LMFDB - Embedded newform 847.2.f.z.323.2

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			323.2
Character	$\chi$	$=$	847.323
Dual form			847.2.f.z.729.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.666271 - 0.484074i) q^{2} +(-0.296857 + 0.913631i) q^{3} +(-0.408445 - 1.25706i) q^{4} +(-2.41544 + 1.75492i) q^{5} +(0.640052 - 0.465025i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.845363 + 2.60176i) q^{8} +(1.68045 + 1.22092i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

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

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	$-0.394045\pi$
$2$	−0.666271	−	0.484074i	−0.471125	−	0.342292i	−0.797879	+	0.602817i	$0.794045\pi$
$3$	−0.296857	+	0.913631i	−0.171390	+	0.527485i	−0.999450	−	0.0331543i	$-0.989445\pi$
$3$	−0.296857	+	0.913631i	−0.171390	+	0.527485i	0.828060	+	0.560640i	$0.189445\pi$
$4$	−0.408445	−	1.25706i	−0.204222	−	0.628532i
$5$	−2.41544	+	1.75492i	−1.08022	+	0.784824i	−0.977721	−	0.209909i	$-0.932683\pi$
$5$	−2.41544	+	1.75492i	−1.08022	+	0.784824i	−0.102497	+	0.994733i	$0.532683\pi$
$6$	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	$-0.201248\pi$
$13$	1.78101	+	1.29398i	0.493962	+	0.358884i	−0.312744	+	0.949837i	$0.601248\pi$
$14$	−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	$-0.520541\pi$
$17$	3.56509	−	2.59019i	0.864661	−	0.628213i	0.929149	+	0.369705i	$0.120541\pi$
$18$	−0.528621	−	1.62693i	−0.124597	−	0.383470i
$19$	0.533248	−	1.64117i	0.122335	−	0.376510i	−0.871071	−	0.491158i	$-0.836574\pi$
$19$	0.533248	−	1.64117i	0.122335	−	0.376510i	0.993406	+	0.114648i	$0.0365739\pi$
$20$	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	$-0.198905\pi$
$29$	−1.01758	−	3.13178i	−0.188959	−	0.581557i	−0.999994	+	0.00344098i	$0.998905\pi$
$30$	−0.729926	+	2.24648i	−0.133266	+	0.410150i
$31$	−6.04800	−	4.39413i	−1.08625	−	0.789208i	−0.107490	−	0.994206i	$-0.534281\pi$
$31$	−6.04800	−	4.39413i	−1.08625	−	0.789208i	−0.978762	+	0.204998i	$0.934281\pi$
$32$	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	−0.881297	−	0.472563i	$-0.843329\pi$
$37$	−2.71339	−	8.35095i	−0.446078	−	1.37289i	0.435219	−	0.900325i	$-0.356671\pi$
$38$	−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	0.732448	+	0.680823i	$0.238378\pi$
$41$	−1.66669	+	5.12954i	−0.260293	+	0.801099i	−0.992741	+	0.120276i	$0.961622\pi$
$42$	−0.640052	−	0.465025i	−0.0987622	−	0.0717550i
$43$	−9.44629			−1.44055			−0.720273	−	0.693691i	$-0.755983\pi$
$43$	−9.44629			−1.44055			−0.720273	+	0.693691i	$0.755983\pi$
$44$		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	0.752665	+	0.658403i	$0.228768\pi$
$47$	−1.66766	+	5.13254i	−0.243254	+	0.748657i	−0.995919	+	0.0902541i	$0.971232\pi$
$48$	−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	−0.0732141	−	0.997316i	$-0.523326\pi$
$53$	−7.60293	−	5.52385i	−1.04434	−	0.758759i	−0.971129	+	0.238557i	$0.923326\pi$
$54$	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	0.996304	−	0.0859007i	$-0.0273768\pi$
$59$	1.07372	+	3.30456i	0.139786	+	0.430217i	−0.856518	+	0.516117i	$0.827377\pi$
$60$	−3.06699	+	2.22830i	−0.395947	+	0.287672i
$61$	10.5126	−	7.63782i	1.34599	−	0.977922i	0.346794	−	0.937941i	$-0.387270\pi$
$61$	10.5126	−	7.63782i	1.34599	−	0.977922i	0.999200	−	0.0399808i	$-0.0127297\pi$
$62$	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	−0.778643	−	0.627467i	$-0.784092\pi$
$71$	−3.56004	+	2.58652i	−0.422500	+	0.306964i	0.356143	+	0.934431i	$0.384092\pi$
$72$	−4.59713	+	3.34001i	−0.541777	+	0.393624i
