LMFDB - Embedded newform 585.2.bt.b.571.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.11
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64129 + 0.947602i) q^{2} +(-1.39724 + 1.02358i) q^{3} +(0.795899 - 1.37854i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.32334 - 3.00402i) q^{6} +(2.82539 - 1.63124i) q^{7} -0.773626i q^{8} +(0.904573 - 2.86038i) q^{9} +O(q^{10})$	\(q+(-1.64129 + 0.947602i) q^{2} +(-1.39724 + 1.02358i) q^{3} +(0.795899 - 1.37854i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.32334 - 3.00402i) q^{6} +(2.82539 - 1.63124i) q^{7} -0.773626i q^{8} +(0.904573 - 2.86038i) q^{9} -1.89520 q^{10} +(-0.866548 + 0.500301i) q^{11} +(0.298978 + 2.74082i) q^{12} +(-2.87709 + 2.17310i) q^{13} +(-3.09153 + 5.35469i) q^{14} +(-1.72184 + 0.187824i) q^{15} +(2.32489 + 4.02682i) q^{16} -7.42651 q^{17} +(1.22583 + 5.55189i) q^{18} -2.59185i q^{19} +(1.37854 - 0.795899i) q^{20} +(-2.27805 + 5.17125i) q^{21} +(0.948173 - 1.64228i) q^{22} +(-4.12263 + 7.14060i) q^{23} +(0.791867 + 1.08094i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.66292 - 6.29303i) q^{26} +(1.66391 + 4.92254i) q^{27} -5.19321i q^{28} +(-2.59582 - 4.49610i) q^{29} +(2.64806 - 1.93989i) q^{30} +(-4.82840 - 2.78768i) q^{31} +(-6.29169 - 3.63251i) q^{32} +(0.698679 - 1.58602i) q^{33} +(12.1891 - 7.03738i) q^{34} +3.26248 q^{35} +(-3.22319 - 3.52356i) q^{36} +3.25387i q^{37} +(2.45604 + 4.25399i) q^{38} +(1.79565 - 5.98127i) q^{39} +(0.386813 - 0.669980i) q^{40} +(3.27005 + 1.88797i) q^{41} +(-1.16133 - 10.6462i) q^{42} +(-4.95061 - 8.57471i) q^{43} +1.59276i q^{44} +(2.21357 - 2.02487i) q^{45} -15.6264i q^{46} +(-9.84967 + 5.68671i) q^{47} +(-7.37020 - 3.24674i) q^{48} +(1.82189 - 3.15560i) q^{49} +(-1.64129 - 0.947602i) q^{50} +(10.3766 - 7.60162i) q^{51} +(0.705827 + 5.69574i) q^{52} +2.76962 q^{53} +(-7.39558 - 6.50261i) q^{54} -1.00060 q^{55} +(-1.26197 - 2.18580i) q^{56} +(2.65296 + 3.62145i) q^{57} +(8.52102 + 4.91961i) q^{58} +(-5.16225 - 2.98043i) q^{59} +(-1.11149 + 2.52311i) q^{60} +(3.45357 + 5.98176i) q^{61} +10.5664 q^{62} +(-2.11019 - 9.55725i) q^{63} +4.46914 q^{64} +(-3.57818 + 0.443415i) q^{65} +(0.356179 + 3.26520i) q^{66} +(-3.37201 - 1.94683i) q^{67} +(-5.91075 + 10.2377i) q^{68} +(-1.54866 - 14.1970i) q^{69} +(-5.35469 + 3.09153i) q^{70} +12.8725i q^{71} +(-2.21286 - 0.699802i) q^{72} -4.10295i q^{73} +(-3.08337 - 5.34055i) q^{74} +(-1.58507 - 0.698258i) q^{75} +(-3.57297 - 2.06285i) q^{76} +(-1.63222 + 2.82709i) q^{77} +(2.72067 + 11.5186i) q^{78} +(1.42966 + 2.47624i) q^{79} +4.64978i q^{80} +(-7.36349 - 5.17484i) q^{81} -7.15616 q^{82} +(2.63423 - 1.52087i) q^{83} +(5.31566 + 7.25617i) q^{84} +(-6.43155 - 3.71326i) q^{85} +(16.2508 + 9.38242i) q^{86} +(8.22911 + 3.62511i) q^{87} +(0.387046 + 0.670384i) q^{88} -17.3066i q^{89} +(-1.71435 + 5.42099i) q^{90} +(-4.58405 + 10.8331i) q^{91} +(6.56239 + 11.3664i) q^{92} +(9.59986 - 1.04719i) q^{93} +(10.7775 - 18.6671i) q^{94} +(1.29593 - 2.24461i) q^{95} +(12.5092 - 1.36454i) q^{96} +(4.09056 - 2.36168i) q^{97} +6.90569i q^{98} +(0.647194 + 2.93121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.64129	+	0.947602i	−1.16057	+	0.670056i	−0.951441	−	0.307832i	$-0.900396\pi$
$2$	−1.64129	+	0.947602i	−1.16057	+	0.670056i	−0.209130	+	0.977888i	$0.567063\pi$
$3$	−1.39724	+	1.02358i	−0.806698	+	0.590963i
$3$	−1.39724	+	1.02358i	−0.806698	+	0.590963i
$4$	0.795899	−	1.37854i	0.397949	−	0.689269i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	1.32334	−	3.00402i	0.540252	−	1.22639i
$7$	2.82539	−	1.63124i	1.06790	−	0.616551i	0.140291	−	0.990110i	$-0.455196\pi$
$7$	2.82539	−	1.63124i	1.06790	−	0.616551i	0.927606	+	0.373560i	$0.121863\pi$
$8$		−	0.773626i		−	0.273518i
$9$	0.904573	−	2.86038i	0.301524	−	0.953458i
$10$	−1.89520			−0.599316
$11$	−0.866548	+	0.500301i	−0.261274	+	0.150847i	−0.624916	−	0.780692i	$-0.714867\pi$
$11$	−0.866548	+	0.500301i	−0.261274	+	0.150847i	0.363642	+	0.931539i	$0.381533\pi$
$12$	0.298978	+	2.74082i	0.0863074	+	0.791206i
$13$	−2.87709	+	2.17310i	−0.797961	+	0.602709i
$13$	−2.87709	+	2.17310i	−0.797961	+	0.602709i
$14$	−3.09153	+	5.35469i	−0.826247	+	1.43110i
$15$	−1.72184	+	0.187824i	−0.444576	+	0.0484959i
$16$	2.32489	+	4.02682i	0.581222	+	1.00671i
$17$	−7.42651			−1.80119			−0.900597	−	0.434655i	$-0.856870\pi$
$17$	−7.42651			−1.80119			−0.900597	+	0.434655i	$0.856870\pi$
$18$	1.22583	+	5.55189i	0.288930	+	1.30859i
$19$		−	2.59185i		−	0.594612i	−0.954782	−	0.297306i	$-0.903912\pi$
$19$		−	2.59185i		−	0.594612i	0.954782	−	0.297306i	$-0.0960881\pi$
$20$	1.37854	−	0.795899i	0.308250	−	0.177968i
$21$	−2.27805	+	5.17125i	−0.497112	+	1.12846i
$22$	0.948173	−	1.64228i	0.202151	−	0.350136i
$23$	−4.12263	+	7.14060i	−0.859628	+	1.48892i	0.0126568	+	0.999920i	$0.495971\pi$
$23$	−4.12263	+	7.14060i	−0.859628	+	1.48892i	−0.872284	+	0.488999i	$0.837362\pi$
$24$	0.791867	+	1.08094i	0.161639	+	0.220647i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.66292	−	6.29303i	0.522241	−	1.23417i
$27$	1.66391	+	4.92254i	0.320220	+	0.947343i
$28$		−	5.19321i		−	0.981424i
$29$	−2.59582	−	4.49610i	−0.482032	−	0.834904i	0.517755	−	0.855529i	$-0.326768\pi$
$29$	−2.59582	−	4.49610i	−0.482032	−	0.834904i	−0.999787	+	0.0206245i	$0.993435\pi$
$30$	2.64806	−	1.93989i	0.483467	−	0.354174i
$31$	−4.82840	−	2.78768i	−0.867207	−	0.500682i	−0.000787699	−	1.00000i	$-0.500251\pi$
$31$	−4.82840	−	2.78768i	−0.867207	−	0.500682i	−0.866419	+	0.499318i	$0.833584\pi$
$32$	−6.29169	−	3.63251i	−1.11222	−	0.642143i
$33$	0.698679	−	1.58602i	0.121624	−	0.276091i
$34$	12.1891	−	7.03738i	2.09041	−	1.20690i
$35$	3.26248			0.551460
$36$	−3.22319	−	3.52356i	−0.537198	−	0.587260i
$37$			3.25387i			0.534932i	0.963567	+	0.267466i	$0.0861864\pi$
$37$			3.25387i			0.534932i	−0.963567	+	0.267466i	$0.913814\pi$
$38$	2.45604	+	4.25399i	0.398423	+	0.690089i
$39$	1.79565	−	5.98127i	0.287534	−	0.957770i
$40$	0.386813	−	0.669980i	0.0611605	−	0.105933i
$41$	3.27005	+	1.88797i	0.510696	+	0.294851i	0.733120	−	0.680099i	$-0.238063\pi$
$41$	3.27005	+	1.88797i	0.510696	+	0.294851i	−0.222423	+	0.974950i	$0.571397\pi$
$42$	−1.16133	−	10.6462i	−0.179197	−	1.64275i
$43$	−4.95061	−	8.57471i	−0.754961	−	1.30763i	−0.945394	−	0.325931i	$-0.894322\pi$
$43$	−4.95061	−	8.57471i	−0.754961	−	1.30763i	0.190432	−	0.981700i	$-0.439011\pi$
$44$			1.59276i			0.240117i
$45$	2.21357	−	2.02487i	0.329980	−	0.301850i
$46$		−	15.6264i		−	2.30399i
$47$	−9.84967	+	5.68671i	−1.43672	+	0.829492i	−0.997620	−	0.0689461i	$-0.978036\pi$
$47$	−9.84967	+	5.68671i	−1.43672	+	0.829492i	−0.439101	+	0.898438i	$0.644703\pi$
$48$	−7.37020	−	3.24674i	−1.06380	−	0.468627i
$49$	1.82189	−	3.15560i	0.260269	−	0.450800i
$50$	−1.64129	−	0.947602i	−0.232114	−	0.134011i
$51$	10.3766	−	7.60162i	1.45302	−	1.06444i
$52$	0.705827	+	5.69574i	0.0978806	+	0.789857i
$53$	2.76962			0.380436			0.190218	−	0.981742i	$-0.439080\pi$
$53$	2.76962			0.380436			0.190218	+	0.981742i	$0.439080\pi$
$54$	−7.39558	−	6.50261i	−1.00641	−	0.884894i
$55$	−1.00060			−0.134921
$56$	−1.26197	−	2.18580i	−0.168638	−	0.292089i
$57$	2.65296	+	3.62145i	0.351394	+	0.479672i
$58$	8.52102	+	4.91961i	1.11887	+	0.645977i
$59$	−5.16225	−	2.98043i	−0.672068	−	0.388019i	0.124792	−	0.992183i	$-0.460174\pi$
$59$	−5.16225	−	2.98043i	−0.672068	−	0.388019i	−0.796860	+	0.604164i	$0.793507\pi$
$60$	−1.11149	+	2.52311i	−0.143492	+	0.325732i
$61$	3.45357	+	5.98176i	0.442185	+	0.765886i	0.997851	−	0.0655188i	$-0.0208702\pi$
$61$	3.45357	+	5.98176i	0.442185	+	0.765886i	−0.555667	+	0.831405i	$0.687537\pi$
$62$	10.5664			1.34194
$63$	−2.11019	−	9.55725i	−0.265858	−	1.20410i
$64$	4.46914			0.558643
$65$	−3.57818	+	0.443415i	−0.443819	+	0.0549989i
$66$	0.356179	+	3.26520i	0.0438426	+	0.401918i
$67$	−3.37201	−	1.94683i	−0.411956	−	0.237843i	0.279674	−	0.960095i	$-0.409774\pi$
$67$	−3.37201	−	1.94683i	−0.411956	−	0.237843i	−0.691630	+	0.722252i	$0.743107\pi$
$68$	−5.91075	+	10.2377i	−0.716784	+	1.24151i
$69$	−1.54866	−	14.1970i	−0.186436	−	1.70912i
$70$	−5.35469	+	3.09153i	−0.640008	+	0.369509i
$71$			12.8725i			1.52768i	0.645403	+	0.763842i	$0.276690\pi$
$71$			12.8725i			1.52768i	−0.645403	+	0.763842i	$0.723310\pi$
$72$	−2.21286	−	0.699802i	−0.260788	−	0.0824724i
$73$		−	4.10295i		−	0.480214i	−0.970746	−	0.240107i	$-0.922817\pi$
$73$		−	4.10295i		−	0.480214i	0.970746	−	0.240107i	$-0.0771825\pi$
$74$	−3.08337	−	5.34055i	−0.358435	−	0.620827i
$75$	−1.58507	−	0.698258i	−0.183028	−	0.0806279i
$76$	−3.57297	−	2.06285i	−0.409847	−	0.236625i
$77$	−1.63222	+	2.82709i	−0.186009	+	0.322177i
$78$	2.72067	+	11.5186i	0.308055	+	1.30422i
