LMFDB - Embedded newform 950.2.w.a.37.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.17
Character	$\chi$	$=$	950.37
Dual form			950.2.w.a.873.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(0.531107 - 1.04236i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.52005 + 1.63996i) q^{5} +(-0.361507 + 1.11261i) q^{6} +(3.11636 + 3.11636i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.958925 + 1.31985i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(0.531107 - 1.04236i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.52005 + 1.63996i) q^{5} +(-0.361507 + 1.11261i) q^{6} +(3.11636 + 3.11636i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.958925 + 1.31985i) q^{9} +(1.24479 - 1.85755i) q^{10} +(-1.54315 - 1.12117i) q^{11} +(0.183007 - 1.15546i) q^{12} +(-0.301973 - 0.0478278i) q^{13} +(-3.56549 - 2.59048i) q^{14} +(0.902110 + 2.45542i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-5.87422 + 2.99307i) q^{17} +(-1.15359 - 1.15359i) q^{18} +(-1.18866 + 4.19370i) q^{19} +(-0.938876 + 2.02941i) q^{20} +(4.90347 - 1.59323i) q^{21} +(1.69954 + 0.865961i) q^{22} +(-2.73440 + 0.433087i) q^{23} +1.16986i q^{24} +(-0.378914 - 4.98562i) q^{25} +0.305737 q^{26} +(5.35142 - 0.847582i) q^{27} +(3.92684 + 2.00082i) q^{28} +(0.431759 + 1.32882i) q^{29} +(-1.27512 - 2.28407i) q^{30} +(-8.35051 - 2.71324i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.98823 + 1.01305i) q^{33} +(5.33368 - 3.87515i) q^{34} +(-9.84770 + 0.373680i) q^{35} +(1.31985 + 0.958925i) q^{36} +(0.551694 - 3.48326i) q^{37} +(0.517984 - 4.32801i) q^{38} +(-0.210233 + 0.289361i) q^{39} +(0.609847 - 2.15130i) q^{40} +(-4.19291 - 5.77105i) q^{41} +(-4.59386 + 2.34069i) q^{42} +(0.0527312 - 0.0527312i) q^{43} +(-1.81409 - 0.589432i) q^{44} +(-3.62210 - 0.433635i) q^{45} +(2.63299 - 0.855510i) q^{46} +(-3.16058 + 6.20300i) q^{47} +(-0.183007 - 1.15546i) q^{48} +12.4234i q^{49} +(1.15417 + 4.86497i) q^{50} +7.71266i q^{51} +(-0.301973 + 0.0478278i) q^{52} +(-1.66143 + 3.26075i) q^{53} +(-5.15294 + 1.67429i) q^{54} +(4.18433 - 0.826478i) q^{55} +(-4.19149 - 1.36190i) q^{56} +(3.74002 + 3.46630i) q^{57} +(-0.634317 - 1.24492i) q^{58} +(5.30085 - 3.85129i) q^{59} +(1.61672 + 2.05648i) q^{60} +(0.782439 + 0.568476i) q^{61} +(8.67214 + 1.37353i) q^{62} +(-1.12476 + 7.10147i) q^{63} +(0.587785 - 0.809017i) q^{64} +(0.537448 - 0.422522i) q^{65} +(1.80528 - 1.31161i) q^{66} +(5.51588 + 10.8255i) q^{67} +(-4.66181 + 4.66181i) q^{68} +(-1.00083 + 3.08024i) q^{69} +(9.66800 - 1.90960i) q^{70} +(-8.35859 + 2.71587i) q^{71} +(-1.45361 - 0.740650i) q^{72} +(9.87358 - 1.56382i) q^{73} +3.52668i q^{74} +(-5.39803 - 2.25293i) q^{75} +(0.165444 + 4.35576i) q^{76} +(-1.31506 - 8.30297i) q^{77} +(0.162379 - 0.318686i) q^{78} +(-1.76102 - 5.41987i) q^{79} +(-0.265802 + 2.22021i) q^{80} +(0.446282 - 1.37352i) q^{81} +(5.04408 + 5.04408i) q^{82} +(7.68745 + 15.0875i) q^{83} +(4.17114 - 3.03051i) q^{84} +(4.02060 - 14.1831i) q^{85} +(-0.0438330 + 0.0603309i) q^{86} +(1.61441 + 0.255698i) q^{87} +(1.88396 + 0.298390i) q^{88} +(12.5989 + 9.15367i) q^{89} +(3.64535 - 0.138326i) q^{90} +(-0.792006 - 1.09010i) q^{91} +(-2.46674 + 1.25687i) q^{92} +(-7.26317 + 7.26317i) q^{93} +(2.15131 - 6.62105i) q^{94} +(-5.07067 - 8.32396i) q^{95} +(0.361507 + 1.11261i) q^{96} +(10.3143 + 5.25542i) q^{97} +(-1.94344 - 12.2704i) q^{98} -3.11184i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	0.531107	−	1.04236i	0.306634	−	0.601804i	−0.685343	−	0.728221i	$-0.740348\pi$
$3$	0.531107	−	1.04236i	0.306634	−	0.601804i	0.991977	+	0.126417i	$0.0403476\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−1.52005	+	1.63996i	−0.679786	+	0.733411i
$5$	−1.52005	+	1.63996i	−0.679786	+	0.733411i
$6$	−0.361507	+	1.11261i	−0.147585	+	0.454219i
$7$	3.11636	+	3.11636i	1.17787	+	1.17787i	0.980285	+	0.197586i	$0.0633103\pi$
$7$	3.11636	+	3.11636i	1.17787	+	1.17787i	0.197586	+	0.980285i	$0.436690\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	0.958925	+	1.31985i	0.319642	+	0.439949i
$10$	1.24479	−	1.85755i	0.393636	−	0.587410i
$11$	−1.54315	−	1.12117i	−0.465278	−	0.338044i	0.330320	−	0.943869i	$-0.392843\pi$
$11$	−1.54315	−	1.12117i	−0.465278	−	0.338044i	−0.795598	+	0.605825i	$0.792843\pi$
$12$	0.183007	−	1.15546i	0.0528295	−	0.333552i
$13$	−0.301973	−	0.0478278i	−0.0837522	−	0.0132650i	0.114418	−	0.993433i	$-0.463500\pi$
$13$	−0.301973	−	0.0478278i	−0.0837522	−	0.0132650i	−0.198170	+	0.980168i	$0.563500\pi$
$14$	−3.56549	−	2.59048i	−0.952918	−	0.692336i
$15$	0.902110	+	2.45542i	0.232924	+	0.633987i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−5.87422	+	2.99307i	−1.42471	+	0.725925i	−0.985055	−	0.172243i	$-0.944899\pi$
$17$	−5.87422	+	2.99307i	−1.42471	+	0.725925i	−0.439653	+	0.898168i	$0.644899\pi$
$18$	−1.15359	−	1.15359i	−0.271904	−	0.271904i
$19$	−1.18866	+	4.19370i	−0.272697	+	0.962100i
$19$	−1.18866	+	4.19370i	−0.272697	+	0.962100i
$20$	−0.938876	+	2.02941i	−0.209939	+	0.453790i
$21$	4.90347	−	1.59323i	1.07002	−	0.347672i
$22$	1.69954	+	0.865961i	0.362344	+	0.184623i
$23$	−2.73440	+	0.433087i	−0.570163	+	0.0903049i	−0.434858	−	0.900499i	$-0.643201\pi$
$23$	−2.73440	+	0.433087i	−0.570163	+	0.0903049i	−0.135305	+	0.990804i	$0.543201\pi$
$24$			1.16986i			0.238797i
$25$	−0.378914	−	4.98562i	−0.0757827	−	0.997124i
$26$	0.305737			0.0599599
$27$	5.35142	−	0.847582i	1.02988	−	0.163117i
$28$	3.92684	+	2.00082i	0.742103	+	0.378120i
$29$	0.431759	+	1.32882i	0.0801757	+	0.246755i	0.983108	−	0.183028i	$-0.0585899\pi$
$29$	0.431759	+	1.32882i	0.0801757	+	0.246755i	−0.902932	+	0.429783i	$0.858590\pi$
$30$	−1.27512	−	2.28407i	−0.232803	−	0.417012i
$31$	−8.35051	−	2.71324i	−1.49980	−	0.487313i	−0.559837	−	0.828603i	$-0.689136\pi$
$31$	−8.35051	−	2.71324i	−1.49980	−	0.487313i	−0.939958	+	0.341290i	$0.889136\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.98823	+	1.01305i	−0.346107	+	0.176350i
$34$	5.33368	−	3.87515i	0.914719	−	0.664582i
$35$	−9.84770	+	0.373680i	−1.66456	+	0.0631634i
$36$	1.31985	+	0.958925i	0.219975	+	0.159821i
$37$	0.551694	−	3.48326i	0.0906980	−	0.572644i	−0.899928	−	0.436039i	$-0.856381\pi$
$37$	0.551694	−	3.48326i	0.0906980	−	0.572644i	0.990626	−	0.136605i	$-0.0436191\pi$
$38$	0.517984	−	4.32801i	0.0840280	−	0.702096i
$39$	−0.210233	+	0.289361i	−0.0336643	+	0.0463349i
$40$	0.609847	−	2.15130i	0.0964253	−	0.340150i
$41$	−4.19291	−	5.77105i	−0.654823	−	0.901286i	0.344473	−	0.938796i	$-0.388057\pi$
$41$	−4.19291	−	5.77105i	−0.654823	−	0.901286i	−0.999296	+	0.0375098i	$0.988057\pi$
$42$	−4.59386	+	2.34069i	−0.708848	+	0.361176i
$43$	0.0527312	−	0.0527312i	0.00804143	−	0.00804143i	−0.703075	−	0.711116i	$-0.748190\pi$
$43$	0.0527312	−	0.0527312i	0.00804143	−	0.00804143i	0.711116	+	0.703075i	$0.248190\pi$
$44$	−1.81409	−	0.589432i	−0.273484	−	0.0888602i
$45$	−3.62210	−	0.433635i	−0.539951	−	0.0646424i
$46$	2.63299	−	0.855510i	0.388213	−	0.126138i
$47$	−3.16058	+	6.20300i	−0.461019	+	0.904800i	0.537102	+	0.843517i	$0.319519\pi$
$47$	−3.16058	+	6.20300i	−0.461019	+	0.904800i	−0.998120	+	0.0612826i	$0.980481\pi$
$48$	−0.183007	−	1.15546i	−0.0264148	−	0.166776i
$49$			12.4234i			1.77476i
$50$	1.15417	+	4.86497i	0.163225	+	0.688010i
$51$			7.71266i			1.07999i
$52$	−0.301973	+	0.0478278i	−0.0418761	+	0.00663252i
$53$	−1.66143	+	3.26075i	−0.228215	+	0.447898i	−0.976511	−	0.215468i	$-0.930872\pi$
$53$	−1.66143	+	3.26075i	−0.228215	+	0.447898i	0.748296	+	0.663365i	$0.230872\pi$
$54$	−5.15294	+	1.67429i	−0.701227	+	0.227842i
$55$	4.18433	−	0.826478i	0.564215	−	0.111442i
$56$	−4.19149	−	1.36190i	−0.560111	−	0.181991i
$57$	3.74002	+	3.46630i	0.495378	+	0.459123i
$58$	−0.634317	−	1.24492i	−0.0832899	−	0.163466i
$59$	5.30085	−	3.85129i	0.690112	−	0.501395i	−0.186585	−	0.982439i	$-0.559742\pi$
$59$	5.30085	−	3.85129i	0.690112	−	0.501395i	0.876697	+	0.481043i	$0.159742\pi$
$60$	1.61672	+	2.05648i	0.208718	+	0.265490i
$61$	0.782439	+	0.568476i	0.100181	+	0.0727858i	0.636748	−	0.771072i	$-0.280279\pi$
$61$	0.782439	+	0.568476i	0.100181	+	0.0727858i	−0.536567	+	0.843858i	$0.680279\pi$
$62$	8.67214	+	1.37353i	1.10136	+	0.174439i
$63$	−1.12476	+	7.10147i	−0.141707	+	0.894701i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	0.537448	−	0.422522i	0.0666623	−	0.0524074i
$66$	1.80528	−	1.31161i	0.222214	−	0.161448i
$67$	5.51588	+	10.8255i	0.673872	+	1.32255i	0.934104	+	0.357002i	$0.116201\pi$
$67$	5.51588	+	10.8255i	0.673872	+	1.32255i	−0.260232	+	0.965546i	$0.583799\pi$
$68$	−4.66181	+	4.66181i	−0.565327	+	0.565327i
$69$	−1.00083	+	3.08024i	−0.120486	+	0.370817i
$70$	9.66800	−	1.90960i	1.15555	−	0.228241i
$71$	−8.35859	+	2.71587i	−0.991982	+	0.322314i	−0.759657	−	0.650324i	$-0.774633\pi$
$71$	−8.35859	+	2.71587i	−0.991982	+	0.322314i	−0.232325	+	0.972638i	$0.574633\pi$
$72$	−1.45361	−	0.740650i	−0.171309	−	0.0872864i
$73$	9.87358	−	1.56382i	1.15562	−	0.183031i	0.450935	−	0.892557i	$-0.351091\pi$
$73$	9.87358	−	1.56382i	1.15562	−	0.183031i	0.704680	+	0.709525i	$0.251091\pi$
$74$			3.52668i			0.409968i
$75$	−5.39803	−	2.25293i	−0.623311	−	0.260146i
$76$	0.165444	+	4.35576i	0.0189777	+	0.499640i
$77$	−1.31506	−	8.30297i	−0.149865	−	0.946211i
$78$	0.162379	−	0.318686i	0.0183858	−	0.0360841i
