LMFDB - Embedded newform 1638.2.r.ba.757.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, 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("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.r (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:	$13.0794958511$
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:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.2
Root			$3.08945 + 1.20635i$ of defining polynomial
Character	$\chi$	$=$	1638.757
Dual form			1638.2.r.ba.1387.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	3.08945	+	5.35109i	0.931505	+	1.61341i	0.780750	+	0.624844i	$0.214837\pi$
$11$	3.08945	+	5.35109i	0.931505	+	1.61341i	0.150756	+	0.988571i	$0.451829\pi$
$12$		0			0
$13$	−1.50000	+	3.27872i	−0.416025	+	0.909353i
$13$	−1.50000	+	3.27872i	−0.416025	+	0.909353i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	−3.08945	+	5.35109i	−0.658674	+	1.14086i
$23$	1.58945	+	2.75302i	0.331424	+	0.574043i	0.982791	−	0.184719i	$-0.0591376\pi$
$23$	1.58945	+	2.75302i	0.331424	+	0.574043i	−0.651367	+	0.758763i	$0.725804\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.58945	+	0.340322i	−0.703950	+	0.0667425i
$27$		0			0
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	4.08945	+	7.08314i	0.759393	+	1.31531i	0.943161	+	0.332337i	$0.107837\pi$
$29$	4.08945	+	7.08314i	0.759393	+	1.31531i	−0.183768	+	0.982970i	$0.558830\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	5.00000			0.857493
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−2.00000			−0.316228
$41$	2.08945	+	3.61904i	0.326318	+	0.565199i	0.981778	−	0.190030i	$-0.0608587\pi$
$41$	2.08945	+	3.61904i	0.326318	+	0.565199i	−0.655460	+	0.755230i	$0.727525\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	−1.58945	+	2.75302i	−0.234352	+	0.405910i
$47$	−4.17891			−0.609556			−0.304778	−	0.952423i	$-0.598582\pi$
$47$	−4.17891			−0.609556			−0.304778	+	0.952423i	$0.598582\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	−2.08945	−	2.93840i	−0.289755	−	0.407482i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		0			0
$55$	6.17891	+	10.7022i	0.833164	+	1.44308i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−4.08945	+	7.08314i	−0.536972	+	0.930062i
$59$	−0.410546	+	0.711086i	−0.0534485	+	0.0925755i	−0.891512	−	0.452998i	$-0.850355\pi$
$59$	−0.410546	+	0.711086i	−0.0534485	+	0.0925755i	0.838063	+	0.545573i	$0.183688\pi$
$60$		0			0
$61$	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			0
$64$	1.00000			0.125000
$65$	−3.00000	+	6.55744i	−0.372104	+	0.813350i
$66$		0			0
$67$	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
$69$		0			0
$70$	2.00000			0.239046
$71$	4.58945	−	7.94917i	0.544668	−	0.943393i	−0.453960	−	0.891022i	$-0.649989\pi$
$71$	4.58945	−	7.94917i	0.544668	−	0.943393i	0.998628	−	0.0523705i	$-0.0166777\pi$
$72$		0			0
$73$	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			0
$76$	4.08945	+	7.08314i	0.469093	+	0.812492i
$77$	6.17891			0.704152
$78$		0			0
$79$	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			0
$82$	−2.08945	+	3.61904i	−0.230742	+	0.399656i
$83$	5.17891			0.568459			0.284230	−	0.958756i	$-0.408262\pi$
$83$	5.17891			0.568459			0.284230	+	0.958756i	$0.408262\pi$
$84$		0			0
$85$	5.00000	−	8.66025i	0.542326	−	0.939336i
$86$	−0.821092			−0.0885406
$87$		0			0
$88$	−3.08945	−	5.35109i	−0.329337	−	0.570428i
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	2.08945	+	2.93840i	0.219034	+	0.308028i
$92$	−3.17891			−0.331424
$93$		0			0
$94$	−2.08945	−	3.61904i	−0.215511	−	0.373276i
$95$	8.17891	−	14.1663i	0.839138	−	1.45343i
$96$		0			0
$97$	−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
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−8.17891	−	14.1663i	−0.813832	−	1.40960i	−0.910164	−	0.414249i	$-0.864044\pi$
$101$	−8.17891	−	14.1663i	−0.813832	−	1.40960i	0.0963319	−	0.995349i	$-0.469289\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	3.91055	+	6.77326i	0.378047	+	0.654796i	0.990778	−	0.135495i	$-0.0432625\pi$
$107$	3.91055	+	6.77326i	0.378047	+	0.654796i	−0.612731	+	0.790291i	$0.709929\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	−2.17891	+	3.77398i	−0.204974	+	0.355026i	−0.950125	−	0.311871i	$-0.899044\pi$
$113$	−2.17891	+	3.77398i	−0.204974	+	0.355026i	0.745150	+	0.666897i	$0.232378\pi$
$114$		0			0
$115$	3.17891	+	5.50603i	0.296435	+	0.513440i
$116$	−8.17891			−0.759393
$117$		0			0
$118$	−0.821092			−0.0755876
$119$	−2.50000	−	4.33013i	−0.229175	−	0.396942i
$120$		0			0
$121$	−13.5895	+	23.5376i	−1.23540	+	2.13978i
$122$	3.00000			0.271607
$123$		0			0
$124$	3.58945	−	6.21712i	0.322343	−	0.558314i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−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			0