$79$	1.42966	+	2.47624i	0.160849	+	0.278599i	0.935173	−	0.354190i	$-0.115243\pi$
$79$	1.42966	+	2.47624i	0.160849	+	0.278599i	−0.774324	+	0.632789i	$0.781910\pi$
$80$			4.64978i			0.519861i
$81$	−7.36349	−	5.17484i	−0.818166	−	0.574982i
$82$	−7.15616			−0.790266
$83$	2.63423	−	1.52087i	0.289144	−	0.166937i	−0.348412	−	0.937342i	$-0.613279\pi$
$83$	2.63423	−	1.52087i	0.289144	−	0.166937i	0.637556	+	0.770404i	$0.279946\pi$
$84$	5.31566	+	7.25617i	0.579986	+	0.791713i
$85$	−6.43155	−	3.71326i	−0.697599	−	0.402759i
$86$	16.2508	+	9.38242i	1.75237	+	1.01173i
$87$	8.22911	+	3.62511i	0.882253	+	0.388653i
$88$	0.387046	+	0.670384i	0.0412593	+	0.0714632i
$89$		−	17.3066i		−	1.83449i	−0.398321	−	0.917246i	$-0.630407\pi$
$89$		−	17.3066i		−	1.83449i	0.398321	−	0.917246i	$-0.369593\pi$
$90$	−1.71435	+	5.42099i	−0.180708	+	0.571423i
$91$	−4.58405	+	10.8331i	−0.480539	+	1.13561i
$92$	6.56239	+	11.3664i	0.684177	+	1.18503i
$93$	9.59986	−	1.04719i	0.995459	−	0.108588i
$94$	10.7775	−	18.6671i	1.11161	−	1.92537i
$95$	1.29593	−	2.24461i	0.132959	−	0.230292i
$96$	12.5092	−	1.36454i	1.27671	−	0.139268i
$97$	4.09056	−	2.36168i	0.415333	−	0.239793i	−0.277745	−	0.960655i	$-0.589587\pi$
$97$	4.09056	−	2.36168i	0.415333	−	0.239793i	0.693079	+	0.720862i	$0.256254\pi$
$98$			6.90569i			0.697580i
$99$	0.647194	+	2.93121i	0.0650455	+	0.294598i
$100$	1.59180			0.159180
$101$	−4.91011	−	8.50455i	−0.488574	−	0.846235i	0.511340	−	0.859379i	$-0.329149\pi$
$101$	−4.91011	−	8.50455i	−0.488574	−	0.846235i	−0.999914	+	0.0131440i	$0.995816\pi$
$102$	−9.82781	+	22.3094i	−0.973099	+	2.20896i
$103$	−6.08635	+	10.5419i	−0.599706	+	1.03872i	0.393158	+	0.919471i	$0.371383\pi$
$103$	−6.08635	+	10.5419i	−0.599706	+	1.03872i	−0.992864	+	0.119251i	$0.961951\pi$
$104$	1.68117	+	2.22579i	0.164852	+	0.218257i
$105$	−4.55848	+	3.33940i	−0.444862	+	0.325893i
$106$	−4.54576	+	2.62449i	−0.441523	+	0.254913i
$107$	9.28235			0.897359			0.448679	−	0.893693i	$-0.351895\pi$
$107$	9.28235			0.897359			0.448679	+	0.893693i	$0.351895\pi$
$108$	8.11021	+	1.62408i	0.780405	+	0.156277i
$109$		−	7.58819i		−	0.726817i	−0.931630	−	0.363409i	$-0.881613\pi$
$109$		−	7.58819i		−	0.726817i	0.931630	−	0.363409i	$-0.118387\pi$
$110$	1.64228	−	0.948173i	0.156586	−	0.0904048i
$111$	−3.33059	−	4.54644i	−0.316126	−	0.431529i
$112$	13.1374	+	7.58490i	1.24137	+	0.716706i
$113$	4.79093	−	8.29813i	0.450693	−	0.780623i	−0.547736	−	0.836651i	$-0.684510\pi$
$113$	4.79093	−	8.29813i	0.450693	−	0.780623i	0.998429	+	0.0560282i	$0.0178437\pi$
$114$	−7.78599	−	3.42991i	−0.729225	−	0.321240i
$115$	−7.14060	+	4.12263i	−0.665865	+	0.384437i
$116$	−8.26405			−0.767298
$117$	3.61334	+	10.1953i	0.334054	+	0.942554i
$118$	11.2970			1.03998
$119$	−20.9828	+	12.1144i	−1.92349	+	1.11053i
$120$	0.145305	+	1.33206i	0.0132645	+	0.121600i
$121$	−4.99940	+	8.65921i	−0.454491	+	0.787201i
$122$	−11.3367	−	6.54522i	−1.02637	−	0.592577i
$123$	−6.50154	+	0.709210i	−0.586224	+	0.0639473i
$124$	−7.68584	+	4.43742i	−0.690209	+	0.398492i
$125$			1.00000i			0.0894427i
$126$	12.5199	+	13.6867i	1.11536	+	1.21930i
$127$	1.74824			0.155131			0.0775655	−	0.996987i	$-0.475285\pi$
$127$	1.74824			0.155131			0.0775655	+	0.996987i	$0.475285\pi$
$128$	5.24820	−	3.03005i	0.463880	−	0.267821i
$129$	15.6941	+	6.91361i	1.38179	+	0.608710i
$130$	5.45267	−	4.11847i	0.478231	−	0.361213i
$131$	−5.40681	+	9.36487i	−0.472395	+	0.818212i	−0.999501	−	0.0315873i	$-0.989944\pi$
$131$	−5.40681	+	9.36487i	−0.472395	+	0.818212i	0.527106	+	0.849800i	$0.323277\pi$
$132$	−1.63031	−	2.22547i	−0.141901	−	0.193702i
$133$	−4.22793	−	7.32299i	−0.366608	−	0.634984i
$134$	7.37928			0.637473
$135$	−1.02028	+	5.09500i	−0.0878118	+	0.438508i
$136$			5.74534i			0.492659i
$137$	−14.1845	+	8.18941i	−1.21186	+	0.699669i	−0.963165	−	0.268913i	$-0.913336\pi$
$137$	−14.1845	+	8.18941i	−1.21186	+	0.699669i	−0.248697	+	0.968581i	$0.580002\pi$
$138$	15.9949	+	21.8339i	1.36158	+	1.85863i
$139$	−8.00021	+	13.8568i	−0.678569	+	1.17532i	0.296843	+	0.954926i	$0.404066\pi$
$139$	−8.00021	+	13.8568i	−0.678569	+	1.17532i	−0.975412	+	0.220390i	$0.929267\pi$
$140$	2.59660	−	4.49745i	0.219453	−	0.380104i
$141$	7.94158	−	18.0276i	0.668802	−	1.51820i
$142$	−12.1980	−	21.1276i	−1.02363	−	1.77299i
$143$	1.40593	−	3.32251i	0.117570	−	0.277842i
$144$	13.6213	−	3.00749i	1.13510	−	0.250624i
$145$		−	5.19165i		−	0.431143i
$146$	3.88796	+	6.73415i	0.321770	+	0.557322i
$147$	0.684387	+	6.27398i	0.0564473	+	0.517469i
$148$	4.48558	+	2.58975i	0.368712	+	0.212876i
$149$	11.8586	+	6.84657i	0.971494	+	0.560893i	0.899692	−	0.436526i	$-0.143791\pi$
$149$	11.8586	+	6.84657i	0.971494	+	0.560893i	0.0718029	+	0.997419i	$0.477125\pi$
$150$	3.26323	−	0.355965i	0.266442	−	0.0290644i
$151$	−8.03167	+	4.63708i	−0.653608	+	0.377361i	−0.789837	−	0.613317i	$-0.789835\pi$
$151$	−8.03167	+	4.63708i	−0.653608	+	0.377361i	0.136229	+	0.990677i	$0.456502\pi$
$152$	−2.00512			−0.162637
$153$	−6.71783	+	21.2426i	−0.543104	+	1.71736i
$154$		−	6.18679i		−	0.498546i
$155$	−2.78768	−	4.82840i	−0.223912	−	0.387827i
$156$	−6.81625	−	7.23586i	−0.545737	−	0.579333i
$157$	−1.19067	+	2.06230i	−0.0950256	+	0.164589i	−0.909619	−	0.415443i	$-0.863627\pi$
$157$	−1.19067	+	2.06230i	−0.0950256	+	0.164589i	0.814594	+	0.580032i	$0.196960\pi$
$158$	−4.69298	−	2.70949i	−0.373354	−	0.215556i
$159$	−3.86983	+	2.83492i	−0.306897	+	0.224824i
$160$	−3.63251	−	6.29169i	−0.287175	−	0.497402i
$161$			26.9000i			2.12002i
$162$	16.9894	+	1.51577i	1.33481	+	0.119090i
$163$		−	15.3867i		−	1.20518i	−0.798051	−	0.602590i	$-0.794136\pi$
$163$		−	15.3867i		−	1.20518i	0.798051	−	0.602590i	$-0.205864\pi$
$164$	5.20526	−	3.00526i	0.406463	−	0.234671i
$165$	1.39809	−	1.02420i	0.108841	−	0.0797335i
$166$	−2.88236	+	4.99240i	−0.223715	+	0.387485i
$167$	−4.63227	−	2.67444i	−0.358456	−	0.206955i	0.309947	−	0.950754i	$-0.399689\pi$
$167$	−4.63227	−	2.67444i	−0.358456	−	0.206955i	−0.668403	+	0.743799i	$0.733022\pi$
$168$	4.00061	+	1.76236i	0.308654	+	0.135969i
$169$	3.55528	−	12.5044i	0.273483	−	0.961877i
$170$	14.0748			1.07948
$171$	−7.41367	−	2.34452i	−0.566938	−	0.179290i
$172$	−15.7607			−1.20175
$173$	−8.37328	−	14.5030i	−0.636609	−	1.10264i	−0.986172	−	0.165726i	$-0.947003\pi$
$173$	−8.37328	−	14.5030i	−0.636609	−	1.10264i	0.349563	−	0.936913i	$-0.386330\pi$
$174$	−16.9415	+	1.84804i	−1.28434	+	0.140100i
$175$	2.82539	+	1.63124i	0.213579	+	0.123310i
$176$	−4.02925	−	2.32629i	−0.303716	−	0.175351i
$177$	10.2636	−	1.11959i	0.771461	−	0.0841536i
$178$	16.3997	+	28.4052i	1.22921	+	2.12906i
$179$	15.9753			1.19405			0.597025	−	0.802223i	$-0.296349\pi$
$179$	15.9753			1.19405			0.597025	+	0.802223i	$0.296349\pi$
$180$	−1.02958	−	4.66308i	−0.0767405	−	0.347566i
$181$	1.76031			0.130843			0.0654214	−	0.997858i	$-0.479161\pi$
$181$	1.76031			0.130843			0.0654214	+	0.997858i	$0.479161\pi$
$182$	−2.74166	−	22.1241i	−0.203226	−	1.63995i
$183$	−10.9483	−	4.82297i	−0.809320	−	0.356524i
$184$	5.52416	+	3.18937i	0.407246	+	0.235124i
$185$	−1.62693	+	2.81793i	−0.119615	+	0.207178i
$186$	−14.7639	+	10.8156i	−1.08254	+	0.793037i
$187$	6.43543	−	3.71550i	0.470605	−	0.271704i
$188$			18.1042i			1.32038i
$189$	12.7310	+	11.1939i	0.926047	+	0.814233i
$190$			4.91209i			0.356360i
$191$	6.38591	+	11.0607i	0.462068	+	0.800325i	0.999064	−	0.0432595i	$-0.0137742\pi$
$191$	6.38591	+	11.0607i	0.462068	+	0.800325i	−0.536996	+	0.843585i	$0.680441\pi$
$192$	−6.24448	+	4.57452i	−0.450656	+	0.330138i
$193$	17.7511	+	10.2486i	1.27776	+	0.737712i	0.976435	−	0.215811i	$-0.0692395\pi$
$193$	17.7511	+	10.2486i	1.27776	+	0.737712i	0.301320	+	0.953523i	$0.402573\pi$
$194$	−4.47587	+	7.75244i	−0.321349	+	0.556593i
$195$	4.54572	−	4.28211i	0.325526	−	0.306648i
$196$	−2.90007	−	5.02308i	−0.207148	−	0.358791i
$197$		−	25.9810i		−	1.85107i	−0.378667	−	0.925533i	$-0.623617\pi$
$197$		−	25.9810i		−	1.85107i	0.378667	−	0.925533i	$-0.376383\pi$
$198$	−3.83986	−	4.19770i	−0.272887	−	0.298317i
$199$	−16.0787			−1.13979			−0.569894	−	0.821718i	$-0.693016\pi$
$199$	−16.0787			−1.13979			−0.569894	+	0.821718i	$0.693016\pi$
$200$	0.669980	−	0.386813i	0.0473747	−	0.0273518i
$201$	6.70425	−	0.731322i	0.472881	−	0.0515835i
$202$	16.1179	+	9.30565i	1.13405	+	0.654743i
$203$	−14.6684	−	8.46882i	−1.02952	−	0.594395i
$204$	−2.22036	−	20.3547i	−0.155456	−	1.42511i
$205$	1.88797	+	3.27005i	0.131861	+	0.228390i
$206$		−	23.0698i		−	1.60735i
$207$	16.6956	+	18.2515i	1.16042	+	1.26856i
$208$	−15.4396	−	6.53332i	−1.07054	−	0.453004i
$209$	1.29671	+	2.24596i	0.0896951	+	0.155357i
$210$	4.31738	−	9.80057i	0.297927	−	0.676303i
$211$	−3.26160	+	5.64926i	−0.224538	+	0.388911i	−0.956181	−	0.292777i	$-0.905421\pi$
