LMFDB - Embedded newform 280.2.ba.b.19.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(19,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("280.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.ba (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.19
Character	$\chi$	$=$	280.19
Dual form			280.2.ba.b.59.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.175210 - 1.40332i) q^{2} +(0.833565 + 1.44378i) q^{3} +(-1.93860 + 0.491749i) q^{4} +(0.660510 + 2.13629i) q^{5} +(1.88003 - 1.42272i) q^{6} +(-2.56833 + 0.635367i) q^{7} +(1.02974 + 2.63432i) q^{8} +(0.110340 - 0.191114i) q^{9} +O(q^{10})$	\(q+(-0.175210 - 1.40332i) q^{2} +(0.833565 + 1.44378i) q^{3} +(-1.93860 + 0.491749i) q^{4} +(0.660510 + 2.13629i) q^{5} +(1.88003 - 1.42272i) q^{6} +(-2.56833 + 0.635367i) q^{7} +(1.02974 + 2.63432i) q^{8} +(0.110340 - 0.191114i) q^{9} +(2.88216 - 1.30120i) q^{10} +(-0.395322 - 0.684718i) q^{11} +(-2.32593 - 2.38900i) q^{12} +6.84388i q^{13} +(1.34162 + 3.49286i) q^{14} +(-2.53375 + 2.73436i) q^{15} +(3.51636 - 1.90661i) q^{16} +(1.46309 + 2.53414i) q^{17} +(-0.287526 - 0.121357i) q^{18} +(1.96683 + 1.13555i) q^{19} +(-2.33098 - 3.81661i) q^{20} +(-3.05820 - 3.17847i) q^{21} +(-0.891613 + 0.674732i) q^{22} +(0.946588 - 1.63954i) q^{23} +(-2.94501 + 3.68259i) q^{24} +(-4.12745 + 2.82208i) q^{25} +(9.60414 - 1.19911i) q^{26} +5.36929 q^{27} +(4.66653 - 2.49470i) q^{28} -2.46658i q^{29} +(4.28112 + 3.07656i) q^{30} +(-2.87365 - 4.97731i) q^{31} +(-3.29169 - 4.60052i) q^{32} +(0.659054 - 1.14151i) q^{33} +(3.29986 - 2.49718i) q^{34} +(-3.05373 - 5.06702i) q^{35} +(-0.119925 + 0.424753i) q^{36} +(2.59082 - 4.48744i) q^{37} +(1.24893 - 2.95905i) q^{38} +(-9.88103 + 5.70482i) q^{39} +(-4.94751 + 3.93982i) q^{40} +3.71071i q^{41} +(-3.92458 + 4.84852i) q^{42} -9.52516i q^{43} +(1.10308 + 1.13300i) q^{44} +(0.481155 + 0.109485i) q^{45} +(-2.46665 - 1.04110i) q^{46} +(0.185107 + 0.106871i) q^{47} +(5.68384 + 3.48756i) q^{48} +(6.19262 - 3.26366i) q^{49} +(4.68344 + 5.29768i) q^{50} +(-2.43916 + 4.22474i) q^{51} +(-3.36547 - 13.2676i) q^{52} +(3.21770 + 5.57322i) q^{53} +(-0.940751 - 7.53482i) q^{54} +(1.20164 - 1.29679i) q^{55} +(-4.31847 - 6.11153i) q^{56} +3.78622i q^{57} +(-3.46140 + 0.432169i) q^{58} +(0.430991 - 0.248833i) q^{59} +(3.56730 - 6.54681i) q^{60} +(5.87951 - 10.1836i) q^{61} +(-6.48126 + 4.90472i) q^{62} +(-0.161961 + 0.560949i) q^{63} +(-5.87926 + 5.42534i) q^{64} +(-14.6205 + 4.52045i) q^{65} +(-1.71738 - 0.724858i) q^{66} +(-2.83429 + 1.63638i) q^{67} +(-4.08251 - 4.19322i) q^{68} +3.15617 q^{69} +(-6.57560 + 5.17315i) q^{70} +4.40847i q^{71} +(0.617076 + 0.0938716i) q^{72} +(3.18360 + 5.51416i) q^{73} +(-6.75124 - 2.84951i) q^{74} +(-7.51495 - 3.60674i) q^{75} +(-4.37131 - 1.23419i) q^{76} +(1.45036 + 1.50741i) q^{77} +(9.73693 + 12.8667i) q^{78} +(5.25074 + 3.03152i) q^{79} +(6.39567 + 6.25263i) q^{80} +(4.14463 + 7.17871i) q^{81} +(5.20731 - 0.650152i) q^{82} -13.5430 q^{83} +(7.49164 + 4.65793i) q^{84} +(-4.44727 + 4.79940i) q^{85} +(-13.3668 + 1.66890i) q^{86} +(3.56120 - 2.05606i) q^{87} +(1.39669 - 1.74649i) q^{88} +(-9.86730 - 5.69689i) q^{89} +(0.0693390 - 0.694396i) q^{90} +(-4.34837 - 17.5773i) q^{91} +(-1.02882 + 3.64390i) q^{92} +(4.79075 - 8.29782i) q^{93} +(0.117542 - 0.278488i) q^{94} +(-1.12675 + 4.95176i) q^{95} +(3.89829 - 8.58729i) q^{96} +13.0656 q^{97} +(-5.66496 - 8.11839i) q^{98} -0.174479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) $ 80 * q + 6 * q^4 - 52 * q^9	$ 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) $ 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.175210	−	1.40332i	−0.123892	−	0.992296i
$2$	−0.175210	−	1.40332i	−0.123892	−	0.992296i
$3$	0.833565	+	1.44378i	0.481259	+	0.833565i	0.999769	−	0.0215069i	$-0.00684639\pi$
$3$	0.833565	+	1.44378i	0.481259	+	0.833565i	−0.518510	+	0.855072i	$0.673513\pi$
$4$	−1.93860	+	0.491749i	−0.969302	+	0.245875i
$5$	0.660510	+	2.13629i	0.295389	+	0.955377i
$5$	0.660510	+	2.13629i	0.295389	+	0.955377i
$6$	1.88003	−	1.42272i	0.767519	−	0.580823i
$7$	−2.56833	+	0.635367i	−0.970737	+	0.240146i
$7$	−2.56833	+	0.635367i	−0.970737	+	0.240146i
$8$	1.02974	+	2.63432i	0.364069	+	0.931372i
$9$	0.110340	−	0.191114i	0.0367799	−	0.0637046i
$10$	2.88216	−	1.30120i	0.911420	−	0.411477i
$11$	−0.395322	−	0.684718i	−0.119194	−	0.206450i	0.800254	−	0.599661i	$-0.204698\pi$
$11$	−0.395322	−	0.684718i	−0.119194	−	0.206450i	−0.919449	+	0.393210i	$0.871364\pi$
$12$	−2.32593	−	2.38900i	−0.671437	−	0.689646i
$13$			6.84388i			1.89815i	0.315049	+	0.949076i	$0.397979\pi$
$13$			6.84388i			1.89815i	−0.315049	+	0.949076i	$0.602021\pi$
$14$	1.34162	+	3.49286i	0.358562	+	0.933506i
$15$	−2.53375	+	2.73436i	−0.654210	+	0.706009i
$16$	3.51636	−	1.90661i	0.879091	−	0.476654i
$17$	1.46309	+	2.53414i	0.354851	+	0.614620i	0.987092	−	0.160152i	$-0.0511983\pi$
$17$	1.46309	+	2.53414i	0.354851	+	0.614620i	−0.632242	+	0.774771i	$0.717865\pi$
$18$	−0.287526	−	0.121357i	−0.0677705	−	0.0286040i
$19$	1.96683	+	1.13555i	0.451222	+	0.260513i	0.708346	−	0.705865i	$-0.249442\pi$
$19$	1.96683	+	1.13555i	0.451222	+	0.260513i	−0.257124	+	0.966378i	$0.582775\pi$
$20$	−2.33098	−	3.81661i	−0.521224	−	0.853420i
$21$	−3.05820	−	3.17847i	−0.667353	−	0.693600i
$22$	−0.891613	+	0.674732i	−0.190093	+	0.143853i
$23$	0.946588	−	1.63954i	0.197377	−	0.341867i	−0.750300	−	0.661098i	$-0.770091\pi$
$23$	0.946588	−	1.63954i	0.197377	−	0.341867i	0.947677	+	0.319230i	$0.103424\pi$
$24$	−2.94501	+	3.68259i	−0.601147	+	0.751706i
$25$	−4.12745	+	2.82208i	−0.825491	+	0.564416i
$26$	9.60414	−	1.19911i	1.88353	−	0.235165i
$27$	5.36929			1.03332
$28$	4.66653	−	2.49470i	0.881891	−	0.471454i
$29$		−	2.46658i		−	0.458033i	−0.973423	−	0.229017i	$-0.926449\pi$
$29$		−	2.46658i		−	0.458033i	0.973423	−	0.229017i	$-0.0735510\pi$
$30$	4.28112	+	3.07656i	0.781621	+	0.561701i
$31$	−2.87365	−	4.97731i	−0.516123	−	0.893951i	−0.999825	−	0.0187183i	$-0.994041\pi$
$31$	−2.87365	−	4.97731i	−0.516123	−	0.893951i	0.483702	−	0.875233i	$-0.339292\pi$
$32$	−3.29169	−	4.60052i	−0.581894	−	0.813265i
$33$	0.659054	−	1.14151i	0.114727	−	0.198712i
$34$	3.29986	−	2.49718i	0.565921	−	0.428263i
$35$	−3.05373	−	5.06702i	−0.516175	−	0.856483i
$36$	−0.119925	+	0.424753i	−0.0199874	+	0.0707922i
$37$	2.59082	−	4.48744i	0.425929	−	0.737730i	−0.570578	−	0.821243i	$-0.693281\pi$
$37$	2.59082	−	4.48744i	0.425929	−	0.737730i	0.996507	+	0.0835133i	$0.0266141\pi$
$38$	1.24893	−	2.95905i	0.202603	−	0.480021i
$39$	−9.88103	+	5.70482i	−1.58223	+	0.913502i
$40$	−4.94751	+	3.93982i	−0.782270	+	0.622940i
$41$			3.71071i			0.579516i	0.957100	+	0.289758i	$0.0935748\pi$
$41$			3.71071i			0.579516i	−0.957100	+	0.289758i	$0.906425\pi$
$42$	−3.92458	+	4.84852i	−0.605576	+	0.748143i
$43$		−	9.52516i		−	1.45257i	−0.687392	−	0.726286i	$-0.741245\pi$
$43$		−	9.52516i		−	1.45257i	0.687392	−	0.726286i	$-0.258755\pi$
$44$	1.10308	+	1.13300i	0.166296	+	0.170806i
$45$	0.481155	+	0.109485i	0.0717263	+	0.0163210i
$46$	−2.46665	−	1.04110i	−0.363687	−	0.153502i
$47$	0.185107	+	0.106871i	0.0270006	+	0.0155888i	0.513440	−	0.858126i	$-0.328371\pi$
$47$	0.185107	+	0.106871i	0.0270006	+	0.0155888i	−0.486439	+	0.873715i	$0.661704\pi$
$48$	5.68384	+	3.48756i	0.820392	+	0.503386i
$49$	6.19262	−	3.26366i	0.884660	−	0.466237i
$50$	4.68344	+	5.29768i	0.662339	+	0.749204i
$51$	−2.43916	+	4.22474i	−0.341550	+	0.591582i
$52$	−3.36547	−	13.2676i	−0.466707	−	1.83988i
$53$	3.21770	+	5.57322i	0.441985	+	0.765540i	0.997837	−	0.0657412i	$-0.0209412\pi$
$53$	3.21770	+	5.57322i	0.441985	+	0.765540i	−0.555852	+	0.831281i	$0.687608\pi$
$54$	−0.940751	−	7.53482i	−0.128020	−	1.02536i
$55$	1.20164	−	1.29679i	0.162029	−	0.174859i
$56$	−4.31847	−	6.11153i	−0.577080	−	0.816687i
$57$			3.78622i			0.501497i
$58$	−3.46140	+	0.432169i	−0.454504	+	0.0567466i
$59$	0.430991	−	0.248833i	0.0561102	−	0.0323953i	−0.471682	−	0.881768i	$-0.656353\pi$
$59$	0.430991	−	0.248833i	0.0561102	−	0.0323953i	0.527793	+	0.849373i	$0.323020\pi$
$60$	3.56730	−	6.54681i	0.460537	−	0.845190i
$61$	5.87951	−	10.1836i	0.752794	−	1.30388i	−0.193670	−	0.981067i	$-0.562039\pi$
$61$	5.87951	−	10.1836i	0.752794	−	1.30388i	0.946464	−	0.322810i	$-0.104628\pi$
$62$	−6.48126	+	4.90472i	−0.823120	+	0.622900i
$63$	−0.161961	+	0.560949i	−0.0204052	+	0.0706730i
$64$	−5.87926	+	5.42534i	−0.734908	+	0.678167i
$65$	−14.6205	+	4.52045i	−1.81345	+	0.560693i
$66$	−1.71738	−	0.724858i	−0.211395	−	0.0892238i
$67$	−2.83429	+	1.63638i	−0.346264	+	0.199916i	−0.663039	−	0.748585i	$-0.730734\pi$
$67$	−2.83429	+	1.63638i	−0.346264	+	0.199916i	0.316774	+	0.948501i	$0.397400\pi$
$68$	−4.08251	−	4.19322i	−0.495077	−	0.508503i
$69$	3.15617			0.379958
$70$	−6.57560	+	5.17315i	−0.785935	+	0.618309i
$71$			4.40847i			0.523189i	0.965178	+	0.261594i	$0.0842483\pi$
$71$			4.40847i			0.523189i	−0.965178	+	0.261594i	$0.915752\pi$
$72$	0.617076	+	0.0938716i	0.0727231	+	0.0110629i
$73$	3.18360	+	5.51416i	0.372612	+	0.645384i	0.989967	−	0.141302i	$-0.0451288\pi$
$73$	3.18360	+	5.51416i	0.372612	+	0.645384i	−0.617354	+	0.786685i	$0.711795\pi$
$74$	−6.75124	−	2.84951i	−0.784816	−	0.331248i
