LMFDB - Embedded newform 58.2.d.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [58,2,Mod(7,58)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(58, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("58.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	58.d (of order $7$, 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:	$0.463132331723$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.2
Root			$-1.56920 - 0.755686i$ of defining polynomial
Character	$\chi$	$=$	58.25
Dual form			58.2.d.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(1.56920 - 0.755686i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.110081 - 0.482295i) q^{5} +(0.387560 + 1.69801i) q^{6} +(-2.82760 + 1.36170i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.0208506 - 0.0261458i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(1.56920 - 0.755686i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.110081 - 0.482295i) q^{5} +(0.387560 + 1.69801i) q^{6} +(-2.82760 + 1.36170i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.0208506 - 0.0261458i) q^{9} +(0.445708 + 0.214642i) q^{10} +(0.870839 + 1.09200i) q^{11} -1.74168 q^{12} +(-3.56353 - 4.46852i) q^{13} +(-0.698359 - 3.05971i) q^{14} +(-0.191725 - 0.840003i) q^{15} +(0.623490 + 0.781831i) q^{16} +5.31800 q^{17} +(0.0208506 + 0.0261458i) q^{18} +(-4.47471 - 2.15491i) q^{19} +(-0.308439 + 0.386771i) q^{20} +(-3.40804 + 4.27355i) q^{21} +(-1.25840 + 0.606013i) q^{22} +(0.181045 + 0.793210i) q^{23} +(0.387560 - 1.69801i) q^{24} +(4.28435 + 2.06324i) q^{25} +(5.14944 - 2.47984i) q^{26} +(-1.14972 + 5.03725i) q^{27} +3.13840 q^{28} +(5.38501 - 0.0414712i) q^{29} +0.861605 q^{30} +(-1.41596 + 6.20373i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(2.19173 + 1.05548i) q^{33} +(-1.18337 + 5.18466i) q^{34} +(0.345477 + 1.51363i) q^{35} +(-0.0301299 + 0.0145098i) q^{36} +(5.56630 - 6.97992i) q^{37} +(3.09660 - 3.88301i) q^{38} +(-8.96867 - 4.31909i) q^{39} +(-0.308439 - 0.386771i) q^{40} -4.01226 q^{41} +(-3.40804 - 4.27355i) q^{42} +(0.310799 + 1.36170i) q^{43} +(-0.310799 - 1.36170i) q^{44} +(-0.0103147 - 0.0129343i) q^{45} -0.813609 q^{46} +(-6.42079 - 8.05142i) q^{47} +(1.56920 + 0.755686i) q^{48} +(1.77665 - 2.22785i) q^{49} +(-2.96486 + 3.71782i) q^{50} +(8.34499 - 4.01873i) q^{51} +(1.27181 + 5.57215i) q^{52} +(-0.944288 + 4.13720i) q^{53} +(-4.65512 - 2.24179i) q^{54} +(0.622528 - 0.299794i) q^{55} +(-0.698359 + 3.05971i) q^{56} -8.65014 q^{57} +(-1.15784 + 5.25922i) q^{58} +11.1598 q^{59} +(-0.191725 + 0.840003i) q^{60} +(-4.38454 + 2.11149i) q^{61} +(-5.73311 - 2.76092i) q^{62} +(-0.0233543 + 0.102322i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-2.54742 + 1.22677i) q^{65} +(-1.51672 + 1.90191i) q^{66} +(4.45072 - 5.58102i) q^{67} +(-4.79135 - 2.30739i) q^{68} +(0.883513 + 1.10789i) q^{69} -1.55256 q^{70} +(3.76423 + 4.72019i) q^{71} +(-0.00744148 - 0.0326033i) q^{72} +(-2.73238 - 11.9713i) q^{73} +(5.56630 + 6.97992i) q^{74} +8.28215 q^{75} +(3.09660 + 3.88301i) q^{76} +(-3.94935 - 1.90191i) q^{77} +(6.20651 - 7.78272i) q^{78} +(-5.86220 + 7.35096i) q^{79} +(0.445708 - 0.214642i) q^{80} +(2.02476 + 8.87107i) q^{81} +(0.892813 - 3.91167i) q^{82} +(-11.4508 - 5.51441i) q^{83} +(4.92476 - 2.37164i) q^{84} +(0.585409 - 2.56484i) q^{85} -1.39672 q^{86} +(8.41880 - 4.13445i) q^{87} +1.39672 q^{88} +(-0.398796 + 1.74724i) q^{89} +(0.0149052 - 0.00717798i) q^{90} +(16.1610 + 7.78272i) q^{91} +(0.181045 - 0.793210i) q^{92} +(2.46615 + 10.8049i) q^{93} +(9.27831 - 4.46820i) q^{94} +(-1.53188 + 1.92092i) q^{95} +(-1.08592 + 1.36170i) q^{96} +(-3.42035 - 1.64715i) q^{97} +(1.77665 + 2.22785i) q^{98} +0.0467086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9} - 7 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} + q^{14} - 9 q^{15} - 2 q^{16} - 12 q^{17} - 11 q^{18} - 6 q^{19} + 7 q^{20} - 13 q^{21} - 2 q^{22} + 35 q^{23} + 4 q^{24} - 6 q^{25} + 8 q^{26} + 39 q^{27} - 6 q^{28} - 14 q^{29} + 54 q^{30} - 8 q^{31} - 2 q^{32} + 33 q^{33} - 5 q^{34} - 18 q^{35} - 4 q^{36} + 31 q^{37} + q^{38} - 22 q^{39} + 7 q^{40} - 30 q^{41} - 13 q^{42} - 5 q^{43} + 5 q^{44} - 20 q^{45} - 28 q^{46} - 33 q^{47} - 3 q^{48} + 37 q^{49} + q^{50} - 15 q^{51} - 6 q^{52} + 13 q^{53} - 24 q^{54} + 36 q^{55} + q^{56} - 38 q^{57} + 38 q^{59} - 9 q^{60} - 5 q^{61} - 8 q^{62} + 4 q^{63} - 2 q^{64} - 20 q^{65} - 30 q^{66} - 7 q^{67} - 19 q^{68} + 20 q^{69} - 18 q^{70} + 3 q^{71} + 3 q^{72} - 22 q^{73} + 31 q^{74} - 2 q^{75} + q^{76} + 10 q^{77} + 41 q^{78} - 60 q^{79} - 7 q^{80} + 88 q^{81} + 26 q^{82} - 39 q^{83} + 43 q^{84} + 38 q^{85} + 2 q^{86} + 9 q^{87} - 2 q^{88} + 39 q^{89} - 34 q^{90} + 61 q^{91} + 35 q^{92} - 54 q^{93} + 16 q^{94} + 55 q^{95} - 3 q^{96} - 19 q^{97} + 37 q^{98} - 8 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9 - 7 * q^10 - 2 * q^11 + 4 * q^12 + q^13 + q^14 - 9 * q^15 - 2 * q^16 - 12 * q^17 - 11 * q^18 - 6 * q^19 + 7 * q^20 - 13 * q^21 - 2 * q^22 + 35 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 39 * q^27 - 6 * q^28 - 14 * q^29 + 54 * q^30 - 8 * q^31 - 2 * q^32 + 33 * q^33 - 5 * q^34 - 18 * q^35 - 4 * q^36 + 31 * q^37 + q^38 - 22 * q^39 + 7 * q^40 - 30 * q^41 - 13 * q^42 - 5 * q^43 + 5 * q^44 - 20 * q^45 - 28 * q^46 - 33 * q^47 - 3 * q^48 + 37 * q^49 + q^50 - 15 * q^51 - 6 * q^52 + 13 * q^53 - 24 * q^54 + 36 * q^55 + q^56 - 38 * q^57 + 38 * q^59 - 9 * q^60 - 5 * q^61 - 8 * q^62 + 4 * q^63 - 2 * q^64 - 20 * q^65 - 30 * q^66 - 7 * q^67 - 19 * q^68 + 20 * q^69 - 18 * q^70 + 3 * q^71 + 3 * q^72 - 22 * q^73 + 31 * q^74 - 2 * q^75 + q^76 + 10 * q^77 + 41 * q^78 - 60 * q^79 - 7 * q^80 + 88 * q^81 + 26 * q^82 - 39 * q^83 + 43 * q^84 + 38 * q^85 + 2 * q^86 + 9 * q^87 - 2 * q^88 + 39 * q^89 - 34 * q^90 + 61 * q^91 + 35 * q^92 - 54 * q^93 + 16 * q^94 + 55 * q^95 - 3 * q^96 - 19 * q^97 + 37 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	1.56920	−	0.755686i	0.905977	−	0.436295i	0.0779327	−	0.996959i	$-0.475168\pi$
$3$	1.56920	−	0.755686i	0.905977	−	0.436295i	0.828044	+	0.560663i	$0.189454\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.110081	−	0.482295i	0.0492296	−	0.215689i	−0.944330	−	0.329000i	$-0.893288\pi$
$5$	0.110081	−	0.482295i	0.0492296	−	0.215689i	0.993560	+	0.113311i	$0.0361456\pi$
$6$	0.387560	+	1.69801i	0.158221	+	0.693210i
$7$	−2.82760	+	1.36170i	−1.06873	+	0.514674i	−0.883697	−	0.468059i	$-0.844954\pi$
$7$	−2.82760	+	1.36170i	−1.06873	+	0.514674i	−0.185033	+	0.982732i	$0.559239\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	0.0208506	−	0.0261458i	0.00695019	−	0.00871526i
$10$	0.445708	+	0.214642i	0.140945	+	0.0678756i
$11$	0.870839	+	1.09200i	0.262568	+	0.329250i	0.895587	−	0.444887i	$-0.146756\pi$
$11$	0.870839	+	1.09200i	0.262568	+	0.329250i	−0.633019	+	0.774136i	$0.718185\pi$
$12$	−1.74168			−0.502779
$13$	−3.56353	−	4.46852i	−0.988344	−	1.23934i	−0.970897	−	0.239497i	$-0.923018\pi$
$13$	−3.56353	−	4.46852i	−0.988344	−	1.23934i	−0.0174472	−	0.999848i	$-0.505554\pi$
$14$	−0.698359	−	3.05971i	−0.186644	−	0.817742i
$15$	−0.191725	−	0.840003i	−0.0495032	−	0.216888i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	5.31800			1.28980			0.644902	−	0.764265i	$-0.276898\pi$
$17$	5.31800			1.28980			0.644902	+	0.764265i	$0.276898\pi$
$18$	0.0208506	+	0.0261458i	0.00491453	+	0.00616262i
$19$	−4.47471	−	2.15491i	−1.02657	−	0.494370i	−0.156697	−	0.987647i	$-0.550085\pi$
$19$	−4.47471	−	2.15491i	−1.02657	−	0.494370i	−0.869872	+	0.493277i	$0.835799\pi$
$20$	−0.308439	+	0.386771i	−0.0689691	+	0.0864845i
$21$	−3.40804	+	4.27355i	−0.743695	+	0.932565i
$22$	−1.25840	+	0.606013i	−0.268292	+	0.129202i
$23$	0.181045	+	0.793210i	0.0377505	+	0.165396i	0.990289	−	0.139021i	$-0.0443956\pi$
$23$	0.181045	+	0.793210i	0.0377505	+	0.165396i	−0.952539	+	0.304417i	$0.901538\pi$
$24$	0.387560	−	1.69801i	0.0791103	−	0.346605i
$25$	4.28435	+	2.06324i	0.856871	+	0.412647i
$26$	5.14944	−	2.47984i	1.00989	−	0.486337i
$27$	−1.14972	+	5.03725i	−0.221263	+	0.969419i
$28$	3.13840			0.593101
$29$	5.38501	−	0.0414712i	0.999970	−	0.00770101i
$29$	5.38501	−	0.0414712i	0.999970	−	0.00770101i
$30$	0.861605			0.157307
$31$	−1.41596	+	6.20373i	−0.254314	+	1.11422i	0.672912	+	0.739722i	$0.265043\pi$
$31$	−1.41596	+	6.20373i	−0.254314	+	1.11422i	−0.927226	+	0.374501i	$0.877814\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	2.19173	+	1.05548i	0.381530	+	0.183735i
$34$	−1.18337	+	5.18466i	−0.202946	+	0.889162i
$35$	0.345477	+	1.51363i	0.0583962	+	0.255851i
$36$	−0.0301299	+	0.0145098i	−0.00502166	+	0.00241830i
$37$	5.56630	−	6.97992i	0.915095	−	1.14749i	−0.0735606	−	0.997291i	$-0.523436\pi$
$37$	5.56630	−	6.97992i	0.915095	−	1.14749i	0.988655	−	0.150202i	$-0.0479923\pi$
$38$	3.09660	−	3.88301i	0.502335	−	0.629908i
$39$	−8.96867	−	4.31909i	−1.43614	−	0.691607i
$40$	−0.308439	−	0.386771i	−0.0487685	−	0.0611538i
$41$	−4.01226			−0.626610			−0.313305	−	0.949652i	$-0.601436\pi$
$41$	−4.01226			−0.626610			−0.313305	+	0.949652i	$0.601436\pi$
$42$	−3.40804	−	4.27355i	−0.525872	−	0.659423i
$43$	0.310799	+	1.36170i	0.0473964	+	0.207657i	0.993082	−	0.117427i	$-0.0374646\pi$
$43$	0.310799	+	1.36170i	0.0473964	+	0.207657i	−0.945685	+	0.325084i	$0.894607\pi$
$44$	−0.310799	−	1.36170i	−0.0468547	−	0.205284i
$45$	−0.0103147	−	0.0129343i	−0.00153763	−	0.00192813i
$46$	−0.813609			−0.119960
$47$	−6.42079	−	8.05142i	−0.936569	−	1.17442i	−0.984467	−	0.175568i	$-0.943824\pi$
$47$	−6.42079	−	8.05142i	−0.936569	−	1.17442i	0.0478986	−	0.998852i	$-0.484748\pi$
$48$	1.56920	+	0.755686i	0.226494	+	0.109074i
$49$	1.77665	−	2.22785i	0.253807	−	0.318264i
$50$	−2.96486	+	3.71782i	−0.419295	+	0.525780i
