LMFDB - Embedded newform 540.2.be.a.11.35

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			11.35
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0367263 + 1.41374i) q^{2} +(-0.570476 + 1.63541i) q^{3} +(-1.99730 + 0.103843i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-2.33299 - 0.746441i) q^{6} +(-1.79764 - 0.316972i) q^{7} +(-0.220160 - 2.81985i) q^{8} +(-2.34911 - 1.86592i) q^{9} +(-1.34104 - 0.449015i) q^{10} +(-1.87642 + 0.682962i) q^{11} +(0.969589 - 3.32564i) q^{12} +(1.61846 - 1.35805i) q^{13} +(0.382094 - 2.55303i) q^{14} +(-1.34167 - 1.09541i) q^{15} +(3.97843 - 0.414810i) q^{16} +(0.548982 - 0.316955i) q^{17} +(2.55165 - 3.38956i) q^{18} +(-4.14161 - 2.39116i) q^{19} +(0.585538 - 1.91237i) q^{20} +(1.54389 - 2.75904i) q^{21} +(-1.03444 - 2.62768i) q^{22} +(0.533434 + 3.02525i) q^{23} +(4.73719 + 1.24860i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(1.97936 + 2.23820i) q^{26} +(4.39166 - 2.77729i) q^{27} +(3.62334 + 0.446417i) q^{28} +(-0.140358 + 0.167272i) q^{29} +(1.49935 - 1.93699i) q^{30} +(-7.73919 + 1.36463i) q^{31} +(0.732545 + 5.60922i) q^{32} +(-0.0464661 - 3.45833i) q^{33} +(0.468253 + 0.764475i) q^{34} +(0.912684 - 1.58081i) q^{35} +(4.88565 + 3.48287i) q^{36} +(-4.24077 - 7.34523i) q^{37} +(3.22837 - 5.94297i) q^{38} +(1.29767 + 3.42157i) q^{39} +(2.72509 + 0.757562i) q^{40} +(4.28132 + 5.10228i) q^{41} +(3.95726 + 2.08132i) q^{42} +(2.95131 + 8.10865i) q^{43} +(3.67686 - 1.55893i) q^{44} +(2.55684 - 1.56926i) q^{45} +(-4.25732 + 0.865241i) q^{46} +(0.145756 - 0.826624i) q^{47} +(-1.59122 + 6.74300i) q^{48} +(-3.44682 - 1.25454i) q^{49} +(0.880598 - 1.10659i) q^{50} +(0.205169 + 1.07862i) q^{51} +(-3.09153 + 2.88050i) q^{52} -12.9527i q^{53} +(4.08765 + 6.10665i) q^{54} -1.99685i q^{55} +(-0.498045 + 5.13884i) q^{56} +(6.27322 - 5.40912i) q^{57} +(-0.241633 - 0.192286i) q^{58} +(-6.22822 - 2.26689i) q^{59} +(2.79346 + 2.04855i) q^{60} +(-1.08847 + 6.17300i) q^{61} +(-2.21346 - 10.8911i) q^{62} +(3.63141 + 4.09885i) q^{63} +(-7.90306 + 1.24163i) q^{64} +(0.722602 + 1.98533i) q^{65} +(4.88746 - 0.192702i) q^{66} +(-9.36054 - 11.1555i) q^{67} +(-1.06357 + 0.690062i) q^{68} +(-5.25183 - 0.853454i) q^{69} +(2.26837 + 1.23224i) q^{70} +(2.25153 + 3.89976i) q^{71} +(-4.74443 + 7.03494i) q^{72} +(-1.53042 + 2.65076i) q^{73} +(10.2285 - 6.26510i) q^{74} +(1.48823 - 0.886099i) q^{75} +(8.52036 + 4.34580i) q^{76} +(3.58960 - 0.632944i) q^{77} +(-4.78955 + 1.96022i) q^{78} +(-7.15688 + 8.52924i) q^{79} +(-0.970910 + 3.88038i) q^{80} +(2.03667 + 8.76653i) q^{81} +(-7.05605 + 6.24005i) q^{82} +(1.56073 + 1.30961i) q^{83} +(-2.79710 + 5.67096i) q^{84} +(0.110077 + 0.624279i) q^{85} +(-11.3551 + 4.47017i) q^{86} +(-0.193487 - 0.324967i) q^{87} +(2.33896 + 5.14086i) q^{88} +(-6.00461 - 3.46676i) q^{89} +(2.31243 + 3.55706i) q^{90} +(-3.33986 + 1.92827i) q^{91} +(-1.37958 - 5.98695i) q^{92} +(2.18330 - 13.4352i) q^{93} +(1.17398 + 0.175702i) q^{94} +(3.66347 - 3.07402i) q^{95} +(-9.59126 - 2.00192i) q^{96} +(-5.00188 + 1.82054i) q^{97} +(1.64700 - 4.91898i) q^{98} +(5.68228 + 1.89690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

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

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.0367263	+	1.41374i	0.0259694	+	0.999663i
$2$	0.0367263	+	1.41374i	0.0259694	+	0.999663i
$3$	−0.570476	+	1.63541i	−0.329365	+	0.944203i
$3$	−0.570476	+	1.63541i	−0.329365	+	0.944203i
$4$	−1.99730	+	0.103843i	−0.998651	+	0.0519213i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−2.33299	−	0.746441i	−0.952438	−	0.304733i
$7$	−1.79764	−	0.316972i	−0.679443	−	0.119804i	−0.176732	−	0.984259i	$-0.556553\pi$
$7$	−1.79764	−	0.316972i	−0.679443	−	0.119804i	−0.502710	+	0.864455i	$0.667664\pi$
$8$	−0.220160	−	2.81985i	−0.0778382	−	0.996966i
$9$	−2.34911	−	1.86592i	−0.783038	−	0.621974i
$10$	−1.34104	−	0.449015i	−0.424074	−	0.141991i
$11$	−1.87642	+	0.682962i	−0.565763	+	0.205921i	−0.609036	−	0.793142i	$-0.708444\pi$
$11$	−1.87642	+	0.682962i	−0.565763	+	0.205921i	0.0432734	+	0.999063i	$0.486221\pi$
$12$	0.969589	−	3.32564i	0.279896	−	0.960030i
$13$	1.61846	−	1.35805i	0.448880	−	0.376655i	−0.390140	−	0.920755i	$-0.627573\pi$
$13$	1.61846	−	1.35805i	0.448880	−	0.376655i	0.839020	+	0.544101i	$0.183129\pi$
$14$	0.382094	−	2.55303i	0.102119	−	0.682325i
$15$	−1.34167	−	1.09541i	−0.346417	−	0.282835i
$16$	3.97843	−	0.414810i	0.994608	−	0.103703i
$17$	0.548982	−	0.316955i	0.133148	−	0.0768728i	−0.431947	−	0.901899i	$-0.642173\pi$
$17$	0.548982	−	0.316955i	0.133148	−	0.0768728i	0.565094	+	0.825026i	$0.308840\pi$
$18$	2.55165	−	3.38956i	0.601429	−	0.798926i
$19$	−4.14161	−	2.39116i	−0.950151	−	0.548570i	−0.0570234	−	0.998373i	$-0.518161\pi$
$19$	−4.14161	−	2.39116i	−0.950151	−	0.548570i	−0.893128	+	0.449803i	$0.851494\pi$
$20$	0.585538	−	1.91237i	0.130930	−	0.427618i
$21$	1.54389	−	2.75904i	0.336904	−	0.602072i
$22$	−1.03444	−	2.62768i	−0.220544	−	0.560224i
$23$	0.533434	+	3.02525i	0.111229	+	0.630809i	0.988549	+	0.150903i	$0.0482181\pi$
$23$	0.533434	+	3.02525i	0.111229	+	0.630809i	−0.877320	+	0.479906i	$0.840671\pi$
$24$	4.73719	+	1.24860i	0.966975	+	0.254870i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	1.97936	+	2.23820i	0.388185	+	0.438947i
$27$	4.39166	−	2.77729i	0.845175	−	0.534490i
$28$	3.62334	+	0.446417i	0.684747	+	0.0843649i
$29$	−0.140358	+	0.167272i	−0.0260638	+	0.0310616i	−0.778919	−	0.627125i	$-0.784232\pi$
$29$	−0.140358	+	0.167272i	−0.0260638	+	0.0310616i	0.752855	+	0.658186i	$0.228676\pi$
$30$	1.49935	−	1.93699i	0.273743	−	0.353645i
$31$	−7.73919	+	1.36463i	−1.39000	+	0.245094i	−0.818028	−	0.575179i	$-0.804932\pi$
$31$	−7.73919	+	1.36463i	−1.39000	+	0.245094i	−0.571972	+	0.820273i	$0.693821\pi$
$32$	0.732545	+	5.60922i	0.129497	+	0.991580i
$33$	−0.0464661	−	3.45833i	−0.00808872	−	0.602018i
$34$	0.468253	+	0.764475i	0.0803047	+	0.131106i
$35$	0.912684	−	1.58081i	0.154272	−	0.267206i
$36$	4.88565	+	3.48287i	0.814275	+	0.580479i
$37$	−4.24077	−	7.34523i	−0.697178	−	1.20755i	−0.969441	−	0.245326i	$-0.921105\pi$
$37$	−4.24077	−	7.34523i	−0.697178	−	1.20755i	0.272262	−	0.962223i	$-0.412228\pi$
$38$	3.22837	−	5.94297i	0.523710	−	0.964077i
$39$	1.29767	+	3.42157i	0.207793	+	0.547890i
$40$	2.72509	+	0.757562i	0.430874	+	0.119781i
$41$	4.28132	+	5.10228i	0.668631	+	0.796843i	0.988597	−	0.150586i	$-0.0481160\pi$
$41$	4.28132	+	5.10228i	0.668631	+	0.796843i	−0.319966	+	0.947429i	$0.603672\pi$
$42$	3.95726	+	2.08132i	0.610618	+	0.321155i
$43$	2.95131	+	8.10865i	0.450070	+	1.23656i	0.932674	+	0.360719i	$0.117469\pi$
$43$	2.95131	+	8.10865i	0.450070	+	1.23656i	−0.482604	+	0.875839i	$0.660309\pi$
$44$	3.67686	−	1.55893i	0.554308	−	0.235018i
$45$	2.55684	−	1.56926i	0.381151	−	0.233932i
$46$	−4.25732	+	0.865241i	−0.627708	+	0.127573i
$47$	0.145756	−	0.826624i	0.0212607	−	0.120575i	−0.972330	−	0.233610i	$-0.924946\pi$
$47$	0.145756	−	0.826624i	0.0212607	−	0.120575i	0.993591	+	0.113035i	$0.0360571\pi$
$48$	−1.59122	+	6.74300i	−0.229673	+	0.973268i
$49$	−3.44682	−	1.25454i	−0.492403	−	0.179220i
$50$	0.880598	−	1.10659i	0.124535	−	0.156496i
$51$	0.205169	+	1.07862i	0.0287294	+	0.151038i
$52$	−3.09153	+	2.88050i	−0.428718	+	0.399453i
$53$		−	12.9527i		−	1.77919i	−0.456750	−	0.889595i	$-0.650987\pi$
$53$		−	12.9527i		−	1.77919i	0.456750	−	0.889595i	$-0.349013\pi$
$54$	4.08765	+	6.10665i	0.556259	+	0.831009i
$55$		−	1.99685i		−	0.269255i
$56$	−0.498045	+	5.13884i	−0.0665540	+	0.686706i
$57$	6.27322	−	5.40912i	0.830908	−	0.716456i
$58$	−0.241633	−	0.192286i	−0.0317280	−	0.0252484i
$59$	−6.22822	−	2.26689i	−0.810845	−	0.295123i	−0.0968722	−	0.995297i	$-0.530884\pi$
$59$	−6.22822	−	2.26689i	−0.810845	−	0.295123i	−0.713973	+	0.700173i	$0.753106\pi$
$60$	2.79346	+	2.04855i	0.360634	+	0.264467i
$61$	−1.08847	+	6.17300i	−0.139364	+	0.790372i	0.832357	+	0.554240i	$0.186991\pi$
$61$	−1.08847	+	6.17300i	−0.139364	+	0.790372i	−0.971721	+	0.236132i	$0.924120\pi$
$62$	−2.21346	−	10.8911i	−0.281109	−	1.38317i
$63$	3.63141	+	4.09885i	0.457514	+	0.516407i
$64$	−7.90306	+	1.24163i	−0.987882	+	0.155204i
$65$	0.722602	+	1.98533i	0.0896278	+	0.246250i
$66$	4.88746	−	0.192702i	0.601605	−	0.0237200i
$67$	−9.36054	−	11.1555i	−1.14357	−	1.36286i	−0.921758	−	0.387767i	$-0.873247\pi$
$67$	−9.36054	−	11.1555i	−1.14357	−	1.36286i	−0.221814	−	0.975089i	$-0.571198\pi$
$68$	−1.06357	+	0.690062i	−0.128977	+	0.0836824i
$69$	−5.25183	−	0.853454i	−0.632247	−	0.102744i
$70$	2.26837	+	1.23224i	0.271123	+	0.147280i
$71$	2.25153	+	3.89976i	0.267207	+	0.462817i	0.968140	−	0.250411i	$-0.0805658\pi$
$71$	2.25153	+	3.89976i	0.267207	+	0.462817i	−0.700932	+	0.713228i	$0.747233\pi$
$72$	−4.74443	+	7.03494i	−0.559137	+	0.829075i
$73$	−1.53042	+	2.65076i	−0.179122	+	0.310248i	−0.941580	−	0.336789i	$-0.890659\pi$
$73$	−1.53042	+	2.65076i	−0.179122	+	0.310248i	0.762458	+	0.647037i	$0.223992\pi$
$74$	10.2285	−	6.26510i	1.18904	−	0.728303i
$75$	1.48823	−	0.886099i	0.171846	−	0.102318i
$76$	8.52036	+	4.34580i	0.977352	+	0.498497i
$77$	3.58960	−	0.632944i	0.409073	−	0.0721307i
$78$	−4.78955	+	1.96022i	−0.542309	+	0.221952i
$79$	−7.15688	+	8.52924i	−0.805212	+	0.959615i	−0.999774	−	0.0212756i	$-0.993227\pi$
