LMFDB - Embedded newform 1638.2.r.ba.1387.1

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			1387.1
Root			$-2.58945 + 2.07237i$ of defining polynomial
Character	$\chi$	$=$	1638.1387
Dual form			1638.2.r.ba.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(-2.58945 + 4.48507i) q^{11} +(-1.50000 + 3.27872i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +(-1.58945 - 2.75302i) q^{19} +(-1.00000 - 1.73205i) q^{20} +(2.58945 + 4.48507i) q^{22} +(-4.08945 + 7.08314i) q^{23} -1.00000 q^{25} +(2.08945 + 2.93840i) q^{26} +(0.500000 - 0.866025i) q^{28} +(-1.58945 + 2.75302i) q^{29} +4.17891 q^{31} +(0.500000 + 0.866025i) q^{32} +5.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(-1.00000 + 1.73205i) q^{37} -3.17891 q^{38} -2.00000 q^{40} +(-3.58945 + 6.21712i) q^{41} +(-6.08945 - 10.5472i) q^{43} +5.17891 q^{44} +(4.08945 + 7.08314i) q^{46} +7.17891 q^{47} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.58945 - 0.340322i) q^{52} +3.00000 q^{53} +(-5.17891 + 8.97013i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(1.58945 + 2.75302i) q^{58} +(-6.08945 - 10.5472i) q^{59} +(1.50000 + 2.59808i) q^{61} +(2.08945 - 3.61904i) q^{62} +1.00000 q^{64} +(-3.00000 + 6.55744i) q^{65} +(1.91055 - 3.30916i) q^{67} +(2.50000 - 4.33013i) q^{68} +2.00000 q^{70} +(-1.08945 - 1.88699i) q^{71} +4.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.58945 + 2.75302i) q^{76} -5.17891 q^{77} +13.1789 q^{79} +(-1.00000 + 1.73205i) q^{80} +(3.58945 + 6.21712i) q^{82} -6.17891 q^{83} +(5.00000 + 8.66025i) q^{85} -12.1789 q^{86} +(2.58945 - 4.48507i) q^{88} +(4.50000 - 7.79423i) q^{89} +(-3.58945 + 0.340322i) q^{91} +8.17891 q^{92} +(3.58945 - 6.21712i) q^{94} +(-3.17891 - 5.50603i) q^{95} +(5.17891 + 8.97013i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$11$	−2.58945	+	4.48507i	−0.780750	+	1.35230i	0.150756	+	0.988571i	$0.451829\pi$
$11$	−2.58945	+	4.48507i	−0.780750	+	1.35230i	−0.931505	+	0.363727i	$0.881504\pi$
$12$		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	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$		0			0
$19$	−1.58945	−	2.75302i	−0.364646	−	0.631585i	0.624073	−	0.781366i	$-0.285477\pi$
$19$	−1.58945	−	2.75302i	−0.364646	−	0.631585i	−0.988719	+	0.149781i	$0.952143\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$	2.58945	+	4.48507i	0.552073	+	0.956219i
$23$	−4.08945	+	7.08314i	−0.852710	+	1.47694i	0.0260431	+	0.999661i	$0.491709\pi$
$23$	−4.08945	+	7.08314i	−0.852710	+	1.47694i	−0.878753	+	0.477276i	$0.841624\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.08945	+	2.93840i	0.409776	+	0.576267i
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−1.58945	+	2.75302i	−0.295154	+	0.511222i	−0.975021	−	0.222114i	$-0.928704\pi$
$29$	−1.58945	+	2.75302i	−0.295154	+	0.511222i	0.679867	+	0.733336i	$0.262038\pi$
$30$		0			0
$31$	4.17891			0.750554			0.375277	−	0.926913i	$-0.377548\pi$
$31$	4.17891			0.750554			0.375277	+	0.926913i	$0.377548\pi$
$32$	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	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−3.17891			−0.515687
$39$		0			0
$40$	−2.00000			−0.316228
$41$	−3.58945	+	6.21712i	−0.560579	+	0.970951i	0.436867	+	0.899526i	$0.356088\pi$
$41$	−3.58945	+	6.21712i	−0.560579	+	0.970951i	−0.997446	+	0.0714247i	$0.977245\pi$
$42$		0			0
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.785612	−	0.618720i	$-0.787652\pi$
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.143022	−	0.989720i	$-0.545682\pi$
$44$	5.17891			0.780750
$45$		0			0
$46$	4.08945	+	7.08314i	0.602957	+	1.04435i
$47$	7.17891			1.04715			0.523576	−	0.851979i	$-0.324598\pi$
$47$	7.17891			1.04715			0.523576	+	0.851979i	$0.324598\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	3.58945	−	0.340322i	0.497768	−	0.0471941i
$53$	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
$55$	−5.17891	+	8.97013i	−0.698324	+	1.20953i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	1.58945	+	2.75302i	0.208706	+	0.361489i
$59$	−6.08945	−	10.5472i	−0.792779	−	1.37313i	−0.924240	−	0.381813i	$-0.875300\pi$
$59$	−6.08945	−	10.5472i	−0.792779	−	1.37313i	0.131460	−	0.991321i	$-0.458033\pi$
$60$		0			0
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	0.945931	−	0.324367i	$-0.105151\pi$
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	−0.753876	+	0.657017i	$0.771818\pi$
$62$	2.08945	−	3.61904i	0.265361	−	0.459619i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	+	6.55744i	−0.372104	+	0.813350i
$66$		0			0
$67$	1.91055	−	3.30916i	0.233410	−	0.404279i	−0.725399	−	0.688328i	$-0.758345\pi$
$67$	1.91055	−	3.30916i	0.233410	−	0.404279i	0.958809	+	0.284050i	$0.0916781\pi$
$68$	2.50000	−	4.33013i	0.303170	−	0.525105i
$69$		0			0
$70$	2.00000			0.239046
$71$	−1.08945	−	1.88699i	−0.129294	−	0.223945i	0.794109	−	0.607775i	$-0.207938\pi$
$71$	−1.08945	−	1.88699i	−0.129294	−	0.223945i	−0.923403	+	0.383831i	$0.874605\pi$
$72$		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
$76$	−1.58945	+	2.75302i	−0.182323	+	0.315793i
$77$	−5.17891			−0.590191
$78$		0			0
$79$	13.1789			1.48274			0.741372	−	0.671095i	$-0.234176\pi$
$79$	13.1789			1.48274			0.741372	+	0.671095i	$0.234176\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$		0			0
$82$	3.58945	+	6.21712i	0.396389	+	0.686566i
$83$	−6.17891			−0.678223			−0.339112	−	0.940746i	$-0.610126\pi$
$83$	−6.17891			−0.678223			−0.339112	+	0.940746i	$0.610126\pi$
$84$		0			0
$85$	5.00000	+	8.66025i	0.542326	+	0.939336i
$86$	−12.1789			−1.31329
$87$		0			0
$88$	2.58945	−	4.48507i	0.276037	−	0.478110i
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	−0.522654	−	0.852545i	$-0.675058\pi$
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	0.999653	+	0.0263586i	$0.00839118\pi$
$90$		0			0
$91$	−3.58945	+	0.340322i	−0.376277	+	0.0356754i
$92$	8.17891			0.852710
$93$		0			0
$94$	3.58945	−	6.21712i	0.370224	−	0.641247i
$95$	−3.17891	−	5.50603i	−0.326149	−	0.564907i
$96$		0			0
$97$	5.17891	+	8.97013i	0.525838	+	0.910779i	0.999547	+	0.0300973i	$0.00958170\pi$
$97$	5.17891	+	8.97013i	0.525838	+	0.910779i	−0.473709	+	0.880682i	$0.657085\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.17891	−	5.50603i	0.316313	−	0.547871i	−0.663403	−	0.748263i	$-0.730888\pi$
$101$	3.17891	−	5.50603i	0.316313	−	0.547871i	0.979716	+	0.200392i	$0.0642216\pi$
