LMFDB - Embedded newform 675.2.l.f.76.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.8
Character	$\chi$	$=$	675.76
Dual form			675.2.l.f.151.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.672508 - 0.564301i) q^{2} +(1.45527 - 0.939248i) q^{3} +(-0.213465 + 1.21062i) q^{4} +(0.448662 - 1.45286i) q^{6} +(-0.0883715 - 0.501180i) q^{7} +(1.41750 + 2.45517i) q^{8} +(1.23563 - 2.73372i) q^{9} +(2.28041 + 0.830001i) q^{11} +(0.826424 + 1.96228i) q^{12} +(4.85915 + 4.07731i) q^{13} +(-0.342247 - 0.287179i) q^{14} +(0.0284139 + 0.0103418i) q^{16} +(-2.86909 + 4.96942i) q^{17} +(-0.711675 - 2.53572i) q^{18} +(-1.94493 - 3.36871i) q^{19} +(-0.599337 - 0.646349i) q^{21} +(2.00197 - 0.728656i) q^{22} +(1.12370 - 6.37282i) q^{23} +(4.36886 + 2.24156i) q^{24} +5.56865 q^{26} +(-0.769474 - 5.13886i) q^{27} +0.625603 q^{28} +(-0.324767 + 0.272512i) q^{29} +(1.47718 - 8.37750i) q^{31} +(-5.30309 + 1.93017i) q^{32} +(4.09819 - 0.933994i) q^{33} +(0.874759 + 4.96101i) q^{34} +(3.04574 + 2.07943i) q^{36} +(-1.19190 + 2.06443i) q^{37} +(-3.20895 - 1.16796i) q^{38} +(10.9010 + 1.36964i) q^{39} +(0.938033 + 0.787103i) q^{41} +(-0.767795 - 0.0964687i) q^{42} +(2.34944 + 0.855127i) q^{43} +(-1.49160 + 2.58353i) q^{44} +(-2.84049 - 4.91988i) q^{46} +(0.143949 + 0.816377i) q^{47} +(0.0510634 - 0.0116376i) q^{48} +(6.33448 - 2.30556i) q^{49} +(0.492208 + 9.92664i) q^{51} +(-5.97334 + 5.01222i) q^{52} -8.88536 q^{53} +(-3.41735 - 3.02171i) q^{54} +(1.10522 - 0.927387i) q^{56} +(-5.99445 - 3.07562i) q^{57} +(-0.0646297 + 0.366533i) q^{58} +(-6.58000 + 2.39492i) q^{59} +(0.558258 + 3.16604i) q^{61} +(-3.73402 - 6.46751i) q^{62} +(-1.47928 - 0.377687i) q^{63} +(-2.50742 + 4.34297i) q^{64} +(2.22901 - 2.94073i) q^{66} +(-5.32923 - 4.47176i) q^{67} +(-5.40363 - 4.53418i) q^{68} +(-4.35037 - 10.3296i) q^{69} +(-1.59927 + 2.77002i) q^{71} +(8.46325 - 0.841362i) q^{72} +(5.99262 + 10.3795i) q^{73} +(0.363398 + 2.06093i) q^{74} +(4.49341 - 1.63547i) q^{76} +(0.214457 - 1.21624i) q^{77} +(8.10390 - 5.23035i) q^{78} +(2.06451 - 1.73233i) q^{79} +(-5.94646 - 6.75571i) q^{81} +1.07500 q^{82} +(-6.00558 + 5.03928i) q^{83} +(0.910421 - 0.587596i) q^{84} +(2.06257 - 0.750714i) q^{86} +(-0.216668 + 0.701616i) q^{87} +(1.19467 + 6.77532i) q^{88} +(-9.24733 - 16.0168i) q^{89} +(1.61406 - 2.79563i) q^{91} +(7.47519 + 2.72075i) q^{92} +(-5.71886 - 13.5790i) q^{93} +(0.557490 + 0.467789i) q^{94} +(-5.90453 + 7.78984i) q^{96} +(7.86099 + 2.86117i) q^{97} +(2.95896 - 5.12506i) q^{98} +(5.08672 - 5.20843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.672508	−	0.564301i	0.475535	−	0.399021i	−0.373274	−	0.927721i	$-0.621765\pi$
$2$	0.672508	−	0.564301i	0.475535	−	0.399021i	0.848809	+	0.528700i	$0.177320\pi$
$3$	1.45527	−	0.939248i	0.840201	−	0.542275i
$3$	1.45527	−	0.939248i	0.840201	−	0.542275i
$4$	−0.213465	+	1.21062i	−0.106733	+	0.605310i
$5$		0			0
$5$		0			0
$6$	0.448662	−	1.45286i	0.183166	−	0.593129i
$7$	−0.0883715	−	0.501180i	−0.0334013	−	0.189428i	0.963542	−	0.267557i	$-0.0862165\pi$
$7$	−0.0883715	−	0.501180i	−0.0334013	−	0.189428i	−0.996943	+	0.0781292i	$0.975105\pi$
$8$	1.41750	+	2.45517i	0.501160	+	0.868035i
$9$	1.23563	−	2.73372i	0.411875	−	0.911240i
$10$		0			0
$11$	2.28041	+	0.830001i	0.687569	+	0.250255i	0.662094	−	0.749421i	$-0.269668\pi$
$11$	2.28041	+	0.830001i	0.687569	+	0.250255i	0.0254752	+	0.999675i	$0.491890\pi$
$12$	0.826424	+	1.96228i	0.238568	+	0.566461i
$13$	4.85915	+	4.07731i	1.34769	+	1.13084i	0.979579	+	0.201059i	$0.0644383\pi$
$13$	4.85915	+	4.07731i	1.34769	+	1.13084i	0.368107	+	0.929784i	$0.380006\pi$
$14$	−0.342247	−	0.287179i	−0.0914694	−	0.0767519i
$15$		0			0
$16$	0.0284139	+	0.0103418i	0.00710347	+	0.00258545i
$17$	−2.86909	+	4.96942i	−0.695857	+	1.20526i	0.274033	+	0.961720i	$0.411642\pi$
$17$	−2.86909	+	4.96942i	−0.695857	+	1.20526i	−0.969891	+	0.243540i	$0.921691\pi$
$18$	−0.711675	−	2.53572i	−0.167743	−	0.597674i
$19$	−1.94493	−	3.36871i	−0.446197	−	0.772835i	0.551938	−	0.833885i	$-0.313889\pi$
$19$	−1.94493	−	3.36871i	−0.446197	−	0.772835i	−0.998135	+	0.0610497i	$0.980555\pi$
$20$		0			0
$21$	−0.599337	−	0.646349i	−0.130786	−	0.141045i
$22$	2.00197	−	0.728656i	0.426820	−	0.155350i
$23$	1.12370	−	6.37282i	0.234308	−	1.32882i	−0.609760	−	0.792586i	$-0.708734\pi$
$23$	1.12370	−	6.37282i	0.234308	−	1.32882i	0.844067	−	0.536238i	$-0.180155\pi$
$24$	4.36886	+	2.24156i	0.891789	+	0.457557i
$25$		0			0
$26$	5.56865			1.09210
$27$	−0.769474	−	5.13886i	−0.148085	−	0.988975i
$28$	0.625603			0.118228
$29$	−0.324767	+	0.272512i	−0.0603078	+	0.0506042i	−0.672443	−	0.740149i	$-0.734755\pi$
$29$	−0.324767	+	0.272512i	−0.0603078	+	0.0506042i	0.612136	+	0.790753i	$0.290311\pi$
$30$		0			0
$31$	1.47718	−	8.37750i	0.265309	−	1.50464i	−0.502844	−	0.864377i	$-0.667713\pi$
$31$	1.47718	−	8.37750i	0.265309	−	1.50464i	0.768153	−	0.640266i	$-0.221176\pi$
$32$	−5.30309	+	1.93017i	−0.937464	+	0.341209i
$33$	4.09819	−	0.933994i	0.713403	−	0.162588i
$34$	0.874759	+	4.96101i	0.150020	+	0.850806i
$35$		0			0
$36$	3.04574	+	2.07943i	0.507623	+	0.346571i
$37$	−1.19190	+	2.06443i	−0.195947	+	0.339390i	−0.947210	−	0.320612i	$-0.896111\pi$
$37$	−1.19190	+	2.06443i	−0.195947	+	0.339390i	0.751264	+	0.660002i	$0.229445\pi$
$38$	−3.20895	−	1.16796i	−0.520560	−	0.189468i
$39$	10.9010	+	1.36964i	1.74555	+	0.219318i
$40$		0			0
$41$	0.938033	+	0.787103i	0.146496	+	0.122925i	0.713090	−	0.701072i	$-0.247295\pi$
$41$	0.938033	+	0.787103i	0.146496	+	0.122925i	−0.566594	+	0.823997i	$0.691739\pi$
$42$	−0.767795	−	0.0964687i	−0.118473	−	0.0148854i
$43$	2.34944	+	0.855127i	0.358287	+	0.130406i	0.514891	−	0.857256i	$-0.327832\pi$
$43$	2.34944	+	0.855127i	0.358287	+	0.130406i	−0.156604	+	0.987661i	$0.550055\pi$
$44$	−1.49160	+	2.58353i	−0.224868	+	0.389482i
$45$		0			0
$46$	−2.84049	−	4.91988i	−0.418808	−	0.725396i
$47$	0.143949	+	0.816377i	0.0209972	+	0.119081i	0.993505	−	0.113790i	$-0.0362991\pi$
$47$	0.143949	+	0.816377i	0.0209972	+	0.119081i	−0.972508	+	0.232871i	$0.925188\pi$
$48$	0.0510634	−	0.0116376i	0.00737037	−	0.00167974i
$49$	6.33448	−	2.30556i	0.904925	−	0.329366i
$50$		0			0
$51$	0.492208	+	9.92664i	0.0689229	+	1.39001i
$52$	−5.97334	+	5.01222i	−0.828353	+	0.695070i
$53$	−8.88536			−1.22050			−0.610249	−	0.792210i	$-0.708931\pi$
$53$	−8.88536			−1.22050			−0.610249	+	0.792210i	$0.708931\pi$
$54$	−3.41735	−	3.02171i	−0.465042	−	0.411203i
$55$		0			0
$56$	1.10522	−	0.927387i	0.147691	−	0.123927i
$57$	−5.99445	−	3.07562i	−0.793984	−	0.407376i
$58$	−0.0646297	+	0.366533i	−0.00848630	+	0.0481282i
$59$	−6.58000	+	2.39492i	−0.856643	+	0.311792i	−0.732746	−	0.680503i	$-0.761762\pi$
$59$	−6.58000	+	2.39492i	−0.856643	+	0.311792i	−0.123897	+	0.992295i	$0.539539\pi$
$60$		0			0
$61$	0.558258	+	3.16604i	0.0714776	+	0.405369i	0.999463	+	0.0327541i	$0.0104278\pi$
$61$	0.558258	+	3.16604i	0.0714776	+	0.405369i	−0.927986	+	0.372615i	$0.878461\pi$
$62$	−3.73402	−	6.46751i	−0.474221	−	0.821375i
$63$	−1.47928	−	0.377687i	−0.186372	−	0.0475841i
$64$	−2.50742	+	4.34297i	−0.313427	+	0.542871i
$65$		0			0
$66$	2.22901	−	2.94073i	0.274372	−	0.361979i
$67$	−5.32923	−	4.47176i	−0.651070	−	0.546312i	0.256326	−	0.966590i	$-0.417488\pi$
$67$	−5.32923	−	4.47176i	−0.651070	−	0.546312i	−0.907395	+	0.420278i	$0.861932\pi$
$68$	−5.40363	−	4.53418i	−0.655286	−	0.549850i
$69$	−4.35037	−	10.3296i	−0.523723	−	1.24354i
$70$		0			0
$71$	−1.59927	+	2.77002i	−0.189799	+	0.328741i	−0.945183	−	0.326541i	$-0.894117\pi$
$71$	−1.59927	+	2.77002i	−0.189799	+	0.328741i	0.755384	+	0.655282i	$0.227450\pi$
$72$	8.46325	−	0.841362i	0.997404	−	0.0991554i
$73$	5.99262	+	10.3795i	0.701383	+	1.21483i	0.967981	+	0.251024i	$0.0807672\pi$
$73$	5.99262	+	10.3795i	0.701383	+	1.21483i	−0.266598	+	0.963808i	$0.585899\pi$
$74$	0.363398	+	2.06093i	0.0422442	+	0.239579i
$75$		0			0
$76$	4.49341	−	1.63547i	0.515429	−	0.187601i
$77$	0.214457	−	1.21624i	0.0244396	−	0.138604i
$78$	8.10390	−	5.23035i	0.917585	−	0.592220i
$79$	2.06451	−	1.73233i	0.232276	−	0.194903i	−0.519220	−	0.854641i	$-0.673777\pi$
$79$	2.06451	−	1.73233i	0.232276	−	0.194903i	0.751495	+	0.659738i	$0.229333\pi$
$80$		0			0
$81$	−5.94646	−	6.75571i	−0.660718	−	0.750634i
