LMFDB - Embedded newform 540.2.be.a.491.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			491.28
Character	$\chi$	$=$	540.491
Dual form			540.2.be.a.11.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.537858 - 1.30794i) q^{2} +(1.12619 - 1.31594i) q^{3} +(-1.42142 + 1.40697i) q^{4} +(0.342020 + 0.939693i) q^{5} +(-2.32690 - 0.765193i) q^{6} +(-4.64650 + 0.819302i) q^{7} +(2.60476 + 1.10238i) q^{8} +(-0.463415 - 2.96399i) q^{9} +(1.04510 - 0.952763i) q^{10} +(-2.41957 - 0.880650i) q^{11} +(0.250715 + 3.45502i) q^{12} +(-0.378011 - 0.317189i) q^{13} +(3.57075 + 5.63667i) q^{14} +(1.62176 + 0.608189i) q^{15} +(0.0408615 - 3.99979i) q^{16} +(-4.19187 - 2.42018i) q^{17} +(-3.62747 + 2.20032i) q^{18} +(-3.67476 + 2.12162i) q^{19} +(-1.80827 - 0.854484i) q^{20} +(-4.15466 + 7.03721i) q^{21} +(0.149544 + 3.63831i) q^{22} +(-0.984432 + 5.58299i) q^{23} +(4.38411 - 2.18623i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(-0.211548 + 0.665018i) q^{26} +(-4.42234 - 2.72818i) q^{27} +(5.45188 - 7.70206i) q^{28} +(3.28825 + 3.91878i) q^{29} +(-0.0768014 - 2.44829i) q^{30} +(-5.46534 - 0.963686i) q^{31} +(-5.25347 + 2.09787i) q^{32} +(-3.88376 + 2.19224i) q^{33} +(-0.910820 + 6.78443i) q^{34} +(-2.35909 - 4.08606i) q^{35} +(4.82896 + 3.56106i) q^{36} +(5.45430 - 9.44713i) q^{37} +(4.75145 + 3.66523i) q^{38} +(-0.843112 + 0.140228i) q^{39} +(-0.145020 + 2.82471i) q^{40} +(-5.41030 + 6.44774i) q^{41} +(11.4389 + 1.64903i) q^{42} +(3.66535 - 10.0705i) q^{43} +(4.67826 - 2.15249i) q^{44} +(2.62674 - 1.44921i) q^{45} +(7.83170 - 1.71527i) q^{46} +(-0.122222 - 0.693155i) q^{47} +(-5.21748 - 4.55828i) q^{48} +(14.3408 - 5.21963i) q^{49} +(1.25275 + 0.656213i) q^{50} +(-7.90564 + 2.79070i) q^{51} +(0.983587 - 0.0809925i) q^{52} -3.75742i q^{53} +(-1.18971 + 7.25152i) q^{54} -2.57485i q^{55} +(-13.0062 - 2.98813i) q^{56} +(-1.34652 + 7.22511i) q^{57} +(3.35692 - 6.40858i) q^{58} +(-4.56304 + 1.66081i) q^{59} +(-3.16090 + 1.41728i) q^{60} +(2.25866 + 12.8095i) q^{61} +(1.67913 + 7.66666i) q^{62} +(4.58166 + 13.3925i) q^{63} +(5.56951 + 5.74287i) q^{64} +(0.168773 - 0.463699i) q^{65} +(4.95623 + 3.90062i) q^{66} +(4.03968 - 4.81430i) q^{67} +(9.36352 - 2.45776i) q^{68} +(6.23825 + 7.58293i) q^{69} +(-4.07547 + 5.28326i) q^{70} +(3.92026 - 6.79009i) q^{71} +(2.06037 - 8.23134i) q^{72} +(-4.53053 - 7.84711i) q^{73} +(-15.2899 - 2.05270i) q^{74} +(-0.0168356 + 1.73197i) q^{75} +(2.23831 - 8.18599i) q^{76} +(11.9640 + 2.10958i) q^{77} +(0.636884 + 1.02732i) q^{78} +(1.45125 + 1.72954i) q^{79} +(3.77255 - 1.32961i) q^{80} +(-8.57049 + 2.74711i) q^{81} +(11.3432 + 3.60838i) q^{82} +(-3.70034 + 3.10495i) q^{83} +(-3.99565 - 15.8483i) q^{84} +(0.840519 - 4.76682i) q^{85} +(-15.1430 + 0.622416i) q^{86} +(8.86007 + 0.0861241i) q^{87} +(-5.33157 - 4.96116i) q^{88} +(-3.52826 + 2.03704i) q^{89} +(-3.30830 - 2.65616i) q^{90} +(2.01630 + 1.16411i) q^{91} +(-6.45582 - 9.32083i) q^{92} +(-7.42314 + 6.10679i) q^{93} +(-0.840867 + 0.532677i) q^{94} +(-3.25051 - 2.72750i) q^{95} +(-3.15569 + 9.27586i) q^{96} +(-5.74588 - 2.09133i) q^{97} +(-14.5403 - 15.9495i) q^{98} +(-1.48898 + 7.57968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	−0.537858	−	1.30794i	−0.380323	−	0.924854i
$2$	−0.537858	−	1.30794i	−0.380323	−	0.924854i
$3$	1.12619	−	1.31594i	0.650203	−	0.759760i
$3$	1.12619	−	1.31594i	0.650203	−	0.759760i
$4$	−1.42142	+	1.40697i	−0.710709	+	0.703486i
$5$	0.342020	+	0.939693i	0.152956	+	0.420243i
$5$	0.342020	+	0.939693i	0.152956	+	0.420243i
$6$	−2.32690	−	0.765193i	−0.949954	−	0.312389i
$7$	−4.64650	+	0.819302i	−1.75621	+	0.309667i	−0.956720	−	0.291011i	$-0.906008\pi$
$7$	−4.64650	+	0.819302i	−1.75621	+	0.309667i	−0.799491	+	0.600679i	$0.794897\pi$
$8$	2.60476	+	1.10238i	0.920920	+	0.389751i
$9$	−0.463415	−	2.96399i	−0.154472	−	0.987997i
$10$	1.04510	−	0.952763i	0.330491	−	0.301290i
$11$	−2.41957	−	0.880650i	−0.729526	−	0.265526i	−0.0495620	−	0.998771i	$-0.515783\pi$
$11$	−2.41957	−	0.880650i	−0.729526	−	0.265526i	−0.679964	+	0.733245i	$0.738005\pi$
$12$	0.250715	+	3.45502i	0.0723752	+	0.997377i
$13$	−0.378011	−	0.317189i	−0.104841	−	0.0879723i	0.588860	−	0.808235i	$-0.299577\pi$
$13$	−0.378011	−	0.317189i	−0.104841	−	0.0879723i	−0.693702	+	0.720263i	$0.744021\pi$
$14$	3.57075	+	5.63667i	0.954324	+	1.50646i
$15$	1.62176	+	0.608189i	0.418737	+	0.157034i
$16$	0.0408615	−	3.99979i	0.0102154	−	0.999948i
$17$	−4.19187	−	2.42018i	−1.01668	−	0.586979i	−0.103538	−	0.994626i	$-0.533016\pi$
$17$	−4.19187	−	2.42018i	−1.01668	−	0.586979i	−0.913140	+	0.407646i	$0.866350\pi$
$18$	−3.62747	+	2.20032i	−0.855004	+	0.518621i
$19$	−3.67476	+	2.12162i	−0.843047	+	0.486733i	−0.858299	−	0.513150i	$-0.828478\pi$
$19$	−3.67476	+	2.12162i	−0.843047	+	0.486733i	0.0152518	+	0.999884i	$0.495145\pi$
$20$	−1.80827	−	0.854484i	−0.404343	−	0.191068i
$21$	−4.15466	+	7.03721i	−0.906621	+	1.53565i
$22$	0.149544	+	3.63831i	0.0318828	+	0.775691i
$23$	−0.984432	+	5.58299i	−0.205268	+	1.16413i	0.691749	+	0.722138i	$0.256840\pi$
$23$	−0.984432	+	5.58299i	−0.205268	+	1.16413i	−0.897017	+	0.441996i	$0.854271\pi$
$24$	4.38411	−	2.18623i	0.894902	−	0.446262i
$25$	−0.766044	+	0.642788i	−0.153209	+	0.128558i
$26$	−0.211548	+	0.665018i	−0.0414880	+	0.130421i
$27$	−4.42234	−	2.72818i	−0.851079	−	0.525038i
$28$	5.45188	−	7.70206i	1.03031	−	1.45555i
$29$	3.28825	+	3.91878i	0.610612	+	0.727699i	0.979426	−	0.201804i	$-0.0646804\pi$
$29$	3.28825	+	3.91878i	0.610612	+	0.727699i	−0.368814	+	0.929503i	$0.620236\pi$
$30$	−0.0768014	−	2.44829i	−0.0140219	−	0.446994i
$31$	−5.46534	−	0.963686i	−0.981604	−	0.173083i	−0.340255	−	0.940333i	$-0.610513\pi$
$31$	−5.46534	−	0.963686i	−0.981604	−	0.173083i	−0.641348	+	0.767250i	$0.721625\pi$
$32$	−5.25347	+	2.09787i	−0.928691	+	0.370855i
$33$	−3.88376	+	2.19224i	−0.676076	+	0.381619i
$34$	−0.910820	+	6.78443i	−0.156204	+	1.16352i
$35$	−2.35909	−	4.08606i	−0.398759	−	0.690670i
$36$	4.82896	+	3.56106i	0.804826	+	0.593510i
$37$	5.45430	−	9.44713i	0.896682	−	1.55310i	0.0649719	−	0.997887i	$-0.479304\pi$
$37$	5.45430	−	9.44713i	0.896682	−	1.55310i	0.831710	−	0.555211i	$-0.187362\pi$
$38$	4.75145	+	3.66523i	0.770787	+	0.594580i
$39$	−0.843112	+	0.140228i	−0.135006	+	0.0224544i
$40$	−0.145020	+	2.82471i	−0.0229297	+	0.446625i
$41$	−5.41030	+	6.44774i	−0.844946	+	1.00697i	0.154872	+	0.987934i	$0.450503\pi$
$41$	−5.41030	+	6.44774i	−0.844946	+	1.00697i	−0.999819	+	0.0190334i	$0.993941\pi$
$42$	11.4389	+	1.64903i	1.76506	+	0.254451i
$43$	3.66535	−	10.0705i	0.558961	−	1.53573i	−0.262186	−	0.965017i	$-0.584443\pi$
$43$	3.66535	−	10.0705i	0.558961	−	1.53573i	0.821147	−	0.570716i	$-0.193334\pi$
$44$	4.67826	−	2.15249i	0.705275	−	0.324500i
$45$	2.62674	−	1.44921i	0.391572	−	0.216036i
$46$	7.83170	−	1.71527i	1.15472	−	0.252903i
$47$	−0.122222	−	0.693155i	−0.0178279	−	0.101107i	0.974595	−	0.223973i	$-0.0719027\pi$
$47$	−0.122222	−	0.693155i	−0.0178279	−	0.101107i	−0.992423	+	0.122866i	$0.960792\pi$
$48$	−5.21748	−	4.55828i	−0.753079	−	0.657931i
$49$	14.3408	−	5.21963i	2.04869	−	0.745661i
$50$	1.25275	+	0.656213i	0.177166	+	0.0928025i
$51$	−7.90564	+	2.79070i	−1.10701	+	0.390776i
$52$	0.983587	−	0.0809925i	0.136399	−	0.0112316i
$53$		−	3.75742i		−	0.516121i	−0.966129	−	0.258061i	$-0.916917\pi$
$53$		−	3.75742i		−	0.516121i	0.966129	−	0.258061i	$-0.0830834\pi$
$54$	−1.18971	+	7.25152i	−0.161898	+	0.986807i
$55$		−	2.57485i		−	0.347192i
$56$	−13.0062	−	2.98813i	−1.73802	−	0.399305i
$57$	−1.34652	+	7.22511i	−0.178351	+	0.956989i
$58$	3.35692	−	6.40858i	0.440786	−	0.841488i
$59$	−4.56304	+	1.66081i	−0.594057	+	0.216219i	−0.621513	−	0.783404i	$-0.713482\pi$
$59$	−4.56304	+	1.66081i	−0.594057	+	0.216219i	0.0274561	+	0.999623i	$0.491259\pi$
$60$	−3.16090	+	1.41728i	−0.408071	+	0.182970i
$61$	2.25866	+	12.8095i	0.289191	+	1.64009i	0.689918	+	0.723888i	$0.257647\pi$
$61$	2.25866	+	12.8095i	0.289191	+	1.64009i	−0.400726	+	0.916198i	$0.631242\pi$
$62$	1.67913	+	7.66666i	0.213249	+	0.973667i
$63$	4.58166	+	13.3925i	0.577235	+	1.68730i
$64$	5.56951	+	5.74287i	0.696189	+	0.717859i
$65$	0.168773	−	0.463699i	0.0209337	−	0.0575148i
$66$	4.95623	+	3.90062i	0.610069	+	0.480133i
$67$	4.03968	−	4.81430i	0.493525	−	0.588160i	−0.460585	−	0.887615i	$-0.652360\pi$
$67$	4.03968	−	4.81430i	0.493525	−	0.588160i	0.954110	+	0.299455i	$0.0968049\pi$
$68$	9.36352	−	2.45776i	1.13549	−	0.298047i
$69$	6.23825	+	7.58293i	0.750997	+	0.912878i
$70$	−4.07547	+	5.28326i	−0.487112	+	0.631471i
$71$	3.92026	−	6.79009i	0.465250	−	0.805836i	−0.533963	−	0.845508i	$-0.679298\pi$
$71$	3.92026	−	6.79009i	0.465250	−	0.805836i	0.999213	+	0.0396719i	$0.0126313\pi$
$72$	2.06037	−	8.23134i	0.242816	−	0.970072i
$73$	−4.53053	−	7.84711i	−0.530259	−	0.918435i	−0.999377	−	0.0352995i	$-0.988761\pi$
$73$	−4.53053	−	7.84711i	−0.530259	−	0.918435i	0.469118	−	0.883135i	$-0.344572\pi$
$74$	−15.2899	−	2.05270i	−1.77742	−	0.238621i
$75$	−0.0168356	+	1.73197i	−0.00194400	+	0.199991i
$76$	2.23831	−	8.18599i	0.256751	−	0.938998i
$77$	11.9640	+	2.10958i	1.36343	+	0.240409i
$78$	0.636884	+	1.02732i	0.0721129	+	0.116321i
$79$	1.45125	+	1.72954i	0.163279	+	0.194588i	0.841480	−	0.540288i	$-0.181685\pi$
