LMFDB - Embedded newform 324.5.d.e.163.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,5,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	324.d (of order $2$, degree $1$, 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:	$33.4918680392$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.7
Character	$\chi$	$=$	324.163
Dual form			324.5.d.e.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43802 - 3.17113i) q^{2} +(-4.11208 + 15.4626i) q^{4} +22.1491 q^{5} +95.5959i q^{7} +(59.0591 - 24.6582i) q^{8} +O(q^{10})$	\(q+(-2.43802 - 3.17113i) q^{2} +(-4.11208 + 15.4626i) q^{4} +22.1491 q^{5} +95.5959i q^{7} +(59.0591 - 24.6582i) q^{8} +(-54.0000 - 70.2376i) q^{10} +21.8693i q^{11} +126.225 q^{13} +(303.147 - 233.065i) q^{14} +(-222.182 - 127.167i) q^{16} +283.865 q^{17} +323.729i q^{19} +(-91.0790 + 342.482i) q^{20} +(69.3502 - 53.3178i) q^{22} +229.131i q^{23} -134.417 q^{25} +(-307.739 - 400.274i) q^{26} +(-1478.16 - 393.098i) q^{28} -1209.64 q^{29} -829.727i q^{31} +(138.422 + 1014.60i) q^{32} +(-692.070 - 900.172i) q^{34} +2117.36i q^{35} -318.650 q^{37} +(1026.59 - 789.259i) q^{38} +(1308.11 - 546.156i) q^{40} -328.837 q^{41} -207.079i q^{43} +(-338.155 - 89.9283i) q^{44} +(726.602 - 558.626i) q^{46} +1226.78i q^{47} -6737.58 q^{49} +(327.712 + 426.253i) q^{50} +(-519.046 + 1951.76i) q^{52} +2834.27 q^{53} +484.385i q^{55} +(2357.22 + 5645.81i) q^{56} +(2949.14 + 3835.93i) q^{58} +1475.86i q^{59} -1872.36 q^{61} +(-2631.17 + 2022.89i) q^{62} +(2879.95 - 2912.58i) q^{64} +2795.76 q^{65} -247.871i q^{67} +(-1167.28 + 4389.28i) q^{68} +(6714.43 - 5162.18i) q^{70} +4308.28i q^{71} +3010.75 q^{73} +(776.875 + 1010.48i) q^{74} +(-5005.68 - 1331.20i) q^{76} -2090.61 q^{77} +7191.93i q^{79} +(-4921.12 - 2816.63i) q^{80} +(801.712 + 1042.78i) q^{82} -3322.48i q^{83} +6287.36 q^{85} +(-656.674 + 504.863i) q^{86} +(539.256 + 1291.58i) q^{88} +1549.85 q^{89} +12066.6i q^{91} +(-3542.95 - 942.204i) q^{92} +(3890.28 - 2990.92i) q^{94} +7170.31i q^{95} +5837.37 q^{97} +(16426.4 + 21365.7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8}+O(q^{10}) $ 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8	$ 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8} + 14 q^{10} + 2 q^{13} + 252 q^{14} + q^{16} + 28 q^{17} - 140 q^{20} + 33 q^{22} + 1752 q^{25} - 548 q^{26} - 258 q^{28} + 526 q^{29} - 121 q^{32} - 385 q^{34} - 4 q^{37} + 1395 q^{38} + 2276 q^{40} - 2762 q^{41} - 3357 q^{44} + 1788 q^{46} - 3428 q^{49} + 6375 q^{50} - 1438 q^{52} + 5044 q^{53} - 7506 q^{56} + 4064 q^{58} + 2 q^{61} + 9162 q^{62} + 4513 q^{64} - 2014 q^{65} - 11405 q^{68} - 3666 q^{70} - 1708 q^{73} + 14620 q^{74} - 1581 q^{76} - 3942 q^{77} - 22760 q^{80} - 4243 q^{82} + 1252 q^{85} + 22113 q^{86} - 1995 q^{88} - 6524 q^{89} - 30294 q^{92} - 7524 q^{94} - 5638 q^{97} + 46469 q^{98}+O(q^{100}) $ 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8 + 14 * q^10 + 2 * q^13 + 252 * q^14 + q^16 + 28 * q^17 - 140 * q^20 + 33 * q^22 + 1752 * q^25 - 548 * q^26 - 258 * q^28 + 526 * q^29 - 121 * q^32 - 385 * q^34 - 4 * q^37 + 1395 * q^38 + 2276 * q^40 - 2762 * q^41 - 3357 * q^44 + 1788 * q^46 - 3428 * q^49 + 6375 * q^50 - 1438 * q^52 + 5044 * q^53 - 7506 * q^56 + 4064 * q^58 + 2 * q^61 + 9162 * q^62 + 4513 * q^64 - 2014 * q^65 - 11405 * q^68 - 3666 * q^70 - 1708 * q^73 + 14620 * q^74 - 1581 * q^76 - 3942 * q^77 - 22760 * q^80 - 4243 * q^82 + 1252 * q^85 + 22113 * q^86 - 1995 * q^88 - 6524 * q^89 - 30294 * q^92 - 7524 * q^94 - 5638 * q^97 + 46469 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.43802	−	3.17113i	−0.609506	−	0.792782i
$2$	−2.43802	−	3.17113i	−0.609506	−	0.792782i
$3$		0			0
$3$		0			0
$4$	−4.11208	+	15.4626i	−0.257005	+	0.966410i
$5$	22.1491			0.885964			0.442982	−	0.896530i	$-0.353920\pi$
$5$	22.1491			0.885964			0.442982	+	0.896530i	$0.353920\pi$
$6$		0			0
$7$			95.5959i			1.95094i	0.220138	+	0.975469i	$0.429349\pi$
$7$			95.5959i			1.95094i	−0.220138	+	0.975469i	$0.570651\pi$
$8$	59.0591	−	24.6582i	0.922798	−	0.385284i
$9$		0			0
$10$	−54.0000	−	70.2376i	−0.540000	−	0.702376i
$11$			21.8693i			0.180738i	0.995908	+	0.0903689i	$0.0288046\pi$
$11$			21.8693i			0.180738i	−0.995908	+	0.0903689i	$0.971195\pi$
$12$		0			0
$13$	126.225			0.746892			0.373446	−	0.927652i	$-0.378176\pi$
$13$	126.225			0.746892			0.373446	+	0.927652i	$0.378176\pi$
$14$	303.147	−	233.065i	1.54667	−	1.18911i
$15$		0			0
$16$	−222.182	−	127.167i	−0.867897	−	0.496745i
$17$	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	$0.852002\pi$
$20$	−91.0790	+	342.482i	−0.227697	+	0.856205i
$21$		0			0
$22$	69.3502	−	53.3178i	0.143286	−	0.110161i
$23$			229.131i			0.433139i	0.976267	+	0.216570i	$0.0694868\pi$
$23$			229.131i			0.433139i	−0.976267	+	0.216570i	$0.930513\pi$
$24$		0			0
$25$	−134.417			−0.215067
$26$	−307.739	−	400.274i	−0.455235	−	0.592122i
$27$		0			0
$28$	−1478.16	−	393.098i	−1.88541	−	0.501401i
$29$	−1209.64			−1.43834			−0.719170	−	0.694835i	$-0.755478\pi$
$29$	−1209.64			−1.43834			−0.719170	+	0.694835i	$0.755478\pi$
$30$		0			0
$31$		−	829.727i		−	0.863399i	−0.902017	−	0.431700i	$-0.857914\pi$
$31$		−	829.727i		−	0.863399i	0.902017	−	0.431700i	$-0.142086\pi$
$32$	138.422	+	1014.60i	0.135178	+	0.990821i
$33$		0			0
$34$	−692.070	−	900.172i	−0.598676	−	0.778695i
$35$			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	$0.537129\pi$
$38$	1026.59	−	789.259i	0.710932	−	0.546578i
$39$		0			0
$40$	1308.11	−	546.156i	0.817566	−	0.341348i
$41$	−328.837			−0.195620			−0.0978099	−	0.995205i	$-0.531184\pi$
$41$	−328.837			−0.195620			−0.0978099	+	0.995205i	$0.531184\pi$
$42$		0			0
$43$		−	207.079i		−	0.111995i	−0.998431	−	0.0559976i	$-0.982166\pi$
$43$		−	207.079i		−	0.111995i	0.998431	−	0.0559976i	$-0.0178339\pi$
$44$	−338.155	−	89.9283i	−0.174667	−	0.0464506i
$45$		0			0
$46$	726.602	−	558.626i	0.343385	−	0.264001i
