LMFDB - Embedded newform 108.5.f.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not 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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.99035 - 0.277636i) q^{2} +(15.8458 + 2.21573i) q^{4} +(23.3466 + 40.4374i) q^{5} +(52.4363 + 30.2741i) q^{7} +(-62.6153 - 13.2409i) q^{8} +O(q^{10})$	\(q+(-3.99035 - 0.277636i) q^{2} +(15.8458 + 2.21573i) q^{4} +(23.3466 + 40.4374i) q^{5} +(52.4363 + 30.2741i) q^{7} +(-62.6153 - 13.2409i) q^{8} +(-81.9341 - 167.841i) q^{10} +(-63.7631 - 36.8136i) q^{11} +(15.5924 + 27.0068i) q^{13} +(-200.834 - 135.363i) q^{14} +(246.181 + 70.2201i) q^{16} -53.8013 q^{17} +54.9619i q^{19} +(280.347 + 692.494i) q^{20} +(244.217 + 164.602i) q^{22} +(243.863 - 140.795i) q^{23} +(-777.624 + 1346.88i) q^{25} +(-54.7210 - 112.096i) q^{26} +(763.818 + 595.904i) q^{28} +(-223.597 + 387.282i) q^{29} +(-240.584 + 138.901i) q^{31} +(-962.854 - 348.552i) q^{32} +(214.686 + 14.9372i) q^{34} +2827.19i q^{35} +1016.51 q^{37} +(15.2594 - 219.317i) q^{38} +(-926.424 - 2841.13i) q^{40} +(946.158 + 1638.79i) q^{41} +(-666.266 - 384.669i) q^{43} +(-928.811 - 724.625i) q^{44} +(-1012.19 + 494.115i) q^{46} +(-2374.81 - 1371.10i) q^{47} +(632.546 + 1095.60i) q^{49} +(3476.94 - 5158.64i) q^{50} +(187.235 + 462.494i) q^{52} +4647.69 q^{53} -3437.89i q^{55} +(-2882.46 - 2589.93i) q^{56} +(999.756 - 1483.31i) q^{58} +(262.792 - 151.723i) q^{59} +(-478.174 + 828.222i) q^{61} +(998.577 - 487.469i) q^{62} +(3745.36 + 1658.17i) q^{64} +(-728.057 + 1261.03i) q^{65} +(-6010.96 + 3470.43i) q^{67} +(-852.527 - 119.209i) q^{68} +(784.928 - 11281.5i) q^{70} -5971.60i q^{71} -4339.17 q^{73} +(-4056.25 - 282.220i) q^{74} +(-121.781 + 870.917i) q^{76} +(-2229.00 - 3860.75i) q^{77} +(3294.15 + 1901.88i) q^{79} +(2907.96 + 11594.3i) q^{80} +(-3320.52 - 6802.05i) q^{82} +(2730.64 + 1576.53i) q^{83} +(-1256.08 - 2175.59i) q^{85} +(2551.84 + 1719.94i) q^{86} +(3505.10 + 3149.38i) q^{88} +7132.44 q^{89} +1888.18i q^{91} +(4176.18 - 1690.67i) q^{92} +(9095.67 + 6130.50i) q^{94} +(-2222.52 + 1283.17i) q^{95} +(980.405 - 1698.11i) q^{97} +(-2219.91 - 4547.46i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−3.99035	−	0.277636i	−0.997588	−	0.0694089i
$2$	−3.99035	−	0.277636i	−0.997588	−	0.0694089i
$3$		0			0
$3$		0			0
$4$	15.8458	+	2.21573i	0.990365	+	0.138483i
$5$	23.3466	+	40.4374i	0.933862	+	1.61750i	0.776650	+	0.629932i	$0.216917\pi$
$5$	23.3466	+	40.4374i	0.933862	+	1.61750i	0.157212	+	0.987565i	$0.449749\pi$
$6$		0			0
$7$	52.4363	+	30.2741i	1.07013	+	0.617839i	0.928217	−	0.372040i	$-0.121341\pi$
$7$	52.4363	+	30.2741i	1.07013	+	0.617839i	0.141913	+	0.989879i	$0.454675\pi$
$8$	−62.6153	−	13.2409i	−0.978364	−	0.206889i
$9$		0			0
$10$	−81.9341	−	167.841i	−0.819341	−	1.67841i
$11$	−63.7631	−	36.8136i	−0.526968	−	0.304245i	0.212813	−	0.977093i	$-0.431737\pi$
$11$	−63.7631	−	36.8136i	−0.526968	−	0.304245i	−0.739781	+	0.672848i	$0.765071\pi$
$12$		0			0
$13$	15.5924	+	27.0068i	0.0922626	+	0.159803i	0.908463	−	0.417966i	$-0.137257\pi$
$13$	15.5924	+	27.0068i	0.0922626	+	0.159803i	−0.816200	+	0.577769i	$0.803923\pi$
$14$	−200.834	−	135.363i	−1.02466	−	0.690626i
$15$		0			0
$16$	246.181	+	70.2201i	0.961645	+	0.274297i
$17$	−53.8013			−0.186164			−0.0930819	−	0.995658i	$-0.529672\pi$
$17$	−53.8013			−0.186164			−0.0930819	+	0.995658i	$0.529672\pi$
$18$		0			0
$19$			54.9619i			0.152249i	0.997098	+	0.0761245i	$0.0242546\pi$
$19$			54.9619i			0.152249i	−0.997098	+	0.0761245i	$0.975745\pi$
$20$	280.347	+	692.494i	0.700869	+	1.73124i
$21$		0			0
$22$	244.217	+	164.602i	0.504580	+	0.340088i
$23$	243.863	−	140.795i	0.460990	−	0.266152i	−0.251471	−	0.967865i	$-0.580914\pi$
$23$	243.863	−	140.795i	0.460990	−	0.266152i	0.712460	+	0.701712i	$0.247581\pi$
$24$		0			0
$25$	−777.624	+	1346.88i	−1.24420	+	2.15501i
$26$	−54.7210	−	112.096i	−0.0809483	−	0.165822i
$27$		0			0
$28$	763.818	+	595.904i	0.974258	+	0.760081i
$29$	−223.597	+	387.282i	−0.265871	+	0.460502i	−0.967791	−	0.251753i	$-0.918993\pi$
$29$	−223.597	+	387.282i	−0.265871	+	0.460502i	0.701921	+	0.712255i	$0.252326\pi$
$30$		0			0
$31$	−240.584	+	138.901i	−0.250347	+	0.144538i	−0.619923	−	0.784663i	$-0.712836\pi$
$31$	−240.584	+	138.901i	−0.250347	+	0.144538i	0.369576	+	0.929200i	$0.379503\pi$
$32$	−962.854	−	348.552i	−0.940287	−	0.340383i
$33$		0			0
$34$	214.686	+	14.9372i	0.185715	+	0.0129214i
$35$			2827.19i			2.30791i
$36$		0			0
$37$	1016.51			0.742522			0.371261	−	0.928528i	$-0.378925\pi$
$37$	1016.51			0.742522			0.371261	+	0.928528i	$0.378925\pi$
$38$	15.2594	−	219.317i	0.0105674	−	0.151882i
$39$		0			0
$40$	−926.424	−	2841.13i	−0.579015	−	1.77571i
$41$	946.158	+	1638.79i	0.562854	+	0.974892i	0.997246	+	0.0741680i	$0.0236301\pi$
$41$	946.158	+	1638.79i	0.562854	+	0.974892i	−0.434392	+	0.900724i	$0.643037\pi$
$42$		0			0
$43$	−666.266	−	384.669i	−0.360339	−	0.208042i	0.308891	−	0.951098i	$-0.400042\pi$
$43$	−666.266	−	384.669i	−0.360339	−	0.208042i	−0.669229	+	0.743056i	$0.733376\pi$
$44$	−928.811	−	724.625i	−0.479758	−	0.374290i
$45$		0			0
$46$	−1012.19	+	494.115i	−0.478351	+	0.233514i
$47$	−2374.81	−	1371.10i	−1.07506	−	0.620687i	−0.145502	−	0.989358i	$-0.546480\pi$
$47$	−2374.81	−	1371.10i	−1.07506	−	0.620687i	−0.929560	+	0.368671i	$0.879813\pi$
$48$		0			0
$49$	632.546	+	1095.60i	0.263451	+	0.456311i
$50$	3476.94	−	5158.64i	1.39077	−	2.06346i
$51$		0			0
$52$	187.235	+	462.494i	0.0692435	+	0.171041i
$53$	4647.69			1.65457			0.827286	−	0.561780i	$-0.189883\pi$
$53$	4647.69			1.65457			0.827286	+	0.561780i	$0.189883\pi$
$54$		0			0
$55$		−	3437.89i		−	1.13649i
$56$	−2882.46	−	2589.93i	−0.919152	−	0.825870i
$57$		0			0
$58$	999.756	−	1483.31i	0.297193	−	0.440937i
$59$	262.792	−	151.723i	0.0754934	−	0.0435861i	−0.461778	−	0.886995i	$-0.652788\pi$
$59$	262.792	−	151.723i	0.0754934	−	0.0435861i	0.537272	+	0.843409i	$0.319455\pi$
$60$		0			0
$61$	−478.174	+	828.222i	−0.128507	+	0.222580i	−0.923098	−	0.384564i	$-0.874352\pi$
$61$	−478.174	+	828.222i	−0.128507	+	0.222580i	0.794591	+	0.607145i	$0.207685\pi$
$62$	998.577	−	487.469i	0.259776	−	0.126813i
$63$		0			0
$64$	3745.36	+	1658.17i	0.914394	+	0.404826i
$65$	−728.057	+	1261.03i	−0.172321	+	0.298469i
$66$		0			0
$67$	−6010.96	+	3470.43i	−1.33904	+	0.773096i	−0.986665	−	0.162762i	$-0.947960\pi$
$67$	−6010.96	+	3470.43i	−1.33904	+	0.773096i	−0.352376	+	0.935858i	$0.614626\pi$
$68$	−852.527	−	119.209i	−0.184370	−	0.0257805i
$69$		0			0
$70$	784.928	−	11281.5i	0.160189	−	2.30234i
$71$		−	5971.60i		−	1.18461i	−0.805715	−	0.592303i	$-0.798219\pi$
$71$		−	5971.60i		−	1.18461i	0.805715	−	0.592303i	$-0.201781\pi$
$72$		0			0
$73$	−4339.17			−0.814257			−0.407128	−	0.913371i	$-0.633470\pi$
$73$	−4339.17			−0.814257			−0.407128	+	0.913371i	$0.633470\pi$
$74$	−4056.25	−	282.220i	−0.740732	−	0.0515377i
$75$		0			0
$76$	−121.781	+	870.917i	−0.0210839	+	0.150782i
$77$	−2229.00	−	3860.75i	−0.375949	−	0.651163i
$78$		0			0
$79$	3294.15	+	1901.88i	0.527824	+	0.304740i	0.740130	−	0.672464i	$-0.234764\pi$
$79$	3294.15	+	1901.88i	0.527824	+	0.304740i	−0.212306	+	0.977203i	$0.568097\pi$
$80$	2907.96	+	11594.3i	0.454369	+	1.81161i
$81$		0			0
$82$	−3320.52	−	6802.05i	−0.493831	−	1.01161i
$83$	2730.64	+	1576.53i	0.396376	+	0.228848i	0.684919	−	0.728619i	$-0.259837\pi$