$82$	1.07500			0.118714
$83$	−6.00558	+	5.03928i	−0.659198	+	0.553133i	−0.909846	−	0.414945i	$-0.863801\pi$
$83$	−6.00558	+	5.03928i	−0.659198	+	0.553133i	0.250648	+	0.968078i	$0.419356\pi$
$84$	0.910421	−	0.587596i	0.0993351	−	0.0641120i
$85$		0			0
$86$	2.06257	−	0.750714i	0.222412	−	0.0809515i
$87$	−0.216668	+	0.701616i	−0.0232292	+	0.0752211i
$88$	1.19467	+	6.77532i	0.127353	+	0.722252i
$89$	−9.24733	−	16.0168i	−0.980215	−	1.69778i	−0.661525	−	0.749923i	$-0.730091\pi$
$89$	−9.24733	−	16.0168i	−0.980215	−	1.69778i	−0.318690	−	0.947859i	$-0.603243\pi$
$90$		0			0
$91$	1.61406	−	2.79563i	0.169199	−	0.293061i
$92$	7.47519	+	2.72075i	0.779343	+	0.283658i
$93$	−5.71886	−	13.5790i	−0.593018	−	1.40807i
$94$	0.557490	+	0.467789i	0.0575007	+	0.0482488i
$95$		0			0
$96$	−5.90453	+	7.78984i	−0.602629	+	0.795047i
$97$	7.86099	+	2.86117i	0.798163	+	0.290508i	0.708725	−	0.705485i	$-0.249271\pi$
$97$	7.86099	+	2.86117i	0.798163	+	0.290508i	0.0894380	+	0.995992i	$0.471493\pi$
$98$	2.95896	−	5.12506i	0.298900	−	0.517710i
$99$	5.08672	−	5.20843i	0.511235	−	0.523467i
$100$		0			0
$101$	0.772822	+	4.38289i	0.0768986	+	0.436114i	0.998813	+	0.0487190i	$0.0155139\pi$
$101$	0.772822	+	4.38289i	0.0768986	+	0.436114i	−0.921914	+	0.387395i	$0.873375\pi$
$102$	5.93263	+	6.39799i	0.587418	+	0.633496i
$103$	−10.4849	+	3.81618i	−1.03310	+	0.376019i	−0.802262	−	0.596972i	$-0.796370\pi$
$103$	−10.4849	+	3.81618i	−1.03310	+	0.376019i	−0.230842	+	0.972991i	$0.574148\pi$
$104$	−3.12269	+	17.7096i	−0.306204	+	1.73657i
$105$		0			0
$106$	−5.97548	+	5.01402i	−0.580390	+	0.487005i
$107$	−11.5176			−1.11345			−0.556724	−	0.830698i	$-0.687942\pi$
$107$	−11.5176			−1.11345			−0.556724	+	0.830698i	$0.687942\pi$
$108$	6.38547	+	0.165427i	0.614442	+	0.0159182i
$109$	−16.8148			−1.61057			−0.805285	−	0.592888i	$-0.797988\pi$
$109$	−16.8148			−1.61057			−0.805285	+	0.592888i	$0.797988\pi$
$110$		0			0
$111$	0.204476	+	4.12379i	0.0194080	+	0.391413i
$112$	0.00267213	−	0.0151544i	0.000252492	−	0.00143195i
$113$	−10.0593	+	3.66129i	−0.946301	+	0.344425i	−0.768651	−	0.639668i	$-0.779072\pi$
$113$	−10.0593	+	3.66129i	−0.946301	+	0.344425i	−0.177650	+	0.984094i	$0.556849\pi$
$114$	−5.76689	+	1.31430i	−0.540119	+	0.123095i
$115$		0			0
$116$	−0.260582	−	0.451342i	−0.0241945	−	0.0419060i
$117$	17.1503	−	8.24553i	1.58555	−	0.762300i
$118$	−3.07364	+	5.32371i	−0.282952	+	0.490087i
$119$	2.74412	+	0.998777i	0.251553	+	0.0915577i
$120$		0			0
$121$	−3.91512	−	3.28518i	−0.355920	−	0.298653i
$122$	2.16203	+	1.81416i	0.195741	+	0.164246i
$123$	2.10438	+	0.264402i	0.189745	+	0.0238404i
$124$	9.82665	+	3.57661i	0.882459	+	0.321189i
$125$		0			0
$126$	−1.20796	+	0.580762i	−0.107613	+	0.0517384i
$127$	3.89640	+	6.74877i	0.345750	+	0.598857i	0.985490	−	0.169735i	$-0.0542912\pi$
$127$	3.89640	+	6.74877i	0.345750	+	0.598857i	−0.639740	+	0.768592i	$0.720958\pi$
$128$	−1.19546	−	6.77978i	−0.105664	−	0.599253i
$129$	4.22225	−	0.962268i	0.371748	−	0.0847230i
$130$		0			0
$131$	1.52245	−	8.63426i	0.133017	−	0.754378i	−0.843203	−	0.537596i	$-0.819333\pi$
$131$	1.52245	−	8.63426i	0.133017	−	0.754378i	0.976220	−	0.216783i	$-0.0695563\pi$
$132$	0.255892	+	5.16073i	0.0222726	+	0.449184i
$133$	−1.51645	+	1.27246i	−0.131493	+	0.110336i
$134$	−6.10737			−0.527597
$135$		0			0
$136$	−16.2677			−1.39494
$137$	12.2406	−	10.2711i	1.04579	−	0.877519i	0.0531421	−	0.998587i	$-0.483076\pi$
$137$	12.2406	−	10.2711i	1.04579	−	0.877519i	0.992644	+	0.121068i	$0.0386319\pi$
$138$	−8.75467	−	4.49182i	−0.745247	−	0.382369i
$139$	−0.582428	+	3.30311i	−0.0494009	+	0.280167i	−0.999494	−	0.0317992i	$-0.989876\pi$
$139$	−0.582428	+	3.30311i	−0.0494009	+	0.280167i	0.950093	+	0.311966i	$0.100987\pi$
$140$		0			0
$141$	0.976266	+	1.05285i	0.0822164	+	0.0886656i
$142$	0.487603	+	2.76534i	0.0409188	+	0.232062i
$143$	7.69668	+	13.3310i	0.643629	+	1.11480i
$144$	0.0633805	−	0.0648970i	0.00528171	−	0.00540808i
$145$		0			0
$146$	9.88727	+	3.59867i	0.818276	+	0.297828i
$147$	7.05288	−	9.30486i	0.581712	−	0.767452i
$148$	−2.24481	−	1.88362i	−0.184522	−	0.154833i
$149$	−1.64045	−	1.37650i	−0.134391	−	0.112767i	0.573114	−	0.819475i	$-0.305735\pi$
$149$	−1.64045	−	1.37650i	−0.134391	−	0.112767i	−0.707505	+	0.706708i	$0.750179\pi$
$150$		0			0
$151$	−14.8096	−	5.39026i	−1.20519	−	0.438653i	−0.340156	−	0.940369i	$-0.610480\pi$
$151$	−14.8096	−	5.39026i	−1.20519	−	0.438653i	−0.865032	+	0.501716i	$0.832702\pi$
$152$	5.51385	−	9.55027i	0.447232	−	0.774629i
$153$	10.0399	+	13.9836i	0.811675	+	1.13051i
$154$	−0.542104	−	0.938952i	−0.0436840	−	0.0756629i
$155$		0			0
$156$	−3.98510	+	12.9046i	−0.319063	+	1.03319i
$157$	20.5892	−	7.49385i	1.64320	−	0.598074i	0.655602	−	0.755106i	$-0.272415\pi$
$157$	20.5892	−	7.49385i	1.64320	−	0.598074i	0.987594	+	0.157032i	$0.0501925\pi$
$158$	0.410845	−	2.33002i	0.0326851	−	0.185366i
$159$	−12.9306	+	8.34556i	−1.02546	+	0.661846i
$160$		0			0
$161$	−3.29323			−0.259543
$162$	−7.81130	−	1.18767i	−0.613714	−	0.0933125i
$163$	19.9707			1.56423			0.782115	−	0.623134i	$-0.214141\pi$
$163$	19.9707			1.56423			0.782115	+	0.623134i	$0.214141\pi$
$164$	−1.15312	+	0.967584i	−0.0900436	+	0.0755556i
$165$		0			0
$166$	−1.19513	+	6.77791i	−0.0927600	+	0.526068i
$167$	−16.2833	+	5.92664i	−1.26004	+	0.458617i	−0.883783	−	0.467897i	$-0.845012\pi$
$167$	−16.2833	+	5.92664i	−1.26004	+	0.458617i	−0.376258	+	0.926515i	$0.622789\pi$
$168$	0.737343	−	2.38767i	0.0568873	−	0.184213i
$169$	4.72945	+	26.8220i	0.363804	+	2.06323i
$170$		0			0
$171$	−11.6123	+	1.15442i	−0.888016	+	0.0882808i
$172$	−1.53676	+	2.66174i	−0.117177	+	0.202956i
$173$	−13.4604	−	4.89919i	−1.02338	−	0.372478i	−0.224821	−	0.974400i	$-0.572180\pi$
$173$	−13.4604	−	4.89919i	−1.02338	−	0.372478i	−0.798555	+	0.601922i	$0.794402\pi$
$174$	0.250212	+	0.594109i	0.0189685	+	0.0450393i
$175$		0			0
$176$	0.0562116	+	0.0471671i	0.00423711	+	0.00355535i
$177$	−7.32625	+	9.66551i	−0.550675	+	0.726505i
$178$	−15.2572	−	5.55318i	−1.14358	−	0.416228i
$179$	12.1807	−	21.0976i	0.910428	−	1.57691i	0.0969684	−	0.995287i	$-0.469085\pi$
$179$	12.1807	−	21.0976i	0.910428	−	1.57691i	0.813460	−	0.581621i	$-0.197581\pi$
$180$		0			0
$181$	2.03955	+	3.53261i	0.151599	+	0.262577i	0.931815	−	0.362933i	$-0.118225\pi$
$181$	2.03955	+	3.53261i	0.151599	+	0.262577i	−0.780217	+	0.625509i	$0.784891\pi$
$182$	−0.492110	−	2.79090i	−0.0364776	−	0.206875i
$183$	3.78611	+	4.08310i	0.279877	+	0.301831i
$184$	17.2392	−	6.27456i	1.27089	−	0.462567i
$185$		0			0
$186$	−11.5086	−	5.90481i	−0.843852	−	0.432962i
$187$	−10.6673	+	8.95095i	−0.780072	+	0.654558i
$188$	−1.01905			−0.0743219
$189$	−2.50749	+	0.839774i	−0.182393	+	0.0610845i
$190$		0			0
$191$	5.70298	−	4.78537i	0.412653	−	0.346257i	−0.412707	−	0.910864i	$-0.635417\pi$
$191$	5.70298	−	4.78537i	0.412653	−	0.346257i	0.825360	+	0.564607i	$0.190972\pi$
$192$	0.430160	+	8.67528i	0.0310441	+	0.626085i
$193$	−1.60633	+	9.10995i	−0.115626	+	0.655749i	0.870812	+	0.491616i	$0.163594\pi$
$193$	−1.60633	+	9.10995i	−0.115626	+	0.655749i	−0.986438	+	0.164133i	$0.947517\pi$
$194$	6.90115	−	2.51181i	0.495473	−	0.180338i
$195$		0			0
$196$	1.43897	+	8.16081i	0.102784	+	0.582915i
$197$	4.51987	+	7.82865i	0.322028	+	0.557768i	0.980906	−	0.194481i	$-0.0623023\pi$
$197$	4.51987	+	7.82865i	0.322028	+	0.557768i	−0.658879	+	0.752249i	$0.728969\pi$
$198$	0.481737	−	6.37316i	0.0342356	−	0.452921i
$199$	3.66921	−	6.35527i	0.260104	−	0.450513i	−0.706166	−	0.708047i	$-0.749577\pi$
$199$	3.66921	−	6.35527i	0.260104	−	0.450513i	0.966269	+	0.257534i	$0.0829099\pi$
$200$		0			0
$201$	−11.9556	−	1.50214i	−0.843281	−	0.105953i
$202$	2.99300	+	2.51143i	0.210587	+	0.176703i
$203$	0.165278	+	0.138684i	0.0116002	+	0.00973374i
$204$	−12.1225	−	1.52311i	−0.848742	−	0.106639i
$205$		0			0
$206$	−4.89768	+	8.48303i	−0.341238	+	0.591041i
$207$	−16.0330	−	10.9463i	−1.11437	−	0.760820i
$208$	0.0959005	+	0.166105i	0.00664950	+	0.0115173i
$209$	−1.63919	−	9.29633i	−0.113385	−	0.643041i
$210$		0			0
$211$	15.6493	−	5.69586i	1.07734	−	0.392119i	0.258423	−	0.966032i	$-0.416797\pi$
$211$	15.6493	−	5.69586i	1.07734	−	0.392119i	0.818917	+	0.573913i	$0.194575\pi$