$130$	−7.17891	+	0.680643i	−0.629632	+	0.0596963i
$131$	−19.5367			−1.70693			−0.853466	−	0.521149i	$-0.825504\pi$
$131$	−19.5367			−1.70693			−0.853466	+	0.521149i	$0.825504\pi$
$132$		0			0
$133$	−4.08945	−	7.08314i	−0.354601	−	0.614186i
$134$	−7.58945	+	13.1453i	−0.655629	+	1.13558i
$135$		0			0
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	−8.17891	+	14.1663i	−0.698771	+	1.21031i	0.270121	+	0.962826i	$0.412936\pi$
$137$	−8.17891	+	14.1663i	−0.698771	+	1.21031i	−0.968893	+	0.247481i	$0.920397\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	9.17891			0.770277
$143$	−22.1789	+	2.10282i	−1.85469	+	0.175846i
$144$		0			0
$145$	8.17891	+	14.1663i	0.679221	+	1.17645i
$146$	2.00000	+	3.46410i	0.165521	+	0.286691i
$147$		0			0
$148$	2.00000			0.164399
$149$	2.41055	−	4.17519i	0.197480	−	0.342045i	−0.750231	−	0.661176i	$-0.770058\pi$
$149$	2.41055	−	4.17519i	0.197480	−	0.342045i	0.947711	+	0.319131i	$0.103391\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	3.08945	+	5.35109i	0.248955	+	0.431203i
$155$	−14.3578			−1.15325
$156$		0			0
$157$	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
$159$		0			0
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	3.17891			0.250533
$162$		0			0
$163$	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
$165$		0			0
$166$	2.58945	+	4.48507i	0.200981	+	0.348109i
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	0.668730	−	0.743505i	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$		0			0
$169$	−8.50000	−	9.83616i	−0.653846	−	0.756628i
$170$	10.0000			0.766965
$171$		0			0
$172$	−0.410546	−	0.711086i	−0.0313038	−	0.0542198i
$173$	2.00000	−	3.46410i	0.152057	−	0.263371i	−0.779926	−	0.625871i	$-0.784744\pi$
$173$	2.00000	−	3.46410i	0.152057	−	0.263371i	0.931984	+	0.362500i	$0.118077\pi$
$174$		0			0
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	3.08945	−	5.35109i	0.232876	−	0.403354i
$177$		0			0
$178$	−4.50000	+	7.79423i	−0.337289	+	0.584202i
$179$	−7.17891	−	12.4342i	−0.536577	−	0.929378i	−0.999085	−	0.0427634i	$-0.986384\pi$
$179$	−7.17891	−	12.4342i	−0.536577	−	0.929378i	0.462508	−	0.886615i	$-0.346949\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−1.58945	−	2.75302i	−0.117176	−	0.202955i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$		0			0
$187$	30.8945			2.25923
$188$	2.08945	−	3.61904i	0.152389	−	0.263946i
$189$		0			0
$190$	16.3578			1.18672
$191$	13.7684	−	23.8475i	0.996244	−	1.72554i	0.423130	−	0.906069i	$-0.360931\pi$
$191$	13.7684	−	23.8475i	0.996244	−	1.72554i	0.573114	−	0.819476i	$-0.305735\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	1.00000			0.0714286
$197$	8.50000	+	14.7224i	0.605600	+	1.04893i	0.991956	+	0.126580i	$0.0404001\pi$
$197$	8.50000	+	14.7224i	0.605600	+	1.04893i	−0.386356	+	0.922350i	$0.626267\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	8.17891	−	14.1663i	0.575466	−	0.996736i
$203$	8.17891			0.574047
$204$		0			0
$205$	4.17891	+	7.23808i	0.291868	+	0.505530i
$206$	1.58945	+	2.75302i	0.110743	+	0.191812i
$207$		0			0
$208$	3.58945	−	0.340322i	0.248884	−	0.0235971i
$209$	50.5367			3.49570
$210$		0			0
$211$	−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
$213$		0			0
$214$	−3.91055	+	6.77326i	−0.267319	+	0.463011i
$215$	−0.821092	+	1.42217i	−0.0559980	+	0.0969914i
$216$		0			0
$217$	−3.58945	+	6.21712i	−0.243668	+	0.422045i
$218$	2.00000	+	3.46410i	0.135457	+	0.234619i
$219$		0			0
$220$	−12.3578			−0.833164
$221$	10.4473	+	14.6920i	0.702759	+	0.988290i
$222$		0			0
$223$	−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			0
$226$	−4.35782			−0.289878
$227$	4.17891	−	7.23808i	0.277364	−	0.480408i	−0.693365	−	0.720587i	$-0.743873\pi$
$227$	4.17891	−	7.23808i	0.277364	−	0.480408i	0.970729	+	0.240178i	$0.0772059\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−4.08945	−	7.08314i	−0.268486	−	0.465031i
$233$	0.357817			0.0234414			0.0117207	−	0.999931i	$-0.496269\pi$
$233$	0.357817			0.0234414			0.0117207	+	0.999931i	$0.496269\pi$
$234$		0			0
$235$	−8.35782			−0.545204
$236$	−0.410546	−	0.711086i	−0.0267243	−	0.0462878i
$237$		0			0
$238$	2.50000	−	4.33013i	0.162051	−	0.280680i
$239$	1.17891			0.0762572			0.0381286	−	0.999273i	$-0.487860\pi$
$239$	1.17891			0.0762572			0.0381286	+	0.999273i	$0.487860\pi$
$240$		0			0
$241$	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			0
$244$	1.50000	+	2.59808i	0.0960277	+	0.166325i
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$		0			0
$247$	17.0895	+	24.0329i	1.08738	+	1.52918i
$248$	7.17891			0.455861
$249$		0			0
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	5.41055	−	9.37134i	0.341511	−	0.591514i	−0.643203	−	0.765696i	$-0.722395\pi$
