LMFDB - Embedded newform 80.2.j.b.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(43,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$1.41323 + 0.0526497i$ of defining polynomial
Character	$\chi$	$=$	80.43
Dual form			80.2.j.b.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31641 + 0.516777i) q^{2} +1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.841703 + 2.07160i) q^{5} +(-0.662041 - 1.68645i) q^{6} +(-1.13975 + 1.13975i) q^{7} +(-1.22659 + 2.54862i) q^{8} +1.35879 q^{9} +O(q^{10})$	\(q+(-1.31641 + 0.516777i) q^{2} +1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.841703 + 2.07160i) q^{5} +(-0.662041 - 1.68645i) q^{6} +(-1.13975 + 1.13975i) q^{7} +(-1.22659 + 2.54862i) q^{8} +1.35879 q^{9} +(0.0374711 - 3.16206i) q^{10} +(-2.32204 + 2.32204i) q^{11} +(1.74304 + 1.87794i) q^{12} +1.36502 q^{13} +(0.911384 - 2.08938i) q^{14} +(-2.65392 - 1.07830i) q^{15} +(0.297625 - 3.98891i) q^{16} +(5.25380 - 5.25380i) q^{17} +(-1.78873 + 0.702192i) q^{18} +(3.69752 - 3.69752i) q^{19} +(1.58475 + 4.18193i) q^{20} +(-1.46013 - 1.46013i) q^{21} +(1.85678 - 4.25673i) q^{22} +(-0.911118 - 0.911118i) q^{23} +(-3.26503 - 1.57138i) q^{24} +(-3.58307 - 3.48735i) q^{25} +(-1.79693 + 0.705412i) q^{26} +5.58403i q^{27} +(-0.120015 + 3.22146i) q^{28} +(2.37343 + 2.37343i) q^{29} +(4.05090 + 0.0480041i) q^{30} +0.242577i q^{31} +(1.66958 + 5.40486i) q^{32} +(-2.97475 - 2.97475i) q^{33} +(-4.20112 + 9.63121i) q^{34} +(-1.40178 - 3.32044i) q^{35} +(1.99183 - 1.84875i) q^{36} -3.34494 q^{37} +(-2.95666 + 6.77825i) q^{38} +1.74872i q^{39} +(-4.24731 - 4.68619i) q^{40} +2.66956i q^{41} +(2.67669 + 1.16757i) q^{42} +9.04874 q^{43} +(-0.244509 + 6.56316i) q^{44} +(-1.14370 + 2.81488i) q^{45} +(1.67025 + 0.728562i) q^{46} +(-7.87820 - 7.87820i) q^{47} +(5.11018 + 0.381287i) q^{48} +4.40194i q^{49} +(6.51898 + 2.73914i) q^{50} +(6.73063 + 6.73063i) q^{51} +(2.00096 - 1.85723i) q^{52} -5.80113i q^{53} +(-2.88570 - 7.35089i) q^{54} +(-2.85587 - 6.76480i) q^{55} +(-1.50679 - 4.30279i) q^{56} +(4.73688 + 4.73688i) q^{57} +(-4.35095 - 1.89788i) q^{58} +(-5.91474 - 5.91474i) q^{59} +(-5.35746 + 2.03022i) q^{60} +(-6.67404 + 6.67404i) q^{61} +(-0.125358 - 0.319332i) q^{62} +(-1.54868 + 1.54868i) q^{63} +(-4.99096 - 6.25222i) q^{64} +(-1.14894 + 2.82778i) q^{65} +(5.45328 + 2.37872i) q^{66} -4.54673 q^{67} +(0.553222 - 14.8497i) q^{68} +(1.16723 - 1.16723i) q^{69} +(3.56124 + 3.64666i) q^{70} +15.4389 q^{71} +(-1.66668 + 3.46305i) q^{72} +(1.49307 - 1.49307i) q^{73} +(4.40332 - 1.72859i) q^{74} +(4.46763 - 4.59026i) q^{75} +(0.389347 - 10.4509i) q^{76} -5.29308i q^{77} +(-0.903701 - 2.30204i) q^{78} +10.3024 q^{79} +(8.01293 + 3.97404i) q^{80} -3.07731 q^{81} +(-1.37957 - 3.51424i) q^{82} +3.26589i q^{83} +(-4.12701 - 0.153751i) q^{84} +(6.46165 + 15.3059i) q^{85} +(-11.9119 + 4.67618i) q^{86} +(-3.04060 + 3.04060i) q^{87} +(-3.06981 - 8.76618i) q^{88} -9.77206 q^{89} +(0.0509154 - 4.29657i) q^{90} +(-1.55578 + 1.55578i) q^{91} +(-2.57524 - 0.0959403i) q^{92} -0.310765 q^{93} +(14.4422 + 6.29969i) q^{94} +(4.54758 + 10.7720i) q^{95} +(-6.92415 + 2.13889i) q^{96} +(-1.63587 + 1.63587i) q^{97} +(-2.27482 - 5.79477i) q^{98} +(-3.15516 + 3.15516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	$ 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) $ 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.31641	+	0.516777i	−0.930844	+	0.365417i
$2$	−1.31641	+	0.516777i	−0.930844	+	0.365417i
$3$			1.28110i			0.739642i	0.929103	+	0.369821i	$0.120581\pi$
$3$			1.28110i			0.739642i	−0.929103	+	0.369821i	$0.879419\pi$
$4$	1.46588	−	1.36058i	0.732941	−	0.680292i
$5$	−0.841703	+	2.07160i	−0.376421	+	0.926449i
$5$	−0.841703	+	2.07160i	−0.376421	+	0.926449i
$6$	−0.662041	−	1.68645i	−0.270277	−	0.688491i
$7$	−1.13975	+	1.13975i	−0.430785	+	0.430785i	−0.888895	−	0.458111i	$-0.848526\pi$
$7$	−1.13975	+	1.13975i	−0.430785	+	0.430785i	0.458111	+	0.888895i	$0.348526\pi$
$8$	−1.22659	+	2.54862i	−0.433664	+	0.901074i
$9$	1.35879			0.452930
$10$	0.0374711	−	3.16206i	0.0118494	−	0.999930i
$11$	−2.32204	+	2.32204i	−0.700120	+	0.700120i	−0.964436	−	0.264316i	$-0.914854\pi$
$11$	−2.32204	+	2.32204i	−0.700120	+	0.700120i	0.264316	+	0.964436i	$0.414854\pi$
$12$	1.74304	+	1.87794i	0.503172	+	0.542114i
$13$	1.36502			0.378589			0.189294	−	0.981920i	$-0.439380\pi$
$13$	1.36502			0.378589			0.189294	+	0.981920i	$0.439380\pi$
$14$	0.911384	−	2.08938i	0.243578	−	0.558409i
$15$	−2.65392	−	1.07830i	−0.685240	−	0.278416i
$16$	0.297625	−	3.98891i	0.0744064	−	0.997228i
$17$	5.25380	−	5.25380i	1.27423	−	1.27423i	0.330389	−	0.943845i	$-0.392820\pi$
$17$	5.25380	−	5.25380i	1.27423	−	1.27423i	0.943845	−	0.330389i	$-0.107180\pi$
$18$	−1.78873	+	0.702192i	−0.421608	+	0.165508i
$19$	3.69752	−	3.69752i	0.848269	−	0.848269i	−0.141648	−	0.989917i	$-0.545240\pi$
$19$	3.69752	−	3.69752i	0.848269	−	0.848269i	0.989917	+	0.141648i	$0.0452403\pi$
$20$	1.58475	+	4.18193i	0.354361	+	0.935109i
$21$	−1.46013	−	1.46013i	−0.318626	−	0.318626i
$22$	1.85678	−	4.25673i	0.395867	−	0.907538i
$23$	−0.911118	−	0.911118i	−0.189981	−	0.189981i	0.605707	−	0.795688i	$-0.292890\pi$
$23$	−0.911118	−	0.911118i	−0.189981	−	0.189981i	−0.795688	+	0.605707i	$0.792890\pi$
$24$	−3.26503	−	1.57138i	−0.666472	−	0.320756i
$25$	−3.58307	−	3.48735i	−0.716615	−	0.697469i
$26$	−1.79693	+	0.705412i	−0.352407	+	0.138343i
$27$			5.58403i			1.07465i
$28$	−0.120015	+	3.22146i	−0.0226807	+	0.608799i
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	0.892259	−	0.451524i	$-0.149119\pi$
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	−0.451524	+	0.892259i	$0.649119\pi$
$30$	4.05090	+	0.0480041i	0.739590	+	0.00876431i
$31$			0.242577i			0.0435681i	0.999763	+	0.0217841i	$0.00693463\pi$
$31$			0.242577i			0.0435681i	−0.999763	+	0.0217841i	$0.993065\pi$
$32$	1.66958	+	5.40486i	0.295143	+	0.955453i
$33$	−2.97475	−	2.97475i	−0.517838	−	0.517838i
$34$	−4.20112	+	9.63121i	−0.720487	+	1.65174i
$35$	−1.40178	−	3.32044i	−0.236944	−	0.561256i
$36$	1.99183	−	1.84875i	0.331971	−	0.308125i
$37$	−3.34494			−0.549905			−0.274953	−	0.961458i	$-0.588662\pi$
$37$	−3.34494			−0.549905			−0.274953	+	0.961458i	$0.588662\pi$
$38$	−2.95666	+	6.77825i	−0.479634	+	1.09958i
$39$			1.74872i			0.280020i
$40$	−4.24731	−	4.68619i	−0.671559	−	0.740951i
$41$			2.66956i			0.416915i	0.978031	+	0.208457i	$0.0668442\pi$
$41$			2.66956i			0.416915i	−0.978031	+	0.208457i	$0.933156\pi$
$42$	2.67669	+	1.16757i	0.413023	+	0.180160i
$43$	9.04874			1.37992			0.689960	−	0.723847i	$-0.257628\pi$
$43$	9.04874			1.37992			0.689960	+	0.723847i	$0.257628\pi$
$44$	−0.244509	+	6.56316i	−0.0368611	+	0.989433i
$45$	−1.14370	+	2.81488i	−0.170492	+	0.419617i
$46$	1.67025	+	0.728562i	0.246265	+	0.107421i
$47$	−7.87820	−	7.87820i	−1.14915	−	1.14915i	−0.986719	−	0.162435i	$-0.948065\pi$
$47$	−7.87820	−	7.87820i	−1.14915	−	1.14915i	−0.162435	−	0.986719i	$-0.551935\pi$
$48$	5.11018	+	0.381287i	0.737591	+	0.0550340i
$49$			4.40194i			0.628849i
$50$	6.51898	+	2.73914i	0.921923	+	0.387372i
$51$	6.73063	+	6.73063i	0.942476	+	0.942476i
$52$	2.00096	−	1.85723i	0.277483	−	0.257551i
$53$		−	5.80113i		−	0.796846i	−0.917202	−	0.398423i	$-0.869558\pi$
$53$		−	5.80113i		−	0.796846i	0.917202	−	0.398423i	$-0.130442\pi$
$54$	−2.88570	−	7.35089i	−0.392694	−	1.00033i
$55$	−2.85587	−	6.76480i	−0.385086	−	0.912165i
$56$	−1.50679	−	4.30279i	−0.201353	−	0.574985i
$57$	4.73688	+	4.73688i	0.627415	+	0.627415i
$58$	−4.35095	−	1.89788i	−0.571308	−	0.249204i
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	0.208079	−	0.978112i	$-0.433279\pi$
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	−0.978112	+	0.208079i	$0.933279\pi$
$60$	−5.35746	+	2.03022i	−0.691645	+	0.262100i
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	−0.990686	−	0.136163i	$-0.956523\pi$
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	0.136163	+	0.990686i	$0.456523\pi$
$62$	−0.125358	−	0.319332i	−0.0159205	−	0.0405551i
$63$	−1.54868	+	1.54868i	−0.195116	+	0.195116i
$64$	−4.99096	−	6.25222i	−0.623870	−	0.781528i
$65$	−1.14894	+	2.82778i	−0.142509	+	0.350743i
$66$	5.45328	+	2.37872i	0.671253	+	0.292800i
$67$	−4.54673			−0.555471			−0.277736	−	0.960658i	$-0.589584\pi$
$67$	−4.54673			−0.555471			−0.277736	+	0.960658i	$0.589584\pi$
$68$	0.553222	−	14.8497i	0.0670881	−	1.80079i
$69$	1.16723	−	1.16723i	0.140518	−	0.140518i
$70$	3.56124	+	3.64666i	0.425650	+	0.435859i
$71$	15.4389			1.83226			0.916128	−	0.400885i	$-0.131297\pi$
$71$	15.4389			1.83226			0.916128	+	0.400885i	$0.131297\pi$
$72$	−1.66668	+	3.46305i	−0.196420	+	0.408124i
$73$	1.49307	−	1.49307i	0.174750	−	0.174750i	−0.614313	−	0.789063i	$-0.710567\pi$
$73$	1.49307	−	1.49307i	0.174750	−	0.174750i	0.789063	+	0.614313i	$0.210567\pi$
$74$	4.40332	−	1.72859i	0.511876	−	0.200944i
$75$	4.46763	−	4.59026i	0.515877	−	0.530038i
$76$	0.389347	−	10.4509i	0.0446611	−	1.19880i
$77$		−	5.29308i		−	0.603202i
$78$	−0.903701	−	2.30204i	−0.102324	−	0.260655i
$79$	10.3024			1.15911			0.579556	−	0.814932i	$-0.303226\pi$
$79$	10.3024			1.15911			0.579556	+	0.814932i	$0.303226\pi$
$80$	8.01293	+	3.97404i	0.895873	+	0.444311i
$81$	−3.07731			−0.341924
