LMFDB - Embedded newform 618.2.i.e.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [618,2,Mod(13,618)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(618, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("618.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 618 = 2 \cdot 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	618.i (of order $17$, degree $16$, 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:	$4.93475484492$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$5$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			133.1
Character	$\chi$	$=$	618.133
Dual form			618.2.i.e.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.739009 + 0.673696i) q^{2} +(-0.932472 - 0.361242i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(-2.35292 + 1.45687i) q^{5} +(-0.445738 - 0.895163i) q^{6} +(-0.0712563 - 0.0943586i) q^{7} +(-0.602635 + 0.798017i) q^{8} +(0.739009 + 0.673696i) q^{9} +O(q^{10})$	\(q+(0.739009 + 0.673696i) q^{2} +(-0.932472 - 0.361242i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(-2.35292 + 1.45687i) q^{5} +(-0.445738 - 0.895163i) q^{6} +(-0.0712563 - 0.0943586i) q^{7} +(-0.602635 + 0.798017i) q^{8} +(0.739009 + 0.673696i) q^{9} +(-2.72031 - 0.508515i) q^{10} +(-2.76340 - 2.51918i) q^{11} +(0.273663 - 0.961826i) q^{12} +(-3.60586 - 4.77493i) q^{13} +(0.0109099 - 0.117737i) q^{14} +(2.72031 - 0.508515i) q^{15} +(-0.982973 + 0.183750i) q^{16} +(1.82194 - 3.65896i) q^{17} +(0.0922684 + 0.995734i) q^{18} +(7.50549 - 2.90764i) q^{19} +(-1.66775 - 2.20846i) q^{20} +(0.0323583 + 0.113728i) q^{21} +(-0.345023 - 3.72339i) q^{22} +(-4.45422 + 4.06055i) q^{23} +(0.850217 - 0.526432i) q^{24} +(1.18508 - 2.37997i) q^{25} +(0.552087 - 5.95797i) q^{26} +(-0.445738 - 0.895163i) q^{27} +(0.0873814 - 0.0796587i) q^{28} +(0.537536 - 0.332828i) q^{29} +(2.35292 + 1.45687i) q^{30} +(-7.70388 + 1.44010i) q^{31} +(-0.850217 - 0.526432i) q^{32} +(1.66677 + 3.34732i) q^{33} +(3.81145 - 1.47657i) q^{34} +(0.305128 + 0.118207i) q^{35} +(-0.602635 + 0.798017i) q^{36} +(0.728205 - 2.55937i) q^{37} +(7.50549 + 2.90764i) q^{38} +(1.63746 + 5.75508i) q^{39} +(0.255347 - 2.75563i) q^{40} +(-1.97121 - 1.22052i) q^{41} +(-0.0527047 + 0.105845i) q^{42} +(-2.45528 - 8.62940i) q^{43} +(2.25345 - 2.98406i) q^{44} +(-2.72031 - 0.508515i) q^{45} -6.02728 q^{46} -11.3876 q^{47} +(0.982973 + 0.183750i) q^{48} +(1.91181 - 6.71933i) q^{49} +(2.47916 - 0.960431i) q^{50} +(-3.02068 + 2.75371i) q^{51} +(4.42185 - 4.03105i) q^{52} +(-4.73055 + 1.83263i) q^{53} +(0.273663 - 0.961826i) q^{54} +(10.1722 + 1.90151i) q^{55} +0.118241 q^{56} -8.04902 q^{57} +(0.621469 + 0.116173i) q^{58} +(-0.504817 + 0.668485i) q^{59} +(0.757344 + 2.66179i) q^{60} +(-1.43634 + 2.88456i) q^{61} +(-6.66342 - 4.12582i) q^{62} +(0.0109099 - 0.117737i) q^{63} +(-0.273663 - 0.961826i) q^{64} +(15.4407 + 5.98177i) q^{65} +(-1.02332 + 3.59659i) q^{66} +(-5.26260 + 6.96881i) q^{67} +(3.81145 + 1.47657i) q^{68} +(5.62027 - 2.17731i) q^{69} +(0.145857 + 0.292920i) q^{70} +(4.85999 + 3.00918i) q^{71} +(-0.982973 + 0.183750i) q^{72} +(11.2307 + 6.95376i) q^{73} +(2.26239 - 1.40081i) q^{74} +(-1.96480 + 1.79115i) q^{75} +(3.58776 + 7.20519i) q^{76} +(-0.0407959 + 0.440258i) q^{77} +(-2.66707 + 5.35620i) q^{78} +(-8.97423 + 5.55661i) q^{79} +(2.04516 - 1.86441i) q^{80} +(0.0922684 + 0.995734i) q^{81} +(-0.634481 - 2.22997i) q^{82} +(-4.42943 - 5.86552i) q^{83} +(-0.110257 + 0.0427137i) q^{84} +(1.04372 + 11.2636i) q^{85} +(3.99912 - 8.03132i) q^{86} +(-0.621469 + 0.116173i) q^{87} +(3.67567 - 0.687101i) q^{88} +(-0.476245 + 5.13950i) q^{89} +(-1.66775 - 2.20846i) q^{90} +(-0.193616 + 0.680488i) q^{91} +(-4.45422 - 4.06055i) q^{92} +(7.70388 + 1.44010i) q^{93} +(-8.41557 - 7.67181i) q^{94} +(-13.4238 + 17.7760i) q^{95} +(0.602635 + 0.798017i) q^{96} +(4.85316 + 9.74645i) q^{97} +(5.93963 - 3.67767i) q^{98} +(-0.345023 - 3.72339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 5 q^{2} + 5 q^{3} - 5 q^{4} + 14 q^{5} + 5 q^{6} - 2 q^{7} - 5 q^{8} - 5 q^{9}+O(q^{10}) $ 80 * q - 5 * q^2 + 5 * q^3 - 5 * q^4 + 14 * q^5 + 5 * q^6 - 2 * q^7 - 5 * q^8 - 5 * q^9	\( 80 q - 5 q^{2} + 5 q^{3} - 5 q^{4} + 14 q^{5} + 5 q^{6} - 2 q^{7} - 5 q^{8} - 5 q^{9} - 3 q^{10} + 18 q^{11} + 5 q^{12} + 14 q^{13} - 2 q^{14} + 3 q^{15} - 5 q^{16} - 4 q^{17} - 5 q^{18} - 14 q^{19} - 3 q^{20} + 2 q^{21} - 16 q^{22} - 13 q^{23} + 5 q^{24} + q^{25} + 31 q^{26} + 5 q^{27} - 2 q^{28} - 22 q^{29} - 14 q^{30} + 26 q^{31} - 5 q^{32} + 33 q^{33} - 4 q^{34} - 2 q^{35} - 5 q^{36} - 25 q^{37} - 14 q^{38} + 20 q^{39} + 14 q^{40} - 35 q^{41} + 19 q^{42} + 16 q^{43} + 18 q^{44} - 3 q^{45} + 72 q^{46} - 34 q^{47} + 5 q^{48} - 5 q^{49} - 16 q^{50} + 4 q^{51} - 3 q^{52} - 72 q^{53} + 5 q^{54} + 6 q^{55} + 32 q^{56} - 54 q^{57} - 5 q^{58} - 96 q^{59} + 3 q^{60} + 4 q^{61} - 8 q^{62} - 2 q^{63} - 5 q^{64} + 31 q^{65} - q^{66} + 48 q^{67} - 4 q^{68} - 4 q^{69} + 32 q^{70} - 14 q^{71} - 5 q^{72} + 48 q^{73} - 8 q^{74} + 16 q^{75} + 3 q^{76} + 2 q^{77} + 3 q^{78} + 34 q^{79} - 3 q^{80} - 5 q^{81} - q^{82} + 24 q^{83} - 15 q^{84} + 26 q^{85} + 16 q^{86} + 5 q^{87} + q^{88} - 18 q^{89} - 3 q^{90} + 46 q^{91} - 13 q^{92} - 26 q^{93} - 34 q^{94} - 45 q^{95} + 5 q^{96} + 89 q^{97} - 39 q^{98} - 16 q^{99}+O(q^{100}) \) 80 * q - 5 * q^2 + 5 * q^3 - 5 * q^4 + 14 * q^5 + 5 * q^6 - 2 * q^7 - 5 * q^8 - 5 * q^9 - 3 * q^10 + 18 * q^11 + 5 * q^12 + 14 * q^13 - 2 * q^14 + 3 * q^15 - 5 * q^16 - 4 * q^17 - 5 * q^18 - 14 * q^19 - 3 * q^20 + 2 * q^21 - 16 * q^22 - 13 * q^23 + 5 * q^24 + q^25 + 31 * q^26 + 5 * q^27 - 2 * q^28 - 22 * q^29 - 14 * q^30 + 26 * q^31 - 5 * q^32 + 33 * q^33 - 4 * q^34 - 2 * q^35 - 5 * q^36 - 25 * q^37 - 14 * q^38 + 20 * q^39 + 14 * q^40 - 35 * q^41 + 19 * q^42 + 16 * q^43 + 18 * q^44 - 3 * q^45 + 72 * q^46 - 34 * q^47 + 5 * q^48 - 5 * q^49 - 16 * q^50 + 4 * q^51 - 3 * q^52 - 72 * q^53 + 5 * q^54 + 6 * q^55 + 32 * q^56 - 54 * q^57 - 5 * q^58 - 96 * q^59 + 3 * q^60 + 4 * q^61 - 8 * q^62 - 2 * q^63 - 5 * q^64 + 31 * q^65 - q^66 + 48 * q^67 - 4 * q^68 - 4 * q^69 + 32 * q^70 - 14 * q^71 - 5 * q^72 + 48 * q^73 - 8 * q^74 + 16 * q^75 + 3 * q^76 + 2 * q^77 + 3 * q^78 + 34 * q^79 - 3 * q^80 - 5 * q^81 - q^82 + 24 * q^83 - 15 * q^84 + 26 * q^85 + 16 * q^86 + 5 * q^87 + q^88 - 18 * q^89 - 3 * q^90 + 46 * q^91 - 13 * q^92 - 26 * q^93 - 34 * q^94 - 45 * q^95 + 5 * q^96 + 89 * q^97 - 39 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/618\mathbb{Z}\right)^\times$.

$n$	$211$	$413$
$\chi(n)$	$e\left(\frac{14}{17}\right)$	$1$

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 $

$2$	0.739009	+	0.673696i	0.522558	+	0.476375i
$2$	0.739009	+	0.673696i	0.522558	+	0.476375i
$3$	−0.932472	−	0.361242i	−0.538363	−	0.208563i
$3$	−0.932472	−	0.361242i	−0.538363	−	0.208563i
$4$	0.0922684	+	0.995734i	0.0461342	+	0.497867i
$5$	−2.35292	+	1.45687i	−1.05226	+	0.651531i	−0.939660	−	0.342110i	$-0.888858\pi$
$5$	−2.35292	+	1.45687i	−1.05226	+	0.651531i	−0.112598	+	0.993641i	$0.535917\pi$
$6$	−0.445738	−	0.895163i	−0.181972	−	0.365449i
$7$	−0.0712563	−	0.0943586i	−0.0269324	−	0.0356642i	0.784352	−	0.620316i	$-0.212996\pi$
$7$	−0.0712563	−	0.0943586i	−0.0269324	−	0.0356642i	−0.811284	+	0.584652i	$0.801231\pi$
$8$	−0.602635	+	0.798017i	−0.213064	+	0.282142i
$9$	0.739009	+	0.673696i	0.246336	+	0.224565i
$10$	−2.72031	−	0.508515i	−0.860239	−	0.160806i
$11$	−2.76340	−	2.51918i	−0.833198	−	0.759560i	0.139848	−	0.990173i	$-0.455339\pi$
$11$	−2.76340	−	2.51918i	−0.833198	−	0.759560i	−0.973046	+	0.230613i	$0.925927\pi$
$12$	0.273663	−	0.961826i	0.0789997	−	0.277655i
$13$	−3.60586	−	4.77493i	−1.00009	−	1.32433i	−0.945431	−	0.325822i	$-0.894359\pi$
$13$	−3.60586	−	4.77493i	−1.00009	−	1.32433i	−0.0546542	−	0.998505i	$-0.517406\pi$
$14$	0.0109099	−	0.117737i	0.00291580	−	0.0314665i
$15$	2.72031	−	0.508515i	0.702382	−	0.131298i
$16$	−0.982973	+	0.183750i	−0.245743	+	0.0459374i
$17$	1.82194	−	3.65896i	0.441886	−	0.887427i	−0.556511	−	0.830840i	$-0.687860\pi$
$17$	1.82194	−	3.65896i	0.441886	−	0.887427i	0.998398	−	0.0565872i	$-0.0180219\pi$
$18$	0.0922684	+	0.995734i	0.0217479	+	0.234697i
$19$	7.50549	−	2.90764i	1.72188	−	0.667059i	0.722182	−	0.691704i	$-0.243139\pi$
$19$	7.50549	−	2.90764i	1.72188	−	0.667059i	0.999696	+	0.0246445i	$0.00784537\pi$
$20$	−1.66775	−	2.20846i	−0.372921	−	0.493827i
$21$	0.0323583	+	0.113728i	0.00706116	+	0.0248174i
$22$	−0.345023	−	3.72339i	−0.0735590	−	0.793829i
$23$	−4.45422	+	4.06055i	−0.928768	+	0.846684i	−0.988452	−	0.151533i	$-0.951579\pi$
$23$	−4.45422	+	4.06055i	−0.928768	+	0.846684i	0.0596838	+	0.998217i	$0.480991\pi$
$24$	0.850217	−	0.526432i	0.173550	−	0.107458i
$25$	1.18508	−	2.37997i	0.237016	−	0.475993i
$26$	0.552087	−	5.95797i	0.108273	−	1.16845i
$27$	−0.445738	−	0.895163i	−0.0857824	−	0.172274i
$28$	0.0873814	−	0.0796587i	0.0165135	−	0.0150541i
$29$	0.537536	−	0.332828i	0.0998180	−	0.0618047i	−0.475615	−	0.879653i	$-0.657775\pi$
$29$	0.537536	−	0.332828i	0.0998180	−	0.0618047i	0.575433	+	0.817849i	$0.304833\pi$
$30$	2.35292	+	1.45687i	0.429583	+	0.265986i
$31$	−7.70388	+	1.44010i	−1.38366	+	0.258650i	−0.822362	−	0.568965i	$-0.807344\pi$
$31$	−7.70388	+	1.44010i	−1.38366	+	0.258650i	−0.561295	+	0.827616i	$0.689697\pi$
$32$	−0.850217	−	0.526432i	−0.150299	−	0.0930609i
$33$	1.66677	+	3.34732i	0.290147	+	0.582693i
$34$	3.81145	−	1.47657i	0.653659	−	0.253229i
$35$	0.305128	+	0.118207i	0.0515761	+	0.0199807i
$36$	−0.602635	+	0.798017i	−0.100439	+	0.133003i
$37$	0.728205	−	2.55937i	0.119716	−	0.420758i	−0.878678	−	0.477416i	$-0.841574\pi$
$37$	0.728205	−	2.55937i	0.119716	−	0.420758i	0.998394	+	0.0566572i	$0.0180442\pi$
$38$	7.50549	+	2.90764i	1.21755	+	0.471682i
$39$	1.63746	+	5.75508i	0.262203	+	0.921550i
$40$	0.255347	−	2.75563i	0.0403739	−	0.435703i
$41$	−1.97121	−	1.22052i	−0.307851	−	0.190613i	0.363807	−	0.931474i	$-0.381477\pi$
$41$	−1.97121	−	1.22052i	−0.307851	−	0.190613i	−0.671659	+	0.740861i	$0.734418\pi$
$42$	−0.0527047	+	0.105845i	−0.00813251	+	0.0163323i
