LMFDB - Embedded newform 300.2.w.a.127.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [300,2,Mod(67,300)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(300, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("300.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	300.127
Dual form			300.2.w.a.163.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25988 + 0.642429i) q^{2} +(-0.891007 + 0.453990i) q^{3} +(1.17457 - 1.61876i) q^{4} +(-2.20628 - 0.363753i) q^{5} +(0.830900 - 1.14438i) q^{6} +(1.56720 - 1.56720i) q^{7} +(-0.439875 + 2.79401i) q^{8} +(0.587785 - 0.809017i) q^{9} +(3.01333 - 0.959095i) q^{10} +(3.58185 + 4.92999i) q^{11} +(-0.311649 + 1.97557i) q^{12} +(-5.17848 + 0.820190i) q^{13} +(-0.967663 + 2.98129i) q^{14} +(2.13095 - 0.677525i) q^{15} +(-1.24077 - 3.80270i) q^{16} +(-1.47126 + 2.88752i) q^{17} +(-0.220800 + 1.39687i) q^{18} +(1.69688 + 5.22245i) q^{19} +(-3.18026 + 3.14419i) q^{20} +(-0.684892 + 2.10788i) q^{21} +(-7.67984 - 3.91009i) q^{22} +(-2.49745 - 0.395558i) q^{23} +(-0.876524 - 2.68918i) q^{24} +(4.73537 + 1.60509i) q^{25} +(5.99732 - 4.36014i) q^{26} +(-0.156434 + 0.987688i) q^{27} +(-0.696133 - 4.37771i) q^{28} +(-4.79694 - 1.55862i) q^{29} +(-2.24947 + 2.22258i) q^{30} +(-3.36051 + 1.09190i) q^{31} +(4.00617 + 3.99382i) q^{32} +(-5.42961 - 2.76653i) q^{33} +(-0.00141553 - 4.58309i) q^{34} +(-4.02776 + 2.88761i) q^{35} +(-0.619209 - 1.90173i) q^{36} +(1.85505 + 11.7124i) q^{37} +(-5.49291 - 5.48952i) q^{38} +(4.24170 - 3.08177i) q^{39} +(1.98682 - 6.00438i) q^{40} +(-0.572121 - 0.415670i) q^{41} +(-0.491285 - 3.09566i) q^{42} +(3.99658 + 3.99658i) q^{43} +(12.1876 - 0.00752853i) q^{44} +(-1.59110 + 1.57111i) q^{45} +(3.40060 - 1.10608i) q^{46} +(2.06893 + 4.06050i) q^{47} +(2.83192 + 2.82493i) q^{48} +2.08776i q^{49} +(-6.99712 + 1.01993i) q^{50} -3.24074i q^{51} +(-4.75480 + 9.34608i) q^{52} +(-1.32853 - 2.60739i) q^{53} +(-0.437431 - 1.34486i) q^{54} +(-6.10926 - 12.1799i) q^{55} +(3.68941 + 5.06815i) q^{56} +(-3.88287 - 3.88287i) q^{57} +(7.04484 - 1.11802i) q^{58} +(-3.73548 - 2.71399i) q^{59} +(1.40621 - 4.24530i) q^{60} +(7.77655 - 5.64999i) q^{61} +(3.53236 - 3.53454i) q^{62} +(-0.346715 - 2.18907i) q^{63} +(-7.61302 - 2.45803i) q^{64} +(11.7235 + 0.0741177i) q^{65} +(8.61793 - 0.00266174i) q^{66} +(2.30218 + 1.17302i) q^{67} +(2.94609 + 5.77321i) q^{68} +(2.40483 - 0.781376i) q^{69} +(3.21939 - 6.22558i) q^{70} +(6.04498 + 1.96413i) q^{71} +(2.00185 + 1.99815i) q^{72} +(2.57943 - 16.2859i) q^{73} +(-9.86149 - 13.5644i) q^{74} +(-4.94794 + 0.719669i) q^{75} +(10.4470 + 3.38730i) q^{76} +(13.3398 + 2.11281i) q^{77} +(-3.36419 + 6.60764i) q^{78} +(-1.05902 + 3.25934i) q^{79} +(1.35424 + 8.84116i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(0.987840 + 0.156146i) q^{82} +(-0.755975 + 1.48368i) q^{83} +(2.60770 + 3.58453i) q^{84} +(4.29637 - 5.83550i) q^{85} +(-7.60270 - 2.46767i) q^{86} +(4.98170 - 0.789024i) q^{87} +(-15.3500 + 7.83915i) q^{88} +(-2.75973 - 3.79844i) q^{89} +(0.995264 - 3.00157i) q^{90} +(-6.83031 + 9.40112i) q^{91} +(-3.57375 + 3.57817i) q^{92} +(2.49853 - 2.49853i) q^{93} +(-5.21517 - 3.78658i) q^{94} +(-1.84411 - 12.1395i) q^{95} +(-5.38268 - 1.73975i) q^{96} +(0.728754 - 0.371318i) q^{97} +(-1.34124 - 2.63032i) q^{98} +6.09380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−1.25988	+	0.642429i	−0.890866	+	0.454266i
$2$	−1.25988	+	0.642429i	−0.890866	+	0.454266i
$3$	−0.891007	+	0.453990i	−0.514423	+	0.262112i
$3$	−0.891007	+	0.453990i	−0.514423	+	0.262112i
$4$	1.17457	−	1.61876i	0.587285	−	0.809380i
$5$	−2.20628	−	0.363753i	−0.986680	−	0.162676i
$5$	−2.20628	−	0.363753i	−0.986680	−	0.162676i
$6$	0.830900	−	1.14438i	0.339214	−	0.467191i
$7$	1.56720	−	1.56720i	0.592346	−	0.592346i	−0.345918	−	0.938265i	$-0.612433\pi$
$7$	1.56720	−	1.56720i	0.592346	−	0.592346i	0.938265	+	0.345918i	$0.112433\pi$
$8$	−0.439875	+	2.79401i	−0.155519	+	0.987833i
$9$	0.587785	−	0.809017i	0.195928	−	0.269672i
$10$	3.01333	−	0.959095i	0.952897	−	0.303293i
$11$	3.58185	+	4.92999i	1.07997	+	1.48645i	0.859557	+	0.511040i	$0.170739\pi$
$11$	3.58185	+	4.92999i	1.07997	+	1.48645i	0.220410	+	0.975407i	$0.429261\pi$
$12$	−0.311649	+	1.97557i	−0.0899652	+	0.570298i
$13$	−5.17848	+	0.820190i	−1.43625	+	0.227480i	−0.825526	−	0.564363i	$-0.809122\pi$
$13$	−5.17848	+	0.820190i	−1.43625	+	0.227480i	−0.610724	+	0.791843i	$0.709122\pi$
$14$	−0.967663	+	2.98129i	−0.258619	+	0.796784i
$15$	2.13095	−	0.677525i	0.550210	−	0.174936i
$16$	−1.24077	−	3.80270i	−0.310192	−	0.950674i
$17$	−1.47126	+	2.88752i	−0.356834	+	0.700326i	−0.997733	−	0.0672996i	$-0.978562\pi$
$17$	−1.47126	+	2.88752i	−0.356834	+	0.700326i	0.640899	+	0.767625i	$0.278562\pi$
$18$	−0.220800	+	1.39687i	−0.0520431	+	0.329246i
$19$	1.69688	+	5.22245i	0.389290	+	1.19811i	0.933320	+	0.359047i	$0.116898\pi$
$19$	1.69688	+	5.22245i	0.389290	+	1.19811i	−0.544029	+	0.839066i	$0.683102\pi$
$20$	−3.18026	+	3.14419i	−0.711129	+	0.703062i
$21$	−0.684892	+	2.10788i	−0.149456	+	0.459977i
$22$	−7.67984	−	3.91009i	−1.63735	−	0.833634i
$23$	−2.49745	−	0.395558i	−0.520755	−	0.0824795i	−0.109477	−	0.993989i	$-0.534918\pi$
$23$	−2.49745	−	0.395558i	−0.520755	−	0.0824795i	−0.411278	+	0.911510i	$0.634918\pi$
$24$	−0.876524	−	2.68918i	−0.178920	−	0.548927i
$25$	4.73537	+	1.60509i	0.947073	+	0.321017i
$26$	5.99732	−	4.36014i	1.17617	−	0.855094i
$27$	−0.156434	+	0.987688i	−0.0301058	+	0.190081i
$28$	−0.696133	−	4.37771i	−0.131557	−	0.827309i
$29$	−4.79694	−	1.55862i	−0.890769	−	0.289428i	−0.172347	−	0.985036i	$-0.555135\pi$
$29$	−4.79694	−	1.55862i	−0.890769	−	0.289428i	−0.718422	+	0.695608i	$0.755135\pi$
$30$	−2.24947	+	2.22258i	−0.410696	+	0.405786i
$31$	−3.36051	+	1.09190i	−0.603566	+	0.196110i	−0.594830	−	0.803851i	$-0.702781\pi$
$31$	−3.36051	+	1.09190i	−0.603566	+	0.196110i	−0.00873571	+	0.999962i	$0.502781\pi$
$32$	4.00617	+	3.99382i	0.708198	+	0.706014i
$33$	−5.42961	−	2.76653i	−0.945175	−	0.481591i
$34$	−0.00141553	−	4.58309i	−0.000242762	−	0.785994i
$35$	−4.02776	+	2.88761i	−0.680816	+	0.488096i
$36$	−0.619209	−	1.90173i	−0.103201	−	0.316955i
$37$	1.85505	+	11.7124i	0.304969	+	1.92550i	0.373032	+	0.927818i	$0.378318\pi$
$37$	1.85505	+	11.7124i	0.304969	+	1.92550i	−0.0680633	+	0.997681i	$0.521682\pi$
$38$	−5.49291	−	5.48952i	−0.891067	−	0.890517i
$39$	4.24170	−	3.08177i	0.679215	−	0.493479i
$40$	1.98682	−	6.00438i	0.314144	−	0.949375i
$41$	−0.572121	−	0.415670i	−0.0893503	−	0.0649168i	0.542213	−	0.840241i	$-0.317587\pi$
$41$	−0.572121	−	0.415670i	−0.0893503	−	0.0649168i	−0.631564	+	0.775324i	$0.717587\pi$
$42$	−0.491285	−	3.09566i	−0.0758069	−	0.477671i
$43$	3.99658	+	3.99658i	0.609472	+	0.609472i	0.942808	−	0.333336i	$-0.108174\pi$
$43$	3.99658	+	3.99658i	0.609472	+	0.609472i	−0.333336	+	0.942808i	$0.608174\pi$
$44$	12.1876	−	0.00752853i	1.83735	−	0.00113497i
$45$	−1.59110	+	1.57111i	−0.237188	+	0.234207i
$46$	3.40060	−	1.10608i	0.501391	−	0.163083i
$47$	2.06893	+	4.06050i	0.301784	+	0.592285i	0.991245	−	0.132039i	$-0.0421523\pi$
$47$	2.06893	+	4.06050i	0.301784	+	0.592285i	−0.689460	+	0.724323i	$0.742152\pi$
$48$	2.83192	+	2.82493i	0.408752	+	0.407744i
$49$			2.08776i			0.298252i
$50$	−6.99712	+	1.01993i	−0.989543	+	0.144240i
$51$		−	3.24074i		−	0.453794i
$52$	−4.75480	+	9.34608i	−0.659372	+	1.29607i
$53$	−1.32853	−	2.60739i	−0.182488	−	0.358152i	0.781582	−	0.623803i	$-0.214413\pi$
$53$	−1.32853	−	2.60739i	−0.182488	−	0.358152i	−0.964069	+	0.265651i	$0.914413\pi$
$54$	−0.437431	−	1.34486i	−0.0595269	−	0.183013i
$55$	−6.10926	−	12.1799i	−0.823773	−	1.64233i
$56$	3.68941	+	5.06815i	0.493018	+	0.677260i
$57$	−3.88287	−	3.88287i	−0.514299	−	0.514299i
$58$	7.04484	−	1.11802i	0.925033	−	0.146804i
$59$	−3.73548	−	2.71399i	−0.486318	−	0.353331i	0.317448	−	0.948276i	$-0.397174\pi$
$59$	−3.73548	−	2.71399i	−0.486318	−	0.353331i	−0.803767	+	0.594945i	$0.797174\pi$
$60$	1.40621	−	4.24530i	0.181540	−	0.548066i
$61$	7.77655	−	5.64999i	0.995685	−	0.723407i	0.0345260	−	0.999404i	$-0.489008\pi$
$61$	7.77655	−	5.64999i	0.995685	−	0.723407i	0.961159	+	0.275997i	$0.0890078\pi$
$62$	3.53236	−	3.53454i	0.448610	−	0.448887i
$63$	−0.346715	−	2.18907i	−0.0436819	−	0.275797i
$64$	−7.61302	−	2.45803i	−0.951628	−	0.307254i
$65$	11.7235	+	0.0741177i	1.45412	+	0.00919317i
$66$	8.61793	−	0.00266174i	1.06079	−	0.000327637i
$67$	2.30218	+	1.17302i	0.281257	+	0.143307i	0.588929	−	0.808185i	$-0.299550\pi$
$67$	2.30218	+	1.17302i	0.281257	+	0.143307i	−0.307672	+	0.951492i	$0.599550\pi$
$68$	2.94609	+	5.77321i	0.357266	+	0.700105i
$69$	2.40483	−	0.781376i	0.289507	−	0.0940666i
$70$	3.21939	−	6.22558i	0.384791	−	0.744099i
$71$	6.04498	+	1.96413i	0.717407	+	0.233100i	0.644898	−	0.764268i	$-0.276900\pi$
$71$	6.04498	+	1.96413i	0.717407	+	0.233100i	0.0725082	+	0.997368i	$0.476900\pi$
$72$	2.00185	+	1.99815i	0.235921	+	0.235484i
$73$	2.57943	−	16.2859i	0.301899	−	1.90612i	−0.108293	−	0.994119i	$-0.534538\pi$
$73$	2.57943	−	16.2859i	0.301899	−	1.90612i	0.410192	−	0.911999i	$-0.365462\pi$
$74$	−9.86149	−	13.5644i	−1.14637	−	1.57683i
$75$	−4.94794	+	0.719669i	−0.571338	+	0.0831003i
$76$	10.4470	+	3.38730i	1.19835	+	0.388550i
$77$	13.3398	+	2.11281i	1.52021	+	0.240777i
$78$	−3.36419	+	6.60764i	−0.380919	+	0.748168i