$83$	2730.64	+	1576.53i	0.396376	+	0.228848i	−0.288543	+	0.957467i	$0.593171\pi$
$84$		0			0
$85$	−1256.08	−	2175.59i	−0.173851	−	0.301119i
$86$	2551.84	+	1719.94i	0.345030	+	0.232551i
$87$		0			0
$88$	3505.10	+	3149.38i	0.452622	+	0.406686i
$89$	7132.44			0.900447			0.450224	−	0.892916i	$-0.351344\pi$
$89$	7132.44			0.900447			0.450224	+	0.892916i	$0.351344\pi$
$90$		0			0
$91$			1888.18i			0.228014i
$92$	4176.18	−	1690.67i	0.493405	−	0.199749i
$93$		0			0
$94$	9095.67	+	6130.50i	1.02939	+	0.693809i
$95$	−2222.52	+	1283.17i	−0.246262	+	0.142180i
$96$		0			0
$97$	980.405	−	1698.11i	0.104199	−	0.180477i	−0.809212	−	0.587517i	$-0.800106\pi$
$97$	980.405	−	1698.11i	0.104199	−	0.180477i	0.913411	+	0.407040i	$0.133439\pi$
$98$	−2219.91	−	4547.46i	−0.231144	−	0.473496i
$99$		0			0
$100$	−15306.4	+	19619.5i	−1.53064	+	1.96195i
$101$	−3849.96	+	6668.32i	−0.377410	+	0.653693i	−0.990685	−	0.136177i	$-0.956519\pi$
$101$	−3849.96	+	6668.32i	−0.377410	+	0.653693i	0.613275	+	0.789870i	$0.289852\pi$
$102$		0			0
$103$	3195.22	−	1844.76i	0.301180	−	0.173886i	−0.341793	−	0.939775i	$-0.611034\pi$
$103$	3195.22	−	1844.76i	0.301180	−	0.173886i	0.642973	+	0.765889i	$0.277701\pi$
$104$	−618.727	−	1897.50i	−0.0572048	−	0.175434i
$105$		0			0
$106$	−18545.9	−	1290.37i	−1.65058	−	0.114842i
$107$			13741.5i			1.20024i	0.799911	+	0.600118i	$0.204880\pi$
$107$			13741.5i			1.20024i	−0.799911	+	0.600118i	$0.795120\pi$
$108$		0			0
$109$	18709.9			1.57478			0.787388	−	0.616458i	$-0.211433\pi$
$109$	18709.9			1.57478			0.787388	+	0.616458i	$0.211433\pi$
$110$	−954.480	+	13718.4i	−0.0788826	+	1.13375i
$111$		0			0
$112$	10783.0	+	11135.0i	0.859613	+	0.887676i
$113$	−5000.50	−	8661.12i	−0.391613	−	0.678293i	0.601050	−	0.799212i	$-0.294749\pi$
$113$	−5000.50	−	8661.12i	−0.391613	−	0.678293i	−0.992662	+	0.120919i	$0.961416\pi$
$114$		0			0
$115$	11386.7	+	6574.14i	0.861002	+	0.497099i
$116$	−4401.20	+	5641.38i	−0.327081	+	0.419246i
$117$		0			0
$118$	−1090.76	+	532.469i	−0.0783366	+	0.0382411i
$119$	−2821.15	−	1628.79i	−0.199219	−	0.115019i
$120$		0			0
$121$	−4610.01	−	7984.77i	−0.314870	−	0.545371i
$122$	2138.03	−	3172.14i	0.143646	−	0.213124i
$123$		0			0
$124$	−4120.01	+	1667.93i	−0.267951	+	0.108477i
$125$	−43436.1			−2.77991
$126$		0			0
$127$		−	18883.8i		−	1.17080i	−0.810745	−	0.585400i	$-0.800937\pi$
$127$		−	18883.8i		−	1.17080i	0.810745	−	0.585400i	$-0.199063\pi$
$128$	−14484.9	−	7656.52i	−0.884090	−	0.467317i
$129$		0			0
$130$	3255.31	−	4829.82i	0.192622	−	0.285788i
$131$	25700.9	−	14838.4i	1.49763	−	0.864660i	0.497639	−	0.867384i	$-0.334201\pi$
$131$	25700.9	−	14838.4i	1.49763	−	0.864660i	0.999996	+	0.00272458i	$0.000867262\pi$
$132$		0			0
$133$	−1663.92	+	2882.00i	−0.0940654	+	0.162926i
$134$	24949.4	−	12179.4i	1.38947	−	0.678290i
$135$		0			0
$136$	3368.79	+	712.379i	0.182136	+	0.0385153i
$137$	8332.79	−	14432.8i	0.443965	−	0.768971i	−0.554014	−	0.832507i	$-0.686905\pi$
$137$	8332.79	−	14432.8i	0.443965	−	0.768971i	0.997980	+	0.0635366i	$0.0202380\pi$
$138$		0			0
$139$	3545.95	−	2047.25i	0.183528	−	0.105960i	−0.405421	−	0.914130i	$-0.632875\pi$
$139$	3545.95	−	2047.25i	0.183528	−	0.105960i	0.588949	+	0.808170i	$0.299542\pi$
$140$	−6264.28	+	44799.1i	−0.319606	+	2.28567i
$141$		0			0
$142$	−1657.93	+	23828.8i	−0.0822222	+	1.18175i
$143$		−	2296.05i		−	0.112282i
$144$		0			0
$145$	−20880.9			−0.993147
$146$	17314.8	+	1204.71i	0.812293	+	0.0565167i
$147$		0			0
$148$	16107.5	+	2252.32i	0.735368	+	0.102827i
$149$	−2934.59	−	5082.86i	−0.132183	−	0.228947i	0.792335	−	0.610086i	$-0.208865\pi$
$149$	−2934.59	−	5082.86i	−0.132183	−	0.228947i	−0.924518	+	0.381139i	$0.875532\pi$
$150$		0			0
$151$	28725.6	+	16584.7i	1.25984	+	0.727369i	0.973043	−	0.230622i	$-0.0740760\pi$
$151$	28725.6	+	16584.7i	1.25984	+	0.727369i	0.286797	+	0.957991i	$0.407409\pi$
$152$	727.745	−	3441.46i	0.0314987	−	0.148955i
$153$		0			0
$154$	7822.63	+	16024.6i	0.329846	+	0.675687i
$155$	−11233.6	−	6485.72i	−0.467579	−	0.269957i
$156$		0			0
$157$	−11089.2	−	19207.1i	−0.449886	−	0.779226i	0.548492	−	0.836156i	$-0.315202\pi$
$157$	−11089.2	−	19207.1i	−0.449886	−	0.779226i	−0.998378	+	0.0569302i	$0.981869\pi$
$158$	−12616.8	−	8503.74i	−0.505400	−	0.340640i
$159$		0			0
$160$	−8384.79	−	47072.8i	−0.327531	−	1.83878i
$161$	17049.7			0.657758
$162$		0			0
$163$		−	31303.8i		−	1.17821i	−0.808057	−	0.589104i	$-0.799481\pi$
$163$		−	31303.8i		−	1.17821i	0.808057	−	0.589104i	$-0.200519\pi$
$164$	11361.5	+	28064.5i	0.422425	+	1.04344i
$165$		0			0
$166$	−10458.5	−	7049.04i	−0.379536	−	0.255808i
$167$	−22551.7	+	13020.2i	−0.808622	+	0.466858i	−0.846477	−	0.532425i	$-0.821281\pi$
$167$	−22551.7	+	13020.2i	−0.808622	+	0.466858i	0.0378548	+	0.999283i	$0.487948\pi$
$168$		0			0
$169$	13794.3	−	23892.4i	0.482975	−	0.836538i
$170$	4408.17	+	9030.10i	0.152532	+	0.312460i
$171$		0			0
$172$	−9705.23	−	7571.67i	−0.328057	−	0.255938i
$173$	7830.38	−	13562.6i	0.261632	−	0.453160i	−0.705044	−	0.709164i	$-0.749073\pi$
$173$	7830.38	−	13562.6i	0.261632	−	0.453160i	0.966676	+	0.256004i	$0.0824060\pi$
$174$		0			0
$175$	−81551.5	+	47083.8i	−2.66290	+	1.53743i
$176$	−13112.2	−	13540.3i	−0.423302	−	0.437122i
$177$		0			0
$178$	−28461.0	−	1980.22i	−0.898276	−	0.0624991i
$179$		−	36836.7i		−	1.14967i	−0.818268	−	0.574837i	$-0.805065\pi$
$179$		−	36836.7i		−	1.14967i	0.818268	−	0.574837i	$-0.194935\pi$
$180$		0			0
$181$	56961.0			1.73868			0.869342	−	0.494211i	$-0.164543\pi$
$181$	56961.0			1.73868			0.869342	+	0.494211i	$0.164543\pi$
$182$	524.227	−	7534.52i	0.0158262	−	0.227464i
$183$		0			0
$184$	−17133.8	+	5586.93i	−0.506080	+	0.165020i
$185$	23732.1	+	41105.2i	0.693414	+	1.20103i
$186$		0			0
$187$	3430.54	+	1980.62i	0.0981024	+	0.0566394i
$188$	−34592.9	−	26988.1i	−0.978749	−	0.763584i
$189$		0			0
$190$	9224.88	−	4503.26i	0.255537	−	0.124744i
$191$	33837.1	+	19535.9i	0.927527	+	0.535508i	0.886029	−	0.463630i	$-0.153453\pi$
$191$	33837.1	+	19535.9i	0.927527	+	0.535508i	0.0414986	+	0.999139i	$0.486787\pi$
$192$		0			0
$193$	−2025.97	−	3509.08i	−0.0543898	−	0.0942059i	0.837549	−	0.546363i	$-0.183988\pi$
$193$	−2025.97	−	3509.08i	−0.0543898	−	0.0942059i	−0.891938	+	0.452157i	$0.850655\pi$
$194$	−4383.62	+	6503.87i	−0.116474	+	0.172810i
$195$		0			0
$196$	7595.67	+	18762.3i	0.197721	+	0.488398i
$197$	44869.6			1.15617			0.578083	−	0.815978i	$-0.303801\pi$
$197$	44869.6			1.15617			0.578083	+	0.815978i	$0.303801\pi$
$198$		0			0
$199$			56256.7i			1.42059i	0.703905	+	0.710294i	$0.251438\pi$
$199$			56256.7i			1.42059i	−0.703905	+	0.710294i	$0.748562\pi$
$200$	66525.1	−	74039.1i	1.66313	−	1.85098i
$201$		0			0
$202$	17214.1	−	25540.1i	0.421872	−	0.625921i
$203$	−23449.3	+	13538.4i	−0.569032	+	0.328531i
$204$		0			0
$205$	−44179.1	+	76520.4i	−1.05126	+	1.82083i
$206$	−13262.2	+	6474.13i	−0.312523	+	0.152562i
$207$		0			0
$208$	1942.13	+	7743.46i	0.0448902	+	0.178982i
$209$	2023.35	−	3504.54i	0.0463210	−	0.0802303i
$210$		0			0
$211$	63309.8	−	36552.0i	1.42202	−	0.821005i	0.425551	−	0.904935i	$-0.360080\pi$
$211$	63309.8	−	36552.0i	1.42202	−	0.821005i	0.996472	+	0.0839298i	$0.0267471\pi$
$212$	73646.6	+	10298.0i	1.63863	+	0.229130i
$213$		0			0
$214$	3815.13	−	54833.4i	0.0833071	−	1.19734i
$215$		−	35922.8i		−	0.777129i
$216$		0			0
