LMFDB - Embedded newform 546.2.l.k.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-43})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} - 11x + 121 $ x^4 - x^3 - 10x^2 - 11x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$-2.58945 - 2.07237i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.2.l.k.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-3.08945 - 5.35109i) q^{11} -1.00000 q^{12} +(-1.50000 + 3.27872i) q^{13} -1.00000 q^{14} +(-1.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(4.08945 - 7.08314i) q^{19} +(1.00000 - 1.73205i) q^{20} +1.00000 q^{21} +(-3.08945 + 5.35109i) q^{22} +(-1.58945 - 2.75302i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(3.58945 - 0.340322i) q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-4.08945 - 7.08314i) q^{29} +(-1.00000 + 1.73205i) q^{30} -7.17891 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.08945 - 5.35109i) q^{33} +5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 - 1.73205i) q^{37} -8.17891 q^{38} +(-3.58945 + 0.340322i) q^{39} -2.00000 q^{40} +(-2.08945 - 3.61904i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-0.410546 + 0.711086i) q^{43} +6.17891 q^{44} +(1.00000 - 1.73205i) q^{45} +(-1.58945 + 2.75302i) q^{46} +4.17891 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} -5.00000 q^{51} +(-2.08945 - 2.93840i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(6.17891 + 10.7022i) q^{55} +(0.500000 - 0.866025i) q^{56} +8.17891 q^{57} +(-4.08945 + 7.08314i) q^{58} +(0.410546 - 0.711086i) q^{59} +2.00000 q^{60} +(1.50000 - 2.59808i) q^{61} +(3.58945 + 6.21712i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(3.00000 - 6.55744i) q^{65} -6.17891 q^{66} +(7.58945 + 13.1453i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(1.58945 - 2.75302i) q^{69} +2.00000 q^{70} +(-4.58945 + 7.94917i) q^{71} +(-0.500000 + 0.866025i) q^{72} +4.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(4.08945 + 7.08314i) q^{76} -6.17891 q^{77} +(2.08945 + 2.93840i) q^{78} +1.82109 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.08945 + 3.61904i) q^{82} -5.17891 q^{83} +(-0.500000 + 0.866025i) q^{84} +(5.00000 - 8.66025i) q^{85} +0.821092 q^{86} +(4.08945 - 7.08314i) q^{87} +(-3.08945 - 5.35109i) q^{88} +(-4.50000 - 7.79423i) q^{89} -2.00000 q^{90} +(2.08945 + 2.93840i) q^{91} +3.17891 q^{92} +(-3.58945 - 6.21712i) q^{93} +(-2.08945 - 3.61904i) q^{94} +(-8.17891 + 14.1663i) q^{95} -1.00000 q^{96} +(-6.17891 + 10.7022i) q^{97} +(-0.500000 + 0.866025i) q^{98} +6.17891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{14} - 4 q^{15} - 2 q^{16} - 10 q^{17} + 4 q^{18} + 5 q^{19} + 4 q^{20} + 4 q^{21} - q^{22} + 5 q^{23} + 2 q^{24} - 4 q^{25} + 3 q^{26} - 4 q^{27} + 2 q^{28} - 5 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} - 4 q^{37} - 10 q^{38} - 3 q^{39} - 8 q^{40} + 3 q^{41} - 2 q^{42} - 13 q^{43} + 2 q^{44} + 4 q^{45} + 5 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} + 3 q^{52} - 12 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 10 q^{57} - 5 q^{58} + 13 q^{59} + 8 q^{60} + 6 q^{61} + 3 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{65} - 2 q^{66} + 19 q^{67} - 10 q^{68} - 5 q^{69} + 8 q^{70} - 7 q^{71} - 2 q^{72} + 16 q^{73} - 4 q^{74} - 2 q^{75} + 5 q^{76} - 2 q^{77} - 3 q^{78} + 30 q^{79} + 4 q^{80} - 2 q^{81} + 3 q^{82} + 2 q^{83} - 2 q^{84} + 20 q^{85} + 26 q^{86} + 5 q^{87} - q^{88} - 18 q^{89} - 8 q^{90} - 3 q^{91} - 10 q^{92} - 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} - 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 6 * q^13 - 4 * q^14 - 4 * q^15 - 2 * q^16 - 10 * q^17 + 4 * q^18 + 5 * q^19 + 4 * q^20 + 4 * q^21 - q^22 + 5 * q^23 + 2 * q^24 - 4 * q^25 + 3 * q^26 - 4 * q^27 + 2 * q^28 - 5 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 - 4 * q^37 - 10 * q^38 - 3 * q^39 - 8 * q^40 + 3 * q^41 - 2 * q^42 - 13 * q^43 + 2 * q^44 + 4 * q^45 + 5 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 + 3 * q^52 - 12 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 10 * q^57 - 5 * q^58 + 13 * q^59 + 8 * q^60 + 6 * q^61 + 3 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^65 - 2 * q^66 + 19 * q^67 - 10 * q^68 - 5 * q^69 + 8 * q^70 - 7 * q^71 - 2 * q^72 + 16 * q^73 - 4 * q^74 - 2 * q^75 + 5 * q^76 - 2 * q^77 - 3 * q^78 + 30 * q^79 + 4 * q^80 - 2 * q^81 + 3 * q^82 + 2 * q^83 - 2 * q^84 + 20 * q^85 + 26 * q^86 + 5 * q^87 - q^88 - 18 * q^89 - 8 * q^90 - 3 * q^91 - 10 * q^92 - 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 - 2 * q^97 - 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−3.08945	−	5.35109i	−0.931505	−	1.61341i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	−3.08945	−	5.35109i	−0.931505	−	1.61341i	−0.150756	−	0.988571i	$-0.548171\pi$
$12$	−1.00000			−0.288675
$13$	−1.50000	+	3.27872i	−0.416025	+	0.909353i
$13$	−1.50000	+	3.27872i	−0.416025	+	0.909353i
$14$	−1.00000			−0.267261
$15$	−1.00000	−	1.73205i	−0.258199	−	0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$	1.00000			0.235702
$19$	4.08945	−	7.08314i	0.938185	−	1.62498i	0.169332	−	0.985559i	$-0.445839\pi$
$19$	4.08945	−	7.08314i	0.938185	−	1.62498i	0.768853	−	0.639425i	$-0.220828\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$	1.00000			0.218218
$22$	−3.08945	+	5.35109i	−0.658674	+	1.14086i
$23$	−1.58945	−	2.75302i	−0.331424	−	0.574043i	0.651367	−	0.758763i	$-0.274196\pi$
$23$	−1.58945	−	2.75302i	−0.331424	−	0.574043i	−0.982791	+	0.184719i	$0.940862\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−1.00000			−0.200000
$26$	3.58945	−	0.340322i	0.703950	−	0.0667425i
$27$	−1.00000			−0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	−4.08945	−	7.08314i	−0.759393	−	1.31531i	−0.943161	−	0.332337i	$-0.892163\pi$
$29$	−4.08945	−	7.08314i	−0.759393	−	1.31531i	0.183768	−	0.982970i	$-0.441170\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−7.17891			−1.28937			−0.644685	−	0.764448i	$-0.723011\pi$
$31$	−7.17891			−1.28937			−0.644685	+	0.764448i	$0.723011\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.08945	−	5.35109i	0.537805	−	0.931505i
$34$	5.00000			0.857493
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−8.17891			−1.32679
$39$	−3.58945	+	0.340322i	−0.574773	+	0.0544951i
$40$	−2.00000			−0.316228
$41$	−2.08945	−	3.61904i	−0.326318	−	0.565199i	0.655460	−	0.755230i	$-0.272475\pi$
$41$	−2.08945	−	3.61904i	−0.326318	−	0.565199i	−0.981778	+	0.190030i	$0.939141\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−0.410546	+	0.711086i	−0.0626077	+	0.108440i	−0.895630	−	0.444799i	$-0.853275\pi$
$43$	−0.410546	+	0.711086i	−0.0626077	+	0.108440i	0.833023	+	0.553239i	$0.186608\pi$
$44$	6.17891			0.931505
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	−1.58945	+	2.75302i	−0.234352	+	0.405910i
$47$	4.17891			0.609556			0.304778	−	0.952423i	$-0.401418\pi$
$47$	4.17891			0.609556			0.304778	+	0.952423i	$0.401418\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−5.00000			−0.700140
$52$	−2.08945	−	2.93840i	−0.289755	−	0.407482i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	6.17891	+	10.7022i	0.833164	+	1.44308i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	8.17891			1.08332
$58$	−4.08945	+	7.08314i	−0.536972	+	0.930062i
$59$	0.410546	−	0.711086i	0.0534485	−	0.0925755i	−0.838063	−	0.545573i	$-0.816312\pi$
$59$	0.410546	−	0.711086i	0.0534485	−	0.0925755i	0.891512	+	0.452998i	$0.149645\pi$
$60$	2.00000			0.258199
$61$	1.50000	−	2.59808i	0.192055	−	0.332650i	−0.753876	−	0.657017i	$-0.771818\pi$
$61$	1.50000	−	2.59808i	0.192055	−	0.332650i	0.945931	+	0.324367i	$0.105151\pi$
$62$	3.58945	+	6.21712i	0.455861	+	0.789575i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	3.00000	−	6.55744i	0.372104	−	0.813350i
$66$	−6.17891			−0.760571
$67$	7.58945	+	13.1453i	0.927199	+	1.60596i	0.787985	+	0.615694i	$0.211124\pi$
$67$	7.58945	+	13.1453i	0.927199	+	1.60596i	0.139214	+	0.990262i	$0.455542\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$	1.58945	−	2.75302i	0.191348	−	0.331424i
$70$	2.00000			0.239046
$71$	−4.58945	+	7.94917i	−0.544668	+	0.943393i	0.453960	+	0.891022i	$0.350011\pi$
$71$	−4.58945	+	7.94917i	−0.544668	+	0.943393i	−0.998628	+	0.0523705i	$0.983322\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	4.08945	+	7.08314i	0.469093	+	0.812492i