$79$	−1.76102	−	5.41987i	−0.198130	−	0.609783i	−0.999926	−	0.0121840i	$-0.996122\pi$
$79$	−1.76102	−	5.41987i	−0.198130	−	0.609783i	0.801795	−	0.597599i	$-0.203878\pi$
$80$	−0.265802	+	2.22021i	−0.0297175	+	0.248227i
$81$	0.446282	−	1.37352i	0.0495869	−	0.152613i
$82$	5.04408	+	5.04408i	0.557026	+	0.557026i
$83$	7.68745	+	15.0875i	0.843807	+	1.65606i	0.750925	+	0.660387i	$0.229608\pi$
$83$	7.68745	+	15.0875i	0.843807	+	1.65606i	0.0928819	+	0.995677i	$0.470392\pi$
$84$	4.17114	−	3.03051i	0.455109	−	0.330656i
$85$	4.02060	−	14.1831i	0.436095	−	1.53837i
$86$	−0.0438330	+	0.0603309i	−0.00472663	+	0.00650565i
$87$	1.61441	+	0.255698i	0.173083	+	0.0274137i
$88$	1.88396	+	0.298390i	0.200831	+	0.0318084i
$89$	12.5989	+	9.15367i	1.33549	+	0.970287i	0.999597	+	0.0283848i	$0.00903638\pi$
$89$	12.5989	+	9.15367i	1.33549	+	0.970287i	0.335888	+	0.941902i	$0.390964\pi$
$90$	3.64535	−	0.138326i	0.384253	−	0.0145808i
$91$	−0.792006	−	1.09010i	−0.0830248	−	0.114274i
$92$	−2.46674	+	1.25687i	−0.257176	+	0.131037i
$93$	−7.26317	+	7.26317i	−0.753156	+	0.753156i
$94$	2.15131	−	6.62105i	0.221891	−	0.682909i
$95$	−5.07067	−	8.32396i	−0.520239	−	0.854020i
$96$	0.361507	+	1.11261i	0.0368962	+	0.113555i
$97$	10.3143	+	5.25542i	1.04726	+	0.533607i	0.890950	−	0.454101i	$-0.150040\pi$
$97$	10.3143	+	5.25542i	1.04726	+	0.533607i	0.156312	+	0.987708i	$0.450040\pi$
$98$	−1.94344	−	12.2704i	−0.196317	−	1.23950i
$99$		−	3.11184i		−	0.312752i
$100$	−1.90101	−	4.62452i	−0.190101	−	0.462452i
$101$	8.37271			0.833116			0.416558	−	0.909109i	$-0.363236\pi$
$101$	8.37271			0.833116			0.416558	+	0.909109i	$0.363236\pi$
$102$	−1.20653	−	7.61771i	−0.119464	−	0.754265i
$103$	−4.22523	+	8.29249i	−0.416325	+	0.817083i	0.583662	+	0.811997i	$0.301619\pi$
$103$	−4.22523	+	8.29249i	−0.416325	+	0.817083i	−0.999987	+	0.00508686i	$0.998381\pi$
$104$	0.290773	−	0.0944779i	0.0285126	−	0.00926432i
$105$	−4.84067	+	10.4633i	−0.472401	+	1.02111i
$106$	1.13088	−	3.48051i	0.109841	−	0.338057i
$107$	−2.40364	+	2.40364i	−0.232369	+	0.232369i	−0.813681	−	0.581312i	$-0.802540\pi$
$107$	−2.40364	+	2.40364i	−0.232369	+	0.232369i	0.581312	+	0.813681i	$0.302540\pi$
$108$	4.82759	−	2.45978i	0.464535	−	0.236692i
$109$	−15.9663	+	11.6002i	−1.52929	+	1.11109i	−0.572658	+	0.819794i	$0.694088\pi$
$109$	−15.9663	+	11.6002i	−1.52929	+	1.11109i	−0.956632	+	0.291300i	$0.905912\pi$
$110$	−4.00352	+	1.47088i	−0.381721	+	0.140243i
$111$	−3.33779	−	2.42504i	−0.316809	−	0.230175i
$112$	4.35293	+	0.689437i	0.411314	+	0.0651457i
$113$	−9.04963	−	1.43332i	−0.851318	−	0.134836i	−0.284497	−	0.958677i	$-0.591827\pi$
$113$	−9.04963	−	1.43332i	−0.851318	−	0.134836i	−0.566821	+	0.823841i	$0.691827\pi$
$114$	−4.23622	−	2.83856i	−0.396759	−	0.265855i
$115$	3.44618	−	5.14262i	0.321358	−	0.479551i
$116$	0.821255	+	1.13036i	0.0762516	+	0.104951i
$117$	−0.226444	−	0.444421i	−0.0209348	−	0.0410868i
$118$	−4.63311	+	4.63311i	−0.426512	+	0.426512i
$119$	−27.6336	−	8.97871i	−2.53317	−	0.823077i
$120$	−1.91852	−	1.77825i	−0.175136	−	0.162331i
$121$	−2.27488	−	7.00136i	−0.206807	−	0.636487i
$122$	−0.861736	−	0.439076i	−0.0780179	−	0.0397521i
$123$	−8.24236	+	1.30546i	−0.743189	+	0.117710i
$124$	−8.78024			−0.788489
$125$	8.75217	+	6.95698i	0.782818	+	0.622251i
$126$		−	7.18999i		−	0.640535i
$127$	13.6206	−	2.15730i	1.20864	−	0.191429i	0.480583	−	0.876949i	$-0.340425\pi$
$127$	13.6206	−	2.15730i	1.20864	−	0.191429i	0.728054	+	0.685520i	$0.240425\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	−0.0269587	−	0.0829705i	−0.00237358	−	0.00730514i
$130$	−0.464734	+	0.501395i	−0.0407599	+	0.0439753i
$131$	5.04055	−	15.5132i	0.440395	−	1.35540i	−0.447061	−	0.894504i	$-0.647529\pi$
$131$	5.04055	−	15.5132i	0.440395	−	1.35540i	0.887456	−	0.460893i	$-0.152471\pi$
$132$	−1.57787	+	1.57787i	−0.137336	+	0.137336i
$133$	−16.7733	+	9.36478i	−1.45443	+	0.812029i
$134$	−7.14145	−	9.82937i	−0.616928	−	0.849128i
$135$	−6.74441	+	10.0645i	−0.580467	+	0.866211i
$136$	3.87515	−	5.33368i	0.332291	−	0.457359i
$137$	13.0079	+	2.06026i	1.11134	+	0.176020i	0.685001	−	0.728542i	$-0.259802\pi$
$137$	13.0079	+	2.06026i	1.11134	+	0.176020i	0.426343	+	0.904562i	$0.359802\pi$
$138$	0.506652	−	3.19888i	0.0431291	−	0.272306i
$139$	5.61587	−	7.72958i	0.476332	−	0.655615i	−0.501463	−	0.865179i	$-0.667205\pi$
$139$	5.61587	−	7.72958i	0.476332	−	0.655615i	0.977795	+	0.209565i	$0.0672046\pi$
$140$	−9.25024	+	3.39850i	−0.781788	+	0.287225i
$141$	4.78712	+	6.58890i	0.403148	+	0.554886i
$142$	7.83083	−	3.99000i	0.657148	−	0.334834i
$143$	0.412367	+	0.412367i	0.0344839	+	0.0344839i
$144$	1.55157	+	0.504137i	0.129298	+	0.0420114i
$145$	−2.83550	−	1.31180i	−0.235475	−	0.108939i
$146$	−9.50739	+	3.08914i	−0.786837	+	0.255659i
$147$	12.9495	+	6.59812i	1.06806	+	0.544204i
$148$	−0.551694	−	3.48326i	−0.0453490	−	0.286322i
$149$		−	10.4727i		−	0.857956i	−0.903315	−	0.428978i	$-0.858874\pi$
$149$		−	10.4727i		−	0.857956i	0.903315	−	0.428978i	$-0.141126\pi$
$150$	5.68401	+	1.38076i	0.464097	+	0.112738i
$151$			1.16344i			0.0946792i	0.998879	+	0.0473396i	$0.0150743\pi$
$151$			1.16344i			0.0946792i	−0.998879	+	0.0473396i	$0.984926\pi$
$152$	−0.844798	−	4.27625i	−0.0685222	−	0.346850i
$153$	−9.58333	−	4.88295i	−0.774766	−	0.394763i
$154$	2.59774	+	7.99502i	0.209332	+	0.644257i
$155$	17.1428	−	9.57021i	1.37694	−	0.768698i
$156$	−0.110526	+	0.340165i	−0.00884917	+	0.0272350i
$157$	15.8948	+	15.8948i	1.26854	+	1.26854i	0.946842	+	0.321698i	$0.104254\pi$
$157$	15.8948	+	15.8948i	1.26854	+	1.26854i	0.321698	+	0.946842i	$0.395746\pi$
$158$	2.58719	+	5.07765i	0.205826	+	0.403957i
$159$	2.51646	+	3.46361i	0.199568	+	0.274682i
$160$	−0.0847887	−	2.23446i	−0.00670313	−	0.176650i
$161$	−9.87103	−	7.17172i	−0.777946	−	0.565211i
$162$	−0.225923	+	1.42642i	−0.0177502	+	0.112070i
$163$	−3.02509	+	19.0996i	−0.236943	+	1.49600i	0.526528	+	0.850157i	$0.323493\pi$
$163$	−3.02509	+	19.0996i	−0.236943	+	1.49600i	−0.763471	+	0.645842i	$0.776507\pi$
$164$	−5.77105	−	4.19291i	−0.450643	−	0.327411i
$165$	1.36084	−	4.80051i	0.105941	−	0.373719i
$166$	−9.95300	−	13.6991i	−0.772503	−	1.06326i
$167$	−7.91693	−	15.5378i	−0.612630	−	1.20235i	−0.963946	−	0.266098i	$-0.914266\pi$
$167$	−7.91693	−	15.5378i	−0.612630	−	1.20235i	0.351316	−	0.936257i	$-0.385734\pi$
$168$	−3.64571	+	3.64571i	−0.281273	+	0.281273i
$169$	−12.2748	−	3.98834i	−0.944218	−	0.306795i
$170$	−1.75238	+	14.6374i	−0.134401	+	1.12264i
$171$	−6.67487	+	2.45260i	−0.510440	+	0.187555i
$172$	0.0338555	−	0.0664451i	0.00258146	−	0.00506639i
$173$	1.94127	+	12.2567i	0.147592	+	0.931858i	0.944680	+	0.327995i	$0.106373\pi$
$173$	1.94127	+	12.2567i	0.147592	+	0.931858i	−0.797088	+	0.603864i	$0.793627\pi$
$174$	−1.63453			−0.123914
$175$	14.3561	−	16.7178i	1.08522	−	1.26375i
$176$	−1.90744			−0.143779
$177$	−1.19910	−	7.57081i	−0.0901298	−	0.569057i
$178$	−13.8758	−	7.07006i	−1.04003	−	0.529923i
$179$	−7.88114	−	24.2557i	−0.589064	−	1.81295i	−0.582297	−	0.812976i	$-0.697846\pi$
$179$	−7.88114	−	24.2557i	−0.589064	−	1.81295i	−0.00676742	−	0.999977i	$-0.502154\pi$
$180$	−3.57883	+	0.706881i	−0.266750	+	0.0526878i
$181$	10.1648	+	3.30275i	0.755545	+	0.245491i	0.661365	−	0.750064i	$-0.269977\pi$
$181$	10.1648	+	3.30275i	0.755545	+	0.245491i	0.0941792	+	0.995555i	$0.469977\pi$
$182$	0.952785	+	0.952785i	0.0706251	+	0.0706251i
$183$	1.00811	−	0.513659i	0.0745218	−	0.0379708i
$184$	2.23975	−	1.62728i	0.165117	−	0.119964i
$185$	4.87379	+	6.19947i	0.358328	+	0.455794i
$186$	6.03754	−	8.30996i	0.442694	−	0.609316i
$187$	12.4205	+	1.96722i	0.908280	+	0.143857i
$188$	−1.08906	+	6.87607i	−0.0794281	+	0.501489i
$189$	19.3183	+	14.0356i	1.40520	+	1.02094i
$190$	6.31039	+	7.42825i	0.457804	+	0.538902i
$191$	2.80175	−	2.03559i	0.202727	−	0.147290i	−0.481790	−	0.876287i	$-0.660013\pi$
$191$	2.80175	−	2.03559i	0.202727	−	0.147290i	0.684517	+	0.728997i	$0.260013\pi$
$192$	−0.531107	−	1.04236i	−0.0383293	−	0.0752255i
$193$	−10.7346	−	10.7346i	−0.772697	−	0.772697i	0.205881	−	0.978577i	$-0.433994\pi$
$193$	−10.7346	−	10.7346i	−0.772697	−	0.772697i	−0.978577	+	0.205881i	$0.933994\pi$
$194$	−11.0095	−	3.57720i	−0.790434	−	0.256828i
$195$	−0.154975	−	0.784616i	−0.0110980	−	0.0561875i
$196$	3.83903	+	11.8153i	0.274216	+	0.843951i
$197$	2.48581	−	4.87867i	0.177107	−	0.347591i	−0.785339	−	0.619066i	$-0.787511\pi$
$197$	2.48581	−	4.87867i	0.177107	−	0.347591i	0.962446	+	0.271475i	$0.0875114\pi$
$198$	0.486799	+	3.07353i	0.0345953	+	0.218426i
$199$			7.16459i			0.507885i	0.967219	+	0.253942i	$0.0817273\pi$
$199$			7.16459i			0.507885i	−0.967219	+	0.253942i	$0.918273\pi$
$200$	2.60104	+	4.27020i	0.183921	+	0.301949i
$201$	14.2136			1.00255
$202$	−8.26963	+	1.30978i	−0.581849	+	0.0921558i
$203$	−2.79556	+	5.48659i	−0.196210	+	0.385083i
$204$	2.38334	+	7.33518i	0.166867	+	0.513565i
$205$	15.8377	+	1.89607i	1.10615	+	0.132427i
$206$	2.87598	−	8.85137i	0.200379	−	0.616704i
$207$	−3.19370	−	3.19370i	−0.221977	−	0.221977i
$208$	−0.272414	+	0.138802i	−0.0188885	+	0.00962416i
$209$	6.53611	−	5.13883i	0.452112	−	0.355461i
$210$	3.14426	−	11.0917i	0.216974	−	0.765399i
$211$	−7.18031	+	9.88284i	−0.494313	+	0.680363i	−0.981176	−	0.193115i	$-0.938141\pi$