$82$	−1.37957	−	3.51424i	−0.152348	−	0.388083i
$83$			3.26589i			0.358478i	0.983806	+	0.179239i	$0.0573636\pi$
$83$			3.26589i			0.358478i	−0.983806	+	0.179239i	$0.942636\pi$
$84$	−4.12701	−	0.153751i	−0.450293	−	0.0167756i
$85$	6.46165	+	15.3059i	0.700864	+	1.66016i
$86$	−11.9119	+	4.67618i	−1.28449	+	0.504246i
$87$	−3.04060	+	3.04060i	−0.325986	+	0.325986i
$88$	−3.06981	−	8.76618i	−0.327243	−	0.934477i
$89$	−9.77206			−1.03584			−0.517918	−	0.855430i	$-0.673293\pi$
$89$	−9.77206			−1.03584			−0.517918	+	0.855430i	$0.673293\pi$
$90$	0.0509154	−	4.29657i	0.00536695	−	0.452899i
$91$	−1.55578	+	1.55578i	−0.163090	+	0.163090i
$92$	−2.57524	−	0.0959403i	−0.268488	−	0.0100025i
$93$	−0.310765			−0.0322248
$94$	14.4422	+	6.29969i	1.48960	+	0.649763i
$95$	4.54758	+	10.7720i	0.466571	+	1.10518i
$96$	−6.92415	+	2.13889i	−0.706693	+	0.218300i
$97$	−1.63587	+	1.63587i	−0.166097	+	0.166097i	−0.785262	−	0.619164i	$-0.787472\pi$
$97$	−1.63587	+	1.63587i	−0.166097	+	0.166097i	0.619164	+	0.785262i	$0.287472\pi$
$98$	−2.27482	−	5.79477i	−0.229792	−	0.585360i
$99$	−3.15516	+	3.15516i	−0.317106	+	0.317106i
$100$	−9.99719	−	0.236971i	−0.999719	−	0.0236971i
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	0.294877	−	0.955535i	$-0.404721\pi$
$101$	−6.63953	−	6.63953i	−0.660658	−	0.660658i	−0.955535	+	0.294877i	$0.904721\pi$
$102$	−12.3385	−	5.38205i	−1.22170	−	0.532902i
$103$	1.62219	+	1.62219i	0.159839	+	0.159839i	0.782496	−	0.622656i	$-0.213946\pi$
$103$	1.62219	+	1.62219i	0.159839	+	0.159839i	−0.622656	+	0.782496i	$0.713946\pi$
$104$	−1.67432	+	3.47893i	−0.164180	+	0.341137i
$105$	4.25380	−	1.79581i	0.415129	−	0.175253i
$106$	2.99789	+	7.63667i	0.291181	+	0.741739i
$107$		−	3.65206i		−	0.353058i	−0.984295	−	0.176529i	$-0.943513\pi$
$107$		−	3.65206i		−	0.353058i	0.984295	−	0.176529i	$-0.0564869\pi$
$108$	7.59754	+	8.18554i	0.731074	+	0.787654i
$109$	−5.20757	−	5.20757i	−0.498795	−	0.498795i	0.412268	−	0.911063i	$-0.364737\pi$
$109$	−5.20757	−	5.20757i	−0.498795	−	0.498795i	−0.911063	+	0.412268i	$0.864737\pi$
$110$	7.25540	+	7.42941i	0.691775	+	0.708367i
$111$		−	4.28519i		−	0.406733i
$112$	4.20714	+	4.88558i	0.397537	+	0.461644i
$113$	−4.27905	−	4.27905i	−0.402539	−	0.402539i	0.476588	−	0.879127i	$-0.341873\pi$
$113$	−4.27905	−	4.27905i	−0.402539	−	0.402539i	−0.879127	+	0.476588i	$0.841873\pi$
$114$	−8.68359	−	3.78777i	−0.813293	−	0.354757i
$115$	2.65437	−	1.12058i	0.247521	−	0.104495i
$116$	6.70843	+	0.249921i	0.622862	+	0.0232046i
$117$	1.85478			0.171474
$118$	10.8428	+	4.72963i	0.998164	+	0.435398i
$119$			11.9760i			1.09784i
$120$	6.00346	−	5.44122i	0.548038	−	0.496713i
$121$			0.216302i			0.0196639i
$122$	5.33680	−	12.2348i	0.483171	−	1.10768i
$123$	−3.41996			−0.308367
$124$	0.330046	+	0.355590i	0.0296390	+	0.0319329i
$125$	10.2403	−	4.48739i	0.915918	−	0.401365i
$126$	1.23838	−	2.83903i	0.110324	−	0.252921i
$127$	7.29257	+	7.29257i	0.647111	+	0.647111i	0.952294	−	0.305183i	$-0.0987175\pi$
$127$	7.29257	+	7.29257i	0.647111	+	0.647111i	−0.305183	+	0.952294i	$0.598718\pi$
$128$	9.80117	+	5.65129i	0.866309	+	0.499508i
$129$			11.5923i			1.02065i
$130$	0.0511488	−	4.31627i	0.00448605	−	0.378562i
$131$	−11.9793	−	11.9793i	−1.04664	−	1.04664i	−0.998858	−	0.0477778i	$-0.984786\pi$
$131$	−11.9793	−	11.9793i	−1.04664	−	1.04664i	−0.0477778	−	0.998858i	$-0.515214\pi$
$132$	−8.40804	−	0.313240i	−0.731826	−	0.0272640i
$133$			8.42848i			0.730842i
$134$	5.98537	−	2.34965i	0.517057	−	0.202978i
$135$	−11.5679	−	4.70010i	−0.995606	−	0.404520i
$136$	6.94571	+	19.8342i	0.595590	+	1.70077i
$137$	4.92762	+	4.92762i	0.420995	+	0.420995i	0.885546	−	0.464551i	$-0.153784\pi$
$137$	4.92762	+	4.92762i	0.420995	+	0.420995i	−0.464551	+	0.885546i	$0.653784\pi$
$138$	−0.933359	+	2.13975i	−0.0794528	+	0.182148i
$139$	−10.3015	−	10.3015i	−0.873761	−	0.873761i	0.119119	−	0.992880i	$-0.461993\pi$
$139$	−10.3015	−	10.3015i	−0.873761	−	0.873761i	−0.992880	+	0.119119i	$0.961993\pi$
$140$	−6.57257	−	2.96014i	−0.555484	−	0.250177i
$141$	10.0927	−	10.0927i	0.849962	−	0.849962i
$142$	−20.3239	+	7.97845i	−1.70555	+	0.669537i
$143$	−3.16963	+	3.16963i	−0.265058	+	0.265058i
$144$	0.404411	−	5.42010i	0.0337009	−	0.451675i
$145$	−6.91454	+	2.91909i	−0.574221	+	0.242417i
$146$	−1.19391	+	2.73707i	−0.0988086	+	0.226522i
$147$	−5.63931			−0.465123
$148$	−4.90329	+	4.55107i	−0.403048	+	0.374096i
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.287896	−	0.957662i	$-0.407044\pi$
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.957662	−	0.287896i	$-0.0929557\pi$
$150$	−3.50910	+	8.35145i	−0.286517	+	0.681893i
$151$	−10.7055			−0.871204			−0.435602	−	0.900139i	$-0.643464\pi$
$151$	−10.7055			−0.871204			−0.435602	+	0.900139i	$0.643464\pi$
$152$	4.88825	+	13.9589i	0.396489	+	1.13222i
$153$	7.13882	−	7.13882i	0.577139	−	0.577139i
$154$	2.73534	+	6.96787i	0.220420	+	0.561487i
$155$	−0.502523	−	0.204178i	−0.0403636	−	0.0164000i
$156$	2.37929	+	2.56343i	0.190495	+	0.205238i
$157$		−	2.34588i		−	0.187222i	−0.995609	−	0.0936108i	$-0.970159\pi$
$157$		−	2.34588i		−	0.187222i	0.995609	−	0.0936108i	$-0.0298409\pi$
$158$	−13.5622	+	5.32405i	−1.07895	+	0.423559i
$159$	7.43180			0.589380
$160$	−12.6020	−	1.09058i	−0.996276	−	0.0862177i
$161$	2.07689			0.163682
$162$	4.05101	−	1.59028i	0.318278	−	0.124945i
$163$		−	2.73625i		−	0.214319i	−0.994242	−	0.107160i	$-0.965824\pi$
$163$		−	2.73625i		−	0.214319i	0.994242	−	0.107160i	$-0.0341756\pi$
$164$	3.63215	+	3.91326i	0.283624	+	0.305574i
$165$	8.66636	−	3.65865i	0.674675	−	0.284825i
$166$	−1.68774	−	4.29926i	−0.130994	−	0.333687i
$167$	10.1328	−	10.1328i	0.784097	−	0.784097i	−0.196423	−	0.980519i	$-0.562932\pi$
$167$	10.1328	−	10.1328i	0.784097	−	0.784097i	0.980519	+	0.196423i	$0.0629325\pi$
$168$	5.51230	−	1.93034i	0.425283	−	0.148929i
$169$	−11.1367			−0.856670
$170$	−16.4159	−	16.8097i	−1.25905	−	1.28924i
$171$	5.02415	−	5.02415i	0.384207	−	0.384207i
$172$	13.2644	−	12.3116i	1.01140	−	0.938748i
$173$	−8.79590			−0.668740			−0.334370	−	0.942442i	$-0.608523\pi$
$173$	−8.79590			−0.668740			−0.334370	+	0.942442i	$0.608523\pi$
$174$	2.43137	−	5.57399i	0.184322	−	0.422563i
$175$	8.05851	−	0.109105i	0.609166	−	0.00824753i
$176$	8.57130	+	9.95349i	0.646086	+	0.750273i
$177$	7.57735	−	7.57735i	0.569549	−	0.569549i
$178$	12.8641	−	5.04998i	0.964202	−	0.378512i
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	−0.909832	−	0.414977i	$-0.863790\pi$
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	0.414977	+	0.909832i	$0.363790\pi$
$180$	2.15335	+	5.68237i	0.160501	+	0.423539i
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	0.455765	−	0.890100i	$-0.349366\pi$
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	−0.890100	+	0.455765i	$0.849366\pi$
$182$	1.24406	−	2.85204i	0.0922157	−	0.211408i
$183$	−8.55009	−	8.55009i	−0.632041	−	0.632041i
$184$	3.43966	−	1.20453i	0.253575	−	0.0887992i
$185$	2.81545	−	6.92939i	0.206996	−	0.509459i
$186$	0.409095	−	0.160596i	0.0299963	−	0.0117755i
$187$			24.3990i			1.78423i
$188$	−22.2675	−	0.829571i	−1.62402	−	0.0605027i
$189$	−6.36440	−	6.36440i	−0.462942	−	0.462942i
$190$	−11.5532	−	11.8303i	−0.838158	−	0.858260i
$191$			1.83906i			0.133070i	0.997784	+	0.0665349i	$0.0211944\pi$
$191$			1.83906i			0.133070i	−0.997784	+	0.0665349i	$0.978806\pi$
$192$	8.00970	−	6.39391i	0.578050	−	0.461440i
$193$	6.18343	+	6.18343i	0.445093	+	0.445093i	0.893719	−	0.448626i	$-0.148087\pi$
$193$	6.18343	+	6.18343i	0.445093	+	0.445093i	−0.448626	+	0.893719i	$0.648087\pi$
$194$	1.30810	−	2.99886i	0.0939160	−	0.215305i
$195$	−3.62266	−	1.47191i	−0.259424	−	0.105405i
$196$	5.98921	+	6.45273i	0.427801	+	0.460910i
$197$	5.55669			0.395898			0.197949	−	0.980212i	$-0.436572\pi$
$197$	5.55669			0.395898			0.197949	+	0.980212i	$0.436572\pi$
$198$	2.52298	−	5.78401i	0.179300	−	0.411052i
$199$		−	6.96413i		−	0.493674i	−0.969057	−	0.246837i	$-0.920609\pi$
$199$		−	6.96413i		−	0.493674i	0.969057	−	0.246837i	$-0.0793912\pi$
$200$	13.2829	−	4.85437i	0.939242	−	0.343256i
$201$		−	5.82480i		−	0.410850i
$202$	12.1715	+	5.30920i	0.856385	+	0.373554i
$203$	−5.41024			−0.379724
$204$	19.0239	+	0.708731i	1.33194	+	0.0496211i
$205$	−5.53026	−	2.24697i	−0.386250	−	0.156935i
$206$	−2.97379	−	1.29716i	−0.207194	−	0.0903776i
$207$	−1.23802	−	1.23802i	−0.0860483	−	0.0860483i
$208$	0.406265	−	5.44495i	0.0281694	−	0.377539i
$209$			17.1715i			1.18778i
$210$	−4.67172	+	4.56230i	−0.322379	+	0.314828i
$211$	5.43389	+	5.43389i	0.374084	+	0.374084i	0.868962	−	0.494878i	$-0.164787\pi$
$211$	5.43389	+	5.43389i	0.374084	+	0.374084i	−0.494878	+	0.868962i	$0.664787\pi$
$212$	−7.89291	−	8.50377i	−0.542088	−	0.584041i
$213$			19.7787i			1.35521i
$214$	1.88730	+	4.80761i	0.129013	+	0.328642i
$215$	−7.61635	+	18.7454i	−0.519431	+	1.27843i
$216$	−14.2316	−	6.84931i	−0.968338	−	0.466036i
$217$	−0.276477	−	0.276477i	−0.0187685	−	0.0187685i
$218$	9.54647	+	4.16416i	0.646568	+	0.282032i
$219$	1.91276	+	1.91276i	0.129253	+	0.129253i
$220$	−13.3904	−	6.03075i	−0.902784	−	0.406593i
$221$	7.17155	−	7.17155i	0.482411	−	0.482411i
$222$	2.21449	+	5.64108i	0.148627	+	0.378605i
$223$	−8.61776	+	8.61776i	−0.577088	+	0.577088i	−0.934100	−	0.357012i	$-0.883796\pi$
