LMFDB - Embedded newform 585.2.bt.b.376.11

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			376.11
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.11

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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	−0.209130	−	0.977888i	$-0.567063\pi$
$2$	−1.64129	−	0.947602i	−1.16057	−	0.670056i	−0.951441	+	0.307832i	$0.900396\pi$
$3$	−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	0.927606	−	0.373560i	$-0.121863\pi$
$7$	2.82539	+	1.63124i	1.06790	+	0.616551i	0.140291	+	0.990110i	$0.455196\pi$
$8$			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	0.363642	−	0.931539i	$-0.381533\pi$
$11$	−0.866548	−	0.500301i	−0.261274	−	0.150847i	−0.624916	+	0.780692i	$0.714867\pi$
$12$	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	$0.0960881\pi$
$19$			2.59185i			0.594612i	−0.954782	+	0.297306i	$0.903912\pi$
$20$	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	−0.872284	−	0.488999i	$-0.837362\pi$
$23$	−4.12263	−	7.14060i	−0.859628	−	1.48892i	0.0126568	−	0.999920i	$-0.495971\pi$
$24$	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	−0.999787	−	0.0206245i	$-0.993435\pi$
$29$	−2.59582	+	4.49610i	−0.482032	+	0.834904i	0.517755	+	0.855529i	$0.326768\pi$
$30$	2.64806	+	1.93989i	0.483467	+	0.354174i
$31$	−4.82840	+	2.78768i	−0.867207	+	0.500682i	−0.866419	−	0.499318i	$-0.833584\pi$
$31$	−4.82840	+	2.78768i	−0.867207	+	0.500682i	−0.000787699		1.00000i	$0.500251\pi$
$32$	−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	$-0.913814\pi$
$37$		−	3.25387i		−	0.534932i	0.963567	−	0.267466i	$-0.0861864\pi$
$38$	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	−0.222423	−	0.974950i	$-0.571397\pi$
$41$	3.27005	−	1.88797i	0.510696	−	0.294851i	0.733120	+	0.680099i	$0.238063\pi$
$42$	−1.16133	+	10.6462i	−0.179197	+	1.64275i
$43$	−4.95061	+	8.57471i	−0.754961	+	1.30763i	0.190432	+	0.981700i	$0.439011\pi$
$43$	−4.95061	+	8.57471i	−0.754961	+	1.30763i	−0.945394	+	0.325931i	$0.894322\pi$
$44$		−	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	−0.439101	−	0.898438i	$-0.644703\pi$
$47$	−9.84967	−	5.68671i	−1.43672	−	0.829492i	−0.997620	+	0.0689461i	$0.978036\pi$
$48$	−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	−0.796860	−	0.604164i	$-0.793507\pi$
$59$	−5.16225	+	2.98043i	−0.672068	+	0.388019i	0.124792	+	0.992183i	$0.460174\pi$
$60$	−1.11149	−	2.52311i	−0.143492	−	0.325732i
$61$	3.45357	−	5.98176i	0.442185	−	0.765886i	−0.555667	−	0.831405i	$-0.687537\pi$
$61$	3.45357	−	5.98176i	0.442185	−	0.765886i	0.997851	+	0.0655188i	$0.0208702\pi$
$62$	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	−0.691630	−	0.722252i	$-0.743107\pi$
$67$	−3.37201	+	1.94683i	−0.411956	+	0.237843i	0.279674	+	0.960095i	$0.409774\pi$
$68$	−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	$-0.723310\pi$
$71$		−	12.8725i		−	1.52768i	0.645403	−	0.763842i	$-0.276690\pi$
$72$	−2.21286	+	0.699802i	−0.260788	+	0.0824724i
$73$			4.10295i			0.480214i	0.970746	+	0.240107i	$0.0771825\pi$
$73$			4.10295i			0.480214i	−0.970746	+	0.240107i	$0.922817\pi$
$74$	−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	−0.774324	−	0.632789i	$-0.781910\pi$