$211$	−7.18031	+	9.88284i	−0.494313	+	0.680363i	0.486863	+	0.873478i	$0.338141\pi$
$212$	−0.572491	+	3.61456i	−0.0393188	+	0.248249i
$213$	−1.60840	+	10.1550i	−0.110206	+	0.695812i
$214$	1.99803	−	2.75006i	0.136583	−	0.187990i
$215$	0.00632296	+	0.166631i	0.000431222	+	0.0113641i
$216$	−4.38336	+	3.18470i	−0.298250	+	0.216691i
$217$	−17.5677	−	34.4786i	−1.19257	−	2.34056i
$218$	13.9550	−	13.9550i	0.945153	−	0.945153i
$219$	3.61387	−	11.1223i	0.244202	−	0.751578i
$220$	3.72414	−	2.07906i	0.251081	−	0.140170i
$221$	1.91701	−	0.622873i	0.128952	−	0.0418990i
$222$	3.67605	+	1.87304i	0.246721	+	0.125710i
$223$	−3.47724	−	21.9544i	−0.232853	−	1.47018i	−0.776102	−	0.630607i	$-0.782806\pi$
$223$	−3.47724	−	21.9544i	−0.232853	−	1.47018i	0.543249	−	0.839572i	$-0.317194\pi$
$224$	−4.40719			−0.294468
$225$	6.21691	−	5.28095i	0.414461	−	0.352063i
$226$	9.16244			0.609476
$227$	−3.27128	+	0.518120i	−0.217122	+	0.0343888i	−0.264048	−	0.964510i	$-0.585058\pi$
$227$	−3.27128	+	0.518120i	−0.217122	+	0.0343888i	0.0469255	+	0.998898i	$0.485058\pi$
$228$	4.62812	+	2.14092i	0.306504	+	0.141786i
$229$	1.37564	−	0.446973i	0.0909050	−	0.0295368i	−0.263211	−	0.964738i	$-0.584782\pi$
$229$	1.37564	−	0.446973i	0.0909050	−	0.0295368i	0.354116	+	0.935201i	$0.384782\pi$
$230$	−2.59927	+	5.61840i	−0.171391	+	0.370467i
$231$	−9.35308	−	3.03900i	−0.615387	−	0.199952i
$232$	−0.987971	−	0.987971i	−0.0648635	−	0.0648635i
$233$	2.70301	+	5.30496i	0.177080	+	0.347539i	0.962437	−	0.271503i	$-0.0875208\pi$
$233$	2.70301	+	5.30496i	0.177080	+	0.347539i	−0.785357	+	0.619043i	$0.787521\pi$
$234$	0.293179	+	0.403526i	0.0191657	+	0.0263793i
$235$	−5.36841	−	14.6121i	−0.350196	−	0.953186i
$236$	3.85129	−	5.30085i	0.250698	−	0.345056i
$237$	−6.58472	−	1.04292i	−0.427723	−	0.0677447i
$238$	28.6980	+	4.54531i	1.86021	+	0.294629i
$239$	−3.97451	+	5.47044i	−0.257090	+	0.353853i	−0.917978	−	0.396630i	$-0.870179\pi$
$239$	−3.97451	+	5.47044i	−0.257090	+	0.353853i	0.660889	+	0.750484i	$0.270179\pi$
$240$	2.17308	+	1.45623i	0.140272	+	0.0939992i
$241$	−0.936509	−	1.28899i	−0.0603258	−	0.0830314i	0.777788	−	0.628527i	$-0.216342\pi$
$241$	−0.936509	−	1.28899i	−0.0603258	−	0.0830314i	−0.838114	+	0.545495i	$0.816342\pi$
$242$	3.34213	+	6.55929i	0.214840	+	0.421647i
$243$	10.2989	+	10.2989i	0.660676	+	0.660676i
$244$	0.919813	+	0.298865i	0.0588850	+	0.0191329i
$245$	−20.3738	−	18.8841i	−1.30163	−	1.20646i
$246$	7.93667	−	2.57878i	0.506023	−	0.164417i
$247$	0.559517	−	1.20953i	0.0356012	−	0.0769606i
$248$	8.67214	−	1.37353i	0.550682	−	0.0872194i
$249$	19.8094			1.25537
$250$	−9.73273	−	5.50219i	−0.615552	−	0.347989i
$251$	25.6906			1.62158			0.810789	−	0.585339i	$-0.199038\pi$
$251$	25.6906			1.62158			0.810789	+	0.585339i	$0.199038\pi$
$252$	1.12476	+	7.10147i	0.0708534	+	0.447351i
$253$	4.70517	+	2.39740i	0.295811	+	0.150723i
$254$	−13.1155	+	4.26148i	−0.822938	+	0.267389i
$255$	−12.6484	−	11.7236i	−0.792075	−	0.734161i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−13.5852	+	13.5852i	−0.847419	+	0.847419i	−0.989810	−	0.142391i	$-0.954521\pi$
$257$	−13.5852	+	13.5852i	−0.847419	+	0.847419i	0.142391	+	0.989810i	$0.454521\pi$
$258$	0.0396063	+	0.0777317i	0.00246578	+	0.00483936i
$259$	12.5744	−	9.13580i	0.781332	−	0.567671i
$260$	0.380577	−	0.567923i	0.0236024	−	0.0352211i
$261$	−1.33981	+	1.84409i	−0.0829323	+	0.114147i
$262$	−2.55169	+	16.1107i	−0.157644	+	0.995325i
$263$	4.70317	−	29.6946i	0.290010	−	1.83105i	−0.225594	−	0.974221i	$-0.572432\pi$
$263$	4.70317	−	29.6946i	0.290010	−	1.83105i	0.515604	−	0.856827i	$-0.327568\pi$
$264$	1.31161	−	1.80528i	0.0807241	−	0.111107i
$265$	−2.82202	−	7.68116i	−0.173356	−	0.471850i
$266$	15.1019	−	11.8734i	0.925954	−	0.728005i
$267$	16.2328	−	8.27100i	0.993428	−	0.506177i
$268$	8.59118	+	8.59118i	0.524790	+	0.524790i
$269$	−3.64927	+	11.2313i	−0.222500	+	0.684785i	0.776036	+	0.630689i	$0.217228\pi$
$269$	−3.64927	+	11.2313i	−0.222500	+	0.684785i	−0.998536	+	0.0540959i	$0.982772\pi$
$270$	5.08695	−	10.9956i	0.309582	−	0.669171i
$271$	3.86661	+	11.9002i	0.234880	+	0.722885i	0.997137	+	0.0756114i	$0.0240909\pi$
$271$	3.86661	+	11.9002i	0.234880	+	0.722885i	−0.762258	+	0.647274i	$0.775909\pi$
$272$	−2.99307	+	5.87422i	−0.181481	+	0.356177i
$273$	−1.55691	+	0.246591i	−0.0942287	+	0.0149244i
$274$	−13.1701			−0.795634
$275$	−5.00499	+	8.11840i	−0.301812	+	0.489558i
$276$			3.23875i			0.194950i
$277$	−1.24562	−	7.86457i	−0.0748423	−	0.472536i	−0.996434	−	0.0843753i	$-0.973111\pi$
$277$	−1.24562	−	7.86457i	−0.0748423	−	0.472536i	0.921592	−	0.388161i	$-0.126889\pi$
$278$	−4.33756	+	8.51293i	−0.260149	+	0.510572i
$279$	−4.42644	−	13.6232i	−0.265004	−	0.815599i
$280$	8.60471	−	4.80371i	0.514230	−	0.287077i
$281$	20.9665	+	6.81244i	1.25076	+	0.406396i	0.858193	−	0.513328i	$-0.171587\pi$
$281$	20.9665	+	6.81244i	1.25076	+	0.406396i	0.392566	+	0.919724i	$0.371587\pi$
$282$	−5.75891	−	5.75891i	−0.342938	−	0.342938i
$283$	−5.31068	−	10.4228i	−0.315687	−	0.619571i	0.677576	−	0.735453i	$-0.263031\pi$
$283$	−5.31068	−	10.4228i	−0.315687	−	0.619571i	−0.993263	+	0.115882i	$0.963031\pi$
$284$	−7.11024	+	5.16589i	−0.421915	+	0.306539i
$285$	−11.3696	+	0.864525i	−0.673476	+	0.0512100i
$286$	−0.471799	−	0.342782i	−0.0278980	−	0.0202691i
$287$	4.91803	−	31.0512i	0.290302	−	1.83290i
$288$	−1.61134	−	0.255211i	−0.0949489	−	0.0150384i
$289$	15.5557	−	21.4106i	0.915040	−	1.25945i
$290$	3.00580	+	0.852080i	0.176507	+	0.0500359i
$291$	10.9560	−	7.96001i	0.642253	−	0.466624i
$292$	8.90709	−	4.53839i	0.521248	−	0.265589i
$293$	6.83793	+	6.83793i	0.399476	+	0.399476i	0.878048	−	0.478572i	$-0.158845\pi$
$293$	6.83793	+	6.83793i	0.399476	+	0.399476i	−0.478572	+	0.878048i	$0.658845\pi$
$294$	−13.8223	−	4.49113i	−0.806132	−	0.261928i
$295$	−1.74159	+	14.5473i	−0.101399	+	0.846977i
$296$	1.08980	+	3.35407i	0.0633436	+	0.194951i
$297$	−9.20834	−	4.69188i	−0.534322	−	0.272251i
$298$	1.63829	+	10.3438i	0.0949035	+	0.599197i
$299$	0.846429			0.0489503
$300$	−5.83003	−	0.474583i	−0.336597	−	0.0274001i
$301$	0.328658			0.0189435
$302$	−0.182002	−	1.14911i	−0.0104730	−	0.0661240i
$303$	4.44680	−	8.72734i	0.255462	−	0.501372i
$304$	1.50335	+	4.09145i	0.0862230	+	0.234661i
$305$	−2.12162	+	0.419057i	−0.121484	+	0.0239951i
$306$	10.2292	+	3.32367i	0.584765	+	0.190002i
$307$	16.3033	−	16.3033i	0.930481	−	0.930481i	−0.0672553	−	0.997736i	$-0.521424\pi$
$307$	16.3033	−	16.3033i	0.930481	−	0.930481i	0.997736	+	0.0672553i	$0.0214242\pi$
$308$	−3.81646	−	7.49022i	−0.217463	−	0.426795i
$309$	6.39967	+	8.80839i	0.364065	+	0.501092i
$310$	−15.4346	+	12.1341i	−0.876626	+	0.689171i
$311$	−4.21666	−	3.06358i	−0.239105	−	0.173720i	0.461780	−	0.886995i	$-0.347211\pi$
$311$	−4.21666	−	3.06358i	−0.239105	−	0.173720i	−0.700884	+	0.713275i	$0.747211\pi$
$312$	0.0559519	−	0.353267i	0.00316765	−	0.0199998i
$313$	1.49917	−	9.46542i	0.0847384	−	0.535017i	−0.908403	−	0.418096i	$-0.862698\pi$
$313$	1.49917	−	9.46542i	0.0847384	−	0.535017i	0.993141	−	0.116921i	$-0.0373024\pi$
$314$	−18.1856	−	13.2126i	−1.02627	−	0.745629i
$315$	−9.93641	−	12.6391i	−0.559853	−	0.712134i
$316$	−3.34966	−	4.61041i	−0.188433	−	0.259356i
$317$	13.6138	+	26.7186i	0.764626	+	1.50066i	0.862828	+	0.505497i	$0.168691\pi$
$317$	13.6138	+	26.7186i	0.764626	+	1.50066i	−0.0982021	+	0.995166i	$0.531309\pi$
$318$	−3.02730	−	3.02730i	−0.169763	−	0.169763i
$319$	0.823556	−	2.53464i	0.0461103	−	0.141913i
$320$	0.433291	+	2.19369i	0.0242217	+	0.122631i
$321$	1.22886	+	3.78203i	0.0685881	+	0.211093i
$322$	10.8714	+	5.53926i	0.605840	+	0.308691i
$323$	−5.56958	−	28.1924i	−0.309900	−	1.56867i
$324$		−	1.44420i		−	0.0802333i
$325$	−0.124030	+	1.52364i	−0.00687993	+	0.0845166i
$326$		−	19.3377i		−	1.07102i
$327$	3.61171	+	22.8034i	0.199728	+	1.26103i
$328$	6.35591	+	3.23850i	0.350947	+	0.178816i
$329$	−29.1803	+	9.48124i	−1.60876	+	0.522718i
$330$	−0.593122	+	4.95429i	−0.0326503	+	0.272724i
$331$	22.8836	+	7.43533i	1.25780	+	0.408683i	0.860709	−	0.509098i	$-0.170021\pi$
$331$	22.8836	+	7.43533i	1.25780	+	0.408683i	0.397088	+	0.917781i	$0.370021\pi$
$332$	11.9735	+	11.9735i	0.657130	+	0.657130i
$333$	5.12641	−	2.61203i	0.280925	−	0.143139i
$334$	10.2501	+	14.1081i	0.560861	+	0.771959i
$335$	−26.1378	−	7.40950i	−1.42806	−	0.404824i
$336$	3.03051	−	4.17114i	0.165328	−	0.227554i
$337$	−1.26928	+	8.01391i	−0.0691420	+	0.436545i	0.928697	+	0.370839i	$0.120930\pi$
$337$	−1.26928	+	8.01391i	−0.0691420	+	0.436545i	−0.997839	+	0.0657060i	$0.979070\pi$
$338$	12.7476	+	2.01903i	0.693379	+	0.109821i
$339$	−6.30035	+	8.67169i	−0.342188	+	0.470981i
$340$	−0.558994	−	14.7313i	−0.0303157	−	0.798919i
$341$	9.84411	+	13.5493i	0.533089	+	0.733733i
$342$	6.20903	−	3.46658i	0.335746	−	0.187451i
$343$	−16.9011	+	16.9011i	−0.912574	+	0.912574i
$344$	−0.0230444	+	0.0709233i	−0.00124247	+	0.00382393i
$345$	−3.53014	−	6.32342i	−0.190057	−	0.340441i
$346$	−3.83473	−	11.8021i	−0.206157	−	0.634485i
$347$	−12.0950	+	23.7378i	−0.649294	+	1.27431i	0.298190	+	0.954507i	$0.403617\pi$
$347$	−12.0950	+	23.7378i	−0.649294	+	1.27431i	−0.947484	+	0.319804i	$0.896383\pi$
$348$	1.61441	−	0.255698i	0.0865415	−	0.0137068i
$349$			14.1397i			0.756880i	0.925626	+	0.378440i	$0.123539\pi$