$211$	−3.26160	+	5.64926i	−0.224538	+	0.388911i	0.731643	+	0.681688i	$0.238754\pi$
$212$	2.20434	−	3.81802i	0.151394	−	0.262223i
$213$	−13.1760	−	17.9860i	−0.902806	−	1.23238i
$214$	−15.2351	+	8.79597i	−1.04145	+	0.601280i
$215$		−	9.90122i		−	0.675258i
$216$	3.80821	−	1.28724i	0.259116	−	0.0875859i
$217$	−18.1895			−1.23478
$218$	7.19059	+	12.4545i	0.487008	+	0.843523i
$219$	4.19969	+	5.73282i	0.283789	+	0.387388i
$220$	−0.796379	+	1.37937i	−0.0536919	+	0.0929970i
$221$	21.3667	−	16.1386i	1.43728	−	1.08560i
$222$	9.77469	+	4.30598i	0.656035	+	0.288998i
$223$	−21.7284	+	12.5449i	−1.45504	+	0.840068i	−0.998761	−	0.0497685i	$-0.984152\pi$
$223$	−21.7284	+	12.5449i	−1.45504	+	0.840068i	−0.456280	+	0.889836i	$0.650818\pi$
$224$	−23.7020			−1.58366
$225$	2.92944	−	0.646804i	0.195296	−	0.0431203i
$226$			18.1596i			1.20796i
$227$	20.3625	−	11.7563i	1.35151	−	0.780292i	0.363045	−	0.931772i	$-0.381737\pi$
$227$	20.3625	−	11.7563i	1.35151	−	0.780292i	0.988460	+	0.151480i	$0.0484039\pi$
$228$	7.10379	−	0.774906i	0.470460	−	0.0513194i
$229$	−7.07705	−	4.08594i	−0.467665	−	0.270006i	0.247597	−	0.968863i	$-0.420359\pi$
$229$	−7.07705	−	4.08594i	−0.467665	−	0.270006i	−0.715262	+	0.698857i	$0.753692\pi$
$230$	7.81322	−	13.5329i	0.515189	−	0.892333i
$231$	−0.613141	−	5.62084i	−0.0403417	−	0.369824i
$232$	−3.47830	+	2.00820i	−0.228362	+	0.131845i
$233$	5.64894			0.370074			0.185037	−	0.982732i	$-0.440759\pi$
$233$	5.64894			0.370074			0.185037	+	0.982732i	$0.440759\pi$
$234$	−15.5916	−	13.3095i	−1.01926	−	0.870066i
$235$	−11.3734			−0.741920
$236$	−8.21726	+	4.74424i	−0.534898	+	0.308824i
$237$	−4.53221	−	1.99654i	−0.294398	−	0.129689i
$238$	22.9593	−	39.7667i	1.48823	−	2.57769i
$239$	−18.5870	−	10.7312i	−1.20230	−	0.694146i	−0.241231	−	0.970468i	$-0.577551\pi$
$239$	−18.5870	−	10.7312i	−1.20230	−	0.694146i	−0.961065	+	0.276322i	$0.910884\pi$
$240$	−4.75941	−	6.49686i	−0.307219	−	0.419371i
$241$	5.80729	−	3.35284i	0.374081	−	0.215976i	−0.301159	−	0.953574i	$-0.597374\pi$
$241$	5.80729	−	3.35284i	0.374081	−	0.215976i	0.675240	+	0.737598i	$0.264040\pi$
$242$		−	18.9498i		−	1.21814i
$243$	15.5854	−	0.306611i	0.999807	−	0.0196691i
$244$	10.9948			0.703869
$245$	3.15560	−	1.82189i	0.201604	−	0.116396i
$246$	9.99889	−	7.32489i	0.637506	−	0.467018i
$247$	5.63235	+	7.45699i	0.358378	+	0.474477i
$248$	−2.15662	+	3.73538i	−0.136946	+	0.237197i
$249$	−2.12392	+	4.82137i	−0.134598	+	0.305542i
$250$	−0.947602	−	1.64129i	−0.0599316	−	0.103805i
$251$	−6.55456			−0.413720			−0.206860	−	0.978371i	$-0.566325\pi$
$251$	−6.55456			−0.413720			−0.206860	+	0.978371i	$0.566325\pi$
$252$	−14.8545	−	4.69764i	−0.935747	−	0.295923i
$253$		−	8.25023i		−	0.518688i
$254$	−2.86937	+	1.65663i	−0.180040	+	0.103946i
$255$	12.7872	−	1.39488i	0.800768	−	0.0873505i
$256$	−10.2117	+	17.6872i	−0.638232	+	1.10545i
$257$	2.70420	−	4.68381i	0.168683	−	0.292168i	−0.769274	−	0.638919i	$-0.779382\pi$
$257$	2.70420	−	4.68381i	0.168683	−	0.292168i	0.937957	+	0.346751i	$0.112715\pi$
$258$	−32.3100	+	3.52449i	−2.01153	+	0.219425i
$259$	5.30784	+	9.19344i	0.329813	+	0.571253i
$260$	−2.23661	+	5.28557i	−0.138708	+	0.327797i
$261$	−15.2086	+	3.35798i	−0.941391	+	0.207854i
$262$		−	20.4940i		−	1.26612i
$263$	5.90237	+	10.2232i	0.363956	+	0.630390i	0.988608	−	0.150513i	$-0.0480925\pi$
$263$	5.90237	+	10.2232i	0.363956	+	0.630390i	−0.624652	+	0.780903i	$0.714759\pi$
$264$	−1.22699	−	0.540517i	−0.0755159	−	0.0332665i
$265$	2.39856	+	1.38481i	0.147342	+	0.0850681i
$266$	13.8786	+	8.01279i	0.850950	+	0.491296i
$267$	17.7146	+	24.1815i	1.08412	+	1.47988i
$268$	−5.36756	+	3.09896i	−0.327876	+	0.189299i
$269$	9.63399			0.587395			0.293697	−	0.955898i	$-0.405114\pi$
$269$	9.63399			0.587395			0.293697	+	0.955898i	$0.405114\pi$
$270$	−3.15345	−	9.32922i	−0.191913	−	0.567758i
$271$			9.51808i			0.578182i	0.957302	+	0.289091i	$0.0933531\pi$
$271$			9.51808i			0.578182i	−0.957302	+	0.289091i	$0.906647\pi$
$272$	−17.2658	−	29.9053i	−1.04689	−	1.81327i
$273$	−4.68347	−	19.8286i	−0.283457	−	1.20008i
$274$	15.5206	−	26.8825i	0.937634	−	1.62403i
$275$	−0.866548	−	0.500301i	−0.0522548	−	0.0301693i
$276$	−20.8037	−	9.16449i	−1.25223	−	0.551637i
$277$	2.99760	+	5.19199i	0.180108	+	0.311956i	0.941917	−	0.335845i	$-0.109022\pi$
$277$	2.99760	+	5.19199i	0.180108	+	0.311956i	−0.761809	+	0.647802i	$0.775689\pi$
$278$		−	30.3241i		−	1.81872i
$279$	−12.3415	+	11.2894i	−0.738864	+	0.675878i
$280$		−	2.52394i		−	0.150834i
$281$	−6.01530	+	3.47293i	−0.358842	+	0.207178i	−0.668573	−	0.743647i	$-0.733095\pi$
$281$	−6.01530	+	3.47293i	−0.358842	+	0.207178i	0.309730	+	0.950824i	$0.399761\pi$
$282$	4.04853	+	37.1141i	0.241087	+	2.21011i
$283$	0.903153	−	1.56431i	0.0536869	−	0.0929884i	−0.837933	−	0.545773i	$-0.816236\pi$
$283$	0.903153	−	1.56431i	0.0536869	−	0.0929884i	0.891620	+	0.452785i	$0.149569\pi$
$284$	17.7452	+	10.2452i	1.05299	+	0.607941i
$285$	0.486812	+	4.46275i	0.0288362	+	0.264350i
$286$	0.840869	+	6.78547i	0.0497216	+	0.401233i
$287$	12.3189			0.727162
$288$	−16.0816	+	14.7107i	−0.947620	+	0.866838i
$289$	38.1531			2.24430
$290$	4.91961	+	8.52102i	0.288890	+	0.500372i
$291$	−3.29813	+	7.48685i	−0.193340	+	0.438887i
$292$	−5.65607	−	3.26553i	−0.330996	−	0.191101i
$293$	2.08194	+	1.20201i	0.121628	+	0.0702220i	0.559580	−	0.828777i	$-0.310963\pi$
$293$	2.08194	+	1.20201i	0.121628	+	0.0702220i	−0.437952	+	0.898999i	$0.644296\pi$
$294$	−7.06852	−	9.64893i	−0.412244	−	0.562737i
$295$	−2.98043	−	5.16225i	−0.173527	−	0.300558i
$296$	2.51728			0.146314
$297$	−3.90461	−	3.43316i	−0.226569	−	0.199212i
$298$	−25.9513			−1.50332
$299$	−3.65607	−	29.5030i	−0.211436	−	1.70620i
$300$	−2.22413	+	1.62933i	−0.128410	+	0.0940694i
$301$	−27.9748	−	16.1513i	−1.61244	−	0.930944i
$302$	8.78822	−	15.2216i	0.505705	−	0.875907i
$303$	15.5657	+	6.85704i	0.894225	+	0.393927i
$304$	10.4369	−	6.02577i	0.598599	−	0.345601i
$305$			6.90715i			0.395502i
$306$	−9.10361	−	41.2312i	−0.520419	−	2.35703i
$307$		−	13.4202i		−	0.765932i	−0.923762	−	0.382966i	$-0.874903\pi$
$307$		−	13.4202i		−	0.765932i	0.923762	−	0.382966i	$-0.125097\pi$
$308$	2.59817	+	4.50016i	0.148044	+	0.256421i
$309$	−2.28632	−	20.9594i	−0.130064	−	1.19234i
$310$	9.15081	+	5.28322i	0.519731	+	0.300067i
$311$	10.4161	−	18.0412i	0.590643	−	1.02302i	−0.403503	−	0.914978i	$-0.632208\pi$
$311$	10.4161	−	18.0412i	0.590643	−	1.02302i	0.994146	−	0.108045i	$-0.0344592\pi$
$312$	−4.62727	−	1.38916i	−0.261968	−	0.0786459i
$313$	14.4104	+	24.9595i	0.814523	+	1.41080i	0.909670	+	0.415332i	$0.136335\pi$
$313$	14.4104	+	24.9595i	0.814523	+	1.41080i	−0.0951470	+	0.995463i	$0.530332\pi$
$314$		−	4.51311i		−	0.254690i
$315$	2.95115	−	9.33192i	0.166279	−	0.525794i
$316$	4.55145			0.256039
$317$	1.54399	−	0.891421i	0.0867190	−	0.0500672i	−0.456013	−	0.889973i	$-0.650723\pi$
$317$	1.54399	−	0.891421i	0.0867190	−	0.0500672i	0.542732	+	0.839906i	$0.317390\pi$
$318$	3.66515	−	8.32000i	0.205531	−	0.466562i
$319$	4.49881	+	2.59739i	0.251885	+	0.145426i
$320$	3.87039	+	2.23457i	0.216362	+	0.124916i
$321$	−12.9697	+	9.50122i	−0.723898	+	0.530306i
$322$	−25.4905	−	44.1508i	−1.42053	−	2.46043i
$323$			19.2484i			1.07101i
$324$	−12.9943	+	6.03220i	−0.721906	+	0.335122i
$325$	−3.32050	−	1.40508i	−0.184188	−	0.0779399i
$326$	14.5805	+	25.2541i	0.807537	+	1.39870i
$327$	7.76711	+	10.6025i	0.429522	+	0.586322i
$328$	1.46058	−	2.52980i	0.0806470	−	0.139685i
$329$	−18.5528	+	32.1343i	−1.02285	+	1.77162i
$330$	−1.32414	+	3.00584i	−0.0728915	+	0.165466i
$331$	−24.7844	+	14.3093i	−1.36227	+	0.786510i	−0.989926	−	0.141583i	$-0.954781\pi$
$331$	−24.7844	+	14.3093i	−1.36227	+	0.786510i	−0.372348	+	0.928093i	$0.621447\pi$
$332$		−	4.84184i		−	0.265731i
$333$	9.30728	+	2.94336i	0.510036	+	0.161295i
$334$	10.1372			0.554684
$335$	−1.94683	−	3.37201i	−0.106367	−	0.184233i
$336$	−26.1199	+	2.84925i	−1.42496	+	0.155439i
$337$	−4.59158	+	7.95285i	−0.250119	+	0.433219i	−0.963558	−	0.267498i	$-0.913803\pi$
$337$	−4.59158	+	7.95285i	−0.250119	+	0.433219i	0.713439	+	0.700717i	$0.247137\pi$
$338$	6.01394	+	23.8924i	0.327115	+	1.29957i
$339$	1.79970	+	16.4984i	0.0977464	+	0.896070i
$340$	−10.2377	+	5.91075i	−0.555219	+	0.320556i
$341$	5.57872			0.302105
$342$	14.3897	−	3.17716i	0.778105	−	0.171801i
$343$			10.9496i			0.591224i
$344$	−6.63362	+	3.82992i	−0.357661	+	0.206496i
$345$	5.75732	−	13.0693i	0.309964	−	0.703627i
$346$	27.4861	+	15.8691i	1.47766	+	0.853127i
$347$	−2.13858	+	3.70413i	−0.114805	+	0.198848i	−0.917702	−	0.397270i	$-0.869958\pi$
$347$	−2.13858	+	3.70413i	−0.114805	+	0.198848i	0.802897	+	0.596118i	$0.203291\pi$
$348$	11.5469	−	8.45891i	0.618978	−	0.453445i
