LMFDB - Embedded newform 108.3.k.a.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.3
Character	$\chi$	$=$	108.65
Dual form			108.3.k.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.727525 + 2.91045i) q^{3} +(0.0686711 - 0.188672i) q^{5} +(-1.47862 + 8.38565i) q^{7} +(-7.94141 - 4.23485i) q^{9} +O(q^{10})$	\(q+(-0.727525 + 2.91045i) q^{3} +(0.0686711 - 0.188672i) q^{5} +(-1.47862 + 8.38565i) q^{7} +(-7.94141 - 4.23485i) q^{9} +(2.58315 + 7.09715i) q^{11} +(-12.5592 + 10.5384i) q^{13} +(0.499161 + 0.337127i) q^{15} +(5.21882 - 3.01309i) q^{17} +(-0.189946 + 0.328995i) q^{19} +(-23.3303 - 10.4042i) q^{21} +(27.6819 - 4.88107i) q^{23} +(19.1202 + 16.0438i) q^{25} +(18.1029 - 20.0321i) q^{27} +(26.6332 - 31.7402i) q^{29} +(2.35612 + 13.3622i) q^{31} +(-22.5352 + 2.35477i) q^{33} +(1.48060 + 0.854825i) q^{35} +(-2.26190 - 3.91773i) q^{37} +(-21.5344 - 44.2199i) q^{39} +(-49.3383 - 58.7991i) q^{41} +(1.63966 - 0.596788i) q^{43} +(-1.34434 + 1.20751i) q^{45} +(75.3795 + 13.2914i) q^{47} +(-22.0879 - 8.03934i) q^{49} +(4.97261 + 17.3812i) q^{51} +85.8739i q^{53} +1.51642 q^{55} +(-0.819334 - 0.792179i) q^{57} +(6.23410 - 17.1281i) q^{59} +(-6.51665 + 36.9578i) q^{61} +(47.2543 - 60.3322i) q^{63} +(1.12585 + 3.09326i) q^{65} +(-53.9204 + 45.2446i) q^{67} +(-5.93319 + 84.1179i) q^{69} +(-38.9179 + 22.4692i) q^{71} +(51.2495 - 88.7667i) q^{73} +(-60.6050 + 43.9762i) q^{75} +(-63.3337 + 11.1674i) q^{77} +(64.7058 + 54.2946i) q^{79} +(45.1321 + 67.2614i) q^{81} +(-44.2042 + 52.6805i) q^{83} +(-0.210104 - 1.19156i) q^{85} +(73.0020 + 100.606i) q^{87} +(-119.245 - 68.8461i) q^{89} +(-69.8014 - 120.900i) q^{91} +(-40.6042 - 2.86398i) q^{93} +(0.0490285 + 0.0584299i) q^{95} +(112.916 - 41.0979i) q^{97} +(9.54147 - 67.3007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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			0
$2$		0			0
$3$	−0.727525	+	2.91045i	−0.242508	+	0.970149i
$3$	−0.727525	+	2.91045i	−0.242508	+	0.970149i
$4$		0			0
$5$	0.0686711	−	0.188672i	0.0137342	−	0.0377344i	−0.932636	−	0.360818i	$-0.882497\pi$
$5$	0.0686711	−	0.188672i	0.0137342	−	0.0377344i	0.946370	+	0.323084i	$0.104720\pi$
$6$		0			0
$7$	−1.47862	+	8.38565i	−0.211231	+	1.19795i	0.676098	+	0.736812i	$0.263670\pi$
$7$	−1.47862	+	8.38565i	−0.211231	+	1.19795i	−0.887328	+	0.461138i	$0.847441\pi$
$8$		0			0
$9$	−7.94141	−	4.23485i	−0.882379	−	0.470539i
$10$		0			0
$11$	2.58315	+	7.09715i	0.234832	+	0.645195i	0.999999	+	0.00136376i	$0.000434100\pi$
$11$	2.58315	+	7.09715i	0.234832	+	0.645195i	−0.765167	+	0.643832i	$0.777344\pi$
$12$		0			0
$13$	−12.5592	+	10.5384i	−0.966094	+	0.810649i	−0.981934	−	0.189226i	$-0.939402\pi$
$13$	−12.5592	+	10.5384i	−0.966094	+	0.810649i	0.0158399	+	0.999875i	$0.494958\pi$
$14$		0			0
$15$	0.499161	+	0.337127i	0.0332774	+	0.0224752i
$16$		0			0
$17$	5.21882	−	3.01309i	0.306990	−	0.177241i	−0.338589	−	0.940934i	$-0.609950\pi$
$17$	5.21882	−	3.01309i	0.306990	−	0.177241i	0.645579	+	0.763694i	$0.276616\pi$
$18$		0			0
$19$	−0.189946	+	0.328995i	−0.00999714	+	0.0173155i	−0.870981	−	0.491317i	$-0.836516\pi$
$19$	−0.189946	+	0.328995i	−0.00999714	+	0.0173155i	0.860984	+	0.508633i	$0.169849\pi$
$20$		0			0
$21$	−23.3303	−	10.4042i	−1.11097	−	0.495438i
$22$		0			0
$23$	27.6819	−	4.88107i	1.20356	−	0.212220i	0.464324	−	0.885665i	$-0.346297\pi$
$23$	27.6819	−	4.88107i	1.20356	−	0.212220i	0.739238	+	0.673445i	$0.235186\pi$
$24$		0			0
$25$	19.1202	+	16.0438i	0.764809	+	0.641751i
$26$		0			0
$27$	18.1029	−	20.0321i	0.670477	−	0.741930i
$28$		0			0
$29$	26.6332	−	31.7402i	0.918387	−	1.09449i	−0.0768538	−	0.997042i	$-0.524487\pi$
$29$	26.6332	−	31.7402i	0.918387	−	1.09449i	0.995241	−	0.0974484i	$-0.0310681\pi$
$30$		0			0
$31$	2.35612	+	13.3622i	0.0760038	+	0.431039i	0.998938	+	0.0460807i	$0.0146731\pi$
$31$	2.35612	+	13.3622i	0.0760038	+	0.431039i	−0.922934	+	0.384959i	$0.874216\pi$
$32$		0			0
$33$	−22.5352	+	2.35477i	−0.682885	+	0.0713568i
$34$		0			0
$35$	1.48060	+	0.854825i	0.0423029	+	0.0244236i
$36$		0			0
$37$	−2.26190	−	3.91773i	−0.0611325	−	0.105885i	0.833839	−	0.552007i	$-0.186138\pi$
$37$	−2.26190	−	3.91773i	−0.0611325	−	0.105885i	−0.894972	+	0.446122i	$0.852805\pi$
$38$		0			0
$39$	−21.5344	−	44.2199i	−0.552165	−	1.13384i
$40$		0			0
$41$	−49.3383	−	58.7991i	−1.20337	−	1.43412i	−0.871217	−	0.490899i	$-0.836668\pi$
$41$	−49.3383	−	58.7991i	−1.20337	−	1.43412i	−0.332156	−	0.943225i	$-0.607776\pi$
$42$		0			0
$43$	1.63966	−	0.596788i	0.0381317	−	0.0138788i	−0.322884	−	0.946439i	$-0.604652\pi$
$43$	1.63966	−	0.596788i	0.0381317	−	0.0138788i	0.361016	+	0.932560i	$0.382430\pi$
$44$		0			0
$45$	−1.34434	+	1.20751i	−0.0298743	+	0.0268336i
$46$		0			0
$47$	75.3795	+	13.2914i	1.60382	+	0.282797i	0.902708	−	0.430255i	$-0.141576\pi$
$47$	75.3795	+	13.2914i	1.60382	+	0.282797i	0.701112	+	0.713051i	$0.252687\pi$
$48$		0			0
$49$	−22.0879	−	8.03934i	−0.450773	−	0.164068i
$50$		0			0
$51$	4.97261	+	17.3812i	0.0975022	+	0.340808i
$52$		0			0
$53$			85.8739i			1.62026i	0.586249	+	0.810131i	$0.300604\pi$
$53$			85.8739i			1.62026i	−0.586249	+	0.810131i	$0.699396\pi$
$54$		0			0
$55$	1.51642			0.0275713
$56$		0			0
$57$	−0.819334	−	0.792179i	−0.0143743	−	0.0138979i
$58$		0			0
$59$	6.23410	−	17.1281i	0.105663	−	0.290306i	−0.875583	−	0.483068i	$-0.839522\pi$
$59$	6.23410	−	17.1281i	0.105663	−	0.290306i	0.981246	+	0.192762i	$0.0617446\pi$
$60$		0			0
$61$	−6.51665	+	36.9578i	−0.106830	+	0.605865i	0.883643	+	0.468161i	$0.155083\pi$
$61$	−6.51665	+	36.9578i	−0.106830	+	0.605865i	−0.990473	+	0.137704i	$0.956028\pi$
$62$		0			0
$63$	47.2543	−	60.3322i	0.750068	−	0.957654i
$64$		0			0
$65$	1.12585	+	3.09326i	0.0173208	+	0.0475886i
$66$		0			0
$67$	−53.9204	+	45.2446i	−0.804783	+	0.675293i	−0.949356	−	0.314201i	$-0.898263\pi$
$67$	−53.9204	+	45.2446i	−0.804783	+	0.675293i	0.144574	+	0.989494i	$0.453819\pi$
$68$		0			0
$69$	−5.93319	+	84.1179i	−0.0859883	+	1.21910i
$70$		0			0
$71$	−38.9179	+	22.4692i	−0.548139	+	0.316468i	−0.748371	−	0.663280i	$-0.769164\pi$
$71$	−38.9179	+	22.4692i	−0.548139	+	0.316468i	0.200232	+	0.979748i	$0.435830\pi$
$72$		0			0
$73$	51.2495	−	88.7667i	0.702047	−	1.21598i	−0.265699	−	0.964056i	$-0.585603\pi$
$73$	51.2495	−	88.7667i	0.702047	−	1.21598i	0.967747	−	0.251926i	$-0.0810639\pi$
$74$		0			0
$75$	−60.6050	+	43.9762i	−0.808067	+	0.586349i
$76$		0			0
$77$	−63.3337	+	11.1674i	−0.822516	+	0.145032i
$78$		0			0
$79$	64.7058	+	54.2946i	0.819060	+	0.687273i	0.952752	−	0.303750i	$-0.0982387\pi$
$79$	64.7058	+	54.2946i	0.819060	+	0.687273i	−0.133692	+	0.991023i	$0.542683\pi$
$80$		0			0
$81$	45.1321	+	67.2614i	0.557187	+	0.830387i
$82$		0			0
$83$	−44.2042	+	52.6805i	−0.532580	+	0.634704i	−0.963507	−	0.267682i	$-0.913742\pi$
