LMFDB - Embedded newform 429.2.bb.b.64.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [429,2,Mod(25,429)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(429, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("429.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.3
Character	$\chi$	$=$	429.64
Dual form			429.2.bb.b.181.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97843 - 0.642831i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.88292 + 1.36802i) q^{4} +(-3.50059 + 1.13741i) q^{5} +(-1.97843 + 0.642831i) q^{6} +(2.06240 - 2.83865i) q^{7} +(-0.400343 - 0.551025i) q^{8} +(0.309017 - 0.951057i) q^{9} +7.65683 q^{10} +(3.29855 - 0.345829i) q^{11} +2.32742 q^{12} +(-0.482267 + 3.57315i) q^{13} +(-5.90508 + 4.29029i) q^{14} +(-2.16348 + 2.97778i) q^{15} +(-1.00059 - 3.07949i) q^{16} +(-1.85474 - 5.70830i) q^{17} +(-1.22274 + 1.68295i) q^{18} +(-1.03348 - 1.42247i) q^{19} +(-8.14732 - 2.64722i) q^{20} -3.50876i q^{21} +(-6.74825 - 1.43621i) q^{22} -2.41381 q^{23} +(-0.647768 - 0.210473i) q^{24} +(6.91532 - 5.02428i) q^{25} +(3.25106 - 6.75921i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(7.76666 - 2.52354i) q^{28} +(-1.66253 - 1.20790i) q^{29} +(6.19450 - 4.50057i) q^{30} +(-9.46029 - 3.07384i) q^{31} +8.09797i q^{32} +(2.46531 - 2.21862i) q^{33} +12.4858i q^{34} +(-3.99090 + 12.2827i) q^{35} +(1.88292 - 1.36802i) q^{36} +(5.38162 - 7.40717i) q^{37} +(1.13027 + 3.47861i) q^{38} +(1.71008 + 3.17421i) q^{39} +(2.02818 + 1.47356i) q^{40} +(1.31107 + 1.80453i) q^{41} +(-2.25554 + 6.94184i) q^{42} -4.98659 q^{43} +(6.68399 + 3.86131i) q^{44} +3.68074i q^{45} +(4.77555 + 1.55167i) q^{46} +(-6.89489 - 9.49000i) q^{47} +(-2.61957 - 1.90323i) q^{48} +(-1.64131 - 5.05145i) q^{49} +(-16.9112 + 5.49480i) q^{50} +(-4.85577 - 3.52792i) q^{51} +(-5.79622 + 6.06820i) q^{52} +(3.88002 - 11.9415i) q^{53} +2.08024i q^{54} +(-11.1535 + 4.96240i) q^{55} -2.38983 q^{56} +(-1.67221 - 0.543335i) q^{57} +(2.51273 + 3.45848i) q^{58} +(-1.15208 + 1.58570i) q^{59} +(-8.14732 + 2.64722i) q^{60} +(1.20764 + 3.71674i) q^{61} +(16.7406 + 12.1627i) q^{62} +(-2.06240 - 2.83865i) q^{63} +(3.20445 - 9.86229i) q^{64} +(-2.37592 - 13.0567i) q^{65} +(-6.30363 + 2.80461i) q^{66} -1.81940i q^{67} +(4.31675 - 13.2856i) q^{68} +(-1.95281 + 1.41880i) q^{69} +(15.7914 - 21.7350i) q^{70} +(-5.47570 + 1.77916i) q^{71} +(-0.647768 + 0.210473i) q^{72} +(-6.70122 + 9.22344i) q^{73} +(-15.4087 + 11.1951i) q^{74} +(2.64142 - 8.12945i) q^{75} -4.09222i q^{76} +(5.82123 - 10.0766i) q^{77} +(-1.34280 - 7.37925i) q^{78} +(-0.713431 + 2.19571i) q^{79} +(7.00529 + 9.64195i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.43385 - 4.41293i) q^{82} +(15.3207 - 4.97801i) q^{83} +(4.80006 - 6.60671i) q^{84} +(12.9853 + 17.8728i) q^{85} +(9.86562 + 3.20553i) q^{86} -2.05501 q^{87} +(-1.51111 - 1.67913i) q^{88} +1.62134i q^{89} +(2.36609 - 7.28208i) q^{90} +(9.14829 + 8.73825i) q^{91} +(-4.54501 - 3.30214i) q^{92} +(-9.46029 + 3.07384i) q^{93} +(7.54059 + 23.2075i) q^{94} +(5.23573 + 3.80398i) q^{95} +(4.75987 + 6.55140i) q^{96} +(8.91121 + 2.89543i) q^{97} +11.0490i q^{98} +(0.690403 - 3.24397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36}+ \cdots + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−1.97843	−	0.642831i	−1.39896	−	0.454550i	−0.490106	−	0.871663i	$-0.663042\pi$
$2$	−1.97843	−	0.642831i	−1.39896	−	0.454550i	−0.908855	+	0.417113i	$0.863042\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	1.88292	+	1.36802i	0.941459	+	0.684010i
$5$	−3.50059	+	1.13741i	−1.56551	+	0.508665i	−0.958273	−	0.285855i	$-0.907722\pi$
$5$	−3.50059	+	1.13741i	−1.56551	+	0.508665i	−0.607237	+	0.794520i	$0.707722\pi$
$6$	−1.97843	+	0.642831i	−0.807691	+	0.262435i
$7$	2.06240	−	2.83865i	0.779513	−	1.07291i	−0.215822	−	0.976433i	$-0.569243\pi$
$7$	2.06240	−	2.83865i	0.779513	−	1.07291i	0.995335	−	0.0964752i	$-0.0307568\pi$
$8$	−0.400343	−	0.551025i	−0.141543	−	0.194817i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	7.65683			2.42130
$11$	3.29855	−	0.345829i	0.994549	−	0.104271i
$11$	3.29855	−	0.345829i	0.994549	−	0.104271i
$12$	2.32742			0.671867
$13$	−0.482267	+	3.57315i	−0.133757	+	0.991014i
$13$	−0.482267	+	3.57315i	−0.133757	+	0.991014i
$14$	−5.90508	+	4.29029i	−1.57820	+	1.14663i
$15$	−2.16348	+	2.97778i	−0.558609	+	0.768859i
$16$	−1.00059	−	3.07949i	−0.250147	−	0.769873i
$17$	−1.85474	−	5.70830i	−0.449840	−	1.38447i	−0.877087	−	0.480331i	$-0.840517\pi$
$17$	−1.85474	−	5.70830i	−0.449840	−	1.38447i	0.427247	−	0.904135i	$-0.359483\pi$
$18$	−1.22274	+	1.68295i	−0.288202	+	0.396676i
$19$	−1.03348	−	1.42247i	−0.237098	−	0.326337i	0.673843	−	0.738875i	$-0.264642\pi$
$19$	−1.03348	−	1.42247i	−0.237098	−	0.326337i	−0.910940	+	0.412538i	$0.864642\pi$
$20$	−8.14732	−	2.64722i	−1.82180	−	0.591937i
$21$		−	3.50876i		−	0.765674i
$22$	−6.74825	−	1.43621i	−1.43873	−	0.306201i
$23$	−2.41381			−0.503314			−0.251657	−	0.967816i	$-0.580976\pi$
$23$	−2.41381			−0.503314			−0.251657	+	0.967816i	$0.580976\pi$
$24$	−0.647768	−	0.210473i	−0.132225	−	0.0429626i
$25$	6.91532	−	5.02428i	1.38306	−	1.00486i
$26$	3.25106	−	6.75921i	0.637586	−	1.32559i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	7.76666	−	2.52354i	1.46776	−	0.476904i
$29$	−1.66253	−	1.20790i	−0.308725	−	0.224302i	0.422624	−	0.906305i	$-0.361109\pi$
$29$	−1.66253	−	1.20790i	−0.308725	−	0.224302i	−0.731349	+	0.682003i	$0.761109\pi$
$30$	6.19450	−	4.50057i	1.13096	−	0.821688i
$31$	−9.46029	−	3.07384i	−1.69912	−	0.552077i	−0.710656	−	0.703540i	$-0.751602\pi$
$31$	−9.46029	−	3.07384i	−1.69912	−	0.552077i	−0.988463	+	0.151463i	$0.951602\pi$
$32$			8.09797i			1.43153i
$33$	2.46531	−	2.21862i	0.429155	−	0.386212i
$34$			12.4858i			2.14129i
$35$	−3.99090	+	12.2827i	−0.674585	+	2.07616i
$36$	1.88292	−	1.36802i	0.313820	−	0.228003i
$37$	5.38162	−	7.40717i	0.884733	−	1.21773i	−0.0903541	−	0.995910i	$-0.528800\pi$
$37$	5.38162	−	7.40717i	0.884733	−	1.21773i	0.975087	−	0.221821i	$-0.0712001\pi$
$38$	1.13027	+	3.47861i	0.183354	+	0.564305i
$39$	1.71008	+	3.17421i	0.273833	+	0.508281i
$40$	2.02818	+	1.47356i	0.320683	+	0.232990i
$41$	1.31107	+	1.80453i	0.204754	+	0.281820i	0.899028	−	0.437891i	$-0.144274\pi$
$41$	1.31107	+	1.80453i	0.204754	+	0.281820i	−0.694274	+	0.719711i	$0.744274\pi$
$42$	−2.25554	+	6.94184i	−0.348037	+	1.07115i
$43$	−4.98659			−0.760448			−0.380224	−	0.924894i	$-0.624153\pi$
$43$	−4.98659			−0.760448			−0.380224	+	0.924894i	$0.624153\pi$
$44$	6.68399	+	3.86131i	1.00765	+	0.582114i
$45$			3.68074i			0.548692i
$46$	4.77555	+	1.55167i	0.704117	+	0.228781i
$47$	−6.89489	−	9.49000i	−1.00572	−	1.38426i	−0.921747	−	0.387791i	$-0.873238\pi$
$47$	−6.89489	−	9.49000i	−1.00572	−	1.38426i	−0.0839753	−	0.996468i	$-0.526762\pi$
$48$	−2.61957	−	1.90323i	−0.378103	−	0.274708i
$49$	−1.64131	−	5.05145i	−0.234473	−	0.721635i
$50$	−16.9112	+	5.49480i	−2.39161	+	0.777082i
$51$	−4.85577	−	3.52792i	−0.679944	−	0.494008i
$52$	−5.79622	+	6.06820i	−0.803791	+	0.841508i
$53$	3.88002	−	11.9415i	0.532962	−	1.64029i	−0.215050	−	0.976603i	$-0.568991\pi$
$53$	3.88002	−	11.9415i	0.532962	−	1.64029i	0.748012	−	0.663686i	$-0.231009\pi$
$54$			2.08024i			0.283085i
$55$	−11.1535	+	4.96240i	−1.50394	+	0.669130i
$56$	−2.38983			−0.319355
$57$	−1.67221	−	0.543335i	−0.221490	−	0.0719664i
$58$	2.51273	+	3.45848i	0.329938	+	0.454120i
$59$	−1.15208	+	1.58570i	−0.149988	+	0.206441i	−0.877399	−	0.479761i	$-0.840723\pi$
$59$	−1.15208	+	1.58570i	−0.149988	+	0.206441i	0.727411	+	0.686202i	$0.240723\pi$
$60$	−8.14732	+	2.64722i	−1.05181	+	0.341755i
$61$	1.20764	+	3.71674i	0.154623	+	0.475879i	0.998122	−	0.0612499i	$-0.0195087\pi$
$61$	1.20764	+	3.71674i	0.154623	+	0.475879i	−0.843500	+	0.537129i	$0.819509\pi$
$62$	16.7406	+	12.1627i	2.12605	+	1.54467i
$63$	−2.06240	−	2.83865i	−0.259838	−	0.357636i
$64$	3.20445	−	9.86229i	0.400556	−	1.23279i
$65$	−2.37592	−	13.0567i	−0.294696	−	1.61948i
$66$	−6.30363	+	2.80461i	−0.775923	+	0.345223i
$67$		−	1.81940i		−	0.222275i	−0.993805	−	0.111137i	$-0.964551\pi$
$67$		−	1.81940i		−	0.222275i	0.993805	−	0.111137i	$-0.0354494\pi$
$68$	4.31675	−	13.2856i	0.523483	−	1.61111i
$69$	−1.95281	+	1.41880i	−0.235091	+	0.170804i
$70$	15.7914	−	21.7350i	1.88744	−	2.59783i
$71$	−5.47570	+	1.77916i	−0.649846	+	0.211148i	−0.615346	−	0.788257i	$-0.710984\pi$
$71$	−5.47570	+	1.77916i	−0.649846	+	0.211148i	−0.0344996	+	0.999405i	$0.510984\pi$
$72$	−0.647768	+	0.210473i	−0.0763402	+	0.0248044i
$73$	−6.70122	+	9.22344i	−0.784319	+	1.07952i	0.210474	+	0.977600i	$0.432499\pi$
$73$	−6.70122	+	9.22344i	−0.784319	+	1.07952i	−0.994792	+	0.101923i	$0.967501\pi$
$74$	−15.4087	+	11.1951i	−1.79123	+	1.30140i
$75$	2.64142	−	8.12945i	0.305005	−	0.938708i
$76$		−	4.09222i		−	0.469410i
$77$	5.82123	−	10.0766i	0.663390	−	1.14834i