$349$			14.1397i			0.756880i	−0.925626	+	0.378440i	$0.876461\pi$
$350$	−11.5642	+	18.7578i	−0.618130	+	1.00265i
$351$	−1.65652			−0.0884186
$352$	1.88396	−	0.298390i	0.100415	−	0.0159042i
$353$	15.1350	+	7.71166i	0.805554	+	0.410450i	0.807734	−	0.589547i	$-0.200694\pi$
$353$	15.1350	+	7.71166i	0.805554	+	0.410450i	−0.00217964	+	0.999998i	$0.500694\pi$
$354$	2.36867	+	7.29002i	0.125893	+	0.387460i
$355$	8.25154	−	17.8360i	0.437946	−	0.946635i
$356$	14.8109	+	4.81237i	0.784978	+	0.255055i
$357$	−24.0354	+	24.0354i	−1.27209	+	1.27209i
$358$	11.5785	+	22.7242i	0.611945	+	1.20101i
$359$	3.16285	+	4.35329i	0.166929	+	0.229758i	0.884284	−	0.466950i	$-0.154647\pi$
$359$	3.16285	+	4.35329i	0.166929	+	0.229758i	−0.717355	+	0.696708i	$0.754647\pi$
$360$	3.42418	−	1.25803i	0.180470	−	0.0663040i
$361$	−16.1742	−	9.96973i	−0.851273	−	0.524723i
$362$	−10.5563	−	1.67196i	−0.554828	−	0.0878762i
$363$	−8.50611	−	1.34723i	−0.446455	−	0.0707115i
$364$	−1.09010	−	0.792006i	−0.0571369	−	0.0415124i
$365$	−12.4437	+	18.5693i	−0.651333	+	0.971963i
$366$	−0.915347	+	0.665038i	−0.0478459	+	0.0347621i
$367$	−9.48832	+	4.83454i	−0.495286	+	0.252361i	−0.683746	−	0.729720i	$-0.739650\pi$
$367$	−9.48832	+	4.83454i	−0.495286	+	0.252361i	0.188460	+	0.982081i	$0.439650\pi$
$368$	−1.95762	+	1.95762i	−0.102048	+	0.102048i
$369$	3.59621	−	11.0680i	0.187211	−	0.576178i
$370$	−5.78360	−	5.36072i	−0.300675	−	0.278691i
$371$	−15.3393	+	4.98403i	−0.796375	+	0.258758i
$372$	−4.66324	+	9.15213i	−0.241778	+	0.474516i
$373$	5.43739	+	34.3303i	0.281537	+	1.77756i	0.571584	+	0.820544i	$0.306329\pi$
$373$	5.43739	+	34.3303i	0.281537	+	1.77756i	−0.290047	+	0.957012i	$0.593671\pi$
$374$	−12.5754			−0.650257
$375$	11.9000	−	5.42797i	0.614512	−	0.280299i
$376$		−	6.96179i		−	0.359027i
$377$	−0.0668251	−	0.421917i	−0.00344167	−	0.0217298i
$378$	−21.2761	−	10.8407i	−1.09432	−	0.557586i
$379$	−4.27979	−	13.1719i	−0.219838	−	0.676593i	−0.998775	−	0.0494897i	$-0.984241\pi$
$379$	−4.27979	−	13.1719i	−0.219838	−	0.676593i	0.778936	−	0.627103i	$-0.215759\pi$
$380$	−7.39474	−	6.34964i	−0.379342	−	0.325729i
$381$	4.98534	−	15.3433i	0.255407	−	0.786061i
$382$	−2.44882	+	2.44882i	−0.125292	+	0.125292i
$383$	−1.22669	+	0.625029i	−0.0626808	+	0.0319375i	−0.485050	−	0.874486i	$-0.661199\pi$
$383$	−1.22669	+	0.625029i	−0.0626808	+	0.0319375i	0.422369	+	0.906424i	$0.361199\pi$
$384$	0.687628	+	0.946439i	0.0350904	+	0.0482977i
$385$	15.6155	+	10.4643i	0.795838	+	0.533308i
$386$	12.2818	+	8.92322i	0.625125	+	0.454180i
$387$	0.120162	+	0.0190318i	0.00610820	+	0.000967443i
$388$	11.4335	+	1.81089i	0.580449	+	0.0919342i
$389$	−4.30445	+	5.92457i	−0.218244	+	0.300387i	−0.904075	−	0.427373i	$-0.859439\pi$
$389$	−4.30445	+	5.92457i	−0.218244	+	0.300387i	0.685831	+	0.727761i	$0.259439\pi$
$390$	0.275808	+	0.750713i	0.0139661	+	0.0380138i
$391$	14.7662	−	10.7283i	0.746761	−	0.542553i
$392$	−5.64008	−	11.0693i	−0.284867	−	0.559083i
$393$	−13.4932	−	13.4932i	−0.680643	−	0.680643i
$394$	−1.69201	+	5.20748i	−0.0852423	+	0.262349i
$395$	11.5652	+	5.35045i	0.581907	+	0.269211i
$396$	−0.961612	−	2.95954i	−0.0483228	−	0.148722i
$397$	−3.95149	+	7.75524i	−0.198320	+	0.389225i	−0.968653	−	0.248417i	$-0.920090\pi$
$397$	−3.95149	+	7.75524i	−0.198320	+	0.389225i	0.770333	+	0.637641i	$0.220090\pi$
$398$	−1.12079	−	7.07638i	−0.0561801	−	0.354707i
$399$	0.852998	+	22.4575i	0.0427033	+	1.12428i
$400$	−3.23702	−	3.81073i	−0.161851	−	0.190537i
$401$			15.0201i			0.750066i	0.927011	+	0.375033i	$0.122369\pi$
$401$			15.0201i			0.750066i	−0.927011	+	0.375033i	$0.877631\pi$
$402$	−14.0386	+	2.22349i	−0.700180	+	0.110898i
$403$	2.39186	+	1.21871i	0.119147	+	0.0607084i
$404$	7.96292	−	2.58731i	0.396170	−	0.128723i
$405$	1.57414	+	2.81969i	0.0782194	+	0.140112i
$406$	1.90285	−	5.85636i	0.0944367	−	0.290646i
$407$	−4.75666	+	4.75666i	−0.235779	+	0.235779i
$408$	−3.50148	−	6.87203i	−0.173349	−	0.340216i
$409$	16.2773	−	11.8262i	0.804863	−	0.584767i	−0.107474	−	0.994208i	$-0.534276\pi$
$409$	16.2773	−	11.8262i	0.804863	−	0.584767i	0.912337	+	0.409441i	$0.134276\pi$
$410$	−15.9393	+	0.604832i	−0.787187	+	0.0298705i
$411$	9.05612	−	12.4647i	0.446706	−	0.614838i
$412$	−1.45592	+	9.19230i	−0.0717279	+	0.452872i
$413$	28.5213	+	4.51733i	1.40344	+	0.222283i
$414$	3.65398	+	2.65477i	0.179583	+	0.130475i
$415$	−36.4281	−	10.3266i	−1.78818	−	0.506912i
$416$	0.247346	−	0.179708i	0.0121272	−	0.00881089i
$417$	−5.07434	−	9.95896i	−0.248492	−	0.487693i
$418$	−5.65175	+	6.09804i	−0.276436	+	0.298265i
$419$	−14.4607	−	4.69858i	−0.706453	−	0.229541i	−0.0663132	−	0.997799i	$-0.521124\pi$
$419$	−14.4607	−	4.69858i	−0.706453	−	0.229541i	−0.640140	+	0.768258i	$0.721124\pi$
$420$	−1.37042	+	11.4470i	−0.0668698	+	0.558557i
$421$	−21.4244	+	6.96121i	−1.04416	+	0.339269i	−0.780375	−	0.625312i	$-0.784972\pi$
$421$	−21.4244	+	6.96121i	−1.04416	+	0.339269i	−0.263787	+	0.964581i	$0.584972\pi$
$422$	5.54589	−	10.8844i	0.269970	−	0.529845i
$423$	−11.2178	+	1.77672i	−0.545427	+	0.0863871i
$424$		−	3.65962i		−	0.177727i
$425$	17.1481	+	28.1525i	0.831806	+	1.36560i
$426$		−	10.2816i		−	0.498146i
$427$	0.666788	+	4.20993i	0.0322681	+	0.203733i
$428$	−1.54323	+	3.02876i	−0.0745949	+	0.146401i
$429$	0.648844	−	0.210822i	0.0313265	−	0.0101786i
$430$	−0.0323119	−	0.163590i	−0.00155822	−	0.00788901i
$431$	−6.93727	−	2.25405i	−0.334156	−	0.108574i	0.137133	−	0.990553i	$-0.456211\pi$
$431$	−6.93727	−	2.25405i	−0.334156	−	0.108574i	−0.471289	+	0.881979i	$0.656211\pi$
$432$	3.83119	−	3.83119i	0.184328	−	0.184328i
$433$	−15.4876	+	7.89132i	−0.744286	+	0.379233i	−0.784639	−	0.619953i	$-0.787152\pi$
$433$	−15.4876	+	7.89132i	−0.744286	+	0.379233i	0.0403530	+	0.999185i	$0.487152\pi$
$434$	22.7451	+	31.3059i	1.09180	+	1.50273i
$435$	−2.87331	+	2.25889i	−0.137765	+	0.108306i
$436$	−11.6002	+	15.9663i	−0.555547	+	0.764645i
$437$	1.43403	−	11.9821i	0.0685990	−	0.573179i
$438$	−1.82946	+	11.5507i	−0.0874148	+	0.551915i
$439$	3.38784	+	2.46141i	0.161693	+	0.117477i	0.665689	−	0.746229i	$-0.268138\pi$
$439$	3.38784	+	2.46141i	0.161693	+	0.117477i	−0.503996	+	0.863706i	$0.668138\pi$
$440$	−3.35305	+	2.63604i	−0.159850	+	0.125668i
$441$	−16.3969	+	11.9131i	−0.780806	+	0.567289i
$442$	−1.79597	+	0.915090i	−0.0854254	+	0.0435264i
$443$	−2.56699	+	2.56699i	−0.121961	+	0.121961i	−0.765453	−	0.643492i	$-0.777485\pi$
$443$	−2.56699	+	2.56699i	−0.121961	+	0.121961i	0.643492	+	0.765453i	$0.277485\pi$
$444$	−3.92380	−	1.27492i	−0.186215	−	0.0605051i
$445$	−34.1626	+	6.74771i	−1.61946	+	0.319872i
$446$	6.86886	+	21.1402i	0.325250	+	1.00102i
$447$	−10.9163	−	5.56211i	−0.516321	−	0.263079i
$448$	4.35293	−	0.689437i	0.205657	−	0.0325728i
$449$	−5.35450			−0.252695			−0.126347	−	0.991986i	$-0.540325\pi$
$449$	−5.35450			−0.252695			−0.126347	+	0.991986i	$0.540325\pi$
$450$	−5.31425	+	6.18847i	−0.250516	+	0.291727i
$451$			13.6066i			0.640708i
$452$	−9.04963	+	1.43332i	−0.425659	+	0.0674178i
$453$	1.21271	+	0.617909i	0.0569783	+	0.0290319i
$454$	3.14995	−	1.02348i	0.147835	−	0.0480344i
$455$	2.99161	+	0.358152i	0.140249	+	0.0167904i
$456$	−4.90605	−	1.39056i	−0.229747	−	0.0651192i
$457$	4.15052	+	4.15052i	0.194153	+	0.194153i	0.797488	−	0.603335i	$-0.206162\pi$
$457$	4.15052	+	4.15052i	0.194153	+	0.194153i	−0.603335	+	0.797488i	$0.706162\pi$
$458$	−1.28878	+	0.656668i	−0.0602209	+	0.0306841i
$459$	−28.8986	+	20.9960i	−1.34887	+	0.980011i
$460$	1.68836	−	5.95585i	0.0787200	−	0.277693i
$461$	−0.434366	−	0.315585i	−0.0202304	−	0.0146983i	0.577624	−	0.816303i	$-0.303980\pi$
$461$	−0.434366	−	0.315585i	−0.0202304	−	0.0146983i	−0.597855	+	0.801605i	$0.703980\pi$
$462$	9.71333	+	1.53844i	0.451905	+	0.0715747i
$463$	−0.562744	+	3.55303i	−0.0261529	+	0.165123i	−0.997308	−	0.0733254i	$-0.976639\pi$
$463$	−0.562744	+	3.55303i	−0.0261529	+	0.165123i	0.971155	+	0.238449i	$0.0766388\pi$
$464$	1.13036	+	0.821255i	0.0524757	+	0.0381258i
$465$	−0.870922	−	22.9517i	−0.0403880	−	1.06436i
$466$	−3.49961	−	4.81680i	−0.162116	−	0.223134i
$467$	27.2132	−	13.8658i	1.25928	−	0.641633i	0.308416	−	0.951252i	$-0.400201\pi$
$467$	27.2132	−	13.8658i	1.25928	−	0.641633i	0.950861	+	0.309618i	$0.100201\pi$
$468$	−0.352695	−	0.352695i	−0.0163033	−	0.0163033i
$469$	−16.5467	+	50.9256i	−0.764057	+	2.35153i
$470$	7.58814	+	13.5924i	0.350015	+	0.626969i
$471$	25.0098	−	8.12618i	1.15239	−	0.374435i
$472$	−2.97464	+	5.83806i	−0.136919	+	0.268718i
$473$	−0.140493	+	0.0222519i	−0.00645986	+	0.00102314i
$474$	6.66680			0.306216
$475$	21.3586	+	4.33714i	0.979999	+	0.199002i
$476$	−29.0557			−1.33177
$477$	−5.89688	+	0.933974i	−0.269999	+	0.0427637i
$478$	3.06981	−	6.02484i	0.140410	−	0.275570i
$479$	−8.21963	+	2.67072i	−0.375564	+	0.122028i	−0.490716	−	0.871320i	$-0.663265\pi$
$479$	−8.21963	+	2.67072i	−0.375564	+	0.122028i	0.115151	+	0.993348i	$0.463265\pi$
$480$	−2.37413	−	1.09836i	−0.108364	−	0.0501329i
$481$	−0.333193	+	1.02546i	−0.0151923	+	0.0467571i
$482$	1.12662	+	1.12662i	0.0513162	+	0.0513162i
$483$	−12.7181	+	6.48017i	−0.578691	+	0.294858i
$484$	−4.32708	−	5.95571i	−0.196685	−	0.270714i
$485$	−24.2969	+	8.92658i	−1.10327	+	0.405335i
$486$	−11.7832	−	8.56101i	−0.534498	−	0.388335i
$487$	2.54308	−	16.0563i	0.115238	−	0.727582i	−0.860632	−	0.509228i	$-0.829931\pi$
