LMFDB - Embedded newform 80.2.s.b.27.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

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, 3, 3]))

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

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

chi := DirichletCharacter("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (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			27.4
Root			$1.41323 + 0.0526497i$ of defining polynomial
Character	$\chi$	$=$	80.27
Dual form			80.2.s.b.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.516777 - 1.31641i) q^{2} +1.28110 q^{3} +(-1.46588 + 1.36058i) q^{4} +(2.07160 - 0.841703i) q^{5} +(-0.662041 - 1.68645i) q^{6} +(-1.13975 - 1.13975i) q^{7} +(2.54862 + 1.22659i) q^{8} -1.35879 q^{9} +(-2.17858 - 2.29211i) q^{10} +(-2.32204 + 2.32204i) q^{11} +(-1.87794 + 1.74304i) q^{12} -1.36502i 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} +(0.702192 + 1.78873i) q^{18} +(-3.69752 + 3.69752i) q^{19} +(-1.89152 + 4.05243i) q^{20} +(-1.46013 - 1.46013i) q^{21} +(4.25673 + 1.85678i) 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} -5.58403 q^{27} +(3.22146 + 0.120015i) q^{28} +(-2.37343 - 2.37343i) q^{29} +(-2.79098 - 2.93641i) q^{30} +0.242577i q^{31} +(-5.40486 + 1.66958i) q^{32} +(-2.97475 + 2.97475i) q^{33} +(4.20112 - 9.63121i) q^{34} +(-3.32044 - 1.40178i) q^{35} +(1.99183 - 1.84875i) q^{36} -3.34494i q^{37} +(6.77825 + 2.95666i) q^{38} -1.74872i q^{39} +(6.31216 + 0.395820i) q^{40} +2.66956i q^{41} +(-1.16757 + 2.67669i) q^{42} -9.04874i q^{43} +(0.244509 - 6.56316i) q^{44} +(-2.81488 + 1.14370i) q^{45} +(1.67025 + 0.728562i) q^{46} +(7.87820 - 7.87820i) q^{47} +(0.381287 - 5.11018i) q^{48} -4.40194i q^{49} +(-6.44244 - 2.91462i) q^{50} +(6.73063 + 6.73063i) q^{51} +(1.85723 + 2.00096i) q^{52} -5.80113 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} +(-1.89788 + 4.35095i) q^{58} +(5.91474 + 5.91474i) q^{59} +(-2.42322 + 5.19155i) q^{60} +(-6.67404 + 6.67404i) q^{61} +(0.319332 - 0.125358i) 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} -4.54673i q^{67} +(-14.8497 - 0.553222i) q^{68} +(-1.16723 + 1.16723i) q^{69} +(-0.129391 + 5.09547i) q^{70} +15.4389 q^{71} +(-3.46305 - 1.66668i) q^{72} +(-1.49307 - 1.49307i) q^{73} +(-4.40332 + 1.72859i) q^{74} +(4.59026 - 4.46763i) q^{75} +(0.389347 - 10.4509i) q^{76} +5.29308 q^{77} +(-2.30204 + 0.903701i) q^{78} -10.3024 q^{79} +(-2.74092 - 8.51395i) q^{80} -3.07731 q^{81} +(3.51424 - 1.37957i) q^{82} +3.26589 q^{83} +(4.12701 + 0.153751i) q^{84} +(15.3059 + 6.46165i) q^{85} +(-11.9119 + 4.67618i) q^{86} +(-3.04060 - 3.04060i) q^{87} +(-8.76618 + 3.06981i) q^{88} +9.77206 q^{89} +(2.96024 + 3.11450i) q^{90} +(-1.55578 + 1.55578i) q^{91} +(0.0959403 - 2.57524i) q^{92} +0.310765i 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} +(-5.79477 + 2.27482i) q^{98} +(3.15516 - 3.15516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25}+ \cdots + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

Character values

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

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

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 $

$2$	−0.516777	−	1.31641i	−0.365417	−	0.930844i
$2$	−0.516777	−	1.31641i	−0.365417	−	0.930844i
$3$	1.28110			0.739642			0.369821	−	0.929103i	$-0.379419\pi$
$3$	1.28110			0.739642			0.369821	+	0.929103i	$0.379419\pi$
$4$	−1.46588	+	1.36058i	−0.732941	+	0.680292i
$5$	2.07160	−	0.841703i	0.926449	−	0.376421i
$5$	2.07160	−	0.841703i	0.926449	−	0.376421i
$6$	−0.662041	−	1.68645i	−0.270277	−	0.688491i
$7$	−1.13975	−	1.13975i	−0.430785	−	0.430785i	0.458111	−	0.888895i	$-0.348526\pi$
$7$	−1.13975	−	1.13975i	−0.430785	−	0.430785i	−0.888895	+	0.458111i	$0.848526\pi$
$8$	2.54862	+	1.22659i	0.901074	+	0.433664i
$9$	−1.35879			−0.452930
$10$	−2.17858	−	2.29211i	−0.688929	−	0.724829i
$11$	−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	$0.414854\pi$
$12$	−1.87794	+	1.74304i	−0.542114	+	0.503172i
$13$		−	1.36502i		−	0.378589i	−0.981920	−	0.189294i	$-0.939380\pi$
$13$		−	1.36502i		−	0.378589i	0.981920	−	0.189294i	$-0.0606201\pi$
$14$	−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	0.943845	+	0.330389i	$0.107180\pi$
$17$	5.25380	+	5.25380i	1.27423	+	1.27423i	0.330389	+	0.943845i	$0.392820\pi$
$18$	0.702192	+	1.78873i	0.165508	+	0.421608i
$19$	−3.69752	+	3.69752i	−0.848269	+	0.848269i	−0.989917	−	0.141648i	$-0.954760\pi$
$19$	−3.69752	+	3.69752i	−0.848269	+	0.848269i	0.141648	+	0.989917i	$0.454760\pi$
$20$	−1.89152	+	4.05243i	−0.422957	+	0.906150i
$21$	−1.46013	−	1.46013i	−0.318626	−	0.318626i
$22$	4.25673	+	1.85678i	0.907538	+	0.395867i
$23$	−0.911118	+	0.911118i	−0.189981	+	0.189981i	−0.795688	−	0.605707i	$-0.792890\pi$
$23$	−0.911118	+	0.911118i	−0.189981	+	0.189981i	0.605707	+	0.795688i	$0.292890\pi$
$24$	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
$27$	−5.58403			−1.07465
$28$	3.22146	+	0.120015i	0.608799	+	0.0226807i
$29$	−2.37343	−	2.37343i	−0.440736	−	0.440736i	0.451524	−	0.892259i	$-0.350881\pi$
$29$	−2.37343	−	2.37343i	−0.440736	−	0.440736i	−0.892259	+	0.451524i	$0.850881\pi$
$30$	−2.79098	−	2.93641i	−0.509560	−	0.536114i
$31$			0.242577i			0.0435681i	0.999763	+	0.0217841i	$0.00693463\pi$
$31$			0.242577i			0.0435681i	−0.999763	+	0.0217841i	$0.993065\pi$
$32$	−5.40486	+	1.66958i	−0.955453	+	0.295143i
$33$	−2.97475	+	2.97475i	−0.517838	+	0.517838i
$34$	4.20112	−	9.63121i	0.720487	−	1.65174i
$35$	−3.32044	−	1.40178i	−0.561256	−	0.236944i
$36$	1.99183	−	1.84875i	0.331971	−	0.308125i
$37$		−	3.34494i		−	0.549905i	−0.961458	−	0.274953i	$-0.911338\pi$
$37$		−	3.34494i		−	0.549905i	0.961458	−	0.274953i	$-0.0886621\pi$
$38$	6.77825	+	2.95666i	1.09958	+	0.479634i
$39$		−	1.74872i		−	0.280020i
$40$	6.31216	+	0.395820i	0.998040	+	0.0625846i
$41$			2.66956i			0.416915i	0.978031	+	0.208457i	$0.0668442\pi$
$41$			2.66956i			0.416915i	−0.978031	+	0.208457i	$0.933156\pi$
$42$	−1.16757	+	2.67669i	−0.180160	+	0.413023i
$43$		−	9.04874i		−	1.37992i	−0.723847	−	0.689960i	$-0.757628\pi$
$43$		−	9.04874i		−	1.37992i	0.723847	−	0.689960i	$-0.242372\pi$
$44$	0.244509	−	6.56316i	0.0368611	−	0.989433i
$45$	−2.81488	+	1.14370i	−0.419617	+	0.170492i
$46$	1.67025	+	0.728562i	0.246265	+	0.107421i
$47$	7.87820	−	7.87820i	1.14915	−	1.14915i	0.162435	−	0.986719i	$-0.448065\pi$
$47$	7.87820	−	7.87820i	1.14915	−	1.14915i	0.986719	−	0.162435i	$-0.0519348\pi$
$48$	0.381287	−	5.11018i	0.0550340	−	0.737591i
$49$		−	4.40194i		−	0.628849i
$50$	−6.44244	−	2.91462i	−0.911098	−	0.412190i
$51$	6.73063	+	6.73063i	0.942476	+	0.942476i
$52$	1.85723	+	2.00096i	0.257551	+	0.277483i
$53$	−5.80113			−0.796846			−0.398423	−	0.917202i	$-0.630442\pi$
$53$	−5.80113			−0.796846			−0.398423	+	0.917202i	$0.630442\pi$
$54$	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
$58$	−1.89788	+	4.35095i	−0.249204	+	0.571308i
$59$	5.91474	+	5.91474i	0.770033	+	0.770033i	0.978112	−	0.208079i	$-0.0667210\pi$
$59$	5.91474	+	5.91474i	0.770033	+	0.770033i	−0.208079	+	0.978112i	$0.566721\pi$
$60$	−2.42322	+	5.19155i	−0.312836	+	0.670226i
$61$	−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	$0.456523\pi$
$62$	0.319332	−	0.125358i	0.0405551	−	0.0159205i
$63$	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
$67$		−	4.54673i		−	0.555471i	−0.960658	−	0.277736i	$-0.910416\pi$
$67$		−	4.54673i		−	0.555471i	0.960658	−	0.277736i	$-0.0895839\pi$
$68$	−14.8497	−	0.553222i	−1.80079	−	0.0670881i
$69$	−1.16723	+	1.16723i	−0.140518	+	0.140518i
$70$	−0.129391	+	5.09547i	−0.0154652	+	0.609025i
$71$	15.4389			1.83226			0.916128	−	0.400885i	$-0.131297\pi$
$71$	15.4389			1.83226			0.916128	+	0.400885i	$0.131297\pi$
