LMFDB - Embedded newform 228.2.m.a.11.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(11,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.m (of order $6$, degree $2$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	228.11
Dual form			228.2.m.a.83.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.262728 + 1.38959i) q^{2} +(1.73065 - 0.0695904i) q^{3} +(-1.86195 + 0.730170i) q^{4} +(-0.0574154 - 0.0331488i) q^{5} +(0.551393 + 2.38662i) q^{6} +3.60595i q^{7} +(-1.50383 - 2.39552i) q^{8} +(2.99031 - 0.240874i) q^{9} +(0.0309788 - 0.0884932i) q^{10} -1.08432 q^{11} +(-3.17157 + 1.39324i) q^{12} +(0.113579 + 0.196724i) q^{13} +(-5.01081 + 0.947383i) q^{14} +(-0.101673 - 0.0533734i) q^{15} +(2.93370 - 2.71908i) q^{16} +(2.43120 + 1.40366i) q^{17} +(1.12036 + 4.09204i) q^{18} +(4.35886 + 0.0194115i) q^{19} +(0.131109 + 0.0197983i) q^{20} +(0.250939 + 6.24065i) q^{21} +(-0.284880 - 1.50676i) q^{22} +(-4.30600 - 7.45822i) q^{23} +(-2.76931 - 4.04116i) q^{24} +(-2.49780 - 4.32632i) q^{25} +(-0.243527 + 0.209513i) q^{26} +(5.15843 - 0.624965i) q^{27} +(-2.63296 - 6.71409i) q^{28} +(-4.65184 + 2.68574i) q^{29} +(0.0474552 - 0.155307i) q^{30} -6.89036i q^{31} +(4.54918 + 3.36228i) q^{32} +(-1.87657 + 0.0754579i) q^{33} +(-1.31177 + 3.74717i) q^{34} +(0.119533 - 0.207037i) q^{35} +(-5.39193 + 2.63193i) q^{36} +1.80655 q^{37} +(1.11822 + 6.06214i) q^{38} +(0.210255 + 0.332557i) q^{39} +(0.00693426 + 0.187390i) q^{40} +(2.63274 + 1.52002i) q^{41} +(-8.60604 + 1.98829i) q^{42} +(-5.11992 - 2.95599i) q^{43} +(2.01894 - 0.791735i) q^{44} +(-0.179675 - 0.0852954i) q^{45} +(9.23260 - 7.94308i) q^{46} +(0.205933 + 0.356687i) q^{47} +(4.88800 - 4.90994i) q^{48} -6.00287 q^{49} +(5.35559 - 4.60758i) q^{50} +(4.30525 + 2.26005i) q^{51} +(-0.355120 - 0.283358i) q^{52} +(-0.727053 + 0.419764i) q^{53} +(2.22371 + 7.00393i) q^{54} +(0.0622564 + 0.0359437i) q^{55} +(8.63812 - 5.42272i) q^{56} +(7.54501 - 0.269740i) q^{57} +(-4.95426 - 5.75856i) q^{58} +(4.44625 - 7.70114i) q^{59} +(0.228281 + 0.0251401i) q^{60} +(4.67311 + 8.09407i) q^{61} +(9.57482 - 1.81029i) q^{62} +(0.868578 + 10.7829i) q^{63} +(-3.47701 + 7.20489i) q^{64} -0.0150600i q^{65} +(-0.597884 - 2.58785i) q^{66} +(-5.00700 + 2.89079i) q^{67} +(-5.55168 - 0.838342i) q^{68} +(-7.97122 - 12.6079i) q^{69} +(0.319102 + 0.111708i) q^{70} +(-5.70164 + 9.87552i) q^{71} +(-5.07393 - 6.80112i) q^{72} +(7.27491 - 12.6005i) q^{73} +(0.474631 + 2.51037i) q^{74} +(-4.62390 - 7.31353i) q^{75} +(-8.13014 + 3.14656i) q^{76} -3.90999i q^{77} +(-0.406880 + 0.379542i) q^{78} +(3.33564 + 1.92583i) q^{79} +(-0.258574 + 0.0588682i) q^{80} +(8.88396 - 1.44058i) q^{81} +(-1.42051 + 4.05780i) q^{82} +9.87713 q^{83} +(-5.02397 - 11.4365i) q^{84} +(-0.0930590 - 0.161183i) q^{85} +(2.76248 - 7.89123i) q^{86} +(-7.86382 + 4.97181i) q^{87} +(1.63062 + 2.59750i) q^{88} +(-13.7070 + 7.91375i) q^{89} +(0.0713206 - 0.272084i) q^{90} +(-0.709378 + 0.409559i) q^{91} +(13.4633 + 10.7427i) q^{92} +(-0.479503 - 11.9248i) q^{93} +(-0.441546 + 0.379876i) q^{94} +(-0.249622 - 0.145605i) q^{95} +(8.10704 + 5.50236i) q^{96} +(4.49303 - 7.78215i) q^{97} +(-1.57712 - 8.34156i) q^{98} +(-3.24244 + 0.261183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) $ 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.262728	+	1.38959i	0.185777	+	0.982592i
$2$	0.262728	+	1.38959i	0.185777	+	0.982592i
$3$	1.73065	−	0.0695904i	0.999193	−	0.0401780i
$3$	1.73065	−	0.0695904i	0.999193	−	0.0401780i
$4$	−1.86195	+	0.730170i	−0.930974	+	0.365085i
$5$	−0.0574154	−	0.0331488i	−0.0256769	−	0.0148246i	0.487107	−	0.873343i	$-0.338052\pi$
$5$	−0.0574154	−	0.0331488i	−0.0256769	−	0.0148246i	−0.512784	+	0.858518i	$0.671386\pi$
$6$	0.551393	+	2.38662i	0.225105	+	0.974334i
$7$			3.60595i			1.36292i	0.731855	+	0.681460i	$0.238655\pi$
$7$			3.60595i			1.36292i	−0.731855	+	0.681460i	$0.761345\pi$
$8$	−1.50383	−	2.39552i	−0.531683	−	0.846943i
$9$	2.99031	−	0.240874i	0.996771	−	0.0802912i
$10$	0.0309788	−	0.0884932i	0.00979634	−	0.0279840i
$11$	−1.08432			−0.326933			−0.163467	−	0.986549i	$-0.552268\pi$
$11$	−1.08432			−0.326933			−0.163467	+	0.986549i	$0.552268\pi$
$12$	−3.17157	+	1.39324i	−0.915554	+	0.402195i
$13$	0.113579	+	0.196724i	0.0315011	+	0.0545615i	0.881346	−	0.472471i	$-0.156638\pi$
$13$	0.113579	+	0.196724i	0.0315011	+	0.0545615i	−0.849845	+	0.527033i	$0.823305\pi$
$14$	−5.01081	+	0.947383i	−1.33920	+	0.253199i
$15$	−0.101673	−	0.0533734i	−0.0262518	−	0.0137810i
$16$	2.93370	−	2.71908i	0.733426	−	0.679770i
$17$	2.43120	+	1.40366i	0.589654	+	0.340437i	0.764961	−	0.644077i	$-0.222758\pi$
$17$	2.43120	+	1.40366i	0.589654	+	0.340437i	−0.175307	+	0.984514i	$0.556092\pi$
$18$	1.12036	+	4.09204i	0.264070	+	0.964503i
$19$	4.35886	+	0.0194115i	0.999990	+	0.00445331i
$19$	4.35886	+	0.0194115i	0.999990	+	0.00445331i
$20$	0.131109	+	0.0197983i	0.0293168	+	0.00442704i
$21$	0.250939	+	6.24065i	0.0547595	+	1.36182i
$22$	−0.284880	−	1.50676i	−0.0607366	−	0.321242i
$23$	−4.30600	−	7.45822i	−0.897864	−	1.55515i	−0.830220	−	0.557436i	$-0.811785\pi$
$23$	−4.30600	−	7.45822i	−0.897864	−	1.55515i	−0.0676443	−	0.997710i	$-0.521548\pi$
$24$	−2.76931	−	4.04116i	−0.565282	−	0.824898i
$25$	−2.49780	−	4.32632i	−0.499560	−	0.865264i
$26$	−0.243527	+	0.209513i	−0.0477595	+	0.0410890i
$27$	5.15843	−	0.624965i	0.992741	−	0.120275i
$28$	−2.63296	−	6.71409i	−0.497582	−	1.26884i
$29$	−4.65184	+	2.68574i	−0.863825	+	0.498730i	−0.865291	−	0.501269i	$-0.832867\pi$
$29$	−4.65184	+	2.68574i	−0.863825	+	0.498730i	0.00146616	+	0.999999i	$0.499533\pi$
$30$	0.0474552	−	0.155307i	0.00866409	−	0.0283550i
$31$		−	6.89036i		−	1.23755i	−0.785570	−	0.618773i	$-0.787630\pi$
$31$		−	6.89036i		−	1.23755i	0.785570	−	0.618773i	$-0.212370\pi$
$32$	4.54918	+	3.36228i	0.804190	+	0.594373i
$33$	−1.87657	+	0.0754579i	−0.326669	+	0.0131355i
$34$	−1.31177	+	3.74717i	−0.224967	+	0.642634i
$35$	0.119533	−	0.207037i	0.0202047	−	0.0349956i
$36$	−5.39193	+	2.63193i	−0.898655	+	0.438655i
$37$	1.80655			0.296995			0.148497	−	0.988913i	$-0.452556\pi$
$37$	1.80655			0.296995			0.148497	+	0.988913i	$0.452556\pi$
$38$	1.11822	+	6.06214i	0.181399	+	0.983410i
$39$	0.210255	+	0.332557i	0.0336678	+	0.0532518i
$40$	0.00693426	+	0.187390i	0.00109640	+	0.0296289i
$41$	2.63274	+	1.52002i	0.411166	+	0.237387i	0.691290	−	0.722577i	$-0.257043\pi$
$41$	2.63274	+	1.52002i	0.411166	+	0.237387i	−0.280125	+	0.959964i	$0.590376\pi$
$42$	−8.60604	+	1.98829i	−1.32794	+	0.306801i
$43$	−5.11992	−	2.95599i	−0.780780	−	0.450784i	0.0559266	−	0.998435i	$-0.482189\pi$
$43$	−5.11992	−	2.95599i	−0.780780	−	0.450784i	−0.836707	+	0.547651i	$0.815522\pi$
$44$	2.01894	−	0.791735i	0.304367	−	0.119359i
$45$	−0.179675	−	0.0852954i	−0.0267843	−	0.0127151i
$46$	9.23260	−	7.94308i	1.36127	−	1.17114i
$47$	0.205933	+	0.356687i	0.0300385	+	0.0520282i	0.880654	−	0.473760i	$-0.157104\pi$
$47$	0.205933	+	0.356687i	0.0300385	+	0.0520282i	−0.850615	+	0.525788i	$0.823770\pi$
$48$	4.88800	−	4.90994i	0.705522	−	0.708688i
$49$	−6.00287			−0.857553
$50$	5.35559	−	4.60758i	0.757395	−	0.651610i
$51$	4.30525	+	2.26005i	0.602856	+	0.316471i
$52$	−0.355120	−	0.283358i	−0.0492463	−	0.0392947i
$53$	−0.727053	+	0.419764i	−0.0998684	+	0.0576590i	−0.549102	−	0.835755i	$-0.685030\pi$
$53$	−0.727053	+	0.419764i	−0.0998684	+	0.0576590i	0.449234	+	0.893414i	$0.351697\pi$
$54$	2.22371	+	7.00393i	0.302609	+	0.953115i
$55$	0.0622564	+	0.0359437i	0.00839464	+	0.00484665i
$56$	8.63812	−	5.42272i	1.15432	−	0.724642i
$57$	7.54501	−	0.269740i	0.999362	−	0.0357279i
$58$	−4.95426	−	5.75856i	−0.650526	−	0.756135i
$59$	4.44625	−	7.70114i	0.578853	−	1.00260i	−0.416758	−	0.909017i	$-0.636834\pi$
$59$	4.44625	−	7.70114i	0.578853	−	1.00260i	0.995611	−	0.0935854i	$-0.0298328\pi$
$60$	0.228281	+	0.0251401i	0.0294710	+	0.00324557i
$61$	4.67311	+	8.09407i	0.598331	+	1.03634i	0.993068	+	0.117545i	$0.0375025\pi$
$61$	4.67311	+	8.09407i	0.598331	+	1.03634i	−0.394737	+	0.918794i	$0.629164\pi$
$62$	9.57482	−	1.81029i	1.21600	−	0.229907i
$63$	0.868578	+	10.7829i	0.109431	+	1.35852i
$64$	−3.47701	+	7.20489i	−0.434626	+	0.900611i
$65$		−	0.0150600i		−	0.00186796i
$66$	−0.597884	−	2.58785i	−0.0735944	−	0.318542i
$67$	−5.00700	+	2.89079i	−0.611703	+	0.353167i	−0.773632	−	0.633636i	$-0.781562\pi$
$67$	−5.00700	+	2.89079i	−0.611703	+	0.353167i	0.161929	+	0.986802i	$0.448229\pi$
$68$	−5.55168	−	0.838342i	−0.673241	−	0.101664i
$69$	−7.97122	−	12.6079i	−0.959622	−	1.51782i
$70$	0.319102	+	0.111708i	0.0381400	+	0.0133516i
$71$	−5.70164	+	9.87552i	−0.676660	+	1.17201i	0.299321	+	0.954152i	$0.403240\pi$
$71$	−5.70164	+	9.87552i	−0.676660	+	1.17201i	−0.975981	+	0.217856i	$0.930094\pi$
$72$	−5.07393	−	6.80112i	−0.597968	−	0.801520i
$73$	7.27491	−	12.6005i	0.851464	−	1.47478i	−0.0284230	−	0.999596i	$-0.509049\pi$
$73$	7.27491	−	12.6005i	0.851464	−	1.47478i	0.879887	−	0.475183i	$-0.157618\pi$
$74$	0.474631	+	2.51037i	0.0551747	+	0.291825i
$75$	−4.62390	−	7.31353i	−0.533922	−	0.844494i
$76$	−8.13014	+	3.14656i	−0.932591	+	0.360936i
$77$		−	3.90999i		−	0.445584i
$78$	−0.406880	+	0.379542i	−0.0460701	+	0.0429747i
$79$	3.33564	+	1.92583i	0.375289	+	0.216673i	0.675767	−	0.737116i	$-0.263813\pi$
