LMFDB - Embedded newform 847.2.f.y.729.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.5
Character	$\chi$	$=$	847.729
Dual form			847.2.f.y.323.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.666271 - 0.484074i) q^{2} +(-0.296857 - 0.913631i) q^{3} +(-0.408445 + 1.25706i) q^{4} +(-2.41544 - 1.75492i) q^{5} +(-0.640052 - 0.465025i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.845363 + 2.60176i) q^{8} +(1.68045 - 1.22092i) q^{9} +O(q^{10})$	\(q+(0.666271 - 0.484074i) q^{2} +(-0.296857 - 0.913631i) q^{3} +(-0.408445 + 1.25706i) q^{4} +(-2.41544 - 1.75492i) q^{5} +(-0.640052 - 0.465025i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.845363 + 2.60176i) q^{8} +(1.68045 - 1.22092i) q^{9} -2.45885 q^{10} +1.26974 q^{12} +(-1.78101 + 1.29398i) q^{13} +(-0.254493 - 0.783248i) q^{14} +(-0.886310 + 2.72778i) q^{15} +(-0.315961 - 0.229559i) q^{16} +(-3.56509 - 2.59019i) q^{17} +(0.528621 - 1.62693i) q^{18} +(-0.533248 - 1.64117i) q^{19} +(3.19262 - 2.31958i) q^{20} -0.960649 q^{21} -8.39774 q^{23} +(2.12610 - 1.54470i) q^{24} +(1.20952 + 3.72253i) q^{25} +(-0.560251 + 1.72428i) q^{26} +(-3.94587 - 2.86684i) q^{27} +(1.06932 + 0.776908i) q^{28} +(1.01758 - 3.13178i) q^{29} +(0.729926 + 2.24648i) q^{30} +(-6.04800 + 4.39413i) q^{31} -5.79294 q^{32} -3.62916 q^{34} +(-2.41544 + 1.75492i) q^{35} +(0.848403 + 2.61112i) q^{36} +(-2.71339 + 8.35095i) q^{37} +(-1.14973 - 0.835331i) q^{38} +(1.71092 + 1.24306i) q^{39} +(2.52396 - 7.76794i) q^{40} +(1.66669 + 5.12954i) q^{41} +(-0.640052 + 0.465025i) q^{42} +9.44629 q^{43} -6.20165 q^{45} +(-5.59517 + 4.06513i) q^{46} +(-1.66766 - 5.13254i) q^{47} +(-0.115937 + 0.356818i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(2.60785 + 1.89471i) q^{50} +(-1.30816 + 4.02609i) q^{51} +(-0.899168 - 2.76736i) q^{52} +(-7.60293 + 5.52385i) q^{53} -4.01678 q^{54} +2.73565 q^{56} +(-1.34112 + 0.974384i) q^{57} +(-0.838032 - 2.57920i) q^{58} +(1.07372 - 3.30456i) q^{59} +(-3.06699 - 2.22830i) q^{60} +(-10.5126 - 7.63782i) q^{61} +(-1.90252 + 5.85536i) q^{62} +(-0.641876 - 1.97549i) q^{63} +(-3.22775 + 2.34510i) q^{64} +6.57274 q^{65} +4.32138 q^{67} +(4.71218 - 3.42360i) q^{68} +(2.49293 + 7.67244i) q^{69} +(-0.759826 + 2.33850i) q^{70} +(-3.56004 - 2.58652i) q^{71} +(4.59713 + 3.34001i) q^{72} +(4.55829 - 14.0290i) q^{73} +(2.23463 + 6.87747i) q^{74} +(3.04196 - 2.21012i) q^{75} +2.28086 q^{76} +1.74167 q^{78} +(5.81495 - 4.22481i) q^{79} +(0.360327 + 1.10897i) q^{80} +(0.477749 - 1.47036i) q^{81} +(3.59354 + 2.61086i) q^{82} +(-6.17640 - 4.48742i) q^{83} +(0.392372 - 1.20760i) q^{84} +(4.06569 + 12.5129i) q^{85} +(6.29379 - 4.57270i) q^{86} -3.16337 q^{87} +10.8428 q^{89} +(-4.13198 + 3.00206i) q^{90} +(0.680283 + 2.09370i) q^{91} +(3.43001 - 10.5565i) q^{92} +(5.81000 + 4.22121i) q^{93} +(-3.59564 - 2.61239i) q^{94} +(-1.59209 + 4.89995i) q^{95} +(1.71967 + 5.29261i) q^{96} +(-2.30973 + 1.67812i) q^{97} -0.823556 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.666271	−	0.484074i	0.471125	−	0.342292i	−0.326755	−	0.945109i	$-0.605955\pi$
$2$	0.666271	−	0.484074i	0.471125	−	0.342292i	0.797879	+	0.602817i	$0.205955\pi$
$3$	−0.296857	−	0.913631i	−0.171390	−	0.527485i	0.828060	−	0.560640i	$-0.189445\pi$
$3$	−0.296857	−	0.913631i	−0.171390	−	0.527485i	−0.999450	+	0.0331543i	$0.989445\pi$
$4$	−0.408445	+	1.25706i	−0.204222	+	0.628532i
$5$	−2.41544	−	1.75492i	−1.08022	−	0.784824i	−0.102497	−	0.994733i	$-0.532683\pi$
$5$	−2.41544	−	1.75492i	−1.08022	−	0.784824i	−0.977721	+	0.209909i	$0.932683\pi$
$6$	−0.640052	−	0.465025i	−0.261300	−	0.189846i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.845363	+	2.60176i	0.298881	+	0.919861i
$9$	1.68045	−	1.22092i	0.560151	−	0.406973i
$10$	−2.45885			−0.777556
$11$		0			0
$11$		0			0
$12$	1.26974			0.366543
$13$	−1.78101	+	1.29398i	−0.493962	+	0.358884i	−0.806706	−	0.590953i	$-0.798752\pi$
$13$	−1.78101	+	1.29398i	−0.493962	+	0.358884i	0.312744	+	0.949837i	$0.398752\pi$
$14$	−0.254493	−	0.783248i	−0.0680161	−	0.209332i
$15$	−0.886310	+	2.72778i	−0.228844	+	0.704310i
$16$	−0.315961	−	0.229559i	−0.0789902	−	0.0573897i
$17$	−3.56509	−	2.59019i	−0.864661	−	0.628213i	0.0644876	−	0.997919i	$-0.479459\pi$
$17$	−3.56509	−	2.59019i	−0.864661	−	0.628213i	−0.929149	+	0.369705i	$0.879459\pi$
$18$	0.528621	−	1.62693i	0.124597	−	0.383470i
$19$	−0.533248	−	1.64117i	−0.122335	−	0.376510i	0.871071	−	0.491158i	$-0.163426\pi$
$19$	−0.533248	−	1.64117i	−0.122335	−	0.376510i	−0.993406	+	0.114648i	$0.963426\pi$
$20$	3.19262	−	2.31958i	0.713892	−	0.518673i
$21$	−0.960649			−0.209631
$22$		0			0
$23$	−8.39774			−1.75105			−0.875525	−	0.483173i	$-0.839484\pi$
$23$	−8.39774			−1.75105			−0.875525	+	0.483173i	$0.839484\pi$
$24$	2.12610	−	1.54470i	0.433988	−	0.315311i
$25$	1.20952	+	3.72253i	0.241904	+	0.744505i
$26$	−0.560251	+	1.72428i	−0.109874	+	0.338158i
$27$	−3.94587	−	2.86684i	−0.759383	−	0.551724i
$28$	1.06932	+	0.776908i	0.202083	+	0.146822i
$29$	1.01758	−	3.13178i	0.188959	−	0.581557i	−0.811035	−	0.584998i	$-0.801095\pi$
$29$	1.01758	−	3.13178i	0.188959	−	0.581557i	0.999994	+	0.00344098i	$0.00109530\pi$
$30$	0.729926	+	2.24648i	0.133266	+	0.410150i
$31$	−6.04800	+	4.39413i	−1.08625	+	0.789208i	−0.978762	−	0.204998i	$-0.934281\pi$
$31$	−6.04800	+	4.39413i	−1.08625	+	0.789208i	−0.107490	+	0.994206i	$0.534281\pi$
$32$	−5.79294			−1.02406
$33$		0			0
$34$	−3.62916			−0.622396
$35$	−2.41544	+	1.75492i	−0.408284	+	0.296636i
$36$	0.848403	+	2.61112i	0.141400	+	0.435186i
$37$	−2.71339	+	8.35095i	−0.446078	+	1.37289i	0.435219	+	0.900325i	$0.356671\pi$
$37$	−2.71339	+	8.35095i	−0.446078	+	1.37289i	−0.881297	+	0.472563i	$0.843329\pi$
$38$	−1.14973	−	0.835331i	−0.186512	−	0.135509i
$39$	1.71092	+	1.24306i	0.273967	+	0.199048i
$40$	2.52396	−	7.76794i	0.399073	−	1.22822i
$41$	1.66669	+	5.12954i	0.260293	+	0.801099i	0.992741	+	0.120276i	$0.0383779\pi$
$41$	1.66669	+	5.12954i	0.260293	+	0.801099i	−0.732448	+	0.680823i	$0.761622\pi$
$42$	−0.640052	+	0.465025i	−0.0987622	+	0.0717550i
$43$	9.44629			1.44055			0.720273	−	0.693691i	$-0.244017\pi$
$43$	9.44629			1.44055			0.720273	+	0.693691i	$0.244017\pi$
$44$		0			0
$45$	−6.20165			−0.924487
$46$	−5.59517	+	4.06513i	−0.824962	+	0.599370i
$47$	−1.66766	−	5.13254i	−0.243254	−	0.748657i	−0.995919	−	0.0902541i	$-0.971232\pi$
$47$	−1.66766	−	5.13254i	−0.243254	−	0.748657i	0.752665	−	0.658403i	$-0.228768\pi$
$48$	−0.115937	+	0.356818i	−0.0167341	+	0.0515022i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	2.60785	+	1.89471i	0.368805	+	0.267953i
$51$	−1.30816	+	4.02609i	−0.183179	+	0.563766i
$52$	−0.899168	−	2.76736i	−0.124692	−	0.383763i
$53$	−7.60293	+	5.52385i	−1.04434	+	0.758759i	−0.971129	−	0.238557i	$-0.923326\pi$
$53$	−7.60293	+	5.52385i	−1.04434	+	0.758759i	−0.0732141	+	0.997316i	$0.523326\pi$
$54$	−4.01678			−0.546615
$55$		0			0
$56$	2.73565			0.365567
$57$	−1.34112	+	0.974384i	−0.177636	+	0.129060i
$58$	−0.838032	−	2.57920i	−0.110039	−	0.338665i
$59$	1.07372	−	3.30456i	0.139786	−	0.430217i	−0.856518	−	0.516117i	$-0.827377\pi$
$59$	1.07372	−	3.30456i	0.139786	−	0.430217i	0.996304	+	0.0859007i	$0.0273768\pi$
$60$	−3.06699	−	2.22830i	−0.395947	−	0.287672i
$61$	−10.5126	−	7.63782i	−1.34599	−	0.977922i	−0.999200	−	0.0399808i	$-0.987270\pi$
$61$	−10.5126	−	7.63782i	−1.34599	−	0.977922i	−0.346794	−	0.937941i	$-0.612730\pi$
$62$	−1.90252	+	5.85536i	−0.241620	+	0.743631i
$63$	−0.641876	−	1.97549i	−0.0808687	−	0.248888i
$64$	−3.22775	+	2.34510i	−0.403468	+	0.293137i
$65$	6.57274			0.815248
$66$		0			0
$67$	4.32138			0.527940			0.263970	−	0.964531i	$-0.414968\pi$
$67$	4.32138			0.527940			0.263970	+	0.964531i	$0.414968\pi$
$68$	4.71218	−	3.42360i	0.571436	−	0.415172i
$69$	2.49293	+	7.67244i	0.300113	+	0.923653i
$70$	−0.759826	+	2.33850i	−0.0908166	+	0.279505i
$71$	−3.56004	−	2.58652i	−0.422500	−	0.306964i	0.356143	−	0.934431i	$-0.384092\pi$
$71$	−3.56004	−	2.58652i	−0.422500	−	0.306964i	−0.778643	+	0.627467i	$0.784092\pi$
$72$	4.59713	+	3.34001i	0.541777	+	0.393624i
$73$	4.55829	−	14.0290i	0.533507	−	1.64197i	−0.213345	−	0.976977i	$-0.568436\pi$
$73$	4.55829	−	14.0290i	0.533507	−	1.64197i	0.746852	−	0.664990i	$-0.231564\pi$
$74$	2.23463	+	6.87747i	0.259770	+	0.799490i
$75$	3.04196	−	2.21012i	0.351256	−	0.255202i
$76$	2.28086			0.261632
$77$		0			0
$78$	1.74167			0.197205
$79$	5.81495	−	4.22481i	0.654233	−	0.475328i	−0.210477	−	0.977599i	$-0.567502\pi$
