LMFDB - Embedded newform 735.2.p.f.509.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(374,735)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("735.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.5
Character	$\chi$	$=$	735.509
Dual form			735.2.p.f.374.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.322403 + 0.558418i) q^{2} +(-1.69458 + 0.358331i) q^{3} +(0.792113 + 1.37198i) q^{4} +(-0.550103 + 2.16735i) q^{5} +(0.346239 - 1.06181i) q^{6} -2.31113 q^{8} +(2.74320 - 1.21444i) q^{9} +(-1.03293 - 1.00595i) q^{10} +(-3.51044 + 2.02675i) q^{11} +(-1.83392 - 2.04109i) q^{12} -4.21339 q^{13} +(0.155565 - 3.86986i) q^{15} +(-0.839111 + 1.45338i) q^{16} +(1.88498 - 1.08830i) q^{17} +(-0.206248 + 1.92339i) q^{18} +(3.87634 + 2.23800i) q^{19} +(-3.40930 + 0.962052i) q^{20} -2.61372i q^{22} +(0.322403 - 0.558418i) q^{23} +(3.91639 - 0.828150i) q^{24} +(-4.39477 - 2.38453i) q^{25} +(1.35841 - 2.35284i) q^{26} +(-4.21339 + 3.04094i) q^{27} -1.16875i q^{29} +(2.11084 + 1.33452i) q^{30} +(0.339111 - 0.195786i) q^{31} +(-2.85219 - 4.94014i) q^{32} +(5.22247 - 4.69239i) q^{33} +1.40348i q^{34} +(3.83911 + 2.80164i) q^{36} +(3.69236 + 2.13178i) q^{37} +(-2.49949 + 1.44308i) q^{38} +(7.13993 - 1.50979i) q^{39} +(1.27136 - 5.00902i) q^{40} +2.27971 q^{41} -6.54419i q^{43} +(-5.56132 - 3.21083i) q^{44} +(1.12307 + 6.61352i) q^{45} +(0.207887 + 0.360071i) q^{46} +(-6.75621 - 3.90070i) q^{47} +(0.901147 - 2.76355i) q^{48} +(2.74845 - 1.68534i) q^{50} +(-2.80428 + 2.51965i) q^{51} +(-3.33748 - 5.78069i) q^{52} +(3.60074 + 6.23667i) q^{53} +(-0.339707 - 3.33324i) q^{54} +(-2.46157 - 8.72325i) q^{55} +(-7.37071 - 2.40346i) q^{57} +(0.652654 + 0.376810i) q^{58} +(-5.66247 - 9.80768i) q^{59} +(5.43259 - 2.85193i) q^{60} +(-6.05456 - 3.49560i) q^{61} +0.252487i q^{62} +0.321779 q^{64} +(2.31780 - 9.13188i) q^{65} +(0.936579 + 4.42916i) q^{66} +(-7.56680 + 4.36870i) q^{67} +(2.98624 + 1.72411i) q^{68} +(-0.346239 + 1.06181i) q^{69} -8.13766i q^{71} +(-6.33988 + 2.80673i) q^{72} +(2.61843 + 4.53525i) q^{73} +(-2.38085 + 1.37459i) q^{74} +(8.30174 + 2.46598i) q^{75} +7.09101i q^{76} +(-1.45884 + 4.47383i) q^{78} +(-1.87634 + 3.24991i) q^{79} +(-2.68838 - 2.61815i) q^{80} +(6.05026 - 6.66291i) q^{81} +(-0.734986 + 1.27303i) q^{82} +5.27461i q^{83} +(1.32178 + 4.68409i) q^{85} +(3.65439 + 2.10987i) q^{86} +(0.418802 + 1.98055i) q^{87} +(8.11308 - 4.68409i) q^{88} +(-0.447379 + 0.774883i) q^{89} +(-4.05520 - 1.50507i) q^{90} +1.02152 q^{92} +(-0.504494 + 0.453288i) q^{93} +(4.35644 - 2.51519i) q^{94} +(-6.98291 + 7.17023i) q^{95} +(6.60347 + 7.34943i) q^{96} +3.89968 q^{97} +(-7.16845 + 9.82300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) $ 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.322403	+	0.558418i	−0.227973	+	0.394861i	−0.957207	−	0.289403i	$-0.906543\pi$
$2$	−0.322403	+	0.558418i	−0.227973	+	0.394861i	0.729234	+	0.684264i	$0.239877\pi$
$3$	−1.69458	+	0.358331i	−0.978366	+	0.206883i
$3$	−1.69458	+	0.358331i	−0.978366	+	0.206883i
$4$	0.792113	+	1.37198i	0.396056	+	0.685990i
$5$	−0.550103	+	2.16735i	−0.246013	+	0.969266i
$5$	−0.550103	+	2.16735i	−0.246013	+	0.969266i
$6$	0.346239	−	1.06181i	0.141351	−	0.433483i
$7$		0			0
$7$		0			0
$8$	−2.31113			−0.817108
$9$	2.74320	−	1.21444i	0.914399	−	0.404814i
$10$	−1.03293	−	1.00595i	−0.326641	−	0.318108i
$11$	−3.51044	+	2.02675i	−1.05844	+	0.611089i	−0.924999	−	0.379968i	$-0.875935\pi$
$11$	−3.51044	+	2.02675i	−1.05844	+	0.611089i	−0.133437	+	0.991057i	$0.542602\pi$
$12$	−1.83392	−	2.04109i	−0.529407	−	0.589212i
$13$	−4.21339			−1.16858			−0.584292	−	0.811543i	$-0.698628\pi$
$13$	−4.21339			−1.16858			−0.584292	+	0.811543i	$0.698628\pi$
$14$		0			0
$15$	0.155565	−	3.86986i	0.0401666	−	0.999193i
$16$	−0.839111	+	1.45338i	−0.209778	+	0.363346i
$17$	1.88498	−	1.08830i	0.457176	−	0.263951i	−0.253680	−	0.967288i	$-0.581641\pi$
$17$	1.88498	−	1.08830i	0.457176	−	0.263951i	0.710856	+	0.703338i	$0.248308\pi$
$18$	−0.206248	+	1.92339i	−0.0486132	+	0.453348i
$19$	3.87634	+	2.23800i	0.889293	+	0.513434i	0.873711	−	0.486445i	$-0.161707\pi$
$19$	3.87634	+	2.23800i	0.889293	+	0.513434i	0.0155818	+	0.999879i	$0.495040\pi$
$20$	−3.40930	+	0.962052i	−0.762342	+	0.215121i
$21$		0			0
$22$		−	2.61372i		−	0.557248i
$23$	0.322403	−	0.558418i	0.0672257	−	0.116438i	−0.830453	−	0.557088i	$-0.811919\pi$
$23$	0.322403	−	0.558418i	0.0672257	−	0.116438i	0.897679	+	0.440650i	$0.145252\pi$
$24$	3.91639	−	0.828150i	0.799430	−	0.169045i
$25$	−4.39477	−	2.38453i	−0.878955	−	0.476905i
$26$	1.35841	−	2.35284i	0.266406	−	0.461429i
$27$	−4.21339	+	3.04094i	−0.810868	+	0.585229i
$28$		0			0
$29$		−	1.16875i		−	0.217032i	−0.994095	−	0.108516i	$-0.965390\pi$
$29$		−	1.16875i		−	0.217032i	0.994095	−	0.108516i	$-0.0346099\pi$
$30$	2.11084	+	1.33452i	0.385386	+	0.243650i
$31$	0.339111	−	0.195786i	0.0609061	−	0.0351641i	−0.469238	−	0.883072i	$-0.655471\pi$
$31$	0.339111	−	0.195786i	0.0609061	−	0.0351641i	0.530144	+	0.847908i	$0.322138\pi$
$32$	−2.85219	−	4.94014i	−0.504201	−	0.873302i
$33$	5.22247	−	4.69239i	0.909115	−	0.816841i
$34$			1.40348i			0.240695i
$35$		0			0
$36$	3.83911	+	2.80164i	0.639852	+	0.466939i
$37$	3.69236	+	2.13178i	0.607020	+	0.350463i	0.771798	−	0.635868i	$-0.219358\pi$
$37$	3.69236	+	2.13178i	0.607020	+	0.350463i	−0.164778	+	0.986331i	$0.552691\pi$
$38$	−2.49949	+	1.44308i	−0.405470	+	0.234098i
$39$	7.13993	−	1.50979i	1.14330	−	0.241760i
$40$	1.27136	−	5.00902i	0.201019	−	0.791995i
$41$	2.27971			0.356031			0.178016	−	0.984028i	$-0.443032\pi$
$41$	2.27971			0.356031			0.178016	+	0.984028i	$0.443032\pi$
$42$		0			0
$43$		−	6.54419i		−	0.997980i	−0.866608	−	0.498990i	$-0.833705\pi$
$43$		−	6.54419i		−	0.997980i	0.866608	−	0.498990i	$-0.166295\pi$
$44$	−5.56132	−	3.21083i	−0.838401	−	0.484051i
$45$	1.12307	+	6.61352i	0.167418	+	0.985886i
$46$	0.207887	+	0.360071i	0.0306513	+	0.0530896i
$47$	−6.75621	−	3.90070i	−0.985494	−	0.568975i	−0.0815698	−	0.996668i	$-0.525993\pi$
$47$	−6.75621	−	3.90070i	−0.985494	−	0.568975i	−0.903924	+	0.427692i	$0.859327\pi$
$48$	0.901147	−	2.76355i	0.130069	−	0.398884i
$49$		0			0
$50$	2.74845	−	1.68534i	0.388690	−	0.238344i
$51$	−2.80428	+	2.51965i	−0.392678	+	0.352822i
$52$	−3.33748	−	5.78069i	−0.462825	−	0.801637i
$53$	3.60074	+	6.23667i	0.494600	+	0.856672i	0.999981	−	0.00622439i	$-0.00198130\pi$
$53$	3.60074	+	6.23667i	0.494600	+	0.856672i	−0.505381	+	0.862896i	$0.668648\pi$
$54$	−0.339707	−	3.33324i	−0.0462283	−	0.453597i
$55$	−2.46157	−	8.72325i	−0.331918	−	1.17624i
$56$		0			0
$57$	−7.37071	−	2.40346i	−0.976274	−	0.318346i
$58$	0.652654	+	0.376810i	0.0856977	+	0.0494776i
$59$	−5.66247	−	9.80768i	−0.737190	−	1.27685i	−0.953756	−	0.300583i	$-0.902819\pi$
$59$	−5.66247	−	9.80768i	−0.737190	−	1.27685i	0.216566	−	0.976268i	$-0.430515\pi$
$60$	5.43259	−	2.85193i	0.701344	−	0.368183i
$61$	−6.05456	−	3.49560i	−0.775207	−	0.447566i	0.0595220	−	0.998227i	$-0.481042\pi$
$61$	−6.05456	−	3.49560i	−0.775207	−	0.447566i	−0.834729	+	0.550661i	$0.814376\pi$
$62$			0.252487i			0.0320659i
$63$		0			0
$64$	0.321779			0.0402224
$65$	2.31780	−	9.13188i	0.287488	−	1.13267i
$66$	0.936579	+	4.42916i	0.115285	+	0.545192i
$67$	−7.56680	+	4.36870i	−0.924432	+	0.533721i	−0.885046	−	0.465503i	$-0.845873\pi$
$67$	−7.56680	+	4.36870i	−0.924432	+	0.533721i	−0.0393859	+	0.999224i	$0.512540\pi$
$68$	2.98624	+	1.72411i	0.362135	+	0.209079i
$69$	−0.346239	+	1.06181i	−0.0416822	+	0.127827i
$70$		0			0
$71$		−	8.13766i		−	0.965762i	−0.875686	−	0.482881i	$-0.839590\pi$
$71$		−	8.13766i		−	0.965762i	0.875686	−	0.482881i	$-0.160410\pi$
$72$	−6.33988	+	2.80673i	−0.747163	+	0.330777i
$73$	2.61843	+	4.53525i	0.306464	+	0.530810i	0.977586	−	0.210536i	$-0.0675209\pi$
$73$	2.61843	+	4.53525i	0.306464	+	0.530810i	−0.671123	+	0.741346i	$0.734188\pi$
$74$	−2.38085	+	1.37459i	−0.276769	+	0.159792i
$75$	8.30174	+	2.46598i	0.958603	+	0.284747i
$76$			7.09101i			0.813394i
$77$		0			0
$78$	−1.45884	+	4.47383i	−0.165181	+	0.506561i
$79$	−1.87634	+	3.24991i	−0.211105	+	0.365644i	−0.952060	−	0.305910i	$-0.901039\pi$
$79$	−1.87634	+	3.24991i	−0.211105	+	0.365644i	0.740956	+	0.671554i	$0.234373\pi$
$80$	−2.68838	−	2.61815i	−0.300571	−	0.292718i
$81$	6.05026	−	6.66291i	0.672251	−	0.740323i
$82$	−0.734986	+	1.27303i	−0.0811656	+	0.140583i
$83$			5.27461i			0.578964i	0.957183	+	0.289482i	$0.0934831\pi$