$79$	3.33564	+	1.92583i	0.375289	+	0.216673i	−0.300478	+	0.953789i	$0.597146\pi$
$80$	−0.258574	+	0.0588682i	−0.0289094	+	0.00658167i
$81$	8.88396	−	1.44058i	0.987107	−	0.160064i
$82$	−1.42051	+	4.05780i	−0.156869	+	0.448109i
$83$	9.87713			1.08416			0.542078	−	0.840328i	$-0.317638\pi$
$83$	9.87713			1.08416			0.542078	+	0.840328i	$0.317638\pi$
$84$	−5.02397	−	11.4365i	−0.548160	−	1.24783i
$85$	−0.0930590	−	0.161183i	−0.0100937	−	0.0174827i
$86$	2.76248	−	7.89123i	0.297886	−	0.850933i
$87$	−7.86382	+	4.97181i	−0.843090	+	0.533034i
$88$	1.63062	+	2.59750i	0.173825	+	0.276894i
$89$	−13.7070	+	7.91375i	−1.45294	+	0.838856i	−0.998647	−	0.0519957i	$-0.983442\pi$
$89$	−13.7070	+	7.91375i	−1.45294	+	0.838856i	−0.454294	+	0.890852i	$0.650108\pi$
$90$	0.0713206	−	0.272084i	0.00751785	−	0.0286802i
$91$	−0.709378	+	0.409559i	−0.0743630	+	0.0429335i
$92$	13.4633	+	10.7427i	1.40365	+	1.12000i
$93$	−0.479503	−	11.9248i	−0.0497222	−	1.23655i
$94$	−0.441546	+	0.379876i	−0.0455420	+	0.0391812i
$95$	−0.249622	−	0.145605i	−0.0256107	−	0.0149388i
$96$	8.10704	+	5.50236i	0.827421	+	0.561582i
$97$	4.49303	−	7.78215i	0.456198	−	0.790158i	−0.542558	−	0.840018i	$-0.682544\pi$
$97$	4.49303	−	7.78215i	0.456198	−	0.790158i	0.998756	+	0.0498604i	$0.0158776\pi$
$98$	−1.57712	−	8.34156i	−0.159313	−	0.842625i
$99$	−3.24244	+	0.261183i	−0.325878	+	0.0262499i
$100$	7.80973	+	6.23156i	0.780973	+	0.623156i
$101$	−14.1683	+	8.18009i	−1.40980	+	0.813949i	−0.995369	−	0.0961309i	$-0.969353\pi$
$101$	−14.1683	+	8.18009i	−1.40980	+	0.813949i	−0.414433	+	0.910080i	$0.636020\pi$
$102$	−2.00945	+	6.57633i	−0.198965	+	0.651154i
$103$			9.27449i			0.913843i	0.889507	+	0.456921i	$0.151048\pi$
$103$			9.27449i			0.913843i	−0.889507	+	0.456921i	$0.848952\pi$
$104$	0.300454	−	0.567919i	0.0294619	−	0.0556890i
$105$	0.192462	−	0.366627i	0.0187824	−	0.0357792i
$106$	−0.774319	−	0.900025i	−0.0752085	−	0.0874182i
$107$	−10.7650			−1.04069			−0.520346	−	0.853955i	$-0.674197\pi$
$107$	−10.7650			−1.04069			−0.520346	+	0.853955i	$0.674197\pi$
$108$	−9.14840	+	4.93019i	−0.880305	+	0.474407i
$109$	−5.77711	+	10.0062i	−0.553347	+	0.958425i	0.444683	+	0.895688i	$0.353316\pi$
$109$	−5.77711	+	10.0062i	−0.553347	+	0.958425i	−0.998030	+	0.0627368i	$0.980017\pi$
$110$	−0.0335907	+	0.0959545i	−0.00320275	+	0.00914891i
$111$	3.12651	−	0.125718i	0.296755	−	0.0119327i
$112$	9.80486	+	10.5788i	0.926472	+	0.999601i
$113$		−	0.563097i		−	0.0529717i	−0.999649	−	0.0264858i	$-0.991568\pi$
$113$		−	0.563097i		−	0.0529717i	0.999649	−	0.0264858i	$-0.00843169\pi$
$114$	2.35711	+	10.4136i	0.220764	+	0.975327i
$115$			0.570955i			0.0532418i
$116$	6.70044	−	8.39735i	0.622120	−	0.779674i
$117$	0.387022	+	0.560909i	0.0357802	+	0.0518561i
$118$	11.8696	+	4.15519i	1.09269	+	0.382516i
$119$	−5.06151	+	8.76680i	−0.463988	+	0.803651i
$120$	0.0250413	+	0.323824i	0.00228595	+	0.0295609i
$121$	−9.82426			−0.893115
$122$	−10.0197	+	8.62027i	−0.907143	+	0.780443i
$123$	4.66214	+	2.44741i	0.420371	+	0.220675i
$124$	5.03114	+	12.8295i	0.451810	+	1.15212i
$125$			0.662684i			0.0592723i
$126$	−14.7557	+	4.03994i	−1.31454	+	0.359907i
$127$	3.96530	−	2.28937i	0.351864	−	0.203149i	−0.313642	−	0.949541i	$-0.601549\pi$
$127$	3.96530	−	2.28937i	0.351864	−	0.203149i	0.665506	+	0.746393i	$0.268216\pi$
$128$	−10.9254	−	2.93871i	−0.965676	−	0.259748i
$129$	−9.06650	−	4.75949i	−0.798261	−	0.419049i
$130$	0.0209273	−	0.00395668i	0.00183544	−	0.000347023i
$131$	−5.09359	+	8.82236i	−0.445029	+	0.770813i	−0.998054	−	0.0623514i	$-0.980140\pi$
$131$	−5.09359	+	8.82236i	−0.445029	+	0.770813i	0.553025	+	0.833165i	$0.313473\pi$
$132$	3.43898	−	1.51072i	0.299325	−	0.131491i
$133$	−0.0699971	+	15.7178i	−0.00606951	+	1.36291i
$134$	−5.33251	−	6.19821i	−0.460659	−	0.535444i
$135$	−0.316890	−	0.135113i	−0.0272736	−	0.0116287i
$136$	−0.293625	−	7.93485i	−0.0251782	−	0.680408i
$137$	0.500698	−	0.289078i	0.0427775	−	0.0246976i	−0.478459	−	0.878110i	$-0.658804\pi$
$137$	0.500698	−	0.289078i	0.0427775	−	0.0246976i	0.521236	+	0.853412i	$0.325471\pi$
$138$	15.4256	−	14.3892i	1.31312	−	1.22489i
$139$	−11.8727	+	6.85472i	−1.00703	+	0.581410i	−0.910321	−	0.413903i	$-0.864165\pi$
$139$	−11.8727	+	6.85472i	−1.00703	+	0.581410i	−0.0967105	+	0.995313i	$0.530832\pi$
$140$	−0.0713917	+	0.472771i	−0.00603370	+	0.0399565i
$141$	0.381221	+	0.602971i	0.0321046	+	0.0507793i
$142$	−15.2210	−	5.32839i	−1.27731	−	0.447149i
$143$	−0.123155	−	0.213311i	−0.0102988	−	0.0178380i
$144$	8.11774	−	8.83755i	0.676478	−	0.736463i
$145$	0.356116			0.0295738
$146$	19.4209	+	6.79868i	1.60729	+	0.562662i
$147$	−10.3889	+	0.417742i	−0.856861	+	0.0344548i
$148$	−3.36370	+	1.31909i	−0.276494	+	0.108428i
$149$	7.60188	+	4.38895i	0.622771	+	0.359557i	0.777947	−	0.628330i	$-0.216261\pi$
$149$	7.60188	+	4.38895i	0.622771	+	0.359557i	−0.155176	+	0.987887i	$0.549595\pi$
$150$	8.94802	−	8.34681i	0.730603	−	0.681514i
$151$		−	16.1081i		−	1.31086i	−0.755257	−	0.655429i	$-0.772488\pi$
$151$		−	16.1081i		−	1.31086i	0.755257	−	0.655429i	$-0.227512\pi$
$152$	−6.50846	−	10.4709i	−0.527906	−	0.849303i
$153$	7.60817	+	3.61176i	0.615084	+	0.291994i
$154$	5.43330	−	1.02726i	0.437828	−	0.0827791i
$155$	−0.228407	+	0.395613i	−0.0183461	+	0.0317764i
$156$	−0.634308	−	0.465682i	−0.0507853	−	0.0372844i
$157$	−2.73796	+	4.74229i	−0.218513	+	0.378476i	−0.954354	−	0.298679i	$-0.903454\pi$
$157$	−2.73796	+	4.74229i	−0.218513	+	0.378476i	0.735840	+	0.677155i	$0.236787\pi$
$158$	−1.79976	+	5.14116i	−0.143181	+	0.409009i
$159$	−1.22906	+	0.777062i	−0.0974711	+	0.0616250i
$160$	−0.149737	−	0.343846i	−0.0118378	−	0.0271834i
$161$	26.8940	−	15.5272i	2.11954	−	1.22372i
$162$	4.33588	+	11.9666i	0.340659	+	0.940187i
$163$			2.54802i			0.199576i	0.995009	+	0.0997880i	$0.0318165\pi$
$163$			2.54802i			0.199576i	−0.995009	+	0.0997880i	$0.968184\pi$
$164$	−6.01191	−	0.907839i	−0.469451	−	0.0708903i
$165$	0.110245	+	0.0578736i	0.00858260	+	0.00450546i
$166$	2.59500	+	13.7252i	0.201411	+	1.06528i
$167$	−6.52564	−	11.3027i	−0.504969	−	0.874633i	−0.999983	−	0.00574771i	$-0.998170\pi$
$167$	−6.52564	−	11.3027i	−0.504969	−	0.874633i	0.495014	−	0.868885i	$-0.335163\pi$
$168$	14.5722	−	9.98598i	1.12427	−	0.770435i
$169$	6.47420	−	11.2136i	0.498015	−	0.862588i
$170$	0.199530	−	0.171661i	0.0153032	−	0.0131658i
$171$	13.0390	−	0.991886i	0.997119	−	0.0758514i
$172$	11.6914	+	1.76548i	0.891460	+	0.134617i
$173$	−10.4328	−	6.02338i	−0.793192	−	0.457949i	0.0478933	−	0.998852i	$-0.484749\pi$
$173$	−10.4328	−	6.02338i	−0.793192	−	0.457949i	−0.841085	+	0.540903i	$0.818083\pi$
$174$	−8.97484	−	9.62129i	−0.680381	−	0.729388i
$175$	15.6005	−	9.00695i	1.17929	−	0.680861i
$176$	−3.18106	+	2.94834i	−0.239781	+	0.222239i
$177$	7.15899	−	13.6374i	0.538103	−	1.02505i
$178$	−14.5981	−	16.9680i	−1.09418	−	1.27181i
$179$	4.43830			0.331734			0.165867	−	0.986148i	$-0.446958\pi$
$179$	4.43830			0.331734			0.165867	+	0.986148i	$0.446958\pi$
$180$	0.396825	+	0.0276226i	0.0295776	+	0.00205886i
$181$	−0.959000	−	1.66104i	−0.0712819	−	0.123464i	0.828181	−	0.560460i	$-0.189376\pi$
$181$	−0.959000	−	1.66104i	−0.0712819	−	0.123464i	−0.899463	+	0.436996i	$0.856042\pi$
$182$	−0.755495	−	0.878145i	−0.0560010	−	0.0650924i
$183$	8.65081	+	13.6828i	0.639486	+	1.01146i
$184$	−11.3908	+	21.5310i	−0.839742	+	1.58728i
$185$	−0.103724	−	0.0598849i	−0.00762591	−	0.00440282i
$186$	16.4447	−	3.79930i	1.20578	−	0.278578i
$187$	−2.63619	−	1.52201i	−0.192777	−	0.111300i
$188$	−0.643880	−	0.513767i	−0.0469598	−	0.0374703i
$189$	2.25359	+	18.6010i	0.163925	+	1.35303i
$190$	0.136750	−	0.385128i	0.00992087	−	0.0279401i
$191$	20.8595			1.50934			0.754669	−	0.656105i	$-0.227797\pi$
$191$	20.8595			1.50934			0.754669	+	0.656105i	$0.227797\pi$
$192$	−5.51611	+	12.7111i	−0.398091	+	0.917346i
$193$	−11.1740	+	19.3539i	−0.804319	+	1.39312i	0.112431	+	0.993660i	$0.464136\pi$
$193$	−11.1740	+	19.3539i	−0.804319	+	1.39312i	−0.916750	+	0.399462i	$0.869197\pi$
$194$	11.9945	+	4.19890i	0.861153	+	0.301463i
$195$	−0.00104803	−	0.0260636i	−7.50510e−5	−	0.00186645i
$196$	11.1770	−	4.38312i	0.798360	−	0.313080i
$197$		−	21.2443i		−	1.51359i	−0.653651	−	0.756796i	$-0.726763\pi$
$197$		−	21.2443i		−	1.51359i	0.653651	−	0.756796i	$-0.273237\pi$
$198$	−1.21482	−	4.43706i	−0.0863334	−	0.315328i
$199$	−1.22792	+	0.708941i	−0.0870451	+	0.0502555i	−0.542891	−	0.839803i	$-0.682670\pi$
$199$	−1.22792	+	0.708941i	−0.0870451	+	0.0502555i	0.455846	+	0.890059i	$0.349337\pi$
$200$	−6.60752	+	12.4896i	−0.467222	+	0.883146i
$201$	−8.46421	+	5.35140i	−0.597019	+	0.377459i
$202$	−15.0894	−	17.5391i	−1.06169	−	1.23405i
$203$	−9.68465	−	16.7743i	−0.679729	−	1.17733i
$204$	−9.66638	−	1.06454i	−0.676782	−	0.0745324i
$205$	−0.100773	−	0.174545i	−0.00703831	−	0.0121907i
$206$	−12.8878	+	2.43667i	−0.897935	+	0.169771i
$207$	−14.6728	−	21.2652i	−1.01983	−	1.47803i
$208$	0.868115	+	0.268301i	0.0601929	+	0.0186033i
$209$	−4.72637	−	0.0210482i	−0.326930	−	0.00145594i
$210$	0.560028	+	0.171121i	0.0386456	+	0.0118085i
$211$	13.7991	+	7.96692i	0.949970	+	0.548466i	0.893072	−	0.449914i	$-0.148546\pi$
$211$	13.7991	+	7.96692i	0.949970	+	0.548466i	0.0568985	+	0.998380i	$0.481879\pi$
$212$	1.04724	−	1.31245i	0.0719244	−	0.0901395i