$251$	5.41055	−	9.37134i	0.341511	−	0.591514i	0.984713	+	0.174182i	$0.0557281\pi$
$252$		0			0
$253$	−9.82109	+	17.0106i	−0.617447	+	1.06945i
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.8578	+	22.2704i	0.802049	+	1.38919i	0.918266	+	0.395965i	$0.129590\pi$
$257$	12.8578	+	22.2704i	0.802049	+	1.38919i	−0.116217	+	0.993224i	$0.537077\pi$
$258$		0			0
$259$	−2.00000			−0.124274
$260$	−4.17891	−	5.87680i	−0.259165	−	0.364463i
$261$		0			0
$262$	−9.76836	−	16.9193i	−0.603491	−	1.04528i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$	4.08945	−	7.08314i	0.250741	−	0.434295i
$267$		0			0
$268$	−15.1789			−0.927199
$269$	9.17891	−	15.8983i	0.559648	−	0.969339i	−0.437878	−	0.899035i	$-0.644270\pi$
$269$	9.17891	−	15.8983i	0.559648	−	0.969339i	0.997526	−	0.0703041i	$-0.0223970\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	−16.3578			−0.988212
$275$	−3.08945	−	5.35109i	−0.186301	−	0.322683i
$276$		0			0
$277$	−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
$279$		0			0
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	−5.64218			−0.336584			−0.168292	−	0.985737i	$-0.553825\pi$
$281$	−5.64218			−0.336584			−0.168292	+	0.985737i	$0.553825\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	−12.9105	−	18.1561i	−0.763417	−	1.07359i
$287$	4.17891			0.246673
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−8.17891	+	14.1663i	−0.480282	+	0.831873i
$291$		0			0
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	−0.635818	−	0.771839i	$-0.719337\pi$
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	0.986341	+	0.164714i	$0.0526703\pi$
$294$		0			0
$295$	−0.821092	+	1.42217i	−0.0478058	+	0.0828021i
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$		0			0
$298$	4.82109			0.279278
$299$	−11.4105	+	1.08185i	−0.659889	+	0.0625651i
$300$		0			0
$301$	0.410546	+	0.711086i	0.0236635	+	0.0409863i
$302$	−7.26836	−	12.5892i	−0.418247	−	0.724426i
$303$		0			0
$304$	−8.17891			−0.469093
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$		0			0
$307$	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
$309$		0			0
$310$	−7.17891	−	12.4342i	−0.407735	−	0.706217i
$311$	8.53673			0.484073			0.242037	−	0.970267i	$-0.422185\pi$
$311$	8.53673			0.484073			0.242037	+	0.970267i	$0.422185\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	−0.910546	+	1.57711i	−0.0512222	+	0.0887195i
$317$	−7.17891			−0.403208			−0.201604	−	0.979467i	$-0.564615\pi$
$317$	−7.17891			−0.403208			−0.201604	+	0.979467i	$0.564615\pi$
$318$		0			0
$319$	−25.2684	+	43.7661i	−1.41476	+	2.45043i
$320$	2.00000			0.111803
$321$		0			0
$322$	1.58945	+	2.75302i	0.0885768	+	0.153420i
$323$	−20.4473	−	35.4157i	−1.13772	−	1.97058i
$324$		0			0
$325$	1.50000	−	3.27872i	0.0832050	−	0.181871i
$326$	8.82109			0.488555
$327$		0			0
$328$	−2.08945	−	3.61904i	−0.115371	−	0.199828i
$329$	−2.08945	+	3.61904i	−0.115195	+	0.199524i
$330$		0			0
$331$	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
$333$		0			0
$334$	4.00000	−	6.92820i	0.218870	−	0.379094i
$335$	15.1789	+	26.2906i	0.829312	+	1.43641i
$336$		0			0
$337$	−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
$339$		0			0
$340$	5.00000	+	8.66025i	0.271163	+	0.469668i
$341$	−22.1789	−	38.4150i	−1.20106	−	2.08029i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	0.410546	−	0.711086i	0.0221351	−	0.0383392i
$345$		0			0
$346$	4.00000			0.215041
$347$	−3.91055	+	6.77326i	−0.209929	+	0.363608i	−0.951692	−	0.307054i	$-0.900657\pi$
$347$	−3.91055	+	6.77326i	−0.209929	+	0.363608i	0.741763	+	0.670662i	$0.233990\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	6.17891			0.329337
$353$	−3.58945	−	6.21712i	−0.191047	−	0.330904i	0.754550	−	0.656242i	$-0.227855\pi$
$353$	−3.58945	−	6.21712i	−0.191047	−	0.330904i	−0.945598	+	0.325339i	$0.894522\pi$
$354$		0			0
$355$	9.17891	−	15.8983i	0.487166	−	0.843796i
$356$	−9.00000			−0.476999
$357$		0			0
$358$	7.17891	−	12.4342i	0.379417	−	0.657170i
$359$	−12.3578			−0.652221			−0.326110	−	0.945332i	$-0.605738\pi$
$359$	−12.3578			−0.652221			−0.326110	+	0.945332i	$0.605738\pi$
$360$		0			0
$361$	−23.9473	−	41.4779i	−1.26038	−	2.18305i
$362$	3.91055	+	6.77326i	0.205534	+	0.355995i
$363$		0			0
$364$	−3.58945	+	0.340322i	−0.188139	+	0.0178377i
$365$	8.00000			0.418739
$366$		0			0
$367$	−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
$369$		0			0
$370$	2.00000	−	3.46410i	0.103975	−	0.180090i
$371$	1.50000	−	2.59808i	0.0778761	−	0.134885i
$372$		0			0
$373$	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
$375$		0			0
$376$	4.17891			0.215511
$377$	−29.3578	+	2.78346i	−1.51200	+	0.143355i
$378$		0			0
$379$	−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
