LMFDB - Embedded newform 1089.2.e.k.364.6

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			364.6
Root			$-0.485097 - 1.32841i$ of defining polynomial
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.k.727.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.907891 + 1.57251i) q^{2} +(0.691682 + 1.58795i) q^{3} +(-0.648531 + 1.12329i) q^{4} +(-1.72104 + 2.98093i) q^{5} +(-1.86910 + 2.52936i) q^{6} +(0.575887 + 0.997466i) q^{7} +1.27638 q^{8} +(-2.04315 + 2.19671i) q^{9} +O(q^{10})$	\(q+(0.907891 + 1.57251i) q^{2} +(0.691682 + 1.58795i) q^{3} +(-0.648531 + 1.12329i) q^{4} +(-1.72104 + 2.98093i) q^{5} +(-1.86910 + 2.52936i) q^{6} +(0.575887 + 0.997466i) q^{7} +1.27638 q^{8} +(-2.04315 + 2.19671i) q^{9} -6.25008 q^{10} +(-2.23230 - 0.252874i) q^{12} +(-1.10285 + 1.91019i) q^{13} +(-1.04569 + 1.81118i) q^{14} +(-5.92398 - 0.671066i) q^{15} +(2.45588 + 4.25370i) q^{16} +7.48558 q^{17} +(-5.30931 - 1.21851i) q^{18} -1.52371 q^{19} +(-2.23230 - 3.86646i) q^{20} +(-1.18559 + 1.60441i) q^{21} +(3.69168 - 6.39418i) q^{23} +(0.882851 + 2.02683i) q^{24} +(-3.42398 - 5.93051i) q^{25} -4.00507 q^{26} +(-4.90147 - 1.72499i) q^{27} -1.49392 q^{28} +(-3.24870 - 5.62692i) q^{29} +(-4.32307 - 9.92479i) q^{30} +(2.02936 - 3.51496i) q^{31} +(-3.18295 + 5.51304i) q^{32} +(6.79609 + 11.7712i) q^{34} -3.96451 q^{35} +(-1.14249 - 3.71968i) q^{36} -4.43702 q^{37} +(-1.38336 - 2.39606i) q^{38} +(-3.79610 - 0.430021i) q^{39} +(-2.19671 + 3.80481i) q^{40} +(-0.638191 + 1.10538i) q^{41} +(-3.59934 - 0.407732i) q^{42} +(3.61913 + 6.26851i) q^{43} +(-3.03190 - 9.87113i) q^{45} +13.4066 q^{46} +(1.01379 + 1.75594i) q^{47} +(-5.05597 + 6.84201i) q^{48} +(2.83671 - 4.91332i) q^{49} +(6.21720 - 10.7685i) q^{50} +(5.17764 + 11.8867i) q^{51} +(-1.43046 - 2.47764i) q^{52} -12.5059 q^{53} +(-1.73743 - 9.27373i) q^{54} +(0.735052 + 1.27315i) q^{56} +(-1.05392 - 2.41957i) q^{57} +(5.89894 - 10.2173i) q^{58} +(6.59062 - 11.4153i) q^{59} +(4.59569 - 6.21913i) q^{60} +(4.46717 + 7.73737i) q^{61} +7.36975 q^{62} +(-3.36777 - 0.772917i) q^{63} -1.73559 q^{64} +(-3.79610 - 6.57505i) q^{65} +(-2.54315 + 4.40487i) q^{67} +(-4.85463 + 8.40847i) q^{68} +(12.7071 + 1.43945i) q^{69} +(-3.59934 - 6.23424i) q^{70} +4.69787 q^{71} +(-2.60784 + 2.80384i) q^{72} +0.163600 q^{73} +(-4.02833 - 6.97727i) q^{74} +(7.04903 - 9.53913i) q^{75} +(0.988175 - 1.71157i) q^{76} +(-2.77023 - 6.35984i) q^{78} +(1.64126 + 2.84275i) q^{79} -16.9067 q^{80} +(-0.651065 - 8.97642i) q^{81} -2.31763 q^{82} +(6.05073 + 10.4802i) q^{83} +(-1.03332 - 2.37227i) q^{84} +(-12.8830 + 22.3140i) q^{85} +(-6.57154 + 11.3822i) q^{86} +(6.68818 - 9.05081i) q^{87} -8.15366 q^{89} +(12.7699 - 13.7296i) q^{90} -2.54047 q^{91} +(4.78834 + 8.29365i) q^{92} +(6.98524 + 0.791285i) q^{93} +(-1.84082 + 3.18840i) q^{94} +(2.62238 - 4.54209i) q^{95} +(-10.9560 - 1.24109i) q^{96} +(1.69346 + 2.93316i) q^{97} +10.3017 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 $

$2$	0.907891	+	1.57251i	0.641976	+	1.11193i	0.984991	+	0.172605i	$0.0552183\pi$
$2$	0.907891	+	1.57251i	0.641976	+	1.11193i	−0.343016	+	0.939330i	$0.611448\pi$
$3$	0.691682	+	1.58795i	0.399343	+	0.916802i
$3$	0.691682	+	1.58795i	0.399343	+	0.916802i
$4$	−0.648531	+	1.12329i	−0.324265	+	0.561644i
$5$	−1.72104	+	2.98093i	−0.769674	+	1.33311i	0.168066	+	0.985776i	$0.446248\pi$
$5$	−1.72104	+	2.98093i	−0.769674	+	1.33311i	−0.937740	+	0.347339i	$0.887085\pi$
$6$	−1.86910	+	2.52936i	−0.763055	+	1.03261i
$7$	0.575887	+	0.997466i	0.217665	+	0.377007i	0.954094	−	0.299508i	$-0.0968227\pi$
$7$	0.575887	+	0.997466i	0.217665	+	0.377007i	−0.736429	+	0.676515i	$0.763489\pi$
$8$	1.27638			0.451269
$9$	−2.04315	+	2.19671i	−0.681050	+	0.732236i
$10$	−6.25008			−1.97645
$11$		0			0
$11$		0			0
$12$	−2.23230	−	0.252874i	−0.644409	−	0.0729984i
$13$	−1.10285	+	1.91019i	−0.305875	+	0.529792i	−0.977456	−	0.211140i	$-0.932282\pi$
$13$	−1.10285	+	1.91019i	−0.305875	+	0.529792i	0.671580	+	0.740932i	$0.265616\pi$
$14$	−1.04569	+	1.81118i	−0.279471	+	0.484058i
$15$	−5.92398	−	0.671066i	−1.52957	−	0.173269i
$16$	2.45588	+	4.25370i	0.613969	+	1.06343i
$17$	7.48558			1.81552			0.907760	−	0.419489i	$-0.137791\pi$
$17$	7.48558			1.81552			0.907760	+	0.419489i	$0.137791\pi$
$18$	−5.30931	−	1.21851i	−1.25142	−	0.287205i
$19$	−1.52371			−0.349564			−0.174782	−	0.984607i	$-0.555922\pi$
$19$	−1.52371			−0.349564			−0.174782	+	0.984607i	$0.555922\pi$
$20$	−2.23230	−	3.86646i	−0.499157	−	0.864566i
$21$	−1.18559	+	1.60441i	−0.258717	+	0.350111i
$22$		0			0
$23$	3.69168	−	6.39418i	0.769769	−	1.33328i	−0.167919	−	0.985801i	$-0.553705\pi$
$23$	3.69168	−	6.39418i	0.769769	−	1.33328i	0.937688	−	0.347478i	$-0.112962\pi$
$24$	0.882851	+	2.02683i	0.180211	+	0.413724i
$25$	−3.42398	−	5.93051i	−0.684796	−	1.18610i
$26$	−4.00507			−0.785458
$27$	−4.90147	−	1.72499i	−0.943288	−	0.331975i
$28$	−1.49392			−0.282325
$29$	−3.24870	−	5.62692i	−0.603269	−	1.04489i	−0.992322	−	0.123678i	$-0.960531\pi$
$29$	−3.24870	−	5.62692i	−0.603269	−	1.04489i	0.389053	−	0.921215i	$-0.372802\pi$
$30$	−4.32307	−	9.92479i	−0.789281	−	1.81201i
$31$	2.02936	−	3.51496i	0.364484	−	0.631305i	−0.624209	−	0.781257i	$-0.714579\pi$
$31$	2.02936	−	3.51496i	0.364484	−	0.631305i	0.988693	+	0.149952i	$0.0479120\pi$
$32$	−3.18295	+	5.51304i	−0.562672	+	0.974577i
$33$		0			0
$34$	6.79609	+	11.7712i	1.16552	+	2.01874i
$35$	−3.96451			−0.670124
$36$	−1.14249	−	3.71968i	−0.190415	−	0.619947i
$37$	−4.43702			−0.729441			−0.364721	−	0.931117i	$-0.618836\pi$
$37$	−4.43702			−0.729441			−0.364721	+	0.931117i	$0.618836\pi$
$38$	−1.38336	−	2.39606i	−0.224411	−	0.388692i
$39$	−3.79610	−	0.430021i	−0.607863	−	0.0688585i
$40$	−2.19671	+	3.80481i	−0.347330	+	0.601594i
$41$	−0.638191	+	1.10538i	−0.0996687	+	0.172631i	−0.911548	−	0.411195i	$-0.865112\pi$
$41$	−0.638191	+	1.10538i	−0.0996687	+	0.172631i	0.811879	+	0.583826i	$0.198445\pi$
$42$	−3.59934	−	0.407732i	−0.555390	−	0.0629144i
$43$	3.61913	+	6.26851i	0.551912	+	0.955939i	0.998137	+	0.0610181i	$0.0194347\pi$
$43$	3.61913	+	6.26851i	0.551912	+	0.955939i	−0.446225	+	0.894921i	$0.647232\pi$
$44$		0			0
$45$	−3.03190	−	9.87113i	−0.451968	−	1.47150i
$46$	13.4066			1.97669
$47$	1.01379	+	1.75594i	0.147876	+	0.256130i	0.930442	−	0.366438i	$-0.119423\pi$
$47$	1.01379	+	1.75594i	0.147876	+	0.256130i	−0.782566	+	0.622568i	$0.786090\pi$
$48$	−5.05597	+	6.84201i	−0.729766	+	0.987560i
$49$	2.83671	−	4.91332i	0.405244	−	0.701903i
$50$	6.21720	−	10.7685i	0.879245	−	1.52290i
$51$	5.17764	+	11.8867i	0.725015	+	1.66447i
$52$	−1.43046	−	2.47764i	−0.198370	−	0.343586i
$53$	−12.5059			−1.71781			−0.858907	−	0.512131i	$-0.828856\pi$
$53$	−12.5059			−1.71781			−0.858907	+	0.512131i	$0.828856\pi$
$54$	−1.73743	−	9.27373i	−0.236434	−	1.26199i
$55$		0			0
$56$	0.735052	+	1.27315i	0.0982255	+	0.170132i
$57$	−1.05392	−	2.41957i	−0.139596	−	0.320481i
$58$	5.89894	−	10.2173i	0.774568	−	1.34159i
$59$	6.59062	−	11.4153i	0.858025	−	1.48614i	−0.0157843	−	0.999875i	$-0.505025\pi$
$59$	6.59062	−	11.4153i	0.858025	−	1.48614i	0.873810	−	0.486268i	$-0.161642\pi$
$60$	4.59569	−	6.21913i	0.593300	−	0.802887i
$61$	4.46717	+	7.73737i	0.571963	+	0.990668i	0.996364	+	0.0851944i	$0.0271511\pi$
$61$	4.46717	+	7.73737i	0.571963	+	0.990668i	−0.424402	+	0.905474i	$0.639516\pi$
$62$	7.36975			0.935960
$63$	−3.36777	−	0.772917i	−0.424299	−	0.0973784i
$64$	−1.73559			−0.216948
$65$	−3.79610	−	6.57505i	−0.470849	−	0.815534i
$66$		0			0
$67$	−2.54315	+	4.40487i	−0.310695	+	0.538140i	−0.978513	−	0.206185i	$-0.933895\pi$
$67$	−2.54315	+	4.40487i	−0.310695	+	0.538140i	0.667818	+	0.744325i	$0.267229\pi$
$68$	−4.85463	+	8.40847i	−0.588710	+	1.01968i
$69$	12.7071	+	1.43945i	1.52975	+	0.173290i
$70$	−3.59934	−	6.23424i	−0.430203	−	0.745134i
$71$	4.69787			0.557535			0.278767	−	0.960359i	$-0.410074\pi$
$71$	4.69787			0.557535			0.278767	+	0.960359i	$0.410074\pi$
$72$	−2.60784	+	2.80384i	−0.307337	+	0.330436i
$73$	0.163600			0.0191479			0.00957396	−	0.999954i	$-0.496952\pi$
$73$	0.163600			0.0191479			0.00957396	+	0.999954i	$0.496952\pi$
$74$	−4.02833	−	6.97727i	−0.468284	−	0.811091i
$75$	7.04903	−	9.53913i	0.813952	−	1.10148i
$76$	0.988175	−	1.71157i	0.113351	−	0.196330i
$77$		0			0