$72$	−3.46305	−	1.66668i	−0.408124	−	0.196420i
$73$	−1.49307	−	1.49307i	−0.174750	−	0.174750i	0.614313	−	0.789063i	$-0.289433\pi$
$73$	−1.49307	−	1.49307i	−0.174750	−	0.174750i	−0.789063	+	0.614313i	$0.789433\pi$
$74$	−4.40332	+	1.72859i	−0.511876	+	0.200944i
$75$	4.59026	−	4.46763i	0.530038	−	0.515877i
$76$	0.389347	−	10.4509i	0.0446611	−	1.19880i
$77$	5.29308			0.603202
$78$	−2.30204	+	0.903701i	−0.260655	+	0.102324i
$79$	−10.3024			−1.15911			−0.579556	−	0.814932i	$-0.696774\pi$
$79$	−10.3024			−1.15911			−0.579556	+	0.814932i	$0.696774\pi$
$80$	−2.74092	−	8.51395i	−0.306444	−	0.951889i
$81$	−3.07731			−0.341924
$82$	3.51424	−	1.37957i	0.388083	−	0.152348i
$83$	3.26589			0.358478			0.179239	−	0.983806i	$-0.442636\pi$
$83$	3.26589			0.358478			0.179239	+	0.983806i	$0.442636\pi$
$84$	4.12701	+	0.153751i	0.450293	+	0.0167756i
$85$	15.3059	+	6.46165i	1.66016	+	0.700864i
$86$	−11.9119	+	4.67618i	−1.28449	+	0.504246i
$87$	−3.04060	−	3.04060i	−0.325986	−	0.325986i
$88$	−8.76618	+	3.06981i	−0.934477	+	0.327243i
$89$	9.77206			1.03584			0.517918	−	0.855430i	$-0.326707\pi$
$89$	9.77206			1.03584			0.517918	+	0.855430i	$0.326707\pi$
$90$	2.96024	+	3.11450i	0.312037	+	0.328297i
$91$	−1.55578	+	1.55578i	−0.163090	+	0.163090i
$92$	0.0959403	−	2.57524i	0.0100025	−	0.268488i
$93$			0.310765i			0.0322248i
$94$	−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	0.619164	−	0.785262i	$-0.287472\pi$
$97$	−1.63587	−	1.63587i	−0.166097	−	0.166097i	−0.785262	+	0.619164i	$0.787472\pi$
$98$	−5.79477	+	2.27482i	−0.585360	+	0.229792i
$99$	3.15516	−	3.15516i	0.317106	−	0.317106i
$100$	−0.507540	+	9.98711i	−0.0507540	+	0.998711i
$101$	−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	$0.904721\pi$
$102$	5.38205	−	12.3385i	0.532902	−	1.22170i
$103$	1.62219	−	1.62219i	0.159839	−	0.159839i	−0.622656	−	0.782496i	$-0.713946\pi$
$103$	1.62219	−	1.62219i	0.159839	−	0.159839i	0.782496	+	0.622656i	$0.213946\pi$
$104$	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
$107$	3.65206			0.353058			0.176529	−	0.984295i	$-0.443513\pi$
$107$	3.65206			0.353058			0.176529	+	0.984295i	$0.443513\pi$
$108$	8.18554	−	7.59754i	0.787654	−	0.731074i
$109$	5.20757	+	5.20757i	0.498795	+	0.498795i	0.911063	−	0.412268i	$-0.135263\pi$
$109$	5.20757	+	5.20757i	0.498795	+	0.498795i	−0.412268	+	0.911063i	$0.635263\pi$
$110$	10.3811	+	0.263611i	0.989800	+	0.0251344i
$111$		−	4.28519i		−	0.406733i
$112$	−4.88558	+	4.20714i	−0.461644	+	0.397537i
$113$	−4.27905	+	4.27905i	−0.402539	+	0.402539i	−0.879127	−	0.476588i	$-0.841873\pi$
$113$	−4.27905	+	4.27905i	−0.402539	+	0.402539i	0.476588	+	0.879127i	$0.341873\pi$
$114$	8.68359	+	3.78777i	0.813293	+	0.354757i
$115$	−1.12058	+	2.65437i	−0.104495	+	0.247521i
$116$	6.70843	+	0.249921i	0.622862	+	0.0232046i
$117$			1.85478i			0.171474i
$118$	4.72963	−	10.8428i	0.435398	−	0.998164i
$119$		−	11.9760i		−	1.09784i
$120$	8.08648	+	0.507083i	0.738192	+	0.0462901i
$121$			0.216302i			0.0196639i
$122$	12.2348	+	5.33680i	1.10768	+	0.483171i
$123$			3.41996i			0.308367i
$124$	−0.330046	−	0.355590i	−0.0296390	−	0.0319329i
$125$	4.48739	−	10.2403i	0.401365	−	0.915918i
$126$	1.23838	−	2.83903i	0.110324	−	0.252921i
$127$	−7.29257	+	7.29257i	−0.647111	+	0.647111i	−0.952294	−	0.305183i	$-0.901282\pi$
$127$	−7.29257	+	7.29257i	−0.647111	+	0.647111i	0.305183	+	0.952294i	$0.401282\pi$
$128$	5.65129	−	9.80117i	0.499508	−	0.866309i
$129$		−	11.5923i		−	1.02065i
$130$	−3.12878	+	2.97381i	−0.274412	+	0.260821i
$131$	−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	$-0.515214\pi$
$132$	0.313240	−	8.40804i	0.0272640	−	0.731826i
$133$	8.42848			0.730842
$134$	−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	$-0.846216\pi$
$137$	−4.92762	+	4.92762i	−0.420995	+	0.420995i	0.464551	+	0.885546i	$0.346216\pi$
$138$	2.13975	+	0.933359i	0.182148	+	0.0794528i
$139$	10.3015	+	10.3015i	0.873761	+	0.873761i	0.992880	−	0.119119i	$-0.0380071\pi$
$139$	10.3015	+	10.3015i	0.873761	+	0.873761i	−0.119119	+	0.992880i	$0.538007\pi$
$140$	6.77461	−	2.46289i	0.572559	−	0.208152i
$141$	10.0927	−	10.0927i	0.849962	−	0.849962i
$142$	−7.97845	−	20.3239i	−0.669537	−	1.70555i
$143$	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
$147$		−	5.63931i		−	0.465123i
$148$	4.55107	+	4.90329i	0.374096	+	0.403048i
$149$	−15.2040	+	15.2040i	−1.24556	+	1.24556i	−0.287896	+	0.957662i	$0.592956\pi$
$149$	−15.2040	+	15.2040i	−1.24556	+	1.24556i	−0.957662	+	0.287896i	$0.907044\pi$
$150$	−8.25338	−	3.73391i	−0.673886	−	0.304873i
$151$	−10.7055			−0.871204			−0.435602	−	0.900139i	$-0.643464\pi$
$151$	−10.7055			−0.871204			−0.435602	+	0.900139i	$0.643464\pi$
$152$	−13.9589	+	4.88825i	−1.13222	+	0.396489i
$153$	−7.13882	−	7.13882i	−0.577139	−	0.577139i
$154$	−2.73534	−	6.96787i	−0.220420	−	0.561487i
$155$	0.204178	+	0.502523i	0.0164000	+	0.0403636i
$156$	2.37929	+	2.56343i	0.190495	+	0.205238i
$157$	2.34588			0.187222			0.0936108	−	0.995609i	$-0.470159\pi$
$157$	2.34588			0.187222			0.0936108	+	0.995609i	$0.470159\pi$
$158$	5.32405	+	13.5622i	0.423559	+	1.07895i
$159$	−7.43180			−0.589380
$160$	−9.79143	+	8.00799i	−0.774080	+	0.633087i
$161$	2.07689			0.163682
$162$	1.59028	+	4.05101i	0.124945	+	0.318278i
$163$	−2.73625			−0.214319			−0.107160	−	0.994242i	$-0.534176\pi$
$163$	−2.73625			−0.214319			−0.107160	+	0.994242i	$0.534176\pi$
$164$	−3.63215	−	3.91326i	−0.283624	−	0.305574i
$165$	−3.65865	+	8.66636i	−0.284825	+	0.674675i
$166$	−1.68774	−	4.29926i	−0.130994	−	0.333687i
$167$	10.1328	+	10.1328i	0.784097	+	0.784097i	0.980519	−	0.196423i	$-0.0629325\pi$
$167$	10.1328	+	10.1328i	0.784097	+	0.784097i	−0.196423	+	0.980519i	$0.562932\pi$
$168$	−1.93034	−	5.51230i	−0.148929	−	0.425283i
$169$	11.1367			0.856670
$170$	0.596443	−	23.4881i	0.0457451	−	1.80146i
$171$	5.02415	−	5.02415i	0.384207	−	0.384207i
$172$	12.3116	+	13.2644i	0.938748	+	1.01140i
$173$			8.79590i			0.668740i	0.942442	+	0.334370i	$0.108523\pi$
$173$			8.79590i			0.668740i	−0.942442	+	0.334370i	$0.891477\pi$
$174$	−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
$178$	−5.04998	−	12.8641i	−0.378512	−	0.964202i
$179$	6.62071	−	6.62071i	0.494855	−	0.494855i	−0.414977	−	0.909832i	$-0.636210\pi$
$179$	6.62071	−	6.62071i	0.494855	−	0.494855i	0.909832	+	0.414977i	$0.136210\pi$
$180$	2.57018	−	5.50640i	0.191570	−	0.410423i
$181$	−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	$0.849366\pi$
$182$	2.85204	+	1.24406i	0.211408	+	0.0922157i
$183$	−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
$187$	−24.3990			−1.78423
$188$	−0.829571	+	22.2675i	−0.0605027	+	1.62402i
$189$	6.36440	+	6.36440i	0.462942	+	0.462942i
$190$	16.5305	+	0.419764i	1.19925	+	0.0304529i
$191$			1.83906i			0.133070i	0.997784	+	0.0665349i	$0.0211944\pi$
$191$			1.83906i			0.133070i	−0.997784	+	0.0665349i	$0.978806\pi$
$192$	6.39391	+	8.00970i	0.461440	+	0.578050i
$193$	6.18343	−	6.18343i	0.445093	−	0.445093i	−0.448626	−	0.893719i	$-0.648087\pi$
$193$	6.18343	−	6.18343i	0.445093	−	0.445093i	0.893719	+	0.448626i	$0.148087\pi$
$194$	−1.30810	+	2.99886i	−0.0939160	+	0.215305i
$195$	−1.47191	−	3.62266i	−0.105405	−	0.259424i
$196$	5.98921	+	6.45273i	0.427801	+	0.460910i
$197$			5.55669i			0.395898i	0.980212	+	0.197949i	$0.0634280\pi$
$197$			5.55669i			0.395898i	−0.980212	+	0.197949i	$0.936572\pi$
$198$	−5.78401	−	2.52298i	−0.411052	−	0.179300i
$199$			6.96413i			0.493674i	0.969057	+	0.246837i	$0.0793912\pi$
$199$			6.96413i			0.493674i	−0.969057	+	0.246837i	$0.920609\pi$
$200$	13.4094	−	4.49298i	0.948191	−	0.317702i
$201$		−	5.82480i		−	0.410850i
$202$	−5.30920	+	12.1715i	−0.373554	+	0.856385i
$203$			5.41024i			0.379724i
$204$	−19.0239	−	0.708731i	−1.33194	−	0.0496211i