$213$	−9.18031	+	17.4879i	−0.629024	+	1.19825i
$214$	−2.82827	−	14.9590i	−0.193336	−	1.02258i
$215$	0.195975	+	0.339438i	0.0133654	+	0.0231495i
$216$	−9.25450	−	11.4173i	−0.629689	−	0.776847i
$217$	24.8463			1.68668
$218$	−15.4224	−	5.39892i	−1.04454	−	0.365661i
$219$	11.7135	−	22.3134i	0.791523	−	1.50780i
$220$	−0.142163	−	0.0214676i	−0.00958464	−	0.00144735i
$221$			0.637702i			0.0428965i
$222$	0.996118	+	4.31155i	0.0668551	+	0.289372i
$223$	−0.981114	−	0.566446i	−0.0657002	−	0.0379320i	0.466790	−	0.884368i	$-0.345410\pi$
$223$	−0.981114	−	0.566446i	−0.0657002	−	0.0379320i	−0.532490	+	0.846436i	$0.678744\pi$
$224$	−12.1242	+	16.4041i	−0.810083	+	1.09605i
$225$	−8.51131	−	12.3354i	−0.567421	−	0.822360i
$226$	0.782476	−	0.147941i	0.0520495	−	0.00984090i
$227$	−9.94899			−0.660338			−0.330169	−	0.943922i	$-0.607106\pi$
$227$	−9.94899			−0.660338			−0.330169	+	0.943922i	$0.607106\pi$
$228$	−13.8515	+	6.01139i	−0.917336	+	0.398114i
$229$	−12.3392			−0.815397			−0.407698	−	0.913117i	$-0.633669\pi$
$229$	−12.3392			−0.815397			−0.407698	+	0.913117i	$0.633669\pi$
$230$	−0.793396	+	0.150006i	−0.0523150	+	0.00989108i
$231$	−0.272098	−	6.76683i	−0.0179027	−	0.445225i
$232$	13.4293	+	7.10468i	0.881677	+	0.466445i
$233$	24.9320	+	14.3945i	1.63335	+	0.943016i	0.983049	+	0.183341i	$0.0586914\pi$
$233$	24.9320	+	14.3945i	1.63335	+	0.943016i	0.650303	+	0.759675i	$0.274642\pi$
$234$	−0.677755	+	0.685170i	−0.0443062	+	0.0447910i
$235$		−	0.0273058i		−	0.00178123i
$236$	−2.65555	+	17.5856i	−0.172862	+	1.14473i
$237$	5.90685	+	3.10082i	0.383691	+	0.201420i
$238$	−13.5121	−	4.73017i	−0.875859	−	0.306612i
$239$	18.7292			1.21149			0.605746	−	0.795658i	$-0.292875\pi$
$239$	18.7292			1.21149			0.605746	+	0.795658i	$0.292875\pi$
$240$	−0.443404	+	0.119875i	−0.0286216	+	0.00773788i
$241$	−0.171030	−	0.296232i	−0.0110170	−	0.0190820i	0.860464	−	0.509511i	$-0.170174\pi$
$241$	−0.171030	−	0.296232i	−0.0110170	−	0.0190820i	−0.871481	+	0.490429i	$0.836840\pi$
$242$	−2.58111	−	13.6517i	−0.165920	−	0.877567i
$243$	15.2748	−	3.11137i	0.979879	−	0.199595i
$244$	−14.6111	−	11.6586i	−0.935383	−	0.746364i
$245$	0.344657	+	0.198988i	0.0220193	+	0.0127129i
$246$	−2.17603	+	7.12149i	−0.138738	+	0.454050i
$247$	0.491255	+	0.859697i	0.0312578	+	0.0547012i
$248$	−16.5060	+	10.3619i	−1.04813	+	0.657982i
$249$	17.0939	−	0.687353i	1.08328	−	0.0435592i
$250$	−0.920862	+	0.174105i	−0.0582404	+	0.0110114i
$251$	10.5008	+	18.1880i	0.662806	+	1.14801i	0.979875	+	0.199612i	$0.0639681\pi$
$251$	10.5008	+	18.1880i	0.662806	+	1.14801i	−0.317069	+	0.948403i	$0.602699\pi$
$252$	−9.49062	−	19.4430i	−0.597853	−	1.22480i
$253$	4.66907	+	8.08706i	0.293542	+	0.508429i
$254$	4.22309	+	4.90868i	0.264980	+	0.307998i
$255$	−0.172269	−	0.272475i	−0.0107879	−	0.0170631i
$256$	1.21322	−	15.9539i	0.0758263	−	0.997121i
$257$	−13.5869	+	7.84438i	−0.847526	+	0.489319i	−0.859815	−	0.510605i	$-0.829421\pi$
$257$	−13.5869	+	7.84438i	−0.847526	+	0.489319i	0.0122895	+	0.999924i	$0.496088\pi$
$258$	4.23174	−	13.8492i	0.263456	−	0.862215i
$259$			6.51432i			0.404780i
$260$	0.0109964	+	0.0280409i	0.000681965	+	0.00173902i
$261$	−13.2635	+	9.15172i	−0.820993	+	0.566477i
$262$	−13.5977	−	4.76015i	−0.840071	−	0.294083i
$263$	14.0127	−	24.2707i	0.864059	−	1.49659i	−0.00391948	−	0.999992i	$-0.501248\pi$
$263$	14.0127	−	24.2707i	0.864059	−	1.49659i	0.867978	−	0.496602i	$-0.165419\pi$
$264$	3.00280	+	4.38189i	0.184810	+	0.269687i
$265$	0.0556587			0.00341908
$266$	−21.8598	+	4.03224i	−1.34031	+	0.247232i
$267$	−23.1714	+	14.6498i	−1.41806	+	0.896555i
$268$	7.21201	−	9.03848i	0.440544	−	0.552113i
$269$	19.4875	+	11.2511i	1.18817	+	0.685991i	0.957891	−	0.287133i	$-0.0927021\pi$
$269$	19.4875	+	11.2511i	1.18817	+	0.685991i	0.230281	+	0.973124i	$0.426035\pi$
$270$	0.104497	−	0.475847i	0.00635946	−	0.0289591i
$271$	−12.9598	−	7.48235i	−0.787252	−	0.454520i	0.0517422	−	0.998660i	$-0.483523\pi$
$271$	−12.9598	−	7.48235i	−0.787252	−	0.454520i	−0.838994	+	0.544140i	$0.816856\pi$
$272$	10.9491	−	2.49273i	0.663886	−	0.151144i
$273$	−1.19918	+	0.758171i	−0.0725779	+	0.0458866i
$274$	0.533249	+	0.619819i	0.0322148	+	0.0374446i
$275$	2.70841	+	4.69110i	0.163323	+	0.282884i
$276$	24.0479	+	17.6550i	1.44751	+	1.06270i
$277$	−10.1303			−0.608668			−0.304334	−	0.952565i	$-0.598434\pi$
$277$	−10.1303			−0.608668			−0.304334	+	0.952565i	$0.598434\pi$
$278$	−12.6446	−	14.6974i	−0.758372	−	0.881489i
$279$	−1.65971	−	20.6044i	−0.0993640	−	1.23355i
$280$	−0.675717	+	0.0250046i	−0.0403818	+	0.00149431i
$281$	18.4562	−	10.6557i	1.10100	−	0.635665i	0.164520	−	0.986374i	$-0.447393\pi$
$281$	18.4562	−	10.6557i	1.10100	−	0.635665i	0.936485	+	0.350709i	$0.114059\pi$
$282$	−0.737728	+	0.688160i	−0.0439310	+	0.0409793i
$283$	4.84844	+	2.79925i	0.288210	+	0.166398i	0.637134	−	0.770753i	$-0.280120\pi$
$283$	4.84844	+	2.79925i	0.288210	+	0.166398i	−0.348924	+	0.937151i	$0.613453\pi$
$284$	3.40534	−	22.5509i	0.202070	−	1.33815i
$285$	−0.442141	−	0.234621i	−0.0261902	−	0.0138977i
$286$	0.264060	−	0.227179i	0.0156142	−	0.0134334i
$287$	−5.48110	+	9.49355i	−0.323539	+	0.560386i
$288$	14.4134	+	8.95850i	0.849316	+	0.527885i
$289$	−4.55950	−	7.89728i	−0.268206	−	0.464546i
$290$	0.0935616	+	0.494857i	0.00549413	+	0.0290590i
$291$	7.23430	−	13.7809i	0.424082	−	0.807849i
$292$	−4.34499	+	28.7734i	−0.254271	+	1.68384i
$293$		−	24.2140i		−	1.41460i	−0.706915	−	0.707299i	$-0.749914\pi$
$293$		−	24.2140i		−	1.41460i	0.706915	−	0.707299i	$-0.250086\pi$
$294$	−3.30994	−	14.3266i	−0.193040	−	0.835544i
$295$	−0.510566	+	0.294776i	−0.0297263	+	0.0171625i
$296$	−2.71674	−	4.32762i	−0.157907	−	0.251538i
$297$	−5.59337	+	0.677660i	−0.324560	+	0.0393218i
$298$	−4.10164	+	11.7166i	−0.237601	+	0.678727i
$299$	0.978141	−	1.69419i	0.0565674	−	0.0979776i
$300$	13.9496	+	10.2412i	0.805380	+	0.591275i
$301$	10.6591	−	18.4622i	0.614382	−	1.06414i
$302$	22.3837	−	4.23204i	1.28804	−	0.243527i
$303$	−23.9512	+	15.1429i	−1.37596	+	0.869935i
$304$	12.8404	−	11.7951i	0.736446	−	0.676497i
$305$		−	0.619632i		−	0.0354800i
$306$	−3.02001	+	11.5212i	−0.172642	+	0.658622i
$307$	−11.2463	−	6.49305i	−0.641860	−	0.370578i	0.143471	−	0.989655i	$-0.454174\pi$
$307$	−11.2463	−	6.49305i	−0.641860	−	0.370578i	−0.785331	+	0.619077i	$0.787507\pi$
$308$	2.85496	+	7.28019i	0.162676	+	0.414828i
$309$	0.645416	+	16.0509i	0.0367164	+	0.913105i
$310$	−0.609750	−	0.213455i	−0.0346315	−	0.0121234i
$311$	7.00672			0.397315			0.198657	−	0.980069i	$-0.436342\pi$
$311$	7.00672			0.397315			0.198657	+	0.980069i	$0.436342\pi$
$312$	0.480459	−	1.00378i	0.0272006	−	0.0568278i
$313$	−8.22035	−	14.2381i	−0.464641	−	0.804783i	0.534544	−	0.845141i	$-0.320483\pi$
$313$	−8.22035	−	14.2381i	−0.464641	−	0.804783i	−0.999185	+	0.0403582i	$0.987150\pi$
$314$	−7.30920	−	2.55873i	−0.412482	−	0.144397i
$315$	0.307571	−	0.647898i	0.0173297	−	0.0365049i
$316$	−7.61698	−	1.15022i	−0.428488	−	0.0647047i
$317$	−12.2361	+	7.06454i	−0.687250	+	0.396784i	−0.802581	−	0.596543i	$-0.796540\pi$
$317$	−12.2361	+	7.06454i	−0.687250	+	0.396784i	0.115331	+	0.993327i	$0.463207\pi$
$318$	−1.40271	−	1.50375i	−0.0786601	−	0.0843259i
$319$	5.04406	−	2.91219i	0.282413	−	0.163051i
$320$	0.438467	−	0.298412i	0.0245110	−	0.0166818i
$321$	−18.6305	+	0.749141i	−1.03985	+	0.0418130i
$322$	28.6424	+	33.2923i	1.59618	+	1.85531i
$323$	10.5700	+	6.16553i	0.588132	+	0.343059i
$324$	−15.4896	+	9.16908i	−0.860534	+	0.509393i
$325$	0.567395	−	0.982756i	0.0314734	−	0.0545135i
$326$	−3.54071	+	0.669435i	−0.196102	+	0.0370766i
$327$	−9.30183	+	17.7194i	−0.514392	+	0.979883i
$328$	−0.317966	−	8.59263i	−0.0175567	−	0.474448i
$329$	−1.28620	+	0.742586i	−0.0709103	+	0.0409401i
$330$	−0.0514564	+	0.168402i	−0.00283258	+	0.00927020i
$331$			26.0553i			1.43213i	0.698034	+	0.716065i	$0.254059\pi$
$331$			26.0553i			1.43213i	−0.698034	+	0.716065i	$0.745941\pi$
$332$	−18.3907	+	7.21199i	−1.00932	+	0.395809i
$333$	5.40215	−	0.435150i	0.296036	−	0.0238461i
$334$	13.9918	−	12.0375i	0.765596	−	0.658665i
$335$	0.383305			0.0209422
$336$	17.7050	+	17.6259i	0.965886	+	0.961570i
$337$	−4.66024	+	8.07177i	−0.253859	+	0.439697i	−0.964585	−	0.263772i	$-0.915033\pi$
$337$	−4.66024	+	8.07177i	−0.253859	+	0.439697i	0.710726	+	0.703469i	$0.248367\pi$
$338$	17.2834	+	6.05038i	0.940092	+	0.329097i
$339$	−0.0391861	−	0.974524i	−0.00212830	−	0.0529289i
$340$	0.290962	+	0.232165i	0.0157796	+	0.0125909i
$341$			7.47133i			0.404595i
$342$	4.80403	+	17.8584i	0.259772	+	0.965670i
$343$			3.59558i			0.194143i
$344$	0.618351	+	16.7101i	0.0333392	+	0.900950i
$345$	0.0397330	+	0.988124i	0.00213915	+	0.0531988i
$346$	5.62908	−	16.0799i	0.302621	−	0.864460i
$347$	−11.7069	+	20.2769i	−0.628459	+	1.08852i	0.359402	+	0.933183i	$0.382981\pi$
$347$	−11.7069	+	20.2769i	−0.628459	+	1.08852i	−0.987861	+	0.155340i	$0.950353\pi$
$348$	11.0118	−	14.9992i	0.590292	−	0.804040i
$349$	19.3123			1.03376			0.516881	−	0.856057i	$-0.327093\pi$
$349$	19.3123			1.03376			0.516881	+	0.856057i	$0.327093\pi$
$350$	16.6147	+	19.3120i	0.888093	+	1.03227i
$351$	0.708834	+	0.943806i	0.0378348	+	0.0503766i
$352$	−4.93275	−	3.64577i	−0.262916	−	0.194320i
$353$		−	0.804702i		−	0.0428300i	−0.999771	−	0.0214150i	$-0.993183\pi$