$381$		0			0
$382$	27.5367			1.40890
$383$	4.91055	−	8.50531i	0.250917	−	0.434601i	−0.712861	−	0.701305i	$-0.752601\pi$
$383$	4.91055	−	8.50531i	0.250917	−	0.434601i	0.963779	+	0.266704i	$0.0859345\pi$
$384$		0			0
$385$	12.3578			0.629813
$386$	10.2684	−	17.7853i	0.522646	−	0.905249i
$387$		0			0
$388$	−6.17891	−	10.7022i	−0.313687	−	0.543321i
$389$	0.821092			0.0416310			0.0208155	−	0.999783i	$-0.493374\pi$
$389$	0.821092			0.0416310			0.0208155	+	0.999783i	$0.493374\pi$
$390$		0			0
$391$	15.8945			0.803822
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	−8.50000	+	14.7224i	−0.428224	+	0.741705i
$395$	3.64218			0.183258
$396$		0			0
$397$	−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
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	16.1789	+	28.0227i	0.807936	+	1.39939i	0.914291	+	0.405058i	$0.132749\pi$
$401$	16.1789	+	28.0227i	0.807936	+	1.39939i	−0.106355	+	0.994328i	$0.533918\pi$
$402$		0			0
$403$	10.7684	−	23.5376i	0.536410	−	1.17249i
$404$	16.3578			0.813832
$405$		0			0
$406$	4.08945	+	7.08314i	0.202956	+	0.351530i
$407$	6.17891	−	10.7022i	0.306277	−	0.530488i
$408$		0			0
$409$	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
$411$		0			0
$412$	−1.58945	+	2.75302i	−0.0783068	+	0.135631i
$413$	0.410546	+	0.711086i	0.0202016	+	0.0349903i
$414$		0			0
$415$	10.3578			0.508445
$416$	2.08945	+	2.93840i	0.102444	+	0.144067i
$417$		0			0
$418$	25.2684	+	43.7661i	1.23592	+	2.14067i
$419$	14.9473	+	25.8894i	0.730222	+	1.26478i	0.956788	+	0.290786i	$0.0939167\pi$
$419$	14.9473	+	25.8894i	0.730222	+	1.26478i	−0.226566	+	0.973996i	$0.572750\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−3.00000			−0.145693
$425$	−2.50000	+	4.33013i	−0.121268	+	0.210042i
$426$		0			0
$427$	−1.50000	−	2.59808i	−0.0725901	−	0.125730i
$428$	−7.82109			−0.378047
$429$		0			0
$430$	−1.64218			−0.0791931
$431$	−0.589454	−	1.02096i	−0.0283930	−	0.0491781i	0.851480	−	0.524387i	$-0.175706\pi$
$431$	−0.589454	−	1.02096i	−0.0283930	−	0.0491781i	−0.879873	+	0.475209i	$0.842372\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	−2.00000	+	3.46410i	−0.0957826	+	0.165900i
$437$	26.0000			1.24375
$438$		0			0
$439$	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
$441$		0			0
$442$	−7.50000	+	16.3936i	−0.356739	+	0.779764i
$443$	8.17891			0.388592			0.194296	−	0.980943i	$-0.437758\pi$
$443$	8.17891			0.388592			0.194296	+	0.980943i	$0.437758\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	4.58945	−	7.94917i	0.217317	−	0.376404i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−7.00000	+	12.1244i	−0.330350	+	0.572184i	−0.982581	−	0.185837i	$-0.940500\pi$
$449$	−7.00000	+	12.1244i	−0.330350	+	0.572184i	0.652230	+	0.758021i	$0.273834\pi$
$450$		0			0
$451$	−12.9105	+	22.3617i	−0.607934	+	1.05297i
$452$	−2.17891	−	3.77398i	−0.102487	−	0.177513i
$453$		0			0
$454$	8.35782			0.392252
$455$	4.17891	+	5.87680i	0.195910	+	0.275508i
$456$		0			0
$457$	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
$459$		0			0
$460$	−6.35782			−0.296435
$461$	−12.3578	+	21.4044i	−0.575561	+	0.996901i	0.420420	+	0.907330i	$0.361883\pi$
$461$	−12.3578	+	21.4044i	−0.575561	+	0.996901i	−0.995980	+	0.0895709i	$0.971450\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	0.178908	+	0.309878i	0.00828777	+	0.0143548i
$467$	−33.8945			−1.56845			−0.784226	−	0.620475i	$-0.786940\pi$
$467$	−33.8945			−1.56845			−0.784226	+	0.620475i	$0.786940\pi$
$468$		0			0
$469$	15.1789			0.700897
$470$	−4.17891	−	7.23808i	−0.192759	−	0.333868i
$471$		0			0
$472$	0.410546	−	0.711086i	0.0188969	−	0.0327304i
$473$	−5.07345			−0.233277
$474$		0			0
$475$	−4.08945	+	7.08314i	−0.187637	+	0.324997i
$476$	5.00000			0.229175
$477$		0			0
$478$	0.589454	+	1.02096i	0.0269610	+	0.0466978i
$479$	−14.9105	−	25.8258i	−0.681280	−	1.18001i	−0.974590	−	0.223995i	$-0.928090\pi$
$479$	−14.9105	−	25.8258i	−0.681280	−	1.18001i	0.293310	−	0.956017i	$-0.405243\pi$
$480$		0			0
$481$	7.17891	−	0.680643i	0.327330	−	0.0310347i
$482$	18.3578			0.836176
$483$		0			0
$484$	−13.5895	−	23.5376i	−0.617702	−	1.06989i
$485$	−12.3578	+	21.4044i	−0.561140	+	0.971922i
$486$		0			0
$487$	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
$489$		0			0
$490$	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	$0.833333\pi$
$492$		0			0
$493$	40.8945			1.84180
$494$	−12.2684	+	26.8163i	−0.551980	+	1.20652i
$495$		0			0
$496$	3.58945	+	6.21712i	0.161171	+	0.279157i
$497$	−4.58945	−	7.94917i	−0.205865	−	0.356569i
$498$		0			0
$499$	−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
$501$		0			0
$502$	10.8211			0.482969
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$		0			0
$505$	−16.3578	−	28.3326i	−0.727913	−	1.26078i