$77$	−6.17891			−0.704152
$78$	2.08945	+	2.93840i	0.236584	+	0.332708i
$79$	1.82109			0.204889			0.102444	−	0.994739i	$-0.467334\pi$
$79$	1.82109			0.204889			0.102444	+	0.994739i	$0.467334\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.08945	+	3.61904i	−0.230742	+	0.399656i
$83$	−5.17891			−0.568459			−0.284230	−	0.958756i	$-0.591738\pi$
$83$	−5.17891			−0.568459			−0.284230	+	0.958756i	$0.591738\pi$
$84$	−0.500000	+	0.866025i	−0.0545545	+	0.0944911i
$85$	5.00000	−	8.66025i	0.542326	−	0.939336i
$86$	0.821092			0.0885406
$87$	4.08945	−	7.08314i	0.438436	−	0.759393i
$88$	−3.08945	−	5.35109i	−0.329337	−	0.570428i
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$	−2.00000			−0.210819
$91$	2.08945	+	2.93840i	0.219034	+	0.308028i
$92$	3.17891			0.331424
$93$	−3.58945	−	6.21712i	−0.372209	−	0.644685i
$94$	−2.08945	−	3.61904i	−0.215511	−	0.373276i
$95$	−8.17891	+	14.1663i	−0.839138	+	1.45343i
$96$	−1.00000			−0.102062
$97$	−6.17891	+	10.7022i	−0.627373	+	1.08664i	0.360704	+	0.932680i	$0.382537\pi$
$97$	−6.17891	+	10.7022i	−0.627373	+	1.08664i	−0.988077	+	0.153962i	$0.950797\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	6.17891			0.621004
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	8.17891	+	14.1663i	0.813832	+	1.40960i	0.910164	+	0.414249i	$0.135956\pi$
$101$	8.17891	+	14.1663i	0.813832	+	1.40960i	−0.0963319	+	0.995349i	$0.530711\pi$
$102$	2.50000	+	4.33013i	0.247537	+	0.428746i
$103$	3.17891			0.313227			0.156614	−	0.987660i	$-0.449942\pi$
$103$	3.17891			0.313227			0.156614	+	0.987660i	$0.449942\pi$
$104$	−1.50000	+	3.27872i	−0.147087	+	0.321505i
$105$	−2.00000			−0.195180
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	−3.91055	−	6.77326i	−0.378047	−	0.654796i	0.612731	−	0.790291i	$-0.290071\pi$
$107$	−3.91055	−	6.77326i	−0.378047	−	0.654796i	−0.990778	+	0.135495i	$0.956737\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	6.17891	−	10.7022i	0.589136	−	1.02041i
$111$	1.00000	−	1.73205i	0.0949158	−	0.164399i
$112$	−1.00000			−0.0944911
$113$	2.17891	−	3.77398i	0.204974	−	0.355026i	−0.745150	−	0.666897i	$-0.767622\pi$
$113$	2.17891	−	3.77398i	0.204974	−	0.355026i	0.950125	+	0.311871i	$0.100956\pi$
$114$	−4.08945	−	7.08314i	−0.383012	−	0.663397i
$115$	3.17891	+	5.50603i	0.296435	+	0.513440i
$116$	8.17891			0.759393
$117$	−2.08945	−	2.93840i	−0.193170	−	0.271655i
$118$	−0.821092			−0.0755876
$119$	2.50000	+	4.33013i	0.229175	+	0.396942i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−13.5895	+	23.5376i	−1.23540	+	2.13978i
$122$	−3.00000			−0.271607
$123$	2.08945	−	3.61904i	0.188400	−	0.326318i
$124$	3.58945	−	6.21712i	0.322343	−	0.558314i
$125$	12.0000			1.07331
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	−0.999284	−	0.0378419i	$-0.987952\pi$
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	0.466870	−	0.884326i	$-0.345382\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.821092			−0.0722931
$130$	−7.17891	+	0.680643i	−0.629632	+	0.0596963i
$131$	19.5367			1.70693			0.853466	−	0.521149i	$-0.174496\pi$
$131$	19.5367			1.70693			0.853466	+	0.521149i	$0.174496\pi$
$132$	3.08945	+	5.35109i	0.268902	+	0.465753i
$133$	−4.08945	−	7.08314i	−0.354601	−	0.614186i
$134$	7.58945	−	13.1453i	0.655629	−	1.13558i
$135$	2.00000			0.172133
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	8.17891	−	14.1663i	0.698771	−	1.21031i	−0.270121	−	0.962826i	$-0.587064\pi$
$137$	8.17891	−	14.1663i	0.698771	−	1.21031i	0.968893	−	0.247481i	$-0.0796028\pi$
$138$	−3.17891			−0.270607
$139$	9.08945	−	15.7434i	0.770957	−	1.33534i	−0.166081	−	0.986112i	$-0.553111\pi$
$139$	9.08945	−	15.7434i	0.770957	−	1.33534i	0.937039	−	0.349225i	$-0.113555\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$	2.08945	+	3.61904i	0.175964	+	0.304778i
$142$	9.17891			0.770277
$143$	22.1789	−	2.10282i	1.85469	−	0.175846i
$144$	1.00000			0.0833333
$145$	8.17891	+	14.1663i	0.679221	+	1.17645i
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	2.00000			0.164399
$149$	−2.41055	+	4.17519i	−0.197480	+	0.342045i	−0.947711	−	0.319131i	$-0.896609\pi$
$149$	−2.41055	+	4.17519i	−0.197480	+	0.342045i	0.750231	+	0.661176i	$0.229942\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−14.5367			−1.18298			−0.591491	−	0.806312i	$-0.701460\pi$
$151$	−14.5367			−1.18298			−0.591491	+	0.806312i	$0.701460\pi$
$152$	4.08945	−	7.08314i	0.331699	−	0.574519i
$153$	−2.50000	−	4.33013i	−0.202113	−	0.350070i
$154$	3.08945	+	5.35109i	0.248955	+	0.431203i
$155$	14.3578			1.15325
$156$	1.50000	−	3.27872i	0.120096	−	0.262508i
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	−0.910546	−	1.57711i	−0.0724391	−	0.125468i
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	−3.17891			−0.250533
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	4.41055	−	7.63929i	0.345461	−	0.598355i	−0.639977	−	0.768394i	$-0.721056\pi$
$163$	4.41055	−	7.63929i	0.345461	−	0.598355i	0.985437	+	0.170039i	$0.0543894\pi$
$164$	4.17891			0.326318
$165$	−6.17891	+	10.7022i	−0.481027	+	0.833164i
$166$	2.58945	+	4.48507i	0.200981	+	0.348109i
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$	1.00000			0.0771517
$169$	−8.50000	−	9.83616i	−0.653846	−	0.756628i
$170$	−10.0000			−0.766965
$171$	4.08945	+	7.08314i	0.312728	+	0.541661i
$172$	−0.410546	−	0.711086i	−0.0313038	−	0.0542198i
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	−0.931984	−	0.362500i	$-0.881923\pi$
$173$	−2.00000	+	3.46410i	−0.152057	+	0.263371i	0.779926	+	0.625871i	$0.215256\pi$
$174$	−8.17891			−0.620041
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	−3.08945	+	5.35109i	−0.232876	+	0.403354i
$177$	0.821092			0.0617170
$178$	−4.50000	+	7.79423i	−0.337289	+	0.584202i
$179$	7.17891	+	12.4342i	0.536577	+	0.929378i	0.999085	+	0.0427634i	$0.0136162\pi$
$179$	7.17891	+	12.4342i	0.536577	+	0.929378i	−0.462508	+	0.886615i	$0.653051\pi$
$180$	1.00000	+	1.73205i	0.0745356	+	0.129099i
$181$	7.82109			0.581337			0.290669	−	0.956824i	$-0.406122\pi$
$181$	7.82109			0.581337			0.290669	+	0.956824i	$0.406122\pi$
$182$	1.50000	−	3.27872i	0.111187	−	0.243035i
$183$	3.00000			0.221766
$184$	−1.58945	−	2.75302i	−0.117176	−	0.202955i
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	−3.58945	+	6.21712i	−0.263192	+	0.455861i
$187$	30.8945			2.25923
$188$	−2.08945	+	3.61904i	−0.152389	+	0.263946i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$	16.3578			1.18672
$191$	−13.7684	+	23.8475i	−0.996244	+	1.72554i	−0.423130	+	0.906069i	$0.639069\pi$
$191$	−13.7684	+	23.8475i	−0.996244	+	1.72554i	−0.573114	+	0.819476i	$0.694265\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−10.2684	−	17.7853i	−0.739133	−	1.28022i	−0.952886	−	0.303328i	$-0.901902\pi$
$193$	−10.2684	−	17.7853i	−0.739133	−	1.28022i	0.213753	−	0.976888i	$-0.431431\pi$
$194$	12.3578			0.887240
$195$	7.17891	−	0.680643i	0.514092	−	0.0487419i
$196$	1.00000			0.0714286
$197$	−8.50000	−	14.7224i	−0.605600	−	1.04893i	−0.991956	−	0.126580i	$-0.959600\pi$
$197$	−8.50000	−	14.7224i	−0.605600	−	1.04893i	0.386356	−	0.922350i	$-0.373733\pi$
$198$	−3.08945	−	5.35109i	−0.219558	−	0.380286i
$199$	−6.41055	+	11.1034i	−0.454432	+	0.787099i	−0.998655	−	0.0518416i	$-0.983491\pi$
$199$	−6.41055	+	11.1034i	−0.454432	+	0.787099i	0.544224	+	0.838940i	$0.316824\pi$
$200$	−1.00000			−0.0707107
$201$	−7.58945	+	13.1453i	−0.535319	+	0.927199i
$202$	8.17891	−	14.1663i	0.575466	−	0.996736i
$203$	−8.17891			−0.574047
$204$	2.50000	−	4.33013i	0.175035	−	0.303170i
$205$	4.17891	+	7.23808i	0.291868	+	0.505530i
$206$	−1.58945	−	2.75302i	−0.110743	−	0.191812i
$207$	3.17891			0.220949
$208$	3.58945	−	0.340322i	0.248884	−	0.0235971i
$209$	−50.5367			−3.49570
$210$	1.00000	+	1.73205i	0.0690066	+	0.119523i
$211$	−8.17891	−	14.1663i	−0.563059	−	0.975247i	−0.997227	−	0.0744154i	$-0.976291\pi$
$211$	−8.17891	−	14.1663i	−0.563059	−	0.975247i	0.434168	−	0.900832i	$-0.357042\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−9.17891			−0.628928
$214$	−3.91055	+	6.77326i	−0.267319	+	0.463011i
$215$	0.821092	−	1.42217i	0.0559980	−	0.0969914i
$216$	−1.00000			−0.0680414
$217$	−3.58945	+	6.21712i	−0.243668	+	0.422045i
$218$	−2.00000	−	3.46410i	−0.135457	−	0.234619i
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$	−12.3578			−0.833164
$221$	−10.4473	−	14.6920i	−0.702759	−	0.988290i
