LMFDB - Embedded newform 108.5.f.a.19.22

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			19.22
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.96529 - 0.525827i) q^{2} +(15.4470 - 4.17011i) q^{4} +(-11.0746 - 19.1817i) q^{5} +(-82.7885 - 47.7980i) q^{7} +(59.0591 - 24.6582i) q^{8} +O(q^{10})$	\(q+(3.96529 - 0.525827i) q^{2} +(15.4470 - 4.17011i) q^{4} +(-11.0746 - 19.1817i) q^{5} +(-82.7885 - 47.7980i) q^{7} +(59.0591 - 24.6582i) q^{8} +(-54.0000 - 70.2376i) q^{10} +(-18.9394 - 10.9346i) q^{11} +(-63.1124 - 109.314i) q^{13} +(-353.414 - 146.000i) q^{14} +(221.220 - 128.832i) q^{16} +283.865 q^{17} +323.729i q^{19} +(-251.059 - 250.118i) q^{20} +(-80.8497 - 33.4002i) q^{22} +(198.433 - 114.565i) q^{23} +(67.2085 - 116.409i) q^{25} +(-307.739 - 400.274i) q^{26} +(-1478.16 - 393.098i) q^{28} +(604.822 - 1047.58i) q^{29} +(-718.565 + 414.863i) q^{31} +(809.459 - 627.178i) q^{32} +(1125.61 - 149.264i) q^{34} +2117.36i q^{35} -318.650 q^{37} +(170.226 + 1283.68i) q^{38} +(-1127.04 - 859.775i) q^{40} +(164.418 + 284.781i) q^{41} +(179.336 + 103.539i) q^{43} +(-338.155 - 89.9283i) q^{44} +(726.602 - 558.626i) q^{46} +(-1062.42 - 613.390i) q^{47} +(3368.79 + 5834.92i) q^{49} +(205.290 - 496.933i) q^{50} +(-1430.75 - 1425.39i) q^{52} +2834.27 q^{53} +484.385i q^{55} +(-6068.02 - 781.492i) q^{56} +(1847.44 - 4471.99i) q^{58} +(1278.13 - 737.929i) q^{59} +(936.180 - 1621.51i) q^{61} +(-2631.17 + 2022.89i) q^{62} +(2879.95 - 2912.58i) q^{64} +(-1397.88 + 2421.20i) q^{65} +(-214.663 + 123.936i) q^{67} +(4384.87 - 1183.75i) q^{68} +(1113.37 + 8395.96i) q^{70} +4308.28i q^{71} +3010.75 q^{73} +(-1263.54 + 167.555i) q^{74} +(1349.99 + 5000.65i) q^{76} +(1045.31 + 1810.52i) q^{77} +(-6228.39 - 3595.96i) q^{79} +(-4921.12 - 2816.63i) q^{80} +(801.712 + 1042.78i) q^{82} +(2877.35 + 1661.24i) q^{83} +(-3143.68 - 5445.01i) q^{85} +(765.561 + 316.264i) q^{86} +(-1388.17 - 178.780i) q^{88} +1549.85 q^{89} +12066.6i q^{91} +(2587.44 - 2597.18i) q^{92} +(-4535.35 - 1873.62i) q^{94} +(6209.67 - 3585.16i) q^{95} +(-2918.68 + 5055.31i) q^{97} +(16426.4 + 21365.7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.96529	−	0.525827i	0.991322	−	0.131457i
$2$	3.96529	−	0.525827i	0.991322	−	0.131457i
$3$		0			0
$3$		0			0
$4$	15.4470	−	4.17011i	0.965438	−	0.260632i
$5$	−11.0746	−	19.1817i	−0.442982	−	0.767268i	0.554927	−	0.831899i	$-0.312746\pi$
$5$	−11.0746	−	19.1817i	−0.442982	−	0.767268i	−0.997909	+	0.0646314i	$0.979413\pi$
$6$		0			0
$7$	−82.7885	−	47.7980i	−1.68956	−	0.975469i	−0.954850	−	0.297089i	$-0.903984\pi$
$7$	−82.7885	−	47.7980i	−1.68956	−	0.975469i	−0.734711	−	0.678380i	$-0.762682\pi$
$8$	59.0591	−	24.6582i	0.922798	−	0.385284i
$9$		0			0
$10$	−54.0000	−	70.2376i	−0.540000	−	0.702376i
$11$	−18.9394	−	10.9346i	−0.156524	−	0.0903689i	0.419692	−	0.907666i	$-0.362138\pi$
$11$	−18.9394	−	10.9346i	−0.156524	−	0.0903689i	−0.576216	+	0.817297i	$0.695471\pi$
$12$		0			0
$13$	−63.1124	−	109.314i	−0.373446	−	0.646827i	0.616647	−	0.787240i	$-0.288491\pi$
$13$	−63.1124	−	109.314i	−0.373446	−	0.646827i	−0.990093	+	0.140412i	$0.955157\pi$
$14$	−353.414	−	146.000i	−1.80313	−	0.744899i
$15$		0			0
$16$	221.220	−	128.832i	0.864142	−	0.503248i
$17$	283.865			0.982232			0.491116	−	0.871094i	$-0.336589\pi$
$17$	283.865			0.982232			0.491116	+	0.871094i	$0.336589\pi$
$18$		0			0
$19$			323.729i			0.896756i	0.893844	+	0.448378i	$0.147998\pi$
$19$			323.729i			0.896756i	−0.893844	+	0.448378i	$0.852002\pi$
$20$	−251.059	−	250.118i	−0.627646	−	0.625294i
$21$		0			0
$22$	−80.8497	−	33.4002i	−0.167045	−	0.0690086i
$23$	198.433	−	114.565i	0.375109	−	0.216570i	−0.300579	−	0.953757i	$-0.597180\pi$
$23$	198.433	−	114.565i	0.375109	−	0.216570i	0.675688	+	0.737187i	$0.263847\pi$
$24$		0			0
$25$	67.2085	−	116.409i	0.107534	−	0.186254i
$26$	−307.739	−	400.274i	−0.455235	−	0.592122i
$27$		0			0
$28$	−1478.16	−	393.098i	−1.88541	−	0.501401i
$29$	604.822	−	1047.58i	0.719170	−	1.24564i	−0.242160	−	0.970236i	$-0.577856\pi$
$29$	604.822	−	1047.58i	0.719170	−	1.24564i	0.961329	−	0.275402i	$-0.0888109\pi$
$30$		0			0
$31$	−718.565	+	414.863i	−0.747726	+	0.431700i	−0.824872	−	0.565320i	$-0.808753\pi$
$31$	−718.565	+	414.863i	−0.747726	+	0.431700i	0.0771458	+	0.997020i	$0.475419\pi$
$32$	809.459	−	627.178i	0.790487	−	0.612478i
$33$		0			0
$34$	1125.61	−	149.264i	0.973708	−	0.129121i
$35$			2117.36i			1.72846i
$36$		0			0
$37$	−318.650			−0.232761			−0.116380	−	0.993205i	$-0.537129\pi$
$37$	−318.650			−0.232761			−0.116380	+	0.993205i	$0.537129\pi$
$38$	170.226	+	1283.68i	0.117885	+	0.888974i
$39$		0			0
$40$	−1127.04	−	859.775i	−0.704399	−	0.537359i
$41$	164.418	+	284.781i	0.0978099	+	0.169412i	0.910778	−	0.412897i	$-0.135483\pi$
$41$	164.418	+	284.781i	0.0978099	+	0.169412i	−0.812968	+	0.582308i	$0.802150\pi$
$42$		0			0
$43$	179.336	+	103.539i	0.0969906	+	0.0559976i	0.547711	−	0.836668i	$-0.315499\pi$
$43$	179.336	+	103.539i	0.0969906	+	0.0559976i	−0.450720	+	0.892665i	$0.648833\pi$
$44$	−338.155	−	89.9283i	−0.174667	−	0.0464506i
$45$		0			0
$46$	726.602	−	558.626i	0.343385	−	0.264001i
$47$	−1062.42	−	613.390i	−0.480952	−	0.277678i	0.239861	−	0.970807i	$-0.422898\pi$
$47$	−1062.42	−	613.390i	−0.480952	−	0.277678i	−0.720813	+	0.693129i	$0.756231\pi$
$48$		0			0
$49$	3368.79	+	5834.92i	1.40308	+	2.43020i
$50$	205.290	−	496.933i	0.0821161	−	0.198773i
$51$		0			0
$52$	−1430.75	−	1425.39i	−0.529123	−	0.527140i
$53$	2834.27			1.00900			0.504499	−	0.863412i	$-0.331677\pi$
$53$	2834.27			1.00900			0.504499	+	0.863412i	$0.331677\pi$
$54$		0			0
$55$			484.385i			0.160127i
$56$	−6068.02	−	781.492i	−1.93496	−	0.249200i
$57$		0			0
$58$	1847.44	−	4471.99i	0.549181	−	1.32937i
$59$	1278.13	−	737.929i	0.367173	−	0.211988i	−0.305049	−	0.952337i	$-0.598673\pi$
$59$	1278.13	−	737.929i	0.367173	−	0.211988i	0.672223	+	0.740349i	$0.265340\pi$
$60$		0			0
$61$	936.180	−	1621.51i	0.251594	−	0.435773i	−0.712371	−	0.701803i	$-0.752379\pi$
$61$	936.180	−	1621.51i	0.251594	−	0.435773i	0.963965	+	0.266030i	$0.0857120\pi$
$62$	−2631.17	+	2022.89i	−0.684487	+	0.526247i
$63$		0			0
$64$	2879.95	−	2912.58i	0.703113	−	0.711078i
$65$	−1397.88	+	2421.20i	−0.330860	+	0.573066i
$66$		0			0
$67$	−214.663	+	123.936i	−0.0478197	+	0.0276087i	−0.523719	−	0.851891i	$-0.675456\pi$
$67$	−214.663	+	123.936i	−0.0478197	+	0.0276087i	0.475900	+	0.879500i	$0.342123\pi$
$68$	4384.87	−	1183.75i	0.948284	−	0.256001i
$69$		0			0
$70$	1113.37	+	8395.96i	0.227218	+	1.71346i
$71$			4308.28i			0.854648i	0.904099	+	0.427324i	$0.140544\pi$
$71$			4308.28i			0.854648i	−0.904099	+	0.427324i	$0.859456\pi$
$72$		0			0
$73$	3010.75			0.564974			0.282487	−	0.959271i	$-0.408841\pi$
$73$	3010.75			0.564974			0.282487	+	0.959271i	$0.408841\pi$
$74$	−1263.54	+	167.555i	−0.230741	+	0.0305980i
$75$		0			0
$76$	1349.99	+	5000.65i	0.233723	+	0.865763i
$77$	1045.31	+	1810.52i	0.176304	+	0.305368i
$78$		0			0
$79$	−6228.39	−	3595.96i	−0.997980	−	0.576184i	−0.0903300	−	0.995912i	$-0.528792\pi$
$79$	−6228.39	−	3595.96i	−0.997980	−	0.576184i	−0.907650	+	0.419728i	$0.862126\pi$
$80$	−4921.12	−	2816.63i	−0.768926	−	0.440098i
$81$		0			0
$82$	801.712	+	1042.78i	0.119231	+	0.155084i
$83$	2877.35	+	1661.24i	0.417673	+	0.241144i	0.694081	−	0.719897i	$-0.255811\pi$