$43$	−2.45528	−	8.62940i	−0.374426	−	1.31597i	−0.888756	−	0.458380i	$-0.848430\pi$
$43$	−2.45528	−	8.62940i	−0.374426	−	1.31597i	0.514330	−	0.857592i	$-0.328041\pi$
$44$	2.25345	−	2.98406i	0.339721	−	0.449863i
$45$	−2.72031	−	0.508515i	−0.405520	−	0.0758049i
$46$	−6.02728			−0.888675
$47$	−11.3876			−1.66106			−0.830530	−	0.556975i	$-0.811962\pi$
$47$	−11.3876			−1.66106			−0.830530	+	0.556975i	$0.811962\pi$
$48$	0.982973	+	0.183750i	0.141880	+	0.0265220i
$49$	1.91181	−	6.71933i	0.273116	−	0.959905i
$50$	2.47916	−	0.960431i	0.350606	−	0.135825i
$51$	−3.02068	+	2.75371i	−0.422980	+	0.385597i
$52$	4.42185	−	4.03105i	0.613201	−	0.559006i
$53$	−4.73055	+	1.83263i	−0.649791	+	0.251730i	−0.663501	−	0.748176i	$-0.730930\pi$
$53$	−4.73055	+	1.83263i	−0.649791	+	0.251730i	0.0137096	+	0.999906i	$0.495636\pi$
$54$	0.273663	−	0.961826i	0.0372408	−	0.130888i
$55$	10.1722	+	1.90151i	1.37162	+	0.256399i
$56$	0.118241			0.0158007
$57$	−8.04902			−1.06612
$58$	0.621469	+	0.116173i	0.0816029	+	0.0152542i
$59$	−0.504817	+	0.668485i	−0.0657215	+	0.0870294i	−0.829691	−	0.558223i	$-0.811483\pi$
$59$	−0.504817	+	0.668485i	−0.0657215	+	0.0870294i	0.763969	+	0.645253i	$0.223248\pi$
$60$	0.757344	+	2.66179i	0.0977727	+	0.343636i
$61$	−1.43634	+	2.88456i	−0.183905	+	0.369331i	−0.967861	−	0.251485i	$-0.919081\pi$
$61$	−1.43634	+	2.88456i	−0.183905	+	0.369331i	0.783956	+	0.620816i	$0.213199\pi$
$62$	−6.66342	−	4.12582i	−0.846256	−	0.523979i
$63$	0.0109099	−	0.117737i	0.00137452	−	0.0148335i
$64$	−0.273663	−	0.961826i	−0.0342079	−	0.120228i
$65$	15.4407	+	5.98177i	1.91519	+	0.741948i
$66$	−1.02332	+	3.59659i	−0.125962	+	0.442710i
$67$	−5.26260	+	6.96881i	−0.642929	+	0.851376i	−0.996462	−	0.0840464i	$-0.973216\pi$
$67$	−5.26260	+	6.96881i	−0.642929	+	0.851376i	0.353533	+	0.935422i	$0.384980\pi$
$68$	3.81145	+	1.47657i	0.462207	+	0.179060i
$69$	5.62027	−	2.17731i	0.676602	−	0.262117i
$70$	0.145857	+	0.292920i	0.0174332	+	0.0350106i
$71$	4.85999	+	3.00918i	0.576774	+	0.357123i	0.783611	−	0.621252i	$-0.213376\pi$
$71$	4.85999	+	3.00918i	0.576774	+	0.357123i	−0.206837	+	0.978375i	$0.566317\pi$
$72$	−0.982973	+	0.183750i	−0.115844	+	0.0216551i
$73$	11.2307	+	6.95376i	1.31445	+	0.813876i	0.991192	−	0.132434i	$-0.0422792\pi$
$73$	11.2307	+	6.95376i	1.31445	+	0.813876i	0.323262	+	0.946309i	$0.395220\pi$
$74$	2.26239	−	1.40081i	0.262997	−	0.162841i
$75$	−1.96480	+	1.79115i	−0.226875	+	0.206824i
$76$	3.58776	+	7.20519i	0.411544	+	0.826492i
$77$	−0.0407959	+	0.440258i	−0.00464913	+	0.0501721i
$78$	−2.66707	+	5.35620i	−0.301986	+	0.606470i
$79$	−8.97423	+	5.55661i	−1.00968	+	0.625167i	−0.928423	−	0.371526i	$-0.878835\pi$
$79$	−8.97423	+	5.55661i	−1.00968	+	0.625167i	−0.0812572	+	0.996693i	$0.525894\pi$
$80$	2.04516	−	1.86441i	0.228656	−	0.208447i
$81$	0.0922684	+	0.995734i	0.0102520	+	0.110637i
$82$	−0.634481	−	2.22997i	−0.0700667	−	0.246259i
$83$	−4.42943	−	5.86552i	−0.486194	−	0.643824i	0.487111	−	0.873340i	$-0.338051\pi$
$83$	−4.42943	−	5.86552i	−0.486194	−	0.643824i	−0.973305	+	0.229515i	$0.926286\pi$
$84$	−0.110257	+	0.0427137i	−0.0120300	+	0.00466045i
$85$	1.04372	+	11.2636i	0.113208	+	1.22170i
$86$	3.99912	−	8.03132i	0.431236	−	0.866039i
$87$	−0.621469	+	0.116173i	−0.0666285	+	0.0124550i
$88$	3.67567	−	0.687101i	0.391828	−	0.0732453i
$89$	−0.476245	+	5.13950i	−0.0504818	+	0.544786i	0.932511	+	0.361142i	$0.117613\pi$
$89$	−0.476245	+	5.13950i	−0.0504818	+	0.544786i	−0.982993	+	0.183644i	$0.941211\pi$
$90$	−1.66775	−	2.20846i	−0.175796	−	0.232792i
$91$	−0.193616	+	0.680488i	−0.0202964	+	0.0713345i
$92$	−4.45422	−	4.06055i	−0.464384	−	0.423342i
$93$	7.70388	+	1.44010i	0.798855	+	0.149332i
$94$	−8.41557	−	7.67181i	−0.868000	−	0.791287i
$95$	−13.4238	+	17.7760i	−1.37725	+	1.82377i
$96$	0.602635	+	0.798017i	0.0615061	+	0.0814473i
$97$	4.85316	+	9.74645i	0.492763	+	0.989602i	0.992364	+	0.123346i	$0.0393626\pi$
$97$	4.85316	+	9.74645i	0.492763	+	0.989602i	−0.499600	+	0.866256i	$0.666520\pi$
$98$	5.93963	−	3.67767i	0.599994	−	0.371500i
$99$	−0.345023	−	3.72339i	−0.0346761	−	0.374214i
$100$	2.47916	+	0.960431i	0.247916	+	0.0960431i
$101$	6.95862	+	6.34362i	0.692408	+	0.631214i	0.941400	−	0.337292i	$-0.109511\pi$
$101$	6.95862	+	6.34362i	0.692408	+	0.631214i	−0.248992	+	0.968506i	$0.580099\pi$
$102$	−4.08747			−0.404720
$103$	2.27427	−	9.89079i	0.224090	−	0.974568i
$103$	2.27427	−	9.89079i	0.224090	−	0.974568i
$104$	5.98349			0.586730
$105$	−0.241822	−	0.220450i	−0.0235994	−	0.0215137i
$106$	−4.73055	−	1.83263i	−0.459472	−	0.178000i
$107$	0.970297	+	10.4712i	0.0938022	+	1.01229i	0.904401	+	0.426684i	$0.140318\pi$
$107$	0.970297	+	10.4712i	0.0938022	+	1.01229i	−0.810598	+	0.585602i	$0.800858\pi$
$108$	0.850217	−	0.526432i	0.0818122	−	0.0506560i
$109$	−2.89562	−	5.81520i	−0.277350	−	0.556995i	0.712064	−	0.702115i	$-0.247761\pi$
$109$	−2.89562	−	5.81520i	−0.277350	−	0.556995i	−0.989414	+	0.145120i	$0.953643\pi$
$110$	6.23629	+	8.25818i	0.594607	+	0.787386i
$111$	−1.60358	+	2.12349i	−0.152205	+	0.201552i
$112$	0.0873814	+	0.0796587i	0.00825677	+	0.00752704i
$113$	−13.5500	−	2.53294i	−1.27468	−	0.238279i	−0.497447	−	0.867494i	$-0.665729\pi$
$113$	−13.5500	−	2.53294i	−1.27468	−	0.238279i	−0.777231	+	0.629216i	$0.783376\pi$
$114$	−5.94830	−	5.42259i	−0.557109	−	0.507872i
$115$	4.56473	−	16.0434i	0.425663	−	1.49605i
$116$	0.381006	+	0.504534i	0.0353755	+	0.0468448i
$117$	0.552087	−	5.95797i	0.0510405	−	0.550814i
$118$	−0.823420	+	0.153924i	−0.0758019	+	0.0141698i
$119$	−0.475079	+	0.0888077i	−0.0435504	+	0.00814099i
$120$	−1.23355	+	2.47731i	−0.112607	+	0.226146i
$121$	0.275204	+	2.96992i	0.0250185	+	0.269993i
$122$	−3.00479	+	1.16406i	−0.272041	+	0.105389i
$123$	1.39719	+	1.85018i	0.125981	+	0.166826i
$124$	−2.14478	−	7.53814i	−0.192607	−	0.676945i
$125$	−0.597845	−	6.45177i	−0.0534728	−	0.577064i
$126$	0.0873814	−	0.0796587i	0.00778456	−	0.00709656i
$127$	7.35945	−	4.55678i	0.653046	−	0.404349i	−0.159539	−	0.987192i	$-0.551001\pi$
$127$	7.35945	−	4.55678i	0.653046	−	0.404349i	0.812585	+	0.582843i	$0.198060\pi$
$128$	0.445738	−	0.895163i	0.0393981	−	0.0791220i
$129$	−0.827823	+	8.93363i	−0.0728857	+	0.786562i
$130$	7.38095	+	14.8229i	0.647352	+	1.30006i
$131$	7.29889	−	6.65381i	0.637707	−	0.581346i	−0.288909	−	0.957357i	$-0.593292\pi$
$131$	7.29889	−	6.65381i	0.637707	−	0.581346i	0.926616	+	0.376010i	$0.122704\pi$
$132$	−3.17925	+	1.96851i	−0.276718	+	0.171337i
$133$	−0.809175	−	0.501020i	−0.0701644	−	0.0434439i
$134$	−8.58397	+	1.60462i	−0.741542	+	0.138618i
$135$	2.35292	+	1.45687i	0.202507	+	0.125387i
$136$	1.82194	+	3.65896i	0.156230	+	0.313753i
$137$	−13.6990	+	5.30701i	−1.17038	+	0.453409i	−0.866440	−	0.499282i	$-0.833597\pi$
$137$	−13.6990	+	5.30701i	−1.17038	+	0.453409i	−0.303943	+	0.952690i	$0.598303\pi$
$138$	5.62027	+	2.17731i	0.478430	+	0.185345i
$139$	7.62686	−	10.0996i	0.646902	−	0.856636i	−0.349880	−	0.936794i	$-0.613778\pi$
$139$	7.62686	−	10.0996i	0.646902	−	0.856636i	0.996782	+	0.0801581i	$0.0255425\pi$
$140$	−0.0895494	+	0.314734i	−0.00756831	+	0.0265998i
$141$	10.6187	+	4.11369i	0.894253	+	0.346435i
$142$	1.56430	+	5.49796i	0.131273	+	0.461378i
$143$	−2.06444	+	22.2788i	−0.172637	+	1.86305i
$144$	−0.850217	−	0.526432i	−0.0708514	−	0.0438693i
$145$	−0.779894	+	1.56624i	−0.0647666	+	0.130069i
$146$	3.61487	+	12.7050i	0.299169	+	1.05147i
$147$	−4.21002	+	5.57496i	−0.347236	+	0.459815i
$148$	2.61565	+	0.488949i	0.215005	+	0.0401914i
$149$	20.6859			1.69466			0.847329	−	0.531068i	$-0.178209\pi$
$149$	20.6859			1.69466			0.847329	+	0.531068i	$0.178209\pi$
$150$	−2.65869			−0.217081
$151$	−12.5541	−	2.34677i	−1.02164	−	0.190977i	−0.353829	−	0.935310i	$-0.615121\pi$
$151$	−12.5541	−	2.34677i	−1.02164	−	0.190977i	−0.667809	+	0.744333i	$0.732768\pi$
$152$	−2.20272	+	7.74176i	−0.178664	+	0.627939i
$153$	3.81145	−	1.47657i	0.308138	−	0.119373i
$154$	−0.326749	+	0.297871i	−0.0263302	+	0.0240031i
$155$	16.0286	−	14.6120i	1.28745	−	1.17366i
$156$	−5.57944	+	2.16149i	−0.446713	+	0.173057i
$157$	4.43125	−	15.5742i	0.353652	−	1.24296i	−0.557253	−	0.830343i	$-0.688145\pi$
$157$	4.43125	−	15.5742i	0.353652	−	1.24296i	0.910905	−	0.412615i	$-0.135385\pi$
$158$	−10.3755	−	1.93952i	−0.825430	−	0.154300i
$159$	5.07313			0.402325
$160$	2.76743			0.218785
$161$	0.700540	+	0.130954i	0.0552103	+	0.0103206i
$162$	−0.602635	+	0.798017i	−0.0473474	+	0.0626982i
$163$	−5.54925	−	19.5036i	−0.434651	−	1.52764i	−0.801866	−	0.597503i	$-0.796159\pi$
$163$	−5.54925	−	19.5036i	−0.434651	−	1.52764i	0.367215	−	0.930136i	$-0.380311\pi$
$164$	1.03343	−	2.07542i	0.0806976	−	0.162063i
$165$	−8.79836	−	5.44772i	−0.684952	−	0.424104i
$166$	0.678183	−	7.31876i	0.0526372	−	0.568046i
$167$	0.790892	+	2.77970i	0.0612010	+	0.215099i	0.986394	−	0.164397i	$-0.0525679\pi$
$167$	0.790892	+	2.77970i	0.0612010	+	0.215099i	−0.925193	+	0.379496i	$0.876097\pi$
$168$	−0.110257	−	0.0427137i	−0.00850650	−	0.00329543i
$169$	−6.24011	+	21.9317i	−0.480008	+	1.68705i
$170$	−6.81689	+	9.02702i	−0.522832	+	0.692341i
$171$	7.50549	+	2.90764i	0.573959	+	0.222353i
$172$	8.36605	−	3.24102i	0.637905	−	0.247126i
$173$	−2.15772	−	4.33329i	−0.164049	−	0.329454i	0.797852	−	0.602853i	$-0.205970\pi$
$173$	−2.15772	−	4.33329i	−0.164049	−	0.329454i	−0.961901	+	0.273399i	$0.911852\pi$
$174$	−0.537536	−	0.332828i	−0.0407505	−	0.0252317i
$175$	−0.309015	+	0.0577649i	−0.0233593	+	0.00436662i
$176$	3.17925	+	1.96851i	0.239645	+	0.148382i
$177$	0.712212	−	0.440983i	0.0535332	−	0.0331463i
$178$	−3.81441	+	3.47729i	−0.285902	+	0.260634i
$179$	2.65369	+	5.32933i	0.198346	+	0.398333i	0.971899	−	0.235399i	$-0.0756398\pi$
$179$	2.65369	+	5.32933i	0.198346	+	0.398333i	−0.773553	+	0.633732i	$0.781522\pi$
$180$	0.255347	−	2.75563i	0.0190324	−	0.205392i
$181$	−0.287207	+	0.576790i	−0.0213480	+	0.0428725i	−0.905581	−	0.424174i	$-0.860564\pi$
$181$	−0.287207	+	0.576790i	−0.0213480	+	0.0428725i	0.884233	+	0.467047i	$0.154682\pi$
$182$	−0.601525	+	0.372449i	−0.0445880	+	0.0276077i
$183$	2.38137	−	2.17091i	0.176036	−	0.160478i
