LMFDB - Embedded newform 618.2.i.e.79.1

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			79.1
Character	$\chi$	$=$	618.79
Dual form			618.2.i.e.133.1

$q$-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 $\left(\mathbb{Z}/618\mathbb{Z}\right)^\times$.

$n$	$211$	$413$
$\chi(n)$	$e\left(\frac{3}{17}\right)$	$1$

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	−0.112598	−	0.993641i	$-0.535917\pi$
$5$	−2.35292	−	1.45687i	−1.05226	−	0.651531i	−0.939660	+	0.342110i	$0.888858\pi$
$6$	−0.445738	+	0.895163i	−0.181972	+	0.365449i
$7$	−0.0712563	+	0.0943586i	−0.0269324	+	0.0356642i	−0.811284	−	0.584652i	$-0.801231\pi$
$7$	−0.0712563	+	0.0943586i	−0.0269324	+	0.0356642i	0.784352	+	0.620316i	$0.212996\pi$
$8$	−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	−0.973046	−	0.230613i	$-0.925927\pi$
$11$	−2.76340	+	2.51918i	−0.833198	+	0.759560i	0.139848	+	0.990173i	$0.455339\pi$
$12$	0.273663	+	0.961826i	0.0789997	+	0.277655i
$13$	−3.60586	+	4.77493i	−1.00009	+	1.32433i	−0.0546542	+	0.998505i	$0.517406\pi$
$13$	−3.60586	+	4.77493i	−1.00009	+	1.32433i	−0.945431	+	0.325822i	$0.894359\pi$
$14$	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	0.998398	+	0.0565872i	$0.0180219\pi$
$17$	1.82194	+	3.65896i	0.441886	+	0.887427i	−0.556511	+	0.830840i	$0.687860\pi$
$18$	0.0922684	−	0.995734i	0.0217479	−	0.234697i
$19$	7.50549	+	2.90764i	1.72188	+	0.667059i	0.999696	−	0.0246445i	$-0.00784537\pi$
$19$	7.50549	+	2.90764i	1.72188	+	0.667059i	0.722182	+	0.691704i	$0.243139\pi$
$20$	−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	0.0596838	−	0.998217i	$-0.480991\pi$
$23$	−4.45422	−	4.06055i	−0.928768	−	0.846684i	−0.988452	+	0.151533i	$0.951579\pi$
$24$	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	0.575433	−	0.817849i	$-0.304833\pi$
$29$	0.537536	+	0.332828i	0.0998180	+	0.0618047i	−0.475615	+	0.879653i	$0.657775\pi$
$30$	2.35292	−	1.45687i	0.429583	−	0.265986i
$31$	−7.70388	−	1.44010i	−1.38366	−	0.258650i	−0.561295	−	0.827616i	$-0.689697\pi$
$31$	−7.70388	−	1.44010i	−1.38366	−	0.258650i	−0.822362	+	0.568965i	$0.807344\pi$
$32$	−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	0.998394	−	0.0566572i	$-0.0180442\pi$
$37$	0.728205	+	2.55937i	0.119716	+	0.420758i	−0.878678	+	0.477416i	$0.841574\pi$
$38$	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	−0.671659	−	0.740861i	$-0.734418\pi$
$41$	−1.97121	+	1.22052i	−0.307851	+	0.190613i	0.363807	+	0.931474i	$0.381477\pi$
$42$	−0.0527047	−	0.105845i	−0.00813251	−	0.0163323i
$43$	−2.45528	+	8.62940i	−0.374426	+	1.31597i	0.514330	+	0.857592i	$0.328041\pi$
$43$	−2.45528	+	8.62940i	−0.374426	+	1.31597i	−0.888756	+	0.458380i	$0.848430\pi$
$44$	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	0.0137096	−	0.999906i	$-0.495636\pi$
$53$	−4.73055	−	1.83263i	−0.649791	−	0.251730i	−0.663501	+	0.748176i	$0.730930\pi$
$54$	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	0.763969	−	0.645253i	$-0.223248\pi$
$59$	−0.504817	−	0.668485i	−0.0657215	−	0.0870294i	−0.829691	+	0.558223i	$0.811483\pi$
$60$	0.757344	−	2.66179i	0.0977727	−	0.343636i
$61$	−1.43634	−	2.88456i	−0.183905	−	0.369331i	0.783956	−	0.620816i	$-0.213199\pi$
$61$	−1.43634	−	2.88456i	−0.183905	−	0.369331i	−0.967861	+	0.251485i	$0.919081\pi$
$62$	−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	0.353533	−	0.935422i	$-0.384980\pi$
$67$	−5.26260	−	6.96881i	−0.642929	−	0.851376i	−0.996462	+	0.0840464i	$0.973216\pi$
$68$	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	−0.206837	−	0.978375i	$-0.566317\pi$
$71$	4.85999	−	3.00918i	0.576774	−	0.357123i	0.783611	+	0.621252i	$0.213376\pi$
$72$	−0.982973	−	0.183750i	−0.115844	−	0.0216551i
$73$	11.2307	−	6.95376i	1.31445	−	0.813876i	0.323262	−	0.946309i	$-0.395220\pi$
