	0.152195i	−0.478099	−	0.878306i	$-0.658674\pi$
$251$	3.31877	−	2.41122i	0.209479	−	0.152195i	0.687578	+	0.726111i	$0.258674\pi$
$252$	−2.10911	+	1.59739i	−0.132862	+	0.100626i
$253$	0.263995	+	1.07486i	0.0165972	+	0.0675759i
$254$	6.30665	−	10.9234i	0.395714	−	0.685398i
$255$	−4.83165	−	2.15119i	−0.302570	−	0.134713i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−9.16684	−	10.1808i	−0.571812	−	0.635062i	0.385986	−	0.922505i	$-0.373861\pi$
$257$	−9.16684	−	10.1808i	−0.571812	−	0.635062i	−0.957798	+	0.287443i	$0.907195\pi$
$258$	−0.974095	−	0.707721i	−0.0606445	−	0.0440608i
$259$	13.4004	−	24.3141i	0.832658	−	1.51081i
$260$	−0.0313059	+	0.0963495i	−0.00194151	+	0.00597534i
$261$	1.67145	+	0.355278i	0.103460	+	0.0219912i
$262$	1.47848	+	0.658262i	0.0913408	+	0.0406676i
$263$	4.31657	+	7.47652i	0.266171	+	0.461022i	0.967870	−	0.251452i	$-0.0809081\pi$
$263$	4.31657	+	7.47652i	0.266171	+	0.461022i	−0.701699	+	0.712474i	$0.747575\pi$
$264$	3.12056	−	1.12342i	0.192057	−	0.0691419i
$265$	−2.46436			−0.151385
$266$	10.4389	−	2.43675i	0.640047	−	0.149407i
$267$	4.26773	+	13.1347i	0.261181	+	0.803831i
$268$	−7.83405	−	8.70059i	−0.478541	−	0.531473i
$269$	1.66232	−	15.8159i	0.101354	−	0.964315i	−0.819150	−	0.573580i	$-0.805554\pi$
$269$	1.66232	−	15.8159i	0.101354	−	0.964315i	0.920503	−	0.390735i	$-0.127779\pi$
$270$	−0.225801	+	2.14835i	−0.0137418	+	0.130745i
$271$	12.4985	+	13.8809i	0.759227	+	0.843207i	0.991590	−	0.129422i	$-0.0413122\pi$
$271$	12.4985	+	13.8809i	0.759227	+	0.843207i	−0.232363	+	0.972629i	$0.574646\pi$
$272$	−0.756584	−	2.32853i	−0.0458746	−	0.141188i
$273$	0.120831	−	0.0282057i	0.00731305	−	0.00170709i
$274$	−17.8865			−1.08057
$275$	0.0347381	+	1.10587i	0.00209478	+	0.0666866i
$276$	−0.166857	−	0.289005i	−0.0100436	−	0.0173961i
$277$	−8.87228	−	3.95019i	−0.533084	−	0.237344i	0.122498	−	0.992469i	$-0.460910\pi$
$277$	−8.87228	−	3.95019i	−0.533084	−	0.237344i	−0.655581	+	0.755125i	$0.727576\pi$
$278$	15.4928	+	3.29309i	0.929196	+	0.197507i
$279$	−2.28077	+	7.01948i	−0.136546	+	0.420245i
$280$	−2.75868	+	5.00545i	−0.164863	+	0.299133i
$281$	−1.67632	−	1.21792i	−0.100001	−	0.0726548i	0.536661	−	0.843798i	$-0.319685\pi$
$281$	−1.67632	−	1.21792i	−0.100001	−	0.0726548i	−0.636662	+	0.771143i	$0.719685\pi$
$282$	−2.16285	−	2.40209i	−0.128796	−	0.143043i
$283$	−14.3696	+	15.9590i	−0.854183	+	0.948666i	−0.999169	−	0.0407678i	$-0.987020\pi$
$283$	−14.3696	+	15.9590i	−0.854183	+	0.948666i	0.144986	+	0.989434i	$0.453686\pi$
$284$	0.615616	+	0.274090i	0.0365301	+	0.0162642i
$285$	4.37609	−	7.57961i	0.259217	−	0.448977i
$286$	−0.155124	−	0.0113938i	−0.00917270	−	0.000673729i
$287$	−11.6989	+	8.86044i	−0.690565	+	0.523015i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	10.7651	+	2.28818i	0.633238	+	0.134599i
$290$	3.61065	−	0.767467i	0.212025	−	0.0450672i
$291$	−0.667795	+	6.35365i	−0.0391469	+	0.372458i
$292$	8.42582	−	3.75142i	0.493084	−	0.219535i
$293$	9.21699	−	28.3670i	0.538463	−	1.65722i	−0.197584	−	0.980286i	$-0.563309\pi$
$293$	9.21699	−	28.3670i	0.538463	−	1.65722i	0.736046	−	0.676931i	$-0.236691\pi$
$294$	6.99447	−	0.278311i	0.407925	−	0.0162314i
$295$	7.75709	−	5.63585i	0.451635	−	0.328132i
$296$	5.24659	−	9.08735i	0.304952	−	0.528192i
$297$	−3.28595	+	0.450072i	−0.190670	+	0.0261158i
$298$	−8.08543	−	14.0044i	−0.468376	−	0.811252i
$299$	0.00163592	+	0.0155647i	9.46076e−5	+	0.000900131i
$300$	−0.103087	−	0.317270i	−0.00595174	−	0.0183176i
$301$	1.04445	+	3.00952i	0.0602013	+	0.173466i
$302$	−17.9311	−	13.0277i	−1.03182	−	0.749660i
$303$	−0.433258	+	0.192899i	−0.0248900	+	0.0110818i
$304$	3.96305	−	0.842372i	0.227296	−	0.0483133i
$305$	−1.09145	+	1.21218i	−0.0624963	+	0.0694092i
$306$	0.255923	+	2.43494i	0.0146301	+	0.139196i
$307$	−13.9653			−0.797044			−0.398522	−	0.917159i	$-0.630477\pi$
$307$	−13.9653			−0.797044			−0.398522	+	0.917159i	$0.630477\pi$
$308$	−8.47352	−	2.28022i	−0.482824	−	0.129928i
$309$	−15.2619			−0.868217
$310$	1.66657	+	15.8564i	0.0946550	+	0.900582i
$311$	−12.5646	+	13.9544i	−0.712472	+	0.791281i	−0.985309	−	0.170780i	$-0.945371\pi$
$311$	−12.5646	+	13.9544i	−0.712472	+	0.791281i	0.272837	+	0.962060i	$0.412038\pi$
$312$	0.0458729	−	0.00975059i	0.00259704	−	0.000552019i
$313$	1.65053	−	0.734863i	0.0932934	−	0.0415369i	−0.359559	−	0.933122i	$-0.617073\pi$
$313$	1.65053	−	0.734863i	0.0932934	−	0.0415369i	0.452853	+	0.891585i	$0.350406\pi$
$314$	17.0609	+	12.3955i	0.962803	+	0.699517i
$315$	3.73909	−	4.32251i	0.210674	−	0.243546i
$316$	0.0307739	+	0.0947123i	0.00173117	+	0.00532798i
$317$	−3.45249	−	32.8483i	−0.193911	−	1.84494i	−0.468601	−	0.883410i	$-0.655242\pi$
$317$	−3.45249	−	32.8483i	−0.193911	−	1.84494i	0.274690	−	0.961533i	$-0.411425\pi$
$318$	0.570405	+	0.987971i	0.0319867	+	0.0554027i
$319$	2.46657	+	5.10252i	0.138101	+	0.285687i
$320$	−1.08009	+	1.87078i	−0.0603790	+	0.104580i
$321$	2.26660	−	1.64678i	0.126509	−	0.0919143i
$322$	−0.0748133	+	0.879750i	−0.00416918	+	0.0490266i
$323$	3.06536	−	9.43422i	0.170561	−	0.524934i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	−0.00163534	+	0.0155593i	−9.07126e−5	+	0.000863073i
$326$	−1.87835	+	0.399255i	−0.104032	+	0.0221127i
$327$	15.4075	+	3.27497i	0.852037	+	0.181106i
$328$	−4.48749	+	3.26035i	−0.247780	+	0.180023i
$329$	1.06285	+	8.48565i	0.0585971	+	0.467829i
$330$	−6.08913	+	3.77530i	−0.335196	+	0.207824i
$331$	7.09871	−	12.2953i	0.390181	−	0.675813i	−0.602292	−	0.798276i	$-0.705746\pi$
$331$	7.09871	−	12.2953i	0.390181	−	0.675813i	0.992473	+	0.122463i	$0.0390792\pi$
$332$	−5.75277	−	2.56130i	−0.315724	−	0.140569i
$333$	−7.02130	+	7.79795i	−0.384765	+	0.427325i
$334$	9.95471	+	11.0558i	0.544697	+	0.604948i
$335$	20.4609	+	14.8657i	1.11790	+	0.812199i
$336$	2.64523	−	0.0526062i	0.144309	−	0.00286990i
$337$	−10.2129	+	31.4321i	−0.556333	+	1.71222i	0.136064	+	0.990700i	$0.456555\pi$
$337$	−10.2129	+	31.4321i	−0.556333	+	1.71222i	−0.692397	+	0.721517i	$0.743445\pi$
$338$	12.7138	+	2.70239i	0.691538	+	0.146991i
$339$	12.2153	+	5.43862i	0.663446	+	0.295385i
$340$	2.64445	+	4.58033i	0.143416	+	0.248403i
$341$	−23.0320	+	8.29167i	−1.24725	+	0.449019i
$342$	−4.05159			−0.219085
$343$	−15.6056	−	9.97330i	−0.842621	−	0.538507i
$344$	0.372071	+	1.14512i	0.0200607	+	0.0617406i
$345$	0.482366	+	0.535722i	0.0259697	+	0.0288423i
$346$	−2.30111	+	21.8936i	−0.123708	+	1.17701i
$347$	−0.630212	+	5.99607i	−0.0338316	+	0.321886i	0.964497	+	0.264094i	$0.0850728\pi$
$347$	−0.630212	+	5.99607i	−0.0338316	+	0.321886i	−0.998329	+	0.0577923i	$0.981594\pi$
$348$	−1.14341	−	1.26988i	−0.0612930	−	0.0680728i
$349$	−3.35159	−	10.3151i	−0.179406	−	0.552156i	0.820401	−	0.571789i	$-0.193750\pi$
$349$	−3.35159	−	10.3151i	−0.179406	−	0.552156i	−0.999807	+	0.0196327i	$0.993750\pi$
$350$	−0.255999	+	0.844674i	−0.0136837	+	0.0451497i
$351$	−0.0468978			−0.00250322
$352$	−3.18492	−	0.925353i	−0.169757	−	0.0493215i
$353$	8.29149	+	14.3613i	0.441311	+	0.764374i	0.997787	−	0.0664901i	$-0.0211801\pi$