$83$	−44.2042	+	52.6805i	−0.532580	+	0.634704i	0.430927	+	0.902387i	$0.358187\pi$
$84$		0			0
$85$	−0.210104	−	1.19156i	−0.00247181	−	0.0140183i
$86$		0			0
$87$	73.0020	+	100.606i	0.839103	+	1.15640i
$88$		0			0
$89$	−119.245	−	68.8461i	−1.33983	−	0.773551i	−0.353048	−	0.935605i	$-0.614855\pi$
$89$	−119.245	−	68.8461i	−1.33983	−	0.773551i	−0.986782	+	0.162054i	$0.948188\pi$
$90$		0			0
$91$	−69.8014	−	120.900i	−0.767048	−	1.32857i
$92$		0			0
$93$	−40.6042	−	2.86398i	−0.436604	−	0.0307955i
$94$		0			0
$95$	0.0490285	+	0.0584299i	0.000516090	+	0.000615052i
$96$		0			0
$97$	112.916	−	41.0979i	1.16408	−	0.423690i	0.313526	−	0.949580i	$-0.398490\pi$
$97$	112.916	−	41.0979i	1.16408	−	0.423690i	0.850553	+	0.525889i	$0.176267\pi$
$98$		0			0
$99$	9.54147	−	67.3007i	0.0963785	−	0.679805i
$100$		0			0
$101$	13.1189	+	2.31321i	0.129890	+	0.0229031i	0.238215	−	0.971212i	$-0.423438\pi$
$101$	13.1189	+	2.31321i	0.129890	+	0.0229031i	−0.108325	+	0.994116i	$0.534549\pi$
$102$		0			0
$103$	−183.161	−	66.6652i	−1.77826	−	0.647235i	−0.999809	−	0.0195327i	$-0.993782\pi$
$103$	−183.161	−	66.6652i	−1.77826	−	0.647235i	−0.778454	−	0.627702i	$-0.783996\pi$
$104$		0			0
$105$	−3.56510	+	3.68731i	−0.0339533	+	0.0351172i
$106$		0			0
$107$			155.702i			1.45516i	0.686024	+	0.727579i	$0.259355\pi$
$107$			155.702i			1.45516i	−0.686024	+	0.727579i	$0.740645\pi$
$108$		0			0
$109$	70.1664			0.643729			0.321864	−	0.946786i	$-0.395691\pi$
$109$	70.1664			0.643729			0.321864	+	0.946786i	$0.395691\pi$
$110$		0			0
$111$	13.0479	−	3.73291i	0.117549	−	0.0336298i
$112$		0			0
$113$	35.8589	−	98.5216i	0.317336	−	0.871873i	−0.673787	−	0.738925i	$-0.735334\pi$
$113$	35.8589	−	98.5216i	0.317336	−	0.871873i	0.991123	−	0.132947i	$-0.0424441\pi$
$114$		0			0
$115$	0.980025	−	5.55800i	0.00852196	−	0.0483304i
$116$		0			0
$117$	144.367	−	30.5037i	1.23390	−	0.260716i
$118$		0			0
$119$	17.5501	+	48.2184i	0.147480	+	0.405197i
$120$		0			0
$121$	48.9945	−	41.1113i	0.404913	−	0.339763i
$122$		0			0
$123$	207.026	−	100.819i	1.68314	−	0.819664i
$124$		0			0
$125$	8.68705	−	5.01547i	0.0694964	−	0.0401238i
$126$		0			0
$127$	77.8451	−	134.832i	0.612954	−	1.06167i	−0.377786	−	0.925893i	$-0.623315\pi$
$127$	77.8451	−	134.832i	0.612954	−	1.06167i	0.990740	−	0.135774i	$-0.0433521\pi$
$128$		0			0
$129$	0.544026	+	5.20633i	0.00421726	+	0.0403592i
$130$		0			0
$131$	−140.642	+	24.7989i	−1.07360	+	0.189305i	−0.682383	−	0.730994i	$-0.739057\pi$
$131$	−140.642	+	24.7989i	−1.07360	+	0.189305i	−0.391216	+	0.920299i	$0.627945\pi$
$132$		0			0
$133$	−2.47798	−	2.07928i	−0.0186315	−	0.0156336i
$134$		0			0
$135$	−2.53636	−	4.79114i	−0.0187878	−	0.0354899i
$136$		0			0
$137$	123.444	−	147.114i	0.901048	−	1.07383i	−0.0958717	−	0.995394i	$-0.530564\pi$
$137$	123.444	−	147.114i	0.901048	−	1.07383i	0.996919	−	0.0784331i	$-0.0249917\pi$
$138$		0			0
$139$	−12.4043	−	70.3485i	−0.0892398	−	0.506104i	−0.996361	−	0.0852345i	$-0.972836\pi$
$139$	−12.4043	−	70.3485i	−0.0892398	−	0.506104i	0.907121	−	0.420870i	$-0.138275\pi$
$140$		0			0
$141$	−93.5245	+	209.718i	−0.663295	+	1.48736i
$142$		0			0
$143$	−107.235	−	61.9123i	−0.749897	−	0.432953i
$144$		0			0
$145$	−4.15957	−	7.20458i	−0.0286867	−	0.0496868i
$146$		0			0
$147$	39.4676	−	58.4369i	0.268487	−	0.397530i
$148$		0			0
$149$	−64.1576	−	76.4600i	−0.430588	−	0.513155i	0.506504	−	0.862238i	$-0.330938\pi$
$149$	−64.1576	−	76.4600i	−0.430588	−	0.513155i	−0.937092	+	0.349083i	$0.886493\pi$
$150$		0			0
$151$	−91.0224	+	33.1295i	−0.602797	+	0.219400i	−0.625349	−	0.780345i	$-0.715043\pi$
$151$	−91.0224	+	33.1295i	−0.602797	+	0.219400i	0.0225513	+	0.999746i	$0.492821\pi$
$152$		0			0
$153$	−54.2048	+	1.82727i	−0.354280	+	0.0119429i
$154$		0			0
$155$	2.68288	+	0.473063i	0.0173089	+	0.00305202i
$156$		0			0
$157$	225.856	+	82.2049i	1.43857	+	0.523598i	0.939376	−	0.342890i	$-0.111406\pi$
$157$	225.856	+	82.2049i	1.43857	+	0.523598i	0.499198	+	0.866488i	$0.333628\pi$
$158$		0			0
$159$	−249.931	−	62.4754i	−1.57190	−	0.392927i
$160$		0			0
$161$			239.348i			1.48663i
$162$		0			0
$163$	−58.5417			−0.359152			−0.179576	−	0.983744i	$-0.557473\pi$
$163$	−58.5417			−0.359152			−0.179576	+	0.983744i	$0.557473\pi$
$164$		0			0
$165$	−1.10324	+	4.41347i	−0.00668628	+	0.0267483i
$166$		0			0
$167$	22.4027	−	61.5510i	0.134148	−	0.368569i	−0.854371	−	0.519663i	$-0.826057\pi$
$167$	22.4027	−	61.5510i	0.134148	−	0.368569i	0.988519	+	0.151094i	$0.0482797\pi$
$168$		0			0
$169$	17.3288	−	98.2765i	0.102537	−	0.581518i
$170$		0			0
$171$	2.90168	−	1.80830i	0.0169689	−	0.0105748i
$172$		0			0
$173$	25.8686	+	71.0734i	0.149530	+	0.410829i	0.991731	−	0.128334i	$-0.0409629\pi$
$173$	25.8686	+	71.0734i	0.149530	+	0.410829i	−0.842201	+	0.539163i	$0.818741\pi$
$174$		0			0
$175$	−162.809	+	136.613i	−0.930337	+	0.780646i
$176$		0			0
$177$	45.3148	+	30.6051i	0.256016	+	0.172910i
$178$		0			0
$179$	259.614	−	149.888i	1.45035	−	0.837363i	0.451854	−	0.892092i	$-0.350763\pi$
$179$	259.614	−	149.888i	1.45035	−	0.837363i	0.998501	+	0.0547292i	$0.0174296\pi$
$180$		0			0
$181$	−148.560	+	257.314i	−0.820774	+	1.42162i	0.0843330	+	0.996438i	$0.473124\pi$
$181$	−148.560	+	257.314i	−0.820774	+	1.42162i	−0.905107	+	0.425184i	$0.860209\pi$
$182$		0			0
$183$	−102.823	−	45.8541i	−0.561872	−	0.250569i
$184$		0			0
$185$	−0.894495	+	0.157724i	−0.00483511	+	0.000852560i
$186$		0			0
$187$	34.8654	+	29.2555i	0.186446	+	0.156447i
$188$		0			0
$189$	141.215	+	181.424i	0.747170	+	0.959917i
$190$		0			0
$191$	−52.6139	+	62.7028i	−0.275466	+	0.328287i	−0.885985	−	0.463714i	$-0.846516\pi$
$191$	−52.6139	+	62.7028i	−0.275466	+	0.328287i	0.610519	+	0.792001i	$0.290961\pi$
$192$		0			0
$193$	20.4421	+	115.933i	0.105918	+	0.600688i	0.990850	+	0.134968i	$0.0430933\pi$
$193$	20.4421	+	115.933i	0.105918	+	0.600688i	−0.884932	+	0.465720i	$0.845796\pi$
$194$		0			0
$195$	−9.82186	+	1.02632i	−0.0503685	+	0.00526317i
$196$		0			0
$197$	−69.8603	−	40.3339i	−0.354621	−	0.204740i	0.312098	−	0.950050i	$-0.398968\pi$
$197$	−69.8603	−	40.3339i	−0.354621	−	0.204740i	−0.666719	+	0.745310i	$0.732302\pi$
$198$		0			0
$199$	87.9561	+	152.345i	0.441991	+	0.765550i	0.997837	−	0.0657347i	$-0.0209391\pi$
$199$	87.9561	+	152.345i	0.441991	+	0.765550i	−0.555846	+	0.831285i	$0.687606\pi$
$200$		0			0
$201$	−92.4536	−	189.849i	−0.459968	−	0.944524i
$202$		0			0
$203$	226.782	+	270.268i	1.11715	+	1.33137i
$204$		0			0
$205$	−14.4819	+	5.27097i	−0.0706432	+	0.0257120i
$206$		0			0
$207$	−240.504	−	78.4661i	−1.16186	−	0.379063i
$208$		0			0
$209$	−2.82559	−	0.498227i	−0.0135196	−	0.00238386i
$210$		0			0
$211$	−34.0107	−	12.3789i	−0.161188	−	0.0586678i	0.260166	−	0.965564i	$-0.416223\pi$
