LMFDB - Embedded newform 125.2.h.a.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	125.109
Dual form			125.2.h.a.39.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0924748 + 0.732014i) q^{2} +(-1.70661 + 1.41183i) q^{3} +(1.40987 + 0.361994i) q^{4} +(2.23072 - 0.154513i) q^{5} +(-0.875660 - 1.37982i) q^{6} +(-2.87488 + 0.934106i) q^{7} +(-0.938590 + 2.37061i) q^{8} +(0.357107 - 1.87202i) q^{9} +O(q^{10})$	\(q+(-0.0924748 + 0.732014i) q^{2} +(-1.70661 + 1.41183i) q^{3} +(1.40987 + 0.361994i) q^{4} +(2.23072 - 0.154513i) q^{5} +(-0.875660 - 1.37982i) q^{6} +(-2.87488 + 0.934106i) q^{7} +(-0.938590 + 2.37061i) q^{8} +(0.357107 - 1.87202i) q^{9} +(-0.0931802 + 1.64721i) q^{10} +(-1.76238 - 0.222640i) q^{11} +(-2.91718 + 1.37272i) q^{12} +(3.74763 + 0.714899i) q^{13} +(-0.417924 - 2.19084i) q^{14} +(-3.58883 + 3.41309i) q^{15} +(0.902590 + 0.496203i) q^{16} +(-0.634082 - 2.46959i) q^{17} +(1.33732 + 0.434522i) q^{18} +(-1.15473 + 1.39583i) q^{19} +(3.20097 + 0.589665i) q^{20} +(3.58750 - 5.65300i) q^{21} +(0.325951 - 1.26950i) q^{22} +(6.08640 - 6.48136i) q^{23} +(-1.74509 - 5.37083i) q^{24} +(4.95225 - 0.689351i) q^{25} +(-0.869877 + 2.67721i) q^{26} +(-1.16757 - 2.12381i) q^{27} +(-4.39137 + 0.276281i) q^{28} +(-0.162497 - 2.58282i) q^{29} +(-2.16656 - 2.94269i) q^{30} +(8.08663 - 2.07629i) q^{31} +(-3.44399 + 4.74025i) q^{32} +(3.32202 - 2.10822i) q^{33} +(1.86641 - 0.235782i) q^{34} +(-6.26874 + 2.52794i) q^{35} +(1.18114 - 2.51004i) q^{36} +(-0.810526 + 1.47434i) q^{37} +(-0.914984 - 0.974359i) q^{38} +(-7.40506 + 4.07097i) q^{39} +(-1.72745 + 5.43320i) q^{40} +(-5.33550 + 5.01037i) q^{41} +(3.80632 + 3.14886i) q^{42} +(4.98522 + 6.86156i) q^{43} +(-2.40414 - 0.951866i) q^{44} +(0.507355 - 4.23114i) q^{45} +(4.18160 + 5.05469i) q^{46} +(-3.77950 - 9.54593i) q^{47} +(-2.24092 + 0.427479i) q^{48} +(1.72928 - 1.25640i) q^{49} +(0.0466558 + 3.68886i) q^{50} +(4.56876 + 3.31940i) q^{51} +(5.02490 + 2.36454i) q^{52} +(0.00179146 + 0.00113689i) q^{53} +(1.66263 - 0.658282i) q^{54} +(-3.96578 - 0.224338i) q^{55} +(0.483938 - 7.69197i) q^{56} -4.01243i q^{57} +(1.90568 + 0.119896i) q^{58} +(-4.16519 - 8.85147i) q^{59} +(-6.29531 + 3.51290i) q^{60} +(-4.96975 - 4.66690i) q^{61} +(0.772066 + 6.11153i) q^{62} +(0.722025 + 5.71542i) q^{63} +(-1.64978 - 1.54924i) q^{64} +(8.47039 + 1.01568i) q^{65} +(1.23604 + 2.62672i) q^{66} +(3.00266 + 0.188911i) q^{67} -3.71134i q^{68} +(-1.23653 + 19.6541i) q^{69} +(-1.27079 - 4.82257i) q^{70} +(-9.18523 + 3.63669i) q^{71} +(4.10265 + 2.60362i) q^{72} +(-6.61756 - 3.11399i) q^{73} +(-1.00428 - 0.729655i) q^{74} +(-7.47831 + 8.16819i) q^{75} +(-2.13331 + 1.54994i) q^{76} +(5.27461 - 1.00619i) q^{77} +(-2.29522 - 5.79707i) q^{78} +(3.35584 + 4.05651i) q^{79} +(2.09010 + 0.967430i) q^{80} +(10.3069 + 4.08079i) q^{81} +(-3.17426 - 4.36899i) q^{82} +(7.00117 + 5.79187i) q^{83} +(7.10428 - 6.67136i) q^{84} +(-1.79604 - 5.41099i) q^{85} +(-5.48376 + 3.01472i) q^{86} +(3.92382 + 4.17844i) q^{87} +(2.18195 - 3.96894i) q^{88} +(0.108067 - 0.229654i) q^{89} +(3.05033 + 0.762665i) q^{90} +(-11.4418 + 1.44544i) q^{91} +(10.9273 - 6.93466i) q^{92} +(-10.8693 + 14.9604i) q^{93} +(7.33726 - 1.88389i) q^{94} +(-2.36021 + 3.29214i) q^{95} +(-0.814876 - 12.9521i) q^{96} +(-18.5231 + 1.16538i) q^{97} +(0.759785 + 1.38204i) q^{98} +(-1.04615 + 3.21970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{27}{50}\right)$

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 $

$2$	−0.0924748	+	0.732014i	−0.0653896	+	0.517612i	0.925069	+	0.379800i	$0.124007\pi$
$2$	−0.0924748	+	0.732014i	−0.0653896	+	0.517612i	−0.990458	+	0.137812i	$0.955993\pi$
$3$	−1.70661	+	1.41183i	−0.985311	+	0.815120i	−0.982762	−	0.184877i	$-0.940811\pi$
$3$	−1.70661	+	1.41183i	−0.985311	+	0.815120i	−0.00254935	+	0.999997i	$0.500811\pi$
$4$	1.40987	+	0.361994i	0.704937	+	0.180997i
$5$	2.23072	−	0.154513i	0.997610	−	0.0691003i
$5$	2.23072	−	0.154513i	0.997610	−	0.0691003i
$6$	−0.875660	−	1.37982i	−0.357487	−	0.563309i
$7$	−2.87488	+	0.934106i	−1.08660	+	0.353059i	−0.796933	−	0.604067i	$-0.793546\pi$
$7$	−2.87488	+	0.934106i	−1.08660	+	0.353059i	−0.289671	+	0.957126i	$0.593546\pi$
$8$	−0.938590	+	2.37061i	−0.331842	+	0.838137i
$9$	0.357107	−	1.87202i	0.119036	−	0.624007i
$10$	−0.0931802	+	1.64721i	−0.0294662	+	0.520893i
$11$	−1.76238	−	0.222640i	−0.531377	−	0.0671286i	−0.144933	−	0.989441i	$-0.546297\pi$
$11$	−1.76238	−	0.222640i	−0.531377	−	0.0671286i	−0.386444	+	0.922313i	$0.626297\pi$
$12$	−2.91718	+	1.37272i	−0.842117	+	0.396270i
$13$	3.74763	+	0.714899i	1.03941	+	0.198277i	0.678710	−	0.734406i	$-0.262539\pi$
$13$	3.74763	+	0.714899i	1.03941	+	0.198277i	0.360696	+	0.932683i	$0.382539\pi$
$14$	−0.417924	−	2.19084i	−0.111695	−	0.585525i
$15$	−3.58883	+	3.41309i	−0.926631	+	0.881257i
$16$	0.902590	+	0.496203i	0.225648	+	0.124051i
$17$	−0.634082	−	2.46959i	−0.153787	−	0.598963i	−0.998015	−	0.0629775i	$-0.979940\pi$
$17$	−0.634082	−	2.46959i	−0.153787	−	0.598963i	0.844227	−	0.535985i	$-0.180060\pi$
$18$	1.33732	+	0.434522i	0.315210	+	0.102418i
$19$	−1.15473	+	1.39583i	−0.264914	+	0.320226i	−0.886151	−	0.463397i	$-0.846630\pi$
$19$	−1.15473	+	1.39583i	−0.264914	+	0.320226i	0.621237	+	0.783623i	$0.286630\pi$
$20$	3.20097	+	0.589665i	0.715759	+	0.131853i
$21$	3.58750	−	5.65300i	0.782857	−	1.23359i
$22$	0.325951	−	1.26950i	0.0694931	−	0.270658i
$23$	6.08640	−	6.48136i	1.26910	−	1.35146i	0.361080	−	0.932535i	$-0.382408\pi$
$23$	6.08640	−	6.48136i	1.26910	−	1.35146i	0.908022	−	0.418922i	$-0.137592\pi$
$24$	−1.74509	−	5.37083i	−0.356215	−	1.09632i
$25$	4.95225	−	0.689351i	0.990450	−	0.137870i
$26$	−0.869877	+	2.67721i	−0.170597	+	0.525044i
$27$	−1.16757	−	2.12381i	−0.224700	−	0.408728i
$28$	−4.39137	+	0.276281i	−0.829890	+	0.0522123i
$29$	−0.162497	−	2.58282i	−0.0301750	−	0.479617i	−0.983875	−	0.178858i	$-0.942760\pi$
$29$	−0.162497	−	2.58282i	−0.0301750	−	0.479617i	0.953700	−	0.300760i	$-0.0972402\pi$
$30$	−2.16656	−	2.94269i	−0.395557	−	0.537260i
$31$	8.08663	−	2.07629i	1.45240	−	0.372913i	0.561639	−	0.827382i	$-0.310171\pi$
$31$	8.08663	−	2.07629i	1.45240	−	0.372913i	0.890763	+	0.454469i	$0.150171\pi$
$32$	−3.44399	+	4.74025i	−0.608818	+	0.837966i
$33$	3.32202	−	2.10822i	0.578290	−	0.366994i
$34$	1.86641	−	0.235782i	0.320086	−	0.0404363i
$35$	−6.26874	+	2.52794i	−1.05961	+	0.427300i
$36$	1.18114	−	2.51004i	0.196856	−	0.418340i
$37$	−0.810526	+	1.47434i	−0.133250	+	0.242380i	−0.934511	−	0.355934i	$-0.884163\pi$
$37$	−0.810526	+	1.47434i	−0.133250	+	0.242380i	0.801261	+	0.598315i	$0.204163\pi$
$38$	−0.914984	−	0.974359i	−0.148430	−	0.158062i
$39$	−7.40506	+	4.07097i	−1.18576	+	0.651876i
$40$	−1.72745	+	5.43320i	−0.273133	+	0.859064i
$41$	−5.33550	+	5.01037i	−0.833265	+	0.782488i	−0.978356	−	0.206930i	$-0.933653\pi$
$41$	−5.33550	+	5.01037i	−0.833265	+	0.782488i	0.145090	+	0.989418i	$0.453653\pi$
$42$	3.80632	+	3.14886i	0.587328	+	0.485880i
$43$	4.98522	+	6.86156i	0.760238	+	1.04638i	0.997194	+	0.0748579i	$0.0238503\pi$
$43$	4.98522	+	6.86156i	0.760238	+	1.04638i	−0.236956	+	0.971520i	$0.576150\pi$
$44$	−2.40414	−	0.951866i	−0.362438	−	0.143499i
$45$	0.507355	−	4.23114i	0.0756321	−	0.630741i
$46$	4.18160	+	5.05469i	0.616544	+	0.745274i
$47$	−3.77950	−	9.54593i	−0.551297	−	1.39242i	−0.891910	−	0.452213i	$-0.850635\pi$
$47$	−3.77950	−	9.54593i	−0.551297	−	1.39242i	0.340613	−	0.940204i	$-0.389365\pi$
$48$	−2.24092	+	0.427479i	−0.323449	+	0.0617013i
$49$	1.72928	−	1.25640i	0.247041	−	0.179485i
$50$	0.0466558	+	3.68886i	0.00659813	+	0.521684i
$51$	4.56876	+	3.31940i	0.639755	+	0.464809i
$52$	5.02490	+	2.36454i	0.696828	+	0.327903i
$53$	0.00179146	+	0.00113689i	0.000246076	+	0.000156164i	0.535950	−	0.844250i	$-0.319954\pi$
$53$	0.00179146	+	0.00113689i	0.000246076	+	0.000156164i	−0.535704	+	0.844406i	$0.679954\pi$
$54$	1.66263	−	0.658282i	0.226255	−	0.0895808i
$55$	−3.96578	−	0.224338i	−0.534746	−	0.0302498i
$56$	0.483938	−	7.69197i	0.0646689	−	1.02788i
$57$		−	4.01243i		−	0.531459i
$58$	1.90568	+	0.119896i	0.250229	+	0.0157431i
$59$	−4.16519	−	8.85147i	−0.542261	−	1.15236i	−0.968788	−	0.247889i	$-0.920263\pi$
$59$	−4.16519	−	8.85147i	−0.542261	−	1.15236i	0.426527	−	0.904475i	$-0.359737\pi$
$60$	−6.29531	+	3.51290i	−0.812721	+	0.453513i
$61$	−4.96975	−	4.66690i	−0.636311	−	0.597536i	0.297753	−	0.954643i	$-0.403763\pi$
$61$	−4.96975	−	4.66690i	−0.636311	−	0.597536i	−0.934063	+	0.357108i	$0.883763\pi$
$62$	0.772066	+	6.11153i	0.0980524	+	0.776165i
$63$	0.722025	+	5.71542i	0.0909666	+	0.720075i
$64$	−1.64978	−	1.54924i	−0.206222	−	0.193656i
$65$	8.47039	+	1.01568i	1.05062	+	0.125980i
$66$	1.23604	+	2.62672i	0.152146	+	0.323327i
$67$	3.00266	+	0.188911i	0.366833	+	0.0230792i	0.245137	−	0.969488i	$-0.421167\pi$
$67$	3.00266	+	0.188911i	0.366833	+	0.0230792i	0.121695	+	0.992568i	$0.461167\pi$
$68$		−	3.71134i		−	0.450066i
$69$	−1.23653	+	19.6541i	−0.148861	+	2.36608i
$70$	−1.27079	−	4.82257i	−0.151888	−	0.576408i
$71$	−9.18523	+	3.63669i	−1.09009	+	0.431596i	−0.843283	−	0.537470i	$-0.819380\pi$
$71$	−9.18523	+	3.63669i	−1.09009	+	0.431596i	−0.246804	+	0.969066i	$0.579380\pi$
$72$	4.10265	+	2.60362i	0.483502	+	0.306840i
$73$	−6.61756	−	3.11399i	−0.774527	−	0.364465i	−0.00245270	−	0.999997i	$-0.500781\pi$
$73$	−6.61756	−	3.11399i	−0.774527	−	0.364465i	−0.772074	+	0.635532i	$0.780781\pi$
$74$	−1.00428	−	0.729655i	−0.116746	−	0.0848207i