$79$	5.81495	−	4.22481i	0.654233	−	0.475328i	0.864711	+	0.502271i	$0.167502\pi$
$80$	0.360327	+	1.10897i	0.0402857	+	0.123987i
$81$	0.477749	−	1.47036i	0.0530832	−	0.163373i
$82$	3.59354	+	2.61086i	0.396840	+	0.288321i
$83$	−6.17640	−	4.48742i	−0.677948	−	0.492558i	0.194728	−	0.980857i	$-0.437617\pi$
$83$	−6.17640	−	4.48742i	−0.677948	−	0.492558i	−0.872676	+	0.488299i	$0.837617\pi$
$84$	0.392372	−	1.20760i	0.0428113	−	0.131760i
$85$	4.06569	+	12.5129i	0.440986	+	1.35721i
$86$	6.29379	−	4.57270i	0.678677	−	0.493087i
$87$	−3.16337			−0.339149
$88$		0			0
$89$	10.8428			1.14934			0.574668	−	0.818386i	$-0.305131\pi$
$89$	10.8428			1.14934			0.574668	+	0.818386i	$0.305131\pi$
$90$	−4.13198	+	3.00206i	−0.435549	+	0.316445i
$91$	0.680283	+	2.09370i	0.0713131	+	0.219479i
$92$	3.43001	−	10.5565i	0.357604	−	1.10059i
$93$	5.81000	+	4.22121i	0.602469	+	0.437719i
$94$	−3.59564	−	2.61239i	−0.370862	−	0.269447i
$95$	−1.59209	+	4.89995i	−0.163345	+	0.502724i
$96$	1.71967	+	5.29261i	0.175514	+	0.540175i
$97$	−2.30973	+	1.67812i	−0.234517	+	0.170387i	−0.698837	−	0.715281i	$-0.746299\pi$
$97$	−2.30973	+	1.67812i	−0.234517	+	0.170387i	0.464320	+	0.885668i	$0.346299\pi$
$98$	−0.823556			−0.0831917
$99$		0			0
$100$	−5.17348			−0.517348
$101$	11.8126	−	8.58234i	1.17539	−	0.853974i	0.183750	−	0.982973i	$-0.441176\pi$
$101$	11.8126	−	8.58234i	1.17539	−	0.853974i	0.991645	+	0.128999i	$0.0411763\pi$
$102$	1.07734	+	3.31571i	0.106673	+	0.328305i
$103$	−0.0333020	+	0.102493i	−0.00328134	+	0.0100989i	−0.952684	−	0.303963i	$-0.901690\pi$
$103$	−0.0333020	+	0.102493i	−0.00328134	+	0.0100989i	0.949402	+	0.314062i	$0.101690\pi$
$104$	−4.87221	−	3.53987i	−0.477759	−	0.347113i
$105$	2.32039	+	1.68586i	0.226447	+	0.164523i
$106$	−2.39166	+	7.36076i	−0.232298	+	0.714940i
$107$	−1.43663	−	4.42148i	−0.138884	−	0.427441i	0.857290	−	0.514834i	$-0.172146\pi$
$107$	−1.43663	−	4.42148i	−0.138884	−	0.427441i	−0.996174	+	0.0873930i	$0.972146\pi$
$108$	5.21547	−	3.78926i	0.501859	−	0.364622i
$109$	3.23140			0.309512			0.154756	−	0.987953i	$-0.450541\pi$
$109$	3.23140			0.309512			0.154756	+	0.987953i	$0.450541\pi$
$110$		0			0
$111$	8.43518			0.800632
$112$	−0.315961	+	0.229559i	−0.0298555	+	0.0216913i
$113$	−3.49789	−	10.7654i	−0.329054	−	1.01272i	−0.969577	−	0.244785i	$-0.921283\pi$
$113$	−3.49789	−	10.7654i	−0.329054	−	1.01272i	0.640523	−	0.767939i	$-0.278717\pi$
$114$	−0.421878	+	1.29841i	−0.0395125	+	0.121607i
$115$	20.2842	+	14.7374i	1.89151	+	1.37427i
$116$	3.52122	+	2.55832i	0.326938	+	0.237534i
$117$	−1.41305	+	4.34893i	−0.130637	+	0.402059i
$118$	−0.884265	−	2.72149i	−0.0814032	−	0.250533i
$119$	−3.56509	+	2.59019i	−0.326811	+	0.237442i
$120$	−7.84629			−0.716265
$121$		0			0
$122$	−10.7015			−0.968866
$123$	4.19174	−	3.04548i	0.377956	−	0.274601i
$124$	−3.05343	−	9.39748i	−0.274206	−	0.843918i
$125$	−1.00187	+	3.08345i	−0.0896102	+	0.275792i
$126$	−1.38395	−	1.00550i	−0.123292	−	0.0895767i
$127$	16.1643	+	11.7440i	1.43435	+	1.04212i	0.989186	+	0.146665i	$0.0468540\pi$
$127$	16.1643	+	11.7440i	1.43435	+	1.04212i	0.445162	+	0.895450i	$0.353146\pi$
$128$	2.56488	−	7.89389i	0.226706	−	0.697728i
$129$	−2.80420	−	8.63043i	−0.246896	−	0.759867i
$130$	4.37922	−	3.18169i	0.384083	−	0.279053i
$131$	8.45523			0.738737			0.369368	−	0.929283i	$-0.379574\pi$
$131$	8.45523			0.738737			0.369368	+	0.929283i	$0.379574\pi$
$132$		0			0
$133$	−1.72563			−0.149631
$134$	2.87921	−	2.09187i	0.248726	−	0.180710i
$135$	4.49993	+	13.8494i	0.387293	+	1.19196i
$136$	3.72526	−	11.4652i	0.319438	−	0.983129i
$137$	−6.75898	−	4.91069i	−0.577459	−	0.419548i	0.260348	−	0.965515i	$-0.416163\pi$
$137$	−6.75898	−	4.91069i	−0.577459	−	0.419548i	−0.837807	+	0.545966i	$0.816163\pi$
$138$	5.37499	+	3.90516i	0.457550	+	0.332429i
$139$	−4.54668	+	13.9932i	−0.385645	+	1.18689i	0.550367	+	0.834923i	$0.314488\pi$
$139$	−4.54668	+	13.9932i	−0.385645	+	1.18689i	−0.936012	+	0.351969i	$0.885512\pi$
$140$	−1.21947	−	3.75315i	−0.103064	−	0.317199i
$141$	−4.19419	+	3.04726i	−0.353215	+	0.256625i
$142$	−3.62402			−0.304121
$143$		0			0
$144$	−0.811230			−0.0676025
$145$	−7.95392	+	5.77886i	−0.660537	+	0.479908i
$146$	−3.75401	−	11.5536i	−0.310684	−	0.956186i
$147$	−0.296857	+	0.913631i	−0.0244843	+	0.0753551i
$148$	−9.38941	−	6.82181i	−0.771805	−	0.560749i
$149$	−7.15391	−	5.19762i	−0.586071	−	0.425805i	0.254837	−	0.966984i	$-0.417978\pi$
$149$	−7.15391	−	5.19762i	−0.586071	−	0.425805i	−0.840908	+	0.541179i	$0.817978\pi$
$150$	0.956911	−	2.94507i	0.0781315	−	0.240464i
$151$	−6.17104	−	18.9925i	−0.502192	−	1.54559i	−0.805441	−	0.592676i	$-0.798071\pi$
$151$	−6.17104	−	18.9925i	−0.502192	−	1.54559i	0.303249	−	0.952911i	$-0.401929\pi$
$152$	3.81914	−	2.77476i	0.309773	−	0.225063i
$153$	−9.15338			−0.740007
$154$		0			0
$155$	22.3199			1.79278
$156$	−2.26142	+	1.64302i	−0.181058	+	0.131547i
$157$	4.03319	+	12.4129i	0.321883	+	0.990655i	0.972828	+	0.231530i	$0.0743731\pi$
$157$	4.03319	+	12.4129i	0.321883	+	0.990655i	−0.650944	+	0.759125i	$0.725627\pi$
$158$	1.82921	−	5.62973i	0.145524	−	0.447878i
$159$	7.30375	+	5.30648i	0.579225	+	0.420831i
$160$	13.9925	+	10.1662i	1.10620	+	0.803705i
$161$	−2.59504	+	7.98672i	−0.204518	+	0.629442i
$162$	−0.393453	−	1.21092i	−0.0309126	−	0.0951391i
$163$	−4.82536	+	3.50583i	−0.377951	+	0.274598i	−0.760500	−	0.649337i	$-0.775046\pi$
$163$	−4.82536	+	3.50583i	−0.377951	+	0.274598i	0.382549	+	0.923935i	$0.375046\pi$
$164$	−7.12891			−0.556674
$165$		0			0
$166$	−6.28740			−0.487997
$167$	−10.7172	+	7.78648i	−0.829320	+	0.602536i	−0.919367	−	0.393401i	$-0.871298\pi$
$167$	−10.7172	+	7.78648i	−0.829320	+	0.602536i	0.0900471	+	0.995938i	$0.471298\pi$
$168$	−0.812097	−	2.49938i	−0.0626546	−	0.192831i
$169$	−2.51962	+	7.75458i	−0.193817	+	0.596506i
$170$	8.76602	+	6.36888i	0.672323	+	0.488471i
$171$	−2.89983	−	2.10685i	−0.221756	−	0.161115i
$172$	−3.85829	+	11.8746i	−0.294192	+	0.905429i
$173$	−0.159983	−	0.492377i	−0.0121633	−	0.0374348i	0.944791	−	0.327675i	$-0.106265\pi$
$173$	−0.159983	−	0.492377i	−0.0121633	−	0.0374348i	−0.956954	+	0.290240i	$0.906265\pi$
$174$	−2.10766	+	1.53130i	−0.159781	+	0.116088i
$175$	3.91410			0.295878
$176$		0			0
$177$	−3.33789			−0.250891
$178$	7.22425	−	5.24873i	0.541481	−	0.393409i
$179$	0.524139	+	1.61314i	0.0391760	+	0.120571i	0.968732	−	0.248110i	$-0.0798094\pi$
$179$	0.524139	+	1.61314i	0.0391760	+	0.120571i	−0.929556	+	0.368681i	$0.879809\pi$
$180$	2.53303	−	7.79587i	0.188801	−	0.581070i
$181$	7.99793	+	5.81084i	0.594482	+	0.431916i	0.843916	−	0.536475i	$-0.180245\pi$
$181$	7.99793	+	5.81084i	0.594482	+	0.431916i	−0.249434	+	0.968392i	$0.580245\pi$
$182$	1.46676	+	1.06566i	0.108723	+	0.0789921i
$183$	−3.85743	+	11.8719i	−0.285149	+	0.877599i
$184$	−7.09914	−	21.8489i	−0.523355	−	1.61072i
$185$	21.2093	−	15.4094i	1.55934	−	1.13292i
$186$	5.91441			0.433666
$187$		0			0
$188$	7.13308			0.520233
$189$	−3.94587	+	2.86684i	−0.287020	+	0.208532i
$190$	1.31118	+	4.03538i	0.0951227	+	0.292758i
$191$	7.14845	−	22.0007i	0.517244	−	1.59191i	−0.261917	−	0.965090i	$-0.584355\pi$
$191$	7.14845	−	22.0007i	0.517244	−	1.59191i	0.779162	−	0.626823i	$-0.215645\pi$
$192$	3.10073	+	2.25281i	0.223776	+	0.162583i
$193$	18.6792	+	13.5712i	1.34456	+	0.976880i	0.999263	+	0.0383859i	$0.0122216\pi$
$193$	18.6792	+	13.5712i	1.34456	+	0.976880i	0.345296	+	0.938494i	$0.387778\pi$
$194$	−0.726572	+	2.23616i	−0.0521648	+	0.160547i
$195$	−1.95116	−	6.00506i	−0.139726	−	0.430031i
$196$	1.06932	−	0.776908i	0.0763802	−	0.0554935i
$197$	6.68989			0.476635			0.238318	−	0.971187i	$-0.423404\pi$
$197$	6.68989			0.476635			0.238318	+	0.971187i	$0.423404\pi$
$198$		0			0
$199$	−15.8233			−1.12169			−0.560844	−	0.827922i	$-0.689523\pi$
$199$	−15.8233			−1.12169			−0.560844	+	0.827922i	$0.689523\pi$
$200$	−8.66263	+	6.29377i	−0.612541	+	0.445037i
$201$	−1.28283	−	3.94815i	−0.0904839	−	0.278481i
$202$	3.71589	−	11.4363i	0.261449	−	0.804657i
$203$	−2.66405	−	1.93555i	−0.186980	−	0.135849i
$204$	−4.52675	−	3.28888i	−0.316936	−	0.230267i
$205$	4.97614	−	15.3150i	0.347549	−	1.06965i
$206$	0.0274260	+	0.0844086i	0.00191086	+	0.00588103i
$207$	−14.1120	+	10.2530i	−0.980852	+	0.712631i
$208$	0.859771			0.0596144
$209$		0			0
$210$	2.36209			0.163000
$211$	−9.18436	+	6.67283i	−0.632277	+	0.459376i	−0.857188	−	0.515003i	$-0.827791\pi$
$211$	−9.18436	+	6.67283i	−0.632277	+	0.459376i	0.224911	+	0.974379i	$0.427791\pi$
