LMFDB - Embedded newform 71.2.c.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(5,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("71.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + \cdots + 961 $ x^20 - 6x^19 + 28x^18 - 91x^17 + 268x^16 - 604x^15 + 1278x^14 - 1990x^13 + 3162x^12 - 4046x^11 + 6406x^10 - 8426x^9 + 12709x^8 - 13621x^7 + 17787x^6 - 13514x^5 + 9316x^4 - 1639x^3 - 228x^2 + 620*x + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.2
Root			$0.561200 - 1.72720i$ of defining polynomial
Character	$\chi$	$=$	71.5
Dual form			71.2.c.a.57.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.561200 - 1.72720i) q^{2} +(0.906993 + 2.79144i) q^{3} +(-1.05022 + 0.763032i) q^{4} +(1.21045 + 0.879441i) q^{5} +(4.31235 - 3.13311i) q^{6} +(-0.388444 - 1.19551i) q^{7} +(-1.03119 - 0.749203i) q^{8} +(-4.54244 + 3.30028i) q^{9} +O(q^{10})$	\(q+(-0.561200 - 1.72720i) q^{2} +(0.906993 + 2.79144i) q^{3} +(-1.05022 + 0.763032i) q^{4} +(1.21045 + 0.879441i) q^{5} +(4.31235 - 3.13311i) q^{6} +(-0.388444 - 1.19551i) q^{7} +(-1.03119 - 0.749203i) q^{8} +(-4.54244 + 3.30028i) q^{9} +(0.839664 - 2.58422i) q^{10} +(-1.22818 - 3.77994i) q^{11} +(-3.08250 - 2.23957i) q^{12} +(-0.173990 + 0.535487i) q^{13} +(-1.84688 + 1.34184i) q^{14} +(-1.35704 + 4.17654i) q^{15} +(-1.51762 + 4.67074i) q^{16} +(1.87505 - 5.77080i) q^{17} +(8.24944 + 5.99357i) q^{18} +(2.31993 + 7.14000i) q^{19} -1.94228 q^{20} +(2.98487 - 2.16864i) q^{21} +(-5.83944 + 4.24260i) q^{22} -8.89324 q^{23} +(1.15607 - 3.55802i) q^{24} +(-0.853320 - 2.62625i) q^{25} +1.02253 q^{26} +(-6.20887 - 4.51100i) q^{27} +(1.32017 + 0.959157i) q^{28} +(1.96757 + 1.42952i) q^{29} +7.97526 q^{30} +(0.162981 + 0.501605i) q^{31} +6.36973 q^{32} +(9.43751 - 6.85675i) q^{33} -11.0196 q^{34} +(0.581189 - 1.78871i) q^{35} +(2.25236 - 6.93206i) q^{36} +1.78389 q^{37} +(11.0302 - 8.01394i) q^{38} -1.65259 q^{39} +(-0.589320 - 1.81374i) q^{40} +2.18573 q^{41} +(-5.42077 - 3.93842i) q^{42} +(0.171513 + 0.124611i) q^{43} +(4.17407 + 3.03264i) q^{44} -8.40078 q^{45} +(4.99088 + 15.3604i) q^{46} +(-3.23735 + 9.96355i) q^{47} -14.4146 q^{48} +(4.38477 - 3.18572i) q^{49} +(-4.05716 + 2.94770i) q^{50} +17.8095 q^{51} +(-0.225865 - 0.695142i) q^{52} +(0.315365 + 0.229126i) q^{53} +(-4.30697 + 13.2555i) q^{54} +(1.83759 - 5.65552i) q^{55} +(-0.495119 + 1.52382i) q^{56} +(-17.8267 + 12.9519i) q^{57} +(1.36486 - 4.20062i) q^{58} +(5.34321 + 3.88207i) q^{59} +(-1.76164 - 5.42176i) q^{60} +(0.163356 - 0.502759i) q^{61} +(0.774905 - 0.563001i) q^{62} +(5.71000 + 4.14856i) q^{63} +(-0.539458 - 1.66028i) q^{64} +(-0.681536 + 0.495165i) q^{65} +(-17.1393 - 12.4524i) q^{66} +(2.66875 - 1.93896i) q^{67} +(2.43409 + 7.49135i) q^{68} +(-8.06611 - 24.8249i) q^{69} -3.41562 q^{70} +(7.75871 + 3.28671i) q^{71} +7.15669 q^{72} +(1.58170 + 4.86797i) q^{73} +(-1.00112 - 3.08113i) q^{74} +(6.55706 - 4.76398i) q^{75} +(-7.88450 - 5.72842i) q^{76} +(-4.04187 + 2.93659i) q^{77} +(0.927432 + 2.85434i) q^{78} +(-7.36486 - 5.35088i) q^{79} +(-5.94463 + 4.31903i) q^{80} +(1.75562 - 5.40324i) q^{81} +(-1.22663 - 3.77518i) q^{82} +(-6.00741 - 4.36464i) q^{83} +(-1.48005 + 4.55511i) q^{84} +(7.34472 - 5.33625i) q^{85} +(0.118975 - 0.366167i) q^{86} +(-2.20585 + 6.78891i) q^{87} +(-1.56546 + 4.81798i) q^{88} +(7.05835 + 5.12819i) q^{89} +(4.71452 + 14.5098i) q^{90} +0.707766 q^{91} +(9.33989 - 6.78583i) q^{92} +(-1.25238 + 0.909905i) q^{93} +19.0258 q^{94} +(-3.47106 + 10.6828i) q^{95} +(5.77730 + 17.7807i) q^{96} -2.53926 q^{97} +(-7.96309 - 5.78552i) q^{98} +(18.0538 + 13.1168i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.561200	−	1.72720i	−0.396828	−	1.22131i	−0.927529	−	0.373752i	$-0.878071\pi$
$2$	−0.561200	−	1.72720i	−0.396828	−	1.22131i	0.530701	−	0.847559i	$-0.321929\pi$
$3$	0.906993	+	2.79144i	0.523653	+	1.61164i	0.766964	+	0.641690i	$0.221766\pi$
$3$	0.906993	+	2.79144i	0.523653	+	1.61164i	−0.243312	+	0.969948i	$0.578234\pi$
$4$	−1.05022	+	0.763032i	−0.525112	+	0.381516i
$5$	1.21045	+	0.879441i	0.541328	+	0.393298i	0.824578	−	0.565748i	$-0.191413\pi$
$5$	1.21045	+	0.879441i	0.541328	+	0.393298i	−0.283250	+	0.959046i	$0.591413\pi$
$6$	4.31235	−	3.13311i	1.76051	−	1.27909i
$7$	−0.388444	−	1.19551i	−0.146818	−	0.451860i	0.850422	−	0.526101i	$-0.176347\pi$
$7$	−0.388444	−	1.19551i	−0.146818	−	0.451860i	−0.997240	+	0.0742410i	$0.976347\pi$
$8$	−1.03119	−	0.749203i	−0.364580	−	0.264883i
$9$	−4.54244	+	3.30028i	−1.51415	+	1.10009i
$10$	0.839664	−	2.58422i	0.265525	−	0.817202i
$11$	−1.22818	−	3.77994i	−0.370309	−	1.13969i	−0.946589	−	0.322442i	$-0.895496\pi$
$11$	−1.22818	−	3.77994i	−0.370309	−	1.13969i	0.576280	−	0.817252i	$-0.304504\pi$
$12$	−3.08250	−	2.23957i	−0.889842	−	0.646508i
$13$	−0.173990	+	0.535487i	−0.0482562	+	0.148517i	−0.972281	−	0.233815i	$-0.924879\pi$
$13$	−0.173990	+	0.535487i	−0.0482562	+	0.148517i	0.924025	+	0.382332i	$0.124879\pi$
$14$	−1.84688	+	1.34184i	−0.493600	+	0.358622i
$15$	−1.35704	+	4.17654i	−0.350386	+	1.07838i
$16$	−1.51762	+	4.67074i	−0.379404	+	1.16769i
$17$	1.87505	−	5.77080i	0.454766	−	1.39962i	−0.416645	−	0.909069i	$-0.636794\pi$
$17$	1.87505	−	5.77080i	0.454766	−	1.39962i	0.871410	−	0.490555i	$-0.163206\pi$
$18$	8.24944	+	5.99357i	1.94441	+	1.41270i
$19$	2.31993	+	7.14000i	0.532228	+	1.63803i	0.749564	+	0.661932i	$0.230263\pi$
$19$	2.31993	+	7.14000i	0.532228	+	1.63803i	−0.217335	+	0.976097i	$0.569737\pi$
$20$	−1.94228			−0.434307
$21$	2.98487	−	2.16864i	0.651353	−	0.473236i
$22$	−5.83944	+	4.24260i	−1.24497	+	0.904525i
$23$	−8.89324			−1.85437			−0.927184	−	0.374606i	$-0.877778\pi$
$23$	−8.89324			−1.85437			−0.927184	+	0.374606i	$0.877778\pi$
$24$	1.15607	−	3.55802i	0.235982	−	0.726278i
$25$	−0.853320	−	2.62625i	−0.170664	−	0.525250i
$26$	1.02253			0.200535
$27$	−6.20887	−	4.51100i	−1.19490	−	0.868143i
$28$	1.32017	+	0.959157i	0.249488	+	0.181264i
$29$	1.96757	+	1.42952i	0.365368	+	0.265456i	0.755288	−	0.655393i	$-0.227497\pi$
$29$	1.96757	+	1.42952i	0.365368	+	0.265456i	−0.389919	+	0.920849i	$0.627497\pi$
$30$	7.97526			1.45608
$31$	0.162981	+	0.501605i	0.0292723	+	0.0900909i	0.964625	−	0.263625i	$-0.0849181\pi$
$31$	0.162981	+	0.501605i	0.0292723	+	0.0900909i	−0.935353	+	0.353716i	$0.884918\pi$
$32$	6.36973			1.12602
$33$	9.43751	−	6.85675i	1.64286	−	1.19361i
$34$	−11.0196			−1.88984
$35$	0.581189	−	1.78871i	0.0982388	−	0.302348i
$36$	2.25236	−	6.93206i	0.375394	−	1.15534i
$37$	1.78389			0.293270			0.146635	−	0.989191i	$-0.453156\pi$
$37$	1.78389			0.293270			0.146635	+	0.989191i	$0.453156\pi$
$38$	11.0302	−	8.01394i	1.78934	−	1.30003i
$39$	−1.65259			−0.264626
$40$	−0.589320	−	1.81374i	−0.0931796	−	0.286777i
$41$	2.18573			0.341353			0.170677	−	0.985327i	$-0.445405\pi$
$41$	2.18573			0.341353			0.170677	+	0.985327i	$0.445405\pi$
$42$	−5.42077	−	3.93842i	−0.836443	−	0.607712i
$43$	0.171513	+	0.124611i	0.0261554	+	0.0190030i	0.600786	−	0.799410i	$-0.294854\pi$
$43$	0.171513	+	0.124611i	0.0261554	+	0.0190030i	−0.574631	+	0.818413i	$0.694854\pi$
$44$	4.17407	+	3.03264i	0.629265	+	0.457188i
$45$	−8.40078			−1.25231
$46$	4.99088	+	15.3604i	0.735865	+	2.26476i
$47$	−3.23735	+	9.96355i	−0.472216	+	1.45333i	0.377459	+	0.926026i	$0.376798\pi$
$47$	−3.23735	+	9.96355i	−0.472216	+	1.45333i	−0.849675	+	0.527306i	$0.823202\pi$
$48$	−14.4146			−2.08056
$49$	4.38477	−	3.18572i	0.626395	−	0.455103i
$50$	−4.05716	+	2.94770i	−0.573769	+	0.416868i
$51$	17.8095			2.49383
$52$	−0.225865	−	0.695142i	−0.0313219	−	0.0963988i
$53$	0.315365	+	0.229126i	0.0433187	+	0.0314729i	0.609234	−	0.792991i	$-0.291477\pi$
$53$	0.315365	+	0.229126i	0.0433187	+	0.0314729i	−0.565915	+	0.824463i	$0.691477\pi$
$54$	−4.30697	+	13.2555i	−0.586105	+	1.80384i
$55$	1.83759	−	5.65552i	0.247781	−	0.762590i
$56$	−0.495119	+	1.52382i	−0.0661630	+	0.203629i
$57$	−17.8267	+	12.9519i	−2.36121	+	1.71552i
$58$	1.36486	−	4.20062i	0.179215	−	0.551569i
$59$	5.34321	+	3.88207i	0.695627	+	0.505403i	0.878505	−	0.477733i	$-0.158541\pi$
$59$	5.34321	+	3.88207i	0.695627	+	0.505403i	−0.182878	+	0.983136i	$0.558541\pi$
$60$	−1.76164	−	5.42176i	−0.227426	−	0.699946i
$61$	0.163356	−	0.502759i	0.0209156	−	0.0643717i	−0.940054	−	0.341026i	$-0.889226\pi$
$61$	0.163356	−	0.502759i	0.0209156	−	0.0643717i	0.960970	+	0.276654i	$0.0892256\pi$
$62$	0.774905	−	0.563001i	0.0984130	−	0.0715012i
$63$	5.71000	+	4.14856i	0.719392	+	0.522669i
$64$	−0.539458	−	1.66028i	−0.0674322	−	0.207535i
$65$	−0.681536	+	0.495165i	−0.0845341	+	0.0614176i
$66$	−17.1393	−	12.4524i	−2.10970	−	1.53279i
$67$	2.66875	−	1.93896i	0.326040	−	0.236882i	−0.412708	−	0.910863i	$-0.635417\pi$
$67$	2.66875	−	1.93896i	0.326040	−	0.236882i	0.738748	+	0.673981i	$0.235417\pi$
$68$	2.43409	+	7.49135i	0.295177	+	0.908460i
$69$	−8.06611	−	24.8249i	−0.971045	−	2.98857i