$73$	11.2307	−	6.95376i	1.31445	−	0.813876i	0.991192	+	0.132434i	$0.0422792\pi$
$74$	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	−0.0812572	−	0.996693i	$-0.525894\pi$
$79$	−8.97423	−	5.55661i	−1.00968	−	0.625167i	−0.928423	+	0.371526i	$0.878835\pi$
$80$	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	−0.973305	−	0.229515i	$-0.926286\pi$
$83$	−4.42943	+	5.86552i	−0.486194	+	0.643824i	0.487111	+	0.873340i	$0.338051\pi$
$84$	−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	−0.982993	−	0.183644i	$-0.941211\pi$
$89$	−0.476245	−	5.13950i	−0.0504818	−	0.544786i	0.932511	−	0.361142i	$-0.117613\pi$
$90$	−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	−0.499600	−	0.866256i	$-0.666520\pi$
$97$	4.85316	−	9.74645i	0.492763	−	0.989602i	0.992364	−	0.123346i	$-0.0393626\pi$
$98$	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	−0.248992	−	0.968506i	$-0.580099\pi$
$101$	6.95862	−	6.34362i	0.692408	−	0.631214i	0.941400	+	0.337292i	$0.109511\pi$
$102$	−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	−0.810598	−	0.585602i	$-0.800858\pi$
$107$	0.970297	−	10.4712i	0.0938022	−	1.01229i	0.904401	−	0.426684i	$-0.140318\pi$
$108$	0.850217	+	0.526432i	0.0818122	+	0.0506560i
$109$	−2.89562	+	5.81520i	−0.277350	+	0.556995i	−0.989414	−	0.145120i	$-0.953643\pi$
$109$	−2.89562	+	5.81520i	−0.277350	+	0.556995i	0.712064	+	0.702115i	$0.247761\pi$
$110$	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	−0.777231	−	0.629216i	$-0.783376\pi$
$113$	−13.5500	+	2.53294i	−1.27468	+	0.238279i	−0.497447	+	0.867494i	$0.665729\pi$
$114$	−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	0.812585	−	0.582843i	$-0.198060\pi$
$127$	7.35945	+	4.55678i	0.653046	+	0.404349i	−0.159539	+	0.987192i	$0.551001\pi$
$128$	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	0.926616	−	0.376010i	$-0.122704\pi$
$131$	7.29889	+	6.65381i	0.637707	+	0.581346i	−0.288909	+	0.957357i	$0.593292\pi$
$132$	−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	−0.303943	−	0.952690i	$-0.598303\pi$
$137$	−13.6990	−	5.30701i	−1.17038	−	0.453409i	−0.866440	+	0.499282i	$0.833597\pi$
$138$	5.62027	−	2.17731i	0.478430	−	0.185345i
$139$	7.62686	+	10.0996i	0.646902	+	0.856636i	0.996782	−	0.0801581i	$-0.0255425\pi$
$139$	7.62686	+	10.0996i	0.646902	+	0.856636i	−0.349880	+	0.936794i	$0.613778\pi$
$140$	−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	−0.667809	−	0.744333i	$-0.732768\pi$
$151$	−12.5541	+	2.34677i	−1.02164	+	0.190977i	−0.353829	+	0.935310i	$0.615121\pi$
$152$	−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	0.910905	+	0.412615i	$0.135385\pi$
$157$	4.43125	+	15.5742i	0.353652	+	1.24296i	−0.557253	+	0.830343i	$0.688145\pi$
$158$	−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	0.367215	+	0.930136i	$0.380311\pi$
$163$	−5.54925	+	19.5036i	−0.434651	+	1.52764i	−0.801866	+	0.597503i	$0.796159\pi$
$164$	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	−0.925193	−	0.379496i	$-0.876097\pi$
$167$	0.790892	−	2.77970i	0.0612010	−	0.215099i	0.986394	+	0.164397i	$0.0525679\pi$
$168$	−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	−0.961901	−	0.273399i	$-0.911852\pi$
$173$	−2.15772	+	4.33329i	−0.164049	+	0.329454i	0.797852	+	0.602853i	$0.205970\pi$
$174$	−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	−0.773553	−	0.633732i	$-0.781522\pi$
$179$	2.65369	−	5.32933i	0.198346	−	0.398333i	0.971899	+	0.235399i	$0.0756398\pi$
$180$	0.255347	+	2.75563i	0.0190324	+	0.205392i
$181$	−0.287207	−	0.576790i	−0.0213480	−	0.0428725i	0.884233	−	0.467047i	$-0.154682\pi$
$181$	−0.287207	−	0.576790i	−0.0213480	−	0.0428725i	−0.905581	+	0.424174i	$0.860564\pi$
$182$	−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	−0.446435	−	0.894816i	$-0.647307\pi$
