LMFDB - Embedded newform 798.2.cc.b.317.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			317.17
Character	$\chi$	$=$	798.317
Dual form			798.2.cc.b.725.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(0.687834 - 1.58962i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.890265 - 2.44598i) q^{5} +(-1.68491 - 0.401350i) q^{6} +(-2.59902 - 0.495088i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.05377 - 2.18679i) q^{9} +(-2.56342 - 0.452000i) q^{10} +(-0.968132 - 0.558951i) q^{11} +(-0.102672 + 1.72901i) q^{12} +(-0.376322 - 1.03393i) q^{13} +(-0.0362518 + 2.64550i) q^{14} +(-3.27582 - 3.09761i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.469922 + 1.29110i) q^{17} +(-1.79693 + 2.40230i) q^{18} +(-1.32697 + 4.15200i) q^{19} +2.60296i q^{20} +(-2.57469 + 3.79090i) q^{21} +(-0.382345 + 1.05049i) q^{22} +(1.94234 - 2.31479i) q^{23} +(1.72057 - 0.199127i) q^{24} +(-1.36004 - 1.14121i) q^{25} +(-0.952880 + 0.550145i) q^{26} +(-4.88881 + 1.76056i) q^{27} +(2.61161 - 0.423686i) q^{28} +(3.58761 + 3.01036i) q^{29} +(-2.48171 + 3.76395i) q^{30} -7.98280i q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.55443 + 1.15449i) q^{33} +(1.35309 + 0.238586i) q^{34} +(-3.52479 + 5.91639i) q^{35} +(2.67784 + 1.35248i) q^{36} +(-4.01120 - 2.31587i) q^{37} +(4.31935 + 0.585824i) q^{38} +(-1.90241 - 0.112969i) q^{39} +(2.56342 - 0.452000i) q^{40} +(-2.98936 - 1.08804i) q^{41} +(4.18040 + 1.87729i) q^{42} +(0.593141 + 3.36387i) q^{43} +(1.10092 + 0.194122i) q^{44} +(-7.17725 + 3.07666i) q^{45} +(-2.61691 - 1.51087i) q^{46} +(-3.38692 - 9.30550i) q^{47} +(-0.494875 - 1.65985i) q^{48} +(6.50978 + 2.57348i) q^{49} +(-0.887706 + 1.53755i) q^{50} +(1.72913 + 1.63506i) q^{51} +(0.707253 + 0.842871i) q^{52} +(5.40713 - 1.96804i) q^{53} +(2.58274 + 4.50882i) q^{54} +(-2.22908 + 1.87042i) q^{55} +(-0.870750 - 2.49836i) q^{56} +(5.68736 + 4.96527i) q^{57} +(2.34165 - 4.05585i) q^{58} +(-1.60078 - 0.582635i) q^{59} +(4.13771 + 1.79041i) q^{60} +(3.23637 + 2.71564i) q^{61} +(-7.86152 + 1.38620i) q^{62} +(4.25512 + 6.70029i) q^{63} +(-0.500000 + 0.866025i) q^{64} -2.86401 q^{65} +(1.40688 + 1.33034i) q^{66} +(1.15342 + 0.203379i) q^{67} -1.37396i q^{68} +(-2.34362 - 4.67977i) q^{69} +(6.43858 + 2.44387i) q^{70} +(-0.436878 - 2.47766i) q^{71} +(0.866929 - 2.87201i) q^{72} +(0.846397 + 4.80015i) q^{73} +(-1.58415 + 4.35241i) q^{74} +(-2.74958 + 1.37698i) q^{75} +(-0.173123 - 4.35546i) q^{76} +(2.23946 + 1.93203i) q^{77} +(0.219097 + 1.89312i) q^{78} +(-1.88575 - 2.24736i) q^{79} +(-0.890265 - 2.44598i) q^{80} +(-0.564076 + 8.98231i) q^{81} +(-0.552412 + 3.13288i) q^{82} +(-15.0823 - 8.70774i) q^{83} +(1.12285 - 4.44288i) q^{84} +(2.73966 + 2.29884i) q^{85} +(3.20977 - 1.16826i) q^{86} +(7.25301 - 3.63230i) q^{87} -1.11790i q^{88} +(2.27005 - 12.8741i) q^{89} +(4.27624 + 6.53395i) q^{90} +(0.466177 + 2.87353i) q^{91} +(-1.03350 + 2.83951i) q^{92} +(-12.6896 - 5.49085i) q^{93} +(-8.57599 + 4.95135i) q^{94} +(8.97438 + 6.94214i) q^{95} +(-1.54870 + 0.775586i) q^{96} +(-8.80844 - 10.4975i) q^{97} +(1.40398 - 6.85776i) q^{98} +(0.766011 + 3.26506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	0.687834	−	1.58962i	0.397121	−	0.917766i
$3$	0.687834	−	1.58962i	0.397121	−	0.917766i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.890265	−	2.44598i	0.398139	−	1.09388i	−0.565051	−	0.825056i	$-0.691144\pi$
$5$	0.890265	−	2.44598i	0.398139	−	1.09388i	0.963190	−	0.268822i	$-0.0866342\pi$
$6$	−1.68491	−	0.401350i	−0.687861	−	0.163851i
$7$	−2.59902	−	0.495088i	−0.982336	−	0.187126i
$7$	−2.59902	−	0.495088i	−0.982336	−	0.187126i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.05377	−	2.18679i	−0.684589	−	0.728929i
$10$	−2.56342	−	0.452000i	−0.810624	−	0.142935i
$11$	−0.968132	−	0.558951i	−0.291903	−	0.168530i	0.346897	−	0.937903i	$-0.387235\pi$
$11$	−0.968132	−	0.558951i	−0.291903	−	0.168530i	−0.638800	+	0.769373i	$0.720569\pi$
$12$	−0.102672	+	1.72901i	−0.0296388	+	0.499121i
$13$	−0.376322	−	1.03393i	−0.104373	−	0.286762i	0.876503	−	0.481396i	$-0.159870\pi$
$13$	−0.376322	−	1.03393i	−0.104373	−	0.286762i	−0.980876	+	0.194634i	$0.937648\pi$
$14$	−0.0362518	+	2.64550i	−0.00968871	+	0.707040i
$15$	−3.27582	−	3.09761i	−0.845814	−	0.799800i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.469922	+	1.29110i	−0.113973	+	0.313138i	−0.983544	−	0.180670i	$-0.942173\pi$
$17$	−0.469922	+	1.29110i	−0.113973	+	0.313138i	0.869571	+	0.493808i	$0.164396\pi$
$18$	−1.79693	+	2.40230i	−0.423541	+	0.566227i
$19$	−1.32697	+	4.15200i	−0.304428	+	0.952535i
$19$	−1.32697	+	4.15200i	−0.304428	+	0.952535i
$20$			2.60296i			0.582040i
$21$	−2.57469	+	3.79090i	−0.561844	+	0.827243i
$22$	−0.382345	+	1.05049i	−0.0815163	+	0.223964i
$23$	1.94234	−	2.31479i	0.405006	−	0.482667i	−0.524534	−	0.851390i	$-0.675760\pi$
$23$	1.94234	−	2.31479i	0.405006	−	0.482667i	0.929539	+	0.368723i	$0.120205\pi$
$24$	1.72057	−	0.199127i	0.351209	−	0.0406466i
$25$	−1.36004	−	1.14121i	−0.272009	−	0.228243i
$26$	−0.952880	+	0.550145i	−0.186875	+	0.107892i
$27$	−4.88881	+	1.76056i	−0.940851	+	0.338820i
$28$	2.61161	−	0.423686i	0.493547	−	0.0800691i
$29$	3.58761	+	3.01036i	0.666203	+	0.559011i	0.911939	−	0.410326i	$-0.134585\pi$
$29$	3.58761	+	3.01036i	0.666203	+	0.559011i	−0.245736	+	0.969337i	$0.579030\pi$
$30$	−2.48171	+	3.76395i	−0.453097	+	0.687200i
$31$		−	7.98280i		−	1.43375i	−0.697200	−	0.716877i	$-0.745571\pi$
$31$		−	7.98280i		−	1.43375i	0.697200	−	0.716877i	$-0.254429\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−1.55443	+	1.15449i	−0.270592	+	0.200972i
$34$	1.35309	+	0.238586i	0.232052	+	0.0409171i
$35$	−3.52479	+	5.91639i	−0.595799	+	1.00005i
$36$	2.67784	+	1.35248i	0.446306	+	0.225413i
$37$	−4.01120	−	2.31587i	−0.659438	−	0.380726i	0.132625	−	0.991166i	$-0.457659\pi$
$37$	−4.01120	−	2.31587i	−0.659438	−	0.380726i	−0.792063	+	0.610440i	$0.790993\pi$
$38$	4.31935	+	0.585824i	0.700692	+	0.0950333i
$39$	−1.90241	−	0.112969i	−0.304629	−	0.0180895i
$40$	2.56342	−	0.452000i	0.405312	−	0.0714674i
$41$	−2.98936	−	1.08804i	−0.466860	−	0.169923i	0.0978694	−	0.995199i	$-0.468797\pi$
$41$	−2.98936	−	1.08804i	−0.466860	−	0.169923i	−0.564729	+	0.825276i	$0.691019\pi$
$42$	4.18040	+	1.87729i	0.645050	+	0.289673i
$43$	0.593141	+	3.36387i	0.0904532	+	0.512985i	0.996046	+	0.0888376i	$0.0283152\pi$
$43$	0.593141	+	3.36387i	0.0904532	+	0.512985i	−0.905593	+	0.424148i	$0.860574\pi$
$44$	1.10092	+	0.194122i	0.165970	+	0.0292650i
$45$	−7.17725	+	3.07666i	−1.06992	+	0.458642i
$46$	−2.61691	−	1.51087i	−0.385842	−	0.222766i
$47$	−3.38692	−	9.30550i	−0.494034	−	1.35735i	−0.896959	−	0.442113i	$-0.854229\pi$
$47$	−3.38692	−	9.30550i	−0.494034	−	1.35735i	0.402926	−	0.915233i	$-0.367993\pi$
$48$	−0.494875	−	1.65985i	−0.0714290	−	0.239579i
$49$	6.50978	+	2.57348i	0.929968	+	0.367640i
$50$	−0.887706	+	1.53755i	−0.125541	+	0.217443i
$51$	1.72913	+	1.63506i	0.242126	+	0.228954i
$52$	0.707253	+	0.842871i	0.0980784	+	0.116885i
$53$	5.40713	−	1.96804i	0.742727	−	0.270331i	0.0571850	−	0.998364i	$-0.481788\pi$
$53$	5.40713	−	1.96804i	0.742727	−	0.270331i	0.685542	+	0.728033i	$0.259565\pi$
$54$	2.58274	+	4.50882i	0.351467	+	0.613572i
$55$	−2.22908	+	1.87042i	−0.300569	+	0.252208i
$56$	−0.870750	−	2.49836i	−0.116359	−	0.333857i
$57$	5.68736	+	4.96527i	0.753310	+	0.657666i
$58$	2.34165	−	4.05585i	0.307473	−	0.532559i
$59$	−1.60078	−	0.582635i	−0.208403	−	0.0758526i	0.235709	−	0.971824i	$-0.424259\pi$
$59$	−1.60078	−	0.582635i	−0.208403	−	0.0758526i	−0.444112	+	0.895971i	$0.646481\pi$
$60$	4.13771	+	1.79041i	0.534177	+	0.231141i
$61$	3.23637	+	2.71564i	0.414375	+	0.347702i	0.826018	−	0.563643i	$-0.190601\pi$
$61$	3.23637	+	2.71564i	0.414375	+	0.347702i	−0.411643	+	0.911345i	$0.635045\pi$
$62$	−7.86152	+	1.38620i	−0.998415	+	0.176047i
$63$	4.25512	+	6.70029i	0.536095	+	0.844157i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.86401			−0.355237
$66$	1.40688	+	1.33034i	0.173175	+	0.163754i
$67$	1.15342	+	0.203379i	0.140913	+	0.0248467i	0.243660	−	0.969861i	$-0.421652\pi$
$67$	1.15342	+	0.203379i	0.140913	+	0.0248467i	−0.102747	+	0.994708i	$0.532763\pi$
$68$		−	1.37396i		−	0.166617i
$69$	−2.34362	−	4.67977i	−0.282139	−	0.563378i
$70$	6.43858	+	2.44387i	0.769558	+	0.292098i
$71$	−0.436878	−	2.47766i	−0.0518478	−	0.294044i	0.947848	−	0.318724i	$-0.103254\pi$
$71$	−0.436878	−	2.47766i	−0.0518478	−	0.294044i	−0.999695	+	0.0246804i	$0.992143\pi$
$72$	0.866929	−	2.87201i	0.102169	−	0.338469i
$73$	0.846397	+	4.80015i	0.0990632	+	0.561816i	0.993426	+	0.114474i	$0.0365182\pi$
$73$	0.846397	+	4.80015i	0.0990632	+	0.561816i	−0.894363	+	0.447342i	$0.852371\pi$
$74$	−1.58415	+	4.35241i	−0.184153	+	0.505957i
$75$	−2.74958	+	1.37698i	−0.317494	+	0.159001i
$76$	−0.173123	−	4.35546i	−0.0198586	−	0.499605i
$77$	2.23946	+	1.93203i	0.255210	+	0.220176i
$78$	0.219097	+	1.89312i	0.0248079	+	0.214354i
$79$	−1.88575	−	2.24736i	−0.212164	−	0.252847i	0.649458	−	0.760397i	$-0.274996\pi$
$79$	−1.88575	−	2.24736i	−0.212164	−	0.252847i	−0.861622	+	0.507550i	$0.830551\pi$
$80$	−0.890265	−	2.44598i	−0.0995347	−	0.273469i
$81$	−0.564076	+	8.98231i	−0.0626751	+	0.998034i