$83$	2877.35	+	1661.24i	0.417673	+	0.241144i	−0.276408	+	0.961040i	$0.589144\pi$
$84$		0			0
$85$	−3143.68	−	5445.01i	−0.435111	−	0.753635i
$86$	765.561	+	316.264i	0.103510	+	0.0427615i
$87$		0			0
$88$	−1388.17	−	178.780i	−0.179257	−	0.0230863i
$89$	1549.85			0.195664			0.0978318	−	0.995203i	$-0.468809\pi$
$89$	1549.85			0.195664			0.0978318	+	0.995203i	$0.468809\pi$
$90$		0			0
$91$			12066.6i			1.45714i
$92$	2587.44	−	2597.18i	0.305700	−	0.306850i
$93$		0			0
$94$	−4535.35	−	1873.62i	−0.513281	−	0.212044i
$95$	6209.67	−	3585.16i	0.688052	−	0.397247i
$96$		0			0
$97$	−2918.68	+	5055.31i	−0.310201	+	0.537285i	−0.978406	−	0.206693i	$-0.933730\pi$
$97$	−2918.68	+	5055.31i	−0.310201	+	0.537285i	0.668204	+	0.743978i	$0.267063\pi$
$98$	16426.4	+	21365.7i	1.71037	+	2.22467i
$99$		0			0
$100$	552.734	−	2078.43i	0.0552734	−	0.207843i
$101$	−2749.50	+	4762.27i	−0.269532	+	0.466844i	−0.968741	−	0.248074i	$-0.920202\pi$
$101$	−2749.50	+	4762.27i	−0.269532	+	0.466844i	0.699209	+	0.714918i	$0.253536\pi$
$102$		0			0
$103$	15530.7	−	8966.63i	1.46391	−	0.845191i	0.464725	−	0.885455i	$-0.346153\pi$
$103$	15530.7	−	8966.63i	1.46391	−	0.845191i	0.999189	+	0.0402641i	$0.0128199\pi$
$104$	−6422.83	−	4899.74i	−0.593827	−	0.453008i
$105$		0			0
$106$	11238.7	−	1490.34i	1.00024	−	0.132640i
$107$		−	8715.17i		−	0.761217i	−0.924736	−	0.380608i	$-0.875715\pi$
$107$		−	8715.17i		−	0.761217i	0.924736	−	0.380608i	$-0.124285\pi$
$108$		0			0
$109$	−12162.1			−1.02366			−0.511830	−	0.859087i	$-0.671032\pi$
$109$	−12162.1			−1.02366			−0.511830	+	0.859087i	$0.671032\pi$
$110$	254.703	+	1920.73i	0.0210498	+	0.158738i
$111$		0			0
$112$	−24472.4	+	91.8909i	−1.95092	+	0.00732549i
$113$	−10236.7	−	17730.5i	−0.801684	−	1.38856i	−0.918507	−	0.395404i	$-0.870604\pi$
$113$	−10236.7	−	17730.5i	−0.801684	−	1.38856i	0.116823	−	0.993153i	$-0.462729\pi$
$114$		0			0
$115$	−4395.11	−	2537.52i	−0.332334	−	0.191873i
$116$	4974.15	−	18704.2i	0.369661	−	1.39003i
$117$		0			0
$118$	4680.13	−	3598.18i	0.336120	−	0.258415i
$119$	−23500.8	−	13568.2i	−1.65954	−	0.958136i
$120$		0			0
$121$	−7081.37	−	12265.3i	−0.483667	−	0.837736i
$122$	2859.59	−	6922.03i	0.192125	−	0.465065i
$123$		0			0
$124$	−9369.65	+	9404.89i	−0.609368	+	0.611661i
$125$	−16820.4			−1.07651
$126$		0			0
$127$		−	8130.42i		−	0.504087i	−0.967716	−	0.252044i	$-0.918897\pi$
$127$		−	8130.42i		−	0.504087i	0.967716	−	0.252044i	$-0.0811026\pi$
$128$	9888.32	−	13063.6i	0.603535	−	0.797336i
$129$		0			0
$130$	−4269.87	+	10335.8i	−0.252655	+	0.611586i
$131$	−14095.1	+	8137.79i	−0.821343	+	0.474203i	−0.850879	−	0.525361i	$-0.823930\pi$
$131$	−14095.1	+	8137.79i	−0.821343	+	0.474203i	0.0295362	+	0.999564i	$0.490597\pi$
$132$		0			0
$133$	15473.6	−	26801.0i	0.874758	−	1.51512i
$134$	−786.030	+	604.315i	−0.0437754	+	0.0336554i
$135$		0			0
$136$	16764.8	−	6999.59i	0.906402	−	0.378438i
$137$	12331.4	−	21358.7i	0.657011	−	1.13798i	−0.324375	−	0.945929i	$-0.605154\pi$
$137$	12331.4	−	21358.7i	0.657011	−	1.13798i	0.981386	−	0.192047i	$-0.0615126\pi$
$138$		0			0
$139$	17078.1	−	9860.04i	0.883913	−	0.510328i	0.0119667	−	0.999928i	$-0.496191\pi$
$139$	17078.1	−	9860.04i	0.883913	−	0.510328i	0.871947	+	0.489601i	$0.162857\pi$
$140$	8829.65	+	32707.0i	0.450492	+	1.66872i
$141$		0			0
$142$	2265.41	+	17083.6i	0.112349	+	0.847231i
$143$			2760.44i			0.134992i
$144$		0			0
$145$	−26792.5			−1.27432
$146$	11938.5	−	1583.13i	0.560072	−	0.0742697i
$147$		0			0
$148$	−4922.18	+	1328.80i	−0.224716	+	0.0606649i
$149$	14942.7	+	25881.6i	0.673066	+	1.16578i	0.977030	+	0.213101i	$0.0683562\pi$
$149$	14942.7	+	25881.6i	0.673066	+	1.16578i	−0.303965	+	0.952683i	$0.598310\pi$
$150$		0			0
$151$	−5164.11	−	2981.50i	−0.226486	−	0.130762i	0.382464	−	0.923970i	$-0.375076\pi$
$151$	−5164.11	−	2981.50i	−0.226486	−	0.130762i	−0.608950	+	0.793209i	$0.708409\pi$
$152$	7982.56	+	19119.1i	0.345506	+	0.827525i
$153$		0			0
$154$	5096.97	+	6629.60i	0.214917	+	0.279541i
$155$	15915.6	+	9188.85i	0.662458	+	0.382471i
$156$		0			0
$157$	17493.5	+	30299.6i	0.709704	+	1.22924i	0.964967	+	0.262372i	$0.0845048\pi$
$157$	17493.5	+	30299.6i	0.709704	+	1.22924i	−0.255262	+	0.966872i	$0.582162\pi$
$158$	−26588.2	−	10984.0i	−1.06506	−	0.439993i
$159$		0			0
$160$	−20994.7	−	8581.08i	−0.820107	−	0.335198i
$161$	−21903.9			−0.845027
$162$		0			0
$163$			14509.8i			0.546118i	0.961997	+	0.273059i	$0.0880354\pi$
$163$			14509.8i			0.546118i	−0.961997	+	0.273059i	$0.911965\pi$
$164$	3727.34	+	3713.37i	0.138584	+	0.138064i
$165$		0			0
$166$	12283.0	+	5074.30i	0.445749	+	0.184145i
$167$	38640.1	−	22308.9i	1.38550	−	0.799917i	0.392693	−	0.919670i	$-0.371543\pi$
$167$	38640.1	−	22308.9i	1.38550	−	0.799917i	0.992804	+	0.119753i	$0.0382102\pi$
$168$		0			0
$169$	6314.16	−	10936.5i	0.221076	−	0.382916i
$170$	−15328.7	−	19938.0i	−0.530406	−	0.689896i
$171$		0			0
$172$	3201.97	+	851.526i	0.108233	+	0.0287833i
$173$	−26443.3	+	45801.1i	−0.883534	+	1.53033i	−0.0361488	+	0.999346i	$0.511509\pi$
$173$	−26443.3	+	45801.1i	−0.883534	+	1.53033i	−0.847385	+	0.530979i	$0.821824\pi$
$174$		0			0
$175$	−11128.2	+	6424.86i	−0.363369	+	0.209791i
$176$	−5598.50	+	21.0217i	−0.180737	+	0.000678644i
$177$		0			0
$178$	6145.61	−	814.954i	0.193966	−	0.0257213i
$179$		−	32840.8i		−	1.02496i	−0.858698	−	0.512482i	$-0.828726\pi$
$179$		−	32840.8i		−	1.02496i	0.858698	−	0.512482i	$-0.171274\pi$
$180$		0			0
$181$	−22758.6			−0.694685			−0.347343	−	0.937738i	$-0.612916\pi$
$181$	−22758.6			−0.694685			−0.347343	+	0.937738i	$0.612916\pi$
$182$	6344.93	+	47847.4i	0.191551	+	1.44449i
$183$		0			0
$184$	8894.30	−	11659.1i	0.262710	−	0.344373i
$185$	3528.90	+	6112.24i	0.103109	+	0.178590i
$186$		0			0
$187$	−5376.22	−	3103.96i	−0.153742	−	0.0887632i
$188$	−18969.2	−	5044.62i	−0.536701	−	0.142729i
$189$		0			0
$190$	22738.0	−	17481.4i	0.629860	−	0.484249i
$191$	49799.3	+	28751.7i	1.36508	+	0.788127i	0.990294	−	0.138986i	$-0.0443843\pi$
$191$	49799.3	+	28751.7i	1.36508	+	0.788127i	0.374782	+	0.927113i	$0.377718\pi$
$192$		0			0
$193$	22470.8	+	38920.5i	0.603259	+	1.04488i	0.992324	+	0.123665i	$0.0394648\pi$
$193$	22470.8	+	38920.5i	0.603259	+	1.04488i	−0.389065	+	0.921210i	$0.627202\pi$
$194$	−8915.21	+	21580.5i	−0.236880	+	0.573400i
$195$		0			0
$196$	76370.0	+	76083.8i	1.98797	+	1.98052i
$197$	44514.7			1.14702			0.573510	−	0.819198i	$-0.305581\pi$
$197$	44514.7			1.14702			0.573510	+	0.819198i	$0.305581\pi$
$198$		0			0
$199$			19066.9i			0.481474i	0.970590	+	0.240737i	$0.0773892\pi$
$199$			19066.9i			0.481474i	−0.970590	+	0.240737i	$0.922611\pi$
$200$	1098.85	−	8532.22i	0.0274713	−	0.213305i
$201$		0			0
$202$	−8398.42	+	20329.5i	−0.205824	+	0.498224i
$203$	−100145.	+	57818.5i	−2.43016	+	1.40305i
$204$		0			0
$205$	3641.72	−	6307.65i	0.0866561	−	0.150093i
$206$	56868.6	−	43721.7i	1.34010	−	1.03030i
$207$		0			0
$208$	−28044.8	−	16051.6i	−0.648225	−	0.371014i
$209$	3539.86	−	6131.22i	0.0810389	−	0.140364i
$210$		0			0
$211$	825.251	−	476.459i	0.0185362	−	0.0107019i	−0.490703	−	0.871327i	$-0.663260\pi$
$211$	825.251	−	476.459i	0.0185362	−	0.0107019i	0.509239	+	0.860625i	$0.329927\pi$
$212$	43781.1	−	11819.2i	0.974125	−	0.262977i
$213$		0			0
$214$	−4582.67	−	34558.1i	−0.100067	−	0.754611i
$215$		−	4586.61i		−	0.0992237i
$216$		0			0