$212$	−3.83846	−	11.8136i	−0.263626	−	0.811359i
$213$	−1.30631	+	4.02040i	−0.0895066	+	0.275473i
$214$	−3.09751	−	2.25047i	−0.211741	−	0.153839i
$215$	−22.8170	−	16.5775i	−1.55610	−	1.13058i
$216$	4.12314	−	12.6897i	0.280544	−	0.863426i
$217$	2.31013	+	7.10984i	0.156822	+	0.482648i
$218$	2.15299	−	1.56424i	0.145819	−	0.105944i
$219$	−14.1705			−0.957552
$220$		0			0
$221$	9.70109			0.652566
$222$	5.62011	−	4.08325i	0.377197	−	0.274050i
$223$	−3.30335	−	10.1667i	−0.221208	−	0.680810i	−0.998654	−	0.0518599i	$-0.983485\pi$
$223$	−3.30335	−	10.1667i	−0.221208	−	0.680810i	0.777446	−	0.628950i	$-0.216515\pi$
$224$	−1.79012	+	5.50942i	−0.119607	+	0.368113i
$225$	6.57745	+	4.77880i	0.438497	+	0.318587i
$226$	−7.54179	−	5.47943i	−0.501673	−	0.364487i
$227$	−1.15505	+	3.55489i	−0.0766636	+	0.235946i	−0.982043	−	0.188657i	$-0.939586\pi$
$227$	−1.15505	+	3.55489i	−0.0766636	+	0.235946i	0.905379	+	0.424604i	$0.139586\pi$
$228$	−0.677088	−	2.08386i	−0.0448412	−	0.138007i
$229$	19.1401	−	13.9061i	1.26482	−	0.918942i	0.265832	−	0.964019i	$-0.414353\pi$
$229$	19.1401	−	13.9061i	1.26482	−	0.918942i	0.998983	+	0.0450774i	$0.0143534\pi$
$230$	20.6488			1.36154
$231$		0			0
$232$	9.00836			0.591428
$233$	−3.12827	+	2.27282i	−0.204940	+	0.148897i	−0.685521	−	0.728053i	$-0.740426\pi$
$233$	−3.12827	+	2.27282i	−0.204940	+	0.148897i	0.480582	+	0.876950i	$0.340426\pi$
$234$	1.16373	+	3.58159i	0.0760753	+	0.234136i
$235$	−4.97905	+	15.3240i	−0.324798	+	0.999624i
$236$	3.71549	+	2.69946i	0.241858	+	0.175720i
$237$	−5.58613	−	4.05856i	−0.362858	−	0.263632i
$238$	−1.12147	+	3.45154i	−0.0726942	+	0.223730i
$239$	−3.11232	−	9.57873i	−0.201319	−	0.619597i	−0.999844	−	0.0176354i	$-0.994386\pi$
$239$	−3.11232	−	9.57873i	−0.201319	−	0.619597i	0.798525	−	0.601961i	$-0.205614\pi$
$240$	0.906226	−	0.658412i	0.0584966	−	0.0425003i
$241$	13.4265			0.864878			0.432439	−	0.901663i	$-0.357653\pi$
$241$	13.4265			0.864878			0.432439	+	0.901663i	$0.357653\pi$
$242$		0			0
$243$	−16.1173			−1.03392
$244$	13.8950	−	10.0953i	0.889538	−	0.646287i
$245$	0.922616	+	2.83952i	0.0589438	+	0.181410i
$246$	1.31860	−	4.05822i	0.0840707	−	0.258743i
$247$	3.07335	+	2.23292i	0.195553	+	0.142077i
$248$	−16.5452	−	12.0208i	−1.05062	−	0.763321i
$249$	−2.26634	+	6.97507i	−0.143623	+	0.442027i
$250$	0.825098	+	2.53939i	0.0521838	+	0.160605i
$251$	−0.0618470	+	0.0449345i	−0.00390375	+	0.00283624i	−0.589735	−	0.807597i	$-0.700768\pi$
$251$	−0.0618470	+	0.0449345i	−0.00390375	+	0.00283624i	0.585832	+	0.810433i	$0.300768\pi$
$252$	2.74549			0.172950
$253$		0			0
$254$	16.4548			1.03246
$255$	10.2253	−	7.42908i	0.640330	−	0.465227i
$256$	−4.57810	−	14.0900i	−0.286131	−	0.880622i
$257$	2.93935	−	9.04639i	0.183352	−	0.564298i	−0.816564	−	0.577254i	$-0.804124\pi$
$257$	2.93935	−	9.04639i	0.183352	−	0.564298i	0.999916	+	0.0129561i	$0.00412416\pi$
$258$	−6.04612	−	4.39276i	−0.376415	−	0.273482i
$259$	7.10374	+	5.16117i	0.441405	+	0.320700i
$260$	−2.68460	+	8.26235i	−0.166492	+	0.512409i
$261$	−2.11366	−	6.50519i	−0.130833	−	0.402661i
$262$	5.63347	−	4.09296i	0.348037	−	0.252864i
$263$	14.7919			0.912107			0.456053	−	0.889952i	$-0.349263\pi$
$263$	14.7919			0.912107			0.456053	+	0.889952i	$0.349263\pi$
$264$		0			0
$265$	28.0583			1.72361
$266$	−1.14973	+	0.835331i	−0.0704947	+	0.0512174i
$267$	−3.21876	−	9.90634i	−0.196985	−	0.606258i
$268$	−1.76505	+	5.43225i	−0.107817	+	0.331828i
$269$	24.3155	+	17.6662i	1.48254	+	1.07713i	0.976726	+	0.214489i	$0.0688086\pi$
$269$	24.3155	+	17.6662i	1.48254	+	1.07713i	0.505816	+	0.862641i	$0.331191\pi$
$270$	9.70229	+	7.04913i	0.590463	+	0.428996i
$271$	−3.21126	+	9.88324i	−0.195070	+	0.600364i	0.804906	+	0.593403i	$0.202216\pi$
$271$	−3.21126	+	9.88324i	−0.195070	+	0.600364i	−0.999976	+	0.00696114i	$0.997784\pi$
$272$	0.531827	+	1.63680i	0.0322468	+	0.0992454i
$273$	1.71092	−	1.24306i	0.103550	−	0.0752332i
$274$	−6.88045			−0.415663
$275$		0			0
$276$	−10.6630			−0.641835
$277$	−22.7445	+	16.5249i	−1.36659	+	0.992883i	−0.368592	+	0.929591i	$0.620160\pi$
$277$	−22.7445	+	16.5249i	−1.36659	+	0.992883i	−0.997995	+	0.0632918i	$0.979840\pi$
$278$	3.74445	+	11.5242i	0.224577	+	0.691177i
$279$	−4.79849	+	14.7682i	−0.287278	+	0.884151i
$280$	−6.60780	−	4.80085i	−0.394892	−	0.286906i
$281$	−7.74237	−	5.62516i	−0.461871	−	0.335569i	0.332394	−	0.943141i	$-0.392144\pi$
$281$	−7.74237	−	5.62516i	−0.461871	−	0.335569i	−0.794265	+	0.607572i	$0.792144\pi$
$282$	−1.31937	+	4.06060i	−0.0785672	+	0.241805i
$283$	−0.511502	−	1.57424i	−0.0304056	−	0.0935789i	0.934702	−	0.355432i	$-0.115666\pi$
$283$	−0.511502	−	1.57424i	−0.0304056	−	0.0935789i	−0.965108	+	0.261853i	$0.915666\pi$
$284$	4.70551	−	3.41875i	0.279221	−	0.202866i
$285$	4.94937			0.293176
$286$		0			0
$287$	5.39351			0.318369
$288$	−9.73476	+	7.07272i	−0.573626	+	0.416764i
$289$	0.747498	+	2.30056i	0.0439705	+	0.135327i
$290$	−2.50207	+	7.70057i	−0.146926	+	0.452193i
$291$	2.21884	+	1.61208i	0.130071	+	0.0945018i
$292$	15.7735	+	11.4601i	0.923075	+	0.670653i
$293$	1.44678	−	4.45274i	0.0845219	−	0.260132i	−0.899860	−	0.436179i	$-0.856331\pi$
$293$	1.44678	−	4.45274i	0.0845219	−	0.260132i	0.984382	+	0.176048i	$0.0563313\pi$
$294$	0.244478	+	0.752427i	0.0142583	+	0.0438824i
$295$	−8.39273	+	6.09768i	−0.488644	+	0.355020i
$296$	−24.0210			−1.39619
$297$		0			0
$298$	−7.28247			−0.421862
$299$	14.9564	−	10.8665i	0.864952	−	0.628424i
$300$	1.53578	+	4.72665i	0.0886684	+	0.272893i
$301$	2.91906	−	8.98396i	0.168252	−	0.517827i
$302$	−13.3054	−	9.66691i	−0.765637	−	0.556268i
$303$	−11.3477	−	8.24461i	−0.651910	−	0.473641i
$304$	−0.208259	+	0.640956i	−0.0119445	+	0.0367614i
$305$	11.9887	+	36.8974i	0.686470	+	2.11274i
$306$	−6.09863	+	4.43091i	−0.348635	+	0.253299i
$307$	−16.9829			−0.969266			−0.484633	−	0.874718i	$-0.661047\pi$
$307$	−16.9829			−0.969266			−0.484633	+	0.874718i	$0.661047\pi$
$308$		0			0
$309$	0.103527			0.00588942
$310$	14.8711	−	10.8045i	0.844622	−	0.613654i
$311$	−6.77540	−	20.8525i	−0.384198	−	1.18244i	−0.937061	−	0.349167i	$-0.886465\pi$
$311$	−6.77540	−	20.8525i	−0.384198	−	1.18244i	0.552863	−	0.833272i	$-0.313535\pi$
$312$	−1.78779	+	5.50224i	−0.101213	+	0.311503i
$313$	−8.13504	−	5.91045i	−0.459820	−	0.334079i	0.333641	−	0.942700i	$-0.391723\pi$
$313$	−8.13504	−	5.91045i	−0.459820	−	0.334079i	−0.793461	+	0.608622i	$0.791723\pi$
$314$	8.69595	+	6.31797i	0.490741	+	0.356544i
$315$	−1.91642	+	5.89812i	−0.107978	+	0.332321i
$316$	2.93577	+	9.03537i	0.165150	+	0.508279i
$317$	−19.0606	+	13.8483i	−1.07055	+	0.777799i	−0.976011	−	0.217722i	$-0.930137\pi$
$317$	−19.0606	+	13.8483i	−1.07055	+	0.777799i	−0.0945377	+	0.995521i	$0.530137\pi$
$318$	7.43500			0.416934
$319$		0			0
$320$	11.9119			0.665895
$321$	−3.61313	+	2.62510i	−0.201665	+	0.146519i
$322$	2.13716	+	6.57751i	0.119099	+	0.366550i
$323$	−2.34986	+	7.23213i	−0.130750	+	0.402406i
$324$	1.65320	+	1.20112i	0.0918446	+	0.0667290i
$325$	−6.97103	−	5.06475i	−0.386683	−	0.280942i
$326$	−1.51792	+	4.67166i	−0.0840695	+	0.258739i
$327$	−0.959265	−	2.95231i	−0.0530475	−	0.163263i
$328$	−11.9369	+	8.67264i	−0.659103	+	0.478866i
$329$	−5.39667			−0.297528
$330$		0			0
$331$	−20.8607			−1.14661			−0.573304	−	0.819343i	$-0.694339\pi$
$331$	−20.8607			−1.14661			−0.573304	+	0.819343i	$0.694339\pi$
$332$	8.16369	−	5.93127i	0.448041	−	0.325521i
$333$	5.63612	+	17.3462i	0.308858	+	0.950566i
$334$	−3.37131	+	10.3758i	−0.184470	+	0.567739i
$335$	−10.4380	−	7.58367i	−0.570291	−	0.414340i
$336$	0.303527	+	0.220525i	0.0165588	+	0.0120307i
$337$	4.12672	−	12.7007i	0.224797	−	0.691854i	−0.773515	−	0.633778i	$-0.781503\pi$
$337$	4.12672	−	12.7007i	0.224797	−	0.691854i	0.998312	−	0.0580761i	$-0.0184966\pi$
$338$	2.07504	+	6.38633i	0.112868	+	0.347371i
$339$	−8.79724	+	6.39157i	−0.477800	+	0.347142i
$340$	−17.3901			−0.943112
$341$		0			0
$342$	−2.95195			−0.159623
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	7.98554	+	24.5770i	0.430552	+	1.32510i
$345$	7.44300	−	22.9072i	0.400718	−	1.23328i
$346$	−0.344939	−	0.250613i	−0.0185440	−	0.0134730i
$347$	1.28841	+	0.936085i	0.0691655	+	0.0502517i	0.621831	−	0.783152i	$-0.286389\pi$
$347$	1.28841	+	0.936085i	0.0691655	+	0.0502517i	−0.552665	+	0.833403i	$0.686389\pi$
$348$	1.29206	−	3.97656i	0.0692618	−	0.213166i
$349$	2.05025	+	6.31002i	0.109747	+	0.337768i	0.990815	−	0.135222i	$-0.0431747\pi$
$349$	2.05025	+	6.31002i	0.109747	+	0.337768i	−0.881068	+	0.472990i	$0.843175\pi$