$217$	−16820.4			−0.357205
$218$	−74659.2	−	5194.54i	−1.57098	−	0.109303i
$219$		0			0
$220$	7617.42	−	54476.2i	0.157385	−	1.12554i
$221$	−838.891	−	1453.00i	−0.0171760	−	0.0297496i
$222$		0			0
$223$	−65737.1	−	37953.3i	−1.32191	−	0.763203i	−0.337873	−	0.941192i	$-0.609708\pi$
$223$	−65737.1	−	37953.3i	−1.32191	−	0.763203i	−0.984032	+	0.177989i	$0.943041\pi$
$224$	−39936.4	−	47426.3i	−0.795927	−	0.945200i
$225$		0			0
$226$	17549.1	+	35949.3i	0.343589	+	0.703839i
$227$	35712.5	+	20618.6i	0.693057	+	0.400136i	0.804756	−	0.593606i	$-0.202296\pi$
$227$	35712.5	+	20618.6i	0.693057	+	0.400136i	−0.111700	+	0.993742i	$0.535629\pi$
$228$		0			0
$229$	−13792.1	−	23888.7i	−0.263003	−	0.455534i	0.704036	−	0.710165i	$-0.251379\pi$
$229$	−13792.1	−	23888.7i	−0.263003	−	0.455534i	−0.967038	+	0.254630i	$0.918046\pi$
$230$	−43611.9	−	29394.5i	−0.824422	−	0.555662i
$231$		0			0
$232$	19128.6	−	21289.2i	0.355391	−	0.395533i
$233$	−49430.2			−0.910502			−0.455251	−	0.890363i	$-0.650450\pi$
$233$	−49430.2			−0.910502			−0.455251	+	0.890363i	$0.650450\pi$
$234$		0			0
$235$		−	128042.i		−	2.31855i
$236$	4500.34	−	1821.91i	0.0808019	−	0.0327116i
$237$		0			0
$238$	10805.2	+	7282.69i	0.190756	+	0.128570i
$239$	−97042.8	+	56027.7i	−1.69890	+	0.980859i	−0.752091	+	0.659060i	$0.770955\pi$
$239$	−97042.8	+	56027.7i	−1.69890	+	0.980859i	−0.946808	+	0.321800i	$0.895712\pi$
$240$		0			0
$241$	−20548.3	+	35590.7i	−0.353787	+	0.612776i	−0.986910	−	0.161275i	$-0.948439\pi$
$241$	−20548.3	+	35590.7i	−0.353787	+	0.612776i	0.633123	+	0.774051i	$0.281773\pi$
$242$	16178.7	+	33142.0i	0.276257	+	0.565910i
$243$		0			0
$244$	−9412.18	+	12064.4i	−0.158092	+	0.202640i
$245$	−29535.6	+	51157.1i	−0.492054	+	0.852263i
$246$		0			0
$247$	−1484.34	+	856.986i	−0.0243299	+	0.0140469i
$248$	16903.4	−	5511.79i	0.274834	−	0.0896167i
$249$		0			0
$250$	173326.	+	12059.4i	2.77321	+	0.192951i
$251$			50848.1i			0.807099i	0.914958	+	0.403550i	$0.132224\pi$
$251$			50848.1i			0.807099i	−0.914958	+	0.403550i	$0.867776\pi$
$252$		0			0
$253$	−20732.7			−0.323902
$254$	−5242.83	+	75353.2i	−0.0812640	+	1.16798i
$255$		0			0
$256$	55674.3	+	34573.7i	0.849522	+	0.527553i
$257$	6405.02	+	11093.8i	0.0969738	+	0.167964i	0.910431	−	0.413662i	$-0.135750\pi$
$257$	6405.02	+	11093.8i	0.0969738	+	0.167964i	−0.813457	+	0.581625i	$0.802417\pi$
$258$		0			0
$259$	53302.2	+	30774.1i	0.794595	+	0.458760i
$260$	−14330.8	+	18368.9i	−0.211994	+	0.271730i
$261$		0			0
$262$	−106675.	+	52075.1i	−1.55404	+	0.758625i
$263$	−27445.5	−	15845.6i	−0.396789	−	0.229086i	0.288309	−	0.957537i	$-0.406907\pi$
$263$	−27445.5	−	15845.6i	−0.396789	−	0.229086i	−0.685097	+	0.728452i	$0.740240\pi$
$264$		0			0
$265$	108508.	+	187941.i	1.54514	+	2.67627i
$266$	7439.79	−	11038.2i	0.105147	−	0.156004i
$267$		0			0
$268$	−102938.	+	41673.2i	−1.43320	+	0.580213i
$269$	54892.9			0.758598			0.379299	−	0.925274i	$-0.376165\pi$
$269$	54892.9			0.758598			0.379299	+	0.925274i	$0.376165\pi$
$270$		0			0
$271$			106332.i			1.44785i	0.689877	+	0.723927i	$0.257665\pi$
$271$			106332.i			1.44785i	−0.689877	+	0.723927i	$0.742335\pi$
$272$	−13244.9	−	3777.94i	−0.179024	−	0.0510643i
$273$		0			0
$274$	−37257.8	+	55278.5i	−0.496268	+	0.736301i
$275$	99167.4	−	57254.3i	1.31130	−	0.757082i
$276$		0			0
$277$	25166.6	−	43589.8i	0.327993	−	0.568100i	−0.654121	−	0.756390i	$-0.726961\pi$
$277$	25166.6	−	43589.8i	0.327993	−	0.568100i	0.982113	+	0.188290i	$0.0602945\pi$
$278$	−14718.0	+	7184.78i	−0.190440	+	0.0929660i
$279$		0			0
$280$	37434.5	−	177025.i	0.477481	−	2.25797i
$281$	−3048.20	+	5279.64i	−0.0386039	+	0.0668640i	−0.884682	−	0.466195i	$-0.845624\pi$
$281$	−3048.20	+	5279.64i	−0.0386039	+	0.0668640i	0.846078	+	0.533059i	$0.178958\pi$
$282$		0			0
$283$	−44494.8	+	25689.1i	−0.555567	+	0.320757i	−0.751364	−	0.659888i	$-0.770604\pi$
$283$	−44494.8	+	25689.1i	−0.555567	+	0.320757i	0.195797	+	0.980644i	$0.437271\pi$
$284$	13231.4	−	94625.0i	0.164048	−	1.17319i
$285$		0			0
$286$	−637.465	+	9162.05i	−0.00779335	+	0.112011i
$287$			114576.i			1.39101i
$288$		0			0
$289$	−80626.4			−0.965343
$290$	83322.2	+	5797.29i	0.990752	+	0.0689332i
$291$		0			0
$292$	−68757.8	−	9614.43i	−0.806411	−	0.112761i
$293$	45640.7	+	79051.9i	0.531639	+	0.920825i	0.999318	+	0.0369270i	$0.0117569\pi$
$293$	45640.7	+	79051.9i	0.531639	+	0.920825i	−0.467679	+	0.883898i	$0.654910\pi$
$294$		0			0
$295$	12270.6	+	7084.43i	0.141001	+	0.0814068i
$296$	−63649.3	−	13459.6i	−0.726457	−	0.153620i
$297$		0			0
$298$	10298.9	+	21097.1i	0.115973	+	0.237570i
$299$	7604.82	+	4390.65i	0.0850642	+	0.0491118i
$300$		0			0
$301$	−23291.0	−	40341.3i	−0.257073	−	0.445263i
$302$	−110021.	−	74154.3i	−1.20632	−	0.813059i
$303$		0			0
$304$	−3859.43	+	13530.6i	−0.0417615	+	0.146409i
$305$	−44654.9			−0.480031
$306$		0			0
$307$			108180.i			1.14781i	0.818923	+	0.573904i	$0.194572\pi$
$307$			108180.i			1.14781i	−0.818923	+	0.573904i	$0.805428\pi$
$308$	−26766.0	−	66115.6i	−0.282152	−	0.696952i
$309$		0			0
$310$	43025.4	+	28999.2i	0.447714	+	0.301760i
$311$	86673.2	−	50040.8i	0.896116	−	0.517373i	0.0201778	−	0.999796i	$-0.493577\pi$
$311$	86673.2	−	50040.8i	0.896116	−	0.517373i	0.875938	+	0.482424i	$0.160243\pi$
$312$		0			0
$313$	75895.3	−	131455.i	0.774687	−	1.34180i	−0.160283	−	0.987071i	$-0.551241\pi$
$313$	75895.3	−	131455.i	0.774687	−	1.34180i	0.934970	−	0.354726i	$-0.115426\pi$
$314$	38917.4	+	79722.0i	0.394716	+	0.808572i
$315$		0			0
$316$	47984.5	+	37435.8i	0.480537	+	0.374898i
$317$	56202.0	−	97344.7i	0.559285	−	0.968710i	−0.438271	−	0.898843i	$-0.644409\pi$
$317$	56202.0	−	97344.7i	0.559285	−	0.968710i	0.997556	−	0.0698672i	$-0.0222575\pi$
$318$		0			0
$319$	28514.5	−	16462.9i	0.280211	−	0.161780i
$320$	20389.2	+	190165.i	0.199113	+	1.85708i
$321$		0			0
$322$	−68034.5	−	4733.62i	−0.656172	−	0.0456543i
$323$		−	2957.02i		−	0.0283433i
$324$		0			0
$325$	−48500.0			−0.459172
$326$	−8691.05	+	124913.i	−0.0817781	+	1.17537i
$327$		0			0
$328$	−37544.9	−	115142.i	−0.348982	−	1.07025i
$329$	−83017.6	−	143791.i	−0.766970	−	1.32843i
$330$		0			0
$331$	−99528.9	−	57463.0i	−0.908433	−	0.524484i	−0.0285065	−	0.999594i	$-0.509075\pi$
$331$	−99528.9	−	57463.0i	−0.908433	−	0.524484i	−0.879927	+	0.475109i	$0.842408\pi$
$332$	39776.0	+	31031.8i	0.360865	+	0.281534i
$333$		0			0
$334$	93604.0	−	45694.1i	0.839076	−	0.409607i
$335$	−280670.	−	162045.i	−2.50096	−	1.44393i
$336$		0			0
$337$	−61646.2	−	106774.i	−0.542808	−	0.940171i	−0.998741	−	0.0501573i	$-0.984028\pi$
$337$	−61646.2	−	106774.i	−0.542808	−	0.940171i	0.455933	−	0.890014i	$-0.349306\pi$
$338$	−61677.3	+	91509.1i	−0.539874	+	0.800997i
$339$		0			0
$340$	−15083.1	−	37257.1i	−0.130476	−	0.322294i
$341$	20453.8			0.175900
$342$		0			0
$343$		−	68777.2i		−	0.584597i
$344$	36625.1	+	32908.2i	0.309501	+	0.278091i
$345$		0			0
$346$	−35011.5	+	51945.7i	−0.292454	+	0.433907i
$347$	82843.4	−	47829.7i	0.688017	−	0.397227i	−0.114852	−	0.993383i	$-0.536639\pi$
$347$	82843.4	−	47829.7i	0.688017	−	0.397227i	0.802869	+	0.596156i	$0.203306\pi$
$348$		0			0
$349$	−21543.6	+	37314.5i	−0.176875	+	0.306357i	−0.940809	−	0.338938i	$-0.889932\pi$
$349$	−21543.6	+	37314.5i	−0.176875	+	0.306357i	0.763934	+	0.645295i	$0.223266\pi$
$350$	338491.	−	165239.i	2.76319	−	1.34889i
$351$		0			0
$352$	48563.1	+	57670.9i	0.391941	+	0.465448i