$51$	8.34499	−	4.01873i	1.16853	−	0.562735i
$52$	1.27181	+	5.57215i	0.176368	+	0.772719i
$53$	−0.944288	+	4.13720i	−0.129708	+	0.568288i	0.867748	+	0.497004i	$0.165567\pi$
$53$	−0.944288	+	4.13720i	−0.129708	+	0.568288i	−0.997456	+	0.0712835i	$0.977291\pi$
$54$	−4.65512	−	2.24179i	−0.633481	−	0.305068i
$55$	0.622528	−	0.299794i	0.0839416	−	0.0404241i
$56$	−0.698359	+	3.05971i	−0.0933221	+	0.408871i
$57$	−8.65014			−1.14574
$58$	−1.15784	+	5.25922i	−0.152032	+	0.690569i
$59$	11.1598			1.45288			0.726438	−	0.687232i	$-0.241174\pi$
$59$	11.1598			1.45288			0.726438	+	0.687232i	$0.241174\pi$
$60$	−0.191725	+	0.840003i	−0.0247516	+	0.108444i
$61$	−4.38454	+	2.11149i	−0.561383	+	0.270348i	−0.692982	−	0.720955i	$-0.743703\pi$
$61$	−4.38454	+	2.11149i	−0.561383	+	0.270348i	0.131598	+	0.991303i	$0.457989\pi$
$62$	−5.73311	−	2.76092i	−0.728106	−	0.350637i
$63$	−0.0233543	+	0.102322i	−0.00294237	+	0.0128913i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−2.54742	+	1.22677i	−0.315969	+	0.152163i
$66$	−1.51672	+	1.90191i	−0.186695	+	0.234109i
$67$	4.45072	−	5.58102i	0.543742	−	0.681830i	−0.431718	−	0.902009i	$-0.642092\pi$
$67$	4.45072	−	5.58102i	0.543742	−	0.681830i	0.975460	+	0.220178i	$0.0706639\pi$
$68$	−4.79135	−	2.30739i	−0.581036	−	0.279812i
$69$	0.883513	+	1.10789i	0.106362	+	0.133374i
$70$	−1.55256			−0.185566
$71$	3.76423	+	4.72019i	0.446732	+	0.560184i	0.953304	−	0.302014i	$-0.0976589\pi$
$71$	3.76423	+	4.72019i	0.446732	+	0.560184i	−0.506572	+	0.862198i	$0.669087\pi$
$72$	−0.00744148	−	0.0326033i	−0.000876987	−	0.00384233i
$73$	−2.73238	−	11.9713i	−0.319801	−	1.40114i	−0.837903	−	0.545819i	$-0.816219\pi$
$73$	−2.73238	−	11.9713i	−0.319801	−	1.40114i	0.518103	−	0.855319i	$-0.326639\pi$
$74$	5.56630	+	6.97992i	0.647070	+	0.811400i
$75$	8.28215			0.956341
$76$	3.09660	+	3.88301i	0.355204	+	0.445412i
$77$	−3.94935	−	1.90191i	−0.450070	−	0.216743i
$78$	6.20651	−	7.78272i	0.702749	−	0.881220i
$79$	−5.86220	+	7.35096i	−0.659549	+	0.827048i	−0.993294	−	0.115615i	$-0.963116\pi$
$79$	−5.86220	+	7.35096i	−0.659549	+	0.827048i	0.333745	+	0.942663i	$0.391687\pi$
$80$	0.445708	−	0.214642i	0.0498316	−	0.0239977i
$81$	2.02476	+	8.87107i	0.224974	+	0.985675i
$82$	0.892813	−	3.91167i	0.0985947	−	0.431971i
$83$	−11.4508	−	5.51441i	−1.25689	−	0.605285i	−0.317538	−	0.948246i	$-0.602856\pi$
$83$	−11.4508	−	5.51441i	−1.25689	−	0.605285i	−0.939350	+	0.342960i	$0.888570\pi$
$84$	4.92476	−	2.37164i	0.537336	−	0.258767i
$85$	0.585409	−	2.56484i	0.0634965	−	0.278196i
$86$	−1.39672			−0.150612
$87$	8.41880	−	4.13445i	0.902590	−	0.443259i
$88$	1.39672			0.148891
$89$	−0.398796	+	1.74724i	−0.0422722	+	0.185207i	−0.991656	−	0.128911i	$-0.958852\pi$
$89$	−0.398796	+	1.74724i	−0.0422722	+	0.185207i	0.949384	+	0.314118i	$0.101709\pi$
$90$	0.0149052	−	0.00717798i	0.00157115	−	0.000756626i
$91$	16.1610	+	7.78272i	1.69413	+	0.815851i
$92$	0.181045	−	0.793210i	0.0188753	−	0.0826979i
$93$	2.46615	+	10.8049i	0.255728	+	1.12042i
$94$	9.27831	−	4.46820i	0.956985	−	0.460860i
$95$	−1.53188	+	1.92092i	−0.157168	+	0.197082i
$96$	−1.08592	+	1.36170i	−0.110831	+	0.138978i
$97$	−3.42035	−	1.64715i	−0.347283	−	0.167243i	0.252108	−	0.967699i	$-0.418876\pi$
$97$	−3.42035	−	1.64715i	−0.347283	−	0.167243i	−0.599391	+	0.800456i	$0.704591\pi$
$98$	1.77665	+	2.22785i	0.179469	+	0.225047i
$99$	0.0467086			0.00469439
$100$	−2.96486	−	3.71782i	−0.296486	−	0.371782i
$101$	0.271881	+	1.19119i	0.0270532	+	0.118528i	0.986652	−	0.162846i	$-0.0520672\pi$
$101$	0.271881	+	1.19119i	0.0270532	+	0.118528i	−0.959598	+	0.281373i	$0.909210\pi$
$102$	2.06104	+	9.03001i	0.204074	+	0.894104i
$103$	1.12736	+	1.41366i	0.111082	+	0.139292i	0.834264	−	0.551365i	$-0.185893\pi$
$103$	1.12736	+	1.41366i	0.111082	+	0.139292i	−0.723182	+	0.690657i	$0.757321\pi$
$104$	−5.71545			−0.560446
$105$	1.68595	+	2.11412i	0.164532	+	0.206317i
$106$	−3.82334	−	1.84123i	−0.371356	−	0.178836i
$107$	2.58788	−	3.24509i	0.250179	−	0.313715i	−0.640845	−	0.767670i	$-0.721416\pi$
$107$	2.58788	−	3.24509i	0.250179	−	0.313715i	0.891025	+	0.453955i	$0.149987\pi$
$108$	3.22144	−	4.03956i	0.309983	−	0.388707i
$109$	−13.0682	+	6.29330i	−1.25170	+	0.602789i	−0.937968	−	0.346721i	$-0.887295\pi$
$109$	−13.0682	+	6.29330i	−1.25170	+	0.602789i	−0.313736	+	0.949510i	$0.601581\pi$
$110$	0.153752	+	0.673630i	0.0146596	+	0.0642281i
$111$	3.46000	−	15.1593i	0.328409	−	1.43885i
$112$	−2.82760	−	1.36170i	−0.267183	−	0.128668i
$113$	−15.0312	+	7.23864i	−1.41402	+	0.680954i	−0.975951	−	0.217989i	$-0.930050\pi$
$113$	−15.0312	+	7.23864i	−1.41402	+	0.680954i	−0.438065	+	0.898943i	$0.644336\pi$
$114$	1.92484	−	8.43327i	0.180278	−	0.789848i
$115$	0.402491			0.0375325
$116$	−4.86972	−	2.29910i	−0.452142	−	0.213466i
$117$	−0.191135			−0.0176704
$118$	−2.48328	+	10.8800i	−0.228604	+	1.00158i
$119$	−15.0371	+	7.24151i	−1.37845	+	0.663828i
$120$	−0.776279	−	0.373836i	−0.0708643	−	0.0341264i
$121$	2.01363	−	8.82230i	0.183057	−	0.802027i
$122$	−1.08289	−	4.74446i	−0.0980405	−	0.429544i
$123$	−6.29603	+	3.03201i	−0.567694	+	0.273387i
$124$	3.96744	−	4.97501i	0.356286	−	0.446769i
$125$	3.00891	−	3.77305i	0.269125	−	0.337472i
$126$	−0.0945597	−	0.0455375i	−0.00842405	−	0.00405681i
$127$	−7.91387	−	9.92368i	−0.702243	−	0.880584i	0.294946	−	0.955514i	$-0.404698\pi$
$127$	−7.91387	−	9.92368i	−0.702243	−	0.880584i	−0.997189	+	0.0749295i	$0.976127\pi$
$128$	1.00000			0.0883883
$129$	1.51672	+	1.90191i	0.133540	+	0.167454i
$130$	−0.629161	−	2.75653i	−0.0551811	−	0.241764i
$131$	3.29243	+	14.4251i	0.287661	+	1.26033i	0.887725	+	0.460374i	$0.152285\pi$
$131$	3.29243	+	14.4251i	0.287661	+	1.26033i	−0.600064	+	0.799952i	$0.704858\pi$
$132$	−1.51672	−	1.90191i	−0.132014	−	0.165540i
$133$	15.5870			1.35157
$134$	4.45072	+	5.58102i	0.384483	+	0.482127i
$135$	2.30288	+	1.10901i	0.198200	+	0.0954482i
$136$	3.31572	−	4.15778i	0.284320	−	0.356526i
$137$	−0.941003	+	1.17998i	−0.0803953	+	0.100813i	−0.820403	−	0.571786i	$-0.806251\pi$
$137$	−0.941003	+	1.17998i	−0.0803953	+	0.100813i	0.740007	+	0.672599i	$0.234822\pi$
$138$	−1.27671	+	0.614833i	−0.108681	+	0.0523380i
$139$	−1.94848	−	8.53684i	−0.165268	−	0.724086i	−0.987846	−	0.155434i	$-0.950322\pi$
$139$	−1.94848	−	8.53684i	−0.165268	−	0.724086i	0.822578	−	0.568652i	$-0.192535\pi$
$140$	0.345477	−	1.51363i	0.0291981	−	0.127925i
$141$	−16.1598	−	7.78216i	−1.36090	−	0.655377i
$142$	−5.43947	+	2.61951i	−0.456470	+	0.219824i
$143$	1.77636	−	7.78272i	0.148546	−	0.650824i
$144$	0.0334417			0.00278681
$145$	0.572784	−	2.60173i	0.0475671	−	0.216062i
$146$	12.2792			1.01623
$147$	1.10436	−	4.83852i	0.0910861	−	0.399074i
$148$	−8.04354	+	3.87357i	−0.661175	+	0.318405i
$149$	4.27124	+	2.05692i	0.349914	+	0.168510i	0.600581	−	0.799564i	$-0.294936\pi$
$149$	4.27124	+	2.05692i	0.349914	+	0.168510i	−0.250668	+	0.968073i	$0.580650\pi$
$150$	−1.84295	+	8.07450i	−0.150476	+	0.659280i
$151$	1.44508	+	6.33133i	0.117599	+	0.515236i	0.999075	+	0.0430064i	$0.0136936\pi$
$151$	1.44508	+	6.33133i	0.117599	+	0.515236i	−0.881475	+	0.472230i	$0.843449\pi$
$152$	−4.47471	+	2.15491i	−0.362947	+	0.174786i
$153$	0.110883	−	0.139043i	0.00896438	−	0.0112410i
$154$	2.73304	−	3.42712i	0.220234	−	0.276165i
$155$	2.83616	+	1.36582i	0.227806	+	0.109706i
$156$	6.20651	+	7.78272i	0.496919	+	0.623117i
$157$	6.56139			0.523656			0.261828	−	0.965115i	$-0.415675\pi$
$157$	6.56139			0.523656			0.261828	+	0.965115i	$0.415675\pi$
$158$	−5.86220	−	7.35096i	−0.466371	−	0.584811i
$159$	1.64465	+	7.20566i	0.130429	+	0.571446i
$160$	0.110081	+	0.482295i	0.00870264	+	0.0381288i
$161$	−1.59204	−	1.99635i	−0.125470	−	0.157334i
$162$	−9.09921			−0.714901
$163$	3.52776	+	4.42367i	0.276315	+	0.346488i	0.900553	−	0.434746i	$-0.143162\pi$
$163$	3.52776	+	4.42367i	0.276315	+	0.346488i	−0.624238	+	0.781234i	$0.714590\pi$
$164$	3.61493	+	1.74086i	0.282278	+	0.135938i
$165$	0.750319	−	0.940870i	0.0584123	−	0.0732467i
$166$	7.92419	−	9.93663i	0.615037	−	0.771232i
$167$	10.8919	−	5.24527i	0.842842	−	0.405891i	0.0379260	−	0.999281i	$-0.487925\pi$
$167$	10.8919	−	5.24527i	0.842842	−	0.405891i	0.804915	+	0.593389i	$0.202211\pi$
$168$	1.21632	+	5.32903i	0.0938408	+	0.411143i
$169$	−4.37618	+	19.1733i	−0.336630	+	1.47487i
$170$	2.37027	+	1.14146i	0.181792	+	0.0875462i
$171$	−0.149642	+	0.0720639i	−0.0114434	+	0.00551086i
$172$	0.310799	−	1.36170i	0.0236982	−	0.103829i
$173$	11.6405			0.885008			0.442504	−	0.896767i	$-0.354090\pi$
$173$	11.6405			0.885008			0.442504	+	0.896767i	$0.354090\pi$
$174$	2.15743	+	9.12772i	0.163554	+	0.691971i
$175$	−14.9239			−1.12814
$176$	−0.310799	+	1.36170i	−0.0234273	+	0.102642i
$177$	17.5119	−	8.43327i	1.31627	−	0.633883i
$178$	−1.61469	−	0.777594i	−0.121026	−	0.0582831i
$179$	4.08440	−	17.8949i	0.305282	−	1.33753i	−0.556752	−	0.830678i	$-0.687953\pi$
$179$	4.08440	−	17.8949i	0.305282	−	1.33753i	0.862034	−	0.506850i	$-0.169190\pi$
$180$	0.00368129	+	0.0161288i	0.000274387	+	0.00120217i
$181$	8.91422	−	4.29286i	0.662589	−	0.319086i	−0.0721917	−	0.997391i	$-0.522999\pi$
$181$	8.91422	−	4.29286i	0.662589	−	0.319086i	0.734781	+	0.678305i	$0.237285\pi$
$182$	−11.1838	+	14.0240i	−0.828995	+	1.03953i
$183$	−5.28460	+	6.62667i	−0.390649	+	0.489858i
$184$	0.733037	+	0.353012i	0.0540402	+	0.0260244i
$185$	−2.75364	−	3.45296i	−0.202452	−	0.253866i
$186$	−11.0828			−0.812629
$187$	4.63112	+	5.80724i	0.338661	+	0.424667i
$188$	2.29155	+	10.0400i	0.167129	+	0.732239i
$189$	−3.60827	−	15.8089i	−0.262463	−	1.14993i
$190$	−1.53188	−	1.92092i	−0.111134	−	0.139358i
$191$	0.424259			0.0306983			0.0153492	−	0.999882i	$-0.495114\pi$
$191$	0.424259			0.0306983			0.0153492	+	0.999882i	$0.495114\pi$
$192$	−1.08592	−	1.36170i	−0.0783694	−	0.0982721i