$353$		−	0.804702i		−	0.0428300i	0.999771	−	0.0214150i	$-0.00681712\pi$
$354$	20.8313	+	6.36518i	1.10717	+	0.338305i
$355$	0.654723	−	0.378004i	0.0347491	−	0.0200624i
$356$	19.7434	−	24.7435i	1.04640	−	1.31140i
$357$	−8.14964	+	15.5245i	−0.431324	+	0.821644i
$358$	1.16606	+	6.16744i	0.0616284	+	0.325959i
$359$	2.14236	−	3.71068i	0.113070	−	0.195842i	−0.803937	−	0.594715i	$-0.797265\pi$
$359$	2.14236	−	3.71068i	0.113070	−	0.195842i	0.917006	+	0.398872i	$0.130598\pi$
$360$	0.0658728	+	0.558683i	0.00347180	+	0.0294452i
$361$	18.9992	+	0.169224i	0.999960	+	0.00890654i
$362$	2.05621	−	1.76902i	0.108072	−	0.0929777i
$363$	−17.0024	+	0.683674i	−0.892393	+	0.0358836i
$364$	1.02178	−	1.28054i	0.0535556	−	0.0671188i
$365$	−0.835383	+	0.482309i	−0.0437260	+	0.0252452i
$366$	−16.7408	+	15.6160i	−0.875054	+	0.816260i
$367$	19.9401	−	11.5124i	1.04086	−	0.600943i	0.120786	−	0.992679i	$-0.461458\pi$
$367$	19.9401	−	11.5124i	1.04086	−	0.600943i	0.920078	+	0.391735i	$0.128125\pi$
$368$	−32.9120	−	10.1718i	−1.71566	−	0.530243i
$369$	8.23887	+	3.91117i	0.428898	+	0.203607i
$370$	0.0559646	−	0.159867i	0.00290946	−	0.00831110i
$371$	−1.51365	−	2.62172i	−0.0785847	−	0.136113i
$372$	9.59996	+	21.8533i	0.497735	+	1.13304i
$373$	−32.6423			−1.69015			−0.845076	−	0.534646i	$-0.820445\pi$
$373$	−32.6423			−1.69015			−0.845076	+	0.534646i	$0.820445\pi$
$374$	1.42237	−	4.06311i	0.0735491	−	0.210099i
$375$	0.0461164	+	1.14688i	0.00238144	+	0.0592244i
$376$	0.544762	−	1.02971i	0.0280940	−	0.0531034i
$377$	−1.05670	−	0.610086i	−0.0544229	−	0.0314211i
$378$	−25.2558	+	8.01859i	−1.29902	+	0.412432i
$379$			9.50252i			0.488112i	0.969761	+	0.244056i	$0.0784780\pi$
$379$			9.50252i			0.488112i	−0.969761	+	0.244056i	$0.921522\pi$
$380$	0.571099	+	0.0888430i	0.0292968	+	0.00455755i
$381$	6.70324	−	4.23805i	0.343418	−	0.217122i
$382$	5.48036	+	28.9862i	0.280400	+	1.48306i
$383$	−18.2486	+	31.6075i	−0.932460	+	1.61507i	−0.153359	+	0.988171i	$0.549009\pi$
$383$	−18.2486	+	31.6075i	−0.932460	+	1.61507i	−0.779101	+	0.626898i	$0.784324\pi$
$384$	−19.1125	−	4.32559i	−0.975333	−	0.220739i
$385$	−0.129611	+	0.224493i	−0.00660560	+	0.0114412i
$386$	−29.8297	−	10.4425i	−1.51829	−	0.531508i
$387$	−16.0222	−	7.60607i	−0.814453	−	0.386638i
$388$	−2.68349	+	17.7706i	−0.136233	+	0.902167i
$389$	4.61960	−	2.66713i	0.234223	−	0.135229i	−0.378296	−	0.925685i	$-0.623490\pi$
$389$	4.61960	−	2.66713i	0.234223	−	0.135229i	0.612519	+	0.790456i	$0.290156\pi$
$390$	0.0359425	−	0.00830397i	0.00182002	−	0.000420488i
$391$		−	24.1766i		−	1.22266i
$392$	9.02728	+	14.3800i	0.455947	+	0.726299i
$393$	−8.20128	+	15.6229i	−0.413700	+	0.788071i
$394$	29.5209	−	5.58146i	1.48724	−	0.281190i
$395$	−0.127678	−	0.221145i	−0.00642418	−	0.0111270i
$396$	5.84655	−	2.85385i	0.293800	−	0.143411i
$397$	4.78790	−	8.29289i	0.240298	−	0.416208i	−0.720501	−	0.693454i	$-0.756088\pi$
$397$	4.78790	−	8.29289i	0.240298	−	0.416208i	0.960799	+	0.277246i	$0.0894216\pi$
$398$	−1.30775	−	1.52006i	−0.0655516	−	0.0761935i
$399$	0.972668	+	27.2069i	0.0486943	+	1.36205i
$400$	−19.0914	−	5.90042i	−0.954571	−	0.295021i
$401$	−23.8972	−	13.7970i	−1.19337	−	0.688991i	−0.234299	−	0.972165i	$-0.575279\pi$
$401$	−23.8972	−	13.7970i	−1.19337	−	0.688991i	−0.959069	+	0.283174i	$0.908613\pi$
$402$	−9.66006	−	10.3559i	−0.481800	−	0.516503i
$403$	1.35550	−	0.782599i	0.0675223	−	0.0389840i
$404$	20.4078	−	25.5762i	1.01533	−	1.27246i
$405$	−0.557829	−	0.211781i	−0.0277187	−	0.0105235i
$406$	20.7651	−	17.8648i	1.03055	−	0.886616i
$407$	−1.95887			−0.0970975
$408$	−1.06035	−	13.7120i	−0.0524953	−	0.678847i
$409$	0.247829	+	0.429253i	0.0122544	+	0.0212252i	0.872088	−	0.489350i	$-0.162766\pi$
$409$	0.247829	+	0.429253i	0.0122544	+	0.0212252i	−0.859833	+	0.510575i	$0.829433\pi$
$410$	0.216070	−	0.185892i	0.0106709	−	0.00918054i
$411$	0.846418	−	0.535138i	0.0417507	−	0.0263964i
$412$	−6.77196	−	17.2686i	−0.333630	−	0.850764i
$413$	27.7699	+	16.0330i	1.36647	+	0.788931i
$414$	25.6951	−	25.9762i	1.26284	−	1.27666i
$415$	−0.567099	−	0.327415i	−0.0278378	−	0.0160722i
$416$	−0.144751	+	1.27682i	−0.00709702	+	0.0626012i
$417$	−20.0705	+	12.6894i	−0.982859	+	0.621401i
$418$	−1.21250	−	6.57328i	−0.0593054	−	0.321509i
$419$	26.4145			1.29043			0.645216	−	0.764000i	$-0.276767\pi$
$419$	26.4145			1.29043			0.645216	+	0.764000i	$0.276767\pi$
$420$	−0.0906539	+	0.823171i	−0.00442346	+	0.0401666i
$421$	13.5509	−	23.4708i	0.660430	−	1.14390i	−0.320073	−	0.947393i	$-0.603708\pi$
$421$	13.5509	−	23.4708i	0.660430	−	1.14390i	0.980503	−	0.196505i	$-0.0629591\pi$
$422$	−7.44538	+	21.2683i	−0.362436	+	1.03533i
$423$	0.701722	+	1.01700i	0.0341189	+	0.0494484i
$424$	2.09891	+	1.11042i	0.101932	+	0.0539265i
$425$		−	14.0242i		−	0.680275i
$426$	−26.7130	−	8.16236i	−1.29425	−	0.395468i
$427$	−29.1868	+	16.8510i	−1.41245	+	0.815478i
$428$	20.0439	−	7.86029i	0.968858	−	0.379942i
$429$	−0.227983	−	0.360597i	−0.0110071	−	0.0174098i
$430$	−0.420193	+	0.361505i	−0.0202635	+	0.0174333i
$431$	−0.166246	−	0.287947i	−0.00800780	−	0.0138699i	0.861994	−	0.506919i	$-0.169216\pi$
$431$	−0.166246	−	0.287947i	−0.00800780	−	0.0138699i	−0.870002	+	0.493049i	$0.835882\pi$
$432$	13.4340	−	15.8596i	0.646342	−	0.763048i
$433$	−9.53952	−	16.5229i	−0.458440	−	0.794041i	0.540439	−	0.841383i	$-0.318258\pi$
$433$	−9.53952	−	16.5229i	−0.458440	−	0.794041i	−0.998879	+	0.0473421i	$0.984925\pi$
$434$	6.52782	+	34.5263i	0.313345	+	1.65732i
$435$	0.616313	−	0.0247823i	0.0295500	−	0.00118822i
$436$	3.45041	−	22.8494i	0.165245	−	1.09429i
$437$	−18.6245	−	32.5929i	−0.890929	−	1.55913i
$438$	34.0840	+	10.4146i	1.62860	+	0.497630i
$439$	−13.6352	−	7.87227i	−0.650772	−	0.375723i	0.137980	−	0.990435i	$-0.455939\pi$
$439$	−13.6352	−	7.87227i	−0.650772	−	0.375723i	−0.788752	+	0.614712i	$0.789272\pi$
$440$	−0.00751893	−	0.203189i	−0.000358451	−	0.00968667i
$441$	−17.9505	+	1.44593i	−0.854785	+	0.0688540i
$442$	−0.886148	+	0.167542i	−0.0421498	+	0.00796916i
$443$	−8.64486	−	14.9733i	−0.410730	−	0.711405i	0.584240	−	0.811581i	$-0.301393\pi$
$443$	−8.64486	−	14.9733i	−0.410730	−	0.711405i	−0.994970	+	0.100176i	$0.968059\pi$
$444$	−5.72960	+	2.51696i	−0.271915	+	0.119450i
$445$	1.04932			0.0497428
$446$	0.529365	−	1.51217i	0.0250662	−	0.0716034i
$447$	13.4616	+	7.06673i	0.636714	+	0.334245i
$448$	−25.9805	−	12.5379i	−1.22746	−	0.592362i
$449$			14.4783i			0.683275i	0.939832	+	0.341637i	$0.110981\pi$
$449$			14.4783i			0.683275i	−0.939832	+	0.341637i	$0.889019\pi$
$450$	14.9051	−	15.0681i	0.702631	−	0.710318i
$451$	−2.85473	−	1.64818i	−0.134424	−	0.0776096i
$452$	0.411156	+	1.04846i	0.0193392	+	0.0493153i
$453$	−1.12097	−	27.8775i	−0.0526677	−	1.30980i
$454$	−2.61388	−	13.8251i	−0.122675	−	0.648842i
$455$	0.0543056			0.00254588
$456$	−11.9926	−	17.6686i	−0.561603	−	0.827407i
$457$	33.7644			1.57943			0.789716	−	0.613472i	$-0.210228\pi$
$457$	33.7644			1.57943			0.789716	+	0.613472i	$0.210228\pi$
$458$	−3.24185	−	17.1465i	−0.151482	−	0.801202i
$459$	13.4184	+	5.72125i	0.626319	+	0.267045i
$460$	−0.416894	−	1.06309i	−0.0194378	−	0.0495668i
$461$	1.31774	+	0.760795i	0.0613731	+	0.0354338i	0.530373	−	0.847765i	$-0.322052\pi$
$461$	1.31774	+	0.760795i	0.0613731	+	0.0354338i	−0.468999	+	0.883198i	$0.655385\pi$
$462$	9.33166	−	2.15594i	0.434148	−	0.100303i
$463$			18.2142i			0.846488i	0.906016	+	0.423244i	$0.139109\pi$
$463$			18.2142i			0.846488i	−0.906016	+	0.423244i	$0.860891\pi$
$464$	−6.34438	+	20.5279i	−0.294530	+	0.952983i
$465$	−0.367762	+	0.700563i	−0.0170546	+	0.0324878i
$466$	−13.4522	+	38.4273i	−0.623162	+	1.78011i
$467$	−29.4320			−1.36195			−0.680975	−	0.732306i	$-0.738444\pi$
$467$	−29.4320			−1.36195			−0.680975	+	0.732306i	$0.738444\pi$
$468$	−1.13017	−	0.761792i	−0.0522423	−	0.0352138i
$469$	−10.4241	−	18.0550i	−0.481338	−	0.833703i
$470$	0.0379440	−	0.00717398i	0.00175022	−	0.000330911i
$471$	−4.40844	+	8.39779i	−0.203130	+	0.386950i
$472$	−25.1346	+	0.930094i	−1.15691	+	0.0428111i
$473$	5.55160	+	3.20522i	0.255263	+	0.147376i
$474$	−2.75699	+	9.02281i	−0.126633	+	0.414431i
$475$	−10.8036	−	18.9063i	−0.495702	−	0.867480i
$476$	3.02302	−	20.0191i	0.138560	−	0.917574i
$477$	−2.07301	+	1.43035i	−0.0949164	+	0.0654914i
$478$	4.92068	+	26.0260i	0.225067	+	1.19040i
$479$	−4.06914	−	7.04796i	−0.185924	−	0.322029i	0.757964	−	0.652297i	$-0.226194\pi$
$479$	−4.06914	−	7.04796i	−0.185924	−	0.322029i	−0.943887	+	0.330267i	$0.892861\pi$
$480$	−0.283072	−	0.584658i	−0.0129204	−	0.0266859i
$481$	0.205186	+	0.355392i	0.00935566	+	0.0162045i
$482$	0.366708	−	0.315490i	0.0167031	−	0.0143702i
$483$	45.4635	−	28.7438i	2.06866	−	1.30789i
$484$	18.2923	−	7.17338i	0.831467	−	0.326063i
$485$	−0.515937	+	0.297877i	−0.0234275	+	0.0135259i
$486$	8.33666	+	20.4083i	0.378159	+	0.925741i
$487$		−	27.5866i		−	1.25007i	−0.780598	−	0.625033i	$-0.785085\pi$
$487$		−	27.5866i		−	1.25007i	0.780598	−	0.625033i	$-0.214915\pi$
$488$	12.3619	−	23.3666i	0.559599	−	1.05776i
$489$	0.177317	+	4.40973i	0.00801857	+	0.199415i
$490$	−0.185962	+	0.531213i	−0.00840089	+	0.0239978i
$491$	−1.88290	+	3.26127i	−0.0849740	+	0.147179i	−0.905380	−	0.424602i	$-0.860414\pi$
$491$	−1.88290	+	3.26127i	−0.0849740	+	0.147179i	0.820406	+	0.571781i	$0.193747\pi$