$78$	−1.34280	−	7.37925i	−0.152042	−	0.835535i
$79$	−0.713431	+	2.19571i	−0.0802672	+	0.247037i	−0.983135	−	0.182881i	$-0.941458\pi$
$79$	−0.713431	+	2.19571i	−0.0802672	+	0.247037i	0.902868	+	0.429918i	$0.141458\pi$
$80$	7.00529	+	9.64195i	0.783215	+	1.07800i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.43385	−	4.41293i	−0.158342	−	0.487327i
$83$	15.3207	−	4.97801i	1.68167	−	0.546408i	0.696436	−	0.717619i	$-0.254768\pi$
$83$	15.3207	−	4.97801i	1.68167	−	0.546408i	0.985234	+	0.171212i	$0.0547682\pi$
$84$	4.80006	−	6.60671i	0.523729	−	0.720851i
$85$	12.9853	+	17.8728i	1.40846	+	1.93858i
$86$	9.86562	+	3.20553i	1.06384	+	0.345662i
$87$	−2.05501			−0.220320
$88$	−1.51111	−	1.67913i	−0.161085	−	0.178996i
$89$			1.62134i			0.171862i	0.996301	+	0.0859310i	$0.0273865\pi$
$89$			1.62134i			0.171862i	−0.996301	+	0.0859310i	$0.972614\pi$
$90$	2.36609	−	7.28208i	0.249408	−	0.767598i
$91$	9.14829	+	8.73825i	0.959002	+	0.916018i
$92$	−4.54501	−	3.30214i	−0.473850	−	0.344272i
$93$	−9.46029	+	3.07384i	−0.980987	+	0.318742i
$94$	7.54059	+	23.2075i	0.777752	+	2.39368i
$95$	5.23573	+	3.80398i	0.537175	+	0.390280i
$96$	4.75987	+	6.55140i	0.485802	+	0.668649i
$97$	8.91121	+	2.89543i	0.904796	+	0.293986i	0.724215	−	0.689574i	$-0.242202\pi$
$97$	8.91121	+	2.89543i	0.904796	+	0.293986i	0.180581	+	0.983560i	$0.442202\pi$
$98$			11.0490i			1.11612i
$99$	0.690403	−	3.24397i	0.0693882	−	0.326031i
$100$	19.8943			1.98943
$101$	−1.77471	+	5.46201i	−0.176591	+	0.543490i	−0.999703	−	0.0243890i	$-0.992236\pi$
$101$	−1.77471	+	5.46201i	−0.176591	+	0.543490i	0.823112	+	0.567879i	$0.192236\pi$
$102$	7.33894	+	10.1012i	0.726663	+	1.00017i
$103$	−5.99786	−	4.35770i	−0.590987	−	0.429377i	0.251682	−	0.967810i	$-0.419016\pi$
$103$	−5.99786	−	4.35770i	−0.590987	−	0.429377i	−0.842668	+	0.538433i	$0.819016\pi$
$104$	2.16197	−	1.16474i	0.211998	−	0.114213i
$105$	3.99090	+	12.2827i	0.389472	+	1.19867i
$106$	−15.3527	+	21.1312i	−1.49119	+	2.05244i
$107$	5.93787	−	4.31411i	0.574035	−	0.417061i	−0.262533	−	0.964923i	$-0.584558\pi$
$107$	5.93787	−	4.31411i	0.574035	−	0.417061i	0.836569	+	0.547862i	$0.184558\pi$
$108$	0.719211	−	2.21350i	0.0692061	−	0.212994i
$109$		−	13.1289i		−	1.25752i	−0.777599	−	0.628760i	$-0.783563\pi$
$109$		−	13.1289i		−	1.25752i	0.777599	−	0.628760i	$-0.216437\pi$
$110$	25.2564	−	2.64795i	2.40810	−	0.252473i
$111$		−	9.15576i		−	0.869027i
$112$	−10.8052	−	3.51082i	−1.02100	−	0.331741i
$113$	9.35891	−	6.79965i	0.880412	−	0.639657i	−0.0529483	−	0.998597i	$-0.516862\pi$
$113$	9.35891	−	6.79965i	0.880412	−	0.639657i	0.933361	+	0.358940i	$0.116862\pi$
$114$	2.95908	+	2.14990i	0.277143	+	0.201356i
$115$	8.44975	−	2.74549i	0.787943	−	0.256018i
$116$	−1.47798	−	4.54876i	−0.137227	−	0.422342i
$117$	3.24924	+	1.56283i	0.300392	+	0.144484i
$118$	3.29865	−	2.39661i	0.303665	−	0.220626i
$119$	−20.0291	−	6.50784i	−1.83606	−	0.596572i
$120$	2.50696			0.228853
$121$	10.7608	−	2.28147i	0.978255	−	0.207406i
$122$		−	8.12961i		−	0.736021i
$123$	2.12135	+	0.689269i	0.191276	+	0.0621493i
$124$	−13.6079	−	18.7297i	−1.22202	−	1.68197i
$125$	−7.67563	+	10.5646i	−0.686529	+	0.944926i
$126$	2.25554	+	6.94184i	0.200939	+	0.618428i
$127$	2.21775	+	6.82552i	0.196793	+	0.605667i	0.999951	+	0.00990058i	$0.00315150\pi$
$127$	2.21775	+	6.82552i	0.196793	+	0.605667i	−0.803158	+	0.595766i	$0.796848\pi$
$128$	−3.15983	+	4.34913i	−0.279292	+	0.384412i
$129$	−4.03424	+	2.93104i	−0.355195	+	0.258064i
$130$	−3.69264	+	27.3590i	−0.323866	+	2.39954i
$131$	12.7487			1.11386			0.556930	−	0.830559i	$-0.311979\pi$
$131$	12.7487			1.11386			0.556930	+	0.830559i	$0.311979\pi$
$132$	7.67709	−	0.804888i	0.668205	−	0.0700565i
$133$	−6.16934			−0.534950
$134$	−1.16956	+	3.59955i	−0.101035	+	0.310954i
$135$	2.16348	+	2.97778i	0.186203	+	0.256286i
$136$	−2.40288	+	3.30728i	−0.206045	+	0.283597i
$137$	7.26809	−	2.36155i	0.620955	−	0.201760i	0.0183906	−	0.999831i	$-0.494146\pi$
$137$	7.26809	−	2.36155i	0.620955	−	0.201760i	0.602564	+	0.798070i	$0.294146\pi$
$138$	4.77555	−	1.55167i	0.406522	−	0.132087i
$139$	4.42946	+	3.21819i	0.375702	+	0.272963i	0.759571	−	0.650424i	$-0.225409\pi$
$139$	4.42946	+	3.21819i	0.375702	+	0.272963i	−0.383870	+	0.923387i	$0.625409\pi$
$140$	−24.3176	+	17.6677i	−2.05521	+	1.49320i
$141$	−11.1562	−	3.62486i	−0.939518	−	0.305268i
$142$	11.9770			1.00509
$143$	−0.355081	+	11.9530i	−0.0296933	+	0.999559i
$144$	−3.23797			−0.269831
$145$	7.19373	+	2.33738i	0.597407	+	0.194109i
$146$	19.1870	−	13.9402i	1.58793	−	1.15370i
$147$	−4.29702	−	3.12197i	−0.354412	−	0.257495i
$148$	20.2663	−	6.58492i	1.66588	−	0.541277i
$149$	−9.60364	+	3.12041i	−0.786761	+	0.255634i	−0.674724	−	0.738070i	$-0.735737\pi$
$149$	−9.60364	+	3.12041i	−0.786761	+	0.255634i	−0.112037	+	0.993704i	$0.535737\pi$
$150$	−10.4517	+	14.3856i	−0.853380	+	1.17458i
$151$	4.10413	+	5.64885i	0.333989	+	0.459697i	0.942674	−	0.333715i	$-0.108302\pi$
$151$	4.10413	+	5.64885i	0.333989	+	0.459697i	−0.608684	+	0.793412i	$0.708302\pi$
$152$	−0.370067	+	1.13895i	−0.0300164	+	0.0923811i
$153$	−6.00206			−0.485238
$154$	−17.9945	+	16.1939i	−1.45004	+	1.30494i
$155$	36.6128			2.94081
$156$	−1.12244	+	8.31621i	−0.0898669	+	0.665830i
$157$	3.42197	−	2.48621i	0.273103	−	0.198421i	−0.442800	−	0.896620i	$-0.646015\pi$
$157$	3.42197	−	2.48621i	0.273103	−	0.198421i	0.715904	+	0.698199i	$0.246015\pi$
$158$	2.82295	−	3.88545i	0.224581	−	0.309110i
$159$	−3.88002	−	11.9415i	−0.307706	−	0.947021i
$160$	−9.21071	−	28.3477i	−0.728171	−	2.24108i
$161$	−4.97824	+	6.85196i	−0.392340	+	0.540010i
$162$	1.22274	+	1.68295i	0.0960673	+	0.132225i
$163$	−2.95410	−	0.959846i	−0.231383	−	0.0751809i	0.191031	−	0.981584i	$-0.438817\pi$
$163$	−2.95410	−	0.959846i	−0.231383	−	0.0751809i	−0.422414	+	0.906403i	$0.638817\pi$
$164$			5.19135i			0.405376i
$165$	−6.10654	+	10.5705i	−0.475394	+	0.822915i
$166$	−33.5110			−2.60096
$167$	1.19544	+	0.388423i	0.0925062	+	0.0300571i	0.354904	−	0.934903i	$-0.384513\pi$
$167$	1.19544	+	0.388423i	0.0925062	+	0.0300571i	−0.262398	+	0.964960i	$0.584513\pi$
$168$	−1.93341	+	1.40471i	−0.149166	+	0.108376i
$169$	−12.5348	−	3.44643i	−0.964218	−	0.265110i
$170$	−14.2014	−	43.7075i	−1.08920	−	3.35221i
$171$	−1.67221	+	0.543335i	−0.127877	+	0.0415498i
$172$	−9.38935	−	6.82176i	−0.715931	−	0.520154i
$173$	−1.57906	+	1.14726i	−0.120054	+	0.0872243i	−0.646192	−	0.763175i	$-0.723640\pi$
$173$	−1.57906	+	1.14726i	−0.120054	+	0.0872243i	0.526138	+	0.850399i	$0.323640\pi$
$174$	4.06569	+	1.32102i	0.308219	+	0.100146i
$175$		−	29.9922i		−	2.26720i
$176$	−4.36546	−	9.81181i	−0.329059	−	0.739593i
$177$			1.96004i			0.147325i
$178$	1.04225	−	3.20771i	0.0781198	−	0.240428i
$179$	−16.1815	+	11.7566i	−1.20946	+	0.878727i	−0.995182	−	0.0980444i	$-0.968741\pi$
$179$	−16.1815	+	11.7566i	−1.20946	+	0.878727i	−0.214282	+	0.976772i	$0.568741\pi$
$180$	−5.03532	+	6.93052i	−0.375311	+	0.516571i
$181$	2.60957	+	8.03142i	0.193967	+	0.596970i	0.999987	+	0.00508164i	$0.00161754\pi$
$181$	2.60957	+	8.03142i	0.193967	+	0.596970i	−0.806020	+	0.591889i	$0.798382\pi$
$182$	−12.4820	−	23.1688i	−0.925230	−	1.71739i
$183$	3.16165	+	2.29707i	0.233716	+	0.169804i
$184$	0.966351	+	1.33007i	0.0712404	+	0.0980540i
$185$	−10.4139	+	32.0505i	−0.765642	+	2.35640i
$186$	20.6925			1.51725
$187$	−8.09204	−	18.1877i	−0.591748	−	1.33001i
$188$		−	27.3012i		−	1.99115i
$189$	−3.33703	−	1.08427i	−0.242733	−	0.0788688i
$190$	−7.91321	−	10.8916i	−0.574085	−	0.790160i
$191$	5.38044	+	3.90912i	0.389315	+	0.282854i	0.765175	−	0.643823i	$-0.222653\pi$
$191$	5.38044	+	3.90912i	0.389315	+	0.282854i	−0.375860	+	0.926677i	$0.622653\pi$
$192$	−3.20445	−	9.86229i	−0.231261	−	0.711749i
$193$	2.04727	−	0.665197i	0.147365	−	0.0478819i	−0.234406	−	0.972139i	$-0.575314\pi$
$193$	2.04727	−	0.665197i	0.147365	−	0.0478819i	0.381771	+	0.924257i	$0.375314\pi$
$194$	−15.7689	−	11.4568i	−1.13214	−	0.822550i
$195$	−9.59668	−	9.16654i	−0.687232	−	0.656429i
$196$	3.82002	−	11.7568i	0.272859	−	0.839772i
$197$		−	1.60486i		−	0.114341i	−0.998364	−	0.0571707i	$-0.981792\pi$
$197$		−	1.60486i		−	0.114341i	0.998364	−	0.0571707i	$-0.0182079\pi$
$198$	−3.45124	+	5.97415i	−0.245269	+	0.424565i
$199$	−14.9512			−1.05987			−0.529933	−	0.848040i	$-0.677783\pi$
$199$	−14.9512			−1.05987			−0.529933	+	0.848040i	$0.677783\pi$
$200$	−5.53700	−	1.79908i	−0.391525	−	0.127214i
$201$	−1.06941	−	1.47192i	−0.0754307	−	0.103821i
$202$	7.02230	−	9.66536i	0.494087	−	0.680052i
$203$	−6.85762	+	2.22818i	−0.481310	+	0.156387i
$204$	−4.31675	−	13.2856i	−0.302233	−	0.930177i
$205$	−6.64200	−	4.82569i	−0.463897	−	0.337041i
$206$	9.06508	+	12.4770i	0.631594	+	0.869315i
$207$	−0.745908	+	2.29567i	−0.0518442	+	0.159560i
$208$	11.4860	−	2.09011i	0.796414	−	0.144923i
$209$	−3.90093	−	4.33467i	−0.269833	−	0.299835i