$73$	−4.55829	−	14.0290i	−0.533507	−	1.64197i	−0.746852	−	0.664990i	$-0.768436\pi$
$73$	−4.55829	−	14.0290i	−0.533507	−	1.64197i	0.213345	−	0.976977i	$-0.431564\pi$
$74$	−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	$-0.432498\pi$
$79$	−5.81495	−	4.22481i	−0.654233	−	0.475328i	−0.864711	+	0.502271i	$0.832498\pi$
$80$	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	$-0.562383\pi$
$83$	6.17640	−	4.48742i	0.677948	−	0.492558i	0.872676	+	0.488299i	$0.162383\pi$
$84$	−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	0.464320	−	0.885668i	$-0.346299\pi$
$97$	−2.30973	−	1.67812i	−0.234517	−	0.170387i	−0.698837	+	0.715281i	$0.746299\pi$
$98$	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	$-0.558824\pi$
$101$	−11.8126	−	8.58234i	−1.17539	−	0.853974i	−0.991645	+	0.128999i	$0.958824\pi$
$102$	1.07734	−	3.31571i	0.106673	−	0.328305i
$103$	−0.0333020	−	0.102493i	−0.00328134	−	0.0100989i	0.949402	−	0.314062i	$-0.101690\pi$
$103$	−0.0333020	−	0.102493i	−0.00328134	−	0.0100989i	−0.952684	+	0.303963i	$0.901690\pi$
$104$	−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	$-0.827854\pi$
$107$	1.43663	−	4.42148i	0.138884	−	0.427441i	0.996174	+	0.0873930i	$0.0278536\pi$
$108$	5.21547	+	3.78926i	0.501859	+	0.364622i
$109$	−3.23140			−0.309512			−0.154756	−	0.987953i	$-0.549459\pi$
$109$	−3.23140			−0.309512			−0.154756	+	0.987953i	$0.549459\pi$
$110$		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	0.640523	+	0.767939i	$0.278717\pi$
$113$	−3.49789	+	10.7654i	−0.329054	+	1.01272i	−0.969577	+	0.244785i	$0.921283\pi$
$114$	−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	−0.445162	+	0.895450i	$0.646854\pi$
$127$	−16.1643	+	11.7440i	−1.43435	+	1.04212i	−0.989186	+	0.146665i	$0.953146\pi$
$128$	−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	$-0.620426\pi$
$131$	−8.45523			−0.738737			−0.369368	+	0.929283i	$0.620426\pi$
$132$		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	−0.837807	−	0.545966i	$-0.816163\pi$
$137$	−6.75898	+	4.91069i	−0.577459	+	0.419548i	0.260348	+	0.965515i	$0.416163\pi$
$138$	−5.37499	+	3.90516i	−0.457550	+	0.332429i
$139$	4.54668	+	13.9932i	0.385645	+	1.18689i	0.936012	+	0.351969i	$0.114488\pi$
$139$	4.54668	+	13.9932i	0.385645	+	1.18689i	−0.550367	+	0.834923i	$0.685512\pi$
$140$	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	$-0.582022\pi$
$149$	7.15391	−	5.19762i	0.586071	−	0.425805i	0.840908	+	0.541179i	$0.182022\pi$
$150$	−0.956911	−	2.94507i	−0.0781315	−	0.240464i
$151$	6.17104	−	18.9925i	0.502192	−	1.54559i	−0.303249	−	0.952911i	$-0.598071\pi$
$151$	6.17104	−	18.9925i	0.502192	−	1.54559i	0.805441	−	0.592676i	$-0.201929\pi$
$152$	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	−0.650944	−	0.759125i	$-0.725627\pi$
$157$	4.03319	−	12.4129i	0.321883	−	0.990655i	0.972828	−	0.231530i	$-0.0743731\pi$
$158$	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	0.382549	−	0.923935i	$-0.375046\pi$
$163$	−4.82536	−	3.50583i	−0.377951	−	0.274598i	−0.760500	+	0.649337i	$0.775046\pi$
$164$	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	$-0.128702\pi$
$167$	10.7172	+	7.78648i	0.829320	+	0.602536i	−0.0900471	+	0.995938i	$0.528702\pi$
$168$	−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	$-0.893735\pi$
$173$	0.159983	−	0.492377i	0.0121633	−	0.0374348i	0.956954	+	0.290240i	$0.0937351\pi$
$174$	−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	−0.929556	−	0.368681i	$-0.879809\pi$
$179$	0.524139	−	1.61314i	0.0391760	−	0.120571i	0.968732	+	0.248110i	$0.0798094\pi$
