LMFDB - Embedded newform 360.2.bk.a.229.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(229,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("360.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bk (of order $6$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.5
Character	$\chi$	$=$	360.229
Dual form			360.2.bk.a.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38109 + 0.304279i) q^{2} +(1.07030 - 1.36178i) q^{3} +(1.81483 - 0.840474i) q^{4} +(-1.96832 + 1.06099i) q^{5} +(-1.06383 + 2.20642i) q^{6} +(-1.60442 + 0.926310i) q^{7} +(-2.25071 + 1.71299i) q^{8} +(-0.708903 - 2.91504i) q^{9} +O(q^{10})$	\(q+(-1.38109 + 0.304279i) q^{2} +(1.07030 - 1.36178i) q^{3} +(1.81483 - 0.840474i) q^{4} +(-1.96832 + 1.06099i) q^{5} +(-1.06383 + 2.20642i) q^{6} +(-1.60442 + 0.926310i) q^{7} +(-2.25071 + 1.71299i) q^{8} +(-0.708903 - 2.91504i) q^{9} +(2.39560 - 2.06425i) q^{10} +(2.88736 - 1.66702i) q^{11} +(0.797874 - 3.37096i) q^{12} +(3.23243 - 5.59873i) q^{13} +(1.93399 - 1.76751i) q^{14} +(-0.661859 + 3.81601i) q^{15} +(2.58721 - 3.05063i) q^{16} -0.590749i q^{17} +(1.86604 + 3.81023i) q^{18} -4.73221i q^{19} +(-2.68043 + 3.57985i) q^{20} +(-0.455778 + 3.17630i) q^{21} +(-3.48047 + 3.18087i) q^{22} +(-7.05625 - 4.07393i) q^{23} +(-0.0762247 + 4.89839i) q^{24} +(2.74859 - 4.17675i) q^{25} +(-2.76071 + 8.71592i) q^{26} +(-4.72839 - 2.15460i) q^{27} +(-2.13320 + 3.02956i) q^{28} +(-0.135659 + 0.0783230i) q^{29} +(-0.247044 - 5.47165i) q^{30} +(-2.77492 + 4.80630i) q^{31} +(-2.64493 + 5.00044i) q^{32} +(0.820235 - 5.71618i) q^{33} +(0.179752 + 0.815878i) q^{34} +(2.17520 - 3.52555i) q^{35} +(-3.73655 - 4.69448i) q^{36} +3.21991 q^{37} +(1.43991 + 6.53561i) q^{38} +(-4.16458 - 10.3942i) q^{39} +(2.61265 - 5.75969i) q^{40} +(-0.929101 + 1.60925i) q^{41} +(-0.337008 - 4.52544i) q^{42} +(1.08597 + 1.88095i) q^{43} +(3.83898 - 5.45211i) q^{44} +(4.48819 + 4.98560i) q^{45} +(10.9849 + 3.47940i) q^{46} +(8.32731 - 4.80777i) q^{47} +(-1.38520 - 6.78831i) q^{48} +(-1.78390 + 3.08981i) q^{49} +(-2.52515 + 6.60482i) q^{50} +(-0.804471 - 0.632280i) q^{51} +(1.16072 - 12.8775i) q^{52} +6.40212 q^{53} +(7.18594 + 1.53696i) q^{54} +(-3.91456 + 6.34471i) q^{55} +(2.02431 - 4.83319i) q^{56} +(-6.44424 - 5.06489i) q^{57} +(0.163526 - 0.149449i) q^{58} +(-1.67616 - 0.967729i) q^{59} +(2.00610 + 7.48168i) q^{60} +(-2.78455 + 1.60766i) q^{61} +(2.36996 - 7.48229i) q^{62} +(3.83760 + 4.02027i) q^{63} +(2.13136 - 7.71086i) q^{64} +(-0.422244 + 14.4497i) q^{65} +(0.606492 + 8.14415i) q^{66} +(3.33522 - 5.77678i) q^{67} +(-0.496509 - 1.07211i) q^{68} +(-13.1001 + 5.24874i) q^{69} +(-1.93140 + 5.53098i) q^{70} +2.20166 q^{71} +(6.58895 + 5.34656i) q^{72} +15.2968i q^{73} +(-4.44699 + 0.979750i) q^{74} +(-2.74601 - 8.21337i) q^{75} +(-3.97730 - 8.58815i) q^{76} +(-3.08835 + 5.34919i) q^{77} +(8.91440 + 13.0882i) q^{78} +(-0.603265 - 1.04489i) q^{79} +(-1.85576 + 8.74964i) q^{80} +(-7.99491 + 4.13296i) q^{81} +(0.793513 - 2.50523i) q^{82} +(-2.12097 - 3.67362i) q^{83} +(1.84243 + 6.14751i) q^{84} +(0.626781 + 1.16278i) q^{85} +(-2.07215 - 2.26733i) q^{86} +(-0.0385378 + 0.268568i) q^{87} +(-3.64303 + 8.69798i) q^{88} +12.3193 q^{89} +(-7.71561 - 5.51990i) q^{90} +11.9769i q^{91} +(-16.2299 - 1.46289i) q^{92} +(3.57513 + 8.92303i) q^{93} +(-10.0379 + 9.17380i) q^{94} +(5.02084 + 9.31451i) q^{95} +(3.97863 + 8.95380i) q^{96} +(12.0457 - 6.95457i) q^{97} +(1.52357 - 4.81011i) q^{98} +(-6.90629 - 7.23502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 136 * q - 2 * q^4 - 8 * q^9	$ 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) $ 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.38109	+	0.304279i	−0.976579	+	0.215158i
$2$	−1.38109	+	0.304279i	−0.976579	+	0.215158i
$3$	1.07030	−	1.36178i	0.617940	−	0.786225i
$3$	1.07030	−	1.36178i	0.617940	−	0.786225i
$4$	1.81483	−	0.840474i	0.907414	−	0.420237i
$5$	−1.96832	+	1.06099i	−0.880260	+	0.474491i
$5$	−1.96832	+	1.06099i	−0.880260	+	0.474491i
$6$	−1.06383	+	2.20642i	−0.434305	+	0.900766i
$7$	−1.60442	+	0.926310i	−0.606412	+	0.350112i	−0.771560	−	0.636157i	$-0.780523\pi$
$7$	−1.60442	+	0.926310i	−0.606412	+	0.350112i	0.165148	+	0.986269i	$0.447190\pi$
$8$	−2.25071	+	1.71299i	−0.795745	+	0.605632i
$9$	−0.708903	−	2.91504i	−0.236301	−	0.971680i
$10$	2.39560	−	2.06425i	0.757554	−	0.652773i
$11$	2.88736	−	1.66702i	0.870573	−	0.502625i	0.00303427	−	0.999995i	$-0.499034\pi$
$11$	2.88736	−	1.66702i	0.870573	−	0.502625i	0.867539	+	0.497370i	$0.165701\pi$
$12$	0.797874	−	3.37096i	0.230326	−	0.973113i
$13$	3.23243	−	5.59873i	0.896514	−	1.55281i	0.0645952	−	0.997912i	$-0.479424\pi$
$13$	3.23243	−	5.59873i	0.896514	−	1.55281i	0.831919	−	0.554897i	$-0.187242\pi$
$14$	1.93399	−	1.76751i	0.516880	−	0.472386i
$15$	−0.661859	+	3.81601i	−0.170891	+	0.985290i
$16$	2.58721	−	3.05063i	0.646802	−	0.762658i
$17$		−	0.590749i		−	0.143278i	−0.997431	−	0.0716388i	$-0.977177\pi$
$17$		−	0.590749i		−	0.143278i	0.997431	−	0.0716388i	$-0.0228229\pi$
$18$	1.86604	+	3.81023i	0.439831	+	0.898081i
$19$		−	4.73221i		−	1.08564i	−0.839848	−	0.542821i	$-0.817356\pi$
$19$		−	4.73221i		−	1.08564i	0.839848	−	0.542821i	$-0.182644\pi$
$20$	−2.68043	+	3.57985i	−0.599363	+	0.800478i
$21$	−0.455778	+	3.17630i	−0.0994590	+	0.693125i
$22$	−3.48047	+	3.18087i	−0.742040	+	0.678164i
$23$	−7.05625	−	4.07393i	−1.47133	−	0.849473i	−0.471848	−	0.881680i	$-0.656413\pi$
$23$	−7.05625	−	4.07393i	−1.47133	−	0.849473i	−0.999481	+	0.0322071i	$0.989746\pi$
$24$	−0.0762247	+	4.89839i	−0.0155593	+	0.999879i
$25$	2.74859	−	4.17675i	0.549717	−	0.835351i
$26$	−2.76071	+	8.71592i	−0.541419	+	1.70933i
$27$	−4.72839	−	2.15460i	−0.909979	−	0.414654i
$28$	−2.13320	+	3.02956i	−0.403137	+	0.572534i
$29$	−0.135659	+	0.0783230i	−0.0251913	+	0.0145442i	−0.512543	−	0.858662i	$-0.671296\pi$
$29$	−0.135659	+	0.0783230i	−0.0251913	+	0.0145442i	0.487351	+	0.873206i	$0.337963\pi$
$30$	−0.247044	−	5.47165i	−0.0451038	−	0.998982i
$31$	−2.77492	+	4.80630i	−0.498390	+	0.863236i	−0.999998	−	0.00185828i	$-0.999408\pi$
$31$	−2.77492	+	4.80630i	−0.498390	+	0.863236i	0.501608	+	0.865095i	$0.332742\pi$
$32$	−2.64493	+	5.00044i	−0.467562	+	0.883960i
$33$	0.820235	−	5.71618i	0.142785	−	0.995059i
$34$	0.179752	+	0.815878i	0.0308273	+	0.139922i
$35$	2.17520	−	3.52555i	0.367676	−	0.595927i
$36$	−3.73655	−	4.69448i	−0.622759	−	0.782414i
$37$	3.21991			0.529350			0.264675	−	0.964338i	$-0.414735\pi$
$37$	3.21991			0.529350			0.264675	+	0.964338i	$0.414735\pi$
$38$	1.43991	+	6.53561i	0.233584	+	1.06022i
$39$	−4.16458	−	10.3942i	−0.666866	−	1.66440i
$40$	2.61265	−	5.75969i	0.413096	−	0.910687i
$41$	−0.929101	+	1.60925i	−0.145101	+	0.251323i	−0.929411	−	0.369047i	$-0.879684\pi$
$41$	−0.929101	+	1.60925i	−0.145101	+	0.251323i	0.784309	+	0.620370i	$0.213017\pi$
$42$	−0.337008	−	4.52544i	−0.0520015	−	0.698291i
$43$	1.08597	+	1.88095i	0.165608	+	0.286842i	0.936871	−	0.349675i	$-0.113708\pi$
$43$	1.08597	+	1.88095i	0.165608	+	0.286842i	−0.771263	+	0.636517i	$0.780375\pi$
$44$	3.83898	−	5.45211i	0.578749	−	0.821936i
$45$	4.48819	+	4.98560i	0.669060	+	0.743209i
$46$	10.9849	+	3.47940i	1.61964	+	0.513010i
$47$	8.32731	−	4.80777i	1.21466	−	0.701286i	0.250891	−	0.968015i	$-0.419276\pi$
$47$	8.32731	−	4.80777i	1.21466	−	0.701286i	0.963771	+	0.266729i	$0.0859430\pi$
$48$	−1.38520	−	6.78831i	−0.199937	−	0.979809i
$49$	−1.78390	+	3.08981i	−0.254843	+	0.441401i
$50$	−2.52515	+	6.60482i	−0.357110	+	0.934062i
$51$	−0.804471	−	0.632280i	−0.112649	−	0.0885369i
$52$	1.16072	−	12.8775i	0.160963	−	1.78579i
$53$	6.40212			0.879398			0.439699	−	0.898145i	$-0.355085\pi$
$53$	6.40212			0.879398			0.439699	+	0.898145i	$0.355085\pi$
$54$	7.18594	+	1.53696i	0.977883	+	0.209153i
$55$	−3.91456	+	6.34471i	−0.527840	+	0.855520i
$56$	2.02431	−	4.83319i	0.270510	−	0.645862i
$57$	−6.44424	−	5.06489i	−0.853560	−	0.670862i
$58$	0.163526	−	0.149449i	0.0214720	−	0.0196237i
$59$	−1.67616	−	0.967729i	−0.218217	−	0.125988i	0.386907	−	0.922119i	$-0.373543\pi$
$59$	−1.67616	−	0.967729i	−0.218217	−	0.125988i	−0.605124	+	0.796131i	$0.706877\pi$
$60$	2.00610	+	7.48168i	0.258986	+	0.965881i
$61$	−2.78455	+	1.60766i	−0.356526	+	0.205840i	−0.667556	−	0.744560i	$-0.732659\pi$
$61$	−2.78455	+	1.60766i	−0.356526	+	0.205840i	0.311030	+	0.950400i	$0.399326\pi$
$62$	2.36996	−	7.48229i	0.300985	−	0.950251i
$63$	3.83760	+	4.02027i	0.483493	+	0.506507i
$64$	2.13136	−	7.71086i	0.266420	−	0.963857i
$65$	−0.422244	+	14.4497i	−0.0523729	+	1.79226i
$66$	0.606492	+	8.14415i	0.0746540	+	1.00248i
$67$	3.33522	−	5.77678i	0.407462	−	0.705745i	−0.587142	−	0.809484i	$-0.699747\pi$
$67$	3.33522	−	5.77678i	0.407462	−	0.705745i	0.994605	+	0.103738i	$0.0330804\pi$
$68$	−0.496509	−	1.07211i	−0.0602105	−	0.130012i
$69$	−13.1001	+	5.24874i	−1.57707	+	0.631874i
$70$	−1.93140	+	5.53098i	−0.230846	+	0.661078i
$71$	2.20166			0.261289			0.130644	−	0.991429i	$-0.458295\pi$
$71$	2.20166			0.261289			0.130644	+	0.991429i	$0.458295\pi$
$72$	6.58895	+	5.34656i	0.776516	+	0.630098i
$73$			15.2968i			1.79035i	0.445710	+	0.895177i	$0.352951\pi$
$73$			15.2968i			1.79035i	−0.445710	+	0.895177i	$0.647049\pi$
