LMFDB - Embedded newform 1089.2.e.k.364.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 3x^{14} + 5x^{12} + 15x^{10} + 45x^{8} + 60x^{6} + 80x^{4} + 192x^{2} + 256 $ x^16 + 3x^14 + 5x^12 + 15x^10 + 45x^8 + 60x^6 + 80x^4 + 192*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.8
Root			$0.263711 - 1.38941i$ of defining polynomial
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.k.727.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33512 + 2.31249i) q^{2} +(-1.60832 + 0.642882i) q^{3} +(-2.56508 + 4.44285i) q^{4} +(0.247410 - 0.428526i) q^{5} +(-3.63396 - 2.86091i) q^{6} +(-2.31660 - 4.01248i) q^{7} -8.35829 q^{8} +(2.17341 - 2.06792i) q^{9} +O(q^{10})$	\(q+(1.33512 + 2.31249i) q^{2} +(-1.60832 + 0.642882i) q^{3} +(-2.56508 + 4.44285i) q^{4} +(0.247410 - 0.428526i) q^{5} +(-3.63396 - 2.86091i) q^{6} +(-2.31660 - 4.01248i) q^{7} -8.35829 q^{8} +(2.17341 - 2.06792i) q^{9} +1.32129 q^{10} +(1.26925 - 8.79459i) q^{12} +(0.379171 - 0.656743i) q^{13} +(6.18588 - 10.7143i) q^{14} +(-0.122423 + 0.848264i) q^{15} +(-6.02914 - 10.4428i) q^{16} -1.55221 q^{17} +(7.68381 + 2.26507i) q^{18} +2.40926 q^{19} +(1.26925 + 2.19841i) q^{20} +(6.30539 + 4.96406i) q^{21} +(1.39168 - 2.41046i) q^{23} +(13.4428 - 5.37339i) q^{24} +(2.37758 + 4.11808i) q^{25} +2.02495 q^{26} +(-2.16611 + 4.72313i) q^{27} +23.7691 q^{28} +(-2.31387 - 4.00774i) q^{29} +(-2.12505 + 0.849430i) q^{30} +(2.36091 - 4.08922i) q^{31} +(7.74094 - 13.4077i) q^{32} +(-2.07238 - 3.58947i) q^{34} -2.29260 q^{35} +(3.61251 + 14.9605i) q^{36} -6.53013 q^{37} +(3.21665 + 5.57139i) q^{38} +(-0.187621 + 1.30002i) q^{39} +(-2.06792 + 3.58175i) q^{40} +(4.17914 - 7.23849i) q^{41} +(-3.06090 + 21.2088i) q^{42} +(-3.75062 - 6.49626i) q^{43} +(-0.348437 - 1.44299i) q^{45} +7.43221 q^{46} +(-3.53432 - 6.12162i) q^{47} +(16.4103 + 12.9193i) q^{48} +(-7.23331 + 12.5285i) q^{49} +(-6.34869 + 10.9963i) q^{50} +(2.49645 - 0.997885i) q^{51} +(1.94521 + 3.36920i) q^{52} -3.20205 q^{53} +(-13.8142 + 1.29682i) q^{54} +(19.3628 + 33.5374i) q^{56} +(-3.87487 + 1.54887i) q^{57} +(6.17859 - 10.7016i) q^{58} +(4.57026 - 7.91593i) q^{59} +(-3.45469 - 2.71978i) q^{60} +(1.03589 + 1.79421i) q^{61} +12.6084 q^{62} +(-13.3324 - 3.93018i) q^{63} +17.2238 q^{64} +(-0.187621 - 0.324969i) q^{65} +(1.67341 - 2.89843i) q^{67} +(3.98154 - 6.89623i) q^{68} +(-0.688629 + 4.77147i) q^{69} +(-3.06090 - 5.30163i) q^{70} +6.89479 q^{71} +(-18.1660 + 17.2843i) q^{72} +1.54674 q^{73} +(-8.71850 - 15.1009i) q^{74} +(-6.47135 - 5.09471i) q^{75} +(-6.17995 + 10.7040i) q^{76} +(-3.25678 + 1.30180i) q^{78} +(0.320843 + 0.555716i) q^{79} -5.96667 q^{80} +(0.447393 - 8.98887i) q^{81} +22.3186 q^{82} +(-4.82476 - 8.35673i) q^{83} +(-38.2284 + 15.2807i) q^{84} +(-0.384031 + 0.665161i) q^{85} +(10.0150 - 17.3466i) q^{86} +(6.29796 + 4.95820i) q^{87} -13.2092 q^{89} +(2.87169 - 2.73232i) q^{90} -3.51356 q^{91} +(7.13953 + 12.3660i) q^{92} +(-1.16823 + 8.09458i) q^{93} +(9.43747 - 16.3462i) q^{94} +(0.596074 - 1.03243i) q^{95} +(-3.83037 + 26.5404i) q^{96} +(8.82123 + 15.2788i) q^{97} -38.6293 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9	$ 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9} - 6 q^{12} + 4 q^{14} - 52 q^{15} - 24 q^{16} - 6 q^{20} + 46 q^{23} - 12 q^{25} - 60 q^{26} - 32 q^{27} + 14 q^{31} + 38 q^{34} + 54 q^{36} - 12 q^{37} + 4 q^{38} - 4 q^{42} - 28 q^{45} + 16 q^{47} + 20 q^{48} - 42 q^{49} - 96 q^{53} + 46 q^{56} + 50 q^{58} + 48 q^{59} + 12 q^{60} - 12 q^{64} - 22 q^{67} - 10 q^{69} - 4 q^{70} + 68 q^{71} - 10 q^{75} - 72 q^{78} - 148 q^{80} - 14 q^{81} + 112 q^{82} + 14 q^{86} - 16 q^{89} - 96 q^{91} + 84 q^{92} + 30 q^{93} - 4 q^{97}+O(q^{100}) $ 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9 - 6 * q^12 + 4 * q^14 - 52 * q^15 - 24 * q^16 - 6 * q^20 + 46 * q^23 - 12 * q^25 - 60 * q^26 - 32 * q^27 + 14 * q^31 + 38 * q^34 + 54 * q^36 - 12 * q^37 + 4 * q^38 - 4 * q^42 - 28 * q^45 + 16 * q^47 + 20 * q^48 - 42 * q^49 - 96 * q^53 + 46 * q^56 + 50 * q^58 + 48 * q^59 + 12 * q^60 - 12 * q^64 - 22 * q^67 - 10 * q^69 - 4 * q^70 + 68 * q^71 - 10 * q^75 - 72 * q^78 - 148 * q^80 - 14 * q^81 + 112 * q^82 + 14 * q^86 - 16 * q^89 - 96 * q^91 + 84 * q^92 + 30 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.33512	+	2.31249i	0.944071	+	1.63518i	0.757600	+	0.652719i	$0.226372\pi$
$2$	1.33512	+	2.31249i	0.944071	+	1.63518i	0.186472	+	0.982460i	$0.440295\pi$
$3$	−1.60832	+	0.642882i	−0.928566	+	0.371168i
$3$	−1.60832	+	0.642882i	−0.928566	+	0.371168i
$4$	−2.56508	+	4.44285i	−1.28254	+	2.22143i
$5$	0.247410	−	0.428526i	0.110645	−	0.191643i	−0.805385	−	0.592751i	$-0.798042\pi$
$5$	0.247410	−	0.428526i	0.110645	−	0.191643i	0.916031	+	0.401109i	$0.131375\pi$
$6$	−3.63396	−	2.86091i	−1.48356	−	1.16796i
$7$	−2.31660	−	4.01248i	−0.875594	−	1.51657i	−0.856129	−	0.516763i	$-0.827137\pi$
$7$	−2.31660	−	4.01248i	−0.875594	−	1.51657i	−0.0194655	−	0.999811i	$-0.506196\pi$
$8$	−8.35829			−2.95510
$9$	2.17341	−	2.06792i	0.724469	−	0.689308i
$10$	1.32129			0.417827
$11$		0			0
$11$		0			0
$12$	1.26925	−	8.79459i	0.366402	−	2.53878i
$13$	0.379171	−	0.656743i	0.105163	−	0.182148i	−0.808642	−	0.588301i	$-0.799797\pi$
$13$	0.379171	−	0.656743i	0.105163	−	0.182148i	0.913805	+	0.406154i	$0.133130\pi$
$14$	6.18588	−	10.7143i	1.65325	−	2.86351i
$15$	−0.122423	+	0.848264i	−0.0316095	+	0.219021i
$16$	−6.02914	−	10.4428i	−1.50728	−	2.61069i
$17$	−1.55221			−0.376465			−0.188233	−	0.982124i	$-0.560276\pi$
$17$	−1.55221			−0.376465			−0.188233	+	0.982124i	$0.560276\pi$
$18$	7.68381	+	2.26507i	1.81109	+	0.533881i
$19$	2.40926			0.552722			0.276361	−	0.961054i	$-0.410871\pi$
$19$	2.40926			0.552722			0.276361	+	0.961054i	$0.410871\pi$
$20$	1.26925	+	2.19841i	0.283814	+	0.491580i
$21$	6.30539	+	4.96406i	1.37595	+	1.08325i
$22$		0			0
$23$	1.39168	−	2.41046i	0.290185	−	0.502615i	−0.683669	−	0.729793i	$-0.739617\pi$
$23$	1.39168	−	2.41046i	0.290185	−	0.502615i	0.973853	+	0.227178i	$0.0729499\pi$
$24$	13.4428	−	5.37339i	2.74401	−	1.09684i
$25$	2.37758	+	4.11808i	0.475515	+	0.823617i
$26$	2.02495			0.397126
$27$	−2.16611	+	4.72313i	−0.416868	+	0.908967i
$28$	23.7691			4.49194
$29$	−2.31387	−	4.00774i	−0.429675	−	0.744219i	0.567169	−	0.823601i	$-0.308039\pi$
$29$	−2.31387	−	4.00774i	−0.429675	−	0.744219i	−0.996844	+	0.0793821i	$0.974705\pi$
$30$	−2.12505	+	0.849430i	−0.387980	+	0.155084i
$31$	2.36091	−	4.08922i	0.424033	−	0.734446i	−0.572297	−	0.820046i	$-0.693948\pi$
$31$	2.36091	−	4.08922i	0.424033	−	0.734446i	0.996330	+	0.0856005i	$0.0272809\pi$
$32$	7.74094	−	13.4077i	1.36842	−	2.37017i
$33$		0			0
$34$	−2.07238	−	3.58947i	−0.355410	−	0.615588i
$35$	−2.29260			−0.387521
$36$	3.61251	+	14.9605i	0.602085	+	2.49342i
$37$	−6.53013			−1.07355			−0.536774	−	0.843726i	$-0.680357\pi$
$37$	−6.53013			−1.07355			−0.536774	+	0.843726i	$0.680357\pi$
$38$	3.21665	+	5.57139i	0.521809	+	0.903800i
$39$	−0.187621	+	1.30002i	−0.0300434	+	0.208169i
$40$	−2.06792	+	3.58175i	−0.326967	+	0.566324i
$41$	4.17914	−	7.23849i	0.652673	−	1.13046i	−0.329799	−	0.944051i	$-0.606981\pi$
$41$	4.17914	−	7.23849i	0.652673	−	1.13046i	0.982472	−	0.186411i	$-0.0596856\pi$
$42$	−3.06090	+	21.2088i	−0.472307	+	3.27259i
$43$	−3.75062	−	6.49626i	−0.571964	−	0.990670i	−0.996364	−	0.0851958i	$-0.972848\pi$
$43$	−3.75062	−	6.49626i	−0.571964	−	0.990670i	0.424400	−	0.905475i	$-0.360485\pi$
$44$		0			0
$45$	−0.348437	−	1.44299i	−0.0519420	−	0.215108i
$46$	7.43221			1.09582
$47$	−3.53432	−	6.12162i	−0.515534	−	0.892930i	−0.999837	−	0.0180305i	$-0.994260\pi$
$47$	−3.53432	−	6.12162i	−0.515534	−	0.892930i	0.484304	−	0.874900i	$-0.339073\pi$
$48$	16.4103	+	12.9193i	2.36862	+	1.86475i
$49$	−7.23331	+	12.5285i	−1.03333	+	1.78978i
$50$	−6.34869	+	10.9963i	−0.897841	+	1.55511i
$51$	2.49645	−	0.997885i	0.349573	−	0.139732i
$52$	1.94521	+	3.36920i	0.269752	+	0.467224i
$53$	−3.20205			−0.439836			−0.219918	−	0.975518i	$-0.570579\pi$
$53$	−3.20205			−0.439836			−0.219918	+	0.975518i	$0.570579\pi$
$54$	−13.8142	+	1.29682i	−1.87988	+	0.176475i
$55$		0			0
$56$	19.3628	+	33.5374i	2.58747	+	4.48163i
$57$	−3.87487	+	1.54887i	−0.513239	+	0.205153i
$58$	6.17859	−	10.7016i	0.811288	−	1.40519i
$59$	4.57026	−	7.91593i	0.594998	−	1.03057i	−0.398550	−	0.917147i	$-0.630486\pi$
$59$	4.57026	−	7.91593i	0.594998	−	1.03057i	0.993547	−	0.113419i	$-0.0361804\pi$
$60$	−3.45469	−	2.71978i	−0.445998	−	0.351122i
$61$	1.03589	+	1.79421i	0.132632	+	0.229725i	0.924690	−	0.380720i	$-0.124324\pi$
