LMFDB - Embedded newform 1638.2.r.x.1387.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1387.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	1638.1387
Dual form			1638.2.r.x.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.27492 q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.63746 - 2.83616i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(3.50000 + 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(4.27492 + 7.40437i) q^{19} +(-1.63746 - 2.83616i) q^{20} +(2.00000 + 3.46410i) q^{22} +(1.13746 - 1.97014i) q^{23} +5.72508 q^{25} +(2.50000 - 2.59808i) q^{26} +(-0.500000 + 0.866025i) q^{28} +(0.362541 - 0.627940i) q^{29} +6.27492 q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(-1.63746 - 2.83616i) q^{35} +(3.63746 - 6.30026i) q^{37} +8.54983 q^{38} -3.27492 q^{40} +(0.362541 - 0.627940i) q^{41} +(-5.41238 - 9.37451i) q^{43} +4.00000 q^{44} +(-1.13746 - 1.97014i) q^{46} -8.54983 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.86254 - 4.95807i) q^{50} +(-1.00000 - 3.46410i) q^{52} -11.5498 q^{53} +(-6.54983 + 11.3446i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.362541 - 0.627940i) q^{58} +(5.41238 + 9.37451i) q^{59} +(4.50000 + 7.79423i) q^{61} +(3.13746 - 5.43424i) q^{62} +1.00000 q^{64} +(11.4622 + 2.83616i) q^{65} +(5.13746 - 8.89834i) q^{67} +(1.50000 - 2.59808i) q^{68} -3.27492 q^{70} +(-1.13746 - 1.97014i) q^{71} +13.2749 q^{73} +(-3.63746 - 6.30026i) q^{74} +(4.27492 - 7.40437i) q^{76} +4.00000 q^{77} -8.00000 q^{79} +(-1.63746 + 2.83616i) q^{80} +(-0.362541 - 0.627940i) q^{82} -10.8248 q^{83} +(4.91238 + 8.50848i) q^{85} -10.8248 q^{86} +(2.00000 - 3.46410i) q^{88} +(4.13746 - 7.16629i) q^{89} +(-1.00000 - 3.46410i) q^{91} -2.27492 q^{92} +(-4.27492 + 7.40437i) q^{94} +(14.0000 + 24.2487i) q^{95} +(-7.27492 - 12.6005i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8} - q^{10} - 8 q^{11} + 14 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{17} + 2 q^{19} + q^{20} + 8 q^{22} - 3 q^{23} + 38 q^{25} + 10 q^{26} - 2 q^{28} + 9 q^{29}+ \cdots + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8 - q^10 - 8 * q^11 + 14 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^17 + 2 * q^19 + q^20 + 8 * q^22 - 3 * q^23 + 38 * q^25 + 10 * q^26 - 2 * q^28 + 9 * q^29 + 10 * q^31 + 2 * q^32 + 12 * q^34 + q^35 + 7 * q^37 + 4 * q^38 + 2 * q^40 + 9 * q^41 + q^43 + 16 * q^44 + 3 * q^46 - 4 * q^47 - 2 * q^49 + 19 * q^50 - 4 * q^52 - 16 * q^53 + 4 * q^55 + 2 * q^56 - 9 * q^58 - q^59 + 18 * q^61 + 5 * q^62 + 4 * q^64 - 7 * q^65 + 13 * q^67 + 6 * q^68 + 2 * q^70 + 3 * q^71 + 38 * q^73 - 7 * q^74 + 2 * q^76 + 16 * q^77 - 32 * q^79 + q^80 - 9 * q^82 + 2 * q^83 - 3 * q^85 + 2 * q^86 + 8 * q^88 + 9 * q^89 - 4 * q^91 + 6 * q^92 - 2 * q^94 + 56 * q^95 - 14 * q^97 + 2 * q^98

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
$5$	3.27492			1.46459			0.732294	−	0.680989i	$-0.238450\pi$
$5$	3.27492			1.46459			0.732294	+	0.680989i	$0.238450\pi$
$6$		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
$10$	1.63746	−	2.83616i	0.517810	−	0.896873i
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	4.27492	+	7.40437i	0.980733	+	1.69868i	0.659546	+	0.751664i	$0.270749\pi$
$19$	4.27492	+	7.40437i	0.980733	+	1.69868i	0.321187	+	0.947016i	$0.395918\pi$
$20$	−1.63746	−	2.83616i	−0.366147	−	0.634185i
$21$		0			0
$22$	2.00000	+	3.46410i	0.426401	+	0.738549i
$23$	1.13746	−	1.97014i	0.237177	−	0.410802i	−0.722726	−	0.691134i	$-0.757111\pi$
$23$	1.13746	−	1.97014i	0.237177	−	0.410802i	0.959903	+	0.280332i	$0.0904447\pi$
$24$		0			0
$25$	5.72508			1.14502
$26$	2.50000	−	2.59808i	0.490290	−	0.509525i
$27$		0			0
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	0.362541	−	0.627940i	0.0673222	−	0.116606i	−0.830400	−	0.557168i	$-0.811888\pi$
$29$	0.362541	−	0.627940i	0.0673222	−	0.116606i	0.897722	+	0.440563i	$0.145221\pi$
$30$		0			0
$31$	6.27492			1.12701			0.563504	−	0.826113i	$-0.309453\pi$
$31$	6.27492			1.12701			0.563504	+	0.826113i	$0.309453\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	−1.63746	−	2.83616i	−0.276781	−	0.479399i
$36$		0			0
$37$	3.63746	−	6.30026i	0.597995	−	1.03576i	−0.395122	−	0.918629i	$-0.629298\pi$
$37$	3.63746	−	6.30026i	0.597995	−	1.03576i	0.993117	−	0.117128i	$-0.0373689\pi$
$38$	8.54983			1.38697
$39$		0			0
$40$	−3.27492			−0.517810
$41$	0.362541	−	0.627940i	0.0566195	−	0.0980678i	−0.836326	−	0.548232i	$-0.815301\pi$
$41$	0.362541	−	0.627940i	0.0566195	−	0.0980678i	0.892946	+	0.450164i	$0.148634\pi$
$42$		0			0
$43$	−5.41238	−	9.37451i	−0.825380	−	1.42960i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−5.41238	−	9.37451i	−0.825380	−	1.42960i	0.0762493	−	0.997089i	$-0.475706\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$	−1.13746	−	1.97014i	−0.167709	−	0.290481i
$47$	−8.54983			−1.24712			−0.623561	−	0.781775i	$-0.714315\pi$
$47$	−8.54983			−1.24712			−0.623561	+	0.781775i	$0.714315\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.86254	−	4.95807i	0.404824	−	0.701177i
$51$		0			0
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	−11.5498			−1.58649			−0.793246	−	0.608901i	$-0.791610\pi$
$53$	−11.5498			−1.58649			−0.793246	+	0.608901i	$0.791610\pi$
$54$		0			0
$55$	−6.54983	+	11.3446i	−0.883179	+	1.52971i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	−0.362541	−	0.627940i	−0.0476040	−	0.0824526i
$59$	5.41238	+	9.37451i	0.704631	+	1.22046i	0.966824	+	0.255442i	$0.0822209\pi$
$59$	5.41238	+	9.37451i	0.704631	+	1.22046i	−0.262193	+	0.965015i	$0.584446\pi$
$60$		0			0
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$	3.13746	−	5.43424i	0.398458	−	0.690149i
$63$		0			0
$64$	1.00000			0.125000
$65$	11.4622	+	2.83616i	1.42171	+	0.351783i
$66$		0			0
$67$	5.13746	−	8.89834i	0.627640	−	1.08711i	−0.360383	−	0.932804i	$-0.617354\pi$
$67$	5.13746	−	8.89834i	0.627640	−	1.08711i	0.988024	−	0.154301i	$-0.0493125\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	−3.27492			−0.391427
$71$	−1.13746	−	1.97014i	−0.134992	−	0.233812i	0.790603	−	0.612329i	$-0.209767\pi$
$71$	−1.13746	−	1.97014i	−0.134992	−	0.233812i	−0.925594	+	0.378517i	$0.876434\pi$
$72$		0			0
$73$	13.2749			1.55371			0.776856	−	0.629679i	$-0.216813\pi$
$73$	13.2749			1.55371			0.776856	+	0.629679i	$0.216813\pi$
$74$	−3.63746	−	6.30026i	−0.422846	−	0.732391i
$75$		0			0
$76$	4.27492	−	7.40437i	0.490367	−	0.849340i
$77$	4.00000			0.455842
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−1.63746	+	2.83616i	−0.183073	+	0.317092i
$81$		0			0
$82$	−0.362541	−	0.627940i	−0.0400360	−	0.0693444i
$83$	−10.8248			−1.18817			−0.594085	−	0.804402i	$-0.702486\pi$
$83$	−10.8248			−1.18817			−0.594085	+	0.804402i	$0.702486\pi$
$84$		0			0
$85$	4.91238	+	8.50848i	0.532822	+	0.922875i
$86$	−10.8248			−1.16726