$74$	−4.44699	+	0.979750i	−0.516952	+	0.113894i
$75$	−2.74601	−	8.21337i	−0.317082	−	0.948398i
$76$	−3.97730	−	8.58815i	−0.456227	−	0.985128i
$77$	−3.08835	+	5.34919i	−0.351951	+	0.609596i
$78$	8.91440	+	13.0882i	1.00936	+	1.48194i
$79$	−0.603265	−	1.04489i	−0.0678727	−	0.117559i	0.830092	−	0.557626i	$-0.188288\pi$
$79$	−0.603265	−	1.04489i	−0.0678727	−	0.117559i	−0.897965	+	0.440068i	$0.854954\pi$
$80$	−1.85576	+	8.74964i	−0.207480	+	0.978239i
$81$	−7.99491	+	4.13296i	−0.888324	+	0.459218i
$82$	0.793513	−	2.50523i	0.0876289	−	0.276656i
$83$	−2.12097	−	3.67362i	−0.232806	−	0.403232i	0.725827	−	0.687878i	$-0.241457\pi$
$83$	−2.12097	−	3.67362i	−0.232806	−	0.403232i	−0.958633	+	0.284645i	$0.908124\pi$
$84$	1.84243	+	6.14751i	0.201026	+	0.670748i
$85$	0.626781	+	1.16278i	0.0679839	+	0.126122i
$86$	−2.07215	−	2.26733i	−0.223446	−	0.244492i
$87$	−0.0385378	+	0.268568i	−0.00413168	+	0.0287935i
$88$	−3.64303	+	8.69798i	−0.388348	+	0.927208i
$89$	12.3193			1.30584			0.652921	−	0.757426i	$-0.273543\pi$
$89$	12.3193			1.30584			0.652921	+	0.757426i	$0.273543\pi$
$90$	−7.71561	−	5.51990i	−0.813297	−	0.581849i
$91$			11.9769i			1.25552i
$92$	−16.2299	−	1.46289i	−1.69209	−	0.152517i
$93$	3.57513	+	8.92303i	0.370724	+	0.925275i
$94$	−10.0379	+	9.17380i	−1.03533	+	0.946205i
$95$	5.02084	+	9.31451i	0.515127	+	0.955648i
$96$	3.97863	+	8.95380i	0.406067	+	0.913843i
$97$	12.0457	−	6.95457i	1.22305	−	0.706130i	0.257485	−	0.966282i	$-0.417106\pi$
$97$	12.0457	−	6.95457i	1.22305	−	0.706130i	0.965568	+	0.260152i	$0.0837727\pi$
$98$	1.52357	−	4.81011i	0.153904	−	0.485894i
$99$	−6.90629	−	7.23502i	−0.694108	−	0.727147i
$100$	1.47776	−	9.89021i	0.147776	−	0.989021i
$101$	12.4676	−	7.19817i	1.24057	−	0.716245i	0.271362	−	0.962477i	$-0.412526\pi$
$101$	12.4676	−	7.19817i	1.24057	−	0.716245i	0.969211	+	0.246233i	$0.0791927\pi$
$102$	1.30344	+	0.628453i	0.129060	+	0.0622262i
$103$	−7.10860	−	4.10415i	−0.700431	−	0.404394i	0.107077	−	0.994251i	$-0.465851\pi$
$103$	−7.10860	−	4.10415i	−0.700431	−	0.404394i	−0.807508	+	0.589857i	$0.799184\pi$
$104$	2.31529	+	18.1382i	0.227033	+	1.77860i
$105$	−2.47291	−	6.73555i	−0.241332	−	0.657323i
$106$	−8.84191	+	1.94803i	−0.858802	+	0.189209i
$107$	−17.4628			−1.68819			−0.844094	−	0.536195i	$-0.819861\pi$
$107$	−17.4628			−1.68819			−0.844094	+	0.536195i	$0.819861\pi$
$108$	−10.3921	+	0.0638520i	−0.999981	+	0.00614416i
$109$			16.1089i			1.54295i	0.636259	+	0.771476i	$0.280481\pi$
$109$			16.1089i			1.54295i	−0.636259	+	0.771476i	$0.719519\pi$
$110$	3.47581	−	9.95374i	0.331406	−	0.949052i
$111$	3.44628	−	4.38481i	0.327106	−	0.416188i
$112$	−1.32513	+	7.29104i	−0.125213	+	0.688938i
$113$	3.62139	+	2.09081i	0.340671	+	0.196687i	0.660569	−	0.750765i	$-0.270315\pi$
$113$	3.62139	+	2.09081i	0.340671	+	0.196687i	−0.319898	+	0.947452i	$0.603649\pi$
$114$	10.4412	+	5.03424i	0.977910	+	0.471500i
$115$	18.2114	+	0.532167i	1.69822	+	0.0496248i
$116$	−0.180370	+	0.256161i	−0.0167469	+	0.0237839i
$117$	−18.6120	−	5.45370i	−1.72068	−	0.504195i
$118$	2.60938	+	0.826504i	0.240213	+	0.0760858i
$119$	0.547216	+	0.947806i	0.0501632	+	0.0868853i
$120$	−5.04712	−	9.72248i	−0.460737	−	0.887537i
$121$	0.0579116	−	0.100306i	0.00526469	−	0.00911872i
$122$	3.35655	−	3.06761i	0.303887	−	0.277728i
$123$	1.19703	+	2.98762i	0.107933	+	0.269385i
$124$	−0.996432	+	11.0549i	−0.0894823	+	0.992755i
$125$	−0.978591	+	11.1374i	−0.0875278	+	0.996162i
$126$	−6.52337	−	4.38466i	−0.581148	−	0.390617i
$127$			1.18401i			0.105064i	0.998619	+	0.0525322i	$0.0167292\pi$
$127$			1.18401i			0.105064i	−0.998619	+	0.0525322i	$0.983271\pi$
$128$	−0.597357	+	11.2979i	−0.0527994	+	0.998605i
$129$	3.72376	+	0.534335i	0.327858	+	0.0470456i
$130$	−3.81358	−	20.0848i	−0.334473	−	1.76156i
$131$	6.15679	+	3.55462i	0.537921	+	0.310569i	0.744236	−	0.667917i	$-0.232814\pi$
$131$	6.15679	+	3.55462i	0.537921	+	0.310569i	−0.206315	+	0.978486i	$0.566147\pi$
$132$	−3.31571	−	11.0633i	−0.288596	−	0.962934i
$133$	4.38349	+	7.59243i	0.380097	+	0.658347i
$134$	−2.84850	+	8.99309i	−0.246073	+	0.776885i
$135$	11.5930	−	0.775838i	0.997768	−	0.0667735i
$136$	1.01194	+	1.32960i	0.0867735	+	0.114012i
$137$	−3.36728	+	1.94410i	−0.287686	+	0.166096i	−0.636898	−	0.770948i	$-0.719783\pi$
$137$	−3.36728	+	1.94410i	−0.287686	+	0.166096i	0.349212	+	0.937044i	$0.386449\pi$
$138$	16.4954	−	11.2351i	1.40418	−	0.956394i
$139$	−2.71801	−	1.56924i	−0.230538	−	0.133101i	0.380282	−	0.924871i	$-0.375827\pi$
$139$	−2.71801	−	1.56924i	−0.230538	−	0.133101i	−0.610820	+	0.791769i	$0.709160\pi$
$140$	0.984479	−	8.22647i	0.0832037	−	0.695263i
$141$	2.36560	−	16.4858i	0.199219	−	1.38835i
$142$	−3.04069	+	0.669918i	−0.255169	+	0.0562183i
$143$		−	21.5541i		−	1.80244i
$144$	−10.7268	−	5.37921i	−0.893899	−	0.448267i
$145$	0.183921	−	0.298099i	0.0152738	−	0.0247557i
$146$	−4.65449	−	21.1263i	−0.385208	−	1.74842i
$147$	2.29833	+	5.73631i	0.189563	+	0.473123i
$148$	5.84358	−	2.70625i	0.480340	−	0.222452i
$149$	−6.27214	−	3.62122i	−0.513834	−	0.296662i	0.220574	−	0.975370i	$-0.429207\pi$
$149$	−6.27214	−	3.62122i	−0.513834	−	0.296662i	−0.734408	+	0.678708i	$0.762540\pi$
$150$	6.29165	+	10.5079i	0.513711	+	0.857963i
$151$	6.77715	+	11.7384i	0.551517	+	0.955255i	0.998165	+	0.0605455i	$0.0192840\pi$
$151$	6.77715	+	11.7384i	0.551517	+	0.955255i	−0.446649	+	0.894709i	$0.647383\pi$
$152$	8.10620	+	10.6508i	0.657500	+	0.863895i
$153$	−1.72206	+	0.418784i	−0.139220	+	0.0338567i
$154$	2.63766	−	8.32744i	0.212548	−	0.671044i
$155$	0.362480	−	12.4045i	0.0291151	−	0.996354i
$156$	−16.2940	−	15.3635i	−1.30457	−	1.23006i
$157$	1.59282	−	2.75885i	0.127121	−	0.220180i	−0.795439	−	0.606034i	$-0.792760\pi$
$157$	1.59282	−	2.75885i	0.127121	−	0.220180i	0.922560	+	0.385854i	$0.126093\pi$
$158$	1.15110	+	1.25952i	0.0915767	+	0.100202i
$159$	6.85221	−	8.71829i	0.543415	−	0.691405i
$160$	−0.0993588	−	12.6487i	−0.00785500	−	0.999969i
$161$	15.0949			1.18964
$162$	9.78414	−	8.14068i	0.768714	−	0.639592i
$163$	−14.4380			−1.13087			−0.565435	−	0.824793i	$-0.691292\pi$
$163$	−14.4380			−1.13087			−0.565435	+	0.824793i	$0.691292\pi$
$164$	−0.333627	+	3.70140i	−0.0260519	+	0.289031i
$165$	4.45034	+	12.1215i	0.346459	+	0.943661i
$166$	4.04705	+	4.42824i	0.314112	+	0.343698i
$167$	10.4193	+	6.01557i	0.806268	+	0.465499i	0.845658	−	0.533725i	$-0.179208\pi$
$167$	10.4193	+	6.01557i	0.806268	+	0.465499i	−0.0393901	+	0.999224i	$0.512542\pi$
$168$	−4.41513	−	7.92965i	−0.340634	−	0.611786i
$169$	−14.3972	−	24.9367i	−1.10748	−	1.91820i
$170$	−1.21945	−	1.41520i	−0.0935277	−	0.108541i
$171$	−13.7946	+	3.35468i	−1.05490	+	0.256539i
$172$	3.55173	+	2.50087i	0.270817	+	0.190690i
$173$	−5.44736	−	9.43511i	−0.414155	−	0.717338i	0.581184	−	0.813772i	$-0.302590\pi$
$173$	−5.44736	−	9.43511i	−0.414155	−	0.717338i	−0.995339	+	0.0964340i	$0.969256\pi$
$174$	−0.0284953	−	0.382643i	−0.00216022	−	0.0290081i
$175$	−0.540904	+	9.24729i	−0.0408885	+	0.699029i
$176$	2.38474	−	13.1212i	0.179757	−	0.989048i
$177$	−3.11183	+	1.24680i	−0.233899	+	0.0937149i
$178$	−17.0141	+	3.74850i	−1.27526	+	0.280962i
$179$			0.363546i			0.0271727i	0.999908	+	0.0135863i	$0.00432480\pi$
$179$			0.363546i			0.0271727i	−0.999908	+	0.0135863i	$0.995675\pi$
$180$	12.3356	+	5.27580i	0.919438	+	0.393235i
$181$		−	3.06981i		−	0.228177i	−0.993471	−	0.114089i	$-0.963605\pi$
$181$		−	3.06981i		−	0.228177i	0.993471	−	0.114089i	$-0.0363948\pi$
$182$	−3.64432	−	16.5412i	−0.270135	−	1.22612i
$183$	−0.791029	+	5.51264i	−0.0584746	+	0.407506i
$184$	22.8601	−	2.91804i	1.68527	−	0.215120i
$185$	−6.33782	+	3.41630i	−0.465966	+	0.251172i
$186$	−7.65267	−	11.2357i	−0.561121	−	0.823840i
$187$	−0.984790	−	1.70571i	−0.0720150	−	0.124734i
$188$	11.0718	−	15.7242i	0.807496	−	1.14680i
$189$	9.58213	−	0.923075i	0.696998	−	0.0671438i
$190$	−9.76845	−	11.3365i	−0.708678	−	0.822433i
$191$	−9.10363	−	15.7680i	−0.658716	−	1.14093i	−0.980948	−	0.194269i	$-0.937767\pi$
$191$	−9.10363	−	15.7680i	−0.658716	−	1.14093i	0.322233	−	0.946661i	$-0.395567\pi$
$192$	−8.21930	−	11.1554i	−0.593177	−	0.805072i
$193$	19.6102	+	11.3220i	1.41158	+	0.814974i	0.995537	−	0.0943730i	$-0.0300846\pi$
$193$	19.6102	+	11.3220i	1.41158	+	0.814974i	0.416039	+	0.909347i	$0.363418\pi$
$194$	−14.5201	+	13.2701i	−1.04248	+	0.952741i
$195$	19.2254	+	16.0406i	1.37676	+	1.14869i
$196$	−0.640573	+	7.10679i	−0.0457552	+	0.507628i
$197$	12.2075			0.869747			0.434873	−	0.900492i	$-0.356793\pi$
$197$	12.2075			0.869747			0.434873	+	0.900492i	$0.356793\pi$
$198$	11.7397	+	7.89079i	0.834303	+	0.560774i
$199$	−14.9325			−1.05854			−0.529269	−	0.848454i	$-0.677534\pi$
$199$	−14.9325			−1.05854			−0.529269	+	0.848454i	$0.677534\pi$
$200$	0.968461	+	14.1089i	0.0684805	+	0.997652i
$201$	−4.29701	−	10.7247i	−0.303088	−	0.756465i
$202$	−15.0286	+	13.7350i	−1.05741	+	0.966389i
$203$	0.145103	−	0.251325i	0.0101842	−	0.0176396i
$204$	−1.99139	−	0.471343i	−0.139425	−	0.0330006i
$205$	0.121366	−	4.15329i	0.00847657	−	0.290079i
$206$	11.0664	+	3.50521i	0.771035	+	0.244220i
$207$	−6.87346	+	23.4573i	−0.477739	+	1.63039i
$208$	−8.71670	−	24.3460i	−0.604395	−	1.68809i
