LMFDB - Embedded newform 266.2.u.c.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [266,2,Mod(43,266)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(266, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("266.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 266 = 2 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	266.u (of order $9$, degree $6$, 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:	$2.12402069377$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 24 x^{16} - 35 x^{15} + 264 x^{14} - 276 x^{13} + 1919 x^{12} - 801 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 24x^16 - 35x^15 + 264x^14 - 276x^13 + 1919x^12 - 801x^11 + 8532x^10 - 414x^9 + 28392x^8 + 8547x^7 + 58143x^6 + 26301x^5 + 84828x^4 + 43250x^3 + 43896x^2 + 210*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.3
Root			$1.65297 + 2.86303i$ of defining polynomial
Character	$\chi$	$=$	266.85
Dual form			266.2.u.c.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(2.53250 - 2.12502i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.50882 - 0.549166i) q^{5} +(2.53250 + 2.12502i) q^{6} +(0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.37690 - 7.80878i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(2.53250 - 2.12502i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.50882 - 0.549166i) q^{5} +(2.53250 + 2.12502i) q^{6} +(0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.37690 - 7.80878i) q^{9} +(0.278819 - 1.58126i) q^{10} +(0.502487 + 0.870333i) q^{11} +(-1.65297 + 2.86303i) q^{12} +(3.05964 + 2.56734i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-4.98808 + 1.81551i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.724195 + 4.10711i) q^{17} +7.92924 q^{18} +(-3.93304 - 1.87916i) q^{19} +1.60566 q^{20} +(-0.574070 - 3.25572i) q^{21} +(-0.769855 + 0.645985i) q^{22} +(3.20835 - 1.16774i) q^{23} +(-3.10657 - 1.13070i) q^{24} +(-1.85526 - 1.55675i) q^{25} +(-1.99704 + 3.45897i) q^{26} +(-8.14789 - 14.1126i) q^{27} +(-0.173648 + 0.984808i) q^{28} +(-1.61276 + 9.14639i) q^{29} +(-2.65410 - 4.59704i) q^{30} +(-1.76085 + 3.04987i) q^{31} +(0.766044 + 0.642788i) q^{32} +(3.12202 + 1.13632i) q^{33} +(-3.91896 + 1.42638i) q^{34} +(-1.23000 + 1.03210i) q^{35} +(1.37690 + 7.80878i) q^{36} +6.29853 q^{37} +(1.16764 - 4.19960i) q^{38} +13.2042 q^{39} +(0.278819 + 1.58126i) q^{40} +(-9.11160 + 7.64554i) q^{41} +(3.10657 - 1.13070i) q^{42} +(3.25130 + 1.18338i) q^{43} +(-0.769855 - 0.645985i) q^{44} +(-6.36581 + 11.0259i) q^{45} +(1.70713 + 2.95683i) q^{46} +(-1.17664 + 6.67305i) q^{47} +(0.574070 - 3.25572i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.21094 - 2.09740i) q^{50} +(10.5617 + 8.86232i) q^{51} +(-3.75320 - 1.36605i) q^{52} +(0.793572 - 0.288837i) q^{53} +(12.4833 - 10.4747i) q^{54} +(-0.280206 - 1.58913i) q^{55} -1.00000 q^{56} +(-13.9536 + 3.59881i) q^{57} -9.28749 q^{58} +(-2.32413 - 13.1808i) q^{59} +(4.06632 - 3.41205i) q^{60} +(2.04017 - 0.742561i) q^{61} +(-3.30931 - 1.20449i) q^{62} +(-6.07415 - 5.09682i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.20655 - 5.55391i) q^{65} +(-0.576926 + 3.27191i) q^{66} +(0.318118 - 1.80414i) q^{67} +(-2.08524 - 3.61173i) q^{68} +(5.64365 - 9.77509i) q^{69} +(-1.23000 - 1.03210i) q^{70} +(-0.948160 - 0.345102i) q^{71} +(-7.45105 + 2.71196i) q^{72} +(3.38857 - 2.84335i) q^{73} +(1.09373 + 6.20284i) q^{74} -8.00656 q^{75} +(4.33855 + 0.420653i) q^{76} +1.00497 q^{77} +(2.29288 + 13.0036i) q^{78} +(2.74926 - 2.30690i) q^{79} +(-1.50882 + 0.549166i) q^{80} +(-28.2708 - 10.2897i) q^{81} +(-9.11160 - 7.64554i) q^{82} +(-4.95398 + 8.58055i) q^{83} +(1.65297 + 2.86303i) q^{84} +(1.16281 - 6.59461i) q^{85} +(-0.600817 + 3.40740i) q^{86} +(15.3519 + 26.5903i) q^{87} +(0.502487 - 0.870333i) q^{88} +(0.659939 + 0.553754i) q^{89} +(-11.9638 - 4.35447i) q^{90} +(3.75320 - 1.36605i) q^{91} +(-2.61547 + 2.19464i) q^{92} +(2.02170 + 11.4656i) q^{93} -6.77599 q^{94} +(4.90228 + 4.99521i) q^{95} +3.30594 q^{96} +(-2.48753 - 14.1075i) q^{97} +(0.766044 - 0.642788i) q^{98} +(7.48811 - 2.72545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 6 q^{13} - 21 q^{17} + 24 q^{18} - 18 q^{19} + 6 q^{20} + 6 q^{21} - 15 q^{22} + 6 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 24 q^{27} + 21 q^{29} + 6 q^{30} - 9 q^{31} - 24 q^{33} + 24 q^{34} - 3 q^{35} - 3 q^{36} + 18 q^{37} + 12 q^{38} + 66 q^{39} + 3 q^{40} - 24 q^{41} - 3 q^{42} - 6 q^{43} - 15 q^{44} - 18 q^{45} - 6 q^{46} - 9 q^{47} - 6 q^{48} - 9 q^{49} + 18 q^{51} + 3 q^{52} - 9 q^{53} + 9 q^{54} - 27 q^{55} - 18 q^{56} + 27 q^{57} - 12 q^{58} + 45 q^{59} + 9 q^{60} + 6 q^{61} - 15 q^{62} - 15 q^{63} - 9 q^{64} + 3 q^{65} + 39 q^{66} + 27 q^{67} - 12 q^{68} - 6 q^{69} - 3 q^{70} - 27 q^{71} - 12 q^{72} + 21 q^{73} - 24 q^{74} - 6 q^{75} + 15 q^{76} + 6 q^{77} + 36 q^{78} - 6 q^{79} - 6 q^{80} - 99 q^{81} - 24 q^{82} - 9 q^{83} + 3 q^{84} + 36 q^{85} - 6 q^{86} + 3 q^{87} + 3 q^{88} + 54 q^{89} - 63 q^{90} - 3 q^{91} - 12 q^{92} - 75 q^{93} + 42 q^{94} + 57 q^{95} + 6 q^{96} + 60 q^{97} - 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 6 * q^13 - 21 * q^17 + 24 * q^18 - 18 * q^19 + 6 * q^20 + 6 * q^21 - 15 * q^22 + 6 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 24 * q^27 + 21 * q^29 + 6 * q^30 - 9 * q^31 - 24 * q^33 + 24 * q^34 - 3 * q^35 - 3 * q^36 + 18 * q^37 + 12 * q^38 + 66 * q^39 + 3 * q^40 - 24 * q^41 - 3 * q^42 - 6 * q^43 - 15 * q^44 - 18 * q^45 - 6 * q^46 - 9 * q^47 - 6 * q^48 - 9 * q^49 + 18 * q^51 + 3 * q^52 - 9 * q^53 + 9 * q^54 - 27 * q^55 - 18 * q^56 + 27 * q^57 - 12 * q^58 + 45 * q^59 + 9 * q^60 + 6 * q^61 - 15 * q^62 - 15 * q^63 - 9 * q^64 + 3 * q^65 + 39 * q^66 + 27 * q^67 - 12 * q^68 - 6 * q^69 - 3 * q^70 - 27 * q^71 - 12 * q^72 + 21 * q^73 - 24 * q^74 - 6 * q^75 + 15 * q^76 + 6 * q^77 + 36 * q^78 - 6 * q^79 - 6 * q^80 - 99 * q^81 - 24 * q^82 - 9 * q^83 + 3 * q^84 + 36 * q^85 - 6 * q^86 + 3 * q^87 + 3 * q^88 + 54 * q^89 - 63 * q^90 - 3 * q^91 - 12 * q^92 - 75 * q^93 + 42 * q^94 + 57 * q^95 + 6 * q^96 + 60 * q^97 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/266\mathbb{Z}\right)^\times$.

$n$	$115$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	2.53250	−	2.12502i	1.46214	−	1.22688i	0.539059	−	0.842268i	$-0.318780\pi$
$3$	2.53250	−	2.12502i	1.46214	−	1.22688i	0.923078	−	0.384612i	$-0.125665\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.50882	−	0.549166i	−0.674766	−	0.245595i	−0.0181674	−	0.999835i	$-0.505783\pi$
$5$	−1.50882	−	0.549166i	−0.674766	−	0.245595i	−0.656599	+	0.754240i	$0.728005\pi$
$6$	2.53250	+	2.12502i	1.03389	+	0.867535i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.37690	−	7.80878i	0.458966	−	2.60293i
$10$	0.278819	−	1.58126i	0.0881703	−	0.500039i
$11$	0.502487	+	0.870333i	0.151506	+	0.262415i	0.931781	−	0.363021i	$-0.118255\pi$
$11$	0.502487	+	0.870333i	0.151506	+	0.262415i	−0.780276	+	0.625436i	$0.784921\pi$
$12$	−1.65297	+	2.86303i	−0.477171	+	0.826485i
$13$	3.05964	+	2.56734i	0.848591	+	0.712052i	0.959479	−	0.281780i	$-0.0909250\pi$
$13$	3.05964	+	2.56734i	0.848591	+	0.712052i	−0.110888	+	0.993833i	$0.535369\pi$
$14$	0.939693	+	0.342020i	0.251143	+	0.0914087i
$15$	−4.98808	+	1.81551i	−1.28792	+	0.468763i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.724195	+	4.10711i	0.175643	+	0.996121i	0.937399	+	0.348257i	$0.113226\pi$
$17$	0.724195	+	4.10711i	0.175643	+	0.996121i	−0.761756	+	0.647864i	$0.775663\pi$
$18$	7.92924			1.86894
$19$	−3.93304	−	1.87916i	−0.902300	−	0.431108i
$19$	−3.93304	−	1.87916i	−0.902300	−	0.431108i
$20$	1.60566			0.359035
$21$	−0.574070	−	3.25572i	−0.125272	−	0.710455i
$22$	−0.769855	+	0.645985i	−0.164134	+	0.137724i
$23$	3.20835	−	1.16774i	0.668986	−	0.243491i	0.0148749	−	0.999889i	$-0.495265\pi$
$23$	3.20835	−	1.16774i	0.668986	−	0.243491i	0.654111	+	0.756398i	$0.273043\pi$
$24$	−3.10657	−	1.13070i	−0.634125	−	0.230803i
$25$	−1.85526	−	1.55675i	−0.371052	−	0.311350i
$26$	−1.99704	+	3.45897i	−0.391651	+	0.678360i
$27$	−8.14789	−	14.1126i	−1.56806	−	2.71596i
$28$	−0.173648	+	0.984808i	−0.0328164	+	0.186111i
$29$	−1.61276	+	9.14639i	−0.299481	+	1.69844i	0.348927	+	0.937150i	$0.386546\pi$
$29$	−1.61276	+	9.14639i	−0.299481	+	1.69844i	−0.648408	+	0.761293i	$0.724565\pi$
$30$	−2.65410	−	4.59704i	−0.484570	−	0.839300i
$31$	−1.76085	+	3.04987i	−0.316257	+	0.547774i	−0.979704	−	0.200450i	$-0.935760\pi$
$31$	−1.76085	+	3.04987i	−0.316257	+	0.547774i	0.663447	+	0.748224i	$0.269093\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	3.12202	+	1.13632i	0.543474	+	0.197808i
$34$	−3.91896	+	1.42638i	−0.672096	+	0.244623i
$35$	−1.23000	+	1.03210i	−0.207909	+	0.174456i
$36$	1.37690	+	7.80878i	0.229483	+	1.30146i
$37$	6.29853			1.03547			0.517736	−	0.855540i	$-0.326775\pi$
$37$	6.29853			1.03547			0.517736	+	0.855540i	$0.326775\pi$
$38$	1.16764	−	4.19960i	0.189417	−	0.681264i
$39$	13.2042			2.11436
$40$	0.278819	+	1.58126i	0.0440852	+	0.250019i
$41$	−9.11160	+	7.64554i	−1.42299	+	1.19403i	−0.473279	+	0.880913i	$0.656930\pi$
$41$	−9.11160	+	7.64554i	−1.42299	+	1.19403i	−0.949714	+	0.313120i	$0.898626\pi$
$42$	3.10657	−	1.13070i	0.479354	−	0.174471i
$43$	3.25130	+	1.18338i	0.495819	+	0.180463i	0.577813	−	0.816169i	$-0.303906\pi$
$43$	3.25130	+	1.18338i	0.495819	+	0.180463i	−0.0819934	+	0.996633i	$0.526129\pi$
$44$	−0.769855	−	0.645985i	−0.116060	−	0.0973859i
$45$	−6.36581	+	11.0259i	−0.948959	+	1.64365i
$46$	1.70713	+	2.95683i	0.251702	+	0.435960i
$47$	−1.17664	+	6.67305i	−0.171630	+	0.973364i	0.770331	+	0.637644i	$0.220091\pi$
$47$	−1.17664	+	6.67305i	−0.171630	+	0.973364i	−0.941962	+	0.335720i	$0.891020\pi$