$78$	−2.77023	−	6.35984i	−0.313667	−	0.720110i
$79$	1.64126	+	2.84275i	0.184656	+	0.319834i	0.943461	−	0.331485i	$-0.107549\pi$
$79$	1.64126	+	2.84275i	0.184656	+	0.319834i	−0.758804	+	0.651319i	$0.774216\pi$
$80$	−16.9067			−1.89023
$81$	−0.651065	−	8.97642i	−0.0723405	−	0.997380i
$82$	−2.31763			−0.255940
$83$	6.05073	+	10.4802i	0.664154	+	1.15035i	0.979514	+	0.201376i	$0.0645413\pi$
$83$	6.05073	+	10.4802i	0.664154	+	1.15035i	−0.315360	+	0.948972i	$0.602125\pi$
$84$	−1.03332	−	2.37227i	−0.112744	−	0.258836i
$85$	−12.8830	+	22.3140i	−1.39736	+	2.42030i
$86$	−6.57154	+	11.3822i	−0.708628	+	1.22738i
$87$	6.68818	−	9.05081i	0.717048	−	0.970349i
$88$		0			0
$89$	−8.15366			−0.864286			−0.432143	−	0.901805i	$-0.642242\pi$
$89$	−8.15366			−0.864286			−0.432143	+	0.901805i	$0.642242\pi$
$90$	12.7699	−	13.7296i	1.34606	−	1.44723i
$91$	−2.54047			−0.266313
$92$	4.78834	+	8.29365i	0.499219	+	0.864673i
$93$	6.98524	+	0.791285i	0.724335	+	0.0820524i
$94$	−1.84082	+	3.18840i	−0.189866	+	0.328858i
$95$	2.62238	−	4.54209i	0.269050	−	0.466008i
$96$	−10.9560	−	1.24109i	−1.11819	−	0.126668i
$97$	1.69346	+	2.93316i	0.171945	+	0.297818i	0.939100	−	0.343644i	$-0.111661\pi$
$97$	1.69346	+	2.93316i	0.171945	+	0.297818i	−0.767155	+	0.641462i	$0.778328\pi$
$98$	10.3017			1.04063
$99$		0			0
$100$	8.88223			0.888223
$101$	0.638191	+	1.10538i	0.0635024	+	0.109989i	0.896029	−	0.443996i	$-0.146440\pi$
$101$	0.638191	+	1.10538i	0.0635024	+	0.109989i	−0.832526	+	0.553986i	$0.813106\pi$
$102$	−13.9913	+	18.9337i	−1.38534	+	1.87472i
$103$	−1.04062	+	1.80240i	−0.102535	+	0.177596i	−0.912728	−	0.408567i	$-0.866029\pi$
$103$	−1.04062	+	1.80240i	−0.102535	+	0.177596i	0.810193	+	0.586163i	$0.199362\pi$
$104$	−1.40766	+	2.43813i	−0.138032	+	0.239079i
$105$	−2.74218	−	6.29543i	−0.267609	−	0.614371i
$106$	−11.3540	−	19.6657i	−1.10279	−	1.91010i
$107$	3.67244			0.355028			0.177514	−	0.984118i	$-0.443194\pi$
$107$	3.67244			0.355028			0.177514	+	0.984118i	$0.443194\pi$
$108$	5.11642	−	4.38705i	0.492327	−	0.422144i
$109$	10.7321			1.02795			0.513976	−	0.857804i	$-0.328172\pi$
$109$	10.7321			1.02795			0.513976	+	0.857804i	$0.328172\pi$
$110$		0			0
$111$	−3.06901	−	7.04575i	−0.291297	−	0.668753i
$112$	−2.82862	+	4.89931i	−0.267279	+	0.462941i
$113$	−0.783272	+	1.35667i	−0.0736840	+	0.127624i	−0.900513	−	0.434829i	$-0.856809\pi$
$113$	−0.783272	+	1.35667i	−0.0736840	+	0.127624i	0.826829	+	0.562453i	$0.190142\pi$
$114$	2.84796	−	3.85402i	0.266736	−	0.360962i
$115$	12.7071	+	22.0093i	1.18494	+	2.05238i
$116$	8.42754			0.782477
$117$	−1.94285	−	6.32545i	−0.179616	−	0.584788i
$118$	23.9342			2.20333
$119$	4.31085	+	7.46661i	0.395175	+	0.684463i
$120$	−7.56127	−	0.856537i	−0.690246	−	0.0781908i
$121$		0			0
$122$	−8.11141	+	14.0494i	−0.734372	+	1.27197i
$123$	−2.19671	−	0.248842i	−0.198071	−	0.0224374i
$124$	2.63221	+	4.55912i	0.236379	+	0.409421i
$125$	6.36085			0.568932
$126$	−1.84214	−	5.99758i	−0.164111	−	0.534307i
$127$	−21.0255			−1.86572			−0.932858	−	0.360245i	$-0.882693\pi$
$127$	−21.0255			−1.86572			−0.932858	+	0.360245i	$0.882693\pi$
$128$	4.79018	+	8.29684i	0.423396	+	0.733344i
$129$	−7.45078	+	10.0828i	−0.656004	+	0.887741i
$130$	6.89290	−	11.9388i	0.604547	−	1.04711i
$131$	8.80728	−	15.2547i	0.769495	−	1.33280i	−0.168342	−	0.985729i	$-0.553841\pi$
$131$	8.80728	−	15.2547i	0.769495	−	1.33280i	0.937837	−	0.347076i	$-0.112825\pi$
$132$		0			0
$133$	−0.877487	−	1.51985i	−0.0760877	−	0.131788i
$134$	−9.23561			−0.797835
$135$	13.5777	−	11.6422i	1.16858	−	1.00200i
$136$	9.55446			0.819289
$137$	3.63124	+	6.28948i	0.310237	+	0.537347i	0.978414	−	0.206656i	$-0.0662581\pi$
$137$	3.63124	+	6.28948i	0.310237	+	0.537347i	−0.668176	+	0.744003i	$0.732925\pi$
$138$	9.27309	+	21.2889i	0.789378	+	1.81223i
$139$	1.56997	−	2.71926i	0.133163	−	0.230645i	−0.791731	−	0.610869i	$-0.790820\pi$
$139$	1.56997	−	2.71926i	0.133163	−	0.230645i	0.924894	+	0.380225i	$0.124153\pi$
$140$	2.57111	−	4.45329i	0.217298	−	0.376371i
$141$	−2.08711	+	2.82439i	−0.175767	+	0.237857i
$142$	4.26515	+	7.38746i	0.357924	+	0.619942i
$143$		0			0
$144$	−14.3619	−	3.29611i	−1.19682	−	0.274676i
$145$	22.3646			1.85728
$146$	0.148531	+	0.257263i	0.0122925	+	0.0212912i
$147$	9.76419	+	1.10608i	0.805337	+	0.0912283i
$148$	2.87754	−	4.98405i	0.236533	−	0.409687i
$149$	10.9889	−	19.0333i	0.900244	−	1.55927i	0.0730669	−	0.997327i	$-0.476721\pi$
$149$	10.9889	−	19.0333i	0.900244	−	1.55927i	0.827177	−	0.561941i	$-0.189945\pi$
$150$	21.4002	+	2.42420i	1.74732	+	0.197935i
$151$	1.06804	+	1.84991i	0.0869162	+	0.150543i	0.906206	−	0.422836i	$-0.138965\pi$
$151$	1.06804	+	1.84991i	0.0869162	+	0.150543i	−0.819290	+	0.573379i	$0.805632\pi$
$152$	−1.94484			−0.157747
$153$	−15.2942	+	16.4436i	−1.23646	+	1.32939i
$154$		0			0
$155$	6.98524	+	12.0988i	0.561068	+	0.971798i
$156$	2.94493	−	3.98524i	0.235783	−	0.319074i
$157$	−8.98173	+	15.5568i	−0.716820	+	1.24157i	0.245433	+	0.969414i	$0.421070\pi$
$157$	−8.98173	+	15.5568i	−0.716820	+	1.24157i	−0.962253	+	0.272156i	$0.912263\pi$
$158$	−2.98017	+	5.16181i	−0.237090	+	0.410651i
$159$	−8.65009	−	19.8587i	−0.685997	−	1.57490i
$160$	−10.9560	−	18.9764i	−0.866148	−	1.50021i
$161$	8.50397			0.670207
$162$	13.5244	−	9.17342i	1.06258	−	0.720732i
$163$	−14.4887			−1.13485			−0.567423	−	0.823427i	$-0.692059\pi$
$163$	−14.4887			−1.13485			−0.567423	+	0.823427i	$0.692059\pi$
$164$	−0.827773	−	1.43375i	−0.0646382	−	0.111957i
$165$		0			0
$166$	−10.9868	+	19.0297i	−0.852741	+	1.47699i
$167$	−0.798593	+	1.38320i	−0.0617969	+	0.107035i	−0.895269	−	0.445527i	$-0.853016\pi$
$167$	−0.798593	+	1.38320i	−0.0617969	+	0.107035i	0.833472	+	0.552562i	$0.186350\pi$
$168$	−1.51327	+	2.04784i	−0.116751	+	0.157994i
$169$	4.06744	+	7.04502i	0.312880	+	0.541925i
$170$	−46.7855			−3.58828
$171$	3.11318	−	3.34715i	0.238070	−	0.255963i
$172$	−9.38846			−0.715863
$173$	1.75594	+	3.04137i	0.133501	+	0.231231i	0.925024	−	0.379909i	$-0.124045\pi$
$173$	1.75594	+	3.04137i	0.133501	+	0.231231i	−0.791523	+	0.611140i	$0.790711\pi$
$174$	20.3047	+	2.30010i	1.53929	+	0.174370i
$175$	3.94366	−	6.83061i	0.298112	−	0.516346i
$176$		0			0
$177$	22.6855	+	2.56980i	1.70515	+	0.193158i
$178$	−7.40263	−	12.8217i	−0.554850	−	0.961029i
$179$	0.555970			0.0415551			0.0207776	−	0.999784i	$-0.493386\pi$
$179$	0.555970			0.0415551			0.0207776	+	0.999784i	$0.493386\pi$
$180$	13.0544	+	2.99604i	0.973018	+	0.223312i
$181$	3.97048			0.295123			0.147562	−	0.989053i	$-0.452858\pi$
$181$	3.97048			0.295123			0.147562	+	0.989053i	$0.452858\pi$
$182$	−2.30647	−	3.99492i	−0.170967	−	0.296123i
$183$	−9.19667	+	12.4454i	−0.679837	+	0.919993i
$184$	4.71200	−	8.16142i	0.347373	−	0.601668i
$185$	7.63630	−	13.2265i	0.561432	−	0.972429i
$186$	5.09753	+	11.7028i	0.373769	+	0.858089i
$187$		0			0
$188$	−2.62990			−0.191805
$189$	−1.10207	−	5.88245i	−0.0801641	−	0.427885i
$190$	9.52332			0.690894
$191$	−5.11379	−	8.85735i	−0.370021	−	0.640895i	0.619547	−	0.784959i	$-0.287316\pi$
$191$	−5.11379	−	8.85735i	−0.370021	−	0.640895i	−0.989568	+	0.144064i	$0.953983\pi$
$192$	−1.20047	−	2.75602i	−0.0866368	−	0.198899i
$193$	1.43678	−	2.48858i	0.103422	−	0.179132i	−0.809670	−	0.586885i	$-0.800354\pi$
$193$	1.43678	−	2.48858i	0.103422	−	0.179132i	0.913092	+	0.407753i	$0.133687\pi$
$194$	−3.07496	+	5.32599i	−0.220769	+	0.382383i
$195$	7.81513	−	10.5759i	0.559653	−	0.757353i
$196$	3.67938	+	6.37288i	0.262813	+	0.455206i
$197$	6.57236			0.468261			0.234131	−	0.972205i	$-0.424776\pi$
$197$	6.57236			0.468261			0.234131	+	0.972205i	$0.424776\pi$
$198$		0			0
$199$	−1.02758			−0.0728432			−0.0364216	−	0.999337i	$-0.511596\pi$
$199$	−1.02758			−0.0728432			−0.0364216	+	0.999337i	$0.511596\pi$
$200$	−4.37031	−	7.56960i	−0.309028	−	0.535251i
$201$	−8.75375	−	0.991621i	−0.617442	−	0.0699436i
$202$	−1.15882	+	2.00713i	−0.0815340	+	0.141221i
$203$	3.74177	−	6.48094i	0.262621	−	0.454873i
$204$	−16.7101	−	1.89291i	−1.16994	−	0.132530i
$205$	−2.19671	−	3.80481i	−0.153425	−	0.265740i
$206$	−3.77907			−0.263300
$207$	6.50349	+	21.1738i	0.452024	+	1.47168i
$208$	−10.8339			−0.751193
$209$		0			0
$210$	7.41004	−	10.0277i	0.511342	−	0.691975i
$211$	−7.21395	+	12.4949i	−0.496629	+	0.860187i	−0.999992	−	0.00388817i	$-0.998762\pi$