$184$	−0.556128	−	6.00157i	−0.0409983	−	0.442442i
$185$	2.01526	+	7.08290i	0.148165	+	0.520745i
$186$	4.72304	+	6.25432i	0.346310	+	0.458589i
$187$	−14.2523	+	5.52138i	−1.04223	+	0.403763i
$188$	−1.05072	−	11.3391i	−0.0766316	−	0.826987i
$189$	−0.0527047	+	0.105845i	−0.00383370	+	0.00769911i
$190$	−21.8959	+	4.09305i	−1.58849	+	0.296941i
$191$	−16.3904	+	3.06390i	−1.18597	+	0.221696i	−0.739533	−	0.673120i	$-0.764954\pi$
$191$	−16.3904	+	3.06390i	−1.18597	+	0.221696i	−0.446435	+	0.894816i	$0.647307\pi$
$192$	−0.0922684	+	0.995734i	−0.00665890	+	0.0718609i
$193$	12.7509	+	16.8849i	0.917829	+	1.21540i	0.976148	+	0.217104i	$0.0696612\pi$
$193$	12.7509	+	16.8849i	0.917829	+	1.21540i	−0.0583192	+	0.998298i	$0.518574\pi$
$194$	−2.97962	+	10.4723i	−0.213924	+	0.751865i
$195$	−12.2372	−	11.1557i	−0.876323	−	0.798874i
$196$	6.86707	+	1.28368i	0.490505	+	0.0916913i
$197$	5.86272	+	5.34458i	0.417702	+	0.380786i	0.855083	−	0.518490i	$-0.173506\pi$
$197$	5.86272	+	5.34458i	0.417702	+	0.380786i	−0.437382	+	0.899276i	$0.644094\pi$
$198$	2.25345	−	2.98406i	0.160146	−	0.212068i
$199$	−13.6415	−	18.0643i	−0.967020	−	1.28054i	−0.959834	−	0.280567i	$-0.909478\pi$
$199$	−13.6415	−	18.0643i	−0.967020	−	1.28054i	−0.00718530	−	0.999974i	$-0.502287\pi$
$200$	1.18508	+	2.37997i	0.0837980	+	0.168289i
$201$	7.42466	−	4.59715i	0.523695	−	0.324258i
$202$	0.868813	+	9.37598i	0.0611294	+	0.659692i
$203$	−0.0697081	−	0.0270051i	−0.00489255	−	0.00189538i
$204$	−3.02068	−	2.75371i	−0.211490	−	0.192798i
$205$	6.41623			0.448129
$206$	8.34409	−	5.77722i	0.581360	−	0.402518i
$207$	−6.02728			−0.418925
$208$	4.42185	+	4.03105i	0.306600	+	0.279503i
$209$	−28.0656	−	10.8727i	−1.94134	−	0.752077i
$210$	−0.0301925	−	0.325829i	−0.00208348	−	0.0224844i
$211$	−21.7953	+	13.4951i	−1.50045	+	0.929038i	−0.502528	+	0.864561i	$0.667597\pi$
$211$	−21.7953	+	13.4951i	−1.50045	+	0.929038i	−0.997919	+	0.0644768i	$0.979462\pi$
$212$	−2.26129	−	4.54128i	−0.155306	−	0.311896i
$213$	−3.44476	−	4.56160i	−0.236031	−	0.312556i
$214$	−6.33733	+	8.39198i	−0.433211	+	0.573664i
$215$	18.3490	+	16.7273i	1.25139	+	1.14079i
$216$	0.982973	+	0.183750i	0.0668828	+	0.0125026i
$217$	0.684836	+	0.624311i	0.0464897	+	0.0423810i
$218$	1.77778	−	6.24825i	0.120406	−	0.423185i
$219$	−7.96033	−	10.5412i	−0.537909	−	0.712307i
$220$	−0.954827	+	10.3042i	−0.0643744	+	0.694711i
$221$	−24.0409	+	4.49403i	−1.61717	+	0.302301i
$222$	−2.61565	+	0.488949i	−0.175551	+	0.0328161i
$223$	1.42985	−	2.87152i	0.0957497	−	0.192291i	−0.842110	−	0.539306i	$-0.818687\pi$
$223$	1.42985	−	2.87152i	0.0957497	−	0.192291i	0.937860	+	0.347014i	$0.112804\pi$
$224$	0.0109099	+	0.117737i	0.000728951	+	0.00786663i
$225$	2.47916	−	0.960431i	0.165277	−	0.0640287i
$226$	−8.30715	−	11.0004i	−0.552584	−	0.731739i
$227$	−1.27668	−	4.48707i	−0.0847363	−	0.297817i	0.907861	−	0.419272i	$-0.137715\pi$
$227$	−1.27668	−	4.48707i	−0.0847363	−	0.297817i	−0.992597	+	0.121455i	$0.961244\pi$
$228$	−0.742670	−	8.01469i	−0.0491845	−	0.530786i
$229$	7.62399	−	6.95018i	0.503807	−	0.459281i	−0.381445	−	0.924391i	$-0.624574\pi$
$229$	7.62399	−	6.95018i	0.503807	−	0.459281i	0.885253	+	0.465110i	$0.153985\pi$
$230$	14.1817	−	8.78095i	0.935115	−	0.578999i
$231$	0.197081	−	0.395791i	0.0129670	−	0.0260412i
$232$	−0.0583352	+	0.629537i	−0.00382989	+	0.0413311i
$233$	−1.56316	−	3.13924i	−0.102406	−	0.205659i	0.838035	−	0.545617i	$-0.183705\pi$
$233$	−1.56316	−	3.13924i	−0.102406	−	0.205659i	−0.940440	+	0.339958i	$0.889587\pi$
$234$	4.42185	−	4.03105i	0.289066	−	0.263518i
$235$	26.7942	−	16.5903i	1.74786	−	1.08223i
$236$	−0.712212	−	0.440983i	−0.0463611	−	0.0287056i
$237$	10.3755	−	1.93952i	0.673961	−	0.125985i
$238$	−0.410917	−	0.254429i	−0.0266358	−	0.0164922i
$239$	−5.00725	−	10.0559i	−0.323892	−	0.650462i	0.672046	−	0.740510i	$-0.265416\pi$
$239$	−5.00725	−	10.0559i	−0.323892	−	0.650462i	−0.995937	+	0.0900473i	$0.971298\pi$
$240$	−2.58056	+	0.999713i	−0.166574	+	0.0645312i
$241$	16.6230	+	6.43979i	1.07078	+	0.414823i	0.831154	−	0.556042i	$-0.187681\pi$
$241$	16.6230	+	6.43979i	1.07078	+	0.414823i	0.239628	+	0.970865i	$0.422975\pi$
$242$	−1.79744	+	2.38020i	−0.115544	+	0.153005i
$243$	0.273663	−	0.961826i	0.0175555	−	0.0617011i
$244$	−3.00479	−	1.16406i	−0.192362	−	0.0745214i
$245$	5.29082	+	18.5953i	0.338018	+	1.18801i
$246$	−0.213922	+	2.30859i	−0.0136392	+	0.147190i
$247$	−40.9475	−	25.3536i	−2.60543	−	1.61321i
$248$	3.49339	−	7.01568i	0.221831	−	0.445496i
$249$	2.01145	+	7.06953i	0.127471	+	0.448013i
$250$	3.90472	−	5.17068i	0.246956	−	0.327023i
$251$	5.09386	+	0.952208i	0.321522	+	0.0601028i	0.342036	−	0.939687i	$-0.388883\pi$
$251$	5.09386	+	0.952208i	0.321522	+	0.0601028i	−0.0205146	+	0.999790i	$0.506530\pi$
$252$	0.118241			0.00744851
$253$	22.5380			1.41695
$254$	8.50858	+	1.59053i	0.533876	+	0.0997987i
$255$	3.09562	−	10.8800i	0.193856	−	0.681332i
$256$	0.932472	−	0.361242i	0.0582795	−	0.0225776i
$257$	13.3757	−	12.1936i	0.834356	−	0.760616i	−0.138908	−	0.990305i	$-0.544359\pi$
$257$	13.3757	−	12.1936i	0.834356	−	0.760616i	0.973264	+	0.229690i	$0.0737711\pi$
$258$	−6.63032	+	6.04433i	−0.412785	+	0.376304i
$259$	−0.293388	+	0.113659i	−0.0182303	+	0.00706244i
$260$	−4.53156	+	15.9268i	−0.281036	+	0.987738i
$261$	0.621469	+	0.116173i	0.0384680	+	0.00719091i
$262$	9.87659			0.610178
$263$	−6.55568			−0.404241			−0.202120	−	0.979361i	$-0.564783\pi$
$263$	−6.55568			−0.404241			−0.202120	+	0.979361i	$0.564783\pi$
$264$	−3.67567	−	0.687101i	−0.226222	−	0.0422882i
$265$	8.46072	−	11.2038i	0.519738	−	0.688244i
$266$	−0.260453	−	0.915396i	−0.0159694	−	0.0561265i
$267$	2.30069	−	4.62040i	0.140800	−	0.282764i
$268$	−7.42466	−	4.59715i	−0.453533	−	0.280816i
$269$	0.754172	−	8.13882i	0.0459827	−	0.496232i	−0.941335	−	0.337474i	$-0.890427\pi$
$269$	0.754172	−	8.13882i	0.0459827	−	0.496232i	0.987317	−	0.158758i	$-0.0507490\pi$
$270$	0.757344	+	2.66179i	0.0460905	+	0.161991i
$271$	16.6798	+	6.46179i	1.01323	+	0.392526i	0.809889	−	0.586583i	$-0.199527\pi$
$271$	16.6798	+	6.46179i	1.01323	+	0.392526i	0.203337	+	0.979109i	$0.434821\pi$
$272$	−1.11859	+	3.93144i	−0.0678245	+	0.238378i
$273$	0.426362	−	0.564594i	0.0258046	−	0.0341708i
$274$	−13.6990	−	5.30701i	−0.827586	−	0.320608i
$275$	−9.27041	+	3.59138i	−0.559027	+	0.216568i
$276$	2.68659	+	5.39540i	0.161714	+	0.324765i
$277$	−2.27533	−	1.40883i	−0.136711	−	0.0846481i	0.456372	−	0.889789i	$-0.349149\pi$
$277$	−2.27533	−	1.40883i	−0.136711	−	0.0846481i	−0.593084	+	0.805141i	$0.702090\pi$
$278$	12.4404	−	2.32551i	0.746124	−	0.139475i
$279$	−6.66342	−	4.12582i	−0.398929	−	0.247006i
$280$	−0.278212	+	0.172262i	−0.0166264	+	0.0102946i
$281$	14.0592	−	12.8167i	0.838704	−	0.764580i	−0.135373	−	0.990795i	$-0.543223\pi$
$281$	14.0592	−	12.8167i	0.838704	−	0.764580i	0.974077	+	0.226215i	$0.0726351\pi$
$282$	5.07591	+	10.1938i	0.302266	+	0.607032i
$283$	−1.51268	+	16.3244i	−0.0899195	+	0.970386i	0.824566	+	0.565766i	$0.191420\pi$
$283$	−1.51268	+	16.3244i	−0.0899195	+	0.970386i	−0.914485	+	0.404619i	$0.867404\pi$
$284$	−2.54792	+	5.11691i	−0.151191	+	0.303633i
$285$	18.9387	−	11.7264i	1.12183	−	0.694609i
$286$	−16.5348	+	15.0735i	−0.977723	+	0.891313i
$287$	0.0252944	+	0.272970i	0.00149308	+	0.0161129i
$288$	−0.273663	−	0.961826i	−0.0161257	−	0.0566761i
$289$	0.176311	+	0.233473i	0.0103712	+	0.0137337i
$290$	−1.63152	+	0.632053i	−0.0958059	+	0.0371154i
$291$	−1.00461	−	10.8415i	−0.0588912	−	0.635537i
$292$	−5.88785	+	11.8244i	−0.344561	+	0.691971i
$293$	−17.7171	+	3.31190i	−1.03504	+	0.193483i	−0.673743	−	0.738966i	$-0.735314\pi$
$293$	−17.7171	+	3.31190i	−1.03504	+	0.193483i	−0.361301	+	0.932449i	$0.617667\pi$
$294$	−6.86707	+	1.28368i	−0.400496	+	0.0748656i
$295$	0.213900	−	2.30834i	0.0124537	−	0.134397i
$296$	1.60358	+	2.12349i	0.0932064	+	0.123425i
$297$	−1.02332	+	3.59659i	−0.0593789	+	0.208695i
$298$	15.2871	+	13.9360i	0.885557	+	0.807292i
$299$	35.4501	+	6.62678i	2.05013	+	0.383237i
$300$	−1.96480	−	1.79115i	−0.113438	−	0.103412i
$301$	−0.639305	+	0.846576i	−0.0368489	+	0.0487959i
$302$	−7.69658	−	10.1919i	−0.442889	−	0.586479i
$303$	−4.19714	−	8.42899i	−0.241119	−	0.484233i
$304$	−6.84342	+	4.23727i	−0.392497	+	0.243024i
$305$	−0.822826	−	8.87971i	−0.0471149	−	0.508451i
$306$	3.81145	+	1.47657i	0.217886	+	0.0844096i
$307$	−24.9768	−	22.7693i	−1.42550	−	1.29951i	−0.890742	−	0.454509i	$-0.849815\pi$
$307$	−24.9768	−	22.7693i	−1.42550	−	1.29951i	−0.534758	−	0.845005i	$-0.679597\pi$
$308$	−0.442144			−0.0251935
$309$	−5.69366	+	8.40133i	−0.323901	+	0.477935i
$310$	21.6893			1.23187
$311$	18.8783	+	17.2098i	1.07049	+	0.975879i	0.999766	−	0.0216175i	$-0.00688161\pi$
$311$	18.8783	+	17.2098i	1.07049	+	0.975879i	0.0707215	+	0.997496i	$0.477470\pi$
$312$	−5.57944	−	2.16149i	−0.315874	−	0.122370i
$313$	1.93702	+	20.9038i	0.109487	+	1.18155i	0.856286	+	0.516503i	$0.172766\pi$
$313$	1.93702	+	20.9038i	0.109487	+	1.18155i	−0.746799	+	0.665050i	$0.768410\pi$
$314$	13.7670	−	8.52417i	0.776918	−	0.481047i
$315$	0.145857	+	0.292920i	0.00821810	+	0.0165042i
$316$	−6.36094	−	8.42325i	−0.357831	−	0.473845i
$317$	18.4481	−	24.4292i	1.03615	−	1.37208i	0.110421	−	0.993885i	$-0.464780\pi$
$317$	18.4481	−	24.4292i	1.03615	−	1.37208i	0.925726	−	0.378195i	$-0.123455\pi$
$318$	3.74909	+	3.41774i	0.210238	+	0.191658i
$319$	−2.32388	−	0.434409i	−0.130112	−	0.0243222i
$320$	2.04516	+	1.86441i	0.114328	+	0.104224i
$321$	2.87785	−	10.1146i	0.160626	−	0.564541i
$322$	0.429482	+	0.568726i	0.0239341	+	0.0316939i
$323$	3.03564	−	32.7598i	0.168908	−	1.82281i
$324$	−0.982973	+	0.183750i	−0.0546096	+	0.0102083i
$325$	−15.6374	+	2.92314i	−0.867407	+	0.162147i
$326$	9.03854	−	18.1518i	0.500598	−	1.00534i
$327$	0.599397	+	6.46853i	0.0331468	+	0.357710i
$328$	2.16192	−	0.837530i	0.119372	−	0.0462449i
$329$	0.811442	+	1.07452i	0.0447362	+	0.0592404i
$330$	−2.83197	−	9.95333i	−0.155895	−	0.547913i
$331$	0.993875	+	10.7256i	0.0546283	+	0.589533i	0.978418	+	0.206634i	$0.0662509\pi$
$331$	0.993875	+	10.7256i	0.0546283	+	0.589533i	−0.923790	+	0.382899i	$0.874926\pi$