$492$	−10.4677	−	1.15278i	−0.471920	−	0.0519714i
$493$	−15.0794			−0.679144
$494$	−1.06556	+	0.908511i	−0.0479420	+	0.0408759i
$495$	0.194824	+	0.0924871i	0.00875669	+	0.00415699i
$496$	−18.7354	−	20.2143i	−0.841246	−	0.907648i
$497$	−35.6106	−	20.5598i	−1.59736	−	0.922234i
$498$	5.44618	+	23.5730i	0.244049	+	1.05633i
$499$	−14.6121	−	8.43629i	−0.654127	−	0.377660i	0.135909	−	0.990721i	$-0.456605\pi$
$499$	−14.6121	−	8.43629i	−0.654127	−	0.377660i	−0.790035	+	0.613061i	$0.789938\pi$
$500$	−0.483872	−	1.23388i	−0.0216394	−	0.0551809i
$501$	−12.0802	−	19.1070i	−0.539703	−	0.853638i
$502$	−22.5151	+	19.3704i	−1.00490	+	0.864543i
$503$	11.9622	+	20.7191i	0.533366	+	0.923818i	0.999241	+	0.0389668i	$0.0124066\pi$
$503$	11.9622	+	20.7191i	0.533366	+	0.923818i	−0.465874	+	0.884851i	$0.654260\pi$
$504$	24.5245	−	18.2963i	1.09241	−	0.814984i
$505$	1.08464			0.0482658
$506$	−10.0110	+	8.61281i	−0.445045	+	0.382886i
$507$	10.4242	−	19.8575i	0.462956	−	0.881901i
$508$	−5.71156	+	7.15803i	−0.253410	+	0.317586i
$509$	−22.1517	+	12.7893i	−0.981858	+	0.566876i	−0.902830	−	0.429997i	$-0.858515\pi$
$509$	−22.1517	+	12.7893i	−0.981858	+	0.566876i	−0.0790271	+	0.996872i	$0.525181\pi$
$510$	0.333371	−	0.310972i	0.0147619	−	0.0137701i
$511$	45.4368	+	26.2330i	2.01001	+	1.16048i
$512$	22.4883	−	2.50566i	0.993850	−	0.110735i
$513$	22.4970	−	2.62400i	0.993266	−	0.115852i
$514$	−14.4702	−	16.8193i	−0.638252	−	0.741868i
$515$	0.307438	−	0.532498i	0.0135473	−	0.0234647i
$516$	20.3566	+	2.24182i	0.896149	+	0.0986908i
$517$	−0.223297	−	0.386761i	−0.00982058	−	0.0170098i
$518$	−9.05227	+	1.71149i	−0.397734	+	0.0751987i
$519$	−18.4747	−	9.69836i	−0.810951	−	0.425711i
$520$	−0.0360765	+	0.0226476i	−0.00158206	+	0.000993163i
$521$		−	0.00191766i		−	8.40143e-5i	−1.00000		4.20072e-5i	$-0.999987\pi$
$521$		−	0.00191766i		−	8.40143e-5i	1.00000		4.20072e-5i	$-1.33713e-5\pi$
$522$	−16.2019	−	16.0265i	−0.709137	−	0.701463i
$523$	−15.9634	+	9.21644i	−0.698029	+	0.403007i	−0.806613	−	0.591080i	$-0.798702\pi$
$523$	−15.9634	+	9.21644i	−0.698029	+	0.403007i	0.108584	+	0.994087i	$0.465368\pi$
$524$	3.04218	−	20.1460i	0.132898	−	0.880081i
$525$	26.3722	−	16.6735i	1.15098	−	0.727693i
$526$	37.4079	+	13.0954i	1.63106	+	0.570985i
$527$	9.67170	−	16.7519i	0.421306	−	0.729723i
$528$	−5.30013	+	5.32392i	−0.230659	+	0.231694i
$529$	−25.5833	+	44.3116i	−1.11232	+	1.92659i
$530$	0.0146231	+	0.0773430i	0.000635186	+	0.00335956i
$531$	11.4407	−	24.0998i	0.496484	−	1.04584i
$532$	−11.3464	−	29.3169i	−0.491927	−	1.27105i
$533$			0.690566i			0.0299117i
$534$	−26.4451	−	28.3499i	−1.14439	−	1.22682i
$535$	0.618077	+	0.356847i	0.0267218	+	0.0154278i
$536$	14.4546	+	7.64711i	0.624344	+	0.330305i
$537$	7.68115	−	0.308863i	0.331466	−	0.0133284i
$538$	−10.5146	+	30.0357i	−0.453315	+	1.29493i
$539$	6.50901			0.280363
$540$	0.688688	+	0.0201898i	0.0296364	+	0.000868832i
$541$	18.6544	+	32.3104i	0.802017	+	1.38913i	0.918287	+	0.395916i	$0.129573\pi$
$541$	18.6544	+	32.3104i	0.802017	+	1.38913i	−0.116270	+	0.993218i	$0.537094\pi$
$542$	6.99253	−	19.9747i	0.300355	−	0.857987i
$543$	−1.77529	−	2.80794i	−0.0761849	−	0.120500i
$544$	6.34051	+	14.5599i	0.271847	+	0.624250i
$545$	0.663390	−	0.383008i	0.0284165	−	0.0164063i
$546$	−1.36861	−	1.46719i	−0.0585711	−	0.0627899i
$547$	−12.2611	+	7.07894i	−0.524246	+	0.302674i	−0.738670	−	0.674067i	$-0.764546\pi$
$547$	−12.2611	+	7.07894i	−0.524246	+	0.302674i	0.214424	+	0.976741i	$0.431213\pi$
$548$	−0.721198	+	0.903844i	−0.0308080	+	0.0386103i
$549$	15.9237	+	23.0782i	0.679608	+	0.984953i
$550$	−5.80715	+	4.99607i	−0.247618	+	0.213033i
$551$	−20.3288	+	11.6165i	−0.866038	+	0.494878i
$552$	−18.2152	+	38.0553i	−0.775290	+	1.61974i
$553$	−6.94446	+	12.0282i	−0.295308	+	0.511489i
$554$	−2.66150	−	14.0769i	−0.113076	−	0.598072i
$555$	−0.183677	−	0.0964217i	−0.00779665	−	0.00409287i
$556$	17.1013	−	21.4323i	0.725256	−	0.908930i
$557$	11.1884	−	6.45965i	0.474069	−	0.273704i	−0.243872	−	0.969807i	$-0.578418\pi$
$557$	11.1884	−	6.45965i	0.474069	−	0.273704i	0.717942	+	0.696103i	$0.245084\pi$
$558$	28.1957	−	7.71966i	1.19362	−	0.326799i
$559$		−	1.34295i		−	0.0568007i
$560$	−0.212276	−	0.932404i	−0.00897029	−	0.0394013i
$561$	−4.66825	−	2.45061i	−0.197094	−	0.103465i
$562$	19.6560	+	22.8471i	0.829140	+	0.963746i
$563$	21.0550			0.887364			0.443682	−	0.896184i	$-0.353672\pi$
$563$	21.0550			0.887364			0.443682	+	0.896184i	$0.353672\pi$
$564$	−1.15009	−	0.844344i	−0.0484273	−	0.0355533i
$565$	−0.0186660	+	0.0323304i	−0.000785283	+	0.00136015i
$566$	−2.61600	+	7.47281i	−0.109959	+	0.314106i
$567$	5.19464	+	32.0351i	0.218154	+	1.34535i
$568$	32.2313	−	1.19270i	1.35239	−	0.0500447i
$569$			20.4572i			0.857609i	0.903397	+	0.428805i	$0.141065\pi$
$569$			20.4572i			0.857609i	−0.903397	+	0.428805i	$0.858935\pi$
$570$	0.209865	−	0.676039i	0.00879028	−	0.0283161i
$571$		−	30.1475i		−	1.26163i	−0.775932	−	0.630816i	$-0.782720\pi$
$571$		−	30.1475i		−	1.26163i	0.775932	−	0.630816i	$-0.217280\pi$
$572$	0.385062	+	0.307250i	0.0161003	+	0.0128468i
$573$	36.1005	−	1.45162i	1.50812	−	0.0606423i
$574$	−14.6322	−	5.12229i	−0.610737	−	0.213800i
$575$	−21.5111	+	37.2583i	−0.897075	+	1.55378i
$576$	−8.66189	+	22.3824i	−0.360912	+	0.932600i
$577$	8.53496			0.355315			0.177658	−	0.984092i	$-0.443148\pi$
$577$	8.53496			0.355315			0.177658	+	0.984092i	$0.443148\pi$
$578$	9.77612	−	8.41069i	0.406633	−	0.349839i
$579$	−17.9914	+	34.2724i	−0.747697	+	1.42431i
$580$	−0.663070	+	0.260025i	−0.0275325	+	0.0107970i
$581$			35.6164i			1.47762i
$582$	21.0505	+	6.43214i	0.872570	+	0.266621i
$583$	0.788354	−	0.455157i	0.0326503	−	0.0188507i
$584$	−41.1250	+	1.52181i	−1.70176	+	0.0629730i
$585$	−0.00362755	−	0.0450341i	−0.000149981	−	0.00186193i
$586$	33.6477	−	6.36169i	1.38997	−	0.262799i
$587$	17.1850	−	29.7654i	0.709303	−	1.22855i	−0.255813	−	0.966726i	$-0.582343\pi$
$587$	17.1850	−	29.7654i	0.709303	−	1.22855i	0.965116	−	0.261822i	$-0.0843235\pi$
$588$	19.0385	−	8.36347i	0.785137	−	0.344904i
$589$	0.133753	−	30.0341i	0.00551118	−	1.23753i
$590$	−0.543759	−	0.632035i	−0.0223862	−	0.0260205i
$591$	−1.47840	−	36.7665i	−0.0608132	−	1.51237i
$592$	5.29988	−	4.91215i	0.217824	−	0.201888i
$593$	24.7534	−	14.2914i	1.01650	−	0.586877i	0.103413	−	0.994639i	$-0.467024\pi$
$593$	24.7534	−	14.2914i	1.01650	−	0.586877i	0.913089	+	0.407761i	$0.133690\pi$
$594$	−2.41121	−	7.59447i	−0.0989329	−	0.311605i
$595$	0.581217	−	0.335566i	0.0238276	−	0.0137569i
$596$	−17.3590	−	2.62133i	−0.711052	−	0.107374i
$597$	−2.07577	+	1.31238i	−0.0849556	+	0.0537122i
$598$	2.61122	+	0.914109i	0.106781	+	0.0373807i
$599$	−1.33281	−	2.30849i	−0.0544571	−	0.0943224i	0.837512	−	0.546419i	$-0.184009\pi$
$599$	−1.33281	−	2.30849i	−0.0544571	−	0.0943224i	−0.891969	+	0.452097i	$0.850676\pi$
$600$	−10.5662	+	22.0749i	−0.431362	+	0.901205i
$601$	8.37653			0.341686			0.170843	−	0.985298i	$-0.445351\pi$
$601$	8.37653			0.341686			0.170843	+	0.985298i	$0.445351\pi$
$602$	28.4554	+	9.96136i	1.15975	+	0.405995i
$603$	−14.2762	+	9.85044i	−0.581372	+	0.401141i
$604$	11.7617	+	29.9924i	0.478575	+	1.22038i
$605$	0.564063	+	0.325662i	0.0229324	+	0.0132400i
$606$	−27.3351	−	29.3040i	−1.11041	−	1.19039i
$607$		−	1.64216i		−	0.0666533i	−0.999445	−	0.0333267i	$-0.989390\pi$
$607$		−	1.64216i		−	0.0666533i	0.999445	−	0.0333267i	$-0.0106102\pi$
$608$	19.7640	+	14.7440i	0.801535	+	0.597948i
$609$	−17.9281	−	28.3565i	−0.726483	−	1.14906i
$610$	0.861037	−	0.162795i	0.0348624	−	0.00659136i
$611$	−0.0467793	+	0.0810242i	−0.00189249	+	0.00327789i
$612$	−16.8032	−	1.16965i	−0.679230	−	0.0472804i
$613$	−15.2963	+	26.4940i	−0.617812	+	1.07008i	0.372072	+	0.928204i	$0.378647\pi$
$613$	−15.2963	+	26.4940i	−0.617812	+	1.07008i	−0.989884	+	0.141878i	$0.954686\pi$
$614$	6.06800	−	17.3337i	0.244884	−	0.699531i
$615$	−0.186550	−	0.295063i	−0.00752243	−	0.0118981i
$616$	−9.36644	+	5.87994i	−0.377385	+	0.236910i
$617$	−6.15678	+	3.55462i	−0.247863	+	0.143104i	−0.618785	−	0.785560i	$-0.712375\pi$
$617$	−6.15678	+	3.55462i	−0.247863	+	0.143104i	0.370922	+	0.928664i	$0.379042\pi$
$618$	−22.1347	+	5.11389i	−0.890389	+	0.205711i
$619$			4.26335i			0.171359i	0.996323	+	0.0856793i	$0.0273061\pi$
$619$			4.26335i			0.171359i	−0.996323	+	0.0856793i	$0.972694\pi$
$620$	0.136418	−	0.903387i	0.00547866	−	0.0362809i
$621$	−26.8734	−	35.7816i	−1.07839	−	1.43587i
$622$	1.84086	+	9.73651i	0.0738118	+	0.390398i
$623$	−28.5366	−	49.4268i	−1.14329	−	1.98024i
$624$	1.52108	+	0.403923i	0.0608918	+	0.0161698i
$625$	−12.4670	+	21.5936i	−0.498682	+	0.863742i
$626$	17.6254	−	15.1637i	0.704453	−	0.606063i
$627$	−8.18118	+	0.292483i	−0.326725	+	0.0116806i
$628$	1.63527	−	10.8291i	0.0652542	−	0.432127i
$629$	4.39209	+	2.53577i	0.175124	+	0.101108i
$630$	0.981123	+	0.257178i	0.0390889	+	0.0102462i
$631$	12.5246	−	7.23110i	0.498598	−	0.287865i	−0.229537	−	0.973300i	$-0.573721\pi$
$631$	12.5246	−	7.23110i	0.498598	−	0.287865i	0.728134	+	0.685435i	$0.240388\pi$
$632$	−0.402858	−	10.8867i	−0.0160248	−	0.433050i
$633$	24.4359	+	12.8277i	0.971239	+	0.509855i
$634$	−13.0316	−	15.1472i	−0.517552	−	0.601573i
$635$	−0.303559			−0.0120464
$636$	1.72107	−	2.34427i	0.0682447	−	0.0929565i