$102$		0			0
$103$	−8.17891			−0.805892			−0.402946	−	0.915224i	$-0.632014\pi$
$103$	−8.17891			−0.805892			−0.402946	+	0.915224i	$0.632014\pi$
$104$	1.50000	−	3.27872i	0.147087	−	0.321505i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	9.58945	−	16.6094i	0.927048	−	1.60569i	0.138813	−	0.990319i	$-0.455671\pi$
$107$	9.58945	−	16.6094i	0.927048	−	1.60569i	0.788235	−	0.615375i	$-0.210995\pi$
$108$		0			0
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	5.17891	+	8.97013i	0.493790	+	0.855269i
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	9.17891	+	15.8983i	0.863479	+	1.49559i	0.868549	+	0.495602i	$0.165053\pi$
$113$	9.17891	+	15.8983i	0.863479	+	1.49559i	−0.00507042	+	0.999987i	$0.501614\pi$
$114$		0			0
$115$	−8.17891	+	14.1663i	−0.762687	+	1.32101i
$116$	3.17891			0.295154
$117$		0			0
$118$	−12.1789			−1.12116
$119$	−2.50000	+	4.33013i	−0.229175	+	0.396942i
$120$		0			0
$121$	−7.91055	−	13.7015i	−0.719141	−	1.24559i
$122$	3.00000			0.271607
$123$		0			0
$124$	−2.08945	−	3.61904i	−0.187639	−	0.324999i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	0.466870	+	0.884326i	$0.345382\pi$
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	−0.999284	+	0.0378419i	$0.987952\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	4.17891	+	5.87680i	0.366515	+	0.515429i
$131$	14.5367			1.27008			0.635040	−	0.772479i	$-0.280984\pi$
$131$	14.5367			1.27008			0.635040	+	0.772479i	$0.280984\pi$
$132$		0			0
$133$	1.58945	−	2.75302i	0.137823	−	0.238717i
$134$	−1.91055	−	3.30916i	−0.165046	−	0.285868i
$135$		0			0
$136$	−2.50000	−	4.33013i	−0.214373	−	0.371305i
$137$	3.17891	+	5.50603i	0.271592	+	0.470412i	0.969270	−	0.246000i	$-0.0791164\pi$
$137$	3.17891	+	5.50603i	0.271592	+	0.470412i	−0.697677	+	0.716412i	$0.745783\pi$
$138$		0			0
$139$	3.41055	+	5.90724i	0.289279	+	0.501045i	0.973638	−	0.228100i	$-0.0732512\pi$
$139$	3.41055	+	5.90724i	0.289279	+	0.501045i	−0.684359	+	0.729145i	$0.739918\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	−2.17891			−0.182850
$143$	−10.8211	−	15.2177i	−0.904905	−	1.27257i
$144$		0			0
$145$	−3.17891	+	5.50603i	−0.263994	+	0.457251i
$146$	2.00000	−	3.46410i	0.165521	−	0.286691i
$147$		0			0
$148$	2.00000			0.164399
$149$	8.08945	+	14.0113i	0.662714	+	1.14785i	0.979900	+	0.199491i	$0.0639288\pi$
$149$	8.08945	+	14.0113i	0.662714	+	1.14785i	−0.317186	+	0.948363i	$0.602738\pi$
$150$		0			0
$151$	19.5367			1.58988			0.794938	−	0.606691i	$-0.207503\pi$
$151$	19.5367			1.58988			0.794938	+	0.606691i	$0.207503\pi$
$152$	1.58945	+	2.75302i	0.128922	+	0.223299i
$153$		0			0
$154$	−2.58945	+	4.48507i	−0.208664	+	0.361417i
$155$	8.35782			0.671316
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	6.58945	−	11.4133i	0.524229	−	0.907991i
$159$		0			0
$160$	1.00000	+	1.73205i	0.0790569	+	0.136931i
$161$	−8.17891			−0.644588
$162$		0			0
$163$	10.0895	+	17.4754i	0.790267	+	1.36878i	0.925801	+	0.378010i	$0.123392\pi$
$163$	10.0895	+	17.4754i	0.790267	+	1.36878i	−0.135534	+	0.990773i	$0.543275\pi$
$164$	7.17891			0.560579
$165$		0			0
$166$	−3.08945	+	5.35109i	−0.239788	+	0.415325i
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$		0			0
$169$	−8.50000	−	9.83616i	−0.653846	−	0.756628i
$170$	10.0000			0.766965
$171$		0			0
$172$	−6.08945	+	10.5472i	−0.464317	+	0.804220i
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−2.58945	−	4.48507i	−0.195187	−	0.338075i
$177$		0			0
$178$	−4.50000	−	7.79423i	−0.337289	−	0.584202i
$179$	4.17891	−	7.23808i	0.312346	−	0.541000i	−0.666524	−	0.745484i	$-0.732218\pi$
$179$	4.17891	−	7.23808i	0.312346	−	0.541000i	0.978870	+	0.204484i	$0.0655518\pi$
$180$		0			0
$181$	19.1789			1.42556			0.712779	−	0.701389i	$-0.247436\pi$
$181$	19.1789			1.42556			0.712779	+	0.701389i	$0.247436\pi$
$182$	−1.50000	+	3.27872i	−0.111187	+	0.243035i
$183$		0			0
$184$	4.08945	−	7.08314i	0.301479	−	0.522176i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	−25.8945			−1.89360
$188$	−3.58945	−	6.21712i	−0.261788	−	0.453430i
$189$		0			0
$190$	−6.35782			−0.461245
$191$	−3.26836	−	5.66097i	−0.236490	−	0.409613i	0.723214	−	0.690624i	$-0.242664\pi$
$191$	−3.26836	−	5.66097i	−0.236490	−	0.409613i	−0.959705	+	0.281010i	$0.909331\pi$
$192$		0			0
$193$	6.76836	−	11.7231i	0.487197	−	0.843851i	−0.512694	−	0.858571i	$-0.671353\pi$
$193$	6.76836	−	11.7231i	0.487197	−	0.843851i	0.999892	+	0.0147206i	$0.00468589\pi$
$194$	10.3578			0.743648
$195$		0			0
$196$	1.00000			0.0714286
$197$	8.50000	−	14.7224i	0.605600	−	1.04893i	−0.386356	−	0.922350i	$-0.626267\pi$
$197$	8.50000	−	14.7224i	0.605600	−	1.04893i	0.991956	−	0.126580i	$-0.0404001\pi$
$198$		0			0
$199$	−12.0895	−	20.9395i	−0.856999	−	1.48437i	−0.874778	−	0.484523i	$-0.838993\pi$
$199$	−12.0895	−	20.9395i	−0.856999	−	1.48437i	0.0177797	−	0.999842i	$-0.494340\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$	−3.17891	−	5.50603i	−0.223667	−	0.387403i
$203$	−3.17891			−0.223116
$204$		0			0
$205$	−7.17891	+	12.4342i	−0.501397	+	0.868445i
$206$	−4.08945	+	7.08314i	−0.284926	+	0.493506i
$207$		0			0
$208$	−2.08945	−	2.93840i	−0.144878	−	0.203741i
$209$	16.4633			1.13879
$210$		0			0
$211$	3.17891	−	5.50603i	0.218845	−	0.379051i	−0.735610	−	0.677405i	$-0.763104\pi$
$211$	3.17891	−	5.50603i	0.218845	−	0.379051i	0.954455	+	0.298354i	$0.0964377\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$		0			0
$214$	−9.58945	−	16.6094i	−0.655522	−	1.13540i
$215$	−12.1789	−	21.0945i	−0.830595	−	1.43863i
$216$		0			0
$217$	2.08945	+	3.61904i	0.141841	+	0.245676i
$218$	2.00000	−	3.46410i	0.135457	−	0.234619i
$219$		0			0
$220$	10.3578			0.698324
$221$	−17.9473	+	1.70161i	−1.20726	+	0.114463i
$222$		0			0
$223$	1.08945	−	1.88699i	0.0729552	−	0.126362i	−0.827240	−	0.561849i	$-0.810090\pi$
$223$	1.08945	−	1.88699i	0.0729552	−	0.126362i	0.900195	+	0.435487i	$0.143424\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$	18.3578			1.22114
$227$	−7.17891	−	12.4342i	−0.476481	−	0.825289i	0.523156	−	0.852237i	$-0.324755\pi$
$227$	−7.17891	−	12.4342i	−0.476481	−	0.825289i	−0.999637	+	0.0269479i	$0.991421\pi$
$228$		0			0
$229$	1.00000			0.0660819			0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000			0.0660819			0.0330409	+	0.999454i	$0.489481\pi$
$230$	8.17891	+	14.1663i	0.539301	+	0.934097i
$231$		0			0
$232$	1.58945	−	2.75302i	0.104353	−	0.180744i