$79$	1.42966	−	2.47624i	0.160849	−	0.278599i	0.935173	+	0.354190i	$0.115243\pi$
$80$		−	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	0.637556	−	0.770404i	$-0.279946\pi$
$83$	2.63423	+	1.52087i	0.289144	+	0.166937i	−0.348412	+	0.937342i	$0.613279\pi$
$84$	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	$0.369593\pi$
$89$			17.3066i			1.83449i	−0.398321	+	0.917246i	$0.630407\pi$
$90$	−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	0.693079	−	0.720862i	$-0.256254\pi$
$97$	4.09056	+	2.36168i	0.415333	+	0.239793i	−0.277745	+	0.960655i	$0.589587\pi$
$98$		−	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	−0.999914	−	0.0131440i	$-0.995816\pi$
$101$	−4.91011	+	8.50455i	−0.488574	+	0.846235i	0.511340	+	0.859379i	$0.329149\pi$
$102$	−9.82781	−	22.3094i	−0.973099	−	2.20896i
$103$	−6.08635	−	10.5419i	−0.599706	−	1.03872i	−0.992864	−	0.119251i	$-0.961951\pi$
$103$	−6.08635	−	10.5419i	−0.599706	−	1.03872i	0.393158	−	0.919471i	$-0.371383\pi$
$104$	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	$0.118387\pi$
$109$			7.58819i			0.726817i	−0.931630	+	0.363409i	$0.881613\pi$
$110$	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	0.998429	−	0.0560282i	$-0.0178437\pi$
$113$	4.79093	+	8.29813i	0.450693	+	0.780623i	−0.547736	+	0.836651i	$0.684510\pi$
$114$	−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	0.527106	−	0.849800i	$-0.323277\pi$
$131$	−5.40681	−	9.36487i	−0.472395	−	0.818212i	−0.999501	+	0.0315873i	$0.989944\pi$
$132$	−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	−0.248697	−	0.968581i	$-0.580002\pi$
$137$	−14.1845	−	8.18941i	−1.21186	−	0.699669i	−0.963165	+	0.268913i	$0.913336\pi$
$138$	15.9949	−	21.8339i	1.36158	−	1.85863i
$139$	−8.00021	−	13.8568i	−0.678569	−	1.17532i	−0.975412	−	0.220390i	$-0.929267\pi$
$139$	−8.00021	−	13.8568i	−0.678569	−	1.17532i	0.296843	−	0.954926i	$-0.404066\pi$
$140$	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	0.0718029	−	0.997419i	$-0.477125\pi$
$149$	11.8586	−	6.84657i	0.971494	−	0.560893i	0.899692	+	0.436526i	$0.143791\pi$
$150$	3.26323	+	0.355965i	0.266442	+	0.0290644i
$151$	−8.03167	−	4.63708i	−0.653608	−	0.377361i	0.136229	−	0.990677i	$-0.456502\pi$
$151$	−8.03167	−	4.63708i	−0.653608	−	0.377361i	−0.789837	+	0.613317i	$0.789835\pi$
$152$	−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	0.814594	−	0.580032i	$-0.196960\pi$
$157$	−1.19067	−	2.06230i	−0.0950256	−	0.164589i	−0.909619	+	0.415443i	$0.863627\pi$
$158$	−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	$0.205864\pi$
$163$			15.3867i			1.20518i	−0.798051	+	0.602590i	$0.794136\pi$
$164$	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	−0.668403	−	0.743799i	$-0.733022\pi$
$167$	−4.63227	+	2.67444i	−0.358456	+	0.206955i	0.309947	+	0.950754i	$0.399689\pi$
$168$	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	0.349563	+	0.936913i	$0.386330\pi$
$173$	−8.37328	+	14.5030i	−0.636609	+	1.10264i	−0.986172	+	0.165726i	$0.947003\pi$
$174$	−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	−0.536996	−	0.843585i	$-0.680441\pi$
$191$	6.38591	−	11.0607i	0.462068	−	0.800325i	0.999064	+	0.0432595i	$0.0137742\pi$