$83$			5.27461i			0.578964i	−0.957183	+	0.289482i	$0.906517\pi$
$84$		0			0
$85$	1.32178	+	4.68409i	0.143367	+	0.508061i
$86$	3.65439	+	2.10987i	0.394064	+	0.227513i
$87$	0.418802	+	1.98055i	0.0449002	+	0.212337i
$88$	8.11308	−	4.68409i	0.864857	−	0.499325i
$89$	−0.447379	+	0.774883i	−0.0474221	+	0.0821375i	−0.888762	−	0.458369i	$-0.848434\pi$
$89$	−0.447379	+	0.774883i	−0.0474221	+	0.0821375i	0.841340	+	0.540506i	$0.181767\pi$
$90$	−4.05520	−	1.50507i	−0.427455	−	0.158649i
$91$		0			0
$92$	1.02152			0.106501
$93$	−0.504494	+	0.453288i	−0.0523135	+	0.0470038i
$94$	4.35644	−	2.51519i	0.449333	−	0.259422i
$95$	−6.98291	+	7.17023i	−0.716432	+	0.735650i
$96$	6.60347	+	7.34943i	0.673964	+	0.750098i
$97$	3.89968			0.395953			0.197976	−	0.980207i	$-0.436563\pi$
$97$	3.89968			0.395953			0.197976	+	0.980207i	$0.436563\pi$
$98$		0			0
$99$	−7.16845	+	9.82300i	−0.720456	+	0.987249i
$100$	−0.209636	−	7.91835i	−0.0209636	−	0.791835i
$101$	−3.29188	−	5.70171i	−0.327555	−	0.567341i	0.654471	−	0.756087i	$-0.272891\pi$
$101$	−3.29188	−	5.70171i	−0.327555	−	0.567341i	−0.982026	+	0.188745i	$0.939558\pi$
$102$	−0.502911	−	2.37831i	−0.0497956	−	0.235487i
$103$	−4.90721	+	8.49954i	−0.483522	+	0.837485i	−0.999821	−	0.0189238i	$-0.993976\pi$
$103$	−4.90721	+	8.49954i	−0.483522	+	0.837485i	0.516299	+	0.856408i	$0.327309\pi$
$104$	9.73770			0.954860
$105$		0			0
$106$	−4.64356			−0.451022
$107$	−9.38974	+	16.2635i	−0.907740	+	1.57225i	−0.0905447	+	0.995892i	$0.528861\pi$
$107$	−9.38974	+	16.2635i	−0.907740	+	1.57225i	−0.817196	+	0.576360i	$0.804473\pi$
$108$	−7.50959	−	3.37192i	−0.722611	−	0.324463i
$109$	−0.453002	−	0.784623i	−0.0433897	−	0.0751532i	0.843515	−	0.537106i	$-0.180482\pi$
$109$	−0.453002	−	0.784623i	−0.0433897	−	0.0751532i	−0.886905	+	0.461952i	$0.847149\pi$
$110$	5.66484	+	1.43782i	0.540121	+	0.137090i
$111$	−7.02088	−	2.28939i	−0.666392	−	0.217299i
$112$		0			0
$113$	8.82955			0.830614			0.415307	−	0.909681i	$-0.363674\pi$
$113$	8.82955			0.830614			0.415307	+	0.909681i	$0.363674\pi$
$114$	3.71848	−	3.34105i	0.348267	−	0.312918i
$115$	1.03293	+	1.00595i	0.0963213	+	0.0938049i
$116$	1.60351	−	0.925786i	0.148882	−	0.0859570i
$117$	−11.5582	+	5.11692i	−1.06855	+	0.473059i
$118$	7.30238			0.672239
$119$		0			0
$120$	−0.359530	+	8.94374i	−0.0328205	+	0.816448i
$121$	2.71545	−	4.70330i	0.246859	−	0.427572i
$122$	3.90402	−	2.25398i	0.353453	−	0.204066i
$123$	−3.86315	+	0.816892i	−0.348329	+	0.0736567i
$124$	0.537228	+	0.310168i	0.0482445	+	0.0278540i
$125$	7.58567	−	8.21326i	0.678483	−	0.734616i
$126$		0			0
$127$			15.8249i			1.40424i	0.712060	+	0.702118i	$0.247762\pi$
$127$			15.8249i			1.40424i	−0.712060	+	0.702118i	$0.752238\pi$
$128$	5.60064	−	9.70060i	0.495032	−	0.857420i
$129$	2.34499	+	11.0896i	0.206465	+	0.976389i
$130$	4.35214	+	4.23845i	0.381708	+	0.371736i
$131$	−8.27814	+	14.3382i	−0.723265	+	1.25273i	0.236419	+	0.971651i	$0.424026\pi$
$131$	−8.27814	+	14.3382i	−0.723265	+	1.25273i	−0.959684	+	0.281080i	$0.909307\pi$
$132$	10.5746	+	3.44821i	0.920405	+	0.300128i
$133$		0			0
$134$		−	5.63392i		−	0.486697i
$135$	−4.27297	−	10.8047i	−0.367759	−	0.929921i
$136$	−4.35644	+	2.51519i	−0.373562	+	0.215676i
$137$	−9.93080	−	17.2007i	−0.848446	−	1.46955i	−0.882595	−	0.470135i	$-0.844205\pi$
$137$	−9.93080	−	17.2007i	−0.848446	−	1.46955i	0.0341490	−	0.999417i	$-0.489128\pi$
$138$	−0.481306	−	0.535677i	−0.0409715	−	0.0455998i
$139$			0.228766i			0.0194037i	0.999953	+	0.00970183i	$0.00308824\pi$
$139$			0.228766i			0.0194037i	−0.999953	+	0.00970183i	$0.996912\pi$
$140$		0			0
$141$	12.8467	+	4.18908i	1.08188	+	0.352784i
$142$	4.54422	+	2.62361i	0.381342	+	0.220168i
$143$	14.7909	−	8.53950i	1.23687	−	0.714109i
$144$	−0.536798	+	5.00596i	−0.0447332	+	0.417164i
$145$	2.53310	+	0.642935i	0.210362	+	0.0533929i
$146$	−3.37675			−0.279462
$147$		0			0
$148$			6.75445i			0.555212i
$149$	8.62438	+	4.97929i	0.706537	+	0.407919i	0.809777	−	0.586737i	$-0.199588\pi$
$149$	8.62438	+	4.97929i	0.706537	+	0.407919i	−0.103240	+	0.994656i	$0.532921\pi$
$150$	−4.05356	+	3.84080i	−0.330971	+	0.313600i
$151$	2.53723	+	4.39461i	0.206477	+	0.357628i	0.950602	−	0.310412i	$-0.100467\pi$
$151$	2.53723	+	4.39461i	0.206477	+	0.357628i	−0.744126	+	0.668040i	$0.767134\pi$
$152$	−8.95872	−	5.17232i	−0.726648	−	0.419530i
$153$	3.84921	−	5.27461i	0.311190	−	0.426427i
$154$		0			0
$155$	0.237789	+	0.842672i	0.0190997	+	0.0676850i
$156$	7.72703	+	8.59991i	0.618657	+	0.688544i
$157$	8.42678	+	14.5956i	0.672531	+	1.16486i	0.977184	+	0.212394i	$0.0681260\pi$
$157$	8.42678	+	14.5956i	0.672531	+	1.16486i	−0.304653	+	0.952463i	$0.598541\pi$
$158$	−1.20987	−	2.09556i	−0.0962524	−	0.166714i
$159$	−8.33653	−	9.27827i	−0.661130	−	0.735814i
$160$	12.2760	−	3.46410i	0.970503	−	0.273861i
$161$		0			0
$162$	1.77007	+	5.52672i	0.139070	+	0.434220i
$163$	−4.16292	−	2.40346i	−0.326065	−	0.188254i	0.328028	−	0.944668i	$-0.393616\pi$
$163$	−4.16292	−	2.40346i	−0.326065	−	0.188254i	−0.654093	+	0.756414i	$0.726949\pi$
$164$	1.80579	+	3.12772i	0.141008	+	0.244234i
$165$	7.29714	+	13.9002i	0.568082	+	1.08213i
$166$	−2.94544	−	1.70055i	−0.228611	−	0.131988i
$167$			4.45089i			0.344420i	0.985060	+	0.172210i	$0.0550908\pi$
$167$			4.45089i			0.344420i	−0.985060	+	0.172210i	$0.944909\pi$
$168$		0			0
$169$	4.75268			0.365590
$170$	−3.04182	−	0.772058i	−0.233297	−	0.0592141i
$171$	13.3515	+	1.43170i	1.02101	+	0.109485i
$172$	8.97849	−	5.18374i	0.684604	−	0.395256i
$173$	9.91963	+	5.72710i	0.754175	+	0.435423i	0.827201	−	0.561907i	$-0.189932\pi$
$173$	9.91963	+	5.72710i	0.754175	+	0.435423i	−0.0730252	+	0.997330i	$0.523265\pi$
$174$	−1.24100	−	0.404668i	−0.0940797	−	0.0306778i
$175$		0			0
$176$		−	6.80268i		−	0.512771i
$177$	13.1099	+	14.5908i	0.985400	+	1.09672i
$178$	−0.288473	−	0.499649i	−0.0216219	−	0.0374503i
$179$	−9.04522	+	5.22226i	−0.676071	+	0.390330i	−0.798373	−	0.602163i	$-0.794306\pi$
$179$	−9.04522	+	5.22226i	−0.676071	+	0.390330i	0.122302	+	0.992493i	$0.460972\pi$
$180$	−8.18402	+	6.77949i	−0.610001	+	0.505314i
$181$			11.9616i			0.889095i	0.895755	+	0.444548i	$0.146636\pi$
$181$			11.9616i			0.889095i	−0.895755	+	0.444548i	$0.853364\pi$
$182$		0			0
$183$	11.5125	+	3.75404i	0.851030	+	0.277506i
$184$	−0.745115	+	1.29058i	−0.0549306	+	0.0951426i
$185$	−6.65149	+	6.82991i	−0.489027	+	0.502145i
$186$	−0.0904741	−	0.427860i	−0.00663389	−	0.0313722i
$187$	−4.41141	+	7.64079i	−0.322594	+	0.558750i
$188$		−	12.3592i		−	0.901385i
$189$		0			0
$190$	−1.75268	−	6.21109i	−0.127153	−	0.450600i
$191$	−12.2522	−	7.07383i	−0.886541	−	0.511844i	−0.0137312	−	0.999906i	$-0.504371\pi$
$191$	−12.2522	−	7.07383i	−0.886541	−	0.511844i	−0.872809	+	0.488061i	$0.837704\pi$
$192$	−0.545280	+	0.115303i	−0.0393522	+	0.00832131i
$193$	−5.36185	+	3.09566i	−0.385954	+	0.222831i	−0.680406	−	0.732836i	$-0.738196\pi$
$193$	−5.36185	+	3.09566i	−0.385954	+	0.222831i	0.294452	+	0.955666i	$0.404863\pi$
$194$	−1.25727	+	2.17765i	−0.0902667	+	0.156346i
$195$	−0.655455	+	16.3052i	−0.0469381	+	1.16764i
$196$		0			0
$197$	−13.0751			−0.931562			−0.465781	−	0.884900i	$-0.654227\pi$
$197$	−13.0751			−0.931562			−0.465781	+	0.884900i	$0.654227\pi$
$198$	−3.17421	−	7.16996i	−0.225582	−	0.509547i
$199$	−14.6810	+	8.47608i	−1.04071	+	0.600854i	−0.920034	−	0.391838i	$-0.871839\pi$
$199$	−14.6810	+	8.47608i	−1.04071	+	0.600854i	−0.120675	+	0.992692i	$0.538506\pi$
$200$	10.1569	+	5.51095i	0.718201	+	0.389683i
$201$	11.2571	−	10.1145i	0.794015	−	0.713424i
$202$	4.24525			0.298695
$203$		0			0
$204$	−5.67822	−	1.85157i	−0.397555	−	0.129636i
$205$	−1.25408	+	4.94092i	−0.0875885	+	0.345089i
$206$	−3.16420	−	5.48055i	−0.220460	−	0.381848i
$207$	0.206248	−	1.92339i	0.0143353	−	0.133685i
$208$	3.53550	−	6.12367i	0.245143	−	0.424600i
$209$	−18.1435			−1.25501
$210$		0			0
$211$	−18.4309			−1.26884			−0.634418	−	0.772990i	$-0.718760\pi$
$211$	−18.4309			−1.26884			−0.634418	+	0.772990i	$0.718760\pi$
$212$	−5.70439	+	9.88029i	−0.391779	+	0.678581i
$213$	2.91598	+	13.7899i	0.199800	+	0.944869i
$214$	−6.05456	−	10.4868i	−0.413881	−	0.716863i
$215$	14.1835	+	3.59998i	0.967308	+	0.245516i
$216$	9.73770	−	7.02801i	0.662566	−	0.478195i
$217$		0			0
$218$	0.584197			0.0395668
$219$	−6.06225	−	6.74707i	−0.409649	−	0.455925i
$220$	10.0183	−	10.2870i	0.675433	−	0.693551i