$637$	−0.681799	−	1.18091i	−0.0270139	−	0.0467894i
$638$	5.37198	+	6.24409i	0.212679	+	0.247206i
$639$	−14.6709	+	30.9043i	−0.580373	+	1.22255i
$640$	0.529870	+	0.530890i	0.0209449	+	0.0209853i
$641$	11.8782	+	6.85786i	0.469159	+	0.270869i	0.715888	−	0.698215i	$-0.246022\pi$
$641$	11.8782	+	6.85786i	0.469159	+	0.270869i	−0.246728	+	0.969085i	$0.579356\pi$
$642$	−5.93575	−	25.6920i	−0.234265	−	1.01398i
$643$	15.8960	+	9.17754i	0.626876	+	0.361927i	0.779541	−	0.626351i	$-0.215452\pi$
$643$	15.8960	+	9.17754i	0.626876	+	0.361927i	−0.152665	+	0.988278i	$0.548786\pi$
$644$	−38.7376	+	48.5481i	−1.52648	+	1.91306i
$645$	0.362785	+	0.573811i	0.0142847	+	0.0225938i
$646$	−5.79055	+	16.3079i	−0.227826	+	0.641626i
$647$	−10.7256			−0.421667			−0.210833	−	0.977522i	$-0.567618\pi$
$647$	−10.7256			−0.421667			−0.210833	+	0.977522i	$0.567618\pi$
$648$	−16.8109	−	19.1153i	−0.660393	−	0.750920i
$649$	−4.82114	+	8.35046i	−0.189246	+	0.327784i
$650$	1.51470	+	0.530251i	0.0594116	+	0.0207982i
$651$	43.0003	−	1.72906i	1.68532	−	0.0677674i
$652$	−1.86049	−	4.74428i	−0.0728623	−	0.185800i
$653$			34.5202i			1.35088i	0.737416	+	0.675439i	$0.236046\pi$
$653$			34.5202i			1.35088i	−0.737416	+	0.675439i	$0.763954\pi$
$654$	−27.0666	−	8.27041i	−1.05839	−	0.323398i
$655$	0.584901	−	0.337693i	0.0228540	−	0.0131947i
$656$	11.8567	−	2.69937i	0.462928	−	0.105393i
$657$	18.7191	−	39.4318i	0.730303	−	1.53838i
$658$	−1.36981	−	1.59219i	−0.0534009	−	0.0620702i
$659$	1.94679	+	3.37194i	0.0758361	+	0.131352i	0.901450	−	0.432884i	$-0.142504\pi$
$659$	1.94679	+	3.37194i	0.0758361	+	0.131352i	−0.825613	+	0.564236i	$0.809171\pi$
$660$	−0.247529	−	0.0272598i	−0.00963505	−	0.00106109i
$661$	−1.71778	−	2.97528i	−0.0668139	−	0.115725i	0.830683	−	0.556745i	$-0.187950\pi$
$661$	−1.71778	−	2.97528i	−0.0668139	−	0.115725i	−0.897497	+	0.441020i	$0.854617\pi$
$662$	−36.2063	+	6.84546i	−1.40720	+	0.266056i
$663$	0.0443779	+	1.10364i	0.00172350	+	0.0428619i
$664$	−14.8535	−	23.6608i	−0.576427	−	0.918218i
$665$	0.525045	−	0.900124i	0.0203604	−	0.0349053i
$666$	2.02398	+	7.39247i	0.0784275	+	0.286453i
$667$	40.0617	+	23.1296i	1.55120	+	0.895583i
$668$	20.4033	+	16.2803i	0.789429	+	0.629904i
$669$	−1.73739	−	0.912045i	−0.0671712	−	0.0352617i
$670$	0.100705	+	0.532639i	0.00389057	+	0.0205776i
$671$	−5.06713	−	8.77653i	−0.195614	−	0.338814i
$672$	−19.8412	+	29.2336i	−0.765392	+	1.12771i
$673$	−10.8539			−0.418388			−0.209194	−	0.977874i	$-0.567084\pi$
$673$	−10.8539			−0.418388			−0.209194	+	0.977874i	$0.567084\pi$
$674$	−12.4409	−	4.35517i	−0.479204	−	0.167755i
$675$	−15.5885	−	20.7560i	−0.600003	−	0.798898i
$676$	−3.86676	+	25.6065i	−0.148721	+	0.984865i
$677$		−	6.67800i		−	0.256657i	−0.991732	−	0.128328i	$-0.959039\pi$
$677$		−	6.67800i		−	0.256657i	0.991732	−	0.128328i	$-0.0409611\pi$
$678$	1.34390	−	0.310487i	0.0516121	−	0.0119242i
$679$	28.0620	+	16.2016i	1.07692	+	0.621761i
$680$	−0.246172	+	0.465315i	−0.00944026	+	0.0178440i
$681$	−17.2182	+	0.692354i	−0.659804	+	0.0265311i
$682$	−10.3821	+	1.96293i	−0.397552	+	0.0751643i
$683$	12.2326			0.468068			0.234034	−	0.972228i	$-0.424807\pi$
$683$	12.2326			0.468068			0.234034	+	0.972228i	$0.424807\pi$
$684$	−23.5537	+	11.3676i	−0.900600	+	0.434649i
$685$	−0.0383304			−0.00146453
$686$	−4.99641	+	0.944660i	−0.190764	+	0.0360673i
$687$	−21.3549	+	0.858689i	−0.814738	+	0.0327610i
$688$	−23.0579	+	5.24948i	−0.879073	+	0.200134i
$689$	−0.165156	−	0.0953526i	−0.00629192	−	0.00363264i
$690$	−1.36265	+	0.314820i	−0.0518753	+	0.0119850i
$691$			9.10551i			0.346390i	0.984888	+	0.173195i	$0.0554091\pi$
$691$			9.10551i			0.346390i	−0.984888	+	0.173195i	$0.944591\pi$
$692$	23.8234	+	3.59750i	0.905631	+	0.136757i
$693$	−0.941812	−	11.6921i	−0.0357765	−	0.444146i
$694$	−31.2525	−	10.9405i	−1.18633	−	0.415297i
$695$	0.908903			0.0344766
$696$	23.7359	+	11.3612i	0.899706	+	0.430644i
$697$	4.26716	+	7.39094i	0.161630	+	0.279952i
$698$	5.07387	+	26.8362i	0.192049	+	1.01577i
$699$	44.1504	+	23.1769i	1.66992	+	0.876630i
$700$	−22.4707	+	28.1615i	−0.849313	+	1.06440i
$701$	2.44982	+	1.41441i	0.0925286	+	0.0534214i	0.545550	−	0.838078i	$-0.316321\pi$
$701$	2.44982	+	1.41441i	0.0925286	+	0.0534214i	−0.453022	+	0.891499i	$0.649654\pi$
$702$	−1.12528	+	1.23296i	−0.0424708	+	0.0465349i
$703$	7.87449	+	0.0350679i	0.296992	+	0.00132261i
$704$	3.77018	−	7.81237i	0.142094	−	0.294440i
$705$	−0.00190022	−	0.0472568i	−7.15664e−5	−	0.00177979i
$706$	1.11821	−	0.211418i	0.0420844	−	0.00795681i
$707$	−29.4970	−	51.0903i	−1.10935	−	1.92145i
$708$	−3.37205	+	30.6194i	−0.126729	+	1.15075i
$709$	6.24505	+	10.8167i	0.234538	+	0.406232i	0.959138	−	0.282938i	$-0.0913090\pi$
$709$	6.24505	+	10.8167i	0.234538	+	0.406232i	−0.724600	+	0.689169i	$0.757976\pi$
$710$	0.697287	+	0.810487i	0.0261687	+	0.0304170i
$711$	10.4385	+	4.95538i	0.391474	+	0.185841i
$712$	39.5705	+	20.9345i	1.48297	+	0.784554i
$713$	−51.3898	+	29.6699i	−1.92456	+	1.11115i
$714$	−23.7139	−	7.24597i	−0.887471	−	0.271174i
$715$			0.0163298i			0.000610699i
$716$	−8.26388	+	3.24071i	−0.308836	+	0.121111i
$717$	32.4137	−	1.30337i	1.21051	−	0.0486753i
$718$	5.71920	+	2.00212i	0.213439	+	0.0747184i
$719$	9.48282	−	16.4247i	0.353649	−	0.612539i	−0.633236	−	0.773958i	$-0.718274\pi$
$719$	9.48282	−	16.4247i	0.353649	−	0.612539i	0.986886	+	0.161420i	$0.0516073\pi$
$720$	−0.759037	+	0.238318i	−0.0282876	+	0.00888159i
$721$	−33.4434			−1.24550
$722$	4.75648	+	26.4457i	0.177018	+	0.984208i
$723$	−0.316608	−	0.500772i	−0.0117748	−	0.0186239i
$724$	2.99845	+	2.39253i	0.111436	+	0.0889177i
$725$	23.2388	+	13.4169i	0.863066	+	0.498291i
$726$	−5.41703	−	23.4468i	−0.201045	−	0.870192i
$727$	−18.1204	−	10.4618i	−0.672049	−	0.388007i	0.124804	−	0.992181i	$-0.460170\pi$
$727$	−18.1204	−	10.4618i	−0.672049	−	0.388007i	−0.796852	+	0.604174i	$0.793503\pi$
$728$	2.04789	+	1.08342i	0.0758998	+	0.0401542i
$729$	26.2188	−	6.44768i	0.971068	−	0.238803i
$730$	−0.889692	−	1.03413i	−0.0329290	−	0.0382748i
$731$	−8.29838	−	14.3732i	−0.306927	−	0.531612i
$732$	−26.0981	−	19.1601i	−0.964615	−	0.708179i
$733$	39.5695			1.46153			0.730766	−	0.682628i	$-0.239163\pi$
$733$	39.5695			1.46153			0.730766	+	0.682628i	$0.239163\pi$
$734$	21.2364	+	24.6840i	0.783850	+	0.911104i
$735$	0.610329	+	0.320394i	0.0225123	+	0.0118179i
$736$	5.48782	−	48.4068i	0.202284	−	1.78430i
$737$	5.42917	−	3.13453i	0.199986	−	0.115462i
$738$	−3.27036	+	12.4763i	−0.120384	+	0.459257i
$739$	30.9794	+	17.8859i	1.13959	+	0.657945i	0.946330	−	0.323202i	$-0.104759\pi$
$739$	30.9794	+	17.8859i	1.13959	+	0.657945i	0.193264	+	0.981147i	$0.438093\pi$
$740$	0.236854	+	0.0357666i	0.00870693	+	0.00131481i
$741$	0.910018	+	1.45365i	0.0334303	+	0.0534012i
$742$	3.24545	−	2.79216i	0.119144	−	0.102503i
$743$	4.68614	−	8.11663i	0.171918	−	0.297770i	−0.767173	−	0.641441i	$-0.778337\pi$
$743$	4.68614	−	8.11663i	0.171918	−	0.297770i	0.939090	+	0.343670i	$0.111670\pi$
$744$	−27.8450	+	19.0815i	−1.02085	+	0.699563i
$745$	−0.290977	−	0.503986i	−0.0106606	−	0.0184646i
$746$	−8.57603	−	45.3595i	−0.313991	−	1.66073i
$747$	29.5357	−	2.37914i	1.08066	−	0.0870481i
$748$	6.01978	+	0.909027i	0.220105	+	0.0332373i
$749$		−	38.8181i		−	1.41838i
$750$	−1.58158	+	0.365399i	−0.0577510	+	0.0133425i
$751$	−8.07650	+	4.66297i	−0.294716	+	0.170154i	−0.640067	−	0.768319i	$-0.721093\pi$
$751$	−8.07650	+	4.66297i	−0.294716	+	0.170154i	0.345351	+	0.938474i	$0.387760\pi$
$752$	1.57401	+	0.486465i	0.0573982	+	0.0177396i
$753$	19.4390	+	30.7463i	0.708396	+	1.12046i
$754$	0.570148	−	1.62867i	0.0207636	−	0.0593128i
$755$	−0.533964	+	0.924852i	−0.0194329	+	0.0336588i
$756$	−17.7780	−	32.9887i	−0.646580	−	1.19979i
$757$	6.55774	−	11.3583i	0.238345	−	0.412826i	−0.721895	−	0.692003i	$-0.756728\pi$
$757$	6.55774	−	11.3583i	0.238345	−	0.412826i	0.960240	+	0.279177i	$0.0900618\pi$
$758$	−13.2047	+	2.49658i	−0.479615	+	0.0906797i
$759$	8.64331	+	13.6710i	0.313732	+	0.496225i
$760$	0.0265879	+	0.816938i	0.000964445	+	0.0296335i
$761$			9.12600i			0.330817i	0.986225	+	0.165409i	$0.0528943\pi$
$761$			9.12600i			0.330817i	−0.986225	+	0.165409i	$0.947106\pi$
$762$	7.65030	+	8.20134i	0.277141	+	0.297103i
$763$	−36.0820	−	20.8320i	−1.30626	−	0.754168i
$764$	−38.8393	+	15.2310i	−1.40516	+	0.551037i
$765$	−0.317100	−	0.459572i	−0.0114648	−	0.0166159i
$766$	−48.7161	−	17.0540i	−1.76018	−	0.616186i
$767$	2.02000			0.0729380
$768$	0.989424	−	27.6951i	0.0357027	−	0.999362i
$769$	13.0400	+	22.5859i	0.470233	+	0.814467i	0.999421	−	0.0340376i	$-0.0108366\pi$
$769$	13.0400	+	22.5859i	0.470233	+	0.814467i	−0.529188	+	0.848505i	$0.677503\pi$
$770$	−0.346007	−	0.121127i	−0.0124692	−	0.00436510i
$771$	−22.9683	+	14.5214i	−0.827181	+	0.522976i
$772$	6.67372	−	44.1948i	0.240192	−	1.59061i
$773$	2.68879	−	1.55237i	0.0967090	−	0.0558350i	−0.450866	−	0.892592i	$-0.648885\pi$
$773$	2.68879	−	1.55237i	0.0967090	−	0.0558350i	0.547575	+	0.836757i	$0.315551\pi$
$774$	6.35989	−	24.2627i	0.228602	−	0.872104i
$775$	−29.8099	+	17.2108i	−1.07080	+	0.618229i
$776$	−25.3990	+	0.939879i	−0.911771	+	0.0337397i
$777$	0.453334	+	11.2740i	0.0162633	+	0.404454i
$778$	4.91992	+	5.71864i	0.176388	+	0.205023i
$779$	11.4462	+	6.67664i	0.410104	+	0.239215i