$205$	2.24697	+	5.53026i	0.156935	+	0.386250i
$206$	−2.97379	−	1.29716i	−0.207194	−	0.0903776i
$207$	1.23802	−	1.23802i	0.0860483	−	0.0860483i
$208$	−5.44495	−	0.406265i	−0.377539	−	0.0281694i
$209$		−	17.1715i		−	1.18778i
$210$	−0.165763	+	6.52779i	−0.0114387	+	0.450460i
$211$	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	$0.664787\pi$
$212$	8.50377	−	7.89291i	0.584041	−	0.542088i
$213$	19.7787			1.35521
$214$	−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
$218$	4.16416	−	9.54647i	0.282032	−	0.646568i
$219$	−1.91276	−	1.91276i	−0.129253	−	0.129253i
$220$	−5.01770	−	13.8021i	−0.338293	−	0.930534i
$221$	7.17155	−	7.17155i	0.482411	−	0.482411i
$222$	−5.64108	+	2.21449i	−0.378605	+	0.148627i
$223$	8.61776	+	8.61776i	0.577088	+	0.577088i	0.934100	−	0.357012i	$-0.116204\pi$
$223$	8.61776	+	8.61776i	0.577088	+	0.577088i	−0.357012	+	0.934100i	$0.616204\pi$
$224$	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
$227$			6.01977i			0.399546i	0.979842	+	0.199773i	$0.0640205\pi$
$227$			6.01977i			0.399546i	−0.979842	+	0.199773i	$0.935980\pi$
$228$	0.498791	−	13.3886i	0.0330332	−	0.886683i
$229$	−0.568504	+	0.568504i	−0.0375678	+	0.0375678i	−0.725641	−	0.688073i	$-0.758457\pi$
$229$	−0.568504	+	0.568504i	−0.0375678	+	0.0375678i	0.688073	+	0.725641i	$0.258457\pi$
$230$	4.07333	+	0.103436i	0.268588	+	0.00682034i
$231$	6.78094			0.446153
$232$	−3.13776	−	8.96022i	−0.206004	−	0.588267i
$233$	12.6979	+	12.6979i	0.831869	+	0.831869i	0.987772	−	0.155904i	$-0.0498289\pi$
$233$	12.6979	+	12.6979i	0.831869	+	0.831869i	−0.155904	+	0.987772i	$0.549829\pi$
$234$	2.44165	−	0.958508i	0.159616	−	0.0626596i
$235$	9.68940	−	22.9516i	0.632067	−	1.49720i
$236$	−16.7178	−	0.622819i	−1.08824	−	0.0405421i
$237$	−13.1984			−0.857327
$238$	−15.7654	+	6.18894i	−1.02192	+	0.401169i
$239$	1.78306			0.115336			0.0576682	−	0.998336i	$-0.481633\pi$
$239$	1.78306			0.115336			0.0576682	+	0.998336i	$0.481633\pi$
$240$	−3.51138	−	10.9072i	−0.226659	−	0.704056i
$241$	10.4440			0.672754			0.336377	−	0.941727i	$-0.390798\pi$
$241$	10.4440			0.672754			0.336377	+	0.941727i	$0.390798\pi$
$242$	0.284743	−	0.111780i	0.0183040	−	0.00718550i
$243$	12.8098			0.821747
$244$	0.702773	−	18.8639i	0.0449904	−	1.20764i
$245$	−3.70513	−	9.11908i	−0.236712	−	0.582596i
$246$	4.50208	−	1.76736i	0.287042	−	0.112683i
$247$	5.04719	+	5.04719i	0.321145	+	0.321145i
$248$	−0.297542	+	0.618238i	−0.0188939	+	0.0392581i
$249$	4.18392			0.265145
$250$	−15.7994	−	0.615321i	−0.999242	−	0.0389163i
$251$	−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	$0.440964\pi$
$252$	−4.37730	−	0.163075i	−0.275744	−	0.0102728i
$253$		−	4.23130i		−	0.266019i
$254$	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	0.566441	−	0.824102i	$-0.308320\pi$
$257$	−4.13062	−	4.13062i	−0.257661	−	0.257661i	−0.824102	+	0.566441i	$0.808320\pi$
$258$	−15.2603	+	5.99064i	−0.950063	+	0.372961i
$259$	−3.81240	+	3.81240i	−0.236891	+	0.236891i
$260$	5.53165	+	2.58197i	0.343058	+	0.160127i
$261$	3.22500	+	3.22500i	0.199623	+	0.199623i
$262$	−9.57907	+	21.9603i	−0.591797	+	1.35671i
$263$	17.1303	−	17.1303i	1.05630	−	1.05630i	0.0579798	−	0.998318i	$-0.481534\pi$
$263$	17.1303	−	17.1303i	1.05630	−	1.05630i	0.998318	−	0.0579798i	$-0.0184659\pi$
$264$	−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
$267$	12.5190			0.766147
$268$	6.18620	+	6.66497i	0.377883	+	0.407128i
$269$	−19.8075	−	19.8075i	−1.20768	−	1.20768i	−0.971775	−	0.235910i	$-0.924193\pi$
$269$	−19.8075	−	19.8075i	−1.20768	−	1.20768i	−0.235910	−	0.971775i	$-0.575807\pi$
$270$	12.1653	+	12.7992i	0.740356	+	0.778936i
$271$		−	27.9542i		−	1.69810i	−0.528316	−	0.849048i	$-0.677176\pi$
$271$		−	27.9542i		−	1.69810i	0.528316	−	0.849048i	$-0.322824\pi$
$272$	22.5206	−	19.3933i	1.36551	−	1.17589i
$273$	−1.99311	+	1.99311i	−0.120628	+	0.120628i
$274$	9.03326	+	3.94030i	0.545719	+	0.238042i
$275$	−0.222281	+	16.4178i	−0.0134041	+	0.990029i
$276$	0.122909	−	3.29914i	0.00739824	−	0.198585i
$277$		−	26.0257i		−	1.56373i	−0.623447	−	0.781866i	$-0.714268\pi$
$277$		−	26.0257i		−	1.56373i	0.623447	−	0.781866i	$-0.285732\pi$
$278$	8.23743	−	18.8846i	0.494048	−	1.13262i
$279$		−	0.329612i		−	0.0197333i
$280$	−6.74314	−	7.64541i	−0.402980	−	0.456901i
$281$			24.1001i			1.43769i	0.695170	+	0.718846i	$0.255329\pi$
$281$			24.1001i			1.43769i	−0.695170	+	0.718846i	$0.744671\pi$
$282$	−18.5019	−	8.07051i	−1.10177	−	0.480592i
$283$		−	4.73708i		−	0.281590i	−0.990039	−	0.140795i	$-0.955034\pi$
$283$		−	4.73708i		−	0.281590i	0.990039	−	0.140795i	$-0.0449658\pi$
$284$	−22.6316	+	21.0059i	−1.34294	+	1.24647i
$285$	−5.82588	+	13.8000i	−0.345096	+	0.817439i
$286$	2.53455	−	5.81053i	0.149871	−	0.343584i
$287$	3.04262	−	3.04262i	0.179600	−	0.179600i
$288$	7.34408	−	2.26861i	0.432754	−	0.133679i
$289$			38.2049i			2.24734i
$290$	−0.269446	+	10.6109i	−0.0158224	+	0.623093i
$291$	−2.09571	−	2.09571i	−0.122852	−	0.122852i
$292$	4.22010	+	0.157219i	0.246963	+	0.00920056i
$293$	−3.11001			−0.181689			−0.0908445	−	0.995865i	$-0.528957\pi$
$293$	−3.11001			−0.181689			−0.0908445	+	0.995865i	$0.528957\pi$
$294$	−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
$298$	27.8718	+	12.1576i	1.61457	+	0.704273i
$299$	1.24370	+	1.24370i	0.0719248	+	0.0719248i
$300$	−0.650208	+	12.7945i	−0.0375398	+	0.738688i
$301$	−10.3133	+	10.3133i	−0.594449	+	0.594449i
$302$	5.53238	+	14.0929i	0.318352	+	0.810955i
$303$	−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
$307$			14.5670i			0.831382i	0.909506	+	0.415691i	$0.136460\pi$
$307$			14.5670i			0.831382i	−0.909506	+	0.415691i	$0.863540\pi$
$308$	−7.75903	+	7.20167i	−0.442112	+	0.410353i
$309$	2.07819	−	2.07819i	0.118224	−	0.118224i
$310$	0.556014	−	0.528475i	0.0315794	−	0.0300153i
$311$	−14.4572			−0.819791			−0.409896	−	0.912132i	$-0.634435\pi$
$311$	−14.4572			−0.819791			−0.409896	+	0.912132i	$0.634435\pi$
$312$	2.14496	−	4.45684i	0.121435	−	0.252319i
$313$	−10.1273	−	10.1273i	−0.572429	−	0.572429i	0.360377	−	0.932807i	$-0.382648\pi$
$313$	−10.1273	−	10.1273i	−0.572429	−	0.572429i	−0.932807	+	0.360377i	$0.882648\pi$
$314$	−1.21230	−	3.08815i	−0.0684139	−	0.174274i
$315$	4.51178	+	1.90472i	0.254210	+	0.107319i
$316$	15.1021	−	14.0173i	0.849561	−	0.788534i
$317$	−13.8750			−0.779295			−0.389648	−	0.920964i	$-0.627403\pi$
$317$	−13.8750			−0.779295			−0.389648	+	0.920964i	$0.627403\pi$
$318$	3.84058	+	9.78332i	0.215369	+	0.548621i
$319$	11.0224			0.617136
$320$	15.6018	+	8.75121i	0.872167	+	0.489208i
$321$	4.67864			0.261136
$322$	−1.07329	−	2.73405i	−0.0598121	−	0.152362i
$323$	−38.8520			−2.16179
$324$	4.51098	−	4.18694i	0.250610	−	0.232608i
$325$	−4.76030	−	4.89097i	−0.264054	−	0.271302i
$326$	1.41403	+	3.60203i	0.0783158	+	0.199498i
$327$	6.67140	+	6.67140i	0.368930	+	0.368930i
$328$	−3.27445	+	6.80369i	−0.180801	+	0.375671i
$329$	−17.9584			−0.990076
$330$	13.2992	+	0.337712i	0.732097	+	0.0185904i
$331$	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	$0.229020\pi$
$332$	−4.78741	+	4.44352i	−0.262743	+	0.243870i
$333$			4.54508i			0.249069i
$334$	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	0.398048	−	0.917364i	$-0.369688\pi$
$337$	−9.53338	−	9.53338i	−0.519316	−	0.519316i	−0.917364	+	0.398048i	$0.869688\pi$
$338$	−5.75520	−	14.6605i	−0.313042	−	0.797427i
$339$	−5.48188	+	5.48188i	−0.297735	+	0.297735i
$340$	−31.2283	+	11.3530i	−1.69359	+	0.615701i
$341$	−0.563273	−	0.563273i	−0.0305029	−	0.0305029i
$342$	−9.21023	−	4.01749i	−0.498032	−	0.217241i
$343$	−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
$347$	−6.67273			−0.358211			−0.179105	−	0.983830i	$-0.557320\pi$
$347$	−6.67273			−0.358211			−0.179105	+	0.983830i	$0.557320\pi$