$70$	−3.41562			−0.408245
$71$	7.75871	+	3.28671i	0.920789	+	0.390060i
$71$	7.75871	+	3.28671i	0.920789	+	0.390060i
$72$	7.15669			0.843424
$73$	1.58170	+	4.86797i	0.185124	+	0.569753i	0.999950	−	0.00995204i	$-0.00316788\pi$
$73$	1.58170	+	4.86797i	0.185124	+	0.569753i	−0.814827	+	0.579705i	$0.803168\pi$
$74$	−1.00112	−	3.08113i	−0.116378	−	0.358174i
$75$	6.55706	−	4.76398i	0.757144	−	0.550097i
$76$	−7.88450	−	5.72842i	−0.904414	−	0.657095i
$77$	−4.04187	+	2.93659i	−0.460614	+	0.334656i
$78$	0.927432	+	2.85434i	0.105011	+	0.323191i
$79$	−7.36486	−	5.35088i	−0.828611	−	0.602021i	0.0905549	−	0.995891i	$-0.471136\pi$
$79$	−7.36486	−	5.35088i	−0.828611	−	0.602021i	−0.919166	+	0.393870i	$0.871136\pi$
$80$	−5.94463	+	4.31903i	−0.664630	+	0.482882i
$81$	1.75562	−	5.40324i	0.195069	−	0.600360i
$82$	−1.22663	−	3.77518i	−0.135459	−	0.416899i
$83$	−6.00741	−	4.36464i	−0.659399	−	0.479081i	0.207061	−	0.978328i	$-0.433610\pi$
$83$	−6.00741	−	4.36464i	−0.659399	−	0.479081i	−0.866460	+	0.499247i	$0.833610\pi$
$84$	−1.48005	+	4.55511i	−0.161486	+	0.497003i
$85$	7.34472	−	5.33625i	0.796647	−	0.578798i
$86$	0.118975	−	0.366167i	0.0128294	−	0.0394848i
$87$	−2.20585	+	6.78891i	−0.236492	+	0.727848i
$88$	−1.56546	+	4.81798i	−0.166878	+	0.513598i
$89$	7.05835	+	5.12819i	0.748183	+	0.543587i	0.895263	−	0.445538i	$-0.146987\pi$
$89$	7.05835	+	5.12819i	0.748183	+	0.543587i	−0.147080	+	0.989125i	$0.546987\pi$
$90$	4.71452	+	14.5098i	0.496954	+	1.52947i
$91$	0.707766			0.0741940
$92$	9.33989	−	6.78583i	0.973751	−	0.707471i
$93$	−1.25238	+	0.909905i	−0.129865	+	0.0943527i
$94$	19.0258			1.96236
$95$	−3.47106	+	10.6828i	−0.356124	+	1.09604i
$96$	5.77730	+	17.7807i	0.589643	+	1.81474i
$97$	−2.53926			−0.257823			−0.128911	−	0.991656i	$-0.541148\pi$
$97$	−2.53926			−0.257823			−0.128911	+	0.991656i	$0.541148\pi$
$98$	−7.96309	−	5.78552i	−0.804393	−	0.584426i
$99$	18.0538	+	13.1168i	1.81447	+	1.31829i
$100$	2.90009	+	2.10704i	0.290009	+	0.210704i
$101$	−10.4097			−1.03580			−0.517902	−	0.855440i	$-0.673287\pi$
$101$	−10.4097			−1.03580			−0.517902	+	0.855440i	$0.673287\pi$
$102$	−9.99468	−	30.7605i	−0.989621	−	3.04574i
$103$	−16.5543			−1.63115			−0.815573	−	0.578655i	$-0.803578\pi$
$103$	−16.5543			−1.63115			−0.815573	+	0.578655i	$0.803578\pi$
$104$	0.580605	−	0.421834i	0.0569330	−	0.0413643i
$105$	5.52022			0.538718
$106$	0.218763	−	0.673282i	0.0212481	−	0.0653949i
$107$	2.61245	−	8.04029i	0.252555	−	0.777284i	−0.741747	−	0.670680i	$-0.766002\pi$
$107$	2.61245	−	8.04029i	0.252555	−	0.777284i	0.994302	−	0.106604i	$-0.0339976\pi$
$108$	9.96274			0.958665
$109$	3.85264	−	2.79911i	0.369016	−	0.268106i	−0.387787	−	0.921749i	$-0.626760\pi$
$109$	3.85264	−	2.79911i	0.369016	−	0.268106i	0.756803	+	0.653643i	$0.226760\pi$
$110$	−10.7994			−1.02969
$111$	1.61798	+	4.97962i	0.153572	+	0.472645i
$112$	6.17342			0.583334
$113$	−2.71074	−	1.96947i	−0.255005	−	0.185272i	0.452937	−	0.891542i	$-0.350376\pi$
$113$	−2.71074	−	1.96947i	−0.255005	−	0.185272i	−0.707942	+	0.706271i	$0.750376\pi$
$114$	32.3748	+	23.5216i	3.03217	+	2.20300i
$115$	−10.7648	−	7.82108i	−1.00382	−	0.729319i
$116$	−3.15716			−0.293135
$117$	−0.976915	−	3.00664i	−0.0903158	−	0.277964i
$118$	3.70648	−	11.4074i	0.341210	−	1.05014i
$119$	−7.62739			−0.699202
$120$	4.52843	−	3.29010i	0.413388	−	0.300344i
$121$	−3.88031	+	2.81921i	−0.352756	+	0.256292i
$122$	−0.960039			−0.0869179
$123$	1.98244	+	6.10132i	0.178751	+	0.550138i
$124$	−0.553908	−	0.402437i	−0.0497424	−	0.0361400i
$125$	3.58848	−	11.0442i	0.320963	−	0.987824i
$126$	3.96092	−	12.1904i	0.352867	−	1.08601i
$127$	2.45999	−	7.57106i	0.218289	−	0.671823i	−0.780615	−	0.625012i	$-0.785094\pi$
$127$	2.45999	−	7.57106i	0.218289	−	0.671823i	0.998904	−	0.0468113i	$-0.0149059\pi$
$128$	7.74155	−	5.62457i	0.684263	−	0.497146i
$129$	−0.192284	+	0.591788i	−0.0169296	+	0.0521040i
$130$	1.23772	+	0.899259i	0.108556	+	0.0788702i
$131$	3.49791	+	10.7655i	0.305614	+	0.940582i	0.979448	+	0.201699i	$0.0646463\pi$
$131$	3.49791	+	10.7655i	0.305614	+	0.940582i	−0.673834	+	0.738883i	$0.735354\pi$
$132$	−4.67958	+	14.4023i	−0.407305	+	1.25356i
$133$	7.63478	−	5.54699i	0.662019	−	0.480985i
$134$	−4.84667	−	3.52131i	−0.418689	−	0.304195i
$135$	−3.54834	−	10.9207i	−0.305392	−	0.939901i
$136$	−6.25702	+	4.54599i	−0.536535	+	0.389816i
$137$	−2.53184	−	1.83949i	−0.216310	−	0.157158i	0.474354	−	0.880334i	$-0.342682\pi$
$137$	−2.53184	−	1.83949i	−0.216310	−	0.157158i	−0.690664	+	0.723176i	$0.742682\pi$
$138$	−38.3508	+	27.8635i	−3.26464	+	2.37190i
$139$	2.79502	+	8.60220i	0.237071	+	0.729629i	0.996840	+	0.0794360i	$0.0253119\pi$
$139$	2.79502	+	8.60220i	0.237071	+	0.729629i	−0.759769	+	0.650193i	$0.774688\pi$
$140$	0.754469	+	2.32202i	0.0637643	+	0.196246i
$141$	−30.7489			−2.58952
$142$	1.32260	−	15.2453i	0.110990	−	1.27936i
$143$	2.23780			0.187134
$144$	−8.52106	−	26.2251i	−0.710088	−	2.18543i
$145$	1.12446	+	3.46072i	0.0933810	+	0.287397i
$146$	7.52028	−	5.46381i	0.622383	−	0.452188i
$147$	12.8697	+	9.35038i	1.06147	+	0.771206i
$148$	−1.87349	+	1.36117i	−0.154000	+	0.111887i
$149$	−0.848861	−	2.61252i	−0.0695414	−	0.214026i	0.910246	−	0.414068i	$-0.135892\pi$
$149$	−0.848861	−	2.61252i	−0.0695414	−	0.214026i	−0.979787	+	0.200041i	$0.935892\pi$
$150$	−11.9081	−	8.65177i	−0.972296	−	0.706414i
$151$	4.72833	−	3.43533i	0.384786	−	0.279563i	−0.378530	−	0.925589i	$-0.623570\pi$
$151$	4.72833	−	3.43533i	0.384786	−	0.279563i	0.763315	+	0.646026i	$0.223570\pi$
$152$	2.95703	−	9.10079i	0.239846	−	0.738171i
$153$	10.5279	+	32.4017i	0.851134	+	2.61952i
$154$	7.34036	+	5.33308i	0.591503	+	0.429752i
$155$	−0.243852	+	0.750499i	−0.0195866	+	0.0602815i
$156$	1.73559	−	1.26098i	0.138958	−	0.100959i
$157$	0.684717	−	2.10734i	0.0546463	−	0.168184i	−0.920008	−	0.391899i	$-0.871818\pi$
$157$	0.684717	−	2.10734i	0.0546463	−	0.168184i	0.974655	+	0.223715i	$0.0718184\pi$
$158$	−5.10886	+	15.7235i	−0.406439	+	1.25089i
$159$	−0.353557	+	1.08814i	−0.0280389	+	0.0862949i
$160$	7.71022	+	5.60180i	0.609546	+	0.442861i
$161$	3.45453	+	10.6319i	0.272255	+	0.837915i
$162$	−10.3177			−0.810635
$163$	5.94620	−	4.32017i	0.465742	−	0.338382i	−0.330037	−	0.943968i	$-0.607061\pi$
$163$	5.94620	−	4.32017i	0.465742	−	0.338382i	0.795780	+	0.605586i	$0.207061\pi$
$164$	−2.29550	+	1.66778i	−0.179249	+	0.130232i
$165$	17.4537			1.35877
$166$	−4.16723	+	12.8254i	−0.323439	+	0.995444i
$167$	−0.311585	−	0.958958i	−0.0241111	−	0.0742064i	0.938277	−	0.345885i	$-0.112421\pi$
$167$	−0.311585	−	0.958958i	−0.0241111	−	0.0742064i	−0.962388	+	0.271679i	$0.912421\pi$
$168$	−4.70272			−0.362823
$169$	10.2607	+	7.45487i	0.789288	+	0.573451i
$170$	−13.3386	−	9.69106i	−1.02302	−	0.743271i
$171$	−34.1021	−	24.7766i	−2.60785	−	1.89472i
$172$	−0.275209			−0.0209845
$173$	−2.56930	−	7.90749i	−0.195340	−	0.601195i	−0.999972	−	0.00742175i	$-0.997638\pi$
$173$	−2.56930	−	7.90749i	−0.195340	−	0.601195i	0.804632	−	0.593773i	$-0.202362\pi$
$174$	12.9637			0.982775
$175$	−2.80824	+	2.04030i	−0.212283	+	0.154232i
$176$	19.5190			1.47130
$177$	−5.99030	+	18.4363i	−0.450259	+	1.38575i
$178$	4.89624	−	15.0691i	0.366989	−	1.12948i
$179$	−21.5570			−1.61124			−0.805621	−	0.592431i	$-0.798168\pi$
$179$	−21.5570			−1.61124			−0.805621	+	0.592431i	$0.798168\pi$
$180$	8.82270	−	6.41007i	0.657605	−	0.477778i
$181$	−13.8487			−1.02936			−0.514682	−	0.857381i	$-0.672090\pi$
$181$	−13.8487			−1.02936			−0.514682	+	0.857381i	$0.672090\pi$
$182$	−0.397198	−	1.22245i	−0.0294423	−	0.0906140i
$183$	1.55159			0.114696
$184$	9.17061	+	6.66284i	0.676066	+	0.491191i
$185$	2.15931	+	1.56883i	0.158755	+	0.115342i
$186$	2.27442	+	1.65246i	0.166768	+	0.121164i
$187$	−24.1161			−1.76355
$188$	−4.20256	−	12.9342i	−0.306503	−	0.943320i
$189$	−2.98115	+	9.17503i	−0.216847	+	0.667385i
$190$	20.3993			1.47992
$191$	−9.84273	+	7.15117i	−0.712195	+	0.517440i	−0.883881	−	0.467712i	$-0.845079\pi$
$191$	−9.84273	+	7.15117i	−0.712195	+	0.517440i	0.171686	+	0.985152i	$0.445079\pi$
$192$	4.14529	−	3.01173i	0.299160	−	0.217353i
$193$	7.17041			0.516137			0.258069	−	0.966127i	$-0.416914\pi$
$193$	7.17041			0.516137			0.258069	+	0.966127i	$0.416914\pi$
$194$	1.42503	+	4.38580i	0.102311	+	0.314882i
$195$	−2.00037	−	1.45335i	−0.143249	−	0.104077i
$196$	−2.17418	+	6.69144i	−0.155299	+	0.477960i
$197$	−4.11397	+	12.6615i	−0.293108	+	0.902093i	0.690743	+	0.723101i	$0.257284\pi$
$197$	−4.11397	+	12.6615i	−0.293108	+	0.902093i	−0.983850	+	0.178993i	$0.942716\pi$
$198$	12.5235	−	38.5435i	0.890010	−	2.73917i
$199$	21.0695	−	15.3079i	1.49358	−	1.08515i	0.520728	−	0.853723i	$-0.325661\pi$
$199$	21.0695	−	15.3079i	1.49358	−	1.08515i	0.972852	−	0.231427i	$-0.0743394\pi$
$200$	−1.08766	+	3.34747i	−0.0769091	+	0.236702i
$201$	7.83304	+	5.69103i	0.552500	+	0.401415i