$48$	0.574070	−	3.25572i	0.0828599	−	0.469922i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	1.21094	−	2.09740i	0.171252	−	0.296617i
$51$	10.5617	+	8.86232i	1.47893	+	1.24097i
$52$	−3.75320	−	1.36605i	−0.520476	−	0.189438i
$53$	0.793572	−	0.288837i	0.109005	−	0.0396748i	−0.286942	−	0.957948i	$-0.592639\pi$
$53$	0.793572	−	0.288837i	0.109005	−	0.0396748i	0.395947	+	0.918273i	$0.370416\pi$
$54$	12.4833	−	10.4747i	1.69876	−	1.42543i
$55$	−0.280206	−	1.58913i	−0.0377830	−	0.214278i
$56$	−1.00000			−0.133631
$57$	−13.9536	+	3.59881i	−1.84821	+	0.476674i
$58$	−9.28749			−1.21951
$59$	−2.32413	−	13.1808i	−0.302576	−	1.71600i	−0.634699	−	0.772760i	$-0.718876\pi$
$59$	−2.32413	−	13.1808i	−0.302576	−	1.71600i	0.332122	−	0.943236i	$-0.392235\pi$
$60$	4.06632	−	3.41205i	0.524959	−	0.440493i
$61$	2.04017	−	0.742561i	0.261217	−	0.0950752i	−0.208092	−	0.978109i	$-0.566725\pi$
$61$	2.04017	−	0.742561i	0.261217	−	0.0950752i	0.469309	+	0.883034i	$0.344503\pi$
$62$	−3.30931	−	1.20449i	−0.420283	−	0.152970i
$63$	−6.07415	−	5.09682i	−0.765271	−	0.642139i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−3.20655	−	5.55391i	−0.397724	−	0.688878i
$66$	−0.576926	+	3.27191i	−0.0710147	+	0.402744i
$67$	0.318118	−	1.80414i	0.0388644	−	0.220411i	−0.959190	−	0.282763i	$-0.908749\pi$
$67$	0.318118	−	1.80414i	0.0388644	−	0.220411i	0.998054	+	0.0623521i	$0.0198602\pi$
$68$	−2.08524	−	3.61173i	−0.252872	−	0.437987i
$69$	5.64365	−	9.77509i	0.679416	−	1.17678i
$70$	−1.23000	−	1.03210i	−0.147014	−	0.123359i
$71$	−0.948160	−	0.345102i	−0.112526	−	0.0409561i	0.285144	−	0.958485i	$-0.407959\pi$
$71$	−0.948160	−	0.345102i	−0.112526	−	0.0409561i	−0.397669	+	0.917529i	$0.630181\pi$
$72$	−7.45105	+	2.71196i	−0.878115	+	0.319608i
$73$	3.38857	−	2.84335i	0.396603	−	0.332789i	−0.422576	−	0.906327i	$-0.638874\pi$
$73$	3.38857	−	2.84335i	0.396603	−	0.332789i	0.819179	+	0.573538i	$0.194430\pi$
$74$	1.09373	+	6.20284i	0.127143	+	0.721066i
$75$	−8.00656			−0.924518
$76$	4.33855	+	0.420653i	0.497666	+	0.0482522i
$77$	1.00497			0.114527
$78$	2.29288	+	13.0036i	0.259618	+	1.47236i
$79$	2.74926	−	2.30690i	0.309316	−	0.259547i	−0.474893	−	0.880043i	$-0.657513\pi$
$79$	2.74926	−	2.30690i	0.309316	−	0.259547i	0.784209	+	0.620496i	$0.213069\pi$
$80$	−1.50882	+	0.549166i	−0.168691	+	0.0613987i
$81$	−28.2708	−	10.2897i	−3.14120	−	1.14330i
$82$	−9.11160	−	7.64554i	−1.00621	−	0.844309i
$83$	−4.95398	+	8.58055i	−0.543770	+	0.941838i	0.454913	+	0.890536i	$0.349670\pi$
$83$	−4.95398	+	8.58055i	−0.543770	+	0.941838i	−0.998683	+	0.0513017i	$0.983663\pi$
$84$	1.65297	+	2.86303i	0.180354	+	0.312382i
$85$	1.16281	−	6.59461i	0.126124	−	0.715285i
$86$	−0.600817	+	3.40740i	−0.0647877	+	0.367430i
$87$	15.3519	+	26.5903i	1.64590	+	2.85078i
$88$	0.502487	−	0.870333i	0.0535653	−	0.0927778i
$89$	0.659939	+	0.553754i	0.0699534	+	0.0586979i	0.677094	−	0.735897i	$-0.263239\pi$
$89$	0.659939	+	0.553754i	0.0699534	+	0.0586979i	−0.607141	+	0.794594i	$0.707684\pi$
$90$	−11.9638	−	4.35447i	−1.26110	−	0.459002i
$91$	3.75320	−	1.36605i	0.393443	−	0.143201i
$92$	−2.61547	+	2.19464i	−0.272681	+	0.228807i
$93$	2.02170	+	11.4656i	0.209640	+	1.18893i
$94$	−6.77599			−0.698890
$95$	4.90228	+	4.99521i	0.502964	+	0.512497i
$96$	3.30594			0.337411
$97$	−2.48753	−	14.1075i	−0.252571	−	1.43240i	−0.802232	−	0.597012i	$-0.796354\pi$
$97$	−2.48753	−	14.1075i	−0.252571	−	1.43240i	0.549661	−	0.835387i	$-0.314757\pi$
$98$	0.766044	−	0.642788i	0.0773822	−	0.0649314i
$99$	7.48811	−	2.72545i	0.752584	−	0.273918i
$100$	2.27581	+	0.828329i	0.227581	+	0.0828329i
$101$	−5.70521	−	4.78724i	−0.567690	−	0.476349i	0.313188	−	0.949691i	$-0.398603\pi$
$101$	−5.70521	−	4.78724i	−0.567690	−	0.476349i	−0.880878	+	0.473342i	$0.843047\pi$
$102$	−6.89366	+	11.9402i	−0.682574	+	1.18225i
$103$	0.104146	+	0.180386i	0.0102618	+	0.0177740i	0.871111	−	0.491087i	$-0.163400\pi$
$103$	0.104146	+	0.180386i	0.0102618	+	0.0177740i	−0.860849	+	0.508861i	$0.830067\pi$
$104$	0.693564	−	3.93340i	0.0680095	−	0.385701i
$105$	−0.921759	+	5.22756i	−0.0899545	+	0.510157i
$106$	0.422251	+	0.731360i	0.0410126	+	0.0710359i
$107$	0.675207	−	1.16949i	0.0652747	−	0.113059i	−0.831541	−	0.555463i	$-0.812541\pi$
$107$	0.675207	−	1.16949i	0.0652747	−	0.113059i	0.896816	+	0.442404i	$0.145874\pi$
$108$	12.4833	+	10.4747i	1.20120	+	1.00793i
$109$	−16.4134	−	5.97397i	−1.57211	−	0.572203i	−0.598644	−	0.801015i	$-0.704293\pi$
$109$	−16.4134	−	5.97397i	−1.57211	−	0.572203i	−0.973470	+	0.228813i	$0.926516\pi$
$110$	1.51633	−	0.551898i	0.144576	−	0.0526214i
$111$	15.9510	−	13.3845i	1.51400	−	1.27040i
$112$	−0.173648	−	0.984808i	−0.0164082	−	0.0930556i
$113$	5.83241			0.548667			0.274334	−	0.961635i	$-0.411543\pi$
$113$	5.83241			0.548667			0.274334	+	0.961635i	$0.411543\pi$
$114$	−5.96716	−	13.1167i	−0.558876	−	1.22849i
$115$	−5.48211			−0.511209
$116$	−1.61276	−	9.14639i	−0.149741	−	0.849221i
$117$	24.2606	−	20.3571i	2.24289	−	1.88201i
$118$	12.5770	−	4.57765i	1.15781	−	0.421407i
$119$	3.91896	+	1.42638i	0.359250	+	0.130756i
$120$	4.06632	+	3.41205i	0.371202	+	0.311476i
$121$	4.99501	−	8.65162i	0.454092	−	0.786511i
$122$	1.08555	+	1.88023i	0.0982812	+	0.170228i
$123$	−6.82819	+	38.7246i	−0.615678	+	3.49168i
$124$	0.611535	−	3.46819i	0.0549175	−	0.311453i
$125$	5.95848	+	10.3204i	0.532943	+	0.923084i
$126$	3.96462	−	6.86692i	0.353196	−	0.611754i
$127$	−0.886687	−	0.744019i	−0.0786807	−	0.0660210i	0.602599	−	0.798044i	$-0.294132\pi$
$127$	−0.886687	−	0.744019i	−0.0786807	−	0.0660210i	−0.681280	+	0.732023i	$0.738576\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	10.7486	−	3.91218i	0.946363	−	0.344448i
$130$	4.91273	−	4.12227i	0.430874	−	0.361547i
$131$	−2.98983	−	16.9562i	−0.261223	−	1.48147i	−0.779579	−	0.626303i	$-0.784567\pi$
$131$	−2.98983	−	16.9562i	−0.261223	−	1.48147i	0.518357	−	0.855165i	$-0.326544\pi$
$132$	−3.32238			−0.289176
$133$	−3.59392	+	2.46653i	−0.311632	+	0.213875i
$134$	1.83197			0.158258
$135$	4.54357	+	25.7679i	0.391049	+	2.21775i
$136$	3.19477	−	2.68073i	0.273949	−	0.229870i
$137$	6.56205	−	2.38839i	0.560634	−	0.204054i	−0.0461310	−	0.998935i	$-0.514689\pi$
$137$	6.56205	−	2.38839i	0.560634	−	0.204054i	0.606765	+	0.794881i	$0.292467\pi$
$138$	10.6066	+	3.86049i	0.902894	+	0.328626i
$139$	16.5305	+	13.8707i	1.40210	+	1.17650i	0.960159	+	0.279454i	$0.0901534\pi$
$139$	16.5305	+	13.8707i	1.40210	+	1.17650i	0.441938	+	0.897046i	$0.354291\pi$
$140$	0.802828	−	1.39054i	0.0678513	−	0.117522i
$141$	11.2005	+	19.3999i	0.943253	+	1.63376i
$142$	0.175213	−	0.993682i	0.0147035	−	0.0833879i
$143$	−0.697014	+	3.95296i	−0.0582872	+	0.330563i
$144$	−3.96462	−	6.86692i	−0.330385	−	0.572244i
$145$	7.45626	−	12.9146i	0.619208	−	1.07250i
$146$	3.38857	+	2.84335i	0.280440	+	0.235317i
$147$	−3.10657	−	1.13070i	−0.256225	−	0.0932584i
$148$	−5.91868	+	2.15422i	−0.486513	+	0.177076i
$149$	−13.3006	+	11.1605i	−1.08963	+	0.914308i	−0.996685	−	0.0813634i	$-0.974073\pi$
$149$	−13.3006	+	11.1605i	−1.08963	+	0.914308i	−0.0929452	+	0.995671i	$0.529628\pi$
$150$	−1.39032	−	7.88492i	−0.113520	−	0.643801i
$151$	19.3294			1.57300			0.786500	−	0.617590i	$-0.211891\pi$
$151$	19.3294			1.57300			0.786500	+	0.617590i	$0.211891\pi$
$152$	0.339120	+	4.34569i	0.0275062	+	0.352482i
$153$	33.0687			2.67344
$154$	0.174512	+	0.989706i	0.0140626	+	0.0797528i
$155$	4.33169	−	3.63472i	0.347930	−	0.291948i
$156$	−12.4079	+	4.51609i	−0.993424	+	0.361577i
$157$	−11.6008	−	4.22234i	−0.925844	−	0.336980i	−0.165283	−	0.986246i	$-0.552854\pi$
$157$	−11.6008	−	4.22234i	−0.925844	−	0.336980i	−0.760561	+	0.649267i	$0.775076\pi$
$158$	2.74926	+	2.30690i	0.218719	+	0.183527i
$159$	1.39594	−	2.41783i	0.110705	−	0.191747i
$160$	−0.802828	−	1.39054i	−0.0634691	−	0.109932i
$161$	0.592878	−	3.36238i	0.0467254	−	0.264993i
$162$	5.22423	−	29.6281i	0.410454	−	2.32780i
$163$	−5.30568	−	9.18971i	−0.415573	−	0.719794i	0.579915	−	0.814677i	$-0.303086\pi$
$163$	−5.30568	−	9.18971i	−0.415573	−	0.719794i	−0.995488	+	0.0948829i	$0.969752\pi$
$164$	5.94717	−	10.3008i	0.464396	−	0.804358i
$165$	−4.08654	−	3.42902i	−0.318137	−	0.266949i
$166$	−9.31044	−	3.38872i	−0.722630	−	0.263016i
$167$	−11.6509	+	4.24058i	−0.901574	+	0.328146i	−0.750883	−	0.660435i	$-0.770372\pi$
$167$	−11.6509	+	4.24058i	−0.901574	+	0.328146i	−0.150690	+	0.988581i	$0.548150\pi$
$168$	−2.53250	+	2.12502i	−0.195386	+	0.163949i
$169$	0.512719	+	2.90777i	0.0394399	+	0.223675i
$170$	6.69634			0.513586
$171$	−20.0893	+	28.1248i	−1.53627	+	2.15076i
$172$	−3.45997			−0.263820
$173$	2.05799	+	11.6715i	0.156466	+	0.887364i	0.957433	+	0.288656i	$0.0932082\pi$
$173$	2.05799	+	11.6715i	0.156466	+	0.887364i	−0.800967	+	0.598709i	$0.795681\pi$
$174$	−23.5205	+	19.7361i	−1.78309	+	1.49619i
$175$	−2.27581	+	0.828329i	−0.172035	+	0.0626158i
$176$	0.944367	+	0.343721i	0.0711843	+	0.0259090i
$177$	−33.8953	−	28.4416i	−2.54773	−	2.13780i
$178$	−0.430744	+	0.746071i	−0.0322857	+	0.0559204i
$179$	2.78686	+	4.82699i	0.208300	+	0.360786i	0.951179	−	0.308639i	$-0.0998736\pi$
$179$	2.78686	+	4.82699i	0.208300	+	0.360786i	−0.742879	+	0.669426i	$0.766540\pi$
$180$	2.21082	−	12.5382i	0.164785	−	0.934543i
$181$	−0.0874274	+	0.495826i	−0.00649843	+	0.0368544i	−0.987885	−	0.155191i	$-0.950401\pi$
$181$	−0.0874274	+	0.495826i	−0.00649843	+	0.0368544i	0.981386	+	0.192045i	$0.0615120\pi$
$182$	1.99704	+	3.45897i	0.148030	+	0.256396i
$183$	3.58877	−	6.21593i	0.265289	−	0.459495i
$184$	−2.61547	−	2.19464i	−0.192815	−	0.161791i
$185$	−9.50336	−	3.45894i	−0.698701	−	0.254306i
$186$	−10.9404	+	3.98197i	−0.802187	+	0.291972i
$187$	−3.21066	+	2.69406i	−0.234786	+	0.197009i
$188$	−1.17664	−	6.67305i	−0.0858152	−	0.486682i
$189$	−16.2958			−1.18534