$61$	1.03589	+	1.79421i	0.132632	+	0.229725i	−0.792059	+	0.610445i	$0.790991\pi$
$62$	12.6084			1.60127
$63$	−13.3324	−	3.93018i	−1.67973	−	0.495157i
$64$	17.2238			2.15297
$65$	−0.187621	−	0.324969i	−0.0232715	−	0.0403075i
$66$		0			0
$67$	1.67341	−	2.89843i	0.204439	−	0.354099i	−0.745515	−	0.666489i	$-0.767796\pi$
$67$	1.67341	−	2.89843i	0.204439	−	0.354099i	0.949954	+	0.312390i	$0.101130\pi$
$68$	3.98154	−	6.89623i	0.482832	−	0.836290i
$69$	−0.688629	+	4.77147i	−0.0829012	+	0.574418i
$70$	−3.06090	−	5.30163i	−0.365847	−	0.633666i
$71$	6.89479			0.818260			0.409130	−	0.912476i	$-0.365832\pi$
$71$	6.89479			0.818260			0.409130	+	0.912476i	$0.365832\pi$
$72$	−18.1660	+	17.2843i	−2.14088	+	2.03697i
$73$	1.54674			0.181032			0.0905162	−	0.995895i	$-0.471148\pi$
$73$	1.54674			0.181032			0.0905162	+	0.995895i	$0.471148\pi$
$74$	−8.71850	−	15.1009i	−1.01351	−	1.75544i
$75$	−6.47135	−	5.09471i	−0.747247	−	0.588286i
$76$	−6.17995	+	10.7040i	−0.708889	+	1.22783i
$77$		0			0
$78$	−3.25678	+	1.30180i	−0.368757	+	0.147400i
$79$	0.320843	+	0.555716i	0.0360976	+	0.0625229i	0.883510	−	0.468413i	$-0.155174\pi$
$79$	0.320843	+	0.555716i	0.0360976	+	0.0625229i	−0.847412	+	0.530936i	$0.821841\pi$
$80$	−5.96667			−0.667094
$81$	0.447393	−	8.98887i	0.0497103	−	0.998764i
$82$	22.3186			2.46468
$83$	−4.82476	−	8.35673i	−0.529586	−	0.917270i	−0.999404	−	0.0345068i	$-0.989014\pi$
$83$	−4.82476	−	8.35673i	−0.529586	−	0.917270i	0.469818	−	0.882763i	$-0.344319\pi$
$84$	−38.2284	+	15.2807i	−4.17107	+	1.66727i
$85$	−0.384031	+	0.665161i	−0.0416540	+	0.0721469i
$86$	10.0150	−	17.3466i	1.07995	−	1.87053i
$87$	6.29796	+	4.95820i	0.675212	+	0.531575i
$88$		0			0
$89$	−13.2092			−1.40017			−0.700084	−	0.714060i	$-0.746854\pi$
$89$	−13.2092			−1.40017			−0.700084	+	0.714060i	$0.746854\pi$
$90$	2.87169	−	2.73232i	0.302703	−	0.288011i
$91$	−3.51356			−0.368321
$92$	7.13953	+	12.3660i	0.744348	+	1.28925i
$93$	−1.16823	+	8.09458i	−0.121139	+	0.839369i
$94$	9.43747	−	16.3462i	0.973401	−	1.68598i
$95$	0.596074	−	1.03243i	0.0611559	−	0.105925i
$96$	−3.83037	+	26.5404i	−0.390936	+	2.70877i
$97$	8.82123	+	15.2788i	0.895660	+	1.55133i	0.832985	+	0.553295i	$0.186630\pi$
$97$	8.82123	+	15.2788i	0.895660	+	1.55133i	0.0626748	+	0.998034i	$0.480037\pi$
$98$	−38.6293			−3.90215
$99$		0			0
$100$	−24.3947			−2.43947
$101$	−4.17914	−	7.23849i	−0.415840	−	0.720257i	0.579676	−	0.814847i	$-0.303179\pi$
$101$	−4.17914	−	7.23849i	−0.415840	−	0.720257i	−0.995516	+	0.0945905i	$0.969846\pi$
$102$	5.64066	+	4.44073i	0.558508	+	0.439697i
$103$	0.160931	−	0.278740i	0.0158570	−	0.0274650i	−0.857988	−	0.513670i	$-0.828286\pi$
$103$	0.160931	−	0.278740i	0.0158570	−	0.0274650i	0.873845	+	0.486205i	$0.161619\pi$
$104$	−3.16922	+	5.48925i	−0.310768	+	0.538265i
$105$	3.68725	−	1.47387i	0.359838	−	0.143835i
$106$	−4.27512	−	7.40473i	−0.415237	−	0.719211i
$107$	−2.78689			−0.269419			−0.134710	−	0.990885i	$-0.543010\pi$
$107$	−2.78689			−0.269419			−0.134710	+	0.990885i	$0.543010\pi$
$108$	−15.4279	−	21.7389i	−1.48455	−	2.09183i
$109$	10.3945			0.995616			0.497808	−	0.867287i	$-0.334138\pi$
$109$	10.3945			0.995616			0.497808	+	0.867287i	$0.334138\pi$
$110$		0			0
$111$	10.5026	−	4.19810i	0.996859	−	0.398466i
$112$	−27.9343	+	48.3836i	−2.63954	+	4.57182i
$113$	−9.16449	+	15.8734i	−0.862122	+	1.49324i	0.00775392	+	0.999970i	$0.497532\pi$
$113$	−9.16449	+	15.8734i	−0.862122	+	1.49324i	−0.869876	+	0.493270i	$0.835802\pi$
$114$	−8.75515	−	6.89268i	−0.819995	−	0.645559i
$115$	−0.688629	−	1.19274i	−0.0642150	−	0.111224i
$116$	23.7411			2.20431
$117$	−0.534002	−	2.21147i	−0.0493685	−	0.204450i
$118$	24.4074			2.24688
$119$	3.59585	+	6.22819i	0.329631	+	0.570937i
$120$	1.02325	−	7.09004i	0.0934094	−	0.647229i
$121$		0			0
$122$	−2.76606	+	4.79096i	−0.250427	+	0.433753i
$123$	−2.06792	+	14.3285i	−0.186458	+	1.29196i
$124$	12.1119	+	20.9784i	1.08768	+	1.88392i
$125$	4.82704			0.431744
$126$	−8.71183	−	36.0784i	−0.776111	−	3.21412i
$127$	−12.5905			−1.11722			−0.558611	−	0.829430i	$-0.688666\pi$
$127$	−12.5905			−1.11722			−0.558611	+	0.829430i	$0.688666\pi$
$128$	7.51387	+	13.0144i	0.664139	+	1.15032i
$129$	10.2085	+	8.03688i	0.898811	+	0.707608i
$130$	0.500993	−	0.867745i	0.0439400	−	0.0761063i
$131$	4.20801	−	7.28848i	0.367655	−	0.636797i	−0.621543	−	0.783380i	$-0.713494\pi$
$131$	4.20801	−	7.28848i	0.367655	−	0.636797i	0.989198	+	0.146582i	$0.0468273\pi$
$132$		0			0
$133$	−5.58130	−	9.66709i	−0.483960	−	0.838243i
$134$	8.93679			0.772021
$135$	1.48807	+	2.09678i	0.128073	+	0.180462i
$136$	12.9738			1.11249
$137$	0.409333	+	0.708986i	0.0349717	+	0.0605728i	0.882982	−	0.469408i	$-0.155533\pi$
$137$	0.409333	+	0.708986i	0.0349717	+	0.0605728i	−0.848010	+	0.529981i	$0.822199\pi$
$138$	−11.9534	+	4.77803i	−1.01754	+	0.406733i
$139$	5.00965	−	8.67696i	0.424913	−	0.735970i	−0.571500	−	0.820602i	$-0.693638\pi$
$139$	5.00965	−	8.67696i	0.424913	−	0.735970i	0.996412	+	0.0846320i	$0.0269715\pi$
$140$	5.88072	−	10.1857i	0.497011	−	0.860849i
$141$	9.61981	+	7.57340i	0.810134	+	0.637795i
$142$	9.20536	+	15.9441i	0.772496	+	1.33800i
$143$		0			0
$144$	−34.6986	−	10.2286i	−2.89155	−	0.852384i
$145$	−2.28990			−0.190166
$146$	2.06508	+	3.57683i	0.170908	+	0.296021i
$147$	3.57918	−	24.8000i	0.295206	−	2.04547i
$148$	16.7503	−	29.0124i	1.37687	−	2.38481i
$149$	8.85778	−	15.3421i	0.725658	−	1.25688i	−0.233045	−	0.972466i	$-0.574869\pi$
$149$	8.85778	−	15.3421i	0.725658	−	1.25688i	0.958703	−	0.284410i	$-0.0917977\pi$
$150$	3.14146	−	21.7670i	0.256499	−	1.77727i
$151$	−9.03550	−	15.6499i	−0.735298	−	1.27357i	−0.954592	−	0.297915i	$-0.903709\pi$
$151$	−9.03550	−	15.6499i	−0.735298	−	1.27357i	0.219294	−	0.975659i	$-0.429625\pi$
$152$	−20.1373			−1.63335
$153$	−3.37357	+	3.20984i	−0.272737	+	0.259500i
$154$		0			0
$155$	−1.16823	−	2.02343i	−0.0938342	−	0.162526i
$156$	−5.29452	−	4.16823i	−0.423901	−	0.333725i
$157$	8.85830	−	15.3430i	0.706969	−	1.22451i	−0.259007	−	0.965875i	$-0.583395\pi$
$157$	8.85830	−	15.3430i	0.706969	−	1.22451i	0.965976	−	0.258631i	$-0.0832713\pi$
$158$	−0.856726	+	1.48389i	−0.0681575	+	0.118052i
$159$	5.14994	−	2.05854i	0.408417	−	0.163253i
$160$	−3.83037	−	6.63440i	−0.302817	−	0.524495i
$161$	−12.8959			−1.01634
$162$	21.3840	−	10.9666i	1.68009	−	0.861619i
$163$	2.12818			0.166692			0.0833460	−	0.996521i	$-0.473439\pi$
$163$	2.12818			0.166692			0.0833460	+	0.996521i	$0.473439\pi$
$164$	21.4397	+	37.1347i	1.67416	+	2.89973i
$165$		0			0
$166$	12.8832	−	22.3144i	0.999934	−	1.73194i
$167$	−11.0806	+	19.1922i	−0.857444	+	1.48514i	0.0169158	+	0.999857i	$0.494615\pi$
$167$	−11.0806	+	19.1922i	−0.857444	+	1.48514i	−0.874359	+	0.485279i	$0.838718\pi$
$168$	−52.7023	−	41.4910i	−4.06607	−	3.20110i
$169$	6.21246	+	10.7603i	0.477881	+	0.827715i
$170$	−2.05091			−0.157297
$171$	5.23630	−	4.98216i	0.400430	−	0.380995i
$172$	38.4826			2.93427
$173$	6.12162	+	10.6030i	0.465418	+	0.806128i	0.999220	−	0.0394814i	$-0.0125706\pi$
$173$	6.12162	+	10.6030i	0.465418	+	0.806128i	−0.533802	+	0.845609i	$0.679237\pi$
$174$	−3.05729	+	21.1838i	−0.231772	+	1.60594i
$175$	11.0158	−	19.0799i	0.832717	−	1.44231i
$176$		0			0
$177$	−2.26146	+	15.6695i	−0.169981	+	1.17779i
$178$	−17.6358	−	30.5461i	−1.32186	−	2.28953i
$179$	−20.9103			−1.56291			−0.781454	−	0.623963i	$-0.785521\pi$
$179$	−20.9103			−1.56291			−0.781454	+	0.623963i	$0.785521\pi$
$180$	7.30475	+	2.15332i	0.544464	+	0.160499i
$181$	−12.3365			−0.916961			−0.458481	−	0.888704i	$-0.651606\pi$
$181$	−12.3365			−0.916961			−0.458481	+	0.888704i	$0.651606\pi$
$182$	−4.69101	−	8.12507i	−0.347721	−	0.602270i
$183$	−2.81950	−	2.21971i	−0.208423	−	0.164086i
$184$	−11.6320	+	20.1473i	−0.857525	+	1.48528i
$185$	−1.61562	+	2.79833i	−0.118783	+	0.205738i
$186$	−20.2784	+	8.10571i	−1.48688	+	0.594339i
$187$		0			0
$188$	36.2633			2.64477
$189$	23.9695	−	2.25016i	1.74352	−	0.163675i
$190$	3.18332			0.230942
$191$	1.07193	+	1.85664i	0.0775622	+	0.134342i	0.902198	−	0.431323i	$-0.141953\pi$
$191$	1.07193	+	1.85664i	0.0775622	+	0.134342i	−0.824635	+	0.565665i	$0.808620\pi$
$192$	−27.7014	+	11.0728i	−1.99917	+	0.799113i
$193$	6.90147	−	11.9537i	0.496779	−	0.860446i	−0.503214	−	0.864162i	$-0.667849\pi$
$193$	6.90147	−	11.9537i	0.496779	−	0.860446i	0.999993	+	0.00371574i	$0.00118276\pi$
$194$	−23.5548	+	40.7981i	−1.69113	+	2.92913i
$195$	0.510672	+	0.402038i	0.0365700	+	0.0287905i
$196$	−37.1081	−	64.2731i	−2.65058	−	4.59094i
$197$	−1.40549			−0.100137			−0.0500686	−	0.998746i	$-0.515944\pi$