$210$		−	26.8660i		−	1.85393i
$211$	4.29630	−	13.2227i	0.295770	−	0.910285i	−0.687192	−	0.726476i	$-0.741157\pi$
$211$	4.29630	−	13.2227i	0.295770	−	0.910285i	0.982962	−	0.183810i	$-0.0588430\pi$
$212$	23.6420	−	17.1769i	1.62374	−	1.17971i
$213$	−3.38417	+	4.65791i	−0.231879	+	0.319155i
$214$	−14.5209	+	4.71813i	−0.992628	+	0.322525i
$215$	17.4560	−	5.67180i	1.19049	−	0.386813i
$216$	−0.400343	+	0.551025i	−0.0272399	+	0.0374925i
$217$	−28.2364	+	20.5150i	−1.91681	+	1.39265i
$218$	−8.43966	+	25.9746i	−0.571606	+	1.75922i
$219$			11.4008i			0.770395i
$220$	−27.7898	−	5.91441i	−1.87359	−	0.398749i
$221$	21.2911	−	3.87434i	1.43219	−	0.260616i
$222$	−5.88561	+	18.1140i	−0.395016	+	1.21573i
$223$	6.68021	+	9.19452i	0.447340	+	0.615711i	0.971823	−	0.235710i	$-0.0757416\pi$
$223$	6.68021	+	9.19452i	0.447340	+	0.615711i	−0.524484	+	0.851421i	$0.675742\pi$
$224$	22.9873	+	16.7012i	1.53590	+	1.11590i
$225$	−2.64142	−	8.12945i	−0.176095	−	0.541963i
$226$	−22.8870	+	7.43643i	−1.52242	+	0.494664i
$227$	−12.1516	+	16.7252i	−0.806528	+	1.11009i	0.185322	+	0.982678i	$0.440667\pi$
$227$	−12.1516	+	16.7252i	−0.806528	+	1.11009i	−0.991850	+	0.127413i	$0.959333\pi$
$228$	−2.40535	−	3.31068i	−0.159298	−	0.219255i
$229$	−10.2086	−	3.31696i	−0.674601	−	0.219191i	−0.0483708	−	0.998829i	$-0.515403\pi$
$229$	−10.2086	−	3.31696i	−0.674601	−	0.219191i	−0.626230	+	0.779638i	$0.715403\pi$
$230$	−18.4821			−1.21868
$231$	−1.21343	−	11.5738i	−0.0798380	−	0.761501i
$232$			1.39967i			0.0918930i
$233$	0.629084	−	1.93612i	0.0412126	−	0.126839i	−0.928333	−	0.371749i	$-0.878758\pi$
$233$	0.629084	−	1.93612i	0.0412126	−	0.126839i	0.969546	+	0.244909i	$0.0787582\pi$
$234$	−5.42376	−	5.18066i	−0.354562	−	0.338670i
$235$	34.9302	+	25.3783i	2.27859	+	1.65549i
$236$	−4.33855	+	1.40968i	−0.282415	+	0.0917623i
$237$	0.713431	+	2.19571i	0.0463423	+	0.142627i
$238$	35.4426	+	25.7506i	2.29741	+	1.66916i
$239$	−2.02172	−	2.78266i	−0.130774	−	0.179995i	0.738609	−	0.674135i	$-0.235483\pi$
$239$	−2.02172	−	2.78266i	−0.130774	−	0.179995i	−0.869383	+	0.494139i	$0.835483\pi$
$240$	11.3348	+	3.68290i	0.731658	+	0.237730i
$241$		−	10.2551i		−	0.660587i	−0.943878	−	0.330293i	$-0.892852\pi$
$241$		−	10.2551i		−	0.660587i	0.943878	−	0.330293i	$-0.107148\pi$
$242$	−22.7561	−	2.40365i	−1.46282	−	0.154513i
$243$	−1.00000			−0.0641500
$244$	−2.81068	+	8.65039i	−0.179936	+	0.553785i
$245$	11.4911	+	15.8162i	0.734141	+	1.01046i
$246$	−3.75386	−	2.72734i	−0.239337	−	0.173889i
$247$	5.58111	−	3.00679i	0.355118	−	0.191317i
$248$	2.09360	+	6.44344i	0.132944	+	0.409159i
$249$	9.46874	−	13.0326i	0.600057	−	0.825908i
$250$	21.9769	−	15.9672i	1.38994	−	1.00985i
$251$	−1.23125	+	3.78941i	−0.0777161	+	0.239186i	−0.982365	−	0.186971i	$-0.940133\pi$
$251$	−1.23125	+	3.78941i	−0.0777161	+	0.239186i	0.904649	+	0.426157i	$0.140133\pi$
$252$		−	8.16634i		−	0.514431i
$253$	−7.96206	+	0.834766i	−0.500571	+	0.0524813i
$254$		−	14.9294i		−	0.936756i
$255$	21.0107	+	6.82680i	1.31574	+	0.427511i
$256$	−7.73148	+	5.61725i	−0.483218	+	0.351078i
$257$	13.1519	+	9.55544i	0.820395	+	0.596052i	0.916826	−	0.399288i	$-0.130743\pi$
$257$	13.1519	+	9.55544i	0.820395	+	0.596052i	−0.0964305	+	0.995340i	$0.530743\pi$
$258$	9.86562	−	3.20553i	0.614207	−	0.199568i
$259$	−9.92729	−	30.5531i	−0.616852	−	1.89847i
$260$	13.3881	−	27.8349i	0.830296	−	1.72625i
$261$	−1.66253	+	1.20790i	−0.102908	+	0.0747673i
$262$	−25.2224	−	8.19527i	−1.55825	−	0.506305i
$263$	−5.53606			−0.341368			−0.170684	−	0.985326i	$-0.554598\pi$
$263$	−5.53606			−0.341368			−0.170684	+	0.985326i	$0.554598\pi$
$264$	−2.20948	−	0.470236i	−0.135984	−	0.0289411i
$265$			46.2154i			2.83899i
$266$	12.2056	+	3.96584i	0.748374	+	0.243161i
$267$	0.953001	+	1.31169i	0.0583227	+	0.0802743i
$268$	2.48897	−	3.42578i	0.152038	−	0.209263i
$269$	3.09474	+	9.52463i	0.188690	+	0.580727i	0.999992	−	0.00389913i	$-0.00124113\pi$
$269$	3.09474	+	9.52463i	0.188690	+	0.580727i	−0.811303	+	0.584626i	$0.801241\pi$
$270$	−2.36609	−	7.28208i	−0.143996	−	0.443173i
$271$	−15.3378	+	21.1107i	−0.931708	+	1.28239i	0.0274819	+	0.999622i	$0.491251\pi$
$271$	−15.3378	+	21.1107i	−0.931708	+	1.28239i	−0.959190	+	0.282763i	$0.908749\pi$
$272$	−15.7228	+	11.4233i	−0.953336	+	0.692639i
$273$	12.5373	+	1.69216i	0.758794	+	0.102414i
$274$	−15.8975			−0.960402
$275$	21.0730	−	18.9643i	1.27075	−	1.14359i
$276$	−5.61794			−0.338160
$277$	−2.69828	+	8.30447i	−0.162124	+	0.498967i	−0.998813	−	0.0487118i	$-0.984488\pi$
$277$	−2.69828	+	8.30447i	−0.162124	+	0.498967i	0.836689	+	0.547679i	$0.184488\pi$
$278$	−6.69462	−	9.21436i	−0.401517	−	0.552640i
$279$	−5.84678	+	8.04741i	−0.350038	+	0.481786i
$280$	8.36581	−	2.71822i	0.499953	−	0.162445i
$281$	2.89258	−	0.939855i	0.172557	−	0.0560671i	−0.221464	−	0.975168i	$-0.571084\pi$
$281$	2.89258	−	0.939855i	0.172557	−	0.0560671i	0.394021	+	0.919101i	$0.371084\pi$
$282$	19.7415	+	14.3430i	1.17559	+	0.854116i
$283$	26.5468	−	19.2874i	1.57804	−	1.14652i	0.659147	−	0.752014i	$-0.270917\pi$
$283$	26.5468	−	19.2874i	1.57804	−	1.14652i	0.918896	−	0.394501i	$-0.129083\pi$
$284$	−12.7442	−	4.14085i	−0.756231	−	0.245714i
$285$	6.47172			0.383352
$286$	8.38625	−	23.4199i	0.495889	−	1.38485i
$287$	7.82637			0.461976
$288$	7.70163	+	2.50241i	0.453823	+	0.147456i
$289$	−15.3913	+	11.1825i	−0.905373	+	0.657792i
$290$	−12.7297	−	9.24870i	−0.747516	−	0.543102i
$291$	8.91121	−	2.89543i	0.522384	−	0.169733i
$292$	−25.2357	+	8.19958i	−1.47681	+	0.479844i
$293$	4.73980	−	6.52378i	0.276902	−	0.381123i	−0.647803	−	0.761808i	$-0.724312\pi$
$293$	4.73980	−	6.52378i	0.276902	−	0.381123i	0.924705	+	0.380685i	$0.124312\pi$
$294$	6.49445	+	8.93884i	0.378764	+	0.521324i
$295$	2.22936	−	6.86128i	0.129799	−	0.399479i
$296$	−6.23603			−0.362462
$297$	−1.34821	−	3.03024i	−0.0782311	−	0.175832i
$298$	21.0060			1.21685
$299$	1.16410	−	8.62491i	0.0673218	−	0.498791i
$300$	16.0948	−	11.6936i	0.929236	−	0.675129i
$301$	−10.2843	+	14.1552i	−0.592779	+	0.815891i
$302$	−4.48848	−	13.8141i	−0.258283	−	0.794913i
$303$	1.77471	+	5.46201i	0.101955	+	0.313784i
$304$	−3.34639	+	4.60591i	−0.191929	+	0.264167i
$305$	−8.45491	−	11.6372i	−0.484127	−	0.666343i
$306$	11.8747	+	3.85831i	0.678829	+	0.220565i
$307$			8.32222i			0.474974i	0.971391	+	0.237487i	$0.0763237\pi$
$307$			8.32222i			0.474974i	−0.971391	+	0.237487i	$0.923676\pi$
$308$	24.7460	−	11.0099i	1.41003	−	0.627350i
$309$	−7.41376			−0.421754
$310$	−72.4358	−	23.5358i	−4.11408	−	1.33675i
$311$	−11.2588	+	8.18003i	−0.638430	+	0.463847i	−0.859311	−	0.511454i	$-0.829107\pi$
$311$	−11.2588	+	8.18003i	−0.638430	+	0.463847i	0.220880	+	0.975301i	$0.429107\pi$
$312$	1.06445	−	2.21307i	0.0602625	−	0.125290i
$313$	−6.50007	−	20.0052i	−0.367406	−	1.13076i	−0.948461	−	0.316895i	$-0.897360\pi$
$313$	−6.50007	−	20.0052i	−0.367406	−	1.13076i	0.581055	−	0.813864i	$-0.302640\pi$
$314$	−8.36835	+	2.71904i	−0.472253	+	0.153444i
$315$	10.4483	+	7.59114i	0.588696	+	0.427712i
$316$	−4.34711	+	3.15836i	−0.244544	+	0.177672i
$317$	17.7491	+	5.76702i	0.996887	+	0.323908i	0.761621	−	0.648023i	$-0.224404\pi$
$317$	17.7491	+	5.76702i	0.996887	+	0.323908i	0.235266	+	0.971931i	$0.424404\pi$
$318$			26.1196i			1.46471i
$319$	−5.90168	−	3.40937i	−0.330430	−	0.190888i
$320$			38.1686i			2.13369i
$321$	2.26806	−	6.98038i	0.126591	−	0.389607i
$322$	14.2537	−	10.3559i	0.794330	−	0.577114i
$323$	−6.20303	+	8.53774i	−0.345146	+	0.475053i
$324$	−0.719211	−	2.21350i	−0.0399562	−	0.122972i
$325$	14.6175	+	27.1326i	0.810832	+	1.50504i
$326$	5.22746	+	3.79797i	0.289522	+	0.210350i
$327$	−7.71698	−	10.6215i	−0.426750	−	0.587371i
$328$	0.469464	−	1.44486i	0.0259218	−	0.0797791i
$329$	−41.1588			−2.26916
$330$	18.8764	−	16.9876i	1.03911	−	0.935135i
$331$		−	29.8420i		−	1.64026i	−0.572175	−	0.820132i	$-0.693900\pi$
$331$		−	29.8420i		−	1.64026i	0.572175	−	0.820132i	$-0.306100\pi$
$332$	35.6577	+	11.5859i	1.95697	+	0.635859i
$333$	−5.38162	−	7.40717i	−0.294911	−	0.405910i
$334$	−2.11541	−	1.53694i	−0.115750	−	0.0840974i
$335$	2.06940	+	6.36896i	0.113063	+	0.347973i
$336$	−10.8052	+	3.51082i	−0.589472	+	0.191531i
$337$	10.0802	+	7.32372i	0.549105	+	0.398948i	0.827456	−	0.561531i	$-0.189788\pi$
$337$	10.0802	+	7.32372i	0.549105	+	0.398948i	−0.278350	+	0.960480i	$0.589788\pi$
$338$	22.5838	+	14.8763i	1.22840	+	0.809164i
$339$	3.57479	−	11.0021i	0.194156	−	0.597550i
$340$			51.4173i			2.78849i
$341$	−32.2682	−	6.86754i	−1.74742	−	0.371898i
$342$	3.65763			0.197782
$343$	5.63489	+	1.83089i	0.304256	+	0.0988586i
$344$	1.99635	+	2.74773i	0.107636	+	0.148148i
$345$	5.22223	−	7.18779i	0.281156	−	0.386978i
$346$	3.86156	−	1.25470i	0.207599	−	0.0674529i
$347$	−1.32884	−	4.08974i	−0.0713357	−	0.219549i	0.909032	−	0.416726i	$-0.136823\pi$
$347$	−1.32884	−	4.08974i	−0.0713357	−	0.219549i	−0.980368	+	0.197177i	$0.936823\pi$