$211$	−34.0107	−	12.3789i	−0.161188	−	0.0586678i	−0.421354	+	0.906896i	$0.638445\pi$
$212$		0			0
$213$	−37.0818	−	129.615i	−0.174093	−	0.608523i
$214$		0			0
$215$		−	0.350341i		−	0.00162949i
$216$		0			0
$217$	−115.535			−0.532418
$218$		0			0
$219$	221.065	+	213.739i	1.00943	+	0.975976i
$220$		0			0
$221$	−33.7911	+	92.8403i	−0.152901	+	0.420092i
$222$		0			0
$223$	−70.0960	+	397.534i	−0.314332	+	1.78266i	0.261611	+	0.965174i	$0.415746\pi$
$223$	−70.0960	+	397.534i	−0.314332	+	1.78266i	−0.575942	+	0.817490i	$0.695365\pi$
$224$		0			0
$225$	−83.8987	−	208.382i	−0.372883	−	0.926140i
$226$		0			0
$227$	−59.9958	−	164.837i	−0.264299	−	0.726155i	−0.998866	−	0.0476187i	$-0.984837\pi$
$227$	−59.9958	−	164.837i	−0.264299	−	0.726155i	0.734567	−	0.678536i	$-0.237385\pi$
$228$		0			0
$229$	102.807	−	86.2654i	0.448939	−	0.376705i	−0.390103	−	0.920771i	$-0.627561\pi$
$229$	102.807	−	86.2654i	0.448939	−	0.376705i	0.839042	+	0.544066i	$0.183116\pi$
$230$		0			0
$231$	13.5746	−	192.454i	0.0587645	−	0.833135i
$232$		0			0
$233$	342.572	−	197.784i	1.47027	−	0.848858i	0.470823	−	0.882228i	$-0.343957\pi$
$233$	342.572	−	197.784i	1.47027	−	0.848858i	0.999443	+	0.0333693i	$0.0106237\pi$
$234$		0			0
$235$	7.68412	−	13.3093i	0.0326984	−	0.0566352i
$236$		0			0
$237$	−205.097	+	148.822i	−0.865386	+	0.627941i
$238$		0			0
$239$	442.556	−	78.0346i	1.85170	−	0.326504i	0.866668	−	0.498885i	$-0.166257\pi$
$239$	442.556	−	78.0346i	1.85170	−	0.326504i	0.985030	+	0.172380i	$0.0551458\pi$
$240$		0			0
$241$	−174.607	−	146.513i	−0.724511	−	0.607937i	0.204118	−	0.978946i	$-0.434567\pi$
$241$	−174.607	−	146.513i	−0.724511	−	0.607937i	−0.928629	+	0.371009i	$0.879012\pi$
$242$		0			0
$243$	−228.595	+	82.4204i	−0.940722	+	0.339179i
$244$		0			0
$245$	−3.03360	+	3.61530i	−0.0123820	+	0.0147563i
$246$		0			0
$247$	−1.08153	−	6.13365i	−0.00437866	−	0.0248326i
$248$		0			0
$249$	−121.164	−	166.980i	−0.486603	−	0.670603i
$250$		0			0
$251$	−307.522	−	177.548i	−1.22519	−	0.707362i	−0.259167	−	0.965832i	$-0.583448\pi$
$251$	−307.522	−	177.548i	−1.22519	−	0.707362i	−0.966019	+	0.258471i	$0.916781\pi$
$252$		0			0
$253$	106.148	+	183.854i	0.419558	+	0.726697i
$254$		0			0
$255$	3.62083	+	0.255392i	0.0141993	+	0.00100154i
$256$		0			0
$257$	−122.816	−	146.366i	−0.477883	−	0.569519i	0.472210	−	0.881486i	$-0.343456\pi$
$257$	−122.816	−	146.366i	−0.477883	−	0.569519i	−0.950093	+	0.311968i	$0.899012\pi$
$258$		0			0
$259$	36.1972	−	13.1747i	0.139758	−	0.0508676i
$260$		0			0
$261$	−345.920	+	139.275i	−1.32537	+	0.533620i
$262$		0			0
$263$	−59.8335	−	10.5503i	−0.227504	−	0.0401150i	0.0587341	−	0.998274i	$-0.481294\pi$
$263$	−59.8335	−	10.5503i	−0.227504	−	0.0401150i	−0.286238	+	0.958159i	$0.592405\pi$
$264$		0			0
$265$	16.2020	+	5.89705i	0.0611397	+	0.0222530i
$266$		0			0
$267$	287.127	−	296.969i	1.07538	−	1.11224i
$268$		0			0
$269$			1.02338i			0.00380438i	0.999998	+	0.00190219i	$0.000605486\pi$
$269$			1.02338i			0.00380438i	−0.999998	+	0.00190219i	$0.999395\pi$
$270$		0			0
$271$	264.552			0.976205			0.488102	−	0.872786i	$-0.337689\pi$
$271$	264.552			0.976205			0.488102	+	0.872786i	$0.337689\pi$
$272$		0			0
$273$	402.654	−	115.196i	1.47492	−	0.421963i
$274$		0			0
$275$	−64.4747	+	177.143i	−0.234453	+	0.644155i
$276$		0			0
$277$	63.0965	−	357.838i	0.227785	−	1.29183i	−0.629503	−	0.776998i	$-0.716742\pi$
$277$	63.0965	−	357.838i	0.227785	−	1.29183i	0.857288	−	0.514837i	$-0.172147\pi$
$278$		0			0
$279$	37.8760	−	116.093i	0.135756	−	0.416103i
$280$		0			0
$281$	−64.8213	−	178.095i	−0.230681	−	0.633790i	0.769306	−	0.638880i	$-0.220602\pi$
$281$	−64.8213	−	178.095i	−0.230681	−	0.633790i	−0.999987	+	0.00509010i	$0.998380\pi$
$282$		0			0
$283$	219.711	−	184.359i	0.776364	−	0.651447i	−0.165966	−	0.986131i	$-0.553074\pi$
$283$	219.711	−	184.359i	0.776364	−	0.651447i	0.942330	+	0.334685i	$0.108630\pi$
$284$		0			0
$285$	−0.205727	+	0.100186i	−0.000721848	+	0.000351529i
$286$		0			0
$287$	566.021	−	326.792i	1.97220	−	1.13865i
$288$		0			0
$289$	−126.343	+	218.832i	−0.437172	+	0.757203i
$290$		0			0
$291$	37.4644	+	358.535i	0.128744	+	1.23208i
$292$		0			0
$293$	197.305	−	34.7903i	0.673397	−	0.118738i	0.173515	−	0.984831i	$-0.444488\pi$
$293$	197.305	−	34.7903i	0.673397	−	0.118738i	0.499883	+	0.866093i	$0.333376\pi$
$294$		0			0
$295$	−2.80348	−	2.35240i	−0.00950334	−	0.00797425i
$296$		0			0
$297$	188.933	+	76.7329i	0.636139	+	0.258360i
$298$		0			0
$299$	−296.225	+	353.027i	−0.990717	+	1.18069i
$300$		0			0
$301$	2.58003	+	14.6321i	0.00857152	+	0.0486115i
$302$		0			0
$303$	−16.2768	+	36.4989i	−0.0537189	+	0.120459i
$304$		0			0
$305$	6.52540	+	3.76744i	0.0213948	+	0.0123523i
$306$		0			0
$307$	−87.7799	−	152.039i	−0.285928	−	0.495242i	0.686906	−	0.726746i	$-0.258968\pi$
$307$	−87.7799	−	152.039i	−0.285928	−	0.495242i	−0.972834	+	0.231505i	$0.925635\pi$
$308$		0			0
$309$	327.280	−	484.580i	1.05916	−	1.56822i
$310$		0			0
$311$	92.2362	+	109.923i	0.296579	+	0.353450i	0.893670	−	0.448724i	$-0.148121\pi$
$311$	92.2362	+	109.923i	0.296579	+	0.353450i	−0.597091	+	0.802174i	$0.703677\pi$
$312$		0			0
$313$	−469.902	+	171.030i	−1.50128	+	0.546422i	−0.956392	−	0.292085i	$-0.905651\pi$
$313$	−469.902	+	171.030i	−1.50128	+	0.546422i	−0.544891	+	0.838507i	$0.683429\pi$
$314$		0			0
$315$	−8.13801	−	13.0586i	−0.0258350	−	0.0414560i
$316$		0			0
$317$	−159.214	−	28.0736i	−0.502251	−	0.0885604i	−0.0832179	−	0.996531i	$-0.526520\pi$
$317$	−159.214	−	28.0736i	−0.502251	−	0.0885604i	−0.419033	+	0.907971i	$0.637631\pi$
$318$		0			0
$319$	294.063	+	107.030i	0.921827	+	0.335518i
$320$		0			0
$321$	−453.162	−	113.277i	−1.41172	−	0.352888i
$322$		0			0
$323$			2.28929i			0.00708759i
$324$		0			0
$325$	−409.211			−1.25911
$326$		0			0
$327$	−51.0478	+	204.216i	−0.156110	+	0.624513i
$328$		0			0
$329$	−222.915	+	612.453i	−0.677553	+	1.86156i
$330$		0			0
$331$	79.9019	−	453.146i	0.241396	−	1.36902i	−0.587321	−	0.809354i	$-0.699817\pi$
$331$	79.9019	−	453.146i	0.241396	−	1.36902i	0.828717	−	0.559668i	$-0.189072\pi$
$332$		0			0
$333$	1.37172	+	40.6912i	0.00411927	+	0.122196i
$334$		0			0
$335$	4.83363	+	13.2803i	0.0144287	+	0.0396426i
$336$		0			0
$337$	262.855	−	220.561i	0.779984	−	0.654484i	−0.163261	−	0.986583i	$-0.552201\pi$
$337$	262.855	−	220.561i	0.779984	−	0.654484i	0.943245	+	0.332099i	$0.107757\pi$
$338$		0			0
$339$	260.654	+	176.042i	0.768890	+	0.519299i
$340$		0			0
$341$	−88.7474	+	51.2384i	−0.260256	+	0.150259i
$342$		0			0
$343$	−108.543	+	188.002i	−0.316453	+	0.548112i
$344$		0			0
$345$	15.4633	+	6.89589i	0.0448211	+	0.0199881i
$346$		0			0
$347$	−270.540	+	47.7035i	−0.779653	+	0.137474i	−0.549291	−	0.835631i	$-0.685102\pi$
$347$	−270.540	+	47.7035i	−0.779653	+	0.137474i	−0.230362	+	0.973105i	$0.573991\pi$