$202$	5.84192	+	17.9796i	0.411036	+	1.26504i
$203$	0.944715	−	2.90754i	0.0663060	−	0.204069i
$204$	−18.7039	+	13.5892i	−1.30954	+	0.951435i
$205$	2.64571	+	1.92222i	0.184784	+	0.134254i
$206$	9.29028	+	28.5925i	0.647284	+	1.99214i
$207$	40.3970	−	29.3501i	2.80779	−	2.03998i
$208$	−2.23707	−	1.62533i	−0.155113	−	0.112696i
$209$	24.1395	−	17.5384i	1.66976	−	1.21315i
$210$	−3.09795	−	9.53450i	−0.213779	−	0.657943i
$211$	−6.50881	−	20.0321i	−0.448085	−	1.37906i	−0.879065	−	0.476703i	$-0.841832\pi$
$211$	−6.50881	−	20.0321i	−0.448085	−	1.37906i	0.430979	−	0.902362i	$-0.358168\pi$
$212$	−0.506034			−0.0347546
$213$	−2.13755	+	24.6390i	−0.146462	+	1.68824i
$214$	−15.3532			−1.04953
$215$	0.0980186	+	0.301670i	0.00668482	+	0.0205737i
$216$	3.02286	+	9.30340i	0.205679	+	0.633016i
$217$	0.536364	−	0.389691i	0.0364108	−	0.0264540i
$218$	−6.99670	−	5.08340i	−0.473876	−	0.344291i
$219$	−12.1540	+	8.83043i	−0.821294	+	0.596705i
$220$	2.38546	+	7.34170i	0.160828	+	0.494977i
$221$	2.76395	+	2.00813i	0.185923	+	0.135081i
$222$	7.69277	−	5.58913i	0.516305	−	0.375118i
$223$	−2.40251	+	7.39418i	−0.160884	+	0.495151i	−0.998709	−	0.0507878i	$-0.983827\pi$
$223$	−2.40251	+	7.39418i	−0.160884	+	0.495151i	0.837825	+	0.545939i	$0.183827\pi$
$224$	−2.47429	−	7.61507i	−0.165320	−	0.508803i
$225$	12.5435	+	9.11339i	0.836234	+	0.607559i
$226$	−1.88039	+	5.78724i	−0.125081	+	0.384961i
$227$	22.1600	−	16.1002i	1.47081	−	1.06861i	0.490431	−	0.871480i	$-0.336839\pi$
$227$	22.1600	−	16.1002i	1.47081	−	1.06861i	0.980378	−	0.197126i	$-0.0631607\pi$
$228$	8.83935	−	27.2047i	0.585401	−	1.80168i
$229$	6.72782	−	20.7061i	0.444587	−	1.36830i	−0.438350	−	0.898804i	$-0.644437\pi$
$229$	6.72782	−	20.7061i	0.444587	−	1.36830i	0.882937	−	0.469492i	$-0.155563\pi$
$230$	−7.46733	+	22.9821i	−0.492381	+	1.51539i
$231$	−11.8633	−	8.61916i	−0.780545	−	0.567099i
$232$	−0.957933	−	2.94821i	−0.0628914	−	0.193560i
$233$	−11.7450			−0.769442			−0.384721	−	0.923033i	$-0.625702\pi$
$233$	−11.7450			−0.769442			−0.384721	+	0.923033i	$0.625702\pi$
$234$	−4.64480	+	3.37465i	−0.303640	+	0.220608i
$235$	−12.6810	+	9.21328i	−0.827217	+	0.601008i
$236$	−8.57372			−0.558101
$237$	8.25678	−	25.4118i	0.536336	−	1.65067i
$238$	4.28049	+	13.1740i	0.277463	+	0.853944i
$239$	−9.97895			−0.645484			−0.322742	−	0.946487i	$-0.604605\pi$
$239$	−9.97895			−0.645484			−0.322742	+	0.946487i	$0.604605\pi$
$240$	−17.4481	−	12.6768i	−1.12627	−	0.818281i
$241$	−0.231623	−	0.168284i	−0.0149202	−	0.0108401i	0.580300	−	0.814403i	$-0.302935\pi$
$241$	−0.231623	−	0.168284i	−0.0149202	−	0.0108401i	−0.595220	+	0.803563i	$0.702935\pi$
$242$	7.04696	+	5.11992i	0.452996	+	0.329121i
$243$	−6.34860			−0.407263
$244$	0.212061	+	0.652656i	0.0135758	+	0.0417820i
$245$	8.10918			0.518076
$246$	9.42563	−	6.84812i	0.600956	−	0.436620i
$247$	−4.22703			−0.268959
$248$	0.207739	−	0.639355i	0.0131915	−	0.0405991i
$249$	6.73494	−	20.7280i	0.426809	−	1.31358i
$250$	−21.0894			−1.33381
$251$	1.70687	−	1.24011i	0.107736	−	0.0782751i	−0.532613	−	0.846359i	$-0.678790\pi$
$251$	1.70687	−	1.24011i	0.107736	−	0.0782751i	0.640349	+	0.768084i	$0.278790\pi$
$252$	−9.16226			−0.577168
$253$	10.9225	+	33.6159i	0.686689	+	2.11341i
$254$	−14.4572			−0.907128
$255$	21.5574	+	15.6624i	1.34998	+	0.980817i
$256$	−16.8839	−	12.2669i	−1.05524	−	0.766680i
$257$	5.88139	+	4.27308i	0.366871	+	0.266547i	0.755912	−	0.654673i	$-0.227194\pi$
$257$	5.88139	+	4.27308i	0.366871	+	0.266547i	−0.389041	+	0.921220i	$0.627194\pi$
$258$	1.13004			0.0703534
$259$	−0.692943	−	2.13266i	−0.0430574	−	0.132517i
$260$	0.337938	−	1.04007i	0.0209580	−	0.0645022i
$261$	−13.6554			−0.845247
$262$	16.6310	−	12.0831i	1.02747	−	0.746499i
$263$	15.2340	−	11.0682i	0.939369	−	0.682492i	−0.00889944	−	0.999960i	$-0.502833\pi$
$263$	15.2340	−	11.0682i	0.939369	−	0.682492i	0.948269	+	0.317469i	$0.102833\pi$
$264$	−14.8690			−0.915121
$265$	0.180230	+	0.554689i	0.0110714	+	0.0340743i
$266$	−13.8654	−	10.0738i	−0.850140	−	0.617663i
$267$	−7.91315	+	24.3542i	−0.484277	+	1.49045i
$268$	−1.32330	+	4.07269i	−0.0808332	+	0.248779i
$269$	−7.78463	+	23.9586i	−0.474638	+	1.46078i	0.371808	+	0.928309i	$0.378738\pi$
$269$	−7.78463	+	23.9586i	−0.474638	+	1.46078i	−0.846446	+	0.532475i	$0.821262\pi$
$270$	−16.8708	+	12.2573i	−1.02672	+	0.745958i
$271$	1.67301	−	5.14900i	0.101628	−	0.312779i	−0.887296	−	0.461200i	$-0.847419\pi$
$271$	1.67301	−	5.14900i	0.101628	−	0.312779i	0.988924	+	0.148421i	$0.0474190\pi$
$272$	24.1083	+	17.5157i	1.46178	+	1.06205i
$273$	0.641939	+	1.97568i	0.0388519	+	0.119574i
$274$	−1.75629	+	5.40530i	−0.106101	+	0.326546i
$275$	−8.87903	+	6.45099i	−0.535425	+	0.389009i
$276$	27.4134	+	19.9170i	1.65010	+	1.19886i
$277$	3.37886	+	10.3991i	0.203016	+	0.624820i	0.999789	+	0.0205407i	$0.00653877\pi$
$277$	3.37886	+	10.3991i	0.203016	+	0.624820i	−0.796773	+	0.604279i	$0.793461\pi$
$278$	13.2891	−	9.65510i	0.797028	−	0.579075i
$279$	−2.39577	−	1.74063i	−0.143431	−	0.104209i
$280$	−1.93942	+	1.40907i	−0.115903	+	0.0842083i
$281$	−5.81312	−	17.8909i	−0.346782	−	1.06728i	−0.960623	−	0.277855i	$-0.910377\pi$
$281$	−5.81312	−	17.8909i	−0.346782	−	1.06728i	0.613842	−	0.789429i	$-0.289623\pi$
$282$	17.2563	+	53.1093i	1.02760	+	3.16261i
$283$	16.3366			0.971113			0.485556	−	0.874205i	$-0.338617\pi$
$283$	16.3366			0.971113			0.485556	+	0.874205i	$0.338617\pi$
$284$	−10.6562	+	2.46837i	−0.632332	+	0.146471i
$285$	−32.9687			−1.95290
$286$	−1.25585	−	3.86511i	−0.0742601	−	0.228549i
$287$	−0.849034	−	2.61306i	−0.0501169	−	0.154244i
$288$	−28.9341	+	21.0219i	−1.70496	+	1.23873i
$289$	−16.0330	−	11.6487i	−0.943120	−	0.685217i
$290$	5.34629	−	3.88431i	0.313945	−	0.228095i
$291$	−2.30309	−	7.08819i	−0.135010	−	0.415517i
$292$	−5.37556	−	3.90557i	−0.314581	−	0.228556i
$293$	3.56679	−	2.59143i	0.208374	−	0.151393i	−0.478704	−	0.877977i	$-0.658893\pi$
$293$	3.56679	−	2.59143i	0.208374	−	0.151393i	0.687078	+	0.726584i	$0.258893\pi$
$294$	8.92746	−	27.4759i	0.520660	−	1.60243i
$295$	3.05362	+	9.39808i	0.177789	+	0.547177i
$296$	−1.83953	−	1.33650i	−0.106920	−	0.0776822i
$297$	−9.42573	+	29.0094i	−0.546936	+	1.68330i
$298$	−4.03596	+	2.93230i	−0.233797	+	0.169863i
$299$	1.54734	−	4.76222i	0.0894848	−	0.275406i
$300$	−3.25131	+	10.0065i	−0.187714	+	0.577725i
$301$	0.0823507	−	0.253449i	0.00474661	−	0.0146086i
$302$	−8.58702	−	6.23884i	−0.494128	−	0.359005i
$303$	−9.44153	−	29.0581i	−0.542402	−	1.66934i
$304$	−36.8699			−2.11463
$305$	0.639882	−	0.464901i	0.0366395	−	0.0266202i
$306$	50.0558	−	36.3676i	2.86150	−	2.07900i
$307$	−28.2017			−1.60956			−0.804779	−	0.593574i	$-0.797716\pi$
$307$	−28.2017			−1.60956			−0.804779	+	0.593574i	$0.797716\pi$
$308$	2.00416	−	6.16816i	0.114197	−	0.351463i
$309$	−15.0147	−	46.2104i	−0.854154	−	2.62882i
$310$	1.43311			0.0813950
$311$	8.75868	+	6.36355i	0.496659	+	0.360844i	0.807739	−	0.589540i	$-0.200691\pi$
$311$	8.75868	+	6.36355i	0.496659	+	0.360844i	−0.311080	+	0.950384i	$0.600691\pi$
$312$	1.70413	+	1.23812i	0.0964774	+	0.0700949i
$313$	3.62287	+	2.63217i	0.204777	+	0.148779i	0.685447	−	0.728122i	$-0.259607\pi$
$313$	3.62287	+	2.63217i	0.204777	+	0.148779i	−0.480671	+	0.876901i	$0.659607\pi$
$314$	−4.02405			−0.227090
$315$	3.26324	+	10.0432i	0.183863	+	0.565871i
$316$	11.8176			0.664795
$317$	−1.21297	+	0.881275i	−0.0681272	+	0.0494973i	−0.621328	−	0.783551i	$-0.713406\pi$
$317$	−1.21297	+	0.881275i	−0.0681272	+	0.0494973i	0.553200	+	0.833048i	$0.313406\pi$
$318$	2.07784			0.116520
$319$	2.98698	−	9.19298i	0.167239	−	0.514708i
$320$	0.807134	−	2.48410i	0.0451202	−	0.138866i
$321$	24.8134			1.38495
$322$	16.4248	−	11.9333i	0.915316	−	0.665016i
$323$	45.5535			2.53466
$324$	2.27905	+	7.01420i	0.126614	+	0.389678i
$325$	1.55479			0.0862444
$326$	−10.7988	−	7.84577i	−0.598089	−	0.434537i
$327$	11.3078	+	8.21563i	0.625325	+	0.454326i
$328$	−2.25390	−	1.63755i	−0.124451	−	0.0904187i
$329$	13.1690			0.726033
$330$	−9.79502	−	30.1460i	−0.539198	−	1.65948i
$331$	8.56068	−	26.3471i	0.470537	−	1.44817i	−0.381345	−	0.924433i	$-0.624539\pi$
$331$	8.56068	−	26.3471i	0.470537	−	1.44817i	0.851883	−	0.523732i	$-0.175461\pi$
$332$	9.63948			0.529035
$333$	−8.10322	+	5.88734i	−0.444054	+	0.322624i
$334$	−1.48145	+	1.07633i	−0.0810612	+	0.0588944i
$335$	4.93559			0.269660
$336$	5.59925	+	17.2327i	0.305464	+	0.940123i
$337$	−13.9792	−	10.1565i	−0.761498	−	0.553261i	0.137871	−	0.990450i	$-0.455974\pi$
$337$	−13.9792	−	10.1565i	−0.761498	−	0.553261i	−0.899370	+	0.437189i	$0.855974\pi$
$338$	7.11769	−	21.9060i	0.387151	−	1.19153i
$339$	3.03902	−	9.35315i	0.165057	−	0.507993i
$340$	−3.64187	+	11.2085i	−0.197508	+	0.607867i
$341$	1.69586	−	1.23212i	0.0918362	−	0.0667229i
$342$	−23.6560	+	72.8057i	−1.27917	+	3.93688i
$343$	−12.6305	−	9.17661i	−0.681984	−	0.495490i