$197$	−1.40549			−0.100137			−0.0500686	+	0.998746i	$0.515944\pi$
$198$		0			0
$199$	8.06864			0.571971			0.285985	−	0.958234i	$-0.407679\pi$
$199$	8.06864			0.571971			0.285985	+	0.958234i	$0.407679\pi$
$200$	−19.8725	−	34.4201i	−1.40520	−	2.43387i
$201$	−0.828034	+	5.73741i	−0.0584050	+	0.404685i
$202$	11.1593	−	19.3285i	0.785166	−	1.35995i
$203$	−10.7207	+	18.5687i	−0.752442	+	1.30327i
$204$	−1.97014	+	13.6510i	−0.137938	+	0.955762i
$205$	−2.06792	−	3.58175i	−0.144430	−	0.250160i
$206$	0.859445			0.0598804
$207$	−1.95995	−	8.11678i	−0.136226	−	0.564155i
$208$	−9.14430			−0.634043
$209$		0			0
$210$	8.33123	+	6.55894i	0.574909	+	0.452610i
$211$	10.6954	−	18.5250i	0.736301	−	1.27531i	−0.217850	−	0.975982i	$-0.569904\pi$
$211$	10.6954	−	18.5250i	0.736301	−	1.27531i	0.954150	−	0.299328i	$-0.0967625\pi$
$212$	8.21354	−	14.2263i	0.564108	−	0.977064i
$213$	−11.0890	+	4.43253i	−0.759809	+	0.303712i
$214$	−3.72083	−	6.44467i	−0.254351	−	0.440549i
$215$	−3.71176			−0.253140
$216$	18.1050	−	39.4773i	1.23189	−	2.68609i
$217$	−21.8772			−1.48512
$218$	13.8779	+	24.0373i	0.939933	+	1.62801i
$219$	−2.48766	+	0.994372i	−0.168101	+	0.0671934i
$220$		0			0
$221$	−0.588551	+	1.01940i	−0.0395902	+	0.0685723i
$222$	23.7303	+	18.6821i	1.59267	+	1.25386i
$223$	4.11044	+	7.11949i	0.275255	+	0.476756i	0.970200	−	0.242307i	$-0.0779043\pi$
$223$	4.11044	+	7.11949i	0.275255	+	0.476756i	−0.694944	+	0.719064i	$0.744571\pi$
$224$	−71.7308			−4.79272
$225$	13.6833	+	4.03363i	0.912221	+	0.268908i
$226$	−48.9427			−3.25562
$227$	3.57059	+	6.18444i	0.236988	+	0.410476i	0.959849	−	0.280518i	$-0.0905064\pi$
$227$	3.57059	+	6.18444i	0.236988	+	0.410476i	−0.722860	+	0.690994i	$0.757173\pi$
$228$	3.05796	−	21.1884i	0.202518	−	1.40324i
$229$	−8.19525	+	14.1946i	−0.541557	+	0.938005i	0.457257	+	0.889334i	$0.348832\pi$
$229$	−8.19525	+	14.1946i	−0.541557	+	0.938005i	−0.998815	+	0.0486706i	$0.984502\pi$
$230$	1.83880	−	3.18490i	0.121247	−	0.210006i
$231$		0			0
$232$	19.3400	+	33.4979i	1.26973	+	2.19924i
$233$	−29.3627			−1.92362			−0.961808	−	0.273724i	$-0.911744\pi$
$233$	−29.3627			−1.92362			−0.961808	+	0.273724i	$0.911744\pi$
$234$	4.40104	−	4.18744i	0.287705	−	0.273742i
$235$	−3.49770			−0.228165
$236$	23.4462	+	40.6100i	1.52622	+	2.64349i
$237$	−0.873278	−	0.687507i	−0.0567255	−	0.0446584i
$238$	−9.60176	+	16.6307i	−0.622390	+	1.07801i
$239$	−2.97451	+	5.15201i	−0.192405	+	0.333256i	−0.946047	−	0.324030i	$-0.894962\pi$
$239$	−2.97451	+	5.15201i	−0.192405	+	0.333256i	0.753641	+	0.657286i	$0.228296\pi$
$240$	9.59634	−	3.83586i	0.619441	−	0.247604i
$241$	2.53821	+	4.39631i	0.163501	+	0.283191i	0.936122	−	0.351676i	$-0.114388\pi$
$241$	2.53821	+	4.39631i	0.163501	+	0.283191i	−0.772621	+	0.634867i	$0.781055\pi$
$242$		0			0
$243$	5.05923	+	14.7446i	0.324550	+	0.945869i
$244$	−10.6285			−0.680422
$245$	3.57918	+	6.19933i	0.228666	+	0.396061i
$246$	−35.8955	+	14.3482i	−2.28862	+	0.914809i
$247$	0.913521	−	1.58226i	0.0581259	−	0.100677i
$248$	−19.7332	+	34.1789i	−1.25306	+	2.17036i
$249$	13.1322	+	10.3386i	0.832217	+	0.655180i
$250$	6.44467	+	11.1625i	0.407597	+	0.705979i
$251$	−7.70399			−0.486271			−0.243136	−	0.969992i	$-0.578176\pi$
$251$	−7.70399			−0.486271			−0.243136	+	0.969992i	$0.578176\pi$
$252$	51.6600	−	49.1527i	3.25427	−	3.09633i
$253$		0			0
$254$	−16.8097	−	29.1153i	−1.05474	−	1.82686i
$255$	0.190026	−	1.31668i	0.0118999	−	0.0824537i
$256$	−2.84006	+	4.91913i	−0.177504	+	0.307446i
$257$	−3.10359	+	5.37558i	−0.193597	+	0.335319i	−0.946440	−	0.322881i	$-0.895349\pi$
$257$	−3.10359	+	5.37558i	−0.193597	+	0.335319i	0.752843	+	0.658200i	$0.228682\pi$
$258$	−4.95564	+	34.3374i	−0.308525	+	2.13775i
$259$	15.1277	+	26.2020i	0.939992	+	1.62811i
$260$	1.92506			0.119387
$261$	−13.3167	−	3.92555i	−0.824282	−	0.242985i
$262$	22.4727			1.38837
$263$	−12.1065	−	20.9691i	−0.746520	−	1.29301i	−0.949481	−	0.313823i	$-0.898390\pi$
$263$	−12.1065	−	20.9691i	−0.746520	−	1.29301i	0.202962	−	0.979187i	$-0.434943\pi$
$264$		0			0
$265$	−0.792220	+	1.37216i	−0.0486657	+	0.0842914i
$266$	14.9034	−	25.8134i	0.913786	−	1.58272i
$267$	21.2446	−	8.49193i	1.30015	−	0.519698i
$268$	8.58486	+	14.8694i	0.524404	+	0.908294i
$269$	−8.18133			−0.498825			−0.249412	−	0.968397i	$-0.580237\pi$
$269$	−8.18133			−0.498825			−0.249412	+	0.968397i	$0.580237\pi$
$270$	−2.86205	+	6.24061i	−0.174179	+	0.379791i
$271$	15.7651			0.957660			0.478830	−	0.877908i	$-0.341061\pi$
$271$	15.7651			0.957660			0.478830	+	0.877908i	$0.341061\pi$
$272$	9.35847	+	16.2093i	0.567440	+	0.982836i
$273$	5.65093	−	2.25880i	0.342010	−	0.136709i
$274$	−1.09302	+	1.89316i	−0.0660316	+	0.114370i
$275$		0			0
$276$	−19.4326	−	15.2987i	−1.16970	−	0.920874i
$277$	−1.12820	−	1.95410i	−0.0677870	−	0.117410i	0.830140	−	0.557555i	$-0.188260\pi$
$277$	−1.12820	−	1.95410i	−0.0677870	−	0.117410i	−0.897927	+	0.440145i	$0.854927\pi$
$278$	26.7539			1.60459
$279$	−3.32497	−	13.7697i	−0.199061	−	0.824372i
$280$	19.1622			1.14516
$281$	7.87903	+	13.6469i	0.470023	+	0.814104i	0.999412	−	0.0342749i	$-0.0109122\pi$
$281$	7.87903	+	13.6469i	0.470023	+	0.814104i	−0.529389	+	0.848379i	$0.677579\pi$
$282$	−4.66985	+	32.3571i	−0.278085	+	1.92684i
$283$	−0.629049	+	1.08954i	−0.0373931	+	0.0647667i	−0.884116	−	0.467267i	$-0.845239\pi$
$283$	−0.629049	+	1.08954i	−0.0373931	+	0.0647667i	0.846723	+	0.532034i	$0.178572\pi$
$284$	−17.6857	+	30.6325i	−1.04945	+	1.81771i
$285$	−0.294949	+	2.04369i	−0.0174713	+	0.121058i
$286$		0			0
$287$	−38.7257			−2.28591
$288$	−10.9019	−	45.1481i	−0.642400	−	2.66038i
$289$	−14.5907			−0.858274
$290$	−3.05729	−	5.29537i	−0.179530	−	0.310955i
$291$	−24.0099	−	18.9023i	−1.40748	−	1.10807i
$292$	−3.96752	+	6.87195i	−0.232182	+	0.402150i
$293$	8.60424	−	14.9030i	0.502665	−	0.870641i	−0.497330	−	0.867561i	$-0.665686\pi$
$293$	8.60424	−	14.9030i	0.502665	−	0.870641i	0.999995	−	0.00307994i	$-0.000980378\pi$
$294$	62.1284	−	24.8341i	3.62340	−	1.44835i
$295$	−2.26146	−	3.91696i	−0.131667	−	0.228054i
$296$	54.5807			3.17244
$297$		0			0
$298$	47.3047			2.74029
$299$	−1.05537	−	1.82795i	−0.0610334	−	0.105713i
$300$	39.2346	−	15.6829i	2.26521	−	0.905454i
$301$	−17.3774	+	30.0985i	−1.00162	+	1.73485i
$302$	24.1269	−	41.7890i	1.38835	−	2.40469i
$303$	11.3749	+	8.95514i	0.653471	+	0.514459i
$304$	−14.5258	−	25.1593i	−0.833109	−	1.44299i
$305$	1.02515			0.0587001
$306$	−11.9269	−	3.51585i	−0.681813	−	0.200988i
$307$	−2.96471			−0.169205			−0.0846026	−	0.996415i	$-0.526962\pi$
$307$	−2.96471			−0.169205			−0.0846026	+	0.996415i	$0.526962\pi$
$308$		0			0
$309$	−0.0796316	+	0.551763i	−0.00453008	+	0.0313887i
$310$	3.11944	−	5.40303i	0.177172	−	0.306872i
$311$	−2.14994	+	3.72380i	−0.121912	+	0.211158i	−0.920522	−	0.390692i	$-0.872236\pi$
$311$	−2.14994	+	3.72380i	−0.121912	+	0.211158i	0.798610	+	0.601849i	$0.205569\pi$
$312$	1.56819	−	10.8659i	0.0887814	−	0.615161i
$313$	2.07657	+	3.59672i	0.117374	+	0.203299i	0.918726	−	0.394895i	$-0.129219\pi$
$313$	2.07657	+	3.59672i	0.117374	+	0.203299i	−0.801352	+	0.598193i	$0.795886\pi$
$314$	47.3075			2.66972
$315$	−4.98276	+	4.74092i	−0.280747	+	0.267121i
$316$	−3.29195			−0.185187
$317$	−10.7395	−	18.6013i	−0.603189	−	1.04475i	−0.992335	−	0.123578i	$-0.960563\pi$
$317$	−10.7395	−	18.6013i	−0.603189	−	1.04475i	0.389145	−	0.921176i	$-0.372770\pi$
$318$	11.6361	+	9.16080i	0.652523	+	0.513712i
$319$		0			0
$320$	4.26133	−	7.38083i	0.238215	−	0.412601i
$321$	4.48223	−	1.79164i	0.250173	−	0.0999997i
$322$	−17.2175	−	29.8216i	−0.959494	−	1.66189i
$323$	−3.73967			−0.208081
$324$	38.7887	+	25.0449i	2.15493	+	1.39138i
$325$	3.60603			0.200027
$326$	2.84137	+	4.92140i	0.157369	+	0.272571i
$327$	−16.7178	+	6.68246i	−0.924495	+	0.369541i
$328$	−34.9305	+	60.5014i	−1.92871	+	3.34063i
$329$	−16.3752	+	28.3627i	−0.902796	+	1.56369i
$330$		0			0
$331$	−9.74105	−	16.8720i	−0.535417	−	0.927369i	−0.999143	−	0.0413905i	$-0.986821\pi$
$331$	−9.74105	−	16.8720i	−0.535417	−	0.927369i	0.463726	−	0.885978i	$-0.346512\pi$
$332$	49.5036			2.71686
$333$	−14.1926	+	13.5038i	−0.777752	+	0.740004i
$334$	−59.1757			−3.23795
$335$	−0.828034	−	1.43420i	−0.0452404	−	0.0783586i
$336$	13.8224	−	95.7748i	0.754075	−	5.22494i
$337$	−0.863293	+	1.49527i	−0.0470266	+	0.0814524i	−0.888581	−	0.458721i	$-0.848308\pi$
$337$	−0.863293	+	1.49527i	−0.0470266	+	0.0814524i	0.841554	+	0.540173i	$0.181641\pi$
$338$	−16.5887	+	28.7325i	−0.902308	+	1.56284i
$339$	4.53477	−	31.4212i	0.246295	−	1.70656i
$340$	−1.97014	−	3.41239i	−0.106846	−	0.185063i