$79$	−7.15688	+	8.52924i	−0.805212	+	0.959615i	0.194561	+	0.980890i	$0.437672\pi$
$80$	−0.970910	+	3.88038i	−0.108551	+	0.433839i
$81$	2.03667	+	8.76653i	0.226296	+	0.974058i
$82$	−7.05605	+	6.24005i	−0.779210	+	0.689099i
$83$	1.56073	+	1.30961i	0.171313	+	0.143748i	0.724413	−	0.689366i	$-0.242111\pi$
$83$	1.56073	+	1.30961i	0.171313	+	0.143748i	−0.553100	+	0.833115i	$0.686555\pi$
$84$	−2.79710	+	5.67096i	−0.305189	+	0.618753i
$85$	0.110077	+	0.624279i	0.0119396	+	0.0677126i
$86$	−11.3551	+	4.47017i	−1.22445	+	0.482031i
$87$	−0.193487	−	0.324967i	−0.0207440	−	0.0348401i
$88$	2.33896	+	5.14086i	0.249334	+	0.548018i
$89$	−6.00461	−	3.46676i	−0.636487	−	0.367476i	0.146773	−	0.989170i	$-0.453111\pi$
$89$	−6.00461	−	3.46676i	−0.636487	−	0.367476i	−0.783260	+	0.621694i	$0.786445\pi$
$90$	2.31243	+	3.55706i	0.243751	+	0.374947i
$91$	−3.33986	+	1.92827i	−0.350113	+	0.202138i
$92$	−1.37958	−	5.98695i	−0.143831	−	0.624183i
$93$	2.18330	−	13.4352i	0.226398	−	1.39317i
$94$	1.17398	+	0.175702i	0.121087	+	0.0181223i
$95$	3.66347	−	3.07402i	0.375864	−	0.315388i
$96$	−9.59126	−	2.00192i	−0.978904	−	0.204320i
$97$	−5.00188	+	1.82054i	−0.507864	+	0.184848i	−0.583228	−	0.812309i	$-0.698211\pi$
$97$	−5.00188	+	1.82054i	−0.507864	+	0.184848i	0.0753635	+	0.997156i	$0.475988\pi$
$98$	1.64700	−	4.91898i	0.166372	−	0.496892i
$99$	5.68228	+	1.89690i	0.571091	+	0.190646i
$100$	1.59677	+	1.20429i	0.159677	+	0.120429i
$101$	6.28092	+	1.10750i	0.624975	+	0.110200i	0.477162	−	0.878815i	$-0.341665\pi$
$101$	6.28092	+	1.10750i	0.624975	+	0.110200i	0.147813	+	0.989015i	$0.452777\pi$
$102$	−1.51736	+	0.329669i	−0.150241	+	0.0326421i
$103$	3.41738	−	9.38916i	0.336724	−	0.925142i	−0.649593	−	0.760282i	$-0.725061\pi$
$103$	3.41738	−	9.38916i	0.336724	−	0.925142i	0.986317	−	0.164860i	$-0.0527171\pi$
$104$	−4.18581	−	4.26482i	−0.410452	−	0.418200i
$105$	2.06461	+	2.39443i	0.201485	+	0.233672i
$106$	18.3117	−	0.475705i	1.77859	−	0.0462045i
$107$	−5.86840			−0.567319			−0.283660	−	0.958925i	$-0.591549\pi$
$107$	−5.86840			−0.567319			−0.283660	+	0.958925i	$0.591549\pi$
$108$	−8.48306	+	6.00313i	−0.816283	+	0.577652i
$109$	−16.8094			−1.61005			−0.805024	−	0.593242i	$-0.797848\pi$
$109$	−16.8094			−1.61005			−0.805024	+	0.593242i	$0.797848\pi$
$110$	2.82302	−	0.0733368i	0.269164	−	0.00699239i
$111$	14.4317	−	2.74511i	1.36980	−	0.260554i
$112$	−7.28326	−	0.515373i	−0.688203	−	0.0486982i
$113$	−5.66844	+	15.5739i	−0.533242	+	1.46507i	0.321949	+	0.946757i	$0.395662\pi$
$113$	−5.66844	+	15.5739i	−0.533242	+	1.46507i	−0.855191	+	0.518313i	$0.826560\pi$
$114$	7.87747	+	8.67002i	0.737793	+	0.812022i
$115$	−3.02525	−	0.533434i	−0.282106	−	0.0497430i
$116$	0.262967	−	0.348668i	0.0244159	−	0.0323730i
$117$	−6.33596	+	0.170291i	−0.585759	+	0.0157434i
$118$	2.97604	−	8.88832i	0.273967	−	0.818236i
$119$	−1.08734	+	0.395758i	−0.0996759	+	0.0362791i
$120$	−2.79352	+	4.02446i	−0.255012	+	0.367381i
$121$	−5.37196	+	4.50761i	−0.488360	+	0.409783i
$122$	−8.76697	−	1.31209i	−0.793724	−	0.118791i
$123$	−10.7867	+	4.09098i	−0.972605	+	0.368871i
$124$	15.3158	−	3.52923i	1.37540	−	0.316934i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	−5.66133	+	5.28439i	−0.504351	+	0.470771i
$127$	7.84257	+	4.52791i	0.695916	+	0.401787i	0.805824	−	0.592154i	$-0.201722\pi$
$127$	7.84257	+	4.52791i	0.695916	+	0.401787i	−0.109909	+	0.993942i	$0.535056\pi$
$128$	−2.04559	−	11.1272i	−0.180806	−	0.983519i
$129$	−14.9446	+	0.200796i	−1.31580	+	0.0176791i
$130$	−2.78020	+	1.09448i	−0.243840	+	0.0959925i
$131$	−0.940729	−	5.33514i	−0.0821919	−	0.466133i	−0.997927	−	0.0643516i	$-0.979502\pi$
$131$	−0.940729	−	5.33514i	−0.0821919	−	0.466133i	0.915735	−	0.401782i	$-0.131609\pi$
$132$	0.451929	+	6.90250i	0.0393353	+	0.600786i
$133$	6.68718	+	5.61121i	0.579852	+	0.486554i
$134$	15.4271	−	13.6430i	1.33270	−	1.17858i
$135$	1.10777	+	5.07670i	0.0953413	+	0.436933i
$136$	−1.01463	−	1.47826i	−0.0870036	−	0.126760i
$137$	−3.75569	+	4.47586i	−0.320871	+	0.382399i	−0.902235	−	0.431245i	$-0.858075\pi$
$137$	−3.75569	+	4.47586i	−0.320871	+	0.382399i	0.581364	+	0.813643i	$0.302519\pi$
$138$	1.01368	−	7.45605i	0.0862901	−	0.634701i
$139$	−6.64276	+	1.17130i	−0.563432	+	0.0993482i	−0.448108	−	0.893980i	$-0.647902\pi$
$139$	−6.64276	+	1.17130i	−0.563432	+	0.0993482i	−0.115324	+	0.993328i	$0.536791\pi$
$140$	−1.65875	+	3.25214i	−0.140190	+	0.274856i
$141$	1.26872	+	0.709940i	0.106845	+	0.0597877i
$142$	−5.43055	+	3.32629i	−0.455721	+	0.279136i
$143$	−2.10942	+	3.65362i	−0.176398	+	0.305531i
$144$	−10.1198	−	6.44901i	−0.843316	−	0.537418i
$145$	−0.109179	−	0.189104i	−0.00906683	−	0.0157042i
$146$	−3.80368	−	2.06625i	−0.314795	−	0.171004i
$147$	4.01802	−	4.92127i	0.331401	−	0.405900i
$148$	9.23285	+	14.2303i	0.758936	+	1.16972i
$149$	8.01650	+	9.55370i	0.656737	+	0.782669i	0.986914	−	0.161250i	$-0.0515526\pi$
$149$	8.01650	+	9.55370i	0.656737	+	0.782669i	−0.330176	+	0.943919i	$0.607108\pi$
$150$	1.30737	+	2.07142i	0.106746	+	0.169131i
$151$	−6.20903	−	17.0592i	−0.505283	−	1.38825i	−0.886053	−	0.463585i	$-0.846563\pi$
$151$	−6.20903	−	17.0592i	−0.505283	−	1.38825i	0.380769	−	0.924670i	$-0.375659\pi$
$152$	−5.83089	+	12.2051i	−0.472948	+	0.989968i
$153$	−1.88103	−	0.279795i	−0.152073	−	0.0226201i
$154$	1.02665	+	5.05151i	0.0827298	+	0.407062i
$155$	1.36463	−	7.73919i	0.109610	−	0.621627i
$156$	−2.94714	−	6.69916i	−0.235960	−	0.536362i
$157$	7.25110	+	2.63918i	0.578701	+	0.210630i	0.614753	−	0.788720i	$-0.289256\pi$
$157$	7.25110	+	2.63918i	0.578701	+	0.210630i	−0.0360517	+	0.999350i	$0.511478\pi$
$158$	−12.3209	−	9.80470i	−0.980202	−	0.780020i
$159$	21.1829	+	7.38921i	1.67992	+	0.586003i
$160$	−5.52149	−	1.23010i	−0.436512	−	0.0972479i
$161$		−	5.60739i		−	0.441924i
$162$	−12.3188	+	3.20127i	−0.967853	+	0.251516i
$163$		−	7.40707i		−	0.580167i	−0.957001	−	0.290083i	$-0.906317\pi$
$163$		−	7.40707i		−	0.580167i	0.957001	−	0.290083i	$-0.0936831\pi$
$164$	−9.08093	−	9.74622i	−0.709102	−	0.761052i
$165$	3.26566	+	1.13915i	0.254231	+	0.0886830i
$166$	−1.79412	+	2.25456i	−0.139251	+	0.174988i
$167$	2.15117	+	0.782961i	0.166462	+	0.0605874i	0.423907	−	0.905706i	$-0.360658\pi$
$167$	2.15117	+	0.782961i	0.166462	+	0.0605874i	−0.257445	+	0.966293i	$0.582881\pi$
$168$	−8.11997	−	3.74609i	−0.626470	−	0.289017i
$169$	−1.48231	+	8.40661i	−0.114024	+	0.646662i
$170$	−0.878524	+	0.178548i	−0.0673797	+	0.0136940i
$171$	5.26740	+	13.3450i	0.402808	+	1.02052i
$172$	−6.73668	−	15.8890i	−0.513667	−	1.21152i
$173$	1.90005	+	5.22034i	0.144458	+	0.396895i	0.990728	−	0.135859i	$-0.0433794\pi$
$173$	1.90005	+	5.22034i	0.144458	+	0.396895i	−0.846270	+	0.532754i	$0.821157\pi$
$174$	0.452312	−	0.285474i	0.0342897	−	0.0216418i
$175$	1.17332	+	1.39831i	0.0886949	+	0.105702i
$176$	−7.18192	+	3.49548i	−0.541358	+	0.263482i
$177$	7.26033	−	8.89247i	0.545720	−	0.668399i
$178$	4.68056	−	8.61625i	0.350823	−	0.645815i
$179$	−1.59348	−	2.75999i	−0.119102	−	0.206291i	0.800310	−	0.599587i	$-0.204668\pi$
$179$	−1.59348	−	2.75999i	−0.119102	−	0.206291i	−0.919412	+	0.393295i	$0.871335\pi$
$180$	−4.94382	+	3.39980i	−0.368491	+	0.253406i
$181$	−11.3643	+	19.6835i	−0.844700	+	1.46306i	0.0411819	+	0.999152i	$0.486888\pi$
$181$	−11.3643	+	19.6835i	−0.844700	+	1.46306i	−0.885882	+	0.463911i	$0.846446\pi$
$182$	−2.84873	−	4.65087i	−0.211162	−	0.344745i
$183$	−9.47443	−	5.30164i	−0.700370	−	0.391908i
$184$	8.41331	−	2.17024i	0.620237	−	0.159992i
$185$	8.35269	−	1.47280i	0.614102	−	0.108283i
$186$	19.0740	+	2.59319i	1.39858	+	0.190142i
$187$	−0.813654	+	0.969675i	−0.0595003	+	0.0709097i
$188$	−0.205280	+	1.66615i	−0.0149716	+	0.121517i
$189$	−8.77492	+	3.60053i	−0.638282	+	0.261900i
$190$	4.48040	+	5.06629i	0.325042	+	0.367547i
$191$	17.3416	+	14.5513i	1.25479	+	1.05289i	0.996217	+	0.0869032i	$0.0276971\pi$
$191$	17.3416	+	14.5513i	1.25479	+	1.05289i	0.258574	+	0.965991i	$0.416747\pi$
$192$	2.47794	−	13.6330i	0.178830	−	0.983880i
$193$	1.39998	+	7.93968i	0.100773	+	0.571511i	0.992825	+	0.119578i	$0.0381542\pi$
$193$	1.39998	+	7.93968i	0.100773	+	0.571511i	−0.892052	+	0.451933i	$0.850735\pi$
$194$	−2.75746	−	7.00448i	−0.197974	−	0.502893i
$195$	−3.65906	+	0.0491631i	−0.262030	+	0.00352064i
$196$	7.01462	+	2.14777i	0.501045	+	0.153412i
$197$	10.1431	+	5.85611i	0.722664	+	0.417230i	0.815732	−	0.578429i	$-0.196334\pi$
$197$	10.1431	+	5.85611i	0.722664	+	0.417230i	−0.0930683	+	0.995660i	$0.529668\pi$
$198$	−2.47303	+	8.10292i	−0.175751	+	0.575849i
$199$	8.69564	−	5.02043i	0.616417	−	0.355889i	−0.159055	−	0.987270i	$-0.550845\pi$
$199$	8.69564	−	5.02043i	0.616417	−	0.355889i	0.775473	+	0.631381i	$0.217512\pi$
$200$	−1.64391	+	2.30164i	−0.116242	+	0.162751i
$201$	23.5837	−	8.94437i	1.66346	−	0.630887i
$202$	−1.33503	+	8.92024i	−0.0939326	+	0.627626i
$203$	0.305333	−	0.256205i	0.0214302	−	0.0179820i
$204$	−0.521792	−	2.13303i	−0.0365327	−	0.149342i
$205$	−6.25888	+	2.27805i	−0.437139	+	0.159106i
$206$	13.3993	+	4.48644i	0.933574	+	0.312585i
$207$	4.39179	−	8.10201i	0.305251	−	0.563129i
$208$	5.87560	−	6.07426i	0.407399	−	0.421174i
$209$	9.40449	+	1.65827i	0.650522	+	0.114705i
$210$	−3.30926	+	3.00675i	−0.228361	+	0.207486i
$211$	4.43498	−	12.1850i	0.305316	−	0.838850i	−0.688237	−	0.725486i	$-0.741615\pi$
