LMFDB - Embedded newform 222.2.j.b.175.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [222,2,Mod(85,222)] 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("222.85"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(222, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	222.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.77267892487$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.4
Root			$0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	222.175
Dual form			222.2.j.b.85.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.92048 - 1.68614i) q^{5} +1.00000i q^{6} +(-0.896143 - 1.55217i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +3.37228 q^{10} -2.57999 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.454090 + 0.262169i) q^{13} -1.79229i q^{14} +(2.92048 + 1.68614i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.41819 - 1.39614i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-3.60662 + 2.08228i) q^{19} +(2.92048 + 1.68614i) q^{20} +(0.896143 - 1.55217i) q^{21} +(-2.23434 - 1.29000i) q^{22} +8.63325i q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.18614 - 5.51856i) q^{25} -0.524338 q^{26} -1.00000 q^{27} +(0.896143 - 1.55217i) q^{28} +2.83638i q^{29} +(1.68614 + 2.92048i) q^{30} -7.10433i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.29000 - 2.23434i) q^{33} +(-1.39614 - 2.41819i) q^{34} +(-5.23434 - 3.02205i) q^{35} -1.00000 q^{36} +(5.70819 - 2.10157i) q^{37} -4.16457 q^{38} +(-0.454090 - 0.262169i) q^{39} +(1.68614 + 2.92048i) q^{40} +(0.0459101 + 0.0795187i) q^{41} +(1.55217 - 0.896143i) q^{42} -12.2735i q^{43} +(-1.29000 - 2.23434i) q^{44} +3.37228i q^{45} +(-4.31662 + 7.47661i) q^{46} -9.93278 q^{47} -1.00000 q^{48} +(1.89385 - 3.28025i) q^{49} +(5.51856 - 3.18614i) q^{50} -2.79229i q^{51} +(-0.454090 - 0.262169i) q^{52} +(0.847944 - 1.46868i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-7.53483 + 4.35023i) q^{55} +(1.55217 - 0.896143i) q^{56} +(-3.60662 - 2.08228i) q^{57} +(-1.41819 + 2.45638i) q^{58} +(8.48119 + 4.89662i) q^{59} +3.37228i q^{60} +(-3.36456 + 1.94253i) q^{61} +(3.55217 - 6.15253i) q^{62} +1.79229 q^{63} -1.00000 q^{64} +(-0.884107 + 1.53132i) q^{65} -2.57999i q^{66} +(4.79276 + 8.30131i) q^{67} -2.79229i q^{68} +(-7.47661 + 4.31662i) q^{69} +(-3.02205 - 5.23434i) q^{70} +(4.66228 + 8.07530i) q^{71} +(-0.866025 - 0.500000i) q^{72} +8.14050 q^{73} +(5.99422 + 1.03408i) q^{74} +6.37228 q^{75} +(-3.60662 - 2.08228i) q^{76} +(2.31205 + 4.00458i) q^{77} +(-0.262169 - 0.454090i) q^{78} +(0.964312 - 0.556746i) q^{79} +3.37228i q^{80} +(-0.500000 - 0.866025i) q^{81} +0.0918203i q^{82} +(0.316625 - 0.548410i) q^{83} +1.79229 q^{84} -9.41638 q^{85} +(6.13674 - 10.6291i) q^{86} +(-2.45638 + 1.41819i) q^{87} -2.57999i q^{88} +(-13.0755 - 7.54915i) q^{89} +(-1.68614 + 2.92048i) q^{90} +(0.813859 + 0.469882i) q^{91} +(-7.47661 + 4.31662i) q^{92} +(6.15253 - 3.55217i) q^{93} +(-8.60204 - 4.96639i) q^{94} +(-7.02205 + 12.1625i) q^{95} +(-0.866025 - 0.500000i) q^{96} +2.45159i q^{97} +(3.28025 - 1.89385i) q^{98} +(1.29000 - 2.23434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{4} - 4 q^{7} - 4 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{16} + 6 q^{17} + 6 q^{19} + 4 q^{21} - 6 q^{22} + 14 q^{25} + 16 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} - 2 q^{33}+ \cdots + 2 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^7 - 4 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^16 + 6 * q^17 + 6 * q^19 + 4 * q^21 - 6 * q^22 + 14 * q^25 + 16 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 - 2 * q^33 - 8 * q^34 - 30 * q^35 - 8 * q^36 + 12 * q^37 - 4 * q^38 - 6 * q^39 + 2 * q^40 - 2 * q^41 - 6 * q^42 - 2 * q^44 - 8 * q^46 - 28 * q^47 - 8 * q^48 + 10 * q^49 - 6 * q^52 + 4 * q^53 + 30 * q^55 - 6 * q^56 + 6 * q^57 + 14 * q^58 + 12 * q^59 - 36 * q^61 + 10 * q^62 + 8 * q^63 - 8 * q^64 + 4 * q^65 - 8 * q^67 - 2 * q^70 + 6 * q^71 + 20 * q^73 + 24 * q^74 + 28 * q^75 + 6 * q^76 - 12 * q^77 + 8 * q^78 - 24 * q^79 - 4 * q^81 - 24 * q^83 + 8 * q^84 - 8 * q^85 + 18 * q^86 - 24 * q^87 - 42 * q^89 - 2 * q^90 + 18 * q^91 + 12 * q^93 - 30 * q^94 - 34 * q^95 + 12 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.92048	−	1.68614i	1.30608	−	0.754065i	0.324640	−	0.945838i	$-0.394757\pi$
$5$	2.92048	−	1.68614i	1.30608	−	0.754065i	0.981439	+	0.191773i	$0.0614237\pi$
$6$			1.00000i			0.408248i
$7$	−0.896143	−	1.55217i	−0.338710	−	0.586664i	0.645480	−	0.763777i	$-0.276657\pi$
$7$	−0.896143	−	1.55217i	−0.338710	−	0.586664i	−0.984190	+	0.177114i	$0.943324\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	3.37228			1.06641
$11$	−2.57999			−0.777898			−0.388949	−	0.921259i	$-0.627162\pi$
$11$	−2.57999			−0.777898			−0.388949	+	0.921259i	$0.627162\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.454090	+	0.262169i	−0.125942	+	0.0727126i	−0.561647	−	0.827377i	$-0.689832\pi$
$13$	−0.454090	+	0.262169i	−0.125942	+	0.0727126i	0.435706	+	0.900089i	$0.356499\pi$
$14$		−	1.79229i		−	0.479009i
$15$	2.92048	+	1.68614i	0.754065	+	0.435360i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.41819	−	1.39614i	−0.586498	−	0.338615i	0.177214	−	0.984172i	$-0.443292\pi$
$17$	−2.41819	−	1.39614i	−0.586498	−	0.338615i	−0.763711	+	0.645558i	$0.776625\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−3.60662	+	2.08228i	−0.827416	+	0.477709i	−0.852967	−	0.521965i	$-0.825199\pi$
$19$	−3.60662	+	2.08228i	−0.827416	+	0.477709i	0.0255512	+	0.999674i	$0.491866\pi$
$20$	2.92048	+	1.68614i	0.653039	+	0.377033i
$21$	0.896143	−	1.55217i	0.195555	−	0.338710i
$22$	−2.23434	−	1.29000i	−0.476363	−	0.275028i
$23$			8.63325i			1.80016i	0.435728	+	0.900078i	$0.356491\pi$
$23$			8.63325i			1.80016i	−0.435728	+	0.900078i	$0.643509\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	3.18614	−	5.51856i	0.637228	−	1.10371i
$26$	−0.524338			−0.102831
$27$	−1.00000			−0.192450
$28$	0.896143	−	1.55217i	0.169355	−	0.293332i
$29$			2.83638i			0.526703i	0.964700	+	0.263352i	$0.0848279\pi$
$29$			2.83638i			0.526703i	−0.964700	+	0.263352i	$0.915172\pi$
$30$	1.68614	+	2.92048i	0.307846	+	0.533204i
$31$		−	7.10433i		−	1.27598i	−0.770046	−	0.637988i	$-0.779767\pi$
$31$		−	7.10433i		−	1.27598i	0.770046	−	0.637988i	$-0.220233\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.29000	−	2.23434i	−0.224560	−	0.388949i
$34$	−1.39614	−	2.41819i	−0.239437	−	0.414716i
$35$	−5.23434	−	3.02205i	−0.884765	−	0.510819i
$36$	−1.00000			−0.166667
$37$	5.70819	−	2.10157i	0.938420	−	0.345495i
$37$	5.70819	−	2.10157i	0.938420	−	0.345495i
$38$	−4.16457			−0.675582
$39$	−0.454090	−	0.262169i	−0.0727126	−	0.0419806i
$40$	1.68614	+	2.92048i	0.266602	+	0.461769i
$41$	0.0459101	+	0.0795187i	0.00716996	+	0.0124187i	0.869588	−	0.493778i	$-0.164384\pi$
$41$	0.0459101	+	0.0795187i	0.00716996	+	0.0124187i	−0.862418	+	0.506197i	$0.831051\pi$
$42$	1.55217	−	0.896143i	0.239504	−	0.138278i
$43$		−	12.2735i		−	1.87169i	−0.352414	−	0.935844i	$-0.614639\pi$
$43$		−	12.2735i		−	1.87169i	0.352414	−	0.935844i	$-0.385361\pi$
$44$	−1.29000	−	2.23434i	−0.194474	−	0.336840i
$45$			3.37228i			0.502710i
$46$	−4.31662	+	7.47661i	−0.636452	+	1.10237i
$47$	−9.93278			−1.44885			−0.724423	−	0.689356i	$-0.757894\pi$
$47$	−9.93278			−1.44885			−0.724423	+	0.689356i	$0.757894\pi$
$48$	−1.00000			−0.144338
$49$	1.89385	−	3.28025i	0.270551	−	0.468607i
$50$	5.51856	−	3.18614i	0.780442	−	0.450588i
$51$		−	2.79229i		−	0.390998i
$52$	−0.454090	−	0.262169i	−0.0629709	−	0.0363563i
$53$	0.847944	−	1.46868i	0.116474	−	0.201739i	−0.801894	−	0.597466i	$-0.796174\pi$
$53$	0.847944	−	1.46868i	0.116474	−	0.201739i	0.918368	+	0.395727i	$0.129507\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−7.53483	+	4.35023i	−1.01600	+	0.586585i
$56$	1.55217	−	0.896143i	0.207417	−	0.119752i
$57$	−3.60662	−	2.08228i	−0.477709	−	0.275805i
$58$	−1.41819	+	2.45638i	−0.186218	+	0.322538i
$59$	8.48119	+	4.89662i	1.10416	+	0.637486i	0.937310	−	0.348497i	$-0.113308\pi$
$59$	8.48119	+	4.89662i	1.10416	+	0.637486i	0.166847	+	0.985983i	$0.446641\pi$
$60$			3.37228i			0.435360i
$61$	−3.36456	+	1.94253i	−0.430788	+	0.248715i	−0.699682	−	0.714454i	$-0.746675\pi$
$61$	−3.36456	+	1.94253i	−0.430788	+	0.248715i	0.268894	+	0.963170i	$0.413342\pi$
$62$	3.55217	−	6.15253i	0.451126	−	0.781372i
$63$	1.79229			0.225807
$64$	−1.00000			−0.125000
$65$	−0.884107	+	1.53132i	−0.109660	+	0.189937i
$66$		−	2.57999i		−	0.317575i
$67$	4.79276	+	8.30131i	0.585529	+	1.01417i	0.994809	+	0.101757i	$0.0324466\pi$
$67$	4.79276	+	8.30131i	0.585529	+	1.01417i	−0.409280	+	0.912409i	$0.634220\pi$
$68$		−	2.79229i		−	0.338615i
$69$	−7.47661	+	4.31662i	−0.900078	+	0.519661i
