LMFDB - Embedded newform 186.2.e.d.25.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [186,2,Mod(25,186)] 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("186.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(186, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	186.25
Dual form			186.2.e.d.67.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.41421 - 2.44949i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.20711 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.41421 - 2.44949i) q^{10} +(-1.20711 + 2.09077i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.82843 + 4.89898i) q^{13} +(-1.20711 - 2.09077i) q^{14} +2.82843 q^{15} +1.00000 q^{16} +(3.12132 + 5.40629i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.70711 - 4.68885i) q^{19} +(1.41421 - 2.44949i) q^{20} +(1.20711 - 2.09077i) q^{21} +(-1.20711 + 2.09077i) q^{22} -6.24264 q^{23} +(0.500000 + 0.866025i) q^{24} +(-1.50000 - 2.59808i) q^{25} +(-2.82843 + 4.89898i) q^{26} -1.00000 q^{27} +(-1.20711 - 2.09077i) q^{28} +5.82843 q^{29} +2.82843 q^{30} +(-0.378680 - 5.55487i) q^{31} +1.00000 q^{32} -2.41421 q^{33} +(3.12132 + 5.40629i) q^{34} -6.82843 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.53553 - 6.12372i) q^{37} +(-2.70711 - 4.68885i) q^{38} -5.65685 q^{39} +(1.41421 - 2.44949i) q^{40} +(-3.29289 + 5.70346i) q^{41} +(1.20711 - 2.09077i) q^{42} +(0.828427 + 1.43488i) q^{43} +(-1.20711 + 2.09077i) q^{44} +(1.41421 + 2.44949i) q^{45} -6.24264 q^{46} +8.24264 q^{47} +(0.500000 + 0.866025i) q^{48} +(0.585786 - 1.01461i) q^{49} +(-1.50000 - 2.59808i) q^{50} +(-3.12132 + 5.40629i) q^{51} +(-2.82843 + 4.89898i) q^{52} +(3.74264 - 6.48244i) q^{53} -1.00000 q^{54} +(3.41421 + 5.91359i) q^{55} +(-1.20711 - 2.09077i) q^{56} +(2.70711 - 4.68885i) q^{57} +5.82843 q^{58} +(3.44975 + 5.97514i) q^{59} +2.82843 q^{60} -7.07107 q^{61} +(-0.378680 - 5.55487i) q^{62} +2.41421 q^{63} +1.00000 q^{64} +(8.00000 + 13.8564i) q^{65} -2.41421 q^{66} +(-3.12132 + 5.40629i) q^{67} +(3.12132 + 5.40629i) q^{68} +(-3.12132 - 5.40629i) q^{69} -6.82843 q^{70} +(0.828427 - 1.43488i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.24264 - 3.88437i) q^{73} +(-3.53553 - 6.12372i) q^{74} +(1.50000 - 2.59808i) q^{75} +(-2.70711 - 4.68885i) q^{76} +5.82843 q^{77} -5.65685 q^{78} +(-6.24264 - 10.8126i) q^{79} +(1.41421 - 2.44949i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.29289 + 5.70346i) q^{82} +(1.79289 - 3.10538i) q^{83} +(1.20711 - 2.09077i) q^{84} +17.6569 q^{85} +(0.828427 + 1.43488i) q^{86} +(2.91421 + 5.04757i) q^{87} +(-1.20711 + 2.09077i) q^{88} -9.31371 q^{89} +(1.41421 + 2.44949i) q^{90} +13.6569 q^{91} -6.24264 q^{92} +(4.62132 - 3.10538i) q^{93} +8.24264 q^{94} -15.3137 q^{95} +(0.500000 + 0.866025i) q^{96} +8.31371 q^{97} +(0.585786 - 1.01461i) q^{98} +(-1.20711 - 2.09077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{11} + 2 q^{12} - 2 q^{14} + 4 q^{16} + 4 q^{17} - 2 q^{18} - 8 q^{19} + 2 q^{21} - 2 q^{22} - 8 q^{23} + 2 q^{24} - 6 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^11 + 2 * q^12 - 2 * q^14 + 4 * q^16 + 4 * q^17 - 2 * q^18 - 8 * q^19 + 2 * q^21 - 2 * q^22 - 8 * q^23 + 2 * q^24 - 6 * q^25 - 4 * q^27 - 2 * q^28 + 12 * q^29 - 10 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 16 * q^35 - 2 * q^36 - 8 * q^38 - 16 * q^41 + 2 * q^42 - 8 * q^43 - 2 * q^44 - 8 * q^46 + 16 * q^47 + 2 * q^48 + 8 * q^49 - 6 * q^50 - 4 * q^51 - 2 * q^53 - 4 * q^54 + 8 * q^55 - 2 * q^56 + 8 * q^57 + 12 * q^58 - 6 * q^59 - 10 * q^62 + 4 * q^63 + 4 * q^64 + 32 * q^65 - 4 * q^66 - 4 * q^67 + 4 * q^68 - 4 * q^69 - 16 * q^70 - 8 * q^71 - 2 * q^72 - 8 * q^73 + 6 * q^75 - 8 * q^76 + 12 * q^77 - 8 * q^79 - 2 * q^81 - 16 * q^82 + 10 * q^83 + 2 * q^84 + 48 * q^85 - 8 * q^86 + 6 * q^87 - 2 * q^88 + 8 * q^89 + 32 * q^91 - 8 * q^92 + 10 * q^93 + 16 * q^94 - 16 * q^95 + 2 * q^96 - 12 * q^97 + 8 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	1.41421	−	2.44949i	0.632456	−	1.09545i	−0.354593	−	0.935021i	$-0.615380\pi$
$5$	1.41421	−	2.44949i	0.632456	−	1.09545i	0.987048	−	0.160424i	$-0.0512862\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−1.20711	−	2.09077i	−0.456243	−	0.790237i	0.542515	−	0.840046i	$-0.317472\pi$
$7$	−1.20711	−	2.09077i	−0.456243	−	0.790237i	−0.998759	+	0.0498090i	$0.984139\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.41421	−	2.44949i	0.447214	−	0.774597i
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	−0.988608	−	0.150513i	$-0.951908\pi$
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	0.624652	+	0.780903i	$0.285241\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.82843	+	4.89898i	−0.784465	+	1.35873i	0.144854	+	0.989453i	$0.453729\pi$
$13$	−2.82843	+	4.89898i	−0.784465	+	1.35873i	−0.929318	+	0.369279i	$0.879605\pi$
$14$	−1.20711	−	2.09077i	−0.322613	−	0.558782i
$15$	2.82843			0.730297
$16$	1.00000			0.250000
$17$	3.12132	+	5.40629i	0.757031	+	1.31122i	0.944358	+	0.328919i	$0.106684\pi$
$17$	3.12132	+	5.40629i	0.757031	+	1.31122i	−0.187327	+	0.982298i	$0.559982\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−2.70711	−	4.68885i	−0.621053	−	1.07570i	−0.989290	−	0.145963i	$-0.953372\pi$
$19$	−2.70711	−	4.68885i	−0.621053	−	1.07570i	0.368237	−	0.929732i	$-0.379961\pi$
$20$	1.41421	−	2.44949i	0.316228	−	0.547723i
$21$	1.20711	−	2.09077i	0.263412	−	0.456243i
$22$	−1.20711	+	2.09077i	−0.257356	+	0.445754i
$23$	−6.24264			−1.30168			−0.650840	−	0.759215i	$-0.725583\pi$
$23$	−6.24264			−1.30168			−0.650840	+	0.759215i	$0.725583\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$	−2.82843	+	4.89898i	−0.554700	+	0.960769i
$27$	−1.00000			−0.192450
$28$	−1.20711	−	2.09077i	−0.228122	−	0.395118i
$29$	5.82843			1.08231			0.541156	−	0.840922i	$-0.317987\pi$
$29$	5.82843			1.08231			0.541156	+	0.840922i	$0.317987\pi$
$30$	2.82843			0.516398
$31$	−0.378680	−	5.55487i	−0.0680129	−	0.997684i
$31$	−0.378680	−	5.55487i	−0.0680129	−	0.997684i
$32$	1.00000			0.176777
$33$	−2.41421			−0.420261
$34$	3.12132	+	5.40629i	0.535302	+	0.927170i
$35$	−6.82843			−1.15421
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.53553	−	6.12372i	−0.581238	−	1.00673i	−0.995333	−	0.0965003i	$-0.969235\pi$
$37$	−3.53553	−	6.12372i	−0.581238	−	1.00673i	0.414095	−	0.910234i	$-0.364098\pi$
$38$	−2.70711	−	4.68885i	−0.439151	−	0.760631i
$39$	−5.65685			−0.905822
$40$	1.41421	−	2.44949i	0.223607	−	0.387298i
$41$	−3.29289	+	5.70346i	−0.514264	+	0.890731i	0.485600	+	0.874181i	$0.338601\pi$
$41$	−3.29289	+	5.70346i	−0.514264	+	0.890731i	−0.999863	+	0.0165492i	$0.994732\pi$
$42$	1.20711	−	2.09077i	0.186261	−	0.322613i
$43$	0.828427	+	1.43488i	0.126334	+	0.218817i	0.922254	−	0.386585i	$-0.126346\pi$
$43$	0.828427	+	1.43488i	0.126334	+	0.218817i	−0.795920	+	0.605402i	$0.793012\pi$
$44$	−1.20711	+	2.09077i	−0.181978	+	0.315195i
$45$	1.41421	+	2.44949i	0.210819	+	0.365148i
$46$	−6.24264			−0.920427
$47$	8.24264			1.20231			0.601156	−	0.799131i	$-0.294707\pi$
$47$	8.24264			1.20231			0.601156	+	0.799131i	$0.294707\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	0.585786	−	1.01461i	0.0836838	−	0.144945i
$50$	−1.50000	−	2.59808i	−0.212132	−	0.367423i
$51$	−3.12132	+	5.40629i	−0.437072	+	0.757031i
$52$	−2.82843	+	4.89898i	−0.392232	+	0.679366i
$53$	3.74264	−	6.48244i	0.514091	−	0.890432i	−0.485775	−	0.874084i	$-0.661463\pi$
$53$	3.74264	−	6.48244i	0.514091	−	0.890432i	0.999866	−	0.0163483i	$-0.00520406\pi$
$54$	−1.00000			−0.136083
$55$	3.41421	+	5.91359i	0.460372	+	0.797388i
$56$	−1.20711	−	2.09077i	−0.161306	−	0.279391i
$57$	2.70711	−	4.68885i	0.358565	−	0.621053i
$58$	5.82843			0.765310
$59$	3.44975	+	5.97514i	0.449119	+	0.777897i	0.998329	−	0.0577877i	$-0.0184046\pi$
$59$	3.44975	+	5.97514i	0.449119	+	0.777897i	−0.549210	+	0.835684i	$0.685071\pi$
$60$	2.82843			0.365148
$61$	−7.07107			−0.905357			−0.452679	−	0.891674i	$-0.649532\pi$
$61$	−7.07107			−0.905357			−0.452679	+	0.891674i	$0.649532\pi$
$62$	−0.378680	−	5.55487i	−0.0480924	−	0.705469i
$63$	2.41421			0.304162
$64$	1.00000			0.125000
$65$	8.00000	+	13.8564i	0.992278	+	1.71868i
$66$	−2.41421			−0.297169
$67$	−3.12132	+	5.40629i	−0.381330	+	0.660483i	−0.991253	−	0.131978i	$-0.957867\pi$
$67$	−3.12132	+	5.40629i	−0.381330	+	0.660483i	0.609923	+	0.792461i	$0.291200\pi$
$68$	3.12132	+	5.40629i	0.378516	+	0.655608i
$69$	−3.12132	−	5.40629i	−0.375763	−	0.650840i
$70$	−6.82843			−0.816153
$71$	0.828427	−	1.43488i	0.0983162	−	0.170289i	−0.812672	−	0.582722i	$-0.801988\pi$