$341$		0			0
$342$	18.5123	+	5.45713i	1.00103	+	0.295088i
$343$	34.5944			1.86792
$344$	31.3487	+	54.2976i	1.69021	+	2.92753i
$345$	1.87433	+	1.47561i	0.100910	+	0.0794439i
$346$	−16.3462	+	28.3124i	−0.878776	+	1.52209i
$347$	−12.6593	+	21.9265i	−0.679586	+	1.17708i	0.295519	+	0.955337i	$0.404507\pi$
$347$	−12.6593	+	21.9265i	−0.679586	+	1.17708i	−0.975106	+	0.221741i	$0.928826\pi$
$348$	−38.1834	+	15.2627i	−2.04684	+	0.818167i
$349$	6.87380	+	11.9058i	0.367946	+	0.637302i	0.989244	−	0.146273i	$-0.0467277\pi$
$349$	6.87380	+	11.9058i	0.367946	+	0.637302i	−0.621298	+	0.783574i	$0.713394\pi$
$350$	58.8296			3.14458
$351$	2.28056	+	3.21345i	0.121727	+	0.171521i
$352$		0			0
$353$	5.16138	+	8.93977i	0.274712	+	0.475816i	0.970063	−	0.242855i	$-0.0780840\pi$
$353$	5.16138	+	8.93977i	0.274712	+	0.475816i	−0.695350	+	0.718671i	$0.744751\pi$
$354$	−39.2550	+	15.6911i	−2.08638	+	0.833970i
$355$	1.70584	−	2.95460i	0.0905365	−	0.156814i
$356$	33.8826	−	58.6864i	1.79578	−	3.11037i
$357$	−9.78727	−	7.70524i	−0.517997	−	0.407804i
$358$	−27.9177	−	48.3549i	−1.47550	−	2.55563i
$359$	6.63940			0.350414			0.175207	−	0.984532i	$-0.443941\pi$
$359$	6.63940			0.350414			0.175207	+	0.984532i	$0.443941\pi$
$360$	2.91234	+	12.0609i	0.153494	+	0.635665i
$361$	−13.1955			−0.694499
$362$	−16.4706	−	28.5280i	−0.865677	−	1.49940i
$363$		0			0
$364$	9.01256	−	15.6102i	0.472387	−	0.818198i
$365$	0.382679	−	0.662820i	0.0200303	−	0.0346936i
$366$	1.36870	−	9.48365i	0.0715431	−	0.495718i
$367$	10.8790	+	18.8430i	0.567880	+	0.983597i	0.996775	+	0.0802430i	$0.0255696\pi$
$367$	10.8790	+	18.8430i	0.567880	+	0.983597i	−0.428895	+	0.903354i	$0.641097\pi$
$368$	−33.5625			−1.74956
$369$	−5.88566	−	24.3743i	−0.306395	−	1.26888i
$370$	−8.62817			−0.448557
$371$	7.41789	+	12.8482i	0.385118	+	0.667044i
$372$	−32.9664	−	25.9535i	−1.70923	−	1.34563i
$373$	10.4190	−	18.0462i	0.539473	−	0.934395i	−0.459459	−	0.888199i	$-0.651957\pi$
$373$	10.4190	−	18.0462i	0.539473	−	0.934395i	0.998932	−	0.0461961i	$-0.0147099\pi$
$374$		0			0
$375$	−7.76344	+	3.10322i	−0.400902	+	0.160249i
$376$	29.5409	+	51.1663i	1.52345	+	2.63870i
$377$	−3.50941			−0.180744
$378$	37.2056	+	52.4250i	1.91365	+	2.69645i
$379$	6.50319			0.334047			0.167023	−	0.985953i	$-0.446584\pi$
$379$	6.50319			0.334047			0.167023	+	0.985953i	$0.446584\pi$
$380$	3.05796	+	5.29654i	0.156870	+	0.271707i
$381$	20.2495	−	8.09417i	1.03741	−	0.414677i
$382$	−2.86231	+	4.95767i	−0.146449	+	0.253656i
$383$	10.0827	−	17.4638i	0.515204	−	0.892359i	−0.484640	−	0.874714i	$-0.661050\pi$
$383$	10.0827	−	17.4638i	0.515204	−	0.892359i	0.999844	−	0.0176459i	$-0.00561716\pi$
$384$	−20.4515	−	16.1008i	−1.04366	−	0.821643i
$385$		0			0
$386$	36.8571			1.87598
$387$	−21.5854	−	6.36303i	−1.09725	−	0.323451i
$388$	−90.5088			−4.59489
$389$	12.4880	+	21.6299i	0.633168	+	1.09668i	0.986900	+	0.161332i	$0.0515789\pi$
$389$	12.4880	+	21.6299i	0.633168	+	1.09668i	−0.353733	+	0.935347i	$0.615088\pi$
$390$	−0.247901	+	1.71769i	−0.0125530	+	0.0869788i
$391$	−2.16017	+	3.74152i	−0.109244	+	0.189217i
$392$	60.4581	−	104.716i	3.05359	−	5.28898i
$393$	−2.08220	+	14.4275i	−0.105033	+	0.727770i
$394$	−1.87650	−	3.25019i	−0.0945366	−	0.163742i
$395$	0.317518			0.0159761
$396$		0			0
$397$	27.5029			1.38033			0.690166	−	0.723651i	$-0.257538\pi$
$397$	27.5029			1.38033			0.690166	+	0.723651i	$0.257538\pi$
$398$	10.7726	+	18.6587i	0.539981	+	0.935275i
$399$	15.1913	+	11.9597i	0.760518	+	0.598734i
$400$	28.6695	−	49.6570i	1.43347	−	2.48285i
$401$	15.5597	−	26.9502i	0.777015	−	1.34583i	−0.156639	−	0.987656i	$-0.550066\pi$
$401$	15.5597	−	26.9502i	0.777015	−	1.34583i	0.933655	−	0.358174i	$-0.116601\pi$
$402$	−14.3732	+	5.74529i	−0.716872	+	0.286549i
$403$	−1.79038	−	3.10103i	−0.0891851	−	0.154473i
$404$	42.8794			2.13333
$405$	−3.74128	−	2.41565i	−0.185906	−	0.120035i
$406$	−57.2534			−2.84144
$407$		0			0
$408$	−20.8660	+	8.34061i	−1.03302	+	0.412922i
$409$	−13.5989	+	23.5540i	−0.672424	+	1.16467i	0.304791	+	0.952419i	$0.401414\pi$
$409$	−13.5989	+	23.5540i	−0.672424	+	1.16467i	−0.977215	+	0.212253i	$0.931920\pi$
$410$	5.52184	−	9.56411i	0.272704	−	0.472338i
$411$	−1.11413	−	0.877126i	−0.0549562	−	0.0432654i
$412$	0.825600	+	1.42998i	0.0406744	+	0.0704501i
$413$	−42.3500			−2.08391
$414$	16.1532	−	15.3692i	0.793888	−	0.755357i
$415$	−4.77477			−0.234384
$416$	−5.87028	−	10.1676i	−0.287814	−	0.498509i
$417$	−2.47887	+	17.1760i	−0.121391	+	0.841111i
$418$		0			0
$419$	2.43604	−	4.21934i	0.119008	−	0.206128i	−0.800367	−	0.599511i	$-0.795362\pi$
$419$	2.43604	−	4.21934i	0.119008	−	0.206128i	0.919375	+	0.393382i	$0.128695\pi$
$420$	−2.90989	+	20.1625i	−0.141988	+	0.983829i
$421$	−0.915507	−	1.58570i	−0.0446191	−	0.0772825i	0.842853	−	0.538143i	$-0.180874\pi$
$421$	−0.915507	−	1.58570i	−0.0446191	−	0.0772825i	−0.887472	+	0.460861i	$0.847541\pi$
$422$	57.1184			2.78048
$423$	−20.3406	−	5.99607i	−0.988992	−	0.291539i
$424$	26.7637			1.29976
$425$	−3.69049	−	6.39211i	−0.179015	−	0.310063i
$426$	−25.0554	−	19.7254i	−1.21394	−	0.955698i
$427$	4.79947	−	8.31293i	0.232263	−	0.402291i
$428$	7.14861	−	12.3818i	0.345541	−	0.598495i
$429$		0			0
$430$	−4.95564	−	8.58342i	−0.238982	−	0.413929i
$431$	−19.3517			−0.932137			−0.466068	−	0.884749i	$-0.654330\pi$
$431$	−19.3517			−0.932137			−0.466068	+	0.884749i	$0.654330\pi$
$432$	62.3824	−	5.85620i	3.00137	−	0.281757i
$433$	20.3759			0.979204			0.489602	−	0.871946i	$-0.337142\pi$
$433$	20.3759			0.979204			0.489602	+	0.871946i	$0.337142\pi$
$434$	−29.2087	−	50.5909i	−1.40206	−	2.42844i
$435$	3.68290	−	1.47213i	0.176581	−	0.0705834i
$436$	−26.6629	+	46.1814i	−1.27692	+	2.21169i
$437$	3.35291	−	5.80741i	0.160391	−	0.277806i
$438$	−5.62080	−	4.42509i	−0.268572	−	0.211439i
$439$	−9.10142	−	15.7641i	−0.434387	−	0.752380i	0.562858	−	0.826553i	$-0.309702\pi$
$439$	−9.10142	−	15.7641i	−0.434387	−	0.752380i	−0.997245	+	0.0741731i	$0.976368\pi$
$440$		0			0
$441$	10.1870	+	42.1874i	0.485093	+	2.00892i
$442$	−3.14314			−0.149504
$443$	−12.8473	−	22.2521i	−0.610392	−	1.05723i	−0.991174	−	0.132565i	$-0.957679\pi$
$443$	−12.8473	−	22.2521i	−0.610392	−	1.05723i	0.380783	−	0.924665i	$-0.375655\pi$
$444$	−8.28839	+	57.4298i	−0.393350	+	2.72550i
$445$	−3.26808	+	5.66048i	−0.154922	+	0.268332i
$446$	−10.9758	+	19.0107i	−0.519721	+	0.900184i
$447$	−4.38300	+	30.3696i	−0.207309	+	1.43643i
$448$	−39.9006	−	69.1099i	−1.88513	−	3.26514i
$449$	4.59869			0.217025			0.108513	−	0.994095i	$-0.465391\pi$
$449$	4.59869			0.217025			0.108513	+	0.994095i	$0.465391\pi$
$450$	8.94112	+	37.0280i	0.421489	+	1.74551i
$451$		0			0
$452$	−47.0153	−	81.4330i	−2.21142	−	3.83028i
$453$	24.5931	+	19.3614i	1.15548	+	0.909678i
$454$	−9.53432	+	16.5139i	−0.447468	+	0.775037i
$455$	−0.869288	+	1.50565i	−0.0407528	+	0.0705860i
$456$	32.3873	−	12.9459i	1.51667	−	0.606247i
$457$	5.50043	+	9.52702i	0.257299	+	0.445655i	0.965517	−	0.260338i	$-0.0838341\pi$
$457$	5.50043	+	9.52702i	0.257299	+	0.445655i	−0.708218	+	0.705994i	$0.750501\pi$
$458$	−43.7665			−2.04508
$459$	3.36225	−	7.33127i	0.156936	−	0.342194i
$460$	7.06556			0.329434
$461$	13.2961	+	23.0295i	0.619262	+	1.07259i	0.989621	+	0.143704i	$0.0459014\pi$
$461$	13.2961	+	23.0295i	0.619262	+	1.07259i	−0.370359	+	0.928889i	$0.620765\pi$
$462$		0			0
$463$	−5.49270	+	9.51364i	−0.255268	+	0.442136i	−0.964968	−	0.262367i	$-0.915497\pi$
$463$	−5.49270	+	9.51364i	−0.255268	+	0.442136i	0.709701	+	0.704503i	$0.248830\pi$
$464$	−27.9013	+	48.3265i	−1.29529	+	2.24350i
$465$	3.17971	+	2.50329i	0.147455	+	0.116087i
$466$	−39.2027	−	67.9011i	−1.81603	−	3.14546i
$467$	27.9906			1.29525			0.647626	−	0.761959i	$-0.275762\pi$
$467$	27.9906			1.29525			0.647626	+	0.761959i	$0.275762\pi$
$468$	11.1950	+	3.30010i	0.517488	+	0.152547i
$469$	−15.5065			−0.716023
$470$	−4.66985	−	8.08841i	−0.215404	−	0.373091i
$471$	−4.38326	+	30.3714i	−0.201970	+	1.39944i
$472$	−38.1996	+	66.1636i	−1.75828	+	3.04543i
$473$		0			0
$474$	0.423925	−	2.93735i	0.0194715	−	0.134917i
$475$	5.72820	+	9.92153i	0.262828	+	0.455231i
$476$	−36.8946			−1.69106
$477$	−6.95937	+	6.62160i	−0.318648	+	0.303182i
$478$	−15.8853			−0.726578
$479$	17.4989	+	30.3090i	0.799546	+	1.38485i	0.919912	+	0.392125i	$0.128260\pi$
$479$	17.4989	+	30.3090i	0.799546	+	1.38485i	−0.120366	+	0.992730i	$0.538407\pi$
$480$	10.4256	+	8.20778i	0.475862	+	0.374632i
$481$	−2.47604	+	4.28862i	−0.112898	+	0.195544i
$482$	−6.77763	+	11.7392i	−0.308713	+	0.534706i
$483$	20.7407	−	8.29051i	0.943735	−	0.377231i