$222$	−2.00000			−0.134231
$223$	−4.58945	−	7.94917i	−0.307333	−	0.532316i	0.670445	−	0.741959i	$-0.266103\pi$
$223$	−4.58945	−	7.94917i	−0.307333	−	0.532316i	−0.977778	+	0.209643i	$0.932770\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−4.35782			−0.289878
$227$	−4.17891	+	7.23808i	−0.277364	+	0.480408i	−0.970729	−	0.240178i	$-0.922794\pi$
$227$	−4.17891	+	7.23808i	−0.277364	+	0.480408i	0.693365	+	0.720587i	$0.256127\pi$
$228$	−4.08945	+	7.08314i	−0.270831	+	0.469093i
$229$	1.00000			0.0660819			0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000			0.0660819			0.0330409	+	0.999454i	$0.489481\pi$
$230$	3.17891	−	5.50603i	0.209611	−	0.363057i
$231$	−3.08945	−	5.35109i	−0.203271	−	0.352076i
$232$	−4.08945	−	7.08314i	−0.268486	−	0.465031i
$233$	−0.357817			−0.0234414			−0.0117207	−	0.999931i	$-0.503731\pi$
$233$	−0.357817			−0.0234414			−0.0117207	+	0.999931i	$0.503731\pi$
$234$	−1.50000	+	3.27872i	−0.0980581	+	0.214337i
$235$	−8.35782			−0.545204
$236$	0.410546	+	0.711086i	0.0267243	+	0.0462878i
$237$	0.910546	+	1.57711i	0.0591463	+	0.102444i
$238$	2.50000	−	4.33013i	0.162051	−	0.280680i
$239$	−1.17891			−0.0762572			−0.0381286	−	0.999273i	$-0.512140\pi$
$239$	−1.17891			−0.0762572			−0.0381286	+	0.999273i	$0.512140\pi$
$240$	−1.00000	+	1.73205i	−0.0645497	+	0.111803i
$241$	9.17891	−	15.8983i	0.591265	−	1.02410i	−0.402797	−	0.915289i	$-0.631962\pi$
$241$	9.17891	−	15.8983i	0.591265	−	1.02410i	0.994062	−	0.108812i	$-0.0347048\pi$
$242$	27.1789			1.74713
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.50000	+	2.59808i	0.0960277	+	0.166325i
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$	−4.17891			−0.266437
$247$	17.0895	+	24.0329i	1.08738	+	1.52918i
$248$	−7.17891			−0.455861
$249$	−2.58945	−	4.48507i	−0.164100	−	0.284230i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−5.41055	+	9.37134i	−0.341511	+	0.591514i	−0.984713	−	0.174182i	$-0.944272\pi$
$251$	−5.41055	+	9.37134i	−0.341511	+	0.591514i	0.643203	+	0.765696i	$0.277605\pi$
$252$	−1.00000			−0.0629941
$253$	−9.82109	+	17.0106i	−0.617447	+	1.06945i
$254$	−6.00000	+	10.3923i	−0.376473	+	0.652071i
$255$	10.0000			0.626224
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.8578	−	22.2704i	−0.802049	−	1.38919i	−0.918266	−	0.395965i	$-0.870410\pi$
$257$	−12.8578	−	22.2704i	−0.802049	−	1.38919i	0.116217	−	0.993224i	$-0.462923\pi$
$258$	0.410546	+	0.711086i	0.0255595	+	0.0442703i
$259$	−2.00000			−0.124274
$260$	4.17891	+	5.87680i	0.259165	+	0.364463i
$261$	8.17891			0.506262
$262$	−9.76836	−	16.9193i	−0.603491	−	1.04528i
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$	3.08945	−	5.35109i	0.190143	−	0.329337i
$265$	6.00000			0.368577
$266$	−4.08945	+	7.08314i	−0.250741	+	0.434295i
$267$	4.50000	−	7.79423i	0.275396	−	0.476999i
$268$	−15.1789			−0.927199
$269$	−9.17891	+	15.8983i	−0.559648	+	0.969339i	0.437878	+	0.899035i	$0.355730\pi$
$269$	−9.17891	+	15.8983i	−0.559648	+	0.969339i	−0.997526	+	0.0703041i	$0.977603\pi$
$270$	−1.00000	−	1.73205i	−0.0608581	−	0.105409i
$271$	−15.5895	−	27.0017i	−0.946992	−	1.64024i	−0.751713	−	0.659490i	$-0.770772\pi$
$271$	−15.5895	−	27.0017i	−0.946992	−	1.64024i	−0.195279	−	0.980748i	$-0.562561\pi$
$272$	5.00000			0.303170
$273$	−1.50000	+	3.27872i	−0.0907841	+	0.198437i
$274$	−16.3578			−0.988212
$275$	3.08945	+	5.35109i	0.186301	+	0.322683i
$276$	1.58945	+	2.75302i	0.0956739	+	0.165712i
$277$	−14.1789	+	24.5586i	−0.851928	+	1.47558i	0.0275379	+	0.999621i	$0.491233\pi$
$277$	−14.1789	+	24.5586i	−0.851928	+	1.47558i	−0.879466	+	0.475962i	$0.842100\pi$
$278$	−18.1789			−1.09030
$279$	3.58945	−	6.21712i	0.214895	−	0.372209i
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	5.64218			0.336584			0.168292	−	0.985737i	$-0.446175\pi$
$281$	5.64218			0.336584			0.168292	+	0.985737i	$0.446175\pi$
$282$	2.08945	−	3.61904i	0.124425	−	0.215511i
$283$	−15.1789	−	26.2906i	−0.902292	−	1.56282i	−0.824511	−	0.565846i	$-0.808550\pi$
$283$	−15.1789	−	26.2906i	−0.902292	−	1.56282i	−0.0777814	−	0.996970i	$-0.524784\pi$
$284$	−4.58945	−	7.94917i	−0.272334	−	0.471696i
$285$	−16.3578			−0.968953
$286$	−12.9105	−	18.1561i	−0.763417	−	1.07359i
$287$	−4.17891			−0.246673
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	8.17891	−	14.1663i	0.480282	−	0.831873i
$291$	−12.3578			−0.724428
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	−0.986341	−	0.164714i	$-0.947330\pi$
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	0.635818	+	0.771839i	$0.280663\pi$
$294$	−1.00000			−0.0583212
$295$	−0.821092	+	1.42217i	−0.0478058	+	0.0828021i
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$	3.08945	+	5.35109i	0.179268	+	0.310502i
$298$	4.82109			0.279278
$299$	11.4105	−	1.08185i	0.659889	−	0.0625651i
$300$	1.00000			0.0577350
$301$	0.410546	+	0.711086i	0.0236635	+	0.0409863i
$302$	7.26836	+	12.5892i	0.418247	+	0.724426i
$303$	−8.17891	+	14.1663i	−0.469866	+	0.813832i
$304$	−8.17891			−0.469093
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$	−2.50000	+	4.33013i	−0.142915	+	0.247537i
$307$	24.8945			1.42081			0.710403	−	0.703795i	$-0.248513\pi$
$307$	24.8945			1.42081			0.710403	+	0.703795i	$0.248513\pi$
$308$	3.08945	−	5.35109i	0.176038	−	0.304907i
$309$	1.58945	+	2.75302i	0.0904209	+	0.156614i
$310$	−7.17891	−	12.4342i	−0.407735	−	0.706217i
$311$	−8.53673			−0.484073			−0.242037	−	0.970267i	$-0.577815\pi$
$311$	−8.53673			−0.484073			−0.242037	+	0.970267i	$0.577815\pi$
$312$	−3.58945	+	0.340322i	−0.203213	+	0.0192669i
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$	−1.00000	−	1.73205i	−0.0564333	−	0.0977453i
$315$	−1.00000	−	1.73205i	−0.0563436	−	0.0975900i
$316$	−0.910546	+	1.57711i	−0.0512222	+	0.0887195i
$317$	7.17891			0.403208			0.201604	−	0.979467i	$-0.435385\pi$
$317$	7.17891			0.403208			0.201604	+	0.979467i	$0.435385\pi$
$318$	−1.50000	+	2.59808i	−0.0841158	+	0.145693i
$319$	−25.2684	+	43.7661i	−1.41476	+	2.45043i
$320$	−2.00000			−0.111803
$321$	3.91055	−	6.77326i	0.218265	−	0.378047i
$322$	1.58945	+	2.75302i	0.0885768	+	0.153420i
$323$	20.4473	+	35.4157i	1.13772	+	1.97058i
$324$	1.00000			0.0555556
$325$	1.50000	−	3.27872i	0.0832050	−	0.181871i
$326$	−8.82109			−0.488555
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	−2.08945	−	3.61904i	−0.115371	−	0.199828i
$329$	2.08945	−	3.61904i	0.115195	−	0.199524i
$330$	12.3578			0.680275
$331$	12.1789	−	21.0945i	0.669413	−	1.15946i	−0.308655	−	0.951174i	$-0.599879\pi$
$331$	12.1789	−	21.0945i	0.669413	−	1.15946i	0.978068	−	0.208284i	$-0.0667878\pi$
$332$	2.58945	−	4.48507i	0.142115	−	0.246150i
$333$	2.00000			0.109599
$334$	4.00000	−	6.92820i	0.218870	−	0.379094i
$335$	−15.1789	−	26.2906i	−0.829312	−	1.43641i
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	−0.536725			−0.0292373			−0.0146186	−	0.999893i	$-0.504653\pi$
$337$	−0.536725			−0.0292373			−0.0146186	+	0.999893i	$0.504653\pi$
$338$	−4.26836	+	12.2793i	−0.232168	+	0.667906i
$339$	4.35782			0.236684
$340$	5.00000	+	8.66025i	0.271163	+	0.469668i
$341$	22.1789	+	38.4150i	1.20106	+	2.08029i
$342$	4.08945	−	7.08314i	0.221132	−	0.383012i
$343$	−1.00000			−0.0539949
$344$	−0.410546	+	0.711086i	−0.0221351	+	0.0383392i
$345$	−3.17891	+	5.50603i	−0.171147	+	0.296435i
$346$	4.00000			0.215041
$347$	3.91055	−	6.77326i	0.209929	−	0.363608i	−0.741763	−	0.670662i	$-0.766010\pi$
$347$	3.91055	−	6.77326i	0.209929	−	0.363608i	0.951692	+	0.307054i	$0.0993433\pi$
$348$	4.08945	+	7.08314i	0.219218	+	0.379696i
$349$	1.58945	+	2.75302i	0.0850815	+	0.147366i	0.905426	−	0.424504i	$-0.139552\pi$
$349$	1.58945	+	2.75302i	0.0850815	+	0.147366i	−0.820344	+	0.571870i	$0.806218\pi$
$350$	1.00000			0.0534522
$351$	1.50000	−	3.27872i	0.0800641	−	0.175005i
$352$	6.17891			0.329337
$353$	3.58945	+	6.21712i	0.191047	+	0.330904i	0.945598	−	0.325339i	$-0.105478\pi$
$353$	3.58945	+	6.21712i	0.191047	+	0.330904i	−0.754550	+	0.656242i	$0.772145\pi$
$354$	−0.410546	−	0.711086i	−0.0218203	−	0.0377938i
$355$	9.17891	−	15.8983i	0.487166	−	0.843796i
$356$	9.00000			0.476999
$357$	−2.50000	+	4.33013i	−0.132314	+	0.229175i
$358$	7.17891	−	12.4342i	0.379417	−	0.657170i
$359$	12.3578			0.652221			0.326110	−	0.945332i	$-0.394262\pi$
$359$	12.3578			0.652221			0.326110	+	0.945332i	$0.394262\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	−23.9473	−	41.4779i	−1.26038	−	2.18305i