$350$	2.60785	−	1.89471i	0.139395	−	0.101277i
$351$	10.7372			0.573111
$352$		0			0
$353$	−25.4141			−1.35265			−0.676327	−	0.736601i	$-0.736430\pi$
$353$	−25.4141			−1.35265			−0.676327	+	0.736601i	$0.736430\pi$
$354$	−2.22394	+	1.61578i	−0.118201	+	0.0858780i
$355$	4.05993	+	12.4952i	0.215479	+	0.663176i
$356$	−4.42869	+	13.6301i	−0.234720	+	0.722395i
$357$	3.42480	+	2.48826i	0.181260	+	0.131693i
$358$	1.13010	+	0.821063i	0.0597274	+	0.0433945i
$359$	4.96875	−	15.2922i	0.262241	−	0.807094i	−0.730076	−	0.683366i	$-0.760515\pi$
$359$	4.96875	−	15.2922i	0.262241	−	0.807094i	0.992316	−	0.123727i	$-0.0394849\pi$
$360$	−5.24264	−	16.1352i	−0.276312	−	0.850400i
$361$	12.9622	−	9.41762i	0.682223	−	0.495664i
$362$	8.14167			0.427916
$363$		0			0
$364$	−2.90977			−0.152513
$365$	−35.6300	+	25.8867i	−1.86496	+	1.35497i
$366$	3.17681	+	9.77720i	0.166054	+	0.511063i
$367$	−0.935105	+	2.87796i	−0.0488121	+	0.150228i	−0.972492	−	0.232938i	$-0.925166\pi$
$367$	−0.935105	+	2.87796i	−0.0488121	+	0.150228i	0.923680	+	0.383166i	$0.125166\pi$
$368$	2.65335	+	1.92778i	0.138316	+	0.100492i
$369$	9.06354	+	6.58505i	0.471829	+	0.342804i
$370$	6.67181	−	20.5337i	0.346851	−	1.06750i
$371$	2.90406	+	8.93778i	0.150771	+	0.464026i
$372$	−7.67940	+	5.57941i	−0.398158	+	0.289279i
$373$	1.73856			0.0900192			0.0450096	−	0.998987i	$-0.485668\pi$
$373$	1.73856			0.0900192			0.0450096	+	0.998987i	$0.485668\pi$
$374$		0			0
$375$	3.11455			0.160834
$376$	11.9438	−	8.67771i	0.615957	−	0.447519i
$377$	2.24014	+	6.89444i	0.115373	+	0.355082i
$378$	−1.24125	+	3.82019i	−0.0638432	+	0.196489i
$379$	−15.8347	−	11.5046i	−0.813373	−	0.590950i	0.101433	−	0.994842i	$-0.467657\pi$
$379$	−15.8347	−	11.5046i	−0.813373	−	0.590950i	−0.914807	+	0.403892i	$0.867657\pi$
$380$	−5.50927	−	4.00272i	−0.282620	−	0.205335i
$381$	5.93125	−	18.2545i	0.303867	−	0.935206i
$382$	−5.88715	−	18.1188i	−0.301213	−	0.927038i
$383$	−3.85474	+	2.80063i	−0.196968	+	0.143106i	−0.681898	−	0.731447i	$-0.738845\pi$
$383$	−3.85474	+	2.80063i	−0.196968	+	0.143106i	0.484930	+	0.874553i	$0.338845\pi$
$384$	−7.97351			−0.406897
$385$		0			0
$386$	19.0149			0.967833
$387$	15.8740	−	11.5332i	0.806923	−	0.586264i
$388$	−1.16610	−	3.58889i	−0.0591999	−	0.182198i
$389$	−0.439447	+	1.35248i	−0.0222809	+	0.0685735i	−0.961579	−	0.274529i	$-0.911478\pi$
$389$	−0.439447	+	1.35248i	−0.0222809	+	0.0685735i	0.939298	+	0.343103i	$0.111478\pi$
$390$	−4.20690	−	3.05649i	−0.213024	−	0.154771i
$391$	29.9387	+	21.7517i	1.51406	+	1.10003i
$392$	0.845363	−	2.60176i	0.0426973	−	0.131409i
$393$	−2.50999	−	7.72496i	−0.126612	−	0.389673i
$394$	4.45728	−	3.23840i	0.224555	−	0.163148i
$395$	−21.4599			−1.07976
$396$		0			0
$397$	−18.3969			−0.923314			−0.461657	−	0.887059i	$-0.652745\pi$
$397$	−18.3969			−0.923314			−0.461657	+	0.887059i	$0.652745\pi$
$398$	−10.5426	+	7.65967i	−0.528455	+	0.383945i
$399$	0.512264	+	1.57659i	0.0256453	+	0.0789280i
$400$	0.472378	−	1.45383i	0.0236189	−	0.0726914i
$401$	1.33705	+	0.971420i	0.0667689	+	0.0485104i	0.620669	−	0.784073i	$-0.286861\pi$
$401$	1.33705	+	0.971420i	0.0667689	+	0.0485104i	−0.553900	+	0.832583i	$0.686861\pi$
$402$	−2.76591	−	2.00955i	−0.137951	−	0.100227i
$403$	5.08562	−	15.6519i	0.253333	−	0.779678i
$404$	5.96376	+	18.3546i	0.296708	+	0.913174i
$405$	−3.73434	+	2.71315i	−0.185561	+	0.134818i
$406$	−2.71193			−0.134591
$407$		0			0
$408$	−11.5808			−0.573335
$409$	29.6795	−	21.5634i	1.46755	−	1.06624i	0.486241	−	0.873825i	$-0.338368\pi$
$409$	29.6795	−	21.5634i	1.46755	−	1.06624i	0.981313	−	0.192416i	$-0.0616324\pi$
$410$	−4.09813	−	12.6128i	−0.202392	−	0.622900i
$411$	−2.48011	+	7.63299i	−0.122335	+	0.376508i
$412$	−0.115238	−	0.0837254i	−0.00567738	−	0.00412485i
$413$	−2.81102	−	2.04233i	−0.138321	−	0.100496i
$414$	−4.43922	+	13.6625i	−0.218176	+	0.671476i
$415$	7.04367	+	21.6782i	0.345760	+	1.06414i
$416$	10.3173	−	7.49593i	0.505845	−	0.367518i
$417$	14.1344			0.692164
$418$		0			0
$419$	−17.3452			−0.847366			−0.423683	−	0.905810i	$-0.639263\pi$
$419$	−17.3452			−0.847366			−0.423683	+	0.905810i	$0.639263\pi$
$420$	−3.06699	+	2.22830i	−0.149654	+	0.108730i
$421$	1.64608	+	5.06612i	0.0802251	+	0.246907i	0.983122	−	0.182949i	$-0.0585643\pi$
$421$	1.64608	+	5.06612i	0.0802251	+	0.246907i	−0.902897	+	0.429856i	$0.858564\pi$
$422$	−2.88913	+	8.89182i	−0.140640	+	0.432847i
$423$	−9.06885	−	6.58890i	−0.440942	−	0.320363i
$424$	−20.7990	−	15.1113i	−1.01009	−	0.733871i
$425$	5.33000	−	16.4040i	0.258543	−	0.795713i
$426$	1.07582	+	3.31102i	0.0521235	+	0.160420i
$427$	−10.5126	+	7.63782i	−0.508738	+	0.369620i
$428$	6.14487			0.297024
$429$		0			0
$430$	−23.2270			−1.12011
$431$	22.8208	−	16.5803i	1.09924	−	0.798644i	0.118304	−	0.992977i	$-0.462254\pi$
$431$	22.8208	−	16.5803i	1.09924	−	0.798644i	0.980936	+	0.194333i	$0.0622543\pi$
$432$	0.588631	+	1.81162i	0.0283205	+	0.0871615i
$433$	5.47145	−	16.8394i	0.262941	−	0.809249i	−0.729220	−	0.684280i	$-0.760117\pi$
$433$	5.47145	−	16.8394i	0.262941	−	0.809249i	0.992161	−	0.124969i	$-0.0398832\pi$
$434$	4.98086	+	3.61881i	0.239089	+	0.173708i
$435$	7.64093	+	5.55146i	0.366354	+	0.266172i
$436$	−1.31985	+	4.06208i	−0.0632094	+	0.194538i
$437$	4.47808	+	13.7821i	0.214215	+	0.659287i
$438$	−9.44137	+	6.85956i	−0.451126	+	0.327762i
$439$	−25.1189			−1.19886			−0.599430	−	0.800427i	$-0.704606\pi$
$439$	−25.1189			−1.19886			−0.599430	+	0.800427i	$0.704606\pi$
$440$		0			0
$441$	−2.07715			−0.0989121
$442$	6.46355	−	4.69605i	0.307440	−	0.223368i
$443$	−8.33008	−	25.6374i	−0.395774	−	1.21807i	−0.928357	−	0.371690i	$-0.878778\pi$
$443$	−8.33008	−	25.6374i	−0.395774	−	1.21807i	0.532583	−	0.846378i	$-0.321222\pi$
$444$	−3.44531	+	10.6036i	−0.163507	+	0.503223i
$445$	−26.1902	−	19.0283i	−1.24153	−	0.902027i
$446$	−7.12234	−	5.17468i	−0.337252	−	0.245028i
$447$	−2.62502	+	8.07898i	−0.124159	+	0.382123i
$448$	1.23289	+	3.79444i	0.0582486	+	0.179271i
$449$	17.0673	−	12.4001i	0.805456	−	0.585198i	−0.107053	−	0.994253i	$-0.534142\pi$
$449$	17.0673	−	12.4001i	0.805456	−	0.585198i	0.912510	+	0.409055i	$0.134142\pi$
$450$	6.69566			0.315636
$451$		0			0
$452$	14.9615			0.703730
$453$	−15.5202	+	11.2761i	−0.729204	+	0.529798i
$454$	0.951251	+	2.92765i	0.0446444	+	0.137401i
$455$	2.03109	−	6.25104i	0.0952188	−	0.293053i
$456$	−3.66885	−	2.66558i	−0.171810	−	0.124827i
$457$	1.54001	+	1.11888i	0.0720387	+	0.0523392i	0.623222	−	0.782045i	$-0.285823\pi$
$457$	1.54001	+	1.11888i	0.0720387	+	0.0523392i	−0.551183	+	0.834384i	$0.685823\pi$
$458$	6.02092	−	18.5305i	0.281339	−	0.865872i
$459$	6.64172	+	20.4411i	0.310009	+	0.954109i
$460$	−26.8108	+	19.4792i	−1.25006	+	0.908222i
$461$	25.0440			1.16641			0.583207	−	0.812324i	$-0.301798\pi$
$461$	25.0440			1.16641			0.583207	+	0.812324i	$0.301798\pi$
$462$		0			0
$463$	−21.1721			−0.983952			−0.491976	−	0.870609i	$-0.663725\pi$
$463$	−21.1721			−0.983952			−0.491976	+	0.870609i	$0.663725\pi$
$464$	−1.04044	+	0.755926i	−0.0483013	+	0.0350930i
$465$	−6.62582	−	20.3922i	−0.307265	−	0.945664i
$466$	−0.984061	+	3.02863i	−0.0455857	+	0.140298i
$467$	−13.4689	−	9.78570i	−0.623265	−	0.452828i	0.230796	−	0.973002i	$-0.425867\pi$
$467$	−13.4689	−	9.78570i	−0.623265	−	0.452828i	−0.854060	+	0.520174i	$0.825867\pi$
$468$	−4.88973	−	3.55260i	−0.226028	−	0.164219i
$469$	1.33538	−	4.10988i	0.0616621	−	0.189776i
$470$	4.10053	+	12.6201i	0.189143	+	0.582123i
$471$	10.1435	−	7.36969i	0.467388	−	0.339578i
$472$	9.50534			0.437519
$473$		0			0
$474$	−5.68652			−0.261190
$475$	5.46432	−	3.97006i	0.250720	−	0.182159i
$476$	−1.79989	−	5.53950i	−0.0824979	−	0.253902i
$477$	−6.03218	+	18.5651i	−0.276195	+	0.850039i
$478$	−6.71046	−	4.87544i	−0.306929	−	0.222997i
$479$	−17.5244	−	12.7322i	−0.800708	−	0.581749i	0.110413	−	0.993886i	$-0.464783\pi$
$479$	−17.5244	−	12.7322i	−0.800708	−	0.581749i	−0.911122	+	0.412137i	$0.864783\pi$
$480$	5.13434	−	15.8019i	0.234350	−	0.721254i
$481$	−5.97337	−	18.3841i	−0.272362	−	0.838245i
$482$	8.94570	−	6.49943i	0.407465	−	0.296041i
$483$	8.06728			0.367074
$484$		0			0
$485$	8.52397			0.387053
$486$	−10.7385	+	7.80196i	−0.487107	+	0.353904i
$487$	−0.869374	−	2.67566i	−0.0393951	−	0.121246i	0.929425	−	0.369011i	$-0.120304\pi$
$487$	−0.869374	−	2.67566i	−0.0393951	−	0.121246i	−0.968820	+	0.247766i	$0.920304\pi$
$488$	10.9848	−	33.8079i	0.497260	−	1.53041i
$489$	4.63548	+	3.36787i	0.209623	+	0.152300i