$221$	−7.94218	+	4.58542i	−0.534249	+	0.308449i
$222$	3.54199	−	3.18248i	0.237723	−	0.213594i
$223$	−0.627418			−0.0420150			−0.0210075	−	0.999779i	$-0.506687\pi$
$223$	−0.627418			−0.0420150			−0.0210075	+	0.999779i	$0.506687\pi$
$224$		0			0
$225$	−14.9516	−	1.20403i	−0.996773	−	0.0802685i
$226$	−2.84667	+	4.93058i	−0.189358	+	0.327977i
$227$	−4.70200	+	2.71470i	−0.312082	+	0.180181i	−0.647858	−	0.761761i	$-0.724335\pi$
$227$	−4.70200	+	2.71470i	−0.312082	+	0.180181i	0.335776	+	0.941942i	$0.391002\pi$
$228$	−2.54093	−	12.0163i	−0.168277	−	0.795797i
$229$	12.4482	+	7.18699i	0.822602	+	0.474930i	0.851313	−	0.524658i	$-0.175807\pi$
$229$	12.4482	+	7.18699i	0.822602	+	0.474930i	−0.0287108	+	0.999588i	$0.509140\pi$
$230$	−0.894758	+	0.252487i	−0.0589986	+	0.0166485i
$231$		0			0
$232$			2.70114i			0.177339i
$233$	4.21524	−	7.30101i	0.276150	−	0.478305i	−0.694275	−	0.719710i	$-0.744275\pi$
$233$	4.21524	−	7.30101i	0.276150	−	0.478305i	0.970425	+	0.241405i	$0.0776081\pi$
$234$	0.869006	−	8.10400i	0.0568087	−	0.529775i
$235$	12.1708	−	12.4973i	0.793934	−	0.815231i
$236$	8.97062	−	15.5376i	0.583938	−	1.01141i
$237$	2.01506	−	6.17959i	0.130892	−	0.401407i
$238$		0			0
$239$		−	2.71852i		−	0.175847i	−0.996127	−	0.0879233i	$-0.971977\pi$
$239$		−	2.71852i		−	0.175847i	0.996127	−	0.0879233i	$-0.0280230\pi$
$240$	5.49385	+	3.47333i	0.354626	+	0.224203i
$241$	1.32457	−	0.764739i	0.0853229	−	0.0492612i	−0.456732	−	0.889605i	$-0.650980\pi$
$241$	1.32457	−	0.764739i	0.0853229	−	0.0492612i	0.542054	+	0.840343i	$0.317647\pi$
$242$	1.75094	+	3.03271i	0.112555	+	0.194950i
$243$	−7.86512	+	13.4588i	−0.504548	+	0.863384i
$244$		−	11.0756i		−	0.709045i
$245$		0			0
$246$	0.789324	−	2.42062i	0.0503255	−	0.154333i
$247$	−16.3325	−	9.42959i	−1.03921	−	0.599991i
$248$	−0.783728	+	0.452486i	−0.0497668	+	0.0287329i
$249$	−1.89006	−	8.93825i	−0.119778	−	0.566439i
$250$	2.14079	+	6.88395i	0.135396	+	0.435379i
$251$	8.81039			0.556107			0.278054	−	0.960566i	$-0.410311\pi$
$251$	8.81039			0.556107			0.278054	+	0.960566i	$0.410311\pi$
$252$		0			0
$253$			2.61372i			0.164323i
$254$	−8.83694	−	5.10201i	−0.554479	−	0.320128i
$255$	−3.91831	−	7.46392i	−0.245374	−	0.467409i
$256$	3.93311	+	6.81234i	0.245819	+	0.425771i
$257$	−17.4101	−	10.0517i	−1.08601	−	0.627011i	−0.153502	−	0.988148i	$-0.549055\pi$
$257$	−17.4101	−	10.0517i	−1.08601	−	0.627011i	−0.932512	+	0.361138i	$0.882388\pi$
$258$	−6.94869	−	2.26585i	−0.432607	−	0.141066i
$259$		0			0
$260$	14.3647	−	4.05350i	0.890861	−	0.251388i
$261$	−1.41938	−	3.20613i	−0.0878577	−	0.198454i
$262$	−5.33780	−	9.24533i	−0.329770	−	0.571179i
$263$	4.37959	+	7.58568i	0.270057	+	0.467753i	0.968876	−	0.247546i	$-0.0796240\pi$
$263$	4.37959	+	7.58568i	0.270057	+	0.467753i	−0.698819	+	0.715299i	$0.746291\pi$
$264$	−12.0698	+	10.8447i	−0.742845	+	0.667447i
$265$	−15.4978	+	4.37324i	−0.952022	+	0.268646i
$266$		0			0
$267$	0.480454	−	1.47341i	0.0294033	−	0.0901713i
$268$	−11.9875	−	6.92100i	−0.732255	−	0.422767i
$269$	8.62438	+	14.9379i	0.525838	+	0.910778i	0.999547	+	0.0300966i	$0.00958150\pi$
$269$	8.62438	+	14.9379i	0.525838	+	0.910778i	−0.473709	+	0.880681i	$0.657085\pi$
$270$	7.41116	+	1.09736i	0.451029	+	0.0667834i
$271$	−19.6117	−	11.3228i	−1.19132	−	0.687812i	−0.232718	−	0.972544i	$-0.574762\pi$
$271$	−19.6117	−	11.3228i	−1.19132	−	0.687812i	−0.958607	+	0.284733i	$0.908095\pi$
$272$			3.65280i			0.221484i
$273$		0			0
$274$	12.8069			0.773692
$275$	20.2604	−	0.536390i	1.22175	−	0.0323455i
$276$	−1.73104	+	0.366042i	−0.104197	+	0.0220331i
$277$	−11.4413	+	6.60561i	−0.687438	+	0.396893i	−0.802652	−	0.596448i	$-0.796578\pi$
$277$	−11.4413	+	6.60561i	−0.687438	+	0.396893i	0.115213	+	0.993341i	$0.463245\pi$
$278$	−0.127747	−	0.0737548i	−0.00766176	−	0.00442352i
$279$	0.692477	−	0.948908i	0.0414575	−	0.0568097i
$280$		0			0
$281$			32.8703i			1.96088i	0.196817	+	0.980440i	$0.436940\pi$
$281$			32.8703i			1.96088i	−0.196817	+	0.980440i	$0.563060\pi$
$282$	−6.48106	+	5.82324i	−0.385942	+	0.346769i
$283$	−7.90575	−	13.6932i	−0.469948	−	0.813974i	0.529462	−	0.848334i	$-0.322394\pi$
$283$	−7.90575	−	13.6932i	−0.469948	−	0.813974i	−0.999410	+	0.0343601i	$0.989061\pi$
$284$	11.1647	−	6.44594i	0.662503	−	0.382496i
$285$	9.26378	−	14.6527i	0.548739	−	0.867952i
$286$			11.0126i			0.651191i
$287$		0			0
$288$	−13.8236	−	10.0880i	−0.814566	−	0.594439i
$289$	−6.13122	+	10.6196i	−0.360660	+	0.624682i
$290$	−1.17570	+	1.20724i	−0.0690397	+	0.0708917i
$291$	−6.60832	+	1.39738i	−0.387387	+	0.0819158i
$292$	−4.14818	+	7.18485i	−0.242754	+	0.420462i
$293$			20.7797i			1.21396i	0.794716	+	0.606982i	$0.207620\pi$
$293$			20.7797i			1.21396i	−0.794716	+	0.606982i	$0.792380\pi$
$294$		0			0
$295$	24.3716	−	6.87729i	1.41897	−	0.400411i
$296$	−8.53351	−	4.92683i	−0.496000	−	0.286366i
$297$	8.62762	−	19.2145i	0.500625	−	1.11494i
$298$	−5.56105	+	3.21068i	−0.322143	+	0.185989i
$299$	−1.35841	+	2.35284i	−0.0785589	+	0.136068i
$300$	3.19264	+	13.3432i	0.184327	+	0.770367i
$301$		0			0
$302$	−3.27204			−0.188285
$303$	7.62146	+	8.48241i	0.437841	+	0.487302i
$304$	−6.50535	+	3.75587i	−0.373108	+	0.215414i
$305$	10.9068	−	11.1994i	0.624522	−	0.641275i
$306$	1.70444	+	3.85002i	0.0974366	+	0.220091i
$307$	−12.9857			−0.741136			−0.370568	−	0.928805i	$-0.620837\pi$
$307$	−12.9857			−0.741136			−0.370568	+	0.928805i	$0.620837\pi$
$308$		0			0
$309$	5.27001	−	16.1616i	0.299800	−	0.919399i
$310$	−0.547227	−	0.138894i	−0.0310804	−	0.00788865i
$311$	0.228825	+	0.396337i	0.0129755	+	0.0224742i	0.872440	−	0.488721i	$-0.162536\pi$
$311$	0.228825	+	0.396337i	0.0129755	+	0.0224742i	−0.859465	+	0.511195i	$0.829203\pi$
$312$	−16.5013	+	3.48932i	−0.934202	+	0.197544i
$313$	13.8710	−	24.0252i	0.784033	−	1.35799i	−0.145542	−	0.989352i	$-0.546493\pi$
$313$	13.8710	−	24.0252i	0.784033	−	1.35799i	0.929575	−	0.368633i	$-0.120174\pi$
$314$	−10.8673			−0.613276
$315$		0			0
$316$	−5.94509			−0.334437
$317$	2.26170	−	3.91737i	0.127030	−	0.220022i	−0.795495	−	0.605960i	$-0.792789\pi$
$317$	2.26170	−	3.91737i	0.127030	−	0.220022i	0.922524	+	0.385939i	$0.126122\pi$
$318$	7.86888	−	1.66393i	0.441265	−	0.0933087i
$319$	2.36878	+	4.10284i	0.132626	+	0.229715i
$320$	−0.177011	+	0.697406i	−0.00989524	+	0.0389862i
$321$	10.0839	−	30.9244i	0.562830	−	1.72603i
$322$		0			0
$323$	9.74245			0.542084
$324$	13.9339	+	3.02306i	0.774103	+	0.167948i
$325$	18.5169	+	10.0469i	1.02713	+	0.557304i
$326$	2.68428	−	1.54977i	0.148668	−	0.0858337i
$327$	1.04880	+	1.16728i	0.0579989	+	0.0645508i
$328$	−5.26871			−0.290916
$329$		0			0
$330$	−10.1147	−	0.406603i	−0.556798	−	0.0223828i
$331$	11.4482	−	19.8289i	0.629252	−	1.08990i	−0.358451	−	0.933549i	$-0.616695\pi$
$331$	11.4482	−	19.8289i	0.629252	−	1.08990i	0.987702	−	0.156347i	$-0.0499718\pi$
$332$	−7.23666	+	4.17809i	−0.397163	+	0.229302i
$333$	12.7178	+	1.36375i	0.696931	+	0.0747330i
$334$	−2.48546	−	1.43498i	−0.135998	−	0.0785186i
$335$	−5.30596	−	18.8031i	−0.289895	−	1.02732i
$336$		0			0
$337$		−	31.2616i		−	1.70293i	−0.524413	−	0.851464i	$-0.675715\pi$
$337$		−	31.2616i		−	1.70293i	0.524413	−	0.851464i	$-0.324285\pi$
$338$	−1.53228	+	2.65398i	−0.0833449	+	0.144358i
$339$	−14.9624	+	3.16390i	−0.812644	+	0.171840i
$340$	−5.37947	+	5.52378i	−0.291743	+	0.299569i
$341$	−0.793618	+	1.37459i	−0.0429768	+	0.0744380i
$342$	−5.10405	+	6.99413i	−0.275995	+	0.378199i
$343$		0			0
$344$			15.1245i			0.815457i
$345$	−2.11084	−	1.33452i	−0.113644	−	0.0718483i
$346$	−6.39623	+	3.69287i	−0.343864	+	0.198530i
$347$	−1.39335	−	2.41336i	−0.0747992	−	0.129556i	0.826200	−	0.563377i	$-0.190498\pi$
$347$	−1.39335	−	2.41336i	−0.0747992	−	0.129556i	−0.900999	+	0.433821i	$0.857165\pi$
$348$	−2.38553	+	2.14340i	−0.127878	+	0.114899i
$349$		−	16.5636i		−	0.886627i	−0.896367	−	0.443314i	$-0.853803\pi$
$349$		−	16.5636i		−	0.886627i	0.896367	−	0.443314i	$-0.146197\pi$
$350$		0			0
$351$	17.7527	−	12.8127i	0.947568	−	0.683890i
$352$	20.0249	+	11.5614i	1.06733	+	0.616223i
$353$	−2.83794	+	1.63849i	−0.151048	+	0.0872078i	−0.573619	−	0.819122i	$-0.694461\pi$
$353$	−2.83794	+	1.63849i	−0.151048	+	0.0872078i	0.422571	+	0.906330i	$0.361128\pi$
$354$	−12.3745	+	2.61667i	−0.657695	+	0.139075i
$355$	17.6371	+	4.47655i	0.936081	+	0.237591i
$356$	−1.41750			−0.0751273
$357$		0			0
$358$		−	6.73469i		−	0.355939i
$359$	14.7282	+	8.50335i	0.777326	+	0.448789i	0.835482	−	0.549518i	$-0.185189\pi$
