LMFDB - Embedded newform 460.2.w.a.167.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.42
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.409811 + 1.35353i) q^{2} +(1.07533 + 1.96932i) q^{3} +(-1.66411 + 1.10939i) q^{4} +(-1.09207 + 1.95125i) q^{5} +(-2.22487 + 2.26255i) q^{6} +(1.84794 + 2.46855i) q^{7} +(-2.18356 - 1.79779i) q^{8} +(-1.09998 + 1.71160i) q^{9} +O(q^{10})$	\(q+(0.409811 + 1.35353i) q^{2} +(1.07533 + 1.96932i) q^{3} +(-1.66411 + 1.10939i) q^{4} +(-1.09207 + 1.95125i) q^{5} +(-2.22487 + 2.26255i) q^{6} +(1.84794 + 2.46855i) q^{7} +(-2.18356 - 1.79779i) q^{8} +(-1.09998 + 1.71160i) q^{9} +(-3.08863 - 0.678508i) q^{10} +(4.61278 - 2.10659i) q^{11} +(-3.97421 - 2.08421i) q^{12} +(1.37983 + 1.03293i) q^{13} +(-2.58397 + 3.51289i) q^{14} +(-5.01699 - 0.0523926i) q^{15} +(1.53852 - 3.69228i) q^{16} +(2.48362 - 0.177632i) q^{17} +(-2.76749 - 0.787425i) q^{18} +(-4.68500 - 5.40678i) q^{19} +(-0.347370 - 4.45862i) q^{20} +(-2.87424 + 6.29370i) q^{21} +(4.74171 + 5.38026i) q^{22} +(-3.71803 - 3.02924i) q^{23} +(1.19238 - 6.23337i) q^{24} +(-2.61477 - 4.26180i) q^{25} +(-0.832635 + 2.29095i) q^{26} +(2.16068 + 0.154535i) q^{27} +(-5.81375 - 2.05787i) q^{28} +(0.385342 + 0.333901i) q^{29} +(-1.98510 - 6.81213i) q^{30} +(-0.480846 - 1.63761i) q^{31} +(5.62813 + 0.569308i) q^{32} +(9.10883 + 6.81879i) q^{33} +(1.25825 + 3.28887i) q^{34} +(-6.83485 + 0.909960i) q^{35} +(-0.0683401 - 4.06859i) q^{36} +(0.607786 + 2.79395i) q^{37} +(5.39830 - 8.55706i) q^{38} +(-0.550395 + 3.82808i) q^{39} +(5.89255 - 2.29737i) q^{40} +(-2.52268 + 1.62123i) q^{41} +(-9.69664 - 1.31115i) q^{42} +(3.22075 + 5.89837i) q^{43} +(-5.33916 + 8.62295i) q^{44} +(-2.13851 - 4.01552i) q^{45} +(2.57649 - 6.27389i) q^{46} +(3.53092 - 3.53092i) q^{47} +(8.92573 - 0.940577i) q^{48} +(-0.706762 + 2.40701i) q^{49} +(4.69694 - 5.28572i) q^{50} +(3.02053 + 4.70004i) q^{51} +(-3.44211 - 0.188141i) q^{52} +(5.67194 + 7.57683i) q^{53} +(0.676301 + 2.98788i) q^{54} +(-0.926993 + 11.3012i) q^{55} +(0.402860 - 8.71245i) q^{56} +(5.60977 - 15.0404i) q^{57} +(-0.294029 + 0.658410i) q^{58} +(-0.414003 - 2.87945i) q^{59} +(8.40694 - 5.47859i) q^{60} +(-7.47212 + 2.19401i) q^{61} +(2.01951 - 1.32195i) q^{62} +(-6.25786 + 0.447571i) q^{63} +(1.53589 + 7.85118i) q^{64} +(-3.52238 + 1.56437i) q^{65} +(-5.49656 + 15.1235i) q^{66} +(-1.73239 - 4.64472i) q^{67} +(-3.93595 + 3.05089i) q^{68} +(1.96744 - 10.5794i) q^{69} +(-4.03266 - 8.87829i) q^{70} +(3.05723 + 1.39619i) q^{71} +(5.47897 - 1.75985i) q^{72} +(-3.95313 - 0.282733i) q^{73} +(-3.53263 + 1.96765i) q^{74} +(5.58113 - 9.73219i) q^{75} +(13.7946 + 3.80000i) q^{76} +(13.7244 + 7.49407i) q^{77} +(-5.40699 + 0.823810i) q^{78} +(-1.76030 - 12.2432i) q^{79} +(5.52440 + 7.03427i) q^{80} +(4.55470 + 9.97341i) q^{81} +(-3.22821 - 2.75014i) q^{82} +(-3.00592 - 13.8180i) q^{83} +(-2.19910 - 13.6621i) q^{84} +(-2.36568 + 5.04016i) q^{85} +(-6.66375 + 6.77662i) q^{86} +(-0.243188 + 1.11792i) q^{87} +(-13.8595 - 3.69296i) q^{88} +(-5.21213 + 17.7509i) q^{89} +(4.55875 - 4.54015i) q^{90} +5.31498i q^{91} +(9.54780 + 0.916260i) q^{92} +(2.70792 - 2.70792i) q^{93} +(6.22622 + 3.33221i) q^{94} +(15.6663 - 3.23704i) q^{95} +(4.93096 + 11.6958i) q^{96} +(-16.4840 - 3.58588i) q^{97} +(-3.54761 + 0.0297925i) q^{98} +(-1.46833 + 10.2124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.409811	+	1.35353i	0.289780	+	0.957093i
$2$	0.409811	+	1.35353i	0.289780	+	0.957093i
$3$	1.07533	+	1.96932i	0.620844	+	1.13699i	0.979102	+	0.203368i	$0.0651887\pi$
$3$	1.07533	+	1.96932i	0.620844	+	1.13699i	−0.358259	+	0.933622i	$0.616629\pi$
$4$	−1.66411	+	1.10939i	−0.832055	+	0.554693i
$5$	−1.09207	+	1.95125i	−0.488388	+	0.872627i
$5$	−1.09207	+	1.95125i	−0.488388	+	0.872627i
$6$	−2.22487	+	2.26255i	−0.908298	+	0.923682i
$7$	1.84794	+	2.46855i	0.698454	+	0.933026i	0.999790	−	0.0204924i	$-0.00652338\pi$
$7$	1.84794	+	2.46855i	0.698454	+	0.933026i	−0.301336	+	0.953518i	$0.597432\pi$
$8$	−2.18356	−	1.79779i	−0.772006	−	0.635615i
$9$	−1.09998	+	1.71160i	−0.366659	+	0.570533i
$10$	−3.08863	−	0.678508i	−0.976710	−	0.214563i
$11$	4.61278	−	2.10659i	1.39081	−	0.635160i	0.427612	−	0.903963i	$-0.359355\pi$
$11$	4.61278	−	2.10659i	1.39081	−	0.635160i	0.963195	+	0.268802i	$0.0866279\pi$
$12$	−3.97421	−	2.08421i	−1.14726	−	0.601661i
$13$	1.37983	+	1.03293i	0.382696	+	0.286483i	0.773255	−	0.634095i	$-0.218627\pi$
$13$	1.37983	+	1.03293i	0.382696	+	0.286483i	−0.390559	+	0.920578i	$0.627718\pi$
$14$	−2.58397	+	3.51289i	−0.690595	+	0.938858i
$15$	−5.01699	−	0.0523926i	−1.29538	−	0.0135277i
$16$	1.53852	−	3.69228i	0.384631	−	0.923070i
$17$	2.48362	−	0.177632i	0.602366	−	0.0430821i	0.233174	−	0.972435i	$-0.425089\pi$
$17$	2.48362	−	0.177632i	0.602366	−	0.0430821i	0.369192	+	0.929353i	$0.379634\pi$
$18$	−2.76749	−	0.787425i	−0.652304	−	0.185598i
$19$	−4.68500	−	5.40678i	−1.07481	−	1.24040i	−0.969274	−	0.245985i	$-0.920889\pi$
$19$	−4.68500	−	5.40678i	−1.07481	−	1.24040i	−0.105539	−	0.994415i	$-0.533657\pi$
$20$	−0.347370	−	4.45862i	−0.0776743	−	0.996979i
$21$	−2.87424	+	6.29370i	−0.627210	+	1.37340i
$22$	4.74171	+	5.38026i	1.01094	+	1.14708i
$23$	−3.71803	−	3.02924i	−0.775262	−	0.631640i
$23$	−3.71803	−	3.02924i	−0.775262	−	0.631640i
$24$	1.19238	−	6.23337i	0.243393	−	1.27238i
$25$	−2.61477	−	4.26180i	−0.522954	−	0.852361i
$26$	−0.832635	+	2.29095i	−0.163293	+	0.449293i
$27$	2.16068	+	0.154535i	0.415822	+	0.0297402i
$28$	−5.81375	−	2.05787i	−1.09870	−	0.388901i
$29$	0.385342	+	0.333901i	0.0715562	+	0.0620038i	0.689905	−	0.723900i	$-0.257652\pi$
$29$	0.385342	+	0.333901i	0.0715562	+	0.0620038i	−0.618348	+	0.785904i	$0.712198\pi$
$30$	−1.98510	−	6.81213i	−0.362428	−	1.24372i
$31$	−0.480846	−	1.63761i	−0.0863624	−	0.294123i	0.904975	−	0.425465i	$-0.139890\pi$
$31$	−0.480846	−	1.63761i	−0.0863624	−	0.294123i	−0.991337	+	0.131342i	$0.958071\pi$
$32$	5.62813	+	0.569308i	0.994923	+	0.100640i
$33$	9.10883	+	6.81879i	1.58564	+	1.18700i
$34$	1.25825	+	3.28887i	0.215787	+	0.564036i
$35$	−6.83485	+	0.909960i	−1.15530	+	0.153811i
$36$	−0.0683401	−	4.06859i	−0.0113900	−	0.678098i
$37$	0.607786	+	2.79395i	0.0999194	+	0.459322i	0.999734	+	0.0230503i	$0.00733779\pi$
$37$	0.607786	+	2.79395i	0.0999194	+	0.459322i	−0.899815	+	0.436272i	$0.856299\pi$
$38$	5.39830	−	8.55706i	0.875719	−	1.38814i
$39$	−0.550395	+	3.82808i	−0.0881337	+	0.612983i
$40$	5.89255	−	2.29737i	0.931693	−	0.363246i
$41$	−2.52268	+	1.62123i	−0.393976	+	0.253193i	−0.722598	−	0.691268i	$-0.757052\pi$
$41$	−2.52268	+	1.62123i	−0.393976	+	0.253193i	0.328622	+	0.944462i	$0.393416\pi$
$42$	−9.69664	−	1.31115i	−1.49622	−	0.202315i
$43$	3.22075	+	5.89837i	0.491160	+	0.899493i	0.999270	+	0.0382009i	$0.0121627\pi$
$43$	3.22075	+	5.89837i	0.491160	+	0.899493i	−0.508110	+	0.861292i	$0.669656\pi$
$44$	−5.33916	+	8.62295i	−0.804909	+	1.29996i
$45$	−2.13851	−	4.01552i	−0.318790	−	0.598598i
$46$	2.57649	−	6.27389i	0.379883	−	0.925035i
$47$	3.53092	−	3.53092i	0.515037	−	0.515037i	−0.401028	−	0.916066i	$-0.631347\pi$
$47$	3.53092	−	3.53092i	0.515037	−	0.515037i	0.916066	+	0.401028i	$0.131347\pi$
$48$	8.92573	−	0.940577i	1.28832	−	0.135761i
$49$	−0.706762	+	2.40701i	−0.100966	+	0.343859i
$50$	4.69694	−	5.28572i	0.664247	−	0.747513i
$51$	3.02053	+	4.70004i	0.422959	+	0.658137i
$52$	−3.44211	−	0.188141i	−0.477335	−	0.0260905i
$53$	5.67194	+	7.57683i	0.779101	+	1.04076i	0.997886	+	0.0649841i	$0.0206997\pi$
$53$	5.67194	+	7.57683i	0.779101	+	1.04076i	−0.218785	+	0.975773i	$0.570209\pi$
$54$	0.676301	+	2.98788i	0.0920329	+	0.406599i
$55$	−0.926993	+	11.3012i	−0.124996	+	1.52386i
$56$	0.402860	−	8.71245i	0.0538345	−	1.16425i
$57$	5.60977	−	15.0404i	0.743032	−	1.99215i
$58$	−0.294029	+	0.658410i	−0.0386079	+	0.0864534i
$59$	−0.414003	−	2.87945i	−0.0538986	−	0.374873i	−0.998862	−	0.0476964i	$-0.984812\pi$
$59$	−0.414003	−	2.87945i	−0.0538986	−	0.374873i	0.944963	−	0.327176i	$-0.106097\pi$
$60$	8.40694	−	5.47859i	1.08533	−	0.707283i
$61$	−7.47212	+	2.19401i	−0.956707	+	0.280915i	−0.722577	−	0.691291i	$-0.757042\pi$
$61$	−7.47212	+	2.19401i	−0.956707	+	0.280915i	−0.234130	+	0.972205i	$0.575224\pi$
$62$	2.01951	−	1.32195i	0.256477	−	0.167888i
$63$	−6.25786	+	0.447571i	−0.788416	+	0.0563887i
$64$	1.53589	+	7.85118i	0.191987	+	0.981398i
$65$	−3.52238	+	1.56437i	−0.436897	+	0.194036i
$66$	−5.49656	+	15.1235i	−0.676580	+	1.86158i
$67$	−1.73239	−	4.64472i	−0.211645	−	0.567443i	0.787137	−	0.616778i	$-0.211563\pi$
$67$	−1.73239	−	4.64472i	−0.211645	−	0.567443i	−0.998782	+	0.0493350i	$0.984290\pi$
$68$	−3.93595	+	3.05089i	−0.477305	+	0.369975i
$69$	1.96744	−	10.5794i	0.236852	−	1.27361i
$70$	−4.03266	−	8.87829i	−0.481995	−	1.06116i
$71$	3.05723	+	1.39619i	0.362826	+	0.165697i	0.588483	−	0.808510i	$-0.299725\pi$
$71$	3.05723	+	1.39619i	0.362826	+	0.165697i	−0.225657	+	0.974207i	$0.572453\pi$
$72$	5.47897	−	1.75985i	0.645702	−	0.207401i
$73$	−3.95313	−	0.282733i	−0.462679	−	0.0330914i	−0.161945	−	0.986800i	$-0.551777\pi$
$73$	−3.95313	−	0.282733i	−0.462679	−	0.0330914i	−0.300733	+	0.953708i	$0.597231\pi$
$74$	−3.53263	+	1.96765i	−0.410660	+	0.228735i
$75$	5.58113	−	9.73219i	0.644453	−	1.12378i
$76$	13.7946	+	3.80000i	1.58234	+	0.435890i
$77$	13.7244	+	7.49407i	1.56404	+	0.854028i
$78$	−5.40699	+	0.823810i	−0.612221	+	0.0932782i
