LMFDB - Embedded newform 675.2.u.e.49.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); 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, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.15
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.564301 + 0.672508i) q^{2} +(-0.939248 - 1.45527i) q^{3} +(0.213465 - 1.21062i) q^{4} +(0.448662 - 1.45286i) q^{6} +(0.501180 - 0.0883715i) q^{7} +(2.45517 - 1.41750i) q^{8} +(-1.23563 + 2.73372i) q^{9} +(2.28041 + 0.830001i) q^{11} +(-1.96228 + 0.826424i) q^{12} +(4.07731 - 4.85915i) q^{13} +(0.342247 + 0.287179i) q^{14} +(0.0284139 + 0.0103418i) q^{16} +(-4.96942 - 2.86909i) q^{17} +(-2.53572 + 0.711675i) q^{18} +(1.94493 + 3.36871i) q^{19} +(-0.599337 - 0.646349i) q^{21} +(0.728656 + 2.00197i) q^{22} +(-6.37282 - 1.12370i) q^{23} +(-4.36886 - 2.24156i) q^{24} +5.56865 q^{26} +(5.13886 - 0.769474i) q^{27} -0.625603i q^{28} +(0.324767 - 0.272512i) q^{29} +(1.47718 - 8.37750i) q^{31} +(-1.93017 - 5.30309i) q^{32} +(-0.933994 - 4.09819i) q^{33} +(-0.874759 - 4.96101i) q^{34} +(3.04574 + 2.07943i) q^{36} +(-2.06443 - 1.19190i) q^{37} +(-1.16796 + 3.20895i) q^{38} +(-10.9010 - 1.36964i) q^{39} +(0.938033 + 0.787103i) q^{41} +(0.0964687 - 0.767795i) q^{42} +(0.855127 - 2.34944i) q^{43} +(1.49160 - 2.58353i) q^{44} +(-2.84049 - 4.91988i) q^{46} +(-0.816377 + 0.143949i) q^{47} +(-0.0116376 - 0.0510634i) q^{48} +(-6.33448 + 2.30556i) q^{49} +(0.492208 + 9.92664i) q^{51} +(-5.01222 - 5.97334i) q^{52} +8.88536i q^{53} +(3.41735 + 3.02171i) q^{54} +(1.10522 - 0.927387i) q^{56} +(3.07562 - 5.99445i) q^{57} +(0.366533 + 0.0646297i) q^{58} +(6.58000 - 2.39492i) q^{59} +(0.558258 + 3.16604i) q^{61} +(6.46751 - 3.73402i) q^{62} +(-0.377687 + 1.47928i) q^{63} +(2.50742 - 4.34297i) q^{64} +(2.22901 - 2.94073i) q^{66} +(4.47176 - 5.32923i) q^{67} +(-4.53418 + 5.40363i) q^{68} +(4.35037 + 10.3296i) q^{69} +(-1.59927 + 2.77002i) q^{71} +(0.841362 + 8.46325i) q^{72} +(10.3795 - 5.99262i) q^{73} +(-0.363398 - 2.06093i) q^{74} +(4.49341 - 1.63547i) q^{76} +(1.21624 + 0.214457i) q^{77} +(-5.23035 - 8.10390i) q^{78} +(-2.06451 + 1.73233i) q^{79} +(-5.94646 - 6.75571i) q^{81} +1.07500i q^{82} +(5.03928 + 6.00558i) q^{83} +(-0.910421 + 0.587596i) q^{84} +(2.06257 - 0.750714i) q^{86} +(-0.701616 - 0.216668i) q^{87} +(6.77532 - 1.19467i) q^{88} +(9.24733 + 16.0168i) q^{89} +(1.61406 - 2.79563i) q^{91} +(-2.72075 + 7.47519i) q^{92} +(-13.5790 + 5.71886i) q^{93} +(-0.557490 - 0.467789i) q^{94} +(-5.90453 + 7.78984i) q^{96} +(-2.86117 + 7.86099i) q^{97} +(-5.12506 - 2.95896i) q^{98} +(-5.08672 + 5.20843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * 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 $

$2$	0.564301	+	0.672508i	0.399021	+	0.475535i	0.927721	−	0.373274i	$-0.121765\pi$
$2$	0.564301	+	0.672508i	0.399021	+	0.475535i	−0.528700	+	0.848809i	$0.677320\pi$
$3$	−0.939248	−	1.45527i	−0.542275	−	0.840201i
$3$	−0.939248	−	1.45527i	−0.542275	−	0.840201i
$4$	0.213465	−	1.21062i	0.106733	−	0.605310i
$5$		0			0
$5$		0			0
$6$	0.448662	−	1.45286i	0.183166	−	0.593129i
$7$	0.501180	−	0.0883715i	0.189428	−	0.0334013i	−0.0781292	−	0.996943i	$-0.524895\pi$
$7$	0.501180	−	0.0883715i	0.189428	−	0.0334013i	0.267557	+	0.963542i	$0.413784\pi$
$8$	2.45517	−	1.41750i	0.868035	−	0.501160i
$9$	−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	$0.491890\pi$
$12$	−1.96228	+	0.826424i	−0.566461	+	0.238568i
$13$	4.07731	−	4.85915i	1.13084	−	1.34769i	0.201059	−	0.979579i	$-0.435562\pi$
$13$	4.07731	−	4.85915i	1.13084	−	1.34769i	0.929784	−	0.368107i	$-0.119994\pi$
$14$	0.342247	+	0.287179i	0.0914694	+	0.0767519i
$15$		0			0
$16$	0.0284139	+	0.0103418i	0.00710347	+	0.00258545i
$17$	−4.96942	−	2.86909i	−1.20526	−	0.695857i	−0.243540	−	0.969891i	$-0.578309\pi$
$17$	−4.96942	−	2.86909i	−1.20526	−	0.695857i	−0.961720	+	0.274033i	$0.911642\pi$
$18$	−2.53572	+	0.711675i	−0.597674	+	0.167743i
$19$	1.94493	+	3.36871i	0.446197	+	0.772835i	0.998135	−	0.0610497i	$-0.0194448\pi$
$19$	1.94493	+	3.36871i	0.446197	+	0.772835i	−0.551938	+	0.833885i	$0.686111\pi$
$20$		0			0
$21$	−0.599337	−	0.646349i	−0.130786	−	0.141045i
$22$	0.728656	+	2.00197i	0.155350	+	0.426820i
$23$	−6.37282	−	1.12370i	−1.32882	−	0.234308i	−0.536238	−	0.844067i	$-0.680155\pi$
$23$	−6.37282	−	1.12370i	−1.32882	−	0.234308i	−0.792586	+	0.609760i	$0.791266\pi$
$24$	−4.36886	−	2.24156i	−0.891789	−	0.457557i
$25$		0			0
$26$	5.56865			1.09210
$27$	5.13886	−	0.769474i	0.988975	−	0.148085i
$28$		−	0.625603i		−	0.118228i
$29$	0.324767	−	0.272512i	0.0603078	−	0.0506042i	−0.612136	−	0.790753i	$-0.709689\pi$
$29$	0.324767	−	0.272512i	0.0603078	−	0.0506042i	0.672443	+	0.740149i	$0.265245\pi$
$30$		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	$-0.221176\pi$
$32$	−1.93017	−	5.30309i	−0.341209	−	0.937464i
$33$	−0.933994	−	4.09819i	−0.162588	−	0.713403i
$34$	−0.874759	−	4.96101i	−0.150020	−	0.850806i
$35$		0			0
$36$	3.04574	+	2.07943i	0.507623	+	0.346571i
$37$	−2.06443	−	1.19190i	−0.339390	−	0.195947i	0.320612	−	0.947210i	$-0.396111\pi$
$37$	−2.06443	−	1.19190i	−0.339390	−	0.195947i	−0.660002	+	0.751264i	$0.729445\pi$
$38$	−1.16796	+	3.20895i	−0.189468	+	0.520560i
$39$	−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	$0.691739\pi$
$42$	0.0964687	−	0.767795i	0.0148854	−	0.118473i
$43$	0.855127	−	2.34944i	0.130406	−	0.358287i	−0.857256	−	0.514891i	$-0.827832\pi$
$43$	0.855127	−	2.34944i	0.130406	−	0.358287i	0.987661	+	0.156604i	$0.0500547\pi$
$44$	1.49160	−	2.58353i	0.224868	−	0.389482i
$45$		0			0
$46$	−2.84049	−	4.91988i	−0.418808	−	0.725396i
$47$	−0.816377	+	0.143949i	−0.119081	+	0.0209972i	−0.232871	−	0.972508i	$-0.574812\pi$
$47$	−0.816377	+	0.143949i	−0.119081	+	0.0209972i	0.113790	+	0.993505i	$0.463701\pi$
$48$	−0.0116376	−	0.0510634i	−0.00167974	−	0.00737037i
$49$	−6.33448	+	2.30556i	−0.904925	+	0.329366i
$50$		0			0
$51$	0.492208	+	9.92664i	0.0689229	+	1.39001i
$52$	−5.01222	−	5.97334i	−0.695070	−	0.828353i
$53$			8.88536i			1.22050i	0.792210	+	0.610249i	$0.208931\pi$
$53$			8.88536i			1.22050i	−0.792210	+	0.610249i	$0.791069\pi$
$54$	3.41735	+	3.02171i	0.465042	+	0.411203i
$55$		0			0
$56$	1.10522	−	0.927387i	0.147691	−	0.123927i
$57$	3.07562	−	5.99445i	0.407376	−	0.793984i
$58$	0.366533	+	0.0646297i	0.0481282	+	0.00848630i
$59$	6.58000	−	2.39492i	0.856643	−	0.311792i	0.123897	−	0.992295i	$-0.460461\pi$
$59$	6.58000	−	2.39492i	0.856643	−	0.311792i	0.732746	+	0.680503i	$0.238238\pi$
$60$		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	$0.878461\pi$
$62$	6.46751	−	3.73402i	0.821375	−	0.474221i
$63$	−0.377687	+	1.47928i	−0.0475841	+	0.186372i
$64$	2.50742	−	4.34297i	0.313427	−	0.542871i
$65$		0			0
$66$	2.22901	−	2.94073i	0.274372	−	0.361979i
$67$	4.47176	−	5.32923i	0.546312	−	0.651070i	−0.420278	−	0.907395i	$-0.638068\pi$
$67$	4.47176	−	5.32923i	0.546312	−	0.651070i	0.966590	+	0.256326i	$0.0825120\pi$
$68$	−4.53418	+	5.40363i	−0.549850	+	0.655286i
$69$	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	$0.227450\pi$
$72$	0.841362	+	8.46325i	0.0991554	+	0.997404i
$73$	10.3795	−	5.99262i	1.21483	−	0.701383i	0.251024	−	0.967981i	$-0.419233\pi$
$73$	10.3795	−	5.99262i	1.21483	−	0.701383i	0.963808	+	0.266598i	$0.0858994\pi$
$74$	−0.363398	−	2.06093i	−0.0422442	−	0.239579i
$75$		0			0
$76$	4.49341	−	1.63547i	0.515429	−	0.187601i
$77$	1.21624	+	0.214457i	0.138604	+	0.0244396i
$78$	−5.23035	−	8.10390i	−0.592220	−	0.917585i
$79$	−2.06451	+	1.73233i	−0.232276	+	0.194903i	−0.751495	−	0.659738i	$-0.770667\pi$