$506$	−19.6422			−0.873202
$507$		0			0
$508$	12.0000			0.532414
$509$	14.3578	+	24.8685i	0.636399	+	1.10228i	0.986217	+	0.165458i	$0.0529101\pi$
$509$	14.3578	+	24.8685i	0.636399	+	1.10228i	−0.349818	+	0.936818i	$0.613757\pi$
$510$		0			0
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−12.8578	+	22.2704i	−0.567134	+	0.982305i
$515$	6.35782			0.280159
$516$		0			0
$517$	−12.9105	−	22.3617i	−0.567805	−	0.983467i
$518$	−1.00000	−	1.73205i	−0.0439375	−	0.0761019i
$519$		0			0
$520$	3.00000	−	6.55744i	0.131559	−	0.287563i
$521$	4.17891			0.183081			0.0915406	−	0.995801i	$-0.470821\pi$
$521$	4.17891			0.183081			0.0915406	+	0.995801i	$0.470821\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	6.00000	−	10.3923i	0.261612	−	0.453126i
$527$	−17.9473	+	31.0856i	−0.781795	+	1.35411i
$528$		0			0
$529$	6.44727	−	11.1670i	0.280316	−	0.485522i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$		0			0
$532$	8.17891			0.354601
$533$	−15.0000	+	1.42217i	−0.649722	+	0.0616011i
$534$		0			0
$535$	7.82109	+	13.5465i	0.338135	+	0.585667i
$536$	−7.58945	−	13.1453i	−0.327814	−	0.567791i
$537$		0			0
$538$	18.3578			0.791462
$539$	3.08945	−	5.35109i	0.133072	−	0.230488i
$540$		0			0
$541$	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
$543$		0			0
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	8.00000			0.342682
$546$		0			0
$547$	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
$549$		0			0
$550$	3.08945	−	5.35109i	0.131735	−	0.228171i
$551$	66.8945			2.84980
$552$		0			0
$553$	0.910546	−	1.57711i	0.0387203	−	0.0670656i
$554$	−28.3578			−1.20481
$555$		0			0
$556$	9.08945	+	15.7434i	0.385479	+	0.667669i
$557$	−10.8578	−	18.8063i	−0.460060	−	0.796848i	0.538903	−	0.842368i	$-0.318839\pi$
$557$	−10.8578	−	18.8063i	−0.460060	−	0.796848i	−0.998963	+	0.0455198i	$0.985506\pi$
$558$		0			0
$559$	−1.71563	−	2.41269i	−0.0725636	−	0.102046i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	−2.82109	−	4.88627i	−0.119001	−	0.206115i
$563$	2.17891	−	3.77398i	0.0918300	−	0.159054i	−0.816451	−	0.577414i	$-0.804062\pi$
$563$	2.17891	−	3.77398i	0.0918300	−	0.159054i	0.908281	+	0.418360i	$0.137395\pi$
$564$		0			0
$565$	−4.35782	+	7.54796i	−0.183335	+	0.317545i
$566$	15.1789	−	26.2906i	0.638017	−	1.10508i
$567$		0			0
$568$	−4.58945	+	7.94917i	−0.192569	+	0.333540i
$569$	−13.1789	−	22.8265i	−0.552489	−	0.956938i	−0.998094	−	0.0617089i	$-0.980345\pi$
$569$	−13.1789	−	22.8265i	−0.552489	−	0.956938i	0.445606	−	0.895229i	$-0.352988\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	2.08945	+	3.61904i	0.0872121	+	0.151056i
$575$	−1.58945	−	2.75302i	−0.0662848	−	0.114809i
$576$		0			0
$577$	−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
$579$		0			0
$580$	−16.3578			−0.679221
$581$	2.58945	−	4.48507i	0.107429	−	0.186072i
$582$		0			0
$583$	9.26836	+	16.0533i	0.383856	+	0.664859i
$584$	−4.00000			−0.165521
$585$		0			0
$586$	12.0000			0.495715
$587$	−5.58945	−	9.68122i	−0.230701	−	0.399587i	0.727313	−	0.686306i	$-0.240769\pi$
$587$	−5.58945	−	9.68122i	−0.230701	−	0.399587i	−0.958015	+	0.286719i	$0.907435\pi$
$588$		0			0
$589$	−29.3578	+	50.8492i	−1.20967	+	2.09521i
$590$	−1.64218			−0.0676076
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	33.0000			1.35515			0.677574	−	0.735455i	$-0.263031\pi$
$593$	33.0000			1.35515			0.677574	+	0.735455i	$0.263031\pi$
$594$		0			0
$595$	−5.00000	−	8.66025i	−0.204980	−	0.355036i
$596$	2.41055	+	4.17519i	0.0987398	+	0.171022i
$597$		0			0
$598$	−6.64218	−	9.34090i	−0.271619	−	0.381978i
$599$	−28.8211			−1.17760			−0.588799	−	0.808280i	$-0.700399\pi$
$599$	−28.8211			−1.17760			−0.588799	+	0.808280i	$0.700399\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	7.26836	−	12.5892i	0.295745	−	0.512246i
$605$	−27.1789	+	47.0753i	−1.10498	+	1.91388i
$606$		0			0
$607$	−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
$609$		0			0
$610$	6.00000			0.242933
$611$	6.26836	−	13.7015i	0.253591	−	0.554302i
$612$		0			0
$613$	−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
$615$		0			0
$616$	−6.17891			−0.248955
$617$	16.0000	−	27.7128i	0.644136	−	1.11568i	−0.340365	−	0.940294i	$-0.610551\pi$
$617$	16.0000	−	27.7128i	0.644136	−	1.11568i	0.984500	−	0.175382i	$-0.0561162\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	4.26836	+	7.39302i	0.171146	+	0.296433i
$623$	9.00000			0.360577
$624$		0			0
$625$	−19.0000			−0.760000
$626$	2.00000	+	3.46410i	0.0799361	+	0.138453i
$627$		0			0
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	−10.0000			−0.398726
$630$		0			0
$631$	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
$633$		0			0
$634$	−3.58945	−	6.21712i	−0.142555	−	0.246913i