$87$		0			0
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	4.13746	−	7.16629i	0.438570	−	0.759625i	−0.559010	−	0.829161i	$-0.688819\pi$
$89$	4.13746	−	7.16629i	0.438570	−	0.759625i	0.997579	+	0.0695360i	$0.0221519\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	−2.27492			−0.237177
$93$		0			0
$94$	−4.27492	+	7.40437i	−0.440924	+	0.763703i
$95$	14.0000	+	24.2487i	1.43637	+	2.48787i
$96$		0			0
$97$	−7.27492	−	12.6005i	−0.738656	−	1.27939i	−0.953101	−	0.302653i	$-0.902128\pi$
$97$	−7.27492	−	12.6005i	−0.738656	−	1.27939i	0.214445	−	0.976736i	$-0.431206\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	−2.86254	−	4.95807i	−0.286254	−	0.495807i
$101$	4.63746	−	8.03231i	0.461444	−	0.799245i	−0.537589	−	0.843207i	$-0.680665\pi$
$101$	4.63746	−	8.03231i	0.461444	−	0.799245i	0.999033	+	0.0439620i	$0.0139981\pi$
$102$		0			0
$103$	−2.27492			−0.224154			−0.112077	−	0.993700i	$-0.535750\pi$
$103$	−2.27492			−0.224154			−0.112077	+	0.993700i	$0.535750\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$		0			0
$106$	−5.77492	+	10.0025i	−0.560910	+	0.971524i
$107$	−6.27492	+	10.8685i	−0.606619	+	1.05070i	0.385174	+	0.922844i	$0.374141\pi$
$107$	−6.27492	+	10.8685i	−0.606619	+	1.05070i	−0.991793	+	0.127851i	$0.959192\pi$
$108$		0			0
$109$	10.5498			1.01049			0.505245	−	0.862976i	$-0.331402\pi$
$109$	10.5498			1.01049			0.505245	+	0.862976i	$0.331402\pi$
$110$	6.54983	+	11.3446i	0.624502	+	1.08167i
$111$		0			0
$112$	1.00000			0.0944911
$113$	−3.91238	−	6.77643i	−0.368045	−	0.637473i	0.621215	−	0.783641i	$-0.286640\pi$
$113$	−3.91238	−	6.77643i	−0.368045	−	0.637473i	−0.989260	+	0.146167i	$0.953306\pi$
$114$		0			0
$115$	3.72508	−	6.45203i	0.347366	−	0.601655i
$116$	−0.725083			−0.0673222
$117$		0			0
$118$	10.8248			0.996499
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	9.00000			0.814822
$123$		0			0
$124$	−3.13746	−	5.43424i	−0.281752	−	0.488009i
$125$	2.37459			0.212389
$126$		0			0
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	−0.987108	−	0.160055i	$-0.948833\pi$
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	0.632166	+	0.774833i	$0.282166\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	8.18729	−	8.50848i	0.718073	−	0.746243i
$131$	10.2749			0.897724			0.448862	−	0.893601i	$-0.351830\pi$
$131$	10.2749			0.897724			0.448862	+	0.893601i	$0.351830\pi$
$132$		0			0
$133$	4.27492	−	7.40437i	0.370682	−	0.642041i
$134$	−5.13746	−	8.89834i	−0.443809	−	0.768699i
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	0.0876242	+	0.151770i	0.00748624	+	0.0129665i	0.869744	−	0.493503i	$-0.164284\pi$
$137$	0.0876242	+	0.151770i	0.00748624	+	0.0129665i	−0.862258	+	0.506469i	$0.830950\pi$
$138$		0			0
$139$	−10.5498	−	18.2728i	−0.894825	−	1.54988i	−0.834021	−	0.551733i	$-0.813967\pi$
$139$	−10.5498	−	18.2728i	−0.894825	−	1.54988i	−0.0608046	−	0.998150i	$-0.519367\pi$
$140$	−1.63746	+	2.83616i	−0.138391	+	0.239699i
$141$		0			0
$142$	−2.27492			−0.190907
$143$	−10.0000	+	10.3923i	−0.836242	+	0.869048i
$144$		0			0
$145$	1.18729	−	2.05645i	0.0985993	−	0.170779i
$146$	6.63746	−	11.4964i	0.549320	−	0.951450i
$147$		0			0
$148$	−7.27492			−0.597995
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$		0			0
$151$	−17.0997			−1.39155			−0.695776	−	0.718259i	$-0.744939\pi$
$151$	−17.0997			−1.39155			−0.695776	+	0.718259i	$0.744939\pi$
$152$	−4.27492	−	7.40437i	−0.346742	−	0.600574i
$153$		0			0
$154$	2.00000	−	3.46410i	0.161165	−	0.279145i
$155$	20.5498			1.65060
$156$		0			0
$157$	−11.2749			−0.899836			−0.449918	−	0.893070i	$-0.648547\pi$
$157$	−11.2749			−0.899836			−0.449918	+	0.893070i	$0.648547\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$		0			0
$160$	1.63746	+	2.83616i	0.129452	+	0.224218i
$161$	−2.27492			−0.179289
$162$		0			0
$163$	2.86254	+	4.95807i	0.224212	+	0.388346i	0.956083	−	0.293097i	$-0.0946860\pi$
$163$	2.86254	+	4.95807i	0.224212	+	0.388346i	−0.731871	+	0.681443i	$0.761353\pi$
$164$	−0.725083			−0.0566195
$165$		0			0
$166$	−5.41238	+	9.37451i	−0.420082	+	0.727603i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	9.82475			0.753524
$171$		0			0
$172$	−5.41238	+	9.37451i	−0.412690	+	0.714800i
$173$	5.27492	+	9.13642i	0.401045	+	0.694630i	0.993852	−	0.110715i	$-0.0353139\pi$
$173$	5.27492	+	9.13642i	0.401045	+	0.694630i	−0.592808	+	0.805344i	$0.701981\pi$
$174$		0			0
$175$	−2.86254	−	4.95807i	−0.216388	−	0.374795i
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$		0			0
$178$	−4.13746	−	7.16629i	−0.310116	−	0.537136i
$179$	8.27492	−	14.3326i	0.618496	−	1.07127i	−0.371264	−	0.928527i	$-0.621075\pi$
$179$	8.27492	−	14.3326i	0.618496	−	1.07127i	0.989760	−	0.142740i	$-0.0455912\pi$
$180$		0			0
$181$	5.82475			0.432950			0.216475	−	0.976288i	$-0.430544\pi$
$181$	5.82475			0.432950			0.216475	+	0.976288i	$0.430544\pi$
$182$	−3.50000	−	0.866025i	−0.259437	−	0.0641941i
$183$		0			0
$184$	−1.13746	+	1.97014i	−0.0838546	+	0.145240i
$185$	11.9124	−	20.6328i	0.875815	−	1.51696i
$186$		0			0
$187$	−12.0000			−0.877527
$188$	4.27492	+	7.40437i	0.311780	+	0.540019i
$189$		0			0
$190$	28.0000			2.03133
$191$	7.13746	+	12.3624i	0.516448	+	0.894515i	0.999818	+	0.0190983i	$0.00607953\pi$
$191$	7.13746	+	12.3624i	0.516448	+	0.894515i	−0.483369	+	0.875417i	$0.660587\pi$
$192$		0			0
$193$	1.08762	−	1.88382i	0.0782889	−	0.135600i	−0.824223	−	0.566266i	$-0.808388\pi$
$193$	1.08762	−	1.88382i	0.0782889	−	0.135600i	0.902512	+	0.430665i	$0.141721\pi$
$194$	−14.5498			−1.04462
$195$		0			0
$196$	1.00000			0.0714286
$197$	0.412376	−	0.714256i	0.0293806	−	0.0508886i	−0.850961	−	0.525228i	$-0.823980\pi$
$197$	0.412376	−	0.714256i	0.0293806	−	0.0508886i	0.880342	+	0.474340i	$0.157313\pi$
$198$		0			0
$199$	5.41238	+	9.37451i	0.383673	+	0.664541i	0.991584	−	0.129464i	$-0.0413256\pi$
$199$	5.41238	+	9.37451i	0.383673	+	0.664541i	−0.607911	+	0.794005i	$0.707992\pi$
$200$	−5.72508			−0.404824
$201$		0			0
$202$	−4.63746	−	8.03231i	−0.326290	−	0.565152i
$203$	−0.725083			−0.0508908
$204$		0			0
$205$	1.18729	−	2.05645i	0.0829241	−	0.143629i
$206$	−1.13746	+	1.97014i	−0.0792505	+	0.137266i
$207$		0			0
$208$	−2.50000	+	2.59808i	−0.173344	+	0.180144i
$209$	−34.1993			−2.36562
$210$		0			0
$211$	4.54983	−	7.88054i	0.313224	−	0.542519i	−0.665835	−	0.746099i	$-0.731924\pi$
$211$	4.54983	−	7.88054i	0.313224	−	0.542519i	0.979058	+	0.203580i	$0.0652578\pi$
$212$	5.77492	+	10.0025i	0.396623	+	0.686971i
$213$		0			0
$214$	6.27492	+	10.8685i	0.428945	+	0.742954i
$215$	−17.7251	−	30.7007i	−1.20884	−	2.09377i
$216$		0			0
$217$	−3.13746	−	5.43424i	−0.212985	−	0.368900i
$218$	5.27492	−	9.13642i	0.357262	−	0.618797i
$219$		0			0
$220$	13.0997			0.883179
$221$	3.00000	+	10.3923i	0.201802	+	0.699062i
$222$		0			0