$211$	4.43498	−	12.1850i	0.305316	−	0.838850i	0.993553	−	0.113364i	$-0.0361627\pi$
$212$	1.34504	+	25.8705i	0.0923779	+	1.77679i
$213$	−7.66214	+	1.45744i	−0.525001	+	0.0998624i
$214$	−0.215524	−	8.29637i	−0.0147329	−	0.567128i
$215$	−8.62905			−0.588496
$216$	−8.79840	−	11.7723i	−0.598655	−	0.801007i
$217$	14.3448			0.973788
$218$	−0.617347	−	23.7641i	−0.0418120	−	1.60951i
$219$	−3.46201	−	4.01505i	−0.233941	−	0.271312i
$220$	0.207358	+	3.98831i	0.0139801	+	0.268892i
$221$	0.458065	−	1.25852i	0.0308128	−	0.0846574i
$222$	4.41088	+	20.3018i	0.296039	+	1.36257i
$223$	24.1360	+	4.25582i	1.61626	+	0.284991i	0.907372	−	0.420327i	$-0.138085\pi$
$223$	24.1360	+	4.25582i	1.61626	+	0.284991i	0.708891	+	0.705318i	$0.249196\pi$
$224$	0.461115	−	10.3155i	0.0308096	−	0.689236i
$225$	0.600133	+	2.93936i	0.0400089	+	0.195957i
$226$	−22.2256	−	7.44171i	−1.47842	−	0.495015i
$227$	−19.9690	+	7.26814i	−1.32539	+	0.482403i	−0.905182	−	0.425024i	$-0.860266\pi$
$227$	−19.9690	+	7.26814i	−1.32539	+	0.482403i	−0.420210	+	0.907427i	$0.638044\pi$
$228$	−11.9678	+	11.4551i	−0.792588	+	0.758631i
$229$	21.3677	−	17.9296i	1.41202	−	1.18482i	0.456557	−	0.889694i	$-0.349082\pi$
$229$	21.3677	−	17.9296i	1.41202	−	1.18482i	0.955458	−	0.295127i	$-0.0953620\pi$
$230$	0.643029	−	4.29650i	0.0424001	−	0.283303i
$231$	−1.01266	+	6.23155i	−0.0666284	+	0.410006i
$232$	0.502582	+	0.358961i	0.0329962	+	0.0235669i
$233$	2.32324	−	1.34132i	0.152200	−	0.0878729i	−0.421966	−	0.906612i	$-0.638660\pi$
$233$	2.32324	−	1.34132i	0.152200	−	0.0878729i	0.574166	+	0.818739i	$0.305326\pi$
$234$	−0.473442	−	8.95112i	−0.0309499	−	0.585153i
$235$	0.726921	+	0.419688i	0.0474191	+	0.0273774i
$236$	12.6750	+	3.88090i	0.825075	+	0.252625i
$237$	−9.86595	−	16.5702i	−0.640862	−	1.07635i
$238$	−0.599431	−	1.52267i	−0.0388553	−	0.0987001i
$239$	0.905124	+	5.13321i	0.0585476	+	0.332040i	0.999987	−	0.00514285i	$-0.00163703\pi$
$239$	0.905124	+	5.13321i	0.0585476	+	0.332040i	−0.941439	+	0.337183i	$0.890526\pi$
$240$	−5.79212	−	3.80150i	−0.373880	−	0.245386i
$241$	4.73933	+	3.97677i	0.305287	+	0.256166i	0.782541	−	0.622599i	$-0.213923\pi$
$241$	4.73933	+	3.97677i	0.305287	+	0.256166i	−0.477254	+	0.878765i	$0.658368\pi$
$242$	−6.56987	−	7.42899i	−0.422327	−	0.477554i
$243$	−15.4987	−	1.67032i	−0.994243	−	0.107151i
$244$	1.53298	−	12.4424i	0.0981388	−	0.796542i
$245$	2.35777	−	2.80988i	0.150632	−	0.179516i
$246$	−6.17972	−	15.0993i	−0.394005	−	0.962697i
$247$	−9.95034	+	1.75451i	−0.633125	+	0.111637i
$248$	5.55190	+	21.5229i	0.352546	+	1.36670i
$249$	−3.03210	+	1.80533i	−0.192152	+	0.114408i
$250$	0.738674	+	1.20597i	0.0467179	+	0.0762722i
$251$	−15.2169	+	26.3564i	−0.960482	+	1.66360i	−0.239189	+	0.970973i	$0.576882\pi$
$251$	−15.2169	+	26.3564i	−0.960482	+	1.66360i	−0.721293	+	0.692631i	$0.756452\pi$
$252$	−7.67865	−	7.80955i	−0.483710	−	0.491956i
$253$	−3.06708	−	5.31234i	−0.192826	−	0.333984i
$254$	−6.11325	+	11.2536i	−0.383579	+	0.706115i
$255$	−1.08375	−	0.176115i	−0.0678669	−	0.0110288i
$256$	15.6559	−	3.30059i	0.978492	−	0.206287i
$257$	17.7094	+	21.1052i	1.10468	+	1.31651i	0.944164	+	0.329475i	$0.106872\pi$
$257$	17.7094	+	21.1052i	1.10468	+	1.31651i	0.160517	+	0.987033i	$0.448684\pi$
$258$	−0.832732	−	21.1204i	−0.0518436	−	1.31490i
$259$	5.29513	+	14.5483i	0.329024	+	0.903985i
$260$	−1.64942	−	3.89027i	−0.102293	−	0.241265i
$261$	0.641833	−	0.131044i	0.0397285	−	0.00811142i
$262$	7.50794	−	1.52588i	0.463842	−	0.0942694i
$263$	1.65170	−	9.36725i	0.101848	−	0.577610i	−0.890584	−	0.454818i	$-0.849704\pi$
$263$	1.65170	−	9.36725i	0.101848	−	0.577610i	0.992432	−	0.122791i	$-0.0391846\pi$
$264$	−9.74172	+	0.892412i	−0.599562	+	0.0549241i
$265$	12.1716	+	4.43008i	0.747693	+	0.272138i
$266$	−7.68718	+	9.66000i	−0.471331	+	0.592292i
$267$	9.09505	−	7.84227i	0.556608	−	0.479939i
$268$	19.8542	+	21.3088i	1.21279	+	1.30164i
$269$		−	20.9036i		−	1.27451i	−0.770651	−	0.637257i	$-0.780069\pi$
$269$		−	20.9036i		−	1.27451i	0.770651	−	0.637257i	$-0.219931\pi$
$270$	−7.13643	+	1.75254i	−0.434309	+	0.106656i
$271$		−	20.4202i		−	1.24044i	−0.784429	−	0.620219i	$-0.787044\pi$
$271$		−	20.4202i		−	1.24044i	0.784429	−	0.620219i	$-0.212956\pi$
$272$	2.05261	−	1.48871i	0.124458	−	0.0902661i
$273$	−1.24819	−	6.56207i	−0.0755442	−	0.397154i
$274$	−6.46562	−	5.14518i	−0.390603	−	0.310832i
$275$	1.87642	+	0.682962i	0.113153	+	0.0411842i
$276$	10.5781	+	1.15924i	0.636728	+	0.0697782i
$277$	0.485051	−	2.75086i	0.0291439	−	0.165283i	−0.966762	−	0.255677i	$-0.917702\pi$
$277$	0.485051	−	2.75086i	0.0291439	−	0.165283i	0.995906	+	0.0903941i	$0.0288127\pi$
$278$	−1.89987	−	9.34810i	−0.113947	−	0.560662i
$279$	20.7265	+	11.2351i	1.24086	+	0.672626i
$280$	−4.65859	−	2.22560i	−0.278404	−	0.133005i
$281$	−8.06726	−	22.1646i	−0.481252	−	1.32223i	−0.908421	−	0.418058i	$-0.862711\pi$
$281$	−8.06726	−	22.1646i	−0.481252	−	1.32223i	0.427168	−	0.904172i	$-0.359511\pi$
$282$	−0.957073	+	1.81970i	−0.0569928	+	0.108362i
$283$	9.51028	+	11.3339i	0.565328	+	0.673731i	0.970665	−	0.240436i	$-0.0772904\pi$
$283$	9.51028	+	11.3339i	0.565328	+	0.673731i	−0.405337	+	0.914167i	$0.632846\pi$
$284$	−4.90194	−	7.55520i	−0.290877	−	0.448319i
$285$	2.93735	+	7.74492i	0.173993	+	0.458770i
$286$	−5.24272	−	2.84798i	−0.310009	−	0.168404i
$287$	−6.07898	−	10.5291i	−0.358831	−	0.621514i
$288$	8.74554	−	14.5436i	0.515336	−	0.856988i
$289$	−8.29908	+	14.3744i	−0.488181	+	0.845555i
$290$	0.263333	−	0.161296i	0.0154634	−	0.00947160i
$291$	−0.123862	−	9.21869i	−0.00726094	−	0.540409i
$292$	2.78144	−	5.45329i	0.162772	−	0.319130i
$293$	−12.6444	+	2.22954i	−0.738692	+	0.130251i	−0.530319	−	0.847798i	$-0.677928\pi$
$293$	−12.6444	+	2.22954i	−0.738692	+	0.130251i	−0.208373	+	0.978049i	$0.566817\pi$
$294$	7.10495	+	5.49968i	0.414369	+	0.320748i
$295$	4.26035	−	5.07729i	0.248047	−	0.295611i
$296$	−19.7788	+	13.5754i	−1.14962	+	0.789057i
$297$	−6.34382	+	8.21071i	−0.368106	+	0.476434i
$298$	−13.2120	+	11.6841i	−0.765350	+	0.676841i
$299$	4.97178	+	4.17182i	0.287526	+	0.241263i
$300$	−2.88043	+	1.92435i	−0.166302	+	0.111102i
$301$	−2.73516	−	15.5119i	−0.157652	−	0.894090i
$302$	23.8891	−	9.40445i	1.37466	−	0.541165i
$303$	−5.39432	+	9.64006i	−0.309896	+	0.553807i
$304$	−17.4690	−	7.79510i	−1.00192	−	0.447079i
$305$	−5.42845	−	3.13411i	−0.310832	−	0.179459i
$306$	0.326473	−	2.66956i	0.0186632	−	0.152609i
$307$	27.9901	−	16.1601i	1.59748	−	0.922305i	0.605508	−	0.795839i	$-0.292970\pi$
$307$	27.9901	−	16.1601i	1.59748	−	0.922305i	0.991971	−	0.126466i	$-0.0403635\pi$
$308$	−7.10380	+	1.63693i	−0.404777	+	0.0932730i
$309$	13.4056	+	10.9451i	0.762616	+	0.622645i
$310$	10.9913	+	1.64499i	0.624264	+	0.0934293i
$311$	16.3687	−	13.7350i	0.928185	−	0.778839i	−0.0473060	−	0.998880i	$-0.515064\pi$
$311$	16.3687	−	13.7350i	0.928185	−	0.778839i	0.975491	+	0.220041i	$0.0706192\pi$
$312$	9.36262	−	4.41252i	0.530054	−	0.249810i
$313$	−14.5358	+	5.29059i	−0.821611	+	0.299042i	−0.718411	−	0.695619i	$-0.755130\pi$
$313$	−14.5358	+	5.29059i	−0.821611	+	0.299042i	−0.103200	+	0.994661i	$0.532908\pi$
$314$	−3.46481	+	10.3481i	−0.195530	+	0.583976i
$315$	−5.09368	+	2.01052i	−0.286996	+	0.113280i
$316$	13.4088	−	17.7787i	0.754302	−	1.00013i
$317$	4.18837	+	0.738522i	0.235242	+	0.0414796i	0.290026	−	0.957019i	$-0.406336\pi$
$317$	4.18837	+	0.738522i	0.235242	+	0.0414796i	−0.0547841	+	0.998498i	$0.517447\pi$
$318$	−9.66843	+	30.2185i	−0.542178	+	1.69457i
$319$	0.149130	−	0.409732i	0.00834969	−	0.0229406i
$320$	1.53625	−	7.85111i	0.0858792	−	0.438890i
$321$	3.34778	−	9.59722i	0.186855	−	0.535664i
$322$	7.92737	−	0.205939i	0.441775	−	0.0114765i
$323$	−3.03156			−0.168681
$324$	−4.97818	−	17.2979i	−0.276566	−	0.960995i
$325$	−2.11275			−0.117194
$326$	10.4717	−	0.272034i	0.579971	−	0.0150666i
$327$	9.58936	−	27.4902i	0.530293	−	1.52021i
$328$	13.4451	−	13.1960i	0.742380	−	0.728627i
$329$	−0.524033	+	1.43977i	−0.0288909	+	0.0793770i
$330$	−1.49053	+	4.65862i	−0.0820509	+	0.256448i
$331$	−11.4008	−	2.01026i	−0.626642	−	0.110494i	−0.148696	−	0.988883i	$-0.547508\pi$
$331$	−11.4008	−	2.01026i	−0.626642	−	0.110494i	−0.477946	+	0.878389i	$0.658619\pi$
$332$	−3.25325	−	2.45361i	−0.178545	−	0.134660i
$333$	−3.74358	+	25.1677i	−0.205147	+	1.37918i
$334$	−1.02790	+	3.06994i	−0.0562440	+	0.167980i
$335$	13.6842	−	4.98064i	0.747647	−	0.272121i
$336$	4.99777	−	11.6171i	0.272651	−	0.633764i
$337$	17.4342	−	14.6290i	0.949700	−	0.796893i	−0.0295468	−	0.999563i	$-0.509406\pi$
$337$	17.4342	−	14.6290i	0.949700	−	0.796893i	0.979247	+	0.202670i	$0.0649620\pi$
$338$	−11.9392	−	1.78686i	−0.649405	−	0.0971921i
$339$	−22.2360	−	18.1548i	−1.20769	−	0.986031i
$340$	−0.284684	−	1.23544i	−0.0154392	−	0.0670013i
$341$	13.5900	−	7.84619i	0.735940	−	0.424895i
$342$	−18.6729	+	7.93683i	−1.00972	+	0.429174i
$343$	16.8642	+	9.73654i	0.910580	+	0.525724i
$344$	22.2154	−	10.1074i	1.19777	−	0.544956i
$345$	2.59822	−	4.64321i	0.139883	−	0.249982i
$346$	−7.31040	+	2.87789i	−0.393010	+	0.154716i
$347$	0.720672	+	4.08713i	0.0386877	+	0.219409i	0.998022	−	0.0628630i	$-0.0200231\pi$
$347$	0.720672	+	4.08713i	0.0386877	+	0.219409i	−0.959334	+	0.282272i	$0.908912\pi$
$348$	0.420197	+	0.628965i	0.0225249	+	0.0337161i