$348$	−3.86941	−	2.81129i	−0.207422	−	0.150701i
$349$	13.2436	+	18.2283i	0.708915	+	0.975738i	0.999820	+	0.0189861i	$0.00604382\pi$
$349$	13.2436	+	18.2283i	0.708915	+	0.975738i	−0.290904	+	0.956752i	$0.593956\pi$
$350$	−19.2799	+	59.3375i	−1.03056	+	3.17172i
$351$	3.54730	−	0.645501i	0.189341	−	0.0344543i
$352$	2.80052	+	26.7115i	0.149268	+	1.42373i
$353$		−	5.16885i		−	0.275110i	−0.990494	−	0.137555i	$-0.956076\pi$
$353$		−	5.16885i		−	0.275110i	0.990494	−	0.137555i	$-0.0439244\pi$
$354$	1.25997	−	3.87779i	0.0669667	−	0.206102i
$355$	17.1445	−	12.4562i	0.909937	−	0.661108i
$356$	−2.21803	+	3.05286i	−0.117555	+	0.161801i
$357$	−20.0291	+	6.50784i	−1.06005	+	0.344431i
$358$	39.5715	−	12.8576i	2.09142	−	0.679543i
$359$	3.68155	−	5.06721i	0.194305	−	0.267437i	−0.700737	−	0.713419i	$-0.747145\pi$
$359$	3.68155	−	5.06721i	0.194305	−	0.267437i	0.895042	+	0.445982i	$0.147145\pi$
$360$	2.02818	−	1.47356i	0.106894	−	0.0776632i
$361$	4.91599	−	15.1299i	0.258737	−	0.796309i
$362$		−	17.5671i		−	0.923306i
$363$	7.36466	−	8.17079i	0.386544	−	0.428855i
$364$	5.27139	+	28.9685i	0.276296	+	1.51836i
$365$	12.9674	−	39.9095i	0.678744	−	2.08896i
$366$	−4.77847	−	6.57699i	−0.249774	−	0.343785i
$367$	−21.6721	−	15.7457i	−1.13128	−	0.821921i	−0.145397	−	0.989373i	$-0.546446\pi$
$367$	−21.6721	−	15.7457i	−1.13128	−	0.821921i	−0.985880	+	0.167453i	$0.946446\pi$
$368$	2.41523	+	7.43331i	0.125902	+	0.387488i
$369$	2.12135	−	0.689269i	0.110433	−	0.0358819i
$370$	41.2062	−	56.7154i	2.14221	−	2.94849i
$371$	−25.8955	−	35.6421i	−1.34443	−	1.85045i
$372$	−22.0180	−	7.15409i	−1.14158	−	0.370922i
$373$	30.3112			1.56945			0.784727	−	0.619841i	$-0.212803\pi$
$373$	30.3112			1.56945			0.784727	+	0.619841i	$0.212803\pi$
$374$	4.31794	+	41.1848i	0.223275	+	2.12962i
$375$			13.0586i			0.674341i
$376$	−2.46890	+	7.59851i	−0.127324	+	0.391863i
$377$	5.11781	−	5.35796i	0.263580	−	0.275949i
$378$	5.90508	+	4.29029i	0.303725	+	0.220669i
$379$	24.0492	−	7.81407i	1.23533	−	0.401382i	0.382686	−	0.923879i	$-0.374999\pi$
$379$	24.0492	−	7.81407i	1.23533	−	0.401382i	0.852641	+	0.522497i	$0.174999\pi$
$380$	4.65453	+	14.3252i	0.238772	+	0.734866i
$381$	5.80613	+	4.21840i	0.297457	+	0.216115i
$382$	−8.13192	−	11.1926i	−0.416065	−	0.572665i
$383$	21.7199	+	7.05722i	1.10983	+	0.360607i	0.805880	−	0.592079i	$-0.201693\pi$
$383$	21.7199	+	7.05722i	1.10983	+	0.360607i	0.303955	+	0.952686i	$0.401693\pi$
$384$			5.37582i			0.274333i
$385$	−8.91644	+	41.8953i	−0.454424	+	2.13518i
$386$	−4.47798			−0.227923
$387$	−1.54094	+	4.74253i	−0.0783305	+	0.241076i
$388$	12.8181	+	17.6426i	0.650739	+	0.895666i
$389$	15.2056	+	11.0475i	0.770953	+	0.560130i	0.902250	−	0.431213i	$-0.141914\pi$
$389$	15.2056	+	11.0475i	0.770953	+	0.560130i	−0.131297	+	0.991343i	$0.541914\pi$
$390$	13.0938	+	24.3044i	0.663031	+	1.23070i
$391$	4.47699	+	13.7787i	0.226411	+	0.696821i
$392$	−2.12638	+	2.92671i	−0.107399	+	0.147821i
$393$	10.3139	−	7.49351i	0.520269	−	0.377998i
$394$	−1.03165	+	3.17510i	−0.0519739	+	0.159959i
$395$		−	8.49775i		−	0.427568i
$396$	5.73779	−	5.16365i	0.288335	−	0.259483i
$397$			9.98777i			0.501272i	0.968081	+	0.250636i	$0.0806397\pi$
$397$			9.98777i			0.501272i	−0.968081	+	0.250636i	$0.919360\pi$
$398$	29.5800	+	9.61112i	1.48271	+	0.481762i
$399$	−4.99110	+	3.62625i	−0.249868	+	0.181540i
$400$	−22.3916	−	16.2685i	−1.11958	−	0.813423i
$401$	−36.6472	+	11.9074i	−1.83008	+	0.594628i	−0.830800	+	0.556571i	$0.812117\pi$
$401$	−36.6472	+	11.9074i	−1.83008	+	0.594628i	−0.999276	+	0.0380562i	$0.987883\pi$
$402$	1.16956	+	3.59955i	0.0583326	+	0.179529i
$403$	15.5457	−	32.3207i	0.774385	−	1.61001i
$404$	−10.8138	+	7.85667i	−0.538006	+	0.390884i
$405$	3.50059	+	1.13741i	0.173946	+	0.0565183i
$406$	14.9997			0.744420
$407$	15.1899	−	26.2940i	0.752936	−	1.30335i
$408$			4.08803i			0.202387i
$409$	17.5607	+	5.70582i	0.868321	+	0.282134i	0.709099	−	0.705108i	$-0.249102\pi$
$409$	17.5607	+	5.70582i	0.868321	+	0.282134i	0.159221	+	0.987243i	$0.449102\pi$
$410$	10.0386	+	13.8170i	0.495772	+	0.682372i
$411$	4.49193	−	6.18261i	0.221570	−	0.304965i
$412$	−5.33206	−	16.4104i	−0.262692	−	0.808482i
$413$	2.12520	+	6.54070i	0.104574	+	0.321847i
$414$	2.95145	−	4.06233i	0.145056	−	0.199653i
$415$	−47.9696	+	34.8519i	−2.35473	+	1.71081i
$416$	−28.9353	−	3.90539i	−1.41867	−	0.191477i
$417$	5.47511			0.268117
$418$	4.93125	+	11.0835i	0.241195	+	0.542110i
$419$	−37.9338			−1.85319			−0.926593	−	0.376064i	$-0.877277\pi$
$419$	−37.9338			−1.85319			−0.926593	+	0.376064i	$0.877277\pi$
$420$	−9.28848	+	28.5870i	−0.453231	+	1.39490i
$421$	9.26703	+	12.7550i	0.451648	+	0.621640i	0.972751	−	0.231854i	$-0.0744792\pi$
$421$	9.26703	+	12.7550i	0.451648	+	0.621640i	−0.521103	+	0.853494i	$0.674479\pi$
$422$	−16.9999	+	23.3983i	−0.827540	+	1.13901i
$423$	−11.1562	+	3.62486i	−0.542431	+	0.176247i
$424$	−8.13339	+	2.64270i	−0.394992	+	0.128341i
$425$	−41.5062	−	30.1560i	−2.01335	−	1.46278i
$426$	9.68958	−	7.03989i	0.469462	−	0.341084i
$427$	13.0411	+	4.23732i	0.631105	+	0.205059i
$428$	17.0823			0.825705
$429$	6.73852	+	9.87888i	0.325339	+	0.476957i
$430$	−38.1815			−1.84127
$431$	11.4631	+	3.72460i	0.552160	+	0.179408i	0.571791	−	0.820400i	$-0.306249\pi$
$431$	11.4631	+	3.72460i	0.552160	+	0.179408i	−0.0196303	+	0.999807i	$0.506249\pi$
$432$	−2.61957	+	1.90323i	−0.126034	+	0.0915692i
$433$	−0.636616	−	0.462528i	−0.0305938	−	0.0222277i	0.572383	−	0.819986i	$-0.306019\pi$
$433$	−0.636616	−	0.462528i	−0.0305938	−	0.0222277i	−0.602977	+	0.797759i	$0.706019\pi$
$434$	69.0514	−	22.4362i	3.31457	−	1.07697i
$435$	7.19373	−	2.33738i	0.344913	−	0.112069i
$436$	17.9606	−	24.7207i	0.860157	−	1.18390i
$437$	2.49463	+	3.43357i	0.119335	+	0.164250i
$438$	7.32878	−	22.5557i	0.350183	−	1.07775i
$439$	15.5544			0.742370			0.371185	−	0.928559i	$-0.378952\pi$
$439$	15.5544			0.742370			0.371185	+	0.928559i	$0.378952\pi$
$440$	7.19963	+	4.15919i	0.343229	+	0.198282i
$441$	−5.31141			−0.252924
$442$	−44.6135	−	6.02147i	−2.12205	−	0.286412i
$443$	−25.5769	+	18.5827i	−1.21519	+	0.882890i	−0.995692	−	0.0927217i	$-0.970443\pi$
$443$	−25.5769	+	18.5827i	−1.21519	+	0.882890i	−0.219502	+	0.975612i	$0.570443\pi$
$444$	12.5253	−	17.2396i	0.594423	−	0.818153i
$445$	−1.84413	−	5.67565i	−0.0874202	−	0.269052i
$446$	−7.30580	−	22.4850i	−0.345940	−	1.06469i
$447$	−5.93538	+	8.16935i	−0.280734	+	0.386397i
$448$	−21.3867	−	29.4363i	−1.01043	−	1.39073i
$449$	17.0792	+	5.54937i	0.806018	+	0.261891i	0.682910	−	0.730502i	$-0.260714\pi$
$449$	17.0792	+	5.54937i	0.806018	+	0.261891i	0.123107	+	0.992393i	$0.460714\pi$
$450$			17.7815i			0.838230i
$451$	4.94867	+	5.49892i	0.233024	+	0.258934i
$452$	26.9241			1.26640
$453$	6.64062	+	2.15767i	0.312004	+	0.101376i
$454$	34.7925	−	25.2782i	1.63289	−	1.18637i
$455$	−41.9634	−	20.1836i	−1.96727	−	0.946224i
$456$	0.370067	+	1.13895i	0.0173300	+	0.0533362i
$457$	−2.65596	+	0.862974i	−0.124241	+	0.0403682i	−0.370477	−	0.928841i	$-0.620806\pi$
$457$	−2.65596	+	0.862974i	−0.124241	+	0.0403682i	0.246237	+	0.969210i	$0.420806\pi$
$458$	18.0647	+	13.1248i	0.844107	+	0.613280i
$459$	−4.85577	+	3.52792i	−0.226648	+	0.164669i
$460$	19.6661	+	6.38990i	0.916936	+	0.297931i
$461$			13.1955i			0.614574i	0.951617	+	0.307287i	$0.0994212\pi$
$461$			13.1955i			0.614574i	−0.951617	+	0.307287i	$0.900579\pi$
$462$	−5.03931	+	23.6780i	−0.234450	+	1.10160i
$463$		−	25.1264i		−	1.16772i	−0.811854	−	0.583861i	$-0.801541\pi$
$463$		−	25.1264i		−	1.16772i	0.811854	−	0.583861i	$-0.198459\pi$
$464$	−2.05621	+	6.32837i	−0.0954573	+	0.293787i
$465$	29.6204	−	21.5205i	1.37361	−	0.997987i
$466$	−2.48920	+	3.42608i	−0.115310	+	0.158710i
$467$	−8.91179	−	27.4277i	−0.412389	−	1.26920i	−0.914566	−	0.404437i	$-0.867467\pi$
$467$	−8.91179	−	27.4277i	−0.412389	−	1.26920i	0.502177	−	0.864765i	$-0.332533\pi$
$468$	3.98008	+	7.38771i	0.183979	+	0.341497i
$469$	−5.16463	−	3.75232i	−0.238480	−	0.173266i
$470$	−52.7930	−	72.6633i	−2.43516	−	3.35171i
$471$	1.30708	−	4.02277i	0.0602270	−	0.185360i
$472$	1.33499			0.0614478
$473$	−16.4485	+	1.72451i	−0.756303	+	0.0792930i
$474$		−	4.80268i		−	0.220594i
$475$	−14.2938	−	4.64432i	−0.655842	−	0.213096i
$476$	−28.8102	−	39.6539i	−1.32051	−	1.81753i
$477$	−10.1580	−	7.38024i	−0.465104	−	0.337918i
$478$	2.21105	+	6.80492i	0.101131	+	0.311250i
$479$	4.44635	−	1.44471i	0.203159	−	0.0660103i	−0.205670	−	0.978621i	$-0.565937\pi$
$479$	4.44635	−	1.44471i	0.203159	−	0.0660103i	0.408829	+	0.912611i	$0.365937\pi$
$480$	−24.1140	−	17.5198i	−1.10065	−	0.799667i
$481$	23.8716	+	22.8016i	1.08845	+	1.03966i
$482$	−6.59227	+	20.2889i	−0.300270	+	0.924135i
$483$			8.46948i			0.385375i
$484$	23.3828	+	10.4252i	1.06286	+	0.473872i
$485$	−34.4878			−1.56601
$486$	1.97843	+	0.642831i	0.0897434	+	0.0291594i