$344$	−0.0835028	−	0.256995i	−0.00450217	−	0.0138563i
$345$	12.0685	−	37.1429i	0.649744	−	1.99971i
$346$	−12.2159	+	8.87536i	−0.656730	+	0.477142i
$347$	14.8815	+	10.8120i	0.798880	+	0.580421i	0.910586	−	0.413321i	$-0.135631\pi$
$347$	14.8815	+	10.8120i	0.798880	+	0.580421i	−0.111705	+	0.993741i	$0.535631\pi$
$348$	−2.86352	−	8.81301i	−0.153501	−	0.472427i
$349$	−11.5214	+	8.37079i	−0.616727	+	0.448078i	−0.851777	−	0.523905i	$-0.824475\pi$
$349$	−11.5214	+	8.37079i	−0.616727	+	0.448078i	0.235050	+	0.971983i	$0.424475\pi$
$350$	5.09999	+	3.70536i	0.272606	+	0.198060i
$351$	3.49587	−	2.53990i	0.186596	−	0.135570i
$352$	−7.82314	−	24.0772i	−0.416975	−	1.28332i
$353$	1.63316	+	5.02635i	0.0869243	+	0.267525i	0.985065	−	0.172183i	$-0.0550819\pi$
$353$	1.63316	+	5.02635i	0.0869243	+	0.267525i	−0.898141	+	0.439708i	$0.855082\pi$
$354$	35.2048			1.87111
$355$	6.50104	+	10.8017i	0.345039	+	0.573295i
$356$	−11.3258			−0.600267
$357$	−6.91800	−	21.2914i	−0.366139	−	1.12686i
$358$	12.0978	+	37.2331i	0.639386	+	1.96783i
$359$	−25.4670	+	18.5028i	−1.34409	+	0.976542i	−0.344812	+	0.938672i	$0.612057\pi$
$359$	−25.4670	+	18.5028i	−1.34409	+	0.976542i	−0.999283	+	0.0378704i	$0.987943\pi$
$360$	8.66279	+	6.29389i	0.456569	+	0.331717i
$361$	−30.2263	+	21.9607i	−1.59086	+	1.15583i
$362$	7.77187	+	23.9194i	0.408480	+	1.25717i
$363$	−11.3891	−	8.27465i	−0.597772	−	0.434307i
$364$	−0.743312	+	0.540048i	−0.0389602	+	0.0283062i
$365$	−2.36653	+	7.28343i	−0.123870	+	0.381232i
$366$	−0.870749	−	2.67989i	−0.0455148	−	0.140080i
$367$	−15.2325	−	11.0671i	−0.795130	−	0.577696i	0.114351	−	0.993440i	$-0.463521\pi$
$367$	−15.2325	−	11.0671i	−0.795130	−	0.577696i	−0.909481	+	0.415744i	$0.863521\pi$
$368$	13.4965	−	41.5380i	0.703555	−	2.16532i
$369$	−9.92854	+	7.21350i	−0.516859	+	0.375520i
$370$	1.49787	−	4.60997i	0.0778705	−	0.239661i
$371$	0.151420	−	0.466024i	0.00786136	−	0.0241948i
$372$	0.620989	−	1.91121i	0.0321968	−	0.0990915i
$373$	22.2616	+	16.1740i	1.15266	+	0.837458i	0.988833	−	0.149031i	$-0.0476154\pi$
$373$	22.2616	+	16.1740i	1.15266	+	0.837458i	0.163829	+	0.986489i	$0.447615\pi$
$374$	13.5340	+	41.6533i	0.699825	+	2.15384i
$375$	34.0840			1.76009
$376$	10.8030	−	7.84886i	0.557124	−	0.404774i
$377$	−1.10783	+	0.804885i	−0.0570561	+	0.0414537i
$378$	17.5201			0.901136
$379$	−2.22452	+	6.84637i	−0.114266	+	0.351674i	−0.991793	−	0.127852i	$-0.959192\pi$
$379$	−2.22452	+	6.84637i	−0.114266	+	0.351674i	0.877527	+	0.479527i	$0.159192\pi$
$380$	−4.50596	−	13.8679i	−0.231151	−	0.711408i
$381$	23.3654			1.19704
$382$	17.8752	+	12.9871i	0.914575	+	0.664477i
$383$	12.0092	+	8.72517i	0.613639	+	0.445835i	0.850694	−	0.525661i	$-0.176182\pi$
$383$	12.0092	+	8.72517i	0.613639	+	0.445835i	−0.237055	+	0.971496i	$0.576182\pi$
$384$	22.7222	+	16.5086i	1.15954	+	0.842452i
$385$	−7.47503			−0.380963
$386$	−4.02403	−	12.3847i	−0.204818	−	0.630364i
$387$	−1.19034			−0.0605082
$388$	2.66679	−	1.93754i	0.135386	−	0.0983636i
$389$	−30.1100			−1.52664			−0.763320	−	0.646021i	$-0.776432\pi$
$389$	−30.1100			−1.52664			−0.763320	+	0.646021i	$0.776432\pi$
$390$	−1.38762	+	4.27065i	−0.0702648	+	0.216253i
$391$	−16.6752	+	51.3211i	−0.843303	+	2.59542i
$392$	−6.90827			−0.348920
$393$	−26.8785	+	19.5284i	−1.35584	+	0.985077i
$394$	24.1776			1.21805
$395$	−4.20898	−	12.9539i	−0.211777	−	0.651782i
$396$	−28.9690			−1.45575
$397$	−2.30746	−	1.67647i	−0.115808	−	0.0841396i	0.528374	−	0.849012i	$-0.322802\pi$
$397$	−2.30746	−	1.67647i	−0.115808	−	0.0841396i	−0.644182	+	0.764872i	$0.722802\pi$
$398$	−38.2640	−	27.8004i	−1.91800	−	1.39351i
$399$	22.4088	+	16.2809i	1.12184	+	0.815066i
$400$	13.5615			0.678077
$401$	2.76407	+	8.50693i	0.138031	+	0.424816i	0.996049	−	0.0888035i	$-0.0283043\pi$
$401$	2.76407	+	8.50693i	0.138031	+	0.424816i	−0.858018	+	0.513619i	$0.828304\pi$
$402$	5.43363	−	16.7230i	0.271005	−	0.834067i
$403$	−0.296960			−0.0147926
$404$	10.9325	−	7.94294i	0.543913	−	0.395176i
$405$	6.87691	−	4.99637i	0.341717	−	0.248272i
$406$	−5.55205			−0.275544
$407$	−2.19093	−	6.74300i	−0.108600	−	0.334238i
$408$	−18.3649	−	13.3429i	−0.909200	−	0.660573i
$409$	7.68520	−	23.6526i	0.380009	−	1.16955i	−0.560028	−	0.828474i	$-0.689210\pi$
$409$	7.68520	−	23.6526i	0.380009	−	1.16955i	0.940037	−	0.341073i	$-0.110790\pi$
$410$	1.83528	−	5.64840i	0.0906378	−	0.278955i
$411$	2.83846	−	8.73587i	0.140011	−	0.430909i
$412$	17.3857	−	12.6315i	0.856534	−	0.622308i
$413$	2.56551	−	7.89583i	0.126241	−	0.388528i
$414$	−73.3642	−	53.3022i	−3.60565	−	2.61966i
$415$	−3.43321	−	10.5663i	−0.168530	−	0.518680i
$416$	−1.10827	+	3.41091i	−0.0543375	+	0.167234i
$417$	−21.4774	+	15.6043i	−1.05175	+	0.764145i
$418$	−43.8392	−	31.8511i	−2.14425	−	1.55789i
$419$	8.06600	+	24.8246i	0.394050	+	1.21276i	0.929699	+	0.368321i	$0.120067\pi$
$419$	8.06600	+	24.8246i	0.394050	+	1.21276i	−0.535649	+	0.844441i	$0.679933\pi$
$420$	−5.79747	+	4.21211i	−0.282887	+	0.205530i
$421$	17.4032	+	12.6441i	0.848178	+	0.616238i	0.924643	−	0.380835i	$-0.124363\pi$
$421$	17.4032	+	12.6441i	0.848178	+	0.616238i	−0.0764649	+	0.997072i	$0.524363\pi$
$422$	−30.9465	+	22.4840i	−1.50645	+	1.09450i
$423$	−18.1770	−	55.9430i	−0.883795	−	2.72004i
$424$	−0.153539	−	0.472544i	−0.00745651	−	0.0229488i
$425$	−16.7556			−0.812765
$426$	43.7559	−	10.1354i	2.11998	−	0.491063i
$427$	−0.664508			−0.0321578
$428$	3.39134	+	10.4375i	0.163927	+	0.504515i
$429$	2.02967	+	6.24668i	0.0979933	+	0.301592i
$430$	0.466036	−	0.338595i	0.0224742	−	0.0163285i
$431$	8.57844	+	6.23260i	0.413209	+	0.300214i	0.774900	−	0.632084i	$-0.217800\pi$
$431$	8.57844	+	6.23260i	0.413209	+	0.300214i	−0.361691	+	0.932298i	$0.617800\pi$
$432$	30.4924	−	22.1540i	1.46707	−	1.06589i
$433$	7.85517	+	24.1757i	0.377495	+	1.16181i	0.941780	+	0.336231i	$0.109152\pi$
$433$	7.85517	+	24.1757i	0.377495	+	1.16181i	−0.564284	+	0.825581i	$0.690848\pi$
$434$	−0.974080	−	0.707711i	−0.0467574	−	0.0339712i
$435$	−8.64051	+	6.27770i	−0.414281	+	0.300993i
$436$	−1.91032	+	5.87937i	−0.0914880	+	0.281571i
$437$	−20.6317	−	63.4978i	−0.986947	−	3.03751i
$438$	22.0727	+	16.0368i	1.05468	+	0.766267i
$439$	−6.76598	+	20.8235i	−0.322923	+	0.993853i	0.649447	+	0.760407i	$0.275000\pi$
$439$	−6.76598	+	20.8235i	−0.322923	+	0.993853i	−0.972370	+	0.233447i	$0.925000\pi$
$440$	−6.13203	+	4.45518i	−0.292333	+	0.212392i
$441$	−9.40379	+	28.9419i	−0.447799	+	1.37818i
$442$	1.91730	−	5.90084i	0.0911966	−	0.280674i
$443$	−6.18668	+	19.0406i	−0.293938	+	0.904648i	0.689638	+	0.724154i	$0.257770\pi$
$443$	−6.18668	+	19.0406i	−0.293938	+	0.904648i	−0.983576	+	0.180494i	$0.942230\pi$
$444$	−5.49885	−	3.99515i	−0.260964	−	0.189601i
$445$	4.03381	+	12.4148i	0.191221	+	0.588518i
$446$	14.1195			0.668577
$447$	6.52279	−	4.73909i	0.308517	−	0.224151i
$448$	−1.77533	+	1.28985i	−0.0838765	+	0.0609399i
$449$	24.7128			1.16627			0.583135	−	0.812375i	$-0.301826\pi$
$449$	24.7128			1.16627			0.583135	+	0.812375i	$0.301826\pi$
$450$	8.70119	−	26.7795i	0.410178	−	1.26240i
$451$	−2.68446	−	8.26191i	−0.126406	−	0.389038i
$452$	4.34965			0.204590
$453$	13.8781	+	10.0830i	0.652049	+	0.473741i
$454$	−40.2443	−	29.2392i	−1.88876	−	1.37226i
$455$	0.856713	+	0.622438i	0.0401633	+	0.0291804i
$456$	28.0863			1.31526
$457$	11.0455	+	33.9947i	0.516688	+	1.59020i	0.780189	+	0.625544i	$0.215123\pi$
$457$	11.0455	+	33.9947i	0.516688	+	1.59020i	−0.263501	+	0.964659i	$0.584877\pi$
$458$	−39.5391			−1.84754
$459$	−37.6740	+	27.3718i	−1.75847	+	1.27760i
$460$	17.2732			0.805366
$461$	9.31042	−	28.6545i	0.433629	−	1.33457i	−0.460855	−	0.887475i	$-0.652457\pi$
$461$	9.31042	−	28.6545i	0.433629	−	1.33457i	0.894485	−	0.447099i	$-0.147543\pi$
$462$	−8.22932	+	25.3272i	−0.382863	+	1.17833i
$463$	17.1138			0.795347			0.397673	−	0.917527i	$-0.369818\pi$
$463$	17.1138			0.795347			0.397673	+	0.917527i	$0.369818\pi$
$464$	−9.66294	+	7.02053i	−0.448591	+	0.325920i
$465$	−2.31614			−0.107409
$466$	6.59130	+	20.2859i	0.305336	+	0.939728i
$467$	4.53643			0.209921			0.104961	−	0.994476i	$-0.466528\pi$
$467$	4.53643			0.209921			0.104961	+	0.994476i	$0.466528\pi$
$468$	3.32014	+	2.41222i	0.153474	+	0.111505i
$469$	−3.35471	−	2.43734i	−0.154906	−	0.112546i
$470$	23.0297	+	16.7321i	1.06228	+	0.771792i
$471$	6.50355			0.299668
$472$	−2.60140	−	8.00630i	−0.119739	−	0.368520i
$473$	0.260375	−	0.801351i	0.0119720	−	0.0368462i
$474$	−48.5248			−2.22882
$475$	16.7718	−	12.1854i	0.769543	−	0.559105i
$476$	8.01047	−	5.81995i	0.367159	−	0.266757i
$477$	−2.18870			−0.100214
$478$	5.60018	+	17.2356i	0.256146	+	0.788337i
$479$	5.80943	+	4.22080i	0.265440	+	0.192853i	0.712542	−	0.701630i	$-0.247544\pi$
$479$	5.80943	+	4.22080i	0.265440	+	0.192853i	−0.447102	+	0.894483i	$0.647544\pi$
$480$	−8.64397	+	26.6034i	−0.394541	+	1.21427i
$481$	−0.310380	+	0.955251i	−0.0141521	+	0.0435557i