$223$	−9.13746	+	15.8265i	−0.611889	+	1.05982i	0.379032	+	0.925383i	$0.376257\pi$
$223$	−9.13746	+	15.8265i	−0.611889	+	1.05982i	−0.990922	+	0.134440i	$0.957076\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	−7.82475			−0.520495
$227$	4.54983	+	7.88054i	0.301983	+	0.523050i	0.976585	−	0.215132i	$-0.0690180\pi$
$227$	4.54983	+	7.88054i	0.301983	+	0.523050i	−0.674602	+	0.738182i	$0.735685\pi$
$228$		0			0
$229$	20.2749			1.33980			0.669902	−	0.742449i	$-0.266336\pi$
$229$	20.2749			1.33980			0.669902	+	0.742449i	$0.266336\pi$
$230$	−3.72508	−	6.45203i	−0.245625	−	0.425434i
$231$		0			0
$232$	−0.362541	+	0.627940i	−0.0238020	+	0.0412263i
$233$	−22.5498			−1.47729			−0.738644	−	0.674095i	$-0.764534\pi$
$233$	−22.5498			−1.47729			−0.738644	+	0.674095i	$0.764534\pi$
$234$		0			0
$235$	−28.0000			−1.82652
$236$	5.41238	−	9.37451i	0.352316	−	0.610229i
$237$		0			0
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	−2.27492			−0.147152			−0.0735761	−	0.997290i	$-0.523441\pi$
$239$	−2.27492			−0.147152			−0.0735761	+	0.997290i	$0.523441\pi$
$240$		0			0
$241$	11.6375	+	20.1567i	0.749635	+	1.29841i	0.947998	+	0.318277i	$0.103104\pi$
$241$	11.6375	+	20.1567i	0.749635	+	1.29841i	−0.198363	+	0.980129i	$0.563563\pi$
$242$	−5.00000			−0.321412
$243$		0			0
$244$	4.50000	−	7.79423i	0.288083	−	0.498974i
$245$	−1.63746	+	2.83616i	−0.104613	+	0.181196i
$246$		0			0
$247$	8.54983	+	29.6175i	0.544013	+	1.88452i
$248$	−6.27492			−0.398458
$249$		0			0
$250$	1.18729	−	2.05645i	0.0750910	−	0.130061i
$251$	2.86254	+	4.95807i	0.180682	+	0.312950i	0.942113	−	0.335296i	$-0.108836\pi$
$251$	2.86254	+	4.95807i	0.180682	+	0.312950i	−0.761431	+	0.648246i	$0.775503\pi$
$252$		0			0
$253$	4.54983	+	7.88054i	0.286046	+	0.495446i
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$	−7.27492			−0.452041
$260$	−3.27492	−	11.3446i	−0.203102	−	0.703565i
$261$		0			0
$262$	5.13746	−	8.89834i	0.317393	−	0.549741i
$263$	−4.54983	+	7.88054i	−0.280555	+	0.485935i	−0.971522	−	0.236951i	$-0.923852\pi$
$263$	−4.54983	+	7.88054i	−0.280555	+	0.485935i	0.690967	+	0.722887i	$0.257185\pi$
$264$		0			0
$265$	−37.8248			−2.32356
$266$	−4.27492	−	7.40437i	−0.262112	−	0.453991i
$267$		0			0
$268$	−10.2749			−0.627640
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	−8.86254	+	15.3504i	−0.538361	+	0.932469i	0.460631	+	0.887591i	$0.347623\pi$
$271$	−8.86254	+	15.3504i	−0.538361	+	0.932469i	−0.998993	+	0.0448772i	$0.985710\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	0.175248			0.0105871
$275$	−11.4502	+	19.8323i	−0.690471	+	1.19593i
$276$		0			0
$277$	3.91238	+	6.77643i	0.235072	+	0.407156i	0.959294	−	0.282411i	$-0.0911341\pi$
$277$	3.91238	+	6.77643i	0.235072	+	0.407156i	−0.724222	+	0.689567i	$0.757801\pi$
$278$	−21.0997			−1.26547
$279$		0			0
$280$	1.63746	+	2.83616i	0.0978569	+	0.169493i
$281$	−1.82475			−0.108856			−0.0544278	−	0.998518i	$-0.517333\pi$
$281$	−1.82475			−0.108856			−0.0544278	+	0.998518i	$0.517333\pi$
$282$		0			0
$283$	12.2749	−	21.2608i	0.729668	−	1.26382i	−0.227355	−	0.973812i	$-0.573008\pi$
$283$	12.2749	−	21.2608i	0.729668	−	1.26382i	0.957024	−	0.290010i	$-0.0936588\pi$
$284$	−1.13746	+	1.97014i	−0.0674958	+	0.116906i
$285$		0			0
$286$	4.00000	+	13.8564i	0.236525	+	0.819346i
$287$	−0.725083			−0.0428003
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−1.18729	−	2.05645i	−0.0697202	−	0.120759i
$291$		0			0
$292$	−6.63746	−	11.4964i	−0.388428	−	0.672777i
$293$	−5.36254	−	9.28819i	−0.313283	−	0.542622i	0.665788	−	0.746141i	$-0.268096\pi$
$293$	−5.36254	−	9.28819i	−0.313283	−	0.542622i	−0.979071	+	0.203519i	$0.934762\pi$
$294$		0			0
$295$	17.7251	+	30.7007i	1.03199	+	1.78747i
$296$	−3.63746	+	6.30026i	−0.211423	+	0.366195i
$297$		0			0
$298$	−1.00000			−0.0579284
$299$	5.68729	−	5.91041i	0.328905	−	0.341808i
$300$		0			0
$301$	−5.41238	+	9.37451i	−0.311964	+	0.540338i
$302$	−8.54983	+	14.8087i	−0.491988	+	0.852148i
$303$		0			0
$304$	−8.54983			−0.490367
$305$	14.7371	+	25.5255i	0.843845	+	1.46158i
$306$		0			0
$307$	−16.5498			−0.944549			−0.472274	−	0.881452i	$-0.656567\pi$
$307$	−16.5498			−0.944549			−0.472274	+	0.881452i	$0.656567\pi$
$308$	−2.00000	−	3.46410i	−0.113961	−	0.197386i
$309$		0			0
$310$	10.2749	−	17.7967i	0.583576	−	1.01078i
$311$	−12.5498			−0.711636			−0.355818	−	0.934555i	$-0.615798\pi$
$311$	−12.5498			−0.711636			−0.355818	+	0.934555i	$0.615798\pi$
$312$		0			0
$313$	−27.6495			−1.56284			−0.781421	−	0.624004i	$-0.785505\pi$
$313$	−27.6495			−1.56284			−0.781421	+	0.624004i	$0.785505\pi$
$314$	−5.63746	+	9.76436i	−0.318140	+	0.551035i
$315$		0			0
$316$	4.00000	+	6.92820i	0.225018	+	0.389742i
$317$	−7.54983			−0.424041			−0.212020	−	0.977265i	$-0.568004\pi$
$317$	−7.54983			−0.424041			−0.212020	+	0.977265i	$0.568004\pi$
$318$		0			0
$319$	1.45017	+	2.51176i	0.0811937	+	0.140632i
$320$	3.27492			0.183073
$321$		0			0
$322$	−1.13746	+	1.97014i	−0.0633881	+	0.109791i
$323$	−12.8248	+	22.2131i	−0.713588	+	1.23597i
$324$		0			0
$325$	20.0378	+	4.95807i	1.11150	+	0.275024i
$326$	5.72508			0.317083
$327$		0			0
$328$	−0.362541	+	0.627940i	−0.0200180	+	0.0346722i
$329$	4.27492	+	7.40437i	0.235684	+	0.408216i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	5.41238	+	9.37451i	0.297043	+	0.514493i
$333$		0			0
$334$		0			0
$335$	16.8248	−	29.1413i	0.919234	−	1.59216i
$336$		0			0
$337$	−7.27492			−0.396290			−0.198145	−	0.980173i	$-0.563492\pi$
$337$	−7.27492			−0.396290			−0.198145	+	0.980173i	$0.563492\pi$
$338$	11.0000	−	6.92820i	0.598321	−	0.376845i
$339$		0			0
$340$	4.91238	−	8.50848i	0.266411	−	0.461437i
$341$	−12.5498	+	21.7370i	−0.679612	+	1.17712i
$342$		0			0
$343$	1.00000			0.0539949
$344$	5.41238	+	9.37451i	0.291816	+	0.505440i
$345$		0			0
$346$	10.5498			0.567163
$347$	7.72508	+	13.3802i	0.414704	+	0.718289i	0.995397	−	0.0958338i	$-0.0305517\pi$
$347$	7.72508	+	13.3802i	0.414704	+	0.718289i	−0.580693	+	0.814122i	$0.697218\pi$
$348$		0			0
$349$	−8.96221	+	15.5230i	−0.479736	+	0.830927i	−0.999730	−	0.0232427i	$-0.992601\pi$
$349$	−8.96221	+	15.5230i	−0.479736	+	0.830927i	0.519994	+	0.854170i	$0.325934\pi$
$350$	−5.72508			−0.306019
$351$		0			0
$352$	−4.00000			−0.213201
$353$	−2.22508	+	3.85396i	−0.118429	+	0.205125i	−0.919145	−	0.393919i	$-0.871119\pi$
$353$	−2.22508	+	3.85396i	−0.118429	+	0.205125i	0.800716	+	0.599044i	$0.204453\pi$
$354$		0			0
$355$	−3.72508	−	6.45203i	−0.197707	−	0.342438i
$356$	−8.27492			−0.438570
$357$		0			0
$358$	−8.27492	−	14.3326i	−0.437343	−	0.757500i
$359$	−29.0997			−1.53582			−0.767911	−	0.640557i	$-0.778704\pi$
$359$	−29.0997			−1.53582			−0.767911	+	0.640557i	$0.778704\pi$
$360$		0			0
$361$	−27.0498	+	46.8517i	−1.42368	+	2.46588i
$362$	2.91238	−	5.04438i	0.153071	−	0.265127i
$363$		0			0
$364$	−2.50000	+	2.59808i	−0.131036	+	0.136176i
