LMFDB - Embedded newform 1638.2.r.ba.757.1

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			757.1
Root			$-2.58945 - 2.07237i$ of defining polynomial
Character	$\chi$	$=$	1638.757
Dual form			1638.2.r.ba.1387.1

$q$-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 $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

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

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
$11$	−2.58945	−	4.48507i	−0.780750	−	1.35230i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−2.58945	−	4.48507i	−0.780750	−	1.35230i	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
$19$	−1.58945	+	2.75302i	−0.364646	+	0.631585i	−0.988719	−	0.149781i	$-0.952143\pi$
$19$	−1.58945	+	2.75302i	−0.364646	+	0.631585i	0.624073	+	0.781366i	$0.285477\pi$
$20$	−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	−0.878753	−	0.477276i	$-0.841624\pi$
$23$	−4.08945	−	7.08314i	−0.852710	−	1.47694i	0.0260431	−	0.999661i	$-0.491709\pi$
$24$		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	0.679867	−	0.733336i	$-0.262038\pi$
$29$	−1.58945	−	2.75302i	−0.295154	−	0.511222i	−0.975021	+	0.222114i	$0.928704\pi$
$30$		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	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−3.17891			−0.515687
$39$		0			0
$40$	−2.00000			−0.316228
$41$	−3.58945	−	6.21712i	−0.560579	−	0.970951i	−0.997446	−	0.0714247i	$-0.977245\pi$
$41$	−3.58945	−	6.21712i	−0.560579	−	0.970951i	0.436867	−	0.899526i	$-0.356088\pi$
$42$		0			0
$43$	−6.08945	+	10.5472i	−0.928633	+	1.60844i	−0.143022	+	0.989720i	$0.545682\pi$
$43$	−6.08945	+	10.5472i	−0.928633	+	1.60844i	−0.785612	+	0.618720i	$0.787652\pi$
$44$	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	0.131460	+	0.991321i	$0.458033\pi$
$59$	−6.08945	+	10.5472i	−0.792779	+	1.37313i	−0.924240	+	0.381813i	$0.875300\pi$
$60$		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	$0.105151\pi$
$62$	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	0.958809	−	0.284050i	$-0.0916781\pi$
$67$	1.91055	+	3.30916i	0.233410	+	0.404279i	−0.725399	+	0.688328i	$0.758345\pi$
$68$	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	−0.923403	−	0.383831i	$-0.874605\pi$
$71$	−1.08945	+	1.88699i	−0.129294	+	0.223945i	0.794109	+	0.607775i	$0.207938\pi$
$72$		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	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	−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	−0.473709	−	0.880682i	$-0.657085\pi$
$97$	5.17891	−	8.97013i	0.525838	−	0.910779i	0.999547	−	0.0300973i	$-0.00958170\pi$
$98$	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	0.979716	−	0.200392i	$-0.0642216\pi$
$101$	3.17891	+	5.50603i	0.316313	+	0.547871i	−0.663403	+	0.748263i	$0.730888\pi$
$102$		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	0.788235	+	0.615375i	$0.210995\pi$
$107$	9.58945	+	16.6094i	0.927048	+	1.60569i	0.138813	+	0.990319i	$0.455671\pi$
$108$		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	−0.00507042	−	0.999987i	$-0.501614\pi$
$113$	9.17891	−	15.8983i	0.863479	−	1.49559i	0.868549	−	0.495602i	$-0.165053\pi$
$114$		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	−0.999284	−	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
$130$	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	−0.697677	−	0.716412i	$-0.745783\pi$
$137$	3.17891	−	5.50603i	0.271592	−	0.470412i	0.969270	+	0.246000i	$0.0791164\pi$
$138$		0			0
$139$	3.41055	−	5.90724i	0.289279	−	0.501045i	−0.684359	−	0.729145i	$-0.739918\pi$
$139$	3.41055	−	5.90724i	0.289279	−	0.501045i	0.973638	+	0.228100i	$0.0732512\pi$
$140$	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	−0.317186	−	0.948363i	$-0.602738\pi$
$149$	8.08945	−	14.0113i	0.662714	−	1.14785i	0.979900	−	0.199491i	$-0.0639288\pi$
$150$		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	−0.135534	−	0.990773i	$-0.543275\pi$
$163$	10.0895	−	17.4754i	0.790267	−	1.36878i	0.925801	−	0.378010i	$-0.123392\pi$