$82$	−0.552412	+	3.13288i	−0.0610037	+	0.345969i
$83$	−15.0823	−	8.70774i	−1.65549	−	0.955799i	−0.974757	−	0.223270i	$-0.928327\pi$
$83$	−15.0823	−	8.70774i	−1.65549	−	0.955799i	−0.680736	−	0.732529i	$-0.738340\pi$
$84$	1.12285	−	4.44288i	0.122514	−	0.484758i
$85$	2.73966	+	2.29884i	0.297157	+	0.249345i
$86$	3.20977	−	1.16826i	0.346118	−	0.125977i
$87$	7.25301	−	3.63230i	0.777604	−	0.389423i
$88$		−	1.11790i		−	0.119169i
$89$	2.27005	−	12.8741i	0.240625	−	1.36465i	−0.589812	−	0.807540i	$-0.700798\pi$
$89$	2.27005	−	12.8741i	0.240625	−	1.36465i	0.830437	−	0.557112i	$-0.188091\pi$
$90$	4.27624	+	6.53395i	0.450755	+	0.688739i
$91$	0.466177	+	2.87353i	0.0488687	+	0.301227i
$92$	−1.03350	+	2.83951i	−0.107749	+	0.296039i
$93$	−12.6896	−	5.49085i	−1.31585	−	0.569374i
$94$	−8.57599	+	4.95135i	−0.884546	+	0.510693i
$95$	8.97438	+	6.94214i	0.920752	+	0.712249i
$96$	−1.54870	+	0.775586i	−0.158063	+	0.0791579i
$97$	−8.80844	−	10.4975i	−0.894362	−	1.06586i	−0.997463	−	0.0711883i	$-0.977321\pi$
$97$	−8.80844	−	10.4975i	−0.894362	−	1.06586i	0.103101	−	0.994671i	$-0.467124\pi$
$98$	1.40398	−	6.85776i	0.141823	−	0.692738i
$99$	0.766011	+	3.26506i	0.0769870	+	0.328150i
$100$	1.66834	+	0.607227i	0.166834	+	0.0607227i
$101$	−2.14541	+	2.55680i	−0.213476	+	0.254411i	−0.862147	−	0.506658i	$-0.830881\pi$
$101$	−2.14541	+	2.55680i	−0.213476	+	0.254411i	0.648671	+	0.761069i	$0.275325\pi$
$102$	1.30996	−	1.98678i	0.129705	−	0.196721i
$103$			12.9217i			1.27321i	0.771188	+	0.636607i	$0.219663\pi$
$103$			12.9217i			1.27321i	−0.771188	+	0.636607i	$0.780337\pi$
$104$	0.707253	−	0.842871i	0.0693519	−	0.0826503i
$105$	6.98033	+	9.67257i	0.681211	+	0.943946i
$106$	−2.87708	−	4.98324i	−0.279446	−	0.484015i
$107$	−3.00269	−	5.20081i	−0.290281	−	0.502781i	0.683595	−	0.729861i	$-0.260415\pi$
$107$	−3.00269	−	5.20081i	−0.290281	−	0.502781i	−0.973876	+	0.227080i	$0.927082\pi$
$108$	3.99183	−	3.32645i	0.384114	−	0.320088i
$109$	10.8134	+	12.8869i	1.03574	+	1.23434i	0.971656	+	0.236398i	$0.0759668\pi$
$109$	10.8134	+	12.8869i	1.03574	+	1.23434i	0.0640799	+	0.997945i	$0.479589\pi$
$110$	2.22908	+	1.87042i	0.212535	+	0.178338i
$111$	−6.44039	+	4.78334i	−0.611295	+	0.454015i
$112$	−2.30920	+	1.29136i	−0.218199	+	0.122022i
$113$	6.36375			0.598651			0.299325	−	0.954151i	$-0.403238\pi$
$113$	6.36375			0.598651			0.299325	+	0.954151i	$0.403238\pi$
$114$	3.90224	−	6.46317i	0.365478	−	0.605331i
$115$	−3.93274	−	6.81171i	−0.366730	−	0.635195i
$116$	−4.40086	−	1.60178i	−0.408609	−	0.148722i
$117$	−1.48812	+	2.94640i	−0.137577	+	0.272395i
$118$	−0.295811	+	1.67763i	−0.0272317	+	0.154438i
$119$	1.86054	−	3.12294i	0.170556	−	0.286279i
$120$	1.04470	−	4.38575i	0.0953676	−	0.400363i
$121$	−4.87515	−	8.44400i	−0.443195	−	0.767637i
$122$	2.11239	−	3.65877i	0.191247	−	0.331249i
$123$	−3.78575	+	4.00355i	−0.341350	+	0.360988i
$124$	2.73028	+	7.50138i	0.245186	+	0.673644i
$125$	7.26897	−	4.19674i	0.650156	−	0.375368i
$126$	5.85960	−	5.35397i	0.522015	−	0.476970i
$127$	−0.844346	−	2.31982i	−0.0749236	−	0.205851i	0.896577	−	0.442888i	$-0.146046\pi$
$127$	−0.844346	−	2.31982i	−0.0749236	−	0.205851i	−0.971501	+	0.237037i	$0.923824\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	5.75525	+	1.37092i	0.506722	+	0.120703i
$130$	0.497331	+	2.82050i	0.0436188	+	0.247375i
$131$	5.94250	−	1.04782i	0.519199	−	0.0915488i	0.0920931	−	0.995750i	$-0.470644\pi$
$131$	5.94250	−	1.04782i	0.519199	−	0.0915488i	0.427106	+	0.904202i	$0.359533\pi$
$132$	1.06583	−	1.61652i	0.0927686	−	0.140700i
$133$	5.50443	−	10.1342i	0.477295	−	0.878743i
$134$		−	1.17121i		−	0.101177i
$135$	−0.0460396	+	13.5253i	−0.00396246	+	1.16407i
$136$	−1.35309	+	0.238586i	−0.116026	+	0.0204586i
$137$	0.0979446	+	0.269101i	0.00836798	+	0.0229908i	0.943806	−	0.330499i	$-0.107217\pi$
$137$	0.0979446	+	0.269101i	0.00836798	+	0.0229908i	−0.935438	+	0.353490i	$0.884995\pi$
$138$	−4.20171	+	3.12065i	−0.357673	+	0.265647i
$139$	9.06026	−	3.29766i	0.768481	−	0.279704i	0.0721202	−	0.997396i	$-0.477023\pi$
$139$	9.06026	−	3.29766i	0.768481	−	0.279704i	0.696361	+	0.717692i	$0.254801\pi$
$140$	1.28869	−	6.76514i	0.108915	−	0.571759i
$141$	−17.1218	−	1.01673i	−1.44192	−	0.0856239i
$142$	−2.36415	+	0.860481i	−0.198395	+	0.0722099i
$143$	−0.213590	+	1.21133i	−0.0178613	+	0.101297i
$144$	−2.97892	−	0.355040i	−0.248243	−	0.0295866i
$145$	10.5572	−	6.09522i	0.876730	−	0.506180i
$146$	4.58025	−	1.66708i	0.379064	−	0.137968i
$147$	8.56850	−	8.57792i	0.706718	−	0.707495i
$148$	4.56137	+	0.804293i	0.374942	+	0.0661125i
$149$	−3.23877	−	3.85982i	−0.265330	−	0.316208i	0.616886	−	0.787052i	$-0.288394\pi$
$149$	−3.23877	−	3.85982i	−0.265330	−	0.316208i	−0.882216	+	0.470844i	$0.843949\pi$
$150$	1.83352	+	2.46869i	0.149707	+	0.201568i
$151$	−12.2792	+	7.08940i	−0.999268	+	0.576927i	−0.908032	−	0.418902i	$-0.862415\pi$
$151$	−12.2792	+	7.08940i	−0.999268	+	0.576927i	−0.0912362	+	0.995829i	$0.529082\pi$
$152$	−4.25923	+	0.926811i	−0.345469	+	0.0751743i
$153$	3.78847	−	1.62400i	0.306280	−	0.131293i
$154$	1.51380	−	2.54093i	0.121986	−	0.204754i
$155$	−19.5258	−	7.10681i	−1.56835	−	0.570833i
$156$	1.82632	−	0.544506i	0.146222	−	0.0435954i
$157$	15.9911	−	13.4182i	1.27623	−	1.07089i	0.282480	−	0.959273i	$-0.408843\pi$
$157$	15.9911	−	13.4182i	1.27623	−	1.07089i	0.993752	−	0.111612i	$-0.0356014\pi$
$158$	−1.88575	+	2.24736i	−0.150023	+	0.178790i
$159$	0.590788	−	9.94896i	0.0468526	−	0.789004i
$160$	−2.25423	+	1.30148i	−0.178213	+	0.102891i
$161$	−6.19419	+	5.05455i	−0.488171	+	0.398354i
$162$	8.94380	−	1.00425i	0.702691	−	0.0789017i
$163$	−16.3604			−1.28144			−0.640722	−	0.767773i	$-0.721365\pi$
$163$	−16.3604			−1.28144			−0.640722	+	0.767773i	$0.721365\pi$
$164$	3.18121			0.248411
$165$	1.44002	+	4.82993i	0.112105	+	0.376009i
$166$	−5.95645	+	16.3652i	−0.462310	+	1.27019i
$167$	−0.438514	+	2.48693i	−0.0339332	+	0.192445i	−0.997062	−	0.0765950i	$-0.975595\pi$
$167$	−0.438514	+	2.48693i	−0.0339332	+	0.192445i	0.963129	+	0.269040i	$0.0867063\pi$
$168$	−4.57037	−	0.334298i	−0.352611	−	0.0257916i
$169$	9.03117	−	7.57805i	0.694706	−	0.582927i
$170$	1.78818	−	3.09722i	0.137147	−	0.237546i
$171$	11.8048	−	5.62545i	0.902739	−	0.430189i
$172$	−1.70788	−	2.95814i	−0.130225	−	0.225556i
$173$	−1.29503	−	7.34445i	−0.0984589	−	0.558388i	−0.993632	−	0.112670i	$-0.964060\pi$
$173$	−1.29503	−	7.34445i	−0.0984589	−	0.558388i	0.895173	−	0.445718i	$-0.147052\pi$
$174$	−4.83659	−	6.51208i	−0.366661	−	0.493679i
$175$	2.96978	+	3.63937i	0.224494	+	0.275111i
$176$	−1.10092	+	0.194122i	−0.0829849	+	0.0146325i
$177$	−2.02724	+	2.14387i	−0.152376	+	0.161143i
$178$	−13.0727			−0.979841
$179$	8.57267	−	14.8483i	0.640752	−	1.10981i	−0.344514	−	0.938781i	$-0.611956\pi$
$179$	8.57267	−	14.8483i	0.640752	−	1.10981i	0.985265	−	0.171033i	$-0.0547105\pi$
$180$	5.69212	−	5.34588i	0.424266	−	0.398458i
$181$	13.7700	−	16.4104i	1.02351	−	1.21978i	0.0482256	−	0.998836i	$-0.484643\pi$
$181$	13.7700	−	16.4104i	1.02351	−	1.21978i	0.975288	−	0.220939i	$-0.0709122\pi$
$182$	2.74892	−	0.958078i	0.203764	−	0.0710174i
$183$	6.54291	−	3.27668i	0.483666	−	0.242219i
$184$	2.97584	+	0.524720i	0.219382	+	0.0386829i
$185$	−9.23561	+	7.74960i	−0.679016	+	0.569762i
$186$	−3.20390	+	13.4503i	−0.234921	+	0.986223i
$187$	1.17661	−	0.987292i	0.0860422	−	0.0721980i
$188$	6.36533	+	7.58591i	0.464240	+	0.553259i
$189$	13.5777	−	2.15533i	0.987634	−	0.156777i
$190$	5.27829	−	10.0435i	0.382927	−	0.728634i
$191$	6.54766	+	3.78029i	0.473772	+	0.273532i	0.717817	−	0.696231i	$-0.245141\pi$
$191$	6.54766	+	3.78029i	0.473772	+	0.273532i	−0.244045	+	0.969764i	$0.578475\pi$
$192$	1.03273	+	1.39049i	0.0745310	+	0.100350i
$193$	10.2727	−	1.81135i	0.739442	−	0.130384i	0.208775	−	0.977964i	$-0.433052\pi$
$193$	10.2727	−	1.81135i	0.739442	−	0.130384i	0.530667	+	0.847580i	$0.321941\pi$
$194$	−8.80844	+	10.4975i	−0.632409	+	0.753676i
$195$	−1.96997	+	4.55269i	−0.141072	+	0.326025i
$196$	−6.99737	−	0.191809i	−0.499812	−	0.0137006i
$197$	−12.7071	−	7.33645i	−0.905343	−	0.522700i	−0.0264133	−	0.999651i	$-0.508409\pi$
$197$	−12.7071	−	7.33645i	−0.905343	−	0.522700i	−0.878930	+	0.476951i	$0.841742\pi$
$198$	3.08244	−	1.32134i	0.219059	−	0.0939039i
$199$	−3.45999	+	19.6226i	−0.245272	+	1.39101i	0.574587	+	0.818444i	$0.305163\pi$
$199$	−3.45999	+	19.6226i	−0.245272	+	1.39101i	−0.819859	+	0.572565i	$0.805948\pi$
$200$	0.308297	−	1.74844i	0.0217999	−	0.123633i
$201$	1.11666	−	1.69360i	0.0787629	−	0.119458i
$202$	2.89051	+	1.66883i	0.203375	+	0.117419i
$203$	−7.83387	−	9.60017i	−0.549830	−	0.673800i
$204$	−2.18407	−	0.945057i	−0.152916	−	0.0661672i
$205$	−5.32265	+	6.34329i	−0.371750	+	0.443035i
$206$	12.7254	−	2.24383i	0.886621	−	0.156335i
$207$	−9.05106	+	0.506558i	−0.629092	+	0.0352082i
$208$	−0.952880	−	0.550145i	−0.0660703	−	0.0381457i
$209$	3.60545	−	3.27798i	0.249394	−	0.226742i
$210$	8.31350	−	8.55391i	0.573686	−	0.590276i
$211$	−0.799909	−	0.953295i	−0.0550680	−	0.0656275i	0.737807	−	0.675011i	$-0.235861\pi$
$211$	−0.799909	−	0.953295i	−0.0550680	−	0.0656275i	−0.792875	+	0.609384i	$0.791417\pi$
$212$	−4.40794	+	3.69870i	−0.302738	+	0.254028i
$213$	−4.23902	−	1.00975i	−0.290453	−	0.0691868i