$79$	−1.05902	+	3.25934i	−0.119150	+	0.366705i	−0.992790	−	0.119868i	$-0.961753\pi$
$79$	−1.05902	+	3.25934i	−0.119150	+	0.366705i	0.873640	+	0.486572i	$0.161753\pi$
$80$	1.35424	+	8.84116i	0.151408	+	0.988471i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	0.987840	+	0.156146i	0.109089	+	0.0172434i
$83$	−0.755975	+	1.48368i	−0.0829791	+	0.162856i	−0.928767	−	0.370663i	$-0.879131\pi$
$83$	−0.755975	+	1.48368i	−0.0829791	+	0.162856i	0.845788	+	0.533518i	$0.179131\pi$
$84$	2.60770	+	3.58453i	0.284523	+	0.391104i
$85$	4.29637	−	5.83550i	0.466006	−	0.632949i
$86$	−7.60270	−	2.46767i	−0.819820	−	0.266096i
$87$	4.98170	−	0.789024i	0.534094	−	0.0845922i
$88$	−15.3500	+	7.83915i	−1.63632	+	0.835656i
$89$	−2.75973	−	3.79844i	−0.292531	−	0.402634i	0.637303	−	0.770613i	$-0.280050\pi$
$89$	−2.75973	−	3.79844i	−0.292531	−	0.402634i	−0.929834	+	0.367979i	$0.880050\pi$
$90$	0.995264	−	3.00157i	0.104910	−	0.316394i
$91$	−6.83031	+	9.40112i	−0.716011	+	0.985505i
$92$	−3.57375	+	3.57817i	−0.372589	+	0.373050i
$93$	2.49853	−	2.49853i	0.259085	−	0.259085i
$94$	−5.21517	−	3.78658i	−0.537904	−	0.390556i
$95$	−1.84411	−	12.1395i	−0.189201	−	1.24548i
$96$	−5.38268	−	1.73975i	−0.549368	−	0.177563i
$97$	0.728754	−	0.371318i	0.0739937	−	0.0377017i	−0.416602	−	0.909089i	$-0.636779\pi$
$97$	0.728754	−	0.371318i	0.0739937	−	0.0377017i	0.490596	+	0.871387i	$0.336779\pi$
$98$	−1.34124	−	2.63032i	−0.135486	−	0.265702i
$99$	6.09380			0.612450
$100$	8.16027	−	5.78013i	0.816027	−	0.578013i
$101$	−2.38257			−0.237075			−0.118537	−	0.992950i	$-0.537821\pi$
$101$	−2.38257			−0.237075			−0.118537	+	0.992950i	$0.537821\pi$
$102$	2.08194	+	4.08292i	0.206143	+	0.404269i
$103$	−8.92572	+	4.54788i	−0.879477	+	0.448116i	−0.834587	−	0.550876i	$-0.814294\pi$
$103$	−8.92572	+	4.54788i	−0.879477	+	0.448116i	−0.0448899	+	0.998992i	$0.514294\pi$
$104$	−0.0137407	−	14.8295i	−0.00134739	−	1.45415i
$105$	2.27781	−	4.40145i	0.222292	−	0.429537i
$106$	3.34884	+	2.43150i	0.325268	+	0.236168i
$107$	10.1918	−	10.1918i	0.985278	−	0.985278i	−0.0146155	−	0.999893i	$-0.504652\pi$
$107$	10.1918	−	10.1918i	0.985278	−	0.985278i	0.999893	+	0.0146155i	$0.00465243\pi$
$108$	1.41509	+	1.41334i	0.136167	+	0.135999i
$109$	−4.95925	+	6.82582i	−0.475010	+	0.653795i	−0.977536	−	0.210767i	$-0.932404\pi$
$109$	−4.95925	+	6.82582i	−0.475010	+	0.653795i	0.502526	+	0.864562i	$0.332404\pi$
$110$	15.5216	+	11.4203i	1.47993	+	1.08889i
$111$	−6.97016	−	9.59361i	−0.661579	−	0.910585i
$112$	−7.90412	−	4.01506i	−0.746869	−	0.379387i
$113$	−8.07749	+	1.27935i	−0.759866	+	0.120351i	−0.524331	−	0.851515i	$-0.675684\pi$
$113$	−8.07749	+	1.27935i	−0.759866	+	0.120351i	−0.235536	+	0.971866i	$0.575684\pi$
$114$	7.38640	+	2.39747i	0.691800	+	0.224543i
$115$	5.36620	+	1.78117i	0.500401	+	0.166095i
$116$	−8.15737	+	5.93438i	−0.757393	+	0.550993i
$117$	−2.38028	+	4.67157i	−0.220057	+	0.431887i
$118$	6.44978	+	1.01950i	0.593751	+	0.0938529i
$119$	2.21955	+	6.83108i	0.203466	+	0.626204i
$120$	0.955660	+	6.25194i	0.0872395	+	0.570721i
$121$	−8.07597	+	24.8553i	−0.734179	+	2.25957i
$122$	−6.16776	+	12.1142i	−0.558403	+	1.09676i
$123$	0.698474	+	0.110627i	0.0629793	+	0.00997494i
$124$	−2.17964	+	6.72237i	−0.195738	+	0.603687i
$125$	−9.86370	−	5.26378i	−0.882236	−	0.470807i
$126$	1.84314	+	2.53522i	0.164200	+	0.225855i
$127$	2.15193	−	13.5867i	0.190953	−	1.20563i	−0.686920	−	0.726733i	$-0.741038\pi$
$127$	2.15193	−	13.5867i	0.190953	−	1.20563i	0.877873	−	0.478894i	$-0.158962\pi$
$128$	11.1706	−	1.79401i	0.987348	−	0.158570i
$129$	−5.37538	−	1.74657i	−0.473276	−	0.153777i
$130$	−14.8178	+	7.43815i	−1.29961	+	0.652369i
$131$	−8.55782	+	2.78060i	−0.747700	+	0.242943i	−0.657991	−	0.753026i	$-0.728594\pi$
$131$	−8.55782	+	2.78060i	−0.747700	+	0.242943i	−0.0897088	+	0.995968i	$0.528594\pi$
$132$	−10.8558	+	5.53976i	−0.944877	+	0.482174i
$133$	10.8440	+	5.52528i	0.940292	+	0.479103i
$134$	−3.65405	+	0.00112859i	−0.315662	+	9.74953e-5i
$135$	0.704414	−	2.12222i	0.0606263	−	0.182651i
$136$	−7.42059	−	5.38087i	−0.636310	−	0.461406i
$137$	−0.597042	−	3.76957i	−0.0510087	−	0.322056i	−0.999978	−	0.00668676i	$-0.997872\pi$
$137$	−0.597042	−	3.76957i	−0.0510087	−	0.322056i	0.948969	−	0.315370i	$-0.102128\pi$
$138$	−2.52780	+	2.52937i	−0.215181	+	0.215314i
$139$	−4.30227	+	3.12579i	−0.364914	+	0.265126i	−0.755099	−	0.655611i	$-0.772411\pi$
$139$	−4.30227	+	3.12579i	−0.364914	+	0.265126i	0.390185	+	0.920737i	$0.372411\pi$
$140$	−0.0565401	+	9.91169i	−0.00477851	+	0.837690i
$141$	−3.68686	−	2.67866i	−0.310489	−	0.225584i
$142$	−8.87773	+	1.40891i	−0.745003	+	0.118233i
$143$	−22.5920	−	22.5920i	−1.88924	−	1.88924i
$144$	−3.80575	−	1.23137i	−0.317146	−	0.102614i
$145$	10.0164	+	5.18366i	0.831821	+	0.430479i
$146$	7.21276	+	22.1753i	0.596932	+	1.83524i
$147$	−0.947824	−	1.86021i	−0.0781752	−	0.153428i
$148$	21.1384	+	10.7541i	1.73756	+	0.883982i
$149$		−	3.08620i		−	0.252832i	−0.991977	−	0.126416i	$-0.959653\pi$
$149$		−	3.08620i		−	0.252832i	0.991977	−	0.126416i	$-0.0403474\pi$
$150$	5.77145	−	4.08539i	0.471237	−	0.333571i
$151$			14.6630i			1.19326i	0.802518	+	0.596628i	$0.203493\pi$
$151$			14.6630i			1.19326i	−0.802518	+	0.596628i	$0.796507\pi$
$152$	−15.3380	+	2.44387i	−1.24408	+	0.198224i
$153$	1.47126	+	2.88752i	0.118945	+	0.233442i
$154$	−18.1638	+	5.90796i	−1.46368	+	0.476077i
$155$	7.81142	−	1.18663i	0.627429	−	0.0953128i
$156$	−0.00647745	−	10.4861i	−0.000518611	−	0.839556i
$157$	−7.88169	−	7.88169i	−0.629027	−	0.629027i	0.318796	−	0.947823i	$-0.396722\pi$
$157$	−7.88169	−	7.88169i	−0.629027	−	0.629027i	−0.947823	+	0.318796i	$0.896722\pi$
$158$	−0.759656	−	4.78671i	−0.0604350	−	0.380810i
$159$	2.36746	+	1.72006i	0.187752	+	0.136410i
$160$	−7.38598	−	10.2688i	−0.583913	−	0.811816i
$161$	−4.53393	+	3.29409i	−0.357324	+	0.259611i
$162$	1.00031	+	0.999691i	0.0785917	+	0.0785432i
$163$	0.428035	+	2.70250i	0.0335263	+	0.211676i	0.998764	−	0.0496955i	$-0.0158251\pi$
$163$	0.428035	+	2.70250i	0.0335263	+	0.211676i	−0.965238	+	0.261372i	$0.915825\pi$
$164$	−1.34487	+	0.437893i	−0.105017	+	0.0341937i
$165$	10.9729	+	8.07878i	0.854242	+	0.628932i
$166$	−0.000727340	−	2.35492i	−5.64526e−5	−	0.182777i
$167$	14.5757	+	7.42667i	1.12790	+	0.574693i	0.915431	−	0.402475i	$-0.131850\pi$
$167$	14.5757	+	7.42667i	1.12790	+	0.574693i	0.212468	+	0.977168i	$0.431850\pi$
$168$	−5.58818	−	2.84080i	−0.431137	−	0.219173i
$169$	13.7802	−	4.47745i	1.06001	−	0.344419i
$170$	−1.66399	+	10.1121i	−0.127622	+	0.775563i
$171$	5.22245	+	1.69688i	0.399371	+	0.129763i
$172$	11.1638	−	1.77524i	0.851229	−	0.135360i
$173$	−1.78038	+	11.2409i	−0.135360	+	0.854627i	0.822787	+	0.568350i	$0.192418\pi$
$173$	−1.78038	+	11.2409i	−0.135360	+	0.854627i	−0.958147	+	0.286277i	$0.907582\pi$
$174$	−5.76943	+	4.19446i	−0.437379	+	0.317981i
$175$	9.93676	−	4.90578i	0.751149	−	0.370842i
$176$	14.3030	−	19.7376i	1.07813	−	1.48778i
$177$	4.56046	+	0.722306i	0.342785	+	0.0542919i
$178$	5.91714	+	3.01263i	0.443508	+	0.225806i
$179$	3.50223	−	10.7788i	0.261769	−	0.805642i	−0.730651	−	0.682751i	$-0.760783\pi$
$179$	3.50223	−	10.7788i	0.261769	−	0.805642i	0.992420	−	0.122891i	$-0.0392166\pi$
$180$	0.674389	+	4.42100i	0.0502660	+	0.329522i
$181$	−2.54239	−	7.82467i	−0.188974	−	0.581603i	0.811020	−	0.585019i	$-0.198913\pi$
$181$	−2.54239	−	7.82467i	−0.188974	−	0.581603i	−0.999994	+	0.00341549i	$0.998913\pi$
$182$	2.56579	−	16.2322i	0.190189	−	1.20321i
$183$	−4.36391	+	8.56466i	−0.322590	+	0.633118i
$184$	2.20376	−	6.80392i	0.162463	−	0.501592i
$185$	0.167635	−	26.5155i	0.0123248	−	1.94946i
$186$	−1.54271	+	4.75296i	−0.113117	+	0.348504i
$187$	−19.5053	+	3.08933i	−1.42637	+	0.225914i
$188$	9.00308	+	1.42025i	0.656617	+	0.103582i
$189$	1.30274	+	1.79307i	0.0947605	+	0.130427i
$190$	10.1221	+	14.1095i	0.734333	+	1.02361i
$191$	11.9137	−	16.3977i	0.862041	−	1.18650i	−0.119037	−	0.992890i	$-0.537981\pi$
$191$	11.9137	−	16.3977i	0.862041	−	1.18650i	0.981079	−	0.193609i	$-0.0620192\pi$
$192$	7.89917	−	1.26612i	0.570074	−	0.0913741i
$193$	1.12084	−	1.12084i	0.0806800	−	0.0806800i	−0.665615	−	0.746295i	$-0.731831\pi$
$193$	1.12084	−	1.12084i	0.0806800	−	0.0806800i	0.746295	+	0.665615i	$0.231831\pi$
$194$	−0.679593	+	0.935987i	−0.0487919	+	0.0672000i
$195$	−10.4794	+	5.25633i	−0.750445	+	0.376414i
$196$	3.37959	+	2.45223i	0.241399	+	0.175159i
$197$	−2.63812	+	1.34419i	−0.187958	+	0.0957695i	−0.545437	−	0.838152i	$-0.683636\pi$
$197$	−2.63812	+	1.34419i	−0.187958	+	0.0957695i	0.357479	+	0.933921i	$0.383636\pi$
$198$	−7.67743	+	3.91483i	−0.545611	+	0.278215i
$199$	−5.66665			−0.401698			−0.200849	−	0.979622i	$-0.564370\pi$
$199$	−5.66665			−0.401698			−0.200849	+	0.979622i	$0.564370\pi$
$200$	−6.56760	+	12.5246i	−0.464399	+	0.885626i
$201$	−2.58380			−0.182247
$202$	3.00174	−	1.53063i	0.211202	−	0.107695i
$203$	−9.96043	+	5.07510i	−0.699085	+	0.356202i
$204$	−5.24597	−	3.80647i	−0.367292	−	0.266506i
$205$	1.11106	+	1.12520i	0.0775998	+	0.0785872i
$206$	8.32360	−	11.4639i	0.579933	−	0.798727i
$207$	−1.78798	+	1.78798i	−0.124273	+	0.124273i
$208$	9.54422	+	18.6745i	0.661772	+	1.29484i
$209$	−19.6687	+	27.0716i	−1.36051	+	1.87258i
$210$	−0.0421446	+	7.00861i	−0.00290825	+	0.483640i
$211$	−1.79030	−	2.46414i	−0.123250	−	0.169638i	0.742934	−	0.669365i	$-0.233434\pi$