$348$		0			0
$349$	−377.022	−	316.359i	−1.08029	−	0.906473i	−0.0843479	−	0.996436i	$-0.526881\pi$
$349$	−377.022	−	316.359i	−1.08029	−	0.906473i	−0.995945	+	0.0899629i	$0.971325\pi$
$350$		0			0
$351$	−16.2509	+	442.364i	−0.0462987	+	1.26030i
$352$		0			0
$353$	71.2407	−	84.9014i	0.201815	−	0.240514i	−0.655639	−	0.755075i	$-0.727601\pi$
$353$	71.2407	−	84.9014i	0.201815	−	0.240514i	0.857454	+	0.514561i	$0.172045\pi$
$354$		0			0
$355$	1.56679	+	8.88570i	0.00441349	+	0.0250302i
$356$		0			0
$357$	−153.105	+	15.9985i	−0.428867	+	0.0448136i
$358$		0			0
$359$	−480.926	−	277.663i	−1.33963	−	0.773433i	−0.352874	−	0.935671i	$-0.614796\pi$
$359$	−480.926	−	277.663i	−1.33963	−	0.773433i	−0.986752	+	0.162237i	$0.948129\pi$
$360$		0			0
$361$	180.428	+	312.510i	0.499800	+	0.865679i
$362$		0			0
$363$	84.0075	+	172.505i	0.231426	+	0.475222i
$364$		0			0
$365$	−13.2284	−	15.7650i	−0.0362423	−	0.0431919i
$366$		0			0
$367$	374.715	−	136.385i	1.02102	−	0.371622i	0.223367	−	0.974734i	$-0.428295\pi$
$367$	374.715	−	136.385i	1.02102	−	0.371622i	0.797656	+	0.603113i	$0.206073\pi$
$368$		0			0
$369$	142.811	+	675.888i	0.387021	+	1.83167i
$370$		0			0
$371$	−720.108	−	126.975i	−1.94099	−	0.342249i
$372$		0			0
$373$	189.416	+	68.9418i	0.507818	+	0.184830i	0.583207	−	0.812324i	$-0.301798\pi$
$373$	189.416	+	68.9418i	0.507818	+	0.184830i	−0.0753893	+	0.997154i	$0.524020\pi$
$374$		0			0
$375$	8.27722	+	28.9321i	0.0220726	+	0.0771523i
$376$		0			0
$377$			679.305i			1.80187i
$378$		0			0
$379$	135.501			0.357522			0.178761	−	0.983892i	$-0.442791\pi$
$379$	135.501			0.357522			0.178761	+	0.983892i	$0.442791\pi$
$380$		0			0
$381$	335.786	+	324.658i	0.881329	+	0.852120i
$382$		0			0
$383$	82.3154	−	226.160i	0.214923	−	0.590495i	−0.784643	−	0.619947i	$-0.787154\pi$
$383$	82.3154	−	226.160i	0.214923	−	0.590495i	0.999566	+	0.0294519i	$0.00937620\pi$
$384$		0			0
$385$	−2.24221	+	12.7162i	−0.00582392	+	0.0330291i
$386$		0			0
$387$	−15.5486	−	2.20438i	−0.0401771	−	0.00569606i
$388$		0			0
$389$	34.2832	+	94.1925i	0.0881317	+	0.242140i	0.975927	−	0.218100i	$-0.0699857\pi$
$389$	34.2832	+	94.1925i	0.0881317	+	0.242140i	−0.887795	+	0.460240i	$0.847764\pi$
$390$		0			0
$391$	129.760	−	108.882i	0.331867	−	0.278469i
$392$		0			0
$393$	30.1443	−	427.372i	0.0767031	−	1.08746i
$394$		0			0
$395$	14.6873	−	8.47971i	0.0371830	−	0.0214676i
$396$		0			0
$397$	−31.5616	+	54.6663i	−0.0795003	+	0.137699i	−0.903034	−	0.429568i	$-0.858666\pi$
$397$	−31.5616	+	54.6663i	−0.0795003	+	0.137699i	0.823534	+	0.567267i	$0.191999\pi$
$398$		0			0
$399$	7.85442	−	5.69932i	0.0196853	−	0.0142840i
$400$		0			0
$401$	−382.225	+	67.3965i	−0.953178	+	0.168071i	−0.628549	−	0.777770i	$-0.716351\pi$
$401$	−382.225	+	67.3965i	−0.953178	+	0.168071i	−0.324630	+	0.945841i	$0.605240\pi$
$402$		0			0
$403$	−170.408	−	142.989i	−0.422848	−	0.354812i
$404$		0			0
$405$	15.7896	−	3.89627i	0.0389867	−	0.00962042i
$406$		0			0
$407$	21.9619	−	26.1732i	0.0539604	−	0.0643075i
$408$		0			0
$409$	−90.7835	−	514.859i	−0.221965	−	1.25882i	−0.868404	−	0.495858i	$-0.834854\pi$
$409$	−90.7835	−	514.859i	−0.221965	−	1.25882i	0.646439	−	0.762966i	$-0.276258\pi$
$410$		0			0
$411$	338.360	+	466.305i	0.823261	+	1.13456i
$412$		0			0
$413$	134.412	+	77.6028i	0.325453	+	0.187900i
$414$		0			0
$415$	6.90379	+	11.9577i	0.0166356	+	0.0288138i
$416$		0			0
$417$	213.770	+	15.0781i	0.512638	+	0.0361585i
$418$		0			0
$419$	324.985	+	387.301i	0.775619	+	0.924347i	0.998727	−	0.0504466i	$-0.0160645\pi$
$419$	324.985	+	387.301i	0.775619	+	0.924347i	−0.223107	+	0.974794i	$0.571620\pi$
$420$		0			0
$421$	−61.4522	+	22.3668i	−0.145967	+	0.0531277i	−0.413971	−	0.910290i	$-0.635858\pi$
$421$	−61.4522	+	22.3668i	−0.145967	+	0.0531277i	0.268003	+	0.963418i	$0.413636\pi$
$422$		0			0
$423$	−542.333	−	424.774i	−1.28211	−	1.00419i
$424$		0			0
$425$	148.126	+	26.1187i	0.348533	+	0.0614557i
$426$		0			0
$427$	−300.279	−	109.293i	−0.703230	−	0.255955i
$428$		0			0
$429$	258.209	−	267.060i	0.601885	−	0.622517i
$430$		0			0
$431$		−	449.973i		−	1.04402i	−0.852939	−	0.522010i	$-0.825182\pi$
$431$		−	449.973i		−	1.04402i	0.852939	−	0.522010i	$-0.174818\pi$
$432$		0			0
$433$	57.6415			0.133121			0.0665606	−	0.997782i	$-0.478797\pi$
$433$	57.6415			0.133121			0.0665606	+	0.997782i	$0.478797\pi$
$434$		0			0
$435$	23.9948	−	6.86469i	0.0551604	−	0.0157809i
$436$		0			0
$437$	−3.65221	+	10.0344i	−0.00835746	+	0.0229619i
$438$		0			0
$439$	−40.0913	+	227.369i	−0.0913241	+	0.517925i	0.904488	+	0.426499i	$0.140253\pi$
$439$	−40.0913	+	227.369i	−0.0913241	+	0.517925i	−0.995812	+	0.0914252i	$0.970858\pi$
$440$		0			0
$441$	141.364	+	157.383i	0.320553	+	0.356877i
$442$		0			0
$443$	97.4032	+	267.613i	0.219872	+	0.604093i	0.999762	−	0.0218237i	$-0.00694726\pi$
$443$	97.4032	+	267.613i	0.219872	+	0.604093i	−0.779890	+	0.625917i	$0.784725\pi$
$444$		0			0
$445$	−21.1780	+	17.7705i	−0.0475910	+	0.0399336i
$446$		0			0
$447$	269.209	−	131.101i	0.602258	−	0.293290i
$448$		0			0
$449$	249.959	−	144.314i	0.556701	−	0.321412i	−0.195119	−	0.980780i	$-0.562509\pi$
$449$	249.959	−	144.314i	0.556701	−	0.321412i	0.751821	+	0.659368i	$0.229176\pi$
$450$		0			0
$451$	289.858	−	502.048i	0.642700	−	1.11319i
$452$		0			0
$453$	−30.2005	−	289.019i	−0.0666677	−	0.638010i
$454$		0			0
$455$	−27.6037	+	4.86728i	−0.0606675	+	0.0106973i
$456$		0			0
$457$	57.0131	+	47.8396i	0.124755	+	0.104682i	0.703031	−	0.711160i	$-0.251830\pi$
$457$	57.0131	+	47.8396i	0.124755	+	0.104682i	−0.578276	+	0.815842i	$0.696274\pi$
$458$		0			0
$459$	34.1172	−	159.090i	0.0743294	−	0.346601i
$460$		0			0
$461$	−81.2197	+	96.7939i	−0.176182	+	0.209965i	−0.846907	−	0.531740i	$-0.821538\pi$
$461$	−81.2197	+	96.7939i	−0.176182	+	0.209965i	0.670726	+	0.741705i	$0.265983\pi$
$462$		0			0
$463$	7.85137	+	44.5273i	0.0169576	+	0.0961713i	0.992112	−	0.125355i	$-0.0400071\pi$
$463$	7.85137	+	44.5273i	0.0169576	+	0.0961713i	−0.975154	+	0.221527i	$0.928896\pi$
$464$		0			0
$465$	−3.32869	+	7.46421i	−0.00715846	+	0.0160521i
$466$		0			0
$467$	−395.495	−	228.339i	−0.846884	−	0.488949i	0.0127140	−	0.999919i	$-0.495953\pi$
$467$	−395.495	−	228.339i	−0.846884	−	0.488949i	−0.859598	+	0.510970i	$0.829286\pi$
$468$		0			0
$469$	−299.678	−	519.057i	−0.638972	−	1.10673i
$470$		0			0
$471$	−403.569	+	597.536i	−0.856835	+	1.26865i
$472$		0			0
$473$	8.47099	+	10.0953i	0.0179091	+	0.0213432i
$474$		0			0
$475$	−8.91013	+	3.24302i	−0.0187582	+	0.00682742i
$476$		0			0
$477$	363.663	−	681.960i	0.762396	−	1.42969i
$478$		0			0
$479$	−370.216	−	65.2790i	−0.772893	−	0.136282i	−0.226726	−	0.973959i	$-0.572802\pi$
$479$	−370.216	−	65.2790i	−0.772893	−	0.136282i	−0.546166	+	0.837677i	$0.683913\pi$
$480$		0			0