$487$	−1.31889	−	1.81529i	−0.0597644	−	0.0822587i	0.778089	−	0.628155i	$-0.216189\pi$
$487$	−1.31889	−	1.81529i	−0.0597644	−	0.0822587i	−0.837853	+	0.545896i	$0.816189\pi$
$488$	1.56454	−	2.15341i	0.0708235	−	0.0974803i
$489$	−2.95410	+	0.959846i	−0.133589	+	0.0434057i
$490$	−12.5673	−	38.6781i	−0.567731	−	1.74730i
$491$	23.0295	+	16.7319i	1.03931	+	0.755100i	0.970150	−	0.242506i	$-0.0779693\pi$
$491$	23.0295	+	16.7319i	1.03931	+	0.755100i	0.0691563	+	0.997606i	$0.477969\pi$
$492$	3.05140	+	4.19989i	0.137568	+	0.189346i
$493$	−3.81150	+	11.7306i	−0.171661	+	0.528319i
$494$	−12.9747	+	2.36100i	−0.583759	+	0.106227i
$495$	1.27291	+	12.1411i	0.0572129	+	0.545701i
$496$			32.2085i			1.44621i
$497$	−6.24265	+	19.2129i	−0.280021	+	0.861817i
$498$	−27.1110	+	19.6973i	−1.21487	+	0.882657i
$499$	13.0930	−	18.0210i	0.586125	−	0.806731i	−0.408226	−	0.912881i	$-0.633852\pi$
$499$	13.0930	−	18.0210i	0.586125	−	0.806731i	0.994350	+	0.106150i	$0.0338523\pi$
$500$	−28.9052	+	9.39185i	−1.29268	+	0.420016i
$501$	1.19544	−	0.388423i	0.0534085	−	0.0173535i
$502$	4.87190	−	6.70560i	0.217444	−	0.299285i
$503$	−1.55187	+	1.12750i	−0.0691943	+	0.0502726i	−0.621845	−	0.783141i	$-0.713616\pi$
$503$	−1.55187	+	1.12750i	−0.0691943	+	0.0502726i	0.552650	+	0.833413i	$0.313616\pi$
$504$	−0.738498	+	2.27286i	−0.0328953	+	0.101241i
$505$		−	21.1388i		−	0.940665i
$506$	16.2890	+	3.46673i	0.724134	+	0.154115i
$507$	−12.1667	+	4.57957i	−0.540340	+	0.203386i
$508$	−5.16161	+	15.8858i	−0.229010	+	0.704819i
$509$	10.2899	+	14.1628i	0.456090	+	0.627754i	0.973692	−	0.227867i	$-0.0731753\pi$
$509$	10.2899	+	14.1628i	0.456090	+	0.627754i	−0.517602	+	0.855621i	$0.673175\pi$
$510$	−37.1798	−	27.0127i	−1.64635	−	1.19614i
$511$	12.3615	+	38.0448i	0.546841	+	1.68300i
$512$	29.1325	−	9.46574i	1.28749	−	0.418330i
$513$	−1.03348	+	1.42247i	−0.0456294	+	0.0628035i
$514$	−19.8776	−	27.3592i	−0.876765	−	1.20676i
$515$	25.9525	+	8.43248i	1.14360	+	0.371580i
$516$	−11.6059			−0.510920
$517$	−26.0250	−	28.9187i	−1.14458	−	1.27184i
$518$			66.8286i			2.93628i
$519$	−0.603149	+	1.85630i	−0.0264753	+	0.0814826i
$520$	−6.24336	+	6.53633i	−0.273790	+	0.286637i
$521$	7.17750	+	5.21476i	0.314452	+	0.228463i	0.733804	−	0.679361i	$-0.237743\pi$
$521$	7.17750	+	5.21476i	0.314452	+	0.228463i	−0.419353	+	0.907823i	$0.637743\pi$
$522$	4.06569	−	1.32102i	0.177950	−	0.0578195i
$523$	−0.831256	−	2.55834i	−0.0363483	−	0.111869i	0.931236	−	0.364416i	$-0.118731\pi$
$523$	−0.831256	−	2.55834i	−0.0363483	−	0.111869i	−0.967584	+	0.252548i	$0.918731\pi$
$524$	24.0048	+	17.4405i	1.04865	+	0.761892i
$525$	−17.6290	−	24.2642i	−0.769392	−	1.05898i
$526$	10.9527	+	3.55875i	0.477560	+	0.155169i
$527$			59.7033i			2.60072i
$528$	−9.29897	−	5.37197i	−0.404686	−	0.233785i
$529$	−17.1735			−0.746675
$530$	29.7087	−	91.4339i	1.29046	−	3.97163i
$531$	1.15208	+	1.58570i	0.0499960	+	0.0688136i
$532$	−11.6164	−	8.43979i	−0.503634	−	0.365911i
$533$	−7.08014	+	3.81438i	−0.306675	+	0.165219i
$534$	−1.04225	−	3.20771i	−0.0451025	−	0.138811i
$535$	−15.8791	+	21.8557i	−0.686514	+	0.944905i
$536$	−1.00253	+	0.728383i	−0.0433028	+	0.0314613i
$537$	−6.18079	+	19.0225i	−0.266721	+	0.820883i
$538$		−	20.8332i		−	0.898184i
$539$	−7.16089	−	16.0948i	−0.308441	−	0.693253i
$540$			8.56660i			0.368648i
$541$	−5.73502	−	1.86342i	−0.246568	−	0.0801147i	0.183126	−	0.983089i	$-0.441378\pi$
$541$	−5.73502	−	1.86342i	−0.246568	−	0.0801147i	−0.429694	+	0.902975i	$0.641378\pi$
$542$	43.9155	−	31.9065i	1.88633	−	1.37050i
$543$	6.83193	+	4.96369i	0.293186	+	0.213012i
$544$	46.2256	−	15.0196i	1.98191	−	0.643961i
$545$	14.9329	+	45.9589i	0.639657	+	1.96866i
$546$	−23.7165	−	11.4072i	−1.01497	−	0.488183i
$547$	−13.7278	+	9.97381i	−0.586957	+	0.426450i	−0.841226	−	0.540684i	$-0.818165\pi$
$547$	−13.7278	+	9.97381i	−0.586957	+	0.426450i	0.254268	+	0.967134i	$0.418165\pi$
$548$	16.9159	+	5.49630i	0.722610	+	0.234790i
$549$	3.90801			0.166790
$550$	−53.8822	+	23.9732i	−2.29755	+	1.02222i
$551$			3.61325i			0.153930i
$552$	1.56359	+	0.508041i	0.0665508	+	0.0216237i
$553$	4.76148	+	6.55361i	0.202479	+	0.278688i
$554$	10.6767	−	14.6953i	0.453611	−	0.624342i
$555$	10.4139	+	32.0505i	0.442043	+	1.36047i
$556$	3.93776	+	12.1192i	0.166998	+	0.513968i
$557$	1.39554	−	1.92080i	0.0591311	−	0.0813869i	−0.778427	−	0.627735i	$-0.783982\pi$
$557$	1.39554	−	1.92080i	0.0591311	−	0.0813869i	0.837558	+	0.546348i	$0.183982\pi$
$558$	16.7406	−	12.1627i	0.708685	−	0.514890i
$559$	2.40487	−	17.8178i	0.101715	−	0.753615i
$560$	41.8178			1.76712
$561$	−17.2370	−	9.95775i	−0.727748	−	0.420416i
$562$	−6.32693			−0.266885
$563$	−1.66022	+	5.10965i	−0.0699701	+	0.215346i	−0.979927	−	0.199357i	$-0.936115\pi$
$563$	−1.66022	+	5.10965i	−0.0699701	+	0.215346i	0.909957	+	0.414703i	$0.136115\pi$
$564$	−16.0473	−	22.0872i	−0.675712	−	0.930038i
$565$	−25.0277	+	34.4477i	−1.05292	+	1.44922i
$566$	−64.9195	+	21.0936i	−2.72877	+	0.886631i
$567$	−3.33703	+	1.08427i	−0.140142	+	0.0455349i
$568$	3.17252	+	2.30497i	0.133116	+	0.0967144i
$569$	20.6296	−	14.9883i	0.864836	−	0.628340i	−0.0643600	−	0.997927i	$-0.520501\pi$
$569$	20.6296	−	14.9883i	0.864836	−	0.628340i	0.929196	+	0.369586i	$0.120501\pi$
$570$	−12.8038	−	4.16022i	−0.536294	−	0.174252i
$571$	−13.5119			−0.565457			−0.282729	−	0.959200i	$-0.591240\pi$
$571$	−13.5119			−0.565457			−0.282729	+	0.959200i	$0.591240\pi$
$572$	−17.0205	+	22.0207i	−0.711664	+	0.920734i
$573$	6.65059			0.277832
$574$	−15.4839	−	5.03103i	−0.646286	−	0.209991i
$575$	−16.6923	+	12.1277i	−0.696116	+	0.505758i
$576$	−8.38936	−	6.09523i	−0.349557	−	0.253968i
$577$	12.6750	−	4.11837i	0.527668	−	0.171450i	−0.0330543	−	0.999454i	$-0.510523\pi$
$577$	12.6750	−	4.11837i	0.527668	−	0.171450i	0.560723	+	0.828004i	$0.310523\pi$
$578$	37.6391	−	12.2297i	1.56558	−	0.508688i
$579$	1.26528	−	1.74151i	0.0525832	−	0.0723746i
$580$	10.3476	+	14.2423i	0.429661	+	0.591378i
$581$	17.4667	−	53.7568i	0.724639	−	2.23021i
$582$	−19.4915			−0.807947
$583$	8.66872	−	40.7313i	0.359022	−	1.68692i
$584$	7.76513			0.321323
$585$	−13.1518	−	1.77510i	−0.543761	−	0.0733913i
$586$	−13.5710	+	9.85994i	−0.560615	+	0.407311i
$587$	1.45278	−	1.99958i	0.0599625	−	0.0825313i	−0.777983	−	0.628286i	$-0.783757\pi$
$587$	1.45278	−	1.99958i	0.0599625	−	0.0825313i	0.837945	+	0.545754i	$0.183757\pi$
$588$	−3.82002	−	11.7568i	−0.157535	−	0.484843i
$589$	5.40463	+	16.6337i	0.222694	+	0.685381i
$590$	−8.82128	+	12.1415i	−0.363166	+	0.499856i
$591$	−0.943312	−	1.29836i	−0.0388027	−	0.0534073i
$592$	−28.1951	−	9.16114i	−1.15881	−	0.376521i
$593$		−	42.5819i		−	1.74863i	−0.485361	−	0.874314i	$-0.661312\pi$
$593$		−	42.5819i		−	1.74863i	0.485361	−	0.874314i	$-0.338688\pi$
$594$	0.719409	+	6.86178i	0.0295177	+	0.281542i
$595$	77.5155			3.17783
$596$	−22.3517	−	7.26250i	−0.915560	−	0.297483i
$597$	−12.0958	+	8.78812i	−0.495049	+	0.359674i
$598$	−7.84745	+	16.3155i	−0.320906	+	0.667189i
$599$	−6.75383	−	20.7862i	−0.275954	−	0.849299i	−0.988965	−	0.148147i	$-0.952669\pi$
$599$	−6.75383	−	20.7862i	−0.275954	−	0.849299i	0.713011	−	0.701152i	$-0.247331\pi$
$600$	−5.53700	+	1.79908i	−0.226047	+	0.0734472i
$601$	18.3112	+	13.3039i	0.746929	+	0.542676i	0.894874	−	0.446320i	$-0.147266\pi$
$601$	18.3112	+	13.3039i	0.746929	+	0.542676i	−0.147944	+	0.988996i	$0.547266\pi$
$602$	29.4462	−	21.3939i	1.20014	−	0.871951i
$603$	−1.73035	−	0.562225i	−0.0704653	−	0.0228956i
$604$			16.2509i			0.661238i
$605$	−35.0742	+	20.2259i	−1.42597	+	0.822300i
$606$		−	11.9470i		−	0.485315i
$607$	−6.77007	+	20.8361i	−0.274789	+	0.845713i	0.714486	+	0.699649i	$0.246660\pi$
$607$	−6.77007	+	20.8361i	−0.274789	+	0.845713i	−0.989275	+	0.146064i	$0.953340\pi$
$608$	11.5191	−	8.36913i	0.467162	−	0.339413i
$609$	−4.23824	+	5.83344i	−0.171742	+	0.236383i
$610$	9.24670	+	28.4584i	0.374388	+	1.15225i
$611$	37.2344	−	20.0598i	1.50634	−	0.811531i
$612$	−11.3014	−	8.21094i	−0.456832	−	0.331908i
$613$	−1.48310	−	2.04132i	−0.0599019	−	0.0824479i	0.778015	−	0.628246i	$-0.216227\pi$
$613$	−1.48310	−	2.04132i	−0.0599019	−	0.0824479i	−0.837917	+	0.545798i	$0.816227\pi$
$614$	5.34978	−	16.4649i	0.215899	−	0.664470i
$615$	−8.20996			−0.331057
$616$	−7.88297	+	0.826473i	−0.317614	+	0.0332996i
$617$			6.28929i			0.253197i	0.991954	+	0.126599i	$0.0404060\pi$
$617$			6.28929i			0.253197i	−0.991954	+	0.126599i	$0.959594\pi$
$618$	14.6676	+	4.76579i	0.590018	+	0.191708i
$619$	10.0359	+	13.8132i	0.403377	+	0.555200i	0.961587	−	0.274499i	$-0.0885119\pi$
$619$	10.0359	+	13.8132i	0.403377	+	0.555200i	−0.558211	+	0.829699i	$0.688512\pi$
$620$	68.9389	+	50.0870i	2.76865	+	2.01154i
$621$	0.745908	+	2.29567i	0.0299323	+	0.0921221i
$622$	27.5332	−	8.94608i	1.10398	−	0.358705i
$623$	4.60242	+	3.34385i	0.184392	+	0.133969i
$624$	8.06387	−	8.44226i	0.322813	−	0.337961i