$780$	0.0209822	+	0.0477638i	0.000751285	+	0.00171022i
$781$	6.18237	−	10.7082i	0.221223	−	0.383169i
$782$	33.5957	−	6.35186i	1.20138	−	0.227142i
$783$	−22.3177	+	16.7615i	−0.797570	+	0.599006i
$784$	−17.6106	+	16.3223i	−0.628952	+	0.582939i
$785$	0.314402	−	0.181520i	0.0112215	−	0.00647873i
$786$	−23.8642	−	7.29189i	−0.851208	−	0.260093i
$787$			9.79232i			0.349058i	0.984652	+	0.174529i	$0.0558404\pi$
$787$			9.79232i			0.349058i	−0.984652	+	0.174529i	$0.944160\pi$
$788$	15.5119	+	39.5558i	0.552590	+	1.40912i
$789$	22.5621	−	42.9793i	0.803231	−	1.53010i
$790$	0.273757	−	0.235522i	0.00973984	−	0.00837948i
$791$	2.03050			0.0721962
$792$	5.50174	+	7.37456i	0.195496	+	0.262044i
$793$	−1.06153	+	1.83863i	−0.0376961	+	0.0652916i
$794$	12.7817	+	4.47447i	0.453604	+	0.158793i
$795$	0.0963258	−	0.00387331i	0.00341632	−	0.000137372i
$796$	1.76868	−	2.21660i	0.0626892	−	0.0785654i
$797$			5.59036i			0.198021i	0.995086	+	0.0990104i	$0.0315677\pi$
$797$			5.59036i			0.198021i	−0.995086	+	0.0990104i	$0.968432\pi$
$798$	−37.5511	+	8.49963i	−1.32929	+	0.300884i
$799$			1.15624i			0.0409048i
$800$	3.18334	−	28.0795i	0.112548	−	0.992762i
$801$	−39.0821	+	26.9663i	−1.38090	+	0.952806i
$802$	12.8938	−	36.8322i	0.455297	−	1.30059i
$803$	−7.88830	+	13.6629i	−0.278372	+	0.482154i
$804$	11.8525	−	16.1443i	0.418005	−	0.569367i
$805$	−2.05883			−0.0725644
$806$	1.44362	+	1.67799i	0.0508495	+	0.0591046i
$807$	34.5090	+	18.1156i	1.21477	+	0.637699i
$808$	40.9023	+	21.6390i	1.43894	+	0.761259i
$809$			8.57218i			0.301382i	0.988581	+	0.150691i	$0.0481498\pi$
$809$			8.57218i			0.301382i	−0.988581	+	0.150691i	$0.951850\pi$
$810$	0.147733	−	0.830797i	0.00519081	−	0.0291912i
$811$	−7.74988	+	4.47439i	−0.272135	+	0.157117i	−0.629857	−	0.776711i	$-0.716887\pi$
$811$	−7.74988	+	4.47439i	−0.272135	+	0.157117i	0.357722	+	0.933828i	$0.383553\pi$
$812$	30.2804	+	24.1614i	1.06263	+	0.847901i
$813$	−22.9496	−	12.0475i	−0.804878	−	0.422523i
$814$	−0.514649	−	2.72203i	−0.0180384	−	0.0954072i
$815$	0.0844636	−	0.146295i	0.00295863	−	0.00512450i
$816$	18.7756	−	5.07599i	0.657277	−	0.177695i
$817$	−22.2596	−	12.9841i	−0.778765	−	0.454256i
$818$	−0.531376	+	0.457159i	−0.0185791	+	0.0159842i
$819$	−2.02261	+	1.39558i	−0.0706757	+	0.0487656i
$820$	0.315082	+	0.251411i	0.0110031	+	0.00877966i
$821$	22.5728	−	13.0324i	0.787794	−	0.454833i	−0.0513910	−	0.998679i	$-0.516365\pi$
$821$	22.5728	−	13.0324i	0.787794	−	0.454833i	0.839186	+	0.543845i	$0.183032\pi$
$822$	0.966002	+	1.03558i	0.0336932	+	0.0361201i
$823$	15.5961	−	9.00439i	0.543645	−	0.313873i	−0.202910	−	0.979197i	$-0.565040\pi$
$823$	15.5961	−	9.00439i	0.543645	−	0.313873i	0.746555	+	0.665324i	$0.231707\pi$
$824$	22.2172	−	13.9472i	0.773973	−	0.485875i
$825$	5.01376	+	7.93018i	0.174557	+	0.276093i
$826$	−14.9834	+	42.8012i	−0.521339	+	1.48925i
$827$	13.4740	+	23.3377i	0.468538	+	0.811531i	0.999353	−	0.0359561i	$-0.0114477\pi$
$827$	13.4740	+	23.3377i	0.468538	+	0.811531i	−0.530816	+	0.847487i	$0.678114\pi$
$828$	42.8472	+	28.8811i	1.48904	+	1.00369i
$829$	23.0503			0.800569			0.400284	−	0.916391i	$-0.368911\pi$
$829$	23.0503			0.800569			0.400284	+	0.916391i	$0.368911\pi$
$830$	0.305981	−	0.874058i	0.0106208	−	0.0303390i
$831$	−17.5319	+	0.704968i	−0.608176	+	0.0244551i
$832$	−1.81229	+	0.134310i	−0.0628299	+	0.00465635i
$833$	−14.5942	−	8.42597i	−0.505660	−	0.291943i
$834$	−22.9062	−	24.5561i	−0.793176	−	0.850307i
$835$			0.865268i			0.0299438i
$836$	8.81563	−	3.41187i	0.304895	−	0.118002i
$837$	−4.30624	−	35.5435i	−0.148845	−	1.22856i
$838$	6.93982	+	36.7054i	0.239732	+	1.26797i
$839$	16.8082	−	29.1127i	0.580284	−	1.00508i	−0.415162	−	0.909748i	$-0.636275\pi$
$839$	16.8082	−	29.1127i	0.580284	−	1.00508i	0.995445	−	0.0953334i	$-0.0303917\pi$
$840$	−1.16769	+	0.0902977i	−0.0402892	+	0.00311557i
$841$	−0.0735821	+	0.127448i	−0.00253731	+	0.00439476i
$842$	36.1751	+	12.6638i	1.24668	+	0.436423i
$843$	31.1997	−	19.7257i	1.07458	−	0.679388i
$844$	−31.5104	−	4.75829i	−1.08463	−	0.163787i
$845$	−0.743437	+	0.429224i	−0.0255750	+	0.0147657i
$846$	−1.22886	+	1.24230i	−0.0422491	+	0.0427113i
$847$		−	35.4258i		−	1.21724i
$848$	−0.991585	+	3.20838i	−0.0340512	+	0.110176i
$849$	8.58577	+	4.50712i	0.294663	+	0.154684i
$850$	19.4880	−	3.68455i	0.668433	−	0.126379i
$851$	−7.77901	−	13.4736i	−0.266661	−	0.461870i
$852$	4.32413	−	39.2647i	0.148142	−	1.34519i
$853$	−4.35531	+	7.54363i	−0.149123	+	0.258289i	−0.930904	−	0.365265i	$-0.880978\pi$
$853$	−4.35531	+	7.54363i	−0.149123	+	0.258289i	0.781780	+	0.623554i	$0.214312\pi$
$854$	−31.0843	−	36.1306i	−1.06368	−	1.23636i
$855$	−0.781520	−	0.375278i	−0.0267274	−	0.0128342i
$856$	16.1887	+	25.7878i	0.553319	+	0.881408i
$857$	13.2683	+	7.66045i	0.453236	+	0.261676i	0.709196	−	0.705011i	$-0.249058\pi$
$857$	13.2683	+	7.66045i	0.453236	+	0.261676i	−0.255960	+	0.966687i	$0.582391\pi$
$858$	0.441186	−	0.411543i	0.0150618	−	0.0140499i
$859$	−13.0828	+	7.55337i	−0.446380	+	0.257718i	−0.706300	−	0.707913i	$-0.749637\pi$
$859$	−13.0828	+	7.55337i	−0.446380	+	0.257718i	0.259920	+	0.965630i	$0.416304\pi$
$860$	−0.612742	−	0.488921i	−0.0208943	−	0.0166721i
$861$	−8.82522	+	16.8115i	−0.300763	+	0.572933i
$862$	0.356452	−	0.306667i	0.0121408	−	0.0104451i
$863$	−16.8019			−0.571945			−0.285973	−	0.958238i	$-0.592317\pi$
$863$	−16.8019			−0.571945			−0.285973	+	0.958238i	$0.592317\pi$
$864$	25.5680	+	14.5010i	0.869840	+	0.493334i
$865$	0.399336	+	0.691669i	0.0135778	+	0.0235175i
$866$	20.4539	−	17.5971i	0.695051	−	0.597974i
$867$	−8.44048	−	13.3502i	−0.286654	−	0.453395i
$868$	−46.2625	+	18.1420i	−1.57025	+	0.615781i
$869$	−3.61689	−	2.08821i	−0.122694	−	0.0708377i
$870$	0.196360	+	0.849915i	0.00665722	+	0.0288148i
$871$	−1.13738	−	0.656666i	−0.0385386	−	0.0222503i
$872$	32.6579	−	1.20849i	1.10594	−	0.0409247i
$873$	11.5610	−	24.3533i	0.391282	−	0.824235i
$874$	40.3977	−	34.4435i	1.36647	−	1.16507i
$875$	−2.38961			−0.0807834
$876$	−5.51730	+	50.0992i	−0.186412	+	1.69269i
$877$	12.0992	−	20.9565i	0.408562	−	0.707650i	−0.586167	−	0.810190i	$-0.699364\pi$
$877$	12.0992	−	20.9565i	0.408562	−	0.707650i	0.994729	+	0.102540i	$0.0326971\pi$
$878$	7.35693	−	21.0156i	0.248284	−	0.709244i
$879$	−1.68506	−	41.9060i	−0.0568357	−	1.41345i
$880$	0.280375	−	0.0638317i	0.00945145	−	0.00215177i
$881$			51.7294i			1.74281i	0.490565	+	0.871405i	$0.336790\pi$
$881$			51.7294i			1.74281i	−0.490565	+	0.871405i	$0.663210\pi$
$882$	−6.72535	−	24.5640i	−0.226454	−	0.827113i
$883$	21.8823	−	12.6337i	0.736397	−	0.425159i	−0.0843609	−	0.996435i	$-0.526885\pi$
$883$	21.8823	−	12.6337i	0.736397	−	0.425159i	0.820758	+	0.571276i	$0.193552\pi$
$884$	−0.465631	−	1.18737i	−0.0156609	−	0.0399355i
$885$	−0.863099	+	0.545685i	−0.0290128	+	0.0183430i
$886$	18.5356	−	15.9468i	0.622717	−	0.535742i
$887$	14.7061	+	25.4718i	0.493784	+	0.855258i	0.999974	−	0.00716328i	$-0.00228016\pi$
$887$	14.7061	+	25.4718i	0.493784	+	0.855258i	−0.506191	+	0.862422i	$0.668947\pi$
$888$	−5.00289	−	7.30055i	−0.167886	−	0.244990i
$889$	8.25535	+	14.2987i	0.276876	+	0.479562i
$890$	0.275687	+	1.45814i	0.00924104	+	0.0488768i
$891$	−9.63301	+	1.56204i	−0.322718	+	0.0523302i
$892$	2.24039	+	0.338314i	0.0750136	+	0.0113276i
$893$	0.890710	+	1.55875i	0.0298065	+	0.0521614i
$894$	−6.28314	+	20.5629i	−0.210140	+	0.687725i
$895$	−0.254826	−	0.147124i	−0.00851791	−	0.00491782i
$896$	10.5969	−	39.3964i	0.354016	−	1.31614i
$897$	1.57492	−	3.00012i	0.0525851	−	0.100171i
$898$	−20.1190	+	3.80386i	−0.671380	+	0.126936i
$899$	18.5057	+	32.0529i	0.617201	+	1.06902i
$900$	24.8546	+	16.7532i	0.828486	+	0.558439i
$901$	−2.35682			−0.0785170
$902$	1.54028	−	4.39993i	0.0512858	−	0.146502i
$903$	17.1625	−	32.6934i	0.571131	−	1.08797i
$904$	−1.34891	+	0.846800i	−0.0448640	+	0.0281641i
$905$			0.127159i			0.00422690i
$906$	38.4439	−	8.88189i	1.27721	−	0.295081i
$907$	−19.1736	−	11.0699i	−0.636649	−	0.367570i	0.146673	−	0.989185i	$-0.453143\pi$
$907$	−19.1736	−	11.0699i	−0.636649	−	0.367570i	−0.783323	+	0.621615i	$0.786477\pi$
$908$	18.5245	−	7.26446i	0.614757	−	0.241079i
$909$	−40.3974	+	27.8738i	−1.33990	+	0.924516i
$910$	0.0142676	+	0.0754627i	0.000472966	+	0.00250156i
$911$	−8.98945			−0.297834			−0.148917	−	0.988850i	$-0.547579\pi$
$911$	−8.98945			−0.297834			−0.148917	+	0.988850i	$0.547579\pi$
$912$	21.4014	−	21.3068i	0.708671	−	0.705539i
$913$	−10.7099			−0.354447
$914$	8.87085	+	46.9189i	0.293422	+	1.55194i
$915$	−0.0431204	−	1.07237i	−0.00142552	−	0.0354514i
$916$	22.9749	−	9.00971i	0.759113	−	0.297689i
$917$	−31.8130	−	18.3672i	−1.05056	−	0.606540i
$918$	−4.42482	+	20.1493i	−0.146041	+	0.665027i
$919$		−	0.380683i		−	0.0125576i	−0.999980	−	0.00627879i	$-0.998001\pi$
$919$		−	0.380683i		−	0.0125576i	0.999980	−	0.00627879i	$-0.00199862\pi$
$920$	1.36773	−	0.858617i	0.0450928	−	0.0283078i
$921$	−19.9153	−	10.4546i	−0.656231	−	0.344490i
$922$	−0.710991	+	2.03100i	−0.0234153	+	0.0668875i
$923$	−2.59034			−0.0852620
$924$	5.44757	+	12.4008i	0.179212	+	0.407957i
$925$	−4.51240	−	7.81571i	−0.148367	−	0.256979i
$926$	−25.3104	+	4.78539i	−0.831752	+	0.157258i
$927$	2.23398	+	27.7336i	0.0733735	+	0.910892i
$928$	−30.1923	−	3.42286i	−0.991111	−	0.112361i