$79$	−2.06451	+	1.73233i	−0.232276	+	0.194903i	0.519220	+	0.854641i	$0.326223\pi$
$80$		0			0
$81$	−5.94646	−	6.75571i	−0.660718	−	0.750634i
$82$			1.07500i			0.118714i
$83$	5.03928	+	6.00558i	0.553133	+	0.659198i	0.968078	−	0.250648i	$-0.0806438\pi$
$83$	5.03928	+	6.00558i	0.553133	+	0.659198i	−0.414945	+	0.909846i	$0.636199\pi$
$84$	−0.910421	+	0.587596i	−0.0993351	+	0.0641120i
$85$		0			0
$86$	2.06257	−	0.750714i	0.222412	−	0.0809515i
$87$	−0.701616	−	0.216668i	−0.0752211	−	0.0232292i
$88$	6.77532	−	1.19467i	0.722252	−	0.127353i
$89$	9.24733	+	16.0168i	0.980215	+	1.69778i	0.661525	+	0.749923i	$0.269909\pi$
$89$	9.24733	+	16.0168i	0.980215	+	1.69778i	0.318690	+	0.947859i	$0.396757\pi$
$90$		0			0
$91$	1.61406	−	2.79563i	0.169199	−	0.293061i
$92$	−2.72075	+	7.47519i	−0.283658	+	0.779343i
$93$	−13.5790	+	5.71886i	−1.40807	+	0.593018i
$94$	−0.557490	−	0.467789i	−0.0575007	−	0.0482488i
$95$		0			0
$96$	−5.90453	+	7.78984i	−0.602629	+	0.795047i
$97$	−2.86117	+	7.86099i	−0.290508	+	0.798163i	0.705485	+	0.708725i	$0.250729\pi$
$97$	−2.86117	+	7.86099i	−0.290508	+	0.798163i	−0.995992	+	0.0894380i	$0.971493\pi$
$98$	−5.12506	−	2.95896i	−0.517710	−	0.298900i
$99$	−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	$0.873375\pi$
$102$	−6.39799	+	5.93263i	−0.633496	+	0.587418i
$103$	3.81618	+	10.4849i	0.376019	+	1.03310i	0.972991	+	0.230842i	$0.0741480\pi$
$103$	3.81618	+	10.4849i	0.376019	+	1.03310i	−0.596972	+	0.802262i	$0.703630\pi$
$104$	3.12269	−	17.7096i	0.306204	−	1.73657i
$105$		0			0
$106$	−5.97548	+	5.01402i	−0.580390	+	0.487005i
$107$		−	11.5176i		−	1.11345i	−0.830698	−	0.556724i	$-0.812058\pi$
$107$		−	11.5176i		−	1.11345i	0.830698	−	0.556724i	$-0.187942\pi$
$108$	0.165427	−	6.38547i	0.0159182	−	0.614442i
$109$	16.8148			1.61057			0.805285	−	0.592888i	$-0.202012\pi$
$109$	16.8148			1.61057			0.805285	+	0.592888i	$0.202012\pi$
$110$		0			0
$111$	0.204476	+	4.12379i	0.0194080	+	0.391413i
$112$	0.0151544	+	0.00267213i	0.00143195	+	0.000252492i
$113$	3.66129	+	10.0593i	0.344425	+	0.946301i	0.984094	+	0.177650i	$0.0568495\pi$
$113$	3.66129	+	10.0593i	0.344425	+	0.946301i	−0.639668	+	0.768651i	$0.720928\pi$
$114$	5.76689	−	1.31430i	0.540119	−	0.123095i
$115$		0			0
$116$	−0.260582	−	0.451342i	−0.0241945	−	0.0419060i
$117$	8.24553	+	17.1503i	0.762300	+	1.58555i
$118$	5.32371	+	3.07364i	0.490087	+	0.282952i
$119$	−2.74412	−	0.998777i	−0.251553	−	0.0915577i
$120$		0			0
$121$	−3.91512	−	3.28518i	−0.355920	−	0.298653i
$122$	−1.81416	+	2.16203i	−0.164246	+	0.195741i
$123$	0.264402	−	2.10438i	0.0238404	−	0.189745i
$124$	−9.82665	−	3.57661i	−0.882459	−	0.321189i
$125$		0			0
$126$	−1.20796	+	0.580762i	−0.107613	+	0.0517384i
$127$	−6.74877	+	3.89640i	−0.598857	+	0.345750i	−0.768592	−	0.639740i	$-0.779042\pi$
$127$	−6.74877	+	3.89640i	−0.598857	+	0.345750i	0.169735	+	0.985490i	$0.445709\pi$
$128$	−6.77978	+	1.19546i	−0.599253	+	0.105664i
$129$	−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	$-0.0695563\pi$
$132$	−5.16073	+	0.255892i	−0.449184	+	0.0222726i
$133$	1.27246	+	1.51645i	0.110336	+	0.131493i
$134$	6.10737			0.527597
$135$		0			0
$136$	−16.2677			−1.39494
$137$	10.2711	+	12.2406i	0.877519	+	1.04579i	0.998587	+	0.0531421i	$0.0169236\pi$
$137$	10.2711	+	12.2406i	0.877519	+	1.04579i	−0.121068	+	0.992644i	$0.538632\pi$
$138$	−4.49182	+	8.75467i	−0.382369	+	0.745247i
$139$	0.582428	−	3.30311i	0.0494009	−	0.280167i	−0.950093	−	0.311966i	$-0.899013\pi$
$139$	0.582428	−	3.30311i	0.0494009	−	0.280167i	0.999494	+	0.0317992i	$0.0101237\pi$
$140$		0			0
$141$	0.976266	+	1.05285i	0.0822164	+	0.0886656i
$142$	−2.76534	+	0.487603i	−0.232062	+	0.0409188i
$143$	13.3310	−	7.69668i	1.11480	−	0.643629i
$144$	−0.0633805	+	0.0648970i	−0.00528171	+	0.00540808i
$145$		0			0
$146$	9.88727	+	3.59867i	0.818276	+	0.297828i
$147$	9.30486	+	7.05288i	0.767452	+	0.581712i
$148$	−1.88362	+	2.24481i	−0.154833	+	0.184522i
$149$	1.64045	+	1.37650i	0.134391	+	0.112767i	0.707505	−	0.706708i	$-0.249821\pi$
$149$	1.64045	+	1.37650i	0.134391	+	0.112767i	−0.573114	+	0.819475i	$0.694265\pi$
$150$		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	$0.832702\pi$
$152$	9.55027	+	5.51385i	0.774629	+	0.447232i
$153$	13.9836	−	10.0399i	1.13051	−	0.811675i
$154$	0.542104	+	0.938952i	0.0436840	+	0.0756629i
$155$		0			0
$156$	−3.98510	+	12.9046i	−0.319063	+	1.03319i
$157$	7.49385	+	20.5892i	0.598074	+	1.64320i	0.755106	+	0.655602i	$0.227585\pi$
$157$	7.49385	+	20.5892i	0.598074	+	1.64320i	−0.157032	+	0.987594i	$0.550193\pi$
$158$	−2.33002	−	0.410845i	−0.185366	−	0.0326851i
$159$	12.9306	−	8.34556i	1.02546	−	0.661846i
$160$		0			0
$161$	−3.29323			−0.259543
$162$	1.18767	−	7.81130i	0.0933125	−	0.613714i
$163$		−	19.9707i		−	1.56423i	−0.623134	−	0.782115i	$-0.714141\pi$
$163$		−	19.9707i		−	1.56423i	0.623134	−	0.782115i	$-0.285859\pi$
$164$	1.15312	−	0.967584i	0.0900436	−	0.0755556i
$165$		0			0
$166$	−1.19513	+	6.77791i	−0.0927600	+	0.526068i
$167$	−5.92664	−	16.2833i	−0.458617	−	1.26004i	−0.926515	−	0.376258i	$-0.877211\pi$
$167$	−5.92664	−	16.2833i	−0.458617	−	1.26004i	0.467897	−	0.883783i	$-0.345012\pi$
$168$	−2.38767	−	0.737343i	−0.184213	−	0.0568873i
$169$	−4.72945	−	26.8220i	−0.363804	−	2.06323i
$170$		0			0
$171$	−11.6123	+	1.15442i	−0.888016	+	0.0882808i
$172$	−2.66174	−	1.53676i	−0.202956	−	0.117177i
$173$	−4.89919	+	13.4604i	−0.372478	+	1.02338i	0.601922	+	0.798555i	$0.294402\pi$
$173$	−4.89919	+	13.4604i	−0.372478	+	1.02338i	−0.974400	+	0.224821i	$0.927820\pi$
$174$	−0.250212	−	0.594109i	−0.0189685	−	0.0450393i
$175$		0			0
$176$	0.0562116	+	0.0471671i	0.00423711	+	0.00355535i
$177$	−9.66551	−	7.32625i	−0.726505	−	0.550675i
$178$	−5.55318	+	15.2572i	−0.416228	+	1.14358i
$179$	−12.1807	+	21.0976i	−0.910428	+	1.57691i	−0.0969684	+	0.995287i	$0.530915\pi$
$179$	−12.1807	+	21.0976i	−0.910428	+	1.57691i	−0.813460	+	0.581621i	$0.802419\pi$
$180$		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	$0.784891\pi$
$182$	2.79090	−	0.492110i	0.206875	−	0.0364776i
$183$	4.08310	−	3.78611i	0.301831	−	0.279877i
$184$	−17.2392	+	6.27456i	−1.27089	+	0.462567i
$185$		0			0
$186$	−11.5086	−	5.90481i	−0.843852	−	0.432962i
$187$	−8.95095	−	10.6673i	−0.654558	−	0.780072i
$188$			1.01905i			0.0743219i
$189$	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	$0.190972\pi$
$192$	−8.67528	+	0.430160i	−0.626085	+	0.0310441i
$193$	9.10995	+	1.60633i	0.655749	+	0.115626i	0.491616	−	0.870812i	$-0.336406\pi$
$193$	9.10995	+	1.60633i	0.655749	+	0.115626i	0.164133	+	0.986438i	$0.447517\pi$
$194$	−6.90115	+	2.51181i	−0.495473	+	0.180338i
$195$		0			0
$196$	1.43897	+	8.16081i	0.102784	+	0.582915i
$197$	−7.82865	+	4.51987i	−0.557768	+	0.322028i	−0.752249	−	0.658879i	$-0.771031\pi$
$197$	−7.82865	+	4.51987i	−0.557768	+	0.322028i	0.194481	+	0.980906i	$0.437698\pi$
$198$	−6.37316	−	0.481737i	−0.452921	−	0.0342356i
$199$	−3.66921	+	6.35527i	−0.260104	+	0.450513i	−0.966269	−	0.257534i	$-0.917090\pi$
$199$	−3.66921	+	6.35527i	−0.260104	+	0.450513i	0.706166	+	0.708047i	$0.250423\pi$
$200$		0			0
$201$	−11.9556	−	1.50214i	−0.843281	−	0.105953i
$202$	−2.51143	+	2.99300i	−0.176703	+	0.210587i
$203$	0.138684	−	0.165278i	0.00973374	−	0.0116002i
$204$	12.1225	+	1.52311i	0.848742	+	0.106639i
$205$		0			0
$206$	−4.89768	+	8.48303i	−0.341238	+	0.591041i
$207$	10.9463	−	16.0330i	0.760820	−	1.11437i
$208$	0.166105	−	0.0959005i	0.0115173	−	0.00664950i
$209$	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	$0.194575\pi$
$212$	10.7568	+	1.89671i	0.738780	+	0.130267i
$213$	5.53325	−	0.274364i	0.379132	−	0.0187991i