$233$	−22.3578			−1.46471			−0.732355	−	0.680923i	$-0.761579\pi$
$233$	−22.3578			−1.46471			−0.732355	+	0.680923i	$0.761579\pi$
$234$		0			0
$235$	14.3578			0.936601
$236$	−6.08945	+	10.5472i	−0.396390	+	0.686567i
$237$		0			0
$238$	2.50000	+	4.33013i	0.162051	+	0.280680i
$239$	−10.1789			−0.658419			−0.329209	−	0.944257i	$-0.606782\pi$
$239$	−10.1789			−0.658419			−0.329209	+	0.944257i	$0.606782\pi$
$240$		0			0
$241$	−2.17891	−	3.77398i	−0.140356	−	0.243103i	0.787275	−	0.616602i	$-0.211491\pi$
$241$	−2.17891	−	3.77398i	−0.140356	−	0.243103i	−0.927631	+	0.373499i	$0.878158\pi$
$242$	−15.8211			−1.01702
$243$		0			0
$244$	1.50000	−	2.59808i	0.0960277	−	0.166325i
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	11.4105	−	1.08185i	0.726036	−	0.0688365i
$248$	−4.17891			−0.265361
$249$		0			0
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	11.0895	+	19.2075i	0.699960	+	1.21237i	0.968480	+	0.249092i	$0.0801323\pi$
$251$	11.0895	+	19.2075i	0.699960	+	1.21237i	−0.268520	+	0.963274i	$0.586534\pi$
$252$		0			0
$253$	−21.1789	−	36.6829i	−1.33151	−	2.30624i
$254$	6.00000	+	10.3923i	0.376473	+	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.85782	+	17.0742i	−0.614914	+	1.06506i	0.375486	+	0.926828i	$0.377476\pi$
$257$	−9.85782	+	17.0742i	−0.614914	+	1.06506i	−0.990400	+	0.138234i	$0.955857\pi$
$258$		0			0
$259$	−2.00000			−0.124274
$260$	7.17891	−	0.680643i	0.445217	−	0.0422117i
$261$		0			0
$262$	7.26836	−	12.5892i	0.449041	−	0.777762i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$	−1.58945	−	2.75302i	−0.0974557	−	0.168798i
$267$		0			0
$268$	−3.82109			−0.233410
$269$	−2.17891	−	3.77398i	−0.132850	−	0.230104i	0.791924	−	0.610620i	$-0.209080\pi$
$269$	−2.17891	−	3.77398i	−0.132850	−	0.230104i	−0.924774	+	0.380516i	$0.875746\pi$
$270$		0			0
$271$	−9.91055	+	17.1656i	−0.602023	+	1.04273i	0.390492	+	0.920606i	$0.372305\pi$
$271$	−9.91055	+	17.1656i	−0.602023	+	1.04273i	−0.992514	+	0.122128i	$0.961028\pi$
$272$	−5.00000			−0.303170
$273$		0			0
$274$	6.35782			0.384090
$275$	2.58945	−	4.48507i	0.156150	−	0.270460i
$276$		0			0
$277$	−2.82109	−	4.88627i	−0.169503	−	0.293588i	0.768742	−	0.639559i	$-0.220883\pi$
$277$	−2.82109	−	4.88627i	−0.169503	−	0.293588i	−0.938245	+	0.345971i	$0.887550\pi$
$278$	6.82109			0.409102
$279$		0			0
$280$	−1.00000	−	1.73205i	−0.0597614	−	0.103510i
$281$	−28.3578			−1.69169			−0.845843	−	0.533432i	$-0.820902\pi$
$281$	−28.3578			−1.69169			−0.845843	+	0.533432i	$0.820902\pi$
$282$		0			0
$283$	−3.82109	+	6.61832i	−0.227140	+	0.393419i	−0.956959	−	0.290222i	$-0.906271\pi$
$283$	−3.82109	+	6.61832i	−0.227140	+	0.393419i	0.729819	+	0.683640i	$0.239604\pi$
$284$	−1.08945	+	1.88699i	−0.0646472	+	0.111972i
$285$		0			0
$286$	−18.5895	+	1.76249i	−1.09922	+	0.104218i
$287$	−7.17891			−0.423758
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	3.17891	+	5.50603i	0.186672	+	0.323325i
$291$		0			0
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	0.986341	−	0.164714i	$-0.0526703\pi$
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	−0.635818	+	0.771839i	$0.719337\pi$
$294$		0			0
$295$	−12.1789	−	21.0945i	−0.709083	−	1.22817i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$		0			0
$298$	16.1789			0.937219
$299$	−17.0895	−	24.0329i	−0.988309	−	1.38986i
$300$		0			0
$301$	6.08945	−	10.5472i	0.350990	−	0.607933i
$302$	9.76836	−	16.9193i	0.562106	−	0.973596i
$303$		0			0
$304$	3.17891			0.182323
$305$	3.00000	+	5.19615i	0.171780	+	0.297531i
$306$		0			0
$307$	−31.8945			−1.82032			−0.910159	−	0.414259i	$-0.864041\pi$
$307$	−31.8945			−1.82032			−0.910159	+	0.414259i	$0.864041\pi$
$308$	2.58945	+	4.48507i	0.147548	+	0.255560i
$309$		0			0
$310$	4.17891	−	7.23808i	0.237346	−	0.411095i
$311$	−25.5367			−1.44805			−0.724027	−	0.689771i	$-0.757711\pi$
$311$	−25.5367			−1.44805			−0.724027	+	0.689771i	$0.757711\pi$
$312$		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
$316$	−6.58945	−	11.4133i	−0.370686	−	0.642047i
$317$	4.17891			0.234711			0.117355	−	0.993090i	$-0.462558\pi$
$317$	4.17891			0.234711			0.117355	+	0.993090i	$0.462558\pi$
$318$		0			0
$319$	−8.23164	−	14.2576i	−0.460883	−	0.798273i
$320$	2.00000			0.111803
$321$		0			0
$322$	−4.08945	+	7.08314i	−0.227896	+	0.394728i
$323$	7.94727	−	13.7651i	0.442198	−	0.765909i
$324$		0			0
$325$	1.50000	−	3.27872i	0.0832050	−	0.181871i
$326$	20.1789			1.11761
$327$		0			0
$328$	3.58945	−	6.21712i	0.198194	−	0.343283i
$329$	3.58945	+	6.21712i	0.197893	+	0.342761i
$330$		0			0
$331$	0.821092	+	1.42217i	0.0451313	+	0.0781697i	0.887709	−	0.460406i	$-0.152296\pi$
$331$	0.821092	+	1.42217i	0.0451313	+	0.0781697i	−0.842577	+	0.538575i	$0.818963\pi$
$332$	3.08945	+	5.35109i	0.169556	+	0.293679i
$333$		0			0
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	3.82109	−	6.61832i	0.208769	−	0.361598i
$336$		0			0
$337$	33.5367			1.82686			0.913431	−	0.406994i	$-0.133423\pi$
$337$	33.5367			1.82686			0.913431	+	0.406994i	$0.133423\pi$
$338$	−12.7684	+	2.44314i	−0.694507	+	0.132889i
$339$		0			0
$340$	5.00000	−	8.66025i	0.271163	−	0.469668i
$341$	−10.8211	+	18.7427i	−0.585995	+	1.01497i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	6.08945	+	10.5472i	0.328321	+	0.568669i
$345$		0			0
$346$	4.00000			0.215041
$347$	−9.58945	−	16.6094i	−0.514789	−	0.891640i	−0.999853	−	0.0171617i	$-0.994537\pi$
$347$	−9.58945	−	16.6094i	−0.514789	−	0.891640i	0.485064	−	0.874479i	$-0.338796\pi$
$348$		0			0
$349$	−4.08945	+	7.08314i	−0.218903	+	0.379152i	−0.954473	−	0.298297i	$-0.903581\pi$
$349$	−4.08945	+	7.08314i	−0.218903	+	0.379152i	0.735570	+	0.677449i	$0.236915\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	−5.17891			−0.276037
$353$	2.08945	−	3.61904i	0.111210	−	0.192622i	−0.805048	−	0.593209i	$-0.797861\pi$
$353$	2.08945	−	3.61904i	0.111210	−	0.192622i	0.916259	+	0.400587i	$0.131194\pi$
$354$		0			0
$355$	−2.17891	−	3.77398i	−0.115644	−	0.200302i
$356$	−9.00000			−0.476999
$357$		0			0
$358$	−4.17891	−	7.23808i	−0.220862	−	0.382544i
$359$	10.3578			0.546665			0.273332	−	0.961920i	$-0.411874\pi$
$359$	10.3578			0.546665			0.273332	+	0.961920i	$0.411874\pi$
$360$		0			0
$361$	4.44727	−	7.70290i	0.234067	−	0.405416i
$362$	9.58945	−	16.6094i	0.504011	−	0.872972i
$363$		0			0
$364$	2.08945	+	2.93840i	0.109517	+	0.154014i
$365$	8.00000			0.418739