$223$	−8.61776	+	8.61776i	−0.577088	+	0.577088i	0.357012	+	0.934100i	$0.383796\pi$
$224$	−8.06309	−	4.25728i	−0.538738	−	0.284452i
$225$	−4.86865	−	4.73858i	−0.324577	−	0.315905i
$226$	7.84431	+	3.42168i	0.521796	+	0.227607i
$227$	6.01977			0.399546			0.199773	−	0.979842i	$-0.435980\pi$
$227$	6.01977			0.399546			0.199773	+	0.979842i	$0.435980\pi$
$228$	13.3886	+	0.498791i	0.886683	+	0.0330332i
$229$	0.568504	−	0.568504i	0.0375678	−	0.0375678i	−0.688073	−	0.725641i	$-0.741543\pi$
$229$	0.568504	−	0.568504i	0.0375678	−	0.0375678i	0.725641	+	0.688073i	$0.241543\pi$
$230$	−2.91515	+	2.84687i	−0.192219	+	0.187717i
$231$	6.78094			0.446153
$232$	−8.96022	+	3.13776i	−0.588267	+	0.206004i
$233$	−12.6979	+	12.6979i	−0.831869	+	0.831869i	−0.987772	−	0.155904i	$-0.950171\pi$
$233$	−12.6979	+	12.6979i	−0.831869	+	0.831869i	0.155904	+	0.987772i	$0.450171\pi$
$234$	−2.44165	+	0.958508i	−0.159616	+	0.0626596i
$235$	22.9516	−	9.68940i	1.49720	−	0.632067i
$236$	−16.7178	−	0.622819i	−1.08824	−	0.0405421i
$237$			13.1984i			0.857327i
$238$	−6.18894	−	15.7654i	−0.401169	−	1.02192i
$239$	−1.78306			−0.115336			−0.0576682	−	0.998336i	$-0.518367\pi$
$239$	−1.78306			−0.115336			−0.0576682	+	0.998336i	$0.518367\pi$
$240$	−5.09113	+	10.2653i	−0.328631	+	0.662625i
$241$	10.4440			0.672754			0.336377	−	0.941727i	$-0.390798\pi$
$241$	10.4440			0.672754			0.336377	+	0.941727i	$0.390798\pi$
$242$	−0.111780	−	0.284743i	−0.00718550	−	0.0183040i
$243$			12.8098i			0.821747i
$244$	−0.702773	+	18.8639i	−0.0449904	+	1.20764i
$245$	−9.11908	−	3.70513i	−0.582596	−	0.236712i
$246$	4.50208	−	1.76736i	0.287042	−	0.112683i
$247$	5.04719	−	5.04719i	0.321145	−	0.321145i
$248$	−0.618238	−	0.297542i	−0.0392581	−	0.0188939i
$249$	−4.18392			−0.265145
$250$	−11.1614	+	11.1992i	−0.705912	+	0.708300i
$251$	−12.6497	+	12.6497i	−0.798445	+	0.798445i	−0.982850	−	0.184406i	$-0.940964\pi$
$251$	−12.6497	+	12.6497i	−0.798445	+	0.798445i	0.184406	+	0.982850i	$0.440964\pi$
$252$	−0.163075	+	4.37730i	−0.0102728	+	0.275744i
$253$	4.23130			0.266019
$254$	−13.3687	−	5.83140i	−0.838825	−	0.365894i
$255$	−19.6084	+	8.27800i	−1.22792	+	0.518388i
$256$	−15.8228	−	2.37440i	−0.988927	−	0.148400i
$257$	−4.13062	+	4.13062i	−0.257661	+	0.257661i	−0.824102	−	0.566441i	$-0.808320\pi$
$257$	−4.13062	+	4.13062i	−0.257661	+	0.257661i	0.566441	+	0.824102i	$0.308320\pi$
$258$	−5.99064	−	15.2603i	−0.372961	−	0.950063i
$259$	3.81240	−	3.81240i	0.236891	−	0.236891i
$260$	2.16322	+	5.70843i	0.134157	+	0.354022i
$261$	3.22500	+	3.22500i	0.199623	+	0.199623i
$262$	21.9603	+	9.57907i	1.35671	+	0.591797i
$263$	17.1303	+	17.1303i	1.05630	+	1.05630i	0.998318	+	0.0579798i	$0.0184659\pi$
$263$	17.1303	+	17.1303i	1.05630	+	1.05630i	0.0579798	+	0.998318i	$0.481534\pi$
$264$	11.2303	−	3.93273i	0.691178	−	0.242043i
$265$	12.0176	+	4.88282i	0.738237	+	0.299949i
$266$	−4.35565	−	11.0954i	−0.267062	−	0.680300i
$267$		−	12.5190i		−	0.766147i
$268$	−6.66497	+	6.18620i	−0.407128	+	0.377883i
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.971775	+	0.235910i	$0.0758070\pi$
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.235910	+	0.971775i	$0.424193\pi$
$270$	17.6570	+	0.209240i	1.07457	+	0.0127339i
$271$		−	27.9542i		−	1.69810i	−0.528316	−	0.849048i	$-0.677176\pi$
$271$		−	27.9542i		−	1.69810i	0.528316	−	0.849048i	$-0.322824\pi$
$272$	−19.3933	−	22.5206i	−1.17589	−	1.36551i
$273$	−1.99311	−	1.99311i	−0.120628	−	0.120628i
$274$	−9.03326	−	3.94030i	−0.545719	−	0.238042i
$275$	16.4178	−	0.222281i	0.990029	−	0.0134041i
$276$	0.122909	−	3.29914i	0.00739824	−	0.198585i
$277$	−26.0257			−1.56373			−0.781866	−	0.623447i	$-0.785732\pi$
$277$	−26.0257			−1.56373			−0.781866	+	0.623447i	$0.785732\pi$
$278$	18.8846	+	8.23743i	1.13262	+	0.494048i
$279$			0.329612i			0.0197333i
$280$	10.1819	+	0.500206i	0.608488	+	0.0298930i
$281$			24.1001i			1.43769i	0.695170	+	0.718846i	$0.255329\pi$
$281$			24.1001i			1.43769i	−0.695170	+	0.718846i	$0.744671\pi$
$282$	−8.07051	+	18.5019i	−0.480592	+	1.10177i
$283$	4.73708			0.281590			0.140795	−	0.990039i	$-0.455034\pi$
$283$	4.73708			0.281590			0.140795	+	0.990039i	$0.455034\pi$
$284$	22.6316	−	21.0059i	1.34294	−	1.24647i
$285$	−13.8000	+	5.82588i	−0.817439	+	0.345096i
$286$	2.53455	−	5.81053i	0.149871	−	0.343584i
$287$	−3.04262	−	3.04262i	−0.179600	−	0.179600i
$288$	2.26861	+	7.34408i	0.133679	+	0.432754i
$289$		−	38.2049i		−	2.24734i
$290$	7.59387	−	7.41600i	0.445927	−	0.435482i
$291$	−2.09571	−	2.09571i	−0.122852	−	0.122852i
$292$	0.157219	−	4.22010i	0.00920056	−	0.246963i
$293$		−	3.11001i		−	0.181689i	−0.995865	−	0.0908445i	$-0.971043\pi$
$293$		−	3.11001i		−	0.181689i	0.995865	−	0.0908445i	$-0.0289566\pi$
$294$	7.42366	−	2.91427i	0.432957	−	0.169964i
$295$	17.2314	−	7.27454i	1.00325	−	0.423540i
$296$	4.10287	−	8.52500i	0.238474	−	0.495505i
$297$	−12.9663	−	12.9663i	−0.752382	−	0.752382i
$298$	−12.1576	+	27.8718i	−0.704273	+	1.61457i
$299$	−1.24370	−	1.24370i	−0.0719248	−	0.0719248i
$300$	0.303583	−	12.8074i	0.0175274	−	0.739434i
$301$	−10.3133	+	10.3133i	−0.594449	+	0.594449i
$302$	14.0929	−	5.53238i	0.810955	−	0.318352i
$303$	8.50588	−	8.50588i	0.488650	−	0.488650i
$304$	−13.6486	−	15.8495i	−0.782801	−	0.909034i
$305$	−8.20840	−	19.4435i	−0.470012	−	1.11333i
$306$	−5.70845	+	13.0868i	−0.326330	+	0.748123i
$307$	14.5670			0.831382			0.415691	−	0.909506i	$-0.363540\pi$
$307$	14.5670			0.831382			0.415691	+	0.909506i	$0.363540\pi$
$308$	−7.20167	−	7.75903i	−0.410353	−	0.442112i
$309$	−2.07819	+	2.07819i	−0.118224	+	0.118224i
$310$	0.767042	+	0.00908963i	0.0435651	+	0.000516256i
$311$	−14.4572			−0.819791			−0.409896	−	0.912132i	$-0.634435\pi$
$311$	−14.4572			−0.819791			−0.409896	+	0.912132i	$0.634435\pi$
$312$	−4.45684	−	2.14496i	−0.252319	−	0.121435i
$313$	10.1273	−	10.1273i	0.572429	−	0.572429i	−0.360377	−	0.932807i	$-0.617352\pi$
$313$	10.1273	−	10.1273i	0.572429	−	0.572429i	0.932807	+	0.360377i	$0.117352\pi$
$314$	1.21230	+	3.08815i	0.0684139	+	0.174274i
$315$	−1.90472	−	4.51178i	−0.107319	−	0.254210i
$316$	15.1021	−	14.0173i	0.849561	−	0.788534i
$317$			13.8750i			0.779295i	0.920964	+	0.389648i	$0.127403\pi$
$317$			13.8750i			0.779295i	−0.920964	+	0.389648i	$0.872597\pi$
$318$	−9.78332	+	3.84058i	−0.548621	+	0.215369i
$319$	−11.0224			−0.617136
$320$	17.1530	−	5.07678i	0.958883	−	0.283801i
$321$	4.67864			0.261136
$322$	−2.73405	+	1.07329i	−0.152362	+	0.0598121i
$323$		−	38.8520i		−	2.16179i
$324$	−4.51098	+	4.18694i	−0.250610	+	0.232608i
$325$	−4.89097	−	4.76030i	−0.271302	−	0.264054i
$326$	1.41403	+	3.60203i	0.0783158	+	0.199498i
$327$	6.67140	−	6.67140i	0.368930	−	0.368930i
$328$	−6.80369	−	3.27445i	−0.375671	−	0.180801i
$329$	17.9584			0.990076
$330$	−9.51780	+	9.29486i	−0.523938	+	0.511665i
$331$	1.69458	−	1.69458i	0.0931425	−	0.0931425i	−0.659000	−	0.752143i	$-0.729020\pi$
$331$	1.69458	−	1.69458i	0.0931425	−	0.0931425i	0.752143	+	0.659000i	$0.229020\pi$
$332$	4.44352	+	4.78741i	0.243870	+	0.262743i
$333$	−4.54508			−0.249069
$334$	−8.10251	+	18.5753i	−0.443350	+	1.01639i
$335$	3.82699	−	9.41902i	0.209091	−	0.514616i
$336$	−6.25890	+	5.38975i	−0.341451	+	0.294035i
$337$	−9.53338	+	9.53338i	−0.519316	+	0.519316i	−0.917364	−	0.398048i	$-0.869688\pi$
$337$	−9.53338	+	9.53338i	−0.519316	+	0.519316i	0.398048	+	0.917364i	$0.369688\pi$
$338$	14.6605	−	5.75520i	0.797427	−	0.313042i
$339$	5.48188	−	5.48188i	0.297735	−	0.297735i
$340$	30.2970	+	13.6451i	1.64309	+	0.740008i
$341$	−0.563273	−	0.563273i	−0.0305029	−	0.0305029i
$342$	−4.01749	+	9.21023i	−0.217241	+	0.498032i
$343$	−12.9954	−	12.9954i	−0.701683	−	0.701683i
$344$	−11.0991	+	23.0618i	−0.598422	+	1.24341i
$345$	1.43558	+	3.40050i	0.0772888	+	0.183077i
$346$	11.5790	−	4.54552i	0.622492	−	0.244369i
$347$			6.67273i			0.358211i	0.983830	+	0.179105i	$0.0573203\pi$
$347$			6.67273i			0.358211i	−0.983830	+	0.179105i	$0.942680\pi$
$348$	−0.320173	+	8.59415i	−0.0171631	+	0.460695i
$349$	−2.02618	−	2.02618i	−0.108459	−	0.108459i	0.650795	−	0.759254i	$-0.274436\pi$
$349$	−2.02618	−	2.02618i	−0.108459	−	0.108459i	−0.759254	+	0.650795i	$0.774436\pi$
$350$	−10.5519	+	4.30808i	−0.564025	+	0.230276i
$351$			7.62233i			0.406850i
$352$	−16.4271	−	8.67345i	−0.875567	−	0.462296i
$353$	−5.36542	−	5.36542i	−0.285572	−	0.285572i	0.549754	−	0.835327i	$-0.314721\pi$
$353$	−5.36542	−	5.36542i	−0.285572	−	0.285572i	−0.835327	+	0.549754i	$0.814721\pi$
$354$	−6.05912	+	13.8907i	−0.322039	+	0.738284i
$355$	−12.9949	+	31.9832i	−0.689700	+	1.69749i
$356$	−14.3247	+	13.2957i	−0.759207	+	0.704671i
$357$	−15.3425			−0.812009
$358$	5.29416	−	12.1370i	0.279805	−	0.641462i
$359$			7.76117i			0.409619i	0.978802	+	0.204809i	$0.0656574\pi$
$359$			7.76117i			0.409619i	−0.978802	+	0.204809i	$0.934343\pi$
$360$	−5.77121	−	6.36755i	−0.304170	−	0.335599i
$361$		−	8.34326i		−	0.439119i
$362$	10.7120	+	4.67258i	0.563012	+	0.245585i
$363$	−0.277104			−0.0145442
$364$	−0.163823	+	4.39737i	−0.00858666	+	0.230485i
$365$	1.83632	+	4.34976i	0.0961175	+	0.227677i
$366$	15.6739	+	6.83695i	0.819290	+	0.357373i
$367$	−18.0536	−	18.0536i	−0.942389	−	0.942389i	0.0560392	−	0.998429i	$-0.482153\pi$