$349$	−8.55416	+	4.93875i	−0.457894	+	0.264365i	−0.711158	−	0.703032i	$-0.751829\pi$
$349$	−8.55416	+	4.93875i	−0.457894	+	0.264365i	0.253264	+	0.967397i	$0.418496\pi$
$350$	−6.18306			−0.330499
$351$	−15.4844	−	10.5467i	−0.826496	−	0.562943i
$352$	7.26940			0.387460
$353$	3.85654	−	2.22658i	0.205263	−	0.118509i	−0.393845	−	0.919177i	$-0.628855\pi$
$353$	3.85654	−	2.22658i	0.205263	−	0.118509i	0.599108	+	0.800668i	$0.295522\pi$
$354$	−15.7847	+	11.5634i	−0.838947	+	0.614588i
$355$	−6.43625	+	11.1479i	−0.341601	+	0.591670i
$356$	−23.8577	−	13.7743i	−1.26446	−	0.730035i
$357$	16.9180	−	38.4043i	0.895395	−	2.03257i
$358$	−26.2202	+	15.1382i	−1.38578	+	0.800080i
$359$			13.1002i			0.691404i	0.938344	+	0.345702i	$0.112359\pi$
$359$			13.1002i			0.691404i	−0.938344	+	0.345702i	$0.887641\pi$
$360$	−1.56649	−	1.71248i	−0.0825614	−	0.0902554i
$361$	12.2823			0.646437
$362$	−2.88919	+	1.66807i	−0.151852	+	0.0876719i
$363$	−1.87801	−	17.2163i	−0.0985701	−	0.903621i
$364$	11.2854	+	14.9413i	0.591513	+	0.783138i
$365$	2.05147	−	3.55326i	0.107379	−	0.185986i
$366$	22.5396	−	2.45870i	1.17816	−	0.128518i
$367$	−2.26826	−	3.92875i	−0.118402	−	0.205079i	0.800732	−	0.599022i	$-0.204444\pi$
$367$	−2.26826	−	3.92875i	−0.118402	−	0.205079i	−0.919135	+	0.393943i	$0.871111\pi$
$368$	−38.3386			−1.99854
$369$	8.35829	−	7.64577i	0.435115	−	0.398023i
$370$		−	6.16674i		−	0.320594i
$371$	7.82525	−	4.51791i	0.406267	−	0.234558i
$372$	6.19693	−	14.0672i	0.321296	−	0.729351i
$373$	1.03048	−	1.78484i	0.0533560	−	0.0924153i	−0.838114	−	0.545495i	$-0.816342\pi$
$373$	1.03048	−	1.78484i	0.0533560	−	0.0924153i	0.891470	+	0.453080i	$0.149675\pi$
$374$	−7.04162	+	12.1964i	−0.364114	+	0.630663i
$375$	−1.02358	−	1.39724i	−0.0528574	−	0.0721533i
$376$	4.39939	+	7.61996i	0.226881	+	0.392969i
$377$	17.2389	+	7.29469i	0.887848	+	0.375696i
$378$	−31.5027	−	6.30846i	−1.62032	−	0.324472i
$379$		−	15.9055i		−	0.817010i	−0.912756	−	0.408505i	$-0.866050\pi$
$379$		−	15.9055i		−	0.817010i	0.912756	−	0.408505i	$-0.133950\pi$
$380$	−2.06285	−	3.57297i	−0.105822	−	0.183289i
$381$	−2.44271	+	1.78946i	−0.125144	+	0.0916767i
$382$	−20.9623	−	12.1026i	−1.07253	−	0.619223i
$383$	11.7910	+	6.80753i	0.602491	+	0.347848i	0.770021	−	0.638019i	$-0.220246\pi$
$383$	11.7910	+	6.80753i	0.602491	+	0.347848i	−0.167530	+	0.985867i	$0.553579\pi$
$384$	−4.23151	+	9.60566i	−0.215939	+	0.490187i
$385$	−2.82709	+	1.63222i	−0.144082	+	0.0831858i
$386$	−38.8465			−1.97723
$387$	−29.0051	+	6.40415i	−1.47441	+	0.325541i
$388$		−	7.51865i		−	0.381702i
$389$	1.18440	+	2.05144i	0.0600515	+	0.104012i	0.894488	−	0.447091i	$-0.147540\pi$
$389$	1.18440	+	2.05144i	0.0600515	+	0.104012i	−0.834437	+	0.551104i	$0.814207\pi$
$390$	−3.40313	+	11.3357i	−0.172324	+	0.574007i
$391$	30.6168	−	53.0298i	1.54836	−	2.68183i
$392$	−2.44125	−	1.40946i	−0.123302	−	0.0711884i
$393$	−2.03106	−	18.6193i	−0.102453	−	0.939219i
$394$	24.6196	+	42.6424i	1.24032	+	2.14829i
$395$			2.85932i			0.143868i
$396$	4.55589	+	1.44077i	0.228942	+	0.0724012i
$397$			20.9582i			1.05186i	0.850527	+	0.525931i	$0.176283\pi$
$397$			20.9582i			1.05186i	−0.850527	+	0.525931i	$0.823717\pi$
$398$	26.3899	−	15.2362i	1.32281	−	0.763722i
$399$	13.4031	+	5.90438i	0.670995	+	0.295589i
$400$	−2.32489	+	4.02682i	−0.116244	+	0.201341i
$401$	10.9949	+	6.34789i	0.549057	+	0.316998i	0.748742	−	0.662862i	$-0.230658\pi$
$401$	10.9949	+	6.34789i	0.549057	+	0.316998i	−0.199684	+	0.979860i	$0.563992\pi$
$402$	−10.3106	+	7.55327i	−0.514248	+	0.376723i
$403$	19.9496	−	2.47220i	0.993763	−	0.123149i
$404$	−15.6318			−0.777711
$405$	−3.78955	−	8.16329i	−0.188304	−	0.405637i
$406$	32.1003			1.59311
$407$	−1.62791	−	2.81963i	−0.0806927	−	0.139764i
$408$	−5.88081	−	8.02764i	−0.291144	−	0.397427i
$409$	−15.2644	−	8.81290i	−0.754776	−	0.435770i	0.0726412	−	0.997358i	$-0.476857\pi$
$409$	−15.2644	−	8.81290i	−0.754776	−	0.435770i	−0.827417	+	0.561588i	$0.810191\pi$
$410$	−6.19742	−	3.57808i	−0.306069	−	0.176709i
$411$	11.4366	−	25.9615i	0.564128	−	1.28059i
$412$	9.68824	+	16.7805i	0.477305	+	0.826717i
$413$	−19.4472			−0.956933
$414$	−44.6975	−	14.1353i	−2.19676	−	0.694710i
$415$	3.04174			0.149313
$416$	25.9956	−	3.22142i	1.27454	−	0.157943i
$417$	−3.00526	−	27.5501i	−0.147168	−	1.34914i
$418$	−4.25656	−	2.45753i	−0.208195	−	0.120201i
$419$	−18.0022	+	31.1808i	−0.879467	+	1.52328i	−0.0275401	+	0.999621i	$0.508767\pi$
$419$	−18.0022	+	31.1808i	−0.879467	+	1.52328i	−0.851927	+	0.523661i	$0.824566\pi$
$420$	0.975408	+	8.94186i	0.0475951	+	0.436318i
$421$	23.5453	−	13.5939i	1.14753	−	0.662527i	0.199246	−	0.979950i	$-0.436151\pi$
$421$	23.5453	−	13.5939i	1.14753	−	0.662527i	0.948284	+	0.317423i	$0.102818\pi$
$422$		−	12.3628i		−	0.601812i
$423$	7.35637	+	33.3178i	0.357679	+	1.61997i
$424$		−	2.14265i		−	0.104056i
$425$	−3.71326	−	6.43155i	−0.180119	−	0.311976i
$426$	38.6693	+	17.0347i	1.87353	+	0.825335i
$427$	19.5154	+	11.2672i	0.944416	+	0.545259i
$428$	7.38781	−	12.7961i	0.357103	−	0.618521i
$429$	1.43642	+	6.08143i	0.0693511	+	0.293614i
$430$	9.38242	+	16.2508i	0.452460	+	0.783685i
$431$			10.2093i			0.491762i	0.969300	+	0.245881i	$0.0790773\pi$
$431$			10.2093i			0.491762i	−0.969300	+	0.245881i	$0.920923\pi$
$432$	−15.9538	+	18.1446i	−0.767577	+	0.872984i
$433$	−21.1855			−1.01811			−0.509056	−	0.860733i	$-0.670005\pi$
$433$	−21.1855			−1.01811			−0.509056	+	0.860733i	$0.670005\pi$
$434$	29.8543	−	17.2364i	1.43305	−	0.827374i
$435$	5.31406	+	7.25399i	0.254790	+	0.347802i
$436$	−10.4606	−	6.03944i	−0.500972	−	0.289237i
$437$	18.5074	+	10.6852i	0.885329	+	0.511145i
$438$	−12.3254	−	5.42960i	−0.588928	−	0.259436i
$439$	3.06941	+	5.31638i	0.146495	+	0.253737i	0.929930	−	0.367737i	$-0.119867\pi$
$439$	3.06941	+	5.31638i	0.146495	+	0.253737i	−0.783435	+	0.621474i	$0.786534\pi$
$440$			0.774093i			0.0369034i
$441$	−7.37817	−	8.06575i	−0.351341	−	0.384083i
$442$	−19.7762	+	46.7353i	−0.940657	+	2.22297i
$443$	2.15458	+	3.73184i	0.102367	+	0.177305i	0.912659	−	0.408721i	$-0.134025\pi$
$443$	2.15458	+	3.73184i	0.102367	+	0.177305i	−0.810292	+	0.586026i	$0.800692\pi$
$444$	−8.91825	+	0.972834i	−0.423242	+	0.0461686i
$445$	8.65328	−	14.9879i	0.410205	−	0.710496i
$446$	23.7751	−	41.1797i	1.12578	−	1.94992i
$447$	−23.5773	+	2.57190i	−1.11517	+	0.121647i
$448$	12.6271	−	7.29025i	0.596573	−	0.344432i
$449$			39.6303i			1.87027i	0.354293	+	0.935134i	$0.384722\pi$
$449$			39.6303i			1.87027i	−0.354293	+	0.935134i	$0.615278\pi$
$450$	−4.19517	+	3.83754i	−0.197762	+	0.180904i
$451$	−3.77821			−0.177909
$452$	−7.62619	−	13.2090i	−0.358706	−	0.621297i
$453$	6.47576	−	14.7002i	0.304258	−	0.690674i
$454$	−22.2806	+	38.5910i	−1.04568	+	1.81117i
$455$	−9.38644	+	7.08969i	−0.440043	+	0.332370i
$456$	2.80165	−	2.05240i	0.131199	−	0.0961126i
$457$	−8.39654	+	4.84775i	−0.392774	+	0.226768i	−0.683361	−	0.730080i	$-0.739483\pi$
$457$	−8.39654	+	4.84775i	−0.392774	+	0.226768i	0.290588	+	0.956848i	$0.406149\pi$
$458$	15.4874			0.723677
$459$	−12.3571	−	36.5573i	−0.576778	−	1.70635i
$460$			13.1248i			0.611946i
$461$	32.2639	−	18.6276i	1.50268	−	0.867573i	0.502685	−	0.864470i	$-0.332346\pi$
$461$	32.2639	−	18.6276i	1.50268	−	0.867573i	0.999995	−	0.00310271i	$-0.000987624\pi$
$462$	6.33267	+	8.64445i	0.294622	+	0.402176i
$463$	10.9320	+	6.31158i	0.508052	+	0.293324i	0.732033	−	0.681270i	$-0.238572\pi$
$463$	10.9320	+	6.31158i	0.508052	+	0.293324i	−0.223981	+	0.974594i	$0.571905\pi$
$464$	12.0700	−	20.9058i	0.560335	−	0.970530i
$465$	8.83731	+	3.89304i	0.409821	+	0.180535i
$466$	−9.27157	+	5.35294i	−0.429497	+	0.247970i
$467$	8.83032			0.408619			0.204309	−	0.978906i	$-0.434505\pi$
$467$	8.83032			0.408619			0.204309	+	0.978906i	$0.434505\pi$
$468$	16.9304	+	3.13329i	0.782610	+	0.144836i
$469$	−12.7030			−0.586570
$470$	18.6671	−	10.7775i	0.861050	−	0.497128i
$471$	−0.447271	−	4.10027i	−0.0206092	−	0.188930i
$472$	−2.30574	+	3.99365i	−0.106130	+	0.183823i
$473$	8.57988	+	4.95360i	0.394503	+	0.227767i
$474$	9.33061	−	1.01782i	0.428569	−	0.0467498i
$475$	2.24461	−	1.29593i	0.102990	−	0.0594612i
$476$			38.5674i			1.76774i
$477$	2.50532	−	7.92215i	0.114711	−	0.362730i
$478$	40.6758			1.86047
$479$	−9.04739	+	5.22351i	−0.413386	+	0.238668i	−0.692243	−	0.721664i	$-0.743378\pi$
$479$	−9.04739	+	5.22351i	−0.413386	+	0.238668i	0.278858	+	0.960332i	$0.410044\pi$
$480$	11.5155	+	5.07286i	0.525610	+	0.231543i
$481$	−7.07098	−	9.36166i	−0.322409	−	0.426855i
$482$	−6.35432	+	11.0060i	−0.289431	+	0.501310i
$483$	−27.5343	−	37.5858i	−1.25285	−	1.71021i
$484$	7.95803	+	13.7837i	0.361729	+	0.626532i
$485$	4.72337			0.214477
$486$	−25.2898	+	15.2720i	−1.14717	+	0.692754i