$332$	5.43180	−	4.95174i	0.298109	−	0.271762i
$333$	2.26239	−	1.40081i	0.123978	−	0.0767640i
$334$	−1.28819	+	2.58704i	−0.0704868	+	0.141557i
$335$	2.22985	−	24.0640i	0.121830	−	1.31475i
$336$	−0.0527047	−	0.105845i	−0.00287528	−	0.00577434i
$337$	9.49807	−	8.65863i	0.517393	−	0.471666i	−0.372373	−	0.928083i	$-0.621456\pi$
$337$	9.49807	−	8.65863i	0.517393	−	0.471666i	0.889766	+	0.456417i	$0.150868\pi$
$338$	−19.3868	+	12.0038i	−1.05450	+	0.652920i
$339$	11.7200	+	7.25672i	0.636544	+	0.394131i
$340$	−11.1192	+	2.07854i	−0.603024	+	0.112725i
$341$	24.9168	+	15.4278i	1.34932	+	0.835464i
$342$	3.58776	+	7.20519i	0.194004	+	0.389612i
$343$	−1.54205	+	0.597395i	−0.0832631	+	0.0322563i
$344$	8.36605	+	3.24102i	0.451067	+	0.174744i
$345$	−10.0520	+	13.3110i	−0.541182	+	0.716641i
$346$	1.32474	−	4.65599i	0.0712187	−	0.250308i
$347$	−26.3098	−	10.1925i	−1.41239	−	0.547161i	−0.470293	−	0.882511i	$-0.655852\pi$
$347$	−26.3098	−	10.1925i	−1.41239	−	0.547161i	−0.942094	+	0.335349i	$0.891146\pi$
$348$	−0.173019	−	0.608099i	−0.00927480	−	0.0325975i
$349$	−2.42613	+	26.1821i	−0.129868	+	1.40149i	0.642484	+	0.766299i	$0.277904\pi$
$349$	−2.42613	+	26.1821i	−0.129868	+	1.40149i	−0.772352	+	0.635195i	$0.780920\pi$
$350$	−0.267281	−	0.165493i	−0.0142868	−	0.00884598i
$351$	−2.66707	+	5.35620i	−0.142358	+	0.285893i
$352$	1.02332	+	3.59659i	0.0545430	+	0.191699i
$353$	8.68239	−	11.4973i	0.462117	−	0.611942i	−0.505972	−	0.862550i	$-0.668866\pi$
$353$	8.68239	−	11.4973i	0.462117	−	0.611942i	0.968089	+	0.250608i	$0.0806307\pi$
$354$	0.823420	+	0.153924i	0.0437643	+	0.00818096i
$355$	−15.8191			−0.839592
$356$	−5.16152			−0.273560
$357$	0.475079	+	0.0888077i	0.0251439	+	0.00470020i
$358$	−1.62924	+	5.72620i	−0.0861083	+	0.302639i
$359$	−25.9928	+	10.0697i	−1.37185	+	0.531457i	−0.930636	−	0.365946i	$-0.880745\pi$
$359$	−25.9928	+	10.0697i	−1.37185	+	0.531457i	−0.441212	+	0.897403i	$0.645451\pi$
$360$	2.04516	−	1.86441i	0.107789	−	0.0982630i
$361$	33.8368	−	30.8464i	1.78089	−	1.62349i
$362$	−0.600830	+	0.232763i	−0.0315789	+	0.0122337i
$363$	0.816239	−	2.86878i	0.0428414	−	0.150572i
$364$	−0.695450	−	0.130002i	−0.0364515	−	0.00681396i
$365$	−36.5556			−1.91341
$366$	3.22239			0.168437
$367$	−9.48981	−	1.77395i	−0.495364	−	0.0925996i	−0.0698613	−	0.997557i	$-0.522256\pi$
$367$	−9.48981	−	1.77395i	−0.495364	−	0.0925996i	−0.425503	+	0.904957i	$0.639903\pi$
$368$	3.63225	−	4.80988i	0.189344	−	0.250732i
$369$	−0.634481	−	2.22997i	−0.0330298	−	0.116088i
$370$	−3.28242	+	6.59200i	−0.170645	+	0.342702i
$371$	0.510006	+	0.315782i	0.0264782	+	0.0163946i
$372$	−0.723137	+	7.80389i	−0.0374929	+	0.404613i
$373$	3.08150	+	10.8303i	0.159554	+	0.560773i	0.999827	+	0.0186099i	$0.00592405\pi$
$373$	3.08150	+	10.8303i	0.159554	+	0.560773i	−0.840273	+	0.542163i	$0.817605\pi$
$374$	−14.2523	−	5.52138i	−0.736970	−	0.285504i
$375$	−1.77317	+	6.23206i	−0.0915664	+	0.321822i
$376$	6.86259	−	9.08754i	0.353911	−	0.468654i
$377$	−3.52751	−	1.36657i	−0.181676	−	0.0703817i
$378$	−0.110257	+	0.0427137i	−0.00567100	+	0.00219696i
$379$	16.5736	+	33.2842i	0.851326	+	1.70969i	0.691284	+	0.722583i	$0.257045\pi$
$379$	16.5736	+	33.2842i	0.851326	+	1.70969i	0.160042	+	0.987110i	$0.448837\pi$
$380$	−18.9387	−	11.7264i	−0.971535	−	0.601549i
$381$	−8.50858	+	1.59053i	−0.435908	+	0.0814853i
$382$	−14.1768	−	8.77790i	−0.725348	−	0.449116i
$383$	21.6300	−	13.3927i	1.10524	−	0.684337i	0.152557	−	0.988295i	$-0.451249\pi$
$383$	21.6300	−	13.3927i	1.10524	−	0.684337i	0.952686	+	0.303957i	$0.0983080\pi$
$384$	−0.739009	+	0.673696i	−0.0377124	+	0.0343794i
$385$	−0.545408	−	1.09533i	−0.0277966	−	0.0558230i
$386$	−1.95227	+	21.0683i	−0.0993678	+	1.07235i
$387$	3.99912	−	8.03132i	0.203287	−	0.408255i
$388$	−9.25708	+	5.73174i	−0.469957	+	0.290985i
$389$	12.7067	−	11.5837i	0.644256	−	0.587317i	−0.284197	−	0.958766i	$-0.591727\pi$
$389$	12.7067	−	11.5837i	0.644256	−	0.587317i	0.928453	+	0.371449i	$0.121139\pi$
$390$	−1.52786	−	16.4883i	−0.0773664	−	0.834917i
$391$	6.74206	+	23.6959i	0.340961	+	1.19835i
$392$	4.21002	+	5.57496i	0.212638	+	0.281578i
$393$	−9.20964	+	3.56784i	−0.464565	+	0.179973i
$394$	0.731986	+	7.89938i	0.0368769	+	0.397965i
$395$	13.0204	−	26.1485i	0.655128	−	1.31567i
$396$	3.67567	−	0.687101i	0.184709	−	0.0345281i
$397$	−20.3153	+	3.79759i	−1.01960	+	0.190596i	−0.666904	−	0.745143i	$-0.732381\pi$
$397$	−20.3153	+	3.79759i	−1.01960	+	0.190596i	−0.352693	+	0.935739i	$0.614734\pi$
$398$	2.08863	−	22.5399i	0.104693	−	1.12982i
$399$	0.573544	+	0.759495i	0.0287131	+	0.0380223i
$400$	−0.727586	+	2.55720i	−0.0363793	+	0.127860i
$401$	−21.2509	−	19.3727i	−1.06122	−	0.967427i	−0.0616872	−	0.998096i	$-0.519648\pi$
$401$	−21.2509	−	19.3727i	−1.06122	−	0.967427i	−0.999530	+	0.0306686i	$0.990236\pi$
$402$	8.58397	+	1.60462i	0.428129	+	0.0800313i
$403$	34.6555	+	31.5926i	1.72631	+	1.57374i
$404$	−5.67450	+	7.51425i	−0.282317	+	0.373848i
$405$	−1.66775	−	2.20846i	−0.0828713	−	0.109739i
$406$	−0.0333217	−	0.0669190i	−0.00165373	−	0.00332114i
$407$	−8.45983	+	5.23811i	−0.419338	+	0.259643i
$408$	−0.377144	−	4.07004i	−0.0186714	−	0.201497i
$409$	−5.50640	−	2.13319i	−0.272274	−	0.105480i	0.221234	−	0.975221i	$-0.428992\pi$
$409$	−5.50640	−	2.13319i	−0.272274	−	0.105480i	−0.493508	+	0.869741i	$0.664286\pi$
$410$	4.74165	+	4.32259i	0.234174	+	0.213477i
$411$	14.6910			0.724655
$412$	10.0584	+	1.35196i	0.495544	+	0.0666063i
$413$	0.0990488			0.00487387
$414$	−4.45422	−	4.06055i	−0.218913	−	0.199565i
$415$	18.9674	+	7.34800i	0.931072	+	0.360699i
$416$	0.552087	+	5.95797i	0.0270683	+	0.292113i
$417$	−10.7602	+	6.66245i	−0.526931	+	0.326262i
$418$	−13.4158	−	26.9426i	−0.656190	−	1.31781i
$419$	−8.70310	−	11.5248i	−0.425174	−	0.563022i	0.534128	−	0.845404i	$-0.320640\pi$
$419$	−8.70310	−	11.5248i	−0.425174	−	0.563022i	−0.959302	+	0.282382i	$0.908875\pi$
$420$	0.197197	−	0.261131i	0.00962224	−	0.0127419i
$421$	−17.8741	−	16.2944i	−0.871131	−	0.794141i	0.108678	−	0.994077i	$-0.465338\pi$
$421$	−17.8741	−	16.2944i	−0.871131	−	0.794141i	−0.979809	+	0.199936i	$0.935927\pi$
$422$	−25.1984	−	4.71041i	−1.22664	−	0.229299i
$423$	−8.41557	−	7.67181i	−0.409179	−	0.373016i
$424$	1.38833	−	4.87946i	0.0674231	−	0.236968i
$425$	−6.54904	−	8.67232i	−0.317675	−	0.420670i
$426$	0.527422	−	5.69179i	0.0255537	−	0.275768i
$427$	0.374532	−	0.0700122i	0.0181249	−	0.00338813i
$428$	−10.3370	+	1.93232i	−0.499657	+	0.0934020i
$429$	9.97308	−	20.0286i	0.481505	−	0.966992i
$430$	2.29094	+	24.7232i	0.110479	+	1.19226i
$431$	4.78065	−	1.85203i	0.230276	−	0.0892094i	−0.243339	−	0.969941i	$-0.578243\pi$
$431$	4.78065	−	1.85203i	0.230276	−	0.0892094i	0.473615	+	0.880732i	$0.342949\pi$
$432$	0.602635	+	0.798017i	0.0289943	+	0.0383946i
$433$	−2.38028	−	8.36581i	−0.114389	−	0.402035i	0.883391	−	0.468637i	$-0.155255\pi$
$433$	−2.38028	−	8.36581i	−0.114389	−	0.402035i	−0.997780	+	0.0666020i	$0.978784\pi$
$434$	0.0855047	+	0.922742i	0.00410436	+	0.0442931i
$435$	1.29302	−	1.17874i	0.0619955	−	0.0565164i
$436$	5.52322	−	3.41983i	0.264514	−	0.163780i
$437$	−21.6244	+	43.4277i	−1.03444	+	2.07743i
$438$	1.21879	−	13.1529i	0.0582362	−	0.628468i
$439$	11.7794	+	23.6563i	0.562202	+	1.12905i	0.975814	+	0.218601i	$0.0701492\pi$
$439$	11.7794	+	23.6563i	0.562202	+	1.12905i	−0.413612	+	0.910453i	$0.635733\pi$
$440$	−7.64754	+	6.97165i	−0.364582	+	0.332361i
$441$	5.93963	−	3.67767i	0.282840	−	0.175127i
$442$	−20.7941	−	12.8751i	−0.989073	−	0.612408i
$443$	−8.78422	+	1.64205i	−0.417351	+	0.0780164i	−0.388237	−	0.921560i	$-0.626916\pi$
$443$	−8.78422	+	1.64205i	−0.417351	+	0.0780164i	−0.0291141	+	0.999576i	$0.509269\pi$
$444$	−2.26239	−	1.40081i	−0.107368	−	0.0664796i
$445$	−6.36700	−	12.7867i	−0.301825	−	0.606146i
$446$	2.99120	−	1.15880i	0.141638	−	0.0548707i
$447$	−19.2891	−	7.47262i	−0.912341	−	0.353443i
$448$	−0.0712563	+	0.0943586i	−0.00336655	+	0.00445803i
$449$	3.76799	−	13.2431i	0.177823	−	0.624982i	−0.820736	−	0.571308i	$-0.806436\pi$
$449$	3.76799	−	13.2431i	0.177823	−	0.624982i	0.998559	−	0.0536739i	$-0.0170931\pi$
$450$	2.47916	+	0.960431i	0.116869	+	0.0452752i
$451$	2.37254	+	8.33861i	0.111719	+	0.392650i
$452$	1.27189	−	13.7259i	0.0598249	−	0.645613i
$453$	10.8586	+	6.72336i	0.510181	+	0.315891i
$454$	2.07944	−	4.17608i	0.0975929	−	0.195993i
$455$	−0.535818	−	1.88321i	−0.0251195	−	0.0882861i
$456$	4.85062	−	6.42326i	0.227151	−	0.300797i
$457$	3.37919	+	0.631680i	0.158072	+	0.0295487i	0.262190	−	0.965016i	$-0.415555\pi$
$457$	3.37919	+	0.631680i	0.158072	+	0.0295487i	−0.104119	+	0.994565i	$0.533202\pi$
$458$	10.3165			0.482059
$459$	−4.08747			−0.190787
$460$	16.3961	+	3.06496i	0.764472	+	0.142905i
$461$	8.63116	−	30.3354i	0.401993	−	1.41286i	−0.451741	−	0.892149i	$-0.649197\pi$
$461$	8.63116	−	30.3354i	0.401993	−	1.41286i	0.853734	−	0.520710i	$-0.174333\pi$
$462$	0.412287	−	0.159721i	0.0191813	−	0.00743089i
$463$	3.13353	−	2.85659i	0.145627	−	0.132757i	−0.597604	−	0.801792i	$-0.703880\pi$
$463$	3.13353	−	2.85659i	0.145627	−	0.132757i	0.743231	+	0.669035i	$0.233292\pi$
$464$	−0.467227	+	0.425933i	−0.0216905	+	0.0197735i
$465$	−20.2246	+	7.83507i	−0.937895	+	0.363343i
$466$	0.959707	−	3.37302i	0.0444576	−	0.156252i
$467$	−13.3179	−	2.48955i	−0.616279	−	0.115202i	−0.133651	−	0.991028i	$-0.542670\pi$
$467$	−13.3179	−	2.48955i	−0.616279	−	0.115202i	−0.482627	+	0.875826i	$0.660317\pi$
$468$	5.98349			0.276587
$469$	1.03256			0.0476793
$470$	30.9780	+	5.79079i	1.42891	+	0.267109i
$471$	−9.75807	+	12.9218i	−0.449628	+	0.595404i
$472$	−0.229243	−	0.805705i	−0.0105518	−	0.0370856i
$473$	−14.9541	+	30.0318i	−0.687588	+	1.38086i
$474$	8.97423	+	5.55661i	0.412200	+	0.255223i
$475$	1.97453	−	21.3086i	0.0905978	−	0.977706i
$476$	−0.132264	−	0.464858i	−0.00606229	−	0.0213067i
$477$	−4.73055	−	1.83263i	−0.216597	−	0.0839102i
$478$	3.07422	−	10.8048i	0.140612	−	0.494198i
$479$	12.7108	−	16.8318i	0.580771	−	0.769066i	−0.408875	−	0.912590i	$-0.634079\pi$
$479$	12.7108	−	16.8318i	0.580771	−	0.769066i	0.989647	+	0.143525i	$0.0458436\pi$