$193$	9.30230	+	4.47975i	0.669594	+	0.322460i	0.737612	−	0.675225i	$-0.235953\pi$
$193$	9.30230	+	4.47975i	0.669594	+	0.322460i	−0.0680181	+	0.997684i	$0.521668\pi$
$194$	2.36695	−	2.96806i	0.169937	−	0.213095i
$195$	−3.07035	+	3.85010i	−0.219872	+	0.275711i
$196$	−2.56733	+	1.23636i	−0.183381	+	0.0883116i
$197$	5.97308	+	26.1698i	0.425564	+	1.86452i	0.498050	+	0.867148i	$0.334050\pi$
$197$	5.97308	+	26.1698i	0.425564	+	1.86452i	−0.0724862	+	0.997369i	$0.523093\pi$
$198$	−0.0103936	+	0.0455375i	−0.000738644	+	0.00323621i
$199$	6.12924	+	2.95169i	0.434490	+	0.209239i	0.638327	−	0.769765i	$-0.279627\pi$
$199$	6.12924	+	2.95169i	0.434490	+	0.209239i	−0.203837	+	0.979005i	$0.565341\pi$
$200$	4.28435	−	2.06324i	0.302950	−	0.145893i
$201$	2.76655	−	12.1211i	0.195138	−	0.854954i
$202$	−1.22182			−0.0859671
$203$	−15.1701	+	7.45002i	−1.06474	+	0.522889i
$204$	−9.26224			−0.648486
$205$	−0.441673	+	1.93510i	−0.0308478	+	0.135153i
$206$	−1.62908	+	0.784523i	−0.113503	+	0.0546603i
$207$	0.0245140	+	0.0118053i	0.00170384	+	0.000820526i
$208$	1.27181	−	5.57215i	0.0881840	−	0.386359i
$209$	−1.54360	−	6.76296i	−0.106773	−	0.467803i
$210$	−2.43627	+	1.17325i	−0.168119	+	0.0809617i
$211$	3.64156	−	4.56638i	0.250696	−	0.314362i	−0.640521	−	0.767941i	$-0.721281\pi$
$211$	3.64156	−	4.56638i	0.250696	−	0.314362i	0.891216	+	0.453579i	$0.149853\pi$
$212$	2.64584	−	3.31777i	0.181717	−	0.227866i
$213$	9.47380	+	4.56234i	0.649134	+	0.312607i
$214$	2.58788	+	3.24509i	0.176904	+	0.221830i
$215$	0.690954			0.0471226
$216$	3.22144	+	4.03956i	0.219191	+	0.274857i
$217$	−4.44385	−	19.4698i	−0.301668	−	1.32169i
$218$	−3.22757	−	14.1409i	−0.218599	−	0.957744i
$219$	−13.3342	−	16.7206i	−0.901042	−	1.12987i
$220$	−0.690954			−0.0465841
$221$	−18.9508	−	23.7636i	−1.27477	−	1.59851i
$222$	14.0093	+	6.74650i	0.940240	+	0.452796i
$223$	−13.6769	+	17.1503i	−0.915874	+	1.14847i	0.0726432	+	0.997358i	$0.476857\pi$
$223$	−13.6769	+	17.1503i	−0.915874	+	1.14847i	−0.988517	+	0.151111i	$0.951715\pi$
$224$	1.95676	−	2.45370i	0.130741	−	0.163944i
$225$	0.143276	−	0.0689982i	0.00955174	−	0.00459988i
$226$	−3.71240	−	16.2651i	−0.246945	−	1.08194i
$227$	0.479626	−	2.10138i	0.0318339	−	0.139474i	−0.956514	−	0.291688i	$-0.905783\pi$
$227$	0.479626	−	2.10138i	0.0318339	−	0.139474i	0.988348	+	0.152214i	$0.0486403\pi$
$228$	7.79351	+	3.75316i	0.516138	+	0.248559i
$229$	−8.37172	+	4.03161i	−0.553219	+	0.266416i	−0.689539	−	0.724249i	$-0.742187\pi$
$229$	−8.37172	+	4.03161i	−0.553219	+	0.266416i	0.136320	+	0.990665i	$0.456472\pi$
$230$	−0.0895627	+	0.392400i	−0.00590559	+	0.0258741i
$231$	−7.63456			−0.502317
$232$	3.32507	−	4.23602i	0.218302	−	0.278109i
$233$	−11.7848			−0.772045			−0.386022	−	0.922489i	$-0.626151\pi$
$233$	−11.7848			−0.772045			−0.386022	+	0.922489i	$0.626151\pi$
$234$	0.0425314	−	0.186342i	0.00278037	−	0.0121816i
$235$	−4.58996	+	2.21041i	−0.299416	+	0.144191i
$236$	−10.0546	−	4.84204i	−0.654498	−	0.315190i
$237$	−3.64393	+	15.9651i	−0.236699	+	1.03704i
$238$	−3.71387	−	16.2715i	−0.240734	−	1.05473i
$239$	12.9462	−	6.23455i	0.837419	−	0.403280i	0.0345265	−	0.999404i	$-0.489008\pi$
$239$	12.9462	−	6.23455i	0.837419	−	0.403280i	0.802892	+	0.596124i	$0.203293\pi$
$240$	0.537202	−	0.673630i	0.0346762	−	0.0434826i
$241$	−5.73880	+	7.19623i	−0.369669	+	0.463550i	−0.931521	−	0.363688i	$-0.881517\pi$
$241$	−5.73880	+	7.19623i	−0.369669	+	0.463550i	0.561852	+	0.827238i	$0.310089\pi$
$242$	8.15303	+	3.92629i	0.524097	+	0.252392i
$243$	0.216675	+	0.271702i	0.0138997	+	0.0174297i
$244$	4.86648			0.311544
$245$	−0.878905	−	1.10211i	−0.0561512	−	0.0704114i
$246$	−1.55499	−	6.81287i	−0.0991427	−	0.434372i
$247$	6.31651	+	27.6744i	0.401910	+	1.76088i
$248$	3.96744	+	4.97501i	0.251933	+	0.315913i
$249$	−22.1357			−1.40279
$250$	3.00891	+	3.77305i	0.190300	+	0.238629i
$251$	−5.33012	−	2.56685i	−0.336434	−	0.162018i	0.258037	−	0.966135i	$-0.416924\pi$
$251$	−5.33012	−	2.56685i	−0.336434	−	0.162018i	−0.594471	+	0.804117i	$0.702639\pi$
$252$	0.0654373	−	0.0820558i	0.00412216	−	0.00516903i
$253$	−0.708523	+	0.888459i	−0.0445444	+	0.0558569i
$254$	11.4359	−	5.50723i	0.717551	−	0.345554i
$255$	−1.01959	−	4.46713i	−0.0638494	−	0.279743i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	24.0750	+	11.5939i	1.50176	+	0.723209i	0.990665	−	0.136316i	$-0.0435263\pi$
$257$	24.0750	+	11.5939i	1.50176	+	0.723209i	0.511094	+	0.859525i	$0.329241\pi$
$258$	−2.19173	+	1.05548i	−0.136451	+	0.0657113i
$259$	−6.23471	+	27.3160i	−0.387406	+	1.69734i
$260$	2.82742			0.175349
$261$	0.111196	−	0.141660i	0.00688287	−	0.00876853i
$262$	−14.7961			−0.914104
$263$	5.19684	−	22.7688i	0.320451	−	1.40399i	−0.516302	−	0.856407i	$-0.672692\pi$
$263$	5.19684	−	22.7688i	0.320451	−	1.40399i	0.836753	−	0.547581i	$-0.184451\pi$
$264$	2.19173	−	1.05548i	0.134891	−	0.0649603i
$265$	1.89140	+	0.910851i	0.116188	+	0.0559531i
$266$	−3.46844	+	15.1962i	−0.212664	+	0.931740i
$267$	0.694573	+	3.04312i	0.0425072	+	0.186236i
$268$	−6.43147	+	3.09723i	−0.392865	+	0.189194i
$269$	9.73222	−	12.2038i	0.593384	−	0.744080i	−0.390946	−	0.920413i	$-0.627852\pi$
$269$	9.73222	−	12.2038i	0.593384	−	0.744080i	0.984331	+	0.176333i	$0.0564236\pi$
$270$	−1.59364	+	1.99836i	−0.0969859	+	0.121616i
$271$	−0.197924	−	0.0953153i	−0.0120230	−	0.00578999i	0.427863	−	0.903844i	$-0.359267\pi$
$271$	−0.197924	−	0.0953153i	−0.0120230	−	0.00578999i	−0.439886	+	0.898054i	$0.644981\pi$
$272$	3.31572	+	4.15778i	0.201045	+	0.252102i
$273$	31.2411			1.89080
$274$	−0.941003	−	1.17998i	−0.0568481	−	0.0712853i
$275$	1.47793	+	6.47525i	0.0891227	+	0.390472i
$276$	−0.315322	−	1.38152i	−0.0189802	−	0.0831575i
$277$	2.33928	+	2.93336i	0.140554	+	0.176249i	0.847126	−	0.531392i	$-0.178331\pi$
$277$	2.33928	+	2.93336i	0.140554	+	0.176249i	−0.706572	+	0.707641i	$0.749759\pi$
$278$	8.75639			0.525173
$279$	0.132678	+	0.166373i	0.00794322	+	0.00996048i
$280$	1.39881	+	0.673630i	0.0835947	+	0.0402571i
$281$	−15.2450	+	19.1167i	−0.909442	+	1.14040i	0.0801905	+	0.996780i	$0.474447\pi$
$281$	−15.2450	+	19.1167i	−0.909442	+	1.14040i	−0.989632	+	0.143624i	$0.954124\pi$
$282$	11.1830	−	14.0230i	0.665935	−	0.835056i
$283$	−6.84512	+	3.29644i	−0.406900	+	0.195953i	−0.626127	−	0.779721i	$-0.715361\pi$
$283$	−6.84512	+	3.29644i	−0.406900	+	0.195953i	0.219227	+	0.975674i	$0.429647\pi$
$284$	−1.34344	−	5.88599i	−0.0797184	−	0.349269i
$285$	−0.952214	+	4.17192i	−0.0564043	+	0.247123i
$286$	7.19232	+	3.46364i	0.425291	+	0.204809i
$287$	11.3451	−	5.46349i	0.669678	−	0.322500i
$288$	−0.00744148	+	0.0326033i	−0.000438494	+	0.00192117i
$289$	11.2811			0.663593
$290$	2.40904	+	1.13736i	0.141464	+	0.0667882i
$291$	−6.61193			−0.387598
$292$	−2.73238	+	11.9713i	−0.159900	+	0.700569i
$293$	23.1750	−	11.1605i	1.35390	−	0.652003i	0.390631	−	0.920547i	$-0.372257\pi$
$293$	23.1750	−	11.1605i	1.35390	−	0.652003i	0.963267	+	0.268545i	$0.0865427\pi$
$294$	4.47147	+	2.15334i	0.260781	+	0.125586i
$295$	1.22847	−	5.38230i	0.0715245	−	0.313369i
$296$	−1.98659	−	8.70382i	−0.115468	−	0.505899i
$297$	−6.50188	+	3.13114i	−0.377277	+	0.181687i
$298$	−2.95579	+	3.70644i	−0.171224	+	0.214709i
$299$	2.89932	−	3.63563i	0.167672	−	0.210254i
$300$	−7.46196	−	3.59349i	−0.430817	−	0.207470i
$301$	−2.73304	−	3.42712i	−0.157530	−	0.197536i
$302$	−6.49415			−0.373696
$303$	1.32680	+	1.66375i	0.0762226	+	0.0955801i
$304$	−1.10516	−	4.84204i	−0.0633855	−	0.277710i
$305$	0.535705	+	2.34708i	0.0306744	+	0.134393i
$306$	0.110883	+	0.139043i	0.00633877	+	0.00794857i
$307$	1.81399			0.103530			0.0517649	−	0.998659i	$-0.483515\pi$
$307$	1.81399			0.103530			0.0517649	+	0.998659i	$0.483515\pi$
$308$	2.73304	+	3.42712i	0.155729	+	0.195278i
$309$	2.83733	+	1.36639i	0.161410	+	0.0777310i
$310$	−1.96268	+	2.46113i	−0.111473	+	0.139783i
$311$	12.1020	−	15.1754i	0.686239	−	0.860517i	−0.309673	−	0.950843i	$-0.600220\pi$
$311$	12.1020	−	15.1754i	0.686239	−	0.860517i	0.995912	+	0.0903265i	$0.0287910\pi$
$312$	−8.96867	+	4.31909i	−0.507751	+	0.244520i
$313$	−7.54006	−	33.0352i	−0.426189	−	1.86726i	−0.493847	−	0.869549i	$-0.664410\pi$
$313$	−7.54006	−	33.0352i	−0.426189	−	1.86726i	0.0676576	−	0.997709i	$-0.478447\pi$
$314$	−1.46005	+	6.39688i	−0.0823952	+	0.360997i
$315$	0.0467785	+	0.0225273i	0.00263567	+	0.00126927i
$316$	8.47112	−	4.07948i	0.476538	−	0.229489i
$317$	−1.22333	+	5.35977i	−0.0687092	+	0.301035i	−0.997593	−	0.0693356i	$-0.977912\pi$
$317$	−1.22333	+	5.35977i	−0.0687092	+	0.301035i	0.928884	+	0.370370i	$0.120769\pi$
$318$	−7.39097			−0.414465
$319$	4.73476	+	5.84430i	0.265096	+	0.327218i
$320$	−0.494698			−0.0276545
$321$	1.60862	−	7.04781i	0.0897843	−	0.393371i
$322$	2.30056	−	1.10789i	0.128205	−	0.0617403i
$323$	−23.7965	−	11.4598i	−1.32407	−	0.637640i
$324$	2.02476	−	8.87107i	0.112487	−	0.492837i
$325$	−6.04779	−	26.4971i	−0.335471	−	1.46980i
$326$	−5.09776	+	2.45495i	−0.282339	+	0.135967i
$327$	−15.7508	+	19.7509i	−0.871021	+	1.09223i
$328$	−2.50161	+	3.13691i	−0.138128	+	0.173207i
$329$	29.1190	+	14.0230i	1.60538	+	0.773112i
$330$	0.750319	+	0.940870i	0.0413037	+	0.0517932i
$331$	−13.6463			−0.750067			−0.375034	−	0.927011i	$-0.622369\pi$
$331$	−13.6463			−0.750067			−0.375034	+	0.927011i	$0.622369\pi$
$332$	7.92419	+	9.93663i	0.434897	+	0.545343i
$333$	−0.0664350	−	0.291071i	−0.00364062	−	0.0159506i
$334$	2.69008	+	11.7860i	0.147195	+	0.644902i
$335$	−2.20176	−	2.76092i	−0.120295	−	0.150845i
$336$	−5.46607			−0.298199
$337$	14.0705	+	17.6438i	0.766469	+	0.961122i	0.999937	−	0.0112429i	$-0.00357882\pi$
$337$	14.0705	+	17.6438i	0.766469	+	0.961122i	−0.233468	+	0.972365i	$0.575007\pi$
$338$	−17.7188	−	8.53293i	−0.963776	−	0.464130i