$214$	7.74568	−	6.49940i	0.529484	−	0.444290i
$215$		0			0
$216$	11.5261	−	9.17350i	0.784250	−	0.624178i
$217$		−	4.32917i		−	0.293883i
$218$	9.48864	+	11.3081i	0.642652	+	0.765882i
$219$	−18.4698	−	9.47646i	−1.24808	−	0.640360i
$220$		0			0
$221$	−34.2032	+	12.4490i	−2.30076	+	0.837407i
$222$	−2.65790	+	2.46457i	−0.178386	+	0.165411i
$223$	−8.34872	+	1.47210i	−0.559072	+	0.0985794i	−0.446042	−	0.895012i	$-0.647167\pi$
$223$	−8.34872	+	1.47210i	−0.559072	+	0.0985794i	−0.113030	+	0.993592i	$0.536056\pi$
$224$	−1.43600	−	2.48723i	−0.0959470	−	0.166185i
$225$		0			0
$226$	−4.69890	+	8.13874i	−0.312566	+	0.541381i
$227$	−3.31658	+	9.11223i	−0.220129	+	0.604800i	−0.999770	−	0.0214263i	$-0.993179\pi$
$227$	−3.31658	+	9.11223i	−0.220129	+	0.604800i	0.779641	+	0.626227i	$0.215401\pi$
$228$	−6.60047	−	5.00301i	−0.437127	−	0.331333i
$229$	−0.120012	−	0.100702i	−0.00793060	−	0.00665457i	0.638814	−	0.769361i	$-0.279425\pi$
$229$	−0.120012	−	0.100702i	−0.00793060	−	0.00665457i	−0.646744	+	0.762707i	$0.723870\pi$
$230$		0			0
$231$	−0.830262	−	1.97139i	−0.0546272	−	0.129708i
$232$	0.411076	−	1.12942i	0.0269884	−	0.0741501i
$233$	14.1015	+	8.14148i	0.923818	+	0.533366i	0.884851	−	0.465874i	$-0.154260\pi$
$233$	14.1015	+	8.14148i	0.923818	+	0.533366i	0.0389667	+	0.999241i	$0.487593\pi$
$234$	−6.88077	+	15.2231i	−0.449810	+	0.995168i
$235$		0			0
$236$	−1.49474	−	8.47711i	−0.0972995	−	0.551813i
$237$	4.46010	+	1.37734i	0.289715	+	0.0894676i
$238$	−0.876823	−	2.40905i	−0.0568360	−	0.156156i
$239$	3.50159	−	19.8585i	0.226499	−	1.28454i	−0.633299	−	0.773907i	$-0.718300\pi$
$239$	3.50159	−	19.8585i	0.226499	−	1.28454i	0.859798	−	0.510634i	$-0.170589\pi$
$240$		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	$-0.0453481\pi$
$242$		−	4.48678i		−	0.288421i
$243$	−4.24618	+	14.9990i	−0.272393	+	0.962186i
$244$	3.95204			0.253003
$245$		0			0
$246$	1.56441	−	1.00969i	0.0997434	−	0.0643755i
$247$	24.2991	+	4.28460i	1.54612	+	0.272622i
$248$	−8.24833	−	22.6621i	−0.523770	−	1.43905i
$249$	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	$-0.401300\pi$
$252$	1.71022	+	0.773011i	0.107734	+	0.0486951i
$253$	−13.6000	−	7.85194i	−0.855022	−	0.493647i
$254$	−6.42871	−	2.33986i	−0.403373	−	0.146816i
$255$		0			0
$256$	−12.3130	−	10.3318i	−0.769560	−	0.645737i
$257$	−7.40277	+	8.82228i	−0.461772	+	0.550319i	−0.945807	−	0.324730i	$-0.894726\pi$
$257$	−7.40277	+	8.82228i	−0.461772	+	0.550319i	0.484034	+	0.875049i	$0.339171\pi$
$258$	−3.02976	−	2.29649i	−0.188624	−	0.142973i
$259$	−1.13998	−	0.414918i	−0.0708348	−	0.0257818i
$260$		0			0
$261$	0.343681	+	1.22455i	0.0212733	+	0.0757975i
$262$	6.66573	−	3.84846i	0.411810	−	0.237759i
$263$	10.6545	−	1.87867i	0.656983	−	0.115844i	0.164789	−	0.986329i	$-0.447306\pi$
$263$	10.6545	−	1.87867i	0.656983	−	0.115844i	0.492195	+	0.870485i	$0.336195\pi$
$264$	−8.10228	−	8.73784i	−0.498661	−	0.537777i
$265$		0			0
$266$	−0.301779	+	1.71147i	−0.0185033	+	0.104937i
$267$	14.6233	−	28.5012i	0.894932	−	1.74424i
$268$	−5.49712	−	6.55121i	−0.335790	−	0.400179i
$269$	27.5918			1.68230			0.841152	−	0.540798i	$-0.181878\pi$
$269$	27.5918			1.68230			0.841152	+	0.540798i	$0.181878\pi$
$270$		0			0
$271$	22.2930			1.35421			0.677103	−	0.735889i	$-0.263235\pi$
$271$	22.2930			1.35421			0.677103	+	0.735889i	$0.263235\pi$
$272$	−0.111529	−	0.132915i	−0.00676242	−	0.00805914i
$273$	−5.58439	+	0.276899i	−0.337983	+	0.0167587i
$274$	−2.43592	+	13.8148i	−0.147159	+	0.834582i
$275$		0			0
$276$	13.4339	−	3.06164i	0.808625	−	0.184289i
$277$	−20.1680	+	3.55616i	−1.21178	+	0.213669i	−0.742783	−	0.669532i	$-0.766495\pi$
$277$	−20.1680	+	3.55616i	−1.21178	+	0.213669i	−0.468994	+	0.883201i	$0.655383\pi$
$278$	2.55004	−	1.47226i	0.152941	−	0.0883006i
$279$	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	$0.455234\pi$
$282$	−0.157139	+	1.25067i	−0.00935749	+	0.0744763i
$283$	−6.78999	+	8.09200i	−0.403623	+	0.481019i	−0.929121	−	0.369776i	$-0.879435\pi$
$283$	−6.78999	+	8.09200i	−0.403623	+	0.481019i	0.525498	+	0.850795i	$0.323879\pi$
$284$	3.01206	+	2.52742i	0.178733	+	0.149975i
$285$		0			0
$286$	12.6988	+	4.62199i	0.750896	+	0.273304i
$287$	0.539681	+	0.311585i	0.0318564	+	0.0183923i
$288$	16.8821	+	1.27610i	0.994790	+	0.0751946i
$289$	7.96339	+	13.7930i	0.468435	+	0.811353i
$290$		0			0
$291$	14.1272	−	3.21965i	0.828152	−	0.188739i
$292$	−5.03913	−	13.8449i	−0.294893	−	0.810211i
$293$	−16.2482	−	2.86499i	−0.949229	−	0.167375i	−0.322463	−	0.946582i	$-0.604511\pi$
$293$	−16.2482	−	2.86499i	−0.949229	−	0.167375i	−0.626766	+	0.779207i	$0.715622\pi$
$294$	0.507624	+	10.2375i	0.0296052	+	0.597066i
$295$		0			0
$296$	−6.75804			−0.392803
$297$	12.3574	+	2.51055i	0.717048	+	0.145677i
$298$			1.87998i			0.108904i
$299$	−31.4442	+	26.3848i	−1.81846	+	1.52587i
$300$		0			0
$301$	0.220949	−	1.25306i	0.0127353	−	0.0722253i
$302$	−4.73209	−	13.0013i	−0.272301	−	0.748142i
$303$	5.65242	−	5.24129i	0.324723	−	0.301104i
$304$	0.0204243	+	0.115832i	0.00117142	+	0.00664343i
$305$		0			0
$306$	14.6429	+	3.73860i	0.837078	+	0.213721i
$307$	12.4125	+	7.16633i	0.708416	+	0.409004i	0.810474	−	0.585774i	$-0.199209\pi$
$307$	12.4125	+	7.16633i	0.708416	+	0.409004i	−0.102058	+	0.994778i	$0.532543\pi$
$308$	0.519251	−	1.42663i	0.0295871	−	0.0812898i
$309$	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	$0.364884\pi$
$312$	−28.7053	+	12.0894i	−1.62512	+	0.684427i
$313$	−5.83964	+	16.0443i	−0.330076	+	0.906876i	0.658015	+	0.753005i	$0.271396\pi$
$313$	−5.83964	+	16.0443i	−0.330076	+	0.906876i	−0.988091	+	0.153871i	$0.950826\pi$
$314$	−9.61761	+	16.6582i	−0.542753	+	0.940076i
$315$		0			0
$316$	1.65650	+	2.86914i	0.0931852	+	0.161401i
$317$	−13.4455	+	2.37080i	−0.755173	+	0.133157i	−0.537964	−	0.842968i	$-0.680806\pi$
$317$	−13.4455	+	2.37080i	−0.755173	+	0.133157i	−0.217209	+	0.976125i	$0.569695\pi$
$318$	12.9092	+	3.98653i	0.723913	+	0.223553i
$319$	0.966788	−	0.351882i	0.0541297	−	0.0197016i
$320$		0			0
$321$	−16.7612	+	10.8179i	−0.935520	+	0.603795i
$322$	−1.85837	−	2.21472i	−0.103563	−	0.123422i
$323$		−	22.3207i		−	1.24196i
$324$	−9.44796	+	5.75680i	−0.524887	+	0.319822i
$325$		0			0
$326$	13.4305	−	11.2695i	0.743846	−	0.624161i
$327$	−15.7933	−	24.4701i	−0.873372	−	1.35320i
$328$	3.41875	+	0.602818i	0.188769	+	0.0332851i
$329$	−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	$0.660625\pi$
$332$	8.34619	−	4.81867i	0.458057	−	0.264459i
$333$	5.80917	−	4.17083i	0.318341	−	0.228560i
$334$	7.60625	−	13.1744i	0.416196	−	0.720872i
$335$		0			0
$336$	−0.0103451	−	0.0245635i	−0.000564369	−	0.00134005i
$337$	−11.1428	+	13.2795i	−0.606987	+	0.723379i	−0.978775	−	0.204938i	$-0.934301\pi$
$337$	−11.1428	+	13.2795i	−0.606987	+	0.723379i	0.371787	+	0.928318i	$0.378745\pi$
$338$	15.3692	−	18.3163i	0.835975	−	0.996276i
$339$	11.2002	−	14.7764i	0.608310	−	0.802542i
$340$		0			0
$341$	10.3219	−	17.8781i	0.558963	−	0.968152i
$342$	−7.32921	−	7.15794i	−0.396318	−	0.387057i
$343$	−6.05608	+	3.49648i	−0.326997	+	0.188792i
$344$	−1.23084	−	6.98043i	−0.0663623	−	0.376359i
$345$		0			0
$346$	−11.8168	+	4.30098i	−0.635278	+	0.231222i
$347$	3.31767	+	0.584994i	0.178102	+	0.0314041i	0.261988	−	0.965071i	$-0.415622\pi$
$347$	3.31767	+	0.584994i	0.178102	+	0.0314041i	−0.0838860	+	0.996475i	$0.526733\pi$
$348$	−0.412073	+	0.803140i	−0.0220894	+	0.0430528i
$349$	−5.25034	+	4.40556i	−0.281045	+	0.235824i	−0.772402	−	0.635133i	$-0.780945\pi$
$349$	−5.25034	+	4.40556i	−0.281045	+	0.235824i	0.491358	+	0.870958i	$0.336501\pi$
$350$		0			0
$351$	17.2138	−	28.1079i	0.918802	−	1.50029i