$192$	−6.24448	−	4.57452i	−0.450656	−	0.330138i
$193$	17.7511	−	10.2486i	1.27776	−	0.737712i	0.301320	−	0.953523i	$-0.402573\pi$
$193$	17.7511	−	10.2486i	1.27776	−	0.737712i	0.976435	+	0.215811i	$0.0692395\pi$
$194$	−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	$0.376383\pi$
$197$			25.9810i			1.85107i	−0.378667	+	0.925533i	$0.623617\pi$
$198$	−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	0.731643	−	0.681688i	$-0.238754\pi$
$211$	−3.26160	−	5.64926i	−0.224538	−	0.388911i	−0.956181	+	0.292777i	$0.905421\pi$
$212$	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	−0.456280	−	0.889836i	$-0.650818\pi$
$223$	−21.7284	−	12.5449i	−1.45504	−	0.840068i	−0.998761	+	0.0497685i	$0.984152\pi$
$224$	−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	0.988460	−	0.151480i	$-0.0484039\pi$
$227$	20.3625	+	11.7563i	1.35151	+	0.780292i	0.363045	+	0.931772i	$0.381737\pi$
$228$	7.10379	+	0.774906i	0.470460	+	0.0513194i
$229$	−7.07705	+	4.08594i	−0.467665	+	0.270006i	−0.715262	−	0.698857i	$-0.753692\pi$
$229$	−7.07705	+	4.08594i	−0.467665	+	0.270006i	0.247597	+	0.968863i	$0.420359\pi$
$230$	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	−0.961065	−	0.276322i	$-0.910884\pi$
$239$	−18.5870	+	10.7312i	−1.20230	+	0.694146i	−0.241231	+	0.970468i	$0.577551\pi$
$240$	−4.75941	+	6.49686i	−0.307219	+	0.419371i
$241$	5.80729	+	3.35284i	0.374081	+	0.215976i	0.675240	−	0.737598i	$-0.264040\pi$
$241$	5.80729	+	3.35284i	0.374081	+	0.215976i	−0.301159	+	0.953574i	$0.597374\pi$
$242$			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	0.937957	−	0.346751i	$-0.112715\pi$
$257$	2.70420	+	4.68381i	0.168683	+	0.292168i	−0.769274	+	0.638919i	$0.779382\pi$
$258$	−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	−0.624652	−	0.780903i	$-0.714759\pi$
$263$	5.90237	−	10.2232i	0.363956	−	0.630390i	0.988608	+	0.150513i	$0.0480925\pi$
$264$	−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	$-0.906647\pi$
$271$		−	9.51808i		−	0.578182i	0.957302	−	0.289091i	$-0.0933531\pi$
$272$	−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	−0.761809	−	0.647802i	$-0.775689\pi$
$277$	2.99760	−	5.19199i	0.180108	−	0.311956i	0.941917	+	0.335845i	$0.109022\pi$
$278$			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	0.309730	−	0.950824i	$-0.399761\pi$
$281$	−6.01530	−	3.47293i	−0.358842	−	0.207178i	−0.668573	+	0.743647i	$0.733095\pi$
$282$	4.04853	−	37.1141i	0.241087	−	2.21011i
$283$	0.903153	+	1.56431i	0.0536869	+	0.0929884i	0.891620	−	0.452785i	$-0.149569\pi$
$283$	0.903153	+	1.56431i	0.0536869	+	0.0929884i	−0.837933	+	0.545773i	$0.816236\pi$
$284$	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	−0.437952	−	0.898999i	$-0.644296\pi$
$293$	2.08194	−	1.20201i	0.121628	−	0.0702220i	0.559580	+	0.828777i	$0.310963\pi$
$294$	−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	$0.125097\pi$
$307$			13.4202i			0.765932i	−0.923762	+	0.382966i	$0.874903\pi$
$308$	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	0.994146	+	0.108045i	$0.0344592\pi$
$311$	10.4161	+	18.0412i	0.590643	+	1.02302i	−0.403503	+	0.914978i	$0.632208\pi$
$312$	−4.62727	+	1.38916i	−0.261968	+	0.0786459i