$191$	−16.3904	−	3.06390i	−1.18597	−	0.221696i	−0.739533	+	0.673120i	$0.764954\pi$
$192$	−0.0922684	−	0.995734i	−0.00665890	−	0.0718609i
$193$	12.7509	−	16.8849i	0.917829	−	1.21540i	−0.0583192	−	0.998298i	$-0.518574\pi$
$193$	12.7509	−	16.8849i	0.917829	−	1.21540i	0.976148	−	0.217104i	$-0.0696612\pi$
$194$	−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	−0.437382	−	0.899276i	$-0.644094\pi$
$197$	5.86272	−	5.34458i	0.417702	−	0.380786i	0.855083	+	0.518490i	$0.173506\pi$
$198$	2.25345	+	2.98406i	0.160146	+	0.212068i
$199$	−13.6415	+	18.0643i	−0.967020	+	1.28054i	−0.00718530	+	0.999974i	$0.502287\pi$
$199$	−13.6415	+	18.0643i	−0.967020	+	1.28054i	−0.959834	+	0.280567i	$0.909478\pi$
$200$	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	−0.997919	−	0.0644768i	$-0.979462\pi$
$211$	−21.7953	−	13.4951i	−1.50045	−	0.929038i	−0.502528	−	0.864561i	$-0.667597\pi$
$212$	−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	0.937860	−	0.347014i	$-0.112804\pi$
$223$	1.42985	+	2.87152i	0.0957497	+	0.192291i	−0.842110	+	0.539306i	$0.818687\pi$
$224$	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	−0.992597	−	0.121455i	$-0.961244\pi$
$227$	−1.27668	+	4.48707i	−0.0847363	+	0.297817i	0.907861	+	0.419272i	$0.137715\pi$
$228$	−0.742670	+	8.01469i	−0.0491845	+	0.530786i
$229$	7.62399	+	6.95018i	0.503807	+	0.459281i	0.885253	−	0.465110i	$-0.153985\pi$
$229$	7.62399	+	6.95018i	0.503807	+	0.459281i	−0.381445	+	0.924391i	$0.624574\pi$
$230$	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	−0.940440	−	0.339958i	$-0.889587\pi$
$233$	−1.56316	+	3.13924i	−0.102406	+	0.205659i	0.838035	+	0.545617i	$0.183705\pi$
$234$	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	−0.995937	−	0.0900473i	$-0.971298\pi$
$239$	−5.00725	+	10.0559i	−0.323892	+	0.650462i	0.672046	+	0.740510i	$0.265416\pi$
$240$	−2.58056	−	0.999713i	−0.166574	−	0.0645312i
$241$	16.6230	−	6.43979i	1.07078	−	0.414823i	0.239628	−	0.970865i	$-0.422975\pi$
$241$	16.6230	−	6.43979i	1.07078	−	0.414823i	0.831154	+	0.556042i	$0.187681\pi$
$242$	−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	−0.0205146	−	0.999790i	$-0.506530\pi$
$251$	5.09386	−	0.952208i	0.321522	−	0.0601028i	0.342036	+	0.939687i	$0.388883\pi$
$252$	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	0.973264	−	0.229690i	$-0.0737711\pi$
$257$	13.3757	+	12.1936i	0.834356	+	0.760616i	−0.138908	+	0.990305i	$0.544359\pi$
$258$	−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	0.987317	+	0.158758i	$0.0507490\pi$
$269$	0.754172	+	8.13882i	0.0459827	+	0.496232i	−0.941335	+	0.337474i	$0.890427\pi$
$270$	0.757344	−	2.66179i	0.0460905	−	0.161991i
$271$	16.6798	−	6.46179i	1.01323	−	0.392526i	0.203337	−	0.979109i	$-0.434821\pi$
$271$	16.6798	−	6.46179i	1.01323	−	0.392526i	0.809889	+	0.586583i	$0.199527\pi$
$272$	−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	−0.593084	−	0.805141i	$-0.702090\pi$
$277$	−2.27533	+	1.40883i	−0.136711	+	0.0846481i	0.456372	+	0.889789i	$0.349149\pi$
$278$	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	0.974077	−	0.226215i	$-0.0726351\pi$
$281$	14.0592	+	12.8167i	0.838704	+	0.764580i	−0.135373	+	0.990795i	$0.543223\pi$
$282$	5.07591	−	10.1938i	0.302266	−	0.607032i
$283$	−1.51268	−	16.3244i	−0.0899195	−	0.970386i	−0.914485	−	0.404619i	$-0.867404\pi$
$283$	−1.51268	−	16.3244i	−0.0899195	−	0.970386i	0.824566	−	0.565766i	$-0.191420\pi$
$284$	−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	−0.361301	−	0.932449i	$-0.617667\pi$
$293$	−17.7171	−	3.31190i	−1.03504	−	0.193483i	−0.673743	+	0.738966i	$0.735314\pi$
$294$	−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	−0.534758	+	0.845005i	$0.679597\pi$
$307$	−24.9768	+	22.7693i	−1.42550	+	1.29951i	−0.890742	+	0.454509i	$0.849815\pi$