$214$	−4.60039	+	3.86018i	−0.314476	+	0.263877i
$215$	8.75603	+	1.54392i	0.597156	+	0.105295i
$216$	−3.96909	−	3.35355i	−0.270062	−	0.228180i
$217$	−3.95219	+	20.7474i	−0.268292	+	1.40843i
$218$	10.8134	−	12.8869i	0.732376	−	0.872812i
$219$	8.21259	+	1.95626i	0.554955	+	0.132192i
$220$	1.45493	−	2.52001i	0.0980913	−	0.169899i
$221$	1.51176			0.101692
$222$	5.82903	+	5.51192i	0.391219	+	0.369936i
$223$	17.1463	−	3.02336i	1.14820	−	0.202459i	0.433011	−	0.901389i	$-0.357451\pi$
$223$	17.1463	−	3.02336i	1.14820	−	0.202459i	0.715190	+	0.698930i	$0.246340\pi$
$224$	1.67273	+	2.04988i	0.111764	+	0.136963i
$225$	0.297626	+	5.31791i	0.0198417	+	0.354528i
$226$	−1.10505	−	6.26707i	−0.0735070	−	0.416879i
$227$	−10.8527	−	18.7975i	−0.720322	−	1.24763i	−0.960871	−	0.276997i	$-0.910661\pi$
$227$	−10.8527	−	18.7975i	−0.720322	−	1.24763i	0.240549	−	0.970637i	$-0.422672\pi$
$228$	−7.04260	−	2.72063i	−0.466407	−	0.180178i
$229$	14.5288	−	25.1647i	0.960092	−	1.66293i	0.237832	−	0.971306i	$-0.423563\pi$
$229$	14.5288	−	25.1647i	0.960092	−	1.66293i	0.722260	−	0.691621i	$-0.243103\pi$
$230$	−6.02531	+	5.05583i	−0.397297	+	0.333372i
$231$	4.61157	−	2.23097i	0.303419	−	0.146787i
$232$	−0.813246	+	4.61214i	−0.0533922	+	0.302802i
$233$	8.18791	−	22.4961i	0.536408	−	1.47377i	−0.314911	−	0.949121i	$-0.601975\pi$
$233$	8.18791	−	22.4961i	0.536408	−	1.47377i	0.851319	−	0.524648i	$-0.175803\pi$
$234$	3.16004	+	0.953874i	0.206579	+	0.0623567i
$235$	−25.7764			−1.68146
$236$	1.70351			0.110889
$237$	−4.86952	+	1.45182i	−0.316309	+	0.0943059i
$238$	−3.39857	−	1.28999i	−0.220297	−	0.0836173i
$239$	7.85952	−	4.53770i	0.508390	−	0.293519i	−0.223782	−	0.974639i	$-0.571840\pi$
$239$	7.85952	−	4.53770i	0.508390	−	0.293519i	0.732172	+	0.681120i	$0.238507\pi$
$240$	−4.50053	−	0.267250i	−0.290508	−	0.0172509i
$241$	−4.82535	+	5.75063i	−0.310828	+	0.370431i	−0.898731	−	0.438501i	$-0.855510\pi$
$241$	−4.82535	+	5.75063i	−0.310828	+	0.370431i	0.587902	+	0.808932i	$0.299954\pi$
$242$	−7.46916	+	6.26737i	−0.480136	+	0.402882i
$243$	13.8904	+	7.07500i	0.891072	+	0.453862i
$244$	−3.97000	−	1.44496i	−0.254153	−	0.0925042i
$245$	12.0901	−	13.6317i	0.772410	−	0.870899i
$246$	4.60012	+	3.03303i	0.293293	+	0.193379i
$247$	4.79227	−	0.190486i	0.304925	−	0.0121203i
$248$	6.91331	−	3.99140i	0.438996	−	0.253454i
$249$	−24.2161	+	17.9855i	−1.53463	+	1.13979i
$250$	−5.39523	−	6.42978i	−0.341224	−	0.406655i
$251$	−29.5757	−	5.21499i	−1.86680	−	0.329167i	−0.878028	−	0.478608i	$-0.841141\pi$
$251$	−29.5757	−	5.21499i	−1.86680	−	0.329167i	−0.988771	+	0.149441i	$0.952252\pi$
$252$	−6.29014	−	4.84088i	−0.396242	−	0.304947i
$253$	−3.17430	+	1.15535i	−0.199566	+	0.0726362i
$254$	−2.13796	+	1.23435i	−0.134148	+	0.0774501i
$255$	5.53871	−	2.77378i	0.346848	−	0.173701i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	6.18569	−	2.25141i	0.385853	−	0.140439i	−0.141808	−	0.989894i	$-0.545292\pi$
$257$	6.18569	−	2.25141i	0.385853	−	0.140439i	0.527661	+	0.849455i	$0.323069\pi$
$258$	0.350702	−	5.90587i	0.0218338	−	0.367684i
$259$	9.27862	+	8.00488i	0.576546	+	0.497399i
$260$	2.69129	−	0.979551i	0.166907	−	0.0607492i
$261$	−0.785097	−	14.0279i	−0.0485963	−	0.868307i
$262$	−2.06381	−	5.67027i	−0.127503	−	0.350311i
$263$	−3.85842	+	0.680343i	−0.237920	+	0.0419518i	−0.291337	−	0.956621i	$-0.594100\pi$
$263$	−3.85842	+	0.680343i	−0.237920	+	0.0419518i	0.0534165	+	0.998572i	$0.482989\pi$
$264$	−1.77704	−	0.768932i	−0.109369	−	0.0473245i
$265$		−	14.9778i		−	0.920081i
$266$	−10.9360	−	3.66103i	−0.670531	−	0.224472i
$267$	−18.9035	−	12.4638i	−1.15687	−	0.762770i
$268$	−1.15342	+	0.203379i	−0.0704563	+	0.0124233i
$269$	4.24238	+	24.0597i	0.258662	+	1.46695i	0.786494	+	0.617598i	$0.211894\pi$
$269$	4.24238	+	24.0597i	0.258662	+	1.46695i	−0.527831	+	0.849349i	$0.676995\pi$
$270$	13.3278	−	2.30331i	0.811106	−	0.140175i
$271$	13.2628	+	4.82727i	0.805658	+	0.293236i	0.711829	−	0.702353i	$-0.247867\pi$
$271$	13.2628	+	4.82727i	0.805658	+	0.293236i	0.0938290	+	0.995588i	$0.470089\pi$
$272$	0.469922	+	1.29110i	0.0284932	+	0.0782845i
$273$	4.88846	+	1.23547i	0.295863	+	0.0747738i
$274$	0.248005	−	0.143185i	0.0149825	−	0.00865015i
$275$	0.678820	+	1.86504i	0.0409344	+	0.112466i
$276$	3.80286	+	3.59598i	0.228905	+	0.216452i
$277$	−1.75593	+	3.04137i	−0.105504	+	0.182738i	−0.913944	−	0.405840i	$-0.866979\pi$
$277$	−1.75593	+	3.04137i	−0.105504	+	0.182738i	0.808440	+	0.588578i	$0.200312\pi$
$278$	−4.82086	−	8.34998i	−0.289136	−	0.500799i
$279$	−17.4567	+	16.3948i	−1.04510	+	0.981532i
$280$	−6.88614	−	0.0943621i	−0.411526	−	0.00563922i
$281$	−4.63222	+	26.2706i	−0.276335	+	1.56717i	0.458354	+	0.888770i	$0.348439\pi$
$281$	−4.63222	+	26.2706i	−0.276335	+	1.56717i	−0.734689	+	0.678404i	$0.762672\pi$
$282$	1.97189	+	17.0383i	0.117424	+	1.01461i
$283$	19.2872	+	7.01997i	1.14651	+	0.417294i	0.844259	−	0.535936i	$-0.180041\pi$
$283$	19.2872	+	7.01997i	1.14651	+	0.417294i	0.302247	+	0.953230i	$0.402263\pi$
$284$	1.25794	+	2.17881i	0.0746449	+	0.129289i
$285$	17.2082	−	9.49079i	1.01933	−	0.562186i
$286$	1.23002			0.0727325
$287$	7.23073	+	4.30783i	0.426816	+	0.254283i
$288$	0.167638	+	2.99531i	0.00987814	+	0.176500i
$289$	11.5766	+	9.71396i	0.680979	+	0.571409i
$290$	−7.83586	−	9.33842i	−0.460138	−	0.548371i
$291$	−22.7458	+	6.78152i	−1.33338	+	0.397540i
$292$	−2.43710	−	4.22118i	−0.142621	−	0.247026i
$293$	13.4257	+	23.2540i	0.784339	+	1.35851i	0.929393	+	0.369091i	$0.120331\pi$
$293$	13.4257	+	23.2540i	0.784339	+	1.35851i	−0.145055	+	0.989424i	$0.546336\pi$
$294$	−9.93551	−	6.94879i	−0.579451	−	0.405261i
$295$	−2.85023	+	3.39677i	−0.165947	+	0.197768i
$296$		−	4.63174i		−	0.269214i
$297$	5.71708	+	1.02815i	0.331739	+	0.0596595i
$298$	−3.23877	+	3.85982i	−0.187617	+	0.223593i
$299$	−3.12429	−	1.13715i	−0.180682	−	0.0657629i
$300$	2.11280	−	2.23435i	0.121983	−	0.129000i
$301$	0.123828	−	9.03641i	0.00713731	−	0.520850i
$302$	9.11396	+	10.8616i	0.524450	+	0.625015i
$303$	2.58865	+	5.16904i	0.148714	+	0.296954i
$304$	1.65234	+	4.03358i	0.0947681	+	0.231342i
$305$	9.52364	−	5.49848i	0.545322	−	0.314842i
$306$	−2.25719	−	3.44891i	−0.129035	−	0.197161i
$307$	5.95890	−	16.3719i	0.340092	−	0.934396i	−0.645275	−	0.763951i	$-0.723257\pi$
$307$	5.95890	−	16.3719i	0.340092	−	0.934396i	0.985367	−	0.170446i	$-0.0545207\pi$
$308$	−2.76520	−	1.04958i	−0.157562	−	0.0598052i
$309$	20.5406	+	8.88800i	1.16851	+	0.505621i
$310$	−3.60822	+	20.4633i	−0.204933	+	1.16223i
$311$			20.5119i			1.16312i	0.813502	+	0.581562i	$0.197558\pi$
$311$			20.5119i			1.16312i	−0.813502	+	0.581562i	$0.802442\pi$
$312$	−0.853370	−	1.70402i	−0.0483126	−	0.0964710i
$313$	13.5601	−	4.93546i	0.766460	−	0.278968i	0.0709448	−	0.997480i	$-0.477399\pi$
$313$	13.5601	−	4.93546i	0.766460	−	0.278968i	0.695515	+	0.718512i	$0.255176\pi$
$314$	−15.9911	−	13.4182i	−0.902432	−	0.757230i
$315$	20.1770	−	4.44293i	1.13685	−	0.250331i
$316$	2.54067	+	1.46686i	0.142924	+	0.0825171i
$317$	−3.52070	+	19.9669i	−0.197742	+	1.12145i	0.710717	+	0.703478i	$0.248370\pi$
$317$	−3.52070	+	19.9669i	−0.197742	+	1.12145i	−0.908459	+	0.417973i	$0.862741\pi$
$318$	−9.90040	+	1.14581i	−0.555187	+	0.0642536i
$319$	−1.79064	−	4.91973i	−0.100256	−	0.275452i
$320$	1.67315	+	1.99398i	0.0935320	+	0.111467i
$321$	−10.3326	+	1.19583i	−0.576712	+	0.0667448i
$322$	6.05337	+	5.22238i	0.337341	+	0.291032i
$323$	−4.73708	−	3.66437i	−0.263578	−	0.203891i
$324$	−2.54207	−	8.63353i	−0.141226	−	0.479641i
$325$	−0.668126	+	1.83566i	−0.0370609	+	0.101824i
$326$	2.84095	+	16.1118i	0.157346	+	0.892351i
$327$	27.9231	−	8.32511i	1.54415	−	0.460380i
$328$	−0.552412	−	3.13288i	−0.0305018	−	0.172985i
$329$	4.19563	+	25.8620i	0.231313	+	1.42582i
$330$	4.50649	−	2.25685i	0.248074	−	0.124235i
$331$			14.9539i			0.821938i	0.911649	+	0.410969i	$0.134810\pi$
$331$			14.9539i			0.821938i	−0.911649	+	0.410969i	$0.865190\pi$
$332$	17.1509	+	3.02417i	0.941278	+	0.165973i
$333$	3.17377	+	13.5279i	0.173921	+	0.741324i
$334$	2.52530			0.138178
$335$	1.52431	−	2.64018i	0.0832820	−	0.144249i
$336$	0.464417	+	4.55898i	0.0253360	+	0.248713i
$337$	−18.7841	+	3.31215i	−1.02324	+	0.180424i	−0.659994	−	0.751270i	$-0.729441\pi$
$337$	−18.7841	+	3.31215i	−1.02324	+	0.180424i	−0.363242	+	0.931695i	$0.618330\pi$
$338$	−9.03117	−	7.57805i	−0.491231	−	0.412192i
$339$	4.37720	−	10.1159i	0.237737	−	0.549422i
$340$	−3.36069	−	1.22319i	−0.182259	−	0.0663368i
$341$	−4.46200	+	7.72841i	−0.241631	+	0.418517i
$342$	−7.58987	−	10.6487i	−0.410413	−	0.575813i
$343$	−15.6449	−	9.91144i	−0.844746	−	0.535167i
$344$	−2.61663	+	2.19561i	−0.141079	+	0.118379i
$345$	−13.5331	+	1.56623i	−0.728597	+	0.0843229i
$346$	−7.00800	+	2.55070i	−0.376752	+	0.137127i
$347$	20.9171	+	24.9280i	1.12289	+	1.33821i	0.934439	+	0.356124i	$0.115902\pi$
$347$	20.9171	+	24.9280i	1.12289	+	1.33821i	0.188450	+	0.982083i	$0.439654\pi$
$348$	−5.57328	+	5.89392i	−0.298759	+	0.315947i
$349$	7.51533	−	13.0169i	0.402286	−	0.696781i	−0.591715	−	0.806147i	$-0.701549\pi$
$349$	7.51533	−	13.0169i	0.402286	−	0.696781i	0.994001	+	0.109367i	$0.0348823\pi$
$350$	3.06839	−	3.55663i	0.164012	−	0.190110i
$351$	3.66007	+	4.39217i	0.195360	+	0.234437i
