LMFDB - Embedded newform 961.2.g.h.338.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,4,-4,-4,12,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.h.816.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.363271i) q^{2} +(-0.129204 + 1.22930i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.381966 + 0.661585i) q^{6} +(4.14350 - 0.880728i) q^{7} +(0.690983 + 2.12663i) q^{8} +(1.43997 + 0.306074i) q^{9} +(0.0646021 + 0.614648i) q^{10} +(1.33826 + 1.48629i) q^{11} +(-1.82709 - 0.813473i) q^{12} +(1.12920 - 0.502754i) q^{13} +(1.75181 - 1.94558i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(3.50361 - 3.89116i) q^{17} +(0.831171 - 0.370061i) q^{18} +(2.04275 + 0.909491i) q^{19} +(-1.08268 - 1.20243i) q^{20} +(0.547318 + 5.20738i) q^{21} +(1.20906 + 0.256993i) q^{22} +(-2.38197 - 7.33094i) q^{23} +(-2.70353 + 0.574654i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.381966 - 0.661585i) q^{26} +(-1.70820 + 5.25731i) q^{27} +(-0.716449 + 6.81655i) q^{28} +(-5.85410 + 4.25325i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(-2.00000 + 1.45309i) q^{33} +(0.338261 - 3.21834i) q^{34} +(-1.30902 + 4.02874i) q^{35} +(-1.19098 + 2.06284i) q^{36} +(1.00000 + 1.73205i) q^{37} +(1.35177 - 0.287327i) q^{38} +(0.472136 + 1.45309i) q^{39} +(-2.18720 - 0.464905i) q^{40} +(-0.731699 - 6.96165i) q^{41} +(2.16535 + 2.40487i) q^{42} +(-2.95630 - 1.31623i) q^{43} +(-2.95630 + 1.31623i) q^{44} +(-0.985051 + 1.09401i) q^{45} +(-3.85410 - 2.80017i) q^{46} +(5.23607 + 3.80423i) q^{47} +(1.53351 - 1.70314i) q^{48} +(9.99809 - 4.45144i) q^{49} +(2.25841 + 1.00551i) q^{50} +(4.33070 + 4.80973i) q^{51} +(0.209057 + 1.98904i) q^{52} +(1.49448 + 0.317661i) q^{53} +(1.05573 + 3.24920i) q^{54} +(-1.95630 + 0.415823i) q^{55} +(4.73607 + 8.20311i) q^{56} +(-1.38197 + 2.39364i) q^{57} +(-1.38197 + 4.25325i) q^{58} +(0.233733 - 2.22382i) q^{59} +(1.61803 - 1.17557i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(0.190983 - 0.138757i) q^{64} +(-0.129204 + 1.22930i) q^{65} +(-0.472136 + 1.45309i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(4.23607 + 7.33708i) q^{68} +(9.31966 - 1.98095i) q^{69} +(0.809017 + 2.48990i) q^{70} +(-12.8923 - 2.74035i) q^{71} +(0.344086 + 3.27376i) q^{72} +(-0.315921 - 0.350865i) q^{73} +(1.12920 + 0.502754i) q^{74} +(-4.51682 + 2.01102i) q^{75} +(-2.42094 + 2.68872i) q^{76} +(6.85410 + 4.97980i) q^{77} +(0.763932 + 0.555029i) q^{78} +(1.14301 - 1.26944i) q^{79} +(1.69381 - 0.754131i) q^{80} +(-2.20750 - 0.982842i) q^{81} +(-2.89482 - 3.21502i) q^{82} +(-0.307760 - 2.92814i) q^{83} +(-8.28700 - 1.76146i) q^{84} +(1.61803 + 4.97980i) q^{85} +(-1.95630 + 0.415823i) q^{86} +(-4.47214 - 7.74597i) q^{87} +(-2.23607 + 3.87298i) q^{88} +(-0.527864 + 1.62460i) q^{89} +(-0.0951031 + 0.904846i) q^{90} +(4.23607 - 3.07768i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(-1.80902 + 1.31433i) q^{95} +(0.725874 - 6.90623i) q^{96} +(0.600813 - 1.84911i) q^{97} +(3.38197 - 5.85774i) q^{98} +(1.47214 + 2.54981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} - q^{14} - 8 q^{15} - 12 q^{16} - 2 q^{17} - 6 q^{18} + 5 q^{19} + 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 - q^14 - 8 * q^15 - 12 * q^16 - 2 * q^17 - 6 * q^18 + 5 * q^19 + 2 * q^20 - 8 * q^21 + 6 * q^22 - 28 * q^23 + 10 * q^24 + 16 * q^25 + 12 * q^26 + 40 * q^27 + 11 * q^28 - 20 * q^29 - 24 * q^30 - 36 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 14 * q^36 + 8 * q^37 - 5 * q^38 - 32 * q^39 - 5 * q^40 + 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 + 13 * q^45 - 4 * q^46 + 24 * q^47 + 24 * q^48 + 22 * q^49 + 8 * q^50 - 8 * q^51 - 2 * q^52 - 16 * q^53 + 80 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 - 20 * q^58 - 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 + 6 * q^64 + 4 * q^65 + 32 * q^66 - 32 * q^67 + 16 * q^68 - 24 * q^69 + 2 * q^70 - 23 * q^71 + 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 + 28 * q^77 + 24 * q^78 - 20 * q^79 + 6 * q^80 - 19 * q^81 + 21 * q^82 + 14 * q^83 - 6 * q^84 + 4 * q^85 + 2 * q^86 - 40 * q^89 - 6 * q^90 + 16 * q^91 + 64 * q^92 + 32 * q^94 - 10 * q^95 - 18 * q^96 + 54 * q^97 + 36 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	0.500000	−	0.363271i	0.353553	−	0.256872i	−0.396805	−	0.917903i	$-0.629881\pi$
$2$	0.500000	−	0.363271i	0.353553	−	0.256872i	0.750358	+	0.661031i	$0.229881\pi$
$3$	−0.129204	+	1.22930i	−0.0745961	+	0.709735i	0.891757	+	0.452515i	$0.149473\pi$
$3$	−0.129204	+	1.22930i	−0.0745961	+	0.709735i	−0.966353	+	0.257220i	$0.917194\pi$
$4$	−0.500000	+	1.53884i	−0.250000	+	0.769421i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	0.381966	+	0.661585i	0.155937	+	0.270091i
$7$	4.14350	−	0.880728i	1.56610	−	0.332884i	0.658451	−	0.752623i	$-0.271212\pi$
$7$	4.14350	−	0.880728i	1.56610	−	0.332884i	0.907645	+	0.419740i	$0.137879\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	1.43997	+	0.306074i	0.479989	+	0.102025i
$10$	0.0646021	+	0.614648i	0.0204290	+	0.194369i
$11$	1.33826	+	1.48629i	0.403501	+	0.448133i	0.910311	−	0.413924i	$-0.135842\pi$
$11$	1.33826	+	1.48629i	0.403501	+	0.448133i	−0.506810	+	0.862058i	$0.669176\pi$
$12$	−1.82709	−	0.813473i	−0.527436	−	0.234830i
$13$	1.12920	−	0.502754i	0.313185	−	0.139439i	−0.244124	−	0.969744i	$-0.578500\pi$
$13$	1.12920	−	0.502754i	0.313185	−	0.139439i	0.557309	+	0.830305i	$0.311834\pi$
$14$	1.75181	−	1.94558i	0.468190	−	0.519978i
$15$	−1.00000	−	0.726543i	−0.258199	−	0.187592i
$16$	−1.50000	−	1.08981i	−0.375000	−	0.272453i
$17$	3.50361	−	3.89116i	0.849751	−	0.943744i	−0.149233	−	0.988802i	$-0.547681\pi$
$17$	3.50361	−	3.89116i	0.849751	−	0.943744i	0.998984	+	0.0450579i	$0.0143472\pi$
$18$	0.831171	−	0.370061i	0.195909	−	0.0872243i
$19$	2.04275	+	0.909491i	0.468639	+	0.208651i	0.627449	−	0.778658i	$-0.284099\pi$
$19$	2.04275	+	0.909491i	0.468639	+	0.208651i	−0.158810	+	0.987309i	$0.550766\pi$
$20$	−1.08268	−	1.20243i	−0.242094	−	0.268872i
$21$	0.547318	+	5.20738i	0.119435	+	1.13634i
$22$	1.20906	+	0.256993i	0.257772	+	0.0547911i
$23$	−2.38197	−	7.33094i	−0.496674	−	1.52861i	−0.814331	−	0.580400i	$-0.802896\pi$
$23$	−2.38197	−	7.33094i	−0.496674	−	1.52861i	0.317657	−	0.948206i	$-0.397104\pi$
$24$	−2.70353	+	0.574654i	−0.551856	+	0.117301i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	0.381966	−	0.661585i	0.0749097	−	0.129747i
$27$	−1.70820	+	5.25731i	−0.328744	+	1.01177i
$28$	−0.716449	+	6.81655i	−0.135396	+	1.28821i
$29$	−5.85410	+	4.25325i	−1.08708	+	0.789809i	−0.978904	−	0.204322i	$-0.934501\pi$
$29$	−5.85410	+	4.25325i	−1.08708	+	0.789809i	−0.108176	+	0.994132i	$0.534501\pi$
$30$	−0.763932			−0.139474
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	−2.00000	+	1.45309i	−0.348155	+	0.252950i
$34$	0.338261	−	3.21834i	0.0580113	−	0.551941i
$35$	−1.30902	+	4.02874i	−0.221264	+	0.680981i
$36$	−1.19098	+	2.06284i	−0.198497	+	0.343807i
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	1.35177	−	0.287327i	0.219286	−	0.0466106i
$39$	0.472136	+	1.45309i	0.0756023	+	0.232680i
$40$	−2.18720	−	0.464905i	−0.345827	−	0.0735079i
$41$	−0.731699	−	6.96165i	−0.114272	−	1.08723i	−0.889937	−	0.456083i	$-0.849252\pi$
$41$	−0.731699	−	6.96165i	−0.114272	−	1.08723i	0.775665	−	0.631145i	$-0.217415\pi$
$42$	2.16535	+	2.40487i	0.334121	+	0.371079i
$43$	−2.95630	−	1.31623i	−0.450831	−	0.200723i	0.168745	−	0.985660i	$-0.446029\pi$
$43$	−2.95630	−	1.31623i	−0.450831	−	0.200723i	−0.619576	+	0.784937i	$0.712695\pi$
$44$	−2.95630	+	1.31623i	−0.445678	+	0.198429i
$45$	−0.985051	+	1.09401i	−0.146843	+	0.163085i
$46$	−3.85410	−	2.80017i	−0.568256	−	0.412862i
$47$	5.23607	+	3.80423i	0.763759	+	0.554903i	0.900061	−	0.435764i	$-0.143522\pi$
$47$	5.23607	+	3.80423i	0.763759	+	0.554903i	−0.136302	+	0.990667i	$0.543522\pi$
$48$	1.53351	−	1.70314i	0.221343	−	0.245827i
$49$	9.99809	−	4.45144i	1.42830	−	0.635919i
$50$	2.25841	+	1.00551i	0.319387	+	0.142200i
$51$	4.33070	+	4.80973i	0.606420	+	0.673498i
$52$	0.209057	+	1.98904i	0.0289910	+	0.275831i
$53$	1.49448	+	0.317661i	0.205282	+	0.0436341i	0.309405	−	0.950930i	$-0.399870\pi$
$53$	1.49448	+	0.317661i	0.205282	+	0.0436341i	−0.104123	+	0.994564i	$0.533203\pi$
$54$	1.05573	+	3.24920i	0.143666	+	0.442160i
$55$	−1.95630	+	0.415823i	−0.263787	+	0.0560696i
$56$	4.73607	+	8.20311i	0.632884	+	1.09619i
$57$	−1.38197	+	2.39364i	−0.183046	+	0.317045i
$58$	−1.38197	+	4.25325i	−0.181461	+	0.558480i
$59$	0.233733	−	2.22382i	0.0304294	−	0.289517i	−0.968716	−	0.248174i	$-0.920170\pi$
$59$	0.233733	−	2.22382i	0.0304294	−	0.289517i	0.999145	−	0.0413430i	$-0.0131636\pi$
$60$	1.61803	−	1.17557i	0.208887	−	0.151765i
$61$	−14.1803			−1.81561			−0.907803	−	0.419396i	$-0.862242\pi$
$61$	−14.1803			−1.81561			−0.907803	+	0.419396i	$0.862242\pi$
$62$		0			0
$63$	6.23607			0.785671
$64$	0.190983	−	0.138757i	0.0238729	−	0.0173447i
$65$	−0.129204	+	1.22930i	−0.0160258	+	0.152475i
$66$	−0.472136	+	1.45309i	−0.0581159	+	0.178862i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	4.23607	+	7.33708i	0.513699	+	0.889752i
$69$	9.31966	−	1.98095i	1.12195	−	0.238479i
$70$	0.809017	+	2.48990i	0.0966960	+	0.297600i
$71$	−12.8923	−	2.74035i	−1.53004	−	0.325219i	−0.635460	−	0.772134i	$-0.719189\pi$
$71$	−12.8923	−	2.74035i	−1.53004	−	0.325219i	−0.894577	+	0.446914i	$0.852523\pi$
$72$	0.344086	+	3.27376i	0.0405510	+	0.385817i
$73$	−0.315921	−	0.350865i	−0.0369757	−	0.0410657i	0.724373	−	0.689408i	$-0.242129\pi$
$73$	−0.315921	−	0.350865i	−0.0369757	−	0.0410657i	−0.761349	+	0.648342i	$0.775463\pi$