$367$	−18.0536	−	18.0536i	−0.942389	−	0.942389i	−0.998429	+	0.0560392i	$0.982153\pi$
$368$	−3.90554	+	3.36320i	−0.203590	+	0.175319i
$369$			3.62737i			0.188833i
$370$	−0.125339	+	10.5769i	−0.00651605	+	0.549866i
$371$	6.61183	+	6.61183i	0.343269	+	0.343269i
$372$	−0.455545	+	0.422821i	−0.0236189	+	0.0219223i
$373$		−	4.36197i		−	0.225854i	−0.993603	−	0.112927i	$-0.963977\pi$
$373$		−	4.36197i		−	0.225854i	0.993603	−	0.112927i	$-0.0360226\pi$
$374$	−12.6089	−	32.1192i	−0.651988	−	1.66084i
$375$	5.74879	+	13.1188i	0.296866	+	0.677451i
$376$	29.7419	−	10.4153i	1.53382	−	0.537126i
$377$	3.23979	+	3.23979i	0.166858	+	0.166858i
$378$	11.6671	+	5.08920i	0.600093	+	0.261760i
$379$	5.93072	+	5.93072i	0.304641	+	0.304641i	0.842826	−	0.538186i	$-0.180890\pi$
$379$	5.93072	+	5.93072i	0.304641	+	0.304641i	−0.538186	+	0.842826i	$0.680890\pi$
$380$	21.3224	+	9.60313i	1.09382	+	0.492630i
$381$	−9.34249	+	9.34249i	−0.478630	+	0.478630i
$382$	−0.950385	−	2.42096i	−0.0486259	−	0.123867i
$383$	19.3340	−	19.3340i	0.987922	−	0.987922i	−0.0120057	−	0.999928i	$-0.503822\pi$
$383$	19.3340	−	19.3340i	0.987922	−	0.987922i	0.999928	+	0.0120057i	$0.00382161\pi$
$384$	−7.23984	+	12.5562i	−0.369457	+	0.640758i
$385$	10.9652	+	4.45520i	0.558836	+	0.227058i
$386$	−11.3354	−	4.94449i	−0.576957	−	0.251668i
$387$	12.2954			0.625008
$388$	−0.172256	+	4.62373i	−0.00874498	+	0.234734i
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	−0.848274	−	0.529558i	$-0.822358\pi$
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	0.529558	+	0.848274i	$0.322358\pi$
$390$	5.52956	+	0.0655266i	0.280000	+	0.00331807i
$391$	−9.57367			−0.484161
$392$	−11.2189	−	5.39937i	−0.566640	−	0.272709i
$393$	15.3466	−	15.3466i	0.774135	−	0.774135i
$394$	−7.31489	+	2.87157i	−0.368519	+	0.144668i
$395$	−8.67157	+	21.3425i	−0.436314	+	1.07386i
$396$	−0.332237	+	8.91796i	−0.0166955	+	0.448144i
$397$		−	6.58413i		−	0.330448i	−0.986256	−	0.165224i	$-0.947165\pi$
$397$		−	6.58413i		−	0.330448i	0.986256	−	0.165224i	$-0.0528347\pi$
$398$	3.59890	+	9.16767i	0.180397	+	0.459534i
$399$	−10.7977			−0.540561
$400$	−14.9771	+	13.2546i	−0.748857	+	0.662732i
$401$	19.7951			0.988522			0.494261	−	0.869313i	$-0.335439\pi$
$401$	19.7951			0.988522			0.494261	+	0.869313i	$0.335439\pi$
$402$	3.01012	+	7.66784i	0.150131	+	0.382437i
$403$			0.331123i			0.0164944i
$404$	−18.7664	−	0.699139i	−0.933664	−	0.0347835i
$405$	2.59018	−	6.37497i	0.128707	−	0.316775i
$406$	7.12211	−	2.79589i	0.353464	−	0.138758i
$407$	7.76707	−	7.76707i	0.385000	−	0.385000i
$408$	−25.4095	+	8.89813i	−1.25796	+	0.440523i
$409$	−5.76937			−0.285277			−0.142638	−	0.989775i	$-0.545559\pi$
$409$	−5.76937			−0.285277			−0.142638	+	0.989775i	$0.545559\pi$
$410$	8.44128	+	0.100031i	0.416885	+	0.00494019i
$411$	−6.31276	+	6.31276i	−0.311385	+	0.311385i
$412$	4.58507	+	0.170816i	0.225890	+	0.00841550i
$413$	13.4826			0.663437
$414$	2.26952	+	0.989964i	0.111541	+	0.0486541i
$415$	−6.76563	−	2.74891i	−0.332112	−	0.134939i
$416$	2.27901	+	7.37775i	0.111738	+	0.361724i
$417$	13.1972	−	13.1972i	0.646270	−	0.646270i
$418$	−8.87385	−	22.6048i	−0.434034	−	1.10564i
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	−0.886750	−	0.462249i	$-0.847043\pi$
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	0.462249	+	0.886750i	$0.347043\pi$
$420$	3.79222	−	8.42010i	0.185041	−	0.410859i
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	0.999815	−	0.0192594i	$-0.00613083\pi$
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	−0.0192594	+	0.999815i	$0.506131\pi$
$422$	−9.96134	−	4.34513i	−0.484911	−	0.211517i
$423$	−10.7048	−	10.7048i	−0.520487	−	0.520487i
$424$	14.7849	+	7.11559i	0.718017	+	0.345564i
$425$	−37.1466	+	0.502930i	−1.80187	+	0.0243957i
$426$	−10.2212	−	26.0369i	−0.495217	−	1.26149i
$427$		−	15.2135i		−	0.736231i
$428$	−4.96893	−	5.35349i	−0.240182	−	0.258770i
$429$	−4.06060	−	4.06060i	−0.196048	−	0.196048i
$430$	0.339066	−	28.6126i	0.0163512	−	1.37982i
$431$			33.6247i			1.61965i	0.586675	+	0.809823i	$0.300437\pi$
$431$			33.6247i			1.61965i	−0.586675	+	0.809823i	$0.699563\pi$
$432$	22.2742	+	1.66195i	1.07167	+	0.0799606i
$433$	7.46558	+	7.46558i	0.358773	+	0.358773i	0.863361	−	0.504588i	$-0.168355\pi$
$433$	7.46558	+	7.46558i	0.358773	+	0.358773i	−0.504588	+	0.863361i	$0.668355\pi$
$434$	0.506835	+	0.221081i	0.0243289	+	0.0106122i
$435$	−3.73963	−	8.85819i	−0.179302	−	0.424718i
$436$	−14.7190	−	0.548355i	−0.704914	−	0.0262614i
$437$	−6.73775			−0.322310
$438$	−3.50646	−	1.52951i	−0.167545	−	0.0730829i
$439$			7.91929i			0.377967i	0.981980	+	0.188984i	$0.0605193\pi$
$439$			7.91929i			0.377967i	−0.981980	+	0.188984i	$0.939481\pi$
$440$	20.7439	+	1.01908i	0.988927	+	0.0485827i
$441$			5.98132i			0.284825i
$442$	−5.73463	+	13.1468i	−0.272768	+	0.625330i
$443$	10.6463			0.505823			0.252911	−	0.967489i	$-0.418612\pi$
$443$	10.6463			0.505823			0.252911	+	0.967489i	$0.418612\pi$
$444$	−5.83036	−	6.28159i	−0.276697	−	0.298111i
$445$	8.22517	−	20.2438i	0.389910	−	0.959649i
$446$	6.89106	−	15.7980i	0.326301	−	0.748056i
$447$	19.4778	+	19.4778i	0.921266	+	0.921266i
$448$	12.8144	+	1.43752i	0.605424	+	0.0679164i
$449$			6.08115i			0.286987i	0.989651	+	0.143494i	$0.0458336\pi$
$449$			6.08115i			0.286987i	−0.989651	+	0.143494i	$0.954166\pi$
$450$	8.85794	+	3.72191i	0.417567	+	0.175453i
$451$	−6.19880	−	6.19880i	−0.291890	−	0.291890i
$452$	−12.0946	−	0.450582i	−0.568882	−	0.0211936i
$453$		−	13.7148i		−	0.644379i
$454$	−7.92450	+	3.11088i	−0.371915	+	0.146001i
$455$	−1.91346	−	4.53247i	−0.0897042	−	0.212485i
$456$	−17.8827	+	6.26232i	−0.837435	+	0.293260i
$457$	−0.313815	−	0.313815i	−0.0146796	−	0.0146796i	0.699729	−	0.714409i	$-0.253304\pi$
$457$	−0.313815	−	0.313815i	−0.0146796	−	0.0146796i	−0.714409	+	0.699729i	$0.753304\pi$
$458$	−0.454596	+	1.04218i	−0.0212419	+	0.0486977i
$459$	29.3374	+	29.3374i	1.36935	+	1.36935i
$460$	2.36634	−	5.25413i	0.110331	−	0.244975i
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	−0.437626	−	0.899157i	$-0.644181\pi$
$461$	9.90949	−	9.90949i	0.461531	−	0.461531i	0.899157	+	0.437626i	$0.144181\pi$
$462$	−8.92652	+	3.50424i	−0.415299	+	0.163032i
$463$	−17.3430	+	17.3430i	−0.805999	+	0.805999i	−0.984026	−	0.178027i	$-0.943029\pi$
$463$	−17.3430	+	17.3430i	−0.805999	+	0.805999i	0.178027	+	0.984026i	$0.443029\pi$
$464$	10.1738	−	8.76103i	0.472307	−	0.406720i
$465$	0.261571	−	0.643781i	0.0121301	−	0.0298546i
$466$	10.1537	−	23.2777i	0.470361	−	1.07832i
$467$	1.52267			0.0704606			0.0352303	−	0.999379i	$-0.488784\pi$
$467$	1.52267			0.0704606			0.0352303	+	0.999379i	$0.488784\pi$
$468$	2.71889	−	2.52358i	0.125681	−	0.116653i
$469$	5.18213	−	5.18213i	0.239289	−	0.239289i
$470$	−25.2065	+	24.6161i	−1.16269	+	1.13546i
$471$	3.00530			0.138477
$472$	22.3294	−	7.81950i	1.02779	−	0.359921i
$473$	−21.0115	+	21.0115i	−0.966110	+	0.966110i
$474$	−6.82062	−	17.3745i	−0.313282	−	0.798038i
$475$	−26.1430	+	0.353952i	−1.19952	+	0.0162404i
$476$	16.2944	+	17.5555i	0.746852	+	0.804653i
$477$		−	7.88252i		−	0.360916i
$478$	2.34724	−	0.921443i	0.107360	−	0.0421458i
$479$	−0.507657			−0.0231955			−0.0115977	−	0.999933i	$-0.503692\pi$
$479$	−0.507657			−0.0231955			−0.0115977	+	0.999933i	$0.503692\pi$
$480$	1.39713	−	16.1444i	0.0637702	−	0.736887i
$481$	−4.56592			−0.208188
$482$	−13.7486	+	5.39720i	−0.626229	+	0.245836i
$483$			2.66070i			0.121066i
$484$	0.294297	+	0.317074i	0.0133772	+	0.0144125i
$485$	−2.01195	−	4.76578i	−0.0913581	−	0.216403i
$486$	−6.61979	−	16.8629i	−0.300280	−	0.764918i
$487$	−25.9809	+	25.9809i	−1.17730	+	1.17730i	−0.196876	+	0.980428i	$0.563080\pi$
$487$	−25.9809	+	25.9809i	−1.17730	+	1.17730i	−0.980428	+	0.196876i	$0.936920\pi$
$488$	−8.82332	−	25.1959i	−0.399413	−	1.14057i
$489$	3.50539			0.158519
$490$	13.9192	+	0.164946i	0.628805	+	0.00745148i
$491$	−3.28208	+	3.28208i	−0.148118	+	0.148118i	−0.777277	−	0.629159i	$-0.783400\pi$
$491$	−3.28208	+	3.28208i	−0.148118	+	0.148118i	0.629159	+	0.777277i	$0.283400\pi$
$492$	−5.01326	+	4.65314i	−0.226015	+	0.209780i
$493$	24.9391			1.12320
$494$	−4.03591	+	9.25246i	−0.181584	+	0.416288i
$495$	−3.88053	−	9.19195i	−0.174417	−	0.413147i
$496$	0.967619	+	0.0721971i	0.0434474	+	0.00324175i
$497$	−17.5964	+	17.5964i	−0.789308	+	0.789308i
$498$	5.50777	−	2.16215i	0.246809	−	0.0968885i
$499$	6.73907	−	6.73907i	0.301682	−	0.301682i	−0.539990	−	0.841672i	$-0.681572\pi$
$499$	6.73907	−	6.73907i	0.301682	−	0.301682i	0.841672	+	0.539990i	$0.181572\pi$
$500$	8.90557	−	20.5107i	0.398269	−	0.917269i
$501$	12.9810	+	12.9810i	0.579950	+	0.579950i
$502$	10.1152	−	23.1894i	0.451463	−	1.03499i
$503$	−6.12090	−	6.12090i	−0.272918	−	0.272918i	0.557356	−	0.830274i	$-0.311816\pi$
$503$	−6.12090	−	6.12090i	−0.272918	−	0.272918i	−0.830274	+	0.557356i	$0.811816\pi$
$504$	−2.04741	−	5.84660i	−0.0911990	−	0.260428i
$505$	19.3430	−	8.16596i	0.860752	−	0.363380i
$506$	−5.57013	+	2.18664i	−0.247623	+	0.0972079i
$507$		−	14.2672i		−	0.633629i
$508$	20.6122	+	0.767904i	0.914519	+	0.0340702i
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	0.329323	−	0.944217i	$-0.393180\pi$
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	−0.944217	+	0.329323i	$0.893180\pi$