$79$	1.45125	+	1.72954i	0.163279	+	0.194588i	−0.678201	+	0.734876i	$0.737240\pi$
$80$	3.77255	−	1.32961i	0.421784	−	0.148655i
$81$	−8.57049	+	2.74711i	−0.952277	+	0.305235i
$82$	11.3432	+	3.60838i	1.25265	+	0.398479i
$83$	−3.70034	+	3.10495i	−0.406165	+	0.340813i	−0.822871	−	0.568229i	$-0.807629\pi$
$83$	−3.70034	+	3.10495i	−0.406165	+	0.340813i	0.416706	+	0.909041i	$0.363185\pi$
$84$	−3.99565	−	15.8483i	−0.435961	−	1.72919i
$85$	0.840519	−	4.76682i	0.0911670	−	0.517034i
$86$	−15.1430	+	0.622416i	−1.63292	+	0.0671168i
$87$	8.86007	+	0.0861241i	0.949899	+	0.00923348i
$88$	−5.33157	−	4.96116i	−0.568347	−	0.528862i
$89$	−3.52826	+	2.03704i	−0.373995	+	0.215926i	−0.675202	−	0.737633i	$-0.735944\pi$
$89$	−3.52826	+	2.03704i	−0.373995	+	0.215926i	0.301207	+	0.953559i	$0.402610\pi$
$90$	−3.30830	−	2.65616i	−0.348725	−	0.279983i
$91$	2.01630	+	1.16411i	0.211366	+	0.122032i
$92$	−6.45582	−	9.32083i	−0.673065	−	0.971764i
$93$	−7.42314	+	6.10679i	−0.769744	+	0.633244i
$94$	−0.840867	+	0.532677i	−0.0867288	+	0.0549415i
$95$	−3.25051	−	2.72750i	−0.333496	−	0.279836i
$96$	−3.15569	+	9.27586i	−0.322077	+	0.946714i
$97$	−5.74588	−	2.09133i	−0.583406	−	0.212342i	0.0334208	−	0.999441i	$-0.489360\pi$
$97$	−5.74588	−	2.09133i	−0.583406	−	0.212342i	−0.616827	+	0.787099i	$0.711582\pi$
$98$	−14.5403	−	15.9495i	−1.46879	−	1.61114i
$99$	−1.48898	+	7.57968i	−0.149648	+	0.761786i
$100$	0.184486	−	1.99147i	0.0184486	−	0.199147i
$101$	11.2191	−	1.97823i	1.11634	−	0.196842i	0.415109	−	0.909772i	$-0.363743\pi$
$101$	11.2191	−	1.97823i	1.11634	−	0.196842i	0.701235	+	0.712930i	$0.252632\pi$
$102$	7.90217	+	8.83911i	0.782432	+	0.875202i
$103$	−5.69431	−	15.6450i	−0.561077	−	1.54155i	−0.818061	−	0.575132i	$-0.804951\pi$
$103$	−5.69431	−	15.6450i	−0.561077	−	1.54155i	0.256984	−	0.966416i	$-0.417271\pi$
$104$	−0.634963	−	1.24291i	−0.0622633	−	0.121877i
$105$	−8.03379	−	1.49723i	−0.784018	−	0.146115i
$106$	−4.91448	+	2.02096i	−0.477337	+	0.196293i
$107$	1.46569			0.141694			0.0708469	−	0.997487i	$-0.477430\pi$
$107$	1.46569			0.141694			0.0708469	+	0.997487i	$0.477430\pi$
$108$	10.1245	−	2.34422i	0.974226	−	0.225573i
$109$	−10.2294			−0.979800			−0.489900	−	0.871779i	$-0.662967\pi$
$109$	−10.2294			−0.979800			−0.489900	+	0.871779i	$0.662967\pi$
$110$	−3.36775	+	1.38490i	−0.321102	+	0.132045i
$111$	−6.28933	−	17.8168i	−0.596957	−	1.69109i
$112$	3.08718	+	18.6185i	0.291711	+	1.75928i
$113$	3.54026	+	9.72677i	0.333039	+	0.915018i	0.987317	+	0.158763i	$0.0507507\pi$
$113$	3.54026	+	9.72677i	0.333039	+	0.915018i	−0.654277	+	0.756255i	$0.727027\pi$
$114$	10.1743	−	2.12491i	0.952906	−	0.199016i
$115$	−5.58299	+	0.984432i	−0.520616	+	0.0917987i
$116$	−10.1876	−	0.943757i	−0.945894	−	0.0876256i
$117$	−0.764969	+	1.26741i	−0.0707214	+	0.117172i
$118$	4.62650	+	5.07490i	0.425904	+	0.467183i
$119$	21.4604	+	7.81093i	1.96727	+	0.716027i
$120$	3.55384	+	3.37198i	0.324419	+	0.307818i
$121$	−3.34774	−	2.80908i	−0.304340	−	0.255371i
$122$	15.5392	−	9.84386i	1.40685	−	0.891222i
$123$	2.39187	+	14.3810i	0.215667	+	1.29669i
$124$	9.12441	−	6.31977i	0.819396	−	0.567532i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	15.0523	−	13.1958i	1.34097	−	1.17557i
$127$	−1.54694	+	0.893124i	−0.137268	+	0.0792519i	−0.567061	−	0.823675i	$-0.691920\pi$
$127$	−1.54694	+	0.893124i	−0.137268	+	0.0792519i	0.429793	+	0.902927i	$0.358586\pi$
$128$	4.51573	−	10.3734i	0.399138	−	0.916891i
$129$	−9.12431	−	16.1646i	−0.803351	−	1.42322i
$130$	−0.697266	+	0.0286594i	−0.0611543	+	0.00251359i
$131$	−0.920076	+	5.21801i	−0.0803874	+	0.455900i	0.917870	+	0.396882i	$0.129908\pi$
$131$	−0.920076	+	5.21801i	−0.0803874	+	0.455900i	−0.998257	+	0.0590175i	$0.981203\pi$
$132$	2.43604	−	8.58043i	0.212030	−	0.746831i
$133$	15.3365	−	12.8688i	1.32984	−	1.11587i
$134$	−8.46959	−	2.69425i	−0.731661	−	0.232748i
$135$	1.05112	−	5.08873i	0.0904659	−	0.437968i
$136$	−8.25084	−	10.9250i	−0.707504	−	0.936812i
$137$	−6.96696	−	8.30290i	−0.595228	−	0.709365i	0.381374	−	0.924421i	$-0.375451\pi$
$137$	−6.96696	−	8.30290i	−0.595228	−	0.709365i	−0.976602	+	0.215056i	$0.931007\pi$
$138$	6.56274	−	12.2378i	0.558658	−	1.04175i
$139$	−2.00673	−	0.353840i	−0.170208	−	0.0300123i	0.0878944	−	0.996130i	$-0.471986\pi$
$139$	−2.00673	−	0.353840i	−0.170208	−	0.0300123i	−0.258103	+	0.966117i	$0.583097\pi$
$140$	9.10222	+	2.48883i	0.769278	+	0.210345i
$141$	−1.04980	−	0.619783i	−0.0884088	−	0.0521952i
$142$	−10.9896	−	1.47537i	−0.922225	−	0.123810i
$143$	0.635290	+	1.10035i	0.0531256	+	0.0920162i
$144$	−11.8743	+	1.73245i	−0.989524	+	0.144371i
$145$	−2.55780	+	4.43024i	−0.212414	+	0.367912i
$146$	−7.82678	+	10.1463i	−0.647749	+	0.839713i
$147$	9.28167	−	24.7500i	0.765539	−	2.04134i
$148$	5.53899	+	21.1024i	0.455303	+	1.73460i
$149$	7.84601	−	9.35051i	0.642770	−	0.766024i	−0.342035	−	0.939687i	$-0.611116\pi$
$149$	7.84601	−	9.35051i	0.642770	−	0.766024i	0.984805	+	0.173663i	$0.0555605\pi$
$150$	2.27437	−	0.909533i	0.185701	−	0.0742630i
$151$	−2.79008	+	7.66567i	−0.227053	+	0.623823i	−0.999943	−	0.0107173i	$-0.996589\pi$
$151$	−2.79008	+	7.66567i	−0.227053	+	0.623823i	0.772889	+	0.634541i	$0.218811\pi$
$152$	−11.9107	+	1.47533i	−0.966084	+	0.119665i
$153$	−5.23081	+	13.5462i	−0.422886	+	1.09515i
$154$	−3.67573	−	16.7829i	−0.296199	−	1.35240i
$155$	−0.963686	−	5.46534i	−0.0774052	−	0.438986i
$156$	1.00112	−	1.38556i	0.0801537	−	0.110933i
$157$	−14.0713	+	5.12153i	−1.12301	+	0.408742i	−0.835750	−	0.549110i	$-0.814967\pi$
$157$	−14.0713	+	5.12153i	−1.12301	+	0.408742i	−0.287260	+	0.957853i	$0.592744\pi$
$158$	1.48157	−	2.82840i	0.117867	−	0.225015i
$159$	−4.94455	−	4.23155i	−0.392129	−	0.335584i
$160$	−3.76815	−	4.21913i	−0.297898	−	0.333552i
$161$		−	26.7479i		−	2.10803i
$162$	8.20277	+	9.73214i	0.644470	+	0.764629i
$163$			7.79458i			0.610519i	0.952269	+	0.305259i	$0.0987432\pi$
$163$			7.79458i			0.610519i	−0.952269	+	0.305259i	$0.901257\pi$
$164$	−1.38149	−	16.7771i	−0.107876	−	1.31007i
$165$	−3.38835	−	2.89975i	−0.263783	−	0.225746i
$166$	6.05135	+	3.16980i	0.469676	+	0.246024i
$167$	3.77904	−	1.37546i	0.292431	−	0.106436i	−0.191639	−	0.981465i	$-0.561380\pi$
$167$	3.77904	−	1.37546i	0.292431	−	0.106436i	0.484070	+	0.875029i	$0.339158\pi$
$168$	−18.5796	+	13.7502i	−1.43344	+	1.06085i
$169$	−2.21514	−	12.5627i	−0.170396	−	0.966361i
$170$	−6.68679	+	1.46452i	−0.512854	+	0.112324i
$171$	7.99141	+	9.90876i	0.611118	+	0.757742i
$172$	8.95888	+	19.4714i	0.683108	+	1.48468i
$173$	−3.96952	+	10.9062i	−0.301797	+	0.829181i	0.692391	+	0.721523i	$0.256558\pi$
$173$	−3.96952	+	10.9062i	−0.301797	+	0.829181i	−0.994188	+	0.107658i	$0.965665\pi$
$174$	−4.65281	−	11.6348i	−0.352729	−	0.882029i
$175$	3.03278	−	3.61433i	0.229257	−	0.273218i
$176$	−3.62128	+	9.64177i	−0.272964	+	0.726776i
$177$	−2.95329	+	7.87507i	−0.221983	+	0.591927i
$178$	4.56203	+	3.51912i	0.341939	+	0.263769i
$179$	7.10571	−	12.3074i	0.531105	−	0.919902i	−0.468236	−	0.883604i	$-0.655110\pi$
$179$	7.10571	−	12.3074i	0.531105	−	0.919902i	0.999341	−	0.0362980i	$-0.0115565\pi$
$180$	−1.69470	+	5.75569i	−0.126316	+	0.429004i
$181$	−3.34868	−	5.80008i	−0.248905	−	0.431117i	0.714317	−	0.699822i	$-0.246737\pi$
$181$	−3.34868	−	5.80008i	−0.248905	−	0.431117i	−0.963222	+	0.268706i	$0.913404\pi$
$182$	0.438106	−	3.26332i	0.0324746	−	0.241894i
$183$	19.4002	+	11.4536i	1.43411	+	0.846673i
$184$	−8.71879	+	13.4571i	−0.642757	+	0.992071i
$185$	10.7429	+	1.89426i	0.789832	+	0.139269i
$186$	11.9799	+	6.42444i	0.878409	+	0.471063i
$187$	8.01117	+	9.54734i	0.585835	+	0.698171i
$188$	1.14898	+	0.813300i	0.0837978	+	0.0593160i
$189$	22.7836	+	9.05322i	1.65726	+	0.658525i
$190$	−1.81910	+	5.71849i	−0.131971	+	0.414863i
$191$	−8.63141	+	7.24262i	−0.624547	+	0.524057i	−0.899229	−	0.437478i	$-0.855872\pi$
$191$	−8.63141	+	7.24262i	−0.624547	+	0.524057i	0.274682	+	0.961535i	$0.411427\pi$
$192$	13.8296	−	0.861630i	0.998065	−	0.0621828i
$193$	0.769275	−	4.36277i	0.0553736	−	0.314039i	−0.944523	−	0.328446i	$-0.893475\pi$
$193$	0.769275	−	4.36277i	0.0553736	−	0.314039i	0.999896	+	0.0144071i	$0.00458609\pi$
$194$	0.355130	+	8.64011i	0.0254968	+	0.620324i
$195$	−0.420132	−	0.744306i	−0.0300863	−	0.0533008i
$196$	−13.0404	+	27.5964i	−0.931459	+	1.97117i
$197$	−14.3030	+	8.25787i	−1.01905	+	0.588349i	−0.913829	−	0.406100i	$-0.866888\pi$
$197$	−14.3030	+	8.25787i	−1.01905	+	0.588349i	−0.105221	+	0.994449i	$0.533555\pi$
$198$	10.7146	−	2.12929i	0.761455	−	0.151322i
$199$	15.7461	+	9.09101i	1.11621	+	0.644445i	0.940431	−	0.339985i	$-0.110422\pi$
$199$	15.7461	+	9.09101i	1.11621	+	0.644445i	0.175780	+	0.984429i	$0.443755\pi$
$200$	−2.70396	+	0.829832i	−0.191199	+	0.0586780i
$201$	−1.78592	−	10.7378i	−0.125969	−	0.757384i
$202$	−8.62170	−	13.6099i	−0.606621	−	0.957592i
$203$	−18.4895	−	15.5145i	−1.29771	−	1.08891i
$204$	7.31079	−	15.0898i	0.511857	−	1.05649i
$205$	−7.90932	−	2.87876i	−0.552411	−	0.201061i
$206$	−17.4000	+	15.8626i	−1.21232	+	1.10520i
$207$	17.0041	+	0.330608i	1.18187	+	0.0229788i
$208$	−1.28413	+	1.49900i	−0.0890387	+	0.103937i
$209$	10.7597	−	1.89723i	0.744265	−	0.131234i
$210$	2.36274	+	11.3130i	0.163045	+	0.780673i
$211$	−0.314356	−	0.863686i	−0.0216412	−	0.0594586i	0.928402	−	0.371578i	$-0.121183\pi$