$75$	−7.47831	+	8.16819i	−0.863521	+	0.943181i
$76$	−2.13331	+	1.54994i	−0.244708	+	0.177790i
$77$	5.27461	−	1.00619i	0.601097	−	0.114665i
$78$	−2.29522	−	5.79707i	−0.259883	−	0.656388i
$79$	3.35584	+	4.05651i	0.377561	+	0.456393i	0.924727	−	0.380631i	$-0.124293\pi$
$79$	3.35584	+	4.05651i	0.377561	+	0.456393i	−0.547166	+	0.837024i	$0.684293\pi$
$80$	2.09010	+	0.967430i	0.233680	+	0.108162i
$81$	10.3069	+	4.08079i	1.14521	+	0.453421i
$82$	−3.17426	−	4.36899i	−0.350538	−	0.482474i
$83$	7.00117	+	5.79187i	0.768478	+	0.635741i	0.936750	−	0.350000i	$-0.113818\pi$
$83$	7.00117	+	5.79187i	0.768478	+	0.635741i	−0.168271	+	0.985741i	$0.553818\pi$
$84$	7.10428	−	6.67136i	0.775141	−	0.727905i
$85$	−1.79604	−	5.41099i	−0.194808	−	0.586904i
$86$	−5.48376	+	3.01472i	−0.591329	+	0.325086i
$87$	3.92382	+	4.17844i	0.420677	+	0.447976i
$88$	2.18195	−	3.96894i	0.232596	−	0.423091i
$89$	0.108067	−	0.229654i	0.0114551	−	0.0243433i	−0.899018	−	0.437912i	$-0.855718\pi$
$89$	0.108067	−	0.229654i	0.0114551	−	0.0243433i	0.910473	+	0.413569i	$0.135718\pi$
$90$	3.05033	+	0.762665i	0.321533	+	0.0803919i
$91$	−11.4418	+	1.44544i	−1.19943	+	0.151523i
$92$	10.9273	−	6.93466i	1.13925	−	0.722988i
$93$	−10.8693	+	14.9604i	−1.12710	+	1.55132i
$94$	7.33726	−	1.88389i	0.756780	−	0.194308i
$95$	−2.36021	+	3.29214i	−0.242153	+	0.337766i
$96$	−0.814876	−	12.9521i	−0.0831679	−	1.32192i
$97$	−18.5231	+	1.16538i	−1.88074	+	0.118326i	−0.961403	−	0.275146i	$-0.911274\pi$
$97$	−18.5231	+	1.16538i	−1.88074	+	0.118326i	−0.919337	+	0.393472i	$0.871274\pi$
$98$	0.759785	+	1.38204i	0.0767499	+	0.139608i
$99$	−1.04615	+	3.21970i	−0.105142	+	0.323592i
$100$	7.23159	+	0.820788i	0.723159	+	0.0820788i
$101$	−4.28152	−	13.1772i	−0.426027	−	1.31118i	−0.902007	−	0.431721i	$-0.857907\pi$
$101$	−4.28152	−	13.1772i	−0.426027	−	1.31118i	0.475980	−	0.879456i	$-0.342093\pi$
$102$	−2.85234	+	3.03744i	−0.282424	+	0.300751i
$103$	0.584947	−	2.27822i	0.0576365	−	0.224479i	−0.933240	−	0.359254i	$-0.883031\pi$
$103$	0.584947	−	2.27822i	0.0576365	−	0.224479i	0.990876	+	0.134775i	$0.0430311\pi$
$104$	−5.21224	+	8.21317i	−0.511102	+	0.805368i
$105$	7.12926	−	13.1646i	0.695745	−	1.28473i
$106$	−0.000997887		0.00120624i	−9.69233e−5		0.000117160i
$107$	1.49574	+	0.485996i	0.144599	+	0.0469830i	0.380422	−	0.924813i	$-0.375779\pi$
$107$	1.49574	+	0.485996i	0.144599	+	0.0469830i	−0.235823	+	0.971796i	$0.575779\pi$
$108$	−0.877327	−	3.41696i	−0.0844208	−	0.328797i
$109$	14.0383	+	7.71763i	1.34463	+	0.739215i	0.981307	−	0.192449i	$-0.0616431\pi$
$109$	14.0383	+	7.71763i	1.34463	+	0.739215i	0.363320	+	0.931664i	$0.381643\pi$
$110$	0.530954	−	2.88226i	0.0506245	−	0.274813i
$111$	−0.698268	−	3.66045i	−0.0662766	−	0.347434i
$112$	−3.05835	−	0.583411i	−0.288987	−	0.0551272i
$113$	−7.71147	+	3.62874i	−0.725434	+	0.341363i	−0.752789	−	0.658262i	$-0.771292\pi$
$113$	−7.71147	+	3.62874i	−0.725434	+	0.341363i	0.0273545	+	0.999626i	$0.491292\pi$
$114$	2.93715	+	0.371048i	0.275089	+	0.0347519i
$115$	12.5756	−	15.3985i	1.17268	−	1.43592i
$116$	0.705864	−	3.70027i	0.0655379	−	0.343562i
$117$	2.67661	−	6.76035i	0.247453	−	0.624994i
$118$	6.86457	−	2.23043i	0.631935	−	0.205328i
$119$	4.12977	+	6.50747i	0.378575	+	0.596539i
$120$	−4.72267	−	11.7112i	−0.431119	−	1.06908i
$121$	−7.59800	−	1.95084i	−0.690727	−	0.177349i
$122$	3.87581	−	3.20635i	0.350899	−	0.290289i
$123$	2.03183	−	16.0836i	0.183204	−	1.45021i
$124$	12.1527			1.09135
$125$	10.9406	−	2.30294i	0.978556	−	0.205981i
$126$	−4.25053			−0.378667
$127$	−1.49565	+	11.8393i	−0.132718	+	1.05057i	0.775287	+	0.631609i	$0.217605\pi$
$127$	−1.49565	+	11.8393i	−0.132718	+	1.05057i	−0.908005	+	0.418960i	$0.862395\pi$
$128$	−7.74266	+	6.40529i	−0.684361	+	0.566153i
$129$	−18.1952	−	4.67173i	−1.60200	−	0.411323i
$130$	−1.52679	+	6.10652i	−0.133909	+	0.535577i
$131$	8.38691	+	13.2157i	0.732767	+	1.15466i	0.982486	+	0.186338i	$0.0596620\pi$
$131$	8.38691	+	13.2157i	0.732767	+	1.15466i	−0.249718	+	0.968319i	$0.580338\pi$
$132$	5.44680	−	1.76977i	0.474083	−	0.154039i
$133$	2.01587	−	5.09150i	0.174798	−	0.441489i
$134$	−0.415955	+	2.18051i	−0.0359331	+	0.188368i
$135$	−2.93269	−	4.55723i	−0.252406	−	0.392224i
$136$	6.44956	+	0.814769i	0.553046	+	0.0698659i
$137$	−1.34908	+	0.634828i	−0.115260	+	0.0542370i	−0.482545	−	0.875871i	$-0.660287\pi$
$137$	−1.34908	+	0.634828i	−0.115260	+	0.0542370i	0.367285	+	0.930108i	$0.380287\pi$
$138$	−14.2727	−	2.72267i	−1.21498	−	0.231769i
$139$	−2.06179	−	10.8083i	−0.174879	−	0.916748i	−0.956221	−	0.292645i	$-0.905465\pi$
$139$	−2.06179	−	10.8083i	−0.174879	−	0.916748i	0.781342	−	0.624103i	$-0.214535\pi$
$140$	−9.75323	+	1.29483i	−0.824298	+	0.109433i
$141$	19.9274	+	10.9552i	1.67819	+	0.922590i
$142$	−1.81270	−	7.06002i	−0.152119	−	0.592464i
$143$	−6.44559	−	2.09430i	−0.539007	−	0.175134i
$144$	1.25122	−	1.51247i	0.104269	−	0.126039i
$145$	−0.761565	−	5.73644i	−0.0632445	−	0.476386i
$146$	2.89144	−	4.55618i	0.239297	−	0.377072i
$147$	−1.17739	+	4.58563i	−0.0971095	+	0.378217i
$148$	−1.67644	+	1.78523i	−0.137803	+	0.146745i
$149$	0.140060	+	0.431059i	0.0114741	+	0.0353138i	0.956630	−	0.291307i	$-0.0940901\pi$
$149$	0.140060	+	0.431059i	0.0114741	+	0.0353138i	−0.945156	+	0.326621i	$0.894090\pi$
$150$	−5.28767	−	6.22958i	−0.431736	−	0.508643i
$151$	−5.23454	+	16.1103i	−0.425981	+	1.31103i	0.476071	+	0.879407i	$0.342061\pi$
$151$	−5.23454	+	16.1103i	−0.425981	+	1.31103i	−0.902052	+	0.431628i	$0.857939\pi$
$152$	−2.22515	−	4.04753i	−0.180484	−	0.328298i
$153$	−4.84955	+	0.305108i	−0.392063	+	0.0246665i
$154$	0.248773	+	3.95413i	0.0200467	+	0.318633i
$155$	17.7182	−	5.88113i	1.42316	−	0.472383i
$156$	−11.9139	+	3.05896i	−0.953873	+	0.244913i
$157$	8.45757	−	11.6408i	0.674988	−	0.929041i	−0.324873	−	0.945758i	$-0.605321\pi$
$157$	8.45757	−	11.6408i	0.674988	−	0.929041i	0.999860	+	0.0167170i	$0.00532142\pi$
$158$	−3.27975	+	2.08139i	−0.260923	+	0.165587i
$159$	−0.00466242		0.000589001i	−0.000369754		4.67108e-5i
$160$	−6.95016	+	11.1063i	−0.549459	+	0.878032i
$161$	−11.4434	+	24.3185i	−0.901868	+	1.91657i
$162$	−3.94032	+	7.16742i	−0.309581	+	0.563125i
$163$	−6.95043	−	7.40146i	−0.544400	−	0.579727i	0.396660	−	0.917965i	$-0.370169\pi$
$163$	−6.95043	−	7.40146i	−0.544400	−	0.579727i	−0.941061	+	0.338238i	$0.890169\pi$
$164$	−9.33611	+	5.13257i	−0.729028	+	0.400786i
$165$	7.08477	−	5.21615i	0.551548	−	0.406077i
$166$	−4.88716	+	4.58935i	−0.379317	+	0.356203i
$167$	−0.849291	−	0.702595i	−0.0657201	−	0.0543684i	0.603984	−	0.796996i	$-0.293579\pi$
$167$	−0.849291	−	0.702595i	−0.0657201	−	0.0543684i	−0.669704	+	0.742628i	$0.733579\pi$
$168$	10.0339	+	13.8104i	0.774129	+	1.06550i
$169$	1.44657	+	0.572739i	0.111275	+	0.0440568i
$170$	4.12701	−	0.814348i	0.316527	−	0.0624577i
$171$	2.20066	+	2.66014i	0.168289	+	0.203426i
$172$	4.54468	+	11.4786i	0.346529	+	0.875232i
$173$	−1.83653	+	0.350336i	−0.139629	+	0.0266356i	−0.256722	−	0.966485i	$-0.582642\pi$
$173$	−1.83653	+	0.350336i	−0.139629	+	0.0266356i	0.117093	+	0.993121i	$0.462642\pi$
$174$	−3.42153	+	2.48589i	−0.259386	+	0.188455i
$175$	−13.5932	+	6.60773i	−1.02755	+	0.499498i
$176$	−1.48023	−	1.07545i	−0.111577	−	0.0810652i
$177$	19.6051	+	9.22547i	1.47361	+	0.693429i
$178$	0.158117	+	0.100344i	0.0118513	+	0.00752109i
$179$	3.28814	−	1.30187i	0.245767	−	0.0973061i	−0.242012	−	0.970273i	$-0.577807\pi$
$179$	3.28814	−	1.30187i	0.245767	−	0.0973061i	0.487779	+	0.872967i	$0.337807\pi$
$180$	2.24695	−	5.78171i	0.167478	−	0.430943i
$181$	0.0588018	−	0.934628i	0.00437070	−	0.0694704i	−0.995237	−	0.0974877i	$-0.968919\pi$
$181$	0.0588018	−	0.934628i	0.00437070	−	0.0694704i	0.999607	+	0.0280173i	$0.00891935\pi$
$182$		−	8.50922i		−	0.630745i
$183$	15.0703	+	0.948142i	1.11403	+	0.0700887i
$184$	9.65213	+	20.5118i	0.711564	+	1.51215i
$185$	−1.58025	+	3.41408i	−0.116183	+	0.251008i
$186$	−9.94605	−	9.33996i	−0.729280	−	0.684839i
$187$	0.567664	+	4.49352i	0.0415117	+	0.328599i
$188$	−1.87305	−	14.8267i	−0.136606	−	1.08135i
$189$	5.34051	+	5.01507i	0.388465	+	0.364793i
$190$	−2.19163	−	2.03215i	−0.158997	−	0.147428i
$191$	6.76524	+	14.3769i	0.489516	+	1.04027i	0.985143	+	0.171738i	$0.0549383\pi$
$191$	6.76524	+	14.3769i	0.489516	+	1.04027i	−0.495627	+	0.868535i	$0.665062\pi$
$192$	5.00279	+	0.314749i	0.361046	+	0.0227151i
$193$		−	27.2674i		−	1.96275i	−0.192101	−	0.981375i	$-0.561530\pi$
$193$		−	27.2674i		−	1.96275i	0.192101	−	0.981375i	$-0.438470\pi$
$194$	0.859852	−	13.6670i	0.0617338	−	0.981230i
$195$	−15.8896	+	10.2254i	−1.13788	+	0.732254i
$196$	2.89288	−	1.14537i	0.206634	−	0.0818123i
$197$	3.69076	+	2.34223i	0.262956	+	0.166877i	0.660768	−	0.750590i	$-0.270231\pi$
$197$	3.69076	+	2.34223i	0.262956	+	0.166877i	−0.397812	+	0.917467i	$0.630231\pi$
$198$	−2.26013	−	1.06353i	−0.160620	−	0.0755821i
$199$	−22.6182	−	16.4331i	−1.60336	−	1.16491i	−0.880661	−	0.473748i	$-0.842901\pi$
$199$	−22.6182	−	16.4331i	−1.60336	−	1.16491i	−0.722700	−	0.691162i	$-0.757099\pi$
$200$	−3.01395	+	12.3869i	−0.213119	+	0.875884i
$201$	−5.39107	+	3.91684i	−0.380257	+	0.276273i
$202$	10.0418	−	1.91557i	0.706538	−	0.134779i
$203$	2.87979	+	7.27351i	0.202121	+	0.510500i
$204$	5.23978	+	6.33380i	0.366858	+	0.443455i
$205$	−11.1279	+	12.0011i	−0.777203	+	0.838197i
$206$	1.61359	+	0.638867i	0.112424	+	0.0445119i
$207$	−9.95974	−	13.7084i	−0.692250	−	0.952800i
$208$	3.02784	+	2.50485i	0.209943	+	0.173680i
$209$	2.34585	−	2.20290i	0.162266	−	0.152378i