$47$			1226.78i			0.555356i	0.960674	+	0.277678i	$0.0895648\pi$
$47$			1226.78i			0.555356i	−0.960674	+	0.277678i	$0.910435\pi$
$48$		0			0
$49$	−6737.58			−2.80616
$50$	327.712	+	426.253i	0.131085	+	0.170501i
$51$		0			0
$52$	−519.046	+	1951.76i	−0.191955	+	0.721804i
$53$	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
$56$	2357.22	+	5645.81i	0.751664	+	1.80032i
$57$		0			0
$58$	2949.14	+	3835.93i	0.876676	+	1.14029i
$59$			1475.86i			0.423975i	0.977272	+	0.211988i	$0.0679937\pi$
$59$			1475.86i			0.423975i	−0.977272	+	0.211988i	$0.932006\pi$
$60$		0			0
$61$	−1872.36			−0.503187			−0.251594	−	0.967833i	$-0.580955\pi$
$61$	−1872.36			−0.503187			−0.251594	+	0.967833i	$0.580955\pi$
$62$	−2631.17	+	2022.89i	−0.684487	+	0.526247i
$63$		0			0
$64$	2879.95	−	2912.58i	0.703113	−	0.711078i
$65$	2795.76			0.661719
$66$		0			0
$67$		−	247.871i		−	0.0552174i	−0.999619	−	0.0276087i	$-0.991211\pi$
$67$		−	247.871i		−	0.0552174i	0.999619	−	0.0276087i	$-0.00878924\pi$
$68$	−1167.28	+	4389.28i	−0.252439	+	0.949239i
$69$		0			0
$70$	6714.43	−	5162.18i	1.37029	−	1.05351i
$71$			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	$0.408841\pi$
$74$	776.875	+	1010.48i	0.141869	+	0.184528i
$75$		0			0
$76$	−5005.68	−	1331.20i	−0.866634	−	0.230471i
$77$	−2090.61			−0.352608
$78$		0			0
$79$			7191.93i			1.15237i	0.817320	+	0.576184i	$0.195459\pi$
$79$			7191.93i			1.15237i	−0.817320	+	0.576184i	$0.804541\pi$
$80$	−4921.12	−	2816.63i	−0.768926	−	0.440098i
$81$		0			0
$82$	801.712	+	1042.78i	0.119231	+	0.155084i
$83$		−	3322.48i		−	0.482287i	−0.970489	−	0.241144i	$-0.922477\pi$
$83$		−	3322.48i		−	0.482287i	0.970489	−	0.241144i	$-0.0775225\pi$
$84$		0			0
$85$	6287.36			0.870222
$86$	−656.674	+	504.863i	−0.0887877	+	0.0682617i
$87$		0			0
$88$	539.256	+	1291.58i	0.0696353	+	0.166785i
$89$	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
$92$	−3542.95	−	942.204i	−0.418590	−	0.111319i
$93$		0			0
$94$	3890.28	−	2990.92i	0.440276	−	0.338493i
$95$			7170.31i			0.794494i
$96$		0			0
$97$	5837.37			0.620403			0.310201	−	0.950671i	$-0.399604\pi$
$97$	5837.37			0.620403			0.310201	+	0.950671i	$0.399604\pi$
$98$	16426.4	+	21365.7i	1.71037	+	2.22467i
$99$		0			0
$100$	552.734	−	2078.43i	0.0552734	−	0.207843i
$101$	5499.00			0.539065			0.269532	−	0.962991i	$-0.413131\pi$
$101$	5499.00			0.539065			0.269532	+	0.962991i	$0.413131\pi$
$102$		0			0
$103$			17933.3i			1.69038i	0.534464	+	0.845191i	$0.320513\pi$
$103$			17933.3i			1.69038i	−0.534464	+	0.845191i	$0.679487\pi$
$104$	7454.72	−	3112.47i	0.689230	−	0.287765i
$105$		0			0
$106$	−6910.03	−	8987.84i	−0.614990	−	0.799915i
$107$		−	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	$0.671032\pi$
$110$	1536.05	−	1180.94i	0.126946	−	0.0975985i
$111$		0			0
$112$	12156.6	−	21239.7i	0.969118	−	1.69321i
$113$	20473.4			1.60337			0.801684	−	0.597748i	$-0.203938\pi$
$113$	20473.4			1.60337			0.801684	+	0.597748i	$0.203938\pi$
$114$		0			0
$115$			5075.04i			0.383746i