$349$	−20.8588	−	17.5026i	−1.11654	−	0.936892i	−0.118119	−	0.992999i	$-0.537686\pi$
$349$	−20.8588	−	17.5026i	−1.11654	−	0.936892i	−0.998425	+	0.0561078i	$0.982131\pi$
$350$	−1.93375	+	1.71013i	−0.103363	+	0.0914100i
$351$	3.33602	−	10.4590i	0.178063	−	0.558261i
$352$	−5.20545	−	10.0250i	−0.277451	−	0.534333i
$353$	−11.5166	+	13.7250i	−0.612969	+	0.730507i	−0.979844	−	0.199762i	$-0.935983\pi$
$353$	−11.5166	+	13.7250i	−0.612969	+	0.730507i	0.366876	+	0.930270i	$0.380427\pi$
$354$	12.8383	+	9.93761i	0.682346	+	0.528178i
$355$	−4.43465	+	0.781948i	−0.235367	+	0.0415015i
$356$	12.3530	+	6.30064i	0.654708	+	0.333933i
$357$	−0.0269259	−	2.00401i	−0.00142507	−	0.106063i
$358$	3.84338	−	2.35413i	0.203129	−	0.124419i
$359$	−9.12927	+	15.8124i	−0.481825	+	0.834545i	−0.999782	−	0.0208615i	$-0.993359\pi$
$359$	−9.12927	+	15.8124i	−0.481825	+	0.834545i	0.517958	+	0.855406i	$0.326692\pi$
$360$	−4.98799	−	6.86440i	−0.262890	−	0.361786i
$361$	1.93531	+	3.35206i	0.101858	+	0.176424i
$362$	−28.2446	−	15.3432i	−1.48451	−	0.806420i
$363$	−4.30720	−	11.3568i	−0.226070	−	0.596079i
$364$	6.47048	−	4.19816i	0.339145	−	0.220043i
$365$	−1.96747	−	2.34473i	−0.102982	−	0.122729i
$366$	7.14716	−	13.5891i	0.373588	−	0.710311i
$367$	−0.533252	−	1.46510i	−0.0278355	−	0.0764774i	0.924997	−	0.379976i	$-0.124068\pi$
$367$	−0.533252	−	1.46510i	−0.0278355	−	0.0764774i	−0.952832	+	0.303498i	$0.901845\pi$
$368$	3.37714	+	11.8145i	0.176045	+	0.615873i
$369$	−0.536851	−	19.9745i	−0.0279474	−	1.03983i
$370$	2.38892	+	11.7544i	0.124194	+	0.611083i
$371$	−4.10564	+	23.2842i	−0.213154	+	1.20886i
$372$	−2.96557	+	27.0609i	−0.153758	+	1.40304i
$373$	−15.1574	−	5.51685i	−0.784821	−	0.285652i	−0.0816398	−	0.996662i	$-0.526016\pi$
$373$	−15.1574	−	5.51685i	−0.784821	−	0.285652i	−0.703182	+	0.711010i	$0.748238\pi$
$374$	−1.40075	−	1.11468i	−0.0724309	−	0.0576387i
$375$	0.323657	+	1.70154i	0.0167136	+	0.0878673i
$376$	−2.36304	−	0.229020i	−0.121865	−	0.0118108i
$377$			0.461336i			0.0237600i
$378$	−5.41247	−	12.2732i	−0.278387	−	0.631265i
$379$			12.7335i			0.654078i	0.945011	+	0.327039i	$0.106051\pi$
$379$			12.7335i			0.654078i	−0.945011	+	0.327039i	$0.893949\pi$
$380$	−6.99785	+	6.52017i	−0.358982	+	0.334478i
$381$	−11.8790	+	10.2427i	−0.608579	+	0.524751i
$382$	−19.9348	+	25.0508i	−1.01995	+	1.28171i
$383$	8.84657	+	3.21989i	0.452039	+	0.164529i	0.557999	−	0.829842i	$-0.311569\pi$
$383$	8.84657	+	3.21989i	0.452039	+	0.164529i	−0.105960	+	0.994370i	$0.533792\pi$
$384$	19.3645	+	3.00246i	0.988192	+	0.153218i
$385$	−0.632944	+	3.58960i	−0.0322578	+	0.182943i
$386$	−11.1732	+	2.27080i	−0.568701	+	0.115581i
$387$	8.19716	−	24.5551i	0.416685	−	1.24820i
$388$	9.80123	−	4.15557i	0.497582	−	0.210967i
$389$	10.7709	+	29.5928i	0.546106	+	1.50041i	0.838926	+	0.544246i	$0.183184\pi$
$389$	10.7709	+	29.5928i	0.546106	+	1.50041i	−0.292820	+	0.956168i	$0.594594\pi$
$390$	−0.203887	−	5.17114i	−0.0103242	−	0.261851i
$391$	1.25171	+	1.49174i	0.0633019	+	0.0754403i
$392$	−2.77876	+	9.99571i	−0.140349	+	0.504860i
$393$	9.26179	+	1.50510i	0.467196	+	0.0759221i
$394$	−7.90647	+	14.5547i	−0.398322	+	0.733256i
$395$	−5.56707	−	9.64244i	−0.280110	−	0.485164i
$396$	−11.5462	−	3.19863i	−0.580219	−	0.160737i
$397$	7.57507	−	13.1204i	0.380182	−	0.658494i	−0.610906	−	0.791703i	$-0.709195\pi$
$397$	7.57507	−	13.1204i	0.380182	−	0.658494i	0.991088	+	0.133209i	$0.0425281\pi$
$398$	7.41692	+	12.1090i	0.371777	+	0.606967i
$399$	−12.9915	+	7.73520i	−0.650388	+	0.387245i
$400$	−3.31429	−	2.23952i	−0.165715	−	0.111976i
$401$	−23.7061	+	4.18003i	−1.18383	+	0.208741i	−0.730696	−	0.682703i	$-0.760804\pi$
$401$	−23.7061	+	4.18003i	−1.18383	+	0.208741i	−0.453132	+	0.891443i	$0.649693\pi$
$402$	13.5111	+	33.0126i	0.673873	+	1.64652i
$403$	−10.6723	+	12.7188i	−0.531627	+	0.633568i
$404$	−12.6599	−	1.55978i	−0.629854	−	0.0776018i
$405$	−8.93442	−	1.08449i	−0.443955	−	0.0538886i
$406$	0.373420	+	0.422251i	0.0185325	+	0.0209560i
$407$	12.9740	+	10.8865i	0.643097	+	0.539622i
$408$	2.99638	−	0.816014i	0.148343	−	0.0403987i
$409$	−5.82923	−	33.0592i	−0.288237	−	1.63467i	−0.693489	−	0.720467i	$-0.743928\pi$
$409$	−5.82923	−	33.0592i	−0.288237	−	1.63467i	0.405253	−	0.914205i	$-0.367184\pi$
$410$	−3.45042	−	8.76474i	−0.170404	−	0.432860i
$411$	−5.17732	−	8.69546i	−0.255378	−	0.428916i
$412$	−5.85054	+	19.1079i	−0.288235	+	0.941377i
$413$	10.4775	+	6.04921i	0.515566	+	0.297662i
$414$	11.6154	+	5.91128i	0.570866	+	0.290524i
$415$	−1.76443	+	1.01869i	−0.0866125	+	0.0500058i
$416$	8.80319	+	8.08346i	0.431612	+	0.396324i
$417$	1.87399	−	11.5318i	0.0917697	−	0.564716i
$418$	−1.99896	+	13.3564i	−0.0977723	+	0.653282i
$419$	3.13986	−	2.63465i	0.153392	−	0.128711i	−0.562862	−	0.826551i	$-0.690300\pi$
$419$	3.13986	−	2.63465i	0.153392	−	0.128711i	0.716254	+	0.697840i	$0.245855\pi$
$420$	−4.37230	−	4.56800i	−0.213346	−	0.222896i
$421$	−22.9848	+	8.36577i	−1.12021	+	0.407723i	−0.834728	−	0.550662i	$-0.814375\pi$
$421$	−22.9848	+	8.36577i	−1.12021	+	0.407723i	−0.285480	+	0.958385i	$0.592153\pi$
$422$	17.3893	+	5.82238i	0.846496	+	0.283429i
$423$	−1.88481	+	1.66986i	−0.0916428	+	0.0811915i
$424$	−36.5246	+	2.85166i	−1.77379	+	0.138489i
$425$	−0.624279	−	0.110077i	−0.0302820	−	0.00533953i
$426$	−2.34184	−	10.7787i	−0.113463	−	0.522231i
$427$	3.91333	−	10.7518i	0.189380	−	0.520316i
$428$	11.7210	−	0.609389i	0.566554	−	0.0294559i
$429$	−4.77178	−	5.53406i	−0.230384	−	0.267187i
$430$	−0.316913	−	12.1992i	−0.0152829	−	0.588298i
$431$	16.4438			0.792069			0.396035	−	0.918236i	$-0.370386\pi$
$431$	16.4438			0.792069			0.396035	+	0.918236i	$0.370386\pi$
$432$	16.3199	−	12.8710i	0.785190	−	0.619255i
$433$	−6.72259			−0.323067			−0.161534	−	0.986867i	$-0.551644\pi$
$433$	−6.72259			−0.323067			−0.161534	+	0.986867i	$0.551644\pi$
$434$	0.526831	+	20.2798i	0.0252887	+	0.973460i
$435$	0.371546	−	0.0706730i	0.0178142	−	0.00338851i
$436$	33.5734	−	1.74553i	1.60788	−	0.0835958i
$437$	5.02460	−	13.8050i	0.240359	−	0.660381i
$438$	5.54908	−	5.04182i	0.265145	−	0.240908i
$439$	−2.80665	−	0.494888i	−0.133954	−	0.0236197i	0.106269	−	0.994337i	$-0.466110\pi$
$439$	−2.80665	−	0.494888i	−0.133954	−	0.0236197i	−0.240223	+	0.970718i	$0.577221\pi$
$440$	−5.63080	+	0.439625i	−0.268438	+	0.0209583i
$441$	5.75610	+	9.37857i	0.274100	+	0.446598i
$442$	1.79604	+	0.601362i	0.0854290	+	0.0286039i
$443$	−6.49106	+	2.36255i	−0.308400	+	0.112248i	−0.491584	−	0.870830i	$-0.663582\pi$
$443$	−6.49106	+	2.36255i	−0.308400	+	0.112248i	0.183184	+	0.983079i	$0.441360\pi$
$444$	−28.5394	+	6.98143i	−1.35442	+	0.331324i
$445$	5.31139	−	4.45678i	0.251784	−	0.211272i
$446$	−5.13019	+	34.2782i	−0.242921	+	1.62312i
$447$	−20.1974	+	7.66009i	−0.955305	+	0.362310i
$448$	14.6004	+	0.273044i	0.689803	+	0.0129001i
$449$	−29.7525	+	17.1776i	−1.40411	+	0.810662i	−0.994811	−	0.101740i	$-0.967559\pi$
$449$	−29.7525	+	17.1776i	−1.40411	+	0.810662i	−0.409296	+	0.912402i	$0.634226\pi$
$450$	−4.13344	+	0.956382i	−0.194852	+	0.0450843i
$451$	−11.5182	−	6.65006i	−0.542373	−	0.313139i
$452$	9.70435	−	31.6944i	0.456454	−	1.49078i
$453$	31.4408	−	0.422439i	1.47722	−	0.0198479i
$454$	−11.0086	−	27.9640i	−0.516660	−	1.31242i
$455$	−0.669681	−	3.79795i	−0.0313951	−	0.178051i
$456$	−16.6340	−	16.4986i	−0.778959	−	0.772619i
$457$	11.5319	+	9.67640i	0.539439	+	0.452643i	0.871346	−	0.490669i	$-0.163248\pi$
$457$	11.5319	+	9.67640i	0.539439	+	0.452643i	−0.331907	+	0.943312i	$0.607692\pi$
$458$	26.1325	+	29.5498i	1.22109	+	1.38077i
$459$	1.53066	−	2.91664i	0.0714453	−	0.136137i
$460$	6.09774	+	0.751279i	0.284309	+	0.0350285i
$461$	2.37404	−	2.82927i	0.110570	−	0.131772i	−0.707921	−	0.706292i	$-0.750367\pi$
$461$	2.37404	−	2.82927i	0.110570	−	0.131772i	0.818491	+	0.574520i	$0.194811\pi$
$462$	−8.84695	−	1.20278i	−0.411598	−	0.0559583i
$463$	−12.4805	+	2.20065i	−0.580018	+	0.102273i	−0.455957	−	0.890002i	$-0.650703\pi$
$463$	−12.4805	+	2.20065i	−0.580018	+	0.102273i	−0.124061	+	0.992275i	$0.539592\pi$
$464$	−0.489018	+	0.723702i	−0.0227021	+	0.0335970i
$465$	11.8782	+	6.64675i	0.550840	+	0.308236i
$466$	1.98160	+	3.23518i	0.0917958	+	0.149867i
$467$	−6.40991	+	11.1023i	−0.296615	+	0.513753i	−0.975359	−	0.220622i	$-0.929191\pi$
$467$	−6.40991	+	11.1023i	−0.296615	+	0.513753i	0.678744	+	0.734375i	$0.262525\pi$
$468$	12.6371	−	0.998064i	0.584152	−	0.0461355i
$469$	13.2909	+	23.0205i	0.613716	+	1.06299i
$470$	−0.566631	+	1.04309i	−0.0261367	+	0.0481141i
$471$	−8.45272	+	10.3529i	−0.389481	+	0.477037i
$472$	−5.02107	+	18.0617i	−0.231113	+	0.831357i
$473$	−11.0758	−	13.1996i	−0.509266	−	0.606920i
$474$	23.0635	−	14.5564i	1.05934	−	0.668598i
$475$	1.63565	+	4.49391i	0.0750488	+	0.206195i
$476$	2.13064	−	0.903360i	0.0976578	−	0.0414054i
$477$	−24.1687	+	30.4274i	−1.10661	+	1.39317i
$478$	−7.22377	+	1.46813i	−0.330408	+	0.0671508i
$479$	−6.64514	+	37.6865i	−0.303624	+	1.72194i	0.326287	+	0.945271i	$0.394202\pi$
$479$	−6.64514	+	37.6865i	−0.303624	+	1.72194i	−0.629911	+	0.776667i	$0.716909\pi$
$480$	5.16159	−	8.32814i	0.235593	−	0.380126i
$481$	−16.8387	−	6.12878i	−0.767778	−	0.279448i
$482$	−5.44804	+	6.84621i	−0.248152	+	0.311836i
$483$	9.17037	+	3.19888i	0.417266	+	0.145554i
$484$	10.2614	−	9.56090i	0.466425	−	0.434587i