$359$	14.7282	+	8.50335i	0.777326	+	0.448789i	−0.0581557	+	0.998308i	$0.518522\pi$
$360$	−2.59557	−	15.2847i	−0.136799	−	0.805575i
$361$	0.517332	+	0.896045i	0.0272280	+	0.0471603i
$362$	−6.67955	−	3.85644i	−0.351069	−	0.202690i
$363$	−2.91620	+	8.94314i	−0.153061	+	0.469393i
$364$		0			0
$365$	−11.2698	+	3.18018i	−0.589891	+	0.166458i
$366$	−5.80799	+	5.21849i	−0.303588	+	0.272775i
$367$	−8.55840	−	14.8236i	−0.446745	−	0.773785i	0.551427	−	0.834223i	$-0.314084\pi$
$367$	−8.55840	−	14.8236i	−0.446745	−	0.773785i	−0.998172	+	0.0604381i	$0.980750\pi$
$368$	0.541063	+	0.937149i	0.0282049	+	0.0488523i
$369$	6.25370	−	2.76858i	0.325555	−	0.144126i
$370$	−1.66949	−	5.91630i	−0.0867926	−	0.307574i
$371$		0			0
$372$	−1.02152	−	0.333100i	−0.0529632	−	0.0172704i
$373$	25.0397	+	14.4567i	1.29651	+	0.748538i	0.979799	−	0.199986i	$-0.0640897\pi$
$373$	25.0397	+	14.4567i	1.29651	+	0.748538i	0.316706	+	0.948524i	$0.397423\pi$
$374$	−2.84450	−	4.92683i	−0.147086	−	0.254760i
$375$	−9.91145	+	16.6362i	−0.511825	+	0.859090i
$376$	15.6145	+	9.01502i	0.805255	+	0.464914i
$377$			4.92442i			0.253621i
$378$		0			0
$379$	−0.559557			−0.0287425			−0.0143712	−	0.999897i	$-0.504575\pi$
$379$	−0.559557			−0.0287425			−0.0143712	+	0.999897i	$0.504575\pi$
$380$	−15.3687	−	3.90078i	−0.788396	−	0.200106i
$381$	−5.67057	−	26.8166i	−0.290512	−	1.37386i
$382$	7.90031	−	4.56125i	0.404215	−	0.233374i
$383$	−3.28951	−	1.89920i	−0.168086	−	0.0970447i	0.413597	−	0.910460i	$-0.364272\pi$
$383$	−3.28951	−	1.89920i	−0.168086	−	0.0970447i	−0.581683	+	0.813415i	$0.697606\pi$
$384$	−6.01470	+	18.4453i	−0.306937	+	0.941284i
$385$		0			0
$386$		−	3.99220i		−	0.203198i
$387$	−7.94754	−	17.9520i	−0.403996	−	0.912552i
$388$	3.08899	+	5.35029i	0.156820	+	0.271620i
$389$	−7.88909	+	4.55477i	−0.399993	+	0.230936i	−0.686481	−	0.727148i	$-0.740845\pi$
$389$	−7.88909	+	4.55477i	−0.399993	+	0.230936i	0.286488	+	0.958084i	$0.407512\pi$
$390$	−8.89382	−	5.62287i	−0.450356	−	0.284725i
$391$		−	1.40348i		−	0.0709770i
$392$		0			0
$393$	8.89016	−	27.2635i	0.448449	−	1.37526i
$394$	4.21545	−	7.30137i	0.212371	−	0.367838i
$395$	−6.01151	−	5.85446i	−0.302472	−	0.294570i
$396$	−19.1552	−	2.05404i	−0.962584	−	0.103219i
$397$	12.1191	−	20.9910i	0.608242	−	1.05351i	−0.383288	−	0.923629i	$-0.625208\pi$
$397$	12.1191	−	20.9910i	0.608242	−	1.05351i	0.991530	−	0.129878i	$-0.0414584\pi$
$398$		−	10.9309i		−	0.547914i
$399$		0			0
$400$	7.15333	−	4.38641i	0.357666	−	0.219320i
$401$	26.1500	+	15.0977i	1.30587	+	0.753944i	0.981404	−	0.191953i	$-0.0614821\pi$
$401$	26.1500	+	15.0977i	1.30587	+	0.753944i	0.324466	+	0.945897i	$0.394815\pi$
$402$	2.01881	+	9.54713i	0.100689	+	0.476167i
$403$	−1.42881	+	0.824921i	−0.0711739	+	0.0410923i
$404$	5.21509	−	9.03279i	0.259460	−	0.449398i
$405$	11.1126	+	16.7783i	0.552187	+	0.833720i
$406$		0			0
$407$	−17.2824			−0.856656
$408$	6.48106	−	5.82324i	0.320860	−	0.288294i
$409$	21.3618	−	12.3332i	1.05627	−	0.609839i	0.131874	−	0.991267i	$-0.457901\pi$
$409$	21.3618	−	12.3332i	1.05627	−	0.609839i	0.924399	+	0.381427i	$0.124567\pi$
$410$	−2.35478	−	2.29327i	−0.116295	−	0.113256i
$411$	22.9921	+	25.5894i	1.13412	+	1.26223i
$412$	−15.5483			−0.766008
$413$		0			0
$414$	1.00756	+	0.735280i	0.0495189	+	0.0361370i
$415$	−11.4319	−	2.90158i	−0.561170	−	0.142433i
$416$	12.0174	+	20.8148i	0.589202	+	1.02053i
$417$	−0.0819740	−	0.387662i	−0.00401428	−	0.0189839i
$418$	5.84953	−	10.1317i	0.286110	−	0.495556i
$419$	39.4615			1.92782			0.963911	−	0.266226i	$-0.0857766\pi$
$419$	39.4615			1.92782			0.963911	+	0.266226i	$0.0857766\pi$
$420$		0			0
$421$	−30.9363			−1.50774			−0.753870	−	0.657023i	$-0.771815\pi$
$421$	−30.9363			−1.50774			−0.753870	+	0.657023i	$0.771815\pi$
$422$	5.94218	−	10.2921i	0.289261	−	0.501014i
$423$	−23.2708	−	2.49536i	−1.13146	−	0.121329i
$424$	−8.32178	−	14.4137i	−0.404141	−	0.699993i
$425$	−10.8791	+	0.288023i	−0.527716	+	0.0139712i
$426$	−8.64066	−	2.81757i	−0.418641	−	0.136512i
$427$		0			0
$428$	−29.7509			−1.43807
$429$	−22.0043	+	19.7709i	−1.06238	+	0.954548i
$430$	−6.58310	+	6.75969i	−0.317465	+	0.325981i
$431$	26.6240	−	15.3713i	1.28243	−	0.740412i	0.305138	−	0.952308i	$-0.401297\pi$
$431$	26.6240	−	15.3713i	1.28243	−	0.740412i	0.977292	+	0.211896i	$0.0679639\pi$
$432$	−0.884148	−	8.67536i	−0.0425386	−	0.417393i
$433$	2.95856			0.142179			0.0710896	−	0.997470i	$-0.477352\pi$
$433$	2.95856			0.142179			0.0710896	+	0.997470i	$0.477352\pi$
$434$		0			0
$435$	−4.52292	−	0.181817i	−0.216857	−	0.00871746i
$436$	0.717658	−	1.24302i	0.0343696	−	0.0595298i
$437$	2.49949	−	1.44308i	0.119567	−	0.0690318i
$438$	5.72217	−	1.21000i	0.273416	−	0.0578159i
$439$	−15.0772	−	8.70485i	−0.719598	−	0.415460i	0.0950070	−	0.995477i	$-0.469713\pi$
$439$	−15.0772	−	8.70485i	−0.719598	−	0.415460i	−0.814605	+	0.580017i	$0.803046\pi$
$440$	5.68901	+	20.1606i	0.271213	+	0.961117i
$441$		0			0
$442$		−	5.91341i		−	0.281272i
$443$	−15.8970	+	27.5344i	−0.755288	+	1.30820i	0.189942	+	0.981795i	$0.439170\pi$
$443$	−15.8970	+	27.5344i	−0.755288	+	1.30820i	−0.945231	+	0.326403i	$0.894163\pi$
$444$	−2.42033	−	11.4460i	−0.114864	−	0.543201i
$445$	−1.43334	−	1.39589i	−0.0679466	−	0.0661716i
$446$	0.202281	−	0.350362i	0.00957830	−	0.0165901i
$447$	−16.3989	−	5.34741i	−0.775643	−	0.252924i
$448$		0			0
$449$			2.99461i			0.141324i	0.997500	+	0.0706621i	$0.0225112\pi$
$449$			2.99461i			0.141324i	−0.997500	+	0.0706621i	$0.977489\pi$
$450$	5.49279	−	7.96106i	0.258933	−	0.375288i
$451$	−8.00279	+	4.62041i	−0.376837	+	0.217567i
$452$	6.99400	+	12.1140i	0.328970	+	0.569793i
$453$	−5.87426	−	6.53784i	−0.275997	−	0.307175i
$454$		−	3.50091i		−	0.164306i
$455$		0			0
$456$	17.0347	+	5.55471i	0.797721	+	0.260123i
$457$	7.62540	+	4.40252i	0.356701	+	0.205941i	0.667633	−	0.744491i	$-0.267308\pi$
$457$	7.62540	+	4.40252i	0.356701	+	0.205941i	−0.310932	+	0.950432i	$0.600641\pi$
$458$	−8.02669	+	4.63421i	−0.375063	+	0.216543i
$459$	−4.63273	+	10.3175i	−0.216237	+	0.481582i
$460$	−0.561940	+	2.21398i	−0.0262006	+	0.103227i
$461$	−31.9710			−1.48904			−0.744519	−	0.667602i	$-0.767321\pi$
$461$	−31.9710			−1.48904			−0.744519	+	0.667602i	$0.767321\pi$
$462$		0			0
$463$			6.94495i			0.322759i	0.986892	+	0.161380i	$0.0515943\pi$
$463$			6.94495i			0.322759i	−0.986892	+	0.161380i	$0.948406\pi$
$464$	1.69865	+	0.980715i	0.0788577	+	0.0455285i
$465$	−0.704909	−	1.34277i	−0.0326894	−	0.0622693i
$466$	2.71801	+	4.70774i	0.125910	+	0.218082i
$467$	21.1944	+	12.2366i	0.980758	+	0.566241i	0.902499	−	0.430692i	$-0.141731\pi$
$467$	21.1944	+	12.2366i	0.980758	+	0.566241i	0.0782589	+	0.996933i	$0.475064\pi$
$468$	−16.1757	−	11.8044i	−0.747721	−	0.545658i
$469$		0			0
$470$	3.05480	+	10.8255i	0.140908	+	0.499344i
$471$	−19.5099	−	21.7139i	−0.898970	−	1.00052i
$472$	13.0867	+	22.6668i	0.602364	+	1.04332i
$473$	13.2635	+	22.9730i	0.609854	+	1.05630i
$474$	2.80113	+	3.11756i	0.128660	+	0.143194i
$475$	−11.6991	−	19.0788i	−0.536789	−	0.875393i
$476$		0			0
$477$	17.4516	+	12.7355i	0.799054	+	0.583119i
$478$	1.51807	+	0.876459i	0.0694350	+	0.0400883i
$479$	12.1451	+	21.0359i	0.554923	+	0.961156i	0.997909	+	0.0646271i	$0.0205858\pi$
$479$	12.1451	+	21.0359i	0.554923	+	0.961156i	−0.442986	+	0.896529i	$0.646081\pi$
$480$	−19.5614	+	10.2691i	−0.892849	+	0.468717i
$481$	−15.5573	−	8.98204i	−0.709354	−	0.409546i
$482$			0.986217i			0.0449209i
$483$		0			0
$484$	8.60377			0.391080
$485$	−2.14523	+	8.45196i	−0.0974097	+	0.383784i
$486$	−4.97991	−	8.73119i	−0.225893	−	0.396055i
$487$	8.44934	−	4.87823i	0.382876	−	0.221054i	−0.296193	−	0.955128i	$-0.595717\pi$
$487$	8.44934	−	4.87823i	0.382876	−	0.221054i	0.679069	+	0.734075i	$0.262384\pi$
$488$	13.9929	+	8.07879i	0.633427	+	0.365710i
$489$	7.91563	+	2.58115i	0.357957	+	0.116724i
$490$		0			0
$491$		−	23.6689i		−	1.06816i	−0.845434	−	0.534080i	$-0.820658\pi$
$491$		−	23.6689i		−	1.06816i	0.845434	−	0.534080i	$-0.179342\pi$
$492$	−4.18081	−	4.65310i	−0.188486	−	0.209778i
$493$	−1.27195	−	2.20308i	−0.0572858	−	0.0992219i
$494$	10.5313	−	6.08026i	0.473826	−	0.273564i
$495$	−17.3465	−	20.9402i	−0.779665	−	0.941191i
$496$			0.657143i			0.0295066i
$497$		0			0
$498$	5.60064	+	1.82627i	0.250971	+	0.0818373i
$499$	5.73534	−	9.93391i	0.256749	−	0.444703i	−0.708620	−	0.705590i	$-0.750682\pi$