$625$	1.64583	−	5.06535i	0.0658333	−	0.202614i
$626$			43.7573i			1.74889i
$627$	−5.70377	−	1.21391i	−0.227787	−	0.0484791i
$628$	9.84448			0.392838
$629$	−52.2638	−	16.9815i	−2.08390	−	0.677099i
$630$	−15.7914	−	21.7350i	−0.629145	−	0.865944i
$631$	16.8201	−	23.1509i	0.669599	−	0.921624i	−0.330152	−	0.943928i	$-0.607100\pi$
$631$	16.8201	−	23.1509i	0.669599	−	0.921624i	0.999751	+	0.0223035i	$0.00710001\pi$
$632$	1.49551	−	0.485920i	0.0594882	−	0.0193289i
$633$	−4.29630	−	13.2227i	−0.170763	−	0.525554i
$634$	−31.4081	−	22.8193i	−1.24737	−	0.906270i
$635$	−15.5268	−	21.3708i	−0.616163	−	0.848076i
$636$	9.03042	−	27.7928i	0.358080	−	1.10206i
$637$	18.8411	−	3.42852i	0.746513	−	0.135843i
$638$	9.48440	+	10.5390i	0.375491	+	0.417242i
$639$			5.75749i			0.227763i
$640$	6.11451	−	18.8185i	0.241697	−	0.743867i
$641$	−7.60105	+	5.52248i	−0.300223	+	0.218125i	−0.727690	−	0.685906i	$-0.759406\pi$
$641$	−7.60105	+	5.52248i	−0.300223	+	0.218125i	0.427467	+	0.904031i	$0.359406\pi$
$642$	−8.97441	+	12.3522i	−0.354192	+	0.487503i
$643$	−7.99545	+	2.59788i	−0.315310	+	0.102450i	−0.462397	−	0.886673i	$-0.653010\pi$
$643$	−7.99545	+	2.59788i	−0.315310	+	0.102450i	0.147087	+	0.989124i	$0.453010\pi$
$644$	−18.7472	+	6.09134i	−0.738744	+	0.240033i
$645$	10.7884	−	14.8490i	0.424793	−	0.584677i
$646$	17.7606	−	12.9038i	0.698781	−	0.507694i
$647$	4.80111	−	14.7763i	0.188751	−	0.580916i	−0.811242	−	0.584711i	$-0.801208\pi$
$647$	4.80111	−	14.7763i	0.188751	−	0.580916i	0.999993	+	0.00379463i	$0.00120787\pi$
$648$			0.681104i			0.0267563i
$649$	−3.25181	+	5.62894i	−0.127645	+	0.220955i
$650$	−11.4780	−	63.0764i	−0.450204	−	2.47406i
$651$	−10.7854	+	33.1939i	−0.422711	+	1.30097i
$652$	−4.24924	−	5.84858i	−0.166413	−	0.229048i
$653$	39.9459	+	29.0224i	1.56320	+	1.13573i	0.933320	+	0.359045i	$0.116898\pi$
$653$	39.9459	+	29.0224i	1.56320	+	1.13573i	0.629884	+	0.776689i	$0.283102\pi$
$654$	8.43966	+	25.9746i	0.330017	+	1.01569i
$655$	−44.6280	+	14.5005i	−1.74376	+	0.566582i
$656$	4.24520	−	5.84301i	0.165747	−	0.228131i
$657$	6.70122	+	9.22344i	0.261440	+	0.359841i
$658$	81.4297	+	26.4581i	3.17446	+	1.03144i
$659$	−14.2033			−0.553283			−0.276642	−	0.960973i	$-0.589221\pi$
$659$	−14.2033			−0.553283			−0.276642	+	0.960973i	$0.589221\pi$
$660$	−25.9588	+	11.5496i	−1.01045	+	0.449567i
$661$		−	10.8145i		−	0.420636i	−0.977633	−	0.210318i	$-0.932550\pi$
$661$		−	10.8145i		−	0.420636i	0.977633	−	0.210318i	$-0.0674500\pi$
$662$	−19.1833	+	59.0402i	−0.745582	+	2.29466i
$663$	14.9476	−	15.6490i	0.580516	−	0.607757i
$664$	−8.87655	−	6.44919i	−0.344477	−	0.250277i
$665$	21.5963	−	7.01707i	0.837469	−	0.272110i
$666$	5.88561	+	18.1140i	0.228063	+	0.701905i
$667$	4.01304	+	2.91565i	0.155386	+	0.112894i
$668$	1.71955	+	2.36676i	0.0665315	+	0.0915727i
$669$	10.8088	+	3.51199i	0.417893	+	0.135782i
$670$		−	13.9308i		−	0.538194i
$671$	5.26882	+	11.8422i	0.203400	+	0.457163i
$672$	28.4139			1.09609
$673$	−0.671181	+	2.06568i	−0.0258721	+	0.0796262i	−0.963159	−	0.268933i	$-0.913329\pi$
$673$	−0.671181	+	2.06568i	−0.0258721	+	0.0796262i	0.937287	+	0.348559i	$0.113329\pi$
$674$	−15.2351	−	20.9694i	−0.586835	−	0.807709i
$675$	−6.91532	−	5.02428i	−0.266171	−	0.193385i
$676$	−18.8873	−	23.6373i	−0.726434	−	0.909125i
$677$	−15.5857	−	47.9678i	−0.599007	−	1.84355i	−0.533674	−	0.845690i	$-0.679189\pi$
$677$	−15.5857	−	47.9678i	−0.599007	−	1.84355i	−0.0653327	−	0.997864i	$-0.520811\pi$
$678$	−14.1449	+	19.4688i	−0.543233	+	0.747695i
$679$	26.5976	−	19.3243i	1.02072	−	0.741597i
$680$	4.64976	−	14.3105i	0.178310	−	0.548782i
$681$			20.6735i			0.792210i
$682$	59.4258	+	34.3300i	2.27553	+	1.31456i
$683$		−	21.5077i		−	0.822970i	−0.911417	−	0.411485i	$-0.865010\pi$
$683$		−	21.5077i		−	0.822970i	0.911417	−	0.411485i	$-0.134990\pi$
$684$	−3.89193	−	1.26457i	−0.148812	−	0.0483519i
$685$	−22.7565	+	16.5336i	−0.869482	+	0.631716i
$686$	−9.97129	−	7.24456i	−0.380705	−	0.276599i
$687$	−10.2086	+	3.31696i	−0.389481	+	0.126550i
$688$	4.98952	+	15.3562i	0.190224	+	0.585448i
$689$	40.7975	+	19.6229i	1.55426	+	0.747573i
$690$	−14.9524	+	10.8635i	−0.569226	+	0.413567i
$691$	22.2593	+	7.23249i	0.846785	+	0.275137i	0.700099	−	0.714046i	$-0.253139\pi$
$691$	22.2593	+	7.23249i	0.846785	+	0.275137i	0.146686	+	0.989183i	$0.453139\pi$
$692$	−4.54272			−0.172688
$693$	−7.78460	−	8.65017i	−0.295713	−	0.328593i
$694$			8.94547i			0.339566i
$695$	−19.1661	−	6.22745i	−0.727012	−	0.236220i
$696$	0.822707	+	1.13236i	0.0311846	+	0.0429220i
$697$	7.86911	−	10.8309i	0.298064	−	0.410249i
$698$	−14.4839	−	44.5768i	−0.548223	−	1.68726i
$699$	−0.629084	−	1.93612i	−0.0237941	−	0.0732308i
$700$	41.0300	−	56.4729i	1.55079	−	2.13448i
$701$	29.1888	−	21.2069i	1.10244	−	0.800972i	0.120987	−	0.992654i	$-0.461394\pi$
$701$	29.1888	−	21.2069i	1.10244	−	0.800972i	0.981457	+	0.191682i	$0.0613941\pi$
$702$	−7.43303	−	1.00323i	−0.280542	−	0.0378646i
$703$	−16.0983			−0.607158
$704$	7.15936	−	33.6394i	0.269829	−	1.26783i
$705$	43.1761			1.62610
$706$	−3.32270	+	10.2262i	−0.125051	+	0.384868i
$707$	11.8446	+	16.3026i	0.445460	+	0.613123i
$708$	−2.68137	+	3.69059i	−0.100772	+	0.138701i
$709$	15.9468	−	5.18143i	0.598894	−	0.194593i	0.00614700	−	0.999981i	$-0.498043\pi$
$709$	15.9468	−	5.18143i	0.598894	−	0.194593i	0.592747	+	0.805389i	$0.298043\pi$
$710$	−41.9265	+	13.6227i	−1.57347	+	0.511252i
$711$	1.86779	+	1.35703i	0.0700474	+	0.0508924i
$712$	0.893400	−	0.649093i	0.0334816	−	0.0243258i
$713$	22.8353	+	7.41965i	0.855191	+	0.277868i
$714$	43.8095			1.63953
$715$	−12.3525	−	42.2463i	−0.461956	−	1.57992i
$716$	−46.5517			−1.73972
$717$	−3.27121	−	1.06288i	−0.122166	−	0.0396940i
$718$	−10.5410	+	7.65851i	−0.393388	+	0.285813i
$719$	17.8592	+	12.9755i	0.666036	+	0.483904i	0.868696	−	0.495346i	$-0.164959\pi$
$719$	17.8592	+	12.9755i	0.666036	+	0.483904i	−0.202660	+	0.979249i	$0.564959\pi$
$720$	11.3348	−	3.68290i	0.422423	−	0.137253i
$721$	−24.7399	+	8.03850i	−0.921364	+	0.299369i
$722$	−19.4519	+	26.7732i	−0.723925	+	0.996397i
$723$	−6.02778	−	8.29652i	−0.224175	−	0.308551i
$724$	−6.07354	+	18.6924i	−0.225721	+	0.694699i
$725$	−17.5658			−0.652378
$726$	−19.8229	+	11.4311i	−0.735697	+	0.424248i
$727$	−0.811161			−0.0300843			−0.0150422	−	0.999887i	$-0.504788\pi$
$727$	−0.811161			−0.0300843			−0.0150422	+	0.999887i	$0.504788\pi$
$728$	1.15254	−	8.53923i	0.0427159	−	0.316485i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−51.3101	+	70.6223i	−1.89907	+	2.61385i
$731$	9.24882	+	28.4650i	0.342080	+	1.05281i
$732$	2.81068	+	8.65039i	0.103886	+	0.319728i
$733$	10.7220	−	14.7575i	0.396025	−	0.545081i	−0.563716	−	0.825969i	$-0.690629\pi$
$733$	10.7220	−	14.7575i	0.396025	−	0.545081i	0.959741	+	0.280887i	$0.0906288\pi$
$734$	32.7550	+	45.0833i	1.20901	+	1.66406i
$735$	18.5930	+	6.04124i	0.685814	+	0.222835i
$736$		−	19.5470i		−	0.720511i
$737$	−0.629201	−	6.00136i	−0.0231769	−	0.221063i
$738$	−4.64003			−0.170802
$739$	−45.1410	−	14.6672i	−1.66054	−	0.539542i	−0.679555	−	0.733625i	$-0.737827\pi$
$739$	−45.1410	−	14.6672i	−1.66054	−	0.539542i	−0.980985	+	0.194083i	$0.937827\pi$
$740$	−63.4542	+	46.1022i	−2.33262	+	1.69475i
$741$	2.74787	−	5.71304i	0.100946	−	0.209874i
$742$	28.3206	+	87.1618i	1.03968	+	3.19981i
$743$	4.13919	−	1.34490i	0.151852	−	0.0493398i	−0.232105	−	0.972691i	$-0.574561\pi$
$743$	4.13919	−	1.34490i	0.151852	−	0.0493398i	0.383957	+	0.923351i	$0.374561\pi$
$744$	5.48112	+	3.98227i	0.200948	+	0.145997i
$745$	30.0692	−	21.8465i	1.10165	−	0.800396i
$746$	−59.9686	−	19.4850i	−2.19561	−	0.713396i
$747$		−	16.1092i		−	0.589404i
$748$	9.64445	−	45.3160i	0.352636	−	1.65692i
$749$		−	25.7529i		−	0.940992i
$750$	8.39444	−	25.8354i	0.306522	−	0.943377i
$751$	2.45515	−	1.78377i	0.0895896	−	0.0650907i	−0.542089	−	0.840321i	$-0.682366\pi$
$751$	2.45515	−	1.78377i	0.0895896	−	0.0650907i	0.631678	+	0.775231i	$0.282366\pi$
$752$	−22.3254	+	30.7283i	−0.814125	+	1.12055i
$753$	1.23125	+	3.78941i	0.0448694	+	0.138094i
$754$	−13.5695	+	7.31046i	−0.494171	+	0.266231i
$755$	−20.7919	−	15.1062i	−0.756696	−	0.549772i
$756$	−4.80006	−	6.60671i	−0.174576	−	0.240284i
$757$	6.08954	−	18.7417i	0.221328	−	0.681178i	−0.777316	−	0.629111i	$-0.783419\pi$
$757$	6.08954	−	18.7417i	0.221328	−	0.681178i	0.998644	−	0.0520668i	$-0.0165809\pi$
$758$	−52.6029			−1.91062
$759$	−5.95078	+	5.35532i	−0.216000	+	0.194386i
$760$		−	4.40791i		−	0.159892i
$761$	45.7209	+	14.8556i	1.65738	+	0.538516i	0.980321	−	0.197412i	$-0.0632537\pi$
$761$	45.7209	+	14.8556i	1.65738	+	0.538516i	0.677060	+	0.735928i	$0.263254\pi$
$762$	−8.77531	−	12.0782i	−0.317896	−	0.437546i
$763$	−37.2683	−	27.0770i	−1.34920	−	0.980254i
$764$	4.78318	+	14.7211i	0.173049	+	0.532591i
$765$	21.0107	−	6.82680i	0.759645	−	0.246824i
$766$	−38.4347	−	27.9244i	−1.38870	−	1.00895i