$70$	−3.02205	−	5.23434i	−0.361204	−	0.625623i
$71$	4.66228	+	8.07530i	0.553311	+	0.958362i	0.998033	+	0.0626936i	$0.0199691\pi$
$71$	4.66228	+	8.07530i	0.553311	+	0.958362i	−0.444722	+	0.895669i	$0.646698\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	8.14050			0.952773			0.476386	−	0.879236i	$-0.341946\pi$
$73$	8.14050			0.952773			0.476386	+	0.879236i	$0.341946\pi$
$74$	5.99422	+	1.03408i	0.696814	+	0.120210i
$75$	6.37228			0.735808
$76$	−3.60662	−	2.08228i	−0.413708	−	0.238854i
$77$	2.31205	+	4.00458i	0.263482	+	0.456364i
$78$	−0.262169	−	0.454090i	−0.0296848	−	0.0514156i
$79$	0.964312	−	0.556746i	0.108494	−	0.0626388i	−0.444771	−	0.895644i	$-0.646715\pi$
$79$	0.964312	−	0.556746i	0.108494	−	0.0626388i	0.553265	+	0.833005i	$0.313382\pi$
$80$			3.37228i			0.377033i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			0.0918203i			0.0101399i
$83$	0.316625	−	0.548410i	0.0347541	−	0.0601958i	−0.848125	−	0.529796i	$-0.822269\pi$
$83$	0.316625	−	0.548410i	0.0347541	−	0.0601958i	0.882879	+	0.469600i	$0.155602\pi$
$84$	1.79229			0.195555
$85$	−9.41638			−1.02135
$86$	6.13674	−	10.6291i	0.661742	−	1.14617i
$87$	−2.45638	+	1.41819i	−0.263352	+	0.152046i
$88$		−	2.57999i		−	0.275028i
$89$	−13.0755	−	7.54915i	−1.38600	−	0.800208i	−0.393140	−	0.919479i	$-0.628611\pi$
$89$	−13.0755	−	7.54915i	−1.38600	−	0.800208i	−0.992862	+	0.119270i	$0.961945\pi$
$90$	−1.68614	+	2.92048i	−0.177735	+	0.307846i
$91$	0.813859	+	0.469882i	0.0853156	+	0.0492570i
$92$	−7.47661	+	4.31662i	−0.779491	+	0.450039i
$93$	6.15253	−	3.55217i	0.637988	−	0.368342i
$94$	−8.60204	−	4.96639i	−0.887233	−	0.512244i
$95$	−7.02205	+	12.1625i	−0.720447	+	1.24785i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$			2.45159i			0.248921i	0.992225	+	0.124461i	$0.0397200\pi$
$97$			2.45159i			0.248921i	−0.992225	+	0.124461i	$0.960280\pi$
$98$	3.28025	−	1.89385i	0.331355	−	0.191308i
$99$	1.29000	−	2.23434i	0.129650	−	0.224560i
$100$	6.37228			0.637228
$101$	18.5855			1.84933			0.924664	−	0.380783i	$-0.124346\pi$
$101$	18.5855			1.84933			0.924664	+	0.380783i	$0.124346\pi$
$102$	1.39614	−	2.41819i	0.138239	−	0.239437i
$103$			0.348209i			0.0343100i	0.999853	+	0.0171550i	$0.00546088\pi$
$103$			0.348209i			0.0343100i	−0.999853	+	0.0171550i	$0.994539\pi$
$104$	−0.262169	−	0.454090i	−0.0257078	−	0.0445272i
$105$		−	6.04410i		−	0.589843i
$106$	1.46868	−	0.847944i	0.142651	−	0.0823596i
$107$	−2.53387	−	4.38880i	−0.244959	−	0.424281i	0.717161	−	0.696907i	$-0.245441\pi$
$107$	−2.53387	−	4.38880i	−0.244959	−	0.424281i	−0.962120	+	0.272626i	$0.912108\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−5.99313	−	3.46014i	−0.574038	−	0.331421i	0.184723	−	0.982791i	$-0.440861\pi$
$109$	−5.99313	−	3.46014i	−0.574038	−	0.331421i	−0.758760	+	0.651370i	$0.774195\pi$
$110$	−8.70047			−0.829557
$111$	4.67410	+	3.89265i	0.443646	+	0.369474i
$112$	1.79229			0.169355
$113$	17.1962	+	9.92820i	1.61768	+	0.933967i	0.987519	+	0.157501i	$0.0503437\pi$
$113$	17.1962	+	9.92820i	1.61768	+	0.933967i	0.630159	+	0.776466i	$0.282990\pi$
$114$	−2.08228	−	3.60662i	−0.195024	−	0.337791i
$115$	14.5569	+	25.2132i	1.35744	+	2.35115i
$116$	−2.45638	+	1.41819i	−0.228069	+	0.131676i
$117$		−	0.524338i		−	0.0484750i
$118$	4.89662	+	8.48119i	0.450770	+	0.780757i
$119$			5.00458i			0.458769i
$120$	−1.68614	+	2.92048i	−0.153923	+	0.266602i
$121$	−4.34363			−0.394875
$122$	−3.88506			−0.351737
$123$	−0.0459101	+	0.0795187i	−0.00413958	+	0.00716996i
$124$	6.15253	−	3.55217i	0.552514	−	0.318994i
$125$		−	4.62772i		−	0.413916i
$126$	1.55217	+	0.896143i	0.138278	+	0.0798348i
$127$	3.29505	−	5.70720i	0.292389	−	0.506432i	−0.681985	−	0.731366i	$-0.738883\pi$
$127$	3.29505	−	5.70720i	0.292389	−	0.506432i	0.974374	+	0.224934i	$0.0722166\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	10.6291	−	6.13674i	0.935844	−	0.540310i
$130$	−1.53132	+	0.884107i	−0.134306	+	0.0775413i
$131$	−9.04963	−	5.22480i	−0.790670	−	0.456493i	0.0495286	−	0.998773i	$-0.484228\pi$
$131$	−9.04963	−	5.22480i	−0.790670	−	0.456493i	−0.840198	+	0.542279i	$0.817561\pi$
$132$	1.29000	−	2.23434i	0.112280	−	0.194474i
$133$	6.46410	+	3.73205i	0.560509	+	0.323610i
$134$			9.58553i			0.828063i
$135$	−2.92048	+	1.68614i	−0.251355	+	0.145120i
$136$	1.39614	−	2.41819i	0.119718	−	0.207358i
$137$	6.02865			0.515063			0.257531	−	0.966270i	$-0.417091\pi$
$137$	6.02865			0.515063			0.257531	+	0.966270i	$0.417091\pi$
$138$	−8.63325			−0.734911
$139$	−4.65024	+	8.05446i	−0.394428	+	0.683170i	−0.993028	−	0.117878i	$-0.962391\pi$
$139$	−4.65024	+	8.05446i	−0.394428	+	0.683170i	0.598600	+	0.801048i	$0.295724\pi$
$140$		−	6.04410i		−	0.510819i
$141$	−4.96639	−	8.60204i	−0.418246	−	0.724423i
$142$			9.32456i			0.782499i
$143$	1.17155	−	0.676394i	0.0979699	−	0.0565629i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.78254	+	8.28360i	0.397168	+	0.687916i
$146$	7.04988	+	4.07025i	0.583452	+	0.336856i
$147$	3.78771			0.312405
$148$	4.67410	+	3.89265i	0.384209	+	0.319974i
$149$	−18.6968			−1.53170			−0.765852	−	0.643016i	$-0.777683\pi$
$149$	−18.6968			−1.53170			−0.765852	+	0.643016i	$0.777683\pi$
$150$	5.51856	+	3.18614i	0.450588	+	0.260147i
$151$	6.17916	+	10.7026i	0.502853	+	0.870967i	0.999995	+	0.00329737i	$0.00104959\pi$
$151$	6.17916	+	10.7026i	0.502853	+	0.870967i	−0.497142	+	0.867669i	$0.665617\pi$
$152$	−2.08228	−	3.60662i	−0.168896	−	0.292536i
$153$	2.41819	−	1.39614i	0.195499	−	0.112872i
$154$			4.62409i			0.372620i
$155$	−11.9789	−	20.7481i	−0.962169	−	1.66653i
$156$		−	0.524338i		−	0.0419806i
$157$	−3.57770	+	6.19677i	−0.285532	+	0.494556i	−0.972738	−	0.231907i	$-0.925504\pi$
$157$	−3.57770	+	6.19677i	−0.285532	+	0.494556i	0.687206	+	0.726462i	$0.258837\pi$
$158$	1.11349			0.0885846
$159$	1.69589			0.134493
$160$	−1.68614	+	2.92048i	−0.133301	+	0.230884i
$161$	13.4002	−	7.73663i	1.05609	−	0.609732i
$162$		−	1.00000i		−	0.0785674i
$163$	9.53025	+	5.50229i	0.746466	+	0.430973i	0.824416	−	0.565985i	$-0.191504\pi$
$163$	9.53025	+	5.50229i	0.746466	+	0.430973i	−0.0779493	+	0.996957i	$0.524837\pi$
$164$	−0.0459101	+	0.0795187i	−0.00358498	+	0.00620937i
$165$	−7.53483	−	4.35023i	−0.586585	−	0.338665i
$166$	0.548410	−	0.316625i	0.0425649	−	0.0245748i
$167$	−0.339746	+	0.196152i	−0.0262903	+	0.0151787i	−0.513088	−	0.858336i	$-0.671498\pi$
$167$	−0.339746	+	0.196152i	−0.0262903	+	0.0151787i	0.486797	+	0.873515i	$0.338165\pi$
$168$	1.55217	+	0.896143i	0.119752	+	0.0691390i
$169$	−6.36253	+	11.0202i	−0.489426	+	0.847710i
$170$	−8.15482	−	4.70819i	−0.625446	−	0.361102i
$171$		−	4.16457i		−	0.318472i
$172$	10.6291	−	6.13674i	0.810465	−	0.467922i
$173$	8.32435	−	14.4182i	0.632888	−	1.09619i	−0.354070	−	0.935219i	$-0.615203\pi$
$173$	8.32435	−	14.4182i	0.632888	−	1.09619i	0.986958	−	0.160976i	$-0.0514641\pi$
$174$	−2.83638			−0.215026
$175$	−11.4210			−0.863343
$176$	1.29000	−	2.23434i	0.0972372	−	0.168420i
$177$			9.79324i			0.736105i
$178$	−7.54915	−	13.0755i	−0.565833	−	0.980051i
$179$			2.56092i			0.191412i	0.995410	+	0.0957062i	$0.0305109\pi$
$179$			2.56092i			0.191412i	−0.995410	+	0.0957062i	$0.969489\pi$
$180$	−2.92048	+	1.68614i	−0.217680	+	0.125678i
$181$	−12.0951	−	20.9493i	−0.899019	−	1.55715i	−0.828751	−	0.559618i	$-0.810948\pi$
$181$	−12.0951	−	20.9493i	−0.899019	−	1.55715i	−0.0702683	−	0.997528i	$-0.522386\pi$
$182$	0.469882	+	0.813859i	0.0348300	+	0.0603273i
$183$	−3.36456	−	1.94253i	−0.248715	−	0.143596i
$184$	−8.63325			−0.636452
$185$	13.1271	−	15.7624i	0.965125	−	1.15887i
$186$	7.10433			0.520915
$187$	6.23892	+	3.60204i	0.456235	+	0.263407i
$188$	−4.96639	−	8.60204i	−0.362211	−	0.627368i
$189$	0.896143	+	1.55217i	0.0651848	+	0.112903i
$190$	−12.1625	+	7.02205i	−0.882364	+	0.509433i
$191$			5.28962i			0.382743i	0.981518	+	0.191372i	$0.0612936\pi$
$191$			5.28962i			0.382743i	−0.981518	+	0.191372i	$0.938706\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$		−	10.2448i		−	0.737439i	−0.929541	−	0.368719i	$-0.879796\pi$
$193$		−	10.2448i		−	0.737439i	0.929541	−	0.368719i	$-0.120204\pi$
$194$	−1.22579	+	2.12314i	−0.0880069	+	0.152432i
$195$	−1.76821			−0.126624
$196$	3.78771			0.270551
$197$	−11.5978	+	20.0880i	−0.826311	+	1.43121i	0.0746023	+	0.997213i	$0.476231\pi$
$197$	−11.5978	+	20.0880i	−0.826311	+	1.43121i	−0.900913	+	0.433999i	$0.857102\pi$
$198$	2.23434	−	1.29000i	0.158788	−	0.0916761i
$199$		−	13.9443i		−	0.988488i	−0.869323	−	0.494244i	$-0.835445\pi$
$199$		−	13.9443i		−	0.988488i	0.869323	−	0.494244i	$-0.164555\pi$
$200$	5.51856	+	3.18614i	0.390221	+	0.225294i
$201$	−4.79276	+	8.30131i	−0.338055	+	0.585529i
$202$	16.0955	+	9.29276i	1.13248	+	0.653836i
$203$	4.40254	−	2.54181i	0.308998	−	0.178400i