$74$	1.12920	+	0.502754i	0.131267	+	0.0584440i
$75$	−4.51682	+	2.01102i	−0.521557	+	0.232212i
$76$	−2.42094	+	2.68872i	−0.277701	+	0.308418i
$77$	6.85410	+	4.97980i	0.781097	+	0.567500i
$78$	0.763932	+	0.555029i	0.0864983	+	0.0628447i
$79$	1.14301	−	1.26944i	0.128599	−	0.142823i	−0.675406	−	0.737446i	$-0.736032\pi$
$79$	1.14301	−	1.26944i	0.128599	−	0.142823i	0.804005	+	0.594622i	$0.202698\pi$
$80$	1.69381	−	0.754131i	0.189373	−	0.0843144i
$81$	−2.20750	−	0.982842i	−0.245278	−	0.109205i
$82$	−2.89482	−	3.21502i	−0.319679	−	0.355040i
$83$	−0.307760	−	2.92814i	−0.0337811	−	0.321405i	−0.998343	−	0.0575479i	$-0.981672\pi$
$83$	−0.307760	−	2.92814i	−0.0337811	−	0.321405i	0.964562	−	0.263858i	$-0.0849949\pi$
$84$	−8.28700	−	1.76146i	−0.904186	−	0.192191i
$85$	1.61803	+	4.97980i	0.175500	+	0.540135i
$86$	−1.95630	+	0.415823i	−0.210953	+	0.0448394i
$87$	−4.47214	−	7.74597i	−0.479463	−	0.830455i
$88$	−2.23607	+	3.87298i	−0.238366	+	0.412861i
$89$	−0.527864	+	1.62460i	−0.0559535	+	0.172207i	−0.975128	−	0.221644i	$-0.928858\pi$
$89$	−0.527864	+	1.62460i	−0.0559535	+	0.172207i	0.919174	+	0.393852i	$0.128858\pi$
$90$	−0.0951031	+	0.904846i	−0.0100248	+	0.0953791i
$91$	4.23607	−	3.07768i	0.444061	−	0.322629i
$92$	12.4721			1.30031
$93$		0			0
$94$	4.00000			0.412568
$95$	−1.80902	+	1.31433i	−0.185601	+	0.134847i
$96$	0.725874	−	6.90623i	0.0740842	−	0.704864i
$97$	0.600813	−	1.84911i	0.0610033	−	0.187749i	−0.915911	−	0.401382i	$-0.868530\pi$
$97$	0.600813	−	1.84911i	0.0610033	−	0.187749i	0.976914	+	0.213634i	$0.0685298\pi$
$98$	3.38197	−	5.85774i	0.341630	−	0.591721i
$99$	1.47214	+	2.54981i	0.147955	+	0.256266i
$100$	−6.33070	+	1.34563i	−0.633070	+	0.134563i
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	0.894281	−	0.447506i	$-0.147688\pi$
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	−0.986526	+	0.163605i	$0.947688\pi$
$102$	3.91259	+	0.831647i	0.387404	+	0.0823453i
$103$	−0.184381	−	1.75427i	−0.0181676	−	0.172853i	0.981676	−	0.190560i	$-0.0610303\pi$
$103$	−0.184381	−	1.75427i	−0.0181676	−	0.172853i	−0.999843	+	0.0177064i	$0.994364\pi$
$104$	1.84943	+	2.05400i	0.181352	+	0.201411i
$105$	−4.78339	−	2.12970i	−0.466811	−	0.207838i
$106$	0.862635	−	0.384070i	0.0837865	−	0.0373042i
$107$	6.84927	−	7.60688i	0.662144	−	0.735385i	−0.314735	−	0.949180i	$-0.601916\pi$
$107$	6.84927	−	7.60688i	0.662144	−	0.735385i	0.976879	+	0.213795i	$0.0685823\pi$
$108$	−7.23607	−	5.25731i	−0.696291	−	0.505885i
$109$	−3.19098	−	2.31838i	−0.305641	−	0.222061i	0.424383	−	0.905483i	$-0.360491\pi$
$109$	−3.19098	−	2.31838i	−0.305641	−	0.222061i	−0.730024	+	0.683422i	$0.760491\pi$
$110$	−0.827091	+	0.918578i	−0.0788600	+	0.0875829i
$111$	−2.25841	+	1.00551i	−0.214359	+	0.0954386i
$112$	−7.17508	−	3.19455i	−0.677981	−	0.301857i
$113$	−3.66157	−	4.06659i	−0.344452	−	0.382553i	0.545881	−	0.837863i	$-0.316195\pi$
$113$	−3.66157	−	4.06659i	−0.344452	−	0.382553i	−0.890333	+	0.455310i	$0.849528\pi$
$114$	0.178556	+	1.69885i	0.0167233	+	0.159112i
$115$	7.53976	+	1.60263i	0.703086	+	0.149446i
$116$	−3.61803	−	11.1352i	−0.335926	−	1.03387i
$117$	1.77990	−	0.378329i	0.164551	−	0.0349765i
$118$	−0.690983	−	1.19682i	−0.0636101	−	0.110176i
$119$	11.0902	−	19.2087i	1.01663	−	1.76086i
$120$	0.854102	−	2.62866i	0.0779685	−	0.239962i
$121$	0.731699	−	6.96165i	0.0665181	−	0.632878i
$122$	−7.09017	+	5.15131i	−0.641914	+	0.466378i
$123$	8.65248			0.780167
$124$		0			0
$125$	−9.00000			−0.804984
$126$	3.11803	−	2.26538i	0.277777	−	0.201816i
$127$	−0.368762	+	3.50854i	−0.0327224	+	0.311332i	0.965902	+	0.258906i	$0.0833621\pi$
$127$	−0.368762	+	3.50854i	−0.0327224	+	0.311332i	−0.998625	+	0.0524261i	$0.983305\pi$
$128$	3.51722	−	10.8249i	0.310881	−	0.956794i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	0.381966	+	0.661585i	0.0335006	+	0.0580248i
$131$	−11.7378	+	2.49494i	−1.02553	+	0.217984i	−0.689821	−	0.723980i	$-0.742311\pi$
$131$	−11.7378	+	2.49494i	−1.02553	+	0.217984i	−0.335713	+	0.941964i	$0.608977\pi$
$132$	−1.23607	−	3.80423i	−0.107586	−	0.331115i
$133$	9.26515	+	1.96937i	0.803390	+	0.170766i
$134$	0.516817	+	4.91719i	0.0446462	+	0.424780i
$135$	−3.69886	−	4.10800i	−0.318347	−	0.353561i
$136$	10.6960	+	4.76216i	0.917172	+	0.408351i
$137$	18.0043	−	8.01605i	1.53821	−	0.684857i	0.549614	−	0.835419i	$-0.314775\pi$
$137$	18.0043	−	8.01605i	1.53821	−	0.684857i	0.988601	+	0.150562i	$0.0481082\pi$
$138$	3.94020	−	4.37604i	0.335413	−	0.372513i
$139$	10.8541	+	7.88597i	0.920633	+	0.668879i	0.943681	−	0.330855i	$-0.107337\pi$
$139$	10.8541	+	7.88597i	0.920633	+	0.668879i	−0.0230486	+	0.999734i	$0.507337\pi$
$140$	−5.54508	−	4.02874i	−0.468645	−	0.340491i
$141$	−5.35304	+	5.94516i	−0.450808	+	0.500673i
$142$	−7.44165	+	3.31324i	−0.624489	+	0.278041i
$143$	2.25841	+	1.00551i	0.188858	+	0.0840848i
$144$	−1.82639	−	2.02841i	−0.152199	−	0.169034i
$145$	−0.756375	−	7.19643i	−0.0628135	−	0.597631i
$146$	−0.285420	−	0.0606678i	−0.0236215	−	0.00502090i
$147$	4.18034	+	12.8658i	0.344789	+	1.06115i
$148$	−3.16535	+	0.672816i	−0.260190	+	0.0553052i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$	−1.52786	+	2.64634i	−0.124750	+	0.216073i
$151$	2.52786	−	7.77997i	0.205715	−	0.633125i	−0.793969	−	0.607959i	$-0.791989\pi$
$151$	2.52786	−	7.77997i	0.205715	−	0.633125i	0.999683	−	0.0251659i	$-0.00801140\pi$
$152$	−0.522642	+	4.97261i	−0.0423919	+	0.403332i
$153$	6.23607	−	4.53077i	0.504156	−	0.366291i
$154$	5.23607			0.421934
$155$		0			0
$156$	−2.47214			−0.197929
$157$	12.0451	−	8.75127i	0.961302	−	0.698427i	0.00784957	−	0.999969i	$-0.497501\pi$
$157$	12.0451	−	8.75127i	0.961302	−	0.698427i	0.953453	+	0.301542i	$0.0975014\pi$
$158$	0.110354	−	1.04994i	0.00877926	−	0.0835291i
$159$	−0.583592	+	1.79611i	−0.0462819	+	0.142441i
$160$	2.80902	−	4.86536i	0.222072	−	0.384640i
$161$	−16.3262	−	28.2779i	−1.28669	−	2.22861i
$162$	−1.46079	+	0.310500i	−0.114770	+	0.0243952i
$163$	−0.836881	−	2.57565i	−0.0655496	−	0.201741i	0.912917	−	0.408144i	$-0.133824\pi$
$163$	−0.836881	−	2.57565i	−0.0655496	−	0.201741i	−0.978467	+	0.206404i	$0.933824\pi$
$164$	11.0787	+	2.35486i	0.865104	+	0.183883i
$165$	−0.258409	−	2.45859i	−0.0201171	−	0.191401i
$166$	−1.21759	−	1.35227i	−0.0945033	−	0.104957i
$167$	2.25841	+	1.00551i	0.174761	+	0.0778086i	0.492252	−	0.870453i	$-0.336174\pi$
$167$	2.25841	+	1.00551i	0.174761	+	0.0778086i	−0.317491	+	0.948261i	$0.602840\pi$
$168$	−10.6960	+	4.76216i	−0.825213	+	0.367408i
$169$	−7.67636	+	8.52546i	−0.590489	+	0.655804i
$170$	2.61803	+	1.90211i	0.200794	+	0.145885i
$171$	2.66312	+	1.93487i	0.203654	+	0.147963i
$172$	3.50361	−	3.89116i	0.267148	−	0.296698i
$173$	−13.6523	+	6.07838i	−1.03796	+	0.462131i	−0.853710	−	0.520748i	$-0.825653\pi$
$173$	−13.6523	+	6.07838i	−1.03796	+	0.462131i	−0.184253	+	0.982879i	$0.558986\pi$
$174$	−5.04996	−	2.24838i	−0.382836	−	0.170450i
$175$	11.3379	+	12.5920i	0.857067	+	0.951869i
$176$	−0.387613	−	3.68789i	−0.0292174	−	0.277985i
$177$	2.70353	+	0.574654i	0.203210	+	0.0431936i
$178$	0.326238	+	1.00406i	0.0244526	+	0.0752573i
$179$	11.4524	−	2.43427i	0.855989	−	0.181946i	0.241042	−	0.970515i	$-0.422511\pi$
$179$	11.4524	−	2.43427i	0.855989	−	0.181946i	0.614947	+	0.788569i	$0.289177\pi$
$180$	−1.19098	−	2.06284i	−0.0887706	−	0.153755i
$181$	−9.09017	+	15.7446i	−0.675667	+	1.17029i	0.300606	+	0.953748i	$0.402811\pi$
$181$	−9.09017	+	15.7446i	−0.675667	+	1.17029i	−0.976273	+	0.216541i	$0.930522\pi$
$182$	1.00000	−	3.07768i	0.0741249	−	0.228133i
$183$	1.83216	−	17.4318i	0.135437	−	1.28860i
$184$	13.9443	−	10.1311i	1.02799	−	0.746875i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	10.4721			0.765798
$188$	−8.47214	+	6.15537i	−0.617894	+	0.448926i
$189$	−2.44768	+	23.2881i	−0.178043	+	1.69396i
$190$	−0.427051	+	1.31433i	−0.0309815	+	0.0953514i
$191$	−1.59017	+	2.75426i	−0.115061	+	0.199291i	−0.917804	−	0.397034i	$-0.870040\pi$
$191$	−1.59017	+	2.75426i	−0.115061	+	0.199291i	0.802743	+	0.596325i	$0.203373\pi$
$192$	0.145898	+	0.252703i	0.0105293	+	0.0182373i
$193$	5.35256	−	1.13772i	0.385285	−	0.0818950i	−0.0111969	−	0.999937i	$-0.503564\pi$
$193$	5.35256	−	1.13772i	0.385285	−	0.0818950i	0.396482	+	0.918042i	$0.370231\pi$
$194$	−0.371323	−	1.14281i	−0.0266594	−	0.0820493i
$195$	−1.49448	−	0.317661i	−0.107022	−	0.0227482i
$196$	1.85101	+	17.6112i	0.132215	+	1.25794i
$197$	−10.3156	−	11.4566i	−0.734955	−	0.816251i	0.253568	−	0.967318i	$-0.418396\pi$
$197$	−10.3156	−	11.4566i	−0.734955	−	0.816251i	−0.988524	+	0.151067i	$0.951729\pi$
$198$	1.66234	+	0.740122i	0.118138	+	0.0525982i
$199$	−0.964456	+	0.429403i	−0.0683684	+	0.0304396i	−0.440636	−	0.897686i	$-0.645247\pi$
$199$	−0.964456	+	0.429403i	−0.0683684	+	0.0304396i	0.372268	+	0.928125i	$0.378580\pi$
$200$	−5.98489	+	6.64689i	−0.423195	+	0.470006i
$201$	−8.00000	−	5.81234i	−0.564276	−	0.409971i
$202$	−1.50000	−	1.08981i	−0.105540	−	0.0766790i
$203$	−20.5105	+	22.7792i	−1.43956	+	1.59879i
$204$	−9.56677	+	4.25940i	−0.669808	+	0.298218i
$205$	6.39482	+	2.84716i	0.446633	+	0.198854i
$206$	−0.729466	−	0.810154i	−0.0508243	−	0.0564461i
$207$	−1.18614	−	11.2854i	−0.0824424	−	0.784387i
$208$	−2.24171	−	0.476491i	−0.155435	−	0.0330387i
$209$	1.38197	+	4.25325i	0.0955926	+	0.294204i
$210$	−3.16535	+	0.672816i	−0.218430	+	0.0464287i
$211$	−0.409830	−	0.709846i	−0.0282139	−	0.0488678i	0.851574	−	0.524235i	$-0.175649\pi$
$211$	−0.409830	−	0.709846i	−0.0282139	−	0.0488678i	−0.879788	+	0.475367i	$0.842315\pi$
$212$	−1.23607	+	2.14093i	−0.0848935	+	0.147040i
$213$	5.03444	−	15.4944i	0.344954	−	1.06166i