$929$	−46.4956	−	26.8443i	−1.52547	−	0.880732i	−0.999544	−	0.0302029i	$-0.990385\pi$
$929$	−46.4956	−	26.8443i	−1.52547	−	0.880732i	−0.525928	−	0.850529i	$-0.676282\pi$
$930$	−1.07012	−	0.326983i	−0.0350906	−	0.0107222i
$931$	−26.1657	−	0.116525i	−0.857545	−	0.00381895i
$932$	−56.9326	−	8.59722i	−1.86489	−	0.281611i
$933$	12.1262	−	0.487601i	0.396994	−	0.0159633i
$934$	−7.73260	−	40.8986i	−0.253019	−	1.33824i
$935$	0.100905	+	0.174773i	0.00329995	+	0.00571569i
$936$	0.761654	−	1.77063i	0.0248954	−	0.0578748i
$937$	−17.4603	−	30.2422i	−0.570404	−	0.987969i	−0.996524	−	0.0833024i	$-0.973453\pi$
$937$	−17.4603	−	30.2422i	−0.570404	−	0.987969i	0.426120	−	0.904667i	$-0.359880\pi$
$938$	22.3505	−	19.2288i	0.729768	−	0.627842i
$939$	−15.2174	−	24.0691i	−0.496601	−	0.785464i
$940$	0.0199379	+	0.0508419i	0.000650301	+	0.00165828i
$941$	27.2658	−	15.7419i	0.888839	−	0.513171i	0.0152764	−	0.999883i	$-0.495137\pi$
$941$	27.2658	−	15.7419i	0.888839	−	0.513171i	0.873563	+	0.486712i	$0.161804\pi$
$942$	−12.8277	−	3.91962i	−0.417951	−	0.127708i
$943$		−	26.1808i		−	0.852563i
$944$	−7.89601	−	34.6826i	−0.256993	−	1.12882i
$945$	0.487211	−	1.14269i	0.0158490	−	0.0371717i
$946$	−2.99540	+	8.55658i	−0.0973888	+	0.278198i
$947$	10.1473	−	17.5756i	0.329743	−	0.571131i	−0.652718	−	0.757601i	$-0.726371\pi$
$947$	10.1473	−	17.5756i	0.329743	−	0.571131i	0.982461	+	0.186470i	$0.0597047\pi$
$948$	−13.2624	−	1.46056i	−0.430742	−	0.0474366i
$949$	3.30510			0.107288
$950$	23.4337	−	19.9798i	0.760289	−	0.648231i
$951$	−20.6849	+	13.0778i	−0.670753	+	0.424076i
$952$	28.6127	−	1.05880i	0.927342	−	0.0343158i
$953$	−38.6657	−	22.3237i	−1.25251	−	0.723135i	−0.280900	−	0.959737i	$-0.590633\pi$
$953$	−38.6657	−	22.3237i	−1.25251	−	0.723135i	−0.971607	+	0.236602i	$0.923966\pi$
$954$	−2.53225	−	2.50485i	−0.0819846	−	0.0810974i
$955$	−1.19765	−	0.691466i	−0.0387552	−	0.0223753i
$956$	−34.8728	+	13.6755i	−1.12787	+	0.442297i
$957$	8.52686	−	5.39101i	0.275634	−	0.174267i
$958$	8.72473	−	7.50615i	0.281883	−	0.242513i
$959$	1.04240	+	1.80549i	0.0336609	+	0.0583024i
$960$	0.738067	−	0.546961i	0.0238210	−	0.0176531i
$961$	−16.4771			−0.531520
$962$	−0.439943	+	0.378496i	−0.0141843	+	0.0122032i
$963$	−32.1908	+	2.59301i	−1.03733	+	0.0835585i
$964$	0.534748	+	0.426688i	0.0172231	+	0.0137427i
$965$	1.28311	−	0.740806i	0.0413049	−	0.0238474i
$966$	51.8868	+	55.6241i	1.66943	+	1.78968i
$967$	−42.3551	−	24.4537i	−1.36205	−	0.786379i	−0.372152	−	0.928172i	$-0.621380\pi$
$967$	−42.3551	−	24.4537i	−1.36205	−	0.786379i	−0.989896	+	0.141793i	$0.954713\pi$
$968$	14.7740	+	23.5342i	0.474854	+	0.756418i
$969$	18.7221	+	9.93481i	0.601440	+	0.319152i
$970$	−0.549479	−	0.638684i	−0.0176427	−	0.0205069i
$971$	−28.7069	+	49.7218i	−0.921249	+	1.59565i	−0.123764	+	0.992312i	$0.539496\pi$
$971$	−28.7069	+	49.7218i	−0.921249	+	1.59565i	−0.797485	+	0.603338i	$0.793837\pi$
$972$	−26.1690	+	16.9464i	−0.839373	+	0.543557i
$973$	−24.7178	−	42.8125i	−0.792416	−	1.37250i
$974$	38.3341	−	7.24775i	1.22830	−	0.232233i
$975$	0.913572	−	1.74029i	0.0292577	−	0.0557340i
$976$	35.7179	+	11.0390i	1.14330	+	0.353351i
$977$		−	31.8377i		−	1.01858i	−0.860595	−	0.509289i	$-0.829908\pi$
$977$		−	31.8377i		−	1.01858i	0.860595	−	0.509289i	$-0.170092\pi$
$978$	−6.08115	+	1.40496i	−0.194454	+	0.0449256i
$979$	14.8627	−	8.58100i	0.475015	−	0.274250i
$980$	−0.787029	−	0.118847i	−0.0251407	−	0.00379642i
$981$	−14.8651	+	31.3134i	−0.474607	+	0.999759i
$982$	−5.02654	−	1.75964i	−0.160403	−	0.0561523i
$983$	−22.2451	+	38.5296i	−0.709508	+	1.22890i	0.255532	+	0.966801i	$0.417749\pi$
$983$	−22.2451	+	38.5296i	−0.709508	+	1.22890i	−0.965040	+	0.262103i	$0.915584\pi$
$984$	−1.14825	−	14.8487i	−0.0366050	−	0.473360i
$985$	−0.704222	+	1.21975i	−0.0224384	+	0.0388644i
$986$	−3.96179	−	20.9543i	−0.126169	−	0.667321i
$987$	−2.17428	+	1.37466i	−0.0692082	+	0.0437561i
$988$	−1.54242	−	1.24201i	−0.0490708	−	0.0395137i
$989$			50.9139i			1.61897i
$990$	−0.0773340	+	0.295025i	−0.00245783	+	0.00937652i
$991$	5.66131	+	3.26856i	0.179837	+	0.103829i	0.587216	−	0.809430i	$-0.300224\pi$
$991$	5.66131	+	3.26856i	0.179837	+	0.103829i	−0.407379	+	0.913259i	$0.633557\pi$
$992$	23.1673	−	31.3455i	0.735564	−	0.995222i
$993$	1.81320	+	45.0927i	0.0575402	+	1.43097i
$994$	19.2139	−	54.8860i	0.609428	−	1.74088i
$995$	0.0940021			0.00298007
$996$	−31.3260	+	13.7613i	−0.992603	+	0.436042i
$997$	−9.26164	−	16.0416i	−0.293319	−	0.508044i	0.681273	−	0.732029i	$-0.261427\pi$
$997$	−9.26164	−	16.0416i	−0.293319	−	0.508044i	−0.974592	+	0.223985i	$0.928093\pi$
$998$	7.88403	−	22.5213i	0.249565	−	0.712900i
$999$	9.31896	−	1.12903i	0.294839	−	0.0357209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.m.a.11.20	yes	72
3.2	odd	2	inner	228.2.m.a.11.17	yes	72
4.3	odd	2	inner	228.2.m.a.11.32	yes	72
12.11	even	2	inner	228.2.m.a.11.5	✓	72
19.7	even	3	inner	228.2.m.a.83.5	yes	72
57.26	odd	6	inner	228.2.m.a.83.32	yes	72
76.7	odd	6	inner	228.2.m.a.83.17	yes	72
228.83	even	6	inner	228.2.m.a.83.20	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.m.a.11.5	✓	72	12.11	even	2	inner
228.2.m.a.11.17	yes	72	3.2	odd	2	inner
228.2.m.a.11.20	yes	72	1.1	even	1	trivial
228.2.m.a.11.32	yes	72	4.3	odd	2	inner
228.2.m.a.83.5	yes	72	19.7	even	3	inner
228.2.m.a.83.17	yes	72	76.7	odd	6	inner
228.2.m.a.83.20	yes	72	228.83	even	6	inner
228.2.m.a.83.32	yes	72	57.26	odd	6	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.262728 + 1.38959i) q^{2} +(1.73065 - 0.0695904i) q^{3} +(-1.86195 + 0.730170i) q^{4} +(-0.0574154 - 0.0331488i) q^{5} +(0.551393 + 2.38662i) q^{6} +3.60595i q^{7} +(-1.50383 - 2.39552i) q^{8} +(2.99031 - 0.240874i) q^{9} +(0.0309788 - 0.0884932i) q^{10} -1.08432 q^{11} +(-3.17157 + 1.39324i) q^{12} +(0.113579 + 0.196724i) q^{13} +(-5.01081 + 0.947383i) q^{14} +(-0.101673 - 0.0533734i) q^{15} +(2.93370 - 2.71908i) q^{16} +(2.43120 + 1.40366i) q^{17} +(1.12036 + 4.09204i) q^{18} +(4.35886 + 0.0194115i) q^{19} +(0.131109 + 0.0197983i) q^{20} +(0.250939 + 6.24065i) q^{21} +(-0.284880 - 1.50676i) q^{22} +(-4.30600 - 7.45822i) q^{23} +(-2.76931 - 4.04116i) q^{24} +(-2.49780 - 4.32632i) q^{25} +(-0.243527 + 0.209513i) q^{26} +(5.15843 - 0.624965i) q^{27} +(-2.63296 - 6.71409i) q^{28} +(-4.65184 + 2.68574i) q^{29} +(0.0474552 - 0.155307i) q^{30} -6.89036i q^{31} +(4.54918 + 3.36228i) q^{32} +(-1.87657 + 0.0754579i) q^{33} +(-1.31177 + 3.74717i) q^{34} +(0.119533 - 0.207037i) q^{35} +(-5.39193 + 2.63193i) q^{36} +1.80655 q^{37} +(1.11822 + 6.06214i) q^{38} +(0.210255 + 0.332557i) q^{39} +(0.00693426 + 0.187390i) q^{40} +(2.63274 + 1.52002i) q^{41} +(-8.60604 + 1.98829i) q^{42} +(-5.11992 - 2.95599i) q^{43} +(2.01894 - 0.791735i) q^{44} +(-0.179675 - 0.0852954i) q^{45} +(9.23260 - 7.94308i) q^{46} +(0.205933 + 0.356687i) q^{47} +(4.88800 - 4.90994i) q^{48} -6.00287 q^{49} +(5.35559 - 4.60758i) q^{50} +(4.30525 + 2.26005i) q^{51} +(-0.355120 - 0.283358i) q^{52} +(-0.727053 + 0.419764i) q^{53} +(2.22371 + 7.00393i) q^{54} +(0.0622564 + 0.0359437i) q^{55} +(8.63812 - 5.42272i) q^{56} +(7.54501 - 0.269740i) q^{57} +(-4.95426 - 5.75856i) q^{58} +(4.44625 - 7.70114i) q^{59} +(0.228281 + 0.0251401i) q^{60} +(4.67311 + 8.09407i) q^{61} +(9.57482 - 1.81029i) q^{62} +(0.868578 + 10.7829i) q^{63} +(-3.47701 + 7.20489i) q^{64} -0.0150600i q^{65} +(-0.597884 - 2.58785i) q^{66} +(-5.00700 + 2.89079i) q^{67} +(-5.55168 - 0.838342i) q^{68} +(-7.97122 - 12.6079i) q^{69} +(0.319102 + 0.111708i) q^{70} +(-5.70164 + 9.87552i) q^{71} +(-5.07393 - 6.80112i) q^{72} +(7.27491 - 12.6005i) q^{73} +(0.474631 + 2.51037i) q^{74} +(-4.62390 - 7.31353i) q^{75} +(-8.13014 + 3.14656i) q^{76} -3.90999i q^{77} +(-0.406880 + 0.379542i) q^{78} +(3.33564 + 1.92583i) q^{79} +(-0.258574 + 0.0588682i) q^{80} +(8.88396 - 1.44058i) q^{81} +(-1.42051 + 4.05780i) q^{82} +9.87713 q^{83} +(-5.02397 - 11.4365i) q^{84} +(-0.0930590 - 0.161183i) q^{85} +(2.76248 - 7.89123i) q^{86} +(-7.86382 + 4.97181i) q^{87} +(1.63062 + 2.59750i) q^{88} +(-13.7070 + 7.91375i) q^{89} +(0.0713206 - 0.272084i) q^{90} +(-0.709378 + 0.409559i) q^{91} +(13.4633 + 10.7427i) q^{92} +(-0.479503 - 11.9248i) q^{93} +(-0.441546 + 0.379876i) q^{94} +(-0.249622 - 0.145605i) q^{95} +(8.10704 + 5.50236i) q^{96} +(4.49303 - 7.78215i) q^{97} +(-1.57712 - 8.34156i) q^{98} +(-3.24244 + 0.261183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 8 q^{10} - 10 q^{12} - 4 q^{16} - 22 q^{18} + 4 q^{21} - 6 q^{22} + 11 q^{24} + 16 q^{25} + 6 q^{28} - 60 q^{30} - 30 q^{33} - 20 q^{34} - 11 q^{36} - 8 q^{37} + 36 q^{40} + 8 q^{42} - 28 q^{45}+ \cdots - 16 q^{97}+O(q^{100}) \) 72 * q + 3 * q^6 - 8 * q^10 - 10 * q^12 - 4 * q^16 - 22 * q^18 + 4 * q^21 - 6 * q^22 + 11 * q^24 + 16 * q^25 + 6 * q^28 - 60 * q^30 - 30 * q^33 - 20 * q^34 - 11 * q^36 - 8 * q^37 + 36 * q^40 + 8 * q^42 - 28 * q^45 - 8 * q^46 - 23 * q^48 - 16 * q^49 + 6 * q^52 - 22 * q^54 - 6 * q^57 - 80 * q^58 - 14 * q^60 - 40 * q^61 + 48 * q^64 - 15 * q^66 + 4 * q^69 + 72 * q^70 + 15 * q^72 - 4 * q^73 + 12 * q^76 + 44 * q^78 + 4 * q^81 - 6 * q^82 + 56 * q^84 - 52 * q^85 - 44 * q^88 + 20 * q^90 + 4 * q^93 + 56 * q^94 - 86 * q^96 - 16 * q^97

Introduction

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