$499$	5.73534	−	9.93391i	0.256749	−	0.444703i	0.965369	+	0.260888i	$0.0840152\pi$
$500$	17.2771	+	3.90155i	0.772657	+	0.174483i
$501$	−1.59489	−	7.54238i	−0.0712545	−	0.336969i
$502$	−2.84050	+	4.91988i	−0.126778	+	0.219585i
$503$			16.8580i			0.751659i	0.926689	+	0.375830i	$0.122642\pi$
$503$			16.8580i			0.751659i	−0.926689	+	0.375830i	$0.877358\pi$
$504$		0			0
$505$	14.1685	−	3.99812i	0.630488	−	0.177914i
$506$	−1.45955	−	0.842672i	−0.0648849	−	0.0374613i
$507$	−8.05379	+	1.70303i	−0.357681	+	0.0756343i
$508$	−21.7115	+	12.5351i	−0.963292	+	0.556157i
$509$	1.47582	−	2.55620i	0.0654147	−	0.113302i	−0.831463	−	0.555580i	$-0.812496\pi$
$509$	1.47582	−	2.55620i	0.0654147	−	0.113302i	0.896878	+	0.442278i	$0.145830\pi$
$510$	5.43127	+	0.218332i	0.240500	+	0.00966790i
$511$		0			0
$512$	17.3304			0.765902
$513$	−23.1382	+	2.35812i	−1.02158	+	0.104114i
$514$	11.2262	−	6.48142i	0.495164	−	0.285883i
$515$	−15.7220	−	15.3112i	−0.692793	−	0.674694i
$516$	−13.3573	+	12.0015i	−0.588021	+	0.528338i
$517$	31.6230			1.39078
$518$		0			0
$519$	−18.8618	−	6.15051i	−0.827941	−	0.269977i
$520$	−5.35673	+	21.1050i	−0.234908	+	0.925513i
$521$	7.91563	+	13.7103i	0.346790	+	0.600658i	0.985677	−	0.168642i	$-0.0539382\pi$
$521$	7.91563	+	13.7103i	0.346790	+	0.600658i	−0.638887	+	0.769300i	$0.720605\pi$
$522$	2.24797	+	0.241054i	0.0983911	+	0.0105506i
$523$	−10.9800	+	19.0179i	−0.480122	+	0.831595i	−0.999740	−	0.0228034i	$-0.992741\pi$
$523$	−10.9800	+	19.0179i	−0.480122	+	0.831595i	0.519618	+	0.854398i	$0.326074\pi$
$524$	−26.2289			−1.14581
$525$		0			0
$526$	−5.64798			−0.246263
$527$	0.426145	−	0.738105i	0.0185632	−	0.0321524i
$528$	2.43761	+	11.5277i	0.106083	+	0.501678i
$529$	11.2921	+	19.5585i	0.490961	+	0.850370i
$530$	2.55443	−	10.0642i	0.110958	−	0.437161i
$531$	−27.4441	−	20.0277i	−1.19097	−	0.869126i
$532$		0			0
$533$	−9.60532			−0.416053
$534$	0.667880	+	0.743327i	0.0289020	+	0.0321669i
$535$	−30.0833	−	29.2974i	−1.30062	−	1.26664i
$536$	17.4879	−	10.0966i	0.755361	−	0.436108i
$537$	13.4565	−	12.0907i	0.580693	−	0.521753i
$538$	−11.1221			−0.479508
$539$		0			0
$540$	11.4392	−	14.4210i	0.492263	−	0.620580i
$541$	−2.34667	+	4.06456i	−0.100891	+	0.174749i	−0.912052	−	0.410074i	$-0.865503\pi$
$541$	−2.34667	+	4.06456i	−0.100891	+	0.174749i	0.811161	+	0.584823i	$0.198836\pi$
$542$	12.6457	−	7.30101i	0.543181	−	0.313605i
$543$	−4.28620	−	20.2698i	−0.183938	−	0.869860i
$544$	−10.7527	−	6.20806i	−0.461017	−	0.266168i
$545$	1.94975	−	0.550189i	0.0835180	−	0.0235675i
$546$		0			0
$547$			14.9485i			0.639151i	0.947561	+	0.319575i	$0.103540\pi$
$547$			14.9485i			0.639151i	−0.947561	+	0.319575i	$0.896460\pi$
$548$	15.7326	−	27.2497i	0.672065	−	1.16405i
$549$	−20.8541	−	2.23622i	−0.890029	−	0.0954393i
$550$	−6.23249	+	11.4867i	−0.265754	+	0.489796i
$551$	2.61568	−	4.53049i	0.111432	−	0.193005i
$552$	0.800202	−	2.45398i	0.0340589	−	0.104448i
$553$		0			0
$554$		−	8.51867i		−	0.361924i
$555$	8.82410	−	13.9573i	0.374562	−	0.592453i
$556$	−0.313862	+	0.181208i	−0.0133107	+	0.00768494i
$557$	−0.614501	−	1.06435i	−0.0260373	−	0.0450979i	0.852713	−	0.522379i	$-0.174956\pi$
$557$	−0.614501	−	1.06435i	−0.0260373	−	0.0450979i	−0.878750	+	0.477282i	$0.841622\pi$
$558$	0.306631	+	0.692623i	0.0129807	+	0.0293211i
$559$			27.5732i			1.16622i
$560$		0			0
$561$	4.73755	−	14.5287i	0.200020	−	0.613401i
$562$	−18.3554	−	10.5975i	−0.774276	−	0.447028i
$563$	−3.64387	+	2.10379i	−0.153571	+	0.0886643i	−0.574816	−	0.818282i	$-0.694926\pi$
$563$	−3.64387	+	2.10379i	−0.153571	+	0.0886643i	0.421245	+	0.906947i	$0.361593\pi$
$564$	4.42868	+	20.9436i	0.186481	+	0.881884i
$565$	−4.85716	+	19.1367i	−0.204342	+	0.805086i
$566$	10.1953			0.428542
$567$		0			0
$568$			18.8072i			0.789132i
$569$	−22.3139	−	12.8829i	−0.935447	−	0.540081i	−0.0469169	−	0.998899i	$-0.514940\pi$
$569$	−22.3139	−	12.8829i	−0.935447	−	0.540081i	−0.888530	+	0.458818i	$0.848273\pi$
$570$	5.19568	+	9.89715i	0.217623	+	0.414546i
$571$	−12.3419	−	21.3768i	−0.516492	−	0.894591i	−0.999817	−	0.0191497i	$-0.993904\pi$
$571$	−12.3419	−	21.3768i	−0.516492	−	0.894591i	0.483324	−	0.875441i	$-0.339429\pi$
$572$	23.4320	+	13.5285i	0.979743	+	0.565655i
$573$	23.2972	+	7.59681i	0.973253	+	0.317361i
$574$		0			0
$575$	−2.74845	+	1.68534i	−0.114618	+	0.0702837i
$576$	0.882703	−	0.390782i	0.0367793	−	0.0162826i
$577$	−2.86692	−	4.96565i	−0.119351	−	0.206723i	0.800159	−	0.599787i	$-0.204748\pi$
$577$	−2.86692	−	4.96565i	−0.119351	−	0.206723i	−0.919511	+	0.393065i	$0.871415\pi$
$578$	−3.95345	−	6.84757i	−0.164442	−	0.284822i
$579$	7.97680	−	7.16716i	0.331504	−	0.297857i
$580$	1.12440	+	3.98463i	0.0466883	+	0.165453i
$581$		0			0
$582$	1.35022	−	4.14073i	0.0559684	−	0.171639i
$583$	−25.2804	−	14.5956i	−1.04701	−	0.604489i
$584$	−6.05152	−	10.4815i	−0.250414	−	0.433729i
$585$	−4.73195	−	27.8654i	−0.195642	−	1.15209i
$586$	−11.6038	−	6.69944i	−0.479347	−	0.276751i
$587$		−	31.0435i		−	1.28130i	−0.767832	−	0.640652i	$-0.778664\pi$
$587$		−	31.0435i		−	1.28130i	0.767832	−	0.640652i	$-0.221336\pi$
$588$		0			0
$589$	1.75268			0.0722178
$590$	−4.01706	+	15.8268i	−0.165380	+	0.651578i
$591$	22.1568	−	4.68522i	0.911408	−	0.192724i
$592$	−6.19659	+	3.57760i	−0.254678	+	0.147039i
$593$	−28.2124	−	16.2884i	−1.15854	−	0.668885i	−0.207588	−	0.978216i	$-0.566561\pi$
$593$	−28.2124	−	16.2884i	−1.15854	−	0.668885i	−0.950954	+	0.309331i	$0.899895\pi$
$594$	7.94818	+	11.0126i	0.326118	+	0.451854i
$595$		0			0
$596$			15.7766i			0.646236i
$597$	21.8409	−	19.6241i	0.893888	−	0.803159i
$598$	−0.875911	−	1.51712i	−0.0358187	−	0.0620397i
$599$	31.8553	−	18.3917i	1.30157	−	0.751463i	0.320899	−	0.947113i	$-0.396015\pi$
$599$	31.8553	−	18.3917i	1.30157	−	0.751463i	0.980674	+	0.195650i	$0.0626817\pi$
$600$	−19.1864	−	5.69920i	−0.783282	−	0.232669i
$601$			42.5075i			1.73392i	0.498380	+	0.866959i	$0.333929\pi$
$601$			42.5075i			1.73392i	−0.498380	+	0.866959i	$0.666071\pi$
$602$		0			0
$603$	−15.4517	+	21.1736i	−0.629242	+	0.862257i
$604$	−4.01954	+	6.96205i	−0.163553	+	0.283282i
$605$	8.69989	+	8.47261i	0.353701	+	0.344461i
$606$	−7.19392	+	1.52121i	−0.292233	+	0.0617948i
$607$	−8.47607	+	14.6810i	−0.344033	+	0.595883i	−0.985178	−	0.171537i	$-0.945127\pi$
$607$	−8.47607	+	14.6810i	−0.344033	+	0.595883i	0.641144	+	0.767420i	$0.278460\pi$
$608$		−	25.5329i		−	1.03550i
$609$		0			0
$610$	2.73755	+	9.70127i	0.110840	+	0.392793i
$611$	28.4666	+	16.4352i	1.15163	+	0.664896i
$612$	10.2857	+	1.10295i	0.415774	+	0.0445841i
$613$	30.0373	−	17.3421i	1.21320	−	0.700439i	0.249742	−	0.968312i	$-0.419654\pi$
$613$	30.0373	−	17.3421i	1.21320	−	0.700439i	0.963454	+	0.267873i	$0.0863207\pi$
$614$	4.18664	−	7.25148i	0.168959	−	0.292646i
$615$	0.354643	−	8.82216i	0.0143006	−	0.355744i
$616$		0			0
$617$	45.7116			1.84028			0.920140	−	0.391590i	$-0.128075\pi$
$617$	45.7116			1.84028			0.920140	+	0.391590i	$0.128075\pi$
$618$	7.32584	+	8.15340i	0.294689	+	0.327978i
$619$	34.2356	−	19.7659i	1.37604	−	0.794459i	0.384363	−	0.923182i	$-0.374421\pi$
$619$	34.2356	−	19.7659i	1.37604	−	0.794459i	0.991681	+	0.128723i	$0.0410877\pi$
$620$	−0.967773	+	0.993733i	−0.0388667	+	0.0399093i
$621$	0.339707	+	3.33324i	0.0136320	+	0.133758i
$622$	−0.295096			−0.0118323
$623$		0			0
$624$	−3.79689	+	11.6439i	−0.151997	+	0.466130i
$625$	13.6281	+	20.9589i	0.545123	+	0.838356i
$626$	8.94408	+	15.4916i	0.357477	+	0.619169i
$627$	30.7456	−	6.50139i	1.22786	−	0.259641i
$628$	−13.3499	+	23.1228i	−0.532720	+	0.922698i
$629$	9.28004			0.370020
$630$		0			0
$631$	−21.1685			−0.842703			−0.421351	−	0.906897i	$-0.638444\pi$
$631$	−21.1685			−0.842703			−0.421351	+	0.906897i	$0.638444\pi$
$632$	4.33646	−	7.51097i	0.172495	−	0.298770i
$633$	31.2326	−	6.60437i	1.24139	−	0.262500i
$634$	1.45835	+	2.52594i	0.0579187	+	0.100318i
$635$	−34.2981	−	8.70534i	−1.36108	−	0.345461i
$636$	6.12612	−	18.7870i	0.242916	−	0.744952i
$637$		0			0
$638$	−3.05480			−0.120941
$639$	−9.88271	−	22.3232i	−0.390954	−	0.883092i
$640$	17.9436	+	17.4749i	0.709284	+	0.690754i
$641$	−30.6083	+	17.6717i	−1.20896	+	0.697991i	−0.962531	−	0.271171i	$-0.912589\pi$
$641$	−30.6083	+	17.6717i	−1.20896	+	0.697991i	−0.246424	+	0.969162i	$0.579256\pi$
$642$	14.0177	+	15.6012i	0.553234	+	0.615730i
$643$	26.0538			1.02746			0.513731	−	0.857951i	$-0.328263\pi$
$643$	26.0538			1.02746			0.513731	+	0.857951i	$0.328263\pi$
$644$		0			0