$75$	−7.51495	−	3.60674i	−0.867752	−	0.416470i
$76$	−4.37131	−	1.23419i	−0.501424	−	0.141572i
$77$	1.45036	+	1.50741i	0.165284	+	0.171785i
$78$	9.73693	+	12.8667i	1.10249	+	1.45687i
$79$	5.25074	+	3.03152i	0.590755	+	0.341072i	0.765396	−	0.643560i	$-0.222543\pi$
$79$	5.25074	+	3.03152i	0.590755	+	0.341072i	−0.174641	+	0.984632i	$0.555877\pi$
$80$	6.39567	+	6.25263i	0.715058	+	0.699065i
$81$	4.14463	+	7.17871i	0.460515	+	0.797635i
$82$	5.20731	−	0.650152i	0.575051	−	0.0717973i
$83$	−13.5430			−1.48654			−0.743271	−	0.668990i	$-0.766727\pi$
$83$	−13.5430			−1.48654			−0.743271	+	0.668990i	$0.766727\pi$
$84$	7.49164	+	4.65793i	0.817405	+	0.508222i
$85$	−4.44727	+	4.79940i	−0.482375	+	0.520568i
$86$	−13.3668	+	1.66890i	−1.44138	+	0.179962i
$87$	3.56120	−	2.05606i	0.381800	−	0.220432i
$88$	1.39669	−	1.74649i	0.148887	−	0.186176i
$89$	−9.86730	−	5.69689i	−1.04593	−	0.603869i	−0.124424	−	0.992229i	$-0.539708\pi$
$89$	−9.86730	−	5.69689i	−1.04593	−	0.603869i	−0.921508	+	0.388360i	$0.873042\pi$
$90$	0.0693390	−	0.694396i	0.00730897	−	0.0731957i
$91$	−4.34837	−	17.5773i	−0.455833	−	1.84261i
$92$	−1.02882	+	3.64390i	−0.107262	+	0.379903i
$93$	4.79075	−	8.29782i	0.496777	−	0.860444i
$94$	0.117542	−	0.278488i	0.0121235	−	0.0287239i
$95$	−1.12675	+	4.95176i	−0.115602	+	0.508040i
$96$	3.89829	−	8.58729i	0.397868	−	0.876437i
$97$	13.0656			1.32661			0.663303	−	0.748351i	$-0.269154\pi$
$97$	13.0656			1.32661			0.663303	+	0.748351i	$0.269154\pi$
$98$	−5.66496	−	8.11839i	−0.572247	−	0.820081i
$99$	−0.174479			−0.0175358
$100$	6.61374	−	7.50056i	0.661374	−	0.750056i
$101$	5.16640	+	8.94847i	0.514076	+	0.890406i	0.999867	+	0.0163310i	$0.00519856\pi$
$101$	5.16640	+	8.94847i	0.514076	+	0.890406i	−0.485790	+	0.874075i	$0.661468\pi$
$102$	6.35602	+	2.68270i	0.629340	+	0.265627i
$103$	−17.1988	−	9.92971i	−1.69464	−	0.978403i	−0.950675	−	0.310189i	$-0.899608\pi$
$103$	−17.1988	−	9.92971i	−1.69464	−	0.978403i	−0.743969	−	0.668214i	$-0.767059\pi$
$104$	−18.0290	+	7.04744i	−1.76788	+	0.691058i
$105$	4.77017	−	8.63260i	0.465521	−	0.842455i
$106$	7.25722	−	5.49193i	0.704884	−	0.533424i
$107$	13.9595	+	8.05950i	1.34951	+	0.779142i	0.988180	−	0.153295i	$-0.0489885\pi$
$107$	13.9595	+	8.05950i	1.34951	+	0.779142i	0.361333	+	0.932437i	$0.382322\pi$
$108$	−10.4089	+	2.64035i	−1.00160	+	0.254067i
$109$	12.8463	−	7.41679i	1.23045	−	0.710400i	0.263326	−	0.964707i	$-0.415181\pi$
$109$	12.8463	−	7.41679i	1.23045	−	0.710400i	0.967124	+	0.254307i	$0.0818473\pi$
$110$	−2.03034	−	1.45908i	−0.193585	−	0.139117i
$111$	8.63847			0.819928
$112$	−7.81978	+	7.13099i	−0.738900	+	0.673815i
$113$		−	4.32459i		−	0.406823i	−0.979093	−	0.203411i	$-0.934797\pi$
$113$		−	4.32459i		−	0.406823i	0.979093	−	0.203411i	$-0.0652029\pi$
$114$	5.31327	−	0.663381i	0.497633	−	0.0621314i
$115$	4.12776	+	0.939254i	0.384915	+	0.0875859i
$116$	1.21294	+	4.78173i	0.112619	+	0.443972i
$117$	1.30796	+	0.755151i	0.120921	+	0.0698138i
$118$	−0.424705	−	0.561220i	−0.0390973	−	0.0516644i
$119$	−5.36780	−	5.57891i	−0.492065	−	0.511418i
$120$	−9.81229	−	3.85900i	−0.895735	−	0.352277i
$121$	5.18744	−	8.98491i	0.471585	−	0.816810i
$122$	−15.3210	−	6.46655i	−1.38710	−	0.585454i
$123$	−5.35744	+	3.09312i	−0.483064	+	0.278897i
$124$	8.01846	+	8.23591i	0.720079	+	0.739607i
$125$	−8.75499	−	6.95342i	−0.783071	−	0.621933i
$126$	0.815567	+	0.128999i	0.0726565	+	0.0114922i
$127$	4.67057			0.414446			0.207223	−	0.978294i	$-0.433557\pi$
$127$	4.67057			0.414446			0.207223	+	0.978294i	$0.433557\pi$
$128$	8.64358	+	7.29990i	0.763992	+	0.645226i
$129$	13.7522	−	7.93983i	1.21081	−	0.699063i
$130$	8.90528	+	19.7252i	0.781045	+	1.73001i
$131$	13.4161	+	7.74576i	1.17217	+	0.676750i	0.954189	−	0.299204i	$-0.0967209\pi$
$131$	13.4161	+	7.74576i	1.17217	+	0.676750i	0.217977	+	0.975954i	$0.430054\pi$
$132$	−0.716304	+	2.53703i	−0.0623463	+	0.220820i
$133$	−5.77295	−	1.66681i	−0.500579	−	0.144530i
$134$	2.79296	+	3.69071i	0.241275	+	0.318829i
$135$	3.54647	+	11.4703i	0.305231	+	0.987210i
$136$	−5.16913	+	6.46375i	−0.443249	+	0.554262i
$137$	−12.5411	+	7.24059i	−1.07146	+	0.618606i	−0.928579	−	0.371135i	$-0.878969\pi$
$137$	−12.5411	+	7.24059i	−1.07146	+	0.618606i	−0.142877	+	0.989740i	$0.545635\pi$
$138$	−0.552991	−	4.42911i	−0.0470737	−	0.377031i
$139$			10.9687i			0.930349i	0.885219	+	0.465175i	$0.154008\pi$
$139$			10.9687i			0.930349i	−0.885219	+	0.465175i	$0.845992\pi$
$140$	8.41168	+	8.32128i	0.710917	+	0.703276i
$141$			0.356337i			0.0300090i
$142$	6.18648	−	0.772405i	0.519158	−	0.0648188i
$143$	4.68613	−	2.70554i	0.391874	−	0.226249i
$144$	0.0236141	−	0.882401i	0.00196784	−	0.0735334i
$145$	5.26933	−	1.62920i	0.437594	−	0.135298i
$146$	7.18032	−	5.43374i	0.594248	−	0.449699i
$147$	9.87394	+	6.22029i	0.814389	+	0.513041i
$148$	−2.81588	+	9.97340i	−0.231464	+	0.819808i
$149$	12.7792	+	7.37808i	1.04691	+	0.604436i	0.921784	−	0.387704i	$-0.126732\pi$
$149$	12.7792	+	7.37808i	1.04691	+	0.604436i	0.125130	+	0.992140i	$0.460065\pi$
$150$	−3.74471	+	11.1778i	−0.305754	+	0.912664i
$151$	13.6780	−	7.89697i	1.11310	−	0.642647i	0.173467	−	0.984840i	$-0.444503\pi$
$151$	13.6780	−	7.89697i	1.11310	−	0.642647i	0.939630	+	0.342193i	$0.111170\pi$
$152$	−0.966070	+	6.35058i	−0.0783586	+	0.515100i
$153$	0.645746			0.0522055
$154$	1.86125	−	2.29944i	0.149984	−	0.185294i
$155$	8.73489	−	9.42651i	0.701603	−	0.757155i
$156$	16.3501	−	15.9184i	1.30905	−	1.27449i
$157$	8.15924	−	4.71074i	0.651178	−	0.375958i	−0.137729	−	0.990470i	$-0.543980\pi$
$157$	8.15924	−	4.71074i	0.651178	−	0.375958i	0.788907	+	0.614512i	$0.210647\pi$
$158$	3.33420	−	7.89961i	0.265255	−	0.628459i
$159$	−5.36432	+	9.29127i	−0.425418	+	0.736846i
$160$	7.65385	−	10.0707i	0.605090	−	0.796157i
$161$	−1.38944	+	4.81230i	−0.109503	+	0.379263i
$162$	9.34784	−	7.07402i	0.734435	−	0.555787i
$163$	−4.19953	−	2.42460i	−0.328932	−	0.189909i	0.326435	−	0.945220i	$-0.394153\pi$
$163$	−4.19953	−	2.42460i	−0.328932	−	0.189909i	−0.655367	+	0.755311i	$0.727486\pi$
$164$	−1.82474	−	7.19360i	−0.142488	−	0.561726i
$165$	2.87391	+	0.653947i	0.223734	+	0.0509097i
$166$	2.37287	+	19.0052i	0.184171	+	1.47509i
$167$		−	10.5301i		−	0.814840i	−0.913241	−	0.407420i	$-0.866428\pi$
$167$		−	10.5301i		−	0.814840i	0.913241	−	0.407420i	$-0.133572\pi$
$168$	5.22395	−	11.3293i	0.403037	−	0.874072i
$169$	−33.8387			−2.60298
$170$	7.51429	+	5.40004i	0.576320	+	0.414164i
$171$	0.434039	−	0.250592i	0.0331918	−	0.0191633i
$172$	4.68399	+	18.4655i	0.357151	+	1.40798i
$173$	−10.0480	−	5.80119i	−0.763933	−	0.441057i	0.0667734	−	0.997768i	$-0.478730\pi$
$173$	−10.0480	−	5.80119i	−0.763933	−	0.441057i	−0.830706	+	0.556712i	$0.812063\pi$
$174$	−3.50926	−	4.63725i	−0.266036	−	0.351549i
$175$	8.80760	−	9.87047i	0.665792	−	0.746137i
$176$	−2.69559	−	1.65399i	−0.203188	−	0.124674i
$177$	0.718518	+	0.414836i	0.0540071	+	0.0311810i
$178$	−6.26570	+	14.8451i	−0.469634	+	1.11269i
$179$	9.70530	+	16.8101i	0.725408	+	1.25644i	0.958806	+	0.284062i	$0.0916822\pi$
$179$	9.70530	+	16.8101i	0.725408	+	1.25644i	−0.233398	+	0.972381i	$0.574984\pi$
$180$	−0.986607	+	0.0243601i	−0.0735373	+	0.00181570i
$181$	−16.8009			−1.24880			−0.624401	−	0.781104i	$-0.714657\pi$
$181$	−16.8009			−1.24880			−0.624401	+	0.781104i	$0.714657\pi$
$182$	−23.9047	+	9.18187i	−1.77194	+	0.680605i
$183$	19.6038			1.44915
$184$	5.29381	+	0.805311i	0.390265	+	0.0593683i
$185$	11.2977	+	2.57075i	0.830625	+	0.189005i
$186$	−12.4839	−	5.26909i	−0.915361	−	0.386348i
$187$	1.15678	−	2.00361i	0.0845923	−	0.146518i
$188$	−0.411402	−	0.116155i	−0.0300046	−	0.00847148i
$189$	−13.7901	+	3.41147i	−1.00308	+	0.248148i
$190$	7.14631	+	0.713595i	0.518448	+	0.0517697i
$191$	−9.58750	−	5.53535i	−0.693727	−	0.400524i	0.111280	−	0.993789i	$-0.464505\pi$
$191$	−9.58750	−	5.53535i	−0.693727	−	0.400524i	−0.805007	+	0.593266i	$0.797838\pi$
$192$	−12.7337	−	3.96597i	−0.918977	−	0.286219i
$193$	−2.30035	+	1.32811i	−0.165583	+	0.0955994i	−0.580501	−	0.814259i	$-0.697143\pi$
$193$	−2.30035	+	1.32811i	−0.165583	+	0.0955994i	0.414918	+	0.909859i	$0.363810\pi$
$194$	−2.28921	−	18.3351i	−0.164356	−	1.31639i
$195$	−18.7137	−	17.3406i	−1.34011	−	1.24179i
$196$	−10.4001	+	9.37216i	−0.742866	+	0.669440i
$197$	−9.96943			−0.710292			−0.355146	−	0.934811i	$-0.615569\pi$
$197$	−9.96943			−0.710292			−0.355146	+	0.934811i	$0.615569\pi$
$198$	0.0305704	+	0.244849i	0.00217254	+	0.0174007i
$199$	0.373969	+	0.647733i	0.0265099	+	0.0459166i	0.878976	−	0.476866i	$-0.158227\pi$
$199$	0.373969	+	0.647733i	0.0265099	+	0.0459166i	−0.852466	+	0.522783i	$0.824894\pi$
$200$	−11.6845	−	7.96701i	−0.826216	−	0.563353i
$201$	−4.72514	−	2.72806i	−0.333285	−	0.192422i
$202$	11.6524	−	8.81797i	0.819857	−	0.620430i
$203$	1.56718	+	6.33500i	0.109995	+	0.444630i
$204$	2.65104	−	9.38955i	0.185610	−	0.657400i
$205$	−7.92715	+	2.45096i	−0.553656	+	0.171183i
$206$	−10.9212	+	25.8751i	−0.760913	+	1.80280i
$207$	−0.208892	−	0.361812i	−0.0145190	−	0.0251477i
$208$	13.0486	+	24.0656i	0.904760	+	1.66865i
$209$		−	1.79563i		−	0.124207i
$210$	−12.9501	−	5.18155i	−0.893639	−	0.357561i
$211$	−13.0773			−0.900281			−0.450140	−	0.892958i	$-0.648626\pi$