$480$	−2.58056	−	0.999713i	−0.117786	−	0.0456304i
$481$	−14.8466	+	5.75162i	−0.676948	+	0.262251i
$482$	7.94609	+	15.9579i	0.361935	+	0.726863i
$483$	−0.605928	−	0.375175i	−0.0275707	−	0.0170710i
$484$	−2.93186	+	0.548059i	−0.133266	+	0.0249118i
$485$	−25.6184	−	15.8622i	−1.16327	−	0.720266i
$486$	0.850217	−	0.526432i	0.0385666	−	0.0238794i
$487$	−21.7729	+	19.8486i	−0.986623	+	0.899426i	−0.994933	−	0.100540i	$-0.967943\pi$
$487$	−21.7729	+	19.8486i	−0.986623	+	0.899426i	0.00830990	+	0.999965i	$0.497355\pi$
$488$	−1.43634	−	2.88456i	−0.0650202	−	0.130578i
$489$	−1.87099	+	20.1912i	−0.0846090	+	0.913077i
$490$	−8.61762	+	17.3065i	−0.389304	+	0.781828i
$491$	1.28236	−	0.794004i	0.0578721	−	0.0358329i	−0.497191	−	0.867641i	$-0.665635\pi$
$491$	1.28236	−	0.794004i	0.0578721	−	0.0358329i	0.555063	+	0.831808i	$0.312694\pi$
$492$	−1.71338	+	1.56195i	−0.0772449	+	0.0704180i
$493$	−0.238444	−	2.57322i	−0.0107390	−	0.115892i
$494$	−13.1800	−	46.3227i	−0.592994	−	2.08416i
$495$	6.23629	+	8.25818i	0.280300	+	0.371178i
$496$	7.30808	−	2.83117i	0.328143	−	0.127123i
$497$	−0.0623631	−	0.673005i	−0.00279737	−	0.0301884i
$498$	−3.27623	+	6.57955i	−0.146811	+	0.294837i
$499$	19.5646	−	3.65726i	0.875834	−	0.163722i	0.273409	−	0.961898i	$-0.411849\pi$
$499$	19.5646	−	3.65726i	0.875834	−	0.163722i	0.602424	+	0.798176i	$0.294202\pi$
$500$	6.36909	−	1.19059i	0.284834	−	0.0532447i
$501$	0.266657	−	2.87769i	0.0119134	−	0.128566i
$502$	3.12291	+	4.13540i	0.139382	+	0.184572i
$503$	5.14657	−	18.0883i	0.229474	−	0.806518i	−0.758470	−	0.651708i	$-0.774053\pi$
$503$	5.14657	−	18.0883i	0.229474	−	0.806518i	0.987944	−	0.154810i	$-0.0494765\pi$
$504$	0.0873814	+	0.0796587i	0.00389228	+	0.00354828i
$505$	−25.6149	−	4.78825i	−1.13985	−	0.213074i
$506$	16.6558	+	15.1838i	0.740441	+	0.675002i
$507$	13.7414	−	18.1965i	0.610276	−	0.808136i
$508$	5.21638	+	6.90761i	0.231440	+	0.306476i
$509$	7.12953	+	14.3180i	0.316011	+	0.634635i	0.995040	−	0.0994760i	$-0.0317167\pi$
$509$	7.12953	+	14.3180i	0.316011	+	0.634635i	−0.679029	+	0.734111i	$0.737599\pi$
$510$	9.61750	−	5.95490i	0.425870	−	0.263688i
$511$	−0.144112	−	1.55521i	−0.00637513	−	0.0687986i
$512$	0.932472	+	0.361242i	0.0412098	+	0.0159648i
$513$	−5.94830	−	5.42259i	−0.262624	−	0.239413i
$514$	18.0996			0.798337
$515$	9.05839	+	26.5855i	0.399160	+	1.17150i
$516$	−8.97190			−0.394966
$517$	31.4687	+	28.6875i	1.38399	+	1.26167i
$518$	−0.293388	−	0.113659i	−0.0128907	−	0.00499390i
$519$	0.446651	+	4.82014i	0.0196058	+	0.211580i
$520$	−14.0787	+	8.71715i	−0.617391	+	0.382272i
$521$	−1.21869	−	2.44746i	−0.0533918	−	0.107225i	0.866860	−	0.498551i	$-0.166134\pi$
$521$	−1.21869	−	2.44746i	−0.0533918	−	0.107225i	−0.920252	+	0.391326i	$0.872017\pi$
$522$	0.381006	+	0.504534i	0.0166762	+	0.0220828i
$523$	2.64370	−	3.50082i	0.115601	−	0.153080i	−0.736538	−	0.676396i	$-0.763541\pi$
$523$	2.64370	−	3.50082i	0.115601	−	0.153080i	0.852139	+	0.523316i	$0.175305\pi$
$524$	7.29889	+	6.65381i	0.318853	+	0.290673i
$525$	0.309015	+	0.0577649i	0.0134865	+	0.00252107i
$526$	−4.84471	−	4.41653i	−0.211239	−	0.192570i
$527$	−8.76675	+	30.8119i	−0.381886	+	1.34219i
$528$	−2.25345	−	2.98406i	−0.0980690	−	0.129864i
$529$	1.22977	−	13.2713i	0.0534681	−	0.577013i
$530$	13.8005	−	2.57976i	0.599455	−	0.112058i
$531$	−0.823420	+	0.153924i	−0.0357334	+	0.00667973i
$532$	0.424221	−	0.851952i	0.0183923	−	0.0369368i
$533$	1.28000	+	13.8134i	0.0554430	+	0.598325i
$534$	4.81297	−	1.86455i	0.208278	−	0.0806872i
$535$	−17.5381	−	23.2242i	−0.758240	−	1.00407i
$536$	−2.38981	−	8.39929i	−0.103224	−	0.362794i
$537$	−0.549317	−	5.92807i	−0.0237048	−	0.255815i
$538$	6.04043	−	5.50658i	0.260421	−	0.237405i
$539$	−22.2103	+	13.7520i	−0.956665	+	0.592342i
$540$	−1.23355	+	2.47731i	−0.0530836	+	0.106606i
$541$	−2.04722	+	22.0931i	−0.0880170	+	0.949855i	0.831166	+	0.556024i	$0.187674\pi$
$541$	−2.04722	+	22.0931i	−0.0880170	+	0.949855i	−0.919183	+	0.393831i	$0.871150\pi$
$542$	7.97325	+	16.0124i	0.342480	+	0.687793i
$543$	0.476174	−	0.434090i	0.0204346	−	0.0186286i
$544$	−3.47524	+	2.15178i	−0.149000	+	0.0922567i
$545$	15.2851	+	9.46416i	0.654743	+	0.405400i
$546$	0.695450	−	0.130002i	0.0297625	−	0.00556358i
$547$	−19.4347	−	12.0335i	−0.830969	−	0.514514i	0.0438082	−	0.999040i	$-0.486051\pi$
$547$	−19.4347	−	12.0335i	−0.830969	−	0.514514i	−0.874777	+	0.484526i	$0.838992\pi$
$548$	−6.54836	−	13.1509i	−0.279732	−	0.561777i
$549$	−3.00479	+	1.16406i	−0.128241	+	0.0496809i
$550$	−9.27041	−	3.59138i	−0.395292	−	0.153137i
$551$	3.06673	−	4.06101i	0.130647	−	0.173005i
$552$	−1.64944	+	5.79720i	−0.0702050	+	0.246745i
$553$	1.16378	+	0.450853i	0.0494892	+	0.0191722i
$554$	−0.732370	−	2.57402i	−0.0311154	−	0.109359i
$555$	0.679466	−	7.33260i	0.0288417	−	0.311252i
$556$	10.7602	+	6.66245i	0.456335	+	0.282551i
$557$	7.12204	−	14.3030i	0.301771	−	0.606037i	−0.691431	−	0.722442i	$-0.743020\pi$
$557$	7.12204	−	14.3030i	0.301771	−	0.606037i	0.993202	+	0.116405i	$0.0371372\pi$
$558$	−2.14478	−	7.53814i	−0.0907960	−	0.319115i
$559$	−32.3514	+	42.8402i	−1.36832	+	1.81195i
$560$	−0.321654	−	0.0601275i	−0.0135923	−	0.00254085i
$561$	15.2844			0.645310
$562$	19.0245			0.802498
$563$	28.4648	+	5.32099i	1.19965	+	0.224253i	0.745397	−	0.666621i	$-0.232260\pi$
$563$	28.4648	+	5.32099i	1.19965	+	0.224253i	0.454250	+	0.890874i	$0.349907\pi$
$564$	−3.11638	+	10.9529i	−0.131223	+	0.461202i
$565$	35.5723	−	13.7808i	1.49654	−	0.579761i
$566$	−12.1156	+	11.0448i	−0.509255	+	0.464248i
$567$	0.0873814	−	0.0796587i	0.00366967	−	0.00334535i
$568$	−5.33017	+	2.06492i	−0.223649	+	0.0866421i
$569$	4.16211	−	14.6283i	0.174485	−	0.613250i	−0.824399	−	0.566009i	$-0.808487\pi$
$569$	4.16211	−	14.6283i	0.174485	−	0.613250i	0.998884	−	0.0472409i	$-0.0150428\pi$
$570$	21.8959	+	4.09305i	0.917117	+	0.171439i
$571$	13.2776			0.555649			0.277825	−	0.960632i	$-0.410387\pi$
$571$	13.2776			0.555649			0.277825	+	0.960632i	$0.410387\pi$
$572$	−22.3743			−0.935516
$573$	16.3904	+	3.06390i	0.684719	+	0.127996i
$574$	−0.165206	+	0.218768i	−0.00689557	+	0.00913121i
$575$	4.38537	+	15.4130i	0.182883	+	0.642765i
$576$	0.445738	−	0.895163i	0.0185724	−	0.0372985i
$577$	−6.93501	−	4.29398i	−0.288708	−	0.178761i	0.374435	−	0.927253i	$-0.377837\pi$
$577$	−6.93501	−	4.29398i	−0.288708	−	0.178761i	−0.663143	+	0.748493i	$0.730778\pi$
$578$	−0.0269946	+	0.291319i	−0.00112283	+	0.0121173i
$579$	−5.79032	−	20.3509i	−0.240637	−	0.845753i
$580$	−1.63152	−	0.632053i	−0.0677450	−	0.0262446i
$581$	−0.237837	+	0.835911i	−0.00986715	+	0.0346794i
$582$	6.56143	−	8.68873i	0.271980	−	0.360160i
$583$	17.6891	+	6.85280i	0.732609	+	0.283814i
$584$	−12.3172	+	4.77172i	−0.509690	+	0.197455i
$585$	7.38095	+	14.8229i	0.305165	+	0.612853i
$586$	−15.3243	−	9.48840i	−0.633041	−	0.391962i
$587$	−17.5340	+	3.27768i	−0.723707	+	0.135284i	−0.532700	−	0.846304i	$-0.678822\pi$
$587$	−17.5340	+	3.27768i	−0.723707	+	0.135284i	−0.191007	+	0.981589i	$0.561175\pi$
$588$	−5.93963	−	3.67767i	−0.244946	−	0.151664i
$589$	−53.6341	+	33.2088i	−2.20995	+	1.36835i
$590$	1.71319	−	1.56178i	0.0705311	−	0.0642976i
$591$	−3.53614	−	7.10153i	−0.145457	−	0.292118i
$592$	−0.245522	+	2.64960i	−0.0100909	+	0.108898i
$593$	−12.9765	+	26.0602i	−0.532879	+	1.07017i	0.451198	+	0.892424i	$0.350997\pi$
$593$	−12.9765	+	26.0602i	−0.532879	+	1.07017i	−0.984077	+	0.177742i	$0.943121\pi$
$594$	−3.17925	+	1.96851i	−0.130446	+	0.0807688i
$595$	0.988442	−	0.901084i	0.0405222	−	0.0369409i
$596$	1.90866	+	20.5977i	0.0781817	+	0.843714i
$597$	6.19475	+	21.7723i	0.253534	+	0.891081i
$598$	21.7335	+	28.7799i	0.888750	+	1.17690i
$599$	2.10957	−	0.817252i	0.0861947	−	0.0333920i	−0.317758	−	0.948172i	$-0.602930\pi$
$599$	2.10957	−	0.817252i	0.0861947	−	0.0333920i	0.403953	+	0.914780i	$0.367636\pi$
$600$	−0.245313	−	2.64735i	−0.0100149	−	0.108078i
$601$	−3.56597	+	7.16144i	−0.145459	+	0.292121i	−0.955896	−	0.293704i	$-0.905112\pi$
$601$	−3.56597	+	7.16144i	−0.145459	+	0.292121i	0.810437	+	0.585825i	$0.199230\pi$
$602$	−1.04279	+	0.194931i	−0.0425008	+	0.00794478i
$603$	−8.58397	+	1.60462i	−0.349566	+	0.0653452i
$604$	1.17841	−	12.7171i	0.0479489	−	0.517451i
$605$	−4.97431	−	6.58705i	−0.202234	−	0.267802i
$606$	2.57685	−	9.05669i	0.104677	−	0.367903i
$607$	13.3307	+	12.1525i	0.541075	+	0.493255i	0.897467	−	0.441082i	$-0.145405\pi$
$607$	13.3307	+	12.1525i	0.541075	+	0.493255i	−0.356392	+	0.934336i	$0.615993\pi$
$608$	−7.91197	−	1.47900i	−0.320873	−	0.0599815i
$609$	0.0552455	+	0.0503630i	0.00223866	+	0.00204081i
$610$	5.37415	−	7.11652i	0.217593	−	0.288139i
$611$	41.0623	+	54.3752i	1.66120	+	2.19979i
$612$	1.82194	+	3.65896i	0.0736477	+	0.147905i
$613$	−31.0913	+	19.2509i	−1.25577	+	0.777538i	−0.982833	−	0.184495i	$-0.940935\pi$
$613$	−31.0913	+	19.2509i	−1.25577	+	0.777538i	−0.272933	+	0.962033i	$0.587994\pi$
$614$	−3.11845	−	33.6535i	−0.125851	−	1.35814i
$615$	−5.98296	−	2.31781i	−0.241256	−	0.0934632i
$616$	−0.326749	−	0.297871i	−0.0131651	−	0.0120016i
$617$	−20.9484			−0.843353			−0.421676	−	0.906746i	$-0.638558\pi$
$617$	−20.9484			−0.843353			−0.421676	+	0.906746i	$0.638558\pi$
$618$	−9.86760	+	2.37286i	−0.396933	+	0.0954505i
$619$	15.7599			0.633445			0.316723	−	0.948518i	$-0.397418\pi$
$619$	15.7599			0.633445			0.316723	+	0.948518i	$0.397418\pi$
$620$	16.0286	+	14.6120i	0.643723	+	0.586831i
$621$	5.62027	+	2.17731i	0.225534	+	0.0873723i
$622$	2.35703	+	25.4364i	0.0945083	+	1.01991i
$623$	0.518892	−	0.321284i	0.0207890	−	0.0128720i
$624$	−2.66707	−	5.35620i	−0.106768	−	0.214420i
$625$	18.8172	+	24.9179i	0.752686	+	0.996718i
$626$	−12.6513	+	16.7531i	−0.505649	+	0.669587i
$627$	22.2427	+	20.2769i	0.888288	+	0.809782i
$628$	15.9166	+	2.97534i	0.635143	+	0.118729i
$629$	−8.03789	−	7.32750i	−0.320492	−	0.292167i
$630$	−0.0895494	+	0.314734i	−0.00356773	+	0.0125393i
$631$	18.0934	+	23.9595i	0.720286	+	0.953813i	0.999980	−	0.00627638i	$-0.00199785\pi$
$631$	18.0934	+	23.9595i	0.720286	+	0.953813i	−0.279694	+	0.960089i	$0.590233\pi$
$632$	0.973913	−	10.5102i	0.0387402	−	0.418073i