$353$	8.29149	+	14.3613i	0.441311	+	0.764374i	−0.556476	+	0.830864i	$0.687847\pi$
$354$	−4.05490	−	1.80536i	−0.215515	−	0.0959536i
$355$	−1.42389	−	0.302656i	−0.0755720	−	0.0160633i
$356$	4.26773	−	13.1347i	0.226189	−	0.696138i
$357$	3.12669	−	5.67318i	0.165482	−	0.300256i
$358$	−14.6727	−	10.6603i	−0.775475	−	0.563416i
$359$	17.1606	+	19.0588i	0.905703	+	1.00588i	0.999947	+	0.0103356i	$0.00328997\pi$
$359$	17.1606	+	19.0588i	0.905703	+	1.00588i	−0.0942439	+	0.995549i	$0.530043\pi$
$360$	1.44545	−	1.60533i	0.0761817	−	0.0846084i
$361$	−2.36120	−	1.05127i	−0.124274	−	0.0553302i
$362$	−7.07762	+	12.2588i	−0.371992	+	0.644308i
$363$	−7.85899	−	7.69651i	−0.412490	−	0.403962i
$364$	−0.114334	−	0.0482040i	−0.00599271	−	0.00252658i
$365$	−16.1187	+	11.7109i	−0.843693	+	0.612979i
$366$	0.738596	+	0.156993i	0.0386070	+	0.00820617i
$367$	1.78956	−	0.380383i	0.0934145	−	0.0198559i	−0.160967	−	0.986960i	$-0.551461\pi$
$367$	1.78956	−	0.380383i	0.0934145	−	0.0198559i	0.254382	+	0.967104i	$0.418128\pi$
$368$	−0.0348827	+	0.331886i	−0.00181838	+	0.0173008i
$369$	5.06729	−	2.25610i	0.263793	−	0.117448i
$370$	−7.00455	+	21.5578i	−0.364149	+	1.12074i
$371$	0.255751	−	3.00745i	0.0132779	−	0.156139i
$372$	5.97113	−	4.33828i	0.309589	−	0.224929i
$373$	−13.2704	+	22.9850i	−0.687116	+	1.19012i	0.285651	+	0.958334i	$0.407790\pi$
$373$	−13.2704	+	22.9850i	−0.687116	+	1.19012i	−0.972767	+	0.231786i	$0.925543\pi$
$374$	−5.86097	+	5.62031i	−0.303064	+	0.290620i
$375$	5.76078	+	9.97796i	0.297485	+	0.515260i
$376$	0.337871	+	3.21463i	0.0174244	+	0.165782i
$377$	0.0247642	+	0.0762163i	0.00127542	+	0.00392534i
$378$	−2.59836	−	0.498517i	−0.133645	−	0.0256410i
$379$	30.7961	+	22.3747i	1.58189	+	1.14931i	0.914487	+	0.404615i	$0.132594\pi$
$379$	30.7961	+	22.3747i	1.58189	+	1.14931i	0.667404	+	0.744696i	$0.267406\pi$
$380$	−7.99551	+	3.55983i	−0.410161	+	0.182615i
$381$	12.3377	−	2.62245i	0.632078	−	0.134352i
$382$	−16.7595	+	18.6133i	−0.857490	+	0.952339i
$383$	−1.38170	−	13.1460i	−0.0706016	−	0.671729i	−0.971393	−	0.237477i	$-0.923679\pi$
$383$	−1.38170	−	13.1460i	−0.0706016	−	0.671729i	0.900791	−	0.434252i	$-0.142987\pi$
$384$	1.00000			0.0510310
$385$	18.9285	+	1.01237i	0.964686	+	0.0515953i
$386$	3.16552			0.161121
$387$	−0.125857	−	1.19745i	−0.00639768	−	0.0608699i
$388$	4.27484	−	4.74769i	0.217022	−	0.241027i
$389$	14.5454	−	3.09172i	0.737480	−	0.156756i	0.176168	−	0.984360i	$-0.443630\pi$
$389$	14.5454	−	3.09172i	0.737480	−	0.156756i	0.561312	+	0.827604i	$0.310297\pi$
$390$	−0.0925494	+	0.0412056i	−0.00468642	+	0.00208653i
$391$	0.661009	+	0.480251i	0.0334287	+	0.0242873i
$392$	−5.82223	−	3.88609i	−0.294067	−	0.196277i
$393$	0.500113	+	1.53919i	0.0252273	+	0.0776418i
$394$	1.91282	+	18.1993i	0.0963665	+	0.916866i
$395$	−0.107563	−	0.186304i	−0.00541206	−	0.00937396i
$396$	2.92293	+	1.56731i	0.146883	+	0.0787605i
$397$	−17.8678	+	30.9480i	−0.896761	+	1.55324i	−0.0651522	+	0.997875i	$0.520753\pi$
$397$	−17.8678	+	30.9480i	−0.896761	+	1.55324i	−0.831609	+	0.555361i	$0.812580\pi$
$398$	5.74333	−	4.17277i	0.287887	−	0.209162i
$399$	8.79581	+	6.12708i	0.440341	+	0.306738i
$400$	−0.103087	+	0.317270i	−0.00515436	+	0.0158635i
$401$	−2.84732	+	1.26771i	−0.142188	+	0.0633063i	−0.476597	−	0.879122i	$-0.658130\pi$
$401$	−2.84732	+	1.26771i	−0.142188	+	0.0633063i	0.334409	+	0.942428i	$0.391463\pi$
$402$	1.22380	−	11.6437i	0.0610375	−	0.580733i
$403$	−0.338575	+	0.0719664i	−0.0168656	+	0.00358490i
$404$	0.463896	+	0.0986042i	0.0230797	+	0.00490574i
$405$	−1.74763	+	1.26973i	−0.0868403	+	0.0630932i
$406$	0.561885	+	4.48599i	0.0278859	+	0.222636i
$407$	−34.7084	−	2.54931i	−1.72043	−	0.126365i
$408$	1.22418	−	2.12034i	0.0606058	−	0.104972i
$409$	6.20163	+	2.76115i	0.306651	+	0.136530i	0.554293	−	0.832322i	$-0.312989\pi$
$409$	6.20163	+	2.76115i	0.306651	+	0.136530i	−0.247642	+	0.968852i	$0.579656\pi$
$410$	8.01766	−	8.90451i	0.395964	−	0.439763i
$411$	−11.9684	−	13.2923i	−0.590359	−	0.655660i
$412$	12.3471	+	8.97070i	0.608298	+	0.441955i
$413$	6.07282	+	10.0514i	0.298824	+	0.494599i
$414$	0.103123	−	0.317381i	0.00506824	−	0.0155984i
$415$	13.3058	+	2.82824i	0.653158	+	0.138833i
$416$	−0.0428432	−	0.0190750i	−0.00210056	−	0.000935231i
$417$	7.91946	+	13.7169i	0.387817	+	0.671719i
$418$	−8.23585	−	10.6179i	−0.402828	−	0.519338i
$419$	20.5184			1.00239			0.501195	−	0.865334i	$-0.332894\pi$
$419$	20.5184			1.00239			0.501195	+	0.865334i	$0.332894\pi$
$420$	−5.56569	+	1.29920i	−0.271578	+	0.0633945i
$421$	−4.49810	−	13.8437i	−0.219224	−	0.674702i	−0.998827	−	0.0484275i	$-0.984579\pi$
$421$	−4.49810	−	13.8437i	−0.219224	−	0.674702i	0.779603	−	0.626274i	$-0.215421\pi$
$422$	−0.164823	−	0.183055i	−0.00802347	−	0.00891097i
$423$	0.337871	−	3.21463i	0.0164278	−	0.156301i
$424$	0.119247	−	1.13456i	0.00579115	−	0.0550991i
$425$	0.546523	+	0.606975i	0.0265102	+	0.0294426i
$426$	0.208239	+	0.640894i	0.0100892	+	0.0310514i
$427$	−1.36604	−	1.45778i	−0.0661074	−	0.0705469i
$428$	−2.80167			−0.135424
$429$	−0.0953313	−	0.122904i	−0.00460264	−	0.00593385i
$430$	−1.30048	−	2.25250i	−0.0627149	−	0.108625i
$431$	−19.5627	−	8.70989i	−0.942303	−	0.419540i	−0.122682	−	0.992446i	$-0.539149\pi$
$431$	−19.5627	−	8.70989i	−0.942303	−	0.419540i	−0.819621	+	0.572906i	$0.805816\pi$
$432$	−0.978148	−	0.207912i	−0.0470611	−	0.0100032i
$433$	7.37500	−	22.6979i	0.354420	−	1.09079i	−0.601925	−	0.798553i	$-0.705599\pi$
$433$	7.37500	−	22.6979i	0.354420	−	1.09079i	0.956345	−	0.292240i	$-0.0944006\pi$
$434$	−19.5237	+	0.388271i	−0.937167	+	0.0186376i
$435$	2.98633	+	2.16970i	0.143184	+	0.104029i
$436$	−10.5400	−	11.7058i	−0.504773	−	0.560607i
$437$	−0.904713	+	1.00479i	−0.0432783	+	0.0480654i
$438$	8.42582	+	3.75142i	0.402601	+	0.179250i
$439$	9.66441	−	16.7393i	0.461257	−	0.798921i	−0.537767	−	0.843094i	$-0.680732\pi$
$439$	9.66441	−	16.7393i	0.461257	−	0.798921i	0.999024	+	0.0441728i	$0.0140652\pi$
$440$	7.14528	+	0.524816i	0.340638	+	0.0250196i
$441$	4.88704	+	5.01167i	0.232716	+	0.238651i
$442$	−0.0928933	+	0.0674909i	−0.00441848	+	0.00321022i
$443$	−34.8535	−	7.40833i	−1.65594	−	0.351980i	−0.717268	−	0.696797i	$-0.754608\pi$
$443$	−34.8535	−	7.40833i	−1.65594	−	0.351980i	−0.938670	+	0.344817i	$0.887941\pi$
$444$	10.2639	−	2.18165i	0.487102	−	0.103537i
$445$	−3.11846	+	29.6701i	−0.147829	+	1.40650i
$446$	−13.3796	+	5.95700i	−0.633544	+	0.282072i
$447$	4.99707	−	15.3794i	0.236353	−	0.727421i
$448$	−2.17096	−	1.51227i	−0.102568	−	0.0714479i
$449$	25.5403	−	18.5561i	1.20532	−	0.875718i	0.210525	−	0.977589i	$-0.432483\pi$
$449$	25.5403	−	18.5561i	1.20532	−	0.875718i	0.994798	+	0.101871i	$0.0324828\pi$
$450$	0.166799	−	0.288904i	0.00786296	−	0.0136191i
$451$	16.2130	+	8.69364i	0.763442	+	0.409368i
$452$	−6.68567	−	11.5799i	−0.314468	−	0.544674i
$453$	−2.31677	−	22.0426i	−0.108851	−	1.03565i
$454$	−7.93514	−	24.4218i	−0.372414	−	1.14617i
$455$	0.263234	+	0.0505037i	0.0123406	+	0.00236765i