$352$	0.382345	+	1.05049i	0.0203791	+	0.0559910i
$353$	12.7233	+	7.34583i	0.677195	+	0.390979i	0.798798	−	0.601600i	$-0.205470\pi$
$353$	12.7233	+	7.34583i	0.677195	+	0.390979i	−0.121602	+	0.992579i	$0.538803\pi$
$354$	2.46332	+	1.62416i	0.130924	+	0.0863231i
$355$	−6.44924	−	1.13718i	−0.342290	−	0.0603550i
$356$	2.27005	+	12.8741i	0.120313	+	0.682326i
$357$	−3.68453	−	5.10562i	−0.195006	−	0.270218i
$358$	−16.1114	−	5.86405i	−0.851511	−	0.309925i
$359$	−18.9603	+	3.34321i	−1.00069	+	0.176448i	−0.649909	−	0.760012i	$-0.725193\pi$
$359$	−18.9603	+	3.34321i	−1.00069	+	0.176448i	−0.350776	+	0.936459i	$0.614082\pi$
$360$	−6.25309	−	4.67735i	−0.329567	−	0.246518i
$361$	−15.4783	−	11.0192i	−0.814647	−	0.579957i
$362$	−18.5522	−	10.7111i	−0.975083	−	0.562964i
$363$	−16.7760	+	1.94154i	−0.880513	+	0.101905i
$364$	−1.42087	−	2.54079i	−0.0744737	−	0.133174i
$365$	12.4946	+	2.20314i	0.653998	+	0.115318i
$366$	−4.36307	−	5.87452i	−0.228061	−	0.307066i
$367$	−9.19799	−	7.71803i	−0.480131	−	0.402878i	0.370343	−	0.928895i	$-0.379240\pi$
$367$	−9.19799	−	7.71803i	−0.480131	−	0.402878i	−0.850474	+	0.526017i	$0.823685\pi$
$368$		−	3.02174i		−	0.157519i
$369$	3.76015	+	8.77168i	0.195745	+	0.456635i
$370$	9.23561	+	7.74960i	0.480137	+	0.402882i
$371$	−15.0276	+	2.43795i	−0.780193	+	0.126572i
$372$	13.8023	+	0.819608i	0.715616	+	0.0424947i
$373$	−6.16796	+	3.56107i	−0.319365	+	0.184385i	−0.651109	−	0.758984i	$-0.725696\pi$
$373$	−6.16796	+	3.56107i	−0.319365	+	0.184385i	0.331745	+	0.943369i	$0.392363\pi$
$374$	−1.17661	−	0.987292i	−0.0608410	−	0.0510517i
$375$	−1.67137	−	14.4415i	−0.0863090	−	0.745758i
$376$	6.36533	−	7.58591i	0.328267	−	0.391213i
$377$	1.76242	−	4.84222i	0.0907695	−	0.249387i
$378$	−4.48033	−	12.9972i	−0.230443	−	0.668503i
$379$			11.7593i			0.604033i	0.953303	+	0.302016i	$0.0976597\pi$
$379$			11.7593i			0.604033i	−0.953303	+	0.302016i	$0.902340\pi$
$380$	−10.8075	−	3.45406i	−0.554414	−	0.177189i
$381$	−4.26840	−	0.253466i	−0.218677	−	0.0129855i
$382$	2.58587	−	7.10463i	0.132305	−	0.363504i
$383$	−1.70812	+	1.43329i	−0.0872810	+	0.0732375i	−0.685384	−	0.728182i	$-0.740366\pi$
$383$	−1.70812	+	1.43329i	−0.0872810	+	0.0732375i	0.598103	+	0.801419i	$0.295921\pi$
$384$	1.19003	−	1.25850i	0.0607287	−	0.0642225i
$385$	6.71944	−	3.75766i	0.342454	−	0.191508i
$386$	−3.56766	−	9.80206i	−0.181589	−	0.498912i
$387$	6.13789	−	8.20568i	0.312007	−	0.417118i
$388$	11.8676	+	6.85175i	0.602485	+	0.347845i
$389$	−1.31460	−	0.231800i	−0.0666531	−	0.0117527i	0.140222	−	0.990120i	$-0.455218\pi$
$389$	−1.31460	−	0.231800i	−0.0666531	−	0.0117527i	−0.206875	+	0.978367i	$0.566329\pi$
$390$	4.82560	+	1.14947i	0.244354	+	0.0582059i
$391$	2.07588	+	3.59552i	0.104982	+	0.181834i
$392$	1.02619	+	6.92437i	0.0518302	+	0.349734i
$393$	2.42182	−	10.1670i	0.122165	−	0.512859i
$394$	−5.01843	+	13.7880i	−0.252825	+	0.694630i
$395$	−7.17582	+	2.61178i	−0.361055	+	0.131413i
$396$	−1.83653	−	2.80616i	−0.0922891	−	0.141015i
$397$	0.930554	+	5.27743i	0.0467032	+	0.264867i	0.999214	−	0.0396375i	$-0.0126203\pi$
$397$	0.930554	+	5.27743i	0.0467032	+	0.264867i	−0.952511	+	0.304504i	$0.901509\pi$
$398$	19.9253			0.998765
$399$	−12.3233	−	15.7206i	−0.616937	−	0.787013i
$400$	−1.77541			−0.0887706
$401$	2.73821	+	15.5292i	0.136740	+	0.775489i	0.973632	+	0.228122i	$0.0732586\pi$
$401$	2.73821	+	15.5292i	0.136740	+	0.775489i	−0.836893	+	0.547367i	$0.815630\pi$
$402$	−1.86178	−	0.805601i	−0.0928572	−	0.0401797i
$403$	−8.25370	+	3.00410i	−0.411146	+	0.149645i
$404$	1.14155	−	3.13638i	0.0567942	−	0.156041i
$405$	21.4684	+	9.37636i	1.06677	+	0.465915i
$406$	−8.09398	+	9.38191i	−0.401698	+	0.465616i
$407$	2.58892	+	4.48413i	0.128328	+	0.222270i
$408$	−0.551440	+	2.31500i	−0.0273003	+	0.114609i
$409$	13.4280	+	2.36771i	0.663970	+	0.117076i	0.495469	−	0.868626i	$-0.334996\pi$
$409$	13.4280	+	2.36771i	0.663970	+	0.117076i	0.168501	+	0.985701i	$0.446107\pi$
$410$	7.17119	+	4.14029i	0.354160	+	0.204474i
$411$	0.495137	+	0.0294022i	0.0244233	+	0.00145030i
$412$	−4.41949	−	12.1424i	−0.217733	−	0.598215i
$413$	3.87199	+	2.30680i	0.190528	+	0.113510i
$414$	2.07056	+	8.82559i	0.101763	+	0.433754i
$415$	−34.7262	+	29.1388i	−1.70464	+	1.43037i
$416$	−0.376322	+	1.03393i	−0.0184507	+	0.0506928i
$417$	0.989932	−	16.6706i	0.0484772	−	0.816363i
$418$	−3.85426	−	2.98146i	−0.188518	−	0.145828i
$419$		−	9.43950i		−	0.461150i	−0.973055	−	0.230575i	$-0.925939\pi$
$419$		−	9.43950i		−	0.461150i	0.973055	−	0.230575i	$-0.0740607\pi$
$420$	−9.86758	−	6.70183i	−0.481489	−	0.327016i
$421$	−3.02079	+	8.29954i	−0.147224	+	0.404495i	−0.991282	−	0.131757i	$-0.957938\pi$
$421$	−3.02079	+	8.29954i	−0.147224	+	0.404495i	0.844058	+	0.536252i	$0.180160\pi$
$422$	−0.799909	+	0.953295i	−0.0389390	+	0.0464057i
$423$	−13.3932	+	26.5178i	−0.651199	+	1.28934i
$424$	4.40794	+	3.69870i	0.214068	+	0.179625i
$425$	2.11254	−	1.21967i	0.102473	−	0.0591628i
$426$	−0.258309	+	4.34996i	−0.0125151	+	0.210756i
$427$	−7.06691	−	8.66028i	−0.341992	−	0.419100i
$428$	4.60039	+	3.86018i	0.222368	+	0.186589i
$429$	1.77864	+	1.17272i	0.0858735	+	0.0566196i
$430$		−	8.89110i		−	0.428767i
$431$	12.9380	+	10.8563i	0.623202	+	0.522929i	0.898808	−	0.438342i	$-0.144434\pi$
$431$	12.9380	+	10.8563i	0.623202	+	0.522929i	−0.275606	+	0.961271i	$0.588878\pi$
$432$	−2.61338	+	4.49113i	−0.125736	+	0.216080i
$433$	−27.0498	−	4.76961i	−1.29993	−	0.229213i	−0.519508	−	0.854466i	$-0.673885\pi$
$433$	−27.0498	−	4.76961i	−1.29993	−	0.229213i	−0.780422	+	0.625253i	$0.784996\pi$
$434$	21.1185	+	0.289391i	1.01372	+	0.0138912i
$435$	−2.42744	−	20.9745i	−0.116387	−	1.00565i
$436$	−14.5689	−	8.41134i	−0.697722	−	0.402830i
$437$	7.03359	+	11.1363i	0.336462	+	0.532720i
$438$	0.500443	−	8.42752i	0.0239121	−	0.402683i
$439$	−21.3932	+	3.77220i	−1.02104	+	0.180037i	−0.659015	−	0.752130i	$-0.729027\pi$
$439$	−21.3932	+	3.77220i	−1.02104	+	0.180037i	−0.362028	+	0.932167i	$0.617915\pi$
$440$	−2.73437	−	0.995230i	−0.130356	−	0.0474457i
$441$	−7.74191	−	19.5208i	−0.368662	−	0.929563i
$442$	−0.262514	−	1.48879i	−0.0124865	−	0.0708145i
$443$	23.4539	+	4.13556i	1.11433	+	0.196486i	0.700350	−	0.713800i	$-0.253027\pi$
$443$	23.4539	+	4.13556i	1.11433	+	0.196486i	0.413980	+	0.910286i	$0.364138\pi$
$444$	4.41599	−	6.69761i	0.209573	−	0.317855i
$445$	−29.4689	−	17.0139i	−1.39696	−	0.806535i
$446$	−5.95485	−	16.3608i	−0.281970	−	0.774707i
$447$	−8.36337	+	2.49349i	−0.395574	+	0.117938i
$448$	1.72827	−	2.00327i	0.0816529	−	0.0946456i
$449$	−18.6884	+	32.3693i	−0.881961	+	1.52760i	−0.0328044	+	0.999462i	$0.510444\pi$
$449$	−18.6884	+	32.3693i	−0.881961	+	1.52760i	−0.849157	+	0.528140i	$0.822890\pi$
$450$	5.18544	−	1.21655i	0.244444	−	0.0573487i
$451$	2.28594	+	2.72427i	0.107641	+	0.128281i
$452$	−5.97997	+	2.17653i	−0.281274	+	0.102375i
$453$	2.82338	+	24.3956i	0.132654	+	1.14620i
$454$	−16.6274	+	13.9520i	−0.780361	+	0.654801i
$455$	7.44362	+	1.41794i	0.348962	+	0.0664740i
$456$	−1.45637	+	7.40804i	−0.0682007	+	0.346913i
$457$	−1.00123	+	1.73418i	−0.0468355	+	0.0811215i	−0.888493	−	0.458891i	$-0.848247\pi$
$457$	−1.00123	+	1.73418i	−0.0468355	+	0.0811215i	0.841657	+	0.540012i	$0.181580\pi$
$458$	−27.3053	−	9.93830i	−1.27589	−	0.464386i
$459$	0.0243018	−	7.13927i	0.00113431	−	0.333232i
$460$	6.02531	+	5.05583i	0.280931	+	0.235729i
$461$	−12.1682	+	2.14559i	−0.566730	+	0.0999299i	−0.449670	−	0.893195i	$-0.648458\pi$
$461$	−12.1682	+	2.14559i	−0.566730	+	0.0999299i	−0.117061	+	0.993125i	$0.537347\pi$
$462$	−2.99787	−	4.15411i	−0.139473	−	0.193267i
$463$	4.35338	−	7.54027i	0.202319	−	0.350426i	−0.746956	−	0.664873i	$-0.768486\pi$
$463$	4.35338	−	7.54027i	0.202319	−	0.350426i	0.949275	+	0.314447i	$0.101819\pi$
$464$	4.68329			0.217416
$465$	−24.7276	+	26.1503i	−1.14672	+	1.21269i
$466$	−23.5762	−	4.15711i	−1.09214	−	0.192575i
$467$		−	22.1727i		−	1.02603i	−0.858379	−	0.513016i	$-0.828528\pi$
$467$		−	22.1727i		−	1.02603i	0.858379	−	0.513016i	$-0.171472\pi$
$468$	0.390647	−	3.27767i	0.0180577	−	0.151511i
$469$	−2.89707	−	1.09963i	−0.133774	−	0.0507762i
$470$	4.47602	+	25.3848i	0.206463	+	1.17091i
$471$	−10.3305	−	34.6493i	−0.476003	−	1.59655i
$472$	−0.295811	−	1.67763i	−0.0136158	−	0.0772192i
$473$	1.30600	−	3.58821i	0.0600500	−	0.164986i
$474$	2.27535	+	4.54344i	0.104510	+	0.208687i
$475$	6.54306	−	4.13255i	0.300216	−	0.189615i
$476$	−0.680231	+	3.57095i	−0.0311783	+	0.163674i
$477$	−15.4087	−	7.78236i	−0.705515	−	0.356330i
$478$	−5.83355	−	6.95215i	−0.266820	−	0.317984i
$479$	−6.10663	−	16.7778i	−0.279019	−	0.766599i	−0.997474	−	0.0710256i	$-0.977373\pi$
$479$	−6.10663	−	16.7778i	−0.279019	−	0.766599i	0.718455	−	0.695573i	$-0.244849\pi$
$480$	0.518319	+	4.47857i	0.0236579	+	0.204418i
$481$	−0.884956	+	5.01883i	−0.0403505	+	0.228839i
$482$	6.50118	+	3.75346i	0.296121	+	0.170965i
$483$	3.77422	+	13.3231i	0.171733	+	0.606222i
$484$	7.46916	+	6.26737i	0.339507	+	0.284880i
$485$	−33.5186	+	12.1998i	−1.52200	+	0.553963i
$486$	4.55547	−	14.9080i	0.206640	−	0.676239i
$487$			15.2673i			0.691829i	0.938266	+	0.345914i	$0.112431\pi$
$487$			15.2673i			0.691829i	−0.938266	+	0.345914i	$0.887569\pi$
$488$	−0.733626	+	4.16060i	−0.0332097	+	0.188342i