$210$	8.97738	+	6.43611i	0.619498	+	0.444134i
$211$	13.1567	−	7.23295i	0.905744	−	0.497937i	0.0404384	−	0.999182i	$-0.487125\pi$
$211$	13.1567	−	7.23295i	0.905744	−	0.497937i	0.865305	+	0.501245i	$0.167125\pi$
$212$	0.00211418	+	0.00225138i	0.000145203	+	0.000154625i
$213$	10.5412	−	19.1744i	0.722272	−	1.31381i
$214$	−0.494075	+	1.04996i	−0.0337742	+	0.0717739i
$215$	12.1808	+	14.5360i	0.830726	+	0.991344i
$216$	6.13060	−	0.774475i	0.417134	−	0.0526963i
$217$	−21.3086	+	13.5229i	−1.44653	+	0.917993i
$218$	−6.94760	+	9.56255i	−0.470551	+	0.647658i
$219$	15.6900	−	4.02851i	1.06023	−	0.272221i
$220$	−5.51004	−	1.75188i	−0.371487	−	0.118112i
$221$	−0.610801	−	9.70840i	−0.0410869	−	0.653058i
$222$	2.74407	−	0.172642i	0.184170	−	0.0115870i
$223$	9.61204	+	17.4842i	0.643670	+	1.17083i	0.973910	+	0.226934i	$0.0728701\pi$
$223$	9.61204	+	17.4842i	0.643670	+	1.17083i	−0.330241	+	0.943897i	$0.607130\pi$
$224$	5.47318	−	16.8447i	0.365692	−	1.12549i
$225$	0.478004	−	9.51689i	0.0318669	−	0.634459i
$226$	−1.94317	−	5.98047i	−0.129258	−	0.397815i
$227$	5.64971	−	6.01633i	0.374985	−	0.399318i	−0.513601	−	0.858029i	$-0.671689\pi$
$227$	5.64971	−	6.01633i	0.374985	−	0.399318i	0.888585	+	0.458711i	$0.151689\pi$
$228$	1.45247	−	5.65701i	0.0961925	−	0.374645i
$229$	−9.13369	+	14.3924i	−0.603571	+	0.951076i	0.395891	+	0.918297i	$0.370436\pi$
$229$	−9.13369	+	14.3924i	−0.603571	+	0.951076i	−0.999463	+	0.0327790i	$0.989564\pi$
$230$	10.1090	+	10.6295i	0.666569	+	0.700889i
$231$	−7.58113	+	9.16401i	−0.498802	+	0.602948i
$232$	6.27537	+	2.03899i	0.411998	+	0.133866i
$233$	−0.231656	−	0.902240i	−0.0151763	−	0.0591077i	0.960544	−	0.278128i	$-0.0897139\pi$
$233$	−0.231656	−	0.902240i	−0.0151763	−	0.0591077i	−0.975720	+	0.219020i	$0.929714\pi$
$234$	4.70115	+	2.58448i	0.307324	+	0.168953i
$235$	−9.90599	−	20.7103i	−0.646195	−	1.35099i
$236$	−2.66821	−	13.9872i	−0.173686	−	0.910491i
$237$	−11.4542	−	2.18501i	−0.744031	−	0.141931i
$238$	−5.14546	+	2.42127i	−0.333530	+	0.156948i
$239$	−13.4192	−	1.69524i	−0.868014	−	0.109656i	−0.321303	−	0.946977i	$-0.604121\pi$
$239$	−13.4192	−	1.69524i	−0.868014	−	0.109656i	−0.546712	+	0.837321i	$0.684121\pi$
$240$	−4.93283	+	1.29984i	−0.318413	+	0.0839042i
$241$	3.39916	−	17.8190i	0.218959	−	1.14783i	−0.687711	−	0.725985i	$-0.741384\pi$
$241$	3.39916	−	17.8190i	0.218959	−	1.14783i	0.906670	−	0.421840i	$-0.138616\pi$
$242$	2.13066	−	5.38144i	0.136964	−	0.345932i
$243$	−16.4363	+	5.34047i	−1.05439	+	0.342592i
$244$	−5.31732	−	8.37876i	−0.340407	−	0.536395i
$245$	3.66342	−	3.06987i	0.234048	−	0.196127i
$246$	11.5855	+	2.97465i	0.738664	+	0.189657i
$247$	−5.32539	+	4.40555i	−0.338847	+	0.280318i
$248$	−2.66795	+	21.1190i	−0.169415	+	1.34106i
$249$	−20.1254			−1.27540
$250$	0.674053	+	8.22162i	0.0426309	+	0.519981i
$251$	0.155589			0.00982068			0.00491034	−	0.999988i	$-0.498437\pi$
$251$	0.155589			0.00982068			0.00491034	+	0.999988i	$0.498437\pi$
$252$	−1.05098	+	8.31939i	−0.0662057	+	0.524072i
$253$	−12.1696	+	10.0675i	−0.765094	+	0.632941i
$254$	−8.52823	−	2.18968i	−0.535108	−	0.137393i
$255$	10.7045	+	6.69873i	0.670344	+	0.419491i
$256$	−6.39809	−	10.0818i	−0.399880	−	0.630111i
$257$	12.7915	−	4.15620i	0.797910	−	0.259257i	0.118441	−	0.992961i	$-0.462210\pi$
$257$	12.7915	−	4.15620i	0.797910	−	0.259257i	0.679469	+	0.733704i	$0.262210\pi$
$258$	5.10236	−	12.8871i	0.317659	−	0.802315i
$259$	0.952976	−	4.99568i	0.0592150	−	0.310416i
$260$	11.5745	+	4.49822i	0.717821	+	0.278968i
$261$	−4.89312	−	0.618144i	−0.302876	−	0.0382622i
$262$	−10.4496	+	4.91721i	−0.645579	+	0.303787i
$263$	−9.93854	−	1.89588i	−0.612837	−	0.116905i	−0.128387	−	0.991724i	$-0.540980\pi$
$263$	−9.93854	−	1.89588i	−0.612837	−	0.116905i	−0.484449	+	0.874819i	$0.660980\pi$
$264$	1.87975	+	9.85397i	0.115690	+	0.606470i
$265$	0.00417191	+	0.00225929i	0.000256279	+	0.000138787i
$266$	3.54063	+	1.94648i	0.217090	+	0.119346i
$267$	0.139805	+	0.544503i	0.00855590	+	0.0333230i
$268$	4.16498	+	1.35328i	0.254417	+	0.0826650i
$269$	8.47608	−	10.2458i	0.516796	−	0.624699i	−0.445966	−	0.895050i	$-0.647140\pi$
$269$	8.47608	−	10.2458i	0.516796	−	0.624699i	0.962762	+	0.270351i	$0.0871398\pi$
$270$	3.60715	−	1.72534i	0.219524	−	0.105001i
$271$	8.76784	−	13.8159i	0.532608	−	0.839256i	−0.466364	−	0.884593i	$-0.654436\pi$
$271$	8.76784	−	13.8159i	0.532608	−	0.839256i	0.998972	+	0.0453370i	$0.0144362\pi$
$272$	0.653100	−	2.54366i	0.0396000	−	0.154232i
$273$	17.4860	−	18.6207i	1.05830	−	1.12697i
$274$	−0.339947	−	1.04625i	−0.0205369	−	0.0632062i
$275$	−8.88122	+	0.112328i	−0.535558	+	0.00677361i
$276$	−8.85803	+	27.2622i	−0.533191	+	1.64099i
$277$	0.507752	+	0.923598i	0.0305079	+	0.0554936i	0.891121	−	0.453765i	$-0.149920\pi$
$277$	0.507752	+	0.923598i	0.0305079	+	0.0554936i	−0.860613	+	0.509259i	$0.829920\pi$
$278$	8.10249	−	0.509765i	0.485955	−	0.0305737i
$279$	−0.999072	−	15.8798i	−0.0598129	−	0.950699i
$280$	−0.108978	−	17.2334i	−0.00651266	−	1.02989i
$281$	5.55694	−	1.42678i	0.331499	−	0.0851146i	−0.0792718	−	0.996853i	$-0.525260\pi$
$281$	5.55694	−	1.42678i	0.331499	−	0.0851146i	0.410771	+	0.911738i	$0.365260\pi$
$282$	−9.86210	+	13.5740i	−0.587279	+	0.808321i
$283$	−10.1827	+	6.46217i	−0.605301	+	0.384136i	−0.802871	−	0.596153i	$-0.796695\pi$
$283$	−10.1827	+	6.46217i	−0.605301	+	0.384136i	0.197570	+	0.980289i	$0.436695\pi$
$284$	−14.2665	+	1.80228i	−0.846560	+	0.106945i
$285$	−0.619972	−	8.95061i	−0.0367239	−	0.530188i
$286$	2.12911	−	4.52459i	0.125897	−	0.267544i
$287$	10.6587	−	19.3882i	0.629165	−	1.14445i
$288$	7.64397	+	8.14000i	0.450425	+	0.479654i
$289$	9.20042	−	5.05797i	0.541201	−	0.297528i
$290$	4.26958	−	0.0269992i	0.250718	−	0.00158545i
$291$	29.9664	−	28.1404i	1.75666	−	1.64962i
$292$	−8.20268	−	6.78585i	−0.480026	−	0.397112i
$293$	18.1027	+	24.9163i	1.05757	+	1.45562i	0.882055	+	0.471147i	$0.156160\pi$
$293$	18.1027	+	24.9163i	1.05757	+	1.45562i	0.175517	+	0.984476i	$0.443840\pi$
$294$	−3.24787	−	1.28592i	−0.189419	−	0.0749965i
$295$	−10.6590	−	19.1016i	−0.620594	−	1.11214i
$296$	−2.73433	−	3.30524i	−0.158930	−	0.192113i
$297$	1.58486	+	4.00291i	0.0919632	+	0.232272i
$298$	−0.328493	+	0.0626634i	−0.0190291	+	0.00363000i
$299$	27.4431	−	19.9386i	1.58708	−	1.15308i
$300$	−13.5003	+	8.80901i	−0.779441	+	0.508589i
$301$	−20.7413	−	15.0695i	−1.19551	−	0.868590i
$302$	−11.3089	−	5.32155i	−0.650752	−	0.306221i
$303$	25.9108	+	16.4435i	1.48854	+	0.944654i
$304$	−1.73487	+	0.686882i	−0.0995015	+	0.0393954i
$305$	−11.8072	−	9.64268i	−0.676080	−	0.552138i
$306$	0.225118	−	3.57815i	0.0128692	−	0.204549i
$307$			4.39954i			0.251095i	0.992088	+	0.125547i	$0.0400687\pi$
$307$			4.39954i			0.251095i	−0.992088	+	0.125547i	$0.959931\pi$
$308$	7.80076	+	0.490782i	0.444490	+	0.0279649i
$309$	2.21818	+	4.71387i	0.126188	+	0.268163i
$310$	2.66657	+	13.5138i	0.151451	+	0.767534i
$311$	−7.54574	−	7.08592i	−0.427880	−	0.401806i	0.440463	−	0.897771i	$-0.354814\pi$
$311$	−7.54574	−	7.08592i	−0.427880	−	0.401806i	−0.868342	+	0.495965i	$0.834814\pi$
$312$	−2.70035	−	21.3755i	−0.152877	−	1.21015i
$313$	0.701659	+	5.55420i	0.0396601	+	0.313942i	0.999448	+	0.0332164i	$0.0105751\pi$
$313$	0.701659	+	5.55420i	0.0396601	+	0.313942i	−0.959788	+	0.280725i	$0.909425\pi$
$314$	7.73915	+	7.26754i	0.436745	+	0.410131i
$315$	2.49374	+	12.6380i	0.140507	+	0.712068i
$316$	3.26288	+	6.93397i	0.183551	+	0.390066i
$317$	4.74762	+	0.298695i	0.266653	+	0.0167764i	0.195554	−	0.980693i	$-0.437349\pi$
$317$	4.74762	+	0.298695i	0.266653	+	0.0167764i	0.0710988	+	0.997469i	$0.477349\pi$
$318$		−	0.00346742i		−	0.000194443i
$319$	−0.288658	+	4.58808i	−0.0161617	+	0.256883i
$320$	−3.91958	−	3.20102i	−0.219111	−	0.178943i
$321$	−3.23879	+	1.28233i	−0.180772	+	0.0715726i
$322$	−16.7432	−	10.6256i	−0.933065	−	0.592141i
$323$	4.17932	+	1.96664i	0.232544	+	0.109427i
$324$	13.0542	+	9.48443i	0.725233	+	0.526913i
$325$	19.0520	+	0.956925i	1.05682	+	0.0530807i
$326$	6.06071	−	4.40336i	0.335672	−	0.243880i
$327$	−34.8539	+	6.64874i	−1.92743	+	0.367676i
$328$	−6.86977	−	17.3511i	−0.379320	−	0.958052i
$329$	19.7825	+	23.9130i	1.09065	+	1.31837i
$330$	3.16313	+	5.66851i	0.174125	+	0.312041i
$331$	20.7621	+	8.22030i	1.14119	+	0.451829i	0.861246	−	0.508188i	$-0.169684\pi$
$331$	20.7621	+	8.22030i	1.14119	+	0.451829i	0.279943	+	0.960017i	$0.409684\pi$
$332$	7.77415	+	10.7002i	0.426662	+	0.587249i
$333$	2.47055	+	2.04382i	0.135385	+	0.112001i
$334$	0.592847	−	0.556720i	0.0324391	−	0.0304624i
$335$	6.72728	−	0.0425408i	0.367551	−	0.00232425i
$336$	6.04308	−	3.32221i	0.329677	−	0.181242i
$337$	10.8386	+	11.5419i	0.590414	+	0.628727i	0.952908	−	0.303259i	$-0.0980748\pi$
$337$	10.8386	+	11.5419i	0.590414	+	0.628727i	−0.362494	+	0.931986i	$0.618075\pi$
$338$	−0.553024	+	1.00595i	−0.0300806	+	0.0547163i
$339$	8.03730	−	17.0801i	0.436526	−	0.927665i
$340$	−0.573450	−	8.27897i	−0.0310997	−	0.448990i
$341$	−14.7140	+	1.85881i	−0.796807	+	0.100660i
$342$	−2.15077	+	1.36492i	−0.116300	+	0.0738064i
$343$	8.63955	−	11.8913i	0.466492	−	0.642071i
$344$	−20.9452	+	5.37780i	−1.12929	+	0.289952i
$345$	0.278454	+	44.0339i	0.0149915	+	2.37071i
$346$	−0.0866184	−	1.37676i	−0.00465664	−	0.0740151i
$347$	−15.2636	+	0.960303i	−0.819392	+	0.0515517i	−0.466952	−	0.884283i	$-0.654648\pi$
$347$	−15.2636	+	0.960303i	−0.819392	+	0.0515517i	−0.352440	+	0.935835i	$0.614648\pi$
$348$	4.01952	+	7.31148i	0.215469	+	0.391936i