$485$		−	5.32289i		−	0.241700i
$486$	1.79218	−	21.9724i	0.0812948	−	0.996690i
$487$			15.8940i			0.720224i	0.932909	+	0.360112i	$0.117261\pi$
$487$			15.8940i			0.720224i	−0.932909	+	0.360112i	$0.882739\pi$
$488$	17.6465	+	1.71026i	0.798822	+	0.0774200i
$489$	12.1136	+	4.22556i	0.547795	+	0.191086i
$490$	4.05902	+	3.23006i	0.183368	+	0.145919i
$491$	1.88678	+	0.686731i	0.0851491	+	0.0309917i	0.384243	−	0.923232i	$-0.374462\pi$
$491$	1.88678	+	0.686731i	0.0851491	+	0.0309917i	−0.299094	+	0.954224i	$0.596685\pi$
$492$	21.1195	−	9.29104i	0.952141	−	0.418872i
$493$	−0.0240363	+	0.136316i	−0.00108254	+	0.00613938i
$494$	−2.84586	−	14.0027i	−0.128041	−	0.630013i
$495$	−3.72596	+	4.69082i	−0.167470	+	0.210837i
$496$	−30.2238	+	8.63938i	−1.35709	+	0.387919i
$497$	−2.81131	−	7.72402i	−0.126105	−	0.346470i
$498$	−2.66362	−	4.22029i	−0.119360	−	0.189116i
$499$	3.69437	+	4.40277i	0.165383	+	0.197095i	0.842370	−	0.538899i	$-0.181160\pi$
$499$	3.69437	+	4.40277i	0.165383	+	0.197095i	−0.676988	+	0.735994i	$0.736715\pi$
$500$	−1.67779	+	1.08858i	−0.0750332	+	0.0486828i
$501$	−2.50765	+	3.07137i	−0.112034	+	0.137219i
$502$	−37.8199	−	20.5447i	−1.68799	−	0.916955i
$503$	−18.1187	−	31.3826i	−0.807874	−	1.39928i	−0.914334	−	0.404962i	$-0.867285\pi$
$503$	−18.1187	−	31.3826i	−0.807874	−	1.39928i	0.106460	−	0.994317i	$-0.466049\pi$
$504$	10.7586	−	11.1424i	0.479228	−	0.496322i
$505$	−3.18891	+	5.52335i	−0.141905	+	0.245786i
$506$	7.39761	−	4.53115i	0.328864	−	0.201434i
$507$	−12.9026	−	7.21996i	−0.573025	−	0.320650i
$508$	−16.1342	−	8.22922i	−0.715839	−	0.365112i
$509$	18.3957	−	3.24366i	0.815376	−	0.143773i	0.249618	−	0.968344i	$-0.419695\pi$
$509$	18.3957	−	3.24366i	0.815376	−	0.143773i	0.565758	+	0.824572i	$0.308584\pi$
$510$	0.209179	−	1.53860i	0.00926259	−	0.0681304i
$511$	3.59135	−	4.28000i	0.158872	−	0.189336i
$512$	5.24114	+	22.0121i	0.231628	+	0.972804i
$513$	−24.8295	+	1.00131i	−1.09625	+	0.0442089i
$514$	−29.1868	+	25.8115i	−1.28738	+	1.13850i
$515$	7.65412	+	6.42257i	0.337281	+	0.283012i
$516$	29.8280	−	1.95294i	1.31311	−	0.0859732i
$517$	0.291053	+	1.65064i	0.0128005	+	0.0725951i
$518$	−20.3729	+	8.02023i	−0.895135	+	0.352389i
$519$	−9.62131	+	0.129272i	−0.422329	+	0.00567441i
$520$	5.43925	−	2.47472i	0.238527	−	0.108524i
$521$	−19.6508	−	11.3454i	−0.860919	−	0.497052i	0.00340120	−	0.999994i	$-0.498917\pi$
$521$	−19.6508	−	11.3454i	−0.860919	−	0.497052i	−0.864320	+	0.502943i	$0.832251\pi$
$522$	0.208834	+	0.902570i	0.00914041	+	0.0395044i
$523$	−16.7664	+	9.68011i	−0.733145	+	0.423282i	−0.819572	−	0.572977i	$-0.805789\pi$
$523$	−16.7664	+	9.68011i	−0.733145	+	0.423282i	0.0864263	+	0.996258i	$0.472455\pi$
$524$	2.43294	+	10.5582i	0.106283	+	0.461237i
$525$	−2.95616	+	1.12116i	−0.129018	+	0.0489313i
$526$	13.3035	+	1.99104i	0.580060	+	0.0868136i
$527$	−3.81615	+	3.20213i	−0.166234	+	0.139487i
$528$	−1.61941	−	13.7395i	−0.0704759	−	0.597933i
$529$	12.7453	−	4.63892i	0.554144	−	0.201692i
$530$	−5.81596	+	17.3701i	−0.252629	+	0.754508i
$531$	10.4010	+	16.9465i	0.451363	+	0.735418i
$532$	−13.9390	−	10.5129i	−0.604333	−	0.455791i
$533$	13.8583	+	2.44359i	0.600269	+	0.105844i
$534$	11.4209	+	12.5700i	0.494232	+	0.543957i
$535$	2.00711	−	5.51449i	0.0867749	−	0.238412i
$536$	−29.3958	+	28.8513i	−1.26971	+	1.24618i
$537$	5.42275	−	1.03148i	0.234009	−	0.0445117i
$538$	29.5522	−	0.767711i	1.27408	−	0.0330984i
$539$	7.32450			0.315489
$540$	−2.73972	−	10.0247i	−0.117899	−	0.431393i
$541$	13.5313			0.581754			0.290877	−	0.956760i	$-0.406053\pi$
$541$	13.5313			0.581754			0.290877	+	0.956760i	$0.406053\pi$
$542$	28.8687	−	0.749957i	1.24002	−	0.0322134i
$543$	−25.7075	−	29.8142i	−1.10321	−	1.27945i
$544$	2.18002	+	2.84718i	0.0934678	+	0.122072i
$545$	5.74915	−	15.7957i	0.246267	−	0.676612i
$546$	9.23119	−	2.00562i	0.395059	−	0.0858326i
$547$	−9.69562	−	1.70960i	−0.414555	−	0.0730972i	−0.0375190	−	0.999296i	$-0.511945\pi$
$547$	−9.69562	−	1.70960i	−0.414555	−	0.0730972i	−0.377036	+	0.926199i	$0.623057\pi$
$548$	7.03647	−	9.32965i	0.300583	−	0.398543i
$549$	14.0753	−	12.4701i	0.600718	−	0.532210i
$550$	−0.896614	+	2.67785i	−0.0382318	+	0.114184i
$551$	0.981283	−	0.357158i	0.0418040	−	0.0152154i
$552$	−1.25037	+	14.9973i	−0.0532192	+	0.638326i
$553$	15.5690	−	13.0639i	0.662061	−	0.555535i
$554$	3.90681	+	0.584705i	0.165984	+	0.0248417i
$555$	−2.35638	+	14.5002i	−0.100023	+	0.615501i
$556$	13.1460	−	3.02924i	0.557514	−	0.128468i
$557$	−33.3576	+	19.2590i	−1.41341	+	0.816031i	−0.995708	−	0.0925535i	$-0.970497\pi$
$557$	−33.3576	+	19.2590i	−1.41341	+	0.816031i	−0.417700	+	0.908585i	$0.637164\pi$
$558$	−15.1222	+	29.7145i	−0.640174	+	1.25791i
$559$	15.7885	+	9.11550i	0.667783	+	0.385545i
$560$	2.97531	−	6.66776i	0.125730	−	0.281764i
$561$	−1.12164	−	1.88383i	−0.0473558	−	0.0795355i
$562$	31.0386	−	12.2190i	1.30929	−	0.515427i
$563$	−7.19325	−	40.7949i	−0.303159	−	1.71930i	−0.632045	−	0.774932i	$-0.717784\pi$
$563$	−7.19325	−	40.7949i	−0.303159	−	1.71930i	0.328885	−	0.944370i	$-0.393327\pi$
$564$	−2.60773	−	1.28622i	−0.109805	−	0.0541595i
$565$	−12.6960	−	10.6532i	−0.534123	−	0.448183i
$566$	−15.6739	+	13.8613i	−0.658823	+	0.582633i
$567$	−0.882446	−	16.4046i	−0.0370592	−	0.688928i
$568$	10.5010	−	7.20753i	0.440613	−	0.302421i
$569$	−19.7075	+	23.4865i	−0.826181	+	0.984605i	−1.00000		0.000173014i	$-0.999945\pi$
$569$	−19.7075	+	23.4865i	−0.826181	+	0.984605i	0.173819	+	0.984778i	$0.444389\pi$
$570$	−10.8414	+	4.43708i	−0.454097	+	0.185849i
$571$	−46.8315	+	8.25766i	−1.95984	+	0.345573i	−0.962640	+	0.270786i	$0.912716\pi$
$571$	−46.8315	+	8.25766i	−1.95984	+	0.345573i	−0.997200	+	0.0747865i	$0.976172\pi$
$572$	3.83374	−	7.51643i	0.160297	−	0.314278i
$573$	−33.6902	+	20.0593i	−1.40743	+	0.837991i
$574$	14.6621	−	8.98078i	0.611985	−	0.374850i
$575$	1.53596	−	2.66036i	0.0640540	−	0.110945i
$576$	20.8820	+	11.8298i	0.870082	+	0.492907i
$577$	17.9968	+	31.1713i	0.749215	+	1.29768i	0.948199	+	0.317676i	$0.102902\pi$
$577$	17.9968	+	31.1713i	0.749215	+	1.29768i	−0.198984	+	0.980003i	$0.563764\pi$
$578$	−20.6264	−	11.2048i	−0.857947	−	0.466058i
$579$	−13.7833	−	2.23986i	−0.572813	−	0.0930856i
$580$	0.237701	+	0.366360i	0.00986998	+	0.0152123i
$581$	−2.39052	−	2.84891i	−0.0991754	−	0.118193i
$582$	13.0283	−	0.513677i	0.540038	−	0.0212926i
$583$	8.84620	+	24.3047i	0.366372	+	1.00660i
$584$	7.81167	+	3.73195i	0.323249	+	0.154429i
$585$	2.00700	−	6.01209i	0.0829794	−	0.248569i
$586$	−3.61637	−	17.7939i	−0.149391	−	0.735060i
$587$	4.07152	−	23.0907i	0.168050	−	0.953056i	−0.777815	−	0.628494i	$-0.783672\pi$
$587$	4.07152	−	23.0907i	0.168050	−	0.953056i	0.945864	−	0.324563i	$-0.105217\pi$
$588$	−7.51416	+	10.2465i	−0.309879	+	0.422559i
$589$	35.3158	+	12.8539i	1.45516	+	0.529636i
$590$	7.33442	+	5.83655i	0.301953	+	0.240287i
$591$	−15.3635	+	13.2473i	−0.631970	+	0.544921i
$592$	−19.9185	−	27.4634i	−0.818645	−	1.12874i
$593$		−	39.0152i		−	1.60216i	−0.598555	−	0.801082i	$-0.704258\pi$
$593$		−	39.0152i		−	1.60216i	0.598555	−	0.801082i	$-0.295742\pi$
$594$	−11.8408	−	8.66694i	−0.485832	−	0.355609i
$595$		−	1.15712i		−	0.0474372i
$596$	−17.0035	−	18.2492i	−0.696489	−	0.747515i
$597$	3.24979	+	17.0849i	0.133005	+	0.699240i
$598$	−5.71526	+	7.18201i	−0.233714	+	0.293694i
$599$	−1.00198	−	0.364693i	−0.0409400	−	0.0149009i	0.321469	−	0.946920i	$-0.395823\pi$
$599$	−1.00198	−	0.364693i	−0.0409400	−	0.0149009i	−0.362409	+	0.932019i	$0.618046\pi$
$600$	−2.82631	−	4.00149i	−0.115384	−	0.163360i
$601$	2.27509	−	12.9027i	0.0928027	−	0.526310i	−0.902596	−	0.430489i	$-0.858341\pi$
$601$	2.27509	−	12.9027i	0.0928027	−	0.526310i	0.995399	−	0.0958213i	$-0.0305477\pi$
$602$	21.8293	−	4.43650i	0.889695	−	0.180818i
$603$	1.17375	+	43.6715i	0.0477989	+	1.77844i
$604$	14.1728	+	33.4275i	0.576682	+	1.36015i
$605$	−2.39845	−	6.58969i	−0.0975109	−	0.267909i
$606$	−13.8266	−	7.27211i	−0.561668	−	0.295409i
$607$	21.9417	+	26.1492i	0.890588	+	1.06136i	0.997745	+	0.0671192i	$0.0213808\pi$
$607$	21.9417	+	26.1492i	0.890588	+	1.06136i	−0.107157	+	0.994242i	$0.534175\pi$
$608$	10.3786	−	24.9829i	0.420909	−	1.01319i
$609$	0.244814	+	0.645502i	0.00992036	+	0.0261571i
$610$	4.23145	−	7.78950i	0.171326	−	0.315388i
$611$	−0.886695	−	1.53580i	−0.0358718	−	0.0621318i
$612$	3.78605	+	0.363503i	0.153042	+	0.0146937i
$613$	23.0961	−	40.0036i	0.932842	−	1.61573i	0.154405	−	0.988008i	$-0.450654\pi$
$613$	23.0961	−	40.0036i	0.932842	−	1.61573i	0.778437	−	0.627723i	$-0.216013\pi$
$614$	23.8741	+	38.9771i	0.963480	+	1.57299i
$615$	−0.154990	−	11.5354i	−0.00624978	−	0.465152i
$616$	−2.57509	−	9.98278i	−0.103753	−	0.402218i
$617$	24.8028	−	4.37341i	0.998524	−	0.176067i	0.349583	−	0.936905i	$-0.386323\pi$
$617$	24.8028	−	4.37341i	0.998524	−	0.176067i	0.648941	+	0.760839i	$0.275212\pi$
$618$	−14.9811	+	19.3539i	−0.602630	+	0.778529i
$619$	−13.0942	+	15.6050i	−0.526299	+	0.627218i	−0.962058	−	0.272845i	$-0.912035\pi$
$619$	−13.0942	+	15.6050i	−0.526299	+	0.627218i	0.435759	+	0.900063i	$0.356480\pi$
$620$	−1.92192	+	15.5992i	−0.0771861	+	0.626479i
$621$	10.7447	+	11.8044i	0.431169	+	0.473693i
$622$	20.0188	+	22.6366i	0.802681	+	0.907646i
$623$	9.69523	+	8.13527i	0.388431	+	0.325933i