$79$	−1.76030	−	12.2432i	−0.198049	−	1.37746i	−0.809936	−	0.586518i	$-0.800498\pi$
$79$	−1.76030	−	12.2432i	−0.198049	−	1.37746i	0.611887	−	0.790945i	$-0.290411\pi$
$80$	5.52440	+	7.03427i	0.617647	+	0.786456i
$81$	4.55470	+	9.97341i	0.506078	+	1.10816i
$82$	−3.22821	−	2.75014i	−0.356496	−	0.303702i
$83$	−3.00592	−	13.8180i	−0.329942	−	1.51672i	−0.781174	−	0.624313i	$-0.785379\pi$
$83$	−3.00592	−	13.8180i	−0.329942	−	1.51672i	0.451232	−	0.892407i	$-0.350985\pi$
$84$	−2.19910	−	13.6621i	−0.239941	−	1.49065i
$85$	−2.36568	+	5.04016i	−0.256594	+	0.546682i
$86$	−6.66375	+	6.77662i	−0.718570	+	0.730742i
$87$	−0.243188	+	1.11792i	−0.0260725	+	0.119853i
$88$	−13.8595	−	3.69296i	−1.47743	−	0.393671i
$89$	−5.21213	+	17.7509i	−0.552484	+	1.88159i	−0.0877406	+	0.996143i	$0.527965\pi$
$89$	−5.21213	+	17.7509i	−0.552484	+	1.88159i	−0.464744	+	0.885445i	$0.653854\pi$
$90$	4.55875	−	4.54015i	0.480535	−	0.478574i
$91$			5.31498i			0.557161i
$92$	9.54780	+	0.916260i	0.995427	+	0.0955267i
$93$	2.70792	−	2.70792i	0.280798	−	0.280798i
$94$	6.22622	+	3.33221i	0.642186	+	0.343691i
$95$	15.6663	−	3.23704i	1.60733	−	0.332114i
$96$	4.93096	+	11.6958i	0.503264	+	1.19370i
$97$	−16.4840	−	3.58588i	−1.67370	−	0.364091i	−0.727106	−	0.686525i	$-0.759135\pi$
$97$	−16.4840	−	3.58588i	−1.67370	−	0.364091i	−0.946592	+	0.322434i	$0.895499\pi$
$98$	−3.54761	+	0.0297925i	−0.358363	+	0.00300950i
$99$	−1.46833	+	10.2124i	−0.147572	+	1.02639i
$100$	9.07925	+	4.19132i	0.907925	+	0.419132i
$101$	5.95402	+	3.82641i	0.592447	+	0.380742i	0.802238	−	0.597004i	$-0.203642\pi$
$101$	5.95402	+	3.82641i	0.592447	+	0.380742i	−0.209792	+	0.977746i	$0.567279\pi$
$102$	−5.12382	+	6.01452i	−0.507334	+	0.595527i
$103$	−6.53972	+	17.5337i	−0.644378	+	1.72764i	0.0406963	+	0.999172i	$0.487042\pi$
$103$	−6.53972	+	17.5337i	−0.644378	+	1.72764i	−0.685074	+	0.728473i	$0.740230\pi$
$104$	−1.15596	−	4.73611i	−0.113351	−	0.464414i
$105$	−9.14174	−	12.4815i	−0.892142	−	1.21807i
$106$	−7.93107	+	10.7822i	−0.770334	+	1.04726i
$107$	4.02093	−	7.36379i	0.388718	−	0.711884i	−0.607904	−	0.794011i	$-0.707989\pi$
$107$	4.02093	−	7.36379i	0.388718	−	0.711884i	0.996622	+	0.0821266i	$0.0261712\pi$
$108$	−3.76704	+	2.13986i	−0.362484	+	0.205908i
$109$	−2.31147	−	2.00290i	−0.221398	−	0.191843i	0.537098	−	0.843520i	$-0.319520\pi$
$109$	−2.31147	−	2.00290i	−0.221398	−	0.191843i	−0.758497	+	0.651677i	$0.774066\pi$
$110$	−15.6765	+	3.37666i	−1.49470	+	0.321952i
$111$	−4.84862	+	4.20135i	−0.460211	+	0.398775i
$112$	11.9577	−	3.02517i	1.12990	−	0.285852i
$113$	−0.909319	−	2.43798i	−0.0855415	−	0.229346i	0.887135	−	0.461510i	$-0.152692\pi$
$113$	−0.909319	−	2.43798i	−0.0855415	−	0.229346i	−0.972677	+	0.232164i	$0.925419\pi$
$114$	22.6566	+	1.42931i	2.12199	+	0.133867i
$115$	9.97115	−	3.94667i	0.929814	−	0.368029i
$116$	−1.01168	−	0.128154i	−0.0939318	−	0.0118988i
$117$	−3.28574	+	1.22552i	−0.303767	+	0.113299i
$118$	3.72777	−	1.74040i	0.343169	−	0.160217i
$119$	5.02807	+	5.80270i	0.460922	+	0.531932i
$120$	10.8607	+	9.13390i	0.991443	+	0.833807i
$121$	9.63660	−	11.1212i	0.876054	−	1.01102i
$122$	−6.03183	−	9.21464i	−0.546096	−	0.834255i
$123$	−5.90544	−	3.22462i	−0.532476	−	0.290754i
$124$	2.61692	+	2.19172i	0.235007	+	0.196822i
$125$	11.1714	−	0.447897i	0.999197	−	0.0400611i
$126$	−3.17034	−	8.28681i	−0.282437	−	0.738248i
$127$	−3.28449	−	1.22505i	−0.291451	−	0.108706i	0.199486	−	0.979901i	$-0.436073\pi$
$127$	−3.28449	−	1.22505i	−0.291451	−	0.108706i	−0.490937	+	0.871195i	$0.663346\pi$
$128$	−9.99742	+	5.29638i	−0.883655	+	0.468138i
$129$	−8.15243	+	12.6854i	−0.717781	+	1.11689i
$130$	−3.56094	−	4.12656i	−0.312315	−	0.361923i
$131$	17.0482	+	2.45116i	1.48951	+	0.214159i	0.838496	−	0.544908i	$-0.183436\pi$
$131$	17.0482	+	2.45116i	1.48951	+	0.214159i	0.651012	+	0.759067i	$0.274345\pi$
$132$	−22.7228	−	1.24200i	−1.97776	−	0.108102i
$133$	4.68934	−	21.5566i	0.406618	−	1.86919i
$134$	5.57684	−	4.24831i	0.481766	−	0.366998i
$135$	−2.66114	+	4.04726i	−0.229035	+	0.348333i
$136$	−5.74249	−	4.07716i	−0.492414	−	0.349614i
$137$	−4.81807	−	4.81807i	−0.411635	−	0.411635i	0.470673	−	0.882308i	$-0.344011\pi$
$137$	−4.81807	−	4.81807i	−0.411635	−	0.411635i	−0.882308	+	0.470673i	$0.844011\pi$
$138$	15.1259	−	1.67257i	1.28760	−	0.142379i
$139$	−14.0067			−1.18803			−0.594014	−	0.804454i	$-0.702458\pi$
$139$	−14.0067			−1.18803			−0.594014	+	0.804454i	$0.702458\pi$
$140$	10.3644	−	9.09676i	0.875955	−	0.768816i
$141$	10.7504	+	3.15661i	0.905350	+	0.265835i
$142$	−0.636905	+	4.71024i	−0.0534478	+	0.395274i
$143$	8.54082	+	1.85794i	0.714219	+	0.155369i
$144$	4.62736	+	6.69476i	0.385613	+	0.557897i
$145$	−1.07234	+	0.387257i	−0.0890534	+	0.0321599i
$146$	−1.23735	−	5.46656i	−0.102403	−	0.452416i
$147$	−5.50019	+	1.19649i	−0.453648	+	0.0986851i
$148$	−4.11099	−	3.97517i	−0.337921	−	0.326757i
$149$	8.81210	−	4.02435i	0.721915	−	0.329688i	−0.0203508	−	0.999793i	$-0.506478\pi$
$149$	8.81210	−	4.02435i	0.721915	−	0.329688i	0.742266	+	0.670105i	$0.233751\pi$
$150$	15.4601	+	3.56589i	1.26231	+	0.291153i
$151$	9.12979	−	1.31267i	0.742972	−	0.106823i	0.239574	−	0.970878i	$-0.422992\pi$
$151$	9.12979	−	1.31267i	0.742972	−	0.106823i	0.503398	+	0.864055i	$0.332083\pi$
$152$	0.509732	+	20.2287i	0.0413447	+	1.64076i
$153$	−2.42789	+	4.44635i	−0.196283	+	0.359466i
$154$	−4.51908	+	21.6475i	−0.364158	+	1.74441i
$155$	3.72051	+	0.850132i	0.298838	+	0.0682842i
$156$	−3.33090	−	6.98094i	−0.266685	−	0.558923i
$157$	0.681453	−	9.52796i	0.0543859	−	0.760414i	−0.894953	−	0.446160i	$-0.852791\pi$
$157$	0.681453	−	9.52796i	0.0543859	−	0.760414i	0.949339	−	0.314254i	$-0.101754\pi$
$158$	15.8502	−	7.40001i	1.26097	−	0.588713i
$159$	−8.82201	+	19.3175i	−0.699631	+	1.53198i
$160$	−7.25717	+	10.3602i	−0.573730	+	0.819045i
$161$	0.607164	−	14.7760i	0.0478512	−	1.16451i
$162$	−11.6328	+	10.2522i	−0.913958	+	0.805486i
$163$	9.53532	−	3.55649i	0.746864	−	0.278566i	0.0529237	−	0.998599i	$-0.483146\pi$
$163$	9.53532	−	3.55649i	0.746864	−	0.278566i	0.693940	+	0.720033i	$0.255873\pi$
$164$	2.39945	−	5.49653i	0.187365	−	0.429207i
$165$	−23.2526	+	10.3270i	−1.81022	+	0.803960i
$166$	17.4713	−	9.73137i	1.35603	−	0.755301i
$167$	0.863053	+	12.0671i	0.0667850	+	0.933777i	0.914827	+	0.403847i	$0.132327\pi$
$167$	0.863053	+	12.0671i	0.0667850	+	0.933777i	−0.848041	+	0.529930i	$0.822218\pi$
$168$	17.5908	−	8.57542i	1.35716	−	0.661608i
$169$	−2.82553	−	9.62287i	−0.217348	−	0.740221i
$170$	−7.79150	−	1.13652i	−0.597581	−	0.0871669i
$171$	14.4076	−	2.07150i	1.10178	−	0.158412i
$172$	−11.9033	−	6.24248i	−0.907615	−	0.475985i
$173$	10.0982	+	3.76643i	0.767752	+	0.286357i	0.702663	−	0.711523i	$-0.251994\pi$
$173$	10.0982	+	3.76643i	0.767752	+	0.286357i	0.0650888	+	0.997879i	$0.479267\pi$
$174$	−1.61280	+	0.128971i	−0.122266	+	0.00977730i
$175$	5.68856	−	14.3302i	0.430015	−	1.08326i
$176$	−0.681235	−	20.2727i	−0.0513500	−	1.52811i
$177$	5.22539	−	3.91167i	0.392764	−	0.294019i
$178$	−26.1624	+	0.219709i	−1.96095	+	0.0164679i
$179$	21.0891	−	13.5531i	1.57627	−	1.01301i	0.599071	−	0.800696i	$-0.295537\pi$
$179$	21.0891	−	13.5531i	1.57627	−	1.01301i	0.977202	−	0.212313i	$-0.0680998\pi$
$180$	8.01347	+	4.30983i	0.597289	+	0.321236i
$181$	−16.9375	−	4.97329i	−1.25895	−	0.369661i	−0.416847	−	0.908977i	$-0.636865\pi$
$181$	−16.9375	−	4.97329i	−1.25895	−	0.369661i	−0.842104	+	0.539315i	$0.818683\pi$
$182$	−7.19400	+	2.17814i	−0.533255	+	0.161454i
$183$	−12.3557	−	12.3557i	−0.913363	−	0.913363i
$184$	2.67260	+	13.2988i	0.197027	+	0.980398i
$185$	−6.11544	−	1.86524i	−0.449616	−	0.137135i
$186$	4.77499	+	2.55552i	0.350119	+	0.187380i
$187$	11.0822	−	6.05134i	0.810411	−	0.442518i
$188$	−1.95868	+	9.79298i	−0.142852	+	0.714227i
$189$	3.61131	+	5.61932i	0.262685	+	0.408745i
$190$	10.8017	+	19.8783i	0.783636	+	1.44213i
$191$	−17.8959	−	2.57304i	−1.29490	−	0.186179i	−0.539804	−	0.841791i	$-0.681501\pi$
$191$	−17.8959	−	2.57304i	−1.29490	−	0.186179i	−0.755098	+	0.655612i	$0.772411\pi$
$192$	−13.8099	+	11.4673i	−0.996646	+	0.827581i
$193$	5.73361	−	1.24727i	0.412715	−	0.0897806i	−0.00141388	−	0.999999i	$-0.500450\pi$
$193$	5.73361	−	1.24727i	0.412715	−	0.0897806i	0.414128	+	0.910218i	$0.364086\pi$
$194$	−1.90172	−	23.7812i	−0.136536	−	1.70739i
$195$	−6.86848	−	5.25448i	−0.491862	−	0.376281i
$196$	−1.49418	−	4.78960i	−0.106727	−	0.342115i
$197$	−4.74178	+	6.33428i	−0.337838	+	0.451299i	−0.937000	−	0.349329i	$-0.886410\pi$
$197$	−4.74178	+	6.33428i	−0.337838	+	0.451299i	0.599162	+	0.800628i	$0.295501\pi$
$198$	−14.4246	+	2.19774i	−1.02511	+	0.156186i
$199$	−17.6935	+	5.19529i	−1.25426	+	0.368284i	−0.840356	−	0.542035i	$-0.817654\pi$
$199$	−17.6935	+	5.19529i	−1.25426	+	0.368284i	−0.413906	+	0.910320i	$0.635836\pi$
$200$	−1.95232	+	14.0067i	−0.138050	+	0.990425i
$201$	7.28407	−	8.40627i	0.513779	−	0.592932i
$202$	−2.73916	+	9.62707i	−0.192727	+	0.677358i
$203$	−0.112165	+	1.56826i	−0.00787240	+	0.110071i
$204$	−10.2407	−	4.47045i	−0.716990	−	0.312994i
$205$	−0.408485	−	6.69288i	−0.0285298	−	0.467451i
$206$	−26.4125	−	1.66625i	−1.84024	−	0.116093i
$207$	9.27458	−	3.03167i	0.644628	−	0.210716i
$208$	5.93677	−	3.50554i	0.411641	−	0.243065i
$209$	−33.0007	−	15.0709i	−2.28271	−	1.04248i
$210$	13.1478	−	17.4887i	0.907283	−	1.20684i
$211$	−0.776715	+	0.673028i	−0.0534713	+	0.0463331i	−0.681186	−	0.732110i	$-0.738536\pi$