$212$	1.89671	−	10.7568i	0.130267	−	0.738780i
$213$	0.274364	+	5.53325i	0.0187991	+	0.379132i
$214$	−7.74568	+	6.49940i	−0.529484	+	0.444290i
$215$		0			0
$216$	11.5261	−	9.17350i	0.784250	−	0.624178i
$217$	−4.32917			−0.293883
$218$	−11.3081	+	9.48864i	−0.765882	+	0.642652i
$219$	18.4698	+	9.47646i	1.24808	+	0.640360i
$220$		0			0
$221$	−34.2032	+	12.4490i	−2.30076	+	0.837407i
$222$	2.46457	+	2.65790i	0.165411	+	0.178386i
$223$	−1.47210	−	8.34872i	−0.0985794	−	0.559072i	−0.993592	−	0.113030i	$-0.963944\pi$
$223$	−1.47210	−	8.34872i	−0.0985794	−	0.559072i	0.895012	−	0.446042i	$-0.147167\pi$
$224$	1.43600	+	2.48723i	0.0959470	+	0.166185i
$225$		0			0
$226$	−4.69890	+	8.13874i	−0.312566	+	0.541381i
$227$	9.11223	+	3.31658i	0.604800	+	0.220129i	0.626227	−	0.779641i	$-0.284599\pi$
$227$	9.11223	+	3.31658i	0.604800	+	0.220129i	−0.0214263	+	0.999770i	$0.506821\pi$
$228$	5.00301	−	6.60047i	0.331333	−	0.437127i
$229$	0.120012	+	0.100702i	0.00793060	+	0.00665457i	0.646744	−	0.762707i	$-0.276130\pi$
$229$	0.120012	+	0.100702i	0.00793060	+	0.00665457i	−0.638814	+	0.769361i	$0.720575\pi$
$230$		0			0
$231$	−0.830262	−	1.97139i	−0.0546272	−	0.129708i
$232$	−1.12942	−	0.411076i	−0.0741501	−	0.0269884i
$233$	−8.14148	+	14.1015i	−0.533366	+	0.923818i	0.465874	+	0.884851i	$0.345740\pi$
$233$	−8.14148	+	14.1015i	−0.533366	+	0.923818i	−0.999241	+	0.0389667i	$0.987593\pi$
$234$	6.88077	−	15.2231i	0.449810	−	0.995168i
$235$		0			0
$236$	−1.49474	−	8.47711i	−0.0972995	−	0.551813i
$237$	1.37734	−	4.46010i	0.0894676	−	0.289715i
$238$	2.40905	−	0.876823i	0.156156	−	0.0568360i
$239$	−3.50159	+	19.8585i	−0.226499	+	1.28454i	0.633299	+	0.773907i	$0.281700\pi$
$239$	−3.50159	+	19.8585i	−0.226499	+	1.28454i	−0.859798	+	0.510634i	$0.829411\pi$
$240$		0			0
$241$	20.2060	−	16.9549i	1.30158	−	1.09216i	0.311716	−	0.950175i	$-0.399096\pi$
$241$	20.2060	−	16.9549i	1.30158	−	1.09216i	0.989869	−	0.141984i	$-0.0453481\pi$
$242$	−4.48678			−0.288421
$243$	−14.9990	−	4.24618i	−0.962186	−	0.272393i
$244$	−3.95204			−0.253003
$245$		0			0
$246$	1.56441	−	1.00969i	0.0997434	−	0.0643755i
$247$	4.28460	−	24.2991i	0.272622	−	1.54612i
$248$	22.6621	−	8.24833i	1.43905	−	0.523770i
$249$	−4.00661	+	12.9742i	−0.253908	+	0.822209i
$250$		0			0
$251$	−10.6490	−	18.4446i	−0.672160	−	1.16422i	−0.977290	−	0.211905i	$-0.932033\pi$
$251$	−10.6490	−	18.4446i	−0.672160	−	1.16422i	0.305130	−	0.952311i	$-0.401300\pi$
$252$	0.773011	−	1.71022i	0.0486951	−	0.107734i
$253$	7.85194	−	13.6000i	0.493647	−	0.855022i
$254$	6.42871	+	2.33986i	0.403373	+	0.146816i
$255$		0			0
$256$	−12.3130	−	10.3318i	−0.769560	−	0.645737i
$257$	8.82228	+	7.40277i	0.550319	+	0.461772i	0.875049	−	0.484034i	$-0.160829\pi$
$257$	8.82228	+	7.40277i	0.550319	+	0.461772i	−0.324730	+	0.945807i	$0.605274\pi$
$258$	2.29649	−	3.02976i	0.142973	−	0.188624i
$259$	1.13998	+	0.414918i	0.0708348	+	0.0257818i
$260$		0			0
$261$	0.343681	+	1.22455i	0.0212733	+	0.0757975i
$262$	−3.84846	−	6.66573i	−0.237759	−	0.411810i
$263$	1.87867	+	10.6545i	0.115844	+	0.656983i	0.986329	+	0.164789i	$0.0526942\pi$
$263$	1.87867	+	10.6545i	0.115844	+	0.656983i	−0.870485	+	0.492195i	$0.836195\pi$
$264$	8.10228	+	8.73784i	0.498661	+	0.537777i
$265$		0			0
$266$	−0.301779	+	1.71147i	−0.0185033	+	0.104937i
$267$	−28.5012	−	14.6233i	−1.74424	−	0.894932i
$268$	6.55121	−	5.49712i	0.400179	−	0.335790i
$269$	−27.5918			−1.68230			−0.841152	−	0.540798i	$-0.818122\pi$
$269$	−27.5918			−1.68230			−0.841152	+	0.540798i	$0.818122\pi$
$270$		0			0
$271$	22.2930			1.35421			0.677103	−	0.735889i	$-0.263235\pi$
$271$	22.2930			1.35421			0.677103	+	0.735889i	$0.263235\pi$
$272$	−0.132915	+	0.111529i	−0.00805914	+	0.00676242i
$273$	−0.276899	−	5.58439i	−0.0167587	−	0.337983i
$274$	2.43592	−	13.8148i	0.147159	−	0.834582i
$275$		0			0
$276$	13.4339	−	3.06164i	0.808625	−	0.184289i
$277$	3.55616	+	20.1680i	0.213669	+	1.21178i	0.883201	+	0.468994i	$0.155383\pi$
$277$	3.55616	+	20.1680i	0.213669	+	1.21178i	−0.669532	+	0.742783i	$0.733505\pi$
$278$	1.47226	+	2.55004i	0.0883006	+	0.152941i
$279$	−21.0765	−	14.3896i	−1.26182	−	0.861486i
$280$		0			0
$281$	14.8184	+	5.39346i	0.883993	+	0.321747i	0.743820	−	0.668380i	$-0.233012\pi$
$281$	14.8184	+	5.39346i	0.883993	+	0.321747i	0.140173	+	0.990127i	$0.455234\pi$
$282$	1.25067	+	0.157139i	0.0744763	+	0.00935749i
$283$	−8.09200	−	6.78999i	−0.481019	−	0.403623i	0.369776	−	0.929121i	$-0.379435\pi$
$283$	−8.09200	−	6.78999i	−0.481019	−	0.403623i	−0.850795	+	0.525498i	$0.823879\pi$
$284$	−3.01206	−	2.52742i	−0.178733	−	0.149975i
$285$		0			0
$286$	12.6988	+	4.62199i	0.750896	+	0.273304i
$287$	0.311585	−	0.539681i	0.0183923	−	0.0318564i
$288$	−1.27610	+	16.8821i	−0.0751946	+	0.994790i
$289$	−7.96339	−	13.7930i	−0.468435	−	0.811353i
$290$		0			0
$291$	14.1272	−	3.21965i	0.828152	−	0.188739i
$292$	−13.8449	+	5.03913i	−0.810211	+	0.294893i
$293$	2.86499	−	16.2482i	0.167375	−	0.949229i	−0.779207	−	0.626766i	$-0.784378\pi$
$293$	2.86499	−	16.2482i	0.167375	−	0.949229i	0.946582	−	0.322463i	$-0.104511\pi$
$294$	−0.507624	−	10.2375i	−0.0296052	−	0.597066i
$295$		0			0
$296$	−6.75804			−0.392803
$297$	2.51055	−	12.3574i	0.145677	−	0.717048i
$298$	−1.87998			−0.108904
$299$	31.4442	−	26.3848i	1.81846	−	1.52587i
$300$		0			0
$301$	0.220949	−	1.25306i	0.0127353	−	0.0722253i
$302$	−13.0013	+	4.73209i	−0.748142	+	0.272301i
$303$	5.24129	+	5.65242i	0.301104	+	0.324723i
$304$	−0.0204243	−	0.115832i	−0.00117142	−	0.00664343i
$305$		0			0
$306$	14.6429	+	3.73860i	0.837078	+	0.213721i
$307$	7.16633	−	12.4125i	0.409004	−	0.708416i	−0.585774	−	0.810474i	$-0.699209\pi$
$307$	7.16633	−	12.4125i	0.409004	−	0.708416i	0.994778	+	0.102058i	$0.0325428\pi$
$308$	1.42663	+	0.519251i	0.0812898	+	0.0295871i
$309$	−11.6740	+	15.4015i	−0.664109	+	0.876158i
$310$		0			0
$311$	24.3502	+	20.4322i	1.38077	+	1.15861i	0.968926	+	0.247352i	$0.0795605\pi$
$311$	24.3502	+	20.4322i	1.38077	+	1.15861i	0.411846	+	0.911253i	$0.364884\pi$
$312$	12.0894	+	28.7053i	0.684427	+	1.62512i
$313$	−16.0443	−	5.83964i	−0.906876	−	0.330076i	−0.153871	−	0.988091i	$-0.549174\pi$
$313$	−16.0443	−	5.83964i	−0.906876	−	0.330076i	−0.753005	+	0.658015i	$0.771396\pi$
$314$	9.61761	−	16.6582i	0.542753	−	0.940076i
$315$		0			0
$316$	1.65650	+	2.86914i	0.0931852	+	0.161401i
$317$	2.37080	+	13.4455i	0.133157	+	0.755173i	0.976125	+	0.217209i	$0.0696952\pi$
$317$	2.37080	+	13.4455i	0.133157	+	0.755173i	−0.842968	+	0.537964i	$0.819194\pi$
$318$	−3.98653	+	12.9092i	−0.223553	+	0.723913i
$319$	−0.966788	+	0.351882i	−0.0541297	+	0.0197016i
$320$		0			0
$321$	−16.7612	+	10.8179i	−0.935520	+	0.603795i
$322$	−2.21472	+	1.85837i	−0.123422	+	0.103563i
$323$	22.3207			1.24196
$324$	9.44796	−	5.75680i	0.524887	−	0.319822i
$325$		0			0
$326$	13.4305	−	11.2695i	0.743846	−	0.624161i
$327$	−24.4701	+	15.7933i	−1.35320	+	0.873372i
$328$	−0.602818	+	3.41875i	−0.0332851	+	0.188769i
$329$	0.396431	−	0.144289i	0.0218559	−	0.00795491i
$330$		0			0
$331$	4.91646	+	27.8827i	0.270233	+	1.53257i	0.753707	+	0.657211i	$0.228264\pi$
$331$	4.91646	+	27.8827i	0.270233	+	1.53257i	−0.483474	+	0.875359i	$0.660625\pi$
$332$	−4.81867	−	8.34619i	−0.264459	−	0.458057i
$333$	4.17083	+	5.80917i	0.228560	+	0.318341i
$334$	−7.60625	+	13.1744i	−0.416196	+	0.720872i
$335$		0			0
$336$	−0.0103451	−	0.0245635i	−0.000564369	−	0.00134005i
$337$	13.2795	+	11.1428i	0.723379	+	0.606987i	0.928318	−	0.371787i	$-0.121255\pi$
$337$	13.2795	+	11.1428i	0.723379	+	0.606987i	−0.204938	+	0.978775i	$0.565699\pi$
$338$	18.3163	+	15.3692i	0.996276	+	0.835975i
$339$	−11.2002	+	14.7764i	−0.608310	+	0.802542i
$340$		0			0
$341$	10.3219	−	17.8781i	0.558963	−	0.968152i
$342$	−7.15794	+	7.32921i	−0.387057	+	0.396318i
$343$	−3.49648	−	6.05608i	−0.188792	−	0.326997i
$344$	1.23084	+	6.98043i	0.0663623	+	0.376359i
$345$		0			0
$346$	−11.8168	+	4.30098i	−0.635278	+	0.231222i
$347$	0.584994	−	3.31767i	0.0314041	−	0.178102i	−0.965071	−	0.261988i	$-0.915622\pi$
$347$	0.584994	−	3.31767i	0.0314041	−	0.178102i	0.996475	+	0.0838860i	$0.0267331\pi$
$348$	−0.803140	−	0.412073i	−0.0430528	−	0.0220894i
$349$	5.25034	−	4.40556i	0.281045	−	0.235824i	−0.491358	−	0.870958i	$-0.663499\pi$