$365$	43.4743			2.27555
$366$		0			0
$367$	−2.86254	+	4.95807i	−0.149423	+	0.258809i	−0.931015	−	0.364982i	$-0.881075\pi$
$367$	−2.86254	+	4.95807i	−0.149423	+	0.258809i	0.781591	+	0.623791i	$0.214408\pi$
$368$	1.13746	+	1.97014i	0.0592941	+	0.102700i
$369$		0			0
$370$	−11.9124	−	20.6328i	−0.619295	−	1.07265i
$371$	5.77492	+	10.0025i	0.299819	+	0.519301i
$372$		0			0
$373$	−2.08762	−	3.61587i	−0.108093	−	0.187223i	0.806905	−	0.590682i	$-0.201141\pi$
$373$	−2.08762	−	3.61587i	−0.108093	−	0.187223i	−0.914998	+	0.403459i	$0.867808\pi$
$374$	−6.00000	+	10.3923i	−0.310253	+	0.537373i
$375$		0			0
$376$	8.54983			0.440924
$377$	1.81271	−	1.88382i	0.0933592	−	0.0970217i
$378$		0			0
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$	14.0000	−	24.2487i	0.718185	−	1.24393i
$381$		0			0
$382$	14.2749			0.730368
$383$	−19.0997	−	33.0816i	−0.975947	−	1.69039i	−0.676772	−	0.736192i	$-0.736622\pi$
$383$	−19.0997	−	33.0816i	−0.975947	−	1.69039i	−0.299175	−	0.954198i	$-0.596712\pi$
$384$		0			0
$385$	13.0997			0.667621
$386$	−1.08762	−	1.88382i	−0.0553586	−	0.0958839i
$387$		0			0
$388$	−7.27492	+	12.6005i	−0.369328	+	0.639695i
$389$	−20.6495			−1.04697			−0.523486	−	0.852034i	$-0.675369\pi$
$389$	−20.6495			−1.04697			−0.523486	+	0.852034i	$0.675369\pi$
$390$		0			0
$391$	6.82475			0.345143
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	−0.412376	−	0.714256i	−0.0207752	−	0.0359837i
$395$	−26.1993			−1.31823
$396$		0			0
$397$	−7.86254	−	13.6183i	−0.394610	−	0.683484i	0.598442	−	0.801166i	$-0.295787\pi$
$397$	−7.86254	−	13.6183i	−0.394610	−	0.683484i	−0.993051	+	0.117682i	$0.962454\pi$
$398$	10.8248			0.542596
$399$		0			0
$400$	−2.86254	+	4.95807i	−0.143127	+	0.247903i
$401$	2.63746	−	4.56821i	0.131708	−	0.228126i	−0.792627	−	0.609707i	$-0.791287\pi$
$401$	2.63746	−	4.56821i	0.131708	−	0.228126i	0.924335	+	0.381581i	$0.124620\pi$
$402$		0			0
$403$	21.9622	+	5.43424i	1.09402	+	0.270699i
$404$	−9.27492			−0.461444
$405$		0			0
$406$	−0.362541	+	0.627940i	−0.0179926	+	0.0311641i
$407$	14.5498	+	25.2011i	0.721209	+	1.24917i
$408$		0			0
$409$	−11.4622	−	19.8531i	−0.566770	−	0.981674i	−0.996883	−	0.0788990i	$-0.974860\pi$
$409$	−11.4622	−	19.8531i	−0.566770	−	0.981674i	0.430113	−	0.902775i	$-0.358474\pi$
$410$	−1.18729	−	2.05645i	−0.0586362	−	0.101561i
$411$		0			0
$412$	1.13746	+	1.97014i	0.0560386	+	0.0970616i
$413$	5.41238	−	9.37451i	0.266326	−	0.461289i
$414$		0			0
$415$	−35.4502			−1.74018
$416$	1.00000	+	3.46410i	0.0490290	+	0.169842i
$417$		0			0
$418$	−17.0997	+	29.6175i	−0.836372	+	1.44864i
$419$	7.68729	−	13.3148i	0.375549	−	0.650470i	−0.614860	−	0.788636i	$-0.710788\pi$
$419$	7.68729	−	13.3148i	0.375549	−	0.650470i	0.990409	+	0.138166i	$0.0441209\pi$
$420$		0			0
$421$	0.725083			0.0353384			0.0176692	−	0.999844i	$-0.494375\pi$
$421$	0.725083			0.0353384			0.0176692	+	0.999844i	$0.494375\pi$
$422$	−4.54983	−	7.88054i	−0.221482	−	0.383619i
$423$		0			0
$424$	11.5498			0.560910
$425$	8.58762	+	14.8742i	0.416561	+	0.721505i
$426$		0			0
$427$	4.50000	−	7.79423i	0.217770	−	0.377189i
$428$	12.5498			0.606619
$429$		0			0
$430$	−35.4502			−1.70956
$431$	−2.86254	+	4.95807i	−0.137884	+	0.238822i	−0.926695	−	0.375813i	$-0.877363\pi$
$431$	−2.86254	+	4.95807i	−0.137884	+	0.238822i	0.788812	+	0.614635i	$0.210697\pi$
$432$		0			0
$433$	1.36254	+	2.35999i	0.0654796	+	0.113414i	0.896907	−	0.442220i	$-0.145809\pi$
$433$	1.36254	+	2.35999i	0.0654796	+	0.113414i	−0.831427	+	0.555634i	$0.812476\pi$
$434$	−6.27492			−0.301206
$435$		0			0
$436$	−5.27492	−	9.13642i	−0.252623	−	0.437555i
$437$	19.4502			0.930428
$438$		0			0
$439$	8.54983	−	14.8087i	0.408061	−	0.706783i	−0.586611	−	0.809869i	$-0.699538\pi$
$439$	8.54983	−	14.8087i	0.408061	−	0.706783i	0.994672	+	0.103086i	$0.0328716\pi$
$440$	6.54983	−	11.3446i	0.312251	−	0.540835i
$441$		0			0
$442$	10.5000	+	2.59808i	0.499434	+	0.123578i
$443$	−19.4502			−0.924105			−0.462053	−	0.886853i	$-0.652887\pi$
$443$	−19.4502			−0.924105			−0.462053	+	0.886853i	$0.652887\pi$
$444$		0			0
$445$	13.5498	−	23.4690i	0.642324	−	1.11254i
$446$	9.13746	+	15.8265i	0.432671	+	0.749409i
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	5.54983	+	9.61260i	0.261913	+	0.453646i	0.966750	−	0.255723i	$-0.0823134\pi$
$449$	5.54983	+	9.61260i	0.261913	+	0.453646i	−0.704837	+	0.709369i	$0.748980\pi$
$450$		0			0
$451$	1.45017	+	2.51176i	0.0682856	+	0.118274i
$452$	−3.91238	+	6.77643i	−0.184023	+	0.318737i
$453$		0			0
$454$	9.09967			0.427069
$455$	−3.27492	−	11.3446i	−0.153530	−	0.531845i
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$	10.1375	−	17.5586i	0.473692	−	0.820459i
$459$		0			0
$460$	−7.45017			−0.347366
$461$	9.18729	+	15.9129i	0.427895	+	0.741136i	0.996686	−	0.0813464i	$-0.0259220\pi$
$461$	9.18729	+	15.9129i	0.427895	+	0.741136i	−0.568791	+	0.822482i	$0.692589\pi$
$462$		0			0
$463$	4.54983			0.211449			0.105724	−	0.994395i	$-0.466284\pi$
$463$	4.54983			0.211449			0.105724	+	0.994395i	$0.466284\pi$
$464$	0.362541	+	0.627940i	0.0168306	+	0.0291514i
$465$		0			0
$466$	−11.2749	+	19.5287i	−0.522300	+	0.904651i
$467$	30.8248			1.42640			0.713200	−	0.700961i	$-0.247245\pi$
$467$	30.8248			1.42640			0.713200	+	0.700961i	$0.247245\pi$
$468$		0			0
$469$	−10.2749			−0.474452
$470$	−14.0000	+	24.2487i	−0.645772	+	1.11851i
$471$		0			0
$472$	−5.41238	−	9.37451i	−0.249125	−	0.431497i
$473$	43.2990			1.99089
$474$		0			0
$475$	24.4743	+	42.3907i	1.12296	+	1.94502i
$476$	−3.00000			−0.137505
$477$		0			0
$478$	−1.13746	+	1.97014i	−0.0520261	+	0.0901119i
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	−0.541884	−	0.840453i	$-0.682289\pi$
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	0.998796	+	0.0490589i	$0.0156222\pi$
$480$		0			0
$481$	18.1873	−	18.9008i	0.829269	−	0.861802i
$482$	23.2749			1.06014
$483$		0			0
$484$	−2.50000	+	4.33013i	−0.113636	+	0.196824i
$485$	−23.8248	−	41.2657i	−1.08183	−	1.87378i
$486$		0			0
$487$	−14.5498	−	25.2011i	−0.659316	−	1.14197i	−0.980793	−	0.195051i	$-0.937513\pi$
$487$	−14.5498	−	25.2011i	−0.659316	−	1.14197i	0.321477	−	0.946917i	$-0.395821\pi$
$488$	−4.50000	−	7.79423i	−0.203705	−	0.352828i
$489$		0			0
$490$	1.63746	+	2.83616i	0.0739728	+	0.128125i
$491$	−2.54983	+	4.41644i	−0.115072	+	0.199311i	−0.917809	−	0.397023i	$-0.870043\pi$
$491$	−2.54983	+	4.41644i	−0.115072	+	0.199311i	0.802736	+	0.596334i	$0.203377\pi$
$492$		0			0
$493$	2.17525			0.0979683
$494$	29.9244	+	7.40437i	1.34636	+	0.333139i
$495$		0			0
$496$	−3.13746	+	5.43424i	−0.140876	+	0.244004i
$497$	−1.13746	+	1.97014i	−0.0510220	+	0.0883727i
$498$		0			0
$499$	−9.17525			−0.410741			−0.205370	−	0.978684i	$-0.565840\pi$
$499$	−9.17525			−0.410741			−0.205370	+	0.978684i	$0.565840\pi$