$209$	−7.88868	−	13.6636i	−0.545672	−	0.945131i
$210$	5.46480	+	8.54996i	0.377107	+	0.590004i
$211$	5.55973	+	3.20991i	0.382748	+	0.220980i	0.679013	−	0.734126i	$-0.262408\pi$
$211$	5.55973	+	3.20991i	0.382748	+	0.220980i	−0.296265	+	0.955106i	$0.595741\pi$
$212$	11.6187	−	5.38081i	0.797979	−	0.369556i
$213$	2.35644	−	2.99818i	0.161461	−	0.205432i
$214$	24.1177	−	5.31355i	1.64865	−	0.363227i
$215$	−4.13321	−	2.55011i	−0.281882	−	0.173916i
$216$	14.3330	−	3.25028i	0.975239	−	0.221154i
$217$		−	10.2817i		−	0.697969i
$218$	−4.90159	−	22.2478i	−0.331978	−	1.50681i
$219$	20.8309	+	16.3722i	1.40762	+	1.10633i
$220$	−1.77170	+	14.8046i	−0.119448	+	0.998129i
$221$	−3.30744	−	1.90955i	−0.222483	−	0.128450i
$222$	−3.42542	+	7.10446i	−0.229899	+	0.476820i
$223$	−20.2535	+	11.6934i	−1.35628	+	0.783046i	−0.989120	−	0.147113i	$-0.953002\pi$
$223$	−20.2535	+	11.6934i	−1.35628	+	0.783046i	−0.367156	+	0.930159i	$0.619668\pi$
$224$	−0.388388	−	10.4728i	−0.0259503	−	0.699743i
$225$	−14.1239	−	5.05132i	−0.941592	−	0.336755i
$226$	−5.63765	−	1.78569i	−0.375011	−	0.118782i
$227$	11.6127	+	20.1137i	0.770760	+	1.33500i	0.937147	+	0.348935i	$0.113457\pi$
$227$	11.6127	+	20.1137i	0.770760	+	1.33500i	−0.166387	+	0.986061i	$0.553210\pi$
$228$	−15.9521	−	3.77571i	−1.05645	−	0.250052i
$229$	−6.49252	−	3.74846i	−0.429038	−	0.247705i	0.269899	−	0.962889i	$-0.413010\pi$
$229$	−6.49252	−	3.74846i	−0.429038	−	0.247705i	−0.698937	+	0.715184i	$0.746343\pi$
$230$	−25.3135	+	4.80637i	−1.66912	+	0.316922i
$231$	3.97895	+	9.93092i	0.261796	+	0.653406i
$232$	0.171163	−	0.408665i	0.0112374	−	0.0268301i
$233$			19.5735i			1.28230i	0.767414	+	0.641152i	$0.221543\pi$
$233$			19.5735i			1.28230i	−0.767414	+	0.641152i	$0.778457\pi$
$234$	27.3643	+	1.86882i	1.78886	+	0.122169i
$235$	−11.2898	+	18.2985i	−0.736466	+	1.19366i
$236$	−3.85529	−	0.347497i	−0.250958	−	0.0226202i
$237$	−2.06858	−	0.296829i	−0.134369	−	0.0192811i
$238$	−1.04415	−	1.14250i	−0.0676824	−	0.0740574i
$239$	2.50305	−	4.33540i	0.161909	−	0.280434i	−0.773645	−	0.633620i	$-0.781568\pi$
$239$	2.50305	−	4.33540i	0.161909	−	0.280434i	0.935553	+	0.353186i	$0.114902\pi$
$240$	9.92888	+	11.8919i	0.640907	+	0.767619i
$241$	5.73015	+	9.92490i	0.369111	+	0.639319i	0.989427	−	0.145033i	$-0.0463288\pi$
$241$	5.73015	+	9.92490i	0.369111	+	0.639319i	−0.620316	+	0.784352i	$0.712995\pi$
$242$	−0.0494603	+	0.156153i	−0.00317943	+	0.0100379i
$243$	−2.92878	+	15.3109i	−0.187882	+	0.982192i
$244$	−3.70229	+	5.25798i	−0.237015	+	0.336608i
$245$	0.233026	−	7.97444i	0.0148875	−	0.509468i
$246$	−2.56228	−	3.76195i	−0.163365	−	0.239853i
$247$	−26.4943	−	15.2965i	−1.68580	−	0.973294i
$248$	−1.98759	−	15.5710i	−0.126212	−	0.988757i
$249$	−7.27275	−	1.04359i	−0.460892	−	0.0661350i
$250$	−2.03736	−	15.6796i	−0.128854	−	0.991664i
$251$		−	5.20608i		−	0.328605i	−0.986410	−	0.164303i	$-0.947463\pi$
$251$		−	5.20608i		−	0.328605i	0.986410	−	0.164303i	$-0.0525373\pi$
$252$	10.3435	+	4.07070i	0.651581	+	0.256430i
$253$	−27.1653			−1.70787
$254$	−0.360271	−	1.63523i	−0.0226054	−	0.102604i
$255$	2.25430	+	0.390992i	0.141170	+	0.0244849i
$256$	−2.61271	−	15.7852i	−0.163295	−	0.986577i
$257$	8.63681	+	4.98647i	0.538750	+	0.311047i	0.744572	−	0.667542i	$-0.232654\pi$
$257$	8.63681	+	4.98647i	0.538750	+	0.311047i	−0.205822	+	0.978589i	$0.565987\pi$
$258$	−5.30543	+	0.395094i	−0.330302	+	0.0245975i
$259$	−5.16607	+	2.98263i	−0.321004	+	0.185332i
$260$	11.3783	+	26.5786i	0.705651	+	1.64833i
$261$	0.324484	+	0.339929i	0.0200851	+	0.0210411i
$262$	−9.58468	−	3.03588i	−0.592144	−	0.187557i
$263$	10.2358	−	5.90965i	0.631167	−	0.364404i	−0.150037	−	0.988680i	$-0.547939\pi$
$263$	10.2358	−	5.90965i	0.631167	−	0.364404i	0.781204	+	0.624276i	$0.214606\pi$
$264$	7.94562	+	14.2705i	0.489019	+	0.878288i
$265$	−12.6014	+	6.79261i	−0.774100	+	0.417266i
$266$	−8.36421	−	9.15203i	−0.512843	−	0.561147i
$267$	13.1854	−	16.7762i	0.806932	−	1.02669i
$268$	1.19763	−	13.2870i	0.0731569	−	0.811634i
$269$		−	16.1799i		−	0.986508i	−0.869885	−	0.493254i	$-0.835807\pi$
$269$		−	16.1799i		−	0.986508i	0.869885	−	0.493254i	$-0.164193\pi$
$270$	−15.7750	+	4.59901i	−0.960033	+	0.279887i
$271$	20.1093			1.22155			0.610776	−	0.791803i	$-0.290857\pi$
$271$	20.1093			1.22155			0.610776	+	0.791803i	$0.290857\pi$
$272$	−1.80216	−	1.52839i	−0.109272	−	0.0926722i
$273$	16.3100	+	12.8189i	0.987124	+	0.775837i
$274$	4.05898	−	3.70958i	0.245212	−	0.224104i
$275$	0.973430	−	16.6418i	0.0587000	−	1.00354i
$276$	−19.3631	+	20.5359i	−1.16552	+	1.23611i
$277$	−1.26920	−	2.19832i	−0.0762588	−	0.132084i	0.825374	−	0.564586i	$-0.190964\pi$
$277$	−1.26920	−	2.19832i	−0.0762588	−	0.132084i	−0.901633	+	0.432502i	$0.857631\pi$
$278$	4.23130	+	1.34023i	0.253777	+	0.0803819i
$279$	15.9777	+	4.68179i	0.956560	+	0.280292i
$280$	1.14348	+	11.6611i	0.0683362	+	0.696882i
$281$	−3.84074	−	6.65235i	−0.229119	−	0.396846i	0.728428	−	0.685122i	$-0.240251\pi$
$281$	−3.84074	−	6.65235i	−0.229119	−	0.396846i	−0.957547	+	0.288276i	$0.906918\pi$
$282$	1.74915	+	23.4881i	0.104161	+	1.39870i
$283$	−1.95480	+	3.38581i	−0.116201	+	0.201266i	−0.918259	−	0.395980i	$-0.870405\pi$
$283$	−1.95480	+	3.38581i	−0.116201	+	0.201266i	0.802058	+	0.597246i	$0.203738\pi$
$284$	3.99563	−	1.85044i	0.237097	−	0.109803i
$285$	18.0582	+	3.13205i	1.06967	+	0.185527i
$286$	6.55845	+	29.7682i	0.387809	+	1.76023i
$287$		−	3.44254i		−	0.203207i
$288$	16.4515	+	4.16525i	0.969412	+	0.245440i
$289$	16.6510			0.979472
$290$	−0.163307	+	0.467665i	−0.00958971	+	0.0274622i
$291$	3.42190	−	23.8471i	0.200596	−	1.39794i
$292$	12.8566	+	27.7611i	0.752373	+	1.62459i
$293$	0.689283	−	1.19387i	0.0402683	−	0.0697468i	−0.845189	−	0.534468i	$-0.820512\pi$
$293$	0.689283	−	1.19387i	0.0402683	−	0.0697468i	0.885457	+	0.464721i	$0.153845\pi$
$294$	−4.91964	−	7.22304i	−0.286919	−	0.421256i
$295$	4.32597	+	0.126412i	0.251868	+	0.00735998i
$296$	−7.24707	+	5.51566i	−0.421227	+	0.320591i
$297$	−17.2444	+	1.66120i	−1.00062	+	0.0963925i
$298$	9.76426	+	3.09276i	0.565629	+	0.179159i
$299$	−45.6176	+	26.3374i	−2.63814	+	1.52313i
$300$	−11.8867	−	12.5979i	−0.686277	−	0.727340i
$301$	−3.48468	−	2.01188i	−0.200854	−	0.115963i
$302$	−12.9316	−	14.1496i	−0.744130	−	0.814219i
$303$	3.54176	−	24.6824i	0.203469	−	1.41797i
$304$	−14.4362	−	12.2432i	−0.827974	−	0.702196i
$305$	3.77518	−	6.11879i	0.216166	−	0.350361i
$306$	2.25089	−	1.10236i	0.128675	−	0.0630179i
$307$	27.3968			1.56362			0.781808	−	0.623519i	$-0.214298\pi$
$307$	27.3968			1.56362			0.781808	+	0.623519i	$0.214298\pi$
$308$	−1.10898	+	12.3035i	−0.0631902	+	0.701059i
$309$	−13.1973	+	5.28768i	−0.750769	+	0.300805i
$310$	3.27381	+	17.2421i	0.185940	+	0.979283i
$311$	2.27190	−	3.93505i	0.128828	−	0.223136i	−0.794395	−	0.607402i	$-0.792212\pi$
$311$	2.27190	−	3.93505i	0.128828	−	0.223136i	0.923223	+	0.384265i	$0.125545\pi$
$312$	27.1784	+	16.2604i	1.53867	+	0.920566i
$313$	15.7733	−	9.10673i	0.891561	−	0.514743i	0.0171079	−	0.999854i	$-0.494554\pi$
$313$	15.7733	−	9.10673i	0.891561	−	0.514743i	0.874453	+	0.485111i	$0.161221\pi$
$314$	−1.36037	+	4.29488i	−0.0767704	+	0.242374i
$315$	−11.8191	−	3.84151i	−0.665932	−	0.216445i
$316$	−1.97302	−	1.38926i	−0.110991	−	0.0781520i
$317$	3.94082	+	6.82570i	0.221338	+	0.383369i	0.955215	−	0.295914i	$-0.0956241\pi$
$317$	3.94082	+	6.82570i	0.221338	+	0.383369i	−0.733876	+	0.679283i	$0.762291\pi$
$318$	−6.81073	+	14.1257i	−0.381927	+	0.792132i
$319$	−0.261132	+	0.452294i	−0.0146206	+	0.0253236i
$320$	3.98596	+	17.4388i	0.222822	+	0.974859i
$321$	−18.6904	+	23.7805i	−1.04320	+	1.32730i
$322$	−20.8474	+	4.59305i	−1.16178	+	0.255961i
$323$	−2.79555			−0.155548
$324$	−11.0358	+	14.2201i	−0.613097	+	0.790007i
$325$	−14.4999	−	28.8896i	−0.804311	−	1.60251i
$326$	19.9402	−	4.39317i	1.10438	−	0.243315i
$327$	21.9368	+	17.2414i	1.21311	+	0.953451i
$328$	−0.665488	−	5.21349i	−0.0367454	−	0.287867i
$329$	−8.90697	+	15.4273i	−0.491057	+	0.850536i
$330$	−9.83466	−	15.3868i	−0.541380	−	0.847017i
$331$	−3.80014	+	2.19401i	−0.208874	+	0.120594i	−0.600788	−	0.799408i	$-0.705146\pi$
$331$	−3.80014	+	2.19401i	−0.208874	+	0.120594i	0.391914	+	0.920002i	$0.371813\pi$
$332$	−6.93677	−	4.88438i	−0.380705	−	0.268065i
$333$	−2.28260	−	9.38616i	−0.125086	−	0.514358i
$334$	−16.2204	−	5.13769i	−0.887540	−	0.281122i
$335$	−0.435671	+	14.9092i	−0.0238033	+	0.814577i
$336$	8.51052	+	9.60815i	0.464287	+	0.524168i
$337$	−9.50739	−	5.48909i	−0.517900	−	0.299010i	0.218175	−	0.975910i	$-0.429990\pi$
$337$	−9.50739	−	5.48909i	−0.517900	−	0.299010i	−0.736075	+	0.676900i	$0.763323\pi$
$338$	27.4715	+	30.0591i	1.49425	+	1.63500i
$339$	6.72320	−	2.69374i	0.365154	−	0.146304i
$340$	2.11479	+	1.58346i	0.114691	+	0.0858752i
$341$			18.5034i			1.00201i
$342$	18.0308	−	8.83051i	0.974995	−	0.477499i
$343$		−	19.5781i		−	1.05712i
$344$	−5.66623	−	2.37322i	−0.305503	−	0.127955i
$345$	20.2164	−	24.2304i	1.08841	−	1.30452i
$346$	10.3942	+	11.3732i	0.558796	+	0.611429i
$347$	1.19627	−	2.07199i	0.0642189	−	0.111230i	−0.832128	−	0.554583i	$-0.812878\pi$
$347$	1.19627	−	2.07199i	0.0642189	−	0.111230i	0.896347	+	0.443353i	$0.146211\pi$