$211$	−0.314356	−	0.863686i	−0.0216412	−	0.0594586i	−0.950043	+	0.312120i	$0.898961\pi$
$212$	5.28658	+	5.34087i	0.363084	+	0.366812i
$213$	−4.52044	−	12.8057i	−0.309735	−	0.877435i
$214$	−0.788334	−	1.91704i	−0.0538894	−	0.131046i
$215$	10.7168			0.730878
$216$	−8.51162	−	11.9813i	−0.579142	−	0.815226i
$217$	26.1842			1.77750
$218$	5.50197	+	13.3795i	0.372640	+	0.906172i
$219$	−15.4286	−	2.87538i	−1.04257	−	0.194300i
$220$	3.62274	+	3.65994i	0.244245	+	0.246753i
$221$	0.816919	+	2.24447i	0.0549519	+	0.150979i
$222$	−19.9205	+	17.8090i	−1.33698	+	1.19526i
$223$	3.09399	−	0.545554i	0.207189	−	0.0365330i	−0.0690904	−	0.997610i	$-0.522010\pi$
$223$	3.09399	−	0.545554i	0.207189	−	0.0365330i	0.276279	+	0.961077i	$0.410899\pi$
$224$	22.6914	−	14.0519i	1.51613	−	0.938885i
$225$	2.26021	+	1.97267i	0.150681	+	0.131511i
$226$	10.8179	−	9.86206i	0.719595	−	0.656015i
$227$	−9.46699	−	3.44570i	−0.628346	−	0.228699i	0.00816514	−	0.999967i	$-0.497401\pi$
$227$	−9.46699	−	3.44570i	−0.628346	−	0.228699i	−0.636511	+	0.771267i	$0.719623\pi$
$228$	−8.25156	−	12.1644i	−0.546473	−	0.805609i
$229$	−13.3658	−	11.2153i	−0.883239	−	0.741125i	0.0836036	−	0.996499i	$-0.473357\pi$
$229$	−13.3658	−	11.2153i	−0.883239	−	0.741125i	−0.966842	+	0.255374i	$0.917801\pi$
$230$	4.29043	+	6.77273i	0.282903	+	0.446581i
$231$	16.2498	−	13.3682i	1.06916	−	0.879563i
$232$	4.24509	+	13.8324i	0.278704	+	0.908140i
$233$	26.3330	+	15.2034i	1.72513	+	0.996006i	0.907211	+	0.420677i	$0.138207\pi$
$233$	26.3330	+	15.2034i	1.72513	+	0.996006i	0.817922	+	0.575329i	$0.195126\pi$
$234$	2.06914	+	0.318848i	0.135264	+	0.0208437i
$235$	0.609550	−	0.351924i	0.0397627	−	0.0229570i
$236$	4.14927	−	8.78077i	0.270095	−	0.571579i
$237$	3.91036	+	0.0380105i	0.254005	+	0.00246905i
$238$	−1.32638	−	32.2700i	−0.0859763	−	2.09176i
$239$	−4.89355	+	27.7527i	−0.316537	+	1.79517i	0.246928	+	0.969034i	$0.420579\pi$
$239$	−4.89355	+	27.7527i	−0.316537	+	1.79517i	−0.563466	+	0.826139i	$0.690532\pi$
$240$	2.49889	−	6.46185i	0.161303	−	0.417111i
$241$	−3.75216	+	3.14844i	−0.241698	+	0.202809i	−0.755588	−	0.655048i	$-0.772649\pi$
$241$	−3.75216	+	3.14844i	−0.241698	+	0.202809i	0.513890	+	0.857856i	$0.328204\pi$
$242$	−1.87351	+	5.88953i	−0.120434	+	0.378593i
$243$	−6.03691	+	14.3720i	−0.387268	+	0.921967i
$244$	−21.2331	−	15.0298i	−1.35931	−	0.962182i
$245$	9.80969	+	11.6907i	0.626718	+	0.746894i
$246$	17.5230	−	10.8633i	1.11723	−	0.692622i
$247$	2.06205	+	0.363595i	0.131205	+	0.0231350i
$248$	−13.1735	−	8.53505i	−0.836520	−	0.541976i
$249$	−0.0813234	+	8.36619i	−0.00515366	+	0.530186i
$250$	−0.188172	+	1.40164i	−0.0119011	+	0.0886474i
$251$	−5.38045	−	9.31922i	−0.339611	−	0.588224i	0.644748	−	0.764395i	$-0.276962\pi$
$251$	−5.38045	−	9.31922i	−0.339611	−	0.588224i	−0.984360	+	0.176171i	$0.943629\pi$
$252$	−25.3553	−	12.5901i	−1.59724	−	0.793100i
$253$	7.29855	−	12.6415i	0.458856	−	0.794762i
$254$	2.00018	+	1.54293i	0.125503	+	0.0968118i
$255$	−5.32628	−	6.47439i	−0.333545	−	0.405442i
$256$	−15.9967	−	0.326875i	−0.999791	−	0.0204297i
$257$	−4.24539	+	5.05946i	−0.264820	+	0.315600i	−0.882025	−	0.471202i	$-0.843820\pi$
$257$	−4.24539	+	5.05946i	−0.264820	+	0.315600i	0.617205	+	0.786802i	$0.288265\pi$
$258$	−16.2348	+	20.6283i	−1.01073	+	1.28426i
$259$	−17.6033	+	48.3648i	−1.09382	+	3.00524i
$260$	0.412515	+	0.896568i	0.0255831	+	0.0556028i
$261$	10.0914	−	11.5624i	0.624643	−	0.715692i
$262$	7.31972	−	1.60314i	0.452214	−	0.0990424i
$263$	0.877239	+	4.97507i	0.0540929	+	0.306776i	0.999835	−	0.0181409i	$-0.00577475\pi$
$263$	0.877239	+	4.97507i	0.0540929	+	0.306776i	−0.945743	+	0.324917i	$0.894664\pi$
$264$	−12.5329	+	1.42886i	−0.771349	+	0.0879400i
$265$	3.53082	−	1.28511i	0.216897	−	0.0789439i
$266$	−25.0805	−	13.1376i	−1.53779	−	0.805519i
$267$	−1.29284	+	6.93708i	−0.0791207	+	0.424542i
$268$	1.03151	+	12.5268i	0.0630096	+	0.765199i
$269$			20.3815i			1.24268i	0.783540	+	0.621342i	$0.213412\pi$
$269$			20.3815i			1.24268i	−0.783540	+	0.621342i	$0.786588\pi$
$270$	−7.22111	+	1.36221i	−0.439463	+	0.0829015i
$271$			9.49990i			0.577078i	0.957468	+	0.288539i	$0.0931695\pi$
$271$			9.49990i			0.577078i	−0.957468	+	0.288539i	$0.906831\pi$
$272$	−9.85149	+	16.6677i	−0.597334	+	1.01063i
$273$	3.80263	−	1.34233i	0.230146	−	0.0812416i
$274$	−7.11247	+	13.5782i	−0.429680	+	0.820286i
$275$	2.41957	−	0.880650i	0.145905	−	0.0531052i
$276$	−19.5361	−	2.00149i	−1.17594	−	0.120475i
$277$	−1.74306	−	9.88537i	−0.104730	−	0.593954i	−0.991328	−	0.131413i	$-0.958049\pi$
$277$	−1.74306	−	9.88537i	−0.104730	−	0.593954i	0.886598	−	0.462542i	$-0.153062\pi$
$278$	0.616531	+	2.81499i	0.0369771	+	0.168832i
$279$	−0.323641	+	16.6458i	−0.0193759	+	0.996558i
$280$	−1.64045	−	13.2438i	−0.0980358	−	0.791469i
$281$	4.32579	−	11.8850i	0.258055	−	0.709000i	−0.741232	−	0.671249i	$-0.765758\pi$
$281$	4.32579	−	11.8850i	0.258055	−	0.709000i	0.999287	−	0.0377516i	$-0.0120196\pi$
$282$	−0.245999	+	1.70643i	−0.0146490	+	0.101616i
$283$	−7.23619	+	8.62375i	−0.430147	+	0.512629i	−0.936965	−	0.349424i	$-0.886377\pi$
$283$	−7.23619	+	8.62375i	−0.430147	+	0.512629i	0.506818	+	0.862053i	$0.330822\pi$
$284$	3.98114	+	15.1673i	0.236237	+	0.900011i
$285$	−7.24992	+	1.20582i	−0.429448	+	0.0714264i
$286$	1.09750	−	1.42275i	0.0648967	−	0.0841293i
$287$	19.8563	−	34.3921i	1.17208	−	2.03010i
$288$	8.65261	+	14.5991i	0.509860	+	0.860257i
$289$	3.21451	+	5.56770i	0.189089	+	0.327512i
$290$	7.17023	+	0.962614i	0.421050	+	0.0565267i
$291$	−9.22300	+	5.20603i	−0.540662	+	0.305183i
$292$	17.4804	+	4.77970i	1.02297	+	0.279711i
$293$	0.595877	+	0.105069i	0.0348115	+	0.00613821i	0.191027	−	0.981585i	$-0.438818\pi$
$293$	0.595877	+	0.105069i	0.0348115	+	0.00613821i	−0.156215	+	0.987723i	$0.549929\pi$
$294$	−37.3637	+	1.17208i	−2.17910	+	0.0683570i
$295$	−3.12130	−	3.71982i	−0.181729	−	0.216576i
$296$	24.6215	−	18.5947i	1.43109	−	1.08080i
$297$	8.29756	+	10.4955i	0.481474	+	0.609012i
$298$	−16.4500	−	5.23288i	−0.952920	−	0.303132i
$299$	2.14299	−	1.79818i	0.123932	−	0.103991i
$300$	−2.41290	−	2.48554i	−0.139309	−	0.143503i
$301$	−8.78029	+	49.7955i	−0.506087	+	2.87016i
$302$	11.5269	−	0.473784i	0.663299	−	0.0272632i
$303$	10.0316	−	16.9916i	0.576298	−	0.976142i
$304$	8.33589	+	14.7850i	0.478096	+	0.847975i
$305$	−11.2645	+	6.50354i	−0.645001	+	0.372392i
$306$	20.5311	−	0.444341i	1.17368	−	0.0254013i
$307$	−0.433918	−	0.250523i	−0.0247650	−	0.0142981i	0.487566	−	0.873086i	$-0.337885\pi$
$307$	−0.433918	−	0.250523i	−0.0247650	−	0.0142981i	−0.512331	+	0.858788i	$0.671218\pi$
$308$	−19.9740	+	13.8344i	−1.13812	+	0.788290i
$309$	−27.0008	−	10.1258i	−1.53602	−	0.576035i
$310$	−6.63001	+	4.20002i	−0.376559	+	0.238545i
$311$	−6.97612	−	5.85366i	−0.395580	−	0.331931i	0.423202	−	0.906035i	$-0.360906\pi$
$311$	−6.97612	−	5.85366i	−0.395580	−	0.331931i	−0.818782	+	0.574104i	$0.805350\pi$
$312$	−2.35069	−	0.564172i	−0.133081	−	0.0319400i
$313$	19.9013	+	7.24348i	1.12489	+	0.409426i	0.836434	−	0.548068i	$-0.184637\pi$
$313$	19.9013	+	7.24348i	1.12489	+	0.409426i	0.288454	+	0.957494i	$0.406859\pi$
$314$	14.2670	+	15.6497i	0.805133	+	0.883166i
$315$	−11.0178	+	8.88586i	−0.620783	+	0.500661i
$316$	−4.49625	−	0.416523i	−0.252934	−	0.0234313i
$317$	−11.6423	+	2.05285i	−0.653897	+	0.115300i	−0.490748	−	0.871302i	$-0.663276\pi$
$317$	−11.6423	+	2.05285i	−0.653897	+	0.115300i	−0.163150	+	0.986601i	$0.552165\pi$
$318$	−2.87515	+	8.74315i	−0.161231	+	0.490292i
$319$	−4.50506	−	12.3775i	−0.252235	−	0.693009i
$320$	−3.49165	+	7.19781i	−0.195189	+	0.402370i
$321$	1.65064	−	1.92877i	0.0921298	−	0.107653i
$322$	−34.9846	+	14.3865i	−1.94962	+	0.801731i
$323$	20.5388			1.14281
$324$	8.31715	−	15.9632i	0.462064	−	0.886847i
$325$	0.493458			0.0273721
$326$	10.1949	−	4.19237i	0.564641	−	0.232194i
$327$	−11.5202	+	13.4613i	−0.637069	+	0.744413i
$328$	−21.2004	+	10.8306i	−1.17059	+	0.598019i
$329$	1.13581	+	3.12060i	0.0626190	+	0.172044i
$330$	−1.97026	+	5.99142i	−0.108459	+	0.329817i
$331$	26.6418	−	4.69766i	1.46436	−	0.258207i	0.616052	−	0.787705i	$-0.288731\pi$
$331$	26.6418	−	4.69766i	1.46436	−	0.258207i	0.848311	+	0.529499i	$0.177620\pi$
$332$	0.891149	−	9.61971i	0.0489082	−	0.527950i
$333$	−30.5288	−	11.7886i	−1.67297	−	0.646009i
$334$	−3.83160	−	4.20296i	−0.209656	−	0.229976i
$335$	5.90561	+	2.14947i	0.322658	+	0.117438i
$336$	27.9776	+	16.9053i	1.52630	+	0.922260i
$337$	−22.0213	−	18.4781i	−1.19958	−	1.00657i	−0.999642	−	0.0267571i	$-0.991482\pi$
$337$	−22.0213	−	18.4781i	−1.19958	−	1.00657i	−0.199937	−	0.979809i	$-0.564074\pi$
$338$	−15.2398	+	9.65422i	−0.828938	+	0.525120i
$339$	16.7869	+	6.29537i	0.911738	+	0.341918i
$340$	5.51205	+	7.95823i	0.298933	+	0.431596i
$341$	12.3751	+	7.14475i	0.670148	+	0.386910i
$342$	8.66183	−	15.7818i	0.468378	−	0.853381i
$343$	−33.7557	+	19.4888i	−1.82263	+	1.05230i
$344$	20.6489	−	22.1905i	1.11331	−	1.19643i
$345$	−4.99202	+	8.45555i	−0.268761	+	0.455231i
$346$	16.3997	−	0.674067i	0.881652	−	0.0362381i
$347$	−0.933492	+	5.29409i	−0.0501125	+	0.284202i	−0.999558	−	0.0297300i	$-0.990535\pi$
$347$	−0.933492	+	5.29409i	−0.0501125	+	0.284202i	0.949446	+	0.313932i	$0.101646\pi$
$348$	−12.7150	+	12.3434i	−0.681598	+	0.661678i