$349$	−8.57536	+	26.3922i	−0.459028	+	1.41274i	0.407312	+	0.913289i	$0.366466\pi$
$349$	−8.57536	+	26.3922i	−0.459028	+	1.41274i	−0.866340	+	0.499455i	$0.833534\pi$
$350$	−3.57992	−	10.5615i	−0.191355	−	0.564534i
$351$	−2.85733	−	8.79396i	−0.152513	−	0.469387i
$352$	7.12499	−	7.58735i	0.379763	−	0.404407i
$353$	−5.56882	+	21.6891i	−0.296399	+	1.15440i	0.629616	+	0.776907i	$0.283212\pi$
$353$	−5.56882	+	21.6891i	−0.296399	+	1.15440i	−0.926014	+	0.377489i	$0.876788\pi$
$354$	−8.56615	+	13.4981i	−0.455286	+	0.717415i
$355$	−19.9278	+	9.53169i	−1.05766	+	0.505890i
$356$	0.235495	−	0.284664i	0.0124812	−	0.0150872i
$357$	−16.2353	−	5.27518i	−0.859265	−	0.279192i
$358$	0.648914	+	2.52735i	0.0342962	+	0.133575i
$359$	−28.3235	−	15.5710i	−1.49486	−	0.821804i	−0.495941	−	0.868356i	$-0.665177\pi$
$359$	−28.3235	−	15.5710i	−1.49486	−	0.821804i	−0.998916	+	0.0465520i	$0.985177\pi$
$360$	9.55417	+	5.17405i	0.503549	+	0.272696i
$361$	2.94531	+	15.4398i	0.155016	+	0.812623i
$362$	0.678723	+	0.129473i	0.0356729	+	0.00680496i
$363$	15.7211	−	7.39777i	0.825142	−	0.388282i
$364$	−16.6547	−	2.10398i	−0.872945	−	0.110279i
$365$	−15.2431	−	5.92395i	−0.797860	−	0.310074i
$366$	−2.08767	+	10.9440i	−0.109124	+	0.572051i
$367$	−6.45184	+	16.2955i	−0.336783	+	0.850618i	0.658407	+	0.752662i	$0.271230\pi$
$367$	−6.45184	+	16.2955i	−0.336783	+	0.850618i	−0.995191	+	0.0979559i	$0.968770\pi$
$368$	8.70960	−	2.82992i	0.454019	−	0.147520i
$369$	7.47417	+	11.7774i	0.389090	+	0.613107i
$370$	−2.35302	−	1.47248i	−0.122328	−	0.0765508i
$371$	−0.00621222	−	0.00159503i	−0.000322522	−	8.28096e-5i
$372$	−20.7400	+	17.1576i	−1.07532	+	0.889580i
$373$	0.468353	−	3.70740i	0.0242504	−	0.191962i	−0.975336	−	0.220726i	$-0.929157\pi$
$373$	0.468353	−	3.70740i	0.0242504	−	0.191962i	0.999586	+	0.0287644i	$0.00915726\pi$
$374$	−3.34181			−0.172801
$375$	−15.4199	+	19.3765i	−0.796283	+	1.00060i
$376$	26.1771			1.34998
$377$	1.23747	−	9.79562i	0.0637332	−	0.504500i
$378$	−4.16496	+	3.44556i	−0.214223	+	0.177220i
$379$	−1.73583	−	0.445685i	−0.0891634	−	0.0228933i	0.203845	−	0.979003i	$-0.434656\pi$
$379$	−1.73583	−	0.445685i	−0.0891634	−	0.0228933i	−0.293008	+	0.956110i	$0.594656\pi$
$380$	−4.51934	+	3.78711i	−0.231837	+	0.194275i
$381$	−14.1626	−	22.3167i	−0.725572	−	1.14332i
$382$	−11.1497	+	3.62275i	−0.570467	+	0.185356i
$383$	−6.82282	+	17.2325i	−0.348630	+	0.880539i	0.644615	+	0.764507i	$0.277018\pi$
$383$	−6.82282	+	17.2325i	−0.348630	+	0.880539i	−0.993245	+	0.116032i	$0.962982\pi$
$384$	4.17052	−	21.8626i	0.212826	−	1.11567i
$385$	11.6107	−	3.05952i	0.591737	−	0.155927i
$386$	19.9601	+	2.52155i	1.01594	+	0.128343i
$387$	14.6252	−	6.88212i	0.743443	−	0.349838i
$388$	−26.5371	−	5.06223i	−1.34722	−	0.256996i
$389$	−2.16608	−	11.3550i	−0.109824	−	0.575720i	−0.994074	−	0.108705i	$-0.965330\pi$
$389$	−2.16608	−	11.3550i	−0.109824	−	0.575720i	0.884250	−	0.467015i	$-0.154670\pi$
$390$	−6.01572	−	12.5770i	−0.304618	−	0.636861i
$391$	−19.8656	−	10.9212i	−1.00464	−	0.552308i
$392$	1.35534	+	5.27870i	0.0684550	+	0.266614i
$393$	−32.9714	−	10.7131i	−1.66319	−	0.540403i
$394$	−2.05585	+	2.48509i	−0.103572	+	0.125197i
$395$	8.11273	+	8.53044i	0.408196	+	0.429213i
$396$	−2.64045	+	4.16068i	−0.132687	+	0.209082i
$397$	2.65378	−	10.3358i	0.133189	−	0.518738i	−0.866615	−	0.498977i	$-0.833709\pi$
$397$	2.65378	−	10.3358i	0.133189	−	0.518738i	0.999805	−	0.0197613i	$-0.00629063\pi$
$398$	14.1208	−	15.0372i	0.707814	−	0.753745i
$399$	3.74803	+	11.5353i	0.187636	+	0.577485i
$400$	4.81191	+	1.83512i	0.240596	+	0.0917561i
$401$	0.469076	−	1.44367i	0.0234245	−	0.0720933i	−0.938661	−	0.344842i	$-0.887933\pi$
$401$	0.469076	−	1.44367i	0.0234245	−	0.0720933i	0.962085	+	0.272748i	$0.0879326\pi$
$402$	−2.36864	−	4.30854i	−0.118137	−	0.214891i
$403$	31.7901	−	2.00006i	1.58358	−	0.0996301i
$404$	−1.26635	−	20.1280i	−0.0630032	−	1.00141i
$405$	23.6224	+	7.51056i	1.17380	+	0.373203i
$406$	−5.59062	+	1.43543i	−0.277458	+	0.0712390i
$407$	1.75670	−	2.41789i	0.0870765	−	0.119850i
$408$	−12.1572	+	7.71519i	−0.601871	+	0.381959i
$409$	−5.81242	+	0.734279i	−0.287406	+	0.0363078i	−0.267714	−	0.963498i	$-0.586268\pi$
$409$	−5.81242	+	0.734279i	−0.287406	+	0.0363078i	−0.0196913	+	0.999806i	$0.506268\pi$
$410$	−7.75596	−	9.25555i	−0.383039	−	0.457099i
$411$	1.40608	−	2.98807i	0.0693568	−	0.147391i
$412$	1.64940	−	3.00025i	0.0812602	−	0.147812i
$413$	20.2426	+	21.5562i	0.996075	+	1.06071i
$414$	10.9558	−	6.02298i	0.538447	−	0.296013i
$415$	16.5126	+	11.8383i	0.810571	+	0.581119i
$416$	−16.2956	+	15.3026i	−0.798958	+	0.750272i
$417$	18.7782	+	15.5346i	0.919570	+	0.760735i
$418$	1.39562	+	1.92090i	0.0682619	+	0.0939545i
$419$	−3.19865	−	1.26644i	−0.156264	−	0.0618694i	0.288690	−	0.957423i	$-0.406780\pi$
$419$	−3.19865	−	1.26644i	−0.156264	−	0.0618694i	−0.444955	+	0.895553i	$0.646780\pi$
$420$	14.8169	−	15.9797i	0.722989	−	0.779728i
$421$	4.94363	+	5.97583i	0.240938	+	0.291244i	0.877096	−	0.480315i	$-0.159478\pi$
$421$	4.94363	+	5.97583i	0.240938	+	0.291244i	−0.636158	+	0.771559i	$0.719478\pi$
$422$	4.07796	+	10.2997i	0.198512	+	0.501383i
$423$	−19.2199	+	3.66638i	−0.934501	+	0.178266i
$424$	−0.00437658	+	0.00317977i	−0.000212545	+	0.000154423i
$425$	−4.84254	−	11.7929i	−0.234898	−	0.572040i
$426$	13.0611	+	9.48946i	0.632813	+	0.459766i
$427$	18.6468	+	8.77453i	0.902383	+	0.424629i
$428$	1.93288	+	1.22664i	0.0934294	+	0.0592921i
$429$	13.9569	−	5.52592i	0.673845	−	0.266794i
$430$	−11.7669	+	7.57233i	−0.567452	+	0.365170i
$431$	0.423400	−	6.72975i	0.0203945	−	0.324161i	−0.974581	−	0.224037i	$-0.928076\pi$
$431$	0.423400	−	6.72975i	0.0203945	−	0.324161i	0.994975	−	0.100123i	$-0.0319238\pi$
$432$		−	2.49629i		−	0.120103i
$433$	2.52844	+	0.159076i	0.121509	+	0.00764469i	0.123428	−	0.992353i	$-0.460611\pi$
$433$	2.52844	+	0.159076i	0.121509	+	0.00764469i	−0.00191965	+	0.999998i	$0.500611\pi$
$434$	−7.92842	−	16.8487i	−0.380576	−	0.808766i
$435$	9.39857	+	8.71467i	0.450627	+	0.417836i
$436$	16.9985	+	15.9627i	0.814082	+	0.764474i
$437$	2.01872	+	15.9798i	0.0965686	+	0.764419i
$438$	1.49799	+	11.8578i	0.0715769	+	0.566589i
$439$	−17.3724	−	16.3138i	−0.829139	−	0.778614i	0.148498	−	0.988913i	$-0.452556\pi$
$439$	−17.3724	−	16.3138i	−0.829139	−	0.778614i	−0.977637	+	0.210299i	$0.932556\pi$
$440$	4.25406	−	9.19075i	0.202805	−	0.438152i
$441$	−1.73446	−	3.68592i	−0.0825935	−	0.175520i
$442$	7.16317	+	0.450668i	0.340717	+	0.0214361i
$443$		−	20.7057i		−	0.983758i	−0.870663	−	0.491879i	$-0.836310\pi$
$443$		−	20.7057i		−	0.983758i	0.870663	−	0.491879i	$-0.163690\pi$
$444$	0.340591	−	5.41354i	0.0161637	−	0.256915i
$445$	0.205583	−	0.528993i	0.00974558	−	0.0250767i
$446$	−13.6876	+	5.41929i	−0.648125	+	0.256611i
$447$	−0.847609	−	0.537909i	−0.0400905	−	0.0254422i
$448$	6.19008	+	2.91283i	0.292454	+	0.137618i
$449$	1.69910	+	1.23447i	0.0801854	+	0.0582581i	0.627156	−	0.778894i	$-0.284219\pi$
$449$	1.69910	+	1.23447i	0.0801854	+	0.0582581i	−0.546970	+	0.837152i	$0.684219\pi$
$450$	6.92229	+	1.22998i	0.326320	+	0.0579817i
$451$	10.5187	−	7.64227i	0.495306	−	0.359861i
$452$	−12.1858	+	2.32456i	−0.573171	+	0.109338i
$453$	−13.8116	−	34.8842i	−0.648927	−	1.63900i
$454$	3.88158	+	4.69203i	0.182172	+	0.220208i
$455$	−25.3001	+	4.99227i	−1.18609	+	0.234041i
$456$	9.51189	+	3.76602i	0.445435	+	0.176360i
$457$	−8.33736	−	11.4754i	−0.390005	−	0.536796i	0.568195	−	0.822894i	$-0.307642\pi$
$457$	−8.33736	−	11.4754i	−0.390005	−	0.536796i	−0.958201	+	0.286097i	$0.907642\pi$
$458$	−9.69079	−	8.01692i	−0.452821	−	0.374606i
$459$	−4.50460	+	4.23010i	−0.210257	+	0.197444i
$460$	23.3042	−	17.1577i	1.08657	−	0.799982i
$461$	−12.5399	+	6.89388i	−0.584042	+	0.321080i	−0.746239	−	0.665679i	$-0.768142\pi$
$461$	−12.5399	+	6.89388i	−0.584042	+	0.321080i	0.162196	+	0.986758i	$0.448142\pi$
$462$	−6.00712	−	6.39693i	−0.279476	−	0.297612i
$463$	−3.65920	+	6.65606i	−0.170058	+	0.309333i	−0.947578	−	0.319524i	$-0.896477\pi$
$463$	−3.65920	+	6.65606i	−0.170058	+	0.309333i	0.777521	+	0.628857i	$0.216477\pi$
$464$	1.13493	−	2.41186i	0.0526880	−	0.111968i
$465$	−21.9349	+	35.0519i	−1.01721	+	1.62549i
$466$	0.681874	−	0.0861407i	0.0315872	−	0.00399039i
$467$	5.10401	−	3.23910i	0.236185	−	0.149888i	−0.412467	−	0.910972i	$-0.635333\pi$
$467$	5.10401	−	3.23910i	0.236185	−	0.149888i	0.648653	+	0.761085i	$0.275333\pi$
$468$	6.22089	−	8.56232i	0.287561	−	0.395794i
$469$	−8.80875	+	2.26170i	−0.406750	+	0.104436i
$470$	16.0763	−	5.33613i	0.741545	−	0.246137i
$471$	2.00113	+	31.8070i	0.0922071	+	1.46559i
$472$	24.8928	−	1.56612i	1.14578	−	0.0720866i
$473$	−7.25818	−	13.2026i	−0.333732	−	0.607056i
$474$	2.65868	−	8.18258i	0.122117	−	0.375838i
$475$	−4.75631	+	7.70853i	−0.218234	+	0.353692i
$476$	3.46679	+	10.6697i	0.158900	+	0.489043i
$477$	0.00276803	−	0.00294765i	0.000126739	−	0.000134964i
$478$	2.48187	−	9.66625i	0.113518	−	0.442124i
$479$	11.4366	−	18.0212i	0.522552	−	0.823410i	−0.475873	−	0.879514i	$-0.657868\pi$
$479$	11.4366	−	18.0212i	0.522552	−	0.823410i	0.998425	+	0.0561038i	$0.0178678\pi$
$480$	−3.81903	−	28.7666i	−0.174314	−	1.31301i
$481$	−4.09156	+	4.94584i	−0.186559	+	0.225511i
$482$	12.7294	+	4.13605i	0.579810	+	0.188392i
$483$	−14.8041	−	57.6583i	−0.673612	−	2.62355i
$484$	−10.0060	−	5.50086i	−0.454820	−	0.250039i
$485$	−41.1399	+	5.46170i	−1.86807	+	0.248003i
$486$	−2.38936	−	12.5254i	−0.108383	−	0.568166i