$71$	0.828427	−	1.43488i	0.0983162	−	0.170289i	0.910988	+	0.412433i	$0.135321\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	2.24264	−	3.88437i	0.262481	−	0.454631i	−0.704419	−	0.709784i	$-0.748793\pi$
$73$	2.24264	−	3.88437i	0.262481	−	0.454631i	0.966901	+	0.255153i	$0.0821259\pi$
$74$	−3.53553	−	6.12372i	−0.410997	−	0.711868i
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$	−2.70711	−	4.68885i	−0.310526	−	0.537848i
$77$	5.82843			0.664211
$78$	−5.65685			−0.640513
$79$	−6.24264	−	10.8126i	−0.702352	−	1.21651i	−0.967639	−	0.252340i	$-0.918800\pi$
$79$	−6.24264	−	10.8126i	−0.702352	−	1.21651i	0.265287	−	0.964170i	$-0.414533\pi$
$80$	1.41421	−	2.44949i	0.158114	−	0.273861i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.29289	+	5.70346i	−0.363639	+	0.629842i
$83$	1.79289	−	3.10538i	0.196796	−	0.340860i	−0.750692	−	0.660652i	$-0.770280\pi$
$83$	1.79289	−	3.10538i	0.196796	−	0.340860i	0.947488	+	0.319792i	$0.103613\pi$
$84$	1.20711	−	2.09077i	0.131706	−	0.228122i
$85$	17.6569			1.91515
$86$	0.828427	+	1.43488i	0.0893316	+	0.154727i
$87$	2.91421	+	5.04757i	0.312436	+	0.541156i
$88$	−1.20711	+	2.09077i	−0.128678	+	0.222877i
$89$	−9.31371			−0.987251			−0.493626	−	0.869675i	$-0.664329\pi$
$89$	−9.31371			−0.987251			−0.493626	+	0.869675i	$0.664329\pi$
$90$	1.41421	+	2.44949i	0.149071	+	0.258199i
$91$	13.6569			1.43163
$92$	−6.24264			−0.650840
$93$	4.62132	−	3.10538i	0.479209	−	0.322013i
$94$	8.24264			0.850163
$95$	−15.3137			−1.57115
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	8.31371			0.844129			0.422065	−	0.906566i	$-0.361306\pi$
$97$	8.31371			0.844129			0.422065	+	0.906566i	$0.361306\pi$
$98$	0.585786	−	1.01461i	0.0591734	−	0.102491i
$99$	−1.20711	−	2.09077i	−0.121319	−	0.210130i
$100$	−1.50000	−	2.59808i	−0.150000	−	0.259808i
$101$	7.82843			0.778958			0.389479	−	0.921035i	$-0.372655\pi$
$101$	7.82843			0.778958			0.389479	+	0.921035i	$0.372655\pi$
$102$	−3.12132	+	5.40629i	−0.309057	+	0.535302i
$103$	−4.79289	+	8.30153i	−0.472258	+	0.817975i	−0.999496	−	0.0317430i	$-0.989894\pi$
$103$	−4.79289	+	8.30153i	−0.472258	+	0.817975i	0.527238	+	0.849717i	$0.323228\pi$
$104$	−2.82843	+	4.89898i	−0.277350	+	0.480384i
$105$	−3.41421	−	5.91359i	−0.333193	−	0.577107i
$106$	3.74264	−	6.48244i	0.363517	−	0.629631i
$107$	−1.62132	−	2.80821i	−0.156739	−	0.271480i	0.776952	−	0.629560i	$-0.216765\pi$
$107$	−1.62132	−	2.80821i	−0.156739	−	0.271480i	−0.933691	+	0.358080i	$0.883431\pi$
$108$	−1.00000			−0.0962250
$109$	9.75736			0.934586			0.467293	−	0.884103i	$-0.345229\pi$
$109$	9.75736			0.934586			0.467293	+	0.884103i	$0.345229\pi$
$110$	3.41421	+	5.91359i	0.325532	+	0.563839i
$111$	3.53553	−	6.12372i	0.335578	−	0.581238i
$112$	−1.20711	−	2.09077i	−0.114061	−	0.197559i
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	−0.614231	−	0.789127i	$-0.710534\pi$
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	0.990519	+	0.137376i	$0.0438669\pi$
$114$	2.70711	−	4.68885i	0.253544	−	0.439151i
$115$	−8.82843	+	15.2913i	−0.823255	+	1.42592i
$116$	5.82843			0.541156
$117$	−2.82843	−	4.89898i	−0.261488	−	0.452911i
$118$	3.44975	+	5.97514i	0.317575	+	0.550056i
$119$	7.53553	−	13.0519i	0.690781	−	1.19647i
$120$	2.82843			0.258199
$121$	2.58579	+	4.47871i	0.235071	+	0.407156i
$122$	−7.07107			−0.640184
$123$	−6.58579			−0.593820
$124$	−0.378680	−	5.55487i	−0.0340064	−	0.498842i
$125$	5.65685			0.505964
$126$	2.41421			0.215075
$127$	10.2071	+	17.6792i	0.905734	+	1.56878i	0.819929	+	0.572466i	$0.194013\pi$
$127$	10.2071	+	17.6792i	0.905734	+	1.56878i	0.0858057	+	0.996312i	$0.472654\pi$
$128$	1.00000			0.0883883
$129$	−0.828427	+	1.43488i	−0.0729389	+	0.126334i
$130$	8.00000	+	13.8564i	0.701646	+	1.21529i
$131$	0.656854	+	1.13770i	0.0573896	+	0.0994017i	0.893293	−	0.449475i	$-0.148389\pi$
$131$	0.656854	+	1.13770i	0.0573896	+	0.0994017i	−0.835903	+	0.548877i	$0.815056\pi$
$132$	−2.41421			−0.210130
$133$	−6.53553	+	11.3199i	−0.566703	+	0.981558i
$134$	−3.12132	+	5.40629i	−0.269641	+	0.467032i
$135$	−1.41421	+	2.44949i	−0.121716	+	0.210819i
$136$	3.12132	+	5.40629i	0.267651	+	0.463585i
$137$	−0.878680	+	1.52192i	−0.0750707	+	0.130026i	−0.901117	−	0.433576i	$-0.857252\pi$
$137$	−0.878680	+	1.52192i	−0.0750707	+	0.130026i	0.826046	+	0.563602i	$0.190585\pi$
$138$	−3.12132	−	5.40629i	−0.265704	−	0.460214i
$139$	−16.2426			−1.37768			−0.688841	−	0.724912i	$-0.741880\pi$
$139$	−16.2426			−1.37768			−0.688841	+	0.724912i	$0.741880\pi$
$140$	−6.82843			−0.577107
$141$	4.12132	+	7.13834i	0.347078	+	0.601156i
$142$	0.828427	−	1.43488i	0.0695201	−	0.120412i
$143$	−6.82843	−	11.8272i	−0.571022	−	0.989039i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	8.24264	−	14.2767i	0.684514	−	1.18561i
$146$	2.24264	−	3.88437i	0.185602	−	0.321473i
$147$	1.17157			0.0966297
$148$	−3.53553	−	6.12372i	−0.290619	−	0.503367i
$149$	−9.74264	−	16.8747i	−0.798148	−	1.38243i	−0.920821	−	0.389986i	$-0.872480\pi$
$149$	−9.74264	−	16.8747i	−0.798148	−	1.38243i	0.122673	−	0.992447i	$-0.460854\pi$
$150$	1.50000	−	2.59808i	0.122474	−	0.212132i
$151$	18.0711			1.47060			0.735301	−	0.677740i	$-0.237041\pi$
$151$	18.0711			1.47060			0.735301	+	0.677740i	$0.237041\pi$
$152$	−2.70711	−	4.68885i	−0.219575	−	0.380316i
$153$	−6.24264			−0.504688
$154$	5.82843			0.469668
$155$	−14.1421	−	6.92820i	−1.13592	−	0.556487i
$156$	−5.65685			−0.452911
$157$	−7.75736			−0.619105			−0.309552	−	0.950882i	$-0.600179\pi$
$157$	−7.75736			−0.619105			−0.309552	+	0.950882i	$0.600179\pi$
$158$	−6.24264	−	10.8126i	−0.496638	−	0.860202i
$159$	7.48528			0.593621
$160$	1.41421	−	2.44949i	0.111803	−	0.193649i
$161$	7.53553	+	13.0519i	0.593883	+	1.02864i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−1.75736			−0.137647			−0.0688235	−	0.997629i	$-0.521925\pi$
$163$	−1.75736			−0.137647			−0.0688235	+	0.997629i	$0.521925\pi$
$164$	−3.29289	+	5.70346i	−0.257132	+	0.445365i
$165$	−3.41421	+	5.91359i	−0.265796	+	0.460372i
$166$	1.79289	−	3.10538i	0.139156	−	0.241024i
$167$	3.94975	+	6.84116i	0.305641	+	0.529385i	0.977404	−	0.211381i	$-0.0677961\pi$
$167$	3.94975	+	6.84116i	0.305641	+	0.529385i	−0.671763	+	0.740766i	$0.734463\pi$
$168$	1.20711	−	2.09077i	0.0931303	−	0.161306i
$169$	−9.50000	−	16.4545i	−0.730769	−	1.26573i
$170$	17.6569			1.35422
$171$	5.41421			0.414035
$172$	0.828427	+	1.43488i	0.0631670	+	0.109408i
$173$	−10.3995	+	18.0125i	−0.790659	+	1.36946i	0.134900	+	0.990859i	$0.456929\pi$
$173$	−10.3995	+	18.0125i	−0.790659	+	1.36946i	−0.925559	+	0.378602i	$0.876405\pi$
$174$	2.91421	+	5.04757i	0.220926	+	0.382655i
$175$	−3.62132	+	6.27231i	−0.273746	+	0.474142i
$176$	−1.20711	+	2.09077i	−0.0909891	+	0.157598i
$177$	−3.44975	+	5.97514i	−0.259299	+	0.449119i
$178$	−9.31371			−0.698092
$179$	−8.37868	−	14.5123i	−0.626252	−	1.08470i	−0.988297	−	0.152540i	$-0.951255\pi$
$179$	−8.37868	−	14.5123i	−0.626252	−	1.08470i	0.362045	−	0.932160i	$-0.382079\pi$
$180$	1.41421	+	2.44949i	0.105409	+	0.182574i
$181$	−9.82843	+	17.0233i	−0.730541	+	1.26533i	0.226111	+	0.974102i	$0.427399\pi$
$181$	−9.82843	+	17.0233i	−0.730541	+	1.26533i	−0.956652	+	0.291233i	$0.905935\pi$
$182$	13.6569			1.01231
$183$	−3.53553	−	6.12372i	−0.261354	−	0.452679i
$184$	−6.24264			−0.460214
$185$	−20.0000			−1.47043
$186$	4.62132	−	3.10538i	0.338852	−	0.227698i
$187$	−15.0711			−1.10211
$188$	8.24264			0.601156
$189$	1.20711	+	2.09077i	0.0878041	+	0.152081i
$190$	−15.3137			−1.11097
$191$	3.12132	−	5.40629i	0.225851	−	0.391185i	−0.730724	−	0.682673i	$-0.760817\pi$
$191$	3.12132	−	5.40629i	0.225851	−	0.391185i	0.956574	+	0.291488i	$0.0941505\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	1.32843	+	2.30090i	0.0956223	+	0.165623i	0.909868	−	0.414898i	$-0.136183\pi$
$193$	1.32843	+	2.30090i	0.0956223	+	0.165623i	−0.814246	+	0.580520i	$0.802849\pi$
$194$	8.31371			0.596889
$195$	−8.00000	+	13.8564i	−0.572892	+	0.992278i
$196$	0.585786	−	1.01461i	0.0418419	−	0.0724723i
$197$	−1.41421	+	2.44949i	−0.100759	+	0.174519i	−0.911997	−	0.410196i	$-0.865460\pi$
$197$	−1.41421	+	2.44949i	−0.100759	+	0.174519i	0.811239	+	0.584715i	$0.198794\pi$
$198$	−1.20711	−	2.09077i	−0.0857853	−	0.148585i
$199$	2.37868	−	4.11999i	0.168620	−	0.292059i	−0.769315	−	0.638870i	$-0.779402\pi$
$199$	2.37868	−	4.11999i	0.168620	−	0.292059i	0.937935	+	0.346811i	$0.112736\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$	−6.24264			−0.440322
$202$	7.82843			0.550806
$203$	−7.03553	−	12.1859i	−0.493798	−	0.855283i
$204$	−3.12132	+	5.40629i	−0.218536	+	0.378516i