$349$	1.44831	−	1.21528i	0.0775262	−	0.0650522i	−0.603201	−	0.797589i	$-0.706108\pi$
$349$	1.44831	−	1.21528i	0.0775262	−	0.0650522i	0.680727	+	0.732537i	$0.261664\pi$
$350$	−6.35854	−	2.02271i	−0.339878	−	0.108118i
$351$	0.806344	+	2.43399i	0.0430395	+	0.129917i
$352$	14.5586	−	0.449476i	0.775976	−	0.0239572i
$353$	−11.4628	−	13.6608i	−0.610101	−	0.727090i	0.369234	−	0.929337i	$-0.379620\pi$
$353$	−11.4628	−	13.6608i	−0.610101	−	0.727090i	−0.979335	+	0.202247i	$0.935176\pi$
$354$	11.8886	−	0.372938i	0.631871	−	0.0198214i
$355$	7.72141	+	1.36149i	0.409810	+	0.0722605i
$356$	2.14908	−	7.85966i	0.113901	−	0.416561i
$357$	34.4471	−	19.4441i	1.82313	−	1.02909i
$358$	−19.9193	−	2.67419i	−1.05277	−	0.141335i
$359$	8.54371	+	14.7981i	0.450920	+	0.781016i	0.998443	−	0.0557742i	$-0.0177627\pi$
$359$	8.54371	+	14.7981i	0.450920	+	0.781016i	−0.547524	+	0.836790i	$0.684429\pi$
$360$	8.43961	−	0.879172i	0.444807	−	0.0463364i
$361$	−0.497442	+	0.861594i	−0.0261811	+	0.0453471i
$362$	−5.78505	+	7.49949i	−0.304056	+	0.394165i
$363$	−7.46677	+	1.24188i	−0.391904	+	0.0651820i
$364$	−4.50387	+	1.18219i	−0.236067	+	0.0619634i
$365$	5.82434	−	6.94118i	0.304860	−	0.363318i
$366$	4.54605	−	31.5347i	0.237626	−	1.64835i
$367$	8.75609	−	24.0572i	0.457064	−	1.25577i	−0.470596	−	0.882349i	$-0.655961\pi$
$367$	8.75609	−	24.0572i	0.457064	−	1.25577i	0.927661	−	0.373425i	$-0.121817\pi$
$368$	22.2906	+	4.16565i	1.16198	+	0.217150i
$369$	21.6183	+	13.0481i	1.12540	+	0.679257i
$370$	−3.30056	−	15.0699i	−0.171588	−	0.783446i
$371$	3.07846	+	17.4588i	0.159826	+	0.906417i
$372$	1.95931	−	19.1244i	0.101586	−	0.991556i
$373$	−20.7962	+	7.56918i	−1.07678	+	0.391918i	−0.818710	−	0.574207i	$-0.805310\pi$
$373$	−20.7962	+	7.56918i	−1.07678	+	0.391918i	−0.258075	+	0.966125i	$0.583088\pi$
$374$	8.17849	−	15.6133i	0.422900	−	0.807342i
$375$	−1.63328	+	0.576548i	−0.0843420	+	0.0297728i
$376$	0.445762	−	1.94023i	0.0229884	−	0.100060i
$377$		−	2.52434i		−	0.130010i
$378$	−0.413232	−	34.6689i	−0.0212544	−	1.78318i
$379$		−	19.4423i		−	0.998684i	−0.866405	−	0.499342i	$-0.833575\pi$
$379$		−	19.4423i		−	0.998684i	0.866405	−	0.499342i	$-0.166425\pi$
$380$	8.45786	−	0.696455i	0.433879	−	0.0357274i
$381$	−0.566835	+	3.04150i	−0.0290399	+	0.155821i
$382$	14.1154	+	7.39388i	0.722206	+	0.378304i
$383$	9.88038	−	3.59617i	0.504864	−	0.183755i	−0.0770164	−	0.997030i	$-0.524539\pi$
$383$	9.88038	−	3.59617i	0.504864	−	0.183755i	0.581880	+	0.813274i	$0.302317\pi$
$384$	−8.56531	−	17.6249i	−0.437097	−	0.899415i
$385$	2.10958	+	11.9640i	0.107514	+	0.609743i
$386$	−6.12001	+	1.34038i	−0.311500	+	0.0682238i
$387$	−31.5474	−	6.19727i	−1.60364	−	0.315025i
$388$	11.1097	−	5.11164i	0.564012	−	0.259504i
$389$	−6.61451	+	18.1732i	−0.335369	+	0.921419i	0.651320	+	0.758803i	$0.274215\pi$
$389$	−6.61451	+	18.1732i	−0.335369	+	0.921419i	−0.986689	+	0.162616i	$0.948007\pi$
$390$	−0.747537	+	0.949839i	−0.0378530	+	0.0480970i
$391$	17.6384	−	21.0207i	0.892014	−	1.06306i
$392$	43.1083	+	2.21318i	2.17730	+	0.111782i
$393$	5.83043	+	7.08721i	0.294106	+	0.357503i
$394$	18.4938	+	14.2660i	0.931704	+	0.718710i
$395$	−1.12888	+	1.95527i	−0.0567999	+	0.0983803i
$396$	−8.54793	−	12.8688i	−0.429550	−	0.646684i
$397$	−2.42245	−	4.19580i	−0.121579	−	0.210581i	0.798811	−	0.601582i	$-0.205463\pi$
$397$	−2.42245	−	4.19580i	−0.121579	−	0.210581i	−0.920391	+	0.391000i	$0.872129\pi$
$398$	3.42135	−	25.4846i	0.171497	−	1.27743i
$399$	0.337054	−	34.6747i	0.0168738	−	1.73590i
$400$	2.53971	+	3.09028i	0.126986	+	0.154514i
$401$	11.4115	+	2.01216i	0.569864	+	0.100482i	0.451153	−	0.892447i	$-0.351013\pi$
$401$	11.4115	+	2.01216i	0.569864	+	0.100482i	0.118710	+	0.992929i	$0.462124\pi$
$402$	−13.0838	+	8.11127i	−0.652561	+	0.404554i
$403$	1.76029	+	2.09783i	0.0876861	+	0.104500i
$404$	−13.1638	+	18.5969i	−0.654921	+	0.925230i
$405$	−5.51272	−	7.11406i	−0.273929	−	0.353501i
$406$	−10.3474	+	32.5278i	−0.513531	+	1.61433i
$407$	−21.5166	+	18.0546i	−1.06654	+	0.894934i
$408$	−23.6687	−	1.44594i	−1.17177	−	0.0715847i
$409$	−1.18862	+	6.74098i	−0.0587733	+	0.333320i	−0.999990	−	0.00448351i	$-0.998573\pi$
$409$	−1.18862	+	6.74098i	−0.0587733	+	0.333320i	0.941217	+	0.337804i	$0.109684\pi$
$410$	0.488844	+	11.8933i	0.0241423	+	0.587368i
$411$	−18.7722	−	0.182475i	−0.925966	−	0.00900084i
$412$	30.1061	+	14.2264i	1.48322	+	0.700882i
$413$	19.8414	−	11.4554i	0.976332	−	0.563686i
$414$	−8.71338	−	22.4182i	−0.428239	−	1.10180i
$415$	−4.18329	−	2.41522i	−0.205350	−	0.118559i
$416$	2.65129	+	0.873322i	0.129990	+	0.0428181i
$417$	−2.72558	+	2.24225i	−0.133472	+	0.109803i
$418$	−8.26866	−	13.0526i	−0.404433	−	0.638425i
$419$	−12.1391	−	10.1860i	−0.593036	−	0.497616i	0.296163	−	0.955137i	$-0.404293\pi$
$419$	−12.1391	−	10.1860i	−0.593036	−	0.497616i	−0.889199	+	0.457521i	$0.848737\pi$
$420$	13.5259	−	9.17512i	0.659999	−	0.447700i
$421$	11.7878	+	4.29039i	0.574500	+	0.209101i	0.612899	−	0.790162i	$-0.290003\pi$
$421$	11.7878	+	4.29039i	0.574500	+	0.209101i	−0.0383985	+	0.999263i	$0.512226\pi$
$422$	−0.960572	+	0.875699i	−0.0467599	+	0.0426284i
$423$	−1.99787	+	0.683483i	−0.0971395	+	0.0332321i
$424$	4.14211	−	9.78716i	0.201159	−	0.475307i
$425$	4.76682	−	0.840519i	0.231225	−	0.0407711i
$426$	−14.3178	+	12.8001i	−0.693700	+	0.620168i
$427$	−20.9897	−	57.6687i	−1.01576	−	2.79078i
$428$	−2.08336	+	2.06219i	−0.100703	+	0.0996796i
$429$	2.16346	+	0.403197i	0.104453	+	0.0194665i
$430$	−5.76410	−	14.0169i	−0.277970	−	0.675956i
$431$	22.3663			1.07735			0.538674	−	0.842514i	$-0.318926\pi$
$431$	22.3663			1.07735			0.538674	+	0.842514i	$0.318926\pi$
$432$	−11.0928	+	17.5769i	−0.533704	+	0.845671i
$433$	18.8249			0.904667			0.452333	−	0.891849i	$-0.350592\pi$
$433$	18.8249			0.904667			0.452333	+	0.891849i	$0.350592\pi$
$434$	−14.0834	−	34.2474i	−0.676024	−	1.64393i
$435$	2.94939	+	8.35520i	0.141413	+	0.400601i
$436$	14.5403	−	14.3925i	0.696353	−	0.689276i
$437$	−8.22744	−	22.6047i	−0.393572	−	1.08133i
$438$	4.53755	+	21.7262i	0.216813	+	1.03812i
$439$	37.8165	−	6.66807i	1.80488	−	0.318250i	0.832922	−	0.553390i	$-0.186666\pi$
$439$	37.8165	−	6.66807i	1.80488	−	0.318250i	0.971961	+	0.235140i	$0.0755549\pi$
$440$	2.83846	−	6.70685i	0.135318	−	0.319737i
$441$	−22.1167	−	40.0872i	−1.05318	−	1.90891i
$442$	2.49624	−	2.27568i	0.118734	−	0.108243i
$443$	24.5676	+	8.94189i	1.16724	+	0.424842i	0.851680	−	0.524062i	$-0.175584\pi$
$443$	24.5676	+	8.94189i	1.16724	+	0.424842i	0.315564	+	0.948904i	$0.397806\pi$
$444$	34.0075	+	16.4762i	1.61392	+	0.781924i
$445$	−3.12093	−	2.61877i	−0.147946	−	0.124142i
$446$	−2.37768	−	3.75332i	−0.112586	−	0.177725i
$447$	−3.46869	−	20.8553i	−0.164063	−	0.986423i
$448$	−30.5839	−	22.1211i	−1.44495	−	1.04512i
$449$	−8.75961	−	5.05736i	−0.413392	−	0.238672i	0.278854	−	0.960333i	$-0.410045\pi$
$449$	−8.75961	−	5.05736i	−0.413392	−	0.238672i	−0.692246	+	0.721662i	$0.743379\pi$
$450$	1.36447	−	4.01724i	0.0643215	−	0.189375i
$451$	18.7688	−	10.8362i	0.883787	−	0.510255i
$452$	−18.7175	−	8.84478i	−0.880396	−	0.416023i
$453$	6.94545	+	12.3045i	0.326326	+	0.578118i
$454$	0.585117	+	14.2356i	0.0274609	+	0.668108i
$455$	−0.404291	+	2.29285i	−0.0189535	+	0.107490i
$456$	−11.4722	+	17.3353i	−0.537234	+	0.811799i
$457$	13.5014	−	11.3290i	0.631567	−	0.529948i	−0.269848	−	0.962903i	$-0.586974\pi$
$457$	13.5014	−	11.3290i	0.631567	−	0.529948i	0.901415	+	0.432955i	$0.142529\pi$
$458$	−7.47999	+	23.5139i	−0.349517	+	1.09873i
$459$	11.9352	+	22.1390i	0.557087	+	1.03336i
$460$	6.55070	−	9.25440i	0.305428	−	0.431488i
$461$	4.38053	+	5.22051i	0.204022	+	0.243143i	0.858347	−	0.513070i	$-0.171492\pi$
$461$	4.38053	+	5.22051i	0.204022	+	0.243143i	−0.654325	+	0.756213i	$0.727047\pi$
$462$	−26.2249	−	14.0636i	−1.22009	−	0.654297i
$463$	1.99743	+	0.352200i	0.0928283	+	0.0163681i	0.219869	−	0.975529i	$-0.429437\pi$
$463$	1.99743	+	0.352200i	0.0928283	+	0.0163681i	−0.127041	+	0.991897i	$0.540548\pi$
$464$	15.8087	−	12.9922i	0.733899	−	0.603147i
$465$	−8.27736	−	4.88682i	−0.383854	−	0.226621i
$466$	5.72170	−	42.6193i	0.265053	−	1.97430i
$467$	2.26262	+	3.91898i	0.104702	+	0.181349i	0.913616	−	0.406577i	$-0.133278\pi$
$467$	2.26262	+	3.91898i	0.104702	+	0.181349i	−0.808915	+	0.587926i	$0.799945\pi$
$468$	−0.695870	−	2.87781i	−0.0321666	−	0.133027i
$469$	−14.8260	+	25.6793i	−0.684600	+	1.18576i
$470$	−0.788147	−	0.607970i	−0.0363545	−	0.0280436i
$471$	−9.10722	+	24.2848i	−0.419639	+	1.11898i
$472$	−13.7164	−	0.704201i	−0.631350	−	0.0324135i
$473$	−17.7371	+	21.1383i	−0.815554	+	0.971940i
$474$	−2.05350	−	5.13496i	−0.0943203	−	0.235856i
$475$	1.45127	−	3.98734i	0.0665891	−	0.182952i
$476$	−41.4939	+	19.0915i	−1.90187	+	0.875058i
$477$	−11.1370	+	1.74124i	−0.509926	+	0.0797261i
$478$	38.9309	−	8.52653i	1.78066	−	0.389994i
$479$	−5.46708	−	31.0053i	−0.249797	−	1.41667i	−0.809082	−	0.587695i	$-0.800035\pi$
$479$	−5.46708	−	31.0053i	−0.249797	−	1.41667i	0.559285	−	0.828975i	$-0.311076\pi$
$480$	−9.79577	+	0.207149i	−0.447114	+	0.00945501i
$481$	−5.05831	+	1.84107i	−0.230639	+	0.0839457i
$482$	6.13610	+	3.21420i	0.279492	+	0.146403i
$483$	−35.1987	−	30.1231i	−1.60160	−	1.37065i
$484$	8.71084	−	0.717285i	0.395947	−	0.0326039i
$485$		−	6.11464i		−	0.277651i