$164$	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	0.668730	−	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
$172$	−6.08945	−	10.5472i	−0.464317	−	0.804220i
$173$	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
$176$	−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	0.978870	−	0.204484i	$-0.0655518\pi$
$179$	4.17891	+	7.23808i	0.312346	+	0.541000i	−0.666524	+	0.745484i	$0.732218\pi$
$180$		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	−0.959705	−	0.281010i	$-0.909331\pi$
$191$	−3.26836	+	5.66097i	−0.236490	+	0.409613i	0.723214	+	0.690624i	$0.242664\pi$
$192$		0			0
$193$	6.76836	+	11.7231i	0.487197	+	0.843851i	0.999892	−	0.0147206i	$-0.00468589\pi$
$193$	6.76836	+	11.7231i	0.487197	+	0.843851i	−0.512694	+	0.858571i	$0.671353\pi$
$194$	10.3578			0.743648
$195$		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
$199$	−12.0895	+	20.9395i	−0.856999	+	1.48437i	0.0177797	+	0.999842i	$0.494340\pi$
$199$	−12.0895	+	20.9395i	−0.856999	+	1.48437i	−0.874778	+	0.484523i	$0.838993\pi$
$200$	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	0.954455	−	0.298354i	$-0.0964377\pi$
$211$	3.17891	+	5.50603i	0.218845	+	0.379051i	−0.735610	+	0.677405i	$0.763104\pi$
$212$	−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	0.900195	−	0.435487i	$-0.143424\pi$
$223$	1.08945	+	1.88699i	0.0729552	+	0.126362i	−0.827240	+	0.561849i	$0.810090\pi$
$224$	−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	−0.999637	−	0.0269479i	$-0.991421\pi$
$227$	−7.17891	+	12.4342i	−0.476481	+	0.825289i	0.523156	+	0.852237i	$0.324755\pi$
$228$		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	−0.927631	−	0.373499i	$-0.878158\pi$
$241$	−2.17891	+	3.77398i	−0.140356	+	0.243103i	0.787275	+	0.616602i	$0.211491\pi$
$242$	−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	−0.268520	−	0.963274i	$-0.586534\pi$
$251$	11.0895	−	19.2075i	0.699960	−	1.21237i	0.968480	−	0.249092i	$-0.0801323\pi$
$252$		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	−0.990400	−	0.138234i	$-0.955857\pi$
$257$	−9.85782	−	17.0742i	−0.614914	−	1.06506i	0.375486	−	0.926828i	$-0.377476\pi$
$258$		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	0.619586	−	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
$266$	−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	−0.924774	−	0.380516i	$-0.875746\pi$
$269$	−2.17891	+	3.77398i	−0.132850	+	0.230104i	0.791924	+	0.610620i	$0.209080\pi$
$270$		0			0
$271$	−9.91055	−	17.1656i	−0.602023	−	1.04273i	−0.992514	−	0.122128i	$-0.961028\pi$
$271$	−9.91055	−	17.1656i	−0.602023	−	1.04273i	0.390492	−	0.920606i	$-0.372305\pi$
$272$	−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	−0.938245	−	0.345971i	$-0.887550\pi$
$277$	−2.82109	+	4.88627i	−0.169503	+	0.293588i	0.768742	+	0.639559i	$0.220883\pi$
$278$	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	0.729819	−	0.683640i	$-0.239604\pi$
$283$	−3.82109	−	6.61832i	−0.227140	−	0.393419i	−0.956959	+	0.290222i	$0.906271\pi$
$284$	−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	−0.635818	−	0.771839i	$-0.719337\pi$
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	0.986341	+	0.164714i	$0.0526703\pi$
$294$		0			0
$295$	−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	−0.842577	−	0.538575i	$-0.818963\pi$
$331$	0.821092	−	1.42217i	0.0451313	−	0.0781697i	0.887709	+	0.460406i	$0.152296\pi$
$332$	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	0.485064	+	0.874479i	$0.338796\pi$
$347$	−9.58945	+	16.6094i	−0.514789	+	0.891640i	−0.999853	+	0.0171617i	$0.994537\pi$
$348$		0			0
$349$	−4.08945	−	7.08314i	−0.218903	−	0.379152i	0.735570	−	0.677449i	$-0.236915\pi$
$349$	−4.08945	−	7.08314i	−0.218903	−	0.379152i	−0.954473	+	0.298297i	$0.903581\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	−5.17891			−0.276037
$353$	2.08945	+	3.61904i	0.111210	+	0.192622i	0.916259	−	0.400587i	$-0.131194\pi$
$353$	2.08945	+	3.61904i	0.111210	+	0.192622i	−0.805048	+	0.593209i	$0.797861\pi$
$354$		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	0.952797	−	0.303607i	$-0.0981908\pi$