$366$		0			0
$367$	4.08945	−	7.08314i	0.213468	−	0.369737i	−0.739330	−	0.673344i	$-0.764857\pi$
$367$	4.08945	−	7.08314i	0.213468	−	0.369737i	0.952797	+	0.303607i	$0.0981908\pi$
$368$	−4.08945	−	7.08314i	−0.213178	−	0.369234i
$369$		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	0.999787	+	0.0206542i	$0.00657489\pi$
$373$	10.0000	+	17.3205i	0.517780	+	0.896822i	−0.482006	+	0.876168i	$0.660092\pi$
$374$	−12.9473	+	22.4253i	−0.669487	+	1.15959i
$375$		0			0
$376$	−7.17891			−0.370224
$377$	−6.64218	−	9.34090i	−0.342090	−	0.481081i
$378$		0			0
$379$	12.3578	−	21.4044i	0.634778	−	1.09947i	−0.351784	−	0.936081i	$-0.614425\pi$
$379$	12.3578	−	21.4044i	0.634778	−	1.09947i	0.986562	−	0.163387i	$-0.0522420\pi$
$380$	−3.17891	+	5.50603i	−0.163075	+	0.282453i
$381$		0			0
$382$	−6.53673			−0.334448
$383$	10.5895	+	18.3415i	0.541096	+	0.937205i	0.998841	+	0.0481223i	$0.0153237\pi$
$383$	10.5895	+	18.3415i	0.541096	+	0.937205i	−0.457746	+	0.889083i	$0.651343\pi$
$384$		0			0
$385$	−10.3578			−0.527883
$386$	−6.76836	−	11.7231i	−0.344501	−	0.596693i
$387$		0			0
$388$	5.17891	−	8.97013i	0.262919	−	0.455389i
$389$	12.1789			0.617495			0.308748	−	0.951144i	$-0.400090\pi$
$389$	12.1789			0.617495			0.308748	+	0.951144i	$0.400090\pi$
$390$		0			0
$391$	−40.8945			−2.06813
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	−8.50000	−	14.7224i	−0.428224	−	0.741705i
$395$	26.3578			1.32621
$396$		0			0
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	0.825926	−	0.563778i	$-0.190653\pi$
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	−0.901209	+	0.433384i	$0.857319\pi$
$398$	−24.1789			−1.21198
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	4.82109	−	8.35038i	0.240754	−	0.416998i	−0.720175	−	0.693792i	$-0.755939\pi$
$401$	4.82109	−	8.35038i	0.240754	−	0.416998i	0.960929	+	0.276794i	$0.0892720\pi$
$402$		0			0
$403$	−6.26836	+	13.7015i	−0.312249	+	0.682519i
$404$	−6.35782			−0.316313
$405$		0			0
$406$	−1.58945	+	2.75302i	−0.0788833	+	0.136630i
$407$	−5.17891	−	8.97013i	−0.256709	−	0.444633i
$408$		0			0
$409$	18.1789	+	31.4868i	0.898889	+	1.55692i	0.828916	+	0.559373i	$0.188958\pi$
$409$	18.1789	+	31.4868i	0.898889	+	1.55692i	0.0699730	+	0.997549i	$0.477709\pi$
$410$	7.17891	+	12.4342i	0.354541	+	0.614083i
$411$		0			0
$412$	4.08945	+	7.08314i	0.201473	+	0.348961i
$413$	6.08945	−	10.5472i	0.299642	−	0.518996i
$414$		0			0
$415$	−12.3578			−0.606621
$416$	−3.58945	+	0.340322i	−0.175987	+	0.0166856i
$417$		0			0
$418$	8.23164	−	14.2576i	0.402623	−	0.697363i
$419$	−13.4473	+	23.2914i	−0.656942	+	1.13786i	0.324461	+	0.945899i	$0.394817\pi$
$419$	−13.4473	+	23.2914i	−0.656942	+	1.13786i	−0.981403	+	0.191958i	$0.938516\pi$
$420$		0			0
$421$	10.7156			0.522248			0.261124	−	0.965305i	$-0.415907\pi$
$421$	10.7156			0.522248			0.261124	+	0.965305i	$0.415907\pi$
$422$	−3.17891	−	5.50603i	−0.154747	−	0.268029i
$423$		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
$428$	−19.1789			−0.927048
$429$		0			0
$430$	−24.3578			−1.17464
$431$	5.08945	−	8.81519i	0.245150	−	0.424613i	−0.717024	−	0.697049i	$-0.754496\pi$
$431$	5.08945	−	8.81519i	0.245150	−	0.424613i	0.962174	+	0.272436i	$0.0878293\pi$
$432$		0			0
$433$	−17.1789	−	29.7547i	−0.825566	−	1.42992i	−0.901486	−	0.432808i	$-0.857523\pi$
$433$	−17.1789	−	29.7547i	−0.825566	−	1.42992i	0.0759206	−	0.997114i	$-0.475810\pi$
$434$	4.17891			0.200594
$435$		0			0
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	26.0000			1.24375
$438$		0			0
$439$	−20.3578	+	35.2608i	−0.971626	+	1.68290i	−0.280977	+	0.959715i	$0.590658\pi$
$439$	−20.3578	+	35.2608i	−0.971626	+	1.68290i	−0.690649	+	0.723190i	$0.742675\pi$
$440$	5.17891	−	8.97013i	0.246895	−	0.427634i
$441$		0			0
$442$	−7.50000	+	16.3936i	−0.356739	+	0.779764i
$443$	−3.17891			−0.151034			−0.0755172	−	0.997144i	$-0.524061\pi$
$443$	−3.17891			−0.151034			−0.0755172	+	0.997144i	$0.524061\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−1.08945	−	1.88699i	−0.0515872	−	0.0893516i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	0.652230	−	0.758021i	$-0.273834\pi$
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	−0.982581	+	0.185837i	$0.940500\pi$
$450$		0			0
$451$	−18.5895	−	32.1979i	−0.875343	−	1.51614i
$452$	9.17891	−	15.8983i	0.431740	−	0.747795i
$453$		0			0
$454$	−14.3578			−0.673846
$455$	−7.17891	+	0.680643i	−0.336552	+	0.0319090i
$456$		0			0
$457$	−12.4473	+	21.5593i	−0.582259	+	1.00850i	0.412952	+	0.910753i	$0.364498\pi$
$457$	−12.4473	+	21.5593i	−0.582259	+	1.00850i	−0.995211	+	0.0977491i	$0.968836\pi$
$458$	0.500000	−	0.866025i	0.0233635	−	0.0404667i
$459$		0			0
$460$	16.3578			0.762687
$461$	10.3578	+	17.9403i	0.482412	+	0.835561i	0.999796	−	0.0201916i	$-0.00642763\pi$
$461$	10.3578	+	17.9403i	0.482412	+	0.835561i	−0.517385	+	0.855753i	$0.673094\pi$
$462$		0			0
$463$	27.8945			1.29637			0.648185	−	0.761483i	$-0.275528\pi$
$463$	27.8945			1.29637			0.648185	+	0.761483i	$0.275528\pi$
$464$	−1.58945	−	2.75302i	−0.0737886	−	0.127806i
$465$		0			0
$466$	−11.1789	+	19.3624i	−0.517853	+	0.896948i
$467$	22.8945			1.05943			0.529717	−	0.848175i	$-0.322298\pi$
$467$	22.8945			1.05943			0.529717	+	0.848175i	$0.322298\pi$
$468$		0			0
$469$	3.82109			0.176442
$470$	7.17891	−	12.4342i	0.331138	−	0.573548i
$471$		0			0
$472$	6.08945	+	10.5472i	0.280290	+	0.485476i
$473$	63.0735			2.90012
$474$		0			0
$475$	1.58945	+	2.75302i	0.0729292	+	0.126317i
$476$	5.00000			0.229175
$477$		0			0
$478$	−5.08945	+	8.81519i	−0.232786	+	0.403198i
$479$	−20.5895	+	35.6620i	−0.940756	+	1.62944i	−0.176723	+	0.984261i	$0.556550\pi$
$479$	−20.5895	+	35.6620i	−0.940756	+	1.62944i	−0.764033	+	0.645177i	$0.776784\pi$
$480$		0			0
$481$	−4.17891	−	5.87680i	−0.190542	−	0.267959i
$482$	−4.35782			−0.198493
$483$		0			0
$484$	−7.91055	+	13.7015i	−0.359570	+	0.622794i
$485$	10.3578	+	17.9403i	0.470324	+	0.814625i
$486$		0			0
$487$	13.4105	+	23.2277i	0.607690	+	1.05255i	0.991620	+	0.129188i	$0.0412369\pi$
$487$	13.4105	+	23.2277i	0.607690	+	1.05255i	−0.383930	+	0.923362i	$0.625430\pi$
$488$	−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	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$	−15.8945			−0.715854
$494$	4.76836	−	10.4227i	0.214539	−	0.468942i
$495$		0			0
$496$	−2.08945	+	3.61904i	−0.0938193	+	0.162500i