$352$		−	13.6953i		−	0.729960i
$353$	−19.5969	−	23.3547i	−1.04304	−	1.24304i	−0.969330	−	0.245763i	$-0.920961\pi$
$353$	−19.5969	−	23.3547i	−1.04304	−	1.24304i	−0.0737074	−	0.997280i	$-0.523483\pi$
$354$	−0.527300	−	10.6344i	−0.0280257	−	0.565209i
$355$		0			0
$356$	21.3643	−	7.77597i	1.13231	−	0.412126i
$357$	1.12392	+	4.93153i	0.0594840	+	0.261004i
$358$	−21.0619	+	3.71378i	−1.11316	+	0.196279i
$359$	−7.50154	−	12.9931i	−0.395916	−	0.685747i	0.597301	−	0.802017i	$-0.296240\pi$
$359$	−7.50154	−	12.9931i	−0.395916	−	0.685747i	−0.993218	+	0.116270i	$0.962906\pi$
$360$		0			0
$361$	1.93452	−	3.35069i	0.101817	−	0.176352i
$362$	−1.22479	+	3.36507i	−0.0643733	+	0.176864i
$363$	−1.10355	+	8.78316i	−0.0579214	+	0.460996i
$364$	−3.03990	−	2.55078i	−0.159334	−	0.133697i
$365$		0			0
$366$	4.85029	+	0.609409i	0.253529	+	0.0318543i
$367$	−5.67728	+	15.5982i	−0.296351	+	0.814219i	0.698751	+	0.715365i	$0.253740\pi$
$367$	−5.67728	+	15.5982i	−0.296351	+	0.814219i	−0.995102	+	0.0988534i	$0.968483\pi$
$368$	−0.169455	−	0.0978351i	−0.00883347	−	0.00510000i
$369$	−3.31078	+	1.59176i	−0.172352	+	0.0828635i
$370$		0			0
$371$	0.785213	+	4.45316i	0.0407662	+	0.231197i
$372$	4.02473	+	17.6598i	0.208673	+	0.915616i
$373$	2.39142	+	6.57037i	0.123823	+	0.340201i	0.986080	−	0.166269i	$-0.0531722\pi$
$373$	2.39142	+	6.57037i	0.123823	+	0.340201i	−0.862257	+	0.506470i	$0.830950\pi$
$374$	2.12283	−	12.0392i	0.109769	−	0.622531i
$375$		0			0
$376$	−1.80030	+	1.51063i	−0.0928434	+	0.0779048i
$377$		−	2.68921i		−	0.138501i
$378$	1.97974	+	1.21243i	0.101827	+	0.0623604i
$379$	13.7794			0.707801			0.353901	−	0.935283i	$-0.384855\pi$
$379$	13.7794			0.707801			0.353901	+	0.935283i	$0.384855\pi$
$380$		0			0
$381$	12.0091	+	6.16160i	0.615245	+	0.315668i
$382$	6.43640	+	1.13491i	0.329315	+	0.0580671i
$383$	3.50965	+	9.64267i	0.179335	+	0.492718i	0.996491	−	0.0836981i	$-0.0266732\pi$
$383$	3.50965	+	9.64267i	0.179335	+	0.492718i	−0.817157	+	0.576416i	$0.804451\pi$
$384$	8.10761	+	8.74358i	0.413740	+	0.446194i
$385$		0			0
$386$	4.06049	+	7.03297i	0.206673	+	0.357969i
$387$	5.36610	+	5.24071i	0.272774	+	0.266400i
$388$	8.90592	+	5.14184i	0.452130	+	0.261037i
$389$	−36.0005	−	13.1031i	−1.82530	−	0.664354i	−0.994112	−	0.108358i	$-0.965441\pi$
$389$	−36.0005	−	13.1031i	−1.82530	−	0.664354i	−0.831185	−	0.555996i	$-0.812337\pi$
$390$		0			0
$391$	28.4452	+	23.8683i	1.43853	+	1.20707i
$392$	−12.2841	+	14.6396i	−0.620442	+	0.739414i
$393$	−13.9951	+	5.89413i	−0.705961	+	0.297320i
$394$	−7.45737	−	2.71426i	−0.375697	−	0.136742i
$395$		0			0
$396$	5.21960	+	7.26991i	0.262295	+	0.365327i
$397$	27.6975	−	15.9911i	1.39010	−	0.802573i	0.396771	−	0.917917i	$-0.370131\pi$
$397$	27.6975	−	15.9911i	1.39010	−	0.802573i	0.993326	+	0.115345i	$0.0367973\pi$
$398$	−6.34451	+	1.11871i	−0.318022	+	0.0560758i
$399$	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	$0.0965554\pi$
$402$	−5.73634	−	8.88788i	−0.286103	−	0.443287i
$403$	−34.6846	−	41.3355i	−1.72776	−	2.05907i
$404$	5.47099			0.272192
$405$		0			0
$406$	0.189410			0.00940028
$407$	−3.71846	−	4.43149i	−0.184317	−	0.219661i
$408$	15.2794	+	23.6739i	0.756444	+	1.17203i
$409$	−4.07496	+	23.1102i	−0.201494	+	1.14273i	0.701369	+	0.712799i	$0.252573\pi$
$409$	−4.07496	+	23.1102i	−0.201494	+	1.14273i	−0.902863	+	0.429929i	$0.858538\pi$
$410$		0			0
$411$	8.16630	−	26.4442i	0.402814	−	1.30440i
$412$	13.5078	−	2.38179i	0.665482	−	0.117342i
$413$	3.08612	−	1.78177i	0.151858	−	0.0876752i
$414$	16.9594	−	1.68599i	0.833507	−	0.0828618i
$415$		0			0
$416$	−33.6384	−	12.2434i	−1.64926	−	0.600281i
$417$	−5.35397	+	2.25485i	−0.262185	+	0.110421i
$418$	−5.32686	+	6.34831i	−0.260545	+	0.310506i
$419$	7.14090	+	5.99192i	0.348856	+	0.292725i	0.800330	−	0.599559i	$-0.204657\pi$
$419$	7.14090	+	5.99192i	0.348856	+	0.292725i	−0.451475	+	0.892284i	$0.649102\pi$
$420$		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	$0.811476\pi$
$422$	12.6614	+	7.31007i	0.616348	+	0.355849i
$423$	0.615219	−	2.40961i	0.0299130	−	0.117159i
$424$	12.5950	+	21.8151i	0.611665	+	1.05943i
$425$		0			0
$426$	3.30693	+	3.56633i	0.160221	+	0.172789i
$427$	0.559575	+	1.53742i	0.0270797	+	0.0744009i
$428$	−13.9434	−	2.45860i	−0.673982	−	0.118841i
$429$	−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	$0.581738\pi$
$432$	0.153973	+	0.0312814i	0.00740802	+	0.00150503i
$433$			4.12615i			0.198290i	0.995073	+	0.0991451i	$0.0316108\pi$
$433$			4.12615i			0.198290i	−0.995073	+	0.0991451i	$0.968389\pi$
$434$	2.91141	−	2.44296i	0.139752	−	0.117266i
$435$		0			0
$436$	3.58938	−	20.3564i	0.171900	−	0.974894i
$437$	−8.60924	−	23.6537i	−0.411836	−	1.13151i
$438$	−4.04956	−	17.7687i	−0.193495	−	0.849021i
$439$	2.08794	+	11.8413i	0.0996517	+	0.565153i	0.993222	+	0.116230i	$0.0370811\pi$
$439$	2.08794	+	11.8413i	0.0996517	+	0.565153i	−0.893571	+	0.448923i	$0.851808\pi$
$440$		0			0
$441$	1.52428	−	20.1655i	0.0725847	−	0.960262i
$442$	−27.6729	−	15.9770i	−1.31627	−	0.759948i
$443$	11.5970	−	31.8626i	0.550992	−	1.51384i	−0.281367	−	0.959600i	$-0.590788\pi$
$443$	11.5970	−	31.8626i	0.550992	−	1.51384i	0.832359	−	0.554237i	$-0.186990\pi$
$444$	5.03599	+	0.632742i	0.238998	+	0.0300286i
$445$		0			0
$446$	−5.70120	−	4.78387i	−0.269960	−	0.226523i
$447$	0.462392	−	3.68018i	0.0218704	−	0.174066i
$448$	0.872871	−	2.39819i	0.0412393	−	0.113304i
$449$	−0.297582	+	0.515427i	−0.0140438	+	0.0243245i	−0.872962	−	0.487788i	$-0.837804\pi$
$449$	−0.297582	+	0.515427i	−0.0140438	+	0.0243245i	0.858918	+	0.512113i	$0.171137\pi$
$450$		0			0
$451$	1.48580	+	2.57349i	0.0699638	+	0.121181i
$452$	12.9596	−	2.28512i	0.609567	−	0.107483i
$453$	6.06562	+	26.6148i	0.284988	+	1.25047i
$454$	−7.99960	+	2.91162i	−0.375440	+	0.136649i
$455$		0			0
$456$	−0.945929	−	19.0771i	−0.0442972	−	0.893367i
$457$	5.70374	+	6.79746i	0.266810	+	0.317972i	0.882770	−	0.469806i	$-0.155676\pi$
$457$	5.70374	+	6.79746i	0.266810	+	0.317972i	−0.615960	+	0.787778i	$0.711232\pi$
$458$		−	0.137535i		−	0.00642659i
$459$	−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	$0.476331\pi$
$462$	0.857259	−	1.67082i	0.0398833	−	0.0777335i
$463$	11.2994	+	1.99238i	0.525126	+	0.0925939i	0.429926	−	0.902864i	$-0.358540\pi$
$463$	11.2994	+	1.99238i	0.525126	+	0.0925939i	0.0952002	+	0.995458i	$0.469651\pi$
$464$	0.0120462	−	0.00438444i	0.000559229	−	0.000203543i
$465$		0			0
$466$	2.48226	+	14.0776i	0.114989	+	0.652132i
$467$	−0.568149	+	0.328021i	−0.0262908	+	0.0151790i	−0.513088	−	0.858336i	$-0.671498\pi$
$467$	−0.568149	+	0.328021i	−0.0262908	+	0.0151790i	0.486797	+	0.873515i	$0.338165\pi$
$468$	22.5227	−	6.32122i	1.04111	−	0.292198i
$469$	1.77020	−	3.06608i	0.0817403	−	0.141578i
$470$		0			0
$471$	22.9243	−	30.2439i	1.05629	−	1.39357i
$472$	12.7602	−	15.2071i	0.587338	−	0.699962i
$473$	3.90008	−	4.64793i	0.179326	−	0.213712i
$474$	1.59057	+	3.77669i	0.0730575	+	0.173469i
$475$		0			0
$476$	−1.79491	+	3.10888i	−0.0822697	+	0.142495i
$477$	−24.2901	−	10.9790i	−1.11217	−	0.502693i
$478$	15.3310	−	8.85134i	0.701223	−	0.404851i
$479$	−3.87971	−	22.0029i	−0.177269	−	1.00534i	−0.935493	−	0.353346i	$-0.885044\pi$
$479$	−3.87971	−	22.0029i	−0.177269	−	1.00534i	0.758224	−	0.651994i	$-0.226067\pi$
$480$		0			0
$481$	−14.2089	+	5.17162i	−0.647871	+	0.235806i
$482$	22.8046	+	4.02106i	1.03872	+	0.183154i
$483$	3.09316	+	4.79254i	0.140744	+	0.218068i
$484$	−4.81285	+	4.03846i	−0.218766	+	0.183566i
$485$		0			0
$486$	−12.4831	+	5.60836i	−0.566244	+	0.254401i
$487$		−	28.3011i		−	1.28245i	−0.767354	−	0.641224i	$-0.778427\pi$
