LMFDB - Embedded newform 260.2.bc.c.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(19,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 5]))

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

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

chi := DirichletCharacter("260.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	260.19
Dual form			260.2.bc.c.219.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32112 - 0.504618i) q^{2} +(0.414936 - 0.718690i) q^{3} +(1.49072 + 1.33332i) q^{4} +(0.439941 + 2.19236i) q^{5} +(-0.910845 + 0.740092i) q^{6} +(0.345572 - 1.28969i) q^{7} +(-1.29660 - 2.51373i) q^{8} +(1.15566 + 2.00166i) q^{9} +O(q^{10})$	\(q+(-1.32112 - 0.504618i) q^{2} +(0.414936 - 0.718690i) q^{3} +(1.49072 + 1.33332i) q^{4} +(0.439941 + 2.19236i) q^{5} +(-0.910845 + 0.740092i) q^{6} +(0.345572 - 1.28969i) q^{7} +(-1.29660 - 2.51373i) q^{8} +(1.15566 + 2.00166i) q^{9} +(0.525091 - 3.11838i) q^{10} +(1.06679 + 3.98133i) q^{11} +(1.57680 - 0.518122i) q^{12} +(-3.36473 + 1.29562i) q^{13} +(-1.10734 + 1.52946i) q^{14} +(1.75818 + 0.593509i) q^{15} +(0.444495 + 3.97523i) q^{16} +(1.72001 + 2.97915i) q^{17} +(-0.516689 - 3.22759i) q^{18} +(1.73392 - 6.47108i) q^{19} +(-2.26730 + 3.85478i) q^{20} +(-0.783498 - 0.783498i) q^{21} +(0.599688 - 5.79814i) q^{22} +(6.36940 + 3.67737i) q^{23} +(-2.34460 - 0.111181i) q^{24} +(-4.61290 + 1.92902i) q^{25} +(5.09900 - 0.0137634i) q^{26} +4.40771 q^{27} +(2.23473 - 1.46181i) q^{28} +(4.61995 - 8.00199i) q^{29} +(-2.02327 - 1.67130i) q^{30} +(-2.05056 - 2.05056i) q^{31} +(1.41874 - 5.47605i) q^{32} +(3.30399 + 0.885302i) q^{33} +(-0.769011 - 4.80376i) q^{34} +(2.97950 + 0.190230i) q^{35} +(-0.946094 + 4.52477i) q^{36} +(0.319083 + 1.19083i) q^{37} +(-5.55614 + 7.67411i) q^{38} +(-0.464999 + 2.95579i) q^{39} +(4.94057 - 3.94851i) q^{40} +(2.03261 + 7.58581i) q^{41} +(0.639728 + 1.43046i) q^{42} +(-3.93517 + 2.27197i) q^{43} +(-3.71811 + 7.35742i) q^{44} +(-3.87993 + 3.41423i) q^{45} +(-6.55907 - 8.07237i) q^{46} +(-8.18265 - 8.18265i) q^{47} +(3.04139 + 1.33001i) q^{48} +(4.51829 + 2.60864i) q^{49} +(7.06762 - 0.220713i) q^{50} +2.85478 q^{51} +(-6.74334 - 2.55487i) q^{52} -1.10572i q^{53} +(-5.82312 - 2.22421i) q^{54} +(-8.25918 + 4.09035i) q^{55} +(-3.69000 + 0.803543i) q^{56} +(-3.93123 - 3.93123i) q^{57} +(-10.1415 + 8.24028i) q^{58} +(-8.91109 - 2.38772i) q^{59} +(1.82961 + 3.22897i) q^{60} +(-3.44018 - 5.95856i) q^{61} +(1.67429 + 3.74379i) q^{62} +(2.98088 - 0.798724i) q^{63} +(-4.63765 + 6.51861i) q^{64} +(-4.32074 - 6.80670i) q^{65} +(-3.91823 - 2.83685i) q^{66} +(-1.13019 - 4.21791i) q^{67} +(-1.40811 + 6.73441i) q^{68} +(5.28578 - 3.05175i) q^{69} +(-3.84029 - 1.75483i) q^{70} +(-1.28747 + 4.80490i) q^{71} +(3.53319 - 5.50035i) q^{72} +(3.25125 - 3.25125i) q^{73} +(0.179369 - 1.73425i) q^{74} +(-0.527691 + 4.11567i) q^{75} +(11.2128 - 7.33469i) q^{76} +5.50333 q^{77} +(2.10587 - 3.67031i) q^{78} -12.4204i q^{79} +(-8.51958 + 2.72336i) q^{80} +(-1.63805 + 2.83719i) q^{81} +(1.14261 - 11.0475i) q^{82} +(-7.98892 + 7.98892i) q^{83} +(-0.123320 - 2.21263i) q^{84} +(-5.77467 + 5.08154i) q^{85} +(6.34531 - 1.01579i) q^{86} +(-3.83397 - 6.64063i) q^{87} +(8.62476 - 7.84382i) q^{88} +(-2.23917 + 0.599985i) q^{89} +(6.84874 - 2.55272i) q^{90} +(0.508191 + 4.78718i) q^{91} +(4.59186 + 13.9744i) q^{92} +(-2.32457 + 0.622867i) q^{93} +(6.68115 + 14.9394i) q^{94} +(14.9498 + 0.954487i) q^{95} +(-3.34690 - 3.29185i) q^{96} +(0.884051 - 3.29932i) q^{97} +(-4.65285 - 5.72634i) q^{98} +(-6.73640 + 6.73640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{4} - 12 q^{5} - 80 q^{9}+O(q^{10}) $ 144 * q - 12 * q^4 - 12 * q^5 - 80 * q^9	$ 144 q - 12 q^{4} - 12 q^{5} - 80 q^{9} - 12 q^{10} - 32 q^{14} - 36 q^{16} + 18 q^{20} + 8 q^{21} - 28 q^{24} + 28 q^{26} - 6 q^{30} + 16 q^{34} + 24 q^{36} - 88 q^{40} - 72 q^{41} + 68 q^{45} + 64 q^{46} - 24 q^{49} - 34 q^{50} + 80 q^{54} + 96 q^{56} - 48 q^{60} - 8 q^{61} + 40 q^{66} - 24 q^{69} - 80 q^{70} - 24 q^{74} - 28 q^{76} - 92 q^{80} - 8 q^{81} + 84 q^{84} + 20 q^{85} - 52 q^{86} - 104 q^{89} - 52 q^{94} - 124 q^{96}+O(q^{100}) $ 144 * q - 12 * q^4 - 12 * q^5 - 80 * q^9 - 12 * q^10 - 32 * q^14 - 36 * q^16 + 18 * q^20 + 8 * q^21 - 28 * q^24 + 28 * q^26 - 6 * q^30 + 16 * q^34 + 24 * q^36 - 88 * q^40 - 72 * q^41 + 68 * q^45 + 64 * q^46 - 24 * q^49 - 34 * q^50 + 80 * q^54 + 96 * q^56 - 48 * q^60 - 8 * q^61 + 40 * q^66 - 24 * q^69 - 80 * q^70 - 24 * q^74 - 28 * q^76 - 92 * q^80 - 8 * q^81 + 84 * q^84 + 20 * q^85 - 52 * q^86 - 104 * q^89 - 52 * q^94 - 124 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$	$-1$

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 $

$2$	−1.32112	−	0.504618i	−0.934173	−	0.356819i
$2$	−1.32112	−	0.504618i	−0.934173	−	0.356819i
$3$	0.414936	−	0.718690i	0.239563	−	0.414936i	−0.721026	−	0.692908i	$-0.756329\pi$
$3$	0.414936	−	0.718690i	0.239563	−	0.414936i	0.960589	+	0.277972i	$0.0896624\pi$
$4$	1.49072	+	1.33332i	0.745360	+	0.666662i
$5$	0.439941	+	2.19236i	0.196748	+	0.980454i
$5$	0.439941	+	2.19236i	0.196748	+	0.980454i
$6$	−0.910845	+	0.740092i	−0.371851	+	0.302141i
$7$	0.345572	−	1.28969i	0.130614	−	0.487457i	−0.869364	−	0.494173i	$-0.835471\pi$
$7$	0.345572	−	1.28969i	0.130614	−	0.487457i	0.999977	+	0.00671553i	$0.00213764\pi$
$8$	−1.29660	−	2.51373i	−0.458418	−	0.888737i
$9$	1.15566	+	2.00166i	0.385219	+	0.667218i
$10$	0.525091	−	3.11838i	0.166048	−	0.986118i
$11$	1.06679	+	3.98133i	0.321650	+	1.20041i	0.917637	+	0.397420i	$0.130095\pi$
$11$	1.06679	+	3.98133i	0.321650	+	1.20041i	−0.595986	+	0.802995i	$0.703239\pi$
$12$	1.57680	−	0.518122i	0.455183	−	0.149569i
$13$	−3.36473	+	1.29562i	−0.933207	+	0.359339i
$13$	−3.36473	+	1.29562i	−0.933207	+	0.359339i
$14$	−1.10734	+	1.52946i	−0.295950	+	0.408764i
$15$	1.75818	+	0.593509i	0.453959	+	0.153243i
$16$	0.444495	+	3.97523i	0.111124	+	0.993807i
$17$	1.72001	+	2.97915i	0.417164	+	0.722550i	0.995653	−	0.0931408i	$-0.0296907\pi$
$17$	1.72001	+	2.97915i	0.417164	+	0.722550i	−0.578489	+	0.815690i	$0.696357\pi$
$18$	−0.516689	−	3.22759i	−0.121785	−	0.760751i
$19$	1.73392	−	6.47108i	0.397789	−	1.48457i	−0.419190	−	0.907899i	$-0.637686\pi$
$19$	1.73392	−	6.47108i	0.397789	−	1.48457i	0.816978	−	0.576668i	$-0.195648\pi$
$20$	−2.26730	+	3.85478i	−0.506984	+	0.861956i
$21$	−0.783498	−	0.783498i	−0.170973	−	0.170973i
$22$	0.599688	−	5.79814i	0.127854	−	1.23617i
$23$	6.36940	+	3.67737i	1.32811	+	0.766785i	0.985007	−	0.172512i	$-0.0551885\pi$
$23$	6.36940	+	3.67737i	1.32811	+	0.766785i	0.343104	+	0.939298i	$0.388522\pi$
$24$	−2.34460	−	0.111181i	−0.478589	−	0.0226946i
$25$	−4.61290	+	1.92902i	−0.922581	+	0.385804i
$26$	5.09900	−	0.0137634i	0.999996	−	0.00269922i
$27$	4.40771			0.848264
$28$	2.23473	−	1.46181i	0.422324	−	0.276256i
$29$	4.61995	−	8.00199i	0.857903	−	1.48593i	−0.0160223	−	0.999872i	$-0.505100\pi$
$29$	4.61995	−	8.00199i	0.857903	−	1.48593i	0.873925	−	0.486060i	$-0.161566\pi$
$30$	−2.02327	−	1.67130i	−0.369397	−	0.305137i
$31$	−2.05056	−	2.05056i	−0.368292	−	0.368292i	0.498562	−	0.866854i	$-0.333862\pi$
$31$	−2.05056	−	2.05056i	−0.368292	−	0.368292i	−0.866854	+	0.498562i	$0.833862\pi$
$32$	1.41874	−	5.47605i	0.250800	−	0.968039i
$33$	3.30399	+	0.885302i	0.575151	+	0.154111i
$34$	−0.769011	−	4.80376i	−0.131884	−	0.823839i
$35$	2.97950	+	0.190230i	0.503628	+	0.0321548i
$36$	−0.946094	+	4.52477i	−0.157682	+	0.754129i
$37$	0.319083	+	1.19083i	0.0524569	+	0.195772i	0.987182	−	0.159601i	$-0.0510207\pi$
$37$	0.319083	+	1.19083i	0.0524569	+	0.195772i	−0.934725	+	0.355372i	$0.884354\pi$
$38$	−5.55614	+	7.67411i	−0.901325	+	1.24490i
$39$	−0.464999	+	2.95579i	−0.0744594	+	0.473306i
$40$	4.94057	−	3.94851i	0.781173	−	0.624315i
$41$	2.03261	+	7.58581i	0.317441	+	1.18470i	0.921696	+	0.387914i	$0.126804\pi$
$41$	2.03261	+	7.58581i	0.317441	+	1.18470i	−0.604255	+	0.796791i	$0.706529\pi$
$42$	0.639728	+	1.43046i	0.0987122	+	0.220725i
$43$	−3.93517	+	2.27197i	−0.600108	+	0.346472i	−0.769084	−	0.639148i	$-0.779287\pi$
$43$	−3.93517	+	2.27197i	−0.600108	+	0.346472i	0.168976	+	0.985620i	$0.445954\pi$
$44$	−3.71811	+	7.35742i	−0.560526	+	1.10917i
$45$	−3.87993	+	3.41423i	−0.578386	+	0.508963i
$46$	−6.55907	−	8.07237i	−0.967082	−	1.19021i
$47$	−8.18265	−	8.18265i	−1.19356	−	1.19356i	−0.976060	−	0.217502i	$-0.930209\pi$
$47$	−8.18265	−	8.18265i	−1.19356	−	1.19356i	−0.217502	−	0.976060i	$-0.569791\pi$
$48$	3.04139	+	1.33001i	0.438987	+	0.191970i
$49$	4.51829	+	2.60864i	0.645471	+	0.372663i
$50$	7.06762	−	0.220713i	0.999513	−	0.0312136i
$51$	2.85478			0.399749
$52$	−6.74334	−	2.55487i	−0.935133	−	0.354296i
$53$		−	1.10572i		−	0.151883i	−0.997112	−	0.0759415i	$-0.975804\pi$
$53$		−	1.10572i		−	0.151883i	0.997112	−	0.0759415i	$-0.0241962\pi$
$54$	−5.82312	−	2.22421i	−0.792426	−	0.302677i
$55$	−8.25918	+	4.09035i	−1.11367	+	0.551542i
$56$	−3.69000	+	0.803543i	−0.493097	+	0.107378i
$57$	−3.93123	−	3.93123i	−0.520705	−	0.520705i
$58$	−10.1415	+	8.24028i	−1.33164	+	1.08200i
$59$	−8.91109	−	2.38772i	−1.16013	−	0.310855i	−0.373110	−	0.927787i	$-0.621708\pi$
$59$	−8.91109	−	2.38772i	−1.16013	−	0.310855i	−0.787016	+	0.616933i	$0.788375\pi$
$60$	1.82961	+	3.22897i	0.236202	+	0.416859i
$61$	−3.44018	−	5.95856i	−0.440470	−	0.762916i	0.557255	−	0.830342i	$-0.311855\pi$
$61$	−3.44018	−	5.95856i	−0.440470	−	0.762916i	−0.997724	+	0.0674260i	$0.978521\pi$
$62$	1.67429	+	3.74379i	0.212635	+	0.475462i
$63$	2.98088	−	0.798724i	0.375555	−	0.100630i