$116$	4974.15	−	18704.2i	0.369661	−	1.39003i
$117$		0			0
$118$	4680.13	−	3598.18i	0.336120	−	0.258415i
$119$			27136.3i			1.91627i
$120$		0			0
$121$	14162.7			0.967334
$122$	4564.86	+	5937.49i	0.306696	+	0.398918i
$123$		0			0
$124$	12829.7	+	3411.90i	0.834398	+	0.221898i
$125$	−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	$-0.0811026\pi$
$128$	−16257.5	−	2031.76i	−0.992281	−	0.124009i
$129$		0			0
$130$	−6816.14	−	8865.72i	−0.403322	−	0.524599i
$131$		−	16275.6i		−	0.948406i	−0.880416	−	0.474203i	$-0.842736\pi$
$131$		−	16275.6i		−	0.948406i	0.880416	−	0.474203i	$-0.157264\pi$
$132$		0			0
$133$	−30947.2			−1.74952
$134$	−786.030	+	604.315i	−0.0437754	+	0.0336554i
$135$		0			0
$136$	16764.8	−	6999.59i	0.906402	−	0.378438i
$137$	−24662.9			−1.31402			−0.657011	−	0.753881i	$-0.728179\pi$
$137$	−24662.9			−1.31402			−0.657011	+	0.753881i	$0.728179\pi$
$138$		0			0
$139$			19720.1i			1.02066i	0.859980	+	0.510328i	$0.170476\pi$
$139$			19720.1i			1.02066i	−0.859980	+	0.510328i	$0.829524\pi$
$140$	−32739.9	−	8706.78i	−1.67040	−	0.444223i
$141$		0			0
$142$	13662.1	−	10503.7i	0.677549	−	0.520913i
$143$			2760.44i			0.134992i
$144$		0			0
$145$	−26792.5			−1.27432
$146$	−7340.28	−	9547.46i	−0.344355	−	0.447901i
$147$		0			0
$148$	1310.31	−	4927.14i	0.0598207	−	0.224942i
$149$	−29885.5			−1.34613			−0.673066	−	0.739583i	$-0.735023\pi$
$149$	−29885.5			−1.34613			−0.673066	+	0.739583i	$0.735023\pi$
$150$		0			0
$151$			5963.00i			0.261524i	0.991414	+	0.130762i	$0.0417423\pi$
$151$			5963.00i			0.261524i	−0.991414	+	0.130762i	$0.958258\pi$
$152$	7982.56	+	19119.1i	0.345506	+	0.827525i
$153$		0			0
$154$	5096.97	+	6629.60i	0.214917	+	0.279541i
$155$		−	18377.7i		−	0.764941i
$156$		0			0
$157$	−34987.0			−1.41941			−0.709704	−	0.704500i	$-0.751172\pi$
$157$	−34987.0			−1.41941			−0.709704	+	0.704500i	$0.751172\pi$
$158$	22806.5	−	17534.1i	0.913576	−	0.702375i
$159$		0			0
$160$	3065.93	+	22472.5i	0.119763	+	0.877832i
$161$	−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	$0.911965\pi$
$164$	1352.20	−	5084.66i	0.0502753	−	0.189049i
$165$		0			0
$166$	−10536.0	+	8100.28i	−0.382349	+	0.293957i
$167$			44617.8i			1.59983i	0.600111	+	0.799917i	$0.295123\pi$
$167$			44617.8i			1.59983i	−0.600111	+	0.799917i	$0.704877\pi$
$168$		0			0
$169$	−12628.3			−0.442153
$170$	−15328.7	−	19938.0i	−0.530406	−	0.689896i
$171$		0			0
$172$	3201.97	+	851.526i	0.108233	+	0.0287833i
$173$	52886.6			1.76707			0.883534	−	0.468367i	$-0.155158\pi$
$173$	52886.6			1.76707			0.883534	+	0.468367i	$0.155158\pi$
$174$		0			0
$175$		−	12849.7i		−	0.419583i
$176$	2781.04	−	4858.95i	0.0897806	−	0.156862i
$177$		0			0
$178$	−3778.57	−	4914.77i	−0.119258	−	0.155119i
$179$		−	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	$0.612916\pi$
$182$	38264.6	−	29418.6i	1.15519	−	0.888135i
$183$		0			0
$184$	5649.94	+	13532.2i	0.166881	+	0.399700i
$185$	−7057.80			−0.206218
$186$		0			0