$456$	3.27780	+	2.38146i	0.153497	+	0.111522i
$457$	9.49950	−	4.22945i	0.444368	−	0.197845i	−0.172340	−	0.985038i	$-0.555133\pi$
$457$	9.49950	−	4.22945i	0.444368	−	0.197845i	0.616708	+	0.787192i	$0.288466\pi$
$458$	7.71319	−	1.63949i	0.360413	−	0.0766082i
$459$	−1.63827	+	1.81948i	−0.0764679	+	0.0849262i
$460$	−0.0753530	−	0.716936i	−0.00351335	−	0.0334273i
$461$	25.2416			1.17562			0.587810	−	0.808999i	$-0.299990\pi$
$461$	25.2416			1.17562			0.587810	+	0.808999i	$0.299990\pi$
$462$	−3.97536	−	7.82282i	−0.184950	−	0.363951i
$463$	32.5304			1.51182			0.755908	−	0.654678i	$-0.227196\pi$
$463$	32.5304			1.51182			0.755908	+	0.654678i	$0.227196\pi$
$464$	0.178618	+	1.69943i	0.00829211	+	0.0788942i
$465$	−10.6684	+	11.8485i	−0.494737	+	0.549461i
$466$	−14.4684	+	3.07535i	−0.670235	+	0.142463i
$467$	9.47874	−	4.22021i	0.438624	−	0.195288i	−0.175530	−	0.984474i	$-0.556164\pi$
$467$	9.47874	−	4.22021i	0.438624	−	0.195288i	0.614154	+	0.789186i	$0.289497\pi$
$468$	0.0379411	+	0.0275658i	0.00175383	+	0.00127423i
$469$	−20.2651	+	23.4272i	−0.935757	+	1.08177i
$470$	−2.15769	−	6.64070i	−0.0995270	−	0.306313i
$471$	2.20434	+	20.9729i	0.101571	+	0.966381i
$472$	2.21932	+	3.84397i	0.102152	+	0.176933i
$473$	2.88230	−	2.76395i	0.132528	−	0.127086i
$474$	−0.0497932	+	0.0862443i	−0.00228708	+	0.00396133i
$475$	−1.09347	+	0.794449i	−0.0501717	+	0.0364518i
$476$	−5.86415	+	2.75188i	−0.268783	+	0.126132i
$477$	−0.352530	+	1.08498i	−0.0161412	+	0.0496776i
$478$	1.22230	−	0.544202i	0.0559066	−	0.0248912i
$479$	−2.75809	+	26.2415i	−0.126020	+	1.19900i	0.730509	+	0.682904i	$0.239283\pi$
$479$	−2.75809	+	26.2415i	−0.126020	+	1.19900i	−0.856529	+	0.516099i	$0.827384\pi$
$480$	−2.11298	+	0.449128i	−0.0964439	+	0.0204998i
$481$	−0.481353	−	0.102315i	−0.0219478	−	0.00466515i
$482$	−17.8327	+	12.9562i	−0.812258	+	0.590140i
$483$	−0.703842	+	0.533071i	−0.0320259	+	0.0242556i
$484$	1.83416	+	10.8460i	0.0833707	+	0.493000i
$485$	−6.90033	+	11.9517i	−0.313328	+	0.542700i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	15.8033	−	17.5514i	0.716118	−	0.795329i	−0.269737	−	0.962934i	$-0.586937\pi$
$487$	15.8033	−	17.5514i	0.716118	−	0.795329i	0.985854	+	0.167605i	$0.0536033\pi$
$488$	−0.505258	−	0.561146i	−0.0228720	−	0.0254019i
$489$	−1.55356	−	1.12873i	−0.0702545	−	0.0510429i
$490$	14.0476	+	5.59630i	0.634606	+	0.252815i
$491$	2.61236	−	8.04002i	0.117894	−	0.362841i	−0.874645	−	0.484763i	$-0.838906\pi$
$491$	2.61236	−	8.04002i	0.117894	−	0.362841i	0.992540	+	0.121922i	$0.0389058\pi$
$492$	−5.42563	−	1.15325i	−0.244606	−	0.0519926i
$493$	3.82203	+	1.70168i	0.172136	+	0.0766397i
$494$	−0.0950052	−	0.164554i	−0.00427448	−	0.00740362i
$495$	−6.88002	−	1.99893i	−0.309234	−	0.0898454i
$496$	−7.38072			−0.331404
$497$	0.517125	−	1.70627i	0.0231962	−	0.0765365i
$498$	−1.94594	−	5.98898i	−0.0871996	−	0.268373i
$499$	−20.5013	−	22.7690i	−0.917762	−	1.01928i	−0.999744	−	0.0226445i	$-0.992791\pi$
$499$	−20.5013	−	22.7690i	−0.917762	−	1.01928i	0.0819812	−	0.996634i	$-0.473875\pi$
$500$	1.20433	−	11.4584i	0.0538593	−	0.512437i
$501$	−1.55508	+	14.7956i	−0.0694758	+	0.661018i
$502$	−2.74492	−	3.04854i	−0.122512	−	0.136063i
$503$	4.56149	+	14.0388i	0.203387	+	0.625960i	0.999776	+	0.0211753i	$0.00674082\pi$
$503$	4.56149	+	14.0388i	0.203387	+	0.625960i	−0.796389	+	0.604785i	$0.793259\pi$
$504$	1.80910	+	1.93059i	0.0805836	+	0.0859952i
$505$	−1.02449			−0.0455892
$506$	1.04138	−	0.374903i	0.0462949	−	0.0166665i
$507$	6.49890	+	11.2564i	0.288626	+	0.499915i
$508$	−11.5228	−	5.13029i	−0.511243	−	0.227620i
$509$	−14.9693	−	3.18181i	−0.663501	−	0.141031i	−0.136162	−	0.990687i	$-0.543477\pi$
$509$	−14.9693	−	3.18181i	−0.663501	−	0.141031i	−0.527339	+	0.849655i	$0.676810\pi$
$510$	−1.63436	+	5.03005i	−0.0723707	+	0.222734i
$511$	−12.6189	−	20.8862i	−0.558229	−	0.923953i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−2.71104	−	3.01091i	−0.119695	−	0.132935i
$514$	−9.16684	+	10.1808i	−0.404332	+	0.449056i
$515$	−30.1182	−	13.4095i	−1.32717	−	0.590892i
$516$	−0.602024	+	1.04274i	−0.0265026	+	0.0459039i
$517$	9.11130	−	5.64907i	0.400715	−	0.248446i
$518$	−25.5817	−	10.7854i	−1.12399	−	0.473885i
$519$	−17.8098	+	12.9396i	−0.781765	+	0.567986i
$520$	0.0990941	+	0.0210631i	0.00434556	+	0.000923678i
$521$	22.6517	−	4.81477i	0.992390	−	0.210939i	0.317020	−	0.948419i	$-0.397318\pi$
$521$	22.6517	−	4.81477i	0.992390	−	0.210939i	0.675369	+	0.737480i	$0.263984\pi$
$522$	0.178618	−	1.69943i	0.00781788	−	0.0743821i
$523$	−20.9076	+	9.30868i	−0.914227	+	0.407040i	−0.809270	−	0.587436i	$-0.800137\pi$
$523$	−20.9076	+	9.30868i	−0.914227	+	0.407040i	−0.104957	+	0.994477i	$0.533471\pi$
$524$	0.500113	−	1.53919i	0.0218475	−	0.0672398i
$525$	−0.799012	+	0.374953i	−0.0348717	+	0.0163643i
$526$	6.98435	−	5.07443i	0.304532	−	0.221256i
$527$	−9.03532	+	15.6496i	−0.393585	+	0.681708i
$528$	−1.44346	−	2.98604i	−0.0628184	−	0.129951i
$529$	11.4443	+	19.8221i	0.497579	+	0.861832i
$530$	0.257596	+	2.45086i	0.0111893	+	0.106459i
$531$	−1.37161	−	4.22140i	−0.0595230	−	0.183193i
$532$	−3.51456	−	10.1270i	−0.152375	−	0.439059i
$533$	0.210453	+	0.152903i	0.00911574	+	0.00662297i
$534$	12.6167	−	5.61730i	0.545976	−	0.243084i
$535$	5.91988	−	1.25831i	0.255939	−	0.0544014i
$536$	−7.83405	+	8.70059i	−0.338379	+	0.375808i
$537$	−1.89577	−	18.0371i	−0.0818086	−	0.778357i
$538$	−15.9031			−0.685630
$539$	−3.19987	+	22.9948i	−0.137828	+	0.990456i
$540$	2.16019			0.0929596
$541$	1.13728	+	10.8205i	0.0488955	+	0.465210i	0.991386	+	0.130976i	$0.0418110\pi$
$541$	1.13728	+	10.8205i	0.0488955	+	0.465210i	−0.942490	+	0.334234i	$0.891522\pi$
$542$	12.4985	−	13.8809i	0.536855	−	0.596237i
$543$	−13.8459	+	2.94304i	−0.594185	+	0.126298i
$544$	−2.23668	+	0.995836i	−0.0958971	+	0.0426961i
$545$	27.5281	+	20.0004i	1.17918	+	0.856721i
$546$	−0.0406816	−	0.117221i	−0.00174101	−	0.00501661i
$547$	−6.17054	−	18.9910i	−0.263833	−	0.811995i	−0.991960	−	0.126552i	$-0.959609\pi$
$547$	−6.17054	−	18.9910i	−0.263833	−	0.811995i	0.728127	−	0.685443i	$-0.240391\pi$
$548$	1.86965	+	17.7885i	0.0798676	+	0.759889i
$549$	0.377548	+	0.653932i	0.0161134	+	0.0279092i
$550$	1.09618	−	0.150143i	0.0467414	−	0.00640211i
$551$	−3.46166	+	5.99577i	−0.147472	+	0.255429i
$552$	−0.269981	+	0.196152i	−0.0114911	+	0.00834880i
$553$	0.238523	−	0.111932i	0.0101430	−	0.00475983i
$554$	−3.00115	+	9.23659i	−0.127507	+	0.392425i
$555$	−20.7075	+	9.21958i	−0.878985	+	0.391349i
$556$	1.65562	−	15.7521i	0.0702138	−	0.668040i
$557$	15.9076	−	3.38126i	0.674026	−	0.143269i	0.141832	−	0.989891i	$-0.454701\pi$
$557$	15.9076	−	3.38126i	0.674026	−	0.143269i	0.532195	+	0.846622i	$0.321367\pi$
$558$	7.21943	+	1.53454i	0.305623	+	0.0649622i
$559$	0.0456829	−	0.0331906i	0.00193218	−	0.00140381i
$560$	5.26639	+	2.22035i	0.222546	+	0.0938271i
$561$	−8.09846	−	0.594827i	−0.341917	−	0.0251136i
$562$	−1.03602	+	1.79444i	−0.0437020	+	0.0756940i
$563$	27.6612	+	12.3156i	1.16578	+	0.519039i	0.896074	−	0.443904i	$-0.146407\pi$