$500$	−1.18729	−	2.05645i	−0.0530974	−	0.0919673i
$501$		0			0
$502$	5.72508			0.255523
$503$	4.54983	+	7.88054i	0.202867	+	0.351376i	0.949451	−	0.313915i	$-0.101641\pi$
$503$	4.54983	+	7.88054i	0.202867	+	0.351376i	−0.746584	+	0.665291i	$0.768307\pi$
$504$		0			0
$505$	15.1873	−	26.3052i	0.675826	−	1.17056i
$506$	9.09967			0.404530
$507$		0			0
$508$	8.00000			0.354943
$509$	−17.9124	+	31.0251i	−0.793952	+	1.37517i	0.129550	+	0.991573i	$0.458647\pi$
$509$	−17.9124	+	31.0251i	−0.793952	+	1.37517i	−0.923502	+	0.383593i	$0.874687\pi$
$510$		0			0
$511$	−6.63746	−	11.4964i	−0.293624	−	0.508571i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$	−7.45017			−0.328294
$516$		0			0
$517$	17.0997	−	29.6175i	0.752043	−	1.30258i
$518$	−3.63746	+	6.30026i	−0.159821	+	0.276818i
$519$		0			0
$520$	−11.4622	−	2.83616i	−0.502651	−	0.124374i
$521$	−1.82475			−0.0799438			−0.0399719	−	0.999201i	$-0.512727\pi$
$521$	−1.82475			−0.0799438			−0.0399719	+	0.999201i	$0.512727\pi$
$522$		0			0
$523$	−17.0997	+	29.6175i	−0.747716	+	1.29508i	0.201199	+	0.979550i	$0.435516\pi$
$523$	−17.0997	+	29.6175i	−0.747716	+	1.29508i	−0.948915	+	0.315532i	$0.897817\pi$
$524$	−5.13746	−	8.89834i	−0.224431	−	0.388726i
$525$		0			0
$526$	4.54983	+	7.88054i	0.198382	+	0.343608i
$527$	9.41238	+	16.3027i	0.410010	+	0.710157i
$528$		0			0
$529$	8.91238	+	15.4367i	0.387495	+	0.671160i
$530$	−18.9124	+	32.7572i	−0.821501	+	1.42288i
$531$		0			0
$532$	−8.54983			−0.370682
$533$	1.81271	−	1.88382i	0.0785171	−	0.0815973i
$534$		0			0
$535$	−20.5498	+	35.5934i	−0.888447	+	1.53884i
$536$	−5.13746	+	8.89834i	−0.221904	+	0.384350i
$537$		0			0
$538$	−18.0000			−0.776035
$539$	−2.00000	−	3.46410i	−0.0861461	−	0.149209i
$540$		0			0
$541$	−12.3746			−0.532025			−0.266013	−	0.963970i	$-0.585706\pi$
$541$	−12.3746			−0.532025			−0.266013	+	0.963970i	$0.585706\pi$
$542$	8.86254	+	15.3504i	0.380679	+	0.659355i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	34.5498			1.47995
$546$		0			0
$547$	33.0997			1.41524			0.707620	−	0.706593i	$-0.249769\pi$
$547$	33.0997			1.41524			0.707620	+	0.706593i	$0.249769\pi$
$548$	0.0876242	−	0.151770i	0.00374312	−	0.00648327i
$549$		0			0
$550$	11.4502	+	19.8323i	0.488237	+	0.845651i
$551$	6.19934			0.264101
$552$		0			0
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	7.82475			0.332442
$555$		0			0
$556$	−10.5498	+	18.2728i	−0.447413	+	0.774941i
$557$	12.5997	−	21.8233i	0.533865	−	0.924681i	−0.465352	−	0.885126i	$-0.654072\pi$
$557$	12.5997	−	21.8233i	0.533865	−	0.924681i	0.999217	−	0.0395559i	$-0.0125943\pi$
$558$		0			0
$559$	−10.8248	−	37.4980i	−0.457838	−	1.58600i
$560$	3.27492			0.138391
$561$		0			0
$562$	−0.912376	+	1.58028i	−0.0384863	+	0.0666601i
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$		0			0
$565$	−12.8127	−	22.1923i	−0.539035	−	0.933635i
$566$	−12.2749	−	21.2608i	−0.515953	−	0.893657i
$567$		0			0
$568$	1.13746	+	1.97014i	0.0477267	+	0.0826651i
$569$	17.5498	−	30.3972i	0.735727	−	1.27432i	−0.218676	−	0.975797i	$-0.570174\pi$
$569$	17.5498	−	30.3972i	0.735727	−	1.27432i	0.954403	−	0.298520i	$-0.0964928\pi$
$570$		0			0
$571$	−22.2749			−0.932176			−0.466088	−	0.884738i	$-0.654337\pi$
$571$	−22.2749			−0.932176			−0.466088	+	0.884738i	$0.654337\pi$
$572$	14.0000	+	3.46410i	0.585369	+	0.144841i
$573$		0			0
$574$	−0.362541	+	0.627940i	−0.0151322	+	0.0262097i
$575$	6.51204	−	11.2792i	0.271571	−	0.470375i
$576$		0			0
$577$	−28.3746			−1.18125			−0.590625	−	0.806946i	$-0.701119\pi$
$577$	−28.3746			−1.18125			−0.590625	+	0.806946i	$0.701119\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	−2.37459			−0.0985993
$581$	5.41238	+	9.37451i	0.224543	+	0.388920i
$582$		0			0
$583$	23.0997	−	40.0098i	0.956691	−	1.65704i
$584$	−13.2749			−0.549320
$585$		0			0
$586$	−10.7251			−0.443049
$587$	−21.9622	+	38.0397i	−0.906477	+	1.57006i	−0.0875558	+	0.996160i	$0.527906\pi$
$587$	−21.9622	+	38.0397i	−0.906477	+	1.57006i	−0.818922	+	0.573905i	$0.805428\pi$
$588$		0			0
$589$	26.8248	+	46.4618i	1.10529	+	1.91443i
$590$	35.4502			1.45946
$591$		0			0
$592$	3.63746	+	6.30026i	0.149499	+	0.258939i
$593$	−19.5498			−0.802815			−0.401408	−	0.915899i	$-0.631479\pi$
$593$	−19.5498			−0.802815			−0.401408	+	0.915899i	$0.631479\pi$
$594$		0			0
$595$	4.91238	−	8.50848i	0.201388	−	0.348814i
$596$	−0.500000	+	0.866025i	−0.0204808	+	0.0354738i
$597$		0			0
$598$	−2.27492	−	7.88054i	−0.0930283	−	0.322259i
$599$	18.2749			0.746693			0.373346	−	0.927692i	$-0.378210\pi$
$599$	18.2749			0.746693			0.373346	+	0.927692i	$0.378210\pi$
$600$		0			0
$601$	7.63746	−	13.2285i	0.311538	−	0.539600i	−0.667157	−	0.744917i	$-0.732489\pi$
$601$	7.63746	−	13.2285i	0.311538	−	0.539600i	0.978696	+	0.205317i	$0.0658224\pi$
$602$	5.41238	+	9.37451i	0.220592	+	0.382077i
$603$		0			0
$604$	8.54983	+	14.8087i	0.347888	+	0.602559i
$605$	−8.18729	−	14.1808i	−0.332861	−	0.576532i
$606$		0			0
$607$	−11.1375	−	19.2906i	−0.452055	−	0.782983i	0.546458	−	0.837486i	$-0.315976\pi$
$607$	−11.1375	−	19.2906i	−0.452055	−	0.782983i	−0.998514	+	0.0545034i	$0.982642\pi$
$608$	−4.27492	+	7.40437i	−0.173371	+	0.300287i
$609$		0			0
$610$	29.4743			1.19338
$611$	−29.9244	−	7.40437i	−1.21061	−	0.299549i
$612$		0			0
$613$	4.18729	−	7.25260i	0.169123	−	0.292930i	−0.768989	−	0.639262i	$-0.779240\pi$
$613$	4.18729	−	7.25260i	0.169123	−	0.292930i	0.938112	+	0.346332i	$0.112573\pi$
$614$	−8.27492	+	14.3326i	−0.333948	+	0.578416i
$615$		0			0
$616$	−4.00000			−0.161165
$617$	−6.46221	−	11.1929i	−0.260159	−	0.450608i	0.706125	−	0.708087i	$-0.250442\pi$
$617$	−6.46221	−	11.1929i	−0.260159	−	0.450608i	−0.966284	+	0.257479i	$0.917108\pi$
$618$		0			0
$619$	29.6495			1.19171			0.595857	−	0.803090i	$-0.296812\pi$
$619$	29.6495			1.19171			0.595857	+	0.803090i	$0.296812\pi$
$620$	−10.2749	−	17.7967i	−0.412651	−	0.714732i
$621$		0			0
$622$	−6.27492	+	10.8685i	−0.251601	+	0.435786i
$623$	−8.27492			−0.331528
$624$		0			0
$625$	−20.8488			−0.833954
$626$	−13.8248	+	23.9452i	−0.552548	+	0.957042i
$627$		0			0
$628$	5.63746	+	9.76436i	0.224959	+	0.389641i
$629$	21.8248			0.870210
$630$		0			0
$631$	−0.549834	−	0.952341i	−0.0218886	−	0.0379121i	0.854874	−	0.518836i	$-0.173635\pi$
$631$	−0.549834	−	0.952341i	−0.0218886	−	0.0379121i	−0.876762	+	0.480924i	$0.840301\pi$
$632$	8.00000			0.318223
$633$		0			0
$634$	−3.77492	+	6.53835i	−0.149921	+	0.259671i
$635$	−13.0997	+	22.6893i	−0.519845	+	0.900397i
$636$		0			0
$637$	−2.50000	+	2.59808i	−0.0990536	+	0.102940i
$638$	2.90033			0.114825
$639$		0			0
$640$	1.63746	−	2.83616i	0.0647262	−	0.112109i
$641$	−1.91238	−	3.31233i	−0.0755343	−	0.130829i	0.825784	−	0.563986i	$-0.190733\pi$
$641$	−1.91238	−	3.31233i	−0.0755343	−	0.130829i	−0.901318	+	0.433157i	$0.857400\pi$
$642$		0			0