$211$	−13.0773			−0.900281			−0.450140	+	0.892958i	$0.648626\pi$
$212$	−8.97847	−	9.22195i	−0.616644	−	0.633366i
$213$	−6.36484	+	3.67474i	−0.436112	+	0.251789i
$214$	8.86422	−	21.0017i	0.605945	−	1.43565i
$215$	20.3485	−	6.29146i	1.38775	−	0.429074i
$216$	5.52899	+	14.1444i	0.376200	+	0.962405i
$217$	10.5429	+	10.9575i	0.715698	+	0.743846i
$218$	−12.6589	−	16.7279i	−0.857370	−	1.13296i
$219$	−5.30748	+	9.19282i	−0.358646	+	0.621193i
$220$	−1.69181	+	3.10486i	−0.114062	+	0.209330i
$221$	−17.3434	+	10.0132i	−1.16664	+	0.673560i
$222$	−1.51354	−	12.1225i	−0.101582	−	0.813611i
$223$		−	4.09586i		−	0.274279i	−0.990552	−	0.137140i	$-0.956209\pi$
$223$		−	4.09586i		−	0.274279i	0.990552	−	0.137140i	$-0.0437909\pi$
$224$	11.3771	+	9.72422i	0.760168	+	0.649727i
$225$	0.0839164	+	1.10020i	0.00559443	+	0.0733467i
$226$	−6.06877	+	0.757709i	−0.403689	+	0.0504020i
$227$	4.93818	+	8.55319i	0.327759	+	0.567695i	0.982067	−	0.188533i	$-0.0603733\pi$
$227$	4.93818	+	8.55319i	0.327759	+	0.567695i	−0.654308	+	0.756228i	$0.727040\pi$
$228$	−1.86187	−	7.33997i	−0.123305	−	0.486102i
$229$	−1.67919	+	2.90845i	−0.110964	+	0.192196i	−0.916159	−	0.400814i	$-0.868727\pi$
$229$	−1.67919	+	2.90845i	−0.110964	+	0.192196i	0.805195	+	0.593010i	$0.202061\pi$
$230$	0.594849	−	5.95712i	0.0392232	−	0.392801i
$231$	−0.967386	+	3.35052i	−0.0636493	+	0.220448i
$232$	6.49776	−	2.53995i	0.426599	−	0.166756i
$233$	−17.2096	−	9.93598i	−1.12744	−	0.650927i	−0.184150	−	0.982898i	$-0.558953\pi$
$233$	−17.2096	−	9.93598i	−1.12744	−	0.650927i	−0.943290	+	0.331971i	$0.892286\pi$
$234$	0.830550	−	1.96779i	0.0542948	−	0.128639i
$235$	−0.106043	+	0.466031i	−0.00691750	+	0.0304005i
$236$	−0.713157	+	0.694328i	−0.0464226	+	0.0451969i
$237$			10.1079i			0.656576i
$238$	−6.88850	+	8.51021i	−0.446515	+	0.551635i
$239$		−	6.74480i		−	0.436285i	−0.975917	−	0.218142i	$-0.930000\pi$
$239$		−	6.74480i		−	0.436285i	0.975917	−	0.218142i	$-0.0699997\pi$
$240$	−3.69620	+	14.4459i	−0.238589	+	0.932478i
$241$	−1.18354	+	0.683317i	−0.0762385	+	0.0440163i	−0.537635	−	0.843178i	$-0.680682\pi$
$241$	−1.18354	+	0.683317i	−0.0762385	+	0.0440163i	0.461396	+	0.887194i	$0.347349\pi$
$242$	−13.5176	−	5.70539i	−0.868943	−	0.366756i
$243$	1.14430	−	1.98198i	0.0734067	−	0.127144i
$244$	−6.39025	+	22.6332i	−0.409094	+	1.44894i
$245$	11.0624	+	11.0735i	0.706751	+	0.707462i
$246$	5.27931	+	6.97625i	0.336596	+	0.444789i
$247$	−7.77157	+	13.4607i	−0.494493	+	0.856487i
$248$	10.1527	−	12.6955i	0.644697	−	0.806162i
$249$	−11.2890	−	19.5531i	−0.715412	−	1.23913i
$250$	−8.22390	+	13.5043i	−0.520125	+	0.854090i
$251$		−	15.4536i		−	0.975423i	−0.873005	−	0.487712i	$-0.837832\pi$
$251$		−	15.4536i		−	0.975423i	0.873005	−	0.487712i	$-0.162168\pi$
$252$	0.0381318	−	1.16710i	0.00240207	−	0.0735205i
$253$	−1.49683			−0.0941049
$254$	−0.818329	−	6.55430i	−0.0513465	−	0.411253i
$255$	−10.6364	−	2.42026i	−0.666074	−	0.151562i
$256$	8.72965	−	13.4087i	0.545603	−	0.838044i
$257$	12.5171	−	21.6802i	0.780792	−	1.35237i	−0.150688	−	0.988581i	$-0.548149\pi$
$257$	12.5171	−	21.6802i	0.780792	−	1.35237i	0.931481	−	0.363791i	$-0.118518\pi$
$258$	−13.5516	−	17.9076i	−0.843688	−	1.11488i
$259$	−3.80292	+	13.1713i	−0.236302	+	0.818427i
$260$	26.1204	−	15.9530i	1.61992	−	0.989362i
$261$	−0.471398	−	0.272162i	−0.0291788	−	0.0168464i
$262$	8.51915	−	20.1841i	0.526315	−	1.24698i
$263$	14.1558	+	24.5185i	0.872883	+	1.51188i	0.859001	+	0.511974i	$0.171086\pi$
$263$	14.1558	+	24.5185i	0.872883	+	1.51188i	0.0138820	+	0.999904i	$0.495581\pi$
$264$	3.68577	+	0.560691i	0.226843	+	0.0345081i
$265$	−9.78068	+	10.5551i	−0.600822	+	0.648394i
$266$	−1.32758	+	8.39333i	−0.0813993	+	0.514628i
$267$		−	18.9949i		−	1.16247i
$268$	4.68988	−	4.56606i	0.286480	−	0.278916i
$269$	1.84643	+	3.19810i	0.112579	+	0.194992i	0.916809	−	0.399325i	$-0.130756\pi$
$269$	1.84643	+	3.19810i	0.112579	+	0.194992i	−0.804231	+	0.594317i	$0.797422\pi$
$270$	15.4752	−	6.98654i	0.941789	−	0.425187i
$271$	−0.382982	+	0.663345i	−0.0232645	+	0.0402953i	−0.877423	−	0.479717i	$-0.840739\pi$
$271$	−0.382982	+	0.663345i	−0.0232645	+	0.0402953i	0.854159	+	0.520012i	$0.174073\pi$
$272$	9.97638	+	6.12142i	0.604907	+	0.371166i
$273$	21.7531	−	20.9299i	1.31656	−	1.26674i
$274$	12.3582	+	16.3305i	0.746585	+	0.986562i
$275$	3.56400	+	1.71051i	0.214918	+	0.103148i
$276$	−6.11856	+	1.55204i	−0.368294	+	0.0934221i
$277$	−9.73148	−	16.8554i	−0.584708	−	1.01274i	−0.994912	−	0.100750i	$-0.967876\pi$
$277$	−9.73148	−	16.8554i	−0.584708	−	1.01274i	0.410204	−	0.911994i	$-0.365458\pi$
$278$	15.3925	−	1.92181i	0.923181	−	0.115263i
$279$	−1.26831			−0.0759318
$280$	10.2036	−	13.2622i	0.609781	−	0.792570i
$281$	−7.20046			−0.429544			−0.214772	−	0.976664i	$-0.568901\pi$
$281$	−7.20046			−0.429544			−0.214772	+	0.976664i	$0.568901\pi$
$282$	0.500054	−	0.0624336i	0.0297778	−	0.00371787i
$283$	5.91380	+	10.2430i	0.351539	+	0.608883i	0.986519	−	0.163645i	$-0.0523252\pi$
$283$	5.91380	+	10.2430i	0.351539	+	0.608883i	−0.634980	+	0.772528i	$0.718992\pi$
$284$	−2.16786	−	8.54627i	−0.128639	−	0.507128i
$285$	−8.08845	+	2.50083i	−0.479118	+	0.148137i
$286$	−4.61779	−	6.10210i	−0.273055	−	0.360825i
$287$	−2.35766	−	9.53033i	−0.139168	−	0.562558i
$288$	−1.24243	+	0.121467i	−0.0732107	+	0.00715752i
$289$	4.21875	−	7.30709i	0.248162	−	0.429829i
$290$	−3.20953	−	7.10910i	−0.188470	−	0.417461i
$291$	10.8910	+	18.8637i	0.638441	+	1.10581i
$292$	−8.88333	−	9.12423i	−0.519857	−	0.533955i
$293$			11.8864i			0.694410i	0.937789	+	0.347205i	$0.112869\pi$
$293$			11.8864i			0.694410i	−0.937789	+	0.347205i	$0.887131\pi$
$294$	6.99903	−	14.9461i	0.408192	−	0.871676i
$295$	0.816252	+	0.756364i	0.0475240	+	0.0440372i
$296$	14.4892	+	2.20415i	0.842169	+	0.128113i
$297$	−2.12260	−	3.67645i	−0.123166	−	0.213329i
$298$	8.11476	−	19.2260i	0.470075	−	1.11373i
$299$	11.2208	+	6.47834i	0.648916	+	0.374652i
$300$	16.3421	+	3.29656i	0.943513	+	0.190327i
$301$	6.05197	+	24.4637i	0.348829	+	1.41007i
$302$	−13.4785	−	17.8109i	−0.775599	−	1.02490i
$303$	−8.61306	+	14.9183i	−0.494808	+	0.857032i
$304$	9.08115	+	0.243022i	0.520840	+	0.0139383i
$305$	25.6386	+	5.83395i	1.46806	+	0.334051i
$306$	−0.113141	−	0.906187i	−0.00646783	−	0.0518033i
$307$	−18.3489			−1.04723			−0.523615	−	0.851955i	$-0.675417\pi$
$307$	−18.3489			−1.04723			−0.523615	+	0.851955i	$0.675417\pi$
$308$	−3.55295	−	2.20905i	−0.202448	−	0.125872i
$309$		−	33.1082i		−	1.88346i
$310$	−14.7588	−	10.6062i	−0.838245	−	0.602393i
$311$	−3.85642	−	6.67951i	−0.218677	−	0.378760i	0.735726	−	0.677279i	$-0.236841\pi$
$311$	−3.85642	−	6.67951i	−0.218677	−	0.378760i	−0.954404	+	0.298518i	$0.903508\pi$
$312$	−25.2032	−	20.1553i	−1.42685	−	1.14107i
$313$	−8.58738	+	14.8738i	−0.485387	+	0.840716i	−0.999859	−	0.0167918i	$-0.994655\pi$
$313$	−8.58738	+	14.8738i	−0.485387	+	0.840716i	0.514472	+	0.857507i	$0.327988\pi$
$314$	−8.04024	−	10.6246i	−0.453737	−	0.599583i
$315$	−1.30533	+	0.0245169i	−0.0735468	+	0.00138137i
$316$	−11.6699	−	3.29486i	−0.656480	−	0.185350i
$317$	−9.77351	+	16.9282i	−0.548935	+	0.950784i	0.449413	+	0.893324i	$0.351633\pi$
$317$	−9.77351	+	16.9282i	−0.548935	+	0.950784i	−0.998348	+	0.0574593i	$0.981700\pi$
$318$	13.9785	+	5.89993i	0.783875	+	0.330851i
$319$	−1.68892	+	0.975096i	−0.0945611	+	0.0545949i
$320$	−15.4734	−	8.97630i	−0.864989	−	0.501791i
$321$			26.8725i			1.49988i
$322$	6.99664	+	1.10667i	0.389907	+	0.0616721i
$323$			6.64563i			0.369773i
$324$	−11.5649	−	11.8786i	−0.642496	−	0.659920i
$325$	−19.3140	−	28.2478i	−1.07135	−	1.56691i
$326$	−2.66668	+	6.31808i	−0.147694	+	0.349926i
$327$	21.4164	+	12.3648i	1.18433	+	0.683773i
$328$	−9.77520	+	3.82108i	−0.539745	+	0.210984i
$329$	−0.543317	−	0.156870i	−0.0299540	−	0.00864853i
$330$	0.414159	−	4.14759i	0.0227987	−	0.228318i
$331$	−1.08473	+	1.87881i	−0.0596222	+	0.103269i	−0.894296	−	0.447476i	$-0.852323\pi$
$331$	−1.08473	+	1.87881i	−0.0596222	+	0.103269i	0.834674	+	0.550745i	$0.185656\pi$
$332$	26.2546	−	6.65979i	1.44091	−	0.365503i
$333$	−0.571741	−	0.990284i	−0.0313312	−	0.0542672i
$334$	−14.7770	+	1.84497i	−0.808563	+	0.100952i
$335$	−5.36786	−	4.97403i	−0.293278	−	0.271760i
$336$	−16.8139	−	5.34587i	−0.917271	−	0.291641i
$337$			0.664494i			0.0361973i	0.999836	+	0.0180986i	$0.00576129\pi$
$337$			0.664494i			0.0361973i	−0.999836	+	0.0180986i	$0.994239\pi$
$338$	5.92886	+	47.4865i	0.322488	+	2.58292i
$339$	6.24374	−	3.60482i	0.339113	−	0.195787i
$340$	6.26140	−	11.4911i	0.339572	−	0.623191i
$341$	−2.27204	+	3.93528i	−0.123038	+	0.213108i
$342$	−0.427708	−	0.565188i	−0.0231278	−	0.0305619i
$343$	−13.8311	+	12.3167i	−0.746807	+	0.665041i
$344$	25.0923	−	9.80846i	1.35289	−	0.528837i
$345$	2.08468	+	6.74249i	0.112235	+	0.363003i
$346$	−6.38042	+	15.1169i	−0.343014	+	0.812690i
$347$	−23.4079	+	13.5146i	−1.25660	+	0.725500i	−0.972412	−	0.233268i	$-0.925058\pi$
$347$	−23.4079	+	13.5146i	−1.25660	+	0.725500i	−0.284190	+	0.958768i	$0.591725\pi$
$348$	−5.89268	+	5.73709i	−0.315881	+	0.307541i
$349$	22.2420			1.19059			0.595295	−	0.803508i	$-0.297035\pi$
$349$	22.2420			1.19059			0.595295	+	0.803508i	$0.297035\pi$
$350$	−15.3946	−	10.6305i	−0.822875	−	0.568222i
$351$			36.7468i			1.96140i