$563$	27.6612	+	12.3156i	1.16578	+	0.519039i	0.269706	+	0.962943i	$0.413074\pi$
$564$	−2.16285	+	2.40209i	−0.0910726	+	0.101146i
$565$	19.3276	+	21.4654i	0.813117	+	0.903058i
$566$	17.3736	+	12.6227i	0.730268	+	0.530571i
$567$	−1.36817	−	2.26453i	−0.0574578	−	0.0951014i
$568$	0.208239	−	0.640894i	0.00873752	−	0.0268913i
$569$	37.7881	+	8.03211i	1.58416	+	0.336723i	0.914070	−	0.405557i	$-0.132922\pi$
$569$	37.7881	+	8.03211i	1.58416	+	0.336723i	0.670089	+	0.742281i	$0.266256\pi$
$570$	−7.99551	−	3.55983i	−0.334895	−	0.149105i
$571$	−4.11664	−	7.13024i	−0.172276	−	0.298391i	0.766939	−	0.641720i	$-0.221779\pi$
$571$	−4.11664	−	7.13024i	−0.172276	−	0.298391i	−0.939215	+	0.343329i	$0.888445\pi$
$572$	0.00488354	+	0.155466i	0.000204191	+	0.00650034i
$573$	−25.0466			−1.04634
$574$	10.0348	+	10.7087i	0.418843	+	0.446971i
$575$	−0.0344017	−	0.105878i	−0.00143465	−	0.00441540i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	0.498375	−	4.74172i	0.0207476	−	0.197400i	−0.979238	−	0.202713i	$-0.935024\pi$
$577$	0.498375	−	4.74172i	0.0207476	−	0.197400i	0.999986	+	0.00531225i	$0.00169095\pi$
$578$	1.15039	−	10.9453i	0.0478501	−	0.455263i
$579$	2.11815	+	2.35244i	0.0880272	+	0.0977641i
$580$	−1.14068	−	3.51065i	−0.0473641	−	0.145772i
$581$	−4.83239	+	15.9446i	−0.200481	+	0.661493i
$582$	6.38865			0.264818
$583$	−3.55997	+	1.28161i	−0.147439	+	0.0530790i
$584$	−4.61160	−	7.98753i	−0.190830	−	0.330526i
$585$	−0.0925494	−	0.0412056i	−0.00382645	−	0.00170364i
$586$	−29.1750	−	6.20134i	−1.20521	−	0.256175i
$587$	−6.57059	+	20.2222i	−0.271197	+	0.834659i	0.719003	+	0.695007i	$0.244599\pi$
$587$	−6.57059	+	20.2222i	−0.271197	+	0.834659i	−0.990201	+	0.139653i	$0.955401\pi$
$588$	−1.00791	−	6.92706i	−0.0415654	−	0.285667i
$589$	−24.1925	−	17.5769i	−0.996836	−	0.724244i
$590$	−6.41581	−	7.12548i	−0.264135	−	0.293352i
$591$	−12.2448	+	13.5992i	−0.503682	+	0.559396i
$592$	−9.58599	−	4.26796i	−0.393982	−	0.175412i
$593$	20.8598	−	36.1302i	0.856609	−	1.48369i	−0.0185359	−	0.999828i	$-0.505900\pi$
$593$	20.8598	−	36.1302i	0.856609	−	1.48369i	0.875145	−	0.483862i	$-0.160766\pi$
$594$	0.791081	+	3.22090i	0.0324585	+	0.132155i
$595$	11.1549	−	8.44842i	0.457306	−	0.346351i
$596$	−13.0825	+	9.50499i	−0.535880	+	0.389340i
$597$	6.94402	+	1.47600i	0.284200	+	0.0604085i
$598$	0.0153085	−	0.00325391i	0.000626010	−	0.000133062i
$599$	−0.959407	+	9.12815i	−0.0392003	+	0.372966i	0.957282	+	0.289157i	$0.0933751\pi$
$599$	−0.959407	+	9.12815i	−0.0392003	+	0.372966i	−0.996482	+	0.0838086i	$0.973292\pi$
$600$	−0.304756	+	0.135686i	−0.0124416	+	0.00553937i
$601$	0.482269	−	1.48427i	0.0196721	−	0.0605446i	−0.940739	−	0.339133i	$-0.889866\pi$
$601$	0.482269	−	1.48427i	0.0196721	−	0.0605446i	0.960411	+	0.278588i	$0.0898664\pi$
$602$	2.88386	−	1.35331i	0.117537	−	0.0551569i
$603$	9.47181	−	6.88167i	0.385722	−	0.280243i
$604$	−11.0820	+	19.1946i	−0.450921	+	0.781018i
$605$	−8.74678	−	22.0936i	−0.355607	−	0.898234i
$606$	0.237130	+	0.410721i	0.00963274	+	0.0166844i
$607$	−2.52893	−	24.0611i	−0.102646	−	0.976612i	−0.917713	−	0.397245i	$-0.869966\pi$
$607$	−2.52893	−	24.0611i	−0.102646	−	0.976612i	0.815067	−	0.579367i	$-0.196700\pi$
$608$	−1.25201	−	3.85329i	−0.0507757	−	0.156271i
$609$	−2.95777	+	3.41928i	−0.119855	+	0.138556i
$610$	1.31963	+	0.958765i	0.0534301	+	0.0388193i
$611$	0.138484	−	0.0616569i	0.00560245	−	0.00249437i
$612$	2.39485	−	0.509042i	0.0968062	−	0.0205768i
$613$	6.99215	−	7.76557i	0.282410	−	0.313648i	−0.585204	−	0.810886i	$-0.698986\pi$
$613$	6.99215	−	7.76557i	0.282410	−	0.313648i	0.867614	+	0.497238i	$0.165652\pi$
$614$	1.45978	+	13.8888i	0.0589118	+	0.560508i
$615$	11.9822			0.483169
$616$	−1.38201	+	8.66545i	−0.0556827	+	0.349141i
$617$	25.7849			1.03806			0.519031	−	0.854756i	$-0.326293\pi$
$617$	25.7849			1.03806			0.519031	+	0.854756i	$0.326293\pi$
$618$	1.59530	+	15.1783i	0.0641723	+	0.610559i
$619$	30.0227	−	33.3436i	1.20672	−	1.34019i	0.282056	−	0.959398i	$-0.408984\pi$
$619$	30.0227	−	33.3436i	1.20672	−	1.34019i	0.924660	−	0.380795i	$-0.124350\pi$
$620$	15.5953	−	3.31489i	0.626323	−	0.133129i
$621$	0.304863	−	0.135734i	0.0122337	−	0.00544681i
$622$	15.1913	+	11.0371i	0.609116	+	0.442548i
$623$	−35.8851	−	6.88485i	−1.43770	−	0.275836i
$624$	−0.0144922	−	0.0446024i	−0.000580153	−	0.00178553i
$625$	2.42723	+	23.0935i	0.0970891	+	0.923741i
$626$	−0.903364	−	1.56467i	−0.0361057	−	0.0625369i
$627$	2.37978	−	13.2252i	0.0950391	−	0.528163i
$628$	10.5442	−	18.2631i	0.420760	−	0.728778i
$629$	−20.7845	+	15.1008i	−0.828731	+	0.602109i
$630$	−4.68967	−	3.26678i	−0.186841	−	0.130152i
$631$	2.01119	−	6.18980i	0.0800642	−	0.246412i	−0.903010	−	0.429619i	$-0.858648\pi$
$631$	2.01119	−	6.18980i	0.0800642	−	0.246412i	0.983074	+	0.183207i	$0.0586478\pi$
$632$	0.0909767	−	0.0405054i	0.00361886	−	0.00161122i
$633$	0.0257479	−	0.244975i	0.00102339	−	0.00973689i
$634$	−32.3074	+	6.86716i	−1.28309	+	0.272730i
$635$	26.6517	+	5.66499i	1.05764	+	0.224808i
$636$	0.922935	−	0.670552i	0.0365968	−	0.0265891i
$637$	−0.0889519	+	0.316003i	−0.00352440	+	0.0125205i
$638$	4.81675	−	2.98642i	0.190697	−	0.118233i
$639$	−0.336938	+	0.583594i	−0.0133291	+	0.0230866i
$640$	1.97343	+	0.878627i	0.0780066	+	0.0347308i
$641$	18.5737	−	20.6282i	0.733617	−	0.814764i	−0.254726	−	0.967013i	$-0.581985\pi$
$641$	18.5737	−	20.6282i	0.733617	−	0.814764i	0.988342	+	0.152250i	$0.0486518\pi$
$642$	−1.87468	−	2.08205i	−0.0739879	−	0.0821719i
$643$	8.48610	+	6.16552i	0.334659	+	0.243144i	0.742405	−	0.669951i	$-0.233685\pi$
$643$	8.48610	+	6.16552i	0.334659	+	0.243144i	−0.407746	+	0.913096i	$0.633685\pi$
$644$	0.882751	−	0.0175554i	0.0347853	−	0.000691781i
$645$	0.803743	−	2.47367i	0.0316473	−	0.0974005i
$646$	−9.70295	−	2.06243i	−0.381758	−	0.0811451i
$647$	−38.9545	−	17.3436i	−1.53146	−	0.681849i	−0.543907	−	0.839146i	$-0.683055\pi$
$647$	−38.9545	−	17.3436i	−1.53146	−	0.681849i	−0.987551	+	0.157297i	$0.949722\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	8.27477	−	12.1756i	0.324813	−	0.477934i
$650$	0.0156450			0.000613646
$651$	−13.3524	−	14.2491i	−0.523323	−	0.558467i
$652$	0.593408	+	1.82632i	0.0232396	+	0.0715243i
$653$	19.6023	+	21.7706i	0.767097	+	0.851948i	0.992491	−	0.122320i	$-0.0390335\pi$
$653$	19.6023	+	21.7706i	0.767097	+	0.851948i	−0.225394	+	0.974268i	$0.572367\pi$
$654$	1.64650	−	15.6654i	0.0643834	−	0.612567i
$655$	−0.365436	+	3.47689i	−0.0142788	+	0.135853i
$656$	3.71156	+	4.12211i	0.144912	+	0.160941i
$657$	2.85013	+	8.77179i	0.111194	+	0.342220i
$658$	8.32806	−	1.94402i	0.324662	−	0.0757860i
$659$	−12.5940			−0.490591			−0.245296	−	0.969448i	$-0.578885\pi$
$659$	−12.5940			−0.490591			−0.245296	+	0.969448i	$0.578885\pi$
$660$	4.39111	+	5.66115i	0.170924	+	0.220360i
$661$	−5.61827	−	9.73112i	−0.218525	−	0.378497i	0.735832	−	0.677164i	$-0.236791\pi$
$661$	−5.61827	−	9.73112i	−0.218525	−	0.378497i	−0.954357	+	0.298667i	$0.903458\pi$
$662$	−12.9700	−	5.77461i	−0.504093	−	0.224437i