$490$	1.98925	+	1.44527i	0.0898652	+	0.0652909i
$491$	0.990648	−	3.04890i	0.0447073	−	0.137595i	−0.926211	−	0.377005i	$-0.876954\pi$
$491$	0.990648	−	3.04890i	0.0447073	−	0.137595i	0.970919	+	0.239410i	$0.0769540\pi$
$492$	2.11627	+	6.51319i	0.0954086	+	0.293637i
$493$	−11.7397	+	8.52936i	−0.528728	+	0.384143i
$494$	3.12858			0.140762
$495$		0			0
$496$	2.91964			0.131096
$497$	−3.56004	+	2.58652i	−0.159690	+	0.116021i
$498$	1.86646	+	5.74436i	0.0836379	+	0.257411i
$499$	−6.19617	+	19.0698i	−0.277379	+	0.853684i	0.711202	+	0.702988i	$0.248151\pi$
$499$	−6.19617	+	19.0698i	−0.277379	+	0.853684i	−0.988580	+	0.150695i	$0.951849\pi$
$500$	−3.46688	−	2.51884i	−0.155044	−	0.112646i
$501$	10.2954	+	7.48008i	0.459966	+	0.334185i
$502$	−0.0194552	+	0.0598771i	−0.000868330	+	0.00267244i
$503$	10.9728	+	33.7709i	0.489255	+	1.50577i	0.825722	+	0.564077i	$0.190768\pi$
$503$	10.9728	+	33.7709i	0.489255	+	1.50577i	−0.336467	+	0.941695i	$0.609232\pi$
$504$	4.59713	−	3.34001i	0.204773	−	0.148776i
$505$	−43.5939			−1.93990
$506$		0			0
$507$	7.83279			0.347867
$508$	−21.3652	+	15.5228i	−0.947929	+	0.688711i
$509$	2.83980	+	8.74002i	0.125872	+	0.387394i	0.994059	−	0.108843i	$-0.0347146\pi$
$509$	2.83980	+	8.74002i	0.125872	+	0.387394i	−0.868187	+	0.496237i	$0.834715\pi$
$510$	3.21656	−	9.89956i	0.142432	−	0.438360i
$511$	−11.9338	−	8.67038i	−0.527918	−	0.383555i
$512$	3.55906	+	2.58581i	0.157290	+	0.114278i
$513$	−2.60084	+	8.00457i	−0.114830	+	0.353410i
$514$	−2.42072	−	7.45021i	−0.106773	−	0.328615i
$515$	0.260306	−	0.189123i	0.0114704	−	0.00833376i
$516$	11.9944			0.528022
$517$		0			0
$518$	7.23140			0.317730
$519$	−0.402359	+	0.292331i	−0.0176616	+	0.0128319i
$520$	5.55635	+	17.1007i	0.243662	+	0.749914i
$521$	3.83176	−	11.7929i	0.167872	−	0.516658i	−0.831364	−	0.555728i	$-0.812440\pi$
$521$	3.83176	−	11.7929i	0.167872	−	0.516658i	0.999236	+	0.0390700i	$0.0124395\pi$
$522$	−4.55727	−	3.31105i	−0.199466	−	0.144921i
$523$	−18.3732	−	13.3489i	−0.803404	−	0.583707i	0.108507	−	0.994096i	$-0.465393\pi$
$523$	−18.3732	−	13.3489i	−0.803404	−	0.583707i	−0.911911	+	0.410388i	$0.865393\pi$
$524$	−3.45350	+	10.6288i	−0.150867	+	0.464320i
$525$	−1.16193	−	3.57604i	−0.0507106	−	0.156071i
$526$	9.85540	−	7.16037i	0.429716	−	0.312207i
$527$	32.9433			1.43503
$528$		0			0
$529$	47.5220			2.06617
$530$	18.6945	−	13.5823i	0.812035	−	0.589978i
$531$	−2.23027	−	6.86407i	−0.0967856	−	0.297875i
$532$	0.704823	−	2.16922i	0.0305580	−	0.0940477i
$533$	−9.60588	−	6.97908i	−0.416077	−	0.302297i
$534$	−6.93997	−	5.04218i	−0.300322	−	0.218197i
$535$	−4.28926	+	13.2010i	−0.185441	+	0.570729i
$536$	3.65313	+	11.2432i	0.157791	+	0.485632i
$537$	1.31822	−	0.957741i	0.0568853	−	0.0413296i
$538$	24.7525			1.06716
$539$		0			0
$540$	−19.2475			−0.828281
$541$	−13.9756	+	10.1539i	−0.600859	+	0.436550i	−0.846184	−	0.532891i	$-0.821105\pi$
$541$	−13.9756	+	10.1539i	−0.600859	+	0.436550i	0.245325	+	0.969441i	$0.421105\pi$
$542$	2.64465	+	8.13940i	0.113597	+	0.349617i
$543$	2.93472	−	9.03215i	0.125941	−	0.387607i
$544$	20.6524	+	15.0048i	0.885463	+	0.643326i
$545$	−7.80526	−	5.67086i	−0.334341	−	0.242913i
$546$	0.538205	−	1.65642i	0.0230330	−	0.0708884i
$547$	−4.07098	−	12.5292i	−0.174062	−	0.535709i	0.825527	−	0.564363i	$-0.190878\pi$
$547$	−4.07098	−	12.5292i	−0.174062	−	0.535709i	−0.999589	+	0.0286536i	$0.990878\pi$
$548$	8.93372	−	6.49073i	0.381630	−	0.277270i
$549$	−26.9910			−1.15195
$550$		0			0
$551$	−5.68240			−0.242078
$552$	−17.8544	+	12.9720i	−0.759934	+	0.552124i
$553$	−2.22111	−	6.83589i	−0.0944514	−	0.290691i
$554$	−7.15476	+	22.0201i	−0.303976	+	0.935543i
$555$	−20.3747	−	14.8031i	−0.864857	−	0.628355i
$556$	−15.7333	−	11.4309i	−0.667242	−	0.484780i
$557$	−3.90028	+	12.0038i	−0.165260	+	0.508618i	−0.999055	−	0.0434555i	$-0.986163\pi$
$557$	−3.90028	+	12.0038i	−0.165260	+	0.508618i	0.833795	+	0.552074i	$0.186163\pi$
$558$	3.95183	+	12.1625i	0.167294	+	0.514878i
$559$	−16.8239	+	12.2233i	−0.711575	+	0.516989i
$560$	1.16604			0.0492743
$561$		0			0
$562$	−7.88151			−0.332462
$563$	−7.94393	+	5.77160i	−0.334797	+	0.243244i	−0.742463	−	0.669887i	$-0.766343\pi$
$563$	−7.94393	+	5.77160i	−0.334797	+	0.243244i	0.407666	+	0.913131i	$0.366343\pi$
$564$	−2.11750	−	6.51700i	−0.0891630	−	0.274415i
$565$	−10.4435	+	32.1417i	−0.439360	+	1.35221i
$566$	−1.10285	−	0.801266i	−0.0463562	−	0.0336797i
$567$	−1.25076	−	0.908732i	−0.0525271	−	0.0381632i
$568$	3.71998	−	11.4489i	0.156087	−	0.480386i
$569$	6.28986	+	19.3582i	0.263684	+	0.811537i	0.991994	+	0.126289i	$0.0403065\pi$
$569$	6.28986	+	19.3582i	0.263684	+	0.811537i	−0.728309	+	0.685249i	$0.759693\pi$
$570$	3.29762	−	2.39586i	0.138122	−	0.100352i
$571$	−32.3174			−1.35244			−0.676221	−	0.736699i	$-0.736384\pi$
$571$	−32.3174			−1.35244			−0.676221	+	0.736699i	$0.736384\pi$
$572$		0			0
$573$	−22.2226			−0.928362
$574$	3.59354	−	2.61086i	0.149992	−	0.108975i
$575$	−10.1573	−	31.2608i	−0.423587	−	1.30367i
$576$	−2.56090	+	7.88164i	−0.106704	+	0.328402i
$577$	9.15654	+	6.65262i	0.381192	+	0.276952i	0.761837	−	0.647769i	$-0.224298\pi$
$577$	9.15654	+	6.65262i	0.381192	+	0.276952i	−0.380645	+	0.924721i	$0.624298\pi$
$578$	1.61168	+	1.17095i	0.0670370	+	0.0487053i
$579$	6.85406	−	21.0946i	0.284845	−	0.876663i
$580$	−4.01566	−	12.3589i	−0.166741	−	0.513177i
$581$	−6.17640	+	4.48742i	−0.256240	+	0.186169i
$582$	2.25871			0.0936266
$583$		0			0
$584$	40.3534			1.66984
$585$	11.0452	−	8.02479i	0.456662	−	0.331784i
$586$	−1.19151	−	3.66708i	−0.0492206	−	0.151486i
$587$	−11.8164	+	36.3672i	−0.487716	+	1.50104i	0.340291	+	0.940320i	$0.389474\pi$
$587$	−11.8164	+	36.3672i	−0.487716	+	1.50104i	−0.828008	+	0.560717i	$0.810526\pi$
$588$	−1.02724	−	0.746336i	−0.0423628	−	0.0307784i
$589$	10.4366	+	7.58262i	0.430032	+	0.312436i
$590$	−2.64010	+	8.12541i	−0.108691	+	0.334518i
$591$	−1.98594	−	6.11210i	−0.0816907	−	0.251418i
$592$	2.77436	−	2.01569i	0.114025	−	0.0828443i
$593$	−26.4263			−1.08520			−0.542598	−	0.839992i	$-0.682559\pi$
$593$	−26.4263			−1.08520			−0.542598	+	0.839992i	$0.682559\pi$
$594$		0			0
$595$	13.1568			0.539378
$596$	9.45572	−	6.86998i	0.387321	−	0.281405i
$597$	4.69727	+	14.4567i	0.192246	+	0.591674i
$598$	4.70484	−	14.4800i	0.192395	−	0.592132i
$599$	16.4226	+	11.9317i	0.671009	+	0.487517i	0.870363	−	0.492411i	$-0.163884\pi$
$599$	16.4226	+	11.9317i	0.671009	+	0.487517i	−0.199354	+	0.979928i	$0.563884\pi$
$600$	8.32175	+	6.04611i	0.339734	+	0.246831i
$601$	−1.57416	+	4.84478i	−0.0642115	+	0.197623i	−0.978015	−	0.208533i	$-0.933131\pi$
$601$	−1.57416	+	4.84478i	−0.0642115	+	0.197623i	0.913804	+	0.406156i	$0.133131\pi$
$602$	−2.40401	−	7.39879i	−0.0979803	−	0.301552i
$603$	7.26187	−	5.27606i	0.295726	−	0.214858i
$604$	26.3953			1.07401
$605$		0			0
$606$	−11.5517			−0.469254
$607$	−24.7888	+	18.0101i	−1.00615	+	0.731008i	−0.963397	−	0.268077i	$-0.913612\pi$
$607$	−24.7888	+	18.0101i	−1.00615	+	0.731008i	−0.0427494	+	0.999086i	$0.513612\pi$
$608$	3.08907	+	9.50719i	0.125278	+	0.385568i
$609$	−0.977534	+	3.00854i	−0.0396117	+	0.121912i
$610$	25.8488	+	18.7802i	1.04659	+	0.760389i
$611$	9.61150	+	6.98316i	0.388839	+	0.282508i
$612$	3.73865	−	11.5064i	0.151126	−	0.465118i
$613$	−7.67569	−	23.6234i	−0.310018	−	0.954138i	−0.977757	−	0.209742i	$-0.932737\pi$
$613$	−7.67569	−	23.6234i	−0.310018	−	0.954138i	0.667738	−	0.744396i	$-0.267263\pi$
$614$	−11.3152	+	8.22099i	−0.456645	+	0.331772i
$615$	−15.4695			−0.623789
$616$		0			0
$617$	0.521714			0.0210034			0.0105017	−	0.999945i	$-0.496657\pi$
$617$	0.521714			0.0210034			0.0105017	+	0.999945i	$0.496657\pi$
$618$	0.0689768	−	0.0501146i	0.00277465	−	0.00201590i
$619$	9.72967	+	29.9449i	0.391069	+	1.20359i	0.931981	+	0.362507i	$0.118079\pi$
$619$	9.72967	+	29.9449i	0.391069	+	1.20359i	−0.540913	+	0.841079i	$0.681921\pi$
$620$	−9.11645	+	28.0576i	−0.366126	+	1.12682i
$621$	33.1364	+	24.0750i	1.32972	+	0.966096i
$622$	−14.6084	−	10.6136i	−0.585744	−	0.425568i
$623$	3.35062	−	10.3121i	0.134240	−	0.413147i
$624$	−0.255229	−	0.785514i	−0.0102173	−	0.0314457i
$625$	23.6640	−	17.1929i	0.946561	−	0.687717i
$626$	−8.28124			−0.330985
$627$		0			0
$628$	−17.2511			−0.688395
$629$	31.3040	−	22.7437i	1.24817	−	0.906851i
$630$	1.57828	+	4.85743i	0.0628800	+	0.193525i
$631$	−0.0352990	+	0.108639i	−0.00140523	+	0.00432486i	−0.951757	−	0.306854i	$-0.900724\pi$
$631$	−0.0352990	+	0.108639i	−0.00140523	+	0.00432486i	0.950351	+	0.311179i	$0.100724\pi$