$211$	−1.79030	−	2.46414i	−0.123250	−	0.169638i	−0.866183	+	0.499727i	$0.833434\pi$
$212$	−5.78119	−	0.911990i	−0.397054	−	0.0626357i
$213$	−6.27781	+	0.994307i	−0.430148	+	0.0681288i
$214$	−6.29289	+	19.3879i	−0.430173	+	1.32533i
$215$	−7.36381	−	10.2713i	−0.502208	−	0.700500i
$216$	−2.69080	−	0.871539i	−0.183086	−	0.0593007i
$217$	−3.55538	+	6.97782i	−0.241355	+	0.473685i
$218$	1.86293	−	11.7856i	0.126174	−	0.798225i
$219$	5.09535	+	15.6819i	0.344312	+	1.05968i
$220$	−26.8920	−	4.41667i	−1.81306	−	0.297772i
$221$	5.25059	−	16.1597i	0.353193	−	1.08702i
$222$	14.9447	+	7.60891i	1.00303	+	0.510677i
$223$	12.2309	+	1.93719i	0.819043	+	0.129724i	0.551876	−	0.833926i	$-0.313912\pi$
$223$	12.2309	+	1.93719i	0.819043	+	0.129724i	0.267168	+	0.963650i	$0.413912\pi$
$224$	12.5376	−	0.0193618i	0.837703	−	0.00129367i
$225$	4.08192	−	2.88755i	0.272128	−	0.192503i
$226$	9.35474	−	6.80103i	0.622268	−	0.452398i
$227$	0.153858	−	0.971418i	0.0102119	−	0.0644753i	−0.982056	−	0.188589i	$-0.939609\pi$
$227$	0.153858	−	0.971418i	0.0102119	−	0.0644753i	0.992268	+	0.124113i	$0.0396087\pi$
$228$	−10.8461	+	1.72473i	−0.718304	+	0.114223i
$229$	4.78404	+	1.55443i	0.316138	+	0.102720i	0.462788	−	0.886469i	$-0.346849\pi$
$229$	4.78404	+	1.55443i	0.316138	+	0.102720i	−0.146650	+	0.989188i	$0.546849\pi$
$230$	−7.90502	+	1.20335i	−0.521242	+	0.0793466i
$231$	−12.8450	+	4.17359i	−0.845139	+	0.274602i
$232$	6.46486	−	12.7171i	0.424439	−	0.834919i
$233$	24.1337	+	12.2967i	1.58105	+	0.805584i	0.999966	−	0.00826064i	$-0.00262947\pi$
$233$	24.1337	+	12.2967i	1.58105	+	0.805584i	0.581082	+	0.813845i	$0.302629\pi$
$234$	−0.00229012	−	7.41476i	−0.000149710	−	0.484718i
$235$	−3.08762	−	9.71119i	−0.201414	−	0.633488i
$236$	−8.78088	+	2.85908i	−0.571587	+	0.186110i
$237$	−0.536113	−	3.38488i	−0.0348243	−	0.219872i
$238$	−7.18484	−	7.18041i	−0.465724	−	0.465437i
$239$	9.19015	−	6.67704i	0.594462	−	0.431902i	−0.249447	−	0.968388i	$-0.580249\pi$
$239$	9.19015	−	6.67704i	0.594462	−	0.431902i	0.843909	+	0.536487i	$0.180249\pi$
$240$	−5.22044	−	7.26272i	−0.336978	−	0.468806i
$241$	−14.5161	−	10.5466i	−0.935064	−	0.679364i	0.0121631	−	0.999926i	$-0.496128\pi$
$241$	−14.5161	−	10.5466i	−0.935064	−	0.679364i	−0.947228	+	0.320562i	$0.896128\pi$
$242$	−5.79303	−	36.5028i	−0.372390	−	2.34649i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−0.0118755	−	19.2247i	−0.000760249	−	1.23073i
$245$	0.759431	−	4.60620i	0.0485183	−	0.294279i
$246$	−0.951061	+	0.309343i	−0.0606374	+	0.0197230i
$247$	−13.0706	−	25.6526i	−0.831665	−	1.63223i
$248$	−1.57257	−	9.86961i	−0.0998582	−	0.626721i
$249$		−	1.66518i		−	0.105526i
$250$	15.8086	+	0.294980i	0.999826	+	0.0186562i
$251$			16.8452i			1.06326i	0.846977	+	0.531630i	$0.178420\pi$
$251$			16.8452i			1.06326i	−0.846977	+	0.531630i	$0.821580\pi$
$252$	−3.95082	−	2.00997i	−0.248878	−	0.126616i
$253$	−6.99540	−	13.7292i	−0.439797	−	0.863150i
$254$	6.01735	+	18.5000i	0.377562	+	1.16080i
$255$	−1.17883	+	7.14998i	−0.0738211	+	0.447749i
$256$	−12.9210	+	9.43652i	−0.807562	+	0.589782i
$257$	18.4325	+	18.4325i	1.14979	+	1.14979i	0.986594	+	0.163196i	$0.0521802\pi$
$257$	18.4325	+	18.4325i	1.14979	+	1.14979i	0.163196	+	0.986594i	$0.447820\pi$
$258$	7.89436	−	1.25284i	0.491481	−	0.0779986i
$259$	21.2629	+	15.4484i	1.32121	+	0.959915i
$260$	13.8901	−	18.8905i	0.861427	−	1.17154i
$261$	−4.08052	+	2.96467i	−0.252578	+	0.183508i
$262$	8.99544	−	9.00100i	0.555740	−	0.556084i
$263$	3.14127	+	19.8332i	0.193699	+	1.22297i	0.872489	+	0.488634i	$0.162505\pi$
$263$	3.14127	+	19.8332i	0.193699	+	1.22297i	−0.678790	+	0.734333i	$0.737495\pi$
$264$	10.1181	−	13.9535i	0.622724	−	0.858778i
$265$	1.98267	+	6.23589i	0.121794	+	0.383068i
$266$	−17.2117	+	0.00531600i	−1.05531	+	0.000325945i
$267$	4.18339	+	2.13154i	0.256019	+	0.130448i
$268$	4.60292	−	2.34889i	0.281168	−	0.143481i
$269$	−9.32155	+	3.02875i	−0.568345	+	0.184666i	−0.579072	−	0.815276i	$-0.696585\pi$
$269$	−9.32155	+	3.02875i	−0.568345	+	0.184666i	0.0107278	+	0.999942i	$0.496585\pi$
$270$	0.475899	+	3.12626i	0.0289623	+	0.190258i
$271$	19.1339	+	6.21699i	1.16230	+	0.377655i	0.825765	−	0.564014i	$-0.190744\pi$
$271$	19.1339	+	6.21699i	1.16230	+	0.377655i	0.336539	+	0.941670i	$0.390744\pi$
$272$	12.8058	+	2.01203i	0.776468	+	0.121997i
$273$	1.81783	−	11.4774i	0.110020	−	0.694641i
$274$	3.17388	+	4.36563i	0.191741	+	0.263738i
$275$	9.04830	+	29.0945i	0.545633	+	1.75446i
$276$	1.55978	−	4.81062i	0.0938877	−	0.289565i
$277$	−3.98677	−	0.631442i	−0.239542	−	0.0379397i	0.0355092	−	0.999369i	$-0.488695\pi$
$277$	−3.98677	−	0.631442i	−0.239542	−	0.0379397i	−0.275051	+	0.961430i	$0.588695\pi$
$278$	3.41223	−	6.70200i	0.204652	−	0.401960i
$279$	−1.09190	+	3.36051i	−0.0653701	+	0.201189i
$280$	−6.29632	−	12.5238i	−0.376277	−	0.748441i
$281$	−7.18206	−	22.1041i	−0.428446	−	1.31862i	−0.899656	−	0.436600i	$-0.856183\pi$
$281$	−7.18206	−	22.1041i	−0.428446	−	1.31862i	0.471210	−	0.882021i	$-0.343817\pi$
$282$	6.36583	+	1.00623i	0.379079	+	0.0599203i
$283$	7.42602	−	14.5744i	0.441431	−	0.866357i	−0.557905	−	0.829905i	$-0.688395\pi$
$283$	7.42602	−	14.5744i	0.441431	−	0.866357i	0.999335	−	0.0364517i	$-0.0116055\pi$
$284$	10.2797	−	7.47835i	0.609989	−	0.443759i
$285$	7.15431	+	9.97912i	0.423785	+	0.591112i
$286$	42.9769	+	13.9494i	2.54128	+	0.824843i
$287$	−1.54807	+	0.245190i	−0.0913796	+	0.0144731i
$288$	5.58584	−	0.893554i	0.329149	−	0.0526532i
$289$	3.81921	+	5.25670i	0.224660	+	0.309217i
$290$	−15.9496	−	0.0959091i	−0.936593	−	0.00563198i
$291$	−0.480749	+	0.661694i	−0.0281820	+	0.0387892i
$292$	−23.3332	−	23.3044i	−1.36547	−	1.36379i
$293$	10.4276	−	10.4276i	0.609185	−	0.609185i	−0.333548	−	0.942733i	$-0.608246\pi$
$293$	10.4276	−	10.4276i	0.609185	−	0.609185i	0.942733	+	0.333548i	$0.108246\pi$
$294$	2.38919	+	1.73472i	0.139341	+	0.101171i
$295$	7.25431	+	7.34662i	0.422362	+	0.427737i
$296$	−33.5405	+	0.0310780i	−1.94950	+	0.00180637i
$297$	−5.42961	+	2.76653i	−0.315058	+	0.160530i
$298$	1.98267	+	3.88823i	0.114853	+	0.225239i
$299$	13.2574			0.766697
$300$	−4.64673	+	8.85482i	−0.268279	+	0.511233i
$301$	12.5269			0.722037
$302$	−9.41992	−	18.4735i	−0.542055	−	1.06303i
$303$	2.12289	−	1.08167i	0.121957	−	0.0621401i
$304$	17.7540	−	12.9326i	1.01826	−	0.741733i
$305$	−19.2125	+	9.63673i	−1.10010	+	0.551798i
$306$	−3.70863	−	2.69273i	−0.212008	−	0.153933i
$307$	−0.708332	+	0.708332i	−0.0404266	+	0.0404266i	−0.727031	−	0.686605i	$-0.759100\pi$
$307$	−0.708332	+	0.708332i	−0.0404266	+	0.0404266i	0.686605	+	0.727031i	$0.259100\pi$
$308$	19.0886	−	19.1122i	1.08767	−	1.08902i
$309$	5.88818	−	8.10438i	0.334967	−	0.461042i
$310$	−9.07909	+	6.51329i	−0.515658	+	0.369930i
$311$	1.70477	+	2.34642i	0.0966688	+	0.133053i	0.854611	−	0.519268i	$-0.173795\pi$
$311$	1.70477	+	2.34642i	0.0966688	+	0.133053i	−0.757943	+	0.652321i	$0.773795\pi$
$312$	6.74470	+	13.2070i	0.381844	+	0.747697i
$313$	−4.23903	+	0.671396i	−0.239604	+	0.0379496i	−0.275081	−	0.961421i	$-0.588705\pi$
$313$	−4.23903	+	0.671396i	−0.239604	+	0.0379496i	0.0354774	+	0.999370i	$0.488705\pi$
$314$	14.9934	+	4.86652i	0.846125	+	0.274634i
$315$	−0.0313314	+	4.95583i	−0.00176532	+	0.279229i
$316$	4.03219	+	5.54263i	0.226829	+	0.311798i
$317$	3.98043	−	7.81203i	0.223563	−	0.438767i	−0.751794	−	0.659398i	$-0.770811\pi$
$317$	3.98043	−	7.81203i	0.223563	−	0.438767i	0.975358	+	0.220630i	$0.0708114\pi$
$318$	−4.08772	−	0.646137i	−0.229228	−	0.0362335i
$319$	−9.49791	−	29.2316i	−0.531781	−	1.63665i
$320$	15.9024	+	8.19238i	0.888969	+	0.457968i
$321$	−4.45398	+	13.7079i	−0.248597	+	0.765102i
$322$	3.59597	−	7.06287i	0.200395	−	0.393598i
$323$	−17.5765	−	2.78384i	−0.977981	−	0.154897i
$324$	−1.90249	−	0.616859i	−0.105694	−	0.0342699i
$325$	−25.8385	−	4.42800i	−1.43326	−	0.245621i
$326$	−2.27544	−	3.12984i	−0.126025	−	0.173346i
$327$	1.31987	−	8.33330i	0.0729887	−	0.460833i
$328$	1.41305	−	1.41567i	0.0780227	−	0.0781674i
$329$	9.60605	+	3.12119i	0.529598	+	0.172077i
$330$	−19.0146	−	3.12893i	−1.04672	−	0.172242i
$331$	−15.1358	+	4.91791i	−0.831938	+	0.270313i	−0.693861	−	0.720109i	$-0.744092\pi$
$331$	−15.1358	+	4.91791i	−0.831938	+	0.270313i	−0.138076	+	0.990422i	$0.544092\pi$
$332$	1.51378	+	2.96644i	0.0830796	+	0.162804i
$333$	10.5659	+	5.38358i	0.579006	+	0.295018i
$334$	−23.1346	+	0.00714537i	−1.26587	+	0.000390977i
$335$	−4.65258	−	3.42545i	−0.254198	−	0.187152i
$336$	8.86542	−	0.0109527i	0.483648	−	0.000597519i
$337$	−4.18546	−	26.4260i	−0.227997	−	1.43951i	−0.790370	−	0.612630i	$-0.790112\pi$
$337$	−4.18546	−	26.4260i	−0.227997	−	1.43951i	0.562373	−	0.826883i	$-0.309888\pi$
$338$	−14.4849	+	14.4938i	−0.787872	+	0.788359i
$339$	6.61628	−	4.80701i	0.359347	−	0.261081i
$340$	−4.39989	−	13.8090i	−0.238617	−	0.748898i
$341$	−17.4199	−	12.6563i	−0.943339	−	0.685376i
$342$	−7.66976	+	1.21720i	−0.414733	+	0.0658186i
$343$	14.2423	+	14.2423i	0.769015	+	0.769015i
$344$	−12.9245	+	9.40849i	−0.696841	+	0.507272i
$345$	−5.58996	+	0.849171i	−0.300953	+	0.0457178i
$346$	−4.97840	−	15.3059i	−0.267640	−	0.822848i
$347$	6.97585	+	13.6909i	0.374483	+	0.734965i	0.998937	−	0.0460972i	$-0.0146784\pi$
$347$	6.97585	+	13.6909i	0.374483	+	0.734965i	−0.624454	+	0.781062i	$0.714678\pi$
$348$	4.57412	−	8.99094i	0.245199	−	0.481965i
$349$		−	2.51038i		−	0.134378i	−0.997740	−	0.0671888i	$-0.978597\pi$