$510$	21.5348	−	21.0304i	0.953578	−	0.931242i
$511$			3.40344i			0.150559i
$512$	22.0564	−	5.05119i	0.974765	−	0.223233i
$513$	20.6471	+	20.6471i	0.911590	+	0.911590i
$514$	3.30299	−	7.57221i	0.145689	−	0.333996i
$515$	−4.72594	+	1.99514i	−0.208250	+	0.0879162i
$516$	15.7723	+	16.9930i	0.694337	+	0.748074i
$517$	36.5869			1.60909
$518$	−3.04853	+	6.98884i	−0.133945	+	0.307072i
$519$		−	11.2684i		−	0.494628i
$520$	−5.79767	−	6.39674i	−0.254245	−	0.280516i
$521$		−	5.87686i		−	0.257470i	−0.991679	−	0.128735i	$-0.958908\pi$
$521$		−	5.87686i		−	0.257470i	0.991679	−	0.128735i	$-0.0410917\pi$
$522$	−5.91204	−	2.57883i	−0.258763	−	0.112872i
$523$	−26.0176			−1.13767			−0.568834	−	0.822452i	$-0.692605\pi$
$523$	−26.0176			−1.13767			−0.568834	+	0.822452i	$0.692605\pi$
$524$	−33.8591	−	1.26141i	−1.47914	−	0.0551051i
$525$	0.139774	+	10.3237i	0.00610022	+	0.450564i
$526$	−31.4030	−	13.6980i	−1.36924	−	0.597260i
$527$	1.27445	+	1.27445i	0.0555160	+	0.0555160i
$528$	−12.7514	+	10.9807i	−0.554933	+	0.477872i
$529$		−	21.3397i		−	0.927814i
$530$	−18.3435	−	0.217374i	−0.796790	−	0.00944214i
$531$	−8.03690	−	8.03690i	−0.348772	−	0.348772i
$532$	11.4677	+	12.3552i	0.497186	+	0.535665i
$533$			3.64400i			0.157839i
$534$	6.46951	+	16.4801i	0.279963	+	0.713164i
$535$	7.56561	+	3.07394i	0.327090	+	0.132898i
$536$	5.57696	−	11.5879i	0.240888	−	0.500521i
$537$	−8.48177	−	8.48177i	−0.366016	−	0.366016i
$538$	−36.3109	−	15.8388i	−1.56547	−	0.682858i
$539$	−10.2215	−	10.2215i	−0.440270	−	0.440270i
$540$	−23.3521	+	8.84930i	−1.00491	+	0.380813i
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	−0.834210	−	0.551447i	$-0.814076\pi$
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	0.551447	+	0.834210i	$0.314076\pi$
$542$	14.4461	+	36.7992i	0.620513	+	1.58066i
$543$	7.48594	−	7.48594i	0.321253	−	0.321253i
$544$	37.1677	+	19.6244i	1.59355	+	0.841390i
$545$	15.1712	−	6.40479i	0.649865	−	0.274351i
$546$	3.65374	+	1.59376i	0.156366	+	0.0682066i
$547$	−10.6170			−0.453951			−0.226976	−	0.973900i	$-0.572884\pi$
$547$	−10.6170			−0.453951			−0.226976	+	0.973900i	$0.572884\pi$
$548$	13.9277	+	0.518876i	0.594964	+	0.0221653i
$549$	−9.06863	+	9.06863i	−0.387040	+	0.387040i
$550$	−21.4977	+	8.77694i	−0.916664	+	0.374250i
$551$	17.5516			0.747724
$552$	1.54312	+	4.40654i	0.0656796	+	0.187555i
$553$	−11.7422	+	11.7422i	−0.499328	+	0.499328i
$554$	34.2605	−	13.4495i	1.45559	−	0.571414i
$555$	8.87722	+	3.60686i	0.376817	+	0.153103i
$556$	−29.1168	−	1.08474i	−1.23483	−	0.0460033i
$557$		−	20.9610i		−	0.888146i	−0.895991	−	0.444073i	$-0.853533\pi$
$557$		−	20.9610i		−	0.888146i	0.895991	−	0.444073i	$-0.146467\pi$
$558$	−0.170336	−	0.433905i	−0.00721089	−	0.0183687i
$559$	12.3517			0.522422
$560$	−13.6621	+	4.60332i	−0.577331	+	0.194526i
$561$	−31.2575			−1.31969
$562$	−12.4544	−	31.7257i	−0.525356	−	1.33827i
$563$			16.5598i			0.697911i	0.937139	+	0.348955i	$0.113464\pi$
$563$			16.5598i			0.697911i	−0.937139	+	0.348955i	$0.886536\pi$
$564$	1.06276	−	28.5268i	0.0447503	−	1.20119i
$565$	12.4662	−	5.26280i	0.524456	−	0.221408i
$566$	−6.23594	+	2.44801i	−0.262116	+	0.102898i
$567$	3.50736	−	3.50736i	0.147295	−	0.147295i
$568$	−18.9371	+	39.3479i	−0.794584	+	1.65100i
$569$	39.6751			1.66327			0.831634	−	0.555325i	$-0.187406\pi$
$569$	39.6751			1.66327			0.831634	+	0.555325i	$0.187406\pi$
$570$	15.1558	−	14.8008i	0.634805	−	0.619936i
$571$	24.0292	−	24.0292i	1.00559	−	1.00559i	0.00560819	−	0.999984i	$-0.498215\pi$
$571$	24.0292	−	24.0292i	1.00559	−	1.00559i	0.999984	−	0.00560819i	$-0.00178515\pi$
$572$	−0.333760	+	8.95885i	−0.0139552	+	0.374588i
$573$	−2.35602			−0.0984240
$574$	5.57771	+	2.43299i	0.232809	+	0.101551i
$575$	0.0872185	+	6.44199i	0.00363726	+	0.268649i
$576$	−6.78168	−	8.49547i	−0.282570	−	0.353978i
$577$	−28.7705	+	28.7705i	−1.19773	+	1.19773i	−0.222888	+	0.974844i	$0.571549\pi$
$577$	−28.7705	+	28.7705i	−1.19773	+	1.19773i	−0.974844	+	0.222888i	$0.928451\pi$
$578$	19.7434	+	50.2933i	0.821217	+	2.09193i
$579$	−7.92157	+	7.92157i	−0.329209	+	0.329209i
$580$	−6.16424	+	13.6868i	−0.255956	+	0.568315i
$581$	−3.72230	−	3.72230i	−0.154427	−	0.154427i
$582$	3.84182	+	1.67580i	0.159249	+	0.0694641i
$583$	13.4704	+	13.4704i	0.557888	+	0.557888i
$584$	1.97389	+	5.63664i	0.0816800	+	0.233246i
$585$	−1.56117	+	3.84237i	−0.0645466	+	0.158862i
$586$	1.60718	+	4.09406i	0.0663922	+	0.169124i
$587$		−	33.4854i		−	1.38209i	−0.722811	−	0.691046i	$-0.757150\pi$
$587$		−	33.4854i		−	1.38209i	0.722811	−	0.691046i	$-0.242850\pi$
$588$	−8.26657	+	7.67276i	−0.340908	+	0.316419i
$589$	0.896933	+	0.896933i	0.0369575	+	0.0369575i
$590$	−18.9244	+	18.4811i	−0.779104	+	0.760855i
$591$			7.11866i			0.292822i
$592$	−0.995540	+	13.3427i	−0.0409164	+	0.548381i
$593$	11.5298	+	11.5298i	0.473472	+	0.473472i	0.903036	−	0.429564i	$-0.141333\pi$
$593$	11.5298	+	11.5298i	0.473472	+	0.473472i	−0.429564	+	0.903036i	$0.641333\pi$
$594$	23.7697	+	10.3683i	0.975284	+	0.425418i
$595$	−24.8096	−	10.0803i	−1.01709	−	0.413250i
$596$	1.60097	−	42.9735i	0.0655783	−	1.76026i
$597$	8.92172			0.365142
$598$	2.27993	+	0.994503i	0.0932333	+	0.0406683i
$599$		−	20.0148i		−	0.817781i	−0.912583	−	0.408891i	$-0.865916\pi$
$599$		−	20.0148i		−	0.817781i	0.912583	−	0.408891i	$-0.134084\pi$
$600$	6.21891	+	17.0167i	0.253886	+	0.694702i
$601$		−	27.5924i		−	1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$601$		−	27.5924i		−	1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$602$	8.24688	−	18.9062i	0.336118	−	0.770560i
$603$	−6.17806			−0.251590
$604$	−15.6931	+	14.5658i	−0.638542	+	0.592673i
$605$	−0.448093	−	0.182062i	−0.0182176	−	0.00740188i
$606$	−6.80160	+	15.5929i	−0.276296	+	0.633418i
$607$	30.4850	+	30.4850i	1.23735	+	1.23735i	0.961081	+	0.276265i	$0.0890968\pi$
$607$	30.4850	+	30.4850i	1.23735	+	1.23735i	0.276265	+	0.961081i	$0.410903\pi$
$608$	26.1579	+	13.8113i	1.06084	+	0.560120i
$609$		−	6.93104i		−	0.280860i
$610$	20.8536	+	21.3538i	0.844338	+	0.864589i
$611$	−10.7539	−	10.7539i	−0.435057	−	0.435057i
$612$	0.751714	−	20.1776i	0.0303862	−	0.815632i
$613$		−	20.2657i		−	0.818523i	−0.912417	−	0.409261i	$-0.865786\pi$
$613$		−	20.2657i		−	0.818523i	0.912417	−	0.409261i	$-0.134214\pi$
$614$	−19.1762	+	7.52788i	−0.773887	+	0.303801i
$615$	2.87859	−	7.08480i	0.116076	−	0.285687i
$616$	13.4901	+	6.49242i	0.543530	+	0.261587i
$617$	−1.61302	−	1.61302i	−0.0649378	−	0.0649378i	0.673892	−	0.738830i	$-0.264621\pi$
$617$	−1.61302	−	1.61302i	−0.0649378	−	0.0649378i	−0.738830	+	0.673892i	$0.764621\pi$
$618$	1.66179	−	3.80971i	0.0668470	−	0.153249i
$619$	2.46756	+	2.46756i	0.0991797	+	0.0991797i	0.754956	−	0.655776i	$-0.227658\pi$
$619$	2.46756	+	2.46756i	0.0991797	+	0.0991797i	−0.655776	+	0.754956i	$0.727658\pi$
$620$	−1.01444	+	0.384424i	−0.0407409	+	0.0154388i
$621$	5.08771	−	5.08771i	0.204163	−	0.204163i
$622$	19.0316	−	7.47114i	0.763098	−	0.299565i
$623$	11.1377	−	11.1377i	0.446222	−	0.446222i
$624$	6.97551	+	0.520465i	0.279244	+	0.0208353i
$625$	0.676829	+	24.9908i	0.0270732	+	0.999633i
$626$	−8.09815	+	18.5653i	−0.323667	+	0.742017i
$627$	−21.9984			−0.878531
$628$	−3.19177	−	3.43879i	−0.127365	−	0.137222i
$629$	−17.5737	+	17.5737i	−0.700708	+	0.700708i
$630$	4.83899	+	4.95505i	0.192790	+	0.197414i
$631$	−29.9602			−1.19270			−0.596348	−	0.802726i	$-0.703382\pi$
$631$	−29.9602			−1.19270			−0.596348	+	0.802726i	$0.703382\pi$
$632$	−12.6368	+	26.2570i	−0.502666	+	1.04445i
$633$	−6.96133	+	6.96133i	−0.276688	+	0.276688i
$634$	−7.17026	−	18.2652i	−0.284767	−	0.725402i
$635$	−21.2455	+	8.96913i	−0.843101	+	0.355929i
$636$	10.8942	−	10.1116i	0.431981	−	0.400950i
$637$			6.00875i			0.238075i
$638$	14.5100	−	5.69612i	0.574457	−	0.225512i
$639$	20.9782			0.829885
$640$	−19.9569	+	15.5474i	−0.788865	+	0.614566i
$641$	−37.3386			−1.47478			−0.737392	−	0.675465i	$-0.763943\pi$
$641$	−37.3386			−1.47478			−0.737392	+	0.675465i	$0.763943\pi$
$642$	−6.15901	+	2.41781i	−0.243077	+	0.0954234i
$643$			24.5635i			0.968691i	0.874877	+	0.484345i	$0.160942\pi$
$643$			24.5635i			0.968691i	−0.874877	+	0.484345i	$0.839058\pi$
$644$	3.04448	−	2.82579i	0.119969	−	0.111352i
$645$	−24.0147	−	9.75728i	−0.945577	−	0.384193i
$646$	20.0778	+	51.1453i	0.789952	+	2.01229i
$647$	−23.1347	+	23.1347i	−0.909519	+	0.909519i	−0.996233	−	0.0867142i	$-0.972363\pi$
$647$	−23.1347	+	23.1347i	−0.909519	+	0.909519i	0.0867142	+	0.996233i	$0.472363\pi$
$648$	3.77459	−	7.84291i	0.148280	−	0.308099i
$649$	27.4685			1.07823
$650$	8.89855	+	3.73898i	0.349030	+	0.146655i
$651$	0.354194	−	0.354194i	0.0138820	−	0.0138820i
$652$	−3.72289	−	4.01101i	−0.145800	−	0.157083i
$653$	−50.8060			−1.98819			−0.994097	−	0.108496i	$-0.965397\pi$
$653$	−50.8060			−1.98819			−0.994097	+	0.108496i	$0.965397\pi$
$654$	−5.33469	+	12.2299i	−0.208603	+	0.478229i
$655$	34.8993	−	14.7333i	1.36363	−	0.575679i
$656$	10.6486	+	0.794528i	0.415759	+	0.0310211i
$657$	2.02877	−	2.02877i	0.0791497	−	0.0791497i
$658$	−23.6406	+	9.28047i	−0.921607	+	0.361790i
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	−0.485537	−	0.874216i	$-0.661376\pi$
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	0.874216	+	0.485537i	$0.161376\pi$