$204$	2.41819	−	1.39614i	0.169307	−	0.0977496i
$205$	0.268159	+	0.154822i	0.0187291	+	0.0108132i
$206$	−0.174104	+	0.301558i	−0.0121304	+	0.0210105i
$207$	−7.47661	−	4.31662i	−0.519661	−	0.300026i
$208$		−	0.524338i		−	0.0363563i
$209$	9.30506	−	5.37228i	0.643645	−	0.371608i
$210$	3.02205	−	5.23434i	0.208541	−	0.361204i
$211$	−16.4255			−1.13078			−0.565390	−	0.824824i	$-0.691274\pi$
$211$	−16.4255			−1.13078			−0.565390	+	0.824824i	$0.691274\pi$
$212$	1.69589			0.116474
$213$	−4.66228	+	8.07530i	−0.319454	+	0.553311i
$214$		−	5.06775i		−	0.346424i
$215$	−20.6948	−	35.8445i	−1.41137	−	2.44457i
$216$		−	1.00000i		−	0.0680414i
$217$	−11.0271	+	6.36650i	−0.748569	+	0.432186i
$218$	−3.46014	−	5.99313i	−0.234350	−	0.405906i
$219$	4.07025	+	7.04988i	0.275042	+	0.476386i
$220$	−7.53483	−	4.35023i	−0.507998	−	0.293293i
$221$	1.46410			0.0984861
$222$	2.10157	+	5.70819i	0.141048	+	0.383109i
$223$	10.3091			0.690349			0.345175	−	0.938538i	$-0.387820\pi$
$223$	10.3091			0.690349			0.345175	+	0.938538i	$0.387820\pi$
$224$	1.55217	+	0.896143i	0.103708	+	0.0598761i
$225$	3.18614	+	5.51856i	0.212409	+	0.367904i
$226$	9.92820	+	17.1962i	0.660414	+	1.14387i
$227$	−15.0957	+	8.71553i	−1.00194	+	0.578470i	−0.908822	−	0.417185i	$-0.863017\pi$
$227$	−15.0957	+	8.71553i	−1.00194	+	0.578470i	−0.0931182	+	0.995655i	$0.529683\pi$
$228$		−	4.16457i		−	0.275805i
$229$	−1.04543	−	1.81075i	−0.0690843	−	0.119657i	0.829414	−	0.558634i	$-0.188674\pi$
$229$	−1.04543	−	1.81075i	−0.0690843	−	0.119657i	−0.898498	+	0.438977i	$0.855341\pi$
$230$			29.1137i			1.91970i
$231$	−2.31205	+	4.00458i	−0.152121	+	0.263482i
$232$	−2.83638			−0.186218
$233$	−5.26097			−0.344657			−0.172329	−	0.985039i	$-0.555129\pi$
$233$	−5.26097			−0.344657			−0.172329	+	0.985039i	$0.555129\pi$
$234$	0.262169	−	0.454090i	0.0171385	−	0.0296848i
$235$	−29.0085	+	16.7481i	−1.89231	+	1.09252i
$236$			9.79324i			0.637486i
$237$	0.964312	+	0.556746i	0.0626388	+	0.0361645i
$238$	−2.50229	+	4.33409i	−0.162199	+	0.280938i
$239$	0.946368	+	0.546386i	0.0612155	+	0.0353428i	0.530295	−	0.847813i	$-0.322081\pi$
$239$	0.946368	+	0.546386i	0.0612155	+	0.0353428i	−0.469080	+	0.883156i	$0.655414\pi$
$240$	−2.92048	+	1.68614i	−0.188516	+	0.108840i
$241$	7.18156	−	4.14628i	0.462605	−	0.267085i	−0.250534	−	0.968108i	$-0.580606\pi$
$241$	7.18156	−	4.14628i	0.462605	−	0.267085i	0.713139	+	0.701023i	$0.247273\pi$
$242$	−3.76169	−	2.17181i	−0.241811	−	0.139610i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.36456	−	1.94253i	−0.215394	−	0.124358i
$245$		−	12.7732i		−	0.816051i
$246$	−0.0795187	+	0.0459101i	−0.00506993	+	0.00292712i
$247$	1.09182	−	1.89109i	0.0694709	−	0.120327i
$248$	7.10433			0.451126
$249$	0.633250			0.0401306
$250$	2.31386	−	4.00772i	0.146341	−	0.253471i
$251$		−	24.4706i		−	1.54457i	−0.635276	−	0.772285i	$-0.719114\pi$
$251$		−	24.4706i		−	1.54457i	0.635276	−	0.772285i	$-0.280886\pi$
$252$	0.896143	+	1.55217i	0.0564517	+	0.0977773i
$253$		−	22.2737i		−	1.40034i
$254$	5.70720	−	3.29505i	0.358101	−	0.206750i
$255$	−4.70819	−	8.15482i	−0.294838	−	0.510675i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	16.7403	+	9.66504i	1.04423	+	0.602889i	0.921030	−	0.389492i	$-0.127350\pi$
$257$	16.7403	+	9.66504i	1.04423	+	0.602889i	0.123204	+	0.992381i	$0.460683\pi$
$258$	12.2735			0.764113
$259$	−8.37734	−	6.97675i	−0.520542	−	0.433514i
$260$	−1.76821			−0.109660
$261$	−2.45638	−	1.41819i	−0.152046	−	0.0877838i
$262$	−5.22480	−	9.04963i	−0.322789	−	0.559088i
$263$	1.09182	+	1.89109i	0.0673245	+	0.116609i	0.897723	−	0.440561i	$-0.145220\pi$
$263$	1.09182	+	1.89109i	0.0673245	+	0.116609i	−0.830398	+	0.557170i	$0.811887\pi$
$264$	2.23434	−	1.29000i	0.137514	−	0.0793938i
$265$		−	5.71901i		−	0.351316i
$266$	3.73205	+	6.46410i	0.228827	+	0.396339i
$267$		−	15.0983i		−	0.924001i
$268$	−4.79276	+	8.30131i	−0.292765	+	0.507083i
$269$	−28.3942			−1.73123			−0.865613	−	0.500714i	$-0.833071\pi$
$269$	−28.3942			−1.73123			−0.865613	+	0.500714i	$0.833071\pi$
$270$	−3.37228			−0.205231
$271$	10.4135	−	18.0367i	0.632575	−	1.09565i	−0.354448	−	0.935076i	$-0.615331\pi$
$271$	10.4135	−	18.0367i	0.632575	−	1.09565i	0.987023	−	0.160577i	$-0.0513354\pi$
$272$	2.41819	−	1.39614i	0.146624	−	0.0846536i
$273$			0.939764i			0.0568771i
$274$	5.22097	+	3.01433i	0.315410	+	0.182102i
$275$	−8.22022	+	14.2378i	−0.495698	+	0.858574i
$276$	−7.47661	−	4.31662i	−0.450039	−	0.259830i
$277$	−13.0277	+	7.52157i	−0.782761	+	0.451927i	−0.837408	−	0.546578i	$-0.815930\pi$
$277$	−13.0277	+	7.52157i	−0.782761	+	0.451927i	0.0546467	+	0.998506i	$0.482597\pi$
$278$	−8.05446	+	4.65024i	−0.483074	+	0.278903i
$279$	6.15253	+	3.55217i	0.368342	+	0.212663i
$280$	3.02205	−	5.23434i	0.180602	−	0.312812i
$281$	10.5100	+	6.06796i	0.626975	+	0.361984i	0.779580	−	0.626303i	$-0.215433\pi$
$281$	10.5100	+	6.06796i	0.626975	+	0.361984i	−0.152605	+	0.988287i	$0.548766\pi$
$282$		−	9.93278i		−	0.591489i
$283$	28.5528	−	16.4849i	1.69729	−	0.979928i	0.748968	−	0.662606i	$-0.230549\pi$
$283$	28.5528	−	16.4849i	1.69729	−	0.979928i	0.948318	−	0.317323i	$-0.102784\pi$
$284$	−4.66228	+	8.07530i	−0.276655	+	0.479181i
$285$	−14.0441			−0.831900
$286$	1.35279			0.0799921
$287$	0.0822842	−	0.142520i	0.00485708	−	0.00841271i
$288$		−	1.00000i		−	0.0589256i
$289$	−4.60157	−	7.97015i	−0.270680	−	0.468832i
$290$			9.56508i			0.561681i
$291$	−2.12314	+	1.22579i	−0.124461	+	0.0718574i
$292$	4.07025	+	7.04988i	0.238193	+	0.412563i
$293$	8.47182	+	14.6736i	0.494929	+	0.857243i	0.999983	−	0.00584537i	$-0.00186065\pi$
$293$	8.47182	+	14.6736i	0.494929	+	0.857243i	−0.505054	+	0.863088i	$0.668527\pi$
$294$	3.28025	+	1.89385i	0.191308	+	0.110452i
$295$	33.0256			1.92282
$296$	2.10157	+	5.70819i	0.122151	+	0.331782i
$297$	2.57999			0.149706
$298$	−16.1919	−	9.34842i	−0.937974	−	0.541539i
$299$	−2.26337	−	3.92027i	−0.130894	−	0.226715i
$300$	3.18614	+	5.51856i	0.183952	+	0.318614i
$301$	−19.0505	+	10.9988i	−1.09805	+	0.633960i
$302$			12.3583i			0.711141i
$303$	9.29276	+	16.0955i	0.533855	+	0.924664i
$304$		−	4.16457i		−	0.238854i
$305$	−6.55076	+	11.3462i	−0.375095	+	0.649684i
$306$	2.79229			0.159624
$307$	29.4992			1.68361			0.841805	−	0.539782i	$-0.181493\pi$
$307$	29.4992			1.68361			0.841805	+	0.539782i	$0.181493\pi$
$308$	−2.31205	+	4.00458i	−0.131741	+	0.228182i
$309$	−0.301558	+	0.174104i	−0.0171550	+	0.00990446i
$310$		−	23.9578i		−	1.36071i
$311$	27.5640	+	15.9141i	1.56301	+	0.902405i	0.996950	+	0.0780420i	$0.0248668\pi$
$311$	27.5640	+	15.9141i	1.56301	+	0.902405i	0.566061	+	0.824363i	$0.308466\pi$
$312$	0.262169	−	0.454090i	0.0148424	−	0.0257078i
$313$	18.1636	+	10.4868i	1.02667	+	0.592747i	0.916028	−	0.401114i	$-0.131377\pi$
$313$	18.1636	+	10.4868i	1.02667	+	0.592747i	0.110639	+	0.993861i	$0.464710\pi$
$314$	−6.19677	+	3.57770i	−0.349704	+	0.201902i
$315$	5.23434	−	3.02205i	0.294922	−	0.170273i
$316$	0.964312	+	0.556746i	0.0542468	+	0.0313194i
$317$	−3.76747	+	6.52546i	−0.211602	+	0.366506i	−0.952216	−	0.305425i	$-0.901202\pi$
$317$	−3.76747	+	6.52546i	−0.211602	+	0.366506i	0.740614	+	0.671931i	$0.234535\pi$
$318$	1.46868	+	0.847944i	0.0823596	+	0.0475503i
$319$		−	7.31785i		−	0.409721i
$320$	−2.92048	+	1.68614i	−0.163260	+	0.0942581i
$321$	2.53387	−	4.38880i	0.141427	−	0.244959i
$322$	15.4733			0.862291
$323$	11.6287			0.647037
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			3.34123i			0.185338i
$326$	5.50229	+	9.53025i	0.304744	+	0.527831i
$327$		−	6.92027i		−	0.382692i
$328$	−0.0795187	+	0.0459101i	−0.00439069	+	0.00253496i
$329$	8.90120	+	15.4173i	0.490739	+	0.849985i
$330$	−4.35023	−	7.53483i	−0.239472	−	0.414778i
$331$	−25.5204	−	14.7342i	−1.40273	−	0.809865i	−0.408056	−	0.912957i	$-0.633793\pi$
$331$	−25.5204	−	14.7342i	−1.40273	−	0.809865i	−0.994672	+	0.103092i	$0.967126\pi$
$332$	0.633250			0.0347541
$333$	−1.03408	+	5.99422i	−0.0566675	+	0.328481i
$334$	−0.392305			−0.0214660
$335$	27.9943	+	16.1625i	1.52949	+	0.883054i
$336$	0.896143	+	1.55217i	0.0488886	+	0.0846776i
$337$	10.3077	+	17.8535i	0.561498	+	0.972543i	0.997366	+	0.0725323i	$0.0231081\pi$
$337$	10.3077	+	17.8535i	0.561498	+	0.972543i	−0.435868	+	0.900011i	$0.643559\pi$
$338$	−11.0202	+	6.36253i	−0.599422	+	0.346076i
$339$			19.8564i			1.07845i
$340$	−4.70819	−	8.15482i	−0.255337	−	0.442257i
$341$			18.3291i			0.992578i
$342$	2.08228	−	3.60662i	0.112597	−	0.195024i
$343$	−19.3347			−1.04397
$344$	12.2735			0.661742
$345$	−14.5569	+	25.2132i	−0.783716	+	1.35744i
$346$	14.4182	−	8.32435i	0.775127	−	0.447520i
$347$		−	32.5286i		−	1.74623i	−0.487515	−	0.873114i	$-0.662097\pi$
$347$		−	32.5286i		−	1.74623i	0.487515	−	0.873114i	$-0.337903\pi$