$217$	79318.5			1.68444
$218$	−48226.2	+	6395.17i	−1.01478	+	0.134567i
$219$		0			0
$220$	2019.94	+	7482.30i	0.0417343	+	0.154593i
$221$	−17915.4	−	31030.4i	−0.366810	−	0.635334i
$222$		0			0
$223$	−37535.4	−	21671.1i	−0.754800	−	0.435784i	0.0726258	−	0.997359i	$-0.476862\pi$
$223$	−37535.4	−	21671.1i	−0.754800	−	0.435784i	−0.827426	+	0.561575i	$0.810195\pi$
$224$	−96991.7	+	13232.6i	−1.93303	+	0.263724i
$225$		0			0
$226$	−49914.6	−	64923.7i	−0.977262	−	1.27112i
$227$	5202.66	+	3003.76i	0.100966	+	0.0582925i	0.549633	−	0.835406i	$-0.314768\pi$
$227$	5202.66	+	3003.76i	0.100966	+	0.0582925i	−0.448667	+	0.893699i	$0.648101\pi$
$228$		0			0
$229$	2038.17	+	3530.22i	0.0388660	+	0.0673180i	0.884804	−	0.465963i	$-0.154292\pi$
$229$	2038.17	+	3530.22i	0.0388660	+	0.0673180i	−0.845938	+	0.533281i	$0.820959\pi$
$230$	−18762.2	−	7750.92i	−0.354673	−	0.146520i
$231$		0			0
$232$	9888.77	−	76783.0i	0.183724	−	1.42656i
$233$	37427.6			0.689414			0.344707	−	0.938710i	$-0.387978\pi$
$233$	37427.6			0.689414			0.344707	+	0.938710i	$0.387978\pi$
$234$		0			0
$235$			27172.1i			0.492025i
$236$	16666.1	−	16728.7i	0.299232	−	0.300358i
$237$		0			0
$238$	−100322.	−	41444.4i	−1.77109	−	0.731664i
$239$	22212.3	−	12824.3i	0.388865	−	0.224511i	−0.292804	−	0.956173i	$-0.594588\pi$
$239$	22212.3	−	12824.3i	0.388865	−	0.224511i	0.681668	+	0.731662i	$0.261255\pi$
$240$		0			0
$241$	−38300.8	+	66339.0i	−0.659438	+	1.14218i	0.321323	+	0.946970i	$0.395872\pi$
$241$	−38300.8	+	66339.0i	−0.659438	+	1.14218i	−0.980761	+	0.195211i	$0.937461\pi$
$242$	−34529.1	−	44911.8i	−0.589596	−	0.766884i
$243$		0			0
$244$	7699.30	−	28951.5i	0.129322	−	0.486285i
$245$	74615.7	−	129238.i	1.24308	−	2.15307i
$246$		0			0
$247$	35388.1	−	20431.3i	0.580046	−	0.334890i
$248$	−32208.0	+	42219.9i	−0.523673	+	0.686458i
$249$		0			0
$250$	−66697.8	+	8844.63i	−1.06716	+	0.141514i
$251$			66642.6i			1.05780i	0.848683	+	0.528902i	$0.177396\pi$
$251$			66642.6i			1.05780i	−0.848683	+	0.528902i	$0.822604\pi$
$252$		0			0
$253$	−5010.92			−0.0782846
$254$	−4275.20	−	32239.5i	−0.0662657	−	0.499713i
$255$		0			0
$256$	32340.9	−	57000.3i	0.493482	−	0.869756i
$257$	29713.2	+	51464.8i	0.449866	+	0.779191i	0.998377	−	0.0569526i	$-0.0181384\pi$
$257$	29713.2	+	51464.8i	0.449866	+	0.779191i	−0.548511	+	0.836143i	$0.684805\pi$
$258$		0			0
$259$	26380.5	+	15230.8i	0.393264	+	0.227051i
$260$	−11496.4	+	43229.7i	−0.170065	+	0.639492i
$261$		0			0
$262$	−51611.9	+	39680.3i	−0.751878	+	0.578059i
$263$	−21772.1	−	12570.2i	−0.314767	−	0.181731i	0.334290	−	0.942470i	$-0.391503\pi$
$263$	−21772.1	−	12570.2i	−0.314767	−	0.181731i	−0.649058	+	0.760739i	$0.724837\pi$
$264$		0			0
$265$	−31388.3	−	54366.2i	−0.446968	−	0.774171i
$266$	47264.5	−	114410.i	0.667993	−	1.61697i
$267$		0			0
$268$	−2799.07	+	2809.60i	−0.0389712	+	0.0391179i
$269$	−2553.46			−0.0352877			−0.0176439	−	0.999844i	$-0.505617\pi$
$269$	−2553.46			−0.0352877			−0.0176439	+	0.999844i	$0.505617\pi$
$270$		0			0
$271$		−	4623.11i		−	0.0629499i	−0.999505	−	0.0314750i	$-0.989980\pi$
$271$		−	4623.11i		−	0.0629499i	0.999505	−	0.0314750i	$-0.0100204\pi$
$272$	62796.7	−	36570.8i	0.848788	−	0.494307i
$273$		0			0
$274$	37666.7	−	91177.4i	0.501714	−	1.21447i
$275$	−2545.77	+	1469.80i	−0.0336631	+	0.0194354i
$276$		0			0
$277$	4927.19	−	8534.14i	0.0642154	−	0.111224i	−0.832130	−	0.554580i	$-0.812879\pi$
$277$	4927.19	−	8534.14i	0.0642154	−	0.111224i	0.896346	+	0.443356i	$0.146212\pi$
$278$	62534.9	−	48078.0i	0.809157	−	0.622095i
$279$		0			0
$280$	52210.3	+	125050.i	0.665948	+	1.59502i
$281$	−24208.6	+	41930.5i	−0.306589	+	0.531028i	−0.977614	−	0.210407i	$-0.932521\pi$
$281$	−24208.6	+	41930.5i	−0.306589	+	0.531028i	0.671025	+	0.741435i	$0.265854\pi$
$282$		0			0
$283$	−114515.	+	66115.1i	−1.42984	+	0.825520i	−0.997108	−	0.0760012i	$-0.975785\pi$
$283$	−114515.	+	66115.1i	−1.42984	+	0.825520i	−0.432735	+	0.901521i	$0.642451\pi$
$284$	17966.0	+	66550.0i	0.222749	+	0.825110i
$285$		0			0
$286$	1451.52	+	10946.0i	0.0177456	+	0.133820i
$287$		−	31435.5i		−	0.381642i
$288$		0			0
$289$	−2941.65			−0.0352205
$290$	−106240.	+	14088.2i	−1.26326	+	0.167518i
$291$		0			0
$292$	46507.1	−	12555.2i	0.545448	−	0.147250i
$293$	−44759.6	−	77525.8i	−0.521375	−	0.903049i	−0.999691	−	0.0248607i	$-0.992086\pi$
$293$	−44759.6	−	77525.8i	−0.521375	−	0.903049i	0.478315	−	0.878188i	$-0.341248\pi$
$294$		0			0
$295$	−28309.5	−	16344.5i	−0.325303	−	0.187814i
$296$	−18819.1	+	7857.31i	−0.214791	+	0.0896789i
$297$		0			0
$298$	72861.5	+	94770.6i	0.820475	+	1.06719i
$299$	−25047.1	−	14461.0i	−0.280166	−	0.161754i
$300$		0			0
$301$	−9897.95	−	17143.8i	−0.109248	−	0.189223i
$302$	−22044.9	−	9107.08i	−0.241710	−	0.0998540i
$303$		0			0
$304$	41706.5	+	71615.4i	0.451291	+	0.774925i
$305$	−41471.1			−0.445806
$306$		0			0
$307$			62726.9i			0.665545i	0.943007	+	0.332772i	$0.107984\pi$
$307$			62726.9i			0.665545i	−0.943007	+	0.332772i	$0.892016\pi$
$308$	23697.0	+	23608.2i	0.249799	+	0.248863i
$309$		0			0
$310$	67941.5	+	28067.6i	0.706988	+	0.292067i
$311$	106333.	−	61391.4i	1.09938	−	0.634726i	0.163321	−	0.986573i	$-0.447779\pi$
$311$	106333.	−	61391.4i	1.09938	−	0.634726i	0.936058	+	0.351847i	$0.114446\pi$
$312$		0			0
$313$	24294.6	−	42079.4i	0.247982	−	0.429518i	−0.714984	−	0.699141i	$-0.753566\pi$
$313$	24294.6	−	42079.4i	0.247982	−	0.429518i	0.962966	+	0.269623i	$0.0868992\pi$
$314$	85299.2	+	110948.i	0.865138	+	1.12528i
$315$		0			0
$316$	−111206.	−	29573.8i	−1.11366	−	0.296164i
$317$	−55066.7	+	95378.4i	−0.547988	+	0.949143i	0.450425	+	0.892815i	$0.351273\pi$
$317$	−55066.7	+	95378.4i	−0.547988	+	0.949143i	−0.998412	+	0.0563282i	$0.982061\pi$
$318$		0			0
$319$	−22909.9	+	13227.0i	−0.225134	+	0.129981i
$320$	−87762.3	−	22986.8i	−0.857054	−	0.224481i
$321$		0			0
$322$	−86855.5	+	11517.7i	−0.837694	+	0.111085i
$323$			91895.4i			0.880823i
$324$		0			0
$325$	−16966.7			−0.160632
$326$	7629.65	+	57535.6i	0.0717909	+	0.541379i
$327$		0			0
$328$	16732.6	+	12764.7i	0.155530	+	0.118648i
$329$	58637.6	+	101563.i	0.541732	+	0.938308i
$330$		0			0
$331$	159800.	+	92260.3i	1.45854	+	0.842091i	0.998940	−	0.0460325i	$-0.0146578\pi$
$331$	159800.	+	92260.3i	1.45854	+	0.842091i	0.459605	+	0.888124i	$0.347991\pi$
$332$	51374.0	+	13662.3i	0.466087	+	0.123950i
$333$		0			0
$334$	141489.	−	108779.i	1.26832	−	0.975108i
$335$	4754.59	+	2745.06i	0.0423665	+	0.0244603i
$336$		0			0
$337$	−32813.1	−	56833.9i	−0.288926	−	0.500435i	0.684628	−	0.728893i	$-0.259965\pi$
$337$	−32813.1	−	56833.9i	−0.288926	−	0.500435i	−0.973554	+	0.228458i	$0.926632\pi$
$338$	19286.8	−	46686.3i	0.168821	−	0.408655i
$339$		0			0
$340$	−71266.7	−	70999.7i	−0.616494	−	0.614184i
$341$	18145.5			0.156049
$342$		0			0
$343$		−	414560.i		−	3.52370i
$344$	13144.5	+	1692.86i	0.111078	+	0.0143055i
$345$		0			0
$346$	−80771.7	+	195519.i	−0.674695	+	1.63319i
$347$	90819.3	−	52434.6i	0.754257	−	0.435470i	−0.0729731	−	0.997334i	$-0.523249\pi$
$347$	90819.3	−	52434.6i	0.754257	−	0.435470i	0.827230	+	0.561864i	$0.189915\pi$
$348$		0			0
$349$	−43672.0	+	75642.1i	−0.358552	+	0.621030i	−0.987719	−	0.156240i	$-0.950063\pi$
$349$	−43672.0	+	75642.1i	−0.358552	+	0.621030i	0.629167	+	0.777270i	$0.283396\pi$
$350$	−40748.1	+	31327.9i	−0.332637	+	0.255738i