$308$	−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	0.0707215	−	0.997496i	$-0.477470\pi$
$311$	18.8783	−	17.2098i	1.07049	−	0.975879i	0.999766	+	0.0216175i	$0.00688161\pi$
$312$	−5.57944	+	2.16149i	−0.315874	+	0.122370i
$313$	1.93702	−	20.9038i	0.109487	−	1.18155i	−0.746799	−	0.665050i	$-0.768410\pi$
$313$	1.93702	−	20.9038i	0.109487	−	1.18155i	0.856286	−	0.516503i	$-0.172766\pi$
$314$	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	0.925726	+	0.378195i	$0.123455\pi$
$317$	18.4481	+	24.4292i	1.03615	+	1.37208i	0.110421	+	0.993885i	$0.464780\pi$
$318$	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	−0.923790	−	0.382899i	$-0.874926\pi$
$331$	0.993875	−	10.7256i	0.0546283	−	0.589533i	0.978418	−	0.206634i	$-0.0662509\pi$
$332$	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	0.889766	−	0.456417i	$-0.150868\pi$
$337$	9.49807	+	8.65863i	0.517393	+	0.471666i	−0.372373	+	0.928083i	$0.621456\pi$
$338$	−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	−0.942094	−	0.335349i	$-0.891146\pi$
$347$	−26.3098	+	10.1925i	−1.41239	+	0.547161i	−0.470293	+	0.882511i	$0.655852\pi$
$348$	−0.173019	+	0.608099i	−0.00927480	+	0.0325975i
$349$	−2.42613	−	26.1821i	−0.129868	−	1.40149i	−0.772352	−	0.635195i	$-0.780920\pi$
$349$	−2.42613	−	26.1821i	−0.129868	−	1.40149i	0.642484	−	0.766299i	$-0.277904\pi$
$350$	−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	0.968089	−	0.250608i	$-0.0806307\pi$
$353$	8.68239	+	11.4973i	0.462117	+	0.611942i	−0.505972	+	0.862550i	$0.668866\pi$
$354$	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	−0.441212	−	0.897403i	$-0.645451\pi$
$359$	−25.9928	−	10.0697i	−1.37185	−	0.531457i	−0.930636	+	0.365946i	$0.880745\pi$
$360$	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	−0.425503	−	0.904957i	$-0.639903\pi$
$367$	−9.48981	+	1.77395i	−0.495364	+	0.0925996i	−0.0698613	+	0.997557i	$0.522256\pi$
$368$	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	−0.840273	−	0.542163i	$-0.817605\pi$
$373$	3.08150	−	10.8303i	0.159554	−	0.560773i	0.999827	−	0.0186099i	$-0.00592405\pi$
$374$	−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	0.160042	−	0.987110i	$-0.448837\pi$
$379$	16.5736	−	33.2842i	0.851326	−	1.70969i	0.691284	−	0.722583i	$-0.257045\pi$
$380$	−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	0.952686	−	0.303957i	$-0.0983080\pi$
$383$	21.6300	+	13.3927i	1.10524	+	0.684337i	0.152557	+	0.988295i	$0.451249\pi$
$384$	−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	0.928453	−	0.371449i	$-0.121139\pi$
$389$	12.7067	+	11.5837i	0.644256	+	0.587317i	−0.284197	+	0.958766i	$0.591727\pi$
$390$	−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	−0.352693	−	0.935739i	$-0.614734\pi$
$397$	−20.3153	−	3.79759i	−1.01960	−	0.190596i	−0.666904	+	0.745143i	$0.732381\pi$
$398$	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	−0.999530	−	0.0306686i	$-0.990236\pi$
$401$	−21.2509	+	19.3727i	−1.06122	+	0.967427i	−0.0616872	+	0.998096i	$0.519648\pi$
$402$	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	−0.493508	−	0.869741i	$-0.664286\pi$
$409$	−5.50640	+	2.13319i	−0.272274	+	0.105480i	0.221234	+	0.975221i	$0.428992\pi$
$410$	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	−0.959302	−	0.282382i	$-0.908875\pi$
$419$	−8.70310	+	11.5248i	−0.425174	+	0.563022i	0.534128	+	0.845404i	$0.320640\pi$
$420$	0.197197	+	0.261131i	0.00962224	+	0.0127419i
$421$	−17.8741	+	16.2944i	−0.871131	+	0.794141i	−0.979809	−	0.199936i	$-0.935927\pi$
$421$	−17.8741	+	16.2944i	−0.871131	+	0.794141i	0.108678	+	0.994077i	$0.465338\pi$
$422$	−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	0.473615	−	0.880732i	$-0.342949\pi$
$431$	4.78065	+	1.85203i	0.230276	+	0.0892094i	−0.243339	+	0.969941i	$0.578243\pi$
$432$	0.602635	−	0.798017i	0.0289943	−	0.0383946i