$663$	−0.112313	−	0.0238729i	−0.00436189	−	0.000927148i
$664$	−1.94594	+	5.98898i	−0.0755170	+	0.232418i
$665$	11.9745	+	19.8196i	0.464351	+	0.768570i
$666$	8.48915	+	6.16773i	0.328948	+	0.238995i
$667$	−0.381571	−	0.423778i	−0.0147745	−	0.0164087i
$668$	9.95471	−	11.0558i	0.385159	−	0.427763i
$669$	−13.3796	−	5.95700i	−0.517287	−	0.230311i
$670$	12.6455	−	21.9027i	0.488539	−	0.846174i
$671$	−0.946286	+	2.31871i	−0.0365310	+	0.0895128i
$672$	−0.328820	−	2.62524i	−0.0126845	−	0.101271i
$673$	16.4519	−	11.9530i	0.634172	−	0.460753i	−0.223671	−	0.974665i	$-0.571804\pi$
$673$	16.4519	−	11.9530i	0.634172	−	0.460753i	0.857843	+	0.513911i	$0.171804\pi$
$674$	32.3275	+	6.87142i	1.24521	+	0.264677i
$675$	0.326307	−	0.0693588i	0.0125596	−	0.00266962i
$676$	1.35864	−	12.9266i	0.0522554	−	0.497177i
$677$	−9.76415	+	4.34728i	−0.375267	+	0.167079i	−0.585698	−	0.810529i	$-0.699180\pi$
$677$	−9.76415	+	4.34728i	−0.375267	+	0.167079i	0.210432	+	0.977609i	$0.432513\pi$
$678$	4.13197	−	12.7169i	0.158687	−	0.488390i
$679$	−13.8695	−	9.66134i	−0.532261	−	0.370768i
$680$	4.27881	−	3.10874i	0.164085	−	0.119215i
$681$	12.8393	−	22.2384i	0.492004	−	0.852176i
$682$	10.6538	+	22.0391i	0.407953	+	0.843922i
$683$	−22.9614	−	39.7703i	−0.878594	−	1.52177i	−0.852884	−	0.522100i	$-0.825149\pi$
$683$	−22.9614	−	39.7703i	−0.878594	−	1.52177i	−0.0257098	−	0.999669i	$-0.508185\pi$
$684$	0.423506	+	4.02939i	0.0161932	+	0.154068i
$685$	−11.9399	−	36.7471i	−0.456199	−	1.40404i
$686$	−8.28744	+	16.5626i	−0.316416	+	0.632361i
$687$	6.37951	+	4.63498i	0.243393	+	0.176836i
$688$	1.09995	−	0.489730i	0.0419353	−	0.0186708i
$689$	−0.0523323	+	0.0111236i	−0.00199370	+	0.000423775i
$690$	0.482366	−	0.535722i	0.0183634	−	0.0203946i
$691$	−0.607278	−	5.77786i	−0.0231019	−	0.219800i	−0.999982	−	0.00601180i	$-0.998086\pi$
$691$	−0.607278	−	5.77786i	−0.0231019	−	0.219800i	0.976880	−	0.213788i	$-0.0685803\pi$
$692$	22.0142			0.836853
$693$	3.15346	−	8.18876i	0.119790	−	0.311065i
$694$	6.02910			0.228861
$695$	3.57644	+	34.0276i	0.135662	+	1.29074i
$696$	−1.14341	+	1.26988i	−0.0433407	+	0.0481347i
$697$	13.2839	−	2.82357i	0.503162	−	0.106950i
$698$	−9.90828	+	4.41145i	−0.375034	+	0.166976i
$699$	−11.9667	−	8.69430i	−0.452621	−	0.328849i
$700$	0.866806	+	0.166304i	0.0327622	+	0.00628570i
$701$	−9.32225	−	28.6909i	−0.352096	−	1.08364i	−0.957674	−	0.287855i	$-0.907058\pi$
$701$	−9.32225	−	28.6909i	−0.352096	−	1.08364i	0.605578	−	0.795786i	$-0.292942\pi$
$702$	0.00490215	+	0.0466409i	0.000185020	+	0.00176035i
$703$	−21.2570	−	36.8182i	−0.801723	−	1.38862i
$704$	−0.587369	+	3.26420i	−0.0221373	+	0.123024i
$705$	3.49122	−	6.04697i	0.131487	−	0.227742i
$706$	13.4159	−	9.74723i	0.504914	−	0.366842i
$707$	0.106321	−	1.25026i	0.00399862	−	0.0470209i
$708$	−1.37161	+	4.22140i	−0.0515484	+	0.158650i
$709$	14.9384	−	6.65100i	0.561023	−	0.249784i	−0.106576	−	0.994305i	$-0.533989\pi$
$709$	14.9384	−	6.65100i	0.561023	−	0.249784i	0.667599	+	0.744521i	$0.267322\pi$
$710$	−0.152162	+	1.44772i	−0.00571053	+	0.0543321i
$711$	−0.0974102	+	0.0207052i	−0.00365317	+	0.000776504i
$712$	−13.5089	−	2.87140i	−0.506266	−	0.107610i
$713$	1.99265	−	1.44775i	0.0746254	−	0.0542185i
$714$	−5.96893	−	2.51655i	−0.223382	−	0.0941795i
$715$	−0.0801428	−	0.326302i	−0.00299717	−	0.0122030i
$716$	−9.06821	+	15.7066i	−0.338895	+	0.586983i
$717$	1.22230	+	0.544202i	0.0456475	+	0.0203236i
$718$	17.1606	−	19.0588i	0.640428	−	0.711268i
$719$	−1.03391	−	1.14828i	−0.0385585	−	0.0428236i	0.723557	−	0.690265i	$-0.242506\pi$
$719$	−1.03391	−	1.14828i	−0.0385585	−	0.0428236i	−0.762116	+	0.647441i	$0.775839\pi$
$720$	−1.74763	−	1.26973i	−0.0651302	−	0.0473199i
$721$	19.4903	−	35.3638i	0.725855	−	1.31702i
$722$	−0.798703	+	2.45815i	−0.0297246	+	0.0914830i
$723$	−21.5608	−	4.58288i	−0.801854	−	0.170439i
$724$	12.9315	+	5.75746i	0.480594	+	0.213974i
$725$	−0.285024	−	0.493677i	−0.0105855	−	0.0183347i
$726$	−6.83286	+	8.62044i	−0.253591	+	0.319934i
$727$	46.5451			1.72626			0.863131	−	0.504980i	$-0.168500\pi$
$727$	46.5451			1.72626			0.863131	+	0.504980i	$0.168500\pi$
$728$	−0.0359888	+	0.118746i	−0.00133383	+	0.00440102i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	13.3317	+	14.8063i	0.493427	+	0.548006i
$731$	0.308143	−	2.93179i	0.0113971	−	0.108436i
$732$	0.0789290	−	0.750960i	0.00291730	−	0.0277563i
$733$	−2.96802	−	3.29633i	−0.109626	−	0.121753i	0.685834	−	0.727758i	$-0.259438\pi$
$733$	−2.96802	−	3.29633i	−0.109626	−	0.121753i	−0.795460	+	0.606005i	$0.792771\pi$
$734$	−0.565360	−	1.74000i	−0.0208678	−	0.0642245i
$735$	5.24082	+	14.1841i	0.193311	+	0.523187i
$736$	0.333714			0.0123009
$737$	37.2884	+	10.8338i	1.37354	+	0.399070i
$738$	−2.77342	−	4.80370i	−0.102091	−	0.176827i
$739$	−27.5795	−	12.2792i	−1.01453	−	0.451697i	−0.168993	−	0.985617i	$-0.554051\pi$
$739$	−27.5795	−	12.2792i	−1.01453	−	0.451697i	−0.845535	+	0.533921i	$0.820718\pi$
$740$	22.1719	+	4.71278i	0.815054	+	0.173245i
$741$	0.0587164	−	0.180711i	0.00215700	−	0.00663857i
$742$	−3.01770	+	0.0600136i	−0.110783	+	0.00220317i
$743$	6.87891	+	4.99782i	0.252363	+	0.183352i	0.706773	−	0.707440i	$-0.250150\pi$
$743$	6.87891	+	4.99782i	0.252363	+	0.183352i	−0.454411	+	0.890792i	$0.650150\pi$
$744$	−4.93867	−	5.48494i	−0.181060	−	0.201088i
$745$	23.3741	−	25.9596i	0.856361	−	0.951085i
$746$	24.2463	+	10.7951i	0.887719	+	0.395238i
$747$	3.14859	−	5.45352i	0.115201	−	0.199534i
$748$	6.20216	+	5.24138i	0.226774	+	0.191644i
$749$	0.921244	+	7.35505i	0.0336615	+	0.268748i
$750$	9.32114	−	6.77220i	0.340360	−	0.247286i
$751$	−18.7255	−	3.98023i	−0.683303	−	0.145241i	−0.146835	−	0.989161i	$-0.546909\pi$
$751$	−18.7255	−	3.98023i	−0.683303	−	0.145241i	−0.536468	+	0.843920i	$0.680242\pi$
$752$	3.16170	−	0.672040i	0.115295	−	0.0245068i
$753$	0.428799	−	4.07975i	0.0156263	−	0.148674i
$754$	0.0732102	−	0.0325953i	0.00266616	−	0.00118705i
$755$	14.7953	−	45.5351i	0.538454	−	1.65719i
$756$	−0.224184	+	2.63624i	−0.00815348	+	0.0958790i
$757$	24.2009	−	17.5830i	0.879596	−	0.639064i	−0.0535489	−	0.998565i	$-0.517053\pi$
$757$	24.2009	−	17.5830i	0.879596	−	0.639064i	0.933144	+	0.359502i	$0.117053\pi$
$758$	19.0331	−	32.9662i	0.691312	−	1.19739i
$759$	0.975424	+	0.523035i	0.0354057	+	0.0189850i
$760$	4.37609	+	7.57961i	0.158737	+	0.274941i
$761$	0.397376	+	3.78078i	0.0144049	+	0.137053i	0.999361	−	0.0357534i	$-0.0113831\pi$
$761$	0.397376	+	3.78078i	0.0144049	+	0.137053i	−0.984956	+	0.172807i	$0.944716\pi$
$762$	−3.89772	−	11.9960i	−0.141200	−	0.434568i
$763$	−27.2648	+	31.5190i	−0.987052	+	1.14106i
$764$	20.2632	+	14.7221i	0.733096	+	0.532625i
$765$	−4.83165	+	2.15119i	−0.174689	+	0.0777765i
$766$	−12.9296	+	2.74826i	−0.467164	+	0.0992988i
$767$	0.139288	−	0.154695i	0.00502939	−	0.00558570i
$768$	−0.104528	−	0.994522i	−0.00377185	−	0.0358867i
$769$	−11.4898			−0.414331			−0.207166	−	0.978306i	$-0.566424\pi$
$769$	−11.4898			−0.414331			−0.207166	+	0.978306i	$0.566424\pi$