$487$	37.4152	+	7.13733i	1.69545	+	0.323423i	0.942385	−	0.334529i	$-0.108577\pi$
$487$	37.4152	+	7.13733i	1.69545	+	0.323423i	0.753060	+	0.657952i	$0.228577\pi$
$488$	15.7280	−	7.40101i	0.711971	−	0.335028i
$489$	22.3113	+	2.81857i	1.00895	+	0.127460i
$490$	1.90841	+	2.96556i	0.0862134	+	0.133970i
$491$	2.53086	−	13.2672i	0.114216	−	0.598741i	−0.878448	−	0.477837i	$-0.841421\pi$
$491$	2.53086	−	13.2672i	0.114216	−	0.598741i	0.992664	−	0.120904i	$-0.0385792\pi$
$492$	8.68677	−	21.9403i	0.391630	−	0.989144i
$493$	−6.27545	+	2.03902i	−0.282632	+	0.0918328i
$494$	−2.73246	−	4.30566i	−0.122939	−	0.193721i
$495$	−1.83617	+	7.34391i	−0.0825299	+	0.330084i
$496$	8.32918	+	2.13857i	0.373991	+	0.0960246i
$497$	23.0094	−	19.0351i	1.03211	−	0.853839i
$498$	1.86109	−	14.7321i	0.0833976	−	0.660160i
$499$	16.0140			0.716887			0.358444	−	0.933551i	$-0.383308\pi$
$499$	16.0140			0.716887			0.358444	+	0.933551i	$0.383308\pi$
$500$	16.2585	+	0.713576i	0.727102	+	0.0319121i
$501$	2.44135			0.109072
$502$	−0.0143880	+	0.113893i	−0.000642170	+	0.00508330i
$503$	−20.9701	+	17.3480i	−0.935011	+	0.773508i	−0.974191	−	0.225724i	$-0.927525\pi$
$503$	−20.9701	+	17.3480i	−0.935011	+	0.773508i	0.0391807	+	0.999232i	$0.487525\pi$
$504$	−14.2267	−	3.65280i	−0.633708	−	0.162708i
$505$	−11.5869	−	28.7331i	−0.515612	−	1.27860i
$506$	−6.24420	−	9.83928i	−0.277588	−	0.437409i
$507$	−3.27734	+	1.06487i	−0.145552	+	0.0472927i
$508$	−6.39444	+	16.1505i	−0.283708	+	0.716563i
$509$	−7.89621	+	41.3934i	−0.349994	+	1.83473i	0.176186	+	0.984357i	$0.443624\pi$
$509$	−7.89621	+	41.3934i	−0.349994	+	1.83473i	−0.526180	+	0.850373i	$0.676376\pi$
$510$	−5.89346	+	7.21640i	−0.260967	+	0.319548i
$511$	21.9335	+	2.77085i	0.970282	+	0.122575i
$512$	−10.2130	+	4.80588i	−0.451356	+	0.212392i
$513$	4.31272	+	0.822695i	0.190411	+	0.0363229i
$514$	1.85951	+	9.74787i	0.0820193	+	0.429960i
$515$	0.952840	−	5.17245i	0.0419872	−	0.227926i
$516$	−23.9618	−	13.1731i	−1.05486	−	0.579913i
$517$	4.53561	+	17.6650i	0.199476	+	0.776907i
$518$	3.56878	+	1.15957i	0.156803	+	0.0509484i
$519$	2.63962	−	3.19075i	0.115866	−	0.140058i
$520$	−10.3580	+	19.1267i	−0.454229	+	0.838760i
$521$	−18.0040	+	28.3698i	−0.788769	+	1.24290i	0.177182	+	0.984178i	$0.443302\pi$
$521$	−18.0040	+	28.3698i	−0.788769	+	1.24290i	−0.965951	+	0.258724i	$0.916698\pi$
$522$	0.904980	−	3.52466i	0.0396099	−	0.154270i
$523$	−12.9200	+	13.7585i	−0.564954	+	0.601615i	−0.946488	−	0.322740i	$-0.895396\pi$
$523$	−12.9200	+	13.7585i	−0.564954	+	0.601615i	0.381533	+	0.924355i	$0.375396\pi$
$524$	7.04049	+	21.6684i	0.307565	+	0.946589i
$525$	13.8693	−	30.4681i	0.605307	−	1.32974i
$526$	2.30687	−	7.09982i	0.100584	−	0.309567i
$527$	−10.2552	−	18.6541i	−0.446722	−	0.812585i
$528$	4.04453	−	0.254460i	0.176016	−	0.0110740i
$529$	−3.51955	−	55.9417i	−0.153024	−	2.43225i
$530$	−0.00203963	+	0.00284497i	−8.85959e−5	+	0.000123578i
$531$	−18.0576	+	4.63639i	−0.783631	+	0.201202i
$532$	4.68521	−	6.44864i	0.203130	−	0.279584i
$533$	−23.5774	+	14.9627i	−1.02125	+	0.648105i
$534$	−0.411512	+	0.0519860i	−0.0178079	+	0.00224965i
$535$	3.41168	+	0.853012i	0.147500	+	0.0368789i
$536$	−3.26610	+	6.94081i	−0.141074	+	0.299797i
$537$	−3.77355	+	6.86407i	−0.162841	+	0.296207i
$538$	6.71626	+	7.15209i	0.289558	+	0.308348i
$539$	−3.32738	+	1.82924i	−0.143320	+	0.0787910i
$540$	−2.48504	−	7.48674i	−0.106939	−	0.322178i
$541$	−11.3015	+	10.6128i	−0.485891	+	0.456282i	−0.888357	−	0.459153i	$-0.848153\pi$
$541$	−11.3015	+	10.6128i	−0.485891	+	0.456282i	0.402467	+	0.915435i	$0.368153\pi$
$542$	9.30262	+	7.69580i	0.399582	+	0.330563i
$543$	1.21918	+	1.67806i	0.0523202	+	0.0720126i
$544$	13.8902	+	5.49953i	0.595539	+	0.235790i
$545$	32.5081	+	15.0468i	1.39249	+	0.644534i
$546$	12.0136	+	14.5219i	0.514133	+	0.621480i
$547$	−7.85782	−	19.8466i	−0.335976	−	0.848578i	−0.995311	−	0.0967289i	$-0.969162\pi$
$547$	−7.85782	−	19.8466i	−0.335976	−	0.848578i	0.659335	−	0.751849i	$-0.270838\pi$
$548$	−2.13183	+	0.406669i	−0.0910675	+	0.0173720i
$549$	−10.5113	+	7.63688i	−0.448610	+	0.325934i
$550$	0.739064	−	6.51156i	0.0315138	−	0.277654i
$551$	3.79282	+	2.75565i	0.161580	+	0.117394i
$552$	−45.4316	−	21.3785i	−1.93370	−	0.909929i
$553$	−13.4369	−	8.52729i	−0.571393	−	0.362617i
$554$	−0.723041	+	0.286272i	−0.0307191	+	0.0121625i
$555$	−2.12323	−	8.05755i	−0.0901260	−	0.342024i
$556$	1.00567	−	15.9847i	0.0426500	−	0.677902i
$557$			32.4344i			1.37429i	0.726521	+	0.687144i	$0.241136\pi$
$557$			32.4344i			1.37429i	−0.726521	+	0.687144i	$0.758864\pi$
$558$	11.7166	+	0.737147i	0.496004	+	0.0312059i
$559$	13.7774	+	29.2785i	0.582723	+	1.23835i
$560$	−6.91248	−	0.828875i	−0.292105	−	0.0350263i
$561$	−7.31287	−	6.86724i	−0.308749	−	0.289935i
$562$	0.530545	+	4.19970i	0.0223797	+	0.177154i
$563$	4.94798	+	39.1673i	0.208532	+	1.65070i	0.654799	+	0.755803i	$0.272753\pi$
$563$	4.94798	+	39.1673i	0.208532	+	1.65070i	−0.446266	+	0.894900i	$0.647247\pi$
$564$	24.1294	+	22.6590i	1.01603	+	0.954115i
$565$	−16.6415	+	9.28624i	−0.700112	+	0.390675i
$566$	−3.78875	−	8.05149i	−0.159253	−	0.338430i
$567$	−33.4430	−	2.10406i	−1.40447	−	0.0883620i
$568$		−	25.1880i		−	1.05686i
$569$	−0.115575	+	1.83701i	−0.00484515	+	0.0770115i	−0.999706	−	0.0242380i	$-0.992284\pi$
$569$	−0.115575	+	1.83701i	−0.00484515	+	0.0770115i	0.994861	+	0.101250i	$0.0322840\pi$
$570$	6.60930	+	0.373878i	0.276833	+	0.0156600i
$571$	18.8093	−	7.44714i	0.787146	−	0.311653i	0.0600557	−	0.998195i	$-0.480872\pi$
$571$	18.8093	−	7.44714i	0.787146	−	0.311653i	0.727090	+	0.686542i	$0.240872\pi$
$572$	−8.32934	−	5.28596i	−0.348267	−	0.221017i
$573$	−31.8433	−	14.9843i	−1.33027	−	0.625979i
$574$	13.2067	+	9.59525i	0.551238	+	0.400498i
$575$	25.6735	−	36.2930i	1.07066	−	1.51352i
$576$	−3.48936	+	2.53517i	−0.145390	+	0.105632i
$577$	15.0443	−	2.86985i	0.626302	−	0.119474i	0.135547	−	0.990771i	$-0.456721\pi$
$577$	15.0443	−	2.86985i	0.626302	−	0.119474i	0.490755	+	0.871297i	$0.336721\pi$
$578$	2.85170	+	7.20257i	0.118615	+	0.299587i
$579$	38.4969	+	46.5348i	1.59988	+	1.93392i
$580$	1.00285	−	8.36334i	0.0416410	−	0.347269i
$581$	−25.5378	−	10.1111i	−1.05949	−	0.419480i
$582$	17.8280	+	24.5381i	0.738993	+	1.01714i
$583$	−0.00290411	−	0.00240249i	−0.000120276	−	9.95010e-5i
$584$	13.5932	−	12.7649i	0.562492	−	0.528215i
$585$	4.92622	−	15.4940i	0.203674	−	0.640600i
$586$	−19.9131	+	10.9473i	−0.822602	+	0.452229i
$587$	−12.2325	−	13.0262i	−0.504888	−	0.537651i	0.425146	−	0.905125i	$-0.360223\pi$
$587$	−12.2325	−	13.0262i	−0.504888	−	0.537651i	−0.930034	+	0.367474i	$0.880223\pi$
$588$	−3.31995	+	6.03896i	−0.136912	+	0.249042i
$589$	−6.43974	+	13.6851i	−0.265345	+	0.563886i
$590$	14.9683	−	6.03615i	0.616236	−	0.248504i
$591$	−9.60552	+	1.21346i	−0.395118	+	0.0499151i
$592$	−1.46315	+	0.928540i	−0.0601349	+	0.0381628i
$593$	10.2368	−	14.0897i	0.420374	−	0.578595i	−0.545337	−	0.838217i	$-0.683598\pi$
$593$	10.2368	−	14.0897i	0.420374	−	0.578595i	0.965710	+	0.259623i	$0.0835981\pi$
$594$	−3.07674	+	0.789974i	−0.126240	+	0.0324130i
$595$	10.2179	+	13.8783i	0.418891	+	0.568954i
$596$	0.0414255	+	0.658440i	0.00169686	+	0.0269708i
$597$	61.8011	−	3.88820i	2.52935	−	0.159133i
$598$	12.0575	+	21.9326i	0.493069	+	0.896889i
$599$	−3.08167	+	9.48439i	−0.125913	+	0.387522i	−0.994066	−	0.108775i	$-0.965307\pi$
$599$	−3.08167	+	9.48439i	−0.125913	+	0.387522i	0.868153	+	0.496297i	$0.165307\pi$
$600$	−12.3445	−	25.3947i	−0.503962	−	1.03674i
$601$	5.42151	+	16.6857i	0.221148	+	0.680624i	0.998660	+	0.0517553i	$0.0164816\pi$
$601$	5.42151	+	16.6857i	0.221148	+	0.680624i	−0.777512	+	0.628868i	$0.783518\pi$
$602$	12.9491	−	13.7894i	0.527766	−	0.562014i
$603$	1.42591	−	5.55357i	0.0580677	−	0.226159i
$604$	−13.2119	+	20.8186i	−0.537583	+	0.847096i
$605$	−17.2505	−	3.17778i	−0.701331	−	0.129195i
$606$	−14.4330	+	17.4464i	−0.586299	+	0.708713i
$607$	−13.5664	−	4.40799i	−0.550643	−	0.178915i	0.0204635	−	0.999791i	$-0.493486\pi$
$607$	−13.5664	−	4.40799i	−0.550643	−	0.178915i	−0.571107	+	0.820876i	$0.693486\pi$
$608$	−2.63970	−	10.2810i	−0.107054	−	0.416948i
$609$	−15.1836	−	8.34727i	−0.615272	−	0.338248i
$610$	8.15044	−	7.75134i	0.330002	−	0.313843i
$611$	−7.33980	−	38.4766i	−0.296937	−	1.55660i
$612$	−6.94770	−	1.32535i	−0.280844	−	0.0535739i
$613$	7.97093	−	3.75084i	0.321943	−	0.151495i	−0.258016	−	0.966141i	$-0.583069\pi$
$613$	7.97093	−	3.75084i	0.321943	−	0.151495i	0.579959	+	0.814646i	$0.303069\pi$
$614$	−3.22052	−	0.406847i	−0.129970	−	0.0164190i
$615$	2.04732	−	36.1919i	0.0825560	−	1.45940i
$616$	−2.56542	+	13.4484i	−0.103364	+	0.541852i
$617$	−9.26749	+	23.4070i	−0.373095	+	0.942331i	0.615006	+	0.788523i	$0.289154\pi$
$617$	−9.26749	+	23.4070i	−0.373095	+	0.942331i	−0.988101	+	0.153808i	$0.950846\pi$
$618$	−3.65574	+	1.18782i	−0.147056	+	0.0477812i
$619$	3.26847	+	5.15029i	0.131371	+	0.207008i	0.903645	−	0.428282i	$-0.140881\pi$
$619$	3.26847	+	5.15029i	0.131371	+	0.207008i	−0.772274	+	0.635289i	$0.780881\pi$
$620$	27.1094	−	1.87776i	1.08874	−	0.0754125i
$621$	−20.8715	−	5.35889i	−0.837545	−	0.215045i
$622$	5.88478	−	4.86831i	0.235958	−	0.195202i
$623$	−0.0961589	+	0.761176i	−0.00385252	+	0.0304959i
$624$	−8.70376			−0.348429
$625$	24.0496	−	6.82768i	0.961984	−	0.273107i
$626$	−4.13063			−0.165093
$627$	−0.893328	+	7.07142i	−0.0356761	+	0.282405i
$628$	16.1380	−	13.3505i	0.643977	−	0.532745i
$629$	4.15495	+	1.06681i	0.165669	+	0.0425365i