$205$	9.31371	+	16.1318i	0.650498	+	1.12669i
$206$	−4.79289	+	8.30153i	−0.333937	+	0.578395i
$207$	3.12132	−	5.40629i	0.216947	−	0.375763i
$208$	−2.82843	+	4.89898i	−0.196116	+	0.339683i
$209$	13.0711			0.904145
$210$	−3.41421	−	5.91359i	−0.235603	−	0.408077i
$211$	−11.7782	−	20.4004i	−0.810843	−	1.40442i	−0.912275	−	0.409579i	$-0.865676\pi$
$211$	−11.7782	−	20.4004i	−0.810843	−	1.40442i	0.101432	−	0.994842i	$-0.467658\pi$
$212$	3.74264	−	6.48244i	0.257046	−	0.445216i
$213$	1.65685			0.113526
$214$	−1.62132	−	2.80821i	−0.110831	−	0.191965i
$215$	4.68629			0.319602
$216$	−1.00000			−0.0680414
$217$	−11.1569	+	7.49706i	−0.757377	+	0.508933i
$218$	9.75736			0.660852
$219$	4.48528			0.303087
$220$	3.41421	+	5.91359i	0.230186	+	0.398694i
$221$	−35.3137			−2.37546
$222$	3.53553	−	6.12372i	0.237289	−	0.410997i
$223$	3.62132	+	6.27231i	0.242502	+	0.420025i	0.961426	−	0.275063i	$-0.0886987\pi$
$223$	3.62132	+	6.27231i	0.242502	+	0.420025i	−0.718925	+	0.695088i	$0.755365\pi$
$224$	−1.20711	−	2.09077i	−0.0806532	−	0.139695i
$225$	3.00000			0.200000
$226$	4.00000	−	6.92820i	0.266076	−	0.460857i
$227$	−9.37868	+	16.2443i	−0.622485	+	1.07818i	0.366537	+	0.930404i	$0.380543\pi$
$227$	−9.37868	+	16.2443i	−0.622485	+	1.07818i	−0.989021	+	0.147772i	$0.952790\pi$
$228$	2.70711	−	4.68885i	0.179283	−	0.310526i
$229$	−12.6066	−	21.8353i	−0.833068	−	1.44292i	−0.895594	−	0.444872i	$-0.853249\pi$
$229$	−12.6066	−	21.8353i	−0.833068	−	1.44292i	0.0625263	−	0.998043i	$-0.480084\pi$
$230$	−8.82843	+	15.2913i	−0.582129	+	1.00828i
$231$	2.91421	+	5.04757i	0.191741	+	0.332105i
$232$	5.82843			0.382655
$233$	27.5563			1.80528			0.902638	−	0.430400i	$-0.141628\pi$
$233$	27.5563			1.80528			0.902638	+	0.430400i	$0.141628\pi$
$234$	−2.82843	−	4.89898i	−0.184900	−	0.320256i
$235$	11.6569	−	20.1903i	0.760409	−	1.31707i
$236$	3.44975	+	5.97514i	0.224559	+	0.388948i
$237$	6.24264	−	10.8126i	0.405503	−	0.702352i
$238$	7.53553	−	13.0519i	0.488456	−	0.846031i
$239$	−3.65685	+	6.33386i	−0.236542	+	0.409703i	−0.959720	−	0.280959i	$-0.909347\pi$
$239$	−3.65685	+	6.33386i	−0.236542	+	0.409703i	0.723178	+	0.690662i	$0.242681\pi$
$240$	2.82843			0.182574
$241$	−7.57107	−	13.1135i	−0.487695	−	0.844713i	0.512205	−	0.858864i	$-0.328829\pi$
$241$	−7.57107	−	13.1135i	−0.487695	−	0.844713i	−0.999900	+	0.0141504i	$0.995496\pi$
$242$	2.58579	+	4.47871i	0.166221	+	0.287903i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−7.07107			−0.452679
$245$	−1.65685	−	2.86976i	−0.105853	−	0.183342i
$246$	−6.58579			−0.419894
$247$	30.6274			1.94878
$248$	−0.378680	−	5.55487i	−0.0240462	−	0.352735i
$249$	3.58579			0.227240
$250$	5.65685			0.357771
$251$	3.75736	+	6.50794i	0.237162	+	0.410777i	0.959899	−	0.280346i	$-0.0904493\pi$
$251$	3.75736	+	6.50794i	0.237162	+	0.410777i	−0.722737	+	0.691124i	$0.757116\pi$
$252$	2.41421			0.152081
$253$	7.53553	−	13.0519i	0.473755	−	0.820568i
$254$	10.2071	+	17.6792i	0.640451	+	1.10929i
$255$	8.82843	+	15.2913i	0.552858	+	0.957577i
$256$	1.00000			0.0625000
$257$	−6.70711	+	11.6170i	−0.418378	+	0.724652i	−0.995776	−	0.0918107i	$-0.970735\pi$
$257$	−6.70711	+	11.6170i	−0.418378	+	0.724652i	0.577399	+	0.816462i	$0.304068\pi$
$258$	−0.828427	+	1.43488i	−0.0515756	+	0.0893316i
$259$	−8.53553	+	14.7840i	−0.530372	+	0.918632i
$260$	8.00000	+	13.8564i	0.496139	+	0.859338i
$261$	−2.91421	+	5.04757i	−0.180385	+	0.312436i
$262$	0.656854	+	1.13770i	0.0405806	+	0.0702876i
$263$	15.1716			0.935519			0.467760	−	0.883856i	$-0.345061\pi$
$263$	15.1716			0.935519			0.467760	+	0.883856i	$0.345061\pi$
$264$	−2.41421			−0.148585
$265$	−10.5858	−	18.3351i	−0.650280	−	1.12632i
$266$	−6.53553	+	11.3199i	−0.400719	+	0.694066i
$267$	−4.65685	−	8.06591i	−0.284995	−	0.493626i
$268$	−3.12132	+	5.40629i	−0.190665	+	0.330241i
$269$	−0.656854	+	1.13770i	−0.0400491	+	0.0693671i	−0.885355	−	0.464915i	$-0.846085\pi$
$269$	−0.656854	+	1.13770i	−0.0400491	+	0.0693671i	0.845306	+	0.534282i	$0.179418\pi$
$270$	−1.41421	+	2.44949i	−0.0860663	+	0.149071i
$271$	29.2426			1.77636			0.888182	−	0.459492i	$-0.151968\pi$
$271$	29.2426			1.77636			0.888182	+	0.459492i	$0.151968\pi$
$272$	3.12132	+	5.40629i	0.189258	+	0.327804i
$273$	6.82843	+	11.8272i	0.413275	+	0.715814i
$274$	−0.878680	+	1.52192i	−0.0530830	+	0.0919424i
$275$	7.24264			0.436748
$276$	−3.12132	−	5.40629i	−0.187881	−	0.325420i
$277$	3.41421			0.205140			0.102570	−	0.994726i	$-0.467293\pi$
$277$	3.41421			0.205140			0.102570	+	0.994726i	$0.467293\pi$
$278$	−16.2426			−0.974169
$279$	5.00000	+	2.44949i	0.299342	+	0.146647i
$280$	−6.82843			−0.408077
$281$	32.6274			1.94639			0.973194	−	0.229985i	$-0.0738676\pi$
$281$	32.6274			1.94639			0.973194	+	0.229985i	$0.0738676\pi$
$282$	4.12132	+	7.13834i	0.245421	+	0.425082i
$283$	−11.3137			−0.672530			−0.336265	−	0.941767i	$-0.609164\pi$
$283$	−11.3137			−0.672530			−0.336265	+	0.941767i	$0.609164\pi$
$284$	0.828427	−	1.43488i	0.0491581	−	0.0851443i
$285$	−7.65685	−	13.2621i	−0.453553	−	0.785577i
$286$	−6.82843	−	11.8272i	−0.403773	−	0.699356i
$287$	15.8995			0.938518
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−10.9853	+	19.0271i	−0.646193	+	1.11924i
$290$	8.24264	−	14.2767i	0.484025	−	0.838355i
$291$	4.15685	+	7.19988i	0.243679	+	0.422065i
$292$	2.24264	−	3.88437i	0.131241	−	0.227315i
$293$	11.7426	+	20.3389i	0.686012	+	1.18821i	0.973117	+	0.230309i	$0.0739738\pi$
$293$	11.7426	+	20.3389i	0.686012	+	1.18821i	−0.287105	+	0.957899i	$0.592693\pi$
$294$	1.17157			0.0683275
$295$	19.5147			1.13619
$296$	−3.53553	−	6.12372i	−0.205499	−	0.355934i
$297$	1.20711	−	2.09077i	0.0700434	−	0.121319i
$298$	−9.74264	−	16.8747i	−0.564376	−	0.977528i
$299$	17.6569	−	30.5826i	1.02112	−	1.76864i
$300$	1.50000	−	2.59808i	0.0866025	−	0.150000i
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$	18.0711			1.03987
$303$	3.91421	+	6.77962i	0.224866	+	0.389479i
$304$	−2.70711	−	4.68885i	−0.155263	−	0.268924i
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$	−6.24264			−0.356868
$307$	8.70711	+	15.0812i	0.496941	+	0.860727i	0.999994	−	0.00352883i	$-0.00112326\pi$
$307$	8.70711	+	15.0812i	0.496941	+	0.860727i	−0.503053	+	0.864256i	$0.667790\pi$
$308$	5.82843			0.332105
$309$	−9.58579			−0.545316
$310$	−14.1421	−	6.92820i	−0.803219	−	0.393496i
$311$	−17.6569			−1.00123			−0.500614	−	0.865671i	$-0.666892\pi$
$311$	−17.6569			−1.00123			−0.500614	+	0.865671i	$0.666892\pi$
$312$	−5.65685			−0.320256
$313$	−11.8137	−	20.4619i	−0.667750	−	1.15658i	−0.978532	−	0.206096i	$-0.933924\pi$
$313$	−11.8137	−	20.4619i	−0.667750	−	1.15658i	0.310781	−	0.950481i	$-0.399409\pi$
$314$	−7.75736			−0.437773
$315$	3.41421	−	5.91359i	0.192369	−	0.333193i
$316$	−6.24264	−	10.8126i	−0.351176	−	0.608255i
$317$	−14.2279	−	24.6435i	−0.799120	−	1.38412i	−0.920190	−	0.391472i	$-0.871966\pi$
$317$	−14.2279	−	24.6435i	−0.799120	−	1.38412i	0.121070	−	0.992644i	$-0.461367\pi$
$318$	7.48528			0.419754
$319$	−7.03553	+	12.1859i	−0.393914	+	0.682280i
$320$	1.41421	−	2.44949i	0.0790569	−	0.136931i
$321$	1.62132	−	2.80821i	0.0904933	−	0.156739i
$322$	7.53553	+	13.0519i	0.419939	+	0.727355i
$323$	16.8995	−	29.2708i	0.940313	−	1.62867i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	16.9706			0.941357
$326$	−1.75736			−0.0973311
$327$	4.87868	+	8.45012i	0.269792	+	0.467293i
$328$	−3.29289	+	5.70346i	−0.181820	+	0.314921i
$329$	−9.94975	−	17.2335i	−0.548547	−	0.950112i
$330$	−3.41421	+	5.91359i	−0.187946	+	0.325532i
$331$	0.878680	−	1.52192i	0.0482966	−	0.0836522i	−0.840866	−	0.541243i	$-0.817954\pi$
$331$	0.878680	−	1.52192i	0.0482966	−	0.0836522i	0.889163	+	0.457590i	$0.151287\pi$
$332$	1.79289	−	3.10538i	0.0983978	−	0.170430i
$333$	7.07107			0.387492
$334$	3.94975	+	6.84116i	0.216121	+	0.374332i
$335$	8.82843	+	15.2913i	0.482349	+	0.835452i
$336$	1.20711	−	2.09077i	0.0658531	−	0.114061i
$337$	1.34315			0.0731658			0.0365829	−	0.999331i	$-0.488353\pi$
$337$	1.34315			0.0731658			0.0365829	+	0.999331i	$0.488353\pi$
$338$	−9.50000	−	16.4545i	−0.516732	−	0.895006i
$339$	8.00000			0.434500
$340$	17.6569			0.957577
$341$	12.0711	+	5.91359i	0.653685	+	0.320239i
$342$	5.41421			0.292767
$343$	−19.7279			−1.06521
$344$	0.828427	+	1.43488i	0.0446658	+	0.0773634i
$345$	−17.6569			−0.950613
$346$	−10.3995	+	18.0125i	−0.559080	+	0.968356i
$347$	6.27817	+	10.8741i	0.337030	+	0.583753i	0.983873	−	0.178870i	$-0.0572443\pi$
$347$	6.27817	+	10.8741i	0.337030	+	0.583753i	−0.646843	+	0.762624i	$0.723911\pi$