$487$		−	28.3011i		−	1.28245i	0.767354	−	0.641224i	$-0.221573\pi$
$488$	5.85846	+	6.98184i	0.265200	+	0.316053i
$489$	−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	$0.971092\pi$
$492$	−2.49116	−	0.769302i	−0.112310	−	0.0346828i
$493$	−2.39577	+	0.422438i	−0.107900	+	0.0190257i
$494$	10.8306	+	18.7592i	0.487293	+	0.844015i
$495$		0			0
$496$	0.128611	−	0.222761i	0.00577480	−	0.0100022i
$497$	−0.556732	+	1.52961i	−0.0249729	+	0.0686124i
$498$	10.9862	−	4.62691i	0.492304	−	0.207337i
$499$	3.09802	+	2.59955i	0.138686	+	0.116372i	0.709492	−	0.704714i	$-0.248924\pi$
$499$	3.09802	+	2.59955i	0.138686	+	0.116372i	−0.570805	+	0.821085i	$0.693369\pi$
$500$		0			0
$501$	−18.1300	+	23.9189i	−0.809991	+	1.06862i
$502$	6.39492	−	17.5699i	0.285419	−	0.784183i
$503$	−20.7321	−	11.9697i	−0.924399	−	0.533702i	−0.0393633	−	0.999225i	$-0.512533\pi$
$503$	−20.7321	−	11.9697i	−0.924399	−	0.533702i	−0.885036	+	0.465523i	$0.845866\pi$
$504$	1.16958	+	4.16726i	0.0520974	+	0.185624i
$505$		0			0
$506$	−2.39398	−	13.5769i	−0.106425	−	0.603569i
$507$	−34.5912	+	32.0752i	−1.53625	+	1.42451i
$508$	3.27644	+	9.00195i	0.145369	+	0.399397i
$509$	4.85069	−	27.5096i	0.215003	−	1.21934i	−0.665898	−	0.746043i	$-0.731951\pi$
$509$	4.85069	−	27.5096i	0.215003	−	1.21934i	0.880901	−	0.473300i	$-0.156937\pi$
$510$		0			0
$511$	4.67243	−	3.92064i	0.206696	−	0.173439i
$512$		−	0.342088i		−	0.0151183i
$513$	12.5868	+	15.8148i	0.555723	+	0.698239i
$514$	−10.1105			−0.445953
$515$		0			0
$516$	0.263639	+	5.31695i	0.0116060	+	0.234066i
$517$	−1.98115	−	0.349331i	−0.0871310	−	0.0153635i
$518$	−0.364256	−	1.00078i	−0.0160045	−	0.0439719i
$519$	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	$0.919045\pi$
$522$	−0.629577	+	0.922142i	−0.0275559	+	0.0403610i
$523$	−19.4691	−	11.2405i	−0.851324	−	0.491512i	0.00977335	−	0.999952i	$-0.496889\pi$
$523$	−19.4691	−	11.2405i	−0.851324	−	0.491512i	−0.861097	+	0.508440i	$0.830222\pi$
$524$	−10.1278	−	3.68622i	−0.442436	−	0.161033i
$525$		0			0
$526$	7.27576	+	6.10509i	0.317238	+	0.266195i
$527$	−31.3765	+	37.3931i	−1.36678	+	1.62887i
$528$	0.0158443	−	0.126105i	0.000689534	−	0.00548800i
$529$	17.7371	+	6.45579i	0.771180	+	0.280687i
$530$		0			0
$531$	−1.58336	+	20.9471i	−0.0687119	+	0.909027i
$532$	2.10748	−	1.21675i	0.0913706	−	0.0527529i
$533$	7.64931	−	1.34878i	0.331328	−	0.0584221i
$534$	27.4192	−	6.24895i	1.18655	−	0.270419i
$535$		0			0
$536$	3.42478	−	19.4229i	0.147928	−	0.838941i
$537$	42.1434	−	2.08966i	1.81862	−	0.0901756i
$538$	15.5701	+	18.5557i	0.671276	+	0.799995i
$539$	−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	$0.657977\pi$
$542$	12.5800	+	14.9922i	0.540357	+	0.643972i
$543$	3.22525	−	6.28609i	0.138409	−	0.269762i
$544$	−5.62326	+	31.8911i	−0.241095	+	1.36732i
$545$		0			0
$546$	−3.33750	−	3.59929i	−0.142832	−	0.154036i
$547$	9.43459	−	1.66357i	0.403394	−	0.0711292i	0.0317297	−	0.999496i	$-0.489898\pi$
$547$	9.43459	−	1.66357i	0.403394	−	0.0711292i	0.371664	+	0.928367i	$0.378787\pi$
$548$	17.0113	−	9.82146i	0.726685	−	0.419552i
$549$	−9.34486	−	2.38591i	−0.398829	−	0.101828i
$550$		0			0
$551$	1.54966	+	0.564031i	0.0660179	+	0.0240285i
$552$	25.3231	+	19.1943i	1.07782	+	0.816966i
$553$	−0.881604	+	1.05065i	−0.0374896	+	0.0446784i
$554$	−13.7724	−	11.5564i	−0.585132	−	0.490984i
$555$		0			0
$556$	−3.87449	−	1.41020i	−0.164315	−	0.0598058i
$557$	0.0783859	+	0.0452561i	0.00332132	+	0.00191756i	0.501660	−	0.865065i	$-0.332723\pi$
$557$	0.0783859	+	0.0452561i	0.00332132	+	0.00191756i	−0.498338	+	0.866983i	$0.666056\pi$
$558$	2.21635	+	22.2942i	0.0938255	+	0.943790i
$559$	−7.92967	−	13.7346i	−0.335389	−	0.580911i
$560$		0			0
$561$	−7.11668	+	23.0453i	−0.300467	+	0.972975i
$562$	4.73491	+	13.0090i	0.199730	+	0.548753i
$563$	−14.4906	−	2.55509i	−0.610707	−	0.107684i	−0.140263	−	0.990114i	$-0.544795\pi$
$563$	−14.4906	−	2.55509i	−0.610707	−	0.107684i	−0.470443	+	0.882430i	$0.655906\pi$
$564$	1.48299	−	0.957142i	0.0624453	−	0.0403029i
$565$		0			0
$566$	−9.27354			−0.389796
$567$	−3.57726	−	2.86033i	−0.150231	−	0.120122i
$568$			9.06785i			0.380479i
$569$	5.30885	−	4.45466i	0.222559	−	0.186749i	−0.524690	−	0.851293i	$-0.675819\pi$
$569$	5.30885	−	4.45466i	0.222559	−	0.186749i	0.747249	+	0.664544i	$0.231374\pi$
$570$		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	$0.842497\pi$
$572$	−6.47205	−	17.7818i	−0.270610	−	0.743495i
$573$	−12.3205	−	3.80473i	−0.514697	−	0.158945i
$574$	0.0949993	+	0.538768i	0.00396519	+	0.0224877i
$575$		0			0
$576$	8.77425	+	12.2209i	0.365594	+	0.509202i
$577$	3.98675	+	2.30175i	0.165970	+	0.0958231i	0.580684	−	0.814129i	$-0.302785\pi$
$577$	3.98675	+	2.30175i	0.165970	+	0.0958231i	−0.414714	+	0.909952i	$0.636118\pi$
$578$	−4.78215	+	13.1389i	−0.198911	+	0.546505i
$579$	−6.21886	−	14.7662i	−0.258447	−	0.613662i
$580$		0			0
$581$	3.05631	+	2.56455i	0.126797	+	0.106395i
$582$	10.1373	+	7.68382i	0.420203	+	0.318505i
$583$	−7.37486	+	20.2623i	−0.305435	+	0.839177i
$584$	16.9890	−	29.4259i	0.703011	−	1.21765i
$585$		0			0
$586$	−7.24214	−	12.5438i	−0.299170	−	0.518178i
$587$	−9.60364	+	1.69338i	−0.396384	+	0.0698933i	−0.368288	−	0.929712i	$-0.620056\pi$
$587$	−9.60364	+	1.69338i	−0.396384	+	0.0698933i	−0.0280969	+	0.999605i	$0.508945\pi$
$588$	10.5246	−	9.75911i	0.434028	−	0.402459i
$589$	31.0944	−	11.3174i	1.28122	−	0.466327i
$590$		0			0
$591$	13.9307	+	7.14752i	0.573032	+	0.294010i
$592$	−0.0463320	−	0.0552163i	−0.00190423	−	0.00226938i
$593$		−	1.52185i		−	0.0624948i	−0.999512	−	0.0312474i	$-0.990052\pi$
$593$		−	1.52185i		−	0.0624948i	0.999512	−	0.0312474i	$-0.00994798\pi$
$594$	5.28492	+	9.72714i	0.216843	+	0.399110i
$595$		0			0
$596$	2.01660	−	1.69213i	0.0826032	−	0.0693123i
$597$	12.6949	−	0.629473i	0.519569	−	0.0257626i
$598$	−35.4880	−	6.25749i	−1.45121	−	0.255888i
$599$	−24.2758	+	8.83566i	−0.991881	+	0.361015i	−0.786448	−	0.617656i	$-0.788082\pi$
$599$	−24.2758	+	8.83566i	−0.991881	+	0.361015i	−0.205433	+	0.978671i	$0.565860\pi$
$600$		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	$-0.169157\pi$
$602$	0.967376	−	0.558515i	0.0394273	−	0.0227634i
$603$	9.04322	+	18.8095i	0.368268	+	0.765981i
$604$	−9.68689	+	16.7782i	−0.394154	+	0.682695i
$605$		0			0
$606$	6.71448	+	0.843633i	0.272757	+	0.0342703i
$607$	−8.08708	+	9.63781i	−0.328244	+	0.391187i	−0.904776	−	0.425889i	$-0.859962\pi$
$607$	−8.08708	+	9.63781i	−0.328244	+	0.391187i	0.576531	+	0.817075i	$0.304406\pi$
$608$	14.1106	−	16.8163i	0.572259	−	0.681991i
$609$	−0.370783	−	0.0465866i	−0.0150249	−	0.00188779i
$610$		0			0
$611$	−2.62915	+	4.55382i	−0.106364	+	0.184228i
$612$	−9.16946	−	19.0720i	−0.370653	−	0.770942i
$613$	−20.4069	+	11.7819i	−0.824226	+	0.475867i	−0.851872	−	0.523750i	$-0.824532\pi$
$613$	−20.4069	+	11.7819i	−0.824226	+	0.475867i	0.0276453	+	0.999618i	$0.491199\pi$
$614$	2.18495	+	12.3914i	0.0881773	+	0.500078i
$615$		0			0
$616$	3.29008	−	1.19749i	0.132561	−	0.0482483i
$617$	11.4279	+	2.01505i	0.460071	+	0.0811229i	0.398880	−	0.917003i	$-0.369399\pi$
$617$	11.4279	+	2.01505i	0.460071	+	0.0811229i	0.0611910	+	0.998126i	$0.480510\pi$
$618$	16.9452	−	0.840222i	0.681638	−	0.0337987i
$619$	15.1620	−	12.7224i	0.609411	−	0.511357i	−0.285044	−	0.958514i	$-0.592008\pi$
$619$	15.1620	−	12.7224i	0.609411	−	0.511357i	0.894455	+	0.447158i	$0.147564\pi$
$620$		0			0
$621$	−33.6137	−	0.870823i	−1.34887	−	0.0349449i
$622$			27.9056i			1.11891i
$623$	6.05001	+	7.21012i	0.242388	+	0.288867i
$624$	−0.295575	−	0.151653i	−0.0118325	−	0.00607097i
$625$		0			0
$626$	−14.0852	+	5.12660i	−0.562959	+	0.204900i