$367$	4.08945	+	7.08314i	0.213468	+	0.369737i	−0.739330	+	0.673344i	$0.764857\pi$
$368$	−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	−0.482006	−	0.876168i	$-0.660092\pi$
$373$	10.0000	−	17.3205i	0.517780	−	0.896822i	0.999787	−	0.0206542i	$-0.00657489\pi$
$374$	−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	0.986562	+	0.163387i	$0.0522420\pi$
$379$	12.3578	+	21.4044i	0.634778	+	1.09947i	−0.351784	+	0.936081i	$0.614425\pi$
$380$	−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	−0.457746	−	0.889083i	$-0.651343\pi$
$383$	10.5895	−	18.3415i	0.541096	−	0.937205i	0.998841	−	0.0481223i	$-0.0153237\pi$
$384$		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	−0.901209	−	0.433384i	$-0.857319\pi$
$397$	−1.50000	+	2.59808i	−0.0752828	+	0.130394i	0.825926	+	0.563778i	$0.190653\pi$
$398$	−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	0.960929	−	0.276794i	$-0.0892720\pi$
$401$	4.82109	+	8.35038i	0.240754	+	0.416998i	−0.720175	+	0.693792i	$0.755939\pi$
$402$		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	0.0699730	−	0.997549i	$-0.477709\pi$
$409$	18.1789	−	31.4868i	0.898889	−	1.55692i	0.828916	−	0.559373i	$-0.188958\pi$
$410$	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	−0.981403	−	0.191958i	$-0.938516\pi$
$419$	−13.4473	−	23.2914i	−0.656942	−	1.13786i	0.324461	−	0.945899i	$-0.394817\pi$
$420$		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	0.962174	−	0.272436i	$-0.0878293\pi$
$431$	5.08945	+	8.81519i	0.245150	+	0.424613i	−0.717024	+	0.697049i	$0.754496\pi$
$432$		0			0
$433$	−17.1789	+	29.7547i	−0.825566	+	1.42992i	0.0759206	+	0.997114i	$0.475810\pi$
$433$	−17.1789	+	29.7547i	−0.825566	+	1.42992i	−0.901486	+	0.432808i	$0.857523\pi$
$434$	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	−0.690649	−	0.723190i	$-0.742675\pi$
$439$	−20.3578	−	35.2608i	−0.971626	−	1.68290i	−0.280977	−	0.959715i	$-0.590658\pi$
$440$	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	−0.982581	−	0.185837i	$-0.940500\pi$
$449$	−7.00000	+	12.1244i	−0.330350	+	0.572184i	0.652230	+	0.758021i	$0.273834\pi$
$450$		0			0
$451$	−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	−0.995211	−	0.0977491i	$-0.968836\pi$
$457$	−12.4473	−	21.5593i	−0.582259	−	1.00850i	0.412952	−	0.910753i	$-0.364498\pi$
$458$	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	−0.517385	−	0.855753i	$-0.673094\pi$
$461$	10.3578	−	17.9403i	0.482412	−	0.835561i	0.999796	+	0.0201916i	$0.00642763\pi$
$462$		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	−0.764033	−	0.645177i	$-0.776784\pi$
$479$	−20.5895	−	35.6620i	−0.940756	−	1.62944i	−0.176723	−	0.984261i	$-0.556550\pi$
$480$		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	−0.383930	−	0.923362i	$-0.625430\pi$
$487$	13.4105	−	23.2277i	0.607690	−	1.05255i	0.991620	−	0.129188i	$-0.0412369\pi$
$488$	−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
$493$	−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	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$		0			0
$505$	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	0.619182	−	0.785248i	$-0.287464\pi$
$509$	−8.35782	−	14.4762i	−0.370454	−	0.641645i	−0.989635	+	0.143603i	$0.954131\pi$
$510$		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	0.711907	−	0.702273i	$-0.247832\pi$
$523$	−5.76836	−	9.99110i	−0.252233	−	0.436880i	−0.964140	+	0.265393i	$0.914498\pi$
$524$	−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	0.999996	+	0.00281030i	$0.000894548\pi$
$557$	11.8578	+	20.5383i	0.502432	+	0.870237i	−0.497564	+	0.867427i	$0.665772\pi$
$558$		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	−0.992023	−	0.126055i	$-0.959768\pi$
$563$	−9.17891	+	15.8983i	−0.386845	+	0.670035i	0.605178	+	0.796090i	$0.293102\pi$
$564$		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	0.825326	−	0.564657i	$-0.190991\pi$
$569$	−1.82109	−	3.15422i	−0.0763441	−	0.132232i	−0.901670	+	0.432425i	$0.857658\pi$
$570$		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	0.867866	−	0.496799i	$-0.165491\pi$