$484$		0			0
$485$	8.72984			0.396401
$486$	−27.3422	+	31.3853i	−1.24027	+	1.42366i
$487$	1.49068			0.0675490			0.0337745	−	0.999429i	$-0.489247\pi$
$487$	1.49068			0.0675490			0.0337745	+	0.999429i	$0.489247\pi$
$488$	−8.65823	−	14.9965i	−0.391940	−	0.678859i
$489$	−3.42280	+	1.36817i	−0.154784	+	0.0618707i
$490$	−9.55727	+	16.5537i	−0.431753	+	0.747819i
$491$	−9.20595	+	15.9452i	−0.415459	+	0.719595i	−0.995476	−	0.0950083i	$-0.969712\pi$
$491$	−9.20595	+	15.9452i	−0.415459	+	0.719595i	0.580018	+	0.814604i	$0.303046\pi$
$492$	−58.3552	−	45.9413i	−2.63085	−	2.07120i
$493$	3.59161	+	6.22084i	0.161758	+	0.280173i
$494$	4.87863			0.219500
$495$		0			0
$496$	−56.9371			−2.55655
$497$	−15.9725	−	27.6652i	−0.716464	−	1.24095i
$498$	−6.37488	+	44.1712i	−0.285665	+	1.97936i
$499$	−16.1587	+	27.9876i	−0.723362	+	1.25290i	0.236283	+	0.971684i	$0.424071\pi$
$499$	−16.1587	+	27.9876i	−0.723362	+	1.25290i	−0.959645	+	0.281215i	$0.909263\pi$
$500$	−12.3818	+	21.4458i	−0.553729	+	0.959087i
$501$	5.48290	−	37.9908i	0.244958	−	1.69730i
$502$	−10.2857	−	17.8154i	−0.459075	−	0.795141i
$503$	42.1918			1.88124			0.940619	−	0.339465i	$-0.110246\pi$
$503$	42.1918			1.88124			0.940619	+	0.339465i	$0.110246\pi$
$504$	111.436	+	32.8496i	4.96376	+	1.46324i
$505$	−4.13585			−0.184043
$506$		0			0
$507$	−16.9092	−	13.3122i	−0.750966	−	0.591214i
$508$	32.2956	−	55.9376i	1.43288	−	2.48183i
$509$	14.6202	−	25.3229i	0.648028	−	1.12242i	−0.335566	−	0.942017i	$-0.608927\pi$
$509$	14.6202	−	25.3229i	0.648028	−	1.12242i	0.983593	−	0.180400i	$-0.0577392\pi$
$510$	3.29852	−	1.31849i	0.146061	−	0.0583838i
$511$	−3.58319	−	6.20626i	−0.158511	−	0.274549i
$512$	14.8882			0.657972
$513$	−5.21872	+	11.3792i	−0.230412	+	0.502406i
$514$	−16.5746			−0.731076
$515$	−0.0796316	−	0.137926i	−0.00350899	−	0.00607774i
$516$	−61.8924	+	24.7397i	−2.72466	+	1.08911i
$517$		0			0
$518$	−40.3946	+	69.9656i	−1.77484	+	3.07411i
$519$	−16.6620	−	13.1175i	−0.731380	−	0.575795i
$520$	1.56819	+	2.71619i	0.0687698	+	0.119113i
$521$	1.33096			0.0583104			0.0291552	−	0.999575i	$-0.490718\pi$
$521$	1.33096			0.0583104			0.0291552	+	0.999575i	$0.490718\pi$
$522$	−8.70155	−	36.0358i	−0.380857	−	1.57725i
$523$	7.29320			0.318909			0.159455	−	0.987205i	$-0.449026\pi$
$523$	7.29320			0.318909			0.159455	+	0.987205i	$0.449026\pi$
$524$	21.5878	+	37.3911i	0.943066	+	1.63344i
$525$	−5.45084	+	37.7686i	−0.237894	+	1.64836i
$526$	32.3273	−	55.9925i	1.40954	−	2.44139i
$527$	−3.66462	+	6.34731i	−0.159634	+	0.276493i
$528$		0			0
$529$	7.62647	+	13.2094i	0.331586	+	0.574323i
$530$	−4.23083			−0.183775
$531$	−6.43649	−	26.6555i	−0.279320	−	1.15675i
$532$	57.2660			2.48280
$533$	−3.16922	−	5.48925i	−0.137274	−	0.237766i
$534$	48.0016	+	37.7903i	2.07723	+	1.63535i
$535$	−0.689505	+	1.19426i	−0.0298099	+	0.0516322i
$536$	−13.9868	+	24.2259i	−0.604138	+	1.04640i
$537$	33.6305	−	13.4428i	1.45126	−	0.580101i
$538$	−10.9231	−	18.9193i	−0.470926	−	0.815668i
$539$		0			0
$540$	−13.1327	+	1.23285i	−0.565143	+	0.0530533i
$541$	20.4463			0.879054			0.439527	−	0.898229i	$-0.355146\pi$
$541$	20.4463			0.879054			0.439527	+	0.898229i	$0.355146\pi$
$542$	21.0482	+	36.4566i	0.904099	+	1.56595i
$543$	19.8410	−	7.93088i	0.851459	−	0.340347i
$544$	−12.0155	+	20.8115i	−0.515162	+	0.892287i
$545$	2.57171	−	4.45433i	0.110160	−	0.190803i
$546$	12.7681	+	10.0520i	0.546425	+	0.430185i
$547$	20.5571	+	35.6060i	0.878959	+	1.52240i	0.852485	+	0.522752i	$0.175095\pi$
$547$	20.5571	+	35.6060i	0.878959	+	1.52240i	0.0264740	+	0.999650i	$0.491572\pi$
$548$	−4.19990			−0.179411
$549$	5.96168	+	1.75741i	0.254438	+	0.0750044i
$550$		0			0
$551$	−5.57472	−	9.65569i	−0.237491	−	0.411346i
$552$	5.75576	−	39.8814i	0.244981	−	1.69746i
$553$	1.48653	−	2.57475i	0.0632137	−	0.109489i
$554$	3.01256	−	5.21791i	0.127991	−	0.221688i
$555$	0.799440	−	5.53928i	0.0339343	−	0.235129i
$556$	25.7003	+	44.5143i	1.08994	+	1.88783i
$557$	−15.6373			−0.662574			−0.331287	−	0.943530i	$-0.607483\pi$
$557$	−15.6373			−0.662574			−0.331287	+	0.943530i	$0.607483\pi$
$558$	27.4032	−	26.0732i	1.16007	−	1.10377i
$559$	−5.68850			−0.240598
$560$	13.8224	+	23.9411i	0.584104	+	1.01170i
$561$		0			0
$562$	−21.0389	+	36.4404i	−0.887471	+	1.53715i
$563$	−14.1825	+	24.5648i	−0.597720	+	1.03528i	0.395437	+	0.918493i	$0.370593\pi$
$563$	−14.1825	+	24.5648i	−0.597720	+	1.03528i	−0.993157	+	0.116788i	$0.962740\pi$
$564$	−58.3231	+	23.3130i	−2.45585	+	0.981655i
$565$	4.53477	+	7.85445i	0.190779	+	0.330439i
$566$	−3.35942			−0.141207
$567$	−37.1041	+	19.0285i	−1.55822	+	0.799122i
$568$	−57.6286			−2.41804
$569$	0.564664	+	0.978027i	0.0236720	+	0.0410010i	0.877619	−	0.479359i	$-0.159131\pi$
$569$	0.564664	+	0.978027i	0.0236720	+	0.0410010i	−0.853947	+	0.520360i	$0.825798\pi$
$570$	−5.11981	+	2.04650i	−0.214445	+	0.0857183i
$571$	10.0361	−	17.3831i	0.419999	−	0.727459i	−0.575940	−	0.817492i	$-0.695364\pi$
$571$	10.0361	−	17.3831i	0.419999	−	0.727459i	0.995939	+	0.0900328i	$0.0286972\pi$
$572$		0			0
$573$	−2.91761	−	2.29695i	−0.121885	−	0.0959565i
$574$	−51.7034	−	89.5529i	−2.15806	−	3.73787i
$575$	13.2353			0.551949
$576$	37.4342	−	35.6174i	1.55976	−	1.48406i
$577$	13.2021			0.549609			0.274804	−	0.961500i	$-0.411387\pi$
$577$	13.2021			0.549609			0.274804	+	0.961500i	$0.411387\pi$
$578$	−19.4803	−	33.7408i	−0.810272	−	1.40343i
$579$	−3.41498	+	23.6622i	−0.141922	+	0.983369i
$580$	5.87378	−	10.1737i	0.243895	−	0.422439i
$581$	−22.3541	+	38.7185i	−0.927405	+	1.60631i
$582$	11.6554	−	80.7594i	0.483130	−	3.34759i
$583$		0			0
$584$	−12.9281			−0.534969
$585$	−1.07979	−	0.318305i	−0.0446438	−	0.0131603i
$586$	45.9507			1.89821
$587$	−18.2186	−	31.5555i	−0.751961	−	1.30244i	−0.946871	−	0.321614i	$-0.895775\pi$
$587$	−18.2186	−	31.5555i	−0.751961	−	1.30244i	0.194910	−	0.980821i	$-0.437559\pi$
$588$	101.002	+	79.5158i	4.16524	+	3.27918i
$589$	5.68805	−	9.85199i	0.234372	−	0.405944i
$590$	6.03862	−	10.4592i	0.248606	−	0.430599i
$591$	2.26048	−	0.903565i	0.0929839	−	0.0371677i
$592$	39.3711	+	68.1927i	1.61814	+	2.80270i
$593$	−31.9074			−1.31028			−0.655141	−	0.755507i	$-0.727391\pi$
$593$	−31.9074			−1.31028			−0.655141	+	0.755507i	$0.727391\pi$
$594$		0			0
$595$	3.55859			0.145888
$596$	45.4419	+	78.7077i	1.86137	+	3.22399i
$597$	−12.9770	+	5.18718i	−0.531112	+	0.212297i
$598$	2.81808	−	4.88106i	0.115240	−	0.199601i
$599$	−4.79213	+	8.30022i	−0.195801	+	0.339138i	−0.947163	−	0.320753i	$-0.896064\pi$
$599$	−4.79213	+	8.30022i	−0.195801	+	0.339138i	0.751362	+	0.659891i	$0.229397\pi$
$600$	54.0894	+	42.5830i	2.20819	+	1.73845i
$601$	8.23932	+	14.2709i	0.336089	+	0.582123i	0.983693	−	0.179854i	$-0.0575624\pi$
$601$	8.23932	+	14.2709i	0.336089	+	0.582123i	−0.647605	+	0.761977i	$0.724229\pi$
$602$	−92.8035			−3.78239
$603$	−2.35673	−	9.75993i	−0.0959733	−	0.397455i
$604$	92.7072			3.77220
$605$		0			0
$606$	−5.52184	+	38.2606i	−0.224310	+	1.55423i
$607$	−6.24059	+	10.8090i	−0.253298	+	0.438725i	−0.964432	−	0.264332i	$-0.914849\pi$
$607$	−6.24059	+	10.8090i	−0.253298	+	0.438725i	0.711134	+	0.703056i	$0.248182\pi$
$608$	18.6499	−	32.3026i	0.756355	−	1.31005i
$609$	5.30479	−	36.7566i	0.214961	−	1.48945i
$610$	1.36870	+	2.37066i	0.0554171	+	0.0959852i
$611$	−5.36044			−0.216860
$612$	−5.60736	−	23.2218i	−0.226664	−	0.938686i
$613$	−41.6568			−1.68250			−0.841252	−	0.540643i	$-0.818181\pi$
$613$	−41.6568			−1.68250			−0.841252	+	0.540643i	$0.818181\pi$
$614$	−3.95824	−	6.85588i	−0.159742	−	0.276681i
$615$	5.62853	+	4.43118i	0.226964	+	0.178682i
$616$		0			0
$617$	−7.98657	+	13.8332i	−0.321527	+	0.556902i	−0.980803	−	0.194999i	$-0.937530\pi$
$617$	−7.98657	+	13.8332i	−0.321527	+	0.556902i	0.659276	+	0.751901i	$0.270863\pi$
$618$	−1.38227	+	0.552521i	−0.0556029	+	0.0222257i
$619$	22.4002	+	38.7983i	0.900341	+	1.55944i	0.827051	+	0.562126i	$0.190016\pi$
$619$	22.4002	+	38.7983i	0.900341	+	1.55944i	0.0732898	+	0.997311i	$0.476650\pi$
$620$	11.9864			0.481385
$621$	8.37037	+	11.7944i	0.335891	+	0.473292i
$622$	−11.4817			−0.460374
$623$	30.6004	+	53.0015i	1.22598	+	2.12346i
$624$	14.7070	−	5.87870i	0.588750	−	0.235336i
$625$	−10.6936	+	18.5219i	−0.427745	+	0.740876i
$626$	−5.54493	+	9.60409i	−0.221620	+	0.383857i
$627$		0			0
$628$	45.4445	+	78.7123i	1.81343	+	3.14096i
$629$	10.1361			0.404153
$630$	−17.6159	−	5.19290i	−0.701835	−	0.206890i
$631$	22.4771			0.894798			0.447399	−	0.894334i	$-0.352350\pi$
$631$	22.4771			0.894798			0.447399	+	0.894334i	$0.352350\pi$