$352$	−1.84878	+	4.07257i	−0.0985405	+	0.217069i
$353$	−6.08471	−	10.5390i	−0.323856	−	0.560936i	0.657424	−	0.753521i	$-0.271646\pi$
$353$	−6.08471	−	10.5390i	−0.323856	−	0.560936i	−0.981280	+	0.192585i	$0.938313\pi$
$354$	0.456256	−	1.08099i	0.0242497	−	0.0574541i
$355$	−9.41776	+	2.91183i	−0.499843	+	0.154544i
$356$	21.9302	+	6.19177i	1.16230	+	0.328163i
$357$	3.58029	−	12.4003i	0.189489	−	0.656293i
$358$	21.8894	−	16.5649i	1.15689	−	0.875482i
$359$	−28.3997	−	16.3965i	−1.49888	−	0.865377i	−0.498877	−	0.866673i	$-0.666254\pi$
$359$	−28.3997	−	16.3965i	−1.49888	−	0.865377i	−0.999999	+	0.00129574i	$0.999588\pi$
$360$	0.207048	+	1.38026i	0.0109124	+	0.0727458i
$361$	−6.92105	−	11.9876i	−0.364266	−	0.630927i
$362$	2.94368	+	23.5770i	0.154716	+	1.23918i
$363$	17.2963			0.907819
$364$	17.0734	+	31.9372i	0.894890	+	1.67396i
$365$	−9.67703	+	10.4432i	−0.506519	+	0.546625i
$366$	−3.43477	−	27.5104i	−0.179538	−	1.43799i
$367$	−0.00646496	+	0.00373255i	−0.000337468	+	0.000194837i	−0.500169	−	0.865928i	$-0.666729\pi$
$367$	−0.00646496	+	0.00373255i	−0.000337468	+	0.000194837i	0.499831	+	0.866123i	$0.333395\pi$
$368$	0.202582	−	7.57000i	0.0105603	−	0.394613i
$369$	0.709169	+	0.409439i	0.0369178	+	0.0213145i
$370$	1.62811	−	16.3047i	0.0846414	−	0.847642i
$371$	−11.8051	−	12.2694i	−0.612892	−	0.636997i
$372$	−5.20691	+	18.4420i	−0.269966	+	0.956175i
$373$	17.5825	−	30.4538i	0.910388	−	1.57684i	0.0968723	−	0.995297i	$-0.469116\pi$
$373$	17.5825	−	30.4538i	0.910388	−	1.57684i	0.813516	−	0.581542i	$-0.197551\pi$
$374$	−3.01438	−	1.27228i	−0.155870	−	0.0657882i
$375$	2.74133	−	18.4364i	0.141562	−	0.952051i
$376$	−0.0909209	+	0.597680i	−0.00468889	+	0.0308230i
$377$	16.8810			0.869416
$378$	7.20353	+	18.7542i	0.370510	+	0.964610i
$379$	17.3297			0.890165			0.445082	−	0.895490i	$-0.353174\pi$
$379$	17.3297			0.890165			0.445082	+	0.895490i	$0.353174\pi$
$380$	−0.250700	−	10.1536i	−0.0128606	−	0.520867i
$381$	3.89322	+	6.74326i	0.199456	+	0.345468i
$382$	−6.08803	+	14.4242i	−0.311491	+	0.738004i
$383$	5.87162	+	3.38998i	0.300026	+	0.173220i	0.642455	−	0.766324i	$-0.277916\pi$
$383$	5.87162	+	3.38998i	0.300026	+	0.173220i	−0.342429	+	0.939544i	$0.611249\pi$
$384$	−3.33444	+	18.5643i	−0.170160	+	0.947357i
$385$	−2.26228	+	4.09405i	−0.115296	+	0.208652i
$386$	2.26680	+	2.99543i	0.115377	+	0.152463i
$387$	−1.82039	−	1.05100i	−0.0925356	−	0.0534254i
$388$	−25.3289	+	6.42498i	−1.28588	+	0.326179i
$389$	−4.97969	+	2.87502i	−0.252480	+	0.145770i	−0.620899	−	0.783890i	$-0.713232\pi$
$389$	−4.97969	+	2.87502i	−0.252480	+	0.145770i	0.368419	+	0.929660i	$0.379899\pi$
$390$	−21.0556	+	29.2995i	−1.06619	+	1.48364i
$391$	5.53977			0.280158
$392$	14.9743	+	12.9526i	0.756317	+	0.654205i
$393$			25.8264i			1.30277i
$394$	1.74674	+	13.9903i	0.0879994	+	0.704820i
$395$	−3.00803	+	13.2194i	−0.151350	+	0.665142i
$396$	0.338245	−	0.0857999i	0.0169975	−	0.00431161i
$397$	4.00016	+	2.30949i	0.200762	+	0.115910i	0.597011	−	0.802233i	$-0.296355\pi$
$397$	4.00016	+	2.30949i	0.200762	+	0.115910i	−0.396249	+	0.918143i	$0.629688\pi$
$398$	0.843452	−	0.638286i	0.0422784	−	0.0319944i
$399$	−2.40564	−	9.72425i	−0.120432	−	0.486821i
$400$	−9.13302	+	17.7929i	−0.456651	+	0.889646i
$401$	8.29423	−	14.3660i	0.414194	−	0.717406i	−0.581149	−	0.813797i	$-0.697397\pi$
$401$	8.29423	−	14.3660i	0.414194	−	0.717406i	0.995344	+	0.0963914i	$0.0307301\pi$
$402$	−3.00045	+	7.10885i	−0.149649	+	0.354557i
$403$	34.0641	−	19.6669i	1.69685	−	0.979679i
$404$	−14.4160	−	14.8070i	−0.717224	−	0.736674i
$405$	−12.5982	+	13.5957i	−0.626011	+	0.675578i
$406$	8.61543	−	3.30921i	0.427577	−	0.164233i
$407$	−4.09684			−0.203073
$408$	−13.6410	−	2.07511i	−0.675331	−	0.102734i
$409$	14.1437	−	8.16589i	0.699363	−	0.403777i	−0.107747	−	0.994178i	$-0.534364\pi$
$409$	14.1437	−	8.16589i	0.699363	−	0.403777i	0.807110	+	0.590401i	$0.201030\pi$
$410$	4.82839	+	10.6949i	0.238457	+	0.528183i
$411$	−20.9076	−	12.0710i	−1.03130	−	0.595419i
$412$	38.2245	+	10.7923i	1.88319	+	0.531698i
$413$	−0.948826	+	0.912921i	−0.0466887	+	0.0449219i
$414$	−0.471138	+	0.356535i	−0.0231552	+	0.0175228i
$415$	−8.94531	−	28.9319i	−0.439108	−	1.42021i
$416$	31.4854	−	22.5279i	1.54370	−	1.10452i
$417$	−15.8363	+	9.14308i	−0.775506	+	0.447739i
$418$	−2.51984	+	0.314612i	−0.123250	+	0.0153882i
$419$		−	25.5119i		−	1.24634i	−0.782087	−	0.623170i	$-0.785845\pi$
$419$		−	25.5119i		−	1.24634i	0.782087	−	0.623170i	$-0.214155\pi$
$420$	−5.00238	+	19.0809i	−0.244091	+	0.931053i
$421$		−	5.65879i		−	0.275793i	−0.990447	−	0.137896i	$-0.955966\pi$
$421$		−	5.65879i		−	0.275793i	0.990447	−	0.137896i	$-0.0440341\pi$
$422$	2.29127	+	18.3517i	0.111537	+	0.893345i
$423$	0.0408492	−	0.0235843i	0.00198616	−	0.00114671i
$424$	−11.3682	+	14.2154i	−0.552090	+	0.690362i
$425$	−13.1904	−	6.33061i	−0.639827	−	0.307080i
$426$	6.27201	+	8.28805i	0.303880	+	0.401557i
$427$	−8.63018	+	29.8905i	−0.417644	+	1.44650i
$428$	−31.0251	−	8.75962i	−1.49966	−	0.423412i
$429$	7.81239	+	4.51048i	0.377186	+	0.217768i
$430$	−12.3942	−	27.4531i	−0.597700	−	1.32390i
$431$	8.15466	−	4.70809i	0.392796	−	0.226781i	−0.290575	−	0.956852i	$-0.593847\pi$
$431$	8.15466	−	4.70809i	0.392796	−	0.226781i	0.683371	+	0.730071i	$0.260513\pi$
$432$	18.8804	−	10.2372i	0.908383	−	0.492536i
$433$	2.39361			0.115030			0.0575148	−	0.998345i	$-0.481682\pi$
$433$	2.39361			0.115030			0.0575148	+	0.998345i	$0.481682\pi$
$434$	13.5297	−	16.7149i	0.649446	−	0.802341i
$435$	6.74453	+	6.24969i	0.323376	+	0.299650i
$436$	−21.2566	+	20.6954i	−1.01801	+	0.991128i
$437$	3.72356	−	2.14980i	0.178122	−	0.102839i
$438$	13.8304	+	5.83741i	0.660841	+	0.278922i
$439$	−17.7739	+	30.7852i	−0.848300	+	1.46930i	0.0344242	+	0.999407i	$0.489040\pi$
$439$	−17.7739	+	30.7852i	−0.848300	+	1.46930i	−0.882724	+	0.469891i	$0.844293\pi$
$440$	4.65353	+	1.83015i	0.221848	+	0.0872490i
$441$	0.0595608	−	1.54361i	0.00283623	−	0.0735051i
$442$	17.0904	+	22.5838i	0.812909	+	1.07420i
$443$	−10.5455	−	6.08847i	−0.501033	−	0.289272i	0.228107	−	0.973636i	$-0.426746\pi$
$443$	−10.5455	−	6.08847i	−0.501033	−	0.289272i	−0.729140	+	0.684364i	$0.760080\pi$
$444$	−16.7466	+	4.24797i	−0.794757	+	0.201599i
$445$	5.65275	−	24.8423i	0.267966	−	1.17764i
$446$	−5.74780	+	0.717634i	−0.272166	+	0.0339810i
$447$			24.6004i			1.16356i
$448$	11.6528	−	17.6695i	0.550543	−	0.834807i
$449$	5.65182			0.266726			0.133363	−	0.991067i	$-0.457422\pi$
$449$	5.65182			0.266726			0.133363	+	0.991067i	$0.457422\pi$
$450$	1.52923	−	0.310527i	0.0720885	−	0.0146384i
$451$	2.54079	−	1.46693i	0.119641	−	0.0690749i
$452$	2.12661	+	8.38366i	0.100027	+	0.394334i
$453$	22.8029	+	13.1653i	1.07138	+	0.618559i
$454$	11.1376	−	8.42844i	0.522715	−	0.395566i
$455$	34.6781	−	20.8994i	1.62573	−	0.979778i
$456$	−9.97410	+	3.89883i	−0.467080	+	0.182579i
$457$	−17.8188	−	10.2877i	−0.833529	−	0.481238i	0.0215305	−	0.999768i	$-0.493146\pi$
$457$	−17.8188	−	10.2877i	−0.833529	−	0.481238i	−0.855059	+	0.518530i	$0.826479\pi$
$458$	4.37569	+	1.84686i	0.204463	+	0.0862979i
$459$	7.85574	+	13.6065i	0.366675	+	0.635099i
$460$	−8.46396	+	0.208982i	−0.394634	+	0.00974384i
$461$	−1.04586			−0.0487106			−0.0243553	−	0.999703i	$-0.507753\pi$
$461$	−1.04586			−0.0487106			−0.0243553	+	0.999703i	$0.507753\pi$
$462$	4.87135	+	0.770506i	0.226636	+	0.0358472i
$463$	−15.3524			−0.713488			−0.356744	−	0.934202i	$-0.616113\pi$
$463$	−15.3524			−0.713488			−0.356744	+	0.934202i	$0.616113\pi$
$464$	−4.70282	−	8.67341i	−0.218323	−	0.402653i
$465$	20.8909	+	4.75363i	0.968791	+	0.220444i
$466$	−10.9280	+	25.8914i	−0.506232	+	1.19940i
$467$	8.02282	−	13.8959i	0.371252	−	0.643027i	−0.618507	−	0.785780i	$-0.712262\pi$
$467$	8.02282	−	13.8959i	0.371252	−	0.643027i	0.989758	+	0.142753i	$0.0455954\pi$
$468$	−2.90696	−	0.820750i	−0.134374	−	0.0379392i
$469$	6.23970	−	6.00358i	0.288122	−	0.277220i
$470$	0.672569	+	0.0671595i	0.0310233	+	0.00309783i
$471$	13.6025	+	7.85341i	0.626770	+	0.361866i
$472$	1.09931	+	0.879133i	0.0506000	+	0.0404654i
$473$	−6.52205	+	3.76551i	−0.299884	+	0.173138i
$474$	14.1845	−	1.77099i	0.651518	−	0.0813444i
$475$	−11.3226	+	0.863618i	−0.519517	+	0.0396255i
$476$	13.1495	+	8.17568i	0.602704	+	0.374732i
$477$	1.42016			0.0650246
$478$	−9.46510	+	1.18175i	−0.432923	+	0.0540521i
$479$	10.5683	+	18.3049i	0.482879	+	0.836371i	0.999807	−	0.0196582i	$-0.00625780\pi$
$479$	10.5683	+	18.3049i	0.482879	+	0.836371i	−0.516928	+	0.856029i	$0.672924\pi$
$480$	20.9198	+	2.65588i	0.954853	+	0.121224i
$481$	30.7115	+	17.7313i	1.40032	+	0.808477i
$482$	1.16628	+	1.54116i	0.0531226	+	0.0701979i
$483$	−8.10608	+	2.00532i	−0.368839	+	0.0912454i
$484$	−5.63806	+	19.9691i	−0.256276	+	0.907686i
$485$	8.62993	+	27.9118i	0.391865	+	1.26741i
$486$	−2.98184	−	1.25855i	−0.135259	−	0.0570890i
$487$	−8.49641	−	14.7162i	−0.385009	−	0.666855i	0.606761	−	0.794884i	$-0.292468\pi$
$487$	−8.49641	−	14.7162i	−0.385009	−	0.666855i	−0.991770	+	0.128029i	$0.959135\pi$
$488$	32.8812	+	5.00200i	1.48846	+	0.226430i
$489$		−	8.08424i		−	0.365582i
$490$	13.6015	−	17.4643i	0.614451	−	0.788955i
$491$	13.6290			0.615070			0.307535	−	0.951537i	$-0.400496\pi$