$64$	−4.63765	+	6.51861i	−0.579706	+	0.814826i
$65$	−4.32074	−	6.80670i	−0.535922	−	0.844267i
$66$	−3.91823	−	2.83685i	−0.482301	−	0.349192i
$67$	−1.13019	−	4.21791i	−0.138074	−	0.515300i	−0.999966	−	0.00820827i	$-0.997387\pi$
$67$	−1.13019	−	4.21791i	−0.138074	−	0.515300i	0.861892	−	0.507092i	$-0.169279\pi$
$68$	−1.40811	+	6.73441i	−0.170759	+	0.816667i
$69$	5.28578	−	3.05175i	0.636334	−	0.367387i
$70$	−3.84029	−	1.75483i	−0.459002	−	0.209742i
$71$	−1.28747	+	4.80490i	−0.152795	+	0.570237i	0.846490	+	0.532405i	$0.178712\pi$
$71$	−1.28747	+	4.80490i	−0.152795	+	0.570237i	−0.999284	+	0.0378318i	$0.987955\pi$
$72$	3.53319	−	5.50035i	0.416390	−	0.648223i
$73$	3.25125	−	3.25125i	0.380530	−	0.380530i	−0.490763	−	0.871293i	$-0.663282\pi$
$73$	3.25125	−	3.25125i	0.380530	−	0.380530i	0.871293	+	0.490763i	$0.163282\pi$
$74$	0.179369	−	1.73425i	0.0208513	−	0.201602i
$75$	−0.527691	+	4.11567i	−0.0609326	+	0.475236i
$76$	11.2128	−	7.33469i	1.28620	−	0.841347i
$77$	5.50333			0.627163
$78$	2.10587	−	3.67031i	0.238443	−	0.415581i
$79$		−	12.4204i		−	1.39740i	−0.715413	−	0.698702i	$-0.753761\pi$
$79$		−	12.4204i		−	1.39740i	0.715413	−	0.698702i	$-0.246239\pi$
$80$	−8.51958	+	2.72336i	−0.952518	+	0.304481i
$81$	−1.63805	+	2.83719i	−0.182006	+	0.315243i
$82$	1.14261	−	11.0475i	0.126181	−	1.21999i
$83$	−7.98892	+	7.98892i	−0.876897	+	0.876897i	−0.993212	−	0.116315i	$-0.962892\pi$
$83$	−7.98892	+	7.98892i	−0.876897	+	0.876897i	0.116315	+	0.993212i	$0.462892\pi$
$84$	−0.123320	−	2.21263i	−0.0134553	−	0.241418i
$85$	−5.77467	+	5.08154i	−0.626351	+	0.551170i
$86$	6.34531	−	1.01579i	0.684232	−	0.109535i
$87$	−3.83397	−	6.64063i	−0.411044	−	0.711950i
$88$	8.62476	−	7.84382i	0.919403	−	0.836154i
$89$	−2.23917	+	0.599985i	−0.237352	+	0.0635983i	−0.375534	−	0.926809i	$-0.622541\pi$
$89$	−2.23917	+	0.599985i	−0.237352	+	0.0635983i	0.138182	+	0.990407i	$0.455874\pi$
$90$	6.84874	−	2.55272i	0.721921	−	0.269080i
$91$	0.508191	+	4.78718i	0.0532729	+	0.501833i
$92$	4.59186	+	13.9744i	0.478735	+	1.45693i
$93$	−2.32457	+	0.622867i	−0.241047	+	0.0645883i
$94$	6.68115	+	14.9394i	0.689108	+	1.54088i
$95$	14.9498	+	0.954487i	1.53381	+	0.0979283i
$96$	−3.34690	−	3.29185i	−0.341592	−	0.335973i
$97$	0.884051	−	3.29932i	0.0897618	−	0.334996i	−0.906411	−	0.422396i	$-0.861189\pi$
$97$	0.884051	−	3.29932i	0.0897618	−	0.334996i	0.996173	+	0.0874002i	$0.0278559\pi$
$98$	−4.65285	−	5.72634i	−0.470008	−	0.578448i
$99$	−6.73640	+	6.73640i	−0.677033	+	0.677033i
$100$	−9.44856	−	3.27486i	−0.944856	−	0.327486i
$101$	−5.80873	−	3.35367i	−0.577990	−	0.333703i	0.182344	−	0.983235i	$-0.441632\pi$
$101$	−5.80873	−	3.35367i	−0.577990	−	0.333703i	−0.760334	+	0.649532i	$0.774965\pi$
$102$	−3.77151	−	1.44057i	−0.373435	−	0.142638i
$103$			2.72870i			0.268867i	0.990923	+	0.134433i	$0.0429215\pi$
$103$			2.72870i			0.268867i	−0.990923	+	0.134433i	$0.957079\pi$
$104$	7.61954	+	6.77810i	0.747157	+	0.664648i
$105$	1.37302	−	2.06240i	0.133993	−	0.201270i
$106$	−0.557969	+	1.46080i	−0.0541947	+	0.141885i
$107$	−1.67053	+	2.89345i	−0.161497	+	0.279720i	−0.935406	−	0.353576i	$-0.884965\pi$
$107$	−1.67053	+	2.89345i	−0.161497	+	0.279720i	0.773909	+	0.633297i	$0.218299\pi$
$108$	6.57066	+	5.87690i	0.632262	+	0.565505i
$109$	4.74987	−	4.74987i	0.454955	−	0.454955i	−0.442040	−	0.896995i	$-0.645745\pi$
$109$	4.74987	−	4.74987i	0.454955	−	0.454955i	0.896995	+	0.442040i	$0.145745\pi$
$110$	12.9754	−	1.23611i	1.23716	−	0.117858i
$111$	0.988239	+	0.264798i	0.0937995	+	0.0251335i
$112$	5.28042	+	0.800464i	0.498953	+	0.0756368i
$113$	6.83509	−	3.94624i	0.642991	−	0.371231i	−0.142774	−	0.989755i	$-0.545602\pi$
$113$	6.83509	−	3.94624i	0.642991	−	0.371231i	0.785766	+	0.618524i	$0.212269\pi$
$114$	3.20986	+	7.17741i	0.300631	+	0.672226i
$115$	−5.25997	+	15.5819i	−0.490495	+	1.45302i
$116$	17.5563	−	5.76884i	1.63006	−	0.535623i
$117$	−6.48184	−	5.23773i	−0.599247	−	0.484229i
$118$	10.5677	+	7.65117i	0.972840	+	0.704347i
$119$	4.43657	−	1.18877i	0.406699	−	0.108975i
$120$	−0.787737	−	5.18912i	−0.0719102	−	0.473700i
$121$	−5.18663	+	2.99450i	−0.471512	+	0.272227i
$122$	1.53809	+	9.60796i	0.139252	+	0.869864i
$123$	6.29525	+	1.68681i	0.567624	+	0.152094i
$124$	−0.322751	−	5.79088i	−0.0289839	−	0.520036i
$125$	−6.25852	−	9.26450i	−0.559779	−	0.828642i
$126$	−4.34115	−	0.448995i	−0.386741	−	0.0399997i
$127$	2.22261	+	1.28322i	0.197224	+	0.113868i	0.595360	−	0.803459i	$-0.297009\pi$
$127$	2.22261	+	1.28322i	0.197224	+	0.113868i	−0.398136	+	0.917326i	$0.630343\pi$
$128$	9.41630	−	6.27163i	0.832291	−	0.554339i
$129$			3.77089i			0.332008i
$130$	2.27343	+	11.1728i	0.199393	+	0.979920i
$131$		−	9.92673i		−	0.867303i	−0.901081	−	0.433651i	$-0.857225\pi$
$131$		−	9.92673i		−	0.867303i	0.901081	−	0.433651i	$-0.142775\pi$
$132$	3.74493	+	5.72503i	0.325955	+	0.498300i
$133$	−7.74650	−	4.47244i	−0.671707	−	0.387810i
$134$	−0.635324	+	6.14268i	−0.0548836	+	0.530647i
$135$	1.93913	+	9.66330i	0.166894	+	0.831684i
$136$	5.25859	−	8.18641i	0.450921	−	0.701979i
$137$	15.8301	+	4.24165i	1.35245	+	0.362389i	0.861039	−	0.508538i	$-0.169814\pi$
$137$	15.8301	+	4.24165i	1.35245	+	0.362389i	0.491413	+	0.870927i	$0.336481\pi$
$138$	−8.52313	+	1.36442i	−0.725537	+	0.116148i
$139$	7.08212	−	4.08886i	0.600697	−	0.346813i	−0.168619	−	0.985681i	$-0.553931\pi$
$139$	7.08212	−	4.08886i	0.600697	−	0.346813i	0.769316	+	0.638869i	$0.220597\pi$
$140$	4.18796	+	4.25622i	0.353948	+	0.359716i
$141$	−9.27607	+	2.48551i	−0.781186	+	0.209318i
$142$	4.12555	−	5.69818i	0.346208	−	0.478180i
$143$	−8.74774	−	12.0139i	−0.731523	−	1.00465i
$144$	−7.44335	+	5.48372i	−0.620279	+	0.456977i
$145$	19.5758	+	6.60820i	1.62568	+	0.548781i
$146$	−5.93594	+	2.65466i	−0.491262	+	0.219701i
$147$	3.74961	−	2.16484i	0.309262	−	0.178553i
$148$	−1.11210	+	2.20064i	−0.0914143	+	0.180891i
$149$	−9.55100	−	2.55918i	−0.782448	−	0.209656i	−0.154584	−	0.987980i	$-0.549404\pi$
$149$	−9.55100	−	2.55918i	−0.782448	−	0.209656i	−0.627864	+	0.778323i	$0.716071\pi$
$150$	2.77399	−	5.17101i	0.226495	−	0.422211i
$151$	3.54345	−	3.54345i	0.288362	−	0.288362i	−0.548070	−	0.836432i	$-0.684637\pi$
$151$	3.54345	−	3.54345i	0.288362	−	0.288362i	0.836432	+	0.548070i	$0.184637\pi$
$152$	−18.5147	+	4.03181i	−1.50174	+	0.327023i
$153$	−3.97548	+	6.88574i	−0.321399	+	0.556679i
$154$	−7.27057	−	2.77708i	−0.585879	−	0.223784i
$155$	3.59345	−	5.39770i	0.288633	−	0.433554i
$156$	−4.63421	+	3.78627i	−0.371034	+	0.303144i
$157$		−	6.43170i		−	0.513305i	−0.966504	−	0.256653i	$-0.917380\pi$
$157$		−	6.43170i		−	0.513305i	0.966504	−	0.256653i	$-0.0826196\pi$
$158$	−6.26756	+	16.4088i	−0.498620	+	1.30542i
$159$	−0.794673	−	0.458805i	−0.0630217	−	0.0363856i
$160$	12.6297	+	0.701252i	0.998462	+	0.0554388i
$161$	6.94376	−	6.94376i	0.547245	−	0.547245i
$162$	3.59576	−	2.92168i	0.282510	−	0.229549i
$163$	5.49440	−	20.5054i	0.430355	−	1.60611i	−0.321589	−	0.946879i	$-0.604217\pi$
$163$	5.49440	−	20.5054i	0.430355	−	1.60611i	0.751944	−	0.659227i	$-0.229116\pi$
$164$	−7.08429	+	14.0185i	−0.553190	+	1.09466i
$165$	−0.487340	+	7.63303i	−0.0379394	+	0.594230i
$166$	14.5857	−	6.52297i	1.13207	−	0.506281i
$167$	7.87017	−	2.10880i	0.609012	−	0.163184i	0.0588842	−	0.998265i	$-0.481246\pi$
$167$	7.87017	−	2.10880i	0.609012	−	0.163184i	0.550128	+	0.835081i	$0.314579\pi$
$168$	−0.953615	+	2.98539i	−0.0735730	+	0.230328i
$169$	9.64276	−	8.71879i	0.741750	−	0.670676i
$170$	10.1933	−	3.79932i	0.781788	−	0.291395i
$171$	14.9567	−	4.00763i	1.14377	−	0.306471i
$172$	−8.89551	−	1.85998i	−0.678276	−	0.141822i
$173$	−2.05910	−	3.56647i	−0.156551	−	0.271154i	0.777072	−	0.629412i	$-0.216704\pi$
$173$	−2.05910	−	3.56647i	−0.156551	−	0.271154i	−0.933623	+	0.358258i	$0.883371\pi$
$174$	1.71415	+	10.7078i	0.129949	+	0.811753i
$175$	0.893752	+	6.61583i	0.0675613	+	0.500110i
$176$	−15.3525	+	6.01042i	−1.15724	+	0.453053i
$177$	−5.41356	+	5.41356i	−0.406908	+	0.406908i
$178$	3.26098	+	0.337276i	0.244421	+	0.0252799i
$179$	−4.77291	+	8.26693i	−0.356744	+	0.617899i	−0.987415	−	0.158151i	$-0.949447\pi$
$179$	−4.77291	+	8.26693i	−0.356744	+	0.617899i	0.630671	+	0.776051i	$0.282780\pi$
$180$	−10.3362	−	0.0835477i	−0.770412	−	0.00622728i
$181$			5.71334i			0.424669i	0.977197	+	0.212334i	$0.0681066\pi$
$181$			5.71334i			0.424669i	−0.977197	+	0.212334i	$0.931893\pi$
$182$	1.74432	−	6.58089i	0.129298	−	0.487808i
$183$	−5.70981			−0.422082
$184$	0.985338	−	20.7790i	0.0726401	−	1.53185i
$185$	−2.47036	+	1.22344i	−0.181624	+	0.0899492i
$186$	3.38535	+	0.350139i	0.248226	+	0.0256734i
$187$	−10.0261	+	10.0261i	−0.733178	+	0.733178i
$188$	−1.28792	−	23.1082i	−0.0939313	−	1.68534i
$189$	1.52318	−	5.68458i	0.110795	−	0.413493i
$190$	−19.2688	−	8.80492i	−1.39791	−	0.638776i
$191$	−20.9721	+	12.1083i	−1.51749	+	0.876124i	−0.517702	+	0.855561i	$0.673213\pi$
$191$	−20.9721	+	12.1083i	−1.51749	+	0.876124i	−0.999789	+	0.0205629i	$0.993454\pi$
$192$	2.76053	+	6.03784i	0.199224	+	0.435743i
$193$	−0.0966189	−	0.360587i	−0.00695478	−	0.0259556i	0.962361	−	0.271773i	$-0.0876101\pi$
$193$	−0.0966189	−	0.360587i	−0.00695478	−	0.0259556i	−0.969316	+	0.245818i	$0.920943\pi$
$194$	−2.83284	+	3.91270i	−0.203386	+	0.280915i
$195$	−6.68474	+	0.280929i	−0.478704	+	0.0201178i
$196$	3.25735	+	9.91310i	0.232668	+	0.708079i
$197$	−4.09507	+	1.09727i	−0.291761	+	0.0781772i	−0.401731	−	0.915758i	$-0.631591\pi$
$197$	−4.09507	+	1.09727i	−0.291761	+	0.0781772i	0.109970	+	0.993935i	$0.464925\pi$
$198$	12.2989	−	5.50028i	0.874045	−	0.390888i