$489$	−11.2532	+	26.0067i	−0.508888	+	1.17607i
$490$	−15.5241	−	9.53933i	−0.701305	−	0.430943i
$491$	−9.16347	+	25.1764i	−0.413541	+	1.13620i	0.541752	+	0.840538i	$0.317761\pi$
$491$	−9.16347	+	25.1764i	−0.413541	+	1.13620i	−0.955294	+	0.295658i	$0.904461\pi$
$492$	2.18815	−	5.05691i	0.0986493	−	0.227983i
$493$	−5.57258	+	3.21733i	−0.250976	+	0.144901i
$494$	−1.01976	−	4.68639i	−0.0458812	−	0.210851i
$495$	8.66823	+	1.03312i	0.389608	+	0.0464351i
$496$	−5.13125	−	6.11518i	−0.230400	−	0.274580i
$497$	−0.0912052	+	6.65576i	−0.00409111	+	0.298552i
$498$	21.9174	+	20.7250i	0.982141	+	0.928711i
$499$	37.6516	+	13.7041i	1.68552	+	0.613478i	0.994049	−	0.108929i	$-0.0347422\pi$
$499$	37.6516	+	13.7041i	1.68552	+	0.613478i	0.691468	+	0.722407i	$0.256964\pi$
$500$	−5.39523	+	6.42978i	−0.241282	+	0.287548i
$501$	3.65165	+	2.40767i	0.163144	+	0.107567i
$502$			30.0319i			1.34039i
$503$	18.4283	−	21.9620i	0.821676	−	0.979235i	−0.178313	−	0.983974i	$-0.557064\pi$
$503$	18.4283	−	21.9620i	0.821676	−	0.979235i	0.999989	+	0.00473862i	$0.00150836\pi$
$504$	−3.67506	+	7.03519i	−0.163700	+	0.313372i
$505$	4.34391	+	7.52388i	0.193302	+	0.334808i
$506$	1.68901	+	2.92545i	0.0750855	+	0.130052i
$507$	−5.83426	−	19.5686i	−0.259108	−	0.869070i
$508$	1.58685	+	1.89114i	0.0704052	+	0.0839056i
$509$	19.3383	+	16.2267i	0.857153	+	0.719237i	0.961353	−	0.275320i	$-0.0887837\pi$
$509$	19.3383	+	16.2267i	0.857153	+	0.719237i	−0.104200	+	0.994556i	$0.533228\pi$
$510$	−3.69343	−	4.97291i	−0.163548	−	0.220204i
$511$	0.176699	−	12.8947i	0.00781670	−	0.570429i
$512$	−1.00000			−0.0441942
$513$	−0.822533	−	22.6346i	−0.0363157	−	0.999340i
$514$	−3.29134	−	5.70076i	−0.145175	−	0.251450i
$515$	31.6063	+	11.5038i	1.39274	+	0.506916i
$516$	−5.87705	+	0.680170i	−0.258723	+	0.0299428i
$517$	−1.92233	+	10.9021i	−0.0845440	+	0.479473i
$518$	6.27205	−	10.5277i	0.275578	−	0.462560i
$519$	−12.5656	−	2.99317i	−0.551570	−	0.131386i
$520$	−1.43201	−	2.48031i	−0.0627977	−	0.108769i
$521$	−17.5600	+	30.4148i	−0.769318	+	1.33250i	0.168614	+	0.985682i	$0.446071\pi$
$521$	−17.5600	+	30.4148i	−0.769318	+	1.33250i	−0.937933	+	0.346817i	$0.887263\pi$
$522$	−13.6785	+	3.20909i	−0.598691	+	0.140458i
$523$	−9.43305	−	25.9171i	−0.412479	−	1.13328i	−0.955868	−	0.293795i	$-0.905082\pi$
$523$	−9.43305	−	25.9171i	−0.412479	−	1.13328i	0.543390	−	0.839480i	$-0.317141\pi$
$524$	−5.22575	+	3.01709i	−0.228288	+	0.131802i
$525$	7.82793	−	2.21752i	0.341639	−	0.0967807i
$526$	1.34001	+	3.68166i	0.0584274	+	0.160528i
$527$	10.3066	+	3.75130i	0.448962	+	0.163409i
$528$	−0.448671	+	1.88356i	−0.0195259	+	0.0819716i
$529$	2.40834	+	13.6584i	0.104710	+	0.593842i
$530$	−14.7503	+	2.60087i	−0.640712	+	0.112975i
$531$	2.01352	+	4.69715i	0.0873795	+	0.203839i
$532$	−1.70638	+	11.4056i	−0.0739812	+	0.494496i
$533$			3.50026i			0.151613i
$534$	−8.99186	+	20.7806i	−0.389116	+	0.899265i
$535$	−15.3943	+	2.71443i	−0.665553	+	0.117355i
$536$	0.400578	+	1.10058i	0.0173024	+	0.0475378i
$537$	−17.7065	−	23.8404i	−0.764094	−	1.02879i
$538$	22.9575	−	8.35586i	0.989769	−	0.360247i
$539$	−4.86387	−	6.13012i	−0.209502	−	0.264043i
$540$	−4.58267	−	12.7254i	−0.197207	−	0.547613i
$541$	27.8091	−	10.1217i	1.19561	−	0.435165i	0.333918	−	0.942602i	$-0.391629\pi$
$541$	27.8091	−	10.1217i	1.19561	−	0.435165i	0.861689	+	0.507437i	$0.169407\pi$
$542$	2.45087	−	13.8996i	0.105274	−	0.597037i
$543$	−16.6148	−	33.1766i	−0.713010	−	1.42374i
$544$	1.18988	−	0.686980i	0.0510159	−	0.0294540i
$545$	41.1480	−	14.9766i	1.76259	−	0.641529i
$546$	0.367825	−	5.02873i	0.0157414	−	0.215210i
$547$	18.3825	+	3.24133i	0.785978	+	0.138589i	0.552212	−	0.833704i	$-0.313784\pi$
$547$	18.3825	+	3.24133i	0.785978	+	0.138589i	0.233766	+	0.972293i	$0.424895\pi$
$548$	−0.184076	−	0.219373i	−0.00786333	−	0.00937115i
$549$	−0.708233	−	12.6545i	−0.0302266	−	0.540083i
$550$	1.71883	−	0.992369i	0.0732913	−	0.0423148i
$551$	−17.2597	+	10.9011i	−0.735288	+	0.464403i
$552$	2.88099	−	4.36952i	0.122623	−	0.185979i
$553$	3.78847	+	6.77453i	0.161102	+	0.288082i
$554$	3.30007	+	1.20113i	0.140207	+	0.0510311i
$555$	5.96633	+	20.0115i	0.253256	+	0.849442i
$556$	−7.38599	+	6.19758i	−0.313236	+	0.262836i
$557$	28.2090	−	33.6182i	1.19526	−	1.42445i	0.315564	−	0.948904i	$-0.397806\pi$
$557$	28.2090	−	33.6182i	1.19526	−	1.42445i	0.879691	−	0.475546i	$-0.157749\pi$
$558$	19.1771	+	14.3446i	0.811830	+	0.607253i
$559$	3.25481	−	1.87917i	0.137664	−	0.0794803i
$560$	1.10284	+	6.79791i	0.0466034	+	0.287264i
$561$	−0.760105	−	2.54945i	−0.0320917	−	0.107638i
$562$	26.6759			1.12525
$563$	−31.9871			−1.34809			−0.674047	−	0.738688i	$-0.735446\pi$
$563$	−31.9871			−1.34809			−0.674047	+	0.738688i	$0.735446\pi$
$564$	16.4370	−	4.90060i	0.692122	−	0.206352i
$565$	5.66542	−	15.5656i	0.238346	−	0.654851i
$566$	3.56413	−	20.2132i	0.149812	−	0.849624i
$567$	5.91307	−	23.0659i	0.248326	−	0.968677i
$568$	1.92727	−	1.61717i	0.0808666	−	0.0678551i
$569$	−11.2287	+	19.4486i	−0.470730	+	0.815329i	−0.999440	−	0.0334743i	$-0.989343\pi$
$569$	−11.2287	+	19.4486i	−0.470730	+	0.815329i	0.528709	+	0.848803i	$0.322676\pi$
$570$	−12.3348	−	15.2987i	−0.516647	−	0.640794i
$571$	−15.1765	−	26.2864i	−0.635115	−	1.10005i	−0.986491	−	0.163817i	$-0.947619\pi$
$571$	−15.1765	−	26.2864i	−0.635115	−	1.10005i	0.351375	−	0.936235i	$-0.385714\pi$
$572$	−0.213590	−	1.21133i	−0.00893066	−	0.0506483i
$573$	10.5129	−	7.80806i	0.439184	−	0.326186i
$574$	2.98678	−	7.86893i	0.124666	−	0.328443i
$575$	−5.28333	+	0.931594i	−0.220330	+	0.0388502i
$576$	2.92070	−	0.685221i	0.121696	−	0.0285509i
$577$	34.7259			1.44566			0.722829	−	0.691027i	$-0.242841\pi$
$577$	34.7259			1.44566			0.722829	+	0.691027i	$0.242841\pi$
$578$	7.55612	−	13.0876i	0.314293	−	0.544371i
$579$	4.18654	−	17.5755i	0.173987	−	0.730413i
$580$	−7.83586	+	9.33842i	−0.325366	+	0.387757i
$581$	34.8879	+	30.0986i	1.44740	+	1.24870i
$582$	10.6283	+	21.2226i	0.440555	+	0.879705i
$583$	−6.33486	−	1.11701i	−0.262363	−	0.0462617i
$584$	−3.73386	+	3.13308i	−0.154508	+	0.129648i
$585$	5.88202	+	6.26299i	0.243192	+	0.258943i
$586$	20.5694	−	17.2598i	0.849714	−	0.712994i
$587$	−23.3883	−	27.8731i	−0.965339	−	1.15045i	−0.988577	−	0.150716i	$-0.951842\pi$
$587$	−23.3883	−	27.8731i	−0.965339	−	1.15045i	0.0232386	−	0.999730i	$-0.492602\pi$
$588$	−5.11794	+	10.9912i	−0.211060	+	0.453270i
$589$	33.1446	+	10.5930i	1.36570	+	0.436475i
$590$	3.84011	+	2.21709i	0.158095	+	0.0912760i
$591$	−20.4025	+	15.1532i	−0.839248	+	0.623318i
$592$	−4.56137	+	0.804293i	−0.187471	+	0.0330562i
$593$	16.1782	−	19.2805i	0.664360	−	0.791754i	−0.323644	−	0.946179i	$-0.604908\pi$
$593$	16.1782	−	19.2805i	0.664360	−	0.791754i	0.988004	+	0.154425i	$0.0493526\pi$
$594$	0.0197728	−	5.80876i	0.000811287	−	0.238336i
$595$	−5.98228	−	7.33111i	−0.245250	−	0.300546i
$596$	4.36358	+	2.51932i	0.178739	+	0.103195i
$597$	28.8125	+	18.9972i	1.17922	+	0.777502i
$598$	−0.577345	+	3.27428i	−0.0236094	+	0.133895i
$599$	−1.51603	+	8.59786i	−0.0619435	+	0.351299i	0.938045	+	0.346513i	$0.112634\pi$
$599$	−1.51603	+	8.59786i	−0.0619435	+	0.351299i	−0.999989	+	0.00478565i	$0.998477\pi$
$600$	−2.56729	−	1.69271i	−0.104809	−	0.0691046i
$601$	28.4413	+	16.4206i	1.16014	+	0.669809i	0.951338	−	0.308148i	$-0.0997091\pi$
$601$	28.4413	+	16.4206i	1.16014	+	0.669809i	0.208805	+	0.977957i	$0.433042\pi$
$602$	−8.92063	+	1.44721i	−0.363578	+	0.0589839i
$603$	−1.92411	−	2.93998i	−0.0783558	−	0.119725i
$604$	9.11396	−	10.8616i	0.370842	−	0.441952i
$605$	−24.9941	+	4.40713i	−1.01615	+	0.179175i
$606$	4.64100	−	3.44692i	0.188528	−	0.140021i
$607$	20.1429	+	11.6295i	0.817573	+	0.472026i	0.849579	−	0.527461i	$-0.176856\pi$
$607$	20.1429	+	11.6295i	0.817573	+	0.472026i	−0.0320055	+	0.999488i	$0.510189\pi$
$608$	3.68538	−	2.32766i	0.149462	−	0.0943990i
$609$	−20.6490	+	5.84953i	−0.836740	+	0.237035i
$610$	−7.06870	−	8.42415i	−0.286203	−	0.341084i
$611$	−8.34670	+	7.00372i	−0.337672	+	0.283340i
$612$	−3.00456	+	2.82180i	−0.121452	+	0.114064i
$613$	23.0602	−	19.3498i	0.931393	−	0.781532i	−0.0446736	−	0.999002i	$-0.514225\pi$
$613$	23.0602	−	19.3498i	0.931393	−	0.781532i	0.976067	+	0.217470i	$0.0697803\pi$
$614$	−17.1580	−	3.02541i	−0.692439	−	0.122096i
$615$	6.42230	+	12.8241i	0.258972	+	0.517118i
$616$	−0.553460	+	2.90545i	−0.0222995	+	0.117064i
$617$	−3.19642	+	3.80934i	−0.128683	+	0.153358i	−0.826539	−	0.562880i	$-0.809693\pi$
$617$	−3.19642	+	3.80934i	−0.128683	+	0.153358i	0.697856	+	0.716239i	$0.254138\pi$
$618$	5.18614	−	21.7719i	0.208617	−	0.875795i
$619$	−7.29465	+	12.6347i	−0.293197	+	0.507832i	−0.974564	−	0.224110i	$-0.928052\pi$
$619$	−7.29465	+	12.6347i	−0.293197	+	0.507832i	0.681367	+	0.731942i	$0.261386\pi$
$620$	20.7789			0.834502
$621$	−5.42040	+	14.7362i	−0.217513	+	0.591342i
$622$	20.2003	−	3.56186i	0.809958	−	0.142818i
$623$	−12.2737	+	32.3361i	−0.491736	+	1.29552i
$624$	−1.52994	+	1.13631i	−0.0612468	+	0.0454886i
$625$	−5.33534	−	30.2582i	−0.213413	−	1.21033i
$626$	−7.21515	−	12.4970i	−0.288376	−	0.499481i
$627$	−2.73077	−	7.98600i	−0.109057	−	0.318930i
$628$	−10.4375	+	18.0782i	−0.416500	+	0.721400i
$629$	4.87497	−	4.09059i	0.194378	−	0.163102i
$630$	−7.87913	−	19.0990i	−0.313912	−	0.760921i