$214$	0.661272	−	6.29158i	0.0452036	−	0.430084i
$215$	2.61803	−	1.90211i	0.178548	−	0.129723i
$216$	−12.3607			−0.841038
$217$		0			0
$218$	−2.43769			−0.165101
$219$	0.472136	−	0.343027i	0.0319040	−	0.0231796i
$220$	0.338261	−	3.21834i	0.0228056	−	0.216980i
$221$	2.00000	−	6.15537i	0.134535	−	0.414055i
$222$	−0.763932	+	1.32317i	−0.0512718	+	0.0888053i
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$	−23.2783	+	4.94796i	−1.55535	+	0.330599i
$225$	1.81966	+	5.60034i	0.121311	+	0.373356i
$226$	−3.30806	−	0.703150i	−0.220049	−	0.0467729i
$227$	−0.258409	−	2.45859i	−0.0171512	−	0.163183i	0.982594	−	0.185767i	$-0.0594771\pi$
$227$	−0.258409	−	2.45859i	−0.0171512	−	0.163183i	−0.999745	+	0.0225848i	$0.992810\pi$
$228$	−2.99244	−	3.32344i	−0.198179	−	0.220101i
$229$	12.2565	+	5.45694i	0.809932	+	0.360605i	0.769556	−	0.638579i	$-0.220478\pi$
$229$	12.2565	+	5.45694i	0.809932	+	0.360605i	0.0403763	+	0.999185i	$0.487144\pi$
$230$	4.35207	−	1.93767i	0.286967	−	0.127766i
$231$	−7.00723	+	7.78231i	−0.461042	+	0.512039i
$232$	−13.0902	−	9.51057i	−0.859412	−	0.624399i
$233$	−0.0450850	−	0.0327561i	−0.00295361	−	0.00214593i	0.586307	−	0.810089i	$-0.300581\pi$
$233$	−0.0450850	−	0.0327561i	−0.00295361	−	0.00214593i	−0.589261	+	0.807943i	$0.700581\pi$
$234$	0.752512	−	0.835749i	0.0491933	−	0.0546346i
$235$	−5.91259	+	2.63245i	−0.385695	+	0.171722i
$236$	3.30524	+	1.47159i	0.215153	+	0.0957922i
$237$	1.41284	+	1.56912i	0.0917738	+	0.101925i
$238$	−1.43290	−	13.6331i	−0.0928809	−	0.883703i
$239$	−1.67088	−	0.355156i	−0.108080	−	0.0229731i	0.153554	−	0.988140i	$-0.450928\pi$
$239$	−1.67088	−	0.355156i	−0.108080	−	0.0229731i	−0.261634	+	0.965167i	$0.584261\pi$
$240$	0.708204	+	2.17963i	0.0457144	+	0.140694i
$241$	29.6972	−	6.31234i	1.91297	−	0.406614i	0.912968	−	0.408032i	$-0.133785\pi$
$241$	29.6972	−	6.31234i	1.91297	−	0.406614i	0.999999	+	0.00141870i	$0.000451585\pi$
$242$	−2.16312	−	3.74663i	−0.139051	−	0.240843i
$243$	−6.79837	+	11.7751i	−0.436116	+	0.755375i
$244$	7.09017	−	21.8213i	0.453902	−	1.39697i
$245$	−1.14399	+	10.8843i	−0.0730867	+	0.695374i
$246$	4.32624	−	3.14320i	0.275831	−	0.200403i
$247$	2.76393			0.175865
$248$		0			0
$249$	3.63932			0.230633
$250$	−4.50000	+	3.26944i	−0.284605	+	0.206778i
$251$	2.52753	−	24.0479i	0.159537	−	1.51789i	−0.562943	−	0.826496i	$-0.690331\pi$
$251$	2.52753	−	24.0479i	0.159537	−	1.51789i	0.722479	−	0.691393i	$-0.243002\pi$
$252$	−3.11803	+	9.59632i	−0.196418	+	0.604511i
$253$	7.70820	−	13.3510i	0.484611	−	0.839370i
$254$	1.09017	+	1.88823i	0.0684033	+	0.118478i
$255$	−6.33070	+	1.34563i	−0.396444	+	0.0842668i
$256$	−2.02786	−	6.24112i	−0.126742	−	0.390070i
$257$	15.5959	+	3.31500i	0.972842	+	0.206784i	0.666802	−	0.745235i	$-0.267663\pi$
$257$	15.5959	+	3.31500i	0.972842	+	0.206784i	0.306040	+	0.952019i	$0.400996\pi$
$258$	−0.258409	−	2.45859i	−0.0160878	−	0.153065i
$259$	5.66897	+	6.29602i	0.352252	+	0.391216i
$260$	−1.82709	−	0.813473i	−0.113311	−	0.0504495i
$261$	−9.73152	+	4.33275i	−0.602366	+	0.268191i
$262$	−4.96255	+	5.51147i	−0.306587	+	0.340499i
$263$	15.1803	+	11.0292i	0.936060	+	0.680087i	0.947469	−	0.319848i	$-0.103632\pi$
$263$	15.1803	+	11.0292i	0.936060	+	0.680087i	−0.0114091	+	0.999935i	$0.503632\pi$
$264$	−4.47214	−	3.24920i	−0.275241	−	0.199974i
$265$	−1.02234	+	1.13542i	−0.0628019	+	0.0697486i
$266$	5.34799	−	2.38108i	0.327906	−	0.145993i
$267$	−1.92891	−	0.858807i	−0.118047	−	0.0525581i
$268$	−8.66141	−	9.61947i	−0.529080	−	0.587603i
$269$	3.02550	+	28.7857i	0.184468	+	1.75510i	0.560191	+	0.828364i	$0.310728\pi$
$269$	3.02550	+	28.7857i	0.184468	+	1.75510i	−0.375723	+	0.926732i	$0.622605\pi$
$270$	−3.34175	−	0.710311i	−0.203372	−	0.0432282i
$271$	2.52786	+	7.77997i	0.153557	+	0.472599i	0.998012	−	0.0630273i	$-0.0200755\pi$
$271$	2.52786	+	7.77997i	0.153557	+	0.472599i	−0.844455	+	0.535627i	$0.820076\pi$
$272$	−9.49606	+	2.01845i	−0.575783	+	0.122386i
$273$	3.23607	+	5.60503i	0.195856	+	0.339232i
$274$	6.09017	−	10.5485i	0.367921	−	0.637257i
$275$	−2.47214	+	7.60845i	−0.149075	+	0.458807i
$276$	−1.61145	+	15.3320i	−0.0969981	+	0.922875i
$277$	−15.0902	+	10.9637i	−0.906680	+	0.658742i	−0.940173	−	0.340697i	$-0.889337\pi$
$277$	−15.0902	+	10.9637i	−0.906680	+	0.658742i	0.0334927	+	0.999439i	$0.489337\pi$
$278$	8.29180			0.497309
$279$		0			0
$280$	−9.47214			−0.566068
$281$	−13.7533	+	9.99235i	−0.820452	+	0.596094i	−0.916842	−	0.399250i	$-0.869271\pi$
$281$	−13.7533	+	9.99235i	−0.820452	+	0.596094i	0.0963896	+	0.995344i	$0.469271\pi$
$282$	−0.516817	+	4.91719i	−0.0307760	+	0.292814i
$283$	6.76393	−	20.8172i	0.402074	−	1.23746i	−0.521240	−	0.853410i	$-0.674530\pi$
$283$	6.76393	−	20.8172i	0.402074	−	1.23746i	0.923314	−	0.384046i	$-0.125470\pi$
$284$	10.6631	−	18.4691i	0.632740	−	1.09594i
$285$	−1.38197	−	2.39364i	−0.0818606	−	0.141787i
$286$	1.49448	−	0.317661i	0.0883703	−	0.0187837i
$287$	−9.16312	−	28.2012i	−0.540882	−	1.66466i
$288$	−8.08978	−	1.71954i	−0.476695	−	0.101325i
$289$	−1.08881	−	10.3593i	−0.0640477	−	0.609373i
$290$	−2.99244	−	3.32344i	−0.175722	−	0.195159i
$291$	2.19548	+	0.977491i	0.128701	+	0.0573015i
$292$	0.697887	−	0.310719i	0.0408407	−	0.0181835i
$293$	5.66897	−	6.29602i	0.331184	−	0.367818i	−0.554437	−	0.832226i	$-0.687066\pi$
$293$	5.66897	−	6.29602i	0.331184	−	0.367818i	0.885621	+	0.464408i	$0.153733\pi$
$294$	6.76393	+	4.91428i	0.394481	+	0.286607i
$295$	1.80902	+	1.31433i	0.105325	+	0.0765231i
$296$	−2.99244	+	3.32344i	−0.173932	+	0.193171i
$297$	−10.0999	+	4.49677i	−0.586056	+	0.260929i
$298$	−5.64602	−	2.51377i	−0.327065	−	0.145619i
$299$	−6.37539	−	7.08058i	−0.368698	−	0.409481i
$300$	−0.836228	−	7.95618i	−0.0482796	−	0.459350i
$301$	−13.4086	−	2.85010i	−0.772862	−	0.164277i
$302$	−1.56231	−	4.80828i	−0.0899006	−	0.276686i
$303$	3.62717	−	0.770979i	0.208376	−	0.0442916i
$304$	−2.07295	−	3.59045i	−0.118892	−	0.205927i
$305$	7.09017	−	12.2805i	0.405982	−	0.703181i
$306$	1.47214	−	4.53077i	0.0841564	−	0.259007i
$307$	1.59843	−	15.2080i	0.0912271	−	0.867968i	−0.849223	−	0.528035i	$-0.822929\pi$
$307$	1.59843	−	15.2080i	0.0912271	−	0.867968i	0.940450	−	0.339933i	$-0.110404\pi$
$308$	−11.0902	+	8.05748i	−0.631921	+	0.459118i
$309$	2.18034			0.124035
$310$		0			0
$311$	−6.81966			−0.386707			−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966			−0.386707			−0.193354	+	0.981129i	$0.561936\pi$
$312$	−2.76393	+	2.00811i	−0.156477	+	0.113687i
$313$	−2.21977	+	21.1197i	−0.125469	+	1.19376i	0.732759	+	0.680489i	$0.238232\pi$
$313$	−2.21977	+	21.1197i	−0.125469	+	1.19376i	−0.858228	+	0.513269i	$0.828434\pi$
$314$	2.84346	−	8.75127i	0.160466	−	0.493863i
$315$	−3.11803	+	5.40059i	−0.175681	+	0.304289i
$316$	1.38197	+	2.39364i	0.0777417	+	0.134653i
$317$	−21.4647	+	4.56247i	−1.20558	+	0.256254i	−0.766530	−	0.642209i	$-0.778018\pi$
$317$	−21.4647	+	4.56247i	−1.20558	+	0.256254i	−0.439050	+	0.898463i	$0.644685\pi$
$318$	0.360680	+	1.11006i	0.0202259	+	0.0622490i
$319$	−14.1559	−	3.00893i	−0.792577	−	0.168468i
$320$	0.0246758	+	0.234775i	0.00137942	+	0.0131243i
$321$	8.46616	+	9.40262i	0.472535	+	0.524803i
$322$	−18.4357	−	8.20808i	−1.02738	−	0.457419i
$323$	10.6960	−	4.76216i	0.595140	−	0.264973i
$324$	2.61619	−	2.90557i	0.145344	−	0.161421i
$325$	4.00000	+	2.90617i	0.221880	+	0.161205i
$326$	−1.35410	−	0.983813i	−0.0749968	−	0.0544883i
$327$	3.26227	−	3.62312i	0.180404	−	0.200359i
$328$	14.2992	−	6.36644i	0.789544	−	0.351528i
$329$	25.0461	+	11.1513i	1.38084	+	0.614789i
$330$	−1.02234	−	1.13542i	−0.0562780	−	0.0625030i
$331$	−0.209057	−	1.98904i	−0.0114908	−	0.109328i	0.987273	−	0.159034i	$-0.0508380\pi$
$331$	−0.209057	−	1.98904i	−0.0114908	−	0.109328i	−0.998764	+	0.0497066i	$0.984171\pi$
$332$	4.65983	+	0.990477i	0.255741	+	0.0543595i
$333$	0.909830	+	2.80017i	0.0498584	+	0.153448i
$334$	1.49448	−	0.317661i	0.0817741	−	0.0173816i
$335$	−4.00000	−	6.92820i	−0.218543	−	0.378528i
$336$	4.85410	−	8.40755i	0.264813	−	0.458670i
$337$	−5.94427	+	18.2946i	−0.323805	+	0.996570i	0.648172	+	0.761494i	$0.275534\pi$
$337$	−5.94427	+	18.2946i	−0.323805	+	0.996570i	−0.971977	+	0.235076i	$0.924466\pi$
$338$	−0.741125	+	7.05133i	−0.0403119	+	0.383542i
$339$	5.47214	−	3.97574i	0.297206	−	0.215933i
$340$	−8.47214			−0.459466
$341$		0			0
$342$	2.03444			0.110010
$343$	13.5172	−	9.82084i	0.729861	−	0.530275i
$344$	0.756375	−	7.19643i	0.0407810	−	0.388005i
$345$	−2.94427	+	9.06154i	−0.158514	+	0.487857i
$346$	−4.61803	+	7.99867i	−0.248267	+	0.430011i
$347$	−0.909830	−	1.57587i	−0.0488422	−	0.0845972i	0.840571	−	0.541702i	$-0.182220\pi$
$347$	−0.909830	−	1.57587i	−0.0488422	−	0.0845972i	−0.889413	+	0.457105i	$0.848886\pi$
$348$	14.1559	−	3.00893i	0.758835	−	0.161295i
$349$	8.61803	+	26.5236i	0.461313	+	1.41977i	0.863561	+	0.504244i	$0.168229\pi$
$349$	8.61803	+	26.5236i	0.461313	+	1.41977i	−0.402248	+	0.915531i	$0.631771\pi$
$350$	10.2433	+	2.17728i	0.547527	+	0.116380i
$351$	0.714224	+	6.79538i	0.0381224	+	0.362711i
$352$	−7.51840	−	8.35003i	−0.400732	−	0.445058i
$353$	−17.7378	−	7.89736i	−0.944086	−	0.420334i	−0.123813	−	0.992306i	$-0.539512\pi$
$353$	−17.7378	−	7.89736i	−0.944086	−	0.420334i	−0.820274	+	0.571971i	$0.806179\pi$
$354$	1.56052	−	0.694789i	0.0829408	−	0.0369276i
$355$	8.81937	−	9.79490i	0.468083	−	0.519859i
$356$	−2.23607	−	1.62460i	−0.118511	−	0.0861035i
$357$	22.1803	+	16.1150i	1.17391	+	0.852894i
$358$	4.84187	−	5.37745i	0.255901	−	0.284207i
$359$	16.2282	−	7.22524i	0.856489	−	0.381334i	0.0689665	−	0.997619i	$-0.478030\pi$
$359$	16.2282	−	7.22524i	0.856489	−	0.381334i	0.787523	+	0.616285i	$0.211363\pi$