$348$	−2.45638	−	1.41819i	−0.131676	−	0.0760230i
$349$	−12.3855	+	21.4524i	−0.662982	+	1.14832i	0.316846	+	0.948477i	$0.397376\pi$
$349$	−12.3855	+	21.4524i	−0.662982	+	1.14832i	−0.979828	+	0.199842i	$0.935957\pi$
$350$	−9.89084	−	5.71048i	−0.528688	−	0.305238i
$351$	0.454090	−	0.262169i	0.0242375	−	0.0139935i
$352$	2.23434	−	1.29000i	0.119091	−	0.0687571i
$353$	28.1999	+	16.2812i	1.50093	+	0.866561i	0.999999	+	0.00107208i	$0.000341254\pi$
$353$	28.1999	+	16.2812i	1.50093	+	0.866561i	0.500928	+	0.865489i	$0.332992\pi$
$354$	−4.89662	+	8.48119i	−0.260252	+	0.450770i
$355$	27.2322	+	15.7225i	1.44533	+	0.834464i
$356$		−	15.0983i		−	0.800208i
$357$	−4.33409	+	2.50229i	−0.229385	+	0.132435i
$358$	−1.28046	+	2.21782i	−0.0676745	+	0.117216i
$359$	−16.5036			−0.871028			−0.435514	−	0.900182i	$-0.643433\pi$
$359$	−16.5036			−0.871028			−0.435514	+	0.900182i	$0.643433\pi$
$360$	−3.37228			−0.177735
$361$	−0.828185	+	1.43446i	−0.0435887	+	0.0754978i
$362$		−	24.1901i		−	1.27140i
$363$	−2.17181	−	3.76169i	−0.113991	−	0.197438i
$364$			0.939764i			0.0492570i
$365$	23.7742	−	13.7260i	1.24440	−	0.718453i
$366$	−1.94253	−	3.36456i	−0.101538	−	0.175868i
$367$	−8.67191	−	15.0202i	−0.452670	−	0.784048i	0.545881	−	0.837863i	$-0.316195\pi$
$367$	−8.67191	−	15.0202i	−0.452670	−	0.784048i	−0.998551	+	0.0538151i	$0.982862\pi$
$368$	−7.47661	−	4.31662i	−0.389745	−	0.225020i
$369$	−0.0918203			−0.00477997
$370$	19.2496	−	7.08707i	1.00074	−	0.368439i
$371$	−3.03952			−0.157804
$372$	6.15253	+	3.55217i	0.318994	+	0.184171i
$373$	−15.1006	−	26.1550i	−0.781879	−	1.35425i	−0.930846	−	0.365412i	$-0.880928\pi$
$373$	−15.1006	−	26.1550i	−0.781879	−	1.35425i	0.148967	−	0.988842i	$-0.452405\pi$
$374$	3.60204	+	6.23892i	0.186257	+	0.322607i
$375$	4.00772	−	2.31386i	0.206958	−	0.119487i
$376$		−	9.93278i		−	0.512244i
$377$	−0.743611	−	1.28797i	−0.0382979	−	0.0663340i
$378$			1.79229i			0.0921853i
$379$	6.55890	−	11.3603i	0.336908	−	0.583542i	−0.646942	−	0.762540i	$-0.723952\pi$
$379$	6.55890	−	11.3603i	0.336908	−	0.583542i	0.983849	+	0.178998i	$0.0572856\pi$
$380$	−14.0441			−0.720447
$381$	6.59010			0.337621
$382$	−2.64481	+	4.58095i	−0.135320	+	0.234382i
$383$	15.2965	−	8.83143i	0.781614	−	0.451265i	−0.0553883	−	0.998465i	$-0.517640\pi$
$383$	15.2965	−	8.83143i	0.781614	−	0.451265i	0.837002	+	0.547200i	$0.184306\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	13.5046	+	7.79687i	0.688257	+	0.397365i
$386$	5.12241	−	8.87228i	0.260724	−	0.451587i
$387$	10.6291	+	6.13674i	0.540310	+	0.311948i
$388$	−2.12314	+	1.22579i	−0.107786	+	0.0622303i
$389$	−8.27567	+	4.77796i	−0.419593	+	0.242252i	−0.694903	−	0.719103i	$-0.744553\pi$
$389$	−8.27567	+	4.77796i	−0.419593	+	0.242252i	0.275310	+	0.961355i	$0.411219\pi$
$390$	−1.53132	−	0.884107i	−0.0775413	−	0.0447685i
$391$	12.0533	−	20.8769i	0.609559	−	1.05579i
$392$	3.28025	+	1.89385i	0.165678	+	0.0956541i
$393$		−	10.4496i		−	0.527113i
$394$	−20.0880	+	11.5978i	−1.01202	+	0.584290i
$395$	1.87750	−	3.25193i	0.0944674	−	0.163622i
$396$	2.57999			0.129650
$397$	−22.7510			−1.14184			−0.570921	−	0.821005i	$-0.693414\pi$
$397$	−22.7510			−1.14184			−0.570921	+	0.821005i	$0.693414\pi$
$398$	6.97217	−	12.0762i	0.349483	−	0.605323i
$399$			7.46410i			0.373672i
$400$	3.18614	+	5.51856i	0.159307	+	0.275928i
$401$		−	9.30548i		−	0.464694i	−0.972633	−	0.232347i	$-0.925360\pi$
$401$		−	9.30548i		−	0.464694i	0.972633	−	0.232347i	$-0.0746405\pi$
$402$	−8.30131	+	4.79276i	−0.414032	+	0.239041i
$403$	1.86253	+	3.22601i	0.0927795	+	0.160699i
$404$	9.29276	+	16.0955i	0.462332	+	0.800783i
$405$	−2.92048	−	1.68614i	−0.145120	−	0.0837850i
$406$	5.08361			0.252295
$407$	−14.7271	+	5.42203i	−0.729995	+	0.268760i
$408$	2.79229			0.138239
$409$	3.52502	+	2.03517i	0.174301	+	0.100633i	0.584612	−	0.811313i	$-0.301247\pi$
$409$	3.52502	+	2.03517i	0.174301	+	0.100633i	−0.410311	+	0.911946i	$0.634580\pi$
$410$	0.154822	+	0.268159i	0.00764611	+	0.0132435i
$411$	3.01433	+	5.22097i	0.148686	+	0.257531i
$412$	−0.301558	+	0.174104i	−0.0148567	+	0.00857751i
$413$		−	17.5523i		−	0.863692i
$414$	−4.31662	−	7.47661i	−0.212151	−	0.367456i
$415$		−	2.13550i		−	0.104827i
$416$	0.262169	−	0.454090i	0.0128539	−	0.0222636i
$417$	−9.30048			−0.455447
$418$	10.7446			0.525534
$419$	−3.32158	+	5.75315i	−0.162270	+	0.281060i	−0.935682	−	0.352843i	$-0.885215\pi$
$419$	−3.32158	+	5.75315i	−0.162270	+	0.281060i	0.773413	+	0.633903i	$0.218548\pi$
$420$	5.23434	−	3.02205i	0.255410	−	0.147461i
$421$			37.5689i			1.83100i	0.402323	+	0.915498i	$0.368203\pi$
$421$			37.5689i			1.83100i	−0.402323	+	0.915498i	$0.631797\pi$
$422$	−14.2249	−	8.21277i	−0.692459	−	0.399791i
$423$	4.96639	−	8.60204i	0.241474	−	0.418246i
$424$	1.46868	+	0.847944i	0.0713255	+	0.0411798i
$425$	−15.4094	+	8.89662i	−0.747466	+	0.431549i
$426$	−8.07530	+	4.66228i	−0.391250	+	0.225888i
$427$	6.03026	+	3.48157i	0.291825	+	0.168485i
$428$	2.53387	−	4.38880i	0.122479	−	0.212141i
$429$	1.17155	+	0.676394i	0.0565629	+	0.0326566i
$430$		−	41.3896i		−	1.99599i
$431$	−19.6529	+	11.3466i	−0.946647	+	0.546547i	−0.892038	−	0.451961i	$-0.850725\pi$
$431$	−19.6529	+	11.3466i	−0.946647	+	0.546547i	−0.0546090	+	0.998508i	$0.517391\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−15.6533			−0.752248			−0.376124	−	0.926569i	$-0.622743\pi$
$433$	−15.6533			−0.752248			−0.376124	+	0.926569i	$0.622743\pi$
$434$	−12.7330			−0.611204
$435$	−4.78254	+	8.28360i	−0.229305	+	0.397168i
$436$		−	6.92027i		−	0.331421i
$437$	−17.9769	−	31.1369i	−0.859951	−	1.48948i
$438$			8.14050i			0.388968i
$439$	−26.6156	+	15.3665i	−1.27029	+	0.733403i	−0.975043	−	0.222017i	$-0.928736\pi$
$439$	−26.6156	+	15.3665i	−1.27029	+	0.733403i	−0.295249	+	0.955420i	$0.595403\pi$
$440$	−4.35023	−	7.53483i	−0.207389	−	0.359209i
$441$	1.89385	+	3.28025i	0.0901835	+	0.156202i
$442$	1.26795	+	0.732051i	0.0603102	+	0.0348201i
$443$	−6.42649			−0.305332			−0.152666	−	0.988278i	$-0.548786\pi$
$443$	−6.42649			−0.305332			−0.152666	+	0.988278i	$0.548786\pi$
$444$	−1.03408	+	5.99422i	−0.0490755	+	0.284473i
$445$	−50.9157			−2.41364
$446$	8.92795	+	5.15456i	0.422751	+	0.244075i
$447$	−9.34842	−	16.1919i	−0.442165	−	0.765852i
$448$	0.896143	+	1.55217i	0.0423388	+	0.0733330i
$449$	10.9328	−	6.31205i	0.515950	−	0.297884i	−0.219326	−	0.975652i	$-0.570386\pi$
$449$	10.9328	−	6.31205i	0.515950	−	0.297884i	0.735276	+	0.677768i	$0.237053\pi$
$450$			6.37228i			0.300392i
$451$	−0.118448	−	0.205158i	−0.00557749	−	0.00966050i
$452$			19.8564i			0.933967i
$453$	−6.17916	+	10.7026i	−0.290322	+	0.502853i
$454$	−17.4311			−0.818081
$455$	3.16915			0.148572
$456$	2.08228	−	3.60662i	0.0975119	−	0.168896i
$457$	18.3977	−	10.6219i	0.860607	−	0.496871i	−0.00360873	−	0.999993i	$-0.501149\pi$
$457$	18.3977	−	10.6219i	0.860607	−	0.496871i	0.864215	+	0.503122i	$0.167815\pi$
$458$		−	2.09087i		−	0.0976999i
$459$	2.41819	+	1.39614i	0.112872	+	0.0651664i
$460$	−14.5569	+	25.2132i	−0.678718	+	1.17557i
$461$	−7.07931	−	4.08724i	−0.329716	−	0.190362i	0.325999	−	0.945370i	$-0.394299\pi$
$461$	−7.07931	−	4.08724i	−0.329716	−	0.190362i	−0.655715	+	0.755008i	$0.727633\pi$
$462$	−4.00458	+	2.31205i	−0.186310	+	0.107566i
$463$	17.0516	−	9.84472i	0.792453	−	0.457523i	−0.0483725	−	0.998829i	$-0.515403\pi$
$463$	17.0516	−	9.84472i	0.792453	−	0.457523i	0.840825	+	0.541306i	$0.182070\pi$
$464$	−2.45638	−	1.41819i	−0.114035	−	0.0658379i
$465$	11.9789	−	20.7481i	0.555508	−	0.962169i
$466$	−4.55613	−	2.63048i	−0.211059	−	0.121855i
$467$		−	4.69452i		−	0.217236i	−0.994084	−	0.108618i	$-0.965357\pi$
$467$		−	4.69452i		−	0.217236i	0.994084	−	0.108618i	$-0.0346426\pi$
$468$	0.454090	−	0.262169i	0.0209903	−	0.0121188i
$469$	8.59001	−	14.8783i	0.396650	−	0.687017i
$470$	−33.4961			−1.54506
$471$	−7.15541			−0.329704
$472$	−4.89662	+	8.48119i	−0.225385	+	0.390379i
$473$			31.6655i			1.45598i
$474$	0.556746	+	0.964312i	0.0255722	+	0.0442923i
$475$			26.5378i			1.21764i
$476$	−4.33409	+	2.50229i	−0.198653	+	0.114692i
$477$	0.847944	+	1.46868i	0.0388247	+	0.0672463i
$478$	0.546386	+	0.946368i	0.0249911	+	0.0432859i
$479$	6.83180	+	3.94434i	0.312153	+	0.180222i	0.647890	−	0.761734i	$-0.275652\pi$
$479$	6.83180	+	3.94434i	0.312153	+	0.180222i	−0.335736	+	0.941956i	$0.608985\pi$
$480$	−3.37228			−0.153923
$481$	−2.04107	+	2.45081i	−0.0930646	+	0.111747i
$482$	8.29255			0.377715
$483$	13.4002	+	7.73663i	0.609732	+	0.352029i
$484$	−2.17181	−	3.76169i	−0.0987188	−	0.170986i
$485$	4.13373	+	7.15982i	0.187703	+	0.325111i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$			2.53780i			0.114999i	0.998346	+	0.0574994i	$0.0183127\pi$
$487$			2.53780i			0.114999i	−0.998346	+	0.0574994i	$0.981687\pi$