$631$	−5.69425	+	32.2937i	−0.226685	+	1.28559i	0.632754	+	0.774353i	$0.281925\pi$
$631$	−5.69425	+	32.2937i	−0.226685	+	1.28559i	−0.859438	+	0.511239i	$0.829187\pi$
$632$	1.00339	−	2.75679i	0.0399127	−	0.109659i
$633$	−2.06558	+	0.615841i	−0.0820994	+	0.0244775i
$634$	20.2749			0.805219
$635$	−6.42594			−0.255006
$636$	2.84758	+	9.55102i	0.112914	+	0.378723i
$637$	0.211045	−	7.69914i	0.00836192	−	0.305051i
$638$	−4.53405	+	2.61773i	−0.179505	+	0.103637i
$639$	−4.52086	+	6.04389i	−0.178842	+	0.239092i
$640$	1.67315	−	1.99398i	0.0661371	−	0.0788192i
$641$	25.2637	−	21.1988i	0.997856	−	0.837301i	0.0111701	−	0.999938i	$-0.496444\pi$
$641$	25.2637	−	21.1988i	0.997856	−	0.837301i	0.986686	+	0.162637i	$0.0519999\pi$
$642$	2.97191	+	9.96802i	0.117292	+	0.393406i
$643$	−21.1348	−	7.69244i	−0.833475	−	0.303360i	−0.110191	−	0.993910i	$-0.535146\pi$
$643$	−21.1348	−	7.69244i	−0.833475	−	0.303360i	−0.723284	+	0.690550i	$0.757368\pi$
$644$	4.09188	−	6.86826i	0.161243	−	0.270647i
$645$	8.47694	−	12.8568i	0.333779	−	0.506235i
$646$	−2.78612	+	5.30143i	−0.109618	+	0.208582i
$647$	42.4581	−	24.5132i	1.66920	−	0.963713i	0.701130	−	0.713033i	$-0.252679\pi$
$647$	42.4581	−	24.5132i	1.66920	−	0.963713i	0.968070	−	0.250680i	$-0.0806541\pi$
$648$	−8.06094	+	4.00265i	−0.316664	+	0.157239i
$649$	1.22410	+	1.45882i	0.0480501	+	0.0572638i
$650$	1.92379	+	0.339216i	0.0754573	+	0.0133052i
$651$	30.2620	+	20.5533i	1.18606	+	0.805546i
$652$	15.3737	−	5.59558i	0.602081	−	0.219140i
$653$	−15.3263	+	8.84864i	−0.599764	+	0.346274i	−0.768949	−	0.639310i	$-0.779220\pi$
$653$	−15.3263	+	8.84864i	−0.599764	+	0.346274i	0.169185	+	0.985584i	$0.445887\pi$
$654$	−13.0474	−	26.0532i	−0.510195	−	1.01876i
$655$	2.72745	−	15.4681i	0.106570	−	0.604389i
$656$	−2.98936	+	1.08804i	−0.116715	+	0.0424808i
$657$	8.75861	−	11.7093i	0.341706	−	0.456823i
$658$	24.7405	−	8.62277i	0.964485	−	0.336151i
$659$	16.7387	−	6.09237i	0.652045	−	0.237325i	0.00524703	−	0.999986i	$-0.498330\pi$
$659$	16.7387	−	6.09237i	0.652045	−	0.237325i	0.646798	+	0.762661i	$0.276108\pi$
$660$	−3.00510	−	4.04613i	−0.116974	−	0.157495i
$661$	6.93087	+	19.0424i	0.269580	+	0.740664i	0.998431	+	0.0559923i	$0.0178322\pi$
$661$	6.93087	+	19.0424i	0.269580	+	0.740664i	−0.728851	+	0.684672i	$0.759946\pi$
$662$	14.7267	−	2.59671i	0.572368	−	0.100924i
$663$	1.03984	−	2.40311i	0.0403839	−	0.0933292i
$664$		−	17.4155i		−	0.675852i
$665$	−19.8876	−	22.4858i	−0.771208	−	0.871964i
$666$	12.7713	−	5.47464i	0.494876	−	0.212138i
$667$	13.9367	−	2.45742i	0.539632	−	0.0951516i
$668$	−0.438514	−	2.48693i	−0.0169666	−	0.0962224i
$669$	6.98784	−	29.3356i	0.270165	−	1.13418i
$670$	−2.86477	−	1.04269i	−0.110676	−	0.0402826i
$671$	−1.61533	−	4.43807i	−0.0623590	−	0.171330i
$672$	4.40908	−	1.24902i	0.170084	−	0.0481820i
$673$	−31.8301	+	18.3771i	−1.22696	+	0.708386i	−0.966393	−	0.257069i	$-0.917243\pi$
$673$	−31.8301	+	18.3771i	−1.22696	+	0.708386i	−0.260568	+	0.965455i	$0.583910\pi$
$674$	6.52366	+	17.9236i	0.251282	+	0.690392i
$675$	8.65817	+	3.18473i	0.333253	+	0.122580i
$676$	−5.89468	+	10.2099i	−0.226718	+	0.392688i
$677$	12.3761	+	21.4360i	0.475652	+	0.823854i	0.999611	−	0.0278897i	$-0.00887873\pi$
$677$	12.3761	+	21.4360i	0.475652	+	0.823854i	−0.523959	+	0.851744i	$0.675545\pi$
$678$	−10.7223	−	2.55409i	−0.411789	−	0.0980893i
$679$	17.6961	+	31.6441i	0.679114	+	1.21439i
$680$	−0.621030	+	3.52203i	−0.0238154	+	0.135064i
$681$	−37.3457	+	4.32214i	−1.43109	+	0.165625i
$682$	8.38581	+	3.05219i	0.321109	+	0.116874i
$683$	−4.19218	−	7.26107i	−0.160409	−	0.277837i	0.774606	−	0.632444i	$-0.217948\pi$
$683$	−4.19218	−	7.26107i	−0.160409	−	0.277837i	−0.935016	+	0.354607i	$0.884615\pi$
$684$	−9.16891	+	9.32369i	−0.350582	+	0.356500i
$685$	0.745413			0.0284808
$686$	−7.04415	+	17.1283i	−0.268947	+	0.653963i
$687$	−30.0088	−	40.4044i	−1.14491	−	1.54152i
$688$	2.61663	+	2.19561i	0.0997580	+	0.0837069i
$689$	−4.06964	−	4.85001i	−0.155041	−	0.184771i
$690$	3.89243	+	13.0555i	0.148182	+	0.497015i
$691$	−24.5656	−	42.5489i	−0.934520	−	1.61864i	−0.775487	−	0.631364i	$-0.782496\pi$
$691$	−24.5656	−	42.5489i	−0.934520	−	1.61864i	−0.159034	−	0.987273i	$-0.550838\pi$
$692$	3.72888	+	6.45860i	0.141751	+	0.245519i
$693$	−0.374386	−	8.86518i	−0.0142218	−	0.336760i
$694$	20.9171	−	24.9280i	0.794002	−	0.946255i
$695$		−	25.0970i		−	0.951985i
$696$	6.77217	+	4.46514i	0.256698	+	0.169251i
$697$	2.80954	−	3.34827i	0.106419	−	0.126825i
$698$	−14.1242	−	5.14079i	−0.534609	−	0.194582i
$699$	−30.1283	−	28.4893i	−1.13956	−	1.07756i
$700$	−4.03542	−	2.40417i	−0.152524	−	0.0908690i
$701$	−11.0867	−	13.2126i	−0.418739	−	0.499034i	0.514899	−	0.857251i	$-0.327829\pi$
$701$	−11.0867	−	13.2126i	−0.418739	−	0.499034i	−0.933638	+	0.358217i	$0.883385\pi$
$702$	3.68988	−	4.36715i	0.139266	−	0.164828i
$703$	14.9383	−	13.5814i	0.563407	−	0.512234i
$704$	0.968132	−	0.558951i	0.0364879	−	0.0210663i
$705$	−17.7299	+	40.9745i	−0.667745	+	1.54319i
$706$	5.02484	−	13.8056i	0.189112	−	0.519582i
$707$	6.84180	−	5.58300i	0.257312	−	0.209970i
$708$	1.17173	−	2.70793i	0.0440364	−	0.101770i
$709$	−6.26475	+	35.5291i	−0.235278	+	1.33433i	0.606751	+	0.794892i	$0.292473\pi$
$709$	−6.26475	+	35.5291i	−0.235278	+	1.33433i	−0.842028	+	0.539433i	$0.818639\pi$
$710$			6.54873i			0.245770i
$711$	−1.04158	+	8.73929i	−0.0390625	+	0.327749i
$712$	12.2843	−	4.47113i	0.460375	−	0.167563i
$713$	−18.4785	−	15.5053i	−0.692025	−	0.580678i
$714$	−4.38824	+	4.51514i	−0.164226	+	0.168975i
$715$	2.77274	+	1.60085i	0.103695	+	0.0598682i
$716$	−2.97726	+	16.8849i	−0.111265	+	0.631017i
$717$	−1.80715	−	15.6148i	−0.0674894	−	0.583146i
$718$	6.58484	+	18.0917i	0.245744	+	0.675176i
$719$	3.38711	+	4.03660i	0.126318	+	0.150540i	0.825496	−	0.564407i	$-0.190895\pi$
$719$	3.38711	+	4.03660i	0.126318	+	0.150540i	−0.699179	+	0.714947i	$0.746451\pi$
$720$	−3.52045	+	6.97030i	−0.131199	+	0.259768i
$721$	6.39738	−	33.5838i	0.238251	−	1.25072i
$722$	−8.16401	+	17.1566i	−0.303833	+	0.638503i
$723$	5.82226	+	11.6259i	0.216532	+	0.432374i
$724$	−7.32684	+	20.1303i	−0.272300	+	0.748138i
$725$	−1.44385	−	8.18846i	−0.0536231	−	0.304112i
$726$	4.82517	+	16.1840i	0.179079	+	0.600645i
$727$	5.53183	+	31.3726i	0.205164	+	1.16354i	0.897181	+	0.441663i	$0.145611\pi$
$727$	5.53183	+	31.3726i	0.205164	+	1.16354i	−0.692017	+	0.721882i	$0.743278\pi$
$728$	−2.25546	+	1.84048i	−0.0835928	+	0.0682129i
$729$	20.8009	−	17.2141i	0.770403	−	0.637558i
$730$		−	12.6874i		−	0.469581i
$731$	−4.62182	−	0.814952i	−0.170944	−	0.0301421i
$732$	−5.02764	+	5.31688i	−0.185827	+	0.196518i
$733$	9.13036			0.337238			0.168619	−	0.985681i	$-0.446069\pi$
$733$	9.13036			0.337238			0.168619	+	0.985681i	$0.446069\pi$
$734$	−6.00356	+	10.3985i	−0.221596	+	0.383815i
$735$	−13.3532	−	28.5951i	−0.492541	−	1.05474i
$736$	−2.97584	+	0.524720i	−0.109691	+	0.0193414i
$737$	−1.00298	−	0.841603i	−0.0369454	−	0.0310009i
$738$	7.98548	−	5.22621i	0.293949	−	0.192379i
$739$	21.5744	+	7.85244i	0.793627	+	0.288857i	0.706843	−	0.707370i	$-0.250119\pi$
$739$	21.5744	+	7.85244i	0.793627	+	0.288857i	0.0867842	+	0.996227i	$0.472341\pi$
$740$	6.02812	−	10.4410i	0.221598	−	0.383819i
$741$	2.99349	−	7.74890i	0.109969	−	0.284663i
$742$	5.01043	+	14.3759i	0.183939	+	0.527757i
$743$	25.4125	−	21.3236i	0.932294	−	0.782287i	−0.0439340	−	0.999034i	$-0.513989\pi$
$743$	25.4125	−	21.3236i	0.932294	−	0.782287i	0.976228	+	0.216747i	$0.0695447\pi$
$744$	−1.58959	−	13.7349i	−0.0582772	−	0.503547i
$745$	−12.3244	+	4.48572i	−0.451532	+	0.164344i
$746$	4.57802	+	5.45588i	0.167613	+	0.199754i
$747$	11.9335	+	50.8654i	0.436623	+	1.86107i
$748$	−0.767977	+	1.33018i	−0.0280800	+	0.0486360i
$749$	5.22918	+	15.0036i	0.191070	+	0.548219i
$750$	−13.9319	+	4.15372i	−0.508721	+	0.151672i
$751$	−11.6792	−	32.0885i	−0.426182	−	1.17092i	−0.948112	−	0.317936i	$-0.897010\pi$
$751$	−11.6792	−	32.0885i	−0.426182	−	1.17092i	0.521930	−	0.852988i	$-0.325212\pi$
$752$	−8.57599	−	4.95135i	−0.312734	−	0.180557i
$753$	−28.6330	+	43.4269i	−1.04344	+	1.58257i
$754$	−5.07470	−	0.894806i	−0.184810	−	0.0325869i
$755$	6.40882	+	36.3462i	0.233241	+	1.32277i
$756$	−12.0217	+	6.66920i	−0.437226	+	0.242557i
$757$	−23.1563	−	8.42819i	−0.841629	−	0.306328i	−0.115006	−	0.993365i	$-0.536689\pi$
$757$	−23.1563	−	8.42819i	−0.841629	−	0.306328i	−0.726622	+	0.687037i	$0.758911\pi$
$758$	11.5806	−	2.04197i	0.420627	−	0.0741679i
$759$	−0.346826	+	5.84060i	−0.0125890	+	0.212000i
$760$	−1.52488	+	11.2431i	−0.0553132	+	0.407831i
$761$	−36.5720	−	21.1148i	−1.32573	−	0.765412i	−0.341097	−	0.940028i	$-0.610798\pi$
$761$	−36.5720	−	21.1148i	−1.32573	−	0.765412i	−0.984637	+	0.174616i	$0.944132\pi$
$762$	0.491585	+	4.24757i	0.0178082	+	0.153873i
$763$	−21.7241	−	38.8469i	−0.786464	−	1.40635i
$764$	−7.44572	−	1.31288i	−0.269377	−	0.0474984i
$765$	−0.599534	−	10.7123i	−0.0216762	−	0.387305i
$766$	1.70812	+	1.43329i	0.0617170	+	0.0517867i
$767$			1.87436i			0.0676791i
$768$	−1.44603	−	0.953419i	−0.0521790	−	0.0344035i
$769$	14.3737	+	12.0610i	0.518329	+	0.434930i	0.864049	−	0.503408i	$-0.167921\pi$
$769$	14.3737	+	12.0610i	0.518329	+	0.434930i	−0.345720	+	0.938338i	$0.612365\pi$
$770$	−4.86740	−	5.96485i	−0.175409	−	0.214958i