$770$	−0.971740	−	18.9306i	−0.0350191	−	0.682213i
$771$	−13.6996			−0.493380
$772$	−0.330887	−	3.14818i	−0.0119089	−	0.113305i
$773$	−19.7966	+	21.9864i	−0.712035	+	0.790795i	−0.985243	−	0.171160i	$-0.945248\pi$
$773$	−19.7966	+	21.9864i	−0.712035	+	0.790795i	0.273209	+	0.961955i	$0.411915\pi$
$774$	−1.17774	+	0.250336i	−0.0423329	+	0.00899813i
$775$	2.24932	−	1.00146i	0.0807980	−	0.0359736i
$776$	−5.16852	−	3.75515i	−0.185539	−	0.134802i
$777$	−9.10232	−	26.2277i	−0.326544	−	0.940915i
$778$	−4.59519	−	14.1425i	−0.164745	−	0.507034i
$779$	2.34912	+	22.3504i	0.0841659	+	0.800786i
$780$	0.0506539	+	0.0877352i	0.00181370	+	0.00314142i
$781$	−2.21432	+	0.303293i	−0.0792346	+	0.0108527i
$782$	0.408526	−	0.707588i	0.0146089	−	0.0253033i
$783$	1.38244	−	1.00440i	0.0494045	−	0.0358945i
$784$	−3.25621	+	6.19654i	−0.116293	+	0.221305i
$785$	−14.0773	+	43.3253i	−0.502439	+	1.54635i
$786$	1.47848	−	0.658262i	0.0527357	−	0.0234794i
$787$	−4.72973	+	45.0004i	−0.168597	+	1.60409i	0.503747	+	0.863851i	$0.331954\pi$
$787$	−4.72973	+	45.0004i	−0.168597	+	1.60409i	−0.672344	+	0.740239i	$0.734712\pi$
$788$	17.8996	−	3.80468i	0.637648	−	0.135536i
$789$	8.44448	+	1.79493i	0.300631	+	0.0639012i
$790$	−0.174040	+	0.126447i	−0.00619206	+	0.00449879i
$791$	−28.2017	+	21.3592i	−1.00274	+	0.759445i
$792$	1.25320	−	3.07075i	0.0445305	−	0.109114i
$793$	−0.0177062	+	0.0306680i	−0.000628764	+	0.00108905i
$794$	32.6462	+	14.5350i	1.15857	+	0.515828i
$795$	−1.64898	+	1.83138i	−0.0584833	+	0.0649523i
$796$	−4.75026	−	5.27570i	−0.168368	−	0.186992i
$797$	−43.9124	−	31.9042i	−1.55546	−	1.13010i	−0.939615	−	0.342234i	$-0.888817\pi$
$797$	−43.9124	−	31.9042i	−1.55546	−	1.13010i	−0.615841	−	0.787871i	$-0.711183\pi$
$798$	5.17410	−	9.38808i	0.183161	−	0.332335i
$799$	2.44553	−	7.52657i	0.0865167	−	0.266271i
$800$	0.326307	+	0.0693588i	0.0115367	+	0.00245220i
$801$	12.6167	+	5.61730i	0.445788	+	0.198478i
$802$	1.55839	+	2.69921i	0.0550286	+	0.0953124i
$803$	−17.1944	+	25.3001i	−0.606778	+	0.892821i
$804$	−11.7078			−0.412902
$805$	−1.85735	+	0.433562i	−0.0654630	+	0.0152811i
$806$	0.106963	+	0.329198i	0.00376761	+	0.0115955i
$807$	−10.6412	−	11.8183i	−0.374589	−	0.416023i
$808$	0.0495737	−	0.471662i	0.00174400	−	0.0165930i
$809$	1.23682	−	11.7675i	0.0434841	−	0.413724i	−0.951028	−	0.309104i	$-0.899971\pi$
$809$	1.23682	−	11.7675i	0.0434841	−	0.413724i	0.994512	−	0.104620i	$-0.0333625\pi$
$810$	1.44545	+	1.60533i	0.0507878	+	0.0564056i
$811$	10.4101	+	32.0390i	0.365548	+	1.12504i	0.949637	+	0.313351i	$0.101452\pi$
$811$	10.4101	+	32.0390i	0.365548	+	1.12504i	−0.584090	+	0.811689i	$0.698548\pi$
$812$	4.40268	−	1.02772i	0.154504	−	0.0360659i
$813$	18.6786			0.655089
$814$	1.09267	+	34.7848i	0.0382981	+	1.21921i
$815$	−2.07411	−	3.59247i	−0.0726530	−	0.125839i
$816$	−2.23668	−	0.995836i	−0.0782996	−	0.0348612i
$817$	4.77170	+	1.01426i	0.166941	+	0.0354843i
$818$	2.09777	−	6.45628i	0.0733469	−	0.225739i
$819$	0.0598911	−	0.108669i	0.00209276	−	0.00379719i
$820$	−9.69381	−	7.04296i	−0.338522	−	0.245951i
$821$	14.6933	+	16.3185i	0.512799	+	0.569521i	0.942822	−	0.333297i	$-0.108161\pi$
$821$	14.6933	+	16.3185i	0.512799	+	0.569521i	−0.430023	+	0.902818i	$0.641495\pi$
$822$	−11.9684	+	13.2923i	−0.417447	+	0.463622i
$823$	−25.1403	−	11.1932i	−0.876336	−	0.390170i	−0.0812698	−	0.996692i	$-0.525898\pi$
$823$	−25.1403	−	11.1932i	−0.876336	−	0.390170i	−0.795067	+	0.606522i	$0.792564\pi$
$824$	7.63093	−	13.2172i	0.265836	−	0.460442i
$825$	0.845067	+	0.714157i	0.0294215	+	0.0248638i
$826$	9.36159	−	7.09022i	0.325731	−	0.246700i
$827$	−11.5618	+	8.40016i	−0.402044	+	0.292102i	−0.770373	−	0.637593i	$-0.779930\pi$
$827$	−11.5618	+	8.40016i	−0.402044	+	0.292102i	0.368329	+	0.929696i	$0.379930\pi$
$828$	−0.326422	−	0.0693831i	−0.0113439	−	0.00241123i
$829$	−1.22000	+	0.259319i	−0.0423723	+	0.00900651i	−0.229049	−	0.973415i	$-0.573562\pi$
$829$	−1.22000	+	0.259319i	−0.0423723	+	0.00900651i	0.186677	+	0.982421i	$0.440228\pi$
$830$	1.42191	−	13.5286i	0.0493552	−	0.469584i
$831$	−8.87228	+	3.95019i	−0.307776	+	0.137031i
$832$	−0.0144922	+	0.0446024i	−0.000502427	+	0.00154631i
$833$	9.15258	+	14.4899i	0.317118	+	0.502046i
$834$	12.8139	−	9.30988i	0.443711	−	0.322375i
$835$	−16.0686	+	27.8317i	−0.556078	+	0.963155i
$836$	−9.69885	+	9.30060i	−0.335442	+	0.321668i
$837$	3.69036	+	6.39189i	0.127558	+	0.220936i
$838$	−2.14476	−	20.4060i	−0.0740894	−	0.704914i
$839$	5.59305	+	17.2137i	0.193094	+	0.594281i	0.999994	+	0.00359297i	$0.00114368\pi$
$839$	5.59305	+	17.2137i	0.193094	+	0.594281i	−0.806900	+	0.590688i	$0.798856\pi$
$840$	1.87386	+	5.39940i	0.0646542	+	0.186297i
$841$	21.0992	+	15.3295i	0.727558	+	0.528602i
$842$	−13.2977	+	5.92052i	−0.458269	+	0.204035i
$843$	−2.02677	+	0.430802i	−0.0698055	+	0.0148376i
$844$	−0.164823	+	0.183055i	−0.00567345	+	0.00630101i
$845$	2.93492	+	27.9239i	0.100964	+	0.960610i
$846$	−3.23233			−0.111130
$847$	27.8703	−	8.38147i	0.957633	−	0.287991i
$848$	−1.14081			−0.0391756
$849$	2.24475	+	21.3574i	0.0770396	+	0.732982i
$850$	0.546523	−	0.606975i	0.0187456	−	0.0208191i
$851$	3.42520	−	0.728049i	0.117414	−	0.0249572i
$852$	0.615616	−	0.274090i	0.0210907	−	0.00939017i
$853$	−35.5025	−	25.7941i	−1.21558	−	0.883173i	−0.219858	−	0.975532i	$-0.570559\pi$
$853$	−35.5025	−	25.7941i	−1.21558	−	0.883173i	−0.995726	+	0.0923584i	$0.970559\pi$
$854$	−1.30700	+	1.51094i	−0.0447247	+	0.0517033i
$855$	−2.70457	−	8.32382i	−0.0924944	−	0.284668i
$856$	0.292854	+	2.78632i	0.0100096	+	0.0952346i
$857$	−7.27175	−	12.5950i	−0.248398	−	0.430238i	0.714683	−	0.699448i	$-0.246571\pi$
$857$	−7.27175	−	12.5950i	−0.248398	−	0.430238i	−0.963082	+	0.269210i	$0.913238\pi$
$858$	−0.112266	+	0.107656i	−0.00383269	+	0.00367531i
$859$	7.99789	−	13.8528i	0.272885	−	0.472650i	−0.696715	−	0.717348i	$-0.745356\pi$
$859$	7.99789	−	13.8528i	0.272885	−	0.472650i	0.969599	+	0.244698i	$0.0786889\pi$
$860$	−2.10423	+	1.52881i	−0.0717535	+	0.0521320i
$861$	−1.24351	+	14.6228i	−0.0423787	+	0.498343i
$862$	−6.61731	+	20.3660i	−0.225387	+	0.693668i
$863$	−24.2270	+	10.7866i	−0.824698	+	0.367179i	−0.775295	−	0.631600i	$-0.782399\pi$
$863$	−24.2270	+	10.7866i	−0.824698	+	0.367179i	−0.0494031	+	0.998779i	$0.515732\pi$
$864$	−0.104528	+	0.994522i	−0.00355613	+	0.0338343i
$865$	−46.5155	+	9.88718i	−1.58157	+	0.336174i
$866$	−23.3445	−	4.96202i	−0.793278	−	0.168616i
$867$	8.90368	−	6.46890i	0.302385	−	0.219695i
$868$	2.42693	+	19.3762i	0.0823752	+	0.657669i
$869$	−0.252272	−	0.213192i	−0.00855773	−	0.00723205i
$870$	1.84566	−	3.19677i	0.0625736	−	0.108381i
$871$	0.501600	+	0.223327i	0.0169961	+	0.00756714i
$872$	−10.5400	+	11.7058i	−0.356928	+	0.396409i
$873$	4.27484	+	4.74769i	0.144681	+	0.160685i
$874$	1.09385	+	0.794728i	0.0370000	+	0.0268821i
$875$	−30.4772	+	0.606105i	−1.03032	+	0.0204901i
$876$	2.85013	−	8.77179i	0.0962969	−	0.296371i
$877$	−17.2479	−	3.66615i	−0.582419	−	0.123797i	−0.0927255	−	0.995692i	$-0.529558\pi$