$348$	0.155785	+	0.519795i	0.00835094	+	0.0278639i
$349$	17.7287	−	10.2357i	0.948995	−	0.547903i	0.0562266	−	0.998418i	$-0.482093\pi$
$349$	17.7287	−	10.2357i	0.948995	−	0.547903i	0.892769	+	0.450515i	$0.148760\pi$
$350$	−2.06672	−	12.9359i	−0.110471	−	0.691455i
$351$	−27.3472	+	19.5084i	−1.45969	+	1.04128i
$352$	0.698957	+	18.8472i	0.0372545	+	1.00456i
$353$	−22.2359	+	12.8379i	−1.18350	+	0.683293i	−0.956821	−	0.290677i	$-0.906119\pi$
$353$	−22.2359	+	12.8379i	−1.18350	+	0.683293i	−0.226677	+	0.973970i	$0.572786\pi$
$354$	3.91835	−	2.66880i	0.208258	−	0.141845i
$355$	−4.33357	+	2.33595i	−0.230002	+	0.123979i
$356$	22.3574	−	10.3540i	1.18494	−	0.548763i
$357$	1.87639	+	0.269250i	0.0993093	+	0.0142502i
$358$	−0.110619	−	0.502090i	−0.00584641	−	0.0265363i
$359$	−13.8514			−0.731051			−0.365525	−	0.930801i	$-0.619111\pi$
$359$	−13.8514			−0.731051			−0.365525	+	0.930801i	$0.619111\pi$
$360$	−18.6418	−	3.53291i	−0.982512	−	0.186201i
$361$	−3.39378			−0.178620
$362$	0.934078	+	4.23969i	0.0490941	+	0.222833i
$363$	−0.0746118	−	0.186221i	−0.00391611	−	0.00977406i
$364$	10.0663	+	21.7361i	0.527617	+	1.13928i
$365$	−16.2298	−	30.1090i	−0.849507	−	1.57598i
$366$	−0.584897	−	7.85416i	−0.0305730	−	0.410544i
$367$	16.1398	−	9.31834i	0.842493	−	0.486414i	−0.0156178	−	0.999878i	$-0.504972\pi$
$367$	16.1398	−	9.31834i	0.842493	−	0.486414i	0.858111	+	0.513464i	$0.171638\pi$
$368$	−30.6840	+	10.9859i	−1.59952	+	0.572681i
$369$	5.34967	+	1.56756i	0.278493	+	0.0816041i
$370$	7.71360	−	6.64669i	0.401011	−	0.345545i
$371$	−10.2717	+	5.93034i	−0.533278	+	0.307888i
$372$	13.9878	+	13.1890i	0.725235	+	0.683816i
$373$	10.8701	−	18.8276i	0.562834	−	0.974858i	−0.434413	−	0.900714i	$-0.643044\pi$
$373$	10.8701	−	18.8276i	0.562834	−	0.974858i	0.997248	−	0.0741441i	$-0.0236225\pi$
$374$	1.87910	+	2.05609i	0.0971657	+	0.106318i
$375$	14.1194	+	13.2531i	0.729121	+	0.684385i
$376$	−10.5067	+	25.0854i	−0.541841	+	1.29368i
$377$			1.01269i			0.0521564i
$378$	−12.9529	+	4.19049i	−0.666227	+	0.215536i
$379$		−	26.5083i		−	1.36164i	−0.732450	−	0.680821i	$-0.761623\pi$
$379$		−	26.5083i		−	1.36164i	0.732450	−	0.680821i	$-0.238377\pi$
$380$	16.9406	+	12.6844i	0.869033	+	0.650694i
$381$	1.61237	+	1.26725i	0.0826042	+	0.0649234i
$382$	17.3708	+	19.0070i	0.888768	+	0.972480i
$383$	−9.17444	−	5.29687i	−0.468792	−	0.270657i	0.246942	−	0.969030i	$-0.420574\pi$
$383$	−9.17444	−	5.29687i	−0.468792	−	0.270657i	−0.715734	+	0.698373i	$0.753908\pi$
$384$	14.7460	+	12.9057i	0.752502	+	0.658590i
$385$	0.403424	−	13.8056i	0.0205604	−	0.703601i
$386$	−30.5286	−	9.66971i	−1.55386	−	0.492175i
$387$	4.71319	−	4.49904i	0.239585	−	0.228699i
$388$	16.0157	−	22.7454i	0.813074	−	1.15472i
$389$	28.8599	−	16.6623i	1.46326	−	0.844811i	0.464095	−	0.885785i	$-0.346379\pi$
$389$	28.8599	−	16.6623i	1.46326	−	0.844811i	0.999160	+	0.0409742i	$0.0130461\pi$
$390$	−31.4329	−	16.3036i	−1.59166	−	0.825564i
$391$	−2.40667	+	4.16847i	−0.121710	+	0.210809i
$392$	−1.27776	−	10.0100i	−0.0645364	−	0.505584i
$393$	11.4303	−	4.57968i	0.576580	−	0.231014i
$394$	−16.8597	+	3.71448i	−0.849377	+	0.187133i
$395$	2.29604	+	1.41661i	0.115526	+	0.0712775i
$396$	−18.6146	−	7.32577i	−0.935418	−	0.368134i
$397$	20.1614			1.01187			0.505936	−	0.862571i	$-0.331147\pi$
$397$	20.1614			1.01187			0.505936	+	0.862571i	$0.331147\pi$
$398$	20.6232	−	4.54365i	1.03375	−	0.227753i
$399$	15.0309	+	2.15684i	0.752486	+	0.107977i
$400$	−5.63058	−	19.1911i	−0.281529	−	0.959553i
$401$	1.93691	−	3.35482i	0.0967246	−	0.167532i	−0.813602	−	0.581422i	$-0.802497\pi$
$401$	1.93691	−	3.35482i	0.0967246	−	0.167532i	0.910327	+	0.413890i	$0.135830\pi$
$402$	9.19788	+	13.5044i	0.458749	+	0.673537i
$403$	17.9394	+	31.0720i	0.893627	+	1.54781i
$404$	16.5767	−	23.5421i	0.824721	−	1.17127i
$405$	11.3515	−	16.6176i	0.564061	−	0.825733i
$406$	−0.123927	+	0.391255i	−0.00615040	+	0.0194176i
$407$	9.29705	−	5.36765i	0.460837	−	0.266065i
$408$	2.89372	+	0.0450296i	0.143260	+	0.00222930i
$409$	15.0600	−	26.0847i	0.744671	−	1.28981i	−0.205678	−	0.978620i	$-0.565940\pi$
$409$	15.0600	−	26.0847i	0.744671	−	1.28981i	0.950348	−	0.311188i	$-0.100727\pi$
$410$	1.09614	+	5.77301i	0.0541346	+	0.285109i
$411$	−0.956569	+	6.66629i	−0.0471841	+	0.328824i
$412$	−16.3503	−	1.47374i	−0.805522	−	0.0726060i
$413$	3.58567			0.176439
$414$	2.35533	−	34.4881i	0.115758	−	1.69500i
$415$	8.07243	+	4.98054i	0.396260	+	0.244485i
$416$	19.4465	+	30.9718i	0.953445	+	1.51852i
$417$	−5.04605	+	2.02177i	−0.247106	+	0.0990064i
$418$	15.0525	+	16.4703i	0.736244	+	0.805590i
$419$	23.7922	+	13.7364i	1.16232	+	0.671067i	0.951860	−	0.306534i	$-0.0991695\pi$
$419$	23.7922	+	13.7364i	1.16232	+	0.671067i	0.210463	+	0.977602i	$0.432503\pi$
$420$	−10.1490	−	10.1455i	−0.495219	−	0.495048i
$421$	−0.0412004	+	0.0237870i	−0.00200798	+	0.00115931i	−0.501004	−	0.865445i	$-0.667036\pi$
$421$	−0.0412004	+	0.0237870i	−0.00200798	+	0.00115931i	0.498996	+	0.866604i	$0.333702\pi$
$422$	−8.65521	−	2.74148i	−0.421329	−	0.133453i
$423$	−19.9181	−	20.8662i	−0.968451	−	1.01455i
$424$	−14.4093	+	10.9667i	−0.699777	+	0.532592i
$425$	−2.46741	−	1.62372i	−0.119687	−	0.0787621i
$426$	−2.34218	+	4.85778i	−0.113479	+	0.235360i
$427$	2.97839	−	5.15872i	0.144134	−	0.249648i
$428$	−31.6919	+	14.6770i	−1.53189	+	0.709439i
$429$	−29.3520	−	23.0694i	−1.41713	−	1.11380i
$430$	6.48428	+	2.26429i	0.312700	+	0.109194i
$431$	−6.98377			−0.336396			−0.168198	−	0.985753i	$-0.553795\pi$
$431$	−6.98377			−0.336396			−0.168198	+	0.985753i	$0.553795\pi$
$432$	−18.8062	+	8.85018i	−0.904815	+	0.425804i
$433$		−	13.4813i		−	0.647869i	−0.946080	−	0.323934i	$-0.894994\pi$
$433$		−	13.4813i		−	0.647869i	0.946080	−	0.323934i	$-0.105006\pi$
$434$	3.12851	+	14.2000i	0.150173	+	0.681622i
$435$	−0.209094	−	0.569516i	−0.0100253	−	0.0273062i
$436$	13.5391	+	29.2349i	0.648405	+	1.40010i
$437$	−19.2787	+	33.3916i	−0.922224	+	1.59734i
$438$	−33.7511	−	16.2731i	−1.61269	−	0.777559i
$439$	2.35018	+	4.07064i	0.112168	+	0.194281i	0.916644	−	0.399704i	$-0.130887\pi$
$439$	2.35018	+	4.07064i	0.112168	+	0.194281i	−0.804476	+	0.593985i	$0.797554\pi$
$440$	−2.05785	−	20.9857i	−0.0981043	−	1.00045i
$441$	10.2715	+	3.00977i	0.489120	+	0.143322i
$442$	5.14892	+	1.63088i	0.244909	+	0.0775732i
$443$	−4.10464	−	7.10944i	−0.195017	−	0.337780i	0.751889	−	0.659290i	$-0.229143\pi$
$443$	−4.10464	−	7.10944i	−0.195017	−	0.337780i	−0.946906	+	0.321510i	$0.895810\pi$
$444$	2.56908	−	10.8542i	0.121923	−	0.515117i
$445$	−24.2483	+	13.0707i	−1.14948	+	0.619610i
$446$	24.4139	−	22.3123i	1.15603	−	1.05652i
$447$	−11.6444	+	4.66549i	−0.550762	+	0.220670i
$448$	3.72305	+	14.3457i	0.175898	+	0.677771i
$449$	−35.1881			−1.66063			−0.830314	−	0.557297i	$-0.811839\pi$
$449$	−35.1881			−1.66063			−0.830314	+	0.557297i	$0.811839\pi$
$450$	21.0434	+	2.67874i	0.991995	+	0.126277i
$451$			6.19532i			0.291726i
$452$	8.32946	+	0.750779i	0.391785	+	0.0353137i
$453$	23.2387	+	3.33461i	1.09185	+	0.156673i
$454$	−22.1584	−	24.2454i	−1.03994	−	1.13789i
$455$	−12.7074	−	23.5744i	−0.595734	−	1.10519i
$456$	23.1802	+	0.360711i	1.08551	+	0.0168918i
$457$	−30.6355	+	17.6874i	−1.43307	+	0.827383i	−0.997354	−	0.0727007i	$-0.976838\pi$
$457$	−30.6355	+	17.6874i	−1.43307	+	0.827383i	−0.435716	+	0.900084i	$0.643505\pi$
$458$	10.1073	+	3.20143i	0.472285	+	0.149593i
$459$	−1.27283	+	2.79329i	−0.0594106	+	0.130380i
$460$	33.4978	−	14.3404i	1.56184	−	0.668625i
$461$	−13.7003	+	7.90989i	−0.638088	+	0.368400i	−0.783878	−	0.620915i	$-0.786761\pi$
$461$	−13.7003	+	7.90989i	−0.638088	+	0.368400i	0.145790	+	0.989316i	$0.453428\pi$
$462$	−8.51707	−	12.5048i	−0.396250	−	0.581776i
$463$	−5.52455	−	3.18960i	−0.256748	−	0.148233i	0.366102	−	0.930575i	$-0.380692\pi$
$463$	−5.52455	−	3.18960i	−0.256748	−	0.148233i	−0.622850	+	0.782341i	$0.714025\pi$
$464$	−0.112044	+	0.616485i	−0.00520153	+	0.0286196i
$465$	−16.5043	−	13.7702i	−0.765368	−	0.638578i
$466$	−5.95581	−	27.0328i	−0.275897	−	1.25227i
$467$	24.9649			1.15524			0.577618	−	0.816307i	$-0.303982\pi$
$467$	24.9649			1.15524			0.577618	+	0.816307i	$0.303982\pi$
$468$	−38.3613	+	5.74537i	−1.77325	+	0.265580i
$469$			12.3578i			0.570630i
$470$	10.0244	−	28.7071i	0.462392	−	1.32416i
$471$	−2.05215	−	5.12188i	−0.0945581	−	0.236004i
$472$	5.43024	−	0.693156i	0.249947	−	0.0319051i
$473$	6.27116	+	3.62065i	0.288348	+	0.166478i
$474$	2.94722	−	0.219479i	0.135370	−	0.0100810i
$475$	−19.7653	−	13.0069i	−0.906893	−	0.596796i
$476$	1.78971	+	1.26019i	0.0820312	+	0.0577605i
$477$	−4.53848	−	18.6624i	−0.207803	−	0.854494i
$478$	−2.13776	+	6.74921i	−0.0977791	+	0.308702i
$479$	−1.38572	−	2.40013i	−0.0633150	−	0.109665i	0.832630	−	0.553829i	$-0.186834\pi$
$479$	−1.38572	−	2.40013i	−0.0633150	−	0.109665i	−0.895945	+	0.444164i	$0.853501\pi$
$480$	−17.3312	−	13.4027i	−0.791055	−	0.611745i
$481$	10.4081	−	18.0274i	0.474570	−	0.821979i
$482$	−10.9338	−	11.9636i	−0.498021	−	0.544929i
$483$	16.1561	−	20.5559i	0.735127	−	0.935327i
$484$	0.0207952	−	0.230711i	0.000945238	−	0.0104869i
$485$	−16.3310	+	26.4692i	−0.741553	+	1.20191i
$486$	−0.613848	−	22.0369i	−0.0278447	−	0.999612i