$491$	13.6290			0.615070			0.307535	+	0.951537i	$0.400496\pi$
$492$	8.86491	−	8.63085i	0.399661	−	0.389109i
$493$	6.25067	−	3.60883i	0.281516	−	0.162533i
$494$	20.2514	+	8.54753i	0.911152	+	0.384572i
$495$	−0.115245	−	0.372737i	−0.00517988	−	0.0167533i
$496$	−19.5946	−	12.0231i	−0.879824	−	0.539853i
$497$	−2.80099	−	11.3224i	−0.125642	−	0.507879i
$498$	−25.4613	+	19.2680i	−1.14095	+	0.863418i
$499$	−7.46818	+	12.9353i	−0.334322	+	0.579062i	−0.983354	−	0.181699i	$-0.941840\pi$
$499$	−7.46818	+	12.9353i	−0.334322	+	0.579062i	0.649033	+	0.760760i	$0.275174\pi$
$500$	20.3918	+	9.17466i	0.911949	+	0.410303i
$501$	15.2030	−	8.77748i	0.679222	−	0.392149i
$502$	−21.6863	+	2.70762i	−0.967908	+	0.120847i
$503$		−	24.2100i		−	1.07947i	−0.841834	−	0.539736i	$-0.818524\pi$
$503$		−	24.2100i		−	1.07947i	0.841834	−	0.539736i	$-0.181476\pi$
$504$	−1.64450	+	0.150976i	−0.0732517	+	0.00672503i
$505$	−15.7041	+	16.9475i	−0.698821	+	0.754153i
$506$	0.262259	+	2.10053i	0.0116588	+	0.0933799i
$507$	−28.2068	−	48.8555i	−1.25271	−	2.16975i
$508$	−9.05438	+	2.29675i	−0.401723	+	0.101902i
$509$	−4.43051	+	7.67386i	−0.196379	+	0.340138i	−0.947352	−	0.320195i	$-0.896252\pi$
$509$	−4.43051	+	7.67386i	−0.196379	+	0.340138i	0.750973	+	0.660333i	$0.229585\pi$
$510$	−1.53280	+	15.3502i	−0.0678735	+	0.679720i
$511$	−11.6800	−	12.1394i	−0.516695	−	0.537016i
$512$	−20.3462	−	9.90114i	−0.899183	−	0.437573i
$513$	10.5605	+	6.09710i	0.466257	+	0.269193i
$514$	−32.6173	−	13.7668i	−1.43869	−	0.607229i
$515$	9.85277	−	43.3002i	0.434165	−	1.90803i
$516$	−22.7556	+	22.1548i	−1.00176	+	0.975312i
$517$		−	0.168995i		−	0.00743237i
$518$	19.1499	+	3.02896i	0.841397	+	0.133085i
$519$		−	19.3427i		−	0.849050i
$520$	−26.9637	−	33.8601i	−1.18243	−	1.48487i
$521$	−26.5478	+	15.3274i	−1.16308	+	0.671505i	−0.952041	−	0.305972i	$-0.901019\pi$
$521$	−26.5478	+	15.3274i	−1.16308	+	0.671505i	−0.211041	+	0.977477i	$0.567685\pi$
$522$	−0.299336	+	0.709207i	−0.0131016	+	0.0310411i
$523$	9.06880	−	15.7076i	0.396551	−	0.686846i	−0.596747	−	0.802430i	$-0.703540\pi$
$523$	9.06880	−	15.7076i	0.396551	−	0.686846i	0.993298	+	0.115583i	$0.0368737\pi$
$524$	−29.8174	−	8.41862i	−1.30258	−	0.367769i
$525$	21.5925	+	4.48853i	0.942372	+	0.195896i
$526$	31.9271	−	24.1609i	1.39209	−	1.05347i
$527$	8.40880	−	14.5645i	0.366293	−	0.634439i
$528$	0.141046	−	5.27054i	0.00613823	−	0.229371i
$529$	9.70794	+	16.8146i	0.422084	+	0.731072i
$530$	16.5258	+	11.8760i	0.717836	+	0.515862i
$531$		−	0.109824i		−	0.00476598i
$532$	12.0111	+	0.392429i	0.520748	+	0.0170140i
$533$	−25.3957			−1.10001
$534$	−26.6559	+	3.32809i	−1.15351	+	0.144021i
$535$	−7.99706	+	35.1448i	−0.345743	+	1.51944i
$536$	−7.22934	−	5.78138i	−0.312260	−	0.249718i
$537$	−16.1800	+	28.0246i	−0.698218	+	1.20935i
$538$	4.16445	−	3.15146i	0.179542	−	0.135869i
$539$	−4.68277	−	2.95000i	−0.201701	−	0.127066i
$540$	−12.5157	−	20.4925i	−0.538591	−	0.881856i
$541$	−23.5104	−	13.5737i	−1.01079	−	0.583580i	−0.0993669	−	0.995051i	$-0.531682\pi$
$541$	−23.5104	−	13.5737i	−1.01079	−	0.583580i	−0.911423	+	0.411471i	$0.865015\pi$
$542$	0.997986	+	0.421222i	0.0428672	+	0.0180930i
$543$	−14.0046	−	24.2567i	−0.600997	−	1.04096i
$544$	6.84235	−	15.0726i	0.293363	−	0.646231i
$545$	24.3295	+	22.5445i	1.04216	+	0.965699i
$546$	−33.1827	−	26.8594i	−1.42009	−	1.14948i
$547$		−	23.0006i		−	0.983436i	−0.870754	−	0.491718i	$-0.836369\pi$
$547$		−	23.0006i		−	0.983436i	0.870754	−	0.491718i	$-0.163631\pi$
$548$	20.7516	−	20.2037i	0.886465	−	0.863060i
$549$	−1.29749	−	2.24731i	−0.0553753	−	0.0959129i
$550$	1.77595	−	5.30113i	0.0757266	−	0.226041i
$551$	2.80093	−	4.85135i	0.119324	−	0.206674i
$552$	3.25004	+	8.31436i	0.138331	+	0.353882i
$553$	−15.4118	−	4.44978i	−0.655374	−	0.189224i
$554$	−21.9485	+	16.6096i	−0.932501	+	0.705674i
$555$	5.70580	+	18.4543i	0.242198	+	0.783340i
$556$	−5.39383	−	21.2639i	−0.228749	−	0.901789i
$557$	5.52574	+	9.57086i	0.234133	+	0.405530i	0.959020	−	0.283337i	$-0.0914415\pi$
$557$	5.52574	+	9.57086i	0.234133	+	0.405530i	−0.724887	+	0.688867i	$0.758108\pi$
$558$	0.222220	+	1.77984i	0.00940733	+	0.0753468i
$559$	65.1890			2.75720
$560$	−20.3989	−	11.9952i	−0.862011	−	0.506890i
$561$	3.85701			0.162843
$562$	1.26159	+	10.1045i	0.0532170	+	0.426234i
$563$	19.8308	+	34.3480i	0.835770	+	1.44760i	0.893402	+	0.449259i	$0.148312\pi$
$563$	19.8308	+	34.3480i	0.835770	+	1.44760i	−0.0576315	+	0.998338i	$0.518355\pi$
$564$	−0.175228	−	0.690796i	−0.00737845	−	0.0290877i
$565$	9.23856	−	2.85643i	0.388669	−	0.120171i
$566$	13.3380	−	10.0936i	0.560639	−	0.424266i
$567$	−15.2059	−	15.8039i	−0.638587	−	0.663703i
$568$	−11.6133	+	4.53959i	−0.487283	+	0.190477i
$569$	14.0325	−	24.3050i	0.588272	−	1.01892i	−0.406187	−	0.913790i	$-0.633142\pi$
$569$	14.0325	−	24.3050i	0.588272	−	1.01892i	0.994459	−	0.105127i	$-0.0335248\pi$
$570$	4.92664	+	10.9125i	0.206354	+	0.457074i
$571$	1.96859	+	3.40970i	0.0823829	+	0.142691i	0.904273	−	0.426955i	$-0.140414\pi$
$571$	1.96859	+	3.40970i	0.0823829	+	0.142691i	−0.821890	+	0.569646i	$0.807080\pi$
$572$	−7.75410	+	7.54937i	−0.324215	+	0.315655i
$573$		−	18.4563i		−	0.771022i
$574$	−12.9610	+	4.97836i	−0.540982	+	0.207793i
$575$	0.719907	+	9.43847i	0.0300222	+	0.393611i
$576$	0.388142	+	1.72224i	0.0161726	+	0.0717599i
$577$	−20.6956	−	35.8459i	−0.861571	−	1.49228i	−0.870412	−	0.492324i	$-0.836148\pi$
$577$	−20.6956	−	35.8459i	−0.861571	−	1.49228i	0.00884126	−	0.999961i	$-0.497186\pi$
$578$	−10.9933	−	4.63998i	−0.457262	−	0.192998i
$579$	−3.83499	−	2.21413i	−0.159377	−	0.0920161i
$580$	−9.41399	+	5.74957i	−0.390895	+	0.238738i
$581$	34.7830	−	8.60480i	1.44304	−	0.356987i
$582$	24.5636	−	18.5886i	1.01820	−	0.770524i
$583$	2.54406	−	4.40643i	0.105364	−	0.182496i
$584$	−11.2478	+	14.0648i	−0.465436	+	0.582005i
$585$	−0.749300	+	3.29297i	−0.0309798	+	0.136147i
$586$	16.6804	−	2.08261i	0.689060	−	0.0860318i
$587$	15.3447			0.633342			0.316671	−	0.948535i	$-0.397435\pi$
$587$	15.3447			0.633342			0.316671	+	0.948535i	$0.397435\pi$
$588$	−22.2005	−	7.20316i	−0.915532	−	0.297053i
$589$		−	13.0527i		−	0.537827i
$590$	0.918405	−	1.27798i	0.0378101	−	0.0526138i
$591$	−8.31016	−	14.3936i	−0.341834	−	0.592075i
$592$	0.554468	−	20.7192i	0.0227885	−	0.851552i
$593$	−20.8596	+	36.1298i	−0.856600	+	1.48367i	0.0185530	+	0.999828i	$0.494094\pi$
$593$	−20.8596	+	36.1298i	−0.856600	+	1.48367i	−0.875153	+	0.483847i	$0.839239\pi$
$594$	−4.78733	+	3.62283i	−0.196427	+	0.148647i
$595$	8.37268	−	15.1521i	0.343246	−	0.621175i
$596$	−28.4020	−	8.01900i	−1.16339	−	0.328471i
$597$	−0.623454	+	1.07985i	−0.0255163	+	0.0441955i
$598$	7.12517	−	16.8814i	0.291370	−	0.690333i
$599$	−19.4999	+	11.2583i	−0.796746	+	0.460001i	−0.842332	−	0.538959i	$-0.818818\pi$
$599$	−19.4999	+	11.2583i	−0.796746	+	0.460001i	0.0455861	+	0.998960i	$0.485484\pi$
$600$	1.76282	−	23.5108i	0.0719670	−	0.959823i
$601$		−	8.10668i		−	0.330679i	−0.986237	−	0.165339i	$-0.947128\pi$
$601$		−	8.10668i		−	0.330679i	0.986237	−	0.165339i	$-0.0528719\pi$
$602$	33.2700	−	12.7791i	1.35599	−	0.520838i
$603$			0.722231i			0.0294115i
$604$	−22.6328	+	22.0352i	−0.920916	+	0.896601i
$605$	22.6207	+	5.14725i	0.919663	+	0.209265i
$606$	22.4442	+	9.47305i	0.911732	+	0.384816i
$607$	−10.6003	−	6.12010i	−0.430254	−	0.248407i	0.269201	−	0.963084i	$-0.413240\pi$
$607$	−10.6003	−	6.12010i	−0.430254	−	0.248407i	−0.699455	+	0.714677i	$0.746574\pi$
$608$	−1.25007	−	12.7863i	−0.0506969	−	0.518554i
$609$	−7.83997	+	7.54329i	−0.317692	+	0.305670i
$610$	3.69476	−	37.0012i	0.149597	−	1.49814i
$611$	−0.731415	+	1.26685i	−0.0295899	+	0.0512512i
$612$	−1.25185	+	0.317545i	−0.0506029	+	0.0128360i
$613$	6.93580	+	12.0132i	0.280134	+	0.485207i	0.971418	−	0.237377i	$-0.0762876\pi$
$613$	6.93580	+	12.0132i	0.280134	+	0.485207i	−0.691283	+	0.722584i	$0.742954\pi$
$614$	3.21491	+	25.7494i	0.129743	+	1.03916i
$615$	−10.1464	−	9.40200i	−0.409144	−	0.379125i
$616$	−2.47749	+	5.37296i	−0.0998208	+	0.216483i
$617$		−	1.91696i		−	0.0771739i	−0.999255	−	0.0385870i	$-0.987714\pi$
$617$		−	1.91696i		−	0.0771739i	0.999255	−	0.0385870i	$-0.0122857\pi$
$618$	−46.4614	+	5.80088i	−1.86895	+	0.233345i
$619$	−19.2245	+	11.0993i	−0.772699	+	0.446118i	−0.833837	−	0.552011i	$-0.813861\pi$
$619$	−19.2245	+	11.0993i	−0.772699	+	0.446118i	0.0611375	+	0.998129i	$0.480527\pi$
$620$	−12.2980	+	22.5696i	−0.493900	+	0.906418i
$621$	5.08251	−	8.80316i	0.203954	−	0.353259i
$622$	−8.69780	+	6.58210i	−0.348750	+	0.263918i
$623$	28.9621	+	8.36213i	1.16034	+	0.335022i
$624$	−23.8684	+	38.8995i	−0.955502	+	1.55723i
$625$	9.07175	−	23.2960i	0.362870	−	0.931840i
$626$	22.3772	+	9.44480i	0.894374	+	0.377490i
$627$	2.59249	−	1.49678i	0.103534	−	0.0597755i
$628$	−13.5010	+	13.1446i	−0.538749	+	0.524525i
$629$	15.1624			0.604565
$630$	0.263111	+	1.82749i	0.0104826	+	0.0728090i
$631$			4.47405i			0.178109i	0.996027	+	0.0890545i	$0.0283845\pi$
$631$			4.47405i			0.178109i	−0.996027	+	0.0890545i	$0.971615\pi$
$632$	−2.57907	+	16.9538i	−0.102590	+	0.674386i
$633$	−10.9008	−	18.8807i	−0.433268	−	0.750442i
$634$	25.4681	+	10.7494i	1.01147	+	0.426912i
$635$	3.08496	+	9.97769i	0.122423	+	0.395952i
$636$	5.83031	−	20.6500i	0.231187	−	0.818826i