$211$	−7.21395	+	12.4949i	−0.496629	+	0.860187i	0.503363	+	0.864075i	$0.332096\pi$
$212$	8.11045	−	14.0477i	0.557028	−	0.964800i
$213$	3.24943	+	7.45997i	0.222648	+	0.511149i
$214$	3.33417	+	5.77496i	0.227919	+	0.394768i
$215$	−24.9147			−1.69917
$216$	−6.25615	−	2.20175i	−0.425677	−	0.149810i
$217$	4.67473			0.317342
$218$	9.74361	+	16.8764i	0.659921	+	1.14302i
$219$	0.113159	+	0.259788i	0.00764659	+	0.0175548i
$220$		0			0
$221$	−8.25547	+	14.2989i	−0.555323	+	0.961848i
$222$	8.29321	−	11.2228i	0.556604	−	0.753227i
$223$	−9.07839	−	15.7242i	−0.607934	−	1.05297i	−0.991580	−	0.129492i	$-0.958665\pi$
$223$	−9.07839	−	15.7242i	−0.607934	−	1.05297i	0.383646	−	0.923480i	$-0.374668\pi$
$224$	−7.33209			−0.489896
$225$	20.0233	+	4.59544i	1.33489	+	0.306363i
$226$	−2.84450			−0.189213
$227$	2.74604	+	4.75628i	0.182261	+	0.315686i	0.942650	−	0.333782i	$-0.108325\pi$
$227$	2.74604	+	4.75628i	0.182261	+	0.315686i	−0.760389	+	0.649468i	$0.774992\pi$
$228$	3.40138	+	0.385307i	0.225262	+	0.0255176i
$229$	−2.44559	+	4.23589i	−0.161609	+	0.279916i	−0.935446	−	0.353470i	$-0.885002\pi$
$229$	−2.44559	+	4.23589i	−0.161609	+	0.279916i	0.773837	+	0.633385i	$0.218335\pi$
$230$	−23.0733	+	39.9641i	−1.52141	+	2.63516i
$231$		0			0
$232$	−4.14659	−	7.18210i	−0.272237	−	0.471528i
$233$	−22.8673			−1.49808			−0.749042	−	0.662523i	$-0.769486\pi$
$233$	−22.8673			−1.49808			−0.749042	+	0.662523i	$0.769486\pi$
$234$	8.18296	−	8.79797i	0.534937	−	0.575141i
$235$	−6.97911			−0.455267
$236$	8.54844	+	14.8063i	0.556456	+	0.963810i
$237$	−3.37890	+	4.57251i	−0.219483	+	0.297017i
$238$	−7.82756	+	13.5577i	−0.507386	+	0.878818i
$239$	−0.123665	+	0.214194i	−0.00799924	+	0.0138551i	−0.869997	−	0.493056i	$-0.835880\pi$
$239$	−0.123665	+	0.214194i	−0.00799924	+	0.0138551i	0.861998	+	0.506912i	$0.169213\pi$
$240$	−11.6941	−	26.8469i	−0.754848	−	1.73296i
$241$	−0.899843	−	1.55857i	−0.0579640	−	0.100397i	0.835587	−	0.549358i	$-0.185128\pi$
$241$	−0.899843	−	1.55857i	−0.0579640	−	0.100397i	−0.893551	+	0.448961i	$0.851794\pi$
$242$		0			0
$243$	13.8037	−	7.24269i	0.885511	−	0.464619i
$244$	−11.5884			−0.741871
$245$	9.76419	+	16.9121i	0.623812	+	1.08047i
$246$	−1.60306	−	3.68028i	−0.102208	−	0.234646i
$247$	1.68043	−	2.91058i	0.106923	−	0.185196i
$248$	2.59024	−	4.48643i	0.164480	−	0.284889i
$249$	−12.4568	+	16.8572i	−0.789416	+	1.06828i
$250$	5.77496	+	10.0025i	0.365240	+	0.632615i
$251$	1.28843			0.0813251			0.0406625	−	0.999173i	$-0.487053\pi$
$251$	1.28843			0.0813251			0.0406625	+	0.999173i	$0.487053\pi$
$252$	3.05231	−	3.28171i	0.192277	−	0.206729i
$253$		0			0
$254$	−19.0889	−	33.0629i	−1.19774	−	2.07455i
$255$	−44.3445	−	5.02332i	−2.77696	−	0.314573i
$256$	−10.4335	+	18.0714i	−0.652095	+	1.12946i
$257$	5.81607	−	10.0737i	0.362796	−	0.628382i	−0.625624	−	0.780125i	$-0.715155\pi$
$257$	5.81607	−	10.0737i	0.362796	−	0.628382i	0.988420	+	0.151743i	$0.0484887\pi$
$258$	−22.6198	−	2.56236i	−1.40825	−	0.159526i
$259$	−2.55522	−	4.42578i	−0.158774	−	0.275004i
$260$	9.84756			0.610720
$261$	18.9983	+	4.36019i	1.17597	+	0.269889i
$262$	31.9842			1.97599
$263$	−4.84543	−	8.39253i	−0.298782	−	0.517506i	0.677076	−	0.735913i	$-0.263247\pi$
$263$	−4.84543	−	8.39253i	−0.298782	−	0.517506i	−0.975858	+	0.218408i	$0.929914\pi$
$264$		0			0
$265$	21.5232	−	37.2792i	1.32216	−	2.29004i
$266$	1.59332	−	2.75972i	0.0976930	−	0.169209i
$267$	−5.63974	−	12.9476i	−0.345146	−	0.792379i
$268$	−3.29862	−	5.71338i	−0.201496	−	0.349001i
$269$	−1.73753			−0.105939			−0.0529695	−	0.998596i	$-0.516869\pi$
$269$	−1.73753			−0.105939			−0.0529695	+	0.998596i	$0.516869\pi$
$270$	30.6346	+	10.7813i	1.86436	+	0.656131i
$271$	18.9387			1.15044			0.575222	−	0.817997i	$-0.304916\pi$
$271$	18.9387			1.15044			0.575222	+	0.817997i	$0.304916\pi$
$272$	18.3837	+	31.8415i	1.11467	+	1.93067i
$273$	−1.75720	−	4.03413i	−0.106350	−	0.244157i
$274$	−6.59353	+	11.4203i	−0.398330	+	0.689927i
$275$		0			0
$276$	−9.85786	+	13.3402i	−0.593374	+	0.802986i
$277$	2.39700	+	4.15173i	0.144022	+	0.249453i	0.929008	−	0.370061i	$-0.120663\pi$
$277$	2.39700	+	4.15173i	0.144022	+	0.249453i	−0.784986	+	0.619514i	$0.787330\pi$
$278$	5.70143			0.341949
$279$	3.57505	+	11.6395i	0.214032	+	0.696839i
$280$	−5.06023			−0.302406
$281$	8.64807	+	14.9789i	0.515900	+	0.893566i	0.999830	+	0.0184585i	$0.00587585\pi$
$281$	8.64807	+	14.9789i	0.515900	+	0.893566i	−0.483929	+	0.875107i	$0.660791\pi$
$282$	−6.33627	−	0.717770i	−0.377319	−	0.0427426i
$283$	8.74592	−	15.1484i	0.519891	−	0.900477i	−0.479842	−	0.877355i	$-0.659306\pi$
$283$	8.74592	−	15.1484i	0.519891	−	0.900477i	0.999733	−	0.0231221i	$-0.00736066\pi$
$284$	−3.04671	+	5.27706i	−0.180789	+	0.313136i
$285$	9.02645	+	1.02251i	0.534681	+	0.0605684i
$286$		0			0
$287$	−1.47010			−0.0867775
$288$	−5.60729	−	18.2560i	−0.330412	−	1.07574i
$289$	39.0339			2.29611
$290$	20.3047	+	35.1687i	1.19233	+	2.06518i
$291$	−3.48637	+	4.71795i	−0.204375	+	0.276571i
$292$	−0.106100	+	0.183770i	−0.00620901	+	0.0107543i
$293$	−0.224388	+	0.388651i	−0.0131089	+	0.0227052i	−0.872505	−	0.488604i	$-0.837506\pi$
$293$	−0.224388	+	0.388651i	−0.0131089	+	0.0227052i	0.859397	+	0.511310i	$0.170839\pi$
$294$	7.12549	+	16.3585i	0.415567	+	0.954049i
$295$	22.6855	+	39.2924i	1.32080	+	2.28769i
$296$	−5.66333			−0.329175
$297$		0			0
$298$	39.9068			2.31174
$299$	8.14274	+	14.1036i	0.470907	+	0.815635i
$300$	6.14368	+	14.1045i	0.354706	+	0.814324i
$301$	−4.16842	+	7.21991i	−0.240264	+	0.416149i
$302$	−1.93933	+	3.35903i	−0.111596	+	0.193290i
$303$	−1.31386	+	1.77799i	−0.0754792	+	0.102143i
$304$	−3.74205	−	6.48142i	−0.214621	−	0.371735i
$305$	−30.7528			−1.76090
$306$	−39.7433	−	9.12125i	−2.27197	−	0.521427i
$307$	12.4154			0.708583			0.354291	−	0.935135i	$-0.384722\pi$
$307$	12.4154			0.708583			0.354291	+	0.935135i	$0.384722\pi$
$308$		0			0
$309$	−3.58190	−	0.405756i	−0.203767	−	0.0230826i
$310$	−12.6837	+	21.9688i	−0.720384	+	1.24774i
$311$	11.6501	−	20.1786i	0.660616	−	1.14422i	−0.319838	−	0.947472i	$-0.603628\pi$
$311$	11.6501	−	20.1786i	0.660616	−	1.14422i	0.980454	−	0.196748i	$-0.0630382\pi$
$312$	−4.84528	−	0.548871i	−0.274310	−	0.0310737i
$313$	−9.24690	−	16.0161i	−0.522666	−	0.905283i	−0.999652	−	0.0263729i	$-0.991604\pi$
$313$	−9.24690	−	16.0161i	−0.522666	−	0.905283i	0.476987	−	0.878911i	$-0.341729\pi$
$314$	−32.6177			−1.84072
$315$	8.10009	−	8.70887i	0.456388	−	0.490689i
$316$	−4.25763			−0.239511
$317$	−10.9983	−	19.0496i	−0.617725	−	1.06993i	−0.989900	−	0.141768i	$-0.954721\pi$
$317$	−10.9983	−	19.0496i	−0.617725	−	1.06993i	0.372175	−	0.928163i	$-0.378612\pi$
$318$	23.3747	−	31.6319i	1.31079	−	1.77383i
$319$		0			0
$320$	2.98702	−	5.17367i	0.166979	−	0.289217i
$321$	2.54016	+	5.83164i	0.141778	+	0.325490i
$322$	7.72068	+	13.3726i	0.430256	+	0.745226i
$323$	−11.4059			−0.634640
$324$	10.5053	+	5.09015i	0.583630	+	0.282786i
$325$	15.1046			0.837850
$326$	−13.1542	−	22.7837i	−0.728543	−	1.26187i
$327$	7.42323	+	17.0421i	0.410506	+	0.942429i
$328$	−0.814576	+	1.41089i	−0.0449774	+	0.0779032i
$329$	−1.16766	+	2.02244i	−0.0643750	+	0.111501i
$330$		0			0
$331$	9.96363	+	17.2575i	0.547651	+	0.948559i	0.998435	+	0.0559257i	$0.0178110\pi$
$331$	9.96363	+	17.2575i	0.547651	+	0.948559i	−0.450784	+	0.892633i	$0.648856\pi$
$332$	−15.6963			−0.861448
$333$	9.06550	−	9.74684i	0.496786	−	0.534124i
$334$	−2.90014			−0.158689
$335$	−8.75375	−	15.1619i	−0.478268	−	0.828385i
$336$	−9.73635	−	1.10293i	−0.531161	−	0.0601697i
$337$	−2.95857	+	5.12439i	−0.161163	+	0.279143i	−0.935286	−	0.353892i	$-0.884858\pi$
$337$	−2.95857	+	5.12439i	−0.161163	+	0.279143i	0.774123	+	0.633035i	$0.218191\pi$
$338$	−7.38559	+	12.7922i	−0.401723	+	0.695805i
$339$	−2.69609	−	0.305412i	−0.146431	−	0.0165877i
$340$	−16.7101	−	28.9427i	−0.906230	−	1.56964i
$341$		0			0
$342$	8.08987	+	1.85666i	0.437450	+	0.100397i
$343$	14.5969			0.788159
$344$	4.61939	+	8.00102i	0.249061	+	0.431386i
$345$	−26.1604	+	35.4017i	−1.40843	+	1.90596i
$346$	−3.18840	+	5.52246i	−0.171409	+	0.296889i
$347$	−12.4994	+	21.6496i	−0.671004	+	1.16221i	0.306616	+	0.951833i	$0.400803\pi$
$347$	−12.4994	+	21.6496i	−0.671004	+	1.16221i	−0.977620	+	0.210379i	$0.932530\pi$