$488$	−1.94253	−	3.36456i	−0.0879342	−	0.152306i
$489$			11.0046i			0.497644i
$490$	6.38661	−	11.0619i	0.288518	−	0.499727i
$491$	−10.1414			−0.457677			−0.228839	−	0.973464i	$-0.573493\pi$
$491$	−10.1414			−0.457677			−0.228839	+	0.973464i	$0.573493\pi$
$492$	−0.0918203			−0.00413958
$493$	3.96000	−	6.85892i	0.178349	−	0.308910i
$494$	1.89109	−	1.09182i	0.0850841	−	0.0491233i
$495$		−	8.70047i		−	0.391057i
$496$	6.15253	+	3.55217i	0.276257	+	0.159497i
$497$	8.35614	−	14.4733i	0.374824	−	0.649214i
$498$	0.548410	+	0.316625i	0.0245748	+	0.0141883i
$499$	−26.4004	+	15.2423i	−1.18184	+	0.682338i	−0.956440	−	0.291928i	$-0.905703\pi$
$499$	−26.4004	+	15.2423i	−1.18184	+	0.682338i	−0.225403	+	0.974266i	$0.572370\pi$
$500$	4.00772	−	2.31386i	0.179231	−	0.103479i
$501$	−0.339746	−	0.196152i	−0.0151787	−	0.00876344i
$502$	12.2353	−	21.1921i	0.546088	−	0.945852i
$503$	−20.2013	−	11.6632i	−0.900732	−	0.520038i	−0.0232942	−	0.999729i	$-0.507415\pi$
$503$	−20.2013	−	11.6632i	−0.900732	−	0.520038i	−0.877438	+	0.479691i	$0.840749\pi$
$504$			1.79229i			0.0798348i
$505$	54.2787	−	31.3378i	2.41537	−	1.39451i
$506$	11.1369	−	19.2896i	0.495094	−	0.857528i
$507$	−12.7251			−0.565140
$508$	6.59010			0.292389
$509$	−1.02721	+	1.77919i	−0.0455305	+	0.0788611i	−0.887893	−	0.460051i	$-0.847831\pi$
$509$	−1.02721	+	1.77919i	−0.0455305	+	0.0788611i	0.842362	+	0.538912i	$0.181164\pi$
$510$		−	9.41638i		−	0.416964i
$511$	−7.29505	−	12.6354i	−0.322714	−	0.558957i
$512$		−	1.00000i		−	0.0441942i
$513$	3.60662	−	2.08228i	0.159236	−	0.0919351i
$514$	9.66504	+	16.7403i	0.426307	+	0.738385i
$515$	0.587129	+	1.01694i	0.0258720	+	0.0448116i
$516$	10.6291	+	6.13674i	0.467922	+	0.270155i
$517$	25.6265			1.12705
$518$	−3.76661	−	10.2307i	−0.165495	−	0.449512i
$519$	16.6487			0.730797
$520$	−1.53132	−	0.884107i	−0.0671528	−	0.0387707i
$521$	−5.21324	−	9.02960i	−0.228396	−	0.395594i	0.728937	−	0.684581i	$-0.240015\pi$
$521$	−5.21324	−	9.02960i	−0.228396	−	0.395594i	−0.957333	+	0.288987i	$0.906682\pi$
$522$	−1.41819	−	2.45638i	−0.0620726	−	0.107513i
$523$	−11.7529	+	6.78556i	−0.513920	+	0.296712i	−0.734443	−	0.678670i	$-0.762557\pi$
$523$	−11.7529	+	6.78556i	−0.513920	+	0.296712i	0.220524	+	0.975382i	$0.429223\pi$
$524$		−	10.4496i		−	0.456493i
$525$	−5.71048	−	9.89084i	−0.249226	−	0.431672i
$526$			2.18364i			0.0952113i
$527$	−9.91867	+	17.1796i	−0.432064	+	0.748357i
$528$	2.57999			0.112280
$529$	−51.5330			−2.24057
$530$	2.85950	−	4.95281i	0.124209	−	0.215136i
$531$	−8.48119	+	4.89662i	−0.368052	+	0.212495i
$532$			7.46410i			0.323610i
$533$	−0.0416947	−	0.0240724i	−0.00180600	−	0.00104269i
$534$	7.54915	−	13.0755i	0.326684	−	0.565833i
$535$	−14.8003	−	8.54494i	−0.639871	−	0.369430i
$536$	−8.30131	+	4.79276i	−0.358562	+	0.207016i
$537$	−2.21782	+	1.28046i	−0.0957062	+	0.0552560i
$538$	−24.5901	−	14.1971i	−1.06015	−	0.612081i
$539$	−4.88613	+	8.46303i	−0.210461	+	0.364528i
$540$	−2.92048	−	1.68614i	−0.125678	−	0.0725599i
$541$			40.1072i			1.72434i	0.506617	+	0.862171i	$0.330896\pi$
$541$			40.1072i			1.72434i	−0.506617	+	0.862171i	$0.669104\pi$
$542$	18.0367	−	10.4135i	0.774743	−	0.447298i
$543$	12.0951	−	20.9493i	0.519049	−	0.899019i
$544$	2.79229			0.119718
$545$	−23.3371			−0.999652
$546$	−0.469882	+	0.813859i	−0.0201091	+	0.0348300i
$547$		−	36.1009i		−	1.54356i	−0.635888	−	0.771782i	$-0.719366\pi$
$547$		−	36.1009i		−	1.54356i	0.635888	−	0.771782i	$-0.280634\pi$
$548$	3.01433	+	5.22097i	0.128766	+	0.223029i
$549$		−	3.88506i		−	0.165810i
$550$	−14.2378	+	8.22022i	−0.607104	+	0.350512i
$551$	−5.90616	−	10.2298i	−0.251611	−	0.435802i
$552$	−4.31662	−	7.47661i	−0.183728	−	0.318226i
$553$	−1.72832	−	0.997848i	−0.0734958	−	0.0424328i
$554$	−15.0431			−0.639122
$555$	20.2142	+	3.48722i	0.858045	+	0.148024i
$556$	−9.30048			−0.394428
$557$	14.8988	+	8.60183i	0.631283	+	0.364471i	0.781249	−	0.624220i	$-0.214583\pi$
$557$	14.8988	+	8.60183i	0.631283	+	0.364471i	−0.149966	+	0.988691i	$0.547916\pi$
$558$	3.55217	+	6.15253i	0.150375	+	0.260457i
$559$	3.21772	+	5.57326i	0.136095	+	0.235724i
$560$	5.23434	−	3.02205i	0.221191	−	0.127705i
$561$			7.20408i			0.304157i
$562$	6.06796	+	10.5100i	0.255961	+	0.443338i
$563$		−	31.5884i		−	1.33129i	−0.746268	−	0.665646i	$-0.768156\pi$
$563$		−	31.5884i		−	1.33129i	0.746268	−	0.665646i	$-0.231844\pi$
$564$	4.96639	−	8.60204i	0.209123	−	0.362211i
$565$	66.9614			2.81709
$566$	32.9699			1.38583
$567$	−0.896143	+	1.55217i	−0.0376345	+	0.0651848i
$568$	−8.07530	+	4.66228i	−0.338832	+	0.195625i
$569$		−	23.9923i		−	1.00581i	−0.864342	−	0.502905i	$-0.832264\pi$
$569$		−	23.9923i		−	1.00581i	0.864342	−	0.502905i	$-0.167736\pi$
$570$	−12.1625	−	7.02205i	−0.509433	−	0.294121i
$571$	4.63022	−	8.01977i	0.193769	−	0.335617i	−0.752728	−	0.658332i	$-0.771262\pi$
$571$	4.63022	−	8.01977i	0.193769	−	0.335617i	0.946496	+	0.322715i	$0.104596\pi$
$572$	1.17155	+	0.676394i	0.0489849	+	0.0282815i
$573$	−4.58095	+	2.64481i	−0.191372	+	0.110489i
$574$	0.142520	−	0.0822842i	0.00594868	−	0.00343447i
$575$	47.6431	+	27.5067i	1.98685	+	1.14711i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	10.7441	+	6.20313i	0.447284	+	0.258240i	0.706683	−	0.707531i	$-0.250191\pi$
$577$	10.7441	+	6.20313i	0.447284	+	0.258240i	−0.259398	+	0.965770i	$0.583524\pi$
$578$		−	9.20313i		−	0.382800i
$579$	8.87228	−	5.12241i	0.368719	−	0.212880i
$580$	−4.78254	+	8.28360i	−0.198584	+	0.343958i
$581$	−1.13496			−0.0470863
$582$	−2.45159			−0.101622
$583$	−2.18769	+	3.78919i	−0.0906048	+	0.156932i
$584$			8.14050i			0.336856i
$585$	−0.884107	−	1.53132i	−0.0365533	−	0.0633122i
$586$			16.9436i			0.699936i
$587$	3.08847	−	1.78313i	0.127475	−	0.0735976i	−0.434907	−	0.900476i	$-0.643219\pi$
$587$	3.08847	−	1.78313i	0.127475	−	0.0735976i	0.562381	+	0.826878i	$0.309885\pi$
$588$	1.89385	+	3.28025i	0.0781012	+	0.135275i
$589$	14.7932	+	25.6226i	0.609545	+	1.05576i
$590$	28.6010	+	16.5128i	1.17748	+	0.679820i
$591$	−23.1957			−0.954142
$592$	−1.03408	+	5.99422i	−0.0425006	+	0.246361i
$593$	−31.7969			−1.30574			−0.652870	−	0.757470i	$-0.726435\pi$
$593$	−31.7969			−1.30574			−0.652870	+	0.757470i	$0.726435\pi$
$594$	2.23434	+	1.29000i	0.0916761	+	0.0529292i
$595$	8.43843	+	14.6158i	0.345942	+	0.599189i
$596$	−9.34842	−	16.1919i	−0.382926	−	0.663248i
$597$	12.0762	−	6.97217i	0.494244	−	0.285352i
$598$		−	4.52674i		−	0.185112i
$599$	1.71000	+	2.96181i	0.0698688	+	0.121016i	0.898843	−	0.438270i	$-0.144409\pi$
$599$	1.71000	+	2.96181i	0.0698688	+	0.121016i	−0.828975	+	0.559286i	$0.811075\pi$
$600$			6.37228i			0.260147i
$601$	0.808693	−	1.40070i	0.0329873	−	0.0571356i	−0.849060	−	0.528296i	$-0.822831\pi$
$601$	0.808693	−	1.40070i	0.0329873	−	0.0571356i	0.882048	+	0.471160i	$0.156165\pi$
$602$	−21.9976			−0.896555
$603$	−9.58553			−0.390353
$604$	−6.17916	+	10.7026i	−0.251426	+	0.435483i
$605$	−12.6855	+	7.32397i	−0.515738	+	0.297762i
$606$			18.5855i			0.754985i
$607$	31.1045	+	17.9582i	1.26249	+	0.728900i	0.973556	−	0.228448i	$-0.0733652\pi$
$607$	31.1045	+	17.9582i	1.26249	+	0.728900i	0.288936	+	0.957348i	$0.406698\pi$
$608$	2.08228	−	3.60662i	0.0844478	−	0.146268i
$609$	4.40254	+	2.54181i	0.178400	+	0.102999i
$610$	−11.3462	+	6.55076i	−0.459396	+	0.265232i
$611$	4.51038	−	2.60407i	0.182470	−	0.105349i
$612$	2.41819	+	1.39614i	0.0977496	+	0.0564358i
$613$	−8.78552	+	15.2170i	−0.354844	+	0.614607i	−0.987091	−	0.160159i	$-0.948799\pi$
$613$	−8.78552	+	15.2170i	−0.354844	+	0.614607i	0.632248	+	0.774766i	$0.282133\pi$
$614$	25.5471	+	14.7496i	1.03100	+	0.595246i
$615$			0.309644i			0.0124860i
$616$	−4.00458	+	2.31205i	−0.161349	+	0.0931550i
$617$	2.32361	−	4.02460i	0.0935448	−	0.162024i	−0.815456	−	0.578820i	$-0.803513\pi$
$617$	2.32361	−	4.02460i	0.0935448	−	0.162024i	0.909000	+	0.416795i	$0.136847\pi$
$618$	−0.348209			−0.0140070
$619$	20.3209			0.816767			0.408384	−	0.912810i	$-0.366093\pi$
$619$	20.3209			0.816767			0.408384	+	0.912810i	$0.366093\pi$
$620$	11.9789	−	20.7481i	0.481084	−	0.833263i
$621$		−	8.63325i		−	0.346440i
$622$	15.9141	+	27.5640i	0.638097	+	1.10522i
$623$			27.0605i			1.08416i
$624$	0.454090	−	0.262169i	0.0181781	−	0.0104952i
$625$	8.12772	+	14.0776i	0.325109	+	0.563105i
$626$	10.4868	+	18.1636i	0.419135	+	0.725964i
$627$	9.30506	+	5.37228i	0.371608	+	0.214548i
$628$	−7.15541			−0.285532
$629$	−16.7376	−	2.88746i	−0.667371	−	0.115131i
$630$	6.04410			0.240803
$631$	−4.25629	−	2.45737i	−0.169440	−	0.0978264i	0.412882	−	0.910785i	$-0.364522\pi$
$631$	−4.25629	−	2.45737i	−0.169440	−	0.0978264i	−0.582322	+	0.812958i	$0.697856\pi$
$632$	0.556746	+	0.964312i	0.0221462	+	0.0383583i
$633$	−8.21277	−	14.2249i	−0.326428	−	0.565390i