$349$		−	2.51038i		−	0.134378i	0.997740	−	0.0671888i	$-0.0214030\pi$
$350$	−9.36747	+	12.5643i	−0.500712	+	0.671592i
$351$		−	5.24303i		−	0.279852i
$352$	−5.33998	+	34.0556i	−0.284622	+	1.81517i
$353$	2.70770	+	5.31417i	0.144116	+	0.282845i	0.951770	−	0.306813i	$-0.0992627\pi$
$353$	2.70770	+	5.31417i	0.144116	+	0.282845i	−0.807653	+	0.589658i	$0.799263\pi$
$354$	−6.20965	+	2.01976i	−0.330039	+	0.107349i
$355$	−12.6225	−	6.53231i	−0.669931	−	0.346699i
$356$	−9.39026	+	0.00580056i	−0.497683	+	0.000307429i
$357$	−5.07888	−	5.07888i	−0.268803	−	0.268803i
$358$	2.51221	+	15.8298i	0.132774	+	0.836632i
$359$	−16.8314	−	12.2287i	−0.888326	−	0.645407i	0.0471147	−	0.998889i	$-0.484997\pi$
$359$	−16.8314	−	12.2287i	−0.888326	−	0.645407i	−0.935441	+	0.353483i	$0.884997\pi$
$360$	−3.68982	−	5.13666i	−0.194471	−	0.270726i
$361$	−9.02329	+	6.55581i	−0.474910	+	0.345042i
$362$	8.22989	+	8.22480i	0.432553	+	0.432286i
$363$	−4.08832	−	25.8126i	−0.214581	−	1.35481i
$364$	7.19547	+	22.0989i	0.377145	+	1.15830i
$365$	−11.6150	+	34.9930i	−0.607957	+	1.83162i
$366$	−0.00419861	−	13.5939i	−0.000219465	−	0.710565i
$367$	29.2608	+	14.9091i	1.52740	+	0.778249i	0.997558	−	0.0698470i	$-0.0222511\pi$
$367$	29.2608	+	14.9091i	1.52740	+	0.778249i	0.529842	+	0.848096i	$0.322251\pi$
$368$	1.59457	+	9.98785i	0.0831228	+	0.520653i
$369$	−0.672569	+	0.218531i	−0.0350125	+	0.0113763i
$370$	16.8232	+	33.5140i	0.874594	+	1.74231i
$371$	−6.16837	−	2.00423i	−0.320246	−	0.104054i
$372$	−1.10982	−	6.97921i	−0.0575414	−	0.361855i
$373$	−1.78423	+	11.2652i	−0.0923841	+	0.583290i	0.897456	+	0.441104i	$0.145413\pi$
$373$	−1.78423	+	11.2652i	−0.0923841	+	0.583290i	−0.989840	+	0.142186i	$0.954587\pi$
$374$	22.5895	−	16.4229i	1.16808	−	0.849208i
$375$	11.1783	+	0.212035i	0.577246	+	0.0109494i
$376$	−12.2552	+	3.99450i	−0.632012	+	0.206001i
$377$	26.1192	+	4.13687i	1.34521	+	0.213060i
$378$	−2.79321	−	1.42213i	−0.143667	−	0.0731463i
$379$	−9.94580	+	30.6100i	−0.510881	+	1.57233i	0.279771	+	0.960067i	$0.409741\pi$
$379$	−9.94580	+	30.6100i	−0.510881	+	1.57233i	−0.790653	+	0.612265i	$0.790259\pi$
$380$	−21.8169	−	11.2735i	−1.11918	−	0.578317i
$381$	4.25087	+	13.0828i	0.217778	+	0.670253i
$382$	−4.47534	+	28.3128i	−0.228978	+	1.44861i
$383$	−3.99591	+	7.84242i	−0.204182	+	0.400729i	−0.970277	−	0.241998i	$-0.922197\pi$
$383$	−3.99591	+	7.84242i	−0.204182	+	0.400729i	0.766095	+	0.642727i	$0.222197\pi$
$384$	−9.13858	+	6.66980i	−0.466351	+	0.340367i
$385$	−28.6627	−	9.51384i	−1.46079	−	0.484870i
$386$	−0.692060	+	2.13218i	−0.0352249	+	0.108525i
$387$	5.58243	−	0.884170i	0.283771	−	0.0449449i
$388$	0.254897	−	1.61582i	0.0129404	−	0.0820307i
$389$	3.16912	+	4.36192i	0.160681	+	0.221158i	0.881765	−	0.471690i	$-0.156356\pi$
$389$	3.16912	+	4.36192i	0.160681	+	0.221158i	−0.721084	+	0.692848i	$0.756356\pi$
$390$	9.82591	−	13.3546i	0.497554	−	0.676236i
$391$	4.81659	−	6.62947i	0.243585	−	0.335267i
$392$	−5.83324	−	0.918354i	−0.294623	−	0.0463839i
$393$	6.36271	−	6.36271i	0.320956	−	0.320956i
$394$	2.46016	−	3.38831i	0.123941	−	0.170701i
$395$	3.52210	−	6.80581i	0.177216	−	0.342437i
$396$	7.15760	−	9.86440i	0.359683	−	0.495705i
$397$	−3.00439	+	1.53081i	−0.150786	+	0.0768294i	−0.527755	−	0.849396i	$-0.676966\pi$
$397$	−3.00439	+	1.53081i	−0.150786	+	0.0768294i	0.376969	+	0.926226i	$0.376966\pi$
$398$	7.13927	−	3.64042i	0.357859	−	0.182478i
$399$	−12.1705			−0.609286
$400$	0.228168	−	19.9987i	0.0114084	−	0.999935i
$401$	30.0238			1.49931			0.749657	−	0.661826i	$-0.230218\pi$
$401$	30.0238			1.49931			0.749657	+	0.661826i	$0.230218\pi$
$402$	3.25527	−	1.65991i	0.162358	−	0.0827887i
$403$	16.5068	−	8.41062i	0.822261	−	0.418963i
$404$	−2.79850	+	3.85681i	−0.139231	+	0.191884i
$405$	0.335829	+	2.21071i	0.0166875	+	0.109851i
$406$	9.28852	−	12.7929i	0.460981	−	0.634899i
$407$	−51.0972	+	51.0972i	−2.53280	+	2.53280i
$408$	9.05466	+	1.42552i	0.448272	+	0.0705736i
$409$	−1.57854	+	2.17268i	−0.0780540	+	0.107432i	−0.846259	−	0.532772i	$-0.821150\pi$
$409$	−1.57854	+	2.17268i	−0.0780540	+	0.107432i	0.768205	+	0.640204i	$0.221150\pi$
$410$	−2.12266	−	0.703832i	−0.104831	−	0.0347598i
$411$	2.24332	+	3.08766i	0.110655	+	0.152303i
$412$	−3.12196	+	19.7904i	−0.153808	+	0.975003i
$413$	−10.1076	+	1.60089i	−0.497363	+	0.0787746i
$414$	1.10398	−	3.40128i	0.0542577	−	0.167164i
$415$	2.20759	−	2.99844i	0.108366	−	0.147188i
$416$	−24.0216	−	17.3961i	−1.17775	−	0.852913i
$417$	2.41428	−	4.73829i	0.118228	−	0.232035i
$418$	7.38850	−	46.7426i	0.361383	−	2.28625i
$419$	3.46958	+	10.6783i	0.169500	+	0.521668i	0.999340	−	0.0363340i	$-0.0115680\pi$
$419$	3.46958	+	10.6783i	0.169500	+	0.521668i	−0.829839	+	0.558002i	$0.811568\pi$
$420$	−4.44943	−	8.85705i	−0.217110	−	0.432180i
$421$	−8.60918	+	26.4963i	−0.419586	+	1.29135i	0.488498	+	0.872565i	$0.337545\pi$
$421$	−8.60918	+	26.4963i	−0.419586	+	1.29135i	−0.908084	+	0.418788i	$0.862455\pi$
$422$	3.83859	+	1.95437i	0.186860	+	0.0951371i
$423$	4.50110	+	0.712904i	0.218851	+	0.0346626i
$424$	7.86946	−	2.56501i	0.382175	−	0.124568i
$425$	−11.6017	+	11.3119i	−0.562764	+	0.548710i
$426$	7.27049	−	5.28575i	0.352256	−	0.256095i
$427$	3.33274	−	21.0421i	0.161282	−	1.01830i
$428$	−4.52708	−	28.4690i	−0.218825	−	1.37610i
$429$	30.3862	+	9.87308i	1.46706	+	0.476677i
$430$	15.8761	+	8.20989i	0.765613	+	0.395916i
$431$	12.5548	−	4.07929i	0.604741	−	0.196492i	0.00938729	−	0.999956i	$-0.497012\pi$
$431$	12.5548	−	4.07929i	0.604741	−	0.196492i	0.595354	+	0.803464i	$0.297012\pi$
$432$	3.94998	−	0.630618i	0.190043	−	0.0303406i
$433$	−20.5350	−	10.4631i	−0.986847	−	0.502824i	−0.115403	−	0.993319i	$-0.536816\pi$
$433$	−20.5350	−	10.4631i	−0.986847	−	0.502824i	−0.871444	+	0.490495i	$0.836816\pi$
$434$	−0.00342071	−	11.0753i	−0.000164199	−	0.531629i
$435$	−11.2781	−	0.0713013i	−0.540741	−	0.00341864i
$436$	5.22438	+	16.0452i	0.250202	+	0.768428i
$437$	−2.17209	−	13.7140i	−0.103905	−	0.656032i
$438$	−16.4940	−	16.4838i	−0.788113	−	0.787626i
$439$	−16.3390	+	11.8709i	−0.779816	+	0.566569i	−0.904924	−	0.425574i	$-0.860072\pi$
$439$	−16.3390	+	11.8709i	−0.779816	+	0.566569i	0.125108	+	0.992143i	$0.460072\pi$
$440$	36.7180	−	11.7118i	1.75046	−	0.558336i
$441$	1.68904	+	1.22716i	0.0804303	+	0.0584360i
$442$	3.76634	+	23.7323i	0.179146	+	1.12883i
$443$	11.6119	+	11.6119i	0.551700	+	0.551700i	0.926931	−	0.375231i	$-0.122437\pi$
$443$	11.6119	+	11.6119i	0.551700	+	0.551700i	−0.375231	+	0.926931i	$0.622437\pi$
$444$	−23.7167	+	0.0146503i	−1.12554	+	0.000695272i
$445$	4.70704	+	9.38429i	0.223135	+	0.444858i
$446$	−16.6539	+	5.41688i	−0.788587	+	0.256497i
$447$	1.40111	+	2.74983i	0.0662701	+	0.130062i
$448$	−15.7834	+	8.07890i	−0.745694	+	0.381692i
$449$			19.4726i			0.918971i	0.888185	+	0.459486i	$0.151966\pi$
$449$			19.4726i			0.918971i	−0.888185	+	0.459486i	$0.848034\pi$
$450$	−3.28767	+	6.26029i	−0.154982	+	0.295113i
$451$		−	4.30942i		−	0.202923i
$452$	−7.41662	+	14.5782i	−0.348849	+	0.685701i
$453$	−6.65685	−	13.0648i	−0.312766	−	0.613838i
$454$	0.430226	+	1.32271i	0.0201915	+	0.0620778i
$455$	18.4893	−	18.2570i	0.866791	−	0.855900i
$456$	12.5568	−	9.14082i	0.588025	−	0.428058i
$457$	−7.70216	−	7.70216i	−0.360292	−	0.360292i	0.503628	−	0.863920i	$-0.331998\pi$
$457$	−7.70216	−	7.70216i	−0.360292	−	0.360292i	−0.863920	+	0.503628i	$0.831998\pi$
$458$	−7.02591	+	1.11502i	−0.328299	+	0.0521014i
$459$	−2.62181	−	1.90486i	−0.122376	−	0.0889111i
$460$	9.18627	−	6.59448i	0.428312	−	0.307469i
$461$	27.1542	−	19.7287i	1.26470	−	0.918856i	0.265718	−	0.964051i	$-0.414391\pi$
$461$	27.1542	−	19.7287i	1.26470	−	0.918856i	0.998978	+	0.0451948i	$0.0143909\pi$
$462$	13.5019	−	13.5102i	0.628163	−	0.628552i
$463$	−4.00410	−	25.2809i	−0.186086	−	1.17490i	−0.887039	−	0.461695i	$-0.847241\pi$
$463$	−4.00410	−	25.2809i	−0.186086	−	1.17490i	0.700952	−	0.713208i	$-0.252759\pi$
$464$	0.0249253	+	20.1752i	0.00115713	+	0.936609i
$465$	−6.42131	+	4.60361i	−0.297781	+	0.213487i
$466$	−38.3051	+	0.0118309i	−1.77445	+	0.000548058i
$467$	−2.69406	−	1.37269i	−0.124666	−	0.0635207i	0.390545	−	0.920584i	$-0.372287\pi$
$467$	−2.69406	−	1.37269i	−0.124666	−	0.0635207i	−0.515211	+	0.857063i	$0.672287\pi$
$468$	4.76634	+	9.34020i	0.220324	+	0.431751i
$469$	5.44635	−	1.76963i	0.251489	−	0.0817137i
$470$	10.1288	+	10.2513i	0.467205	+	0.472858i
$471$	10.6008	+	3.44442i	0.488461	+	0.158711i
$472$	9.22606	−	9.24317i	0.424664	−	0.425452i
$473$	−5.38795	+	34.0182i	−0.247738	+	1.56416i
$474$	2.84998	+	3.92011i	0.130904	+	0.180057i
$475$	−0.347148	+	27.4539i	−0.0159282	+	1.25967i
$476$	13.6649	+	4.43067i	0.626330	+	0.203079i
$477$	−2.89031	−	0.457780i	−0.132338	−	0.0209603i
$478$	−7.28893	+	14.3163i	−0.333388	+	0.654810i
$479$	7.10777	−	21.8755i	0.324762	−	0.999515i	−0.646786	−	0.762672i	$-0.723887\pi$
$479$	7.10777	−	21.8755i	0.324762	−	0.999515i	0.971548	−	0.236843i	$-0.0761128\pi$
$480$	11.2429	+	5.79636i	0.513165	+	0.264566i
$481$	−19.2127	−	59.1307i	−0.876024	−	2.69613i
$482$	25.0639	+	3.96180i	1.14163	+	0.180455i
$483$	2.54427	−	4.99342i	0.115768	−	0.227208i
$484$	30.7489	+	42.2673i	1.39768	+	1.92124i
$485$	−1.74290	+	0.554147i	−0.0791412	+	0.0251625i
$486$	−1.34513	−	0.436601i	−0.0610164	−	0.0198046i
$487$	6.30501	−	0.998616i	0.285707	−	0.0452516i	−0.0119359	−	0.999929i	$-0.503799\pi$