$643$	−21.3746	−	37.0219i	−0.842931	−	1.46000i	−0.887406	−	0.460989i	$-0.847495\pi$
$643$	−21.3746	−	37.0219i	−0.842931	−	1.46000i	0.0444742	−	0.999011i	$-0.485839\pi$
$644$	1.13746	+	1.97014i	0.0448221	+	0.0776342i
$645$		0			0
$646$	12.8248	+	22.2131i	0.504583	+	0.873964i
$647$	12.2749	−	21.2608i	0.482577	−	0.835848i	−0.517223	−	0.855851i	$-0.673034\pi$
$647$	12.2749	−	21.2608i	0.482577	−	0.835848i	0.999800	+	0.0200031i	$0.00636760\pi$
$648$		0			0
$649$	−43.2990			−1.69963
$650$	14.3127	−	14.8742i	0.561391	−	0.583414i
$651$		0			0
$652$	2.86254	−	4.95807i	0.112106	−	0.194173i
$653$	−17.2371	+	29.8556i	−0.674541	+	1.16834i	0.302062	+	0.953288i	$0.402325\pi$
$653$	−17.2371	+	29.8556i	−0.674541	+	1.16834i	−0.976603	+	0.215051i	$0.931008\pi$
$654$		0			0
$655$	33.6495			1.31479
$656$	0.362541	+	0.627940i	0.0141549	+	0.0245169i
$657$		0			0
$658$	8.54983			0.333307
$659$	−14.2749	−	24.7249i	−0.556072	−	0.963145i	−0.997819	−	0.0660052i	$-0.978975\pi$
$659$	−14.2749	−	24.7249i	−0.556072	−	0.963145i	0.441747	−	0.897139i	$-0.354359\pi$
$660$		0			0
$661$	−20.0498	+	34.7273i	−0.779848	+	1.35074i	0.152181	+	0.988353i	$0.451370\pi$
$661$	−20.0498	+	34.7273i	−0.779848	+	1.35074i	−0.932029	+	0.362384i	$0.881963\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	10.8248			0.420082
$665$	14.0000	−	24.2487i	0.542897	−	0.940325i
$666$		0			0
$667$	−0.824752	−	1.42851i	−0.0319345	−	0.0553122i
$668$		0			0
$669$		0			0
$670$	−16.8248	−	29.1413i	−0.649997	−	1.12583i
$671$	−36.0000			−1.38976
$672$		0			0
$673$	−6.04983	+	10.4786i	−0.233204	+	0.403921i	−0.958749	−	0.284253i	$-0.908254\pi$
$673$	−6.04983	+	10.4786i	−0.233204	+	0.403921i	0.725545	+	0.688174i	$0.241588\pi$
$674$	−3.63746	+	6.30026i	−0.140110	+	0.242677i
$675$		0			0
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$	−11.6495			−0.447727			−0.223863	−	0.974621i	$-0.571867\pi$
$677$	−11.6495			−0.447727			−0.223863	+	0.974621i	$0.571867\pi$
$678$		0			0
$679$	−7.27492	+	12.6005i	−0.279186	+	0.483564i
$680$	−4.91238	−	8.50848i	−0.188381	−	0.326285i
$681$		0			0
$682$	12.5498	+	21.7370i	0.480558	+	0.832351i
$683$	−24.8248	−	42.9977i	−0.949893	−	1.64526i	−0.745645	−	0.666343i	$-0.767859\pi$
$683$	−24.8248	−	42.9977i	−0.949893	−	1.64526i	−0.204248	−	0.978919i	$-0.565475\pi$
$684$		0			0
$685$	0.286962	+	0.497033i	0.0109643	+	0.0189906i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	10.8248			0.412690
$689$	−40.4244	−	10.0025i	−1.54005	−	0.381063i
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	5.27492	−	9.13642i	0.200522	−	0.347315i
$693$		0			0
$694$	15.4502			0.586480
$695$	−34.5498	−	59.8421i	−1.31055	−	2.26994i
$696$		0			0
$697$	2.17525			0.0823934
$698$	8.96221	+	15.5230i	0.339225	+	0.587554i
$699$		0			0
$700$	−2.86254	+	4.95807i	−0.108194	+	0.187397i
$701$	37.9244			1.43239			0.716193	−	0.697902i	$-0.245883\pi$
$701$	37.9244			1.43239			0.716193	+	0.697902i	$0.245883\pi$
$702$		0			0
$703$	62.1993			2.34589
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	2.22508	+	3.85396i	0.0837421	+	0.145046i
$707$	−9.27492			−0.348819
$708$		0			0
$709$	4.81271	+	8.33585i	0.180745	+	0.313060i	0.942134	−	0.335235i	$-0.108816\pi$
$709$	4.81271	+	8.33585i	0.180745	+	0.313060i	−0.761389	+	0.648295i	$0.775482\pi$
$710$	−7.45017			−0.279600
$711$		0			0
$712$	−4.13746	+	7.16629i	−0.155058	+	0.268568i
$713$	7.13746	−	12.3624i	0.267300	−	0.462977i
$714$		0			0
$715$	−32.7492	+	34.0339i	−1.22475	+	1.27280i
$716$	−16.5498			−0.618496
$717$		0			0
$718$	−14.5498	+	25.2011i	−0.542995	+	0.940495i
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	0.781748	−	0.623595i	$-0.214328\pi$
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	−0.930923	+	0.365216i	$0.880995\pi$
$720$		0			0
$721$	1.13746	+	1.97014i	0.0423612	+	0.0733717i
$722$	27.0498	+	46.8517i	1.00669	+	1.74364i
$723$		0			0
$724$	−2.91238	−	5.04438i	−0.108238	−	0.187473i
$725$	2.07558	−	3.59501i	0.0770851	−	0.133515i
$726$		0			0
$727$	−2.82475			−0.104764			−0.0523821	−	0.998627i	$-0.516681\pi$
$727$	−2.82475			−0.104764			−0.0523821	+	0.998627i	$0.516681\pi$
$728$	1.00000	+	3.46410i	0.0370625	+	0.128388i
$729$		0			0
$730$	21.7371	−	37.6498i	0.804527	−	1.39348i
$731$	16.2371	−	28.1235i	0.600552	−	1.04019i
$732$		0			0
$733$	12.6495			0.467220			0.233610	−	0.972330i	$-0.424946\pi$
$733$	12.6495			0.467220			0.233610	+	0.972330i	$0.424946\pi$
$734$	2.86254	+	4.95807i	0.105658	+	0.183006i
$735$		0			0
$736$	2.27492			0.0838546
$737$	20.5498	+	35.5934i	0.756963	+	1.31110i
$738$		0			0
$739$	20.8625	−	36.1350i	0.767441	−	1.32925i	−0.171505	−	0.985183i	$-0.554863\pi$
$739$	20.8625	−	36.1350i	0.767441	−	1.32925i	0.938946	−	0.344064i	$-0.111804\pi$
$740$	−23.8248			−0.875815
$741$		0			0
$742$	11.5498			0.424008
$743$	−13.4124	+	23.2309i	−0.492052	+	0.852260i	−0.999958	−	0.00915297i	$-0.997086\pi$
$743$	−13.4124	+	23.2309i	−0.492052	+	0.852260i	0.507906	+	0.861413i	$0.330420\pi$
$744$		0			0
$745$	−1.63746	−	2.83616i	−0.0599918	−	0.103909i
$746$	−4.17525			−0.152867
$747$		0			0
$748$	6.00000	+	10.3923i	0.219382	+	0.379980i
$749$	12.5498			0.458561
$750$		0			0
$751$	1.72508	−	2.98793i	0.0629492	−	0.109031i	−0.832833	−	0.553524i	$-0.813283\pi$
$751$	1.72508	−	2.98793i	0.0629492	−	0.109031i	0.895782	+	0.444493i	$0.146616\pi$
$752$	4.27492	−	7.40437i	0.155890	−	0.270010i
$753$		0			0
$754$	−0.725083	−	2.51176i	−0.0264060	−	0.0914729i
$755$	−56.0000			−2.03805
$756$		0			0
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	−0.527011	−	0.849858i	$-0.676688\pi$
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	0.999505	+	0.0314762i	$0.0100208\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$		0			0
$760$	−14.0000	−	24.2487i	−0.507833	−	0.879593i
$761$	−20.0997	−	34.8136i	−0.728612	−	1.26199i	−0.957470	−	0.288534i	$-0.906832\pi$
$761$	−20.0997	−	34.8136i	−0.728612	−	1.26199i	0.228857	−	0.973460i	$-0.426501\pi$
$762$		0			0
$763$	−5.27492	−	9.13642i	−0.190965	−	0.330761i
$764$	7.13746	−	12.3624i	0.258224	−	0.447257i
$765$		0			0
$766$	−38.1993			−1.38020
$767$	10.8248	+	37.4980i	0.390859	+	1.35398i
$768$		0			0
$769$	1.82475	−	3.16056i	0.0658022	−	0.113973i	−0.831247	−	0.555903i	$-0.812373\pi$
$769$	1.82475	−	3.16056i	0.0658022	−	0.113973i	0.897050	+	0.441930i	$0.145706\pi$
$770$	6.54983	−	11.3446i	0.236040	−	0.408833i
$771$		0			0
$772$	−2.17525			−0.0782889
$773$	−25.5498	−	44.2536i	−0.918964	−	1.59169i	−0.800992	−	0.598675i	$-0.795694\pi$
$773$	−25.5498	−	44.2536i	−0.918964	−	1.59169i	−0.117971	−	0.993017i	$-0.537639\pi$
$774$		0			0
$775$	35.9244			1.29044
$776$	7.27492	+	12.6005i	0.261154	+	0.452333i
$777$		0			0
$778$	−10.3248	+	17.8830i	−0.370160	+	0.641136i
$779$	6.19934			0.222114
$780$		0			0
$781$	9.09967			0.325612