$587$	0.0894542	+	0.154939i	0.00369217	+	0.00639502i	−0.864173	+	0.503194i	$0.832158\pi$
$588$		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	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$	−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	−0.860528	−	0.509404i	$-0.829866\pi$
$607$	0.268363	−	0.464818i	0.0108925	−	0.0188664i	0.871420	+	0.490537i	$0.163199\pi$
$608$	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	0.663736	−	0.747967i	$-0.268970\pi$
$613$	−7.82109	−	13.5465i	−0.315891	−	0.547139i	−0.979626	+	0.200828i	$0.935637\pi$
$614$	−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	−0.340365	−	0.940294i	$-0.610551\pi$
$617$	16.0000	−	27.7128i	0.644136	−	1.11568i	0.984500	−	0.175382i	$-0.0561162\pi$
$618$		0			0
$619$	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	0.484417	+	0.874837i	$0.339032\pi$
$631$	−12.9473	+	22.4253i	−0.515423	+	0.892738i	−0.999840	+	0.0179011i	$0.994302\pi$
$632$	−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	−0.464511	−	0.885567i	$-0.653770\pi$
$641$	13.5367	−	23.4463i	0.534668	−	0.926073i	0.999179	−	0.0405056i	$-0.0128968\pi$
$642$		0			0
$643$	4.41055	−	7.63929i	0.173935	−	0.301264i	−0.765857	−	0.643011i	$-0.777685\pi$
$643$	4.41055	−	7.63929i	0.173935	−	0.301264i	0.939792	+	0.341746i	$0.111018\pi$
$644$	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	0.762680	+	0.646776i	$0.223883\pi$
$647$	23.9473	+	41.4779i	0.941464	+	1.63066i	0.178784	+	0.983888i	$0.442784\pi$
$648$		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	0.994988	−	0.0999939i	$-0.0318823\pi$
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	−0.584091	+	0.811688i	$0.698549\pi$
$654$		0			0
$655$	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	−0.643157	−	0.765734i	$-0.722376\pi$
$659$	8.76836	−	15.1872i	0.341567	−	0.591611i	0.984724	+	0.174123i	$0.0557091\pi$
$660$		0			0
$661$	−8.26836	−	14.3212i	−0.321602	−	0.557031i	0.659217	−	0.751953i	$-0.270888\pi$
$661$	−8.26836	−	14.3212i	−0.321602	−	0.557031i	−0.980819	+	0.194922i	$0.937555\pi$
$662$	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	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	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	−0.774931	−	0.632045i	$-0.782216\pi$
$683$	4.17891	−	7.23808i	0.159901	−	0.276957i	0.934833	+	0.355088i	$0.115549\pi$
$684$		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	0.942420	+	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
$694$	−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	−0.675791	−	0.737093i	$-0.736198\pi$
$709$	8.00000	−	13.8564i	0.300446	−	0.520388i	0.976237	+	0.216705i	$0.0695310\pi$
$710$	−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	0.277491	+	0.960728i	$0.410497\pi$
$719$	−18.5895	+	32.1979i	−0.693270	+	1.20078i	−0.970761	+	0.240050i	$0.922836\pi$
$720$		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	0.975581	−	0.219641i	$-0.0704887\pi$
$739$	8.08945	+	14.0113i	0.297575	+	0.515416i	−0.678005	+	0.735057i	$0.737155\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	3.00000			0.110133
$743$	15.9105	+	27.5579i	0.583701	+	1.01100i	0.995036	+	0.0995159i	$0.0317294\pi$
$743$	15.9105	+	27.5579i	0.583701	+	1.01100i	−0.411335	+	0.911484i	$0.634937\pi$
$744$		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	0.981918	+	0.189309i	$0.0606248\pi$
$751$	17.9473	+	31.0856i	0.654905	+	1.13433i	−0.327012	+	0.945020i	$0.606042\pi$
$752$	−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	0.989559	−	0.144130i	$-0.0460385\pi$
$757$	10.1789	+	17.6304i	0.369959	+	0.640787i	−0.619600	+	0.784918i	$0.712705\pi$
$758$	−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	0.140490	+	0.990082i	$0.455132\pi$
$761$	−21.7156	+	37.6126i	−0.787191	+	1.36345i	−0.927681	+	0.373373i	$0.878201\pi$
$762$		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	0.651708	−	0.758470i	$-0.274053\pi$
$769$	−9.17891	−	15.8983i	−0.331000	−	0.573309i	−0.982708	+	0.185161i	$0.940719\pi$
$770$	−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	−0.702828	−	0.711360i	$-0.748079\pi$