$487$		−	12.7680i		−	0.578574i	−0.957242	−	0.289287i	$-0.906582\pi$
$487$		−	12.7680i		−	0.578574i	0.957242	−	0.289287i	$-0.0934181\pi$
$488$	4.62765	−	2.67177i	0.209484	−	0.120946i
$489$	15.7495	+	21.4989i	0.712217	+	0.972216i
$490$	−3.45285	+	5.98050i	−0.155984	+	0.270172i
$491$	−8.76862	+	15.1877i	−0.395722	+	0.685411i	−0.993193	−	0.116479i	$-0.962839\pi$
$491$	−8.76862	+	15.1877i	−0.395722	+	0.685411i	0.597471	+	0.801891i	$0.296172\pi$
$492$	−4.19690	+	9.52707i	−0.189211	+	0.429514i
$493$	19.2779	+	33.3903i	0.868234	+	1.50382i
$494$	−16.3106	−	6.90189i	−0.733849	−	0.310531i
$495$	−0.905119	+	2.86210i	−0.0406821	+	0.128642i
$496$		−	25.9242i		−	1.16403i
$497$	20.9981	+	36.3698i	0.941895	+	1.63141i
$498$	−1.08275	−	9.92592i	−0.0485193	−	0.444791i
$499$	−14.3518	−	8.28603i	−0.642476	−	0.370933i	0.143092	−	0.989709i	$-0.454296\pi$
$499$	−14.3518	−	8.28603i	−0.642476	−	0.370933i	−0.785568	+	0.618776i	$0.787629\pi$
$500$	1.37854	+	0.795899i	0.0616501	+	0.0355937i
$501$	9.20991	−	1.00465i	0.411468	−	0.0448844i
$502$	10.7580	−	6.21112i	0.480152	−	0.277216i
$503$	−31.9034			−1.42250			−0.711251	−	0.702938i	$-0.751871\pi$
$503$	−31.9034			−1.42250			−0.711251	+	0.702938i	$0.751871\pi$
$504$	−7.39374	+	1.63249i	−0.329343	+	0.0727171i
$505$		−	9.82021i		−	0.436994i
$506$	7.81793	+	13.5411i	0.347550	+	0.601974i
$507$	7.83165	+	21.1108i	0.347816	+	0.937563i
$508$	1.39142	−	2.41001i	0.0617343	−	0.106927i
$509$	10.3173	+	5.95672i	0.457308	+	0.264027i	0.710912	−	0.703281i	$-0.248283\pi$
$509$	10.3173	+	5.95672i	0.457308	+	0.264027i	−0.253604	+	0.967308i	$0.581616\pi$
$510$	−19.6658	+	14.4066i	−0.870818	+	0.637936i
$511$	−6.69289	−	11.5924i	−0.296076	−	0.512819i
$512$		−	26.5863i		−	1.17496i
$513$	12.7585	−	4.31261i	0.563301	−	0.190406i
$514$			10.2500i			0.452109i
$515$	−10.5419	+	6.08635i	−0.464530	+	0.268197i
$516$	22.0216	−	16.1324i	0.969446	−	0.710188i
$517$	5.69014	−	9.85561i	0.250252	−	0.433449i
$518$	−17.4235	−	10.0594i	−0.765542	−	0.441986i
$519$	26.5444	+	11.6934i	1.16517	+	0.513284i
$520$	0.343038	+	2.76817i	0.0150432	+	0.121392i
$521$	−3.54378			−0.155256			−0.0776279	−	0.996982i	$-0.524735\pi$
$521$	−3.54378			−0.155256			−0.0776279	+	0.996982i	$0.524735\pi$
$522$	21.7798	−	19.9232i	0.953277	−	0.872014i
$523$	19.0310			0.832167			0.416083	−	0.909326i	$-0.363402\pi$
$523$	19.0310			0.832167			0.416083	+	0.909326i	$0.363402\pi$
$524$	8.60655	+	14.9070i	0.375979	+	0.651214i
$525$	−5.61746	+	0.612772i	−0.245166	+	0.0267435i
$526$	−19.3751	−	11.1862i	−0.844793	−	0.487742i
$527$	35.8582	+	20.7027i	1.56201	+	0.901825i
$528$	8.01098	−	0.873865i	0.348633	−	0.0380301i
$529$	−22.4921	−	38.9575i	−0.977919	−	1.69381i
$530$	−5.24899			−0.228002
$531$	−13.1948	+	12.0700i	−0.572605	+	0.523792i
$532$	−13.4600			−0.583566
$533$	−13.5110	+	1.67431i	−0.585225	+	0.0725222i
$534$	−51.9893	−	22.9025i	−2.24980	−	0.991088i
$535$	8.03875	+	4.64118i	0.347546	+	0.200655i
$536$	−1.50612	+	2.60867i	−0.0650544	+	0.112678i
$537$	−22.3214	+	16.3520i	−0.963238	+	0.705640i
$538$	−15.8122	+	9.12919i	−0.681713	+	0.393587i
$539$			3.64597i			0.157043i
$540$	6.21161	+	5.46160i	0.267305	+	0.235030i
$541$			37.3200i			1.60451i	0.596981	+	0.802255i	$0.296367\pi$
$541$			37.3200i			1.60451i	−0.596981	+	0.802255i	$0.703633\pi$
$542$	−9.01935	−	15.6220i	−0.387414	−	0.671021i
$543$	−2.45958	+	1.80181i	−0.105551	+	0.0773233i
$544$	46.7253	+	26.9769i	2.00333	+	1.15662i
$545$	3.79410	−	6.57157i	0.162521	−	0.281495i
$546$	26.4766	+	28.1065i	1.13309	+	1.20285i
$547$	−2.03031	−	3.51660i	−0.0868098	−	0.150359i	0.819351	−	0.573292i	$-0.194334\pi$
$547$	−2.03031	−	3.51660i	−0.0868098	−	0.150359i	−0.906161	+	0.422933i	$0.861001\pi$
$548$			26.0718i			1.11373i
$549$	20.2341	−	4.46757i	0.863570	−	0.190671i
$550$	1.89635			0.0808605
$551$	−11.6532	+	6.72799i	−0.496444	+	0.286622i
$552$	−10.9832	+	1.19808i	−0.467474	+	0.0509937i
$553$	8.07869	+	4.66423i	0.343541	+	0.198343i
$554$	−9.83988	−	5.68106i	−0.418056	−	0.241365i
$555$	−0.611154	−	5.60263i	−0.0259420	−	0.237818i
$556$	12.7347	+	22.0572i	0.540073	+	0.935433i
$557$			0.758048i			0.0321195i	0.999871	+	0.0160598i	$0.00511220\pi$
$557$			0.758048i			0.0321195i	−0.999871	+	0.0160598i	$0.994888\pi$
$558$	9.55812	−	30.2240i	0.404628	−	1.27948i
$559$	32.8771	+	13.9120i	1.39055	+	0.588416i
$560$	7.58490	+	13.1374i	0.320520	+	0.555158i
$561$	−5.18875	+	11.7786i	−0.219069	+	0.497293i
$562$	6.58192	−	11.4002i	0.277641	−	0.480889i
$563$	14.6638	−	25.3984i	0.618005	−	1.07042i	−0.371844	−	0.928295i	$-0.621274\pi$
$563$	14.6638	−	25.3984i	0.618005	−	1.07042i	0.989849	−	0.142121i	$-0.0453922\pi$
$564$	−18.5311	−	25.2959i	−0.780298	−	1.06515i
$565$	8.29813	−	4.79093i	0.349105	−	0.201556i
$566$			3.42332i			0.143893i
$567$	−29.2461	−	2.60931i	−1.22822	−	0.109581i
$568$	9.95850			0.417849
$569$	13.4725	+	23.3351i	0.564798	+	0.978258i	0.997068	+	0.0765144i	$0.0243791\pi$
$569$	13.4725	+	23.3351i	0.564798	+	0.978258i	−0.432271	+	0.901744i	$0.642288\pi$
$570$	−5.02791	−	6.86338i	−0.210596	−	0.287475i
$571$	−9.83988	+	17.0432i	−0.411786	+	0.713235i	−0.995085	−	0.0990228i	$-0.968428\pi$
$571$	−9.83988	+	17.0432i	−0.411786	+	0.713235i	0.583299	+	0.812258i	$0.301762\pi$
$572$	−3.46122	−	4.58251i	−0.144721	−	0.191604i
$573$	−20.2442	−	8.91803i	−0.845713	−	0.372556i
$574$	−20.2189	+	11.6734i	−0.843923	+	0.487239i
$575$	−8.24526			−0.343851
$576$	4.04267	−	12.7834i	0.168445	−	0.532643i
$577$			3.25178i			0.135373i	0.997707	+	0.0676867i	$0.0215618\pi$
$577$			3.25178i			0.135373i	−0.997707	+	0.0676867i	$0.978438\pi$
$578$	−62.6205	+	36.1539i	−2.60467	+	1.50381i
$579$	−35.2929	+	3.84987i	−1.46672	+	0.159995i
$580$	−7.15688	−	4.13203i	−0.297173	−	0.171573i
$581$	4.96181	−	8.59411i	0.205851	−	0.356544i
$582$	−1.68135	−	15.4134i	−0.0696943	−	0.638908i
$583$	−2.40001	+	1.38564i	−0.0993981	+	0.0573875i
$584$	−3.17415			−0.131347
$585$	−1.96839	+	10.6360i	−0.0813831	+	0.439746i
$586$	−4.55610			−0.188211
$587$	−34.6602	+	20.0111i	−1.43058	+	0.825945i	−0.997165	−	0.0752491i	$-0.976025\pi$
$587$	−34.6602	+	20.0111i	−1.43058	+	0.825945i	−0.433415	+	0.901195i	$0.642691\pi$
$588$	9.19362	+	4.05000i	0.379139	+	0.167019i
$589$	−7.22525	+	12.5145i	−0.297711	+	0.515651i
$590$	9.78352	+	5.64852i	0.402781	+	0.232546i
$591$	26.5935	+	36.3017i	1.09391	+	1.49325i
$592$	−13.1027	+	7.56488i	−0.538520	+	0.310914i
$593$			15.3656i			0.630988i	0.948928	+	0.315494i	$0.102170\pi$
$593$			15.3656i			0.630988i	−0.948928	+	0.315494i	$0.897830\pi$
$594$	9.66189	+	1.93481i	0.396432	+	0.0793861i
$595$	−24.2288			−0.993286
$596$	18.8765	−	10.8984i	0.773211	−	0.446414i
$597$	22.4658	−	16.4578i	0.919466	−	0.673573i
$598$	33.9578	+	44.9587i	1.38864	+	1.83850i
$599$	−5.54111	+	9.59748i	−0.226403	+	0.392142i	−0.956740	−	0.290946i	$-0.906030\pi$
$599$	−5.54111	+	9.59748i	−0.226403	+	0.392142i	0.730336	+	0.683088i	$0.239363\pi$
$600$	−0.540191	+	1.22625i	−0.0220532	+	0.0500614i
$601$	−20.1265	−	34.8602i	−0.820979	−	1.42198i	−0.904954	−	0.425509i	$-0.860095\pi$
$601$	−20.1265	−	34.8602i	−0.820979	−	1.42198i	0.0839755	−	0.996468i	$-0.473238\pi$
$602$	61.2199			2.49514
$603$	−8.61890	+	7.88416i	−0.350989	+	0.321068i
$604$			14.7626i			0.600682i
$605$	−8.65921	+	4.99940i	−0.352047	+	0.203254i
$606$	−32.0456	+	3.49565i	−1.30176	+	0.142001i
$607$	7.41688	−	12.8464i	0.301042	−	0.521420i	−0.675330	−	0.737515i	$-0.735999\pi$
$607$	7.41688	−	12.8464i	0.301042	−	0.521420i	0.976372	+	0.216096i	$0.0693323\pi$
$608$	−9.41493	+	16.3071i	−0.381826	+	0.661342i
$609$	29.1639	−	3.18129i	1.18178	−	0.128913i
$610$	−6.54522	−	11.3367i	−0.265008	−	0.459008i
$611$	15.9806	−	37.7655i	0.646505	−	1.52783i
$612$	23.9370	+	26.1677i	0.967597	+	1.05777i
$613$			13.2745i			0.536153i	0.963398	+	0.268077i	$0.0863881\pi$
$613$			13.2745i			0.536153i	−0.963398	+	0.268077i	$0.913612\pi$
$614$	12.7170	+	22.0265i	0.513217	+	0.888918i
$615$	−5.98510	−	2.63658i	−0.241343	−	0.106317i
$616$	2.18711	+	1.26273i	0.0881213	+	0.0508769i
$617$	−9.94291	−	5.74054i	−0.400287	−	0.231106i	0.286321	−	0.958134i	$-0.407568\pi$
$617$	−9.94291	−	5.74054i	−0.400287	−	0.231106i	−0.686608	+	0.727028i	$0.740901\pi$
$618$	23.6137	+	32.2340i	0.949883	+	1.29664i
$619$	12.4593	−	7.19336i	0.500780	−	0.289125i	−0.228256	−	0.973601i	$-0.573302\pi$
$619$	12.4593	−	7.19336i	0.500780	−	0.289125i	0.729036	+	0.684476i	$0.239969\pi$
$620$	−8.87484			−0.356422
$621$	−42.0096	−	8.41248i	−1.68579	−	0.337581i
$622$			39.4813i			1.58305i
$623$	−28.2312	−	48.8978i	−1.13106	−	1.95905i
$624$	28.2602	−	6.67501i	1.13131	−	0.267214i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−47.3034	−	27.3106i	−1.89062	−	1.09155i
$627$	−4.11074	−	1.81087i	−0.164167	−	0.0723193i