$487$	2.54308	−	16.0563i	0.115238	−	0.727582i	0.975869	−	0.218355i	$-0.0700689\pi$
$488$	−0.955241	−	0.151295i	−0.0432417	−	0.00684882i
$489$	18.3020	+	13.2972i	0.827643	+	0.601318i
$490$	23.0770	+	15.4644i	1.04251	+	0.698612i
$491$	−3.99124	+	2.89980i	−0.180122	+	0.130866i	−0.674193	−	0.738555i	$-0.735508\pi$
$491$	−3.99124	+	2.89980i	−0.180122	+	0.130866i	0.494071	+	0.869422i	$0.335508\pi$
$492$	−7.43554	+	3.78860i	−0.335220	+	0.170803i
$493$	−6.51349	−	6.51349i	−0.293353	−	0.293353i
$494$	−0.363416	+	1.28217i	−0.0163509	+	0.0576875i
$495$	5.10329	+	4.73015i	0.229376	+	0.212604i
$496$	−8.35051	+	2.71324i	−0.374949	+	0.121828i
$497$	−34.5120	−	17.5847i	−1.54807	−	0.788783i
$498$	−19.5655	+	3.09887i	−0.876749	+	0.138863i
$499$		−	5.28741i		−	0.236697i	−0.992972	−	0.118348i	$-0.962240\pi$
$499$		−	5.28741i		−	0.236697i	0.992972	−	0.118348i	$-0.0377600\pi$
$500$	10.4736	+	3.91191i	0.468395	+	0.174946i
$501$	−20.4007			−0.911436
$502$	−25.3743	+	4.01890i	−1.13251	+	0.179372i
$503$	11.5526	+	5.88634i	0.515105	+	0.262459i	0.692163	−	0.721741i	$-0.256658\pi$
$503$	11.5526	+	5.88634i	0.515105	+	0.262459i	−0.177058	+	0.984200i	$0.556658\pi$
$504$	−2.22183	−	6.83809i	−0.0989681	−	0.304593i
$505$	−12.7269	+	13.7309i	−0.566340	+	0.611016i
$506$	−5.02227	−	1.63184i	−0.223267	−	0.0725440i
$507$	−10.6765	+	10.6765i	−0.474160	+	0.474160i
$508$	12.2874	−	6.26072i	0.545164	−	0.277775i
$509$	14.8189	−	10.7666i	0.656837	−	0.477220i	−0.208756	−	0.977968i	$-0.566941\pi$
$509$	14.8189	−	10.7666i	0.656837	−	0.477220i	0.865593	+	0.500747i	$0.166941\pi$
$510$	14.3267	+	9.60062i	0.634396	+	0.425123i
$511$	35.6430	+	25.8962i	1.57675	+	1.14558i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	−2.80650	+	23.4497i	−0.123910	+	1.03533i
$514$	11.2927	−	15.5431i	0.498101	−	0.685577i
$515$	−7.17677	−	19.5342i	−0.316246	−	0.860779i
$516$	−0.0512786	−	0.0705789i	−0.00225741	−	0.00310706i
$517$	11.8319	−	6.02863i	0.520364	−	0.265139i
$518$	−10.9904	+	10.9904i	−0.482890	+	0.482890i
$519$	13.8068	+	4.48611i	0.606053	+	0.196918i
$520$	−0.287049	+	0.620466i	−0.0125879	+	0.0272092i
$521$	19.8142	−	6.43804i	0.868078	−	0.282056i	0.159080	−	0.987266i	$-0.449147\pi$
$521$	19.8142	−	6.43804i	0.868078	−	0.282056i	0.708998	+	0.705210i	$0.249147\pi$
$522$	1.03484	−	2.03098i	0.0452936	−	0.0888937i
$523$	−4.65622	−	29.3982i	−0.203602	−	1.28549i	−0.851738	−	0.523968i	$-0.824451\pi$
$523$	−4.65622	−	29.3982i	−0.203602	−	1.28549i	0.648136	−	0.761525i	$-0.275549\pi$
$524$		−	16.3116i		−	0.712574i
$525$	−9.80125	−	23.8431i	−0.427762	−	1.04060i
$526$			30.0648i			1.31089i
$527$	57.1736	−	9.05542i	2.49052	−	0.394460i
$528$	−1.01305	+	1.98823i	−0.0440876	+	0.0865267i
$529$	−14.5849	+	4.73892i	−0.634126	+	0.206040i
$530$	3.98888	+	7.14513i	0.173266	+	0.310365i
$531$	10.1662	+	3.30321i	0.441177	+	0.143347i
$532$	−13.0585	+	14.0897i	−0.566158	+	0.610865i
$533$	0.990129	+	1.94324i	0.0428872	+	0.0841709i
$534$	−14.7390	+	10.7085i	−0.637820	+	0.463404i
$535$	−0.288219	−	7.59551i	−0.0124608	−	0.328382i
$536$	−9.82937	−	7.14145i	−0.424564	−	0.308464i
$537$	−29.4687	−	4.66739i	−1.27167	−	0.201413i
$538$	1.84738	−	11.6639i	0.0796462	−	0.502867i
$539$	13.9286	−	19.1711i	0.599949	−	0.825759i
$540$	−3.30423	+	11.6560i	−0.142191	+	0.501595i
$541$	27.1451	−	19.7221i	1.16706	−	0.847919i	0.176407	−	0.984317i	$-0.443553\pi$
$541$	27.1451	−	19.7221i	1.16706	−	0.847919i	0.990654	+	0.136398i	$0.0435526\pi$
$542$	−5.68060	−	11.1488i	−0.244003	−	0.478882i
$543$	8.84123	−	8.84123i	0.379414	−	0.379414i
$544$	2.03728	−	6.27012i	0.0873479	−	0.268829i
$545$	5.24570	−	43.8168i	0.224701	−	1.87690i
$546$	1.49917	−	0.487110i	0.0641586	−	0.0208464i
$547$	0.139061	+	0.0708549i	0.00594580	+	0.00302954i	0.456961	−	0.889487i	$-0.348938\pi$
$547$	0.139061	+	0.0708549i	0.00594580	+	0.00302954i	−0.451015	+	0.892516i	$0.648938\pi$
$548$	13.0079	−	2.06026i	0.555672	−	0.0880098i
$549$			1.57783i			0.0673400i
$550$	3.67337	−	8.80140i	0.156633	−	0.375293i
$551$	−6.08588	+	0.231159i	−0.259267	+	0.00984770i
$552$	−0.506652	−	3.19888i	−0.0215646	−	0.136153i
$553$	11.4023	−	22.3782i	0.484874	−	0.951618i
$554$	2.46058	+	7.57288i	0.104540	+	0.321741i
$555$	9.05056	−	1.78764i	0.384175	−	0.0758812i
$556$	2.95244	−	9.08667i	0.125211	−	0.385361i
$557$	−14.2778	−	14.2778i	−0.604969	−	0.604969i	0.336658	−	0.941627i	$-0.390703\pi$
$557$	−14.2778	−	14.2778i	−0.604969	−	0.604969i	−0.941627	+	0.336658i	$0.890703\pi$
$558$	6.50309	+	12.7630i	0.275298	+	0.540302i
$559$	−0.0184454	+	0.0134014i	−0.000780157	+	0.000566817i
$560$	−7.74731	+	6.09064i	−0.327384	+	0.257377i
$561$	8.64718	−	11.9018i	0.365084	−	0.502495i
$562$	−21.7741	−	3.44868i	−0.918485	−	0.145474i
$563$	−17.4424	−	2.76260i	−0.735108	−	0.116430i	−0.222355	−	0.974966i	$-0.571374\pi$
$563$	−17.4424	−	2.76260i	−0.735108	−	0.116430i	−0.512753	+	0.858536i	$0.671374\pi$
$564$	6.58890	+	4.78712i	0.277443	+	0.201574i
$565$	16.1065	−	12.6623i	0.677604	−	0.532707i
$566$	6.87578	+	9.46370i	0.289011	+	0.397789i
$567$	5.67114	−	2.88959i	0.238165	−	0.121351i
$568$	6.21458	−	6.21458i	0.260758	−	0.260758i
$569$	−3.73129	+	11.4837i	−0.156424	+	0.481423i	−0.998302	−	0.0582439i	$-0.981450\pi$
$569$	−3.73129	+	11.4837i	−0.156424	+	0.481423i	0.841878	+	0.539667i	$0.181450\pi$
$570$	11.0944	−	2.63248i	0.464692	−	0.110262i
$571$	−10.1062	−	31.1037i	−0.422931	−	1.30165i	−0.904962	−	0.425493i	$-0.860101\pi$
$571$	−10.1062	−	31.1037i	−0.422931	−	1.30165i	0.482031	−	0.876154i	$-0.339899\pi$
$572$	0.519613	+	0.264756i	0.0217261	+	0.0110700i
$573$	−0.633780	−	4.00153i	−0.0264766	−	0.167166i
$574$			31.4383i			1.31221i
$575$	3.19531	+	13.4686i	0.133254	+	0.561679i
$576$	1.63142			0.0679759
$577$	0.126800	+	0.800586i	0.00527877	+	0.0333288i	0.990187	−	0.139748i	$-0.0446292\pi$
$577$	0.126800	+	0.800586i	0.00527877	+	0.0333288i	−0.984908	+	0.173077i	$0.944629\pi$
$578$	−12.0148	+	23.5804i	−0.499751	+	0.980816i
$579$	−16.8906	+	5.48807i	−0.701947	+	0.228077i
$580$	−3.10209	−	0.371379i	−0.128807	−	0.0154207i
$581$	−23.0611	+	70.9747i	−0.956735	+	2.94453i
$582$	−9.57591	+	9.57591i	−0.396934	+	0.396934i
$583$	6.21968	−	3.16909i	0.257593	−	0.131250i
$584$	−8.08746	+	5.87589i	−0.334662	+	0.243146i
$585$	1.07304	+	0.304183i	0.0443646	+	0.0125764i
$586$	−7.82343	−	5.68405i	−0.323183	−	0.234806i
$587$	−15.3383	−	2.42935i	−0.633081	−	0.100270i	−0.168357	−	0.985726i	$-0.553846\pi$
$587$	−15.3383	−	2.42935i	−0.633081	−	0.100270i	−0.464724	+	0.885456i	$0.653846\pi$
$588$	14.3547	+	2.27356i	0.591977	+	0.0937600i
$589$	21.3044	−	31.7944i	0.877833	−	1.31006i
$590$	−0.555553	−	14.6406i	−0.0228718	−	0.602746i
$591$	−3.76508	−	5.18219i	−0.154875	−	0.213167i
$592$	−1.60108	−	3.14229i	−0.0658039	−	0.129148i
$593$	15.3000	−	15.3000i	0.628297	−	0.628297i	−0.319342	−	0.947639i	$-0.603462\pi$
$593$	15.3000	−	15.3000i	0.628297	−	0.628297i	0.947639	+	0.319342i	$0.103462\pi$
$594$	9.82894	+	3.19362i	0.403286	+	0.131036i
$595$	56.7291	−	31.6699i	2.32567	−	1.29834i
$596$	−3.23624	−	9.96012i	−0.132561	−	0.407982i
$597$	7.46805	+	3.80516i	0.305647	+	0.155735i
$598$	−0.836008	+	0.132411i	−0.0341869	+	0.00541468i
$599$	−1.11135			−0.0454087			−0.0227043	−	0.999742i	$-0.507228\pi$
$599$	−1.11135			−0.0454087			−0.0227043	+	0.999742i	$0.507228\pi$
$600$	5.83249	−	0.443277i	0.238111	−	0.0180967i
$601$		−	4.63424i		−	0.189035i	−0.995523	−	0.0945173i	$-0.969869\pi$
$601$		−	4.63424i		−	0.189035i	0.995523	−	0.0945173i	$-0.0301308\pi$
$602$	−0.324612	+	0.0514135i	−0.0132302	+	0.00209546i
$603$	−8.99872	+	17.6610i	−0.366456	+	0.719211i
$604$	0.359522	+	1.10649i	0.0146287	+	0.0450226i
$605$	14.9398	+	6.91169i	0.607391	+	0.281000i
$606$	−3.02680	+	9.31552i	−0.122955	+	0.378417i
$607$	13.3981	−	13.3981i	0.543811	−	0.543811i	−0.380833	−	0.924644i	$-0.624363\pi$
$607$	13.3981	−	13.3981i	0.543811	−	0.543811i	0.924644	+	0.380833i	$0.124363\pi$
$608$	−2.12488	−	3.80590i	−0.0861754	−	0.154350i
$609$	4.23424	+	5.82792i	0.171580	+	0.236159i
$610$	2.02994	−	0.745792i	0.0821900	−	0.0301962i
$611$	1.25109	−	1.72197i	0.0506135	−	0.0696635i
$612$	−10.6232	−	1.68255i	−0.429418	−	0.0680131i
$613$	−1.68138	+	10.6158i	−0.0679104	+	0.428770i	0.930186	+	0.367090i	$0.119646\pi$
$613$	−1.68138	+	10.6158i	−0.0679104	+	0.428770i	−0.998096	+	0.0616799i	$0.980354\pi$
$614$	−13.5522	+	18.6530i	−0.546923	+	0.752775i
$615$	10.3879	−	15.5015i	0.418880	−	0.625080i
$616$	4.94120	+	6.80097i	0.199086	+	0.274019i
$617$	2.94860	−	1.50239i	0.118706	−	0.0604839i	−0.393629	−	0.919269i	$-0.628781\pi$
$617$	2.94860	−	1.50239i	0.118706	−	0.0604839i	0.512335	+	0.858786i	$0.328781\pi$
$618$	−7.69882	−	7.69882i	−0.309692	−	0.309692i
$619$	6.22057	+	2.02119i	0.250026	+	0.0812383i	0.431349	−	0.902185i	$-0.358038\pi$
$619$	6.22057	+	2.02119i	0.250026	+	0.0812383i	−0.181323	+	0.983424i	$0.558038\pi$
$620$	13.3464	−	14.3992i	0.536004	−	0.578286i
$621$	−14.2659	+	4.63526i	−0.572470	+	0.186007i
$622$	4.64400	+	2.36623i	0.186207	+	0.0948773i
$623$	10.7367	+	67.7889i	0.430157	+	2.71590i
$624$			0.357670i			0.0143183i
$625$	−24.7128	+	3.77824i	−0.988514	+	0.151130i
$626$			9.58340i			0.383030i
$627$	−1.88512	−	9.54222i	−0.0752844	−	0.381079i
$628$	20.0286	+	10.2051i	0.799227	+	0.407227i