$180$	2.53303	+	7.79587i	0.188801	+	0.581070i
$181$	7.99793	−	5.81084i	0.594482	−	0.431916i	−0.249434	−	0.968392i	$-0.580245\pi$
$181$	7.99793	−	5.81084i	0.594482	−	0.431916i	0.843916	+	0.536475i	$0.180245\pi$
$182$	−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	0.779162	+	0.626823i	$0.215645\pi$
$191$	7.14845	+	22.0007i	0.517244	+	1.59191i	−0.261917	+	0.965090i	$0.584355\pi$
$192$	3.10073	−	2.25281i	0.223776	−	0.162583i
$193$	−18.6792	+	13.5712i	−1.34456	+	0.976880i	−0.345296	+	0.938494i	$0.612222\pi$
$193$	−18.6792	+	13.5712i	−1.34456	+	0.976880i	−0.999263	+	0.0383859i	$0.987778\pi$
$194$	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	$-0.576596\pi$
$197$	−6.68989			−0.476635			−0.238318	+	0.971187i	$0.576596\pi$
$198$		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	$-0.172209\pi$
$211$	9.18436	+	6.67283i	0.632277	+	0.459376i	−0.224911	+	0.974379i	$0.572209\pi$
$212$	−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	0.777446	+	0.628950i	$0.216515\pi$
$223$	−3.30335	+	10.1667i	−0.221208	+	0.680810i	−0.998654	+	0.0518599i	$0.983485\pi$
$224$	−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	$-0.0604135\pi$
$227$	1.15505	+	3.55489i	0.0766636	+	0.235946i	−0.905379	+	0.424604i	$0.860414\pi$
$228$	0.677088	−	2.08386i	0.0448412	−	0.138007i
$229$	19.1401	+	13.9061i	1.26482	+	0.918942i	0.998983	−	0.0450774i	$-0.0143534\pi$
$229$	19.1401	+	13.9061i	1.26482	+	0.918942i	0.265832	+	0.964019i	$0.414353\pi$
$230$	−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	$-0.259574\pi$
$233$	3.12827	+	2.27282i	0.204940	+	0.148897i	−0.480582	+	0.876950i	$0.659574\pi$
$234$	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	−0.798525	−	0.601961i	$-0.794386\pi$
$239$	3.11232	−	9.57873i	0.201319	−	0.619597i	0.999844	−	0.0176354i	$-0.00561383\pi$
$240$	0.906226	+	0.658412i	0.0584966	+	0.0425003i
$241$	−13.4265			−0.864878			−0.432439	−	0.901663i	$-0.642347\pi$
$241$	−13.4265			−0.864878			−0.432439	+	0.901663i	$0.642347\pi$
$242$		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	0.585832	−	0.810433i	$-0.300768\pi$
$251$	−0.0618470	−	0.0449345i	−0.00390375	−	0.00283624i	−0.589735	+	0.807597i	$0.700768\pi$
$252$	−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	0.999916	−	0.0129561i	$-0.00412416\pi$
$257$	2.93935	+	9.04639i	0.183352	+	0.564298i	−0.816564	+	0.577254i	$0.804124\pi$
$258$	−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	$-0.650737\pi$
$263$	−14.7919			−0.912107			−0.456053	+	0.889952i	$0.650737\pi$
$264$		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	0.505816	−	0.862641i	$-0.331191\pi$
$269$	24.3155	−	17.6662i	1.48254	−	1.07713i	0.976726	−	0.214489i	$-0.0688086\pi$
$270$	−9.70229	+	7.04913i	−0.590463	+	0.428996i
$271$	3.21126	+	9.88324i	0.195070	+	0.600364i	0.999976	+	0.00696114i	$0.00221582\pi$
$271$	3.21126	+	9.88324i	0.195070	+	0.600364i	−0.804906	+	0.593403i	$0.797784\pi$
$272$	−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	0.997995	+	0.0632918i	$0.0201599\pi$
$277$	22.7445	+	16.5249i	1.36659	+	0.992883i	0.368592	+	0.929591i	$0.379840\pi$
$278$	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	$-0.607856\pi$
$281$	7.74237	−	5.62516i	0.461871	−	0.335569i	0.794265	+	0.607572i	$0.207856\pi$
$282$	1.31937	+	4.06060i	0.0785672	+	0.241805i
$283$	0.511502	−	1.57424i	0.0304056	−	0.0935789i	−0.934702	−	0.355432i	$-0.884334\pi$
$283$	0.511502	−	1.57424i	0.0304056	−	0.0935789i	0.965108	+	0.261853i	$0.0843337\pi$
$284$	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	$-0.143669\pi$