$877$	−17.2479	−	3.66615i	−0.582419	−	0.123797i	−0.489693	+	0.871895i	$0.662891\pi$
$878$	−17.6578	−	7.86174i	−0.595920	−	0.265321i
$879$	−14.9134	−	25.8308i	−0.503017	−	0.871251i
$880$	−0.224944	−	7.16099i	−0.00758285	−	0.241397i
$881$	0.924407			0.0311441			0.0155720	−	0.999879i	$-0.495043\pi$
$881$	0.924407			0.0311441			0.0155720	+	0.999879i	$0.495043\pi$
$882$	4.47339	−	5.38413i	0.150627	−	0.181293i
$883$	12.9682	+	39.9121i	0.436415	+	1.34315i	0.891630	+	0.452766i	$0.149563\pi$
$883$	12.9682	+	39.9121i	0.436415	+	1.34315i	−0.455214	+	0.890382i	$0.650437\pi$
$884$	0.0768312	+	0.0853297i	0.00258411	+	0.00286995i
$885$	1.00225	−	9.53576i	0.0336902	−	0.320541i
$886$	−3.72457	+	35.4369i	−0.125129	+	1.19053i
$887$	5.53763	+	6.15016i	0.185935	+	0.206502i	0.828905	−	0.559390i	$-0.188964\pi$
$887$	5.53763	+	6.15016i	0.185935	+	0.206502i	−0.642969	+	0.765892i	$0.722298\pi$
$888$	−3.24257	−	9.97960i	−0.108813	−	0.334893i
$889$	−9.67931	+	31.9371i	−0.324634	+	1.07114i
$890$	29.8336			1.00002
$891$	−1.86426	+	2.74309i	−0.0624550	+	0.0918970i
$892$	7.32292	+	12.6837i	0.245189	+	0.424681i
$893$	11.9639	+	5.32665i	0.400355	+	0.178250i
$894$	−15.8175	−	3.36211i	−0.529016	−	0.112446i
$895$	12.1067	−	37.2605i	0.404682	−	1.24548i
$896$	−1.27706	+	2.31714i	−0.0426634	+	0.0774101i
$897$	0.0126615	+	0.00919911i	0.000422755	+	0.000307149i
$898$	−21.1242	−	23.4608i	−0.704923	−	0.782896i
$899$	8.43916	−	9.37264i	0.281462	−	0.312595i
$900$	−0.304756	−	0.135686i	−0.0101585	−	0.00452288i
$901$	−1.39656	+	2.41890i	−0.0465260	+	0.0805854i
$902$	6.95129	−	17.0329i	0.231453	−	0.567135i
$903$	2.93539	+	1.23758i	0.0976836	+	0.0411842i
$904$	−10.8176	+	7.85948i	−0.359790	+	0.261402i
$905$	−29.9098	−	6.35751i	−0.994234	−	0.211331i
$906$	−21.6797	+	4.60816i	−0.720260	+	0.153096i
$907$	0.133786	−	1.27289i	0.00444228	−	0.0422655i	−0.992076	−	0.125638i	$-0.959902\pi$
$907$	0.133786	−	1.27289i	0.00444228	−	0.0422655i	0.996518	+	0.0833721i	$0.0265690\pi$
$908$	−23.4586	+	10.4444i	−0.778501	+	0.346611i
$909$	−0.146554	+	0.451048i	−0.00486090	+	0.0149603i
$910$	0.0227116	−	0.267072i	0.000752881	−	0.00885334i
$911$	45.5333	−	33.0819i	1.50859	−	1.09605i	0.541787	−	0.840516i	$-0.317748\pi$
$911$	45.5333	−	33.0819i	1.50859	−	1.09605i	0.966800	−	0.255536i	$-0.0822520\pi$
$912$	2.02579	−	3.50878i	0.0670807	−	0.116187i
$913$	20.6922	−	2.83419i	0.684812	−	0.0937979i
$914$	−5.19925	−	9.00537i	−0.171976	−	0.297871i
$915$	0.170501	+	1.62221i	0.00563660	+	0.0536287i
$916$	−2.43675	−	7.49956i	−0.0805126	−	0.247792i
$917$	−4.20518	−	0.806800i	−0.138867	−	0.0266429i
$918$	1.98076	+	1.43911i	0.0653749	+	0.0474976i
$919$	−22.6138	+	10.0683i	−0.745959	+	0.332122i	−0.744272	−	0.667876i	$-0.767204\pi$
$919$	−22.6138	+	10.0683i	−0.745959	+	0.332122i	−0.00168683	+	0.999999i	$0.500537\pi$
$920$	−0.705132	+	0.149880i	−0.0232475	+	0.00494141i
$921$	−9.34464	+	10.3783i	−0.307916	+	0.341976i
$922$	−2.63847	−	25.1034i	−0.0868934	−	0.826735i
$923$	−0.0316033			−0.00104023
$924$	−7.36443	+	4.77129i	−0.242272	+	0.156964i
$925$	3.50049			0.115096
$926$	−3.40035	−	32.3522i	−0.111743	−	1.06316i
$927$	−10.2122	+	11.3418i	−0.335412	+	0.372513i
$928$	1.67145	−	0.355278i	0.0548681	−	0.0116626i
$929$	28.6414	−	12.7520i	0.939695	−	0.418379i	0.121029	−	0.992649i	$-0.461381\pi$
$929$	28.6414	−	12.7520i	0.939695	−	0.418379i	0.818666	+	0.574270i	$0.194714\pi$
$930$	12.8987	+	9.37149i	0.422967	+	0.307303i
$931$	−25.4300	+	12.5565i	−0.833436	+	0.411522i
$932$	4.57086	+	14.0677i	0.149724	+	0.460802i
$933$	1.96278	+	18.6746i	0.0642586	+	0.611379i
$934$	−5.18789	−	8.98568i	−0.169753	−	0.294020i
$935$	−15.4591	−	8.28937i	−0.505567	−	0.271092i
$936$	0.0234489	−	0.0406147i	0.000766451	−	0.00132753i
$937$	2.54471	−	1.84884i	0.0831322	−	0.0603991i	−0.545443	−	0.838148i	$-0.683639\pi$
$937$	2.54471	−	1.84884i	0.0831322	−	0.0603991i	0.628575	+	0.777749i	$0.283639\pi$
$938$	25.4171	+	17.7053i	0.829898	+	0.578099i
$939$	0.558310	−	1.71830i	0.0182197	−	0.0560746i
$940$	−6.37878	+	2.84002i	−0.208053	+	0.0926311i
$941$	−4.63289	+	44.0790i	−0.151028	+	1.43693i	0.612148	+	0.790743i	$0.290306\pi$
$941$	−4.63289	+	44.0790i	−0.151028	+	1.43693i	−0.763176	+	0.646191i	$0.776361\pi$
$942$	20.6276	−	4.38453i	0.672084	−	0.142856i
$943$	−1.81061	−	0.384857i	−0.0589616	−	0.0125327i
$944$	3.59093	−	2.60897i	0.116875	−	0.0849146i
$945$	−0.710311	−	5.67100i	−0.0231064	−	0.184478i
$946$	−3.05009	−	2.57760i	−0.0991669	−	0.0838049i
$947$	5.07378	−	8.78804i	0.164876	−	0.285573i	−0.771736	−	0.635944i	$-0.780611\pi$
$947$	5.07378	−	8.78804i	0.164876	−	0.285573i	0.936611	+	0.350371i	$0.113944\pi$
$948$	0.0909767	+	0.0405054i	0.00295478	+	0.00131555i
$949$	−0.289431	+	0.321446i	−0.00939533	+	0.0104346i
$950$	0.904396	+	1.00443i	0.0293425	+	0.0325881i
$951$	−26.7212	−	19.4141i	−0.866494	−	0.629545i
$952$	3.34977	+	5.54438i	0.108567	+	0.179694i
$953$	5.42980	−	16.7112i	0.175888	−	0.541329i	−0.823785	−	0.566903i	$-0.808141\pi$
$953$	5.42980	−	16.7112i	0.175888	−	0.541329i	0.999673	+	0.0255743i	$0.00814144\pi$
$954$	1.11588	+	0.237188i	0.0361280	+	0.00767924i
$955$	−49.4278	−	22.0067i	−1.59944	−	0.712119i
$956$	−0.668985	−	1.15872i	−0.0216365	−	0.0374756i
$957$	5.44237	+	1.58124i	0.175927	+	0.0511141i
$958$	26.3860			0.852493
$959$	46.0844	−	10.7575i	1.48814	−	0.347378i
$960$	0.667534	+	2.05446i	0.0215446	+	0.0663074i
$961$	15.7079	+	17.4454i	0.506705	+	0.562753i
$962$	−0.0514391	+	0.489411i	−0.00165846	+	0.0157792i
$963$	0.292854	−	2.78632i	0.00943710	−	0.0897880i
$964$	14.7493	+	16.3807i	0.475042	+	0.527588i
$965$	2.11309	+	6.50343i	0.0680229	+	0.209353i
$966$	0.603722	+	0.644265i	0.0194244	+	0.0207289i
$967$	−26.6543			−0.857144			−0.428572	−	0.903508i	$-0.640983\pi$
$967$	−26.6543			−0.857144			−0.428572	+	0.903508i	$0.640983\pi$
$968$	10.5949	−	2.95782i	0.340532	−	0.0950681i
$969$	−4.95986	−	8.59073i	−0.159334	−	0.275974i
$970$	12.6075	+	5.61324i	0.404804	+	0.180230i
$971$	−12.2743	−	2.60897i	−0.393900	−	0.0837260i	0.00670367	−	0.999978i	$-0.497866\pi$
$971$	−12.2743	−	2.60897i	−0.393900	−	0.0837260i	−0.400603	+	0.916252i	$0.631199\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−41.8975	+	0.833224i	−1.34317	+	0.0267119i
$974$	−19.1071	−	13.8821i	−0.612232	−	0.444813i
$975$	0.0104685	+	0.0116265i	0.000335261	+	0.000372345i
$976$	−0.505258	+	0.561146i	−0.0161729	+	0.0179618i
$977$	−29.0630	−	12.9397i	−0.929807	−	0.413977i	−0.114774	−	0.993392i	$-0.536614\pi$
$977$	−29.0630	−	12.9397i	−0.929807	−	0.413977i	−0.815033	+	0.579415i	$0.803281\pi$
$978$	−0.960154	+	1.66304i	−0.0307023	+	0.0531780i
$979$	10.9254	+	44.4827i	0.349176	+	1.42167i
$980$	4.09727	−	14.5556i	0.130882	−	0.464962i
$981$	12.7434	−	9.25863i	0.406866	−	0.295605i
$982$	−8.26905	−	1.75764i	−0.263876	−	0.0560885i
$983$	−0.311593	+	0.0662311i	−0.00993826	+	0.00211244i	−0.212878	−	0.977079i	$-0.568284\pi$
$983$	−0.311593	+	0.0662311i	−0.00993826	+	0.00211244i	0.202940	+	0.979191i	$0.434950\pi$
$984$	−0.579803	+	5.51645i	−0.0184834	+	0.175858i