$634$	−6.52546	+	3.76747i	−0.259159	+	0.149625i
$635$		−	22.2237i		−	0.881920i
$636$	0.847944	+	1.46868i	0.0336231	+	0.0582370i
$637$			1.98604i			0.0786897i
$638$	3.65893	−	6.33745i	0.144858	−	0.250902i
$639$	−9.32456			−0.368874
$640$	−3.37228			−0.133301
$641$	−2.20037	+	3.81115i	−0.0869093	+	0.150531i	−0.906203	−	0.422842i	$-0.861032\pi$
$641$	−2.20037	+	3.81115i	−0.0869093	+	0.150531i	0.819294	+	0.573374i	$0.194366\pi$
$642$	4.38880	−	2.53387i	0.173212	−	0.100004i
$643$		−	2.06482i		−	0.0814284i	−0.999171	−	0.0407142i	$-0.987037\pi$
$643$		−	2.06482i		−	0.0814284i	0.999171	−	0.0407142i	$-0.0129633\pi$
$644$	13.4002	+	7.73663i	0.528043	+	0.304866i
$645$	20.6948	−	35.8445i	0.814857	−	1.41137i
$646$	10.0707	+	5.81433i	0.396227	+	0.228762i
$647$	19.4948	−	11.2553i	0.766419	−	0.442492i	−0.0651768	−	0.997874i	$-0.520761\pi$
$647$	19.4948	−	11.2553i	0.766419	−	0.442492i	0.831596	+	0.555382i	$0.187428\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−21.8814	−	12.6332i	−0.858921	−	0.495898i
$650$	−1.67061	+	2.89359i	−0.0655269	+	0.113496i
$651$	−11.0271	−	6.36650i	−0.432186	−	0.249523i
$652$			11.0046i			0.430973i
$653$	5.13830	−	2.96660i	0.201077	−	0.116092i	−0.396081	−	0.918216i	$-0.629630\pi$
$653$	5.13830	−	2.96660i	0.201077	−	0.116092i	0.597158	+	0.802124i	$0.296297\pi$
$654$	3.46014	−	5.99313i	0.135302	−	0.234350i
$655$	−35.2390			−1.37690
$656$	−0.0918203			−0.00358498
$657$	−4.07025	+	7.04988i	−0.158795	+	0.275042i
$658$			17.8024i			0.694010i
$659$	1.21565	+	2.10556i	0.0473548	+	0.0820209i	0.888731	−	0.458429i	$-0.151588\pi$
$659$	1.21565	+	2.10556i	0.0473548	+	0.0820209i	−0.841376	+	0.540450i	$0.818254\pi$
$660$		−	8.70047i		−	0.338665i
$661$	9.45095	−	5.45651i	0.367599	−	0.212234i	−0.304810	−	0.952413i	$-0.598593\pi$
$661$	9.45095	−	5.45651i	0.367599	−	0.212234i	0.672409	+	0.740180i	$0.265260\pi$
$662$	−14.7342	−	25.5204i	−0.572661	−	0.991878i
$663$	0.732051	+	1.26795i	0.0284305	+	0.0492431i
$664$	0.548410	+	0.316625i	0.0212824	+	0.0122874i
$665$	25.1711			0.976091
$666$	−3.89265	+	4.67410i	−0.150837	+	0.181118i
$667$	−24.4872			−0.948148
$668$	−0.339746	−	0.196152i	−0.0131452	−	0.00758937i
$669$	5.15456	+	8.92795i	0.199287	+	0.345175i
$670$	16.1625	+	27.9943i	0.624414	+	1.08152i
$671$	8.68054	−	5.01171i	0.335109	−	0.193475i
$672$			1.79229i			0.0691390i
$673$	−11.3927	−	19.7328i	−0.439157	−	0.760643i	0.558467	−	0.829526i	$-0.311390\pi$
$673$	−11.3927	−	19.7328i	−0.439157	−	0.760643i	−0.997625	+	0.0688837i	$0.978056\pi$
$674$			20.6155i			0.794078i
$675$	−3.18614	+	5.51856i	−0.122635	+	0.212409i
$676$	−12.7251			−0.489426
$677$	−46.1470			−1.77357			−0.886786	−	0.462180i	$-0.847067\pi$
$677$	−46.1470			−1.77357			−0.886786	+	0.462180i	$0.847067\pi$
$678$	−9.92820	+	17.1962i	−0.381290	+	0.660414i
$679$	3.80527	−	2.19698i	0.146033	−	0.0843122i
$680$		−	9.41638i		−	0.361102i
$681$	−15.0957	−	8.71553i	−0.578470	−	0.333980i
$682$	−9.16457	+	15.8735i	−0.350929	+	0.607828i
$683$	3.85698	+	2.22683i	0.147583	+	0.0852072i	0.571973	−	0.820272i	$-0.306178\pi$
$683$	3.85698	+	2.22683i	0.147583	+	0.0852072i	−0.424390	+	0.905480i	$0.639511\pi$
$684$	3.60662	−	2.08228i	0.137903	−	0.0796181i
$685$	17.6066	−	10.1652i	0.672712	−	0.388391i
$686$	−16.7443	−	9.66733i	−0.639301	−	0.369101i
$687$	1.04543	−	1.81075i	0.0398858	−	0.0690843i
$688$	10.6291	+	6.13674i	0.405232	+	0.233961i
$689$			0.889218i			0.0338765i
$690$	−25.2132	+	14.5569i	−0.959852	+	0.554171i
$691$	−3.87447	+	6.71078i	−0.147392	+	0.255290i	−0.930263	−	0.366894i	$-0.880421\pi$
$691$	−3.87447	+	6.71078i	−0.147392	+	0.255290i	0.782871	+	0.622184i	$0.213755\pi$
$692$	16.6487			0.632888
$693$	−4.62409			−0.175655
$694$	16.2643	−	28.1706i	0.617385	−	1.06934i
$695$			31.3639i			1.18970i
$696$	−1.41819	−	2.45638i	−0.0537564	−	0.0931088i
$697$		−	0.256389i		−	0.00971141i
$698$	−21.4524	+	12.3855i	−0.811984	+	0.468799i
$699$	−2.63048	−	4.55613i	−0.0994940	−	0.172329i
$700$	−5.71048	−	9.89084i	−0.215836	−	0.373839i
$701$	−24.7024	−	14.2619i	−0.932996	−	0.538665i	−0.0452379	−	0.998976i	$-0.514405\pi$
$701$	−24.7024	−	14.2619i	−0.932996	−	0.538665i	−0.887758	+	0.460311i	$0.847738\pi$
$702$	0.524338			0.0197899
$703$	−16.2112	+	19.4656i	−0.611418	+	0.734160i
$704$	2.57999			0.0972372
$705$	−29.0085	−	16.7481i	−1.09252	−	0.630769i
$706$	16.2812	+	28.1999i	0.612751	+	1.06132i
$707$	−16.6553	−	28.8478i	−0.626387	−	1.08493i
$708$	−8.48119	+	4.89662i	−0.318743	+	0.184026i
$709$		−	37.6954i		−	1.41568i	−0.706373	−	0.707840i	$-0.749670\pi$
$709$		−	37.6954i		−	1.41568i	0.706373	−	0.707840i	$-0.250330\pi$
$710$	15.7225	+	27.2322i	0.590055	+	1.02201i
$711$			1.11349i			0.0417592i
$712$	7.54915	−	13.0755i	0.282916	−	0.490026i
$713$	61.3335			2.29696
$714$	−5.00458			−0.187292
$715$	2.28099	−	3.95079i	0.0853043	−	0.147751i
$716$	−2.21782	+	1.28046i	−0.0828840	+	0.0478531i
$717$			1.09277i			0.0408103i
$718$	−14.2926	−	8.25181i	−0.533393	−	0.307955i
$719$	7.32216	−	12.6823i	0.273070	−	0.472972i	−0.696576	−	0.717483i	$-0.745294\pi$
$719$	7.32216	−	12.6823i	0.273070	−	0.472972i	0.969646	+	0.244511i	$0.0786275\pi$
$720$	−2.92048	−	1.68614i	−0.108840	−	0.0628388i
$721$	0.540478	−	0.312045i	0.0201285	−	0.0116212i
$722$	−1.43446	+	0.828185i	−0.0533850	+	0.0308219i
$723$	7.18156	+	4.14628i	0.267085	+	0.154202i
$724$	12.0951	−	20.9493i	0.449509	−	0.778573i
$725$	15.6527	+	9.03712i	0.581328	+	0.335630i
$726$		−	4.34363i		−	0.161207i
$727$	−13.9482	+	8.05301i	−0.517311	+	0.298669i	−0.735834	−	0.677162i	$-0.763209\pi$
$727$	−13.9482	+	8.05301i	−0.517311	+	0.298669i	0.218523	+	0.975832i	$0.429876\pi$
$728$	−0.469882	+	0.813859i	−0.0174150	+	0.0301636i
$729$	1.00000			0.0370370
$730$	27.4520			1.01605
$731$	−17.1355	+	29.6796i	−0.633781	+	1.09774i
$732$		−	3.88506i		−	0.143596i
$733$	18.9483	+	32.8195i	0.699872	+	1.21221i	0.968510	+	0.248973i	$0.0800931\pi$
$733$	18.9483	+	32.8195i	0.699872	+	1.21221i	−0.268638	+	0.963241i	$0.586574\pi$
$734$		−	17.3438i		−	0.640172i
$735$	11.0619	−	6.38661i	0.408025	−	0.235574i
$736$	−4.31662	−	7.47661i	−0.159113	−	0.275592i
$737$	−12.3653	−	21.4173i	−0.455482	−	0.788917i
$738$	−0.0795187	−	0.0459101i	−0.00292712	−	0.00168998i
$739$	19.1508			0.704475			0.352237	−	0.935911i	$-0.385421\pi$
$739$	19.1508			0.704475			0.352237	+	0.935911i	$0.385421\pi$
$740$	20.2142	+	3.48722i	0.743089	+	0.128193i
$741$	2.18364			0.0802180
$742$	−2.63230	−	1.51976i	−0.0966347	−	0.0557921i
$743$	6.75117	+	11.6934i	0.247676	+	0.428988i	0.962881	−	0.269927i	$-0.0869997\pi$
$743$	6.75117	+	11.6934i	0.247676	+	0.428988i	−0.715204	+	0.698915i	$0.753666\pi$
$744$	3.55217	+	6.15253i	0.130229	+	0.225563i
$745$	−54.6038	+	31.5255i	−2.00053	+	1.15500i
$746$		−	30.2012i		−	1.10574i
$747$	0.316625	+	0.548410i	0.0115847	+	0.0200653i
$748$			7.20408i			0.263407i
$749$	−4.54143	+	7.86599i	−0.165940	+	0.287417i
$750$	4.62772			0.168980
$751$	−3.32765			−0.121428			−0.0607139	−	0.998155i	$-0.519338\pi$
$751$	−3.32765			−0.121428			−0.0607139	+	0.998155i	$0.519338\pi$
$752$	4.96639	−	8.60204i	0.181106	−	0.313684i
$753$	21.1921	−	12.2353i	0.772285	−	0.445879i
$754$		−	1.48722i		−	0.0541615i
$755$	36.0922	+	20.8379i	1.31353	+	0.758368i
$756$	−0.896143	+	1.55217i	−0.0325924	+	0.0564517i
$757$	29.5828	+	17.0796i	1.07521	+	0.620770i	0.929599	−	0.368572i	$-0.120153\pi$
$757$	29.5828	+	17.0796i	1.07521	+	0.620770i	0.145607	+	0.989343i	$0.453487\pi$
$758$	11.3603	−	6.55890i	0.412626	−	0.238230i
$759$	19.2896	−	11.1369i	0.700169	−	0.404243i
$760$	−12.1625	−	7.02205i	−0.441182	−	0.254716i
$761$	−18.8763	+	32.6946i	−0.684264	+	1.18518i	0.289403	+	0.957207i	$0.406543\pi$
$761$	−18.8763	+	32.6946i	−0.684264	+	1.18518i	−0.973667	+	0.227973i	$0.926790\pi$
$762$	5.70720	+	3.29505i	0.206750	+	0.119367i
$763$			12.4031i			0.449023i
$764$	−4.58095	+	2.64481i	−0.165733	+	0.0956859i
$765$	4.70819	−	8.15482i	0.170225	−	0.294838i
$766$	17.6629			0.638185
$767$	−5.13496			−0.185413
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$		−	19.4434i		−	0.701146i	−0.936535	−	0.350573i	$-0.885987\pi$
$769$		−	19.4434i		−	0.701146i	0.936535	−	0.350573i	$-0.114013\pi$
$770$	7.79687	+	13.5046i	0.280980	+	0.486671i
$771$			19.3301i			0.696156i
$772$	8.87228	−	5.12241i	0.319320	−	0.184360i
$773$	−3.99781	−	6.92441i	−0.143791	−	0.249054i	0.785130	−	0.619331i	$-0.212596\pi$
$773$	−3.99781	−	6.92441i	−0.143791	−	0.249054i	−0.928921	+	0.370277i	$0.879263\pi$
$774$	6.13674	+	10.6291i	0.220581	+	0.382057i
$775$	−39.2057	−	22.6354i	−1.40831	−	0.813088i
$776$	−2.45159			−0.0880069
$777$	1.85338	−	10.7434i	0.0664895	−	0.385416i
$778$	−9.55592			−0.342596
$779$	−0.331161	−	0.191196i	−0.0118651	−	0.00685031i