$362$	−3.91055	−	6.77326i	−0.205534	−	0.355995i
$363$	−27.1789			−1.42652
$364$	−3.58945	+	0.340322i	−0.188139	+	0.0178377i
$365$	−8.00000			−0.418739
$366$	−1.50000	−	2.59808i	−0.0784063	−	0.135804i
$367$	−1.58945	−	2.75302i	−0.0829688	−	0.143706i	0.821555	−	0.570129i	$-0.193107\pi$
$367$	−1.58945	−	2.75302i	−0.0829688	−	0.143706i	−0.904524	+	0.426423i	$0.859774\pi$
$368$	−1.58945	+	2.75302i	−0.0828560	+	0.143511i
$369$	4.17891			0.217545
$370$	2.00000	−	3.46410i	0.103975	−	0.180090i
$371$	−1.50000	+	2.59808i	−0.0778761	+	0.134885i
$372$	7.17891			0.372209
$373$	10.0000	−	17.3205i	0.517780	−	0.896822i	−0.482006	−	0.876168i	$-0.660092\pi$
$373$	10.0000	−	17.3205i	0.517780	−	0.896822i	0.999787	−	0.0206542i	$-0.00657489\pi$
$374$	−15.4473	−	26.7555i	−0.798759	−	1.38349i
$375$	6.00000	+	10.3923i	0.309839	+	0.536656i
$376$	4.17891			0.215511
$377$	29.3578	−	2.78346i	1.51200	−	0.143355i
$378$	1.00000			0.0514344
$379$	−10.3578	−	17.9403i	−0.532045	−	0.921530i	−0.999300	−	0.0374068i	$-0.988090\pi$
$379$	−10.3578	−	17.9403i	−0.532045	−	0.921530i	0.467255	−	0.884123i	$-0.345243\pi$
$380$	−8.17891	−	14.1663i	−0.419569	−	0.726715i
$381$	6.00000	−	10.3923i	0.307389	−	0.532414i
$382$	27.5367			1.40890
$383$	−4.91055	+	8.50531i	−0.250917	+	0.434601i	−0.963779	−	0.266704i	$-0.914066\pi$
$383$	−4.91055	+	8.50531i	−0.250917	+	0.434601i	0.712861	+	0.701305i	$0.247399\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	12.3578			0.629813
$386$	−10.2684	+	17.7853i	−0.522646	+	0.905249i
$387$	−0.410546	−	0.711086i	−0.0208692	−	0.0361465i
$388$	−6.17891	−	10.7022i	−0.313687	−	0.543321i
$389$	−0.821092			−0.0416310			−0.0208155	−	0.999783i	$-0.506626\pi$
$389$	−0.821092			−0.0416310			−0.0208155	+	0.999783i	$0.506626\pi$
$390$	−4.17891	−	5.87680i	−0.211607	−	0.297583i
$391$	15.8945			0.803822
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	9.76836	+	16.9193i	0.492749	+	0.853466i
$394$	−8.50000	+	14.7224i	−0.428224	+	0.741705i
$395$	−3.64218			−0.183258
$396$	−3.08945	+	5.35109i	−0.155251	+	0.268902i
$397$	−1.50000	+	2.59808i	−0.0752828	+	0.130394i	−0.901209	−	0.433384i	$-0.857319\pi$
$397$	−1.50000	+	2.59808i	−0.0752828	+	0.130394i	0.825926	+	0.563778i	$0.190653\pi$
$398$	12.8211			0.642663
$399$	4.08945	−	7.08314i	0.204729	−	0.354601i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−16.1789	−	28.0227i	−0.807936	−	1.39939i	−0.914291	−	0.405058i	$-0.867251\pi$
$401$	−16.1789	−	28.0227i	−0.807936	−	1.39939i	0.106355	−	0.994328i	$-0.466082\pi$
$402$	15.1789			0.757055
$403$	10.7684	−	23.5376i	0.536410	−	1.17249i
$404$	−16.3578			−0.813832
$405$	1.00000	+	1.73205i	0.0496904	+	0.0860663i
$406$	4.08945	+	7.08314i	0.202956	+	0.351530i
$407$	−6.17891	+	10.7022i	−0.306277	+	0.530488i
$408$	−5.00000			−0.247537
$409$	6.82109	−	11.8145i	0.337281	−	0.584188i	−0.646639	−	0.762796i	$-0.723826\pi$
$409$	6.82109	−	11.8145i	0.337281	−	0.584188i	0.983920	+	0.178608i	$0.0571593\pi$
$410$	4.17891	−	7.23808i	0.206382	−	0.357463i
$411$	16.3578			0.806872
$412$	−1.58945	+	2.75302i	−0.0783068	+	0.135631i
$413$	−0.410546	−	0.711086i	−0.0202016	−	0.0349903i
$414$	−1.58945	−	2.75302i	−0.0781174	−	0.135303i
$415$	10.3578			0.508445
$416$	−2.08945	−	2.93840i	−0.102444	−	0.144067i
$417$	18.1789			0.890225
$418$	25.2684	+	43.7661i	1.23592	+	2.14067i
$419$	−14.9473	−	25.8894i	−0.730222	−	1.26478i	−0.956788	−	0.290786i	$-0.906083\pi$
$419$	−14.9473	−	25.8894i	−0.730222	−	1.26478i	0.226566	−	0.973996i	$-0.427250\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	−34.7156			−1.69194			−0.845968	−	0.533233i	$-0.820977\pi$
$421$	−34.7156			−1.69194			−0.845968	+	0.533233i	$0.820977\pi$
$422$	−8.17891	+	14.1663i	−0.398143	+	0.689604i
$423$	−2.08945	+	3.61904i	−0.101593	+	0.175964i
$424$	−3.00000			−0.145693
$425$	2.50000	−	4.33013i	0.121268	−	0.210042i
$426$	4.58945	+	7.94917i	0.222360	+	0.385138i
$427$	−1.50000	−	2.59808i	−0.0725901	−	0.125730i
$428$	7.82109			0.378047
$429$	12.9105	+	18.1561i	0.623327	+	0.876584i
$430$	−1.64218			−0.0791931
$431$	0.589454	+	1.02096i	0.0283930	+	0.0491781i	0.879873	−	0.475209i	$-0.157628\pi$
$431$	0.589454	+	1.02096i	0.0283930	+	0.0491781i	−0.851480	+	0.524387i	$0.824294\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−5.82109	+	10.0824i	−0.279744	+	0.484530i	−0.971321	−	0.237772i	$-0.923583\pi$
$433$	−5.82109	+	10.0824i	−0.279744	+	0.484530i	0.691577	+	0.722303i	$0.256916\pi$
$434$	7.17891			0.344599
$435$	−8.17891	+	14.1663i	−0.392149	+	0.679221i
$436$	−2.00000	+	3.46410i	−0.0957826	+	0.165900i
$437$	−26.0000			−1.24375
$438$	2.00000	−	3.46410i	0.0955637	−	0.165521i
$439$	2.35782	+	4.08386i	0.112532	+	0.194912i	0.916791	−	0.399368i	$-0.130770\pi$
$439$	2.35782	+	4.08386i	0.112532	+	0.194912i	−0.804258	+	0.594280i	$0.797437\pi$
$440$	6.17891	+	10.7022i	0.294568	+	0.510207i
$441$	1.00000			0.0476190
$442$	−7.50000	+	16.3936i	−0.356739	+	0.779764i
$443$	−8.17891			−0.388592			−0.194296	−	0.980943i	$-0.562242\pi$
$443$	−8.17891			−0.388592			−0.194296	+	0.980943i	$0.562242\pi$
$444$	1.00000	+	1.73205i	0.0474579	+	0.0821995i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	−4.58945	+	7.94917i	−0.217317	+	0.376404i
$447$	−4.82109			−0.228030
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	7.00000	−	12.1244i	0.330350	−	0.572184i	−0.652230	−	0.758021i	$-0.726166\pi$
$449$	7.00000	−	12.1244i	0.330350	−	0.572184i	0.982581	+	0.185837i	$0.0594997\pi$
$450$	−1.00000			−0.0471405
$451$	−12.9105	+	22.3617i	−0.607934	+	1.05297i
$452$	2.17891	+	3.77398i	0.102487	+	0.177513i
$453$	−7.26836	−	12.5892i	−0.341497	−	0.591491i
$454$	8.35782			0.392252
$455$	−4.17891	−	5.87680i	−0.195910	−	0.275508i
$456$	8.17891			0.383012
$457$	15.9473	+	27.6215i	0.745982	+	1.29208i	0.949735	+	0.313056i	$0.101353\pi$
$457$	15.9473	+	27.6215i	0.745982	+	1.29208i	−0.203753	+	0.979022i	$0.565314\pi$
$458$	−0.500000	−	0.866025i	−0.0233635	−	0.0404667i
$459$	2.50000	−	4.33013i	0.116690	−	0.202113i
$460$	−6.35782			−0.296435
$461$	12.3578	−	21.4044i	0.575561	−	0.996901i	−0.420420	−	0.907330i	$-0.638117\pi$
$461$	12.3578	−	21.4044i	0.575561	−	0.996901i	0.995980	−	0.0895709i	$-0.0285496\pi$
$462$	−3.08945	+	5.35109i	−0.143734	+	0.248955i
$463$	−28.8945			−1.34284			−0.671422	−	0.741076i	$-0.734316\pi$
$463$	−28.8945			−1.34284			−0.671422	+	0.741076i	$0.734316\pi$
$464$	−4.08945	+	7.08314i	−0.189848	+	0.328827i
$465$	7.17891	+	12.4342i	0.332914	+	0.576624i
$466$	0.178908	+	0.309878i	0.00828777	+	0.0143548i
$467$	33.8945			1.56845			0.784226	−	0.620475i	$-0.213060\pi$
$467$	33.8945			1.56845			0.784226	+	0.620475i	$0.213060\pi$
$468$	3.58945	−	0.340322i	0.165923	−	0.0157314i
$469$	15.1789			0.700897
$470$	4.17891	+	7.23808i	0.192759	+	0.333868i
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$	0.410546	−	0.711086i	0.0188969	−	0.0327304i
$473$	5.07345			0.233277
$474$	0.910546	−	1.57711i	0.0418228	−	0.0724391i
$475$	−4.08945	+	7.08314i	−0.187637	+	0.324997i
$476$	−5.00000			−0.229175
$477$	1.50000	−	2.59808i	0.0686803	−	0.118958i
$478$	0.589454	+	1.02096i	0.0269610	+	0.0466978i
$479$	14.9105	+	25.8258i	0.681280	+	1.18001i	0.974590	+	0.223995i	$0.0719098\pi$
$479$	14.9105	+	25.8258i	0.681280	+	1.18001i	−0.293310	+	0.956017i	$0.594757\pi$
$480$	2.00000			0.0912871
$481$	7.17891	−	0.680643i	0.327330	−	0.0310347i
$482$	−18.3578			−0.836176
$483$	−1.58945	−	2.75302i	−0.0723227	−	0.125267i
$484$	−13.5895	−	23.5376i	−0.617702	−	1.06989i
$485$	12.3578	−	21.4044i	0.561140	−	0.971922i
$486$	−1.00000			−0.0453609
$487$	19.0895	−	33.0639i	0.865026	−	1.49827i	−0.00199588	−	0.999998i	$-0.500635\pi$
$487$	19.0895	−	33.0639i	0.865026	−	1.49827i	0.867022	−	0.498271i	$-0.166031\pi$
$488$	1.50000	−	2.59808i	0.0679018	−	0.117609i
$489$	8.82109			0.398904
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	2.08945	+	3.61904i	0.0941999	+	0.163159i
$493$	40.8945			1.84180
$494$	12.2684	−	26.8163i	0.551980	−	1.20652i
$495$	−12.3578			−0.555443
$496$	3.58945	+	6.21712i	0.161171	+	0.279157i
$497$	4.58945	+	7.94917i	0.205865	+	0.356569i
$498$	−2.58945	+	4.48507i	−0.116036	+	0.200981i
$499$	−3.17891			−0.142307			−0.0711537	−	0.997465i	$-0.522668\pi$
$499$	−3.17891			−0.142307			−0.0711537	+	0.997465i	$0.522668\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$	10.8211			0.482969