$293$	−1.44678	−	4.45274i	−0.0845219	−	0.260132i	−0.984382	+	0.176048i	$0.943669\pi$
$294$	−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	$-0.338953\pi$
$307$	16.9829			0.969266			0.484633	+	0.874718i	$0.338953\pi$
$308$		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	0.552863	+	0.833272i	$0.313535\pi$
$311$	−6.77540	+	20.8525i	−0.384198	+	1.18244i	−0.937061	+	0.349167i	$0.886465\pi$
$312$	−1.78779	−	5.50224i	−0.101213	−	0.311503i
$313$	−8.13504	+	5.91045i	−0.459820	+	0.334079i	−0.793461	−	0.608622i	$-0.791723\pi$
$313$	−8.13504	+	5.91045i	−0.459820	+	0.334079i	0.333641	+	0.942700i	$0.391723\pi$
$314$	−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	−0.0945377	−	0.995521i	$-0.530137\pi$
$317$	−19.0606	−	13.8483i	−1.07055	−	0.777799i	−0.976011	+	0.217722i	$0.930137\pi$
$318$	−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	−0.998312	−	0.0580761i	$-0.981503\pi$
$337$	−4.12672	−	12.7007i	−0.224797	−	0.691854i	0.773515	−	0.633778i	$-0.218497\pi$
$338$	−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	$-0.713611\pi$
$347$	−1.28841	+	0.936085i	−0.0691655	+	0.0502517i	0.552665	+	0.833403i	$0.313611\pi$
$348$	−1.29206	−	3.97656i	−0.0692618	−	0.213166i
$349$	−2.05025	+	6.31002i	−0.109747	+	0.337768i	−0.990815	−	0.135222i	$-0.956825\pi$
$349$	−2.05025	+	6.31002i	−0.109747	+	0.337768i	0.881068	+	0.472990i	$0.156825\pi$
$350$	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	−0.992316	−	0.123727i	$-0.960515\pi$
$359$	−4.96875	−	15.2922i	−0.262241	−	0.807094i	0.730076	−	0.683366i	$-0.239485\pi$
$360$	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	0.923680	−	0.383166i	$-0.125166\pi$
$367$	−0.935105	−	2.87796i	−0.0488121	−	0.150228i	−0.972492	+	0.232938i	$0.925166\pi$
$368$	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	$-0.514332\pi$
$373$	−1.73856			−0.0900192			−0.0450096	+	0.998987i	$0.514332\pi$
$374$		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	−0.914807	−	0.403892i	$-0.867657\pi$
$379$	−15.8347	+	11.5046i	−0.813373	+	0.590950i	0.101433	+	0.994842i	$0.467657\pi$
$380$	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	0.484930	−	0.874553i	$-0.338845\pi$
$383$	−3.85474	−	2.80063i	−0.196968	−	0.143106i	−0.681898	+	0.731447i	$0.738845\pi$
$384$	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	0.939298	−	0.343103i	$-0.111478\pi$
$389$	−0.439447	−	1.35248i	−0.0222809	−	0.0685735i	−0.961579	+	0.274529i	$0.911478\pi$
$390$	−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	−0.553900	−	0.832583i	$-0.686861\pi$
$401$	1.33705	−	0.971420i	0.0667689	−	0.0485104i	0.620669	+	0.784073i	$0.286861\pi$
$402$	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	−0.981313	−	0.192416i	$-0.938368\pi$
$409$	−29.6795	−	21.5634i	−1.46755	−	1.06624i	−0.486241	−	0.873825i	$-0.661632\pi$
$410$	−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	−0.902897	−	0.429856i	$-0.858564\pi$
$421$	1.64608	−	5.06612i	0.0802251	−	0.246907i	0.983122	+	0.182949i	$0.0585643\pi$
$422$	−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	$-0.537746\pi$
$431$	−22.8208	−	16.5803i	−1.09924	−	0.798644i	−0.980936	+	0.194333i	$0.937746\pi$
$432$	0.588631	−	1.81162i	0.0283205	−	0.0871615i
$433$	5.47145	+	16.8394i	0.262941	+	0.809249i	0.992161	+	0.124969i	$0.0398832\pi$
$433$	5.47145	+	16.8394i	0.262941	+	0.809249i	−0.729220	+	0.684280i	$0.760117\pi$
$434$	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	$-0.295394\pi$
$439$	25.1189			1.19886			0.599430	+	0.800427i	$0.295394\pi$