$767$	−5.11035	−	4.88129i	−0.184524	−	0.176253i
$768$	−2.95316	+	9.08890i	−0.106563	+	0.327967i
$769$		−	29.2195i		−	1.05368i	−0.849964	−	0.526841i	$-0.823376\pi$
$769$		−	29.2195i		−	1.05368i	0.849964	−	0.526841i	$-0.176624\pi$
$770$	44.5721	−	77.1551i	1.60627	−	2.78048i
$771$	16.2567			0.585470
$772$	4.76484	+	1.54819i	0.171490	+	0.0557205i
$773$	−25.8704	−	35.6076i	−0.930494	−	1.28072i	−0.959666	−	0.281141i	$-0.909287\pi$
$773$	−25.8704	−	35.6076i	−0.930494	−	1.28072i	0.0291722	−	0.999574i	$-0.490713\pi$
$774$	6.09729	−	8.39220i	0.219163	−	0.301651i
$775$	−80.8648	+	26.2746i	−2.90475	+	0.943810i
$776$	−1.97209	−	6.06946i	−0.0707938	−	0.217881i
$777$	−25.9900	−	18.8828i	−0.932385	−	0.677418i
$778$	−22.9815	−	31.6313i	−0.823926	−	1.13404i
$779$	1.21192	−	3.72990i	0.0434215	−	0.133638i
$780$	−5.52975	−	30.3883i	−0.197997	−	1.08808i
$781$	−17.4466	+	7.76230i	−0.624287	+	0.277757i
$782$		−	30.1382i		−	1.07774i
$783$	−0.635032	+	1.95443i	−0.0226942	+	0.0698455i
$784$	−13.9136	+	10.1088i	−0.496914	+	0.361030i
$785$	−9.15108	+	12.5954i	−0.326616	+	0.449548i
$786$	−25.2224	+	8.19527i	−0.899655	+	0.292316i
$787$	16.0635	−	5.21936i	0.572604	−	0.186050i	−0.00838075	−	0.999965i	$-0.502668\pi$
$787$	16.0635	−	5.21936i	0.572604	−	0.186050i	0.580984	+	0.813915i	$0.302668\pi$
$788$	2.19548	−	3.02182i	0.0782107	−	0.107648i
$789$	−4.47877	+	3.25401i	−0.159448	+	0.115846i
$790$	−5.46262	+	16.8122i	−0.194351	+	0.598151i
$791$		−	40.5902i		−	1.44322i
$792$	−2.06391	+	0.918271i	−0.0733377	+	0.0326293i
$793$	−13.8629	+	2.52262i	−0.492285	+	0.0895810i
$794$	6.42044	−	19.7601i	0.227853	−	0.701260i
$795$	27.1647	+	37.3890i	0.963433	+	1.32605i
$796$	−28.1520	−	20.4536i	−0.997821	−	0.724959i
$797$	−1.05160	−	3.23648i	−0.0372494	−	0.114642i	0.930703	−	0.365776i	$-0.119196\pi$
$797$	−1.05160	−	3.23648i	−0.0372494	−	0.114642i	−0.967952	+	0.251134i	$0.919196\pi$
$798$	12.2056	−	3.96584i	0.432074	−	0.140389i
$799$	−41.3835	+	56.9596i	−1.46404	+	2.01508i
$800$	40.6865	+	56.0001i	1.43848	+	1.97990i
$801$	1.54199	+	0.501022i	0.0544835	+	0.0177028i
$802$	80.1584			2.83049
$803$	−18.9146	+	32.7414i	−0.667480	+	1.15542i
$804$		−	4.23449i		−	0.149339i
$805$	9.63327	−	29.6482i	0.339528	−	1.04496i
$806$	−51.5327	+	53.9509i	−1.81516	+	1.90034i
$807$	8.10214	+	5.88655i	0.285209	+	0.207216i
$808$	3.72020	−	1.20876i	0.130876	−	0.0425242i
$809$	12.1936	+	37.5280i	0.428704	+	1.31942i	0.899402	+	0.437121i	$0.144002\pi$
$809$	12.1936	+	37.5280i	0.428704	+	1.31942i	−0.470698	+	0.882294i	$0.655998\pi$
$810$	−6.19450	−	4.50057i	−0.217653	−	0.158134i
$811$	−26.4123	−	36.3534i	−0.927462	−	1.27654i	−0.960841	−	0.277099i	$-0.910627\pi$
$811$	−26.4123	−	36.3534i	−0.927462	−	1.27654i	0.0333796	−	0.999443i	$-0.489373\pi$
$812$	−15.9605	−	5.18589i	−0.560105	−	0.181989i
$813$			26.0943i			0.915167i
$814$	−46.9548	+	42.2563i	−1.64576	+	1.48108i
$815$	11.4328			0.400475
$816$	−6.00559	+	18.4833i	−0.210238	+	0.647045i
$817$	5.15356	+	7.09327i	0.180300	+	0.248162i
$818$	−31.0747	−	22.5771i	−1.08650	−	0.789390i
$819$	11.1375	−	6.00028i	0.389177	−	0.209667i
$820$	−5.90469	−	18.1728i	−0.206201	−	0.634621i
$821$	−27.7645	+	38.2146i	−0.968989	+	1.33370i	−0.0264337	+	0.999651i	$0.508415\pi$
$821$	−27.7645	+	38.2146i	−0.968989	+	1.33370i	−0.942556	+	0.334049i	$0.891585\pi$
$822$	−12.8613	+	9.34430i	−0.448590	+	0.325920i
$823$	0.661075	−	2.03458i	0.0230436	−	0.0709210i	−0.938873	−	0.344263i	$-0.888129\pi$
$823$	0.661075	−	2.03458i	0.0230436	−	0.0709210i	0.961917	+	0.273342i	$0.0881289\pi$
$824$			5.04954i			0.175909i
$825$	5.90144	−	27.7288i	0.205462	−	0.965394i
$826$		−	14.3065i		−	0.497785i
$827$	16.5552	+	5.37911i	0.575681	+	0.187050i	0.582365	−	0.812928i	$-0.302128\pi$
$827$	16.5552	+	5.37911i	0.575681	+	0.187050i	−0.00668379	+	0.999978i	$0.502128\pi$
$828$	−4.54501	+	3.30214i	−0.157950	+	0.114757i
$829$	7.89061	+	5.73286i	0.274052	+	0.199111i	0.716319	−	0.697773i	$-0.245826\pi$
$829$	7.89061	+	5.73286i	0.274052	+	0.199111i	−0.442267	+	0.896884i	$0.645826\pi$
$830$	117.308	−	38.1158i	4.07183	−	1.32302i
$831$	2.69828	+	8.30447i	0.0936025	+	0.288079i
$832$	33.6941	+	16.2063i	1.16813	+	0.561851i
$833$	−25.7910	+	18.7382i	−0.893604	+	0.649241i
$834$	−10.8321	−	3.51957i	−0.375086	−	0.121873i
$835$	−4.62655			−0.160108
$836$	−1.41521	−	13.4984i	−0.0489460	−	0.466851i
$837$			9.94714i			0.343823i
$838$	75.0493	+	24.3850i	2.59254	+	0.842366i
$839$	−8.36142	−	11.5085i	−0.288668	−	0.397318i	0.639913	−	0.768448i	$-0.278971\pi$
$839$	−8.36142	−	11.5085i	−0.288668	−	0.397318i	−0.928581	+	0.371130i	$0.878971\pi$
$840$	5.17036	−	7.11638i	0.178394	−	0.245539i
$841$	−7.65650	−	23.5643i	−0.264017	−	0.812561i
$842$	−10.1349	−	31.1920i	−0.349271	−	1.07495i
$843$	1.78771	−	2.46057i	0.0615720	−	0.0847466i
$844$	26.1785	−	19.0198i	0.901100	−	0.654687i
$845$	47.7993	−	2.19271i	1.64435	−	0.0754317i
$846$	24.4019			0.838953
$847$	15.7168	−	35.2514i	0.540035	−	1.21125i
$848$	−40.6560			−1.39613
$849$	10.1400	−	31.2076i	0.348003	−	1.07104i
$850$	62.7319	+	86.3430i	2.15169	+	2.96154i
$851$	−12.9902	+	17.8795i	−0.445299	+	0.612901i
$852$	−12.7442	+	4.14085i	−0.436610	+	0.141863i
$853$	0.926659	−	0.301090i	0.0317282	−	0.0103091i	−0.293110	−	0.956079i	$-0.594690\pi$
$853$	0.926659	−	0.301090i	0.0317282	−	0.0103091i	0.324838	+	0.945770i	$0.394690\pi$
$854$	−23.0771	−	16.7665i	−0.789682	−	0.573738i
$855$	5.23573	−	3.80398i	0.179058	−	0.130093i
$856$	−4.75437	−	1.54479i	−0.162501	−	0.0527997i
$857$	−53.5596			−1.82956			−0.914781	−	0.403950i	$-0.867637\pi$
$857$	−53.5596			−1.82956			−0.914781	+	0.403950i	$0.867637\pi$
$858$	−6.98125	−	23.8764i	−0.238336	−	0.815127i
$859$	38.3373			1.30805			0.654026	−	0.756472i	$-0.273079\pi$
$859$	38.3373			1.30805			0.654026	+	0.756472i	$0.273079\pi$
$860$	40.6274	+	13.2006i	1.38538	+	0.450138i
$861$	6.33166	−	4.60022i	0.215783	−	0.156775i
$862$	−20.2847	−	14.7377i	−0.690901	−	0.501969i
$863$	−11.2419	+	3.65270i	−0.382677	+	0.124339i	−0.494037	−	0.869441i	$-0.664479\pi$
$863$	−11.2419	+	3.65270i	−0.382677	+	0.124339i	0.111360	+	0.993780i	$0.464479\pi$
$864$	7.70163	−	2.50241i	0.262015	−	0.0851338i
$865$	4.22275	−	5.81211i	0.143578	−	0.197618i
$866$	0.962172	+	1.32432i	0.0326959	+	0.0450021i
$867$	−5.87897	+	18.0936i	−0.199660	+	0.614491i
$868$	−81.2318			−2.75719
$869$	−1.59394	+	7.48939i	−0.0540708	+	0.254060i
$870$	−15.7348			−0.533461
$871$	6.50098	+	0.877436i	0.220277	+	0.0297308i
$872$	−7.23435	+	5.25606i	−0.244986	+	0.177993i
$873$	5.50743	−	7.58033i	0.186398	−	0.256555i
$874$	−2.72825	−	8.39670i	−0.0922846	−	0.284023i
$875$	14.1590	+	43.5768i	0.478660	+	1.47316i
$876$	−15.5965	+	21.4668i	−0.526958	+	0.725295i
$877$	23.8912	+	32.8834i	0.806747	+	1.11039i	0.991817	+	0.127667i	$0.0407489\pi$
$877$	23.8912	+	32.8834i	0.806747	+	1.11039i	−0.185070	+	0.982725i	$0.559251\pi$
$878$	−30.7732	−	9.99883i	−1.03855	−	0.337444i
$879$		−	8.06383i		−	0.271986i
$880$	26.4417	+	29.3818i	0.891350	+	0.990459i
$881$	0.607260			0.0204591			0.0102296	−	0.999948i	$-0.496744\pi$
$881$	0.607260			0.0204591			0.0102296	+	0.999948i	$0.496744\pi$
$882$	10.5082	+	3.41433i	0.353831	+	0.114967i
$883$	−19.9337	+	14.4827i	−0.670824	+	0.487382i	−0.870301	−	0.492521i	$-0.836076\pi$
$883$	−19.9337	+	14.4827i	−0.670824	+	0.487382i	0.199477	+	0.979902i	$0.436076\pi$
$884$	45.3896	+	21.8316i	1.52662	+	0.734276i
$885$	−2.22936	−	6.86128i	−0.0749393	−	0.230639i
$886$	62.5476	−	20.3229i	2.10133	−	0.682763i
$887$	−26.0352	−	18.9157i	−0.874175	−	0.635126i	0.0575286	−	0.998344i	$-0.481678\pi$
$887$	−26.0352	−	18.9157i	−0.874175	−	0.635126i	−0.931704	+	0.363218i	$0.881678\pi$
$888$	−5.04505	+	3.66544i	−0.169301	+	0.123004i
$889$	23.9491	+	7.78154i	0.803227	+	0.260984i
$890$			12.4143i			0.416130i
$891$	−2.87185	−	1.65905i	−0.0962107	−	0.0555804i
$892$			26.4512i			0.885652i
$893$	−6.37347	+	19.6155i	−0.213280	+	0.656409i
$894$	16.9942	−	12.3470i	0.568372	−	0.412947i
$895$	43.2728	−	59.5599i	1.44645	−	1.99087i
$896$	5.82882	+	17.9393i	0.194727	+	0.599309i
$897$	−4.12782	−	7.66194i	−0.137824	−	0.255825i
$898$	−30.2227	−	21.9581i	−1.00854	−	0.732751i
$899$	12.0152	+	16.5375i	0.400728	+	0.551555i
$900$	6.14768	−	18.9206i	0.204923	−	0.630687i
$901$	−75.3620			−2.51067
$902$	−6.25573	−	14.0604i	−0.208293	−	0.468159i
$903$			17.4968i			0.582256i
$904$	−7.49354	−	2.43480i	−0.249232	−	0.0809803i
$905$	−18.2700	−	25.1465i	−0.607316	−	0.835899i
$906$	−11.7510	−	8.53759i	−0.390401	−	0.283643i
$907$	12.0229	+	37.0028i	0.399215	+	1.22866i	0.925630	+	0.378429i	$0.123536\pi$
$907$	12.0229	+	37.0028i	0.399215	+	1.22866i	−0.526416	+	0.850227i	$0.676464\pi$
$908$	−45.7608	+	14.8686i	−1.51863	+	0.493432i
$909$	4.64626	+	3.37571i	0.154107	+	0.111965i
$910$	70.0469	+	66.9073i	2.32203	+	2.21795i