$348$	8.59415	+	0.320173i	0.460695	+	0.0171631i
$349$	2.02618	+	2.02618i	0.108459	+	0.108459i	0.759254	−	0.650795i	$-0.225564\pi$
$349$	2.02618	+	2.02618i	0.108459	+	0.108459i	−0.650795	+	0.759254i	$0.725564\pi$
$350$	4.02082	+	10.6647i	0.214922	+	0.570052i
$351$			7.62233i			0.406850i
$352$	8.67345	−	16.4271i	0.462296	−	0.875567i
$353$	−5.36542	+	5.36542i	−0.285572	+	0.285572i	−0.835327	−	0.549754i	$-0.814721\pi$
$353$	−5.36542	+	5.36542i	−0.285572	+	0.285572i	0.549754	+	0.835327i	$0.314721\pi$
$354$	6.05912	−	13.8907i	0.322039	−	0.738284i
$355$	31.9832	−	12.9949i	1.69749	−	0.689700i
$356$	−14.3247	+	13.2957i	−0.759207	+	0.704671i
$357$		−	15.3425i		−	0.812009i
$358$	−12.1370	−	5.29416i	−0.641462	−	0.279805i
$359$		−	7.76117i		−	0.409619i	−0.978802	−	0.204809i	$-0.934343\pi$
$359$		−	7.76117i		−	0.409619i	0.978802	−	0.204809i	$-0.0656574\pi$
$360$	−8.57690	−	0.537836i	−0.452043	−	0.0283465i
$361$		−	8.34326i		−	0.439119i
$362$	−4.67258	+	10.7120i	−0.245585	+	0.563012i
$363$			0.277104i			0.0145442i
$364$	0.163823	−	4.39737i	0.00858666	−	0.230485i
$365$	−4.34976	−	1.83632i	−0.227677	−	0.0961175i
$366$	15.6739	+	6.83695i	0.819290	+	0.357373i
$367$	18.0536	−	18.0536i	0.942389	−	0.942389i	−0.0560392	−	0.998429i	$-0.517847\pi$
$367$	18.0536	−	18.0536i	0.942389	−	0.942389i	0.998429	+	0.0560392i	$0.0178472\pi$
$368$	3.36320	+	3.90554i	0.175319	+	0.203590i
$369$		−	3.62737i		−	0.188833i
$370$	−7.66698	+	7.28724i	−0.398587	+	0.378845i
$371$	6.61183	+	6.61183i	0.343269	+	0.343269i
$372$	−0.422821	−	0.455545i	−0.0219223	−	0.0236189i
$373$	−4.36197			−0.225854			−0.112927	−	0.993603i	$-0.536023\pi$
$373$	−4.36197			−0.225854			−0.112927	+	0.993603i	$0.536023\pi$
$374$	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
$378$	5.08920	−	11.6671i	0.261760	−	0.600093i
$379$	−5.93072	−	5.93072i	−0.304641	−	0.304641i	0.538186	−	0.842826i	$-0.319110\pi$
$379$	−5.93072	−	5.93072i	−0.304641	−	0.304641i	−0.842826	+	0.538186i	$0.819110\pi$
$380$	−7.98998	−	21.9778i	−0.409878	−	1.12744i
$381$	−9.34249	+	9.34249i	−0.478630	+	0.478630i
$382$	2.42096	−	0.950385i	0.123867	−	0.0486259i
$383$	−19.3340	−	19.3340i	−0.987922	−	0.987922i	0.0120057	−	0.999928i	$-0.496178\pi$
$383$	−19.3340	−	19.3340i	−0.987922	−	0.987922i	−0.999928	+	0.0120057i	$0.996178\pi$
$384$	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
$387$			12.2954i			0.625008i
$388$	4.62373	+	0.172256i	0.234734	+	0.00874498i
$389$	6.28607	−	6.28607i	0.318716	−	0.318716i	−0.529558	−	0.848274i	$-0.677642\pi$
$389$	6.28607	−	6.28607i	0.318716	−	0.318716i	0.848274	+	0.529558i	$0.177642\pi$
$390$	−4.00827	+	3.80974i	−0.202967	+	0.192914i
$391$	−9.57367			−0.484161
$392$	5.39937	−	11.2189i	0.272709	−	0.566640i
$393$	−15.3466	−	15.3466i	−0.774135	−	0.774135i
$394$	7.31489	−	2.87157i	0.368519	−	0.144668i
$395$	−21.3425	+	8.67157i	−1.07386	+	0.436314i
$396$	−0.332237	+	8.91796i	−0.0166955	+	0.448144i
$397$	6.58413			0.330448			0.165224	−	0.986256i	$-0.447165\pi$
$397$	6.58413			0.330448			0.165224	+	0.986256i	$0.447165\pi$
$398$	9.16767	−	3.59890i	0.459534	−	0.180397i
$399$	10.7977			0.540561
$400$	−12.8443	−	15.3305i	−0.642215	−	0.766524i
$401$	19.7951			0.988522			0.494261	−	0.869313i	$-0.335439\pi$
$401$	19.7951			0.988522			0.494261	+	0.869313i	$0.335439\pi$
$402$	−7.66784	+	3.01012i	−0.382437	+	0.150131i
$403$	0.331123			0.0164944
$404$	18.7664	+	0.699139i	0.933664	+	0.0347835i
$405$	−6.37497	+	2.59018i	−0.316775	+	0.128707i
$406$	7.12211	−	2.79589i	0.353464	−	0.138758i
$407$	7.76707	+	7.76707i	0.385000	+	0.385000i
$408$	8.89813	+	25.4095i	0.440523	+	1.25796i
$409$	5.76937			0.285277			0.142638	−	0.989775i	$-0.454441\pi$
$409$	5.76937			0.285277			0.142638	+	0.989775i	$0.454441\pi$
$410$	6.11892	−	5.81585i	0.302192	−	0.287225i
$411$	−6.31276	+	6.31276i	−0.311385	+	0.311385i
$412$	−0.170816	+	4.58507i	−0.00841550	+	0.225890i
$413$		−	13.4826i		−	0.663437i
$414$	−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
$418$	−22.6048	+	8.87385i	−1.10564	+	0.434034i
$419$	8.68932	−	8.68932i	0.424501	−	0.424501i	−0.462249	−	0.886750i	$-0.652957\pi$
$419$	8.68932	−	8.68932i	0.424501	−	0.424501i	0.886750	+	0.462249i	$0.152957\pi$
$420$	8.67893	−	3.15520i	0.423488	−	0.153958i
$421$	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	$0.506131\pi$
$422$	4.34513	−	9.96134i	0.211517	−	0.484911i
$423$	−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
$427$	15.2135			0.736231
$428$	−5.35349	+	4.96893i	−0.258770	+	0.240182i
$429$	4.06060	+	4.06060i	0.196048	+	0.196048i
$430$	−20.7407	+	19.7134i	−1.00021	+	0.950667i
$431$			33.6247i			1.61965i	0.586675	+	0.809823i	$0.300437\pi$
$431$			33.6247i			1.61965i	−0.586675	+	0.809823i	$0.699563\pi$
$432$	−1.66195	+	22.2742i	−0.0799606	+	1.07167i
$433$	7.46558	−	7.46558i	0.358773	−	0.358773i	−0.504588	−	0.863361i	$-0.668355\pi$
$433$	7.46558	−	7.46558i	0.358773	−	0.358773i	0.863361	+	0.504588i	$0.168355\pi$
$434$	−0.506835	−	0.221081i	−0.0243289	−	0.0106122i
$435$	−8.85819	−	3.73963i	−0.424718	−	0.179302i
$436$	−14.7190	−	0.548355i	−0.704914	−	0.0262614i
$437$		−	6.73775i		−	0.322310i
$438$	−1.52951	+	3.50646i	−0.0730829	+	0.167545i
$439$		−	7.91929i		−	0.377967i	−0.981980	−	0.188984i	$-0.939481\pi$
$439$		−	7.91929i		−	0.377967i	0.981980	−	0.188984i	$-0.0605193\pi$
$440$	−15.5762	+	13.7379i	−0.742564	+	0.654931i
$441$			5.98132i			0.284825i
$442$	−13.1468	−	5.73463i	−0.625330	−	0.272768i
$443$		−	10.6463i		−	0.505823i	−0.967489	−	0.252911i	$-0.918612\pi$
$443$		−	10.6463i		−	0.505823i	0.967489	−	0.252911i	$-0.0813881\pi$
$444$	5.83036	+	6.28159i	0.276697	+	0.298111i
$445$	20.2438	−	8.22517i	0.959649	−	0.389910i
$446$	6.89106	−	15.7980i	0.326301	−	0.748056i
$447$	−19.4778	+	19.4778i	−0.921266	+	0.921266i
$448$	1.43752	−	12.8144i	0.0679164	−	0.605424i
$449$		−	6.08115i		−	0.286987i	−0.989651	−	0.143494i	$-0.954166\pi$
$449$		−	6.08115i		−	0.286987i	0.989651	−	0.143494i	$-0.0458336\pi$
$450$	8.75393	+	3.96036i	0.412664	+	0.186693i
$451$	−6.19880	−	6.19880i	−0.291890	−	0.291890i
$452$	0.450582	−	12.0946i	0.0211936	−	0.568882i
$453$	−13.7148			−0.644379
$454$	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	$-0.746696\pi$
$457$	0.313815	−	0.313815i	0.0146796	−	0.0146796i	0.714409	+	0.699729i	$0.246696\pi$
$458$	1.04218	+	0.454596i	0.0486977	+	0.0212419i
$459$	−29.3374	−	29.3374i	−1.36935	−	1.36935i
$460$	−1.96884	−	5.41564i	−0.0917977	−	0.252505i
$461$	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	$0.144181\pi$
$462$	−3.50424	−	8.92652i	−0.163032	−	0.415299i
$463$	17.3430	+	17.3430i	0.805999	+	0.805999i	0.984026	−	0.178027i	$-0.0569714\pi$
$463$	17.3430	+	17.3430i	0.805999	+	0.805999i	−0.178027	+	0.984026i	$0.556971\pi$
$464$	−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
$467$			1.52267i			0.0704606i	0.999379	+	0.0352303i	$0.0112165\pi$
$467$			1.52267i			0.0704606i	−0.999379	+	0.0352303i	$0.988784\pi$
$468$	−2.52358	−	2.71889i	−0.116653	−	0.125681i
$469$	−5.18213	+	5.18213i	−0.239289	+	0.239289i
$470$	−35.2210	−	0.894381i	−1.62463	−	0.0412547i
$471$	3.00530			0.138477
$472$	7.81950	+	22.3294i	0.359921	+	1.02779i
$473$	21.0115	+	21.0115i	0.966110	+	0.966110i
$474$	6.82062	+	17.3745i	0.313282	+	0.798038i
$475$	−0.353952	+	26.1430i	−0.0162404	+	1.19952i
$476$	16.2944	+	17.5555i	0.746852	+	0.804653i
$477$	7.88252			0.360916
$478$	−0.921443	−	2.34724i	−0.0421458	−	0.107360i
$479$	0.507657			0.0231955			0.0115977	−	0.999933i	$-0.496308\pi$
$479$	0.507657			0.0231955			0.0115977	+	0.999933i	$0.496308\pi$
$480$	−12.5438	+	10.2590i	−0.572542	+	0.468258i
$481$	−4.56592			−0.208188
$482$	−5.39720	−	13.7486i	−0.245836	−	0.626229i
$483$	2.66070			0.121066