$339$	−18.1168	+	22.7177i	−0.983968	+	1.23386i
$340$	−1.64028	+	2.05684i	−0.0889566	+	0.111548i
$341$	−8.00754	+	3.85623i	−0.433632	+	0.208826i
$342$	−0.0369586	−	0.161926i	−0.00199849	−	0.00875596i
$343$	2.89852	−	12.6993i	0.156505	−	0.685695i
$344$	1.25840	+	0.606013i	0.0678483	+	0.0326740i
$345$	0.631588	−	0.304157i	0.0340036	−	0.0163752i
$346$	−2.59025	+	11.3486i	−0.139253	+	0.610105i
$347$	−2.97305			−0.159602			−0.0798008	−	0.996811i	$-0.525428\pi$
$347$	−2.97305			−0.159602			−0.0798008	+	0.996811i	$0.525428\pi$
$348$	−9.37894	+	0.0722295i	−0.502764	+	0.00387191i
$349$	−5.73913			−0.307208			−0.153604	−	0.988132i	$-0.549088\pi$
$349$	−5.73913			−0.307208			−0.153604	+	0.988132i	$0.549088\pi$
$350$	3.32089	−	14.5498i	0.177509	−	0.777717i
$351$	26.6061	−	12.8128i	1.42013	−	0.683898i
$352$	−1.25840	−	0.606013i	−0.0670729	−	0.0323006i
$353$	1.44019	−	6.30988i	0.0766536	−	0.335841i	−0.922031	−	0.387116i	$-0.873471\pi$
$353$	1.44019	−	6.30988i	0.0766536	−	0.335841i	0.998685	+	0.0512748i	$0.0163284\pi$
$354$	4.32507	+	18.9494i	0.229875	+	1.00715i
$355$	2.69090	−	1.29587i	0.142818	−	0.0687775i
$356$	1.11740	−	1.40118i	0.0592221	−	0.0742622i
$357$	−18.1239	+	22.7267i	−0.959221	+	1.20283i
$358$	16.5374	+	7.96398i	0.874028	+	0.420910i
$359$	6.69717	+	8.39798i	0.353463	+	0.443229i	0.926496	−	0.376303i	$-0.122805\pi$
$359$	6.69717	+	8.39798i	0.353463	+	0.443229i	−0.573034	+	0.819532i	$0.694234\pi$
$360$	−0.0165436			−0.000871922
$361$	3.53313	+	4.43041i	0.185954	+	0.233179i
$362$	2.20163	+	9.64598i	0.115715	+	0.506981i
$363$	−3.50710	−	15.3656i	−0.184075	−	0.806485i
$364$	−11.1838	−	14.0240i	−0.586188	−	0.735056i
$365$	−6.07449			−0.317954
$366$	−5.28460	−	6.62667i	−0.276230	−	0.346382i
$367$	−17.0637	−	8.21747i	−0.890720	−	0.428948i	−0.0681919	−	0.997672i	$-0.521723\pi$
$367$	−17.0637	−	8.21747i	−0.890720	−	0.428948i	−0.822529	+	0.568724i	$0.807437\pi$
$368$	−0.507277	+	0.636105i	−0.0264436	+	0.0331593i
$369$	−0.0836580	+	0.104904i	−0.00435506	+	0.00546107i
$370$	3.97913	−	1.91625i	0.206865	−	0.0996209i
$371$	−2.96355	−	12.9842i	−0.153860	−	0.674104i
$372$	2.46615	−	10.8049i	0.127864	−	0.560208i
$373$	−2.19298	−	1.05608i	−0.113548	−	0.0546819i	0.376247	−	0.926519i	$-0.377214\pi$
$373$	−2.19298	−	1.05608i	−0.113548	−	0.0546819i	−0.489796	+	0.871837i	$0.662929\pi$
$374$	−6.69216	+	3.22277i	−0.346043	+	0.166646i
$375$	1.87033	−	8.19446i	0.0965835	−	0.423160i
$376$	−10.2982			−0.531087
$377$	−19.3749	−	23.9152i	−0.997859	−	1.23170i
$378$	16.2154			0.834031
$379$	3.81433	−	16.7117i	0.195929	−	0.858422i	−0.777400	−	0.629007i	$-0.783462\pi$
$379$	3.81433	−	16.7117i	0.195929	−	0.858422i	0.973329	−	0.229415i	$-0.0736812\pi$
$380$	2.21363	−	1.06603i	0.113557	−	0.0546862i
$381$	−19.9176	−	9.59182i	−1.02041	−	0.491404i
$382$	−0.0944066	+	0.413622i	−0.00483026	+	0.0211628i
$383$	5.29096	+	23.1812i	0.270355	+	1.18450i	0.909595	+	0.415497i	$0.136392\pi$
$383$	5.29096	+	23.1812i	0.270355	+	1.18450i	−0.639239	+	0.769008i	$0.720751\pi$
$384$	1.56920	−	0.755686i	0.0800778	−	0.0385634i
$385$	−1.35203	+	1.69539i	−0.0689057	+	0.0864051i
$386$	−6.43739	+	8.07223i	−0.327655	+	0.410866i
$387$	0.0420830	+	0.0202661i	0.00213920	+	0.00103018i
$388$	2.36695	+	2.96806i	0.120164	+	0.150681i
$389$	−11.5272			−0.584453			−0.292227	−	0.956349i	$-0.594396\pi$
$389$	−11.5272			−0.584453			−0.292227	+	0.956349i	$0.594396\pi$
$390$	−3.07035	−	3.85010i	−0.155473	−	0.194957i
$391$	0.962797	+	4.21829i	0.0486907	+	0.213328i
$392$	−0.634079	−	2.77808i	−0.0320258	−	0.140314i
$393$	16.0673	+	20.1478i	0.810489	+	1.01632i
$394$	−26.8428			−1.35232
$395$	2.90002	+	3.63651i	0.145916	+	0.182973i
$396$	−0.0420830	−	0.0202661i	−0.00211475	−	0.00101841i
$397$	18.0708	−	22.6601i	0.906948	−	1.13728i	−0.0830990	−	0.996541i	$-0.526482\pi$
$397$	18.0708	−	22.6601i	0.906948	−	1.13728i	0.990047	−	0.140736i	$-0.0449468\pi$
$398$	−4.24156	+	5.31875i	−0.212610	+	0.266605i
$399$	24.4591	−	11.7789i	1.22449	−	0.589682i
$400$	1.05815	+	4.63605i	0.0529074	+	0.231802i
$401$	−2.29856	+	10.0707i	−0.114785	+	0.502905i	0.884550	+	0.466445i	$0.154465\pi$
$401$	−2.29856	+	10.0707i	−0.114785	+	0.502905i	−0.999335	+	0.0364602i	$0.988392\pi$
$402$	11.2016	+	5.39438i	0.558683	+	0.269047i
$403$	32.7673	−	15.7799i	1.63226	−	0.786054i
$404$	0.271881	−	1.19119i	0.0135266	−	0.0592638i
$405$	4.50136			0.223674
$406$	−3.88755	−	16.4476i	−0.192936	−	0.816280i
$407$	12.4694			0.618086
$408$	2.06104	−	9.03001i	0.102037	−	0.447052i
$409$	−8.97519	+	4.32222i	−0.443794	+	0.213720i	−0.642416	−	0.766356i	$-0.722068\pi$
$409$	−8.97519	+	4.32222i	−0.443794	+	0.213720i	0.198622	+	0.980076i	$0.436354\pi$
$410$	−1.78830	−	0.861198i	−0.0883177	−	0.0425316i
$411$	−0.584925	+	2.56273i	−0.0288522	+	0.126410i
$412$	−0.402349	−	1.76281i	−0.0198223	−	0.0868473i
$413$	−31.5553	+	15.1962i	−1.55273	+	0.747757i
$414$	−0.0169642	+	0.0212725i	−0.000833746	+	0.00104548i
$415$	−3.92009	+	4.91563i	−0.192429	+	0.241299i
$416$	5.14944	+	2.47984i	0.252472	+	0.121584i
$417$	−9.50872	−	11.9236i	−0.465644	−	0.583899i
$418$	6.93688			0.339294
$419$	17.6773	+	22.1667i	0.863595	+	1.08291i	0.995788	+	0.0916894i	$0.0292267\pi$
$419$	17.6773	+	22.1667i	0.863595	+	1.08291i	−0.132193	+	0.991224i	$0.542202\pi$
$420$	−0.601709	−	2.63626i	−0.0293604	−	0.128636i
$421$	2.11840	+	9.28130i	0.103244	+	0.452343i	0.999953	+	0.00972116i	$0.00309439\pi$
$421$	2.11840	+	9.28130i	0.103244	+	0.452343i	−0.896708	+	0.442622i	$0.854048\pi$
$422$	3.64156	+	4.56638i	0.177268	+	0.222288i
$423$	−0.344388			−0.0167447
$424$	2.64584	+	3.31777i	0.128493	+	0.161125i
$425$	22.7842	+	10.9723i	1.10519	+	0.532234i
$426$	−6.55608	+	8.22106i	−0.317643	+	0.398312i
$427$	9.52251	−	11.9409i	0.460827	−	0.577859i
$428$	−3.73959	+	1.80089i	−0.180760	+	0.0870493i
$429$	−3.09384	−	13.5550i	−0.149372	−	0.654441i
$430$	−0.153752	+	0.673630i	−0.00741456	+	0.0324853i
$431$	17.0958	+	8.23291i	0.823477	+	0.396566i	0.797665	−	0.603101i	$-0.206069\pi$
$431$	17.0958	+	8.23291i	0.823477	+	0.396566i	0.0258122	+	0.999667i	$0.491783\pi$
$432$	−4.65512	+	2.24179i	−0.223969	+	0.107858i
$433$	−6.30063	+	27.6049i	−0.302789	+	1.32661i	0.563108	+	0.826383i	$0.309605\pi$
$433$	−6.30063	+	27.6049i	−0.302789	+	1.32661i	−0.865897	+	0.500222i	$0.833252\pi$
$434$	19.9705			0.958613
$435$	−1.06728	−	4.51547i	−0.0511720	−	0.216500i
$436$	14.5046			0.694644
$437$	0.899171	−	3.93953i	0.0430132	−	0.188453i
$438$	19.2685	−	9.27921i	0.920683	−	0.443378i
$439$	17.9255	+	8.63248i	0.855539	+	0.412006i	0.809631	−	0.586940i	$-0.199667\pi$
$439$	17.9255	+	8.63248i	0.855539	+	0.412006i	0.0459084	+	0.998946i	$0.485382\pi$
$440$	0.153752	−	0.673630i	0.00732982	−	0.0321140i
$441$	−0.0212047	−	0.0929038i	−0.00100975	−	0.00442399i
$442$	27.3847	−	13.1878i	1.30256	−	0.627279i
$443$	−22.1713	+	27.8019i	−1.05339	+	1.32091i	−0.108292	+	0.994119i	$0.534538\pi$
$443$	−22.1713	+	27.8019i	−1.05339	+	1.32091i	−0.945097	+	0.326790i	$0.894033\pi$
$444$	−9.69471	+	12.1568i	−0.460091	+	0.576935i
$445$	0.798784	+	0.384674i	0.0378660	+	0.0182353i
$446$	−13.6769	−	17.1503i	−0.647620	−	0.812090i
$447$	8.25681			0.390534
$448$	1.95676	+	2.45370i	0.0924481	+	0.115926i
$449$	−2.41460	−	10.5790i	−0.113952	−	0.499256i	−0.999404	−	0.0345250i	$-0.989008\pi$
$449$	−2.41460	−	10.5790i	−0.113952	−	0.499256i	0.885452	−	0.464731i	$-0.153849\pi$
$450$	0.0353863	+	0.155037i	0.00166813	+	0.00730853i
$451$	−3.49404	−	4.38138i	−0.164528	−	0.206311i
$452$	16.6834			0.784720
$453$	7.05212	+	8.84307i	0.331337	+	0.415484i
$454$	1.94197	+	0.935202i	0.0911411	+	0.0438912i
$455$	5.53258	−	6.93764i	0.259371	−	0.325242i
$456$	−5.39328	+	6.76296i	−0.252563	+	0.316704i
$457$	−29.1336	+	14.0300i	−1.36281	+	0.656296i	−0.965262	−	0.261285i	$-0.915854\pi$
$457$	−29.1336	+	14.0300i	−1.36281	+	0.656296i	−0.397550	+	0.917580i	$0.630140\pi$
$458$	−2.06764	−	9.05894i	−0.0966146	−	0.423296i
$459$	−6.11420	+	26.7881i	−0.285386	+	1.25036i
$460$	−0.362632	−	0.174634i	−0.0169078	−	0.00814237i
$461$	−22.8888	+	11.0227i	−1.06604	+	0.513377i	−0.882828	−	0.469696i	$-0.844363\pi$
$461$	−22.8888	+	11.0227i	−1.06604	+	0.513377i	−0.183211	+	0.983074i	$0.558649\pi$
$462$	1.69885	−	7.44314i	0.0790376	−	0.346286i
$463$	3.22072			0.149680			0.0748398	−	0.997196i	$-0.476155\pi$
$463$	3.22072			0.149680			0.0748398	+	0.997196i	$0.476155\pi$
$464$	3.38992	+	4.18431i	0.157373	+	0.194252i
$465$	5.48263			0.254251
$466$	2.62235	−	11.4893i	0.121478	−	0.532231i
$467$	−20.5930	+	9.91706i	−0.952929	+	0.458907i	−0.844712	−	0.535221i	$-0.820228\pi$
$467$	−20.5930	+	9.91706i	−0.952929	+	0.458907i	−0.108217	+	0.994127i	$0.534514\pi$
$468$	0.172206	+	0.0829302i	0.00796024	+	0.00383345i
$469$	−4.98516	+	21.8414i	−0.230193	+	1.00854i
$470$	−1.13363	−	4.96675i	−0.0522903	−	0.229099i
$471$	10.2961	−	4.95835i	0.474420	−	0.228469i
$472$	6.95799	−	8.72505i	0.320268	−	0.401603i
$473$	−1.21632	+	1.52521i	−0.0559263	+	0.0701293i
$474$	−14.7540	−	7.10513i	−0.677672	−	0.326350i
$475$	−14.7252	−	18.4648i	−0.675637	−	0.847222i
$476$	16.6900			0.764984
$477$	0.0884813	+	0.110952i	0.00405128	+	0.00508015i
$478$	3.19744	+	14.0089i	0.146248	+	0.640753i
$479$	−0.477409	−	2.09166i	−0.0218134	−	0.0955706i	0.962849	−	0.270039i	$-0.0870365\pi$
$479$	−0.477409	−	2.09166i	−0.0218134	−	0.0955706i	−0.984663	+	0.174468i	$0.944179\pi$
$480$	0.537202	+	0.673630i	0.0245198	+	0.0307469i
$481$	−51.0256			−2.32657
$482$	−5.73880	−	7.19623i	−0.261395	−	0.327779i
$483$	−4.00683	−	1.92959i	−0.182317	−	0.0877993i
$484$	−5.64207	+	7.07493i	−0.256458	+	0.321588i
$485$	−1.17093	+	1.46830i	−0.0531691	+	0.0666719i
$486$	−0.313105	+	0.150783i	−0.0142027	+	0.00683968i
$487$	−4.84560	−	21.2300i	−0.219575	−	0.962021i	−0.957793	−	0.287459i	$-0.907190\pi$