$482$	−0.160673	+	0.494499i	−0.00731843	+	0.0225238i
$483$	−26.5452	+	19.2862i	−1.20785	+	0.877553i
$484$	1.92405	−	5.92161i	0.0874567	−	0.269164i
$485$	−3.07364	−	2.23313i	−0.139567	−	0.101401i
$486$	3.56283	+	10.9653i	0.161613	+	0.497395i
$487$	−4.24689	+	13.0706i	−0.192445	+	0.592285i	0.807552	+	0.589797i	$0.200792\pi$
$487$	−4.24689	+	13.0706i	−0.192445	+	0.592285i	−0.999997	+	0.00248847i	$0.999208\pi$
$488$	−0.545120	+	0.396053i	−0.0246764	+	0.0179285i
$489$	17.4526	+	12.6801i	0.789236	+	0.573414i
$490$	−4.55087	−	14.0061i	−0.205587	−	0.632733i
$491$	−0.716581	+	0.520627i	−0.0323389	+	0.0234956i	−0.603837	−	0.797108i	$-0.706362\pi$
$491$	−0.716581	+	0.520627i	−0.0323389	+	0.0234956i	0.571498	+	0.820603i	$0.306362\pi$
$492$	−6.73751	−	4.89509i	−0.303751	−	0.220688i
$493$	11.9388	−	8.67402i	0.537695	−	0.390658i
$494$	2.37221	+	7.30090i	0.106731	+	0.328483i
$495$	10.3176	+	31.7544i	0.463743	+	1.42726i
$496$	−2.59021			−0.116304
$497$	0.915462	−	10.5523i	0.0410641	−	0.473336i
$498$	−39.5810			−1.77367
$499$	2.32785	+	7.16438i	0.104209	+	0.320722i	0.989544	−	0.144232i	$-0.0460711\pi$
$499$	2.32785	+	7.16438i	0.104209	+	0.320722i	−0.885335	+	0.464953i	$0.846071\pi$
$500$	4.65838	+	14.3370i	0.208329	+	0.641171i
$501$	2.39427	−	1.73954i	0.106968	−	0.0777168i
$502$	−3.09980	−	2.25214i	−0.138351	−	0.100518i
$503$	−2.31691	+	1.68334i	−0.103306	+	0.0750562i	−0.638239	−	0.769838i	$-0.720337\pi$
$503$	−2.31691	+	1.68334i	−0.103306	+	0.0750562i	0.534933	+	0.844894i	$0.320337\pi$
$504$	−2.77998	−	8.55589i	−0.123830	−	0.381110i
$505$	−12.6004	−	9.15472i	−0.560710	−	0.407380i
$506$	51.9315	−	37.7304i	2.30864	−	1.67732i
$507$	−11.5034	+	35.4038i	−0.510883	+	1.57234i
$508$	3.19343	+	9.82836i	0.141685	+	0.436063i
$509$	−6.90853	−	5.01934i	−0.306215	−	0.222478i	0.424056	−	0.905636i	$-0.360606\pi$
$509$	−6.90853	−	5.01934i	−0.306215	−	0.222478i	−0.730271	+	0.683158i	$0.760606\pi$
$510$	14.9540	−	46.0236i	0.662174	−	2.03796i
$511$	5.20530	−	3.78187i	0.230269	−	0.167300i
$512$	−5.79803	+	17.8445i	−0.256239	+	0.788624i
$513$	17.8045	−	54.7965i	0.786087	−	2.41933i
$514$	4.07981	−	12.5564i	0.179953	−	0.553837i
$515$	−20.0381	−	14.5585i	−0.882985	−	0.641526i
$516$	−0.249613	−	0.768229i	−0.0109886	−	0.0338194i
$517$	41.6376			1.83122
$518$	−3.29464	+	2.39369i	−0.144758	+	0.105173i
$519$	19.7429	−	14.3441i	0.866618	−	0.629635i
$520$	1.07377			0.0470879
$521$	−9.81625	+	30.2113i	−0.430058	+	1.32358i	0.468010	+	0.883723i	$0.344971\pi$
$521$	−9.81625	+	30.2113i	−0.430058	+	1.32358i	−0.898067	+	0.439858i	$0.855029\pi$
$522$	7.66339	+	23.5855i	0.335418	+	1.03231i
$523$	−2.33673			−0.102178			−0.0510891	−	0.998694i	$-0.516269\pi$
$523$	−2.33673			−0.102178			−0.0510891	+	0.998694i	$0.516269\pi$
$524$	−11.8880	−	8.63712i	−0.519329	−	0.377314i
$525$	−8.24244	−	5.98848i	−0.359729	−	0.261359i
$526$	−27.6662	−	20.1007i	−1.20630	−	0.876431i
$527$	3.20026			0.139405
$528$	17.7036	+	54.4861i	0.770450	+	2.37120i
$529$	56.0897			2.43868
$530$	0.856912	−	0.622583i	0.0372219	−	0.0270433i
$531$	−37.0831			−1.60927
$532$	−3.78569	+	11.6512i	−0.164131	+	0.505142i
$533$	−0.380295	+	1.17043i	−0.0164724	+	0.0506969i
$534$	46.5053			2.01248
$535$	10.2332	−	7.43485i	0.442419	−	0.321436i
$536$	−4.20466			−0.181614
$537$	−19.5520	−	60.1749i	−0.843732	−	2.59674i
$538$	45.7500			1.97242
$539$	−17.4271	−	12.6615i	−0.750637	−	0.545370i
$540$	12.0594	+	8.76164i	0.518953	+	0.377041i
$541$	2.10411	+	1.52873i	0.0904629	+	0.0657251i	0.632097	−	0.774889i	$-0.282194\pi$
$541$	2.10411	+	1.52873i	0.0904629	+	0.0657251i	−0.541634	+	0.840614i	$0.682194\pi$
$542$	−9.83222			−0.422330
$543$	−12.5607	−	38.6577i	−0.539029	−	1.65896i
$544$	11.9435	−	36.7584i	0.512075	−	1.57600i
$545$	7.12506			0.305204
$546$	3.05214	−	2.21751i	0.130619	−	0.0949005i
$547$	37.6127	−	27.3272i	1.60820	−	1.16843i	0.739403	−	0.673263i	$-0.235108\pi$
$547$	37.6127	−	27.3272i	1.60820	−	1.16843i	0.868799	−	0.495164i	$-0.164892\pi$
$548$	4.06259			0.173545
$549$	0.917208	+	2.82288i	0.0391455	+	0.120477i
$550$	16.1250	+	11.7155i	0.687573	+	0.499551i
$551$	−5.64218	+	17.3648i	−0.240365	+	0.739767i
$552$	−10.2812	+	31.6423i	−0.437598	+	1.34679i
$553$	−3.53619	+	10.8833i	−0.150374	+	0.462804i
$554$	16.0650	−	11.6719i	0.682537	−	0.495892i
$555$	−2.42081	+	7.45049i	−0.102758	+	0.316255i
$556$	−9.49916	−	6.90154i	−0.402854	−	0.292691i
$557$	1.02763	+	3.16272i	0.0435421	+	0.134009i	0.970464	−	0.241245i	$-0.0775557\pi$
$557$	1.02763	+	3.16272i	0.0435421	+	0.134009i	−0.926922	+	0.375253i	$0.877556\pi$
$558$	−1.66190	+	5.11480i	−0.0703538	+	0.216527i
$559$	−0.0965692	+	0.0701616i	−0.00408444	+	0.00296752i
$560$	7.47260	+	5.42916i	0.315775	+	0.229424i
$561$	−21.8732	−	67.3187i	−0.923486	−	2.84220i
$562$	−27.6388	+	20.0808i	−1.16587	+	0.847057i
$563$	−3.71636	−	2.70010i	−0.156626	−	0.113795i	0.506712	−	0.862115i	$-0.330861\pi$
$563$	−3.71636	−	2.70010i	−0.156626	−	0.113795i	−0.663338	+	0.748320i	$0.730861\pi$
$564$	32.2932	−	23.4624i	1.35979	−	0.987945i
$565$	−1.54917	−	4.76787i	−0.0651742	−	0.200586i
$566$	−9.16812	−	28.2166i	−0.385365	−	1.18603i
$567$	−7.14158			−0.299918
$568$	−5.53828	−	9.20206i	−0.232381	−	0.386110i
$569$	−19.3146			−0.809710			−0.404855	−	0.914381i	$-0.632678\pi$
$569$	−19.3146			−0.809710			−0.404855	+	0.914381i	$0.632678\pi$
$570$	18.5020	+	56.9434i	0.774965	+	2.38510i
$571$	−5.38904	−	16.5858i	−0.225524	−	0.694093i	−0.998238	−	0.0593378i	$-0.981101\pi$
$571$	−5.38904	−	16.5858i	−0.225524	−	0.694093i	0.772714	−	0.634755i	$-0.218899\pi$
$572$	−2.35019	+	1.70751i	−0.0982664	+	0.0713947i
$573$	−28.8893	−	20.9893i	−1.20687	−	0.876842i
$574$	−4.03678	+	2.93289i	−0.168492	+	0.122417i
$575$	7.58878	+	23.3559i	0.316474	+	0.974007i
$576$	7.92984	+	5.76137i	0.330410	+	0.240057i
$577$	−27.4380	+	19.9349i	−1.14226	+	0.829900i	−0.987433	−	0.158041i	$-0.949482\pi$
$577$	−27.4380	+	19.9349i	−1.14226	+	0.829900i	−0.154827	+	0.987942i	$0.549482\pi$
$578$	−11.1218	+	34.2294i	−0.462606	+	1.42376i
$579$	6.50351	+	20.0157i	0.270277	+	0.831826i
$580$	−3.82157	−	2.77653i	−0.158682	−	0.115289i
$581$	−2.88442	+	8.87733i	−0.119666	+	0.368294i
$582$	−10.9502	+	7.95578i	−0.453900	+	0.329778i
$583$	0.478758	−	1.47347i	0.0198281	−	0.0610247i
$584$	2.01606	−	6.20481i	0.0834253	−	0.256757i
$585$	1.46166	−	4.49851i	0.0604320	−	0.185991i
$586$	−6.47758	−	4.70624i	−0.267587	−	0.194413i
$587$	−13.3830	−	41.1887i	−0.552376	−	1.70004i	−0.702774	−	0.711414i	$-0.748055\pi$
$587$	−13.3830	−	41.1887i	−0.552376	−	1.70004i	0.150397	−	0.988626i	$-0.451945\pi$
$588$	−20.6507			−0.851620
$589$	−3.20336	+	2.32737i	−0.131992	+	0.0958978i
$590$	14.5186	−	10.5484i	0.597722	−	0.434271i
$591$	−39.0751			−1.60733
$592$	−2.70726	+	8.33209i	−0.111268	+	0.342447i
$593$	−2.60425	−	8.01507i	−0.106944	−	0.329139i	0.883238	−	0.468925i	$-0.155359\pi$
$593$	−2.60425	−	8.01507i	−0.106944	−	0.329139i	−0.990182	+	0.139786i	$0.955359\pi$
$594$	55.3946			2.27287
$595$	−9.23256	−	6.70784i	−0.378498	−	0.274995i
$596$	2.88493	+	2.09603i	0.118172	+	0.0858566i
$597$	61.8410	+	44.9302i	2.53099	+	1.83887i
$598$	−9.09364			−0.371867
$599$	−10.2626	−	31.5849i	−0.419317	−	1.29052i	−0.908332	−	0.418250i	$-0.862644\pi$
$599$	−10.2626	−	31.5849i	−0.419317	−	1.29052i	0.489015	−	0.872275i	$-0.337356\pi$
$600$	−10.3308			−0.421751
$601$	−10.1974	+	7.40881i	−0.415959	+	0.302212i	−0.776010	−	0.630721i	$-0.782759\pi$
$601$	−10.1974	+	7.40881i	−0.415959	+	0.302212i	0.360051	+	0.932933i	$0.382759\pi$
$602$	−0.483972			−0.0197252
$603$	−5.72354	+	17.6152i	−0.233081	+	0.717348i
$604$	−2.34453	+	7.21573i	−0.0953977	+	0.293604i
$605$	−7.17625			−0.291756
$606$	−44.8903	+	32.6147i	−1.82355	+	1.32488i
$607$	−26.2145			−1.06402			−0.532008	−	0.846739i	$-0.678562\pi$
$607$	−26.2145			−1.06402			−0.532008	+	0.846739i	$0.678562\pi$
$608$	14.7773	+	45.4799i	0.599299	+	1.84445i
$609$	8.97306			0.363607
$610$	−1.16208	−	0.844298i	−0.0470511	−	0.0341846i
$611$	−4.77208	−	3.46712i	−0.193058	−	0.140265i
$612$	−35.7802	−	25.9959i	−1.44633	−	1.05082i
$613$	−10.6762			−0.431208			−0.215604	−	0.976481i	$-0.569172\pi$
$613$	−10.6762			−0.431208			−0.215604	+	0.976481i	$0.569172\pi$
$614$	15.8268	+	48.7099i	0.638718	+	1.96577i
$615$	−2.96612	+	9.12877i	−0.119605	+	0.368107i
$616$	6.36803			0.256575
$617$	2.16632	−	1.57393i	0.0872129	−	0.0633639i	−0.543324	−	0.839523i	$-0.682835\pi$
$617$	2.16632	−	1.57393i	0.0872129	−	0.0633639i	0.630537	+	0.776159i	$0.282835\pi$
$618$	−71.3881	+	51.8665i	−2.87165	+	2.08638i
$619$	23.9511			0.962678			0.481339	−	0.876535i	$-0.340151\pi$
$619$	23.9511			0.962678			0.481339	+	0.876535i	$0.340151\pi$
$620$	−0.316556	−	0.974258i	−0.0127132	−	0.0391272i
$621$	55.2169	+	40.1174i	2.21578	+	1.60986i
$622$	6.07573	−	18.6992i	0.243615	−	0.749768i
$623$	3.38902	−	10.4303i	0.135778	−	0.417883i