$773$	7.35782	−	12.7441i	0.264642	−	0.458374i	0.967470	+	0.252986i	$0.0814128\pi$
$774$		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	−0.753333	−	0.657639i	$-0.771555\pi$
$787$	5.41055	−	9.37134i	0.192865	−	0.334052i	0.946199	+	0.323587i	$0.104889\pi$
$788$	−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	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		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	0.634945	−	0.772557i	$-0.281023\pi$
$809$	−10.0000	−	17.3205i	−0.351581	−	0.608957i	−0.986527	+	0.163600i	$0.947689\pi$
$810$		0			0
$811$	−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	0.868496	−	0.495696i	$-0.165087\pi$
$821$	0.142183	+	0.246269i	0.00496223	+	0.00859484i	−0.863534	+	0.504291i	$0.831754\pi$
$822$		0			0
$823$	−16.3578	+	28.3326i	−0.570198	+	0.987611i	0.426348	+	0.904559i	$0.359800\pi$
$823$	−16.3578	+	28.3326i	−0.570198	+	0.987611i	−0.996545	+	0.0830519i	$0.973533\pi$
$824$	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	0.892307	−	0.451429i	$-0.149086\pi$
$829$	1.58945	+	2.75302i	0.0552040	+	0.0956162i	−0.837103	+	0.547046i	$0.815752\pi$
$830$	−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	−0.747874	−	0.663841i	$-0.768925\pi$
$839$	5.82109	−	10.0824i	0.200966	−	0.348084i	0.948840	+	0.315757i	$0.102258\pi$
$840$		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	−0.293162	−	0.956063i	$-0.594708\pi$
$877$	20.1789	−	34.9509i	0.681393	−	1.18021i	0.974556	−	0.224145i	$-0.0719590\pi$
$878$	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	0.946277	−	0.323356i	$-0.104811\pi$
$881$	5.73164	+	9.92749i	0.193104	+	0.334466i	−0.753173	+	0.657822i	$0.771478\pi$
$882$		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	−0.940517	−	0.339745i	$-0.889659\pi$
$887$	−22.7684	−	39.4360i	−0.764487	−	1.32413i	0.176031	−	0.984385i	$-0.443674\pi$
$888$		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	−0.902955	−	0.429736i	$-0.858607\pi$
$907$	−24.8051	−	42.9637i	−0.823639	−	1.42659i	0.0793153	−	0.996850i	$-0.474727\pi$
$908$	−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	0.240245	−	0.970712i	$-0.422772\pi$
$919$	29.1262	−	50.4480i	0.960784	−	1.66413i	0.720539	−	0.693414i	$-0.243894\pi$
$920$	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	−0.345708	−	0.938342i	$-0.612361\pi$
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	0.985482	−	0.169779i	$-0.0543055\pi$
$930$		0			0
$931$	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	−0.982140	−	0.188150i	$-0.939751\pi$
$947$	−20.1262	−	34.8596i	−0.654013	−	1.13278i	0.328127	−	0.944634i	$-0.393582\pi$
$948$		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	−0.887179	−	0.461425i	$-0.847338\pi$
$953$	−1.35782	+	2.35181i	−0.0439840	+	0.0761825i	0.843195	+	0.537607i	$0.180672\pi$
$954$		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	−0.998519	−	0.0543952i	$-0.982677\pi$
$971$	−14.0895	+	24.4037i	−0.452152	+	0.783150i	0.546367	+	0.837546i	$0.316010\pi$
$972$		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	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	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	0.927922	+	0.372774i	$0.121593\pi$
$991$	24.7684	+	42.9001i	0.786793	+	1.36277i	−0.141129	+	0.989991i	$0.545073\pi$
$992$	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	−0.946745	−	0.321985i	$-0.895650\pi$
$997$	−6.14218	+	10.6386i	−0.194525	+	0.336927i	0.752220	+	0.658912i	$0.228983\pi$
$998$	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.757.1		4
3.2	odd	2		546.2.l.k.211.2	✓	4
13.9	even	3	inner	1638.2.r.ba.1387.1		4
39.23	odd	6		7098.2.a.bk.1.2		2
39.29	odd	6		7098.2.a.br.1.1		2
39.35	odd	6		546.2.l.k.295.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.k.211.2	✓	4	3.2	odd	2
546.2.l.k.295.2	yes	4	39.35	odd	6
1638.2.r.ba.757.1		4	1.1	even	1	trivial
1638.2.r.ba.1387.1		4	13.9	even	3	inner
7098.2.a.bk.1.2		2	39.23	odd	6
7098.2.a.br.1.1		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)

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