$497$	1.08945	−	1.88699i	0.0488687	−	0.0846431i
$498$		0			0
$499$	8.17891			0.366138			0.183069	−	0.983100i	$-0.441397\pi$
$499$	8.17891			0.366138			0.183069	+	0.983100i	$0.441397\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	22.1789			0.989893
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	−0.999161	−	0.0409609i	$-0.986958\pi$
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	0.464107	−	0.885779i	$-0.346375\pi$
$504$		0			0
$505$	6.35782	−	11.0121i	0.282919	−	0.490030i
$506$	−42.3578			−1.88303
$507$		0			0
$508$	12.0000			0.532414
$509$	−8.35782	+	14.4762i	−0.370454	+	0.641645i	−0.989635	−	0.143603i	$-0.954131\pi$
$509$	−8.35782	+	14.4762i	−0.370454	+	0.641645i	0.619182	+	0.785248i	$0.287464\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	9.85782	+	17.0742i	0.434810	+	0.753112i
$515$	−16.3578			−0.720812
$516$		0			0
$517$	−18.5895	+	32.1979i	−0.817563	+	1.41606i
$518$	−1.00000	+	1.73205i	−0.0439375	+	0.0761019i
$519$		0			0
$520$	3.00000	−	6.55744i	0.131559	−	0.287563i
$521$	−7.17891			−0.314514			−0.157257	−	0.987558i	$-0.550265\pi$
$521$	−7.17891			−0.314514			−0.157257	+	0.987558i	$0.550265\pi$
$522$		0			0
$523$	−5.76836	+	9.99110i	−0.252233	+	0.436880i	−0.964140	−	0.265393i	$-0.914498\pi$
$523$	−5.76836	+	9.99110i	−0.252233	+	0.436880i	0.711907	+	0.702273i	$0.247832\pi$
$524$	−7.26836	−	12.5892i	−0.317520	−	0.549961i
$525$		0			0
$526$	6.00000	+	10.3923i	0.261612	+	0.453126i
$527$	10.4473	+	18.0952i	0.455090	+	0.788239i
$528$		0			0
$529$	−21.9473	−	38.0138i	−0.954229	−	1.65277i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$		0			0
$532$	−3.17891			−0.137823
$533$	−15.0000	−	21.0945i	−0.649722	−	0.913704i
$534$		0			0
$535$	19.1789	−	33.2188i	0.829177	−	1.43618i
$536$	−1.91055	+	3.30916i	−0.0825230	+	0.142934i
$537$		0			0
$538$	−4.35782			−0.187879
$539$	−2.58945	−	4.48507i	−0.111536	−	0.193185i
$540$		0			0
$541$	−20.3578			−0.875251			−0.437625	−	0.899157i	$-0.644180\pi$
$541$	−20.3578			−0.875251			−0.437625	+	0.899157i	$0.644180\pi$
$542$	9.91055	+	17.1656i	0.425694	+	0.737324i
$543$		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	$0.220443\pi$
$548$	3.17891	−	5.50603i	0.135796	−	0.235206i
$549$		0			0
$550$	−2.58945	−	4.48507i	−0.110415	−	0.191244i
$551$	10.1055			0.430507
$552$		0			0
$553$	6.58945	+	11.4133i	0.280212	+	0.485342i
$554$	−5.64218			−0.239713
$555$		0			0
$556$	3.41055	−	5.90724i	0.144639	−	0.250523i
$557$	11.8578	−	20.5383i	0.502432	−	0.870237i	−0.497564	−	0.867427i	$-0.665772\pi$
$557$	11.8578	−	20.5383i	0.502432	−	0.870237i	0.999996	−	0.00281030i	$-0.000894548\pi$
$558$		0			0
$559$	43.7156	−	4.14474i	1.84897	−	0.175304i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	−14.1789	+	24.5586i	−0.598101	+	1.03594i
$563$	−9.17891	−	15.8983i	−0.386845	−	0.670035i	0.605178	−	0.796090i	$-0.293102\pi$
$563$	−9.17891	−	15.8983i	−0.386845	−	0.670035i	−0.992023	+	0.126055i	$0.959768\pi$
$564$		0			0
$565$	18.3578	+	31.7967i	0.772319	+	1.33770i
$566$	3.82109	+	6.61832i	0.160612	+	0.278189i
$567$		0			0
$568$	1.08945	+	1.88699i	0.0457125	+	0.0791763i
$569$	−1.82109	+	3.15422i	−0.0763441	+	0.132232i	−0.901670	−	0.432425i	$-0.857658\pi$
$569$	−1.82109	+	3.15422i	−0.0763441	+	0.132232i	0.825326	+	0.564657i	$0.190991\pi$
$570$		0			0
$571$	−34.1789			−1.43034			−0.715171	−	0.698949i	$-0.753651\pi$
$571$	−34.1789			−1.43034			−0.715171	+	0.698949i	$0.753651\pi$
$572$	−7.76836	+	16.9802i	−0.324812	+	0.709977i
$573$		0			0
$574$	−3.58945	+	6.21712i	−0.149821	+	0.259497i
$575$	4.08945	−	7.08314i	0.170542	−	0.295387i
$576$		0			0
$577$	−28.3578			−1.18055			−0.590276	−	0.807202i	$-0.700981\pi$
$577$	−28.3578			−1.18055			−0.590276	+	0.807202i	$0.700981\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$		0			0
$580$	6.35782			0.263994
$581$	−3.08945	−	5.35109i	−0.128172	−	0.222001i
$582$		0			0
$583$	−7.76836	+	13.4552i	−0.321733	+	0.557257i
$584$	−4.00000			−0.165521
$585$		0			0
$586$	12.0000			0.495715
$587$	0.0894542	−	0.154939i	0.00369217	−	0.00639502i	−0.864173	−	0.503194i	$-0.832158\pi$
$587$	0.0894542	−	0.154939i	0.00369217	−	0.00639502i	0.867866	+	0.496799i	$0.165491\pi$
$588$		0			0
$589$	−6.64218	−	11.5046i	−0.273686	−	0.474039i
$590$	−24.3578			−1.00280
$591$		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
$596$	8.08945	−	14.0113i	0.331357	−	0.573927i
$597$		0			0
$598$	−29.3578	+	2.78346i	−1.20053	+	0.113824i
$599$	−40.1789			−1.64167			−0.820833	−	0.571168i	$-0.806490\pi$
$599$	−40.1789			−1.64167			−0.820833	+	0.571168i	$0.806490\pi$
$600$		0			0
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	−0.549602	−	0.835426i	$-0.685221\pi$
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	0.998302	+	0.0582563i	$0.0185541\pi$
$602$	−6.08945	−	10.5472i	−0.248188	−	0.429874i
$603$		0			0
$604$	−9.76836	−	16.9193i	−0.397469	−	0.688437i
$605$	−15.8211	−	27.4029i	−0.643219	−	1.11409i
$606$		0			0
$607$	0.268363	+	0.464818i	0.0108925	+	0.0188664i	0.871420	−	0.490537i	$-0.163199\pi$
$607$	0.268363	+	0.464818i	0.0108925	+	0.0188664i	−0.860528	+	0.509404i	$0.829866\pi$
$608$	1.58945	−	2.75302i	0.0644609	−	0.111650i
$609$		0			0
$610$	6.00000			0.242933
$611$	−10.7684	+	23.5376i	−0.435641	+	0.952230i
$612$		0			0
$613$	−7.82109	+	13.5465i	−0.315891	+	0.547139i	−0.979626	−	0.200828i	$-0.935637\pi$
$613$	−7.82109	+	13.5465i	−0.315891	+	0.547139i	0.663736	+	0.747967i	$0.268970\pi$
$614$	−15.9473	+	27.6215i	−0.643579	+	1.11471i
$615$		0			0
$616$	5.17891			0.208664
$617$	16.0000	+	27.7128i	0.644136	+	1.11568i	0.984500	+	0.175382i	$0.0561162\pi$
$617$	16.0000	+	27.7128i	0.644136	+	1.11568i	−0.340365	+	0.940294i	$0.610551\pi$
$618$		0			0
$619$	25.5367			1.02641			0.513204	−	0.858267i	$-0.328458\pi$
$619$	25.5367			1.02641			0.513204	+	0.858267i	$0.328458\pi$
$620$	−4.17891	−	7.23808i	−0.167829	−	0.290688i
$621$		0			0
$622$	−12.7684	+	22.1155i	−0.511965	+	0.886749i
$623$	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
$631$	−12.9473	−	22.4253i	−0.515423	−	0.892738i	−0.999840	−	0.0179011i	$-0.994302\pi$
$631$	−12.9473	−	22.4253i	−0.515423	−	0.892738i	0.484417	−	0.874837i	$-0.339032\pi$
$632$	−13.1789			−0.524229
$633$		0			0
$634$	2.08945	−	3.61904i	0.0829828	−	0.143730i
$635$	−12.0000	+	20.7846i	−0.476205	+	0.824812i
$636$		0			0
$637$	−2.08945	−	2.93840i	−0.0827872	−	0.116424i