$348$	2.91421	+	5.04757i	0.156218	+	0.270578i
$349$	−23.8995			−1.27931			−0.639655	−	0.768662i	$-0.720923\pi$
$349$	−23.8995			−1.27931			−0.639655	+	0.768662i	$0.720923\pi$
$350$	−3.62132	+	6.27231i	−0.193568	+	0.335269i
$351$	2.82843	−	4.89898i	0.150970	−	0.261488i
$352$	−1.20711	+	2.09077i	−0.0643390	+	0.111438i
$353$	−1.82843	−	3.16693i	−0.0973174	−	0.168559i	0.813256	−	0.581906i	$-0.197693\pi$
$353$	−1.82843	−	3.16693i	−0.0973174	−	0.168559i	−0.910573	+	0.413347i	$0.864360\pi$
$354$	−3.44975	+	5.97514i	−0.183352	+	0.317575i
$355$	−2.34315	−	4.05845i	−0.124361	−	0.215400i
$356$	−9.31371			−0.493626
$357$	15.0711			0.797645
$358$	−8.37868	−	14.5123i	−0.442827	−	0.766999i
$359$	−0.0502525	+	0.0870399i	−0.00265223	+	0.00459379i	−0.867348	−	0.497701i	$-0.834178\pi$
$359$	−0.0502525	+	0.0870399i	−0.00265223	+	0.00459379i	0.864696	+	0.502295i	$0.167511\pi$
$360$	1.41421	+	2.44949i	0.0745356	+	0.129099i
$361$	−5.15685	+	8.93193i	−0.271413	+	0.470102i
$362$	−9.82843	+	17.0233i	−0.516571	+	0.894727i
$363$	−2.58579	+	4.47871i	−0.135719	+	0.235071i
$364$	13.6569			0.715814
$365$	−6.34315	−	10.9867i	−0.332015	−	0.575068i
$366$	−3.53553	−	6.12372i	−0.184805	−	0.320092i
$367$	−6.34315	+	10.9867i	−0.331110	+	0.573498i	−0.982730	−	0.185047i	$-0.940756\pi$
$367$	−6.34315	+	10.9867i	−0.331110	+	0.573498i	0.651620	+	0.758545i	$0.274090\pi$
$368$	−6.24264			−0.325420
$369$	−3.29289	−	5.70346i	−0.171421	−	0.296910i
$370$	−20.0000			−1.03975
$371$	−18.0711			−0.938203
$372$	4.62132	−	3.10538i	0.239604	−	0.161007i
$373$	−17.0711			−0.883906			−0.441953	−	0.897038i	$-0.645714\pi$
$373$	−17.0711			−0.883906			−0.441953	+	0.897038i	$0.645714\pi$
$374$	−15.0711			−0.779306
$375$	2.82843	+	4.89898i	0.146059	+	0.252982i
$376$	8.24264			0.425082
$377$	−16.4853	+	28.5533i	−0.849035	+	1.47057i
$378$	1.20711	+	2.09077i	0.0620869	+	0.107538i
$379$	2.41421	+	4.18154i	0.124010	+	0.214791i	0.921345	−	0.388745i	$-0.127091\pi$
$379$	2.41421	+	4.18154i	0.124010	+	0.214791i	−0.797336	+	0.603536i	$0.793758\pi$
$380$	−15.3137			−0.785577
$381$	−10.2071	+	17.6792i	−0.522926	+	0.905734i
$382$	3.12132	−	5.40629i	0.159701	−	0.276610i
$383$	−1.94975	+	3.37706i	−0.0996274	+	0.172560i	−0.911530	−	0.411233i	$-0.865098\pi$
$383$	−1.94975	+	3.37706i	−0.0996274	+	0.172560i	0.811903	+	0.583792i	$0.198432\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	8.24264	−	14.2767i	0.420084	−	0.727607i
$386$	1.32843	+	2.30090i	0.0676152	+	0.117113i
$387$	−1.65685			−0.0842226
$388$	8.31371			0.422065
$389$	1.65685	+	2.86976i	0.0840058	+	0.145502i	0.904967	−	0.425481i	$-0.139895\pi$
$389$	1.65685	+	2.86976i	0.0840058	+	0.145502i	−0.820961	+	0.570984i	$0.806562\pi$
$390$	−8.00000	+	13.8564i	−0.405096	+	0.701646i
$391$	−19.4853	−	33.7495i	−0.985413	−	1.70679i
$392$	0.585786	−	1.01461i	0.0295867	−	0.0512456i
$393$	−0.656854	+	1.13770i	−0.0331339	+	0.0573896i
$394$	−1.41421	+	2.44949i	−0.0712470	+	0.123404i
$395$	−35.3137			−1.77683
$396$	−1.20711	−	2.09077i	−0.0606594	−	0.105065i
$397$	11.4853	+	19.8931i	0.576430	+	0.998406i	0.995885	+	0.0906295i	$0.0288879\pi$
$397$	11.4853	+	19.8931i	0.576430	+	0.998406i	−0.419455	+	0.907776i	$0.637779\pi$
$398$	2.37868	−	4.11999i	0.119232	−	0.206517i
$399$	−13.0711			−0.654372
$400$	−1.50000	−	2.59808i	−0.0750000	−	0.129904i
$401$	17.6569			0.881741			0.440871	−	0.897571i	$-0.354670\pi$
$401$	17.6569			0.881741			0.440871	+	0.897571i	$0.354670\pi$
$402$	−6.24264			−0.311355
$403$	28.2843	+	13.8564i	1.40894	+	0.690237i
$404$	7.82843			0.389479
$405$	−2.82843			−0.140546
$406$	−7.03553	−	12.1859i	−0.349168	−	0.604776i
$407$	17.0711			0.846181
$408$	−3.12132	+	5.40629i	−0.154528	+	0.267651i
$409$	16.0563	+	27.8104i	0.793935	+	1.37514i	0.923513	+	0.383567i	$0.125305\pi$
$409$	16.0563	+	27.8104i	0.793935	+	1.37514i	−0.129578	+	0.991569i	$0.541362\pi$
$410$	9.31371	+	16.1318i	0.459971	+	0.796694i
$411$	−1.75736			−0.0866841
$412$	−4.79289	+	8.30153i	−0.236129	+	0.408987i
$413$	8.32843	−	14.4253i	0.409815	−	0.709821i
$414$	3.12132	−	5.40629i	0.153405	−	0.265704i
$415$	−5.07107	−	8.78335i	−0.248929	−	0.431158i
$416$	−2.82843	+	4.89898i	−0.138675	+	0.240192i
$417$	−8.12132	−	14.0665i	−0.397703	−	0.688841i
$418$	13.0711			0.639327
$419$	−33.5269			−1.63790			−0.818948	−	0.573867i	$-0.805443\pi$
$419$	−33.5269			−1.63790			−0.818948	+	0.573867i	$0.805443\pi$
$420$	−3.41421	−	5.91359i	−0.166597	−	0.288554i
$421$	9.87868	−	17.1104i	0.481457	−	0.833909i	−0.518316	−	0.855189i	$-0.673441\pi$
$421$	9.87868	−	17.1104i	0.481457	−	0.833909i	0.999774	+	0.0212804i	$0.00677428\pi$
$422$	−11.7782	−	20.4004i	−0.573353	−	0.993076i
$423$	−4.12132	+	7.13834i	−0.200385	+	0.347078i
$424$	3.74264	−	6.48244i	0.181759	−	0.314815i
$425$	9.36396	−	16.2189i	0.454219	−	0.786730i
$426$	1.65685			0.0802749
$427$	8.53553	+	14.7840i	0.413063	+	0.715447i
$428$	−1.62132	−	2.80821i	−0.0783695	−	0.135740i
$429$	6.82843	−	11.8272i	0.329680	−	0.571022i
$430$	4.68629			0.225993
$431$	−3.29289	−	5.70346i	−0.158613	−	0.274726i	0.775756	−	0.631033i	$-0.217369\pi$
$431$	−3.29289	−	5.70346i	−0.158613	−	0.274726i	−0.934369	+	0.356307i	$0.884036\pi$
$432$	−1.00000			−0.0481125
$433$	−26.1421			−1.25631			−0.628155	−	0.778088i	$-0.716190\pi$
$433$	−26.1421			−1.25631			−0.628155	+	0.778088i	$0.716190\pi$
$434$	−11.1569	+	7.49706i	−0.535546	+	0.359870i
$435$	16.4853			0.790409
$436$	9.75736			0.467293
$437$	16.8995	+	29.2708i	0.808412	+	1.40021i
$438$	4.48528			0.214315
$439$	19.1066	−	33.0936i	0.911908	−	1.57947i	0.100543	−	0.994933i	$-0.467942\pi$
$439$	19.1066	−	33.0936i	0.911908	−	1.57947i	0.811366	−	0.584539i	$-0.198725\pi$
$440$	3.41421	+	5.91359i	0.162766	+	0.281919i
$441$	0.585786	+	1.01461i	0.0278946	+	0.0483149i
$442$	−35.3137			−1.67970
$443$	−5.00000	+	8.66025i	−0.237557	+	0.411461i	−0.960013	−	0.279956i	$-0.909680\pi$
$443$	−5.00000	+	8.66025i	−0.237557	+	0.411461i	0.722456	+	0.691417i	$0.243013\pi$
$444$	3.53553	−	6.12372i	0.167789	−	0.290619i
$445$	−13.1716	+	22.8138i	−0.624392	+	1.08148i
$446$	3.62132	+	6.27231i	0.171474	+	0.297003i
$447$	9.74264	−	16.8747i	0.460811	−	0.798148i
$448$	−1.20711	−	2.09077i	−0.0570304	−	0.0987796i
$449$	−22.2843			−1.05166			−0.525830	−	0.850590i	$-0.676245\pi$
$449$	−22.2843			−1.05166			−0.525830	+	0.850590i	$0.676245\pi$
$450$	3.00000			0.141421
$451$	−7.94975	−	13.7694i	−0.374339	−	0.648374i
$452$	4.00000	−	6.92820i	0.188144	−	0.325875i
$453$	9.03553	+	15.6500i	0.424526	+	0.735301i
$454$	−9.37868	+	16.2443i	−0.440163	+	0.762385i
$455$	19.3137	−	33.4523i	0.905441	−	1.56827i
$456$	2.70711	−	4.68885i	0.126772	−	0.219575i
$457$	−23.7990			−1.11327			−0.556635	−	0.830757i	$-0.687908\pi$
$457$	−23.7990			−1.11327			−0.556635	+	0.830757i	$0.687908\pi$
$458$	−12.6066	−	21.8353i	−0.589068	−	1.02030i
$459$	−3.12132	−	5.40629i	−0.145691	−	0.252344i
$460$	−8.82843	+	15.2913i	−0.411628	+	0.712960i
$461$	−24.1716			−1.12578			−0.562891	−	0.826531i	$-0.690311\pi$
$461$	−24.1716			−1.12578			−0.562891	+	0.826531i	$0.690311\pi$
$462$	2.91421	+	5.04757i	0.135581	+	0.234834i
$463$	0.414214			0.0192501			0.00962507	−	0.999954i	$-0.496936\pi$
$463$	0.414214			0.0192501			0.00962507	+	0.999954i	$0.496936\pi$
$464$	5.82843			0.270578
$465$	−1.07107	−	15.7116i	−0.0496696	−	0.728606i
$466$	27.5563			1.27652
$467$	−0.0710678			−0.00328863			−0.00164431	−	0.999999i	$-0.500523\pi$
$467$	−0.0710678			−0.00328863			−0.00164431	+	0.999999i	$0.500523\pi$
$468$	−2.82843	−	4.89898i	−0.130744	−	0.226455i
$469$	15.0711			0.695917
$470$	11.6569	−	20.1903i	0.537691	−	0.931307i
$471$	−3.87868	−	6.71807i	−0.178720	−	0.309552i
$472$	3.44975	+	5.97514i	0.158787	+	0.275028i
$473$	−4.00000			−0.183920
$474$	6.24264	−	10.8126i	0.286734	−	0.496638i
$475$	−8.12132	+	14.0665i	−0.372632	+	0.645417i
$476$	7.53553	−	13.0519i	0.345391	−	0.598234i
$477$	3.74264	+	6.48244i	0.171364	+	0.296811i
$478$	−3.65685	+	6.33386i	−0.167261	+	0.289704i
$479$	0.221825	+	0.384213i	0.0101355	+	0.0175551i	0.871049	−	0.491197i	$-0.163440\pi$
$479$	0.221825	+	0.384213i	0.0101355	+	0.0175551i	−0.860913	+	0.508752i	$0.830107\pi$
$480$	2.82843			0.129099
$481$	40.0000			1.82384
$482$	−7.57107	−	13.1135i	−0.344853	−	0.597302i
$483$	−7.53553	+	13.0519i	−0.342879	+	0.593883i
$484$	2.58579	+	4.47871i	0.117536	+	0.203578i
$485$	11.7574	−	20.3643i	0.533874	−	0.924697i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	9.34924	−	16.1934i	0.423655	−	0.733791i	−0.572639	−	0.819808i	$-0.694080\pi$
$487$	9.34924	−	16.1934i	0.423655	−	0.733791i	0.996294	+	0.0860162i	$0.0274137\pi$