$360$	−3.00721	−	1.33889i	−0.158494	−	0.0705659i
$361$	−9.36783	−	10.4040i	−0.493044	−	0.547580i
$362$	1.17449	+	11.1745i	0.0617298	+	0.587320i
$363$	8.46340	+	1.79895i	0.444213	+	0.0944204i
$364$	2.61803	+	8.05748i	0.137222	+	0.422327i
$365$	0.461819	−	0.0981626i	0.0241727	−	0.00513806i
$366$	−5.41641	−	9.38149i	−0.283120	−	0.490379i
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	−0.999404	−	0.0345320i	$-0.989006\pi$
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	0.529607	+	0.848243i	$0.322339\pi$
$368$	−4.41641	+	13.5923i	−0.230221	+	0.708548i
$369$	1.07716	−	10.2485i	0.0560747	−	0.533516i
$370$	−1.00000	+	0.726543i	−0.0519875	+	0.0377711i
$371$	6.47214			0.336017
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	5.23607	−	3.80423i	0.270751	−	0.196712i
$375$	1.16284	−	11.0637i	0.0600487	−	0.571325i
$376$	−4.47214	+	13.7638i	−0.230633	+	0.709815i
$377$	−4.47214	+	7.74597i	−0.230327	+	0.398938i
$378$	7.23607	+	12.5332i	0.372183	+	0.644640i
$379$	37.0606	−	7.87747i	1.90367	−	0.404639i	0.903940	−	0.427660i	$-0.140662\pi$
$379$	37.0606	−	7.87747i	1.90367	−	0.404639i	0.999735	+	0.0230217i	$0.00732867\pi$
$380$	−1.11803	−	3.44095i	−0.0573539	−	0.176517i
$381$	−4.26539	−	0.906636i	−0.218522	−	0.0464484i
$382$	0.205457	+	1.95479i	0.0105121	+	0.100016i
$383$	7.95499	+	8.83491i	0.406481	+	0.451443i	0.911276	−	0.411797i	$-0.135099\pi$
$383$	7.95499	+	8.83491i	0.406481	+	0.451443i	−0.504795	+	0.863239i	$0.668432\pi$
$384$	12.8526	+	5.72233i	0.655880	+	0.292016i
$385$	−7.73968	+	3.44593i	−0.394451	+	0.175621i
$386$	2.26298	−	2.51329i	0.115182	−	0.127923i
$387$	−3.85410	−	2.80017i	−0.195915	−	0.142341i
$388$	2.54508	+	1.84911i	0.129207	+	0.0938745i
$389$	11.9698	−	13.2938i	0.606892	−	0.674021i	−0.358890	−	0.933380i	$-0.616845\pi$
$389$	11.9698	−	13.2938i	0.606892	−	0.674021i	0.965781	+	0.259359i	$0.0835112\pi$
$390$	−0.862635	+	0.384070i	−0.0436812	+	0.0194481i
$391$	−36.8713	−	16.4162i	−1.86466	−	0.830201i
$392$	16.3751	+	18.1863i	0.827065	+	0.918549i
$393$	−1.55045	−	14.7516i	−0.0782099	−	0.744118i
$394$	−9.31966	−	1.98095i	−0.469518	−	0.0997990i
$395$	0.527864	+	1.62460i	0.0265597	+	0.0817424i
$396$	−4.65983	+	0.990477i	−0.234165	+	0.0497734i
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	0.940389	−	0.340099i	$-0.110461\pi$
$397$	3.50000	+	6.06218i	0.175660	+	0.304252i	−0.764730	+	0.644351i	$0.777127\pi$
$398$	−0.326238	+	0.565061i	−0.0163528	+	0.0283239i
$399$	−3.61803	+	11.1352i	−0.181128	+	0.557455i
$400$	0.775226	−	7.37578i	0.0387613	−	0.368789i
$401$	−12.7984	+	9.29856i	−0.639120	+	0.464348i	−0.859548	−	0.511055i	$-0.829255\pi$
$401$	−12.7984	+	9.29856i	−0.639120	+	0.464348i	0.220428	+	0.975403i	$0.429255\pi$
$402$	−6.11146			−0.304812
$403$		0			0
$404$	4.85410			0.241501
$405$	1.95492	−	1.42033i	0.0971405	−	0.0705767i
$406$	−1.98022	+	18.8405i	−0.0982765	+	0.935038i
$407$	−1.23607	+	3.80423i	−0.0612696	+	0.188568i
$408$	−7.23607	+	12.5332i	−0.358239	+	0.620488i
$409$	13.0902	+	22.6728i	0.647267	+	1.12110i	0.983773	+	0.179418i	$0.0574216\pi$
$409$	13.0902	+	22.6728i	0.647267	+	1.12110i	−0.336506	+	0.941681i	$0.609245\pi$
$410$	4.23170	−	0.899475i	0.208989	−	0.0444219i
$411$	7.52786	+	23.1684i	0.371322	+	1.14281i
$412$	2.79173	+	0.593401i	0.137539	+	0.0292348i
$413$	−0.990108	−	9.42025i	−0.0487200	−	0.463540i
$414$	−4.69272	−	5.21179i	−0.230634	−	0.256146i
$415$	2.68973	+	1.19754i	0.132033	+	0.0587851i
$416$	−6.34391	+	2.82449i	−0.311036	+	0.138482i
$417$	−11.0966	+	12.3240i	−0.543402	+	0.603509i
$418$	2.23607	+	1.62460i	0.109370	+	0.0794617i
$419$	−24.3713	−	17.7068i	−1.19062	−	0.865034i	−0.197288	−	0.980346i	$-0.563213\pi$
$419$	−24.3713	−	17.7068i	−1.19062	−	0.865034i	−0.993329	+	0.115312i	$0.963213\pi$
$420$	5.66897	−	6.29602i	0.276617	−	0.307215i
$421$	−14.0327	+	6.24775i	−0.683911	+	0.304497i	−0.719123	−	0.694883i	$-0.755456\pi$
$421$	−14.0327	+	6.24775i	−0.683911	+	0.304497i	0.0352118	+	0.999380i	$0.488789\pi$
$422$	−0.462782	−	0.206044i	−0.0225279	−	0.0100301i
$423$	6.37539	+	7.08058i	0.309982	+	0.344270i
$424$	0.357112	+	3.39769i	0.0173429	+	0.165007i
$425$	20.4866	+	4.35456i	0.993746	+	0.211227i
$426$	−3.11146	−	9.57608i	−0.150751	−	0.463962i
$427$	−58.7562	+	12.4890i	−2.84341	+	0.604386i
$428$	8.28115	+	14.3434i	0.400285	+	0.693313i
$429$	−1.52786	+	2.64634i	−0.0737660	+	0.127766i
$430$	0.618034	−	1.90211i	0.0298042	−	0.0917280i
$431$	−1.25434	+	11.9343i	−0.0604195	+	0.574853i	0.921872	+	0.387494i	$0.126659\pi$
$431$	−1.25434	+	11.9343i	−0.0604195	+	0.574853i	−0.982292	+	0.187359i	$0.940007\pi$
$432$	8.29180	−	6.02434i	0.398939	−	0.289846i
$433$	−12.1803			−0.585350			−0.292675	−	0.956212i	$-0.594545\pi$
$433$	−12.1803			−0.585350			−0.292675	+	0.956212i	$0.594545\pi$
$434$		0			0
$435$	8.94427			0.428845
$436$	5.16312	−	3.75123i	0.247269	−	0.179651i
$437$	1.80166	−	17.1416i	0.0861851	−	0.819996i
$438$	0.111456	−	0.343027i	0.00532558	−	0.0163905i
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	0.494539	+	0.869155i	$0.335337\pi$
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	−0.999980	+	0.00629443i	$0.997996\pi$
$440$	−2.23607	−	3.87298i	−0.106600	−	0.184637i
$441$	15.7594	−	3.34976i	0.750447	−	0.159512i
$442$	−1.23607	−	3.80423i	−0.0587938	−	0.180949i
$443$	−16.9139	−	3.59517i	−0.803605	−	0.170812i	−0.212242	−	0.977217i	$-0.568077\pi$
$443$	−16.9139	−	3.59517i	−0.803605	−	0.170812i	−0.591363	+	0.806406i	$0.701410\pi$
$444$	−0.418114	−	3.97809i	−0.0198428	−	0.188792i
$445$	−1.14301	−	1.26944i	−0.0541839	−	0.0601774i
$446$	−2.25841	−	1.00551i	−0.106939	−	0.0476122i
$447$	11.2920	−	5.02754i	0.534095	−	0.237795i
$448$	0.669131	−	0.743145i	0.0316134	−	0.0351103i
$449$	−25.3262	−	18.4006i	−1.19522	−	0.868377i	−0.201413	−	0.979506i	$-0.564553\pi$
$449$	−25.3262	−	18.4006i	−1.19522	−	0.868377i	−0.993806	+	0.111129i	$0.964553\pi$
$450$	2.94427	+	2.13914i	0.138794	+	0.100840i
$451$	9.36783	−	10.4040i	0.441114	−	0.489907i
$452$	8.08862	−	3.60129i	0.380457	−	0.169390i
$453$	9.23727	+	4.11270i	0.434005	+	0.193231i
$454$	−1.02234	−	1.13542i	−0.0479808	−	0.0532881i
$455$	0.547318	+	5.20738i	0.0256587	+	0.244126i
$456$	−6.04528	−	1.28496i	−0.283096	−	0.0601740i
$457$	−6.47214	−	19.9192i	−0.302754	−	0.931780i	−0.980506	−	0.196490i	$-0.937046\pi$
$457$	−6.47214	−	19.9192i	−0.302754	−	0.931780i	0.677752	−	0.735290i	$-0.262954\pi$
$458$	8.11060	−	1.72396i	0.378983	−	0.0805554i
$459$	14.4721	+	25.0665i	0.675501	+	1.17000i
$460$	−6.23607	+	10.8012i	−0.290758	+	0.503608i
$461$	−3.20163	+	9.85359i	−0.149115	+	0.458928i	−0.997517	−	0.0704241i	$-0.977565\pi$
$461$	−3.20163	+	9.85359i	−0.149115	+	0.458928i	0.848403	+	0.529352i	$0.177565\pi$
$462$	−0.676522	+	6.43668i	−0.0314747	+	0.299461i
$463$	23.7984	−	17.2905i	1.10600	−	0.803559i	0.123975	−	0.992285i	$-0.460436\pi$
$463$	23.7984	−	17.2905i	1.10600	−	0.803559i	0.982030	+	0.188726i	$0.0604359\pi$
$464$	13.4164			0.622841
$465$		0			0
$466$	−0.0344419			−0.00159549
$467$	7.04508	−	5.11855i	0.326008	−	0.236858i	−0.412727	−	0.910855i	$-0.635424\pi$
$467$	7.04508	−	5.11855i	0.326008	−	0.236858i	0.738735	+	0.673996i	$0.235424\pi$
$468$	−0.307760	+	2.92814i	−0.0142262	+	0.135353i
$469$	−10.4721	+	32.2299i	−0.483558	+	1.48824i
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	9.20163	+	15.9377i	0.423989	+	0.734370i
$472$	4.89074	−	1.03956i	0.225114	−	0.0478496i
$473$	−2.00000	−	6.15537i	−0.0919601	−	0.283024i
$474$	1.27644	+	0.271315i	0.0586286	+	0.0124619i
$475$	0.934931	+	8.89527i	0.0428976	+	0.408143i
$476$	24.0141	+	26.6704i	1.10069	+	1.22244i
$477$	2.05477	+	0.914842i	0.0940814	+	0.0418877i
$478$	−0.964456	+	0.429403i	−0.0441132	+	0.0196404i
$479$	24.5626	−	27.2795i	1.12229	−	1.24643i	0.156343	−	0.987703i	$-0.450029\pi$
$479$	24.5626	−	27.2795i	1.12229	−	1.24643i	0.965950	−	0.258730i	$-0.0833040\pi$
$480$	5.61803	+	4.08174i	0.256427	+	0.186305i
$481$	2.00000	+	1.45309i	0.0911922	+	0.0662550i
$482$	12.5555	−	13.9443i	0.571888	−	0.635146i
$483$	36.8713	−	16.4162i	1.67770	−	0.746961i
$484$	10.3470	+	4.60680i	0.470320	+	0.209400i
$485$	1.30097	+	1.44488i	0.0590741	+	0.0656084i
$486$	0.878379	+	8.35722i	0.0398441	+	0.379091i
$487$	14.4413	+	3.06959i	0.654398	+	0.139097i	0.523133	−	0.852251i	$-0.324763\pi$
$487$	14.4413	+	3.06959i	0.654398	+	0.139097i	0.131265	+	0.991347i	$0.458096\pi$
$488$	−9.79837	−	30.1563i	−0.443552	−	1.36511i
$489$	3.27437	−	0.695989i	0.148072	−	0.0314737i
$490$	3.38197	+	5.85774i	0.152782	+	0.264626i
$491$	20.1803	−	34.9534i	0.910726	−	1.57742i	0.0976849	−	0.995217i	$-0.468856\pi$
$491$	20.1803	−	34.9534i	0.910726	−	1.57742i	0.813041	−	0.582206i	$-0.197810\pi$
$492$	−4.32624	+	13.3148i	−0.195042	+	0.600277i
$493$	−3.96043	+	37.6810i	−0.178369	+	1.69707i
$494$	1.38197	−	1.00406i	0.0621776	−	0.0451747i
$495$	−2.94427			−0.132335
$496$		0			0
$497$	−55.8328			−2.50444
$498$	1.81966	−	1.32206i	0.0815409	−	0.0592429i
$499$	3.49297	−	33.2333i	0.156367	−	1.48773i	−0.581922	−	0.813244i	$-0.697699\pi$
$499$	3.49297	−	33.2333i	0.156367	−	1.48773i	0.738289	−	0.674485i	$-0.235634\pi$
$500$	4.50000	−	13.8496i	0.201246	−	0.619372i
$501$	−1.52786	+	2.64634i	−0.0682599	+	0.118230i
$502$	−7.47214	−	12.9421i	−0.333498	−	0.577635i
$503$	1.61637	−	0.343569i	0.0720702	−	0.0153190i	−0.171735	−	0.985143i	$-0.554937\pi$
$503$	1.61637	−	0.343569i	0.0720702	−	0.0153190i	0.243806	+	0.969824i	$0.421604\pi$
$504$	4.30902	+	13.2618i	0.191939	+	0.590727i
$505$	2.93444	+	0.623735i	0.130581	+	0.0277558i
$506$	−0.995933	−	9.47567i	−0.0442746	−	0.421245i