$632$	−2.68170	−	4.64483i	−0.106672	−	0.184762i
$633$	−5.29229	+	36.6700i	−0.210350	+	1.45750i
$634$	28.6770	−	49.6700i	1.13891	−	1.97265i
$635$	−3.11500	+	5.39534i	−0.123615	+	0.214108i
$636$	−4.06422	+	28.1608i	−0.161157	+	1.11665i
$637$	5.48532	+	9.50085i	0.217336	+	0.376438i
$638$		0			0
$639$	14.9852	−	14.2579i	0.592804	−	0.564033i
$640$	7.43602			0.293935
$641$	−14.8509	−	25.7225i	−0.586576	−	1.01598i	−0.994677	−	0.103042i	$-0.967142\pi$
$641$	−14.8509	−	25.7225i	−0.586576	−	1.01598i	0.408101	−	0.912937i	$-0.366191\pi$
$642$	10.1275	+	7.97306i	0.399699	+	0.314672i
$643$	12.6103	−	21.8416i	0.497300	−	0.861349i	−0.502695	−	0.864464i	$-0.667658\pi$
$643$	12.6103	−	21.8416i	0.497300	−	0.861349i	0.999995	+	0.00311497i	$0.000991526\pi$
$644$	33.0790	−	57.2944i	1.30349	−	2.25772i
$645$	5.96971	−	2.38622i	0.235057	−	0.0939574i
$646$	−4.99290	−	8.64795i	−0.196443	−	0.340249i
$647$	−11.3729			−0.447113			−0.223557	−	0.974691i	$-0.571767\pi$
$647$	−11.3729			−0.447113			−0.223557	+	0.974691i	$0.571767\pi$
$648$	−3.73944	+	75.1316i	−0.146899	+	2.95145i
$649$		0			0
$650$	4.81448	+	8.33892i	0.188839	+	0.327079i
$651$	35.1856	−	14.0645i	1.37903	−	0.551229i
$652$	−5.45896	+	9.45520i	−0.213789	+	0.370294i
$653$	−13.7646	+	23.8409i	−0.538649	+	0.932968i	0.460328	+	0.887749i	$0.347732\pi$
$653$	−13.7646	+	23.8409i	−0.538649	+	0.932968i	−0.998977	+	0.0452186i	$0.985602\pi$
$654$	−37.7733	−	29.7379i	−1.47705	−	1.16284i
$655$	−2.08220	−	3.60648i	−0.0813584	−	0.140917i
$656$	−100.787			−3.93505
$657$	3.36170	−	3.19854i	0.131152	−	0.124787i
$658$	−87.4516			−3.40922
$659$	−21.8300	−	37.8106i	−0.850375	−	1.47289i	−0.880870	−	0.473358i	$-0.843042\pi$
$659$	−21.8300	−	37.8106i	−0.850375	−	1.47289i	0.0304948	−	0.999535i	$-0.490292\pi$
$660$		0			0
$661$	−0.628181	+	1.08804i	−0.0244334	+	0.0423199i	−0.877984	−	0.478691i	$-0.841112\pi$
$661$	−0.628181	+	1.08804i	−0.0244334	+	0.0423199i	0.853550	+	0.521011i	$0.174445\pi$
$662$	26.0109	−	45.0522i	1.01094	−	1.75101i
$663$	0.291227	−	2.01789i	0.0113103	−	0.0783685i
$664$	40.3267	+	69.8479i	1.56498	+	2.71063i
$665$	−5.52347			−0.214191
$666$	−50.1763	−	14.7912i	−1.94429	−	0.573147i
$667$	−12.8806			−0.498741
$668$	−56.8454	−	98.4591i	−2.19941	−	3.80950i
$669$	−11.1879	−	8.80791i	−0.432549	−	0.340534i
$670$	2.21105	−	3.82965i	0.0854203	−	0.147952i
$671$		0			0
$672$	115.366	−	46.1144i	4.45035	−	1.77890i
$673$	−10.1624	−	17.6018i	−0.391732	−	0.678501i	0.600946	−	0.799290i	$-0.294791\pi$
$673$	−10.1624	−	17.6018i	−0.391732	−	0.678501i	−0.992678	+	0.120789i	$0.961457\pi$
$674$	−4.61040			−0.177586
$675$	−24.6003	+	2.30938i	−0.946868	+	0.0888881i
$676$	−63.7419			−2.45161
$677$	−7.97630	−	13.8154i	−0.306554	−	0.530968i	0.671052	−	0.741410i	$-0.265843\pi$
$677$	−7.97630	−	13.8154i	−0.306554	−	0.530968i	−0.977606	+	0.210443i	$0.932509\pi$
$678$	78.7157	−	31.4644i	3.02306	−	1.20838i
$679$	40.8706	−	70.7899i	1.56847	−	2.71667i
$680$	3.20984	−	5.55961i	0.123092	−	0.213201i
$681$	−9.71852	−	7.65111i	−0.372415	−	0.293191i
$682$		0			0
$683$	14.8478			0.568134			0.284067	−	0.958804i	$-0.408316\pi$
$683$	14.8478			0.568134			0.284067	+	0.958804i	$0.408316\pi$
$684$	8.70347	+	36.0438i	0.332786	+	1.37817i
$685$	0.405092			0.0154778
$686$	46.1876	+	79.9993i	1.76345	+	3.05439i
$687$	4.05517	−	28.0981i	0.154714	−	1.07201i
$688$	−45.2260	+	78.3337i	−1.72422	+	2.98645i
$689$	−1.21413	+	2.10293i	−0.0462545	+	0.0801152i
$690$	−0.909876	+	6.30448i	−0.0346384	+	0.240007i
$691$	4.86411	+	8.42488i	0.185039	+	0.320498i	0.943590	−	0.331117i	$-0.107425\pi$
$691$	4.86411	+	8.42488i	0.185039	+	0.320498i	−0.758550	+	0.651614i	$0.774092\pi$
$692$	−62.8099			−2.38767
$693$		0			0
$694$	−67.6066			−2.56631
$695$	−2.47887	−	4.29353i	−0.0940290	−	0.162863i
$696$	−52.6402	−	41.4421i	−1.99532	−	1.57086i
$697$	−6.48689	+	11.2356i	−0.245709	+	0.425580i
$698$	−18.3547	+	31.7912i	−0.694735	+	1.20332i
$699$	47.2248	−	18.8768i	1.78620	−	0.713984i
$700$	56.5129	+	97.8833i	2.13599	+	3.69964i
$701$	24.5582			0.927551			0.463775	−	0.885953i	$-0.346494\pi$
$701$	24.5582			0.927551			0.463775	+	0.885953i	$0.346494\pi$
$702$	−4.38627	+	9.56411i	−0.165549	+	0.360974i
$703$	−15.7328			−0.593373
$704$		0			0
$705$	5.62543	−	2.24861i	0.211866	−	0.0846875i
$706$	−13.7821	+	23.8713i	−0.518696	+	0.898408i
$707$	−19.3628	+	33.5374i	−0.728215	+	1.26130i
$708$	−63.8165	−	50.2409i	−2.39837	−	1.88817i
$709$	−15.5268	−	26.8933i	−0.583123	−	1.01000i	−0.995107	−	0.0988071i	$-0.968497\pi$
$709$	−15.5268	−	26.8933i	−0.583123	−	1.01000i	0.411984	−	0.911191i	$-0.364836\pi$
$710$	9.10998			0.341892
$711$	1.84650	+	0.544319i	0.0692491	+	0.0204135i
$712$	110.406			4.13764
$713$	−6.57126	−	11.3818i	−0.246096	−	0.426250i
$714$	4.75114	−	32.9204i	0.177807	−	1.23202i
$715$		0			0
$716$	53.6366	−	92.9013i	2.00449	−	3.47188i
$717$	1.47185	−	10.1984i	0.0549672	−	0.380865i
$718$	8.86438	+	15.3536i	0.330816	+	0.572990i
$719$	12.7230			0.474487			0.237244	−	0.971450i	$-0.423756\pi$
$719$	12.7230			0.474487			0.237244	+	0.971450i	$0.423756\pi$
$720$	−12.9680	+	12.3386i	−0.483289	+	0.459833i
$721$	−1.49125			−0.0555370
$722$	−17.6175	−	30.5144i	−0.655656	−	1.13563i
$723$	−6.90857	−	5.43892i	−0.256933	−	0.202276i
$724$	31.6440	−	54.8091i	1.17604	−	2.03696i
$725$	11.0028	−	19.0574i	0.408634	−	0.707775i
$726$		0			0
$727$	−11.7394	−	20.3333i	−0.435391	−	0.754120i	0.561936	−	0.827181i	$-0.310057\pi$
$727$	−11.7394	−	20.3333i	−0.435391	−	0.754120i	−0.997327	+	0.0730607i	$0.976723\pi$
$728$	29.3673			1.08842
$729$	−17.6159	−	20.4616i	−0.652442	−	0.757839i
$730$	2.04369			0.0756403
$731$	5.82173	+	10.0835i	0.215325	+	0.372953i
$732$	17.0941	−	6.83288i	0.631816	−	0.252551i
$733$	12.5601	−	21.7547i	0.463916	−	0.803526i	−0.535236	−	0.844703i	$-0.679777\pi$
$733$	12.5601	−	21.7547i	0.463916	−	0.803526i	0.999152	+	0.0411763i	$0.0131105\pi$
$734$	−29.0496	+	50.3153i	−1.07224	+	1.85717i
$735$	−9.74192	−	7.66953i	−0.359336	−	0.282895i
$736$	−21.5458	−	37.3184i	−0.794188	−	1.37557i
$737$		0			0
$738$	48.5074	−	46.1532i	1.78558	−	1.69892i
$739$	−1.23246			−0.0453366			−0.0226683	−	0.999743i	$-0.507216\pi$
$739$	−1.23246			−0.0453366			−0.0226683	+	0.999743i	$0.507216\pi$
$740$	−8.28839	−	14.3559i	−0.304687	−	0.527734i
$741$	−0.452028	+	3.13208i	−0.0166057	+	0.115060i
$742$	−19.8075	+	34.3077i	−0.727158	+	1.25947i
$743$	18.7783	−	32.5249i	0.688908	−	1.19322i	−0.283284	−	0.959036i	$-0.591424\pi$
$743$	18.7783	−	32.5249i	0.688908	−	1.19322i	0.972192	−	0.234187i	$-0.0752427\pi$
$744$	9.76437	−	67.6568i	0.357979	−	2.48042i
$745$	−4.38300	−	7.59158i	−0.160581	−	0.278134i
$746$	55.6422			2.03720
$747$	−27.7672	−	8.18534i	−1.01595	−	0.299486i
$748$		0			0
$749$	6.45613	+	11.1823i	0.235902	+	0.408594i
$750$	−17.5413	−	13.8097i	−0.640517	−	0.504261i
$751$	15.4269	−	26.7202i	0.562935	−	0.975033i	−0.434303	−	0.900767i	$-0.643005\pi$
$751$	15.4269	−	26.7202i	0.562935	−	0.975033i	0.997238	−	0.0742658i	$-0.0236613\pi$
$752$	−42.6178	+	73.8162i	−1.55411	+	2.69180i
$753$	12.3905	−	4.95275i	0.451535	−	0.180488i
$754$	−4.68548	−	8.11549i	−0.170635	−	0.295549i
$755$	−8.94188			−0.325428
$756$	−51.4866	+	112.265i	−1.87255	+	4.08303i
$757$	30.0266			1.09133			0.545667	−	0.838002i	$-0.316276\pi$
$757$	30.0266			1.09133			0.545667	+	0.838002i	$0.316276\pi$
$758$	8.68254	+	15.0386i	0.315364	+	0.546226i
$759$		0			0
$760$	−4.98216	+	8.62936i	−0.180722	+	0.313020i
$761$	7.38279	−	12.7874i	0.267626	−	0.463542i	−0.700622	−	0.713532i	$-0.747094\pi$
$761$	7.38279	−	12.7874i	0.267626	−	0.463542i	0.968248	+	0.249991i	$0.0804275\pi$
$762$	45.7532	+	36.0202i	1.65746	+	1.30487i
$763$	−24.0800	−	41.7078i	−0.871755	−	1.50992i
$764$	−10.9984			−0.397907
$765$	0.540846	+	2.23981i	0.0195543	+	0.0809806i
$766$	53.8466			1.94556
$767$	−3.46582	−	6.00298i	−0.125144	−	0.216755i
$768$	1.40532	−	9.73738i	0.0507101	−	0.351367i
$769$	−6.31941	+	10.9455i	−0.227884	+	0.394706i	−0.957181	−	0.289491i	$-0.906514\pi$
$769$	−6.31941	+	10.9455i	−0.227884	+	0.394706i	0.729297	+	0.684197i	$0.239847\pi$
$770$		0			0
$771$	1.53572	−	10.6409i	0.0553075	−	0.383223i
$772$	35.4057	+	61.3245i	1.27428	+	2.20712i
$773$	−13.4752			−0.484669			−0.242334	−	0.970193i	$-0.577913\pi$
$773$	−13.4752			−0.484669			−0.242334	+	0.970193i	$0.577913\pi$
$774$	−14.1046	−	58.4114i	−0.506979	−	2.09956i
$775$	22.4530			0.806536
$776$	−73.7304	−	127.705i	−2.64677	−	4.58433i
$777$	−41.1751	−	32.4159i	−1.47715	−	1.16292i
$778$	−33.3460	+	57.7569i	−1.19551	+	2.07069i
$779$	10.0686	−	17.4394i	0.360746	−	0.624831i