$481$	69.6945	+	25.3667i	0.144895	+	0.0527375i
$482$		0			0
$483$	−696.610	−	174.132i	−1.44226	−	0.360521i
$484$		0			0
$485$		−	24.1263i		−	0.0497449i
$486$		0			0
$487$	51.3988			0.105542			0.0527708	−	0.998607i	$-0.483195\pi$
$487$	51.3988			0.105542			0.0527708	+	0.998607i	$0.483195\pi$
$488$		0			0
$489$	42.5906	−	170.383i	0.0870973	−	0.348431i
$490$		0			0
$491$	254.558	−	699.393i	0.518449	−	1.42443i	−0.353780	−	0.935329i	$-0.615104\pi$
$491$	254.558	−	699.393i	0.518449	−	1.42443i	0.872229	−	0.489098i	$-0.162674\pi$
$492$		0			0
$493$	43.3579	−	245.895i	0.0879471	−	0.498773i
$494$		0			0
$495$	−12.0425	−	6.42182i	−0.0243284	−	0.0129734i
$496$		0			0
$497$	−130.875	−	359.575i	−0.263329	−	0.723491i
$498$		0			0
$499$	−292.343	+	245.305i	−0.585858	+	0.491593i	−0.886865	−	0.462029i	$-0.847122\pi$
$499$	−292.343	+	245.305i	−0.585858	+	0.491593i	0.301007	+	0.953622i	$0.402677\pi$
$500$		0			0
$501$	162.842	+	109.982i	0.325035	+	0.219525i
$502$		0			0
$503$	169.431	−	97.8211i	0.336841	−	0.194475i	−0.322033	−	0.946728i	$-0.604366\pi$
$503$	169.431	−	97.8211i	0.336841	−	0.194475i	0.658874	+	0.752253i	$0.271033\pi$
$504$		0			0
$505$	1.33733	−	2.31632i	0.00264817	−	0.00458677i
$506$		0			0
$507$	273.422	+	121.933i	0.539293	+	0.240499i
$508$		0			0
$509$	429.935	−	75.8091i	0.844666	−	0.148937i	0.265463	−	0.964121i	$-0.414475\pi$
$509$	429.935	−	75.8091i	0.844666	−	0.148937i	0.579203	+	0.815184i	$0.303364\pi$
$510$		0			0
$511$	668.588	+	561.012i	1.30839	+	1.09787i
$512$		0			0
$513$	3.15191	+	9.76078i	0.00614408	+	0.0190269i
$514$		0			0
$515$	−25.1557	+	29.9794i	−0.0488461	+	0.0582125i
$516$		0			0
$517$	100.385	+	569.314i	0.194169	+	1.10119i
$518$		0			0
$519$	−225.676	+	23.5816i	−0.434828	+	0.0454365i
$520$		0			0
$521$	253.777	+	146.518i	0.487097	+	0.281226i	0.723369	−	0.690461i	$-0.242592\pi$
$521$	253.777	+	146.518i	0.487097	+	0.281226i	−0.236272	+	0.971687i	$0.575926\pi$
$522$		0			0
$523$	166.756	+	288.830i	0.318845	+	0.552256i	0.980247	−	0.197775i	$-0.0633716\pi$
$523$	166.756	+	288.830i	0.318845	+	0.552256i	−0.661402	+	0.750032i	$0.730038\pi$
$524$		0			0
$525$	−279.157	−	573.236i	−0.531728	−	1.09188i
$526$		0			0
$527$	52.5577	+	62.6358i	0.0997300	+	0.118854i
$528$		0			0
$529$	245.367	−	89.3062i	0.463831	−	0.168821i
$530$		0			0
$531$	−122.042	+	109.620i	−0.229835	+	0.206442i
$532$		0			0
$533$	1239.30	+	218.522i	2.32514	+	0.409985i
$534$		0			0
$535$	29.3766	+	10.6922i	0.0549096	+	0.0199855i
$536$		0			0
$537$	247.366	+	864.639i	0.460644	+	1.61013i
$538$		0			0
$539$		−	177.528i		−	0.329365i
$540$		0			0
$541$	−51.1409			−0.0945304			−0.0472652	−	0.998882i	$-0.515051\pi$
$541$	−51.1409			−0.0945304			−0.0472652	+	0.998882i	$0.515051\pi$
$542$		0			0
$543$	−640.817	−	619.578i	−1.18014	−	1.14103i
$544$		0			0
$545$	4.81840	−	13.2385i	0.00884110	−	0.0242907i
$546$		0			0
$547$	−78.2579	+	443.823i	−0.143068	+	0.811376i	0.825831	+	0.563918i	$0.190707\pi$
$547$	−78.2579	+	443.823i	−0.143068	+	0.811376i	−0.968898	+	0.247459i	$0.920405\pi$
$548$		0			0
$549$	208.262	−	265.900i	0.379348	−	0.484335i
$550$		0			0
$551$	5.38353	+	14.7911i	0.00977047	+	0.0268441i
$552$		0			0
$553$	−550.970	+	462.319i	−0.996330	+	0.836020i
$554$		0			0
$555$	0.191721	−	2.71813i	0.000345443	−	0.00489753i
$556$		0			0
$557$	−255.303	+	147.399i	−0.458354	+	0.264631i	−0.711352	−	0.702836i	$-0.751917\pi$
$557$	−255.303	+	147.399i	−0.458354	+	0.264631i	0.252998	+	0.967467i	$0.418583\pi$
$558$		0			0
$559$	−14.3037	+	24.7747i	−0.0255880	+	0.0443196i
$560$		0			0
$561$	−110.512	+	80.1897i	−0.196991	+	0.142941i
$562$		0			0
$563$	−570.607	+	100.613i	−1.01351	+	0.178709i	−0.655650	−	0.755065i	$-0.727605\pi$
$563$	−570.607	+	100.613i	−1.01351	+	0.178709i	−0.357861	+	0.933775i	$0.616494\pi$
$564$		0			0
$565$	−16.1258	−	13.5312i	−0.0285413	−	0.0239490i
$566$		0			0
$567$	−630.763	+	279.009i	−1.11246	+	0.492079i
$568$		0			0
$569$	134.264	−	160.010i	0.235965	−	0.281212i	−0.635047	−	0.772473i	$-0.719019\pi$
$569$	134.264	−	160.010i	0.235965	−	0.281212i	0.871012	+	0.491261i	$0.163464\pi$
$570$		0			0
$571$	−83.0575	−	471.043i	−0.145460	−	0.824943i	−0.966997	−	0.254788i	$-0.917994\pi$
$571$	−83.0575	−	471.043i	−0.145460	−	0.824943i	0.821537	−	0.570155i	$-0.193117\pi$
$572$		0			0
$573$	−144.215	−	198.748i	−0.251685	−	0.346855i
$574$		0			0
$575$	607.596	+	350.795i	1.05669	+	0.610079i
$576$		0			0
$577$	94.3702	+	163.454i	0.163553	+	0.283282i	0.936141	−	0.351626i	$-0.114371\pi$
$577$	94.3702	+	163.454i	0.163553	+	0.283282i	−0.772587	+	0.634908i	$0.781038\pi$
$578$		0			0
$579$	−352.288	−	24.8484i	−0.608443	−	0.0429161i
$580$		0			0
$581$	−376.399	−	448.575i	−0.647847	−	0.772074i
$582$		0			0
$583$	−609.460	+	221.825i	−1.04539	+	0.380489i
$584$		0			0
$585$	4.15861	−	29.3327i	0.00710873	−	0.0501414i
$586$		0			0
$587$	563.429	+	99.3478i	0.959846	+	0.169247i	0.631556	−	0.775330i	$-0.282417\pi$
$587$	563.429	+	99.3478i	0.959846	+	0.169247i	0.328290	+	0.944577i	$0.393528\pi$
$588$		0			0
$589$	−4.84364	−	1.76294i	−0.00822350	−	0.00299311i
$590$		0			0
$591$	168.215	−	173.981i	0.284627	−	0.294384i
$592$		0			0
$593$			1075.40i			1.81349i	0.421682	+	0.906744i	$0.361440\pi$
$593$			1075.40i			1.81349i	−0.421682	+	0.906744i	$0.638560\pi$
$594$		0			0
$595$	10.3027			0.0173154
$596$		0			0
$597$	−507.381	+	145.157i	−0.849885	+	0.243145i
$598$		0			0
$599$	145.620	−	400.088i	0.243106	−	0.667927i	−0.756793	−	0.653655i	$-0.773235\pi$
$599$	145.620	−	400.088i	0.243106	−	0.667927i	0.999898	−	0.0142721i	$-0.00454310\pi$
$600$		0			0
$601$	−128.421	+	728.311i	−0.213679	+	1.21183i	0.669506	+	0.742807i	$0.266506\pi$
$601$	−128.421	+	728.311i	−0.213679	+	1.21183i	−0.883185	+	0.469026i	$0.844605\pi$
$602$		0			0
$603$	619.809	−	130.961i	1.02788	−	0.217183i
$604$		0			0
$605$	−4.39205	−	12.0671i	−0.00725959	−	0.0199455i
$606$		0			0
$607$	−379.228	+	318.210i	−0.624758	+	0.524235i	−0.899295	−	0.437342i	$-0.855920\pi$
$607$	−379.228	+	318.210i	−0.624758	+	0.524235i	0.274537	+	0.961577i	$0.411475\pi$
$608$		0			0
$609$	−951.592	+	463.411i	−1.56255	+	0.760937i
$610$		0			0
$611$	−1086.78	+	627.452i	−1.77869	+	1.02693i
$612$		0			0
$613$	−521.519	+	903.298i	−0.850766	+	1.47357i	0.0297525	+	0.999557i	$0.490528\pi$
$613$	−521.519	+	903.298i	−0.850766	+	1.47357i	−0.880518	+	0.474012i	$0.842805\pi$
$614$		0			0
$615$	−4.80496	−	45.9835i	−0.00781294	−	0.0747699i
$616$		0			0
$617$	154.839	−	27.3024i	0.250955	−	0.0442502i	−0.0467552	−	0.998906i	$-0.514888\pi$
$617$	154.839	−	27.3024i	0.250955	−	0.0442502i	0.297711	+	0.954656i	$0.403777\pi$
$618$		0			0
$619$	207.387	+	174.018i	0.335035	+	0.281128i	0.794748	−	0.606940i	$-0.207603\pi$
$619$	207.387	+	174.018i	0.335035	+	0.281128i	−0.459713	+	0.888068i	$0.652048\pi$