$487$			20.8545i			0.945008i	0.881329	+	0.472504i	$0.156650\pi$
$487$			20.8545i			0.945008i	−0.881329	+	0.472504i	$0.843350\pi$
$488$	3.51331	−	8.38828i	0.159040	−	0.379720i
$489$	−15.4530	+	19.6614i	−0.698810	+	0.889119i
$490$	2.10462	+	11.0843i	0.0950772	+	0.500739i
$491$	32.5679	+	18.8031i	1.46977	+	0.848571i	0.999425	−	0.0339131i	$-0.0107970\pi$
$491$	32.5679	+	18.8031i	1.46977	+	0.848571i	0.470343	+	0.882484i	$0.344130\pi$
$492$	4.68342	+	4.41595i	0.211145	+	0.199086i
$493$	0.0462692	+	0.0801406i	0.00208386	+	0.00360935i
$494$	41.2455	+	13.0642i	1.85572	+	0.587787i
$495$	21.2701	+	6.91333i	0.956021	+	0.310731i
$496$	7.48296	+	20.9001i	0.335995	+	0.938444i
$497$	−3.53238	+	2.03942i	−0.158449	+	0.0914804i
$498$	10.3619	−	0.771646i	0.464327	−	0.0345783i
$499$	−26.4715	−	15.2833i	−1.18503	−	0.684175i	−0.227854	−	0.973695i	$-0.573171\pi$
$499$	−26.4715	−	15.2833i	−1.18503	−	0.684175i	−0.957172	+	0.289520i	$0.906504\pi$
$500$	7.58474	+	21.0350i	0.339200	+	0.940714i
$501$	19.3437	−	7.75031i	0.864212	−	0.346258i
$502$	1.58410	+	7.19008i	0.0707019	+	0.320909i
$503$			20.6381i			0.920208i	0.887865	+	0.460104i	$0.152188\pi$
$503$			20.6381i			0.920208i	−0.887865	+	0.460104i	$0.847812\pi$
$504$	−15.5240	−	2.47469i	−0.691493	−	0.110231i
$505$	−16.9030	+	27.3964i	−0.752175	+	1.21912i
$506$	37.5177	−	8.26582i	1.66787	−	0.367460i
$507$	−49.3677	−	7.08394i	−2.19249	−	0.314609i
$508$	0.995133	+	2.14878i	0.0441519	+	0.0953369i
$509$	−1.15035	−	0.664155i	−0.0509884	−	0.0294381i	0.474289	−	0.880369i	$-0.342705\pi$
$509$	−1.15035	−	0.664155i	−0.0509884	−	0.0294381i	−0.525277	+	0.850931i	$0.676038\pi$
$510$	−3.23237	+	0.145941i	−0.143132	+	0.00646237i
$511$	−14.1696	−	24.5424i	−0.626825	−	1.08569i
$512$	8.41151	+	21.0059i	0.371740	+	0.928337i
$513$	−10.1960	+	22.3757i	−0.450166	+	0.987912i
$514$	−13.4455	−	4.25877i	−0.593056	−	0.187846i
$515$	18.3465	+	0.536114i	0.808443	+	0.0236240i
$516$	7.20707	−	2.15999i	0.317274	−	0.0950884i
$517$	16.0293	−	27.7636i	0.704968	−	1.22104i
$518$	6.22727	−	5.69121i	0.273610	−	0.250058i
$519$	−18.6789	−	2.68030i	−0.819913	−	0.117652i
$520$	−23.8018	−	33.2453i	−1.04378	−	1.45790i
$521$	0.811244			0.0355412			0.0177706	−	0.999842i	$-0.494343\pi$
$521$	0.811244			0.0355412			0.0177706	+	0.999842i	$0.494343\pi$
$522$	−0.551575	−	0.370740i	−0.0241418	−	0.0162268i
$523$	−30.4237			−1.33034			−0.665169	−	0.746693i	$-0.731640\pi$
$523$	−30.4237			−1.33034			−0.665169	+	0.746693i	$0.731640\pi$
$524$	14.1611	+	1.27641i	0.618630	+	0.0557604i
$525$	12.0139	+	10.6340i	0.524328	+	0.464106i
$526$	−12.3384	+	11.2763i	−0.537980	+	0.491670i
$527$	2.83931	+	1.63928i	0.123682	+	0.0714081i
$528$	−15.3158	−	17.2912i	−0.666536	−	0.752502i
$529$	21.6938	+	37.5747i	0.943207	+	1.63368i
$530$	15.3369	−	13.2156i	0.666192	−	0.574047i
$531$	−1.63274	+	5.57209i	−0.0708547	+	0.241808i
$532$	14.3365	+	10.0947i	0.621567	+	0.437663i
$533$	6.00651	+	10.4036i	0.260171	+	0.450629i
$534$	−13.1056	+	27.1815i	−0.567133	+	1.17626i
$535$	34.3723	−	18.5279i	1.48605	−	0.801030i
$536$	2.38892	+	18.7150i	0.103186	+	0.808366i
$537$	0.495070	+	0.389104i	0.0213639	+	0.0167911i
$538$	4.92321	+	22.3460i	0.212255	+	0.963404i
$539$			11.8952i			0.512362i
$540$	20.3873	−	11.1516i	0.877329	−	0.479890i
$541$			11.9797i			0.515048i	0.966272	+	0.257524i	$0.0829067\pi$
$541$			11.9797i			0.515048i	−0.966272	+	0.257524i	$0.917093\pi$
$542$	−27.7728	+	6.11883i	−1.19294	+	0.262826i
$543$	−4.18041	−	3.28563i	−0.179399	−	0.141000i
$544$	2.95400	+	1.56249i	0.126652	+	0.0669911i
$545$	−17.0914	−	31.7075i	−0.732116	−	1.35820i
$546$	−26.4261	−	12.7413i	−1.13093	−	0.545279i
$547$	4.69681	+	8.13511i	0.200821	+	0.347832i	0.948793	−	0.315898i	$-0.102306\pi$
$547$	4.69681	+	8.13511i	0.200821	+	0.347832i	−0.747972	+	0.663730i	$0.768972\pi$
$548$	−4.47708	+	6.35833i	−0.191251	+	0.271614i
$549$	6.66038	+	6.97741i	0.284258	+	0.297789i
$550$	3.71934	+	23.2800i	0.158593	+	0.992662i
$551$	0.370640	+	0.641968i	0.0157898	+	0.0273488i
$552$	20.4935	−	34.2537i	0.872263	−	1.45793i
$553$	1.93578	+	1.11762i	0.0823176	+	0.0475261i
$554$	2.42178	+	2.64989i	0.102892	+	0.112583i
$555$	−2.13112	+	12.2872i	−0.0904612	+	0.521563i
$556$	−6.25162	−	0.563492i	−0.265128	−	0.0238974i
$557$	8.56289			0.362821			0.181411	−	0.983407i	$-0.441934\pi$
$557$	8.56289			0.362821			0.181411	+	0.983407i	$0.441934\pi$
$558$	−23.4912	−	1.60431i	−0.994463	−	0.0679160i
$559$	14.0412			0.593881
$560$	−5.12747	−	15.7571i	−0.216675	−	0.665857i
$561$	−3.37682	−	0.484553i	−0.142570	−	0.0204578i
$562$	7.32858	+	8.01885i	0.309137	+	0.338255i
$563$	5.86483	−	10.1582i	0.247173	−	0.428116i	−0.715567	−	0.698544i	$-0.753832\pi$
$563$	5.86483	−	10.1582i	0.247173	−	0.428116i	0.962740	+	0.270427i	$0.0871650\pi$
$564$	−9.56269	−	31.9071i	−0.402662	−	1.34353i
$565$	−9.34639	−	0.273117i	−0.393205	−	0.0114901i
$566$	1.66953	−	5.27092i	0.0701755	−	0.221553i
$567$	8.99876	−	14.0368i	0.377912	−	0.589488i
$568$	−4.95529	+	3.77141i	−0.207919	+	0.158245i
$569$	19.7153	+	34.1479i	0.826509	+	1.43156i	0.900761	+	0.434316i	$0.143010\pi$
$569$	19.7153	+	34.1479i	0.826509	+	1.43156i	−0.0742514	+	0.997240i	$0.523657\pi$
$570$	−25.8930	+	1.16906i	−1.08454	+	0.0489666i
$571$	−7.92266	−	4.57415i	−0.331553	−	0.191422i	0.324977	−	0.945722i	$-0.394643\pi$
$571$	−7.92266	−	4.57415i	−0.331553	−	0.191422i	−0.656530	+	0.754300i	$0.727977\pi$
$572$	−18.1157	−	39.1170i	−0.757453	−	1.63556i
$573$	−31.2162	−	4.47932i	−1.30407	−	0.187126i
$574$	1.04749	+	4.75447i	0.0437215	+	0.198448i
$575$	−36.4105	+	18.2747i	−1.51842	+	0.762107i
$576$	−23.9884	−	0.746756i	−0.999516	−	0.0311148i
$577$		−	20.4943i		−	0.853190i	−0.904443	−	0.426595i	$-0.859713\pi$
$577$		−	20.4943i		−	0.853190i	0.904443	−	0.426595i	$-0.140287\pi$
$578$	−22.9966	+	5.06655i	−0.956532	+	0.210741i
$579$	36.4070	−	14.5869i	1.51302	−	0.606212i
$580$	0.0832414	−	0.695579i	0.00345641	−	0.0288823i
$581$	6.80582	+	3.92934i	0.282353	+	0.163017i
$582$	2.53020	+	33.9762i	0.104880	+	1.40836i
$583$	18.4852	−	10.6725i	0.765580	−	0.442008i
$584$	−26.2032	−	34.4286i	−1.08430	−	1.42467i
$585$	42.4208	−	9.01257i	1.75388	−	0.372624i
$586$	−0.588693	+	1.85858i	−0.0243187	+	0.0767773i
$587$	12.1463	+	21.0379i	0.501330	+	0.868329i	0.999999	+	0.00153627i	$0.000489009\pi$
$587$	12.1463	+	21.0379i	0.501330	+	0.868329i	−0.498669	+	0.866793i	$0.666178\pi$
$588$	8.99230	+	8.47874i	0.370836	+	0.349657i
$589$	22.7444	+	13.1315i	0.937166	+	0.541073i
$590$	−6.01302	+	1.14171i	−0.247552	+	0.0470036i
$591$	13.0657	−	16.6239i	0.537451	−	0.683817i
$592$	8.33057	−	9.82276i	0.342384	−	0.403713i
$593$			6.89686i			0.283220i	0.989923	+	0.141610i	$0.0452279\pi$
$593$			6.89686i			0.283220i	−0.989923	+	0.141610i	$0.954772\pi$
$594$	23.3106	−	7.54136i	0.956444	−	0.309426i
$595$	−2.08271	−	1.28500i	−0.0853830	−	0.0526797i
$596$	−14.4264	−	1.30033i	−0.590929	−	0.0532635i
$597$	−15.9823	+	20.3349i	−0.654113	+	0.832250i
$598$	54.9882	−	50.2548i	2.24864	−	2.05507i
$599$	−1.81418	+	3.14225i	−0.0741254	+	0.128389i	−0.900706	−	0.434430i	$-0.856950\pi$
$599$	−1.81418	+	3.14225i	−0.0741254	+	0.128389i	0.826580	+	0.562819i	$0.190283\pi$
$600$	20.2498	+	13.7820i	0.826697	+	0.562648i
$601$	0.432510	+	0.749129i	0.0176424	+	0.0305576i	0.874712	−	0.484643i	$-0.161051\pi$
$601$	0.432510	+	0.749129i	0.0176424	+	0.0305576i	−0.857069	+	0.515201i	$0.827717\pi$
$602$	5.42484	+	1.71828i	0.221100	+	0.0700318i
$603$	−19.2039	−	5.62713i	−0.782042	−	0.229155i
$604$	22.1652	+	15.6071i	0.901888	+	0.635044i
$605$	−0.00756485	+	0.258878i	−0.000307555	+	0.0105249i
$606$	2.61882	+	35.1663i	0.106382	+	1.42853i
$607$	−2.81348	−	1.62436i	−0.114196	−	0.0659309i	0.441814	−	0.897107i	$-0.354335\pi$
$607$	−2.81348	−	1.62436i	−0.114196	−	0.0659309i	−0.556010	+	0.831176i	$0.687668\pi$
$608$	23.6631	+	12.5163i	0.959665	+	0.507605i
$609$	−0.186946	−	0.466592i	−0.00757545	−	0.0189073i
$610$	−3.35205	+	9.59932i	−0.135721	+	0.388665i
$611$		−	62.1631i		−	2.51485i
$612$	−2.77326	+	2.20736i	−0.112102	+	0.0892274i
$613$	13.7010			0.553380			0.276690	−	0.960959i	$-0.410762\pi$
$613$	13.7010			0.553380			0.276690	+	0.960959i	$0.410762\pi$
$614$	−37.8375	+	8.33626i	−1.52700	+	0.336424i
$615$	−5.52598	−	4.61056i	−0.222829	−	0.185916i
$616$	−2.21210	−	17.3298i	−0.0891280	−	0.698236i
$617$	13.1108	+	7.56954i	0.527822	+	0.304738i	0.740129	−	0.672465i	$-0.234764\pi$
$617$	13.1108	+	7.56954i	0.527822	+	0.304738i	−0.212307	+	0.977203i	$0.568098\pi$
$618$	16.6178	−	11.3184i	0.668465	−	0.455294i
$619$	7.93920	−	4.58370i	0.319103	−	0.184234i	−0.331889	−	0.943318i	$-0.607686\pi$
$619$	7.93920	−	4.58370i	0.319103	−	0.184234i	0.650993	+	0.759084i	$0.274353\pi$
$620$	−9.76783	−	22.8167i	−0.392285	−	0.916342i
$621$	24.5870	+	34.4665i	0.986643	+	1.38309i
$622$	−1.94035	+	6.12596i	−0.0778011	+	0.245629i
$623$	−19.7653	+	11.4115i	−0.791878	+	0.457191i
$624$	−42.4835	−	14.1874i	−1.70070	−	0.567949i
$625$	−9.89056	−	22.9603i	−0.395622	−	0.918413i
$626$	−19.0134	+	17.3767i	−0.759929	+	0.694513i
$627$	−27.0501	−	3.88152i	−1.08028	−	0.155013i
$628$	0.571959	−	6.34556i	0.0228237	−	0.253216i
$629$		−	1.90216i		−	0.0758440i
$630$	17.4922	+	1.70918i	0.696905	+	0.0680952i