$488$	−7.07107			−0.320092
$489$	−0.878680	−	1.52192i	−0.0397353	−	0.0688235i
$490$	−1.65685	−	2.86976i	−0.0748490	−	0.129642i
$491$	−19.1066	+	33.0936i	−0.862269	+	1.49349i	0.00746482	+	0.999972i	$0.497624\pi$
$491$	−19.1066	+	33.0936i	−0.862269	+	1.49349i	−0.869734	+	0.493521i	$0.835709\pi$
$492$	−6.58579			−0.296910
$493$	18.1924	+	31.5101i	0.819344	+	1.41915i
$494$	30.6274			1.37799
$495$	−6.82843			−0.306915
$496$	−0.378680	−	5.55487i	−0.0170032	−	0.249421i
$497$	−4.00000			−0.179425
$498$	3.58579			0.160683
$499$	7.02082	+	12.1604i	0.314295	+	0.544375i	0.979287	−	0.202475i	$-0.0648986\pi$
$499$	7.02082	+	12.1604i	0.314295	+	0.544375i	−0.664992	+	0.746850i	$0.731565\pi$
$500$	5.65685			0.252982
$501$	−3.94975	+	6.84116i	−0.176462	+	0.305641i
$502$	3.75736	+	6.50794i	0.167699	+	0.290463i
$503$	17.9497	+	31.0899i	0.800340	+	1.38623i	0.919393	+	0.393341i	$0.128681\pi$
$503$	17.9497	+	31.0899i	0.800340	+	1.38623i	−0.119053	+	0.992888i	$0.537986\pi$
$504$	2.41421			0.107538
$505$	11.0711	−	19.1757i	0.492656	−	0.853305i
$506$	7.53553	−	13.0519i	0.334995	−	0.580229i
$507$	9.50000	−	16.4545i	0.421910	−	0.730769i
$508$	10.2071	+	17.6792i	0.452867	+	0.784389i
$509$	−1.15685	+	2.00373i	−0.0512767	+	0.0888138i	−0.890524	−	0.454935i	$-0.849662\pi$
$509$	−1.15685	+	2.00373i	−0.0512767	+	0.0888138i	0.839248	+	0.543749i	$0.182996\pi$
$510$	8.82843	+	15.2913i	0.390929	+	0.677109i
$511$	−10.8284			−0.479021
$512$	1.00000			0.0441942
$513$	2.70711	+	4.68885i	0.119522	+	0.207018i
$514$	−6.70711	+	11.6170i	−0.295838	+	0.512406i
$515$	13.5563	+	23.4803i	0.597364	+	1.03467i
$516$	−0.828427	+	1.43488i	−0.0364695	+	0.0631670i
$517$	−9.94975	+	17.2335i	−0.437589	+	0.757927i
$518$	−8.53553	+	14.7840i	−0.375030	+	0.649571i
$519$	−20.7990			−0.912974
$520$	8.00000	+	13.8564i	0.350823	+	0.607644i
$521$	14.1421	+	24.4949i	0.619578	+	1.07314i	0.989563	+	0.144103i	$0.0460297\pi$
$521$	14.1421	+	24.4949i	0.619578	+	1.07314i	−0.369984	+	0.929038i	$0.620637\pi$
$522$	−2.91421	+	5.04757i	−0.127552	+	0.220926i
$523$	35.3137			1.54416			0.772080	−	0.635525i	$-0.219216\pi$
$523$	35.3137			1.54416			0.772080	+	0.635525i	$0.219216\pi$
$524$	0.656854	+	1.13770i	0.0286948	+	0.0497009i
$525$	−7.24264			−0.316095
$526$	15.1716			0.661512
$527$	28.8492	−	19.3858i	1.25669	−	0.844458i
$528$	−2.41421			−0.105065
$529$	15.9706			0.694372
$530$	−10.5858	−	18.3351i	−0.459817	−	0.796427i
$531$	−6.89949			−0.299413
$532$	−6.53553	+	11.3199i	−0.283351	+	0.490779i
$533$	−18.6274	−	32.2636i	−0.806843	−	1.39749i
$534$	−4.65685	−	8.06591i	−0.201522	−	0.349046i
$535$	−9.17157			−0.396522
$536$	−3.12132	+	5.40629i	−0.134821	+	0.233516i
$537$	8.37868	−	14.5123i	0.361567	−	0.626252i
$538$	−0.656854	+	1.13770i	−0.0283190	+	0.0490499i
$539$	1.41421	+	2.44949i	0.0609145	+	0.105507i
$540$	−1.41421	+	2.44949i	−0.0608581	+	0.105409i
$541$	−21.0919	−	36.5322i	−0.906811	−	1.57064i	−0.818468	−	0.574552i	$-0.805176\pi$
$541$	−21.0919	−	36.5322i	−0.906811	−	1.57064i	−0.0883431	−	0.996090i	$-0.528157\pi$
$542$	29.2426			1.25608
$543$	−19.6569			−0.843556
$544$	3.12132	+	5.40629i	0.133826	+	0.231793i
$545$	13.7990	−	23.9006i	0.591084	−	1.02379i
$546$	6.82843	+	11.8272i	0.292230	+	0.506157i
$547$	−0.757359	+	1.31178i	−0.0323823	+	0.0560879i	−0.881762	−	0.471694i	$-0.843643\pi$
$547$	−0.757359	+	1.31178i	−0.0323823	+	0.0560879i	0.849380	+	0.527782i	$0.176976\pi$
$548$	−0.878680	+	1.52192i	−0.0375353	+	0.0650131i
$549$	3.53553	−	6.12372i	0.150893	−	0.261354i
$550$	7.24264			0.308827
$551$	−15.7782	−	27.3286i	−0.672173	−	1.16424i
$552$	−3.12132	−	5.40629i	−0.132852	−	0.230107i
$553$	−15.0711	+	26.1039i	−0.640887	+	1.11005i
$554$	3.41421			0.145056
$555$	−10.0000	−	17.3205i	−0.424476	−	0.735215i
$556$	−16.2426			−0.688841
$557$	−23.0000			−0.974541			−0.487271	−	0.873251i	$-0.662007\pi$
$557$	−23.0000			−0.974541			−0.487271	+	0.873251i	$0.662007\pi$
$558$	5.00000	+	2.44949i	0.211667	+	0.103695i
$559$	−9.37258			−0.396418
$560$	−6.82843			−0.288554
$561$	−7.53553	−	13.0519i	−0.318150	−	0.551053i
$562$	32.6274			1.37630
$563$	2.37868	−	4.11999i	0.100249	−	0.173637i	−0.811538	−	0.584300i	$-0.801369\pi$
$563$	2.37868	−	4.11999i	0.100249	−	0.173637i	0.911787	+	0.410663i	$0.134703\pi$
$564$	4.12132	+	7.13834i	0.173539	+	0.300578i
$565$	−11.3137	−	19.5959i	−0.475971	−	0.824406i
$566$	−11.3137			−0.475551
$567$	−1.20711	+	2.09077i	−0.0506937	+	0.0878041i
$568$	0.828427	−	1.43488i	0.0347600	−	0.0602061i
$569$	−1.17157	+	2.02922i	−0.0491149	+	0.0850695i	−0.889538	−	0.456862i	$-0.848973\pi$
$569$	−1.17157	+	2.02922i	−0.0491149	+	0.0850695i	0.840423	+	0.541931i	$0.182307\pi$
$570$	−7.65685	−	13.2621i	−0.320710	−	0.555487i
$571$	−4.89949	+	8.48617i	−0.205037	+	0.355135i	−0.950145	−	0.311809i	$-0.899065\pi$
$571$	−4.89949	+	8.48617i	−0.205037	+	0.355135i	0.745107	+	0.666945i	$0.232398\pi$
$572$	−6.82843	−	11.8272i	−0.285511	−	0.494519i
$573$	6.24264			0.260790
$574$	15.8995			0.663632
$575$	9.36396	+	16.2189i	0.390504	+	0.676373i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−3.41421	−	5.91359i	−0.142136	−	0.246186i	0.786165	−	0.618017i	$-0.212064\pi$
$577$	−3.41421	−	5.91359i	−0.142136	−	0.246186i	−0.928301	+	0.371831i	$0.878730\pi$
$578$	−10.9853	+	19.0271i	−0.456927	+	0.791422i
$579$	−1.32843	+	2.30090i	−0.0552075	+	0.0956223i
$580$	8.24264	−	14.2767i	0.342257	−	0.592807i
$581$	−8.65685			−0.359147
$582$	4.15685	+	7.19988i	0.172307	+	0.298445i
$583$	9.03553	+	15.6500i	0.374214	+	0.648157i
$584$	2.24264	−	3.88437i	0.0928011	−	0.160736i
$585$	−16.0000			−0.661519
$586$	11.7426	+	20.3389i	0.485084	+	0.840190i
$587$	1.58579			0.0654524			0.0327262	−	0.999464i	$-0.489581\pi$
$587$	1.58579			0.0654524			0.0327262	+	0.999464i	$0.489581\pi$
$588$	1.17157			0.0483149
$589$	−25.0208	+	16.8132i	−1.03096	+	0.692776i
$590$	19.5147			0.803408
$591$	−2.82843			−0.116346
$592$	−3.53553	−	6.12372i	−0.145310	−	0.251684i
$593$	9.55635			0.392432			0.196216	−	0.980561i	$-0.437135\pi$
$593$	9.55635			0.392432			0.196216	+	0.980561i	$0.437135\pi$
$594$	1.20711	−	2.09077i	0.0495282	−	0.0857853i
$595$	−21.3137	−	36.9164i	−0.873777	−	1.51343i
$596$	−9.74264	−	16.8747i	−0.399074	−	0.691217i
$597$	4.75736			0.194706
$598$	17.6569	−	30.5826i	0.722042	−	1.25061i
$599$	−16.0000	+	27.7128i	−0.653742	+	1.13231i	0.328465	+	0.944516i	$0.393469\pi$
$599$	−16.0000	+	27.7128i	−0.653742	+	1.13231i	−0.982208	+	0.187799i	$0.939865\pi$
$600$	1.50000	−	2.59808i	0.0612372	−	0.106066i
$601$	21.3137	+	36.9164i	0.869404	+	1.50585i	0.862606	+	0.505876i	$0.168830\pi$
$601$	21.3137	+	36.9164i	0.869404	+	1.50585i	0.00679782	+	0.999977i	$0.497836\pi$
$602$	2.00000	−	3.46410i	0.0815139	−	0.141186i
$603$	−3.12132	−	5.40629i	−0.127110	−	0.220161i
$604$	18.0711			0.735301
$605$	14.6274			0.594689
$606$	3.91421	+	6.77962i	0.159004	+	0.275403i
$607$	−12.9706	+	22.4657i	−0.526459	+	0.911854i	0.473066	+	0.881027i	$0.343147\pi$
$607$	−12.9706	+	22.4657i	−0.526459	+	0.911854i	−0.999525	+	0.0308265i	$0.990186\pi$
$608$	−2.70711	−	4.68885i	−0.109788	−	0.190158i
$609$	7.03553	−	12.1859i	0.285094	−	0.493798i
$610$	−10.0000	+	17.3205i	−0.404888	+	0.701287i
$611$	−23.3137	+	40.3805i	−0.943172	+	1.63362i
$612$	−6.24264			−0.252344
$613$	18.8284	+	32.6118i	0.760473	+	1.31718i	0.942607	+	0.333904i	$0.108366\pi$
$613$	18.8284	+	32.6118i	0.760473	+	1.31718i	−0.182134	+	0.983274i	$0.558300\pi$
$614$	8.70711	+	15.0812i	0.351390	+	0.608626i
$615$	−9.31371	+	16.1318i	−0.375565	+	0.650498i
$616$	5.82843			0.234834
$617$	−8.60660	−	14.9071i	−0.346489	−	0.600136i	0.639134	−	0.769095i	$-0.279293\pi$
$617$	−8.60660	−	14.9071i	−0.346489	−	0.600136i	−0.985623	+	0.168959i	$0.945959\pi$
$618$	−9.58579			−0.385597
$619$	−1.79899			−0.0723075			−0.0361538	−	0.999346i	$-0.511511\pi$
$619$	−1.79899			−0.0723075			−0.0361538	+	0.999346i	$0.511511\pi$
$620$	−14.1421	−	6.92820i	−0.567962	−	0.278243i
$621$	6.24264			0.250509
$622$	−17.6569			−0.707975
$623$	11.2426	+	19.4728i	0.450427	+	0.780162i
$624$	−5.65685			−0.226455
$625$	15.5000	−	26.8468i	0.620000	−	1.07387i
$626$	−11.8137	−	20.4619i	−0.472171	−	0.817824i
$627$	6.53553	+	11.3199i	0.261004	+	0.452072i
$628$	−7.75736			−0.309552
$629$	22.0711	−	38.2282i	0.880031	−	1.52426i
$630$	3.41421	−	5.91359i	0.136026	−	0.235603i
$631$	−2.86396	+	4.96053i	−0.114012	+	0.197475i	−0.917385	−	0.398002i	$-0.869704\pi$
$631$	−2.86396	+	4.96053i	−0.114012	+	0.197475i	0.803372	+	0.595477i	$0.203037\pi$