$507$	−9.48850	−	10.5380i	−0.421399	−	0.468011i
$508$	−5.21470	−	2.32174i	−0.231365	−	0.103010i
$509$	−17.9025	+	7.97072i	−0.793515	+	0.353296i	−0.763132	−	0.646243i	$-0.776339\pi$
$509$	−17.9025	+	7.97072i	−0.793515	+	0.353296i	−0.0303832	+	0.999538i	$0.509673\pi$
$510$	−2.67652	+	2.97258i	−0.118518	+	0.131628i
$511$	−1.61803	−	1.17557i	−0.0715776	−	0.0520042i
$512$	15.1353	+	10.9964i	0.668890	+	0.485977i
$513$	−8.27091	+	9.18578i	−0.365170	+	0.405562i
$514$	9.00217	−	4.00802i	0.397069	−	0.176786i
$515$	1.61143	+	0.717456i	0.0710082	+	0.0316149i
$516$	4.33070	+	4.80973i	0.190649	+	0.211737i
$517$	1.35304	+	12.8734i	0.0595068	+	0.566170i
$518$	5.12165	+	1.08864i	0.225032	+	0.0478321i
$519$	−5.70820	−	17.5680i	−0.250562	−	0.771152i
$520$	−2.70353	+	0.574654i	−0.118558	+	0.0252002i
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	0.843288	−	0.537461i	$-0.180617\pi$
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	−0.887099	+	0.461579i	$0.847283\pi$
$522$	−3.29180	+	5.70156i	−0.144078	+	0.249550i
$523$	−1.32624	+	4.08174i	−0.0579923	+	0.178482i	−0.975857	−	0.218413i	$-0.929912\pi$
$523$	−1.32624	+	4.08174i	−0.0579923	+	0.178482i	0.917864	+	0.396895i	$0.129912\pi$
$524$	2.02957	−	19.3100i	0.0886621	−	0.843563i
$525$	−16.9443	+	12.3107i	−0.739509	+	0.537284i
$526$	11.5967			0.505642
$527$		0			0
$528$	4.58359			0.199475
$529$	−29.4615	+	21.4050i	−1.28093	+	0.930653i
$530$	−0.0987033	+	0.939099i	−0.00428740	+	0.0407919i
$531$	1.01722	−	3.13068i	0.0441436	−	0.135860i
$532$	−7.66312	+	13.2729i	−0.332238	+	0.575454i
$533$	−4.32624	−	7.49326i	−0.187390	−	0.324569i
$534$	−1.27644	+	0.271315i	−0.0552368	+	0.0117409i
$535$	3.16312	+	9.73508i	0.136754	+	0.420884i
$536$	−17.4976	−	3.71924i	−0.755783	−	0.160647i
$537$	1.51275	+	14.3929i	0.0652800	+	0.621098i
$538$	11.9698	+	13.2938i	0.516054	+	0.573135i
$539$	19.9962	+	8.90287i	0.861296	+	0.383474i
$540$	8.17100	−	3.63796i	0.351624	−	0.156553i
$541$	12.9548	−	14.3878i	0.556971	−	0.618579i	−0.397239	−	0.917715i	$-0.630032\pi$
$541$	12.9548	−	14.3878i	0.556971	−	0.618579i	0.954211	+	0.299136i	$0.0966983\pi$
$542$	4.09017	+	2.97168i	0.175688	+	0.127645i
$543$	−18.1803	−	13.2088i	−0.780193	−	0.566843i
$544$	−19.6834	+	21.8607i	−0.843920	+	0.937268i
$545$	3.60327	−	1.60428i	0.154347	−	0.0687198i
$546$	3.65418	+	1.62695i	0.156385	+	0.0696269i
$547$	18.8190	+	20.9007i	0.804644	+	0.893648i	0.996134	−	0.0878469i	$-0.0279986\pi$
$547$	18.8190	+	20.9007i	0.804644	+	0.893648i	−0.191490	+	0.981495i	$0.561332\pi$
$548$	3.33326	+	31.7139i	0.142390	+	1.35475i
$549$	−20.4192	−	4.34024i	−0.871471	−	0.185237i
$550$	1.52786	+	4.70228i	0.0651483	+	0.200506i
$551$	−15.8268	+	3.36408i	−0.674243	+	0.143315i
$552$	10.6525	+	18.4506i	0.453399	+	0.785311i
$553$	3.61803	−	6.26662i	0.153854	−	0.266484i
$554$	−3.56231	+	10.9637i	−0.151348	+	0.465801i
$555$	0.258409	−	2.45859i	0.0109688	−	0.104361i
$556$	−17.5623	+	12.7598i	−0.744808	+	0.541134i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	6.35410	−	4.61653i	0.268510	−	0.195084i
$561$	−1.35304	+	12.8734i	−0.0571256	+	0.543514i
$562$	−3.24671	+	9.99235i	−0.136954	+	0.421502i
$563$	19.7705	−	34.2435i	0.833228	−	1.44319i	−0.0622377	−	0.998061i	$-0.519824\pi$
$563$	19.7705	−	34.2435i	0.833228	−	1.44319i	0.895465	−	0.445131i	$-0.146843\pi$
$564$	−6.47214	−	11.2101i	−0.272526	−	0.472029i
$565$	5.35256	−	1.13772i	0.225184	−	0.0478643i
$566$	−4.18034	−	12.8658i	−0.175713	−	0.540788i
$567$	−10.0124	−	2.12820i	−0.420481	−	0.0893759i
$568$	−3.08068	−	29.3107i	−0.129262	−	1.22985i
$569$	9.68375	+	10.7549i	0.405964	+	0.450869i	0.911109	−	0.412166i	$-0.135228\pi$
$569$	9.68375	+	10.7549i	0.405964	+	0.450869i	−0.505145	+	0.863035i	$0.668561\pi$
$570$	−1.56052	−	0.694789i	−0.0653631	−	0.0291015i
$571$	5.31652	−	2.36707i	0.222490	−	0.0990588i	−0.292465	−	0.956276i	$-0.594475\pi$
$571$	5.31652	−	2.36707i	0.222490	−	0.0990588i	0.514955	+	0.857217i	$0.327809\pi$
$572$	−2.67652	+	2.97258i	−0.111911	+	0.124290i
$573$	−3.18034	−	2.31065i	−0.132861	−	0.0965289i
$574$	−14.8262	−	10.7719i	−0.618835	−	0.449610i
$575$	20.6312	−	22.9132i	0.860380	−	0.955548i
$576$	0.317479	−	0.141351i	0.0132283	−	0.00588962i
$577$	22.6859	+	10.1004i	0.944427	+	0.420486i	0.820398	−	0.571793i	$-0.193752\pi$
$577$	22.6859	+	10.1004i	0.944427	+	0.420486i	0.124029	+	0.992279i	$0.460419\pi$
$578$	−4.30766	−	4.78414i	−0.179175	−	0.198994i
$579$	0.707023	+	6.72688i	0.0293829	+	0.279560i
$580$	11.4524	+	2.43427i	0.475533	+	0.101078i
$581$	−3.85410	−	11.8617i	−0.159895	−	0.492106i
$582$	1.45283	−	0.308809i	0.0602219	−	0.0128006i
$583$	1.52786	+	2.64634i	0.0632777	+	0.109600i
$584$	0.527864	−	0.914287i	0.0218432	−	0.0378335i
$585$	−0.562306	+	1.73060i	−0.0232485	+	0.0715515i
$586$	0.547318	−	5.20738i	0.0226095	−	0.215115i
$587$	−2.00000	+	1.45309i	−0.0825488	+	0.0599752i	−0.628294	−	0.777976i	$-0.716247\pi$
$587$	−2.00000	+	1.45309i	−0.0825488	+	0.0599752i	0.545745	+	0.837951i	$0.316247\pi$
$588$	−21.8885			−0.902668
$589$		0			0
$590$	1.38197			0.0568946
$591$	15.4164	−	11.2007i	0.634146	−	0.460734i
$592$	0.387613	−	3.68789i	0.0159308	−	0.151571i
$593$	−4.78115	+	14.7149i	−0.196338	+	0.604268i	0.803620	+	0.595143i	$0.202905\pi$
$593$	−4.78115	+	14.7149i	−0.196338	+	0.604268i	−0.999958	+	0.00912470i	$0.997095\pi$
$594$	−3.41641	+	5.91739i	−0.140177	+	0.242794i
$595$	11.0902	+	19.2087i	0.454653	+	0.787481i
$596$	15.8268	−	3.36408i	0.648289	−	0.137798i
$597$	−0.403252	−	1.24108i	−0.0165040	−	0.0507941i
$598$	−5.75987	−	1.22430i	−0.235538	−	0.0500652i
$599$	−3.61634	−	34.4072i	−0.147760	−	1.40584i	−0.777426	−	0.628975i	$-0.783475\pi$
$599$	−3.61634	−	34.4072i	−0.147760	−	1.40584i	0.629666	−	0.776866i	$-0.283192\pi$
$600$	−7.39773	−	8.21601i	−0.302011	−	0.335417i
$601$	−33.3819	−	14.8626i	−1.36168	−	0.606257i	−0.409641	−	0.912247i	$-0.634346\pi$
$601$	−33.3819	−	14.8626i	−1.36168	−	0.606257i	−0.952035	+	0.305990i	$0.901013\pi$
$602$	−7.73968	+	3.44593i	−0.315446	+	0.140446i
$603$	−7.88041	+	8.75208i	−0.320915	+	0.356412i
$604$	10.7082	+	7.77997i	0.435711	+	0.316562i
$605$	5.66312	+	4.11450i	0.230239	+	0.167278i
$606$	1.53351	−	1.70314i	0.0622946	−	0.0691852i
$607$	12.3583	−	5.50228i	0.501609	−	0.223331i	−0.140304	−	0.990109i	$-0.544808\pi$
$607$	12.3583	−	5.50228i	0.501609	−	0.223331i	0.641912	+	0.766778i	$0.278141\pi$
$608$	−11.4762	−	5.10955i	−0.465423	−	0.207220i
$609$	−25.3524	−	28.1567i	−1.02733	−	1.14097i
$610$	−0.916080	−	8.71592i	−0.0370910	−	0.352897i
$611$	7.82518	+	1.66329i	0.316573	+	0.0672897i
$612$	3.85410	+	11.8617i	0.155793	+	0.479481i
$613$	7.93420	−	1.68647i	0.320459	−	0.0681157i	−0.0448735	−	0.998993i	$-0.514288\pi$
$613$	7.93420	−	1.68647i	0.320459	−	0.0681157i	0.365333	+	0.930877i	$0.380955\pi$
$614$	−4.72542	−	8.18468i	−0.190703	−	0.330307i
$615$	−4.32624	+	7.49326i	−0.174451	+	0.302158i
$616$	−5.85410	+	18.0171i	−0.235868	+	0.725929i
$617$	−2.45933	+	23.3990i	−0.0990090	+	0.942007i	0.826412	+	0.563066i	$0.190378\pi$
$617$	−2.45933	+	23.3990i	−0.0990090	+	0.942007i	−0.925421	+	0.378941i	$0.876288\pi$
$618$	1.09017	−	0.792055i	0.0438531	−	0.0318611i
$619$	−16.1803			−0.650343			−0.325171	−	0.945655i	$-0.605422\pi$
$619$	−16.1803			−0.650343			−0.325171	+	0.945655i	$0.605422\pi$
$620$		0			0
$621$	42.6099			1.70988
$622$	−3.40983	+	2.47739i	−0.136722	+	0.0993342i
$623$	−0.756375	+	7.19643i	−0.0303035	+	0.288319i
$624$	0.875388	−	2.69417i	0.0350436	−	0.107853i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	6.56231	+	11.3662i	0.262282	+	0.454287i
$627$	−5.40707	+	1.14931i	−0.215937	+	0.0458989i
$628$	7.44427	+	22.9111i	0.297059	+	0.914253i
$629$	10.2433	+	2.17728i	0.408427	+	0.0868138i
$630$	0.402863	+	3.83299i	0.0160505	+	0.152710i
$631$	−6.93265	−	7.69949i	−0.275984	−	0.306512i	0.589178	−	0.808003i	$-0.299452\pi$
$631$	−6.93265	−	7.69949i	−0.275984	−	0.306512i	−0.865163	+	0.501491i	$0.832785\pi$
$632$	3.48943	+	1.55360i	0.138802	+	0.0617987i
$633$	0.925564	−	0.412088i	0.0367879	−	0.0163790i
$634$	−9.07495	+	10.0788i	−0.360412	+	0.400279i
$635$	−2.85410	−	2.07363i	−0.113262	−	0.0822894i
$636$	−2.47214	−	1.79611i	−0.0980266	−	0.0712205i
$637$	9.05191	−	10.0532i	0.358650	−	0.398321i
$638$	−8.17100	+	3.63796i	−0.323493	+	0.144028i
$639$	−17.7258	−	7.89201i	−0.701220	−	0.312203i
$640$	7.61602	+	8.45845i	0.301050	+	0.334350i
$641$	−1.25434	−	11.9343i	−0.0495435	−	0.471375i	−0.990963	−	0.134137i	$-0.957174\pi$
$641$	−1.25434	−	11.9343i	−0.0495435	−	0.471375i	0.941419	−	0.337238i	$-0.109493\pi$
$642$	7.64878	+	1.62580i	0.301873	+	0.0641652i
$643$	8.79837	+	27.0786i	0.346974	+	1.06788i	0.960519	+	0.278216i	$0.0897431\pi$
$643$	8.79837	+	27.0786i	0.346974	+	1.06788i	−0.613545	+	0.789660i	$0.710257\pi$
$644$	51.6783	−	10.9846i	2.03641	−	0.432852i
$645$	2.00000	+	3.46410i	0.0787499	+	0.136399i
$646$	3.61803	−	6.26662i	0.142350	−	0.246557i
$647$	5.23607	−	16.1150i	0.205851	−	0.633544i	−0.793826	−	0.608145i	$-0.791914\pi$
$647$	5.23607	−	16.1150i	0.205851	−	0.633544i	0.999677	−	0.0253999i	$-0.00808591\pi$
$648$	0.564794	−	5.37365i	0.0221872	−	0.211097i
$649$	3.61803	−	2.62866i	0.142020	−	0.103184i
$650$	3.05573			0.119856
$651$		0			0
$652$	4.38197			0.171611
$653$	−12.3820	+	8.99602i	−0.484544	+	0.352042i	−0.803082	−	0.595868i	$-0.796808\pi$
$653$	−12.3820	+	8.99602i	−0.484544	+	0.352042i	0.318538	+	0.947910i	$0.396808\pi$
$654$	0.314961	−	2.99665i	0.0123159	−	0.117178i
$655$	3.70820	−	11.4127i	0.144892	−	0.445930i
$656$	−6.48936	+	11.2399i	−0.253367	+	0.438844i
$657$	−0.347524	−	0.601929i	−0.0135582	−	0.0234835i