$780$	−3.09611	+	1.23758i	−0.110859	+	0.0443126i
$781$		0			0
$782$	−11.5363			−0.412538
$783$	23.9412	−	2.24750i	0.855589	−	0.0803192i
$784$	174.443			6.23009
$785$	−4.38326	−	7.59203i	−0.156445	−	0.270971i
$786$	−36.1434	+	14.4473i	−1.28919	+	0.515319i
$787$	−4.76840	+	8.25911i	−0.169975	+	0.294406i	−0.938411	−	0.345521i	$-0.887702\pi$
$787$	−4.76840	+	8.25911i	−0.169975	+	0.294406i	0.768436	+	0.639927i	$0.221035\pi$
$788$	3.60520	−	6.24439i	0.128430	−	0.222447i
$789$	32.9518	+	25.9420i	1.17312	+	0.923561i
$790$	0.423925	+	0.734259i	0.0150826	+	0.0261238i
$791$	84.9220			3.01948
$792$		0			0
$793$	1.57111			0.0557917
$794$	36.7197	+	63.6003i	1.30313	+	2.25709i
$795$	0.392006	−	2.71619i	0.0139030	−	0.0963333i
$796$	−20.6967	+	35.8478i	−0.733576	+	1.27059i
$797$	19.7327	−	34.1780i	0.698967	−	1.21065i	−0.269858	−	0.962900i	$-0.586977\pi$
$797$	19.7327	−	34.1780i	0.698967	−	1.21065i	0.968825	−	0.247747i	$-0.0796901\pi$
$798$	−7.37449	+	51.0975i	−0.261054	+	1.80883i
$799$	5.48599	+	9.50202i	0.194080	+	0.336157i
$800$	73.6188			2.60282
$801$	−28.7089	+	27.3155i	−1.01438	+	0.965147i
$802$	83.0963			2.93423
$803$		0			0
$804$	−23.3665	−	18.3958i	−0.824072	−	0.648769i
$805$	−3.19056	+	5.52621i	−0.112453	+	0.194773i
$806$	4.78074	−	8.28048i	0.168394	−	0.291667i
$807$	13.1582	−	5.25963i	0.463192	−	0.185148i
$808$	34.9305	+	60.5014i	1.22885	+	2.12843i
$809$	−1.41298			−0.0496777			−0.0248389	−	0.999691i	$-0.507907\pi$
$809$	−1.41298			−0.0496777			−0.0248389	+	0.999691i	$0.507907\pi$
$810$	0.591134	−	11.8769i	0.0207703	−	0.417311i
$811$	−9.45530			−0.332021			−0.166010	−	0.986124i	$-0.553088\pi$
$811$	−9.45530			−0.332021			−0.166010	+	0.986124i	$0.553088\pi$
$812$	−54.9987	−	95.2606i	−1.93008	−	3.34299i
$813$	−25.3553	+	10.1351i	−0.889250	+	0.355452i
$814$		0			0
$815$	0.526533	−	0.911982i	0.0184436	−	0.0319453i
$816$	−25.4721	−	20.0535i	−0.891703	−	0.702012i
$817$	−9.03621	−	15.6512i	−0.316137	−	0.547565i
$818$	−72.6248			−2.53927
$819$	−7.63638	+	7.26576i	−0.266837	+	0.253886i
$820$	21.2176			0.740950
$821$	−16.7423	−	28.9985i	−0.584310	−	1.01206i	−0.994961	−	0.100262i	$-0.968032\pi$
$821$	−16.7423	−	28.9985i	−0.584310	−	1.01206i	0.410651	−	0.911793i	$-0.365302\pi$
$822$	0.540846	−	3.74750i	0.0188642	−	0.130709i
$823$	14.3521	−	24.8586i	0.500284	−	0.866517i	−0.499716	−	0.866189i	$-0.666562\pi$
$823$	14.3521	−	24.8586i	0.500284	−	0.866517i	1.00000		0.000327451i	$-0.000104231\pi$
$824$	−1.34510	+	2.32979i	−0.0468589	+	0.0811620i
$825$		0			0
$826$	−56.5422	−	97.9340i	−1.96736	−	3.40756i
$827$	12.7378			0.442938			0.221469	−	0.975167i	$-0.428915\pi$
$827$	12.7378			0.442938			0.221469	+	0.975167i	$0.428915\pi$
$828$	41.0891	+	12.1124i	1.42795	+	0.420936i
$829$	27.8268			0.966463			0.483232	−	0.875493i	$-0.339463\pi$
$829$	27.8268			0.966463			0.483232	+	0.875493i	$0.339463\pi$
$830$	−6.37488	−	11.0416i	−0.221275	−	0.383260i
$831$	3.07077	+	2.41753i	0.106524	+	0.0838630i
$832$	6.53075	−	11.3116i	0.226413	−	0.392159i
$833$	11.2276	−	19.4468i	0.389013	−	0.673790i
$834$	−43.0289	+	17.1996i	−1.48997	+	0.595573i
$835$	5.48290	+	9.49667i	0.189744	+	0.328646i
$836$		0			0
$837$	14.1999	+	20.0086i	0.490821	+	0.691599i
$838$	13.0096			0.449409
$839$	28.3745	+	49.1460i	0.979595	+	1.69671i	0.663852	+	0.747864i	$0.268920\pi$
$839$	28.3745	+	49.1460i	0.979595	+	1.69671i	0.315743	+	0.948845i	$0.397746\pi$
$840$	−30.8191	+	12.3190i	−1.06336	+	0.425047i
$841$	3.79199	−	6.56793i	0.130758	−	0.226480i
$842$	2.44462	−	4.23421i	0.0842472	−	0.145920i
$843$	−21.4453	−	16.8833i	−0.738617	−	0.581492i
$844$	54.8691	+	95.0361i	1.88867	+	3.27128i
$845$	6.14809			0.211501
$846$	−13.2912	−	55.0429i	−0.456960	−	1.89241i
$847$		0			0
$848$	19.3056	+	33.4383i	0.662958	+	1.14828i
$849$	0.311266	−	2.15674i	0.0106826	−	0.0740192i
$850$	9.85448	−	17.0685i	0.338006	−	0.585443i
$851$	−9.08783	+	15.7406i	−0.311527	+	0.539581i
$852$	8.75123	−	60.6368i	0.299812	−	2.07738i
$853$	−2.46528	−	4.26998i	−0.0844094	−	0.146201i	0.820730	−	0.571316i	$-0.193567\pi$
$853$	−2.46528	−	4.26998i	−0.0844094	−	0.146201i	−0.905139	+	0.425115i	$0.860234\pi$
$854$	25.6315			0.877090
$855$	−0.839475	−	3.47653i	−0.0287095	−	0.118895i
$856$	23.2937			0.796161
$857$	12.5789	+	21.7873i	0.429688	+	0.744242i	0.996845	−	0.0793679i	$-0.0252902\pi$
$857$	12.5789	+	21.7873i	0.429688	+	0.744242i	−0.567157	+	0.823609i	$0.691957\pi$
$858$		0			0
$859$	6.60823	−	11.4458i	0.225470	−	0.390525i	−0.730991	−	0.682388i	$-0.760942\pi$
$859$	6.60823	−	11.4458i	0.225470	−	0.390525i	0.956460	+	0.291863i	$0.0942750\pi$
$860$	9.52097	−	16.4908i	0.324662	−	0.562332i
$861$	62.2834	−	24.8960i	2.12261	−	0.848455i
$862$	−25.8368	−	44.7506i	−0.880004	−	1.52421i
$863$	−31.8990			−1.08586			−0.542928	−	0.839780i	$-0.682684\pi$
$863$	−31.8990			−1.08586			−0.542928	+	0.839780i	$0.682684\pi$
$864$	46.5586	+	65.6041i	1.58396	+	2.23190i
$865$	6.05820			0.205985
$866$	27.2043	+	47.1192i	0.924438	+	1.60117i
$867$	23.4665	−	9.38006i	0.796964	−	0.318564i
$868$	56.1169	−	97.1973i	1.90473	−	3.29909i
$869$		0			0
$870$	8.32140	+	6.55120i	0.282122	+	0.222107i
$871$	−1.26901	−	2.19800i	−0.0429989	−	0.0744763i
$872$	−86.8805			−2.94215
$873$	50.7675	+	14.9655i	1.71822	+	0.506504i
$874$	17.9061			0.605684
$875$	−11.1823	−	19.3684i	−0.378032	−	0.654771i
$876$	1.96321	−	13.6030i	0.0663306	−	0.459601i
$877$	7.73455	−	13.3966i	0.261177	−	0.452372i	−0.705378	−	0.708831i	$-0.749223\pi$
$877$	7.73455	−	13.3966i	0.261177	−	0.452372i	0.966555	+	0.256459i	$0.0825560\pi$
$878$	24.3029	−	42.0939i	0.820185	−	1.42060i
$879$	−4.25755	+	29.5003i	−0.143603	+	0.995021i
$880$		0			0
$881$	27.6370			0.931113			0.465557	−	0.885018i	$-0.345854\pi$
$881$	27.6370			0.931113			0.465557	+	0.885018i	$0.345854\pi$
$882$	−83.9572	+	79.8824i	−2.82699	+	2.68978i
$883$	21.6292			0.727881			0.363941	−	0.931422i	$-0.381431\pi$
$883$	21.6292			0.727881			0.363941	+	0.931422i	$0.381431\pi$
$884$	−3.01937	−	5.22970i	−0.101552	−	0.175894i
$885$	6.15529	+	4.84588i	0.206908	+	0.162893i
$886$	34.3052	−	59.4184i	1.15251	−	1.99620i
$887$	10.2036	−	17.6731i	0.342603	−	0.593406i	−0.642312	−	0.766443i	$-0.722025\pi$
$887$	10.2036	−	17.6731i	0.342603	−	0.593406i	0.984915	+	0.173037i	$0.0553581\pi$
$888$	−87.7835	+	35.0889i	−2.94582	+	1.17751i
$889$	29.1671	+	50.5189i	0.978233	+	1.69435i
$890$	−17.4531			−0.585029
$891$		0			0
$892$	−42.1745			−1.41211
$893$	−8.51509	−	14.7486i	−0.284947	−	0.493542i
$894$	−76.0813	+	30.4113i	−2.54454	+	1.01711i
$895$	−5.17341	+	8.96060i	−0.172928	+	0.299520i
$896$	34.8133	−	60.2985i	1.16303	−	2.01443i
$897$	2.87252	+	2.26146i	0.0959108	+	0.0755078i
$898$	6.13979	+	10.6344i	0.204887	+	0.354876i
$899$	−21.8514			−0.728785
$900$	−53.0197	+	50.4464i	−1.76732	+	1.68155i
$901$	4.97025			0.165583
$902$		0			0
$903$	8.59868	−	59.5798i	0.286146	−	1.98269i
$904$	76.5994	−	132.674i	2.54766	−	4.41267i
$905$	−3.05216	+	5.28650i	−0.101457	+	0.175729i
$906$	−11.9385	+	82.7210i	−0.396629	+	2.74822i
$907$	−0.274115	−	0.474782i	−0.00910185	−	0.0157649i	0.861439	−	0.507862i	$-0.169564\pi$
$907$	−0.274115	−	0.474782i	−0.00910185	−	0.0157649i	−0.870540	+	0.492097i	$0.836231\pi$
$908$	−36.6354			−1.21579
$909$	−24.0516	−	7.09004i	−0.797742	−	0.235162i
$910$	−4.64241			−0.153894
$911$	9.40470	+	16.2894i	0.311592	+	0.539692i	0.978707	−	0.205262i	$-0.0658046\pi$
$911$	9.40470	+	16.2894i	0.311592	+	0.539692i	−0.667116	+	0.744954i	$0.732471\pi$
$912$	39.5366	+	31.1260i	1.30919	+	1.03069i
$913$		0			0
$914$	−14.6875	+	25.4394i	−0.485818	+	0.841461i
$915$	−1.64878	+	0.659052i	−0.0545069	+	0.0217876i
$916$	−42.0430	−	72.8206i	−1.38914	−	2.40606i
$917$	−38.9931			−1.28767
$918$	21.4425	−	2.01294i	0.707709	−	0.0664368i
$919$	−31.1901			−1.02886			−0.514432	−	0.857531i	$-0.671997\pi$
$919$	−31.1901			−1.02886			−0.514432	+	0.857531i	$0.671997\pi$
$920$	5.75576	+	9.96927i	0.189762	+	0.328677i
$921$	4.76822	−	1.90596i	0.157118	−	0.0628035i
$922$	−35.5038	+	61.4943i	−1.16925	+	2.02521i
$923$	2.61430	−	4.52810i	0.0860508	−	0.149044i
$924$		0			0
$925$	−15.5259	−	26.8916i	−0.510488	−	0.884191i
$926$	−29.3336			−0.963963
$927$	−0.226645	−	0.938607i	−0.00744400	−	0.0308279i
$928$	−71.6462			−2.35190
$929$	25.4124	+	44.0156i	0.833755	+	1.44411i	0.895040	+	0.445986i	$0.147147\pi$
$929$	25.4124	+	44.0156i	0.833755	+	1.44411i	−0.0612848	+	0.998120i	$0.519520\pi$
$930$	−1.54356	+	10.6953i	−0.0506153	+	0.350711i
$931$	−17.4269	+	30.1843i	−0.571144	+	0.989251i
$932$	75.3178	−	130.454i	2.46712	−	4.27317i