$627$	11.9891	−	11.1170i	0.478797	−	0.443972i
$628$	26.5254	−	4.67714i	1.05848	−	0.186638i
$629$	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	$0.260276\pi$
$632$	−2.61317	+	7.17962i	−0.103946	+	0.285590i
$633$	−22.9876	−	17.4241i	−0.913673	−	0.692545i
$634$	−9.18168	−	7.70434i	−0.364651	−	0.305979i
$635$		0			0
$636$	−7.34307	−	17.4355i	−0.291172	−	0.691364i
$637$	−14.6246	+	40.1807i	−0.579446	+	1.59202i
$638$	0.782203	+	0.451605i	0.0309677	+	0.0178792i
$639$	−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	$0.818819\pi$
$642$	−16.7335	−	5.16751i	−0.660418	−	0.203945i
$643$	−1.08118	−	2.97050i	−0.0426374	−	0.117145i	0.916547	−	0.399928i	$-0.130965\pi$
$643$	−1.08118	−	2.97050i	−0.0426374	−	0.117145i	−0.959184	+	0.282782i	$0.908743\pi$
$644$	−0.702989	+	3.98685i	−0.0277017	+	0.157104i
$645$		0			0
$646$	15.0109	−	12.5956i	0.590594	−	0.495567i
$647$			18.5045i			0.727489i	0.931499	+	0.363744i	$0.118502\pi$
$647$			18.5045i			0.727489i	−0.931499	+	0.363744i	$0.881498\pi$
$648$	−24.1758	−	8.15736i	−0.949714	−	0.320451i
$649$	16.9929			0.667029
$650$		0			0
$651$	−6.30012	+	4.06617i	−0.246921	+	0.159366i
$652$	−24.1770	−	4.26306i	−0.946844	−	0.166954i
$653$	3.88059	+	10.6618i	0.151859	+	0.417230i	0.992173	−	0.124870i	$-0.0398515\pi$
$653$	3.88059	+	10.6618i	0.151859	+	0.417230i	−0.840314	+	0.542100i	$0.817629\pi$
$654$	7.54418	−	24.4297i	0.295001	−	0.955276i
$655$		0			0
$656$	0.0185131	+	0.0320656i	0.000722815	+	0.00125195i
$657$	3.55695	+	35.7794i	0.138770	+	1.39589i
$658$	−0.320742	−	0.185180i	−0.0125038	−	0.00721908i
$659$	24.1280	+	8.78187i	0.939893	+	0.342093i	0.766124	−	0.642693i	$-0.222183\pi$
$659$	24.1280	+	8.78187i	0.939893	+	0.342093i	0.173769	+	0.984786i	$0.444405\pi$
$660$		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	$0.772196\pi$
$662$	−15.9770	+	19.0406i	−0.620962	+	0.740033i
$663$	50.2419	+	38.0823i	1.95123	+	1.47899i
$664$	20.8852	+	7.60159i	0.810502	+	0.294999i
$665$		0			0
$666$	6.08304	+	1.55311i	0.235713	+	0.0601819i
$667$	−2.37590	+	1.37173i	−0.0919954	+	0.0531135i
$668$	−20.9781	+	3.69900i	−0.811665	+	0.143118i
$669$	9.98383	+	10.7670i	0.385997	+	0.416275i
$670$		0			0
$671$	−1.35476	+	7.68321i	−0.0522999	+	0.296607i
$672$	−2.27083	+	4.42590i	−0.0875992	+	0.170733i
$673$	8.78341	+	10.4677i	0.338576	+	0.403499i	0.908288	−	0.418346i	$-0.137390\pi$
$673$	8.78341	+	10.4677i	0.338576	+	0.403499i	−0.569712	+	0.821844i	$0.692945\pi$
$674$	−15.2185			−0.586193
$675$		0			0
$676$	−33.4809			−1.28773
$677$	−28.2299	−	33.6430i	−1.08496	−	1.29301i	−0.953404	−	0.301698i	$-0.902447\pi$
$677$	−28.2299	−	33.6430i	−1.08496	−	1.29301i	−0.131558	−	0.991308i	$-0.541998\pi$
$678$	16.2575	−	0.806121i	0.624366	−	0.0309589i
$679$	−0.739271	+	4.19262i	−0.0283706	+	0.160898i
$680$		0			0
$681$	16.3759	−	3.73213i	0.627524	−	0.143015i
$682$	17.8478	−	3.14705i	0.683428	−	0.120507i
$683$	−3.72885	+	2.15285i	−0.142681	+	0.0823767i	−0.569641	−	0.821894i	$-0.692918\pi$
$683$	−3.72885	+	2.15285i	−0.142681	+	0.0823767i	0.426960	+	0.904270i	$0.359584\pi$
$684$	−1.08126	+	14.3045i	−0.0413429	+	0.546948i
$685$		0			0
$686$	−5.76886	−	2.09969i	−0.220256	−	0.0801667i
$687$	−0.0338276	+	0.269234i	−0.00129060	+	0.0102719i
$688$	0.0485949	−	0.0579132i	0.00185266	−	0.00220792i
$689$	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	$0.464255\pi$
$692$	15.2496	+	8.80438i	0.579704	+	0.334692i
$693$	−2.08909	+	3.05988i	−0.0793578	+	0.116235i
$694$	1.47875	+	2.56127i	0.0561326	+	0.0972245i
$695$		0			0
$696$	−2.02971	+	0.462580i	−0.0769361	+	0.0175341i
$697$	−2.40320	−	6.60275i	−0.0910279	−	0.250097i
$698$	−5.92555	−	1.04484i	−0.224286	−	0.0395476i
$699$	−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	$0.408401\pi$
$702$	28.6165	−	4.28493i	1.08006	−	0.161724i
$703$		−	9.27261i		−	0.349723i
$704$	9.32261	−	7.82260i	0.351359	−	0.294825i
$705$		0			0
$706$	4.64765	−	26.3581i	0.174917	−	0.992002i
$707$	0.774645	+	2.12832i	0.0291335	+	0.0800437i
$708$	−10.9326	+	10.1374i	−0.410871	+	0.380986i
$709$	−4.68507	−	26.5704i	−0.175952	−	0.997871i	−0.937040	−	0.349223i	$-0.886446\pi$
$709$	−4.68507	−	26.5704i	−0.175952	−	0.997871i	0.761088	−	0.648648i	$-0.224665\pi$
$710$		0			0
$711$	−2.18475	−	7.78432i	−0.0819345	−	0.291935i
$712$	45.4076	+	26.2161i	1.70172	+	0.982489i
$713$	−18.8276	+	51.7284i	−0.705098	+	1.93724i
$714$	−2.68227	+	3.53871i	−0.100381	+	0.132433i
$715$		0			0
$716$	22.9410	+	19.2498i	0.857347	+	0.719399i
$717$	−32.1884	+	13.5563i	−1.20210	+	0.506270i
$718$	4.50480	−	12.3768i	0.168118	−	0.461900i
$719$	21.0623	−	36.4809i	0.785490	−	1.36051i	−0.143216	−	0.989691i	$-0.545745\pi$
$719$	21.0623	−	36.4809i	0.785490	−	1.36051i	0.928706	−	0.370817i	$-0.120922\pi$
$720$		0			0
$721$	2.83915	+	4.91756i	0.105736	+	0.183139i
$722$	3.34502	−	0.589817i	0.124489	−	0.0219507i
$723$	−43.6524	−	13.4804i	−1.62345	−	0.501342i
$724$	4.71202	−	1.71503i	0.175121	−	0.0637388i
$725$		0			0
$726$	−6.52948	+	4.21420i	−0.242332	+	0.156404i
$727$	6.68233	+	7.96369i	0.247834	+	0.295357i	0.875592	−	0.483052i	$-0.160472\pi$
$727$	6.68233	+	7.96369i	0.247834	+	0.295357i	−0.627758	+	0.778409i	$0.716027\pi$
$728$		−	9.15166i		−	0.339183i
$729$	25.8158	−	7.90844i	0.956142	−	0.292905i
$730$		0			0
$731$	−10.9902	+	9.22191i	−0.406489	+	0.341085i
$732$	−3.71194	−	5.75128i	−0.137197	−	0.212574i
$733$	44.1484	+	7.78456i	1.63066	+	0.287529i	0.912723	−	0.408579i	$-0.133976\pi$
$733$	44.1484	+	7.78456i	1.63066	+	0.287529i	0.717937	+	0.696108i	$0.245087\pi$
$734$	−13.6936	+	4.98406i	−0.505440	+	0.183965i
$735$		0			0
$736$	6.34152	+	35.9646i	0.233752	+	1.32567i
$737$	14.6207	−	8.44127i	0.538561	−	0.310938i
$738$	−2.93875	−	1.32830i	−0.108177	−	0.0488952i
$739$	−8.15749	+	14.1292i	−0.300078	+	0.519751i	−0.976153	−	0.217082i	$-0.930346\pi$
$739$	−8.15749	+	14.1292i	−0.300078	+	0.519751i	0.676075	+	0.736833i	$0.263679\pi$
$740$		0			0
$741$	−16.5877	−	39.3861i	−0.609364	−	1.44689i
$742$	−2.55169	+	3.04099i	−0.0936755	+	0.111638i
$743$	7.43409	−	8.85961i	0.272730	−	0.325028i	−0.612242	−	0.790670i	$-0.709732\pi$
$743$	7.43409	−	8.85961i	0.272730	−	0.325028i	0.884973	+	0.465643i	$0.154177\pi$
$744$	−25.2323	+	33.2889i	−0.925060	+	1.22043i
$745$		0			0
$746$	−3.06915	+	5.31592i	−0.112369	+	0.194630i
$747$	−22.6442	+	6.35534i	−0.828509	+	0.232530i
$748$	−14.8248	+	8.55910i	−0.542049	+	0.312952i
$749$	−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	$0.502505\pi$
$752$	−0.0246851	−	0.00435265i	−0.000900174	−	0.000158725i
$753$	−16.8399	+	32.8213i	−0.613679	+	1.19607i
$754$	1.80852	−	1.51753i	0.0658623	−	0.0552650i
$755$		0			0
$756$	−0.481385	−	3.21489i	−0.0175078	−	0.116924i
$757$		−	8.63554i		−	0.313864i	−0.987609	−	0.156932i	$-0.949840\pi$
$757$		−	8.63554i		−	0.313864i	0.987609	−	0.156932i	$-0.0501603\pi$
$758$	7.77575	+	9.26677i	0.282428	+	0.336584i
$759$	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	$0.395069\pi$
$762$	2.63302	+	11.5532i	0.0953844	+	0.418529i
$763$	8.42726	−	1.48595i	0.305087	−	0.0537951i
$764$	−4.57588	−	7.92566i	−0.165550	−	0.286740i
$765$		0			0
$766$	−4.50428	+	7.80164i	−0.162746	+	0.281885i
$767$	15.1914	−	41.7380i	0.548530	−	1.50707i
$768$	−3.47064	+	27.6228i	−0.125236	+	0.996752i
$769$	−7.27290	−	6.10268i	−0.262267	−	0.220068i	0.502166	−	0.864771i	$-0.332537\pi$
$769$	−7.27290	−	6.10268i	−0.262267	−	0.220068i	−0.764433	+	0.644703i	$0.776981\pi$
$770$		0			0
$771$	19.7918	+	2.48672i	0.712786	+	0.0895572i
$772$	3.88931	−	10.6858i	0.139979	−	0.384590i
$773$	0.670964	+	0.387381i	0.0241329	+	0.0139331i	0.512018	−	0.858975i	$-0.328898\pi$