$660$	7.72597	−	17.1545i	0.300733	−	0.667736i
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	0.601012	−	0.799240i	$-0.294764\pi$
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	−0.799240	+	0.601012i	$0.794764\pi$
$662$	−1.35505	+	3.10648i	−0.0526653	+	0.120737i
$663$	9.18745	+	9.18745i	0.356811	+	0.356811i
$664$	−8.32353	−	4.00590i	−0.323015	−	0.155459i
$665$	−17.4605	−	7.09428i	−0.677088	−	0.275104i
$666$	5.98320	−	2.34879i	0.231844	−	0.0910139i
$667$		−	4.32496i		−	0.167463i
$668$	1.06697	−	28.6399i	0.0412825	−	1.10811i
$669$	−11.0402	−	11.0402i	−0.426838	−	0.426838i
$670$	−0.170371	+	14.3770i	−0.00658200	+	0.555432i
$671$		−	30.9947i		−	1.19654i
$672$	5.45399	−	10.3296i	0.210392	−	0.398473i
$673$	−31.6322	−	31.6322i	−1.21933	−	1.21933i	−0.967867	−	0.251464i	$-0.919088\pi$
$673$	−31.6322	−	31.6322i	−1.21933	−	1.21933i	−0.251464	−	0.967867i	$-0.580912\pi$
$674$	7.62323	−	17.4765i	0.293636	−	0.673169i
$675$	19.4735	−	20.0080i	0.749534	−	0.770108i
$676$	−16.3251	+	15.1524i	−0.627889	+	0.582786i
$677$	25.6600			0.986196			0.493098	−	0.869974i	$-0.335864\pi$
$677$	25.6600			0.986196			0.493098	+	0.869974i	$0.335864\pi$
$678$	−4.38350	+	10.0493i	−0.168347	+	0.385942i
$679$		−	3.72896i		−	0.143104i
$680$	−46.9348	−	2.30575i	−1.79987	−	0.0884216i
$681$			7.71190i			0.295521i
$682$	1.03259	+	0.450413i	0.0395397	+	0.0172472i
$683$	12.3536			0.472698			0.236349	−	0.971668i	$-0.424049\pi$
$683$	12.3536			0.472698			0.236349	+	0.971668i	$0.424049\pi$
$684$	0.529041	−	14.2006i	0.0202284	−	0.542974i
$685$	−14.3557	+	6.06048i	−0.548501	+	0.231559i
$686$	23.8230	+	10.3915i	0.909564	+	0.396751i
$687$	0.728309	+	0.728309i	0.0277867	+	0.0277867i
$688$	2.69314	−	36.0946i	0.102675	−	1.37610i
$689$		−	7.91866i		−	0.301677i
$690$	−3.64711	−	3.73458i	−0.138843	−	0.142173i
$691$	22.5426	+	22.5426i	0.857561	+	0.857561i	0.991050	−	0.133489i	$-0.0426180\pi$
$691$	22.5426	+	22.5426i	0.857561	+	0.857561i	−0.133489	+	0.991050i	$0.542618\pi$
$692$	−12.8938	+	11.9676i	−0.490147	+	0.454938i
$693$		−	7.19219i		−	0.273209i
$694$	−3.44831	−	8.78406i	−0.130896	−	0.333438i
$695$	30.0114	−	12.6698i	1.13840	−	0.480593i
$696$	−4.01978	−	11.4789i	−0.152369	−	0.435107i
$697$	14.0253	+	14.0253i	0.531247	+	0.531247i
$698$	3.71438	+	1.62021i	0.140591	+	0.0613258i
$699$	−16.2673	−	16.2673i	−0.615285	−	0.615285i
$700$	11.6644	−	11.1242i	0.440872	−	0.420455i
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.0181663	−	0.999835i	$-0.494217\pi$
$701$	26.9530	−	26.9530i	1.01800	−	1.01800i	0.999835	−	0.0181663i	$-0.00578284\pi$
$702$	−3.93904	−	10.0341i	−0.148670	−	0.378714i
$703$	−12.3680	+	12.3680i	−0.466467	+	0.466467i
$704$	26.1071	+	2.92869i	0.983947	+	0.110379i
$705$	12.4131	+	29.4032i	0.467503	+	1.10739i
$706$	9.83583	+	4.29038i	0.370176	+	0.161471i
$707$	15.1348			0.569203
$708$	0.797891	−	21.4171i	0.0299866	−	0.804905i
$709$	−7.78615	+	7.78615i	−0.292415	+	0.292415i	−0.838034	−	0.545619i	$-0.816295\pi$
$709$	−7.78615	+	7.78615i	−0.292415	+	0.292415i	0.545619	+	0.838034i	$0.316295\pi$
$710$	0.578511	−	48.8186i	0.0217111	−	1.83213i
$711$	13.9988			0.524997
$712$	11.9863	−	24.9053i	0.449205	−	0.933365i
$713$	0.221016	−	0.221016i	0.00827713	−	0.00827713i
$714$	20.1970	−	7.92863i	0.755854	−	0.296721i
$715$	−3.89833	−	9.23410i	−0.145789	−	0.345336i
$716$	−0.697158	+	18.7132i	−0.0260540	+	0.699346i
$717$		−	2.28427i		−	0.0853076i
$718$	−4.01079	−	10.2169i	−0.149681	−	0.381291i
$719$	−20.6777			−0.771150			−0.385575	−	0.922677i	$-0.625997\pi$
$719$	−20.6777			−0.771150			−0.385575	+	0.922677i	$0.625997\pi$
$720$	10.8879	+	5.39989i	0.405768	+	0.201242i
$721$	−3.69779			−0.137713
$722$	4.31161	+	10.9832i	0.160461	+	0.408751i
$723$			13.3797i			0.497597i
$724$	−16.5161	−	0.615306i	−0.613817	−	0.0228677i
$725$	−0.227201	−	16.7812i	−0.00843805	−	0.623237i
$726$	0.364783	−	0.143201i	0.0135384	−	0.00531469i
$727$	20.4994	−	20.4994i	0.760280	−	0.760280i	−0.216093	−	0.976373i	$-0.569331\pi$
$727$	20.4994	−	20.4994i	0.760280	−	0.760280i	0.976373	+	0.216093i	$0.0693315\pi$
$728$	−2.05680	−	5.87341i	−0.0762301	−	0.217683i
$729$	−25.6425			−0.949722
$730$	−4.66521	−	4.77711i	−0.172667	−	0.176809i
$731$	47.5403	−	47.5403i	1.75834	−	1.75834i
$732$	−24.1665	−	0.900320i	−0.893221	−	0.0332768i
$733$	10.7306			0.396344			0.198172	−	0.980167i	$-0.436500\pi$
$733$	10.7306			0.396344			0.198172	+	0.980167i	$0.436500\pi$
$734$	33.0956	+	14.4363i	1.22158	+	0.532853i
$735$	4.74663	−	11.6824i	0.175082	−	0.430912i
$736$	3.40328	−	6.44565i	0.125447	−	0.237590i
$737$	10.5577	−	10.5577i	0.388897	−	0.388897i
$738$	−1.87454	−	4.77511i	−0.0690028	−	0.175774i
$739$	−2.93837	+	2.93837i	−0.108090	+	0.108090i	−0.759083	−	0.650994i	$-0.774352\pi$
$739$	−2.93837	+	2.93837i	−0.108090	+	0.108090i	0.650994	+	0.759083i	$0.274352\pi$
$740$	−5.30090	−	13.9883i	−0.194865	−	0.514221i
$741$	6.46594	+	6.46594i	0.237532	+	0.237532i
$742$	−12.1207	−	5.28705i	−0.444966	−	0.194094i
$743$	−0.223404	−	0.223404i	−0.00819590	−	0.00819590i	0.702997	−	0.711193i	$-0.251845\pi$
$743$	−0.223404	−	0.223404i	−0.00819590	−	0.00819590i	−0.711193	+	0.702997i	$0.751845\pi$
$744$	0.381180	−	0.792022i	0.0139747	−	0.0290369i
$745$	18.6994	+	44.2938i	0.685091	+	1.62280i
$746$	2.25416	+	5.74215i	0.0825308	+	0.210235i
$747$			4.43766i			0.162366i
$748$	33.1969	+	35.7661i	1.21380	+	1.30774i
$749$	4.16243	+	4.16243i	0.152092	+	0.152092i
$750$	−14.3473	−	14.2989i	−0.523888	−	0.522122i
$751$			39.9939i			1.45940i	0.683769	+	0.729699i	$0.260340\pi$
$751$			39.9939i			1.45940i	−0.683769	+	0.729699i	$0.739660\pi$
$752$	−33.7702	+	29.0807i	−1.23147	+	1.06046i
$753$	−16.2055	−	16.2055i	−0.590563	−	0.590563i
$754$	−5.93915	−	2.59065i	−0.216291	−	0.0943459i
$755$	9.01088	−	22.1776i	0.327939	−	0.807126i
$756$	−17.9888	−	0.670168i	−0.654245	−	0.0243738i
$757$	32.9120			1.19621			0.598103	−	0.801419i	$-0.295921\pi$
$757$	32.9120			1.19621			0.598103	+	0.801419i	$0.295921\pi$
$758$	−10.8721	−	4.74241i	−0.394894	−	0.172252i
$759$			5.42070i			0.196759i
$760$	−33.0318	−	1.62274i	−1.19819	−	0.0588631i
$761$		−	33.9591i		−	1.23102i	−0.788130	−	0.615509i	$-0.788951\pi$
$761$		−	33.9591i		−	1.23102i	0.788130	−	0.615509i	$-0.211049\pi$
$762$	7.47058	−	17.1266i	0.270631	−	0.620430i
$763$	11.8707			0.429747
$764$	2.50220	+	2.69585i	0.0905263	+	0.0975324i
$765$	8.78003	+	20.7976i	0.317443	+	0.751937i
$766$	−15.4602	+	35.4429i	−0.558598	+	1.28060i
$767$	−8.07375	−	8.07375i	−0.291526	−	0.291526i
$768$	3.04184	−	20.2706i	0.109763	−	0.731452i
$769$			40.2535i			1.45158i	0.687917	+	0.725789i	$0.258525\pi$
$769$			40.2535i			1.45158i	−0.687917	+	0.725789i	$0.741475\pi$
$770$	−16.7370	−	0.198337i	−0.603160	−	0.00714758i
$771$	−5.29172	−	5.29172i	−0.190577	−	0.190577i
$772$	17.4773	+	0.651112i	0.629020	+	0.0234340i
$773$			9.47175i			0.340675i	0.985386	+	0.170338i	$0.0544858\pi$
$773$			9.47175i			0.340675i	−0.985386	+	0.170338i	$0.945514\pi$
$774$	−16.1858	+	6.35396i	−0.581785	+	0.228388i
$775$	0.845950	−	0.869172i	0.0303874	−	0.0312216i
$776$	−2.16268	−	6.17575i	−0.0776355	−	0.221696i
$777$	4.88405	+	4.88405i	0.175214	+	0.175214i
$778$	5.02656	−	11.5236i	0.180211	−	0.413139i
$779$	9.87073	+	9.87073i	0.353656	+	0.353656i
$780$	−7.31305	+	2.77129i	−0.261849	+	0.0992282i
$781$	−35.8496	+	35.8496i	−1.28280	+	1.28280i
$782$	12.6029	−	4.94745i	0.450679	−	0.176921i
$783$	−13.2533	+	13.2533i	−0.473636	+	0.473636i
$784$	17.5590	+	1.31013i	0.627106	+	0.0467904i
$785$	4.85973	+	1.97453i	0.173451	+	0.0704741i
$786$	−12.2717	+	28.1333i	−0.437717	+	1.00348i
$787$	−48.1367			−1.71589			−0.857945	−	0.513742i	$-0.828259\pi$
$787$	−48.1367			−1.71589			−0.857945	+	0.513742i	$0.828259\pi$
$788$	8.14546	−	7.56034i	0.290170	−	0.269326i
$789$	−21.9455	+	21.9455i	−0.781282	+	0.781282i
$790$	0.386043	−	32.5768i	0.0137348	−	1.15903i
$791$	9.75409			0.346815
$792$	−4.17124	−	11.9114i	−0.148218	−	0.423253i
$793$	−9.11021	+	9.11021i	−0.323513	+	0.323513i
$794$	3.40253	+	8.66743i	0.120751	+	0.307596i
$795$	−6.25537	+	15.3957i	−0.221855	+	0.546031i
$796$	−9.47528	−	10.2086i	−0.335842	−	0.361834i
$797$			33.8962i			1.20066i	0.799751	+	0.600332i	$0.204965\pi$
$797$			33.8962i			1.20066i	−0.799751	+	0.600332i	$0.795035\pi$
$798$	14.2142	−	5.58001i	0.503178	−	0.197530i
$799$	−82.7810			−2.92858
$800$	12.8664	−	25.1884i	0.454895	−	0.890545i
$801$	−13.2782			−0.469162
$802$	−26.0586	+	10.2297i	−0.920160	+	0.361222i
$803$			6.93391i			0.244692i
$804$	−7.92513	−	8.53847i	−0.279498	−	0.301129i
$805$	−1.74813	+	4.30250i	−0.0616133	+	0.151643i
$806$	−0.171117	−	0.435894i	−0.00602733	−	0.0153537i
$807$	−25.3753	+	25.3753i	−0.893254	+	0.893254i
$808$	25.0656	−	8.77770i	0.881806	−	0.308798i
$809$	−27.5625			−0.969047			−0.484523	−	0.874778i	$-0.661007\pi$
$809$	−27.5625			−0.969047			−0.484523	+	0.874778i	$0.661007\pi$
$810$	−0.115310	+	9.73063i	−0.00405159	+	0.341900i
$811$	−24.1817	+	24.1817i	−0.849133	+	0.849133i	−0.990025	−	0.140892i	$-0.955003\pi$
$811$	−24.1817	+	24.1817i	−0.849133	+	0.849133i	0.140892	+	0.990025i	$0.455003\pi$
$812$	−7.93078	+	7.36108i	−0.278316	+	0.258323i
$813$	35.8120			1.25598
$814$	−6.21083	+	14.2385i	−0.217689	+	0.499060i