$645$	−25.3251	−	1.01805i	−0.997174	−	0.0400855i
$646$	−3.14099	+	5.44036i	−0.123581	+	0.214048i
$647$	−35.3707	+	20.4213i	−1.39057	+	0.802844i	−0.993378	−	0.114894i	$-0.963347\pi$
$647$	−35.3707	+	20.4213i	−1.39057	+	0.802844i	−0.397188	+	0.917737i	$0.630014\pi$
$648$	−13.9829	+	15.3988i	−0.549302	+	0.604924i
$649$	39.7555	+	22.9528i	1.56054	+	0.900977i
$650$	−11.5803	+	7.10102i	−0.454217	+	0.278525i
$651$		0			0
$652$		−	7.61525i		−	0.298236i
$653$	−12.0041	+	20.7918i	−0.469758	+	0.813645i	−0.999402	−	0.0345747i	$-0.988992\pi$
$653$	−12.0041	+	20.7918i	−0.469758	+	0.813645i	0.529644	+	0.848220i	$0.322326\pi$
$654$	−0.989968	+	0.209336i	−0.0387108	+	0.00818569i
$655$	−26.5219	−	25.8291i	−1.03630	−	1.00923i
$656$	−1.91293	+	3.31329i	−0.0746874	+	0.129362i
$657$	12.6906	+	9.26115i	0.495109	+	0.361312i
$658$		0			0
$659$			38.7398i			1.50909i	0.656248	+	0.754545i	$0.272142\pi$
$659$			38.7398i			1.50909i	−0.656248	+	0.754545i	$0.727858\pi$
$660$	−13.2906	+	21.0220i	−0.517336	+	0.818282i
$661$	−44.0826	+	25.4511i	−1.71461	+	0.989933i	−0.786539	+	0.617541i	$0.788129\pi$
$661$	−44.0826	+	25.4511i	−1.71461	+	0.989933i	−0.928075	+	0.372392i	$0.878538\pi$
$662$	7.38188	+	12.7858i	0.286905	+	0.496934i
$663$	11.8156	−	10.6163i	0.458878	−	0.412302i
$664$		−	12.1903i		−	0.473076i
$665$		0			0
$666$	−4.86179	+	6.66217i	−0.188391	+	0.258154i
$667$	−0.652654	−	0.376810i	−0.0252709	−	0.0145901i
$668$	−6.10653	+	3.52560i	−0.236269	+	0.136410i
$669$	1.06321	−	0.224823i	0.0411060	−	0.00869218i
$670$	12.2107	+	3.09924i	0.471739	+	0.119734i
$671$	28.3389			1.09401
$672$		0			0
$673$			3.33192i			0.128436i	0.997936	+	0.0642181i	$0.0204553\pi$
$673$			3.33192i			0.128436i	−0.997936	+	0.0642181i	$0.979545\pi$
$674$	17.4570	+	10.0788i	0.672420	+	0.388222i
$675$	25.7681	−	3.31731i	0.991815	−	0.127683i
$676$	3.76466	+	6.52057i	0.144794	+	0.250791i
$677$	28.0352	+	16.1861i	1.07748	+	0.622083i	0.930215	−	0.367014i	$-0.119620\pi$
$677$	28.0352	+	16.1861i	1.07748	+	0.622083i	0.147264	+	0.989097i	$0.452953\pi$
$678$	3.05713	−	9.37531i	0.117408	−	0.360057i
$679$		0			0
$680$	−3.05480	−	10.8255i	−0.117146	−	0.415140i
$681$	6.99514	−	6.28515i	0.268055	−	0.240847i
$682$	−0.511729	−	0.886341i	−0.0195951	−	0.0339398i
$683$	−10.8868	−	18.8566i	−0.416573	−	0.721526i	0.579019	−	0.815314i	$-0.303436\pi$
$683$	−10.8868	−	18.8566i	−0.416573	−	0.721526i	−0.995592	+	0.0937881i	$0.970102\pi$
$684$	8.61162	+	19.4520i	0.329273	+	0.743767i
$685$	42.7427	−	12.0614i	1.63312	−	0.460841i
$686$		0			0
$687$	−23.6698	−	7.71833i	−0.903060	−	0.294473i
$688$	9.51121	+	5.49130i	0.362611	+	0.209354i
$689$	−15.1713	−	26.2775i	−0.577982	−	1.00109i
$690$	1.42576	−	0.748480i	0.0542779	−	0.0284941i
$691$	−5.15554	−	2.97655i	−0.196126	−	0.113233i	0.398721	−	0.917072i	$-0.369454\pi$
$691$	−5.15554	−	2.97655i	−0.196126	−	0.113233i	−0.594847	+	0.803839i	$0.702787\pi$
$692$			18.1460i			0.689809i
$693$		0			0
$694$	1.79689			0.0682088
$695$	−0.495815	−	0.125845i	−0.0188073	−	0.00477356i
$696$	−0.967905	−	4.57730i	−0.0366883	−	0.173502i
$697$	4.29722	−	2.48100i	0.162769	−	0.0939747i
$698$	9.24939	+	5.34014i	0.350095	+	0.202127i
$699$	−4.52688	+	13.8826i	−0.171222	+	0.525088i
$700$		0			0
$701$			19.3393i			0.730434i	0.930922	+	0.365217i	$0.119005\pi$
$701$			19.3393i			0.730434i	−0.930922	+	0.365217i	$0.880995\pi$
$702$	1.43132	+	14.0443i	0.0540217	+	0.530067i
$703$	9.54188	+	16.5270i	0.359879	+	0.623329i
$704$	−1.12958	+	0.652166i	−0.0425728	+	0.0245794i
$705$	−16.1462	+	25.5388i	−0.608100	+	0.961845i
$706$		−	2.11301i		−	0.0795242i
$707$		0			0
$708$	−9.63383	+	29.5441i	−0.362061	+	1.11034i
$709$	16.9012	−	29.2738i	0.634739	−	1.09940i	−0.351831	−	0.936063i	$-0.614441\pi$
$709$	16.9012	−	29.2738i	0.634739	−	1.09940i	0.986570	−	0.163337i	$-0.0522257\pi$
$710$	−8.18605	+	8.40564i	−0.307217	+	0.315458i
$711$	−1.20034	+	11.1939i	−0.0450161	+	0.419802i
$712$	1.03395	−	1.79086i	0.0387490	−	0.0671152i
$713$		−	0.252487i		−	0.00945573i
$714$		0			0
$715$	10.3716	+	36.7545i	0.387875	+	1.37454i
$716$	−14.3297	−	8.27324i	−0.535525	−	0.309185i
$717$	0.974132	+	4.60675i	0.0363796	+	0.172042i
$718$	−9.49685	+	5.48301i	−0.354419	+	0.204624i
$719$	−13.7118	+	23.7495i	−0.511363	+	0.885707i	0.488550	+	0.872536i	$0.337526\pi$
$719$	−13.7118	+	23.7495i	−0.511363	+	0.885707i	−0.999913	+	0.0131713i	$0.995807\pi$
$720$	−10.5544	−	3.91722i	−0.393338	−	0.145986i
$721$		0			0
$722$	−0.667157			−0.0248290
$723$	−1.97055	+	1.77055i	−0.0732857	+	0.0658473i
$724$	−16.4110	+	9.47490i	−0.609910	+	0.352132i
$725$	−2.78693	+	5.13641i	−0.103504	+	0.190762i
$726$	−4.05382	−	4.51176i	−0.150451	−	0.167447i
$727$	6.14612			0.227947			0.113973	−	0.993484i	$-0.463642\pi$
$727$	6.14612			0.227947			0.113973	+	0.993484i	$0.463642\pi$
$728$		0			0
$729$	8.50535	−	25.6254i	0.315013	−	0.949087i
$730$	1.85756	−	7.31859i	0.0687514	−	0.270873i
$731$	−7.12202	−	12.3357i	−0.263417	−	0.456252i
$732$	3.96875	+	18.7686i	0.146689	+	0.693706i
$733$	−8.41748	+	14.5795i	−0.310907	+	0.538506i	−0.978559	−	0.205967i	$-0.933966\pi$
$733$	−8.41748	+	14.5795i	−0.310907	+	0.538506i	0.667652	+	0.744473i	$0.267299\pi$
$734$	11.0370			0.407384
$735$		0			0
$736$	−3.67822			−0.135581
$737$	17.7085	−	30.6721i	0.652302	−	1.12982i
$738$	−0.470187	+	4.38478i	−0.0173078	+	0.161406i
$739$	19.3419	+	33.5012i	0.711503	+	1.23236i	0.964293	+	0.264838i	$0.0853186\pi$
$739$	19.3419	+	33.5012i	0.711503	+	1.23236i	−0.252790	+	0.967521i	$0.581348\pi$
$740$	−14.6392	−	3.71564i	−0.538149	−	0.136590i
$741$	31.0557	+	10.1267i	1.14086	+	0.372015i
$742$		0			0
$743$	39.3563			1.44384			0.721920	−	0.691976i	$-0.243260\pi$
$743$	39.3563			1.44384			0.721920	+	0.691976i	$0.243260\pi$
$744$	1.16595	−	1.04761i	0.0427458	−	0.0384072i
$745$	−15.5361	+	15.9529i	−0.569200	+	0.584469i
$746$	−16.1457	+	9.32174i	−0.591137	+	0.341293i
$747$	6.40571	+	14.4693i	0.234373	+	0.529404i
$748$	−13.9773			−0.511062
$749$		0			0
$750$	−6.09448	−	10.8983i	−0.222539	−	0.397949i
$751$	−16.1416	+	27.9580i	−0.589014	+	1.02020i	0.405347	+	0.914163i	$0.367151\pi$
$751$	−16.1416	+	27.9580i	−0.589014	+	1.02020i	−0.994362	+	0.106040i	$0.966183\pi$
$752$	11.3384	−	6.54623i	0.413469	−	0.238717i
$753$	−14.9299	+	3.15704i	−0.544076	+	0.115049i
$754$	−2.74989	−	1.58765i	−0.100145	−	0.0578187i
$755$	−10.9204	+	3.08156i	−0.397433	+	0.112150i
$756$		0			0
$757$			40.0667i			1.45625i	0.685446	+	0.728124i	$0.259607\pi$
$757$			40.0667i			1.45625i	−0.685446	+	0.728124i	$0.740393\pi$
$758$	0.180403	−	0.312467i	0.00655252	−	0.0113493i
$759$	−0.936579	−	4.42916i	−0.0339957	−	0.160768i
$760$	16.1384	−	16.5713i	0.585402	−	0.601105i
$761$	6.58977	−	11.4138i	0.238879	−	0.413750i	−0.721514	−	0.692400i	$-0.756553\pi$
$761$	6.58977	−	11.4138i	0.238879	−	0.413750i	0.960393	+	0.278649i	$0.0898868\pi$
$762$	16.8031	+	5.47920i	0.608712	+	0.198491i
$763$		0			0
$764$		−	22.4131i		−	0.810877i
$765$	9.31445	+	11.2442i	0.336765	+	0.406533i
$766$	2.12110	−	1.22462i	0.0766384	−	0.0442472i
$767$	23.8582	+	41.3236i	0.861469	+	1.49211i
$768$	−9.10604	−	10.1347i	−0.328586	−	0.365704i
$769$		−	12.7709i		−	0.460530i	−0.973128	−	0.230265i	$-0.926041\pi$
$769$		−	12.7709i		−	0.460530i	0.973128	−	0.230265i	$-0.0739593\pi$
$770$		0			0
$771$	33.1047	+	10.7949i	1.19224	+	0.388768i
$772$	−8.49437	−	4.90423i	−0.305719	−	0.176507i
$773$	15.7518	−	9.09428i	0.566551	−	0.327099i	−0.189219	−	0.981935i	$-0.560596\pi$
$773$	15.7518	−	9.09428i	0.566551	−	0.327099i	0.755771	+	0.654836i	$0.227262\pi$
$774$	12.5870	+	1.34973i	0.452432	+	0.0485150i
$775$	−1.95717	+	0.0518156i	−0.0703036	+	0.00186127i
$776$	−9.01267			−0.323536
$777$		0			0
$778$		−	5.87388i		−	0.210589i
$779$	8.83694	+	5.10201i	0.316616	+	0.182798i
$780$	−22.8896	+	12.0163i	−0.819580	+	0.430253i
$781$	16.4930	+	28.5667i	0.590167	+	1.02220i
$782$	0.783728	+	0.452486i	0.0280261	+	0.0161809i
$783$	3.55412	+	4.92442i	0.127014	+	0.175985i
$784$		0			0
$785$	−36.2693	+	10.2347i	−1.29451	+	0.365291i
$786$	12.3582	+	13.7543i	0.440803	+	0.490598i
$787$	0.619297	+	1.07265i	0.0220756	+	0.0382360i	0.876852	−	0.480760i	$-0.159639\pi$
$787$	0.619297	+	1.07265i	0.0220756	+	0.0382360i	−0.854777	+	0.518996i	$0.826306\pi$
$788$	−10.3569	−	17.9388i	−0.368951	−	0.639042i
$789$	−10.1398	−	11.2852i	−0.360985	−	0.401763i
$790$	5.20736	−	1.46944i	0.185270	−	0.0522803i
$791$		0			0