$313$	14.4104	−	24.9595i	0.814523	−	1.41080i	−0.0951470	−	0.995463i	$-0.530332\pi$
$313$	14.4104	−	24.9595i	0.814523	−	1.41080i	0.909670	−	0.415332i	$-0.136335\pi$
$314$			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	0.542732	−	0.839906i	$-0.317390\pi$
$317$	1.54399	+	0.891421i	0.0867190	+	0.0500672i	−0.456013	+	0.889973i	$0.650723\pi$
$318$	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	−0.372348	−	0.928093i	$-0.621447\pi$
$331$	−24.7844	−	14.3093i	−1.36227	−	0.786510i	−0.989926	+	0.141583i	$0.954781\pi$
$332$			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	0.713439	−	0.700717i	$-0.247137\pi$
$337$	−4.59158	−	7.95285i	−0.250119	−	0.433219i	−0.963558	+	0.267498i	$0.913803\pi$
$338$	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	0.802897	−	0.596118i	$-0.203291\pi$
$347$	−2.13858	−	3.70413i	−0.114805	−	0.198848i	−0.917702	+	0.397270i	$0.869958\pi$
$348$	11.5469	+	8.45891i	0.618978	+	0.453445i
$349$	−8.55416	−	4.93875i	−0.457894	−	0.264365i	0.253264	−	0.967397i	$-0.418496\pi$
$349$	−8.55416	−	4.93875i	−0.457894	−	0.264365i	−0.711158	+	0.703032i	$0.751829\pi$
$350$	−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	0.599108	−	0.800668i	$-0.295522\pi$
$353$	3.85654	+	2.22658i	0.205263	+	0.118509i	−0.393845	+	0.919177i	$0.628855\pi$
$354$	−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	$-0.887641\pi$
$359$		−	13.1002i		−	0.691404i	0.938344	−	0.345702i	$-0.112359\pi$
$360$	−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	−0.919135	−	0.393943i	$-0.871111\pi$
$367$	−2.26826	+	3.92875i	−0.118402	+	0.205079i	0.800732	+	0.599022i	$0.204444\pi$
$368$	−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	0.891470	−	0.453080i	$-0.149675\pi$
$373$	1.03048	+	1.78484i	0.0533560	+	0.0924153i	−0.838114	+	0.545495i	$0.816342\pi$
$374$	−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	$0.133950\pi$
$379$			15.9055i			0.817010i	−0.912756	+	0.408505i	$0.866050\pi$
$380$	−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	−0.167530	−	0.985867i	$-0.553579\pi$
$383$	11.7910	−	6.80753i	0.602491	−	0.347848i	0.770021	+	0.638019i	$0.220246\pi$
$384$	−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	−0.834437	−	0.551104i	$-0.814207\pi$
$389$	1.18440	−	2.05144i	0.0600515	−	0.104012i	0.894488	+	0.447091i	$0.147540\pi$
$390$	−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	$-0.823717\pi$
$397$		−	20.9582i		−	1.05186i	0.850527	−	0.525931i	$-0.176283\pi$
$398$	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	−0.199684	−	0.979860i	$-0.563992\pi$
$401$	10.9949	−	6.34789i	0.549057	−	0.316998i	0.748742	+	0.662862i	$0.230658\pi$
$402$	−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	−0.827417	−	0.561588i	$-0.810191\pi$
$409$	−15.2644	+	8.81290i	−0.754776	+	0.435770i	0.0726412	+	0.997358i	$0.476857\pi$
$410$	−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	−0.851927	−	0.523661i	$-0.824566\pi$
$419$	−18.0022	−	31.1808i	−0.879467	−	1.52328i	−0.0275401	−	0.999621i	$-0.508767\pi$
$420$	0.975408	−	8.94186i	0.0475951	−	0.436318i
$421$	23.5453	+	13.5939i	1.14753	+	0.662527i	0.948284	−	0.317423i	$-0.102818\pi$