$635$	−12.0000	−	20.7846i	−0.476205	−	0.824812i
$636$		0			0
$637$	3.58945	−	0.340322i	0.142219	−	0.0134840i
$638$	−50.5367			−2.00077
$639$		0			0
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	−20.5367	+	35.5707i	−0.811152	+	1.40496i	0.100907	+	0.994896i	$0.467826\pi$
$641$	−20.5367	+	35.5707i	−0.811152	+	1.40496i	−0.912058	+	0.410060i	$0.865508\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	20.4473	−	35.4157i	0.804487	−	1.39341i
$647$	−4.44727	−	7.70290i	−0.174840	−	0.302832i	0.765266	−	0.643715i	$-0.222608\pi$
$647$	−4.44727	−	7.70290i	−0.174840	−	0.302832i	−0.940106	+	0.340882i	$0.889274\pi$
$648$		0			0
$649$	−5.07345			−0.199150
$650$	3.58945	−	0.340322i	0.140790	−	0.0133485i
$651$		0			0
$652$	4.41055	+	7.63929i	0.172730	+	0.299178i
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	0.994988	−	0.0999939i	$-0.0318823\pi$
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	−0.584091	+	0.811688i	$0.698549\pi$
$654$		0			0
$655$	−39.0735			−1.52673
$656$	2.08945	−	3.61904i	0.0815795	−	0.141300i
$657$		0			0
$658$	−4.17891			−0.162911
$659$	−8.26836	+	14.3212i	−0.322090	+	0.557876i	−0.980919	−	0.194417i	$-0.937719\pi$
$659$	−8.26836	+	14.3212i	−0.322090	+	0.557876i	0.658829	+	0.752292i	$0.271052\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	−5.17891			−0.200981
$665$	−8.17891	−	14.1663i	−0.317164	−	0.549345i
$666$		0			0
$667$	−13.0000	+	22.5167i	−0.503362	+	0.871849i
$668$	8.00000			0.309529
$669$		0			0
$670$	−15.1789	+	26.2906i	−0.586412	+	1.01570i
$671$	18.5367			0.715602
$672$		0			0
$673$	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
$675$		0			0
$676$	12.7684	−	2.44314i	0.491091	−	0.0939668i
$677$	−12.0000			−0.461197			−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000			−0.461197			−0.230599	+	0.973049i	$0.574068\pi$
$678$		0			0
$679$	6.17891	+	10.7022i	0.237125	+	0.410712i
$680$	−5.00000	+	8.66025i	−0.191741	+	0.332106i
$681$		0			0
$682$	22.1789	−	38.4150i	0.849274	−	1.47099i
$683$	−7.17891	+	12.4342i	−0.274693	+	0.475783i	−0.970058	−	0.242875i	$-0.921910\pi$
$683$	−7.17891	+	12.4342i	−0.274693	+	0.475783i	0.695364	+	0.718657i	$0.255243\pi$
$684$		0			0
$685$	−16.3578	+	28.3326i	−0.625000	+	1.08253i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	0.821092			0.0313038
$689$	−4.50000	+	9.83616i	−0.171436	+	0.374728i
$690$		0			0
$691$	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
$693$		0			0
$694$	−7.82109			−0.296885
$695$	18.1789	−	31.4868i	0.689565	−	1.19436i
$696$		0			0
$697$	20.8945			0.791437
$698$	−1.58945	+	2.75302i	−0.0601617	+	0.104203i
$699$		0			0
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	−23.7156			−0.895727			−0.447864	−	0.894102i	$-0.647815\pi$
$701$	−23.7156			−0.895727			−0.447864	+	0.894102i	$0.647815\pi$
$702$		0			0
$703$	−16.3578			−0.616947
$704$	3.08945	+	5.35109i	0.116438	+	0.201677i
$705$		0			0
$706$	3.58945	−	6.21712i	0.135091	−	0.233984i
$707$	−16.3578			−0.615199
$708$		0			0
$709$	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			0
$712$	−4.50000	−	7.79423i	−0.168645	−	0.292101i
$713$	−11.4105	−	19.7636i	−0.427328	−	0.740154i
$714$		0			0
$715$	−44.3578	+	4.20563i	−1.65889	+	0.157282i
$716$	14.3578			0.536577
$717$		0			0
$718$	−6.17891	−	10.7022i	−0.230595	−	0.399402i
$719$	−12.9105	+	22.3617i	−0.481482	+	0.833951i	−0.999774	−	0.0212522i	$-0.993235\pi$
$719$	−12.9105	+	22.3617i	−0.481482	+	0.833951i	0.518292	+	0.855204i	$0.326568\pi$
$720$		0			0
$721$	1.58945	−	2.75302i	0.0591944	−	0.102528i
$722$	23.9473	−	41.4779i	0.891225	−	1.54365i
$723$		0			0
$724$	−3.91055	+	6.77326i	−0.145334	+	0.251726i
$725$	−4.08945	−	7.08314i	−0.151879	−	0.263061i
$726$		0			0
$727$	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
$729$		0			0
$730$	4.00000	+	6.92820i	0.148047	+	0.256424i
$731$	2.05273	+	3.55543i	0.0759229	+	0.131502i
$732$		0			0
$733$	−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
$735$		0			0
$736$	3.17891			0.117176
$737$	−46.8945	+	81.2237i	−1.72738	+	2.99191i
$738$		0			0
$739$	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
$741$		0			0
$742$	3.00000			0.110133
$743$	21.5895	+	37.3940i	0.792040	+	1.37185i	0.924702	+	0.380693i	$0.124314\pi$
$743$	21.5895	+	37.3940i	0.792040	+	1.37185i	−0.132661	+	0.991161i	$0.542352\pi$
$744$		0			0
$745$	4.82109	−	8.35038i	0.176631	−	0.305934i
$746$	20.0000			0.732252
$747$		0			0
$748$	−15.4473	+	26.7555i	−0.564808	+	0.978276i
$749$	7.82109			0.285776
$750$		0			0
$751$	−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
$753$		0			0
$754$	−17.0895	−	24.0329i	−0.622361	−	0.875226i
$755$	−29.0735			−1.05809
$756$		0			0
$757$	−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
$759$		0			0