$487$	−4.84560	−	21.2300i	−0.219575	−	0.962021i	0.738218	−	0.674562i	$-0.235668\pi$
$488$	−1.08289	+	4.74446i	−0.0490203	+	0.214772i
$489$	8.87865	+	4.27573i	0.401507	+	0.193355i
$490$	1.27005	−	0.611626i	0.0573752	−	0.0276304i
$491$	8.64786	−	37.8888i	0.390273	−	1.70990i	−0.273423	−	0.961894i	$-0.588156\pi$
$491$	8.64786	−	37.8888i	0.390273	−	1.70990i	0.663696	−	0.748002i	$-0.268987\pi$
$492$	6.98807			0.315047
$493$	28.6374	−	0.220544i	1.28977	−	0.00993279i
$494$	−28.3861			−1.27715
$495$	0.00514172	−	0.0225273i	0.000231103	−	0.00101253i
$496$	−5.73311	+	2.76092i	−0.257424	+	0.123969i
$497$	−17.0712	−	8.22106i	−0.765748	−	0.368765i
$498$	4.92566	−	21.5807i	0.220724	−	0.967056i
$499$	−8.74490	−	38.3139i	−0.391476	−	1.71517i	−0.659457	−	0.751742i	$-0.729214\pi$
$499$	−8.74490	−	38.3139i	−0.391476	−	1.71517i	0.267981	−	0.963424i	$-0.413643\pi$
$500$	−4.34800	+	2.09389i	−0.194449	+	0.0936415i
$501$	13.1278	−	16.4617i	0.586506	−	0.735456i
$502$	3.68856	−	4.62530i	0.164628	−	0.206437i
$503$	−25.2735	−	12.1711i	−1.12689	−	0.542680i	−0.224874	−	0.974388i	$-0.572197\pi$
$503$	−25.2735	−	12.1711i	−1.12689	−	0.542680i	−0.902014	+	0.431707i	$0.857911\pi$
$504$	0.0654373	+	0.0820558i	0.00291481	+	0.00365506i
$505$	0.604433			0.0268969
$506$	−0.708523	−	0.888459i	−0.0314977	−	0.0394968i
$507$	7.62190	+	33.3937i	0.338501	+	1.48307i
$508$	2.82443	+	12.3746i	0.125314	+	0.549035i
$509$	1.06278	+	1.33268i	0.0471069	+	0.0590701i	0.804827	−	0.593510i	$-0.202258\pi$
$509$	1.06278	+	1.33268i	0.0471069	+	0.0590701i	−0.757720	+	0.652580i	$0.773687\pi$
$510$	4.58201			0.202895
$511$	24.0274	+	30.1294i	1.06291	+	1.33285i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	15.9995	−	20.0627i	0.706394	−	0.885790i
$514$	−16.6604	+	20.8915i	−0.734860	+	0.921486i
$515$	0.805903	−	0.388102i	0.0355123	−	0.0171018i
$516$	−0.541311	−	2.37164i	−0.0238299	−	0.104406i
$517$	3.20065	−	14.0230i	0.140765	−	0.616730i
$518$	−25.2438	−	12.1568i	−1.10915	−	0.534138i
$519$	18.2662	−	8.79653i	0.801797	−	0.386125i
$520$	−0.629161	+	2.75653i	−0.0275905	+	0.120882i
$521$	−21.0834			−0.923678			−0.461839	−	0.886964i	$-0.652810\pi$
$521$	−21.0834			−0.923678			−0.461839	+	0.886964i	$0.652810\pi$
$522$	0.113365	+	0.139930i	0.00496184	+	0.00612459i
$523$	−8.93606			−0.390747			−0.195373	−	0.980729i	$-0.562592\pi$
$523$	−8.93606			−0.390747			−0.195373	+	0.980729i	$0.562592\pi$
$524$	3.29243	−	14.4251i	0.143831	−	0.630163i
$525$	−23.4186	+	11.2778i	−1.02207	+	0.492203i
$526$	21.0416	+	10.1331i	0.917457	+	0.441824i
$527$	−7.53008	+	32.9914i	−0.328015	+	1.43713i
$528$	0.541311	+	2.37164i	0.0235576	+	0.103212i
$529$	20.1259	−	9.69211i	0.875038	−	0.421396i
$530$	−1.30889	+	1.64130i	−0.0568546	+	0.0712934i
$531$	0.232687	−	0.291781i	0.0100978	−	0.0126622i
$532$	−14.0434	−	6.76296i	−0.608860	−	0.293211i
$533$	14.2978	+	17.9289i	0.619307	+	0.776586i
$534$	−3.12138			−0.135076
$535$	−1.28022	−	1.60534i	−0.0553486	−	0.0694050i
$536$	−1.58844	−	6.95942i	−0.0686103	−	0.300601i
$537$	−7.11370	−	31.1672i	−0.306979	−	1.34496i
$538$	9.73222	+	12.2038i	0.419586	+	0.526144i
$539$	3.97998			0.171430
$540$	−1.59364	−	1.99836i	−0.0685794	−	0.0859958i
$541$	10.7827	+	5.19269i	0.463586	+	0.223251i	0.651072	−	0.759016i	$-0.274320\pi$
$541$	10.7827	+	5.19269i	0.463586	+	0.223251i	−0.187486	+	0.982267i	$0.560034\pi$
$542$	0.136968	−	0.171752i	0.00588327	−	0.00737739i
$543$	10.7441	−	13.4727i	0.461074	−	0.578169i
$544$	−4.79135	+	2.30739i	−0.205427	+	0.0989286i
$545$	1.59668	+	6.99549i	0.0683940	+	0.299654i
$546$	−6.95179	+	30.4578i	−0.297509	+	1.30347i
$547$	21.7331	+	10.4661i	0.929239	+	0.447498i	0.836361	−	0.548180i	$-0.184679\pi$
$547$	21.7331	+	10.4661i	0.929239	+	0.447498i	0.0928783	+	0.995677i	$0.470393\pi$
$548$	1.35979	−	0.654840i	0.0580873	−	0.0279734i
$549$	−0.0362138	+	0.158663i	−0.00154557	+	0.00677157i
$550$	−6.64177			−0.283206
$551$	−24.1857	−	11.4186i	−1.03035	−	0.486450i
$552$	1.41705			0.0603134
$553$	6.56613	−	28.7681i	0.279220	−	1.22334i
$554$	−3.38036	+	1.62789i	−0.143618	+	0.0691626i
$555$	−6.93036	−	3.33748i	−0.294177	−	0.141668i
$556$	−1.94848	+	8.53684i	−0.0826339	+	0.362043i
$557$	4.05033	+	17.7456i	0.171618	+	0.751907i	0.985333	+	0.170643i	$0.0545844\pi$
$557$	4.05033	+	17.7456i	0.171618	+	0.751907i	−0.813715	+	0.581264i	$0.802558\pi$
$558$	−0.191725	+	0.0923300i	−0.00811637	+	0.00390864i
$559$	4.97724	−	6.24126i	0.210515	−	0.263977i
$560$	−0.968004	+	1.21384i	−0.0409057	+	0.0512941i
$561$	11.6556	+	5.61303i	0.492099	+	0.236982i
$562$	−15.2450	−	19.1167i	−0.643072	−	0.806387i
$563$	−31.5149			−1.32820			−0.664098	−	0.747646i	$-0.731184\pi$
$563$	−31.5149			−1.32820			−0.664098	+	0.747646i	$0.731184\pi$
$564$	11.1830	+	14.0230i	0.470887	+	0.590474i
$565$	1.83652	+	8.04631i	0.0772629	+	0.338511i
$566$	−1.69060	−	7.40702i	−0.0710614	−	0.311340i
$567$	−17.8049	−	22.3267i	−0.747737	−	0.937633i
$568$	6.03736			0.253322
$569$	−17.7477	−	22.2549i	−0.744023	−	0.932975i	0.255404	−	0.966834i	$-0.417792\pi$
$569$	−17.7477	−	22.2549i	−0.744023	−	0.932975i	−0.999427	+	0.0338594i	$0.989220\pi$
$570$	−3.85544	−	1.85668i	−0.161486	−	0.0777678i
$571$	−2.65790	+	3.33290i	−0.111230	+	0.139478i	−0.834330	−	0.551266i	$-0.814145\pi$
$571$	−2.65790	+	3.33290i	−0.111230	+	0.139478i	0.723100	+	0.690743i	$0.242717\pi$
$572$	−4.97724	+	6.24126i	−0.208109	+	0.260960i
$573$	0.665747	−	0.320607i	0.0278120	−	0.0133935i
$574$	2.80200	+	12.2764i	0.116953	+	0.512405i
$575$	−0.860919	+	3.77193i	−0.0359028	+	0.157300i
$576$	−0.0301299	−	0.0145098i	−0.00125541	−	0.000604576i
$577$	−20.3474	+	9.79878i	−0.847072	+	0.407929i	−0.806490	−	0.591248i	$-0.798636\pi$
$577$	−20.3474	+	9.79878i	−0.847072	+	0.407929i	−0.0405823	+	0.999176i	$0.512921\pi$
$578$	−2.51028	+	10.9982i	−0.104414	+	0.457467i
$579$	17.9824			0.747324
$580$	−1.64491	+	2.09555i	−0.0683011	+	0.0870131i
$581$	39.8872			1.65480
$582$	1.47129	−	6.44615i	0.0609870	−	0.267202i
$583$	−5.34013	+	2.57167i	−0.221166	+	0.106508i
$584$	−11.0632	−	5.32774i	−0.457797	−	0.220463i
$585$	−0.0210402	+	0.0921833i	−0.000869906	+	0.00381131i
$586$	5.72375	+	25.0774i	0.236446	+	1.03594i
$587$	30.1868	−	14.5372i	1.24594	−	0.600015i	0.309523	−	0.950892i	$-0.399831\pi$
$587$	30.1868	−	14.5372i	1.24594	−	0.600015i	0.936422	+	0.350877i	$0.114116\pi$
$588$	−3.09435	+	3.88019i	−0.127609	+	0.160016i
$589$	19.7045	−	24.7087i	0.811910	−	1.01810i
$590$	4.97399	+	2.39535i	0.204776	+	0.0986149i
$591$	29.1490	+	36.5517i	1.19903	+	1.50354i
$592$	8.92766			0.366925
$593$	8.32767	+	10.4426i	0.341977	+	0.428825i	0.922844	−	0.385173i	$-0.125858\pi$
$593$	8.32767	+	10.4426i	0.341977	+	0.428825i	−0.580868	+	0.813998i	$0.697287\pi$
$594$	−1.60583	−	7.03561i	−0.0658881	−	0.288675i
$595$	1.83724	+	8.04949i	0.0753197	+	0.329997i
$596$	−2.95579	−	3.70644i	−0.121074	−	0.151822i
$597$	11.8485			0.484928
$598$	2.89932	+	3.63563i	0.118562	+	0.148672i
$599$	−0.824990	−	0.397294i	−0.0337082	−	0.0162330i	0.416954	−	0.908928i	$-0.363098\pi$
$599$	−0.824990	−	0.397294i	−0.0337082	−	0.0162330i	−0.450662	+	0.892695i	$0.648812\pi$
$600$	5.16384	−	6.47525i	0.210813	−	0.264351i
$601$	3.60037	−	4.51472i	0.146862	−	0.184159i	−0.702959	−	0.711230i	$-0.748138\pi$
$601$	3.60037	−	4.51472i	0.146862	−	0.184159i	0.849821	+	0.527071i	$0.176710\pi$
$602$	3.94935	−	1.90191i	0.160964	−	0.0775160i
$603$	−0.0531202	−	0.232735i	−0.00216322	−	0.00947770i
$604$	1.44508	−	6.33133i	0.0587996	−	0.257618i
$605$	−4.03329	−	1.94233i	−0.163977	−	0.0789669i
$606$	−1.91728	+	0.923313i	−0.0778842	+	0.0375070i
$607$	3.33385	−	14.6065i	0.135317	−	0.592861i	−0.861111	−	0.508416i	$-0.830231\pi$
$607$	3.33385	−	14.6065i	0.135317	−	0.592861i	0.996428	−	0.0844449i	$-0.0269117\pi$
$608$	4.96656			0.201421
$609$	−18.1751	+	23.1544i	−0.736492	+	0.938264i
$610$	−2.40744			−0.0974743
$611$	−13.0973	+	57.3829i	−0.529859	+	2.32146i
$612$	−0.160231	+	0.0771631i	−0.00647695	+	0.00311914i
$613$	21.5458	+	10.3759i	0.870228	+	0.419080i	0.815046	−	0.579396i	$-0.196712\pi$
$613$	21.5458	+	10.3759i	0.870228	+	0.419080i	0.0551825	+	0.998476i	$0.482426\pi$
$614$	−0.403651	+	1.76851i	−0.0162900	+	0.0713712i
$615$	0.769252	+	3.37031i	0.0310192	+	0.135904i
$616$	−3.94935	+	1.90191i	−0.159124	+	0.0766300i
$617$	−9.16964	+	11.4984i	−0.369156	+	0.462907i	−0.931364	−	0.364089i	$-0.881380\pi$
$617$	−9.16964	+	11.4984i	−0.369156	+	0.462907i	0.562208	+	0.826996i	$0.309952\pi$
$618$	−1.96349	+	2.46214i	−0.0789833	+	0.0990419i
$619$	−20.6449	−	9.94208i	−0.829790	−	0.399606i	−0.0297537	−	0.999557i	$-0.509472\pi$
$619$	−20.6449	−	9.94208i	−0.829790	−	0.399606i	−0.800036	+	0.599951i	$0.795187\pi$
$620$	−1.96268	−	2.46113i	−0.0788233	−	0.0988413i
$621$	−4.20375			−0.168691
$622$	12.1020	+	15.1754i	0.485244	+	0.608477i
$623$	−1.25158	−	5.48352i	−0.0501434	−	0.219693i
$624$	−2.21508	−	9.70490i	−0.0886741	−	0.388507i
$625$	13.3358	+	16.7226i	0.533433	+	0.668904i
$626$	33.8847			1.35431
$627$	−7.53288	−	9.44594i	−0.300834	−	0.377234i
$628$	−5.91161	−	2.84688i	−0.235899	−	0.113603i
$629$	29.6016	−	37.1192i	1.18029	−	1.48004i
$630$	−0.0323717	+	0.0405929i	−0.00128972	+	0.00161726i
$631$	−11.8128	+	5.68872i	−0.470258	+	0.226465i	−0.653977	−	0.756514i	$-0.726901\pi$
$631$	−11.8128	+	5.68872i	−0.470258	+	0.226465i	0.183719	+	0.982979i	$0.441186\pi$
$632$	2.09219	+	9.16650i	0.0832230	+	0.364624i
$633$	2.26359	−	9.91742i	0.0899695	−	0.394182i
$634$	−4.95317	−	2.38532i	−0.196716	−	0.0947333i
$635$	−5.65731	+	2.72442i	−0.224503	+	0.108115i
$636$	1.64465	−	7.20566i	0.0652144	−	0.285723i
$637$	−16.2863			−0.645287
$638$	−6.75135	+	3.31557i	−0.267289	+	0.131265i
$639$	0.201900			0.00798702