$624$	2.50799	−	7.71881i	0.100400	−	0.309000i
$625$	2.88629	−	2.09701i	0.115452	−	0.0838805i
$626$	2.51312	−	7.73458i	0.100444	−	0.309136i
$627$	70.8516	+	51.4767i	2.82954	+	2.05578i
$628$	0.888864	+	2.73564i	0.0354695	+	0.109164i
$629$	3.34488	−	10.2945i	0.133369	−	0.410468i
$630$	15.5153	−	11.2725i	0.618143	−	0.449107i
$631$	−27.8107	−	20.2056i	−1.10713	−	0.804373i	−0.124917	−	0.992167i	$-0.539866\pi$
$631$	−27.8107	−	20.2056i	−1.10713	−	0.804373i	−0.982208	+	0.187794i	$0.939866\pi$
$632$	3.58566	+	11.0355i	0.142630	+	0.438970i
$633$	50.0148	−	36.3379i	1.98791	−	1.44430i
$634$	2.20285	+	1.60047i	0.0874865	+	0.0635626i
$635$	9.63599	−	7.00096i	0.382393	−	0.277824i
$636$	−0.458970	−	1.41256i	−0.0181993	−	0.0560118i
$637$	0.943005	+	2.90227i	0.0373632	+	0.114992i
$638$	−17.5544			−0.694984
$639$	−46.0905	+	10.6762i	−1.82331	+	0.422344i
$640$	14.3172			0.565937
$641$	5.63142	+	17.3317i	0.222428	+	0.684562i	0.998543	+	0.0539706i	$0.0171877\pi$
$641$	5.63142	+	17.3317i	0.222428	+	0.684562i	−0.776115	+	0.630592i	$0.782812\pi$
$642$	−13.9253	−	42.8576i	−0.549588	−	1.69146i
$643$	20.4897	−	14.8867i	0.808036	−	0.587073i	−0.105224	−	0.994449i	$-0.533556\pi$
$643$	20.4897	−	14.8867i	0.808036	−	0.587073i	0.913261	+	0.407376i	$0.133556\pi$
$644$	−11.7405	−	8.53001i	−0.462642	−	0.336129i
$645$	−0.753192	+	0.547226i	−0.0296569	+	0.0215470i
$646$	−25.5646	−	78.6798i	−1.00583	−	3.09561i
$647$	−8.51837	−	6.18895i	−0.334891	−	0.243313i	0.407612	−	0.913155i	$-0.366362\pi$
$647$	−8.51837	−	6.18895i	−0.334891	−	0.243313i	−0.742503	+	0.669842i	$0.766362\pi$
$648$	−5.85849	+	4.25645i	−0.230143	+	0.167209i
$649$	8.11158	−	24.9649i	0.318407	−	0.979957i
$650$	−0.872549	−	2.68543i	−0.0342242	−	0.105331i
$651$	1.57428	+	1.14378i	0.0617008	+	0.0448283i
$652$	−2.94841	+	9.07429i	−0.115469	+	0.355377i
$653$	−16.9049	+	12.2821i	−0.661538	+	0.480636i	−0.867182	−	0.497991i	$-0.834071\pi$
$653$	−16.9049	+	12.2821i	−0.661538	+	0.480636i	0.205644	+	0.978627i	$0.434071\pi$
$654$	7.84404	−	24.1415i	0.306726	−	0.944006i
$655$	−5.23355	+	16.1072i	−0.204492	+	0.629361i
$656$	−3.31709	+	10.2090i	−0.129511	+	0.398593i
$657$	−23.2504	−	16.8924i	−0.907085	−	0.659036i
$658$	−7.39046	−	22.7455i	−0.288110	−	0.886712i
$659$	20.9191			0.814893			0.407447	−	0.913229i	$-0.366419\pi$
$659$	20.9191			0.814893			0.407447	+	0.913229i	$0.366419\pi$
$660$	−18.3303	+	13.3178i	−0.713506	+	0.518393i
$661$	−21.9702	+	15.9623i	−0.854542	+	0.620861i	−0.926395	−	0.376554i	$-0.877109\pi$
$661$	−21.9702	+	15.9623i	−0.854542	+	0.620861i	0.0718524	+	0.997415i	$0.477109\pi$
$662$	−50.3108			−1.95538
$663$	−3.09868	+	9.53675i	−0.120343	+	0.370377i
$664$	2.92478	+	9.00153i	0.113503	+	0.349327i
$665$	14.1197			0.547540
$666$	14.7161	+	10.6919i	0.570237	+	0.414302i
$667$	−17.4980	−	12.7131i	−0.677527	−	0.492252i
$668$	1.05895	+	0.769372i	0.0409720	+	0.0297679i
$669$	−22.8195			−0.882251
$670$	−2.76985	−	8.52472i	−0.107009	−	0.329339i
$671$	−2.10103			−0.0811093
$672$	19.0128	−	13.8136i	0.733436	−	0.532872i
$673$	−35.7372			−1.37757			−0.688783	−	0.724967i	$-0.741855\pi$
$673$	−35.7372			−1.37757			−0.688783	+	0.724967i	$0.741855\pi$
$674$	−9.69714	+	29.8447i	−0.373520	+	1.14958i
$675$	−6.54887	+	20.1554i	−0.252066	+	0.775780i
$676$	−16.4644			−0.633246
$677$	−13.5945	+	9.87695i	−0.522478	+	0.379602i	−0.817536	−	0.575877i	$-0.804661\pi$
$677$	−13.5945	+	9.87695i	−0.522478	+	0.379602i	0.295059	+	0.955479i	$0.404661\pi$
$678$	−17.8602			−0.685917
$679$	0.986362	+	3.03571i	0.0378531	+	0.116500i
$680$	−11.5717			−0.443756
$681$	65.0416	+	47.2555i	2.49240	+	1.81083i
$682$	−3.07983	−	2.23763i	−0.117933	−	0.0856831i
$683$	37.1533	+	26.9935i	1.42163	+	1.03288i	0.991499	+	0.130111i	$0.0415335\pi$
$683$	37.1533	+	26.9935i	1.42163	+	1.03288i	0.430133	+	0.902765i	$0.358467\pi$
$684$	54.7203			2.09228
$685$	−1.44693	−	4.45321i	−0.0552845	−	0.170148i
$686$	−8.76155	+	26.9653i	−0.334518	+	1.02954i
$687$	63.9019			2.43801
$688$	−0.842317	+	0.611979i	−0.0321130	+	0.0233315i
$689$	−0.177564	+	0.129008i	−0.00676467	+	0.00491482i
$690$	−70.9259			−2.70010
$691$	−3.76742	−	11.5949i	−0.143319	−	0.441092i	0.853472	−	0.521139i	$-0.174493\pi$
$691$	−3.76742	−	11.5949i	−0.143319	−	0.441092i	−0.996791	+	0.0800474i	$0.974493\pi$
$692$	8.73201	+	6.34417i	0.331941	+	0.241169i
$693$	8.66840	−	26.6786i	0.329285	−	1.01344i
$694$	10.3230	−	31.7710i	0.391856	−	1.20601i
$695$	−4.18190	+	12.8706i	−0.158628	+	0.488208i
$696$	7.36092	−	5.34802i	0.279015	−	0.202716i
$697$	4.09834	−	12.6134i	0.155236	−	0.477766i
$698$	20.9238	+	15.2020i	0.791977	+	0.575405i
$699$	−10.6527	−	32.7855i	−0.402920	−	1.24006i
$700$	1.39246	−	4.28555i	0.0526301	−	0.161979i
$701$	17.1148	−	12.4346i	0.646417	−	0.469649i	−0.215632	−	0.976475i	$-0.569181\pi$
$701$	17.1148	−	12.4346i	0.646417	−	0.469649i	0.862049	+	0.506825i	$0.169181\pi$
$702$	−6.34878	−	4.61266i	−0.239619	−	0.174094i
$703$	4.13850	+	12.7370i	0.156086	+	0.480385i
$704$	−5.61321	+	4.07823i	−0.211556	+	0.153704i
$705$	−37.2199	−	27.0418i	−1.40178	−	1.01845i
$706$	7.76495	−	5.64157i	0.292238	−	0.212323i
$707$	4.04359	+	12.4449i	0.152075	+	0.468039i
$708$	−7.77630	−	23.9330i	−0.292251	−	0.899457i
$709$	−0.722189			−0.0271224			−0.0135612	−	0.999908i	$-0.504317\pi$
$709$	−0.722189			−0.0271224			−0.0135612	+	0.999908i	$0.504317\pi$
$710$	15.0083	−	17.2905i	0.563251	−	0.648900i
$711$	51.1138			1.91692
$712$	−3.43644	−	10.5763i	−0.128786	−	0.396362i
$713$	−1.44943	−	4.46089i	−0.0542816	−	0.167062i
$714$	−32.8920	+	23.8975i	−1.23095	+	0.894340i
$715$	2.70874	+	1.96801i	0.101301	+	0.0735995i
$716$	22.6396	−	16.4487i	0.846083	−	0.614715i
$717$	−9.05084	−	27.8556i	−0.338010	−	1.04029i
$718$	46.2501	+	33.6026i	1.72604	+	1.25404i
$719$	1.53176	−	1.11289i	0.0571249	−	0.0415036i	−0.558856	−	0.829264i	$-0.688760\pi$
$719$	1.53176	−	1.11289i	0.0571249	−	0.0415036i	0.615981	+	0.787761i	$0.288760\pi$
$720$	12.7492	−	39.2379i	0.475133	−	1.46231i
$721$	6.43043	+	19.7908i	0.239482	+	0.737049i
$722$	54.8933	+	39.8824i	2.04292	+	1.48427i
$723$	0.259674	−	0.799194i	0.00965738	−	0.0297223i
$724$	14.5442	−	10.5670i	0.540531	−	0.392719i
$725$	2.07532	−	6.38716i	0.0770753	−	0.237213i
$726$	−7.90039	+	24.3149i	−0.293211	+	0.902410i
$727$	−10.4737	+	32.2347i	−0.388448	+	1.19552i	0.545500	+	0.838111i	$0.316340\pi$
$727$	−10.4737	+	32.2347i	−0.388448	+	1.19552i	−0.933948	+	0.357409i	$0.883660\pi$
$728$	−0.729840	−	0.530260i	−0.0270497	−	0.0196527i
$729$	−11.0250	−	33.9314i	−0.408333	−	1.25672i
$730$	13.9080			0.514758
$731$	1.04070	−	0.756113i	0.0384917	−	0.0279658i
$732$	−1.62951	+	1.18391i	−0.0602285	+	0.0437586i
$733$	40.4316			1.49337			0.746687	−	0.665175i	$-0.231643\pi$
$733$	40.4316			1.49337			0.746687	+	0.665175i	$0.231643\pi$
$734$	−10.5665	+	32.5203i	−0.390017	+	1.20035i
$735$	7.35497	+	22.6363i	0.271292	+	0.834951i
$736$	−56.6475			−2.08805
$737$	−10.6069	−	7.70633i	−0.390708	−	0.283866i
$738$	18.0310	+	13.1003i	0.663731	+	0.482229i
$739$	−3.40958	−	2.47720i	−0.125423	−	0.0911253i	0.523305	−	0.852145i	$-0.324699\pi$
$739$	−3.40958	−	2.47720i	−0.125423	−	0.0911253i	−0.648728	+	0.761020i	$0.724699\pi$
$740$	−3.46482			−0.127369
$741$	−3.83389	−	11.7995i	−0.140841	−	0.433465i
$742$	−0.889892			−0.0326690
$743$	−10.4542	+	7.59540i	−0.383526	+	0.278648i	−0.762798	−	0.646637i	$-0.776175\pi$
$743$	−10.4542	+	7.59540i	−0.383526	+	0.278648i	0.379271	+	0.925286i	$0.376175\pi$
$744$	1.97314			0.0723388
$745$	1.27006	−	3.90885i	0.0465314	−	0.143209i
$746$	15.4424	−	47.5270i	0.565388	−	1.74009i
$747$	41.6928			1.52546
$748$	25.3273	−	18.4014i	0.926059	−	0.672822i
$749$	−10.6270			−0.388303
$750$	−19.1279	−	58.8696i	−0.698452	−	2.14962i
$751$	28.5228			1.04081			0.520406	−	0.853919i	$-0.325781\pi$
$751$	28.5228			1.04081			0.520406	+	0.853919i	$0.325781\pi$
$752$	−41.6241	−	30.2417i	−1.51787	−	1.10280i
$753$	5.00981	+	3.63984i	0.182568	+	0.132643i
$754$	2.01191	+	1.46174i	0.0732693	+	0.0532333i
$755$	8.74456			0.318247
$756$	−3.86997	−	11.9105i	−0.140750	−	0.433182i
$757$	−12.3713	+	38.0749i	−0.449642	+	1.38386i	0.427669	+	0.903935i	$0.359335\pi$
$757$	−12.3713	+	38.0749i	−0.449642	+	1.38386i	−0.877311	+	0.479922i	$0.840665\pi$
$758$	13.0734			0.474848
$759$	−83.9300	+	60.9787i	−3.04647	+	2.21339i
$760$	11.5829	−	8.41549i	0.420157	−	0.305262i
$761$	−21.4091			−0.776080			−0.388040	−	0.921643i	$-0.626848\pi$
$761$	−21.4091			−0.776080			−0.388040	+	0.921643i	$0.626848\pi$
$762$	−13.1126	−	40.3565i	−0.475020	−	1.46196i
$763$	−4.84289	−	3.51857i	−0.175324	−	0.127381i
$764$	4.88050	−	15.0206i	0.176570	−	0.543428i
$765$	−15.7519	+	48.4792i	−0.569510	+	1.75277i
$766$	8.33053	−	25.6387i	0.300994	−	0.926365i
$767$	−3.00847	+	2.18578i	−0.108629	+	0.0789239i
$768$	18.9287	−	58.2564i	0.683029	−	2.10215i