$421$	23.5453	+	13.5939i	1.14753	+	0.662527i	0.199246	+	0.979950i	$0.436151\pi$
$422$			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	$-0.920923\pi$
$431$		−	10.2093i		−	0.491762i	0.969300	−	0.245881i	$-0.0790773\pi$
$432$	−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	−0.783435	−	0.621474i	$-0.786534\pi$
$439$	3.06941	−	5.31638i	0.146495	−	0.253737i	0.929930	+	0.367737i	$0.119867\pi$
$440$		−	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	−0.810292	−	0.586026i	$-0.800692\pi$
$443$	2.15458	−	3.73184i	0.102367	−	0.177305i	0.912659	+	0.408721i	$0.134025\pi$
$444$	−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	$-0.615278\pi$
$449$		−	39.6303i		−	1.87027i	0.354293	−	0.935134i	$-0.384722\pi$
$450$	−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	0.290588	−	0.956848i	$-0.406149\pi$
$457$	−8.39654	−	4.84775i	−0.392774	−	0.226768i	−0.683361	+	0.730080i	$0.739483\pi$
$458$	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	0.999995	+	0.00310271i	$0.000987624\pi$
$461$	32.2639	+	18.6276i	1.50268	+	0.867573i	0.502685	+	0.864470i	$0.332346\pi$
$462$	6.33267	−	8.64445i	0.294622	−	0.402176i
$463$	10.9320	−	6.31158i	0.508052	−	0.293324i	−0.223981	−	0.974594i	$-0.571905\pi$
$463$	10.9320	−	6.31158i	0.508052	−	0.293324i	0.732033	+	0.681270i	$0.238572\pi$
$464$	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	0.278858	−	0.960332i	$-0.410044\pi$
$479$	−9.04739	−	5.22351i	−0.413386	−	0.238668i	−0.692243	+	0.721664i	$0.743378\pi$
$480$	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	$0.0934181\pi$
$487$			12.7680i			0.578574i	−0.957242	+	0.289287i	$0.906582\pi$
$488$	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	0.597471	−	0.801891i	$-0.296172\pi$
$491$	−8.76862	−	15.1877i	−0.395722	−	0.685411i	−0.993193	+	0.116479i	$0.962839\pi$
$492$	−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	−0.785568	−	0.618776i	$-0.787629\pi$
$499$	−14.3518	+	8.28603i	−0.642476	+	0.370933i	0.143092	+	0.989709i	$0.454296\pi$
$500$	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	−0.253604	−	0.967308i	$-0.581616\pi$
$509$	10.3173	−	5.95672i	0.457308	−	0.264027i	0.710912	+	0.703281i	$0.248283\pi$
$510$	−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	$-0.703633\pi$
$541$		−	37.3200i		−	1.60451i	0.596981	−	0.802255i	$-0.296367\pi$
$542$	−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	−0.906161	−	0.422933i	$-0.861001\pi$
$547$	−2.03031	+	3.51660i	−0.0868098	+	0.150359i	0.819351	+	0.573292i	$0.194334\pi$
$548$		−	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	$-0.994888\pi$
$557$		−	0.758048i		−	0.0321195i	0.999871	−	0.0160598i	$-0.00511220\pi$
$558$	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	0.989849	+	0.142121i	$0.0453922\pi$
$563$	14.6638	+	25.3984i	0.618005	+	1.07042i	−0.371844	+	0.928295i	$0.621274\pi$
$564$	−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	−0.432271	−	0.901744i	$-0.642288\pi$
$569$	13.4725	−	23.3351i	0.564798	−	0.978258i	0.997068	−	0.0765144i	$-0.0243791\pi$
$570$	−5.02791	+	6.86338i	−0.210596	+	0.287475i
$571$	−9.83988	−	17.0432i	−0.411786	−	0.713235i	0.583299	−	0.812258i	$-0.301762\pi$