$631$	26.2470			1.04488			0.522439	−	0.852677i	$-0.325022\pi$
$631$	26.2470			1.04488			0.522439	+	0.852677i	$0.325022\pi$
$632$	3.14765	+	1.31835i	0.125207	+	0.0524411i
$633$	10.3218	−	4.13557i	0.410255	−	0.164374i
$634$	−7.51955	−	8.22781i	−0.298639	−	0.326768i
$635$	−1.25623	−	2.33052i	−0.0498520	−	0.0924840i
$636$	5.10808	−	21.5813i	0.202549	−	0.855754i
$637$	11.5327	+	19.9752i	0.456941	+	0.791445i
$638$	0.223024	−	0.704116i	0.00882960	−	0.0278762i
$639$	−1.56076	−	6.41792i	−0.0617428	−	0.253889i
$640$	−10.8112	−	22.8718i	−0.427352	−	0.904085i
$641$	−20.3809	−	35.3008i	−0.804998	−	1.39430i	−0.916292	−	0.400510i	$-0.868833\pi$
$641$	−20.3809	−	35.3008i	−0.804998	−	1.39430i	0.111294	−	0.993788i	$-0.464500\pi$
$642$	18.5773	−	38.5301i	0.733188	−	1.52066i
$643$	15.9839	−	27.6850i	0.630345	−	1.09179i	−0.357137	−	0.934052i	$-0.616247\pi$
$643$	15.9839	−	27.6850i	0.630345	−	1.09179i	0.987481	−	0.157737i	$-0.0504197\pi$
$644$	27.3946	−	12.6868i	1.07950	−	0.499932i
$645$	−7.89648	+	2.89914i	−0.310923	+	0.114153i
$646$	3.86090	−	0.850625i	0.151905	−	0.0334674i
$647$			31.4488i			1.23638i	0.786029	+	0.618190i	$0.212134\pi$
$647$			31.4488i			1.23638i	−0.786029	+	0.618190i	$0.787866\pi$
$648$	10.9145	−	22.9973i	0.428762	−	0.903417i
$649$	−6.45289			−0.253298
$650$	28.8162	+	35.4872i	1.13027	+	1.39192i
$651$	−14.0015	−	11.0046i	−0.548761	−	0.431303i
$652$	−26.2025	+	12.1348i	−1.02617	+	0.475234i
$653$	4.85136	−	8.40281i	0.189849	−	0.328827i	−0.755351	−	0.655320i	$-0.772534\pi$
$653$	4.85136	−	8.40281i	0.189849	−	0.328827i	0.945200	+	0.326493i	$0.105867\pi$
$654$	−35.5429	−	17.1370i	−1.38984	−	0.670111i
$655$	−15.8900	−	0.464331i	−0.620873	−	0.0181429i
$656$	2.50545	+	6.99781i	0.0978215	+	0.273219i
$657$	44.5908	−	10.8439i	1.73965	−	0.423063i
$658$	7.60714	−	24.0168i	0.296557	−	0.936271i
$659$	−17.1787	+	9.91816i	−0.669189	+	0.386356i	−0.795769	−	0.605600i	$-0.792933\pi$
$659$	−17.1787	+	9.91816i	−0.669189	+	0.386356i	0.126580	+	0.991956i	$0.459600\pi$
$660$	18.2644	+	18.2581i	0.710943	+	0.710697i
$661$	−34.2332	−	19.7646i	−1.33152	−	0.768753i	−0.345986	−	0.938240i	$-0.612456\pi$
$661$	−34.2332	−	19.7646i	−1.33152	−	0.768753i	−0.985532	+	0.169487i	$0.945789\pi$
$662$	4.58075	−	4.18643i	0.178036	−	0.162710i
$663$	−6.14036	+	2.46022i	−0.238472	+	0.0955469i
$664$	11.0665	+	4.63506i	0.429465	+	0.179875i
$665$	−16.6836	−	10.2935i	−0.646964	−	0.399164i
$666$	6.00849	+	12.2686i	0.232824	+	0.475399i
$667$	1.27633			0.0494196
$668$	23.9651	+	2.16011i	0.927239	+	0.0835770i
$669$	−5.75357	+	40.0963i	−0.222446	+	1.55021i
$670$	−3.93485	−	20.7235i	−0.152017	−	0.800620i
$671$	−5.36001	+	9.28381i	−0.206921	+	0.358398i
$672$	−14.6774	−	10.6802i	−0.566192	−	0.411996i
$673$	−13.7903	+	7.96182i	−0.531576	+	0.306905i	−0.741658	−	0.670778i	$-0.765960\pi$
$673$	−13.7903	+	7.96182i	−0.531576	+	0.306905i	0.210082	+	0.977684i	$0.432627\pi$
$674$	14.8008	+	4.68804i	0.570105	+	0.180577i
$675$	−21.9956	+	13.8272i	−0.846612	+	0.532210i
$676$	−47.0870	−	33.1553i	−1.81104	−	1.27520i
$677$	−2.57113	−	4.45333i	−0.0988166	−	0.171155i	0.812379	−	0.583130i	$-0.198172\pi$
$677$	−2.57113	−	4.45333i	−0.0988166	−	0.171155i	−0.911195	+	0.411975i	$0.864839\pi$
$678$	−8.46571	+	5.76603i	−0.325124	+	0.221443i
$679$	−12.8842	+	22.3161i	−0.494449	+	0.856411i
$680$	−3.40253	−	1.54342i	−0.130481	−	0.0591874i
$681$	39.8196	+	5.71386i	1.52589	+	0.218956i
$682$	−5.63018	−	25.5549i	−0.215591	−	0.978546i
$683$	−32.5301			−1.24473			−0.622364	−	0.782728i	$-0.713828\pi$
$683$	−32.5301			−1.24473			−0.622364	+	0.782728i	$0.713828\pi$
$684$	−22.2153	+	17.6821i	−0.849422	+	0.676093i
$685$	4.56522	−	7.39929i	0.174428	−	0.282712i
$686$	5.95720	+	27.0392i	0.227447	+	1.03236i
$687$	−12.0535	+	4.82941i	−0.459871	+	0.184254i
$688$	8.54770	+	1.55352i	0.325878	+	0.0592274i
$689$	20.6944	−	35.8437i	0.788393	−	1.36554i
$690$	−20.5479	+	39.6158i	−0.782245	+	1.50815i
$691$	21.0875	−	12.1749i	0.802207	−	0.463154i	−0.0420353	−	0.999116i	$-0.513384\pi$
$691$	21.0875	−	12.1749i	0.802207	−	0.463154i	0.844242	+	0.535962i	$0.180051\pi$
$692$	−17.8160	−	12.5447i	−0.677263	−	0.476880i
$693$	17.7824	+	5.21062i	0.675499	+	0.197935i
$694$	−1.02169	+	3.22561i	−0.0387828	+	0.122442i
$695$	7.01486	+	0.204986i	0.266089	+	0.00777556i
$696$	−0.373316	−	0.670482i	−0.0141505	−	0.0254146i
$697$	0.950663	+	0.548865i	0.0360089	+	0.0207898i
$698$	−21.3705	+	19.5309i	−0.808884	+	0.739254i
$699$	26.6549	+	20.9496i	1.00818	+	0.792386i
$700$	6.79046	+	17.2369i	0.256655	+	0.651492i
$701$			29.3780i			1.10959i	0.831987	+	0.554796i	$0.187204\pi$
$701$			29.3780i			1.10959i	−0.831987	+	0.554796i	$0.812796\pi$
$702$	31.8330	−	35.2641i	1.20146	−	1.33096i
$703$		−	15.2373i		−	0.574685i
$704$	−6.70013	−	25.8171i	−0.252521	−	0.973017i
$705$	12.8350	+	34.9592i	0.483395	+	1.31664i
$706$	26.8035	−	24.4962i	1.00876	−	0.921928i
$707$	−13.3355	+	23.0977i	−0.501532	+	0.868679i
$708$	−4.59954	+	4.87813i	−0.172861	+	0.183331i
$709$	−12.2117	+	7.05045i	−0.458622	+	0.264785i	−0.711464	−	0.702722i	$-0.751968\pi$
$709$	−12.2117	+	7.05045i	−0.458622	+	0.264785i	0.252843	+	0.967507i	$0.418634\pi$
$710$	5.27429	−	4.54477i	0.197940	−	0.170562i
$711$	−2.61823	+	2.49927i	−0.0981912	+	0.0937298i
$712$	−27.7271	+	21.1028i	−1.03912	+	0.790859i
$713$	39.1610	−	22.6096i	1.46659	−	0.846737i
$714$	−2.67340	+	0.199087i	−0.100049	+	0.00745065i
$715$	22.8688	+	42.4254i	0.855243	+	1.58662i
$716$	0.305551	+	0.659774i	0.0114190	+	0.0246569i
$717$	−3.22486	−	8.04880i	−0.120435	−	0.300588i
$718$	19.1301	−	4.21470i	0.713929	−	0.157291i
$719$	45.4953			1.69669			0.848345	−	0.529444i	$-0.177600\pi$
$719$	45.4953			1.69669			0.848345	+	0.529444i	$0.177600\pi$
$720$	26.8211	−	0.793041i	0.999563	−	0.0295549i
$721$	15.2069			0.566333
$722$	4.68712	−	1.03266i	0.174437	−	0.0384315i
$723$	19.6486	+	2.81944i	0.730738	+	0.104856i
$724$	−2.58010	−	5.57118i	−0.0958885	−	0.207051i
$725$	−0.0457355	+	0.781893i	−0.00169857	+	0.0290388i
$726$	0.159709	+	0.234485i	0.00592735	+	0.00870256i
$727$	13.8164	−	7.97688i	0.512420	−	0.295846i	−0.221408	−	0.975181i	$-0.571065\pi$
$727$	13.8164	−	7.97688i	0.512420	−	0.295846i	0.733828	+	0.679335i	$0.237732\pi$
$728$	−20.5163	−	26.9565i	−0.760384	−	0.999076i
$729$	17.7154	+	20.3756i	0.656125	+	0.754653i
$730$	31.5764	+	36.6449i	1.16869	+	1.35629i
$731$	1.11117	−	0.641533i	0.0410980	−	0.0237280i
$732$	3.19765	+	10.6693i	0.118189	+	0.394350i
$733$	−17.2293	+	29.8421i	−0.636380	+	1.10224i	0.349841	+	0.936809i	$0.386236\pi$
$733$	−17.2293	+	29.8421i	−0.636380	+	1.10224i	−0.986221	+	0.165434i	$0.947098\pi$
$734$	−19.4552	+	17.7805i	−0.718106	+	0.656290i
$735$	−10.6100	−	8.85240i	−0.391357	−	0.326526i
$736$	39.0347	−	24.5091i	1.43884	−	0.903416i
$737$		−	22.2395i		−	0.819204i
$738$	−7.86536	−	0.537158i	−0.289528	−	0.0197731i
$739$		−	16.8961i		−	0.621532i	−0.950487	−	0.310766i	$-0.899415\pi$
$739$		−	16.8961i		−	0.621532i	0.950487	−	0.310766i	$-0.100585\pi$
$740$	−8.63074	+	11.5268i	−0.317272	+	0.423733i
$741$	−49.1875	+	19.7076i	−1.80695	+	0.723978i
$742$	12.3816	−	11.3158i	0.454544	−	0.415416i
$743$	−17.4220	−	10.0586i	−0.639152	−	0.369015i	0.145136	−	0.989412i	$-0.453638\pi$
$743$	−17.4220	−	10.0586i	−0.639152	−	0.369015i	−0.784288	+	0.620397i	$0.786971\pi$
$744$	−23.3316	−	13.9590i	−0.855377	−	0.511761i
$745$	16.1877	+	0.473031i	0.593071	+	0.0173305i
$746$	−9.28381	+	29.3102i	−0.339904	+	1.07312i
$747$	−9.20519	+	8.78694i	−0.336800	+	0.321497i
$748$	−3.22083	−	2.26787i	−0.117765	−	0.0829217i
$749$	28.0175	−	16.1759i	1.02374	−	0.591055i
$750$	−23.5328	−	14.0075i	−0.859295	−	0.511480i
$751$	−4.26382	+	7.38515i	−0.155589	+	0.269488i	−0.933273	−	0.359167i	$-0.883061\pi$
$751$	−4.26382	+	7.38515i	−0.155589	+	0.269488i	0.777684	+	0.628655i	$0.216394\pi$
$752$	6.87772	−	37.8423i	0.250805	−	1.37997i
$753$	−7.08955	−	5.57209i	−0.258358	−	0.203058i
$754$	−0.308141	−	1.39862i	−0.0112218	−	0.0509348i
$755$	−25.7940	−	15.9144i	−0.938738	−	0.579184i
$756$	16.6141	−	9.72876i	0.604249	−	0.353831i
$757$	−30.3158			−1.10185			−0.550924	−	0.834556i	$-0.685724\pi$
$757$	−30.3158			−1.10185			−0.550924	+	0.834556i	$0.685724\pi$
$758$	8.06592	+	36.6104i	0.292967	+	1.32975i
$759$	−29.0751	+	36.9932i	−1.05536	+	1.34277i
$760$	−27.2561	−	12.3636i	−0.988681	−	0.448475i
$761$	−20.0870	+	34.7918i	−0.728154	+	1.26120i	0.229508	+	0.973307i	$0.426288\pi$
$761$	−20.0870	+	34.7918i	−0.728154	+	1.26120i	−0.957662	+	0.287894i	$0.907045\pi$
$762$	−2.61243	−	1.25958i	−0.0946384	−	0.0456299i
$763$	−14.9218	−	25.8453i	−0.540206	−	0.935664i
$764$	−29.7741	−	20.9648i	−1.07719	−	0.758479i
$765$	2.94523	−	2.65139i	0.106485	−	0.0958613i
$766$	14.2825	+	4.52387i	0.516047	+	0.163454i
$767$	−10.8361	+	6.25623i	−0.391269	+	0.225899i
$768$	−24.2925	−	13.3370i	−0.876579	−	0.481259i
$769$	−18.9297	+	32.7872i	−0.682623	+	1.18234i	0.291554	+	0.956554i	$0.405828\pi$
$769$	−18.9297	+	32.7872i	−0.682623	+	1.18234i	−0.974177	+	0.225784i	$0.927506\pi$
$770$	3.64360	+	19.1896i	0.131306	+	0.691546i
$771$	16.0345	−	6.42443i	0.577468	−	0.231370i
$772$	45.1051	+	4.06556i	1.62337	+	0.146323i