$486$	22.0448	+	0.165814i	0.999972	+	0.00752146i
$487$			5.78692i			0.262231i	0.991367	+	0.131115i	$0.0418558\pi$
$487$			5.78692i			0.262231i	−0.991367	+	0.131115i	$0.958144\pi$
$488$	−8.23768	+	35.8555i	−0.372902	+	1.62310i
$489$	10.2572	+	8.77814i	0.463848	+	0.396961i
$490$	10.0146	−	19.1185i	0.452412	−	0.863684i
$491$	−27.3925	+	9.97004i	−1.23620	+	0.449941i	−0.875718	−	0.482823i	$-0.839611\pi$
$491$	−27.3925	+	9.97004i	−1.23620	+	0.449941i	−0.360486	+	0.932765i	$0.617389\pi$
$492$	−23.6335	−	17.0761i	−1.06548	−	0.769851i
$493$	−4.29976	−	24.3852i	−0.193651	−	1.09825i
$494$	−0.633529	−	2.89260i	−0.0285038	−	0.130144i
$495$	−7.63183	+	1.19322i	−0.343025	+	0.0536314i
$496$	−4.07787	+	21.8208i	−0.183102	+	0.979784i
$497$	−12.6523	+	34.7620i	−0.567535	+	1.55929i
$498$	10.9862	−	4.39345i	0.492304	−	0.196875i
$499$	−23.3872	+	27.8718i	−1.04695	+	1.24771i	−0.0789236	+	0.996881i	$0.525148\pi$
$499$	−23.3872	+	27.8718i	−1.04695	+	1.24771i	−0.968031	+	0.250831i	$0.919296\pi$
$500$	1.93447	−	0.507764i	0.0865121	−	0.0227079i
$501$	2.44587	−	6.52202i	0.109274	−	0.291383i
$502$	−9.29507	+	12.0497i	−0.414859	+	0.537806i
$503$	7.64369	−	13.2393i	0.340815	−	0.590309i	−0.643769	−	0.765220i	$-0.722630\pi$
$503$	7.64369	−	13.2393i	0.340815	−	0.590309i	0.984584	+	0.174910i	$0.0559636\pi$
$504$	−2.82953	+	39.9349i	−0.126037	+	1.77884i
$505$	5.69610	+	9.86593i	0.253473	+	0.439028i
$506$	−20.4599	−	2.74677i	−0.909552	−	0.122109i
$507$	−19.0265	−	11.2329i	−0.844995	−	0.498872i
$508$	0.942243	−	3.44600i	0.0418053	−	0.152891i
$509$	−9.01436	−	1.58948i	−0.399555	−	0.0704522i	−0.0297396	−	0.999558i	$-0.509468\pi$
$509$	−9.01436	−	1.58948i	−0.399555	−	0.0704522i	−0.369815	+	0.929105i	$0.620579\pi$
$510$	−5.60334	+	10.4488i	−0.248120	+	0.462679i
$511$	27.4803	+	32.7497i	1.21565	+	1.44876i
$512$	8.17639	+	21.0985i	0.361349	+	0.932431i
$513$	22.0392	+	0.642856i	0.973053	+	0.0283828i
$514$	8.90088	+	2.83145i	0.392601	+	0.124890i
$515$	12.7539	−	10.7018i	0.562005	−	0.471578i
$516$	35.7126	+	10.1390i	1.57216	+	0.446346i
$517$	−0.314703	+	1.78477i	−0.0138406	+	0.0784940i
$518$	72.7263	−	2.98923i	3.19541	−	0.131339i
$519$	9.88150	+	17.5060i	0.433750	+	0.768430i
$520$	0.950784	−	1.02177i	0.0416946	−	0.0448076i
$521$	3.71240	−	2.14335i	0.162643	−	0.0939020i	−0.416469	−	0.909150i	$-0.636733\pi$
$521$	3.71240	−	2.14335i	0.162643	−	0.0939020i	0.579112	+	0.815248i	$0.303399\pi$
$522$	−20.5506	−	6.98007i	−0.899476	−	0.305509i
$523$	−14.6706	−	8.47009i	−0.641502	−	0.370371i	0.143691	−	0.989623i	$-0.454103\pi$
$523$	−14.6706	−	8.47009i	−0.641502	−	0.370371i	−0.785193	+	0.619251i	$0.787436\pi$
$524$	−6.03378	−	8.71150i	−0.263587	−	0.380564i
$525$	−1.34078	−	8.06138i	−0.0585164	−	0.351827i
$526$	6.03527	−	3.82326i	0.263150	−	0.166702i
$527$	20.5777	+	17.2667i	0.896378	+	0.752151i
$528$	8.60979	+	15.6238i	0.374693	+	0.679940i
$529$	−8.58773	−	3.12568i	−0.373379	−	0.135899i
$530$	−3.57993	−	3.92690i	−0.155502	−	0.170573i
$531$	7.03720	+	12.7552i	0.305389	+	0.553527i
$532$	−3.69347	+	39.8700i	−0.160132	+	1.72858i
$533$	4.09030	−	0.721230i	0.177171	−	0.0312400i
$534$	9.76866	−	2.04020i	0.422731	−	0.0882881i
$535$	0.501296	+	1.37730i	0.0216729	+	0.0595459i
$536$	15.8296	−	8.08681i	0.683733	−	0.349297i
$537$	−8.19356	−	23.2112i	−0.353578	−	1.00164i
$538$	26.6578	−	10.9624i	1.14930	−	0.472621i
$539$	−39.2952			−1.69256
$540$	5.66562	+	8.71211i	0.243809	+	0.374909i
$541$	−40.3960			−1.73676			−0.868380	−	0.495900i	$-0.834838\pi$
$541$	−40.3960			−1.73676			−0.868380	+	0.495900i	$0.834838\pi$
$542$	12.4253	−	5.10959i	0.533713	−	0.219476i
$543$	−11.4038	−	2.12529i	−0.489384	−	0.0912051i
$544$	27.0991	+	3.92031i	1.16186	+	0.168082i
$545$	−3.49867	−	9.61251i	−0.149866	−	0.411755i
$546$	−3.80096	−	4.25163i	−0.162666	−	0.181953i
$547$	−25.4998	+	4.49631i	−1.09029	+	0.192248i	−0.689763	−	0.724035i	$-0.742285\pi$
$547$	−25.4998	+	4.49631i	−1.09029	+	0.192248i	−0.400531	+	0.916283i	$0.631174\pi$
$548$	21.5849	+	1.99958i	0.922062	+	0.0854179i
$549$	36.9205	−	12.6307i	1.57573	−	0.539067i
$550$	−2.45322	−	2.69098i	−0.104606	−	0.114744i
$551$	−20.3977	−	7.42415i	−0.868970	−	0.316279i
$552$	7.88983	+	26.6286i	0.335813	+	1.13339i
$553$	−8.16026	−	6.84728i	−0.347010	−	0.291176i
$554$	−11.9920	+	7.59674i	−0.509490	+	0.322754i
$555$	14.5912	−	12.0037i	0.619362	−	0.509530i
$556$	3.35024	−	2.32045i	0.142082	−	0.0984091i
$557$	−34.4097	−	19.8664i	−1.45799	−	0.841768i	−0.459073	−	0.888399i	$-0.651818\pi$
$557$	−34.4097	−	19.8664i	−1.45799	−	0.841768i	−0.998912	+	0.0466304i	$0.985152\pi$
$558$	21.9458	−	8.52977i	0.929040	−	0.361094i
$559$	−4.57979	+	2.64414i	−0.193704	+	0.111835i
$560$	−16.4398	+	9.26890i	−0.694708	+	0.391682i
$561$	21.5858	+	0.209825i	0.911354	+	0.00885880i
$562$	−17.8716	+	0.734565i	−0.753866	+	0.0309858i
$563$	1.93033	−	10.9475i	0.0813539	−	0.461381i	−0.916730	−	0.399507i	$-0.869181\pi$
$563$	1.93033	−	10.9475i	0.0813539	−	0.461381i	0.998084	−	0.0618737i	$-0.0197076\pi$
$564$	2.36422	−	0.596063i	0.0995515	−	0.0250988i
$565$	−7.92934	+	6.65351i	−0.333590	+	0.279915i
$566$	15.1714	+	4.82616i	0.637701	+	0.202858i
$567$	37.5720	−	19.7863i	1.57788	−	0.830946i
$568$	17.6966	−	13.3649i	0.742533	−	0.560779i
$569$	−27.7490	−	33.0700i	−1.16330	−	1.38637i	−0.907719	−	0.419579i	$-0.862178\pi$
$569$	−27.7490	−	33.0700i	−1.16330	−	1.38637i	−0.255581	−	0.966788i	$-0.582267\pi$
$570$	5.47656	+	8.83391i	0.229388	+	0.370012i
$571$	−4.64768	−	0.819512i	−0.194499	−	0.0342955i	0.0755497	−	0.997142i	$-0.475929\pi$
$571$	−4.64768	−	0.819512i	−0.194499	−	0.0342955i	−0.270049	+	0.962847i	$0.587040\pi$
$572$	−2.45118	−	0.670229i	−0.102489	−	0.0280237i
$573$	−0.189695	+	19.5150i	−0.00792462	+	0.815250i
$574$	−55.6626	−	7.47279i	−2.32331	−	0.311908i
$575$	−2.83456	−	4.90960i	−0.118209	−	0.204744i
$576$	14.4408	−	19.1693i	0.601701	−	0.798722i
$577$	−17.5133	+	30.3340i	−0.729089	+	1.26282i	0.228180	+	0.973619i	$0.426723\pi$
$577$	−17.5133	+	30.3340i	−0.729089	+	1.26282i	−0.957269	+	0.289200i	$0.906611\pi$
$578$	5.55327	−	7.19902i	0.230986	−	0.299440i
$579$	−4.87482	−	5.92561i	−0.202590	−	0.246260i
$580$	−2.59752	−	9.89599i	−0.107856	−	0.410908i
$581$	14.6497	−	17.4588i	0.607772	−	0.724315i
$582$	11.7698	+	9.26303i	0.487876	+	0.383965i
$583$	−3.30897	+	9.09132i	−0.137044	+	0.376524i
$584$	−3.15042	−	25.4342i	−0.130365	−	1.05247i
$585$	−1.45261	−	0.285356i	−0.0600581	−	0.0117980i
$586$	−0.183073	−	0.835885i	−0.00756267	−	0.0345301i
$587$	2.40704	+	13.6510i	0.0993491	+	0.563437i	0.993328	+	0.115327i	$0.0367916\pi$
$587$	2.40704	+	13.6510i	0.0993491	+	0.563437i	−0.893978	+	0.448110i	$0.852097\pi$
$588$	21.6294	+	48.2391i	0.891980	+	1.98935i
$589$	22.1284	−	8.05407i	0.911783	−	0.331862i
$590$	−3.18649	+	6.08321i	−0.131186	+	0.250442i
$591$	−5.24099	+	28.1219i	−0.215585	+	1.15678i
$592$	−37.5637	−	22.2021i	−1.54386	−	0.912500i
$593$		−	31.0415i		−	1.27472i	−0.770566	−	0.637360i	$-0.780026\pi$
$593$		−	31.0415i		−	1.27472i	0.770566	−	0.637360i	$-0.219974\pi$
$594$	9.26462	−	16.4978i	0.380132	−	0.676914i
$595$			22.8376i			0.936252i
$596$	2.00344	+	24.3301i	0.0820641	+	0.996600i
$597$	29.6963	−	10.4828i	1.21539	−	0.429033i
$598$	−3.50453	−	1.83574i	−0.143311	−	0.0750688i
$599$	−9.97602	+	3.63097i	−0.407609	+	0.148358i	−0.537684	−	0.843147i	$-0.680701\pi$
$599$	−9.97602	+	3.63097i	−0.407609	+	0.148358i	0.130075	+	0.991504i	$0.458478\pi$
$600$	−1.95314	+	4.49280i	−0.0797367	+	0.183418i
$601$	2.13569	+	12.1121i	0.0871165	+	0.494062i	0.996880	+	0.0789347i	$0.0251518\pi$
$601$	2.13569	+	12.1121i	0.0871165	+	0.494062i	−0.909763	+	0.415127i	$0.863737\pi$
$602$	69.8521	−	15.2988i	2.84696	−	0.623532i
$603$	−16.1416	−	9.74255i	−0.657336	−	0.396747i
$604$	−6.81952	−	14.8217i	−0.277482	−	0.603086i
$605$	1.49468	−	4.10661i	0.0607675	−	0.166957i
$606$	−27.6196	−	3.98164i	−1.12197	−	0.161743i
$607$	1.05269	−	1.25455i	0.0427273	−	0.0509204i	−0.744258	−	0.667893i	$-0.767196\pi$
$607$	1.05269	−	1.25455i	0.0427273	−	0.0509204i	0.786985	+	0.616972i	$0.211641\pi$
$608$	14.8543	−	18.8550i	0.602422	−	0.764673i
$609$	−41.2388	+	6.85890i	−1.67108	+	0.277937i
$610$	14.5649	+	11.2353i	0.589717	+	0.454903i
$611$	−0.173660	+	0.300787i	−0.00702552	+	0.0121686i
$612$	−11.6240	−	26.6144i	−0.469871	−	1.07582i
$613$	5.75043	+	9.96003i	0.232258	+	0.402282i	0.958472	−	0.285186i	$-0.0920554\pi$
$613$	5.75043	+	9.96003i	0.232258	+	0.402282i	−0.726215	+	0.687468i	$0.758722\pi$
$614$	−0.0942828	+	0.702285i	−0.00380495	+	0.0283419i
$615$	−12.6956	+	7.16621i	−0.511938	+	0.288969i
$616$	28.8378	+	18.6838i	1.16191	+	0.752794i
$617$	−21.6963	−	3.82565i	−0.873461	−	0.154015i	−0.281092	−	0.959681i	$-0.590696\pi$
$617$	−21.6963	−	3.82565i	−0.873461	−	0.154015i	−0.592370	+	0.805666i	$0.701808\pi$
$618$	1.27867	+	40.7616i	0.0514357	+	1.63967i
$619$	−21.8107	−	25.9929i	−0.876645	−	1.04474i	−0.998636	−	0.0522135i	$-0.983372\pi$
$619$	−21.8107	−	25.9929i	−0.876645	−	1.04474i	0.121991	−	0.992531i	$-0.461072\pi$
$620$	9.05938	+	6.41265i	0.363833	+	0.257538i
$621$	19.5849	−	22.0042i	0.785913	−	0.882996i
$622$	−3.90408	+	12.2728i	−0.156540	+	0.492094i
$623$	14.7251	−	12.3558i	0.589949	−	0.495026i