$571$	−9.83988	−	17.0432i	−0.411786	−	0.713235i	−0.995085	+	0.0990228i	$0.968428\pi$
$572$	−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	$-0.978438\pi$
$577$		−	3.25178i		−	0.135373i	0.997707	−	0.0676867i	$-0.0215618\pi$
$578$	−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	−0.433415	−	0.901195i	$-0.642691\pi$
$587$	−34.6602	−	20.0111i	−1.43058	−	0.825945i	−0.997165	+	0.0752491i	$0.976025\pi$
$588$	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	$-0.897830\pi$
$593$		−	15.3656i		−	0.630988i	0.948928	−	0.315494i	$-0.102170\pi$
$594$	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	0.730336	−	0.683088i	$-0.239363\pi$
$599$	−5.54111	−	9.59748i	−0.226403	−	0.392142i	−0.956740	+	0.290946i	$0.906030\pi$
$600$	−0.540191	−	1.22625i	−0.0220532	−	0.0500614i
$601$	−20.1265	+	34.8602i	−0.820979	+	1.42198i	0.0839755	+	0.996468i	$0.473238\pi$
$601$	−20.1265	+	34.8602i	−0.820979	+	1.42198i	−0.904954	+	0.425509i	$0.860095\pi$
$602$	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	0.976372	−	0.216096i	$-0.0693323\pi$
$607$	7.41688	+	12.8464i	0.301042	+	0.521420i	−0.675330	+	0.737515i	$0.735999\pi$
$608$	−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	$-0.913612\pi$
$613$		−	13.2745i		−	0.536153i	0.963398	−	0.268077i	$-0.0863881\pi$
$614$	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	−0.686608	−	0.727028i	$-0.740901\pi$
$617$	−9.94291	+	5.74054i	−0.400287	+	0.231106i	0.286321	+	0.958134i	$0.407568\pi$
$618$	23.6137	−	32.2340i	0.949883	−	1.29664i
$619$	12.4593	+	7.19336i	0.500780	+	0.289125i	0.729036	−	0.684476i	$-0.239969\pi$
$619$	12.4593	+	7.19336i	0.500780	+	0.289125i	−0.228256	+	0.973601i	$0.573302\pi$
$620$	−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	$0.125274\pi$
$631$			19.2657i			0.766957i	−0.923550	+	0.383479i	$0.874726\pi$
$632$	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	−0.966316	−	0.257359i	$-0.917148\pi$
$641$	−6.58973	+	11.4137i	−0.260279	+	0.450816i	0.706037	+	0.708175i	$0.250481\pi$
$642$	12.2837	+	27.8844i	0.484800	+	1.10051i
$643$	−13.6088	+	7.85706i	−0.536680	+	0.309852i	−0.743732	−	0.668478i	$-0.766946\pi$
$643$	−13.6088	+	7.85706i	−0.536680	+	0.309852i	0.207053	+	0.978330i	$0.433613\pi$
$644$	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	0.990753	−	0.135678i	$-0.0433212\pi$
$653$	9.65619	+	16.7250i	0.377876	+	0.654500i	−0.612877	+	0.790178i	$0.709988\pi$
$654$	−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	−0.774565	−	0.632494i	$-0.782031\pi$
$659$	4.11952	−	7.13522i	0.160474	−	0.277949i	0.935039	+	0.354546i	$0.115364\pi$
$660$	−0.299158	+	2.74247i	−0.0116447	+	0.106750i
$661$	−16.4579	+	9.50199i	−0.640139	+	0.369585i	−0.784668	−	0.619916i	$-0.787167\pi$
$661$	−16.4579	+	9.50199i	−0.640139	+	0.369585i	0.144529	+	0.989501i	$0.453833\pi$
$662$	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	−0.933329	−	0.359021i	$-0.883111\pi$
$673$	−4.04033	+	6.99805i	−0.155743	+	0.269755i	0.777586	+	0.628776i	$0.216444\pi$
$674$			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	−0.915810	−	0.401611i	$-0.868450\pi$
$677$	−2.86472	+	4.96183i	−0.110100	+	0.190699i	0.805710	+	0.592310i	$0.201784\pi$