$771$	0.675854	−	11.3815i	0.0243403	−	0.409894i
$772$	−9.03363	+	5.21557i	−0.325127	+	0.187712i
$773$	1.19382	+	1.00174i	0.0429388	+	0.0360299i	0.664005	−	0.747729i	$-0.268856\pi$
$773$	1.19382	+	1.00174i	0.0429388	+	0.0360299i	−0.621066	+	0.783758i	$0.713300\pi$
$774$	−9.14685	−	4.61974i	−0.328777	−	0.166053i
$775$	−9.11007	+	10.8570i	−0.327244	+	0.389994i
$776$	4.68688	−	12.8771i	0.168249	−	0.462260i
$777$	19.1069	−	9.24343i	0.685454	−	0.331606i
$778$			1.33488i			0.0478579i
$779$	8.48435	−	10.9681i	0.303983	−	0.392971i
$780$	0.294053	−	4.95190i	0.0105288	−	0.177306i
$781$	−0.961934	+	2.64289i	−0.0344207	+	0.0945701i
$782$	3.18043	−	2.66870i	0.113732	−	0.0954324i
$783$	−22.8391	−	8.40089i	−0.816201	−	0.300223i
$784$	6.64098	−	2.21300i	0.237178	−	0.0790357i
$785$	−18.5842	−	51.0598i	−0.663300	−	1.82240i
$786$	−10.4331	−	0.619539i	−0.372137	−	0.0220982i
$787$	44.8445	+	25.8910i	1.59853	+	0.922913i	0.991770	+	0.128029i	$0.0408652\pi$
$787$	44.8445	+	25.8910i	1.59853	+	0.922913i	0.606762	+	0.794884i	$0.292468\pi$
$788$	14.4500	+	2.54792i	0.514759	+	0.0907659i
$789$	−1.57247	+	6.60137i	−0.0559813	+	0.235015i
$790$	3.81817	+	6.61327i	0.135845	+	0.235290i
$791$	−16.5395	−	3.15061i	−0.588076	−	0.112023i
$792$	−2.44462	+	2.29591i	−0.0868656	+	0.0815817i
$793$	1.58988	−	4.36815i	0.0564582	−	0.155118i
$794$	5.03567	−	1.83283i	0.178709	−	0.0650448i
$795$	−23.8090	−	10.3023i	−0.844419	−	0.365384i
$796$	−3.45999	−	19.6226i	−0.122636	−	0.695504i
$797$	26.3598			0.933713			0.466856	−	0.884333i	$-0.345386\pi$
$797$	26.3598			0.933713			0.466856	+	0.884333i	$0.345386\pi$
$798$	−13.3418	+	14.8659i	−0.472295	+	0.526248i
$799$	13.6059			0.481343
$800$	0.308297	+	1.74844i	0.0108999	+	0.0618167i
$801$	−32.8151	+	21.4763i	−1.15946	+	0.758828i
$802$	14.8178	−	5.39322i	0.523233	−	0.190441i
$803$	1.86363	−	5.12028i	0.0657660	−	0.180691i
$804$	−0.470067	+	1.97339i	−0.0165780	+	0.0695960i
$805$	6.84887	+	19.6508i	0.241391	+	0.692599i
$806$	4.39170	+	7.60665i	0.154691	+	0.267933i
$807$	41.1638	+	9.80535i	1.44904	+	0.345165i
$808$	−3.28696	−	0.579580i	−0.115635	−	0.0203896i
$809$	−17.1172	−	9.88263i	−0.601809	−	0.347455i	0.167944	−	0.985797i	$-0.446287\pi$
$809$	−17.1172	−	9.88263i	−0.601809	−	0.347455i	−0.769753	+	0.638342i	$0.779621\pi$
$810$	5.50596	−	22.7704i	0.193460	−	0.800072i
$811$	−2.08632	−	5.73213i	−0.0732607	−	0.201282i	0.897657	−	0.440694i	$-0.145268\pi$
$811$	−2.08632	−	5.73213i	−0.0732607	−	0.201282i	−0.970918	+	0.239412i	$0.923045\pi$
$812$	10.6449	+	6.34187i	0.373562	+	0.222556i
$813$	16.7961	−	17.7624i	0.589066	−	0.622956i
$814$	3.96645	−	3.32825i	0.139024	−	0.116655i
$815$	−14.5651	+	40.0172i	−0.510192	+	1.40174i
$816$	2.37558	+	0.141067i	0.0831621	+	0.00493833i
$817$	−14.7539	−	2.00104i	−0.516173	−	0.0700074i
$818$		−	13.6351i		−	0.476741i
$819$	5.32637	−	6.92099i	0.186118	−	0.241839i
$820$	2.83212	−	7.78120i	0.0989021	−	0.271731i
$821$	10.8270	−	12.9031i	0.377866	−	0.450323i	−0.543274	−	0.839556i	$-0.682815\pi$
$821$	10.8270	−	12.9031i	0.377866	−	0.450323i	0.921139	+	0.389233i	$0.127260\pi$
$822$	−0.0570241	−	0.492720i	−0.00198894	−	0.0171856i
$823$	−17.0972	−	14.3462i	−0.595970	−	0.500078i	0.294178	−	0.955751i	$-0.404954\pi$
$823$	−17.0972	−	14.3462i	−0.595970	−	0.500078i	−0.890147	+	0.455673i	$0.849399\pi$
$824$	−11.1905	+	6.46086i	−0.389841	+	0.225075i
$825$	3.43162	+	0.203776i	0.119474	+	0.00709458i
$826$	1.59939	−	4.21374i	0.0556500	−	0.146615i
$827$	−27.4862	−	23.0637i	−0.955789	−	0.802002i	0.0244738	−	0.999700i	$-0.492209\pi$
$827$	−27.4862	−	23.0637i	−0.955789	−	0.802002i	−0.980263	+	0.197698i	$0.936653\pi$
$828$	8.33196	−	3.57165i	0.289556	−	0.124124i
$829$		−	50.6545i		−	1.75930i	−0.475618	−	0.879652i	$-0.657775\pi$
$829$		−	50.6545i		−	1.75930i	0.475618	−	0.879652i	$-0.342225\pi$
$830$	34.7262	+	29.1388i	1.20536	+	1.01142i
$831$	3.62682	+	4.88322i	0.125813	+	0.169397i
$832$	1.08357	+	0.191063i	0.0375662	+	0.00662393i
$833$	−6.38171	+	7.19544i	−0.221113	+	0.249307i
$834$	−16.5892	+	1.91993i	−0.574438	+	0.0664816i
$835$	5.69261	+	3.28663i	0.197001	+	0.113738i
$836$	−2.26688	+	4.31343i	−0.0784018	+	0.149183i
$837$	14.0542	+	39.0264i	0.485784	+	1.34895i
$838$	−9.29610	+	1.63915i	−0.321128	+	0.0566236i
$839$	−3.57967	−	1.30289i	−0.123584	−	0.0449809i	0.279488	−	0.960149i	$-0.409835\pi$
$839$	−3.57967	−	1.30289i	−0.123584	−	0.0449809i	−0.403072	+	0.915168i	$0.632058\pi$
$840$	−4.88653	+	10.8814i	−0.168601	+	0.375445i
$841$	−1.22713	−	6.95939i	−0.0423148	−	0.239979i
$842$	8.69801	+	1.53369i	0.299753	+	0.0528546i
$843$	38.5740	+	25.4333i	1.32856	+	0.875969i
$844$	1.07772	+	0.622219i	0.0370965	+	0.0214177i
$845$	−10.4957	−	28.8366i	−0.361062	−	0.992009i
$846$	28.4406	+	8.58494i	0.977810	+	0.295156i
$847$	8.49007	+	24.3597i	0.291722	+	0.837010i
$848$	2.87708	−	4.98324i	0.0987992	−	0.171125i
$849$	24.4255	−	25.8307i	0.838280	−	0.886507i
$850$	−1.56798	−	1.86865i	−0.0537813	−	0.0640941i
$851$	−13.1519	+	4.78689i	−0.450840	+	0.164092i
$852$	4.32873	−	0.500978i	0.148300	−	0.0171632i
$853$	−20.6495	+	17.3270i	−0.707026	+	0.593265i	−0.923763	−	0.382965i	$-0.874903\pi$
$853$	−20.6495	+	17.3270i	−0.707026	+	0.593265i	0.216737	+	0.976230i	$0.430459\pi$
$854$	−7.30155	+	8.46339i	−0.249854	+	0.289611i
$855$	−3.25031	−	33.8826i	−0.111158	−	1.15876i
$856$	3.00269	−	5.20081i	0.102630	−	0.177760i
$857$	−31.9415	−	11.6257i	−1.09110	−	0.397128i	−0.267072	−	0.963677i	$-0.586056\pi$
$857$	−31.9415	−	11.6257i	−1.09110	−	0.397128i	−0.824028	+	0.566549i	$0.808278\pi$
$858$	0.846049	−	1.95526i	0.0288836	−	0.0667514i
$859$	−26.0121	−	21.8267i	−0.887521	−	0.744719i	0.0801902	−	0.996780i	$-0.474447\pi$
$859$	−26.0121	−	21.8267i	−0.887521	−	0.744719i	−0.967711	+	0.252061i	$0.918892\pi$
$860$	−8.75603	+	1.54392i	−0.298578	+	0.0526474i
$861$	11.8213	−	8.53102i	0.402870	−	0.290736i
$862$	8.44469	−	14.6266i	0.287627	−	0.498185i
$863$	35.4482			1.20667			0.603335	−	0.797488i	$-0.293838\pi$
$863$	35.4482			1.20667			0.603335	+	0.797488i	$0.293838\pi$
$864$	4.87671	+	1.79380i	0.165909	+	0.0610263i
$865$	−19.1173	−	3.37090i	−0.650009	−	0.114614i
$866$			27.4671i			0.933369i
$867$	23.4043	−	11.7208i	0.794851	−	0.398061i
$868$	−3.38220	−	20.8479i	−0.114799	−	0.707625i
$869$	0.569498	+	3.22978i	0.0193189	+	0.109563i
$870$	−20.2343	+	6.03274i	−0.686007	+	0.204529i
$871$	−0.223776	−	1.26910i	−0.00758236	−	0.0430017i
$872$	−5.75369	+	15.8081i	−0.194845	+	0.535331i
$873$	−4.86529	+	40.8216i	−0.164665	+	1.38160i
$874$	9.74571	−	8.86052i	0.329653	−	0.299712i
$875$	−20.9699	+	7.30862i	−0.708913	+	0.247076i
$876$	−8.38639	+	0.970584i	−0.283350	+	0.0327930i
$877$	2.61470	+	3.11608i	0.0882921	+	0.105222i	0.808382	−	0.588659i	$-0.200344\pi$
$877$	2.61470	+	3.11608i	0.0882921	+	0.105222i	−0.720090	+	0.693881i	$0.755899\pi$
$878$	7.42978	+	20.4132i	0.250743	+	0.688911i
$879$	46.1997	−	5.34684i	1.55828	−	0.180344i
$880$	−0.505292	+	2.86565i	−0.0170334	+	0.0966011i
$881$	−38.2535	−	22.0857i	−1.28879	−	0.744086i	−0.310355	−	0.950621i	$-0.600448\pi$
$881$	−38.2535	−	22.0857i	−1.28879	−	0.744086i	−0.978439	+	0.206535i	$0.933781\pi$
$882$	−17.8799	+	11.0140i	−0.602047	+	0.370862i
$883$	3.70911	+	3.11232i	0.124822	+	0.104738i	0.703062	−	0.711129i	$-0.251816\pi$
$883$	3.70911	+	3.11232i	0.124822	+	0.104738i	−0.578240	+	0.815867i	$0.696260\pi$
$884$	−1.42059	+	0.517051i	−0.0477795	+	0.0173903i
$885$	3.43908	+	6.86719i	0.115604	+	0.230838i
$886$		−	23.8157i		−	0.800105i
$887$	3.43582	−	19.4855i	0.115364	−	0.654260i	−0.871206	−	0.490918i	$-0.836661\pi$
$887$	3.43582	−	19.4855i	0.115364	−	0.654260i	0.986569	−	0.163342i	$-0.0522274\pi$
$888$	−7.36269	−	3.18587i	−0.247076	−	0.106911i
$889$	1.04595	+	6.44728i	0.0350802	+	0.216235i
$890$	−11.6382	+	31.9756i	−0.390113	+	1.07183i
$891$	5.56677	−	8.38077i	0.186494	−	0.280766i
$892$	−15.0782	+	8.70541i	−0.504856	+	0.291479i
$893$	43.1308	−	1.71439i	1.44332	−	0.0573698i
$894$	3.90789	+	7.80332i	0.130699	+	0.260982i
$895$	−28.6868	−	34.1876i	−0.958893	−	1.14276i
$896$	−2.27295	−	1.35415i	−0.0759338	−	0.0452389i
$897$	−3.95662	+	4.18425i	−0.132108	+	0.139708i
$898$	35.1228	+	12.7836i	1.17206	+	0.426596i
$899$	24.0311	−	28.6392i	0.801483	−	0.955171i
$900$	−2.09851	−	4.89541i	−0.0699503	−	0.163180i
$901$			7.90598i			0.263386i
$902$	2.28594	−	2.72427i	0.0761134	−	0.0907084i
$903$	−14.2793	−	6.41239i	−0.475184	−	0.213391i
$904$	3.18187	+	5.51117i	0.105828	+	0.183299i
$905$	−27.8807	−	48.2907i	−0.926785	−	1.60524i
$906$	23.5347	−	7.01673i	0.781887	−	0.233115i
$907$	28.3274	+	33.7593i	0.940596	+	1.12096i	0.992492	+	0.122307i	$0.0390292\pi$
$907$	28.3274	+	33.7593i	0.940596	+	1.12096i	−0.0518959	+	0.998653i	$0.516526\pi$
$908$	16.6274	+	13.9520i	0.551798	+	0.463014i
$909$	9.99736	−	0.559519i	0.331591	−	0.0185581i
$910$	0.103826	−	7.57676i	0.00344179	−	0.251167i
$911$	13.6933			0.453679			0.226840	−	0.973932i	$-0.427161\pi$
$911$	13.6933			0.453679			0.226840	+	0.973932i	$0.427161\pi$
$912$	7.54839	+	0.147851i	0.249952	+	0.00489584i
$913$	9.73441	+	16.8605i	0.322162	+	0.558001i
$914$	1.88170	+	0.684881i	0.0622410	+	0.0226539i
$915$	−2.18979	−	18.9210i	−0.0723921	−	0.625508i