$640$	0.110081	−	0.482295i	0.00435132	−	0.0190644i
$641$	38.8282	−	18.6987i	1.53362	−	0.738553i	0.539017	−	0.842295i	$-0.318796\pi$
$641$	38.8282	−	18.6987i	1.53362	−	0.738553i	0.994604	+	0.103742i	$0.0330816\pi$
$642$	6.51316	+	3.13657i	0.257054	+	0.123791i
$643$	1.92324	−	8.42626i	0.0758451	−	0.332299i	−0.922743	−	0.385415i	$-0.874058\pi$
$643$	1.92324	−	8.42626i	0.0758451	−	0.332299i	0.998588	+	0.0531161i	$0.0169153\pi$
$644$	0.568191	+	2.48941i	0.0223899	+	0.0980964i
$645$	1.08424	−	0.522144i	0.0426920	−	0.0205594i
$646$	16.4677	−	20.6498i	0.647913	−	0.812457i
$647$	−2.98700	+	3.74558i	−0.117431	+	0.147254i	−0.837073	−	0.547092i	$-0.815735\pi$
$647$	−2.98700	+	3.74558i	−0.117431	+	0.147254i	0.719641	+	0.694346i	$0.244306\pi$
$648$	8.19810	+	3.94800i	0.322052	+	0.155092i
$649$	9.71835	+	12.1864i	0.381479	+	0.478359i
$650$	27.1785			1.06603
$651$	−21.6863	−	27.1938i	−0.849953	−	1.06581i
$652$	−1.25904	−	5.51622i	−0.0493079	−	0.216032i
$653$	−1.22812	−	5.38073i	−0.0480599	−	0.210564i	0.945197	−	0.326502i	$-0.105870\pi$
$653$	−1.22812	−	5.38073i	−0.0480599	−	0.210564i	−0.993257	+	0.115938i	$0.963013\pi$
$654$	−15.7508	−	19.7509i	−0.615905	−	0.772320i
$655$	7.31958			0.286000
$656$	−2.50161	−	3.13691i	−0.0976713	−	0.122476i
$657$	−0.369971	−	0.178169i	−0.0144340	−	0.00695103i
$658$	−20.1510	+	25.2685i	−0.785567	+	0.985070i
$659$	−1.14932	+	1.44120i	−0.0447712	+	0.0561413i	−0.803713	−	0.595017i	$-0.797145\pi$
$659$	−1.14932	+	1.44120i	−0.0447712	+	0.0561413i	0.758942	+	0.651158i	$0.225717\pi$
$660$	−1.08424	+	0.522144i	−0.0422041	+	0.0203244i
$661$	5.80735	+	25.4436i	0.225880	+	0.989643i	0.952961	+	0.303092i	$0.0980190\pi$
$661$	5.80735	+	25.4436i	0.225880	+	0.989643i	−0.727082	+	0.686551i	$0.759124\pi$
$662$	3.03658	−	13.3041i	0.118020	−	0.517080i
$663$	−47.6954	−	22.9689i	−1.85233	−	0.892037i
$664$	−11.4508	+	5.51441i	−0.444377	+	0.214001i
$665$	1.71583	−	7.51754i	0.0665371	−	0.291518i
$666$	0.298556			0.0115688
$667$	1.00782	+	4.26393i	0.0390231	+	0.165100i
$668$	−12.0891			−0.467742
$669$	−8.50153	+	37.2477i	−0.328688	+	1.44008i
$670$	3.18164	−	1.53220i	0.122917	−	0.0591939i
$671$	−6.12397	−	2.94915i	−0.236413	−	0.113851i
$672$	1.21632	−	5.32903i	0.0469204	−	0.205572i
$673$	−4.88021	−	21.3816i	−0.188118	−	0.824200i	−0.977608	−	0.210436i	$-0.932512\pi$
$673$	−4.88021	−	21.3816i	−0.188118	−	0.824200i	0.789489	−	0.613764i	$-0.210345\pi$
$674$	−20.3325	+	9.79160i	−0.783177	+	0.377158i
$675$	−15.3188	+	19.2092i	−0.589622	+	0.739363i
$676$	12.2618	−	15.3758i	0.471608	−	0.591377i
$677$	−9.15884	−	4.41066i	−0.352003	−	0.169516i	0.249523	−	0.968369i	$-0.419726\pi$
$677$	−9.15884	−	4.41066i	−0.352003	−	0.169516i	−0.601526	+	0.798853i	$0.705440\pi$
$678$	−18.1168	−	22.7177i	−0.695771	−	0.872469i
$679$	11.9143			0.457228
$680$	−1.64028	−	2.05684i	−0.0629018	−	0.0788764i
$681$	−0.835355	−	3.65993i	−0.0320109	−	0.140249i
$682$	−1.97770	−	8.66486i	−0.0757300	−	0.331795i
$683$	12.7734	+	16.0173i	0.488760	+	0.612886i	0.963653	−	0.267158i	$-0.0860845\pi$
$683$	12.7734	+	16.0173i	0.488760	+	0.612886i	−0.474893	+	0.880044i	$0.657513\pi$
$684$	0.166090			0.00635062
$685$	0.465513	+	0.583735i	0.0177863	+	0.0223033i
$686$	11.7359	+	5.65170i	0.448078	+	0.215783i
$687$	−10.0903	+	12.6528i	−0.384967	+	0.482733i
$688$	−0.870839	+	1.09200i	−0.0332004	+	0.0416320i
$689$	21.8521	−	10.5234i	0.832500	−	0.400911i
$690$	0.155989	+	0.683434i	0.00593841	+	0.0260179i
$691$	6.86393	−	30.0728i	0.261116	−	1.14402i	−0.658927	−	0.752207i	$-0.728989\pi$
$691$	6.86393	−	30.0728i	0.261116	−	1.14402i	0.920043	−	0.391817i	$-0.128154\pi$
$692$	−10.4877	−	5.05061i	−0.398682	−	0.191995i
$693$	−0.132073	+	0.0636031i	−0.00501704	+	0.00241608i
$694$	0.661565	−	2.89851i	0.0251127	−	0.110026i
$695$	−4.33177			−0.164313
$696$	2.01659	−	9.15987i	0.0764388	−	0.347204i
$697$	−21.3372			−0.808204
$698$	1.27708	−	5.59523i	0.0483380	−	0.211783i
$699$	−18.4926	+	8.90557i	−0.699455	+	0.336840i
$700$	13.4460	+	6.47525i	0.508211	+	0.244741i
$701$	4.60087	−	20.1577i	0.173773	−	0.761347i	−0.810650	−	0.585530i	$-0.800886\pi$
$701$	4.60087	−	20.1577i	0.173773	−	0.761347i	0.984423	−	0.175817i	$-0.0562566\pi$
$702$	6.57116	+	28.7901i	0.248013	+	1.08661i
$703$	−39.9487	+	19.2383i	−1.50669	+	0.725586i
$704$	0.870839	−	1.09200i	0.0328210	−	0.0411562i
$705$	−5.53219	+	6.93714i	−0.208354	+	0.261268i
$706$	5.83121	+	2.80816i	0.219460	+	0.105687i
$707$	−2.39081	−	2.99798i	−0.0899156	−	0.112751i
$708$	−19.4367			−0.730476
$709$	−28.0695	−	35.1981i	−1.05417	−	1.32189i	−0.944712	−	0.327901i	$-0.893659\pi$
$709$	−28.0695	−	35.1981i	−1.05417	−	1.32189i	−0.109461	−	0.993991i	$-0.534913\pi$
$710$	0.664596	+	2.91179i	0.0249419	+	0.109277i
$711$	0.0699666	+	0.306544i	0.00262395	+	0.0114963i
$712$	1.11740	+	1.40118i	0.0418763	+	0.0525113i
$713$	−5.17722			−0.193888
$714$	−18.1239	−	22.7267i	−0.678272	−	0.850526i
$715$	−3.55803	−	1.71346i	−0.133063	−	0.0640796i
$716$	−11.4442	+	14.3506i	−0.427691	+	0.536307i
$717$	15.6038	−	19.5665i	0.582733	−	0.730724i
$718$	−9.67769	+	4.66053i	−0.361168	+	0.173929i
$719$	2.24249	+	9.82501i	0.0836309	+	0.366411i	0.999375	−	0.0353512i	$-0.0112550\pi$
$719$	2.24249	+	9.82501i	0.0836309	+	0.366411i	−0.915744	+	0.401762i	$0.868398\pi$
$720$	0.00368129	−	0.0161288i	0.000137194	−	0.000601084i
$721$	−5.11269	−	2.46214i	−0.190407	−	0.0916950i
$722$	−5.10552	+	2.45869i	−0.190008	+	0.0915029i
$723$	−3.56722	+	15.6290i	−0.132666	+	0.581250i
$724$	−9.89404			−0.367709
$725$	23.1568	+	10.9329i	0.860023	+	0.406036i
$726$	15.7608			0.584937
$727$	−4.98758	+	21.8520i	−0.184979	+	0.810447i	0.794234	+	0.607612i	$0.207872\pi$
$727$	−4.98758	+	21.8520i	−0.184979	+	0.810447i	−0.979213	+	0.202835i	$0.934985\pi$
$728$	16.1610	−	7.78272i	0.598966	−	0.288447i
$729$	−24.0490	−	11.5814i	−0.890703	−	0.428940i
$730$	1.35170	−	5.92219i	0.0500287	−	0.219190i
$731$	1.65283	+	7.24151i	0.0611320	+	0.267837i
$732$	7.63646	−	3.67753i	0.282252	−	0.135925i
$733$	2.46035	−	3.08518i	0.0908749	−	0.113954i	−0.734315	−	0.678809i	$-0.762497\pi$
$733$	2.46035	−	3.08518i	0.0908749	−	0.113954i	0.825190	+	0.564855i	$0.191068\pi$
$734$	11.8085	−	14.8074i	0.435859	−	0.546550i
$735$	−2.21203	−	1.06526i	−0.0815918	−	0.0392925i
$736$	−0.507277	−	0.636105i	−0.0186985	−	0.0234472i
$737$	9.97032			0.367261
$738$	−0.0836580	−	0.104904i	−0.00307949	−	0.00386156i
$739$	−1.38003	−	6.04632i	−0.0507653	−	0.222417i	0.943182	−	0.332277i	$-0.107817\pi$
$739$	−1.38003	−	6.04632i	−0.0507653	−	0.222417i	−0.993947	+	0.109860i	$0.964960\pi$
$740$	0.982763	+	4.30577i	0.0361271	+	0.158283i
$741$	30.8250	+	38.6533i	1.13239	+	1.41997i
$742$	13.3181			0.488922
$743$	30.3589	+	38.0689i	1.11376	+	1.39661i	0.908490	+	0.417907i	$0.137236\pi$
$743$	30.3589	+	38.0689i	1.11376	+	1.39661i	0.205271	+	0.978705i	$0.434192\pi$
$744$	9.98524	+	4.80864i	0.366077	+	0.176293i
$745$	1.46222	−	1.83357i	0.0535718	−	0.0671769i
$746$	1.51759	−	1.90300i	0.0555629	−	0.0696737i
$747$	−0.382934	+	0.184411i	−0.0140108	+	0.00674726i
$748$	−1.65283	−	7.24151i	−0.0604333	−	0.264776i
$749$	−2.89863	+	12.6997i	−0.105914	+	0.464038i
$750$	7.57282	+	3.64688i	0.276520	+	0.133165i
$751$	−23.7677	+	11.4459i	−0.867296	+	0.417668i	−0.813968	−	0.580909i	$-0.802697\pi$
$751$	−23.7677	+	11.4459i	−0.867296	+	0.417668i	−0.0533277	+	0.998577i	$0.516983\pi$
$752$	2.29155	−	10.0400i	0.0835644	−	0.366119i
$753$	−10.3037			−0.375489
$754$	27.6269	−	13.5675i	1.00611	−	0.494100i
$755$	3.21264			0.116920
$756$	−3.60827	+	15.8089i	−0.131232	+	0.574963i
$757$	−34.4086	+	16.5703i	−1.25060	+	0.602259i	−0.937673	−	0.347518i	$-0.887025\pi$
$757$	−34.4086	+	16.5703i	−1.25060	+	0.602259i	−0.312930	+	0.949776i	$0.601310\pi$
$758$	15.4439	+	7.43740i	0.560949	+	0.270139i
$759$	−0.440416	+	1.92959i	−0.0159861	+	0.0700396i
$760$	0.546722	+	2.39535i	0.0198317	+	0.0868884i
$761$	−5.62055	+	2.70672i	−0.203745	+	0.0981183i	−0.532974	−	0.846132i	$-0.678926\pi$
$761$	−5.62055	+	2.70672i	−0.203745	+	0.0981183i	0.329229	+	0.944250i	$0.393211\pi$
$762$	13.7834	−	17.2839i	0.499320	−	0.626128i
$763$	28.3820	−	35.5898i	1.02750	−	1.28844i
$764$	−0.382244	−	0.184079i	−0.0138291	−	0.00665975i
$765$	−0.0548537	−	0.0687844i	−0.00198324	−	0.00248691i
$766$	−23.7774			−0.859111
$767$	−39.7681	−	49.8676i	−1.43594	−	1.80061i
$768$	0.387560	+	1.69801i	0.0139849	+	0.0612717i
$769$	6.26532	+	27.4502i	0.225933	+	0.989879i	0.952919	+	0.303226i	$0.0980637\pi$
$769$	6.26532	+	27.4502i	0.225933	+	0.989879i	−0.726985	+	0.686653i	$0.759079\pi$
$770$	−1.35203	−	1.69539i	−0.0487237	−	0.0610976i
$771$	46.5398			1.67609
$772$	−6.43739	−	8.07223i	−0.231687	−	0.290526i
$773$	−31.5991	−	15.2173i	−1.13654	−	0.547329i	−0.231576	−	0.972817i	$-0.574388\pi$
$773$	−31.5991	−	15.2173i	−1.13654	−	0.547329i	−0.904964	+	0.425488i	$0.860103\pi$
$774$	−0.0291223	+	0.0365183i	−0.00104678	+	0.00131262i
$775$	−18.8663	+	23.6575i	−0.677696	+	0.849804i
$776$	−3.42035	+	1.64715i	−0.122783	+	0.0591293i
$777$	10.8589	+	47.5757i	0.389559	+	1.70677i
$778$	2.56505	−	11.2382i	0.0919614	−	0.402909i
$779$	17.9537	+	8.64606i	0.643259	+	0.309777i
$780$	4.43679	−	2.13664i	0.158862	−	0.0765041i
$781$	−1.87640	+	8.22106i	−0.0671430	+	0.294173i
$782$	−4.32677			−0.154725
$783$	−5.98234	+	27.1733i	−0.213791	+	0.971094i
$784$	2.84952			0.101769
$785$	0.722283	−	3.16453i	0.0257794	−	0.112947i
$786$	−23.2179	+	11.1812i	−0.828157	+	0.398819i
$787$	24.5984	+	11.8459i	0.876837	+	0.422262i	0.817468	−	0.575974i	$-0.195377\pi$
$787$	24.5984	+	11.8459i	0.876837	+	0.422262i	0.0593688	+	0.998236i	$0.481091\pi$
$788$	5.97308	−	26.1698i	0.212782	−	0.932259i
$789$	−9.05122	−	39.6560i	−0.322232	−	1.41179i
$790$	−4.19065	+	2.01811i	−0.149097	+	0.0718011i