$348$	5.82918	+	13.3825i	0.312477	+	0.717376i
$349$	−12.8792	−	22.3073i	−0.689405	−	1.19408i	−0.972031	−	0.234854i	$-0.924539\pi$
$349$	−12.8792	−	22.3073i	−0.689405	−	1.19408i	0.282625	−	0.959230i	$-0.408795\pi$
$350$	14.3216			0.765523
$351$	8.70065	−	7.46034i	0.464406	−	0.398204i
$352$		0			0
$353$	1.27708	+	2.21197i	0.0679723	+	0.117731i	0.898009	−	0.439978i	$-0.145014\pi$
$353$	1.27708	+	2.21197i	0.0679723	+	0.117731i	−0.830036	+	0.557709i	$0.811680\pi$
$354$	16.5549	+	38.0063i	0.879882	+	2.02001i
$355$	−8.08524	+	14.0040i	−0.429120	+	0.743258i
$356$	5.28790	−	9.15891i	0.280258	−	0.485421i
$357$	−8.87485	+	12.0099i	−0.469707	+	0.635633i
$358$	0.504760	+	0.874270i	0.0266774	+	0.0462066i
$359$	6.28175			0.331538			0.165769	−	0.986165i	$-0.446989\pi$
$359$	6.28175			0.331538			0.165769	+	0.986165i	$0.446989\pi$
$360$	−3.86986	−	12.5993i	−0.203959	−	0.664044i
$361$	−16.6783			−0.877805
$362$	3.60476	+	6.24363i	0.189462	+	0.328158i
$363$		0			0
$364$	1.64757	−	2.85368i	0.0863563	−	0.149573i
$365$	−0.281563	+	0.487681i	−0.0147377	+	0.0255264i
$366$	−27.9202	−	3.16279i	−1.45941	−	0.165321i
$367$	8.78662	+	15.2189i	0.458658	+	0.794418i	0.998890	−	0.0470974i	$-0.0149971\pi$
$367$	8.78662	+	15.2189i	0.458658	+	0.794418i	−0.540233	+	0.841516i	$0.681664\pi$
$368$	36.2653			1.89046
$369$	−1.12428	−	3.66038i	−0.0585275	−	0.190552i
$370$	27.7317			1.44170
$371$	−7.20198	−	12.4742i	−0.373908	−	0.647628i
$372$	−5.41898	+	7.33326i	−0.280961	+	0.380212i
$373$	−3.32460	+	5.75837i	−0.172141	+	0.298157i	−0.939168	−	0.343457i	$-0.888402\pi$
$373$	−3.32460	+	5.75837i	−0.172141	+	0.298157i	0.767027	+	0.641615i	$0.221735\pi$
$374$		0			0
$375$	4.39969	+	10.1007i	0.227199	+	0.521598i
$376$	1.29398	+	2.24125i	0.0667321	+	0.115583i
$377$	14.3313			0.738101
$378$	8.24966	−	7.07365i	0.424317	−	0.363829i
$379$	−2.34371			−0.120388			−0.0601940	−	0.998187i	$-0.519172\pi$
$379$	−2.34371			−0.120388			−0.0601940	+	0.998187i	$0.519172\pi$
$380$	3.40138	+	5.89137i	0.174487	+	0.302221i
$381$	−14.5430	−	33.3874i	−0.745060	−	1.71049i
$382$	9.28553	−	16.0830i	0.475089	−	0.822878i
$383$	9.08808	−	15.7410i	0.464379	−	0.804329i	−0.534794	−	0.844983i	$-0.679611\pi$
$383$	9.08808	−	15.7410i	0.464379	−	0.804329i	0.999173	+	0.0406538i	$0.0129441\pi$
$384$	−9.86166	+	13.3453i	−0.503251	+	0.681026i
$385$		0			0
$386$	5.21777			0.265577
$387$	−21.1645	−	4.85735i	−1.07585	−	0.246913i
$388$	−4.39305			−0.223023
$389$	−6.50237	−	11.2624i	−0.329683	−	0.571028i	0.652766	−	0.757560i	$-0.273609\pi$
$389$	−6.50237	−	11.2624i	−0.329683	−	0.571028i	−0.982449	+	0.186532i	$0.940275\pi$
$390$	23.7259	+	2.68767i	1.20141	+	0.136095i
$391$	27.6344	−	47.8642i	1.39753	−	2.42060i
$392$	3.62072	−	6.27128i	0.182874	−	0.316747i
$393$	30.3154	+	3.43412i	1.52921	+	0.173228i
$394$	5.96698	+	10.3351i	0.300612	+	0.520676i
$395$	−11.2987			−0.568501
$396$		0			0
$397$	−34.8041			−1.74677			−0.873384	−	0.487032i	$-0.838080\pi$
$397$	−34.8041			−1.74677			−0.873384	+	0.487032i	$0.838080\pi$
$398$	−0.932930	−	1.61588i	−0.0467636	−	0.0809969i
$399$	1.80650	−	2.44466i	0.0904382	−	0.122386i
$400$	16.8178	−	29.1292i	0.840888	−	1.45646i
$401$	2.29884	−	3.98171i	0.114799	−	0.198837i	−0.802901	−	0.596113i	$-0.796711\pi$
$401$	2.29884	−	3.98171i	0.114799	−	0.198837i	0.917699	+	0.397276i	$0.130044\pi$
$402$	−6.38811	−	14.6657i	−0.318610	−	0.731457i
$403$	4.47616	+	7.75294i	0.222973	+	0.386201i
$404$	−1.65555			−0.0823665
$405$	27.8786	+	13.5080i	1.38530	+	0.671219i
$406$	13.5885			0.674385
$407$		0			0
$408$	6.60865	+	15.1720i	0.327177	+	0.751125i
$409$	16.3746	−	28.3617i	0.809673	−	1.40239i	−0.103418	−	0.994638i	$-0.532978\pi$
$409$	16.3746	−	28.3617i	0.809673	−	1.40239i	0.913091	−	0.407756i	$-0.133689\pi$
$410$	3.98874	−	6.90871i	0.196990	−	0.341197i
$411$	−7.47571	+	10.1165i	−0.368749	+	0.499012i
$412$	−1.34974	−	2.33783i	−0.0664972	−	0.115176i
$413$	15.1818			0.747048
$414$	−27.3917	+	29.4504i	−1.34623	+	1.44741i
$415$	−41.6543			−2.04473
$416$	−7.02064	−	12.1601i	−0.344215	−	0.596198i
$417$	5.40396	+	0.612159i	0.264633	+	0.0299775i
$418$		0			0
$419$	−12.9281	+	22.3922i	−0.631581	+	1.09393i	0.355648	+	0.934620i	$0.384260\pi$
$419$	−12.9281	+	22.3922i	−0.631581	+	1.09393i	−0.987229	+	0.159310i	$0.949073\pi$
$420$	8.84997	+	1.00252i	0.431834	+	0.0489180i
$421$	−14.4662	−	25.0562i	−0.705040	−	1.22117i	−0.966677	−	0.255999i	$-0.917596\pi$
$421$	−14.4662	−	25.0562i	−0.705040	−	1.22117i	0.261637	−	0.965166i	$-0.415738\pi$
$422$	−26.1979			−1.27529
$423$	−5.92861	−	1.36064i	−0.288259	−	0.0661566i
$424$	−15.9623			−0.775197
$425$	−25.6305	−	44.3933i	−1.24326	−	2.15339i
$426$	−8.78077	+	11.8826i	−0.425430	+	0.575714i
$427$	−5.14517	+	8.91170i	−0.248992	+	0.431268i
$428$	−2.38169	+	4.12521i	−0.115123	+	0.199399i
$429$		0			0
$430$	−22.6198	−	39.1787i	−1.09082	−	1.88936i
$431$	21.9002			1.05490			0.527448	−	0.849588i	$-0.323149\pi$
$431$	21.9002			1.05490			0.527448	+	0.849588i	$0.323149\pi$
$432$	−4.69981	−	25.0858i	−0.226119	−	1.20694i
$433$	22.7804			1.09476			0.547379	−	0.836885i	$-0.315626\pi$
$433$	22.7804			1.09476			0.547379	+	0.836885i	$0.315626\pi$
$434$	4.24415	+	7.35108i	0.203726	+	0.352863i
$435$	15.4692	+	35.5139i	0.741693	+	1.70276i
$436$	−6.96013	+	12.0553i	−0.333330	+	0.577344i
$437$	−5.62506	+	9.74289i	−0.269083	+	0.466066i
$438$	−0.305784	+	0.413803i	−0.0146109	+	0.0197723i
$439$	−6.34912	−	10.9970i	−0.303027	−	0.524858i	0.673793	−	0.738920i	$-0.264664\pi$
$439$	−6.34912	−	10.9970i	−0.303027	−	0.524858i	−0.976820	+	0.214062i	$0.931331\pi$
$440$		0			0
$441$	4.99732	+	16.2701i	0.237967	+	0.774766i
$442$	−29.9803			−1.42602
$443$	−1.73140	−	2.99887i	−0.0822612	−	0.142481i	0.821960	−	0.569546i	$-0.192881\pi$
$443$	−1.73140	−	2.99887i	−0.0822612	−	0.142481i	−0.904221	+	0.427065i	$0.859548\pi$
$444$	9.90476	+	1.12201i	0.470059	+	0.0532481i
$445$	14.0328	−	24.3055i	0.665218	−	1.15219i
$446$	16.4844	−	28.5518i	0.780558	−	1.35197i
$447$	37.8247	+	4.28476i	1.78905	+	0.202662i
$448$	−0.999502	−	1.73119i	−0.0472220	−	0.0817910i
$449$	32.0547			1.51275			0.756376	−	0.654137i	$-0.226968\pi$
$449$	32.0547			1.51275			0.756376	+	0.654137i	$0.226968\pi$
$450$	10.9526	+	35.6591i	0.516311	+	1.68099i
$451$		0			0
$452$	−1.01595	−	1.75968i	−0.0477863	−	0.0827684i
$453$	−2.19881	+	2.97554i	−0.103309	+	0.139803i
$454$	−4.98621	+	8.63637i	−0.234014	+	0.405325i
$455$	4.37226	−	7.57297i	0.204975	−	0.355026i
$456$	−1.34521	−	3.08830i	−0.0629953	−	0.144623i
$457$	−6.88827	−	11.9308i	−0.322220	−	0.558101i	0.658726	−	0.752383i	$-0.271096\pi$
$457$	−6.88827	−	11.9308i	−0.322220	−	0.558101i	−0.980946	+	0.194282i	$0.937762\pi$
$458$	−8.88132			−0.414997
$459$	−36.6904	−	12.9126i	−1.71256	−	0.602707i
$460$	−32.9638			−1.53694
$461$	1.79607	+	3.11089i	0.0836515	+	0.144889i	0.904816	−	0.425803i	$-0.140008\pi$
$461$	1.79607	+	3.11089i	0.0836515	+	0.144889i	−0.821164	+	0.570692i	$0.806675\pi$
$462$		0			0
$463$	−12.4446	+	21.5547i	−0.578351	+	1.00173i	0.417318	+	0.908760i	$0.362970\pi$
$463$	−12.4446	+	21.5547i	−0.578351	+	1.00173i	−0.995669	+	0.0929721i	$0.970363\pi$
$464$	15.9568	−	27.6380i	0.740777	−	1.28306i
$465$	−14.3807	+	19.4607i	−0.666888	+	0.902469i
$466$	−20.7610	−	35.9590i	−0.961733	−	1.66577i
$467$	−23.8940			−1.10568			−0.552841	−	0.833287i	$-0.686456\pi$
$467$	−23.8940			−1.10568			−0.552841	+	0.833287i	$0.686456\pi$
$468$	8.36530	+	1.91987i	0.386686	+	0.0887461i
$469$	−5.85827			−0.270510
$470$	−6.33627	−	10.9747i	−0.292270	−	0.506227i
$471$	−30.9159	−	3.50214i	−1.42453	−	0.161370i
$472$	8.41215	−	14.5703i	0.387200	−	0.670651i
$473$		0			0
$474$	−10.2580	−	1.16202i	−0.471166	−	0.0533735i
$475$	5.21716	+	9.03639i	0.239380	+	0.414618i
$476$	−11.1829			−0.512567
$477$	25.5514	−	27.4718i	1.16992	−	1.25785i
$478$	−0.449098			−0.0205413
$479$	−9.29886	−	16.1061i	−0.424876	−	0.735906i	0.571533	−	0.820579i	$-0.306349\pi$
$479$	−9.29886	−	16.1061i	−0.424876	−	0.735906i	−0.996409	+	0.0846727i	$0.973016\pi$
$480$	22.5554	−	30.5232i	1.02951	−	1.39319i
$481$	4.89337	−	8.47556i	0.223118	−	0.386452i
$482$	1.63392	−	2.83003i	0.0744229	−	0.128904i
$483$	5.88205	+	13.5039i	0.267642	+	0.614447i
$484$		0			0
$485$	−11.6581			−0.529367
$486$	23.9215	+	15.1310i	1.08510	+	0.686356i