$638$	−16.4633			−0.651787
$639$		0			0
$640$	1.00000	−	1.73205i	0.0395285	−	0.0684653i
$641$	13.5367	+	23.4463i	0.534668	+	0.926073i	0.999179	+	0.0405056i	$0.0128968\pi$
$641$	13.5367	+	23.4463i	0.534668	+	0.926073i	−0.464511	+	0.885567i	$0.653770\pi$
$642$		0			0
$643$	4.41055	+	7.63929i	0.173935	+	0.301264i	0.939792	−	0.341746i	$-0.111018\pi$
$643$	4.41055	+	7.63929i	0.173935	+	0.301264i	−0.765857	+	0.643011i	$0.777685\pi$
$644$	4.08945	+	7.08314i	0.161147	+	0.279115i
$645$		0			0
$646$	−7.94727	−	13.7651i	−0.312681	−	0.541580i
$647$	23.9473	−	41.4779i	0.941464	−	1.63066i	0.178784	−	0.983888i	$-0.442784\pi$
$647$	23.9473	−	41.4779i	0.941464	−	1.63066i	0.762680	−	0.646776i	$-0.223883\pi$
$648$		0			0
$649$	63.0735			2.47585
$650$	−2.08945	−	2.93840i	−0.0819551	−	0.115253i
$651$		0			0
$652$	10.0895	−	17.4754i	0.395134	−	0.684391i
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	−0.584091	−	0.811688i	$-0.698549\pi$
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	0.994988	+	0.0999939i	$0.0318823\pi$
$654$		0			0
$655$	29.0735			1.13599
$656$	−3.58945	−	6.21712i	−0.140145	−	0.242738i
$657$		0			0
$658$	7.17891			0.279863
$659$	8.76836	+	15.1872i	0.341567	+	0.591611i	0.984724	−	0.174123i	$-0.0557091\pi$
$659$	8.76836	+	15.1872i	0.341567	+	0.591611i	−0.643157	+	0.765734i	$0.722376\pi$
$660$		0			0
$661$	−8.26836	+	14.3212i	−0.321602	+	0.557031i	−0.980819	−	0.194922i	$-0.937555\pi$
$661$	−8.26836	+	14.3212i	−0.321602	+	0.557031i	0.659217	+	0.751953i	$0.270888\pi$
$662$	1.64218			0.0638253
$663$		0			0
$664$	6.17891			0.239788
$665$	3.17891	−	5.50603i	0.123273	−	0.213515i
$666$		0			0
$667$	−13.0000	−	22.5167i	−0.503362	−	0.871849i
$668$	8.00000			0.309529
$669$		0			0
$670$	−3.82109	−	6.61832i	−0.147622	−	0.255688i
$671$	−15.5367			−0.599789
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	16.7684	−	29.0437i	0.645893	−	1.11872i
$675$		0			0
$676$	−4.26836	+	12.2793i	−0.164168	+	0.472281i
$677$	−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
$679$	−5.17891	+	8.97013i	−0.198748	+	0.344242i
$680$	−5.00000	−	8.66025i	−0.191741	−	0.332106i
$681$		0			0
$682$	10.8211	+	18.7427i	0.414361	+	0.717694i
$683$	4.17891	+	7.23808i	0.159901	+	0.276957i	0.934833	−	0.355088i	$-0.115549\pi$
$683$	4.17891	+	7.23808i	0.159901	+	0.276957i	−0.774931	+	0.632045i	$0.782216\pi$
$684$		0			0
$685$	6.35782	+	11.0121i	0.242920	+	0.420749i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	12.1789			0.464317
$689$	−4.50000	+	9.83616i	−0.171436	+	0.374728i
$690$		0			0
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$	2.00000	−	3.46410i	0.0760286	−	0.131685i
$693$		0			0
$694$	−19.1789			−0.728021
$695$	6.82109	+	11.8145i	0.258739	+	0.448149i
$696$		0			0
$697$	−35.8945			−1.35960
$698$	4.08945	+	7.08314i	0.154788	+	0.268101i
$699$		0			0
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	21.7156			0.820188			0.410094	−	0.912043i	$-0.365496\pi$
$701$	21.7156			0.820188			0.410094	+	0.912043i	$0.365496\pi$
$702$		0			0
$703$	6.35782			0.239790
$704$	−2.58945	+	4.48507i	−0.0975937	+	0.169037i
$705$		0			0
$706$	−2.08945	−	3.61904i	−0.0786376	−	0.136204i
$707$	6.35782			0.239110
$708$		0			0
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$	−4.35782			−0.163546
$711$		0			0
$712$	−4.50000	+	7.79423i	−0.168645	+	0.292101i
$713$	−17.0895	+	29.5998i	−0.640005	+	1.10852i
$714$		0			0
$715$	−21.6422	−	30.4354i	−0.809372	−	1.13822i
$716$	−8.35782			−0.312346
$717$		0			0
$718$	5.17891	−	8.97013i	0.193275	−	0.334762i
$719$	−18.5895	−	32.1979i	−0.693270	−	1.20078i	−0.970761	−	0.240050i	$-0.922836\pi$
$719$	−18.5895	−	32.1979i	−0.693270	−	1.20078i	0.277491	−	0.960728i	$-0.410497\pi$
$720$		0			0
$721$	−4.08945	−	7.08314i	−0.152299	−	0.263790i
$722$	−4.44727	−	7.70290i	−0.165510	−	0.286672i
$723$		0			0
$724$	−9.58945	−	16.6094i	−0.356389	−	0.617284i
$725$	1.58945	−	2.75302i	0.0590308	−	0.102244i
$726$		0			0
$727$	34.5367			1.28090			0.640448	−	0.768001i	$-0.278749\pi$
$727$	34.5367			1.28090			0.640448	+	0.768001i	$0.278749\pi$
$728$	3.58945	−	0.340322i	0.133034	−	0.0126132i
$729$		0			0
$730$	4.00000	−	6.92820i	0.148047	−	0.256424i
$731$	30.4473	−	52.7362i	1.12613	−	1.95052i
$732$		0			0
$733$	19.7156			0.728214			0.364107	−	0.931357i	$-0.381374\pi$
$733$	19.7156			0.728214			0.364107	+	0.931357i	$0.381374\pi$
$734$	−4.08945	−	7.08314i	−0.150945	−	0.261444i
$735$		0			0
$736$	−8.17891			−0.301479
$737$	9.89454	+	17.1378i	0.364470	+	0.631281i
$738$		0			0
$739$	8.08945	−	14.0113i	0.297575	−	0.515416i	−0.678005	−	0.735057i	$-0.737155\pi$
$739$	8.08945	−	14.0113i	0.297575	−	0.515416i	0.975581	+	0.219641i	$0.0704887\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	3.00000			0.110133
$743$	15.9105	−	27.5579i	0.583701	−	1.01100i	−0.411335	−	0.911484i	$-0.634937\pi$
$743$	15.9105	−	27.5579i	0.583701	−	1.01100i	0.995036	−	0.0995159i	$-0.0317294\pi$
$744$		0			0
$745$	16.1789	+	28.0227i	0.592749	+	1.02667i
$746$	20.0000			0.732252
$747$		0			0
$748$	12.9473	+	22.4253i	0.473399	+	0.819951i
$749$	19.1789			0.700782
$750$		0			0
$751$	17.9473	−	31.0856i	0.654905	−	1.13433i	−0.327012	−	0.945020i	$-0.606042\pi$
$751$	17.9473	−	31.0856i	0.654905	−	1.13433i	0.981918	−	0.189309i	$-0.0606248\pi$
$752$	−3.58945	+	6.21712i	−0.130894	+	0.226715i
$753$		0			0
$754$	−11.4105	+	1.08185i	−0.415548	+	0.0393987i
$755$	39.0735			1.42203
$756$		0			0
$757$	10.1789	−	17.6304i	0.369959	−	0.640787i	−0.619600	−	0.784918i	$-0.712705\pi$
$757$	10.1789	−	17.6304i	0.369959	−	0.640787i	0.989559	+	0.144130i	$0.0460385\pi$
$758$	−12.3578	−	21.4044i	−0.448856	−	0.777442i
$759$		0			0
$760$	3.17891	+	5.50603i	0.115311	+	0.199725i
$761$	−21.7156	−	37.6126i	−0.787191	−	1.36345i	−0.927681	−	0.373373i	$-0.878201\pi$
$761$	−21.7156	−	37.6126i	−0.787191	−	1.36345i	0.140490	−	0.990082i	$-0.455132\pi$
$762$		0			0
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	−3.26836	+	5.66097i	−0.118245	+	0.204807i
$765$		0			0
$766$	21.1789			0.765225
$767$	43.7156	−	4.14474i	1.57848	−	0.149658i
$768$		0			0
$769$	−9.17891	+	15.8983i	−0.331000	+	0.573309i	−0.982708	−	0.185161i	$-0.940719\pi$
$769$	−9.17891	+	15.8983i	−0.331000	+	0.573309i	0.651708	+	0.758470i	$0.274053\pi$
$770$	−5.17891	+	8.97013i	−0.186635	+	0.323261i
$771$		0			0
$772$	−13.5367			−0.487197