$629$	7.18485	+	22.1127i	0.286479	+	0.881691i
$630$	11.7913	+	10.9291i	0.469775	+	0.435427i
$631$	−8.84805	+	27.2315i	−0.352235	+	1.08407i	0.605360	+	0.795952i	$0.293029\pi$
$631$	−8.84805	+	27.2315i	−0.352235	+	1.08407i	−0.957595	+	0.288117i	$0.906971\pi$
$632$	4.02965	+	4.02965i	0.160291	+	0.160291i
$633$	6.48793	+	12.7333i	0.257872	+	0.506102i
$634$	−17.6259	−	24.2599i	−0.700013	−	0.963485i
$635$	−17.1661	+	25.6165i	−0.681218	+	1.01656i
$636$	3.46361	+	2.51646i	0.137341	+	0.0997840i
$637$	0.594181	−	3.75151i	0.0235423	−	0.148640i
$638$	−0.416911	+	2.63227i	−0.0165057	+	0.104213i
$639$	−11.5998	−	8.42775i	−0.458881	−	0.333397i
$640$	−0.771125	−	2.09890i	−0.0304814	−	0.0829662i
$641$	7.89387	+	10.8650i	0.311789	+	0.429141i	0.935938	−	0.352164i	$-0.114554\pi$
$641$	7.89387	+	10.8650i	0.311789	+	0.429141i	−0.624149	+	0.781305i	$0.714554\pi$
$642$	−1.80537	−	3.54324i	−0.0712522	−	0.139840i
$643$	−2.87653	+	2.87653i	−0.113439	+	0.113439i	−0.761548	−	0.648109i	$-0.775560\pi$
$643$	−2.87653	+	2.87653i	−0.113439	+	0.113439i	0.648109	+	0.761548i	$0.275560\pi$
$644$	−11.6041	−	3.77040i	−0.457265	−	0.148574i
$645$	0.177047	+	0.0819079i	0.00697120	+	0.00322512i
$646$	9.91127	+	26.9741i	0.389954	+	1.06128i
$647$	5.13688	−	10.0817i	0.201952	−	0.396353i	−0.767712	−	0.640795i	$-0.778605\pi$
$647$	5.13688	−	10.0817i	0.201952	−	0.396353i	0.969664	+	0.244442i	$0.0786049\pi$
$648$	0.225923	+	1.42642i	0.00887508	+	0.0560350i
$649$	−12.4980			−0.490588
$650$	−0.115848	−	1.52429i	−0.00454393	−	0.0597875i
$651$	−45.2693			−1.77424
$652$	3.02509	+	19.0996i	0.118471	+	0.748000i
$653$	−19.5661	−	9.96943i	−0.765681	−	0.390134i	0.0271061	−	0.999633i	$-0.491371\pi$
$653$	−19.5661	−	9.96943i	−0.765681	−	0.390134i	−0.792787	+	0.609499i	$0.791371\pi$
$654$	−7.13449	−	21.9577i	−0.278980	−	0.858614i
$655$	17.7791	+	31.8471i	0.694688	+	1.24437i
$656$	−6.78427	−	2.20434i	−0.264881	−	0.0860652i
$657$	11.5320	+	11.5320i	0.449908	+	0.449908i
$658$	27.3378	−	13.9293i	1.06574	−	0.543021i
$659$	23.4084	−	17.0072i	0.911862	−	0.662506i	−0.0296233	−	0.999561i	$-0.509431\pi$
$659$	23.4084	−	17.0072i	0.911862	−	0.662506i	0.941485	+	0.337055i	$0.109431\pi$
$660$	−0.189201	−	4.98607i	−0.00736465	−	0.194083i
$661$	10.3581	−	14.2567i	0.402884	−	0.554523i	−0.558581	−	0.829450i	$-0.688654\pi$
$661$	10.3581	−	14.2567i	0.402884	−	0.554523i	0.961465	+	0.274927i	$0.0886538\pi$
$662$	−23.7650	−	3.76401i	−0.923653	−	0.146292i
$663$	0.368880	−	2.32901i	0.0143261	−	0.0904514i
$664$	−13.6991	−	9.95300i	−0.531629	−	0.386251i
$665$	10.1384	−	41.7424i	0.393151	−	1.61870i
$666$	−4.65468	+	3.38182i	−0.180365	+	0.131043i
$667$	−1.75610	−	3.44654i	−0.0679964	−	0.133450i
$668$	−12.3309	−	12.3309i	−0.477097	−	0.477097i
$669$	−24.7311	−	8.03563i	−0.956160	−	0.310675i
$670$	26.9751	+	3.22943i	1.04214	+	0.124764i
$671$	−0.570068	−	1.75449i	−0.0220072	−	0.0677313i
$672$	−2.34069	+	4.59386i	−0.0902940	+	0.177212i
$673$	−4.78832	−	30.2323i	−0.184576	−	1.16537i	−0.889789	−	0.456373i	$-0.849148\pi$
$673$	−4.78832	−	30.2323i	−0.184576	−	1.16537i	0.705212	−	0.708996i	$-0.250852\pi$
$674$		−	8.11380i		−	0.312532i
$675$	−6.25345	−	26.3590i	−0.240695	−	1.01456i
$676$	−12.9065			−0.496405
$677$	3.32411	−	0.526487i	0.127756	−	0.0202345i	−0.0922291	−	0.995738i	$-0.529399\pi$
$677$	3.32411	−	0.526487i	0.127756	−	0.0202345i	0.219985	+	0.975503i	$0.429399\pi$
$678$	4.86623	−	9.55052i	0.186886	−	0.366785i
$679$	15.7654	+	48.5209i	0.605020	+	1.86206i
$680$	2.85660	+	14.4625i	0.109546	+	0.554612i
$681$	−1.19733	+	3.68501i	−0.0458819	+	0.141210i
$682$	−11.8425	−	11.8425i	−0.453472	−	0.453472i
$683$	29.9696	−	15.2703i	1.14676	−	0.584301i	0.225879	−	0.974155i	$-0.427474\pi$
$683$	29.9696	−	15.2703i	1.14676	−	0.584301i	0.920877	+	0.389854i	$0.127474\pi$
$684$	−5.59029	+	4.39521i	−0.213750	+	0.168055i
$685$	−23.1514	+	18.2008i	−0.884570	+	0.695416i
$686$	14.0491	−	19.3369i	0.536397	−	0.738287i
$687$	0.264708	−	1.67130i	0.0100992	−	0.0637640i
$688$	0.0116658	−	0.0736550i	0.000444755	−	0.00280807i
$689$	0.657662	−	0.905194i	0.0250549	−	0.0344851i
$690$	4.47588	+	5.69333i	0.170394	+	0.216741i
$691$	−25.2021	+	18.3104i	−0.958734	+	0.696561i	−0.952856	−	0.303422i	$-0.901871\pi$
$691$	−25.2021	+	18.3104i	−0.958734	+	0.696561i	−0.00587736	+	0.999983i	$0.501871\pi$
$692$	5.63378	+	11.0569i	0.214164	+	0.420321i
$693$	9.69761	−	9.69761i	0.368382	−	0.368382i
$694$	8.23269	−	25.3376i	0.312509	−	0.961803i
$695$	4.13979	+	20.9591i	0.157031	+	0.795024i
$696$	−1.55454	+	0.505099i	−0.0589245	+	0.0191457i
$697$	41.9032	+	21.3508i	1.58720	+	0.808717i
$698$	−2.21193	−	13.9656i	−0.0837230	−	0.528606i
$699$	6.96523			0.263449
$700$	8.48742	−	20.3359i	0.320794	−	0.768624i
$701$	−10.9437			−0.413339			−0.206669	−	0.978411i	$-0.566262\pi$
$701$	−10.9437			−0.413339			−0.206669	+	0.978411i	$0.566262\pi$
$702$	1.63613	−	0.259137i	0.0617516	−	0.00978050i
$703$	13.9520	+	6.45404i	0.526208	+	0.243419i
$704$	−1.81409	+	0.589432i	−0.0683709	+	0.0222151i
$705$	−18.0822	−	2.16478i	−0.681014	−	0.0815303i
$706$	−16.1550	−	5.24909i	−0.608002	−	0.197552i
$707$	26.0923	+	26.0923i	0.981304	+	0.981304i
$708$	−3.47992	−	6.82973i	−0.130783	−	0.256677i
$709$	19.0556	+	26.2278i	0.715649	+	0.985007i	0.999657	+	0.0261847i	$0.00833579\pi$
$709$	19.0556	+	26.2278i	0.715649	+	0.985007i	−0.284008	+	0.958822i	$0.591664\pi$
$710$	−5.35979	+	18.9072i	−0.201149	+	0.709575i
$711$	5.46471	−	7.52153i	0.204943	−	0.282079i
$712$	−15.3814	−	2.43618i	−0.576443	−	0.0912996i
$713$	24.0087	+	3.80261i	0.899134	+	0.142409i
$714$	19.9795	−	27.4995i	0.747715	−	1.02914i
$715$	−1.30308	+	0.0494467i	−0.0487325	+	0.00184920i
$716$	−14.9908	−	20.6331i	−0.560233	−	0.771095i
$717$	3.59126	+	7.04824i	0.134118	+	0.263221i
$718$	−3.80491	−	3.80491i	−0.141998	−	0.141998i
$719$	−50.0441	−	16.2603i	−1.86633	−	0.606408i	−0.992822	−	0.119600i	$-0.961839\pi$
$719$	−50.0441	−	16.2603i	−1.86633	−	0.606408i	−0.873509	−	0.486808i	$-0.838161\pi$
$720$	−3.18523	+	1.77820i	−0.118706	+	0.0662697i
$721$	−39.0097	+	12.6750i	−1.45280	+	0.472042i
$722$	17.5347	+	7.31679i	0.652573	+	0.272303i
$723$	−1.84098	+	0.291582i	−0.0684666	+	0.0108440i
$724$	10.6879			0.397213
$725$	6.46139	−	2.65610i	0.239970	−	0.0986449i
$726$	8.61214			0.319626
$727$	−4.63107	−	29.2394i	−0.171757	−	1.08443i	−0.911427	−	0.411461i	$-0.865019\pi$
$727$	−4.63107	−	29.2394i	−0.171757	−	1.08443i	0.739670	−	0.672969i	$-0.234981\pi$
$728$	1.20058	+	0.611726i	0.0444964	+	0.0226721i
$729$	20.3255	−	6.60415i	0.752796	−	0.244598i
$730$	9.38562	−	20.2873i	0.347378	−	0.750868i
$731$	−0.151927	+	0.467582i	−0.00561921	+	0.0172942i
$732$	0.800042	−	0.800042i	0.0295704	−	0.0295704i
$733$	−17.3523	−	34.0557i	−0.640921	−	1.25788i	−0.951593	−	0.307360i	$-0.900554\pi$
$733$	−17.3523	−	34.0557i	−0.640921	−	1.25788i	0.310673	−	0.950517i	$-0.399446\pi$
$734$	8.61522	−	6.25932i	0.317993	−	0.231036i
$735$	−30.5046	+	11.2072i	−1.12518	+	0.413385i
$736$	1.62728	−	2.23975i	0.0599822	−	0.0825584i
$737$	3.62537	−	22.8897i	0.133542	−	0.843151i
$738$	−1.82052	+	11.4943i	−0.0670143	+	0.423112i
$739$	28.1797	−	38.7861i	1.03661	−	1.42677i	0.136739	−	0.990607i	$-0.456338\pi$
$739$	28.1797	−	38.7861i	1.03661	−	1.42677i	0.899869	−	0.436161i	$-0.143662\pi$
$740$	6.55100	+	4.38997i	0.240819	+	0.161378i
$741$	−0.963598	−	1.22561i	−0.0353987	−	0.0450237i
$742$	14.3707	−	7.32226i	0.527566	−	0.268808i
$743$	35.2969	+	35.2969i	1.29492	+	1.29492i	0.931707	+	0.363212i	$0.118320\pi$
$743$	35.2969	+	35.2969i	1.29492	+	1.29492i	0.363212	+	0.931707i	$0.381680\pi$
$744$	3.17412	−	9.76895i	0.116369	−	0.358147i
$745$	17.1747	+	15.9190i	0.629234	+	0.583226i
$746$	−10.7409	−	33.0571i	−0.393252	−	1.21030i
$747$	−12.5415	+	24.6140i	−0.458868	+	0.900580i
$748$	12.4205	−	1.96722i	0.454140	−	0.0719287i
$749$	−14.9812			−0.547401
$750$	−10.9043	+	7.22271i	−0.398170	+	0.263736i
$751$			37.8452i			1.38099i	0.723336	+	0.690496i	$0.242608\pi$
$751$			37.8452i			1.38099i	−0.723336	+	0.690496i	$0.757392\pi$
$752$	1.08906	+	6.87607i	0.0397140	+	0.250745i
$753$	13.6445	−	26.7788i	0.497232	−	0.975872i
$754$	0.132005	+	0.406269i	0.00480733	+	0.0147954i
$755$	−1.90799	−	1.76848i	−0.0694387	−	0.0643616i
$756$	22.7100	+	7.37893i	0.825956	+	0.268369i
$757$	−5.95423	−	5.95423i	−0.216410	−	0.216410i	0.590574	−	0.806984i	$-0.298902\pi$
$757$	−5.95423	−	5.95423i	−0.216410	−	0.216410i	−0.806984	+	0.590574i	$0.798902\pi$
$758$	6.28764	+	12.3402i	0.228377	+	0.448215i
$759$	4.99789	−	3.63118i	0.181412	−	0.131803i
$760$	8.29700	+	5.11467i	0.300964	+	0.185529i
$761$	17.8659	+	12.9803i	0.647639	+	0.470537i	0.862466	−	0.506115i	$-0.168919\pi$
$761$	17.8659	+	12.9803i	0.647639	+	0.470537i	−0.214827	+	0.976652i	$0.568919\pi$
$762$	−2.52374	+	15.9343i	−0.0914256	+	0.577238i
$763$	−85.9068	−	13.6063i	−3.11003	−	0.492581i
$764$	2.03559	−	2.80175i	0.0736450	−	0.101364i
$765$	22.5749	−	8.29393i	0.816199	−	0.299868i
$766$	1.11381	−	0.809230i	0.0402436	−	0.0292387i
$767$	−1.78491	+	0.909457i	−0.0644494	+	0.0328386i
$768$	−0.827218	−	0.827218i	−0.0298497	−	0.0298497i
$769$	45.7958	+	14.8800i	1.65144	+	0.536585i	0.979051	−	0.203614i	$-0.0652688\pi$
$769$	45.7958	+	14.8800i	1.65144	+	0.536585i	0.672388	+	0.740199i	$0.265269\pi$