$632$	−6.24264	−	10.8126i	−0.248319	−	0.430101i
$633$	11.7782	−	20.4004i	0.468140	−	0.810843i
$634$	−14.2279	−	24.6435i	−0.565063	−	0.978718i
$635$	57.7401			2.29135
$636$	7.48528			0.296811
$637$	3.31371	+	5.73951i	0.131294	+	0.227408i
$638$	−7.03553	+	12.1859i	−0.278539	+	0.482444i
$639$	0.828427	+	1.43488i	0.0327721	+	0.0567629i
$640$	1.41421	−	2.44949i	0.0559017	−	0.0968246i
$641$	3.87868	−	6.71807i	0.153199	−	0.265348i	−0.779203	−	0.626772i	$-0.784376\pi$
$641$	3.87868	−	6.71807i	0.153199	−	0.265348i	0.932402	+	0.361424i	$0.117709\pi$
$642$	1.62132	−	2.80821i	0.0639884	−	0.110831i
$643$	15.6985			0.619088			0.309544	−	0.950885i	$-0.399824\pi$
$643$	15.6985			0.619088			0.309544	+	0.950885i	$0.399824\pi$
$644$	7.53553	+	13.0519i	0.296942	+	0.514318i
$645$	2.34315	+	4.05845i	0.0922613	+	0.159801i
$646$	16.8995	−	29.2708i	0.664902	−	1.15164i
$647$	3.07107			0.120736			0.0603681	−	0.998176i	$-0.480773\pi$
$647$	3.07107			0.120736			0.0603681	+	0.998176i	$0.480773\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−16.6569			−0.653839
$650$	16.9706			0.665640
$651$	−12.0711	−	5.91359i	−0.473102	−	0.231772i
$652$	−1.75736			−0.0688235
$653$	−13.6274			−0.533282			−0.266641	−	0.963796i	$-0.585914\pi$
$653$	−13.6274			−0.533282			−0.266641	+	0.963796i	$0.585914\pi$
$654$	4.87868	+	8.45012i	0.190771	+	0.330426i
$655$	3.71573			0.145186
$656$	−3.29289	+	5.70346i	−0.128566	+	0.222683i
$657$	2.24264	+	3.88437i	0.0874937	+	0.151544i
$658$	−9.94975	−	17.2335i	−0.387882	−	0.671831i
$659$	−16.2132			−0.631577			−0.315788	−	0.948830i	$-0.602269\pi$
$659$	−16.2132			−0.631577			−0.315788	+	0.948830i	$0.602269\pi$
$660$	−3.41421	+	5.91359i	−0.132898	+	0.230186i
$661$	17.0919	−	29.6040i	0.664797	−	1.15146i	−0.314543	−	0.949243i	$-0.601851\pi$
$661$	17.0919	−	29.6040i	0.664797	−	1.15146i	0.979340	−	0.202219i	$-0.0648154\pi$
$662$	0.878680	−	1.52192i	0.0341509	−	0.0591510i
$663$	−17.6569	−	30.5826i	−0.685735	−	1.18773i
$664$	1.79289	−	3.10538i	0.0695778	−	0.120512i
$665$	18.4853	+	32.0174i	0.716828	+	1.24158i
$666$	7.07107			0.273998
$667$	−36.3848			−1.40882
$668$	3.94975	+	6.84116i	0.152820	+	0.264693i
$669$	−3.62132	+	6.27231i	−0.140008	+	0.242502i
$670$	8.82843	+	15.2913i	0.341072	+	0.590754i
$671$	8.53553	−	14.7840i	0.329511	−	0.570729i
$672$	1.20711	−	2.09077i	0.0465652	−	0.0806532i
$673$	8.15685	−	14.1281i	0.314424	−	0.544598i	−0.664891	−	0.746940i	$-0.731522\pi$
$673$	8.15685	−	14.1281i	0.314424	−	0.544598i	0.979315	+	0.202343i	$0.0648554\pi$
$674$	1.34315			0.0517360
$675$	1.50000	+	2.59808i	0.0577350	+	0.100000i
$676$	−9.50000	−	16.4545i	−0.365385	−	0.632865i
$677$	−3.39949	+	5.88810i	−0.130653	+	0.226298i	−0.923929	−	0.382565i	$-0.875041\pi$
$677$	−3.39949	+	5.88810i	−0.130653	+	0.226298i	0.793275	+	0.608863i	$0.208374\pi$
$678$	8.00000			0.307238
$679$	−10.0355	−	17.3821i	−0.385128	−	0.667062i
$680$	17.6569			0.677109
$681$	−18.7574			−0.718784
$682$	12.0711	+	5.91359i	0.462225	+	0.226443i
$683$	−6.75736			−0.258563			−0.129282	−	0.991608i	$-0.541267\pi$
$683$	−6.75736			−0.258563			−0.129282	+	0.991608i	$0.541267\pi$
$684$	5.41421			0.207018
$685$	2.48528	+	4.30463i	0.0949577	+	0.164472i
$686$	−19.7279			−0.753216
$687$	12.6066	−	21.8353i	0.480972	−	0.833068i
$688$	0.828427	+	1.43488i	0.0315835	+	0.0547042i
$689$	21.1716	+	36.6702i	0.806573	+	1.39702i
$690$	−17.6569			−0.672185
$691$	10.4645	−	18.1250i	0.398087	−	0.689507i	−0.595403	−	0.803427i	$-0.703008\pi$
$691$	10.4645	−	18.1250i	0.398087	−	0.689507i	0.993490	+	0.113920i	$0.0363409\pi$
$692$	−10.3995	+	18.0125i	−0.395329	+	0.684731i
$693$	−2.91421	+	5.04757i	−0.110702	+	0.191741i
$694$	6.27817	+	10.8741i	0.238316	+	0.412776i
$695$	−22.9706	+	39.7862i	−0.871323	+	1.50918i
$696$	2.91421	+	5.04757i	0.110463	+	0.191327i
$697$	−41.1127			−1.55725
$698$	−23.8995			−0.904609
$699$	13.7782	+	23.8645i	0.521138	+	0.902638i
$700$	−3.62132	+	6.27231i	−0.136873	+	0.237071i
$701$	11.3284	+	19.6214i	0.427869	+	0.741090i	0.996684	−	0.0813752i	$-0.0259312\pi$
$701$	11.3284	+	19.6214i	0.427869	+	0.741090i	−0.568815	+	0.822466i	$0.692598\pi$
$702$	2.82843	−	4.89898i	0.106752	−	0.184900i
$703$	−19.1421	+	33.1552i	−0.721959	+	1.25047i
$704$	−1.20711	+	2.09077i	−0.0454945	+	0.0787989i
$705$	23.3137			0.878045
$706$	−1.82843	−	3.16693i	−0.0688138	−	0.119189i
$707$	−9.44975	−	16.3674i	−0.355394	−	0.615561i
$708$	−3.44975	+	5.97514i	−0.129649	+	0.224559i
$709$	21.2132			0.796679			0.398339	−	0.917238i	$-0.369587\pi$
$709$	21.2132			0.796679			0.398339	+	0.917238i	$0.369587\pi$
$710$	−2.34315	−	4.05845i	−0.0879367	−	0.152311i
$711$	12.4853			0.468235
$712$	−9.31371			−0.349046
$713$	2.36396	+	34.6771i	0.0885310	+	1.29867i
$714$	15.0711			0.564021
$715$	−38.6274			−1.44458
$716$	−8.37868	−	14.5123i	−0.313126	−	0.542350i
$717$	−7.31371			−0.273135
$718$	−0.0502525	+	0.0870399i	−0.00187541	+	0.00324830i
$719$	−21.1924	−	36.7063i	−0.790343	−	1.36891i	−0.925755	−	0.378124i	$-0.876569\pi$
$719$	−21.1924	−	36.7063i	−0.790343	−	1.36891i	0.135412	−	0.990789i	$-0.456764\pi$
$720$	1.41421	+	2.44949i	0.0527046	+	0.0912871i
$721$	23.1421			0.861858
$722$	−5.15685	+	8.93193i	−0.191918	+	0.332412i
$723$	7.57107	−	13.1135i	0.281571	−	0.487695i
$724$	−9.82843	+	17.0233i	−0.365271	+	0.632667i
$725$	−8.74264	−	15.1427i	−0.324694	−	0.562386i
$726$	−2.58579	+	4.47871i	−0.0959675	+	0.166221i
$727$	−6.55025	−	11.3454i	−0.242935	−	0.420776i	0.718614	−	0.695409i	$-0.244777\pi$
$727$	−6.55025	−	11.3454i	−0.242935	−	0.420776i	−0.961549	+	0.274633i	$0.911444\pi$
$728$	13.6569			0.506157
$729$	1.00000			0.0370370
$730$	−6.34315	−	10.9867i	−0.234770	−	0.406634i
$731$	−5.17157	+	8.95743i	−0.191278	+	0.331302i
$732$	−3.53553	−	6.12372i	−0.130677	−	0.226339i
$733$	22.7990	−	39.4890i	0.842100	−	1.45856i	−0.0460162	−	0.998941i	$-0.514653\pi$
$733$	22.7990	−	39.4890i	0.842100	−	1.45856i	0.888116	−	0.459619i	$-0.152014\pi$
$734$	−6.34315	+	10.9867i	−0.234130	+	0.405525i
$735$	1.65685	−	2.86976i	0.0611140	−	0.105853i
$736$	−6.24264			−0.230107
$737$	−7.53553	−	13.0519i	−0.277575	−	0.480774i
$738$	−3.29289	−	5.70346i	−0.121213	−	0.209947i
$739$	10.6066	−	18.3712i	0.390170	−	0.675795i	−0.602302	−	0.798269i	$-0.705750\pi$
$739$	10.6066	−	18.3712i	0.390170	−	0.675795i	0.992472	+	0.122474i	$0.0390828\pi$
$740$	−20.0000			−0.735215
$741$	15.3137	+	26.5241i	0.562563	+	0.974388i
$742$	−18.0711			−0.663410
$743$	6.48528			0.237922			0.118961	−	0.992899i	$-0.462044\pi$
$743$	6.48528			0.237922			0.118961	+	0.992899i	$0.462044\pi$
$744$	4.62132	−	3.10538i	0.169426	−	0.113849i
$745$	−55.1127			−2.01917
$746$	−17.0711			−0.625016
$747$	1.79289	+	3.10538i	0.0655985	+	0.113620i
$748$	−15.0711			−0.551053
$749$	−3.91421	+	6.77962i	−0.143022	+	0.247722i
$750$	2.82843	+	4.89898i	0.103280	+	0.178885i
$751$	1.27817	+	2.21386i	0.0466413	+	0.0807850i	0.888404	−	0.459063i	$-0.151815\pi$
$751$	1.27817	+	2.21386i	0.0466413	+	0.0807850i	−0.841762	+	0.539848i	$0.818482\pi$
$752$	8.24264			0.300578
$753$	−3.75736	+	6.50794i	−0.136926	+	0.237162i
$754$	−16.4853	+	28.5533i	−0.600359	+	1.03985i
$755$	25.5563	−	44.2649i	0.930091	−	1.61096i
$756$	1.20711	+	2.09077i	0.0439020	+	0.0760406i
$757$	−3.65685	+	6.33386i	−0.132911	+	0.230208i	−0.924797	−	0.380460i	$-0.875766\pi$
$757$	−3.65685	+	6.33386i	−0.132911	+	0.230208i	0.791887	+	0.610668i	$0.209099\pi$
$758$	2.41421	+	4.18154i	0.0876882	+	0.151880i
$759$	15.0711			0.547045
$760$	−15.3137			−0.555487
$761$	−7.84924	−	13.5953i	−0.284535	−	0.492829i	0.687961	−	0.725747i	$-0.258506\pi$
$761$	−7.84924	−	13.5953i	−0.284535	−	0.492829i	−0.972496	+	0.232918i	$0.925172\pi$
$762$	−10.2071	+	17.6792i	−0.369764	+	0.640451i
$763$	−11.7782	−	20.4004i	−0.426399	−	0.738544i
$764$	3.12132	−	5.40629i	0.112925	−	0.195593i
$765$	−8.82843	+	15.2913i	−0.319192	+	0.552858i
$766$	−1.94975	+	3.37706i	−0.0704472	+	0.122018i
$767$	−39.0294			−1.40927
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	5.67157	+	9.82345i	0.204522	+	0.354243i	0.949980	−	0.312310i	$-0.101103\pi$
$769$	5.67157	+	9.82345i	0.204522	+	0.354243i	−0.745458	+	0.666552i	$0.767769\pi$
$770$	8.24264	−	14.2767i	0.297044	−	0.514496i
$771$	−13.4142			−0.483101
$772$	1.32843	+	2.30090i	0.0478111	+	0.0828113i
$773$	−13.1716			−0.473749			−0.236874	−	0.971540i	$-0.576123\pi$
$773$	−13.1716			−0.473749			−0.236874	+	0.971540i	$0.576123\pi$
$774$	−1.65685			−0.0595544
$775$	−13.8640	+	9.31615i	−0.498008	+	0.334646i
$776$	8.31371			0.298445
$777$	−17.0711			−0.612421