$487$	6.30501	−	0.998616i	0.285707	−	0.0452516i	0.297643	+	0.954677i	$0.403799\pi$
$488$	12.3654	+	24.2131i	0.559757	+	1.09607i
$489$	−1.60829	−	2.21363i	−0.0727295	−	0.100104i
$490$	2.00236	+	6.29111i	0.0904576	+	0.284203i
$491$	−8.13350	+	11.1948i	−0.367060	+	0.505214i	−0.952099	−	0.305791i	$-0.901079\pi$
$491$	−8.13350	+	11.1948i	−0.367060	+	0.505214i	0.585039	+	0.811005i	$0.301079\pi$
$492$	0.999487	−	1.00072i	0.0450603	−	0.0451160i
$493$	11.5581	−	11.5581i	0.520550	−	0.520550i
$494$	32.9473	+	23.9221i	1.48237	+	1.07631i
$495$	−13.4446	−	2.21664i	−0.604292	−	0.0996306i
$496$	8.32176	+	11.4242i	0.373658	+	0.512963i
$497$	12.5519	−	6.39550i	0.563029	−	0.286878i
$498$	1.06976	+	2.09792i	0.0479370	+	0.0940099i
$499$	24.8664			1.11317			0.556587	−	0.830789i	$-0.312111\pi$
$499$	24.8664			1.11317			0.556587	+	0.830789i	$0.312111\pi$
$500$	−20.1064	+	9.78428i	−0.899186	+	0.437566i
$501$	−16.3587			−0.730851
$502$	−10.8218	−	21.2229i	−0.483003	−	0.947223i
$503$	10.0381	−	5.11465i	0.447576	−	0.228051i	−0.215650	−	0.976471i	$-0.569187\pi$
$503$	10.0381	−	5.11465i	0.447576	−	0.228051i	0.663226	+	0.748420i	$0.269187\pi$
$504$	6.26880	−	0.00580855i	0.279235	−	0.000258733i
$505$	5.25663	+	0.866669i	0.233917	+	0.0385663i
$506$	17.6334	+	12.8031i	0.783900	+	0.569167i
$507$	−10.2455	+	10.2455i	−0.455019	+	0.455019i
$508$	−19.4661	−	19.4420i	−0.863667	−	0.862601i
$509$	15.1447	−	20.8448i	0.671275	−	0.923931i	−0.328513	−	0.944499i	$-0.606548\pi$
$509$	15.1447	−	20.8448i	0.671275	−	0.923931i	0.999788	+	0.0205685i	$0.00654763\pi$
$510$	−3.10817	−	9.76539i	−0.137632	−	0.432419i
$511$	−21.4808	−	29.5657i	−0.950253	−	1.30791i
$512$	10.2165	−	20.1897i	0.451512	−	0.892265i
$513$	−5.42361	+	0.859015i	−0.239458	+	0.0379264i
$514$	−35.0643	−	11.3811i	−1.54662	−	0.501999i
$515$	21.3470	−	6.78715i	0.940659	−	0.299077i
$516$	−9.14104	+	6.64999i	−0.402412	+	0.292749i
$517$	−12.6076	+	24.7439i	−0.554483	+	1.08823i
$518$	−36.7130	−	5.80315i	−1.61308	−	0.254976i
$519$	−3.51692	−	10.8240i	−0.154376	−	0.475119i
$520$	−5.36397	+	32.7231i	−0.235226	+	1.43500i
$521$	−6.89632	+	21.2247i	−0.302133	+	0.929871i	0.678598	+	0.734510i	$0.262588\pi$
$521$	−6.89632	+	21.2247i	−0.302133	+	0.929871i	−0.980731	+	0.195361i	$0.937412\pi$
$522$	3.23635	−	6.35656i	0.141651	−	0.278219i
$523$	28.7316	+	4.55064i	1.25635	+	0.198986i	0.748891	−	0.662693i	$-0.230586\pi$
$523$	28.7316	+	4.55064i	1.25635	+	0.198986i	0.507455	+	0.861678i	$0.330586\pi$
$524$	−5.55063	+	17.1191i	−0.242481	+	0.747850i
$525$	−6.62654	+	8.88228i	−0.289206	+	0.387654i
$526$	−16.6990	−	22.9693i	−0.728112	−	1.00151i
$527$	1.79133	−	11.3100i	0.0780315	−	0.492671i
$528$	−3.78337	+	24.0798i	−0.164650	+	1.04794i
$529$	−15.7935	−	5.13162i	−0.686674	−	0.223114i
$530$	−6.50403	−	6.58272i	−0.282517	−	0.285935i
$531$	−4.39132	+	1.42683i	−0.190567	+	0.0619190i
$532$	21.6811	−	11.0640i	0.939996	−	0.479684i
$533$	3.30365	+	1.68329i	0.143097	+	0.0729115i
$534$	−6.63992	+	0.00205081i	−0.287337	+	8.87471e-5i
$535$	−26.1933	+	18.7787i	−1.13243	+	0.811873i
$536$	−4.29011	+	5.91635i	−0.185305	+	0.255547i
$537$	1.77294	+	11.1939i	0.0765082	+	0.483053i
$538$	9.79822	−	9.80428i	0.422431	−	0.422692i
$539$	−10.2926	+	7.47804i	−0.443336	+	0.322102i
$540$	−2.60797	−	3.63297i	−0.112229	−	0.156338i
$541$	33.0063	+	23.9805i	1.41905	+	1.03100i	0.991927	+	0.126808i	$0.0404731\pi$
$541$	33.0063	+	23.9805i	1.41905	+	1.03100i	0.427124	+	0.904193i	$0.359527\pi$
$542$	−28.1003	+	4.45956i	−1.20701	+	0.191554i
$543$	5.81761	+	5.81761i	0.249658	+	0.249658i
$544$	−17.4263	+	5.69193i	−0.747148	+	0.244040i
$545$	13.4244	−	13.2557i	0.575039	−	0.567814i
$546$	5.08314	+	15.6279i	0.217538	+	0.668811i
$547$	−8.10157	−	15.9002i	−0.346398	−	0.679845i	0.650418	−	0.759576i	$-0.274594\pi$
$547$	−8.10157	−	15.9002i	−0.346398	−	0.679845i	−0.996816	+	0.0797317i	$0.974594\pi$
$548$	−6.80330	−	3.46116i	−0.290623	−	0.147854i
$549$		−	9.61234i		−	0.410245i
$550$	−30.0908	−	30.8425i	−1.28308	−	1.31513i
$551$		−	27.6966i		−	1.17991i
$552$	1.12535	+	7.06283i	0.0478981	+	0.300614i
$553$	3.44834	+	6.76775i	0.146638	+	0.287794i
$554$	5.42849	−	1.76568i	0.230634	−	0.0750164i
$555$	11.8884	+	23.7016i	0.504636	+	1.00608i
$556$	0.00656996	+	10.6358i	0.000278628	+	0.451059i
$557$	−29.1894	−	29.1894i	−1.23679	−	1.23679i	−0.961304	−	0.275491i	$-0.911160\pi$
$557$	−29.1894	−	29.1894i	−1.23679	−	1.23679i	−0.275491	−	0.961304i	$-0.588840\pi$
$558$	−0.783236	−	4.93529i	−0.0331570	−	0.208928i
$559$	−23.9741	−	17.4182i	−1.01400	−	0.736712i
$560$	15.9782	+	11.7335i	0.675204	+	0.495831i
$561$	15.9768	−	11.6078i	0.674540	−	0.490082i
$562$	23.2488	+	23.2345i	0.980692	+	0.980087i
$563$	2.47255	+	15.6111i	0.104206	+	0.657929i	0.983398	+	0.181462i	$0.0580829\pi$
$563$	2.47255	+	15.6111i	0.104206	+	0.657929i	−0.879192	+	0.476467i	$0.841917\pi$
$564$	−8.66658	+	2.82186i	−0.364929	+	0.118822i
$565$	18.2866	+	0.115610i	0.769323	+	0.00486376i
$566$	0.00714473	+	23.1326i	0.000300316	+	0.972335i
$567$	−1.97479	−	1.00620i	−0.0829333	−	0.0422566i
$568$	−8.14684	+	16.0258i	−0.341834	+	0.672426i
$569$	−7.32420	+	2.37978i	−0.307046	+	0.0997654i	−0.458487	−	0.888701i	$-0.651609\pi$
$569$	−7.32420	+	2.37978i	−0.307046	+	0.0997654i	0.151441	+	0.988466i	$0.451609\pi$
$570$	−15.4244	−	7.97632i	−0.646057	−	0.334091i
$571$	−16.1627	−	5.25157i	−0.676387	−	0.219771i	−0.0493740	−	0.998780i	$-0.515723\pi$
$571$	−16.1627	−	5.25157i	−0.676387	−	0.219771i	−0.627013	+	0.779009i	$0.715723\pi$
$572$	−63.1070	+	10.0351i	−2.63864	+	0.419590i
$573$	−3.17073	+	20.0192i	−0.132459	+	0.836313i
$574$	1.79286	−	1.30343i	0.0748323	−	0.0544042i
$575$	−11.1915	−	5.88174i	−0.466716	−	0.245285i
$576$	−6.46341	+	4.71427i	−0.269309	+	0.196428i
$577$	18.2821	+	2.89561i	0.761095	+	0.120546i	0.524905	−	0.851161i	$-0.324101\pi$
$577$	18.2821	+	2.89561i	0.761095	+	0.120546i	0.236191	+	0.971707i	$0.424101\pi$
$578$	−8.18879	−	4.16921i	−0.340609	−	0.173416i
$579$	−0.489826	+	1.50753i	−0.0203565	+	0.0626508i
$580$	20.1561	−	10.1256i	0.836937	−	0.420445i
$581$	1.14047	+	3.51000i	0.0473146	+	0.145619i
$582$	0.180592	−	1.14250i	0.00748580	−	0.0473581i
$583$	8.09580	−	15.8889i	0.335294	−	0.658051i
$584$	44.3683	+	14.3707i	1.83597	+	0.594664i
$585$	6.95088	−	9.44097i	0.287384	−	0.390336i
$586$	−6.43846	+	19.8364i	−0.265970	+	0.819434i
$587$	−36.0677	+	5.71256i	−1.48867	+	0.235782i	−0.847163	−	0.531333i	$-0.821691\pi$
$587$	−36.0677	+	5.71256i	−1.48867	+	0.235782i	−0.641509	+	0.767116i	$0.721691\pi$
$588$	−4.12452	−	0.650648i	−0.170092	−	0.0268323i
$589$	−11.4048	−	15.6973i	−0.469925	−	0.646796i
$590$	−13.8592	−	4.59544i	−0.570574	−	0.189191i
$591$	1.74033	−	2.39536i	0.0715877	−	0.0985320i
$592$	42.2368	−	21.5865i	1.73592	−	0.887200i
$593$	−11.6274	+	11.6274i	−0.477479	+	0.477479i	−0.904325	−	0.426845i	$-0.859625\pi$
$593$	−11.6274	+	11.6274i	−0.477479	+	0.477479i	0.426845	+	0.904325i	$0.359625\pi$
$594$	5.06334	−	6.97362i	0.207751	−	0.286131i
$595$	−2.41213	−	15.8787i	−0.0988878	−	0.650962i
$596$	−4.99582	−	3.62497i	−0.204637	−	0.148484i
$597$	5.04902	−	2.57260i	0.206643	−	0.105290i
$598$	−16.7027	+	8.51696i	−0.683025	+	0.348284i
$599$	−17.1691			−0.701509			−0.350755	−	0.936467i	$-0.614075\pi$
$599$	−17.1691			−0.701509			−0.350755	+	0.936467i	$0.614075\pi$
$600$	0.165707	−	14.1412i	0.00676495	−	0.577311i
$601$	28.7389			1.17229			0.586143	−	0.810208i	$-0.300646\pi$
$601$	28.7389			1.17229			0.586143	+	0.810208i	$0.300646\pi$
$602$	−15.7823	+	8.04762i	−0.643239	+	0.327997i
$603$	2.30218	−	1.17302i	0.0937522	−	0.0477691i
$604$	23.7358	+	17.2227i	0.965798	+	0.700782i
$605$	26.8591	−	51.9001i	1.09198	−	2.11004i
$606$	−1.97968	+	2.72657i	−0.0804190	+	0.110759i
$607$	−0.862810	+	0.862810i	−0.0350204	+	0.0350204i	−0.724400	−	0.689380i	$-0.757883\pi$
$607$	−0.862810	+	0.862810i	−0.0350204	+	0.0350204i	0.689380	+	0.724400i	$0.257883\pi$
$608$	−14.0595	+	27.6991i	−0.570190	+	1.12335i
$609$	6.57077	−	9.04389i	0.266261	−	0.366477i
$610$	18.0144	−	24.4837i	0.729381	−	0.991317i
$611$	−14.0443	−	19.3303i	−0.568171	−	0.782020i
$612$	6.40230	+	1.00997i	0.258798	+	0.0408256i
$613$	26.1403	−	4.14022i	1.05580	−	0.167222i	0.395683	−	0.918387i	$-0.370508\pi$
$613$	26.1403	−	4.14022i	1.05580	−	0.167222i	0.660114	+	0.751165i	$0.270508\pi$
$614$	0.437357	−	1.34746i	0.0176503	−	0.0543791i
$615$	−1.50079	−	0.498148i	−0.0605177	−	0.0200873i
$616$	−11.7710	+	36.3421i	−0.474269	+	1.46426i
$617$	−3.06300	+	6.01149i	−0.123312	+	0.242013i	−0.944407	−	0.328778i	$-0.893363\pi$
$617$	−3.06300	+	6.01149i	−0.123312	+	0.242013i	0.821095	+	0.570791i	$0.193363\pi$
$618$	−2.21188	+	13.9932i	−0.0889749	+	0.562891i
$619$	−12.1030	−	37.2492i	−0.486461	−	1.49717i	−0.829854	−	0.557981i	$-0.811576\pi$
$619$	−12.1030	−	37.2492i	−0.486461	−	1.49717i	0.343393	−	0.939192i	$-0.388424\pi$
$620$	7.25419	−	14.0386i	0.291335	−	0.563804i
$621$	0.781376	−	2.40483i	0.0313555	−	0.0965024i
$622$	−3.65521	−	1.86100i	−0.146560	−	0.0746192i
$623$	−10.2780	−	1.62787i	−0.411778	−	0.0652192i
$624$	−16.9820	−	12.3061i	−0.679824	−	0.492639i
$625$	19.8474	+	15.2013i	0.793896	+	0.608054i
$626$	4.90932	−	3.56915i	0.196216	−	0.142652i
$627$	5.23466	−	33.0504i	0.209052	−	1.31990i
$628$	−22.0162	+	3.50096i	−0.878541	+	0.139704i
$629$	−36.5489	−	11.8755i	−1.45730	−	0.473505i