$620$		0			0
$621$	403.344	−	642.889i	0.649508	−	1.03525i
$622$		0			0
$623$	753.636	−	898.149i	1.20969	−	1.44165i
$624$		0			0
$625$	108.005	+	612.529i	0.172809	+	0.980046i
$626$		0			0
$627$	3.50575	−	7.86125i	0.00559131	−	0.0125379i
$628$		0			0
$629$	−23.6090	−	13.6306i	−0.0375341	−	0.0216703i
$630$		0			0
$631$	−226.092	−	391.603i	−0.358308	−	0.620608i	0.629370	−	0.777106i	$-0.283313\pi$
$631$	−226.092	−	391.603i	−0.358308	−	0.620608i	−0.987678	+	0.156498i	$0.949980\pi$
$632$		0			0
$633$	60.7718	−	89.9805i	0.0960060	−	0.142149i
$634$		0			0
$635$	−20.0933	−	23.9462i	−0.0316430	−	0.0377106i
$636$		0			0
$637$	362.129	−	131.804i	0.568491	−	0.206914i
$638$		0			0
$639$	404.217	−	13.6263i	0.632577	−	0.0213245i
$640$		0			0
$641$	682.172	+	120.285i	1.06423	+	0.187653i	0.678233	−	0.734847i	$-0.262746\pi$
$641$	682.172	+	120.285i	1.06423	+	0.187653i	0.385998	+	0.922500i	$0.373857\pi$
$642$		0			0
$643$	−738.955	−	268.958i	−1.14923	−	0.418286i	−0.303992	−	0.952675i	$-0.598319\pi$
$643$	−738.955	−	268.958i	−1.14923	−	0.418286i	−0.845239	+	0.534389i	$0.820542\pi$
$644$		0			0
$645$	1.01965	+	0.254882i	0.00158085	+	0.000395166i
$646$		0			0
$647$			62.1427i			0.0960475i	0.998846	+	0.0480237i	$0.0152923\pi$
$647$			62.1427i			0.0960475i	−0.998846	+	0.0480237i	$0.984708\pi$
$648$		0			0
$649$	137.664			0.212117
$650$		0			0
$651$	84.0544	−	336.258i	0.129116	−	0.516525i
$652$		0			0
$653$	101.323	−	278.384i	0.155166	−	0.426315i	−0.837614	−	0.546262i	$-0.816050\pi$
$653$	101.323	−	278.384i	0.155166	−	0.426315i	0.992780	+	0.119947i	$0.0382725\pi$
$654$		0			0
$655$	−4.97914	+	28.2381i	−0.00760174	+	0.0431116i
$656$		0			0
$657$	−782.906	+	487.899i	−1.19164	+	0.742617i
$658$		0			0
$659$	94.7068	+	260.205i	0.143713	+	0.394848i	0.990576	−	0.136963i	$-0.0437340\pi$
$659$	94.7068	+	260.205i	0.143713	+	0.394848i	−0.846863	+	0.531811i	$0.821512\pi$
$660$		0			0
$661$	489.455	−	410.702i	0.740477	−	0.621334i	−0.192489	−	0.981299i	$-0.561656\pi$
$661$	489.455	−	410.702i	0.740477	−	0.621334i	0.932966	+	0.359965i	$0.117212\pi$
$662$		0			0
$663$	−245.623	−	165.891i	−0.370472	−	0.250212i
$664$		0			0
$665$	−0.562467	+	0.324741i	−0.000845815	+	0.000488332i
$666$		0			0
$667$	582.332	−	1008.63i	0.873062	−	1.51219i
$668$		0			0
$669$	−1106.01	−	493.227i	−1.65322	−	0.737260i
$670$		0			0
$671$	−279.128	+	49.2179i	−0.415989	+	0.0733500i
$672$		0			0
$673$	361.710	+	303.510i	0.537459	+	0.450981i	0.870668	−	0.491872i	$-0.163687\pi$
$673$	361.710	+	303.510i	0.537459	+	0.450981i	−0.333209	+	0.942853i	$0.608132\pi$
$674$		0			0
$675$	667.522	−	92.5801i	0.988922	−	0.137156i
$676$		0			0
$677$	−198.994	+	237.152i	−0.293935	+	0.350298i	−0.892720	−	0.450612i	$-0.851206\pi$
$677$	−198.994	+	237.152i	−0.293935	+	0.350298i	0.598785	+	0.800910i	$0.295650\pi$
$678$		0			0
$679$	177.674	+	1007.64i	0.261670	+	1.48401i
$680$		0			0
$681$	523.399	−	54.6916i	0.768574	−	0.0803107i
$682$		0			0
$683$	654.635	+	377.954i	0.958470	+	0.553373i	0.895702	−	0.444655i	$-0.146674\pi$
$683$	654.635	+	377.954i	0.958470	+	0.553373i	0.0627681	+	0.998028i	$0.480007\pi$
$684$		0			0
$685$	−19.2794	−	33.3929i	−0.0281451	−	0.0487487i
$686$		0			0
$687$	176.276	+	361.975i	0.256588	+	0.526892i
$688$		0			0
$689$	−904.976	−	1078.51i	−1.31346	−	1.56533i
$690$		0			0
$691$	711.871	−	259.100i	1.03020	−	0.374963i	0.229045	−	0.973416i	$-0.426440\pi$
$691$	711.871	−	259.100i	1.03020	−	0.374963i	0.801158	+	0.598452i	$0.204217\pi$
$692$		0			0
$693$	550.252	+	179.523i	0.794014	+	0.259052i
$694$		0			0
$695$	−14.1246	−	2.49055i	−0.0203232	−	0.00358353i
$696$		0			0
$697$	−434.654	−	158.201i	−0.623608	−	0.226975i
$698$		0			0
$699$	326.410	+	1140.93i	0.466968	+	1.63223i
$700$		0			0
$701$		−	1368.47i		−	1.95217i	−0.217397	−	0.976083i	$-0.569757\pi$
$701$		−	1368.47i		−	1.95217i	0.217397	−	0.976083i	$-0.430243\pi$
$702$		0			0
$703$	1.71855			0.00244460
$704$		0			0
$705$	33.1456	+	32.0471i	0.0470150	+	0.0454568i
$706$		0			0
$707$	−38.7956	+	106.590i	−0.0548736	+	0.150764i
$708$		0			0
$709$	70.8018	−	401.537i	0.0998615	−	0.566343i	−0.893287	−	0.449486i	$-0.851607\pi$
$709$	70.8018	−	401.537i	0.0998615	−	0.566343i	0.993149	−	0.116857i	$-0.0372818\pi$
$710$		0			0
$711$	−283.926	−	705.195i	−0.399333	−	0.991835i
$712$		0			0
$713$	130.444	+	358.391i	0.182951	+	0.502653i
$714$		0			0
$715$	−19.0451	+	15.9807i	−0.0266365	+	0.0223507i
$716$		0			0
$717$	−94.8550	+	1344.81i	−0.132294	+	1.87560i
$718$		0			0
$719$	−214.968	+	124.112i	−0.298982	+	0.172617i	−0.641985	−	0.766717i	$-0.721889\pi$
$719$	−214.968	+	124.112i	−0.298982	+	0.172617i	0.343004	+	0.939334i	$0.388556\pi$
$720$		0			0
$721$	829.856	−	1437.35i	1.15098	−	1.99355i
$722$		0			0
$723$	553.449	−	401.593i	0.765490	−	0.555454i
$724$		0			0
$725$	1018.47	−	179.583i	1.40478	−	0.247701i
$726$		0			0
$727$	229.792	+	192.819i	0.316083	+	0.265225i	0.787001	−	0.616952i	$-0.211633\pi$
$727$	229.792	+	192.819i	0.316083	+	0.265225i	−0.470918	+	0.882177i	$0.656077\pi$
$728$		0			0
$729$	−73.5714	−	725.278i	−0.100921	−	0.994894i
$730$		0			0
$731$	6.75893	−	8.05498i	0.00924615	−	0.0110191i
$732$		0			0
$733$	−132.659	−	752.346i	−0.180981	−	1.02639i	−0.931011	−	0.364990i	$-0.881072\pi$
$733$	−132.659	−	752.346i	−0.180981	−	1.02639i	0.750031	−	0.661403i	$-0.230039\pi$
$734$		0			0
$735$	−8.31513	−	11.4594i	−0.0113131	−	0.0155910i
$736$		0			0
$737$	−460.393	−	265.808i	−0.624685	−	0.360662i
$738$		0			0
$739$	−437.913	−	758.487i	−0.592575	−	1.02637i	−0.993884	−	0.110427i	$-0.964778\pi$
$739$	−437.913	−	758.487i	−0.592575	−	1.02637i	0.401309	−	0.915943i	$-0.368555\pi$
$740$		0			0
$741$	18.6385	+	1.31465i	0.0251532	+	0.00177416i
$742$		0			0
$743$	57.9224	+	69.0292i	0.0779574	+	0.0929060i	0.803613	−	0.595152i	$-0.202908\pi$
$743$	57.9224	+	69.0292i	0.0779574	+	0.0929060i	−0.725656	+	0.688058i	$0.758464\pi$
$744$		0			0
$745$	−18.8317	+	6.85416i	−0.0252774	+	0.00920022i
$746$		0			0
$747$	574.137	−	231.160i	0.768591	−	0.309450i
$748$		0			0
$749$	−1305.66	−	230.223i	−1.74321	−	0.307374i
$750$		0			0
$751$	−423.400	−	154.105i	−0.563782	−	0.205200i	0.0443772	−	0.999015i	$-0.485870\pi$
$751$	−423.400	−	154.105i	−0.563782	−	0.205200i	−0.608159	+	0.793815i	$0.708092\pi$
$752$		0			0
$753$	740.473	−	765.856i	0.983364	−	1.01707i
$754$		0			0
$755$			19.4484i			0.0257595i
$756$		0			0
$757$	67.0196			0.0885332			0.0442666	−	0.999020i	$-0.485905\pi$
$757$	67.0196			0.0885332			0.0442666	+	0.999020i	$0.485905\pi$
$758$		0			0
$759$	−612.324	+	175.181i	−0.806751	+	0.230804i
$760$		0			0
$761$	−309.817	+	851.216i	−0.407119	+	1.11855i	0.551579	+	0.834123i	$0.314026\pi$
$761$	−309.817	+	851.216i	−0.407119	+	1.11855i	−0.958698	+	0.284427i	$0.908197\pi$