$351$		0			0
$352$	−22188.6	+	3027.20i	−0.179079	+	0.0244318i
$353$	−24354.3	+	42182.9i	−0.195446	+	0.338522i	−0.947047	−	0.321096i	$-0.895949\pi$
$353$	−24354.3	+	42182.9i	−0.195446	+	0.338522i	0.751601	+	0.659618i	$0.229282\pi$
$354$		0			0
$355$	82640.1	−	47712.3i	0.655744	−	0.378594i
$356$	23940.6	−	6463.06i	0.188901	−	0.0509962i
$357$		0			0
$358$	−17268.6	−	130223.i	−0.134738	−	1.01607i
$359$		−	109409.i		−	0.848911i	−0.905449	−	0.424456i	$-0.860465\pi$
$359$		−	109409.i		−	0.848911i	0.905449	−	0.424456i	$-0.139535\pi$
$360$		0			0
$361$	25520.5			0.195828
$362$	−90244.4	+	11967.1i	−0.688657	+	0.0913211i
$363$		0			0
$364$	50318.9	+	186392.i	0.379777	+	1.40678i
$365$	−33342.7	−	57751.3i	−0.250274	−	0.433487i
$366$		0			0
$367$	−1112.82	−	642.487i	−0.00826215	−	0.00477015i	0.495863	−	0.868401i	$-0.334852\pi$
$367$	−1112.82	−	642.487i	−0.00826215	−	0.00477015i	−0.504125	+	0.863630i	$0.668185\pi$
$368$	29137.8	−	50908.6i	0.215160	−	0.375920i
$369$		0			0
$370$	17207.1	+	22381.2i	0.125691	+	0.163486i
$371$	−234645.	−	135473.i	−1.70476	−	0.984246i
$372$		0			0
$373$	36777.2	+	63699.9i	0.264339	+	0.457848i	0.967390	−	0.253291i	$-0.0815130\pi$
$373$	36777.2	+	63699.9i	0.264339	+	0.457848i	−0.703052	+	0.711139i	$0.748180\pi$
$374$	−22950.4	−	9481.14i	−0.164077	−	0.0677825i
$375$		0			0
$376$	−77870.8	−	10028.9i	−0.550807	−	0.0709376i
$377$	−152687.			−1.07428
$378$		0			0
$379$			139070.i			0.968176i	0.875019	+	0.484088i	$0.160848\pi$
$379$			139070.i			0.968176i	−0.875019	+	0.484088i	$0.839152\pi$
$380$	80970.4	−	81275.0i	0.560737	−	0.562846i
$381$		0			0
$382$	212587.	+	87822.8i	1.45683	+	0.601839i
$383$	−90000.3	+	51961.7i	−0.613545	+	0.354230i	−0.774352	−	0.632756i	$-0.781924\pi$
$383$	−90000.3	+	51961.7i	−0.613545	+	0.354230i	0.160807	+	0.986986i	$0.448590\pi$
$384$		0			0
$385$	23152.6	−	40101.5i	0.156199	−	0.270545i
$386$	109569.	+	142515.i	0.735380	+	0.956505i
$387$		0			0
$388$	−24003.7	+	90260.7i	−0.159447	+	0.599563i
$389$	−50040.9	+	86673.4i	−0.330694	+	0.572778i	−0.982648	−	0.185480i	$-0.940616\pi$
$389$	−50040.9	+	86673.4i	−0.330694	+	0.572778i	0.651954	+	0.758258i	$0.273949\pi$
$390$		0			0
$391$	56328.2	−	32521.1i	0.368444	−	0.212721i
$392$	342836.	+	261537.i	2.23108	+	1.70200i
$393$		0			0
$394$	176514.	−	23407.1i	1.13707	−	0.150784i
$395$			159295.i			1.02096i
$396$		0			0
$397$	164388.			1.04301			0.521507	−	0.853247i	$-0.325370\pi$
$397$	164388.			1.04301			0.521507	+	0.853247i	$0.325370\pi$
$398$	10025.9	+	75605.6i	0.0632931	+	0.477296i
$399$		0			0
$400$	−129.207	−	34410.5i	−0.000807546	−	0.215066i
$401$	−78226.6	−	135492.i	−0.486481	−	0.842609i	0.513399	−	0.858150i	$-0.328386\pi$
$401$	−78226.6	−	135492.i	−0.486481	−	0.842609i	−0.999879	+	0.0155412i	$0.995053\pi$
$402$		0			0
$403$	90700.6	+	52366.0i	0.558470	+	0.322433i
$404$	−22612.3	+	85028.6i	−0.138542	+	0.520958i
$405$		0			0
$406$	−366699.	+	281926.i	−2.22463	+	1.71034i
$407$	6035.02	+	3484.32i	0.0364325	+	0.0210343i
$408$		0			0
$409$	−135351.	−	234435.i	−0.809125	−	1.40145i	−0.913471	−	0.406904i	$-0.866608\pi$
$409$	−135351.	−	234435.i	−0.809125	−	1.40145i	0.104346	−	0.994541i	$-0.466725\pi$
$410$	11123.7	−	26926.6i	0.0661734	−	0.160182i
$411$		0			0
$412$	202510.	−	203272.i	1.19303	−	1.19752i
$413$	−141086.			−0.827149
$414$		0			0
$415$		−	73589.9i		−	0.427290i
$416$	−119646.	−	48902.4i	−0.691372	−	0.282581i
$417$		0			0
$418$	10812.6	−	26173.4i	0.0618839	−	0.149799i
$419$	−49366.2	+	28501.6i	−0.281191	+	0.162346i	−0.633963	−	0.773364i	$-0.718573\pi$
$419$	−49366.2	+	28501.6i	−0.281191	+	0.162346i	0.352771	+	0.935710i	$0.385239\pi$
$420$		0			0
$421$	−116812.	+	202325.i	−0.659059	+	1.14152i	0.321801	+	0.946807i	$0.395712\pi$
$421$	−116812.	+	202325.i	−0.659059	+	1.14152i	−0.980860	+	0.194716i	$0.937621\pi$
$422$	3021.82	−	2323.24i	0.0169685	−	0.0130457i
$423$		0			0
$424$	167390.	−	69888.0i	0.931101	−	0.388750i
$425$	19078.1	−	33044.3i	0.105623	−	0.182944i
$426$		0			0
$427$	−155010.	+	89495.0i	−0.850166	+	0.490843i
$428$	−36343.2	−	134623.i	−0.198397	−	0.734908i
$429$		0			0
$430$	−2411.77	−	18187.2i	−0.0130436	−	0.0983626i
$431$		−	333180.i		−	1.79360i	−0.442439	−	0.896798i	$-0.645887\pi$
$431$		−	333180.i		−	1.79360i	0.442439	−	0.896798i	$-0.354113\pi$
$432$		0			0
$433$	−215343.			−1.14856			−0.574282	−	0.818657i	$-0.694719\pi$
$433$	−215343.			−1.14856			−0.574282	+	0.818657i	$0.694719\pi$
$434$	314521.	−	41707.8i	1.66982	−	0.221431i
$435$		0			0
$436$	−187868.	+	50717.3i	−0.988280	+	0.266799i
$437$	37088.1	+	64238.5i	0.194210	+	0.336382i
$438$		0			0
$439$	27053.2	+	15619.2i	0.140375	+	0.0810455i	0.568543	−	0.822654i	$-0.307507\pi$
$439$	27053.2	+	15619.2i	0.140375	+	0.0810455i	−0.428168	+	0.903699i	$0.640841\pi$
$440$	11944.0	+	28607.3i	0.0616944	+	0.147765i
$441$		0			0
$442$	−87356.3	−	113624.i	−0.447146	−	0.581601i
$443$	184829.	+	106711.i	0.941809	+	0.543754i	0.890527	−	0.454930i	$-0.150336\pi$
$443$	184829.	+	106711.i	0.941809	+	0.543754i	0.0512822	+	0.998684i	$0.483669\pi$
$444$		0			0
$445$	−17163.9	−	29728.8i	−0.0866755	−	0.150126i
$446$	−160234.	−	66195.0i	−0.805536	−	0.332779i
$447$		0			0
$448$	−377642.	+	103472.i	−1.88159	+	0.515546i
$449$	393053.			1.94966			0.974828	−	0.222956i	$-0.0715707\pi$
$449$	393053.			1.94966			0.974828	+	0.222956i	$0.0715707\pi$
$450$		0			0
$451$		−	7191.43i		−	0.0353559i
$452$	−232065.	−	231195.i	−1.13588	−	1.13162i
$453$		0			0
$454$	22209.5	+	9175.06i	0.107752	+	0.0445141i
$455$	231457.	−	133632.i	1.11802	−	0.645487i
$456$		0			0
$457$	36178.7	−	62663.4i	0.173229	−	0.300042i	−0.766318	−	0.642462i	$-0.777913\pi$
$457$	36178.7	−	62663.4i	0.173229	−	0.300042i	0.939547	+	0.342420i	$0.111247\pi$
$458$	9938.23	+	12926.6i	0.0473782	+	0.0616246i
$459$		0			0
$460$	−78473.1	−	20869.0i	−0.370856	−	0.0986246i
$461$	29095.9	−	50395.5i	0.136908	−	0.237132i	−0.789417	−	0.613858i	$-0.789617\pi$
$461$	29095.9	−	50395.5i	0.136908	−	0.237132i	0.926325	+	0.376726i	$0.122950\pi$
$462$		0			0
$463$	−64721.6	+	37367.0i	−0.301917	+	0.174312i	−0.643304	−	0.765611i	$-0.722437\pi$
$463$	−64721.6	+	37367.0i	−0.301917	+	0.174312i	0.341387	+	0.939923i	$0.389103\pi$
$464$	−1162.76	−	309666.i	−0.00540075	−	1.43833i
$465$		0			0
$466$	148411.	−	19680.5i	0.683431	−	0.0906282i
$467$			264366.i			1.21219i	0.795392	+	0.606096i	$0.207265\pi$
$467$			264366.i			1.21219i	−0.795392	+	0.606096i	$0.792735\pi$
$468$		0			0
$469$	23695.5			0.107726
$470$	14287.8	+	107745.i	0.0646801	+	0.487756i
$471$		0			0
$472$	57289.3	−	75097.8i	0.257152	−	0.337088i
$473$	−2264.33	−	3921.94i	−0.0101209	−	0.0175299i
$474$		0			0
$475$	37684.8	+	21757.3i	0.167024	+	0.0964314i
$476$	−419597.	−	111587.i	−1.85191	−	0.492492i
$477$		0			0
$478$	81334.9	−	62531.9i	0.355976	−	0.273682i
$479$	242211.	+	139840.i	1.05566	+	0.609483i	0.924228	−	0.381842i	$-0.124710\pi$
$479$	242211.	+	139840.i	1.05566	+	0.609483i	0.131429	+	0.991326i	$0.458044\pi$
$480$		0			0
$481$	20110.7	+	34832.8i	0.0869236	+	0.150556i
$482$	−116991.	+	283193.i	−0.503568	+	1.21896i
$483$		0			0
$484$	−160534.	−	159932.i	−0.685291	−	0.682723i
$485$	129293.			0.549655
$486$		0			0
$487$			62506.3i			0.263552i	0.991280	+	0.131776i	$0.0420679\pi$
$487$			62506.3i			0.263552i	−0.991280	+	0.131776i	$0.957932\pi$