$628$	1.89530	+	3.28276i	0.0756307	+	0.130996i
$629$		−	24.1649i		−	0.963517i
$630$	3.99923	+	18.1129i	0.159333	+	0.721637i
$631$		−	19.2657i		−	0.766957i	−0.923550	−	0.383479i	$-0.874726\pi$
$631$		−	19.2657i		−	0.766957i	0.923550	−	0.383479i	$-0.125274\pi$
$632$	1.91568	−	1.10602i	0.0762018	−	0.0439952i
$633$	−1.22521	−	11.2319i	−0.0486979	−	0.446428i
$634$	−1.68943	+	2.92617i	−0.0670957	+	0.116213i
$635$	1.51402	+	0.874119i	0.0600820	+	0.0346883i
$636$	0.828054	+	7.59101i	0.0328345	+	0.301003i
$637$	1.61570	+	13.0381i	0.0640165	+	0.516588i
$638$	−9.84516			−0.389774
$639$	36.8202	+	11.6441i	1.45658	+	0.460634i
$640$	6.06010			0.239547
$641$	−6.58973	−	11.4137i	−0.260279	−	0.450816i	0.706037	−	0.708175i	$-0.250481\pi$
$641$	−6.58973	−	11.4137i	−0.260279	−	0.450816i	−0.966316	+	0.257359i	$0.917148\pi$
$642$	12.2837	−	27.8844i	0.484800	−	1.10051i
$643$	−13.6088	−	7.85706i	−0.536680	−	0.309852i	0.207053	−	0.978330i	$-0.433613\pi$
$643$	−13.6088	−	7.85706i	−0.536680	−	0.309852i	−0.743732	+	0.668478i	$0.766946\pi$
$644$	37.0826	+	21.4097i	1.46126	+	0.843659i
$645$	10.1347	+	13.8344i	0.399053	+	0.544729i
$646$	−18.2398	−	31.5923i	−0.717637	−	1.24298i
$647$	21.2633			0.835948			0.417974	−	0.908459i	$-0.362740\pi$
$647$	21.2633			0.835948			0.417974	+	0.908459i	$0.362740\pi$
$648$	−4.00339	+	5.69659i	−0.157268	+	0.223783i
$649$	5.96445			0.234125
$650$	6.78138	−	0.840362i	0.265988	−	0.0329617i
$651$	25.4151	−	18.6184i	0.996098	−	0.729712i
$652$	−21.2111	−	12.2463i	−0.830692	−	0.479600i
$653$	9.65619	−	16.7250i	0.377876	−	0.654500i	−0.612877	−	0.790178i	$-0.709988\pi$
$653$	9.65619	−	16.7250i	0.377876	−	0.654500i	0.990753	+	0.135678i	$0.0433212\pi$
$654$	−22.7951	−	10.0418i	−0.891360	−	0.392664i
$655$	−9.36487	+	5.40681i	−0.365916	+	0.211261i
$656$			17.5572i			0.685495i
$657$	−11.7360	−	3.71142i	−0.457864	−	0.144796i
$658$		−	70.3226i		−	2.74146i
$659$	4.11952	+	7.13522i	0.160474	+	0.277949i	0.935039	−	0.354546i	$-0.115364\pi$
$659$	4.11952	+	7.13522i	0.160474	+	0.277949i	−0.774565	+	0.632494i	$0.782031\pi$
$660$	−0.299158	−	2.74247i	−0.0116447	−	0.106750i
$661$	−16.4579	−	9.50199i	−0.640139	−	0.369585i	0.144529	−	0.989501i	$-0.453833\pi$
$661$	−16.4579	−	9.50199i	−0.640139	−	0.369585i	−0.784668	+	0.619916i	$0.787167\pi$
$662$	27.1190	−	46.9715i	1.05401	−	1.82560i
$663$	−13.3354	+	44.4200i	−0.517905	+	1.72513i
$664$	−1.17659	−	2.03791i	−0.0456604	−	0.0790861i
$665$		−	8.45587i		−	0.327904i
$666$	−18.0651	+	3.98867i	−0.700009	+	0.154558i
$667$	42.8065			1.65747
$668$	−7.37364	+	4.25717i	−0.285295	+	0.164715i
$669$	17.5191	−	39.7690i	0.677329	−	1.53756i
$670$	6.39064	+	3.68964i	0.246892	+	0.142543i
$671$	−5.98537	−	3.45566i	−0.231063	−	0.133404i
$672$	33.1174	−	24.2608i	1.27753	−	0.935882i
$673$	−4.04033	−	6.99805i	−0.155743	−	0.269755i	0.777586	−	0.628776i	$-0.216444\pi$
$673$	−4.04033	−	6.99805i	−0.155743	−	0.269755i	−0.933329	+	0.359021i	$0.883111\pi$
$674$		−	17.4040i		−	0.670376i
$675$	−3.43109	+	3.90226i	−0.132063	+	0.150198i
$676$	−14.4081	−	14.8533i	−0.554159	−	0.571282i
$677$	−2.86472	−	4.96183i	−0.110100	−	0.190699i	0.805710	−	0.592310i	$-0.201784\pi$
$677$	−2.86472	−	4.96183i	−0.110100	−	0.190699i	−0.915810	+	0.401611i	$0.868450\pi$
$678$	−18.5878	−	25.3733i	−0.713858	−	0.974457i
$679$	7.70495	−	13.3454i	0.295689	−	0.512148i
$680$	−2.87267	+	4.97561i	−0.110162	+	0.190806i
$681$	−16.4178	+	37.2690i	−0.629133	+	1.42815i
$682$	−9.15633	+	5.28641i	−0.350614	+	0.202427i
$683$		−	28.8081i		−	1.10231i	−0.834403	−	0.551155i	$-0.814187\pi$
$683$		−	28.8081i		−	1.10231i	0.834403	−	0.551155i	$-0.185813\pi$
$684$	−9.13254	+	8.35402i	−0.349191	+	0.319424i
$685$	−16.3788			−0.625803
$686$	−10.3759	−	17.9716i	−0.396153	−	0.686157i
$687$	14.0706	−	1.53487i	0.536828	−	0.0585590i
$688$	23.0192	−	39.8705i	0.877600	−	1.52005i
$689$	−7.96843	+	6.01865i	−0.303573	+	0.229292i
$690$	2.93502	+	26.9062i	0.111734	+	1.02430i
$691$	36.1886	−	20.8935i	1.37668	−	0.794827i	0.384922	−	0.922949i	$-0.374228\pi$
$691$	36.1886	−	20.8935i	1.37668	−	0.794827i	0.991758	+	0.128122i	$0.0408949\pi$
$692$	−26.6572			−1.01335
$693$	6.61008	+	7.22609i	0.251096	+	0.274496i
$694$		−	8.10610i		−	0.307703i
$695$	−13.8568	+	8.00021i	−0.525617	+	0.303465i
$696$	2.80448	−	6.36625i	0.106304	−	0.241312i
$697$	−24.2851	−	14.0210i	−0.919863	−	0.531083i
$698$	9.35994	−	16.2119i	0.354279	−	0.613629i
$699$	−7.89294	+	5.78213i	−0.298538	+	0.218700i
$700$	4.49745	−	2.59660i	0.169988	−	0.0981424i
$701$	−50.0124			−1.88894			−0.944472	−	0.328593i	$-0.893426\pi$
$701$	−50.0124			−1.88894			−0.944472	+	0.328593i	$0.893426\pi$
$702$	35.4086	+	2.63727i	1.33641	+	0.0995374i
$703$	8.43354			0.318077
$704$	−3.87273	+	2.23592i	−0.145959	+	0.0842694i
$705$	15.8914	−	11.6416i	0.598505	−	0.438447i
$706$	−4.21981	+	7.30893i	−0.158815	+	0.275075i
$707$	−27.7459	−	16.0191i	−1.04349	−	0.602461i
$708$	6.62541	−	15.0399i	0.248998	−	0.565233i
$709$	28.1835	−	16.2718i	1.05846	−	0.611099i	0.133451	−	0.991055i	$-0.457394\pi$
$709$	28.1835	−	16.2718i	1.05846	−	0.611099i	0.925005	+	0.379956i	$0.124061\pi$
$710$		−	24.3960i		−	0.915566i
$711$	8.37621	−	1.84942i	0.314132	−	0.0693586i
$712$	−13.3888			−0.501767
$713$	39.8114	−	22.9851i	1.49095	−	0.860800i
$714$	8.62461	+	79.0643i	0.322768	+	2.95891i
$715$	2.87882	−	2.17441i	0.107662	−	0.0813183i
$716$	12.7147	−	22.0226i	0.475172	−	0.823022i
$717$	36.9549	−	4.03116i	1.38011	−	0.150547i
$718$	−12.4138	−	21.5013i	−0.463279	−	0.802423i
$719$	−24.3361			−0.907584			−0.453792	−	0.891108i	$-0.649929\pi$
$719$	−24.3361			−0.907584			−0.453792	+	0.891108i	$0.649929\pi$
$720$	13.3001	+	4.20606i	0.495666	+	0.156751i
$721$			39.7132i			1.47900i
$722$	−20.1589	+	11.6387i	−0.750236	+	0.433149i
$723$	−4.68230	+	10.6290i	−0.174137	+	0.395295i
$724$	1.40103	−	2.42665i	0.0520688	−	0.0901858i
$725$	2.59582	−	4.49610i	0.0964065	−	0.166981i
$726$	19.3966	+	26.4774i	0.719874	+	0.982669i
$727$	−8.54013	−	14.7919i	−0.316736	−	0.548603i	0.663069	−	0.748558i	$-0.269254\pi$
$727$	−8.54013	−	14.7919i	−0.316736	−	0.548603i	−0.979805	+	0.199955i	$0.935920\pi$
$728$	8.38075	+	3.54634i	0.310611	+	0.131436i
$729$	−21.4628	+	16.3813i	−0.794919	+	0.606716i
$730$			7.77593i			0.287800i
$731$	36.7658	+	63.6802i	1.35983	+	2.35530i
$732$	−15.3624	+	11.2540i	−0.567810	+	0.415961i
$733$	−19.4870	−	11.2508i	−0.719768	−	0.415558i	0.0948995	−	0.995487i	$-0.469747\pi$
$733$	−19.4870	−	11.2508i	−0.719768	−	0.415558i	−0.814667	+	0.579929i	$0.803080\pi$
$734$	7.44577	+	4.29882i	0.274829	+	0.158672i
$735$	−2.54429	+	5.77562i	−0.0938477	+	0.213037i
$736$	51.8766	−	29.9510i	1.91220	−	1.10401i
$737$	3.89601			0.143511
$738$	−6.47327	+	20.4693i	−0.238284	+	0.753486i
$739$		−	27.5036i		−	1.01174i	−0.862611	−	0.505869i	$-0.831172\pi$
$739$		−	27.5036i		−	1.01174i	0.862611	−	0.505869i	$-0.168828\pi$
$740$	2.58975	+	4.48558i	0.0952011	+	0.164893i
$741$	−15.5026	−	4.65407i	−0.569501	−	0.170971i
$742$	−8.56236	+	14.8304i	−0.314334	+	0.544443i
$743$	38.1227	+	22.0101i	1.39859	+	0.807474i	0.994244	−	0.107135i	$-0.0341677\pi$
$743$	38.1227	+	22.0101i	1.39859	+	0.807474i	0.404341	+	0.914608i	$0.367501\pi$
$744$	−0.810130	−	7.42670i	−0.0297008	−	0.272276i
$745$	6.84657	+	11.8586i	0.250839	+	0.434466i
$746$			3.90592i			0.143006i
$747$	−1.96741	−	8.91062i	−0.0719839	−	0.326023i
$748$		−	11.8286i		−	0.432498i
$749$	26.2263	−	15.1417i	0.958287	−	0.553267i
$750$	3.00402	+	1.32334i	0.109691	+	0.0483216i
$751$	3.71033	−	6.42648i	0.135392	−	0.234506i	−0.790355	−	0.612649i	$-0.790104\pi$
$751$	3.71033	−	6.42648i	0.135392	−	0.234506i	0.925747	+	0.378143i	$0.123437\pi$
$752$	−45.7987	−	26.4419i	−1.67011	−	0.964237i
$753$	9.15831	−	6.70911i	0.333748	−	0.244494i
$754$	−35.2065	+	4.36286i	−1.28215	+	0.158886i
$755$	−9.27417			−0.337522
$756$	25.5638	−	8.64104i	0.929746	−	0.314271i
$757$	−21.1578			−0.768992			−0.384496	−	0.923127i	$-0.625625\pi$
$757$	−21.1578			−0.768992			−0.384496	+	0.923127i	$0.625625\pi$
$758$	15.0721	+	26.1056i	0.547442	+	0.948198i
$759$	8.44476	+	11.5276i	0.306525	+	0.418424i
$760$	−1.73649	−	1.00256i	−0.0629891	−	0.0363668i
$761$	−21.2853	−	12.2891i	−0.771591	−	0.445478i	0.0618512	−	0.998085i	$-0.480300\pi$
$761$	−21.2853	−	12.2891i	−0.771591	−	0.445478i	−0.833442	+	0.552607i	$0.813633\pi$
$762$	2.31351	−	5.25175i	0.0838098	−	0.190251i
$763$	−12.3782	−	21.4396i	−0.448120	−	0.776166i
$764$	20.3302			0.735519
$765$	−16.4391	+	15.0377i	−0.594357	+	0.543690i
$766$	−25.8033			−0.932312
$767$	21.3290	−	2.64313i	0.770146	−	0.0954380i
$768$	−3.83600	−	35.1658i	−0.138420	−	1.26894i
$769$	−34.3401	−	19.8263i	−1.23834	−	0.714954i	−0.269583	−	0.962977i	$-0.586886\pi$