$791$	32.6453	−	40.9359i	1.16073	−	1.45551i
$792$	0.0291223	−	0.0365183i	0.00103482	−	0.00129762i
$793$	25.0597	+	12.0681i	0.889894	+	0.428551i
$794$	18.0708	+	22.6601i	0.641309	+	0.804176i
$795$	3.65630			0.129676
$796$	−4.24156	−	5.31875i	−0.150338	−	0.188518i
$797$	−9.11491	−	39.9350i	−0.322867	−	1.41457i	−0.832426	−	0.554136i	$-0.813049\pi$
$797$	−9.11491	−	39.9350i	−0.322867	−	1.41457i	0.509560	−	0.860435i	$-0.329808\pi$
$798$	6.04090	+	26.4669i	0.213846	+	0.936919i
$799$	−34.1457	−	42.8174i	−1.20799	−	1.51477i
$800$	−4.75527			−0.168124
$801$	0.0373678	+	0.0468577i	0.00132033	+	0.00165564i
$802$	−9.30669	−	4.48187i	−0.328631	−	0.158260i
$803$	10.6932	−	13.4088i	0.377355	−	0.473188i
$804$	−7.75171	+	9.72034i	−0.273382	+	0.342810i
$805$	−1.13808	+	0.548071i	−0.0401121	+	0.0193170i
$806$	8.09286	+	35.4572i	0.285059	+	1.24892i
$807$	6.04953	−	26.5047i	0.212953	−	0.933010i
$808$	1.10082	+	0.530129i	0.0387268	+	0.0186499i
$809$	38.8637	−	18.7158i	1.36638	−	0.658012i	0.400327	−	0.916372i	$-0.368896\pi$
$809$	38.8637	−	18.7158i	1.36638	−	0.658012i	0.966049	+	0.258360i	$0.0831821\pi$
$810$	−1.00165	+	4.38850i	−0.0351943	+	0.154196i
$811$	38.0001			1.33436			0.667182	−	0.744894i	$-0.267500\pi$
$811$	38.0001			1.33436			0.667182	+	0.744894i	$0.267500\pi$
$812$	16.9003	−	0.130153i	0.593083	−	0.00456748i
$813$	−0.382611			−0.0134187
$814$	−2.77471	+	12.1568i	−0.0972534	+	0.426095i
$815$	2.52185	−	1.21446i	0.0883366	−	0.0425407i
$816$	8.34499	+	4.01873i	0.292133	+	0.140684i
$817$	1.54360	−	6.76296i	0.0540037	−	0.236606i
$818$	−2.21669	−	9.71194i	−0.0775047	−	0.339570i
$819$	0.540451	−	0.260268i	0.0188849	−	0.00909449i
$820$	1.23754	−	1.55183i	0.0432168	−	0.0541921i
$821$	−7.61753	+	9.55208i	−0.265854	+	0.333370i	−0.896783	−	0.442470i	$-0.854102\pi$
$821$	−7.61753	+	9.55208i	−0.265854	+	0.333370i	0.630930	+	0.775840i	$0.282674\pi$
$822$	−2.36831	−	1.14052i	−0.0826045	−	0.0397802i
$823$	22.8365	+	28.6361i	0.796030	+	0.998190i	0.999816	+	0.0191747i	$0.00610387\pi$
$823$	22.8365	+	28.6361i	0.796030	+	0.998190i	−0.203786	+	0.979015i	$0.565325\pi$
$824$	1.80814			0.0629896
$825$	7.21242	+	9.04409i	0.251104	+	0.314875i
$826$	−7.79351	−	34.1456i	−0.271171	−	1.18808i
$827$	5.74425	+	25.1672i	0.199747	+	0.875149i	0.971087	+	0.238726i	$0.0767297\pi$
$827$	5.74425	+	25.1672i	0.199747	+	0.875149i	−0.771340	+	0.636423i	$0.780413\pi$
$828$	−0.0169642	−	0.0212725i	−0.000589547	−	0.000739269i
$829$	−15.7732			−0.547825			−0.273913	−	0.961755i	$-0.588318\pi$
$829$	−15.7732			−0.547825			−0.273913	+	0.961755i	$0.588318\pi$
$830$	−3.92009	−	4.91563i	−0.136068	−	0.170624i
$831$	5.88750	+	2.83527i	0.204235	+	0.0983544i
$832$	−3.56353	+	4.46852i	−0.123543	+	0.154918i
$833$	9.44821	−	11.8477i	0.327361	−	0.410498i
$834$	13.7405	−	6.61707i	0.475795	−	0.229131i
$835$	−1.33078	−	5.83052i	−0.0460535	−	0.201773i
$836$	−1.54360	+	6.76296i	−0.0533865	+	0.233902i
$837$	−29.6218	−	14.2651i	−1.02388	−	0.493074i
$838$	−25.5445	+	12.3016i	−0.882420	+	0.424951i
$839$	−0.479893	+	2.10255i	−0.0165677	+	0.0725880i	−0.982536	−	0.186073i	$-0.940424\pi$
$839$	−0.479893	+	2.10255i	−0.0165677	+	0.0725880i	0.965968	+	0.258661i	$0.0832812\pi$
$840$	2.70406			0.0932988
$841$	28.9966	−	0.446646i	0.999881	−	0.0154016i
$842$	−9.51999			−0.328080
$843$	−9.47627	+	41.5183i	−0.326380	+	1.42996i
$844$	−5.26221	+	2.53415i	−0.181133	+	0.0872289i
$845$	8.76546	+	4.22123i	0.301541	+	0.145215i
$846$	0.0766335	−	0.335753i	0.00263471	−	0.0115434i
$847$	6.31957	+	27.6879i	0.217143	+	0.951366i
$848$	−3.82334	+	1.84123i	−0.131294	+	0.0632279i
$849$	−8.25027	+	10.3455i	−0.283149	+	0.355057i
$850$	−15.7671	+	19.7714i	−0.540808	+	0.678152i
$851$	6.54430	+	3.15157i	0.224336	+	0.108034i
$852$	−6.55608	−	8.22106i	−0.224607	−	0.281649i
$853$	−21.6578			−0.741548			−0.370774	−	0.928723i	$-0.620908\pi$
$853$	−21.6578			−0.741548			−0.370774	+	0.928723i	$0.620908\pi$
$854$	9.52251	+	11.9409i	0.325854	+	0.408608i
$855$	0.0182833	+	0.0801045i	0.000625277	+	0.00273952i
$856$	−0.923602	−	4.04656i	−0.0315681	−	0.138309i
$857$	−7.86892	−	9.86732i	−0.268797	−	0.337061i	0.629053	−	0.777363i	$-0.283443\pi$
$857$	−7.86892	−	9.86732i	−0.268797	−	0.337061i	−0.897850	+	0.440302i	$0.854872\pi$
$858$	13.9036			0.474661
$859$	−12.1127	−	15.1888i	−0.413280	−	0.518236i	0.531004	−	0.847369i	$-0.321815\pi$
$859$	−12.1127	−	15.1888i	−0.413280	−	0.518236i	−0.944284	+	0.329133i	$0.893244\pi$
$860$	−0.622528	−	0.299794i	−0.0212280	−	0.0102229i
$861$	13.6740	−	17.1466i	0.466007	−	0.584355i
$862$	−11.8307	+	14.8352i	−0.402954	+	0.505289i
$863$	41.3801	−	19.9276i	1.40860	−	0.678344i	0.433711	−	0.901052i	$-0.357204\pi$
$863$	41.3801	−	19.9276i	1.40860	−	0.678344i	0.974885	+	0.222708i	$0.0714896\pi$
$864$	−1.14972	−	5.03725i	−0.0391142	−	0.171371i
$865$	1.28139	−	5.61414i	0.0435686	−	0.190886i
$866$	−25.5107	−	12.2853i	−0.866890	−	0.417472i
$867$	17.7022	−	8.52495i	0.601200	−	0.289523i
$868$	−4.44385	+	19.4698i	−0.150834	+	0.660847i
$869$	−13.1323			−0.445482
$870$	4.63975	−	0.0357318i	0.157302	−	0.00121142i
$871$	−40.7992			−1.38243
$872$	−3.22757	+	14.1409i	−0.109299	+	0.478872i
$873$	−0.114382	+	0.0550836i	−0.00387125	+	0.00186430i
$874$	3.64067	+	1.75325i	0.123147	+	0.0593047i
$875$	−3.37022	+	14.7659i	−0.113934	+	0.499179i
$876$	4.75892	+	20.8502i	0.160789	+	0.704463i
$877$	−7.29358	+	3.51240i	−0.246287	+	0.118605i	−0.552955	−	0.833211i	$-0.686500\pi$
$877$	−7.29358	+	3.51240i	−0.246287	+	0.118605i	0.306669	+	0.951816i	$0.400786\pi$
$878$	−12.4049	+	15.5552i	−0.418644	+	0.524962i
$879$	27.9323	−	35.0260i	0.942134	−	1.18140i
$880$	0.622528	+	0.299794i	0.0209854	+	0.0101060i
$881$	1.87163	+	2.34695i	0.0630569	+	0.0790709i	0.812360	−	0.583157i	$-0.198183\pi$
$881$	1.87163	+	2.34695i	0.0630569	+	0.0790709i	−0.749303	+	0.662228i	$0.769611\pi$
$882$	0.0952930			0.00320868
$883$	−24.0764	−	30.1908i	−0.810235	−	1.01600i	−0.999420	−	0.0340614i	$-0.989156\pi$
$883$	−24.0764	−	30.1908i	−0.810235	−	1.01600i	0.189184	−	0.981942i	$-0.439416\pi$
$884$	6.76347	+	29.6327i	0.227480	+	0.996655i
$885$	−2.13961	−	9.37422i	−0.0719221	−	0.315111i
$886$	−22.1713	−	27.8019i	−0.744859	−	0.934023i
$887$	−29.4281			−0.988100			−0.494050	−	0.869433i	$-0.664484\pi$
$887$	−29.4281			−0.988100			−0.494050	+	0.869433i	$0.664484\pi$
$888$	−9.69471	−	12.1568i	−0.325333	−	0.407955i
$889$	35.8903	+	17.2839i	1.20372	+	0.579682i
$890$	−0.552776	+	0.693159i	−0.0185291	+	0.0232347i
$891$	−7.92394	+	9.93631i	−0.265462	+	0.332879i
$892$	19.7637	−	9.51770i	0.661738	−	0.318676i
$893$	11.3811	+	49.8640i	0.380855	+	1.66864i
$894$	−1.83731	+	8.04979i	−0.0614489	+	0.269225i
$895$	−8.18101	−	3.93977i	−0.273461	−	0.131692i
$896$	−2.82760	+	1.36170i	−0.0944634	+	0.0454912i
$897$	1.80221	−	7.89599i	0.0601740	−	0.263640i
$898$	10.8511			0.362106
$899$	−7.36769	+	33.4659i	−0.245726	+	1.11615i
$900$	−0.159025			−0.00530082
$901$	−5.02172	+	22.0016i	−0.167298	+	0.732979i
$902$	5.04903	−	2.43148i	0.168114	−	0.0809596i
$903$	−6.87850	−	3.31251i	−0.228902	−	0.110233i
$904$	−3.71240	+	16.2651i	−0.123473	+	0.540969i
$905$	−1.08914	−	4.77185i	−0.0362043	−	0.158622i
$906$	−10.1906	+	4.90754i	−0.338560	+	0.163042i
$907$	2.90939	−	3.64825i	0.0966046	−	0.121138i	−0.731179	−	0.682185i	$-0.761030\pi$
$907$	2.90939	−	3.64825i	0.0966046	−	0.121138i	0.827784	+	0.561047i	$0.189601\pi$
$908$	−1.34388	+	1.68518i	−0.0445983	+	0.0559245i
$909$	0.0368134	+	0.0177284i	0.00122102	+	0.000588014i
$910$	5.53258	+	6.93764i	0.183403	+	0.229981i
$911$	−37.9571			−1.25758			−0.628788	−	0.777577i	$-0.716449\pi$
$911$	−37.9571			−1.25758			−0.628788	+	0.777577i	$0.716449\pi$
$912$	−5.39328	−	6.76296i	−0.178589	−	0.223944i
$913$	−3.95007	−	17.3064i	−0.130728	−	0.572758i
$914$	−7.19540	−	31.5251i	−0.238003	−	1.04276i
$915$	2.61428	+	3.27820i	0.0864255	+	0.108374i
$916$	9.29190			0.307013
$917$	−28.9523	−	36.3050i	−0.956089	−	1.19890i
$918$	−24.7559	−	11.9218i	−0.817066	−	0.393478i
$919$	15.8113	−	19.8268i	0.521568	−	0.654026i	−0.449373	−	0.893344i	$-0.648353\pi$
$919$	15.8113	−	19.8268i	0.521568	−	0.654026i	0.970941	+	0.239318i	$0.0769240\pi$
$920$	0.250949	−	0.314680i	0.00827355	−	0.0103747i
$921$	2.84651	−	1.37081i	0.0937956	−	0.0451696i
$922$	−5.65307	−	24.7677i	−0.186174	−	0.815682i
$923$	7.67836	−	33.6411i	0.252736	−	1.10731i
$924$	6.87850	+	3.31251i	0.226286	+	0.108974i
$925$	38.2492	−	18.4199i	1.25763	−	0.605641i
$926$	−0.716678	+	3.13997i	−0.0235515	+	0.103186i
$927$	0.0604674			0.00198601
$928$	−4.83373	+	2.37383i	−0.158675	+	0.0779248i
$929$	36.8642			1.20947			0.604737	−	0.796425i	$-0.293278\pi$
$929$	36.8642			1.20947			0.604737	+	0.796425i	$0.293278\pi$
$930$	−1.22000	+	5.34517i	−0.0400054	+	0.175275i
$931$	−12.7508	+	6.14046i	−0.417891	+	0.201246i
$932$	10.6177	+	5.11321i	0.347794	+	0.167489i
$933$	7.52255	−	32.9584i	0.246277	−	1.07901i
$934$	−5.08605	−	22.2834i	−0.166421	−	0.729136i
$935$	3.31060	−	1.59430i	0.108268	−	0.0521392i
$936$	−0.119170	+	0.149435i	−0.00389521	+	0.00488444i
$937$	−1.45551	+	1.82515i	−0.0475493	+	0.0596249i	−0.805038	−	0.593224i	$-0.797855\pi$
$937$	−1.45551	+	1.82515i	−0.0475493	+	0.0596249i	0.757488	+	0.652849i	$0.226426\pi$
$938$	−20.1845	−	9.72034i	−0.659047	−	0.317380i
$939$	−36.7960	−	46.1408i	−1.20079	−	1.50575i
$940$	5.09448			0.166164
$941$	5.47972	+	6.87136i	0.178634	+	0.224000i	0.863085	−	0.505059i	$-0.168529\pi$
$941$	5.47972	+	6.87136i	0.178634	+	0.224000i	−0.684451	+	0.729059i	$0.739958\pi$
$942$	2.54293	+	11.1413i	0.0828532	+	0.363003i
$943$	−0.726401	−	3.18257i	−0.0236549	−	0.103639i
$944$	6.95799	+	8.72505i	0.226463	+	0.283976i
$945$	−8.02174			−0.260947