$349$	5.25034	−	4.40556i	0.281045	−	0.235824i	0.772402	+	0.635133i	$0.219055\pi$
$350$		0			0
$351$	17.2138	−	28.1079i	0.918802	−	1.50029i
$352$	−13.6953			−0.729960
$353$	23.3547	−	19.5969i	1.24304	−	1.04304i	0.245763	−	0.969330i	$-0.420961\pi$
$353$	23.3547	−	19.5969i	1.24304	−	1.04304i	0.997280	−	0.0737074i	$-0.0234831\pi$
$354$	0.527300	+	10.6344i	0.0280257	+	0.565209i
$355$		0			0
$356$	21.3643	−	7.77597i	1.13231	−	0.412126i
$357$	4.93153	−	1.12392i	0.261004	−	0.0594840i
$358$	−3.71378	−	21.0619i	−0.196279	−	1.11316i
$359$	7.50154	+	12.9931i	0.395916	+	0.685747i	0.993218	−	0.116270i	$-0.0370937\pi$
$359$	7.50154	+	12.9931i	0.395916	+	0.685747i	−0.597301	+	0.802017i	$0.703760\pi$
$360$		0			0
$361$	1.93452	−	3.35069i	0.101817	−	0.176352i
$362$	3.36507	+	1.22479i	0.176864	+	0.0643733i
$363$	−8.78316	−	1.10355i	−0.460996	−	0.0579214i
$364$	3.03990	+	2.55078i	0.159334	+	0.133697i
$365$		0			0
$366$	4.85029	+	0.609409i	0.253529	+	0.0318543i
$367$	15.5982	+	5.67728i	0.814219	+	0.296351i	0.715365	−	0.698751i	$-0.246260\pi$
$367$	15.5982	+	5.67728i	0.814219	+	0.296351i	0.0988534	+	0.995102i	$0.468483\pi$
$368$	0.0978351	−	0.169455i	0.00510000	−	0.00883347i
$369$	3.31078	−	1.59176i	0.172352	−	0.0828635i
$370$		0			0
$371$	0.785213	+	4.45316i	0.0407662	+	0.231197i
$372$	17.6598	−	4.02473i	0.915616	−	0.208673i
$373$	−6.57037	+	2.39142i	−0.340201	+	0.123823i	−0.506470	−	0.862257i	$-0.669050\pi$
$373$	−6.57037	+	2.39142i	−0.340201	+	0.123823i	0.166269	+	0.986080i	$0.446828\pi$
$374$	−2.12283	+	12.0392i	−0.109769	+	0.622531i
$375$		0			0
$376$	−1.80030	+	1.51063i	−0.0928434	+	0.0779048i
$377$	−2.68921			−0.138501
$378$	−1.21243	+	1.97974i	−0.0623604	+	0.101827i
$379$	−13.7794			−0.707801			−0.353901	−	0.935283i	$-0.615145\pi$
$379$	−13.7794			−0.707801			−0.353901	+	0.935283i	$0.615145\pi$
$380$		0			0
$381$	12.0091	+	6.16160i	0.615245	+	0.315668i
$382$	1.13491	−	6.43640i	0.0580671	−	0.329315i
$383$	−9.64267	+	3.50965i	−0.492718	+	0.179335i	−0.576416	−	0.817157i	$-0.695549\pi$
$383$	−9.64267	+	3.50965i	−0.492718	+	0.179335i	0.0836981	+	0.996491i	$0.473327\pi$
$384$	−8.10761	−	8.74358i	−0.413740	−	0.446194i
$385$		0			0
$386$	4.06049	+	7.03297i	0.206673	+	0.357969i
$387$	5.24071	−	5.36610i	0.266400	−	0.272774i
$388$	−5.14184	+	8.90592i	−0.261037	+	0.452130i
$389$	36.0005	+	13.1031i	1.82530	+	0.664354i	0.994112	+	0.108358i	$0.0345594\pi$
$389$	36.0005	+	13.1031i	1.82530	+	0.664354i	0.831185	+	0.555996i	$0.187663\pi$
$390$		0			0
$391$	28.4452	+	23.8683i	1.43853	+	1.20707i
$392$	14.6396	+	12.2841i	0.739414	+	0.620442i
$393$	−5.89413	−	13.9951i	−0.297320	−	0.705961i
$394$	7.45737	+	2.71426i	0.375697	+	0.136742i
$395$		0			0
$396$	5.21960	+	7.26991i	0.262295	+	0.365327i
$397$	−15.9911	−	27.6975i	−0.802573	−	1.39010i	−0.917917	−	0.396771i	$-0.870131\pi$
$397$	−15.9911	−	27.6975i	−0.802573	−	1.39010i	0.115345	−	0.993326i	$-0.463203\pi$
$398$	−1.11871	−	6.34451i	−0.0560758	−	0.318022i
$399$	−1.01170	+	3.27609i	−0.0506483	+	0.164010i
$400$		0			0
$401$	−0.893312	+	5.06623i	−0.0446099	+	0.252995i	−0.998955	−	0.0457121i	$-0.985444\pi$
$401$	−0.893312	+	5.06623i	−0.0446099	+	0.252995i	0.954345	+	0.298707i	$0.0965554\pi$
$402$	−8.88788	+	5.73634i	−0.443287	+	0.286103i
$403$	41.3355	−	34.6846i	2.05907	−	1.72776i
$404$	−5.47099			−0.272192
$405$		0			0
$406$	0.189410			0.00940028
$407$	−4.43149	+	3.71846i	−0.219661	+	0.184317i
$408$	−23.6739	+	15.2794i	−1.17203	+	0.756444i
$409$	4.07496	−	23.1102i	0.201494	−	1.14273i	−0.701369	−	0.712799i	$-0.747427\pi$
$409$	4.07496	−	23.1102i	0.201494	−	1.14273i	0.902863	−	0.429929i	$-0.141462\pi$
$410$		0			0
$411$	8.16630	−	26.4442i	0.402814	−	1.30440i
$412$	−2.38179	−	13.5078i	−0.117342	−	0.665482i
$413$	1.78177	+	3.08612i	0.0876752	+	0.151858i
$414$	−16.9594	+	1.68599i	−0.833507	+	0.0828618i
$415$		0			0
$416$	−33.6384	−	12.2434i	−1.64926	−	0.600281i
$417$	2.25485	+	5.35397i	0.110421	+	0.262185i
$418$	−6.34831	−	5.32686i	−0.310506	−	0.260545i
$419$	−7.14090	−	5.99192i	−0.348856	−	0.292725i	0.451475	−	0.892284i	$-0.350898\pi$
$419$	−7.14090	−	5.99192i	−0.348856	−	0.292725i	−0.800330	+	0.599559i	$0.795343\pi$
$420$		0			0
$421$	−22.7017	−	8.26276i	−1.10641	−	0.402702i	−0.276738	−	0.960945i	$-0.589253\pi$
$421$	−22.7017	−	8.26276i	−1.10641	−	0.402702i	−0.829677	+	0.558243i	$0.811476\pi$
$422$	7.31007	−	12.6614i	0.355849	−	0.616348i
$423$	2.40961	+	0.615219i	0.117159	+	0.0299130i
$424$	−12.5950	−	21.8151i	−0.611665	−	1.05943i
$425$		0			0
$426$	3.30693	+	3.56633i	0.160221	+	0.172789i
$427$	1.53742	−	0.559575i	0.0744009	−	0.0270797i
$428$	2.45860	−	13.9434i	0.118841	−	0.673982i
$429$	23.7219	+	12.1712i	1.14530	+	0.587630i
$430$		0			0
$431$	−10.5453			−0.507950			−0.253975	−	0.967211i	$-0.581738\pi$
$431$	−10.5453			−0.507950			−0.253975	+	0.967211i	$0.581738\pi$
$432$	0.0312814	−	0.153973i	0.00150503	−	0.00740802i
$433$	−4.12615			−0.198290			−0.0991451	−	0.995073i	$-0.531611\pi$
$433$	−4.12615			−0.198290			−0.0991451	+	0.995073i	$0.531611\pi$
$434$	−2.91141	+	2.44296i	−0.139752	+	0.117266i
$435$		0			0
$436$	3.58938	−	20.3564i	0.171900	−	0.974894i
$437$	−23.6537	+	8.60924i	−1.13151	+	0.411836i
$438$	17.7687	−	4.04956i	0.849021	−	0.193495i
$439$	−2.08794	−	11.8413i	−0.0996517	−	0.565153i	−0.993222	−	0.116230i	$-0.962919\pi$
$439$	−2.08794	−	11.8413i	−0.0996517	−	0.565153i	0.893571	−	0.448923i	$-0.148192\pi$
$440$		0			0
$441$	1.52428	−	20.1655i	0.0725847	−	0.960262i
$442$	−15.9770	+	27.6729i	−0.759948	+	1.31627i
$443$	31.8626	+	11.5970i	1.51384	+	0.550992i	0.959600	−	0.281367i	$-0.0907877\pi$
$443$	31.8626	+	11.5970i	1.51384	+	0.550992i	0.554237	+	0.832359i	$0.313010\pi$
$444$	−5.03599	−	0.632742i	−0.238998	−	0.0300286i
$445$		0			0
$446$	−5.70120	−	4.78387i	−0.269960	−	0.226523i
$447$	−3.68018	−	0.462392i	−0.174066	−	0.0218704i
$448$	2.39819	+	0.872871i	0.113304	+	0.0412393i
$449$	0.297582	−	0.515427i	0.0140438	−	0.0243245i	−0.858918	−	0.512113i	$-0.828863\pi$
$449$	0.297582	−	0.515427i	0.0140438	−	0.0243245i	0.872962	+	0.487788i	$0.162196\pi$
$450$		0			0
$451$	1.48580	+	2.57349i	0.0699638	+	0.121181i
$452$	−2.28512	−	12.9596i	−0.107483	−	0.609567i
$453$	−26.6148	+	6.06562i	−1.25047	+	0.284988i
$454$	7.99960	−	2.91162i	0.375440	−	0.136649i
$455$		0			0
$456$	−0.945929	−	19.0771i	−0.0442972	−	0.893367i
$457$	6.79746	−	5.70374i	0.317972	−	0.266810i	−0.469806	−	0.882770i	$-0.655676\pi$
$457$	6.79746	−	5.70374i	0.317972	−	0.266810i	0.787778	+	0.615960i	$0.211232\pi$
$458$	0.137535			0.00642659
$459$	27.7448	+	10.9200i	1.29502	+	0.509704i
$460$		0			0
$461$	−19.2142	+	16.1226i	−0.894895	+	0.750906i	−0.969186	−	0.246331i	$-0.920775\pi$
$461$	−19.2142	+	16.1226i	−0.894895	+	0.750906i	0.0742911	+	0.997237i	$0.476331\pi$
$462$	−1.67082	−	0.857259i	−0.0777335	−	0.0398833i
$463$	−1.99238	+	11.2994i	−0.0925939	+	0.525126i	0.902864	+	0.429926i	$0.141460\pi$
$463$	−1.99238	+	11.2994i	−0.0925939	+	0.525126i	−0.995458	+	0.0952002i	$0.969651\pi$
$464$	−0.0120462	+	0.00438444i	−0.000559229	+	0.000203543i
$465$		0			0
$466$	2.48226	+	14.0776i	0.114989	+	0.652132i
$467$	0.328021	+	0.568149i	0.0151790	+	0.0262908i	0.873515	−	0.486797i	$-0.161835\pi$
$467$	0.328021	+	0.568149i	0.0151790	+	0.0262908i	−0.858336	+	0.513088i	$0.828502\pi$
$468$	6.32122	+	22.5227i	0.292198	+	1.04111i
$469$	−1.77020	+	3.06608i	−0.0817403	+	0.141578i
$470$		0			0
$471$	22.9243	−	30.2439i	1.05629	−	1.39357i
$472$	−15.2071	−	12.7602i	−0.699962	−	0.587338i
$473$	4.64793	+	3.90008i	0.213712	+	0.179326i
$474$	−1.59057	−	3.77669i	−0.0730575	−	0.173469i
$475$		0			0
$476$	−1.79491	+	3.10888i	−0.0822697	+	0.142495i
$477$	−10.9790	+	24.2901i	−0.502693	+	1.11217i
$478$	8.85134	+	15.3310i	0.404851	+	0.701223i
$479$	3.87971	+	22.0029i	0.177269	+	1.00534i	0.935493	+	0.353346i	$0.114956\pi$
$479$	3.87971	+	22.0029i	0.177269	+	1.00534i	−0.758224	+	0.651994i	$0.773933\pi$
$480$		0			0
$481$	−14.2089	+	5.17162i	−0.647871	+	0.235806i
$482$	4.02106	−	22.8046i	0.183154	−	1.03872i
$483$	−4.79254	+	3.09316i	−0.218068	+	0.140744i
$484$	4.81285	−	4.03846i	0.218766	−	0.183566i
$485$		0			0
$486$	−12.4831	+	5.60836i	−0.566244	+	0.254401i