$633$	25.1984	−	4.71041i	1.00155	−	0.187222i
$634$	30.0911	−	5.62501i	1.19507	−	0.223398i
$635$	−10.6776	+	21.4435i	−0.423727	+	0.850958i
$636$	0.468089	+	5.05149i	0.0185609	+	0.200305i
$637$	−38.9781	+	15.1002i	−1.54437	+	0.598291i
$638$	−1.42471	−	1.88662i	−0.0564048	−	0.0746921i
$639$	1.56430	+	5.49796i	0.0618829	+	0.217496i
$640$	0.255347	+	2.75563i	0.0100935	+	0.108926i
$641$	3.98281	−	3.63081i	0.157311	−	0.143408i	−0.591213	−	0.806515i	$-0.701351\pi$
$641$	3.98281	−	3.63081i	0.157311	−	0.143408i	0.748525	+	0.663107i	$0.230763\pi$
$642$	8.94091	−	5.53598i	0.352870	−	0.218488i
$643$	−3.62729	+	7.28458i	−0.143046	+	0.287276i	−0.955087	−	0.296325i	$-0.904239\pi$
$643$	−3.62729	+	7.28458i	−0.143046	+	0.287276i	0.812041	+	0.583600i	$0.198357\pi$
$644$	−0.0657573	+	0.709634i	−0.00259120	+	0.0279635i
$645$	−11.0673	−	22.2261i	−0.435775	−	0.875154i
$646$	24.3135	−	22.1647i	0.956603	−	0.872058i
$647$	13.6762	−	8.46796i	0.537668	−	0.332910i	−0.230589	−	0.973051i	$-0.574065\pi$
$647$	13.6762	−	8.46796i	0.537668	−	0.332910i	0.768257	+	0.640141i	$0.221124\pi$
$648$	−0.850217	−	0.526432i	−0.0333997	−	0.0206802i
$649$	3.07904	−	0.575573i	0.120863	−	0.0225932i
$650$	−13.5255	−	8.37463i	−0.530513	−	0.328480i
$651$	−0.413064	−	0.829544i	−0.0161892	−	0.0325124i
$652$	18.9084	−	7.32514i	0.740509	−	0.286875i
$653$	5.93406	+	2.29887i	0.232218	+	0.0899616i	0.474539	−	0.880234i	$-0.342615\pi$
$653$	5.93406	+	2.29887i	0.232218	+	0.0899616i	−0.242322	+	0.970196i	$0.577909\pi$
$654$	−3.91486	+	5.18411i	−0.153083	+	0.202715i
$655$	−7.47998	+	26.2894i	−0.292267	+	1.02721i
$656$	2.16192	+	0.837530i	0.0844086	+	0.0327001i
$657$	3.61487	+	12.7050i	0.141030	+	0.495668i
$658$	−0.124239	+	1.34075i	−0.00484332	+	0.0522678i
$659$	29.7480	+	18.4192i	1.15882	+	0.717509i	0.964669	−	0.263464i	$-0.0848649\pi$
$659$	29.7480	+	18.4192i	1.15882	+	0.717509i	0.194147	+	0.980972i	$0.437806\pi$
$660$	4.61267	−	9.26348i	0.179548	−	0.360581i
$661$	−0.0715863	−	0.251600i	−0.00278439	−	0.00978610i	0.960421	−	0.278552i	$-0.0898546\pi$
$661$	−0.0715863	−	0.251600i	−0.00278439	−	0.00978610i	−0.963205	+	0.268766i	$0.913384\pi$
$662$	−6.49132	+	8.59590i	−0.252292	+	0.334089i
$663$	24.0409	+	4.49403i	0.933672	+	0.174534i
$664$	7.35012			0.285240
$665$	2.63384			0.102136
$666$	2.61565	+	0.488949i	0.101354	+	0.0189464i
$667$	−1.04284	+	3.66519i	−0.0403787	+	0.141917i
$668$	−2.69486	+	1.04400i	−0.104267	+	0.0403934i
$669$	−2.37061	+	2.16109i	−0.0916530	+	0.0835527i
$670$	17.8597	−	16.2812i	0.689979	−	0.628999i
$671$	11.2359	−	4.35282i	0.433758	−	0.168039i
$672$	0.0323583	−	0.113728i	0.00124825	−	0.00438714i
$673$	30.0983	+	5.62635i	1.16020	+	0.216880i	0.728442	−	0.685108i	$-0.240245\pi$
$673$	30.0983	+	5.62635i	1.16020	+	0.216880i	0.431762	+	0.901988i	$0.357892\pi$
$674$	12.8524			0.495057
$675$	−2.65869			−0.102333
$676$	−22.4139	−	4.18989i	−0.862074	−	0.161150i
$677$	−6.90674	+	9.14600i	−0.265448	+	0.351509i	−0.911146	−	0.412083i	$-0.864801\pi$
$677$	−6.90674	+	9.14600i	−0.265448	+	0.351509i	0.645699	+	0.763592i	$0.276566\pi$
$678$	3.77237	+	13.2585i	0.144877	+	0.509190i
$679$	0.573844	−	1.15243i	0.0220221	−	0.0442263i
$680$	−9.61750	−	5.95490i	−0.368814	−	0.228360i
$681$	−0.430446	+	4.64525i	−0.0164947	+	0.178007i
$682$	8.02007	+	28.1876i	0.307104	+	1.07936i
$683$	−9.16459	−	3.55038i	−0.350673	−	0.135852i	0.179461	−	0.983765i	$-0.442565\pi$
$683$	−9.16459	−	3.55038i	−0.350673	−	0.135852i	−0.530135	+	0.847913i	$0.677859\pi$
$684$	−2.20272	+	7.74176i	−0.0842231	+	0.296014i
$685$	24.5010	−	32.4446i	0.936135	−	1.23964i
$686$	−1.54205	−	0.597395i	−0.0588759	−	0.0228086i
$687$	−9.61985	+	3.72675i	−0.367020	+	0.142184i
$688$	3.99912	+	8.03132i	0.152465	+	0.306191i
$689$	25.8084	+	15.9799i	0.983220	+	0.608784i
$690$	−16.3961	+	3.06496i	−0.624189	+	0.116681i
$691$	−10.2848	−	6.36807i	−0.391252	−	0.242253i	0.316682	−	0.948532i	$-0.397431\pi$
$691$	−10.2848	−	6.36807i	−0.391252	−	0.242253i	−0.707934	+	0.706279i	$0.750372\pi$
$692$	4.11572	−	2.54835i	0.156456	−	0.0968736i
$693$	−0.326749	+	0.297871i	−0.0124122	+	0.0113152i
$694$	−12.5766	−	25.2572i	−0.477400	−	0.958749i
$695$	−3.23163	+	34.8749i	−0.122583	+	1.32288i
$696$	0.281811	−	0.565953i	0.0106820	−	0.0214524i
$697$	−8.05726	+	4.98885i	−0.305191	+	0.188966i
$698$	−19.4317	+	17.7143i	−0.735499	+	0.670496i
$699$	0.323575	+	3.49193i	0.0122387	+	0.132077i
$700$	−0.0860308	−	0.302367i	−0.00325166	−	0.0114284i
$701$	−22.8608	−	30.2726i	−0.863442	−	1.14338i	−0.988498	−	0.151232i	$-0.951676\pi$
$701$	−22.8608	−	30.2726i	−0.863442	−	1.14338i	0.125057	−	0.992150i	$-0.460089\pi$
$702$	−5.57944	+	2.16149i	−0.210582	+	0.0815800i
$703$	−1.97621	−	21.3267i	−0.0745342	−	0.804352i
$704$	−1.66677	+	3.34732i	−0.0628186	+	0.126157i
$705$	−30.9780	+	5.79079i	−1.16670	+	0.218094i
$706$	14.1621	−	2.64735i	0.532997	−	0.0996343i
$707$	0.102730	−	1.10863i	0.00386354	−	0.0416943i
$708$	0.504817	+	0.668485i	0.0189722	+	0.0251232i
$709$	0.187739	−	0.659833i	0.00705067	−	0.0247805i	−0.958220	−	0.286031i	$-0.907664\pi$
$709$	0.187739	−	0.659833i	0.00705067	−	0.0247805i	0.965271	+	0.261250i	$0.0841347\pi$
$710$	−11.6905	−	10.6573i	−0.438736	−	0.399960i
$711$	−10.3755	−	1.93952i	−0.389112	−	0.0727376i
$712$	−3.81441	−	3.47729i	−0.142951	−	0.130317i
$713$	28.4671	−	37.6965i	1.06610	−	1.41175i
$714$	0.291258	+	0.385688i	0.0109001	+	0.0144340i
$715$	−27.5998	−	55.4280i	−1.03218	−	2.07289i
$716$	−5.06174	+	3.13410i	−0.189166	+	0.117127i
$717$	1.03651	+	11.1857i	0.0387090	+	0.417737i
$718$	−25.9928	−	10.0697i	−0.970043	−	0.375797i
$719$	−6.60648	−	6.02260i	−0.246380	−	0.224605i	0.541079	−	0.840972i	$-0.318016\pi$
$719$	−6.60648	−	6.02260i	−0.246380	−	0.224605i	−0.787460	+	0.616366i	$0.788604\pi$
$720$	2.76743			0.103136
$721$	−1.09534	+	0.490184i	−0.0407925	+	0.0182554i
$722$	45.7868			1.70401
$723$	−13.1742	−	12.0098i	−0.489953	−	0.446651i
$724$	−0.600830	−	0.232763i	−0.0223297	−	0.00865056i
$725$	−0.155096	−	1.67375i	−0.00576010	−	0.0621614i
$726$	2.53589	−	1.57016i	0.0941159	−	0.0582741i
$727$	−17.3324	−	34.8082i	−0.642825	−	1.29097i	−0.941629	−	0.336652i	$-0.890706\pi$
$727$	−17.3324	−	34.8082i	−0.642825	−	1.29097i	0.298805	−	0.954314i	$-0.403412\pi$
$728$	−0.426362	−	0.564594i	−0.0158020	−	0.0209253i
$729$	−0.602635	+	0.798017i	−0.0223198	+	0.0295562i
$730$	−27.0149	−	24.6274i	−0.999868	−	0.911500i
$731$	−36.0480	−	6.73854i	−1.33328	−	0.249234i
$732$	2.38137	+	2.17091i	0.0880181	+	0.0802391i
$733$	8.23864	−	28.9558i	0.304301	−	1.06951i	−0.647316	−	0.762222i	$-0.724109\pi$
$733$	8.23864	−	28.9558i	0.304301	−	1.06951i	0.951617	−	0.307286i	$-0.0994208\pi$
$734$	−5.81795	−	7.70421i	−0.214744	−	0.284368i
$735$	1.78386	−	19.2509i	0.0657985	−	0.710079i
$736$	5.92466	−	1.10751i	0.218386	−	0.0408234i
$737$	32.0984	−	6.00022i	1.18236	−	0.221021i
$738$	1.03343	−	2.07542i	0.0380412	−	0.0763971i
$739$	−1.36484	−	14.7290i	−0.0502065	−	0.541814i	−0.983276	−	0.182119i	$-0.941704\pi$
$739$	−1.36484	−	14.7290i	−0.0502065	−	0.541814i	0.933070	−	0.359695i	$-0.117119\pi$
$740$	−6.86674	+	2.66019i	−0.252426	+	0.0977905i
$741$	29.0236	+	38.4335i	1.06621	+	1.41189i
$742$	0.164158	+	0.576955i	0.00602642	+	0.0211807i
$743$	0.262471	+	2.83252i	0.00962914	+	0.103915i	0.999192	−	0.0401852i	$-0.0127948\pi$
$743$	0.262471	+	2.83252i	0.00962914	+	0.103915i	−0.989563	+	0.144100i	$0.953971\pi$
$744$	−5.79185	+	5.27997i	−0.212340	+	0.193573i
$745$	−48.6724	+	30.1366i	−1.78322	+	1.10412i
$746$	−5.01909	+	10.0797i	−0.183762	+	0.369044i
$747$	0.678183	−	7.31876i	0.0248134	−	0.267780i
$748$	−6.81286	−	13.6821i	−0.249103	−	0.500266i
$749$	0.918906	−	0.837694i	0.0335761	−	0.0306087i
$750$	−5.50891	+	3.41097i	−0.201157	+	0.124551i
$751$	34.6401	+	21.4483i	1.26404	+	0.782658i	0.984144	−	0.177374i	$-0.0567601\pi$
$751$	34.6401	+	21.4483i	1.26404	+	0.782658i	0.279892	+	0.960031i	$0.409701\pi$
$752$	11.1938	−	2.09247i	0.408194	−	0.0763047i
$753$	−4.40591	−	2.72802i	−0.160560	−	0.0994147i
$754$	−1.68621	−	3.38637i	−0.0614083	−	0.123324i
$755$	32.9577	−	12.7679i	1.19945	−	0.464671i
$756$	−0.110257	−	0.0427137i	−0.00401000	−	0.00155348i
$757$	23.2954	−	30.8482i	0.846687	−	1.12120i	−0.144601	−	0.989490i	$-0.546190\pi$
$757$	23.2954	−	30.8482i	0.846687	−	1.12120i	0.991289	−	0.131705i	$-0.0420453\pi$
$758$	−10.1754	+	35.7628i	−0.369587	+	1.29896i
$759$	−21.0161	−	8.14168i	−0.762836	−	0.295524i
$760$	−6.09588	−	21.4248i	−0.221121	−	0.777159i
$761$	1.91104	−	20.6235i	0.0692753	−	0.747600i	−0.888271	−	0.459320i	$-0.848093\pi$
$761$	1.91104	−	20.6235i	0.0692753	−	0.747600i	0.957546	−	0.288280i	$-0.0930833\pi$
$762$	−7.35945	−	4.55678i	−0.266605	−	0.165075i
$763$	−0.342382	+	0.687597i	−0.0123951	+	0.0248927i
$764$	−4.56314	−	16.0378i	−0.165089	−	0.580227i
$765$	−6.81689	+	9.02702i	−0.246465	+	0.326373i
$766$	25.0074	+	4.67470i	0.903555	+	0.168904i
$767$	5.01227			0.180983
$768$	−1.00000			−0.0360844
$769$	−0.930865	−	0.174009i	−0.0335679	−	0.00627492i	0.166939	−	0.985967i	$-0.446612\pi$
$769$	−0.930865	−	0.174009i	−0.0335679	−	0.00627492i	−0.200507	+	0.979692i	$0.564259\pi$
$770$	0.334856	−	1.17690i	0.0120674	−	0.0424124i
$771$	−16.8773	+	6.53832i	−0.607822	+	0.235472i
$772$	−15.6364	+	14.2544i	−0.562766	+	0.513029i
$773$	39.6424	−	36.1389i	1.42584	−	1.29982i	0.535495	−	0.844539i	$-0.320125\pi$
$773$	39.6424	−	36.1389i	1.42584	−	1.29982i	0.890345	−	0.455286i	$-0.150463\pi$
$774$	8.36605	−	3.24102i	0.300711	−	0.116496i
$775$	−5.70233	+	20.0416i	−0.204834	+	0.719915i
$776$	−10.7025	−	2.00065i	−0.384198	−	0.0718190i
$777$	0.314635			0.0112875
$778$	17.1943			0.616444
$779$	−18.3437	−	3.42904i	−0.657232	−	0.122858i
$780$	9.97898	−	13.2143i	0.357305	−	0.473148i
$781$	−5.84946	−	20.5587i	−0.209310	−	0.735649i
$782$	−10.9814	+	22.0536i	−0.392693	+	0.788634i
$783$	−0.537536	−	0.332828i	−0.0192100	−	0.0118943i
$784$	−0.644589	+	6.95622i	−0.0230210	+	0.248436i
$785$	12.2632	+	43.1006i	0.437692	+	1.53833i
$786$	−9.20964	−	3.56784i	−0.328497	−	0.127260i
$787$	0.575757	−	2.02358i	0.0205235	−	0.0721328i	−0.950887	−	0.309537i	$-0.899826\pi$