$769$	−26.0071	−	18.8953i	−0.937842	−	0.681382i	0.0100585	−	0.999949i	$-0.496798\pi$
$769$	−26.0071	−	18.8953i	−0.937842	−	0.681382i	−0.947900	+	0.318568i	$0.896798\pi$
$770$	4.19498	+	12.9108i	0.151177	+	0.465274i
$771$	−6.59366	+	20.2932i	−0.237465	+	0.730841i
$772$	−7.53053	+	5.47125i	−0.271030	+	0.196915i
$773$	−28.2193	−	20.5025i	−1.01498	−	0.737423i	−0.0497292	−	0.998763i	$-0.515836\pi$
$773$	−28.2193	−	20.5025i	−1.01498	−	0.737423i	−0.965247	+	0.261339i	$0.915836\pi$
$774$	0.668017	+	2.05594i	0.0240114	+	0.0738994i
$775$	1.17826	−	0.856059i	0.0423245	−	0.0307506i
$776$	2.61846	+	1.90242i	0.0939971	+	0.0682929i
$777$	5.32469	−	3.86861i	0.191022	−	0.138786i
$778$	16.8977	+	52.0059i	0.605814	+	1.86450i
$779$	5.07073	+	15.6061i	0.181678	+	0.559147i
$780$	3.20979			0.114929
$781$	2.89449	−	33.3641i	0.103573	−	1.19386i
$782$	97.9997			3.50446
$783$	−5.76778	−	17.7514i	−0.206124	−	0.634384i
$784$	8.22528	+	25.3148i	0.293760	+	0.904100i
$785$	2.68210	−	1.94866i	0.0957281	−	0.0695505i
$786$	48.8136	+	35.4651i	1.74112	+	1.26500i
$787$	11.1740	−	8.11842i	0.398312	−	0.289390i	−0.370541	−	0.928816i	$-0.620828\pi$
$787$	11.1740	−	8.11842i	0.398312	−	0.289390i	0.768853	+	0.639426i	$0.220828\pi$
$788$	−5.34054	−	16.4365i	−0.190249	−	0.585525i
$789$	44.7132	+	32.4861i	1.59183	+	1.15653i
$790$	−20.0119	+	14.5395i	−0.711990	+	0.517291i
$791$	−1.30154	+	4.00574i	−0.0462776	+	0.142428i
$792$	−8.78967	−	27.0518i	−0.312327	−	0.961245i
$793$	0.240799	+	0.174951i	0.00855102	+	0.00621268i
$794$	−1.60064	+	4.92627i	−0.0568047	+	0.174827i
$795$	−1.38491	+	1.00620i	−0.0491179	+	0.0356862i
$796$	−10.4473	+	32.1535i	−0.370295	+	1.13965i
$797$	−7.68028	+	23.6375i	−0.272049	+	0.837282i	0.717936	+	0.696109i	$0.245087\pi$
$797$	−7.68028	+	23.6375i	−0.272049	+	0.837282i	−0.989985	+	0.141172i	$0.954913\pi$
$798$	15.5445	−	47.8412i	0.550271	−	1.69356i
$799$	51.4274	+	37.3642i	1.81937	+	1.32185i
$800$	−5.43542	−	16.7285i	−0.192171	−	0.591442i
$801$	−48.9866			−1.73086
$802$	13.1419	−	9.54818i	0.464058	−	0.337158i
$803$	16.4580	−	11.9574i	0.580791	−	0.421969i
$804$	−12.5689			−0.443270
$805$	−5.16865	+	15.9075i	−0.182171	+	0.560664i
$806$	0.166654	+	0.512908i	0.00587014	+	0.0180664i
$807$	−73.9397			−2.60280
$808$	10.7344	+	7.79898i	0.377634	+	0.274367i
$809$	4.51340	+	3.27918i	0.158683	+	0.115290i	0.664293	−	0.747472i	$-0.268733\pi$
$809$	4.51340	+	3.27918i	0.158683	+	0.115290i	−0.505610	+	0.862762i	$0.668733\pi$
$810$	−12.4890	−	9.07381i	−0.438820	−	0.318821i
$811$	9.88194			0.347002			0.173501	−	0.984834i	$-0.444492\pi$
$811$	9.88194			0.347002			0.173501	+	0.984834i	$0.444492\pi$
$812$	1.22638	+	3.77441i	0.0430375	+	0.132456i
$813$	15.8905			0.557305
$814$	−10.4169	+	7.56833i	−0.365113	+	0.265270i
$815$	10.9969			0.385204
$816$	−27.0280	+	83.1835i	−0.946168	+	2.91200i
$817$	−0.491827	+	1.51369i	−0.0172069	+	0.0529573i
$818$	−45.1656			−1.57918
$819$	−3.21498	+	2.33582i	−0.112341	+	0.0816202i
$820$	−4.24530			−0.148252
$821$	−2.43070	−	7.48091i	−0.0848319	−	0.261086i	0.899639	−	0.436635i	$-0.143830\pi$
$821$	−2.43070	−	7.48091i	−0.0848319	−	0.261086i	−0.984471	+	0.175549i	$0.943830\pi$
$822$	−16.6815			−0.581834
$823$	−19.4247	−	14.1128i	−0.677101	−	0.491943i	0.195294	−	0.980745i	$-0.437434\pi$
$823$	−19.4247	−	14.1128i	−0.677101	−	0.491943i	−0.872395	+	0.488802i	$0.837434\pi$
$824$	17.0706	+	12.4025i	0.594683	+	0.432063i
$825$	−26.0608	−	18.9343i	−0.907319	−	0.659206i
$826$	−15.0774			−0.524610
$827$	−9.58370	−	29.4956i	−0.333258	−	1.02566i	−0.967574	−	0.252589i	$-0.918718\pi$
$827$	−9.58370	−	29.4956i	−0.333258	−	1.02566i	0.634316	−	0.773074i	$-0.281282\pi$
$828$	−20.0308	+	61.6484i	−0.696118	+	2.14243i
$829$	−5.39212			−0.187276			−0.0936381	−	0.995606i	$-0.529850\pi$
$829$	−5.39212			−0.187276			−0.0936381	+	0.995606i	$0.529850\pi$
$830$	−16.3234	+	11.8596i	−0.566593	+	0.411654i
$831$	−25.9638	+	18.8638i	−0.900673	+	0.654377i
$832$	0.982920			0.0340766
$833$	−10.1625	−	31.2770i	−0.352110	−	1.08368i
$834$	39.0048	+	28.3386i	1.35062	+	0.981286i
$835$	0.466191	−	1.43479i	0.0161332	−	0.0496529i
$836$	−11.9695	+	36.8384i	−0.413975	+	1.27408i
$837$	1.25081	−	3.84961i	0.0432344	−	0.133062i
$838$	38.3503	−	27.8631i	1.32479	−	0.962516i
$839$	11.5105	−	35.4255i	0.397385	−	1.22303i	−0.529703	−	0.848183i	$-0.677697\pi$
$839$	11.5105	−	35.4255i	0.397385	−	1.22303i	0.927088	−	0.374843i	$-0.122303\pi$
$840$	−5.69239	−	4.13576i	−0.196406	−	0.142697i
$841$	−7.13370	−	21.9553i	−0.245990	−	0.757079i
$842$	12.0722	−	37.1545i	0.416037	−	1.28043i
$843$	44.6690	−	32.4539i	1.53848	−	1.11777i
$844$	22.1208	+	16.0717i	0.761430	+	0.553211i
$845$	5.86397	+	18.0474i	0.201727	+	0.620851i
$846$	−86.4235	+	62.7904i	−2.97130	+	2.15878i
$847$	4.87768	+	3.54384i	0.167599	+	0.121768i
$848$	−1.54879	+	1.12526i	−0.0531857	+	0.0386417i
$849$	14.8172	+	45.6027i	0.508526	+	1.56508i
$850$	9.40322	+	28.9401i	0.322528	+	0.992639i
$851$	−15.8646			−0.543830
$852$	−16.5554	−	27.5075i	−0.567180	−	0.942390i
$853$	−14.2440			−0.487704			−0.243852	−	0.969812i	$-0.578411\pi$
$853$	−14.2440			−0.487704			−0.243852	+	0.969812i	$0.578411\pi$
$854$	0.372922	+	1.14774i	0.0127611	+	0.0392747i
$855$	−19.4892	−	59.9816i	−0.666517	−	2.05133i
$856$	−8.71773	+	6.33380i	−0.297966	+	0.216485i
$857$	−7.03772	−	5.11320i	−0.240404	−	0.174664i	0.461059	−	0.887369i	$-0.347470\pi$
$857$	−7.03772	−	5.11320i	−0.240404	−	0.174664i	−0.701463	+	0.712706i	$0.747470\pi$
$858$	9.65018	−	7.01127i	0.329452	−	0.239361i
$859$	−10.2237	−	31.4652i	−0.348827	−	1.07358i	−0.959503	−	0.281699i	$-0.909102\pi$
$859$	−10.2237	−	31.4652i	−0.348827	−	1.07358i	0.610676	−	0.791881i	$-0.290898\pi$
$860$	−0.333126	−	0.242030i	−0.0113595	−	0.00825316i
$861$	6.52412	−	4.74005i	0.222341	−	0.161540i
$862$	5.95070	−	18.3144i	0.202682	−	0.623790i
$863$	10.5355	+	32.4250i	0.358633	+	1.10376i	0.953873	+	0.300211i	$0.0970570\pi$
$863$	10.5355	+	32.4250i	0.358633	+	1.10376i	−0.595240	+	0.803548i	$0.702943\pi$
$864$	−39.5488	−	28.7339i	−1.34548	−	0.977546i
$865$	3.84417	−	11.8311i	0.130706	−	0.402271i
$866$	37.3479	−	27.1348i	1.26913	−	0.922079i
$867$	17.9747	−	55.3205i	0.610454	−	1.87878i
$868$	−0.265955	+	0.818526i	−0.00902711	+	0.0277826i
$869$	−11.1807	+	34.4105i	−0.379278	+	1.16730i
$870$	15.6919	+	11.4008i	0.532004	+	0.386524i
$871$	0.573952	+	1.76644i	0.0194476	+	0.0598537i
$872$	−6.06989			−0.205553
$873$	11.5344	−	8.38026i	0.390382	−	0.283629i
$874$	−98.0945	+	71.2698i	−3.31810	+	2.41074i
$875$	−14.5974			−0.493481
$876$	6.02657	−	18.5479i	0.203619	−	0.626674i
$877$	11.8730	+	36.5413i	0.400923	+	1.23391i	0.924252	+	0.381782i	$0.124690\pi$
$877$	11.8730	+	36.5413i	0.400923	+	1.23391i	−0.523330	+	0.852130i	$0.675310\pi$
$878$	39.7634			1.34195
$879$	10.4689	+	7.60608i	0.353106	+	0.256547i
$880$	23.6267	+	17.1658i	0.796456	+	0.578659i
$881$	4.22632	+	3.07060i	0.142388	+	0.103451i	0.656699	−	0.754153i	$-0.271952\pi$
$881$	4.22632	+	3.07060i	0.142388	+	0.103451i	−0.514311	+	0.857604i	$0.671952\pi$
$882$	55.2657			1.86089
$883$	17.8931	+	55.0692i	0.602149	+	1.85322i	0.515313	+	0.857002i	$0.327676\pi$
$883$	17.8931	+	55.0692i	0.602149	+	1.85322i	0.0868366	+	0.996223i	$0.472324\pi$
$884$	−4.43503			−0.149166
$885$	−23.4646	+	17.0480i	−0.788752	+	0.573062i
$886$	36.3589			1.22150
$887$	12.8265	−	39.4758i	0.430670	−	1.32547i	−0.466789	−	0.884369i	$-0.654589\pi$
$887$	12.8265	−	39.4758i	0.430670	−	1.32547i	0.897459	−	0.441098i	$-0.145411\pi$
$888$	2.06231	−	6.34712i	0.0692065	−	0.212996i
$889$	−10.0068			−0.335619
$890$	19.1790	−	13.9344i	0.642882	−	0.467081i
$891$	−22.5801			−0.756462
$892$	−3.11882	−	9.59874i	−0.104426	−	0.321389i
$893$	−78.6502			−2.63193
$894$	−11.8459	−	8.60656i	−0.396187	−	0.287846i
$895$	−26.0935	−	18.9581i	−0.872211	−	0.633698i
$896$	−9.73138	−	7.07026i	−0.325103	−	0.236201i
$897$	14.6969			0.490714
$898$	−13.8688	−	42.6839i	−0.462809	−	1.42438i
$899$	−0.396378	+	1.21993i	−0.0132200	+	0.0406868i
$900$	−20.1273			−0.670910
$901$	1.91356	−	1.39028i	0.0637500	−	0.0463171i
$902$	−12.7634	+	9.27316i	−0.424975	+	0.308763i
$903$	0.782180			0.0260293
$904$	1.31975	+	4.06178i	0.0438943	+	0.135093i
$905$	−16.7631	−	12.1791i	−0.557224	−	0.404847i
$906$	9.62696	−	29.6287i	0.319834	−	0.984349i
$907$	1.84276	−	5.67142i	0.0611877	−	0.188317i	−0.915790	−	0.401657i	$-0.868434\pi$
$907$	1.84276	−	5.67142i	0.0611877	−	0.188317i	0.976978	+	0.213341i	$0.0684344\pi$
$908$	−10.9880	+	33.8176i	−0.364649	+	1.12228i
$909$	47.2855	−	34.3549i	1.56836	−	1.13948i
$910$	0.594285	−	1.82902i	0.0197004	−	0.0606315i
$911$	23.6711	+	17.1981i	0.784259	+	0.569798i	0.906254	−	0.422733i	$-0.138929\pi$
$911$	23.6711	+	17.1981i	0.784259	+	0.569798i	−0.121995	+	0.992531i	$0.538929\pi$
$912$	−33.4407	−	102.920i	−1.10733	−	3.40802i
$913$	−9.11990	+	28.0682i	−0.301825	+	0.928921i