$678$	−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	$0.185813\pi$
$683$			28.8081i			1.10231i	−0.834403	+	0.551155i	$0.814187\pi$
$684$	−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	0.991758	−	0.128122i	$-0.0408949\pi$
$691$	36.1886	+	20.8935i	1.37668	+	0.794827i	0.384922	+	0.922949i	$0.374228\pi$
$692$	−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	0.925005	−	0.379956i	$-0.124061\pi$
$709$	28.1835	+	16.2718i	1.05846	+	0.611099i	0.133451	+	0.991055i	$0.457394\pi$
$710$			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	−0.979805	−	0.199955i	$-0.935920\pi$
$727$	−8.54013	+	14.7919i	−0.316736	+	0.548603i	0.663069	+	0.748558i	$0.269254\pi$
$728$	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	−0.814667	−	0.579929i	$-0.803080\pi$
$733$	−19.4870	+	11.2508i	−0.719768	+	0.415558i	0.0948995	+	0.995487i	$0.469747\pi$
$734$	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	$0.168828\pi$
$739$			27.5036i			1.01174i	−0.862611	+	0.505869i	$0.831172\pi$
$740$	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	0.404341	−	0.914608i	$-0.367501\pi$
$743$	38.1227	−	22.0101i	1.39859	−	0.807474i	0.994244	+	0.107135i	$0.0341677\pi$
$744$	−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	0.925747	−	0.378143i	$-0.123437\pi$
$751$	3.71033	+	6.42648i	0.135392	+	0.234506i	−0.790355	+	0.612649i	$0.790104\pi$
$752$	−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	−0.833442	−	0.552607i	$-0.813633\pi$
$761$	−21.2853	+	12.2891i	−0.771591	+	0.445478i	0.0618512	+	0.998085i	$0.480300\pi$
$762$	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	−0.968754	−	0.248023i	$-0.920219\pi$
$769$	−34.3401	+	19.8263i	−1.23834	+	0.714954i	−0.269583	+	0.962977i	$0.586886\pi$
$770$	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	$-0.921282\pi$
$773$		−	13.6116i		−	0.489574i	0.969577	−	0.244787i	$-0.0787180\pi$
$774$	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	−0.619965	−	0.784629i	$-0.712853\pi$
$787$	−7.02569	+	4.05628i	−0.250439	+	0.144591i	0.369526	+	0.929220i	$0.379520\pi$
$788$	−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	0.669906	−	0.742446i	$-0.266334\pi$
$797$	−8.69587	−	15.0617i	−0.308023	−	0.533512i	−0.977930	+	0.208933i	$0.933001\pi$
$798$	−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	$-0.762000\pi$
$811$		−	38.7276i		−	1.35991i	0.733255	−	0.679954i	$-0.238000\pi$
$812$	−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	0.177201	−	0.984175i	$-0.443296\pi$
$821$	−16.8056	−	9.70271i	−0.586519	−	0.338627i	−0.763720	+	0.645548i	$0.776629\pi$
$822$	5.83028	−	53.4479i	0.203354	−	1.86421i
$823$	−9.46514	−	16.3941i	−0.329934	−	0.571463i	0.652564	−	0.757733i	$-0.273693\pi$
$823$	−9.46514	−	16.3941i	−0.329934	−	0.571463i	−0.982498	+	0.186271i	$0.940360\pi$
$824$	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	$0.0128403\pi$
$827$			2.31948i			0.0806562i	−0.999186	+	0.0403281i	$0.987160\pi$
$828$	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	0.240654	−	0.970611i	$-0.422638\pi$
$839$	−13.8917	−	8.02035i	−0.479593	−	0.276893i	−0.720247	+	0.693718i	$0.755972\pi$
$840$	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	−0.357650	−	0.933856i	$-0.616422\pi$