$911$	9.63055	−	29.6398i	0.319074	−	0.982010i	−0.654970	−	0.755655i	$-0.727319\pi$
$911$	9.63055	−	29.6398i	0.319074	−	0.982010i	0.974045	−	0.226356i	$-0.0726811\pi$
$912$			5.69322i			0.188521i
$913$	48.8146	−	21.7186i	1.61553	−	0.718779i
$914$	5.80938			0.192157
$915$	−13.6803	−	4.44501i	−0.452258	−	0.146947i
$916$	−14.6842	−	20.2111i	−0.485180	−	0.667793i
$917$	26.2929	−	36.1891i	0.868269	−	1.19507i
$918$	11.8747	−	3.85831i	0.391922	−	0.127343i
$919$	11.6328	+	35.8022i	0.383732	+	1.18101i	0.937396	+	0.348266i	$0.113229\pi$
$919$	11.6328	+	35.8022i	0.383732	+	1.18101i	−0.553664	+	0.832740i	$0.686771\pi$
$920$	−4.89563	−	3.55688i	−0.161404	−	0.117267i
$921$	4.89168	+	6.73281i	0.161186	+	0.221854i
$922$	8.48245	−	26.1063i	0.279355	−	0.859765i
$923$	−3.71647	−	20.4235i	−0.122329	−	0.672249i
$924$	13.5484	−	23.4525i	0.445710	−	0.771532i
$925$		−	78.2617i		−	2.57323i
$926$	−16.1520	+	49.7108i	−0.530788	+	1.63360i
$927$	−5.99786	+	4.35770i	−0.196996	+	0.143126i
$928$	9.78156	−	13.4632i	0.321095	−	0.441950i
$929$	−35.4084	+	11.5049i	−1.16171	+	0.377463i	−0.825543	−	0.564340i	$-0.809131\pi$
$929$	−35.4084	+	11.5049i	−1.16171	+	0.377463i	−0.336168	+	0.941802i	$0.609131\pi$
$930$	−72.4358	+	23.5358i	−2.37526	+	0.771770i
$931$	−5.48925	+	7.55531i	−0.179903	+	0.247615i
$932$	3.83316	−	2.78496i	0.125559	−	0.0912243i
$933$	−4.30049	+	13.2356i	−0.140792	+	0.433313i
$934$			59.9925i			1.96302i
$935$	49.0137	+	54.4635i	1.60292	+	1.78115i
$936$	−0.439653	−	2.41608i	−0.0143705	−	0.0789720i
$937$	−12.5082	+	38.4964i	−0.408627	+	1.25762i	0.509202	+	0.860647i	$0.329940\pi$
$937$	−12.5082	+	38.4964i	−0.408627	+	1.25762i	−0.917829	+	0.396976i	$0.870060\pi$
$938$	7.80574	+	10.7437i	0.254867	+	0.350794i
$939$	−17.0174	−	12.3639i	−0.555342	−	0.403480i
$940$	31.0527	+	95.5704i	1.01283	+	3.11716i
$941$	−15.3776	+	4.99649i	−0.501296	+	0.162881i	−0.548740	−	0.835993i	$-0.684892\pi$
$941$	−15.3776	+	4.99649i	−0.501296	+	0.162881i	0.0474441	+	0.998874i	$0.484892\pi$
$942$	−5.17192	+	7.11854i	−0.168510	+	0.231935i
$943$	−3.16467	−	4.35579i	−0.103056	−	0.141844i
$944$	6.03591	+	1.96119i	0.196452	+	0.0638312i
$945$	12.9148			0.420119
$946$	33.6508	+	7.16178i	1.09408	+	0.232850i
$947$			34.0755i			1.10730i	0.832748	+	0.553652i	$0.186766\pi$
$947$			34.0755i			1.10730i	−0.832748	+	0.553652i	$0.813234\pi$
$948$	−1.66045	+	5.11034i	−0.0539289	+	0.165976i
$949$	−29.7250	−	28.3927i	−0.964914	−	0.921665i
$950$	25.2937	+	18.3769i	0.820635	+	0.596226i
$951$	17.7491	−	5.76702i	0.575553	−	0.187008i
$952$	4.43251	+	13.6419i	0.143659	+	0.442136i
$953$	6.57087	+	4.77402i	0.212851	+	0.154646i	0.689103	−	0.724664i	$-0.258005\pi$
$953$	6.57087	+	4.77402i	0.212851	+	0.154646i	−0.476252	+	0.879309i	$0.658005\pi$
$954$	15.3527	+	21.1312i	0.497062	+	0.684147i
$955$	−23.2810	−	7.56445i	−0.753355	−	0.244780i
$956$		−	8.00527i		−	0.258909i
$957$	−6.77853	+	0.710681i	−0.219119	+	0.0229731i
$958$	−9.72549			−0.314216
$959$	8.28610	−	25.5020i	0.267572	−	0.823502i
$960$	22.4349	+	30.8790i	0.724084	+	0.996616i
$961$	54.9691	+	39.9374i	1.77320	+	1.28830i
$962$	−32.5706	−	60.4567i	−1.05012	−	1.94920i
$963$	−2.26806	−	6.98038i	−0.0730873	−	0.224940i
$964$	14.0291	−	19.3094i	0.451848	−	0.621916i
$965$	−6.41003	+	4.65716i	−0.206346	+	0.149919i
$966$	5.44444	−	16.7563i	0.175172	−	0.539124i
$967$			24.9363i			0.801899i	0.916100	+	0.400949i	$0.131320\pi$
$967$			24.9363i			0.801899i	−0.916100	+	0.400949i	$0.868680\pi$
$968$	−5.56515	−	5.01610i	−0.178871	−	0.161224i
$969$			10.5532i			0.339019i
$970$	68.2316	+	22.1698i	2.19078	+	0.711829i
$971$	26.4594	−	19.2239i	0.849124	−	0.616925i	−0.0757805	−	0.997125i	$-0.524145\pi$
$971$	26.4594	−	19.2239i	0.849124	−	0.616925i	0.924904	+	0.380200i	$0.124145\pi$
$972$	−1.88292	−	1.36802i	−0.0603946	−	0.0438793i
$973$	18.2706	−	5.93648i	0.585729	−	0.190315i
$974$	1.44240	+	4.43925i	0.0462174	+	0.142243i
$975$	27.7739	+	13.3588i	0.889477	+	0.427823i
$976$	10.2373	−	7.43784i	0.327688	−	0.238079i
$977$	−23.7863	−	7.72862i	−0.760990	−	0.247261i	−0.0972863	−	0.995256i	$-0.531016\pi$
$977$	−23.7863	−	7.72862i	−0.760990	−	0.247261i	−0.663703	+	0.747996i	$0.731016\pi$
$978$	6.46150			0.206616
$979$	0.560708	+	5.34807i	0.0179203	+	0.170925i
$980$			45.5007i			1.45347i
$981$	−12.4863	−	4.05705i	−0.398658	−	0.129532i
$982$	−34.8064	−	47.9070i	−1.11072	−	1.52877i
$983$	−5.79271	+	7.97298i	−0.184759	+	0.254298i	−0.891342	−	0.453331i	$-0.850235\pi$
$983$	−5.79271	+	7.97298i	−0.184759	+	0.254298i	0.706583	+	0.707630i	$0.250235\pi$
$984$	−0.469464	−	1.44486i	−0.0149660	−	0.0460605i
$985$	1.82538	+	5.61794i	0.0581615	+	0.179003i
$986$	15.0816	−	20.7580i	0.480295	−	0.661069i
$987$	−33.2981	+	24.1925i	−1.05989	+	0.770056i
$988$	14.6221	+	1.97354i	0.465192	+	0.0627868i
$989$	12.0367			0.382744
$990$	5.28630	−	24.8385i	0.168010	−	0.789420i
$991$	60.7844			1.93088			0.965440	−	0.260627i	$-0.0839293\pi$
$991$	60.7844			1.93088			0.965440	+	0.260627i	$0.0839293\pi$
$992$	24.8918	−	76.6092i	0.790316	−	2.43234i
$993$	−17.5407	−	24.1427i	−0.556636	−	0.766144i
$994$	24.7013	−	33.9984i	0.783478	−	1.07836i
$995$	52.3381	−	17.0057i	1.65923	−	0.539117i
$996$	35.6577	−	11.5859i	1.12986	−	0.367113i
$997$	0.513148	+	0.372824i	0.0162515	+	0.0118074i	0.595881	−	0.803072i	$-0.296803\pi$
$997$	0.513148	+	0.372824i	0.0162515	+	0.0118074i	−0.579630	+	0.814880i	$0.696803\pi$
$998$	−37.4881	+	27.2367i	−1.18667	+	0.862163i
$999$	−8.70765	−	2.82929i	−0.275498	−	0.0895147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.64.3	✓	56
11.5	even	5	inner	429.2.bb.b.181.12	yes	56
13.12	even	2	inner	429.2.bb.b.64.12	yes	56
143.38	even	10	inner	429.2.bb.b.181.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.64.3	✓	56	1.1	even	1	trivial
429.2.bb.b.64.12	yes	56	13.12	even	2	inner
429.2.bb.b.181.3	yes	56	143.38	even	10	inner
429.2.bb.b.181.12	yes	56	11.5	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97843 - 0.642831i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.88292 + 1.36802i) q^{4} +(-3.50059 + 1.13741i) q^{5} +(-1.97843 + 0.642831i) q^{6} +(2.06240 - 2.83865i) q^{7} +(-0.400343 - 0.551025i) q^{8} +(0.309017 - 0.951057i) q^{9} +7.65683 q^{10} +(3.29855 - 0.345829i) q^{11} +2.32742 q^{12} +(-0.482267 + 3.57315i) q^{13} +(-5.90508 + 4.29029i) q^{14} +(-2.16348 + 2.97778i) q^{15} +(-1.00059 - 3.07949i) q^{16} +(-1.85474 - 5.70830i) q^{17} +(-1.22274 + 1.68295i) q^{18} +(-1.03348 - 1.42247i) q^{19} +(-8.14732 - 2.64722i) q^{20} -3.50876i q^{21} +(-6.74825 - 1.43621i) q^{22} -2.41381 q^{23} +(-0.647768 - 0.210473i) q^{24} +(6.91532 - 5.02428i) q^{25} +(3.25106 - 6.75921i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(7.76666 - 2.52354i) q^{28} +(-1.66253 - 1.20790i) q^{29} +(6.19450 - 4.50057i) q^{30} +(-9.46029 - 3.07384i) q^{31} +8.09797i q^{32} +(2.46531 - 2.21862i) q^{33} +12.4858i q^{34} +(-3.99090 + 12.2827i) q^{35} +(1.88292 - 1.36802i) q^{36} +(5.38162 - 7.40717i) q^{37} +(1.13027 + 3.47861i) q^{38} +(1.71008 + 3.17421i) q^{39} +(2.02818 + 1.47356i) q^{40} +(1.31107 + 1.80453i) q^{41} +(-2.25554 + 6.94184i) q^{42} -4.98659 q^{43} +(6.68399 + 3.86131i) q^{44} +3.68074i q^{45} +(4.77555 + 1.55167i) q^{46} +(-6.89489 - 9.49000i) q^{47} +(-2.61957 - 1.90323i) q^{48} +(-1.64131 - 5.05145i) q^{49} +(-16.9112 + 5.49480i) q^{50} +(-4.85577 - 3.52792i) q^{51} +(-5.79622 + 6.06820i) q^{52} +(3.88002 - 11.9415i) q^{53} +2.08024i q^{54} +(-11.1535 + 4.96240i) q^{55} -2.38983 q^{56} +(-1.67221 - 0.543335i) q^{57} +(2.51273 + 3.45848i) q^{58} +(-1.15208 + 1.58570i) q^{59} +(-8.14732 + 2.64722i) q^{60} +(1.20764 + 3.71674i) q^{61} +(16.7406 + 12.1627i) q^{62} +(-2.06240 - 2.83865i) q^{63} +(3.20445 - 9.86229i) q^{64} +(-2.37592 - 13.0567i) q^{65} +(-6.30363 + 2.80461i) q^{66} -1.81940i q^{67} +(4.31675 - 13.2856i) q^{68} +(-1.95281 + 1.41880i) q^{69} +(15.7914 - 21.7350i) q^{70} +(-5.47570 + 1.77916i) q^{71} +(-0.647768 + 0.210473i) q^{72} +(-6.70122 + 9.22344i) q^{73} +(-15.4087 + 11.1951i) q^{74} +(2.64142 - 8.12945i) q^{75} -4.09222i q^{76} +(5.82123 - 10.0766i) q^{77} +(-1.34280 - 7.37925i) q^{78} +(-0.713431 + 2.19571i) q^{79} +(7.00529 + 9.64195i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.43385 - 4.41293i) q^{82} +(15.3207 - 4.97801i) q^{83} +(4.80006 - 6.60671i) q^{84} +(12.9853 + 17.8728i) q^{85} +(9.86562 + 3.20553i) q^{86} -2.05501 q^{87} +(-1.51111 - 1.67913i) q^{88} +1.62134i q^{89} +(2.36609 - 7.28208i) q^{90} +(9.14829 + 8.73825i) q^{91} +(-4.54501 - 3.30214i) q^{92} +(-9.46029 + 3.07384i) q^{93} +(7.54059 + 23.2075i) q^{94} +(5.23573 + 3.80398i) q^{95} +(4.75987 + 6.55140i) q^{96} +(8.91121 + 2.89543i) q^{97} +11.0490i q^{98} +(0.690403 - 3.24397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36}+ \cdots + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more