$211$	−0.776715	+	0.673028i	−0.0534713	+	0.0463331i	0.627715	+	0.778443i	$0.283990\pi$
$212$	−17.8444	−	6.31630i	−1.22556	−	0.433805i
$213$	0.537987	+	7.52204i	0.0368623	+	0.515402i
$214$	11.6150	+	2.42471i	0.793982	+	0.165750i
$215$	−15.0265	−	0.156922i	−1.02480	−	0.0107020i
$216$	−4.44015	−	4.22188i	−0.302114	−	0.287263i
$217$	3.15396	−	4.21319i	0.214105	−	0.286010i
$218$	1.76373	−	3.94946i	0.119455	−	0.267491i
$219$	−3.69413	−	8.08903i	−0.249626	−	0.546606i
$220$	−10.9948	−	19.8349i	−0.741271	−	1.33727i
$221$	3.61046	+	2.32030i	0.242866	+	0.156080i
$222$	−7.67369	−	4.84101i	−0.515024	−	0.324907i
$223$	−3.77263	+	2.82415i	−0.252634	+	0.189119i	−0.718087	−	0.695953i	$-0.754982\pi$
$223$	−3.77263	+	2.82415i	−0.252634	+	0.189119i	0.465454	+	0.885072i	$0.345891\pi$
$224$	8.99507	+	14.9454i	0.601008	+	0.998581i
$225$	10.1707	+	0.212449i	0.678046	+	0.0141633i
$226$	2.92724	−	2.22990i	0.194717	−	0.148331i
$227$	1.08387	−	0.591838i	0.0719390	−	0.0392817i	−0.442877	−	0.896582i	$-0.646042\pi$
$227$	1.08387	−	0.591838i	0.0719390	−	0.0392817i	0.514816	+	0.857301i	$0.327860\pi$
$228$	7.35031	+	31.2522i	0.486786	+	2.06973i
$229$			3.68529i			0.243531i	0.992559	+	0.121765i	$0.0388555\pi$
$229$			3.68529i			0.243531i	−0.992559	+	0.121765i	$0.961144\pi$
$230$	9.42824	+	11.8789i	0.621680	+	0.783272i
$231$			35.0863i			2.30851i
$232$	−0.241134	−	1.42186i	−0.0158313	−	0.0933495i
$233$	−20.2841	+	11.0760i	−1.32886	+	0.725612i	−0.977561	−	0.210652i	$-0.932441\pi$
$233$	−20.2841	+	11.0760i	−1.32886	+	0.725612i	−0.351297	+	0.936264i	$0.614259\pi$
$234$	−3.00531	−	3.94513i	−0.196464	−	0.257902i
$235$	3.03371	+	10.7457i	0.197897	+	0.700973i
$236$	3.88337	+	4.33244i	0.252786	+	0.282018i
$237$	22.2179	−	16.6321i	1.44321	−	1.08037i
$238$	−5.79359	+	9.18367i	−0.375543	+	0.595289i
$239$	15.1847	+	9.75860i	0.982215	+	0.631231i	0.930060	−	0.367408i	$-0.119755\pi$
$239$	15.1847	+	9.75860i	0.982215	+	0.631231i	0.0521550	+	0.998639i	$0.483391\pi$
$240$	−7.91221	+	18.4435i	−0.510731	+	1.19052i
$241$	11.6379	+	25.4834i	0.749661	+	1.64153i	0.766974	+	0.641678i	$0.221762\pi$
$241$	11.6379	+	25.4834i	0.749661	+	1.64153i	−0.0173130	+	0.999850i	$0.505511\pi$
$242$	19.0021	+	8.48587i	1.22150	+	0.545492i
$243$	−10.8486	+	14.4920i	−0.695938	+	0.929665i
$244$	10.0004	−	11.9406i	0.640212	−	0.764415i
$245$	−3.92485	−	4.00769i	−0.250750	−	0.256042i
$246$	1.94451	−	9.31470i	0.123978	−	0.593884i
$247$	−0.879693	−	12.2997i	−0.0559735	−	0.782612i
$248$	−1.89412	+	4.44028i	−0.120277	+	0.281958i
$249$	23.9797	−	20.7786i	1.51965	−	1.31679i
$250$	5.18439	+	14.9373i	0.327890	+	0.944716i
$251$	−25.0627	−	11.4458i	−1.58195	−	0.722450i	−0.585824	−	0.810438i	$-0.699229\pi$
$251$	−25.0627	−	11.4458i	−1.58195	−	0.722450i	−0.996122	+	0.0879881i	$0.971956\pi$
$252$	9.91724	−	7.68719i	0.624727	−	0.484248i
$253$	−23.5318	−	6.14088i	−1.47943	−	0.386074i
$254$	0.312129	−	4.94770i	0.0195847	−	0.310447i
$255$	−12.4696	+	0.761054i	−0.780876	+	0.0476591i
$256$	−11.2659	−	11.3613i	−0.704118	−	0.710083i
$257$	1.88206	−	26.3146i	0.117400	−	1.64146i	−0.508143	−	0.861272i	$-0.669668\pi$
$257$	1.88206	−	26.3146i	0.117400	−	1.64146i	0.625543	−	0.780190i	$-0.284877\pi$
$258$	−20.5111	−	5.83596i	−1.27697	−	0.363331i
$259$	−5.77386	+	6.66339i	−0.358770	+	0.414043i
$260$	4.12613	−	6.51096i	0.255892	−	0.403793i
$261$	−0.995371	+	0.292267i	−0.0616119	+	0.0180909i
$262$	3.66881	+	24.0798i	0.226660	+	1.48766i
$263$	12.0605	−	16.1109i	0.743679	−	0.993439i	−0.255963	−	0.966687i	$-0.582392\pi$
$263$	12.0605	−	16.1109i	0.743679	−	0.993439i	0.999642	−	0.0267528i	$-0.00851669\pi$
$264$	−7.63095	−	31.2650i	−0.469653	−	1.92423i
$265$	−20.9784	+	2.79297i	−1.28870	+	0.171571i
$266$	31.0993	−	2.48693i	1.90682	−	0.152483i
$267$	−40.5620	+	8.82372i	−2.48235	+	0.540003i
$268$	8.03568	+	5.80744i	0.490858	+	0.354746i
$269$	25.0663	+	3.60398i	1.52832	+	0.219739i	0.854614	−	0.519263i	$-0.173794\pi$
$269$	25.0663	+	3.60398i	1.52832	+	0.219739i	0.673703	+	0.739002i	$0.264703\pi$
$270$	−6.56867	−	1.94334i	−0.399757	−	0.118268i
$271$	−0.251823	−	0.391845i	−0.0152972	−	0.0238029i	0.833521	−	0.552488i	$-0.186322\pi$
$271$	−0.251823	−	0.391845i	−0.0152972	−	0.0238029i	−0.848818	+	0.528685i	$0.822685\pi$
$272$	3.16524	−	9.44352i	0.191921	−	0.572597i
$273$	−10.4669	+	5.71537i	−0.633486	+	0.345910i
$274$	4.54692	−	8.49591i	0.274690	−	0.513257i
$275$	−21.0392	−	14.1505i	−1.26871	−	0.853309i
$276$	8.46265	+	19.7880i	0.509392	+	1.19110i
$277$	−4.26655	−	4.26655i	−0.256352	−	0.256352i	0.567216	−	0.823569i	$-0.308020\pi$
$277$	−4.26655	−	4.26655i	−0.256352	−	0.256352i	−0.823569	+	0.567216i	$0.808020\pi$
$278$	−5.74008	−	18.9585i	−0.344267	−	1.13705i
$279$	3.33185	+	0.978319i	0.199473	+	0.0585705i
$280$	16.5602	+	10.3007i	0.989663	+	0.615583i
$281$	3.98054	−	2.55814i	0.237459	−	0.152606i	−0.416500	−	0.909136i	$-0.636743\pi$
$281$	3.98054	−	2.55814i	0.237459	−	0.152606i	0.653959	+	0.756530i	$0.273107\pi$
$282$	0.133062	+	15.8447i	0.00792374	+	0.943538i
$283$	2.57815	−	1.92998i	0.153255	−	0.114725i	−0.519899	−	0.854228i	$-0.674030\pi$
$283$	2.57815	−	1.92998i	0.153255	−	0.114725i	0.673153	+	0.739503i	$0.264939\pi$
$284$	−6.63648	+	1.06823i	−0.393802	+	0.0633880i
$285$	23.2213	+	27.3712i	1.37551	+	1.62133i
$286$	0.985334	+	12.3217i	0.0582640	+	0.728597i
$287$	−8.66384	−	3.23144i	−0.511410	−	0.190746i
$288$	−7.16525	+	9.00688i	−0.422216	+	0.530735i
$289$	−10.6901	+	1.53701i	−0.628832	+	0.0904124i
$290$	−0.963624	−	1.29275i	−0.0565859	−	0.0759131i
$291$	−10.6640	−	36.3184i	−0.625137	−	2.12902i
$292$	6.89210	−	3.91505i	0.403330	−	0.229111i
$293$	−1.68217	−	23.5198i	−0.0982735	−	1.37404i	−0.772263	−	0.635303i	$-0.780875\pi$
$293$	−1.68217	−	23.5198i	−0.0982735	−	1.37404i	0.673990	−	0.738741i	$-0.264579\pi$
$294$	−3.87353	−	6.95436i	−0.225909	−	0.405587i
$295$	6.07066	+	2.33674i	0.353447	+	0.136050i
$296$	3.69580	−	7.19343i	0.214814	−	0.418110i
$297$	10.2923	−	3.83882i	0.597218	−	0.222751i
$298$	9.05839	+	10.2783i	0.524738	+	0.595403i
$299$	−2.00126	−	8.02029i	−0.115736	−	0.463826i
$300$	1.50915	+	22.3871i	0.0871309	+	1.29252i
$301$	−8.60870	+	18.8504i	−0.496197	+	1.08652i
$302$	5.51823	+	11.8195i	0.317538	+	0.680138i
$303$	−1.13290	+	15.8401i	−0.0650836	+	0.909988i
$304$	−27.1713	+	8.97988i	−1.55838	+	0.515031i
$305$	3.87900	−	16.9760i	0.222111	−	0.972044i
$306$	−7.01327	−	1.46407i	−0.400922	−	0.0836954i
$307$	−1.54834	+	2.83557i	−0.0883684	+	0.161835i	−0.918125	−	0.396291i	$-0.870297\pi$
$307$	−1.54834	+	2.83557i	−0.0883684	+	0.161835i	0.829757	+	0.558125i	$0.188479\pi$
$308$	−31.1527	+	2.75466i	−1.77509	+	0.156961i
$309$	−41.5619	+	5.97570i	−2.36437	+	0.339946i
$310$	0.374022	+	5.38423i	0.0212430	+	0.305804i
$311$	−7.66400	+	3.50003i	−0.434585	+	0.198469i	−0.620681	−	0.784063i	$-0.713144\pi$
$311$	−7.66400	+	3.50003i	−0.434585	+	0.198469i	0.186096	+	0.982532i	$0.440417\pi$
$312$	8.08391	−	7.36936i	0.457661	−	0.417208i
$313$	21.9564	−	4.77633i	1.24105	−	0.269974i	0.456323	−	0.889814i	$-0.349166\pi$
$313$	21.9564	−	4.77633i	1.24105	−	0.269974i	0.784728	+	0.619840i	$0.212802\pi$
$314$	13.1757	−	2.98229i	0.743547	−	0.168300i
$315$	5.96069	−	12.6994i	0.335847	−	0.715533i
$316$	16.5117	+	18.4211i	0.928858	+	1.03627i
$317$	10.9085	+	2.37299i	0.612680	+	0.133280i	0.508189	−	0.861245i	$-0.330315\pi$
$317$	10.9085	+	2.37299i	0.612680	+	0.133280i	0.104491	+	0.994526i	$0.466679\pi$
$318$	−29.7623	−	4.02437i	−1.66898	−	0.225675i
$319$	2.48089	+	0.728455i	0.138903	+	0.0407857i
$320$	−16.9969	−	5.57712i	−0.950158	−	0.311770i
$321$	18.8255			1.05074
$322$	20.2486	−	5.23354i	1.12841	−	0.291654i
$323$	−12.5962	−	12.5962i	−0.700870	−	0.700870i
$324$	−18.6439	−	11.5439i	−1.03577	−	0.641329i
$325$	0.794196	−	8.58144i	0.0440541	−	0.476013i
$326$	8.72151	+	11.4489i	0.483040	+	0.634095i
$327$	1.45876	−	6.70581i	0.0806696	−	0.370832i
$328$	8.42306	+	0.995199i	0.465086	+	0.0549507i
$329$	15.2412	+	2.19135i	0.840273	+	0.120813i
$330$	−23.5072	−	27.2411i	−1.29403	−	1.49957i
$331$	9.74822	−	15.1685i	0.535811	−	0.833738i	−0.462798	−	0.886464i	$-0.653155\pi$
$331$	9.74822	−	15.1685i	0.535811	−	0.833738i	0.998609	+	0.0527260i	$0.0167910\pi$
$332$	20.3317	+	19.6599i	1.11584	+	1.07898i
$333$	−5.45067	−	2.03299i	−0.298695	−	0.111407i
$334$	−15.9795	+	6.11338i	−0.874359	+	0.334509i
$335$	10.9549	+	1.69202i	0.598531	+	0.0924451i
$336$	18.8160	+	20.2955i	1.02650	+	1.10721i
$337$	−20.2475	−	11.0559i	−1.10295	−	0.602256i	−0.178645	−	0.983914i	$-0.557171\pi$
$337$	−20.2475	−	11.0559i	−1.10295	−	0.602256i	−0.924304	+	0.381658i	$0.875353\pi$
$338$	11.8670	−	7.76801i	0.645477	−	0.422524i
$339$	3.82335	−	4.41238i	0.207656	−	0.239648i
$340$	−1.65473	−	11.0118i	−0.0897403	−	0.597200i
$341$	−5.66781	−	6.54100i	−0.306929	−	0.354215i
$342$	8.70825	+	18.6523i	0.470888	+	1.00860i
$343$	12.9764	−	4.83995i	0.700660	−	0.261333i
$344$	3.57132	−	18.6697i	0.192553	−	1.00660i
$345$	18.4946	+	15.3924i	0.995715	+	0.828701i
$346$	−0.959644	+	15.2118i	−0.0515908	+	0.817790i
$347$	7.14869	+	19.1664i	0.383762	+	1.02891i	0.974960	+	0.222379i	$0.0713824\pi$
$347$	7.14869	+	19.1664i	0.383762	+	1.02891i	−0.591198	+	0.806526i	$0.701345\pi$
$348$	−0.835511	−	2.13013i	−0.0447881	−	0.114187i
$349$	−5.93731	+	5.14471i	−0.317817	+	0.275390i	−0.799129	−	0.601159i	$-0.794706\pi$
$349$	−5.93731	+	5.14471i	−0.317817	+	0.275390i	0.481312	+	0.876549i	$0.340160\pi$