$199$	−2.29735	−	3.97914i	−0.162855	−	0.282073i	0.773036	−	0.634362i	$-0.218737\pi$
$199$	−2.29735	−	3.97914i	−0.162855	−	0.282073i	−0.935892	+	0.352288i	$0.885404\pi$
$200$	10.8301	+	9.09441i	0.765806	+	0.643072i
$201$	−3.50033	−	0.937910i	−0.246894	−	0.0661551i
$202$	5.98171	+	7.36180i	0.420872	+	0.517974i
$203$	−8.72357	−	8.72357i	−0.612274	−	0.612274i
$204$	4.25568	+	3.80635i	0.297957	+	0.266497i
$205$	−15.7366	+	7.79353i	−1.09909	+	0.544324i
$206$	1.37695	−	3.60494i	0.0959369	−	0.251168i
$207$			16.9991i			1.18152i
$208$	−6.64597	−	12.7997i	−0.460815	−	0.887496i
$209$	27.6132			1.91005
$210$	−2.85465	+	2.03184i	−0.196990	+	0.140210i
$211$	0.134596	+	0.0777093i	0.00926600	+	0.00534973i	0.504626	−	0.863338i	$-0.331630\pi$
$211$	0.134596	+	0.0777093i	0.00926600	+	0.00534973i	−0.495360	+	0.868688i	$0.664964\pi$
$212$	1.47429	−	1.64833i	0.101255	−	0.113208i
$213$	2.91902	+	2.91902i	0.200008	+	0.200008i
$214$	3.66707	−	2.97962i	0.250676	−	0.203682i
$215$	−6.71222	−	7.62778i	−0.457770	−	0.520210i
$216$	−5.71505	−	11.0798i	−0.388860	−	0.753883i
$217$	−3.35321	+	1.93597i	−0.227630	+	0.131423i
$218$	−8.67203	+	3.87828i	−0.587344	+	0.262670i
$219$	−0.987582	−	3.68571i	−0.0667346	−	0.249057i
$220$	−17.7659	−	4.91460i	−1.19778	−	0.331342i
$221$	−9.64720	−	7.79554i	−0.648941	−	0.524385i
$222$	−1.17196	−	0.848513i	−0.0786569	−	0.0569485i
$223$	1.02642	+	3.83064i	0.0687339	+	0.256518i	0.991740	−	0.128268i	$-0.0409418\pi$
$223$	1.02642	+	3.83064i	0.0687339	+	0.256518i	−0.923006	+	0.384786i	$0.874275\pi$
$224$	−6.57214	−	3.72211i	−0.439120	−	0.248694i
$225$	−9.19217	−	7.00416i	−0.612811	−	0.466944i
$226$	−11.0213	+	1.76435i	−0.733128	+	0.117363i
$227$	11.6371	+	3.11814i	0.772379	+	0.206958i	0.623422	−	0.781885i	$-0.285742\pi$
$227$	11.6371	+	3.11814i	0.772379	+	0.206958i	0.148957	+	0.988844i	$0.452408\pi$
$228$	−0.618763	−	11.1020i	−0.0409786	−	0.735247i
$229$	9.78162	+	9.78162i	0.646387	+	0.646387i	0.952118	−	0.305731i	$-0.0989007\pi$
$229$	9.78162	+	9.78162i	0.646387	+	0.646387i	−0.305731	+	0.952118i	$0.598901\pi$
$230$	14.8119	−	17.9312i	0.976671	−	1.18235i
$231$	2.28353	−	3.95519i	0.150245	−	0.260233i
$232$	−26.1050	−	1.23790i	−1.71388	−	0.0812720i
$233$	0.969109			0.0634885			0.0317442	−	0.999496i	$-0.489894\pi$
$233$	0.969109			0.0634885			0.0317442	+	0.999496i	$0.489894\pi$
$234$	5.92024	+	10.1905i	0.387018	+	0.666176i
$235$	14.3394	−	21.5392i	0.935402	−	1.40506i
$236$	−10.1003	−	15.4408i	−0.657477	−	1.00511i
$237$	−8.92641	−	5.15367i	−0.579833	−	0.334767i
$238$	−6.46112	−	0.668259i	−0.418812	−	0.0433168i
$239$	−5.67429	−	5.67429i	−0.367039	−	0.367039i	0.499357	−	0.866396i	$-0.333570\pi$
$239$	−5.67429	−	5.67429i	−0.367039	−	0.367039i	−0.866396	+	0.499357i	$0.833570\pi$
$240$	−1.57783	+	7.25296i	−0.101848	+	0.468177i
$241$	−2.26834	+	8.46555i	−0.146116	+	0.545314i	0.853587	+	0.520951i	$0.174422\pi$
$241$	−2.26834	+	8.46555i	−0.146116	+	0.545314i	−0.999703	+	0.0243631i	$0.992244\pi$
$242$	8.36325	−	1.33883i	0.537610	−	0.0860633i
$243$	7.97094	+	13.8061i	0.511336	+	0.885660i
$244$	2.81635	−	13.4694i	0.180298	−	0.862291i
$245$	−3.73130	+	11.0534i	−0.238384	+	0.706175i
$246$	−7.46559	−	5.40518i	−0.475989	−	0.344622i
$247$	2.54987	+	24.0199i	0.162244	+	1.52835i
$248$	−2.49579	+	7.81331i	−0.158483	+	0.496146i
$249$	2.42667	+	9.05644i	0.153784	+	0.573929i
$250$	3.59322	+	15.3977i	0.227255	+	0.973835i
$251$	−2.68796	−	4.65568i	−0.169662	−	0.293864i	0.768639	−	0.639683i	$-0.220934\pi$
$251$	−2.68796	−	4.65568i	−0.169662	−	0.293864i	−0.938301	+	0.345819i	$0.887601\pi$
$252$	5.50862	+	2.78380i	0.347010	+	0.175363i
$253$	−7.84599	+	29.2816i	−0.493273	+	1.84092i
$254$	−2.28879	−	2.81686i	−0.143612	−	0.176745i
$255$	1.25593	+	6.25871i	0.0786497	+	0.391936i
$256$	−15.6048	+	3.53394i	−0.975303	+	0.220871i
$257$	1.40704	−	2.43706i	0.0877684	−	0.152019i	−0.818799	−	0.574080i	$-0.805360\pi$
$257$	1.40704	−	2.43706i	0.0877684	−	0.152019i	0.906568	+	0.422061i	$0.138693\pi$
$258$	1.90286	−	4.98180i	0.118467	−	0.310153i
$259$	1.64607			0.102282
$260$	2.63452	−	15.9078i	0.163386	−	0.986562i
$261$	21.3563			1.32192
$262$	−5.00921	+	13.1144i	−0.309470	+	0.810211i
$263$	−6.34314	+	10.9866i	−0.391135	+	0.677465i	−0.992599	−	0.121434i	$-0.961251\pi$
$263$	−6.34314	+	10.9866i	−0.391135	+	0.677465i	0.601465	+	0.798899i	$0.294584\pi$
$264$	−2.05855	−	9.45321i	−0.126695	−	0.581805i
$265$	2.42415	−	0.486454i	0.148914	−	0.0298826i
$266$	7.97718	+	9.81766i	0.489112	+	0.601959i
$267$	−0.497911	+	1.85823i	−0.0304716	+	0.113722i
$268$	3.93905	−	7.79463i	0.240616	−	0.476133i
$269$	−10.7216	−	18.5703i	−0.653705	−	1.13225i	−0.982217	−	0.187750i	$-0.939881\pi$
$269$	−10.7216	−	18.5703i	−0.653705	−	1.13225i	0.328512	−	0.944500i	$-0.393453\pi$
$270$	2.31445	−	13.7449i	0.140853	−	0.836488i
$271$	−2.74463	−	10.2431i	−0.166724	−	0.622224i	−0.997814	−	0.0660855i	$-0.978949\pi$
$271$	−2.74463	−	10.2431i	−0.166724	−	0.622224i	0.831089	−	0.556139i	$-0.187718\pi$
$272$	−11.0783	+	8.16165i	−0.671718	+	0.494873i
$273$	3.65137	+	1.62114i	0.220991	+	0.0981160i
$274$	−18.7730	−	13.5919i	−1.13412	−	0.821115i
$275$	−12.6011	−	16.3076i	−0.759873	−	0.983386i
$276$	11.9486	+	2.49836i	0.719221	+	0.150383i
$277$	9.49960	+	16.4538i	0.570775	+	0.988612i	0.996487	+	0.0837530i	$0.0266907\pi$
$277$	9.49960	+	16.4538i	0.570775	+	0.988612i	−0.425711	+	0.904859i	$0.639976\pi$
$278$	−11.4196	+	1.82811i	−0.684905	+	0.109643i
$279$	1.73477	−	6.47426i	0.103858	−	0.387604i
$280$	−3.38504	−	7.73630i	−0.202295	−	0.462333i
$281$	14.7428	+	14.7428i	0.879485	+	0.879485i	0.993481	−	0.113997i	$-0.0363653\pi$
$281$	14.7428	+	14.7428i	0.879485	+	0.879485i	−0.113997	+	0.993481i	$0.536365\pi$
$282$	13.5090	+	1.39721i	0.804452	+	0.0832026i
$283$	3.16760	+	1.82882i	0.188295	+	0.108712i	0.591184	−	0.806537i	$-0.298661\pi$
$283$	3.16760	+	1.82882i	0.188295	+	0.108712i	−0.402889	+	0.915249i	$0.631994\pi$
$284$	−8.32575	+	5.44615i	−0.494042	+	0.323170i
$285$	6.88918	−	10.3482i	0.408080	−	0.612975i
$286$	5.49438	+	20.2861i	0.324889	+	1.19954i
$287$	10.4858			0.618955
$288$	12.6008	−	3.48861i	0.742506	−	0.205568i
$289$	2.58312	−	4.47409i	0.151948	−	0.263182i
$290$	−22.5273	−	18.6085i	−1.32285	−	1.09273i
$291$	−2.00437	−	2.00437i	−0.117498	−	0.117498i
$292$	9.18169	−	0.511737i	0.537317	−	0.0299471i
$293$	−0.420769	−	0.112745i	−0.0245816	−	0.00658662i	0.246507	−	0.969141i	$-0.420717\pi$
$293$	−0.420769	−	0.112745i	−0.0245816	−	0.00658662i	−0.271089	+	0.962554i	$0.587384\pi$
$294$	−6.04610	+	0.967890i	−0.352616	+	0.0564485i
$295$	1.31439	−	20.5868i	0.0765268	−	1.19861i
$296$	2.57970	−	2.34612i	0.149942	−	0.136366i
$297$	4.70211	+	17.5485i	0.272844	+	1.01827i
$298$	11.3266	+	8.20060i	0.656133	+	0.475048i
$299$	−26.1957	−	4.12106i	−1.51494	−	0.238327i
$300$	−6.27416	+	5.43173i	−0.362239	+	0.313601i
$301$	1.57026	+	5.86028i	0.0905081	+	0.337781i
$302$	−6.46942	+	2.89324i	−0.372273	+	0.166487i
$303$	−4.82050	+	2.78312i	−0.276931	+	0.159886i
$304$	26.4947	+	4.01636i	1.51958	+	0.230354i
$305$	11.5498	−	10.1635i	0.661342	−	0.581962i
$306$	8.72677	−	7.09079i	0.498876	−	0.405354i
$307$	7.16402	+	7.16402i	0.408872	+	0.408872i	0.881345	−	0.472473i	$-0.156639\pi$
$307$	7.16402	+	7.16402i	0.408872	+	0.408872i	−0.472473	+	0.881345i	$0.656639\pi$
$308$	8.20393	+	7.33773i	0.467462	+	0.418106i
$309$	1.96109	+	1.13224i	0.111563	+	0.0644107i
$310$	−7.47116	+	5.31769i	−0.424333	+	0.302025i
$311$	27.4354			1.55572			0.777860	−	0.628437i	$-0.216305\pi$
$311$	27.4354			1.55572			0.777860	+	0.628437i	$0.216305\pi$
$312$	8.03298	−	2.66361i	0.454778	−	0.150797i
$313$		−	14.6463i		−	0.827856i	−0.910310	−	0.413928i	$-0.864156\pi$
$313$		−	14.6463i		−	0.827856i	0.910310	−	0.413928i	$-0.135844\pi$
$314$	−3.24555	+	8.49705i	−0.183157	+	0.479516i
$315$	3.06250	+	6.18377i	0.172553	+	0.348416i
$316$	16.5604	−	18.5153i	0.931596	−	1.04157i
$317$	−15.7071	−	15.7071i	−0.882197	−	0.882197i	0.111560	−	0.993758i	$-0.464415\pi$
$317$	−15.7071	−	15.7071i	−0.882197	−	0.882197i	−0.993758	+	0.111560i	$0.964415\pi$
$318$	0.818338	+	1.00714i	0.0458901	+	0.0564778i
$319$	36.7871	+	9.85706i	2.05968	+	0.551889i
$320$	−16.3314	−	7.29960i	−0.912955	−	0.408060i
$321$	1.38633	+	2.40119i	0.0773774	+	0.134022i
$322$	−12.6775	+	5.66959i	−0.706489	+	0.315954i
$323$	22.2607	−	5.96473i	1.23862	−	0.331886i
$324$	−6.22477	+	2.04540i	−0.345820	+	0.113633i
$325$	13.0219	−	12.4672i	0.722324	−	0.691555i
$326$	−17.6062	+	24.3175i	−0.975115	+	1.34682i
$327$	−1.44279	−	5.38458i	−0.0797867	−	0.297768i
$328$	16.4332	−	14.9452i	0.907370	−	0.825211i
$329$	−13.3808	+	7.72540i	−0.737706	+	0.425915i
$330$	4.49560	−	9.83823i	0.247475	−	0.541577i
$331$	−8.28760	+	30.9298i	−0.455528	+	1.70005i	0.231003	+	0.972953i	$0.425799\pi$
$331$	−8.28760	+	30.9298i	−0.455528	+	1.70005i	−0.686531	+	0.727100i	$0.740868\pi$
$332$	−22.5611	+	1.25743i	−1.23820	+	0.0690104i
$333$	−2.01489	+	2.01489i	−0.110415	+	0.110415i
$334$	−11.4616	−	1.18545i	−0.627150	−	0.0648647i
$335$	8.74998	−	4.33341i	0.478062	−	0.236760i
$336$	2.76632	−	3.46284i	0.150915	−	0.188914i
$337$	−23.1080			−1.25877			−0.629387	−	0.777092i	$-0.716694\pi$
$337$	−23.1080			−1.25877			−0.629387	+	0.777092i	$0.716694\pi$
$338$	−17.1389	+	6.65266i	−0.932234	+	0.361857i
$339$		−	6.54975i		−	0.355734i
$340$	−15.3838	−	0.124348i	−0.834301	−	0.00674369i
$341$	5.97643	−	10.3515i	0.323642	−	0.560564i
$342$	−21.7819	−	2.25285i	−1.17783	−	0.121820i
$343$	11.5346	−	11.5346i	0.622808	−	0.622808i
$344$	10.8135	+	6.94610i	0.583023	+	0.374508i