$433$	−2.38028	+	8.36581i	−0.114389	+	0.402035i	−0.997780	−	0.0666020i	$-0.978784\pi$
$433$	−2.38028	+	8.36581i	−0.114389	+	0.402035i	0.883391	+	0.468637i	$0.155255\pi$
$434$	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	−0.413612	−	0.910453i	$-0.635733\pi$
$439$	11.7794	−	23.6563i	0.562202	−	1.12905i	0.975814	−	0.218601i	$-0.0701492\pi$
$440$	−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	−0.0291141	−	0.999576i	$-0.509269\pi$
$443$	−8.78422	−	1.64205i	−0.417351	−	0.0780164i	−0.388237	+	0.921560i	$0.626916\pi$
$444$	−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	0.998559	+	0.0536739i	$0.0170931\pi$
$449$	3.76799	+	13.2431i	0.177823	+	0.624982i	−0.820736	+	0.571308i	$0.806436\pi$
$450$	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	−0.104119	−	0.994565i	$-0.533202\pi$
$457$	3.37919	−	0.631680i	0.158072	−	0.0295487i	0.262190	+	0.965016i	$0.415555\pi$
$458$	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	0.853734	+	0.520710i	$0.174333\pi$
$461$	8.63116	+	30.3354i	0.401993	+	1.41286i	−0.451741	+	0.892149i	$0.649197\pi$
$462$	0.412287	+	0.159721i	0.0191813	+	0.00743089i
$463$	3.13353	+	2.85659i	0.145627	+	0.132757i	0.743231	−	0.669035i	$-0.233292\pi$
$463$	3.13353	+	2.85659i	0.145627	+	0.132757i	−0.597604	+	0.801792i	$0.703880\pi$
$464$	−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	−0.482627	−	0.875826i	$-0.660317\pi$
$467$	−13.3179	+	2.48955i	−0.616279	+	0.115202i	−0.133651	+	0.991028i	$0.542670\pi$
$468$	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	0.989647	−	0.143525i	$-0.0458436\pi$
$479$	12.7108	+	16.8318i	0.580771	+	0.769066i	−0.408875	+	0.912590i	$0.634079\pi$
$480$	−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	0.00830990	−	0.999965i	$-0.497355\pi$
$487$	−21.7729	−	19.8486i	−0.986623	−	0.899426i	−0.994933	+	0.100540i	$0.967943\pi$
$488$	−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	0.555063	−	0.831808i	$-0.312694\pi$
$491$	1.28236	+	0.794004i	0.0578721	+	0.0358329i	−0.497191	+	0.867641i	$0.665635\pi$
$492$	−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	0.602424	−	0.798176i	$-0.294202\pi$
$499$	19.5646	+	3.65726i	0.875834	+	0.163722i	0.273409	+	0.961898i	$0.411849\pi$
$500$	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	0.987944	+	0.154810i	$0.0494765\pi$
$503$	5.14657	+	18.0883i	0.229474	+	0.806518i	−0.758470	+	0.651708i	$0.774053\pi$
$504$	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	−0.679029	−	0.734111i	$-0.737599\pi$
$509$	7.12953	−	14.3180i	0.316011	−	0.634635i	0.995040	+	0.0994760i	$0.0317167\pi$
$510$	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	−0.920252	−	0.391326i	$-0.872017\pi$
$521$	−1.21869	+	2.44746i	−0.0533918	+	0.107225i	0.866860	+	0.498551i	$0.166134\pi$
$522$	0.381006	−	0.504534i	0.0166762	−	0.0220828i
$523$	2.64370	+	3.50082i	0.115601	+	0.153080i	0.852139	−	0.523316i	$-0.175305\pi$
$523$	2.64370	+	3.50082i	0.115601	+	0.153080i	−0.736538	+	0.676396i	$0.763541\pi$
$524$	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	−0.919183	−	0.393831i	$-0.871150\pi$
$541$	−2.04722	−	22.0931i	−0.0880170	−	0.949855i	0.831166	−	0.556024i	$-0.187674\pi$
$542$	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	−0.874777	−	0.484526i	$-0.838992\pi$
$547$	−19.4347	+	12.0335i	−0.830969	+	0.514514i	0.0438082	+	0.999040i	$0.486051\pi$
$548$	−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	0.993202	−	0.116405i	$-0.0371372\pi$
$557$	7.12204	+	14.3030i	0.301771	+	0.606037i	−0.691431	+	0.722442i	$0.743020\pi$
$558$	−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	0.454250	−	0.890874i	$-0.349907\pi$
$563$	28.4648	−	5.32099i	1.19965	−	0.224253i	0.745397	+	0.666621i	$0.232260\pi$