$350$	21.7277	+	1.82697i	1.16140	+	0.0976557i
$351$	2.82175	+	2.44506i	0.150614	+	0.130507i
$352$	27.1607	−	9.23006i	1.44767	−	0.491964i
$353$	2.16026	−	3.95623i	0.114979	−	0.210569i	−0.813852	−	0.581073i	$-0.802633\pi$
$353$	2.16026	−	3.95623i	0.114979	−	0.210569i	0.928831	+	0.370504i	$0.120815\pi$
$354$	7.43601	+	5.46969i	0.395219	+	0.290711i
$355$	−6.06302	+	4.44069i	−0.321792	+	0.235687i
$356$	−11.0190	−	35.3217i	−0.584007	−	1.87204i
$357$	−6.02055	+	16.1417i	−0.318641	+	0.854311i
$358$	26.9872	+	22.9906i	1.42632	+	1.21509i
$359$	1.22504	+	0.787283i	0.0646549	+	0.0415512i	0.572569	−	0.819857i	$-0.305947\pi$
$359$	1.22504	+	0.787283i	0.0646549	+	0.0415512i	−0.507914	+	0.861408i	$0.669583\pi$
$360$	−2.54949	+	12.6127i	−0.134370	+	0.664749i
$361$	−4.58004	+	31.8549i	−0.241055	+	1.67657i
$362$	−0.209642	−	24.9635i	−0.0110185	−	1.31205i
$363$	32.2639	+	7.01857i	1.69341	+	0.368380i
$364$	−5.89636	−	8.84470i	−0.309053	−	0.463588i
$365$	4.86877	−	7.40479i	0.254843	−	0.387584i
$366$	11.6604	−	21.7874i	0.609499	−	1.13885i
$367$	−9.85288	+	9.85288i	−0.514316	+	0.514316i	−0.915846	−	0.401530i	$-0.868479\pi$
$367$	−9.85288	+	9.85288i	−0.514316	+	0.514316i	0.401530	+	0.915846i	$0.368479\pi$
$368$	−16.9051	+	9.06744i	−0.881238	+	0.472673i
$369$		−	6.10113i		−	0.317612i
$370$	0.0184902	−	9.04186i	0.000961262	−	0.470064i
$371$	−8.22242	+	28.0030i	−0.426887	+	1.45384i
$372$	−1.50215	+	7.51040i	−0.0778826	+	0.389396i
$373$	−7.60611	+	34.9647i	−0.393829	+	1.81040i	0.171088	+	0.985256i	$0.445272\pi$
$373$	−7.60611	+	34.9647i	−0.393829	+	1.81040i	−0.564917	+	0.825148i	$0.691092\pi$
$374$	12.7323	+	12.5202i	0.658372	+	0.647406i
$375$	12.8950	+	21.5184i	0.665894	+	1.11121i
$376$	−14.0578	+	1.36213i	−0.724977	+	0.0702463i
$377$	0.186811	+	0.858758i	0.00962127	+	0.0442283i
$378$	−6.12598	+	7.19090i	−0.315086	+	0.369860i
$379$	7.55313	+	16.5390i	0.387978	+	0.849553i	0.998349	+	0.0574378i	$0.0182931\pi$
$379$	7.55313	+	16.5390i	0.387978	+	0.849553i	−0.610371	+	0.792116i	$0.708980\pi$
$380$	−22.4794	+	22.7668i	−1.15317	+	1.16791i
$381$	−1.11939	−	7.78556i	−0.0573483	−	0.398866i
$382$	−3.85123	−	25.2772i	−0.197046	−	1.29329i
$383$	−2.75570	−	1.50473i	−0.140810	−	0.0768880i	0.407300	−	0.913295i	$-0.366470\pi$
$383$	−2.75570	−	1.50473i	−0.140810	−	0.0768880i	−0.548109	+	0.836407i	$0.684652\pi$
$384$	−21.1808	−	13.9928i	−1.08088	−	0.714066i
$385$	−29.6108	+	18.5957i	−1.50910	+	0.947722i
$386$	4.03792	+	7.24950i	0.205525	+	0.368990i
$387$	−13.6384	−	0.975438i	−0.693279	−	0.0495843i
$388$	31.4093	−	12.3198i	1.59457	−	0.625445i
$389$	−3.10463	−	1.41784i	−0.157411	−	0.0718873i	0.335151	−	0.942164i	$-0.391213\pi$
$389$	−3.10463	−	1.41784i	−0.157411	−	0.0718873i	−0.492563	+	0.870277i	$0.663940\pi$
$390$	4.29735	−	11.4501i	0.217605	−	0.579797i
$391$	−9.77225	−	6.86304i	−0.494204	−	0.347079i
$392$	5.87056	−	3.98525i	0.296508	−	0.201286i
$393$	13.5054	+	36.2093i	0.681255	+	1.82652i
$394$	−10.5169	−	3.82231i	−0.529834	−	0.192565i
$395$	25.8119	+	9.93559i	1.29874	+	0.499914i
$396$	−8.88608	−	18.6236i	−0.446542	−	0.935869i
$397$	29.7954	−	2.13101i	1.49539	−	0.106952i	0.700476	−	0.713676i	$-0.252971\pi$
$397$	29.7954	−	2.13101i	1.49539	−	0.106952i	0.794913	+	0.606723i	$0.207516\pi$
$398$	−14.2830	−	21.8197i	−0.715943	−	1.09372i
$399$	47.4945	−	13.9456i	2.37770	−	0.698155i
$400$	−19.7587	+	3.09758i	−0.987933	+	0.154879i
$401$	2.74836	+	19.1153i	0.137247	+	0.954572i	0.935771	+	0.352609i	$0.114705\pi$
$401$	2.74836	+	19.1153i	0.137247	+	0.954572i	−0.798524	+	0.601963i	$0.794386\pi$
$402$	14.3633	+	6.41426i	0.716374	+	0.319914i
$403$	1.02805	−	2.75631i	0.0512108	−	0.137301i
$404$	−14.1531	+	0.237730i	−0.704143	+	0.0118275i
$405$	−24.4347	−	2.00427i	−1.21417	−	0.0995931i
$406$	−2.16867	+	0.490873i	−0.107629	+	0.0243616i
$407$	8.68928	+	11.6075i	0.430712	+	0.575364i
$408$	1.85417	−	15.6931i	0.0917951	−	0.776925i
$409$	−4.96809	−	7.73050i	−0.245656	−	0.382249i	0.696427	−	0.717628i	$-0.254772\pi$
$409$	−4.96809	−	7.73050i	−0.245656	−	0.382249i	−0.942083	+	0.335379i	$0.891136\pi$
$410$	8.89164	−	3.29571i	0.439127	−	0.162764i
$411$	4.30731	−	14.6694i	0.212464	−	0.723586i
$412$	−8.56880	−	36.4330i	−0.422155	−	1.79493i
$413$	6.34303	−	6.34303i	0.312120	−	0.312120i
$414$	7.90430	+	11.3111i	0.388475	+	0.555908i
$415$	30.2450	+	9.22488i	1.48467	+	0.452832i
$416$	7.17782	+	6.59901i	0.351922	+	0.323543i
$417$	−15.0618	−	27.5836i	−0.737580	−	1.35078i
$418$	6.87496	−	50.8439i	0.336265	−	2.48686i
$419$	23.9786	−	15.4101i	1.17143	−	0.752834i	0.197641	−	0.980275i	$-0.436672\pi$
$419$	23.9786	−	15.4101i	1.17143	−	0.752834i	0.973792	+	0.227440i	$0.0730357\pi$
$420$	29.0597	+	10.6289i	1.41797	+	0.518638i
$421$	0.441564	−	3.07114i	0.0215205	−	0.149678i	−0.976228	−	0.216747i	$-0.930455\pi$
$421$	0.441564	−	3.07114i	0.0215205	−	0.149678i	0.997748	+	0.0670683i	$0.0213645\pi$
$422$	−1.22927	−	0.775497i	−0.0598401	−	0.0377506i
$423$	2.15958	+	9.92744i	0.105002	+	0.482689i
$424$	1.23651	−	26.7414i	0.0600504	−	1.29868i
$425$	−7.25113	−	10.1202i	−0.351732	−	0.490903i
$426$	−9.96087	+	3.81080i	−0.482606	+	0.184634i
$427$	−19.2240	−	14.3909i	−0.930317	−	0.696427i
$428$	1.47801	+	16.7149i	0.0714423	+	0.807946i
$429$	5.52533	+	18.8176i	0.266766	+	0.908520i
$430$	−5.94562	−	20.4032i	−0.286723	−	0.983929i
$431$	−12.6646	−	10.9739i	−0.610032	−	0.528596i	0.294141	−	0.955762i	$-0.404966\pi$
$431$	−12.6646	−	10.9739i	−0.610032	−	0.528596i	−0.904173	+	0.427166i	$0.859512\pi$
$432$	3.89484	−	7.74007i	0.187390	−	0.372394i
$433$	31.4220	+	2.24735i	1.51005	+	0.108001i	0.801641	−	0.597806i	$-0.203961\pi$
$433$	31.4220	+	2.24735i	1.51005	+	0.108001i	0.708404	+	0.705807i	$0.249415\pi$
$434$	6.99523	+	2.54238i	0.335782	+	0.122038i
$435$	−1.91576	−	1.69536i	−0.0918537	−	0.0812865i
$436$	6.06852	+	0.768733i	0.290630	+	0.0368156i
$437$	1.04053	+	34.2945i	0.0497753	+	1.64053i
$438$	9.43488	−	8.31511i	0.450816	−	0.397311i
$439$	−10.9357	+	23.9458i	−0.521932	+	1.14287i	0.446771	+	0.894648i	$0.352574\pi$
$439$	−10.9357	+	23.9458i	−0.521932	+	1.14287i	−0.968703	+	0.248223i	$0.920153\pi$
$440$	22.3414	−	23.0104i	1.06509	−	1.09698i
$441$	−3.34241	−	3.85735i	−0.159163	−	0.183683i
$442$	−1.66100	+	5.83776i	−0.0790058	+	0.277674i
$443$	23.1979	−	1.65914i	1.10216	−	0.0788283i	0.491620	−	0.870810i	$-0.336405\pi$
$443$	23.1979	−	1.65914i	1.10216	−	0.0788283i	0.610545	+	0.791982i	$0.290951\pi$
$444$	3.40771	−	12.3705i	0.161723	−	0.587078i
$445$	−28.9444	−	29.5553i	−1.37210	−	1.40106i
$446$	−5.36865	−	3.94901i	−0.254213	−	0.186991i
$447$	17.4012	+	13.0264i	0.823048	+	0.616126i
$448$	−16.5428	+	18.2999i	−0.781575	+	0.864590i
$449$	1.00347	−	0.458269i	0.0473567	−	0.0216271i	−0.391596	−	0.920137i	$-0.628077\pi$
$449$	1.00347	−	0.458269i	0.0473567	−	0.0216271i	0.438953	+	0.898510i	$0.355350\pi$
$450$	3.88050	+	13.8534i	0.182929	+	0.653057i
$451$	−8.22132	+	12.7926i	−0.387127	+	0.602381i
$452$	4.21786	+	3.04828i	0.198392	+	0.143379i
$453$	12.4026	+	16.5680i	0.582726	+	0.778431i
$454$	1.24525	+	1.22451i	0.0584427	+	0.0574693i
$455$	−10.3709	−	5.80432i	−0.486193	−	0.272111i
$456$	−39.2887	+	22.7564i	−1.83986	+	1.06567i
$457$	8.82468	+	16.1612i	0.412801	+	0.755989i	0.998512	−	0.0545311i	$-0.0173664\pi$
$457$	8.82468	+	16.1612i	0.412801	+	0.755989i	−0.585711	+	0.810520i	$0.699185\pi$
$458$	−4.98816	+	1.51027i	−0.233081	+	0.0705703i
$459$	5.39375			0.251759
$460$	−12.2147	+	17.6295i	−0.569514	+	0.821982i
$461$	−27.6996			−1.29010			−0.645050	−	0.764141i	$-0.723163\pi$
$461$	−27.6996			−1.29010			−0.645050	+	0.764141i	$0.723163\pi$
$462$	−47.4906	+	14.3788i	−2.20946	+	0.668961i
$463$	−14.2127	−	26.0286i	−0.660520	−	1.20965i	−0.966268	−	0.257540i	$-0.917088\pi$
$463$	−14.2127	−	26.0286i	−0.660520	−	1.20965i	0.305748	−	0.952113i	$-0.401094\pi$
$464$	1.82571	−	0.909077i	0.0847566	−	0.0422028i
$465$	2.32660	+	8.24106i	0.107893	+	0.382170i
$466$	−23.3044	−	22.9162i	−1.07955	−	1.06157i
$467$	5.35027	+	7.14712i	0.247581	+	0.330729i	0.907066	−	0.420988i	$-0.138317\pi$
$467$	5.35027	+	7.14712i	0.247581	+	0.330729i	−0.659485	+	0.751717i	$0.729226\pi$
$468$	4.10826	−	5.68456i	0.189905	−	0.262769i
$469$	8.26440	−	12.8597i	0.381615	−	0.593804i
$470$	−13.3014	+	8.50994i	−0.613550	+	0.392534i
$471$	19.4964	−	8.90372i	0.898348	−	0.410262i
$472$	−4.27265	+	7.03175i	−0.196665	+	0.323663i
$473$	27.2821	+	20.4231i	1.25443	+	0.939056i
$474$	31.6172	+	23.2566i	1.45223	+	1.06821i
$475$	−10.7924	+	34.1040i	−0.495190	+	1.56480i
$476$	−14.8047	−	4.07826i	−0.678572	−	0.186927i
$477$	−19.2075	+	1.37375i	−0.879451	+	0.0628995i
$478$	−6.98575	+	24.5522i	−0.319521	+	1.12299i
$479$	−14.3543	−	16.5658i	−0.655866	−	0.756910i	0.326230	−	0.945290i	$-0.394222\pi$
$479$	−14.3543	−	16.5658i	−0.655866	−	0.756910i	−0.982096	+	0.188381i	$0.939676\pi$
$480$	−28.2064	−	3.15109i	−1.28744	−	0.143827i
$481$	−2.04731	+	4.48298i	−0.0933492	+	0.204406i
$482$	−29.7233	+	26.1956i	−1.35386	+	1.19318i
$483$	29.7516	−	14.6934i	1.35375	−	0.668573i
$484$	−3.69862	+	29.1977i	−0.168119	+	1.32717i
$485$	24.9986	−	28.2485i	1.13513	−	1.28270i
$486$	−24.0613	−	8.74496i	−1.09144	−	0.396679i
$487$	10.1628	+	0.726857i	0.460520	+	0.0329370i	0.299672	−	0.954042i	$-0.403123\pi$
$487$	10.1628	+	0.726857i	0.460520	+	0.0329370i	0.160848	+	0.986979i	$0.448577\pi$
$488$	20.2602	+	8.64255i	0.917137	+	0.391230i
$489$	17.2575	+	14.9537i	0.780412	+	0.676231i