$853$	−39.2886	−	22.6833i	−1.34522	−	0.776662i	−0.987568	+	0.157194i	$0.949755\pi$
$854$	−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	−0.997861	−	0.0653657i	$-0.979179\pi$
$857$	−12.9488	+	22.4280i	−0.442322	+	0.766125i	0.555539	+	0.831490i	$0.312512\pi$
$858$	−8.12036	+	8.62026i	−0.277225	+	0.294291i
$859$	−6.25204	−	10.8289i	−0.213317	−	0.369476i	0.739434	−	0.673229i	$-0.235093\pi$
$859$	−6.25204	−	10.8289i	−0.213317	−	0.369476i	−0.952751	+	0.303754i	$0.901760\pi$
$860$	−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	$0.267953\pi$
$863$			43.8210i			1.49168i	−0.666123	+	0.745842i	$0.732047\pi$
$864$	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	−0.989313	−	0.145808i	$-0.953422\pi$
$877$	−40.2071	+	23.2136i	−1.35770	+	0.783866i	−0.368383	+	0.929674i	$0.620089\pi$
$878$	−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	0.997672	+	0.0682024i	$0.0217264\pi$
$887$	16.6157	+	28.7792i	0.557901	+	0.966312i	−0.439771	+	0.898110i	$0.644940\pi$
$888$	−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	−0.859935	−	0.510403i	$-0.829496\pi$
$907$	0.363034	−	0.628793i	0.0120543	−	0.0208787i	0.871990	+	0.489524i	$0.162830\pi$
$908$			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	−0.996108	−	0.0881449i	$-0.971906\pi$
$911$	−12.7286	+	22.0466i	−0.421718	+	0.730437i	0.574390	+	0.818582i	$0.305239\pi$
$912$	−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	−0.0318806	−	0.999492i	$-0.510150\pi$
$929$	−27.8402	−	16.0735i	−0.913406	−	0.527355i	−0.881526	+	0.472136i	$0.843483\pi$
$930$	−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	0.135698	−	0.990750i	$-0.456672\pi$
$941$	32.5642	−	18.8009i	1.06156	−	0.612893i	0.925864	+	0.377857i	$0.123339\pi$
$942$	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	0.958493	−	0.285115i	$-0.0920317\pi$
$947$	36.6456	+	21.1574i	1.19082	+	0.687522i	0.232330	+	0.972637i	$0.425365\pi$
$948$	−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	−0.691763	−	0.722125i	$-0.743166\pi$
$967$	−12.8201	+	7.40166i	−0.412265	+	0.238021i	0.279497	+	0.960146i	$0.409832\pi$
$968$	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	−0.418380	−	0.908272i	$-0.637402\pi$
$977$	4.97041	−	2.86967i	0.159017	−	0.0918088i	0.577397	+	0.816463i	$0.304068\pi$
$978$	−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	−0.265708	−	0.964054i	$-0.585606\pi$
$983$	−38.6724	−	22.3275i	−1.23346	−	0.712136i	−0.967749	+	0.251917i	$0.918939\pi$
$984$	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	−0.767691	−	0.640820i	$-0.778594\pi$
$997$	5.40321	−	9.35864i	0.171121	−	0.296391i	0.938812	+	0.344429i	$0.111928\pi$
$998$	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.376.11	✓	108
9.4	even	3	inner	585.2.bt.b.571.44	yes	108
13.12	even	2	inner	585.2.bt.b.376.44	yes	108
117.103	even	6	inner	585.2.bt.b.571.11	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.11	✓	108	1.1	even	1	trivial
585.2.bt.b.376.44	yes	108	13.12	even	2	inner
585.2.bt.b.571.11	yes	108	117.103	even	6	inner
585.2.bt.b.571.44	yes	108	9.4	even	3	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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