$787$	0.575757	−	2.02358i	0.0205235	−	0.0721328i	0.971411	+	0.237404i	$0.0762966\pi$
$788$	−4.78084	+	6.33085i	−0.170310	+	0.225527i
$789$	6.11299	+	2.36819i	0.217628	+	0.0843096i
$790$	27.2383	−	10.5522i	0.969097	−	0.375430i
$791$	0.726520	+	1.45905i	0.0258321	+	0.0518778i
$792$	3.17925	+	1.96851i	0.112970	+	0.0699479i
$793$	18.9528	−	3.54290i	0.673035	−	0.125812i
$794$	−17.5716	−	10.8799i	−0.623594	−	0.386113i
$795$	−11.9367	+	7.39087i	−0.423350	+	0.262127i
$796$	16.7285	−	15.2501i	0.592927	−	0.540524i
$797$	−7.52737	−	15.1170i	−0.266633	−	0.535471i	0.720870	−	0.693070i	$-0.243742\pi$
$797$	−7.52737	−	15.1170i	−0.266633	−	0.535471i	−0.987503	+	0.157599i	$0.949625\pi$
$798$	−0.0878143	+	0.947668i	−0.00310859	+	0.0335471i
$799$	−20.7476	+	41.6669i	−0.733999	+	1.47407i
$800$	−2.26047	+	1.39962i	−0.0799196	+	0.0494841i
$801$	−3.81441	+	3.47729i	−0.134775	+	0.122864i
$802$	−2.65326	−	28.6332i	−0.0936898	−	1.01107i
$803$	−13.5172	−	47.5081i	−0.477013	−	1.67653i
$804$	5.26260	+	6.96881i	0.185598	+	0.245771i
$805$	−1.83910	+	0.712469i	−0.0648196	+	0.0251112i
$806$	4.32688	+	46.6945i	0.152408	+	1.64474i
$807$	−3.64332	+	7.31678i	−0.128251	+	0.257563i
$808$	−9.25582	+	1.73021i	−0.325619	+	0.0608687i
$809$	17.4546	−	3.26283i	0.613671	−	0.114715i	0.132268	−	0.991214i	$-0.457774\pi$
$809$	17.4546	−	3.26283i	0.613671	−	0.114715i	0.481404	+	0.876499i	$0.340127\pi$
$810$	0.255347	−	2.75563i	0.00897197	−	0.0968229i
$811$	−13.1886	−	17.4646i	−0.463115	−	0.613263i	0.505198	−	0.863004i	$-0.331420\pi$
$811$	−13.1886	−	17.4646i	−0.463115	−	0.613263i	−0.968313	+	0.249740i	$0.919655\pi$
$812$	0.0204580	−	0.0719025i	0.000717936	−	0.00252328i
$813$	−13.2192	−	12.0509i	−0.463617	−	0.422643i
$814$	−9.78078	−	1.82835i	−0.342816	−	0.0640835i
$815$	41.4711	+	37.8059i	1.45267	+	1.32428i
$816$	2.46325	−	3.26187i	0.0862311	−	0.114188i
$817$	−43.5193	−	57.6289i	−1.52255	−	2.01618i
$818$	−2.63216	−	5.28609i	−0.0920313	−	0.184824i
$819$	−0.601525	+	0.372449i	−0.0210190	+	0.0130144i
$820$	0.592015	+	6.38886i	0.0206741	+	0.223109i
$821$	49.4400	+	19.1531i	1.72547	+	0.668449i	0.999808	−	0.0196055i	$-0.00624104\pi$
$821$	49.4400	+	19.1531i	1.72547	+	0.668449i	0.725659	+	0.688055i	$0.241535\pi$
$822$	10.8568	+	9.89728i	0.378675	+	0.345207i
$823$	6.86409			0.239267			0.119634	−	0.992818i	$-0.461828\pi$
$823$	6.86409			0.239267			0.119634	+	0.992818i	$0.461828\pi$
$824$	6.52247	+	7.77544i	0.227221	+	0.270870i
$825$	9.94175			0.346127
$826$	0.0731979	+	0.0667287i	0.00254688	+	0.00232179i
$827$	−8.68337	−	3.36396i	−0.301950	−	0.116976i	0.205500	−	0.978657i	$-0.434118\pi$
$827$	−8.68337	−	3.36396i	−0.301950	−	0.116976i	−0.507451	+	0.861681i	$0.669412\pi$
$828$	−0.556128	−	6.00157i	−0.0193268	−	0.208569i
$829$	−23.0138	+	14.2496i	−0.799303	+	0.494908i	−0.864299	−	0.502978i	$-0.832238\pi$
$829$	−23.0138	+	14.2496i	−0.799303	+	0.494908i	0.0649959	+	0.997886i	$0.479297\pi$
$830$	9.06675	+	18.2085i	0.314711	+	0.632026i
$831$	1.61276	+	2.13563i	0.0559459	+	0.0740844i
$832$	−3.60586	+	4.77493i	−0.125011	+	0.165541i
$833$	−21.1025	−	19.2375i	−0.731159	−	0.666539i
$834$	−12.4404	−	2.32551i	−0.430775	−	0.0805258i
$835$	−5.91055	−	5.38818i	−0.204543	−	0.186466i
$836$	8.23671	−	28.9490i	0.284873	−	1.00122i
$837$	4.72304	+	6.25432i	0.163252	+	0.216181i
$838$	1.33252	−	14.3802i	0.0460310	−	0.496754i
$839$	−1.74134	+	0.325513i	−0.0601177	+	0.0112379i	−0.213722	−	0.976894i	$-0.568559\pi$
$839$	−1.74134	+	0.325513i	−0.0601177	+	0.0112379i	0.153605	+	0.988132i	$0.450912\pi$
$840$	0.321654	−	0.0601275i	0.0110981	−	0.00207460i
$841$	−12.7482	+	25.6019i	−0.439595	+	0.882825i
$842$	−2.23166	−	24.0834i	−0.0769080	−	0.829970i
$843$	−17.7398	+	6.87243i	−0.610990	+	0.236699i
$844$	−15.4485	−	20.4571i	−0.531759	−	0.704163i
$845$	−17.2691	−	60.6946i	−0.594075	−	2.08796i
$846$	−1.05072	−	11.3391i	−0.0361245	−	0.389845i
$847$	0.260628	−	0.237593i	0.00895527	−	0.00816381i
$848$	4.31326	−	2.67066i	0.148118	−	0.0917108i
$849$	7.30759	−	14.6756i	0.250796	−	0.503666i
$850$	1.00271	−	10.8210i	0.0343927	−	0.371157i
$851$	7.14890	+	14.3569i	0.245061	+	0.492149i
$852$	4.22430	−	3.85096i	0.144722	−	0.131932i
$853$	15.2007	−	9.41190i	0.520463	−	0.322257i	−0.240935	−	0.970541i	$-0.577454\pi$
$853$	15.2007	−	9.41190i	0.520463	−	0.322257i	0.761399	+	0.648284i	$0.224513\pi$
$854$	0.323949	+	0.200581i	0.0110853	+	0.00686374i
$855$	−21.8959	+	4.09305i	−0.748823	+	0.139979i
$856$	−8.94091	−	5.53598i	−0.305594	−	0.189216i
$857$	−2.91481	−	5.85372i	−0.0995679	−	0.199959i	0.839779	−	0.542929i	$-0.182685\pi$
$857$	−2.91481	−	5.85372i	−0.0995679	−	0.199959i	−0.939346	+	0.342970i	$0.888567\pi$
$858$	20.8634	−	8.08253i	0.712265	−	0.275933i
$859$	−25.3281	−	9.81215i	−0.864183	−	0.334786i	−0.111974	−	0.993711i	$-0.535717\pi$
$859$	−25.3281	−	9.81215i	−0.864183	−	0.334786i	−0.752209	+	0.658925i	$0.771012\pi$
$860$	−14.9629	+	19.8141i	−0.510231	+	0.675655i
$861$	0.0750219	−	0.263675i	0.00255674	−	0.00898601i
$862$	4.78065	+	1.85203i	0.162830	+	0.0630805i
$863$	13.0967	+	46.0301i	0.445817	+	1.56688i	0.780876	+	0.624687i	$0.214773\pi$
$863$	13.0967	+	46.0301i	0.445817	+	1.56688i	−0.335059	+	0.942197i	$0.608756\pi$
$864$	−0.0922684	+	0.995734i	−0.00313903	+	0.0338756i
$865$	11.3900	+	7.05238i	0.387271	+	0.239788i
$866$	3.87696	−	7.78599i	0.131745	−	0.264579i
$867$	−0.0800647	−	0.281398i	−0.00271914	−	0.00955678i
$868$	−0.558459	+	0.739519i	−0.0189553	+	0.0251009i
$869$	38.7975	+	7.25251i	1.31611	+	0.246024i
$870$	1.74967			0.0593193
$871$	52.2518			1.77048
$872$	6.38563	+	1.19368i	0.216245	+	0.0404231i
$873$	−2.97962	+	10.4723i	−0.100845	+	0.354432i
$874$	−45.2377	+	17.5252i	−1.53019	+	0.592798i
$875$	−0.566180	+	0.516141i	−0.0191404	+	0.0174488i
$876$	9.76173	−	8.89899i	0.329818	−	0.300669i
$877$	18.3177	−	7.09630i	0.618544	−	0.239625i	−0.0315221	−	0.999503i	$-0.510035\pi$
$877$	18.3177	−	7.09630i	0.618544	−	0.239625i	0.650066	+	0.759878i	$0.274741\pi$
$878$	−7.23204	+	25.4180i	−0.244069	+	0.857815i
$879$	17.7171	+	3.31190i	0.597583	+	0.111708i
$880$	−10.3484			−0.348844
$881$	−48.2826			−1.62668			−0.813341	−	0.581787i	$-0.802354\pi$
$881$	−48.2826			−1.62668			−0.813341	+	0.581787i	$0.802354\pi$
$882$	6.86707	+	1.28368i	0.231226	+	0.0432237i
$883$	−24.2284	+	32.0836i	−0.815350	+	1.07970i	0.180028	+	0.983662i	$0.442381\pi$
$883$	−24.2284	+	32.0836i	−0.815350	+	1.07970i	−0.995378	+	0.0960367i	$0.969383\pi$
$884$	−6.69307	−	23.5237i	−0.225112	−	0.791188i
$885$	−1.03333	+	2.07520i	−0.0347348	+	0.0697570i
$886$	−7.59786	−	4.70440i	−0.255255	−	0.158047i
$887$	2.34432	−	25.2992i	0.0787146	−	0.849465i	−0.861247	−	0.508186i	$-0.830316\pi$
$887$	2.34432	−	25.2992i	0.0787146	−	0.849465i	0.939962	−	0.341279i	$-0.110860\pi$
$888$	−0.728205	−	2.55937i	−0.0244369	−	0.0858870i
$889$	−0.954379	−	0.369728i	−0.0320088	−	0.0124003i
$890$	3.90905	−	13.7389i	0.131032	−	0.460528i
$891$	2.25345	−	2.98406i	0.0754936	−	0.0999696i
$892$	2.99120	+	1.15880i	0.100153	+	0.0387994i
$893$	−85.4699	+	33.1112i	−2.86014	+	1.10802i
$894$	−9.22052	−	18.5173i	−0.308380	−	0.619311i
$895$	−14.0080	−	8.67341i	−0.468237	−	0.289920i
$896$	−0.116228	+	0.0217268i	−0.00388291	+	0.000725841i
$897$	−30.6624	−	18.9854i	−1.02379	−	0.633903i
$898$	11.7064	−	7.24831i	0.390648	−	0.241879i
$899$	−3.66181	+	3.33818i	−0.122128	+	0.111334i
$900$	1.18508	+	2.37997i	0.0395027	+	0.0793322i
$901$	−1.91330	+	20.6478i	−0.0637413	+	0.687879i
$902$	−3.86436	+	7.76068i	−0.128669	+	0.258402i
$903$	0.901953	−	0.558465i	0.0300151	−	0.0185846i
$904$	10.1870	−	9.28671i	0.338816	−	0.308871i
$905$	−0.164530	−	1.77556i	−0.00546917	−	0.0590218i
$906$	3.49510	+	12.2840i	0.116117	+	0.408109i
$907$	−31.0162	−	41.0720i	−1.02987	−	1.36377i	−0.929499	−	0.368825i	$-0.879760\pi$
$907$	−31.0162	−	41.0720i	−1.02987	−	1.36377i	−0.100376	−	0.994950i	$-0.532005\pi$
$908$	4.35013	−	1.68525i	0.144364	−	0.0559269i
$909$	0.868813	+	9.37598i	0.0288167	+	0.310982i
$910$	0.872733	−	1.75268i	0.0289308	−	0.0581009i
$911$	19.2304	−	3.59479i	0.637133	−	0.119101i	0.144734	−	0.989471i	$-0.453767\pi$
$911$	19.2304	−	3.59479i	0.637133	−	0.119101i	0.492399	+	0.870370i	$0.336120\pi$
$912$	7.91197	−	1.47900i	0.261992	−	0.0489747i
$913$	−2.53596	+	27.3673i	−0.0839279	+	0.905726i
$914$	2.07169	+	2.74336i	0.0685254	+	0.0907423i
$915$	−2.44046	+	8.57732i	−0.0806791	+	0.283558i
$916$	7.62399	+	6.95018i	0.251904	+	0.229641i
$917$	−1.14794	−	0.214587i	−0.0379082	−	0.00708627i
$918$	−3.02068	−	2.75371i	−0.0996973	−	0.0908861i
$919$	−10.5184	+	13.9287i	−0.346971	+	0.459464i	−0.937720	−	0.347391i	$-0.887068\pi$
$919$	−10.5184	+	13.9287i	−0.346971	+	0.459464i	0.590749	+	0.806855i	$0.298832\pi$
$920$	10.0520	+	13.3110i	0.331405	+	0.438851i
$921$	15.0649	+	30.2544i	0.496406	+	0.996917i
$922$	26.8153	−	16.6033i	0.883115	−	0.546802i
$923$	−3.15582	−	34.0568i	−0.103875	−	1.12099i
$924$	0.412287	+	0.159721i	0.0135633	+	0.00525443i
$925$	−5.22824	−	4.76617i	−0.171903	−	0.156711i
$926$	4.24018			0.139341
$927$	8.34409	−	5.77722i	0.274056	−	0.189749i
$928$	−0.632234			−0.0207541
$929$	18.1443	+	16.5407i	0.595296	+	0.542684i	0.914283	−	0.405075i	$-0.132755\pi$
$929$	18.1443	+	16.5407i	0.595296	+	0.542684i	−0.318988	+	0.947759i	$0.603343\pi$
$930$	−20.2246	−	7.83507i	−0.663192	−	0.256922i
$931$	−5.18831	−	55.9908i	−0.170040	−	1.83502i
$932$	2.98162	−	1.84614i	0.0976663	−	0.0604724i
$933$	−11.3866	−	22.8673i	−0.372779	−	0.748641i
$934$	−8.16484	−	10.8120i	−0.267162	−	0.353779i
$935$	25.4907	−	33.7551i	0.833634	−	1.10391i
$936$	4.42185	+	4.03105i	0.144533	+	0.131759i
$937$	−56.5701	−	10.5748i	−1.84806	−	0.345463i	−0.861360	−	0.507995i	$-0.830387\pi$
$937$	−56.5701	−	10.5748i	−1.84806	−	0.345463i	−0.986703	+	0.162533i	$0.948034\pi$
$938$	0.763072	+	0.695632i	0.0249152	+	0.0227132i
$939$	5.74511	−	20.1920i	0.187484	−	0.658939i
$940$	18.9918	+	25.1492i	0.619443	+	0.820275i
$941$	0.822394	−	8.87504i	0.0268093	−	0.289318i	−0.971766	−	0.235949i	$-0.924180\pi$
$941$	0.822394	−	8.87504i	0.0268093	−	0.289318i	0.998575	−	0.0533696i	$-0.0169962\pi$