$190$	−4.06805	+	5.69521i	−0.295127	+	0.413174i
$191$	20.5992			1.49051			0.745255	−	0.666780i	$-0.232328\pi$
$191$	20.5992			1.49051			0.745255	+	0.666780i	$0.232328\pi$
$192$	0.574070	+	3.25572i	0.0414300	+	0.234961i
$193$	−7.21780	+	6.05646i	−0.519549	+	0.435953i	−0.864474	−	0.502677i	$-0.832349\pi$
$193$	−7.21780	+	6.05646i	−0.519549	+	0.435953i	0.344926	+	0.938630i	$0.387904\pi$
$194$	13.4612	−	4.89948i	0.966459	−	0.351762i
$195$	−19.9228	−	7.25129i	−1.42670	−	0.519276i
$196$	0.766044	+	0.642788i	0.0547175	+	0.0459134i
$197$	3.05420	−	5.29003i	0.217603	−	0.376899i	−0.736472	−	0.676468i	$-0.763510\pi$
$197$	3.05420	−	5.29003i	0.217603	−	0.376899i	0.954075	+	0.299569i	$0.0968430\pi$
$198$	3.98434	+	6.90108i	0.283155	+	0.490438i
$199$	3.48842	−	19.7838i	0.247287	−	1.40244i	−0.567832	−	0.823144i	$-0.692218\pi$
$199$	3.48842	−	19.7838i	0.247287	−	1.40244i	0.815120	−	0.579293i	$-0.196671\pi$
$200$	−0.420553	+	2.38508i	−0.0297376	+	0.168650i
$201$	−3.02819	−	5.24498i	−0.213592	−	0.369953i
$202$	3.72381	−	6.44984i	0.262007	−	0.453809i
$203$	7.11463	+	5.96988i	0.499349	+	0.419004i
$204$	−12.9558	−	4.71554i	−0.907091	−	0.330154i
$205$	17.9465	−	6.53198i	1.25344	−	0.456213i
$206$	−0.159561	+	0.133887i	−0.0111171	+	0.00932838i
$207$	−4.70107	−	26.6611i	−0.326747	−	1.85308i
$208$	3.99407			0.276939
$209$	−0.340806	−	4.36730i	−0.0235741	−	0.302093i
$210$	−5.30820			−0.366301
$211$	2.87600	+	16.3106i	0.197992	+	1.12287i	0.908093	+	0.418769i	$0.137538\pi$
$211$	2.87600	+	16.3106i	0.197992	+	1.12287i	−0.710101	+	0.704100i	$0.751351\pi$
$212$	−0.646926	+	0.542835i	−0.0444310	+	0.0372821i
$213$	−3.13456	+	1.14089i	−0.214777	+	0.0781723i
$214$	1.26897	+	0.461869i	0.0867453	+	0.0315727i
$215$	−4.25577	−	3.57101i	−0.290241	−	0.243541i
$216$	−8.14789	+	14.1126i	−0.554394	+	0.960238i
$217$	1.76085	+	3.04987i	0.119534	+	0.207039i
$218$	3.03307	−	17.2014i	0.205425	−	1.16502i
$219$	2.53938	−	14.4016i	0.171596	−	0.973167i
$220$	0.806821	+	1.39746i	0.0543959	+	0.0942164i
$221$	−8.32858	+	14.4255i	−0.560241	+	0.970366i
$222$	15.9510	+	13.3845i	1.07056	+	0.898308i
$223$	8.51990	+	3.10099i	0.570535	+	0.207658i	0.611147	−	0.791517i	$-0.290709\pi$
$223$	8.51990	+	3.10099i	0.570535	+	0.207658i	−0.0406119	+	0.999175i	$0.512931\pi$
$224$	0.939693	−	0.342020i	0.0627859	−	0.0228522i
$225$	−14.7108	+	12.3438i	−0.980721	+	0.822922i
$226$	1.01279	+	5.74380i	0.0673696	+	0.382072i
$227$	14.1539			0.939426			0.469713	−	0.882819i	$-0.344357\pi$
$227$	14.1539			0.939426			0.469713	+	0.882819i	$0.344357\pi$
$228$	11.8813	−	8.15420i	0.786856	−	0.540025i
$229$	−28.9957			−1.91609			−0.958044	−	0.286622i	$-0.907468\pi$
$229$	−28.9957			−1.91609			−0.958044	+	0.286622i	$0.907468\pi$
$230$	−0.951958	−	5.39882i	−0.0627703	−	0.355988i
$231$	2.54509	−	2.13559i	0.167455	−	0.140511i
$232$	8.72739	−	3.17651i	0.572981	−	0.208548i
$233$	−20.9883	−	7.63912i	−1.37499	−	0.500455i	−0.454334	−	0.890831i	$-0.650123\pi$
$233$	−20.9883	−	7.63912i	−1.37499	−	0.500455i	−0.920655	+	0.390376i	$0.872345\pi$
$234$	24.2606	+	20.3571i	1.58597	+	1.33078i
$235$	5.43995	−	9.42227i	0.354863	−	0.614641i
$236$	6.69207	+	11.5910i	0.435617	+	0.754511i
$237$	2.06028	−	11.6845i	0.133830	−	0.758987i
$238$	−0.724195	+	4.10711i	−0.0469426	+	0.266224i
$239$	−0.131614	−	0.227962i	−0.00851340	−	0.0147456i	0.861737	−	0.507355i	$-0.169377\pi$
$239$	−0.131614	−	0.227962i	−0.00851340	−	0.0147456i	−0.870251	+	0.492609i	$0.836043\pi$
$240$	−2.65410	+	4.59704i	−0.171321	+	0.296737i
$241$	−10.5488	−	8.85147i	−0.679506	−	0.570174i	0.236356	−	0.971667i	$-0.424047\pi$
$241$	−10.5488	−	8.85147i	−0.679506	−	0.570174i	−0.915862	+	0.401493i	$0.868491\pi$
$242$	9.38755	+	3.41679i	0.603455	+	0.219640i
$243$	−47.5224	+	17.2968i	−3.04857	+	1.10959i
$244$	−1.66316	+	1.39556i	−0.106473	+	0.0893415i
$245$	0.278819	+	1.58126i	0.0178131	+	0.101023i
$246$	−39.3220			−2.50708
$247$	−7.20923	−	15.8470i	−0.458712	−	1.00832i
$248$	3.52169			0.223628
$249$	5.68787	+	32.2575i	0.360454	+	2.04424i
$250$	−9.12893	+	7.66008i	−0.577364	+	0.484466i
$251$	−5.30785	+	1.93190i	−0.335028	+	0.121940i	−0.504056	−	0.863671i	$-0.668159\pi$
$251$	−5.30785	+	1.93190i	−0.335028	+	0.121940i	0.169028	+	0.985611i	$0.445937\pi$
$252$	7.45105	+	2.71196i	0.469372	+	0.170837i
$253$	2.62848	+	2.20555i	0.165251	+	0.138662i
$254$	0.578744	−	1.00241i	0.0363136	−	0.0628970i
$255$	−11.0688	−	19.1718i	−0.693158	−	1.20058i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.02989	+	5.84081i	−0.0642429	+	0.364340i	0.935691	+	0.352821i	$0.114778\pi$
$257$	−1.02989	+	5.84081i	−0.0642429	+	0.364340i	−0.999934	+	0.0115184i	$0.996334\pi$
$258$	5.71922	+	9.90598i	0.356063	+	0.616719i
$259$	3.14927	−	5.45469i	0.195686	−	0.338938i
$260$	4.91273	+	4.12227i	0.304674	+	0.255652i
$261$	69.2016	+	25.1873i	4.28347	+	1.55906i
$262$	16.1794	−	5.88882i	0.999566	−	0.363812i
$263$	19.2742	−	16.1730i	1.18850	−	0.997269i	0.188615	−	0.982051i	$-0.439600\pi$
$263$	19.2742	−	16.1730i	1.18850	−	0.997269i	0.999884	−	0.0152178i	$-0.00484416\pi$
$264$	−0.576926	−	3.27191i	−0.0355073	−	0.201372i
$265$	−1.35598			−0.0832971
$266$	−3.05313	−	3.11101i	−0.187200	−	0.190748i
$267$	2.84803			0.174297
$268$	0.318118	+	1.80414i	0.0194322	+	0.110205i
$269$	−15.5332	+	13.0339i	−0.947075	+	0.794691i	−0.978803	−	0.204806i	$-0.934344\pi$
$269$	−15.5332	+	13.0339i	−0.947075	+	0.794691i	0.0317272	+	0.999497i	$0.489899\pi$
$270$	−24.5874	+	8.94909i	−1.49634	+	0.544624i
$271$	−13.4950	−	4.91178i	−0.819763	−	0.298369i	−0.102112	−	0.994773i	$-0.532560\pi$
$271$	−13.4950	−	4.91178i	−0.819763	−	0.298369i	−0.717650	+	0.696404i	$0.754782\pi$
$272$	3.19477	+	2.68073i	0.193711	+	0.162543i
$273$	6.60209	−	11.4351i	0.399576	−	0.692087i
$274$	3.49160	+	6.04762i	0.210935	+	0.365350i
$275$	0.422645	−	2.39694i	0.0254865	−	0.144541i
$276$	−1.96002	+	11.1158i	−0.117979	+	0.669094i
$277$	2.22742	+	3.85801i	0.133833	+	0.231805i	0.925151	−	0.379599i	$-0.123938\pi$
$277$	2.22742	+	3.85801i	0.133833	+	0.231805i	−0.791318	+	0.611405i	$0.790605\pi$
$278$	−10.7895	+	18.6880i	−0.647112	+	1.12083i
$279$	21.3913	+	17.9494i	1.28066	+	1.07460i
$280$	1.50882	+	0.549166i	0.0901694	+	0.0328190i
$281$	21.5334	−	7.83751i	1.28457	−	0.467547i	0.392632	−	0.919696i	$-0.371565\pi$
$281$	21.5334	−	7.83751i	1.28457	−	0.467547i	0.891943	+	0.452149i	$0.149342\pi$
$282$	−17.1602	+	14.3991i	−1.02187	+	0.857454i
$283$	−0.678165	−	3.84607i	−0.0403128	−	0.228625i	0.957994	−	0.286787i	$-0.0925872\pi$
$283$	−0.678165	−	3.84607i	−0.0403128	−	0.228625i	−0.998307	+	0.0581619i	$0.981476\pi$
$284$	1.00901			0.0598738
$285$	23.0299	+	2.23291i	1.36417	+	0.132266i
$286$	−4.01394			−0.237349
$287$	2.06543	+	11.7136i	0.121919	+	0.691435i
$288$	6.07415	−	5.09682i	0.357923	−	0.300333i
$289$	−0.369131	+	0.134353i	−0.0217136	+	0.00790309i
$290$	14.0132	+	5.10038i	0.822882	+	0.299505i
$291$	−36.2784	−	30.4412i	−2.12667	−	1.78449i
$292$	−2.21173	+	3.83084i	−0.129432	+	0.224183i
$293$	−4.59217	−	7.95388i	−0.268278	−	0.464671i	0.700139	−	0.714006i	$-0.253121\pi$
$293$	−4.59217	−	7.95388i	−0.268278	−	0.464671i	−0.968417	+	0.249335i	$0.919788\pi$
$294$	0.574070	−	3.25572i	0.0334805	−	0.189877i
$295$	−3.73176	+	21.1638i	−0.217271	+	1.23221i
$296$	−3.14927	−	5.45469i	−0.183047	−	0.317047i
$297$	8.18842	−	14.1828i	0.475140	−	0.822967i
$298$	−13.3006	−	11.1605i	−0.770485	−	0.646513i
$299$	12.8144	+	4.66405i	0.741074	+	0.269729i
$300$	7.52371	−	2.73840i	0.434381	−	0.158102i
$301$	2.65049	−	2.22402i	0.152772	−	0.128191i
$302$	3.35651	+	19.0357i	0.193145	+	1.09538i
$303$	−24.6214			−1.41446
$304$	−4.22078	+	1.08859i	−0.242078	+	0.0624348i
$305$	−3.48604			−0.199610
$306$	5.74231	+	32.5663i	0.328266	+	1.86169i
$307$	−14.4604	+	12.1337i	−0.825298	+	0.692507i	−0.954206	−	0.299150i	$-0.903297\pi$
$307$	−14.4604	+	12.1337i	−0.825298	+	0.692507i	0.128909	+	0.991656i	$0.458853\pi$
$308$	−0.944367	+	0.343721i	−0.0538103	+	0.0195853i
$309$	0.647073	+	0.235515i	0.0368107	+	0.0133980i
$310$	4.33169	+	3.63472i	0.246024	+	0.206438i
$311$	7.14989	−	12.3840i	0.405433	−	0.702231i	−0.588938	−	0.808178i	$-0.700454\pi$
$311$	7.14989	−	12.3840i	0.405433	−	0.702231i	0.994372	+	0.105947i	$0.0337873\pi$
$312$	−6.60209	−	11.4351i	−0.373769	−	0.647388i
$313$	−1.61039	+	9.13296i	−0.0910245	+	0.516225i	0.904869	+	0.425691i	$0.139969\pi$
$313$	−1.61039	+	9.13296i	−0.0910245	+	0.516225i	−0.995893	+	0.0905349i	$0.971142\pi$
$314$	2.14374	−	12.1578i	0.120978	−	0.686102i
$315$	6.36581	+	11.0259i	0.358673	+	0.621240i
$316$	−1.79445	+	3.10808i	−0.100946	+	0.174843i
$317$	−11.5570	−	9.69750i	−0.649108	−	0.544666i	0.257692	−	0.966227i	$-0.417038\pi$
$317$	−11.5570	−	9.69750i	−0.649108	−	0.544666i	−0.906800	+	0.421561i	$0.861482\pi$
$318$	2.62350	+	0.954876i	0.147119	+	0.0535468i
$319$	−8.77080	+	3.19231i	−0.491070	+	0.178735i
$320$	1.23000	−	1.03210i	0.0687593	−	0.0576959i
$321$	−0.775233	−	4.39656i	−0.0432693	−	0.245392i
$322$	3.41425			0.190269
$323$	4.86963	−	17.5143i	0.270953	−	0.974521i
$324$	30.0851			1.67140
$325$	−1.67972	−	9.52618i	−0.0931742	−	0.528417i
$326$	8.12878	−	6.82086i	0.450211	−	0.377772i
$327$	−54.2616	+	19.7496i	−3.00067	+	1.09216i
$328$	11.1770	+	4.06811i	0.617148	+	0.224624i
$329$	5.19071	+	4.35552i	0.286173	+	0.240128i
$330$	2.66730	−	4.61990i	0.146830	−	0.254317i
$331$	16.4751	+	28.5357i	0.905552	+	1.56846i	0.820174	+	0.572114i	$0.193876\pi$
$331$	16.4751	+	28.5357i	0.905552	+	1.56846i	0.0853778	+	0.996349i	$0.472790\pi$
$332$	1.72050	−	9.75744i	0.0944247	−	0.535509i
$333$	8.67243	−	49.1838i	0.475247	−	2.69526i
$334$	−6.19931	−	10.7375i	−0.339211	−	0.587531i
$335$	−1.47076	+	2.54743i	−0.0803560	+	0.139181i
$336$	−2.53250	−	2.12502i	−0.138159	−	0.115929i