$780$	−0.884107	−	1.53132i	−0.0316561	−	0.0548300i
$781$	−12.0287	−	20.8342i	−0.430419	−	0.745508i
$782$	20.8769	−	12.0533i	0.746555	−	0.431024i
$783$		−	2.83638i		−	0.101364i
$784$	1.89385	+	3.28025i	0.0676376	+	0.117152i
$785$			24.1301i			0.861238i
$786$	5.22480	−	9.04963i	0.186363	−	0.322789i
$787$	6.17948			0.220275			0.110137	−	0.993916i	$-0.464871\pi$
$787$	6.17948			0.220275			0.110137	+	0.993916i	$0.464871\pi$
$788$	−23.1957			−0.826311
$789$	−1.09182	+	1.89109i	−0.0388698	+	0.0673245i
$790$	3.25193	−	1.87750i	0.115699	−	0.0667986i
$791$		−	35.5884i		−	1.26538i
$792$	2.23434	+	1.29000i	0.0793938	+	0.0458381i
$793$	1.01854	−	1.76417i	0.0361695	−	0.0626474i
$794$	−19.7030	−	11.3755i	−0.699233	−	0.403702i
$795$	4.95281	−	2.85950i	0.175658	−	0.101416i
$796$	12.0762	−	6.97217i	0.428028	−	0.247122i
$797$	−22.4298	−	12.9499i	−0.794506	−	0.458708i	0.0470407	−	0.998893i	$-0.485021\pi$
$797$	−22.4298	−	12.9499i	−0.794506	−	0.458708i	−0.841546	+	0.540185i	$0.818354\pi$
$798$	−3.73205	+	6.46410i	−0.132113	+	0.228827i
$799$	24.0194	+	13.8676i	0.849744	+	0.490600i
$800$			6.37228i			0.225294i
$801$	13.0755	−	7.54915i	0.462001	−	0.266736i
$802$	4.65274	−	8.05879i	0.164294	−	0.284566i
$803$	−21.0024			−0.741160
$804$	−9.58553			−0.338055
$805$	26.0901	−	45.1894i	0.919555	−	1.59272i
$806$			3.72507i			0.131210i
$807$	−14.1971	−	24.5901i	−0.499762	−	0.865613i
$808$			18.5855i			0.653836i
$809$	−9.91103	+	5.72214i	−0.348453	+	0.201180i	−0.664004	−	0.747729i	$-0.731144\pi$
$809$	−9.91103	+	5.72214i	−0.348453	+	0.201180i	0.315550	+	0.948909i	$0.397811\pi$
$810$	−1.68614	−	2.92048i	−0.0592449	−	0.102615i
$811$	−12.6964	−	21.9908i	−0.445832	−	0.772203i	0.552278	−	0.833660i	$-0.313759\pi$
$811$	−12.6964	−	21.9908i	−0.445832	−	0.772203i	−0.998110	+	0.0614570i	$0.980425\pi$
$812$	4.40254	+	2.54181i	0.154499	+	0.0891999i
$813$	20.8270			0.730435
$814$	−15.4651	−	2.66793i	−0.542050	−	0.0935109i
$815$	37.1105			1.29993
$816$	2.41819	+	1.39614i	0.0846536	+	0.0488748i
$817$	25.5569	+	44.2658i	0.894122	+	1.54866i
$818$	2.03517	+	3.52502i	0.0711582	+	0.123250i
$819$	−0.813859	+	0.469882i	−0.0284385	+	0.0164190i
$820$			0.309644i			0.0108132i
$821$	16.9192	+	29.3050i	0.590486	+	1.02275i	0.994167	+	0.107851i	$0.0343971\pi$
$821$	16.9192	+	29.3050i	0.590486	+	1.02275i	−0.403681	+	0.914900i	$0.632270\pi$
$822$			6.02865i			0.210273i
$823$	−4.97603	+	8.61873i	−0.173453	+	0.300430i	−0.939625	−	0.342206i	$-0.888826\pi$
$823$	−4.97603	+	8.61873i	−0.173453	+	0.300430i	0.766172	+	0.642636i	$0.222159\pi$
$824$	−0.348209			−0.0121304
$825$	−16.4404			−0.572383
$826$	8.77615	−	15.2007i	0.305361	−	0.528901i
$827$	−22.5062	+	12.9940i	−0.782618	+	0.451845i	−0.837357	−	0.546656i	$-0.815901\pi$
$827$	−22.5062	+	12.9940i	−0.782618	+	0.451845i	0.0547394	+	0.998501i	$0.482567\pi$
$828$		−	8.63325i		−	0.300026i
$829$	−29.0942	−	16.7976i	−1.01048	−	0.583404i	−0.0991512	−	0.995072i	$-0.531613\pi$
$829$	−29.0942	−	16.7976i	−1.01048	−	0.583404i	−0.911334	+	0.411669i	$0.864946\pi$
$830$	1.06775	−	1.84939i	0.0370621	−	0.0641934i
$831$	−13.0277	−	7.52157i	−0.451927	−	0.260920i
$832$	0.454090	−	0.262169i	0.0157427	−	0.00908907i
$833$	−9.15940	+	5.28818i	−0.317354	+	0.183225i
$834$	−8.05446	−	4.65024i	−0.278903	−	0.161025i
$835$	−0.661481	+	1.14572i	−0.0228915	+	0.0396492i
$836$	9.30506	+	5.37228i	0.321822	+	0.185804i
$837$			7.10433i			0.245562i
$838$	−5.75315	+	3.32158i	−0.198739	+	0.114742i
$839$	9.83733	−	17.0388i	0.339622	−	0.588243i	−0.644739	−	0.764403i	$-0.723034\pi$
$839$	9.83733	−	17.0388i	0.339622	−	0.588243i	0.984362	+	0.176159i	$0.0563674\pi$
$840$	6.04410			0.208541
$841$	20.9549			0.722584
$842$	−18.7844	+	32.5356i	−0.647355	+	1.12125i
$843$			12.1359i			0.417983i
$844$	−8.21277	−	14.2249i	−0.282695	−	0.489642i
$845$			42.9125i			1.47624i
$846$	8.60204	−	4.96639i	0.295744	−	0.170748i
$847$	3.89252	+	6.74203i	0.133748	+	0.231659i
$848$	0.847944	+	1.46868i	0.0291185	+	0.0504347i
$849$	28.5528	+	16.4849i	0.979928	+	0.565762i
$850$	−17.7932			−0.610303
$851$	18.1433	+	49.2802i	0.621946	+	1.68930i
$852$	−9.32456			−0.319454
$853$	−30.4004	−	17.5517i	−1.04089	−	0.600959i	−0.120806	−	0.992676i	$-0.538548\pi$
$853$	−30.4004	−	17.5517i	−1.04089	−	0.600959i	−0.920086	+	0.391717i	$0.871881\pi$
$854$	3.48157	+	6.03026i	0.119137	+	0.206351i
$855$	−7.02205	−	12.1625i	−0.240149	−	0.415950i
$856$	4.38880	−	2.53387i	0.150006	−	0.0866060i
$857$		−	30.8848i		−	1.05501i	−0.849553	−	0.527503i	$-0.823128\pi$
$857$		−	30.8848i		−	1.05501i	0.849553	−	0.527503i	$-0.176872\pi$
$858$	0.676394	+	1.17155i	0.0230917	+	0.0399960i
$859$		−	39.7916i		−	1.35767i	−0.734290	−	0.678836i	$-0.762485\pi$
$859$		−	39.7916i		−	1.35767i	0.734290	−	0.678836i	$-0.237515\pi$
$860$	20.6948	−	35.8445i	0.705687	−	1.22229i
$861$	0.164568			0.00560847
$862$	−22.6932			−0.772934
$863$	−19.5249	+	33.8181i	−0.664634	+	1.15118i	0.314750	+	0.949175i	$0.398079\pi$
$863$	−19.5249	+	33.8181i	−0.664634	+	1.15118i	−0.979384	+	0.202006i	$0.935254\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		−	56.1441i		−	1.90896i
$866$	−13.5561	−	7.82664i	−0.460656	−	0.265960i
$867$	4.60157	−	7.97015i	0.156277	−	0.270680i
$868$	−11.0271	−	6.36650i	−0.374284	−	0.216093i
$869$	−2.48792	+	1.43640i	−0.0843969	+	0.0487266i
$870$	−8.28360	+	4.78254i	−0.280840	+	0.162143i
$871$	−4.35269	−	2.51303i	−0.147485	−	0.0851507i
$872$	3.46014	−	5.99313i	0.117175	−	0.202953i
$873$	−2.12314	−	1.22579i	−0.0718574	−	0.0414869i
$874$		−	35.9538i		−	1.21615i
$875$	−7.18299	+	4.14710i	−0.242829	+	0.140198i
$876$	−4.07025	+	7.04988i	−0.137521	+	0.238193i
$877$	−6.61281			−0.223299			−0.111649	−	0.993748i	$-0.535613\pi$
$877$	−6.61281			−0.223299			−0.111649	+	0.993748i	$0.535613\pi$
$878$	−30.7330			−1.03719
$879$	−8.47182	+	14.6736i	−0.285748	+	0.494929i
$880$		−	8.70047i		−	0.293293i
$881$	−1.90137	−	3.29326i	−0.0640586	−	0.110953i	0.832217	−	0.554449i	$-0.187071\pi$
$881$	−1.90137	−	3.29326i	−0.0640586	−	0.110953i	−0.896276	+	0.443497i	$0.853738\pi$
$882$			3.78771i			0.127539i
$883$	−42.2287	+	24.3807i	−1.42111	+	0.820477i	−0.996394	−	0.0848499i	$-0.972959\pi$
$883$	−42.2287	+	24.3807i	−1.42111	+	0.820477i	−0.424715	+	0.905327i	$0.639626\pi$
$884$	0.732051	+	1.26795i	0.0246215	+	0.0426457i
$885$	16.5128	+	28.6010i	0.555071	+	0.961411i
$886$	−5.56550	−	3.21324i	−0.186977	−	0.107951i
$887$	−19.4520			−0.653136			−0.326568	−	0.945174i	$-0.605892\pi$
$887$	−19.4520			−0.653136			−0.326568	+	0.945174i	$0.605892\pi$
$888$	−3.89265	+	4.67410i	−0.130629	+	0.156853i
$889$	−11.8114			−0.396140
$890$	−44.0943	−	25.4579i	−1.47804	−	0.853349i
$891$	1.29000	+	2.23434i	0.0432165	+	0.0748532i
$892$	5.15456	+	8.92795i	0.172587	+	0.298930i
$893$	35.8238	−	20.6829i	1.19880	−	0.692126i
$894$		−	18.6968i		−	0.625316i
$895$	4.31807	+	7.47912i	0.144337	+	0.250000i
$896$			1.79229i			0.0598761i
$897$	2.26337	−	3.92027i	0.0755717	−	0.130894i
$898$	12.6241			0.421271
$899$	20.1506			0.672060
$900$	−3.18614	+	5.51856i	−0.106205	+	0.183952i
$901$	−4.10098	+	2.36770i	−0.136623	+	0.0788796i
$902$		−	0.236896i		−	0.00788777i
$903$	−19.0505	−	10.9988i	−0.633960	−	0.366017i
$904$	−9.92820	+	17.1962i	−0.330207	+	0.571936i
$905$	−70.6468	−	40.7879i	−2.34838	−	1.35584i
$906$	−10.7026	+	6.17916i	−0.355571	+	0.205289i
$907$	13.7882	−	7.96061i	0.457829	−	0.264328i	−0.253302	−	0.967387i	$-0.581517\pi$
$907$	13.7882	−	7.96061i	0.457829	−	0.264328i	0.711131	+	0.703060i	$0.248183\pi$
$908$	−15.0957	−	8.71553i	−0.500970	−	0.289235i
$909$	−9.29276	+	16.0955i	−0.308221	+	0.533855i
$910$	2.74456	+	1.58457i	0.0909814	+	0.0525281i
$911$		−	10.7075i		−	0.354755i	−0.984143	−	0.177377i	$-0.943239\pi$
$911$		−	10.7075i		−	0.354755i	0.984143	−	0.177377i	$-0.0567613\pi$
$912$	3.60662	−	2.08228i	0.119427	−	0.0689513i
$913$	−0.816890	+	1.41490i	−0.0270351	+	0.0468262i
$914$	21.2438			0.702682
$915$	−13.1015			−0.433123
$916$	1.04543	−	1.81075i	0.0345421	−	0.0598287i
$917$			18.7287i			0.618476i
$918$	1.39614	+	2.41819i	0.0460796	+	0.0798122i
$919$		−	13.4434i		−	0.443456i	−0.975109	−	0.221728i	$-0.928830\pi$
$919$		−	13.4434i		−	0.443456i	0.975109	−	0.221728i	$-0.0711697\pi$
$920$	−25.2132	+	14.5569i	−0.831256	+	0.479926i
$921$	14.7496	+	25.5471i	0.486016	+	0.841805i
$922$	−4.08724	−	7.07931i	−0.134606	−	0.233145i
$923$	−4.23419	−	2.44461i	−0.139370	−	0.0804653i
$924$	−4.62409			−0.152121
$925$	6.58948	−	38.1969i	0.216661	−	1.25590i
$926$	19.6894			0.647035
$927$	−0.301558	−	0.174104i	−0.00990446	−	0.00571834i
$928$	−1.41819	−	2.45638i	−0.0465544	−	0.0806346i
$929$	−11.5949	−	20.0829i	−0.380415	−	0.658898i	0.610707	−	0.791857i	$-0.290885\pi$
$929$	−11.5949	−	20.0829i	−0.380415	−	0.658898i	−0.991122	+	0.132959i	$0.957552\pi$