$637$	22.3361	+	42.3815i	0.884988	+	1.67922i
$638$	1.66428	+	2.19924i	0.0658896	+	0.0870687i
$639$	0.842519	+	0.486429i	0.0333295	+	0.0192428i
$640$	−9.88552	+	23.2868i	−0.390760	+	0.920493i
$641$	−16.7611	−	29.0311i	−0.662025	−	1.14666i	−0.980083	−	0.198590i	$-0.936364\pi$
$641$	−16.7611	−	29.0311i	−0.662025	−	1.14666i	0.318058	−	0.948071i	$-0.396969\pi$
$642$	37.7106	−	4.70831i	1.48832	−	0.185822i
$643$	−1.67625			−0.0661048			−0.0330524	−	0.999454i	$-0.510523\pi$
$643$	−1.67625			−0.0661048			−0.0330524	+	0.999454i	$0.510523\pi$
$644$	0.327127	−	10.0124i	0.0128906	−	0.394544i
$645$	26.0452	+	24.1343i	1.02553	+	0.950288i
$646$	9.32594	−	1.16438i	0.366924	−	0.0458119i
$647$	−18.8153	+	10.8630i	−0.739707	+	0.427070i	−0.821963	−	0.569541i	$-0.807121\pi$
$647$	−18.8153	+	10.8630i	−0.739707	+	0.427070i	0.0822561	+	0.996611i	$0.473787\pi$
$648$	−14.6431	+	18.3105i	−0.575236	+	0.719304i
$649$	−0.340761	−	0.196738i	−0.0133760	−	0.00772265i
$650$	−36.2567	+	32.0529i	−1.42210	+	1.25722i
$651$	−7.03206	+	24.3554i	−0.275608	+	0.954563i
$652$	9.33351	+	2.63522i	0.365528	+	0.103203i
$653$	4.45603	−	7.71807i	0.174378	−	0.302031i	−0.765568	−	0.643355i	$-0.777542\pi$
$653$	4.45603	−	7.71807i	0.174378	−	0.302031i	0.939946	+	0.341324i	$0.110875\pi$
$654$	13.5993	−	32.2204i	0.531776	−	1.25992i
$655$	−7.68575	+	33.7767i	−0.300307	+	1.31977i
$656$	7.07490	+	13.0482i	0.276228	+	0.509447i
$657$	1.40511			0.0548186
$658$	−0.124944	+	0.789932i	−0.00487084	+	0.0307947i
$659$	11.6434			0.453562			0.226781	−	0.973946i	$-0.427180\pi$
$659$	11.6434			0.453562			0.226781	+	0.973946i	$0.427180\pi$
$660$	−5.89296	+	0.145502i	−0.229383	+	0.00566366i
$661$	−3.07763	−	5.33061i	−0.119706	−	0.207337i	0.799945	−	0.600073i	$-0.204862\pi$
$661$	−3.07763	−	5.33061i	−0.119706	−	0.207337i	−0.919651	+	0.392736i	$0.871528\pi$
$662$	2.82662	+	1.19304i	0.109860	+	0.0463687i
$663$	−28.9136	−	16.6933i	−1.12291	−	0.648314i
$664$	−13.9459	−	35.6767i	−0.541204	−	1.38452i
$665$	−0.252313	−	13.4336i	−0.00978430	−	0.520934i
$666$	−1.28951	+	0.975842i	−0.0499675	+	0.0378131i
$667$	−4.04406	−	2.33484i	−0.156587	−	0.0904053i
$668$	5.17815	+	20.4136i	0.200349	+	0.789826i
$669$	5.91351	−	3.41417i	0.228630	−	0.131999i
$670$	−6.03964	+	8.40431i	−0.233332	+	0.324687i
$671$	−9.29720			−0.358914
$672$	−4.55601	+	24.5318i	−0.175752	+	0.946336i
$673$		−	29.9527i		−	1.15459i	−0.816535	−	0.577296i	$-0.804108\pi$
$673$		−	29.9527i		−	1.15459i	0.816535	−	0.577296i	$-0.195892\pi$
$674$	0.932496	−	0.116426i	0.0359184	−	0.00448455i
$675$	−22.1615	+	15.1526i	−0.852996	+	0.583222i
$676$	65.5998	−	16.6402i	2.52307	−	0.640006i
$677$	−19.0794	−	11.0155i	−0.733281	−	0.423360i	0.0863404	−	0.996266i	$-0.472483\pi$
$677$	−19.0794	−	11.0155i	−0.733281	−	0.423360i	−0.819621	+	0.572906i	$0.805816\pi$
$678$	−6.15268	−	8.13035i	−0.236292	−	0.312244i
$679$	−33.5566	+	8.30142i	−1.28779	+	0.318579i
$680$	−17.2227	−	6.77338i	−0.660460	−	0.259747i
$681$	−8.23259	+	14.2593i	−0.315474	+	0.546416i
$682$	5.92054	+	2.49889i	0.226709	+	0.0956875i
$683$	−1.35827	+	0.784199i	−0.0519728	+	0.0300065i	−0.525761	−	0.850632i	$-0.676219\pi$
$683$	−1.35827	+	0.784199i	−0.0519728	+	0.0300065i	0.473788	+	0.880639i	$0.342886\pi$
$684$	−0.718200	+	0.699237i	−0.0274611	+	0.0267360i
$685$	−23.7515	−	22.0089i	−0.907498	−	0.840916i
$686$	19.7076	+	17.2514i	0.752441	+	0.658660i
$687$	−5.59887			−0.213610
$688$	−18.1608	−	33.4939i	−0.692374	−	1.27694i
$689$	−38.1424	+	22.0215i	−1.45311	+	0.838954i
$690$	9.09660	−	4.10682i	0.346302	−	0.156344i
$691$	−36.1431	−	20.8673i	−1.37495	−	0.793828i	−0.383404	−	0.923581i	$-0.625248\pi$
$691$	−36.1431	−	20.8673i	−1.37495	−	0.793828i	−0.991546	+	0.129753i	$0.958581\pi$
$692$	22.3317	+	6.30513i	0.848926	+	0.239685i
$693$	0.448119	−	0.110858i	0.0170226	−	0.00421115i
$694$	23.0665	+	30.4809i	0.875593	+	1.15704i
$695$	−23.4322	+	7.24490i	−0.888834	+	0.274815i
$696$	9.08342	+	7.26411i	0.344306	+	0.275345i
$697$	−9.40347	+	5.42910i	−0.356182	+	0.205642i
$698$	−3.89702	−	31.2127i	−0.147504	−	1.18142i
$699$		−	33.1291i		−	1.25306i
$700$	−12.2206	+	23.4661i	−0.461897	+	0.886934i
$701$		−	39.2592i		−	1.48280i	−0.671065	−	0.741399i	$-0.734163\pi$
$701$		−	39.2592i		−	1.48280i	0.671065	−	0.741399i	$-0.265837\pi$
$702$	51.5674	−	6.43839i	1.94629	−	0.243001i
$703$	10.1914	−	5.88402i	0.384377	−	0.221920i
$704$	6.03903	+	1.88088i	0.227605	+	0.0708883i
$705$	−0.761238	+	0.235364i	−0.0286699	+	0.00886432i
$706$	−13.7235	+	10.3853i	−0.516491	+	0.390857i
$707$	−18.9546	−	19.7001i	−0.712860	−	0.740897i
$708$	−1.59692	−	0.450872i	−0.0600158	−	0.0169448i
$709$	7.57554	+	4.37374i	0.284505	+	0.164259i	0.635461	−	0.772133i	$-0.280810\pi$
$709$	7.57554	+	4.37374i	0.284505	+	0.164259i	−0.350956	+	0.936392i	$0.614143\pi$
$710$	5.73631	+	12.7059i	0.215280	+	0.476845i
$711$	1.15873	−	0.668993i	0.0434558	−	0.0250892i
$712$	4.84664	−	31.8599i	0.181635	−	1.19400i
$713$	−10.8807			−0.407484
$714$	−18.0288	−	2.85164i	−0.674713	−	0.106720i
$715$	8.87505	+	8.22389i	0.331908	+	0.307556i
$716$	−27.0811	−	27.8155i	−1.01207	−	1.03951i
$717$	9.73798	−	5.62223i	0.363672	−	0.209966i
$718$	−18.0337	+	42.7266i	−0.673011	+	1.59454i
$719$	1.13078	−	1.95857i	0.0421709	−	0.0730422i	−0.844170	−	0.536076i	$-0.819906\pi$
$719$	1.13078	−	1.95857i	0.0421709	−	0.0730422i	0.886340	+	0.463034i	$0.153239\pi$
$720$	1.90066	−	0.532388i	0.0708334	−	0.0198409i
$721$	50.4811	+	14.5752i	1.88001	+	0.542810i
$722$	−15.6098	+	11.8128i	−0.580937	+	0.439626i
$723$	−1.97312	−	1.13918i	−0.0733809	−	0.0423665i
$724$	32.5703	−	8.26183i	1.21046	−	0.307049i
$725$	6.96089	+	10.1807i	0.258521	+	0.378102i
$726$	−3.03047	−	24.2722i	−0.112471	−	0.900825i
$727$		−	14.0073i		−	0.519502i	−0.965676	−	0.259751i	$-0.916359\pi$
$727$		−	14.0073i		−	0.519502i	0.965676	−	0.259751i	$-0.0836406\pi$
$728$	41.8266	−	29.5551i	1.55020	−	1.09539i
$729$	28.6832			1.06234
$730$	16.3507	+	11.7502i	0.605167	+	0.434894i
$731$	24.1381	−	13.9361i	0.892780	−	0.515447i
$732$	−38.0040	+	9.64016i	−1.40467	+	0.356310i
$733$	−0.730569	−	0.421794i	−0.0269842	−	0.0155793i	0.486447	−	0.873710i	$-0.338293\pi$
$733$	−0.730569	−	0.421794i	−0.0269842	−	0.0155793i	−0.513431	+	0.858131i	$0.671626\pi$
$734$	0.00637067	+	0.00841842i	0.000235146	+	0.000310730i
$735$	−6.76649	+	25.2021i	−0.249586	+	0.929595i
$736$	−10.6586	+	1.04205i	−0.392881	+	0.0384104i
$737$	2.24092	+	1.29380i	0.0825454	+	0.0476576i
$738$	0.450320	−	1.06693i	0.0165765	−	0.0392741i
$739$	−24.2171	−	41.9452i	−0.890840	−	1.54298i	−0.838870	−	0.544331i	$-0.816784\pi$
$739$	−24.2171	−	41.9452i	−0.890840	−	1.54298i	−0.0519693	−	0.998649i	$-0.516550\pi$
$740$	−23.1660	+	0.571987i	−0.851598	+	0.0210266i
$741$	−25.9124			−0.951916
$742$	−15.1495	+	18.7161i	−0.556157	+	0.687089i
$743$	23.9932			0.880226			0.440113	−	0.897942i	$-0.354938\pi$
$743$	23.9932			0.880226			0.440113	+	0.897942i	$0.354938\pi$
$744$	26.7923	+	4.07573i	0.982254	+	0.149424i
$745$	−7.32092	+	32.1734i	−0.268218	+	1.17874i
$746$	−45.8170	−	19.3381i	−1.67748	−	0.708017i
$747$	−1.49434	+	2.58826i	−0.0546749	+	0.0946996i
$748$	−1.25727	+	4.45304i	−0.0459703	+	0.162819i
$749$	−40.9732	−	11.8301i	−1.49713	−	0.432261i
$750$	−26.3524	−	0.616729i	−0.962254	−	0.0225198i
$751$	−15.5172	−	8.95889i	−0.566232	−	0.326914i	0.189411	−	0.981898i	$-0.439342\pi$
$751$	−15.5172	−	8.95889i	−0.566232	−	0.326914i	−0.755643	+	0.654983i	$0.772676\pi$
$752$	0.854665	+	0.0228718i	0.0311664	+	0.000834049i
$753$	22.3116	−	12.8816i	0.813078	−	0.469431i
$754$	−2.95771	−	23.6894i	−0.107714	−	0.862718i
$755$	25.9046	+	24.0040i	0.942766	+	0.873596i
$756$	25.0559	−	13.3948i	0.911276	−	0.487162i
$757$	9.11215			0.331187			0.165593	−	0.986194i	$-0.447046\pi$
$757$	9.11215			0.331187			0.165593	+	0.986194i	$0.447046\pi$
$758$	−3.03632	−	24.3190i	−0.110284	−	0.883307i
$759$	−1.24770	−	2.16109i	−0.0452888	−	0.0784425i
$760$	−14.2048	+	2.13081i	−0.515261	+	0.0772928i
$761$	−0.873293	−	0.504196i	−0.0316568	−	0.0182771i	0.484088	−	0.875019i	$-0.339151\pi$
$761$	−0.873293	−	0.504196i	−0.0316568	−	0.0182771i	−0.515745	+	0.856742i	$0.672485\pi$
$762$	8.78081	−	6.64491i	0.318095	−	0.240720i
$763$	−28.2810	+	27.2108i	−1.02384	+	0.985099i
$764$	21.3084	+	6.01619i	0.770910	+	0.217658i
$765$	0.426522	+	1.37950i	0.0154209	+	0.0498759i
$766$	3.72846	−	8.83371i	0.134715	−	0.319175i
$767$	1.70298	+	2.94965i	0.0614911	+	0.106506i
$768$	26.6359	+	1.42664i	0.961140	+	0.0514793i
$769$			11.3063i			0.407716i	0.979000	+	0.203858i	$0.0653481\pi$
$769$			11.3063i			0.407716i	−0.979000	+	0.203858i	$0.934652\pi$
$770$	6.14163	+	2.45738i	0.221329	+	0.0885577i
$771$	41.7351			1.50305
$772$	3.80638	−	3.70588i	0.136994	−	0.133377i
$773$	−17.9809	+	10.3813i	−0.646729	+	0.373389i	−0.787202	−	0.616695i	$-0.788471\pi$
$773$	−17.9809	+	10.3813i	−0.646729	+	0.373389i	0.140473	+	0.990085i	$0.455138\pi$
$774$	−1.15594	+	2.73873i	−0.0415494	+	0.0984416i
$775$	25.9072	+	12.4339i	0.930615	+	0.446641i
$776$	13.4542	+	34.4188i	0.482976	+	1.23556i
$777$	−22.1864	+	5.48860i	−0.795934	+	0.196902i
$778$	4.90706	+	6.48436i	0.175927	+	0.232475i
$779$	−4.21370	+	7.29834i	−0.150971	+	0.261490i