$624$	6.58199	+	13.0742i	0.263491	+	0.523388i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−8.01335	−	20.3555i	−0.320278	−	0.813568i
$627$	−8.07698	+	14.4342i	−0.322563	+	0.576445i
$628$	−14.7567	−	4.51828i	−0.588856	−	0.180299i
$629$	−4.65621	−	2.68827i	−0.185655	−	0.107188i
$630$	−3.02941	−	7.12728i	−0.120695	−	0.283957i
$631$	−2.31630	+	1.33732i	−0.0922104	+	0.0532377i	−0.545396	−	0.838178i	$-0.683621\pi$
$631$	−2.31630	+	1.33732i	−0.0922104	+	0.0532377i	0.453186	+	0.891416i	$0.350287\pi$
$632$	25.6268	+	18.3035i	1.01938	+	0.728075i
$633$	17.3974	+	14.2043i	0.691484	+	0.564568i
$634$	−0.890253	+	5.94837i	−0.0353565	+	0.236240i
$635$	−6.93716	+	5.82097i	−0.275293	+	0.230998i
$636$	−43.0761	−	12.5588i	−1.70808	−	0.497989i
$637$	−7.28227	+	2.65053i	−0.288534	+	0.105018i
$638$	0.584730	+	0.195783i	0.0231497	+	0.00775112i
$639$	1.98756	−	13.3622i	0.0786265	−	0.528599i
$640$	11.1558	+	1.88352i	0.440973	+	0.0744525i
$641$	−34.1906	−	6.02873i	−1.35045	−	0.238121i	−0.548819	−	0.835941i	$-0.684922\pi$
$641$	−34.1906	−	6.02873i	−1.35045	−	0.238121i	−0.801630	+	0.597820i	$0.796034\pi$
$642$	13.6909	+	4.38041i	0.540336	+	0.172881i
$643$	13.3443	−	36.6632i	0.526249	−	1.44586i	−0.337206	−	0.941431i	$-0.609482\pi$
$643$	13.3443	−	36.6632i	0.526249	−	1.44586i	0.863455	−	0.504426i	$-0.168296\pi$
$644$	0.582286	+	11.1997i	0.0229453	+	0.441328i
$645$	4.92267	−	14.1120i	0.193830	−	0.555660i
$646$	−0.111338	−	4.28583i	−0.00438053	−	0.168624i
$647$	−17.1767			−0.675286			−0.337643	−	0.941274i	$-0.609630\pi$
$647$	−17.1767			−0.675286			−0.337643	+	0.941274i	$0.609630\pi$
$648$	24.2719	−	7.67312i	0.953489	−	0.301429i
$649$	13.2350			0.519518
$650$	−0.0775934	−	2.98687i	−0.00304346	−	0.117155i
$651$	−8.18337	+	23.4596i	−0.320731	+	0.919454i
$652$	0.769170	+	14.7942i	0.0301230	+	0.579384i
$653$	−12.2512	+	33.6598i	−0.479425	+	1.31721i	0.430557	+	0.902563i	$0.358317\pi$
$653$	−12.2512	+	33.6598i	−0.479425	+	1.31721i	−0.909982	+	0.414647i	$0.863905\pi$
$654$	39.2161	+	12.5472i	1.53347	+	0.490635i
$655$	5.33514	+	0.940729i	0.208461	+	0.0367573i
$656$	19.1494	+	18.5232i	0.747660	+	0.723208i
$657$	8.54124	−	3.37130i	0.333225	−	0.131527i
$658$	−2.05470	−	0.687967i	−0.0801005	−	0.0268197i
$659$	11.0911	−	4.03684i	0.432049	−	0.157253i	−0.116835	−	0.993151i	$-0.537275\pi$
$659$	11.0911	−	4.03684i	0.432049	−	0.157253i	0.548884	+	0.835898i	$0.315053\pi$
$660$	−6.64080	−	1.93612i	−0.258493	−	0.0753634i
$661$	−16.6869	+	14.0020i	−0.649047	+	0.544615i	−0.906782	−	0.421601i	$-0.861468\pi$
$661$	−16.6869	+	14.0020i	−0.649047	+	0.544615i	0.257735	+	0.966216i	$0.417024\pi$
$662$	2.42327	−	16.1915i	0.0941831	−	0.629300i
$663$	1.79688	+	1.46708i	0.0697851	+	0.0569766i
$664$	3.34929	−	4.68934i	0.129977	−	0.181982i
$665$	−7.55997	+	4.36475i	−0.293163	+	0.169258i
$666$	−35.7180	−	4.36812i	−1.38405	−	0.169261i
$667$	−0.580912	−	0.335390i	−0.0224930	−	0.0129863i
$668$	−4.37784	−	1.34043i	−0.169384	−	0.0518627i
$669$	−20.7290	+	37.0443i	−0.801429	+	1.43221i
$670$	7.54388	+	19.1629i	0.291445	+	0.740328i
$671$	−2.17350	−	12.3265i	−0.0839071	−	0.475861i
$672$	16.6070	+	6.63888i	0.640631	+	0.256100i
$673$	11.4540	+	9.61104i	0.441519	+	0.370478i	0.836277	−	0.548307i	$-0.184727\pi$
$673$	11.4540	+	9.61104i	0.441519	+	0.370478i	−0.394758	+	0.918785i	$0.629172\pi$
$674$	21.3219	+	24.1101i	0.821288	+	0.928685i
$675$	−5.14941	−	0.695373i	−0.198201	−	0.0267649i
$676$	2.08766	−	16.9445i	0.0802947	−	0.651710i
$677$	−4.70805	+	5.61084i	−0.180945	+	0.215642i	−0.848891	−	0.528568i	$-0.822729\pi$
$677$	−4.70805	+	5.61084i	−0.180945	+	0.215642i	0.667946	+	0.744210i	$0.267174\pi$
$678$	24.8494	−	32.1026i	0.954335	−	1.23289i
$679$	9.56863	−	1.68721i	0.367210	−	0.0647491i
$680$	1.73614	−	0.447842i	0.0665778	−	0.0171740i
$681$	−0.494497	−	36.8038i	−0.0189491	−	1.41033i
$682$	11.5916	+	18.9245i	0.443864	+	0.724657i
$683$	8.85033	−	15.3292i	0.338648	−	0.586556i	−0.645530	−	0.763735i	$-0.723364\pi$
$683$	8.85033	−	15.3292i	0.338648	−	0.586556i	0.984179	+	0.177178i	$0.0566970\pi$
$684$	−11.9064	−	26.1071i	−0.455251	−	0.998230i
$685$	−2.92141	−	5.06003i	−0.111621	−	0.193334i
$686$	−13.1455	+	24.1991i	−0.501899	+	0.923926i
$687$	17.1324	+	45.1732i	0.653644	+	1.72347i
$688$	15.1051	+	31.0355i	0.575878	+	1.18322i
$689$	−17.5904	−	20.9634i	−0.670141	−	0.798642i
$690$	6.65970	+	3.50267i	0.253530	+	0.133344i
$691$	−1.45607	−	4.00052i	−0.0553916	−	0.152187i	0.908911	−	0.416990i	$-0.136915\pi$
$691$	−1.45607	−	4.00052i	−0.0553916	−	0.152187i	−0.964302	+	0.264803i	$0.914693\pi$
$692$	−4.33706	−	10.2293i	−0.164870	−	0.388859i
$693$	−9.61341	−	5.21107i	−0.365183	−	0.197952i
$694$	−5.75166	+	1.16895i	−0.218330	+	0.0443726i
$695$	1.17130	−	6.64276i	0.0444299	−	0.251974i
$696$	−0.873759	+	0.617148i	−0.0331197	+	0.0233929i
$697$	3.96756	+	1.44408i	0.150282	+	0.0546982i
$698$	23.9780	−	30.1316i	0.907580	−	1.14050i
$699$	0.868255	+	4.56463i	0.0328404	+	0.172650i
$700$	−2.48869	−	2.67101i	−0.0940635	−	0.100955i
$701$		−	18.7273i		−	0.707321i	−0.935374	−	0.353660i	$-0.884937\pi$
$701$		−	18.7273i		−	0.707321i	0.935374	−	0.353660i	$-0.115063\pi$
$702$	14.9088	+	4.33213i	0.562697	+	0.163506i
$703$			40.5615i			1.52981i
$704$	13.9815	−	7.72732i	0.526947	−	0.291234i
$705$	−1.10105	+	0.949389i	−0.0414680	+	0.0357561i
$706$	−19.8265	−	15.7774i	−0.746179	−	0.593791i
$707$	−10.9398	−	3.98175i	−0.411432	−	0.149749i
$708$	−13.5777	+	18.5149i	−0.510280	+	0.695832i
$709$	3.65965	−	20.7549i	0.137441	−	0.779468i	−0.835687	−	0.549205i	$-0.814930\pi$
$709$	3.65965	−	20.7549i	0.137441	−	0.779468i	0.973129	−	0.230262i	$-0.0739584\pi$
$710$	−1.26834	−	6.24070i	−0.0475998	−	0.234209i
$711$	32.7272	−	6.68197i	1.22737	−	0.250593i
$712$	−8.45376	+	17.6953i	−0.316818	+	0.663160i
$713$	−8.25669	−	22.6851i	−0.309216	−	0.849563i
$714$	2.83215	−	0.111666i	0.105991	−	0.00417899i
$715$	−2.71181	−	3.23182i	−0.101416	−	0.120863i
$716$	3.46927	+	5.34706i	0.129653	+	0.199829i
$717$	−8.91125	−	1.44813i	−0.332797	−	0.0540814i
$718$	−22.6898	−	12.3257i	−0.846776	−	0.459990i
$719$	−11.7373	−	20.3296i	−0.437728	−	0.758167i	0.559786	−	0.828637i	$-0.310883\pi$
$719$	−11.7373	−	20.3296i	−0.437728	−	0.758167i	−0.997514	+	0.0704705i	$0.977550\pi$
$720$	9.52126	−	7.30380i	0.354837	−	0.272197i
$721$	−9.11930	+	15.7951i	−0.339620	+	0.588240i
$722$	−4.66785	+	2.85913i	−0.173719	+	0.106406i
$723$	−9.20731	+	5.48208i	−0.342424	+	0.203881i
$724$	20.6539	−	40.4940i	0.767596	−	1.50495i
$725$	0.215041	−	0.0379175i	0.00798641	−	0.00140822i
$726$	15.8974	−	6.50635i	0.590007	−	0.241473i
$727$	5.75632	−	6.86011i	0.213490	−	0.254428i	−0.648663	−	0.761076i	$-0.724671\pi$
$727$	5.75632	−	6.86011i	0.213490	−	0.254428i	0.862153	+	0.506649i	$0.169116\pi$
$728$	6.17273	+	8.99337i	0.228777	+	0.333316i
$729$	11.5733	−	24.3938i	0.428641	−	0.903475i
$730$	3.24258	−	2.86759i	0.120013	−	0.106134i
$731$	4.19029	+	3.51607i	0.154984	+	0.130047i
$732$	19.4738	+	9.60512i	0.719773	+	0.355016i
$733$	−4.01245	−	22.7557i	−0.148203	−	0.840502i	−0.964739	−	0.263207i	$-0.915220\pi$
$733$	−4.01245	−	22.7557i	−0.148203	−	0.840502i	0.816536	−	0.577294i	$-0.195891\pi$
$734$	2.05168	−	0.807685i	0.0757288	−	0.0298122i
$735$	3.25024	+	5.45888i	0.119887	+	0.201354i
$736$	−16.5786	+	5.20829i	−0.611094	+	0.191980i
$737$	25.1831	+	14.5395i	0.927631	+	0.535568i
$738$	28.2189	−	1.49255i	1.03875	−	0.0549417i
$739$	17.8718	−	10.3183i	0.657423	−	0.379564i	−0.133871	−	0.990999i	$-0.542741\pi$
$739$	17.8718	−	10.3183i	0.657423	−	0.379564i	0.791295	+	0.611435i	$0.209407\pi$
$740$	−16.5299	+	3.80900i	−0.607651	+	0.140022i
$741$	2.80709	−	17.2738i	0.103121	−	0.634568i
$742$	−33.0686	−	4.94915i	−1.21399	−	0.181689i
$743$	14.0231	−	11.7668i	0.514457	−	0.431681i	−0.348237	−	0.937407i	$-0.613220\pi$
$743$	14.0231	−	11.7668i	0.514457	−	0.431681i	0.862694	+	0.505725i	$0.168775\pi$
$744$	−38.3659	−	3.19869i	−1.40656	−	0.117270i
$745$	−11.7193	+	4.26549i	−0.429363	+	0.156276i
$746$	7.24270	−	21.6312i	0.265174	−	0.791975i
$747$	−1.22271	−	5.98862i	−0.0447365	−	0.219112i
$748$	1.52442	−	2.02123i	0.0557383	−	0.0739034i
$749$	10.5492	+	1.86012i	0.385461	+	0.0679671i
$750$	−2.39365	+	0.520056i	−0.0874036	+	0.0189898i
$751$	4.02629	−	11.0621i	0.146921	−	0.403663i	−0.844301	−	0.535870i	$-0.819984\pi$
$751$	4.02629	−	11.0621i	0.146921	−	0.403663i	0.991222	+	0.132206i	$0.0422061\pi$
$752$	0.236989	−	3.34913i	0.00864210	−	0.122130i
$753$	−34.4226	−	39.9215i	−1.25443	−	1.45482i
$754$	−0.652207	+	0.0169431i	−0.0237520	+	0.000617033i
$755$	18.1540			0.660691
$756$	17.1523	−	8.10256i	0.623823	−	0.294687i
$757$	12.5869			0.457479			0.228740	−	0.973488i	$-0.426540\pi$
$757$	12.5869			0.457479			0.228740	+	0.973488i	$0.426540\pi$
$758$	−18.0019	+	0.467655i	−0.653857	+	0.0169860i
$759$	10.4375	−	1.98536i	0.378859	−	0.0720641i
$760$	−9.47481	−	9.65365i	−0.343687	−	0.350175i
$761$	14.3649	−	39.4673i	0.520728	−	1.43069i	−0.348985	−	0.937128i	$-0.613474\pi$
$761$	14.3649	−	39.4673i	0.520728	−	1.43069i	0.869712	−	0.493559i	$-0.164304\pi$
$762$	−14.9168	−	16.4176i	−0.540379	−	0.594746i
$763$	30.2172	+	5.32810i	1.09394	+	0.192890i
$764$	−36.1474	−	27.2625i	−1.30777	−	0.986324i
$765$	0.906273	−	1.67190i	0.0327664	−	0.0604476i
$766$	−4.22717	+	12.6250i	−0.152734	+	0.456159i