$630$	−9.48176	+	0.656762i	−0.377762	+	0.0261660i
$631$	8.07803	+	12.7289i	0.321581	+	0.506731i	0.966207	−	0.257767i	$-0.0829867\pi$
$631$	8.07803	+	12.7289i	0.321581	+	0.506731i	−0.644626	+	0.764498i	$0.722987\pi$
$632$	−12.7662	+	4.14798i	−0.507811	+	0.164998i
$633$	−12.2416	+	30.9188i	−0.486561	+	1.22891i
$634$	−0.657684	+	3.44770i	−0.0261200	+	0.136926i
$635$	−1.50706	+	26.6413i	−0.0598059	+	1.05723i
$636$	−0.00678664		0.000857352i	−0.000269108		3.39962e-5i
$637$	7.37892	−	3.47225i	0.292363	−	0.137576i
$638$	−3.33185	−	0.635584i	−0.131909	−	0.0251630i
$639$	3.52785	+	18.4936i	0.139560	+	0.731597i
$640$	−16.2820	+	15.4848i	−0.643604	+	0.612089i
$641$	33.9692	+	18.6747i	1.34170	+	0.737607i	0.980804	−	0.194999i	$-0.0624702\pi$
$641$	33.9692	+	18.6747i	1.34170	+	0.737607i	0.360898	+	0.932605i	$0.382470\pi$
$642$	−0.639175	−	2.48942i	−0.0252262	−	0.0982497i
$643$	30.5541	+	9.92762i	1.20494	+	0.391507i	0.841574	−	0.540141i	$-0.181629\pi$
$643$	30.5541	+	9.92762i	1.20494	+	0.391507i	0.363361	+	0.931648i	$0.381629\pi$
$644$	−24.9369	+	30.1436i	−0.982653	+	1.18782i
$645$	−41.3102	−	7.60994i	−1.62659	−	0.299641i
$646$	−1.82609	+	2.87746i	−0.0718465	+	0.113212i
$647$	0.0343264	−	0.133693i	0.00134951	−	0.00525600i	−0.967905	−	0.251317i	$-0.919136\pi$
$647$	0.0343264	−	0.133693i	0.00134951	−	0.00525600i	0.969254	+	0.246061i	$0.0791363\pi$
$648$	−19.3479	+	20.6034i	−0.760057	+	0.809379i
$649$	5.36995	+	16.5270i	0.210789	+	0.648741i
$650$	−2.46232	+	13.8579i	−0.0965800	+	0.543550i
$651$	17.2735	−	53.1624i	0.677003	−	2.08360i
$652$	−7.11995	−	12.9511i	−0.278839	−	0.507206i
$653$	−19.9043	+	1.25227i	−0.778915	+	0.0490052i	−0.447270	−	0.894399i	$-0.647604\pi$
$653$	−19.9043	+	1.25227i	−0.778915	+	0.0490052i	−0.331645	+	0.943404i	$0.607604\pi$
$654$	−1.64386	−	26.1284i	−0.0642799	−	1.02170i
$655$	20.7509	+	28.1846i	0.810803	+	1.10126i
$656$	−7.30193	+	1.87482i	−0.285093	+	0.0731993i
$657$	−8.19263	+	11.2762i	−0.319625	+	0.439926i
$658$	−19.3340	+	12.2697i	−0.753718	+	0.478324i
$659$	20.5594	−	2.59725i	0.800879	−	0.101175i	0.285769	−	0.958299i	$-0.407751\pi$
$659$	20.5594	−	2.59725i	0.800879	−	0.101175i	0.515110	+	0.857124i	$0.327751\pi$
$660$	11.8768	−	4.78947i	0.462306	−	0.186430i
$661$	−3.51431	+	7.46828i	−0.136691	+	0.290482i	−0.961439	−	0.275017i	$-0.911317\pi$
$661$	−3.51431	+	7.46828i	−0.136691	+	0.290482i	0.824749	+	0.565499i	$0.191317\pi$
$662$	−7.93735	+	14.4380i	−0.308494	+	0.561148i
$663$	14.7490	+	15.7061i	0.572804	+	0.609974i
$664$	−20.3015	+	11.1608i	−0.787851	+	0.433125i
$665$	3.71014	−	11.6692i	0.143873	−	0.452512i
$666$	−1.72457	+	1.61948i	−0.0668256	+	0.0627534i
$667$	−17.7292	−	14.6669i	−0.686477	−	0.567903i
$668$	−0.943058	−	1.29801i	−0.0364880	−	0.0502214i
$669$	−41.0887	−	16.2682i	−1.58858	−	0.628964i
$670$	−0.590964	+	4.92840i	−0.0228309	+	0.190401i
$671$	7.71954	+	9.33132i	0.298009	+	0.360232i
$672$	14.4413	+	36.4746i	0.557085	+	1.40704i
$673$	−8.46859	+	1.61547i	−0.326440	+	0.0622718i	−0.347996	−	0.937496i	$-0.613138\pi$
$673$	−8.46859	+	1.61547i	−0.326440	+	0.0622718i	0.0215563	+	0.999768i	$0.493138\pi$
$674$	−9.45111	+	6.86664i	−0.364043	+	0.264493i
$675$	−7.24618	−	9.71278i	−0.278905	−	0.373845i
$676$	1.83216	+	1.33114i	0.0704676	+	0.0511977i
$677$	16.9220	+	7.96287i	0.650364	+	0.306038i	0.722515	−	0.691356i	$-0.242986\pi$
$677$	16.9220	+	7.96287i	0.650364	+	0.306038i	−0.0721505	+	0.997394i	$0.522986\pi$
$678$	11.7596	+	7.46289i	0.451626	+	0.286611i
$679$	52.1633	−	20.6529i	2.00184	−	0.792586i
$680$	14.5131	+	0.820984i	0.556551	+	0.0314833i
$681$	−1.14781	+	18.2440i	−0.0439843	+	0.699110i
$682$		−	10.9427i		−	0.419019i
$683$	−33.3961	−	2.10111i	−1.27787	−	0.0803966i	−0.590698	−	0.806893i	$-0.701147\pi$
$683$	−33.3961	−	2.10111i	−1.27787	−	0.0803966i	−0.687170	+	0.726496i	$0.741147\pi$
$684$	2.13970	+	4.54710i	0.0818135	+	0.173863i
$685$	−2.91133	+	1.62458i	−0.111236	+	0.0620718i
$686$	7.90567	+	7.42392i	0.301840	+	0.283446i
$687$	−4.73197	−	37.4574i	−0.180536	−	1.42909i
$688$	1.09488	+	8.66686i	0.0417419	+	0.330421i
$689$	0.00590096	+	0.00554137i	0.000224809	+	0.000211110i
$690$	−32.2592	−	3.86820i	−1.22809	−	0.147260i
$691$	−19.3987	−	41.2244i	−0.737962	−	1.56825i	−0.820491	−	0.571660i	$-0.806300\pi$
$691$	−19.3987	−	41.2244i	−0.737962	−	1.56825i	0.0825290	−	0.996589i	$-0.473700\pi$
$692$	−2.71609	−	0.170882i	−0.103250	−	0.00649596i
$693$		−	10.2335i		−	0.388738i
$694$	0.708542	−	11.2619i	0.0268959	−	0.427498i
$695$	−6.26931	−	23.7918i	−0.237809	−	0.902473i
$696$	−13.5883	+	5.37999i	−0.515063	+	0.203928i
$697$	15.7567	+	9.99949i	0.596827	+	0.378758i
$698$	−18.5265	−	8.71790i	−0.701237	−	0.329977i
$699$	1.66916	+	1.21271i	0.0631332	+	0.0458690i
$700$	−21.5567	+	4.39541i	−0.814766	+	0.166131i
$701$	18.5891	−	13.5058i	0.702101	−	0.510106i	−0.178515	−	0.983937i	$-0.557129\pi$
$701$	18.5891	−	13.5058i	0.702101	−	0.510106i	0.880616	+	0.473831i	$0.157129\pi$
$702$	6.70153	−	1.27839i	0.252933	−	0.0482495i
$703$	−1.12199	−	2.83383i	−0.0423167	−	0.106880i
$704$	2.56261	+	3.09766i	0.0965820	+	0.116748i
$705$	46.1451	+	21.3589i	1.73793	+	0.804422i
$706$	−15.3618	−	6.08215i	−0.578148	−	0.228905i
$707$	24.6177	+	33.8834i	0.925846	+	1.27432i
$708$	24.3012	+	20.1037i	0.913294	+	0.755543i
$709$	−16.5668	+	15.5573i	−0.622181	+	0.584267i	−0.930173	−	0.367122i	$-0.880343\pi$
$709$	−16.5668	+	15.5573i	−0.622181	+	0.584267i	0.307992	+	0.951389i	$0.400343\pi$
$710$	−5.13451	−	15.4689i	−0.192695	−	0.580536i
$711$	8.79227	−	4.83359i	0.329736	−	0.181274i
$712$	0.442990	+	0.471736i	0.0166017	+	0.0176791i
$713$	35.7613	−	65.0495i	1.33927	−	2.43612i
$714$	5.36287	−	11.3967i	0.200700	−	0.426510i
$715$	−14.7019	−	3.67587i	−0.549820	−	0.137470i
$716$	5.10713	−	0.645181i	0.190862	−	0.0241115i
$717$	25.2947	−	16.0525i	0.944647	−	0.599491i
$718$	14.0174	−	19.2933i	0.523124	−	0.720018i
$719$	3.22364	−	0.827690i	0.120221	−	0.0308676i	−0.188100	−	0.982150i	$-0.560233\pi$
$719$	3.22364	−	0.827690i	0.120221	−	0.0308676i	0.308321	+	0.951282i	$0.400233\pi$
$720$	2.55744	−	3.56723i	0.0953101	−	0.132943i
$721$	0.446443	+	7.09601i	0.0166264	+	0.264269i
$722$	−11.5745	+	0.728208i	−0.430760	+	0.0271011i
$723$	19.3564	+	35.2092i	0.719872	+	1.30944i
$724$	0.421233	−	1.29642i	0.0156550	−	0.0481811i
$725$	−2.58519	−	12.6787i	−0.0960117	−	0.470877i
$726$	3.96147	+	12.1921i	0.147024	+	0.452493i
$727$	−22.0258	+	23.4551i	−0.816891	+	0.869901i	−0.993436	−	0.114392i	$-0.963508\pi$
$727$	−22.0258	+	23.4551i	−0.816891	+	0.869901i	0.176544	+	0.984293i	$0.443508\pi$
$728$	7.31260	−	28.4807i	0.271023	−	1.05556i
$729$	2.69100	−	4.24034i	0.0996668	−	0.157050i
$730$	5.74601	−	10.6103i	0.212669	−	0.392706i
$731$	13.7842	−	16.6622i	0.509826	−	0.616274i
$732$	20.9040	+	6.79211i	0.772633	+	0.251044i
$733$	−6.68472	−	26.0353i	−0.246906	−	0.961634i	−0.964267	−	0.264933i	$-0.914650\pi$
$733$	−6.68472	−	26.0353i	−0.246906	−	0.961634i	0.717361	−	0.696701i	$-0.245350\pi$
$734$	−11.3319	−	6.22976i	−0.418268	−	0.229945i
$735$	−1.91789	+	10.4112i	−0.0707425	+	0.384023i
$736$	9.76174	+	51.1728i	0.359822	+	1.88626i
$737$	−5.24976	−	1.00145i	−0.193377	−	0.0368887i
$738$	−9.31239	+	4.38208i	−0.342794	+	0.161307i
$739$	8.75708	+	1.10628i	0.322134	+	0.0406950i	0.284738	−	0.958605i	$-0.408093\pi$
$739$	8.75708	+	1.10628i	0.322134	+	0.0406950i	0.0373967	+	0.999301i	$0.488093\pi$
$740$	−3.46384	+	4.24138i	−0.127333	+	0.155916i
$741$	2.86848	−	15.0371i	0.105376	−	0.552401i
$742$	0.00174205	−	0.00439993i	6.39528e−5	−	0.000161526i
$743$	−35.1937	+	11.4351i	−1.29113	+	0.419514i	−0.872487	−	0.488637i	$-0.837494\pi$
$743$	−35.1937	+	11.4351i	−1.29113	+	0.419514i	−0.418644	+	0.908151i	$0.637494\pi$
$744$	−25.2633	−	39.8086i	−0.926198	−	1.45945i
$745$	0.379039	+	0.939933i	0.0138869	+	0.0344365i
$746$	2.67056	+	0.685682i	0.0977760	+	0.0251046i
$747$	13.3427	−	11.0380i	0.488183	−	0.403860i
$748$	−0.826294	+	6.54079i	−0.0302123	+	0.239155i
$749$	−4.75406			−0.173710
$750$	−12.7579	−	13.0794i	−0.465852	−	0.477594i
$751$	−18.7214			−0.683153			−0.341576	−	0.939854i	$-0.610961\pi$
$751$	−18.7214			−0.683153			−0.341576	+	0.939854i	$0.610961\pi$
$752$	1.32538	−	10.4915i	0.0483316	−	0.382584i
$753$	−0.265529	+	0.219665i	−0.00967642	+	0.00800503i
$754$	7.05609	+	1.81170i	0.256968	+	0.0659781i
$755$	−9.18757	+	36.7463i	−0.334370	+	1.33734i
$756$	5.71402	+	9.00385i	0.207817	+	0.327467i
$757$	2.93130	−	0.952438i	0.106540	−	0.0346169i	−0.255262	−	0.966872i	$-0.582162\pi$
$757$	2.93130	−	0.952438i	0.106540	−	0.0346169i	0.361802	+	0.932255i	$0.382162\pi$
$758$	0.486767	−	1.22943i	0.0176802	−	0.0446551i
$759$	6.55504	−	34.3627i	0.237933	−	1.24729i
$760$	−5.58909	−	8.68511i	−0.202738	−	0.315042i
$761$	−31.2825	−	3.95190i	−1.13399	−	0.143256i	−0.464147	−	0.885758i	$-0.653639\pi$
$761$	−31.2825	−	3.95190i	−1.13399	−	0.143256i	−0.669844	+	0.742502i	$0.733639\pi$
$762$	17.6458	−	8.30348i	0.639240	−	0.300803i
$763$	−47.5676	−	9.07401i	−1.72206	−	0.328501i
$764$	4.33379	+	22.7185i	0.156791	+	0.821928i
$765$	−10.7709	+	1.42993i	−0.389421	+	0.0516992i
$766$	−11.9835	−	6.58797i	−0.432981	−	0.238033i
$767$	−9.28168	−	36.1498i	−0.335142	−	1.30529i
$768$	25.1528	+	8.17263i	0.907622	+	0.294904i
$769$	29.8491	−	36.0814i	1.07639	−	1.30113i	0.125330	−	0.992115i	$-0.460001\pi$
$769$	29.8491	−	36.0814i	1.07639	−	1.30113i	0.951058	−	0.309014i	$-0.0999988\pi$
$770$	1.16591	+	8.78213i	0.0420164	+	0.316486i
$771$	−15.9622	+	25.1524i	−0.574864	+	0.905841i