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	−0.464107	−	0.885779i	$-0.653625\pi$
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	0.999161	−	0.0409609i	$-0.0130419\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$	−16.3578	−	28.3326i	−0.727913	−	1.26078i
$506$	19.6422			0.873202
$507$	4.26836	−	12.2793i	0.189565	−	0.545343i
$508$	12.0000			0.532414
$509$	−14.3578	−	24.8685i	−0.636399	−	1.10228i	−0.986217	−	0.165458i	$-0.947090\pi$
$509$	−14.3578	−	24.8685i	−0.636399	−	1.10228i	0.349818	−	0.936818i	$-0.386243\pi$
$510$	−5.00000	−	8.66025i	−0.221404	−	0.383482i
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$	1.00000			0.0441942
$513$	−4.08945	+	7.08314i	−0.180554	+	0.312728i
$514$	−12.8578	+	22.2704i	−0.567134	+	0.982305i
$515$	−6.35782			−0.280159
$516$	0.410546	−	0.711086i	0.0180733	−	0.0313038i
$517$	−12.9105	−	22.3617i	−0.567805	−	0.983467i
$518$	1.00000	+	1.73205i	0.0439375	+	0.0761019i
$519$	−4.00000			−0.175581
$520$	3.00000	−	6.55744i	0.131559	−	0.287563i
$521$	−4.17891			−0.183081			−0.0915406	−	0.995801i	$-0.529179\pi$
$521$	−4.17891			−0.183081			−0.0915406	+	0.995801i	$0.529179\pi$
$522$	−4.08945	−	7.08314i	−0.178991	−	0.310021i
$523$	11.2684	+	19.5174i	0.492731	+	0.853435i	0.999965	−	0.00837317i	$-0.00266530\pi$
$523$	11.2684	+	19.5174i	0.492731	+	0.853435i	−0.507234	+	0.861808i	$0.669332\pi$
$524$	−9.76836	+	16.9193i	−0.426733	+	0.739123i
$525$	−1.00000			−0.0436436
$526$	6.00000	−	10.3923i	0.261612	−	0.453126i
$527$	17.9473	−	31.0856i	0.781795	−	1.35411i
$528$	−6.17891			−0.268902
$529$	6.44727	−	11.1670i	0.280316	−	0.485522i
$530$	−3.00000	−	5.19615i	−0.130312	−	0.225706i
$531$	0.410546	+	0.711086i	0.0178162	+	0.0308585i
$532$	8.17891			0.354601
$533$	15.0000	−	1.42217i	0.649722	−	0.0616011i
$534$	−9.00000			−0.389468
$535$	7.82109	+	13.5465i	0.338135	+	0.585667i
$536$	7.58945	+	13.1453i	0.327814	+	0.567791i
$537$	−7.17891	+	12.4342i	−0.309793	+	0.536577i
$538$	18.3578			0.791462
$539$	−3.08945	+	5.35109i	−0.133072	+	0.230488i
$540$	−1.00000	+	1.73205i	−0.0430331	+	0.0745356i
$541$	2.35782			0.101370			0.0506852	−	0.998715i	$-0.483859\pi$
$541$	2.35782			0.101370			0.0506852	+	0.998715i	$0.483859\pi$
$542$	−15.5895	+	27.0017i	−0.669624	+	1.15982i
$543$	3.91055	+	6.77326i	0.167818	+	0.290669i
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	−8.00000			−0.342682
$546$	3.58945	−	0.340322i	0.153614	−	0.0145644i
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	8.17891	+	14.1663i	0.349386	+	0.605154i
$549$	1.50000	+	2.59808i	0.0640184	+	0.110883i
$550$	3.08945	−	5.35109i	0.131735	−	0.228171i
$551$	−66.8945			−2.84980
$552$	1.58945	−	2.75302i	0.0676517	−	0.117176i
$553$	0.910546	−	1.57711i	0.0387203	−	0.0670656i
$554$	28.3578			1.20481
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	9.08945	+	15.7434i	0.385479	+	0.667669i
$557$	10.8578	+	18.8063i	0.460060	+	0.796848i	0.998963	−	0.0455198i	$-0.0144944\pi$
$557$	10.8578	+	18.8063i	0.460060	+	0.796848i	−0.538903	+	0.842368i	$0.681161\pi$
$558$	−7.17891			−0.303907
$559$	−1.71563	−	2.41269i	−0.0725636	−	0.102046i
$560$	2.00000			0.0845154
$561$	15.4473	+	26.7555i	0.652184	+	1.12962i
$562$	−2.82109	−	4.88627i	−0.119001	−	0.206115i
$563$	−2.17891	+	3.77398i	−0.0918300	+	0.159054i	−0.908281	−	0.418360i	$-0.862605\pi$
$563$	−2.17891	+	3.77398i	−0.0918300	+	0.159054i	0.816451	+	0.577414i	$0.195938\pi$
$564$	−4.17891			−0.175964
$565$	−4.35782	+	7.54796i	−0.183335	+	0.317545i
$566$	−15.1789	+	26.2906i	−0.638017	+	1.10508i
$567$	−1.00000			−0.0419961
$568$	−4.58945	+	7.94917i	−0.192569	+	0.333540i
$569$	13.1789	+	22.8265i	0.552489	+	0.956938i	0.998094	+	0.0617089i	$0.0196550\pi$
$569$	13.1789	+	22.8265i	0.552489	+	0.956938i	−0.445606	+	0.895229i	$0.647012\pi$
$570$	8.17891	+	14.1663i	0.342577	+	0.593360i
$571$	−22.8211			−0.955033			−0.477516	−	0.878623i	$-0.658463\pi$
$571$	−22.8211			−0.955033			−0.477516	+	0.878623i	$0.658463\pi$
$572$	−9.26836	+	20.2589i	−0.387530	+	0.847067i
$573$	−27.5367			−1.15036
$574$	2.08945	+	3.61904i	0.0872121	+	0.151056i
$575$	1.58945	+	2.75302i	0.0662848	+	0.114809i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−5.64218			−0.234887			−0.117444	−	0.993080i	$-0.537470\pi$
$577$	−5.64218			−0.234887			−0.117444	+	0.993080i	$0.537470\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$	10.2684	−	17.7853i	0.426739	−	0.739133i
$580$	−16.3578			−0.679221
$581$	−2.58945	+	4.48507i	−0.107429	+	0.186072i
$582$	6.17891	+	10.7022i	0.256124	+	0.443620i
$583$	9.26836	+	16.0533i	0.383856	+	0.664859i
$584$	4.00000			0.165521
$585$	4.17891	+	5.87680i	0.172777	+	0.242976i
$586$	12.0000			0.495715
$587$	5.58945	+	9.68122i	0.230701	+	0.399587i	0.958015	−	0.286719i	$-0.0925646\pi$
$587$	5.58945	+	9.68122i	0.230701	+	0.399587i	−0.727313	+	0.686306i	$0.759231\pi$
$588$	0.500000	+	0.866025i	0.0206197	+	0.0357143i
$589$	−29.3578	+	50.8492i	−1.20967	+	2.09521i
$590$	1.64218			0.0676076
$591$	8.50000	−	14.7224i	0.349643	−	0.605600i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−33.0000			−1.35515			−0.677574	−	0.735455i	$-0.736969\pi$
$593$	−33.0000			−1.35515			−0.677574	+	0.735455i	$0.736969\pi$
$594$	3.08945	−	5.35109i	0.126762	−	0.219558i
$595$	−5.00000	−	8.66025i	−0.204980	−	0.355036i
$596$	−2.41055	−	4.17519i	−0.0987398	−	0.171022i
$597$	−12.8211			−0.524732
$598$	−6.64218	−	9.34090i	−0.271619	−	0.381978i
$599$	28.8211			1.17760			0.588799	−	0.808280i	$-0.299601\pi$
$599$	28.8211			1.17760			0.588799	+	0.808280i	$0.299601\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$	0.410546	−	0.711086i	0.0167326	−	0.0289817i
$603$	−15.1789			−0.618133
$604$	7.26836	−	12.5892i	0.295745	−	0.512246i
$605$	27.1789	−	47.0753i	1.10498	−	1.91388i
$606$	16.3578			0.664491
$607$	−16.7684	+	29.0437i	−0.680607	+	1.17885i	0.294189	+	0.955747i	$0.404950\pi$
$607$	−16.7684	+	29.0437i	−0.680607	+	1.17885i	−0.974796	+	0.223098i	$0.928383\pi$
$608$	4.08945	+	7.08314i	0.165849	+	0.287259i
$609$	−4.08945	−	7.08314i	−0.165713	−	0.287023i
$610$	6.00000			0.242933
$611$	−6.26836	+	13.7015i	−0.253591	+	0.554302i
$612$	5.00000			0.202113
$613$	−19.1789	−	33.2188i	−0.774629	−	1.34170i	−0.935003	−	0.354640i	$-0.884603\pi$
$613$	−19.1789	−	33.2188i	−0.774629	−	1.34170i	0.160374	−	0.987056i	$-0.448730\pi$
$614$	−12.4473	−	21.5593i	−0.502331	−	0.870063i
$615$	−4.17891	+	7.23808i	−0.168510	+	0.291868i
$616$	−6.17891			−0.248955
$617$	−16.0000	+	27.7128i	−0.644136	+	1.11568i	0.340365	+	0.940294i	$0.389449\pi$
$617$	−16.0000	+	27.7128i	−0.644136	+	1.11568i	−0.984500	+	0.175382i	$0.943884\pi$
$618$	1.58945	−	2.75302i	0.0639372	−	0.110743i
$619$	−8.53673			−0.343120			−0.171560	−	0.985174i	$-0.554881\pi$
$619$	−8.53673			−0.343120			−0.171560	+	0.985174i	$0.554881\pi$
$620$	−7.17891	+	12.4342i	−0.288312	+	0.499371i
$621$	1.58945	+	2.75302i	0.0637826	+	0.110475i
$622$	4.26836	+	7.39302i	0.171146	+	0.296433i
$623$	−9.00000			−0.360577
$624$	2.08945	+	2.93840i	0.0836451	+	0.117630i
$625$	−19.0000			−0.760000
$626$	−2.00000	−	3.46410i	−0.0799361	−	0.138453i
$627$	−25.2684	−	43.7661i	−1.00912	−	1.74785i
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	10.0000			0.398726
$630$	−1.00000	+	1.73205i	−0.0398410	+	0.0690066i
$631$	15.4473	−	26.7555i	0.614946	−	1.06512i	−0.375448	−	0.926844i	$-0.622511\pi$
$631$	15.4473	−	26.7555i	0.614946	−	1.06512i	0.990394	−	0.138274i	$-0.0441556\pi$
$632$	1.82109			0.0724391
$633$	8.17891	−	14.1663i	0.325082	−	0.563059i
$634$	−3.58945	−	6.21712i	−0.142555	−	0.246913i
$635$	12.0000	+	20.7846i	0.476205	+	0.824812i
$636$	3.00000			0.118958
$637$	3.58945	−	0.340322i	0.142219	−	0.0134840i
$638$	50.5367			2.00077
$639$	−4.58945	−	7.94917i	−0.181556	−	0.314464i
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	20.5367	−	35.5707i	0.811152	−	1.40496i	−0.100907	−	0.994896i	$-0.532174\pi$
$641$	20.5367	−	35.5707i	0.811152	−	1.40496i	0.912058	−	0.410060i	$-0.134492\pi$
$642$	−7.82109			−0.308674
$643$	10.0895	−	17.4754i	0.397889	−	0.689164i	−0.595576	−	0.803299i	$-0.703076\pi$
$643$	10.0895	−	17.4754i	0.397889	−	0.689164i	0.993465	+	0.114135i	$0.0364095\pi$
$644$	1.58945	−	2.75302i	0.0626333	−	0.108484i
$645$	1.64218			0.0646609
$646$	20.4473	−	35.4157i	0.804487	−	1.39341i