$484$	−0.294297	−	0.317074i	−0.0133772	−	0.0144125i
$485$	−4.76578	−	2.01195i	−0.216403	−	0.0913581i
$486$	−6.61979	−	16.8629i	−0.300280	−	0.764918i
$487$	−25.9809	−	25.9809i	−1.17730	−	1.17730i	−0.980428	−	0.196876i	$-0.936920\pi$
$487$	−25.9809	−	25.9809i	−1.17730	−	1.17730i	−0.196876	−	0.980428i	$-0.563080\pi$
$488$	−25.1959	+	8.82332i	−1.14057	+	0.399413i
$489$	−3.50539			−0.158519
$490$	−10.0897	+	9.59000i	−0.455808	+	0.433232i
$491$	−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	$0.283400\pi$
$492$	−4.65314	−	5.01326i	−0.209780	−	0.226015i
$493$		−	24.9391i		−	1.12320i
$494$	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
$498$	−2.16215	−	5.50777i	−0.0968885	−	0.246809i
$499$	−6.73907	+	6.73907i	−0.301682	+	0.301682i	−0.841672	−	0.539990i	$-0.818428\pi$
$499$	−6.73907	+	6.73907i	−0.301682	+	0.301682i	0.539990	+	0.841672i	$0.318428\pi$
$500$	7.35476	+	21.1165i	0.328915	+	0.944360i
$501$	12.9810	+	12.9810i	0.579950	+	0.579950i
$502$	23.1894	+	10.1152i	1.03499	+	0.451463i
$503$	−6.12090	+	6.12090i	−0.272918	+	0.272918i	−0.830274	−	0.557356i	$-0.811816\pi$
$503$	−6.12090	+	6.12090i	−0.272918	+	0.272918i	0.557356	+	0.830274i	$0.311816\pi$
$504$	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
$507$	14.2672			0.633629
$508$	0.767904	−	20.6122i	0.0340702	−	0.914519i
$509$	13.8727	+	13.8727i	0.614894	+	0.614894i	0.944217	−	0.329323i	$-0.106820\pi$
$509$	13.8727	+	13.8727i	0.614894	+	0.614894i	−0.329323	+	0.944217i	$0.606820\pi$
$510$	0.764101	−	30.0906i	0.0338350	−	1.33243i
$511$			3.40344i			0.150559i
$512$	5.05119	+	22.0564i	0.223233	+	0.974765i
$513$	20.6471	−	20.6471i	0.911590	−	0.911590i
$514$	−3.30299	+	7.57221i	−0.145689	+	0.333996i
$515$	1.99514	−	4.72594i	0.0879162	−	0.208250i
$516$	15.7723	+	16.9930i	0.694337	+	0.748074i
$517$			36.5869i			1.60909i
$518$	6.98884	+	3.04853i	0.307072	+	0.133945i
$519$			11.2684i			0.494628i
$520$	0.540302	−	8.61623i	0.0236938	−	0.377847i
$521$		−	5.87686i		−	0.257470i	−0.991679	−	0.128735i	$-0.958908\pi$
$521$		−	5.87686i		−	0.257470i	0.991679	−	0.128735i	$-0.0410917\pi$
$522$	2.57883	−	5.91204i	0.112872	−	0.258763i
$523$			26.0176i			1.13767i	0.822452	+	0.568834i	$0.192605\pi$
$523$			26.0176i			1.13767i	−0.822452	+	0.568834i	$0.807395\pi$
$524$	33.8591	+	1.26141i	1.47914	+	0.0551051i
$525$	−10.3237	−	0.139774i	−0.450564	−	0.00610022i
$526$	−31.4030	−	13.6980i	−1.36924	−	0.597260i
$527$	−1.27445	+	1.27445i	−0.0555160	+	0.0555160i
$528$	10.9807	+	12.7514i	0.477872	+	0.554933i
$529$			21.3397i			0.927814i
$530$	12.6382	+	13.2968i	0.548970	+	0.577577i
$531$	−8.03690	−	8.03690i	−0.348772	−	0.348772i
$532$	−12.3552	+	11.4677i	−0.535665	+	0.497186i
$533$	3.64400			0.157839
$534$	−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
$538$	−15.8388	+	36.3109i	−0.682858	+	1.56547i
$539$	10.2215	+	10.2215i	0.440270	+	0.440270i
$540$	10.5623	−	22.6289i	0.454529	−	0.973792i
$541$	−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	$0.314076\pi$
$542$	−36.7992	+	14.4461i	−1.58066	+	0.620513i
$543$	−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
$547$		−	10.6170i		−	0.453951i	−0.973900	−	0.226976i	$-0.927116\pi$
$547$		−	10.6170i		−	0.453951i	0.973900	−	0.226976i	$-0.0728838\pi$
$548$	0.518876	−	13.9277i	0.0221653	−	0.594964i
$549$	9.06863	−	9.06863i	0.387040	−	0.387040i
$550$	21.7274	−	8.19171i	0.926460	−	0.349296i
$551$	17.5516			0.747724
$552$	−4.40654	+	1.54312i	−0.187555	+	0.0656796i
$553$	11.7422	+	11.7422i	0.499328	+	0.499328i
$554$	−34.2605	+	13.4495i	−1.45559	+	0.571414i
$555$	−3.60686	−	8.87722i	−0.153103	−	0.376817i
$556$	−29.1168	−	1.08474i	−1.23483	−	0.0460033i
$557$	20.9610			0.888146			0.444073	−	0.895991i	$-0.353533\pi$
$557$	20.9610			0.888146			0.444073	+	0.895991i	$0.353533\pi$
$558$	−0.433905	+	0.170336i	−0.0183687	+	0.00721089i
$559$	−12.3517			−0.522422
$560$	−6.57981	+	12.8277i	−0.278048	+	0.542070i
$561$	−31.2575			−1.31969
$562$	31.7257	−	12.4544i	1.33827	−	0.525356i
$563$	16.5598			0.697911			0.348955	−	0.937139i	$-0.386536\pi$
$563$	16.5598			0.697911			0.348955	+	0.937139i	$0.386536\pi$
$564$	−1.06276	+	28.5268i	−0.0447503	+	1.20119i
$565$	−5.26280	+	12.4662i	−0.221408	+	0.524456i
$566$	−6.23594	+	2.44801i	−0.262116	+	0.102898i
$567$	3.50736	+	3.50736i	0.147295	+	0.147295i
$568$	39.3479	+	18.9371i	1.65100	+	0.794584i
$569$	−39.6751			−1.66327			−0.831634	−	0.555325i	$-0.812594\pi$
$569$	−39.6751			−1.66327			−0.831634	+	0.555325i	$0.812594\pi$
$570$	21.1771	+	0.537759i	0.887012	+	0.0225242i
$571$	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	$-0.00178515\pi$
$572$	−8.95885	−	0.333760i	−0.374588	−	0.0139552i
$573$			2.35602i			0.0984240i
$574$	−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	−0.974844	−	0.222888i	$-0.928451\pi$
$577$	−28.7705	−	28.7705i	−1.19773	−	1.19773i	−0.222888	−	0.974844i	$-0.571549\pi$
$578$	50.2933	−	19.7434i	2.09193	−	0.821217i
$579$	7.92157	−	7.92157i	0.329209	−	0.329209i
$580$	14.1076	−	5.12877i	0.585785	−	0.212960i
$581$	−3.72230	−	3.72230i	−0.154427	−	0.154427i
$582$	−1.67580	+	3.84182i	−0.0694641	+	0.159249i
$583$	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
$587$	33.4854			1.38209			0.691046	−	0.722811i	$-0.257150\pi$
$587$	33.4854			1.38209			0.691046	+	0.722811i	$0.257150\pi$
$588$	7.67276	+	8.26657i	0.316419	+	0.340908i
$589$	−0.896933	−	0.896933i	−0.0369575	−	0.0369575i
$590$	0.671477	−	26.4430i	0.0276443	−	1.08864i
$591$			7.11866i			0.292822i
$592$	−13.3427	−	0.995540i	−0.548381	−	0.0409164i
$593$	11.5298	−	11.5298i	0.473472	−	0.473472i	−0.429564	−	0.903036i	$-0.641333\pi$
$593$	11.5298	−	11.5298i	0.473472	−	0.473472i	0.903036	+	0.429564i	$0.141333\pi$
$594$	−23.7697	−	10.3683i	−0.975284	−	0.425418i
$595$	−10.0803	−	24.8096i	−0.413250	−	1.01709i
$596$	1.60097	−	42.9735i	0.0655783	−	1.76026i
$597$			8.92172i			0.365142i
$598$	0.994503	−	2.27993i	0.0406683	−	0.0932333i
$599$			20.0148i			0.817781i	0.912583	+	0.408891i	$0.134084\pi$
$599$			20.0148i			0.817781i	−0.912583	+	0.408891i	$0.865916\pi$
$600$	17.1788	−	5.75594i	0.701321	−	0.234985i
$601$		−	27.5924i		−	1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$601$		−	27.5924i		−	1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$602$	18.9062	+	8.24688i	0.770560	+	0.336118i
$603$			6.17806i			0.251590i
$604$	15.6931	−	14.5658i	0.638542	−	0.592673i
$605$	0.182062	+	0.448093i	0.00740188	+	0.0182176i
$606$	−6.80160	+	15.5929i	−0.276296	+	0.633418i
$607$	−30.4850	+	30.4850i	−1.23735	+	1.23735i	−0.276265	+	0.961081i	$0.589097\pi$
$607$	−30.4850	+	30.4850i	−1.23735	+	1.23735i	−0.961081	+	0.276265i	$0.910903\pi$
$608$	13.8113	−	26.1579i	0.560120	−	1.06084i
$609$			6.93104i			0.280860i
$610$	29.8376	+	0.757677i	1.20809	+	0.0306774i
$611$	−10.7539	−	10.7539i	−0.435057	−	0.435057i
$612$	20.1776	+	0.751714i	0.815632	+	0.0303862i
$613$	−20.2657			−0.818523			−0.409261	−	0.912417i	$-0.634214\pi$
$613$	−20.2657			−0.818523			−0.409261	+	0.912417i	$0.634214\pi$
$614$	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	$-0.735379\pi$
$617$	1.61302	−	1.61302i	0.0649378	−	0.0649378i	0.738830	+	0.673892i	$0.235379\pi$
$618$	−3.80971	−	1.66179i	−0.153249	−	0.0668470i
$619$	−2.46756	−	2.46756i	−0.0991797	−	0.0991797i	0.655776	−	0.754956i	$-0.272342\pi$
$619$	−2.46756	−	2.46756i	−0.0991797	−	0.0991797i	−0.754956	+	0.655776i	$0.772342\pi$
$620$	−0.983026	−	0.458839i	−0.0394793	−	0.0184274i
$621$	5.08771	−	5.08771i	0.204163	−	0.204163i
$622$	7.47114	+	19.0316i	0.299565	+	0.763098i
$623$	−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
$627$		−	21.9984i		−	0.878531i
$628$	−3.43879	+	3.19177i	−0.137222	+	0.127365i
$629$	17.5737	−	17.5737i	0.700708	−	0.700708i