$440$		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	0.532583	+	0.846378i	$0.321222\pi$
$443$	−8.33008	+	25.6374i	−0.395774	+	1.21807i	−0.928357	+	0.371690i	$0.878778\pi$
$444$	−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	0.912510	−	0.409055i	$-0.134142\pi$
$449$	17.0673	+	12.4001i	0.805456	+	0.585198i	−0.107053	+	0.994253i	$0.534142\pi$
$450$	−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	$-0.714177\pi$
$457$	−1.54001	+	1.11888i	−0.0720387	+	0.0523392i	0.551183	+	0.834384i	$0.314177\pi$
$458$	−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	$-0.698202\pi$
$461$	−25.0440			−1.16641			−0.583207	+	0.812324i	$0.698202\pi$
$462$		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	−0.854060	−	0.520174i	$-0.825867\pi$
$467$	−13.4689	+	9.78570i	−0.623265	+	0.452828i	0.230796	+	0.973002i	$0.425867\pi$
$468$	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	$-0.535217\pi$
$479$	17.5244	−	12.7322i	0.800708	−	0.581749i	0.911122	+	0.412137i	$0.135217\pi$
$480$	−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	−0.968820	−	0.247766i	$-0.920304\pi$
$487$	−0.869374	+	2.67566i	−0.0393951	+	0.121246i	0.929425	+	0.369011i	$0.120304\pi$
$488$	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	$-0.123046\pi$
$491$	−0.990648	−	3.04890i	−0.0447073	−	0.137595i	−0.970919	+	0.239410i	$0.923046\pi$
$492$	−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	−0.988580	−	0.150695i	$-0.951849\pi$
$499$	−6.19617	−	19.0698i	−0.277379	−	0.853684i	0.711202	−	0.702988i	$-0.248151\pi$
$500$	−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	0.336467	+	0.941695i	$0.390768\pi$
$503$	−10.9728	+	33.7709i	−0.489255	+	1.50577i	−0.825722	+	0.564077i	$0.809232\pi$
$504$	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	−0.868187	−	0.496237i	$-0.834715\pi$
$509$	2.83980	−	8.74002i	0.125872	−	0.387394i	0.994059	+	0.108843i	$0.0347146\pi$
$510$	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	0.999236	−	0.0390700i	$-0.0124395\pi$
$521$	3.83176	+	11.7929i	0.167872	+	0.516658i	−0.831364	+	0.555728i	$0.812440\pi$
$522$	−4.55727	+	3.31105i	−0.199466	+	0.144921i
$523$	18.3732	−	13.3489i	0.803404	−	0.583707i	−0.108507	−	0.994096i	$-0.534607\pi$
$523$	18.3732	−	13.3489i	0.803404	−	0.583707i	0.911911	+	0.410388i	$0.134607\pi$
$524$	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	$-0.178895\pi$
$541$	13.9756	+	10.1539i	0.600859	+	0.436550i	−0.245325	+	0.969441i	$0.578895\pi$
$542$	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	$-0.809122\pi$
$547$	4.07098	−	12.5292i	0.174062	−	0.535709i	0.999589	+	0.0286536i	$0.00912198\pi$
$548$	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	$-0.0138367\pi$
$557$	3.90028	+	12.0038i	0.165260	+	0.508618i	−0.833795	+	0.552074i	$0.813837\pi$
$558$	−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	$-0.233657\pi$
$563$	7.94393	+	5.77160i	0.334797	+	0.243244i	−0.407666	+	0.913131i	$0.633657\pi$
$564$	−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	0.728309	+	0.685249i	$0.240307\pi$
$569$	−6.28986	+	19.3582i	−0.263684	+	0.811537i	−0.991994	+	0.126289i	$0.959693\pi$
$570$	3.29762	+	2.39586i	0.138122	+	0.100352i
$571$	32.3174			1.35244			0.676221	−	0.736699i	$-0.263616\pi$
$571$	32.3174			1.35244			0.676221	+	0.736699i	$0.263616\pi$
$572$		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	−0.380645	−	0.924721i	$-0.624298\pi$
$577$	9.15654	−	6.65262i	0.381192	−	0.276952i	0.761837	+	0.647769i	$0.224298\pi$
$578$	−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	−0.828008	−	0.560717i	$-0.810526\pi$