$778$	1.65685	+	2.86976i	0.0594011	+	0.102886i
$779$	35.6569			1.27754
$780$	−8.00000	+	13.8564i	−0.286446	+	0.496139i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	−19.4853	−	33.7495i	−0.696792	−	1.20688i
$783$	−5.82843			−0.208291
$784$	0.585786	−	1.01461i	0.0209209	−	0.0362361i
$785$	−10.9706	+	19.0016i	−0.391556	+	0.678195i
$786$	−0.656854	+	1.13770i	−0.0234292	+	0.0405806i
$787$	−9.94975	−	17.2335i	−0.354670	−	0.614307i	0.632391	−	0.774649i	$-0.282074\pi$
$787$	−9.94975	−	17.2335i	−0.354670	−	0.614307i	−0.987061	+	0.160342i	$0.948740\pi$
$788$	−1.41421	+	2.44949i	−0.0503793	+	0.0872595i
$789$	7.58579	+	13.1390i	0.270061	+	0.467760i
$790$	−35.3137			−1.25641
$791$	−19.3137			−0.686716
$792$	−1.20711	−	2.09077i	−0.0428927	−	0.0742923i
$793$	20.0000	−	34.6410i	0.710221	−	1.23014i
$794$	11.4853	+	19.8931i	0.407597	+	0.705979i
$795$	10.5858	−	18.3351i	0.375439	−	0.650280i
$796$	2.37868	−	4.11999i	0.0843101	−	0.146029i
$797$	10.8431	−	18.7809i	0.384084	−	0.665253i	−0.607558	−	0.794276i	$-0.707851\pi$
$797$	10.8431	−	18.7809i	0.384084	−	0.665253i	0.991642	+	0.129023i	$0.0411840\pi$
$798$	−13.0711			−0.462711
$799$	25.7279	+	44.5621i	0.910188	+	1.57649i
$800$	−1.50000	−	2.59808i	−0.0530330	−	0.0918559i
$801$	4.65685	−	8.06591i	0.164542	−	0.284995i
$802$	17.6569			0.623485
$803$	5.41421	+	9.37769i	0.191063	+	0.330932i
$804$	−6.24264			−0.220161
$805$	42.6274			1.50242
$806$	28.2843	+	13.8564i	0.996271	+	0.488071i
$807$	−1.31371			−0.0462447
$808$	7.82843			0.275403
$809$	−9.36396	−	16.2189i	−0.329219	−	0.570225i	0.653138	−	0.757239i	$-0.273452\pi$
$809$	−9.36396	−	16.2189i	−0.329219	−	0.570225i	−0.982357	+	0.187014i	$0.940119\pi$
$810$	−2.82843			−0.0993808
$811$	1.92893	−	3.34101i	0.0677340	−	0.117319i	−0.830170	−	0.557511i	$-0.811756\pi$
$811$	1.92893	−	3.34101i	0.0677340	−	0.117319i	0.897903	+	0.440192i	$0.145090\pi$
$812$	−7.03553	−	12.1859i	−0.246899	−	0.427641i
$813$	14.6213	+	25.3249i	0.512792	+	0.888182i
$814$	17.0711			0.598341
$815$	−2.48528	+	4.30463i	−0.0870556	+	0.150785i
$816$	−3.12132	+	5.40629i	−0.109268	+	0.189258i
$817$	4.48528	−	7.76874i	0.156920	−	0.271794i
$818$	16.0563	+	27.8104i	0.561397	+	0.972368i
$819$	−6.82843	+	11.8272i	−0.238605	+	0.413275i
$820$	9.31371	+	16.1318i	0.325249	+	0.563347i
$821$	−11.0000			−0.383903			−0.191951	−	0.981404i	$-0.561482\pi$
$821$	−11.0000			−0.383903			−0.191951	+	0.981404i	$0.561482\pi$
$822$	−1.75736			−0.0612949
$823$	−12.8640	−	22.2810i	−0.448409	−	0.776668i	0.549873	−	0.835248i	$-0.314676\pi$
$823$	−12.8640	−	22.2810i	−0.448409	−	0.776668i	−0.998283	+	0.0585801i	$0.981343\pi$
$824$	−4.79289	+	8.30153i	−0.166968	+	0.289198i
$825$	3.62132	+	6.27231i	0.126078	+	0.218374i
$826$	8.32843	−	14.4253i	0.289783	−	0.501919i
$827$	1.48528	−	2.57258i	0.0516483	−	0.0894575i	−0.839045	−	0.544061i	$-0.816886\pi$
$827$	1.48528	−	2.57258i	0.0516483	−	0.0894575i	0.890694	+	0.454604i	$0.150219\pi$
$828$	3.12132	−	5.40629i	0.108473	−	0.187881i
$829$	−9.07107			−0.315051			−0.157526	−	0.987515i	$-0.550352\pi$
$829$	−9.07107			−0.315051			−0.157526	+	0.987515i	$0.550352\pi$
$830$	−5.07107	−	8.78335i	−0.176019	−	0.304874i
$831$	1.70711	+	2.95680i	0.0592189	+	0.102570i
$832$	−2.82843	+	4.89898i	−0.0980581	+	0.169842i
$833$	7.31371			0.253405
$834$	−8.12132	−	14.0665i	−0.281218	−	0.487084i
$835$	22.3431			0.773216
$836$	13.0711			0.452072
$837$	0.378680	+	5.55487i	0.0130891	+	0.192004i
$838$	−33.5269			−1.15817
$839$	40.5269			1.39914			0.699572	−	0.714562i	$-0.253374\pi$
$839$	40.5269			1.39914			0.699572	+	0.714562i	$0.253374\pi$
$840$	−3.41421	−	5.91359i	−0.117802	−	0.204038i
$841$	4.97056			0.171399
$842$	9.87868	−	17.1104i	0.340442	−	0.589662i
$843$	16.3137	+	28.2562i	0.561874	+	0.973194i
$844$	−11.7782	−	20.4004i	−0.405421	−	0.702211i
$845$	−53.7401			−1.84872
$846$	−4.12132	+	7.13834i	−0.141694	+	0.245421i
$847$	6.24264	−	10.8126i	0.214500	−	0.371524i
$848$	3.74264	−	6.48244i	0.128523	−	0.222608i
$849$	−5.65685	−	9.79796i	−0.194143	−	0.336265i
$850$	9.36396	−	16.2189i	0.321181	−	0.556302i
$851$	22.0711	+	38.2282i	0.756586	+	1.31045i
$852$	1.65685			0.0567629
$853$	−12.6863			−0.434370			−0.217185	−	0.976130i	$-0.569688\pi$
$853$	−12.6863			−0.434370			−0.217185	+	0.976130i	$0.569688\pi$
$854$	8.53553	+	14.7840i	0.292080	+	0.505897i
$855$	7.65685	−	13.2621i	0.261859	−	0.453553i
$856$	−1.62132	−	2.80821i	−0.0554156	−	0.0959826i
$857$	9.51472	−	16.4800i	0.325017	−	0.562945i	−0.656499	−	0.754327i	$-0.727963\pi$
$857$	9.51472	−	16.4800i	0.325017	−	0.562945i	0.981516	+	0.191382i	$0.0612968\pi$
$858$	6.82843	−	11.8272i	0.233119	−	0.403773i
$859$	−28.0919	+	48.6566i	−0.958483	+	1.66014i	−0.232294	+	0.972646i	$0.574623\pi$
$859$	−28.0919	+	48.6566i	−0.958483	+	1.66014i	−0.726189	+	0.687495i	$0.758710\pi$
$860$	4.68629			0.159801
$861$	7.94975	+	13.7694i	0.270927	+	0.469259i
$862$	−3.29289	−	5.70346i	−0.112156	−	0.194261i
$863$	17.3137	−	29.9882i	0.589365	−	1.02081i	−0.404950	−	0.914339i	$-0.632711\pi$
$863$	17.3137	−	29.9882i	0.589365	−	1.02081i	0.994316	−	0.106472i	$-0.0339555\pi$
$864$	−1.00000			−0.0340207
$865$	29.4142	+	50.9469i	1.00011	+	1.73225i
$866$	−26.1421			−0.888346
$867$	−21.9706			−0.746159
$868$	−11.1569	+	7.49706i	−0.378688	+	0.254467i
$869$	30.1421			1.02250
$870$	16.4853			0.558903
$871$	−17.6569	−	30.5826i	−0.598280	−	1.03625i
$872$	9.75736			0.330426
$873$	−4.15685	+	7.19988i	−0.140688	+	0.243679i
$874$	16.8995	+	29.2708i	0.571634	+	0.990099i
$875$	−6.82843	−	11.8272i	−0.230843	−	0.399832i
$876$	4.48528			0.151544
$877$	23.1924	−	40.1704i	0.783151	−	1.35646i	−0.146946	−	0.989145i	$-0.546944\pi$
$877$	23.1924	−	40.1704i	0.783151	−	1.35646i	0.930097	−	0.367313i	$-0.119722\pi$
$878$	19.1066	−	33.0936i	0.644817	−	1.11686i
$879$	−11.7426	+	20.3389i	−0.396069	+	0.686012i
$880$	3.41421	+	5.91359i	0.115093	+	0.199347i
$881$	3.43503	−	5.94964i	0.115729	−	0.200449i	−0.802342	−	0.596865i	$-0.796413\pi$
$881$	3.43503	−	5.94964i	0.115729	−	0.200449i	0.918071	+	0.396416i	$0.129746\pi$
$882$	0.585786	+	1.01461i	0.0197245	+	0.0341638i
$883$	−3.41421			−0.114897			−0.0574487	−	0.998348i	$-0.518297\pi$
$883$	−3.41421			−0.114897			−0.0574487	+	0.998348i	$0.518297\pi$
$884$	−35.3137			−1.18773
$885$	9.75736	+	16.9002i	0.327990	+	0.568095i
$886$	−5.00000	+	8.66025i	−0.167978	+	0.290947i
$887$	7.92893	+	13.7333i	0.266227	+	0.461120i	0.967884	−	0.251395i	$-0.0808894\pi$
$887$	7.92893	+	13.7333i	0.266227	+	0.461120i	−0.701657	+	0.712515i	$0.747556\pi$
$888$	3.53553	−	6.12372i	0.118645	−	0.205499i
$889$	24.6421	−	42.6814i	0.826471	−	1.43149i
$890$	−13.1716	+	22.8138i	−0.441512	+	0.764721i
$891$	2.41421			0.0808792
$892$	3.62132	+	6.27231i	0.121251	+	0.210012i
$893$	−22.3137	−	38.6485i	−0.746700	−	1.29332i
$894$	9.74264	−	16.8747i	0.325843	−	0.564376i
$895$	−47.3970			−1.58431
$896$	−1.20711	−	2.09077i	−0.0403266	−	0.0698477i
$897$	35.3137			1.17909
$898$	−22.2843			−0.743636
$899$	−2.20711	−	32.3762i	−0.0736111	−	1.07981i
$900$	3.00000			0.100000
$901$	46.7279			1.55673
$902$	−7.94975	−	13.7694i	−0.264698	−	0.458470i
$903$	4.00000			0.133112
$904$	4.00000	−	6.92820i	0.133038	−	0.230429i
$905$	27.7990	+	48.1493i	0.924070	+	1.60054i
$906$	9.03553	+	15.6500i	0.300186	+	0.519937i
$907$	51.5980			1.71328			0.856641	−	0.515912i	$-0.172547\pi$
$907$	51.5980			1.71328			0.856641	+	0.515912i	$0.172547\pi$
$908$	−9.37868	+	16.2443i	−0.311242	+	0.539088i
$909$	−3.91421	+	6.77962i	−0.129826	+	0.224866i
$910$	19.3137	−	33.4523i	0.640243	−	1.10893i
$911$	−18.1213	−	31.3870i	−0.600386	−	1.03990i	−0.992762	−	0.120095i	$-0.961680\pi$
$911$	−18.1213	−	31.3870i	−0.600386	−	1.03990i	0.392376	−	0.919805i	$-0.371653\pi$
$912$	2.70711	−	4.68885i	0.0896413	−	0.155263i
$913$	4.32843	+	7.49706i	0.143250	+	0.248116i
$914$	−23.7990			−0.787201
$915$	−20.0000			−0.661180
$916$	−12.6066	−	21.8353i	−0.416534	−	0.721458i
$917$	1.58579	−	2.74666i	0.0523673	−	0.0907028i
$918$	−3.12132	−	5.40629i	−0.103019	−	0.178434i
$919$	−25.2071	+	43.6600i	−0.831506	+	1.44021i	0.0653383	+	0.997863i	$0.479187\pi$
$919$	−25.2071	+	43.6600i	−0.831506	+	1.44021i	−0.896844	+	0.442347i	$0.854146\pi$
$920$	−8.82843	+	15.2913i	−0.291065	+	0.504139i
$921$	−8.70711	+	15.0812i	−0.286909	+	0.496941i
$922$	−24.1716			−0.796048
$923$	4.68629	+	8.11689i	0.154251	+	0.267171i
$924$	2.91421	+	5.04757i	0.0958706	+	0.166053i
$925$	−10.6066	+	18.3712i	−0.348743	+	0.604040i
$926$	0.414214			0.0136119
$927$	−4.79289	−	8.30153i	−0.157419	−	0.272658i
$928$	5.82843			0.191327