$916$	−5.04581	+	28.6162i	−0.166718	+	0.945506i
$917$	−15.9634	−	0.218750i	−0.527159	−	0.00722376i
$918$	−7.03502	+	1.21579i	−0.232190	+	0.0401270i
$919$	11.8445	+	20.5152i	0.390713	+	0.676735i	0.992544	−	0.121889i	$-0.0388951\pi$
$919$	11.8445	+	20.5152i	0.390713	+	0.676735i	−0.601831	+	0.798624i	$0.705562\pi$
$920$	3.93274	−	6.81171i	0.129659	−	0.224575i
$921$	−21.9264	−	20.7336i	−0.722499	−	0.683194i
$922$	4.22598	+	11.6108i	0.139175	+	0.382381i
$923$	−2.39733	+	1.38410i	−0.0789090	+	0.0455581i
$924$	−3.57043	+	3.67368i	−0.117458	+	0.120855i
$925$	2.81251	+	7.72732i	0.0924749	+	0.254073i
$926$	−8.18167	−	2.97789i	−0.268867	−	0.0978594i
$927$	28.2570	−	26.5382i	0.928083	−	0.871629i
$928$	−0.813246	−	4.61214i	−0.0266961	−	0.151401i
$929$	18.5812	−	3.27637i	0.609630	−	0.107494i	0.139694	−	0.990195i	$-0.455388\pi$
$929$	18.5812	−	3.27637i	0.609630	−	0.107494i	0.469936	+	0.882701i	$0.344277\pi$
$930$	30.0469	+	19.8110i	0.985276	+	0.649629i
$931$	−19.3234	+	23.6137i	−0.633299	+	0.773907i
$932$			23.9399i			0.784176i
$933$	32.6061	+	14.1088i	1.06748	+	0.461902i
$934$	−21.8359	+	3.85025i	−0.714492	+	0.125984i
$935$	−1.36741	−	3.75692i	−0.0447190	−	0.122864i
$936$	−3.29571	+	0.184450i	−0.107724	+	0.00602894i
$937$	−20.8403	+	7.58525i	−0.680823	+	0.247799i	−0.659201	−	0.751967i	$-0.729105\pi$
$937$	−20.8403	+	7.58525i	−0.680823	+	0.247799i	−0.0216219	+	0.999766i	$0.506883\pi$
$938$	−0.579853	+	3.04400i	−0.0189329	+	0.0993902i
$939$	1.48158	−	24.9501i	0.0483497	−	0.814215i
$940$	24.2219	−	8.81603i	0.790030	−	0.287547i
$941$	1.74075	−	9.87230i	0.0567469	−	0.321828i	−0.943199	−	0.332228i	$-0.892200\pi$
$941$	1.74075	−	9.87230i	0.0567469	−	0.321828i	0.999946	+	0.0104005i	$0.00331064\pi$
$942$	−32.3290	+	16.1903i	−1.05334	+	0.527509i
$943$	−8.32494	+	4.80640i	−0.271097	+	0.156518i
$944$	−1.60078	+	0.582635i	−0.0521008	+	0.0189631i
$945$	6.81587	−	35.1297i	0.221720	−	1.14277i
$946$	−3.76048	−	0.663074i	−0.122264	−	0.0215584i
$947$	16.3357	+	19.4681i	0.530839	+	0.632630i	0.963108	−	0.269115i	$-0.0867313\pi$
$947$	16.3357	+	19.4681i	0.530839	+	0.632630i	−0.432269	+	0.901745i	$0.642287\pi$
$948$	4.07930	−	3.02974i	0.132490	−	0.0984014i
$949$	4.64453	−	2.68152i	0.150768	−	0.0870458i
$950$	−5.20596	−	5.72605i	−0.168904	−	0.185778i
$951$	29.3180	+	19.3305i	0.950702	+	0.626833i
$952$	3.63482	+	0.0498086i	0.117805	+	0.00161431i
$953$	−40.3622	−	14.6906i	−1.30746	−	0.475877i	−0.408041	−	0.912964i	$-0.633788\pi$
$953$	−40.3622	−	14.6906i	−1.30746	−	0.475877i	−0.899419	+	0.437087i	$0.856010\pi$
$954$	−4.98844	+	16.5260i	−0.161507	+	0.535048i
$955$	15.0757	−	12.6500i	0.487838	−	0.409345i
$956$	−5.83355	+	6.95215i	−0.188670	+	0.224849i
$957$	−9.05215	−	0.537534i	−0.292614	−	0.0173760i
$958$	−15.4625	+	8.92730i	−0.499572	+	0.288428i
$959$	−0.121331	−	0.747888i	−0.00391799	−	0.0241506i
$960$	4.32052	−	1.28814i	0.139444	−	0.0415745i
$961$	−32.7251			−1.05565
$962$	5.09626			0.164310
$963$	−5.20624	+	17.2475i	−0.167769	+	0.555793i
$964$	2.56752	−	7.05419i	0.0826941	−	0.227200i
$965$	4.71487	−	26.7393i	0.151777	−	0.860770i
$966$	12.4653	−	6.03041i	0.401064	−	0.194025i
$967$	−1.38160	+	1.15930i	−0.0444293	+	0.0372806i	−0.664732	−	0.747082i	$-0.731454\pi$
$967$	−1.38160	+	1.15930i	−0.0444293	+	0.0372806i	0.620303	+	0.784363i	$0.287010\pi$
$968$	4.87515	−	8.44400i	0.156693	−	0.271400i
$969$	−9.08328	+	5.00967i	−0.291797	+	0.160934i
$970$	17.8349	+	30.8909i	0.572643	+	0.991846i
$971$	6.66208	+	37.7826i	0.213796	+	1.21250i	0.882983	+	0.469405i	$0.155532\pi$
$971$	6.66208	+	37.7826i	0.213796	+	1.21250i	−0.669186	+	0.743095i	$0.733357\pi$
$972$	−15.4725	−	1.89752i	−0.496282	−	0.0608629i
$973$	−25.1804	+	4.08506i	−0.807247	+	0.130961i
$974$	15.0354	−	2.65114i	0.481765	−	0.0849481i
$975$	2.45844	+	2.32469i	0.0787330	+	0.0744498i
$976$	4.22478			0.135232
$977$	−16.4482	+	28.4892i	−0.526225	+	0.911449i	0.473308	+	0.880897i	$0.343060\pi$
$977$	−16.4482	+	28.4892i	−0.526225	+	0.911449i	−0.999533	+	0.0305521i	$0.990273\pi$
$978$	27.5657	+	6.56624i	0.881455	+	0.209965i
$979$	−9.39371	+	11.1950i	−0.300224	+	0.357793i
$980$	−6.69868	+	16.9447i	−0.213981	+	0.541279i
$981$	5.97272	−	50.1133i	0.190694	−	1.60000i
$982$	26.3852	+	4.65241i	0.841984	+	0.148464i
$983$	13.5510	−	11.3706i	0.432210	−	0.362667i	−0.400575	−	0.916264i	$-0.631190\pi$
$983$	13.5510	−	11.3706i	0.432210	−	0.362667i	0.832785	+	0.553597i	$0.186745\pi$
$984$	−5.36005	−	1.27678i	−0.170872	−	0.0407023i
$985$	−29.2575	+	24.5500i	−0.932222	+	0.782227i
$986$	4.13612	+	4.92924i	0.131721	+	0.156979i
$987$	43.9965	+	11.1193i	1.40043	+	0.353931i
$988$	−4.43811	+	1.81805i	−0.141195	+	0.0578399i
$989$	8.93873	+	5.16078i	0.284235	+	0.164103i
$990$	−0.487802	−	8.71594i	−0.0155034	−	0.277011i
$991$	49.7346	−	8.76955i	1.57987	−	0.278574i	0.686239	−	0.727376i	$-0.259260\pi$
$991$	49.7346	−	8.76955i	1.57987	−	0.278574i	0.893631	+	0.448802i	$0.148149\pi$
$992$	−5.13125	+	6.11518i	−0.162917	+	0.194157i
$993$	23.7709	+	10.2858i	0.754347	+	0.326409i
$994$	6.57048	−	1.06594i	0.208403	−	0.0338096i
$995$	44.9162	+	25.9324i	1.42394	+	0.822112i
$996$	16.6043	−	25.1833i	0.526126	−	0.797962i
$997$	7.94071	−	45.0340i	0.251485	−	1.42624i	−0.553452	−	0.832881i	$-0.686690\pi$
$997$	7.94071	−	45.0340i	0.251485	−	1.42624i	0.804937	−	0.593361i	$-0.202199\pi$
$998$	6.95773	−	39.4593i	0.220243	−	1.24906i
$999$	23.6872	+	4.25988i	0.749430	+	0.134777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cc.b.317.17	yes	162
3.2	odd	2		798.2.cc.a.317.20	yes	162
7.4	even	3		798.2.bu.b.431.2	yes	162
19.3	odd	18		798.2.bu.a.611.16	yes	162
21.11	odd	6		798.2.bu.a.431.16	✓	162
57.41	even	18		798.2.bu.b.611.2	yes	162
133.60	odd	18		798.2.cc.a.725.20	yes	162
399.326	even	18	inner	798.2.cc.b.725.17	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.16	✓	162	21.11	odd	6
798.2.bu.a.611.16	yes	162	19.3	odd	18
798.2.bu.b.431.2	yes	162	7.4	even	3
798.2.bu.b.611.2	yes	162	57.41	even	18
798.2.cc.a.317.20	yes	162	3.2	odd	2
798.2.cc.a.725.20	yes	162	133.60	odd	18
798.2.cc.b.317.17	yes	162	1.1	even	1	trivial
798.2.cc.b.725.17	yes	162	399.326	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.687834 - 1.58962i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.890265 - 2.44598i) q^{5} +(-1.68491 - 0.401350i) q^{6} +(-2.59902 - 0.495088i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.05377 - 2.18679i) q^{9} +(-2.56342 - 0.452000i) q^{10} +(-0.968132 - 0.558951i) q^{11} +(-0.102672 + 1.72901i) q^{12} +(-0.376322 - 1.03393i) q^{13} +(-0.0362518 + 2.64550i) q^{14} +(-3.27582 - 3.09761i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.469922 + 1.29110i) q^{17} +(-1.79693 + 2.40230i) q^{18} +(-1.32697 + 4.15200i) q^{19} +2.60296i q^{20} +(-2.57469 + 3.79090i) q^{21} +(-0.382345 + 1.05049i) q^{22} +(1.94234 - 2.31479i) q^{23} +(1.72057 - 0.199127i) q^{24} +(-1.36004 - 1.14121i) q^{25} +(-0.952880 + 0.550145i) q^{26} +(-4.88881 + 1.76056i) q^{27} +(2.61161 - 0.423686i) q^{28} +(3.58761 + 3.01036i) q^{29} +(-2.48171 + 3.76395i) q^{30} -7.98280i q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.55443 + 1.15449i) q^{33} +(1.35309 + 0.238586i) q^{34} +(-3.52479 + 5.91639i) q^{35} +(2.67784 + 1.35248i) q^{36} +(-4.01120 - 2.31587i) q^{37} +(4.31935 + 0.585824i) q^{38} +(-1.90241 - 0.112969i) q^{39} +(2.56342 - 0.452000i) q^{40} +(-2.98936 - 1.08804i) q^{41} +(4.18040 + 1.87729i) q^{42} +(0.593141 + 3.36387i) q^{43} +(1.10092 + 0.194122i) q^{44} +(-7.17725 + 3.07666i) q^{45} +(-2.61691 - 1.51087i) q^{46} +(-3.38692 - 9.30550i) q^{47} +(-0.494875 - 1.65985i) q^{48} +(6.50978 + 2.57348i) q^{49} +(-0.887706 + 1.53755i) q^{50} +(1.72913 + 1.63506i) q^{51} +(0.707253 + 0.842871i) q^{52} +(5.40713 - 1.96804i) q^{53} +(2.58274 + 4.50882i) q^{54} +(-2.22908 + 1.87042i) q^{55} +(-0.870750 - 2.49836i) q^{56} +(5.68736 + 4.96527i) q^{57} +(2.34165 - 4.05585i) q^{58} +(-1.60078 - 0.582635i) q^{59} +(4.13771 + 1.79041i) q^{60} +(3.23637 + 2.71564i) q^{61} +(-7.86152 + 1.38620i) q^{62} +(4.25512 + 6.70029i) q^{63} +(-0.500000 + 0.866025i) q^{64} -2.86401 q^{65} +(1.40688 + 1.33034i) q^{66} +(1.15342 + 0.203379i) q^{67} -1.37396i q^{68} +(-2.34362 - 4.67977i) q^{69} +(6.43858 + 2.44387i) q^{70} +(-0.436878 - 2.47766i) q^{71} +(0.866929 - 2.87201i) q^{72} +(0.846397 + 4.80015i) q^{73} +(-1.58415 + 4.35241i) q^{74} +(-2.74958 + 1.37698i) q^{75} +(-0.173123 - 4.35546i) q^{76} +(2.23946 + 1.93203i) q^{77} +(0.219097 + 1.89312i) q^{78} +(-1.88575 - 2.24736i) q^{79} +(-0.890265 - 2.44598i) q^{80} +(-0.564076 + 8.98231i) q^{81} +(-0.552412 + 3.13288i) q^{82} +(-15.0823 - 8.70774i) q^{83} +(1.12285 - 4.44288i) q^{84} +(2.73966 + 2.29884i) q^{85} +(3.20977 - 1.16826i) q^{86} +(7.25301 - 3.63230i) q^{87} -1.11790i q^{88} +(2.27005 - 12.8741i) q^{89} +(4.27624 + 6.53395i) q^{90} +(0.466177 + 2.87353i) q^{91} +(-1.03350 + 2.83951i) q^{92} +(-12.6896 - 5.49085i) q^{93} +(-8.57599 + 4.95135i) q^{94} +(8.97438 + 6.94214i) q^{95} +(-1.54870 + 0.775586i) q^{96} +(-8.80844 - 10.4975i) q^{97} +(1.40398 - 6.85776i) q^{98} +(0.766011 + 3.26506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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