$587$	−11.8164	−	36.3672i	−0.487716	−	1.50104i	0.340291	−	0.940320i	$-0.389474\pi$
$588$	−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	$-0.317441\pi$
$593$	26.4263			1.08520			0.542598	+	0.839992i	$0.317441\pi$
$594$		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	−0.199354	−	0.979928i	$-0.563884\pi$
$599$	16.4226	−	11.9317i	0.671009	−	0.487517i	0.870363	+	0.492411i	$0.163884\pi$
$600$	−8.32175	+	6.04611i	−0.339734	+	0.246831i
$601$	1.57416	+	4.84478i	0.0642115	+	0.197623i	0.978015	−	0.208533i	$-0.0668690\pi$
$601$	1.57416	+	4.84478i	0.0642115	+	0.197623i	−0.913804	+	0.406156i	$0.866869\pi$
$602$	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	$-0.0863883\pi$
$607$	24.7888	+	18.0101i	1.00615	+	0.731008i	0.0427494	+	0.999086i	$0.486388\pi$
$608$	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	−0.667738	−	0.744396i	$-0.732737\pi$
$613$	7.67569	−	23.6234i	0.310018	−	0.954138i	0.977757	−	0.209742i	$-0.0672625\pi$
$614$	−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	−0.540913	−	0.841079i	$-0.681921\pi$
$619$	9.72967	−	29.9449i	0.391069	−	1.20359i	0.931981	−	0.362507i	$-0.118079\pi$
$620$	−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	0.950351	−	0.311179i	$-0.100724\pi$
$631$	−0.0352990	−	0.108639i	−0.00140523	−	0.00432486i	−0.951757	+	0.306854i	$0.900724\pi$
$632$	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	−0.837459	−	0.546500i	$-0.815960\pi$
$641$	4.08339	−	12.5674i	0.161284	−	0.496382i	0.998743	+	0.0501182i	$0.0159598\pi$
$642$	−1.13658	−	3.49805i	−0.0448574	−	0.138057i
$643$	−1.98694	+	1.44360i	−0.0783573	+	0.0569299i	−0.626274	−	0.779603i	$-0.715421\pi$
$643$	−1.98694	+	1.44360i	−0.0783573	+	0.0569299i	0.547917	+	0.836533i	$0.315421\pi$
$644$	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	0.843015	−	0.537891i	$-0.180779\pi$
$647$	15.0571	+	10.9396i	0.591956	+	0.430081i	−0.251059	+	0.967972i	$0.580779\pi$
$648$	−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	0.997097	+	0.0761389i	$0.0242592\pi$
$653$	6.00981	+	18.4963i	0.235182	+	0.723816i	−0.761915	+	0.647677i	$0.775741\pi$
$654$	−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	$-0.529281\pi$
$659$	−4.71629			−0.183721			−0.0918603	+	0.995772i	$0.529281\pi$
$660$		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	$-0.331522\pi$
$673$	−4.15003	−	3.01517i	−0.159972	−	0.116226i	−0.664891	+	0.746940i	$0.731522\pi$
$674$	−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	−0.695706	+	0.718327i	$0.744908\pi$
$677$	−41.4710	+	30.1304i	−1.59386	+	1.15801i	−0.898154	+	0.439680i	$0.855092\pi$
$678$	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	0.391482	−	0.920186i	$-0.371962\pi$
$691$	−9.53403	−	6.92688i	−0.362692	−	0.263511i	−0.754174	+	0.656675i	$0.771962\pi$
$692$	−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	−0.584141	−	0.811652i	$-0.698569\pi$
$701$	9.67755	−	29.7844i	0.365516	−	1.12494i	0.949657	−	0.313291i	$-0.101431\pi$
$702$	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	0.261384	−	0.965235i	$-0.415821\pi$
$709$	33.5540	−	24.3784i	1.26015	−	0.915552i	0.998765	+	0.0496834i	$0.0158212\pi$
$710$	−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	0.895241	−	0.445582i	$-0.147003\pi$
$719$	−2.43823	−	7.50410i	−0.0909306	−	0.279856i	−0.986172	+	0.165726i	$0.947003\pi$
$720$	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	0.936128	+	0.351660i	$0.114383\pi$
$733$	10.4366	+	32.1206i	0.385485	+	1.18640i	−0.550643	+	0.834741i	$0.685617\pi$