$632$	15.9077	+	11.5576i	0.632774	+	0.459737i
$633$	8.82294	+	6.41024i	0.350680	+	0.254784i
$634$	−5.99589	+	18.4535i	−0.238127	+	0.732880i
$635$	−18.4340	−	56.7341i	−0.731532	−	2.25142i
$636$	−9.65377	+	7.01387i	−0.382797	+	0.278118i
$637$	2.20144			0.0872244
$638$		0			0
$639$	−9.14043			−0.361590
$640$	−20.0485	+	14.5661i	−0.792485	+	0.575774i
$641$	4.08339	+	12.5674i	0.161284	+	0.496382i	0.998743	−	0.0501182i	$-0.0159598\pi$
$641$	4.08339	+	12.5674i	0.161284	+	0.496382i	−0.837459	+	0.546500i	$0.815960\pi$
$642$	−1.13658	+	3.49805i	−0.0448574	+	0.138057i
$643$	−1.98694	−	1.44360i	−0.0783573	−	0.0569299i	0.547917	−	0.836533i	$-0.315421\pi$
$643$	−1.98694	−	1.44360i	−0.0783573	−	0.0569299i	−0.626274	+	0.779603i	$0.715421\pi$
$644$	−8.97989	−	6.52427i	−0.353857	−	0.257092i
$645$	−8.37234	+	25.7674i	−0.329661	+	1.01459i
$646$	1.93524	+	5.95606i	0.0761411	+	0.234338i
$647$	15.0571	−	10.9396i	0.591956	−	0.430081i	−0.251059	−	0.967972i	$-0.580779\pi$
$647$	15.0571	−	10.9396i	0.591956	−	0.430081i	0.843015	+	0.537891i	$0.180779\pi$
$648$	4.22939			0.166146
$649$		0			0
$650$	−7.09630			−0.278340
$651$	5.81000	−	4.22121i	0.227712	−	0.165442i
$652$	−2.43616	−	7.49772i	−0.0954073	−	0.293634i
$653$	6.00981	−	18.4963i	0.235182	−	0.723816i	−0.761915	−	0.647677i	$-0.775741\pi$
$653$	6.00981	−	18.4963i	0.235182	−	0.723816i	0.997097	−	0.0761389i	$-0.0242592\pi$
$654$	−2.06827	−	1.50268i	−0.0808757	−	0.0587596i
$655$	−20.4231	−	14.8383i	−0.797997	−	0.579778i
$656$	0.650923	−	2.00333i	0.0254143	−	0.0782171i
$657$	−9.46827	−	29.1403i	−0.369392	−	1.13687i
$658$	−3.59564	+	2.61239i	−0.140173	+	0.101841i
$659$	4.71629			0.183721			0.0918603	−	0.995772i	$-0.470719\pi$
$659$	4.71629			0.183721			0.0918603	+	0.995772i	$0.470719\pi$
$660$		0			0
$661$	24.9330			0.969782			0.484891	−	0.874575i	$-0.338859\pi$
$661$	24.9330			0.969782			0.484891	+	0.874575i	$0.338859\pi$
$662$	−13.8989	+	10.0981i	−0.540195	+	0.392475i
$663$	−2.87983	−	8.86322i	−0.111844	−	0.344219i
$664$	6.45388	−	19.8630i	0.250459	−	0.770834i
$665$	4.16815	+	3.02834i	0.161634	+	0.117434i
$666$	12.1520	+	8.82897i	0.470882	+	0.342116i
$667$	−8.54535	+	26.2999i	−0.330877	+	1.01833i
$668$	−5.41073	−	16.6525i	−0.209348	−	0.644305i
$669$	−8.30796	+	6.03608i	−0.321204	+	0.233368i
$670$	−10.6256			−0.410503
$671$		0			0
$672$	5.56498			0.214674
$673$	4.15003	−	3.01517i	0.159972	−	0.116226i	−0.504919	−	0.863166i	$-0.668478\pi$
$673$	4.15003	−	3.01517i	0.159972	−	0.116226i	0.664891	+	0.746940i	$0.268478\pi$
$674$	−3.39859	−	10.4598i	−0.130909	−	0.402896i
$675$	5.89928	−	18.1561i	0.227063	−	0.698829i
$676$	−8.71888	−	6.33464i	−0.335342	−	0.243640i
$677$	41.4710	+	30.1304i	1.59386	+	1.15801i	0.898154	+	0.439680i	$0.144908\pi$
$677$	41.4710	+	30.1304i	1.59386	+	1.15801i	0.695706	+	0.718327i	$0.255092\pi$
$678$	−2.76735	+	8.51703i	−0.106279	+	0.327094i
$679$	0.882237	+	2.71525i	0.0338572	+	0.104202i
$680$	−29.1186	+	21.1559i	−1.11665	+	0.811291i
$681$	3.59074			0.137598
$682$		0			0
$683$	−24.9448			−0.954485			−0.477242	−	0.878772i	$-0.658364\pi$
$683$	−24.9448			−0.954485			−0.477242	+	0.878772i	$0.658364\pi$
$684$	3.83287	−	2.78474i	0.146553	−	0.106477i
$685$	7.70805	+	23.7230i	0.294510	+	0.906407i
$686$	−0.254493	+	0.783248i	−0.00971658	+	0.0299046i
$687$	−18.3869	−	13.3589i	−0.701506	−	0.509674i
$688$	−2.98466	−	2.16848i	−0.113789	−	0.0826725i
$689$	6.39313	−	19.6760i	0.243559	−	0.749597i
$690$	−6.12973	−	18.8654i	−0.233355	−	0.718192i
$691$	−9.53403	+	6.92688i	−0.362692	+	0.263511i	−0.754174	−	0.656675i	$-0.771962\pi$
$691$	−9.53403	+	6.92688i	−0.362692	+	0.263511i	0.391482	+	0.920186i	$0.371962\pi$
$692$	0.684294			0.0260130
$693$		0			0
$694$	1.31156			0.0497863
$695$	35.5393	−	25.8208i	1.34808	−	0.979439i
$696$	−2.67419	−	8.23032i	−0.101365	−	0.311970i
$697$	7.34458	−	22.6043i	0.278196	−	0.856199i
$698$	4.42054	+	3.21171i	0.167320	+	0.121565i
$699$	3.00517	+	2.18338i	0.113666	+	0.0825831i
$700$	−1.59869	+	4.92027i	−0.0604249	+	0.185969i
$701$	−9.67755	−	29.7844i	−0.365516	−	1.12494i	−0.949657	−	0.313291i	$-0.898569\pi$
$701$	−9.67755	−	29.7844i	−0.365516	−	1.12494i	0.584141	−	0.811652i	$-0.301431\pi$
$702$	7.15391	−	5.19762i	0.270007	−	0.196171i
$703$	15.1522			0.571477
$704$		0			0
$705$	15.4785			0.582954
$706$	−16.9327	+	12.3023i	−0.637269	+	0.463003i
$707$	−4.51200	−	13.8865i	−0.169691	−	0.522256i
$708$	1.36334	−	4.19594i	0.0512376	−	0.157693i
$709$	33.5540	+	24.3784i	1.26015	+	0.915552i	0.998765	−	0.0496834i	$-0.0158212\pi$
$709$	33.5540	+	24.3784i	1.26015	+	0.915552i	0.261384	+	0.965235i	$0.415821\pi$
$710$	8.75361	+	6.35987i	0.328517	+	0.238682i
$711$	4.61359	−	14.1992i	0.173023	−	0.532511i
$712$	9.16612	+	28.2104i	0.343515	+	1.05723i
$713$	50.7895	−	36.9007i	1.90208	−	1.38194i
$714$	3.48635			0.130473
$715$		0			0
$716$	−2.24190			−0.0837836
$717$	−7.82752	+	5.68702i	−0.292324	+	0.212386i
$718$	−4.09205	−	12.5940i	−0.152714	−	0.470005i
$719$	−2.43823	+	7.50410i	−0.0909306	+	0.279856i	−0.986172	−	0.165726i	$-0.947003\pi$
$719$	−2.43823	+	7.50410i	−0.0909306	+	0.279856i	0.895241	+	0.445582i	$0.147003\pi$
$720$	1.95948	+	1.42364i	0.0730254	+	0.0530561i
$721$	0.0871857	+	0.0633441i	0.00324696	+	0.00235906i
$722$	4.07754	−	12.5494i	0.151750	−	0.467039i
$723$	−3.98575	−	12.2669i	−0.148232	−	0.456210i
$724$	−10.5713	+	7.68051i	−0.392880	+	0.285444i
$725$	12.8889			0.478682
$726$		0			0
$727$	5.12729			0.190161			0.0950803	−	0.995470i	$-0.469689\pi$
$727$	5.12729			0.190161			0.0950803	+	0.995470i	$0.469689\pi$
$728$	−4.87221	+	3.53987i	−0.180576	+	0.131196i
$729$	3.35128	+	10.3142i	0.124121	+	0.382006i
$730$	−11.2081	+	34.4951i	−0.414832	+	1.27672i
$731$	−33.6769	−	24.4677i	−1.24558	−	0.904970i
$732$	−13.3482	−	9.69806i	−0.493365	−	0.358451i
$733$	−10.4366	+	32.1206i	−0.385485	+	1.18640i	0.550643	+	0.834741i	$0.314383\pi$
$733$	−10.4366	+	32.1206i	−0.385485	+	1.18640i	−0.936128	+	0.351660i	$0.885617\pi$
$734$	0.770111	+	2.37016i	0.0284253	+	0.0874842i
$735$	2.32039	−	1.68586i	0.0855889	−	0.0621840i
$736$	48.6476			1.79317
$737$		0			0
$738$	9.22643			0.339629
$739$	34.5799	−	25.1237i	1.27204	−	0.924192i	0.272759	−	0.962082i	$-0.412064\pi$
$739$	34.5799	−	25.1237i	1.27204	−	0.924192i	0.999282	+	0.0378907i	$0.0120639\pi$
$740$	10.7078	+	32.9553i	0.393628	+	1.21146i
$741$	1.12772	−	3.47077i	0.0414278	−	0.127502i
$742$	6.26144	+	4.54920i	0.229865	+	0.167006i
$743$	−18.5722	−	13.4935i	−0.681348	−	0.495028i	0.192457	−	0.981305i	$-0.438354\pi$
$743$	−18.5722	−	13.4935i	−0.681348	−	0.495028i	−0.873804	+	0.486277i	$0.838354\pi$
$744$	−6.07102	+	18.6847i	−0.222574	+	0.685014i
$745$	8.15843	+	25.1091i	0.298902	+	0.919925i
$746$	1.15835	−	0.841592i	0.0424103	−	0.0308129i
$747$	−15.8579			−0.580211
$748$		0			0
$749$	−4.64902			−0.169872
$750$	2.07513	−	1.50767i	0.0757731	−	0.0550524i
$751$	−0.287608	−	0.885166i	−0.0104950	−	0.0323002i	0.945672	−	0.325123i	$-0.105406\pi$
$751$	−0.287608	−	0.885166i	−0.0104950	−	0.0323002i	−0.956167	+	0.292822i	$0.905406\pi$
$752$	−0.651304	+	2.00451i	−0.0237506	+	0.0730968i
$753$	0.0594133	+	0.0431663i	0.00216514	+	0.00157307i
$754$	4.82996	+	3.50917i	0.175897	+	0.127796i
$755$	−18.4245	+	56.7049i	−0.670538	+	2.06370i
$756$	−1.99213	−	6.13116i	−0.0724532	−	0.222988i
$757$	9.28944	−	6.74917i	0.337630	−	0.245303i	−0.406031	−	0.913859i	$-0.633087\pi$
$757$	9.28944	−	6.74917i	0.337630	−	0.245303i	0.743661	+	0.668556i	$0.233087\pi$
$758$	−16.1193			−0.585478
$759$		0			0
$760$	−14.0944			−0.511257
$761$	−31.4416	+	22.8437i	−1.13976	+	0.828083i	−0.987086	−	0.160194i	$-0.948788\pi$
$761$	−31.4416	+	22.8437i	−1.13976	+	0.828083i	−0.152673	+	0.988277i	$0.548788\pi$
$762$	−4.88471	−	15.0336i	−0.176954	−	0.544610i
$763$	0.998559	−	3.07325i	0.0361503	−	0.111259i
$764$	24.7365	+	17.9721i	0.894936	+	0.650209i
$765$	22.1094	+	16.0635i	0.799369	+	0.580775i
$766$	−1.21259	+	3.73196i	−0.0438126	+	0.134841i
$767$	2.36372	+	7.27480i	0.0853491	+	0.262678i
$768$	−11.5140	+	8.36540i	−0.415475	+	0.301860i
$769$	−35.6509			−1.28560			−0.642802	−	0.766032i	$-0.722228\pi$
$769$	−35.6509			−1.28560			−0.642802	+	0.766032i	$0.722228\pi$
$770$		0			0
$771$	−9.13763			−0.329084
$772$	−24.6894	+	17.9379i	−0.888589	+	0.645598i
$773$	−0.547100	−	1.68380i	−0.0196778	−	0.0605621i	0.940735	−	0.339141i	$-0.110137\pi$
$773$	−0.547100	−	1.68380i	−0.0196778	−	0.0605621i	−0.960413	+	0.278579i	$0.910137\pi$