$487$	−19.3139			−0.875196			−0.437598	−	0.899171i	$-0.644171\pi$
$487$	−19.3139			−0.875196			−0.437598	+	0.899171i	$0.644171\pi$
$488$	5.70182	+	9.87584i	0.258109	+	0.447058i
$489$	−10.0216	−	23.0073i	−0.453192	−	1.04043i
$490$	−17.7296	+	30.7086i	−0.800944	+	1.38728i
$491$	−21.0297	+	36.4246i	−0.949058	+	1.64382i	−0.201644	+	0.979459i	$0.564629\pi$
$491$	−21.0297	+	36.4246i	−0.949058	+	1.64382i	−0.747414	+	0.664359i	$0.768705\pi$
$492$	1.70416	−	2.30616i	0.0768293	−	0.103970i
$493$	−24.3184	−	42.1208i	−1.09525	−	1.89702i
$494$	6.10257			0.274568
$495$		0			0
$496$	19.9354			0.895128
$497$	2.70544	+	4.68597i	0.121356	+	0.210194i
$498$	−37.8175	−	4.28395i	−1.69464	−	0.191969i
$499$	0.884117	−	1.53134i	0.0395785	−	0.0685520i	−0.845558	−	0.533884i	$-0.820732\pi$
$499$	0.884117	−	1.53134i	0.0395785	−	0.0685520i	0.885136	+	0.465332i	$0.154065\pi$
$500$	−4.12521	+	7.14507i	−0.184485	+	0.319537i
$501$	−2.74883	−	0.311386i	−0.122808	−	0.0139117i
$502$	1.16975	+	2.02607i	0.0522087	+	0.0904281i
$503$	18.6392			0.831080			0.415540	−	0.909575i	$-0.363593\pi$
$503$	18.6392			0.831080			0.415540	+	0.909575i	$0.363593\pi$
$504$	−4.29856	−	0.986538i	−0.191473	−	0.0439439i
$505$	−4.39342			−0.195505
$506$		0			0
$507$	−8.37374	+	11.3318i	−0.371891	+	0.503263i
$508$	13.6357	−	23.6177i	0.604987	−	1.04787i
$509$	4.58048	−	7.93363i	0.203026	−	0.351652i	−0.746476	−	0.665413i	$-0.768256\pi$
$509$	4.58048	−	7.93363i	0.203026	−	0.351652i	0.949502	+	0.313761i	$0.101589\pi$
$510$	−32.3607	−	74.2928i	−1.43295	−	3.28974i
$511$	0.0942151	+	0.163185i	0.00416783	+	0.00721890i
$512$	−18.7292			−0.827722
$513$	7.46843	+	2.62839i	0.329739	+	0.116046i
$514$	21.1214			0.931626
$515$	−3.58190	−	6.20403i	−0.157837	−	0.273382i
$516$	−6.49383	−	14.9084i	−0.285875	−	0.656305i
$517$		0			0
$518$	4.63973	−	8.03624i	0.203858	−	0.353092i
$519$	−3.61499	+	4.89199i	−0.158680	+	0.214735i
$520$	−4.84528	−	8.39227i	−0.212480	−	0.368026i
$521$	−2.64766			−0.115996			−0.0579981	−	0.998317i	$-0.518472\pi$
$521$	−2.64766			−0.115996			−0.0579981	+	0.998317i	$0.518472\pi$
$522$	10.3919	+	33.8336i	0.454842	+	1.48086i
$523$	27.7951			1.21539			0.607697	−	0.794169i	$-0.292094\pi$
$523$	27.7951			1.21539			0.607697	+	0.794169i	$0.292094\pi$
$524$	11.4236	+	19.7862i	0.499041	+	0.864365i
$525$	13.5744	+	1.53770i	0.592436	+	0.0671109i
$526$	8.79824	−	15.2390i	0.383621	−	0.664452i
$527$	15.1910	−	26.3115i	0.661728	−	1.14615i
$528$		0			0
$529$	−15.7570	−	27.2920i	−0.685088	−	1.18661i
$530$	78.1627			3.39517
$531$	11.6104	+	37.8008i	0.503850	+	1.64042i
$532$	2.27631			0.0986905
$533$	−1.40766	−	2.43813i	−0.0609724	−	0.105607i
$534$	15.2400	−	20.6235i	0.659497	−	0.892468i
$535$	−6.32043	+	10.9473i	−0.273256	+	0.473293i
$536$	−3.24603	+	5.62229i	−0.140207	+	0.242846i
$537$	0.384555	+	0.882851i	0.0165948	+	0.0380978i
$538$	−1.57749	−	2.73229i	−0.0680103	−	0.117797i
$539$		0			0
$540$	4.27195	+	22.8020i	0.183835	+	0.981243i
$541$	8.70614			0.374306			0.187153	−	0.982331i	$-0.440074\pi$
$541$	8.70614			0.374306			0.187153	+	0.982331i	$0.440074\pi$
$542$	17.1943	+	29.7814i	0.738557	+	1.27922i
$543$	2.74631	+	6.30491i	0.117855	+	0.270569i
$544$	−23.8263	+	41.2683i	−1.02154	+	1.76936i
$545$	−18.4705	+	31.9918i	−0.791189	+	1.37038i
$546$	4.74838	−	6.42576i	0.203212	−	0.274997i
$547$	−3.29512	−	5.70732i	−0.140889	−	0.244028i	0.786942	−	0.617026i	$-0.211663\pi$
$547$	−3.29512	−	5.70732i	−0.140889	−	0.244028i	−0.927832	+	0.372999i	$0.878330\pi$
$548$	−9.41987			−0.402397
$549$	−26.1239	−	5.99554i	−1.11494	−	0.255883i
$550$		0			0
$551$	4.95009	+	8.57381i	0.210881	+	0.365257i
$552$	16.2191	+	1.83729i	0.690331	+	0.0782004i
$553$	−1.89036	+	3.27420i	−0.0803864	+	0.139233i
$554$	−4.35243	+	7.53863i	−0.184917	+	0.320286i
$555$	26.2848	+	2.97753i	1.11573	+	0.126389i
$556$	2.03634	+	3.52705i	0.0863602	+	0.149580i
$557$	43.7019			1.85171			0.925855	−	0.377878i	$-0.123346\pi$
$557$	43.7019			1.85171			0.925855	+	0.377878i	$0.123346\pi$
$558$	−15.0575	+	16.1892i	−0.637436	+	0.685344i
$559$	−15.9654			−0.675265
$560$	−9.73635	−	16.8638i	−0.411436	−	0.712628i
$561$		0			0
$562$	−15.7030	+	27.1984i	−0.662391	+	1.14729i
$563$	22.4667	−	38.9134i	0.946858	−	1.64001i	0.194869	−	0.980829i	$-0.437572\pi$
$563$	22.4667	−	38.9134i	0.946858	−	1.64001i	0.751988	−	0.659176i	$-0.229095\pi$
$564$	−1.81905	−	4.17614i	−0.0765959	−	0.175847i
$565$	−2.69609	−	4.66976i	−0.113425	−	0.196458i
$566$	31.7613			1.33503
$567$	8.57873	−	5.81882i	0.360273	−	0.244368i
$568$	5.99628			0.251598
$569$	−15.1172	−	26.1838i	−0.633746	−	1.09768i	−0.986779	−	0.162069i	$-0.948183\pi$
$569$	−15.1172	−	26.1838i	−0.633746	−	1.09768i	0.353033	−	0.935611i	$-0.385150\pi$
$570$	6.58711	+	15.1225i	0.275904	+	0.633413i
$571$	−21.0781	+	36.5083i	−0.882090	+	1.52783i	−0.0330775	+	0.999453i	$0.510531\pi$
$571$	−21.0781	+	36.5083i	−0.882090	+	1.52783i	−0.849013	+	0.528372i	$0.822803\pi$
$572$		0			0
$573$	10.5279	−	14.2469i	0.439808	−	0.595173i
$574$	−1.33469	−	2.31176i	−0.0557091	−	0.0964909i
$575$	−50.5610			−2.10854
$576$	3.54607	−	3.81258i	0.147753	−	0.158857i
$577$	22.5059			0.936932			0.468466	−	0.883482i	$-0.344807\pi$
$577$	22.5059			0.936932			0.468466	+	0.883482i	$0.344807\pi$
$578$	35.4386	+	61.3814i	1.47405	+	2.55313i
$579$	4.94553	+	0.560228i	0.205529	+	0.0232823i
$580$	−14.5042	+	25.1219i	−0.602253	+	1.04313i
$581$	−6.96908	+	12.0708i	−0.289126	+	0.500781i
$582$	−10.5843	−	1.19898i	−0.438732	−	0.0496994i
$583$		0			0
$584$	0.208816			0.00864087
$585$	22.1995	+	5.09488i	0.917836	+	0.210647i
$586$	−0.814878			−0.0336623
$587$	4.67767	+	8.10197i	0.193068	+	0.334404i	0.946266	−	0.323391i	$-0.104823\pi$
$587$	4.67767	+	8.10197i	0.193068	+	0.334404i	−0.753197	+	0.657795i	$0.771489\pi$
$588$	−7.57483	+	10.2507i	−0.312381	+	0.422731i
$589$	−3.09216	+	5.35578i	−0.127410	+	0.220681i
$590$	−41.1919	+	71.3464i	−1.69584	+	2.93729i
$591$	4.54598	+	10.4366i	0.186997	+	0.429303i
$592$	−10.8968	−	18.8738i	−0.447855	−	0.775707i
$593$	16.8332			0.691255			0.345628	−	0.938372i	$-0.387666\pi$
$593$	16.8332			0.691255			0.345628	+	0.938372i	$0.387666\pi$
$594$		0			0
$595$	−29.6767			−1.21662
$596$	14.2533	+	24.6874i	0.583836	+	1.01123i
$597$	−0.710759	−	1.63174i	−0.0290894	−	0.0667828i
$598$	−14.7854	+	25.6091i	−0.604622	+	1.04724i
$599$	13.1733	−	22.8168i	0.538245	−	0.932268i	−0.460754	−	0.887528i	$-0.652421\pi$
$599$	13.1733	−	22.8168i	0.538245	−	0.932268i	0.998999	−	0.0447397i	$-0.0142459\pi$
$600$	8.99726	−	12.1756i	0.367311	−	0.497066i
$601$	−1.47992	−	2.56329i	−0.0603671	−	0.104559i	0.834262	−	0.551368i	$-0.185894\pi$
$601$	−1.47992	−	2.56329i	−0.0603671	−	0.104559i	−0.894630	+	0.446809i	$0.852560\pi$
$602$	−15.1379			−0.616973
$603$	−4.48017	−	14.5864i	−0.182447	−	0.594003i
$604$	−2.77064			−0.112736
$605$		0			0
$606$	−3.98874	−	0.451843i	−0.162032	−	0.0183549i
$607$	−1.95947	+	3.39390i	−0.0795325	+	0.137754i	−0.903048	−	0.429539i	$-0.858676\pi$
$607$	−1.95947	+	3.39390i	−0.0795325	+	0.137754i	0.823516	+	0.567293i	$0.192009\pi$
$608$	4.84991	−	8.40028i	0.196690	−	0.340677i
$609$	12.8795	+	1.45899i	0.521904	+	0.0591211i
$610$	−27.9202	−	48.3591i	−1.13045	−	1.95800i
$611$	−4.47223			−0.180927
$612$	−8.55221	−	27.8440i	−0.345703	−	1.12553i
$613$	−12.7621			−0.515456			−0.257728	−	0.966217i	$-0.582974\pi$
$613$	−12.7621			−0.515456			−0.257728	+	0.966217i	$0.582974\pi$
$614$	11.2718	+	19.5233i	0.454893	+	0.787897i
$615$	4.52242	−	6.11998i	0.182361	−	0.246781i
$616$		0			0
$617$	14.7130	−	25.4836i	0.592322	−	1.02593i	−0.401597	−	0.915816i	$-0.631545\pi$
$617$	14.7130	−	25.4836i	0.592322	−	1.02593i	0.993919	−	0.110115i	$-0.0351219\pi$
$618$	−2.61391	−	6.00096i	−0.105147	−	0.241394i
$619$	14.0501	+	24.3354i	0.564719	+	0.978123i	0.997076	+	0.0764200i	$0.0243490\pi$
$619$	14.0501	+	24.3354i	0.564719	+	0.978123i	−0.432356	+	0.901703i	$0.642318\pi$
$620$	−18.1206			−0.727740
$621$	−29.1246	+	24.9728i	−1.16873	+	1.00212i
$622$	42.3080			1.69640
$623$	−4.69559	−	8.13299i	−0.188125	−	0.325842i
$624$	−7.49358	−	17.2036i	−0.299983	−	0.688695i
$625$	6.17261	−	10.6913i	0.246904	−	0.427651i
$626$	16.7903	−	29.0817i	0.671077	−	1.16234i
$627$		0			0
$628$	−11.6499	−	20.1782i	−0.464880	−	0.805196i