$658$	16.5740	−	3.52291i	0.646122	−	0.137337i
$659$	−1.74671	−	5.37582i	−0.0680422	−	0.209412i	0.911254	−	0.411845i	$-0.135115\pi$
$659$	−1.74671	−	5.37582i	−0.0680422	−	0.209412i	−0.979296	+	0.202432i	$0.935115\pi$
$660$	3.91259	+	0.831647i	0.152297	+	0.0323718i
$661$	4.74148	+	45.1122i	0.184422	+	1.75466i	0.560575	+	0.828103i	$0.310580\pi$
$661$	4.74148	+	45.1122i	0.184422	+	1.75466i	−0.376153	+	0.926557i	$0.622753\pi$
$662$	−0.827091	−	0.918578i	−0.0321458	−	0.0357015i
$663$	7.30836	+	3.25389i	0.283833	+	0.126371i
$664$	6.01441	−	2.67779i	0.233404	−	0.103918i
$665$	−6.33810	+	7.03917i	−0.245781	+	0.272967i
$666$	1.47214	+	1.06957i	0.0570441	+	0.0414450i
$667$	45.1246	+	32.7849i	1.74723	+	1.26944i
$668$	−2.67652	+	2.97258i	−0.103558	+	0.115013i
$669$	4.51682	−	2.01102i	0.174630	−	0.0777504i
$670$	−4.51682	−	2.01102i	−0.174500	−	0.0776923i
$671$	−18.9770	−	21.0761i	−0.732599	−	0.813634i
$672$	−3.07485	−	29.2553i	−0.118615	−	1.12855i
$673$	−45.9858	−	9.77458i	−1.77262	−	0.376783i	−0.798357	−	0.602185i	$-0.794297\pi$
$673$	−45.9858	−	9.77458i	−1.77262	−	0.376783i	−0.974266	+	0.225402i	$0.927630\pi$
$674$	3.67376	+	11.3067i	0.141508	+	0.435517i
$675$	−21.6283	+	4.59723i	−0.832472	+	0.176947i
$676$	−9.28115	−	16.0754i	−0.356967	−	0.618286i
$677$	−21.3607	+	36.9978i	−0.820958	+	1.42194i	0.0840123	+	0.996465i	$0.473226\pi$
$677$	−21.3607	+	36.9978i	−0.820958	+	1.42194i	−0.904970	+	0.425476i	$0.860107\pi$
$678$	1.29180	−	3.97574i	0.0496111	−	0.152687i
$679$	0.860904	−	8.19095i	0.0330384	−	0.314340i
$680$	−9.47214	+	6.88191i	−0.363240	+	0.263909i
$681$	3.05573			0.117096
$682$		0			0
$683$	−17.1803			−0.657387			−0.328694	−	0.944437i	$-0.606608\pi$
$683$	−17.1803			−0.657387			−0.328694	+	0.944437i	$0.606608\pi$
$684$	−4.30902	+	3.13068i	−0.164759	+	0.119705i
$685$	−2.06007	+	19.6002i	−0.0787112	+	0.748887i
$686$	3.19098	−	9.82084i	0.121832	−	0.374961i
$687$	−8.29180	+	14.3618i	−0.316352	+	0.547937i
$688$	3.00000	+	5.19615i	0.114374	+	0.198101i
$689$	1.84727	−	0.392650i	0.0703756	−	0.0149588i
$690$	1.81966	+	5.60034i	0.0692733	+	0.213201i
$691$	18.7612	+	3.98782i	0.713710	+	0.151704i	0.550436	−	0.834877i	$-0.314461\pi$
$691$	18.7612	+	3.98782i	0.713710	+	0.151704i	0.163273	+	0.986581i	$0.447795\pi$
$692$	−2.52753	−	24.0479i	−0.0960824	−	0.914163i
$693$	8.34549	+	9.26860i	0.317019	+	0.352085i
$694$	−1.02738	−	0.457421i	−0.0389990	−	0.0173635i
$695$	−12.2565	+	5.45694i	−0.464915	+	0.206994i
$696$	13.3826	−	14.8629i	0.507267	−	0.563377i
$697$	−29.6525	−	21.5438i	−1.12317	−	0.816029i
$698$	13.9443	+	10.1311i	0.527798	+	0.383468i
$699$	0.0460922	−	0.0511906i	0.00174337	−	0.00193621i
$700$	−25.0461	+	11.1513i	−0.946655	+	0.421478i
$701$	6.39482	+	2.84716i	0.241529	+	0.107536i	0.523932	−	0.851760i	$-0.324465\pi$
$701$	6.39482	+	2.84716i	0.241529	+	0.107536i	−0.282403	+	0.959296i	$0.591131\pi$
$702$	2.82568	+	3.13824i	0.106648	+	0.118445i
$703$	0.467465	+	4.44764i	0.0176308	+	0.167746i
$704$	0.461819	+	0.0981626i	0.0174054	+	0.00369964i
$705$	−2.47214	−	7.60845i	−0.0931060	−	0.286551i
$706$	−11.7378	+	2.49494i	−0.441757	+	0.0938983i
$707$	−6.35410	−	11.0056i	−0.238971	−	0.413909i
$708$	−2.23607	+	3.87298i	−0.0840366	+	0.145556i
$709$	10.6525	−	32.7849i	0.400062	−	1.23126i	−0.524886	−	0.851172i	$-0.675892\pi$
$709$	10.6525	−	32.7849i	0.400062	−	1.23126i	0.924949	−	0.380092i	$-0.124108\pi$
$710$	0.851478	−	8.10127i	0.0319554	−	0.304035i
$711$	2.03444	−	1.47811i	0.0762975	−	0.0554334i
$712$	−3.81966			−0.143148
$713$		0			0
$714$	16.9443			0.634123
$715$	−2.00000	+	1.45309i	−0.0747958	+	0.0543423i
$716$	−1.98022	+	18.8405i	−0.0740041	+	0.704102i
$717$	0.652476	−	2.00811i	0.0243672	−	0.0749944i
$718$	5.48936	−	9.50785i	0.204861	−	0.354830i
$719$	18.0902	+	31.3331i	0.674649	+	1.16853i	0.976571	+	0.215194i	$0.0690385\pi$
$719$	18.0902	+	31.3331i	0.674649	+	1.16853i	−0.301922	+	0.953333i	$0.597628\pi$
$720$	2.66984	−	0.567493i	0.0994992	−	0.0211492i
$721$	−2.30902	−	7.10642i	−0.0859923	−	0.264657i
$722$	−8.46340	−	1.79895i	−0.314975	−	0.0669500i
$723$	3.92273	+	37.3223i	0.145888	+	1.38803i
$724$	−19.6834	−	21.8607i	−0.731528	−	0.812445i
$725$	−26.4419	−	11.7727i	−0.982028	−	0.437227i
$726$	4.88521	−	2.17503i	0.181307	−	0.0807231i
$727$	−26.6073	+	29.5504i	−0.986809	+	1.09596i	0.00857264	+	0.999963i	$0.497271\pi$
$727$	−26.6073	+	29.5504i	−0.986809	+	1.09596i	−0.995381	+	0.0959989i	$0.969395\pi$
$728$	9.47214	+	6.88191i	0.351061	+	0.255061i
$729$	−19.4615	−	14.1396i	−0.720796	−	0.523689i
$730$	0.195250	−	0.216847i	0.00722651	−	0.00802586i
$731$	−15.4794	+	6.89186i	−0.572525	+	0.254905i
$732$	25.9088	+	11.5353i	0.957616	+	0.426358i
$733$	−3.66157	−	4.06659i	−0.135243	−	0.150203i	0.671719	−	0.740806i	$-0.265556\pi$
$733$	−3.66157	−	4.06659i	−0.135243	−	0.150203i	−0.806962	+	0.590603i	$0.798890\pi$
$734$	1.16284	+	11.0637i	0.0429212	+	0.408368i
$735$	−13.2322	−	2.81260i	−0.488079	−	0.103744i
$736$	13.3820	+	41.1855i	0.493266	+	1.51812i
$737$	−15.6504	+	3.32659i	−0.576488	+	0.122536i
$738$	−3.18441	−	5.51555i	−0.117220	−	0.203030i
$739$	8.09017	−	14.0126i	0.297602	−	0.515461i	−0.677985	−	0.735076i	$-0.737147\pi$
$739$	8.09017	−	14.0126i	0.297602	−	0.515461i	0.975587	+	0.219614i	$0.0704799\pi$
$740$	1.00000	−	3.07768i	0.0367607	−	0.113138i
$741$	−0.357112	+	3.39769i	−0.0131188	+	0.124817i
$742$	3.23607	−	2.35114i	0.118800	−	0.0863131i
$743$	27.8197			1.02060			0.510302	−	0.859995i	$-0.329534\pi$
$743$	27.8197			1.02060			0.510302	+	0.859995i	$0.329534\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	9.50000	−	6.90215i	0.347820	−	0.252706i
$747$	0.453065	−	4.31062i	0.0165768	−	0.157717i
$748$	−5.23607	+	16.1150i	−0.191450	+	0.589221i
$749$	21.6803	−	37.5515i	0.792182	−	1.37210i
$750$	−3.43769	−	5.95426i	−0.125527	−	0.217419i
$751$	−44.5458	+	9.46851i	−1.62550	+	0.345511i	−0.928435	−	0.371496i	$-0.878845\pi$
$751$	−44.5458	+	9.46851i	−1.62550	+	0.345511i	−0.697066	+	0.717007i	$0.745512\pi$
$752$	−3.70820	−	11.4127i	−0.135224	−	0.416178i
$753$	29.2354	+	6.21418i	1.06540	+	0.226457i
$754$	0.577819	+	5.49758i	0.0210429	+	0.200210i
$755$	5.47372	+	6.07918i	0.199209	+	0.221244i
$756$	−34.6129	−	15.4107i	−1.25886	−	0.560480i
$757$	−20.6941	+	9.21359i	−0.752139	+	0.334874i	−0.746744	−	0.665112i	$-0.768384\pi$
$757$	−20.6941	+	9.21359i	−0.752139	+	0.334874i	−0.00539480	+	0.999985i	$0.501717\pi$
$758$	15.6686	−	17.4018i	0.569110	−	0.632061i
$759$	15.4164	+	11.2007i	0.559580	+	0.406559i
$760$	−4.04508	−	2.93893i	−0.146731	−	0.106606i
$761$	1.33826	−	1.48629i	0.0485119	−	0.0538780i	−0.718400	−	0.695630i	$-0.755125\pi$
$761$	1.33826	−	1.48629i	0.0485119	−	0.0538780i	0.766912	+	0.641752i	$0.221792\pi$
$762$	−2.46205	+	1.09617i	−0.0891906	+	0.0397102i
$763$	−15.2637	−	6.79584i	−0.552583	−	0.246026i
$764$	−3.44328	−	3.82415i	−0.124573	−	0.138353i
$765$	0.805727	+	7.66598i	0.0291311	+	0.277164i
$766$	7.18696	+	1.52764i	0.259676	+	0.0551957i
$767$	−0.854102	−	2.62866i	−0.0308398	−	0.0949153i
$768$	7.93420	−	1.68647i	0.286301	−	0.0608551i
$769$	1.31966	+	2.28572i	0.0475882	+	0.0824251i	0.888838	−	0.458221i	$-0.151513\pi$
$769$	1.31966	+	2.28572i	0.0475882	+	0.0824251i	−0.841250	+	0.540646i	$0.818180\pi$
$770$	−2.61803	+	4.53457i	−0.0943474	+	0.163414i
$771$	−6.09017	+	18.7436i	−0.219332	+	0.675035i
$772$	−0.925506	+	8.80560i	−0.0333097	+	0.316920i
$773$	−23.5623	+	17.1190i	−0.847477	+	0.615728i	−0.924449	−	0.381305i	$-0.875475\pi$
$773$	−23.5623	+	17.1190i	−0.847477	+	0.615728i	0.0769721	+	0.997033i	$0.475475\pi$
$774$	−2.94427			−0.105830
$775$		0			0
$776$	4.34752			0.156067
$777$	−8.47214	+	6.15537i	−0.303936	+	0.220823i
$778$	1.15564	−	10.9952i	0.0414316	−	0.394196i
$779$	4.83688	−	14.8864i	0.173299	−	0.533360i
$780$	1.23607	−	2.14093i	0.0442583	−	0.0766577i
$781$	−13.1803	−	22.8290i	−0.471630	−	0.816887i
$782$	−24.3992	+	5.18621i	−0.872513	+	0.185458i
$783$	−12.3607	−	38.0423i	−0.441735	−	1.35952i
$784$	−19.8484	−	4.21890i	−0.708870	−	0.150675i
$785$	1.55628	+	14.8070i	0.0555459	+	0.528484i
$786$	−6.13404	−	6.81255i	−0.218794	−	0.242995i
$787$	35.3108	+	15.7214i	1.25869	+	0.560407i	0.924170	−	0.381981i	$-0.124758\pi$
$787$	35.3108	+	15.7214i	1.25869	+	0.560407i	0.334524	+	0.942387i	$0.391425\pi$
$788$	22.7877	−	10.1457i	0.811779	−	0.361427i
$789$	−15.5195	+	17.2361i	−0.552508	+	0.613622i
$790$	0.854102	+	0.620541i	0.0303876	+	0.0220779i
$791$	−18.7533	−	13.6251i	−0.666790	−	0.484451i
$792$	−4.40528	+	4.89256i	−0.156535	+	0.173850i
$793$	−16.0125	+	7.12922i	−0.568621	+	0.253166i
$794$	3.95222	+	1.75964i	0.140259	+	0.0624473i
$795$	−1.26368	−	1.40346i	−0.0448182	−	0.0497757i
$796$	−0.178556	−	1.69885i	−0.00632875	−	0.0602140i
$797$	27.9590	+	5.94286i	0.990358	+	0.210507i	0.674480	−	0.738293i	$-0.264368\pi$
$797$	27.9590	+	5.94286i	0.990358	+	0.210507i	0.315877	+	0.948800i	$0.397701\pi$
$798$	2.23607	+	6.88191i	0.0791559	+	0.243617i
$799$	33.1480	−	7.04582i	1.17269	−	0.249263i
$800$	−11.2361	−	19.4614i	−0.397255	−	0.688066i
$801$	−1.25735	+	2.17780i	−0.0444264	+	0.0769488i
$802$	−3.02129	+	9.29856i	−0.106685	+	0.328344i
$803$	0.0987033	−	0.939099i	0.00348316	−	0.0331401i
$804$	12.9443	−	9.40456i	0.456509	−	0.331673i
$805$	32.6525			1.15085
$806$		0			0
$807$	−35.7771			−1.25941
$808$	5.42705	−	3.94298i	0.190923	−	0.138714i
$809$	0.357112	−	3.39769i	0.0125554	−	0.119457i	−0.986449	−	0.164068i	$-0.947538\pi$
$809$	0.357112	−	3.39769i	0.0125554	−	0.119457i	0.999004	+	0.0446115i	$0.0142050\pi$
$810$	0.461493	−	1.42033i	0.0162152	−	0.0499053i