$946$	−1.21632	−	1.52521i	−0.0395458	−	0.0495889i
$947$	11.4402	+	5.50930i	0.371756	+	0.179028i	0.610428	−	0.792072i	$-0.290998\pi$
$947$	11.4402	+	5.50930i	0.371756	+	0.179028i	−0.238672	+	0.971100i	$0.576712\pi$
$948$	10.2101	−	12.8030i	0.331607	−	0.415822i
$949$	−43.7572	+	54.8698i	−1.42042	+	1.78115i
$950$	21.2785	−	10.2472i	0.690365	−	0.332462i
$951$	2.13065	+	9.33500i	0.0690911	+	0.302708i
$952$	−3.71387	+	16.2715i	−0.120367	+	0.527363i
$953$	−49.0633	−	23.6277i	−1.58932	−	0.765375i	−0.590195	−	0.807261i	$-0.700949\pi$
$953$	−49.0633	−	23.6277i	−1.58932	−	0.765375i	−0.999122	+	0.0418854i	$0.986664\pi$
$954$	−0.127859	+	0.0615737i	−0.00413959	+	0.00199352i
$955$	0.0467028	−	0.204618i	0.00151127	−	0.00662129i
$956$	−14.3692			−0.464732
$957$	11.8462	+	5.59287i	0.382934	+	0.180792i
$958$	2.14546			0.0693165
$959$	1.05400	−	4.61787i	0.0340354	−	0.149119i
$960$	−0.776279	+	0.373836i	−0.0250543	+	0.0120655i
$961$	−8.55134	−	4.11811i	−0.275850	−	0.132842i
$962$	11.3543	−	49.7463i	0.366076	−	1.60388i
$963$	−0.0308868	−	0.135324i	−0.000995314	−	0.00436076i
$964$	8.29280	−	3.99360i	0.267093	−	0.128625i
$965$	3.18457	−	3.99332i	0.102515	−	0.128549i
$966$	2.77281	−	3.47700i	0.0892138	−	0.111871i
$967$	−44.6567	−	21.5055i	−1.43606	−	0.691572i	−0.455949	−	0.890006i	$-0.650700\pi$
$967$	−44.6567	−	21.5055i	−1.43606	−	0.691572i	−0.980114	+	0.198434i	$0.936414\pi$
$968$	−5.64207	−	7.07493i	−0.181343	−	0.227397i
$969$	−46.0014			−1.47778
$970$	−1.17093	−	1.46830i	−0.0375962	−	0.0471442i
$971$	6.13766	+	26.8909i	0.196967	+	0.862969i	0.972729	+	0.231944i	$0.0745085\pi$
$971$	6.13766	+	26.8909i	0.196967	+	0.862969i	−0.775762	+	0.631025i	$0.782634\pi$
$972$	−0.0773306	−	0.338807i	−0.00248038	−	0.0108672i
$973$	17.1341	+	21.4855i	0.549295	+	0.688794i
$974$	21.7759			0.697746
$975$	−29.5137	−	37.0090i	−0.945194	−	1.18524i
$976$	−4.38454	−	2.11149i	−0.140346	−	0.0675870i
$977$	−27.7654	+	34.8167i	−0.888294	+	1.11389i	0.104556	+	0.994519i	$0.466658\pi$
$977$	−27.7654	+	34.8167i	−0.888294	+	1.11389i	−0.992850	+	0.119367i	$0.961914\pi$
$978$	−6.14422	+	7.70461i	−0.196470	+	0.246366i
$979$	−2.25527	+	1.08608i	−0.0720786	+	0.0347112i
$980$	0.313678	+	1.37431i	0.0100201	+	0.0439008i
$981$	−0.107936	+	0.472897i	−0.00344612	+	0.0150984i
$982$	35.0145	+	16.8621i	1.11736	+	0.538091i
$983$	1.07817	−	0.519217i	0.0343882	−	0.0165605i	−0.416611	−	0.909085i	$-0.636782\pi$
$983$	1.07817	−	0.519217i	0.0343882	−	0.0165605i	0.450999	+	0.892525i	$0.351068\pi$
$984$	−1.55499	+	6.81287i	−0.0495713	+	0.217186i
$985$	13.2791			0.423106
$986$	−6.15741	+	27.9685i	−0.196092	+	0.890699i
$987$	56.2904			1.79174
$988$	6.31651	−	27.6744i	0.200955	−	0.880441i
$989$	−1.02384	+	0.493058i	−0.0325564	+	0.0156783i
$990$	0.0208184	+	0.0100256i	0.000661652	+	0.000318635i
$991$	−7.79435	+	34.1493i	−0.247596	+	1.08479i	0.686321	+	0.727298i	$0.259224\pi$
$991$	−7.79435	+	34.1493i	−0.247596	+	1.08479i	−0.933917	+	0.357490i	$0.883633\pi$
$992$	−1.41596	−	6.20373i	−0.0449568	−	0.196969i
$993$	−21.4137	+	10.3123i	−0.679544	+	0.327251i
$994$	11.8136	−	14.8138i	0.374706	−	0.469866i
$995$	2.09829	−	2.63118i	0.0665204	−	0.0834139i
$996$	19.9436	+	9.60433i	0.631937	+	0.304325i
$997$	19.4359	+	24.3719i	0.615543	+	0.771866i	0.987710	−	0.156300i	$-0.0499566\pi$
$997$	19.4359	+	24.3719i	0.615543	+	0.771866i	−0.372167	+	0.928166i	$0.621385\pi$
$998$	39.2992			1.24400
$999$	28.7599	+	36.0638i	0.909924	+	1.14101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.2.d.b.25.2	yes	12
3.2	odd	2		522.2.k.h.199.1		12
4.3	odd	2		464.2.u.h.257.1		12
29.6	even	14		1682.2.a.q.1.5		6
29.7	even	7	inner	58.2.d.b.7.2	✓	12
29.14	odd	28		1682.2.b.i.1681.5		12
29.15	odd	28		1682.2.b.i.1681.8		12
29.23	even	7		1682.2.a.t.1.2		6
87.65	odd	14		522.2.k.h.181.1		12
116.7	odd	14		464.2.u.h.65.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.7.2	✓	12	29.7	even	7	inner
58.2.d.b.25.2	yes	12	1.1	even	1	trivial
464.2.u.h.65.1		12	116.7	odd	14
464.2.u.h.257.1		12	4.3	odd	2
522.2.k.h.181.1		12	87.65	odd	14
522.2.k.h.199.1		12	3.2	odd	2
1682.2.a.q.1.5		6	29.6	even	14
1682.2.a.t.1.2		6	29.23	even	7
1682.2.b.i.1681.5		12	29.14	odd	28
1682.2.b.i.1681.8		12	29.15	odd	28

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:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(1.56920 - 0.755686i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.110081 - 0.482295i) q^{5} +(0.387560 + 1.69801i) q^{6} +(-2.82760 + 1.36170i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.0208506 - 0.0261458i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(1.56920 - 0.755686i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.110081 - 0.482295i) q^{5} +(0.387560 + 1.69801i) q^{6} +(-2.82760 + 1.36170i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.0208506 - 0.0261458i) q^{9} +(0.445708 + 0.214642i) q^{10} +(0.870839 + 1.09200i) q^{11} -1.74168 q^{12} +(-3.56353 - 4.46852i) q^{13} +(-0.698359 - 3.05971i) q^{14} +(-0.191725 - 0.840003i) q^{15} +(0.623490 + 0.781831i) q^{16} +5.31800 q^{17} +(0.0208506 + 0.0261458i) q^{18} +(-4.47471 - 2.15491i) q^{19} +(-0.308439 + 0.386771i) q^{20} +(-3.40804 + 4.27355i) q^{21} +(-1.25840 + 0.606013i) q^{22} +(0.181045 + 0.793210i) q^{23} +(0.387560 - 1.69801i) q^{24} +(4.28435 + 2.06324i) q^{25} +(5.14944 - 2.47984i) q^{26} +(-1.14972 + 5.03725i) q^{27} +3.13840 q^{28} +(5.38501 - 0.0414712i) q^{29} +0.861605 q^{30} +(-1.41596 + 6.20373i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(2.19173 + 1.05548i) q^{33} +(-1.18337 + 5.18466i) q^{34} +(0.345477 + 1.51363i) q^{35} +(-0.0301299 + 0.0145098i) q^{36} +(5.56630 - 6.97992i) q^{37} +(3.09660 - 3.88301i) q^{38} +(-8.96867 - 4.31909i) q^{39} +(-0.308439 - 0.386771i) q^{40} -4.01226 q^{41} +(-3.40804 - 4.27355i) q^{42} +(0.310799 + 1.36170i) q^{43} +(-0.310799 - 1.36170i) q^{44} +(-0.0103147 - 0.0129343i) q^{45} -0.813609 q^{46} +(-6.42079 - 8.05142i) q^{47} +(1.56920 + 0.755686i) q^{48} +(1.77665 - 2.22785i) q^{49} +(-2.96486 + 3.71782i) q^{50} +(8.34499 - 4.01873i) q^{51} +(1.27181 + 5.57215i) q^{52} +(-0.944288 + 4.13720i) q^{53} +(-4.65512 - 2.24179i) q^{54} +(0.622528 - 0.299794i) q^{55} +(-0.698359 + 3.05971i) q^{56} -8.65014 q^{57} +(-1.15784 + 5.25922i) q^{58} +11.1598 q^{59} +(-0.191725 + 0.840003i) q^{60} +(-4.38454 + 2.11149i) q^{61} +(-5.73311 - 2.76092i) q^{62} +(-0.0233543 + 0.102322i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-2.54742 + 1.22677i) q^{65} +(-1.51672 + 1.90191i) q^{66} +(4.45072 - 5.58102i) q^{67} +(-4.79135 - 2.30739i) q^{68} +(0.883513 + 1.10789i) q^{69} -1.55256 q^{70} +(3.76423 + 4.72019i) q^{71} +(-0.00744148 - 0.0326033i) q^{72} +(-2.73238 - 11.9713i) q^{73} +(5.56630 + 6.97992i) q^{74} +8.28215 q^{75} +(3.09660 + 3.88301i) q^{76} +(-3.94935 - 1.90191i) q^{77} +(6.20651 - 7.78272i) q^{78} +(-5.86220 + 7.35096i) q^{79} +(0.445708 - 0.214642i) q^{80} +(2.02476 + 8.87107i) q^{81} +(0.892813 - 3.91167i) q^{82} +(-11.4508 - 5.51441i) q^{83} +(4.92476 - 2.37164i) q^{84} +(0.585409 - 2.56484i) q^{85} -1.39672 q^{86} +(8.41880 - 4.13445i) q^{87} +1.39672 q^{88} +(-0.398796 + 1.74724i) q^{89} +(0.0149052 - 0.00717798i) q^{90} +(16.1610 + 7.78272i) q^{91} +(0.181045 - 0.793210i) q^{92} +(2.46615 + 10.8049i) q^{93} +(9.27831 - 4.46820i) q^{94} +(-1.53188 + 1.92092i) q^{95} +(-1.08592 + 1.36170i) q^{96} +(-3.42035 - 1.64715i) q^{97} +(1.77665 + 2.22785i) q^{98} +0.0467086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + 4 q^{6} + q^{7} - 2 q^{8} - 11 q^{9} - 7 q^{10} - 2 q^{11} + 4 q^{12} + q^{13} + q^{14} - 9 q^{15} - 2 q^{16} - 12 q^{17} - 11 q^{18} - 6 q^{19} + 7 q^{20} - 13 q^{21} - 2 q^{22} + 35 q^{23} + 4 q^{24} - 6 q^{25} + 8 q^{26} + 39 q^{27} - 6 q^{28} - 14 q^{29} + 54 q^{30} - 8 q^{31} - 2 q^{32} + 33 q^{33} - 5 q^{34} - 18 q^{35} - 4 q^{36} + 31 q^{37} + q^{38} - 22 q^{39} + 7 q^{40} - 30 q^{41} - 13 q^{42} - 5 q^{43} + 5 q^{44} - 20 q^{45} - 28 q^{46} - 33 q^{47} - 3 q^{48} + 37 q^{49} + q^{50} - 15 q^{51} - 6 q^{52} + 13 q^{53} - 24 q^{54} + 36 q^{55} + q^{56} - 38 q^{57} + 38 q^{59} - 9 q^{60} - 5 q^{61} - 8 q^{62} + 4 q^{63} - 2 q^{64} - 20 q^{65} - 30 q^{66} - 7 q^{67} - 19 q^{68} + 20 q^{69} - 18 q^{70} + 3 q^{71} + 3 q^{72} - 22 q^{73} + 31 q^{74} - 2 q^{75} + q^{76} + 10 q^{77} + 41 q^{78} - 60 q^{79} - 7 q^{80} + 88 q^{81} + 26 q^{82} - 39 q^{83} + 43 q^{84} + 38 q^{85} + 2 q^{86} + 9 q^{87} - 2 q^{88} + 39 q^{89} - 34 q^{90} + 61 q^{91} + 35 q^{92} - 54 q^{93} + 16 q^{94} + 55 q^{95} - 3 q^{96} - 19 q^{97} + 37 q^{98} - 8 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + 4 * q^6 + q^7 - 2 * q^8 - 11 * q^9 - 7 * q^10 - 2 * q^11 + 4 * q^12 + q^13 + q^14 - 9 * q^15 - 2 * q^16 - 12 * q^17 - 11 * q^18 - 6 * q^19 + 7 * q^20 - 13 * q^21 - 2 * q^22 + 35 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 39 * q^27 - 6 * q^28 - 14 * q^29 + 54 * q^30 - 8 * q^31 - 2 * q^32 + 33 * q^33 - 5 * q^34 - 18 * q^35 - 4 * q^36 + 31 * q^37 + q^38 - 22 * q^39 + 7 * q^40 - 30 * q^41 - 13 * q^42 - 5 * q^43 + 5 * q^44 - 20 * q^45 - 28 * q^46 - 33 * q^47 - 3 * q^48 + 37 * q^49 + q^50 - 15 * q^51 - 6 * q^52 + 13 * q^53 - 24 * q^54 + 36 * q^55 + q^56 - 38 * q^57 + 38 * q^59 - 9 * q^60 - 5 * q^61 - 8 * q^62 + 4 * q^63 - 2 * q^64 - 20 * q^65 - 30 * q^66 - 7 * q^67 - 19 * q^68 + 20 * q^69 - 18 * q^70 + 3 * q^71 + 3 * q^72 - 22 * q^73 + 31 * q^74 - 2 * q^75 + q^76 + 10 * q^77 + 41 * q^78 - 60 * q^79 - 7 * q^80 + 88 * q^81 + 26 * q^82 - 39 * q^83 + 43 * q^84 + 38 * q^85 + 2 * q^86 + 9 * q^87 - 2 * q^88 + 39 * q^89 - 34 * q^90 + 61 * q^91 + 35 * q^92 - 54 * q^93 + 16 * q^94 + 55 * q^95 - 3 * q^96 - 19 * q^97 + 37 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more