$762$		0			0
$763$	−103.749	+	588.391i	−0.135975	+	0.771155i
$764$		0			0
$765$	−3.37755	+	10.3524i	−0.00441509	+	0.0135326i
$766$		0			0
$767$	102.207	+	280.813i	0.133256	+	0.366118i
$768$		0			0
$769$	−706.730	+	593.017i	−0.919024	+	0.771153i	−0.973814	−	0.227345i	$-0.926995\pi$
$769$	−706.730	+	593.017i	−0.919024	+	0.771153i	0.0547901	+	0.998498i	$0.482551\pi$
$770$		0			0
$771$	515.343	−	250.964i	0.668409	−	0.325505i
$772$		0			0
$773$	−1317.32	+	760.554i	−1.70416	+	0.983900i	−0.762721	+	0.646728i	$0.776137\pi$
$773$	−1317.32	+	760.554i	−1.70416	+	0.983900i	−0.941443	+	0.337172i	$0.890530\pi$
$774$		0			0
$775$	−169.331	+	293.290i	−0.218491	+	0.378438i
$776$		0			0
$777$	12.0099	+	114.935i	0.0154568	+	0.147922i
$778$		0			0
$779$	28.7162	−	5.06344i	0.0368629	−	0.00649993i
$780$		0			0
$781$	−259.998	−	218.164i	−0.332904	−	0.279340i
$782$		0			0
$783$	−153.686	−	1108.11i	−0.196279	−	1.41521i
$784$		0			0
$785$	31.0196	−	36.9677i	0.0395154	−	0.0470926i
$786$		0			0
$787$	−136.517	−	774.228i	−0.173465	−	0.983771i	−0.939900	−	0.341449i	$-0.889082\pi$
$787$	−136.517	−	774.228i	−0.173465	−	0.983771i	0.766435	−	0.642322i	$-0.222029\pi$
$788$		0			0
$789$	74.2363	−	166.467i	0.0940891	−	0.210984i
$790$		0			0
$791$	773.146	+	446.376i	0.977429	+	0.564319i
$792$		0			0
$793$	−307.633	−	532.836i	−0.387936	−	0.671924i
$794$		0			0
$795$	−28.9504	+	42.8649i	−0.0364156	+	0.0539181i
$796$		0			0
$797$	−442.583	−	527.450i	−0.555311	−	0.661794i	0.413236	−	0.910624i	$-0.364398\pi$
$797$	−442.583	−	527.450i	−0.555311	−	0.661794i	−0.968547	+	0.248830i	$0.919954\pi$
$798$		0			0
$799$	433.441	−	157.759i	0.542479	−	0.197446i
$800$		0			0
$801$	655.420	+	1051.72i	0.818253	+	1.31301i
$802$		0			0
$803$	762.375	+	134.427i	0.949409	+	0.167406i
$804$		0			0
$805$	45.1584	+	16.4363i	0.0560973	+	0.0204178i
$806$		0			0
$807$	−2.97849	−	0.744533i	−0.00369081	−	0.000922593i
$808$		0			0
$809$		−	267.972i		−	0.331238i	−0.986190	−	0.165619i	$-0.947038\pi$
$809$		−	267.972i		−	0.331238i	0.986190	−	0.165619i	$-0.0529623\pi$
$810$		0			0
$811$	457.328			0.563906			0.281953	−	0.959428i	$-0.409018\pi$
$811$	457.328			0.563906			0.281953	+	0.959428i	$0.409018\pi$
$812$		0			0
$813$	−192.468	+	769.963i	−0.236738	+	0.947064i
$814$		0			0
$815$	−4.02012	+	11.0452i	−0.00493266	+	0.0135524i
$816$		0			0
$817$	−0.115106	+	0.652799i	−0.000140889	+	0.000799019i
$818$		0			0
$819$	42.3306	+	1255.71i	0.0516857	+	1.53323i
$820$		0			0
$821$	71.1226	+	195.408i	0.0866292	+	0.238012i	0.975441	−	0.220260i	$-0.0706907\pi$
$821$	71.1226	+	195.408i	0.0866292	+	0.238012i	−0.888812	+	0.458272i	$0.848468\pi$
$822$		0			0
$823$	−239.194	+	200.707i	−0.290636	+	0.243873i	−0.776434	−	0.630198i	$-0.782974\pi$
$823$	−239.194	+	200.707i	−0.290636	+	0.243873i	0.485798	+	0.874071i	$0.338529\pi$
$824$		0			0
$825$	−468.658	−	316.526i	−0.568070	−	0.383668i
$826$		0			0
$827$	−905.439	+	522.755i	−1.09485	+	0.632111i	−0.934863	−	0.355009i	$-0.884478\pi$
$827$	−905.439	+	522.755i	−1.09485	+	0.632111i	−0.159985	+	0.987119i	$0.551144\pi$
$828$		0			0
$829$	370.655	−	641.994i	0.447111	−	0.774419i	−0.551085	−	0.834449i	$-0.685786\pi$
$829$	370.655	−	641.994i	0.447111	−	0.774419i	0.998197	+	0.0600295i	$0.0191195\pi$
$830$		0			0
$831$	995.565	+	443.975i	1.19803	+	0.534266i
$832$		0			0
$833$	−139.496	+	24.5969i	−0.167462	+	0.0295281i
$834$		0			0
$835$	−10.0745	−	8.45355i	−0.0120653	−	0.0101240i
$836$		0			0
$837$	310.326	+	194.697i	0.370760	+	0.232612i
$838$		0			0
$839$	−54.1406	+	64.5222i	−0.0645299	+	0.0769037i	−0.797344	−	0.603525i	$-0.793762\pi$
$839$	−54.1406	+	64.5222i	−0.0645299	+	0.0769037i	0.732814	+	0.680429i	$0.238207\pi$
$840$		0			0
$841$	−152.076	−	862.466i	−0.180828	−	1.02552i
$842$		0			0
$843$	565.495	−	59.0904i	0.670813	−	0.0700954i
$844$		0			0
$845$	−17.3521	−	10.0182i	−0.0205350	−	0.0118559i
$846$		0			0
$847$	272.301	+	471.639i	0.321488	+	0.556834i
$848$		0			0
$849$	376.723	+	773.583i	0.443726	+	0.911170i
$850$		0			0
$851$	−81.7366	−	97.4099i	−0.0960477	−	0.114465i
$852$		0			0
$853$	−16.4245	+	5.97804i	−0.0192550	+	0.00700825i	−0.351630	−	0.936139i	$-0.614372\pi$
$853$	−16.4245	+	5.97804i	−0.0192550	+	0.00700825i	0.332375	+	0.943147i	$0.392150\pi$
$854$		0			0
$855$	−0.141914	−	0.671644i	−0.000165981	−	0.000785549i
$856$		0			0
$857$	−749.943	−	132.235i	−0.875079	−	0.154300i	−0.281971	−	0.959423i	$-0.590988\pi$
$857$	−749.943	−	132.235i	−0.875079	−	0.154300i	−0.593108	+	0.805123i	$0.702099\pi$
$858$		0			0
$859$	889.121	+	323.614i	1.03507	+	0.376733i	0.803008	−	0.595969i	$-0.203232\pi$
$859$	889.121	+	323.614i	1.03507	+	0.376733i	0.232058	+	0.972702i	$0.425454\pi$
$860$		0			0
$861$	539.318	+	1885.12i	0.626385	+	2.18946i
$862$		0			0
$863$			357.864i			0.414675i	0.978270	+	0.207337i	$0.0664798\pi$
$863$			357.864i			0.414675i	−0.978270	+	0.207337i	$0.933520\pi$
$864$		0			0
$865$	15.1860			0.0175561
$866$		0			0
$867$	−544.981	−	526.919i	−0.628583	−	0.607750i
$868$		0			0
$869$	−218.192	+	599.478i	−0.251084	+	0.689848i
$870$		0			0
$871$	200.391	−	1136.47i	0.230070	−	1.30479i
$872$		0			0
$873$	−1070.75	−	151.805i	−1.22652	−	0.173889i
$874$		0			0
$875$	29.2132	+	80.2625i	0.0333865	+	0.0917286i
$876$		0			0
$877$	833.488	−	699.380i	0.950386	−	0.797468i	−0.0289766	−	0.999580i	$-0.509225\pi$
$877$	833.488	−	699.380i	0.950386	−	0.797468i	0.979362	+	0.202112i	$0.0647804\pi$
$878$		0			0
$879$	−42.2894	+	599.558i	−0.0481108	+	0.682091i
$880$		0			0
$881$	−668.191	+	385.780i	−0.758446	+	0.437889i	−0.828738	−	0.559638i	$-0.810940\pi$
$881$	−668.191	+	385.780i	−0.758446	+	0.437889i	0.0702915	+	0.997526i	$0.477607\pi$
$882$		0			0
$883$	−605.002	+	1047.89i	−0.685166	+	1.18674i	0.288219	+	0.957565i	$0.406937\pi$
$883$	−605.002	+	1047.89i	−0.685166	+	1.18674i	−0.973385	+	0.229178i	$0.926396\pi$
$884$		0			0
$885$	8.88615	−	6.44796i	0.0100409	−	0.00728584i
$886$		0			0
$887$	−1334.02	+	235.224i	−1.50397	+	0.265190i	−0.864110	−	0.503303i	$-0.832118\pi$
$887$	−1334.02	+	235.224i	−1.50397	+	0.265190i	−0.639858	+	0.768493i	$0.721007\pi$
$888$		0			0
$889$	1015.55	+	852.146i	1.14235	+	0.958545i
$890$		0			0
$891$	−360.781	+	494.056i	−0.404917	+	0.554496i
$892$		0			0
$893$	−18.6908	+	22.2749i	−0.0209304	+	0.0249439i
$894$		0			0
$895$	−10.4518	−	59.2748i	−0.0116779	−	0.0662289i
$896$		0			0
$897$	−811.955	−	1118.98i	−0.905189	−	1.24747i
$898$		0			0
$899$	486.871	+	281.095i	0.541569	+	0.312675i
$900$		0			0
$901$	258.746	+	448.161i	0.287176	+	0.497404i
$902$		0			0
$903$	−44.4629	−	3.13616i	−0.0492391	−	0.00347304i
$904$		0			0
$905$	38.3461	+	45.6991i	0.0423714	+	0.0504963i
$906$		0			0
$907$	−1446.41	+	526.450i	−1.59472	+	0.580430i	−0.978337	−	0.207019i	$-0.933624\pi$