$630$	−3.14429	−	6.26385i	−0.125272	−	0.249558i
$631$	33.1596	−	10.7742i	1.32006	−	0.428914i	0.437546	−	0.899196i	$-0.355848\pi$
$631$	33.1596	−	10.7742i	1.32006	−	0.428914i	0.882516	+	0.470282i	$0.155848\pi$
$632$	−8.64081	−	4.39263i	−0.343713	−	0.174729i
$633$	2.71387	+	1.38278i	0.107867	+	0.0549608i
$634$	0.00382966	+	12.3993i	0.000152095	+	0.492440i
$635$	−9.68998	+	29.1934i	−0.384535	+	1.15850i
$636$	5.56511	−	1.81202i	0.220671	−	0.0718511i
$637$	−1.71236	−	10.8114i	−0.0678463	−	0.428364i
$638$	30.7454	+	30.7264i	1.21722	+	1.21647i
$639$	5.14216	−	3.73600i	0.203421	−	0.147794i
$640$	−25.2980	−	0.105241i	−0.999991	−	0.00416001i
$641$	37.8737	+	27.5168i	1.49592	+	1.08685i	0.971971	+	0.235099i	$0.0755415\pi$
$641$	37.8737	+	27.5168i	1.49592	+	1.08685i	0.523948	+	0.851750i	$0.324459\pi$
$642$	−3.19491	−	20.1316i	−0.126093	−	0.794533i
$643$	−19.9654	−	19.9654i	−0.787360	−	0.787360i	0.193701	−	0.981061i	$-0.437951\pi$
$643$	−19.9654	−	19.9654i	−0.787360	−	0.787360i	−0.981061	+	0.193701i	$0.937951\pi$
$644$	0.00692371	+	11.2085i	0.000272833	+	0.441676i
$645$	11.2243	+	5.80874i	0.441956	+	0.228719i
$646$	23.9326	−	7.78434i	0.941615	−	0.306271i
$647$	7.49471	+	14.7092i	0.294647	+	0.578278i	0.990111	−	0.140283i	$-0.0448012\pi$
$647$	7.49471	+	14.7092i	0.294647	+	0.578278i	−0.695464	+	0.718561i	$0.744801\pi$
$648$	2.79319	−	0.445052i	0.109727	−	0.0174833i
$649$		−	28.1370i		−	1.10447i
$650$	35.3979	−	11.0206i	1.38842	−	0.432265i
$651$		−	7.83139i		−	0.306936i
$652$	4.87746	+	2.48140i	0.191016	+	0.0971790i
$653$	−3.58646	−	7.03882i	−0.140349	−	0.275450i	0.810123	−	0.586259i	$-0.199400\pi$
$653$	−3.58646	−	7.03882i	−0.140349	−	0.275450i	−0.950472	+	0.310809i	$0.899400\pi$
$654$	3.69069	+	11.3468i	0.144317	+	0.443697i
$655$	19.8924	−	3.02186i	0.777261	−	0.118074i
$656$	−0.870799	+	2.69135i	−0.0339990	+	0.105080i
$657$	−11.6594	−	11.6594i	−0.454877	−	0.454877i
$658$	−14.1076	+	2.23889i	−0.549970	+	0.0872808i
$659$	−32.6086	−	23.6915i	−1.27025	−	0.922890i	−0.271036	−	0.962569i	$-0.587366\pi$
$659$	−32.6086	−	23.6915i	−1.27025	−	0.922890i	−0.999212	+	0.0396792i	$0.987366\pi$
$660$	25.9661	−	8.27344i	1.01073	−	0.322043i
$661$	−17.3275	+	12.5892i	−0.673962	+	0.489662i	−0.871349	−	0.490663i	$-0.836755\pi$
$661$	−17.3275	+	12.5892i	−0.673962	+	0.489662i	0.197387	+	0.980326i	$0.436755\pi$
$662$	15.9098	−	15.9196i	0.618351	−	0.618734i
$663$	2.65802	+	16.7821i	0.103229	+	0.651762i
$664$	−3.81290	−	2.76484i	−0.147969	−	0.107297i
$665$	−21.9150	−	16.1349i	−0.849829	−	0.625684i
$666$	−16.7702	+	0.00517966i	−0.649834	+	0.000200708i
$667$	11.3636	+	5.79005i	0.440001	+	0.224191i
$668$	29.1421	−	14.8713i	1.12754	−	0.575390i
$669$	−11.7773	+	3.82668i	−0.455337	+	0.147948i
$670$	8.06227	+	1.32668i	0.311473	+	0.0512542i
$671$	55.7088	+	18.1009i	2.15061	+	0.698777i
$672$	−11.1623	+	5.70920i	−0.430595	+	0.220237i
$673$	2.87386	−	18.1449i	0.110779	−	0.699433i	−0.868313	−	0.496017i	$-0.834795\pi$
$673$	2.87386	−	18.1449i	0.110779	−	0.699433i	0.979092	−	0.203417i	$-0.0652046\pi$
$674$	22.2499	+	30.6045i	0.857036	+	1.17884i
$675$	−2.32610	+	4.42598i	−0.0895316	+	0.170356i
$676$	8.93787	−	27.5659i	0.343764	−	1.06023i
$677$	8.32771	+	1.31898i	0.320060	+	0.0506925i	0.314397	−	0.949291i	$-0.398198\pi$
$677$	8.32771	+	1.31898i	0.320060	+	0.0506925i	0.00566258	+	0.999984i	$0.498198\pi$
$678$	−5.24753	+	10.3067i	−0.201530	+	0.395827i
$679$	0.560173	−	1.72403i	0.0214974	−	0.0661623i
$680$	14.4146	+	14.5710i	0.552775	+	0.558772i
$681$	0.303927	+	0.935390i	0.0116465	+	0.0358442i
$682$	30.0776	+	4.75430i	1.15173	+	0.182052i
$683$	4.15158	−	8.14793i	0.158856	−	0.311772i	−0.797836	−	0.602874i	$-0.794022\pi$
$683$	4.15158	−	8.14793i	0.158856	−	0.311772i	0.956692	+	0.291102i	$0.0940220\pi$
$684$	8.88098	−	6.46079i	0.339573	−	0.247035i
$685$	−0.0539525	+	8.53392i	−0.00206142	+	0.326064i
$686$	−27.0933	−	8.79389i	−1.03443	−	0.335752i
$687$	−4.96831	+	0.786903i	−0.189553	+	0.0300222i
$688$	10.2389	−	20.1566i	0.390356	−	0.768463i
$689$	9.01832	+	12.4126i	0.343571	+	0.472884i
$690$	6.49711	−	4.66100i	0.247341	−	0.177441i
$691$	19.7057	−	27.1226i	0.749640	−	1.03179i	−0.248366	−	0.968666i	$-0.579893\pi$
$691$	19.7057	−	27.1226i	0.749640	−	1.03179i	0.998006	−	0.0631245i	$-0.0201065\pi$
$692$	16.1051	+	16.0852i	0.612223	+	0.611467i
$693$	9.55021	−	9.55021i	0.362782	−	0.362782i
$694$	−17.5841	−	12.7673i	−0.667484	−	0.484640i
$695$	10.6291	−	5.33140i	0.403183	−	0.202232i
$696$	0.0132186	+	14.2660i	0.000501050	+	0.540752i
$697$	2.04200	−	1.04045i	0.0773461	−	0.0394098i
$698$	1.61274	+	3.16277i	0.0610431	+	0.119712i
$699$	−27.0858			−1.02448
$700$	3.73015	−	21.8474i	0.140987	−	0.825755i
$701$	−14.0765			−0.531661			−0.265831	−	0.964020i	$-0.585646\pi$
$701$	−14.0765			−0.531661			−0.265831	+	0.964020i	$0.585646\pi$
$702$	3.36827	+	6.60556i	0.127127	+	0.249311i
$703$	−58.0194	+	29.5624i	−2.18824	+	1.11497i
$704$	−15.1506	−	46.3364i	−0.571010	−	1.74637i
$705$	7.15988	+	7.25099i	0.269657	+	0.273088i
$706$	−6.82534	−	4.95568i	−0.256875	−	0.186509i
$707$	−3.73397	+	3.73397i	−0.140430	+	0.140430i
$708$	6.52583	−	6.53390i	0.245256	−	0.245559i
$709$	13.6111	−	18.7340i	0.511175	−	0.703572i	−0.472942	−	0.881094i	$-0.656808\pi$
$709$	13.6111	−	18.7340i	0.511175	−	0.703572i	0.984117	+	0.177522i	$0.0568080\pi$
$710$	20.0993	+	0.120862i	0.754312	+	0.00453587i
$711$	2.01438	+	2.77256i	0.0755453	+	0.103979i
$712$	11.8268	−	6.03988i	0.443229	−	0.226354i
$713$	8.82463	−	1.39768i	0.330485	−	0.0523437i
$714$	9.66158	+	3.13594i	0.361575	+	0.117360i
$715$	41.6265	+	58.0623i	1.55674	+	2.17141i
$716$	−13.3346	−	18.3297i	−0.498338	−	0.685013i
$717$	−5.15718	+	10.1215i	−0.192598	+	0.377995i
$718$	29.0615	+	4.59369i	1.08457	+	0.171435i
$719$	2.56231	+	7.88598i	0.0955581	+	0.294098i	0.987399	−	0.158252i	$-0.0505859\pi$
$719$	2.56231	+	7.88598i	0.0955581	+	0.294098i	−0.891841	+	0.452350i	$0.850586\pi$
$720$	7.94865	+	4.10110i	0.296229	+	0.152839i
$721$	−6.86095	+	21.1158i	−0.255515	+	0.786395i
$722$	7.15658	−	14.0563i	0.266341	−	0.523122i
$723$	17.7220	+	2.80689i	0.659088	+	0.104389i
$724$	−15.6525	−	5.07511i	−0.581720	−	0.188615i
$725$	−20.2135	−	15.0801i	−0.750712	−	0.560062i
$726$	21.7335	+	29.8942i	0.806608	+	1.10948i
$727$	−7.11230	+	44.9053i	−0.263781	+	1.66544i	0.399242	+	0.916845i	$0.369273\pi$
$727$	−7.11230	+	44.9053i	−0.263781	+	1.66544i	−0.663023	+	0.748599i	$0.730727\pi$
$728$	−23.2624	−	23.2193i	−0.862160	−	0.860564i
$729$	−0.951057	−	0.309017i	−0.0352243	−	0.0114451i
$730$	−7.84705	−	51.5486i	−0.290432	−	1.90790i
$731$	−17.4202	+	5.66016i	−0.644309	+	0.209349i
$732$	8.73840	+	17.1239i	0.322981	+	0.632918i
$733$	−1.32413	−	0.674677i	−0.0489078	−	0.0249198i	0.429366	−	0.903131i	$-0.358737\pi$
$733$	−1.32413	−	0.674677i	−0.0489078	−	0.0249198i	−0.478273	+	0.878211i	$0.658737\pi$
$734$	−46.4430	+	0.0143444i	−1.71424	+	0.000529461i
$735$	1.41451	+	4.44892i	0.0521750	+	0.164101i
$736$	−8.42544	−	11.5590i	−0.310566	−	0.426072i
$737$	2.46309	+	15.5513i	0.0907290	+	0.572840i
$738$	0.706962	−	0.707399i	0.0260236	−	0.0260397i
$739$	30.8267	−	22.3969i	1.13398	−	0.823884i	0.147710	−	0.989031i	$-0.452810\pi$
$739$	30.8267	−	22.3969i	1.13398	−	0.823884i	0.986269	+	0.165146i	$0.0528096\pi$
$740$	−42.7254	−	31.4157i	−1.57062	−	1.15487i
$741$	23.2921	+	16.9227i	0.855655	+	0.621670i
$742$	9.05895	−	1.43767i	0.332565	−	0.0527784i
$743$	7.12015	+	7.12015i	0.261213	+	0.261213i	0.825547	−	0.564334i	$-0.190867\pi$
$743$	7.12015	+	7.12015i	0.261213	+	0.261213i	−0.564334	+	0.825547i	$0.690867\pi$
$744$	5.88188	+	8.07996i	0.215640	+	0.296226i
$745$	−1.12262	+	6.80904i	−0.0411295	+	0.249464i
$746$	−4.98918	−	15.3390i	−0.182667	−	0.561601i
$747$	0.755975	+	1.48368i	0.0276597	+	0.0542852i
$748$	−17.9094	+	35.2030i	−0.654833	+	1.28715i
$749$		−	31.9452i		−	1.16725i
$750$	−14.2195	+	6.91414i	−0.519223	+	0.252469i
$751$			36.8810i			1.34581i	0.739730	+	0.672904i	$0.234953\pi$
$751$			36.8810i			1.34581i	−0.739730	+	0.672904i	$0.765047\pi$
$752$	12.8738	−	12.9056i	0.469459	−	0.470620i
$753$	−7.64757	−	15.0092i	−0.278693	−	0.546965i
$754$	−35.5646	+	11.5678i	−1.29519	+	0.421273i
$755$	5.33371	−	32.3507i	0.194114	−	1.17736i
$756$	4.43271	−	0.00273818i	0.161216	−	9.95866e-5i
$757$	−11.7663	−	11.7663i	−0.427655	−	0.427655i	0.460174	−	0.887829i	$-0.347787\pi$
$757$	−11.7663	−	11.7663i	−0.427655	−	0.427655i	−0.887829	+	0.460174i	$0.847787\pi$
$758$	−7.13429	−	44.9543i	−0.259129	−	1.63281i
$759$	12.4659	+	9.05700i	0.452483	+	0.328748i
$760$	34.7290	+	0.187381i	1.25975	+	0.00679701i
$761$	32.3918	−	23.5341i	1.17420	−	0.853109i	0.182697	−	0.983169i	$-0.441517\pi$
$761$	32.3918	−	23.5341i	1.17420	−	0.853109i	0.991506	+	0.130060i	$0.0415171\pi$
$762$	−13.7603	−	13.7518i	−0.498484	−	0.498177i
$763$	2.92529	+	18.4696i	0.105903	+	0.668644i
$764$	−12.5506	−	38.5456i	−0.454064	−	1.39453i
$765$	−2.19568	−	6.90585i	−0.0793849	−	0.249682i
$766$	−0.00384455	−	12.4476i	−0.000138909	−	0.449748i
$767$	21.5701	+	10.9905i	0.778851	+	0.396844i
$768$	7.22860	−	14.2740i	0.260840	−	0.515069i
$769$	15.5649	−	5.05733i	0.561284	−	0.182372i	−0.0146150	−	0.999893i	$-0.504652\pi$
$769$	15.5649	−	5.05733i	0.561284	−	0.182372i	0.575899	+	0.817521i	$0.304652\pi$
$770$	42.2234	−	6.42751i	1.52163	−	0.231631i