$770$	−17.0602	−	7.89263i	−0.614806	−	0.284431i
$771$	6.94540	+	21.3757i	0.250132	+	0.769828i
$772$	−13.5264	−	6.89207i	−0.486827	−	0.248051i
$773$	−2.82779	−	17.8540i	−0.101709	−	0.642162i	−0.984897	−	0.173143i	$-0.944608\pi$
$773$	−2.82779	−	17.8540i	−0.101709	−	0.642162i	0.883188	−	0.469019i	$-0.155392\pi$
$774$	−0.121660			−0.00437299
$775$	−10.3631	+	42.6606i	−0.372253	+	1.53241i
$776$	−11.5760			−0.415556
$777$	−2.84443	−	17.9590i	−0.102043	−	0.644277i
$778$	3.32465	−	6.52499i	0.119194	−	0.233932i
$779$	29.1860	−	10.7240i	1.04570	−	0.384227i
$780$	−0.389850	−	0.698324i	−0.0139589	−	0.0250040i
$781$	15.9435	+	5.18037i	0.570504	+	0.185368i
$782$	−12.9062	+	12.9062i	−0.461523	+	0.461523i
$783$	3.43681	+	6.74512i	0.122822	+	0.241051i
$784$	7.30226	+	10.0507i	0.260795	+	0.358954i
$785$	−50.2275	+	1.90593i	−1.79270	+	0.0680255i
$786$	15.4379	+	11.2163i	0.550652	+	0.400072i
$787$	−0.323072	+	2.03980i	−0.0115163	+	0.0727109i	−0.992777	−	0.119973i	$-0.961719\pi$
$787$	−0.323072	+	2.03980i	−0.0115163	+	0.0727109i	0.981261	+	0.192684i	$0.0617192\pi$
$788$	0.856551	−	5.40805i	0.0305134	−	0.192654i
$789$	−28.4545	−	20.6734i	−1.01301	−	0.735992i
$790$	−12.2598	−	3.47539i	−0.436184	−	0.123649i
$791$	−23.7351	−	32.6686i	−0.843925	−	1.16156i
$792$	1.41275	+	2.77267i	0.0501998	+	0.0985226i
$793$	−0.209086	−	0.209086i	−0.00742488	−	0.00742488i
$794$	2.68966	−	8.27791i	0.0954524	−	0.293772i
$795$	−9.50530	−	1.13796i	−0.337118	−	0.0403594i
$796$	2.21398	+	6.81393i	0.0784725	+	0.241513i
$797$	43.2623	+	22.0432i	1.53243	+	0.780812i	0.997927	−	0.0643557i	$-0.0204992\pi$
$797$	43.2623	+	22.0432i	1.53243	+	0.780812i	0.534502	+	0.845167i	$0.320499\pi$
$798$	−4.35562	−	22.0475i	−0.154187	−	0.780474i
$799$		−	45.8976i		−	1.62374i
$800$	3.79330	+	3.25743i	0.134113	+	0.115168i
$801$			25.4064i			0.897690i
$802$	−2.34966	−	14.8351i	−0.0829692	−	0.523847i
$803$	−16.9898	−	8.65671i	−0.599555	−	0.305489i
$804$	13.5179	−	4.39223i	0.476740	−	0.154902i
$805$	26.7657	−	5.28670i	0.943369	−	0.186332i
$806$	−2.55306	−	0.829539i	−0.0899276	−	0.0292193i
$807$	9.76886	+	9.76886i	0.343880	+	0.343880i
$808$	−7.46014	+	3.80113i	−0.262447	+	0.133723i
$809$	1.18720	+	1.63404i	0.0417398	+	0.0574499i	0.829377	−	0.558690i	$-0.188696\pi$
$809$	1.18720	+	1.63404i	0.0417398	+	0.0574499i	−0.787637	+	0.616140i	$0.788696\pi$
$810$	−1.99585	−	2.53873i	−0.0701271	−	0.0892018i
$811$	−18.0560	+	24.8520i	−0.634033	+	0.872671i	−0.998280	−	0.0586310i	$-0.981326\pi$
$811$	−18.0560	+	24.8520i	−0.634033	+	0.872671i	0.364247	+	0.931302i	$0.381326\pi$
$812$	−0.963283	+	6.08193i	−0.0338046	+	0.213434i
$813$	14.4578	+	2.28989i	0.507057	+	0.0803100i
$814$	3.95399	−	5.44221i	0.138587	−	0.190749i
$815$	−26.7243	−	33.9934i	−0.936111	−	1.19074i
$816$	4.53339	+	6.23967i	0.158700	+	0.218432i
$817$	0.158459	+	0.283818i	0.00554379	+	0.00992953i
$818$	−14.2269	+	14.2269i	−0.497433	+	0.497433i
$819$	0.679295	−	2.09066i	0.0237365	−	0.0730534i
$820$	15.6485	−	3.09084i	0.546468	−	0.107937i
$821$	−8.59598	−	26.4557i	−0.300002	−	0.923310i	−0.981495	−	0.191486i	$-0.938669\pi$
$821$	−8.59598	−	26.4557i	−0.300002	−	0.923310i	0.681494	−	0.731824i	$-0.261331\pi$
$822$	−6.99472	+	13.7279i	−0.243969	+	0.478816i
$823$	−8.99669	+	1.42494i	−0.313605	+	0.0496701i	−0.311253	−	0.950327i	$-0.600749\pi$
$823$	−8.99669	+	1.42494i	−0.313605	+	0.0496701i	−0.00235196	+	0.999997i	$0.500749\pi$
$824$		−	9.30688i		−	0.324221i
$825$	5.80408	+	9.52871i	0.202072	+	0.331747i
$826$	−28.8768			−1.00475
$827$	−16.3156	+	2.58413i	−0.567348	+	0.0898591i	−0.433518	−	0.901145i	$-0.642728\pi$
$827$	−16.3156	+	2.58413i	−0.567348	+	0.0898591i	−0.133831	+	0.991004i	$0.542728\pi$
$828$	−4.02429	−	2.05048i	−0.139854	−	0.0712591i
$829$	1.68633	+	5.18999i	0.0585686	+	0.180256i	0.976061	−	0.217498i	$-0.0697897\pi$
$829$	1.68633	+	5.18999i	0.0585686	+	0.180256i	−0.917492	+	0.397754i	$0.869790\pi$
$830$	37.5950	+	4.50084i	1.30494	+	0.156226i
$831$	−8.85923	−	2.87854i	−0.307323	−	0.0998554i
$832$	−0.216189	+	0.216189i	−0.00749499	+	0.00749499i
$833$	−37.1839	−	72.9775i	−1.28835	−	2.52852i
$834$	6.56980	+	9.04255i	0.227493	+	0.313118i
$835$	37.5155	+	10.6348i	1.29828	+	0.368034i
$836$	4.62822	−	6.90709i	0.160070	−	0.238887i
$837$	−46.9868	−	7.44197i	−1.62410	−	0.257232i
$838$	15.0177	+	2.37857i	0.518779	+	0.0821664i
$839$	28.3143	+	20.5715i	0.977517	+	0.710208i	0.957152	−	0.289585i	$-0.0935172\pi$
$839$	28.3143	+	20.5715i	0.977517	+	0.710208i	0.0203649	+	0.999793i	$0.493517\pi$
$840$	−0.437154	−	11.5205i	−0.0150833	−	0.397493i
$841$	21.8822	−	15.8983i	0.754557	−	0.548218i
$842$	20.0717	−	10.2270i	0.691715	−	0.352447i
$843$	18.2364	−	18.2364i	0.628097	−	0.628097i
$844$	−3.77491	+	11.6180i	−0.129938	+	0.399907i
$845$	25.1990	−	14.0677i	0.866873	−	0.483945i
$846$	10.8017	−	3.50969i	0.371371	−	0.120666i
$847$	14.7294	−	28.9081i	0.506108	−	0.993293i
$848$	0.572491	+	3.61456i	0.0196594	+	0.124125i
$849$	−13.6848			−0.469661
$850$	−21.3410	−	25.1234i	−0.731991	−	0.861725i
$851$			9.76357i			0.334691i
$852$	1.60840	+	10.1550i	0.0551029	+	0.347906i
$853$	13.5183	+	6.88790i	0.462857	+	0.235837i	0.669838	−	0.742508i	$-0.266364\pi$
$853$	13.5183	+	6.88790i	0.462857	+	0.235837i	−0.206981	+	0.978345i	$0.566364\pi$
$854$	−1.31716	−	4.05379i	−0.0450722	−	0.138718i
$855$	6.12397	−	14.6746i	0.209435	−	0.501860i
$856$	1.05043	−	3.23289i	0.0359029	−	0.110498i
$857$	−12.3429	+	12.3429i	−0.421626	+	0.421626i	−0.885763	−	0.464137i	$-0.846364\pi$
$857$	−12.3429	+	12.3429i	−0.421626	+	0.421626i	0.464137	+	0.885763i	$0.346364\pi$
$858$	−0.607876	+	0.309728i	−0.0207525	+	0.0105739i
$859$	1.51905	+	2.09080i	0.0518295	+	0.0713372i	0.834145	−	0.551545i	$-0.185962\pi$
$859$	1.51905	+	2.09080i	0.0518295	+	0.0713372i	−0.782316	+	0.622882i	$0.785962\pi$
$860$	0.0575052	+	0.156521i	0.00196091	+	0.00533733i
$861$	−29.7544	−	21.6179i	−1.01403	−	0.736735i
$862$	7.20447	+	1.14108i	0.245385	+	0.0388652i
$863$	21.8029	+	3.45324i	0.742178	+	0.117549i	0.516062	−	0.856551i	$-0.327397\pi$
$863$	21.8029	+	3.45324i	0.742178	+	0.117549i	0.226116	+	0.974100i	$0.427397\pi$
$864$	−3.18470	+	4.38336i	−0.108346	+	0.149125i
$865$	−23.0512	−	15.4471i	−0.783766	−	0.525218i
$866$	14.0624	−	10.2170i	0.477861	−	0.347186i
$867$	−14.0557	−	27.5858i	−0.477356	−	0.936864i
$868$	−27.3624	−	27.3624i	−0.928739	−	0.928739i
$869$	−3.35905	+	10.3381i	−0.113948	+	0.350695i
$870$	2.48457	−	2.68057i	0.0842348	−	0.0908797i
$871$	−1.14788	−	3.53283i	−0.0388946	−	0.119705i
$872$	8.95967	−	17.5844i	0.303413	−	0.595481i
$873$	2.95433	+	18.6529i	0.0999889	+	0.631305i
$874$	0.458030	+	12.0589i	0.0154931	+	0.407897i
$875$	5.59445	+	48.9553i	0.189127	+	1.65499i
$876$		−	11.6947i		−	0.395128i
$877$	7.45359	−	1.18053i	0.251690	−	0.0398637i	−0.0293146	−	0.999570i	$-0.509332\pi$
$877$	7.45359	−	1.18053i	0.251690	−	0.0398637i	0.281004	+	0.959706i	$0.409332\pi$
$878$	−3.73118	−	1.90113i	−0.125921	−	0.0641601i
$879$	10.7592	−	3.49588i	0.362899	−	0.117913i
$880$	2.89940	−	3.12812i	0.0977388	−	0.105449i
$881$	−2.91462	+	8.97028i	−0.0981960	+	0.302216i	−0.988073	−	0.153983i	$-0.950790\pi$
$881$	−2.91462	+	8.97028i	−0.0981960	+	0.302216i	0.889877	+	0.456200i	$0.150790\pi$
$882$	14.3314	−	14.3314i	0.482565	−	0.482565i
$883$	−4.82283	−	9.46534i	−0.162301	−	0.318534i	0.795506	−	0.605946i	$-0.207205\pi$
$883$	−4.82283	−	9.46534i	−0.162301	−	0.318534i	−0.957807	+	0.287412i	$0.907205\pi$
$884$	1.63070	−	1.18478i	0.0548465	−	0.0398483i
$885$	14.2385	+	9.54152i	0.478622	+	0.320735i
$886$	2.13382	−	2.93695i	0.0716871	−	0.0986688i
$887$	2.61378	−	16.5027i	0.0877621	−	0.554108i	−0.904153	−	0.427208i	$-0.859497\pi$
$887$	2.61378	−	16.5027i	0.0877621	−	0.554108i	0.991916	−	0.126900i	$-0.0405028\pi$
$888$	4.07494	+	0.645406i	0.136746	+	0.0216584i
$889$	49.1697	+	35.7239i	1.64910	+	1.19814i
$890$	32.6864	−	12.0088i	1.09565	−	0.402537i
$891$	−2.22862	+	1.61919i	−0.0746616	+	0.0542448i
$892$	−10.0914	−	19.8054i	−0.337883	−	0.663134i
$893$	−22.2566	−	20.6278i	−0.744790	−	0.690282i
$894$	11.6520	+	3.78595i	0.389700	+	0.126621i
$895$	51.7579	+	23.9450i	1.73008	+	0.800394i
$896$	−4.19149	+	1.36190i	−0.140028	+	0.0454978i
$897$	0.449544	−	0.882280i	0.0150098	−	0.0294585i
$898$	5.28858	−	0.837629i	0.176482	−	0.0279520i
$899$		−	12.2678i		−	0.409153i
$900$	4.28073	−	6.94361i	0.142691	−	0.231454i
$901$		−	24.1271i		−	0.803791i
$902$	−2.12854	−	13.4390i	−0.0708725	−	0.447471i
$903$	0.174553	−	0.342579i	0.00580874	−	0.0114003i
$904$	8.71400	−	2.83135i	0.289823	−	0.0941693i
$905$	−20.8674	+	11.6495i	−0.693654	+	0.387243i
$906$	−1.29445	−	0.420591i	−0.0430051	−	0.0139732i
$907$	−6.03441	+	6.03441i	−0.200369	+	0.200369i	−0.800158	−	0.599789i	$-0.795251\pi$
$907$	−6.03441	+	6.03441i	−0.200369	+	0.200369i	0.599789	+	0.800158i	$0.295251\pi$
$908$	−2.95106	+	1.50364i	−0.0979344	+	0.0499001i
$909$	8.02880	+	11.0507i	0.266299	+	0.366529i
$910$	−3.01080	+	0.114248i	−0.0998072	+	0.00378728i
$911$	−10.0027	+	13.7676i	−0.331405	+	0.456140i	−0.941906	−	0.335875i	$-0.890968\pi$
$911$	−10.0027	+	13.7676i	−0.331405	+	0.456140i	0.610502	+	0.792015i	$0.290968\pi$
$912$	5.06318	+	0.605970i	0.167659	+	0.0200657i
$913$	5.05265	−	31.9012i	0.167218	−	1.05577i