$353$	−56436.9	+	97751.7i	−0.452912	+	0.784467i	−0.998565	−	0.0535440i	$-0.982948\pi$
$353$	−56436.9	+	97751.7i	−0.452912	+	0.784467i	0.545653	+	0.838011i	$0.316282\pi$
$354$		0			0
$355$	241476.	−	139416.i	1.91610	−	1.10626i
$356$	113020.	+	15803.6i	0.891771	+	0.124697i
$357$		0			0
$358$	−10227.2	+	146992.i	−0.0797977	+	1.14690i
$359$		−	223134.i		−	1.73132i	−0.500632	−	0.865660i	$-0.666899\pi$
$359$		−	223134.i		−	1.73132i	0.500632	−	0.865660i	$-0.333101\pi$
$360$		0			0
$361$	127300.			0.976820
$362$	−227295.	−	15814.4i	−1.73449	−	0.120680i
$363$		0			0
$364$	−4183.70	+	29919.8i	−0.0315760	+	0.225817i
$365$	−101305.	−	175465.i	−0.760404	−	1.31706i
$366$		0			0
$367$	−92257.6	−	53265.0i	−0.684968	−	0.395466i	0.116756	−	0.993161i	$-0.462750\pi$
$367$	−92257.6	−	53265.0i	−0.684968	−	0.395466i	−0.801724	+	0.597694i	$0.796084\pi$
$368$	69921.2	−	17536.9i	0.516313	−	0.129496i
$369$		0			0
$370$	−83287.1	−	170613.i	−0.608379	−	1.24626i
$371$	243708.	+	140705.i	1.77061	+	1.02226i
$372$		0			0
$373$	−71440.5	−	123739.i	−0.513484	−	0.889380i	−0.999878	−	0.0156403i	$-0.995021\pi$
$373$	−71440.5	−	123739.i	−0.513484	−	0.889380i	0.486394	−	0.873740i	$-0.338312\pi$
$374$	−13139.2	−	8855.83i	−0.0939345	−	0.0633120i
$375$		0			0
$376$	130545.	+	117296.i	0.923389	+	0.829677i
$377$	−13945.7			−0.0981197
$378$		0			0
$379$			95242.7i			0.663061i	0.943445	+	0.331530i	$0.107565\pi$
$379$			95242.7i			0.663061i	−0.943445	+	0.331530i	$0.892435\pi$
$380$	−38060.8	+	15408.4i	−0.263579	+	0.106707i
$381$		0			0
$382$	−129598.	−	87349.4i	−0.888121	−	0.598595i
$383$	−46899.6	+	27077.5i	−0.319721	+	0.184591i	−0.651268	−	0.758848i	$-0.725763\pi$
$383$	−46899.6	+	27077.5i	−0.319721	+	0.184591i	0.331547	+	0.943439i	$0.392429\pi$
$384$		0			0
$385$	104079.	−	180270.i	0.702169	−	1.21619i
$386$	7110.07	+	14564.9i	0.0477199	+	0.0977538i
$387$		0			0
$388$	19297.9	−	24735.7i	0.128188	−	0.164309i
$389$	6513.23	−	11281.2i	0.0430425	−	0.0745518i	−0.843702	−	0.536813i	$-0.819628\pi$
$389$	6513.23	−	11281.2i	0.0430425	−	0.0745518i	0.886744	+	0.462261i	$0.152962\pi$
$390$		0			0
$391$	−13120.2	+	7574.94i	−0.0858196	+	0.0495480i
$392$	−25100.3	−	76977.0i	−0.163346	−	0.500943i
$393$		0			0
$394$	−179046.	−	12457.4i	−1.15338	−	0.0802481i
$395$			177609.i			1.13834i
$396$		0			0
$397$	54407.2			0.345204			0.172602	−	0.984992i	$-0.444783\pi$
$397$	54407.2			0.345204			0.172602	+	0.984992i	$0.444783\pi$
$398$	15618.9	−	224484.i	0.0986014	−	1.41716i
$399$		0			0
$400$	−286015.	+	276972.i	−1.78759	+	1.73108i
$401$	25211.2	+	43667.1i	0.156785	+	0.271560i	0.933708	−	0.358036i	$-0.116554\pi$
$401$	25211.2	+	43667.1i	0.156785	+	0.271560i	−0.776922	+	0.629596i	$0.783220\pi$
$402$		0			0
$403$	−7502.54	−	4331.59i	−0.0461953	−	0.0266709i
$404$	−75781.0	+	97134.7i	−0.464299	+	0.595130i
$405$		0			0
$406$	97329.6	−	47512.8i	0.590463	−	0.288243i
$407$	−64816.0	−	37421.6i	−0.391285	−	0.225909i
$408$		0			0
$409$	−20416.9	−	35363.2i	−0.122052	−	0.211400i	0.798525	−	0.601962i	$-0.205614\pi$
$409$	−20416.9	−	35363.2i	−0.122052	−	0.211400i	−0.920577	+	0.390562i	$0.872281\pi$
$410$	197535.	−	293078.i	1.17510	−	1.74347i
$411$		0			0
$412$	54718.4	−	22152.0i	0.322358	−	0.130503i
$413$	18373.2			0.107717
$414$		0			0
$415$			147226.i			0.854850i
$416$	−5599.92	−	31438.3i	−0.0323590	−	0.181666i
$417$		0			0
$418$	−9046.86	+	13422.6i	−0.0517780	+	0.0768217i
$419$	−28866.9	+	16666.3i	−0.164427	+	0.0949318i	−0.579955	−	0.814648i	$-0.696930\pi$
$419$	−28866.9	+	16666.3i	−0.164427	+	0.0949318i	0.415529	+	0.909580i	$0.363597\pi$
$420$		0			0
$421$	−4180.31	+	7240.51i	−0.0235855	+	0.0408512i	−0.877577	−	0.479435i	$-0.840842\pi$
$421$	−4180.31	+	7240.51i	−0.0235855	+	0.0408512i	0.853992	+	0.520287i	$0.174175\pi$
$422$	−262777.	+	128278.i	−1.47558	+	0.720324i
$423$		0			0
$424$	−291017.	−	61539.7i	−1.61877	−	0.342313i
$425$	41837.2	−	72464.1i	0.231625	−	0.401186i
$426$		0			0
$427$	−50147.4	+	28952.6i	−0.275038	+	0.158793i
$428$	−30447.4	+	217746.i	−0.166212	+	1.18867i
$429$		0			0
$430$	−9973.45	+	143345.i	−0.0539397	+	0.775255i
$431$			88445.3i			0.476124i	0.971250	+	0.238062i	$0.0765122\pi$
$431$			88445.3i			0.476124i	−0.971250	+	0.238062i	$0.923488\pi$
$432$		0			0
$433$	119092.			0.635195			0.317598	−	0.948226i	$-0.397124\pi$
$433$	119092.			0.635195			0.317598	+	0.948226i	$0.397124\pi$
$434$	67119.5	+	4669.95i	0.356344	+	0.0247932i
$435$		0			0
$436$	296474.	+	41456.1i	1.55960	+	0.218080i
$437$	7738.34	+	13403.2i	0.0405214	+	0.0701852i
$438$		0			0
$439$	103483.	+	59746.2i	0.536960	+	0.310014i	0.743846	−	0.668351i	$-0.233000\pi$
$439$	103483.	+	59746.2i	0.536960	+	0.310014i	−0.206886	+	0.978365i	$0.566333\pi$
$440$	−45520.7	+	215264.i	−0.235128	+	1.11190i
$441$		0			0
$442$	2944.07	+	6030.90i	0.0150696	+	0.0308700i
$443$	176414.	+	101853.i	0.898930	+	0.518998i	0.876853	−	0.480759i	$-0.159639\pi$
$443$	176414.	+	101853.i	0.898930	+	0.518998i	0.0220772	+	0.999756i	$0.492972\pi$
$444$		0			0
$445$	166518.	+	288418.i	0.840894	+	1.45647i
$446$	251777.	+	169698.i	1.26574	+	0.853114i
$447$		0			0
$448$	146193.	+	200336.i	0.728402	+	0.998165i
$449$	−77156.2			−0.382717			−0.191359	−	0.981520i	$-0.561289\pi$
$449$	−77156.2			−0.382717			−0.191359	+	0.981520i	$0.561289\pi$
$450$		0			0
$451$		−	139326.i		−	0.684982i
$452$	−60046.4	−	148322.i	−0.293907	−	0.725989i
$453$		0			0
$454$	−136781.	−	92190.7i	−0.663612	−	0.447276i
$455$	−76353.2	+	44082.6i	−0.368812	+	0.212934i
$456$		0			0
$457$	−140420.	+	243215.i	−0.672353	+	1.16455i	0.304882	+	0.952390i	$0.401383\pi$
$457$	−140420.	+	243215.i	−0.672353	+	1.16455i	−0.977235	+	0.212159i	$0.931951\pi$
$458$	48403.1	+	99153.4i	0.230750	+	0.472690i
$459$		0			0
$460$	165866.	+	129403.i	0.783866	+	0.611544i
$461$	−200811.	+	347814.i	−0.944898	+	1.63661i	−0.188942	+	0.981988i	$0.560506\pi$
$461$	−200811.	+	347814.i	−0.944898	+	1.63661i	−0.755956	+	0.654623i	$0.772827\pi$
$462$		0			0
$463$	51806.1	−	29910.3i	0.241668	−	0.139527i	−0.374275	−	0.927318i	$-0.622108\pi$
$463$	51806.1	−	29910.3i	0.241668	−	0.139527i	0.615943	+	0.787791i	$0.288775\pi$
$464$	−82240.4	+	79640.5i	−0.381988	+	0.369912i
$465$		0			0
$466$	197244.	+	13723.6i	0.908306	+	0.0631969i
$467$		−	208473.i		−	0.955909i	−0.878385	−	0.477955i	$-0.841378\pi$
$467$		−	208473.i		−	0.955909i	0.878385	−	0.477955i	$-0.158622\pi$
$468$		0			0
$469$	−420257.			−1.91060
$470$	−35548.9	+	510931.i	−0.160928	+	2.31295i
$471$		0			0
$472$	−18463.8	+	6020.59i	−0.0828775	+	0.0270243i
$473$	28322.1	+	49055.4i	0.126591	+	0.219263i
$474$		0			0
$475$	−74027.3	−	42739.7i	−0.328099	−	0.189428i
$476$	−41094.5	−	32060.4i	−0.181372	−	0.141500i
$477$		0			0
$478$	402790.	−	196628.i	1.76288	−	0.860575i
$479$	−138667.	−	80059.3i	−0.604368	−	0.348932i	0.166390	−	0.986060i	$-0.446789\pi$
$479$	−138667.	−	80059.3i	−0.604368	−	0.348932i	−0.770758	+	0.637128i	$0.780122\pi$
$480$		0			0
$481$	15849.9	+	27452.8i	0.0685070	+	0.118658i
$482$	91876.1	−	136314.i	0.395466	−	0.586743i
$483$		0			0
$484$	−55357.4	−	136740.i	−0.236312	−	0.583720i
$485$	91556.4			0.389229
$486$		0			0
$487$			371960.i			1.56834i	0.620549	+	0.784168i	$0.286910\pi$
$487$			371960.i			1.56834i	−0.620549	+	0.784168i	$0.713090\pi$
$488$	40907.4	−	45527.9i	0.171776	−	0.191178i
$489$		0			0