$647$	4.44727	+	7.70290i	0.174840	+	0.302832i	0.940106	−	0.340882i	$-0.110726\pi$
$647$	4.44727	+	7.70290i	0.174840	+	0.302832i	−0.765266	+	0.643715i	$0.777392\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−5.07345			−0.199150
$650$	−3.58945	+	0.340322i	−0.140790	+	0.0133485i
$651$	−7.17891			−0.281364
$652$	4.41055	+	7.63929i	0.172730	+	0.299178i
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	0.584091	−	0.811688i	$-0.301451\pi$
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	−0.994988	+	0.0999939i	$0.968118\pi$
$654$	2.00000	−	3.46410i	0.0782062	−	0.135457i
$655$	−39.0735			−1.52673
$656$	−2.08945	+	3.61904i	−0.0815795	+	0.141300i
$657$	−2.00000	+	3.46410i	−0.0780274	+	0.135147i
$658$	−4.17891			−0.162911
$659$	8.26836	−	14.3212i	0.322090	−	0.557876i	−0.658829	−	0.752292i	$-0.728948\pi$
$659$	8.26836	−	14.3212i	0.322090	−	0.557876i	0.980919	+	0.194417i	$0.0622814\pi$
$660$	−6.17891	−	10.7022i	−0.240514	−	0.416582i
$661$	8.76836	+	15.1872i	0.341050	+	0.590716i	0.984628	−	0.174665i	$-0.0558842\pi$
$661$	8.76836	+	15.1872i	0.341050	+	0.590716i	−0.643578	+	0.765380i	$0.722551\pi$
$662$	−24.3578			−0.946693
$663$	7.50000	−	16.3936i	0.291276	−	0.636675i
$664$	−5.17891			−0.200981
$665$	8.17891	+	14.1663i	0.317164	+	0.549345i
$666$	−1.00000	−	1.73205i	−0.0387492	−	0.0671156i
$667$	−13.0000	+	22.5167i	−0.503362	+	0.871849i
$668$	−8.00000			−0.309529
$669$	4.58945	−	7.94917i	0.177439	−	0.307333i
$670$	−15.1789	+	26.2906i	−0.586412	+	1.01570i
$671$	−18.5367			−0.715602
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	0.268363	+	0.464818i	0.0103369	+	0.0179041i
$675$	1.00000			0.0384900
$676$	12.7684	−	2.44314i	0.491091	−	0.0939668i
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$	−2.17891	−	3.77398i	−0.0836805	−	0.144939i
$679$	6.17891	+	10.7022i	0.237125	+	0.410712i
$680$	5.00000	−	8.66025i	0.191741	−	0.332106i
$681$	−8.35782			−0.320272
$682$	22.1789	−	38.4150i	0.849274	−	1.47099i
$683$	7.17891	−	12.4342i	0.274693	−	0.475783i	−0.695364	−	0.718657i	$-0.744757\pi$
$683$	7.17891	−	12.4342i	0.274693	−	0.475783i	0.970058	+	0.242875i	$0.0780903\pi$
$684$	−8.17891			−0.312728
$685$	−16.3578	+	28.3326i	−0.625000	+	1.08253i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	0.500000	+	0.866025i	0.0190762	+	0.0330409i
$688$	0.821092			0.0313038
$689$	4.50000	−	9.83616i	0.171436	−	0.374728i
$690$	6.35782			0.242038
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	0.942420	+	0.334431i	$0.108544\pi$
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	−0.181584	+	0.983375i	$0.558123\pi$
$692$	−2.00000	−	3.46410i	−0.0760286	−	0.131685i
$693$	3.08945	−	5.35109i	0.117359	−	0.203271i
$694$	−7.82109			−0.296885
$695$	−18.1789	+	31.4868i	−0.689565	+	1.19436i
$696$	4.08945	−	7.08314i	0.155010	−	0.268486i
$697$	20.8945			0.791437
$698$	1.58945	−	2.75302i	0.0601617	−	0.104203i
$699$	−0.178908	−	0.309878i	−0.00676694	−	0.0117207i
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	23.7156			0.895727			0.447864	−	0.894102i	$-0.352185\pi$
$701$	23.7156			0.895727			0.447864	+	0.894102i	$0.352185\pi$
$702$	−3.58945	+	0.340322i	−0.135475	+	0.0128446i
$703$	−16.3578			−0.616947
$704$	−3.08945	−	5.35109i	−0.116438	−	0.201677i
$705$	−4.17891	−	7.23808i	−0.157387	−	0.272602i
$706$	3.58945	−	6.21712i	0.135091	−	0.233984i
$707$	16.3578			0.615199
$708$	−0.410546	+	0.711086i	−0.0154293	+	0.0267243i
$709$	8.00000	−	13.8564i	0.300446	−	0.520388i	−0.675791	−	0.737093i	$-0.736198\pi$
$709$	8.00000	−	13.8564i	0.300446	−	0.520388i	0.976237	+	0.216705i	$0.0695310\pi$
$710$	−18.3578			−0.688957
$711$	−0.910546	+	1.57711i	−0.0341481	+	0.0591463i
$712$	−4.50000	−	7.79423i	−0.168645	−	0.292101i
$713$	11.4105	+	19.7636i	0.427328	+	0.740154i
$714$	5.00000			0.187120
$715$	−44.3578	+	4.20563i	−1.65889	+	0.157282i
$716$	−14.3578			−0.536577
$717$	−0.589454	−	1.02096i	−0.0220136	−	0.0381286i
$718$	−6.17891	−	10.7022i	−0.230595	−	0.399402i
$719$	12.9105	−	22.3617i	0.481482	−	0.833951i	−0.518292	−	0.855204i	$-0.673432\pi$
$719$	12.9105	−	22.3617i	0.481482	−	0.833951i	0.999774	+	0.0212522i	$0.00676530\pi$
$720$	−2.00000			−0.0745356
$721$	1.58945	−	2.75302i	0.0591944	−	0.102528i
$722$	−23.9473	+	41.4779i	−0.891225	+	1.54365i
$723$	18.3578			0.682735
$724$	−3.91055	+	6.77326i	−0.145334	+	0.251726i
$725$	4.08945	+	7.08314i	0.151879	+	0.263061i
$726$	13.5895	+	23.5376i	0.504352	+	0.873563i
$727$	0.463275			0.0171819			0.00859096	−	0.999963i	$-0.497265\pi$
$727$	0.463275			0.0171819			0.00859096	+	0.999963i	$0.497265\pi$
$728$	2.08945	+	2.93840i	0.0774403	+	0.108904i
$729$	1.00000			0.0370370
$730$	4.00000	+	6.92820i	0.148047	+	0.256424i
$731$	−2.05273	−	3.55543i	−0.0759229	−	0.131502i
$732$	−1.50000	+	2.59808i	−0.0554416	+	0.0960277i
$733$	−25.7156			−0.949829			−0.474914	−	0.880032i	$-0.657521\pi$
$733$	−25.7156			−0.949829			−0.474914	+	0.880032i	$0.657521\pi$
$734$	−1.58945	+	2.75302i	−0.0586678	+	0.101616i
$735$	−1.00000	+	1.73205i	−0.0368856	+	0.0638877i
$736$	3.17891			0.117176
$737$	46.8945	−	81.2237i	1.72738	−	2.99191i
$738$	−2.08945	−	3.61904i	−0.0769139	−	0.133219i
$739$	2.41055	+	4.17519i	0.0886734	+	0.153587i	0.906951	−	0.421237i	$-0.138404\pi$
$739$	2.41055	+	4.17519i	0.0886734	+	0.153587i	−0.818277	+	0.574824i	$0.805071\pi$
$740$	−4.00000			−0.147043
$741$	−12.2684	+	26.8163i	−0.450690	+	0.985123i
$742$	3.00000			0.110133
$743$	−21.5895	−	37.3940i	−0.792040	−	1.37185i	−0.924702	−	0.380693i	$-0.875686\pi$
$743$	−21.5895	−	37.3940i	−0.792040	−	1.37185i	0.132661	−	0.991161i	$-0.457648\pi$
$744$	−3.58945	−	6.21712i	−0.131596	−	0.227931i
$745$	4.82109	−	8.35038i	0.176631	−	0.305934i
$746$	−20.0000			−0.732252
$747$	2.58945	−	4.48507i	0.0947432	−	0.164100i
$748$	−15.4473	+	26.7555i	−0.564808	+	0.978276i
$749$	−7.82109			−0.285776
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	−10.4473	−	18.0952i	−0.381226	−	0.660303i	0.610012	−	0.792393i	$-0.291165\pi$
$751$	−10.4473	−	18.0952i	−0.381226	−	0.660303i	−0.991238	+	0.132089i	$0.957831\pi$
$752$	−2.08945	−	3.61904i	−0.0761946	−	0.131973i
$753$	−10.8211			−0.394343
$754$	−17.0895	−	24.0329i	−0.622361	−	0.875226i
$755$	29.0735			1.05809
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	−1.17891	−	2.04193i	−0.0428482	−	0.0742152i	0.843806	−	0.536648i	$-0.180310\pi$
$757$	−1.17891	−	2.04193i	−0.0428482	−	0.0742152i	−0.886654	+	0.462433i	$0.846977\pi$
$758$	−10.3578	+	17.9403i	−0.376213	+	0.651620i
$759$	−19.6422			−0.712966
$760$	−8.17891	+	14.1663i	−0.296680	+	0.513865i
$761$	−23.7156	+	41.0767i	−0.859691	+	1.48903i	0.0125327	+	0.999921i	$0.496011\pi$
$761$	−23.7156	+	41.0767i	−0.859691	+	1.48903i	−0.872224	+	0.489107i	$0.837323\pi$
$762$	−12.0000			−0.434714
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	−13.7684	−	23.8475i	−0.498122	−	0.862772i
$765$	5.00000	+	8.66025i	0.180775	+	0.313112i
$766$	9.82109			0.354850
$767$	1.71563	+	2.41269i	0.0619479	+	0.0871173i
$768$	−1.00000			−0.0360844
$769$	2.17891	+	3.77398i	0.0785734	+	0.136093i	0.902635	−	0.430408i	$-0.141630\pi$
$769$	2.17891	+	3.77398i	0.0785734	+	0.136093i	−0.824061	+	0.566501i	$0.808297\pi$
$770$	−6.17891	−	10.7022i	−0.222672	−	0.385680i
$771$	12.8578	−	22.2704i	0.463063	−	0.802049i
$772$	20.5367			0.739133
$773$	15.3578	−	26.6005i	0.552382	−	0.956754i	−0.445720	−	0.895173i	$-0.647052\pi$
$773$	15.3578	−	26.6005i	0.552382	−	0.956754i	0.998102	−	0.0615816i	$-0.0196144\pi$
$774$	−0.410546	+	0.711086i	−0.0147568	+	0.0255595i
$775$	7.17891			0.257874
$776$	−6.17891	+	10.7022i	−0.221810	+	0.384186i
$777$	−1.00000	−	1.73205i	−0.0358748	−	0.0621370i
$778$	0.410546	+	0.711086i	0.0147188	+	0.0254937i
$779$	−34.1789			−1.22459
$780$	−3.00000	+	6.55744i	−0.107417	+	0.234794i
$781$	56.7156			2.02944
$782$	−7.94727	−	13.7651i	−0.284194	−	0.492238i
$783$	4.08945	+	7.08314i	0.146145	+	0.253131i
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−4.00000			−0.142766
$786$	9.76836	−	16.9193i	0.348426	−	0.603491i
$787$	11.0895	−	19.2075i	0.395296	−	0.684673i	−0.597843	−	0.801614i	$-0.703975\pi$
$787$	11.0895	−	19.2075i	0.395296	−	0.684673i	0.993139	+	0.116940i	$0.0373086\pi$
$788$	17.0000			0.605600
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$	1.82109	+	3.15422i	0.0647915	+	0.112222i
$791$	−2.17891	−	3.77398i	−0.0774731	−	0.134187i
$792$	6.17891			0.219558