$564$	−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	0.998884	+	0.0472409i	$0.0150428\pi$
$569$	4.16211	+	14.6283i	0.174485	+	0.613250i	−0.824399	+	0.566009i	$0.808487\pi$
$570$	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	−0.663143	−	0.748493i	$-0.730778\pi$
$577$	−6.93501	+	4.29398i	−0.288708	+	0.178761i	0.374435	+	0.927253i	$0.377837\pi$
$578$	−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	−0.191007	−	0.981589i	$-0.561175\pi$
$587$	−17.5340	−	3.27768i	−0.723707	−	0.135284i	−0.532700	+	0.846304i	$0.678822\pi$
$588$	−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	−0.984077	−	0.177742i	$-0.943121\pi$
$593$	−12.9765	−	26.0602i	−0.532879	−	1.07017i	0.451198	−	0.892424i	$-0.350997\pi$
$594$	−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	0.403953	−	0.914780i	$-0.367636\pi$
$599$	2.10957	+	0.817252i	0.0861947	+	0.0333920i	−0.317758	+	0.948172i	$0.602930\pi$
$600$	−0.245313	+	2.64735i	−0.0100149	+	0.108078i
$601$	−3.56597	−	7.16144i	−0.145459	−	0.292121i	0.810437	−	0.585825i	$-0.199230\pi$
$601$	−3.56597	−	7.16144i	−0.145459	−	0.292121i	−0.955896	+	0.293704i	$0.905112\pi$
$602$	−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	−0.356392	−	0.934336i	$-0.615993\pi$
$607$	13.3307	−	12.1525i	0.541075	−	0.493255i	0.897467	+	0.441082i	$0.145405\pi$
$608$	−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	−0.272933	−	0.962033i	$-0.587994\pi$
$613$	−31.0913	−	19.2509i	−1.25577	−	0.777538i	−0.982833	+	0.184495i	$0.940935\pi$
$614$	−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	−0.279694	−	0.960089i	$-0.590233\pi$
$631$	18.0934	−	23.9595i	0.720286	−	0.953813i	0.999980	+	0.00627638i	$0.00199785\pi$
$632$	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	0.748525	−	0.663107i	$-0.230763\pi$
$641$	3.98281	+	3.63081i	0.157311	+	0.143408i	−0.591213	+	0.806515i	$0.701351\pi$
$642$	8.94091	+	5.53598i	0.352870	+	0.218488i
$643$	−3.62729	−	7.28458i	−0.143046	−	0.287276i	0.812041	−	0.583600i	$-0.198357\pi$
$643$	−3.62729	−	7.28458i	−0.143046	−	0.287276i	−0.955087	+	0.296325i	$0.904239\pi$
$644$	−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	0.768257	−	0.640141i	$-0.221124\pi$
$647$	13.6762	+	8.46796i	0.537668	+	0.332910i	−0.230589	+	0.973051i	$0.574065\pi$
$648$	−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	−0.242322	−	0.970196i	$-0.577909\pi$
$653$	5.93406	−	2.29887i	0.232218	−	0.0899616i	0.474539	+	0.880234i	$0.342615\pi$
$654$	−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	0.194147	−	0.980972i	$-0.437806\pi$
$659$	29.7480	−	18.4192i	1.15882	−	0.717509i	0.964669	+	0.263464i	$0.0848649\pi$
$660$	4.61267	+	9.26348i	0.179548	+	0.360581i
$661$	−0.0715863	+	0.251600i	−0.00278439	+	0.00978610i	−0.963205	−	0.268766i	$-0.913384\pi$
$661$	−0.0715863	+	0.251600i	−0.00278439	+	0.00978610i	0.960421	+	0.278552i	$0.0898546\pi$
$662$	−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	0.431762	−	0.901988i	$-0.357892\pi$
$673$	30.0983	−	5.62635i	1.16020	−	0.216880i	0.728442	+	0.685108i	$0.240245\pi$
$674$	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	0.645699	−	0.763592i	$-0.276566\pi$
$677$	−6.90674	−	9.14600i	−0.265448	−	0.351509i	−0.911146	+	0.412083i	$0.864801\pi$
$678$	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	−0.530135	−	0.847913i	$-0.677859\pi$
$683$	−9.16459	+	3.55038i	−0.350673	+	0.135852i	0.179461	+	0.983765i	$0.442565\pi$
$684$	−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	−0.707934	−	0.706279i	$-0.750372\pi$
$691$	−10.2848	+	6.36807i	−0.391252	+	0.242253i	0.316682	+	0.948532i	$0.397431\pi$
$692$	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	0.125057	+	0.992150i	$0.460089\pi$
$701$	−22.8608	+	30.2726i	−0.863442	+	1.14338i	−0.988498	+	0.151232i	$0.951676\pi$