$487$	−28.3011			−1.28245			−0.641224	−	0.767354i	$-0.721573\pi$
$487$	−28.3011			−1.28245			−0.641224	+	0.767354i	$0.721573\pi$
$488$	−6.98184	+	5.85846i	−0.316053	+	0.265200i
$489$	29.0628	−	18.7575i	1.31427	−	0.848243i
$490$		0			0
$491$	−40.2634	+	14.6547i	−1.81706	+	0.661357i	−0.821184	+	0.570664i	$0.806686\pi$
$491$	−40.2634	+	14.6547i	−1.81706	+	0.661357i	−0.995879	+	0.0906928i	$0.971092\pi$
$492$	−0.769302	+	2.49116i	−0.0346828	+	0.112310i
$493$	−0.422438	−	2.39577i	−0.0190257	−	0.107900i
$494$	−10.8306	−	18.7592i	−0.487293	−	0.844015i
$495$		0			0
$496$	0.128611	−	0.222761i	0.00577480	−	0.0100022i
$497$	1.52961	+	0.556732i	0.0686124	+	0.0249729i
$498$	4.62691	+	10.9862i	0.207337	+	0.492304i
$499$	−3.09802	−	2.59955i	−0.138686	−	0.116372i	0.570805	−	0.821085i	$-0.306631\pi$
$499$	−3.09802	−	2.59955i	−0.138686	−	0.116372i	−0.709492	+	0.704714i	$0.751076\pi$
$500$		0			0
$501$	−18.1300	+	23.9189i	−0.809991	+	1.06862i
$502$	−17.5699	−	6.39492i	−0.784183	−	0.285419i
$503$	11.9697	−	20.7321i	0.533702	−	0.924399i	−0.465523	−	0.885036i	$-0.654134\pi$
$503$	11.9697	−	20.7321i	0.533702	−	0.924399i	0.999225	−	0.0393633i	$-0.0125330\pi$
$504$	−1.16958	−	4.16726i	−0.0520974	−	0.185624i
$505$		0			0
$506$	−2.39398	−	13.5769i	−0.106425	−	0.603569i
$507$	32.0752	+	34.5912i	1.42451	+	1.53625i
$508$	−9.00195	+	3.27644i	−0.399397	+	0.145369i
$509$	−4.85069	+	27.5096i	−0.215003	+	1.21934i	0.665898	+	0.746043i	$0.268049\pi$
$509$	−4.85069	+	27.5096i	−0.215003	+	1.21934i	−0.880901	+	0.473300i	$0.843063\pi$
$510$		0			0
$511$	4.67243	−	3.92064i	0.206696	−	0.173439i
$512$	−0.342088			−0.0151183
$513$	−15.8148	+	12.5868i	−0.698239	+	0.555723i
$514$	10.1105			0.445953
$515$		0			0
$516$	0.263639	+	5.31695i	0.0116060	+	0.234066i
$517$	−0.349331	+	1.98115i	−0.0153635	+	0.0871310i
$518$	1.00078	−	0.364256i	0.0439719	−	0.0160045i
$519$	−24.1901	+	5.51302i	−1.06183	+	0.241995i
$520$		0			0
$521$	−6.07222	−	10.5174i	−0.266029	−	0.460775i	0.701804	−	0.712370i	$-0.252378\pi$
$521$	−6.07222	−	10.5174i	−0.266029	−	0.460775i	−0.967833	+	0.251595i	$0.919045\pi$
$522$	0.922142	+	0.629577i	0.0403610	+	0.0275559i
$523$	11.2405	−	19.4691i	0.491512	−	0.851324i	−0.508440	−	0.861097i	$-0.669778\pi$
$523$	11.2405	−	19.4691i	0.491512	−	0.851324i	0.999952	+	0.00977335i	$0.00311100\pi$
$524$	10.1278	+	3.68622i	0.442436	+	0.161033i
$525$		0			0
$526$	7.27576	+	6.10509i	0.317238	+	0.266195i
$527$	37.3931	+	31.3765i	1.62887	+	1.36678i
$528$	0.126105	+	0.0158443i	0.00548800	+	0.000689534i
$529$	−17.7371	−	6.45579i	−0.771180	−	0.280687i
$530$		0			0
$531$	−1.58336	+	20.9471i	−0.0687119	+	0.909027i
$532$	−1.21675	−	2.10748i	−0.0527529	−	0.0913706i
$533$	1.34878	+	7.64931i	0.0584221	+	0.331328i
$534$	−27.4192	+	6.24895i	−1.18655	+	0.270419i
$535$		0			0
$536$	3.42478	−	19.4229i	0.147928	−	0.838941i
$537$	−2.08966	−	42.1434i	−0.0901756	−	1.81862i
$538$	−18.5557	+	15.5701i	−0.799995	+	0.671276i
$539$	16.3588			0.704624
$540$		0			0
$541$	−22.1510			−0.952347			−0.476173	−	0.879351i	$-0.657977\pi$
$541$	−22.1510			−0.952347			−0.476173	+	0.879351i	$0.657977\pi$
$542$	14.9922	−	12.5800i	0.643972	−	0.540357i
$543$	6.28609	+	3.22525i	0.269762	+	0.138409i
$544$	5.62326	−	31.8911i	0.241095	−	1.36732i
$545$		0			0
$546$	−3.33750	−	3.59929i	−0.142832	−	0.154036i
$547$	−1.66357	−	9.43459i	−0.0711292	−	0.403394i	−0.999496	−	0.0317297i	$-0.989898\pi$
$547$	−1.66357	−	9.43459i	−0.0711292	−	0.403394i	0.928367	−	0.371664i	$-0.121213\pi$
$548$	9.82146	+	17.0113i	0.419552	+	0.726685i
$549$	9.34486	+	2.38591i	0.398829	+	0.101828i
$550$		0			0
$551$	1.54966	+	0.564031i	0.0660179	+	0.0240285i
$552$	19.1943	−	25.3231i	0.816966	−	1.07782i
$553$	−1.05065	−	0.881604i	−0.0446784	−	0.0374896i
$554$	13.7724	+	11.5564i	0.585132	+	0.490984i
$555$		0			0
$556$	−3.87449	−	1.41020i	−0.164315	−	0.0598058i
$557$	0.0452561	−	0.0783859i	0.00191756	−	0.00332132i	−0.865065	−	0.501660i	$-0.832723\pi$
$557$	0.0452561	−	0.0783859i	0.00191756	−	0.00332132i	0.866983	+	0.498338i	$0.166056\pi$
$558$	−22.2942	+	2.21635i	−0.943790	+	0.0938255i
$559$	7.92967	+	13.7346i	0.335389	+	0.580911i
$560$		0			0
$561$	−7.11668	+	23.0453i	−0.300467	+	0.972975i
$562$	13.0090	−	4.73491i	0.548753	−	0.199730i
$563$	2.55509	−	14.4906i	0.107684	−	0.610707i	−0.882430	−	0.470443i	$-0.844094\pi$
$563$	2.55509	−	14.4906i	0.107684	−	0.610707i	0.990114	−	0.140263i	$-0.0447949\pi$
$564$	−1.48299	+	0.957142i	−0.0624453	+	0.0403029i
$565$		0			0
$566$	−9.27354			−0.389796
$567$	−2.86033	+	3.57726i	−0.120122	+	0.150231i
$568$	−9.06785			−0.380479
$569$	−5.30885	+	4.45466i	−0.222559	+	0.186749i	−0.747249	−	0.664544i	$-0.768626\pi$
$569$	−5.30885	+	4.45466i	−0.222559	+	0.186749i	0.524690	+	0.851293i	$0.324181\pi$
$570$		0			0
$571$	−5.14921	+	29.2026i	−0.215488	+	1.22209i	0.664570	+	0.747226i	$0.268615\pi$
$571$	−5.14921	+	29.2026i	−0.215488	+	1.22209i	−0.880058	+	0.474866i	$0.842497\pi$
$572$	−17.7818	+	6.47205i	−0.743495	+	0.270610i
$573$	3.80473	−	12.3205i	0.158945	−	0.514697i
$574$	−0.0949993	−	0.538768i	−0.00396519	−	0.0224877i
$575$		0			0
$576$	8.77425	+	12.2209i	0.365594	+	0.509202i
$577$	2.30175	−	3.98675i	0.0958231	−	0.165970i	−0.814129	−	0.580684i	$-0.802785\pi$
$577$	2.30175	−	3.98675i	0.0958231	−	0.165970i	0.909952	+	0.414714i	$0.136118\pi$
$578$	−13.1389	−	4.78215i	−0.546505	−	0.198911i
$579$	6.21886	+	14.7662i	0.258447	+	0.613662i
$580$		0			0
$581$	3.05631	+	2.56455i	0.126797	+	0.106395i
$582$	7.68382	−	10.1373i	0.318505	−	0.420203i
$583$	−20.2623	−	7.37486i	−0.839177	−	0.305435i
$584$	−16.9890	+	29.4259i	−0.703011	+	1.21765i
$585$		0			0
$586$	−7.24214	−	12.5438i	−0.299170	−	0.518178i
$587$	1.69338	+	9.60364i	0.0698933	+	0.396384i	0.999605	+	0.0280969i	$0.00894470\pi$
$587$	1.69338	+	9.60364i	0.0698933	+	0.396384i	−0.929712	+	0.368288i	$0.879944\pi$
$588$	9.75911	+	10.5246i	0.402459	+	0.434028i
$589$	−31.0944	+	11.3174i	−1.28122	+	0.466327i
$590$		0			0
$591$	13.9307	+	7.14752i	0.573032	+	0.294010i
$592$	−0.0552163	+	0.0463320i	−0.00226938	+	0.00190423i
$593$	1.52185			0.0624948			0.0312474	−	0.999512i	$-0.490052\pi$
$593$	1.52185			0.0624948			0.0312474	+	0.999512i	$0.490052\pi$
$594$	−5.28492	−	9.72714i	−0.216843	−	0.399110i
$595$		0			0
$596$	2.01660	−	1.69213i	0.0826032	−	0.0693123i
$597$	−0.629473	−	12.6949i	−0.0257626	−	0.519569i
$598$	6.25749	−	35.4880i	0.255888	−	1.45121i
$599$	24.2758	−	8.83566i	0.991881	−	0.361015i	0.205433	−	0.978671i	$-0.434140\pi$
$599$	24.2758	−	8.83566i	0.991881	−	0.361015i	0.786448	+	0.617656i	$0.211918\pi$
$600$		0			0
$601$	−2.97450	−	16.8692i	−0.121332	−	0.688109i	−0.983419	−	0.181348i	$-0.941954\pi$
$601$	−2.97450	−	16.8692i	−0.121332	−	0.688109i	0.862087	−	0.506761i	$-0.169157\pi$
$602$	−0.558515	−	0.967376i	−0.0227634	−	0.0394273i
$603$	−18.8095	+	9.04322i	−0.765981	+	0.368268i
$604$	9.68689	−	16.7782i	0.394154	−	0.682695i
$605$		0			0
$606$	6.71448	+	0.843633i	0.272757	+	0.0342703i
$607$	9.63781	+	8.08708i	0.391187	+	0.328244i	0.817075	−	0.576531i	$-0.195594\pi$
$607$	9.63781	+	8.08708i	0.391187	+	0.328244i	−0.425889	+	0.904776i	$0.640038\pi$
$608$	16.8163	+	14.1106i	0.681991	+	0.572259i
$609$	0.370783	+	0.0465866i	0.0150249	+	0.00188779i
$610$		0			0
$611$	−2.62915	+	4.55382i	−0.106364	+	0.184228i
$612$	−19.0720	+	9.16946i	−0.770942	+	0.370653i
$613$	−11.7819	−	20.4069i	−0.475867	−	0.824226i	0.523750	−	0.851872i	$-0.324532\pi$
$613$	−11.7819	−	20.4069i	−0.475867	−	0.824226i	−0.999618	+	0.0276453i	$0.991199\pi$
$614$	−2.18495	−	12.3914i	−0.0881773	−	0.500078i
$615$		0			0
$616$	3.29008	−	1.19749i	0.132561	−	0.0482483i
$617$	2.01505	−	11.4279i	0.0811229	−	0.460071i	−0.917003	−	0.398880i	$-0.869399\pi$
$617$	2.01505	−	11.4279i	0.0811229	−	0.460071i	0.998126	−	0.0611910i	$-0.0194899\pi$
$618$	0.840222	+	16.9452i	0.0337987	+	0.681638i
$619$	−15.1620	+	12.7224i	−0.609411	+	0.511357i	−0.894455	−	0.447158i	$-0.852436\pi$
$619$	−15.1620	+	12.7224i	−0.609411	+	0.511357i	0.285044	+	0.958514i	$0.407992\pi$
$620$		0			0
$621$	−33.6137	−	0.870823i	−1.34887	−	0.0349449i
$622$	27.9056			1.11891
$623$	−7.21012	+	6.05001i	−0.288867	+	0.242388i
$624$	0.295575	+	0.151653i	0.0118325	+	0.00607097i
$625$		0			0
$626$	−14.0852	+	5.12660i	−0.562959	+	0.204900i