$774$	4.99350	−	15.3684i	0.179488	−	0.552407i
$775$	−23.6724	−	17.1990i	−0.850339	−	0.617807i
$776$	−6.31861	−	4.59074i	−0.226825	−	0.164798i
$777$	2.60661	−	8.02233i	0.0935117	−	0.287800i
$778$	0.361910	+	1.11384i	0.0129751	+	0.0399332i
$779$	7.52967	−	5.47063i	0.269779	−	0.196006i
$780$	8.34569			0.298824
$781$		0			0
$782$	30.4767			1.08985
$783$	−12.9935	+	9.44036i	−0.464351	+	0.337371i
$784$	0.120686	+	0.371434i	0.00431022	+	0.0132655i
$785$	12.0417	−	37.0605i	0.429786	−	1.32275i
$786$	−5.41179	−	3.93189i	−0.193032	−	0.140246i
$787$	−2.71276	−	1.97093i	−0.0966993	−	0.0702562i	0.538385	−	0.842699i	$-0.319035\pi$
$787$	−2.71276	−	1.97093i	−0.0966993	−	0.0702562i	−0.635084	+	0.772443i	$0.719035\pi$
$788$	−2.73245	+	8.40963i	−0.0973396	+	0.299581i
$789$	−4.39107	−	13.5143i	−0.156326	−	0.481123i
$790$	−14.2981	+	10.3882i	−0.508703	+	0.369594i
$791$	−11.3194			−0.402472
$792$		0			0
$793$	28.6061			1.01583
$794$	−12.2573	+	8.90546i	−0.434996	+	0.316043i
$795$	−8.32931	−	25.6350i	−0.295410	−	0.909179i
$796$	6.46297	−	19.8910i	0.229074	−	0.705017i
$797$	−3.98475	−	2.89509i	−0.141147	−	0.102549i	0.514971	−	0.857208i	$-0.327803\pi$
$797$	−3.98475	−	2.89509i	−0.141147	−	0.102549i	−0.656118	+	0.754658i	$0.727803\pi$
$798$	1.10449	+	0.802460i	0.0390986	+	0.0284068i
$799$	−7.34888	+	22.6175i	−0.259985	+	0.800150i
$800$	−7.00669	−	21.5644i	−0.247724	−	0.762416i
$801$	18.2208	−	13.2382i	0.643802	−	0.467749i
$802$	1.36107			0.0480612
$803$		0			0
$804$	5.48704			0.193513
$805$	20.2842	−	14.7374i	0.714925	−	0.519424i
$806$	−4.18829	−	12.8902i	−0.147526	−	0.454039i
$807$	8.92222	−	27.4598i	0.314077	−	0.966629i
$808$	32.3151	+	23.4783i	1.13684	+	0.825963i
$809$	5.64145	+	4.09875i	0.198343	+	0.144105i	0.682524	−	0.730863i	$-0.260882\pi$
$809$	5.64145	+	4.09875i	0.198343	+	0.144105i	−0.484181	+	0.874968i	$0.660882\pi$
$810$	−1.17471	+	3.61539i	−0.0412752	+	0.127032i
$811$	1.83364	+	5.64335i	0.0643877	+	0.198165i	0.978075	−	0.208253i	$-0.0667777\pi$
$811$	1.83364	+	5.64335i	0.0643877	+	0.198165i	−0.913687	+	0.406418i	$0.866778\pi$
$812$	3.52122	−	2.55832i	0.123571	−	0.0897794i
$813$	9.98292			0.350116
$814$		0			0
$815$	17.8078			0.623781
$816$	1.33755	−	0.971788i	0.0468237	−	0.0340194i
$817$	−5.03721	−	15.5030i	−0.176230	−	0.542380i
$818$	9.33628	−	28.7341i	0.326435	−	1.00466i
$819$	3.69942	+	2.68779i	0.129268	+	0.0939189i
$820$	17.2195	+	12.5107i	0.601329	+	0.436891i
$821$	12.9005	−	39.7036i	0.450230	−	1.38566i	−0.426416	−	0.904527i	$-0.640224\pi$
$821$	12.9005	−	39.7036i	0.450230	−	1.38566i	0.876645	−	0.481137i	$-0.159776\pi$
$822$	2.04251	+	6.28620i	0.0712407	+	0.219256i
$823$	18.7695	−	13.6368i	0.654263	−	0.475350i	−0.210458	−	0.977603i	$-0.567495\pi$
$823$	18.7695	−	13.6368i	0.654263	−	0.475350i	0.864721	+	0.502253i	$0.167495\pi$
$824$	−0.294814			−0.0102703
$825$		0			0
$826$	−2.86154			−0.0995658
$827$	10.6611	−	7.74577i	0.370724	−	0.269347i	−0.386787	−	0.922169i	$-0.626415\pi$
$827$	10.6611	−	7.74577i	0.370724	−	0.269347i	0.757511	+	0.652822i	$0.226415\pi$
$828$	−7.12466	−	21.9275i	−0.247599	−	0.762032i
$829$	1.32596	−	4.08089i	0.0460526	−	0.141735i	−0.925386	−	0.379026i	$-0.876259\pi$
$829$	1.32596	−	4.08089i	0.0460526	−	0.141735i	0.971439	+	0.237290i	$0.0762592\pi$
$830$	15.1868	+	11.0339i	0.527143	+	0.382992i
$831$	21.8495	+	15.8746i	0.757951	+	0.550684i
$832$	2.71414	−	8.35325i	0.0940958	−	0.289597i
$833$	1.36174	+	4.19102i	0.0471816	+	0.145210i
$834$	9.41733	−	6.84209i	0.326095	−	0.236922i
$835$	39.5513			1.36873
$836$		0			0
$837$	36.4619			1.26031
$838$	−11.5566	+	8.39634i	−0.399215	+	0.290047i
$839$	−4.86557	−	14.9747i	−0.167978	−	0.516983i	0.831265	−	0.555876i	$-0.187617\pi$
$839$	−4.86557	−	14.9747i	−0.167978	−	0.516983i	−0.999243	+	0.0388925i	$0.987617\pi$
$840$	−2.42464	+	7.46226i	−0.0836579	+	0.257473i
$841$	14.6889	+	10.6721i	0.506514	+	0.368004i
$842$	3.54911	+	2.57858i	0.122310	+	0.0888637i
$843$	−2.84095	+	8.74354i	−0.0978475	+	0.301144i
$844$	−4.63687	−	14.2708i	−0.159608	−	0.491221i
$845$	19.6946	−	14.3090i	0.677516	−	0.492245i
$846$	−9.23182			−0.317397
$847$		0			0
$848$	3.67028			0.126038
$849$	−1.28643	+	0.934649i	−0.0441503	+	0.0320771i
$850$	−4.38955	−	13.5096i	−0.150560	−	0.463377i
$851$	22.7863	−	70.1291i	0.781105	−	2.40399i
$852$	−4.52034	−	3.28422i	−0.154864	−	0.112516i
$853$	−4.96749	−	3.60909i	−0.170084	−	0.123573i	0.499487	−	0.866321i	$-0.333522\pi$
$853$	−4.96749	−	3.60909i	−0.170084	−	0.123573i	−0.669571	+	0.742748i	$0.733522\pi$
$854$	−3.30694	+	10.1777i	−0.113161	+	0.348274i
$855$	3.30702	+	10.1780i	0.113098	+	0.348079i
$856$	10.2892	−	7.47552i	0.351676	−	0.255508i
$857$	34.4740			1.17761			0.588804	−	0.808276i	$-0.299599\pi$
$857$	34.4740			1.17761			0.588804	+	0.808276i	$0.299599\pi$
$858$		0			0
$859$	8.21553			0.280310			0.140155	−	0.990130i	$-0.455240\pi$
$859$	8.21553			0.280310			0.140155	+	0.990130i	$0.455240\pi$
$860$	30.1584	−	21.9114i	1.02839	−	0.747172i
$861$	−1.60110	−	4.92768i	−0.0545654	−	0.167935i
$862$	7.17875	−	22.0939i	0.244509	−	0.752522i
$863$	−10.5488	−	7.66413i	−0.359084	−	0.260890i	0.393586	−	0.919288i	$-0.371234\pi$
$863$	−10.5488	−	7.66413i	−0.359084	−	0.260890i	−0.752670	+	0.658398i	$0.771234\pi$
$864$	22.8582	+	16.6074i	0.777651	+	0.564997i
$865$	−0.477653	+	1.47007i	−0.0162407	+	0.0499837i
$866$	−4.50604	−	13.8682i	−0.153122	−	0.471260i
$867$	1.87997	−	1.36588i	0.0638470	−	0.0463876i
$868$	−9.88109			−0.335386
$869$		0			0
$870$	7.77824			0.263707
$871$	−7.69640	+	5.59176i	−0.260782	+	0.189470i
$872$	2.73171	+	8.40734i	0.0925073	+	0.284708i
$873$	−1.83254	+	5.63999i	−0.0620222	+	0.190885i
$874$	9.65517	+	7.01489i	0.326591	+	0.237282i
$875$	2.62294	+	1.90567i	0.0886714	+	0.0644235i
$876$	5.78786	−	17.8132i	0.195554	−	0.601852i
$877$	5.53942	+	17.0486i	0.187053	+	0.575690i	0.999978	−	0.00667896i	$-0.00212599\pi$
$877$	5.53942	+	17.0486i	0.187053	+	0.575690i	−0.812925	+	0.582369i	$0.802126\pi$
$878$	−16.7360	+	12.1594i	−0.564813	+	0.410360i
$879$	−4.49765			−0.151702
$880$		0			0
$881$	−17.3276			−0.583780			−0.291890	−	0.956452i	$-0.594284\pi$
$881$	−17.3276			−0.583780			−0.291890	+	0.956452i	$0.594284\pi$
$882$	−1.38395	+	1.00550i	−0.0465999	+	0.0338568i
$883$	6.75945	+	20.8034i	0.227474	+	0.700092i	0.998031	+	0.0627212i	$0.0199779\pi$
$883$	6.75945	+	20.8034i	0.227474	+	0.700092i	−0.770558	+	0.637370i	$0.780022\pi$
$884$	−3.96236	+	12.1949i	−0.133269	+	0.410159i
$885$	8.06247	+	5.85773i	0.271017	+	0.196905i
$886$	−17.9605	−	13.0490i	−0.603394	−	0.438391i
$887$	7.91386	−	24.3564i	0.265721	−	0.817806i	−0.725805	−	0.687901i	$-0.758532\pi$
$887$	7.91386	−	24.3564i	0.265721	−	0.817806i	0.991526	−	0.129906i	$-0.0414675\pi$
$888$	7.13079	+	21.9463i	0.239294	+	0.736470i
$889$	16.1643	−	11.7440i	0.542133	−	0.393883i
$890$	−26.6608			−0.893674
$891$		0			0
$892$	14.1294			0.473087
$893$	−7.53408	+	5.47383i	−0.252118	+	0.183175i
$894$	2.16185	+	6.65349i	0.0723031	+	0.222526i
$895$	1.56490	−	4.81625i	0.0523087	−	0.160990i
$896$	−6.71495	−	4.87869i	−0.224331	−	0.162986i
$897$	−14.3679	−	10.4389i	−0.479729	−	0.348544i
$898$	5.36887	−	16.5237i	0.179162	−	0.551403i
$899$	7.60713	+	23.4124i	0.253712	+	0.780846i
$900$	−8.69379	+	6.31640i	−0.289793	+	0.210547i
$901$	41.4130			1.37967
$902$		0			0
$903$	−9.07457			−0.301983
$904$	25.0520	−	18.2013i	0.833217	−	0.605368i
$905$	−9.12097	−	28.0715i	−0.303191	−	0.933127i
$906$	−4.88220	+	15.0259i	−0.162200	+	0.499201i
$907$	11.6812	+	8.48689i	0.387868	+	0.281802i	0.764581	−	0.644527i	$-0.222946\pi$
$907$	11.6812	+	8.48689i	0.387868	+	0.281802i	−0.376713	+	0.926330i	$0.622946\pi$
$908$	−3.99695	−	2.90395i	−0.132643	−	0.0963711i
$909$	9.37212	−	28.8444i	0.310854	−	0.956709i
$910$	−1.67271	−	5.14808i	−0.0554499	−	0.170657i
$911$	−30.0839	+	21.8572i	−0.996724	+	0.724163i	−0.961383	−	0.275213i	$-0.911252\pi$
$911$	−30.0839	+	21.8572i	−0.996724	+	0.724163i	−0.0353410	+	0.999375i	$0.511252\pi$
$912$	0.647421			0.0214383
$913$		0			0
$914$	1.56769			0.0518545
$915$	30.1517	−	21.9065i	0.996784	−	0.724206i
$916$	9.66319	+	29.7403i	0.319281	+	0.982646i
$917$	2.61281	−	8.04140i	0.0862826	−	0.265550i
$918$	14.3202	+	10.4042i	0.472637	+	0.343391i
$919$	12.9844	+	9.43369i	0.428315	+	0.311189i	0.780975	−	0.624563i	$-0.214723\pi$
$919$	12.9844	+	9.43369i	0.428315	+	0.311189i	−0.352660	+	0.935752i	$0.614723\pi$
$920$	−21.1955	+	65.2331i	−0.698796	+	2.15067i
$921$	5.04149	+	15.5161i	0.166123	+	0.511274i