$782$	3.41238	−	5.91041i	0.122026	−	0.211356i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−36.9244			−1.31789
$786$		0			0
$787$	4.54983	+	7.88054i	0.162184	+	0.280911i	0.935652	−	0.352925i	$-0.114813\pi$
$787$	4.54983	+	7.88054i	0.162184	+	0.280911i	−0.773468	+	0.633836i	$0.781479\pi$
$788$	−0.824752			−0.0293806
$789$		0			0
$790$	−13.0997	+	22.6893i	−0.466065	+	0.807249i
$791$	−3.91238	+	6.77643i	−0.139108	+	0.240942i
$792$		0			0
$793$	9.00000	+	31.1769i	0.319599	+	1.10712i
$794$	−15.7251			−0.558062
$795$		0			0
$796$	5.41238	−	9.37451i	0.191837	−	0.332271i
$797$	0.725083	+	1.25588i	0.0256837	+	0.0444856i	0.878582	−	0.477592i	$-0.158490\pi$
$797$	0.725083	+	1.25588i	0.0256837	+	0.0444856i	−0.852898	+	0.522078i	$0.825157\pi$
$798$		0			0
$799$	−12.8248	−	22.2131i	−0.453707	−	0.785844i
$800$	2.86254	+	4.95807i	0.101206	+	0.175294i
$801$		0			0
$802$	−2.63746	−	4.56821i	−0.0931319	−	0.161309i
$803$	−26.5498	+	45.9857i	−0.936923	+	1.62280i
$804$		0			0
$805$	−7.45017			−0.262584
$806$	15.6873	−	16.3027i	0.552561	−	0.574239i
$807$		0			0
$808$	−4.63746	+	8.03231i	−0.163145	+	0.282576i
$809$	8.63746	−	14.9605i	0.303677	−	0.525984i	−0.673289	−	0.739379i	$-0.735119\pi$
$809$	8.63746	−	14.9605i	0.303677	−	0.525984i	0.976966	+	0.213396i	$0.0684523\pi$
$810$		0			0
$811$	−25.0997			−0.881369			−0.440684	−	0.897662i	$-0.645264\pi$
$811$	−25.0997			−0.881369			−0.440684	+	0.897662i	$0.645264\pi$
$812$	0.362541	+	0.627940i	0.0127227	+	0.0220364i
$813$		0			0
$814$	29.0997			1.01994
$815$	9.37459	+	16.2373i	0.328377	+	0.568766i
$816$		0			0
$817$	46.2749	−	80.1505i	1.61895	−	2.80411i
$818$	−22.9244			−0.801534
$819$		0			0
$820$	−2.37459			−0.0829241
$821$	3.86254	−	6.69012i	0.134804	−	0.233487i	−0.790719	−	0.612180i	$-0.790293\pi$
$821$	3.86254	−	6.69012i	0.134804	−	0.233487i	0.925522	+	0.378693i	$0.123626\pi$
$822$		0			0
$823$	18.5498	+	32.1293i	0.646607	+	1.11996i	0.983928	+	0.178566i	$0.0571458\pi$
$823$	18.5498	+	32.1293i	0.646607	+	1.11996i	−0.337321	+	0.941390i	$0.609521\pi$
$824$	2.27492			0.0792505
$825$		0			0
$826$	−5.41238	−	9.37451i	−0.188321	−	0.326181i
$827$	25.0997			0.872801			0.436401	−	0.899753i	$-0.356253\pi$
$827$	25.0997			0.872801			0.436401	+	0.899753i	$0.356253\pi$
$828$		0			0
$829$	11.0876	−	19.2043i	0.385089	−	0.666994i	−0.606692	−	0.794937i	$-0.707504\pi$
$829$	11.0876	−	19.2043i	0.385089	−	0.666994i	0.991782	+	0.127943i	$0.0408374\pi$
$830$	−17.7251	+	30.7007i	−0.615247	+	1.06564i
$831$		0			0
$832$	3.50000	+	0.866025i	0.121341	+	0.0300240i
$833$	−3.00000			−0.103944
$834$		0			0
$835$		0			0
$836$	17.0997	+	29.6175i	0.591404	+	1.02434i
$837$		0			0
$838$	−7.68729	−	13.3148i	−0.265553	−	0.459952i
$839$	27.3746	+	47.4142i	0.945076	+	1.63692i	0.755600	+	0.655034i	$0.227346\pi$
$839$	27.3746	+	47.4142i	0.945076	+	1.63692i	0.189476	+	0.981885i	$0.439321\pi$
$840$		0			0
$841$	14.2371	+	24.6594i	0.490935	+	0.850325i
$842$	0.362541	−	0.627940i	0.0124940	−	0.0216402i
$843$		0			0
$844$	−9.09967			−0.313224
$845$	37.6615	+	19.8531i	1.29560	+	0.682968i
$846$		0			0
$847$	−2.50000	+	4.33013i	−0.0859010	+	0.148785i
$848$	5.77492	−	10.0025i	0.198311	−	0.343486i
$849$		0			0
$850$	17.1752			0.589106
$851$	−8.27492	−	14.3326i	−0.283661	−	0.491314i
$852$		0			0
$853$	−29.5498			−1.01177			−0.505884	−	0.862602i	$-0.668833\pi$
$853$	−29.5498			−1.01177			−0.505884	+	0.862602i	$0.668833\pi$
$854$	−4.50000	−	7.79423i	−0.153987	−	0.266713i
$855$		0			0
$856$	6.27492	−	10.8685i	0.214472	−	0.371477i
$857$	14.1752			0.484217			0.242109	−	0.970249i	$-0.422161\pi$
$857$	14.1752			0.484217			0.242109	+	0.970249i	$0.422161\pi$
$858$		0			0
$859$	17.6495			0.602193			0.301097	−	0.953594i	$-0.402647\pi$
$859$	17.6495			0.602193			0.301097	+	0.953594i	$0.402647\pi$
$860$	−17.7251	+	30.7007i	−0.604420	+	1.04689i
$861$		0			0
$862$	2.86254	+	4.95807i	0.0974985	+	0.168872i
$863$	55.2990			1.88240			0.941200	−	0.337850i	$-0.109700\pi$
$863$	55.2990			1.88240			0.941200	+	0.337850i	$0.109700\pi$
$864$		0			0
$865$	17.2749	+	29.9210i	0.587365	+	1.01735i
$866$	2.72508			0.0926021
$867$		0			0
$868$	−3.13746	+	5.43424i	−0.106492	+	0.184450i
$869$	16.0000	−	27.7128i	0.542763	−	0.940093i
$870$		0			0
$871$	25.6873	−	26.6950i	0.870381	−	0.904526i
$872$	−10.5498			−0.357262
$873$		0			0
$874$	9.72508	−	16.8443i	0.328956	−	0.569768i
$875$	−1.18729	−	2.05645i	−0.0401378	−	0.0695208i
$876$		0			0
$877$	5.63746	+	9.76436i	0.190363	+	0.329719i	0.945371	−	0.325997i	$-0.105700\pi$
$877$	5.63746	+	9.76436i	0.190363	+	0.329719i	−0.755007	+	0.655716i	$0.772367\pi$
$878$	−8.54983	−	14.8087i	−0.288543	−	0.499771i
$879$		0			0
$880$	−6.54983	−	11.3446i	−0.220795	−	0.382428i
$881$	−6.77492	+	11.7345i	−0.228253	+	0.395345i	−0.957290	−	0.289128i	$-0.906635\pi$
$881$	−6.77492	+	11.7345i	−0.228253	+	0.395345i	0.729038	+	0.684474i	$0.239968\pi$
$882$		0			0
$883$	−25.0241			−0.842128			−0.421064	−	0.907031i	$-0.638343\pi$
$883$	−25.0241			−0.842128			−0.421064	+	0.907031i	$0.638343\pi$
$884$	7.50000	−	7.79423i	0.252252	−	0.262148i
$885$		0			0
$886$	−9.72508	+	16.8443i	−0.326721	+	0.565897i
$887$	15.7251	−	27.2366i	0.527997	−	0.914517i	−0.471471	−	0.881882i	$-0.656277\pi$
$887$	15.7251	−	27.2366i	0.527997	−	0.914517i	0.999467	−	0.0326352i	$-0.0103900\pi$
$888$		0			0
$889$	8.00000			0.268311
$890$	−13.5498	−	23.4690i	−0.454191	−	0.786683i
$891$		0			0
$892$	18.2749			0.611889
$893$	−36.5498	−	63.3062i	−1.22309	−	2.11846i
$894$		0			0
$895$	27.0997	−	46.9380i	0.905842	−	1.56896i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	11.0997			0.370401
$899$	2.27492	−	3.94027i	0.0758727	−	0.131415i
$900$		0			0
$901$	−17.3248	−	30.0074i	−0.577171	−	0.999690i
$902$	2.90033			0.0965705
$903$		0			0
$904$	3.91238	+	6.77643i	0.130124	+	0.225381i
$905$	19.0756			0.634094
$906$		0			0
$907$	8.58762	−	14.8742i	0.285147	−	0.493890i	−0.687498	−	0.726187i	$-0.741291\pi$
$907$	8.58762	−	14.8742i	0.285147	−	0.493890i	0.972645	+	0.232297i	$0.0746241\pi$
$908$	4.54983	−	7.88054i	0.150992	−	0.261525i
$909$		0			0
$910$	−11.4622	−	2.83616i	−0.379969	−	0.0940178i
$911$	−5.09967			−0.168960			−0.0844798	−	0.996425i	$-0.526923\pi$
$911$	−5.09967			−0.168960			−0.0844798	+	0.996425i	$0.526923\pi$
$912$		0			0
$913$	21.6495	−	37.4980i	0.716494	−	1.24100i
$914$	−8.50000	−	14.7224i	−0.281155	−	0.486975i
$915$		0			0
$916$	−10.1375	−	17.5586i	−0.334951	−	0.580152i
$917$	−5.13746	−	8.89834i	−0.169654	−	0.293849i
$918$		0			0
$919$	2.82475	+	4.89261i	0.0931800	+	0.161392i	0.908848	−	0.417128i	$-0.136963\pi$
$919$	2.82475	+	4.89261i	0.0931800	+	0.161392i	−0.815668	+	0.578521i	$0.803630\pi$
$920$	−3.72508	+	6.45203i	−0.122812	+	0.212717i
$921$		0			0
$922$	18.3746			0.605135
$923$	−2.27492	−	7.88054i	−0.0748798	−	0.259391i
$924$		0			0