$629$	−33.2137			−1.32432
$630$	21.0488	+	4.83079i	0.838605	+	0.192463i
$631$	−28.4345			−1.13196			−0.565979	−	0.824420i	$-0.691502\pi$
$631$	−28.4345			−1.13196			−0.565979	+	0.824420i	$0.691502\pi$
$632$	2.09488	+	3.62843i	0.0833297	+	0.144331i
$633$	−24.8311	−	2.81285i	−0.986946	−	0.111801i
$634$	19.9705	−	34.5899i	0.793128	−	1.37374i
$635$	36.1859	−	62.6758i	1.43599	−	2.48721i
$636$	27.9169	+	3.16241i	1.10698	+	0.125398i
$637$	6.25692	+	10.8373i	0.247908	+	0.429390i
$638$		0			0
$639$	−9.59846	+	10.3199i	−0.379709	+	0.408247i
$640$	−32.9765			−1.30351
$641$	−8.31278	−	14.3982i	−0.328335	−	0.568693i	0.653847	−	0.756627i	$-0.273154\pi$
$641$	−8.31278	−	14.3982i	−0.328335	−	0.568693i	−0.982182	+	0.187934i	$0.939821\pi$
$642$	−6.86414	+	9.28893i	−0.270906	+	0.366605i
$643$	−7.98599	+	13.8321i	−0.314937	+	0.545486i	−0.979424	−	0.201813i	$-0.935317\pi$
$643$	−7.98599	+	13.8321i	−0.314937	+	0.545486i	0.664487	+	0.747300i	$0.268650\pi$
$644$	−5.51509	+	9.55241i	−0.217325	+	0.376418i
$645$	−17.2331	−	39.5632i	−0.678551	−	1.55780i
$646$	−10.3553	−	17.9359i	−0.407423	−	0.705678i
$647$	−15.0590			−0.592031			−0.296016	−	0.955183i	$-0.595658\pi$
$647$	−15.0590			−0.592031			−0.296016	+	0.955183i	$0.595658\pi$
$648$	−0.831008	−	11.4573i	−0.0326451	−	0.450087i
$649$		0			0
$650$	13.7133	+	23.7521i	0.537879	+	0.931634i
$651$	3.23343	+	7.42323i	0.126728	+	0.290939i
$652$	9.39639	−	16.2750i	0.367991	−	0.637379i
$653$	15.6793	−	27.1573i	0.613578	−	1.06275i	−0.377054	−	0.926191i	$-0.623063\pi$
$653$	15.6793	−	27.1573i	0.613578	−	1.06275i	0.990632	−	0.136557i	$-0.0436038\pi$
$654$	−20.0594	+	27.1455i	−0.784384	+	1.06147i
$655$	30.3154	+	52.5078i	1.18452	+	2.05165i
$656$	−6.26928			−0.244774
$657$	−0.334259	+	0.359381i	−0.0130407	+	0.0140208i
$658$	−4.24042			−0.165309
$659$	−9.05194	−	15.6784i	−0.352613	−	0.610744i	0.634093	−	0.773257i	$-0.281374\pi$
$659$	−9.05194	−	15.6784i	−0.352613	−	0.610744i	−0.986706	+	0.162512i	$0.948040\pi$
$660$		0			0
$661$	15.9887	−	27.6933i	0.621890	−	1.07714i	−0.367244	−	0.930125i	$-0.619699\pi$
$661$	15.9887	−	27.6933i	0.621890	−	1.07714i	0.989134	−	0.147020i	$-0.0469681\pi$
$662$	−18.0918	+	31.3359i	−0.703157	+	1.21790i
$663$	−28.4161	−	3.21896i	−1.10359	−	0.125014i
$664$	7.72304	+	13.3767i	0.299712	+	0.519117i
$665$	6.04077			0.234251
$666$	23.5575	+	5.40655i	0.912835	+	0.209500i
$667$	−47.9727			−1.85751
$668$	−1.03582	−	1.79410i	−0.0400772	−	0.0694158i
$669$	18.6899	−	25.2922i	0.722593	−	0.977852i
$670$	15.8949	−	27.5308i	0.614073	−	1.06361i
$671$		0			0
$672$	−5.07148	−	11.6430i	−0.195636	−	0.449137i
$673$	−16.8381	−	29.1645i	−0.649062	−	1.12421i	−0.983347	−	0.181736i	$-0.941828\pi$
$673$	−16.8381	−	29.1645i	−0.649062	−	1.12421i	0.334286	−	0.942472i	$-0.391505\pi$
$674$	−10.7442			−0.413852
$675$	6.55246	+	34.9746i	0.252204	+	1.34617i
$676$	−10.5515			−0.405825
$677$	−19.0838	−	33.0540i	−0.733448	−	1.27037i	−0.955401	−	0.295312i	$-0.904576\pi$
$677$	−19.0838	−	33.0540i	−0.733448	−	1.27037i	0.221953	−	0.975057i	$-0.428757\pi$
$678$	−1.96749	−	4.51692i	−0.0755610	−	0.173471i
$679$	−1.95049	+	3.37834i	−0.0748529	+	0.129649i
$680$	−16.4436	+	28.4812i	−0.630585	+	1.09221i
$681$	−5.65334	+	7.65040i	−0.216636	+	0.293164i
$682$		0			0
$683$	32.1292			1.22939			0.614695	−	0.788765i	$-0.289279\pi$
$683$	32.1292			1.22939			0.614695	+	0.788765i	$0.289279\pi$
$684$	1.74083	+	5.66773i	0.0665622	+	0.216711i
$685$	−24.9981			−0.955127
$686$	13.2524	+	22.9538i	0.505979	+	0.876382i
$687$	−8.41794	−	0.953581i	−0.321165	−	0.0363814i
$688$	−17.7763	+	30.7894i	−0.677713	+	1.17383i
$689$	13.7921	−	23.8886i	0.525437	−	0.910084i
$690$	−79.4203	−	8.99670i	−3.02348	−	0.342499i
$691$	−4.31434	−	7.47266i	−0.164125	−	0.284274i	0.772219	−	0.635357i	$-0.219147\pi$
$691$	−4.31434	−	7.47266i	−0.164125	−	0.284274i	−0.936344	+	0.351083i	$0.885814\pi$
$692$	−4.55511			−0.173159
$693$		0			0
$694$	−45.3924			−1.72307
$695$	5.40396	+	9.35994i	0.204984	+	0.355043i
$696$	8.53667	−	11.5523i	0.323582	−	0.437889i
$697$	−4.77723	+	8.27441i	−0.180951	+	0.313416i
$698$	23.3857	−	40.5053i	0.885163	−	1.53315i
$699$	−15.8169	−	36.3120i	−0.598249	−	1.37345i
$700$	5.11516	+	8.85972i	0.193335	+	0.334866i
$701$	12.7081			0.479977			0.239989	−	0.970776i	$-0.422856\pi$
$701$	12.7081			0.479977			0.239989	+	0.970776i	$0.422856\pi$
$702$	19.6307	+	6.90871i	0.740914	+	0.260752i
$703$	6.76074			0.254986
$704$		0			0
$705$	−4.82732	−	11.0825i	−0.181808	−	0.417389i
$706$	−2.31890	+	4.01646i	−0.0872731	+	0.151161i
$707$	−0.735052	+	1.27315i	−0.0276445	+	0.0478817i
$708$	−17.5989	+	23.8157i	−0.661406	+	0.895050i
$709$	−10.5232	−	18.2268i	−0.395208	−	0.684521i	0.597920	−	0.801556i	$-0.295994\pi$
$709$	−10.5232	−	18.2268i	−0.395208	−	0.684521i	−0.993128	+	0.117035i	$0.962661\pi$
$710$	−29.3621			−1.10194
$711$	−9.59803	−	2.20279i	−0.359954	−	0.0826111i
$712$	−10.4072			−0.390026
$713$	−14.9835	−	25.9522i	−0.561137	−	0.971918i
$714$	−26.9432	−	3.05211i	−1.00832	−	0.114222i
$715$		0			0
$716$	−0.360564	+	0.624515i	−0.0134749	+	0.0233392i
$717$	−0.425666	−	0.0482193i	−0.0158968	−	0.00180078i
$718$	5.70314	+	9.87814i	0.212839	+	0.368649i
$719$	−40.6509			−1.51602			−0.758011	−	0.652242i	$-0.773829\pi$
$719$	−40.6509			−1.51602			−0.758011	+	0.652242i	$0.773829\pi$
$720$	34.5429	−	37.1391i	1.28734	−	1.38409i
$721$	−2.39711			−0.0892732
$722$	−15.1421	−	26.2268i	−0.563530	−	0.976062i
$723$	1.85253	−	2.50694i	0.0688962	−	0.0932341i
$724$	−2.57498	+	4.45999i	−0.0956983	+	0.165754i
$725$	−22.2470	+	38.5329i	−0.826233	+	1.43108i
$726$		0			0
$727$	19.0818	+	33.0507i	0.707706	+	1.22578i	0.965706	+	0.259638i	$0.0836031\pi$
$727$	19.0818	+	33.0507i	0.707706	+	1.22578i	−0.258000	+	0.966145i	$0.583064\pi$
$728$	−3.24261			−0.120179
$729$	21.0488	+	16.9100i	0.779586	+	0.626296i
$730$	−1.02251			−0.0378449
$731$	27.0913	+	46.9234i	1.00201	+	1.73553i
$732$	−8.01549	−	18.4018i	−0.296261	−	0.680148i
$733$	10.5342	−	18.2458i	0.389089	−	0.673923i	−0.603238	−	0.797561i	$-0.706123\pi$
$733$	10.5342	−	18.2458i	0.389089	−	0.673923i	0.992327	+	0.123639i	$0.0394564\pi$
$734$	−15.9546	+	27.6341i	−0.588894	+	1.01999i
$735$	−20.1018	+	27.2028i	−0.741465	+	1.00339i
$736$	23.5009	+	40.7048i	0.866255	+	1.50040i
$737$		0			0
$738$	4.73527	−	5.09116i	0.174308	−	0.187408i
$739$	17.3113			0.636807			0.318403	−	0.947955i	$-0.396853\pi$
$739$	17.3113			0.636807			0.318403	+	0.947955i	$0.396853\pi$
$740$	9.90476	+	17.1555i	0.364106	+	0.630650i
$741$	5.78417	+	0.655229i	0.212487	+	0.0240704i
$742$	13.0772	−	22.6504i	0.480080	−	0.831522i
$743$	2.64725	−	4.58517i	0.0971181	−	0.168214i	−0.813373	−	0.581743i	$-0.802371\pi$
$743$	2.64725	−	4.58517i	0.0971181	−	0.168214i	0.910491	+	0.413530i	$0.135704\pi$
$744$	8.91583	+	1.00998i	0.326870	+	0.0370277i
$745$	37.8247	+	65.5143i	1.38579	+	2.40026i
$746$	−12.0735			−0.442042
$747$	−35.3844	−	8.12088i	−1.29465	−	0.297127i
$748$		0			0
$749$	2.11491	+	3.66313i	0.0772772	+	0.133848i
$750$	−11.8890	+	16.0889i	−0.434126	+	0.587483i
$751$	7.81329	−	13.5330i	0.285111	−	0.493827i	−0.687525	−	0.726161i	$-0.741303\pi$
$751$	7.81329	−	13.5330i	0.285111	−	0.493827i	0.972636	+	0.232334i	$0.0746362\pi$
$752$	−4.97949	+	8.62473i	−0.181583	+	0.314511i
$753$	0.891185	+	2.04596i	0.0324766	+	0.0745590i
$754$	13.0113	+	22.5362i	0.473843	+	0.820720i
$755$	−7.35260			−0.267589
$756$	7.32242	+	2.57700i	0.266314	+	0.0937247i
$757$	21.9655			0.798351			0.399175	−	0.916875i	$-0.369296\pi$
$757$	21.9655			0.798351			0.399175	+	0.916875i	$0.369296\pi$
$758$	−2.12783	−	3.68551i	−0.0772862	−	0.133864i
$759$		0			0
$760$	3.34715	−	5.79744i	0.121414	−	0.210295i
$761$	−13.6441	+	23.6323i	−0.494600	+	0.856672i	−0.999981	−	0.00622458i	$-0.998019\pi$
$761$	−13.6441	+	23.6323i	−0.494600	+	0.856672i	0.505381	+	0.862896i	$0.331352\pi$
$762$	39.2987	−	53.1812i	1.42364	−	1.92655i
$763$	6.18051	+	10.7049i	0.223749	+	0.387545i
$764$	13.2658			0.479940
$765$	−22.6955	−	73.8912i	−0.820558	−	2.67154i
$766$	33.0039			1.19248
$767$	14.5369	+	25.1787i	0.524898	+	0.909150i
$768$	−35.9131	−	4.06822i	−1.29590	−	0.146799i
$769$	6.14632	−	10.6457i	0.221642	−	0.383895i	−0.733665	−	0.679512i	$-0.762192\pi$
$769$	6.14632	−	10.6457i	0.221642	−	0.383895i	0.955307	+	0.295616i	$0.0955250\pi$