$780$	44.8056	+	24.4142i	1.60430	+	0.874169i
$781$	3.01856	−	1.74277i	0.108013	−	0.0623611i
$782$	−0.970620	−	7.77405i	−0.0347093	−	0.278000i
$783$		−	13.2438i		−	0.473295i
$784$	15.5530	−	23.2832i	0.555463	−	0.831541i
$785$	15.4527	+	14.3190i	0.551532	+	0.511067i
$786$	36.2426	−	4.52503i	1.29273	−	0.161402i
$787$	−1.98158	−	3.43220i	−0.0706357	−	0.122345i	0.828544	−	0.559923i	$-0.189169\pi$
$787$	−1.98158	−	3.43220i	−0.0706357	−	0.122345i	−0.899180	+	0.437579i	$0.855836\pi$
$788$	19.3268	−	4.90246i	0.688487	−	0.174643i
$789$	−23.5995	+	40.8756i	−0.840165	+	1.45521i
$790$	19.0781	+	1.90505i	0.678769	+	0.0677786i
$791$	2.74770	+	11.1070i	0.0976969	+	0.394918i
$792$	−0.179668	−	0.459633i	−0.00638424	−	0.0163323i
$793$	69.6954	+	40.2386i	2.47496	+	1.42892i
$794$	2.54009	−	6.01814i	0.0901443	−	0.213576i
$795$	−23.3920	−	5.32276i	−0.829630	−	0.188779i
$796$	−1.04350	−	1.07180i	−0.0369858	−	0.0379889i
$797$			21.7688i			0.771090i	0.922689	+	0.385545i	$0.125987\pi$
$797$			21.7688i			0.771090i	−0.922689	+	0.385545i	$0.874013\pi$
$798$	−13.2247	+	5.07965i	−0.468150	+	0.179818i
$799$			0.625448i			0.0221268i
$800$	26.5693	+	9.69904i	0.939367	+	0.342913i
$801$	−2.17751	+	1.25719i	−0.0769385	+	0.0444205i
$802$	−21.6133	−	9.12238i	−0.763194	−	0.322123i
$803$	2.51710	−	4.35974i	0.0888265	−	0.153852i
$804$	10.5017	+	2.96504i	0.370366	+	0.104569i
$805$	−11.1982	+	0.210327i	−0.394685	+	0.00741306i
$806$	−33.5673	−	44.3570i	−1.18236	−	1.56241i
$807$	−3.07823	+	5.33165i	−0.108359	+	0.187683i
$808$	−18.2531	+	22.8246i	−0.642140	+	0.802966i
$809$	13.0987	+	22.6876i	0.460525	+	0.797652i	0.998987	−	0.0449975i	$-0.0143280\pi$
$809$	13.0987	+	22.6876i	0.460525	+	0.797652i	−0.538462	+	0.842649i	$0.680995\pi$
$810$	21.2865	+	15.2972i	0.747930	+	0.537489i
$811$			35.2550i			1.23797i	0.785403	+	0.618985i	$0.212456\pi$
$811$			35.2550i			1.23797i	−0.785403	+	0.618985i	$0.787544\pi$
$812$	−6.15338	−	11.5104i	−0.215941	−	0.403935i
$813$	−1.27696			−0.0447850
$814$	0.717806	+	5.74917i	0.0251591	+	0.201508i
$815$	2.40581	−	10.5729i	0.0842719	−	0.370351i
$816$	−0.522010	+	19.5063i	−0.0182740	+	0.682856i
$817$	10.8163	−	18.7344i	0.378414	−	0.655432i
$818$	−13.9375	−	18.4174i	−0.487312	−	0.643950i
$819$	−3.83907	−	1.10844i	−0.134148	−	0.0387321i
$820$	14.1623	−	8.64962i	0.494571	−	0.302058i
$821$	15.6779	+	9.05167i	0.547164	+	0.315905i	0.747977	−	0.663724i	$-0.231025\pi$
$821$	15.6779	+	9.05167i	0.547164	+	0.315905i	−0.200813	+	0.979630i	$0.564358\pi$
$822$	−13.2763	+	31.4550i	−0.463063	+	1.09712i
$823$	5.91819	+	10.2506i	0.206295	+	0.357314i	0.950545	−	0.310588i	$-0.100526\pi$
$823$	5.91819	+	10.2506i	0.206295	+	0.357314i	−0.744249	+	0.667902i	$0.767193\pi$
$824$	8.44771	−	55.5320i	0.294290	−	1.93455i
$825$	0.501229	+	6.57145i	0.0174506	+	0.228788i
$826$	1.44736	+	1.17155i	0.0503602	+	0.0407635i
$827$			36.3034i			1.26239i	0.775623	+	0.631196i	$0.217436\pi$
$827$			36.3034i			1.26239i	−0.775623	+	0.631196i	$0.782564\pi$
$828$	0.582880	+	0.598688i	0.0202565	+	0.0208058i
$829$	12.1073	+	20.9704i	0.420502	+	0.728331i	0.995989	−	0.0894800i	$-0.0285205\pi$
$829$	12.1073	+	20.9704i	0.420502	+	0.728331i	−0.575486	+	0.817811i	$0.695187\pi$
$830$	−39.0333	+	17.6223i	−1.35487	+	0.611678i
$831$	16.2236	−	28.1002i	0.562792	−	0.974784i
$832$	−37.1304	−	40.2370i	−1.28726	−	1.39497i
$833$	17.3309	+	10.9180i	0.600481	+	0.378285i
$834$	15.6053	+	20.6214i	0.540368	+	0.714060i
$835$	22.4952	−	6.95520i	0.778480	−	0.240695i
$836$	0.883001	+	3.48102i	0.0305392	+	0.120394i
$837$	−15.4295	−	26.7246i	−0.533320	−	0.923738i
$838$	−35.8014	+	4.46993i	−1.23674	+	0.154411i
$839$	−9.71534			−0.335411			−0.167705	−	0.985837i	$-0.553636\pi$
$839$	−9.71534			−0.335411			−0.167705	+	0.985837i	$0.553636\pi$
$840$	27.6530	+	3.67678i	0.954121	+	0.126861i
$841$	22.9160			0.790206
$842$	−7.94108	+	0.991474i	−0.273668	+	0.0341685i
$843$	−6.00205	−	10.3959i	−0.206722	−	0.358052i
$844$	25.3518	−	6.43077i	0.872644	−	0.221356i
$845$	−22.3508	−	72.2892i	−0.768891	−	2.48682i
$846$	−0.0402534	−	0.0531922i	−0.00138394	−	0.00182879i
$847$	−7.61434	+	26.3721i	−0.261632	+	0.906157i
$848$	21.9406	+	13.4626i	0.753442	+	0.462306i
$849$	−9.85907	+	17.0764i	−0.338362	+	0.586061i
$850$	−6.57278	+	19.6195i	−0.225444	+	0.672942i
$851$	−4.90488	−	8.49551i	−0.168137	−	0.291222i
$852$	10.5318	−	10.2538i	0.360815	−	0.351289i
$853$			30.1601i			1.03266i	0.856389	+	0.516331i	$0.172703\pi$
$853$			30.1601i			1.03266i	−0.856389	+	0.516331i	$0.827297\pi$
$854$	43.4579	+	6.87379i	1.48710	+	0.235216i
$855$	0.822024	+	0.761713i	0.0281126	+	0.0260500i
$856$	−6.85663	+	45.0729i	−0.234355	+	1.54056i
$857$	−13.3793	−	23.1737i	−0.457029	−	0.791597i	0.541774	−	0.840524i	$-0.317753\pi$
$857$	−13.3793	−	23.1737i	−0.457029	−	0.791597i	−0.998802	+	0.0489275i	$0.984420\pi$
$858$	4.96084	−	11.7535i	0.169360	−	0.401259i
$859$	24.3388	+	14.0520i	0.830428	+	0.479448i	0.853999	−	0.520274i	$-0.174170\pi$
$859$	24.3388	+	14.0520i	0.830428	+	0.479448i	−0.0235714	+	0.999722i	$0.507504\pi$
$860$	−36.3538	+	22.2030i	−1.23965	+	0.757116i
$861$	11.7944	−	11.3481i	0.401952	−	0.386742i
$862$	−8.03573	−	10.6187i	−0.273698	−	0.361673i
$863$	−21.9016	+	37.9347i	−0.745539	+	1.29131i	0.204404	+	0.978887i	$0.434474\pi$
$863$	−21.9016	+	37.9347i	−0.745539	+	1.29131i	−0.949943	+	0.312424i	$0.898859\pi$
$864$	−17.6740	−	24.7015i	−0.601282	−	0.840363i
$865$	5.75625	−	25.2971i	0.195718	−	0.860127i
$866$	−0.419383	−	3.35900i	−0.0142512	−	0.114143i
$867$	14.0664			0.477720
$868$	−25.8269	−	16.0579i	−0.876621	−	0.545039i
$869$		−	4.79371i		−	0.162615i
$870$	7.58860	−	10.5597i	0.257278	−	0.358008i
$871$	−11.1992	−	19.3976i	−0.379470	−	0.657262i
$872$	32.7665	+	26.2038i	1.10962	+	0.887371i
$873$	1.44165	−	2.49701i	0.0487924	−	0.0845110i
$874$	−3.66925	−	4.84867i	−0.124114	−	0.164009i
$875$	26.9037	+	12.2960i	0.909510	+	0.415682i
$876$	5.76853	−	20.4312i	0.194900	−	0.690306i
$877$	−17.7221	+	30.6955i	−0.598431	+	1.03651i	0.394622	+	0.918844i	$0.370876\pi$
$877$	−17.7221	+	30.6955i	−0.598431	+	1.03651i	−0.993053	+	0.117670i	$0.962458\pi$
$878$	46.3156	+	19.5485i	1.56308	+	0.659730i
$879$	−17.1613	+	9.90808i	−0.578836	+	0.334191i
$880$	1.75294	−	6.85104i	0.0590916	−	0.230948i
$881$		−	11.0583i		−	0.372564i	−0.982496	−	0.186282i	$-0.940356\pi$
$881$		−	11.0583i		−	0.372564i	0.982496	−	0.186282i	$-0.0596438\pi$
$882$	−2.17661	+	0.186872i	−0.0732901	+	0.00629230i
$883$		−	18.2084i		−	0.612760i	−0.951909	−	0.306380i	$-0.900882\pi$
$883$		−	18.2084i		−	0.612760i	0.951909	−	0.306380i	$-0.0991178\pi$
$884$	28.6979	−	27.9402i	0.965215	−	0.939731i
$885$	−0.411622	+	1.80896i	−0.0138365	+	0.0608077i
$886$	−6.69638	+	15.8655i	−0.224969	+	0.533012i
$887$	24.4553	+	14.1193i	0.821128	+	0.474078i	0.850805	−	0.525481i	$-0.176115\pi$
$887$	24.4553	+	14.1193i	0.821128	+	0.474078i	−0.0296774	+	0.999560i	$0.509448\pi$
$888$	8.89541	+	22.7565i	0.298510	+	0.763658i
$889$	−11.9956	+	2.96752i	−0.402318	+	0.0995276i
$890$	−35.8520	−	3.58001i	−1.20176	−	0.120002i
$891$	3.27693	−	5.67581i	0.109781	−	0.190147i
$892$	2.01414	+	7.94025i	0.0674383	+	0.265859i
$893$	0.242715	+	0.420395i	0.00812216	+	0.0140680i
$894$	34.5222	−	4.31023i	1.15460	−	0.144156i
$895$	−29.5007	+	31.8365i	−0.986100	+	1.06418i
$896$	−26.8377	−	13.2567i	−0.896583	−	0.442875i
$897$			21.6005i			0.721218i
$898$	−0.990253	−	7.93131i	−0.0330452	−	0.264671i
$899$	−12.2769	+	7.08810i	−0.409459	+	0.236401i
$900$	−0.703704	−	2.09159i	−0.0234568	−	0.0697196i
$901$	−9.41555	+	16.3082i	−0.313677	+	0.543305i
$902$	−2.50374	−	3.30852i	−0.0833653	−	0.110162i
$903$	−30.2754	+	29.1298i	−1.00750	+	0.969379i
$904$	11.3923	−	4.45321i	0.378903	−	0.148112i
$905$	−11.0972	−	35.8916i	−0.368882	−	1.19308i
$906$	14.4798	−	34.3064i	0.481059	−	1.13976i
$907$	28.3649	−	16.3765i	0.941840	−	0.543771i	0.0513031	−	0.998683i	$-0.483663\pi$
$907$	28.3649	−	16.3765i	0.941840	−	0.543771i	0.890536	+	0.454912i	$0.150329\pi$
$908$	−13.7792	−	14.1529i	−0.457279	−	0.469680i
$909$	2.28024			0.0756307
$910$	−35.4044	−	45.0026i	−1.17364	−	1.49182i
$911$			6.20517i			0.205587i	0.994703	+	0.102793i	$0.0327780\pi$
$911$			6.20517i			0.205587i	−0.994703	+	0.102793i	$0.967222\pi$
$912$	7.21885	+	13.3137i	0.239040	+	0.440861i
$913$	5.35387	+	9.27318i	0.177187	+	0.306897i
$914$	−11.3149	+	26.8080i	−0.374263	+	0.886729i
$915$	12.9485	+	41.8794i	0.428064	+	1.38449i
$916$	1.82506	−	6.46408i	0.0603018	−	0.213579i
$917$	−39.3782	−	11.3695i	−1.30038	−	0.375456i
$918$	17.7179	−	13.4081i	0.584778	−	0.442533i
$919$	42.5171	+	24.5473i	1.40251	+	0.809740i	0.994650	−	0.103304i	$-0.0329415\pi$
$919$	42.5171	+	24.5473i	1.40251	+	0.809740i	0.407861	+	0.913044i	$0.366275\pi$
$920$	1.77624	+	11.8410i	0.0585607	+	0.390387i
$921$	−15.2950	−	26.4918i	−0.503988	−	0.872934i
$922$	0.183245	+	1.46768i	0.00603485	+	0.0483353i
$923$	−30.1710			−0.993091
$924$	0.227759	−	6.97105i	0.00749273	−	0.229331i
$925$	1.97039	+	25.8332i	0.0647862	+	0.849390i
$926$	2.68989	+	21.5444i	0.0883954	+	0.707991i
$927$	−3.79541	+	2.19128i	−0.124658	+	0.0719711i
$928$	−11.3476	+	8.11922i	−0.372502	+	0.266526i
$929$	16.5181	+	9.53671i	0.541940	+	0.312889i	0.745865	−	0.666097i	$-0.232036\pi$