$929$	52.8701			1.73461			0.867305	−	0.497777i	$-0.165850\pi$
$929$	52.8701			1.73461			0.867305	+	0.497777i	$0.165850\pi$
$930$	−1.07107	−	15.7116i	−0.0351217	−	0.515202i
$931$	−6.34315			−0.207888
$932$	27.5563			0.902638
$933$	−8.82843	−	15.2913i	−0.289030	−	0.500614i
$934$	−0.0710678			−0.00232541
$935$	−21.3137	+	36.9164i	−0.697033	+	1.20730i
$936$	−2.82843	−	4.89898i	−0.0924500	−	0.160128i
$937$	−1.27208	−	2.20330i	−0.0415570	−	0.0719788i	0.844499	−	0.535557i	$-0.179898\pi$
$937$	−1.27208	−	2.20330i	−0.0415570	−	0.0719788i	−0.886056	+	0.463579i	$0.846565\pi$
$938$	15.0711			0.492088
$939$	11.8137	−	20.4619i	0.385526	−	0.667750i
$940$	11.6569	−	20.1903i	0.380205	−	0.658534i
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	−0.642567	−	0.766229i	$-0.722131\pi$
$941$	10.5000	−	18.1865i	0.342290	−	0.592864i	0.984858	+	0.173365i	$0.0554641\pi$
$942$	−3.87868	−	6.71807i	−0.126374	−	0.218887i
$943$	20.5563	−	35.6046i	0.669407	−	1.15945i
$944$	3.44975	+	5.97514i	0.112280	+	0.194474i
$945$	6.82843			0.222129
$946$	−4.00000			−0.130051
$947$	23.0711	+	39.9603i	0.749709	+	1.29853i	0.947962	+	0.318383i	$0.103140\pi$
$947$	23.0711	+	39.9603i	0.749709	+	1.29853i	−0.198253	+	0.980151i	$0.563527\pi$
$948$	6.24264	−	10.8126i	0.202752	−	0.351176i
$949$	12.6863	+	21.9733i	0.411814	+	0.713284i
$950$	−8.12132	+	14.0665i	−0.263490	+	0.456379i
$951$	14.2279	−	24.6435i	0.461372	−	0.799120i
$952$	7.53553	−	13.0519i	0.244228	−	0.423015i
$953$	24.0416			0.778785			0.389392	−	0.921072i	$-0.372685\pi$
$953$	24.0416			0.778785			0.389392	+	0.921072i	$0.372685\pi$
$954$	3.74264	+	6.48244i	0.121172	+	0.209877i
$955$	−8.82843	−	15.2913i	−0.285681	−	0.494814i
$956$	−3.65685	+	6.33386i	−0.118271	+	0.204852i
$957$	−14.0711			−0.454853
$958$	0.221825	+	0.384213i	0.00716685	+	0.0124134i
$959$	4.24264			0.137002
$960$	2.82843			0.0912871
$961$	−30.7132	+	4.20703i	−0.990748	+	0.135711i
$962$	40.0000			1.28965
$963$	3.24264			0.104493
$964$	−7.57107	−	13.1135i	−0.243848	−	0.422357i
$965$	7.51472			0.241907
$966$	−7.53553	+	13.0519i	−0.242452	+	0.419939i
$967$	−20.1716	−	34.9382i	−0.648674	−	1.12354i	−0.983440	−	0.181235i	$-0.941991\pi$
$967$	−20.1716	−	34.9382i	−0.648674	−	1.12354i	0.334766	−	0.942301i	$-0.391343\pi$
$968$	2.58579	+	4.47871i	0.0831103	+	0.143951i
$969$	33.7990			1.08578
$970$	11.7574	−	20.3643i	0.377506	−	0.653860i
$971$	2.20711	−	3.82282i	0.0708294	−	0.122680i	−0.828436	−	0.560084i	$-0.810769\pi$
$971$	2.20711	−	3.82282i	0.0708294	−	0.122680i	0.899265	+	0.437404i	$0.144102\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	19.6066	+	33.9596i	0.628559	+	1.08870i
$974$	9.34924	−	16.1934i	0.299569	−	0.518869i
$975$	8.48528	+	14.6969i	0.271746	+	0.470679i
$976$	−7.07107			−0.226339
$977$	−46.6274			−1.49174			−0.745872	−	0.666090i	$-0.767967\pi$
$977$	−46.6274			−1.49174			−0.745872	+	0.666090i	$0.767967\pi$
$978$	−0.878680	−	1.52192i	−0.0280971	−	0.0486656i
$979$	11.2426	−	19.4728i	0.359316	−	0.622354i
$980$	−1.65685	−	2.86976i	−0.0529263	−	0.0916710i
$981$	−4.87868	+	8.45012i	−0.155764	+	0.269792i
$982$	−19.1066	+	33.0936i	−0.609716	+	1.05606i
$983$	−10.5563	+	18.2841i	−0.336695	+	0.583173i	−0.983809	−	0.179220i	$-0.942643\pi$
$983$	−10.5563	+	18.2841i	−0.336695	+	0.583173i	0.647114	+	0.762393i	$0.275976\pi$
$984$	−6.58579			−0.209947
$985$	4.00000	+	6.92820i	0.127451	+	0.220751i
$986$	18.1924	+	31.5101i	0.579364	+	1.00349i
$987$	9.94975	−	17.2335i	0.316704	−	0.548547i
$988$	30.6274			0.974388
$989$	−5.17157	−	8.95743i	−0.164446	−	0.284830i
$990$	−6.82843			−0.217022
$991$	7.51472			0.238713			0.119356	−	0.992851i	$-0.461917\pi$
$991$	7.51472			0.238713			0.119356	+	0.992851i	$0.461917\pi$
$992$	−0.378680	−	5.55487i	−0.0120231	−	0.176367i
$993$	1.75736			0.0557681
$994$	−4.00000			−0.126872
$995$	−6.72792	−	11.6531i	−0.213289	−	0.369428i
$996$	3.58579			0.113620
$997$	−5.87868	+	10.1822i	−0.186180	+	0.322473i	−0.943973	−	0.330022i	$-0.892944\pi$
$997$	−5.87868	+	10.1822i	−0.186180	+	0.322473i	0.757794	+	0.652494i	$0.226277\pi$
$998$	7.02082	+	12.1604i	0.222240	+	0.384931i
$999$	3.53553	+	6.12372i	0.111859	+	0.193746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.e.d.25.2	✓	4
3.2	odd	2		558.2.e.e.397.1		4
4.3	odd	2		1488.2.q.f.769.2		4
31.5	even	3	inner	186.2.e.d.67.2	yes	4
31.6	odd	6		5766.2.a.t.1.1		2
31.25	even	3		5766.2.a.r.1.1		2
93.5	odd	6		558.2.e.e.253.1		4
124.67	odd	6		1488.2.q.f.625.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.e.d.25.2	✓	4	1.1	even	1	trivial
186.2.e.d.67.2	yes	4	31.5	even	3	inner
558.2.e.e.253.1		4	93.5	odd	6
558.2.e.e.397.1		4	3.2	odd	2
1488.2.q.f.625.2		4	124.67	odd	6
1488.2.q.f.769.2		4	4.3	odd	2
5766.2.a.r.1.1		2	31.25	even	3
5766.2.a.t.1.1		2	31.6	odd	6

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:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(1.41421 - 2.44949i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-1.20711 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.41421 - 2.44949i) q^{10} +(-1.20711 + 2.09077i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.82843 + 4.89898i) q^{13} +(-1.20711 - 2.09077i) q^{14} +2.82843 q^{15} +1.00000 q^{16} +(3.12132 + 5.40629i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.70711 - 4.68885i) q^{19} +(1.41421 - 2.44949i) q^{20} +(1.20711 - 2.09077i) q^{21} +(-1.20711 + 2.09077i) q^{22} -6.24264 q^{23} +(0.500000 + 0.866025i) q^{24} +(-1.50000 - 2.59808i) q^{25} +(-2.82843 + 4.89898i) q^{26} -1.00000 q^{27} +(-1.20711 - 2.09077i) q^{28} +5.82843 q^{29} +2.82843 q^{30} +(-0.378680 - 5.55487i) q^{31} +1.00000 q^{32} -2.41421 q^{33} +(3.12132 + 5.40629i) q^{34} -6.82843 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.53553 - 6.12372i) q^{37} +(-2.70711 - 4.68885i) q^{38} -5.65685 q^{39} +(1.41421 - 2.44949i) q^{40} +(-3.29289 + 5.70346i) q^{41} +(1.20711 - 2.09077i) q^{42} +(0.828427 + 1.43488i) q^{43} +(-1.20711 + 2.09077i) q^{44} +(1.41421 + 2.44949i) q^{45} -6.24264 q^{46} +8.24264 q^{47} +(0.500000 + 0.866025i) q^{48} +(0.585786 - 1.01461i) q^{49} +(-1.50000 - 2.59808i) q^{50} +(-3.12132 + 5.40629i) q^{51} +(-2.82843 + 4.89898i) q^{52} +(3.74264 - 6.48244i) q^{53} -1.00000 q^{54} +(3.41421 + 5.91359i) q^{55} +(-1.20711 - 2.09077i) q^{56} +(2.70711 - 4.68885i) q^{57} +5.82843 q^{58} +(3.44975 + 5.97514i) q^{59} +2.82843 q^{60} -7.07107 q^{61} +(-0.378680 - 5.55487i) q^{62} +2.41421 q^{63} +1.00000 q^{64} +(8.00000 + 13.8564i) q^{65} -2.41421 q^{66} +(-3.12132 + 5.40629i) q^{67} +(3.12132 + 5.40629i) q^{68} +(-3.12132 - 5.40629i) q^{69} -6.82843 q^{70} +(0.828427 - 1.43488i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.24264 - 3.88437i) q^{73} +(-3.53553 - 6.12372i) q^{74} +(1.50000 - 2.59808i) q^{75} +(-2.70711 - 4.68885i) q^{76} +5.82843 q^{77} -5.65685 q^{78} +(-6.24264 - 10.8126i) q^{79} +(1.41421 - 2.44949i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.29289 + 5.70346i) q^{82} +(1.79289 - 3.10538i) q^{83} +(1.20711 - 2.09077i) q^{84} +17.6569 q^{85} +(0.828427 + 1.43488i) q^{86} +(2.91421 + 5.04757i) q^{87} +(-1.20711 + 2.09077i) q^{88} -9.31371 q^{89} +(1.41421 + 2.44949i) q^{90} +13.6569 q^{91} -6.24264 q^{92} +(4.62132 - 3.10538i) q^{93} +8.24264 q^{94} -15.3137 q^{95} +(0.500000 + 0.866025i) q^{96} +8.31371 q^{97} +(0.585786 - 1.01461i) q^{98} +(-1.20711 - 2.09077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} - 2 q^{11} + 2 q^{12} - 2 q^{14} + 4 q^{16} + 4 q^{17} - 2 q^{18} - 8 q^{19} + 2 q^{21} - 2 q^{22} - 8 q^{23} + 2 q^{24} - 6 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 - 2 * q^11 + 2 * q^12 - 2 * q^14 + 4 * q^16 + 4 * q^17 - 2 * q^18 - 8 * q^19 + 2 * q^21 - 2 * q^22 - 8 * q^23 + 2 * q^24 - 6 * q^25 - 4 * q^27 - 2 * q^28 + 12 * q^29 - 10 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 16 * q^35 - 2 * q^36 - 8 * q^38 - 16 * q^41 + 2 * q^42 - 8 * q^43 - 2 * q^44 - 8 * q^46 + 16 * q^47 + 2 * q^48 + 8 * q^49 - 6 * q^50 - 4 * q^51 - 2 * q^53 - 4 * q^54 + 8 * q^55 - 2 * q^56 + 8 * q^57 + 12 * q^58 - 6 * q^59 - 10 * q^62 + 4 * q^63 + 4 * q^64 + 32 * q^65 - 4 * q^66 - 4 * q^67 + 4 * q^68 - 4 * q^69 - 16 * q^70 - 8 * q^71 - 2 * q^72 - 8 * q^73 + 6 * q^75 - 8 * q^76 + 12 * q^77 - 8 * q^79 - 2 * q^81 - 16 * q^82 + 10 * q^83 + 2 * q^84 + 48 * q^85 - 8 * q^86 + 6 * q^87 - 2 * q^88 + 8 * q^89 + 32 * q^91 - 8 * q^92 + 10 * q^93 + 16 * q^94 - 16 * q^95 + 2 * q^96 - 12 * q^97 + 8 * q^98 - 2 * q^99

Introduction

L-functions

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