$793$	6.26836	+	8.81519i	0.222596	+	0.313037i
$794$	3.00000			0.106466
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	−6.41055	−	11.1034i	−0.227216	−	0.393549i
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$	−8.17891			−0.289530
$799$	−10.4473	+	18.0952i	−0.369598	+	0.640162i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	9.00000			0.317999
$802$	−16.1789	+	28.0227i	−0.571297	+	0.989516i
$803$	−12.3578	−	21.4044i	−0.436098	−	0.755344i
$804$	−7.58945	−	13.1453i	−0.267659	−	0.463600i
$805$	6.35782			0.224084
$806$	−25.7684	+	2.44314i	−0.907652	+	0.0860558i
$807$	−18.3578			−0.646226
$808$	8.17891	+	14.1663i	0.287733	+	0.498368i
$809$	10.0000	+	17.3205i	0.351581	+	0.608957i	0.986527	−	0.163600i	$-0.0523108\pi$
$809$	10.0000	+	17.3205i	0.351581	+	0.608957i	−0.634945	+	0.772557i	$0.718977\pi$
$810$	1.00000	−	1.73205i	0.0351364	−	0.0608581i
$811$	32.7156			1.14880			0.574401	−	0.818574i	$-0.305235\pi$
$811$	32.7156			1.14880			0.574401	+	0.818574i	$0.305235\pi$
$812$	4.08945	−	7.08314i	0.143512	−	0.248570i
$813$	15.5895	−	27.0017i	0.546746	−	0.946992i
$814$	12.3578			0.433141
$815$	−8.82109	+	15.2786i	−0.308989	+	0.535185i
$816$	2.50000	+	4.33013i	0.0875175	+	0.151585i
$817$	3.35782	+	5.81591i	0.117475	+	0.203473i
$818$	−13.6422			−0.476988
$819$	−3.58945	+	0.340322i	−0.125426	+	0.0118918i
$820$	−8.35782			−0.291868
$821$	−22.8578	−	39.5909i	−0.797743	−	1.38173i	−0.921083	−	0.389367i	$-0.872694\pi$
$821$	−22.8578	−	39.5909i	−0.797743	−	1.38173i	0.123339	−	0.992365i	$-0.460640\pi$
$822$	−8.17891	−	14.1663i	−0.285272	−	0.494106i
$823$	6.35782	−	11.0121i	0.221620	−	0.383856i	−0.733680	−	0.679495i	$-0.762199\pi$
$823$	6.35782	−	11.0121i	0.221620	−	0.383856i	0.955300	+	0.295638i	$0.0955324\pi$
$824$	3.17891			0.110743
$825$	−3.08945	+	5.35109i	−0.107561	+	0.186301i
$826$	−0.410546	+	0.711086i	−0.0142847	+	0.0247419i
$827$	4.71563			0.163979			0.0819893	−	0.996633i	$-0.473873\pi$
$827$	4.71563			0.163979			0.0819893	+	0.996633i	$0.473873\pi$
$828$	−1.58945	+	2.75302i	−0.0552374	+	0.0956739i
$829$	−4.08945	−	7.08314i	−0.142033	−	0.246008i	0.786229	−	0.617935i	$-0.212030\pi$
$829$	−4.08945	−	7.08314i	−0.142033	−	0.246008i	−0.928262	+	0.371927i	$0.878697\pi$
$830$	−5.17891	−	8.97013i	−0.179763	−	0.311358i
$831$	−28.3578			−0.983722
$832$	−1.50000	+	3.27872i	−0.0520031	+	0.113669i
$833$	5.00000			0.173240
$834$	−9.08945	−	15.7434i	−0.314742	−	0.545149i
$835$	−8.00000	−	13.8564i	−0.276851	−	0.479521i
$836$	25.2684	−	43.7661i	0.873925	−	1.51368i
$837$	7.17891			0.248139
$838$	−14.9473	+	25.8894i	−0.516345	+	0.894336i
$839$	−17.1789	+	29.7547i	−0.593082	+	1.02725i	0.400733	+	0.916195i	$0.368756\pi$
$839$	−17.1789	+	29.7547i	−0.593082	+	1.02725i	−0.993815	+	0.111053i	$0.964578\pi$
$840$	−2.00000			−0.0690066
$841$	−18.9473	+	32.8176i	−0.653354	+	1.13164i
$842$	17.3578	+	30.0646i	0.598190	+	1.03610i
$843$	2.82109	+	4.88627i	0.0971636	+	0.168292i
$844$	16.3578			0.563059
$845$	17.0000	+	19.6723i	0.584818	+	0.676748i
$846$	4.17891			0.143674
$847$	13.5895	+	23.5376i	0.466939	+	0.808762i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	15.1789	−	26.2906i	0.520939	−	0.902292i
$850$	−5.00000			−0.171499
$851$	−3.17891	+	5.50603i	−0.108972	+	0.188744i
$852$	4.58945	−	7.94917i	0.157232	−	0.272334i
$853$	−17.7156			−0.606572			−0.303286	−	0.952900i	$-0.598084\pi$
$853$	−17.7156			−0.606572			−0.303286	+	0.952900i	$0.598084\pi$
$854$	−1.50000	+	2.59808i	−0.0513289	+	0.0889043i
$855$	−8.17891	−	14.1663i	−0.279713	−	0.484477i
$856$	−3.91055	−	6.77326i	−0.133660	−	0.231505i
$857$	34.7156			1.18586			0.592932	−	0.805253i	$-0.297970\pi$
$857$	34.7156			1.18586			0.592932	+	0.805253i	$0.297970\pi$
$858$	9.26836	−	20.2589i	0.316417	−	0.691628i
$859$	−36.8945			−1.25883			−0.629413	−	0.777071i	$-0.716705\pi$
$859$	−36.8945			−1.25883			−0.629413	+	0.777071i	$0.716705\pi$
$860$	0.821092	+	1.42217i	0.0279990	+	0.0484957i
$861$	−2.08945	−	3.61904i	−0.0712084	−	0.123337i
$862$	0.589454	−	1.02096i	0.0200769	−	0.0347742i
$863$	36.3578			1.23763			0.618817	−	0.785535i	$-0.287612\pi$
$863$	36.3578			1.23763			0.618817	+	0.785535i	$0.287612\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	4.00000	−	6.92820i	0.136004	−	0.235566i
$866$	11.6422			0.395617
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	−3.58945	−	6.21712i	−0.121834	−	0.211023i
$869$	−5.62618	−	9.74483i	−0.190855	−	0.330571i
$870$	16.3578			0.554582
$871$	−54.4840	+	5.16571i	−1.84612	+	0.175033i
$872$	4.00000			0.135457
$873$	−6.17891	−	10.7022i	−0.209124	−	0.362214i
$874$	13.0000	+	22.5167i	0.439732	+	0.761637i
$875$	6.00000	−	10.3923i	0.202837	−	0.351324i
$876$	−4.00000			−0.135147
$877$	8.82109	−	15.2786i	0.297867	−	0.515921i	−0.677781	−	0.735264i	$-0.737058\pi$
$877$	8.82109	−	15.2786i	0.297867	−	0.515921i	0.975648	+	0.219343i	$0.0703914\pi$
$878$	2.35782	−	4.08386i	0.0795725	−	0.137824i
$879$	−12.0000			−0.404750
$880$	6.17891	−	10.7022i	0.208291	−	0.360771i
$881$	−22.7684	−	39.4360i	−0.767086	−	1.32863i	−0.939137	−	0.343543i	$-0.888373\pi$
$881$	−22.7684	−	39.4360i	−0.767086	−	1.32863i	0.172051	−	0.985088i	$-0.444961\pi$
$882$	−0.500000	−	0.866025i	−0.0168359	−	0.0291606i
$883$	−37.5367			−1.26321			−0.631606	−	0.775290i	$-0.717604\pi$
$883$	−37.5367			−1.26321			−0.631606	+	0.775290i	$0.717604\pi$
$884$	17.9473	−	1.70161i	0.603632	−	0.0572313i
$885$	−1.64218			−0.0552014
$886$	4.08945	+	7.08314i	0.137388	+	0.237963i
$887$	5.73164	+	9.92749i	0.192450	+	0.333332i	0.946061	−	0.323987i	$-0.105023\pi$
$887$	5.73164	+	9.92749i	0.192450	+	0.333332i	−0.753612	+	0.657320i	$0.771690\pi$
$888$	1.00000	−	1.73205i	0.0335578	−	0.0581238i
$889$	−12.0000			−0.402467
$890$	9.00000	−	15.5885i	0.301681	−	0.522526i
$891$	−3.08945	+	5.35109i	−0.103501	+	0.179268i
$892$	9.17891			0.307333
$893$	17.0895	−	29.5998i	0.571877	−	0.990520i
$894$	2.41055	+	4.17519i	0.0806207	+	0.139639i
$895$	−14.3578	−	24.8685i	−0.479929	−	0.831261i
$896$	−1.00000			−0.0334077
$897$	6.64218	+	9.34090i	0.221776	+	0.311883i
$898$	−14.0000			−0.467186
$899$	29.3578	+	50.8492i	0.979138	+	1.69592i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	7.50000	−	12.9904i	0.249861	−	0.432772i
$902$	25.8211			0.859748
$903$	−0.410546	+	0.711086i	−0.0136621	+	0.0236635i
$904$	2.17891	−	3.77398i	0.0724694	−	0.125521i
$905$	−15.6422			−0.519964
$906$	−7.26836	+	12.5892i	−0.241475	+	0.418247i
$907$	26.3051	+	45.5617i	0.873446	+	1.51285i	0.858409	+	0.512966i	$0.171453\pi$
$907$	26.3051	+	45.5617i	0.873446	+	1.51285i	0.0150372	+	0.999887i	$0.495213\pi$
$908$	−4.17891	−	7.23808i	−0.138682	−	0.240204i
$909$	−16.3578			−0.542555
$910$	−3.00000	+	6.55744i	−0.0994490	+	0.217377i
$911$	−16.7156			−0.553814			−0.276907	−	0.960897i	$-0.589309\pi$
$911$	−16.7156			−0.553814			−0.276907	+	0.960897i	$0.589309\pi$
$912$	−4.08945	−	7.08314i	−0.135415	−	0.234546i
$913$	16.0000	+	27.7128i	0.529523	+	0.917160i
$914$	15.9473	−	27.6215i	0.527489	−	0.913637i
$915$	−6.00000			−0.198354
$916$	−0.500000	+	0.866025i	−0.0165205	+	0.0286143i
$917$	9.76836	−	16.9193i	0.322580	−	0.558725i
$918$	−5.00000			−0.165025
$919$	−10.6262	+	18.4051i	−0.350525	+	0.607128i	−0.986342	−	0.164713i	$-0.947330\pi$
$919$	−10.6262	+	18.4051i	−0.350525	+	0.607128i	0.635816	+	0.771840i	$0.280664\pi$
$920$	3.17891	+	5.50603i	0.104806	+	0.181528i
$921$	12.4473	+	21.5593i	0.410152	+	0.710403i
$922$	−24.7156			−0.813966
$923$	−19.1789	−	26.9713i	−0.631281	−	0.887771i
$924$	6.17891			0.203271
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$	14.4473	+	25.0234i	0.474767	+	0.822320i
$927$	−1.58945	+	2.75302i	−0.0522045	+	0.0904209i
$928$	8.17891			0.268486
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	0.345708	+	0.938342i	$0.387639\pi$
$929$	−19.5000	+	33.7750i	−0.639774	+	1.10812i	−0.985482	+	0.169779i	$0.945695\pi$
$930$	7.17891	−	12.4342i	0.235406	−	0.407735i
$931$	−8.17891			−0.268053
$932$	0.178908	−	0.309878i	0.00586034	−	0.0101504i
$933$	−4.26836	−	7.39302i	−0.139740	−	0.242037i
$934$	−16.9473	−	29.3535i	−0.554532	−	0.960477i
$935$	−61.7891			−2.02072
$936$	−2.08945	−	2.93840i	−0.0682959	−	0.0960445i
$937$	−47.0735			−1.53782			−0.768911	−	0.639355i	$-0.779201\pi$
$937$	−47.0735			−1.53782			−0.768911	+	0.639355i	$0.779201\pi$
$938$	−7.58945	−	13.1453i	−0.247804	−	0.429210i