$490$	3.81610	−	6.95482i	0.172394	−	0.314187i
$491$	0.223793	+	0.762169i	0.0100996	+	0.0343962i	0.964389	−	0.264489i	$-0.0852034\pi$
$491$	0.223793	+	0.762169i	0.0100996	+	0.0343962i	−0.954289	+	0.298885i	$0.903385\pi$
$492$	13.4047	−	1.18530i	0.604328	−	0.0534375i
$493$	1.01635	+	0.760833i	0.0457743	+	0.0342662i
$494$	16.2876	−	6.23125i	0.732813	−	0.280357i
$495$	−18.3235	−	14.0178i	−0.823581	−	0.630051i
$496$	−6.78631	−	0.744085i	−0.304714	−	0.0334104i
$497$	2.20299	+	10.1270i	0.0988178	+	0.454258i
$498$	37.9516	+	23.9421i	1.70065	+	1.07287i
$499$	2.47246	−	17.1963i	0.110683	−	0.769814i	−0.856576	−	0.516021i	$-0.827413\pi$
$499$	2.47246	−	17.1963i	0.110683	−	0.769814i	0.967259	−	0.253793i	$-0.0816782\pi$
$500$	−18.0935	+	13.1387i	−0.809165	+	0.587581i
$501$	−22.8359	+	14.6757i	−1.02023	+	0.655663i
$502$	5.22126	−	38.6139i	0.233036	−	1.72342i
$503$	7.18511	+	13.1586i	0.320368	+	0.586711i	0.987386	−	0.158331i	$-0.0506113\pi$
$503$	7.18511	+	13.1586i	0.320368	+	0.586711i	−0.667018	+	0.745042i	$0.732430\pi$
$504$	14.4691	+	10.2730i	0.644504	+	0.457597i
$505$	−13.9685	+	7.43908i	−0.621590	+	0.331035i
$506$	−1.33171	−	34.3677i	−0.0592016	−	1.52783i
$507$	15.9122	−	15.9122i	0.706685	−	0.706685i
$508$	6.82480	−	1.60515i	0.302802	−	0.0712168i
$509$	0.944050	−	3.21514i	0.0418443	−	0.142508i	−0.935921	−	0.352209i	$-0.885431\pi$
$509$	0.944050	−	3.21514i	0.0418443	−	0.142508i	0.977766	+	0.209700i	$0.0672489\pi$
$510$	−6.14029	−	16.5661i	−0.271897	−	0.733561i
$511$	−6.60719	−	10.2810i	−0.292285	−	0.454804i
$512$	10.7611	−	19.9048i	0.475576	−	0.879674i
$513$	−9.28723	−	12.4063i	−0.410041	−	0.547751i
$514$	36.3891	−	8.23659i	1.60505	−	0.363301i
$515$	−27.0708	−	31.9086i	−1.19288	−	1.40606i
$516$	−0.506499	−	30.1541i	−0.0222974	−	1.32746i
$517$	8.84917	−	23.7255i	0.389186	−	1.04345i
$518$	−11.3853	−	5.08439i	−0.500242	−	0.223395i
$519$	3.44159	+	23.9368i	0.151069	+	1.05071i
$520$	10.5037	+	2.91660i	0.460619	+	0.127901i
$521$	−30.7268	+	9.02220i	−1.34616	+	0.395270i	−0.873865	−	0.486168i	$-0.838394\pi$
$521$	−30.7268	+	9.02220i	−1.34616	+	0.395270i	−0.472300	+	0.881438i	$0.656576\pi$
$522$	−0.803508	−	1.22749i	−0.0351686	−	0.0537260i
$523$	−13.2466	+	0.947418i	−0.579235	+	0.0414277i	−0.357883	−	0.933766i	$-0.616501\pi$
$523$	−13.2466	+	0.947418i	−0.579235	+	0.0414277i	−0.221352	+	0.975194i	$0.571047\pi$
$524$	−31.0894	+	14.8340i	−1.35815	+	0.648028i
$525$	34.3380	−	4.20716i	1.49863	−	0.183616i
$526$	26.7491	+	9.72182i	1.16632	+	0.423892i
$527$	−1.48513	−	3.98179i	−0.0646933	−	0.173449i
$528$	39.1910	−	23.1415i	1.70557	−	1.00710i
$529$	4.64743	+	22.5256i	0.202062	+	0.979373i
$530$	−12.3776	−	27.2505i	−0.537648	−	1.18368i
$531$	5.38386	+	2.45873i	0.233640	+	0.106700i
$532$	16.1110	+	41.0748i	0.698499	+	1.78082i
$533$	−5.15549	−	0.368728i	−0.223309	−	0.0159714i
$534$	−28.5660	−	51.2860i	−1.23617	−	2.21936i
$535$	9.97747	+	15.8876i	0.431364	+	0.686881i
$536$	−4.56746	+	13.2565i	−0.197284	+	0.572595i
$537$	49.3683	+	26.9571i	2.13040	+	1.16329i
$538$	5.39431	+	35.4050i	0.232565	+	1.52642i
$539$	1.81044	+	12.5919i	0.0779811	+	0.542371i
$540$	−0.0615420	−	9.68732i	−0.00264835	−	0.416876i
$541$	−9.73590	−	21.3187i	−0.418579	−	0.916560i	−0.995044	−	0.0994383i	$-0.968295\pi$
$541$	−9.73590	−	21.3187i	−0.418579	−	0.916560i	0.576465	−	0.817122i	$-0.304432\pi$
$542$	0.427175	−	0.501434i	0.0183488	−	0.0215384i
$543$	−8.41939	−	38.7033i	−0.361310	−	1.66092i
$544$	14.0793	+	0.414209i	0.603644	+	0.0177591i
$545$	6.43244	−	2.32295i	0.275536	−	0.0995044i
$546$	−12.0254	−	11.8251i	−0.514640	−	0.506068i
$547$	0.158399	−	0.728148i	0.00677265	−	0.0311334i	−0.973637	−	0.228105i	$-0.926747\pi$
$547$	0.158399	−	0.728148i	0.00677265	−	0.0311334i	0.980409	+	0.196972i	$0.0631107\pi$
$548$	13.3629	+	2.67270i	0.570834	+	0.114172i
$549$	4.46390	−	15.2026i	0.190514	−	0.648833i
$550$	10.5311	−	34.2764i	0.449049	−	1.46155i
$551$		−	3.64778i		−	0.155401i
$552$	−23.3157	+	19.5638i	−0.992380	+	0.832692i
$553$	26.9700	−	26.9700i	1.14688	−	1.14688i
$554$	4.02644	−	7.52340i	0.171067	−	0.319639i
$555$	−2.90287	−	14.0490i	−0.123220	−	0.596349i
$556$	23.3086	−	15.5388i	0.988505	−	0.658991i
$557$	−7.16183	−	1.55796i	−0.303456	−	0.0660129i	0.0582589	−	0.998302i	$-0.481445\pi$
$557$	−7.16183	−	1.55796i	−0.303456	−	0.0660129i	−0.361715	+	0.932289i	$0.617809\pi$
$558$	0.0412396	+	4.91070i	0.00174581	+	0.207886i
$559$	−1.64850	+	11.4656i	−0.0697241	+	0.484942i
$560$	−7.15575	+	26.6362i	−0.302386	+	1.12558i
$561$	23.8341	+	15.3173i	1.00628	+	0.646695i
$562$	5.09380	+	4.33944i	0.214869	+	0.183048i
$563$	−9.32739	+	25.0077i	−0.393103	+	1.05395i	0.578157	+	0.815926i	$0.303772\pi$
$563$	−9.32739	+	25.0077i	−0.393103	+	1.05395i	−0.971259	+	0.238024i	$0.923500\pi$
$564$	−21.3918	+	6.67343i	−0.900757	+	0.281002i
$565$	5.75015	+	0.888129i	0.241911	+	0.0373639i
$566$	3.66884	+	2.69868i	0.154213	+	0.113434i
$567$	−16.2031	+	29.6738i	−0.680466	+	1.24618i
$568$	−4.16559	−	8.54492i	−0.174784	−	0.358537i
$569$	−3.46966	−	3.00648i	−0.145456	−	0.126038i	0.579094	−	0.815261i	$-0.303407\pi$
$569$	−3.46966	−	3.00648i	−0.145456	−	0.126038i	−0.724549	+	0.689223i	$0.757952\pi$
$570$	−27.5315	+	42.6479i	−1.15317	+	1.78632i
$571$	4.25566	−	3.68755i	0.178094	−	0.154319i	−0.561252	−	0.827645i	$-0.689680\pi$
$571$	4.25566	−	3.68755i	0.178094	−	0.154319i	0.739346	+	0.673326i	$0.235135\pi$
$572$	−16.2740	+	6.38325i	−0.680452	+	0.266897i
$573$	−14.1769	−	38.0097i	−0.592248	−	1.58788i
$574$	0.823336	−	13.0511i	0.0343654	−	0.544742i
$575$	−3.18823	+	23.7663i	−0.132958	+	0.991122i
$576$	−15.1275	−	6.00729i	−0.630313	−	0.250304i
$577$	−12.3170	+	4.59401i	−0.512765	+	0.191251i	−0.592509	−	0.805564i	$-0.701862\pi$
$577$	−12.3170	+	4.59401i	−0.512765	+	0.191251i	0.0797441	+	0.996815i	$0.474590\pi$
$578$	−6.46134	−	13.8396i	−0.268756	−	0.575651i
$579$	8.62183	+	9.95012i	0.358311	+	0.413513i
$580$	1.35488	−	1.83408i	0.0562584	−	0.0761561i
$581$	28.5557	−	32.9550i	1.18469	−	1.36720i
$582$	44.7880	−	29.3178i	1.85652	−	1.21526i
$583$	42.1247	+	23.0018i	1.74463	+	0.952638i
$584$	8.12361	+	7.72426i	0.336157	+	0.319632i
$585$	1.19696	−	7.74966i	0.0494882	−	0.320409i
$586$	31.1455	−	11.9156i	1.28661	−	0.492227i
$587$	0.494624	+	0.184485i	0.0204153	+	0.00761452i	0.359651	−	0.933087i	$-0.382896\pi$
$587$	0.494624	+	0.184485i	0.0204153	+	0.00761452i	−0.339236	+	0.940701i	$0.610168\pi$
$588$	7.82555	−	8.09294i	0.322720	−	0.333747i
$589$	−6.60143	+	10.2720i	−0.272007	+	0.423252i
$590$	−0.675031	+	9.17446i	−0.0277906	+	0.377707i
$591$	−17.5733	−	2.52665i	−0.722867	−	0.103933i
$592$	11.2511	+	2.05444i	0.462419	+	0.0844370i
$593$	−2.81012	+	12.9179i	−0.115398	+	0.530476i	0.882761	+	0.469822i	$0.155682\pi$
$593$	−2.81012	+	12.9179i	−0.115398	+	0.530476i	−0.998159	+	0.0606534i	$0.980682\pi$
$594$	9.41386	+	12.3578i	0.386255	+	0.507045i
$595$	−16.8135	+	3.47408i	−0.689287	+	0.142423i
$596$	−10.1997	+	16.4730i	−0.417798	+	0.674760i
$597$	−29.2577	−	29.2577i	−1.19744	−	1.19744i
$598$	10.0356	−	5.99558i	0.410386	−	0.245177i
$599$	−11.2781			−0.460809			−0.230404	−	0.973095i	$-0.574005\pi$
$599$	−11.2781			−0.460809			−0.230404	+	0.973095i	$0.574005\pi$
$600$	−29.6832	+	11.2172i	−1.21181	+	0.457938i
$601$	27.3704	+	8.03667i	1.11646	+	0.327822i	0.787373	−	0.616477i	$-0.211441\pi$
$601$	27.3704	+	8.03667i	1.11646	+	0.327822i	0.329088	+	0.944299i	$0.393259\pi$
$602$	−29.0426	−	3.92706i	−1.18369	−	0.160055i
$603$	9.85549	+	2.14393i	0.401347	+	0.0873076i
$604$	−13.7367	+	12.3129i	−0.558939	+	0.501004i
$605$	11.1765	+	30.9486i	0.454389	+	1.25824i
$606$	−21.9043	+	4.95801i	−0.889803	+	0.201405i
$607$	20.1361	−	4.38034i	0.817299	−	0.177792i	0.215565	−	0.976489i	$-0.430841\pi$
$607$	20.1361	−	4.38034i	0.817299	−	0.177792i	0.601734	+	0.798697i	$0.294477\pi$
$608$	−23.2897	−	33.0973i	−0.944521	−	1.34227i
$609$	−3.20904	+	1.46552i	−0.130037	+	0.0593858i
$610$	24.5673	−	1.70660i	0.994700	−	0.0690981i
$611$	8.51926	−	1.22488i	0.344652	−	0.0495535i
$612$	−0.892442	−	10.0927i	−0.0360748	−	0.407973i
$613$	11.3940	−	20.8666i	0.460200	−	0.842793i	−0.539800	−	0.841793i	$-0.681500\pi$
$613$	11.3940	−	20.8666i	0.460200	−	0.842793i	1.00000		0.000999459i	$-0.000318138\pi$
$614$	−4.47257	−	0.933682i	−0.180498	−	0.0376803i
$615$	12.7412	−	8.00151i	0.513774	−	0.322652i
$616$	−16.4952	−	41.0373i	−0.664612	−	1.65344i
$617$	−3.17754	+	44.4278i	−0.127923	+	1.78859i	0.377789	+	0.925892i	$0.376684\pi$
$617$	−3.17754	+	44.4278i	−0.127923	+	1.78859i	−0.505712	+	0.862702i	$0.668770\pi$
$618$	−25.1208	−	53.8065i	−1.01051	−	2.16442i
$619$	2.71098	−	5.93621i	0.108963	−	0.238597i	−0.847293	−	0.531125i	$-0.821769\pi$
$619$	2.71098	−	5.93621i	0.108963	−	0.238597i	0.956257	+	0.292529i	$0.0944967\pi$
$620$	−7.13446	+	2.71277i	−0.286527	+	0.108947i
$621$	−7.56533	−	7.11977i	−0.303586	−	0.285706i
$622$	−7.87820	−	8.93913i	−0.315887	−	0.358427i
$623$	−53.4507	+	19.9361i	−2.14146	+	0.798722i
$624$	13.2875	+	7.92180i	0.531928	+	0.317126i
$625$	−11.3259	+	22.2873i	−0.453038	+	0.891491i
$626$	15.4629	+	27.7614i	0.618022	+	1.10957i
$627$	−5.80721	−	81.1955i	−0.231918	−	3.24263i
$628$	9.43617	+	16.6116i	0.376544	+	0.662874i
$629$	2.00580	+	6.83114i	0.0799767	+	0.272376i
$630$	19.6319	+	2.86363i	0.782153	+	0.114090i
$631$	−44.9803	+	6.46720i	−1.79064	+	0.257455i	−0.956005	−	0.293350i	$-0.905230\pi$