$815$	5.66841	+	2.30310i	0.198556	+	0.0806742i
$816$	28.8511	−	24.8447i	1.00999	−	0.869738i
$817$	33.4579	−	33.4579i	1.17054	−	1.17054i
$818$	7.59486	−	2.98148i	0.265548	−	0.104245i
$819$	−2.11398	+	2.11398i	−0.0738686	+	0.0738686i
$820$	−11.1639	+	4.23058i	−0.389860	+	0.147738i
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	0.708111	−	0.706101i	$-0.249548\pi$
$821$	0.0575735	+	0.0575735i	0.00200933	+	0.00200933i	−0.706101	+	0.708111i	$0.749548\pi$
$822$	5.04790	−	11.5725i	0.176066	−	0.403636i
$823$	28.5594	+	28.5594i	0.995518	+	0.995518i	0.999990	−	0.00447159i	$-0.00142335\pi$
$823$	28.5594	+	28.5594i	0.995518	+	0.995518i	−0.00447159	+	0.999990i	$0.501423\pi$
$824$	−6.12412	+	2.14460i	−0.213344	+	0.0747106i
$825$	0.284764	+	21.0327i	0.00991420	+	0.732266i
$826$	−17.7487	+	6.96752i	−0.617557	+	0.242431i
$827$			23.0863i			0.802788i	0.915905	+	0.401394i	$0.131474\pi$
$827$			23.0863i			0.802788i	−0.915905	+	0.401394i	$0.868526\pi$
$828$	−3.49922	−	0.130363i	−0.121606	−	0.00453042i
$829$	33.3543	+	33.3543i	1.15844	+	1.15844i	0.984811	+	0.173631i	$0.0555499\pi$
$829$	33.3543	+	33.3543i	1.15844	+	1.15844i	0.173631	+	0.984811i	$0.444450\pi$
$830$	10.3269	+	0.122376i	0.358453	+	0.00424775i
$831$		−	33.3414i		−	1.15660i
$832$	−6.81277	−	8.53442i	−0.236190	−	0.295878i
$833$	23.1269	+	23.1269i	0.801301	+	0.801301i
$834$	−10.5529	+	24.1930i	−0.365419	+	0.837734i
$835$	12.4623	+	29.5198i	0.431275	+	1.02158i
$836$	23.3633	+	25.1715i	0.808037	+	0.870573i
$837$	−1.35456			−0.0468204
$838$	6.94829	−	15.9292i	0.240025	−	0.550264i
$839$		−	49.4524i		−	1.70729i	−0.520859	−	0.853643i	$-0.674388\pi$
$839$		−	49.4524i		−	1.70729i	0.520859	−	0.853643i	$-0.325612\pi$
$840$	−0.640812	+	13.0441i	−0.0221101	+	0.450063i
$841$		−	17.7336i		−	0.611504i
$842$	−36.8825	−	16.0881i	−1.27106	−	0.554433i
$843$	−30.8746			−1.06338
$844$	15.3587	+	0.572185i	0.528668	+	0.0196954i
$845$	9.37380	−	23.0708i	0.322469	−	0.793661i
$846$	19.6240	+	8.55996i	0.674687	+	0.294298i
$847$	−0.246530	−	0.246530i	−0.00847089	−	0.00847089i
$848$	−23.1402	−	1.72656i	−0.794637	−	0.0592904i
$849$			6.06865i			0.208276i
$850$	48.6403	−	19.8586i	1.66835	−	0.681143i
$851$	3.04764	+	3.04764i	0.104472	+	0.104472i
$852$	26.9105	+	28.9932i	0.921940	+	0.993292i
$853$		−	31.3639i		−	1.07388i	−0.843621	−	0.536939i	$-0.819581\pi$
$853$		−	31.3639i		−	1.07388i	0.843621	−	0.536939i	$-0.180419\pi$
$854$	7.86197	+	20.0272i	0.269031	+	0.685316i
$855$	6.17921	+	14.6369i	0.211324	+	0.500571i
$856$	9.30771	+	4.47957i	0.318131	+	0.153108i
$857$	−16.1594	−	16.1594i	−0.551996	−	0.551996i	0.375021	−	0.927016i	$-0.377636\pi$
$857$	−16.1594	−	16.1594i	−0.551996	−	0.551996i	−0.927016	+	0.375021i	$0.877636\pi$
$858$	7.44385	+	3.24700i	0.254129	+	0.110851i
$859$	30.7369	+	30.7369i	1.04873	+	1.04873i	0.998750	+	0.0499792i	$0.0159155\pi$
$859$	30.7369	+	30.7369i	1.04873	+	1.04873i	0.0499792	+	0.998750i	$0.484085\pi$
$860$	14.3400	+	37.8412i	0.488990	+	1.29038i
$861$	3.89790	−	3.89790i	0.132840	−	0.132840i
$862$	−17.3765	−	44.2640i	−0.591845	−	1.50764i
$863$	18.9353	−	18.9353i	0.644565	−	0.644565i	−0.307109	−	0.951674i	$-0.599362\pi$
$863$	18.9353	−	18.9353i	0.644565	−	0.644565i	0.951674	+	0.307109i	$0.0993618\pi$
$864$	−30.1809	+	9.32299i	−1.02678	+	0.317175i
$865$	7.40353	−	18.2216i	0.251728	−	0.619553i
$866$	−13.6858	−	5.96974i	−0.465063	−	0.202860i
$867$	48.9441			1.66223
$868$	−0.781453	−	0.0291129i	−0.0265242	−	0.000988156i
$869$	−23.9226	+	23.9226i	−0.811517	+	0.811517i
$870$	9.50061	+	9.72848i	0.322101	+	0.329826i
$871$	−6.20638			−0.210295
$872$	19.6597	−	6.88460i	0.665761	−	0.233142i
$873$	−2.22280	+	2.22280i	−0.0752305	+	0.0752305i
$874$	8.86966	−	3.48191i	0.300021	−	0.117778i
$875$	−6.55684	+	16.7859i	−0.221662	+	0.567465i
$876$	5.40636	+	0.201413i	0.182664	+	0.00680511i
$877$		−	49.7461i		−	1.67981i	−0.542737	−	0.839903i	$-0.682612\pi$
$877$		−	49.7461i		−	1.67981i	0.542737	−	0.839903i	$-0.317388\pi$
$878$	−4.09251	−	10.4250i	−0.138115	−	0.351828i
$879$	3.98423			0.134385
$880$	−27.8342	+	9.37844i	−0.938289	+	0.316147i
$881$	27.7694			0.935574			0.467787	−	0.883841i	$-0.345051\pi$
$881$	27.7694			0.935574			0.467787	+	0.883841i	$0.345051\pi$
$882$	−3.09101	−	7.87389i	−0.104080	−	0.265128i
$883$		−	42.4602i		−	1.42890i	−0.699686	−	0.714450i	$-0.746677\pi$
$883$		−	42.4602i		−	1.42890i	0.699686	−	0.714450i	$-0.253323\pi$
$884$	0.755161	−	20.2702i	0.0253988	−	0.681759i
$885$	9.31938	+	22.0751i	0.313268	+	0.742048i
$886$	−14.0150	+	5.50178i	−0.470842	+	0.184836i
$887$	−16.1076	+	16.1076i	−0.540842	+	0.540842i	−0.923776	−	0.382934i	$-0.874914\pi$
$887$	−16.1076	+	16.1076i	−0.540842	+	0.540842i	0.382934	+	0.923776i	$0.374914\pi$
$888$	10.9213	+	5.25617i	0.366496	+	0.176385i
$889$	−16.6234			−0.557531
$890$	−0.366170	+	30.8998i	−0.0122740	+	1.03576i
$891$	7.14563	−	7.14563i	0.239388	−	0.239388i
$892$	−0.907445	+	24.3578i	−0.0303835	+	0.815560i
$893$	−58.2596			−1.94958
$894$	−35.7064	−	15.5751i	−1.19420	−	0.520909i
$895$	−8.14281	−	19.2882i	−0.272184	−	0.644732i
$896$	−17.6119	+	4.72983i	−0.588373	+	0.158012i
$897$	1.59329	−	1.59329i	0.0531986	−	0.0531986i
$898$	−3.14260	−	8.00530i	−0.104870	−	0.267140i
$899$	−0.575741	+	0.575741i	−0.0192020	+	0.0192020i
$900$	−13.5841	−	0.321995i	−0.452803	−	0.0107332i
$901$	−30.4780	−	30.4780i	−1.01537	−	1.01537i
$902$	11.3636	+	4.95678i	0.378366	+	0.165043i
$903$	−13.2123	−	13.2123i	−0.439679	−	0.439679i
$904$	16.1543	−	5.65706i	0.537285	−	0.188151i
$905$	17.0236	−	7.18678i	0.565883	−	0.238897i
$906$	7.08751	+	18.0544i	0.235467	+	0.599816i
$907$			9.20991i			0.305810i	0.988241	+	0.152905i	$0.0488628\pi$
$907$			9.20991i			0.305810i	−0.988241	+	0.152905i	$0.951137\pi$
$908$	8.82427	−	8.19040i	0.292844	−	0.271808i
$909$	−9.02174	−	9.02174i	−0.299232	−	0.299232i
$910$	4.86117	+	4.97777i	0.161146	+	0.165011i
$911$			45.8065i			1.51764i	0.651302	+	0.758819i	$0.274223\pi$
$911$			45.8065i			1.51764i	−0.651302	+	0.758819i	$0.725777\pi$
$912$	20.3048	−	17.4852i	0.672359	−	0.578992i
$913$	−7.58351	−	7.58351i	−0.250978	−	0.250978i
$914$	0.575282	+	0.250938i	0.0190286	+	0.00830028i
$915$	24.9090	−	10.5158i	0.823467	−	0.347640i
$916$	0.0598632	−	1.60686i	0.00197794	−	0.0530921i
$917$	27.3068			0.901749
$918$	−53.7810	−	23.4592i	−1.77504	−	0.774270i
$919$		−	5.52468i		−	0.182242i	−0.995840	−	0.0911211i	$-0.970955\pi$
$919$		−	5.52468i		−	0.182242i	0.995840	−	0.0911211i	$-0.0290450\pi$
$920$	−0.399866	+	8.13947i	−0.0131832	+	0.268350i
$921$			18.6617i			0.614924i
$922$	−7.92398	+	18.1660i	−0.260962	+	0.598264i
$923$	21.0744			0.693672
$924$	9.94007	−	9.22604i	0.327004	−	0.303514i
$925$	11.9852	+	11.6650i	0.394070	+	0.383542i
$926$	13.8681	−	31.7930i	0.455734	−	1.04478i
$927$	2.20422	+	2.20422i	0.0723961	+	0.0723961i
$928$	−8.86544	+	16.7907i	−0.291022	+	0.551182i
$929$		−	43.4288i		−	1.42485i	−0.701746	−	0.712427i	$-0.747596\pi$
$929$		−	43.4288i		−	1.42485i	0.701746	−	0.712427i	$-0.252404\pi$
$930$	−0.0116447	+	0.982655i	−0.000381845	+	0.0322225i
$931$	16.2763	+	16.2763i	0.533433	+	0.533433i
$932$	−1.33708	+	35.8903i	−0.0437977	+	1.17562i
$933$		−	18.5210i		−	0.606352i
$934$	−2.00446	+	0.786879i	−0.0655878	+	0.0257475i
$935$	−50.5451	−	20.5367i	−1.65300	−	0.671623i
$936$	−2.27505	+	4.72713i	−0.0743623	+	0.154511i
$937$	−20.7275	−	20.7275i	−0.677138	−	0.677138i	0.282213	−	0.959352i	$-0.408931\pi$
$937$	−20.7275	−	20.7275i	−0.677138	−	0.677138i	−0.959352	+	0.282213i	$0.908931\pi$
$938$	−4.14381	+	9.49983i	−0.135300	+	0.310180i
$939$	12.9741	+	12.9741i	0.423392	+	0.423392i
$940$	20.4611	−	45.4311i	0.667369	−	1.48180i
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	−0.476775	−	0.879026i	$-0.658194\pi$
$941$	12.3393	−	12.3393i	0.402251	−	0.402251i	0.879026	+	0.476775i	$0.158194\pi$
$942$	−3.95621	+	1.55307i	−0.128900	+	0.0506017i
$943$	2.43228	−	2.43228i	0.0792060	−	0.0792060i
$944$	−25.3538	+	21.8330i	−0.825194	+	0.710604i
$945$	18.5414	−	7.82757i	0.603153	−	0.254631i
$946$	16.8015	−	38.5181i	0.546265	−	1.25233i
$947$	−48.3611			−1.57152			−0.785762	−	0.618529i	$-0.787729\pi$
$947$	−48.3611			−1.57152			−0.785762	+	0.618529i	$0.787729\pi$
$948$	17.9575	+	19.3473i	0.583233	+	0.628371i
$949$	2.03807	−	2.03807i	0.0661585	−	0.0661585i
$950$	34.2320	−	13.9760i	1.11063	−	0.453443i
$951$	−17.7752			−0.576399
$952$	−30.5224	−	14.6897i	−0.989237	−	0.476095i
$953$	34.0371	−	34.0371i	1.10257	−	1.10257i	0.108471	−	0.994100i	$-0.465405\pi$
$953$	34.0371	−	34.0371i	1.10257	−	1.10257i	0.994100	−	0.108471i	$-0.0345953\pi$
$954$	4.07350	+	10.3766i	0.131885	+	0.335956i
$955$	−3.80980	−	1.54794i	−0.123282	−	0.0500903i
$956$	−2.61375	+	2.42600i	−0.0845348	+	0.0784624i
$957$		−	14.1208i		−	0.456459i
$958$	0.668286	−	0.262346i	0.0215913	−	0.00847600i
$959$	−11.2325			−0.362716
$960$	6.50385	+	21.9747i	0.209911	+	0.709230i
$961$	30.9412			0.998102
$962$	6.01063	−	2.35956i	0.193791	−	0.0760753i
$963$		−	4.96238i		−	0.159911i
$964$	15.3096	−	14.2099i	0.493090	−	0.457669i
$965$	−18.0142	+	7.60500i	−0.579898	+	0.244814i
$966$	−1.37499	−	3.50258i	−0.0442395	−	0.112694i
$967$	−18.9307	+	18.9307i	−0.608770	+	0.608770i	−0.942625	−	0.333855i	$-0.891651\pi$