$187$			6207.92i			0.177526i
$188$	−18969.2	−	5044.62i	−0.536701	−	0.142729i
$189$		0			0
$190$	22738.0	−	17481.4i	0.629860	−	0.484249i
$191$		−	57503.3i		−	1.57625i	−0.615513	−	0.788127i	$-0.711051\pi$
$191$		−	57503.3i		−	1.57625i	0.615513	−	0.788127i	$-0.288949\pi$
$192$		0			0
$193$	−44941.6			−1.20652			−0.603259	−	0.797545i	$-0.706131\pi$
$193$	−44941.6			−1.20652			−0.603259	+	0.797545i	$0.706131\pi$
$194$	−14231.6	−	18511.0i	−0.378139	−	0.491844i
$195$		0			0
$196$	27705.5	−	104180.i	0.721197	−	2.71190i
$197$	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	$0.922611\pi$
$200$	−7938.54	+	3314.48i	−0.198464	+	0.0828619i
$201$		0			0
$202$	−13406.7	−	17438.0i	−0.328563	−	0.427361i
$203$		−	115637.i		−	2.80611i
$204$		0			0
$205$	−7283.44			−0.173312
$206$	56868.6	−	43721.7i	1.34010	−	1.03030i
$207$		0			0
$208$	−28044.8	−	16051.6i	−0.648225	−	0.371014i
$209$	−7079.72			−0.162078
$210$		0			0
$211$			952.918i			0.0214038i	0.999943	+	0.0107019i	$0.00340658\pi$
$211$			952.918i			0.0214038i	−0.999943	+	0.0107019i	$0.996593\pi$
$212$	−11654.8	+	43825.1i	−0.259318	+	0.975106i
$213$		0			0
$214$	−27636.9	+	21247.8i	−0.603478	+	0.463966i
$215$		−	4586.61i		−	0.0992237i
$216$		0			0
$217$	79318.5			1.68444
$218$	29651.5	+	38567.6i	0.623927	+	0.811539i
$219$		0			0
$220$	−7489.83	−	1991.83i	−0.154749	−	0.0411535i
$221$	35830.8			0.733621
$222$		0			0
$223$			43342.2i			0.871568i	0.900051	+	0.435784i	$0.143529\pi$
$223$			43342.2i			0.871568i	−0.900051	+	0.435784i	$0.856471\pi$
$224$	−96991.7	+	13232.6i	−1.93303	+	0.263724i
$225$		0			0
$226$	−49914.6	−	64923.7i	−0.977262	−	1.27112i
$227$		−	6007.51i		−	0.116585i	−0.998300	−	0.0582925i	$-0.981434\pi$
$227$		−	6007.51i		−	0.116585i	0.998300	−	0.0582925i	$-0.0185656\pi$
$228$		0			0
$229$	−4076.35			−0.0777321			−0.0388660	−	0.999244i	$-0.512375\pi$
$229$	−4076.35			−0.0777321			−0.0388660	+	0.999244i	$0.512375\pi$
$230$	16093.6	−	12373.1i	0.304227	−	0.233895i
$231$		0			0
$232$	−71440.4	+	29827.6i	−1.32730	+	0.554169i
$233$	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
$236$	−22820.5	−	6068.85i	−0.409734	−	0.108964i
$237$		0			0
$238$	86052.8	−	66159.0i	1.51919	−	1.16798i
$239$			25648.6i			0.449022i	0.974472	+	0.224511i	$0.0720785\pi$
$239$			25648.6i			0.449022i	−0.974472	+	0.224511i	$0.927922\pi$
$240$		0			0
$241$	76601.6			1.31888			0.659438	−	0.751759i	$-0.270794\pi$
$241$	76601.6			1.31888			0.659438	+	0.751759i	$0.270794\pi$
$242$	−34529.1	−	44911.8i	−0.589596	−	0.766884i
$243$		0			0
$244$	7699.30	−	28951.5i	0.129322	−	0.486285i
$245$	−149231.			−2.48615
$246$		0			0
$247$			40862.6i			0.669780i
$248$	−20459.5	−	49002.9i	−0.332654	−	0.796743i
$249$		0			0
$250$	41008.6	+	53339.6i	0.656137	+	0.853434i
$251$			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
$254$	−25782.6	+	19822.2i	−0.399631	+	0.307244i
$255$		0			0
$256$	33193.3	+	56508.2i	0.506489	+	0.862246i
$257$	−59426.4			−0.899732			−0.449866	−	0.893096i	$-0.648528\pi$