$488$	15306.5	−	118849.i	0.0642739	−	0.499065i
$489$		0			0
$490$	227916.	−	551702.i	0.949254	−	2.29780i
$491$	−291742.	+	168437.i	−1.21014	+	0.698674i	−0.962790	−	0.270252i	$-0.912893\pi$
$491$	−291742.	+	168437.i	−1.21014	+	0.698674i	−0.247350	+	0.968926i	$0.579560\pi$
$492$		0			0
$493$	171688.	−	297372.i	0.706391	−	1.22351i
$494$	129580.	−	99624.0i	0.530989	−	0.408235i
$495$		0			0
$496$	−105514.	+	184350.i	−0.428889	+	0.749342i
$497$	205927.	−	356676.i	0.833682	−	1.44398i
$498$		0			0
$499$	−276635.	+	159715.i	−1.11098	+	0.641424i	−0.939083	−	0.343691i	$-0.888323\pi$
$499$	−276635.	+	159715.i	−1.11098	+	0.641424i	−0.171896	+	0.985115i	$0.554989\pi$
$500$	−259825.	+	70143.0i	−1.03930	+	0.280572i
$501$		0			0
$502$	35042.5	+	264257.i	0.139055	+	1.04862i
$503$			28287.7i			0.111805i	0.998436	+	0.0559025i	$0.0178036\pi$
$503$			28287.7i			0.111805i	−0.998436	+	0.0559025i	$0.982196\pi$
$504$		0			0
$505$	121798.			0.477592
$506$	−19869.7	+	2634.88i	−0.0776053	+	0.0102910i
$507$		0			0
$508$	−33904.8	−	125591.i	−0.131381	−	0.486665i
$509$	47278.6	+	81888.9i	0.182486	+	0.316074i	0.942726	−	0.333567i	$-0.108252\pi$
$509$	47278.6	+	81888.9i	0.182486	+	0.316074i	−0.760241	+	0.649641i	$0.774919\pi$
$510$		0			0
$511$	−249255.	−	143908.i	−0.954559	−	0.551115i
$512$	98268.5	−	243028.i	0.374865	−	0.927080i
$513$		0			0
$514$	144883.	+	188449.i	0.548392	+	0.713291i
$515$	−343990.	−	198603.i	−1.29698	−	0.748809i
$516$		0			0
$517$	13414.4	+	23234.4i	0.0501869	+	0.0869263i
$518$	112615.	+	46522.9i	0.419698	+	0.173383i
$519$		0			0
$520$	−22855.2	+	177463.i	−0.0845238	+	0.656299i
$521$	−369932.			−1.36285			−0.681423	−	0.731890i	$-0.738638\pi$
$521$	−369932.			−1.36285			−0.681423	+	0.731890i	$0.738638\pi$
$522$		0			0
$523$		−	65267.4i		−	0.238612i	−0.992858	−	0.119306i	$-0.961933\pi$
$523$		−	65267.4i		−	0.238612i	0.992858	−	0.119306i	$-0.0380670\pi$
$524$	−183791.	+	184483.i	−0.669364	+	0.671882i
$525$		0			0
$526$	−92942.5	−	38395.9i	−0.335925	−	0.138776i
$527$	−203975.	+	117765.i	−0.734440	+	0.424029i
$528$		0			0
$529$	−113670.	+	196882.i	−0.406195	+	0.703551i
$530$	−153051.	−	199073.i	−0.544859	−	0.708696i
$531$		0			0
$532$	127257.	−	478523.i	0.449634	−	1.69075i
$533$	20753.7	−	35946.4i	0.0730534	−	0.126532i
$534$		0			0
$535$	−167172.	+	96516.6i	−0.584057	+	0.337205i
$536$	−9621.76	+	12612.7i	−0.0334907	+	0.0439014i
$537$		0			0
$538$	−10125.2	+	1342.68i	−0.0349815	+	0.00463882i
$539$		−	147346.i		−	0.507179i
$540$		0			0
$541$	176002.			0.601343			0.300671	−	0.953728i	$-0.402789\pi$
$541$	176002.			0.601343			0.300671	+	0.953728i	$0.402789\pi$
$542$	−2430.96	−	18331.9i	−0.00827520	−	0.0624036i
$543$		0			0
$544$	229777.	−	178034.i	0.776442	−	0.601596i
$545$	134690.	+	233290.i	0.453463	+	0.785421i
$546$		0			0
$547$	236509.	+	136549.i	0.790448	+	0.456365i	0.840120	−	0.542400i	$-0.182484\pi$
$547$	236509.	+	136549.i	0.790448	+	0.456365i	−0.0496725	+	0.998766i	$0.515818\pi$
$548$	101416.	−	381351.i	0.337710	−	1.26988i
$549$		0			0
$550$	−9321.85	+	7166.82i	−0.0308160	+	0.0236920i
$551$	339133.	+	195798.i	1.11703	+	0.644920i
$552$		0			0
$553$	343760.	+	595409.i	1.12410	+	1.94700i
$554$	15050.2	−	36431.2i	0.0490370	−	0.118701i
$555$		0			0
$556$	222688.	−	223526.i	0.720356	−	0.723066i
$557$	454335.			1.46442			0.732211	−	0.681078i	$-0.238489\pi$
$557$	454335.			1.46442			0.732211	+	0.681078i	$0.238489\pi$
$558$		0			0
$559$		−	26138.5i		−	0.0836482i
$560$	272783.	+	468404.i	0.869845	+	1.49364i
$561$		0			0
$562$	−73945.8	+	178996.i	−0.234121	+	0.566723i
$563$	−27753.2	+	16023.3i	−0.0875582	+	0.0505518i	−0.543140	−	0.839642i	$-0.682765\pi$
$563$	−27753.2	+	16023.3i	−0.0875582	+	0.0505518i	0.455582	+	0.890194i	$0.349431\pi$
$564$		0			0
$565$	−226734.	+	392714.i	−0.710263	+	1.23021i
$566$	−419318.	+	322380.i	−1.30891	+	1.00632i
$567$		0			0
$568$	106234.	+	254443.i	0.329282	+	0.788667i
$569$	−138564.	+	240000.i	−0.427982	+	0.741287i	−0.996694	−	0.0812502i	$-0.974109\pi$
$569$	−138564.	+	240000.i	−0.427982	+	0.741287i	0.568712	+	0.822537i	$0.307442\pi$
$570$		0			0
$571$	556449.	−	321266.i	1.70668	−	0.985355i	0.768085	−	0.640348i	$-0.221210\pi$
$571$	556449.	−	321266.i	1.70668	−	0.985355i	0.938600	−	0.345007i	$-0.112123\pi$
$572$	11511.4	+	42640.6i	0.0351831	+	0.130326i
$573$		0			0
$574$	−16529.6	−	124651.i	−0.0501694	−	0.378330i
$575$		−	30799.0i		−	0.0931540i
$576$		0			0
$577$	451002.			1.35465			0.677324	−	0.735685i	$-0.263140\pi$
$577$	451002.			1.35465			0.677324	+	0.735685i	$0.263140\pi$
$578$	−11664.5	+	1546.80i	−0.0349148	+	0.00462997i
$579$		0			0
$580$	−413864.	+	111728.i	−1.23027	+	0.332128i
$581$	−158808.	−	275063.i	−0.470456	−	0.814854i
$582$		0			0
$583$	−53679.3	−	30991.8i	−0.157932	−	0.0911820i
$584$	177812.	−	74239.5i	0.521357	−	0.217675i
$585$		0			0
$586$	−218250.	−	283876.i	−0.635563	−	0.826674i
$587$	327761.	+	189233.i	0.951221	+	0.549188i	0.893460	−	0.449143i	$-0.148271\pi$
$587$	327761.	+	189233.i	0.951221	+	0.549188i	0.0577610	+	0.998330i	$0.481604\pi$
$588$		0			0
$589$	−134303.	−	232620.i	−0.387129	−	0.670528i
$590$	−120850.	−	49924.6i	−0.347169	−	0.143420i
$591$		0			0
$592$	−70491.8	+	41052.1i	−0.201138	+	0.117136i
$593$	−137966.			−0.392339			−0.196170	−	0.980570i	$-0.562850\pi$
$593$	−137966.			−0.392339			−0.196170	+	0.980570i	$0.562850\pi$
$594$		0			0
$595$			601046.i			1.69775i
$596$	338750.	+	337480.i	0.953644	+	0.950070i
$597$		0			0
$598$	−106923.	−	44171.4i	−0.298998	−	0.123521i
$599$	180870.	−	104426.i	0.504096	−	0.291040i	−0.226307	−	0.974056i	$-0.572665\pi$
$599$	180870.	−	104426.i	0.504096	−	0.291040i	0.730404	+	0.683016i	$0.239332\pi$
$600$		0			0
$601$	−180004.	+	311775.i	−0.498348	+	0.863163i	−0.999998	−	0.00190701i	$-0.999393\pi$
$601$	−180004.	+	311775.i	−0.498348	+	0.863163i	0.501651	+	0.865070i	$0.332726\pi$
$602$	−48262.9	−	62775.3i	−0.133174	−	0.173219i
$603$		0			0
$604$	−92203.3	−	24520.4i	−0.252739	−	0.0672130i
$605$	−156846.	+	271665.i	−0.428512	+	0.742204i
$606$		0			0
$607$	279709.	−	161490.i	0.759152	−	0.438297i	−0.0698392	−	0.997558i	$-0.522249\pi$
$607$	279709.	−	161490.i	0.759152	−	0.438297i	0.828991	+	0.559262i	$0.188915\pi$
$608$	203036.	+	262045.i	0.549244	+	0.708875i
$609$		0			0
$610$	−164445.	+	21806.6i	−0.441937	+	0.0586042i
$611$			154850.i			0.414791i
$612$		0			0
$613$	−392554.			−1.04467			−0.522334	−	0.852741i	$-0.674939\pi$
$613$	−392554.			−1.04467			−0.522334	+	0.852741i	$0.674939\pi$
$614$	32983.5	+	248730.i	0.0874904	+	0.659769i
$615$		0			0
$616$	106379.	+	81152.6i	0.280346	+	0.213866i
$617$	192102.	+	332730.i	0.504616	+	0.874020i	0.999986	+	0.00533786i	$0.00169910\pi$
$617$	192102.	+	332730.i	0.504616	+	0.874020i	−0.495370	+	0.868682i	$0.664968\pi$
$618$		0			0
$619$	−602573.	−	347896.i	−1.57264	−	0.907962i	−0.995844	−	0.0910712i	$-0.970971\pi$
$619$	−602573.	−	347896.i	−1.57264	−	0.907962i	−0.576792	−	0.816891i	$-0.695696\pi$
$620$	284166.	+	75570.6i	0.739247	+	0.196594i
$621$		0			0
$622$	389360.	−	299347.i	1.00640	−	0.773739i
$623$	−128310.	−	74079.7i	−0.330586	−	0.190864i
$624$		0			0
$625$	144273.	+	249889.i	0.369339	+	0.639715i
$626$	74208.4	−	179632.i	0.189367	−	0.458389i
$627$		0			0
$628$	396575.	+	395089.i	1.00556	+	1.00179i
$629$	−90453.5			−0.228625