$967$	−18.9307	+	18.9307i	−0.608770	+	0.608770i	0.333855	+	0.942625i	$0.391651\pi$
$968$	−0.551273	−	0.265314i	−0.0177186	−	0.00852751i
$969$	49.7732			1.59895
$970$	5.11141	+	5.23400i	0.164117	+	0.168054i
$971$	−21.2698	+	21.2698i	−0.682580	+	0.682580i	−0.960581	−	0.278001i	$-0.910328\pi$
$971$	−21.2698	+	21.2698i	−0.682580	+	0.682580i	0.278001	+	0.960581i	$0.410328\pi$
$972$	17.4288	+	18.7776i	0.559028	+	0.602292i
$973$	23.4822			0.752805
$974$	20.7752	−	47.6278i	0.665681	−	1.52609i
$975$	6.09841	−	6.26581i	0.195305	−	0.200666i
$976$	24.6358	+	28.6085i	0.788573	+	0.915736i
$977$	2.13884	−	2.13884i	0.0684275	−	0.0684275i	−0.672065	−	0.740492i	$-0.734592\pi$
$977$	2.13884	−	2.13884i	0.0684275	−	0.0684275i	0.740492	+	0.672065i	$0.234592\pi$
$978$	−4.61454	+	1.81151i	−0.147557	+	0.0579256i
$979$	22.6911	−	22.6911i	0.725210	−	0.725210i
$980$	−18.4086	+	6.97598i	−0.588042	+	0.222840i
$981$	−7.07601	−	7.07601i	−0.225919	−	0.225919i
$982$	2.62447	−	6.01667i	0.0837501	−	0.192000i
$983$	−6.18193	−	6.18193i	−0.197173	−	0.197173i	0.601614	−	0.798787i	$-0.294525\pi$
$983$	−6.18193	−	6.18193i	−0.197173	−	0.197173i	−0.798787	+	0.601614i	$0.794525\pi$
$984$	4.19488	−	8.71619i	0.133728	−	0.277862i
$985$	−4.67708	+	11.5113i	−0.149024	+	0.366779i
$986$	−32.8301	+	12.8880i	−1.04552	+	0.410436i
$987$			23.0064i			0.732302i
$988$	0.531466	−	14.2657i	0.0169082	−	0.453853i
$989$	−8.24447	−	8.24447i	−0.262159	−	0.262159i
$990$	9.85857	+	10.0950i	0.313326	+	0.320841i
$991$		−	43.4847i		−	1.38134i	−0.723172	−	0.690668i	$-0.757317\pi$
$991$		−	43.4847i		−	1.38134i	0.723172	−	0.690668i	$-0.242683\pi$
$992$	−1.31110	+	0.405002i	−0.0416273	+	0.0128588i
$993$	2.17092	+	2.17092i	0.0688921	+	0.0688921i
$994$	14.0707	−	32.2576i	0.446297	−	1.02315i
$995$	14.4269	+	5.86173i	0.457364	+	0.185829i
$996$	−6.13314	+	5.69257i	−0.194336	+	0.180376i
$997$	−33.4043			−1.05793			−0.528963	−	0.848645i	$-0.677419\pi$
$997$	−33.4043			−1.05793			−0.528963	+	0.848645i	$0.677419\pi$
$998$	−5.38879	+	12.3540i	−0.170579	+	0.391059i
$999$		−	18.6783i		−	0.590954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.j.b.43.2	✓	18
3.2	odd	2		720.2.bd.g.523.8		18
4.3	odd	2		320.2.j.b.143.3		18
5.2	odd	4		80.2.s.b.27.4	yes	18
5.3	odd	4		400.2.s.d.107.6		18
5.4	even	2		400.2.j.d.43.8		18
8.3	odd	2		640.2.j.c.543.7		18
8.5	even	2		640.2.j.d.543.3		18
15.2	even	4		720.2.z.g.667.6		18
16.3	odd	4		80.2.s.b.3.4	yes	18
16.5	even	4		640.2.s.c.223.7		18
16.11	odd	4		640.2.s.d.223.3		18
16.13	even	4		320.2.s.b.303.3		18
20.3	even	4		1600.2.s.d.207.7		18
20.7	even	4		320.2.s.b.207.3		18
20.19	odd	2		1600.2.j.d.143.7		18
40.27	even	4		640.2.s.c.287.7		18
40.37	odd	4		640.2.s.d.287.3		18
48.35	even	4		720.2.z.g.163.6		18
80.3	even	4		400.2.j.d.307.8		18
80.13	odd	4		1600.2.j.d.1007.3		18
80.19	odd	4		400.2.s.d.243.6		18
80.27	even	4		640.2.j.d.607.7		18
80.29	even	4		1600.2.s.d.943.7		18
80.37	odd	4		640.2.j.c.607.3		18
80.67	even	4	inner	80.2.j.b.67.2	yes	18
80.77	odd	4		320.2.j.b.47.7		18
240.227	odd	4		720.2.bd.g.307.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.2	✓	18	1.1	even	1	trivial
80.2.j.b.67.2	yes	18	80.67	even	4	inner
80.2.s.b.3.4	yes	18	16.3	odd	4
80.2.s.b.27.4	yes	18	5.2	odd	4
320.2.j.b.47.7		18	80.77	odd	4
320.2.j.b.143.3		18	4.3	odd	2
320.2.s.b.207.3		18	20.7	even	4
320.2.s.b.303.3		18	16.13	even	4
400.2.j.d.43.8		18	5.4	even	2
400.2.j.d.307.8		18	80.3	even	4
400.2.s.d.107.6		18	5.3	odd	4
400.2.s.d.243.6		18	80.19	odd	4
640.2.j.c.543.7		18	8.3	odd	2
640.2.j.c.607.3		18	80.37	odd	4
640.2.j.d.543.3		18	8.5	even	2
640.2.j.d.607.7		18	80.27	even	4
640.2.s.c.223.7		18	16.5	even	4
640.2.s.c.287.7		18	40.27	even	4
640.2.s.d.223.3		18	16.11	odd	4
640.2.s.d.287.3		18	40.37	odd	4
720.2.z.g.163.6		18	48.35	even	4
720.2.z.g.667.6		18	15.2	even	4
720.2.bd.g.307.8		18	240.227	odd	4
720.2.bd.g.523.8		18	3.2	odd	2
1600.2.j.d.143.7		18	20.19	odd	2
1600.2.j.d.1007.3		18	80.13	odd	4
1600.2.s.d.207.7		18	20.3	even	4
1600.2.s.d.943.7		18	80.29	even	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31641 + 0.516777i) q^{2} +1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.841703 + 2.07160i) q^{5} +(-0.662041 - 1.68645i) q^{6} +(-1.13975 + 1.13975i) q^{7} +(-1.22659 + 2.54862i) q^{8} +1.35879 q^{9} +O(q^{10})\)	\(q+(-1.31641 + 0.516777i) q^{2} +1.28110i q^{3} +(1.46588 - 1.36058i) q^{4} +(-0.841703 + 2.07160i) q^{5} +(-0.662041 - 1.68645i) q^{6} +(-1.13975 + 1.13975i) q^{7} +(-1.22659 + 2.54862i) q^{8} +1.35879 q^{9} +(0.0374711 - 3.16206i) q^{10} +(-2.32204 + 2.32204i) q^{11} +(1.74304 + 1.87794i) q^{12} +1.36502 q^{13} +(0.911384 - 2.08938i) q^{14} +(-2.65392 - 1.07830i) q^{15} +(0.297625 - 3.98891i) q^{16} +(5.25380 - 5.25380i) q^{17} +(-1.78873 + 0.702192i) q^{18} +(3.69752 - 3.69752i) q^{19} +(1.58475 + 4.18193i) q^{20} +(-1.46013 - 1.46013i) q^{21} +(1.85678 - 4.25673i) q^{22} +(-0.911118 - 0.911118i) q^{23} +(-3.26503 - 1.57138i) q^{24} +(-3.58307 - 3.48735i) q^{25} +(-1.79693 + 0.705412i) q^{26} +5.58403i q^{27} +(-0.120015 + 3.22146i) q^{28} +(2.37343 + 2.37343i) q^{29} +(4.05090 + 0.0480041i) q^{30} +0.242577i q^{31} +(1.66958 + 5.40486i) q^{32} +(-2.97475 - 2.97475i) q^{33} +(-4.20112 + 9.63121i) q^{34} +(-1.40178 - 3.32044i) q^{35} +(1.99183 - 1.84875i) q^{36} -3.34494 q^{37} +(-2.95666 + 6.77825i) q^{38} +1.74872i q^{39} +(-4.24731 - 4.68619i) q^{40} +2.66956i q^{41} +(2.67669 + 1.16757i) q^{42} +9.04874 q^{43} +(-0.244509 + 6.56316i) q^{44} +(-1.14370 + 2.81488i) q^{45} +(1.67025 + 0.728562i) q^{46} +(-7.87820 - 7.87820i) q^{47} +(5.11018 + 0.381287i) q^{48} +4.40194i q^{49} +(6.51898 + 2.73914i) q^{50} +(6.73063 + 6.73063i) q^{51} +(2.00096 - 1.85723i) q^{52} -5.80113i q^{53} +(-2.88570 - 7.35089i) q^{54} +(-2.85587 - 6.76480i) q^{55} +(-1.50679 - 4.30279i) q^{56} +(4.73688 + 4.73688i) q^{57} +(-4.35095 - 1.89788i) q^{58} +(-5.91474 - 5.91474i) q^{59} +(-5.35746 + 2.03022i) q^{60} +(-6.67404 + 6.67404i) q^{61} +(-0.125358 - 0.319332i) q^{62} +(-1.54868 + 1.54868i) q^{63} +(-4.99096 - 6.25222i) q^{64} +(-1.14894 + 2.82778i) q^{65} +(5.45328 + 2.37872i) q^{66} -4.54673 q^{67} +(0.553222 - 14.8497i) q^{68} +(1.16723 - 1.16723i) q^{69} +(3.56124 + 3.64666i) q^{70} +15.4389 q^{71} +(-1.66668 + 3.46305i) q^{72} +(1.49307 - 1.49307i) q^{73} +(4.40332 - 1.72859i) q^{74} +(4.46763 - 4.59026i) q^{75} +(0.389347 - 10.4509i) q^{76} -5.29308i q^{77} +(-0.903701 - 2.30204i) q^{78} +10.3024 q^{79} +(8.01293 + 3.97404i) q^{80} -3.07731 q^{81} +(-1.37957 - 3.51424i) q^{82} +3.26589i q^{83} +(-4.12701 - 0.153751i) q^{84} +(6.46165 + 15.3059i) q^{85} +(-11.9119 + 4.67618i) q^{86} +(-3.04060 + 3.04060i) q^{87} +(-3.06981 - 8.76618i) q^{88} -9.77206 q^{89} +(0.0509154 - 4.29657i) q^{90} +(-1.55578 + 1.55578i) q^{91} +(-2.57524 - 0.0959403i) q^{92} -0.310765 q^{93} +(14.4422 + 6.29969i) q^{94} +(4.54758 + 10.7720i) q^{95} +(-6.92415 + 2.13889i) q^{96} +(-1.63587 + 1.63587i) q^{97} +(-2.27482 - 5.79477i) q^{98} +(-3.15516 + 3.15516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9	\( 18 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 8 q^{6} + 2 q^{7} - 4 q^{8} - 10 q^{9} - 12 q^{10} - 2 q^{11} + 4 q^{12} + 12 q^{14} + 20 q^{15} - 6 q^{17} + 16 q^{18} + 2 q^{19} - 4 q^{20} - 16 q^{21} + 4 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 16 q^{26} - 4 q^{28} - 14 q^{29} + 20 q^{30} - 4 q^{32} - 8 q^{33} - 28 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} + 16 q^{38} + 20 q^{40} + 28 q^{42} - 44 q^{43} + 44 q^{44} - 4 q^{45} + 12 q^{46} - 38 q^{47} + 60 q^{48} + 20 q^{50} + 8 q^{51} - 40 q^{52} - 4 q^{54} - 6 q^{55} + 20 q^{56} + 24 q^{57} - 20 q^{58} - 10 q^{59} - 68 q^{60} + 14 q^{61} + 6 q^{63} - 16 q^{64} + 4 q^{66} + 12 q^{67} + 36 q^{68} + 32 q^{69} - 36 q^{70} + 24 q^{71} - 36 q^{72} + 14 q^{73} + 48 q^{74} + 64 q^{75} - 16 q^{76} - 84 q^{78} + 16 q^{79} - 20 q^{80} + 2 q^{81} - 28 q^{82} - 24 q^{84} - 10 q^{85} - 36 q^{86} + 24 q^{87} - 96 q^{88} - 12 q^{89} - 64 q^{90} + 52 q^{92} + 16 q^{93} + 28 q^{94} - 34 q^{95} - 40 q^{96} + 18 q^{97} + 32 q^{98} - 22 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 8 * q^6 + 2 * q^7 - 4 * q^8 - 10 * q^9 - 12 * q^10 - 2 * q^11 + 4 * q^12 + 12 * q^14 + 20 * q^15 - 6 * q^17 + 16 * q^18 + 2 * q^19 - 4 * q^20 - 16 * q^21 + 4 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 16 * q^26 - 4 * q^28 - 14 * q^29 + 20 * q^30 - 4 * q^32 - 8 * q^33 - 28 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 + 16 * q^38 + 20 * q^40 + 28 * q^42 - 44 * q^43 + 44 * q^44 - 4 * q^45 + 12 * q^46 - 38 * q^47 + 60 * q^48 + 20 * q^50 + 8 * q^51 - 40 * q^52 - 4 * q^54 - 6 * q^55 + 20 * q^56 + 24 * q^57 - 20 * q^58 - 10 * q^59 - 68 * q^60 + 14 * q^61 + 6 * q^63 - 16 * q^64 + 4 * q^66 + 12 * q^67 + 36 * q^68 + 32 * q^69 - 36 * q^70 + 24 * q^71 - 36 * q^72 + 14 * q^73 + 48 * q^74 + 64 * q^75 - 16 * q^76 - 84 * q^78 + 16 * q^79 - 20 * q^80 + 2 * q^81 - 28 * q^82 - 24 * q^84 - 10 * q^85 - 36 * q^86 + 24 * q^87 - 96 * q^88 - 12 * q^89 - 64 * q^90 + 52 * q^92 + 16 * q^93 + 28 * q^94 - 34 * q^95 - 40 * q^96 + 18 * q^97 + 32 * q^98 - 22 * q^99

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