$490$	132060.	−	195935.i	0.550022	−	0.816055i
$491$	−57863.4	+	33407.4i	−0.240016	+	0.138574i	−0.615184	−	0.788383i	$-0.710918\pi$
$491$	−57863.4	+	33407.4i	−0.240016	+	0.138574i	0.375168	+	0.926957i	$0.377585\pi$
$492$		0			0
$493$	12029.8	−	20836.3i	0.0494955	−	0.0857288i
$494$	6160.99	−	3007.57i	0.0252462	−	0.0123243i
$495$		0			0
$496$	−68980.8	+	17301.0i	−0.280391	+	0.0703246i
$497$	180785.	−	313129.i	0.731896	−	1.26768i
$498$		0			0
$499$	288151.	−	166364.i	1.15723	−	0.668127i	0.206591	−	0.978427i	$-0.433763\pi$
$499$	288151.	−	166364.i	1.15723	−	0.668127i	0.950638	+	0.310301i	$0.100430\pi$
$500$	−688282.	−	96242.7i	−2.75313	−	0.384971i
$501$		0			0
$502$	14117.2	−	202902.i	0.0560199	−	0.805153i
$503$		−	12673.0i		−	0.0500892i	−0.999686	−	0.0250446i	$-0.992027\pi$
$503$		−	12673.0i		−	0.0500892i	0.999686	−	0.0250446i	$-0.00797278\pi$
$504$		0			0
$505$	−359533.			−1.40980
$506$	82730.6	+	5756.12i	0.323121	+	0.0224817i
$507$		0			0
$508$	41841.5	−	299230.i	0.162136	−	1.15952i
$509$	−19452.7	−	33693.0i	−0.0750834	−	0.130048i	0.826039	−	0.563613i	$-0.190589\pi$
$509$	−19452.7	−	33693.0i	−0.0750834	−	0.130048i	−0.901123	+	0.433564i	$0.857256\pi$
$510$		0			0
$511$	−227530.	−	131365.i	−0.871360	−	0.503080i
$512$	−212561.	−	153419.i	−0.810856	−	0.585245i
$513$		0			0
$514$	−22478.3	−	46046.5i	−0.0850817	−	0.174289i
$515$	149195.	+	86137.5i	0.562521	+	0.324772i
$516$		0			0
$517$	100950.	+	174851.i	0.377682	+	0.654164i
$518$	−204151.	−	137598.i	−0.760837	−	0.512805i
$519$		0			0
$520$	62284.7	−	69319.7i	0.230343	−	0.256360i
$521$	−28001.3			−0.103158			−0.0515790	−	0.998669i	$-0.516425\pi$
$521$	−28001.3			−0.103158			−0.0515790	+	0.998669i	$0.516425\pi$
$522$		0			0
$523$		−	306435.i		−	1.12030i	−0.828391	−	0.560151i	$-0.810743\pi$
$523$		−	306435.i		−	1.12030i	0.828391	−	0.560151i	$-0.189257\pi$
$524$	440130.	−	178181.i	1.60295	−	0.648932i
$525$		0			0
$526$	105118.	+	70849.6i	0.379931	+	0.256074i
$527$	12943.7	−	7473.06i	0.0466056	−	0.0269077i
$528$		0			0
$529$	−100274.	+	173680.i	−0.358326	+	0.620638i
$530$	−380805.	−	780076.i	−1.35566	−	2.77706i
$531$		0			0
$532$	−32752.0	+	41980.9i	−0.115722	+	0.148330i
$533$	−29505.7	+	51105.4i	−0.103861	+	0.179892i
$534$		0			0
$535$	−555671.	+	320817.i	−1.94138	+	1.12086i
$536$	422330.	−	137711.i	1.47002	−	0.479336i
$537$		0			0
$538$	−219042.	−	15240.2i	−0.756768	−	0.0526534i
$539$		−	93145.3i		−	0.320615i
$540$		0			0
$541$	387269.			1.32318			0.661590	−	0.749866i	$-0.269882\pi$
$541$	387269.			1.32318			0.661590	+	0.749866i	$0.269882\pi$
$542$	29521.5	−	424302.i	0.100494	−	1.44436i
$543$		0			0
$544$	51802.8	+	18752.6i	0.175047	+	0.0633669i
$545$	436812.	+	756581.i	1.47062	+	2.54720i
$546$		0			0
$547$	220183.	+	127123.i	0.735883	+	0.424862i	0.820570	−	0.571545i	$-0.193656\pi$
$547$	220183.	+	127123.i	0.735883	+	0.424862i	−0.0846877	+	0.996408i	$0.526989\pi$
$548$	164019.	−	210237.i	0.546177	−	0.700080i
$549$		0			0
$550$	−411609.	+	200933.i	−1.36069	+	0.664240i
$551$	−21285.8	−	12289.3i	−0.0701109	−	0.0404786i
$552$		0			0
$553$	115156.	+	199455.i	0.376560	+	0.652221i
$554$	−112526.	+	166951.i	−0.366633	+	0.543965i
$555$		0			0
$556$	60724.6	−	24583.6i	0.196433	−	0.0795235i
$557$	154243.			0.497159			0.248580	−	0.968611i	$-0.420036\pi$
$557$	154243.			0.497159			0.248580	+	0.968611i	$0.420036\pi$
$558$		0			0
$559$		−	23991.6i		−	0.0767779i
$560$	−198525.	+	696000.i	−0.633053	+	2.21939i
$561$		0			0
$562$	13629.2	−	20221.4i	0.0431518	−	0.0640232i
$563$	−188653.	+	108919.i	−0.595177	+	0.343626i	−0.767142	−	0.641477i	$-0.778322\pi$
$563$	−188653.	+	108919.i	−0.595177	+	0.343626i	0.171965	+	0.985103i	$0.444988\pi$
$564$		0			0
$565$	233489.	−	404415.i	0.731425	−	1.26686i
$566$	184682.	−	90155.2i	0.576490	−	0.281422i
$567$		0			0
$568$	−79069.4	+	373914.i	−0.245082	+	1.15898i
$569$	112165.	−	194275.i	0.346443	−	0.600057i	−0.639172	−	0.769064i	$-0.720723\pi$
$569$	112165.	−	194275.i	0.346443	−	0.600057i	0.985615	+	0.169007i	$0.0540561\pi$
$570$		0			0
$571$	227168.	−	131156.i	0.696748	−	0.402268i	−0.109387	−	0.993999i	$-0.534889\pi$
$571$	227168.	−	131156.i	0.696748	−	0.402268i	0.806135	+	0.591732i	$0.201555\pi$
$572$	5087.42	−	36382.8i	0.0155491	−	0.111200i
$573$		0			0
$574$	31810.5	−	457201.i	0.0965488	−	1.38766i
$575$			437941.i			1.32458i
$576$		0			0
$577$	450994.			1.35462			0.677312	−	0.735696i	$-0.263145\pi$
$577$	450994.			1.35462			0.677312	+	0.735696i	$0.263145\pi$
$578$	321728.	+	22384.8i	0.963015	+	0.0670034i
$579$		0			0
$580$	−330876.	−	46266.4i	−0.983578	−	0.137534i
$581$	95456.3	+	165335.i	0.282782	+	0.489794i
$582$		0			0
$583$	−296351.	−	171099.i	−0.871907	−	0.503396i
$584$	271699.	+	57454.6i	0.796640	+	0.168461i
$585$		0			0
$586$	−160175.	−	328117.i	−0.466443	−	0.955505i
$587$	−307738.	−	177673.i	−0.893111	−	0.515638i	−0.0181523	−	0.999835i	$-0.505778\pi$
$587$	−307738.	−	177673.i	−0.893111	−	0.515638i	−0.874959	+	0.484197i	$0.839112\pi$
$588$		0			0
$589$	−7634.26	−	13222.9i	−0.0220058	−	0.0381151i
$590$	−46997.1	−	31676.1i	−0.135010	−	0.0909972i
$591$		0			0
$592$	250246.	+	71379.7i	0.714043	+	0.203672i
$593$	−89819.5			−0.255424			−0.127712	−	0.991811i	$-0.540763\pi$
$593$	−89819.5			−0.255424			−0.127712	+	0.991811i	$0.540763\pi$
$594$		0			0
$595$		−	152106.i		−	0.429649i
$596$	−35238.8	−	87044.4i	−0.0992038	−	0.245046i
$597$		0			0
$598$	−29126.9	−	19631.6i	−0.0814502	−	0.0548976i
$599$	−357687.	+	206511.i	−0.996896	+	0.575558i	−0.907328	−	0.420422i	$-0.861882\pi$
$599$	−357687.	+	206511.i	−0.996896	+	0.575558i	−0.0895677	+	0.995981i	$0.528549\pi$
$600$		0			0
$601$	−129317.	+	223984.i	−0.358020	+	0.620110i	−0.987630	−	0.156802i	$-0.949882\pi$
$601$	−129317.	+	223984.i	−0.358020	+	0.620110i	0.629610	+	0.776912i	$0.283215\pi$
$602$	81739.3	+	167442.i	0.225548	+	0.462032i
$603$		0			0
$604$	418434.	+	326447.i	1.14697	+	0.894828i
$605$	215256.	−	372834.i	0.588090	−	1.01860i
$606$		0			0
$607$	−267430.	+	154401.i	−0.725825	+	0.419055i	−0.816893	−	0.576789i	$-0.804305\pi$
$607$	−267430.	+	154401.i	−0.725825	+	0.419055i	0.0910678	+	0.995845i	$0.470972\pi$
$608$	19157.1	−	52920.3i	0.0518229	−	0.143158i
$609$		0			0
$610$	178189.	+	12397.8i	0.478873	+	0.0333184i
$611$		−	85514.7i		−	0.229065i
$612$		0			0
$613$	−464349.			−1.23573			−0.617865	−	0.786284i	$-0.712002\pi$
$613$	−464349.			−1.23573			−0.617865	+	0.786284i	$0.712002\pi$
$614$	30034.6	−	431675.i	0.0796681	−	1.14504i
$615$		0			0
$616$	88449.9	+	271256.i	0.233097	+	0.714855i
$617$	−253688.	−	439401.i	−0.666392	−	1.15423i	−0.978906	−	0.204312i	$-0.934504\pi$
$617$	−253688.	−	439401.i	−0.666392	−	1.15423i	0.312513	−	0.949913i	$-0.398829\pi$
$618$		0			0
$619$	−244884.	−	141384.i	−0.639115	−	0.368993i	0.145159	−	0.989408i	$-0.453631\pi$
$619$	−244884.	−	141384.i	−0.639115	−	0.368993i	−0.784273	+	0.620415i	$0.786964\pi$
$620$	−163635.	−	127662.i	−0.425690	−	0.332108i
$621$		0			0
$622$	−359750.	+	175617.i	−0.929865	+	0.453927i
$623$	373999.	+	215929.i	0.963595	+	0.556332i
$624$		0			0
$625$	−528069.	−	914643.i	−1.35186	−	2.34149i
$626$	−339346.	+	503479.i	−0.865951	+	1.28479i
$627$		0			0
$628$	−133161.	−	328924.i	−0.337642	−	0.834019i
$629$	−54689.8			−0.138231
$630$		0			0
$631$		−	403620.i		−	1.01371i	−0.862031	−	0.506855i	$-0.830808\pi$