$769$	−34.3401	−	19.8263i	−1.23834	−	0.714954i	−0.968754	+	0.248023i	$0.920219\pi$
$770$	3.09340	−	5.35792i	0.111478	−	0.193086i
$771$	1.01583	+	9.31239i	0.0365841	+	0.335377i
$772$	28.2562	−	16.3137i	1.01696	−	0.587144i
$773$			13.6116i			0.489574i	0.969577	+	0.244787i	$0.0787180\pi$
$773$			13.6116i			0.489574i	−0.969577	+	0.244787i	$0.921282\pi$
$774$	41.5373	−	37.9964i	1.49303	−	1.36575i
$775$		−	5.57536i		−	0.200273i
$776$	−1.82706	−	3.16456i	−0.0655877	−	0.113601i
$777$	−16.8265	−	7.41248i	−0.603649	−	0.265921i
$778$	−3.88790	−	2.24468i	−0.139388	−	0.0804758i
$779$	4.89333	−	8.47549i	0.175322	−	0.303666i
$780$	−2.28512	−	9.67457i	−0.0818203	−	0.346405i
$781$	−6.44013	−	11.1546i	−0.230446	−	0.399144i
$782$			116.050i			4.14994i
$783$	17.8130	−	20.2592i	0.636585	−	0.724003i
$784$	16.9427			0.605097
$785$	−2.06230	+	1.19067i	−0.0736065	+	0.0424967i
$786$	20.9772	+	28.6351i	0.748233	+	1.02138i
$787$	−7.02569	−	4.05628i	−0.250439	−	0.144591i	0.369526	−	0.929220i	$-0.379520\pi$
$787$	−7.02569	−	4.05628i	−0.250439	−	0.144591i	−0.619965	+	0.784629i	$0.712853\pi$
$788$	−35.8157	−	20.6782i	−1.27588	−	0.736631i
$789$	−18.7113	−	8.24276i	−0.666140	−	0.293450i
$790$	−2.70949	−	4.69298i	−0.0963995	−	0.166969i
$791$		−	31.2606i		−	1.11150i
$792$	2.26766	−	0.500686i	0.0805778	−	0.0177911i
$793$	−22.9352	−	9.70511i	−0.814453	−	0.344638i
$794$	−19.8600	−	34.3986i	−0.704807	−	1.22076i
$795$	−4.76883	+	0.520200i	−0.169133	+	0.0184496i
$796$	−12.7970	+	22.1651i	−0.453578	+	0.785621i
$797$	−8.69587	+	15.0617i	−0.308023	+	0.533512i	−0.977930	−	0.208933i	$-0.933001\pi$
$797$	−8.69587	+	15.0617i	−0.308023	+	0.533512i	0.669906	+	0.742446i	$0.266334\pi$
$798$	−27.5935	+	3.00999i	−0.976798	+	0.106552i
$799$	73.1487	−	42.2324i	2.58781	−	1.49408i
$800$		−	7.26502i		−	0.256857i
$801$	−49.5033	−	15.6551i	−1.74911	−	0.553144i
$802$	−24.0611			−0.849626
$803$	2.05271	+	3.55540i	0.0724386	+	0.125467i
$804$	4.32775	−	9.82412i	0.152628	−	0.346470i
$805$	−13.4500	+	23.2961i	−0.474050	+	0.821079i
$806$	−30.4006	+	22.9619i	−1.07082	+	0.808800i
$807$	−13.4610	+	9.86115i	−0.473850	+	0.347129i
$808$	−6.57934	+	3.79859i	−0.231461	+	0.133634i
$809$	16.1304			0.567115			0.283558	−	0.958955i	$-0.408485\pi$
$809$	16.1304			0.567115			0.283558	+	0.958955i	$0.408485\pi$
$810$	13.9553	+	9.80737i	0.490340	+	0.344596i
$811$			38.7276i			1.35991i	0.733255	+	0.679954i	$0.238000\pi$
$811$			38.7276i			1.35991i	−0.733255	+	0.679954i	$0.762000\pi$
$812$	−23.3492	+	13.4807i	−0.819395	+	0.473078i
$813$	−9.74251	−	13.2991i	−0.341685	−	0.466419i
$814$	5.34378	+	3.08523i	0.187299	+	0.108137i
$815$	7.69335	−	13.3253i	0.269486	−	0.466764i
$816$	54.7349	+	24.1120i	1.91610	+	0.844088i
$817$	−22.2244	+	12.8313i	−0.777533	+	0.448909i
$818$	33.4045			1.16796
$819$	26.8401	+	22.9114i	0.937867	+	0.800590i
$820$	6.01052			0.209896
$821$	−16.8056	+	9.70271i	−0.586519	+	0.338627i	−0.763720	−	0.645548i	$-0.776629\pi$
$821$	−16.8056	+	9.70271i	−0.586519	+	0.338627i	0.177201	+	0.984175i	$0.443296\pi$
$822$	5.83028	+	53.4479i	0.203354	+	1.86421i
$823$	−9.46514	+	16.3941i	−0.329934	+	0.571463i	−0.982498	−	0.186271i	$-0.940360\pi$
$823$	−9.46514	+	16.3941i	−0.329934	+	0.571463i	0.652564	+	0.757733i	$0.273693\pi$
$824$	8.15547	+	4.70856i	0.284109	+	0.164031i
$825$	1.72288	−	0.187937i	0.0599828	−	0.00654313i
$826$	31.9185	−	18.4282i	1.11059	−	0.641198i
$827$		−	2.31948i		−	0.0806562i	−0.999186	−	0.0403281i	$-0.987160\pi$
$827$		−	2.31948i		−	0.0806562i	0.999186	−	0.0403281i	$-0.0128403\pi$
$828$	38.4483	−	8.48917i	1.33617	−	0.295019i
$829$	20.9493			0.727601			0.363800	−	0.931477i	$-0.381479\pi$
$829$	20.9493			0.727601			0.363800	+	0.931477i	$0.381479\pi$
$830$	−4.99240	+	2.88236i	−0.173289	+	0.100048i
$831$	−9.50278	−	4.18619i	−0.329648	−	0.145217i
$832$	−12.8581	+	9.71189i	−0.445775	+	0.336699i
$833$	−13.5303	+	23.4351i	−0.468796	+	0.811978i
$834$	31.0391	+	42.3701i	1.07480	+	1.46716i
$835$	−2.67444	−	4.63227i	−0.0925529	−	0.160306i
$836$	4.12819			0.142777
$837$	5.68843	−	28.4065i	0.196621	−	0.981871i
$838$		−	68.2358i		−	2.35717i
$839$	−13.8917	+	8.02035i	−0.479593	+	0.276893i	−0.720247	−	0.693718i	$-0.755972\pi$
$839$	−13.8917	+	8.02035i	−0.479593	+	0.276893i	0.240654	+	0.970611i	$0.422638\pi$
$840$	2.58345	+	3.52656i	0.0891375	+	0.121678i
$841$	1.02340	−	1.77258i	0.0352897	−	0.0611235i
$842$	−25.7632	+	44.6232i	−0.887859	+	1.53782i
$843$	4.85001	−	11.0097i	0.167043	−	0.379193i
$844$	5.19181	+	8.99249i	0.178710	+	0.309534i
$845$	9.33116	−	9.05149i	0.321002	−	0.311381i
$846$	−43.6460	−	47.7134i	−1.50058	−	1.64042i
$847$			32.6209i			1.12087i
$848$	6.43905	+	11.1528i	0.221118	+	0.382987i
$849$	0.339268	+	3.11017i	0.0116436	+	0.106741i
$850$	12.1891	+	7.03738i	0.418083	+	0.241380i
$851$	−23.2346	−	13.4145i	−0.796471	−	0.459843i
$852$	−35.2812	+	3.84859i	−1.20871	+	0.131851i
$853$	−39.2886	+	22.6833i	−1.34522	+	0.776662i	−0.987568	−	0.157194i	$-0.949755\pi$
$853$	−39.2886	+	22.6833i	−1.34522	+	0.776662i	−0.357650	+	0.933856i	$0.616422\pi$
$854$	−42.7073			−1.46141
$855$	−5.24817	−	5.73725i	−0.179484	−	0.196210i
$856$		−	7.18107i		−	0.245444i
$857$	−12.9488	−	22.4280i	−0.442322	−	0.766125i	0.555539	−	0.831490i	$-0.312512\pi$
$857$	−12.9488	−	22.4280i	−0.442322	−	0.766125i	−0.997861	+	0.0653657i	$0.979179\pi$
$858$	−8.12036	−	8.62026i	−0.277225	−	0.294291i
$859$	−6.25204	+	10.8289i	−0.213317	+	0.369476i	−0.952751	−	0.303754i	$-0.901760\pi$
$859$	−6.25204	+	10.8289i	−0.213317	+	0.369476i	0.739434	+	0.673229i	$0.235093\pi$
$860$	−13.6492	−	7.88037i	−0.465434	−	0.268719i
$861$	−17.2125	+	12.6094i	−0.586600	+	0.429726i
$862$	−9.67431	−	16.7564i	−0.329508	−	0.570725i
$863$		−	43.8210i		−	1.49168i	−0.666123	−	0.745842i	$-0.732047\pi$
$863$		−	43.8210i		−	1.49168i	0.666123	−	0.745842i	$-0.267953\pi$
$864$	7.41236	−	37.0153i	0.252174	−	1.25929i
$865$		−	16.7466i		−	0.569400i
$866$	34.7717	−	20.0755i	1.18159	−	0.682192i
$867$	−53.3091	+	39.0527i	−1.81047	+	1.32630i
$868$	−14.4770	+	25.0749i	−0.491381	+	0.851098i
$869$	−2.47773	−	1.43052i	−0.0840514	−	0.0485271i
$870$	−15.5958	−	6.87032i	−0.528748	−	0.232926i
$871$	13.9322	−	1.72651i	0.472075	−	0.0585005i
$872$	−5.87043			−0.198798
$873$	−3.05509	−	13.8368i	−0.103399	−	0.468306i
$874$	−40.5014			−1.36998
$875$	1.63124	+	2.82539i	0.0551460	+	0.0955156i
$876$	11.2454	−	1.22669i	0.379948	−	0.0414460i
$877$	−40.2071	−	23.2136i	−1.35770	−	0.783866i	−0.368383	−	0.929674i	$-0.620089\pi$
$877$	−40.2071	−	23.2136i	−1.35770	−	0.783866i	−0.989313	+	0.145808i	$0.953422\pi$
$878$	−10.0756	−	5.81717i	−0.340036	−	0.196320i
$879$	−4.13932	+	0.451531i	−0.139616	+	0.0152298i
$880$	−2.32629	−	4.02925i	−0.0784192	−	0.135826i
$881$	6.26211			0.210976			0.105488	−	0.994421i	$-0.466360\pi$
$881$	6.26211			0.210976			0.105488	+	0.994421i	$0.466360\pi$
$882$	19.7529	+	6.24671i	0.665114	+	0.210338i
$883$	13.0001			0.437488			0.218744	−	0.975782i	$-0.429804\pi$
$883$	13.0001			0.437488			0.218744	+	0.975782i	$0.429804\pi$
$884$	−5.24184	−	42.2995i	−0.176302	−	1.42269i
$885$	9.44835	+	4.16222i	0.317603	+	0.139911i
$886$	−7.07259	−	4.08336i	−0.237608	−	0.137183i
$887$	16.6157	−	28.7792i	0.557901	−	0.966312i	−0.439771	−	0.898110i	$-0.644940\pi$
$887$	16.6157	−	28.7792i	0.557901	−	0.966312i	0.997672	−	0.0682024i	$-0.0217264\pi$
$888$	−3.51725	+	2.57663i	−0.118031	+	0.0864661i
$889$	4.93945	−	2.85179i	0.165664	−	0.0956461i
$890$			32.7995i			1.09944i
$891$	8.96980	+	0.800277i	0.300500	+	0.0268103i
$892$			39.9379i			1.33722i
$893$	14.7391	+	25.5289i	0.493225	+	0.854291i
$894$	36.2602	−	26.5632i	1.21272	−	0.888406i
$895$	13.8350	+	7.98765i	0.462454	+	0.266998i
$896$	9.88548	−	17.1221i	0.330251	−	0.572011i
$897$	35.3071	+	37.4806i	1.17887	+	1.25144i
$898$	−37.5537	−	65.0450i	−1.25318	−	2.17058i
$899$			28.9453i			0.965380i
$900$	1.43990	−	4.55314i	0.0479966	−	0.151771i
$901$	−20.5686			−0.685239
$902$	6.20115	−	3.58024i	0.206476	−	0.119209i
$903$	55.6197	−	6.06719i	1.85091	−	0.201903i
$904$	−6.41965	−	3.70639i	−0.213514	−	0.123273i
$905$	1.52447	+	0.880154i	0.0506752	+	0.0292573i
$906$	3.30128	+	30.2638i	0.109678	+	1.00545i
$907$	0.363034	+	0.628793i	0.0120543	+	0.0208787i	0.871990	−	0.489524i	$-0.162830\pi$
$907$	0.363034	+	0.628793i	0.0120543	+	0.0208787i	−0.859935	+	0.510403i	$0.829496\pi$
$908$		−	37.4272i		−	1.24207i
$909$	−28.7678	+	6.35175i	−0.954166	+	0.210674i
$910$	8.68771	−	20.5309i	0.287995	−	0.680592i
$911$	−12.7286	−	22.0466i	−0.421718	−	0.730437i	0.574390	−	0.818582i	$-0.305239\pi$
$911$	−12.7286	−	22.0466i	−0.421718	−	0.730437i	−0.996108	+	0.0881449i	$0.971906\pi$
$912$	−8.41508	+	19.1025i	−0.278651	+	0.632546i