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	−0.508347	−	0.861152i	$-0.669743\pi$
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	0.999953	+	0.00966502i	$0.00307652\pi$
$812$	−24.7984	−	42.9520i	−0.870252	−	1.50732i
$813$	−9.89050	+	2.10229i	−0.346875	+	0.0737305i
$814$	0.763932	+	2.35114i	0.0267758	+	0.0824074i
$815$	2.64902	+	0.563067i	0.0927912	+	0.0197234i
$816$	−1.25434	−	11.9343i	−0.0439107	−	0.417783i
$817$	−4.84187	−	5.37745i	−0.169396	−	0.188133i
$818$	14.7815	+	6.58114i	0.516822	+	0.230104i
$819$	7.04179	−	3.13521i	0.246060	−	0.109553i
$820$	−7.57873	+	8.41704i	−0.264661	+	0.293936i
$821$	29.5623	+	21.4783i	1.03173	+	0.749597i	0.968655	−	0.248412i	$-0.0799086\pi$
$821$	29.5623	+	21.4783i	1.03173	+	0.749597i	0.0630771	+	0.998009i	$0.479909\pi$
$822$	12.1803	+	8.84953i	0.424838	+	0.308663i
$823$	−18.5404	+	20.5912i	−0.646278	+	0.717764i	−0.973883	−	0.227050i	$-0.927092\pi$
$823$	−18.5404	+	20.5912i	−0.646278	+	0.717764i	0.327605	+	0.944815i	$0.393758\pi$
$824$	3.60327	−	1.60428i	0.125526	−	0.0558877i
$825$	−9.03363	−	4.02203i	−0.314511	−	0.140029i
$826$	−3.91716	−	4.35045i	−0.136295	−	0.151371i
$827$	−5.08557	−	48.3860i	−0.176843	−	1.68254i	−0.618831	−	0.785524i	$-0.712394\pi$
$827$	−5.08557	−	48.3860i	−0.176843	−	1.68254i	0.441989	−	0.897021i	$-0.354273\pi$
$828$	17.9595	+	3.81740i	0.624134	+	0.132664i
$829$	−11.3820	−	35.0301i	−0.395312	−	1.21665i	−0.928718	−	0.370786i	$-0.879088\pi$
$829$	−11.3820	−	35.0301i	−0.395312	−	1.21665i	0.533406	−	0.845859i	$-0.320912\pi$
$830$	1.77990	−	0.378329i	0.0617811	−	0.0131320i
$831$	−11.5279	−	19.9668i	−0.399897	−	0.692642i
$832$	0.145898	−	0.252703i	0.00505810	−	0.00876089i
$833$	17.7082	−	54.5002i	0.613553	−	1.88832i
$834$	−1.07134	+	10.1931i	−0.0370973	+	0.352957i
$835$	−2.00000	+	1.45309i	−0.0692129	+	0.0502861i
$836$	−7.23607			−0.250265
$837$		0			0
$838$	−18.6180			−0.643149
$839$	−8.94427	+	6.49839i	−0.308791	+	0.224349i	−0.731377	−	0.681973i	$-0.761122\pi$
$839$	−8.94427	+	6.49839i	−0.308791	+	0.224349i	0.422587	+	0.906322i	$0.361122\pi$
$840$	1.22384	−	11.6441i	0.0422265	−	0.401758i
$841$	7.21885	−	22.2173i	0.248926	−	0.766115i
$842$	−4.74671	+	8.22154i	−0.163582	+	0.283333i
$843$	−10.5066	−	18.1979i	−0.361866	−	0.626770i
$844$	1.29726	−	0.275740i	0.0446534	−	0.00949137i
$845$	−3.54508	−	10.9106i	−0.121955	−	0.375338i
$846$	5.75987	+	1.22430i	0.198028	+	0.0420922i
$847$	−3.09953	−	29.4900i	−0.106501	−	1.01329i
$848$	−1.89552	−	2.10519i	−0.0650926	−	0.0722926i
$849$	24.7166	+	11.0046i	0.848273	+	0.377675i
$850$	11.8252	−	5.26491i	0.405600	−	0.180585i
$851$	10.3156	−	11.4566i	0.353614	−	0.392728i
$852$	21.3262	+	15.4944i	0.730625	+	0.530830i
$853$	−30.2705	−	21.9928i	−1.03644	−	0.753020i	−0.0668546	−	0.997763i	$-0.521296\pi$
$853$	−30.2705	−	21.9928i	−1.03644	−	0.753020i	−0.969588	+	0.244743i	$0.921296\pi$
$854$	−24.8412	+	27.5890i	−0.850049	+	0.944075i
$855$	−3.00721	+	1.33889i	−0.102844	+	0.0457892i
$856$	20.9097	+	9.30961i	0.714680	+	0.318196i
$857$	34.5711	+	38.3950i	1.18092	+	1.31155i	0.940067	+	0.340989i	$0.110762\pi$
$857$	34.5711	+	38.3950i	1.18092	+	1.31155i	0.240858	+	0.970560i	$0.422571\pi$
$858$	0.197407	+	1.87820i	0.00673935	+	0.0641206i
$859$	−37.0606	−	7.87747i	−1.26449	−	0.268776i	−0.473604	−	0.880738i	$-0.657047\pi$
$859$	−37.0606	−	7.87747i	−1.26449	−	0.268776i	−0.790887	+	0.611962i	$0.790380\pi$
$860$	1.61803	+	4.97980i	0.0551745	+	0.169810i
$861$	35.8515	−	7.62048i	1.22182	−	0.259705i
$862$	3.70820	+	6.42280i	0.126302	+	0.218761i
$863$	16.0902	−	27.8690i	0.547716	−	0.948672i	−0.450715	−	0.892668i	$-0.648831\pi$
$863$	16.0902	−	27.8690i	0.547716	−	0.948672i	0.998431	−	0.0560035i	$-0.0178358\pi$
$864$	9.59675	−	29.5358i	0.326488	−	1.00483i
$865$	1.56210	−	14.8624i	0.0531131	−	0.505337i
$866$	−6.09017	+	4.42477i	−0.206952	+	0.150360i
$867$	12.8754			0.437271
$868$		0			0
$869$	3.41641			0.115894
$870$	4.47214	−	3.24920i	0.151620	−	0.110158i
$871$	−1.03363	+	9.83437i	−0.0350234	+	0.333225i
$872$	2.72542	−	8.38800i	0.0922945	−	0.284053i
$873$	1.43112	−	2.47877i	0.0484359	−	0.0838935i
$874$	−5.32624	−	9.22531i	−0.180163	−	0.312051i
$875$	−37.2915	+	7.92655i	−1.26068	+	0.267966i
$876$	0.291796	+	0.898056i	0.00985888	+	0.0303425i
$877$	35.1588	+	7.47323i	1.18723	+	0.252353i	0.758862	−	0.651252i	$-0.225756\pi$
$877$	35.1588	+	7.47323i	1.18723	+	0.252353i	0.428367	+	0.903605i	$0.359089\pi$
$878$	1.36830	+	13.0185i	0.0461777	+	0.439352i
$879$	7.00723	+	7.78231i	0.236348	+	0.262491i
$880$	3.38761	+	1.50826i	0.114196	+	0.0508435i
$881$	22.2546	−	9.90838i	0.749776	−	0.333822i	0.00397643	−	0.999992i	$-0.498734\pi$
$881$	22.2546	−	9.90838i	0.749776	−	0.333822i	0.745800	+	0.666170i	$0.232068\pi$
$882$	6.66282	−	7.39981i	0.224349	−	0.249165i
$883$	−32.1803	−	23.3804i	−1.08295	−	0.786813i	−0.104759	−	0.994498i	$-0.533407\pi$
$883$	−32.1803	−	23.3804i	−1.08295	−	0.786813i	−0.978196	+	0.207685i	$0.933407\pi$
$884$	8.47214	+	6.15537i	0.284949	+	0.207027i
$885$	−1.84943	+	2.05400i	−0.0621680	+	0.0690445i
$886$	−9.76299	+	4.34676i	−0.327994	+	0.146032i
$887$	−28.3828	−	12.6369i	−0.953002	−	0.424304i	−0.129476	−	0.991583i	$-0.541330\pi$
$887$	−28.3828	−	12.6369i	−0.953002	−	0.424304i	−0.823526	+	0.567278i	$0.807996\pi$
$888$	−3.69886	−	4.10800i	−0.124126	−	0.137856i
$889$	1.56210	+	14.8624i	0.0523912	+	0.498469i
$890$	−1.03266	−	0.219498i	−0.0346148	−	0.00735760i
$891$	−1.49342	−	4.59628i	−0.0500315	−	0.153981i
$892$	6.33070	−	1.34563i	0.211968	−	0.0450551i
$893$	7.23607	+	12.5332i	0.242146	+	0.419409i
$894$	3.81966	−	6.61585i	0.127749	−	0.221267i
$895$	−3.61803	+	11.1352i	−0.120938	+	0.372207i
$896$	5.03982	−	47.9507i	0.168368	−	1.60192i
$897$	9.52786	−	6.92240i	0.318126	−	0.231132i
$898$	−19.3475			−0.645635
$899$		0			0
$900$	−9.52786			−0.317595
$901$	6.47214	−	4.70228i	0.215618	−	0.156656i
$902$	0.904430	−	8.60508i	0.0301142	−	0.286518i
$903$	5.23607	−	16.1150i	0.174245	−	0.536272i
$904$	6.11803	−	10.5967i	0.203483	−	0.352443i
$905$	−9.09017	−	15.7446i	−0.302167	−	0.523369i
$906$	6.11266	−	1.29929i	0.203080	−	0.0431659i
$907$	−6.10739	−	18.7966i	−0.202793	−	0.624131i	−0.999797	−	0.0201577i	$-0.993583\pi$
$907$	−6.10739	−	18.7966i	−0.202793	−	0.624131i	0.797004	−	0.603974i	$-0.206417\pi$
$908$	3.91259	+	0.831647i	0.129844	+	0.0275992i
$909$	−0.461640	−	4.39221i	−0.0153116	−	0.145681i
$910$	2.16535	+	2.40487i	0.0717807	+	0.0797206i
$911$	−3.81893	−	1.70030i	−0.126527	−	0.0563334i	0.342497	−	0.939519i	$-0.388727\pi$
$911$	−3.81893	−	1.70030i	−0.126527	−	0.0563334i	−0.469024	+	0.883186i	$0.655394\pi$
$912$	4.68157	−	2.08437i	0.155022	−	0.0690203i
$913$	3.94020	−	4.37604i	0.130402	−	0.144826i
$914$	−10.4721	−	7.60845i	−0.346387	−	0.251665i
$915$	14.1803	+	10.3026i	0.468788	+	0.340594i
$916$	−14.5256	+	16.1323i	−0.479940	+	0.533027i
$917$	−46.4381	+	20.6756i	−1.53352	+	0.682767i
$918$	16.3420	+	7.27593i	0.539366	+	0.240141i
$919$	−3.69886	−	4.10800i	−0.122014	−	0.135511i	0.679043	−	0.734099i	$-0.262395\pi$
$919$	−3.69886	−	4.10800i	−0.122014	−	0.135511i	−0.801057	+	0.598588i	$0.795729\pi$
$920$	1.80166	+	17.1416i	0.0593990	+	0.565143i
$921$	18.4887	+	3.92988i	0.609222	+	0.129494i
$922$	1.97871	+	6.08985i	0.0651655	+	0.200559i
$923$	−15.9358	+	3.38725i	−0.524533	+	0.111493i
$924$	−8.47214	−	14.6742i	−0.278713	−	0.482745i
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$	5.61803	−	17.2905i	0.184620	−	0.568202i
$927$	0.271434	−	2.58252i	0.00891506	−	0.0848212i
$928$	32.8885	−	23.8949i	1.07962	−	0.784389i
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	24.4721			0.802042
$932$	0.0729490	−	0.0530006i	0.00238952	−	0.00173609i
$933$	0.881129	−	8.38339i	0.0288469	−	0.274460i
$934$	1.66312	−	5.11855i	0.0544189	−	0.167484i
$935$	−5.23607	+	9.06914i	−0.171238	+	0.296592i
$936$	2.03444	+	3.52376i	0.0664978	+	0.115178i
$937$	−26.3555	+	5.60203i	−0.860996	+	0.183010i	−0.617190	−	0.786814i	$-0.711729\pi$
$937$	−26.3555	+	5.60203i	−0.860996	+	0.183010i	−0.243805	+	0.969824i	$0.578396\pi$
$938$	6.47214	+	19.9192i	0.211323	+	0.650384i
$939$	−25.6756	−	5.45752i	−0.837892	−	0.178099i
$940$	−1.09464	−	10.4148i	−0.0357031	−	0.339692i
$941$	−25.4270	−	28.2395i	−0.828895	−	0.920581i	0.168988	−	0.985618i	$-0.445950\pi$
$941$	−25.4270	−	28.2395i	−0.828895	−	0.920581i	−0.997883	+	0.0650367i	$0.979284\pi$
$942$	10.3905	+	4.62616i	0.338541	+	0.150728i
$943$	−49.2926	+	21.9465i	−1.60519	+	0.714675i
$944$	−2.77415	+	3.08100i	−0.0902908	+	0.100278i
$945$	−18.9443	−	13.7638i	−0.616257	−	0.447737i
$946$	−3.23607	−	2.35114i	−0.105214	−	0.0764422i
$947$	−20.7058	+	22.9961i	−0.672847	+	0.747272i	−0.978810	−	0.204771i	$-0.934355\pi$
$947$	−20.7058	+	22.9961i	−0.672847	+	0.747272i	0.305963	+	0.952043i	$0.401022\pi$
$948$	−3.12104	+	1.38958i	−0.101367	+	0.0451314i
$949$	−0.533138	−	0.237368i	−0.0173064	−	0.00770530i
$950$	3.69886	+	4.10800i	0.120007	+	0.133281i
$951$	−2.83529	−	26.9760i	−0.0919407	−	0.874757i
$952$	48.5129	+	10.3117i	1.57231	+	0.334206i
$953$	9.97871	+	30.7113i	0.323242	+	0.994837i	0.972228	+	0.234037i	$0.0751936\pi$
$953$	9.97871	+	30.7113i	0.323242	+	0.994837i	−0.648986	+	0.760801i	$0.724806\pi$
$954$	1.35972	−	0.289017i	0.0440226	−	0.00935728i
$955$	−1.59017	−	2.75426i	−0.0514567	−	0.0891256i
$956$	1.38197	−	2.39364i	0.0446960	−	0.0774157i
$957$	5.52786	−	17.0130i	0.178690	−	0.549953i
$958$	2.37143	−	22.5626i	0.0766174	−	0.728966i
$959$	67.5410	−	49.0714i	2.18101	−	1.58460i
$960$	−0.291796			−0.00941768
$961$		0			0
$962$	1.52786			0.0492603
$963$	12.1910	−	8.85727i	0.392849	−	0.285421i