$929$	16.5181	+	9.53671i	0.541940	+	0.312889i	−0.203925	+	0.978987i	$0.565370\pi$
$930$	3.01057	−	30.1494i	0.0987206	−	0.988638i
$931$	15.8859	+	0.612964i	0.520639	+	0.0200891i
$932$	38.2486	+	10.7991i	1.25288	+	0.353736i
$933$	6.42915	−	11.1356i	0.210481	−	0.364564i
$934$	−20.9061	−	8.82387i	−0.684068	−	0.288726i
$935$	5.04435	+	1.14782i	0.164968	+	0.0375377i
$936$	−0.642446	+	4.22319i	−0.0209990	+	0.138039i
$937$	−4.46637			−0.145910			−0.0729549	−	0.997335i	$-0.523243\pi$
$937$	−4.46637			−0.145910			−0.0729549	+	0.997335i	$0.523243\pi$
$938$	−9.51819	−	7.70440i	−0.310780	−	0.251557i
$939$	−28.6325			−0.934388
$940$	−0.0235944	−	0.955595i	−0.000769565	−	0.0311681i
$941$	12.8629	+	22.2793i	0.419320	+	0.726283i	0.995871	−	0.0907779i	$-0.0289353\pi$
$941$	12.8629	+	22.2793i	0.419320	+	0.726283i	−0.576552	+	0.817061i	$0.695602\pi$
$942$	8.63754	−	20.4646i	0.281426	−	0.666774i
$943$	6.08386	+	3.51252i	0.198118	+	0.114383i
$944$	1.04109	−	1.69672i	0.0338847	−	0.0552235i
$945$	−16.3964	−	27.2063i	−0.533374	−	0.885021i
$946$	6.42693	+	8.49276i	0.208957	+	0.276123i
$947$	14.4410	+	8.33751i	0.469269	+	0.270933i	0.715934	−	0.698168i	$-0.246001\pi$
$947$	14.4410	+	8.33751i	0.469269	+	0.270933i	−0.246665	+	0.969101i	$0.579335\pi$
$948$	−4.97054	−	19.5951i	−0.161435	−	0.636420i
$949$	−37.7383	+	21.7882i	−1.22504	+	0.707275i
$950$	3.19576	+	15.7379i	0.103684	+	0.510605i
$951$	−32.5874			−1.05672
$952$	9.16917	−	19.8853i	0.297175	−	0.644487i
$953$			13.1368i			0.425544i	0.977102	+	0.212772i	$0.0682492\pi$
$953$			13.1368i			0.425544i	−0.977102	+	0.212772i	$0.931751\pi$
$954$	−0.248825	−	1.99293i	−0.00805602	−	0.0645236i
$955$	5.49246	−	24.1378i	0.177732	−	0.781081i
$956$	3.31675	+	13.0755i	0.107271	+	0.422891i
$957$	−2.81564	−	1.62561i	−0.0910167	−	0.0525485i
$958$	23.8359	−	18.0379i	0.770102	−	0.582778i
$959$	27.6092	−	26.5644i	0.891547	−	0.857809i
$960$	0.0617014	−	29.8225i	0.00199140	−	0.962516i
$961$	−1.01574	+	1.75931i	−0.0327657	+	0.0567519i
$962$	19.5017	−	46.2047i	0.628760	−	1.48970i
$963$	3.08057	−	1.77857i	0.0992699	−	0.0573135i
$964$	1.95839	−	1.90669i	0.0630756	−	0.0614102i
$965$	−4.35663	−	4.03699i	−0.140245	−	0.129955i
$966$	4.23437	+	11.0241i	0.136239	+	0.354693i
$967$	34.0366			1.09454			0.547272	−	0.836955i	$-0.315666\pi$
$967$	34.0366			1.09454			0.547272	+	0.836955i	$0.315666\pi$
$968$	29.0108	+	4.41322i	0.932444	+	0.141846i
$969$	−9.59481	+	5.53957i	−0.308230	+	0.177957i
$970$	37.6571	−	17.0009i	1.20910	−	0.545868i
$971$	31.6711	+	18.2853i	1.01637	+	0.586804i	0.913052	−	0.407844i	$-0.133719\pi$
$971$	31.6711	+	18.2853i	1.01637	+	0.586804i	0.103323	+	0.994648i	$0.467052\pi$
$972$	−1.24370	+	4.40498i	−0.0398917	+	0.141290i
$973$	−6.96912	−	28.1711i	−0.223420	−	0.903124i
$974$	−19.1629	+	14.5016i	−0.614018	+	0.464661i
$975$	24.6841	−	51.4314i	0.790523	−	1.64712i
$976$	1.25829	−	47.0192i	0.0402768	−	1.50505i
$977$	21.9380	−	12.6659i	0.701859	−	0.405218i	−0.106180	−	0.994347i	$-0.533862\pi$
$977$	21.9380	−	12.6659i	0.701859	−	0.405218i	0.808039	+	0.589128i	$0.200529\pi$
$978$	−11.3448	+	1.41644i	−0.362765	+	0.0452926i
$979$			9.00843i			0.287911i
$980$	−26.8910	−	16.0273i	−0.859002	−	0.511972i
$981$		−	3.27347i		−	0.104514i
$982$	−2.38794	−	19.1259i	−0.0762022	−	0.610332i
$983$	39.3227	−	22.7030i	1.25420	−	0.724113i	0.282259	−	0.959338i	$-0.408916\pi$
$983$	39.3227	−	22.7030i	1.25420	−	0.724113i	0.971941	+	0.235225i	$0.0755828\pi$
$984$	−13.6650	−	10.9281i	−0.435626	−	0.348375i
$985$	−6.58490	−	21.2976i	−0.209812	−	0.678597i
$986$	−6.15951	−	8.13938i	−0.196159	−	0.259211i
$987$	−0.226404	−	0.915190i	−0.00720653	−	0.0291308i
$988$	8.44667	−	29.9167i	0.268724	−	0.951778i
$989$	−15.6169	−	9.01640i	−0.496587	−	0.286705i
$990$	−0.502877	+	0.227033i	−0.0159825	+	0.00721557i
$991$	−13.6639	+	7.88884i	−0.434047	+	0.250597i	−0.701069	−	0.713093i	$-0.747294\pi$
$991$	−13.6639	+	7.88884i	−0.434047	+	0.250597i	0.267022	+	0.963690i	$0.413960\pi$
$992$	−13.4391	+	29.6040i	−0.426691	+	0.939929i
$993$	−3.61677			−0.114775
$994$	−15.3982	+	5.91447i	−0.488400	+	0.187596i
$995$	−1.13673	+	1.22674i	−0.0360369	+	0.0388902i
$996$	31.5002	+	32.3544i	0.998121	+	1.02519i
$997$	−1.31350	+	0.758348i	−0.0415989	+	0.0240171i	−0.520655	−	0.853767i	$-0.674312\pi$
$997$	−1.31350	+	0.758348i	−0.0415989	+	0.0240171i	0.479056	+	0.877784i	$0.340979\pi$
$998$	19.4608	+	8.21385i	0.616020	+	0.260005i
$999$	13.9109	−	24.0943i	0.440121	−	0.762311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.ba.b.19.19	yes	80
4.3	odd	2		1120.2.bq.b.719.11		80
5.4	even	2	inner	280.2.ba.b.19.22	yes	80
7.3	odd	6	inner	280.2.ba.b.59.35	yes	80
8.3	odd	2	inner	280.2.ba.b.19.6	✓	80
8.5	even	2		1120.2.bq.b.719.12		80
20.19	odd	2		1120.2.bq.b.719.29		80
28.3	even	6		1120.2.bq.b.1039.30		80
35.24	odd	6	inner	280.2.ba.b.59.6	yes	80
40.19	odd	2	inner	280.2.ba.b.19.35	yes	80
40.29	even	2		1120.2.bq.b.719.30		80
56.3	even	6	inner	280.2.ba.b.59.22	yes	80
56.45	odd	6		1120.2.bq.b.1039.29		80
140.59	even	6		1120.2.bq.b.1039.12		80
280.59	even	6	inner	280.2.ba.b.59.19	yes	80
280.269	odd	6		1120.2.bq.b.1039.11		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.6	✓	80	8.3	odd	2	inner
280.2.ba.b.19.19	yes	80	1.1	even	1	trivial
280.2.ba.b.19.22	yes	80	5.4	even	2	inner
280.2.ba.b.19.35	yes	80	40.19	odd	2	inner
280.2.ba.b.59.6	yes	80	35.24	odd	6	inner
280.2.ba.b.59.19	yes	80	280.59	even	6	inner
280.2.ba.b.59.22	yes	80	56.3	even	6	inner
280.2.ba.b.59.35	yes	80	7.3	odd	6	inner
1120.2.bq.b.719.11		80	4.3	odd	2
1120.2.bq.b.719.12		80	8.5	even	2
1120.2.bq.b.719.29		80	20.19	odd	2
1120.2.bq.b.719.30		80	40.29	even	2
1120.2.bq.b.1039.11		80	280.269	odd	6
1120.2.bq.b.1039.12		80	140.59	even	6
1120.2.bq.b.1039.29		80	56.45	odd	6
1120.2.bq.b.1039.30		80	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.175210 - 1.40332i) q^{2} +(0.833565 + 1.44378i) q^{3} +(-1.93860 + 0.491749i) q^{4} +(0.660510 + 2.13629i) q^{5} +(1.88003 - 1.42272i) q^{6} +(-2.56833 + 0.635367i) q^{7} +(1.02974 + 2.63432i) q^{8} +(0.110340 - 0.191114i) q^{9} +O(q^{10})\)	\(q+(-0.175210 - 1.40332i) q^{2} +(0.833565 + 1.44378i) q^{3} +(-1.93860 + 0.491749i) q^{4} +(0.660510 + 2.13629i) q^{5} +(1.88003 - 1.42272i) q^{6} +(-2.56833 + 0.635367i) q^{7} +(1.02974 + 2.63432i) q^{8} +(0.110340 - 0.191114i) q^{9} +(2.88216 - 1.30120i) q^{10} +(-0.395322 - 0.684718i) q^{11} +(-2.32593 - 2.38900i) q^{12} +6.84388i q^{13} +(1.34162 + 3.49286i) q^{14} +(-2.53375 + 2.73436i) q^{15} +(3.51636 - 1.90661i) q^{16} +(1.46309 + 2.53414i) q^{17} +(-0.287526 - 0.121357i) q^{18} +(1.96683 + 1.13555i) q^{19} +(-2.33098 - 3.81661i) q^{20} +(-3.05820 - 3.17847i) q^{21} +(-0.891613 + 0.674732i) q^{22} +(0.946588 - 1.63954i) q^{23} +(-2.94501 + 3.68259i) q^{24} +(-4.12745 + 2.82208i) q^{25} +(9.60414 - 1.19911i) q^{26} +5.36929 q^{27} +(4.66653 - 2.49470i) q^{28} -2.46658i q^{29} +(4.28112 + 3.07656i) q^{30} +(-2.87365 - 4.97731i) q^{31} +(-3.29169 - 4.60052i) q^{32} +(0.659054 - 1.14151i) q^{33} +(3.29986 - 2.49718i) q^{34} +(-3.05373 - 5.06702i) q^{35} +(-0.119925 + 0.424753i) q^{36} +(2.59082 - 4.48744i) q^{37} +(1.24893 - 2.95905i) q^{38} +(-9.88103 + 5.70482i) q^{39} +(-4.94751 + 3.93982i) q^{40} +3.71071i q^{41} +(-3.92458 + 4.84852i) q^{42} -9.52516i q^{43} +(1.10308 + 1.13300i) q^{44} +(0.481155 + 0.109485i) q^{45} +(-2.46665 - 1.04110i) q^{46} +(0.185107 + 0.106871i) q^{47} +(5.68384 + 3.48756i) q^{48} +(6.19262 - 3.26366i) q^{49} +(4.68344 + 5.29768i) q^{50} +(-2.43916 + 4.22474i) q^{51} +(-3.36547 - 13.2676i) q^{52} +(3.21770 + 5.57322i) q^{53} +(-0.940751 - 7.53482i) q^{54} +(1.20164 - 1.29679i) q^{55} +(-4.31847 - 6.11153i) q^{56} +3.78622i q^{57} +(-3.46140 + 0.432169i) q^{58} +(0.430991 - 0.248833i) q^{59} +(3.56730 - 6.54681i) q^{60} +(5.87951 - 10.1836i) q^{61} +(-6.48126 + 4.90472i) q^{62} +(-0.161961 + 0.560949i) q^{63} +(-5.87926 + 5.42534i) q^{64} +(-14.6205 + 4.52045i) q^{65} +(-1.71738 - 0.724858i) q^{66} +(-2.83429 + 1.63638i) q^{67} +(-4.08251 - 4.19322i) q^{68} +3.15617 q^{69} +(-6.57560 + 5.17315i) q^{70} +4.40847i q^{71} +(0.617076 + 0.0938716i) q^{72} +(3.18360 + 5.51416i) q^{73} +(-6.75124 - 2.84951i) q^{74} +(-7.51495 - 3.60674i) q^{75} +(-4.37131 - 1.23419i) q^{76} +(1.45036 + 1.50741i) q^{77} +(9.73693 + 12.8667i) q^{78} +(5.25074 + 3.03152i) q^{79} +(6.39567 + 6.25263i) q^{80} +(4.14463 + 7.17871i) q^{81} +(5.20731 - 0.650152i) q^{82} -13.5430 q^{83} +(7.49164 + 4.65793i) q^{84} +(-4.44727 + 4.79940i) q^{85} +(-13.3668 + 1.66890i) q^{86} +(3.56120 - 2.05606i) q^{87} +(1.39669 - 1.74649i) q^{88} +(-9.86730 - 5.69689i) q^{89} +(0.0693390 - 0.694396i) q^{90} +(-4.34837 - 17.5773i) q^{91} +(-1.02882 + 3.64390i) q^{92} +(4.79075 - 8.29782i) q^{93} +(0.117542 - 0.278488i) q^{94} +(-1.12675 + 4.95176i) q^{95} +(3.89829 - 8.58729i) q^{96} +13.0656 q^{97} +(-5.66496 - 8.11839i) q^{98} -0.174479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) \) 80 * q + 6 * q^4 - 52 * q^9	\( 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) \) 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

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