$630$		0			0
$631$			230753.i			0.579546i	0.957095	+	0.289773i	$0.0935798\pi$
$631$			230753.i			0.579546i	−0.957095	+	0.289773i	$0.906420\pi$
$632$	−456513.	−	58793.7i	−1.14293	−	0.147196i
$633$		0			0
$634$	−168203.	+	407158.i	−0.418461	+	1.01294i
$635$	−155955.	+	90040.8i	−0.386770	+	0.223302i
$636$		0			0
$637$	425225.	−	736511.i	1.04795	−	1.81510i
$638$	−83889.0	+	64495.5i	−0.206093	+	0.158449i
$639$		0			0
$640$	−360090.	−	45001.6i	−0.879126	−	0.109867i
$641$	259471.	−	449416.i	0.631498	−	1.09379i	−0.355747	−	0.934582i	$-0.615774\pi$
$641$	259471.	−	449416.i	0.631498	−	1.09379i	0.987246	−	0.159205i	$-0.0508931\pi$
$642$		0			0
$643$	−195039.	+	112606.i	−0.471738	+	0.272358i	−0.716967	−	0.697107i	$-0.754470\pi$
$643$	−195039.	+	112606.i	−0.471738	+	0.272358i	0.245229	+	0.969465i	$0.421137\pi$
$644$	−338351.	+	91341.9i	−0.815821	+	0.220241i
$645$		0			0
$646$	48321.1	+	364392.i	0.115790	+	0.873179i
$647$			153505.i			0.366703i	0.983047	+	0.183352i	$0.0586947\pi$
$647$			153505.i			0.366703i	−0.983047	+	0.183352i	$0.941305\pi$
$648$		0			0
$649$	−32276.0			−0.0766284
$650$	−67278.0	+	8921.58i	−0.159238	+	0.0211162i
$651$		0			0
$652$	60507.5	+	224133.i	0.142336	+	0.527243i
$653$	36120.4	+	62562.3i	0.0847082	+	0.146719i	0.905267	−	0.424843i	$-0.139671\pi$
$653$	36120.4	+	62562.3i	0.0847082	+	0.146719i	−0.820559	+	0.571562i	$0.806338\pi$
$654$		0			0
$655$	312193.	+	180245.i	0.727681	+	0.420127i
$656$	73061.5	+	41817.1i	0.169778	+	0.0971731i
$657$		0			0
$658$	285920.	+	371895.i	0.660378	+	0.858950i
$659$	−203157.	−	117293.i	−0.467802	−	0.270086i	0.247517	−	0.968883i	$-0.420385\pi$
$659$	−203157.	−	117293.i	−0.467802	−	0.270086i	−0.715319	+	0.698798i	$0.753719\pi$
$660$		0			0
$661$	−298973.	−	517837.i	−0.684274	−	1.18520i	−0.973665	−	0.227986i	$-0.926786\pi$
$661$	−298973.	−	517837.i	−0.684274	−	1.18520i	0.289391	−	0.957211i	$-0.406547\pi$
$662$	682164.	+	281812.i	1.55659	+	0.643048i
$663$		0			0
$664$	210897.	+	27161.1i	0.478337	+	0.0616043i
$665$	−685452.			−1.55001
$666$		0			0
$667$		−	277166.i		−	0.623001i
$668$	503844.	−	505739.i	1.12913	−	1.13338i
$669$		0			0
$670$	20296.7	+	8384.87i	0.0452144	+	0.0186787i
$671$	−35461.3	+	20473.6i	−0.0787607	+	0.0454725i
$672$		0			0
$673$	375852.	−	650996.i	0.829826	−	1.43730i	−0.0683477	−	0.997662i	$-0.521773\pi$
$673$	375852.	−	650996.i	0.829826	−	1.43730i	0.898174	−	0.439640i	$-0.144894\pi$
$674$	−159998.	−	208109.i	−0.352204	−	0.458111i
$675$		0			0
$676$	51928.7	−	195266.i	0.113636	−	0.427301i
$677$	−42323.8	+	73307.0i	−0.0923437	+	0.159944i	−0.908497	−	0.417892i	$-0.862769\pi$
$677$	−42323.8	+	73307.0i	−0.0923437	+	0.159944i	0.816153	+	0.577836i	$0.196103\pi$
$678$		0			0
$679$	483267.	−	279014.i	1.04821	−	0.605183i
$680$	−319927.	−	244060.i	−0.691883	−	0.527812i
$681$		0			0
$682$	71952.2	−	9541.41i	0.154695	−	0.0205137i
$683$		−	635506.i		−	1.36232i	−0.732136	−	0.681159i	$-0.761476\pi$
$683$		−	635506.i		−	1.36232i	0.732136	−	0.681159i	$-0.238524\pi$
$684$		0			0
$685$	−546260.			−1.16418
$686$	−217987.	−	1.64385e6i	−0.463214	−	3.49312i
$687$		0			0
$688$	53011.8	−	199.053i	0.111994	−	0.000420525i
$689$	−178878.	−	309825.i	−0.376806	−	0.652647i
$690$		0			0
$691$	−384843.	−	222189.i	−0.805986	−	0.465336i	0.0395741	−	0.999217i	$-0.487400\pi$
$691$	−384843.	−	222189.i	−0.805986	−	0.465336i	−0.845560	+	0.533881i	$0.820733\pi$
$692$	−217474.	+	817762.i	−0.454145	+	1.70771i
$693$		0			0
$694$	332553.	−	255673.i	0.690466	−	0.530844i
$695$	−378265.	−	218391.i	−0.783116	−	0.452132i
$696$		0			0
$697$	46672.6	+	80839.4i	0.0960720	+	0.166402i
$698$	−133397.	+	322906.i	−0.273802	+	0.662775i
$699$		0			0
$700$	−145105.	+	145651.i	−0.296132	+	0.297246i
$701$	374624.			0.762359			0.381179	−	0.924501i	$-0.375518\pi$
$701$	374624.			0.762359			0.381179	+	0.924501i	$0.375518\pi$
$702$		0			0
$703$		−	103156.i		−	0.208730i
$704$	−86392.4	+	23671.1i	−0.174313	+	0.0477609i
$705$		0			0
$706$	−74390.9	+	180073.i	−0.149249	+	0.361277i
$707$	455254.	−	262841.i	0.910783	−	0.525841i
$708$		0			0
$709$	−92815.5	+	160761.i	−0.184641	+	0.319808i	−0.943456	−	0.331499i	$-0.892446\pi$
$709$	−92815.5	+	160761.i	−0.184641	+	0.319808i	0.758814	+	0.651307i	$0.225779\pi$
$710$	302603.	−	232647.i	0.600284	−	0.461510i
$711$		0			0
$712$	91532.8	−	38216.5i	0.180558	−	0.0753860i
$713$	−95057.9	+	164645.i	−0.186986	+	0.323869i
$714$		0			0
$715$	52950.0	−	30570.7i	0.103575	−	0.0597989i
$716$	−136950.	−	507293.i	−0.267138	−	0.989539i
$717$		0			0
$718$	−57530.0	−	433836.i	−0.111595	−	0.841544i
$719$		−	651163.i		−	1.25960i	−0.776759	−	0.629799i	$-0.783137\pi$
$719$		−	651163.i		−	1.25960i	0.776759	−	0.629799i	$-0.216863\pi$
$720$		0			0
$721$	−1.71435e6			−3.29783
$722$	101196.	−	13419.4i	0.194129	−	0.0257429i
$723$		0			0
$724$	−351552.	+	94905.9i	−0.670676	+	0.181057i
$725$	−81298.3	−	140813.i	−0.154670	−	0.267896i
$726$		0			0
$727$	−207917.	−	120041.i	−0.393389	−	0.227123i	0.290239	−	0.956954i	$-0.406265\pi$
$727$	−207917.	−	120041.i	−0.393389	−	0.227123i	−0.683627	+	0.729831i	$0.739599\pi$
$728$	297539.	+	712640.i	0.561412	+	1.34465i
$729$		0			0
$730$	−162581.	−	211468.i	−0.305086	−	0.396825i
$731$	50907.1	+	29391.2i	0.0952673	+	0.0550026i
$732$		0			0
$733$	27840.0	+	48220.4i	0.0518158	+	0.0897475i	0.890770	−	0.454455i	$-0.150166\pi$
$733$	27840.0	+	48220.4i	0.0518158	+	0.0897475i	−0.838954	+	0.544202i	$0.816832\pi$
$734$	−4750.49	−	1962.49i	−0.00881752	−	0.00364264i
$735$		0			0
$736$	88770.5	−	217189.i	0.163875	−	0.400942i
$737$	5420.76			0.00997988
$738$		0			0
$739$		−	327859.i		−	0.600341i	−0.953886	−	0.300170i	$-0.902957\pi$
$739$		−	327859.i		−	0.600341i	0.953886	−	0.300170i	$-0.0970435\pi$
$740$	79999.7	+	79699.9i	0.146091	+	0.145544i
$741$		0			0
$742$	−1.00167e6	−	413805.i	−1.81936	−	0.751602i
$743$	−11150.8	+	6437.91i	−0.0201989	+	0.0116618i	−0.510065	−	0.860136i	$-0.670379\pi$
$743$	−11150.8	+	6437.91i	−0.0201989	+	0.0116618i	0.489867	+	0.871797i	$0.337045\pi$
$744$		0			0
$745$	330968.	−	573254.i	0.596312	−	1.03284i
$746$	179327.	+	233250.i	0.322232	+	0.419126i
$747$		0			0
$748$	−95990.4	−	25527.5i	−0.171563	−	0.0456252i
$749$	−416567.	+	721516.i	−0.742543	+	1.28612i
$750$		0			0
$751$	−460430.	+	265829.i	−0.816363	+	0.471328i	−0.849161	−	0.528134i	$-0.822892\pi$
$751$	−460430.	+	265829.i	−0.816363	+	0.471328i	0.0327975	+	0.999462i	$0.489558\pi$
$752$	−314054.	+	1179.23i	−0.555352	+	0.00208528i
$753$		0			0
$754$	−605447.	+	80286.9i	−1.06496	+	0.141222i
$755$			132075.i			0.231701i
$756$		0			0
$757$	614542.			1.07241			0.536204	−	0.844089i	$-0.319858\pi$
$757$	614542.			1.07241			0.536204	+	0.844089i	$0.319858\pi$
$758$	73126.6	+	551451.i	0.127273	+	0.959774i
$759$		0			0
$760$	278334.	−	364855.i	0.481880	−	0.631674i
$761$	−410349.	−	710745.i	−0.708571	−	1.22728i	−0.965387	−	0.260821i	$-0.916007\pi$
$761$	−410349.	−	710745.i	−0.708571	−	1.22728i	0.256816	−	0.966460i	$-0.417327\pi$
$762$		0			0
$763$	1.00688e6	+	581324.i	1.72954	+	0.998548i
$764$	889149.	+	236458.i	1.52331	+	0.405105i
$765$		0			0
$766$	−329554.	+	253368.i	−0.561654	+	0.431811i
$767$	−161332.	−	93144.9i	−0.274239	−	0.158332i
$768$		0			0
$769$	65721.6	+	113833.i	0.111136	+	0.192494i	0.916229	−	0.400656i	$-0.131218\pi$