$760$	−8.17891	+	14.1663i	−0.296680	+	0.513865i
$761$	23.7156	−	41.0767i	0.859691	−	1.48903i	−0.0125327	−	0.999921i	$-0.503989\pi$
$761$	23.7156	−	41.0767i	0.859691	−	1.48903i	0.872224	−	0.489107i	$-0.162677\pi$
$762$		0			0
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	13.7684	+	23.8475i	0.498122	+	0.862772i
$765$		0			0
$766$	9.82109			0.354850
$767$	−1.71563	−	2.41269i	−0.0619479	−	0.0871173i
$768$		0			0
$769$	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
$771$		0			0
$772$	20.5367			0.739133
$773$	−15.3578	+	26.6005i	−0.552382	+	0.956754i	0.445720	+	0.895173i	$0.352948\pi$
$773$	−15.3578	+	26.6005i	−0.552382	+	0.956754i	−0.998102	+	0.0615816i	$0.980386\pi$
$774$		0			0
$775$	7.17891			0.257874
$776$	6.17891	−	10.7022i	0.221810	−	0.384186i
$777$		0			0
$778$	0.410546	+	0.711086i	0.0147188	+	0.0254937i
$779$	34.1789			1.22459
$780$		0			0
$781$	56.7156			2.02944
$782$	7.94727	+	13.7651i	0.284194	+	0.492238i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	4.00000			0.142766
$786$		0			0
$787$	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
$789$		0			0
$790$	1.82109	+	3.15422i	0.0647915	+	0.112222i
$791$	2.17891	+	3.77398i	0.0774731	+	0.134187i
$792$		0			0
$793$	6.26836	+	8.81519i	0.222596	+	0.313037i
$794$	−3.00000			−0.106466
$795$		0			0
$796$	−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	$0.166667\pi$
$798$		0			0
$799$	−10.4473	+	18.0952i	−0.369598	+	0.640162i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	−16.1789	+	28.0227i	−0.571297	+	0.989516i
$803$	12.3578	+	21.4044i	0.436098	+	0.755344i
$804$		0			0
$805$	6.35782			0.224084
$806$	25.7684	−	2.44314i	0.907652	−	0.0860558i
$807$		0			0
$808$	8.17891	+	14.1663i	0.287733	+	0.498368i
$809$	−10.0000	−	17.3205i	−0.351581	−	0.608957i	0.634945	−	0.772557i	$-0.281023\pi$
$809$	−10.0000	−	17.3205i	−0.351581	−	0.608957i	−0.986527	+	0.163600i	$0.947689\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	12.3578			0.433141
$815$	8.82109	−	15.2786i	0.308989	−	0.535185i
$816$		0			0
$817$	3.35782	+	5.81591i	0.117475	+	0.203473i
$818$	13.6422			0.476988
$819$		0			0
$820$	−8.35782			−0.291868
$821$	22.8578	+	39.5909i	0.797743	+	1.38173i	0.921083	+	0.389367i	$0.127306\pi$
$821$	22.8578	+	39.5909i	0.797743	+	1.38173i	−0.123339	+	0.992365i	$0.539360\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	−0.410546	+	0.711086i	−0.0142847	+	0.0247419i
$827$	−4.71563			−0.163979			−0.0819893	−	0.996633i	$-0.526127\pi$
$827$	−4.71563			−0.163979			−0.0819893	+	0.996633i	$0.526127\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	−1.50000	+	3.27872i	−0.0520031	+	0.113669i
$833$	−5.00000			−0.173240
$834$		0			0
$835$	−8.00000	−	13.8564i	−0.276851	−	0.479521i
$836$	−25.2684	+	43.7661i	−0.873925	+	1.51368i
$837$		0			0
$838$	−14.9473	+	25.8894i	−0.516345	+	0.894336i
$839$	17.1789	−	29.7547i	0.593082	−	1.02725i	−0.400733	−	0.916195i	$-0.631244\pi$
$839$	17.1789	−	29.7547i	0.593082	−	1.02725i	0.993815	−	0.111053i	$-0.0354223\pi$
$840$		0			0
$841$	−18.9473	+	32.8176i	−0.653354	+	1.13164i
$842$	−17.3578	−	30.0646i	−0.598190	−	1.03610i
$843$		0			0
$844$	16.3578			0.563059
$845$	−17.0000	−	19.6723i	−0.584818	−	0.676748i
$846$		0			0
$847$	13.5895	+	23.5376i	0.466939	+	0.808762i
$848$	−1.50000	−	2.59808i	−0.0515102	−	0.0892183i
$849$		0			0
$850$	−5.00000			−0.171499
$851$	3.17891	−	5.50603i	0.108972	−	0.188744i
$852$		0			0
$853$	−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
$855$		0			0
$856$	−3.91055	−	6.77326i	−0.133660	−	0.231505i
$857$	−34.7156			−1.18586			−0.592932	−	0.805253i	$-0.702030\pi$
$857$	−34.7156			−1.18586			−0.592932	+	0.805253i	$0.702030\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	0.589454	−	1.02096i	0.0200769	−	0.0347742i
$863$	−36.3578			−1.23763			−0.618817	−	0.785535i	$-0.712388\pi$
$863$	−36.3578			−1.23763			−0.618817	+	0.785535i	$0.712388\pi$
$864$		0			0
$865$	4.00000	−	6.92820i	0.136004	−	0.235566i
$866$	−11.6422			−0.395617
$867$		0			0
$868$	−3.58945	−	6.21712i	−0.121834	−	0.211023i
$869$	5.62618	+	9.74483i	0.190855	+	0.330571i
$870$		0			0
$871$	−54.4840	+	5.16571i	−1.84612	+	0.175033i
$872$	−4.00000			−0.135457
$873$		0			0
$874$	13.0000	+	22.5167i	0.439732	+	0.761637i
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$		0			0
$877$	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
$879$		0			0
$880$	6.17891	−	10.7022i	0.208291	−	0.360771i
$881$	22.7684	+	39.4360i	0.767086	+	1.32863i	0.939137	+	0.343543i	$0.111627\pi$
$881$	22.7684	+	39.4360i	0.767086	+	1.32863i	−0.172051	+	0.985088i	$0.555039\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	4.08945	+	7.08314i	0.137388	+	0.237963i