$627$	−11.1170	−	11.9891i	−0.443972	−	0.478797i
$628$	4.67714	+	26.5254i	0.186638	+	1.05848i
$629$	−6.83933	−	11.8461i	−0.272702	−	0.472334i
$630$		0			0
$631$	−7.28122	+	12.6114i	−0.289861	+	0.502054i	−0.973776	−	0.227508i	$-0.926942\pi$
$631$	−7.28122	+	12.6114i	−0.289861	+	0.502054i	0.683916	+	0.729561i	$0.260276\pi$
$632$	7.17962	+	2.61317i	0.285590	+	0.103946i
$633$	17.4241	−	22.9876i	0.692545	−	0.913673i
$634$	9.18168	+	7.70434i	0.364651	+	0.305979i
$635$		0			0
$636$	−7.34307	−	17.4355i	−0.291172	−	0.691364i
$637$	40.1807	+	14.6246i	1.59202	+	0.579446i
$638$	−0.451605	+	0.782203i	−0.0178792	+	0.0309677i
$639$	5.59637	+	7.79468i	0.221389	+	0.308353i
$640$		0			0
$641$	3.38084	+	19.1737i	0.133535	+	0.757315i	0.975869	+	0.218358i	$0.0700702\pi$
$641$	3.38084	+	19.1737i	0.133535	+	0.757315i	−0.842334	+	0.538957i	$0.818819\pi$
$642$	−5.16751	+	16.7335i	−0.203945	+	0.660418i
$643$	2.97050	−	1.08118i	0.117145	−	0.0426374i	−0.282782	−	0.959184i	$-0.591257\pi$
$643$	2.97050	−	1.08118i	0.117145	−	0.0426374i	0.399928	+	0.916547i	$0.369035\pi$
$644$	0.702989	−	3.98685i	0.0277017	−	0.157104i
$645$		0			0
$646$	15.0109	−	12.5956i	0.590594	−	0.495567i
$647$	18.5045			0.727489			0.363744	−	0.931499i	$-0.381498\pi$
$647$	18.5045			0.727489			0.363744	+	0.931499i	$0.381498\pi$
$648$	8.15736	−	24.1758i	0.320451	−	0.949714i
$649$	−16.9929			−0.667029
$650$		0			0
$651$	−6.30012	+	4.06617i	−0.246921	+	0.159366i
$652$	−4.26306	+	24.1770i	−0.166954	+	0.946844i
$653$	−10.6618	+	3.88059i	−0.417230	+	0.151859i	−0.542100	−	0.840314i	$-0.682371\pi$
$653$	−10.6618	+	3.88059i	−0.417230	+	0.151859i	0.124870	+	0.992173i	$0.460149\pi$
$654$	−7.54418	+	24.4297i	−0.295001	+	0.955276i
$655$		0			0
$656$	0.0185131	+	0.0320656i	0.000722815	+	0.00125195i
$657$	35.7794	−	3.55695i	1.39589	−	0.138770i
$658$	0.185180	−	0.320742i	0.00721908	−	0.0125038i
$659$	−24.1280	−	8.78187i	−0.939893	−	0.342093i	−0.173769	−	0.984786i	$-0.555595\pi$
$659$	−24.1280	−	8.78187i	−0.939893	−	0.342093i	−0.766124	+	0.642693i	$0.777817\pi$
$660$		0			0
$661$	−6.15873	−	5.16779i	−0.239547	−	0.201004i	0.515109	−	0.857125i	$-0.327752\pi$
$661$	−6.15873	−	5.16779i	−0.239547	−	0.201004i	−0.754655	+	0.656121i	$0.772196\pi$
$662$	19.0406	+	15.9770i	0.740033	+	0.620962i
$663$	−38.0823	+	50.2419i	−1.47899	+	1.95123i
$664$	−20.8852	−	7.60159i	−0.810502	−	0.294999i
$665$		0			0
$666$	6.08304	+	1.55311i	0.235713	+	0.0601819i
$667$	1.37173	+	2.37590i	0.0531135	+	0.0919954i
$668$	−3.69900	−	20.9781i	−0.143118	−	0.811665i
$669$	−9.98383	−	10.7670i	−0.385997	−	0.416275i
$670$		0			0
$671$	−1.35476	+	7.68321i	−0.0522999	+	0.296607i
$672$	4.42590	+	2.27083i	0.170733	+	0.0875992i
$673$	−10.4677	+	8.78341i	−0.403499	+	0.338576i	−0.821844	−	0.569712i	$-0.807055\pi$
$673$	−10.4677	+	8.78341i	−0.403499	+	0.338576i	0.418346	+	0.908288i	$0.362610\pi$
$674$	15.2185			0.586193
$675$		0			0
$676$	−33.4809			−1.28773
$677$	−33.6430	+	28.2299i	−1.29301	+	1.08496i	−0.301698	+	0.953404i	$0.597553\pi$
$677$	−33.6430	+	28.2299i	−1.29301	+	1.08496i	−0.991308	+	0.131558i	$0.958002\pi$
$678$	0.806121	+	16.2575i	0.0309589	+	0.624366i
$679$	0.739271	−	4.19262i	0.0283706	−	0.160898i
$680$		0			0
$681$	16.3759	−	3.73213i	0.627524	−	0.143015i
$682$	−3.14705	−	17.8478i	−0.120507	−	0.683428i
$683$	−2.15285	−	3.72885i	−0.0823767	−	0.142681i	0.821894	−	0.569641i	$-0.192918\pi$
$683$	−2.15285	−	3.72885i	−0.0823767	−	0.142681i	−0.904270	+	0.426960i	$0.859584\pi$
$684$	1.08126	−	14.3045i	0.0413429	−	0.546948i
$685$		0			0
$686$	−5.76886	−	2.09969i	−0.220256	−	0.0801667i
$687$	0.269234	+	0.0338276i	0.0102719	+	0.00129060i
$688$	0.0579132	+	0.0485949i	0.00220792	+	0.00185266i
$689$	−43.1753	−	36.2284i	−1.64485	−	1.38019i
$690$		0			0
$691$	21.9927	+	8.00468i	0.836641	+	0.304512i	0.724581	−	0.689189i	$-0.242033\pi$
$691$	21.9927	+	8.00468i	0.836641	+	0.304512i	0.112059	+	0.993702i	$0.464255\pi$
$692$	8.80438	−	15.2496i	0.334692	−	0.579704i
$693$	−3.05988	−	2.08909i	−0.116235	−	0.0793578i
$694$	−1.47875	−	2.56127i	−0.0561326	−	0.0972245i
$695$		0			0
$696$	−2.02971	+	0.462580i	−0.0769361	+	0.0175341i
$697$	−6.60275	+	2.40320i	−0.250097	+	0.0910279i
$698$	1.04484	−	5.92555i	0.0395476	−	0.224286i
$699$	1.39671	+	28.1683i	0.0528286	+	1.06542i
$700$		0			0
$701$	15.0287			0.567624			0.283812	−	0.958880i	$-0.408401\pi$
$701$	15.0287			0.567624			0.283812	+	0.958880i	$0.408401\pi$
$702$	−4.28493	−	28.6165i	−0.161724	−	1.08006i
$703$	9.27261			0.349723
$704$	−9.32261	+	7.82260i	−0.351359	+	0.294825i
$705$		0			0
$706$	4.64765	−	26.3581i	0.174917	−	0.992002i
$707$	2.12832	−	0.774645i	0.0800437	−	0.0291335i
$708$	−10.1374	−	10.9326i	−0.380986	−	0.410871i
$709$	4.68507	+	26.5704i	0.175952	+	0.997871i	0.937040	+	0.349223i	$0.113554\pi$
$709$	4.68507	+	26.5704i	0.175952	+	0.997871i	−0.761088	+	0.648648i	$0.775335\pi$
$710$		0			0
$711$	−2.18475	−	7.78432i	−0.0819345	−	0.291935i
$712$	26.2161	−	45.4076i	0.982489	−	1.70172i
$713$	−51.7284	−	18.8276i	−1.93724	−	0.705098i
$714$	2.68227	−	3.53871i	0.100381	−	0.132433i
$715$		0			0
$716$	22.9410	+	19.2498i	0.857347	+	0.719399i
$717$	13.5563	+	32.1884i	0.506270	+	1.20210i
$718$	12.3768	+	4.50480i	0.461900	+	0.168118i
$719$	−21.0623	+	36.4809i	−0.785490	+	1.36051i	0.143216	+	0.989691i	$0.454255\pi$
$719$	−21.0623	+	36.4809i	−0.785490	+	1.36051i	−0.928706	+	0.370817i	$0.879078\pi$
$720$		0			0
$721$	2.83915	+	4.91756i	0.105736	+	0.183139i
$722$	−0.589817	−	3.34502i	−0.0219507	−	0.124489i
$723$	13.4804	−	43.6524i	0.501342	−	1.62345i
$724$	−4.71202	+	1.71503i	−0.175121	+	0.0637388i
$725$		0			0
$726$	−6.52948	+	4.21420i	−0.242332	+	0.156404i
$727$	7.96369	−	6.68233i	0.295357	−	0.247834i	−0.483052	−	0.875592i	$-0.660472\pi$
$727$	7.96369	−	6.68233i	0.295357	−	0.247834i	0.778409	+	0.627758i	$0.216027\pi$
$728$	9.15166			0.339183
$729$	−25.8158	+	7.90844i	−0.956142	+	0.292905i
$730$		0			0
$731$	−10.9902	+	9.22191i	−0.406489	+	0.341085i
$732$	−5.75128	+	3.71194i	−0.212574	+	0.137197i
$733$	−7.78456	+	44.1484i	−0.287529	+	1.63066i	0.408579	+	0.912723i	$0.366024\pi$
$733$	−7.78456	+	44.1484i	−0.287529	+	1.63066i	−0.696108	+	0.717937i	$0.745087\pi$
$734$	13.6936	−	4.98406i	0.505440	−	0.183965i
$735$		0			0
$736$	6.34152	+	35.9646i	0.233752	+	1.32567i
$737$	−8.44127	−	14.6207i	−0.310938	−	0.538561i
$738$	1.32830	−	2.93875i	0.0488952	−	0.108177i
$739$	8.15749	−	14.1292i	0.300078	−	0.519751i	−0.676075	−	0.736833i	$-0.736321\pi$
$739$	8.15749	−	14.1292i	0.300078	−	0.519751i	0.976153	+	0.217082i	$0.0696539\pi$
$740$		0			0
$741$	−16.5877	−	39.3861i	−0.609364	−	1.44689i
$742$	3.04099	+	2.55169i	0.111638	+	0.0936755i
$743$	8.85961	+	7.43409i	0.325028	+	0.272730i	0.790670	−	0.612242i	$-0.209732\pi$
$743$	8.85961	+	7.43409i	0.325028	+	0.272730i	−0.465643	+	0.884973i	$0.654177\pi$
$744$	25.2323	−	33.2889i	0.925060	−	1.22043i
$745$		0			0
$746$	−3.06915	+	5.31592i	−0.112369	+	0.194630i
$747$	6.35534	+	22.6442i	0.232530	+	0.828509i
$748$	−8.55910	−	14.8248i	−0.312952	−	0.542049i
$749$	1.01783	+	5.77239i	0.0371906	+	0.210918i
$750$		0			0
$751$	−17.9955	+	6.54983i	−0.656666	+	0.239007i	−0.648796	−	0.760962i	$-0.724727\pi$
$751$	−17.9955	+	6.54983i	−0.656666	+	0.239007i	−0.00786953	+	0.999969i	$0.502505\pi$
$752$	−0.00435265	+	0.0246851i	−0.000158725	+	0.000900174i
$753$	−32.8213	−	16.8399i	−1.19607	−	0.613679i
$754$	−1.80852	+	1.51753i	−0.0658623	+	0.0552650i
$755$		0			0
$756$	−0.481385	−	3.21489i	−0.0175078	−	0.116924i
$757$	−8.63554			−0.313864			−0.156932	−	0.987609i	$-0.550160\pi$
$757$	−8.63554			−0.313864			−0.156932	+	0.987609i	$0.550160\pi$
$758$	−9.26677	+	7.77575i	−0.336584	+	0.282428i
$759$	−1.34704	−	27.1665i	−0.0488945	−	0.986083i
$760$		0			0
$761$	−1.00649	+	0.366334i	−0.0364854	+	0.0132796i	−0.360198	−	0.932876i	$-0.617291\pi$
$761$	−1.00649	+	0.366334i	−0.0364854	+	0.0132796i	0.323713	+	0.946155i	$0.395069\pi$
$762$	11.5532	−	2.63302i	0.418529	−	0.0953844i
$763$	1.48595	+	8.42726i	0.0537951	+	0.305087i
$764$	4.57588	+	7.92566i	0.165550	+	0.286740i
$765$		0			0
$766$	−4.50428	+	7.80164i	−0.162746	+	0.281885i
$767$	−41.7380	−	15.1914i	−1.50707	−	0.548530i