$345$	9.01597	+	10.2458i	0.485404	+	0.551613i
$346$	0.920617	+	5.75080i	0.0494927	+	0.309165i
$347$	−4.54455	−	7.87139i	−0.243964	−	0.422558i	0.717876	−	0.696171i	$-0.245115\pi$
$347$	−4.54455	−	7.87139i	−0.243964	−	0.422558i	−0.961840	+	0.273613i	$0.911781\pi$
$348$	3.13873	−	15.0112i	0.168254	−	0.804687i
$349$	−24.6347	+	6.60086i	−1.31867	+	0.353336i	−0.848478	−	0.529230i	$-0.822481\pi$
$349$	−24.6347	+	6.60086i	−1.31867	+	0.353336i	−0.470189	+	0.882566i	$0.655814\pi$
$350$	2.15772	−	9.19132i	0.115335	−	0.491297i
$351$	−14.8307	+	5.71070i	−0.791606	+	0.304815i
$352$	23.3155	−	0.193348i	1.24272	−	0.0103055i
$353$	30.3754	−	8.13905i	1.61672	−	0.433198i	0.666682	−	0.745342i	$-0.267714\pi$
$353$	30.3754	−	8.13905i	1.61672	−	0.433198i	0.950035	+	0.312144i	$0.101047\pi$
$354$	9.88376	−	4.42019i	0.525316	−	0.234930i
$355$	−11.1005	−	0.708726i	−0.589153	−	0.0376153i
$356$	−4.13796	−	2.09113i	−0.219311	−	0.110830i
$357$	0.986531	−	3.68178i	0.0522127	−	0.194861i
$358$	10.4772	−	8.51311i	0.553739	−	0.449932i
$359$	3.81391	−	3.81391i	0.201290	−	0.201290i	−0.599262	−	0.800553i	$-0.704539\pi$
$359$	3.81391	−	3.81391i	0.201290	−	0.201290i	0.800553	+	0.599262i	$0.204539\pi$
$360$	13.6132	+	5.32620i	0.717477	+	0.280715i
$361$	−22.4139	−	12.9407i	−1.17968	−	0.681088i
$362$	2.88305	−	7.54801i	0.151530	−	0.396714i
$363$			4.97011i			0.260863i
$364$	−5.62530	+	7.81394i	−0.294846	+	0.409562i
$365$	8.55829	+	5.69757i	0.447961	+	0.298224i
$366$	7.54335	+	2.88128i	0.394297	+	0.150607i
$367$	0.340645	−	0.590015i	0.0177815	−	0.0307985i	−0.856998	−	0.515320i	$-0.827673\pi$
$367$	0.340645	−	0.590015i	0.0177815	−	0.0307985i	0.874779	+	0.484522i	$0.161006\pi$
$368$	−11.7872	+	26.9544i	−0.614451	+	1.40509i
$369$	−12.8352	+	12.8352i	−0.668173	+	0.668173i
$370$	3.88101	−	0.369725i	0.201764	−	0.0192211i
$371$	−1.42604	−	0.382107i	−0.0740365	−	0.0198380i
$372$	−4.29577	−	2.17088i	−0.222725	−	0.112555i
$373$	1.31994	−	0.762066i	0.0683438	−	0.0394583i	−0.465439	−	0.885080i	$-0.654103\pi$
$373$	1.31994	−	0.762066i	0.0683438	−	0.0394583i	0.533783	+	0.845622i	$0.320770\pi$
$374$	18.3050	−	8.18630i	0.946528	−	0.423304i
$375$	−9.25519	+	0.653761i	−0.477936	+	0.0337601i
$376$	−9.95931	+	31.1786i	−0.513612	+	1.60791i
$377$	−5.17736	+	32.9102i	−0.266647	+	1.69496i
$378$	−4.88085	+	6.74140i	−0.251044	+	0.346740i
$379$	11.7673	−	3.15305i	0.604448	−	0.161961i	0.0563999	−	0.998408i	$-0.482038\pi$
$379$	11.7673	−	3.15305i	0.604448	−	0.161961i	0.548048	+	0.836447i	$0.315371\pi$
$380$	21.0133	+	21.3558i	1.07796	+	1.09553i
$381$	1.84448	−	1.06491i	0.0944955	−	0.0545570i
$382$	33.8168	−	5.41356i	1.73022	−	0.276982i
$383$	−25.6244	−	6.86603i	−1.30935	−	0.350838i	−0.464369	−	0.885642i	$-0.653719\pi$
$383$	−25.6244	−	6.86603i	−1.30935	−	0.350838i	−0.844976	+	0.534804i	$0.820385\pi$
$384$	−0.600195	−	9.36973i	−0.0306286	−	0.478147i
$385$	2.42114	+	12.0653i	0.123393	+	0.614905i
$386$	−0.0543134	+	0.525134i	−0.00276448	+	0.0267286i
$387$	−9.09540	−	5.25123i	−0.462345	−	0.266935i
$388$	5.71694	−	3.73964i	0.290234	−	0.189852i
$389$			9.22898i			0.467928i	0.972245	+	0.233964i	$0.0751698\pi$
$389$			9.22898i			0.467928i	−0.972245	+	0.233964i	$0.924830\pi$
$390$	8.97311	+	3.00210i	0.454371	+	0.152017i
$391$			25.3005i			1.27950i
$392$	0.698975	−	14.7401i	0.0353036	−	0.744489i
$393$	−7.13425	−	4.11896i	−0.359875	−	0.207774i
$394$	5.96378	+	0.616820i	0.300451	+	0.0310749i
$395$	27.2300	−	5.46424i	1.37009	−	0.274936i
$396$	−19.0239	+	1.06029i	−0.955986	+	0.0532814i
$397$	−4.71974	−	1.26465i	−0.236877	−	0.0634710i	0.138427	−	0.990373i	$-0.455795\pi$
$397$	−4.71974	−	1.26465i	−0.236877	−	0.0634710i	−0.375305	+	0.926902i	$0.622462\pi$
$398$	1.02714	+	6.41621i	0.0514858	+	0.321615i
$399$	−6.42860	+	3.71155i	−0.321833	+	0.185810i
$400$	−9.71871	−	17.4799i	−0.485935	−	0.873995i
$401$	21.0267	−	5.63408i	1.05002	−	0.281353i	0.307762	−	0.951463i	$-0.400420\pi$
$401$	21.0267	−	5.63408i	1.05002	−	0.281353i	0.742261	+	0.670111i	$0.233753\pi$
$402$	4.15107	+	3.00542i	0.207036	+	0.149897i
$403$	9.55632	+	4.24284i	0.476034	+	0.211351i
$404$	−4.18766	−	12.7443i	−0.208344	−	0.634053i
$405$	−6.94079	−	2.34301i	−0.344891	−	0.116425i
$406$	7.12281	+	15.9270i	0.353499	+	0.790442i
$407$	−4.40070	+	2.54074i	−0.218135	+	0.125940i
$408$	−3.70151	−	7.17614i	−0.183252	−	0.355272i
$409$	−14.7699	−	3.95759i	−0.730325	−	0.195690i	−0.125551	−	0.992087i	$-0.540070\pi$
$409$	−14.7699	−	3.95759i	−0.730325	−	0.195690i	−0.604774	+	0.796397i	$0.706737\pi$
$410$	24.7227	−	2.35521i	1.22097	−	0.116316i
$411$	9.61689	−	9.61689i	0.474366	−	0.474366i
$412$	−3.63824	+	4.06773i	−0.179243	+	0.200403i
$413$	−6.15884	+	10.6674i	−0.303057	+	0.524910i
$414$	8.57807	−	22.4579i	0.421589	−	1.10374i
$415$	−21.0292	−	13.9999i	−1.03229	−	0.687230i
$416$	2.32119	+	20.2636i	0.113806	+	0.993503i
$417$		−	6.78646i		−	0.332335i
$418$	−36.4804	−	13.9341i	−1.78431	−	0.681541i
$419$	2.27810	+	1.31526i	0.111292	+	0.0642547i	0.554613	−	0.832108i	$-0.312866\pi$
$419$	2.27810	+	1.31526i	0.111292	+	0.0642547i	−0.443321	+	0.896363i	$0.646200\pi$
$420$	4.79664	−	1.24379i	0.234052	−	0.0606908i
$421$	12.3029	−	12.3029i	0.599607	−	0.599607i	−0.340601	−	0.940208i	$-0.610630\pi$
$421$	12.3029	−	12.3029i	0.599607	−	0.599607i	0.940208	+	0.340601i	$0.110630\pi$
$422$	−0.138605	−	0.170583i	−0.00674717	−	0.00830386i
$423$	6.92251	−	25.8352i	0.336584	−	1.25615i
$424$	−2.77949	+	1.43368i	−0.134984	+	0.0696259i
$425$	−13.6811	−	10.4246i	−0.663630	−	0.505667i
$426$	−2.38339	−	5.32937i	−0.115475	−	0.258209i
$427$	−8.87353	+	2.37766i	−0.429420	+	0.115063i
$428$	−6.34821	+	2.08596i	−0.306852	+	0.100829i
$429$	−12.2640	+	1.30191i	−0.592113	+	0.0628567i
$430$	5.01854	+	13.4643i	0.242016	+	0.649308i
$431$	22.1406	−	5.93257i	1.06648	−	0.285762i	0.317432	−	0.948281i	$-0.397179\pi$
$431$	22.1406	−	5.93257i	1.06648	−	0.285762i	0.749045	+	0.662519i	$0.230513\pi$
$432$	1.95921	+	17.5216i	0.0942623	+	0.843010i
$433$	−2.08660	−	3.61409i	−0.100276	−	0.173682i	0.811523	−	0.584321i	$-0.198639\pi$
$433$	−2.08660	−	3.61409i	−0.100276	−	0.173682i	−0.911798	+	0.410639i	$0.865306\pi$
$434$	5.40692	−	0.865567i	0.259540	−	0.0415485i
$435$	12.8719	−	11.3269i	0.617162	−	0.543085i
$436$	13.4138	−	0.747614i	0.642407	−	0.0358042i
$437$	34.8406	−	34.8406i	1.66665	−	1.66665i
$438$	−0.555160	+	5.36762i	−0.0265266	+	0.256475i
$439$	−11.0188	+	19.0850i	−0.525896	+	0.910879i	0.473648	+	0.880714i	$0.342937\pi$
$439$	−11.0188	+	19.0850i	−0.525896	+	0.910879i	−0.999545	+	0.0301654i	$0.990397\pi$
$440$	20.9909	+	15.4578i	1.00070	+	0.736921i
$441$			12.0588i			0.574227i
$442$	8.81135	+	15.1670i	0.419113	+	0.721421i
$443$	−28.6572			−1.36155			−0.680773	−	0.732495i	$-0.738356\pi$
$443$	−28.6572			−1.36155			−0.680773	+	0.732495i	$0.738356\pi$
$444$	1.12013	+	1.71238i	0.0531589	+	0.0812660i
$445$	−2.30049	−	4.64512i	−0.109054	−	0.220200i
$446$	0.576990	−	5.57868i	0.0273213	−	0.264158i
$447$	−5.80231	+	5.80231i	−0.274440	+	0.274440i
$448$	6.80435	+	8.23378i	0.321475	+	0.389009i
$449$	−2.05906	+	7.68453i	−0.0971732	+	0.362655i	−0.997340	−	0.0728901i	$-0.976778\pi$
$449$	−2.05906	+	7.68453i	−0.0971732	+	0.362655i	0.900167	+	0.435545i	$0.143444\pi$
$450$	8.60953	+	13.8919i	0.405857	+	0.654869i
$451$	−28.0332	+	16.1850i	−1.32003	+	0.762121i
$452$	15.4508	+	3.23065i	0.726746	+	0.151957i
$453$	−1.07634	−	4.01695i	−0.0505708	−	0.188733i
$454$	−13.8005	−	9.99172i	−0.647689	−	0.468935i
$455$	−10.2717	+	3.22022i	−0.481543	+	0.150966i
$456$	−4.78480	+	14.9793i	−0.224069	+	0.701470i
$457$	−3.69980	+	0.991357i	−0.173069	+	0.0463737i	−0.344313	−	0.938855i	$-0.611888\pi$
$457$	−3.69980	+	0.991357i	−0.173069	+	0.0463737i	0.171244	+	0.985229i	$0.445221\pi$
$458$	−7.98671	−	17.8587i	−0.373195	−	0.834481i
$459$	7.58131	+	13.1312i	0.353865	+	0.612913i
$460$	−28.6168	+	16.2149i	−1.33427	+	0.756025i
$461$	−12.8333	−	3.43866i	−0.597705	−	0.160155i	−0.0527328	−	0.998609i	$-0.516793\pi$
$461$	−12.8333	−	3.43866i	−0.597705	−	0.160155i	−0.544972	+	0.838454i	$0.683460\pi$
$462$	−5.01268	+	4.07297i	−0.233211	+	0.189492i
$463$	9.90076	+	9.90076i	0.460128	+	0.460128i	0.898697	−	0.438570i	$-0.144515\pi$
$463$	9.90076	+	9.90076i	0.460128	+	0.460128i	−0.438570	+	0.898697i	$0.644515\pi$
$464$	33.8633	+	14.8085i	1.57206	+	0.687467i
$465$	−2.38822	−	4.82227i	−0.110751	−	0.223628i
$466$	−1.28031	−	0.489030i	−0.0593092	−	0.0226539i
$467$		−	15.1540i		−	0.701242i	−0.936518	−	0.350621i	$-0.885971\pi$
$467$		−	15.1540i		−	0.701242i	0.936518	−	0.350621i	$-0.114029\pi$
$468$	−2.67902	−	16.4504i	−0.123838	−	0.760420i
$469$	−5.83036			−0.269221
$470$	−29.8132	+	21.2200i	−1.37518	+	0.978804i
$471$	−4.62240	−	2.66874i	−0.212989	−	0.122969i
$472$	5.55207	+	25.4960i	0.255555	+	1.17355i
$473$	−13.2435	−	13.2435i	−0.608935	−	0.608935i
$474$	9.19224	+	11.3131i	0.422213	+	0.519626i
$475$	4.48444	+	33.1952i	0.205760	+	1.52310i
$476$	8.19870	+	4.14325i	0.375787	+	0.189906i
$477$	2.21328	−	1.27784i	0.101339	−	0.0585082i
$478$	4.63307	+	10.3598i	0.211912	+	0.473845i
$479$	9.29577	+	34.6923i	0.424735	+	1.58513i	0.764501	+	0.644622i	$0.222985\pi$
$479$	9.29577	+	34.6923i	0.424735	+	1.58513i	−0.339767	+	0.940510i	$0.610348\pi$
$480$	5.74448	−	8.78584i	0.262199	−	0.401017i
$481$	−2.61649	−	3.59342i	−0.119302	−	0.163846i
$482$	7.26862	−	10.0394i	0.331076	−	0.457281i
$483$	−2.10920	−	7.87162i	−0.0959717	−	0.358171i
$484$	−11.7245	−	2.45149i	−0.532930	−	0.111431i
$485$	7.62225	+	0.486652i	0.346108	+	0.0220977i
$486$	−3.56377	−	22.2618i	−0.161656	−	1.00981i