$922$	16.6861	−	12.1231i	0.549526	−	0.399254i
$923$	9.68736			0.318863
$924$		0			0
$925$	−34.3685			−1.13003
$926$	−14.1064	+	10.2489i	−0.463564	+	0.336799i
$927$	0.0691733	+	0.212893i	0.00227195	+	0.00699234i
$928$	−5.89477	+	18.1422i	−0.193505	+	0.595548i
$929$	−27.4187	−	19.9209i	−0.899578	−	0.653582i	0.0387793	−	0.999248i	$-0.487653\pi$
$929$	−27.4187	−	19.9209i	−0.899578	−	0.653582i	−0.938358	+	0.345666i	$0.887653\pi$
$930$	−14.2859	−	10.3793i	−0.468453	−	0.340351i
$931$	−0.533248	+	1.64117i	−0.0174765	+	0.0537871i
$932$	−1.57936	−	4.86076i	−0.0517335	−	0.159219i
$933$	−17.0402	+	12.3804i	−0.557871	+	0.405317i
$934$	−13.7109			−0.448635
$935$		0			0
$936$	−12.5094			−0.408883
$937$	7.46419	−	5.42305i	0.243844	−	0.177163i	−0.459150	−	0.888359i	$-0.651846\pi$
$937$	7.46419	−	5.42305i	0.243844	−	0.177163i	0.702994	+	0.711195i	$0.251846\pi$
$938$	−1.09976	−	3.38471i	−0.0359084	−	0.110515i
$939$	−2.98503	+	9.18699i	−0.0974129	+	0.299806i
$940$	−17.2295	−	12.5180i	−0.561965	−	0.408292i
$941$	43.1712	+	31.3657i	1.40734	+	1.02249i	0.993702	+	0.112054i	$0.0357429\pi$
$941$	43.1712	+	31.3657i	1.40734	+	1.02249i	0.413640	+	0.910440i	$0.364257\pi$
$942$	3.19085	−	9.82042i	0.103963	−	0.319967i
$943$	−13.9964	−	43.0765i	−0.455786	−	1.40276i
$944$	−1.09784	+	0.797629i	−0.0357317	+	0.0259606i
$945$	14.5621			0.473705
$946$		0			0
$947$	31.0986			1.01057			0.505285	−	0.862953i	$-0.331388\pi$
$947$	31.0986			1.01057			0.505285	+	0.862953i	$0.331388\pi$
$948$	7.38349	−	5.36442i	0.239805	−	0.174228i
$949$	10.0348	+	30.8840i	0.325744	+	1.00254i
$950$	1.71891	−	5.29027i	0.0557689	−	0.171639i
$951$	18.3105	+	13.3034i	0.593759	+	0.431391i
$952$	−9.75285	−	7.08586i	−0.316092	−	0.229654i
$953$	10.7935	−	33.2191i	0.349637	−	1.07607i	−0.609418	−	0.792849i	$-0.708597\pi$
$953$	10.7935	−	33.2191i	0.349637	−	1.07607i	0.959054	−	0.283222i	$-0.0914032\pi$
$954$	4.96784	+	15.2894i	0.160840	+	0.495014i
$955$	−55.8761	+	40.5964i	−1.80811	+	1.31367i
$956$	13.3123			0.430550
$957$		0			0
$958$	−17.8393			−0.576361
$959$	−6.75898	+	4.91069i	−0.218259	+	0.158574i
$960$	−3.53612	−	10.8831i	−0.114128	−	0.351250i
$961$	7.69038	−	23.6686i	0.248077	−	0.763502i
$962$	−12.8792	−	9.35726i	−0.415241	−	0.301690i
$963$	−7.81246	−	5.67609i	−0.251753	−	0.182909i
$964$	−5.48399	+	16.8780i	−0.176628	+	0.543604i
$965$	−21.3021	−	65.5611i	−0.685738	−	2.11049i
$966$	5.37499	−	3.90516i	0.172938	−	0.125646i
$967$	−20.8029			−0.668975			−0.334488	−	0.942400i	$-0.608563\pi$
$967$	−20.8029			−0.668975			−0.334488	+	0.942400i	$0.608563\pi$
$968$		0			0
$969$	7.30507			0.234673
$970$	5.67927	−	4.12623i	0.182350	−	0.132485i
$971$	−12.3702	−	38.0716i	−0.396979	−	1.22177i	−0.927410	−	0.374046i	$-0.877970\pi$
$971$	−12.3702	−	38.0716i	−0.396979	−	1.22177i	0.530431	−	0.847728i	$-0.322030\pi$
$972$	6.58302	−	20.2605i	0.211150	−	0.649854i
$973$	11.9034	+	8.64830i	0.381604	+	0.277252i
$974$	−1.87445	−	1.36187i	−0.0600614	−	0.0436372i
$975$	−2.55792	+	7.87245i	−0.0819188	+	0.252120i
$976$	1.56822	+	4.82650i	0.0501976	+	0.154492i
$977$	−5.24736	+	3.81243i	−0.167878	+	0.121970i	−0.668552	−	0.743665i	$-0.733086\pi$
$977$	−5.24736	+	3.81243i	−0.167878	+	0.121970i	0.500674	+	0.865636i	$0.333086\pi$
$978$	4.71878			0.150890
$979$		0			0
$980$	−3.94630			−0.126060
$981$	5.43022	−	3.94529i	0.173374	−	0.125963i
$982$	−0.815854	−	2.51094i	−0.0260349	−	0.0801273i
$983$	3.39245	−	10.4409i	0.108202	−	0.333012i	−0.882266	−	0.470750i	$-0.843983\pi$
$983$	3.39245	−	10.4409i	0.108202	−	0.333012i	0.990469	+	0.137738i	$0.0439832\pi$
$984$	11.4671	+	8.33136i	0.365559	+	0.265594i
$985$	−16.1590	−	11.7402i	−0.514870	−	0.374075i
$986$	−3.69295	+	11.3657i	−0.117607	+	0.361959i
$987$	1.60204	+	4.93057i	0.0509934	+	0.156942i
$988$	−4.06222	+	2.95137i	−0.129236	+	0.0938957i
$989$	−79.3275			−2.52247
$990$		0			0
$991$	−59.2666			−1.88267			−0.941333	−	0.337479i	$-0.890426\pi$
$991$	−59.2666			−1.88267			−0.941333	+	0.337479i	$0.890426\pi$
$992$	35.0357	−	25.4549i	1.11238	−	0.808194i
$993$	6.19264	+	19.0590i	0.196518	+	0.604819i
$994$	−1.11988	+	3.44665i	−0.0355206	+	0.109321i
$995$	38.2204	+	27.7687i	1.21167	+	0.880327i
$996$	−7.84244	−	5.69787i	−0.248497	−	0.180544i
$997$	−13.3964	+	41.2299i	−0.424269	+	1.30576i	0.479424	+	0.877583i	$0.340845\pi$
$997$	−13.3964	+	41.2299i	−0.424269	+	1.30576i	−0.903693	+	0.428181i	$0.859155\pi$
$998$	5.10289	+	15.7051i	0.161529	+	0.497136i
$999$	34.6475	−	25.1729i	1.09620	−	0.796435i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.729.5		24
11.2	odd	10		847.2.a.m.1.5	✓	6
11.3	even	5	inner	847.2.f.y.148.2		24
11.4	even	5	inner	847.2.f.y.323.5		24
11.5	even	5	inner	847.2.f.y.372.2		24
11.6	odd	10		847.2.f.z.372.5		24
11.7	odd	10		847.2.f.z.323.2		24
11.8	odd	10		847.2.f.z.148.5		24
11.9	even	5		847.2.a.n.1.2	yes	6
11.10	odd	2		847.2.f.z.729.2		24
33.2	even	10		7623.2.a.cs.1.2		6
33.20	odd	10		7623.2.a.cp.1.5		6
77.13	even	10		5929.2.a.bj.1.5		6
77.20	odd	10		5929.2.a.bm.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.5	✓	6	11.2	odd	10
847.2.a.n.1.2	yes	6	11.9	even	5
847.2.f.y.148.2		24	11.3	even	5	inner
847.2.f.y.323.5		24	11.4	even	5	inner
847.2.f.y.372.2		24	11.5	even	5	inner
847.2.f.y.729.5		24	1.1	even	1	trivial
847.2.f.z.148.5		24	11.8	odd	10
847.2.f.z.323.2		24	11.7	odd	10
847.2.f.z.372.5		24	11.6	odd	10
847.2.f.z.729.2		24	11.10	odd	2
5929.2.a.bj.1.5		6	77.13	even	10
5929.2.a.bm.1.2		6	77.20	odd	10
7623.2.a.cp.1.5		6	33.20	odd	10
7623.2.a.cs.1.2		6	33.2	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.666271 - 0.484074i) q^{2} +(-0.296857 - 0.913631i) q^{3} +(-0.408445 + 1.25706i) q^{4} +(-2.41544 - 1.75492i) q^{5} +(-0.640052 - 0.465025i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.845363 + 2.60176i) q^{8} +(1.68045 - 1.22092i) q^{9} +O(q^{10})\)	\(q+(0.666271 - 0.484074i) q^{2} +(-0.296857 - 0.913631i) q^{3} +(-0.408445 + 1.25706i) q^{4} +(-2.41544 - 1.75492i) q^{5} +(-0.640052 - 0.465025i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.845363 + 2.60176i) q^{8} +(1.68045 - 1.22092i) q^{9} -2.45885 q^{10} +1.26974 q^{12} +(-1.78101 + 1.29398i) q^{13} +(-0.254493 - 0.783248i) q^{14} +(-0.886310 + 2.72778i) q^{15} +(-0.315961 - 0.229559i) q^{16} +(-3.56509 - 2.59019i) q^{17} +(0.528621 - 1.62693i) q^{18} +(-0.533248 - 1.64117i) q^{19} +(3.19262 - 2.31958i) q^{20} -0.960649 q^{21} -8.39774 q^{23} +(2.12610 - 1.54470i) q^{24} +(1.20952 + 3.72253i) q^{25} +(-0.560251 + 1.72428i) q^{26} +(-3.94587 - 2.86684i) q^{27} +(1.06932 + 0.776908i) q^{28} +(1.01758 - 3.13178i) q^{29} +(0.729926 + 2.24648i) q^{30} +(-6.04800 + 4.39413i) q^{31} -5.79294 q^{32} -3.62916 q^{34} +(-2.41544 + 1.75492i) q^{35} +(0.848403 + 2.61112i) q^{36} +(-2.71339 + 8.35095i) q^{37} +(-1.14973 - 0.835331i) q^{38} +(1.71092 + 1.24306i) q^{39} +(2.52396 - 7.76794i) q^{40} +(1.66669 + 5.12954i) q^{41} +(-0.640052 + 0.465025i) q^{42} +9.44629 q^{43} -6.20165 q^{45} +(-5.59517 + 4.06513i) q^{46} +(-1.66766 - 5.13254i) q^{47} +(-0.115937 + 0.356818i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(2.60785 + 1.89471i) q^{50} +(-1.30816 + 4.02609i) q^{51} +(-0.899168 - 2.76736i) q^{52} +(-7.60293 + 5.52385i) q^{53} -4.01678 q^{54} +2.73565 q^{56} +(-1.34112 + 0.974384i) q^{57} +(-0.838032 - 2.57920i) q^{58} +(1.07372 - 3.30456i) q^{59} +(-3.06699 - 2.22830i) q^{60} +(-10.5126 - 7.63782i) q^{61} +(-1.90252 + 5.85536i) q^{62} +(-0.641876 - 1.97549i) q^{63} +(-3.22775 + 2.34510i) q^{64} +6.57274 q^{65} +4.32138 q^{67} +(4.71218 - 3.42360i) q^{68} +(2.49293 + 7.67244i) q^{69} +(-0.759826 + 2.33850i) q^{70} +(-3.56004 - 2.58652i) q^{71} +(4.59713 + 3.34001i) q^{72} +(4.55829 - 14.0290i) q^{73} +(2.23463 + 6.87747i) q^{74} +(3.04196 - 2.21012i) q^{75} +2.28086 q^{76} +1.74167 q^{78} +(5.81495 - 4.22481i) q^{79} +(0.360327 + 1.10897i) q^{80} +(0.477749 - 1.47036i) q^{81} +(3.59354 + 2.61086i) q^{82} +(-6.17640 - 4.48742i) q^{83} +(0.392372 - 1.20760i) q^{84} +(4.06569 + 12.5129i) q^{85} +(6.29379 - 4.57270i) q^{86} -3.16337 q^{87} +10.8428 q^{89} +(-4.13198 + 3.00206i) q^{90} +(0.680283 + 2.09370i) q^{91} +(3.43001 - 10.5565i) q^{92} +(5.81000 + 4.22121i) q^{93} +(-3.59564 - 2.61239i) q^{94} +(-1.59209 + 4.89995i) q^{95} +(1.71967 + 5.29261i) q^{96} +(-2.30973 + 1.67812i) q^{97} -0.823556 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Introduction

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