$792$	16.5672	−	22.7022i	0.588690	−	0.806689i
$793$	25.5102	+	14.7283i	0.905895	+	0.523019i
$794$	7.81449	+	13.5351i	0.277326	+	0.480343i
$795$	24.6952	−	12.9642i	0.875847	−	0.459791i
$796$	−23.2580	−	13.4280i	−0.824359	−	0.475944i
$797$		−	51.4416i		−	1.82216i	−0.412235	−	0.911078i	$-0.635252\pi$
$797$		−	51.4416i		−	1.82216i	0.412235	−	0.911078i	$-0.364748\pi$
$798$		0			0
$799$	−16.9805			−0.600725
$800$	0.754847	+	28.5119i	0.0266879	+	1.00805i
$801$	−0.286199	+	2.66897i	−0.0101123	+	0.0943036i
$802$	−16.8617	+	9.73510i	−0.595407	+	0.343758i
$803$	−18.3836	−	10.6138i	−0.648745	−	0.374553i
$804$	22.7938	+	7.43268i	0.803876	+	0.262130i
$805$		0			0
$806$		−	1.06383i		−	0.0374718i
$807$	−19.9674	−	22.2230i	−0.702886	−	0.782287i
$808$	7.60797	+	13.1774i	0.267647	+	0.463579i
$809$	2.44518	−	1.41172i	0.0859679	−	0.0496336i	−0.456400	−	0.889775i	$-0.650861\pi$
$809$	2.44518	−	1.41172i	0.0859679	−	0.0496336i	0.542368	+	0.840141i	$0.317528\pi$
$810$	−12.9520	+	0.796083i	−0.455088	+	0.0279715i
$811$			0.162805i			0.00571687i	0.999996	+	0.00285843i	$0.000909869\pi$
$811$			0.162805i			0.00571687i	−0.999996	+	0.00285843i	$0.999090\pi$
$812$		0			0
$813$	37.2909	+	12.1599i	1.30785	+	0.426467i
$814$	5.57189	−	9.65080i	0.195295	−	0.338260i
$815$	7.49917	−	7.70033i	0.262684	−	0.269731i
$816$	−1.30891	−	6.18996i	−0.0458211	−	0.216692i
$817$	14.6459	−	25.3675i	0.512396	−	0.887496i
$818$			15.9051i			0.556108i
$819$		0			0
$820$	−7.77222	+	2.19320i	−0.271418	+	0.0765900i
$821$	−43.3765	−	25.0434i	−1.51385	−	0.874022i	−0.999868	−	0.0162217i	$-0.994836\pi$
$821$	−43.3765	−	25.0434i	−1.51385	−	0.874022i	−0.513983	−	0.857801i	$-0.671830\pi$
$822$	−21.7023	+	4.58911i	−0.756954	+	0.160063i
$823$	33.1050	−	19.1132i	1.15397	−	0.666243i	0.204116	−	0.978947i	$-0.434568\pi$
$823$	33.1050	−	19.1132i	1.15397	−	0.666243i	0.949851	+	0.312704i	$0.101235\pi$
$824$	11.3412	−	19.6435i	0.395090	−	0.684315i
$825$	−34.1407	+	8.16890i	−1.18863	+	0.284405i
$826$		0			0
$827$	−7.13112			−0.247973			−0.123987	−	0.992284i	$-0.539568\pi$
$827$	−7.13112			−0.247973			−0.123987	+	0.992284i	$0.539568\pi$
$828$	2.80222	−	1.24057i	0.0973840	−	0.0431129i
$829$	−0.876338	+	0.505954i	−0.0304365	+	0.0175725i	−0.515141	−	0.857105i	$-0.672260\pi$
$829$	−0.876338	+	0.505954i	−0.0304365	+	0.0175725i	0.484705	+	0.874678i	$0.338927\pi$
$830$	5.30598	−	5.44831i	0.184173	−	0.189114i
$831$	17.0211	−	15.2935i	0.590456	−	0.530525i
$832$	−1.35578			−0.0470032
$833$		0			0
$834$	0.242906	+	0.0792075i	0.00841115	+	0.00274273i
$835$	−9.64661	−	2.44845i	−0.333835	−	0.0847319i
$836$	−14.3717	−	24.8925i	−0.497056	−	0.860927i
$837$	−0.833433	+	1.85614i	−0.0288077	+	0.0641575i
$838$	−12.7225	+	22.0360i	−0.439492	+	0.761222i
$839$	−29.5215			−1.01920			−0.509598	−	0.860412i	$-0.670206\pi$
$839$	−29.5215			−1.01920			−0.509598	+	0.860412i	$0.670206\pi$
$840$		0			0
$841$	27.6340			0.952897
$842$	9.97394	−	17.2754i	0.343725	−	0.595348i
$843$	−11.7785	−	55.7014i	−0.405672	−	1.91846i
$844$	−14.5993	−	25.2868i	−0.502530	−	0.870408i
$845$	−2.61446	+	10.3007i	−0.0899402	+	0.354355i
$846$	8.89603	−	12.1903i	0.305852	−	0.419112i
$847$		0			0
$848$	−12.0857			−0.415024
$849$	18.3036	+	20.3713i	0.628178	+	0.699140i
$850$	3.34663	−	6.16797i	0.114789	−	0.211560i
$851$	2.38085	−	1.37459i	0.0816146	−	0.0471202i
$852$	−16.6097	+	14.9238i	−0.569038	+	0.511282i
$853$	22.0904			0.756362			0.378181	−	0.925732i	$-0.376550\pi$
$853$	22.0904			0.756362			0.378181	+	0.925732i	$0.376550\pi$
$854$		0			0
$855$	−10.4477	+	28.1497i	−0.357303	+	0.962700i
$856$	21.7009	−	37.5871i	0.741722	−	1.28470i
$857$	12.4112	−	7.16559i	0.423957	−	0.244772i	−0.272812	−	0.962067i	$-0.587954\pi$
$857$	12.4112	−	7.16559i	0.423957	−	0.244772i	0.696769	+	0.717296i	$0.254620\pi$
$858$	−3.94617	−	18.6618i	−0.134720	−	0.637103i
$859$	−23.7901	−	13.7352i	−0.811709	−	0.468640i	0.0358402	−	0.999358i	$-0.488589\pi$
$859$	−23.7901	−	13.7352i	−0.811709	−	0.468640i	−0.847549	+	0.530717i	$0.821923\pi$
$860$	6.29585	+	22.3111i	0.214687	+	0.760802i
$861$		0			0
$862$			19.8231i			0.675176i
$863$	−8.11130	+	14.0492i	−0.276112	+	0.478240i	−0.970415	−	0.241443i	$-0.922379\pi$
$863$	−8.11130	+	14.0492i	−0.276112	+	0.478240i	0.694303	+	0.719683i	$0.255713\pi$
$864$	27.0401	+	12.1414i	0.919923	+	0.413059i
$865$	−17.8694	+	18.3488i	−0.607578	+	0.623877i
$866$	−0.953847	+	1.65211i	−0.0324131	+	0.0561411i
$867$	6.58451	−	20.1927i	0.223622	−	0.685782i
$868$		0			0
$869$		−	15.2115i		−	0.516014i
$870$	1.55973	−	2.46706i	0.0528798	−	0.0836412i
$871$	31.8819	−	18.4070i	1.08028	−	0.623698i
$872$	1.04695	+	1.81336i	0.0354541	+	0.0614083i
$873$	10.6976	−	4.73594i	0.362059	−	0.160287i
$874$			1.86101i			0.0629496i
$875$		0			0
$876$	4.45486	−	13.6617i	0.150516	−	0.461587i
$877$	−38.5317	−	22.2463i	−1.30112	−	0.751204i	−0.320527	−	0.947240i	$-0.603860\pi$
$877$	−38.5317	−	22.2463i	−1.30112	−	0.751204i	−0.980597	+	0.196036i	$0.937193\pi$
$878$	9.72189	−	5.61294i	0.328098	−	0.189427i
$879$	−7.44602	−	35.2129i	−0.251148	−	1.18770i
$880$	14.7438	+	3.74217i	0.497012	+	0.126149i
$881$	−0.841670			−0.0283566			−0.0141783	−	0.999899i	$-0.504513\pi$
$881$	−0.841670			−0.0283566			−0.0141783	+	0.999899i	$0.504513\pi$
$882$		0			0
$883$		−	51.7706i		−	1.74222i	−0.491088	−	0.871110i	$-0.663400\pi$
$883$		−	51.7706i		−	1.74222i	0.491088	−	0.871110i	$-0.336600\pi$
$884$	−12.5822	−	7.26434i	−0.423185	−	0.244326i
$885$	−38.8352	+	20.3872i	−1.30543	+	0.685308i
$886$	−10.2505	−	17.7543i	−0.344371	−	0.596468i
$887$	48.4743	+	27.9867i	1.62761	+	0.939700i	0.984804	+	0.173669i	$0.0555623\pi$
$887$	48.4743	+	27.9867i	1.62761	+	0.939700i	0.642804	+	0.766031i	$0.277771\pi$
$888$	16.2262	+	5.29107i	0.544514	+	0.177557i
$889$		0			0
$890$	1.24160	−	0.350362i	0.0416186	−	0.0117441i
$891$	−7.73501	+	35.6521i	−0.259133	+	1.19439i
$892$	−0.496986	−	0.860804i	−0.0166403	−	0.0288219i
$893$	−17.4596	−	30.2409i	−0.584262	−	1.01197i
$894$	8.27316	−	7.43344i	0.276696	−	0.248612i
$895$	−6.34264	−	22.4769i	−0.212011	−	0.751320i
$896$		0			0
$897$	1.45884	−	4.47383i	0.0487092	−	0.149377i
$898$	−1.67224	−	0.965470i	−0.0558035	−	0.0322182i
$899$	−0.228825	−	0.396337i	−0.00763175	−	0.0132186i
$900$	−10.1915	−	21.4670i	−0.339715	−	0.715567i
$901$	13.5747	+	7.83734i	0.452238	+	0.261100i
$902$		−	5.95854i		−	0.198398i
$903$		0			0
$904$	−20.4062			−0.678701
$905$	−25.9248	−	6.58008i	−0.861770	−	0.218729i
$906$	5.54473	−	1.17247i	0.184211	−	0.0389528i
$907$	31.4075	−	18.1332i	1.04287	−	0.602102i	0.122226	−	0.992502i	$-0.460997\pi$
$907$	31.4075	−	18.1332i	1.04287	−	0.602102i	0.920645	+	0.390401i	$0.127664\pi$
$908$	−7.44902	−	4.30070i	−0.247205	−	0.142724i
$909$	−15.9547	−	11.6431i	−0.529183	−	0.386178i
$910$		0			0
$911$			5.35784i			0.177513i	0.996053	+	0.0887565i	$0.0282893\pi$
$911$			5.35784i			0.177513i	−0.996053	+	0.0887565i	$0.971711\pi$
$912$	9.67799	−	8.69569i	0.320470	−	0.287943i
$913$	−10.6903	−	18.5162i	−0.353798	−	0.612797i
$914$	−4.91690	+	2.83877i	−0.162637	+	0.0938983i
$915$	−14.4694	+	22.8865i	−0.478342	+	0.756604i
$916$			22.7716i			0.752396i
$917$		0			0
$918$	−4.26790	−	5.91341i	−0.140862	−	0.195172i
$919$	−10.0571	+	17.4194i	−0.331754	+	0.574615i	−0.982856	−	0.184376i	$-0.940974\pi$
$919$	−10.0571	+	17.4194i	−0.331754	+	0.574615i	0.651102	+	0.758990i	$0.274307\pi$
$920$	−2.38724	−	2.32487i	−0.0787048	−	0.0766487i
$921$	22.0054	−	4.65320i	0.725102	−	0.153328i
$922$	10.3075	−	17.8532i	0.339461	−	0.587963i
$923$			34.2872i			1.12858i
$924$		0			0
$925$	−11.1438	−	18.1732i	−0.366405	−	0.597532i
$926$	−3.87818	−	2.23907i	−0.127445	−	0.0735804i
$927$	−3.13925	+	29.2754i	−0.103107	+	0.961532i
$928$	−5.77382	+	3.33351i	−0.189535	+	0.109428i
$929$	3.39903	−	5.88728i	0.111518	−	0.193156i	−0.804864	−	0.593459i	$-0.797762\pi$
$929$	3.39903	−	5.88728i	0.111518	−	0.193156i	0.916383	+	0.400303i	$0.131095\pi$
$930$	0.977090	+	0.0392781i	0.0320401	+	0.00128798i
$931$		0			0
$932$	13.3558			0.437483
$933$	−0.529783	−	0.589629i	−0.0173443	−	0.0193036i
$934$	−13.6662	+	7.89021i	−0.447173	+	0.258176i
$935$	−14.1335	−	13.7643i	−0.462215	−	0.450140i
$936$	26.7124	−	11.8259i	0.873123	−	0.386540i
$937$	−44.1327			−1.44175			−0.720877	−	0.693063i	$-0.756261\pi$
$937$	−44.1327			−1.44175			−0.720877	+	0.693063i	$0.756261\pi$
$938$		0			0
$939$	−14.8965	+	45.6830i	−0.486128	+	1.49081i