$337$	4.97141	+	1.80945i	0.270810	+	0.0985668i	0.473856	−	0.880602i	$-0.342862\pi$
$337$	4.97141	+	1.80945i	0.270810	+	0.0985668i	−0.203046	+	0.979169i	$0.565084\pi$
$338$	−2.77457	+	1.00986i	−0.150916	+	0.0549291i
$339$	14.7706	−	12.3940i	0.802227	−	0.673148i
$340$	1.16281	+	6.59461i	0.0630621	+	0.357643i
$341$	−3.53921			−0.191659
$342$	−31.1860	−	14.9003i	−1.68634	−	0.805715i
$343$	−1.00000			−0.0539949
$344$	−0.600817	−	3.40740i	−0.0323939	−	0.183715i
$345$	−13.8834	+	11.6496i	−0.747458	+	0.627192i
$346$	−11.1368	+	4.05345i	−0.598717	+	0.217915i
$347$	−25.0842	−	9.12990i	−1.34659	−	0.490119i	−0.434708	−	0.900572i	$-0.643148\pi$
$347$	−25.0842	−	9.12990i	−1.34659	−	0.490119i	−0.911882	+	0.410453i	$0.865371\pi$
$348$	−23.5205	−	19.7361i	−1.26083	−	1.05796i
$349$	−9.26472	+	16.0470i	−0.495929	+	0.858975i	−0.999989	−	0.00469409i	$-0.998506\pi$
$349$	−9.26472	+	16.0470i	−0.495929	+	0.858975i	0.504060	+	0.863669i	$0.331839\pi$
$350$	−1.21094	−	2.09740i	−0.0647272	−	0.112111i
$351$	11.3022	−	64.0977i	0.603265	−	3.42128i
$352$	−0.174512	+	0.989706i	−0.00930152	+	0.0527515i
$353$	−7.58280	−	13.1338i	−0.403592	−	0.699042i	0.590565	−	0.806990i	$-0.298905\pi$
$353$	−7.58280	−	13.1338i	−0.403592	−	0.699042i	−0.994156	+	0.107949i	$0.965572\pi$
$354$	22.1236	−	38.3192i	1.17586	−	2.03664i
$355$	1.24109	+	1.04140i	0.0658700	+	0.0552715i
$356$	−0.809535	−	0.294647i	−0.0429053	−	0.0156162i
$357$	12.9558	−	4.71554i	0.685696	−	0.249573i
$358$	−4.26972	+	3.58272i	−0.225662	+	0.189353i
$359$	0.844597	+	4.78995i	0.0445761	+	0.252804i	0.998950	−	0.0458101i	$-0.0145869\pi$
$359$	0.844597	+	4.78995i	0.0445761	+	0.252804i	−0.954374	+	0.298614i	$0.903476\pi$
$360$	12.7316			0.671016
$361$	11.9375	+	14.7816i	0.628291	+	0.777978i
$362$	−0.503474			−0.0264620
$363$	−5.73498	−	32.5247i	−0.301008	−	1.70710i
$364$	−3.05964	+	2.56734i	−0.160369	+	0.134565i
$365$	−6.67423	+	2.42922i	−0.349345	+	0.127151i
$366$	6.74468	+	2.45486i	0.352550	+	0.128318i
$367$	−11.6045	−	9.73736i	−0.605752	−	0.508286i	0.287537	−	0.957770i	$-0.407164\pi$
$367$	−11.6045	−	9.73736i	−0.605752	−	0.508286i	−0.893289	+	0.449483i	$0.851608\pi$
$368$	1.70713	−	2.95683i	0.0889900	−	0.154135i
$369$	47.1566	+	81.6776i	2.45487	+	4.25196i
$370$	1.75615	−	9.95963i	0.0912979	−	0.517776i
$371$	0.146646	−	0.831672i	0.00761349	−	0.0431782i
$372$	−5.82125	−	10.0827i	−0.301818	−	0.522764i
$373$	−6.04445	+	10.4693i	−0.312970	+	0.542080i	−0.979004	−	0.203842i	$-0.934657\pi$
$373$	−6.04445	+	10.4693i	−0.312970	+	0.542080i	0.666034	+	0.745921i	$0.267991\pi$
$374$	−3.21066	−	2.69406i	−0.166019	−	0.139307i
$375$	37.0209	+	13.4745i	1.91175	+	0.695820i
$376$	6.36735	−	2.31753i	0.328371	−	0.119517i
$377$	−28.4164	+	23.8442i	−1.46352	+	1.22804i
$378$	−2.82973	−	16.0482i	−0.145546	−	0.825431i
$379$	−2.53167			−0.130043			−0.0650215	−	0.997884i	$-0.520712\pi$
$379$	−2.53167			−0.130043			−0.0650215	+	0.997884i	$0.520712\pi$
$380$	−6.31510	−	3.01728i	−0.323958	−	0.154783i
$381$	−3.82658			−0.196042
$382$	3.57702	+	20.2863i	0.183016	+	1.03794i
$383$	−13.6105	+	11.4205i	−0.695462	+	0.583562i	−0.920479	−	0.390793i	$-0.872201\pi$
$383$	−13.6105	+	11.4205i	−0.695462	+	0.583562i	0.225017	+	0.974355i	$0.427756\pi$
$384$	−3.10657	+	1.13070i	−0.158531	+	0.0577007i
$385$	−1.51633	−	0.551898i	−0.0772792	−	0.0281273i
$386$	−7.21780	−	6.05646i	−0.367377	−	0.308266i
$387$	13.7175	−	23.7593i	0.697297	−	1.20775i
$388$	7.16257	+	12.4059i	0.363624	+	0.629816i
$389$	−1.28773	+	7.30310i	−0.0652907	+	0.370282i	0.934603	+	0.355693i	$0.115755\pi$
$389$	−1.28773	+	7.30310i	−0.0652907	+	0.370282i	−0.999894	+	0.0145889i	$0.995356\pi$
$390$	3.68158	−	20.8793i	0.186424	−	1.05726i
$391$	7.11951	+	12.3314i	0.360049	+	0.623624i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−43.6039	−	36.5880i	−2.19953	−	1.84562i
$394$	5.74002	+	2.08920i	0.289178	+	0.105252i
$395$	−5.41502	+	1.97091i	−0.272459	+	0.0991671i
$396$	−6.10436	+	5.12217i	−0.306756	+	0.257399i
$397$	4.00069	+	22.6891i	0.200789	+	1.13873i	0.903930	+	0.427681i	$0.140669\pi$
$397$	4.00069	+	22.6891i	0.200789	+	1.13873i	−0.703141	+	0.711051i	$0.748220\pi$
$398$	20.0890			1.00697
$399$	−3.86016	+	13.8836i	−0.193250	+	0.695050i
$400$	−2.42187			−0.121094
$401$	−3.78020	−	21.4386i	−0.188774	−	1.07059i	−0.921009	−	0.389540i	$-0.872634\pi$
$401$	−3.78020	−	21.4386i	−0.188774	−	1.07059i	0.732235	−	0.681052i	$-0.238477\pi$
$402$	4.63946	−	3.89297i	0.231395	−	0.194164i
$403$	−13.2176	+	4.81082i	−0.658417	+	0.239644i
$404$	6.99848	+	2.54724i	0.348188	+	0.126730i
$405$	37.0048	+	31.0507i	1.83878	+	1.54292i
$406$	−4.64375	+	8.04320i	−0.230465	+	0.399177i
$407$	3.16493	+	5.48182i	0.156880	+	0.271724i
$408$	2.39414	−	13.5779i	0.118528	−	0.672204i
$409$	−1.88340	+	10.6813i	−0.0931281	+	0.528156i	0.902177	+	0.431367i	$0.141968\pi$
$409$	−1.88340	+	10.6813i	−0.0931281	+	0.528156i	−0.995305	+	0.0967893i	$0.969143\pi$
$410$	9.54911	+	16.5395i	0.471597	+	0.816830i
$411$	11.5430	−	19.9931i	0.569374	−	0.986185i
$412$	−0.159561	−	0.133887i	−0.00786100	−	0.00659616i
$413$	−12.5770	−	4.57765i	−0.618873	−	0.225251i
$414$	25.4397	−	9.25931i	1.25030	−	0.455070i
$415$	12.1868	−	10.2260i	0.598228	−	0.501973i
$416$	0.693564	+	3.93340i	0.0340048	+	0.192851i
$417$	71.3389			3.49348
$418$	4.24177	−	1.09400i	0.207472	−	0.0535094i
$419$	−10.3984			−0.507994			−0.253997	−	0.967205i	$-0.581745\pi$
$419$	−10.3984			−0.507994			−0.253997	+	0.967205i	$0.581745\pi$
$420$	−0.921759	−	5.22756i	−0.0449773	−	0.255079i
$421$	5.54236	−	4.65059i	0.270118	−	0.226656i	−0.497659	−	0.867373i	$-0.665807\pi$
$421$	5.54236	−	4.65059i	0.270118	−	0.226656i	0.767778	+	0.640717i	$0.221363\pi$
$422$	−15.5634	+	5.66461i	−0.757614	+	0.275749i
$423$	50.4882	+	18.3762i	2.45482	+	0.893482i
$424$	−0.646926	−	0.542835i	−0.0314175	−	0.0263624i
$425$	5.05017	−	8.74715i	0.244969	−	0.424299i
$426$	−1.66786	−	2.88883i	−0.0808083	−	0.139964i
$427$	0.377008	−	2.13812i	0.0182447	−	0.103471i
$428$	−0.234497	+	1.32990i	−0.0113348	+	0.0642831i
$429$	6.63493	+	11.4920i	0.320337	+	0.554840i
$430$	2.77776	−	4.81122i	0.133955	−	0.232017i
$431$	8.64539	+	7.25434i	0.416434	+	0.349429i	0.826805	−	0.562489i	$-0.190156\pi$
$431$	8.64539	+	7.25434i	0.416434	+	0.349429i	−0.410371	+	0.911919i	$0.634601\pi$
$432$	−15.3130	−	5.57348i	−0.736748	−	0.268154i
$433$	26.0556	−	9.48348i	1.25215	−	0.455747i	0.371025	−	0.928623i	$-0.379006\pi$
$433$	26.0556	−	9.48348i	1.25215	−	0.455747i	0.881129	+	0.472876i	$0.156784\pi$
$434$	−2.69777	+	2.26370i	−0.129497	+	0.108661i
$435$	−8.56083	−	48.5509i	−0.410460	−	2.32784i
$436$	17.4667			0.836505
$437$	−14.8129	−	1.43621i	−0.708597	−	0.0687035i
$438$	14.6237			0.698749
$439$	−2.81222	−	15.9489i	−0.134220	−	0.761200i	−0.975400	−	0.220444i	$-0.929249\pi$
$439$	−2.81222	−	15.9489i	−0.134220	−	0.761200i	0.841180	−	0.540756i	$-0.181862\pi$
$440$	−1.23612	+	1.03723i	−0.0589298	+	0.0494480i
$441$	−7.45105	+	2.71196i	−0.354812	+	0.129141i
$442$	−15.6526	−	5.69709i	−0.744519	−	0.270983i
$443$	−1.47190	−	1.23507i	−0.0699320	−	0.0586799i	0.607152	−	0.794586i	$-0.292312\pi$
$443$	−1.47190	−	1.23507i	−0.0699320	−	0.0586799i	−0.677084	+	0.735906i	$0.736756\pi$
$444$	−10.4113	+	18.0329i	−0.494098	+	0.855802i
$445$	−0.691627	−	1.19793i	−0.0327863	−	0.0567875i
$446$	−1.57441	+	8.92895i	−0.0745507	+	0.422798i
$447$	−9.96743	+	56.5281i	−0.471443	+	2.67369i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−3.55403	+	6.15577i	−0.167725	+	0.290509i	−0.937620	−	0.347663i	$-0.886975\pi$
$449$	−3.55403	+	6.15577i	−0.167725	+	0.290509i	0.769895	+	0.638171i	$0.220309\pi$
$450$	−14.7108	−	12.3438i	−0.693474	−	0.581894i
$451$	−11.2326	−	4.08834i	−0.528924	−	0.192512i
$452$	−5.48067	+	1.99480i	−0.257789	+	0.0938276i
$453$	48.9515	−	41.0752i	2.29994	−	1.92988i
$454$	2.45780	+	13.9388i	0.115350	+	0.654183i
$455$	−6.41311			−0.300651
$456$	10.0935	+	10.2848i	0.472671	+	0.481630i
$457$	21.4257			1.00225			0.501126	−	0.865374i	$-0.332919\pi$
$457$	21.4257			1.00225			0.501126	+	0.865374i	$0.332919\pi$
$458$	−5.03504	−	28.5552i	−0.235272	−	1.33429i
$459$	52.0612	−	43.6845i	2.43001	−	2.03902i
$460$	5.15150	−	1.87499i	0.240190	−	0.0874219i
$461$	−1.80600	−	0.657331i	−0.0841139	−	0.0306150i	0.299620	−	0.954058i	$-0.403140\pi$
$461$	−1.80600	−	0.657331i	−0.0841139	−	0.0306150i	−0.383734	+	0.923444i	$0.625362\pi$
$462$	2.54509	+	2.13559i	0.118408	+	0.0993565i
$463$	−6.66817	+	11.5496i	−0.309896	+	0.536756i	−0.978339	−	0.207007i	$-0.933628\pi$
$463$	−6.66817	+	11.5496i	−0.309896	+	0.536756i	0.668443	+	0.743763i	$0.266961\pi$
$464$	4.64375	+	8.04320i	0.215580	+	0.373396i
$465$	3.24615	−	18.4098i	0.150537	−	0.853736i
$466$	3.87848	−	21.9960i	0.179667	−	1.01894i
$467$	−6.27506	−	10.8687i	−0.290375	−	0.502945i	0.683523	−	0.729929i	$-0.260447\pi$
$467$	−6.27506	−	10.8687i	−0.290375	−	0.502945i	−0.973898	+	0.226984i	$0.927113\pi$
$468$	−15.8350	+	27.4270i	−0.731973	+	1.26781i
$469$	−1.40337	−	1.17757i	−0.0648017	−	0.0543751i
$470$	10.2238	+	3.72115i	0.471587	+	0.171644i
$471$	−38.3515	+	13.9588i	−1.76714	+	0.643188i
$472$	−10.2529	+	8.60317i	−0.471926	+	0.395993i
$473$	0.603805	+	3.42435i	0.0277630	+	0.157452i
$474$	11.8647			0.544964
$475$	4.37143	+	9.60907i	0.200575	+	0.440895i
$476$	−4.17047			−0.191153
$477$	−1.16279	−	6.59452i	−0.0532406	−	0.301943i
$478$	0.201644	−	0.169200i	0.00922299	−	0.00773901i
$479$	13.7742	−	5.01341i	0.629361	−	0.229069i	−0.00759211	−	0.999971i	$-0.502417\pi$
$479$	13.7742	−	5.01341i	0.629361	−	0.229069i	0.636953	+	0.770902i	$0.280194\pi$
$480$	−4.98808	−	1.81551i	−0.227674	−	0.0828664i
$481$	19.2712	+	16.1705i	0.878692	+	0.737310i