$631$		−	403620.i		−	1.01371i	0.862031	−	0.506855i	$-0.169192\pi$
$632$	−181082.	−	162704.i	−0.453357	−	0.407347i
$633$		0			0
$634$	−251292.	+	372836.i	−0.625173	+	0.927554i
$635$	763614.	−	440873.i	1.89377	−	1.09337i
$636$		0			0
$637$	−19725.8	+	34166.1i	−0.0486134	+	0.0842008i
$638$	−118354.	+	57776.0i	−0.290764	+	0.141940i
$639$		0			0
$640$	−28563.4	−	764487.i	−0.0697350	−	1.86642i
$641$	−181028.	+	313549.i	−0.440584	+	0.763114i	−0.997733	−	0.0672990i	$-0.978562\pi$
$641$	−181028.	+	313549.i	−0.440584	+	0.763114i	0.557149	+	0.830413i	$0.311895\pi$
$642$		0			0
$643$	−346651.	+	200139.i	−0.838437	+	0.484072i	−0.856733	−	0.515761i	$-0.827509\pi$
$643$	−346651.	+	200139.i	−0.838437	+	0.484072i	0.0182957	+	0.999833i	$0.494176\pi$
$644$	270167.	+	37777.6i	0.651420	+	0.0910883i
$645$		0			0
$646$	−820.975	+	11799.6i	−0.00196727	+	0.0282749i
$647$		−	98990.1i		−	0.236474i	−0.992985	−	0.118237i	$-0.962276\pi$
$647$		−	98990.1i		−	0.236474i	0.992985	−	0.118237i	$-0.0377242\pi$
$648$		0			0
$649$	−22341.9			−0.0530434
$650$	193532.	+	13465.3i	0.458064	+	0.0318706i
$651$		0			0
$652$	69360.7	−	496035.i	0.163162	−	1.16686i
$653$	−269165.	−	466208.i	−0.631237	−	1.09333i	−0.987299	−	0.158872i	$-0.949214\pi$
$653$	−269165.	−	466208.i	−0.631237	−	1.09333i	0.356062	−	0.934462i	$-0.384119\pi$
$654$		0			0
$655$	1.20006e6	+	692852.i	2.79717	+	1.61495i
$656$	117850.	+	469879.i	0.273856	+	1.09189i
$657$		0			0
$658$	291348.	+	596824.i	0.672915	+	1.37846i
$659$	−126219.	−	72872.6i	−0.290639	−	0.167801i	0.347591	−	0.937646i	$-0.387000\pi$
$659$	−126219.	−	72872.6i	−0.290639	−	0.167801i	−0.638230	+	0.769846i	$0.720333\pi$
$660$		0			0
$661$	126176.	+	218543.i	0.288784	+	0.500189i	0.973520	−	0.228603i	$-0.0734157\pi$
$661$	126176.	+	218543.i	0.288784	+	0.500189i	−0.684736	+	0.728792i	$0.740082\pi$
$662$	381201.	+	256930.i	0.869838	+	0.586273i
$663$		0			0
$664$	−150105.	−	134871.i	−0.340454	−	0.305903i
$665$	−155388.			−0.351377
$666$		0			0
$667$			125925.i			0.283049i
$668$	−386199.	+	156348.i	−0.865483	+	0.350380i
$669$		0			0
$670$	1.07498e6	+	724541.i	2.39471	+	1.61404i
$671$	60979.7	−	35206.7i	0.135438	−	0.0781951i
$672$		0			0
$673$	−327332.	+	566956.i	−0.722701	+	1.25175i	0.237213	+	0.971458i	$0.423766\pi$
$673$	−327332.	+	566956.i	−0.722701	+	1.25175i	−0.959913	+	0.280297i	$0.909567\pi$
$674$	216346.	+	443182.i	0.476243	+	0.975580i
$675$		0			0
$676$	271520.	−	348030.i	0.594168	−	0.761594i
$677$	−106756.	+	184907.i	−0.232924	+	0.403437i	−0.958667	−	0.284529i	$-0.908163\pi$
$677$	−106756.	+	184907.i	−0.232924	+	0.403437i	0.725743	+	0.687966i	$0.241496\pi$
$678$		0			0
$679$	102818.	−	59361.8i	0.223012	−	0.128756i
$680$	49842.9	+	152857.i	0.107792	+	0.330572i
$681$		0			0
$682$	−81617.9	−	5678.71i	−0.175476	−	0.0122090i
$683$		−	885039.i		−	1.89724i	−0.316425	−	0.948618i	$-0.602483\pi$
$683$		−	885039.i		−	1.89724i	0.316425	−	0.948618i	$-0.397517\pi$
$684$		0			0
$685$	778168.			1.65841
$686$	−19095.0	+	274445.i	−0.0405762	+	0.583187i
$687$		0			0
$688$	−137011.	−	141484.i	−0.289453	−	0.298902i
$689$	72468.6	+	125519.i	0.152655	+	0.264406i
$690$		0			0
$691$	382656.	+	220927.i	0.801406	+	0.462692i	0.843963	−	0.536402i	$-0.180217\pi$
$691$	382656.	+	220927.i	0.801406	+	0.462692i	−0.0425567	+	0.999094i	$0.513550\pi$
$692$	154130.	−	197561.i	0.321866	−	0.412562i
$693$		0			0
$694$	−343854.	+	167857.i	−0.713929	+	0.348514i
$695$	165571.	+	95592.6i	0.342780	+	0.197904i
$696$		0			0
$697$	−50904.6	−	88169.3i	−0.104783	−	0.181490i
$698$	96326.3	−	142917.i	0.197712	−	0.293341i
$699$		0			0
$700$	−1.39658e6	+	565386.i	−2.85015	+	1.15385i
$701$	−340679.			−0.693281			−0.346640	−	0.937998i	$-0.612678\pi$
$701$	−340679.			−0.693281			−0.346640	+	0.937998i	$0.612678\pi$
$702$		0			0
$703$			55869.5i			0.113048i
$704$	−177772.	−	243610.i	−0.358690	−	0.491530i
$705$		0			0
$706$	252343.	−	374395.i	0.506269	−	0.751139i
$707$	−403755.	+	233108.i	−0.807755	+	0.466357i
$708$		0			0
$709$	292720.	−	507006.i	0.582318	−	1.00860i	−0.412886	−	0.910783i	$-0.635479\pi$
$709$	292720.	−	507006.i	0.582318	−	1.00860i	0.995204	−	0.0978214i	$-0.0311874\pi$
$710$	−1.00228e6	+	489278.i	−1.98826	+	0.970597i
$711$		0			0
$712$	−446600.	−	94440.0i	−0.880966	−	0.186293i
$713$	−39113.0	+	67745.8i	−0.0769383	+	0.133261i
$714$		0			0
$715$	92846.3	−	53604.8i	0.181615	−	0.104856i
$716$	81620.2	−	583709.i	0.159210	−	1.13860i
$717$		0			0
$718$	−61950.0	+	890385.i	−0.120169	+	1.72715i
$719$		−	306988.i		−	0.593832i	−0.954904	−	0.296916i	$-0.904042\pi$
$719$		−	306988.i		−	0.593832i	0.954904	−	0.296916i	$-0.0959581\pi$
$720$		0			0
$721$	223394.			0.429735
$722$	−507973.	−	35343.1i	−0.974464	−	0.0678000i
$723$		0			0
$724$	902595.	+	126210.i	1.72193	+	0.240778i
$725$	−347749.	−	602319.i	−0.661592	−	1.14591i
$726$		0			0
$727$	−488481.	−	282025.i	−0.924227	−	0.533603i	−0.0392459	−	0.999230i	$-0.512496\pi$
$727$	−488481.	−	282025.i	−0.924227	−	0.533603i	−0.884981	+	0.465627i	$0.845829\pi$
$728$	25001.2	−	118229.i	0.0471736	−	0.223081i
$729$		0			0
$730$	355526.	+	728293.i	0.667154	+	1.36666i
$731$	35846.0	+	20695.7i	0.0670821	+	0.0387298i
$732$		0			0
$733$	−290960.	−	503957.i	−0.541533	−	0.937963i	−0.998816	−	0.0486418i	$-0.984511\pi$
$733$	−290960.	−	503957.i	−0.541533	−	0.937963i	0.457283	−	0.889321i	$-0.348823\pi$
$734$	353352.	+	238160.i	0.655867	+	0.442055i
$735$		0			0
$736$	−283879.	+	50565.6i	−0.524056	+	0.0933469i
$737$	511037.			0.940843
$738$		0			0
$739$		−	193774.i		−	0.354818i	−0.984137	−	0.177409i	$-0.943228\pi$
$739$		−	193774.i		−	0.354818i	0.984137	−	0.177409i	$-0.0567715\pi$
$740$	284977.	+	703930.i	0.520411	+	1.28548i
$741$		0			0
$742$	−933417.	−	629124.i	−1.69538	−	1.14269i
$743$	−76480.8	+	44156.2i	−0.138540	+	0.0799861i	−0.567668	−	0.823258i	$-0.692154\pi$
$743$	−76480.8	+	44156.2i	−0.138540	+	0.0799861i	0.429128	+	0.903244i	$0.358821\pi$
$744$		0			0
$745$	137025.	−	237334.i	0.246881	−	0.427610i
$746$	250719.	+	513595.i	0.450514	+	0.922875i
$747$		0			0
$748$	49971.3	+	38985.8i	0.0893135	+	0.0696792i
$749$	−416012.	+	720554.i	−0.741553	+	1.28441i
$750$		0			0
$751$	474180.	−	273768.i	0.840743	−	0.485403i	−0.0167738	−	0.999859i	$-0.505340\pi$
$751$	474180.	−	273768.i	0.840743	−	0.485403i	0.857517	+	0.514456i	$0.172006\pi$
$752$	−488355.	−	504298.i	−0.863575	−	0.891767i
$753$		0			0
$754$	55648.1	+	3871.81i	0.0978831	+	0.00681038i
$755$			1.54879e6i			2.71705i
$756$		0			0
$757$	−45164.0			−0.0788135			−0.0394068	−	0.999223i	$-0.512547\pi$
$757$	−45164.0			−0.0788135			−0.0394068	+	0.999223i	$0.512547\pi$
$758$	26442.8	−	380052.i	0.0460223	−	0.661462i
$759$		0			0
$760$	156154.	−	50918.0i	0.270350	−	0.0881545i
$761$	−100185.	−	173525.i	−0.172995	−	0.299636i	0.766471	−	0.642279i	$-0.222011\pi$
$761$	−100185.	−	173525.i	−0.172995	−	0.299636i	−0.939465	+	0.342644i	$0.888678\pi$
$762$		0			0
$763$	981079.	+	566426.i	1.68521	+	0.972959i
$764$	492891.	+	384536.i	0.844432	+	0.658795i
$765$		0			0
$766$	194663.	−	95027.7i	0.331762	−	0.161954i
$767$	8195.11	+	4731.45i	0.0139304	+	0.00804273i
$768$		0			0
$769$	−212834.	−	368639.i	−0.359905	−	0.623374i	0.628039	−	0.778181i	$-0.283858\pi$
$769$	−212834.	−	368639.i	−0.359905	−	0.623374i	−0.987945	+	0.154807i	$0.950524\pi$
$770$	−465362.	+	690446.i	−0.784891	+	1.16452i
$771$		0			0