$734$	−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	$-0.587936\pi$
$739$	−34.5799	−	25.1237i	−1.27204	−	0.924192i	−0.999282	+	0.0378907i	$0.987936\pi$
$740$	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	$-0.561646\pi$
$743$	18.5722	−	13.4935i	0.681348	−	0.495028i	0.873804	+	0.486277i	$0.161646\pi$
$744$	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	−0.956167	−	0.292822i	$-0.905406\pi$
$751$	−0.287608	+	0.885166i	−0.0104950	+	0.0323002i	0.945672	+	0.325123i	$0.105406\pi$
$752$	−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	0.743661	−	0.668556i	$-0.233087\pi$
$757$	9.28944	+	6.74917i	0.337630	+	0.245303i	−0.406031	+	0.913859i	$0.633087\pi$
$758$	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	$-0.0512119\pi$
$761$	31.4416	+	22.8437i	1.13976	+	0.828083i	0.152673	+	0.988277i	$0.451212\pi$
$762$	−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	$-0.277772\pi$
$769$	35.6509			1.28560			0.642802	+	0.766032i	$0.277772\pi$
$770$		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	−0.960413	−	0.278579i	$-0.910137\pi$
$773$	−0.547100	+	1.68380i	−0.0196778	+	0.0605621i	0.940735	+	0.339141i	$0.110137\pi$
$774$	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	$-0.680965\pi$
$787$	2.71276	−	1.97093i	0.0966993	−	0.0702562i	0.635084	+	0.772443i	$0.280965\pi$
$788$	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	−0.656118	−	0.754658i	$-0.727803\pi$
$797$	−3.98475	+	2.89509i	−0.141147	+	0.102549i	0.514971	+	0.857208i	$0.327803\pi$
$798$	−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	$-0.739118\pi$
$809$	−5.64145	+	4.09875i	−0.198343	+	0.144105i	0.484181	+	0.874968i	$0.339118\pi$
$810$	1.17471	+	3.61539i	0.0412752	+	0.127032i
$811$	−1.83364	+	5.64335i	−0.0643877	+	0.198165i	−0.978075	−	0.208253i	$-0.933222\pi$
$811$	−1.83364	+	5.64335i	−0.0643877	+	0.198165i	0.913687	+	0.406418i	$0.133222\pi$
$812$	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	−0.876645	−	0.481137i	$-0.840224\pi$
$821$	−12.9005	−	39.7036i	−0.450230	−	1.38566i	0.426416	−	0.904527i	$-0.359776\pi$
$822$	−2.04251	+	6.28620i	−0.0712407	+	0.219256i
$823$	18.7695	+	13.6368i	0.654263	+	0.475350i	0.864721	−	0.502253i	$-0.167495\pi$
$823$	18.7695	+	13.6368i	0.654263	+	0.475350i	−0.210458	+	0.977603i	$0.567495\pi$
$824$	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	$-0.373585\pi$
$827$	−10.6611	−	7.74577i	−0.370724	−	0.269347i	−0.757511	+	0.652822i	$0.773585\pi$
$828$	−7.12466	+	21.9275i	−0.247599	+	0.762032i
$829$	1.32596	+	4.08089i	0.0460526	+	0.141735i	0.971439	−	0.237290i	$-0.0762592\pi$
$829$	1.32596	+	4.08089i	0.0460526	+	0.141735i	−0.925386	+	0.379026i	$0.876259\pi$
$830$	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	−0.999243	−	0.0388925i	$-0.987617\pi$
$839$	−4.86557	+	14.9747i	−0.167978	+	0.516983i	0.831265	+	0.555876i	$0.187617\pi$
$840$	−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	$-0.666478\pi$
$853$	4.96749	−	3.60909i	0.170084	−	0.123573i	0.669571	+	0.742748i	$0.266478\pi$
$854$	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	$-0.700401\pi$
$857$	−34.4740			−1.17761			−0.588804	+	0.808276i	$0.700401\pi$
$858$		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	−0.752670	−	0.658398i	$-0.771234\pi$
$863$	−10.5488	+	7.66413i	−0.359084	+	0.260890i	0.393586	+	0.919288i	$0.371234\pi$
$864$	−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	$-0.997874\pi$
$877$	−5.53942	+	17.0486i	−0.187053	+	0.575690i	0.812925	+	0.582369i	$0.197874\pi$
$878$	−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	−0.770558	−	0.637370i	$-0.780022\pi$