$772$	9.87064	−	38.4436i	0.355252	−	1.38362i
$773$	23.7450	−	25.2858i	0.854048	−	0.909469i	−0.142723	−	0.989763i	$-0.545586\pi$
$773$	23.7450	−	25.2858i	0.854048	−	0.909469i	0.996771	+	0.0802938i	$0.0255859\pi$
$774$	3.68534	+	11.3423i	0.132467	+	0.407690i
$775$	38.6157	−	15.8569i	1.38712	−	0.569595i
$776$	14.6230	−	45.0049i	0.524934	−	1.61558i
$777$	5.42669	+	9.87110i	0.194681	+	0.354124i
$778$	8.51230	−	0.535549i	0.305181	−	0.0192003i
$779$	−0.832556	−	13.2331i	−0.0298294	−	0.474125i
$780$	−26.1039	+	8.66454i	−0.934669	+	0.310240i
$781$	16.9975	−	4.36423i	0.608220	−	0.156164i
$782$	9.83152	−	13.5319i	0.351574	−	0.483900i
$783$	−5.29569	+	3.36075i	−0.189252	+	0.120103i
$784$	2.18426	−	0.275937i	0.0780094	−	0.00985488i
$785$	17.0678	−	27.2743i	0.609177	−	0.973462i
$786$	10.8911	−	23.1448i	0.388474	−	0.825549i
$787$	5.83444	−	10.6128i	0.207975	−	0.378306i	−0.751661	−	0.659550i	$-0.770747\pi$
$787$	5.83444	−	10.6128i	0.207975	−	0.378306i	0.959636	+	0.281244i	$0.0907470\pi$
$788$	4.35564	+	4.63829i	0.155163	+	0.165232i
$789$	19.6379	−	10.7960i	0.699126	−	0.384348i
$790$	−6.99462	+	5.14978i	−0.248857	+	0.183221i
$791$	18.7799	−	17.6355i	0.667738	−	0.627048i
$792$	−6.65076	−	5.50198i	−0.236324	−	0.195505i
$793$	−15.2884	−	21.0427i	−0.542908	−	0.747248i
$794$	7.32052	+	2.89840i	0.259796	+	0.102860i
$795$	−0.0103096	+	0.00203430i	−0.000365642	+	7.21492e-5i
$796$	−25.9401	−	31.3562i	−0.919423	−	1.11139i
$797$	−6.77395	−	17.1091i	−0.239946	−	0.606034i	0.759041	−	0.651043i	$-0.225668\pi$
$797$	−6.77395	−	17.1091i	−0.239946	−	0.606034i	−0.998987	+	0.0450092i	$0.985668\pi$
$798$	−8.79056	+	1.67689i	−0.311183	+	0.0593612i
$799$	−21.1780	+	15.3867i	−0.749223	+	0.544342i
$800$	−13.7878	+	25.8490i	−0.487473	+	0.913901i
$801$	−0.391326	−	0.284315i	−0.0138268	−	0.0100458i
$802$	1.01341	+	0.476873i	0.0357846	+	0.0168390i
$803$	10.9694	+	6.96137i	0.387100	+	0.245661i
$804$	−9.01860	+	3.57072i	−0.318062	+	0.125929i
$805$	−21.7696	+	56.0160i	−0.767277	+	1.97430i
$806$	−1.47571	+	23.4557i	−0.0519796	+	0.826192i
$807$			29.4524i			1.03677i
$808$	35.2565	+	2.21815i	1.24032	+	0.0780343i
$809$	0.996679	+	2.11805i	0.0350414	+	0.0744667i	0.921581	−	0.388185i	$-0.126898\pi$
$809$	0.996679	+	2.11805i	0.0350414	+	0.0744667i	−0.886540	+	0.462652i	$0.846898\pi$
$810$	−7.68230	+	16.5973i	−0.269929	+	0.583171i
$811$	12.2946	+	11.5454i	0.431721	+	0.405413i	0.869707	−	0.493569i	$-0.164308\pi$
$811$	12.2946	+	11.5454i	0.431721	+	0.405413i	−0.437985	+	0.898982i	$0.644308\pi$
$812$	1.42717	+	11.2972i	0.0500838	+	0.396454i
$813$	4.54243	+	35.9570i	0.159310	+	1.26107i
$814$	1.60748	+	1.50952i	0.0563421	+	0.0529088i
$815$	−16.6481	−	15.4367i	−0.583158	−	0.540723i
$816$	2.47663	+	5.26310i	0.0866992	+	0.184245i
$817$	−15.3342	−	0.964745i	−0.536475	−	0.0337521i
$818$		−	4.32267i		−	0.151139i
$819$	−1.38006	+	21.9355i	−0.0482233	+	0.766487i
$820$	−20.0332	+	12.8919i	−0.699591	+	0.450204i
$821$	−9.06782	+	3.59020i	−0.316469	+	0.125299i	−0.520989	−	0.853563i	$-0.674437\pi$
$821$	−9.06782	+	3.59020i	−0.316469	+	0.125299i	0.204520	+	0.978862i	$0.434437\pi$
$822$	2.05728	+	1.30559i	0.0717560	+	0.0455377i
$823$	21.1706	+	9.96212i	0.737960	+	0.347258i	0.757749	−	0.652546i	$-0.226299\pi$
$823$	21.1706	+	9.96212i	0.737960	+	0.347258i	−0.0197885	+	0.999804i	$0.506299\pi$
$824$	4.85174	+	3.52499i	0.169018	+	0.122799i
$825$	14.9982	−	12.7305i	0.522170	−	0.443218i
$826$	−17.6514	+	12.8245i	−0.614170	+	0.446221i
$827$	−42.9595	+	8.19496i	−1.49385	+	0.284967i	−0.868621	−	0.495476i	$-0.834994\pi$
$827$	−42.9595	+	8.19496i	−1.49385	+	0.284967i	−0.625227	+	0.780443i	$0.714994\pi$
$828$	−9.07962	−	22.9325i	−0.315539	−	0.796959i
$829$	−24.7604	−	29.9301i	−0.859963	−	1.03952i	−0.998789	−	0.0491998i	$-0.984333\pi$
$829$	−24.7604	−	29.9301i	−0.859963	−	1.03952i	0.138826	−	0.990317i	$-0.455667\pi$
$830$	−10.1928	+	10.9927i	−0.353797	+	0.381562i
$831$	−2.17050	−	0.859361i	−0.0752938	−	0.0298109i
$832$	−5.07521	−	6.98542i	−0.175951	−	0.242176i
$833$	−4.19929	−	3.47396i	−0.145497	−	0.120365i
$834$	−13.1081	+	12.3093i	−0.453896	+	0.426236i
$835$	−2.00309	−	1.43607i	−0.0693199	−	0.0496972i
$836$	4.10478	−	2.25662i	0.141967	−	0.0780470i
$837$	−13.8514	−	14.7502i	−0.478775	−	0.509843i
$838$	1.22284	−	2.22434i	0.0422424	−	0.0768386i
$839$	−10.3280	+	21.9481i	−0.356561	+	0.757731i	−0.999970	−	0.00779208i	$-0.997520\pi$
$839$	−10.3280	+	21.9481i	−0.356561	+	0.757731i	0.643409	+	0.765523i	$0.277520\pi$
$840$	24.5166	+	29.2569i	0.845905	+	1.00946i
$841$	22.1268	−	2.79526i	0.762993	−	0.0963884i
$842$	−4.83155	+	3.06619i	−0.166506	+	0.105668i
$843$	−7.46916	+	10.2804i	−0.257251	+	0.354076i
$844$	21.1676	−	5.43491i	0.728617	−	0.187077i
$845$	3.31540	+	1.05411i	0.114053	+	0.0362624i
$846$	−0.906490	−	14.4082i	−0.0311658	−	0.495366i
$847$	23.6657	−	1.48892i	0.813162	−	0.0511598i
$848$	0.00105282	+	0.00191508i	3.61541e−5	+	6.57640e-5i
$849$	8.25448	−	25.4047i	0.283293	−	0.871887i
$850$	9.08038	−	2.45426i	0.311454	−	0.0841805i
$851$	4.62255	+	14.2267i	0.158459	+	0.487686i
$852$	21.8028	−	23.2176i	0.746952	−	0.795423i
$853$	2.93689	−	11.4384i	0.100557	−	0.391644i	−0.898303	−	0.439376i	$-0.855199\pi$
$853$	2.93689	−	11.4384i	0.100557	−	0.391644i	0.998860	+	0.0477325i	$0.0151995\pi$
$854$	−8.14744	+	12.8383i	−0.278800	+	0.439318i
$855$	5.32010	+	5.59402i	0.181943	+	0.191311i
$856$	−2.55600	+	3.08967i	−0.0873622	+	0.105603i
$857$	−14.2552	−	4.63179i	−0.486948	−	0.158219i	0.0552451	−	0.998473i	$-0.482406\pi$
$857$	−14.2552	−	4.63179i	−0.486948	−	0.158219i	−0.542193	+	0.840254i	$0.682406\pi$
$858$	2.75439	+	10.7276i	0.0940333	+	0.366236i
$859$	−6.66635	−	3.66486i	−0.227453	−	0.125043i	0.363953	−	0.931417i	$-0.381427\pi$
$859$	−6.66635	−	3.66486i	−0.227453	−	0.125043i	−0.591406	+	0.806374i	$0.701427\pi$
$860$	11.9115	+	24.9033i	0.406179	+	0.849194i
$861$	9.18249	+	48.1363i	0.312938	+	1.64048i
$862$	4.88712	+	0.932268i	0.166456	+	0.0317532i
$863$	−2.30521	+	1.08475i	−0.0784703	+	0.0369253i	−0.464614	−	0.885513i	$-0.653807\pi$
$863$	−2.30521	+	1.08475i	−0.0784703	+	0.0369253i	0.386144	+	0.922439i	$0.373807\pi$
$864$	14.0885	+	1.77979i	0.479301	+	0.0605498i
$865$	−4.04265	+	1.06527i	−0.137454	+	0.0362203i
$866$	−0.350262	+	1.83614i	−0.0119024	+	0.0623945i
$867$	−8.56052	+	21.6214i	−0.290731	+	0.734301i
$868$	−34.9377	+	11.3519i	−1.18586	+	0.385310i
$869$	−5.01112	−	7.89626i	−0.169991	−	0.267862i
$870$	−7.24838	+	6.07400i	−0.245743	+	0.205928i
$871$	11.1178	+	2.85456i	0.376712	+	0.0967232i
$872$	−31.4717	+	26.0357i	−1.06577	+	0.881679i
$873$	−4.43313	+	35.0918i	−0.150039	+	1.18768i
$874$	−11.8841			−0.401987
$875$	−29.3017	+	16.8404i	−0.990579	+	0.569308i
$876$	23.5792			0.796669
$877$	−0.425885	+	3.37122i	−0.0143811	+	0.113838i	−0.997671	−	0.0682077i	$-0.978272\pi$
$877$	−0.425885	+	3.37122i	−0.0143811	+	0.113838i	0.983290	+	0.182046i	$0.0582719\pi$
$878$	13.5484	−	11.2082i	0.457237	−	0.378259i
$879$	−66.0718	−	16.9643i	−2.22855	−	0.572193i
$880$	−3.46816	−	2.17032i	−0.116912	−	0.0731615i
$881$	18.1188	+	28.5506i	0.610437	+	0.961895i	0.999178	+	0.0405478i	$0.0129103\pi$
$881$	18.1188	+	28.5506i	0.610437	+	0.961895i	−0.388740	+	0.921347i	$0.627090\pi$
$882$	2.85854	−	0.928796i	0.0962520	−	0.0312742i
$883$	18.7453	−	47.3453i	0.630830	−	1.59330i	−0.163998	−	0.986461i	$-0.552439\pi$
$883$	18.7453	−	47.3453i	0.630830	−	1.59330i	0.794828	−	0.606835i	$-0.207561\pi$
$884$	2.65323	−	13.9087i	0.0892379	−	0.467801i
$885$	45.1590	+	17.5502i	1.51800	+	0.589944i
$886$	15.1569	+	1.91476i	0.509205	+	0.0643275i
$887$	31.1363	−	14.6516i	1.04546	−	0.491954i	0.175189	−	0.984535i	$-0.443946\pi$
$887$	31.1363	−	14.6516i	1.04546	−	0.491954i	0.870267	+	0.492581i	$0.163946\pi$
$888$	9.33287	+	1.78034i	0.313191	+	0.0597443i
$889$	−6.75935	−	35.4337i	−0.226701	−	1.18841i
$890$	0.368219	+	0.199408i	0.0123427	+	0.00668418i
$891$	−17.2561	−	9.48663i	−0.578101	−	0.317814i
$892$	7.22257	+	28.1301i	0.241830	+	0.941864i
$893$	17.6888	+	5.74745i	0.591934	+	0.192331i
$894$	0.472139	−	0.570719i	0.0157907	−	0.0190877i
$895$	7.13377	−	3.41216i	0.238456	−	0.114056i
$896$	16.2760	−	25.6469i	0.543744	−	0.856803i
$897$	−18.6848	+	72.7724i	−0.623866	+	2.42980i
$898$	−1.06077	+	1.12961i	−0.0353984	+	0.0376954i
$899$	−6.67674	−	20.5489i	−0.222682	−	0.685344i
$900$	4.11898	−	13.2446i	0.137299	−	0.441486i
$901$	0.00167173	−	0.00514505i	5.56933e−5	−	0.000171406i
$902$	4.62153	+	8.40654i	0.153880	+	0.279907i
$903$	56.6729	−	3.56556i	1.88596	−	0.118654i
$904$	−1.36442	−	21.6868i	−0.0453798	−	0.721292i
$905$	−0.0132416	−	2.09398i	−0.000440164	−	0.0696063i
$906$	26.8129	−	6.88439i	0.890800	−	0.228719i
$907$	−17.9590	+	24.7185i	−0.596320	+	0.820764i	−0.995365	−	0.0961672i	$-0.969342\pi$
$907$	−17.9590	+	24.7185i	−0.596320	+	0.820764i	0.399045	+	0.916931i	$0.369342\pi$
$908$	10.1433	−	6.43711i	0.336616	−	0.213623i
$909$	−26.1969	+	3.30944i	−0.868896	+	0.109767i
$910$	−1.31478	−	18.9817i	−0.0435847	−	0.629238i
$911$	11.3628	−	24.1471i	0.376466	−	0.800030i	−0.623370	−	0.781927i	$-0.714237\pi$
$911$	11.3628	−	24.1471i	0.376466	−	0.800030i	0.999836	−	0.0181037i	$-0.00576289\pi$
$912$	1.99098	−	3.62158i	0.0659279	−	0.119922i
$913$	−11.0492	−	11.7662i	−0.365676	−	0.389405i
$914$	9.17114	−	5.04188i	0.303354	−	0.166771i
$915$	33.7641	−	0.213512i	1.11621	−	0.00705848i
$916$	−18.0873	+	16.9851i	−0.597622	+	0.561204i
$917$	−36.4562	−	30.1592i	−1.20389	−	0.995944i