$624$	0.526431	+	3.37800i	0.0210741	+	0.135228i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−1.23002	−	29.9257i	−0.0491615	−	1.19607i
$627$	9.62079	−	16.2958i	0.384217	−	0.650792i
$628$	12.7953	−	27.0777i	0.510589	−	1.08052i
$629$	−45.7274	+	26.4007i	−1.82327	+	1.05267i
$630$	17.5482	+	9.63132i	0.699136	+	0.383721i
$631$	−10.1460	−	5.85781i	−0.403907	−	0.233196i	0.284261	−	0.958747i	$-0.408252\pi$
$631$	−10.1460	−	5.85781i	−0.403907	−	0.233196i	−0.688168	+	0.725551i	$0.741585\pi$
$632$	1.87356	+	6.10486i	0.0745260	+	0.242838i
$633$	−1.49059	−	0.558996i	−0.0592454	−	0.0222181i
$634$	8.94692	+	14.1233i	0.355327	+	0.560908i
$635$	−1.36834	−	1.14818i	−0.0543011	−	0.0455640i
$636$	12.9819	−	0.942041i	0.514768	−	0.0373544i
$637$	−7.07659	−	2.57567i	−0.280385	−	0.102052i
$638$	−13.7660	+	12.5497i	−0.545002	+	0.496847i
$639$	−21.9425	−	8.47300i	−0.868031	−	0.335187i
$640$	11.2923	+	0.695473i	0.446368	+	0.0274910i
$641$	14.3613	−	2.53229i	0.567238	−	0.100019i	0.117328	−	0.993093i	$-0.462567\pi$
$641$	14.3613	−	2.53229i	0.567238	−	0.100019i	0.449910	+	0.893074i	$0.351456\pi$
$642$	−3.41053	−	1.12154i	−0.134603	−	0.0442636i
$643$	−2.42174	−	6.65368i	−0.0955041	−	0.262395i	0.882737	−	0.469868i	$-0.155698\pi$
$643$	−2.42174	−	6.65368i	−0.0955041	−	0.262395i	−0.978241	+	0.207473i	$0.933476\pi$
$644$	37.6335	+	38.0199i	1.48297	+	1.49820i
$645$	12.0691	−	14.1027i	0.475219	−	0.555292i
$646$	−11.0469	−	26.8635i	−0.434636	−	1.05693i
$647$	−27.0829			−1.06474			−0.532370	−	0.846512i	$-0.678699\pi$
$647$	−27.0829			−1.06474			−0.532370	+	0.846512i	$0.678699\pi$
$648$	−25.3524	−	2.29239i	−0.995937	−	0.0900534i
$649$	12.5032			0.490792
$650$	−0.265410	−	0.645414i	−0.0104102	−	0.0253152i
$651$	29.4883	−	34.4569i	1.15574	−	1.35047i
$652$	−10.9668	−	11.0794i	−0.429491	−	0.433901i
$653$	15.4485	+	42.4444i	0.604547	+	1.66098i	0.741943	+	0.670462i	$0.233904\pi$
$653$	15.4485	+	42.4444i	0.604547	+	1.66098i	−0.137397	+	0.990516i	$0.543874\pi$
$654$	23.8029	+	7.82748i	0.930765	+	0.306079i
$655$	−5.21801	+	0.920076i	−0.203885	+	0.0359503i
$656$	25.5685	+	21.9035i	0.998284	+	0.855189i
$657$	−21.1593	+	17.0649i	−0.825501	+	0.665766i
$658$	3.47066	−	3.16401i	0.135300	−	0.123346i
$659$	23.6987	+	8.62563i	0.923171	+	0.336007i	0.759499	−	0.650508i	$-0.225444\pi$
$659$	23.6987	+	8.62563i	0.923171	+	0.336007i	0.163672	+	0.986515i	$0.447666\pi$
$660$	8.89614	−	0.645553i	0.346282	−	0.0251281i
$661$	6.37351	+	5.34801i	0.247901	+	0.208014i	0.758268	−	0.651943i	$-0.226046\pi$
$661$	6.37351	+	5.34801i	0.247901	+	0.208014i	−0.510367	+	0.859957i	$0.670490\pi$
$662$	−20.4737	−	32.3192i	−0.795734	−	1.25612i
$663$	3.87359	+	1.45267i	0.150438	+	0.0564168i
$664$	−13.0613	+	4.00846i	−0.506878	+	0.155558i
$665$	17.3381	+	10.0102i	0.672344	+	0.388178i
$666$	1.00140	+	46.2704i	0.0388035	+	1.79294i
$667$	−25.1156	+	14.5005i	−0.972478	+	0.561461i
$668$	−3.43637	+	7.27210i	−0.132957	+	0.281366i
$669$	2.76649	−	4.68591i	0.106959	−	0.181168i
$670$	−0.365002	−	8.88030i	−0.0141013	−	0.343076i
$671$	5.81570	−	32.9825i	0.224512	−	1.27327i
$672$	7.06318	−	45.6857i	0.272468	−	1.76236i
$673$	−11.9400	+	10.0188i	−0.460253	+	0.386198i	−0.843224	−	0.537562i	$-0.819345\pi$
$673$	−11.9400	+	10.0188i	−0.460253	+	0.386198i	0.382971	+	0.923760i	$0.374901\pi$
$674$	−12.3239	+	38.7412i	−0.474699	+	1.49225i
$675$	5.14134	−	0.752719i	0.197890	−	0.0289722i
$676$	20.8240	+	14.7402i	0.800923	+	0.566931i
$677$	30.7857	+	36.6890i	1.18319	+	1.41007i	0.891176	+	0.453658i	$0.149881\pi$
$677$	30.7857	+	36.6890i	1.18319	+	1.41007i	0.292015	+	0.956414i	$0.405674\pi$
$678$	−0.794972	−	25.3422i	−0.0305307	−	0.973263i
$679$	28.4116	+	5.00974i	1.09034	+	0.192256i
$680$	7.44420	−	11.4898i	0.285472	−	0.440615i
$681$	−15.1959	+	8.57753i	−0.582309	+	0.328691i
$682$	2.68889	−	20.0287i	0.102963	−	0.766939i
$683$	19.2564	+	33.3531i	0.736827	+	1.27622i	0.953917	+	0.300070i	$0.0970100\pi$
$683$	19.2564	+	33.3531i	0.736827	+	1.27622i	−0.217090	+	0.976151i	$0.569657\pi$
$684$	−25.3005	−	2.84081i	−0.967388	−	0.108621i
$685$	5.41933	−	9.38656i	0.207062	−	0.358642i
$686$	43.6460	+	33.6682i	1.66641	+	1.28546i
$687$	−29.8110	+	4.95822i	−1.13736	+	0.189168i
$688$	−40.1300	−	15.0721i	−1.52994	−	0.574620i
$689$	−1.19181	+	1.42035i	−0.0454044	+	0.0541108i
$690$	13.7444	+	1.98139i	0.523239	+	0.0754302i
$691$	1.21335	−	3.33366i	0.0461581	−	0.126818i	−0.914472	−	0.404650i	$-0.867393\pi$
$691$	1.21335	−	3.33366i	0.0461581	−	0.126818i	0.960630	+	0.277831i	$0.0896157\pi$
$692$	−9.70233	−	21.0873i	−0.368827	−	0.801617i
$693$	0.708473	−	36.4389i	0.0269127	−	1.38420i
$694$	7.42645	−	1.62652i	0.281904	−	0.0617417i
$695$	−0.353840	−	2.00673i	−0.0134219	−	0.0761194i
$696$	22.9834	+	9.99150i	0.871183	+	0.378727i
$697$	38.2839	−	13.9342i	1.45011	−	0.527796i
$698$	−2.36849	−	1.24066i	−0.0896488	−	0.0469596i
$699$	49.6626	−	17.5309i	1.87841	−	0.663081i
$700$	0.774406	+	9.40452i	0.0292698	+	0.355457i
$701$		−	45.7105i		−	1.72646i	−0.504808	−	0.863231i	$-0.668437\pi$
$701$		−	45.7105i		−	1.72646i	0.504808	−	0.863231i	$-0.331563\pi$
$702$	2.74982	−	2.36379i	0.103785	−	0.0892156i
$703$			46.2879i			1.74578i
$704$	−8.41834	−	18.8000i	−0.317278	−	0.708553i
$705$	0.223354	−	1.19846i	0.00841200	−	0.0451368i
$706$	−11.7022	+	22.3402i	−0.440417	+	0.840783i
$707$	−50.5088	+	18.3837i	−1.89958	+	0.691391i
$708$	−6.88214	−	15.3490i	−0.258647	−	0.576850i
$709$	−0.100853	−	0.571966i	−0.00378761	−	0.0214806i	0.982855	−	0.184378i	$-0.0590271\pi$
$709$	−0.100853	−	0.571966i	−0.00378761	−	0.0214806i	−0.986643	+	0.162898i	$0.947916\pi$
$710$	−2.37227	−	10.8314i	−0.0890296	−	0.406497i
$711$	4.45380	−	5.10300i	0.167031	−	0.191377i
$712$	−11.4359	+	1.41651i	−0.428577	+	0.0530860i
$713$	10.7605	−	29.5642i	0.402984	−	1.10719i
$714$	−43.9593	−	34.5966i	−1.64514	−	1.29475i
$715$	−0.816713	+	0.973320i	−0.0305433	+	0.0364001i
$716$	7.21604	+	27.4916i	0.269676	+	1.02741i
$717$	31.0099	+	37.6943i	1.15809	+	1.40772i
$718$	14.7598	−	19.1340i	0.550831	−	0.714073i
$719$	−16.9740	+	29.3998i	−0.633022	+	1.09643i	0.353909	+	0.935280i	$0.384852\pi$
$719$	−16.9740	+	29.3998i	−0.633022	+	1.09643i	−0.986931	+	0.161146i	$0.948481\pi$
$720$	−5.68921	−	10.5656i	−0.212024	−	0.393758i
$721$	39.2766	+	68.0290i	1.46274	+	2.53353i
$722$	1.39447	+	0.187209i	0.0518967	+	0.00696721i
$723$	−0.0824624	+	8.48336i	−0.00306681	+	0.315500i
$724$	12.9204	+	3.53285i	0.480184	+	0.131297i
$725$	−5.03789	−	0.888315i	−0.187102	−	0.0329912i
$726$	5.64037	+	9.09813i	0.209334	+	0.337663i
$727$	28.6821	+	34.1821i	1.06376	+	1.26774i	0.962034	+	0.272930i	$0.0879927\pi$
$727$	28.6821	+	34.1821i	1.06376	+	1.26774i	0.101728	+	0.994812i	$0.467563\pi$
$728$	3.96867	+	5.25495i	0.147089	+	0.194762i
$729$	12.1141	+	24.1298i	0.448671	+	0.893697i
$730$	−12.2113	−	3.88453i	−0.451961	−	0.143773i
$731$	−39.7370	+	33.3433i	−1.46973	+	1.23325i
$732$	−43.6907	+	11.0152i	−1.61485	+	0.407134i
$733$	−3.03636	+	17.2201i	−0.112151	+	0.636037i	0.875971	+	0.482364i	$0.160222\pi$
$733$	−3.03636	+	17.2201i	−0.112151	+	0.636037i	−0.988122	+	0.153674i	$0.950890\pi$
$734$	−36.1749	+	1.48688i	−1.33524	+	0.0548816i
$735$	26.4319	+	0.256931i	0.974955	+	0.00947703i
$736$	−6.54072	−	31.3953i	−0.241094	−	1.15724i
$737$	−14.0140	+	8.09097i	−0.516211	+	0.298035i
$738$	5.43859	−	35.2934i	0.200197	−	1.29917i
$739$	−44.6954	−	25.8049i	−1.64415	−	0.949250i	−0.979336	−	0.202240i	$-0.935178\pi$
$739$	−44.6954	−	25.8049i	−1.64415	−	0.949250i	−0.664813	−	0.747010i	$-0.731489\pi$
$740$	−17.9353	+	12.4224i	−0.659314	+	0.456656i
$741$	2.80072	−	2.30407i	0.102887	−	0.0846421i
$742$	21.1793	−	13.4168i	0.777518	−	0.492547i
$743$	−38.3012	−	32.1385i	−1.40513	−	1.17905i	−0.958766	−	0.284197i	$-0.908273\pi$
$743$	−38.3012	−	32.1385i	−1.40513	−	1.17905i	−0.446367	−	0.894850i	$-0.647283\pi$
$744$	−26.0675	+	7.72356i	−0.955680	+	0.283160i
$745$	11.4701	+	4.17478i	0.420232	+	0.152952i
$746$	21.0854	+	23.1290i	0.771992	+	0.846813i
$747$	10.9178	+	9.52889i	0.399463	+	0.348644i
$748$	−24.8201	−	2.29928i	−0.907512	−	0.0840700i
$749$	−6.81033	+	1.20085i	−0.248844	+	0.0438779i
$750$	1.63256	+	1.82613i	0.0596127	+	0.0666808i
$751$	−7.67408	−	21.0844i	−0.280031	−	0.769379i	−0.997358	−	0.0726425i	$-0.976857\pi$
$751$	−7.67408	−	21.0844i	−0.280031	−	0.769379i	0.717327	−	0.696737i	$-0.245365\pi$
$752$	−2.77747	+	0.460539i	−0.101284	+	0.0167941i
$753$	−18.3229	−	3.41479i	−0.667725	−	0.124442i
$754$	−3.30168	+	1.35773i	−0.120240	+	0.0494457i
$755$	−8.15764			−0.296887
$756$	−45.1226	+	19.1874i	−1.64109	+	0.697839i
$757$	−7.75110			−0.281718			−0.140859	−	0.990030i	$-0.544986\pi$
$757$	−7.75110			−0.281718			−0.140859	+	0.990030i	$0.544986\pi$
$758$	−25.4294	+	10.4572i	−0.923637	+	0.379822i
$759$	−8.41593	−	23.8411i	−0.305479	−	0.865378i
$760$	−5.46005	−	10.6878i	−0.198057	−	0.387687i
$761$	−3.57145	−	9.81247i	−0.129465	−	0.355702i	0.857976	−	0.513689i	$-0.171722\pi$
$761$	−3.57145	−	9.81247i	−0.129465	−	0.355702i	−0.987441	+	0.157988i	$0.949499\pi$
$762$	4.28298	−	0.894508i	0.155156	−	0.0324046i
$763$	47.5309	−	8.38099i	1.72074	−	0.303412i
$764$	2.07870	−	22.4389i	0.0752046	−	0.811813i
$765$	−14.5183	−	0.282277i	−0.524911	−	0.0102057i
$766$	−10.0178	−	10.9887i	−0.361958	−	0.397039i
$767$	2.25167	+	0.819539i	0.0813030	+	0.0295919i