$487$	18.0495	+	4.83635i	0.817901	+	0.219156i	0.643428	−	0.765506i	$-0.277511\pi$
$487$	18.0495	+	4.83635i	0.817901	+	0.219156i	0.174472	+	0.984662i	$0.444178\pi$
$488$	−10.5177	+	16.3735i	−0.476112	+	0.741196i
$489$	−12.4572	−	12.4572i	−0.563334	−	0.563334i
$490$	10.5072	−	12.7200i	0.474669	−	0.574630i
$491$	15.5336	−	26.9050i	0.701023	−	1.21421i	−0.267085	−	0.963673i	$-0.586060\pi$
$491$	15.5336	−	26.9050i	0.701023	−	1.21421i	0.968108	−	0.250535i	$-0.0806064\pi$
$492$	7.13540	+	10.9082i	0.321689	+	0.491778i
$493$	31.7855			1.43155
$494$	8.75220	−	33.0199i	0.393780	−	1.48564i
$495$	−17.7322	−	11.8050i	−0.797005	−	0.530595i
$496$	7.23998	−	9.06291i	0.325085	−	0.406937i
$497$	5.75193	+	3.32088i	0.258009	+	0.148962i
$498$	1.36413	−	13.1892i	0.0611281	−	0.591022i
$499$	2.23837	+	2.23837i	0.100203	+	0.100203i	0.755431	−	0.655228i	$-0.227427\pi$
$499$	2.23837	+	2.23837i	0.100203	+	0.100203i	−0.655228	+	0.755431i	$0.727427\pi$
$500$	3.02288	−	22.1554i	0.135187	−	0.990820i
$501$	1.75004	−	6.53123i	0.0781859	−	0.291794i
$502$	1.20178	+	7.50711i	0.0536379	+	0.335059i
$503$	18.0614	+	31.2833i	0.805318	+	1.39485i	0.916076	+	0.401005i	$0.131339\pi$
$503$	18.0614	+	31.2833i	0.805318	+	1.39485i	−0.110758	+	0.993847i	$0.535328\pi$
$504$	−5.87279	−	6.45749i	−0.261595	−	0.287639i
$505$	4.79696	−	14.2103i	0.213462	−	0.632348i
$506$	25.1416	−	34.7254i	1.11768	−	1.54373i
$507$	−2.26498	−	10.5479i	−0.100591	−	0.468448i
$508$	1.60233	+	4.87638i	0.0710920	+	0.216354i
$509$	4.82086	+	17.9917i	0.213681	+	0.797468i	0.986627	+	0.162996i	$0.0521157\pi$
$509$	4.82086	+	17.9917i	0.213681	+	0.797468i	−0.772946	+	0.634472i	$0.781218\pi$
$510$	1.49902	−	8.90228i	0.0663777	−	0.394200i
$511$	−3.06957	−	5.31665i	−0.135790	−	0.235195i
$512$	22.3992	+	3.20574i	0.989913	+	0.141675i
$513$	7.64262	−	28.5226i	0.337430	−	1.25930i
$514$	−3.08865	+	2.50963i	−0.136234	+	0.110695i
$515$	−5.98230	+	1.20047i	−0.263612	+	0.0528989i
$516$	−5.02782	+	5.62134i	−0.221337	+	0.247466i
$517$	23.8486	−	41.3070i	1.04886	−	1.81668i
$518$	−2.17466	−	0.830638i	−0.0955491	−	0.0364962i
$519$	−3.41758			−0.150015
$520$	−11.5079	+	19.6867i	−0.504655	+	0.863321i
$521$	−19.8179			−0.868237			−0.434119	−	0.900856i	$-0.642940\pi$
$521$	−19.8179			−0.868237			−0.434119	+	0.900856i	$0.642940\pi$
$522$	−28.2142	−	10.7768i	−1.23490	−	0.471687i
$523$	3.79521	−	6.57350i	0.165953	−	0.287439i	−0.771040	−	0.636786i	$-0.780263\pi$
$523$	3.79521	−	6.57350i	0.165953	−	0.287439i	0.936993	+	0.349347i	$0.113597\pi$
$524$	13.2356	−	14.7980i	0.578198	−	0.646453i
$525$	5.12559	+	2.10282i	0.223699	+	0.0917745i
$526$	13.9241	−	11.3138i	0.607120	−	0.493305i
$527$	2.58194	−	9.63592i	0.112471	−	0.419747i
$528$	−2.05067	+	13.5276i	−0.0892438	+	0.588714i
$529$	15.5461	+	26.9267i	0.675919	+	1.17073i
$530$	−3.44807	−	0.580606i	−0.149774	−	0.0252199i
$531$	−5.51877	−	20.5963i	−0.239494	−	0.893804i
$532$	−5.58465	−	16.9958i	−0.242125	−	0.736859i
$533$	−16.6675	−	22.8907i	−0.721949	−	0.991506i
$534$	1.59550	−	2.20369i	0.0690439	−	0.0953629i
$535$	−7.07843	−	2.38947i	−0.306027	−	0.103306i
$536$	−9.13728	+	8.30993i	−0.394670	+	0.358934i
$537$	3.96091	+	6.86049i	0.170926	+	0.296052i
$538$	4.79357	+	29.9439i	0.206665	+	1.29097i
$539$	−5.56576	+	20.7717i	−0.239734	+	0.894700i
$540$	−9.99360	+	16.9908i	−0.430056	+	0.731166i
$541$	−15.2438	−	15.2438i	−0.655382	−	0.655382i	0.298902	−	0.954284i	$-0.403380\pi$
$541$	−15.2438	−	15.2438i	−0.655382	−	0.655382i	−0.954284	+	0.298902i	$0.903380\pi$
$542$	−1.54287	+	14.9174i	−0.0662719	+	0.640756i
$543$	4.10612	+	2.37067i	0.176210	+	0.101735i
$544$	18.7542	−	5.19224i	0.804081	−	0.222615i
$545$	12.5031	+	8.32377i	0.535574	+	0.356551i
$546$	−4.00584	−	3.98427i	−0.171434	−	0.170511i
$547$	−45.8880			−1.96203			−0.981015	−	0.193929i	$-0.937877\pi$
$547$	−45.8880			−1.96203			−0.981015	+	0.193929i	$0.937877\pi$
$548$	17.9427	+	27.4297i	0.766474	+	1.17174i
$549$	7.95132	−	13.7721i	0.339354	−	0.587779i
$550$	8.41842	+	27.9031i	0.358963	+	1.18979i
$551$	−43.7709	−	43.7709i	−1.86470	−	1.86470i
$552$	−14.5248	−	9.33011i	−0.618217	−	0.397116i
$553$	−16.0185	−	4.29214i	−0.681175	−	0.182520i
$554$	−4.24723	−	26.5311i	−0.180448	−	1.12720i
$555$	−0.145766	+	2.28307i	−0.00618741	+	0.0969110i
$556$	16.0092	+	3.34740i	0.678943	+	0.141962i
$557$	2.52443	+	9.42130i	0.106963	+	0.399193i	0.998561	−	0.0536366i	$-0.0170812\pi$
$557$	2.52443	+	9.42130i	0.106963	+	0.399193i	−0.891597	+	0.452830i	$0.850415\pi$
$558$	−5.55888	+	7.67788i	−0.235326	+	0.325031i
$559$	10.2972	−	12.7430i	0.435523	−	0.538973i
$560$	0.568166	+	11.9287i	0.0240094	+	0.504082i
$561$	3.04546	+	11.3658i	0.128579	+	0.479865i
$562$	−12.0376	−	26.9166i	−0.507774	−	1.13541i
$563$	−21.2618	+	12.2755i	−0.896079	+	0.517351i	−0.875926	−	0.482446i	$-0.839749\pi$
$563$	−21.2618	+	12.2755i	−0.896079	+	0.517351i	−0.0201528	+	0.999797i	$0.506415\pi$
$564$	−17.1420	−	8.66279i	−0.721809	−	0.364769i
$565$	11.6586	+	13.2489i	0.490482	+	0.557385i
$566$	−3.26193	−	4.01452i	−0.137109	−	0.168743i
$567$	3.09303	+	3.09303i	0.129895	+	0.129895i
$568$	13.7476	−	2.99370i	0.576834	−	0.125613i
$569$	−32.1136	−	18.5408i	−1.34627	−	0.777271i	−0.358553	−	0.933509i	$-0.616730\pi$
$569$	−32.1136	−	18.5408i	−1.34627	−	0.777271i	−0.987719	+	0.156238i	$0.950063\pi$
$570$	−14.3233	+	10.1948i	−0.599938	+	0.427014i
$571$	−24.9953			−1.04602			−0.523011	−	0.852326i	$-0.675191\pi$
$571$	−24.9953			−1.04602			−0.523011	+	0.852326i	$0.675191\pi$
$572$	2.97801	−	29.5730i	0.124517	−	1.23651i
$573$			20.0966i			0.839549i
$574$	−13.8530	−	5.29131i	−0.578211	−	0.220855i
$575$	−36.4751	−	4.67667i	−1.52112	−	0.195031i
$576$	−18.4075	−	1.74970i	−0.766980	−	0.0729041i
$577$	−3.50820	−	3.50820i	−0.146048	−	0.146048i	0.630302	−	0.776350i	$-0.282931\pi$
$577$	−3.50820	−	3.50820i	−0.146048	−	0.146048i	−0.776350	+	0.630302i	$0.782931\pi$
$578$	−5.67032	+	4.60733i	−0.235854	+	0.191640i
$579$	−0.299241	−	0.0801813i	−0.0124360	−	0.00333222i
$580$	20.3711	+	35.9518i	0.845865	+	1.49282i
$581$	7.54249	+	13.0640i	0.312915	+	0.541985i
$582$	1.63657	+	3.65945i	0.0678381	+	0.151689i
$583$	4.40225	−	1.17958i	0.182323	−	0.0488532i
$584$	−12.3883	−	3.95718i	−0.512633	−	0.163749i
$585$	8.63138	−	16.5148i	0.356864	−	0.682805i
$586$	0.498994	+	0.361277i	0.0206132	+	0.0149242i
$587$	7.41610	+	27.6773i	0.306095	+	1.14236i	0.931998	+	0.362462i	$0.118064\pi$
$587$	7.41610	+	27.6773i	0.306095	+	1.14236i	−0.625903	+	0.779901i	$0.715270\pi$
$588$	8.47604	+	1.77227i	0.349546	+	0.0730873i
$589$	−16.8249	+	9.71383i	−0.693256	+	0.400252i
$590$	−12.1249	+	26.5344i	−0.499176	+	1.09240i
$591$	−0.910593	+	3.39838i	−0.0374568	+	0.139791i
$592$	−4.59200	+	1.79775i	−0.188730	+	0.0738869i
$593$	−20.1242	+	20.1242i	−0.826402	+	0.826402i	−0.987017	−	0.160615i	$-0.948652\pi$
$593$	−20.1242	+	20.1242i	−0.826402	+	0.826402i	0.160615	+	0.987017i	$0.448652\pi$
$594$	2.64325	−	25.5565i	0.108454	−	1.04860i
$595$	4.55805	+	9.20357i	0.186862	+	0.377310i
$596$	−10.8257	−	16.5496i	−0.443436	−	0.677898i
$597$	−3.81302			−0.156057
$598$	32.5282	+	18.6633i	1.33018	+	0.763198i
$599$			11.6497i			0.475993i	0.971266	+	0.237996i	$0.0764906\pi$
$599$			11.6497i			0.475993i	−0.971266	+	0.237996i	$0.923509\pi$
$600$	11.0299	−	4.00991i	0.450293	−	0.163704i
$601$	7.85831	−	13.6110i	0.320547	−	0.555204i	−0.660054	−	0.751218i	$-0.729467\pi$
$601$	7.85831	−	13.6110i	0.320547	−	0.555204i	0.980601	+	0.196014i	$0.0627998\pi$
$602$	0.882706	−	8.53452i	0.0359764	−	0.347841i
$603$	7.13670	−	7.13670i	0.290629	−	0.290629i
$604$	10.0069	−	0.557728i	0.407174	−	0.0226936i
$605$	−8.84685	−	10.0536i	−0.359675	−	0.408736i
$606$	7.77288	−	1.24432i	0.315752	−	0.0505471i
$607$	−8.68520	−	15.0432i	−0.352521	−	0.610585i	0.634169	−	0.773194i	$-0.281342\pi$
$607$	−8.68520	−	15.0432i	−0.352521	−	0.610585i	−0.986690	+	0.162610i	$0.948009\pi$
$608$	−32.9760	−	18.6758i	−1.33735	−	0.757405i
$609$	−9.88926	+	2.64982i	−0.400733	+	0.107376i
$610$	−20.3875	+	7.59899i	−0.825464	+	0.307674i
$611$	38.1339	+	16.9308i	1.54273	+	0.684947i
$612$	−15.1073	+	4.96411i	−0.610675	+	0.200662i
$613$	2.50400	−	0.670946i	0.101136	−	0.0270992i	−0.207896	−	0.978151i	$-0.566662\pi$
$613$	2.50400	−	0.670946i	0.101136	−	0.0270992i	0.309032	+	0.951052i	$0.399995\pi$
$614$	−5.84944	−	13.0796i	−0.236064	−	0.527851i
$615$	−0.928553	+	14.5436i	−0.0374429	+	0.586453i
$616$	−7.13563	−	13.8339i	−0.287503	−	0.557383i
$617$	−10.9519	+	40.8730i	−0.440906	+	1.64548i	0.285618	+	0.958343i	$0.407801\pi$
$617$	−10.9519	+	40.8730i	−0.440906	+	1.64548i	−0.726524	+	0.687141i	$0.758866\pi$
$618$	−2.01949	−	2.48542i	−0.0812358	−	0.0999784i
$619$	−16.7395	+	16.7395i	−0.672816	+	0.672816i	−0.958364	−	0.285548i	$-0.907824\pi$
$619$	−16.7395	+	16.7395i	−0.672816	+	0.672816i	0.285548	+	0.958364i	$0.407824\pi$
$620$	12.5537	−	3.25523i	0.504169	−	0.130733i
$621$	28.0744	+	16.2088i	1.12659	+	0.650436i
$622$	−36.2455	−	13.8444i	−1.45331	−	0.555111i
$623$			3.09518i			0.124006i
$624$	−11.9566	−	0.534640i	−0.478649	−	0.0214027i
$625$	17.5578	−	17.7968i	0.702310	−	0.711871i
$626$	−7.39078	+	19.3495i	−0.295395	+	0.773362i
$627$	11.4577	−	19.8453i	0.457577	−	0.792547i
$628$	8.57554	−	9.58786i	0.342201	−	0.382597i
$629$	−2.99884	+	2.99884i	−0.119572	+	0.119572i
$630$	−0.925491	−	9.71491i	−0.0368724	−	0.387051i
$631$	9.08138	+	2.43335i	0.361524	+	0.0968701i	0.435009	−	0.900426i	$-0.356745\pi$
$631$	9.08138	+	2.43335i	0.361524	+	0.0968701i	−0.0734846	+	0.997296i	$0.523412\pi$
$632$	−31.2215	+	16.1043i	−1.24192	+	0.640595i