$887$	−5.73164	−	9.92749i	−0.192450	−	0.333332i	0.753612	−	0.657320i	$-0.228310\pi$
$887$	−5.73164	−	9.92749i	−0.192450	−	0.333332i	−0.946061	+	0.323987i	$0.894977\pi$
$888$		0			0
$889$	−12.0000			−0.402467
$890$	−9.00000	+	15.5885i	−0.301681	+	0.522526i
$891$		0			0
$892$	9.17891			0.307333
$893$	−17.0895	+	29.5998i	−0.571877	+	0.990520i
$894$		0			0
$895$	−14.3578	−	24.8685i	−0.479929	−	0.831261i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−14.0000			−0.467186
$899$	−29.3578	−	50.8492i	−0.979138	−	1.69592i
$900$		0			0
$901$	7.50000	−	12.9904i	0.249861	−	0.432772i
$902$	−25.8211			−0.859748
$903$		0			0
$904$	2.17891	−	3.77398i	0.0724694	−	0.125521i
$905$	15.6422			0.519964
$906$		0			0
$907$	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
$909$		0			0
$910$	−3.00000	+	6.55744i	−0.0994490	+	0.217377i
$911$	16.7156			0.553814			0.276907	−	0.960897i	$-0.410691\pi$
$911$	16.7156			0.553814			0.276907	+	0.960897i	$0.410691\pi$
$912$		0			0
$913$	16.0000	+	27.7128i	0.529523	+	0.917160i
$914$	−15.9473	+	27.6215i	−0.527489	+	0.913637i
$915$		0			0
$916$	−0.500000	+	0.866025i	−0.0165205	+	0.0286143i
$917$	−9.76836	+	16.9193i	−0.322580	+	0.558725i
$918$		0			0
$919$	−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
$921$		0			0
$922$	−24.7156			−0.813966
$923$	19.1789	+	26.9713i	0.631281	+	0.887771i
$924$		0			0
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$	−14.4473	−	25.0234i	−0.474767	−	0.822320i
$927$		0			0
$928$	8.17891			0.268486
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	−0.345708	−	0.938342i	$-0.612361\pi$
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	0.985482	−	0.169779i	$-0.0543055\pi$
$930$		0			0
$931$	−8.17891			−0.268053
$932$	−0.178908	+	0.309878i	−0.00586034	+	0.0101504i
$933$		0			0
$934$	−16.9473	−	29.3535i	−0.554532	−	0.960477i
$935$	61.7891			2.02072
$936$		0			0
$937$	−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
$939$		0			0
$940$	4.17891	−	7.23808i	0.136301	−	0.236080i
$941$	20.0000			0.651981			0.325991	−	0.945373i	$-0.394302\pi$
$941$	20.0000			0.651981			0.325991	+	0.945373i	$0.394302\pi$
$942$		0			0
$943$	−6.64218	+	11.5046i	−0.216299	+	0.374641i
$944$	0.821092			0.0267243
$945$		0			0
$946$	−2.53673	−	4.39374i	−0.0824760	−	0.142853i
$947$	19.6262	+	33.9935i	0.637765	+	1.10464i	0.985922	+	0.167205i	$0.0534743\pi$
$947$	19.6262	+	33.9935i	0.637765	+	1.10464i	−0.348157	+	0.937436i	$0.613192\pi$
$948$		0			0
$949$	−6.00000	+	13.1149i	−0.194768	+	0.425727i
$950$	−8.17891			−0.265359
$951$		0			0
$952$	2.50000	+	4.33013i	0.0810255	+	0.140340i
$953$	21.3578	−	36.9928i	0.691848	−	1.19832i	−0.279384	−	0.960179i	$-0.590130\pi$
$953$	21.3578	−	36.9928i	0.691848	−	1.19832i	0.971232	−	0.238136i	$-0.0765363\pi$
$954$		0			0
$955$	27.5367	−	47.6950i	0.891067	−	1.54337i
$956$	−0.589454	+	1.02096i	−0.0190643	+	0.0330204i
$957$		0			0
$958$	14.9105	−	25.8258i	0.481738	−	0.834394i
$959$	8.17891	+	14.1663i	0.264111	+	0.457453i
$960$		0			0
$961$	20.5367			0.662475
$962$	4.17891	+	5.87680i	0.134733	+	0.189475i
$963$		0			0
$964$	9.17891	+	15.8983i	0.295633	+	0.512051i
$965$	−20.5367	−	35.5707i	−0.661101	−	1.14506i
$966$		0			0
$967$	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
$969$		0			0
$970$	−24.7156			−0.793571
$971$	−8.41055	+	14.5675i	−0.269907	+	0.467493i	−0.968838	−	0.247697i	$-0.920326\pi$
$971$	−8.41055	+	14.5675i	−0.269907	+	0.467493i	0.698930	+	0.715190i	$0.253660\pi$
$972$		0			0
$973$	−9.08945	−	15.7434i	−0.291395	−	0.504710i
$974$	38.1789			1.22333
$975$		0			0
$976$	−3.00000			−0.0960277
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	−27.8051	+	48.1598i	−0.888654	+	1.53919i
$980$	2.00000			0.0638877
$981$		0			0
$982$		0			0
$983$	−55.0735			−1.75657			−0.878285	−	0.478137i	$-0.841312\pi$
$983$	−55.0735			−1.75657			−0.878285	+	0.478137i	$0.841312\pi$
$984$		0			0
$985$	17.0000	+	29.4449i	0.541665	+	0.938191i
$986$	20.4473	+	35.4157i	0.651174	+	1.12787i
$987$		0			0
$988$	−29.3578	+	2.78346i	−0.933997	+	0.0885536i
$989$	−2.61018			−0.0829987
$990$		0			0
$991$	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
$993$		0			0
$994$	4.58945	−	7.94917i	0.145569	−	0.252132i
$995$	−12.8211	+	22.2068i	−0.406456	+	0.704002i
$996$		0			0
$997$	−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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.k.211.1	✓	4	3.2	odd	2
546.2.l.k.295.1	yes	4	39.35	odd	6
1638.2.r.ba.757.2		4	1.1	even	1	trivial
1638.2.r.ba.1387.2		4	13.9	even	3	inner
7098.2.a.bk.1.1		2	39.23	odd	6
7098.2.a.br.1.2		2	39.29	odd	6

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

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

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