$940$	26.7866	+	6.79881i	0.873682	+	0.221753i
$941$	−4.53288	−	7.85118i	−0.147768	−	0.255941i	0.782634	−	0.622482i	$-0.213875\pi$
$941$	−4.53288	−	7.85118i	−0.147768	−	0.255941i	−0.930402	+	0.366540i	$0.880542\pi$
$942$	18.4155	−	3.89409i	0.600008	−	0.126876i
$943$	0.734986	−	1.27303i	0.0239344	−	0.0414557i
$944$	19.0057			0.618584
$945$		0			0
$946$	−17.1047			−0.556122
$947$	17.7437	−	30.7330i	0.576593	−	0.998689i	−0.419273	−	0.907860i	$-0.637715\pi$
$947$	17.7437	−	30.7330i	0.576593	−	0.998689i	0.995867	−	0.0908285i	$-0.0289515\pi$
$948$	10.0744	−	2.13031i	0.327202	−	0.0691893i
$949$	−11.0325	−	19.1088i	−0.358129	−	0.620297i
$950$	14.4257	−	0.381918i	0.468033	−	0.0123910i
$951$	−2.42891	+	7.44873i	−0.0787627	+	0.241542i
$952$		0			0
$953$	−10.8726			−0.352198			−0.176099	−	0.984373i	$-0.556348\pi$
$953$	−10.8726			−0.352198			−0.176099	+	0.984373i	$0.556348\pi$
$954$	−12.7382	+	5.63933i	−0.412414	+	0.182580i
$955$	22.0714	−	22.6635i	0.714214	−	0.733373i
$956$	3.72976	−	2.15338i	0.120629	−	0.0696452i
$957$	−5.48426	−	6.10378i	−0.177281	−	0.197307i
$958$	−15.6625			−0.506031
$959$		0			0
$960$	0.0500574	−	1.24524i	0.00161560	−	0.0401899i
$961$	−15.4233	+	26.7140i	−0.497527	+	0.861742i
$962$	10.0315	−	5.79167i	0.323428	−	0.186731i
$963$	−6.00683	+	56.0173i	−0.193567	+	1.80513i
$964$	2.09841	+	1.21152i	0.0675853	+	0.0390204i
$965$	−3.75981	−	13.3239i	−0.121032	−	0.428912i
$966$		0			0
$967$		−	21.3855i		−	0.687711i	−0.939023	−	0.343855i	$-0.888267\pi$
$967$		−	21.3855i		−	0.687711i	0.939023	−	0.343855i	$-0.111733\pi$
$968$	−6.27575	+	10.8699i	−0.201710	+	0.349373i
$969$	−16.5093	+	3.49102i	−0.530357	+	0.112148i
$970$	−4.02810	−	3.92287i	−0.129335	−	0.125956i
$971$	−4.43174	+	7.67600i	−0.142221	+	0.246335i	−0.928333	−	0.371750i	$-0.878758\pi$
$971$	−4.43174	+	7.67600i	−0.142221	+	0.246335i	0.786112	+	0.618085i	$0.212091\pi$
$972$	−24.6953	−	0.129881i	−0.792102	−	0.00416593i
$973$		0			0
$974$			6.29102i			0.201577i
$975$	−34.9785	−	10.3901i	−1.12021	−	0.332751i
$976$	10.1609	−	5.86639i	0.325242	−	0.187779i
$977$	0.365536	+	0.633128i	0.0116945	+	0.0202555i	0.871813	−	0.489838i	$-0.162944\pi$
$977$	0.365536	+	0.633128i	0.0116945	+	0.0202555i	−0.860119	+	0.510094i	$0.829611\pi$
$978$	−3.99339	+	3.58806i	−0.127694	+	0.114734i
$979$		−	3.62691i		−	0.115916i
$980$		0			0
$981$	−2.19555	−	1.60223i	−0.0700986	−	0.0511553i
$982$	13.2171	+	7.63091i	0.421775	+	0.243512i
$983$	3.23213	−	1.86607i	0.103089	−	0.0595184i	−0.447569	−	0.894249i	$-0.647710\pi$
$983$	3.23213	−	1.86607i	0.103089	−	0.0595184i	0.550658	+	0.834731i	$0.314377\pi$
$984$	8.92825	−	1.88794i	0.284622	−	0.0601855i
$985$	7.19265	−	28.3382i	0.229177	−	0.902932i
$986$	1.64032			0.0522385
$987$		0			0
$988$		−	29.8772i		−	0.950520i
$989$	−3.65439	−	2.10987i	−0.116203	−	0.0670898i
$990$	17.2859	−	2.93541i	0.549383	−	0.0932933i
$991$	2.74255	+	4.75024i	0.0871200	+	0.150896i	0.906293	−	0.422651i	$-0.138900\pi$
$991$	2.74255	+	4.75024i	0.0871200	+	0.150896i	−0.819173	+	0.573547i	$0.805567\pi$
$992$	−1.93442	−	1.11684i	−0.0614178	−	0.0354596i
$993$	−12.2946	+	37.7039i	−0.390158	+	1.19650i
$994$		0			0
$995$	−10.2945	−	36.4815i	−0.326359	−	1.15654i
$996$	10.7660	−	9.67323i	0.341132	−	0.306508i
$997$	2.53609	+	4.39264i	0.0803189	+	0.139116i	0.903387	−	0.428826i	$-0.141073\pi$
$997$	2.53609	+	4.39264i	0.0803189	+	0.139116i	−0.823068	+	0.567943i	$0.807739\pi$
$998$	3.69818	+	6.40544i	0.117064	+	0.202761i
$999$	−22.0400	+	2.24620i	−0.697314	+	0.0710666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.f.509.5		24
3.2	odd	2	inner	735.2.p.f.509.7		24
5.4	even	2	inner	735.2.p.f.509.8		24
7.2	even	3		735.2.g.b.734.15		24
7.3	odd	6	inner	735.2.p.f.374.6		24
7.4	even	3		105.2.p.a.59.5	✓	24
7.5	odd	6		735.2.g.b.734.14		24
7.6	odd	2		105.2.p.a.89.6	yes	24
15.14	odd	2	inner	735.2.p.f.509.6		24
21.2	odd	6		735.2.g.b.734.12		24
21.5	even	6		735.2.g.b.734.9		24
21.11	odd	6		105.2.p.a.59.7	yes	24
21.17	even	6	inner	735.2.p.f.374.8		24
21.20	even	2		105.2.p.a.89.8	yes	24
35.4	even	6		105.2.p.a.59.8	yes	24
35.9	even	6		735.2.g.b.734.10		24
35.13	even	4		525.2.t.j.26.7		24
35.18	odd	12		525.2.t.j.101.5		24
35.19	odd	6		735.2.g.b.734.11		24
35.24	odd	6	inner	735.2.p.f.374.7		24
35.27	even	4		525.2.t.j.26.6		24
35.32	odd	12		525.2.t.j.101.8		24
35.34	odd	2		105.2.p.a.89.7	yes	24
105.32	even	12		525.2.t.j.101.6		24
105.44	odd	6		735.2.g.b.734.13		24
105.53	even	12		525.2.t.j.101.7		24
105.59	even	6	inner	735.2.p.f.374.5		24
105.62	odd	4		525.2.t.j.26.8		24
105.74	odd	6		105.2.p.a.59.6	yes	24
105.83	odd	4		525.2.t.j.26.5		24
105.89	even	6		735.2.g.b.734.16		24
105.104	even	2		105.2.p.a.89.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.5	✓	24	7.4	even	3
105.2.p.a.59.6	yes	24	105.74	odd	6
105.2.p.a.59.7	yes	24	21.11	odd	6
105.2.p.a.59.8	yes	24	35.4	even	6
105.2.p.a.89.5	yes	24	105.104	even	2
105.2.p.a.89.6	yes	24	7.6	odd	2
105.2.p.a.89.7	yes	24	35.34	odd	2
105.2.p.a.89.8	yes	24	21.20	even	2
525.2.t.j.26.5		24	105.83	odd	4
525.2.t.j.26.6		24	35.27	even	4
525.2.t.j.26.7		24	35.13	even	4
525.2.t.j.26.8		24	105.62	odd	4
525.2.t.j.101.5		24	35.18	odd	12
525.2.t.j.101.6		24	105.32	even	12
525.2.t.j.101.7		24	105.53	even	12
525.2.t.j.101.8		24	35.32	odd	12
735.2.g.b.734.9		24	21.5	even	6
735.2.g.b.734.10		24	35.9	even	6
735.2.g.b.734.11		24	35.19	odd	6
735.2.g.b.734.12		24	21.2	odd	6
735.2.g.b.734.13		24	105.44	odd	6
735.2.g.b.734.14		24	7.5	odd	6
735.2.g.b.734.15		24	7.2	even	3
735.2.g.b.734.16		24	105.89	even	6
735.2.p.f.374.5		24	105.59	even	6	inner
735.2.p.f.374.6		24	7.3	odd	6	inner
735.2.p.f.374.7		24	35.24	odd	6	inner
735.2.p.f.374.8		24	21.17	even	6	inner
735.2.p.f.509.5		24	1.1	even	1	trivial
735.2.p.f.509.6		24	15.14	odd	2	inner
735.2.p.f.509.7		24	3.2	odd	2	inner
735.2.p.f.509.8		24	5.4	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.322403 + 0.558418i) q^{2} +(-1.69458 + 0.358331i) q^{3} +(0.792113 + 1.37198i) q^{4} +(-0.550103 + 2.16735i) q^{5} +(0.346239 - 1.06181i) q^{6} -2.31113 q^{8} +(2.74320 - 1.21444i) q^{9} +(-1.03293 - 1.00595i) q^{10} +(-3.51044 + 2.02675i) q^{11} +(-1.83392 - 2.04109i) q^{12} -4.21339 q^{13} +(0.155565 - 3.86986i) q^{15} +(-0.839111 + 1.45338i) q^{16} +(1.88498 - 1.08830i) q^{17} +(-0.206248 + 1.92339i) q^{18} +(3.87634 + 2.23800i) q^{19} +(-3.40930 + 0.962052i) q^{20} -2.61372i q^{22} +(0.322403 - 0.558418i) q^{23} +(3.91639 - 0.828150i) q^{24} +(-4.39477 - 2.38453i) q^{25} +(1.35841 - 2.35284i) q^{26} +(-4.21339 + 3.04094i) q^{27} -1.16875i q^{29} +(2.11084 + 1.33452i) q^{30} +(0.339111 - 0.195786i) q^{31} +(-2.85219 - 4.94014i) q^{32} +(5.22247 - 4.69239i) q^{33} +1.40348i q^{34} +(3.83911 + 2.80164i) q^{36} +(3.69236 + 2.13178i) q^{37} +(-2.49949 + 1.44308i) q^{38} +(7.13993 - 1.50979i) q^{39} +(1.27136 - 5.00902i) q^{40} +2.27971 q^{41} -6.54419i q^{43} +(-5.56132 - 3.21083i) q^{44} +(1.12307 + 6.61352i) q^{45} +(0.207887 + 0.360071i) q^{46} +(-6.75621 - 3.90070i) q^{47} +(0.901147 - 2.76355i) q^{48} +(2.74845 - 1.68534i) q^{50} +(-2.80428 + 2.51965i) q^{51} +(-3.33748 - 5.78069i) q^{52} +(3.60074 + 6.23667i) q^{53} +(-0.339707 - 3.33324i) q^{54} +(-2.46157 - 8.72325i) q^{55} +(-7.37071 - 2.40346i) q^{57} +(0.652654 + 0.376810i) q^{58} +(-5.66247 - 9.80768i) q^{59} +(5.43259 - 2.85193i) q^{60} +(-6.05456 - 3.49560i) q^{61} +0.252487i q^{62} +0.321779 q^{64} +(2.31780 - 9.13188i) q^{65} +(0.936579 + 4.42916i) q^{66} +(-7.56680 + 4.36870i) q^{67} +(2.98624 + 1.72411i) q^{68} +(-0.346239 + 1.06181i) q^{69} -8.13766i q^{71} +(-6.33988 + 2.80673i) q^{72} +(2.61843 + 4.53525i) q^{73} +(-2.38085 + 1.37459i) q^{74} +(8.30174 + 2.46598i) q^{75} +7.09101i q^{76} +(-1.45884 + 4.47383i) q^{78} +(-1.87634 + 3.24991i) q^{79} +(-2.68838 - 2.61815i) q^{80} +(6.05026 - 6.66291i) q^{81} +(-0.734986 + 1.27303i) q^{82} +5.27461i q^{83} +(1.32178 + 4.68409i) q^{85} +(3.65439 + 2.10987i) q^{86} +(0.418802 + 1.98055i) q^{87} +(8.11308 - 4.68409i) q^{88} +(-0.447379 + 0.774883i) q^{89} +(-4.05520 - 1.50507i) q^{90} +1.02152 q^{92} +(-0.504494 + 0.453288i) q^{93} +(4.35644 - 2.51519i) q^{94} +(-6.98291 + 7.17023i) q^{95} +(6.60347 + 7.34943i) q^{96} +3.89968 q^{97} +(-7.16845 + 9.82300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) \) 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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