$768$	−18.4453	+	20.6826i	−0.665589	+	0.746318i
$769$	21.5151	+	18.0533i	0.775855	+	0.651020i	0.942201	−	0.335048i	$-0.108752\pi$
$769$	21.5151	+	18.0533i	0.775855	+	0.651020i	−0.166346	+	0.986067i	$0.553197\pi$
$770$	14.5136	−	9.19414i	0.523033	−	0.331334i
$771$	1.87687	+	11.2846i	0.0675937	+	0.406404i
$772$	5.04484	+	7.28367i	0.181568	+	0.262145i
$773$	−2.10109	−	1.21307i	−0.0755711	−	0.0436310i	0.461738	−	0.887016i	$-0.347226\pi$
$773$	−2.10109	−	1.21307i	−0.0755711	−	0.0436310i	−0.537309	+	0.843385i	$0.680559\pi$
$774$	8.86234	+	44.5954i	0.318550	+	1.60295i
$775$	4.80614	−	2.77482i	0.172642	−	0.0996746i
$776$	−12.6612	−	11.7816i	−0.454510	−	0.422933i
$777$	43.8207	+	77.6326i	1.57206	+	2.78506i
$778$	27.3272	−	1.12321i	0.979727	−	0.0402692i
$779$	6.20186	−	35.1725i	0.222205	−	1.26018i
$780$	1.64440	+	0.466856i	0.0588790	+	0.0167161i
$781$	−15.4650	+	12.9767i	−0.553382	+	0.464343i
$782$	−36.9807	−	11.7639i	−1.32243	−	0.420676i
$783$	−3.85061	−	26.3011i	−0.137610	−	0.939924i
$784$	−20.2914	−	57.5735i	−0.724694	−	2.05620i
$785$	−9.62532	−	11.4710i	−0.343542	−	0.409418i
$786$	6.13371	−	11.4378i	0.218782	−	0.407972i
$787$	10.4339	+	1.83978i	0.371929	+	0.0655812i	0.356489	−	0.934300i	$-0.383974\pi$
$787$	10.4339	+	1.83978i	0.371929	+	0.0655812i	0.0154406	+	0.999881i	$0.495085\pi$
$788$	8.71203	−	31.8619i	0.310353	−	1.13503i
$789$	7.53485	+	4.44845i	0.268248	+	0.158369i
$790$	3.16455	+	0.424846i	0.112590	+	0.0151153i
$791$	−24.4190	−	42.2949i	−0.868238	−	1.50383i
$792$	−12.2341	+	18.1018i	−0.434720	+	0.643219i
$793$	3.20923	−	5.55854i	0.113963	−	0.197390i
$794$	−4.18493	+	5.42516i	−0.148518	+	0.192532i
$795$	2.28522	−	6.09363i	0.0810484	−	0.216119i
$796$	−35.1726	+	9.23218i	−1.24666	+	0.327226i
$797$	−14.2888	+	17.0287i	−0.506135	+	0.603188i	−0.957244	−	0.289280i	$-0.906584\pi$
$797$	−14.2888	+	17.0287i	−0.506135	+	0.603188i	0.451109	+	0.892469i	$0.351028\pi$
$798$	−45.5337	+	18.2092i	−1.61187	+	0.644598i
$799$	−1.16522	+	3.20141i	−0.0412225	+	0.113258i
$800$	2.67590	−	4.98393i	0.0946075	−	0.176208i
$801$	7.67283	+	9.51374i	0.271106	+	0.336152i
$802$	−3.50598	−	16.0078i	−0.123801	−	0.565256i
$803$	4.05136	+	22.9764i	0.142969	+	0.810820i
$804$	17.6463	+	12.7501i	0.622337	+	0.449663i
$805$	25.1348	−	9.14831i	0.885885	−	0.322436i
$806$	1.79705	−	3.43068i	0.0632984	−	0.120841i
$807$	26.8209	+	22.9534i	0.944141	+	0.807997i
$808$	31.4039	+	7.21493i	1.10478	+	0.253820i
$809$		−	42.8284i		−	1.50577i	−0.658155	−	0.752883i	$-0.728663\pi$
$809$		−	42.8284i		−	1.50577i	0.658155	−	0.752883i	$-0.271337\pi$
$810$	−6.33971	+	11.0367i	−0.222755	+	0.387789i
$811$			19.5579i			0.686771i	0.939195	+	0.343386i	$0.111574\pi$
$811$			19.5579i			0.686771i	−0.939195	+	0.343386i	$0.888426\pi$
$812$	48.1098	−	3.96156i	1.68832	−	0.139023i
$813$	12.5013	+	10.6986i	0.438441	+	0.375218i
$814$	35.1873	+	18.4317i	1.23331	+	0.646031i
$815$	−7.32451	+	2.66590i	−0.256566	+	0.0933825i
$816$	10.8392	+	31.7349i	0.379447	+	1.11094i
$817$	7.89646	+	44.7831i	0.276262	+	1.56676i
$818$	9.45611	−	2.07105i	0.330625	−	0.0724125i
$819$	2.51603	−	6.51576i	0.0879173	−	0.227679i
$820$	15.2928	−	7.03627i	0.534047	−	0.245717i
$821$	−1.87458	+	5.15036i	−0.0654232	+	0.179749i	−0.968096	−	0.250578i	$-0.919379\pi$
$821$	−1.87458	+	5.15036i	−0.0654232	+	0.179749i	0.902673	+	0.430327i	$0.141602\pi$
$822$	9.85812	+	24.6511i	0.343842	+	0.859807i
$823$	27.8850	−	33.2320i	0.972008	−	1.15839i	−0.0153486	−	0.999882i	$-0.504886\pi$
$823$	27.8850	−	33.2320i	0.972008	−	1.15839i	0.987357	−	0.158512i	$-0.0506698\pi$
$824$	2.41445	−	47.0287i	0.0841114	−	1.63832i
$825$	1.56599	−	4.17579i	0.0545209	−	0.145382i
$826$	−25.6549	−	19.7900i	−0.892648	−	0.688582i
$827$	5.05665	−	8.75837i	0.175837	−	0.304558i	−0.764614	−	0.644489i	$-0.777070\pi$
$827$	5.05665	−	8.75837i	0.175837	−	0.304558i	0.940451	+	0.339930i	$0.110404\pi$
$828$	−24.6351	+	23.4544i	−0.856130	+	0.815097i
$829$	−10.6877	−	18.5116i	−0.371198	−	0.642934i	0.618552	−	0.785744i	$-0.287720\pi$
$829$	−10.6877	−	18.5116i	−0.371198	−	0.642934i	−0.989750	+	0.142810i	$0.954386\pi$
$830$	−0.908956	+	6.77054i	−0.0315503	+	0.235009i
$831$	−14.9716	−	8.83899i	−0.519359	−	0.306621i
$832$	−0.283762	−	3.93745i	−0.00983769	−	0.136507i
$833$	−72.7472	−	12.8273i	−2.52054	−	0.444440i
$834$	4.39870	+	2.35888i	0.152315	+	0.0816815i
$835$	2.58502	+	3.08070i	0.0894582	+	0.106612i
$836$	−12.6247	+	17.8354i	−0.436635	+	0.616849i
$837$	21.5405	+	19.1721i	0.744547	+	0.662686i
$838$	−6.79349	+	21.3559i	−0.234677	+	0.737726i
$839$	−25.4888	+	21.3877i	−0.879972	+	0.738384i	−0.966173	−	0.257893i	$-0.916972\pi$
$839$	−25.4888	+	21.3877i	−0.879972	+	0.738384i	0.0862011	+	0.996278i	$0.472527\pi$
$840$	−19.2756	−	12.7562i	−0.665070	−	0.440132i
$841$	0.491527	−	2.78759i	0.0169492	−	0.0961237i
$842$	−0.728554	−	17.7253i	−0.0251076	−	0.610854i
$843$	−10.7684	−	19.0772i	−0.370882	−	0.657054i
$844$	1.66201	+	0.785370i	0.0572089	+	0.0270335i
$845$	11.0475	−	6.37825i	0.380044	−	0.219418i
$846$	1.96852	+	2.24547i	0.0676792	+	0.0772010i
$847$	17.8567	+	10.3096i	0.613565	+	0.354242i
$848$	−15.0289	−	0.153534i	−0.516094	−	0.00527237i
$849$	3.19909	+	19.2344i	0.109792	+	0.660121i
$850$	−3.66322	−	5.78264i	−0.125647	−	0.198343i
$851$	47.3738	+	39.7513i	1.62395	+	1.36266i
$852$	24.4428	+	11.8422i	0.837395	+	0.405707i
$853$	−32.9258	−	11.9840i	−1.12736	−	0.410324i	−0.290025	−	0.957019i	$-0.593664\pi$
$853$	−32.9258	−	11.9840i	−1.12736	−	0.410324i	−0.837332	+	0.546695i	$0.815886\pi$
$854$	−64.1377	+	58.4708i	−2.19475	+	2.00083i
$855$	−6.57797	+	10.8985i	−0.224962	+	0.372719i
$856$	3.81777	+	1.61575i	0.130489	+	0.0552253i
$857$	−50.2542	+	8.86117i	−1.71665	+	0.302692i	−0.943461	−	0.331484i	$-0.892451\pi$
$857$	−50.2542	+	8.86117i	−1.71665	+	0.302692i	−0.773189	+	0.634175i	$0.781340\pi$
$858$	−0.636274	−	3.04654i	−0.0217220	−	0.104007i
$859$	−4.68516	−	12.8724i	−0.159856	−	0.439199i	0.833745	−	0.552149i	$-0.186192\pi$
$859$	−4.68516	−	12.8724i	−0.159856	−	0.439199i	−0.993601	+	0.112950i	$0.963970\pi$
$860$	−15.2330	+	15.0782i	−0.519442	+	0.514163i
$861$	−22.8962	−	64.8616i	−0.780300	−	2.21048i
$862$	−12.0299	−	29.2538i	−0.409740	−	0.996389i
$863$	13.0651			0.444742			0.222371	−	0.974962i	$-0.428620\pi$
$863$	13.0651			0.444742			0.222371	+	0.974962i	$0.428620\pi$
$864$	28.9560	+	5.05488i	0.985102	+	0.171971i
$865$	−11.6061			−0.394620
$866$	−10.1251	−	24.6218i	−0.344065	−	0.836684i
$867$	10.9469	+	2.04014i	0.371776	+	0.0692868i
$868$	−37.2187	+	36.8404i	−1.26329	+	1.25045i
$869$	−1.98829	−	5.46278i	−0.0674481	−	0.185312i
$870$	9.34175	−	8.35154i	0.316715	−	0.283144i
$871$	−3.05408	+	0.538517i	−0.103484	+	0.0182470i
$872$	−26.6451	−	11.2767i	−0.902318	−	0.381878i
$873$	−3.53596	+	17.9999i	−0.119674	+	0.609204i
$874$	−25.1404	+	22.9191i	−0.850388	+	0.775251i
$875$	4.43363	+	1.61371i	0.149884	+	0.0545534i
$876$	25.9760	−	17.6205i	0.877649	−	0.595340i
$877$	−9.84351	−	8.25968i	−0.332392	−	0.278910i	0.461282	−	0.887254i	$-0.347390\pi$
$877$	−9.84351	−	8.25968i	−0.332392	−	0.278910i	−0.793673	+	0.608344i	$0.791834\pi$
$878$	−29.0613	−	45.8753i	−0.980773	−	1.54822i
$879$	0.809333	−	0.665814i	0.0272981	−	0.0224573i
$880$	−10.2989	−	0.105212i	−0.347174	−	0.00354670i
$881$	18.6875	+	10.7893i	0.629599	+	0.363499i	0.780597	−	0.625035i	$-0.214915\pi$
$881$	18.6875	+	10.7893i	0.629599	+	0.363499i	−0.150998	+	0.988534i	$0.548249\pi$
$882$	−40.5361	+	50.4885i	−1.36492	+	1.70004i
$883$	−25.0561	+	14.4661i	−0.843204	+	0.486824i	−0.858352	−	0.513061i	$-0.828511\pi$
$883$	−25.0561	+	14.4661i	−0.843204	+	0.486824i	0.0151481	+	0.999885i	$0.495178\pi$
$884$	−4.31908	−	2.04094i	−0.145267	−	0.0686444i
$885$	−8.41023	−	0.0817515i	−0.282707	−	0.00274805i
$886$	−1.51843	−	36.9425i	−0.0510126	−	1.24111i
$887$	−0.917869	+	5.20549i	−0.0308190	+	0.174783i	−0.996332	−	0.0855715i	$-0.972728\pi$
$887$	−0.917869	+	5.20549i	−0.0308190	+	0.174783i	0.965513	+	0.260355i	$0.0838395\pi$
$888$	3.25868	−	53.3416i	0.109354	−	1.79003i
$889$	6.45609	−	5.41730i	0.216530	−	0.181691i
$890$	−1.74658	+	5.49052i	−0.0585456	+	0.184043i
$891$	23.1561	+	0.900780i	0.775759	+	0.0301773i
$892$	−3.63027	+	5.12861i	−0.121551	+	0.171719i
$893$	1.91975	+	2.28787i	0.0642419	+	0.0765605i
$894$	−25.4119	+	15.7540i	−0.849900	+	0.526893i
$895$	13.9955	+	2.46779i	0.467818	+	0.0824890i
$896$	−12.4833	+	51.8999i	−0.417039	+	1.73385i
$897$	0.0470970	−	4.84513i	0.00157252	−	0.161774i
$898$	−1.90331	+	14.1772i	−0.0635143	+	0.473099i
$899$	−14.1949	−	24.5863i	−0.473427	−	0.819999i
$900$	−5.98820	+	0.376063i	−0.199607	+	0.0125354i
$901$	−9.09362	+	15.7506i	−0.302952	+	0.524729i
$902$	−24.2680	−	18.7201i	−0.808035	−	0.623312i
$903$	55.6398	+	67.6333i	1.85158	+	2.25069i
$904$	−1.50111	+	29.2386i	−0.0499261	+	0.972461i
$905$	4.30498	−	5.13047i	0.143102	−	0.170543i
$906$	12.3580	−	15.7023i	0.410566	−	0.521675i
$907$	15.6345	−	42.9553i	0.519134	−	1.42631i	−0.352343	−	0.935871i	$-0.614615\pi$
$907$	15.6345	−	42.9553i	0.519134	−	1.42631i	0.871477	−	0.490437i	$-0.163163\pi$
$908$	18.3046	−	8.42200i	0.607458	−	0.279494i
$909$	−11.0626	−	32.3367i	−0.366923	−	1.07254i
$910$	3.21636	−	0.704438i	0.106621	−	0.0233519i