$769$	65721.6	+	113833.i	0.111136	+	0.192494i	−0.805092	+	0.593149i	$0.797884\pi$
$770$	70720.3	−	171188.i	0.119279	−	0.288730i
$771$		0			0
$772$	509410.	+	507500.i	0.854737	+	0.851534i
$773$	629.598			0.00105367			0.000526834	−	1.00000i	$-0.499832\pi$
$773$	629.598			0.00105367			0.000526834		1.00000i	$0.499832\pi$
$774$		0			0
$775$			111529.i			0.185689i
$776$	−47720.2	+	370531.i	−0.0792463	+	0.615321i
$777$		0			0
$778$	−152851.	+	369998.i	−0.252528	+	0.611280i
$779$	−92191.9	+	53227.0i	−0.151921	+	0.0877117i
$780$		0			0
$781$	47109.5	−	81596.0i	0.0772336	−	0.133773i
$782$	206257.	−	158574.i	0.337283	−	0.259310i
$783$		0			0
$784$	1.49697e6	+	856796.i	2.43545	+	1.39394i
$785$	387466.	−	671110.i	0.628773	−	1.08907i
$786$		0			0
$787$	415038.	−	239622.i	0.670098	−	0.386881i	−0.126016	−	0.992028i	$-0.540219\pi$
$787$	415038.	−	239622.i	0.670098	−	0.386881i	0.796114	+	0.605147i	$0.206886\pi$
$788$	687619.	−	185631.i	1.10738	−	0.298950i
$789$		0			0
$790$	83761.6	+	631650.i	0.134212	+	1.01210i
$791$			1.95717e6i			3.12807i
$792$		0			0
$793$	−236338.			−0.375826
$794$	651847.	−	86439.9i	1.03396	−	0.137111i
$795$		0			0
$796$	79511.0	+	294526.i	0.125488	+	0.464834i
$797$	−344008.	−	595840.i	−0.541567	−	0.938021i	−0.998814	−	0.0486819i	$-0.984498\pi$
$797$	−344008.	−	595840.i	−0.541567	−	0.938021i	0.457247	−	0.889340i	$-0.348835\pi$
$798$		0			0
$799$	−301585.	−	174120.i	−0.472407	−	0.272744i
$800$	−18606.3	−	136380.i	−0.0290724	−	0.213093i
$801$		0			0
$802$	−381436.	−	496133.i	−0.593026	−	0.771346i
$803$	−57021.6	−	32921.5i	−0.0884318	−	0.0510561i
$804$		0			0
$805$	242576.	+	420155.i	0.374332	+	0.648362i
$806$	387189.	+	159953.i	0.596010	+	0.246220i
$807$		0			0
$808$	−44954.1	+	349053.i	−0.0688567	+	0.534649i
$809$	423910.			0.647703			0.323852	−	0.946108i	$-0.395022\pi$
$809$	423910.			0.647703			0.323852	+	0.946108i	$0.395022\pi$
$810$		0			0
$811$			257508.i			0.391515i	0.980652	+	0.195757i	$0.0627165\pi$
$811$			257508.i			0.391515i	−0.980652	+	0.195757i	$0.937283\pi$
$812$	−1.30582e6	+	1.31074e6i	−1.98049	+	1.98794i
$813$		0			0
$814$	25762.7	+	10642.9i	0.0388815	+	0.0160625i
$815$	278323.	−	160690.i	0.419019	−	0.241921i
$816$		0			0
$817$	−33518.7	+	58056.2i	−0.0502162	+	0.0869770i
$818$	−659979.	−	858432.i	−0.986333	−	1.28292i
$819$		0			0
$820$	29950.1	−	112621.i	0.0445421	−	0.167491i
$821$	−439034.	+	760430.i	−0.651347	+	1.12817i	0.331450	+	0.943473i	$0.392462\pi$
$821$	−439034.	+	760430.i	−0.651347	+	1.12817i	−0.982796	+	0.184692i	$0.940871\pi$
$822$		0			0
$823$	571229.	−	329799.i	0.843355	−	0.486911i	−0.0150484	−	0.999887i	$-0.504790\pi$
$823$	571229.	−	329799.i	0.843355	−	0.486911i	0.858403	+	0.512976i	$0.171457\pi$
$824$	696126.	−	912519.i	1.02526	−	1.34396i
$825$		0			0
$826$	−559447.	+	74186.9i	−0.819971	+	0.108734i
$827$		−	853638.i		−	1.24814i	−0.781369	−	0.624069i	$-0.785478\pi$
$827$		−	853638.i		−	1.24814i	0.781369	−	0.624069i	$-0.214522\pi$
$828$		0			0
$829$	542017.			0.788685			0.394343	−	0.918963i	$-0.370972\pi$
$829$	542017.			0.788685			0.394343	+	0.918963i	$0.370972\pi$
$830$	−38695.6	−	291805.i	−0.0561701	−	0.423581i
$831$		0			0
$832$	−500145.	−	130999.i	−0.722519	−	0.189243i
$833$	956282.	+	1.65633e6i	1.37815	+	2.38702i
$834$		0			0
$835$	−855844.	−	494122.i	−1.22750	−	0.708698i
$836$	29112.4	−	109471.i	0.0416548	−	0.156634i
$837$		0			0
$838$	−180764.	+	138975.i	−0.257410	+	0.197901i
$839$	−1.01749e6	−	587450.i	−1.44547	−	0.834540i	−0.447259	−	0.894404i	$-0.647600\pi$
$839$	−1.01749e6	−	587450.i	−1.44547	−	0.834540i	−0.998207	+	0.0598644i	$0.980933\pi$
$840$		0			0
$841$	−377978.	−	654677.i	−0.534410	−	0.925625i
$842$	−356806.	+	863699.i	−0.503278	+	1.21826i
$843$		0			0
$844$	10760.8	−	10801.3i	0.0151063	−	0.0151632i
$845$	−279706.			−0.391732
$846$		0			0
$847$			1.35390e6i			1.88721i
$848$	626999.	−	365144.i	0.871917	−	0.507776i
$849$		0			0
$850$	58274.7	−	141062.i	0.0806570	−	0.195242i
$851$	−63230.5	+	36506.2i	−0.0873108	+	0.0504089i
$852$		0			0
$853$	−587574.	+	1.01771e6i	−0.807541	+	1.39870i	0.107021	+	0.994257i	$0.465869\pi$
$853$	−587574.	+	1.01771e6i	−0.807541	+	1.39870i	−0.914562	+	0.404445i	$0.867465\pi$
$854$	−567600.	+	436382.i	−0.778263	+	0.598344i
$855$		0			0
$856$	−214900.	−	514710.i	−0.293284	−	0.702449i
$857$	447698.	−	775436.i	0.609570	−	1.05581i	−0.381741	−	0.924269i	$-0.624675\pi$
$857$	447698.	−	775436.i	0.609570	−	1.05581i	0.991311	−	0.131538i	$-0.0419914\pi$
$858$		0			0
$859$	918319.	−	530192.i	1.24454	−	0.718533i	0.274521	−	0.961581i	$-0.411481\pi$
$859$	918319.	−	530192.i	1.24454	−	0.718533i	0.970014	+	0.243048i	$0.0781473\pi$
$860$	−19126.7	−	70849.5i	−0.0258609	−	0.0957943i
$861$		0			0
$862$	−175195.	−	1.32116e6i	−0.235781	−	1.77803i
$863$			150213.i			0.201691i	0.994902	+	0.100845i	$0.0321547\pi$
$863$			150213.i			0.201691i	−0.994902	+	0.100845i	$0.967845\pi$
$864$		0			0
$865$	1.17139e6			1.56556
$866$	−853898.	+	113233.i	−1.13860	+	0.150987i
$867$		0			0
$868$	1.22523e6	−	330767.i	1.62622	−	0.439019i
$869$	78641.1	+	136210.i	0.104138	+	0.180373i
$870$		0			0
$871$	27095.7	+	15643.7i	0.0357161	+	0.0206207i
$872$	−718283.	+	299895.i	−0.944631	+	0.394399i
$873$		0			0
$874$	180843.	+	235222.i	0.236744	+	0.307932i
$875$	1.39254e6	+	803981.i	1.81882	+	1.05010i
$876$		0			0
$877$	588870.	+	1.01995e6i	0.765632	+	1.32611i	0.939912	+	0.341418i	$0.110907\pi$
$877$	588870.	+	1.01995e6i	0.765632	+	1.32611i	−0.174280	+	0.984696i	$0.555760\pi$
$878$	115487.	+	47709.2i	0.149811	+	0.0618890i
$879$		0			0
$880$	62404.1	+	107156.i	0.0805838	+	0.138373i
$881$	−1.15136e6			−1.48341			−0.741703	−	0.670728i	$-0.765982\pi$
$881$	−1.15136e6			−1.48341			−0.741703	+	0.670728i	$0.765982\pi$
$882$		0			0
$883$		−	109897.i		−	0.140950i	−0.997514	−	0.0704752i	$-0.977548\pi$
$883$		−	109897.i		−	0.140950i	0.997514	−	0.0704752i	$-0.0224516\pi$
$884$	−406139.	−	404617.i	−0.519721	−	0.517773i
$885$		0			0
$886$	789012.	+	325952.i	1.00512	+	0.415228i
$887$	856444.	−	494468.i	1.08856	−	0.628480i	0.155366	−	0.987857i	$-0.450344\pi$
$887$	856444.	−	494468.i	1.08856	−	0.628480i	0.933192	+	0.359377i	$0.117011\pi$
$888$		0			0
$889$	−388618.	+	673105.i	−0.491721	+	0.851686i
$890$	−83692.1	−	108858.i	−0.105658	−	0.137429i
$891$		0			0
$892$	−670181.	−	178227.i	−0.842292	−	0.223997i
$893$	198572.	−	343937.i	0.249009	−	0.431297i
$894$		0			0
$895$	−629943.	+	363698.i	−0.786421	+	0.454040i
$896$	−1.44305e6	+	608871.i	−1.79749	+	0.758419i
$897$		0			0
$898$	1.55857e6	−	206678.i	1.93274	−	0.256296i
$899$			1.00367e6i			1.24186i
$900$		0			0
$901$	804551.			0.991070
$902$	−3781.45	−	28516.1i	−0.00464777	−	0.0350491i
$903$		0			0
$904$	−1.04177e6	−	794728.i	−1.27478	−	0.972482i
$905$	252041.	+	436548.i	0.307733	+	0.533010i
$906$		0			0
$907$	−445673.	−	257309.i	−0.541753	−	0.312781i	0.204036	−	0.978963i	$-0.434594\pi$
$907$	−445673.	−	257309.i	−0.541753	−	0.312781i	−0.745789	+	0.666182i	$0.767927\pi$
$908$	92891.5	+	24703.4i	0.112669	+	0.0299630i
$909$		0			0
$910$	847527.	−	651595.i	1.02346	−	0.786856i
$911$	−992039.	−	572754.i	−1.19534	−	0.690131i	−0.235829	−	0.971795i	$-0.575780\pi$
$911$	−992039.	−	572754.i	−1.19534	−	0.690131i	−0.959513	+	0.281664i	$0.909114\pi$
$912$		0			0
$913$	−36330.1	−	62925.6i	−0.0435838	−	0.0754894i