$907$	−1446.41	+	526.450i	−1.59472	+	0.580430i	−0.616381	+	0.787448i	$0.711402\pi$
$908$		0			0
$909$	−94.3865	−	73.9267i	−0.103835	−	0.0813275i
$910$		0			0
$911$	309.888	+	54.6416i	0.340162	+	0.0599798i	0.341120	−	0.940020i	$-0.389194\pi$
$911$	309.888	+	54.6416i	0.340162	+	0.0599798i	−0.000957797		1.00000i	$0.500305\pi$
$912$		0			0
$913$	−488.067	−	177.642i	−0.534575	−	0.194569i
$914$		0			0
$915$	−15.7123	+	16.2509i	−0.0171719	+	0.0177606i
$916$		0			0
$917$		−	1216.04i		−	1.32611i
$918$		0			0
$919$	−956.851			−1.04119			−0.520594	−	0.853805i	$-0.674289\pi$
$919$	−956.851			−1.04119			−0.520594	+	0.853805i	$0.674289\pi$
$920$		0			0
$921$	506.364	−	144.866i	0.549798	−	0.157293i
$922$		0			0
$923$	251.987	−	692.329i	0.273009	−	0.750086i
$924$		0			0
$925$	19.6071	−	111.197i	0.0211969	−	0.120213i
$926$		0			0
$927$	1172.24	+	1305.08i	1.26455	+	1.40785i
$928$		0			0
$929$	−373.128	−	1025.16i	−0.401645	−	1.10351i	−0.961472	−	0.274902i	$-0.911355\pi$
$929$	−373.128	−	1025.16i	−0.401645	−	1.10351i	0.559827	−	0.828610i	$-0.310868\pi$
$930$		0			0
$931$	6.84040	−	5.73978i	0.00734737	−	0.00616518i
$932$		0			0
$933$	−387.029	+	188.477i	−0.414822	+	0.202012i
$934$		0			0
$935$	7.91394	−	4.56912i	0.00846411	−	0.00488676i
$936$		0			0
$937$	−223.525	+	387.156i	−0.238554	+	0.413187i	−0.960299	−	0.278971i	$-0.910007\pi$
$937$	−223.525	+	387.156i	−0.238554	+	0.413187i	0.721746	+	0.692158i	$0.243340\pi$
$938$		0			0
$939$	−155.909	−	1492.05i	−0.166038	−	1.58898i
$940$		0			0
$941$	−1.45674	+	0.256863i	−0.00154808	+	0.000272968i	−0.174422	−	0.984671i	$-0.555806\pi$
$941$	−1.45674	+	0.256863i	−0.00154808	+	0.000272968i	0.172874	+	0.984944i	$0.444695\pi$
$942$		0			0
$943$	−1652.78	−	1386.85i	−1.75268	−	1.47068i
$944$		0			0
$945$	43.9271	−	14.1848i	0.0464837	−	0.0150103i
$946$		0			0
$947$	−997.650	+	1188.95i	−1.05348	+	1.25549i	−0.0877005	+	0.996147i	$0.527952\pi$
$947$	−997.650	+	1188.95i	−1.05348	+	1.25549i	−0.965784	+	0.259347i	$0.916493\pi$
$948$		0			0
$949$	291.809	+	1654.93i	0.307491	+	1.74387i
$950$		0			0
$951$	197.539	−	442.958i	0.207717	−	0.465782i
$952$		0			0
$953$	1466.92	+	846.929i	1.53927	+	0.888698i	0.998882	+	0.0472820i	$0.0150559\pi$
$953$	1466.92	+	846.929i	1.53927	+	0.888698i	0.540388	+	0.841416i	$0.318277\pi$
$954$		0			0
$955$	8.21723	+	14.2327i	0.00860443	+	0.0149033i
$956$		0			0
$957$	−525.444	+	777.987i	−0.549053	+	0.812944i
$958$		0			0
$959$	1051.12	+	1252.68i	1.09606	+	1.30624i
$960$		0			0
$961$	730.047	−	265.715i	0.759674	−	0.276499i
$962$		0			0
$963$	659.374	−	1236.49i	0.684708	−	1.28400i
$964$		0			0
$965$	23.2771	+	4.10438i	0.0241213	+	0.00425324i
$966$		0			0
$967$	557.509	+	202.917i	0.576535	+	0.209841i	0.613797	−	0.789464i	$-0.289641\pi$
$967$	557.509	+	202.917i	0.576535	+	0.209841i	−0.0372622	+	0.999306i	$0.511864\pi$
$968$		0			0
$969$	−6.66286	−	1.66552i	−0.00687602	−	0.00171880i
$970$		0			0
$971$		−	597.827i		−	0.615682i	−0.951438	−	0.307841i	$-0.900394\pi$
$971$		−	597.827i		−	0.615682i	0.951438	−	0.307841i	$-0.0996065\pi$
$972$		0			0
$973$	608.259			0.625138
$974$		0			0
$975$	297.712	−	1190.99i	0.305345	−	1.22153i
$976$		0			0
$977$	−44.3601	+	121.878i	−0.0454044	+	0.124748i	−0.960322	−	0.278892i	$-0.910033\pi$
$977$	−44.3601	+	121.878i	−0.0454044	+	0.124748i	0.914918	+	0.403640i	$0.132255\pi$
$978$		0			0
$979$	180.583	−	1024.14i	0.184457	−	1.04611i
$980$		0			0
$981$	−557.221	−	297.144i	−0.568013	−	0.302899i
$982$		0			0
$983$	−145.726	−	400.380i	−0.148246	−	0.407304i	0.843236	−	0.537543i	$-0.180648\pi$
$983$	−145.726	−	400.380i	−0.148246	−	0.407304i	−0.991483	+	0.130240i	$0.958425\pi$
$984$		0			0
$985$	−12.4073	+	10.4109i	−0.0125962	+	0.0105695i
$986$		0			0
$987$	−1620.34	−	1094.36i	−1.64168	−	1.10877i
$988$		0			0
$989$	42.4761	−	24.5236i	0.0429485	−	0.0247963i
$990$		0			0
$991$	−194.763	+	337.340i	−0.196532	+	0.340403i	−0.947402	−	0.320047i	$-0.896301\pi$
$991$	−194.763	+	337.340i	−0.196532	+	0.340403i	0.750870	+	0.660450i	$0.229635\pi$
$992$		0			0
$993$	1260.73	+	562.226i	1.26962	+	0.566189i
$994$		0			0
$995$	34.7832	−	6.13322i	0.0349580	−	0.00616404i
$996$		0			0
$997$	−505.149	−	423.871i	−0.506669	−	0.425146i	0.353286	−	0.935515i	$-0.385064\pi$
$997$	−505.149	−	423.871i	−0.506669	−	0.425146i	−0.859955	+	0.510369i	$0.829509\pi$
$998$		0			0
$999$	−119.427	−	25.6115i	−0.119547	−	0.0256372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.65.3	yes	36
3.2	odd	2		324.3.k.a.197.4		36
4.3	odd	2		432.3.bc.b.65.4		36
27.5	odd	18	inner	108.3.k.a.5.3	✓	36
27.7	even	9		2916.3.c.b.1457.19		36
27.20	odd	18		2916.3.c.b.1457.18		36
27.22	even	9		324.3.k.a.125.4		36
108.59	even	18		432.3.bc.b.113.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.5.3	✓	36	27.5	odd	18	inner
108.3.k.a.65.3	yes	36	1.1	even	1	trivial
324.3.k.a.125.4		36	27.22	even	9
324.3.k.a.197.4		36	3.2	odd	2
432.3.bc.b.65.4		36	4.3	odd	2
432.3.bc.b.113.4		36	108.59	even	18
2916.3.c.b.1457.18		36	27.20	odd	18
2916.3.c.b.1457.19		36	27.7	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.727525 + 2.91045i) q^{3} +(0.0686711 - 0.188672i) q^{5} +(-1.47862 + 8.38565i) q^{7} +(-7.94141 - 4.23485i) q^{9} +O(q^{10})\)	\(q+(-0.727525 + 2.91045i) q^{3} +(0.0686711 - 0.188672i) q^{5} +(-1.47862 + 8.38565i) q^{7} +(-7.94141 - 4.23485i) q^{9} +(2.58315 + 7.09715i) q^{11} +(-12.5592 + 10.5384i) q^{13} +(0.499161 + 0.337127i) q^{15} +(5.21882 - 3.01309i) q^{17} +(-0.189946 + 0.328995i) q^{19} +(-23.3303 - 10.4042i) q^{21} +(27.6819 - 4.88107i) q^{23} +(19.1202 + 16.0438i) q^{25} +(18.1029 - 20.0321i) q^{27} +(26.6332 - 31.7402i) q^{29} +(2.35612 + 13.3622i) q^{31} +(-22.5352 + 2.35477i) q^{33} +(1.48060 + 0.854825i) q^{35} +(-2.26190 - 3.91773i) q^{37} +(-21.5344 - 44.2199i) q^{39} +(-49.3383 - 58.7991i) q^{41} +(1.63966 - 0.596788i) q^{43} +(-1.34434 + 1.20751i) q^{45} +(75.3795 + 13.2914i) q^{47} +(-22.0879 - 8.03934i) q^{49} +(4.97261 + 17.3812i) q^{51} +85.8739i q^{53} +1.51642 q^{55} +(-0.819334 - 0.792179i) q^{57} +(6.23410 - 17.1281i) q^{59} +(-6.51665 + 36.9578i) q^{61} +(47.2543 - 60.3322i) q^{63} +(1.12585 + 3.09326i) q^{65} +(-53.9204 + 45.2446i) q^{67} +(-5.93319 + 84.1179i) q^{69} +(-38.9179 + 22.4692i) q^{71} +(51.2495 - 88.7667i) q^{73} +(-60.6050 + 43.9762i) q^{75} +(-63.3337 + 11.1674i) q^{77} +(64.7058 + 54.2946i) q^{79} +(45.1321 + 67.2614i) q^{81} +(-44.2042 + 52.6805i) q^{83} +(-0.210104 - 1.19156i) q^{85} +(73.0020 + 100.606i) q^{87} +(-119.245 - 68.8461i) q^{89} +(-69.8014 - 120.900i) q^{91} +(-40.6042 - 2.86398i) q^{93} +(0.0490285 + 0.0584299i) q^{95} +(112.916 - 41.0979i) q^{97} +(9.54147 - 67.3007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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