$630$	0.175816	−	6.92368i	0.00700466	−	0.275846i
$631$	−29.9602			−1.19270			−0.596348	−	0.802726i	$-0.703382\pi$
$631$	−29.9602			−1.19270			−0.596348	+	0.802726i	$0.703382\pi$
$632$	−26.2570	−	12.6368i	−1.04445	−	0.502666i
$633$	6.96133	+	6.96133i	0.276688	+	0.276688i
$634$	7.17026	+	18.2652i	0.284767	+	0.725402i
$635$	−8.96913	+	21.2455i	−0.355929	+	0.843101i
$636$	10.8942	−	10.1116i	0.431981	−	0.400950i
$637$	−6.00875			−0.238075
$638$	−5.69612	−	14.5100i	−0.225512	−	0.574457i
$639$	−20.9782			−0.829885
$640$	3.45755	−	25.0608i	0.136672	−	0.990616i
$641$	−37.3386			−1.47478			−0.737392	−	0.675465i	$-0.763943\pi$
$641$	−37.3386			−1.47478			−0.737392	+	0.675465i	$0.763943\pi$
$642$	−2.41781	−	6.15901i	−0.0954234	−	0.243077i
$643$	24.5635			0.968691			0.484345	−	0.874877i	$-0.339058\pi$
$643$	24.5635			0.968691			0.484345	+	0.874877i	$0.339058\pi$
$644$	−3.04448	+	2.82579i	−0.119969	+	0.111352i
$645$	−9.75728	−	24.0147i	−0.384193	−	0.945577i
$646$	20.0778	+	51.1453i	0.789952	+	2.01229i
$647$	−23.1347	−	23.1347i	−0.909519	−	0.909519i	0.0867142	−	0.996233i	$-0.472363\pi$
$647$	−23.1347	−	23.1347i	−0.909519	−	0.909519i	−0.996233	+	0.0867142i	$0.972363\pi$
$648$	−7.84291	−	3.77459i	−0.308099	−	0.148280i
$649$	−27.4685			−1.07823
$650$	−3.97852	+	8.79406i	−0.156050	+	0.344932i
$651$	0.354194	−	0.354194i	0.0138820	−	0.0138820i
$652$	4.01101	−	3.72289i	0.157083	−	0.145800i
$653$			50.8060i			1.98819i	0.108496	+	0.994097i	$0.465397\pi$
$653$			50.8060i			1.98819i	−0.108496	+	0.994097i	$0.534603\pi$
$654$	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
$658$	9.28047	+	23.6406i	0.361790	+	0.921607i
$659$	−9.97780	+	9.97780i	−0.388680	+	0.388680i	−0.874216	−	0.485537i	$-0.838624\pi$
$659$	−9.97780	+	9.97780i	−0.388680	+	0.388680i	0.485537	+	0.874216i	$0.338624\pi$
$660$	−6.42816	−	17.6818i	−0.250216	−	0.688262i
$661$	−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	$0.794764\pi$
$662$	−3.10648	−	1.35505i	−0.120737	−	0.0526653i
$663$	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
$667$	4.32496			0.167463
$668$	−28.6399	−	1.06697i	−1.10811	−	0.0412825i
$669$	11.0402	+	11.0402i	0.426838	+	0.426838i
$670$	−10.4216	+	9.90543i	−0.402622	+	0.382680i
$671$		−	30.9947i		−	1.19654i
$672$	10.3296	+	5.45399i	0.398473	+	0.210392i
$673$	−31.6322	+	31.6322i	−1.21933	+	1.21933i	−0.251464	+	0.967867i	$0.580912\pi$
$673$	−31.6322	+	31.6322i	−1.21933	+	1.21933i	−0.967867	+	0.251464i	$0.919088\pi$
$674$	−7.62323	+	17.4765i	−0.293636	+	0.673169i
$675$	−20.0080	+	19.4735i	−0.770108	+	0.749534i
$676$	−16.3251	+	15.1524i	−0.627889	+	0.582786i
$677$			25.6600i			0.986196i	0.869974	+	0.493098i	$0.164136\pi$
$677$			25.6600i			0.986196i	−0.869974	+	0.493098i	$0.835864\pi$
$678$	10.0493	+	4.38350i	0.385942	+	0.168347i
$679$			3.72896i			0.143104i
$680$	31.0833	+	35.2424i	1.19199	+	1.35148i
$681$			7.71190i			0.295521i
$682$	−0.450413	+	1.03259i	−0.0172472	+	0.0395397i
$683$		−	12.3536i		−	0.472698i	−0.971668	−	0.236349i	$-0.924049\pi$
$683$		−	12.3536i		−	0.472698i	0.971668	−	0.236349i	$-0.0759509\pi$
$684$	−0.529041	+	14.2006i	−0.0202284	+	0.542974i
$685$	−6.06048	+	14.3557i	−0.231559	+	0.548501i
$686$	23.8230	+	10.3915i	0.909564	+	0.396751i
$687$	−0.728309	+	0.728309i	−0.0277867	+	0.0277867i
$688$	−36.0946	−	2.69314i	−1.37610	−	0.102675i
$689$			7.91866i			0.301677i
$690$	5.21833	+	0.132511i	0.198658	+	0.00504461i
$691$	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	$0.542618\pi$
$692$	−11.9676	−	12.8938i	−0.454938	−	0.490147i
$693$	−7.19219			−0.273209
$694$	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
$698$	1.62021	−	3.71438i	0.0613258	−	0.140591i
$699$	16.2673	+	16.2673i	0.615285	+	0.615285i
$700$	11.9613	−	10.8043i	0.452094	−	0.408365i
$701$	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	$-0.00578284\pi$
$702$	10.0341	−	3.93904i	0.378714	−	0.148670i
$703$	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
$707$			15.1348i			0.569203i
$708$	−21.4171	−	0.797891i	−0.804905	−	0.0299866i
$709$	7.78615	−	7.78615i	0.292415	−	0.292415i	−0.545619	−	0.838034i	$-0.683705\pi$
$709$	7.78615	−	7.78615i	0.292415	−	0.292415i	0.838034	+	0.545619i	$0.183705\pi$
$710$	−33.6349	−	35.3876i	−1.26229	−	1.32807i
$711$	13.9988			0.524997
$712$	24.9053	+	11.9863i	0.933365	+	0.449205i
$713$	−0.221016	−	0.221016i	−0.00827713	−	0.00827713i
$714$	−20.1970	+	7.92863i	−0.755854	+	0.296721i
$715$	9.23410	+	3.89833i	0.345336	+	0.145789i
$716$	−0.697158	+	18.7132i	−0.0260540	+	0.699346i
$717$	2.28427			0.0853076
$718$	−10.2169	+	4.01079i	−0.381291	+	0.149681i
$719$	20.6777			0.771150			0.385575	−	0.922677i	$-0.374003\pi$
$719$	20.6777			0.771150			0.385575	+	0.922677i	$0.374003\pi$
$720$	3.72433	+	11.5687i	0.138798	+	0.431139i
$721$	−3.69779			−0.137713
$722$	−10.9832	+	4.31161i	−0.408751	+	0.160461i
$723$	13.3797			0.497597
$724$	16.5161	+	0.615306i	0.613817	+	0.0228677i
$725$	−16.7812	−	0.227201i	−0.623237	−	0.00843805i
$726$	0.364783	−	0.143201i	0.0135384	−	0.00531469i
$727$	20.4994	+	20.4994i	0.760280	+	0.760280i	0.976373	−	0.216093i	$-0.0693315\pi$
$727$	20.4994	+	20.4994i	0.760280	+	0.760280i	−0.216093	+	0.976373i	$0.569331\pi$
$728$	−5.87341	+	2.05680i	−0.217683	+	0.0762301i
$729$	25.6425			0.949722
$730$	−0.169502	+	6.67505i	−0.00627355	+	0.247055i
$731$	47.5403	−	47.5403i	1.75834	−	1.75834i
$732$	0.900320	−	24.1665i	0.0332768	−	0.893221i
$733$		−	10.7306i		−	0.396344i	−0.980167	−	0.198172i	$-0.936500\pi$
$733$		−	10.7306i		−	0.396344i	0.980167	−	0.198172i	$-0.0635005\pi$
$734$	−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
$738$	−4.77511	+	1.87454i	−0.175774	+	0.0690028i
$739$	2.93837	−	2.93837i	0.108090	−	0.108090i	−0.650994	−	0.759083i	$-0.725648\pi$
$739$	2.93837	−	2.93837i	0.108090	−	0.108090i	0.759083	+	0.650994i	$0.225648\pi$
$740$	13.5551	+	6.32702i	0.498296	+	0.232586i
$741$	6.46594	+	6.46594i	0.237532	+	0.237532i
$742$	5.28705	−	12.1207i	0.194094	−	0.444966i
$743$	−0.223404	+	0.223404i	−0.00819590	+	0.00819590i	−0.711193	−	0.702997i	$-0.751845\pi$
$743$	−0.223404	+	0.223404i	−0.00819590	+	0.00819590i	0.702997	+	0.711193i	$0.251845\pi$
$744$	−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
$747$	−4.43766			−0.162366
$748$	35.7661	−	33.1969i	1.30774	−	1.21380i
$749$	−4.16243	−	4.16243i	−0.152092	−	0.152092i
$750$	−20.2406	−	0.788286i	−0.739081	−	0.0287841i
$751$			39.9939i			1.45940i	0.683769	+	0.729699i	$0.260340\pi$
$751$			39.9939i			1.45940i	−0.683769	+	0.729699i	$0.739660\pi$
$752$	−29.0807	−	33.7702i	−1.06046	−	1.23147i
$753$	−16.2055	+	16.2055i	−0.590563	+	0.590563i
$754$	5.93915	+	2.59065i	0.216291	+	0.0943459i
$755$	−22.1776	+	9.01088i	−0.807126	+	0.327939i
$756$	−17.9888	−	0.670168i	−0.654245	−	0.0243738i
$757$			32.9120i			1.19621i	0.801419	+	0.598103i	$0.204079\pi$
$757$			32.9120i			1.19621i	−0.801419	+	0.598103i	$0.795921\pi$
$758$	−4.74241	+	10.8721i	−0.172252	+	0.394894i
$759$		−	5.42070i		−	0.196759i
$760$	−24.8029	+	21.8758i	−0.899694	+	0.793517i
$761$		−	33.9591i		−	1.23102i	−0.788130	−	0.615509i	$-0.788951\pi$
$761$		−	33.9591i		−	1.23102i	0.788130	−	0.615509i	$-0.211049\pi$
$762$	17.1266	+	7.47058i	0.620430	+	0.270631i
$763$		−	11.8707i		−	0.429747i
$764$	−2.50220	−	2.69585i	−0.0905263	−	0.0975324i
$765$	−20.7976	−	8.78003i	−0.751937	−	0.317443i
$766$	−15.4602	+	35.4429i	−0.558598	+	1.28060i
$767$	8.07375	−	8.07375i	0.291526	−	0.291526i
$768$	−20.2706	−	3.04184i	−0.731452	−	0.109763i
$769$		−	40.2535i		−	1.45158i	−0.687917	−	0.725789i	$-0.741475\pi$
$769$		−	40.2535i		−	1.45158i	0.687917	−	0.725789i	$-0.258525\pi$
$770$	−11.5314	−	12.1323i	−0.415563	−	0.437218i
$771$	−5.29172	−	5.29172i	−0.190577	−	0.190577i