$773$	0.670964	+	0.387381i	0.0241329	+	0.0139331i	−0.487885	+	0.872908i	$0.662231\pi$
$774$	−0.496320	+	6.56609i	−0.0178399	+	0.236013i
$775$		0			0
$776$	4.11826	+	23.3558i	0.147837	+	0.838424i
$777$	0.466905	+	2.04869i	0.0167501	+	0.0734963i
$778$	−11.5032	−	31.6047i	−0.412409	−	1.13308i
$779$	−0.827119	+	4.69082i	−0.0296346	+	0.168066i
$780$		0			0
$781$	−5.94612	+	4.98939i	−0.212769	+	0.178534i
$782$			32.5985i			1.16572i
$783$	1.45924	−	1.65030i	0.0521491	−	0.0589770i
$784$	−0.203831			−0.00727967
$785$		0			0
$786$	−11.8613	−	6.08578i	−0.423080	−	0.217073i
$787$	−7.13632	−	1.25833i	−0.254382	−	0.0448545i	0.0450026	−	0.998987i	$-0.485670\pi$
$787$	−7.13632	−	1.25833i	−0.254382	−	0.0448545i	−0.299385	+	0.954132i	$0.596781\pi$
$788$	3.80071	+	10.4424i	0.135395	+	0.371994i
$789$	−12.7412	−	13.7406i	−0.453598	−	0.489179i
$790$		0			0
$791$	2.72392	+	4.71797i	0.0968515	+	0.167752i
$792$	−5.10586	+	19.9980i	−0.181429	+	0.710598i
$793$	17.6604	+	10.1963i	0.627140	+	0.362080i
$794$	26.3839	+	9.60296i	0.936330	+	0.340796i
$795$		0			0
$796$	6.91057	+	5.79865i	0.244939	+	0.205528i
$797$	−20.4001	+	24.3118i	−0.722607	+	0.861170i	−0.994881	−	0.101050i	$-0.967780\pi$
$797$	−20.4001	+	24.3118i	−0.722607	+	0.861170i	0.272274	+	0.962220i	$0.412224\pi$
$798$	2.77410	−	1.16833i	0.0982022	−	0.0413584i
$799$	4.46992	+	1.62692i	0.158134	+	0.0575562i
$800$		0			0
$801$	−55.2118	+	5.48880i	−1.95081	+	0.193937i
$802$	−3.91118	+	2.25812i	−0.138108	+	0.0797369i
$803$	28.6435	−	5.05061i	1.01081	−	0.178232i
$804$	−4.37062	+	14.1530i	−0.154140	+	0.499138i
$805$		0			0
$806$	8.22590	−	46.6514i	0.289745	−	1.64322i
$807$	−25.9156	−	40.1536i	−0.912272	−	1.41347i
$808$	8.11014	+	9.66529i	0.285314	+	0.340024i
$809$	−48.9871			−1.72230			−0.861148	−	0.508355i	$-0.830254\pi$
$809$	−48.9871			−1.72230			−0.861148	+	0.508355i	$0.830254\pi$
$810$		0			0
$811$	34.5483			1.21316			0.606578	−	0.795024i	$-0.292542\pi$
$811$	34.5483			1.21316			0.606578	+	0.795024i	$0.292542\pi$
$812$	−0.170484	−	0.203175i	−0.00598283	−	0.00713006i
$813$	−20.9387	−	32.4424i	−0.734352	−	1.13780i
$814$	0.881881	−	5.00139i	0.0309099	−	0.175299i
$815$		0			0
$816$	−0.0886738	+	0.287144i	−0.00310420	+	0.0100521i
$817$	9.57775	−	1.68882i	0.335083	−	0.0590842i
$818$	−17.8413	+	10.3007i	−0.623808	+	0.360156i
$819$	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	$0.525618\pi$
$822$	22.3922	−	9.43060i	0.781018	−	0.328930i
$823$	4.08912	−	4.87323i	0.142538	−	0.169870i	−0.690052	−	0.723759i	$-0.742413\pi$
$823$	4.08912	−	4.87323i	0.142538	−	0.169870i	0.832590	+	0.553889i	$0.186857\pi$
$824$	24.2316	+	20.3327i	0.844148	+	0.708324i
$825$		0			0
$826$	2.93976	+	1.06998i	0.102287	+	0.0372295i
$827$	−41.7075	−	24.0799i	−1.45031	−	0.837339i	−0.451815	−	0.892112i	$-0.649223\pi$
$827$	−41.7075	−	24.0799i	−1.45031	−	0.837339i	−0.998499	+	0.0547729i	$0.982557\pi$
$828$	−17.0733	−	16.6743i	−0.593337	−	0.579472i
$829$	−23.1268	−	40.0568i	−0.803227	−	1.39123i	−0.917482	−	0.397778i	$-0.869782\pi$
$829$	−23.1268	−	40.0568i	−0.803227	−	1.39123i	0.114255	−	0.993451i	$-0.463552\pi$
$830$		0			0
$831$	24.1179	+	26.0098i	0.836641	+	0.902269i
$832$	−10.8796	−	29.8916i	−0.377184	−	1.03630i
$833$	38.0935	+	6.71691i	1.31986	+	0.232727i
$834$	−4.53766	−	2.32817i	−0.157126	−	0.0806180i
$835$		0			0
$836$	11.6042			0.401341
$837$	1.14476	−	44.1875i	0.0395686	−	1.52734i
$838$			8.18356i			0.282696i
$839$	−18.8397	+	15.8084i	−0.650418	+	0.545765i	−0.907198	−	0.420705i	$-0.861783\pi$
$839$	−18.8397	+	15.8084i	−0.650418	+	0.545765i	0.256780	+	0.966470i	$0.417338\pi$
$840$		0			0
$841$	−5.00459	+	28.3824i	−0.172572	+	0.978704i
$842$	−7.25385	−	19.9298i	−0.249984	−	0.686826i
$843$	−6.06922	−	26.6306i	−0.209035	−	0.917207i
$844$	−3.55496	−	20.1612i	−0.122367	−	0.693976i
$845$		0			0
$846$	1.96765	−	0.946009i	0.0676493	−	0.0325245i
$847$	−2.25250	−	1.30048i	−0.0773967	−	0.0446850i
$848$	−0.0918906	+	0.252467i	−0.00315554	+	0.00866977i
$849$	18.1535	+	2.28088i	0.623028	+	0.0782796i
$850$		0			0
$851$	11.8169	+	9.91554i	0.405077	+	0.339900i
$852$	0.849005	−	6.75723i	0.0290864	−	0.231499i
$853$	5.09720	−	14.0044i	0.174525	−	0.479503i	−0.821331	−	0.570452i	$-0.806768\pi$
$853$	5.09720	−	14.0044i	0.174525	−	0.479503i	0.995856	+	0.0909495i	$0.0289902\pi$
$854$	−0.718158	+	1.24389i	−0.0245749	+	0.0425649i
$855$		0			0
$856$	−16.3261	−	28.2777i	−0.558016	−	0.966512i
$857$	35.0389	−	6.17830i	1.19690	−	0.211047i	0.460545	−	0.887636i	$-0.347654\pi$
$857$	35.0389	−	6.17830i	1.19690	−	0.211047i	0.736360	+	0.676590i	$0.236543\pi$
$858$	−5.20109	−	22.8214i	−0.177562	−	0.779110i
$859$	−20.6271	+	7.50764i	−0.703787	+	0.256157i	−0.669027	−	0.743238i	$-0.733289\pi$
$859$	−20.6271	+	7.50764i	−0.703787	+	0.256157i	−0.0347598	+	0.999396i	$0.511067\pi$
$860$		0			0
$861$	−0.0534540	−	1.07804i	−0.00182171	−	0.0367394i
$862$	−5.95074	−	7.09181i	−0.202683	−	0.241548i
$863$			6.43512i			0.219054i	0.993984	+	0.109527i	$0.0349336\pi$
$863$			6.43512i			0.219054i	−0.993984	+	0.109527i	$0.965066\pi$
$864$	−13.9995	−	25.7667i	−0.476271	−	0.876600i
$865$		0			0
$866$	−2.77487	+	2.32839i	−0.0942940	+	0.0791220i
$867$	12.5929	−	24.5439i	0.427679	−	0.833556i
$868$	−5.24099	−	0.924127i	−0.177891	−	0.0313669i
$869$	−6.14578	+	2.23688i	−0.208481	+	0.0758809i
$870$		0			0
$871$	−7.66280	−	43.4579i	−0.259644	−	1.47251i
$872$	41.2833	−	23.8350i	1.39803	−	0.807153i
$873$	−17.9544	−	17.5349i	−0.607666	−	0.593466i
$874$	11.0491	−	19.1376i	0.373741	−	0.647339i
$875$		0			0
$876$	−15.4151	+	20.3371i	−0.520827	+	0.687126i
$877$	8.66977	−	10.3322i	0.292757	−	0.348895i	−0.599538	−	0.800346i	$-0.704649\pi$
$877$	8.66977	−	10.3322i	0.292757	−	0.348895i	0.892296	+	0.451451i	$0.149094\pi$
$878$	−6.78513	+	8.08620i	−0.228987	+	0.272896i
$879$	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	$-0.00265199\pi$
$882$	14.4216	−	10.3543i	0.485601	−	0.348648i
$883$	−6.71129	+	3.87477i	−0.225853	+	0.130396i	−0.608658	−	0.793433i	$-0.708292\pi$
$883$	−6.71129	+	3.87477i	−0.225853	+	0.130396i	0.382804	+	0.923829i	$0.374958\pi$
$884$	7.76977	+	44.0645i	0.261325	+	1.48205i
$885$		0			0
$886$	27.9721	−	10.1810i	0.939741	−	0.342038i
$887$	29.7761	+	5.25033i	0.999784	+	0.176289i	0.649506	−	0.760357i	$-0.274976\pi$
$887$	29.7761	+	5.25033i	0.999784	+	0.176289i	0.350278	+	0.936646i	$0.386087\pi$
$888$	6.34747	+	9.83477i	0.213007	+	0.330033i
$889$	−3.03802	+	2.54920i	−0.101892	+	0.0854974i
$890$		0			0
$891$	−7.95312	−	20.3414i	−0.266439	−	0.681461i
$892$			10.4214i			0.348934i
$893$	−2.07272	−	2.47017i	−0.0693608	−	0.0826610i
$894$	2.73588	−	1.76577i	0.0915014	−	0.0590561i
$895$		0			0
$896$	−3.29224	+	1.19828i	−0.109986	+	0.0400317i
$897$	67.9309	+	20.9779i	2.26815	+	0.700432i
$898$	−0.514555	+	0.0907299i	−0.0171709	+	0.00302769i
$899$	−1.80323	−	3.12329i	−0.0601411	−	0.104167i
$900$		0			0
$901$	25.4929	−	44.1550i	0.849292	−	1.47102i
$902$	−0.892250	+	2.45144i	−0.0297087	+	0.0816240i
$903$	−2.03107	+	0.855396i	−0.0675897	+	0.0284658i
$904$	23.2481	+	19.5075i	0.773222	+	0.648810i
$905$		0			0
$906$	−14.4758	+	19.0979i	−0.480927	+	0.634486i
$907$	−7.42916	+	20.4114i	−0.246681	+	0.677751i	0.753122	+	0.657881i	$0.228547\pi$
$907$	−7.42916	+	20.4114i	−0.246681	+	0.677751i	−0.999803	+	0.0198692i	$0.993675\pi$
$908$	10.3235	+	5.96027i	0.342597	+	0.197798i
$909$	−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	$-0.191541\pi$
$912$	0.149384	−	0.138518i	0.00494659	−	0.00458679i
$913$	6.50698	+	17.8778i	0.215350	+	0.591668i