$770$		0			0
$771$	20.0194	+	2.26779i	0.720982	+	0.0816725i
$772$	1.86360	+	3.22784i	0.0670723	+	0.116173i
$773$	−11.9400			−0.429450			−0.214725	−	0.976675i	$-0.568886\pi$
$773$	−11.9400			−0.429450			−0.214725	+	0.976675i	$0.568886\pi$
$774$	−11.5768	−	37.6914i	−0.416120	−	1.35479i
$775$	−27.7940			−0.998389
$776$	2.16151	+	3.74384i	0.0775936	+	0.134396i
$777$	5.26050	−	7.11879i	0.188719	−	0.255385i
$778$	11.8069	−	20.4501i	0.423297	−	0.733173i
$779$	0.972420	−	1.68428i	0.0348406	−	0.0603456i
$780$	6.81139	+	15.6374i	0.243887	+	0.559909i
$781$		0			0
$782$	100.356			3.58872
$783$	6.21704	+	33.1842i	0.222179	+	1.18591i
$784$	27.8664			0.995229
$785$	−30.9159	−	53.5479i	−1.10344	−	1.91121i
$786$	22.1229	+	50.7892i	0.789097	+	1.81159i
$787$	3.53121	−	6.11623i	0.125874	−	0.218020i	−0.796200	−	0.605033i	$-0.793160\pi$
$787$	3.53121	−	6.11623i	0.125874	−	0.218020i	0.922074	+	0.387013i	$0.126493\pi$
$788$	−4.26238	+	7.38266i	−0.151841	+	0.262996i
$789$	9.97539	−	13.4992i	0.355133	−	0.480586i
$790$	−10.2580	−	17.7674i	−0.364964	−	0.632135i
$791$	−1.80430			−0.0641537
$792$		0			0
$793$	−19.7065			−0.699797
$794$	−31.5983	−	54.7299i	−1.12138	−	1.94229i
$795$	74.0846	+	8.39227i	2.62751	+	0.297643i
$796$	0.666417	−	1.15427i	0.0236205	−	0.0409120i
$797$	4.93799	−	8.55285i	0.174913	−	0.302958i	−0.765218	−	0.643771i	$-0.777369\pi$
$797$	4.93799	−	8.55285i	0.174913	−	0.302958i	0.940131	+	0.340813i	$0.110702\pi$
$798$	5.48436	+	0.621266i	0.194144	+	0.0219926i
$799$	7.58881	+	13.1442i	0.268473	+	0.465008i
$800$	43.5935			1.54126
$801$	16.6592	−	17.9112i	0.588622	−	0.632862i
$802$	8.34839			0.294792
$803$		0			0
$804$	6.79095	−	9.18989i	0.239498	−	0.324102i
$805$	−14.6357	+	25.3498i	−0.515841	+	0.893463i
$806$	−8.12773	+	14.0776i	−0.286287	+	0.495864i
$807$	−1.20182	−	2.75910i	−0.0423060	−	0.0971251i
$808$	0.814576	+	1.41089i	0.0286567	+	0.0496348i
$809$	−0.274918			−0.00966559			−0.00483279	−	0.999988i	$-0.501538\pi$
$809$	−0.274918			−0.00966559			−0.00483279	+	0.999988i	$0.501538\pi$
$810$	4.06921	+	56.1033i	0.142977	+	1.97127i
$811$	−19.5890			−0.687863			−0.343932	−	0.938995i	$-0.611759\pi$
$811$	−19.5890			−0.687863			−0.343932	+	0.938995i	$0.611759\pi$
$812$	4.85331	+	8.40618i	0.170318	+	0.294999i
$813$	13.0996	+	30.0737i	0.459422	+	1.05473i
$814$		0			0
$815$	24.9357	−	43.1900i	0.873461	−	1.51288i
$816$	−37.8469	+	51.2165i	−1.32491	+	1.79293i
$817$	−5.51451	−	9.55141i	−0.192928	−	0.334161i
$818$	59.4654			2.07916
$819$	5.19056	−	5.58067i	0.181373	−	0.195004i
$820$	5.69854			0.199001
$821$	18.1660	+	31.4644i	0.633997	+	1.09812i	0.986727	+	0.162390i	$0.0519202\pi$
$821$	18.1660	+	31.4644i	0.633997	+	1.09812i	−0.352730	+	0.935725i	$0.614746\pi$
$822$	−22.6955	−	2.57094i	−0.791597	−	0.0896717i
$823$	−13.8167	+	23.9313i	−0.481620	+	0.834191i	−0.999777	−	0.0210944i	$-0.993285\pi$
$823$	−13.8167	+	23.9313i	−0.481620	+	0.834191i	0.518157	+	0.855286i	$0.326618\pi$
$824$	−1.32823	+	2.30055i	−0.0462709	+	0.0801436i
$825$		0			0
$826$	13.7834	+	23.8736i	0.479587	+	0.830669i
$827$	31.9450			1.11084			0.555418	−	0.831571i	$-0.312558\pi$
$827$	31.9450			1.11084			0.555418	+	0.831571i	$0.312558\pi$
$828$	−28.0020	−	6.42659i	−0.973138	−	0.223339i
$829$	−24.0996			−0.837012			−0.418506	−	0.908214i	$-0.637446\pi$
$829$	−24.0996			−0.837012			−0.418506	+	0.908214i	$0.637446\pi$
$830$	−37.8175	−	65.5019i	−1.31267	−	2.27360i
$831$	−4.93476	+	6.67798i	−0.171185	+	0.231657i
$832$	1.91409	−	3.31530i	0.0663592	−	0.114937i
$833$	21.2344	−	36.7791i	0.735729	−	1.27432i
$834$	3.94358	+	9.05357i	0.136555	+	0.313500i
$835$	−2.74883	−	4.76110i	−0.0951270	−	0.164765i
$836$		0			0
$837$	−16.0101	+	13.7278i	−0.553391	+	0.474503i
$838$	−46.9493			−1.62184
$839$	−23.3329	−	40.4137i	−0.805540	−	1.39524i	−0.915926	−	0.401348i	$-0.868542\pi$
$839$	−23.3329	−	40.4137i	−0.805540	−	1.39524i	0.110385	−	0.993889i	$-0.464792\pi$
$840$	−3.50007	−	8.03537i	−0.120764	−	0.277247i
$841$	−6.60815	+	11.4457i	−0.227867	+	0.394678i
$842$	26.2675	−	45.4966i	0.905237	−	1.56792i
$843$	−17.8040	+	24.0933i	−0.613201	+	0.829817i
$844$	−9.35694	−	16.2067i	−0.322079	−	0.557858i
$845$	−28.0010			−0.963264
$846$	−3.24290	−	10.5581i	−0.111493	−	0.362996i
$847$		0			0
$848$	−30.7129	−	53.1963i	−1.05469	−	1.82677i
$849$	30.1042	+	3.41019i	1.03317	+	0.117037i
$850$	46.5394	−	80.6086i	1.59629	−	2.76485i
$851$	−16.3801	+	28.3711i	−0.561501	+	0.972549i
$852$	−10.4871	−	1.18797i	−0.359281	−	0.0406992i
$853$	9.95958	+	17.2505i	0.341009	+	0.590646i	0.984620	−	0.174707i	$-0.0558978\pi$
$853$	9.95958	+	17.2505i	0.341009	+	0.590646i	−0.643611	+	0.765353i	$0.722565\pi$
$854$	−18.6850			−0.639388
$855$	4.61974	+	15.0408i	0.157992	+	0.514384i
$856$	4.68744			0.160213
$857$	19.5593	+	33.8778i	0.668134	+	1.15724i	0.978425	+	0.206601i	$0.0662401\pi$
$857$	19.5593	+	33.8778i	0.668134	+	1.15724i	−0.310291	+	0.950642i	$0.600427\pi$
$858$		0			0
$859$	−7.44918	+	12.9024i	−0.254163	+	0.440223i	−0.964668	−	0.263469i	$-0.915133\pi$
$859$	−7.44918	+	12.9024i	−0.254163	+	0.440223i	0.710505	+	0.703692i	$0.248467\pi$
$860$	16.1579	−	27.9864i	0.550981	−	0.954328i
$861$	−1.01685	−	2.33445i	−0.0346540	−	0.0795578i
$862$	19.8830	+	34.4383i	0.677217	+	1.17297i
$863$	−7.92445			−0.269752			−0.134876	−	0.990863i	$-0.543064\pi$
$863$	−7.92445			−0.269752			−0.134876	+	0.990863i	$0.543064\pi$
$864$	25.1111	−	21.5314i	0.854297	−	0.732514i
$865$	−12.0882			−0.411010
$866$	20.6821	+	35.8225i	0.702808	+	1.21730i
$867$	26.9991	+	61.9838i	0.916937	+	2.10508i
$868$	−3.03171	+	5.25107i	−0.102903	+	0.178233i
$869$		0			0
$870$	−41.8016	+	56.5683i	−1.41721	+	1.91784i
$871$	−5.60943	−	9.71581i	−0.190068	−	0.329208i
$872$	13.6983			0.463884
$873$	−9.90331	−	2.27285i	−0.335176	−	0.0769244i
$874$	−20.4278			−0.690980
$875$	3.66313	+	6.34473i	0.123837	+	0.214491i
$876$	−0.365204	−	0.0413702i	−0.0123391	−	0.00139777i
$877$	−18.2147	+	31.5488i	−0.615067	+	1.06533i	0.375306	+	0.926901i	$0.377538\pi$
$877$	−18.2147	+	31.5488i	−0.615067	+	1.06533i	−0.990373	+	0.138426i	$0.955796\pi$
$878$	11.5286	−	19.9681i	0.389072	−	0.673892i
$879$	−0.772362	−	0.0874929i	−0.0260511	−	0.00295106i
$880$		0			0
$881$	25.7097			0.866183			0.433092	−	0.901350i	$-0.357423\pi$
$881$	25.7097			0.866183			0.433092	+	0.901350i	$0.357423\pi$
$882$	−21.0479	+	22.6298i	−0.708719	+	0.761985i
$883$	−7.91844			−0.266477			−0.133238	−	0.991084i	$-0.542538\pi$
$883$	−7.91844			−0.266477			−0.133238	+	0.991084i	$0.542538\pi$
$884$	−10.7079	−	18.5466i	−0.360144	−	0.623788i
$885$	−46.7031	+	63.2012i	−1.56991	+	2.12449i
$886$	3.14384	−	5.44529i	0.105619	−	0.182938i
$887$	−6.00395	+	10.3991i	−0.201593	+	0.349169i	−0.949042	−	0.315150i	$-0.897945\pi$
$887$	−6.00395	+	10.3991i	−0.201593	+	0.349169i	0.747449	+	0.664319i	$0.231278\pi$
$888$	−3.91723	−	8.99307i	−0.131454	−	0.301788i
$889$	−12.1083	−	20.9723i	−0.406101	−	0.703387i
$890$	50.9610			1.70822
$891$		0			0
$892$	23.5505			0.788528
$893$	−1.54472	−	2.67554i	−0.0516922	−	0.0895336i
$894$	27.6028	+	63.3699i	0.923177	+	2.11941i
$895$	−0.956849	+	1.65731i	−0.0319839	+	0.0553978i
$896$	−5.51721	+	9.55609i	−0.184317	+	0.319247i
$897$	−16.7636	+	22.6855i	−0.559722	+	0.757446i
$898$	29.1021	+	50.4064i	0.971150	+	1.68208i
$899$	−26.3712			−0.879528
$900$	−18.1477	+	19.5117i	−0.604925	+	0.650389i
$901$	−93.6138			−3.11873
$902$		0			0
$903$	−14.3481	−	1.62534i	−0.477473	−	0.0540880i
$904$	−0.999754	+	1.73162i	−0.0332513	+	0.0575930i
$905$	−6.83336	+	11.8357i	−0.227149	+	0.393433i
$906$	−6.67536	−	0.756182i	−0.221774	−	0.0251225i
$907$	20.2804	+	35.1267i	0.673400	+	1.16636i	0.976934	+	0.213542i	$0.0685002\pi$
$907$	20.2804	+	35.1267i	0.673400	+	1.16636i	−0.303534	+	0.952821i	$0.598166\pi$
$908$	−7.12357			−0.236404
$909$	−3.73212	−	0.856537i	−0.123787	−	0.0284095i
$910$	15.8781			0.526355
$911$	17.7643	+	30.7687i	0.588559	+	1.01941i	0.994421	+	0.105480i	$0.0336379\pi$
$911$	17.7643	+	30.7687i	0.588559	+	1.01941i	−0.405862	+	0.913934i	$0.633029\pi$
$912$	7.70385	−	10.4253i	0.255100	−	0.345215i
$913$		0			0
$914$	12.5076	−	21.6638i	0.413714	−	0.716574i
$915$	−21.2712	−	48.8338i	−0.703203	−	1.61440i
$916$	−3.17208	−	5.49421i	−0.104809	−	0.181534i