$702$	−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	0.965271	−	0.261250i	$-0.0841347\pi$
$709$	0.187739	+	0.659833i	0.00705067	+	0.0247805i	−0.958220	+	0.286031i	$0.907664\pi$
$710$	−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	−0.787460	−	0.616366i	$-0.788604\pi$
$719$	−6.60648	+	6.02260i	−0.246380	+	0.224605i	0.541079	+	0.840972i	$0.318016\pi$
$720$	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	0.298805	+	0.954314i	$0.403412\pi$
$727$	−17.3324	+	34.8082i	−0.642825	+	1.29097i	−0.941629	+	0.336652i	$0.890706\pi$
$728$	−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	0.951617	+	0.307286i	$0.0994208\pi$
$733$	8.23864	+	28.9558i	0.304301	+	1.06951i	−0.647316	+	0.762222i	$0.724109\pi$
$734$	−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	0.933070	+	0.359695i	$0.117119\pi$
$739$	−1.36484	+	14.7290i	−0.0502065	+	0.541814i	−0.983276	+	0.182119i	$0.941704\pi$
$740$	−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	−0.989563	−	0.144100i	$-0.953971\pi$
$743$	0.262471	−	2.83252i	0.00962914	−	0.103915i	0.999192	+	0.0401852i	$0.0127948\pi$
$744$	−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	0.279892	−	0.960031i	$-0.409701\pi$
$751$	34.6401	−	21.4483i	1.26404	−	0.782658i	0.984144	+	0.177374i	$0.0567601\pi$
$752$	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	0.991289	+	0.131705i	$0.0420453\pi$
$757$	23.2954	+	30.8482i	0.846687	+	1.12120i	−0.144601	+	0.989490i	$0.546190\pi$
$758$	−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	0.957546	+	0.288280i	$0.0930833\pi$
$761$	1.91104	+	20.6235i	0.0692753	+	0.747600i	−0.888271	+	0.459320i	$0.848093\pi$
$762$	−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	−0.200507	−	0.979692i	$-0.564259\pi$
$769$	−0.930865	+	0.174009i	−0.0335679	+	0.00627492i	0.166939	+	0.985967i	$0.446612\pi$
$770$	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	0.890345	+	0.455286i	$0.150463\pi$
$773$	39.6424	+	36.1389i	1.42584	+	1.29982i	0.535495	+	0.844539i	$0.320125\pi$
$774$	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	0.971411	−	0.237404i	$-0.0762966\pi$
$787$	0.575757	+	2.02358i	0.0205235	+	0.0721328i	−0.950887	+	0.309537i	$0.899826\pi$
$788$	−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	−0.987503	−	0.157599i	$-0.949625\pi$
$797$	−7.52737	+	15.1170i	−0.266633	+	0.535471i	0.720870	+	0.693070i	$0.243742\pi$
$798$	−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	0.481404	−	0.876499i	$-0.340127\pi$
$809$	17.4546	+	3.26283i	0.613671	+	0.114715i	0.132268	+	0.991214i	$0.457774\pi$
$810$	0.255347	+	2.75563i	0.00897197	+	0.0968229i
$811$	−13.1886	+	17.4646i	−0.463115	+	0.613263i	−0.968313	−	0.249740i	$-0.919655\pi$
$811$	−13.1886	+	17.4646i	−0.463115	+	0.613263i	0.505198	+	0.863004i	$0.331420\pi$
$812$	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	0.725659	−	0.688055i	$-0.241535\pi$
$821$	49.4400	−	19.1531i	1.72547	−	0.668449i	0.999808	+	0.0196055i	$0.00624104\pi$
$822$	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	−0.507451	−	0.861681i	$-0.669412\pi$
$827$	−8.68337	+	3.36396i	−0.301950	+	0.116976i	0.205500	+	0.978657i	$0.434118\pi$
$828$	−0.556128	+	6.00157i	−0.0193268	+	0.208569i
$829$	−23.0138	−	14.2496i	−0.799303	−	0.494908i	0.0649959	−	0.997886i	$-0.479297\pi$
$829$	−23.0138	−	14.2496i	−0.799303	−	0.494908i	−0.864299	+	0.502978i	$0.832238\pi$
$830$	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	0.153605	−	0.988132i	$-0.450912\pi$
$839$	−1.74134	−	0.325513i	−0.0601177	−	0.0112379i	−0.213722	+	0.976894i	$0.568559\pi$
$840$	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	0.761399	−	0.648284i	$-0.224513\pi$
$853$	15.2007	+	9.41190i	0.520463	+	0.322257i	−0.240935	+	0.970541i	$0.577454\pi$
$854$	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	−0.939346	−	0.342970i	$-0.888567\pi$