$911$	0.319650	+	1.81283i	0.0105905	+	0.0600616i	0.989645	−	0.143537i	$-0.0458475\pi$
$911$	0.319650	+	1.81283i	0.0105905	+	0.0600616i	−0.979055	+	0.203598i	$0.934736\pi$
$912$	28.8439	+	5.68103i	0.955117	+	0.188118i
$913$	11.6876	−	4.25393i	0.386803	−	0.140785i
$914$	−22.0795	−	11.5656i	−0.730323	−	0.382556i
$915$	−4.12758	+	22.1476i	−0.136454	+	0.732177i
$916$	34.7780	−	2.86376i	1.14910	−	0.0946213i
$917$		−	24.9993i		−	0.825549i
$918$	22.5371	−	27.5181i	0.743834	−	0.908234i
$919$		−	37.9428i		−	1.25162i	−0.779977	−	0.625808i	$-0.784769\pi$
$919$		−	37.9428i		−	1.25162i	0.779977	−	0.625808i	$-0.215231\pi$
$920$	−15.6275	−	3.59038i	−0.515225	−	0.118371i
$921$	−0.818346	+	0.288877i	−0.0269654	+	0.00951882i
$922$	4.47202	−	8.53737i	0.147278	−	0.281163i
$923$	−3.63564	+	1.32327i	−0.119669	+	0.0435558i
$924$	−4.28907	+	41.8648i	−0.141100	+	1.37725i
$925$	1.89426	+	10.7429i	0.0622828	+	0.353224i
$926$	−0.613674	−	2.80195i	−0.0201666	−	0.0920777i
$927$	−43.7328	+	24.1280i	−1.43637	+	0.792468i
$928$	−25.4958	−	13.6889i	−0.836941	−	0.449359i
$929$	18.1780	−	49.9436i	0.596401	−	1.63860i	−0.161986	−	0.986793i	$-0.551790\pi$
$929$	18.1780	−	49.9436i	0.596401	−	1.63860i	0.758387	−	0.651805i	$-0.225988\pi$
$930$	−1.93963	+	13.4547i	−0.0636031	+	0.441198i
$931$	−41.6249	+	49.6067i	−1.36420	+	1.62579i
$932$	−58.8209	+	15.4394i	−1.92674	+	0.505736i
$933$	−15.5595	+	2.58788i	−0.509395	+	0.0847233i
$934$	3.90882	−	5.06723i	0.127901	−	0.165805i
$935$	−6.23159	+	10.7934i	−0.203795	+	0.352983i
$936$	−3.38973	+	2.45801i	−0.110797	+	0.0803425i
$937$	−15.0186	−	26.0130i	−0.490636	−	0.849807i	0.509306	−	0.860586i	$-0.329902\pi$
$937$	−15.0186	−	26.0130i	−0.490636	−	0.849807i	−0.999942	+	0.0107790i	$0.996569\pi$
$938$	41.5613	+	5.57967i	1.35702	+	0.182183i
$939$	31.9445	−	18.0315i	1.04247	−	0.588435i
$940$	−0.371279	+	1.35785i	−0.0121098	+	0.0442882i
$941$	−7.04275	−	1.24183i	−0.229587	−	0.0404824i	0.0576708	−	0.998336i	$-0.481633\pi$
$941$	−7.04275	−	1.24183i	−0.229587	−	0.0404824i	−0.287258	+	0.957853i	$0.592744\pi$
$942$	36.6615	−	1.15005i	1.19449	−	0.0374706i
$943$	−30.6716	−	36.5530i	−0.998805	−	1.19033i
$944$	6.45644	+	18.3191i	0.210139	+	0.596234i
$945$	−0.714809	+	24.5059i	−0.0232527	+	0.797178i
$946$	37.1877	+	11.8297i	1.20908	+	0.384618i
$947$	28.1205	−	23.5959i	0.913795	−	0.766765i	−0.0590422	−	0.998255i	$-0.518805\pi$
$947$	28.1205	−	23.5959i	0.913795	−	0.766765i	0.972837	+	0.231490i	$0.0743602\pi$
$948$	−5.61173	+	5.44773i	−0.182261	+	0.176934i
$949$	−0.776425	+	4.40333i	−0.0252038	+	0.142938i
$950$	−5.99579	+	0.246442i	−0.194529	+	0.00799563i
$951$	−10.4100	+	17.6325i	−0.337566	+	0.571774i
$952$	47.2884	+	44.0031i	1.53263	+	1.42615i
$953$	−34.5147	+	19.9271i	−1.11804	+	0.645501i	−0.940900	−	0.338684i	$-0.890018\pi$
$953$	−34.5147	+	19.9271i	−1.11804	+	0.645501i	−0.177141	+	0.984185i	$0.556685\pi$
$954$	8.26754	+	13.6299i	0.267672	+	0.441286i
$955$	−9.75795	−	5.63376i	−0.315760	−	0.182304i
$956$	−32.0915	−	46.3333i	−1.03791	−	1.49853i
$957$	−21.3617	−	8.01100i	−0.690525	−	0.258959i
$958$	−37.6126	+	23.8271i	−1.21521	+	0.769818i
$959$	39.1745	+	32.8713i	1.26501	+	1.06147i
$960$	5.53967	+	12.7009i	0.178792	+	0.409919i
$961$	−0.189250	−	0.0688812i	−0.00610482	−	0.00222197i
$962$	5.12866	+	5.62573i	0.165355	+	0.181381i
$963$	−0.679224	−	4.34430i	−0.0218877	−	0.139993i
$964$	0.903631	−	9.75444i	0.0291040	−	0.314169i
$965$	4.36277	−	0.769275i	0.140443	−	0.0247638i
$966$	−20.4673	+	62.2397i	−0.658524	+	2.00253i
$967$	17.3693	+	47.7219i	0.558560	+	1.53463i	0.821727	+	0.569881i	$0.193011\pi$
$967$	17.3693	+	47.7219i	0.558560	+	1.53463i	−0.263167	+	0.964750i	$0.584767\pi$
$968$	−5.62336	−	11.0075i	−0.180741	−	0.353793i
$969$	23.1305	−	27.0279i	0.743058	−	0.868261i
$970$	−7.99759	+	3.28880i	−0.256787	+	0.105597i
$971$	4.92361			0.158006			0.0790030	−	0.996874i	$-0.474826\pi$
$971$	4.92361			0.158006			0.0790030	+	0.996874i	$0.474826\pi$
$972$	−11.6401	−	28.9225i	−0.373356	−	0.927688i
$973$	9.61414			0.308215
$974$	7.56896	−	3.11254i	0.242525	−	0.0997322i
$975$	0.555725	−	0.649363i	0.0177974	−	0.0207963i
$976$	51.3275	−	8.51074i	1.64295	−	0.272422i
$977$	−8.40804	−	23.1009i	−0.268997	−	0.739063i	−0.998483	−	0.0550671i	$-0.982463\pi$
$977$	−8.40804	−	23.1009i	−0.268997	−	0.739063i	0.729486	−	0.683996i	$-0.239759\pi$
$978$	5.96436	−	18.1372i	0.190719	−	0.579965i
$979$	10.3308	−	1.82160i	0.330173	−	0.0582184i
$980$	−30.3922	−	2.81547i	−0.970844	−	0.0899369i
$981$	4.74046	+	30.3199i	0.151351	+	0.968040i
$982$	27.7735	+	30.4652i	0.886287	+	0.972185i
$983$	−13.3996	−	4.87706i	−0.427381	−	0.155554i	0.119369	−	0.992850i	$-0.461913\pi$
$983$	−13.3996	−	4.87706i	−0.427381	−	0.155554i	−0.546750	+	0.837296i	$0.684135\pi$
$984$	−9.62310	+	40.0957i	−0.306773	+	1.27821i
$985$	−12.6518	−	10.6161i	−0.403119	−	0.338257i
$986$	−29.5817	+	18.7396i	−0.942073	+	0.596790i
$987$	5.38567	+	2.01972i	0.171428	+	0.0642884i
$988$	−3.44261	+	2.38443i	−0.109524	+	0.0758587i
$989$	52.6151	+	30.3773i	1.67306	+	0.965943i
$990$	5.66550	+	9.34020i	0.180061	+	0.296851i
$991$	36.0831	−	20.8326i	1.14622	−	0.661770i	0.198256	−	0.980150i	$-0.436472\pi$
$991$	36.0831	−	20.8326i	1.14622	−	0.661770i	0.947963	+	0.318380i	$0.103139\pi$
$992$	30.7337	−	6.40289i	0.975795	−	0.203292i
$993$	23.8217	−	40.3495i	0.755958	−	1.28045i
$994$	52.2718	−	2.14850i	1.65796	−	0.0681463i
$995$	−3.15728	+	17.9058i	−0.100092	+	0.567652i
$996$	−11.6554	−	12.0063i	−0.369315	−	0.380433i
$997$	8.14804	−	6.83702i	0.258051	−	0.216531i	−0.504579	−	0.863366i	$-0.668352\pi$
$997$	8.14804	−	6.83702i	0.258051	−	0.216531i	0.762630	+	0.646835i	$0.223908\pi$
$998$	49.0336	+	15.5980i	1.55213	+	0.493747i
$999$	−49.8942	+	26.8981i	−1.57858	+	0.851018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.491.28	yes	432
4.3	odd	2	inner	540.2.be.a.491.14	yes	432
27.11	odd	18	inner	540.2.be.a.11.14	✓	432
108.11	even	18	inner	540.2.be.a.11.28	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.14	✓	432	27.11	odd	18	inner
540.2.be.a.11.28	yes	432	108.11	even	18	inner
540.2.be.a.491.14	yes	432	4.3	odd	2	inner
540.2.be.a.491.28	yes	432	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537858 - 1.30794i) q^{2} +(1.12619 - 1.31594i) q^{3} +(-1.42142 + 1.40697i) q^{4} +(0.342020 + 0.939693i) q^{5} +(-2.32690 - 0.765193i) q^{6} +(-4.64650 + 0.819302i) q^{7} +(2.60476 + 1.10238i) q^{8} +(-0.463415 - 2.96399i) q^{9} +(1.04510 - 0.952763i) q^{10} +(-2.41957 - 0.880650i) q^{11} +(0.250715 + 3.45502i) q^{12} +(-0.378011 - 0.317189i) q^{13} +(3.57075 + 5.63667i) q^{14} +(1.62176 + 0.608189i) q^{15} +(0.0408615 - 3.99979i) q^{16} +(-4.19187 - 2.42018i) q^{17} +(-3.62747 + 2.20032i) q^{18} +(-3.67476 + 2.12162i) q^{19} +(-1.80827 - 0.854484i) q^{20} +(-4.15466 + 7.03721i) q^{21} +(0.149544 + 3.63831i) q^{22} +(-0.984432 + 5.58299i) q^{23} +(4.38411 - 2.18623i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(-0.211548 + 0.665018i) q^{26} +(-4.42234 - 2.72818i) q^{27} +(5.45188 - 7.70206i) q^{28} +(3.28825 + 3.91878i) q^{29} +(-0.0768014 - 2.44829i) q^{30} +(-5.46534 - 0.963686i) q^{31} +(-5.25347 + 2.09787i) q^{32} +(-3.88376 + 2.19224i) q^{33} +(-0.910820 + 6.78443i) q^{34} +(-2.35909 - 4.08606i) q^{35} +(4.82896 + 3.56106i) q^{36} +(5.45430 - 9.44713i) q^{37} +(4.75145 + 3.66523i) q^{38} +(-0.843112 + 0.140228i) q^{39} +(-0.145020 + 2.82471i) q^{40} +(-5.41030 + 6.44774i) q^{41} +(11.4389 + 1.64903i) q^{42} +(3.66535 - 10.0705i) q^{43} +(4.67826 - 2.15249i) q^{44} +(2.62674 - 1.44921i) q^{45} +(7.83170 - 1.71527i) q^{46} +(-0.122222 - 0.693155i) q^{47} +(-5.21748 - 4.55828i) q^{48} +(14.3408 - 5.21963i) q^{49} +(1.25275 + 0.656213i) q^{50} +(-7.90564 + 2.79070i) q^{51} +(0.983587 - 0.0809925i) q^{52} -3.75742i q^{53} +(-1.18971 + 7.25152i) q^{54} -2.57485i q^{55} +(-13.0062 - 2.98813i) q^{56} +(-1.34652 + 7.22511i) q^{57} +(3.35692 - 6.40858i) q^{58} +(-4.56304 + 1.66081i) q^{59} +(-3.16090 + 1.41728i) q^{60} +(2.25866 + 12.8095i) q^{61} +(1.67913 + 7.66666i) q^{62} +(4.58166 + 13.3925i) q^{63} +(5.56951 + 5.74287i) q^{64} +(0.168773 - 0.463699i) q^{65} +(4.95623 + 3.90062i) q^{66} +(4.03968 - 4.81430i) q^{67} +(9.36352 - 2.45776i) q^{68} +(6.23825 + 7.58293i) q^{69} +(-4.07547 + 5.28326i) q^{70} +(3.92026 - 6.79009i) q^{71} +(2.06037 - 8.23134i) q^{72} +(-4.53053 - 7.84711i) q^{73} +(-15.2899 - 2.05270i) q^{74} +(-0.0168356 + 1.73197i) q^{75} +(2.23831 - 8.18599i) q^{76} +(11.9640 + 2.10958i) q^{77} +(0.636884 + 1.02732i) q^{78} +(1.45125 + 1.72954i) q^{79} +(3.77255 - 1.32961i) q^{80} +(-8.57049 + 2.74711i) q^{81} +(11.3432 + 3.60838i) q^{82} +(-3.70034 + 3.10495i) q^{83} +(-3.99565 - 15.8483i) q^{84} +(0.840519 - 4.76682i) q^{85} +(-15.1430 + 0.622416i) q^{86} +(8.86007 + 0.0861241i) q^{87} +(-5.33157 - 4.96116i) q^{88} +(-3.52826 + 2.03704i) q^{89} +(-3.30830 - 2.65616i) q^{90} +(2.01630 + 1.16411i) q^{91} +(-6.45582 - 9.32083i) q^{92} +(-7.42314 + 6.10679i) q^{93} +(-0.840867 + 0.532677i) q^{94} +(-3.25051 - 2.72750i) q^{95} +(-3.15569 + 9.27586i) q^{96} +(-5.74588 - 2.09133i) q^{97} +(-14.5403 - 15.9495i) q^{98} +(-1.48898 + 7.57968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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