$771$	−24.7917	−	8.05531i	−0.892851	−	0.290105i
$772$	−0.497866	−	3.13088i	−0.0179186	−	0.112683i
$773$	−7.77928	+	49.1164i	−0.279801	+	1.76659i	0.302043	+	0.953294i	$0.402331\pi$
$773$	−7.77928	+	49.1164i	−0.279801	+	1.76659i	−0.581844	+	0.813301i	$0.697669\pi$
$774$	−6.46514	+	4.70025i	−0.232385	+	0.168947i
$775$	−17.6658	−	0.223380i	−0.634576	−	0.00802406i
$776$	0.716908	+	2.19948i	0.0257355	+	0.0789568i
$777$	−25.9588	−	4.11146i	−0.931265	−	0.147498i
$778$	−6.79491	−	3.45954i	−0.243609	−	0.124030i
$779$	1.20000	−	3.69322i	0.0429944	−	0.132323i
$780$	−3.80005	+	23.1376i	−0.136064	+	0.828457i
$781$	11.9690	+	36.8369i	0.428285	+	1.31813i
$782$	−1.80934	+	11.4466i	−0.0647019	+	0.409330i
$783$	2.28984	−	4.49406i	0.0818321	−	0.160605i
$784$	7.93913	−	2.59043i	0.283540	−	0.0925153i
$785$	14.5222	+	20.2562i	0.518321	+	0.722976i
$786$	−3.92863	+	12.1038i	−0.140130	+	0.431728i
$787$	−37.3225	+	5.91130i	−1.33040	+	0.210715i	−0.780837	−	0.624735i	$-0.785207\pi$
$787$	−37.3225	+	5.91130i	−1.33040	+	0.210715i	−0.549566	+	0.835450i	$0.685207\pi$
$788$	−0.922739	+	5.84933i	−0.0328712	+	0.208374i
$789$	−11.8030	−	16.2454i	−0.420197	−	0.578351i
$790$	−0.0651667	+	10.8372i	−0.00231853	+	0.385569i
$791$	−10.6541	+	14.6640i	−0.378814	+	0.521393i
$792$	−2.68051	+	17.0262i	−0.0952477	+	0.604998i
$793$	−35.6366	+	35.6366i	−1.26549	+	1.26549i
$794$	2.80172	−	3.85874i	0.0994293	−	0.136942i
$795$	−4.59760	−	4.65611i	−0.163060	−	0.165135i
$796$	−6.65588	+	9.17294i	−0.235911	+	0.325126i
$797$	8.78360	−	4.47547i	0.311131	−	0.158529i	−0.291452	−	0.956586i	$-0.594138\pi$
$797$	8.78360	−	4.47547i	0.311131	−	0.158529i	0.602583	+	0.798056i	$0.294138\pi$
$798$	15.3333	−	7.81867i	0.542793	−	0.276778i
$799$	−14.7687			−0.522479
$800$	12.5603	+	25.3424i	0.444073	+	0.895991i
$801$	−4.69513			−0.165894
$802$	−37.8262	+	19.2881i	−1.33569	+	0.681087i
$803$	89.5283	−	45.6169i	3.15939	−	1.60979i
$804$	−3.03486	+	4.18256i	−0.107031	+	0.147507i
$805$	11.2014	−	5.61847i	0.394796	−	0.198025i
$806$	−15.3932	+	21.2008i	−0.542204	+	0.746765i
$807$	6.93053	−	6.93053i	0.243966	−	0.243966i
$808$	1.04803	−	6.65694i	0.0368697	−	0.234190i
$809$	7.57206	−	10.4220i	0.266219	−	0.366420i	−0.654889	−	0.755725i	$-0.727285\pi$
$809$	7.57206	−	10.4220i	0.266219	−	0.366420i	0.921109	+	0.389305i	$0.127285\pi$
$810$	−1.84332	−	2.56947i	−0.0647678	−	0.0902819i
$811$	−10.6030	−	14.5938i	−0.372322	−	0.512458i	0.581208	−	0.813755i	$-0.302580\pi$
$811$	−10.6030	−	14.5938i	−0.372322	−	0.512458i	−0.953530	+	0.301297i	$0.902580\pi$
$812$	−3.48388	+	22.0846i	−0.122260	+	0.775018i
$813$	−19.8709	+	3.14724i	−0.696904	+	0.110379i
$814$	31.5498	−	97.2025i	1.10582	−	3.40694i
$815$	0.0386800	−	6.11819i	0.00135490	−	0.214311i
$816$	−12.3235	+	4.02100i	−0.431410	+	0.140763i
$817$	−14.0902	+	27.6536i	−0.492955	+	0.967478i
$818$	0.592977	−	3.75141i	0.0207329	−	0.131165i
$819$	3.59091	+	11.0517i	0.125476	+	0.386177i
$820$	3.12644	−	0.476915i	0.109180	−	0.0166546i
$821$	−7.97616	+	24.5481i	−0.278370	+	0.856735i	0.709938	+	0.704264i	$0.248723\pi$
$821$	−7.97616	+	24.5481i	−0.278370	+	0.856735i	−0.988308	+	0.152471i	$0.951277\pi$
$822$	−4.80990	−	2.44890i	−0.167765	−	0.0854151i
$823$	−5.46376	−	0.865375i	−0.190455	−	0.0301651i	0.0604783	−	0.998170i	$-0.480737\pi$
$823$	−5.46376	−	0.865375i	−0.190455	−	0.0301651i	−0.250933	+	0.968004i	$0.580737\pi$
$824$	−8.78064	−	26.9391i	−0.305888	−	0.938467i
$825$	−21.2707	−	21.8155i	−0.740551	−	0.759519i
$826$	11.7059	−	8.51034i	0.407299	−	0.296113i
$827$	7.20498	−	45.4905i	0.250542	−	1.58186i	−0.466302	−	0.884625i	$-0.654414\pi$
$827$	7.20498	−	45.4905i	0.250542	−	1.58186i	0.716844	−	0.697233i	$-0.245586\pi$
$828$	0.794201	+	4.99442i	0.0276004	+	0.173568i
$829$	28.7204	+	9.33181i	0.997499	+	0.324107i	0.761866	−	0.647735i	$-0.224284\pi$
$829$	28.7204	+	9.33181i	0.997499	+	0.324107i	0.235633	+	0.971842i	$0.424284\pi$
$830$	−0.855005	+	5.19588i	−0.0296777	+	0.180352i
$831$	3.83891	−	1.24734i	0.133170	−	0.0432696i
$832$	41.4399	+	6.48474i	1.43667	+	0.224818i
$833$	−6.02845	−	3.07165i	−0.208873	−	0.106426i
$834$	0.00232283	+	7.52065i	8.04330e−5	+	0.260419i
$835$	−29.4566	−	21.6873i	−1.01939	−	0.750520i
$836$	20.7202	+	63.6364i	0.716622	+	2.20091i
$837$	−0.552754	−	3.48995i	−0.0191060	−	0.120630i
$838$	−11.2313	−	11.2243i	−0.387978	−	0.387739i
$839$	−23.0238	+	16.7278i	−0.794870	+	0.577507i	−0.909405	−	0.415913i	$-0.863462\pi$
$839$	−23.0238	+	16.7278i	−0.794870	+	0.577507i	0.114535	+	0.993419i	$0.463462\pi$
$840$	11.2958	+	8.30033i	0.389740	+	0.286389i
$841$	−2.88018	−	2.09257i	−0.0993164	−	0.0721576i
$842$	−6.17551	−	38.9129i	−0.212822	−	1.34103i
$843$	16.4343	+	16.4343i	0.566028	+	0.566028i
$844$	−6.09169	+	0.00376296i	−0.209685	+	0.000129526i
$845$	−32.0316	+	4.86593i	−1.10192	+	0.167393i
$846$	−6.12881	+	1.99347i	−0.210713	+	0.0685367i
$847$	26.2965	+	51.6099i	0.903560	+	1.77334i
$848$	−8.26671	+	8.28716i	−0.283880	+	0.284582i
$849$			16.3572i			0.561378i
$850$	7.34955	−	21.7049i	0.252088	−	0.744472i
$851$		−	29.9848i		−	1.02787i
$852$	−5.76419	+	11.3302i	−0.197478	+	0.388165i
$853$	10.7002	+	21.0003i	0.366367	+	0.719037i	0.998438	−	0.0558745i	$-0.0177947\pi$
$853$	10.7002	+	21.0003i	0.366367	+	0.719037i	−0.632070	+	0.774911i	$0.717795\pi$
$854$	9.31920	+	28.6514i	0.318897	+	0.980432i
$855$	−10.9050	−	5.64348i	−0.372942	−	0.193003i
$856$	23.9929	+	32.9591i	0.820060	+	1.12652i
$857$	−18.4664	−	18.4664i	−0.630801	−	0.630801i	0.317468	−	0.948269i	$-0.397167\pi$
$857$	−18.4664	−	18.4664i	−0.630801	−	0.630801i	−0.948269	+	0.317468i	$0.897167\pi$
$858$	−44.6256	+	7.08213i	−1.52349	+	0.241780i
$859$	39.7392	+	28.8722i	1.35589	+	0.985108i	0.998695	+	0.0510767i	$0.0162653\pi$
$859$	39.7392	+	28.8722i	1.35589	+	0.985108i	0.357191	+	0.934032i	$0.383735\pi$
$860$	−25.2762	−	0.144185i	−0.861910	−	0.00491667i
$861$	1.26802	−	0.921274i	0.0432142	−	0.0313969i
$862$	−13.1968	+	13.2049i	−0.449484	+	0.449761i
$863$	5.65910	+	35.7301i	0.192638	+	1.21627i	0.874587	+	0.484868i	$0.161132\pi$
$863$	5.65910	+	35.7301i	0.192638	+	1.21627i	−0.681949	+	0.731400i	$0.738868\pi$
$864$	−4.57135	+	3.33208i	−0.155521	+	0.113360i
$865$	8.01692	−	24.1529i	0.272584	−	0.821224i
$866$	32.5933	−	0.0100668i	1.10756	−	0.000342083i
$867$	−5.78944	−	2.94986i	−0.196620	−	0.100183i
$868$	7.11937	+	13.9512i	0.241647	+	0.473536i
$869$	−19.8618	+	6.45348i	−0.673765	+	0.218919i
$870$	14.2547	−	7.15551i	0.483281	−	0.242595i
$871$	−12.8839	−	4.18624i	−0.436555	−	0.141845i
$872$	−16.8900	−	16.8587i	−0.571967	−	0.570908i
$873$	0.127948	−	0.807830i	0.00433037	−	0.0273409i
$874$	11.5469	+	15.8826i	0.390578	+	0.537236i
$875$	−23.7078	+	7.20900i	−0.801470	+	0.243709i
$876$	31.3700	+	10.1713i	1.05989	+	0.343657i
$877$	−22.5821	−	3.57666i	−0.762545	−	0.120775i	−0.236963	−	0.971519i	$-0.576152\pi$
$877$	−22.5821	−	3.57666i	−0.762545	−	0.120775i	−0.525581	+	0.850743i	$0.676152\pi$
$878$	12.9588	−	25.4525i	0.437339	−	0.858981i
$879$	−4.55701	+	14.0250i	−0.153704	+	0.473053i
$880$	−38.7361	+	38.3440i	−1.30579	+	1.29258i
$881$	3.50327	+	10.7820i	0.118028	+	0.363254i	0.992567	−	0.121703i	$-0.0388354\pi$
$881$	3.50327	+	10.7820i	0.118028	+	0.363254i	−0.874538	+	0.484956i	$0.838835\pi$
$882$	−2.91633	−	0.460979i	−0.0981981	−	0.0155220i
$883$	−7.75461	+	15.2193i	−0.260963	+	0.512170i	−0.983894	−	0.178751i	$-0.942794\pi$
$883$	−7.75461	+	15.2193i	−0.260963	+	0.512170i	0.722931	+	0.690920i	$0.242794\pi$
$884$	−19.9914	−	27.4801i	−0.672384	−	0.924256i
$885$	−9.79893	−	3.25250i	−0.329387	−	0.109331i
$886$	−22.0894	−	7.16975i	−0.742110	−	0.240873i
$887$	3.48285	−	0.551630i	0.116943	−	0.0185219i	−0.0976887	−	0.995217i	$-0.531145\pi$
$887$	3.48285	−	0.551630i	0.116943	−	0.0185219i	0.214631	+	0.976695i	$0.431145\pi$
$888$	29.8707	−	15.2547i	1.00239	−	0.511916i
$889$	−17.9206	−	24.6656i	−0.601039	−	0.827259i
$890$	−11.9590	−	8.79910i	−0.400868	−	0.294946i
$891$	3.58185	−	4.92999i	0.119996	−	0.165161i
$892$	17.5019	−	17.5236i	0.586008	−	0.586732i
$893$	−17.6951	+	17.6951i	−0.592142	+	0.592142i
$894$	−3.53179	−	2.56433i	−0.118121	−	0.0857640i
$895$	−11.6477	+	22.5070i	−0.389340	+	0.752327i
$896$	14.6949	−	20.3181i	0.490924	−	0.678780i
$897$	−11.8125	+	6.01875i	−0.394407	+	0.200960i
$898$	−12.5098	−	24.5331i	−0.417457	−	0.818680i
$899$	17.8220			0.594398
$900$	0.120261	−	9.99928i	0.00400869	−	0.333309i
$901$	9.48349			0.315941
$902$	2.76849	+	5.42933i	0.0921808	+	0.180777i
$903$	−11.1615	+	5.68708i	−0.371432	+	0.189254i
$904$	−0.0214331	−	23.1314i	−0.000712854	−	0.769338i
$905$	2.76298	+	18.1882i	0.0918445	+	0.604597i
$906$	16.7800	+	12.1835i	0.557479	+	0.404769i
$907$	−16.3669	+	16.3669i	−0.543456	+	0.543456i	−0.924540	−	0.381085i	$-0.875551\pi$
$907$	−16.3669	+	16.3669i	−0.543456	+	0.543456i	0.381085	+	0.924540i	$0.375551\pi$
$908$	−1.39178	−	1.39006i	−0.0461877	−	0.0461307i
$909$	−1.40044	+	1.92754i	−0.0464497	+	0.0639325i
$910$	−11.5654	+	34.8795i	−0.383389	+	1.15625i
$911$	−0.0597304	−	0.0822118i	−0.00197896	−	0.00272380i	0.808026	−	0.589146i	$-0.200536\pi$
$911$	−0.0597304	−	0.0822118i	−0.00197896	−	0.00272380i	−0.810005	+	0.586423i	$0.800536\pi$
$912$	−9.94765	+	19.5831i	−0.329399	+	0.648462i
$913$	−10.0223	+	1.58738i	−0.331691	+	0.0525347i
$914$	14.6519	+	4.75567i	0.484640	+	0.157304i