$633$	0.111698	−	0.0644888i	0.00443959	−	0.00256320i
$634$	12.8249	+	28.6770i	0.509340	+	1.13891i
$635$	−1.83547	+	5.43730i	−0.0728385	+	0.215773i
$636$	−0.572900	−	1.74351i	−0.0227170	−	0.0691345i
$637$	−18.5826	−	2.92338i	−0.736270	−	0.115828i
$638$	−43.6261	−	31.5858i	−1.72717	−	1.25049i
$639$	−11.1056	+	2.97575i	−0.439332	+	0.117719i
$640$	17.8923	+	17.8848i	0.707255	+	0.706959i
$641$	15.2500	−	8.80460i	0.602339	−	0.347761i	−0.167622	−	0.985851i	$-0.553609\pi$
$641$	15.2500	−	8.80460i	0.602339	−	0.347761i	0.769961	+	0.638091i	$0.220276\pi$
$642$	−0.619823	−	3.87184i	−0.0244625	−	0.152809i
$643$	−9.33591	−	2.50155i	−0.368172	−	0.0986515i	0.0699891	−	0.997548i	$-0.477704\pi$
$643$	−9.33591	−	2.50155i	−0.368172	−	0.0986515i	−0.438162	+	0.898896i	$0.644370\pi$
$644$	19.6095	−	1.09292i	0.772722	−	0.0430672i
$645$	−8.26715	+	1.65897i	−0.325519	+	0.0653219i
$646$	−32.4189	−	3.35302i	−1.27551	−	0.131923i
$647$	−34.8996	−	20.1493i	−1.37204	−	0.792150i	−0.380859	−	0.924633i	$-0.624372\pi$
$647$	−34.8996	−	20.1493i	−1.37204	−	0.792150i	−0.991185	+	0.132483i	$0.957705\pi$
$648$	9.25582	+	0.438910i	0.363603	+	0.0172420i
$649$		−	38.0252i		−	1.49262i
$650$	−23.4946	+	9.89957i	−0.921536	+	0.388293i
$651$			3.21322i			0.125936i
$652$	35.5309	−	23.2420i	1.39150	−	0.910226i
$653$	12.5083	+	7.22167i	0.489488	+	0.282606i	0.724362	−	0.689420i	$-0.242134\pi$
$653$	12.5083	+	7.22167i	0.489488	+	0.282606i	−0.234874	+	0.972026i	$0.575468\pi$
$654$	−0.811053	+	7.84174i	−0.0317147	+	0.306636i
$655$	21.7630	−	4.36718i	0.850351	−	0.170640i
$656$	−29.2518	+	11.4519i	−1.14209	+	0.447123i
$657$	10.2652	+	2.75056i	0.400484	+	0.107309i
$658$	21.5760	−	3.45399i	0.841120	−	0.134651i
$659$	24.1161	−	13.9234i	0.939428	−	0.542379i	0.0496473	−	0.998767i	$-0.484190\pi$
$659$	24.1161	−	13.9234i	0.939428	−	0.542379i	0.889781	+	0.456388i	$0.150857\pi$
$660$	−10.9038	+	10.7289i	−0.424429	+	0.417623i
$661$	−26.5343	+	7.10984i	−1.03206	+	0.276541i	−0.734821	−	0.678261i	$-0.762734\pi$
$661$	−26.5343	+	7.10984i	−1.03206	+	0.276541i	−0.297243	+	0.954802i	$0.596067\pi$
$662$	26.5567	−	36.6799i	1.03215	−	1.42560i
$663$	−9.60555	+	3.69870i	−0.373049	+	0.143646i
$664$	30.4404	+	9.72351i	1.18132	+	0.377345i
$665$	6.39721	−	18.9507i	0.248073	−	0.734878i
$666$	3.67866	−	1.64516i	0.142545	−	0.0637487i
$667$	58.8526	−	33.9786i	2.27878	−	1.31565i
$668$	14.5439	+	7.34984i	0.562722	+	0.284374i
$669$	3.17894	+	0.851794i	0.122905	+	0.0329322i
$670$	−13.7465	+	1.30956i	−0.531073	+	0.0505927i
$671$	20.0530	−	20.0530i	0.774138	−	0.774138i
$672$	−5.40206	+	3.17890i	−0.208389	+	0.122629i
$673$	−11.4297	+	19.7969i	−0.440584	+	0.763114i	−0.997733	−	0.0672987i	$-0.978562\pi$
$673$	−11.4297	+	19.7969i	−0.440584	+	0.763114i	0.557149	+	0.830413i	$0.311895\pi$
$674$	30.5285	+	11.6607i	1.17591	+	0.449155i
$675$	−20.3323	+	8.50256i	−0.782592	+	0.327264i
$676$	25.9996	−	0.140359i	0.999985	−	0.00539842i
$677$		−	36.2850i		−	1.39454i	−0.716806	−	0.697272i	$-0.754397\pi$
$677$		−	36.2850i		−	1.39454i	0.716806	−	0.697272i	$-0.245603\pi$
$678$	−3.30513	+	8.65301i	−0.126933	+	0.332317i
$679$	−3.94961	−	2.28031i	−0.151572	−	0.0875101i
$680$	20.2610	+	7.92720i	0.776976	+	0.303994i
$681$	7.06961	−	7.06961i	0.270908	−	0.270908i
$682$	−13.1191	+	10.6597i	−0.502357	+	0.408182i
$683$	−11.9831	+	44.7214i	−0.458519	+	1.71122i	0.219013	+	0.975722i	$0.429716\pi$
$683$	−11.9831	+	44.7214i	−0.458519	+	1.71122i	−0.677532	+	0.735493i	$0.736950\pi$
$684$	27.6397	+	13.9678i	1.05683	+	0.534074i
$685$	−2.33494	+	36.5713i	−0.0892135	+	1.39732i
$686$	−21.0591	+	9.41800i	−0.804041	+	0.359581i
$687$	11.0887	−	2.97121i	0.423060	−	0.113359i
$688$	−10.7808	−	14.6333i	−0.411013	−	0.557890i
$689$	1.43259	+	3.72046i	0.0545775	+	0.141738i
$690$	−6.74099	−	18.0855i	−0.256625	−	0.688504i
$691$	16.2812	−	4.36254i	0.619367	−	0.165959i	0.0645271	−	0.997916i	$-0.479446\pi$
$691$	16.2812	−	4.36254i	0.619367	−	0.165959i	0.554840	+	0.831957i	$0.312779\pi$
$692$	1.68571	−	8.06206i	0.0640812	−	0.306474i
$693$	6.35996	+	11.0158i	0.241595	+	0.418455i
$694$	2.03185	+	12.6923i	0.0771280	+	0.481794i
$695$	12.0800	+	13.7277i	0.458220	+	0.520721i
$696$	−11.7216	+	18.2478i	−0.444306	+	0.691681i
$697$	−19.1031	+	19.1031i	−0.723583	+	0.723583i
$698$	35.8764	+	3.71061i	1.35794	+	0.140449i
$699$	0.402118	−	0.696489i	0.0152095	−	0.0263436i
$700$	−7.48872	+	11.0540i	−0.283047	+	0.417803i
$701$			7.78625i			0.294083i	0.989130	+	0.147041i	$0.0469750\pi$
$701$			7.78625i			0.294083i	−0.989130	+	0.147041i	$0.953025\pi$
$702$	22.4749	−	0.0606650i	0.848261	−	0.00228965i
$703$	8.25924			0.311503
$704$	−30.9001	−	11.5100i	−1.16459	−	0.433799i
$705$	−9.53007	−	19.2430i	−0.358923	−	0.724734i
$706$	−44.2366	−	4.57529i	−1.66487	−	0.172193i
$707$	−6.33253	+	6.33253i	−0.238159	+	0.238159i
$708$	−15.2881	+	0.852077i	−0.574564	+	0.0320230i
$709$	−11.0402	+	41.2025i	−0.414623	+	1.54739i	0.370967	+	0.928646i	$0.379026\pi$
$709$	−11.0402	+	41.2025i	−0.414623	+	1.54739i	−0.785590	+	0.618747i	$0.787640\pi$
$710$	14.3075	+	6.53783i	0.536950	+	0.245360i
$711$	24.8613	−	14.3537i	0.932373	−	0.538306i
$712$	4.41152	+	4.85073i	0.165329	+	0.181789i
$713$	−5.52016	−	20.6015i	−0.206732	−	0.771533i
$714$	−3.16122	+	4.36626i	−0.118306	+	0.163403i
$715$	22.4904	−	24.4636i	0.841092	−	0.914888i
$716$	−18.1376	+	5.95984i	−0.677833	+	0.222730i
$717$	−6.43253	+	1.72359i	−0.240227	+	0.0643686i
$718$	−6.96320	+	3.11407i	−0.259864	+	0.116216i
$719$	−2.54277	−	4.40420i	−0.0948293	−	0.164249i	0.814708	−	0.579871i	$-0.196897\pi$
$719$	−2.54277	−	4.40420i	−0.0948293	−	0.164249i	−0.909537	+	0.415622i	$0.863564\pi$
$720$	−15.2969	−	13.9060i	−0.570083	−	0.518246i
$721$	3.51918	+	0.942962i	0.131061	+	0.0351177i
$722$	23.0814	+	28.4066i	0.858999	+	1.05719i
$723$	5.14289	+	5.14289i	0.191266	+	0.191266i
$724$	−7.61773	+	8.51699i	−0.283111	+	0.316531i
$725$	−5.87538	+	45.8244i	−0.218206	+	1.70187i
$726$	2.50801	−	6.56611i	0.0930809	−	0.243691i
$727$		−	24.9711i		−	0.926128i	−0.886325	−	0.463064i	$-0.846750\pi$
$727$		−	24.9711i		−	0.926128i	0.886325	−	0.463064i	$-0.153250\pi$
$728$	11.3748	−	7.48453i	0.421576	−	0.277395i
$729$	3.40141			0.125978
$730$	−8.43143	−	11.8458i	−0.312061	−	0.438434i
$731$	−13.5371	−	7.81563i	−0.500687	−	0.289072i
$732$	−8.51174	−	7.61303i	−0.314603	−	0.281386i
$733$	29.2530	+	29.2530i	1.08048	+	1.08048i	0.996464	+	0.0840182i	$0.0267754\pi$
$733$	29.2530	+	29.2530i	1.08048	+	1.08048i	0.0840182	+	0.996464i	$0.473225\pi$
$734$	−0.747766	+	0.607585i	−0.0276006	+	0.0224264i
$735$	6.39571	+	7.26809i	0.235909	+	0.268088i
$736$	29.1740	−	29.6619i	1.07537	−	1.09335i
$737$	15.5872	−	8.99928i	0.574162	−	0.331493i
$738$	23.4337	−	10.4800i	0.862606	−	0.385772i
$739$	2.09462	+	7.81723i	0.0770519	+	0.287562i	0.993691	−	0.112155i	$-0.0357753\pi$
$739$	2.09462	+	7.81723i	0.0770519	+	0.287562i	−0.916639	+	0.399716i	$0.869109\pi$
$740$	−5.31386	−	1.46998i	−0.195341	−	0.0540375i
$741$	18.3209	+	8.13415i	0.673035	+	0.298816i
$742$	1.69116	+	1.22442i	0.0620843	+	0.0449498i
$743$	−2.19958	−	8.20893i	−0.0806946	−	0.301156i	0.913770	−	0.406233i	$-0.133158\pi$
$743$	−2.19958	−	8.20893i	−0.0806946	−	0.301156i	−0.994464	+	0.105077i	$0.966491\pi$
$744$	4.57976	+	5.03572i	0.167902	+	0.184619i
$745$	1.40878	−	22.0651i	0.0516136	−	0.808404i
$746$	−2.12835	+	0.340717i	−0.0779244	+	0.0124745i
$747$	−25.2235	−	6.75862i	−0.922879	−	0.247285i
$748$	−28.3140	+	1.57807i	−1.03526	+	0.0576999i
$749$	3.15437	+	3.15437i	0.115258	+	0.115258i
$750$	12.5571	+	3.80664i	0.458521	+	0.138999i
$751$	−21.8111	+	37.7780i	−0.795899	+	1.37854i	0.126368	+	0.991983i	$0.459668\pi$
$751$	−21.8111	+	37.7780i	−0.795899	+	1.37854i	−0.922267	+	0.386554i	$0.873665\pi$
$752$	28.8907	−	36.1650i	1.05354	−	1.31880i
$753$	−4.46132			−0.162580
$754$	23.4470	−	40.8657i	0.853889	−	1.48824i
$755$	9.32745	+	6.20962i	0.339461	+	0.225991i
$756$	9.85002	−	6.44323i	0.358242	−	0.234338i
$757$	45.7902	+	26.4370i	1.66427	+	0.960869i	0.970638	+	0.240544i	$0.0773259\pi$
$757$	45.7902	+	26.4370i	1.66427	+	0.960869i	0.693636	+	0.720325i	$0.256007\pi$
$758$	−17.1372	−	1.77246i	−0.622450	−	0.0643786i
$759$	17.7888	+	17.7888i	0.645694	+	0.645694i
$760$	−16.9846	−	38.8172i	−0.616096	−	1.40805i
$761$	3.57028	−	13.3245i	0.129423	−	0.483012i	−0.870536	−	0.492105i	$-0.836228\pi$
$761$	3.57028	−	13.3245i	0.129423	−	0.483012i	0.999959	+	0.00909302i	$0.00289444\pi$
$762$	−2.97415	+	0.476117i	−0.107742	+	0.0172479i
$763$	−4.48445	−	7.76729i	−0.162348	−	0.281195i
$764$	−47.4078	−	9.91261i	−1.71516	−	0.358626i
$765$	−16.8450	−	5.68638i	−0.609033	−	0.205592i
$766$	30.3882	+	22.0014i	1.09797	+	0.794943i
$767$	33.0770	−	3.51134i	1.19434	−	0.126787i
$768$	−3.93521	+	12.6814i	−0.142000	+	0.457601i
$769$	−5.15902	−	19.2537i	−0.186039	−	0.694308i	−0.994406	−	0.105628i	$-0.966315\pi$
$769$	−5.15902	−	19.2537i	−0.186039	−	0.694308i	0.808367	−	0.588679i	$-0.200352\pi$
$770$	2.88975	−	17.1615i	0.104139	−	0.618457i
$771$	−1.16766	−	2.02244i	−0.0420522	−	0.0728366i
$772$	0.336747	−	0.666358i	0.0121198	−	0.0239827i
$773$	0.760833	−	2.83947i	0.0273653	−	0.102129i	−0.950892	−	0.309521i	$-0.899831\pi$
$773$	0.760833	−	2.83947i	0.0273653	−	0.102129i	0.978258	+	0.207393i	$0.0664978\pi$
$774$	9.36626	+	11.5272i	0.336663	+	0.414337i
$775$	13.4146	+	5.50347i	0.481867	+	0.197690i
$776$	−9.43986	+	2.05565i	−0.338871	+	0.0737934i
$777$	0.683015	−	1.18302i	0.0245030	−	0.0424405i
$778$	4.65711	−	12.1926i	0.166966	−	0.437126i
$779$	52.6128			1.88505