$482$	6.88522	−	11.9256i	0.313613	−	0.543194i
$483$	−5.64365	−	9.77509i	−0.256795	−	0.444782i
$484$	−1.73475	+	9.83826i	−0.0788523	+	0.447193i
$485$	−3.99412	+	22.6518i	−0.181364	+	1.02856i
$486$	−25.2862	−	43.7969i	−1.14700	−	1.98667i
$487$	−13.5064	+	23.3937i	−0.612033	+	1.06007i	0.378865	+	0.925452i	$0.376315\pi$
$487$	−13.5064	+	23.3937i	−0.612033	+	1.06007i	−0.990897	+	0.134620i	$0.957019\pi$
$488$	−1.66316	−	1.39556i	−0.0752878	−	0.0631740i
$489$	−32.9649	−	11.9983i	−1.49073	−	0.542580i
$490$	−1.50882	+	0.549166i	−0.0681617	+	0.0248088i
$491$	10.4522	−	8.77047i	0.471703	−	0.395806i	−0.375712	−	0.926736i	$-0.622602\pi$
$491$	10.4522	−	8.77047i	0.471703	−	0.395806i	0.847415	+	0.530931i	$0.178158\pi$
$492$	−6.82819	−	38.7246i	−0.307839	−	1.74584i
$493$	−38.7332			−1.74446
$494$	14.3544	−	9.85150i	0.645834	−	0.443240i
$495$	−12.7950			−0.575091
$496$	0.611535	+	3.46819i	0.0274588	+	0.155726i
$497$	−0.772947	+	0.648580i	−0.0346714	+	0.0290928i
$498$	−30.7798	+	11.2029i	−1.37927	+	0.502015i
$499$	16.0827	+	5.85364i	0.719962	+	0.262045i	0.675910	−	0.736984i	$-0.263751\pi$
$499$	16.0827	+	5.85364i	0.719962	+	0.262045i	0.0440526	+	0.999029i	$0.485973\pi$
$500$	−9.12893	−	7.66008i	−0.408258	−	0.342569i
$501$	−20.4946	+	35.4976i	−0.915629	+	1.58592i
$502$	−2.82425	−	4.89174i	−0.126052	−	0.218329i
$503$	3.75919	−	21.3194i	0.167614	−	0.950587i	−0.778714	−	0.627379i	$-0.784128\pi$
$503$	3.75919	−	21.3194i	0.167614	−	0.950587i	0.946328	−	0.323208i	$-0.104761\pi$
$504$	−1.37690	+	7.80878i	−0.0613319	+	0.347831i
$505$	5.97916	+	10.3562i	0.266069	+	0.460845i
$506$	−1.71562	+	2.97153i	−0.0762685	+	0.132101i
$507$	7.47753	+	6.27439i	0.332089	+	0.278656i
$508$	1.08768	+	0.395884i	0.0482581	+	0.0175645i
$509$	3.64220	−	1.32565i	0.161438	−	0.0587586i	−0.260037	−	0.965599i	$-0.583735\pi$
$509$	3.64220	−	1.32565i	0.161438	−	0.0587586i	0.421475	+	0.906840i	$0.361513\pi$
$510$	16.9585	−	14.2298i	0.750933	−	0.630108i
$511$	−0.768127	−	4.35627i	−0.0339800	−	0.192710i
$512$	1.00000			0.0441942
$513$	5.52622	+	70.8163i	0.243988	+	3.12662i
$514$	−5.93091			−0.261601
$515$	−0.0580758	−	0.329364i	−0.00255912	−	0.0145135i
$516$	−8.76235	+	7.35249i	−0.385741	+	0.323675i
$517$	−6.39902	+	2.32905i	−0.281429	+	0.102432i
$518$	5.91868	+	2.15422i	0.260052	+	0.0946512i
$519$	30.0139	+	25.1847i	1.31746	+	1.10548i
$520$	−3.20655	+	5.55391i	−0.140617	+	0.243555i
$521$	16.6918	+	28.9111i	0.731283	+	1.26662i	0.956335	+	0.292273i	$0.0944115\pi$
$521$	16.6918	+	28.9111i	0.731283	+	1.26662i	−0.225052	+	0.974347i	$0.572255\pi$
$522$	−12.7879	+	72.5240i	−0.559712	+	3.17429i
$523$	4.86980	−	27.6180i	0.212941	−	1.20765i	−0.671502	−	0.741003i	$-0.734351\pi$
$523$	4.86980	−	27.6180i	0.212941	−	1.20765i	0.884443	−	0.466648i	$-0.154538\pi$
$524$	8.60888	+	14.9110i	0.376081	+	0.651391i
$525$	−4.00328	+	6.93388i	−0.174717	+	0.302620i
$526$	19.2742	+	16.1730i	0.840396	+	0.705176i
$527$	−13.8014	−	5.02329i	−0.601197	−	0.218818i
$528$	3.12202	−	1.13632i	0.135868	−	0.0494521i
$529$	−8.68916	+	7.29107i	−0.377790	+	0.317003i
$530$	−0.235463	−	1.33538i	−0.0102279	−	0.0580051i
$531$	−106.126			−4.60548
$532$	2.53357	−	3.54697i	0.109844	−	0.153781i
$533$	−47.5069			−2.05775
$534$	0.494555	+	2.80476i	0.0214015	+	0.121374i
$535$	−1.66101	+	1.39376i	−0.0718119	+	0.0602573i
$536$	−1.72149	+	0.626571i	−0.0743570	+	0.0270637i
$537$	17.3152	+	6.30220i	0.747204	+	0.271960i
$538$	−15.5332	−	13.0339i	−0.669683	−	0.561931i
$539$	0.502487	−	0.870333i	0.0216437	−	0.0374879i
$540$	−13.0827	−	22.6599i	−0.562990	−	0.975127i
$541$	1.27576	−	7.23520i	0.0548492	−	0.311065i	−0.945024	−	0.327002i	$-0.893962\pi$
$541$	1.27576	−	7.23520i	0.0548492	−	0.311065i	0.999873	+	0.0159362i	$0.00507286\pi$
$542$	2.49377	−	14.1429i	0.107117	−	0.607490i
$543$	0.832228	+	1.44146i	0.0357143	+	0.0618590i
$544$	−2.08524	+	3.61173i	−0.0894037	+	0.154852i
$545$	21.4841	+	18.0273i	0.920279	+	0.772206i
$546$	12.4079	+	4.51609i	0.531007	+	0.193271i
$547$	27.0051	−	9.82904i	1.15465	−	0.420259i	0.307469	−	0.951558i	$-0.400518\pi$
$547$	27.0051	−	9.82904i	1.15465	−	0.420259i	0.847184	+	0.531299i	$0.178296\pi$
$548$	−5.34943	+	4.48871i	−0.228516	+	0.191748i
$549$	−2.98939	−	16.9537i	−0.127584	−	0.723565i
$550$	2.43392			0.103783
$551$	23.5305	−	32.9425i	1.00243	−	1.40340i
$552$	−11.2873			−0.480420
$553$	−0.623207	−	3.53438i	−0.0265015	−	0.150297i
$554$	−3.41261	+	2.86352i	−0.144988	+	0.121659i
$555$	−31.4176	+	11.4351i	−1.33360	+	0.485391i
$556$	−20.2776	−	7.38046i	−0.859963	−	0.313001i
$557$	−33.8482	−	28.4020i	−1.43419	−	1.20343i	−0.943181	−	0.332280i	$-0.892182\pi$
$557$	−33.8482	−	28.4020i	−1.43419	−	1.20343i	−0.491013	−	0.871152i	$-0.663373\pi$
$558$	−13.9622	+	24.1832i	−0.591066	+	1.02376i
$559$	6.90968	+	11.9679i	0.292248	+	0.506189i
$560$	−0.278819	+	1.58126i	−0.0117823	+	0.0668205i
$561$	−2.40605	+	13.6454i	−0.101584	+	0.576109i
$562$	11.4577	+	19.8453i	0.483313	+	0.837123i
$563$	9.91937	−	17.1808i	0.418051	−	0.724086i	−0.577692	−	0.816255i	$-0.696047\pi$
$563$	9.91937	−	17.1808i	0.418051	−	0.724086i	0.995743	+	0.0921685i	$0.0293798\pi$
$564$	−17.1602	−	14.3991i	−0.722574	−	0.606311i
$565$	−8.80007	−	3.20296i	−0.370222	−	0.134750i
$566$	3.66987	−	1.33573i	0.154256	−	0.0561447i
$567$	−23.0465	+	19.3384i	−0.967864	+	0.812134i
$568$	0.175213	+	0.993682i	0.00735177	+	0.0416940i
$569$	10.2122			0.428119			0.214060	−	0.976821i	$-0.431331\pi$
$569$	10.2122			0.428119			0.214060	+	0.976821i	$0.431331\pi$
$570$	1.80012	+	23.0678i	0.0753985	+	0.966203i
$571$	−29.1274			−1.21894			−0.609472	−	0.792808i	$-0.708619\pi$
$571$	−29.1274			−1.21894			−0.609472	+	0.792808i	$0.708619\pi$
$572$	−0.697014	−	3.95296i	−0.0291436	−	0.165282i
$573$	52.1675	−	43.7738i	2.17933	−	1.82867i
$574$	−11.1770	+	4.06811i	−0.466520	+	0.169799i
$575$	−7.77020	−	2.82812i	−0.324040	−	0.117941i
$576$	6.07415	+	5.09682i	0.253090	+	0.212367i
$577$	−20.9685	+	36.3185i	−0.872930	+	1.51196i	−0.0139788	+	0.999902i	$0.504450\pi$
$577$	−20.9685	+	36.3185i	−0.872930	+	1.51196i	−0.858951	+	0.512057i	$0.828884\pi$
$578$	−0.196410	−	0.340193i	−0.00816959	−	0.0141501i
$579$	−5.40899	+	30.6759i	−0.224790	+	1.27485i
$580$	−2.58953	+	14.6860i	−0.107524	+	0.609801i
$581$	4.95398	+	8.58055i	0.205526	+	0.355981i
$582$	23.6790	−	41.0133i	0.981527	−	1.70005i
$583$	0.650144	+	0.545535i	0.0269262	+	0.0225938i
$584$	−4.15670	−	1.51292i	−0.172006	−	0.0626049i
$585$	−47.7844	+	17.3921i	−1.97564	+	0.719074i
$586$	7.03562	−	5.90359i	0.290639	−	0.243875i
$587$	2.24398	+	12.7262i	0.0926189	+	0.525268i	0.995451	+	0.0952748i	$0.0303730\pi$
$587$	2.24398	+	12.7262i	0.0926189	+	0.525268i	−0.902832	+	0.429993i	$0.858516\pi$
$588$	3.30594			0.136335
$589$	12.6567	−	8.68636i	0.521509	−	0.357915i
$590$	−21.4903			−0.884743
$591$	−3.50665	−	19.8872i	−0.144244	−	0.818051i
$592$	4.82495	−	4.04862i	0.198304	−	0.166397i
$593$	−1.38043	+	0.502434i	−0.0566873	+	0.0206325i	−0.370208	−	0.928949i	$-0.620714\pi$
$593$	−1.38043	+	0.502434i	−0.0566873	+	0.0206325i	0.313521	+	0.949581i	$0.398491\pi$
$594$	15.3892	+	5.60121i	0.631426	+	0.229820i
$595$	−5.12969	−	4.30432i	−0.210297	−	0.176460i
$596$	8.68137	−	15.0366i	0.355603	−	0.615922i
$597$	−33.2065	−	57.5154i	−1.35905	−	2.35395i
$598$	−2.36800	+	13.4296i	−0.0968347	+	0.549177i
$599$	−4.99738	+	28.3416i	−0.204188	+	1.15800i	0.694526	+	0.719468i	$0.255614\pi$
$599$	−4.99738	+	28.3416i	−0.204188	+	1.15800i	−0.898713	+	0.438537i	$0.855497\pi$
$600$	4.00328	+	6.93388i	0.163433	+	0.283075i
$601$	23.0989	−	40.0085i	0.942224	−	1.63198i	0.181008	−	0.983482i	$-0.442064\pi$
$601$	23.0989	−	40.0085i	0.942224	−	1.63198i	0.761216	−	0.648498i	$-0.224603\pi$
$602$	2.65049	+	2.22402i	0.108026	+	0.0906444i
$603$	−13.6501	−	4.96823i	−0.555875	−	0.202322i
$604$	−18.1637	+	6.61103i	−0.739069	+	0.268999i
$605$	−12.2878	+	10.3107i	−0.499569	+	0.419188i
$606$	−4.27546	−	24.2474i	−0.173679	−	0.984982i
$607$	24.3713			0.989202			0.494601	−	0.869120i	$-0.335314\pi$
$607$	24.3713			0.989202			0.494601	+	0.869120i	$0.335314\pi$
$608$	−1.80498	−	3.96762i	−0.0732016	−	0.160908i
$609$	30.7039			1.24418
$610$	−0.605345	−	3.43308i	−0.0245097	−	0.139001i
$611$	−20.7321	+	17.3963i	−0.838730	+	0.703778i
$612$	−31.0744	+	11.3101i	−1.25611	+	0.457186i
$613$	5.66899	+	2.06334i	0.228968	+	0.0833376i	0.453956	−	0.891024i	$-0.350012\pi$
$613$	5.66899	+	2.06334i	0.228968	+	0.0833376i	−0.224988	+	0.974361i	$0.572234\pi$
$614$	−14.4604	−	12.1337i	−0.583574	−	0.489676i
$615$	31.5688	−	54.6788i	1.27298	−	2.20486i
$616$	−0.502487	−	0.870333i	−0.0202458	−	0.0350667i
$617$	4.14403	−	23.5020i	0.166832	−	0.946153i	−0.780323	−	0.625377i	$-0.784945\pi$
$617$	4.14403	−	23.5020i	0.166832	−	0.946153i	0.947155	−	0.320776i	$-0.103944\pi$
$618$	−0.119574	+	0.678139i	−0.00480998	+	0.0272788i
$619$	11.4694	+	19.8656i	0.460994	+	0.798464i	0.999011	−	0.0444696i	$-0.0141598\pi$
$619$	11.4694	+	19.8656i	0.460994	+	0.798464i	−0.538017	+	0.842934i	$0.680826\pi$
$620$	−2.82731	+	4.89705i	−0.113548	+	0.196670i
$621$	−42.6211	−	35.7633i	−1.71032	−	1.43513i
$622$	13.4374	+	4.89082i	0.538791	+	0.196104i
$623$	0.809535	−	0.294647i	0.0324333	−	0.0118048i
$624$	10.1150	−	8.48748i	0.404923	−	0.339771i
$625$	−1.21991	−	6.91846i	−0.0487964	−	0.276738i
$626$	−9.27385			−0.370658
$627$	−10.1437	−	10.3360i	−0.405100	−	0.412779i
$628$	12.3453			0.492631
$629$	4.56136	+	25.8688i	0.181873	+	1.03146i
$630$	−9.75299	+	8.18373i	−0.388569	+	0.326048i
$631$	39.2050	−	14.2694i	1.56072	−	0.568057i	0.589822	−	0.807533i	$-0.299198\pi$
$631$	39.2050	−	14.2694i	1.56072	−	0.568057i	0.970902	+	0.239476i	$0.0769755\pi$
$632$	−3.37247	−	1.22748i	−0.134150	−	0.0488265i
$633$	41.9438	+	35.1950i	1.66712	+	1.39888i