$768$	−27.6228	−	3.47064i	−0.996752	−	0.125236i
$769$	7.27290	+	6.10268i	0.262267	+	0.220068i	0.764433	−	0.644703i	$-0.223019\pi$
$769$	7.27290	+	6.10268i	0.262267	+	0.220068i	−0.502166	+	0.864771i	$0.667463\pi$
$770$		0			0
$771$	19.7918	+	2.48672i	0.712786	+	0.0895572i
$772$	−10.6858	−	3.88931i	−0.384590	−	0.139979i
$773$	−0.387381	+	0.670964i	−0.0139331	+	0.0241329i	−0.872908	−	0.487885i	$-0.837769\pi$
$773$	−0.387381	+	0.670964i	−0.0139331	+	0.0241329i	0.858975	+	0.512018i	$0.171102\pi$
$774$	0.496320	−	6.56609i	0.0178399	−	0.236013i
$775$		0			0
$776$	4.11826	+	23.3558i	0.147837	+	0.838424i
$777$	2.04869	−	0.466905i	0.0734963	−	0.0167501i
$778$	31.6047	−	11.5032i	1.13308	−	0.412409i
$779$	0.827119	−	4.69082i	0.0296346	−	0.168066i
$780$		0			0
$781$	−5.94612	+	4.98939i	−0.212769	+	0.178534i
$782$	32.5985			1.16572
$783$	1.65030	+	1.45924i	0.0589770	+	0.0521491i
$784$	0.203831			0.00727967
$785$		0			0
$786$	−11.8613	−	6.08578i	−0.423080	−	0.217073i
$787$	−1.25833	+	7.13632i	−0.0448545	+	0.254382i	−0.998987	−	0.0450026i	$-0.985670\pi$
$787$	−1.25833	+	7.13632i	−0.0448545	+	0.254382i	0.954132	+	0.299385i	$0.0967815\pi$
$788$	−10.4424	+	3.80071i	−0.371994	+	0.135395i
$789$	12.7412	+	13.7406i	0.453598	+	0.489179i
$790$		0			0
$791$	2.72392	+	4.71797i	0.0968515	+	0.167752i
$792$	19.9980	+	5.10586i	0.710598	+	0.181429i
$793$	−10.1963	+	17.6604i	−0.362080	+	0.627140i
$794$	−26.3839	−	9.60296i	−0.936330	−	0.340796i
$795$		0			0
$796$	6.91057	+	5.79865i	0.244939	+	0.205528i
$797$	24.3118	+	20.4001i	0.861170	+	0.722607i	0.962220	−	0.272274i	$-0.0877757\pi$
$797$	24.3118	+	20.4001i	0.861170	+	0.722607i	−0.101050	+	0.994881i	$0.532220\pi$
$798$	1.16833	+	2.77410i	0.0413584	+	0.0982022i
$799$	−4.46992	−	1.62692i	−0.158134	−	0.0575562i
$800$		0			0
$801$	−55.2118	+	5.48880i	−1.95081	+	0.193937i
$802$	2.25812	+	3.91118i	0.0797369	+	0.138108i
$803$	5.05061	+	28.6435i	0.178232	+	1.01081i
$804$	4.37062	−	14.1530i	0.154140	−	0.499138i
$805$		0			0
$806$	8.22590	−	46.6514i	0.289745	−	1.64322i
$807$	−40.1536	+	25.9156i	−1.41347	+	0.912272i
$808$	−9.66529	+	8.11014i	−0.340024	+	0.285314i
$809$	48.9871			1.72230			0.861148	−	0.508355i	$-0.169746\pi$
$809$	48.9871			1.72230			0.861148	+	0.508355i	$0.169746\pi$
$810$		0			0
$811$	34.5483			1.21316			0.606578	−	0.795024i	$-0.292542\pi$
$811$	34.5483			1.21316			0.606578	+	0.795024i	$0.292542\pi$
$812$	−0.203175	+	0.170484i	−0.00713006	+	0.00598283i
$813$	32.4424	−	20.9387i	1.13780	−	0.734352i
$814$	−0.881881	+	5.00139i	−0.0309099	+	0.175299i
$815$		0			0
$816$	−0.0886738	+	0.287144i	−0.00310420	+	0.0100521i
$817$	−1.68882	−	9.57775i	−0.0590842	−	0.335083i
$818$	−10.3007	−	17.8413i	−0.360156	−	0.623808i
$819$	−5.64809	−	7.86672i	−0.197360	−	0.274886i
$820$		0			0
$821$	14.2900	+	5.20114i	0.498725	+	0.181521i	0.579120	−	0.815242i	$-0.303396\pi$
$821$	14.2900	+	5.20114i	0.498725	+	0.181521i	−0.0803955	+	0.996763i	$0.525618\pi$
$822$	−9.43060	−	22.3922i	−0.328930	−	0.781018i
$823$	4.87323	+	4.08912i	0.169870	+	0.142538i	0.723759	−	0.690052i	$-0.242413\pi$
$823$	4.87323	+	4.08912i	0.169870	+	0.142538i	−0.553889	+	0.832590i	$0.686857\pi$
$824$	−24.2316	−	20.3327i	−0.844148	−	0.708324i
$825$		0			0
$826$	2.93976	+	1.06998i	0.102287	+	0.0372295i
$827$	−24.0799	+	41.7075i	−0.837339	+	1.45031i	0.0547729	+	0.998499i	$0.482557\pi$
$827$	−24.0799	+	41.7075i	−0.837339	+	1.45031i	−0.892112	+	0.451815i	$0.850777\pi$
$828$	16.6743	−	17.0733i	0.579472	−	0.593337i
$829$	23.1268	+	40.0568i	0.803227	+	1.39123i	0.917482	+	0.397778i	$0.130218\pi$
$829$	23.1268	+	40.0568i	0.803227	+	1.39123i	−0.114255	+	0.993451i	$0.536448\pi$
$830$		0			0
$831$	24.1179	+	26.0098i	0.836641	+	0.902269i
$832$	−29.8916	+	10.8796i	−1.03630	+	0.377184i
$833$	−6.71691	+	38.0935i	−0.232727	+	1.31986i
$834$	4.53766	+	2.32817i	0.157126	+	0.0806180i
$835$		0			0
$836$	11.6042			0.401341
$837$	−44.1875	−	1.14476i	−1.52734	−	0.0395686i
$838$	−8.18356			−0.282696
$839$	18.8397	−	15.8084i	0.650418	−	0.545765i	−0.256780	−	0.966470i	$-0.582662\pi$
$839$	18.8397	−	15.8084i	0.650418	−	0.545765i	0.907198	+	0.420705i	$0.138217\pi$
$840$		0			0
$841$	−5.00459	+	28.3824i	−0.172572	+	0.978704i
$842$	−19.9298	+	7.25385i	−0.686826	+	0.249984i
$843$	26.6306	−	6.06922i	0.917207	−	0.209035i
$844$	3.55496	+	20.1612i	0.122367	+	0.693976i
$845$		0			0
$846$	1.96765	−	0.946009i	0.0676493	−	0.0325245i
$847$	−1.30048	+	2.25250i	−0.0446850	+	0.0773967i
$848$	−0.252467	−	0.0918906i	−0.00866977	−	0.00315554i
$849$	−18.1535	−	2.28088i	−0.623028	−	0.0782796i
$850$		0			0
$851$	11.8169	+	9.91554i	0.405077	+	0.339900i
$852$	−6.75723	−	0.849005i	−0.231499	−	0.0290864i
$853$	14.0044	+	5.09720i	0.479503	+	0.174525i	0.570452	−	0.821331i	$-0.306768\pi$
$853$	14.0044	+	5.09720i	0.479503	+	0.174525i	−0.0909495	+	0.995856i	$0.528990\pi$
$854$	0.718158	−	1.24389i	0.0245749	−	0.0425649i
$855$		0			0
$856$	−16.3261	−	28.2777i	−0.558016	−	0.966512i
$857$	−6.17830	−	35.0389i	−0.211047	−	1.19690i	−0.887636	−	0.460545i	$-0.847654\pi$
$857$	−6.17830	−	35.0389i	−0.211047	−	1.19690i	0.676590	−	0.736360i	$-0.263457\pi$
$858$	22.8214	−	5.20109i	0.779110	−	0.177562i
$859$	20.6271	−	7.50764i	0.703787	−	0.256157i	0.0347598	−	0.999396i	$-0.488933\pi$
$859$	20.6271	−	7.50764i	0.703787	−	0.256157i	0.669027	+	0.743238i	$0.266711\pi$
$860$		0			0
$861$	−0.0534540	−	1.07804i	−0.00182171	−	0.0367394i
$862$	−7.09181	+	5.95074i	−0.241548	+	0.202683i
$863$	−6.43512			−0.219054			−0.109527	−	0.993984i	$-0.534934\pi$
$863$	−6.43512			−0.219054			−0.109527	+	0.993984i	$0.534934\pi$
$864$	13.9995	+	25.7667i	0.476271	+	0.876600i
$865$		0			0
$866$	−2.77487	+	2.32839i	−0.0942940	+	0.0791220i
$867$	−24.5439	−	12.5929i	−0.833556	−	0.427679i
$868$	0.924127	−	5.24099i	0.0313669	−	0.177891i
$869$	6.14578	−	2.23688i	0.208481	−	0.0758809i
$870$		0			0
$871$	−7.66280	−	43.4579i	−0.259644	−	1.47251i
$872$	−23.8350	−	41.2833i	−0.807153	−	1.39803i
$873$	17.5349	−	17.9544i	0.593466	−	0.607666i
$874$	−11.0491	+	19.1376i	−0.373741	+	0.647339i
$875$		0			0
$876$	−15.4151	+	20.3371i	−0.520827	+	0.687126i
$877$	−10.3322	−	8.66977i	−0.348895	−	0.292757i	0.451451	−	0.892296i	$-0.350906\pi$
$877$	−10.3322	−	8.66977i	−0.348895	−	0.292757i	−0.800346	+	0.599538i	$0.795351\pi$
$878$	−8.08620	−	6.78513i	−0.272896	−	0.228987i
$879$	−11.0917	−	26.3364i	−0.374115	−	0.888306i
$880$		0			0
$881$	15.0545	−	26.0751i	0.507198	−	0.878492i	−0.492767	−	0.870161i	$-0.664015\pi$
$881$	15.0545	−	26.0751i	0.507198	−	0.878492i	0.999965	−	0.00833136i	$-0.00265199\pi$
$882$	−10.3543	−	14.4216i	−0.348648	−	0.485601i
$883$	−3.87477	−	6.71129i	−0.130396	−	0.225853i	0.793433	−	0.608658i	$-0.208292\pi$
$883$	−3.87477	−	6.71129i	−0.130396	−	0.225853i	−0.923829	+	0.382804i	$0.874958\pi$
$884$	−7.76977	−	44.0645i	−0.261325	−	1.48205i
$885$		0			0
$886$	27.9721	−	10.1810i	0.939741	−	0.342038i
$887$	5.25033	−	29.7761i	0.176289	−	0.999784i	−0.760357	−	0.649506i	$-0.774976\pi$
$887$	5.25033	−	29.7761i	0.176289	−	0.999784i	0.936646	−	0.350278i	$-0.113913\pi$
$888$	−9.83477	+	6.34747i	−0.330033	+	0.213007i
$889$	3.03802	−	2.54920i	0.101892	−	0.0854974i
$890$		0			0
$891$	−7.95312	−	20.3414i	−0.266439	−	0.681461i
$892$	10.4214			0.348934
$893$	2.47017	−	2.07272i	0.0826610	−	0.0693608i
$894$	−2.73588	+	1.76577i	−0.0915014	+	0.0590561i
$895$		0			0
$896$	−3.29224	+	1.19828i	−0.109986	+	0.0400317i
$897$	20.9779	−	67.9309i	0.700432	−	2.26815i
$898$	−0.0907299	−	0.514555i	−0.00302769	−	0.0171709i
$899$	1.80323	+	3.12329i	0.0601411	+	0.104167i
$900$		0			0
$901$	25.4929	−	44.1550i	0.849292	−	1.47102i
$902$	2.45144	+	0.892250i	0.0816240	+	0.0297087i
$903$	−0.855396	−	2.03107i	−0.0284658	−	0.0675897i
$904$	−23.2481	−	19.5075i	−0.773222	−	0.648810i
$905$		0			0
$906$	−14.4758	+	19.0979i	−0.480927	+	0.634486i
$907$	20.4114	+	7.42916i	0.677751	+	0.246681i	0.657881	−	0.753122i	$-0.271453\pi$
$907$	20.4114	+	7.42916i	0.677751	+	0.246681i	0.0198692	+	0.999803i	$0.493675\pi$
$908$	−5.96027	+	10.3235i	−0.197798	+	0.342597i
$909$	12.9365	+	3.30293i	0.429077	+	0.109551i
$910$		0			0
$911$	−4.34320	−	24.6315i	−0.143897	−	0.816078i	−0.968246	−	0.249998i	$-0.919570\pi$