$914$	−4.74870	−	3.45014i	−0.157073	−	0.114120i
$915$	−0.690000	+	2.43405i	−0.0228107	+	0.0804671i
$916$	1.17019	−	0.850193i	0.0386642	−	0.0280912i
$917$	64.0529	−	32.6366i	2.11521	−	1.07775i
$918$	25.2583	−	25.2583i	0.833647	−	0.833647i
$919$	−29.6404	−	9.63075i	−0.977746	−	0.317689i	−0.223807	−	0.974633i	$-0.571849\pi$
$919$	−29.6404	−	9.63075i	−0.977746	−	0.317689i	−0.753939	+	0.656944i	$0.771849\pi$
$920$	−0.735869	+	6.14664i	−0.0242609	+	0.202649i
$921$	−8.33506	−	25.6527i	−0.274650	−	0.845284i
$922$	0.478386	+	0.243750i	0.0157548	+	0.00802748i
$923$	2.65396	−	0.420346i	0.0873562	−	0.0138359i
$924$	−9.83441			−0.323528
$925$	−17.5753	−	1.43068i	−0.577871	−	0.0470406i
$926$		−	3.59732i		−	0.118215i
$927$	−14.9965	+	2.37521i	−0.492550	+	0.0780123i
$928$	−1.24492	−	0.634317i	−0.0408664	−	0.0208225i
$929$	14.7431	−	4.79032i	0.483705	−	0.157165i	−0.0570057	−	0.998374i	$-0.518155\pi$
$929$	14.7431	−	4.79032i	0.483705	−	0.157165i	0.540711	+	0.841209i	$0.318155\pi$
$930$	4.45063	+	22.5328i	0.145942	+	0.738881i
$931$	−52.0998	−	14.7671i	−1.70750	−	0.483972i
$932$	4.21004	+	4.21004i	0.137904	+	0.137904i
$933$	−5.43284	+	2.76817i	−0.177863	+	0.0906258i
$934$	−24.7091	+	17.9522i	−0.808505	+	0.587413i
$935$	−22.1060	+	17.3789i	−0.722943	+	0.568350i
$936$	0.403526	+	0.293179i	0.0131897	+	0.00958285i
$937$	−48.7042	−	7.71398i	−1.59110	−	0.252005i	−0.702838	−	0.711350i	$-0.748084\pi$
$937$	−48.7042	−	7.71398i	−1.59110	−	0.252005i	−0.888258	+	0.459345i	$0.848084\pi$
$938$	8.37650	−	52.8871i	0.273502	−	1.72683i
$939$	−9.07010	−	6.58982i	−0.295992	−	0.215051i
$940$	−9.62103	−	12.2380i	−0.313804	−	0.399159i
$941$	23.3424	+	32.1280i	0.760939	+	1.04734i	0.997135	+	0.0756376i	$0.0240992\pi$
$941$	23.3424	+	32.1280i	0.760939	+	1.04734i	−0.236196	+	0.971705i	$0.575901\pi$
$942$	−23.4307	+	11.9385i	−0.763413	+	0.388978i
$943$	13.9645	+	13.9645i	0.454746	+	0.454746i
$944$	2.02474	−	6.23152i	0.0658998	−	0.202819i
$945$	−52.3824	+	10.3464i	−1.70400	+	0.336570i
$946$	0.135282	−	0.0439558i	0.00439840	−	0.00142913i
$947$	−5.16100	+	10.1290i	−0.167710	+	0.329149i	−0.959531	−	0.281605i	$-0.909133\pi$
$947$	−5.16100	+	10.1290i	−0.167710	+	0.329149i	0.791821	+	0.610754i	$0.209133\pi$
$948$	−6.58472	+	1.04292i	−0.213862	+	0.0338724i
$949$	−3.05635			−0.0992132
$950$	−21.7741	−	0.942527i	−0.706445	−	0.0305796i
$951$	35.0806			1.13757
$952$	28.6980	−	4.54531i	0.930107	−	0.147314i
$953$	−7.99579	+	15.6926i	−0.259009	+	0.508334i	−0.983490	−	0.180961i	$-0.942079\pi$
$953$	−7.99579	+	15.6926i	−0.259009	+	0.508334i	0.724481	+	0.689294i	$0.242079\pi$
$954$	5.67817	−	1.84495i	0.183838	−	0.0597325i
$955$	−0.920512	+	7.68894i	−0.0297871	+	0.248808i
$956$	−2.08952	+	6.43089i	−0.0675800	+	0.207990i
$957$	−2.20460	−	2.20460i	−0.0712647	−	0.0712647i
$958$	7.70064	−	3.92367i	0.248796	−	0.126768i
$959$	34.1169	+	46.9579i	1.10169	+	1.51635i
$960$	2.51672	+	0.713438i	0.0812269	+	0.0230261i
$961$	37.2897	+	27.0926i	1.20289	+	0.873954i
$962$	0.168673	−	1.06496i	0.00543824	−	0.0343357i
$963$	−5.47735	−	0.867527i	−0.176505	−	0.0279557i
$964$	−1.28899	−	0.936509i	−0.0415157	−	0.0301629i
$965$	33.9215	−	1.28718i	1.09197	−	0.0414359i
$966$	11.5477	−	8.38993i	0.371543	−	0.269942i
$967$	−9.96019	+	5.07497i	−0.320298	+	0.163200i	−0.606746	−	0.794896i	$-0.707525\pi$
$967$	−9.96019	+	5.07497i	−0.320298	+	0.163200i	0.286448	+	0.958096i	$0.407525\pi$
$968$	5.20548	+	5.20548i	0.167311	+	0.167311i
$969$	−32.3446	−	9.16771i	−1.03906	−	0.294509i
$970$	22.6014	−	12.6176i	0.725686	−	0.405125i
$971$	18.8979	−	6.14030i	0.606463	−	0.197052i	0.0103420	−	0.999947i	$-0.496708\pi$
$971$	18.8979	−	6.14030i	0.606463	−	0.197052i	0.596121	+	0.802895i	$0.296708\pi$
$972$	12.9774	+	6.61231i	0.416250	+	0.212090i
$973$	41.5892	−	6.58708i	1.33329	−	0.211172i
$974$			16.2565i			0.520892i
$975$	1.52231	+	0.938500i	0.0487528	+	0.0300561i
$976$	0.967148			0.0309577
$977$	−18.9691	+	3.00442i	−0.606877	+	0.0961198i	−0.452307	−	0.891862i	$-0.649399\pi$
$977$	−18.9691	+	3.00442i	−0.606877	+	0.0961198i	−0.154569	+	0.987982i	$0.549399\pi$
$978$	−20.1568	−	10.2704i	−0.644542	−	0.328411i
$979$	−9.17931	−	28.2510i	−0.293372	−	0.902906i
$980$	−25.2121	−	11.6640i	−0.805371	−	0.372593i
$981$	−30.6209	−	9.94933i	−0.977650	−	0.317658i
$982$	3.48847	−	3.48847i	0.111322	−	0.111322i
$983$	−39.3268	+	20.0380i	−1.25433	+	0.639114i	−0.949642	−	0.313338i	$-0.898553\pi$
$983$	−39.3268	+	20.0380i	−1.25433	+	0.639114i	−0.304689	+	0.952452i	$0.598553\pi$
$984$	6.75133	−	4.90513i	0.215225	−	0.156370i
$985$	4.22227	+	11.4924i	0.134533	+	0.366179i
$986$	7.45223	+	5.41436i	0.237327	+	0.172428i
$987$	−5.61500	+	35.4517i	−0.178728	+	1.12844i
$988$	0.158367	−	1.32323i	0.00503831	−	0.0420977i
$989$	−0.121351	+	0.167025i	−0.00385874	+	0.00531110i
$990$	−5.78041	−	3.87358i	−0.183714	−	0.123110i
$991$	−34.9336	−	48.0819i	−1.10970	−	1.52737i	−0.821855	−	0.569696i	$-0.807061\pi$
$991$	−34.9336	−	48.0819i	−1.10970	−	1.52737i	−0.287846	−	0.957677i	$-0.592939\pi$
$992$	7.82325	−	3.98615i	0.248389	−	0.126560i
$993$	19.9039	−	19.9039i	0.631631	−	0.631631i
$994$	36.8379	+	11.9694i	1.16843	+	0.379645i
$995$	−11.7496	−	10.8905i	−0.372488	−	0.345253i
$996$	18.8398	−	6.12143i	0.596962	−	0.193965i
$997$	−21.0344	+	41.2824i	−0.666167	+	1.30743i	0.272352	+	0.962198i	$0.412198\pi$
$997$	−21.0344	+	41.2824i	−0.666167	+	1.30743i	−0.938519	+	0.345228i	$0.887802\pi$
$998$	0.827133	+	5.22231i	0.0261824	+	0.165309i
$999$		−	19.1080i		−	0.604550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.37.17	✓	400
19.18	odd	2	inner	950.2.w.a.37.34	yes	400
25.23	odd	20	inner	950.2.w.a.873.34	yes	400
475.398	even	20	inner	950.2.w.a.873.17	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.37.17	✓	400	1.1	even	1	trivial
950.2.w.a.37.34	yes	400	19.18	odd	2	inner
950.2.w.a.873.17	yes	400	475.398	even	20	inner
950.2.w.a.873.34	yes	400	25.23	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.531107 - 1.04236i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.52005 + 1.63996i) q^{5} +(-0.361507 + 1.11261i) q^{6} +(3.11636 + 3.11636i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.958925 + 1.31985i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.531107 - 1.04236i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.52005 + 1.63996i) q^{5} +(-0.361507 + 1.11261i) q^{6} +(3.11636 + 3.11636i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.958925 + 1.31985i) q^{9} +(1.24479 - 1.85755i) q^{10} +(-1.54315 - 1.12117i) q^{11} +(0.183007 - 1.15546i) q^{12} +(-0.301973 - 0.0478278i) q^{13} +(-3.56549 - 2.59048i) q^{14} +(0.902110 + 2.45542i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-5.87422 + 2.99307i) q^{17} +(-1.15359 - 1.15359i) q^{18} +(-1.18866 + 4.19370i) q^{19} +(-0.938876 + 2.02941i) q^{20} +(4.90347 - 1.59323i) q^{21} +(1.69954 + 0.865961i) q^{22} +(-2.73440 + 0.433087i) q^{23} +1.16986i q^{24} +(-0.378914 - 4.98562i) q^{25} +0.305737 q^{26} +(5.35142 - 0.847582i) q^{27} +(3.92684 + 2.00082i) q^{28} +(0.431759 + 1.32882i) q^{29} +(-1.27512 - 2.28407i) q^{30} +(-8.35051 - 2.71324i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.98823 + 1.01305i) q^{33} +(5.33368 - 3.87515i) q^{34} +(-9.84770 + 0.373680i) q^{35} +(1.31985 + 0.958925i) q^{36} +(0.551694 - 3.48326i) q^{37} +(0.517984 - 4.32801i) q^{38} +(-0.210233 + 0.289361i) q^{39} +(0.609847 - 2.15130i) q^{40} +(-4.19291 - 5.77105i) q^{41} +(-4.59386 + 2.34069i) q^{42} +(0.0527312 - 0.0527312i) q^{43} +(-1.81409 - 0.589432i) q^{44} +(-3.62210 - 0.433635i) q^{45} +(2.63299 - 0.855510i) q^{46} +(-3.16058 + 6.20300i) q^{47} +(-0.183007 - 1.15546i) q^{48} +12.4234i q^{49} +(1.15417 + 4.86497i) q^{50} +7.71266i q^{51} +(-0.301973 + 0.0478278i) q^{52} +(-1.66143 + 3.26075i) q^{53} +(-5.15294 + 1.67429i) q^{54} +(4.18433 - 0.826478i) q^{55} +(-4.19149 - 1.36190i) q^{56} +(3.74002 + 3.46630i) q^{57} +(-0.634317 - 1.24492i) q^{58} +(5.30085 - 3.85129i) q^{59} +(1.61672 + 2.05648i) q^{60} +(0.782439 + 0.568476i) q^{61} +(8.67214 + 1.37353i) q^{62} +(-1.12476 + 7.10147i) q^{63} +(0.587785 - 0.809017i) q^{64} +(0.537448 - 0.422522i) q^{65} +(1.80528 - 1.31161i) q^{66} +(5.51588 + 10.8255i) q^{67} +(-4.66181 + 4.66181i) q^{68} +(-1.00083 + 3.08024i) q^{69} +(9.66800 - 1.90960i) q^{70} +(-8.35859 + 2.71587i) q^{71} +(-1.45361 - 0.740650i) q^{72} +(9.87358 - 1.56382i) q^{73} +3.52668i q^{74} +(-5.39803 - 2.25293i) q^{75} +(0.165444 + 4.35576i) q^{76} +(-1.31506 - 8.30297i) q^{77} +(0.162379 - 0.318686i) q^{78} +(-1.76102 - 5.41987i) q^{79} +(-0.265802 + 2.22021i) q^{80} +(0.446282 - 1.37352i) q^{81} +(5.04408 + 5.04408i) q^{82} +(7.68745 + 15.0875i) q^{83} +(4.17114 - 3.03051i) q^{84} +(4.02060 - 14.1831i) q^{85} +(-0.0438330 + 0.0603309i) q^{86} +(1.61441 + 0.255698i) q^{87} +(1.88396 + 0.298390i) q^{88} +(12.5989 + 9.15367i) q^{89} +(3.64535 - 0.138326i) q^{90} +(-0.792006 - 1.09010i) q^{91} +(-2.46674 + 1.25687i) q^{92} +(-7.26317 + 7.26317i) q^{93} +(2.15131 - 6.62105i) q^{94} +(-5.07067 - 8.32396i) q^{95} +(0.361507 + 1.11261i) q^{96} +(10.3143 + 5.25542i) q^{97} +(-1.94344 - 12.2704i) q^{98} -3.11184i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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