$634$	7.54332	−	13.0654i	0.299583	−	0.518894i
$635$	0.929263	+	1.60953i	0.0368767	+	0.0638723i
$636$	−0.484803	+	2.74946i	−0.0192237	+	0.109023i
$637$	0.693564	−	3.93340i	0.0274800	−	0.155847i
$638$	−4.66684	−	8.08321i	−0.184762	−	0.320017i
$639$	−4.00034	+	6.92880i	−0.158251	+	0.274099i
$640$	1.23000	+	1.03210i	0.0486202	+	0.0407972i
$641$	18.4643	+	6.72046i	0.729297	+	0.265442i	0.679867	−	0.733335i	$-0.262037\pi$
$641$	18.4643	+	6.72046i	0.729297	+	0.265442i	0.0494295	+	0.998778i	$0.484260\pi$
$642$	4.19515	−	1.52691i	0.165569	−	0.0602624i
$643$	3.74445	−	3.14197i	0.147667	−	0.123907i	−0.565962	−	0.824432i	$-0.691495\pi$
$643$	3.74445	−	3.14197i	0.147667	−	0.123907i	0.713628	+	0.700524i	$0.247051\pi$
$644$	0.592878	+	3.36238i	0.0233627	+	0.132496i
$645$	−18.3662			−0.723168
$646$	18.0938	+	1.75432i	0.711891	+	0.0690228i
$647$	28.2737			1.11155			0.555777	−	0.831331i	$-0.312421\pi$
$647$	28.2737			1.11155			0.555777	+	0.831331i	$0.312421\pi$
$648$	5.22423	+	29.6281i	0.205227	+	1.16390i
$649$	10.3039	−	8.64596i	0.404462	−	0.339384i
$650$	9.08977	−	3.30841i	0.356530	−	0.129766i
$651$	10.9404	+	3.98197i	0.428787	+	0.156066i
$652$	8.12878	+	6.82086i	0.318348	+	0.267125i
$653$	−0.228500	+	0.395774i	−0.00894190	+	0.0154878i	−0.870462	−	0.492236i	$-0.836180\pi$
$653$	−0.228500	+	0.395774i	−0.00894190	+	0.0154878i	0.861520	+	0.507724i	$0.169513\pi$
$654$	−28.8720	−	50.0077i	−1.12898	−	1.95546i
$655$	−4.80064	+	27.2258i	−0.187576	+	1.06380i
$656$	−2.06543	+	11.7136i	−0.0806416	+	0.457341i
$657$	−17.5374	−	30.3756i	−0.684198	−	1.18507i
$658$	−3.38800	+	5.86818i	−0.132078	+	0.228765i
$659$	26.5591	+	22.2857i	1.03460	+	0.868129i	0.991391	−	0.130937i	$-0.0417987\pi$
$659$	26.5591	+	22.2857i	1.03460	+	0.868129i	0.0432051	+	0.999066i	$0.486243\pi$
$660$	5.01289	+	1.82454i	0.195126	+	0.0710202i
$661$	46.5168	−	16.9307i	1.80929	−	0.658529i	0.812114	−	0.583499i	$-0.198317\pi$
$661$	46.5168	−	16.9307i	1.80929	−	0.658529i	0.997181	−	0.0750300i	$-0.0239053\pi$
$662$	−25.2413	+	21.1800i	−0.981030	+	0.823182i
$663$	9.56239	+	54.2310i	0.371372	+	2.10616i
$664$	9.90796			0.384504
$665$	6.77712	−	1.74790i	0.262805	−	0.0677806i
$666$	49.9426			1.93523
$667$	5.50635	+	31.2281i	0.213207	+	1.20916i
$668$	9.49790	−	7.96968i	0.367485	−	0.308356i
$669$	28.1663	−	10.2517i	1.08897	−	0.396353i
$670$	−2.76412	−	1.00606i	−0.106787	−	0.0388674i
$671$	1.67143	+	1.40250i	0.0645250	+	0.0541429i
$672$	1.65297	−	2.86303i	0.0637647	−	0.110444i
$673$	17.3414	+	30.0362i	0.668463	+	1.15781i	0.978334	+	0.207033i	$0.0663808\pi$
$673$	17.3414	+	30.0362i	0.668463	+	1.15781i	−0.309871	+	0.950779i	$0.600286\pi$
$674$	−0.918680	+	5.21009i	−0.0353862	+	0.200685i
$675$	−6.85324	+	38.8667i	−0.263781	+	1.49598i
$676$	−1.47632	−	2.55705i	−0.0567814	−	0.0983482i
$677$	−3.54484	+	6.13984i	−0.136239	+	0.235973i	−0.926070	−	0.377351i	$-0.876835\pi$
$677$	−3.54484	+	6.13984i	−0.136239	+	0.235973i	0.789831	+	0.613325i	$0.210168\pi$
$678$	14.7706	+	12.3940i	0.567260	+	0.475988i
$679$	−13.4612	−	4.89948i	−0.516594	−	0.188025i
$680$	−6.29250	+	2.29028i	−0.241306	+	0.0878283i
$681$	35.8447	−	30.0772i	1.37357	−	1.15256i
$682$	−0.614577	−	3.48544i	−0.0235334	−	0.133464i
$683$	6.70433			0.256534			0.128267	−	0.991740i	$-0.459059\pi$
$683$	6.70433			0.256534			0.128267	+	0.991740i	$0.459059\pi$
$684$	9.25853	−	33.2996i	0.354009	−	1.27324i
$685$	−11.2126			−0.428411
$686$	−0.173648	−	0.984808i	−0.00662992	−	0.0376001i
$687$	−73.4314	+	61.6163i	−2.80158	+	2.35081i
$688$	3.25130	−	1.18338i	0.123955	−	0.0451159i
$689$	3.16959	+	1.15363i	0.120752	+	0.0439500i
$690$	−13.8834	−	11.6496i	−0.528533	−	0.443492i
$691$	−4.81093	+	8.33277i	−0.183016	+	0.316994i	−0.942906	−	0.333058i	$-0.891919\pi$
$691$	−4.81093	+	8.33277i	−0.183016	+	0.316994i	0.759890	+	0.650052i	$0.225253\pi$
$692$	−5.92575	−	10.2637i	−0.225263	−	0.390168i
$693$	1.38375	−	7.84762i	0.0525642	−	0.298106i
$694$	4.63537	−	26.2885i	0.175956	−	0.997897i
$695$	−17.3242	−	30.0064i	−0.657145	−	1.13821i
$696$	15.3519	−	26.5903i	0.581914	−	1.00790i
$697$	−37.9997	−	31.8855i	−1.43934	−	1.20775i
$698$	−17.4120	−	6.33744i	−0.659053	−	0.239876i
$699$	−69.3861	+	25.2545i	−2.62442	+	0.955212i
$700$	1.85526	−	1.55675i	0.0701223	−	0.0588396i
$701$	−8.16280	−	46.2935i	−0.308305	−	1.74848i	−0.607527	−	0.794299i	$-0.707839\pi$
$701$	−8.16280	−	46.2935i	−0.308305	−	1.74848i	0.299223	−	0.954183i	$-0.403273\pi$
$702$	65.0865			2.45653
$703$	−24.7723	−	11.8359i	−0.934307	−	0.446401i
$704$	−1.00497			−0.0378764
$705$	−6.24583	−	35.4219i	−0.235232	−	1.33407i
$706$	11.6175	−	9.74826i	0.437231	−	0.366881i
$707$	−6.99848	+	2.54724i	−0.263205	+	0.0957988i
$708$	41.5788	+	15.1334i	1.56263	+	0.568749i
$709$	23.2867	+	19.5399i	0.874551	+	0.733836i	0.965051	−	0.262061i	$-0.0844021\pi$
$709$	23.2867	+	19.5399i	0.874551	+	0.733836i	−0.0905001	+	0.995896i	$0.528847\pi$
$710$	−0.810062	+	1.40307i	−0.0304011	+	0.0526562i
$711$	−14.2286	−	24.6447i	−0.533616	−	0.924250i
$712$	0.149596	−	0.848401i	0.00560635	−	0.0317952i
$713$	−2.08793	+	11.8413i	−0.0781938	+	0.443459i
$714$	6.89366	+	11.9402i	0.257989	+	0.446850i
$715$	3.22250	−	5.58154i	0.120515	−	0.208738i
$716$	−4.26972	−	3.58272i	−0.159567	−	0.133893i
$717$	−0.817735	−	0.297631i	−0.0305389	−	0.0111152i
$718$	−4.57051	+	1.66353i	−0.170570	+	0.0620824i
$719$	5.87274	−	4.92781i	0.219016	−	0.183776i	−0.526678	−	0.850065i	$-0.676563\pi$
$719$	5.87274	−	4.92781i	0.219016	−	0.183776i	0.745694	+	0.666289i	$0.232118\pi$
$720$	2.21082	+	12.5382i	0.0823925	+	0.467271i
$721$	0.208292			0.00775720
$722$	−12.4841	+	14.3230i	−0.464610	+	0.533046i
$723$	−45.5243			−1.69307
$724$	−0.0874274	−	0.495826i	−0.00324921	−	0.0184272i
$725$	17.2307	−	14.4583i	0.639933	−	0.536967i
$726$	31.0347	−	11.2957i	1.15181	−	0.419223i
$727$	−6.57052	−	2.39147i	−0.243687	−	0.0886948i	0.217289	−	0.976107i	$-0.430278\pi$
$727$	−6.57052	−	2.39147i	−0.243687	−	0.0886948i	−0.460976	+	0.887412i	$0.652501\pi$
$728$	−3.05964	−	2.56734i	−0.113398	−	0.0951520i
$729$	−38.4668	+	66.6265i	−1.42470	+	2.46765i
$730$	−3.55128	−	6.15100i	−0.131439	−	0.227659i
$731$	−2.50569	+	14.2105i	−0.0926762	+	0.525593i
$732$	−1.24637	+	7.06849i	−0.0460670	+	0.261259i
$733$	−7.36247	−	12.7522i	−0.271939	−	0.471012i	0.697419	−	0.716663i	$-0.254332\pi$
$733$	−7.36247	−	12.7522i	−0.271939	−	0.471012i	−0.969358	+	0.245651i	$0.920998\pi$
$734$	7.57433	−	13.1191i	0.279573	−	0.484235i
$735$	4.06632	+	3.41205i	0.149988	+	0.125855i
$736$	3.20835	+	1.16774i	0.118261	+	0.0430436i
$737$	1.73005	−	0.629688i	0.0637273	−	0.0231948i
$738$	−72.2481	+	60.6233i	−2.65949	+	2.23158i
$739$	7.82611	+	44.3841i	0.287888	+	1.63269i	0.694783	+	0.719219i	$0.255500\pi$
$739$	7.82611	+	44.3841i	0.287888	+	1.63269i	−0.406895	+	0.913475i	$0.633389\pi$
$740$	10.1133			0.371771
$741$	−51.9325	−	24.8127i	−1.90779	−	0.911518i
$742$	0.844502			0.0310026
$743$	−6.52876	−	37.0265i	−0.239517	−	1.35837i	−0.832889	−	0.553441i	$-0.813315\pi$
$743$	−6.52876	−	37.0265i	−0.239517	−	1.35837i	0.593372	−	0.804929i	$-0.297797\pi$
$744$	8.91868	−	7.48366i	0.326974	−	0.274364i
$745$	26.1973	−	9.53503i	0.959794	−	0.349337i
$746$	−11.3599	−	4.13465i	−0.415914	−	0.151380i
$747$	60.1825	+	50.4991i	2.20196	+	1.84767i
$748$	2.09561	−	3.62970i	0.0766230	−	0.132715i
$749$	−0.675207	−	1.16949i	−0.0246715	−	0.0427323i
$750$	−6.84118	+	38.7983i	−0.249805	+	1.41671i
$751$	−0.203981	+	1.15684i	−0.00744339	+	0.0422135i	−0.988303	−	0.152502i	$-0.951267\pi$
$751$	−0.203981	+	1.15684i	−0.00744339	+	0.0422135i	0.980860	+	0.194715i	$0.0623782\pi$
$752$	3.38800	+	5.86818i	0.123547	+	0.213991i
$753$	−9.33679	+	16.1718i	−0.340251	+	0.589333i
$754$	−28.4164	−	23.8442i	−1.03486	−	0.868353i
$755$	−29.1646	−	10.6150i	−1.06141	−	0.386321i
$756$	15.3130	−	5.57348i	0.556929	−	0.202706i
$757$	20.1620	−	16.9180i	0.732802	−	0.614894i	−0.198092	−	0.980183i	$-0.563475\pi$
$757$	20.1620	−	16.9180i	0.732802	−	0.614894i	0.930894	+	0.365290i	$0.119030\pi$
$758$	−0.439619	−	2.49320i	−0.0159677	−	0.0905572i
$759$	11.3435			0.411741
$760$	1.87483	−	6.74310i	0.0680074	−	0.244598i
$761$	18.0097			0.652850			0.326425	−	0.945223i	$-0.394156\pi$
$761$	18.0097			0.652850			0.326425	+	0.945223i	$0.394156\pi$
$762$	−0.664479	−	3.76845i	−0.0240716	−	0.136517i
$763$	−13.3803	+	11.2274i	−0.484399	+	0.406459i
$764$	−19.3570	+	7.04536i	−0.700310	+	0.254892i
$765$	−49.8947	−	18.1602i	−1.80395	−	0.656583i
$766$	−13.6105	−	11.4205i	−0.491766	−	0.412641i
$767$	26.7286	−	46.2954i	0.965115	−	1.67163i
$768$	−1.65297	−	2.86303i	−0.0596464	−	0.103311i
$769$	0.215459	−	1.22193i	0.00776966	−	0.0440640i	−0.980676	−	0.195637i	$-0.937323\pi$
$769$	0.215459	−	1.22193i	0.00776966	−	0.0440640i	0.988446	+	0.151573i	$0.0484338\pi$
$770$	0.280206	−	1.58913i	0.0100979	−	0.0572682i
$771$	9.80362	+	16.9804i	0.353069	+	0.611533i
$772$	4.71109	−	8.15984i	0.169556	−	0.293679i
$773$	23.0858	+	19.3713i	0.830340	+	0.696738i	0.955369	−	0.295415i	$-0.0954579\pi$
$773$	23.0858	+	19.3713i	0.830340	+	0.696738i	−0.125029	+	0.992153i	$0.539902\pi$
$774$	25.7804	+	9.38329i	0.926656	+	0.337275i
$775$	8.01472	−	2.91712i	0.287897	−	0.104786i
$776$	−10.9737	+	9.20802i	−0.393932	+	0.330549i
$777$	−3.61580	−	20.5062i	−0.129716	−	0.735657i
$778$	−7.41576			−0.265868
$779$	50.2034	−	12.9480i	1.79872	−	0.463912i
$780$	21.2013			0.759130
$781$	−0.176084	−	0.998624i	−0.00630080	−	0.0357336i
$782$	−10.9077	+	9.15267i	−0.390060	+	0.327299i
$783$	142.220	−	51.7637i	5.08251	−	1.84988i
$784$	−0.939693	−	0.342020i	−0.0335605	−	0.0122150i
$785$	15.1848	+	12.7415i	0.541967	+	0.454765i
$786$	28.4604	−	49.2949i	1.01515	−	1.75829i
$787$	−15.9073	−	27.5522i	−0.567033	−	0.982130i	−0.996857	−	0.0792174i	$-0.974758\pi$