$772$	−0.651112	+	17.4773i	−0.0234340	+	0.629020i
$773$	9.47175			0.340675			0.170338	−	0.985386i	$-0.445514\pi$
$773$	9.47175			0.340675			0.170338	+	0.985386i	$0.445514\pi$
$774$	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
$778$	−11.5236	−	5.02656i	−0.413139	−	0.180211i
$779$	−9.87073	−	9.87073i	−0.353656	−	0.353656i
$780$	7.08658	+	3.30775i	0.253740	+	0.118436i
$781$	−35.8496	+	35.8496i	−1.28280	+	1.28280i
$782$	4.94745	+	12.6029i	0.176921	+	0.450679i
$783$	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
$787$		−	48.1367i		−	1.71589i	−0.513742	−	0.857945i	$-0.671741\pi$
$787$		−	48.1367i		−	1.71589i	0.513742	−	0.857945i	$-0.328259\pi$
$788$	−7.56034	−	8.14546i	−0.269326	−	0.290170i
$789$	21.9455	−	21.9455i	0.781282	−	0.781282i
$790$	22.4447	+	23.6143i	0.798546	+	0.840158i
$791$	9.75409			0.346815
$792$	11.9114	−	4.17124i	0.423253	−	0.148218i
$793$	9.11021	+	9.11021i	0.323513	+	0.323513i
$794$	−3.40253	−	8.66743i	−0.120751	−	0.307596i
$795$	−15.3957	+	6.25537i	−0.546031	+	0.221855i
$796$	−9.47528	−	10.2086i	−0.335842	−	0.361834i
$797$	−33.8962			−1.20066			−0.600332	−	0.799751i	$-0.704965\pi$
$797$	−33.8962			−1.20066			−0.600332	+	0.799751i	$0.704965\pi$
$798$	−5.58001	−	14.2142i	−0.197530	−	0.503178i
$799$	82.7810			2.92858
$800$	−13.5436	+	24.8308i	−0.478839	+	0.877903i
$801$	−13.2782			−0.469162
$802$	−10.2297	−	26.0586i	−0.361222	−	0.920160i
$803$	6.93391			0.244692
$804$	7.92513	+	8.53847i	0.279498	+	0.301129i
$805$	4.30250	−	1.74813i	0.151643	−	0.0616133i
$806$	−0.171117	−	0.435894i	−0.00602733	−	0.0153537i
$807$	−25.3753	−	25.3753i	−0.893254	−	0.893254i
$808$	−8.77770	−	25.0656i	−0.308798	−	0.881806i
$809$	27.5625			0.969047			0.484523	−	0.874778i	$-0.338993\pi$
$809$	27.5625			0.969047			0.484523	+	0.874778i	$0.338993\pi$
$810$	6.70418	+	7.05354i	0.235561	+	0.247836i
$811$	−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	$0.455003\pi$
$812$	−7.36108	−	7.93078i	−0.258323	−	0.278316i
$813$		−	35.8120i		−	1.25598i
$814$	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
$818$	−2.98148	−	7.59486i	−0.104245	−	0.265548i
$819$	2.11398	−	2.11398i	0.0738686	−	0.0738686i
$820$	−10.8182	−	5.04952i	−0.377787	−	0.176337i
$821$	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	$0.749548\pi$
$822$	11.5725	+	5.04790i	0.403636	+	0.176066i
$823$	28.5594	−	28.5594i	0.995518	−	0.995518i	−0.00447159	−	0.999990i	$-0.501423\pi$
$823$	28.5594	−	28.5594i	0.995518	−	0.995518i	0.999990	+	0.00447159i	$0.00142335\pi$
$824$	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
$827$	−23.0863			−0.802788			−0.401394	−	0.915905i	$-0.631474\pi$
$827$	−23.0863			−0.802788			−0.401394	+	0.915905i	$0.631474\pi$
$828$	−0.130363	+	3.49922i	−0.00453042	+	0.121606i
$829$	−33.3543	−	33.3543i	−1.15844	−	1.15844i	−0.984811	−	0.173631i	$-0.944450\pi$
$829$	−33.3543	−	33.3543i	−1.15844	−	1.15844i	−0.173631	−	0.984811i	$-0.555550\pi$
$830$	−7.11502	−	7.48578i	−0.246966	−	0.259835i
$831$		−	33.3414i		−	1.15660i
$832$	8.53442	−	6.81277i	0.295878	−	0.236190i
$833$	23.1269	−	23.1269i	0.801301	−	0.801301i
$834$	10.5529	−	24.1930i	0.365419	−	0.837734i
$835$	29.5198	+	12.4623i	1.02158	+	0.431275i
$836$	23.3633	+	25.1715i	0.808037	+	0.870573i
$837$		−	1.35456i		−	0.0468204i
$838$	−15.9292	−	6.94829i	−0.550264	−	0.240025i
$839$			49.4524i			1.70729i	0.520859	+	0.853643i	$0.325612\pi$
$839$			49.4524i			1.70729i	−0.520859	+	0.853643i	$0.674388\pi$
$840$	−8.63862	−	9.79451i	−0.298061	−	0.337943i
$841$		−	17.7336i		−	0.611504i
$842$	16.0881	−	36.8825i	0.554433	−	1.27106i
$843$			30.8746i			1.06338i
$844$	−15.3587	−	0.572185i	−0.528668	−	0.0196954i
$845$	23.0708	−	9.37380i	0.793661	−	0.322469i
$846$	19.6240	+	8.55996i	0.674687	+	0.294298i
$847$	0.246530	−	0.246530i	0.00847089	−	0.00847089i
$848$	−1.72656	+	23.1402i	−0.0592904	+	0.794637i
$849$		−	6.06865i		−	0.208276i
$850$	−18.5344	−	49.1601i	−0.635726	−	1.68618i
$851$	3.04764	+	3.04764i	0.104472	+	0.104472i
$852$	−28.9932	+	26.9105i	−0.993292	+	0.921940i
$853$	−31.3639			−1.07388			−0.536939	−	0.843621i	$-0.680419\pi$
$853$	−31.3639			−1.07388			−0.536939	+	0.843621i	$0.680419\pi$
$854$	−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	$-0.622364\pi$
$857$	16.1594	−	16.1594i	0.551996	−	0.551996i	0.927016	+	0.375021i	$0.122364\pi$
$858$	3.24700	−	7.44385i	0.110851	−	0.254129i
$859$	−30.7369	−	30.7369i	−1.04873	−	1.04873i	−0.998750	−	0.0499792i	$-0.984085\pi$
$859$	−30.7369	−	30.7369i	−1.04873	−	1.04873i	−0.0499792	−	0.998750i	$-0.515915\pi$
$860$	36.6694	+	17.1159i	1.25041	+	0.583647i
$861$	3.89790	−	3.89790i	0.132840	−	0.132840i
$862$	44.2640	−	17.3765i	1.50764	−	0.591845i
$863$	−18.9353	−	18.9353i	−0.644565	−	0.644565i	0.307109	−	0.951674i	$-0.400638\pi$
$863$	−18.9353	−	18.9353i	−0.644565	−	0.644565i	−0.951674	+	0.307109i	$0.900638\pi$
$864$	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
$867$			48.9441i			1.66223i
$868$	−0.0291129	+	0.781453i	−0.000988156	+	0.0265242i
$869$	23.9226	−	23.9226i	0.811517	−	0.811517i
$870$	−0.345187	+	13.5936i	−0.0117029	+	0.460866i
$871$	−6.20638			−0.210295
$872$	6.88460	+	19.6597i	0.233142	+	0.665761i
$873$	2.22280	+	2.22280i	0.0752305	+	0.0752305i
$874$	−8.86966	+	3.48191i	−0.300021	+	0.117778i
$875$	−16.7859	+	6.55684i	−0.567465	+	0.221662i
$876$	5.40636	+	0.201413i	0.182664	+	0.00680511i
$877$	49.7461			1.67981			0.839903	−	0.542737i	$-0.182612\pi$
$877$	49.7461			1.67981			0.839903	+	0.542737i	$0.182612\pi$
$878$	−10.4250	+	4.09251i	−0.351828	+	0.138115i
$879$	−3.98423			−0.134385
$880$	26.1342	+	13.4052i	0.880984	+	0.451889i
$881$	27.7694			0.935574			0.467787	−	0.883841i	$-0.345051\pi$
$881$	27.7694			0.935574			0.467787	+	0.883841i	$0.345051\pi$
$882$	7.87389	−	3.09101i	0.265128	−	0.104080i
$883$	−42.4602			−1.42890			−0.714450	−	0.699686i	$-0.753323\pi$
$883$	−42.4602			−1.42890			−0.714450	+	0.699686i	$0.753323\pi$
$884$	−0.755161	+	20.2702i	−0.0253988	+	0.681759i
$885$	22.0751	+	9.31938i	0.742048	+	0.313268i
$886$	−14.0150	+	5.50178i	−0.470842	+	0.184836i
$887$	−16.1076	−	16.1076i	−0.540842	−	0.540842i	0.382934	−	0.923776i	$-0.374914\pi$
$887$	−16.1076	−	16.1076i	−0.540842	−	0.540842i	−0.923776	+	0.382934i	$0.874914\pi$
$888$	5.25617	−	10.9213i	0.176385	−	0.366496i
$889$	16.6234			0.557531
$890$	−21.2893	−	22.3986i	−0.713617	−	0.750804i
$891$	7.14563	−	7.14563i	0.239388	−	0.239388i
$892$	−24.3578	−	0.907445i	−0.815560	−	0.0303835i
$893$			58.2596i			1.94958i
$894$	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
$898$	−8.00530	+	3.14260i	−0.267140	+	0.104870i
$899$	0.575741	−	0.575741i	0.0192020	−	0.0192020i
$900$	0.689641	−	13.5704i	0.0229880	−	0.452347i
$901$	−30.4780	−	30.4780i	−1.01537	−	1.01537i
$902$	−4.95678	+	11.3636i	−0.165043	+	0.378366i
$903$	−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
$907$	−9.20991			−0.305810			−0.152905	−	0.988241i	$-0.548863\pi$
$907$	−9.20991			−0.305810			−0.152905	+	0.988241i	$0.548863\pi$
$908$	−8.19040	−	8.82427i	−0.271808	−	0.292844i
$909$	9.02174	+	9.02174i	0.299232	+	0.299232i
$910$	6.95543	+	0.176622i	0.230570	+	0.00585495i
$911$			45.8065i			1.51764i	0.651302	+	0.758819i	$0.274223\pi$
$911$			45.8065i			1.51764i	−0.651302	+	0.758819i	$0.725777\pi$
$912$	17.4852	+	20.3048i	0.578992	+	0.672359i
$913$	−7.58351	+	7.58351i	−0.250978	+	0.250978i
$914$	−0.575282	−	0.250938i	−0.0190286	−	0.00830028i
$915$	−10.5158	+	24.9090i	−0.347640	+	0.823467i
$916$	0.0598632	−	1.60686i	0.00197794	−	0.0530921i
$917$			27.3068i			0.901749i
$918$	−23.4592	+	53.7810i	−0.774270	+	1.77504i
$919$			5.52468i			0.182242i	0.995840	+	0.0911211i	$0.0290450\pi$
$919$			5.52468i			0.182242i	−0.995840	+	0.0911211i	$0.970955\pi$