$773$	7.35782	+	12.7441i	0.264642	+	0.458374i	0.967470	−	0.252986i	$-0.0814128\pi$
$773$	7.35782	+	12.7441i	0.264642	+	0.458374i	−0.702828	+	0.711360i	$0.748079\pi$
$774$		0			0
$775$	−4.17891			−0.150111
$776$	−5.17891	−	8.97013i	−0.185912	−	0.322009i
$777$		0			0
$778$	6.08945	−	10.5472i	0.218318	−	0.378137i
$779$	22.8211			0.817650
$780$		0			0
$781$	11.2844			0.403786
$782$	−20.4473	+	35.4157i	−0.731193	+	1.26646i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	4.00000			0.142766
$786$		0			0
$787$	5.41055	+	9.37134i	0.192865	+	0.334052i	0.946199	−	0.323587i	$-0.104889\pi$
$787$	5.41055	+	9.37134i	0.192865	+	0.334052i	−0.753333	+	0.657639i	$0.771555\pi$
$788$	−17.0000			−0.605600
$789$		0			0
$790$	13.1789	−	22.8265i	0.468885	−	0.812132i
$791$	−9.17891	+	15.8983i	−0.326364	+	0.565280i
$792$		0			0
$793$	−10.7684	+	1.02096i	−0.382396	+	0.0362555i
$794$	−3.00000			−0.106466
$795$		0			0
$796$	−12.0895	+	20.9395i	−0.428499	+	0.742183i
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$	17.9473	+	31.0856i	0.634929	+	1.09973i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−4.82109	−	8.35038i	−0.170239	−	0.294862i
$803$	−10.3578	+	17.9403i	−0.365519	+	0.633098i
$804$		0			0
$805$	−16.3578			−0.576537
$806$	8.73164	+	12.2793i	0.307559	+	0.432520i
$807$		0			0
$808$	−3.17891	+	5.50603i	−0.111834	+	0.193701i
$809$	−10.0000	+	17.3205i	−0.351581	+	0.608957i	−0.986527	−	0.163600i	$-0.947689\pi$
$809$	−10.0000	+	17.3205i	−0.351581	+	0.608957i	0.634945	+	0.772557i	$0.281023\pi$
$810$		0			0
$811$	−12.7156			−0.446506			−0.223253	−	0.974761i	$-0.571668\pi$
$811$	−12.7156			−0.446506			−0.223253	+	0.974761i	$0.571668\pi$
$812$	1.58945	+	2.75302i	0.0557789	+	0.0966119i
$813$		0			0
$814$	−10.3578			−0.363041
$815$	20.1789	+	34.9509i	0.706836	+	1.22428i
$816$		0			0
$817$	−19.3578	+	33.5287i	−0.677244	+	1.17302i
$818$	36.3578			1.27122
$819$		0			0
$820$	14.3578			0.501397
$821$	0.142183	−	0.246269i	0.00496223	−	0.00859484i	−0.863534	−	0.504291i	$-0.831754\pi$
$821$	0.142183	−	0.246269i	0.00496223	−	0.00859484i	0.868496	+	0.495696i	$0.165087\pi$
$822$		0			0
$823$	−16.3578	−	28.3326i	−0.570198	−	0.987611i	−0.996545	−	0.0830519i	$-0.973533\pi$
$823$	−16.3578	−	28.3326i	−0.570198	−	0.987611i	0.426348	−	0.904559i	$-0.359800\pi$
$824$	8.17891			0.284926
$825$		0			0
$826$	−6.08945	−	10.5472i	−0.211879	−	0.366986i
$827$	40.7156			1.41582			0.707911	−	0.706302i	$-0.249638\pi$
$827$	40.7156			1.41582			0.707911	+	0.706302i	$0.249638\pi$
$828$		0			0
$829$	1.58945	−	2.75302i	0.0552040	−	0.0956162i	−0.837103	−	0.547046i	$-0.815752\pi$
$829$	1.58945	−	2.75302i	0.0552040	−	0.0956162i	0.892307	+	0.451429i	$0.149086\pi$
$830$	−6.17891	+	10.7022i	−0.214473	+	0.371478i
$831$		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
$836$	−8.23164	−	14.2576i	−0.284697	−	0.493110i
$837$		0			0
$838$	13.4473	+	23.2914i	0.464528	+	0.804587i
$839$	5.82109	+	10.0824i	0.200966	+	0.348084i	0.948840	−	0.315757i	$-0.102258\pi$
$839$	5.82109	+	10.0824i	0.200966	+	0.348084i	−0.747874	+	0.663841i	$0.768925\pi$
$840$		0			0
$841$	9.44727	+	16.3632i	0.325768	+	0.564247i
$842$	5.35782	−	9.28001i	0.184643	−	0.319810i
$843$		0			0
$844$	−6.35782			−0.218845
$845$	−17.0000	−	19.6723i	−0.584818	−	0.676748i
$846$		0			0
$847$	7.91055	−	13.7015i	0.271810	−	0.470788i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$		0			0
$850$	−5.00000			−0.171499
$851$	−8.17891	−	14.1663i	−0.280369	−	0.485614i
$852$		0			0
$853$	27.7156			0.948965			0.474483	−	0.880265i	$-0.342635\pi$
$853$	27.7156			0.948965			0.474483	+	0.880265i	$0.342635\pi$
$854$	1.50000	+	2.59808i	0.0513289	+	0.0889043i
$855$		0			0
$856$	−9.58945	+	16.6094i	−0.327761	+	0.567698i
$857$	10.7156			0.366039			0.183020	−	0.983109i	$-0.441413\pi$
$857$	10.7156			0.366039			0.183020	+	0.983109i	$0.441413\pi$
$858$		0			0
$859$	19.8945			0.678793			0.339397	−	0.940643i	$-0.389777\pi$
$859$	19.8945			0.678793			0.339397	+	0.940643i	$0.389777\pi$
$860$	−12.1789	+	21.0945i	−0.415297	+	0.719316i
$861$		0			0
$862$	−5.08945	−	8.81519i	−0.173347	−	0.300247i
$863$	−13.6422			−0.464385			−0.232193	−	0.972670i	$-0.574590\pi$
$863$	−13.6422			−0.464385			−0.232193	+	0.972670i	$0.574590\pi$
$864$		0			0
$865$	4.00000	+	6.92820i	0.136004	+	0.235566i
$866$	−34.3578			−1.16753
$867$		0			0
$868$	2.08945	−	3.61904i	0.0709207	−	0.122838i
$869$	−34.1262	+	59.1083i	−1.15765	+	2.00511i
$870$		0			0
$871$	7.98400	+	11.2279i	0.270527	+	0.380442i
$872$	−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
$877$	20.1789	+	34.9509i	0.681393	+	1.18021i	0.974556	+	0.224145i	$0.0719590\pi$
$877$	20.1789	+	34.9509i	0.681393	+	1.18021i	−0.293162	+	0.956063i	$0.594708\pi$
$878$	20.3578	+	35.2608i	0.687043	+	1.18999i
$879$		0			0
$880$	−5.17891	−	8.97013i	−0.174581	−	0.302383i
$881$	5.73164	−	9.92749i	0.193104	−	0.334466i	−0.753173	−	0.657822i	$-0.771478\pi$
$881$	5.73164	−	9.92749i	0.193104	−	0.334466i	0.946277	+	0.323356i	$0.104811\pi$
$882$		0			0
$883$	−3.46327			−0.116548			−0.0582742	−	0.998301i	$-0.518560\pi$
$883$	−3.46327			−0.116548			−0.0582742	+	0.998301i	$0.518560\pi$
$884$	10.4473	+	14.6920i	0.351380	+	0.494145i
$885$		0			0
$886$	−1.58945	+	2.75302i	−0.0533988	+	0.0924894i
$887$	−22.7684	+	39.4360i	−0.764487	+	1.32413i	0.176031	+	0.984385i	$0.443674\pi$
$887$	−22.7684	+	39.4360i	−0.764487	+	1.32413i	−0.940517	+	0.339745i	$0.889659\pi$
$888$		0			0
$889$	−12.0000			−0.402467
$890$	−9.00000	−	15.5885i	−0.301681	−	0.522526i
$891$		0			0
$892$	−2.17891			−0.0729552
$893$	−11.4105	−	19.7636i	−0.381839	−	0.661365i
$894$		0			0
$895$	8.35782	−	14.4762i	0.279371	−	0.483885i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−14.0000			−0.467186
$899$	−6.64218	+	11.5046i	−0.221529	+	0.383700i
$900$		0			0
$901$	7.50000	+	12.9904i	0.249861	+	0.432772i
$902$	−37.1789			−1.23792
$903$		0			0
$904$	−9.17891	−	15.8983i	−0.305286	−	0.528771i
$905$	38.3578			1.27506
$906$		0			0
$907$	−24.8051	+	42.9637i	−0.823639	+	1.42659i	0.0793153	+	0.996850i	$0.474727\pi$
$907$	−24.8051	+	42.9637i	−0.823639	+	1.42659i	−0.902955	+	0.429736i	$0.858607\pi$
$908$	−7.17891	+	12.4342i	−0.238240	+	0.412645i
$909$		0			0
$910$	−3.00000	+	6.55744i	−0.0994490	+	0.217377i
$911$	−28.7156			−0.951391			−0.475696	−	0.879610i	$-0.657804\pi$
$911$	−28.7156			−0.951391			−0.475696	+	0.879610i	$0.657804\pi$