$767$	−13.1587	+	4.78936i	−0.475132	+	0.172934i
$768$	−3.53350	+	27.4866i	−0.127504	+	0.991838i
$769$	−5.47611	+	4.59500i	−0.197474	+	0.165700i	−0.736163	−	0.676805i	$-0.763364\pi$
$769$	−5.47611	+	4.59500i	−0.197474	+	0.165700i	0.538689	+	0.842505i	$0.318920\pi$
$770$	−5.09800	−	0.762984i	−0.183719	−	0.0274960i
$771$	−44.6184	+	16.9220i	−1.60689	+	0.609432i
$772$	−3.62066	−	15.7126i	−0.130310	−	0.565508i
$773$	31.5780	−	18.2315i	1.13578	−	0.655743i	0.190398	−	0.981707i	$-0.439022\pi$
$773$	31.5780	−	18.2315i	1.13578	−	0.655743i	0.945382	+	0.325964i	$0.105689\pi$
$774$	35.0154	+	10.6868i	1.25860	+	0.384129i
$775$	6.80573	+	3.92929i	0.244469	+	0.141144i
$776$	6.23485	+	13.7037i	0.223818	+	0.491935i
$777$	−26.8131	+	0.360261i	−0.961914	+	0.0129243i
$778$	−41.4408	+	16.3140i	−1.48573	+	0.584887i
$779$	−5.53121	−	31.3690i	−0.198176	−	1.12391i
$780$	7.30314	−	0.478159i	0.261494	−	0.0171209i
$781$	−6.88821	−	5.77989i	−0.246479	−	0.206821i
$782$	−2.06295	+	1.82438i	−0.0737709	+	0.0652397i
$783$	−0.151840	+	1.12442i	−0.00542633	+	0.0401834i
$784$	−14.2334	−	3.56133i	−0.508334	−	0.127190i
$785$	−4.96004	+	5.91115i	−0.177032	+	0.210978i
$786$	−1.78766	+	13.1490i	−0.0637637	+	0.469010i
$787$	−29.7784	+	5.25073i	−1.06148	+	0.187168i	−0.677015	−	0.735969i	$-0.736727\pi$
$787$	−29.7784	+	5.25073i	−1.06148	+	0.187168i	−0.384470	+	0.923138i	$0.625616\pi$
$788$	−20.8669	−	10.6431i	−0.743353	−	0.379146i
$789$	14.3770	+	8.04500i	0.511835	+	0.286410i
$790$	13.4274	−	8.22450i	0.477726	−	0.292615i
$791$	15.1263	−	26.1995i	0.537829	−	0.931546i
$792$	4.09797	−	16.4408i	0.145615	−	0.584198i
$793$	6.62159	+	11.4689i	0.235140	+	0.407274i
$794$	18.8270	+	10.2273i	0.668145	+	0.362953i
$795$	−14.1886	+	17.3782i	−0.503217	+	0.616341i
$796$	−16.8465	+	10.9303i	−0.597108	+	0.387414i
$797$	13.8653	+	16.5240i	0.491134	+	0.585310i	0.953505	−	0.301376i	$-0.0974459\pi$
$797$	13.8653	+	16.5240i	0.491134	+	0.585310i	−0.462372	+	0.886686i	$0.653001\pi$
$798$	−11.4127	−	18.0825i	−0.404004	−	0.640113i
$799$	−0.181985	−	0.500000i	−0.00643817	−	0.0176887i
$800$	3.04438	−	4.76778i	0.107635	−	0.168567i
$801$	7.63679	+	19.3479i	0.269833	+	0.683626i
$802$	−6.78010	−	33.3607i	−0.239414	−	1.17801i
$803$	1.06134	−	6.01916i	0.0374539	−	0.212412i
$804$	−46.1749	+	20.3136i	−1.62846	+	0.716405i
$805$	5.26922	+	1.91784i	0.185716	+	0.0675950i
$806$	−18.3730	−	14.6207i	−0.647160	−	0.514994i
$807$	34.1859	+	11.9250i	1.20340	+	0.419780i
$808$	1.74016	−	17.9551i	0.0612187	−	0.631657i
$809$		−	13.2902i		−	0.467257i	−0.972326	−	0.233628i	$-0.924940\pi$
$809$		−	13.2902i		−	0.467257i	0.972326	−	0.233628i	$-0.0750599\pi$
$810$	1.20505	−	12.6707i	0.0423412	−	0.445205i
$811$		−	24.0398i		−	0.844151i	−0.906561	−	0.422075i	$-0.861302\pi$
$811$		−	24.0398i		−	0.844151i	0.906561	−	0.422075i	$-0.138698\pi$
$812$	−0.583237	+	0.543425i	−0.0204676	+	0.0190705i
$813$	33.3953	+	11.6492i	1.17122	+	0.408556i
$814$	−14.9141	+	18.7416i	−0.522740	+	0.656894i
$815$	6.96037	+	2.53337i	0.243811	+	0.0887400i
$816$	1.26368	+	4.20613i	0.0442375	+	0.147244i
$817$	7.16592	−	40.6400i	0.250704	−	1.42181i
$818$	46.5229	−	9.45513i	1.62663	−	0.330591i
$819$	11.4437	+	1.70220i	0.399876	+	0.0594796i
$820$	12.2643	−	5.19988i	0.428288	−	0.181588i
$821$	−11.1315	−	30.5836i	−0.388493	−	1.06738i	−0.967680	−	0.252181i	$-0.918852\pi$
$821$	−11.1315	−	30.5836i	−0.388493	−	1.06738i	0.579187	−	0.815194i	$-0.303370\pi$
$822$	12.1030	−	7.63872i	0.422139	−	0.266431i
$823$	−0.550940	−	0.656585i	−0.0192046	−	0.0228871i	0.756357	−	0.654159i	$-0.226977\pi$
$823$	−0.550940	−	0.656585i	−0.0192046	−	0.0228871i	−0.775561	+	0.631272i	$0.782533\pi$
$824$	−27.2284	−	7.56936i	−0.948545	−	0.263691i
$825$	−2.18738	+	2.67910i	−0.0761547	+	0.0932743i
$826$	−8.16718	+	15.0346i	−0.284173	+	0.523122i
$827$	−10.0879	−	17.4728i	−0.350792	−	0.607590i	0.635596	−	0.772022i	$-0.280754\pi$
$827$	−10.0879	−	17.4728i	−0.350792	−	0.607590i	−0.986388	+	0.164432i	$0.947421\pi$
$828$	−7.93040	+	16.6382i	−0.275601	+	0.578218i
$829$	−8.31167	+	14.3962i	−0.288676	+	0.500002i	−0.973494	−	0.228712i	$-0.926548\pi$
$829$	−8.31167	+	14.3962i	−0.288676	+	0.500002i	0.684818	+	0.728714i	$0.259882\pi$
$830$	−1.50497	−	2.45703i	−0.0522382	−	0.0852847i
$831$	4.22207	+	2.36256i	0.146462	+	0.0819562i
$832$	−11.1046	+	12.7423i	−0.384982	+	0.441759i
$833$	−2.28988	+	0.403767i	−0.0793395	+	0.0139897i
$834$	16.3718	+	2.22581i	0.566908	+	0.0770734i
$835$	−1.47149	+	1.75365i	−0.0509229	+	0.0606875i
$836$	−18.9558	−	2.33547i	−0.655600	−	0.0807740i
$837$	−30.1979	+	27.4870i	−1.04379	+	0.950089i
$838$	3.84002	+	4.34217i	0.132651	+	0.149998i
$839$	−33.0065	−	27.6957i	−1.13951	−	0.956163i	−0.140088	−	0.990139i	$-0.544739\pi$
$839$	−33.0065	−	27.6957i	−1.13951	−	0.956163i	−0.999423	+	0.0339759i	$0.989183\pi$
$840$	6.29737	−	6.34904i	0.217280	−	0.219063i
$841$	5.02752	+	28.5125i	0.173363	+	0.983189i
$842$	−12.6711	−	32.1871i	−0.436676	−	1.10924i
$843$	40.8503	−	0.548866i	1.40696	−	0.0189039i
$844$	−7.59267	+	24.7977i	−0.261350	+	0.853571i
$845$	−7.39265	−	4.26815i	−0.254315	−	0.146829i
$846$	−2.42997	−	2.60330i	−0.0835441	−	0.0895033i
$847$	11.0856	−	6.40029i	0.380906	−	0.219916i
$848$	−5.37291	−	51.5315i	−0.184507	−	1.76960i
$849$	−23.9610	+	9.08746i	−0.822338	+	0.311881i
$850$	0.132693	−	0.886609i	0.00455133	−	0.0304104i
$851$	19.9590	−	16.7476i	0.684186	−	0.574101i
$852$	15.1523	−	3.70661i	0.519108	−	0.126986i
$853$	23.3527	−	8.49967i	0.799580	−	0.291023i	0.0902675	−	0.995918i	$-0.471228\pi$
$853$	23.3527	−	8.49967i	0.799580	−	0.291023i	0.709312	+	0.704894i	$0.249006\pi$
$854$	15.3439	+	5.13755i	0.525059	+	0.175803i
$855$	−14.3418	+	0.385463i	−0.490479	+	0.0131825i
$856$	1.29198	+	16.5480i	0.0441591	+	0.565598i
$857$	−47.7410	−	8.41803i	−1.63080	−	0.287555i	−0.718027	−	0.696015i	$-0.754955\pi$
$857$	−47.7410	−	8.41803i	−1.63080	−	0.287555i	−0.912776	+	0.408461i	$0.866066\pi$
$858$	7.64845	−	6.94929i	0.261114	−	0.237245i
$859$	9.90001	−	27.2001i	0.337784	−	0.928054i	−0.648238	−	0.761438i	$-0.724494\pi$
$859$	9.90001	−	27.2001i	0.337784	−	0.928054i	0.986022	−	0.166616i	$-0.0532840\pi$
$860$	17.2348	−	0.896063i	0.587702	−	0.0305555i
$861$	20.6873	−	3.93501i	0.705021	−	0.134105i
$862$	0.603919	+	23.2472i	0.0205696	+	0.791802i
$863$	−9.90306			−0.337104			−0.168552	−	0.985693i	$-0.553909\pi$
$863$	−9.90306			−0.337104			−0.168552	+	0.985693i	$0.553909\pi$
$864$	18.7955	+	22.5993i	0.639437	+	0.768843i
$865$	−5.55537			−0.188888
$866$	−0.246896	−	9.50397i	−0.00838986	−	0.322958i
$867$	−18.7736	−	21.7726i	−0.637585	−	0.739438i
$868$	−28.6509	+	1.48960i	−0.972475	+	0.0505603i
$869$	7.60419	−	20.8923i	0.257955	−	0.708724i
$870$	0.113559	+	0.522672i	0.00385000	+	0.0177202i
$871$	−30.2993	−	5.34258i	−1.02665	−	0.181026i
$872$	3.70075	+	47.3999i	0.125323	+	1.60516i
$873$	15.1470	+	5.05648i	0.512647	+	0.171136i
$874$	19.7011	+	6.59645i	0.666400	+	0.223128i
$875$	−1.71528	+	0.624312i	−0.0579872	+	0.0211056i
$876$	7.33160	+	7.65977i	0.247712	+	0.258800i
$877$	2.56480	−	2.15212i	0.0866072	−	0.0726721i	−0.598456	−	0.801156i	$-0.704219\pi$
$877$	2.56480	−	2.15212i	0.0866072	−	0.0726721i	0.685063	+	0.728483i	$0.259774\pi$
$878$	0.596563	−	3.98604i	0.0201330	−	0.134522i
$879$	3.56710	−	21.9506i	0.120315	−	0.740375i
$880$	−0.828312	−	7.94432i	−0.0279224	−	0.267803i
$881$	−26.8170	+	15.4828i	−0.903488	+	0.521629i	−0.878330	−	0.478054i	$-0.841342\pi$
$881$	−26.8170	+	15.4828i	−0.903488	+	0.521629i	−0.0251578	+	0.999683i	$0.508009\pi$
$882$	−13.0474	+	8.48205i	−0.439330	+	0.285606i
$883$	−32.9477	−	19.0224i	−1.10878	−	0.640154i	−0.170266	−	0.985398i	$-0.554463\pi$
$883$	−32.9477	−	19.0224i	−1.10878	−	0.640154i	−0.938513	+	0.345245i	$0.887796\pi$
$884$	−0.784205	+	2.56122i	−0.0263757	+	0.0861430i
$885$	5.87301	+	9.86389i	0.197419	+	0.331571i
$886$	−3.57842	−	9.08989i	−0.120219	−	0.305381i
$887$	1.18842	+	6.73988i	0.0399033	+	0.226303i	0.998237	−	0.0593467i	$-0.0189017\pi$
$887$	1.18842	+	6.73988i	0.0399033	+	0.226303i	−0.958334	+	0.285650i	$0.907791\pi$
$888$	−10.9181	−	40.0908i	−0.366386	−	1.34536i
$889$	−12.6629	−	10.6254i	−0.424699	−	0.356365i
$890$	6.49578	+	7.34522i	0.217739	+	0.246212i
$891$	−9.80885	−	15.0587i	−0.328609	−	0.504487i
$892$	−48.6487	−	5.99382i	−1.62888	−	0.200688i
$893$	−2.58026	+	3.07503i	−0.0863450	+	0.102902i
$894$	−11.5711	−	28.2725i	−0.386996	−	0.945573i
$895$	3.13855	−	0.553410i	0.104910	−	0.0184985i
$896$	0.150205	+	20.6511i	0.00501801	+	0.689906i
$897$	−9.65891	+	5.75096i	−0.322502	+	0.192019i
$898$	−25.3773	−	41.4313i	−0.846852	−	1.38258i
$899$	0.857992	−	1.48609i	0.0286156	−	0.0495638i
$900$	−1.50388	−	5.80847i	−0.0501293	−	0.193616i
$901$	−4.10542	−	7.11080i	−0.136771	−	0.236895i
$902$	8.97841	−	16.5280i	0.298948	−	0.550322i
$903$	26.9286	+	4.37606i	0.896128	+	0.145626i
$904$	45.1640	+	12.5554i	1.50213	+	0.417586i
$905$	−14.6096	−	17.4111i	−0.485640	−	0.578764i
$906$	1.75192	+	44.4335i	0.0582036	+	1.47620i
$907$	14.1763	+	38.9491i	0.470717	+	1.29328i	0.917177	+	0.398481i	$0.130462\pi$
$907$	14.1763	+	38.9491i	0.470717	+	1.29328i	−0.446459	+	0.894804i	$0.647315\pi$
$908$	39.1295	−	16.5903i	1.29856	−	0.550569i
$909$	−12.6881	−	14.3213i	−0.420838	−	0.475009i
$910$	5.34471	−	1.08624i	0.177175	−	0.0360084i