$939$	2.00000	+	3.46410i	0.0652675	+	0.113047i
$940$	4.17891	−	7.23808i	0.136301	−	0.236080i
$941$	−20.0000			−0.651981			−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000			−0.651981			−0.325991	+	0.945373i	$0.605698\pi$
$942$	1.00000	−	1.73205i	0.0325818	−	0.0564333i
$943$	−6.64218	+	11.5046i	−0.216299	+	0.374641i
$944$	−0.821092			−0.0267243
$945$	1.00000	−	1.73205i	0.0325300	−	0.0563436i
$946$	−2.53673	−	4.39374i	−0.0824760	−	0.142853i
$947$	−19.6262	−	33.9935i	−0.637765	−	1.10464i	−0.985922	−	0.167205i	$-0.946526\pi$
$947$	−19.6262	−	33.9935i	−0.637765	−	1.10464i	0.348157	−	0.937436i	$-0.386808\pi$
$948$	−1.82109			−0.0591463
$949$	−6.00000	+	13.1149i	−0.194768	+	0.425727i
$950$	8.17891			0.265359
$951$	3.58945	+	6.21712i	0.116396	+	0.201604i
$952$	2.50000	+	4.33013i	0.0810255	+	0.140340i
$953$	−21.3578	+	36.9928i	−0.691848	+	1.19832i	0.279384	+	0.960179i	$0.409870\pi$
$953$	−21.3578	+	36.9928i	−0.691848	+	1.19832i	−0.971232	+	0.238136i	$0.923464\pi$
$954$	−3.00000			−0.0971286
$955$	27.5367	−	47.6950i	0.891067	−	1.54337i
$956$	0.589454	−	1.02096i	0.0190643	−	0.0330204i
$957$	−50.5367			−1.63362
$958$	14.9105	−	25.8258i	0.481738	−	0.834394i
$959$	−8.17891	−	14.1663i	−0.264111	−	0.457453i
$960$	−1.00000	−	1.73205i	−0.0322749	−	0.0559017i
$961$	20.5367			0.662475
$962$	−4.17891	−	5.87680i	−0.134733	−	0.189475i
$963$	7.82109			0.252031
$964$	9.17891	+	15.8983i	0.295633	+	0.512051i
$965$	20.5367	+	35.5707i	0.661101	+	1.14506i
$966$	−1.58945	+	2.75302i	−0.0511398	+	0.0885768i
$967$	34.3578			1.10487			0.552436	−	0.833555i	$-0.313698\pi$
$967$	34.3578			1.10487			0.552436	+	0.833555i	$0.313698\pi$
$968$	−13.5895	+	23.5376i	−0.436782	+	0.756528i
$969$	−20.4473	+	35.4157i	−0.656861	+	1.13772i
$970$	−24.7156			−0.793571
$971$	8.41055	−	14.5675i	0.269907	−	0.467493i	−0.698930	−	0.715190i	$-0.746340\pi$
$971$	8.41055	−	14.5675i	0.269907	−	0.467493i	0.968838	+	0.247697i	$0.0796736\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−9.08945	−	15.7434i	−0.291395	−	0.504710i
$974$	−38.1789			−1.22333
$975$	3.58945	−	0.340322i	0.114955	−	0.0108990i
$976$	−3.00000			−0.0960277
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	0.753942	−	0.656941i	$-0.228150\pi$
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	−0.945899	+	0.324462i	$0.894817\pi$
$978$	−4.41055	−	7.63929i	−0.141034	−	0.244278i
$979$	−27.8051	+	48.1598i	−0.888654	+	1.53919i
$980$	−2.00000			−0.0638877
$981$	−2.00000	+	3.46410i	−0.0638551	+	0.110600i
$982$		0			0
$983$	55.0735			1.75657			0.878285	−	0.478137i	$-0.158688\pi$
$983$	55.0735			1.75657			0.878285	+	0.478137i	$0.158688\pi$
$984$	2.08945	−	3.61904i	0.0666094	−	0.115371i
$985$	17.0000	+	29.4449i	0.541665	+	0.938191i
$986$	−20.4473	−	35.4157i	−0.651174	−	1.12787i
$987$	4.17891			0.133016
$988$	−29.3578	+	2.78346i	−0.933997	+	0.0885536i
$989$	2.61018			0.0829987
$990$	6.17891	+	10.7022i	0.196379	+	0.340138i
$991$	7.73164	+	13.3916i	0.245604	+	0.425398i	0.962301	−	0.271986i	$-0.0876805\pi$
$991$	7.73164	+	13.3916i	0.245604	+	0.425398i	−0.716698	+	0.697384i	$0.754347\pi$
$992$	3.58945	−	6.21712i	0.113965	−	0.197394i
$993$	24.3578			0.772972
$994$	4.58945	−	7.94917i	0.145569	−	0.252132i
$995$	12.8211	−	22.2068i	0.406456	−	0.704002i
$996$	5.17891			0.164100
$997$	−28.8578	+	49.9832i	−0.913936	+	1.58298i	−0.105485	+	0.994421i	$0.533639\pi$
$997$	−28.8578	+	49.9832i	−0.913936	+	1.58298i	−0.808451	+	0.588563i	$0.799694\pi$
$998$	1.58945	+	2.75302i	0.0503133	+	0.0871452i
$999$	1.00000	+	1.73205i	0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.k.211.1	✓	4
3.2	odd	2		1638.2.r.ba.757.2		4
13.3	even	3		7098.2.a.br.1.2		2
13.9	even	3	inner	546.2.l.k.295.1	yes	4
13.10	even	6		7098.2.a.bk.1.1		2
39.35	odd	6		1638.2.r.ba.1387.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.k.211.1	✓	4	1.1	even	1	trivial
546.2.l.k.295.1	yes	4	13.9	even	3	inner
1638.2.r.ba.757.2		4	3.2	odd	2
1638.2.r.ba.1387.2		4	39.35	odd	6
7098.2.a.bk.1.1		2	13.10	even	6
7098.2.a.br.1.2		2	13.3	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-3.08945 - 5.35109i) q^{11} -1.00000 q^{12} +(-1.50000 + 3.27872i) q^{13} -1.00000 q^{14} +(-1.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(4.08945 - 7.08314i) q^{19} +(1.00000 - 1.73205i) q^{20} +1.00000 q^{21} +(-3.08945 + 5.35109i) q^{22} +(-1.58945 - 2.75302i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(3.58945 - 0.340322i) q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-4.08945 - 7.08314i) q^{29} +(-1.00000 + 1.73205i) q^{30} -7.17891 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.08945 - 5.35109i) q^{33} +5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 - 1.73205i) q^{37} -8.17891 q^{38} +(-3.58945 + 0.340322i) q^{39} -2.00000 q^{40} +(-2.08945 - 3.61904i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-0.410546 + 0.711086i) q^{43} +6.17891 q^{44} +(1.00000 - 1.73205i) q^{45} +(-1.58945 + 2.75302i) q^{46} +4.17891 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} -5.00000 q^{51} +(-2.08945 - 2.93840i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(6.17891 + 10.7022i) q^{55} +(0.500000 - 0.866025i) q^{56} +8.17891 q^{57} +(-4.08945 + 7.08314i) q^{58} +(0.410546 - 0.711086i) q^{59} +2.00000 q^{60} +(1.50000 - 2.59808i) q^{61} +(3.58945 + 6.21712i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(3.00000 - 6.55744i) q^{65} -6.17891 q^{66} +(7.58945 + 13.1453i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(1.58945 - 2.75302i) q^{69} +2.00000 q^{70} +(-4.58945 + 7.94917i) q^{71} +(-0.500000 + 0.866025i) q^{72} +4.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(4.08945 + 7.08314i) q^{76} -6.17891 q^{77} +(2.08945 + 2.93840i) q^{78} +1.82109 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.08945 + 3.61904i) q^{82} -5.17891 q^{83} +(-0.500000 + 0.866025i) q^{84} +(5.00000 - 8.66025i) q^{85} +0.821092 q^{86} +(4.08945 - 7.08314i) q^{87} +(-3.08945 - 5.35109i) q^{88} +(-4.50000 - 7.79423i) q^{89} -2.00000 q^{90} +(2.08945 + 2.93840i) q^{91} +3.17891 q^{92} +(-3.58945 - 6.21712i) q^{93} +(-2.08945 - 3.61904i) q^{94} +(-8.17891 + 14.1663i) q^{95} -1.00000 q^{96} +(-6.17891 + 10.7022i) q^{97} +(-0.500000 + 0.866025i) q^{98} +6.17891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{14} - 4 q^{15} - 2 q^{16} - 10 q^{17} + 4 q^{18} + 5 q^{19} + 4 q^{20} + 4 q^{21} - q^{22} + 5 q^{23} + 2 q^{24} - 4 q^{25} + 3 q^{26} - 4 q^{27} + 2 q^{28} - 5 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} - 4 q^{37} - 10 q^{38} - 3 q^{39} - 8 q^{40} + 3 q^{41} - 2 q^{42} - 13 q^{43} + 2 q^{44} + 4 q^{45} + 5 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} + 3 q^{52} - 12 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 10 q^{57} - 5 q^{58} + 13 q^{59} + 8 q^{60} + 6 q^{61} + 3 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{65} - 2 q^{66} + 19 q^{67} - 10 q^{68} - 5 q^{69} + 8 q^{70} - 7 q^{71} - 2 q^{72} + 16 q^{73} - 4 q^{74} - 2 q^{75} + 5 q^{76} - 2 q^{77} - 3 q^{78} + 30 q^{79} + 4 q^{80} - 2 q^{81} + 3 q^{82} + 2 q^{83} - 2 q^{84} + 20 q^{85} + 26 q^{86} + 5 q^{87} - q^{88} - 18 q^{89} - 8 q^{90} - 3 q^{91} - 10 q^{92} - 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} - 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 6 * q^13 - 4 * q^14 - 4 * q^15 - 2 * q^16 - 10 * q^17 + 4 * q^18 + 5 * q^19 + 4 * q^20 + 4 * q^21 - q^22 + 5 * q^23 + 2 * q^24 - 4 * q^25 + 3 * q^26 - 4 * q^27 + 2 * q^28 - 5 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 - 4 * q^37 - 10 * q^38 - 3 * q^39 - 8 * q^40 + 3 * q^41 - 2 * q^42 - 13 * q^43 + 2 * q^44 + 4 * q^45 + 5 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 + 3 * q^52 - 12 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 10 * q^57 - 5 * q^58 + 13 * q^59 + 8 * q^60 + 6 * q^61 + 3 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^65 - 2 * q^66 + 19 * q^67 - 10 * q^68 - 5 * q^69 + 8 * q^70 - 7 * q^71 - 2 * q^72 + 16 * q^73 - 4 * q^74 - 2 * q^75 + 5 * q^76 - 2 * q^77 - 3 * q^78 + 30 * q^79 + 4 * q^80 - 2 * q^81 + 3 * q^82 + 2 * q^83 - 2 * q^84 + 20 * q^85 + 26 * q^86 + 5 * q^87 - q^88 - 18 * q^89 - 8 * q^90 - 3 * q^91 - 10 * q^92 - 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 - 2 * q^97 - 2 * q^98 + 2 * q^99

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