$911$	−4.34320	−	24.6315i	−0.143897	−	0.816078i	0.824350	−	0.566081i	$-0.191541\pi$
$912$	−0.138518	−	0.149384i	−0.00458679	−	0.00494659i
$913$	−17.8778	+	6.50698i	−0.591668	+	0.215350i
$914$	1.35272	−	7.67163i	0.0447438	−	0.253755i
$915$		0			0
$916$	−0.147530	+	0.123792i	−0.00487453	+	0.00409022i
$917$	−4.46185			−0.147343
$918$	24.8208	−	8.31263i	0.819209	−	0.274358i
$919$	56.7307			1.87137			0.935686	−	0.352835i	$-0.114782\pi$
$919$	56.7307			1.87137			0.935686	+	0.352835i	$0.114782\pi$
$920$		0			0
$921$	−1.22942	−	24.7944i	−0.0405108	−	0.817005i
$922$	−3.82369	+	21.6852i	−0.125926	+	0.714164i
$923$	−19.0654	+	6.93922i	−0.627544	+	0.228407i
$924$	2.56384	−	0.584309i	0.0843441	−	0.0192224i
$925$		0			0
$926$	5.03635	+	8.72322i	0.165505	+	0.286663i
$927$	−2.52299	+	33.3780i	−0.0828660	+	1.09628i
$928$	1.19628	−	2.07201i	0.0392697	−	0.0680172i
$929$	−0.152953	−	0.0556703i	−0.00501822	−	0.00182648i	0.339510	−	0.940603i	$-0.389739\pi$
$929$	−0.152953	−	0.0556703i	−0.00501822	−	0.00182648i	−0.344528	+	0.938776i	$0.611961\pi$
$930$		0			0
$931$	−20.0869	−	16.8549i	−0.658320	−	0.552396i
$932$	−15.3336	−	12.8664i	−0.502269	−	0.421454i
$933$	54.6270	+	6.86356i	1.78841	+	0.224703i
$934$	0.541204	+	0.196982i	0.0177087	+	0.00644545i
$935$		0			0
$936$	44.5547	+	30.4190i	1.45632	+	0.994277i
$937$	25.2528	+	43.7391i	0.824973	+	1.42890i	0.901940	+	0.431862i	$0.142143\pi$
$937$	25.2528	+	43.7391i	0.824973	+	1.42890i	−0.0769668	+	0.997034i	$0.524524\pi$
$938$	0.539718	+	3.06089i	0.0176224	+	0.0999417i
$939$	−28.8336	+	6.57131i	−0.940950	+	0.214446i
$940$		0			0
$941$	4.03430	−	22.8796i	0.131514	−	0.745855i	−0.845709	−	0.533644i	$-0.820822\pi$
$941$	4.03430	−	22.8796i	0.131514	−	0.745855i	0.977224	−	0.212211i	$-0.0680665\pi$
$942$	−1.64995	−	33.2755i	−0.0537583	−	1.08417i
$943$	6.07013	−	5.09345i	0.197671	−	0.165865i
$944$	−0.211731			−0.00689126
$945$		0			0
$946$	5.32659			0.173183
$947$	18.4151	−	15.4521i	0.598410	−	0.502126i	−0.292524	−	0.956258i	$-0.594495\pi$
$947$	18.4151	−	15.4521i	0.598410	−	0.502126i	0.890934	+	0.454132i	$0.150051\pi$
$948$	5.10548	+	2.61951i	0.165818	+	0.0850776i
$949$	−13.2015	+	74.8695i	−0.428539	+	2.43037i
$950$		0			0
$951$	16.0788	+	17.3400i	0.521390	+	0.562289i
$952$	1.43760	+	8.15304i	0.0465929	+	0.264242i
$953$	−24.9256	−	43.1725i	−0.807421	−	1.39849i	−0.914645	−	0.404259i	$-0.867529\pi$
$953$	−24.9256	−	43.1725i	−0.807421	−	1.39849i	0.107224	−	0.994235i	$-0.465804\pi$
$954$	6.32348	+	22.5307i	0.204730	+	0.729460i
$955$		0			0
$956$	−23.2937	−	8.47820i	−0.753371	−	0.274205i
$957$	−1.07643	+	1.42014i	−0.0347961	+	0.0459065i
$958$	15.0254	+	12.6078i	0.485450	+	0.407341i
$959$	−6.22939	−	5.22708i	−0.201157	−	0.168791i
$960$		0			0
$961$	−38.8700	−	14.1475i	−1.25387	−	0.456371i
$962$	−6.63726	+	11.4961i	−0.213994	+	0.370648i
$963$	−14.2314	+	31.4859i	−0.458602	+	1.01462i
$964$	16.2126	+	28.0811i	0.522174	+	0.904432i
$965$		0			0
$966$	−1.47755	+	4.78461i	−0.0475393	+	0.153942i
$967$	−20.6916	+	7.53113i	−0.665398	+	0.242185i	−0.652565	−	0.757733i	$-0.726307\pi$
$967$	−20.6916	+	7.53113i	−0.665398	+	0.242185i	−0.0128326	+	0.999918i	$0.504085\pi$
$968$	2.51602	−	14.2690i	0.0808678	−	0.458624i
$969$	32.4827	−	20.9647i	1.04349	−	0.673483i
$970$		0			0
$971$	53.2340			1.70836			0.854181	−	0.519977i	$-0.174059\pi$
$971$	53.2340			1.70836			0.854181	+	0.519977i	$0.174059\pi$
$972$	8.34228	−	17.2517i	0.267579	−	0.553348i
$973$	1.70692			0.0547215
$974$	−19.0328	+	15.9704i	−0.609849	+	0.511724i
$975$		0			0
$976$	−0.0168803	+	0.0957327i	−0.000540324	+	0.00306433i
$977$	−29.9489	+	10.9005i	−0.958149	+	0.348738i	−0.773308	−	0.634031i	$-0.781399\pi$
$977$	−29.9489	+	10.9005i	−0.958149	+	0.348738i	−0.184841	+	0.982768i	$0.559177\pi$
$978$	8.96012	−	29.0148i	0.286513	−	0.927790i
$979$	−7.79370	−	44.2003i	−0.249088	−	1.41265i
$980$		0			0
$981$	−20.7768	+	45.9671i	−0.663353	+	1.46762i
$982$	−18.8078	+	32.5761i	−0.600182	+	1.03955i
$983$	56.3354	+	20.5044i	1.79682	+	0.653989i	0.998671	+	0.0515295i	$0.0164096\pi$
$983$	56.3354	+	20.5044i	1.79682	+	0.653989i	0.798149	+	0.602460i	$0.205813\pi$
$984$	2.33379	+	5.54140i	0.0743986	+	0.176653i
$985$		0			0
$986$	−1.63603	−	1.37279i	−0.0521017	−	0.0437185i
$987$	0.441391	−	0.582326i	0.0140496	−	0.0185356i
$988$	28.5024	+	10.3740i	0.906783	+	0.330042i
$989$	8.08963	−	14.0117i	0.257235	−	0.445545i
$990$		0			0
$991$	6.87505	+	11.9079i	0.218393	+	0.378268i	0.954317	−	0.298796i	$-0.0965852\pi$
$991$	6.87505	+	11.9079i	0.218393	+	0.378268i	−0.735924	+	0.677064i	$0.763252\pi$
$992$	8.33637	+	47.2779i	0.264680	+	1.50107i
$993$	33.3435	+	35.9590i	1.05812	+	1.14113i
$994$	1.34284	−	0.488754i	0.0425923	−	0.0155023i
$995$		0			0
$996$	−14.8516	−	7.62003i	−0.470592	−	0.241450i
$997$	−4.56295	+	3.82877i	−0.144510	+	0.121258i	−0.712177	−	0.702000i	$-0.752291\pi$
$997$	−4.56295	+	3.82877i	−0.144510	+	0.121258i	0.567667	+	0.823258i	$0.307846\pi$
$998$	−3.55037			−0.112385
$999$	11.5259	+	4.53648i	0.364665	+	0.143528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.f.76.8	✓	66
5.2	odd	4		675.2.u.e.49.15		132
5.3	odd	4		675.2.u.e.49.8		132
5.4	even	2		675.2.l.g.76.4	yes	66
27.16	even	9	inner	675.2.l.f.151.8	yes	66
135.43	odd	36		675.2.u.e.124.15		132
135.97	odd	36		675.2.u.e.124.8		132
135.124	even	18		675.2.l.g.151.4	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.8	✓	66	1.1	even	1	trivial
675.2.l.f.151.8	yes	66	27.16	even	9	inner
675.2.l.g.76.4	yes	66	5.4	even	2
675.2.l.g.151.4	yes	66	135.124	even	18
675.2.u.e.49.8		132	5.3	odd	4
675.2.u.e.49.15		132	5.2	odd	4
675.2.u.e.124.8		132	135.97	odd	36
675.2.u.e.124.15		132	135.43	odd	36

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.672508 - 0.564301i) q^{2} +(1.45527 - 0.939248i) q^{3} +(-0.213465 + 1.21062i) q^{4} +(0.448662 - 1.45286i) q^{6} +(-0.0883715 - 0.501180i) q^{7} +(1.41750 + 2.45517i) q^{8} +(1.23563 - 2.73372i) q^{9} +(2.28041 + 0.830001i) q^{11} +(0.826424 + 1.96228i) q^{12} +(4.85915 + 4.07731i) q^{13} +(-0.342247 - 0.287179i) q^{14} +(0.0284139 + 0.0103418i) q^{16} +(-2.86909 + 4.96942i) q^{17} +(-0.711675 - 2.53572i) q^{18} +(-1.94493 - 3.36871i) q^{19} +(-0.599337 - 0.646349i) q^{21} +(2.00197 - 0.728656i) q^{22} +(1.12370 - 6.37282i) q^{23} +(4.36886 + 2.24156i) q^{24} +5.56865 q^{26} +(-0.769474 - 5.13886i) q^{27} +0.625603 q^{28} +(-0.324767 + 0.272512i) q^{29} +(1.47718 - 8.37750i) q^{31} +(-5.30309 + 1.93017i) q^{32} +(4.09819 - 0.933994i) q^{33} +(0.874759 + 4.96101i) q^{34} +(3.04574 + 2.07943i) q^{36} +(-1.19190 + 2.06443i) q^{37} +(-3.20895 - 1.16796i) q^{38} +(10.9010 + 1.36964i) q^{39} +(0.938033 + 0.787103i) q^{41} +(-0.767795 - 0.0964687i) q^{42} +(2.34944 + 0.855127i) q^{43} +(-1.49160 + 2.58353i) q^{44} +(-2.84049 - 4.91988i) q^{46} +(0.143949 + 0.816377i) q^{47} +(0.0510634 - 0.0116376i) q^{48} +(6.33448 - 2.30556i) q^{49} +(0.492208 + 9.92664i) q^{51} +(-5.97334 + 5.01222i) q^{52} -8.88536 q^{53} +(-3.41735 - 3.02171i) q^{54} +(1.10522 - 0.927387i) q^{56} +(-5.99445 - 3.07562i) q^{57} +(-0.0646297 + 0.366533i) q^{58} +(-6.58000 + 2.39492i) q^{59} +(0.558258 + 3.16604i) q^{61} +(-3.73402 - 6.46751i) q^{62} +(-1.47928 - 0.377687i) q^{63} +(-2.50742 + 4.34297i) q^{64} +(2.22901 - 2.94073i) q^{66} +(-5.32923 - 4.47176i) q^{67} +(-5.40363 - 4.53418i) q^{68} +(-4.35037 - 10.3296i) q^{69} +(-1.59927 + 2.77002i) q^{71} +(8.46325 - 0.841362i) q^{72} +(5.99262 + 10.3795i) q^{73} +(0.363398 + 2.06093i) q^{74} +(4.49341 - 1.63547i) q^{76} +(0.214457 - 1.21624i) q^{77} +(8.10390 - 5.23035i) q^{78} +(2.06451 - 1.73233i) q^{79} +(-5.94646 - 6.75571i) q^{81} +1.07500 q^{82} +(-6.00558 + 5.03928i) q^{83} +(0.910421 - 0.587596i) q^{84} +(2.06257 - 0.750714i) q^{86} +(-0.216668 + 0.701616i) q^{87} +(1.19467 + 6.77532i) q^{88} +(-9.24733 - 16.0168i) q^{89} +(1.61406 - 2.79563i) q^{91} +(7.47519 + 2.72075i) q^{92} +(-5.71886 - 13.5790i) q^{93} +(0.557490 + 0.467789i) q^{94} +(-5.90453 + 7.78984i) q^{96} +(7.86099 + 2.86117i) q^{97} +(2.95896 - 5.12506i) q^{98} +(5.08672 - 5.20843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

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Database

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