$917$	20.2880			0.669969
$918$	−13.0057	−	69.4192i	−0.429251	−	2.29118i
$919$	−51.4484			−1.69713			−0.848563	−	0.529094i	$-0.822532\pi$
$919$	−51.4484			−1.69713			−0.848563	+	0.529094i	$0.822532\pi$
$920$	16.2191	+	28.0923i	0.534728	+	0.926176i
$921$	8.58749	+	19.7149i	0.282967	+	0.649630i
$922$	−3.26128	+	5.64870i	−0.107404	+	0.186030i
$923$	−5.18105	+	8.97383i	−0.170536	+	0.295377i
$924$		0			0
$925$	15.1923	+	26.3138i	0.499519	+	0.865192i
$926$	−45.1934			−1.48515
$927$	−1.83322	−	5.96851i	−0.0602107	−	0.196032i
$928$	41.3619			1.35777
$929$	24.1374	+	41.8072i	0.791923	+	1.37165i	0.924775	+	0.380515i	$0.124253\pi$
$929$	24.1374	+	41.8072i	0.791923	+	1.37165i	−0.132851	+	0.991136i	$0.542413\pi$
$930$	−43.6583	−	4.94559i	−1.43161	−	0.162172i
$931$	−4.32233	+	7.48649i	−0.141659	+	0.245360i
$932$	14.8301	−	25.6865i	0.485777	−	0.841390i
$933$	40.1006	+	4.54258i	1.31284	+	0.148718i
$934$	−21.6931	−	37.5736i	−0.709821	−	1.22945i
$935$		0			0
$936$	−2.47982	−	8.07369i	−0.0810553	−	0.263897i
$937$	−44.8251			−1.46437			−0.732185	−	0.681105i	$-0.761500\pi$
$937$	−44.8251			−1.46437			−0.732185	+	0.681105i	$0.761500\pi$
$938$	−5.31867	−	9.21221i	−0.173661	−	0.300789i
$939$	19.0368	−	25.7616i	0.621243	−	0.840699i
$940$	4.52617	−	7.83955i	0.147627	−	0.255698i
$941$	0.136842	−	0.237017i	0.00446092	−	0.00772653i	−0.863786	−	0.503858i	$-0.831913\pi$
$941$	0.136842	−	0.237017i	0.00446092	−	0.00772653i	0.868247	+	0.496132i	$0.165247\pi$
$942$	−22.5611	−	51.7952i	−0.735080	−	1.68758i
$943$	4.71200	+	8.16142i	0.153444	+	0.265772i
$944$	64.7430			2.10720
$945$	19.4319	+	6.83874i	0.632120	+	0.222464i
$946$		0			0
$947$	−11.1580	−	19.3262i	−0.362586	−	0.628017i	0.625800	−	0.779984i	$-0.284773\pi$
$947$	−11.1580	−	19.3262i	−0.362586	−	0.628017i	−0.988386	+	0.151966i	$0.951439\pi$
$948$	−2.94493	−	6.76090i	−0.0956468	−	0.219584i
$949$	−0.180426	+	0.312507i	−0.00585688	+	0.0101444i
$950$	−9.47323	+	16.4081i	−0.307352	+	0.532350i
$951$	22.6424	−	30.6409i	0.734230	−	0.993600i
$952$	5.50229	+	9.53025i	0.178330	+	0.308877i
$953$	−38.9268			−1.26096			−0.630481	−	0.776205i	$-0.717142\pi$
$953$	−38.9268			−1.26096			−0.630481	+	0.776205i	$0.717142\pi$
$954$	66.3976	+	15.2385i	2.14970	+	0.493366i
$955$	35.2042			1.13918
$956$	−0.160401	−	0.277823i	−0.00518775	−	0.00898545i
$957$		0			0
$958$	16.8847	−	29.2452i	0.545520	−	0.944868i
$959$	−4.18236	+	7.24407i	−0.135056	+	0.233923i
$960$	10.2816	+	1.16469i	0.331837	+	0.0375903i
$961$	7.26339	+	12.5806i	0.234303	+	0.405824i
$962$	17.7706			0.572946
$963$	−7.50335	+	8.06728i	−0.241792	+	0.259965i
$964$	2.33430			0.0751829
$965$	4.94553	+	8.56592i	0.159202	+	0.275747i
$966$	−15.8947	+	21.5096i	−0.511405	+	0.692061i
$967$	−13.3803	+	23.1754i	−0.430283	+	0.745271i	−0.996897	−	0.0787115i	$-0.974919\pi$
$967$	−13.3803	+	23.1754i	−0.430283	+	0.745271i	0.566615	+	0.823983i	$0.308253\pi$
$968$		0			0
$969$	−7.88924	−	18.1119i	−0.253439	−	0.581839i
$970$	−10.5843	−	18.3325i	−0.339841	−	0.588621i
$971$	1.83070			0.0587501			0.0293750	−	0.999568i	$-0.490648\pi$
$971$	1.83070			0.0587501			0.0293750	+	0.999568i	$0.490648\pi$
$972$	−0.816532	+	20.2027i	−0.0261903	+	0.648002i
$973$	3.61650			0.115940
$974$	−17.5349	−	30.3713i	−0.561854	−	0.973160i
$975$	10.4475	+	23.9852i	0.334589	+	0.768142i
$976$	−21.9416	+	38.0040i	−0.702335	+	1.21648i
$977$	19.6855	−	34.0963i	0.629794	−	1.09084i	−0.357798	−	0.933799i	$-0.616472\pi$
$977$	19.6855	−	34.0963i	0.629794	−	1.09084i	0.987593	−	0.157037i	$-0.0501942\pi$
$978$	27.0808	−	36.6472i	0.865949	−	1.17185i
$979$		0			0
$980$	−25.3295			−0.809122
$981$	−21.9274	+	23.5754i	−0.700088	+	0.752705i
$982$	−76.3708			−2.43709
$983$	17.9987	+	31.1747i	0.574070	+	0.994318i	0.996142	+	0.0877560i	$0.0279696\pi$
$983$	17.9987	+	31.1747i	0.574070	+	0.994318i	−0.422072	+	0.906562i	$0.638697\pi$
$984$	−2.80384	−	0.317618i	−0.0893832	−	0.0101253i
$985$	−11.3113	+	19.5918i	−0.360409	+	0.624246i
$986$	44.1570	−	76.4821i	1.40624	−	2.43569i
$987$	−4.01918	−	0.455291i	−0.127932	−	0.0144921i
$988$	2.17962	+	3.77521i	0.0693428	+	0.120105i
$989$	53.4427			1.69938
$990$		0			0
$991$	23.0540			0.732334			0.366167	−	0.930549i	$-0.380670\pi$
$991$	23.0540			0.732334			0.366167	+	0.930549i	$0.380670\pi$
$992$	12.9187	+	22.3759i	0.410170	+	0.710435i
$993$	−20.5123	+	27.7584i	−0.650940	+	0.880887i
$994$	−4.91249	+	8.50869i	−0.155815	+	0.269879i
$995$	1.76851	−	3.06315i	0.0560655	−	0.0971084i
$996$	−10.8569	−	24.9250i	−0.344013	−	0.789777i
$997$	18.8281	+	32.6112i	0.596291	+	1.03281i	0.993363	+	0.115018i	$0.0366927\pi$
$997$	18.8281	+	32.6112i	0.596291	+	1.03281i	−0.397073	+	0.917787i	$0.629974\pi$
$998$	3.21073			0.101634
$999$	21.7479	+	7.65382i	0.688074	+	0.242156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.k.364.6	yes	16
9.4	even	3		9801.2.a.bz.1.3		8
9.5	odd	6		9801.2.a.ca.1.6		8
9.7	even	3	inner	1089.2.e.k.727.6	yes	16
11.10	odd	2	inner	1089.2.e.k.364.3	✓	16
99.32	even	6		9801.2.a.ca.1.3		8
99.43	odd	6	inner	1089.2.e.k.727.3	yes	16
99.76	odd	6		9801.2.a.bz.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1089.2.e.k.364.3	✓	16	11.10	odd	2	inner
1089.2.e.k.364.6	yes	16	1.1	even	1	trivial
1089.2.e.k.727.3	yes	16	99.43	odd	6	inner
1089.2.e.k.727.6	yes	16	9.7	even	3	inner
9801.2.a.bz.1.3		8	9.4	even	3
9801.2.a.bz.1.6		8	99.76	odd	6
9801.2.a.ca.1.3		8	99.32	even	6
9801.2.a.ca.1.6		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)

\(f(q)\)	\(=\)	\(q+(0.907891 + 1.57251i) q^{2} +(0.691682 + 1.58795i) q^{3} +(-0.648531 + 1.12329i) q^{4} +(-1.72104 + 2.98093i) q^{5} +(-1.86910 + 2.52936i) q^{6} +(0.575887 + 0.997466i) q^{7} +1.27638 q^{8} +(-2.04315 + 2.19671i) q^{9} +O(q^{10})\)	\(q+(0.907891 + 1.57251i) q^{2} +(0.691682 + 1.58795i) q^{3} +(-0.648531 + 1.12329i) q^{4} +(-1.72104 + 2.98093i) q^{5} +(-1.86910 + 2.52936i) q^{6} +(0.575887 + 0.997466i) q^{7} +1.27638 q^{8} +(-2.04315 + 2.19671i) q^{9} -6.25008 q^{10} +(-2.23230 - 0.252874i) q^{12} +(-1.10285 + 1.91019i) q^{13} +(-1.04569 + 1.81118i) q^{14} +(-5.92398 - 0.671066i) q^{15} +(2.45588 + 4.25370i) q^{16} +7.48558 q^{17} +(-5.30931 - 1.21851i) q^{18} -1.52371 q^{19} +(-2.23230 - 3.86646i) q^{20} +(-1.18559 + 1.60441i) q^{21} +(3.69168 - 6.39418i) q^{23} +(0.882851 + 2.02683i) q^{24} +(-3.42398 - 5.93051i) q^{25} -4.00507 q^{26} +(-4.90147 - 1.72499i) q^{27} -1.49392 q^{28} +(-3.24870 - 5.62692i) q^{29} +(-4.32307 - 9.92479i) q^{30} +(2.02936 - 3.51496i) q^{31} +(-3.18295 + 5.51304i) q^{32} +(6.79609 + 11.7712i) q^{34} -3.96451 q^{35} +(-1.14249 - 3.71968i) q^{36} -4.43702 q^{37} +(-1.38336 - 2.39606i) q^{38} +(-3.79610 - 0.430021i) q^{39} +(-2.19671 + 3.80481i) q^{40} +(-0.638191 + 1.10538i) q^{41} +(-3.59934 - 0.407732i) q^{42} +(3.61913 + 6.26851i) q^{43} +(-3.03190 - 9.87113i) q^{45} +13.4066 q^{46} +(1.01379 + 1.75594i) q^{47} +(-5.05597 + 6.84201i) q^{48} +(2.83671 - 4.91332i) q^{49} +(6.21720 - 10.7685i) q^{50} +(5.17764 + 11.8867i) q^{51} +(-1.43046 - 2.47764i) q^{52} -12.5059 q^{53} +(-1.73743 - 9.27373i) q^{54} +(0.735052 + 1.27315i) q^{56} +(-1.05392 - 2.41957i) q^{57} +(5.89894 - 10.2173i) q^{58} +(6.59062 - 11.4153i) q^{59} +(4.59569 - 6.21913i) q^{60} +(4.46717 + 7.73737i) q^{61} +7.36975 q^{62} +(-3.36777 - 0.772917i) q^{63} -1.73559 q^{64} +(-3.79610 - 6.57505i) q^{65} +(-2.54315 + 4.40487i) q^{67} +(-4.85463 + 8.40847i) q^{68} +(12.7071 + 1.43945i) q^{69} +(-3.59934 - 6.23424i) q^{70} +4.69787 q^{71} +(-2.60784 + 2.80384i) q^{72} +0.163600 q^{73} +(-4.02833 - 6.97727i) q^{74} +(7.04903 - 9.53913i) q^{75} +(0.988175 - 1.71157i) q^{76} +(-2.77023 - 6.35984i) q^{78} +(1.64126 + 2.84275i) q^{79} -16.9067 q^{80} +(-0.651065 - 8.97642i) q^{81} -2.31763 q^{82} +(6.05073 + 10.4802i) q^{83} +(-1.03332 - 2.37227i) q^{84} +(-12.8830 + 22.3140i) q^{85} +(-6.57154 + 11.3822i) q^{86} +(6.68818 - 9.05081i) q^{87} -8.15366 q^{89} +(12.7699 - 13.7296i) q^{90} -2.54047 q^{91} +(4.78834 + 8.29365i) q^{92} +(6.98524 + 0.791285i) q^{93} +(-1.84082 + 3.18840i) q^{94} +(2.62238 - 4.54209i) q^{95} +(-10.9560 - 1.24109i) q^{96} +(1.69346 + 2.93316i) q^{97} +10.3017 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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