$925$	20.8248	−	36.0695i	0.684714	−	1.18596i
$926$	2.27492	−	3.94027i	0.0747584	−	0.129485i
$927$		0			0
$928$	0.725083			0.0238020
$929$	19.2251	+	33.2988i	0.630755	+	1.09250i	0.987398	+	0.158258i	$0.0505878\pi$
$929$	19.2251	+	33.2988i	0.630755	+	1.09250i	−0.356643	+	0.934241i	$0.616079\pi$
$930$		0			0
$931$	−8.54983			−0.280210
$932$	11.2749	+	19.5287i	0.369322	+	0.639685i
$933$		0			0
$934$	15.4124	−	26.6950i	0.504308	−	0.873488i
$935$	−39.2990			−1.28521
$936$		0			0
$937$	41.8248			1.36636			0.683178	−	0.730252i	$-0.260598\pi$
$937$	41.8248			1.36636			0.683178	+	0.730252i	$0.260598\pi$
$938$	−5.13746	+	8.89834i	−0.167744	+	0.290541i
$939$		0			0
$940$	14.0000	+	24.2487i	0.456630	+	0.790906i
$941$	7.64950			0.249367			0.124683	−	0.992197i	$-0.460209\pi$
$941$	7.64950			0.249367			0.124683	+	0.992197i	$0.460209\pi$
$942$		0			0
$943$	−0.824752	−	1.42851i	−0.0268576	−	0.0465187i
$944$	−10.8248			−0.352316
$945$		0			0
$946$	21.6495	−	37.4980i	0.703886	−	1.21917i
$947$	10.5498	−	18.2728i	0.342824	−	0.593788i	−0.642132	−	0.766594i	$-0.721950\pi$
$947$	10.5498	−	18.2728i	0.342824	−	0.593788i	0.984956	+	0.172806i	$0.0552834\pi$
$948$		0			0
$949$	46.4622	+	11.4964i	1.50823	+	0.373189i
$950$	48.9485			1.58810
$951$		0			0
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	9.54983	+	16.5408i	0.309349	+	0.535809i	0.978220	−	0.207570i	$-0.0665554\pi$
$953$	9.54983	+	16.5408i	0.309349	+	0.535809i	−0.668871	+	0.743379i	$0.733222\pi$
$954$		0			0
$955$	23.3746	+	40.4860i	0.756384	+	1.31010i
$956$	1.13746	+	1.97014i	0.0367880	+	0.0637188i
$957$		0			0
$958$	−10.0000	−	17.3205i	−0.323085	−	0.559600i
$959$	0.0876242	−	0.151770i	0.00282953	−	0.00490089i
$960$		0			0
$961$	8.37459			0.270148
$962$	−7.27492	−	25.2011i	−0.234553	−	0.812515i
$963$		0			0
$964$	11.6375	−	20.1567i	0.374817	−	0.649203i
$965$	3.56188	−	6.16936i	0.114661	−	0.198599i
$966$		0			0
$967$	−3.45017			−0.110950			−0.0554749	−	0.998460i	$-0.517667\pi$
$967$	−3.45017			−0.110950			−0.0554749	+	0.998460i	$0.517667\pi$
$968$	2.50000	+	4.33013i	0.0803530	+	0.139176i
$969$		0			0
$970$	−47.6495			−1.52993
$971$	−24.7870	−	42.9323i	−0.795451	−	1.37776i	−0.922552	−	0.385873i	$-0.873900\pi$
$971$	−24.7870	−	42.9323i	−0.795451	−	1.37776i	0.127101	−	0.991890i	$-0.459433\pi$
$972$		0			0
$973$	−10.5498	+	18.2728i	−0.338212	+	0.585801i
$974$	−29.0997			−0.932414
$975$		0			0
$976$	−9.00000			−0.288083
$977$	31.1873	−	54.0180i	0.997770	−	1.72819i	0.441080	−	0.897468i	$-0.354596\pi$
$977$	31.1873	−	54.0180i	0.997770	−	1.72819i	0.556690	−	0.830720i	$-0.312071\pi$
$978$		0			0
$979$	16.5498	+	28.6652i	0.528935	+	0.916142i
$980$	3.27492			0.104613
$981$		0			0
$982$	2.54983	+	4.41644i	0.0813685	+	0.140934i
$983$	51.8488			1.65372			0.826861	−	0.562407i	$-0.190125\pi$
$983$	51.8488			1.65372			0.826861	+	0.562407i	$0.190125\pi$
$984$		0			0
$985$	1.35050	−	2.33913i	0.0430304	−	0.0745308i
$986$	1.08762	−	1.88382i	0.0346370	−	0.0599931i
$987$		0			0
$988$	21.3746	−	22.2131i	0.680016	−	0.706694i
$989$	−24.6254			−0.783043
$990$		0			0
$991$	−19.3746	+	33.5578i	−0.615454	+	1.06600i	0.374851	+	0.927085i	$0.377694\pi$
$991$	−19.3746	+	33.5578i	−0.615454	+	1.06600i	−0.990305	+	0.138912i	$0.955639\pi$
$992$	3.13746	+	5.43424i	0.0996144	+	0.172537i
$993$		0			0
$994$	1.13746	+	1.97014i	0.0360780	+	0.0624889i
$995$	17.7251	+	30.7007i	0.561923	+	0.973279i
$996$		0			0
$997$	17.0498	+	29.5312i	0.539974	+	0.935262i	0.998905	+	0.0467900i	$0.0148991\pi$
$997$	17.0498	+	29.5312i	0.539974	+	0.935262i	−0.458931	+	0.888472i	$0.651768\pi$
$998$	−4.58762	+	7.94600i	−0.145219	+	0.251526i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.x.1387.2		4
3.2	odd	2		546.2.l.j.295.1	yes	4
13.3	even	3	inner	1638.2.r.x.757.2		4
39.17	odd	6		7098.2.a.bm.1.2		2
39.29	odd	6		546.2.l.j.211.1	✓	4
39.35	odd	6		7098.2.a.ca.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.j.211.1	✓	4	39.29	odd	6
546.2.l.j.295.1	yes	4	3.2	odd	2
1638.2.r.x.757.2		4	13.3	even	3	inner
1638.2.r.x.1387.2		4	1.1	even	1	trivial
7098.2.a.bm.1.2		2	39.17	odd	6
7098.2.a.ca.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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.27492 q^{5} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.63746 - 2.83616i) q^{10} +(-2.00000 + 3.46410i) q^{11} +(3.50000 + 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(4.27492 + 7.40437i) q^{19} +(-1.63746 - 2.83616i) q^{20} +(2.00000 + 3.46410i) q^{22} +(1.13746 - 1.97014i) q^{23} +5.72508 q^{25} +(2.50000 - 2.59808i) q^{26} +(-0.500000 + 0.866025i) q^{28} +(0.362541 - 0.627940i) q^{29} +6.27492 q^{31} +(0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(-1.63746 - 2.83616i) q^{35} +(3.63746 - 6.30026i) q^{37} +8.54983 q^{38} -3.27492 q^{40} +(0.362541 - 0.627940i) q^{41} +(-5.41238 - 9.37451i) q^{43} +4.00000 q^{44} +(-1.13746 - 1.97014i) q^{46} -8.54983 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.86254 - 4.95807i) q^{50} +(-1.00000 - 3.46410i) q^{52} -11.5498 q^{53} +(-6.54983 + 11.3446i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.362541 - 0.627940i) q^{58} +(5.41238 + 9.37451i) q^{59} +(4.50000 + 7.79423i) q^{61} +(3.13746 - 5.43424i) q^{62} +1.00000 q^{64} +(11.4622 + 2.83616i) q^{65} +(5.13746 - 8.89834i) q^{67} +(1.50000 - 2.59808i) q^{68} -3.27492 q^{70} +(-1.13746 - 1.97014i) q^{71} +13.2749 q^{73} +(-3.63746 - 6.30026i) q^{74} +(4.27492 - 7.40437i) q^{76} +4.00000 q^{77} -8.00000 q^{79} +(-1.63746 + 2.83616i) q^{80} +(-0.362541 - 0.627940i) q^{82} -10.8248 q^{83} +(4.91238 + 8.50848i) q^{85} -10.8248 q^{86} +(2.00000 - 3.46410i) q^{88} +(4.13746 - 7.16629i) q^{89} +(-1.00000 - 3.46410i) q^{91} -2.27492 q^{92} +(-4.27492 + 7.40437i) q^{94} +(14.0000 + 24.2487i) q^{95} +(-7.27492 - 12.6005i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 2 q^{7} - 4 q^{8} - q^{10} - 8 q^{11} + 14 q^{13} - 4 q^{14} - 2 q^{16} + 6 q^{17} + 2 q^{19} + q^{20} + 8 q^{22} - 3 q^{23} + 38 q^{25} + 10 q^{26} - 2 q^{28} + 9 q^{29}+ \cdots + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 2 * q^7 - 4 * q^8 - q^10 - 8 * q^11 + 14 * q^13 - 4 * q^14 - 2 * q^16 + 6 * q^17 + 2 * q^19 + q^20 + 8 * q^22 - 3 * q^23 + 38 * q^25 + 10 * q^26 - 2 * q^28 + 9 * q^29 + 10 * q^31 + 2 * q^32 + 12 * q^34 + q^35 + 7 * q^37 + 4 * q^38 + 2 * q^40 + 9 * q^41 + q^43 + 16 * q^44 + 3 * q^46 - 4 * q^47 - 2 * q^49 + 19 * q^50 - 4 * q^52 - 16 * q^53 + 4 * q^55 + 2 * q^56 - 9 * q^58 - q^59 + 18 * q^61 + 5 * q^62 + 4 * q^64 - 7 * q^65 + 13 * q^67 + 6 * q^68 + 2 * q^70 + 3 * q^71 + 38 * q^73 - 7 * q^74 + 2 * q^76 + 16 * q^77 - 32 * q^79 + q^80 - 9 * q^82 + 2 * q^83 - 3 * q^85 + 2 * q^86 + 8 * q^88 + 9 * q^89 - 4 * q^91 + 6 * q^92 - 2 * q^94 + 56 * q^95 - 14 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more