$985$	−36.1128	+	16.0784i	−1.15065	+	0.512302i
$986$	1.29285	−	3.97897i	0.0411726	−	0.126716i
$987$	7.01725	+	4.88815i	0.223362	+	0.155592i
$988$	−0.153722	+	0.111685i	−0.00489053	+	0.00355318i
$989$	−0.200904	+	0.347976i	−0.00638838	+	0.0110650i
$990$	−1.26883	+	7.05128i	−0.0403259	+	0.224104i
$991$	11.8337	+	20.4966i	0.375910	+	0.651095i	0.990463	−	0.137781i	$-0.0439970\pi$
$991$	11.8337	+	20.4966i	0.375910	+	0.651095i	−0.614553	+	0.788875i	$0.710664\pi$
$992$	0.771495	+	7.34029i	0.0244950	+	0.233054i
$993$	−4.38725	−	13.5026i	−0.139225	−	0.428491i
$994$	−1.75097	−	0.335939i	−0.0555375	−	0.0106553i
$995$	12.4067	+	9.01397i	0.393318	+	0.285762i
$996$	−5.75277	+	2.56130i	−0.182283	+	0.0811578i
$997$	40.0675	−	8.51662i	1.26895	−	0.269724i	0.476237	−	0.879317i	$-0.342000\pi$
$997$	40.0675	−	8.51662i	1.26895	−	0.269724i	0.792715	+	0.609593i	$0.208667\pi$
$998$	−20.5013	+	22.7690i	−0.648956	+	0.720739i
$999$	1.09684	+	10.4357i	0.0347023	+	0.330171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.b.289.3	yes	24
7.4	even	3	inner	462.2.y.b.25.1	✓	24
11.4	even	5	inner	462.2.y.b.37.1	yes	24
77.4	even	15	inner	462.2.y.b.235.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.b.25.1	✓	24	7.4	even	3	inner
462.2.y.b.37.1	yes	24	11.4	even	5	inner
462.2.y.b.235.3	yes	24	77.4	even	15	inner
462.2.y.b.289.3	yes	24	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.97343 - 0.878627i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.867452 + 2.49951i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.104528 - 0.994522i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.97343 - 0.878627i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.867452 + 2.49951i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.08009 - 1.87078i) q^{10} +(2.39384 - 2.29555i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.0379411 - 0.0275658i) q^{13} +(2.39514 - 1.12397i) q^{14} +(0.667534 - 2.05446i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.255923 - 2.43494i) q^{17} +(-0.978148 + 0.207912i) q^{18} +(3.96305 + 0.842372i) q^{19} +(-1.74763 + 1.26973i) q^{20} +(2.43793 + 1.02785i) q^{21} +(-2.53320 - 2.14078i) q^{22} +(-0.166857 + 0.289005i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-0.223220 + 0.247911i) q^{25} +(-0.0313807 - 0.0348518i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.36817 - 2.26453i) q^{28} +(-0.528046 + 1.62516i) q^{29} +(-2.11298 - 0.449128i) q^{30} +(-6.74262 - 3.00201i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.104132 - 3.31499i) q^{33} -2.44836 q^{34} +(3.90799 + 4.17043i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-7.02130 - 7.79795i) q^{37} +(0.423506 - 4.02939i) q^{38} +(0.00490215 - 0.0466409i) q^{39} +(1.44545 + 1.60533i) q^{40} +(1.71407 + 5.27536i) q^{41} +(0.767389 - 2.53202i) q^{42} +1.20405 q^{43} +(-1.86426 + 2.74309i) q^{44} +(-1.08009 - 1.87078i) q^{45} +(0.304863 + 0.135734i) q^{46} +(3.16170 + 0.672040i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-5.49505 + 4.33640i) q^{49} +(0.269886 + 0.196084i) q^{50} +(-1.63827 - 1.81948i) q^{51} +(-0.0313807 + 0.0348518i) q^{52} +(-1.04218 - 0.464009i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.70714 - 6.63339i) q^{55} +(-2.10911 + 1.59739i) q^{56} +(3.27780 - 2.38146i) q^{57} +(1.67145 + 0.355278i) q^{58} +(4.34164 - 0.922845i) q^{59} +(-0.225801 + 2.14835i) q^{60} +(-0.689815 + 0.307125i) q^{61} +(-2.28077 + 7.01948i) q^{62} +(2.39514 - 1.12397i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.0506539 - 0.0877352i) q^{65} +(-3.28595 + 0.450072i) q^{66} +(5.85390 + 10.1393i) q^{67} +(0.255923 + 2.43494i) q^{68} +(0.103123 + 0.317381i) q^{69} +(3.73909 - 4.32251i) q^{70} +(-0.545177 - 0.396094i) q^{71} +(0.913545 - 0.406737i) q^{72} +(-9.02166 + 1.91761i) q^{73} +(-7.02130 + 7.79795i) q^{74} +(0.0348704 + 0.331770i) q^{75} -4.05159 q^{76} +(7.81427 + 3.99214i) q^{77} -0.0468978 q^{78} +(-0.0104096 - 0.0990408i) q^{79} +(1.44545 - 1.60533i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(5.06729 - 2.25610i) q^{82} +(5.09453 + 3.70139i) q^{83} +(-2.59836 - 0.498517i) q^{84} +(-1.63436 - 5.03005i) q^{85} +(-0.125857 - 1.19745i) q^{86} +(0.854397 + 1.47986i) q^{87} +(2.92293 + 1.56731i) q^{88} +(-6.90533 + 11.9604i) q^{89} +(-1.74763 + 1.26973i) q^{90} +(0.101813 + 0.0709219i) q^{91} +(0.103123 - 0.317381i) q^{92} +(-6.74262 + 3.00201i) q^{93} +(0.337871 - 3.21463i) q^{94} +(8.56092 - 1.81968i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-5.16852 + 3.75515i) q^{97} +(4.88704 + 5.01167i) q^{98} +(-2.53320 - 2.14078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 5 q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 3 q^{9} + 10 q^{10} - 2 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{14} + 20 q^{15} + 3 q^{16} + 8 q^{17} + 3 q^{18} + 7 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{22} + 24 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{27} - 2 q^{28} + 2 q^{29} - 10 q^{30} - 19 q^{31} - 12 q^{32} - 7 q^{33} + 24 q^{34} + 14 q^{35} - 6 q^{36} - q^{37} - 8 q^{38} - 5 q^{39} - 10 q^{40} + 16 q^{41} + 10 q^{42} - 68 q^{43} - 2 q^{44} + 10 q^{45} - 6 q^{46} + 25 q^{47} - 6 q^{48} - 21 q^{49} + 14 q^{50} - 2 q^{51} - 5 q^{53} - 12 q^{54} - 10 q^{55} - 10 q^{56} + 16 q^{57} - q^{58} - 36 q^{59} + 5 q^{60} - q^{61} - 52 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} + 8 q^{66} + 56 q^{67} + 8 q^{68} + 12 q^{69} - 17 q^{70} - 6 q^{71} + 3 q^{72} + 35 q^{73} - q^{74} - 7 q^{75} - 4 q^{76} + 38 q^{77} - 20 q^{78} - 3 q^{79} - 10 q^{80} + 3 q^{81} + 2 q^{82} - 28 q^{83} + 7 q^{84} - 80 q^{85} - 11 q^{86} + 4 q^{87} - 7 q^{88} - 6 q^{89} - 10 q^{90} - 24 q^{91} + 12 q^{92} - 19 q^{93} - 30 q^{94} - 44 q^{95} + 3 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 3 * q^9 + 10 * q^10 - 2 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^14 + 20 * q^15 + 3 * q^16 + 8 * q^17 + 3 * q^18 + 7 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^22 + 24 * q^23 + 3 * q^24 + 8 * q^25 - 6 * q^27 - 2 * q^28 + 2 * q^29 - 10 * q^30 - 19 * q^31 - 12 * q^32 - 7 * q^33 + 24 * q^34 + 14 * q^35 - 6 * q^36 - q^37 - 8 * q^38 - 5 * q^39 - 10 * q^40 + 16 * q^41 + 10 * q^42 - 68 * q^43 - 2 * q^44 + 10 * q^45 - 6 * q^46 + 25 * q^47 - 6 * q^48 - 21 * q^49 + 14 * q^50 - 2 * q^51 - 5 * q^53 - 12 * q^54 - 10 * q^55 - 10 * q^56 + 16 * q^57 - q^58 - 36 * q^59 + 5 * q^60 - q^61 - 52 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 + 8 * q^66 + 56 * q^67 + 8 * q^68 + 12 * q^69 - 17 * q^70 - 6 * q^71 + 3 * q^72 + 35 * q^73 - q^74 - 7 * q^75 - 4 * q^76 + 38 * q^77 - 20 * q^78 - 3 * q^79 - 10 * q^80 + 3 * q^81 + 2 * q^82 - 28 * q^83 + 7 * q^84 - 80 * q^85 - 11 * q^86 + 4 * q^87 - 7 * q^88 - 6 * q^89 - 10 * q^90 - 24 * q^91 + 12 * q^92 - 19 * q^93 - 30 * q^94 - 44 * q^95 + 3 * q^96 - 8 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

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