$883$	6.75945	−	20.8034i	0.227474	−	0.700092i	0.998031	−	0.0627212i	$-0.0199779\pi$
$884$	−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	−0.991526	−	0.129906i	$-0.958532\pi$
$887$	−7.91386	−	24.3564i	−0.265721	−	0.817806i	0.725805	−	0.687901i	$-0.241468\pi$
$888$	−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	−0.376713	−	0.926330i	$-0.622946\pi$
$907$	11.6812	−	8.48689i	0.387868	−	0.281802i	0.764581	+	0.644527i	$0.222946\pi$
$908$	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	−0.0353410	−	0.999375i	$-0.511252\pi$
$911$	−30.0839	−	21.8572i	−0.996724	−	0.724163i	−0.961383	+	0.275213i	$0.911252\pi$
$912$	−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	$-0.785277\pi$
$919$	−12.9844	+	9.43369i	−0.428315	+	0.311189i	0.352660	+	0.935752i	$0.385277\pi$
$920$	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	−0.938358	−	0.345666i	$-0.887653\pi$
$929$	−27.4187	+	19.9209i	−0.899578	+	0.653582i	0.0387793	+	0.999248i	$0.487653\pi$
$930$	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	$-0.348154\pi$
$937$	−7.46419	−	5.42305i	−0.243844	−	0.177163i	−0.702994	+	0.711195i	$0.748154\pi$
$938$	−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	−0.413640	+	0.910440i	$0.635743\pi$
$941$	−43.1712	+	31.3657i	−1.40734	+	1.02249i	−0.993702	+	0.112054i	$0.964257\pi$
$942$	−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	−0.959054	−	0.283222i	$-0.908597\pi$
$953$	−10.7935	−	33.2191i	−0.349637	−	1.07607i	0.609418	−	0.792849i	$-0.291403\pi$
$954$	−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	$-0.391437\pi$
$967$	20.8029			0.668975			0.334488	+	0.942400i	$0.391437\pi$
$968$		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	0.530431	+	0.847728i	$0.322030\pi$
$971$	−12.3702	+	38.0716i	−0.396979	+	1.22177i	−0.927410	+	0.374046i	$0.877970\pi$
$972$	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	0.500674	−	0.865636i	$-0.333086\pi$
$977$	−5.24736	−	3.81243i	−0.167878	−	0.121970i	−0.668552	+	0.743665i	$0.733086\pi$
$978$	−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	0.990469	−	0.137738i	$-0.0439832\pi$
$983$	3.39245	+	10.4409i	0.108202	+	0.333012i	−0.882266	+	0.470750i	$0.843983\pi$
$984$	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	0.903693	+	0.428181i	$0.140845\pi$
$997$	13.3964	+	41.2299i	0.424269	+	1.30576i	−0.479424	+	0.877583i	$0.659155\pi$
$998$	−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.z.323.2		24
11.2	odd	10		847.2.f.y.148.2		24
11.3	even	5	inner	847.2.f.z.729.2		24
11.4	even	5	inner	847.2.f.z.372.5		24
11.5	even	5		847.2.a.m.1.5	✓	6
11.6	odd	10		847.2.a.n.1.2	yes	6
11.7	odd	10		847.2.f.y.372.2		24
11.8	odd	10		847.2.f.y.729.5		24
11.9	even	5	inner	847.2.f.z.148.5		24
11.10	odd	2		847.2.f.y.323.5		24
33.5	odd	10		7623.2.a.cs.1.2		6
33.17	even	10		7623.2.a.cp.1.5		6
77.6	even	10		5929.2.a.bm.1.2		6
77.27	odd	10		5929.2.a.bj.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.5	✓	6	11.5	even	5
847.2.a.n.1.2	yes	6	11.6	odd	10
847.2.f.y.148.2		24	11.2	odd	10
847.2.f.y.323.5		24	11.10	odd	2
847.2.f.y.372.2		24	11.7	odd	10
847.2.f.y.729.5		24	11.8	odd	10
847.2.f.z.148.5		24	11.9	even	5	inner
847.2.f.z.323.2		24	1.1	even	1	trivial
847.2.f.z.372.5		24	11.4	even	5	inner
847.2.f.z.729.2		24	11.3	even	5	inner
5929.2.a.bj.1.5		6	77.27	odd	10
5929.2.a.bm.1.2		6	77.6	even	10
7623.2.a.cp.1.5		6	33.17	even	10
7623.2.a.cs.1.2		6	33.5	odd	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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more