$933$	1.06383	−	7.37123i	0.0348283	−	0.241323i
$934$	37.3708	+	64.7281i	1.22281	+	2.11797i
$935$		0			0
$936$	4.46334	+	18.4841i	0.145889	+	0.604171i
$937$	−32.0738			−1.04781			−0.523903	−	0.851778i	$-0.675524\pi$
$937$	−32.0738			−1.04781			−0.523903	+	0.851778i	$0.675524\pi$
$938$	−20.7030	−	35.8586i	−0.675977	−	1.17083i
$939$	−5.65205	−	4.44970i	−0.184448	−	0.145210i
$940$	8.97190	−	15.5398i	0.292631	−	0.506852i
$941$	−3.23625	+	5.60536i	−0.105499	+	0.182729i	−0.913942	−	0.405845i	$-0.866977\pi$
$941$	−3.23625	+	5.60536i	−0.105499	+	0.182729i	0.808443	+	0.588574i	$0.200311\pi$
$942$	−76.0858	+	30.4131i	−2.47901	+	0.990913i
$943$	−11.6320	−	20.1473i	−0.378791	−	0.656086i
$944$	−110.219			−3.58732
$945$	4.96603	−	10.8283i	0.161545	−	0.352243i
$946$		0			0
$947$	16.0363	+	27.7758i	0.521111	+	0.902591i	0.999699	+	0.0245509i	$0.00781557\pi$
$947$	16.0363	+	27.7758i	0.521111	+	0.902591i	−0.478588	+	0.878040i	$0.658851\pi$
$948$	5.29452	−	2.11634i	0.171958	−	0.0687354i
$949$	0.586479	−	1.01581i	0.0190379	−	0.0329747i
$950$	−15.2956	+	26.4928i	−0.496256	+	0.859541i
$951$	29.2310	+	23.0127i	0.947880	+	0.746239i
$952$	−30.0551	−	52.0570i	−0.974092	−	1.68718i
$953$	28.3525			0.918427			0.459213	−	0.888326i	$-0.348131\pi$
$953$	28.3525			0.918427			0.459213	+	0.888326i	$0.348131\pi$
$954$	−24.6040	−	7.25287i	−0.796584	−	0.234820i
$955$	1.06083			0.0343275
$956$	−15.2598	−	26.4307i	−0.493536	−	0.854829i
$957$		0			0
$958$	−46.7263	+	80.9323i	−1.50966	+	2.61480i
$959$	1.89653	−	3.28488i	0.0612420	−	0.106074i
$960$	−2.10859	+	14.6103i	−0.0680544	+	0.471545i
$961$	4.35218	+	7.53819i	0.140393	+	0.243167i
$962$	−13.2232			−0.426333
$963$	−6.05705	+	5.76308i	−0.195186	+	0.185713i
$964$	−26.0429			−0.838785
$965$	−3.41498	−	5.91492i	−0.109932	−	0.190408i
$966$	46.8630	+	36.8939i	1.50779	+	1.18704i
$967$	−22.4732	+	38.9247i	−0.722689	+	1.25173i	0.237229	+	0.971454i	$0.423761\pi$
$967$	−22.4732	+	38.9247i	−0.722689	+	1.25173i	−0.959918	+	0.280281i	$0.909572\pi$
$968$		0			0
$969$	6.01459	−	2.40416i	0.193217	−	0.0772328i
$970$	11.6554	+	20.1877i	0.374231	+	0.648188i
$971$	−35.4235			−1.13679			−0.568396	−	0.822755i	$-0.692436\pi$
$971$	−35.4235			−1.13679			−0.568396	+	0.822755i	$0.692436\pi$
$972$	−78.4856	−	15.3438i	−2.51743	−	0.492152i
$973$	−46.4215			−1.48820
$974$	1.99023	+	3.44718i	0.0637710	+	0.110455i
$975$	−5.79966	+	2.31825i	−0.185738	+	0.0742434i
$976$	12.4910	−	21.6350i	0.399827	−	0.692521i
$977$	−5.26146	+	9.11311i	−0.168329	+	0.291554i	−0.937832	−	0.347088i	$-0.887170\pi$
$977$	−5.26146	+	9.11311i	−0.168329	+	0.291554i	0.769504	+	0.638643i	$0.220504\pi$
$978$	−7.73373	−	6.08854i	−0.247297	−	0.194690i
$979$		0			0
$980$	−36.7236			−1.17309
$981$	22.5916	−	21.4951i	0.721293	−	0.686286i
$982$	−49.1641			−1.56889
$983$	−8.50360	−	14.7287i	−0.271223	−	0.469772i	0.697952	−	0.716144i	$-0.254095\pi$
$983$	−8.50360	−	14.7287i	−0.271223	−	0.469772i	−0.969175	+	0.246373i	$0.920761\pi$
$984$	17.2843	−	119.762i	0.551003	−	3.81787i
$985$	−0.347732	+	0.602290i	−0.0110797	+	0.0191906i
$986$	−9.59044	+	16.6111i	−0.305422	+	0.529006i
$987$	8.10279	−	56.1438i	0.257915	−	1.78708i
$988$	4.68651	+	8.11728i	0.149098	+	0.258245i
$989$	−20.8786			−0.663901
$990$		0			0
$991$	61.6979			1.95990			0.979949	−	0.199251i	$-0.0638509\pi$
$991$	61.6979			1.95990			0.979949	+	0.199251i	$0.0638509\pi$
$992$	−36.5514	−	63.3089i	−1.16051	−	2.01006i
$993$	26.5135	+	20.8733i	0.841379	+	0.662394i
$994$	42.6503	−	73.8725i	1.35279	−	2.34309i
$995$	1.99626	−	3.45762i	0.0632857	−	0.109614i
$996$	−79.6178	+	31.8250i	−2.52279	+	1.00841i
$997$	−13.0678	−	22.6340i	−0.413860	−	0.716827i	0.581448	−	0.813584i	$-0.302487\pi$
$997$	−13.0678	−	22.6340i	−0.413860	−	0.716827i	−0.995308	+	0.0967565i	$0.969153\pi$
$998$	−86.2950			−2.73162
$999$	14.1450	−	30.8427i	0.447528	−	0.975819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.k.364.8	yes	16
9.4	even	3		9801.2.a.bz.1.1		8
9.5	odd	6		9801.2.a.ca.1.8		8
9.7	even	3	inner	1089.2.e.k.727.8	yes	16
11.10	odd	2	inner	1089.2.e.k.364.1	✓	16
99.32	even	6		9801.2.a.ca.1.1		8
99.43	odd	6	inner	1089.2.e.k.727.1	yes	16
99.76	odd	6		9801.2.a.bz.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1089.2.e.k.364.1	✓	16	11.10	odd	2	inner
1089.2.e.k.364.8	yes	16	1.1	even	1	trivial
1089.2.e.k.727.1	yes	16	99.43	odd	6	inner
1089.2.e.k.727.8	yes	16	9.7	even	3	inner
9801.2.a.bz.1.1		8	9.4	even	3
9801.2.a.bz.1.8		8	99.76	odd	6
9801.2.a.ca.1.1		8	99.32	even	6
9801.2.a.ca.1.8		8	9.5	odd	6

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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33512 + 2.31249i) q^{2} +(-1.60832 + 0.642882i) q^{3} +(-2.56508 + 4.44285i) q^{4} +(0.247410 - 0.428526i) q^{5} +(-3.63396 - 2.86091i) q^{6} +(-2.31660 - 4.01248i) q^{7} -8.35829 q^{8} +(2.17341 - 2.06792i) q^{9} +O(q^{10})\)	\(q+(1.33512 + 2.31249i) q^{2} +(-1.60832 + 0.642882i) q^{3} +(-2.56508 + 4.44285i) q^{4} +(0.247410 - 0.428526i) q^{5} +(-3.63396 - 2.86091i) q^{6} +(-2.31660 - 4.01248i) q^{7} -8.35829 q^{8} +(2.17341 - 2.06792i) q^{9} +1.32129 q^{10} +(1.26925 - 8.79459i) q^{12} +(0.379171 - 0.656743i) q^{13} +(6.18588 - 10.7143i) q^{14} +(-0.122423 + 0.848264i) q^{15} +(-6.02914 - 10.4428i) q^{16} -1.55221 q^{17} +(7.68381 + 2.26507i) q^{18} +2.40926 q^{19} +(1.26925 + 2.19841i) q^{20} +(6.30539 + 4.96406i) q^{21} +(1.39168 - 2.41046i) q^{23} +(13.4428 - 5.37339i) q^{24} +(2.37758 + 4.11808i) q^{25} +2.02495 q^{26} +(-2.16611 + 4.72313i) q^{27} +23.7691 q^{28} +(-2.31387 - 4.00774i) q^{29} +(-2.12505 + 0.849430i) q^{30} +(2.36091 - 4.08922i) q^{31} +(7.74094 - 13.4077i) q^{32} +(-2.07238 - 3.58947i) q^{34} -2.29260 q^{35} +(3.61251 + 14.9605i) q^{36} -6.53013 q^{37} +(3.21665 + 5.57139i) q^{38} +(-0.187621 + 1.30002i) q^{39} +(-2.06792 + 3.58175i) q^{40} +(4.17914 - 7.23849i) q^{41} +(-3.06090 + 21.2088i) q^{42} +(-3.75062 - 6.49626i) q^{43} +(-0.348437 - 1.44299i) q^{45} +7.43221 q^{46} +(-3.53432 - 6.12162i) q^{47} +(16.4103 + 12.9193i) q^{48} +(-7.23331 + 12.5285i) q^{49} +(-6.34869 + 10.9963i) q^{50} +(2.49645 - 0.997885i) q^{51} +(1.94521 + 3.36920i) q^{52} -3.20205 q^{53} +(-13.8142 + 1.29682i) q^{54} +(19.3628 + 33.5374i) q^{56} +(-3.87487 + 1.54887i) q^{57} +(6.17859 - 10.7016i) q^{58} +(4.57026 - 7.91593i) q^{59} +(-3.45469 - 2.71978i) q^{60} +(1.03589 + 1.79421i) q^{61} +12.6084 q^{62} +(-13.3324 - 3.93018i) q^{63} +17.2238 q^{64} +(-0.187621 - 0.324969i) q^{65} +(1.67341 - 2.89843i) q^{67} +(3.98154 - 6.89623i) q^{68} +(-0.688629 + 4.77147i) q^{69} +(-3.06090 - 5.30163i) q^{70} +6.89479 q^{71} +(-18.1660 + 17.2843i) q^{72} +1.54674 q^{73} +(-8.71850 - 15.1009i) q^{74} +(-6.47135 - 5.09471i) q^{75} +(-6.17995 + 10.7040i) q^{76} +(-3.25678 + 1.30180i) q^{78} +(0.320843 + 0.555716i) q^{79} -5.96667 q^{80} +(0.447393 - 8.98887i) q^{81} +22.3186 q^{82} +(-4.82476 - 8.35673i) q^{83} +(-38.2284 + 15.2807i) q^{84} +(-0.384031 + 0.665161i) q^{85} +(10.0150 - 17.3466i) q^{86} +(6.29796 + 4.95820i) q^{87} -13.2092 q^{89} +(2.87169 - 2.73232i) q^{90} -3.51356 q^{91} +(7.13953 + 12.3660i) q^{92} +(-1.16823 + 8.09458i) q^{93} +(9.43747 - 16.3462i) q^{94} +(0.596074 - 1.03243i) q^{95} +(-3.83037 + 26.5404i) q^{96} +(8.82123 + 15.2788i) q^{97} -38.6293 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9	\( 16 q - 2 q^{3} - 16 q^{4} + 4 q^{5} - 14 q^{9} - 6 q^{12} + 4 q^{14} - 52 q^{15} - 24 q^{16} - 6 q^{20} + 46 q^{23} - 12 q^{25} - 60 q^{26} - 32 q^{27} + 14 q^{31} + 38 q^{34} + 54 q^{36} - 12 q^{37} + 4 q^{38} - 4 q^{42} - 28 q^{45} + 16 q^{47} + 20 q^{48} - 42 q^{49} - 96 q^{53} + 46 q^{56} + 50 q^{58} + 48 q^{59} + 12 q^{60} - 12 q^{64} - 22 q^{67} - 10 q^{69} - 4 q^{70} + 68 q^{71} - 10 q^{75} - 72 q^{78} - 148 q^{80} - 14 q^{81} + 112 q^{82} + 14 q^{86} - 16 q^{89} - 96 q^{91} + 84 q^{92} + 30 q^{93} - 4 q^{97}+O(q^{100}) \) 16 * q - 2 * q^3 - 16 * q^4 + 4 * q^5 - 14 * q^9 - 6 * q^12 + 4 * q^14 - 52 * q^15 - 24 * q^16 - 6 * q^20 + 46 * q^23 - 12 * q^25 - 60 * q^26 - 32 * q^27 + 14 * q^31 + 38 * q^34 + 54 * q^36 - 12 * q^37 + 4 * q^38 - 4 * q^42 - 28 * q^45 + 16 * q^47 + 20 * q^48 - 42 * q^49 - 96 * q^53 + 46 * q^56 + 50 * q^58 + 48 * q^59 + 12 * q^60 - 12 * q^64 - 22 * q^67 - 10 * q^69 - 4 * q^70 + 68 * q^71 - 10 * q^75 - 72 * q^78 - 148 * q^80 - 14 * q^81 + 112 * q^82 + 14 * q^86 - 16 * q^89 - 96 * q^91 + 84 * q^92 + 30 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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