$773$	11.8902			0.427662			0.213831	−	0.976871i	$-0.431406\pi$
$773$	11.8902			0.427662			0.213831	+	0.976871i	$0.431406\pi$
$774$	−5.14039	+	7.64772i	−0.184768	+	0.274892i
$775$	12.4476	+	24.8007i	0.447132	+	0.890866i
$776$	−15.1982	+	36.2868i	−0.545584	+	1.30262i
$777$	−1.46756	+	10.2274i	−0.0526486	+	0.366905i
$778$	−34.7882	+	31.7936i	−1.24722	+	1.13986i
$779$	7.61531	+	4.39670i	0.272847	+	0.157528i
$780$	48.3725	+	12.9524i	1.73201	+	0.463770i
$781$	6.35699	−	3.67021i	0.227471	−	0.131330i
$782$	2.05545	−	6.48934i	0.0735028	−	0.232058i
$783$	0.810206	−	0.0780495i	0.0289544	−	0.00278926i
$784$	4.81054	+	13.4360i	0.171805	+	0.479857i
$785$	−0.208066	+	7.12028i	−0.00742620	+	0.254134i
$786$	−14.3927	+	9.80294i	−0.513371	+	0.349659i
$787$	3.21964	−	5.57658i	0.114768	−	0.198784i	−0.802919	−	0.596088i	$-0.796721\pi$
$787$	3.21964	−	5.57658i	0.114768	−	0.198784i	0.917687	+	0.397304i	$0.130054\pi$
$788$	22.1545	−	10.2601i	0.789221	−	0.365500i
$789$	2.90776	−	20.2641i	0.103519	−	0.721419i
$790$	−3.60208	−	1.25784i	−0.128156	−	0.0447518i
$791$	−7.74694			−0.275450
$792$	27.9375	+	4.45354i	0.992717	+	0.158250i
$793$			20.7866i			0.738155i
$794$	−27.8447	+	6.13469i	−0.988173	+	0.217712i
$795$	−4.23730	+	24.4306i	−0.150281	+	0.866462i
$796$	−27.1000	+	12.5504i	−0.960533	+	0.444837i
$797$	−15.1379	+	26.2197i	−0.536213	+	0.928748i	0.462891	+	0.886415i	$0.346812\pi$
$797$	−15.1379	+	26.2197i	−0.536213	+	0.928748i	−0.999104	+	0.0423326i	$0.986521\pi$
$798$	−21.4153	+	1.59479i	−0.758094	+	0.0564550i
$799$	−2.84019	−	4.91935i	−0.100479	−	0.174034i
$800$	13.6158	+	24.7913i	0.481391	+	0.876506i
$801$	−8.73318	−	35.9112i	−0.308572	−	1.26886i
$802$	−1.65425	+	5.22268i	−0.0584135	+	0.184419i
$803$	25.5001	+	44.1674i	0.899878	+	1.55863i
$804$	−16.8122	−	15.8521i	−0.592921	−	0.559059i
$805$	−29.7116	+	16.0156i	−1.04720	+	0.564475i
$806$	−34.2306	−	37.4547i	−1.20572	−	1.31929i
$807$	−22.0336	−	17.3174i	−0.775618	−	0.609603i
$808$	−15.7305	+	37.5578i	−0.553399	+	1.32128i
$809$	3.79502			0.133426			0.0667130	−	0.997772i	$-0.478749\pi$
$809$	3.79502			0.133426			0.0667130	+	0.997772i	$0.478749\pi$
$810$	−10.6211	+	26.4044i	−0.373188	+	0.927756i
$811$		−	25.9465i		−	0.911105i	−0.890209	−	0.455552i	$-0.849442\pi$
$811$		−	25.9465i		−	0.911105i	0.890209	−	0.455552i	$-0.150558\pi$
$812$	0.0521043	−	0.578067i	0.00182850	−	0.0202862i
$813$	21.5230	−	27.3845i	0.754846	−	0.960416i
$814$	−11.2068	+	10.2421i	−0.392799	+	0.358986i
$815$	28.4186	−	15.3186i	0.995461	−	0.536588i
$816$	−4.01019	+	0.818306i	−0.140385	+	0.0286464i
$817$	8.90104	−	5.13902i	0.311408	−	0.179791i
$818$	−12.8623	+	40.6079i	−0.449718	+	1.41982i
$819$	34.9132	−	8.49048i	1.21997	−	0.296681i
$820$	−3.27048	−	7.63952i	−0.114210	−	0.266784i
$821$	−39.0578	+	22.5500i	−1.36313	+	0.787002i	−0.990039	−	0.140794i	$-0.955035\pi$
$821$	−39.0578	+	22.5500i	−1.36313	+	0.787002i	−0.373089	+	0.927796i	$0.621701\pi$
$822$	−0.707299	−	9.49782i	−0.0246699	−	0.331274i
$823$	36.8115	+	21.2532i	1.28317	+	0.740838i	0.977427	−	0.211276i	$-0.0677617\pi$
$823$	36.8115	+	21.2532i	1.28317	+	0.740838i	0.305743	+	0.952114i	$0.401095\pi$
$824$	23.0297	−	2.93968i	0.802278	−	0.102409i
$825$	−21.6206	−	19.1373i	−0.752732	−	0.666276i
$826$	−4.95213	+	1.09104i	−0.172307	+	0.0379622i
$827$	−26.0006			−0.904131			−0.452065	−	0.891985i	$-0.649313\pi$
$827$	−26.0006			−0.904131			−0.452065	+	0.891985i	$0.649313\pi$
$828$	7.24106	+	48.3479i	0.251644	+	1.68021i
$829$			31.5003i			1.09405i	0.837116	+	0.547025i	$0.184240\pi$
$829$			31.5003i			1.09405i	−0.837116	+	0.547025i	$0.815760\pi$
$830$	−12.6642	−	4.42231i	−0.439582	−	0.153501i
$831$	−4.35206	−	0.624493i	−0.150971	−	0.0216634i
$832$	−36.2815	−	36.8577i	−1.25784	−	1.27781i
$833$	1.82530	+	1.05384i	0.0632429	+	0.0365133i
$834$	6.35388	−	4.32766i	0.220017	−	0.149854i
$835$	−26.8910	−	0.785799i	−0.930601	−	0.0271937i
$836$	−25.8005	−	18.1669i	−0.892329	−	0.628314i
$837$	23.4766	−	16.7472i	0.811469	−	0.578868i
$838$	−37.0388	−	11.7318i	−1.27949	−	0.405268i
$839$	28.7717	+	49.8341i	0.993310	+	1.72046i	0.596661	+	0.802493i	$0.296494\pi$
$839$	28.7717	+	49.8341i	0.993310	+	1.72046i	0.396649	+	0.917971i	$0.370173\pi$
$840$	17.1037	+	10.9237i	0.590134	+	0.376903i
$841$	−14.4877	+	25.0935i	−0.499577	+	0.865293i
$842$	0.0496636	−	0.0453885i	0.00171152	−	0.00156419i
$843$	−13.1698	−	1.88978i	−0.453592	−	0.0650876i
$844$	12.7878	+	1.15263i	0.440175	+	0.0396753i
$845$	54.7959	+	33.8081i	1.88504	+	1.16303i
$846$	33.8579	+	22.7575i	1.16406	+	0.782418i
$847$			0.214576i			0.00737293i
$848$	16.5636	−	19.5305i	0.568797	−	0.670680i
$849$	2.51851	+	6.28586i	0.0864351	+	0.215730i
$850$	3.90179	+	1.49173i	0.133830	+	0.0511659i
$851$	−22.7205	−	13.1177i	−0.778848	−	0.449668i
$852$	1.75665	−	7.42171i	0.0601817	−	0.254264i
$853$	21.6573	+	37.5115i	0.741532	+	1.28437i	0.951798	+	0.306726i	$0.0992336\pi$
$853$	21.6573	+	37.5115i	0.741532	+	1.28437i	−0.210266	+	0.977644i	$0.567433\pi$
$854$	−2.54374	+	8.03092i	−0.0870449	+	0.274813i
$855$	23.5929	−	21.2390i	0.806859	−	0.726360i
$856$	39.3036	−	29.9135i	1.34337	−	1.02242i
$857$	46.1891	−	26.6673i	1.57779	−	0.910938i	0.582624	−	0.812742i	$-0.302026\pi$
$857$	46.1891	−	26.6673i	1.57779	−	0.910938i	0.995167	−	0.0981959i	$-0.0313072\pi$
$858$	47.5573	+	22.9298i	1.62358	+	0.782810i
$859$	−14.2097	−	8.20399i	−0.484830	−	0.279916i	0.237597	−	0.971364i	$-0.423640\pi$
$859$	−14.2097	−	8.20399i	−0.484830	−	0.279916i	−0.722427	+	0.691447i	$0.756973\pi$
$860$	−9.64436	−	1.15416i	−0.328870	−	0.0393566i
$861$	−4.68799	−	3.68456i	−0.159766	−	0.125570i
$862$	9.64523	−	2.12501i	0.328518	−	0.0723782i
$863$			29.1271i			0.991499i	0.868466	+	0.495750i	$0.165107\pi$
$863$			29.1271i			0.991499i	−0.868466	+	0.495750i	$0.834893\pi$
$864$	23.2802	−	17.9452i	0.792009	−	0.610510i
$865$	20.7328	+	12.7917i	0.704935	+	0.434932i
$866$	4.10207	+	18.6189i	0.139394	+	0.632695i
$867$	17.8216	−	22.6751i	0.605254	−	0.770085i
$868$	−8.64153	−	18.6596i	−0.293312	−	0.633347i
$869$	−3.48369	−	2.01131i	−0.118176	−	0.0682290i
$870$	0.462070	+	0.722932i	0.0156656	+	0.0245097i
$871$	−21.5617	−	37.3460i	−0.730592	−	1.26542i
$872$	−27.5943	−	36.2564i	−0.934460	−	1.22780i
$873$	−28.8121	−	30.1835i	−0.975141	−	1.02156i
$874$	16.4652	−	51.9830i	0.556945	−	1.75835i
$875$	−8.74664	−	18.7755i	−0.295691	−	0.634729i
$876$	51.5649	+	12.2049i	1.74222	+	0.412366i
$877$	8.30152	−	14.3786i	0.280322	−	0.485532i	−0.691142	−	0.722719i	$-0.742892\pi$
$877$	8.30152	−	14.3786i	0.280322	−	0.485532i	0.971464	+	0.237187i	$0.0762253\pi$
$878$	−4.48443	−	4.90681i	−0.151342	−	0.165597i
$879$	−0.888054	−	2.21646i	−0.0299533	−	0.0747593i
$880$	9.22758	+	28.3570i	0.311062	+	0.955913i
$881$	22.4187			0.755305			0.377652	−	0.925947i	$-0.376731\pi$
$881$	22.4187			0.755305			0.377652	+	0.925947i	$0.376731\pi$
$882$	−15.1017	−	1.03136i	−0.508501	−	0.0347277i
$883$	1.09932			0.0369951			0.0184976	−	0.999829i	$-0.494112\pi$
$883$	1.09932			0.0369951			0.0184976	+	0.999829i	$0.494112\pi$
$884$	−7.60737	−	0.685693i	−0.255864	−	0.0230623i
$885$	4.80224	−	5.75573i	0.161426	−	0.193477i
$886$	7.83213	+	8.56984i	0.263126	+	0.287909i
$887$	−2.99508	−	1.72921i	−0.100565	−	0.0580612i	0.448874	−	0.893595i	$-0.351825\pi$
$887$	−2.99508	−	1.72921i	−0.100565	−	0.0580612i	−0.549439	+	0.835534i	$0.685159\pi$
$888$	−0.245436	+	15.7724i	−0.00823631	+	0.529286i
$889$	−1.09676	−	1.89965i	−0.0367843	−	0.0637123i
$890$	29.5120	−	25.4301i	0.989246	−	0.852418i
$891$	−16.1945	+	25.2610i	−0.542536	+	0.846277i
$892$	−26.9287	+	38.2440i	−0.901639	+	1.28050i
$893$	−22.7514	−	39.4065i	−0.761346	−	1.31869i
$894$	14.6624	−	9.98661i	0.490384	−	0.334002i
$895$	−0.385720	−	0.715575i	−0.0128932	−	0.0239191i
$896$	−9.50697	−	18.6799i	−0.317606	−	0.624052i
$897$	−12.9589	+	90.3103i	−0.432687	+	3.01537i
$898$	48.5979	−	10.7070i	1.62173	−	0.357297i
$899$		−	0.869359i		−	0.0289947i
$900$	−29.8779	+	2.70348i	−0.995931	+	0.0901159i
$901$		−	3.78204i		−	0.125998i
$902$	−1.88510	−	8.55631i	−0.0627671	−	0.284894i
$903$	−6.46941	+	2.59206i	−0.215289	+	0.0862582i
$904$	−11.7322	+	1.49758i	−0.390207	+	0.0498089i
$905$	3.25705	+	6.04238i	0.108268	+	0.200855i
$906$	−33.1094	+	2.46565i	−1.09999	+	0.0819157i
$907$	−16.7205	−	28.9607i	−0.555194	−	0.961625i	−0.997888	−	0.0649519i	$-0.979311\pi$
$907$	−16.7205	−	28.9607i	−0.555194	−	0.961625i	0.442694	−	0.896673i	$-0.354023\pi$
$908$	37.9801	+	26.7429i	1.26041	+	0.887493i
$909$	−29.8213	−	31.2407i	−0.989109	−	1.03619i
$910$	24.7233	+	28.6919i	0.819571	+	0.951126i
$911$	4.97939	+	8.62456i	0.164975	+	0.285745i	0.936646	−	0.350277i	$-0.113912\pi$
$911$	4.97939	+	8.62456i	0.164975	+	0.285745i	−0.771672	+	0.636021i	$0.780579\pi$
$912$	−32.1237	+	6.55506i	−1.06372	+	0.217060i
$913$	−12.2480	−	7.07139i	−0.405350	−	0.234029i
$914$	36.9286	−	33.7497i	1.22149	−	1.11634i
$915$	−4.29188	−	11.6899i	−0.141885	−	0.386457i
$916$	−14.9333	−	1.34602i	−0.493410	−	0.0444736i
$917$	−13.1707			−0.434936
$918$	0.907955	−	4.24509i	0.0299670	−	0.140109i
$919$	−26.5683			−0.876408			−0.438204	−	0.898875i	$-0.644385\pi$
$919$	−26.5683			−0.876408			−0.438204	+	0.898875i	$0.644385\pi$