$930$	20.7481	−	11.9789i	0.680356	−	0.392804i
$931$			15.7742i			0.516977i
$932$	−2.63048	−	4.55613i	−0.0861644	−	0.149241i
$933$			31.8282i			1.04201i
$934$	2.34726	−	4.06557i	0.0768046	−	0.133029i
$935$	24.2942			0.794505
$936$	0.524338			0.0171385
$937$	20.3619	−	35.2679i	0.665195	−	1.15215i	−0.314037	−	0.949411i	$-0.601682\pi$
$937$	20.3619	−	35.2679i	0.665195	−	1.15215i	0.979232	−	0.202742i	$-0.0649851\pi$
$938$	14.8783	−	8.59001i	0.485795	−	0.280474i
$939$			20.9735i			0.684445i
$940$	−29.0085	−	16.7481i	−0.946153	−	0.546262i
$941$	7.64700	−	13.2450i	0.249285	−	0.431774i	−0.714043	−	0.700102i	$-0.753138\pi$
$941$	7.64700	−	13.2450i	0.249285	−	0.431774i	0.963328	+	0.268328i	$0.0864710\pi$
$942$	−6.19677	−	3.57770i	−0.201902	−	0.116568i
$943$	−0.686505	+	0.396354i	−0.0223557	+	0.0129071i
$944$	−8.48119	+	4.89662i	−0.276039	+	0.159371i
$945$	5.23434	+	3.02205i	0.170273	+	0.0983072i
$946$	−15.8328	+	27.4231i	−0.514767	+	0.891603i
$947$	−44.3701	−	25.6171i	−1.44184	−	0.832444i	−0.443863	−	0.896094i	$-0.646392\pi$
$947$	−44.3701	−	25.6171i	−1.44184	−	0.832444i	−0.997972	+	0.0636503i	$0.979726\pi$
$948$			1.11349i			0.0361645i
$949$	−3.69652	+	2.13418i	−0.119994	+	0.0692786i
$950$	−13.2689	+	22.9824i	−0.430500	+	0.745648i
$951$	−7.53495			−0.244337
$952$	−5.00458			−0.162199
$953$	2.79782	−	4.84596i	0.0906302	−	0.156976i	−0.817146	−	0.576430i	$-0.804445\pi$
$953$	2.79782	−	4.84596i	0.0906302	−	0.156976i	0.907776	+	0.419454i	$0.137779\pi$
$954$			1.69589i			0.0549064i
$955$	8.91904	+	15.4482i	0.288613	+	0.499893i
$956$			1.09277i			0.0353428i
$957$	6.33745	−	3.65893i	0.204861	−	0.118276i
$958$	3.94434	+	6.83180i	0.127436	+	0.220726i
$959$	−5.40254	−	9.35747i	−0.174457	−	0.302168i
$960$	−2.92048	−	1.68614i	−0.0942581	−	0.0544200i
$961$	−19.4715			−0.628114
$962$	−2.99302	+	1.10193i	−0.0964988	+	0.0355277i
$963$	5.06775			0.163306
$964$	7.18156	+	4.14628i	0.231303	+	0.133543i
$965$	−17.2742	−	29.9198i	−0.556077	−	0.963153i
$966$	7.73663	+	13.4002i	0.248922	+	0.431146i
$967$	29.8179	−	17.2154i	0.958880	−	0.553610i	0.0630521	−	0.998010i	$-0.479917\pi$
$967$	29.8179	−	17.2154i	0.958880	−	0.553610i	0.895828	+	0.444400i	$0.146583\pi$
$968$		−	4.34363i		−	0.139610i
$969$	5.81433	+	10.0707i	0.186783	+	0.323518i
$970$			8.26745i			0.265452i
$971$	−18.6807	+	32.3559i	−0.599492	+	1.03835i	0.393404	+	0.919366i	$0.371297\pi$
$971$	−18.6807	+	32.3559i	−0.599492	+	1.03835i	−0.992896	+	0.118985i	$0.962036\pi$
$972$	1.00000			0.0320750
$973$	16.6691			0.534388
$974$	−1.26890	+	2.19780i	−0.0406582	+	0.0704221i
$975$	−2.89359	+	1.67061i	−0.0926690	+	0.0535025i
$976$		−	3.88506i		−	0.124358i
$977$	15.3643	+	8.87057i	0.491547	+	0.283795i	0.725216	−	0.688522i	$-0.241740\pi$
$977$	15.3643	+	8.87057i	0.491547	+	0.283795i	−0.233669	+	0.972316i	$0.575073\pi$
$978$	−5.50229	+	9.53025i	−0.175944	+	0.304744i
$979$	33.7348	+	19.4768i	1.07817	+	0.622480i
$980$	11.0619	−	6.38661i	0.353360	−	0.204013i
$981$	5.99313	−	3.46014i	0.191346	−	0.110474i
$982$	−8.78275	−	5.07072i	−0.280269	−	0.161813i
$983$	9.78828	−	16.9538i	0.312198	−	0.540742i	−0.666640	−	0.745380i	$-0.732268\pi$
$983$	9.78828	−	16.9538i	0.312198	−	0.540742i	0.978838	+	0.204637i	$0.0656015\pi$
$984$	−0.0795187	−	0.0459101i	−0.00253496	−	0.00146356i
$985$			78.2223i			2.49237i
$986$	6.85892	−	3.96000i	0.218432	−	0.126112i
$987$	−8.90120	+	15.4173i	−0.283328	+	0.490739i
$988$	2.18364			0.0694709
$989$	105.960			3.36933
$990$	4.35023	−	7.53483i	0.138259	−	0.239472i
$991$			41.8595i			1.32971i	0.746973	+	0.664855i	$0.231507\pi$
$991$			41.8595i			1.32971i	−0.746973	+	0.664855i	$0.768493\pi$
$992$	3.55217	+	6.15253i	0.112781	+	0.195343i
$993$		−	29.4684i		−	0.935152i
$994$	14.4733	−	8.35614i	0.459064	−	0.265041i
$995$	−23.5121	−	40.7242i	−0.745384	−	1.29104i
$996$	0.316625	+	0.548410i	0.0100326	+	0.0173770i
$997$	36.1915	+	20.8952i	1.14620	+	0.661757i	0.947957	−	0.318397i	$-0.103145\pi$
$997$	36.1915	+	20.8952i	1.14620	+	0.661757i	0.198239	+	0.980154i	$0.436478\pi$
$998$	−30.4845			−0.964971
$999$	−5.70819	+	2.10157i	−0.180599	+	0.0664906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.2.j.b.175.4	yes	8
3.2	odd	2		666.2.s.f.397.1		8
4.3	odd	2		1776.2.bz.i.1729.4		8
37.11	even	6	inner	222.2.j.b.85.4	✓	8
37.14	odd	12		8214.2.a.ba.1.4		4
37.23	odd	12		8214.2.a.z.1.2		4
111.11	odd	6		666.2.s.f.307.1		8
148.11	odd	6		1776.2.bz.i.529.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.j.b.85.4	✓	8	37.11	even	6	inner
222.2.j.b.175.4	yes	8	1.1	even	1	trivial
666.2.s.f.307.1		8	111.11	odd	6
666.2.s.f.397.1		8	3.2	odd	2
1776.2.bz.i.529.4		8	148.11	odd	6
1776.2.bz.i.1729.4		8	4.3	odd	2
8214.2.a.z.1.2		4	37.23	odd	12
8214.2.a.ba.1.4		4	37.14	odd	12

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:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	222.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.92048 - 1.68614i) q^{5} +1.00000i q^{6} +(-0.896143 - 1.55217i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +3.37228 q^{10} -2.57999 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.454090 + 0.262169i) q^{13} -1.79229i q^{14} +(2.92048 + 1.68614i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.41819 - 1.39614i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-3.60662 + 2.08228i) q^{19} +(2.92048 + 1.68614i) q^{20} +(0.896143 - 1.55217i) q^{21} +(-2.23434 - 1.29000i) q^{22} +8.63325i q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.18614 - 5.51856i) q^{25} -0.524338 q^{26} -1.00000 q^{27} +(0.896143 - 1.55217i) q^{28} +2.83638i q^{29} +(1.68614 + 2.92048i) q^{30} -7.10433i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.29000 - 2.23434i) q^{33} +(-1.39614 - 2.41819i) q^{34} +(-5.23434 - 3.02205i) q^{35} -1.00000 q^{36} +(5.70819 - 2.10157i) q^{37} -4.16457 q^{38} +(-0.454090 - 0.262169i) q^{39} +(1.68614 + 2.92048i) q^{40} +(0.0459101 + 0.0795187i) q^{41} +(1.55217 - 0.896143i) q^{42} -12.2735i q^{43} +(-1.29000 - 2.23434i) q^{44} +3.37228i q^{45} +(-4.31662 + 7.47661i) q^{46} -9.93278 q^{47} -1.00000 q^{48} +(1.89385 - 3.28025i) q^{49} +(5.51856 - 3.18614i) q^{50} -2.79229i q^{51} +(-0.454090 - 0.262169i) q^{52} +(0.847944 - 1.46868i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-7.53483 + 4.35023i) q^{55} +(1.55217 - 0.896143i) q^{56} +(-3.60662 - 2.08228i) q^{57} +(-1.41819 + 2.45638i) q^{58} +(8.48119 + 4.89662i) q^{59} +3.37228i q^{60} +(-3.36456 + 1.94253i) q^{61} +(3.55217 - 6.15253i) q^{62} +1.79229 q^{63} -1.00000 q^{64} +(-0.884107 + 1.53132i) q^{65} -2.57999i q^{66} +(4.79276 + 8.30131i) q^{67} -2.79229i q^{68} +(-7.47661 + 4.31662i) q^{69} +(-3.02205 - 5.23434i) q^{70} +(4.66228 + 8.07530i) q^{71} +(-0.866025 - 0.500000i) q^{72} +8.14050 q^{73} +(5.99422 + 1.03408i) q^{74} +6.37228 q^{75} +(-3.60662 - 2.08228i) q^{76} +(2.31205 + 4.00458i) q^{77} +(-0.262169 - 0.454090i) q^{78} +(0.964312 - 0.556746i) q^{79} +3.37228i q^{80} +(-0.500000 - 0.866025i) q^{81} +0.0918203i q^{82} +(0.316625 - 0.548410i) q^{83} +1.79229 q^{84} -9.41638 q^{85} +(6.13674 - 10.6291i) q^{86} +(-2.45638 + 1.41819i) q^{87} -2.57999i q^{88} +(-13.0755 - 7.54915i) q^{89} +(-1.68614 + 2.92048i) q^{90} +(0.813859 + 0.469882i) q^{91} +(-7.47661 + 4.31662i) q^{92} +(6.15253 - 3.55217i) q^{93} +(-8.60204 - 4.96639i) q^{94} +(-7.02205 + 12.1625i) q^{95} +(-0.866025 - 0.500000i) q^{96} +2.45159i q^{97} +(3.28025 - 1.89385i) q^{98} +(1.29000 - 2.23434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{4} - 4 q^{7} - 4 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{16} + 6 q^{17} + 6 q^{19} + 4 q^{21} - 6 q^{22} + 14 q^{25} + 16 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} - 2 q^{33}+ \cdots + 2 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^4 - 4 * q^7 - 4 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 6 * q^13 - 4 * q^16 + 6 * q^17 + 6 * q^19 + 4 * q^21 - 6 * q^22 + 14 * q^25 + 16 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 - 2 * q^33 - 8 * q^34 - 30 * q^35 - 8 * q^36 + 12 * q^37 - 4 * q^38 - 6 * q^39 + 2 * q^40 - 2 * q^41 - 6 * q^42 - 2 * q^44 - 8 * q^46 - 28 * q^47 - 8 * q^48 + 10 * q^49 - 6 * q^52 + 4 * q^53 + 30 * q^55 - 6 * q^56 + 6 * q^57 + 14 * q^58 + 12 * q^59 - 36 * q^61 + 10 * q^62 + 8 * q^63 - 8 * q^64 + 4 * q^65 - 8 * q^67 - 2 * q^70 + 6 * q^71 + 20 * q^73 + 24 * q^74 + 28 * q^75 + 6 * q^76 - 12 * q^77 + 8 * q^78 - 24 * q^79 - 4 * q^81 - 24 * q^83 + 8 * q^84 - 8 * q^85 + 18 * q^86 - 24 * q^87 - 42 * q^89 - 2 * q^90 + 18 * q^91 + 12 * q^93 - 30 * q^94 - 34 * q^95 + 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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