$631$	−44.9803	+	6.46720i	−1.79064	+	0.257455i	−0.834634	+	0.550805i	$0.814321\pi$
$632$	−18.1669	+	29.8984i	−0.722642	+	1.18929i
$633$	−2.16064	−	0.805876i	−0.0858776	−	0.0320307i
$634$	1.25848	+	15.7374i	0.0499807	+	0.625014i
$635$	5.97727	−	5.07102i	0.237201	−	0.201237i
$636$	−6.74978	−	41.9335i	−0.267646	−	1.66277i
$637$	−3.46149	+	2.59124i	−0.137149	+	0.102668i
$638$	0.0307069	+	3.65650i	0.00121570	+	0.144762i
$639$	−5.75260	+	3.69697i	−0.227569	+	0.146250i
$640$	0.583288	−	25.2915i	0.0230565	−	0.999734i
$641$	−1.50766	−	0.442690i	−0.0595492	−	0.0174852i	0.251822	−	0.967773i	$-0.418970\pi$
$641$	−1.50766	−	0.442690i	−0.0595492	−	0.0174852i	−0.311371	+	0.950288i	$0.600788\pi$
$642$	7.71491	+	25.4810i	0.304483	+	1.00565i
$643$	−9.16800	−	9.16800i	−0.361551	−	0.361551i	0.502833	−	0.864384i	$-0.332291\pi$
$643$	−9.16800	−	9.16800i	−0.361551	−	0.361551i	−0.864384	+	0.502833i	$0.832291\pi$
$644$	15.3819	+	25.2624i	0.606131	+	0.995480i
$645$	−15.8495	−	29.7608i	−0.624072	−	1.17183i
$646$	11.8873	−	22.2114i	0.467700	−	0.873896i
$647$	−19.8716	+	10.8507i	−0.781234	+	0.426586i	−0.819786	−	0.572671i	$-0.805907\pi$
$647$	−19.8716	+	10.8507i	−0.781234	+	0.426586i	0.0385516	+	0.999257i	$0.487726\pi$
$648$	7.98463	−	29.9660i	0.313666	−	1.17717i
$649$	−7.97552	−	12.4102i	−0.313067	−	0.487141i
$650$	11.9407	−	2.44180i	0.468355	−	0.0957752i
$651$	11.6887	+	1.68058i	0.458116	+	0.0658672i
$652$	−11.9223	+	16.4967i	−0.466913	+	0.646062i
$653$	−27.1212	+	5.89986i	−1.06133	+	0.230879i	−0.709155	−	0.705053i	$-0.750923\pi$
$653$	−27.1212	+	5.89986i	−1.06133	+	0.230879i	−0.352180	+	0.935932i	$0.614560\pi$
$654$	9.67436	−	0.773633i	0.378298	−	0.0302515i
$655$	−23.4006	+	30.5885i	−0.914339	+	1.19519i
$656$	2.10482	+	11.8087i	0.0821796	+	0.461054i
$657$	4.83228	−	6.45517i	0.188525	−	0.251840i
$658$	3.27993	+	21.5275i	0.127865	+	0.839229i
$659$	0.817039	−	0.239904i	0.0318273	−	0.00934534i	−0.265780	−	0.964034i	$-0.585630\pi$
$659$	0.817039	−	0.239904i	0.0318273	−	0.00934534i	0.297607	+	0.954688i	$0.403811\pi$
$660$	27.2383	−	42.9815i	1.06025	−	1.67305i
$661$	0.431048	−	0.497456i	0.0167658	−	0.0193488i	−0.747305	−	0.664481i	$-0.768652\pi$
$661$	0.431048	−	0.497456i	0.0167658	−	0.0193488i	0.764071	+	0.645133i	$0.223198\pi$
$662$	24.5260	+	6.97832i	0.953232	+	0.271220i
$663$	−0.686982	+	9.60526i	−0.0266802	+	0.373037i
$664$	−18.2782	+	35.5764i	−0.709333	+	1.38063i
$665$	36.9412	+	32.6913i	1.43252	+	1.26772i
$666$	0.517984	−	8.21081i	0.0200715	−	0.318162i
$667$	−0.421246	−	2.40874i	−0.0163107	−	0.0932669i
$668$	−14.8232	−	19.1235i	−0.573528	−	0.739909i
$669$	−9.61850	−	4.39262i	−0.371873	−	0.169829i
$670$	2.19923	+	15.5213i	0.0849638	+	0.599639i
$671$	−29.8454	+	25.8612i	−1.15217	+	0.998360i
$672$	−19.7597	+	33.7855i	−0.762245	+	1.30330i
$673$	−0.762757	−	10.6647i	−0.0294021	−	0.411095i	−0.990745	−	0.135740i	$-0.956659\pi$
$673$	−0.762757	−	10.6647i	−0.0294021	−	0.411095i	0.961342	−	0.275356i	$-0.0887956\pi$
$674$	6.66697	−	31.9365i	0.256802	−	1.23015i
$675$	−4.99108	−	9.61245i	−0.192107	−	0.369983i
$676$	15.3775	+	12.8789i	0.591441	+	0.495343i
$677$	−22.6562	+	30.2652i	−0.870750	+	1.16319i	0.114731	+	0.993397i	$0.463399\pi$
$677$	−22.6562	+	30.2652i	−0.870750	+	1.16319i	−0.985480	+	0.169789i	$0.945691\pi$
$678$	7.53916	+	3.36679i	0.289540	+	0.129301i
$679$	−21.6095	−	47.3182i	−0.829296	−	1.81590i
$680$	14.2268	−	6.75250i	0.545571	−	0.258947i
$681$	2.33104	+	1.49807i	0.0893257	+	0.0574062i
$682$	6.53074	−	10.3521i	0.250075	−	0.396404i
$683$	21.7573	−	16.2873i	0.832520	−	0.623217i	−0.0956322	−	0.995417i	$-0.530487\pi$
$683$	21.7573	−	16.2873i	0.832520	−	0.623217i	0.928153	+	0.372200i	$0.121396\pi$
$684$	−21.6778	+	19.4308i	−0.828871	+	0.742956i
$685$	14.6629	−	4.13960i	0.560242	−	0.158166i
$686$	11.8689	+	15.5805i	0.453157	+	0.594868i
$687$	−7.25753	+	3.96291i	−0.276892	+	0.151194i
$688$	26.7337	−	2.81714i	1.01921	−	0.107403i
$689$			16.3135i			0.621493i
$690$	−13.2549	+	31.3410i	−0.504606	+	1.19313i
$691$		−	11.1634i		−	0.424675i	−0.977196	−	0.212338i	$-0.931892\pi$
$691$		−	11.1634i		−	0.424675i	0.977196	−	0.212338i	$-0.0681077\pi$
$692$	−20.9829	+	4.93504i	−0.797652	+	0.187602i
$693$	−27.9233	+	15.2473i	−1.06072	+	0.579196i
$694$	−23.0128	+	17.5306i	−0.873552	+	0.665452i
$695$	15.2962	−	27.3305i	0.580219	−	1.03671i
$696$	2.54080	−	2.00384i	0.0963088	−	0.0759554i
$697$	−5.97740	+	4.47462i	−0.226410	+	0.169488i
$698$	−9.39672	−	5.92800i	−0.355671	−	0.224378i
$699$	−43.6244	−	28.0357i	−1.65003	−	1.06041i
$700$	6.43139	+	30.1579i	0.243084	+	1.13986i
$701$	−1.66485	−	3.64551i	−0.0628804	−	0.137689i	0.875583	−	0.483068i	$-0.160478\pi$
$701$	−1.66485	−	3.64551i	−0.0628804	−	0.137689i	−0.938463	+	0.345379i	$0.887750\pi$
$702$	−2.15309	+	4.82134i	−0.0812630	+	0.181970i
$703$	12.2588	−	16.3758i	0.462349	−	0.617625i
$704$	23.6239	+	32.9803i	0.890361	+	1.24299i
$705$	−17.8996	+	17.5296i	−0.674136	+	0.660202i
$706$	6.24019	+	1.30269i	0.234853	+	0.0490272i
$707$	1.55693	+	21.7688i	0.0585545	+	0.818699i
$708$	−4.35606	+	12.3064i	−0.163711	+	0.462504i
$709$	−1.23836	+	1.07304i	−0.0465075	+	0.0402990i	−0.677804	−	0.735242i	$-0.737068\pi$
$709$	−1.23836	+	1.07304i	−0.0465075	+	0.0402990i	0.631297	+	0.775541i	$0.282523\pi$
$710$	−8.49532	−	6.38666i	−0.318824	−	0.239687i
$711$	22.8917	+	10.4543i	0.858505	+	0.392066i
$712$	43.2934	−	29.3898i	1.62249	−	1.10143i
$713$	−3.17291	+	7.54527i	−0.118827	+	0.282573i
$714$	−24.3157	−	1.53397i	−0.909991	−	0.0574073i
$715$	−12.9525	+	14.6363i	−0.484395	+	0.547366i
$716$	−20.0589	+	45.9499i	−0.749637	+	1.71723i
$717$	−2.88927	+	40.3973i	−0.107902	+	1.50866i
$718$	−0.563581	+	1.98077i	−0.0210327	+	0.0739215i
$719$	−30.7041	+	35.4344i	−1.14507	+	1.32148i	−0.205685	+	0.978618i	$0.565942\pi$
$719$	−30.7041	+	35.4344i	−1.14507	+	1.32148i	−0.939385	+	0.342864i	$0.888603\pi$
$720$	−18.1166	+	1.71801i	−0.675165	+	0.0640264i
$721$	−55.3678	+	16.2575i	−2.06201	+	0.605459i
$722$	−44.9937	+	6.85524i	−1.67449	+	0.255126i
$723$	−37.6705	+	50.3218i	−1.40098	+	1.87149i
$724$	33.7031	−	10.5141i	1.25257	−	0.390753i
$725$	0.415438	−	2.51533i	0.0154290	−	0.0934168i
$726$	3.72220	+	46.5465i	0.138144	+	1.72750i
$727$	38.9112	−	8.46462i	1.44314	−	0.313935i	0.578233	−	0.815872i	$-0.303742\pi$
$727$	38.9112	−	8.46462i	1.44314	−	0.313935i	0.864905	+	0.501936i	$0.167379\pi$
$728$	9.55522	−	11.6056i	0.354140	−	0.430132i
$729$	−7.64751	−	1.09955i	−0.283241	−	0.0407239i
$730$	12.0179	+	3.55549i	0.444803	+	0.131594i
$731$	9.04687	+	14.0772i	0.334611	+	0.520664i
$732$	34.2686	+	6.85403i	1.26660	+	0.253332i
$733$	−31.0486	+	16.9538i	−1.14681	+	0.626204i	−0.936235	−	0.351375i	$-0.885714\pi$
$733$	−31.0486	+	16.9538i	−1.14681	+	0.626204i	−0.210572	+	0.977578i	$0.567533\pi$
$734$	−17.3740	−	9.29840i	−0.641287	−	0.343210i
$735$	3.67193	−	12.0389i	0.135441	−	0.444062i
$736$	−19.2010	−	19.1657i	−0.707757	−	0.706456i
$737$	−17.7757	−	17.7757i	−0.654775	−	0.654775i
$738$	8.25809	−	2.50031i	0.303984	−	0.0920376i
$739$	−22.0599	−	6.47736i	−0.811486	−	0.238274i	−0.150440	−	0.988619i	$-0.548069\pi$
$739$	−22.0599	−	6.47736i	−0.811486	−	0.238274i	−0.661046	+	0.750345i	$0.729887\pi$
$740$	12.2460	−	3.68042i	0.450173	−	0.135295i
$741$	23.2762	−	14.9587i	0.855072	−	0.549521i
$742$	−41.2726	+	0.346604i	−1.51517	+	0.0127242i
$743$	−12.8211	+	9.59776i	−0.470361	+	0.352108i	−0.808014	−	0.589163i	$-0.799458\pi$
$743$	−12.8211	+	9.59776i	−0.470361	+	0.352108i	0.337654	+	0.941270i	$0.390367\pi$
$744$	−10.7812	+	1.04464i	−0.395257	+	0.0382982i
$745$	−1.77089	+	21.5895i	−0.0648805	+	0.790978i
$746$	−50.4430	+	4.03379i	−1.84685	+	0.147688i
$747$	26.9573	+	10.0545i	0.986315	+	0.367876i
$748$	−11.7287	+	22.3645i	−0.428845	+	0.817729i
$749$	25.6083	−	3.68192i	0.935708	−	0.134535i
$750$	−23.8414	+	26.2723i	−0.870565	+	0.959328i
$751$	−10.6146	−	36.1501i	−0.387333	−	1.31914i	−0.890514	−	0.454955i	$-0.849655\pi$
$751$	−10.6146	−	36.1501i	−0.387333	−	1.31914i	0.503181	−	0.864181i	$-0.332163\pi$
$752$	−7.60474	−	18.4695i	−0.277316	−	0.673515i
$753$	−4.41034	−	61.6647i	−0.160722	−	2.24719i
$754$	−1.08580	+	0.604784i	−0.0395425	+	0.0220249i
$755$	−7.40902	+	19.2480i	−0.269642	+	0.700508i
$756$	−12.2436	−	5.34482i	−0.445296	−	0.194389i
$757$	−33.3455	+	12.4372i	−1.21196	+	0.452039i	−0.872516	−	0.488585i	$-0.837513\pi$
$757$	−33.3455	+	12.4372i	−1.21196	+	0.452039i	−0.339448	+	0.940625i	$0.610240\pi$
$758$	−19.2908	+	17.0013i	−0.700674	+	0.617515i
$759$	−13.2111	−	52.9453i	−0.479534	−	1.92179i
$760$	−40.0279	−	21.0965i	−1.45197	−	0.765251i
$761$	17.1688	−	37.5944i	0.622368	−	1.36279i	−0.291417	−	0.956596i	$-0.594127\pi$
$761$	17.1688	−	37.5944i	0.622368	−	1.36279i	0.913785	−	0.406199i	$-0.133146\pi$
$762$	10.0793	−	4.70575i	0.365134	−	0.170471i
$763$	0.672817	−	9.40721i	0.0243576	−	0.340564i
$764$	32.6352	−	15.5716i	1.18070	−	0.563362i
$765$	−6.02453	−	9.59315i	−0.217817	−	0.346841i
$766$	0.907383	−	4.34659i	0.0327851	−	0.157049i
$767$	2.40302	−	4.40079i	0.0867678	−	0.158903i
$768$	10.2596	−	34.4034i	0.370211	−	1.24143i
$769$	21.8148	−	3.13649i	0.786661	−	0.113105i	0.262734	−	0.964868i	$-0.415376\pi$
$769$	21.8148	−	3.13649i	0.786661	−	0.113105i	0.523927	+	0.851763i	$0.324467\pi$
$770$	−37.3047	−	32.4585i	−1.34437	−	1.16972i
$771$	53.8459	−	24.5906i	1.93921	−	0.885609i
$772$	−8.15766	+	8.43639i	−0.293601	+	0.303632i