$913$	−1.52179	+	2.63582i	−0.0503639	+	0.0872328i
$914$	9.18747	−	15.9132i	0.303894	−	0.526361i
$915$	−7.07001	−	9.65096i	−0.233727	−	0.319051i
$916$	−11.2652	+	6.50398i	−0.372214	+	0.214898i
$917$			35.2792i			1.16502i
$918$	54.9233	+	48.2917i	1.81274	+	1.59387i
$919$	−49.4400			−1.63088			−0.815438	−	0.578845i	$-0.803504\pi$
$919$	−49.4400			−1.63088			−0.815438	+	0.578845i	$0.803504\pi$
$920$	3.18937	+	5.52416i	0.105151	+	0.182126i
$921$	13.7366	+	18.7513i	0.452638	+	0.617876i
$922$	−35.3031	+	61.1467i	−1.16264	+	2.01376i
$923$	−27.9732	−	37.0353i	−0.920750	−	1.21903i
$924$	−8.23654	−	3.62839i	−0.270962	−	0.119365i
$925$	−2.81793	+	1.62693i	−0.0926530	+	0.0534932i
$926$	−23.9235			−0.786174
$927$	24.6482	+	26.9451i	0.809552	+	0.884995i
$928$			37.7174i			1.23813i
$929$	−27.8402	+	16.0735i	−0.913406	+	0.527355i	−0.881526	−	0.472136i	$-0.843483\pi$
$929$	−27.8402	+	16.0735i	−0.913406	+	0.527355i	−0.0318806	+	0.999492i	$0.510150\pi$
$930$	−18.1937	+	1.98463i	−0.596595	+	0.0650786i
$931$	−8.17885	−	4.72206i	−0.268051	−	0.154759i
$932$	4.49598	−	7.78727i	0.147271	−	0.255081i
$933$	3.91279	+	35.8697i	0.128099	+	1.17432i
$934$	−14.4932	+	8.36763i	−0.474231	+	0.273797i
$935$	7.43099			0.243019
$936$	7.88734	−	2.79538i	0.257806	−	0.0913697i
$937$	53.0269			1.73231			0.866157	−	0.499772i	$-0.166583\pi$
$937$	53.0269			1.73231			0.866157	+	0.499772i	$0.166583\pi$
$938$	20.8493	−	12.0374i	0.680755	−	0.393034i
$939$	−45.6828	−	20.1243i	−1.49080	−	0.656733i
$940$	−9.05209	+	15.6787i	−0.295247	+	0.511382i
$941$	32.5642	+	18.8009i	1.06156	+	0.612893i	0.925864	−	0.377857i	$-0.123339\pi$
$941$	32.5642	+	18.8009i	1.06156	+	0.612893i	0.135698	+	0.990750i	$0.456672\pi$
$942$	4.61953	+	6.30591i	0.150512	+	0.205458i
$943$	−26.9624	+	15.5668i	−0.878018	+	0.506924i
$944$		−	27.7166i		−	0.902100i
$945$	5.42847	+	16.0597i	0.176588	+	0.522422i
$946$	−18.7762			−0.610465
$947$	36.6456	−	21.1574i	1.19082	−	0.687522i	0.232330	−	0.972637i	$-0.425365\pi$
$947$	36.6456	−	21.1574i	1.19082	−	0.687522i	0.958493	+	0.285115i	$0.0920317\pi$
$948$	−6.35949	+	4.65877i	−0.206547	+	0.151310i
$949$	8.91612	+	11.8045i	0.289429	+	0.383192i
$950$	−2.45604	+	4.25399i	−0.0796846	+	0.138018i
$951$	−1.24488	+	2.82592i	−0.0403681	+	0.0916369i
$952$	9.37203	+	16.2328i	0.303749	+	0.526109i
$953$	28.3661			0.918867			0.459434	−	0.888212i	$-0.348052\pi$
$953$	28.3661			0.918867			0.459434	+	0.888212i	$0.348052\pi$
$954$	3.39507	+	15.3766i	0.109919	+	0.497837i
$955$			12.7718i			0.413286i
$956$	−29.5868	+	17.0820i	−0.956906	+	0.552470i
$957$	−8.94456	+	0.975703i	−0.289137	+	0.0315400i
$958$	9.89962	−	17.1466i	0.319842	−	0.553983i
$959$	−26.7178	+	46.2766i	−0.862762	+	1.49435i
$960$	−7.69514	+	0.839412i	−0.248359	+	0.0270919i
$961$	0.0423136	+	0.0732893i	0.00136496	+	0.00236417i
$962$	20.4767	+	8.66478i	0.660195	+	0.279364i
$963$	8.39657	−	26.5510i	0.270576	−	0.855594i
$964$		−	10.6741i		−	0.343789i
$965$	10.2486	+	17.7511i	0.329915	+	0.571429i
$966$	80.8082	+	35.5979i	2.59996	+	1.14534i
$967$	−12.8201	−	7.40166i	−0.412265	−	0.238021i	0.279497	−	0.960146i	$-0.409832\pi$
$967$	−12.8201	−	7.40166i	−0.412265	−	0.238021i	−0.691763	+	0.722125i	$0.743166\pi$
$968$	6.69899	+	3.86766i	0.215314	+	0.124311i
$969$	−19.7023	−	26.8947i	−0.632928	−	0.863983i
$970$	−7.75244	+	4.47587i	−0.248916	+	0.143712i
$971$	−8.86211			−0.284399			−0.142199	−	0.989838i	$-0.545417\pi$
$971$	−8.86211			−0.284399			−0.142199	+	0.989838i	$0.545417\pi$
$972$	11.9818	−	21.7291i	0.384315	−	0.696963i
$973$			52.2011i			1.67349i
$974$	12.0990	+	20.9561i	0.387677	+	0.671476i
$975$	6.07776	−	1.43556i	0.194644	−	0.0459746i
$976$	−16.0583	+	27.8139i	−0.514015	+	0.890300i
$977$	4.97041	+	2.86967i	0.159017	+	0.0918088i	0.577397	−	0.816463i	$-0.304068\pi$
$977$	4.97041	+	2.86967i	0.159017	+	0.0918088i	−0.418380	+	0.908272i	$0.637402\pi$
$978$	−46.2220	−	20.3619i	−1.47802	−	0.651100i
$979$	8.65850	+	14.9970i	0.276727	+	0.479305i
$980$		−	5.80015i		−	0.185279i
$981$	−21.7051	−	6.86408i	−0.692990	−	0.219153i
$982$		−	33.2367i		−	1.06062i
$983$	−38.6724	+	22.3275i	−1.23346	+	0.712136i	−0.967749	−	0.251917i	$-0.918939\pi$
$983$	−38.6724	+	22.3275i	−1.23346	+	0.712136i	−0.265708	+	0.964054i	$0.585606\pi$
$984$	0.548663	+	5.02976i	0.0174908	+	0.160343i
$985$	12.9905	−	22.5002i	0.413911	−	0.716915i
$986$	−63.2815	−	36.5356i	−2.01529	−	1.16353i
$987$	−6.96931	−	63.8897i	−0.221835	−	2.03363i
$988$	14.7625	−	1.82940i	0.469658	−	0.0582010i
$989$	81.6382			2.59594
$990$	−1.22656	−	5.55524i	−0.0389828	−	0.176557i
$991$	57.3689			1.82238			0.911191	−	0.411984i	$-0.135164\pi$
$991$	57.3689			1.82238			0.911191	+	0.411984i	$0.135164\pi$
$992$	20.2525	+	35.0784i	0.643019	+	1.11374i
$993$	19.9832	−	45.3623i	0.634146	−	1.43953i
$994$	−68.9283	−	39.7957i	−2.18627	−	1.26224i
$995$	−13.9246	−	8.03935i	−0.441438	−	0.254864i
$996$	4.95601	+	6.76523i	0.157037	+	0.214364i
$997$	5.40321	+	9.35864i	0.171121	+	0.296391i	0.938812	−	0.344429i	$-0.111928\pi$
$997$	5.40321	+	9.35864i	0.171121	+	0.296391i	−0.767691	+	0.640820i	$0.778594\pi$
$998$	31.4074			0.994184
$999$	−16.0173	+	5.41414i	−0.506765	+	0.171296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.11	yes	108
9.7	even	3	inner	585.2.bt.b.376.44	yes	108
13.12	even	2	inner	585.2.bt.b.571.44	yes	108
117.25	even	6	inner	585.2.bt.b.376.11	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.11	✓	108	117.25	even	6	inner
585.2.bt.b.376.44	yes	108	9.7	even	3	inner
585.2.bt.b.571.11	yes	108	1.1	even	1	trivial
585.2.bt.b.571.44	yes	108	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64129 + 0.947602i) q^{2} +(-1.39724 + 1.02358i) q^{3} +(0.795899 - 1.37854i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.32334 - 3.00402i) q^{6} +(2.82539 - 1.63124i) q^{7} -0.773626i q^{8} +(0.904573 - 2.86038i) q^{9} +O(q^{10})\)	\(q+(-1.64129 + 0.947602i) q^{2} +(-1.39724 + 1.02358i) q^{3} +(0.795899 - 1.37854i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.32334 - 3.00402i) q^{6} +(2.82539 - 1.63124i) q^{7} -0.773626i q^{8} +(0.904573 - 2.86038i) q^{9} -1.89520 q^{10} +(-0.866548 + 0.500301i) q^{11} +(0.298978 + 2.74082i) q^{12} +(-2.87709 + 2.17310i) q^{13} +(-3.09153 + 5.35469i) q^{14} +(-1.72184 + 0.187824i) q^{15} +(2.32489 + 4.02682i) q^{16} -7.42651 q^{17} +(1.22583 + 5.55189i) q^{18} -2.59185i q^{19} +(1.37854 - 0.795899i) q^{20} +(-2.27805 + 5.17125i) q^{21} +(0.948173 - 1.64228i) q^{22} +(-4.12263 + 7.14060i) q^{23} +(0.791867 + 1.08094i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.66292 - 6.29303i) q^{26} +(1.66391 + 4.92254i) q^{27} -5.19321i q^{28} +(-2.59582 - 4.49610i) q^{29} +(2.64806 - 1.93989i) q^{30} +(-4.82840 - 2.78768i) q^{31} +(-6.29169 - 3.63251i) q^{32} +(0.698679 - 1.58602i) q^{33} +(12.1891 - 7.03738i) q^{34} +3.26248 q^{35} +(-3.22319 - 3.52356i) q^{36} +3.25387i q^{37} +(2.45604 + 4.25399i) q^{38} +(1.79565 - 5.98127i) q^{39} +(0.386813 - 0.669980i) q^{40} +(3.27005 + 1.88797i) q^{41} +(-1.16133 - 10.6462i) q^{42} +(-4.95061 - 8.57471i) q^{43} +1.59276i q^{44} +(2.21357 - 2.02487i) q^{45} -15.6264i q^{46} +(-9.84967 + 5.68671i) q^{47} +(-7.37020 - 3.24674i) q^{48} +(1.82189 - 3.15560i) q^{49} +(-1.64129 - 0.947602i) q^{50} +(10.3766 - 7.60162i) q^{51} +(0.705827 + 5.69574i) q^{52} +2.76962 q^{53} +(-7.39558 - 6.50261i) q^{54} -1.00060 q^{55} +(-1.26197 - 2.18580i) q^{56} +(2.65296 + 3.62145i) q^{57} +(8.52102 + 4.91961i) q^{58} +(-5.16225 - 2.98043i) q^{59} +(-1.11149 + 2.52311i) q^{60} +(3.45357 + 5.98176i) q^{61} +10.5664 q^{62} +(-2.11019 - 9.55725i) q^{63} +4.46914 q^{64} +(-3.57818 + 0.443415i) q^{65} +(0.356179 + 3.26520i) q^{66} +(-3.37201 - 1.94683i) q^{67} +(-5.91075 + 10.2377i) q^{68} +(-1.54866 - 14.1970i) q^{69} +(-5.35469 + 3.09153i) q^{70} +12.8725i q^{71} +(-2.21286 - 0.699802i) q^{72} -4.10295i q^{73} +(-3.08337 - 5.34055i) q^{74} +(-1.58507 - 0.698258i) q^{75} +(-3.57297 - 2.06285i) q^{76} +(-1.63222 + 2.82709i) q^{77} +(2.72067 + 11.5186i) q^{78} +(1.42966 + 2.47624i) q^{79} +4.64978i q^{80} +(-7.36349 - 5.17484i) q^{81} -7.15616 q^{82} +(2.63423 - 1.52087i) q^{83} +(5.31566 + 7.25617i) q^{84} +(-6.43155 - 3.71326i) q^{85} +(16.2508 + 9.38242i) q^{86} +(8.22911 + 3.62511i) q^{87} +(0.387046 + 0.670384i) q^{88} -17.3066i q^{89} +(-1.71435 + 5.42099i) q^{90} +(-4.58405 + 10.8331i) q^{91} +(6.56239 + 11.3664i) q^{92} +(9.59986 - 1.04719i) q^{93} +(10.7775 - 18.6671i) q^{94} +(1.29593 - 2.24461i) q^{95} +(12.5092 - 1.36454i) q^{96} +(4.09056 - 2.36168i) q^{97} +6.90569i q^{98} +(0.647194 + 2.93121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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