$787$	−15.9073	−	27.5522i	−0.567033	−	0.982130i	0.429824	−	0.902912i	$-0.358575\pi$
$788$	−1.06071	+	6.01560i	−0.0377863	+	0.214297i
$789$	14.4440	−	81.9161i	0.514221	−	2.91629i
$790$	−2.88127	−	4.99051i	−0.102511	−	0.177554i
$791$	2.91621	−	5.05102i	0.103688	−	0.179593i
$792$	−6.10436	−	5.12217i	−0.216909	−	0.182008i
$793$	8.14859	+	2.96584i	0.289365	+	0.105320i
$794$	−21.6497	+	7.87983i	−0.768318	+	0.279645i
$795$	−3.43401	+	2.88148i	−0.121792	+	0.102195i
$796$	3.48842	+	19.7838i	0.123644	+	0.701219i
$797$	2.40659			0.0852458			0.0426229	−	0.999091i	$-0.486429\pi$
$797$	2.40659			0.0852458			0.0426229	+	0.999091i	$0.486429\pi$
$798$	−14.3430	−	1.39065i	−0.507737	−	0.0492286i
$799$	−28.2591			−0.999734
$800$	−0.420553	−	2.38508i	−0.0148688	−	0.0843252i
$801$	5.23281	−	4.39085i	0.184892	−	0.155143i
$802$	20.4565	−	7.44555i	0.722343	−	0.262911i
$803$	4.17738	+	1.52044i	0.147416	+	0.0536552i
$804$	4.63946	+	3.89297i	0.163621	+	0.137294i
$805$	−2.74105	+	4.74765i	−0.0966095	+	0.167333i
$806$	−7.03295	−	12.1814i	−0.247725	−	0.429072i
$807$	−11.6405	+	66.0166i	−0.409765	+	2.32389i
$808$	−1.29327	+	7.33448i	−0.0454970	+	0.258026i
$809$	−25.2802	−	43.7866i	−0.888805	−	1.53946i	−0.841290	−	0.540585i	$-0.818203\pi$
$809$	−25.2802	−	43.7866i	−0.888805	−	1.53946i	−0.0475154	−	0.998871i	$-0.515130\pi$
$810$	−24.1532	+	41.8345i	−0.848656	+	1.46992i
$811$	−4.62274	−	3.87894i	−0.162326	−	0.136208i	0.558006	−	0.829837i	$-0.311566\pi$
$811$	−4.62274	−	3.87894i	−0.162326	−	0.136208i	−0.720333	+	0.693629i	$0.756011\pi$
$812$	−8.72739	−	3.17651i	−0.306271	−	0.111474i
$813$	−44.6137	+	16.2380i	−1.56467	+	0.569493i
$814$	−4.84895	+	4.06876i	−0.169956	+	0.142610i
$815$	2.95865	+	16.7794i	0.103637	+	0.587755i
$816$	13.7873			0.482653
$817$	−10.5637	−	10.7640i	−0.369579	−	0.376584i
$818$	−10.8461			−0.379224
$819$	−5.49943	−	31.1888i	−0.192166	−	1.08983i
$820$	−14.6301	+	12.2761i	−0.510905	+	0.428700i
$821$	−21.5825	+	7.85537i	−0.753233	+	0.274154i	−0.689965	−	0.723842i	$-0.742374\pi$
$821$	−21.5825	+	7.85537i	−0.753233	+	0.274154i	−0.0632673	+	0.997997i	$0.520152\pi$
$822$	21.6938	+	7.89588i	0.756657	+	0.275400i
$823$	15.8715	+	13.3177i	0.553244	+	0.464227i	0.876038	−	0.482242i	$-0.160178\pi$
$823$	15.8715	+	13.3177i	0.553244	+	0.464227i	−0.322794	+	0.946469i	$0.604622\pi$
$824$	0.104146	−	0.180386i	0.00362810	−	0.00628405i
$825$	−4.02319	−	6.96837i	−0.140070	−	0.242608i
$826$	2.32413	−	13.1808i	0.0808669	−	0.458619i
$827$	−2.52595	+	14.3254i	−0.0878359	+	0.498142i	0.908873	+	0.417074i	$0.136944\pi$
$827$	−2.52595	+	14.3254i	−0.0878359	+	0.498142i	−0.996709	+	0.0810684i	$0.974167\pi$
$828$	13.5362	+	23.4454i	0.470416	+	0.814784i
$829$	−20.6328	+	35.7371i	−0.716607	+	1.24120i	0.245729	+	0.969339i	$0.420973\pi$
$829$	−20.6328	+	35.7371i	−0.716607	+	1.24120i	−0.962336	+	0.271862i	$0.912361\pi$
$830$	12.1868	+	10.2260i	0.423011	+	0.354948i
$831$	13.8393	+	5.03708i	0.480079	+	0.174734i
$832$	−3.75320	+	1.36605i	−0.130119	+	0.0473594i
$833$	3.19477	−	2.68073i	0.110692	−	0.0928817i
$834$	12.3879	+	70.2551i	0.428957	+	2.43274i
$835$	19.9079			0.688942
$836$	1.81396	+	3.98736i	0.0627371	+	0.137906i
$837$	57.3887			1.98364
$838$	−1.80566	−	10.2404i	−0.0623755	−	0.353749i
$839$	13.7623	−	11.5479i	0.475126	−	0.398678i	−0.373534	−	0.927616i	$-0.621854\pi$
$839$	13.7623	−	11.5479i	0.475126	−	0.398678i	0.848660	+	0.528938i	$0.177410\pi$
$840$	4.98808	−	1.81551i	0.172105	−	0.0626411i
$841$	−53.8044	−	19.5832i	−1.85533	−	0.675283i
$842$	5.54236	+	4.65059i	0.191002	+	0.160270i
$843$	37.8784	−	65.6073i	1.30460	−	2.25964i
$844$	−8.28111	−	14.3433i	−0.285048	−	0.493717i
$845$	0.823250	−	4.66888i	0.0283207	−	0.160614i
$846$	−9.32985	+	52.9122i	−0.320767	+	1.81916i
$847$	−4.99501	−	8.65162i	−0.171631	−	0.297273i
$848$	0.422251	−	0.731360i	0.0145002	−	0.0251150i
$849$	−9.89041	−	8.29904i	−0.339438	−	0.284822i
$850$	9.49121	+	3.45452i	0.325546	+	0.118489i
$851$	20.2079	−	7.35506i	0.692717	−	0.252128i
$852$	2.55532	−	2.14417i	0.0875437	−	0.0734579i
$853$	9.25251	+	52.4736i	0.316800	+	1.79666i	0.561945	+	0.827174i	$0.310053\pi$
$853$	9.25251	+	52.4736i	0.316800	+	1.79666i	−0.245146	+	0.969486i	$0.578836\pi$
$854$	2.17110			0.0742936
$855$	45.7564	−	31.4029i	1.56484	−	1.07396i
$856$	−1.35041			−0.0461562
$857$	3.54097	+	20.0818i	0.120957	+	0.685982i	0.983627	+	0.180215i	$0.0576793\pi$
$857$	3.54097	+	20.0818i	0.120957	+	0.685982i	−0.862670	+	0.505767i	$0.831210\pi$
$858$	−10.1653	+	8.52970i	−0.347037	+	0.291199i
$859$	−11.5134	+	4.19054i	−0.392832	+	0.142979i	−0.530881	−	0.847446i	$-0.678139\pi$
$859$	−11.5134	+	4.19054i	−0.392832	+	0.142979i	0.138049	+	0.990425i	$0.455917\pi$
$860$	5.22047	+	1.90010i	0.178017	+	0.0647928i
$861$	30.1224	+	25.2757i	1.02657	+	0.861393i
$862$	−5.64288	+	9.77375i	−0.192197	+	0.332895i
$863$	−19.2464	−	33.3357i	−0.655154	−	1.13476i	−0.981855	−	0.189632i	$-0.939271\pi$
$863$	−19.2464	−	33.3357i	−0.655154	−	1.13476i	0.326702	−	0.945127i	$-0.394063\pi$
$864$	2.82973	−	16.0482i	0.0962694	−	0.545971i
$865$	3.30443	−	18.7403i	0.112354	−	0.637191i
$866$	13.8639	+	24.0130i	0.471115	+	0.815995i
$867$	−0.649321	+	1.12466i	−0.0220521	+	0.0381953i
$868$	−2.69777	−	2.26370i	−0.0915684	−	0.0768350i
$869$	3.38924	+	1.23358i	0.114972	+	0.0418465i
$870$	46.3267	−	16.8615i	1.57062	−	0.571660i
$871$	5.60517	−	4.70330i	0.189924	−	0.159365i
$872$	3.03307	+	17.2014i	0.102713	+	0.582512i
$873$	−113.587			−3.84435
$874$	−1.15784	−	14.8373i	−0.0391645	−	0.501878i
$875$	11.9170			0.402867
$876$	2.53938	+	14.4016i	0.0857978	+	0.486584i
$877$	25.2675	−	21.2019i	0.853222	−	0.715938i	−0.107275	−	0.994229i	$-0.534213\pi$
$877$	25.2675	−	21.2019i	0.853222	−	0.715938i	0.960497	+	0.278291i	$0.0897681\pi$
$878$	15.2183	−	5.53900i	0.513592	−	0.186932i
$879$	−28.5318	−	10.3847i	−0.962354	−	0.350268i
$880$	−1.23612	−	1.03723i	−0.0416696	−	0.0349650i
$881$	−2.53551	+	4.39163i	−0.0854236	+	0.147958i	−0.905572	−	0.424193i	$-0.860558\pi$
$881$	−2.53551	+	4.39163i	−0.0854236	+	0.147958i	0.820148	+	0.572151i	$0.193891\pi$
$882$	−3.96462	−	6.86692i	−0.133496	−	0.231221i
$883$	4.80773	−	27.2660i	0.161793	−	0.917573i	−0.790517	−	0.612440i	$-0.790188\pi$
$883$	4.80773	−	27.2660i	0.161793	−	0.917573i	0.952310	−	0.305133i	$-0.0987009\pi$
$884$	2.89249	−	16.4041i	0.0972849	−	0.551730i
$885$	35.5229	+	61.5274i	1.19409	+	2.06822i
$886$	0.960714	−	1.66400i	0.0322758	−	0.0559033i
$887$	27.0380	+	22.6876i	0.907848	+	0.761775i	0.971708	−	0.236184i	$-0.0758968\pi$
$887$	27.0380	+	22.6876i	0.907848	+	0.761775i	−0.0638605	+	0.997959i	$0.520341\pi$
$888$	−19.5668	−	7.12174i	−0.656619	−	0.238990i
$889$	−1.08768	+	0.395884i	−0.0364797	+	0.0132775i
$890$	1.05963	−	0.889139i	0.0355190	−	0.0298040i
$891$	−5.25021	−	29.7754i	−0.175889	−	0.997515i
$892$	−9.06669			−0.303575
$893$	17.1675	−	24.0342i	0.574487	−	0.804275i
$894$	−57.4002			−1.91975
$895$	−1.55406	−	8.81352i	−0.0519466	−	0.294604i
$896$	−0.766044	+	0.642788i	−0.0255917	+	0.0214740i
$897$	42.3635	−	15.4191i	1.41448	−	0.514828i
$898$	−6.67940	−	2.43110i	−0.222894	−	0.0811269i
$899$	−25.0555	−	21.0241i	−0.835649	−	0.701193i
$900$	9.60180	−	16.6308i	0.320060	−	0.554360i
$901$	1.76098	+	3.05011i	0.0586669	+	0.101614i
$902$	2.07571	−	11.7719i	0.0691134	−	0.391962i
$903$	1.98626	−	11.2647i	0.0660987	−	0.374865i
$904$	−2.91621	−	5.05102i	−0.0969916	−	0.167994i
$905$	0.404203	−	0.700101i	0.0134362	−	0.0232721i
$906$	48.9515	+	41.0752i	1.62631	+	1.36463i
$907$	−23.5943	−	8.58762i	−0.783436	−	0.285147i	−0.0808311	−	0.996728i	$-0.525757\pi$
$907$	−23.5943	−	8.58762i	−0.783436	−	0.285147i	−0.702605	+	0.711581i	$0.747980\pi$
$908$	−13.3003	+	4.84091i	−0.441386	+	0.160651i
$909$	−45.2380	+	37.9592i	−1.50045	+	1.25903i
$910$	−1.11362	−	6.31568i	−0.0369163	−	0.209363i
$911$	18.6010			0.616278			0.308139	−	0.951341i	$-0.400294\pi$
$911$	18.6010			0.616278			0.308139	+	0.951341i	$0.400294\pi$
$912$	−8.37584	+	11.7261i	−0.277352	+	0.388289i
$913$	−9.95725			−0.329537
$914$	3.72054	+	21.1002i	0.123064	+	0.697933i
$915$	−8.82840	+	7.40790i	−0.291858	+	0.244898i
$916$	27.2470	−	9.91710i	0.900267	−	0.327670i
$917$	−16.1794	−	5.88882i	−0.534291	−	0.194466i
$918$	52.0612	+	43.6845i	1.71827	+	1.44180i
$919$	−8.46367	+	14.6595i	−0.279191	+	0.483573i	−0.971184	−	0.238332i	$-0.923400\pi$
$919$	−8.46367	+	14.6595i	−0.279191	+	0.483573i	0.691993	+	0.721904i	$0.256733\pi$
$920$	2.74105	+	4.74765i	0.0903699	+	0.156525i
$921$	−10.8366	+	61.4571i	−0.357076	+	2.02508i
$922$	0.333736	−	1.89271i	0.0109910	−	0.0623331i
$923$	−2.01503	−	3.49014i	−0.0663256	−	0.114879i
$924$	−1.66119	+	2.87727i	−0.0546492	+	0.0946552i
$925$	−11.6854	−	9.80523i	−0.384214	−	0.322394i
$926$	−12.5321	−	4.56130i	−0.411829	−	0.149893i
$927$	1.55199	−	0.564879i	0.0509742	−	0.0185531i
$928$	−7.11463	+	5.96988i	−0.233549	+	0.195971i
$929$	0.862885	+	4.89367i	0.0283104	+	0.160556i	0.995685	−	0.0927923i	$-0.0295793\pi$
$929$	0.862885	+	4.89367i	0.0283104	+	0.160556i	−0.967375	+	0.253348i	$0.918468\pi$
$930$	18.6938			0.612995
$931$	0.339120	+	4.34569i	0.0111142	+	0.142424i
$932$	22.3353			0.731617
$933$	−8.20909	−	46.5560i	−0.268753	−	1.52418i
$934$	9.61396	−	8.06707i	0.314578	−	0.263962i
$935$	6.32380	−	2.30167i	0.206810	−	0.0752728i
$936$	−29.7600	−	10.8318i	−0.972737	−	0.354047i
$937$	−10.3549	−	8.68877i	−0.338279	−	0.283850i	0.457784	−	0.889063i	$-0.348643\pi$
$937$	−10.3549	−	8.68877i	−0.338279	−	0.283850i	−0.796063	+	0.605214i	$0.793088\pi$
$938$	0.915986	−	1.58653i	0.0299080	−	0.0518022i
$939$	15.3294	+	26.5513i	0.500256	+	0.866469i
$940$	−1.88928	+	10.7146i	−0.0616214	+	0.349472i