$773$	7.98504	−	1.73704i	0.287202	−	0.0624769i	−0.0666565	−	0.997776i	$-0.521233\pi$
$773$	7.98504	−	1.73704i	0.287202	−	0.0624769i	0.353858	+	0.935299i	$0.384870\pi$
$774$	−4.26888	−	18.8598i	−0.153442	−	0.677901i
$775$	−5.72187	+	6.33125i	−0.205536	+	0.227425i
$776$	29.5472	+	37.4648i	1.06068	+	1.34491i
$777$	−19.3312	−	4.20525i	−0.693503	−	0.150862i
$778$	0.646781	−	4.78328i	0.0231882	−	0.171489i
$779$	20.5844	+	6.04412i	0.737512	+	0.216553i
$780$	17.2592	+	1.12424i	0.617977	+	0.0402544i
$781$	17.0435			0.609865
$782$	5.28458	−	16.0396i	0.188976	−	0.573576i
$783$	0.781000	+	0.781000i	0.0279107	+	0.0279107i
$784$	7.79999	+	6.31281i	0.278571	+	0.225458i
$785$	17.8473	+	11.7349i	0.636996	+	0.418836i
$786$	−43.4758	+	33.1189i	−1.55073	+	1.18131i
$787$	−6.61075	+	30.3891i	−0.235648	+	1.08325i	0.695476	+	0.718550i	$0.255194\pi$
$787$	−6.61075	+	30.3891i	−0.235648	+	1.08325i	−0.931123	+	0.364705i	$0.881170\pi$
$788$	0.863685	−	15.8014i	0.0307675	−	0.562902i
$789$	44.6966	+	6.42639i	1.59124	+	0.228786i
$790$	−2.87017	+	39.0090i	−0.102116	+	1.38788i
$791$	4.33792	−	6.74993i	0.154239	−	0.240000i
$792$	21.5660	−	19.6597i	0.766315	−	0.698579i
$793$	−12.5765	−	4.69080i	−0.446606	−	0.166575i
$794$	15.0949	+	39.4558i	0.535697	+	1.40023i
$795$	−28.0591	−	38.3100i	−0.995153	−	1.35872i
$796$	23.6804	−	28.2745i	0.839330	−	1.00216i
$797$	3.84064	+	2.09715i	0.136042	+	0.0742848i	0.545829	−	0.837897i	$-0.316215\pi$
$797$	3.84064	+	2.09715i	0.136042	+	0.0742848i	−0.409786	+	0.912182i	$0.634397\pi$
$798$	38.3396	+	58.5703i	1.35721	+	2.07337i
$799$	8.14225	−	9.39666i	0.288052	−	0.332430i
$800$	−12.2900	−	25.4746i	−0.434517	−	0.900664i
$801$	−24.6491	−	28.4466i	−0.870935	−	1.00511i
$802$	−24.7469	+	11.5537i	−0.873843	+	0.407974i
$803$	−18.8305	+	7.02342i	−0.664515	+	0.247851i
$804$	−2.79570	+	22.0698i	−0.0985967	+	0.778342i
$805$	28.1686	+	17.3211i	0.992813	+	0.610489i
$806$	4.15206	+	0.261935i	0.146250	+	0.00922627i
$807$	19.8572	+	53.2391i	0.699005	+	1.87411i
$808$	−6.12187	−	19.0593i	−0.215367	−	0.670504i
$809$	−16.0202	+	13.8816i	−0.563240	+	0.488050i	−0.889316	−	0.457293i	$-0.848819\pi$
$809$	−16.0202	+	13.8816i	−0.563240	+	0.488050i	0.326076	+	0.945344i	$0.394274\pi$
$810$	−7.30075	−	33.8946i	−0.256522	−	1.19093i
$811$	9.23414	+	8.00142i	0.324254	+	0.280968i	0.801742	−	0.597671i	$-0.203907\pi$
$811$	9.23414	+	8.00142i	0.324254	+	0.280968i	−0.477487	+	0.878639i	$0.658452\pi$
$812$	−1.55316	−	2.73420i	−0.0545051	−	0.0959516i
$813$	0.500876	−	0.917286i	0.0175665	−	0.0321706i
$814$	−12.1502	+	16.5181i	−0.425865	+	0.578960i
$815$	−3.47361	+	22.4897i	−0.121675	+	0.787781i
$816$	22.0010	−	3.92153i	0.770190	−	0.137281i
$817$	16.8020	−	45.0478i	0.587826	−	1.57602i
$818$	8.42752	−	9.89253i	0.294661	−	0.345884i
$819$	−9.09710	−	5.84635i	−0.317879	−	0.204288i
$820$	8.10475	+	10.6845i	0.283030	+	0.373119i
$821$	6.31505	−	43.9221i	0.220397	−	1.53289i	−0.516145	−	0.856501i	$-0.672634\pi$
$821$	6.31505	−	43.9221i	0.220397	−	1.53289i	0.736542	−	0.676392i	$-0.236457\pi$
$822$	21.6207	−	0.181568i	0.754107	−	0.00633293i
$823$	−15.2140	−	3.30960i	−0.530327	−	0.115365i	−0.0605742	−	0.998164i	$-0.519293\pi$
$823$	−15.2140	−	3.30960i	−0.530327	−	0.115365i	−0.469752	+	0.882798i	$0.655657\pi$
$824$	45.8018	−	26.5288i	1.59558	−	0.924175i
$825$	5.24281	−	56.6496i	0.182531	−	1.97229i
$826$	11.1850	+	5.98607i	0.389174	+	0.208282i
$827$	−29.8870	+	29.8870i	−1.03927	+	1.03927i	−0.0400755	+	0.999197i	$0.512760\pi$
$827$	−29.8870	+	29.8870i	−1.03927	+	1.03927i	−0.999197	+	0.0400755i	$0.987240\pi$
$828$	−12.0706	+	15.3341i	−0.419483	+	0.532898i
$829$			20.6244i			0.716314i	0.933661	+	0.358157i	$0.116595\pi$
$829$			20.6244i			0.716314i	−0.933661	+	0.358157i	$0.883405\pi$
$830$	−0.0914468	+	44.7181i	−0.00317417	+	1.55219i
$831$	3.81426	−	12.9902i	0.132315	−	0.450625i
$832$	−5.99044	+	12.4198i	−0.207681	+	0.430578i
$833$	−1.32777	+	6.10365i	−0.0460044	+	0.211479i
$834$	31.1629	−	31.6908i	1.07908	−	1.09736i
$835$	−24.4884	−	11.4940i	−0.847456	−	0.397767i
$836$	71.6364	−	11.5309i	2.47760	−	0.398804i
$837$	−0.785884	−	3.61265i	−0.0271641	−	0.124872i
$838$	30.6848	+	26.1407i	1.05999	+	0.903014i
$839$	−14.2293	−	31.1578i	−0.491250	−	1.07569i	−0.979215	−	0.202824i	$-0.934988\pi$
$839$	−14.2293	−	31.1578i	−0.491250	−	1.07569i	0.487966	−	0.872863i	$-0.337739\pi$
$840$	−2.47761	+	43.6891i	−0.0854857	+	1.50742i
$841$	−4.09013	−	28.4475i	−0.141039	−	0.980948i
$842$	4.33786	−	0.660917i	0.149492	−	0.0227767i
$843$	9.31821	+	5.08813i	0.320936	+	0.175244i
$844$	0.545892	−	1.98167i	0.0187904	−	0.0682119i
$845$	21.8623	+	4.99552i	0.752087	+	0.171851i
$846$	−12.5521	+	6.99144i	−0.431550	+	0.240371i
$847$	45.2612	+	3.23714i	1.55519	+	0.111230i
$848$	36.7022	−	9.28527i	1.26036	−	0.318858i
$849$	6.57312	+	3.00184i	0.225589	+	0.103023i
$850$	10.7265	−	13.9620i	0.367916	−	0.478894i
$851$	6.20377	−	12.2291i	0.212663	−	0.419208i
$852$	−9.24012	−	11.9207i	−0.316561	−	0.408395i
$853$	7.63309	+	20.4651i	0.261352	+	0.700712i	0.999656	+	0.0262432i	$0.00835444\pi$
$853$	7.63309	+	20.4651i	0.261352	+	0.700712i	−0.738304	+	0.674468i	$0.764373\pi$
$854$	11.6004	−	31.9180i	0.396958	−	1.09221i
$855$	−11.6921	+	30.3751i	−0.399861	+	1.03881i
$856$	−22.0185	+	8.85049i	−0.752577	+	0.302504i
$857$	−7.54096	+	0.539340i	−0.257594	+	0.0184235i	−0.199539	−	0.979890i	$-0.563944\pi$
$857$	−7.54096	+	0.539340i	−0.257594	+	0.0184235i	−0.0580552	+	0.998313i	$0.518490\pi$
$858$	−23.2059	+	15.1904i	−0.792235	+	0.518591i
$859$	20.6543	−	6.06466i	0.704716	−	0.206923i	0.0903106	−	0.995914i	$-0.471214\pi$
$859$	20.6543	−	6.06466i	0.704716	−	0.206923i	0.614406	+	0.788990i	$0.289396\pi$
$860$	25.1798	−	16.4091i	0.858625	−	0.559544i
$861$	−2.95275	−	20.5368i	−0.100629	−	0.699892i
$862$	9.66350	−	21.6392i	0.329140	−	0.737034i
$863$	16.9068	−	45.3289i	0.575514	−	1.54301i	−0.243893	−	0.969802i	$-0.578425\pi$
$863$	16.9068	−	45.3289i	0.575514	−	1.54301i	0.819407	−	0.573212i	$-0.194303\pi$
$864$	12.0726	+	2.09983i	0.410718	+	0.0714377i
$865$	−18.3772	+	15.5909i	−0.624843	+	0.530107i
$866$	9.83522	+	43.4517i	0.334214	+	1.47655i
$867$	−14.5223	−	19.3996i	−0.493205	−	0.658844i
$868$	−0.574473	+	10.5102i	−0.0194989	+	0.356739i
$869$	−33.9112	−	52.7669i	−1.15036	−	1.78999i
$870$	1.50963	−	3.28783i	0.0511814	−	0.111468i
$871$	2.40726	−	8.19837i	0.0815669	−	0.277791i
$872$	1.44644	+	8.52899i	0.0489827	+	0.288828i
$873$	24.2696	−	24.2696i	0.821402	−	0.821402i
$874$	−45.9924	+	15.4627i	−1.55572	+	0.523032i
$875$	21.7496	+	26.7494i	0.735272	+	0.904296i
$876$	15.1213	+	9.36281i	0.510901	+	0.316340i
$877$	8.01891	+	14.6855i	0.270779	+	0.495895i	0.977317	−	0.211780i	$-0.0679259\pi$
$877$	8.01891	+	14.6855i	0.270779	+	0.495895i	−0.706538	+	0.707675i	$0.749744\pi$
$878$	−36.8931	−	4.98857i	−1.24508	−	0.168356i
$879$	44.5093	−	28.6044i	1.50126	−	0.964802i
$880$	40.3012	+	20.8100i	1.35855	+	0.701504i
$881$	3.82856	−	26.6282i	0.128987	−	0.897127i	−0.817854	−	0.575426i	$-0.804836\pi$
$881$	3.82856	−	26.6282i	0.128987	−	0.897127i	0.946841	−	0.321701i	$-0.104255\pi$
$882$	3.85130	−	6.10486i	0.129680	−	0.205561i
$883$	0.982088	+	4.51458i	0.0330499	+	0.151928i	0.990715	−	0.135958i	$-0.0434112\pi$
$883$	0.982088	+	4.51458i	0.0330499	+	0.151928i	−0.957665	+	0.287886i	$0.907048\pi$
$884$	−8.58231	+	0.144157i	−0.288654	+	0.00484853i
$885$	1.92618	+	14.4679i	0.0647480	+	0.486332i
$886$	11.7525	+	30.7192i	0.394831	+	1.03203i
$887$	−8.51597	−	6.37497i	−0.285938	−	0.214051i	0.446674	−	0.894697i	$-0.352608\pi$
$887$	−8.51597	−	6.37497i	−0.285938	−	0.214051i	−0.732612	+	0.680646i	$0.761699\pi$
$888$	18.1404	−	0.457111i	0.608753	−	0.0153396i
$889$	−3.04542	−	10.3717i	−0.102140	−	0.347857i
$890$	28.1424	−	51.2894i	0.943336	−	1.71922i
$891$	42.0197	+	36.4103i	1.40771	+	1.21979i
$892$	3.14499	−	8.88500i	0.105302	−	0.297492i
$893$	−35.6332	−	2.54854i	−1.19242	−	0.0852836i
$894$	−10.5004	+	28.8915i	−0.351187	+	0.966275i
$895$	3.41485	+	55.9511i	0.114146	+	1.87024i
$896$	−31.5490	−	14.8918i	−1.05398	−	0.497500i
$897$	13.6425	−	12.5656i	0.455511	−	0.419554i
$898$	1.03152	+	1.17043i	0.0344221	+	0.0390576i
$899$	0.361509	−	0.791595i	0.0120570	−	0.0264012i
$900$	−17.1608	+	10.9297i	−0.572028	+	0.364323i
$901$	15.4328	+	17.8104i	0.514142	+	0.593352i
$902$	−20.6844	−	5.88528i	−0.688716	−	0.195958i
$903$	−46.3798	+	3.31715i	−1.54342	+	0.110388i
$904$	−2.39742	+	6.95824i	−0.0797370	+	0.231428i
$905$	28.2010	−	27.6181i	0.937433	−	0.918056i
$906$	−17.3426	+	23.5771i	−0.576169	+	0.783297i
$907$	13.2661	+	9.93085i	0.440492	+	0.329748i	0.796397	−	0.604774i	$-0.206736\pi$
$907$	13.2661	+	9.93085i	0.440492	+	0.329748i	−0.355905	+	0.934522i	$0.615827\pi$
$908$	−1.14710	+	2.18731i	−0.0380679	+	0.0725886i
$909$	−13.0986	+	5.98191i	−0.434452	+	0.198408i
$910$	3.60625	−	16.4160i	0.119546	−	0.544185i
$911$	−15.2324	+	23.7021i	−0.504672	+	0.785284i	−0.996338	−	0.0854991i	$-0.972752\pi$
$911$	−15.2324	+	23.7021i	−0.504672	+	0.785284i	0.491667	+	0.870784i	$0.336388\pi$
$912$	−46.9025	−	43.8528i	−1.55310	−	1.45211i
$913$	−42.9744	−	57.4071i	−1.42225	−	1.89990i
$914$	−18.2583	+	18.5675i	−0.603930	+	0.614160i
$915$	37.6025	−	10.6159i	1.24310	−	0.350949i
$916$	−4.08841	−	6.13272i	−0.135085	−	0.202631i
$917$	25.4532	+	46.6140i	0.840537	+	1.53933i
$918$	2.21042	+	7.30062i	0.0729546	+	0.240956i