$915$	12.7434	−	17.3087i	0.421285	−	0.572207i
$916$	8.13545	−	5.91843i	0.268803	−	0.195550i
$917$	−9.05406	+	17.7696i	−0.298991	+	0.586803i
$918$	4.52689	+	0.715555i	0.149410	+	0.0236168i
$919$	7.64215	+	23.5201i	0.252091	+	0.775857i	0.994389	+	0.105787i	$0.0337360\pi$
$919$	7.64215	+	23.5201i	0.252091	+	0.775857i	−0.742298	+	0.670070i	$0.766264\pi$
$920$	−7.33707	+	14.2098i	−0.241896	+	0.468482i
$921$	0.309552	−	0.952704i	0.0102001	−	0.0313927i
$922$	−21.5366	+	42.3003i	−0.709271	+	1.39309i
$923$	−32.9147	−	5.21318i	−1.08340	−	0.171594i
$924$	−8.33132	+	25.6952i	−0.274080	+	0.845308i
$925$	−10.0150	+	58.4398i	−0.329290	+	1.92149i
$926$	21.2858	+	29.2784i	0.699496	+	0.962149i
$927$	−1.56709	+	9.89423i	−0.0514701	+	0.324969i
$928$	−12.9925	−	25.4022i	−0.426500	−	0.833868i
$929$	−7.48245	−	2.43119i	−0.245491	−	0.0797649i	0.183687	−	0.982985i	$-0.441197\pi$
$929$	−7.48245	−	2.43119i	−0.245491	−	0.0797649i	−0.429178	+	0.903220i	$0.641197\pi$
$930$	5.13255	−	9.92521i	0.168303	−	0.325460i
$931$	−10.9032	+	3.54268i	−0.357339	+	0.116107i
$932$	48.2521	−	24.6232i	1.58055	−	0.806561i
$933$	−2.58421	−	1.31672i	−0.0846034	−	0.0431076i
$934$	4.27604	−	0.00132070i	0.139916	−	4.32146e-5i
$935$	44.1579	+	0.279172i	1.44412	+	0.00912989i
$936$	−12.0054	−	8.70545i	−0.392409	−	0.284547i
$937$	−3.26461	−	20.6120i	−0.106650	−	0.673364i	−0.981858	−	0.189617i	$-0.939276\pi$
$937$	−3.26461	−	20.6120i	−0.106650	−	0.673364i	0.875208	−	0.483747i	$-0.160724\pi$
$938$	−5.72486	+	5.72840i	−0.186923	+	0.187039i
$939$	3.47220	−	2.52270i	0.113311	−	0.0823251i
$940$	−19.3467	−	6.40837i	−0.631020	−	0.209018i
$941$	−36.2709	−	26.3523i	−1.18240	−	0.859061i	−0.189956	−	0.981793i	$-0.560835\pi$
$941$	−36.2709	−	26.3523i	−1.18240	−	0.859061i	−0.992440	+	0.122731i	$0.960835\pi$
$942$	−15.5685	+	2.47074i	−0.507251	+	0.0805012i
$943$	1.26442	+	1.26442i	0.0411753	+	0.0411753i
$944$	−5.68560	+	17.5723i	−0.185051	+	0.571931i
$945$	−2.22198	−	4.42990i	−0.0722811	−	0.144105i
$946$	−15.0661	−	46.3200i	−0.489842	−	1.50599i
$947$	−12.7930	−	25.1078i	−0.415718	−	0.815893i	−0.999991	−	0.00433534i	$-0.998620\pi$
$947$	−12.7930	−	25.1078i	−0.415718	−	0.815893i	0.584272	−	0.811558i	$-0.301380\pi$
$948$	−6.10901	−	3.10795i	−0.198412	−	0.100941i
$949$			86.4517i			2.80634i
$950$	−17.1998	−	34.8115i	−0.558035	−	1.12943i
$951$			8.76765i			0.284310i
$952$	−20.0625	+	3.19664i	−0.650228	+	0.103604i
$953$	−7.57067	−	14.8583i	−0.245238	−	0.481307i	0.735273	−	0.677771i	$-0.237054\pi$
$953$	−7.57067	−	14.8583i	−0.245238	−	0.481307i	−0.980511	+	0.196464i	$0.937054\pi$
$954$	3.93552	−	1.28007i	0.127417	−	0.0414439i
$955$	−32.2496	+	31.8444i	−1.04357	+	1.03046i
$956$	−0.0140342	−	22.7193i	−0.000453898	−	0.734795i
$957$	21.7336	+	21.7336i	0.702546	+	0.702546i
$958$	5.09852	+	32.1266i	0.164726	+	1.03796i
$959$	−6.84336	−	4.97199i	−0.220984	−	0.160554i
$960$	−17.8884	−	0.0799416i	−0.577345	−	0.00258010i
$961$	−14.9787	+	10.8827i	−0.483185	+	0.351054i
$962$	62.1929	+	62.1544i	2.00518	+	2.00394i
$963$	−2.25475	−	14.2359i	−0.0726582	−	0.458746i
$964$	−34.1226	+	11.1104i	−1.09901	+	0.357842i
$965$	−2.88061	+	2.06519i	−0.0927300	+	0.0664807i
$966$	0.00244790	+	7.92560i	7.87600e−5	+	0.255002i
$967$	34.1591	+	17.4049i	1.09848	+	0.559705i	0.906719	−	0.421736i	$-0.138579\pi$
$967$	34.1591	+	17.4049i	1.09848	+	0.559705i	0.191764	+	0.981441i	$0.438579\pi$
$968$	−65.8936	−	33.4976i	−2.11790	−	1.07665i
$969$	16.9246	−	5.49913i	0.543696	−	0.176658i
$970$	1.83984	−	1.81785i	0.0590738	−	0.0583676i
$971$	42.1675	+	13.7010i	1.35322	+	0.439688i	0.893774	−	0.448518i	$-0.148048\pi$
$971$	42.1675	+	13.7010i	1.35322	+	0.439688i	0.459446	+	0.888206i	$0.348048\pi$
$972$	1.97518	−	0.314089i	0.0633540	−	0.0100744i
$973$	−1.84379	+	11.6413i	−0.0591094	+	0.373202i
$974$	−7.30199	+	5.30865i	−0.233971	+	0.170100i
$975$	25.0325	−	7.78504i	0.801682	−	0.249321i
$976$	−31.1341	−	22.5615i	−0.996578	−	0.722177i
$977$	−7.26654	−	1.15091i	−0.232477	−	0.0368208i	0.0391087	−	0.999235i	$-0.487548\pi$
$977$	−7.26654	−	1.15091i	−0.232477	−	0.0368208i	−0.271586	+	0.962414i	$0.587548\pi$
$978$	3.44834	+	1.75568i	0.110266	+	0.0561404i
$979$	8.84134	−	27.2108i	0.282570	−	0.869663i
$980$	−6.56432	−	6.63964i	−0.209689	−	0.212095i
$981$	2.60723	+	8.02424i	0.0832425	+	0.256194i
$982$	3.05533	−	19.3292i	0.0974996	−	0.616821i
$983$	−19.1149	+	37.5151i	−0.609671	+	1.19655i	0.355438	+	0.934700i	$0.384332\pi$
$983$	−19.1149	+	37.5151i	−0.609671	+	1.19655i	−0.965109	+	0.261847i	$0.915668\pi$
$984$	−0.616336	+	1.90288i	−0.0196481	+	0.0606617i
$985$	6.30939	−	2.00604i	0.201034	−	0.0639176i
$986$	−7.13651	+	21.9870i	−0.227273	+	0.700209i
$987$	−9.97604	+	1.58005i	−0.317541	+	0.0502935i
$988$	−56.8778	−	8.97254i	−1.80952	−	0.285455i
$989$	−8.40039	−	11.5621i	−0.267117	−	0.367655i
$990$	18.3626	−	5.84453i	0.583602	−	0.185751i
$991$	30.1799	−	41.5390i	0.958695	−	1.31953i	0.0111399	−	0.999938i	$-0.496454\pi$
$991$	30.1799	−	41.5390i	0.958695	−	1.31953i	0.947555	−	0.319593i	$-0.103546\pi$
$992$	−17.8236	−	9.04695i	−0.565901	−	0.287241i
$993$	11.2534	−	11.2534i	0.357116	−	0.357116i
$994$	−11.7051	+	16.1212i	−0.371265	+	0.511334i
$995$	12.5022	+	2.06126i	0.396347	+	0.0653464i
$996$	−2.69552	−	1.95587i	−0.0854109	−	0.0619741i
$997$	3.95999	−	2.01771i	0.125414	−	0.0639016i	−0.390158	−	0.920748i	$-0.627580\pi$
$997$	3.95999	−	2.01771i	0.125414	−	0.0639016i	0.515572	+	0.856846i	$0.327580\pi$
$998$	−31.3286	+	15.9749i	−0.991689	+	0.505677i
$999$	−11.8584			−0.375182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.127.4	✓	240
3.2	odd	2		900.2.bj.f.127.27		240
4.3	odd	2	inner	300.2.w.a.127.8	yes	240
12.11	even	2		900.2.bj.f.127.23		240
25.13	odd	20	inner	300.2.w.a.163.8	yes	240
75.38	even	20		900.2.bj.f.163.23		240
100.63	even	20	inner	300.2.w.a.163.4	yes	240
300.263	odd	20		900.2.bj.f.163.27		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.4	✓	240	1.1	even	1	trivial
300.2.w.a.127.8	yes	240	4.3	odd	2	inner
300.2.w.a.163.4	yes	240	100.63	even	20	inner
300.2.w.a.163.8	yes	240	25.13	odd	20	inner
900.2.bj.f.127.23		240	12.11	even	2
900.2.bj.f.127.27		240	3.2	odd	2
900.2.bj.f.163.23		240	75.38	even	20
900.2.bj.f.163.27		240	300.263	odd	20

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25988 + 0.642429i) q^{2} +(-0.891007 + 0.453990i) q^{3} +(1.17457 - 1.61876i) q^{4} +(-2.20628 - 0.363753i) q^{5} +(0.830900 - 1.14438i) q^{6} +(1.56720 - 1.56720i) q^{7} +(-0.439875 + 2.79401i) q^{8} +(0.587785 - 0.809017i) q^{9} +(3.01333 - 0.959095i) q^{10} +(3.58185 + 4.92999i) q^{11} +(-0.311649 + 1.97557i) q^{12} +(-5.17848 + 0.820190i) q^{13} +(-0.967663 + 2.98129i) q^{14} +(2.13095 - 0.677525i) q^{15} +(-1.24077 - 3.80270i) q^{16} +(-1.47126 + 2.88752i) q^{17} +(-0.220800 + 1.39687i) q^{18} +(1.69688 + 5.22245i) q^{19} +(-3.18026 + 3.14419i) q^{20} +(-0.684892 + 2.10788i) q^{21} +(-7.67984 - 3.91009i) q^{22} +(-2.49745 - 0.395558i) q^{23} +(-0.876524 - 2.68918i) q^{24} +(4.73537 + 1.60509i) q^{25} +(5.99732 - 4.36014i) q^{26} +(-0.156434 + 0.987688i) q^{27} +(-0.696133 - 4.37771i) q^{28} +(-4.79694 - 1.55862i) q^{29} +(-2.24947 + 2.22258i) q^{30} +(-3.36051 + 1.09190i) q^{31} +(4.00617 + 3.99382i) q^{32} +(-5.42961 - 2.76653i) q^{33} +(-0.00141553 - 4.58309i) q^{34} +(-4.02776 + 2.88761i) q^{35} +(-0.619209 - 1.90173i) q^{36} +(1.85505 + 11.7124i) q^{37} +(-5.49291 - 5.48952i) q^{38} +(4.24170 - 3.08177i) q^{39} +(1.98682 - 6.00438i) q^{40} +(-0.572121 - 0.415670i) q^{41} +(-0.491285 - 3.09566i) q^{42} +(3.99658 + 3.99658i) q^{43} +(12.1876 - 0.00752853i) q^{44} +(-1.59110 + 1.57111i) q^{45} +(3.40060 - 1.10608i) q^{46} +(2.06893 + 4.06050i) q^{47} +(2.83192 + 2.82493i) q^{48} +2.08776i q^{49} +(-6.99712 + 1.01993i) q^{50} -3.24074i q^{51} +(-4.75480 + 9.34608i) q^{52} +(-1.32853 - 2.60739i) q^{53} +(-0.437431 - 1.34486i) q^{54} +(-6.10926 - 12.1799i) q^{55} +(3.68941 + 5.06815i) q^{56} +(-3.88287 - 3.88287i) q^{57} +(7.04484 - 1.11802i) q^{58} +(-3.73548 - 2.71399i) q^{59} +(1.40621 - 4.24530i) q^{60} +(7.77655 - 5.64999i) q^{61} +(3.53236 - 3.53454i) q^{62} +(-0.346715 - 2.18907i) q^{63} +(-7.61302 - 2.45803i) q^{64} +(11.7235 + 0.0741177i) q^{65} +(8.61793 - 0.00266174i) q^{66} +(2.30218 + 1.17302i) q^{67} +(2.94609 + 5.77321i) q^{68} +(2.40483 - 0.781376i) q^{69} +(3.21939 - 6.22558i) q^{70} +(6.04498 + 1.96413i) q^{71} +(2.00185 + 1.99815i) q^{72} +(2.57943 - 16.2859i) q^{73} +(-9.86149 - 13.5644i) q^{74} +(-4.94794 + 0.719669i) q^{75} +(10.4470 + 3.38730i) q^{76} +(13.3398 + 2.11281i) q^{77} +(-3.36419 + 6.60764i) q^{78} +(-1.05902 + 3.25934i) q^{79} +(1.35424 + 8.84116i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(0.987840 + 0.156146i) q^{82} +(-0.755975 + 1.48368i) q^{83} +(2.60770 + 3.58453i) q^{84} +(4.29637 - 5.83550i) q^{85} +(-7.60270 - 2.46767i) q^{86} +(4.98170 - 0.789024i) q^{87} +(-15.3500 + 7.83915i) q^{88} +(-2.75973 - 3.79844i) q^{89} +(0.995264 - 3.00157i) q^{90} +(-6.83031 + 9.40112i) q^{91} +(-3.57375 + 3.57817i) q^{92} +(2.49853 - 2.49853i) q^{93} +(-5.21517 - 3.78658i) q^{94} +(-1.84411 - 12.1395i) q^{95} +(-5.38268 - 1.73975i) q^{96} +(0.728754 - 0.371318i) q^{97} +(-1.34124 - 2.63032i) q^{98} +6.09380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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