$941$	−3.56489	+	20.2175i	−0.116212	+	0.659072i	0.869931	+	0.493174i	$0.164163\pi$
$941$	−3.56489	+	20.2175i	−0.116212	+	0.659072i	−0.986143	+	0.165898i	$0.946948\pi$
$942$	−20.4064	−	35.3450i	−0.664877	−	1.15160i
$943$	−20.3051	+	35.1695i	−0.661226	+	1.14528i
$944$	−10.2529	−	8.60317i	−0.333702	−	0.280009i
$945$	24.5874	+	8.94909i	0.799829	+	0.291114i
$946$	−3.26748	+	1.18926i	−0.106235	+	0.0386663i
$947$	0.735524	−	0.617178i	0.0239013	−	0.0200556i	−0.630759	−	0.775979i	$-0.717256\pi$
$947$	0.735524	−	0.617178i	0.0239013	−	0.0200556i	0.654660	+	0.755923i	$0.272812\pi$
$948$	2.06028	+	11.6845i	0.0669149	+	0.379493i
$949$	17.6677			0.573517
$950$	−8.70400	+	5.97362i	−0.282395	+	0.193810i
$951$	−49.8755			−1.61732
$952$	−0.724195	−	4.10711i	−0.0234713	−	0.133112i
$953$	10.8390	−	9.09503i	0.351111	−	0.294617i	−0.450125	−	0.892965i	$-0.648621\pi$
$953$	10.8390	−	9.09503i	0.351111	−	0.294617i	0.801236	+	0.598349i	$0.204176\pi$
$954$	6.29242	−	2.29025i	0.203725	−	0.0741497i
$955$	−31.0806	−	11.3124i	−1.00574	−	0.366061i
$956$	0.201644	+	0.169200i	0.00652164	+	0.00547231i
$957$	−15.4283	+	26.7226i	−0.498726	+	0.863819i
$958$	7.32912	+	12.6944i	0.236793	+	0.410138i
$959$	1.21262	−	6.87710i	0.0391575	−	0.222073i
$960$	0.921759	−	5.22756i	0.0297497	−	0.168719i
$961$	9.29884	+	16.1061i	0.299963	+	0.519551i
$962$	−12.5784	+	21.7864i	−0.405544	+	0.702423i
$963$	−8.20262	−	6.88281i	−0.264326	−	0.221796i
$964$	12.9400	+	4.70977i	0.416769	+	0.151692i
$965$	14.2164	−	5.17434i	0.457642	−	0.166568i
$966$	8.64658	−	7.25534i	0.278199	−	0.233437i
$967$	1.03232	+	5.85459i	0.0331973	+	0.188271i	0.996897	−	0.0787175i	$-0.0250825\pi$
$967$	1.03232	+	5.85459i	0.0331973	+	0.188271i	−0.963700	+	0.266989i	$0.913971\pi$
$968$	−9.99003			−0.321092
$969$	−24.8859	−	54.7029i	−0.799449	−	1.75731i
$970$	−23.0012			−0.738525
$971$	3.56517	+	20.2191i	0.114412	+	0.648862i	0.987040	+	0.160476i	$0.0513030\pi$
$971$	3.56517	+	20.2191i	0.114412	+	0.648862i	−0.872628	+	0.488386i	$0.837586\pi$
$972$	38.7407	−	32.5073i	1.24261	−	1.04267i
$973$	20.2776	−	7.38046i	0.650071	−	0.236607i
$974$	−25.3837	−	9.23891i	−0.813346	−	0.296034i
$975$	−24.4972	−	20.5556i	−0.784538	−	0.658305i
$976$	1.08555	−	1.88023i	0.0347477	−	0.0601847i
$977$	−9.89884	−	17.1453i	−0.316692	−	0.548526i	0.663104	−	0.748527i	$-0.269239\pi$
$977$	−9.89884	−	17.1453i	−0.316692	−	0.548526i	−0.979796	+	0.200001i	$0.935905\pi$
$978$	6.09167	−	34.5476i	0.194790	−	1.10471i
$979$	−0.150340	+	0.852621i	−0.00480489	+	0.0272499i
$980$	−0.802828	−	1.39054i	−0.0256454	−	0.0444191i
$981$	−69.2489	+	119.943i	−2.21095	+	3.82948i
$982$	10.4522	+	8.77047i	0.333544	+	0.279877i
$983$	55.1482	+	20.0723i	1.75895	+	0.640207i	0.999941	−	0.0108685i	$-0.00345963\pi$
$983$	55.1482	+	20.0723i	1.75895	+	0.640207i	0.759013	+	0.651075i	$0.225682\pi$
$984$	36.9506	−	13.4489i	1.17794	−	0.428736i
$985$	−7.51335	+	6.30445i	−0.239395	+	0.200877i
$986$	−6.72595	−	38.1448i	−0.214198	−	1.21478i
$987$	22.4010			0.713032
$988$	12.1944	+	12.4256i	0.387957	+	0.395311i
$989$	11.8132			0.375638
$990$	−2.22182	−	12.6006i	−0.0706141	−	0.400472i
$991$	13.2105	−	11.0849i	0.419645	−	0.352124i	−0.408383	−	0.912811i	$-0.633907\pi$
$991$	13.2105	−	11.0849i	0.419645	−	0.352124i	0.828028	+	0.560686i	$0.189463\pi$
$992$	−3.30931	+	1.20449i	−0.105071	+	0.0382426i
$993$	102.362	+	37.2567i	3.24836	+	1.18230i
$994$	−0.772947	−	0.648580i	−0.0245164	−	0.0205717i
$995$	−16.1280	+	27.9345i	−0.511292	+	0.885584i
$996$	−16.3776	−	28.3668i	−0.518943	−	0.898836i
$997$	−2.08307	+	11.8137i	−0.0659715	+	0.374143i	0.933891	+	0.357558i	$0.116391\pi$
$997$	−2.08307	+	11.8137i	−0.0659715	+	0.374143i	−0.999862	+	0.0165850i	$0.994721\pi$
$998$	−2.97197	+	16.8549i	−0.0940761	+	0.533532i
$999$	−51.3197	−	88.8884i	−1.62368	−	2.81230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	266.2.u.c.85.3	✓	18
19.6	even	9		5054.2.a.bk.1.9		9
19.13	odd	18		5054.2.a.bj.1.1		9
19.17	even	9	inner	266.2.u.c.169.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.c.85.3	✓	18	1.1	even	1	trivial
266.2.u.c.169.3	yes	18	19.17	even	9	inner
5054.2.a.bj.1.1		9	19.13	odd	18
5054.2.a.bk.1.9		9	19.6	even	9

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:	\( N \)	\(=\)	\( 266 = 2 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	266.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(2.53250 - 2.12502i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.50882 - 0.549166i) q^{5} +(2.53250 + 2.12502i) q^{6} +(0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.37690 - 7.80878i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(2.53250 - 2.12502i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.50882 - 0.549166i) q^{5} +(2.53250 + 2.12502i) q^{6} +(0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.37690 - 7.80878i) q^{9} +(0.278819 - 1.58126i) q^{10} +(0.502487 + 0.870333i) q^{11} +(-1.65297 + 2.86303i) q^{12} +(3.05964 + 2.56734i) q^{13} +(0.939693 + 0.342020i) q^{14} +(-4.98808 + 1.81551i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.724195 + 4.10711i) q^{17} +7.92924 q^{18} +(-3.93304 - 1.87916i) q^{19} +1.60566 q^{20} +(-0.574070 - 3.25572i) q^{21} +(-0.769855 + 0.645985i) q^{22} +(3.20835 - 1.16774i) q^{23} +(-3.10657 - 1.13070i) q^{24} +(-1.85526 - 1.55675i) q^{25} +(-1.99704 + 3.45897i) q^{26} +(-8.14789 - 14.1126i) q^{27} +(-0.173648 + 0.984808i) q^{28} +(-1.61276 + 9.14639i) q^{29} +(-2.65410 - 4.59704i) q^{30} +(-1.76085 + 3.04987i) q^{31} +(0.766044 + 0.642788i) q^{32} +(3.12202 + 1.13632i) q^{33} +(-3.91896 + 1.42638i) q^{34} +(-1.23000 + 1.03210i) q^{35} +(1.37690 + 7.80878i) q^{36} +6.29853 q^{37} +(1.16764 - 4.19960i) q^{38} +13.2042 q^{39} +(0.278819 + 1.58126i) q^{40} +(-9.11160 + 7.64554i) q^{41} +(3.10657 - 1.13070i) q^{42} +(3.25130 + 1.18338i) q^{43} +(-0.769855 - 0.645985i) q^{44} +(-6.36581 + 11.0259i) q^{45} +(1.70713 + 2.95683i) q^{46} +(-1.17664 + 6.67305i) q^{47} +(0.574070 - 3.25572i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.21094 - 2.09740i) q^{50} +(10.5617 + 8.86232i) q^{51} +(-3.75320 - 1.36605i) q^{52} +(0.793572 - 0.288837i) q^{53} +(12.4833 - 10.4747i) q^{54} +(-0.280206 - 1.58913i) q^{55} -1.00000 q^{56} +(-13.9536 + 3.59881i) q^{57} -9.28749 q^{58} +(-2.32413 - 13.1808i) q^{59} +(4.06632 - 3.41205i) q^{60} +(2.04017 - 0.742561i) q^{61} +(-3.30931 - 1.20449i) q^{62} +(-6.07415 - 5.09682i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.20655 - 5.55391i) q^{65} +(-0.576926 + 3.27191i) q^{66} +(0.318118 - 1.80414i) q^{67} +(-2.08524 - 3.61173i) q^{68} +(5.64365 - 9.77509i) q^{69} +(-1.23000 - 1.03210i) q^{70} +(-0.948160 - 0.345102i) q^{71} +(-7.45105 + 2.71196i) q^{72} +(3.38857 - 2.84335i) q^{73} +(1.09373 + 6.20284i) q^{74} -8.00656 q^{75} +(4.33855 + 0.420653i) q^{76} +1.00497 q^{77} +(2.29288 + 13.0036i) q^{78} +(2.74926 - 2.30690i) q^{79} +(-1.50882 + 0.549166i) q^{80} +(-28.2708 - 10.2897i) q^{81} +(-9.11160 - 7.64554i) q^{82} +(-4.95398 + 8.58055i) q^{83} +(1.65297 + 2.86303i) q^{84} +(1.16281 - 6.59461i) q^{85} +(-0.600817 + 3.40740i) q^{86} +(15.3519 + 26.5903i) q^{87} +(0.502487 - 0.870333i) q^{88} +(0.659939 + 0.553754i) q^{89} +(-11.9638 - 4.35447i) q^{90} +(3.75320 - 1.36605i) q^{91} +(-2.61547 + 2.19464i) q^{92} +(2.02170 + 11.4656i) q^{93} -6.77599 q^{94} +(4.90228 + 4.99521i) q^{95} +3.30594 q^{96} +(-2.48753 - 14.1075i) q^{97} +(0.766044 - 0.642788i) q^{98} +(7.48811 - 2.72545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 6 q^{5} + 3 q^{6} + 9 q^{7} - 9 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 6 q^{13} - 21 q^{17} + 24 q^{18} - 18 q^{19} + 6 q^{20} + 6 q^{21} - 15 q^{22} + 6 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 24 q^{27} + 21 q^{29} + 6 q^{30} - 9 q^{31} - 24 q^{33} + 24 q^{34} - 3 q^{35} - 3 q^{36} + 18 q^{37} + 12 q^{38} + 66 q^{39} + 3 q^{40} - 24 q^{41} - 3 q^{42} - 6 q^{43} - 15 q^{44} - 18 q^{45} - 6 q^{46} - 9 q^{47} - 6 q^{48} - 9 q^{49} + 18 q^{51} + 3 q^{52} - 9 q^{53} + 9 q^{54} - 27 q^{55} - 18 q^{56} + 27 q^{57} - 12 q^{58} + 45 q^{59} + 9 q^{60} + 6 q^{61} - 15 q^{62} - 15 q^{63} - 9 q^{64} + 3 q^{65} + 39 q^{66} + 27 q^{67} - 12 q^{68} - 6 q^{69} - 3 q^{70} - 27 q^{71} - 12 q^{72} + 21 q^{73} - 24 q^{74} - 6 q^{75} + 15 q^{76} + 6 q^{77} + 36 q^{78} - 6 q^{79} - 6 q^{80} - 99 q^{81} - 24 q^{82} - 9 q^{83} + 3 q^{84} + 36 q^{85} - 6 q^{86} + 3 q^{87} + 3 q^{88} + 54 q^{89} - 63 q^{90} - 3 q^{91} - 12 q^{92} - 75 q^{93} + 42 q^{94} + 57 q^{95} + 6 q^{96} + 60 q^{97} - 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 6 * q^5 + 3 * q^6 + 9 * q^7 - 9 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 6 * q^13 - 21 * q^17 + 24 * q^18 - 18 * q^19 + 6 * q^20 + 6 * q^21 - 15 * q^22 + 6 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 24 * q^27 + 21 * q^29 + 6 * q^30 - 9 * q^31 - 24 * q^33 + 24 * q^34 - 3 * q^35 - 3 * q^36 + 18 * q^37 + 12 * q^38 + 66 * q^39 + 3 * q^40 - 24 * q^41 - 3 * q^42 - 6 * q^43 - 15 * q^44 - 18 * q^45 - 6 * q^46 - 9 * q^47 - 6 * q^48 - 9 * q^49 + 18 * q^51 + 3 * q^52 - 9 * q^53 + 9 * q^54 - 27 * q^55 - 18 * q^56 + 27 * q^57 - 12 * q^58 + 45 * q^59 + 9 * q^60 + 6 * q^61 - 15 * q^62 - 15 * q^63 - 9 * q^64 + 3 * q^65 + 39 * q^66 + 27 * q^67 - 12 * q^68 - 6 * q^69 - 3 * q^70 - 27 * q^71 - 12 * q^72 + 21 * q^73 - 24 * q^74 - 6 * q^75 + 15 * q^76 + 6 * q^77 + 36 * q^78 - 6 * q^79 - 6 * q^80 - 99 * q^81 - 24 * q^82 - 9 * q^83 + 3 * q^84 + 36 * q^85 - 6 * q^86 + 3 * q^87 + 3 * q^88 + 54 * q^89 - 63 * q^90 - 3 * q^91 - 12 * q^92 - 75 * q^93 + 42 * q^94 + 57 * q^95 + 6 * q^96 + 60 * q^97 - 27 * q^99

Introduction

L-functions

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