$914$	52.5166	−	38.1556i	1.73710	−	1.26207i
$915$	1.87811	+	1.36453i	0.0620884	+	0.0451099i
$916$	8.73370	+	26.8796i	0.288570	+	0.888126i
$917$	11.5115	−	8.36356i	0.380142	−	0.276189i
$918$	68.4190	+	49.7093i	2.25816	+	1.64065i
$919$	−40.7634	+	29.6163i	−1.34466	+	0.976953i	−0.345402	+	0.938455i	$0.612257\pi$
$919$	−40.7634	+	29.6163i	−1.34466	+	0.976953i	−0.999259	+	0.0384983i	$0.987743\pi$
$920$	5.24096	+	16.1300i	0.172789	+	0.531791i
$921$	−25.5788	−	78.7234i	−0.842850	−	2.59403i
$922$	−54.7170			−1.80201
$923$	−3.10993	+	3.58283i	−0.102365	+	0.117930i
$924$	19.0358			0.626231
$925$	−1.52223	−	4.68494i	−0.0500506	−	0.154040i
$926$	−9.60427	−	29.5589i	−0.315616	−	0.971366i
$927$	75.1970	−	54.6338i	2.46979	−	1.79441i
$928$	12.5329	+	9.10566i	0.411412	+	0.298908i
$929$	−7.51107	+	5.45711i	−0.246430	+	0.179042i	−0.704143	−	0.710058i	$-0.748669\pi$
$929$	−7.51107	+	5.45711i	−0.246430	+	0.179042i	0.457713	+	0.889100i	$0.348669\pi$
$930$	1.29982	+	4.00043i	0.0426227	+	0.131179i
$931$	32.9184	+	23.9166i	1.07886	+	0.783835i
$932$	12.3349	−	8.96183i	0.404043	−	0.293555i
$933$	−9.81940	+	30.2210i	−0.321473	+	0.989392i
$934$	−2.54584	−	7.83530i	−0.0833026	−	0.256379i
$935$	−29.1913	−	21.2087i	−0.954658	−	0.693599i
$936$	−1.24520	+	3.83232i	−0.0407005	+	0.125263i
$937$	−39.4650	+	28.6730i	−1.28926	+	0.936705i	−0.999790	−	0.0204809i	$-0.993480\pi$
$937$	−39.4650	+	28.6730i	−1.28926	+	0.936705i	−0.289474	+	0.957186i	$0.593480\pi$
$938$	−2.32710	+	7.16207i	−0.0759825	+	0.233850i
$939$	−4.06162	+	12.5004i	−0.132546	+	0.407935i
$940$	6.28785	−	19.3520i	0.205087	−	0.631193i
$941$	−7.75418	−	5.63374i	−0.252779	−	0.183655i	0.454179	−	0.890911i	$-0.349933\pi$
$941$	−7.75418	−	5.63374i	−0.252779	−	0.183655i	−0.706957	+	0.707256i	$0.749933\pi$
$942$	−3.64979	−	11.2329i	−0.118917	−	0.365987i
$943$	−19.4382			−0.632995
$944$	−26.2411	+	19.0653i	−0.854075	+	0.620522i
$945$	−11.6774	+	8.48414i	−0.379867	+	0.275989i
$946$	−1.53021			−0.0497515
$947$	−2.78174	+	8.56131i	−0.0903943	+	0.278205i	−0.986026	−	0.166591i	$-0.946724\pi$
$947$	−2.78174	+	8.56131i	−0.0903943	+	0.278205i	0.895632	+	0.444796i	$0.146724\pi$
$948$	10.7185	+	32.9882i	0.348122	+	1.07141i
$949$	−2.88194			−0.0935516
$950$	−30.4589	−	22.1297i	−0.988218	−	0.717982i
$951$	−3.56018	−	2.58662i	−0.115447	−	0.0838770i
$952$	7.86528	+	5.71446i	0.254915	+	0.185207i
$953$	26.4568			0.857018			0.428509	−	0.903537i	$-0.359039\pi$
$953$	26.4568			0.857018			0.428509	+	0.903537i	$0.359039\pi$
$954$	1.22830	+	3.78032i	0.0397677	+	0.122392i
$955$	−18.2031			−0.589040
$956$	10.4801	−	7.61426i	0.338952	−	0.246263i
$957$	28.3708			0.917098
$958$	4.02989	−	12.4027i	0.130200	−	0.400714i
$959$	−1.21565	+	3.74138i	−0.0392553	+	0.120815i
$960$	7.66629			0.247428
$961$	24.8545	−	18.0578i	0.801757	−	0.582511i
$962$	1.82409			0.0588110
$963$	14.6683	+	45.1443i	0.472679	+	1.45476i
$964$	0.371662			0.0119704
$965$	8.67939	+	6.30595i	0.279400	+	0.202996i
$966$	48.2082	+	35.0253i	1.55107	+	1.12692i
$967$	−38.2683	−	27.8036i	−1.23063	−	0.894102i	−0.233689	−	0.972311i	$-0.575080\pi$
$967$	−38.2683	−	27.8036i	−1.23063	−	0.894102i	−0.996937	+	0.0782094i	$0.975080\pi$
$968$	6.11350			0.196495
$969$	41.3167	+	127.160i	1.32728	+	4.08496i
$970$	−2.13213	+	6.56201i	−0.0684584	+	0.210693i
$971$	−53.6776			−1.72260			−0.861298	−	0.508100i	$-0.830348\pi$
$971$	−53.6776			−1.72260			−0.861298	+	0.508100i	$0.830348\pi$
$972$	6.66745	−	4.84418i	0.213859	−	0.155377i
$973$	9.19830	−	6.68295i	0.294884	−	0.214246i
$974$	24.9588			0.799732
$975$	1.41019	+	4.34011i	0.0451621	+	0.138995i
$976$	2.10035	+	1.52599i	0.0672305	+	0.0488458i
$977$	−6.82959	+	21.0193i	−0.218498	+	0.672467i	0.780389	+	0.625294i	$0.215021\pi$
$977$	−6.82959	+	21.0193i	−0.218498	+	0.672467i	−0.998887	+	0.0471727i	$0.984979\pi$
$978$	12.1066	−	37.2602i	0.387125	−	1.19145i
$979$	10.7153	−	32.9784i	0.342464	−	1.05399i
$980$	−8.51645	+	6.18756i	−0.272048	+	0.197655i
$981$	−8.26256	+	25.4295i	−0.263803	+	0.811903i
$982$	1.30137	+	0.945500i	0.0415284	+	0.0301721i
$983$	2.72293	+	8.38032i	0.0868480	+	0.267291i	0.985044	−	0.172305i	$-0.0551216\pi$
$983$	2.72293	+	8.38032i	0.0868480	+	0.267291i	−0.898196	+	0.439596i	$0.855122\pi$
$984$	2.52686	−	7.77687i	0.0805532	−	0.247917i
$985$	−16.1148	+	11.7081i	−0.513459	+	0.373050i
$986$	−21.6818	−	15.7527i	−0.690488	−	0.501669i
$987$	11.9442	+	36.7606i	0.380189	+	1.17010i
$988$	4.43932	−	3.22536i	0.141234	−	0.102612i
$989$	−1.52530	−	1.10820i	−0.0485018	−	0.0352386i
$990$	49.0558	−	35.6411i	1.55910	−	1.13275i
$991$	−4.35026	−	13.3887i	−0.138191	−	0.425307i	0.857882	−	0.513847i	$-0.171780\pi$
$991$	−4.35026	−	13.3887i	−0.138191	−	0.425307i	−0.996073	+	0.0885398i	$0.971780\pi$
$992$	1.03815	+	3.19509i	0.0329612	+	0.101444i
$993$	81.3107			2.58032
$994$	−18.7397	+	4.34077i	−0.594386	+	0.137681i
$995$	38.9660			1.23530
$996$	8.74295	+	26.9080i	0.277031	+	0.852614i
$997$	14.5902	+	44.9042i	0.462078	+	1.42213i	0.862621	+	0.505851i	$0.168822\pi$
$997$	14.5902	+	44.9042i	0.462078	+	1.42213i	−0.400543	+	0.916278i	$0.631178\pi$
$998$	11.0679	−	8.04129i	0.350348	−	0.254543i
$999$	−11.0759	−	8.04714i	−0.350427	−	0.254600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.c.a.5.2	✓	20
3.2	odd	2		639.2.f.c.289.4		20
71.25	even	5		5041.2.a.i.1.2		10
71.46	odd	10		5041.2.a.j.1.2		10
71.57	even	5	inner	71.2.c.a.57.2	yes	20
213.128	odd	10		639.2.f.c.199.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.c.a.5.2	✓	20	1.1	even	1	trivial
71.2.c.a.57.2	yes	20	71.57	even	5	inner
639.2.f.c.199.4		20	213.128	odd	10
639.2.f.c.289.4		20	3.2	odd	2
5041.2.a.i.1.2		10	71.25	even	5
5041.2.a.j.1.2		10	71.46	odd	10

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.561200 - 1.72720i) q^{2} +(0.906993 + 2.79144i) q^{3} +(-1.05022 + 0.763032i) q^{4} +(1.21045 + 0.879441i) q^{5} +(4.31235 - 3.13311i) q^{6} +(-0.388444 - 1.19551i) q^{7} +(-1.03119 - 0.749203i) q^{8} +(-4.54244 + 3.30028i) q^{9} +O(q^{10})\)	\(q+(-0.561200 - 1.72720i) q^{2} +(0.906993 + 2.79144i) q^{3} +(-1.05022 + 0.763032i) q^{4} +(1.21045 + 0.879441i) q^{5} +(4.31235 - 3.13311i) q^{6} +(-0.388444 - 1.19551i) q^{7} +(-1.03119 - 0.749203i) q^{8} +(-4.54244 + 3.30028i) q^{9} +(0.839664 - 2.58422i) q^{10} +(-1.22818 - 3.77994i) q^{11} +(-3.08250 - 2.23957i) q^{12} +(-0.173990 + 0.535487i) q^{13} +(-1.84688 + 1.34184i) q^{14} +(-1.35704 + 4.17654i) q^{15} +(-1.51762 + 4.67074i) q^{16} +(1.87505 - 5.77080i) q^{17} +(8.24944 + 5.99357i) q^{18} +(2.31993 + 7.14000i) q^{19} -1.94228 q^{20} +(2.98487 - 2.16864i) q^{21} +(-5.83944 + 4.24260i) q^{22} -8.89324 q^{23} +(1.15607 - 3.55802i) q^{24} +(-0.853320 - 2.62625i) q^{25} +1.02253 q^{26} +(-6.20887 - 4.51100i) q^{27} +(1.32017 + 0.959157i) q^{28} +(1.96757 + 1.42952i) q^{29} +7.97526 q^{30} +(0.162981 + 0.501605i) q^{31} +6.36973 q^{32} +(9.43751 - 6.85675i) q^{33} -11.0196 q^{34} +(0.581189 - 1.78871i) q^{35} +(2.25236 - 6.93206i) q^{36} +1.78389 q^{37} +(11.0302 - 8.01394i) q^{38} -1.65259 q^{39} +(-0.589320 - 1.81374i) q^{40} +2.18573 q^{41} +(-5.42077 - 3.93842i) q^{42} +(0.171513 + 0.124611i) q^{43} +(4.17407 + 3.03264i) q^{44} -8.40078 q^{45} +(4.99088 + 15.3604i) q^{46} +(-3.23735 + 9.96355i) q^{47} -14.4146 q^{48} +(4.38477 - 3.18572i) q^{49} +(-4.05716 + 2.94770i) q^{50} +17.8095 q^{51} +(-0.225865 - 0.695142i) q^{52} +(0.315365 + 0.229126i) q^{53} +(-4.30697 + 13.2555i) q^{54} +(1.83759 - 5.65552i) q^{55} +(-0.495119 + 1.52382i) q^{56} +(-17.8267 + 12.9519i) q^{57} +(1.36486 - 4.20062i) q^{58} +(5.34321 + 3.88207i) q^{59} +(-1.76164 - 5.42176i) q^{60} +(0.163356 - 0.502759i) q^{61} +(0.774905 - 0.563001i) q^{62} +(5.71000 + 4.14856i) q^{63} +(-0.539458 - 1.66028i) q^{64} +(-0.681536 + 0.495165i) q^{65} +(-17.1393 - 12.4524i) q^{66} +(2.66875 - 1.93896i) q^{67} +(2.43409 + 7.49135i) q^{68} +(-8.06611 - 24.8249i) q^{69} -3.41562 q^{70} +(7.75871 + 3.28671i) q^{71} +7.15669 q^{72} +(1.58170 + 4.86797i) q^{73} +(-1.00112 - 3.08113i) q^{74} +(6.55706 - 4.76398i) q^{75} +(-7.88450 - 5.72842i) q^{76} +(-4.04187 + 2.93659i) q^{77} +(0.927432 + 2.85434i) q^{78} +(-7.36486 - 5.35088i) q^{79} +(-5.94463 + 4.31903i) q^{80} +(1.75562 - 5.40324i) q^{81} +(-1.22663 - 3.77518i) q^{82} +(-6.00741 - 4.36464i) q^{83} +(-1.48005 + 4.55511i) q^{84} +(7.34472 - 5.33625i) q^{85} +(0.118975 - 0.366167i) q^{86} +(-2.20585 + 6.78891i) q^{87} +(-1.56546 + 4.81798i) q^{88} +(7.05835 + 5.12819i) q^{89} +(4.71452 + 14.5098i) q^{90} +0.707766 q^{91} +(9.33989 - 6.78583i) q^{92} +(-1.25238 + 0.909905i) q^{93} +19.0258 q^{94} +(-3.47106 + 10.6828i) q^{95} +(5.77730 + 17.7807i) q^{96} -2.53926 q^{97} +(-7.96309 - 5.78552i) q^{98} +(18.0538 + 13.1168i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

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