$857$	−2.91481	+	5.85372i	−0.0995679	+	0.199959i	0.839779	+	0.542929i	$0.182685\pi$
$858$	20.8634	+	8.08253i	0.712265	+	0.275933i
$859$	−25.3281	+	9.81215i	−0.864183	+	0.334786i	−0.752209	−	0.658925i	$-0.771012\pi$
$859$	−25.3281	+	9.81215i	−0.864183	+	0.334786i	−0.111974	+	0.993711i	$0.535717\pi$
$860$	−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	−0.335059	−	0.942197i	$-0.608756\pi$
$863$	13.0967	−	46.0301i	0.445817	−	1.56688i	0.780876	−	0.624687i	$-0.214773\pi$
$864$	−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	0.650066	−	0.759878i	$-0.274741\pi$
$877$	18.3177	+	7.09630i	0.618544	+	0.239625i	−0.0315221	+	0.999503i	$0.510035\pi$
$878$	−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	−0.995378	−	0.0960367i	$-0.969383\pi$
$883$	−24.2284	−	32.0836i	−0.815350	−	1.07970i	0.180028	−	0.983662i	$-0.442381\pi$
$884$	−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	0.939962	+	0.341279i	$0.110860\pi$
$887$	2.34432	+	25.2992i	0.0787146	+	0.849465i	−0.861247	+	0.508186i	$0.830316\pi$
$888$	−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	−0.100376	+	0.994950i	$0.532005\pi$
$907$	−31.0162	+	41.0720i	−1.02987	+	1.36377i	−0.929499	+	0.368825i	$0.879760\pi$
$908$	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	0.492399	−	0.870370i	$-0.336120\pi$
$911$	19.2304	+	3.59479i	0.637133	+	0.119101i	0.144734	+	0.989471i	$0.453767\pi$
$912$	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	0.590749	−	0.806855i	$-0.298832\pi$
$919$	−10.5184	−	13.9287i	−0.346971	−	0.459464i	−0.937720	+	0.347391i	$0.887068\pi$
$920$	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	−0.318988	−	0.947759i	$-0.603343\pi$
$929$	18.1443	−	16.5407i	0.595296	−	0.542684i	0.914283	+	0.405075i	$0.132755\pi$
$930$	−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	−0.986703	−	0.162533i	$-0.948034\pi$
$937$	−56.5701	+	10.5748i	−1.84806	+	0.345463i	−0.861360	+	0.507995i	$0.830387\pi$
$938$	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	0.998575	+	0.0533696i	$0.0169962\pi$
$941$	0.822394	+	8.87504i	0.0268093	+	0.289318i	−0.971766	+	0.235949i	$0.924180\pi$
$942$	−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	−0.954337	−	0.298734i	$-0.903436\pi$
$947$	−12.4891	+	16.5382i	−0.405840	+	0.537420i	0.548496	+	0.836153i	$0.315201\pi$
$948$	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	0.992398	+	0.123070i	$0.0392740\pi$
$953$	1.21975	+	13.1632i	0.0395115	+	0.426397i	−0.952886	+	0.303327i	$0.901903\pi$
$954$	−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	0.966975	+	0.254869i	$0.0820325\pi$
$967$	1.96831	+	21.2415i	0.0632967	+	0.683080i	−0.903679	+	0.428211i	$0.859144\pi$
$968$	−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	−0.990028	−	0.140870i	$-0.955010\pi$
$971$	−26.6297	−	35.2634i	−0.854587	−	1.13166i	0.135441	−	0.990785i	$-0.456755\pi$
$972$	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	−0.359726	−	0.933058i	$-0.617130\pi$
$977$	−39.2014	−	15.1867i	−1.25416	−	0.485865i	−0.894438	+	0.447193i	$0.852424\pi$
$978$	−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	0.706935	+	0.707278i	$0.250077\pi$
$991$	−8.38780	+	29.4800i	−0.266447	+	0.936464i	−0.973383	+	0.229186i	$0.926393\pi$
$992$	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	−0.965059	−	0.262034i	$-0.915607\pi$
$997$	−5.50590	+	11.0573i	−0.174374	+	0.350189i	0.790685	+	0.612223i	$0.209725\pi$
$998$	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.79.1	✓	80
103.30	even	17	inner	618.2.i.e.133.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
618.2.i.e.79.1	✓	80	1.1	even	1	trivial
618.2.i.e.133.1	yes	80	103.30	even	17	inner

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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