$964$	−5.13492	+	48.8555i	−0.165385	+	1.57353i
$965$	−1.69098	+	5.20431i	−0.0544347	+	0.167533i
$966$	12.4721	−	21.6024i	0.401284	−	0.695045i
$967$	−7.81966	−	13.5440i	−0.251463	−	0.435547i	0.712466	−	0.701707i	$-0.247578\pi$
$967$	−7.81966	−	13.5440i	−0.251463	−	0.435547i	−0.963929	+	0.266160i	$0.914245\pi$
$968$	15.3104	−	3.25433i	0.492096	−	0.104598i
$969$	4.47214	+	13.7638i	0.143666	+	0.442158i
$970$	1.17537	+	0.249832i	0.0377388	+	0.00802163i
$971$	2.92680	+	27.8466i	0.0939254	+	0.893640i	0.935459	+	0.353435i	$0.114987\pi$
$971$	2.92680	+	27.8466i	0.0939254	+	0.893640i	−0.841534	+	0.540205i	$0.818347\pi$
$972$	−14.7209	−	16.3492i	−0.472172	−	0.524400i
$973$	51.9194	+	23.1160i	1.66446	+	0.741065i
$974$	8.33575	−	3.71131i	0.267095	−	0.118918i
$975$	−4.08936	+	4.54170i	−0.130964	+	0.145451i
$976$	21.2705	+	15.4539i	0.680852	+	0.494668i
$977$	−26.8992	−	19.5434i	−0.860581	−	0.625249i	0.0674618	−	0.997722i	$-0.478510\pi$
$977$	−26.8992	−	19.5434i	−0.860581	−	0.625249i	−0.928043	+	0.372473i	$0.878510\pi$
$978$	1.38435	−	1.53748i	0.0442667	−	0.0491632i
$979$	−3.12104	+	1.38958i	−0.0997490	+	0.0444111i
$980$	−16.1772	−	7.20258i	−0.516763	−	0.230078i
$981$	−3.88531	−	4.31507i	−0.124048	−	0.137770i
$982$	−2.60739	−	24.8076i	−0.0832050	−	0.791643i
$983$	−47.4129	−	10.0779i	−1.51224	−	0.321436i	−0.624221	−	0.781248i	$-0.714583\pi$
$983$	−47.4129	−	10.0779i	−1.51224	−	0.321436i	−0.888016	+	0.459812i	$0.847917\pi$
$984$	5.97871	+	18.4006i	0.190594	+	0.586589i
$985$	15.0795	−	3.20525i	0.480474	−	0.102128i
$986$	11.7082	+	20.2792i	0.372865	+	0.645821i
$987$	−16.9443	+	29.3483i	−0.539342	+	0.934168i
$988$	−1.38197	+	4.25325i	−0.0439662	+	0.135314i
$989$	−2.60739	+	24.8076i	−0.0829101	+	0.788837i
$990$	−1.47214	+	1.06957i	−0.0467876	+	0.0339931i
$991$	50.5410			1.60549			0.802744	−	0.596324i	$-0.203372\pi$
$991$	50.5410			1.60549			0.802744	+	0.596324i	$0.203372\pi$
$992$		0			0
$993$	2.47214			0.0784509
$994$	−27.9164	+	20.2825i	−0.885455	+	0.643320i
$995$	0.110354	−	1.04994i	0.00349845	−	0.0332855i
$996$	−1.81966	+	5.60034i	−0.0576581	+	0.177453i
$997$	−7.68034	+	13.3027i	−0.243239	+	0.421302i	−0.961635	−	0.274332i	$-0.911543\pi$
$997$	−7.68034	+	13.3027i	−0.243239	+	0.421302i	0.718396	+	0.695634i	$0.244877\pi$
$998$	−10.3262	−	17.8856i	−0.326871	−	0.566158i
$999$	−10.8141	+	2.29862i	−0.342144	+	0.0727250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.h.338.1		8
31.2	even	5	inner	961.2.g.h.732.1		8
31.3	odd	30		961.2.d.a.531.1		4
31.4	even	5		961.2.g.a.448.1		8
31.5	even	3	inner	961.2.g.h.235.1		8
31.6	odd	6		961.2.d.g.388.1		4
31.7	even	15		961.2.d.c.628.1		4
31.8	even	5		961.2.c.e.521.1		4
31.9	even	15		961.2.c.e.439.1		4
31.10	even	15	inner	961.2.g.h.816.1		8
31.11	odd	30		961.2.g.d.846.1		8
31.12	odd	30		961.2.d.g.374.1		4
31.13	odd	30		961.2.g.d.547.1		8
31.14	even	15		31.2.a.a.1.1	✓	2
31.15	odd	10		961.2.g.d.844.1		8
31.16	even	5		961.2.g.a.844.1		8
31.17	odd	30		961.2.a.f.1.1		2
31.18	even	15		961.2.g.a.547.1		8
31.19	even	15		961.2.d.d.374.1		4
31.20	even	15		961.2.g.a.846.1		8
31.21	odd	30		961.2.g.e.816.1		8
31.22	odd	30		961.2.c.c.439.1		4
31.23	odd	10		961.2.c.c.521.1		4
31.24	odd	30		961.2.d.a.628.1		4
31.25	even	3		961.2.d.d.388.1		4
31.26	odd	6		961.2.g.e.235.1		8
31.27	odd	10		961.2.g.d.448.1		8
31.28	even	15		961.2.d.c.531.1		4
31.29	odd	10		961.2.g.e.732.1		8
31.30	odd	2		961.2.g.e.338.1		8
93.14	odd	30		279.2.a.a.1.2		2
93.17	even	30		8649.2.a.c.1.2		2
124.107	odd	30		496.2.a.i.1.1		2
155.14	even	30		775.2.a.d.1.2		2
155.107	odd	60		775.2.b.d.249.2		4
155.138	odd	60		775.2.b.d.249.3		4
217.76	odd	30		1519.2.a.a.1.1		2
248.45	even	30		1984.2.a.r.1.1		2
248.107	odd	30		1984.2.a.n.1.2		2
341.76	odd	30		3751.2.a.b.1.2		2
372.107	even	30		4464.2.a.bf.1.2		2
403.324	even	30		5239.2.a.f.1.2		2
465.14	odd	30		6975.2.a.y.1.1		2
527.169	even	30		8959.2.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.1	✓	2	31.14	even	15
279.2.a.a.1.2		2	93.14	odd	30
496.2.a.i.1.1		2	124.107	odd	30
775.2.a.d.1.2		2	155.14	even	30
775.2.b.d.249.2		4	155.107	odd	60
775.2.b.d.249.3		4	155.138	odd	60
961.2.a.f.1.1		2	31.17	odd	30
961.2.c.c.439.1		4	31.22	odd	30
961.2.c.c.521.1		4	31.23	odd	10
961.2.c.e.439.1		4	31.9	even	15
961.2.c.e.521.1		4	31.8	even	5
961.2.d.a.531.1		4	31.3	odd	30
961.2.d.a.628.1		4	31.24	odd	30
961.2.d.c.531.1		4	31.28	even	15
961.2.d.c.628.1		4	31.7	even	15
961.2.d.d.374.1		4	31.19	even	15
961.2.d.d.388.1		4	31.25	even	3
961.2.d.g.374.1		4	31.12	odd	30
961.2.d.g.388.1		4	31.6	odd	6
961.2.g.a.448.1		8	31.4	even	5
961.2.g.a.547.1		8	31.18	even	15
961.2.g.a.844.1		8	31.16	even	5
961.2.g.a.846.1		8	31.20	even	15
961.2.g.d.448.1		8	31.27	odd	10
961.2.g.d.547.1		8	31.13	odd	30
961.2.g.d.844.1		8	31.15	odd	10
961.2.g.d.846.1		8	31.11	odd	30
961.2.g.e.235.1		8	31.26	odd	6
961.2.g.e.338.1		8	31.30	odd	2
961.2.g.e.732.1		8	31.29	odd	10
961.2.g.e.816.1		8	31.21	odd	30
961.2.g.h.235.1		8	31.5	even	3	inner
961.2.g.h.338.1		8	1.1	even	1	trivial
961.2.g.h.732.1		8	31.2	even	5	inner
961.2.g.h.816.1		8	31.10	even	15	inner
1519.2.a.a.1.1		2	217.76	odd	30
1984.2.a.n.1.2		2	248.107	odd	30
1984.2.a.r.1.1		2	248.45	even	30
3751.2.a.b.1.2		2	341.76	odd	30
4464.2.a.bf.1.2		2	372.107	even	30
5239.2.a.f.1.2		2	403.324	even	30
6975.2.a.y.1.1		2	465.14	odd	30
8649.2.a.c.1.2		2	93.17	even	30
8959.2.a.b.1.1		2	527.169	even	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.363271i) q^{2} +(-0.129204 + 1.22930i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.381966 + 0.661585i) q^{6} +(4.14350 - 0.880728i) q^{7} +(0.690983 + 2.12663i) q^{8} +(1.43997 + 0.306074i) q^{9} +(0.0646021 + 0.614648i) q^{10} +(1.33826 + 1.48629i) q^{11} +(-1.82709 - 0.813473i) q^{12} +(1.12920 - 0.502754i) q^{13} +(1.75181 - 1.94558i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(3.50361 - 3.89116i) q^{17} +(0.831171 - 0.370061i) q^{18} +(2.04275 + 0.909491i) q^{19} +(-1.08268 - 1.20243i) q^{20} +(0.547318 + 5.20738i) q^{21} +(1.20906 + 0.256993i) q^{22} +(-2.38197 - 7.33094i) q^{23} +(-2.70353 + 0.574654i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.381966 - 0.661585i) q^{26} +(-1.70820 + 5.25731i) q^{27} +(-0.716449 + 6.81655i) q^{28} +(-5.85410 + 4.25325i) q^{29} -0.763932 q^{30} -5.61803 q^{32} +(-2.00000 + 1.45309i) q^{33} +(0.338261 - 3.21834i) q^{34} +(-1.30902 + 4.02874i) q^{35} +(-1.19098 + 2.06284i) q^{36} +(1.00000 + 1.73205i) q^{37} +(1.35177 - 0.287327i) q^{38} +(0.472136 + 1.45309i) q^{39} +(-2.18720 - 0.464905i) q^{40} +(-0.731699 - 6.96165i) q^{41} +(2.16535 + 2.40487i) q^{42} +(-2.95630 - 1.31623i) q^{43} +(-2.95630 + 1.31623i) q^{44} +(-0.985051 + 1.09401i) q^{45} +(-3.85410 - 2.80017i) q^{46} +(5.23607 + 3.80423i) q^{47} +(1.53351 - 1.70314i) q^{48} +(9.99809 - 4.45144i) q^{49} +(2.25841 + 1.00551i) q^{50} +(4.33070 + 4.80973i) q^{51} +(0.209057 + 1.98904i) q^{52} +(1.49448 + 0.317661i) q^{53} +(1.05573 + 3.24920i) q^{54} +(-1.95630 + 0.415823i) q^{55} +(4.73607 + 8.20311i) q^{56} +(-1.38197 + 2.39364i) q^{57} +(-1.38197 + 4.25325i) q^{58} +(0.233733 - 2.22382i) q^{59} +(1.61803 - 1.17557i) q^{60} -14.1803 q^{61} +6.23607 q^{63} +(0.190983 - 0.138757i) q^{64} +(-0.129204 + 1.22930i) q^{65} +(-0.472136 + 1.45309i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(4.23607 + 7.33708i) q^{68} +(9.31966 - 1.98095i) q^{69} +(0.809017 + 2.48990i) q^{70} +(-12.8923 - 2.74035i) q^{71} +(0.344086 + 3.27376i) q^{72} +(-0.315921 - 0.350865i) q^{73} +(1.12920 + 0.502754i) q^{74} +(-4.51682 + 2.01102i) q^{75} +(-2.42094 + 2.68872i) q^{76} +(6.85410 + 4.97980i) q^{77} +(0.763932 + 0.555029i) q^{78} +(1.14301 - 1.26944i) q^{79} +(1.69381 - 0.754131i) q^{80} +(-2.20750 - 0.982842i) q^{81} +(-2.89482 - 3.21502i) q^{82} +(-0.307760 - 2.92814i) q^{83} +(-8.28700 - 1.76146i) q^{84} +(1.61803 + 4.97980i) q^{85} +(-1.95630 + 0.415823i) q^{86} +(-4.47214 - 7.74597i) q^{87} +(-2.23607 + 3.87298i) q^{88} +(-0.527864 + 1.62460i) q^{89} +(-0.0951031 + 0.904846i) q^{90} +(4.23607 - 3.07768i) q^{91} +12.4721 q^{92} +4.00000 q^{94} +(-1.80902 + 1.31433i) q^{95} +(0.725874 - 6.90623i) q^{96} +(0.600813 - 1.84911i) q^{97} +(3.38197 - 5.85774i) q^{98} +(1.47214 + 2.54981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 12 q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} - q^{14} - 8 q^{15} - 12 q^{16} - 2 q^{17} - 6 q^{18} + 5 q^{19} + 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 12 * q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 - q^14 - 8 * q^15 - 12 * q^16 - 2 * q^17 - 6 * q^18 + 5 * q^19 + 2 * q^20 - 8 * q^21 + 6 * q^22 - 28 * q^23 + 10 * q^24 + 16 * q^25 + 12 * q^26 + 40 * q^27 + 11 * q^28 - 20 * q^29 - 24 * q^30 - 36 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 14 * q^36 + 8 * q^37 - 5 * q^38 - 32 * q^39 - 5 * q^40 + 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 + 13 * q^45 - 4 * q^46 + 24 * q^47 + 24 * q^48 + 22 * q^49 + 8 * q^50 - 8 * q^51 - 2 * q^52 - 16 * q^53 + 80 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 - 20 * q^58 - 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 + 6 * q^64 + 4 * q^65 + 32 * q^66 - 32 * q^67 + 16 * q^68 - 24 * q^69 + 2 * q^70 - 23 * q^71 + 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 + 28 * q^77 + 24 * q^78 - 20 * q^79 + 6 * q^80 - 19 * q^81 + 21 * q^82 + 14 * q^83 - 6 * q^84 + 4 * q^85 + 2 * q^86 - 40 * q^89 - 6 * q^90 + 16 * q^91 + 64 * q^92 + 32 * q^94 - 10 * q^95 - 18 * q^96 + 54 * q^97 + 36 * q^98 - 24 * q^99

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