$911$	6.43342	−	36.4857i	0.213149	−	1.20883i	−0.670942	−	0.741510i	$-0.734110\pi$
$911$	6.43342	−	36.4857i	0.213149	−	1.20883i	0.884090	−	0.467316i	$-0.154779\pi$
$912$	22.7138	−	24.1220i	0.752130	−	0.798760i
$913$	−3.82300	−	1.39146i	−0.126523	−	0.0460506i
$914$	−13.2564	+	16.6584i	−0.438481	+	0.551011i
$915$	8.22235	−	7.08978i	0.271823	−	0.234381i
$916$	−40.8158	+	38.0297i	−1.34859	+	1.25654i
$917$			9.88883i			0.326558i
$918$	4.17958	+	2.05684i	0.137947	+	0.0678858i
$919$		−	24.8654i		−	0.820233i	−0.912033	−	0.410116i	$-0.865488\pi$
$919$		−	24.8654i		−	0.820233i	0.912033	−	0.410116i	$-0.134512\pi$
$920$	−0.838163	+	8.64819i	−0.0276334	+	0.285122i
$921$	10.4606	+	54.9942i	0.344690	+	1.81212i
$922$	4.08703	+	3.25236i	0.134599	+	0.107111i
$923$	8.94007	+	3.25392i	0.294266	+	0.107104i
$924$	1.37550	−	12.5514i	0.0452505	−	0.412912i
$925$	−1.47280	+	8.35269i	−0.0484255	+	0.274635i
$926$	−3.56950	−	17.5633i	−0.117301	−	0.577166i
$927$	−25.5473	+	15.6797i	−0.839082	+	0.514987i
$928$	−1.04108	−	0.664764i	−0.0341753	−	0.0218220i
$929$	8.47285	+	23.2790i	0.277985	+	0.763758i	0.997591	+	0.0693748i	$0.0221004\pi$
$929$	8.47285	+	23.2790i	0.277985	+	0.763758i	−0.719606	+	0.694383i	$0.755677\pi$
$930$	−8.96051	+	17.0368i	−0.293827	+	0.558659i
$931$	11.2756	+	13.4377i	0.369543	+	0.440404i
$932$	−4.50092	+	2.92028i	−0.147433	+	0.0956568i
$933$	13.1243	+	34.6050i	0.429671	+	1.13292i
$934$	−15.9311	−	8.65418i	−0.521283	−	0.283174i
$935$	−0.632910	−	1.09623i	−0.0206984	−	0.0358507i
$936$	1.87511	+	17.8289i	0.0612900	+	0.582757i
$937$	24.5549	−	42.5304i	0.802175	−	1.38941i	−0.116007	−	0.993248i	$-0.537010\pi$
$937$	24.5549	−	42.5304i	0.802175	−	1.38941i	0.918182	−	0.396159i	$-0.129657\pi$
$938$	−32.0568	+	19.6353i	−1.04669	+	0.641114i
$939$	−0.359952	−	26.7901i	−0.0117466	−	0.874261i
$940$	−1.49546	−	0.762758i	−0.0487766	−	0.0248784i
$941$	51.5700	−	9.09319i	1.68113	−	0.296429i	0.750090	−	0.661336i	$-0.230010\pi$
$941$	51.5700	−	9.09319i	1.68113	−	0.296429i	0.931044	+	0.364906i	$0.118899\pi$
$942$	−14.9467	−	11.5697i	−0.486991	−	0.376961i
$943$	−13.1519	+	15.6738i	−0.428285	+	0.510410i
$944$	−25.7189	−	6.43513i	−0.837078	−	0.209446i
$945$	−0.382191	−	9.47718i	−0.0124327	−	0.308293i
$946$	18.2540	−	16.1430i	0.593489	−	0.524856i
$947$	9.45691	+	7.93529i	0.307308	+	0.257862i	0.783378	−	0.621545i	$-0.213495\pi$
$947$	9.45691	+	7.93529i	0.307308	+	0.257862i	−0.476070	+	0.879407i	$0.657939\pi$
$948$	21.4260	+	32.0711i	0.695883	+	1.04162i
$949$	1.12294	+	6.36853i	0.0364523	+	0.206731i
$950$	−6.29314	+	2.47742i	−0.204176	+	0.0803783i
$951$	−3.59715	+	6.42838i	−0.116646	+	0.208454i
$952$	1.35536	+	2.97899i	0.0439276	+	0.0965496i
$953$	48.5488	+	28.0297i	1.57265	+	0.907970i	0.995843	+	0.0910892i	$0.0290348\pi$
$953$	48.5488	+	28.0297i	1.57265	+	0.907970i	0.576807	+	0.816881i	$0.304298\pi$
$954$	−43.9039	−	33.0507i	−1.42144	−	1.07006i
$955$	−19.6049	+	11.3189i	−0.634400	+	0.366271i
$956$	−2.34085	−	10.1586i	−0.0757086	−	0.328552i
$957$	0.585004	+	0.477631i	0.0189105	+	0.0154396i
$958$	−53.5228	−	8.01039i	−1.72924	−	0.258804i
$959$	8.17009	−	6.85552i	0.263826	−	0.221376i
$960$	11.9634	+	6.99127i	0.386116	+	0.225642i
$961$	28.9024	−	10.5196i	0.932335	−	0.339342i
$962$	8.04606	−	24.0306i	0.259415	−	0.774776i
$963$	13.7855	+	10.9500i	0.444232	+	0.352858i
$964$	−9.87883	−	7.45066i	−0.318176	−	0.239970i
$965$	−7.93968	−	1.39998i	−0.255587	−	0.0450670i
$966$	−4.18558	+	13.0820i	−0.134669	+	0.420905i
$967$	−16.4008	+	45.0610i	−0.527416	+	1.44906i	0.334687	+	0.942329i	$0.391369\pi$
$967$	−16.4008	+	45.0610i	−0.527416	+	1.44906i	−0.862103	+	0.506733i	$0.830853\pi$
$968$	13.8935	+	14.1557i	0.446553	+	0.454982i
$969$	1.72943	−	4.95784i	0.0555574	−	0.159269i
$970$	7.52517	−	0.195490i	0.241619	−	0.00627681i
$971$	54.3406			1.74387			0.871937	−	0.489619i	$-0.162864\pi$
$971$	54.3406			1.74387			0.871937	+	0.489619i	$0.162864\pi$
$972$	31.1291	+	1.72670i	0.998465	+	0.0553839i
$973$	12.3125			0.394722
$974$	−22.4699	+	0.583726i	−0.719981	+	0.0187038i
$975$	1.20527	−	3.45520i	0.0385996	−	0.110655i
$976$	−1.76977	+	25.0104i	−0.0566489	+	0.800563i
$977$	−13.5670	+	37.2750i	−0.434046	+	1.19253i	0.509261	+	0.860612i	$0.329919\pi$
$977$	−13.5670	+	37.2750i	−0.434046	+	1.19253i	−0.943307	+	0.331920i	$0.892303\pi$
$978$	−5.52894	+	17.2806i	−0.176796	+	0.552573i
$979$	13.6348	+	2.40419i	0.435772	+	0.0768383i
$980$	−4.41739	+	5.85701i	−0.141108	+	0.187095i
$981$	39.4872	+	31.3650i	1.26073	+	1.00141i
$982$	−0.901562	+	2.69263i	−0.0287700	+	0.0859252i
$983$	44.6418	−	16.2483i	1.42385	−	0.518240i	0.488690	−	0.872458i	$-0.337475\pi$
$983$	44.6418	−	16.2483i	1.42385	−	0.518240i	0.935163	+	0.354218i	$0.115253\pi$
$984$	13.9107	+	29.5162i	0.443458	+	0.940942i
$985$	−8.97208	+	7.52847i	−0.285874	+	0.239877i
$986$	−0.193598	−	0.0289746i	−0.00616543	−	0.000922738i
$987$	−2.05566	−	1.67836i	−0.0654323	−	0.0534228i
$988$	19.6917	−	4.53756i	0.626475	−	0.144359i
$989$	−22.9564	+	13.2539i	−0.729971	+	0.421449i
$990$	−6.76843	−	5.09525i	−0.215115	−	0.161938i
$991$	33.4825	+	19.3311i	1.06361	+	0.614073i	0.926427	−	0.376473i	$-0.122863\pi$
$991$	33.4825	+	19.3311i	1.06361	+	0.614073i	0.137178	+	0.990546i	$0.456197\pi$
$992$	−13.3238	−	42.4112i	−0.423031	−	1.34656i
$993$	9.79146	−	17.4981i	0.310723	−	0.555285i
$994$	10.8165	−	4.25813i	0.343078	−	0.135060i
$995$	1.74358	+	9.88832i	0.0552751	+	0.313481i
$996$	5.86856	−	3.92065i	0.185952	−	0.124231i
$997$	−28.3669	−	23.8026i	−0.898389	−	0.753837i	0.0714862	−	0.997442i	$-0.477226\pi$
$997$	−28.3669	−	23.8026i	−0.898389	−	0.753837i	−0.969875	+	0.243604i	$0.921670\pi$
$998$	−6.08868	+	5.38456i	−0.192734	+	0.170445i
$999$	−39.0239	−	20.4799i	−1.23466	−	0.647954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.35	yes	432
4.3	odd	2	inner	540.2.be.a.11.5	✓	432
27.5	odd	18	inner	540.2.be.a.491.5	yes	432
108.59	even	18	inner	540.2.be.a.491.35	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.5	✓	432	4.3	odd	2	inner
540.2.be.a.11.35	yes	432	1.1	even	1	trivial
540.2.be.a.491.5	yes	432	27.5	odd	18	inner
540.2.be.a.491.35	yes	432	108.59	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0367263 + 1.41374i) q^{2} +(-0.570476 + 1.63541i) q^{3} +(-1.99730 + 0.103843i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-2.33299 - 0.746441i) q^{6} +(-1.79764 - 0.316972i) q^{7} +(-0.220160 - 2.81985i) q^{8} +(-2.34911 - 1.86592i) q^{9} +(-1.34104 - 0.449015i) q^{10} +(-1.87642 + 0.682962i) q^{11} +(0.969589 - 3.32564i) q^{12} +(1.61846 - 1.35805i) q^{13} +(0.382094 - 2.55303i) q^{14} +(-1.34167 - 1.09541i) q^{15} +(3.97843 - 0.414810i) q^{16} +(0.548982 - 0.316955i) q^{17} +(2.55165 - 3.38956i) q^{18} +(-4.14161 - 2.39116i) q^{19} +(0.585538 - 1.91237i) q^{20} +(1.54389 - 2.75904i) q^{21} +(-1.03444 - 2.62768i) q^{22} +(0.533434 + 3.02525i) q^{23} +(4.73719 + 1.24860i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(1.97936 + 2.23820i) q^{26} +(4.39166 - 2.77729i) q^{27} +(3.62334 + 0.446417i) q^{28} +(-0.140358 + 0.167272i) q^{29} +(1.49935 - 1.93699i) q^{30} +(-7.73919 + 1.36463i) q^{31} +(0.732545 + 5.60922i) q^{32} +(-0.0464661 - 3.45833i) q^{33} +(0.468253 + 0.764475i) q^{34} +(0.912684 - 1.58081i) q^{35} +(4.88565 + 3.48287i) q^{36} +(-4.24077 - 7.34523i) q^{37} +(3.22837 - 5.94297i) q^{38} +(1.29767 + 3.42157i) q^{39} +(2.72509 + 0.757562i) q^{40} +(4.28132 + 5.10228i) q^{41} +(3.95726 + 2.08132i) q^{42} +(2.95131 + 8.10865i) q^{43} +(3.67686 - 1.55893i) q^{44} +(2.55684 - 1.56926i) q^{45} +(-4.25732 + 0.865241i) q^{46} +(0.145756 - 0.826624i) q^{47} +(-1.59122 + 6.74300i) q^{48} +(-3.44682 - 1.25454i) q^{49} +(0.880598 - 1.10659i) q^{50} +(0.205169 + 1.07862i) q^{51} +(-3.09153 + 2.88050i) q^{52} -12.9527i q^{53} +(4.08765 + 6.10665i) q^{54} -1.99685i q^{55} +(-0.498045 + 5.13884i) q^{56} +(6.27322 - 5.40912i) q^{57} +(-0.241633 - 0.192286i) q^{58} +(-6.22822 - 2.26689i) q^{59} +(2.79346 + 2.04855i) q^{60} +(-1.08847 + 6.17300i) q^{61} +(-2.21346 - 10.8911i) q^{62} +(3.63141 + 4.09885i) q^{63} +(-7.90306 + 1.24163i) q^{64} +(0.722602 + 1.98533i) q^{65} +(4.88746 - 0.192702i) q^{66} +(-9.36054 - 11.1555i) q^{67} +(-1.06357 + 0.690062i) q^{68} +(-5.25183 - 0.853454i) q^{69} +(2.26837 + 1.23224i) q^{70} +(2.25153 + 3.89976i) q^{71} +(-4.74443 + 7.03494i) q^{72} +(-1.53042 + 2.65076i) q^{73} +(10.2285 - 6.26510i) q^{74} +(1.48823 - 0.886099i) q^{75} +(8.52036 + 4.34580i) q^{76} +(3.58960 - 0.632944i) q^{77} +(-4.78955 + 1.96022i) q^{78} +(-7.15688 + 8.52924i) q^{79} +(-0.970910 + 3.88038i) q^{80} +(2.03667 + 8.76653i) q^{81} +(-7.05605 + 6.24005i) q^{82} +(1.56073 + 1.30961i) q^{83} +(-2.79710 + 5.67096i) q^{84} +(0.110077 + 0.624279i) q^{85} +(-11.3551 + 4.47017i) q^{86} +(-0.193487 - 0.324967i) q^{87} +(2.33896 + 5.14086i) q^{88} +(-6.00461 - 3.46676i) q^{89} +(2.31243 + 3.55706i) q^{90} +(-3.33986 + 1.92827i) q^{91} +(-1.37958 - 5.98695i) q^{92} +(2.18330 - 13.4352i) q^{93} +(1.17398 + 0.175702i) q^{94} +(3.66347 - 3.07402i) q^{95} +(-9.59126 - 2.00192i) q^{96} +(-5.00188 + 1.82054i) q^{97} +(1.64700 - 4.91898i) q^{98} +(5.68228 + 1.89690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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