$920$	−41.9001	+	29.9981i	−1.38140	+	0.989007i
$921$	29.3228	−	37.3084i	0.966221	−	1.22936i
$922$	16.5146	−	15.0930i	0.543879	−	0.497061i
$923$	7.11671	−	12.3265i	0.234249	−	0.405732i
$924$	15.5678	+	14.6787i	0.512143	+	0.482894i
$925$	8.85019	−	13.4488i	0.290993	−	0.442193i
$926$	8.60044	+	2.72413i	0.282628	+	0.0895204i
$927$	−6.92445	+	23.6313i	−0.227429	+	0.776153i
$928$	−0.0328397	−	0.885515i	−0.00107801	−	0.0290684i
$929$	−29.4711	−	51.0454i	−0.966915	−	1.67475i	−0.704378	−	0.709825i	$-0.748774\pi$
$929$	−29.4711	−	51.0454i	−0.966915	−	1.67475i	−0.262537	−	0.964922i	$-0.584559\pi$
$930$	26.9839	+	13.9960i	0.884837	+	0.458947i
$931$	14.6216	+	8.44179i	0.479204	+	0.276668i
$932$	16.4510	+	35.5226i	0.538871	+	1.16358i
$933$	−2.92706	−	7.30554i	−0.0958276	−	0.239173i
$934$	−34.4788	+	7.59628i	−1.12818	+	0.248558i
$935$	3.74813	+	2.31252i	0.122577	+	0.0756276i
$936$	51.2323	−	19.6074i	1.67458	−	0.640888i
$937$		−	35.6730i		−	1.16538i	−0.812693	−	0.582692i	$-0.801999\pi$
$937$		−	35.6730i		−	1.16538i	0.812693	−	0.582692i	$-0.198001\pi$
$938$	−3.76022	−	17.0673i	−0.122775	−	0.557266i
$939$	4.48084	−	31.2268i	0.146227	−	1.01905i
$940$	−5.10969	+	42.6974i	−0.166660	+	1.39263i
$941$	−18.8543	−	10.8855i	−0.614632	−	0.354858i	0.160144	−	0.987094i	$-0.448804\pi$
$941$	−18.8543	−	10.8855i	−0.614632	−	0.354858i	−0.774776	+	0.632236i	$0.782137\pi$
$942$	4.39269	+	6.44936i	0.143121	+	0.210132i
$943$	13.1119	−	7.57018i	0.426983	−	0.246519i
$944$	−7.28875	+	2.60962i	−0.237228	+	0.0849358i
$945$	−17.8814	+	11.9835i	−0.581680	+	0.389823i
$946$	−9.76273	−	3.09228i	−0.317414	−	0.100539i
$947$	−16.9667	−	29.3872i	−0.551344	−	0.954955i	−0.998178	−	0.0603385i	$-0.980782\pi$
$947$	−16.9667	−	29.3872i	−0.551344	−	0.954955i	0.446834	−	0.894617i	$-0.352551\pi$
$948$	−4.00360	+	1.19990i	−0.130031	+	0.0389709i
$949$	85.6426	+	49.4458i	2.78008	+	1.60508i
$950$	31.2554	+	11.9495i	1.01406	+	0.387694i
$951$	13.5130	+	1.93903i	0.438189	+	0.0628773i
$952$	−2.85520	−	1.19586i	−0.0925376	−	0.0387581i
$953$		−	29.8028i		−	0.965408i	−0.875783	−	0.482704i	$-0.839655\pi$
$953$		−	29.8028i		−	0.965408i	0.875783	−	0.482704i	$-0.160345\pi$
$954$	11.9466	+	24.3936i	0.386787	+	0.789771i
$955$	34.6486	+	21.3775i	1.12120	+	0.691760i
$956$	0.898807	−	9.97176i	0.0290695	−	0.322510i
$957$	0.336435	+	0.839696i	0.0108754	+	0.0271435i
$958$	2.64411	+	2.89316i	0.0854273	+	0.0934737i
$959$	3.60168	−	6.23829i	0.116304	−	0.201445i
$960$	28.0141	+	13.2368i	0.904150	+	0.427216i
$961$	0.0996707	+	0.172635i	0.00321518	+	0.00556886i
$962$	−8.88922	+	28.0645i	−0.286600	+	0.904835i
$963$	12.3794	+	50.9046i	0.398921	+	1.64038i
$964$	18.7409	+	13.1960i	0.603602	+	0.425013i
$965$	−50.6118	−	1.47896i	−1.62925	−	0.0476094i
$966$	−16.0583	+	33.3056i	−0.516668	+	1.07159i
$967$	−8.50028	−	4.90764i	−0.273351	−	0.157819i	0.357059	−	0.934082i	$-0.383780\pi$
$967$	−8.50028	−	4.90764i	−0.273351	−	0.157819i	−0.630409	+	0.776263i	$0.717113\pi$
$968$	0.0414804	+	0.324961i	0.00133323	+	0.0104446i
$969$	−2.99208	+	3.80692i	−0.0961195	+	0.122296i
$970$	14.5006	−	41.5256i	0.465586	−	1.33331i
$971$		−	16.8674i		−	0.541300i	−0.962678	−	0.270650i	$-0.912761\pi$
$971$		−	16.8674i		−	0.541300i	0.962678	−	0.270650i	$-0.0872386\pi$
$972$	7.55313	+	30.2481i	0.242267	+	0.970210i
$973$	5.81441			0.186402
$974$	−6.34558	−	28.8020i	−0.203326	−	0.922875i
$975$	−54.8607	−	11.1749i	−1.75695	−	0.357884i
$976$	−2.29983	+	12.6540i	−0.0736158	+	0.405045i
$977$	−24.3616	−	14.0652i	−0.779396	−	0.449984i	0.0568205	−	0.998384i	$-0.481904\pi$
$977$	−24.3616	−	14.0652i	−0.779396	−	0.449984i	−0.836216	+	0.548400i	$0.815237\pi$
$978$	15.3595	−	31.8562i	0.491143	−	1.01865i
$979$	35.5703	−	20.5365i	1.13683	−	0.656349i
$980$	−6.27941	−	14.6681i	−0.200588	−	0.468555i
$981$	46.9580	−	11.4196i	1.49925	−	0.364601i
$982$	−50.7006	−	16.0591i	−1.61792	−	0.512465i
$983$	−15.1286	+	8.73451i	−0.482528	+	0.278588i	−0.721469	−	0.692446i	$-0.756533\pi$
$983$	−15.1286	+	8.73451i	−0.482528	+	0.278588i	0.238941	+	0.971034i	$0.423200\pi$
$984$	−7.81191	−	4.67376i	−0.249035	−	0.148994i
$985$	−24.0283	+	12.9521i	−0.765604	+	0.412687i
$986$	−0.0882871	−	0.0966028i	−0.00281163	−	0.00307646i
$987$	11.4755	+	28.6413i	0.365269	+	0.911662i
$988$	−60.9390	−	5.49276i	−1.93873	−	0.174748i
$989$		−	17.6966i		−	0.562719i
$990$	−31.4796	−	3.07589i	−1.00049	−	0.0977583i
$991$	−55.1709			−1.75256			−0.876280	−	0.481801i	$-0.839983\pi$
$991$	−55.1709			−1.75256			−0.876280	+	0.481801i	$0.839983\pi$
$992$	−16.6941	−	26.5881i	−0.530039	−	0.844173i
$993$	−1.07953	+	7.52322i	−0.0342580	+	0.238742i
$994$	4.25798	−	3.89145i	0.135055	−	0.123429i
$995$	29.3920	−	15.8433i	0.931790	−	0.502267i
$996$	−14.0759	+	4.21861i	−0.446012	+	0.133672i
$997$	−12.3131	−	21.3268i	−0.389959	−	0.675428i	0.602485	−	0.798130i	$-0.294177\pi$
$997$	−12.3131	−	21.3268i	−0.389959	−	0.675428i	−0.992444	+	0.122702i	$0.960844\pi$
$998$	41.2099	+	13.0529i	1.30448	+	0.413184i
$999$	−15.2250	−	6.93763i	−0.481697	−	0.219497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bk.a.229.5	✓	136
5.4	even	2	inner	360.2.bk.a.229.64	yes	136
8.5	even	2	inner	360.2.bk.a.229.18	yes	136
9.7	even	3	inner	360.2.bk.a.349.51	yes	136
40.29	even	2	inner	360.2.bk.a.229.51	yes	136
45.34	even	6	inner	360.2.bk.a.349.18	yes	136
72.61	even	6	inner	360.2.bk.a.349.64	yes	136
360.349	even	6	inner	360.2.bk.a.349.5	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bk.a.229.5	✓	136	1.1	even	1	trivial
360.2.bk.a.229.18	yes	136	8.5	even	2	inner
360.2.bk.a.229.51	yes	136	40.29	even	2	inner
360.2.bk.a.229.64	yes	136	5.4	even	2	inner
360.2.bk.a.349.5	yes	136	360.349	even	6	inner
360.2.bk.a.349.18	yes	136	45.34	even	6	inner
360.2.bk.a.349.51	yes	136	9.7	even	3	inner
360.2.bk.a.349.64	yes	136	72.61	even	6	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38109 + 0.304279i) q^{2} +(1.07030 - 1.36178i) q^{3} +(1.81483 - 0.840474i) q^{4} +(-1.96832 + 1.06099i) q^{5} +(-1.06383 + 2.20642i) q^{6} +(-1.60442 + 0.926310i) q^{7} +(-2.25071 + 1.71299i) q^{8} +(-0.708903 - 2.91504i) q^{9} +O(q^{10})\)	\(q+(-1.38109 + 0.304279i) q^{2} +(1.07030 - 1.36178i) q^{3} +(1.81483 - 0.840474i) q^{4} +(-1.96832 + 1.06099i) q^{5} +(-1.06383 + 2.20642i) q^{6} +(-1.60442 + 0.926310i) q^{7} +(-2.25071 + 1.71299i) q^{8} +(-0.708903 - 2.91504i) q^{9} +(2.39560 - 2.06425i) q^{10} +(2.88736 - 1.66702i) q^{11} +(0.797874 - 3.37096i) q^{12} +(3.23243 - 5.59873i) q^{13} +(1.93399 - 1.76751i) q^{14} +(-0.661859 + 3.81601i) q^{15} +(2.58721 - 3.05063i) q^{16} -0.590749i q^{17} +(1.86604 + 3.81023i) q^{18} -4.73221i q^{19} +(-2.68043 + 3.57985i) q^{20} +(-0.455778 + 3.17630i) q^{21} +(-3.48047 + 3.18087i) q^{22} +(-7.05625 - 4.07393i) q^{23} +(-0.0762247 + 4.89839i) q^{24} +(2.74859 - 4.17675i) q^{25} +(-2.76071 + 8.71592i) q^{26} +(-4.72839 - 2.15460i) q^{27} +(-2.13320 + 3.02956i) q^{28} +(-0.135659 + 0.0783230i) q^{29} +(-0.247044 - 5.47165i) q^{30} +(-2.77492 + 4.80630i) q^{31} +(-2.64493 + 5.00044i) q^{32} +(0.820235 - 5.71618i) q^{33} +(0.179752 + 0.815878i) q^{34} +(2.17520 - 3.52555i) q^{35} +(-3.73655 - 4.69448i) q^{36} +3.21991 q^{37} +(1.43991 + 6.53561i) q^{38} +(-4.16458 - 10.3942i) q^{39} +(2.61265 - 5.75969i) q^{40} +(-0.929101 + 1.60925i) q^{41} +(-0.337008 - 4.52544i) q^{42} +(1.08597 + 1.88095i) q^{43} +(3.83898 - 5.45211i) q^{44} +(4.48819 + 4.98560i) q^{45} +(10.9849 + 3.47940i) q^{46} +(8.32731 - 4.80777i) q^{47} +(-1.38520 - 6.78831i) q^{48} +(-1.78390 + 3.08981i) q^{49} +(-2.52515 + 6.60482i) q^{50} +(-0.804471 - 0.632280i) q^{51} +(1.16072 - 12.8775i) q^{52} +6.40212 q^{53} +(7.18594 + 1.53696i) q^{54} +(-3.91456 + 6.34471i) q^{55} +(2.02431 - 4.83319i) q^{56} +(-6.44424 - 5.06489i) q^{57} +(0.163526 - 0.149449i) q^{58} +(-1.67616 - 0.967729i) q^{59} +(2.00610 + 7.48168i) q^{60} +(-2.78455 + 1.60766i) q^{61} +(2.36996 - 7.48229i) q^{62} +(3.83760 + 4.02027i) q^{63} +(2.13136 - 7.71086i) q^{64} +(-0.422244 + 14.4497i) q^{65} +(0.606492 + 8.14415i) q^{66} +(3.33522 - 5.77678i) q^{67} +(-0.496509 - 1.07211i) q^{68} +(-13.1001 + 5.24874i) q^{69} +(-1.93140 + 5.53098i) q^{70} +2.20166 q^{71} +(6.58895 + 5.34656i) q^{72} +15.2968i q^{73} +(-4.44699 + 0.979750i) q^{74} +(-2.74601 - 8.21337i) q^{75} +(-3.97730 - 8.58815i) q^{76} +(-3.08835 + 5.34919i) q^{77} +(8.91440 + 13.0882i) q^{78} +(-0.603265 - 1.04489i) q^{79} +(-1.85576 + 8.74964i) q^{80} +(-7.99491 + 4.13296i) q^{81} +(0.793513 - 2.50523i) q^{82} +(-2.12097 - 3.67362i) q^{83} +(1.84243 + 6.14751i) q^{84} +(0.626781 + 1.16278i) q^{85} +(-2.07215 - 2.26733i) q^{86} +(-0.0385378 + 0.268568i) q^{87} +(-3.64303 + 8.69798i) q^{88} +12.3193 q^{89} +(-7.71561 - 5.51990i) q^{90} +11.9769i q^{91} +(-16.2299 - 1.46289i) q^{92} +(3.57513 + 8.92303i) q^{93} +(-10.0379 + 9.17380i) q^{94} +(5.02084 + 9.31451i) q^{95} +(3.97863 + 8.95380i) q^{96} +(12.0457 - 6.95457i) q^{97} +(1.52357 - 4.81011i) q^{98} +(-6.90629 - 7.23502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 136 * q - 2 * q^4 - 8 * q^9	\( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

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