$920$	−6.11176	+	5.39048i	−0.201499	+	0.177719i
$921$			18.6617i			0.614924i
$922$	−18.1660	−	7.92398i	−0.598264	−	0.260962i
$923$		−	21.0744i		−	0.693672i
$924$	−9.94007	+	9.22604i	−0.327004	+	0.303514i
$925$	−11.6650	−	11.9852i	−0.383542	−	0.394070i
$926$	13.8681	−	31.7930i	0.455734	−	1.04478i
$927$	−2.20422	+	2.20422i	−0.0723961	+	0.0723961i
$928$	16.7907	+	8.86544i	0.551182	+	0.291022i
$929$			43.4288i			1.42485i	0.701746	+	0.712427i	$0.252404\pi$
$929$			43.4288i			1.42485i	−0.701746	+	0.712427i	$0.747596\pi$
$930$	0.712307	−	0.677027i	0.0233575	−	0.0222006i
$931$	16.2763	+	16.2763i	0.533433	+	0.533433i
$932$	−35.8903	−	1.33708i	−1.17562	−	0.0437977i
$933$	−18.5210			−0.606352
$934$	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	$-0.591069\pi$
$937$	20.7275	−	20.7275i	0.677138	−	0.677138i	0.959352	+	0.282213i	$0.0910686\pi$
$938$	9.49983	+	4.14381i	0.310180	+	0.135300i
$939$	−12.9741	−	12.9741i	−0.423392	−	0.423392i
$940$	17.0241	+	46.8276i	0.555264	+	1.52735i
$941$	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	$0.158194\pi$
$942$	−1.55307	−	3.95621i	−0.0506017	−	0.128900i
$943$	−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
$947$		−	48.3611i		−	1.57152i	−0.618529	−	0.785762i	$-0.712271\pi$
$947$		−	48.3611i		−	1.57152i	0.618529	−	0.785762i	$-0.287729\pi$
$948$	19.3473	−	17.9575i	0.628371	−	0.583233i
$949$	−2.03807	+	2.03807i	−0.0661585	+	0.0661585i
$950$	34.5979	−	13.0442i	1.12250	−	0.423208i
$951$	−17.7752			−0.576399
$952$	14.6897	−	30.5224i	0.476095	−	0.989237i
$953$	−34.0371	−	34.0371i	−1.10257	−	1.10257i	−0.994100	−	0.108471i	$-0.965405\pi$
$953$	−34.0371	−	34.0371i	−1.10257	−	1.10257i	−0.108471	−	0.994100i	$-0.534595\pi$
$954$	−4.07350	−	10.3766i	−0.131885	−	0.335956i
$955$	1.54794	+	3.80980i	0.0500903	+	0.123282i
$956$	−2.61375	+	2.42600i	−0.0845348	+	0.0784624i
$957$	14.1208			0.456459
$958$	−0.262346	−	0.668286i	−0.00847600	−	0.0215913i
$959$	11.2325			0.362716
$960$	19.9874	+	11.2111i	0.645091	+	0.361838i
$961$	30.9412			0.998102
$962$	2.35956	+	6.01063i	0.0760753	+	0.193791i
$963$	−4.96238			−0.159911
$964$	−15.3096	+	14.2099i	−0.493090	+	0.457669i
$965$	7.60500	−	18.0142i	0.244814	−	0.579898i
$966$	−1.37499	−	3.50258i	−0.0442395	−	0.112694i
$967$	−18.9307	−	18.9307i	−0.608770	−	0.608770i	0.333855	−	0.942625i	$-0.391651\pi$
$967$	−18.9307	−	18.9307i	−0.608770	−	0.608770i	−0.942625	+	0.333855i	$0.891651\pi$
$968$	−0.265314	+	0.551273i	−0.00852751	+	0.0177186i
$969$	−49.7732			−1.59895
$970$	−0.185714	+	7.31347i	−0.00596290	+	0.234821i
$971$	−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	$0.410328\pi$
$972$	−18.7776	+	17.4288i	−0.602292	+	0.559028i
$973$		−	23.4822i		−	0.752805i
$974$	−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	0.740492	−	0.672065i	$-0.234592\pi$
$977$	2.13884	+	2.13884i	0.0684275	+	0.0684275i	−0.672065	+	0.740492i	$0.734592\pi$
$978$	1.81151	+	4.61454i	0.0579256	+	0.147557i
$979$	−22.6911	+	22.6911i	−0.725210	+	0.725210i
$980$	17.8385	+	8.32636i	0.569831	+	0.265976i
$981$	−7.07601	−	7.07601i	−0.225919	−	0.225919i
$982$	6.01667	+	2.62447i	0.192000	+	0.0837501i
$983$	−6.18193	+	6.18193i	−0.197173	+	0.197173i	−0.798787	−	0.601614i	$-0.794525\pi$
$983$	−6.18193	+	6.18193i	−0.197173	+	0.197173i	0.601614	+	0.798787i	$0.294525\pi$
$984$	−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
$987$	−23.0064			−0.732302
$988$	−14.2657	−	0.531466i	−0.453853	−	0.0169082i
$989$	8.24447	+	8.24447i	0.262159	+	0.262159i
$990$	−14.1058	−	0.358193i	−0.448311	−	0.0113841i
$991$		−	43.4847i		−	1.38134i	−0.723172	−	0.690668i	$-0.757317\pi$
$991$		−	43.4847i		−	1.38134i	0.723172	−	0.690668i	$-0.242683\pi$
$992$	−0.405002	−	1.31110i	−0.0128588	−	0.0416273i
$993$	2.17092	−	2.17092i	0.0688921	−	0.0688921i
$994$	−14.0707	+	32.2576i	−0.446297	+	1.02315i
$995$	5.86173	+	14.4269i	0.185829	+	0.457364i
$996$	−6.13314	+	5.69257i	−0.194336	+	0.180376i
$997$		−	33.4043i		−	1.05793i	−0.848645	−	0.528963i	$-0.822581\pi$
$997$		−	33.4043i		−	1.05793i	0.848645	−	0.528963i	$-0.177419\pi$
$998$	12.3540	+	5.38879i	0.391059	+	0.170579i
$999$			18.6783i			0.590954i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.2	✓	18	5.3	odd	4
80.2.j.b.67.2	yes	18	16.3	odd	4
80.2.s.b.3.4	yes	18	80.3	even	4	inner
80.2.s.b.27.4	yes	18	1.1	even	1	trivial
320.2.j.b.47.7		18	16.13	even	4
320.2.j.b.143.3		18	20.3	even	4
320.2.s.b.207.3		18	4.3	odd	2
320.2.s.b.303.3		18	80.13	odd	4
400.2.j.d.43.8		18	5.2	odd	4
400.2.j.d.307.8		18	80.19	odd	4
400.2.s.d.107.6		18	5.4	even	2
400.2.s.d.243.6		18	80.67	even	4
640.2.j.c.543.7		18	40.3	even	4
640.2.j.c.607.3		18	16.5	even	4
640.2.j.d.543.3		18	40.13	odd	4
640.2.j.d.607.7		18	16.11	odd	4
640.2.s.c.223.7		18	80.53	odd	4
640.2.s.c.287.7		18	8.3	odd	2
640.2.s.d.223.3		18	80.43	even	4
640.2.s.d.287.3		18	8.5	even	2
720.2.z.g.163.6		18	240.83	odd	4
720.2.z.g.667.6		18	3.2	odd	2
720.2.bd.g.307.8		18	48.35	even	4
720.2.bd.g.523.8		18	15.8	even	4
1600.2.j.d.143.7		18	20.7	even	4
1600.2.j.d.1007.3		18	80.29	even	4
1600.2.s.d.207.7		18	20.19	odd	2
1600.2.s.d.943.7		18	80.77	odd	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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.516777 - 1.31641i) q^{2} +1.28110 q^{3} +(-1.46588 + 1.36058i) q^{4} +(2.07160 - 0.841703i) q^{5} +(-0.662041 - 1.68645i) q^{6} +(-1.13975 - 1.13975i) q^{7} +(2.54862 + 1.22659i) q^{8} -1.35879 q^{9} +(-2.17858 - 2.29211i) q^{10} +(-2.32204 + 2.32204i) q^{11} +(-1.87794 + 1.74304i) q^{12} -1.36502i 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} +(0.702192 + 1.78873i) q^{18} +(-3.69752 + 3.69752i) q^{19} +(-1.89152 + 4.05243i) q^{20} +(-1.46013 - 1.46013i) q^{21} +(4.25673 + 1.85678i) 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} -5.58403 q^{27} +(3.22146 + 0.120015i) q^{28} +(-2.37343 - 2.37343i) q^{29} +(-2.79098 - 2.93641i) q^{30} +0.242577i q^{31} +(-5.40486 + 1.66958i) q^{32} +(-2.97475 + 2.97475i) q^{33} +(4.20112 - 9.63121i) q^{34} +(-3.32044 - 1.40178i) q^{35} +(1.99183 - 1.84875i) q^{36} -3.34494i q^{37} +(6.77825 + 2.95666i) q^{38} -1.74872i q^{39} +(6.31216 + 0.395820i) q^{40} +2.66956i q^{41} +(-1.16757 + 2.67669i) q^{42} -9.04874i q^{43} +(0.244509 - 6.56316i) q^{44} +(-2.81488 + 1.14370i) q^{45} +(1.67025 + 0.728562i) q^{46} +(7.87820 - 7.87820i) q^{47} +(0.381287 - 5.11018i) q^{48} -4.40194i q^{49} +(-6.44244 - 2.91462i) q^{50} +(6.73063 + 6.73063i) q^{51} +(1.85723 + 2.00096i) q^{52} -5.80113 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} +(-1.89788 + 4.35095i) q^{58} +(5.91474 + 5.91474i) q^{59} +(-2.42322 + 5.19155i) q^{60} +(-6.67404 + 6.67404i) q^{61} +(0.319332 - 0.125358i) 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} -4.54673i q^{67} +(-14.8497 - 0.553222i) q^{68} +(-1.16723 + 1.16723i) q^{69} +(-0.129391 + 5.09547i) q^{70} +15.4389 q^{71} +(-3.46305 - 1.66668i) q^{72} +(-1.49307 - 1.49307i) q^{73} +(-4.40332 + 1.72859i) q^{74} +(4.59026 - 4.46763i) q^{75} +(0.389347 - 10.4509i) q^{76} +5.29308 q^{77} +(-2.30204 + 0.903701i) q^{78} -10.3024 q^{79} +(-2.74092 - 8.51395i) q^{80} -3.07731 q^{81} +(3.51424 - 1.37957i) q^{82} +3.26589 q^{83} +(4.12701 + 0.153751i) q^{84} +(15.3059 + 6.46165i) q^{85} +(-11.9119 + 4.67618i) q^{86} +(-3.04060 - 3.04060i) q^{87} +(-8.76618 + 3.06981i) q^{88} +9.77206 q^{89} +(2.96024 + 3.11450i) q^{90} +(-1.55578 + 1.55578i) q^{91} +(0.0959403 - 2.57524i) q^{92} +0.310765i 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} +(-5.79477 + 2.27482i) q^{98} +(3.15516 - 3.15516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25}+ \cdots + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

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