$772$	−24328.0	−	60093.2i	−0.0408198	−	0.100830i
$773$	−199528.			−0.333922			−0.166961	−	0.985964i	$-0.553395\pi$
$773$	−199528.			−0.333922			−0.166961	+	0.985964i	$0.553395\pi$
$774$		0			0
$775$		−	432051.i		−	0.719335i
$776$	−83872.9	+	93346.4i	−0.139283	+	0.155015i
$777$		0			0
$778$	−29122.2	+	43207.9i	−0.0481132	+	0.0713844i
$779$	−90071.2	+	52002.6i	−0.148426	+	0.0856940i
$780$		0			0
$781$	−219836.	+	380768.i	−0.360411	+	0.624249i
$782$	54457.2	−	26584.1i	0.0890517	−	0.0434718i
$783$		0			0
$784$	78787.6	+	314134.i	0.128182	+	0.511073i
$785$	517791.	−	896841.i	0.840263	−	1.45538i
$786$		0			0
$787$	−899924.	+	519571.i	−1.45297	+	0.838872i	−0.998649	−	0.0519669i	$-0.983451\pi$
$787$	−899924.	+	519571.i	−1.45297	+	0.838872i	−0.454320	+	0.890839i	$0.650118\pi$
$788$	710997.	+	99418.9i	1.14503	+	0.160109i
$789$		0			0
$790$	49310.7	−	708724.i	0.0790109	−	1.13559i
$791$		−	605543.i		−	0.967815i
$792$		0			0
$793$	−29823.5			−0.0474255
$794$	−217104.	−	15105.4i	−0.344371	−	0.0239602i
$795$		0			0
$796$	−124650.	+	891434.i	−0.196727	+	1.40690i
$797$	12577.0	+	21783.9i	0.0197997	+	0.0342941i	0.875755	−	0.482755i	$-0.160364\pi$
$797$	12577.0	+	21783.9i	0.0197997	+	0.0342941i	−0.855956	+	0.517049i	$0.827030\pi$
$798$		0			0
$799$	127768.	+	73766.9i	0.200138	+	0.115549i
$800$	1.21820e6	−	1.02581e6i	1.90343	−	1.60283i
$801$		0			0
$802$	−88478.1	−	181247.i	−0.137558	−	0.281787i
$803$	276679.	+	159741.i	0.429087	+	0.247734i
$804$		0			0
$805$	398053.	+	689448.i	0.614255	+	1.06392i
$806$	28735.2	+	19367.6i	0.0442327	+	0.0298129i
$807$		0			0
$808$	329361.	−	366562.i	0.504486	−	0.561468i
$809$	−975055.			−1.48981			−0.744907	−	0.667168i	$-0.767506\pi$
$809$	−975055.			−1.48981			−0.744907	+	0.667168i	$0.767506\pi$
$810$		0			0
$811$		−	240015.i		−	0.364919i	−0.983213	−	0.182460i	$-0.941594\pi$
$811$		−	240015.i		−	0.364919i	0.983213	−	0.182460i	$-0.0584059\pi$
$812$	−401571.	+	162571.i	−0.609046	+	0.246564i
$813$		0			0
$814$	248249.	+	167320.i	0.374662	+	0.252523i
$815$	1.26584e6	−	730836.i	1.90575	−	1.10028i
$816$		0			0
$817$	21142.1	−	36619.3i	0.0316741	−	0.0548612i
$818$	71652.7	+	146780.i	0.107084	+	0.219361i
$819$		0			0
$820$	−869603.	+	1.11464e6i	−1.29328	+	1.65770i
$821$	−406806.	+	704608.i	−0.603533	+	1.04535i	0.388749	+	0.921344i	$0.372907\pi$
$821$	−406806.	+	704608.i	−0.603533	+	1.04535i	−0.992282	+	0.124005i	$0.960426\pi$
$822$		0			0
$823$	−24117.0	+	13924.0i	−0.0356061	+	0.0205572i	−0.517697	−	0.855564i	$-0.673211\pi$
$823$	−24117.0	+	13924.0i	−0.0356061	+	0.0205572i	0.482091	+	0.876121i	$0.339877\pi$
$824$	−224496.	+	73202.6i	−0.330639	+	0.107813i
$825$		0			0
$826$	−73315.4	−	5101.04i	−0.107457	−	0.00747651i
$827$			1.05969e6i			1.54941i	0.632323	+	0.774705i	$0.282102\pi$
$827$			1.05969e6i			1.54941i	−0.632323	+	0.774705i	$0.717898\pi$
$828$		0			0
$829$	−904280.			−1.31581			−0.657906	−	0.753100i	$-0.728558\pi$
$829$	−904280.			−1.31581			−0.657906	+	0.753100i	$0.728558\pi$
$830$	40875.3	−	587486.i	0.0593342	−	0.852788i
$831$		0			0
$832$	13617.2	+	127005.i	0.0196717	+	0.183474i
$833$	−34031.8	−	58944.9i	−0.0490451	−	0.0849486i
$834$		0			0
$835$	−1.05301e6	−	607954.i	−1.51028	−	0.871963i
$836$	39826.7	−	51049.2i	0.0569852	−	0.0730426i
$837$		0			0
$838$	119816.	−	58490.0i	0.170619	−	0.0832902i
$839$	−308829.	−	178303.i	−0.438727	−	0.253299i	0.264330	−	0.964432i	$-0.414849\pi$
$839$	−308829.	−	178303.i	−0.438727	−	0.253299i	−0.703058	+	0.711133i	$0.748182\pi$
$840$		0			0
$841$	253649.	+	439333.i	0.358625	+	0.621157i
$842$	18691.1	−	27731.6i	0.0263640	−	0.0391156i
$843$		0			0
$844$	1.08419e6	−	438919.i	1.52202	−	0.616168i
$845$	1.28819e6			1.80413
$846$		0			0
$847$		−	558256.i		−	0.778156i
$848$	1.14417e6	+	326362.i	1.59111	+	0.453845i
$849$		0			0
$850$	−187064.	+	277542.i	−0.258912	+	0.384141i
$851$	247890.	−	143120.i	0.342295	−	0.197624i
$852$		0			0
$853$	93966.4	−	162755.i	0.129144	−	0.223684i	−0.794201	−	0.607655i	$-0.792110\pi$
$853$	93966.4	−	162755.i	0.129144	−	0.223684i	0.923345	+	0.383971i	$0.125444\pi$
$854$	208144.	−	101608.i	0.285396	−	0.139320i
$855$		0			0
$856$	181950.	−	860429.i	0.248316	−	1.17427i
$857$	424830.	−	735827.i	0.578434	−	1.00188i	−0.417226	−	0.908803i	$-0.636998\pi$
$857$	424830.	−	735827.i	0.578434	−	1.00188i	0.995659	−	0.0930735i	$-0.0296692\pi$
$858$		0			0
$859$	−1.04585e6	+	603819.i	−1.41736	+	0.818315i	−0.996067	−	0.0886072i	$-0.971758\pi$
$859$	−1.04585e6	+	603819.i	−1.41736	+	0.818315i	−0.421297	+	0.906923i	$0.638425\pi$
$860$	79595.2	−	569227.i	0.107619	−	0.769641i
$861$		0			0
$862$	24555.6	−	352928.i	0.0330473	−	0.474976i
$863$		−	77194.2i		−	0.103648i	−0.998656	−	0.0518242i	$-0.983496\pi$
$863$		−	77194.2i		−	0.103648i	0.998656	−	0.0518242i	$-0.0165036\pi$
$864$		0			0
$865$	731250.			0.977313
$866$	−475220.	−	33064.2i	−0.633664	−	0.0440882i
$867$		0			0
$868$	−266534.	−	37269.5i	−0.353763	−	0.0494668i
$869$	−140030.	−	242539.i	−0.185431	−	0.321176i
$870$		0			0
$871$	−187450.	−	108224.i	−0.247087	−	0.142656i
$872$	−1.17153e6	−	247736.i	−1.54070	−	0.325804i
$873$		0			0
$874$	−27157.5	−	55631.9i	−0.0355522	−	0.0728285i
$875$	−2.27763e6	−	1.31499e6i	−2.97487	−	1.71754i
$876$		0			0
$877$	−71455.2	−	123764.i	−0.0929040	−	0.160914i	0.815828	−	0.578295i	$-0.196282\pi$
$877$	−71455.2	−	123764.i	−0.0929040	−	0.160914i	−0.908732	+	0.417380i	$0.862948\pi$
$878$	−396348.	−	267139.i	−0.514147	−	0.346536i
$879$		0			0
$880$	241409.	−	846343.i	0.311737	−	1.09290i
$881$	305226.			0.393250			0.196625	−	0.980479i	$-0.437002\pi$
$881$	305226.			0.393250			0.196625	+	0.980479i	$0.437002\pi$
$882$		0			0
$883$			902045.i			1.15693i	0.815707	+	0.578465i	$0.196348\pi$
$883$			902045.i			1.15693i	−0.815707	+	0.578465i	$0.803652\pi$
$884$	−10073.5	−	24882.8i	−0.0128906	−	0.0318416i
$885$		0			0
$886$	−675677.	−	455407.i	−0.860739	−	0.580140i
$887$	−797270.	+	460304.i	−1.01335	+	0.585056i	−0.912170	−	0.409813i	$-0.865594\pi$
$887$	−797270.	+	460304.i	−1.01335	+	0.585056i	−0.101177	+	0.994868i	$0.532261\pi$
$888$		0			0
$889$	571692.	−	990199.i	0.723367	−	1.25291i
$890$	−584391.	−	1.19712e6i	−0.737774	−	1.51132i
$891$		0			0
$892$	−957564.	−	747057.i	−1.20348	−	0.938911i
$893$	75358.1	−	130524.i	0.0944990	−	0.163677i
$894$		0			0
$895$	1.48958e6	−	860011.i	1.85960	−	1.07364i
$896$	−527742.	−	839998.i	−0.657364	−	1.04631i
$897$		0			0
$898$	307881.	+	21421.3i	0.381794	+	0.0265640i
$899$		−	124232.i		−	0.153714i
$900$		0			0
$901$	−250052.			−0.308022
$902$	−38681.9	+	555960.i	−0.0475439	+	0.683330i
$903$		0			0
$904$	198427.	+	608530.i	0.242808	+	0.744638i
$905$	1.32984e6	+	2.30336e6i	1.62369	+	2.81232i
$906$		0			0
$907$	−426945.	−	246497.i	−0.518988	−	0.299638i	0.217533	−	0.976053i	$-0.430199\pi$
$907$	−426945.	−	246497.i	−0.518988	−	0.299638i	−0.736520	+	0.676415i	$0.763532\pi$
$908$	520209.	+	405849.i	0.630967	+	0.492258i
$909$		0			0
$910$	316915.	−	154707.i	0.382702	−	0.186821i
$911$	208640.	+	120458.i	0.251397	+	0.145144i	0.620404	−	0.784283i	$-0.286969\pi$
$911$	208640.	+	120458.i	0.251397	+	0.145144i	−0.369007	+	0.929427i	$0.620302\pi$
$912$		0			0
$913$	−116076.	−	201049.i	−0.139252	−	0.241191i
$914$	627851.	−	931528.i	0.751561	−	1.11507i
$915$		0			0
$916$	−165617.	−	409095.i	−0.197385	−	0.487566i
$917$	1.79688e6			2.13688