$919$	−19.4770			−0.642487			−0.321243	−	0.946997i	$-0.604101\pi$
$919$	−19.4770			−0.642487			−0.321243	+	0.946997i	$0.604101\pi$
$920$	−28.8679	−	9.30824i	−0.951747	−	0.306884i
$921$	−7.24914			−0.238867
$922$	−11.3516	−	37.4924i	−0.373845	−	1.23475i
$923$	2.77629	+	5.08440i	0.0913829	+	0.167355i
$924$	−38.9243	−	58.3875i	−1.28052	−	1.92081i
$925$	10.3180	−	9.89580i	0.339255	−	0.325372i
$926$	29.4061	−	29.9042i	0.966344	−	0.982712i
$927$	−22.8171	−	30.4800i	−0.749411	−	1.00110i
$928$	1.97866	+	2.09862i	0.0649528	+	0.0688904i
$929$	−8.58525	+	13.3589i	−0.281673	+	0.438292i	−0.953045	−	0.302829i	$-0.902069\pi$
$929$	−8.58525	+	13.3589i	−0.281673	+	0.438292i	0.671372	+	0.741121i	$0.265705\pi$
$930$	−10.2011	+	6.52641i	−0.334507	+	0.214009i
$931$	16.3254	−	7.45554i	0.535042	−	0.244346i
$932$	21.4675	−	40.9346i	0.703191	−	1.34086i
$933$	−15.1340	−	11.3292i	−0.495466	−	0.370902i
$934$	−7.48127	+	10.1707i	−0.244795	+	0.332797i
$935$	−0.294835	+	28.2327i	−0.00964214	+	0.923307i
$936$	9.37785	+	3.23108i	0.306525	+	0.105611i
$937$	−26.8849	+	1.92284i	−0.878291	+	0.0628166i	−0.503199	−	0.864171i	$-0.667844\pi$
$937$	−26.8849	+	1.92284i	−0.878291	+	0.0628166i	−0.375092	+	0.926987i	$0.622389\pi$
$938$	20.7928	+	5.91612i	0.678910	+	0.193168i
$939$	33.0166	+	38.1032i	1.07746	+	1.24345i
$940$	−16.9696	−	14.5165i	−0.553486	−	0.473476i
$941$	12.4941	−	27.3583i	0.407296	−	0.891854i	−0.589182	−	0.808000i	$-0.700550\pi$
$941$	12.4941	−	27.3583i	0.407296	−	0.891854i	0.996478	−	0.0838536i	$-0.0267228\pi$
$942$	20.0413	+	22.7403i	0.652982	+	0.740917i
$943$	14.2905	+	1.61403i	0.465362	+	0.0525601i
$944$	−11.2687	−	2.90149i	−0.366765	−	0.0944355i
$945$	−14.9085	+	0.909908i	−0.484974	+	0.0295993i
$946$	−16.4629	+	45.2969i	−0.535255	+	1.47273i
$947$	41.0805	+	2.93813i	1.33494	+	0.0954765i	0.720481	−	0.693475i	$-0.243921\pi$
$947$	41.0805	+	2.93813i	1.33494	+	0.0954765i	0.614455	+	0.788952i	$0.289376\pi$
$948$	−18.5216	+	52.3258i	−0.601552	+	1.69946i
$949$	−5.16261	−	4.47342i	−0.167585	−	0.145214i
$950$	−50.5838	−	0.631705i	−1.64116	−	0.0204952i
$951$	7.05703	+	24.0340i	0.228840	+	0.779357i
$952$	−0.547058	−	21.7100i	−0.0177302	−	0.703624i
$953$	18.8116	+	14.0822i	0.609368	+	0.456167i	0.858861	−	0.512210i	$-0.171173\pi$
$953$	18.8116	+	14.0822i	0.609368	+	0.456167i	−0.249493	+	0.968377i	$0.580264\pi$
$954$	−9.73085	−	25.4350i	−0.315048	−	0.823489i
$955$	24.5642	−	32.1095i	0.794879	−	1.03904i
$956$	−36.0950	+	0.606288i	−1.16740	+	0.0196088i
$957$	1.23322	+	5.66901i	0.0398643	+	0.183253i
$958$	16.5398	−	26.2179i	0.534376	−	0.847062i
$959$	2.99018	−	20.7971i	0.0965579	−	0.671575i
$960$	−7.29421	−	39.4697i	−0.235420	−	1.27388i
$961$	23.6283	−	15.1850i	0.762203	−	0.489838i
$962$	−6.90687	−	0.933927i	−0.222687	−	0.0301110i
$963$	8.18091	+	14.9822i	0.263626	+	0.482795i
$964$	−47.6376	−	29.4962i	−1.53430	−	0.950010i
$965$	−3.82776	+	12.5498i	−0.123220	+	0.403994i
$966$	32.0806	+	34.2483i	1.03218	+	1.10192i
$967$	7.66849	−	7.66849i	0.246602	−	0.246602i	−0.572973	−	0.819575i	$-0.694210\pi$
$967$	7.66849	−	7.66849i	0.246602	−	0.246602i	0.819575	+	0.572973i	$0.194210\pi$
$968$	−41.0358	+	6.95930i	−1.31894	+	0.223681i
$969$	11.2609	−	38.3510i	0.361752	−	1.23201i
$970$	48.4800	+	22.2600i	1.55660	+	0.714725i
$971$	6.78562	+	10.5586i	0.217761	+	0.338843i	0.932897	−	0.360142i	$-0.117272\pi$
$971$	6.78562	+	10.5586i	0.217761	+	0.338843i	−0.715136	+	0.698985i	$0.753635\pi$
$972$	1.97600	−	36.1516i	0.0633803	−	1.15956i
$973$	−25.8834	−	34.5762i	−0.829784	−	1.10846i
$974$	3.18099	+	14.0535i	0.101926	+	0.450305i
$975$	17.7537	−	7.66388i	0.568573	−	0.245441i
$976$	−3.39513	+	30.9647i	−0.108675	+	0.991157i
$977$	14.2476	−	38.1992i	0.455820	−	1.22210i	−0.482366	−	0.875970i	$-0.660222\pi$
$977$	14.2476	−	38.1992i	0.455820	−	1.22210i	0.938186	−	0.346132i	$-0.112505\pi$
$978$	−13.1681	+	29.4869i	−0.421068	+	0.942886i
$979$	13.3514	+	92.8607i	0.426711	+	2.96784i
$980$	10.9775	+	2.31506i	0.350662	+	0.0739520i
$981$	5.97072	−	1.75316i	0.190630	−	0.0559741i
$982$	−0.939909	+	0.615257i	−0.0299937	+	0.0196336i
$983$	36.2146	−	2.59012i	1.15507	−	0.0826119i	0.519368	−	0.854551i	$-0.326167\pi$
$983$	36.2146	−	2.59012i	1.15507	−	0.0826119i	0.635697	+	0.771939i	$0.280713\pi$
$984$	7.09772	+	17.6579i	0.226267	+	0.562914i
$985$	−7.18143	−	16.1699i	−0.228819	−	0.515215i
$986$	−0.613301	+	1.68747i	−0.0195315	+	0.0537399i
$987$	12.0738	+	32.3712i	0.384315	+	1.03039i
$988$	15.1090	+	19.4922i	0.480683	+	0.620128i
$989$	5.89273	−	31.6867i	0.187378	−	1.00758i
$990$	11.4643	−	30.5461i	0.364360	−	0.970820i
$991$	−27.3924	−	12.5097i	−0.870148	−	0.397383i	−0.0702573	−	0.997529i	$-0.522382\pi$
$991$	−27.3924	−	12.5097i	−0.870148	−	0.397383i	−0.799891	+	0.600146i	$0.795109\pi$
$992$	−1.77396	−	9.49044i	−0.0563233	−	0.301322i
$993$	40.3543	+	2.88620i	1.28061	+	0.0915908i
$994$	−12.8044	+	7.13198i	−0.406132	+	0.226213i
$995$	9.18524	−	40.1982i	0.291192	−	1.27437i
$996$	−16.8535	+	61.1806i	−0.534023	+	1.93858i
$997$	17.0846	+	9.32891i	0.541075	+	0.295450i	0.726451	−	0.687218i	$-0.241168\pi$
$997$	17.0846	+	9.32891i	0.541075	+	0.295450i	−0.185376	+	0.982668i	$0.559350\pi$
$998$	24.2891	−	3.70069i	0.768857	−	0.117143i
$999$	0.881467	+	6.13074i	0.0278884	+	0.193968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.42	yes	1360
4.3	odd	2	inner	460.2.w.a.167.27	yes	1360
5.3	odd	4	inner	460.2.w.a.443.62	yes	1360
20.3	even	4	inner	460.2.w.a.443.10	yes	1360
23.4	even	11	inner	460.2.w.a.27.10	✓	1360
92.27	odd	22	inner	460.2.w.a.27.62	yes	1360
115.73	odd	44	inner	460.2.w.a.303.27	yes	1360
460.303	even	44	inner	460.2.w.a.303.42	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.10	✓	1360	23.4	even	11	inner
460.2.w.a.27.62	yes	1360	92.27	odd	22	inner
460.2.w.a.167.27	yes	1360	4.3	odd	2	inner
460.2.w.a.167.42	yes	1360	1.1	even	1	trivial
460.2.w.a.303.27	yes	1360	115.73	odd	44	inner
460.2.w.a.303.42	yes	1360	460.303	even	44	inner
460.2.w.a.443.10	yes	1360	20.3	even	4	inner
460.2.w.a.443.62	yes	1360	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.409811 + 1.35353i) q^{2} +(1.07533 + 1.96932i) q^{3} +(-1.66411 + 1.10939i) q^{4} +(-1.09207 + 1.95125i) q^{5} +(-2.22487 + 2.26255i) q^{6} +(1.84794 + 2.46855i) q^{7} +(-2.18356 - 1.79779i) q^{8} +(-1.09998 + 1.71160i) q^{9} +O(q^{10})\)	\(q+(0.409811 + 1.35353i) q^{2} +(1.07533 + 1.96932i) q^{3} +(-1.66411 + 1.10939i) q^{4} +(-1.09207 + 1.95125i) q^{5} +(-2.22487 + 2.26255i) q^{6} +(1.84794 + 2.46855i) q^{7} +(-2.18356 - 1.79779i) q^{8} +(-1.09998 + 1.71160i) q^{9} +(-3.08863 - 0.678508i) q^{10} +(4.61278 - 2.10659i) q^{11} +(-3.97421 - 2.08421i) q^{12} +(1.37983 + 1.03293i) q^{13} +(-2.58397 + 3.51289i) q^{14} +(-5.01699 - 0.0523926i) q^{15} +(1.53852 - 3.69228i) q^{16} +(2.48362 - 0.177632i) q^{17} +(-2.76749 - 0.787425i) q^{18} +(-4.68500 - 5.40678i) q^{19} +(-0.347370 - 4.45862i) q^{20} +(-2.87424 + 6.29370i) q^{21} +(4.74171 + 5.38026i) q^{22} +(-3.71803 - 3.02924i) q^{23} +(1.19238 - 6.23337i) q^{24} +(-2.61477 - 4.26180i) q^{25} +(-0.832635 + 2.29095i) q^{26} +(2.16068 + 0.154535i) q^{27} +(-5.81375 - 2.05787i) q^{28} +(0.385342 + 0.333901i) q^{29} +(-1.98510 - 6.81213i) q^{30} +(-0.480846 - 1.63761i) q^{31} +(5.62813 + 0.569308i) q^{32} +(9.10883 + 6.81879i) q^{33} +(1.25825 + 3.28887i) q^{34} +(-6.83485 + 0.909960i) q^{35} +(-0.0683401 - 4.06859i) q^{36} +(0.607786 + 2.79395i) q^{37} +(5.39830 - 8.55706i) q^{38} +(-0.550395 + 3.82808i) q^{39} +(5.89255 - 2.29737i) q^{40} +(-2.52268 + 1.62123i) q^{41} +(-9.69664 - 1.31115i) q^{42} +(3.22075 + 5.89837i) q^{43} +(-5.33916 + 8.62295i) q^{44} +(-2.13851 - 4.01552i) q^{45} +(2.57649 - 6.27389i) q^{46} +(3.53092 - 3.53092i) q^{47} +(8.92573 - 0.940577i) q^{48} +(-0.706762 + 2.40701i) q^{49} +(4.69694 - 5.28572i) q^{50} +(3.02053 + 4.70004i) q^{51} +(-3.44211 - 0.188141i) q^{52} +(5.67194 + 7.57683i) q^{53} +(0.676301 + 2.98788i) q^{54} +(-0.926993 + 11.3012i) q^{55} +(0.402860 - 8.71245i) q^{56} +(5.60977 - 15.0404i) q^{57} +(-0.294029 + 0.658410i) q^{58} +(-0.414003 - 2.87945i) q^{59} +(8.40694 - 5.47859i) q^{60} +(-7.47212 + 2.19401i) q^{61} +(2.01951 - 1.32195i) q^{62} +(-6.25786 + 0.447571i) q^{63} +(1.53589 + 7.85118i) q^{64} +(-3.52238 + 1.56437i) q^{65} +(-5.49656 + 15.1235i) q^{66} +(-1.73239 - 4.64472i) q^{67} +(-3.93595 + 3.05089i) q^{68} +(1.96744 - 10.5794i) q^{69} +(-4.03266 - 8.87829i) q^{70} +(3.05723 + 1.39619i) q^{71} +(5.47897 - 1.75985i) q^{72} +(-3.95313 - 0.282733i) q^{73} +(-3.53263 + 1.96765i) q^{74} +(5.58113 - 9.73219i) q^{75} +(13.7946 + 3.80000i) q^{76} +(13.7244 + 7.49407i) q^{77} +(-5.40699 + 0.823810i) q^{78} +(-1.76030 - 12.2432i) q^{79} +(5.52440 + 7.03427i) q^{80} +(4.55470 + 9.97341i) q^{81} +(-3.22821 - 2.75014i) q^{82} +(-3.00592 - 13.8180i) q^{83} +(-2.19910 - 13.6621i) q^{84} +(-2.36568 + 5.04016i) q^{85} +(-6.66375 + 6.77662i) q^{86} +(-0.243188 + 1.11792i) q^{87} +(-13.8595 - 3.69296i) q^{88} +(-5.21213 + 17.7509i) q^{89} +(4.55875 - 4.54015i) q^{90} +5.31498i q^{91} +(9.54780 + 0.916260i) q^{92} +(2.70792 - 2.70792i) q^{93} +(6.22622 + 3.33221i) q^{94} +(15.6663 - 3.23704i) q^{95} +(4.93096 + 11.6958i) q^{96} +(-16.4840 - 3.58588i) q^{97} +(-3.54761 + 0.0297925i) q^{98} +(-1.46833 + 10.2124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

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