$780$	−10.3397	−	8.49414i	−0.370219	−	0.304139i
$781$	−20.5033			−0.733668
$782$	12.7671	−	33.4250i	0.456550	−	1.19528i
$783$	20.3634	−	35.2704i	0.727728	−	1.26046i
$784$	−8.36157	+	19.1208i	−0.298627	+	0.682885i
$785$	14.1006	−	2.82957i	0.503272	−	0.100992i
$786$	7.34670	+	9.04172i	0.262048	+	0.322507i
$787$	−2.91010	+	10.8606i	−0.103734	+	0.387139i	−0.998198	−	0.0599991i	$-0.980890\pi$
$787$	−2.91010	+	10.8606i	−0.103734	+	0.387139i	0.894465	+	0.447139i	$0.147557\pi$
$788$	−7.56762	−	3.82433i	−0.269585	−	0.136236i
$789$	5.26399	+	9.11750i	0.187403	+	0.324592i
$790$	−38.7315	−	6.52184i	−1.37800	−	0.232036i
$791$	−2.72742	−	10.1789i	−0.0969759	−	0.361919i
$792$	25.6679	+	8.19904i	0.912069	+	0.291340i
$793$	19.2953	+	15.5918i	0.685195	+	0.553680i
$794$	5.59718	+	4.05243i	0.198637	+	0.143815i
$795$	0.656257	−	1.94406i	0.0232750	−	0.0689487i
$796$	1.88076	−	8.99490i	0.0666618	−	0.318816i
$797$	−6.86713	−	11.8942i	−0.243246	−	0.421315i	0.718391	−	0.695640i	$-0.244879\pi$
$797$	−6.86713	−	11.8942i	−0.243246	−	0.421315i	−0.961637	+	0.274325i	$0.911546\pi$
$798$	10.3659	−	1.65942i	0.366948	−	0.0587429i
$799$	10.3031	−	38.4516i	0.364496	−	1.36032i
$800$	4.01891	+	27.9973i	0.142090	+	0.989854i
$801$	−3.78868	−	3.78868i	−0.133866	−	0.133866i
$802$	−30.6219	−	3.16715i	−1.08130	−	0.111836i
$803$	16.4127	+	9.47589i	0.579192	+	0.334397i
$804$	−3.96747	−	6.06523i	−0.139922	−	0.213904i
$805$	18.2781	+	12.1684i	0.644217	+	0.428879i
$806$	−10.4840	−	10.4276i	−0.369284	−	0.367296i
$807$	−17.7950			−0.626415
$808$	−0.898604	+	18.9499i	−0.0316128	+	0.666657i
$809$	−22.6524	+	39.2351i	−0.796416	+	1.37943i	0.125521	+	0.992091i	$0.459940\pi$
$809$	−22.6524	+	39.2351i	−0.796416	+	1.37943i	−0.921936	+	0.387341i	$0.873393\pi$
$810$	7.98730	+	6.59785i	0.280645	+	0.231825i
$811$	−23.5721	−	23.5721i	−0.827729	−	0.827729i	0.159474	−	0.987202i	$-0.449020\pi$
$811$	−23.5721	−	23.5721i	−0.827729	−	0.827729i	−0.987202	+	0.159474i	$0.949020\pi$
$812$	−1.37306	−	24.6357i	−0.0481850	−	0.864545i
$813$	−8.50046	−	2.27769i	−0.298124	−	0.0798822i
$814$	7.09596	−	1.13596i	0.248713	−	0.0398153i
$815$	47.3725	+	3.02456i	1.65938	+	0.105946i
$816$	1.26894	+	11.3484i	0.0444216	+	0.397273i
$817$	7.87883	+	29.4042i	0.275645	+	1.02872i
$818$	17.5158	+	12.6816i	0.612425	+	0.443403i
$819$	−8.99500	+	6.54956i	−0.314311	+	0.228860i
$820$	−33.8502	−	9.36403i	−1.18210	−	0.327006i
$821$	11.5339	+	43.0449i	0.402534	+	1.50228i	0.808558	+	0.588416i	$0.200248\pi$
$821$	11.5339	+	43.0449i	0.402534	+	1.50228i	−0.406024	+	0.913862i	$0.633085\pi$
$822$	−17.5579	+	7.85221i	−0.612403	+	0.273877i
$823$	10.6404	−	6.14326i	0.370902	−	0.214141i	−0.302950	−	0.953006i	$-0.597972\pi$
$823$	10.6404	−	6.14326i	0.370902	−	0.214141i	0.673853	+	0.738866i	$0.264638\pi$
$824$	6.85921	−	3.53804i	0.238952	−	0.123253i
$825$	−16.9488	+	2.28966i	−0.590080	+	0.0797156i
$826$	13.5196	−	10.9851i	0.470406	−	0.382220i
$827$	21.4036	+	21.4036i	0.744276	+	0.744276i	0.973398	−	0.229122i	$-0.0735855\pi$
$827$	21.4036	+	21.4036i	0.744276	+	0.744276i	−0.229122	+	0.973398i	$0.573586\pi$
$828$	−22.6653	+	25.3409i	−0.787674	+	0.880658i
$829$	21.3655	+	12.3354i	0.742054	+	0.428425i	0.822816	−	0.568308i	$-0.192402\pi$
$829$	21.3655	+	12.3354i	0.742054	+	0.428425i	−0.0807616	+	0.996733i	$0.525735\pi$
$830$	20.7175	+	29.1074i	0.719117	+	1.01033i
$831$	15.7669			0.546948
$832$	7.15879	−	27.9419i	0.248186	−	0.968712i
$833$			17.9476i			0.621846i
$834$	−3.42457	+	8.96574i	−0.118583	+	0.310458i
$835$	8.08567	+	16.3265i	0.279816	+	0.565002i
$836$	41.1636	+	36.8173i	1.42367	+	1.27335i
$837$	−9.03828	−	9.03828i	−0.312409	−	0.312409i
$838$	−2.34594	−	2.88719i	−0.0810391	−	0.0997363i
$839$	−26.6188	−	7.13249i	−0.918984	−	0.246241i	−0.231833	−	0.972756i	$-0.574472\pi$
$839$	−26.6188	−	7.13249i	−0.918984	−	0.246241i	−0.687151	+	0.726515i	$0.741139\pi$
$840$	−6.96458	−	0.777275i	−0.240301	−	0.0268186i
$841$	−28.1879	−	48.8228i	−0.971995	−	1.68355i
$842$	−22.4619	+	10.0454i	−0.774089	+	0.346186i
$843$	16.7129	−	4.47820i	0.575622	−	0.154237i
$844$	0.0970340	+	0.295304i	0.00334005	+	0.0101648i
$845$	23.3570	+	17.3047i	0.803505	+	0.595298i
$846$	−22.1824	+	30.6382i	−0.762646	+	1.05336i
$847$	2.06963	+	7.72397i	0.0711133	+	0.265399i
$848$	4.39551	−	0.491489i	0.150942	−	0.0168778i
$849$	2.62871	−	1.51768i	0.0902170	−	0.0520868i
$850$	12.8139	+	20.6759i	0.439514	+	0.709176i
$851$	−2.34677	+	8.75827i	−0.0804463	+	0.300230i
$852$	0.459444	+	8.24344i	0.0157403	+	0.282416i
$853$	13.7552	−	13.7552i	0.470970	−	0.470970i	−0.431258	−	0.902228i	$-0.641930\pi$
$853$	13.7552	−	13.7552i	0.470970	−	0.470970i	0.902228	+	0.431258i	$0.141930\pi$
$854$	12.9228	+	1.33658i	0.442210	+	0.0457367i
$855$	15.3662	+	31.0273i	0.525514	+	1.06111i
$856$	9.43937	+	0.447613i	0.322631	+	0.0152991i
$857$	−26.2889			−0.898011			−0.449005	−	0.893529i	$-0.648222\pi$
$857$	−26.2889			−0.898011			−0.449005	+	0.893529i	$0.648222\pi$
$858$	16.8592	+	4.46868i	0.575565	+	0.152558i
$859$			20.7783i			0.708947i	0.935066	+	0.354474i	$0.115340\pi$
$859$			20.7783i			0.708947i	−0.935066	+	0.354474i	$0.884660\pi$
$860$	0.164251	−	20.3205i	0.00560092	−	0.692922i
$861$	4.35092	−	7.53602i	0.148279	−	0.256827i
$862$	−32.2441	−	3.33494i	−1.09824	−	0.113588i
$863$	−14.9022	+	14.9022i	−0.507276	+	0.507276i	−0.913689	−	0.406413i	$-0.866779\pi$
$863$	−14.9022	+	14.9022i	−0.507276	+	0.507276i	0.406413	+	0.913689i	$0.366779\pi$
$864$	6.25340	−	24.1369i	0.212745	−	0.821153i
$865$	6.91311	−	6.08334i	0.235053	−	0.206840i
$866$	0.932910	+	5.82759i	0.0317016	+	0.198030i
$867$	−2.14366	−	3.71292i	−0.0728024	−	0.126098i
$868$	−7.57997	−	1.58491i	−0.257281	−	0.0537954i
$869$	49.4496	−	13.2500i	1.67746	−	0.449475i
$870$	−22.7212	+	8.46882i	−0.770319	+	0.287120i
$871$	9.26756	+	12.7278i	0.314019	+	0.431266i
$872$	−18.0986	−	5.78119i	−0.612895	−	0.195776i
$873$	7.62577	−	2.04332i	0.258093	−	0.0691559i
$874$	−63.6098	+	28.4474i	−2.15163	+	0.962249i
$875$	−14.1111	+	4.87001i	−0.477043	+	0.164636i
$876$	3.44203	−	6.81113i	0.116295	−	0.230127i
$877$	7.00962	−	26.1603i	0.236698	−	0.883370i	−0.740678	−	0.671860i	$-0.765495\pi$
$877$	7.00962	−	26.1603i	0.236698	−	0.883370i	0.977376	−	0.211509i	$-0.0678379\pi$
$878$	24.1878	−	19.6534i	0.816298	−	0.663270i
$879$	−0.255621	+	0.255621i	−0.00862187	+	0.00862187i
$880$	−19.9312	−	31.0140i	−0.671881	−	1.04548i
$881$	35.4160	+	20.4474i	1.19319	+	0.688891i	0.959030	−	0.283306i	$-0.0914311\pi$
$881$	35.4160	+	20.4474i	1.19319	+	0.688891i	0.234165	+	0.972197i	$0.424764\pi$
$882$	6.08507	−	15.9311i	0.204895	−	0.536427i
$883$		−	9.91074i		−	0.333523i	−0.985997	−	0.166761i	$-0.946669\pi$
$883$		−	9.91074i		−	0.333523i	0.985997	−	0.166761i	$-0.0533310\pi$
$884$	−3.98730	−	24.4838i	−0.134107	−	0.823480i
$885$	−14.2501	−	9.48684i	−0.479013	−	0.318897i
$886$	37.8597	+	14.4610i	1.27192	+	0.485826i
$887$	8.86296	−	15.3511i	0.297589	−	0.515439i	−0.677995	−	0.735067i	$-0.737151\pi$
$887$	8.86296	−	15.3511i	0.297589	−	0.515439i	0.975584	+	0.219627i	$0.0704842\pi$
$888$	−0.615723	−	2.82750i	−0.0206623	−	0.0948847i
$889$	2.42303	−	2.42303i	0.0812658	−	0.0812658i
$890$	0.695209	+	7.29764i	0.0233035	+	0.244617i
$891$	−13.0432	−	3.49492i	−0.436965	−	0.117084i
$892$	−3.57738	+	7.07895i	−0.119780	+	0.237021i
$893$	−67.1386	+	38.7625i	−2.24671	+	1.29714i
$894$	10.5935	−	4.73760i	0.354300	−	0.158449i
$895$	−20.2239	−	6.82699i	−0.676011	−	0.228201i
$896$	−4.83445	−	14.3114i	−0.161508	−	0.478111i
$897$	−13.8313	+	17.1166i	−0.461814	+	0.571508i
$898$	6.59803	−	9.11315i	0.220179	−	0.304110i
$899$	−25.8821	+	6.93508i	−0.863215	+	0.231298i
$900$	−4.36414	−	22.6974i	−0.145471	−	0.756579i
$901$	3.29412	−	1.90186i	0.109743	−	0.0633601i
$902$	45.2025	−	7.23624i	1.50508	−	0.240941i
$903$	4.86328	+	1.30311i	0.161840	+	0.0433649i
$904$	−18.7822	−	12.0649i	−0.624686	−	0.401271i
$905$	−12.5257	+	2.51353i	−0.416368	+	0.0835526i
$906$	−0.605054	+	5.85002i	−0.0201016	+	0.194354i
$907$	−18.8081	−	10.8589i	−0.624512	−	0.360562i	0.154111	−	0.988053i	$-0.450749\pi$
$907$	−18.8081	−	10.8589i	−0.624512	−	0.360562i	−0.778624	+	0.627491i	$0.784082\pi$
$908$	13.1901	+	20.1643i	0.437729	+	0.669174i
$909$		−	15.5028i		−	0.514194i
$910$	15.1951	+	0.928975i	0.503713	+	0.0307952i
$911$			47.1018i			1.56055i	0.625436	+	0.780276i	$0.284921\pi$
$911$			47.1018i			1.56055i	−0.625436	+	0.780276i	$0.715079\pi$
$912$	13.8801	−	17.3750i	0.459617	−	0.575342i
$913$	−40.3290	−	23.2840i	−1.33470	−	0.770587i
$914$	5.38814	+	0.557282i	0.178224	+	0.0184333i
$915$	−2.51198	−	12.5180i	−0.0830436	−	0.413832i
$916$	1.53959	+	27.6237i	0.0508696	+	0.912713i
$917$	−12.8024	−	3.43040i	−0.422773	−	0.113282i
$918$	−3.38958	−	21.1736i	−0.111873	−	0.698833i
$919$	4.91537	−	2.83789i	0.162143	−	0.0936134i	−0.416733	−	0.909029i	$-0.636825\pi$
$919$	4.91537	−	2.83789i	0.162143	−	0.0936134i	0.578876	+	0.815416i	$0.303492\pi$
$920$	45.9886	−	6.98132i	1.51620	−	0.230167i
$921$	8.12133	−	2.17610i	0.267607	−	0.0717050i
$922$	15.2191	+	11.0188i	0.501214	+	0.362885i
$923$	−1.89333	−	17.8352i	−0.0623197	−	0.587054i
$924$	8.67766	−	2.85140i	0.285474	−	0.0938041i
$925$	−3.76904	−	4.87768i	−0.123925	−	0.160377i
$926$	−8.08400	−	18.0762i	−0.265657	−	0.594021i
$927$	−5.46192	+	3.15344i	−0.179393	+	0.103573i
$928$	−37.2648	−	36.6518i	−1.22328	−	1.20316i
$929$	−17.2102	−	4.61147i	−0.564649	−	0.151297i	−0.0348078	−	0.999394i	$-0.511082\pi$
$929$	−17.2102	−	4.61147i	−0.564649	−	0.151297i	−0.529841	+	0.848097i	$0.677749\pi$
$930$	0.721723	+	7.57595i	0.0236662	+	0.248425i