$918$	−2.67993	−	3.68860i	−0.0884508	−	0.121742i
$919$	−2.70303	−	1.07020i	−0.0891646	−	0.0353028i	0.323119	−	0.946358i	$-0.395269\pi$
$919$	−2.70303	−	1.07020i	−0.0891646	−	0.0353028i	−0.412283	+	0.911056i	$0.635269\pi$
$920$	24.7006	+	44.2648i	0.814354	+	1.45937i
$921$	−6.21140	−	7.50829i	−0.204673	−	0.247407i
$922$	−3.88678	−	9.81690i	−0.128004	−	0.323302i
$923$	−37.0227	+	7.06247i	−1.21862	+	0.232464i
$924$	−14.0058	+	10.1758i	−0.460756	+	0.334758i
$925$	−2.99759	+	7.86004i	−0.0985601	+	0.258437i
$926$	−4.53394	−	3.29410i	−0.148995	−	0.108251i
$927$	−4.05598	−	1.90860i	−0.133216	−	0.0626866i
$928$	12.8028	+	8.12493i	0.420274	+	0.266714i
$929$	21.7173	−	8.59850i	0.712523	−	0.282108i	0.0162327	−	0.999868i	$-0.494833\pi$
$929$	21.7173	−	8.59850i	0.712523	−	0.282108i	0.696290	+	0.717761i	$0.254833\pi$
$930$	−23.6300	−	19.2981i	−0.774859	−	0.632809i
$931$	−0.243140	+	3.86459i	−0.00796858	+	0.126657i
$932$		−	1.35590i		−	0.0444141i
$933$	22.8817	+	1.43960i	0.749114	+	0.0471303i
$934$	1.89908	+	4.03574i	0.0621396	+	0.132053i
$935$	1.96061	+	9.93609i	0.0641187	+	0.324945i
$936$	13.5139	+	12.6904i	0.441716	+	0.414799i
$937$	0.983544	+	7.78555i	0.0321310	+	0.254343i	0.999996	+	0.00287209i	$0.000914215\pi$
$937$	0.983544	+	7.78555i	0.0321310	+	0.254343i	−0.967865	+	0.251471i	$0.919086\pi$
$938$	−0.841009	−	6.65727i	−0.0274599	−	0.217368i
$939$	−9.03904	−	8.48822i	−0.294978	−	0.277003i
$940$	−6.46917	−	32.7849i	−0.211001	−	1.06932i
$941$	−3.76974	−	8.01110i	−0.122890	−	0.261154i	0.833911	−	0.551900i	$-0.186097\pi$
$941$	−3.76974	−	8.01110i	−0.122890	−	0.261154i	−0.956801	+	0.290745i	$0.906097\pi$
$942$	−23.4682	−	1.47650i	−0.764636	−	0.0481068i
$943$			65.0764i			2.11918i
$944$	0.632672	−	10.0560i	0.0205917	−	0.327296i
$945$	12.6881	+	10.3621i	0.412744	+	0.337078i
$946$	10.3357	−	4.09218i	0.336042	−	0.133048i
$947$	26.8128	+	17.0159i	0.871299	+	0.552943i	0.894642	−	0.446785i	$-0.147431\pi$
$947$	26.8128	+	17.0159i	0.871299	+	0.552943i	−0.0233429	+	0.999728i	$0.507431\pi$
$948$	−15.3580	−	7.22694i	−0.498806	−	0.234720i
$949$	−22.5740	−	16.4010i	−0.732783	−	0.532398i
$950$	−5.20291	−	4.19453i	−0.168805	−	0.136088i
$951$	−8.52404	+	6.19308i	−0.276411	+	0.200824i
$952$	−19.3028	+	3.68221i	−0.625608	+	0.119341i
$953$	−2.99552	−	7.56582i	−0.0970344	−	0.245081i	0.873149	−	0.487454i	$-0.162074\pi$
$953$	−2.99552	−	7.56582i	−0.0970344	−	0.245081i	−0.970183	+	0.242373i	$0.922074\pi$
$954$	0.00190175	+	0.00229882i	6.15714e−5	+	7.44271e-5i
$955$	17.3128	+	31.0255i	0.560229	+	1.00396i
$956$	−18.3057	−	7.24773i	−0.592048	−	0.234408i
$957$	−5.98497	−	8.23760i	−0.193467	−	0.266284i
$958$	12.1342	+	10.0383i	0.392037	+	0.324322i
$959$	3.28545	−	3.08524i	0.106093	−	0.0996276i
$960$	11.2085	−	0.0708782i	0.361752	−	0.00228759i
$961$	33.9171	−	18.6461i	1.09410	−	0.601487i
$962$	−3.24206	−	3.45244i	−0.104528	−	0.111311i
$963$	1.44394	−	2.62651i	0.0465302	−	0.0846381i
$964$	11.2428	−	23.8921i	0.362106	−	0.769513i
$965$	−4.21317	−	60.8260i	−0.135627	−	1.95806i
$966$	43.5757	−	5.50489i	1.40202	−	0.177117i
$967$	−36.1328	+	22.9306i	−1.16195	+	0.737397i	−0.969784	−	0.243965i	$-0.921552\pi$
$967$	−36.1328	+	22.9306i	−1.16195	+	0.737397i	−0.192168	+	0.981362i	$0.561552\pi$
$968$	11.7561	−	16.1809i	0.377855	−	0.520072i
$969$	−9.90903	+	2.54421i	−0.318324	+	0.0817317i
$970$	−0.193630	−	30.6200i	−0.00621707	−	0.983150i
$971$	1.59001	+	25.2724i	0.0510258	+	0.811031i	0.937442	+	0.348142i	$0.113187\pi$
$971$	1.59001	+	25.2724i	0.0510258	+	0.811031i	−0.886416	+	0.462889i	$0.846813\pi$
$972$	−25.1063	+	1.57956i	−0.805286	+	0.0506643i
$973$	16.0235	+	29.1467i	0.513691	+	0.934400i
$974$	−8.68459	+	26.7284i	−0.278272	+	0.856434i
$975$	−33.8654	+	25.2651i	−1.08456	+	0.809132i
$976$	−2.16991	−	6.67830i	−0.0694572	−	0.213767i
$977$	−5.51856	+	5.87667i	−0.176554	+	0.188011i	−0.811159	−	0.584826i	$-0.801163\pi$
$977$	−5.51856	+	5.87667i	−0.176554	+	0.188011i	0.634605	+	0.772837i	$0.281163\pi$
$978$	−4.12646	+	16.0715i	−0.131950	+	0.513910i
$979$	−0.241586	+	0.380678i	−0.00772111	+	0.0121665i
$980$	6.27624	−	3.00200i	0.200487	−	0.0958953i
$981$	19.4607	−	23.5240i	0.621334	−	0.751064i
$982$	9.47774	+	3.07950i	0.302447	+	0.0982709i
$983$	−7.05833	−	27.4904i	−0.225126	−	0.876807i	−0.976250	−	0.216646i	$-0.930488\pi$
$983$	−7.05833	−	27.4904i	−0.225126	−	0.876807i	0.751124	−	0.660161i	$-0.229512\pi$
$984$	36.2208	+	19.9125i	1.15468	+	0.634788i
$985$	8.59498	+	4.65460i	0.273859	+	0.148308i
$986$	−0.912268	−	4.78227i	−0.0290525	−	0.152299i
$987$	−67.5221	−	12.8805i	−2.14925	−	0.409992i
$988$	−9.10292	+	4.28351i	−0.289602	+	0.136277i
$989$	74.8143	+	9.45124i	2.37896	+	0.300532i
$990$	−5.20604	−	2.02323i	−0.165459	−	0.0643025i
$991$	−10.3346	+	54.1757i	−0.328289	+	1.72095i	0.309641	+	0.950854i	$0.399791\pi$
$991$	−10.3346	+	54.1757i	−0.328289	+	1.72095i	−0.637929	+	0.770095i	$0.720209\pi$
$992$	−18.0081	+	45.4834i	−0.571759	+	1.44410i
$993$	−47.0385	+	15.2837i	−1.49272	+	0.485014i
$994$	11.8061	+	18.6035i	0.374467	+	0.590066i
$995$	−52.9940	−	33.1628i	−1.68002	−	1.05133i
$996$	−28.3743	−	7.28528i	−0.899073	−	0.230843i
$997$	10.3989	−	8.60272i	0.329337	−	0.272451i	−0.458029	−	0.888937i	$-0.651444\pi$
$997$	10.3989	−	8.60272i	0.329337	−	0.272451i	0.787366	+	0.616486i	$0.211444\pi$
$998$	−1.48090	+	11.7225i	−0.0468769	+	0.371069i
$999$	4.07757			0.129009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.109.6	yes	240
5.2	odd	4		625.2.g.b.451.11		480
5.3	odd	4		625.2.g.b.451.14		480
5.4	even	2		625.2.h.a.174.7		240
125.27	odd	100		625.2.g.b.176.11		480
125.39	even	50	inner	125.2.h.a.39.6	✓	240
125.86	even	25		625.2.h.a.449.7		240
125.98	odd	100		625.2.g.b.176.14		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.39.6	✓	240	125.39	even	50	inner
125.2.h.a.109.6	yes	240	1.1	even	1	trivial
625.2.g.b.176.11		480	125.27	odd	100
625.2.g.b.176.14		480	125.98	odd	100
625.2.g.b.451.11		480	5.2	odd	4
625.2.g.b.451.14		480	5.3	odd	4
625.2.h.a.174.7		240	5.4	even	2
625.2.h.a.449.7		240	125.86	even	25

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0924748 + 0.732014i) q^{2} +(-1.70661 + 1.41183i) q^{3} +(1.40987 + 0.361994i) q^{4} +(2.23072 - 0.154513i) q^{5} +(-0.875660 - 1.37982i) q^{6} +(-2.87488 + 0.934106i) q^{7} +(-0.938590 + 2.37061i) q^{8} +(0.357107 - 1.87202i) q^{9} +O(q^{10})\)	\(q+(-0.0924748 + 0.732014i) q^{2} +(-1.70661 + 1.41183i) q^{3} +(1.40987 + 0.361994i) q^{4} +(2.23072 - 0.154513i) q^{5} +(-0.875660 - 1.37982i) q^{6} +(-2.87488 + 0.934106i) q^{7} +(-0.938590 + 2.37061i) q^{8} +(0.357107 - 1.87202i) q^{9} +(-0.0931802 + 1.64721i) q^{10} +(-1.76238 - 0.222640i) q^{11} +(-2.91718 + 1.37272i) q^{12} +(3.74763 + 0.714899i) q^{13} +(-0.417924 - 2.19084i) q^{14} +(-3.58883 + 3.41309i) q^{15} +(0.902590 + 0.496203i) q^{16} +(-0.634082 - 2.46959i) q^{17} +(1.33732 + 0.434522i) q^{18} +(-1.15473 + 1.39583i) q^{19} +(3.20097 + 0.589665i) q^{20} +(3.58750 - 5.65300i) q^{21} +(0.325951 - 1.26950i) q^{22} +(6.08640 - 6.48136i) q^{23} +(-1.74509 - 5.37083i) q^{24} +(4.95225 - 0.689351i) q^{25} +(-0.869877 + 2.67721i) q^{26} +(-1.16757 - 2.12381i) q^{27} +(-4.39137 + 0.276281i) q^{28} +(-0.162497 - 2.58282i) q^{29} +(-2.16656 - 2.94269i) q^{30} +(8.08663 - 2.07629i) q^{31} +(-3.44399 + 4.74025i) q^{32} +(3.32202 - 2.10822i) q^{33} +(1.86641 - 0.235782i) q^{34} +(-6.26874 + 2.52794i) q^{35} +(1.18114 - 2.51004i) q^{36} +(-0.810526 + 1.47434i) q^{37} +(-0.914984 - 0.974359i) q^{38} +(-7.40506 + 4.07097i) q^{39} +(-1.72745 + 5.43320i) q^{40} +(-5.33550 + 5.01037i) q^{41} +(3.80632 + 3.14886i) q^{42} +(4.98522 + 6.86156i) q^{43} +(-2.40414 - 0.951866i) q^{44} +(0.507355 - 4.23114i) q^{45} +(4.18160 + 5.05469i) q^{46} +(-3.77950 - 9.54593i) q^{47} +(-2.24092 + 0.427479i) q^{48} +(1.72928 - 1.25640i) q^{49} +(0.0466558 + 3.68886i) q^{50} +(4.56876 + 3.31940i) q^{51} +(5.02490 + 2.36454i) q^{52} +(0.00179146 + 0.00113689i) q^{53} +(1.66263 - 0.658282i) q^{54} +(-3.96578 - 0.224338i) q^{55} +(0.483938 - 7.69197i) q^{56} -4.01243i q^{57} +(1.90568 + 0.119896i) q^{58} +(-4.16519 - 8.85147i) q^{59} +(-6.29531 + 3.51290i) q^{60} +(-4.96975 - 4.66690i) q^{61} +(0.772066 + 6.11153i) q^{62} +(0.722025 + 5.71542i) q^{63} +(-1.64978 - 1.54924i) q^{64} +(8.47039 + 1.01568i) q^{65} +(1.23604 + 2.62672i) q^{66} +(3.00266 + 0.188911i) q^{67} -3.71134i q^{68} +(-1.23653 + 19.6541i) q^{69} +(-1.27079 - 4.82257i) q^{70} +(-9.18523 + 3.63669i) q^{71} +(4.10265 + 2.60362i) q^{72} +(-6.61756 - 3.11399i) q^{73} +(-1.00428 - 0.729655i) q^{74} +(-7.47831 + 8.16819i) q^{75} +(-2.13331 + 1.54994i) q^{76} +(5.27461 - 1.00619i) q^{77} +(-2.29522 - 5.79707i) q^{78} +(3.35584 + 4.05651i) q^{79} +(2.09010 + 0.967430i) q^{80} +(10.3069 + 4.08079i) q^{81} +(-3.17426 - 4.36899i) q^{82} +(7.00117 + 5.79187i) q^{83} +(7.10428 - 6.67136i) q^{84} +(-1.79604 - 5.41099i) q^{85} +(-5.48376 + 3.01472i) q^{86} +(3.92382 + 4.17844i) q^{87} +(2.18195 - 3.96894i) q^{88} +(0.108067 - 0.229654i) q^{89} +(3.05033 + 0.762665i) q^{90} +(-11.4418 + 1.44544i) q^{91} +(10.9273 - 6.93466i) q^{92} +(-10.8693 + 14.9604i) q^{93} +(7.33726 - 1.88389i) q^{94} +(-2.36021 + 3.29214i) q^{95} +(-0.814876 - 12.9521i) q^{96} +(-18.5231 + 1.16538i) q^{97} +(0.759785 + 1.38204i) q^{98} +(-1.04615 + 3.21970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

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