$914$	−1.35272	+	7.67163i	−0.0447438	+	0.253755i
$915$		0			0
$916$	−0.147530	+	0.123792i	−0.00487453	+	0.00409022i
$917$		−	4.46185i		−	0.147343i
$918$	−8.31263	−	24.8208i	−0.274358	−	0.819209i
$919$	−56.7307			−1.87137			−0.935686	−	0.352835i	$-0.885218\pi$
$919$	−56.7307			−1.87137			−0.935686	+	0.352835i	$0.885218\pi$
$920$		0			0
$921$	−1.22942	−	24.7944i	−0.0405108	−	0.817005i
$922$	−21.6852	−	3.82369i	−0.714164	−	0.125926i
$923$	6.93922	+	19.0654i	0.228407	+	0.627544i
$924$	−2.56384	+	0.584309i	−0.0843441	+	0.0192224i
$925$		0			0
$926$	5.03635	+	8.72322i	0.165505	+	0.286663i
$927$	−33.3780	−	2.52299i	−1.09628	−	0.0828660i
$928$	−2.07201	−	1.19628i	−0.0680172	−	0.0392697i
$929$	0.152953	+	0.0556703i	0.00501822	+	0.00182648i	0.344528	−	0.938776i	$-0.388039\pi$
$929$	0.152953	+	0.0556703i	0.00501822	+	0.00182648i	−0.339510	+	0.940603i	$0.610261\pi$
$930$		0			0
$931$	−20.0869	−	16.8549i	−0.658320	−	0.552396i
$932$	12.8664	−	15.3336i	0.421454	−	0.502269i
$933$	6.86356	−	54.6270i	0.224703	−	1.78841i
$934$	−0.541204	−	0.196982i	−0.0177087	−	0.00644545i
$935$		0			0
$936$	44.5547	+	30.4190i	1.45632	+	0.994277i
$937$	−43.7391	+	25.2528i	−1.42890	+	0.824973i	−0.997034	−	0.0769668i	$-0.975476\pi$
$937$	−43.7391	+	25.2528i	−1.42890	+	0.824973i	−0.431862	+	0.901940i	$0.642143\pi$
$938$	3.06089	−	0.539718i	0.0999417	−	0.0176224i
$939$	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	$-0.0680665\pi$
$942$	33.2755	−	1.64995i	1.08417	−	0.0537583i
$943$	−5.09345	−	6.07013i	−0.165865	−	0.197671i
$944$	0.211731			0.00689126
$945$		0			0
$946$	5.32659			0.173183
$947$	15.4521	+	18.4151i	0.502126	+	0.598410i	0.956258	−	0.292524i	$-0.0944951\pi$
$947$	15.4521	+	18.4151i	0.502126	+	0.598410i	−0.454132	+	0.890934i	$0.650051\pi$
$948$	2.61951	−	5.10548i	0.0850776	−	0.165818i
$949$	13.2015	−	74.8695i	0.428539	−	2.43037i
$950$		0			0
$951$	16.0788	+	17.3400i	0.521390	+	0.562289i
$952$	−8.15304	+	1.43760i	−0.264242	+	0.0465929i
$953$	−43.1725	+	24.9256i	−1.39849	+	0.807421i	−0.994235	−	0.107224i	$-0.965804\pi$
$953$	−43.1725	+	24.9256i	−1.39849	+	0.807421i	−0.404259	+	0.914645i	$0.632471\pi$
$954$	−6.32348	−	22.5307i	−0.204730	−	0.729460i
$955$		0			0
$956$	−23.2937	−	8.47820i	−0.753371	−	0.274205i
$957$	−1.42014	−	1.07643i	−0.0459065	−	0.0347961i
$958$	12.6078	−	15.0254i	0.407341	−	0.485450i
$959$	6.22939	+	5.22708i	0.201157	+	0.168791i
$960$		0			0
$961$	−38.8700	−	14.1475i	−1.25387	−	0.456371i
$962$	−11.4961	−	6.63726i	−0.370648	−	0.213994i
$963$	31.4859	+	14.2314i	1.01462	+	0.458602i
$964$	−16.2126	−	28.0811i	−0.522174	−	0.904432i
$965$		0			0
$966$	−1.47755	+	4.78461i	−0.0475393	+	0.153942i
$967$	−7.53113	−	20.6916i	−0.242185	−	0.665398i	−0.999918	−	0.0128326i	$-0.995915\pi$
$967$	−7.53113	−	20.6916i	−0.242185	−	0.665398i	0.757733	−	0.652565i	$-0.226307\pi$
$968$	−14.2690	−	2.51602i	−0.458624	−	0.0808678i
$969$	−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	$0.174059\pi$
$972$	17.2517	+	8.34228i	0.553348	+	0.267579i
$973$		−	1.70692i		−	0.0547215i
$974$	19.0328	−	15.9704i	0.609849	−	0.511724i
$975$		0			0
$976$	−0.0168803	+	0.0957327i	−0.000540324	+	0.00306433i
$977$	−10.9005	−	29.9489i	−0.348738	−	0.958149i	−0.982768	−	0.184841i	$-0.940823\pi$
$977$	−10.9005	−	29.9489i	−0.348738	−	0.958149i	0.634031	−	0.773308i	$-0.281399\pi$
$978$	−29.0148	−	8.96012i	−0.927790	−	0.286513i
$979$	7.79370	+	44.2003i	0.249088	+	1.41265i
$980$		0			0
$981$	−20.7768	+	45.9671i	−0.663353	+	1.46762i
$982$	−32.5761	−	18.8078i	−1.03955	−	0.600182i
$983$	20.5044	−	56.3354i	0.653989	−	1.79682i	0.0515295	−	0.998671i	$-0.483590\pi$
$983$	20.5044	−	56.3354i	0.653989	−	1.79682i	0.602460	−	0.798149i	$-0.294187\pi$
$984$	−2.33379	−	5.54140i	−0.0743986	−	0.176653i
$985$		0			0
$986$	−1.63603	−	1.37279i	−0.0521017	−	0.0437185i
$987$	0.582326	+	0.441391i	0.0185356	+	0.0140496i
$988$	10.3740	−	28.5024i	0.330042	−	0.906783i
$989$	−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	$0.763252\pi$
$992$	−47.2779	+	8.33637i	−1.50107	+	0.264680i
$993$	35.9590	−	33.3435i	1.14113	−	1.05812i
$994$	−1.34284	+	0.488754i	−0.0425923	+	0.0155023i
$995$		0			0
$996$	−14.8516	−	7.62003i	−0.470592	−	0.241450i
$997$	−3.82877	−	4.56295i	−0.121258	−	0.144510i	0.702000	−	0.712177i	$-0.252291\pi$
$997$	−3.82877	−	4.56295i	−0.121258	−	0.144510i	−0.823258	+	0.567667i	$0.807846\pi$
$998$			3.55037i			0.112385i
$999$	−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.u.e.49.15		132
5.2	odd	4		675.2.l.g.76.4	yes	66
5.3	odd	4		675.2.l.f.76.8	✓	66
5.4	even	2	inner	675.2.u.e.49.8		132
27.16	even	9	inner	675.2.u.e.124.8		132
135.43	odd	36		675.2.l.f.151.8	yes	66
135.97	odd	36		675.2.l.g.151.4	yes	66
135.124	even	18	inner	675.2.u.e.124.15		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.8	✓	66	5.3	odd	4
675.2.l.f.151.8	yes	66	135.43	odd	36
675.2.l.g.76.4	yes	66	5.2	odd	4
675.2.l.g.151.4	yes	66	135.97	odd	36
675.2.u.e.49.8		132	5.4	even	2	inner
675.2.u.e.49.15		132	1.1	even	1	trivial
675.2.u.e.124.8		132	27.16	even	9	inner
675.2.u.e.124.15		132	135.124	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.564301 + 0.672508i) q^{2} +(-0.939248 - 1.45527i) q^{3} +(0.213465 - 1.21062i) q^{4} +(0.448662 - 1.45286i) q^{6} +(0.501180 - 0.0883715i) q^{7} +(2.45517 - 1.41750i) q^{8} +(-1.23563 + 2.73372i) q^{9} +(2.28041 + 0.830001i) q^{11} +(-1.96228 + 0.826424i) q^{12} +(4.07731 - 4.85915i) q^{13} +(0.342247 + 0.287179i) q^{14} +(0.0284139 + 0.0103418i) q^{16} +(-4.96942 - 2.86909i) q^{17} +(-2.53572 + 0.711675i) q^{18} +(1.94493 + 3.36871i) q^{19} +(-0.599337 - 0.646349i) q^{21} +(0.728656 + 2.00197i) q^{22} +(-6.37282 - 1.12370i) q^{23} +(-4.36886 - 2.24156i) q^{24} +5.56865 q^{26} +(5.13886 - 0.769474i) q^{27} -0.625603i q^{28} +(0.324767 - 0.272512i) q^{29} +(1.47718 - 8.37750i) q^{31} +(-1.93017 - 5.30309i) q^{32} +(-0.933994 - 4.09819i) q^{33} +(-0.874759 - 4.96101i) q^{34} +(3.04574 + 2.07943i) q^{36} +(-2.06443 - 1.19190i) q^{37} +(-1.16796 + 3.20895i) q^{38} +(-10.9010 - 1.36964i) q^{39} +(0.938033 + 0.787103i) q^{41} +(0.0964687 - 0.767795i) q^{42} +(0.855127 - 2.34944i) q^{43} +(1.49160 - 2.58353i) q^{44} +(-2.84049 - 4.91988i) q^{46} +(-0.816377 + 0.143949i) q^{47} +(-0.0116376 - 0.0510634i) q^{48} +(-6.33448 + 2.30556i) q^{49} +(0.492208 + 9.92664i) q^{51} +(-5.01222 - 5.97334i) q^{52} +8.88536i q^{53} +(3.41735 + 3.02171i) q^{54} +(1.10522 - 0.927387i) q^{56} +(3.07562 - 5.99445i) q^{57} +(0.366533 + 0.0646297i) q^{58} +(6.58000 - 2.39492i) q^{59} +(0.558258 + 3.16604i) q^{61} +(6.46751 - 3.73402i) q^{62} +(-0.377687 + 1.47928i) q^{63} +(2.50742 - 4.34297i) q^{64} +(2.22901 - 2.94073i) q^{66} +(4.47176 - 5.32923i) q^{67} +(-4.53418 + 5.40363i) q^{68} +(4.35037 + 10.3296i) q^{69} +(-1.59927 + 2.77002i) q^{71} +(0.841362 + 8.46325i) q^{72} +(10.3795 - 5.99262i) q^{73} +(-0.363398 - 2.06093i) q^{74} +(4.49341 - 1.63547i) q^{76} +(1.21624 + 0.214457i) q^{77} +(-5.23035 - 8.10390i) q^{78} +(-2.06451 + 1.73233i) q^{79} +(-5.94646 - 6.75571i) q^{81} +1.07500i q^{82} +(5.03928 + 6.00558i) q^{83} +(-0.910421 + 0.587596i) q^{84} +(2.06257 - 0.750714i) q^{86} +(-0.701616 - 0.216668i) q^{87} +(6.77532 - 1.19467i) q^{88} +(9.24733 + 16.0168i) q^{89} +(1.61406 - 2.79563i) q^{91} +(-2.72075 + 7.47519i) q^{92} +(-13.5790 + 5.71886i) q^{93} +(-0.557490 - 0.467789i) q^{94} +(-5.90453 + 7.78984i) q^{96} +(-2.86117 + 7.86099i) q^{97} +(-5.12506 - 2.95896i) q^{98} +(-5.08672 + 5.20843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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