$931$	24.7151	−	24.7151i	0.810004	−	0.810004i
$932$	1.44467	+	1.29214i	0.0473218	+	0.0423253i
$933$	11.3839	−	19.7176i	0.372694	−	0.645524i
$934$	−7.64697	+	20.0202i	−0.250216	+	0.655081i
$935$	−26.3916	−	17.5699i	−0.863099	−	0.574597i
$936$	−4.76186	+	23.0848i	−0.155646	+	0.754552i
$937$			54.2189i			1.77125i	0.464398	+	0.885626i	$0.346271\pi$
$937$			54.2189i			1.77125i	−0.464398	+	0.885626i	$0.653729\pi$
$938$	7.70261	+	2.94211i	0.251499	+	0.0960633i
$939$	−10.5261	−	6.07727i	−0.343507	−	0.198324i
$940$	50.0949	−	12.9898i	1.63391	−	0.423681i
$941$	8.39890	−	8.39890i	0.273796	−	0.273796i	−0.556830	−	0.830626i	$-0.687983\pi$
$941$	8.39890	−	8.39890i	0.273796	−	0.273796i	0.830626	+	0.556830i	$0.187983\pi$
$942$	4.76005	+	5.85828i	0.155091	+	0.190873i
$943$	−14.9493	+	55.7917i	−0.486818	+	1.81683i
$944$	5.53079	−	36.4849i	0.180012	−	1.18748i
$945$	13.1328	+	0.838479i	0.427209	+	0.0272757i
$946$	10.8133	+	24.1791i	0.351571	+	0.786131i
$947$	19.5000	−	5.22500i	0.633664	−	0.169790i	0.0723324	−	0.997381i	$-0.476956\pi$
$947$	19.5000	−	5.22500i	0.633664	−	0.169790i	0.561332	+	0.827591i	$0.310289\pi$
$948$	−6.43528	−	19.5845i	−0.209008	−	0.636074i
$949$	−6.72720	+	15.1520i	−0.218374	+	0.491853i
$950$	10.8264	−	46.1178i	0.351256	−	1.49626i
$951$	−17.8060	+	4.77109i	−0.577398	+	0.154713i
$952$	−8.74072	−	9.61095i	−0.283288	−	0.311493i
$953$	−0.676299	−	1.17138i	−0.0219075	−	0.0379448i	0.854864	−	0.518852i	$-0.173641\pi$
$953$	−0.676299	−	1.17138i	−0.0219075	−	0.0379448i	−0.876771	+	0.480908i	$0.840307\pi$
$954$	−3.56883	+	0.571316i	−0.115545	+	0.0184970i
$955$	−35.7722	−	40.6516i	−1.15756	−	1.31545i
$956$	−0.893115	−	16.0245i	−0.0288854	−	0.518268i
$957$	22.3484	−	22.3484i	0.722423	−	0.722423i
$958$	5.22553	−	50.5235i	0.168829	−	1.63234i
$959$	10.9408	−	18.9501i	0.353298	−	0.611930i
$960$	−12.0226	+	8.70838i	−0.388029	+	0.281062i
$961$		−	22.5904i		−	0.728722i
$962$	1.64339	+	6.06767i	0.0529851	+	0.195629i
$963$	−7.72226			−0.248846
$964$	−14.6688	+	9.59534i	−0.472449	+	0.309045i
$965$	0.748030	−	0.370460i	0.0240799	−	0.0119255i
$966$	−1.18566	+	11.4637i	−0.0381481	+	0.368839i
$967$	−20.4626	+	20.4626i	−0.658034	+	0.658034i	−0.954915	−	0.296880i	$-0.904054\pi$
$967$	−20.4626	+	20.4626i	−0.658034	+	0.658034i	0.296880	+	0.954915i	$0.404054\pi$
$968$	14.2524	+	9.15509i	0.458088	+	0.294256i
$969$	4.94996	−	18.4735i	0.159016	−	0.593454i
$970$	−9.82433	−	4.48925i	−0.315440	−	0.144141i
$971$	−40.9491	+	23.6419i	−1.31412	+	0.758706i	−0.982775	−	0.184804i	$-0.940835\pi$
$971$	−40.9491	+	23.6419i	−1.31412	+	0.758706i	−0.331342	+	0.943511i	$0.607502\pi$
$972$	−6.52552	+	31.2088i	−0.209306	+	1.00102i
$973$	−2.82599	−	10.5467i	−0.0905971	−	0.338113i
$974$	−21.4051	−	15.4975i	−0.685862	−	0.496572i
$975$	−3.55679	−	14.5318i	−0.113908	−	0.465389i
$976$	22.1575	−	16.3240i	0.709244	−	0.522520i
$977$	−37.1301	+	9.94898i	−1.18790	+	0.318296i	−0.798054	−	0.602586i	$-0.794137\pi$
$977$	−37.1301	+	9.94898i	−1.18790	+	0.318296i	−0.389843	+	0.920882i	$0.627471\pi$
$978$	10.1713	+	22.7436i	0.325243	+	0.727260i
$979$	−4.77747	−	8.27482i	−0.152689	−	0.264464i
$980$	−20.3001	+	11.5025i	−0.648462	+	0.367433i
$981$	14.9968	+	4.01839i	0.478812	+	0.128297i
$982$	−34.0986	+	27.7063i	−1.08813	+	0.884142i
$983$	−11.7874	−	11.7874i	−0.375961	−	0.375961i	0.493682	−	0.869643i	$-0.335651\pi$
$983$	−11.7874	−	11.7874i	−0.375961	−	0.375961i	−0.869643	+	0.493682i	$0.835651\pi$
$984$	−3.92226	−	18.0117i	−0.125037	−	0.574191i
$985$	−4.20720	−	8.49513i	−0.134053	−	0.270677i
$986$	−41.9924	−	16.0395i	−1.33731	−	0.510803i
$987$			12.8222i			0.408135i
$988$	−28.2252	+	39.2068i	−0.897962	+	1.24733i
$989$	−33.4195			−1.06268
$990$	17.4694	+	24.5438i	0.555214	+	0.780055i
$991$	8.48660	+	4.89974i	0.269586	+	0.155645i	0.628699	−	0.777648i	$-0.283588\pi$
$991$	8.48660	+	4.89974i	0.269586	+	0.155645i	−0.359114	+	0.933294i	$0.616921\pi$
$992$	−14.1382	+	8.31977i	−0.448888	+	0.264153i
$993$	18.7901	+	18.7901i	0.596285	+	0.596285i
$994$	−5.92321	−	7.28981i	−0.187873	−	0.231219i
$995$	7.71300	−	6.78722i	0.244519	−	0.215169i
$996$	−8.45769	+	16.7362i	−0.267992	+	0.530306i
$997$	49.1333	−	28.3671i	1.55607	−	0.898396i	0.558440	−	0.829545i	$-0.311400\pi$
$997$	49.1333	−	28.3671i	1.55607	−	0.898396i	0.997627	−	0.0688509i	$-0.0219333\pi$
$998$	−1.82764	−	4.08669i	−0.0578528	−	0.129362i
$999$	1.40642	+	5.24884i	0.0444973	+	0.166066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bc.c.19.5	✓	144
4.3	odd	2	inner	260.2.bc.c.19.10	yes	144
5.4	even	2	inner	260.2.bc.c.19.32	yes	144
13.11	odd	12	inner	260.2.bc.c.219.27	yes	144
20.19	odd	2	inner	260.2.bc.c.19.27	yes	144
52.11	even	12	inner	260.2.bc.c.219.32	yes	144
65.24	odd	12	inner	260.2.bc.c.219.10	yes	144
260.219	even	12	inner	260.2.bc.c.219.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bc.c.19.5	✓	144	1.1	even	1	trivial
260.2.bc.c.19.10	yes	144	4.3	odd	2	inner
260.2.bc.c.19.27	yes	144	20.19	odd	2	inner
260.2.bc.c.19.32	yes	144	5.4	even	2	inner
260.2.bc.c.219.5	yes	144	260.219	even	12	inner
260.2.bc.c.219.10	yes	144	65.24	odd	12	inner
260.2.bc.c.219.27	yes	144	13.11	odd	12	inner
260.2.bc.c.219.32	yes	144	52.11	even	12	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32112 - 0.504618i) q^{2} +(0.414936 - 0.718690i) q^{3} +(1.49072 + 1.33332i) q^{4} +(0.439941 + 2.19236i) q^{5} +(-0.910845 + 0.740092i) q^{6} +(0.345572 - 1.28969i) q^{7} +(-1.29660 - 2.51373i) q^{8} +(1.15566 + 2.00166i) q^{9} +O(q^{10})\)	\(q+(-1.32112 - 0.504618i) q^{2} +(0.414936 - 0.718690i) q^{3} +(1.49072 + 1.33332i) q^{4} +(0.439941 + 2.19236i) q^{5} +(-0.910845 + 0.740092i) q^{6} +(0.345572 - 1.28969i) q^{7} +(-1.29660 - 2.51373i) q^{8} +(1.15566 + 2.00166i) q^{9} +(0.525091 - 3.11838i) q^{10} +(1.06679 + 3.98133i) q^{11} +(1.57680 - 0.518122i) q^{12} +(-3.36473 + 1.29562i) q^{13} +(-1.10734 + 1.52946i) q^{14} +(1.75818 + 0.593509i) q^{15} +(0.444495 + 3.97523i) q^{16} +(1.72001 + 2.97915i) q^{17} +(-0.516689 - 3.22759i) q^{18} +(1.73392 - 6.47108i) q^{19} +(-2.26730 + 3.85478i) q^{20} +(-0.783498 - 0.783498i) q^{21} +(0.599688 - 5.79814i) q^{22} +(6.36940 + 3.67737i) q^{23} +(-2.34460 - 0.111181i) q^{24} +(-4.61290 + 1.92902i) q^{25} +(5.09900 - 0.0137634i) q^{26} +4.40771 q^{27} +(2.23473 - 1.46181i) q^{28} +(4.61995 - 8.00199i) q^{29} +(-2.02327 - 1.67130i) q^{30} +(-2.05056 - 2.05056i) q^{31} +(1.41874 - 5.47605i) q^{32} +(3.30399 + 0.885302i) q^{33} +(-0.769011 - 4.80376i) q^{34} +(2.97950 + 0.190230i) q^{35} +(-0.946094 + 4.52477i) q^{36} +(0.319083 + 1.19083i) q^{37} +(-5.55614 + 7.67411i) q^{38} +(-0.464999 + 2.95579i) q^{39} +(4.94057 - 3.94851i) q^{40} +(2.03261 + 7.58581i) q^{41} +(0.639728 + 1.43046i) q^{42} +(-3.93517 + 2.27197i) q^{43} +(-3.71811 + 7.35742i) q^{44} +(-3.87993 + 3.41423i) q^{45} +(-6.55907 - 8.07237i) q^{46} +(-8.18265 - 8.18265i) q^{47} +(3.04139 + 1.33001i) q^{48} +(4.51829 + 2.60864i) q^{49} +(7.06762 - 0.220713i) q^{50} +2.85478 q^{51} +(-6.74334 - 2.55487i) q^{52} -1.10572i q^{53} +(-5.82312 - 2.22421i) q^{54} +(-8.25918 + 4.09035i) q^{55} +(-3.69000 + 0.803543i) q^{56} +(-3.93123 - 3.93123i) q^{57} +(-10.1415 + 8.24028i) q^{58} +(-8.91109 - 2.38772i) q^{59} +(1.82961 + 3.22897i) q^{60} +(-3.44018 - 5.95856i) q^{61} +(1.67429 + 3.74379i) q^{62} +(2.98088 - 0.798724i) q^{63} +(-4.63765 + 6.51861i) q^{64} +(-4.32074 - 6.80670i) q^{65} +(-3.91823 - 2.83685i) q^{66} +(-1.13019 - 4.21791i) q^{67} +(-1.40811 + 6.73441i) q^{68} +(5.28578 - 3.05175i) q^{69} +(-3.84029 - 1.75483i) q^{70} +(-1.28747 + 4.80490i) q^{71} +(3.53319 - 5.50035i) q^{72} +(3.25125 - 3.25125i) q^{73} +(0.179369 - 1.73425i) q^{74} +(-0.527691 + 4.11567i) q^{75} +(11.2128 - 7.33469i) q^{76} +5.50333 q^{77} +(2.10587 - 3.67031i) q^{78} -12.4204i q^{79} +(-8.51958 + 2.72336i) q^{80} +(-1.63805 + 2.83719i) q^{81} +(1.14261 - 11.0475i) q^{82} +(-7.98892 + 7.98892i) q^{83} +(-0.123320 - 2.21263i) q^{84} +(-5.77467 + 5.08154i) q^{85} +(6.34531 - 1.01579i) q^{86} +(-3.83397 - 6.64063i) q^{87} +(8.62476 - 7.84382i) q^{88} +(-2.23917 + 0.599985i) q^{89} +(6.84874 - 2.55272i) q^{90} +(0.508191 + 4.78718i) q^{91} +(4.59186 + 13.9744i) q^{92} +(-2.32457 + 0.622867i) q^{93} +(6.68115 + 14.9394i) q^{94} +(14.9498 + 0.954487i) q^{95} +(-3.34690 - 3.29185i) q^{96} +(0.884051 - 3.29932i) q^{97} +(-4.65285 - 5.72634i) q^{98} +(-6.73640 + 6.73640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{4} - 12 q^{5} - 80 q^{9}+O(q^{10}) \) 144 * q - 12 * q^4 - 12 * q^5 - 80 * q^9	\( 144 q - 12 q^{4} - 12 q^{5} - 80 q^{9} - 12 q^{10} - 32 q^{14} - 36 q^{16} + 18 q^{20} + 8 q^{21} - 28 q^{24} + 28 q^{26} - 6 q^{30} + 16 q^{34} + 24 q^{36} - 88 q^{40} - 72 q^{41} + 68 q^{45} + 64 q^{46} - 24 q^{49} - 34 q^{50} + 80 q^{54} + 96 q^{56} - 48 q^{60} - 8 q^{61} + 40 q^{66} - 24 q^{69} - 80 q^{70} - 24 q^{74} - 28 q^{76} - 92 q^{80} - 8 q^{81} + 84 q^{84} + 20 q^{85} - 52 q^{86} - 104 q^{89} - 52 q^{94} - 124 q^{96}+O(q^{100}) \) 144 * q - 12 * q^4 - 12 * q^5 - 80 * q^9 - 12 * q^10 - 32 * q^14 - 36 * q^16 + 18 * q^20 + 8 * q^21 - 28 * q^24 + 28 * q^26 - 6 * q^30 + 16 * q^34 + 24 * q^36 - 88 * q^40 - 72 * q^41 + 68 * q^45 + 64 * q^46 - 24 * q^49 - 34 * q^50 + 80 * q^54 + 96 * q^56 - 48 * q^60 - 8 * q^61 + 40 * q^66 - 24 * q^69 - 80 * q^70 - 24 * q^74 - 28 * q^76 - 92 * q^80 - 8 * q^81 + 84 * q^84 + 20 * q^85 - 52 * q^86 - 104 * q^89 - 52 * q^94 - 124 * q^96

Introduction

L-functions

Modular forms

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