$918$		0			0
$919$		−	155183.i		−	0.183744i	−0.995771	−	0.0918719i	$-0.970715\pi$
$919$		−	155183.i		−	0.183744i	0.995771	−	0.0918719i	$-0.0292850\pi$
$920$	−625937.	−	562413.i	−0.739529	−	0.664476i
$921$		0			0
$922$	897871.	−	1.33215e6i	1.05621	−	1.56708i
$923$	161274.	−	93111.4i	0.189304	−	0.109295i
$924$		0			0
$925$	−790464.	+	1.36912e6i	−0.923844	+	1.60015i
$926$	−215029.	+	104969.i	−0.250769	+	0.122417i
$927$		0			0
$928$	350279.	−	294961.i	0.406742	−	0.342506i
$929$	−352354.	+	610296.i	−0.408271	+	0.707145i	−0.994696	−	0.102858i	$-0.967201\pi$
$929$	−352354.	+	610296.i	−0.408271	+	0.707145i	0.586425	+	0.810003i	$0.300535\pi$
$930$		0			0
$931$	−60216.4	+	34765.9i	−0.0694729	+	0.0401102i
$932$	−783263.	−	109524.i	−0.901729	−	0.126089i
$933$		0			0
$934$	−57879.6	+	831882.i	−0.0663486	+	0.953604i
$935$			184963.i			0.211574i
$936$		0			0
$937$	−237273.			−0.270252			−0.135126	−	0.990828i	$-0.543144\pi$
$937$	−237273.			−0.270252			−0.135126	+	0.990828i	$0.543144\pi$
$938$	1.67697e6	+	116678.i	1.90599	+	0.132612i
$939$		0			0
$940$	283706.	−	2.02893e6i	0.321079	−	2.29621i
$941$	57476.2	+	99551.7i	0.0649096	+	0.112427i	0.896654	−	0.442732i	$-0.145991\pi$
$941$	57476.2	+	99551.7i	0.0649096	+	0.112427i	−0.831744	+	0.555159i	$0.812657\pi$
$942$		0			0
$943$	461467.	+	266428.i	0.518940	+	0.299610i
$944$	75348.5	−	18898.1i	0.0845534	−	0.0212067i
$945$		0			0
$946$	−99395.8	−	203612.i	−0.111067	−	0.227520i
$947$	890326.	+	514030.i	0.992772	+	0.573177i	0.906102	−	0.423060i	$-0.139044\pi$
$947$	890326.	+	514030.i	0.992772	+	0.573177i	0.0866700	+	0.996237i	$0.472377\pi$
$948$		0			0
$949$	−67658.0	−	117187.i	−0.0751254	−	0.130121i
$950$	283529.	+	191099.i	0.314159	+	0.211744i
$951$		0			0
$952$	155080.	+	139342.i	0.171113	+	0.153747i
$953$	−837599.			−0.922253			−0.461127	−	0.887334i	$-0.652555\pi$
$953$	−837599.			−0.922253			−0.461127	+	0.887334i	$0.652555\pi$
$954$		0			0
$955$			1.82438e6i			2.00036i
$956$	−1.66187e6	+	672785.i	−1.81836	+	0.736140i
$957$		0			0
$958$	531102.	+	357964.i	0.578692	+	0.390039i
$959$	873882.	−	504536.i	0.950201	−	0.548599i
$960$		0			0
$961$	−423174.	+	732958.i	−0.458218	+	0.793656i
$962$	−55624.7	−	113947.i	−0.0601059	−	0.123126i
$963$		0			0
$964$	−404464.	+	518435.i	−0.435237	+	0.557879i
$965$	94598.6	−	163850.i	0.101585	−	0.175951i
$966$		0			0
$967$	−92494.4	+	53401.7i	−0.0989151	+	0.0571087i	−0.548642	−	0.836058i	$-0.684855\pi$
$967$	−92494.4	+	53401.7i	−0.0989151	+	0.0571087i	0.449726	+	0.893166i	$0.351521\pi$
$968$	182932.	+	561010.i	0.195226	+	0.598714i
$969$		0			0
$970$	−365342.	−	25419.3i	−0.388290	−	0.0270159i
$971$		−	689120.i		−	0.730897i	−0.930832	−	0.365448i	$-0.880916\pi$
$971$		−	689120.i		−	0.730897i	0.930832	−	0.365448i	$-0.119084\pi$
$972$		0			0
$973$	247915.			0.261865
$974$	103269.	−	1.48425e6i	0.108856	−	1.56455i
$975$		0			0
$976$	−175875.	+	170315.i	−0.184631	+	0.178794i
$977$	−293734.	−	508762.i	−0.307726	−	0.532998i	0.670138	−	0.742236i	$-0.266235\pi$
$977$	−293734.	−	508762.i	−0.307726	−	0.532998i	−0.977865	+	0.209239i	$0.932901\pi$
$978$		0			0
$979$	−454787.	−	262571.i	−0.474507	−	0.273957i
$980$	−581366.	+	745184.i	−0.605337	+	0.775910i
$981$		0			0
$982$	240170.	−	117243.i	0.249056	−	0.121580i
$983$	338570.	+	195474.i	0.350382	+	0.202293i	0.664853	−	0.746974i	$-0.268494\pi$
$983$	338570.	+	195474.i	0.350382	+	0.202293i	−0.314472	+	0.949267i	$0.601827\pi$
$984$		0			0
$985$	1.04755e6	+	1.81441e6i	1.07970	+	1.87009i
$986$	−53788.2	+	79804.3i	−0.0553265	+	0.0820866i
$987$		0			0
$988$	−25419.5	+	10290.8i	−0.0260408	+	0.0105423i
$989$	−216637.			−0.221483
$990$		0			0
$991$		−	462949.i		−	0.471396i	−0.971826	−	0.235698i	$-0.924262\pi$
$991$		−	462949.i		−	0.471396i	0.971826	−	0.235698i	$-0.0757376\pi$
$992$	280061.	−	49885.5i	0.284596	−	0.0506934i
$993$		0			0
$994$	−808332.	+	1.19930e6i	−0.818120	+	1.21382i
$995$	−2.27488e6	+	1.31340e6i	−2.29780	+	1.32663i
$996$		0			0
$997$	−386642.	+	669683.i	−0.388972	+	0.673720i	−0.992312	−	0.123765i	$-0.960503\pi$
$997$	−386642.	+	669683.i	−0.388972	+	0.673720i	0.603339	+	0.797485i	$0.293836\pi$
$998$	−1.19601e6	+	583851.i	−1.20081	+	0.586193i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.1		44
3.2	odd	2		36.5.f.a.7.22	yes	44
4.3	odd	2	inner	108.5.f.a.19.16		44
9.2	odd	6		324.5.d.f.163.7		22
9.4	even	3	inner	108.5.f.a.91.16		44
9.5	odd	6		36.5.f.a.31.7	yes	44
9.7	even	3		324.5.d.e.163.16		22
12.11	even	2		36.5.f.a.7.7	✓	44
36.7	odd	6		324.5.d.e.163.15		22
36.11	even	6		324.5.d.f.163.8		22
36.23	even	6		36.5.f.a.31.22	yes	44
36.31	odd	6	inner	108.5.f.a.91.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.7	✓	44	12.11	even	2
36.5.f.a.7.22	yes	44	3.2	odd	2
36.5.f.a.31.7	yes	44	9.5	odd	6
36.5.f.a.31.22	yes	44	36.23	even	6
108.5.f.a.19.1		44	1.1	even	1	trivial
108.5.f.a.19.16		44	4.3	odd	2	inner
108.5.f.a.91.1		44	36.31	odd	6	inner
108.5.f.a.91.16		44	9.4	even	3	inner
324.5.d.e.163.15		22	36.7	odd	6
324.5.d.e.163.16		22	9.7	even	3
324.5.d.f.163.7		22	9.2	odd	6
324.5.d.f.163.8		22	36.11	even	6

Overview	Random
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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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.99035 - 0.277636i) q^{2} +(15.8458 + 2.21573i) q^{4} +(23.3466 + 40.4374i) q^{5} +(52.4363 + 30.2741i) q^{7} +(-62.6153 - 13.2409i) q^{8} +O(q^{10})\)	\(q+(-3.99035 - 0.277636i) q^{2} +(15.8458 + 2.21573i) q^{4} +(23.3466 + 40.4374i) q^{5} +(52.4363 + 30.2741i) q^{7} +(-62.6153 - 13.2409i) q^{8} +(-81.9341 - 167.841i) q^{10} +(-63.7631 - 36.8136i) q^{11} +(15.5924 + 27.0068i) q^{13} +(-200.834 - 135.363i) q^{14} +(246.181 + 70.2201i) q^{16} -53.8013 q^{17} +54.9619i q^{19} +(280.347 + 692.494i) q^{20} +(244.217 + 164.602i) q^{22} +(243.863 - 140.795i) q^{23} +(-777.624 + 1346.88i) q^{25} +(-54.7210 - 112.096i) q^{26} +(763.818 + 595.904i) q^{28} +(-223.597 + 387.282i) q^{29} +(-240.584 + 138.901i) q^{31} +(-962.854 - 348.552i) q^{32} +(214.686 + 14.9372i) q^{34} +2827.19i q^{35} +1016.51 q^{37} +(15.2594 - 219.317i) q^{38} +(-926.424 - 2841.13i) q^{40} +(946.158 + 1638.79i) q^{41} +(-666.266 - 384.669i) q^{43} +(-928.811 - 724.625i) q^{44} +(-1012.19 + 494.115i) q^{46} +(-2374.81 - 1371.10i) q^{47} +(632.546 + 1095.60i) q^{49} +(3476.94 - 5158.64i) q^{50} +(187.235 + 462.494i) q^{52} +4647.69 q^{53} -3437.89i q^{55} +(-2882.46 - 2589.93i) q^{56} +(999.756 - 1483.31i) q^{58} +(262.792 - 151.723i) q^{59} +(-478.174 + 828.222i) q^{61} +(998.577 - 487.469i) q^{62} +(3745.36 + 1658.17i) q^{64} +(-728.057 + 1261.03i) q^{65} +(-6010.96 + 3470.43i) q^{67} +(-852.527 - 119.209i) q^{68} +(784.928 - 11281.5i) q^{70} -5971.60i q^{71} -4339.17 q^{73} +(-4056.25 - 282.220i) q^{74} +(-121.781 + 870.917i) q^{76} +(-2229.00 - 3860.75i) q^{77} +(3294.15 + 1901.88i) q^{79} +(2907.96 + 11594.3i) q^{80} +(-3320.52 - 6802.05i) q^{82} +(2730.64 + 1576.53i) q^{83} +(-1256.08 - 2175.59i) q^{85} +(2551.84 + 1719.94i) q^{86} +(3505.10 + 3149.38i) q^{88} +7132.44 q^{89} +1888.18i q^{91} +(4176.18 - 1690.67i) q^{92} +(9095.67 + 6130.50i) q^{94} +(-2222.52 + 1283.17i) q^{95} +(980.405 - 1698.11i) q^{97} +(-2219.91 - 4547.46i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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