$912$		0			0
$913$	16.0000	−	27.7128i	0.529523	−	0.917160i
$914$	12.4473	+	21.5593i	0.411719	+	0.713118i
$915$		0			0
$916$	−0.500000	−	0.866025i	−0.0165205	−	0.0286143i
$917$	7.26836	+	12.5892i	0.240022	+	0.415731i
$918$		0			0
$919$	29.1262	+	50.4480i	0.960784	+	1.66413i	0.720539	+	0.693414i	$0.243894\pi$
$919$	29.1262	+	50.4480i	0.960784	+	1.66413i	0.240245	+	0.970712i	$0.422772\pi$
$920$	8.17891	−	14.1663i	0.269651	−	0.467049i
$921$		0			0
$922$	20.7156			0.682233
$923$	7.82109	−	0.741529i	0.257434	−	0.0244077i
$924$		0			0
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	13.9473	−	24.1574i	0.458336	−	0.793861i
$927$		0			0
$928$	−3.17891			−0.104353
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	0.985482	+	0.169779i	$0.0543055\pi$
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	−0.345708	+	0.938342i	$0.612361\pi$
$930$		0			0
$931$	3.17891			0.104185
$932$	11.1789	+	19.3624i	0.366177	+	0.634238i
$933$		0			0
$934$	11.4473	−	19.8273i	0.374566	−	0.648768i
$935$	−51.7891			−1.69368
$936$		0			0
$937$	21.0735			0.688440			0.344220	−	0.938889i	$-0.388143\pi$
$937$	21.0735			0.688440			0.344220	+	0.938889i	$0.388143\pi$
$938$	1.91055	−	3.30916i	0.0623815	−	0.108048i
$939$		0			0
$940$	−7.17891	−	12.4342i	−0.234150	−	0.405560i
$941$	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
$943$	−29.3578	−	50.8492i	−0.956022	−	1.65588i
$944$	12.1789			0.396390
$945$		0			0
$946$	31.5367	−	54.6232i	1.02535	−	1.77595i
$947$	−20.1262	+	34.8596i	−0.654013	+	1.13278i	0.328127	+	0.944634i	$0.393582\pi$
$947$	−20.1262	+	34.8596i	−0.654013	+	1.13278i	−0.982140	+	0.188150i	$0.939751\pi$
$948$		0			0
$949$	−6.00000	+	13.1149i	−0.194768	+	0.425727i
$950$	3.17891			0.103137
$951$		0			0
$952$	2.50000	−	4.33013i	0.0810255	−	0.140340i
$953$	−1.35782	−	2.35181i	−0.0439840	−	0.0761825i	0.843195	−	0.537607i	$-0.180672\pi$
$953$	−1.35782	−	2.35181i	−0.0439840	−	0.0761825i	−0.887179	+	0.461425i	$0.847338\pi$
$954$		0			0
$955$	−6.53673	−	11.3219i	−0.211523	−	0.366369i
$956$	5.08945	+	8.81519i	0.164605	+	0.285104i
$957$		0			0
$958$	20.5895	+	35.6620i	0.665215	+	1.15219i
$959$	−3.17891	+	5.50603i	−0.102652	+	0.177799i
$960$		0			0
$961$	−13.5367			−0.436669
$962$	−7.17891	+	0.680643i	−0.231457	+	0.0219448i
$963$		0			0
$964$	−2.17891	+	3.77398i	−0.0701779	+	0.121552i
$965$	13.5367	−	23.4463i	0.435763	−	0.754763i
$966$		0			0
$967$	11.6422			0.374387			0.187194	−	0.982323i	$-0.440061\pi$
$967$	11.6422			0.374387			0.187194	+	0.982323i	$0.440061\pi$
$968$	7.91055	+	13.7015i	0.254255	+	0.440382i
$969$		0			0
$970$	20.7156			0.665139
$971$	−14.0895	−	24.4037i	−0.452152	−	0.783150i	0.546367	−	0.837546i	$-0.316010\pi$
$971$	−14.0895	−	24.4037i	−0.452152	−	0.783150i	−0.998519	+	0.0543952i	$0.982677\pi$
$972$		0			0
$973$	−3.41055	+	5.90724i	−0.109337	+	0.189377i
$974$	26.8211			0.859403
$975$		0			0
$976$	−3.00000			−0.0960277
$977$	6.00000	−	10.3923i	0.191957	−	0.332479i	−0.753942	−	0.656941i	$-0.771850\pi$
$977$	6.00000	−	10.3923i	0.191957	−	0.332479i	0.945899	+	0.324462i	$0.105183\pi$
$978$		0			0
$979$	23.3051	+	40.3656i	0.744834	+	1.29009i
$980$	2.00000			0.0638877
$981$		0			0
$982$		0			0
$983$	13.0735			0.416978			0.208489	−	0.978025i	$-0.433145\pi$
$983$	13.0735			0.416978			0.208489	+	0.978025i	$0.433145\pi$
$984$		0			0
$985$	17.0000	−	29.4449i	0.541665	−	0.938191i
$986$	−7.94727	+	13.7651i	−0.253093	+	0.438369i
$987$		0			0
$988$	−6.64218	−	9.34090i	−0.211316	−	0.297174i
$989$	99.6102			3.16742
$990$		0			0
$991$	24.7684	−	42.9001i	0.786793	−	1.36277i	−0.141129	−	0.989991i	$-0.545073\pi$
$991$	24.7684	−	42.9001i	0.786793	−	1.36277i	0.927922	−	0.372774i	$-0.121593\pi$
$992$	2.08945	+	3.61904i	0.0663402	+	0.114905i
$993$		0			0
$994$	−1.08945	−	1.88699i	−0.0345554	−	0.0598517i
$995$	−24.1789	−	41.8791i	−0.766523	−	1.32766i
$996$		0			0
$997$	−6.14218	−	10.6386i	−0.194525	−	0.336927i	0.752220	−	0.658912i	$-0.228983\pi$
$997$	−6.14218	−	10.6386i	−0.194525	−	0.336927i	−0.946745	+	0.321985i	$0.895650\pi$
$998$	4.08945	−	7.08314i	0.129449	−	0.224213i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.ba.1387.1		4
3.2	odd	2		546.2.l.k.295.2	yes	4
13.3	even	3	inner	1638.2.r.ba.757.1		4
39.17	odd	6		7098.2.a.bk.1.2		2
39.29	odd	6		546.2.l.k.211.2	✓	4
39.35	odd	6		7098.2.a.br.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.k.211.2	✓	4	39.29	odd	6
546.2.l.k.295.2	yes	4	3.2	odd	2
1638.2.r.ba.757.1		4	13.3	even	3	inner
1638.2.r.ba.1387.1		4	1.1	even	1	trivial
7098.2.a.bk.1.2		2	39.17	odd	6
7098.2.a.br.1.1		2	39.35	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(-2.58945 + 4.48507i) q^{11} +(-1.50000 + 3.27872i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +(-1.58945 - 2.75302i) q^{19} +(-1.00000 - 1.73205i) q^{20} +(2.58945 + 4.48507i) q^{22} +(-4.08945 + 7.08314i) q^{23} -1.00000 q^{25} +(2.08945 + 2.93840i) q^{26} +(0.500000 - 0.866025i) q^{28} +(-1.58945 + 2.75302i) q^{29} +4.17891 q^{31} +(0.500000 + 0.866025i) q^{32} +5.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(-1.00000 + 1.73205i) q^{37} -3.17891 q^{38} -2.00000 q^{40} +(-3.58945 + 6.21712i) q^{41} +(-6.08945 - 10.5472i) q^{43} +5.17891 q^{44} +(4.08945 + 7.08314i) q^{46} +7.17891 q^{47} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.58945 - 0.340322i) q^{52} +3.00000 q^{53} +(-5.17891 + 8.97013i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(1.58945 + 2.75302i) q^{58} +(-6.08945 - 10.5472i) q^{59} +(1.50000 + 2.59808i) q^{61} +(2.08945 - 3.61904i) q^{62} +1.00000 q^{64} +(-3.00000 + 6.55744i) q^{65} +(1.91055 - 3.30916i) q^{67} +(2.50000 - 4.33013i) q^{68} +2.00000 q^{70} +(-1.08945 - 1.88699i) q^{71} +4.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.58945 + 2.75302i) q^{76} -5.17891 q^{77} +13.1789 q^{79} +(-1.00000 + 1.73205i) q^{80} +(3.58945 + 6.21712i) q^{82} -6.17891 q^{83} +(5.00000 + 8.66025i) q^{85} -12.1789 q^{86} +(2.58945 - 4.48507i) q^{88} +(4.50000 - 7.79423i) q^{89} +(-3.58945 + 0.340322i) q^{91} +8.17891 q^{92} +(3.58945 - 6.21712i) q^{94} +(-3.17891 - 5.50603i) q^{95} +(5.17891 + 8.97013i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 8 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 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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