$914$	110509.	−	267502.i	0.132283	−	0.320210i
$915$		0			0
$916$	46205.1	+	46032.0i	0.0550680	+	0.0548616i
$917$	1.55588e6			1.85028
$918$		0			0
$919$		−	329486.i		−	0.390127i	−0.980791	−	0.195063i	$-0.937509\pi$
$919$		−	329486.i		−	0.390127i	0.980791	−	0.195063i	$-0.0624913\pi$
$920$	−322142.	−	41488.2i	−0.380602	−	0.0490172i
$921$		0			0
$922$	88874.2	−	215132.i	0.104548	−	0.253072i
$923$	470954.	−	271906.i	0.552809	−	0.319165i
$924$		0			0
$925$	−21416.0	+	37093.5i	−0.0250296	+	0.0433525i
$926$	−236991.	+	182203.i	−0.276382	+	0.212488i
$927$		0			0
$928$	−167442.	−	1.22731e6i	−0.194432	−	1.42514i
$929$	−453534.	+	785545.i	−0.525507	+	0.910205i	0.474051	+	0.880497i	$0.342791\pi$
$929$	−453534.	+	785545.i	−0.525507	+	0.910205i	−0.999559	+	0.0297082i	$0.990542\pi$
$930$		0			0
$931$	−1.88893e6	+	1.09058e6i	−2.17930	+	1.25822i
$932$	578145.	−	156077.i	0.665587	−	0.179683i
$933$		0			0
$934$	139011.	+	1.04829e6i	0.159351	+	1.20167i
$935$			137500.i			0.157282i
$936$		0			0
$937$	1.29741e6			1.47774			0.738872	−	0.673846i	$-0.235359\pi$
$937$	1.29741e6			1.47774			0.738872	+	0.673846i	$0.235359\pi$
$938$	93959.3	−	12459.7i	0.106791	−	0.0141613i
$939$		0			0
$940$	113311.	+	419728.i	0.128238	+	0.475020i
$941$	54978.4	+	95225.4i	0.0620888	+	0.107541i	0.895399	−	0.445265i	$-0.146890\pi$
$941$	54978.4	+	95225.4i	0.0620888	+	0.107541i	−0.833310	+	0.552806i	$0.813557\pi$
$942$		0			0
$943$	65252.1	+	37673.3i	0.0733788	+	0.0423653i
$944$	187680.	−	327908.i	0.210608	−	0.367967i
$945$		0			0
$946$	−11041.0	−	14361.0i	−0.0123375	−	0.0160473i
$947$	476861.	+	275316.i	0.531730	+	0.306995i	0.741721	−	0.670709i	$-0.234010\pi$
$947$	476861.	+	275316.i	0.531730	+	0.306995i	−0.209990	+	0.977703i	$0.567343\pi$
$948$		0			0
$949$	−190015.	−	329116.i	−0.210987	−	0.365441i
$950$	160872.	+	66458.4i	0.178251	+	0.0736381i
$951$		0			0
$952$	−1.72250e6	−	221838.i	−1.90058	−	0.244772i
$953$	802951.			0.884104			0.442052	−	0.896989i	$-0.354251\pi$
$953$	802951.			0.884104			0.442052	+	0.896989i	$0.354251\pi$
$954$		0			0
$955$		−	1.27365e6i		−	1.39650i
$956$	289635.	−	290725.i	0.316910	−	0.318102i
$957$		0			0
$958$	1.03397e6	+	427147.i	1.12662	+	0.465421i
$959$	−2.04180e6	+	1.17883e6i	−2.22012	+	1.28179i
$960$		0			0
$961$	−117537.	+	203580.i	−0.127271	+	0.220439i
$962$	98060.8	+	127547.i	0.105961	+	0.137823i
$963$		0			0
$964$	−314992.	+	1.18446e6i	−0.338958	+	1.27458i
$965$	497708.	−	862055.i	0.534466	−	0.925722i
$966$		0			0
$967$	−826524.	+	477194.i	−0.883898	+	0.510319i	−0.871942	−	0.489610i	$-0.837139\pi$
$967$	−826524.	+	477194.i	−0.883898	+	0.510319i	−0.0119565	+	0.999929i	$0.503806\pi$
$968$	−720658.	−	549763.i	−0.769093	−	0.586712i
$969$		0			0
$970$	512682.	−	67985.5i	0.544885	−	0.0722559i
$971$		−	708749.i		−	0.751716i	−0.926677	−	0.375858i	$-0.877348\pi$
$971$		−	708749.i		−	0.751716i	0.926677	−	0.375858i	$-0.122652\pi$
$972$		0			0
$973$	−1.88516e6			−1.99123
$974$	32867.5	+	247856.i	0.0346457	+	0.261265i
$975$		0			0
$976$	−1799.79	−	479321.i	−0.00188939	−	0.503184i
$977$	−311552.	−	539625.i	−0.326394	−	0.565331i	0.655400	−	0.755282i	$-0.272500\pi$
$977$	−311552.	−	539625.i	−0.326394	−	0.565331i	−0.981793	+	0.189952i	$0.939167\pi$
$978$		0			0
$979$	−29353.2	−	16947.1i	−0.0306260	−	0.0176819i
$980$	613652.	−	2.30750e6i	0.638954	−	2.40264i
$981$		0			0
$982$	−1.06827e6	+	821307.i	−1.10779	+	0.851692i
$983$	1.50312e6	+	867829.i	1.55556	+	0.898105i	0.997672	+	0.0681909i	$0.0217227\pi$
$983$	1.50312e6	+	867829.i	1.55556	+	0.898105i	0.557891	+	0.829914i	$0.311611\pi$
$984$		0			0
$985$	−492981.	−	853867.i	−0.508110	−	0.880072i
$986$	524425.	−	1.26944e6i	0.539423	−	1.30575i
$987$		0			0
$988$	461439.	−	463175.i	0.472716	−	0.474494i
$989$	47448.1			0.0485095
$990$		0			0
$991$			106256.i			0.108195i	0.998536	+	0.0540974i	$0.0172282\pi$
$991$			106256.i			0.108195i	−0.998536	+	0.0540974i	$0.982772\pi$
$992$	−321455.	+	786483.i	−0.326661	+	0.799219i
$993$		0			0
$994$	629010.	−	1.52261e6i	0.636626	−	1.54104i
$995$	365735.	−	211157.i	0.369420	−	0.213285i
$996$		0			0
$997$	765045.	−	1.32510e6i	0.769656	−	1.33308i	−0.168094	−	0.985771i	$-0.553761\pi$
$997$	765045.	−	1.32510e6i	0.769656	−	1.33308i	0.937750	−	0.347312i	$-0.112905\pi$
$998$	−1.01295e6	+	778779.i	−1.01702	+	0.781903i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.22		44
3.2	odd	2		36.5.f.a.7.1	✓	44
4.3	odd	2	inner	108.5.f.a.19.8		44
9.2	odd	6		324.5.d.f.163.16		22
9.4	even	3	inner	108.5.f.a.91.8		44
9.5	odd	6		36.5.f.a.31.15	yes	44
9.7	even	3		324.5.d.e.163.7		22
12.11	even	2		36.5.f.a.7.15	yes	44
36.7	odd	6		324.5.d.e.163.8		22
36.11	even	6		324.5.d.f.163.15		22
36.23	even	6		36.5.f.a.31.1	yes	44
36.31	odd	6	inner	108.5.f.a.91.22		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.1	✓	44	3.2	odd	2
36.5.f.a.7.15	yes	44	12.11	even	2
36.5.f.a.31.1	yes	44	36.23	even	6
36.5.f.a.31.15	yes	44	9.5	odd	6
108.5.f.a.19.8		44	4.3	odd	2	inner
108.5.f.a.19.22		44	1.1	even	1	trivial
108.5.f.a.91.8		44	9.4	even	3	inner
108.5.f.a.91.22		44	36.31	odd	6	inner
324.5.d.e.163.7		22	9.7	even	3
324.5.d.e.163.8		22	36.7	odd	6
324.5.d.f.163.15		22	36.11	even	6
324.5.d.f.163.16		22	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.96529 - 0.525827i) q^{2} +(15.4470 - 4.17011i) q^{4} +(-11.0746 - 19.1817i) q^{5} +(-82.7885 - 47.7980i) q^{7} +(59.0591 - 24.6582i) q^{8} +O(q^{10})\)	\(q+(3.96529 - 0.525827i) q^{2} +(15.4470 - 4.17011i) q^{4} +(-11.0746 - 19.1817i) q^{5} +(-82.7885 - 47.7980i) q^{7} +(59.0591 - 24.6582i) q^{8} +(-54.0000 - 70.2376i) q^{10} +(-18.9394 - 10.9346i) q^{11} +(-63.1124 - 109.314i) q^{13} +(-353.414 - 146.000i) q^{14} +(221.220 - 128.832i) q^{16} +283.865 q^{17} +323.729i q^{19} +(-251.059 - 250.118i) q^{20} +(-80.8497 - 33.4002i) q^{22} +(198.433 - 114.565i) q^{23} +(67.2085 - 116.409i) q^{25} +(-307.739 - 400.274i) q^{26} +(-1478.16 - 393.098i) q^{28} +(604.822 - 1047.58i) q^{29} +(-718.565 + 414.863i) q^{31} +(809.459 - 627.178i) q^{32} +(1125.61 - 149.264i) q^{34} +2117.36i q^{35} -318.650 q^{37} +(170.226 + 1283.68i) q^{38} +(-1127.04 - 859.775i) q^{40} +(164.418 + 284.781i) q^{41} +(179.336 + 103.539i) q^{43} +(-338.155 - 89.9283i) q^{44} +(726.602 - 558.626i) q^{46} +(-1062.42 - 613.390i) q^{47} +(3368.79 + 5834.92i) q^{49} +(205.290 - 496.933i) q^{50} +(-1430.75 - 1425.39i) q^{52} +2834.27 q^{53} +484.385i q^{55} +(-6068.02 - 781.492i) q^{56} +(1847.44 - 4471.99i) q^{58} +(1278.13 - 737.929i) q^{59} +(936.180 - 1621.51i) q^{61} +(-2631.17 + 2022.89i) q^{62} +(2879.95 - 2912.58i) q^{64} +(-1397.88 + 2421.20i) q^{65} +(-214.663 + 123.936i) q^{67} +(4384.87 - 1183.75i) q^{68} +(1113.37 + 8395.96i) q^{70} +4308.28i q^{71} +3010.75 q^{73} +(-1263.54 + 167.555i) q^{74} +(1349.99 + 5000.65i) q^{76} +(1045.31 + 1810.52i) q^{77} +(-6228.39 - 3595.96i) q^{79} +(-4921.12 - 2816.63i) q^{80} +(801.712 + 1042.78i) q^{82} +(2877.35 + 1661.24i) q^{83} +(-3143.68 - 5445.01i) q^{85} +(765.561 + 316.264i) q^{86} +(-1388.17 - 178.780i) q^{88} +1549.85 q^{89} +12066.6i q^{91} +(2587.44 - 2597.18i) q^{92} +(-4535.35 - 1873.62i) q^{94} +(6209.67 - 3585.16i) q^{95} +(-2918.68 + 5055.31i) q^{97} +(16426.4 + 21365.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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