$942$	−15.9166	+	2.97534i	−0.518592	+	0.0969417i
$943$	13.7362	−	2.56774i	0.447312	−	0.0836170i
$944$	0.373387	−	0.749863i	0.0121527	−	0.0244060i
$945$	−0.0301925	−	0.325829i	−0.000982163	−	0.0105992i
$946$	−31.2835	+	12.1193i	−1.01711	+	0.394032i
$947$	−12.4891	−	16.5382i	−0.405840	−	0.537420i	0.548496	−	0.836153i	$-0.315201\pi$
$947$	−12.4891	−	16.5382i	−0.405840	−	0.537420i	−0.954337	+	0.298734i	$0.903436\pi$
$948$	2.88857	+	10.1523i	0.0938165	+	0.329731i
$949$	−7.29264	−	78.7001i	−0.236729	−	2.55471i
$950$	15.8147	−	14.4170i	0.513097	−	0.467750i
$951$	−26.0272	+	16.1153i	−0.843988	+	0.522576i
$952$	0.215429	−	0.432640i	0.00698210	−	0.0140219i
$953$	1.21975	−	13.1632i	0.0395115	−	0.426397i	−0.952886	−	0.303327i	$-0.901903\pi$
$953$	1.21975	−	13.1632i	0.0395115	−	0.426397i	0.992398	−	0.123070i	$-0.0392740\pi$
$954$	−2.26129	−	4.54128i	−0.0732119	−	0.147029i
$955$	34.1016	−	31.0877i	1.10350	−	1.00598i
$956$	9.55100	−	5.91373i	0.308901	−	0.191264i
$957$	2.01003	+	1.24456i	0.0649750	+	0.0402308i
$958$	20.7329	−	3.87565i	0.669850	−	0.125217i
$959$	1.47690	+	0.914459i	0.0476916	+	0.0295294i
$960$	−1.23355	−	2.47731i	−0.0398127	−	0.0799547i
$961$	28.3692	−	10.9903i	0.915134	−	0.354525i
$962$	−14.8466	−	5.75162i	−0.478675	−	0.185440i
$963$	−6.33733	+	8.39198i	−0.204218	+	0.270428i
$964$	−4.87854	+	17.1463i	−0.157127	+	0.552245i
$965$	−54.6009	−	21.1525i	−1.75766	−	0.680923i
$966$	−0.195033	−	0.685468i	−0.00627507	−	0.0220546i
$967$	1.96831	−	21.2415i	0.0632967	−	0.683080i	−0.903679	−	0.428211i	$-0.859144\pi$
$967$	1.96831	−	21.2415i	0.0632967	−	0.683080i	0.966975	−	0.254869i	$-0.0820325\pi$
$968$	−2.53589	−	1.57016i	−0.0815067	−	0.0504668i
$969$	−14.6649	+	29.4510i	−0.471103	+	0.946103i
$970$	−8.24589	−	28.9813i	−0.264760	−	0.930534i
$971$	−26.6297	+	35.2634i	−0.854587	+	1.13166i	0.135441	+	0.990785i	$0.456755\pi$
$971$	−26.6297	+	35.2634i	−0.854587	+	1.13166i	−0.990028	+	0.140870i	$0.955010\pi$
$972$	0.982973	+	0.183750i	0.0315289	+	0.00589377i
$973$	−1.49645			−0.0479739
$974$	−29.4623			−0.944032
$975$	15.6374	+	2.92314i	0.500798	+	0.0936153i
$976$	0.881849	−	3.09938i	0.0282273	−	0.0992086i
$977$	−39.2014	+	15.1867i	−1.25416	+	0.485865i	−0.894438	−	0.447193i	$-0.852424\pi$
$977$	−39.2014	+	15.1867i	−1.25416	+	0.485865i	−0.359726	+	0.933058i	$0.617130\pi$
$978$	−14.9854	+	13.6610i	−0.479180	+	0.436830i
$979$	14.2634	−	13.0028i	0.455859	−	0.415570i
$980$	−18.0278	+	6.98401i	−0.575877	+	0.223096i
$981$	1.77778	−	6.24825i	0.0567602	−	0.199491i
$982$	1.48259	+	0.277145i	0.0473114	+	0.00884404i
$983$	41.6854			1.32956			0.664778	−	0.747041i	$-0.268526\pi$
$983$	41.6854			1.32956			0.664778	+	0.747041i	$0.268526\pi$
$984$	−2.31848			−0.0739103
$985$	−21.5809	−	4.03416i	−0.687623	−	0.128539i
$986$	1.55735	−	2.06227i	0.0495962	−	0.0656760i
$987$	−0.368485	−	1.29509i	−0.0117290	−	0.0412232i
$988$	21.4673	−	43.1122i	0.682967	−	1.37158i
$989$	45.9765	+	28.4674i	1.46197	+	0.905212i
$990$	−0.954827	+	10.3042i	−0.0303464	+	0.327490i
$991$	−8.38780	−	29.4800i	−0.266447	−	0.936464i	−0.973383	−	0.229186i	$-0.926393\pi$
$991$	−8.38780	−	29.4800i	−0.266447	−	0.936464i	0.706935	−	0.707278i	$-0.250077\pi$
$992$	7.30808	+	2.83117i	0.232032	+	0.0898896i
$993$	2.94778	−	10.3604i	0.0935450	−	0.328776i
$994$	0.407313	−	0.539370i	0.0129192	−	0.0171078i
$995$	58.4146	+	22.6299i	1.85187	+	0.717417i
$996$	−6.85378	+	2.65517i	−0.217170	+	0.0841322i
$997$	−5.50590	−	11.0573i	−0.174374	−	0.350189i	0.790685	−	0.612223i	$-0.209725\pi$
$997$	−5.50590	−	11.0573i	−0.174374	−	0.350189i	−0.965059	+	0.262034i	$0.915607\pi$
$998$	16.9223	+	10.4779i	0.535667	+	0.331671i
$999$	−2.61565	+	0.488949i	−0.0827554	+	0.0154697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	618.2.i.e.133.1	yes	80
103.79	even	17	inner	618.2.i.e.79.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
618.2.i.e.79.1	✓	80	103.79	even	17	inner
618.2.i.e.133.1	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 618 = 2 \cdot 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	618.i (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.739009 + 0.673696i) q^{2} +(-0.932472 - 0.361242i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(-2.35292 + 1.45687i) q^{5} +(-0.445738 - 0.895163i) q^{6} +(-0.0712563 - 0.0943586i) q^{7} +(-0.602635 + 0.798017i) q^{8} +(0.739009 + 0.673696i) q^{9} +O(q^{10})\)	\(q+(0.739009 + 0.673696i) q^{2} +(-0.932472 - 0.361242i) q^{3} +(0.0922684 + 0.995734i) q^{4} +(-2.35292 + 1.45687i) q^{5} +(-0.445738 - 0.895163i) q^{6} +(-0.0712563 - 0.0943586i) q^{7} +(-0.602635 + 0.798017i) q^{8} +(0.739009 + 0.673696i) q^{9} +(-2.72031 - 0.508515i) q^{10} +(-2.76340 - 2.51918i) q^{11} +(0.273663 - 0.961826i) q^{12} +(-3.60586 - 4.77493i) q^{13} +(0.0109099 - 0.117737i) q^{14} +(2.72031 - 0.508515i) q^{15} +(-0.982973 + 0.183750i) q^{16} +(1.82194 - 3.65896i) q^{17} +(0.0922684 + 0.995734i) q^{18} +(7.50549 - 2.90764i) q^{19} +(-1.66775 - 2.20846i) q^{20} +(0.0323583 + 0.113728i) q^{21} +(-0.345023 - 3.72339i) q^{22} +(-4.45422 + 4.06055i) q^{23} +(0.850217 - 0.526432i) q^{24} +(1.18508 - 2.37997i) q^{25} +(0.552087 - 5.95797i) q^{26} +(-0.445738 - 0.895163i) q^{27} +(0.0873814 - 0.0796587i) q^{28} +(0.537536 - 0.332828i) q^{29} +(2.35292 + 1.45687i) q^{30} +(-7.70388 + 1.44010i) q^{31} +(-0.850217 - 0.526432i) q^{32} +(1.66677 + 3.34732i) q^{33} +(3.81145 - 1.47657i) q^{34} +(0.305128 + 0.118207i) q^{35} +(-0.602635 + 0.798017i) q^{36} +(0.728205 - 2.55937i) q^{37} +(7.50549 + 2.90764i) q^{38} +(1.63746 + 5.75508i) q^{39} +(0.255347 - 2.75563i) q^{40} +(-1.97121 - 1.22052i) q^{41} +(-0.0527047 + 0.105845i) q^{42} +(-2.45528 - 8.62940i) q^{43} +(2.25345 - 2.98406i) q^{44} +(-2.72031 - 0.508515i) q^{45} -6.02728 q^{46} -11.3876 q^{47} +(0.982973 + 0.183750i) q^{48} +(1.91181 - 6.71933i) q^{49} +(2.47916 - 0.960431i) q^{50} +(-3.02068 + 2.75371i) q^{51} +(4.42185 - 4.03105i) q^{52} +(-4.73055 + 1.83263i) q^{53} +(0.273663 - 0.961826i) q^{54} +(10.1722 + 1.90151i) q^{55} +0.118241 q^{56} -8.04902 q^{57} +(0.621469 + 0.116173i) q^{58} +(-0.504817 + 0.668485i) q^{59} +(0.757344 + 2.66179i) q^{60} +(-1.43634 + 2.88456i) q^{61} +(-6.66342 - 4.12582i) q^{62} +(0.0109099 - 0.117737i) q^{63} +(-0.273663 - 0.961826i) q^{64} +(15.4407 + 5.98177i) q^{65} +(-1.02332 + 3.59659i) q^{66} +(-5.26260 + 6.96881i) q^{67} +(3.81145 + 1.47657i) q^{68} +(5.62027 - 2.17731i) q^{69} +(0.145857 + 0.292920i) q^{70} +(4.85999 + 3.00918i) q^{71} +(-0.982973 + 0.183750i) q^{72} +(11.2307 + 6.95376i) q^{73} +(2.26239 - 1.40081i) q^{74} +(-1.96480 + 1.79115i) q^{75} +(3.58776 + 7.20519i) q^{76} +(-0.0407959 + 0.440258i) q^{77} +(-2.66707 + 5.35620i) q^{78} +(-8.97423 + 5.55661i) q^{79} +(2.04516 - 1.86441i) q^{80} +(0.0922684 + 0.995734i) q^{81} +(-0.634481 - 2.22997i) q^{82} +(-4.42943 - 5.86552i) q^{83} +(-0.110257 + 0.0427137i) q^{84} +(1.04372 + 11.2636i) q^{85} +(3.99912 - 8.03132i) q^{86} +(-0.621469 + 0.116173i) q^{87} +(3.67567 - 0.687101i) q^{88} +(-0.476245 + 5.13950i) q^{89} +(-1.66775 - 2.20846i) q^{90} +(-0.193616 + 0.680488i) q^{91} +(-4.45422 - 4.06055i) q^{92} +(7.70388 + 1.44010i) q^{93} +(-8.41557 - 7.67181i) q^{94} +(-13.4238 + 17.7760i) q^{95} +(0.602635 + 0.798017i) q^{96} +(4.85316 + 9.74645i) q^{97} +(5.93963 - 3.67767i) q^{98} +(-0.345023 - 3.72339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 5 q^{2} + 5 q^{3} - 5 q^{4} + 14 q^{5} + 5 q^{6} - 2 q^{7} - 5 q^{8} - 5 q^{9}+O(q^{10}) \) 80 * q - 5 * q^2 + 5 * q^3 - 5 * q^4 + 14 * q^5 + 5 * q^6 - 2 * q^7 - 5 * q^8 - 5 * q^9	\( 80 q - 5 q^{2} + 5 q^{3} - 5 q^{4} + 14 q^{5} + 5 q^{6} - 2 q^{7} - 5 q^{8} - 5 q^{9} - 3 q^{10} + 18 q^{11} + 5 q^{12} + 14 q^{13} - 2 q^{14} + 3 q^{15} - 5 q^{16} - 4 q^{17} - 5 q^{18} - 14 q^{19} - 3 q^{20} + 2 q^{21} - 16 q^{22} - 13 q^{23} + 5 q^{24} + q^{25} + 31 q^{26} + 5 q^{27} - 2 q^{28} - 22 q^{29} - 14 q^{30} + 26 q^{31} - 5 q^{32} + 33 q^{33} - 4 q^{34} - 2 q^{35} - 5 q^{36} - 25 q^{37} - 14 q^{38} + 20 q^{39} + 14 q^{40} - 35 q^{41} + 19 q^{42} + 16 q^{43} + 18 q^{44} - 3 q^{45} + 72 q^{46} - 34 q^{47} + 5 q^{48} - 5 q^{49} - 16 q^{50} + 4 q^{51} - 3 q^{52} - 72 q^{53} + 5 q^{54} + 6 q^{55} + 32 q^{56} - 54 q^{57} - 5 q^{58} - 96 q^{59} + 3 q^{60} + 4 q^{61} - 8 q^{62} - 2 q^{63} - 5 q^{64} + 31 q^{65} - q^{66} + 48 q^{67} - 4 q^{68} - 4 q^{69} + 32 q^{70} - 14 q^{71} - 5 q^{72} + 48 q^{73} - 8 q^{74} + 16 q^{75} + 3 q^{76} + 2 q^{77} + 3 q^{78} + 34 q^{79} - 3 q^{80} - 5 q^{81} - q^{82} + 24 q^{83} - 15 q^{84} + 26 q^{85} + 16 q^{86} + 5 q^{87} + q^{88} - 18 q^{89} - 3 q^{90} + 46 q^{91} - 13 q^{92} - 26 q^{93} - 34 q^{94} - 45 q^{95} + 5 q^{96} + 89 q^{97} - 39 q^{98} - 16 q^{99}+O(q^{100}) \) 80 * q - 5 * q^2 + 5 * q^3 - 5 * q^4 + 14 * q^5 + 5 * q^6 - 2 * q^7 - 5 * q^8 - 5 * q^9 - 3 * q^10 + 18 * q^11 + 5 * q^12 + 14 * q^13 - 2 * q^14 + 3 * q^15 - 5 * q^16 - 4 * q^17 - 5 * q^18 - 14 * q^19 - 3 * q^20 + 2 * q^21 - 16 * q^22 - 13 * q^23 + 5 * q^24 + q^25 + 31 * q^26 + 5 * q^27 - 2 * q^28 - 22 * q^29 - 14 * q^30 + 26 * q^31 - 5 * q^32 + 33 * q^33 - 4 * q^34 - 2 * q^35 - 5 * q^36 - 25 * q^37 - 14 * q^38 + 20 * q^39 + 14 * q^40 - 35 * q^41 + 19 * q^42 + 16 * q^43 + 18 * q^44 - 3 * q^45 + 72 * q^46 - 34 * q^47 + 5 * q^48 - 5 * q^49 - 16 * q^50 + 4 * q^51 - 3 * q^52 - 72 * q^53 + 5 * q^54 + 6 * q^55 + 32 * q^56 - 54 * q^57 - 5 * q^58 - 96 * q^59 + 3 * q^60 + 4 * q^61 - 8 * q^62 - 2 * q^63 - 5 * q^64 + 31 * q^65 - q^66 + 48 * q^67 - 4 * q^68 - 4 * q^69 + 32 * q^70 - 14 * q^71 - 5 * q^72 + 48 * q^73 - 8 * q^74 + 16 * q^75 + 3 * q^76 + 2 * q^77 + 3 * q^78 + 34 * q^79 - 3 * q^80 - 5 * q^81 - q^82 + 24 * q^83 - 15 * q^84 + 26 * q^85 + 16 * q^86 + 5 * q^87 + q^88 - 18 * q^89 - 3 * q^90 + 46 * q^91 - 13 * q^92 - 26 * q^93 - 34 * q^94 - 45 * q^95 + 5 * q^96 + 89 * q^97 - 39 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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Database

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