$257$	−59426.4			−0.899732			−0.449866	+	0.893096i	$0.648528\pi$
$258$		0			0
$259$		−	30461.6i		−	0.454102i
$260$	−11496.4	+	43229.7i	−0.170065	+	0.639492i
$261$		0			0
$262$	−51611.9	+	39680.3i	−0.751878	+	0.578059i
$263$			25140.3i			0.363462i	0.983348	+	0.181731i	$0.0581700\pi$
$263$			25140.3i			0.363462i	−0.983348	+	0.181731i	$0.941830\pi$
$264$		0			0
$265$	62776.7			0.893936
$266$	75450.0	+	98137.4i	1.06634	+	1.38698i
$267$		0			0
$268$	3832.72	+	1019.27i	0.0533627	+	0.0141912i
$269$	−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	$-0.0100204\pi$
$272$	−63069.6	−	36098.2i	−0.852476	−	0.487918i
$273$		0			0
$274$	60128.6	+	78209.0i	0.800904	+	1.04173i
$275$		−	2939.60i		−	0.0388708i
$276$		0			0
$277$	−9854.37			−0.128431			−0.0642154	−	0.997936i	$-0.520454\pi$
$277$	−9854.37			−0.128431			−0.0642154	+	0.997936i	$0.520454\pi$
$278$	62534.9	−	48078.0i	0.809157	−	0.622095i
$279$		0			0
$280$	52210.3	+	125050.i	0.665948	+	1.59502i
$281$	48417.2			0.613178			0.306589	−	0.951842i	$-0.400812\pi$
$281$	48417.2			0.613178			0.306589	+	0.951842i	$0.400812\pi$
$282$		0			0
$283$		−	132230.i		−	1.65104i	−0.564373	−	0.825520i	$-0.690882\pi$
$283$		−	132230.i		−	1.65104i	0.564373	−	0.825520i	$-0.309118\pi$
$284$	−66617.0	−	17716.0i	−0.825940	−	0.219649i
$285$		0			0
$286$	8753.71	−	6730.03i	0.107019	−	0.0822782i
$287$		−	31435.5i		−	0.381642i
$288$		0			0
$289$	−2941.65			−0.0352205
$290$	65320.8	+	84962.5i	0.776704	+	1.01026i
$291$		0			0
$292$	−12380.4	+	46553.9i	−0.145201	+	0.545997i
$293$	89519.1			1.04275			0.521375	−	0.853327i	$-0.325419\pi$
$293$	89519.1			1.04275			0.521375	+	0.853327i	$0.325419\pi$
$294$		0			0
$295$			32688.9i			0.375627i
$296$	−18819.1	+	7857.31i	−0.214791	+	0.0896789i
$297$		0			0
$298$	72861.5	+	94770.6i	0.820475	+	1.06719i
$299$			28921.9i			0.323508i
$300$		0			0
$301$	19795.9			0.218495
$302$	18909.4	−	14537.9i	0.207331	−	0.159400i
$303$		0			0
$304$	41167.5	−	71926.6i	0.445459	−	0.778292i
$305$	−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	$0.892016\pi$
$308$	8596.78	−	32326.2i	0.0906221	−	0.340764i
$309$		0			0
$310$	−58278.0	+	44805.3i	−0.606431	+	0.466236i
$311$			122783.i			1.26945i	0.772737	+	0.634726i	$0.218887\pi$
$311$			122783.i			1.26945i	−0.772737	+	0.634726i	$0.781113\pi$
$312$		0			0
$313$	−48589.1			−0.495964			−0.247982	−	0.968765i	$-0.579767\pi$
$313$	−48589.1			−0.495964			−0.247982	+	0.968765i	$0.579767\pi$
$314$	85299.2	+	110948.i	0.865138	+	1.12528i
$315$		0			0
$316$	−111206.	−	29573.8i	−1.11366	−	0.296164i
$317$	110133.			1.09598			0.547988	−	0.836486i	$-0.315394\pi$
$317$	110133.			1.09598			0.547988	+	0.836486i	$0.315394\pi$
$318$		0			0
$319$		−	26454.0i		−	0.259962i
$320$	63788.3	−	64511.0i	0.622933	−	0.629990i
$321$		0			0
$322$	53402.3	+	69460.2i	0.515049	+	0.669922i
$323$			91895.4i			0.880823i
$324$		0			0
$325$	−16966.7			−0.160632
$326$	46012.4	−	35375.3i	0.432952	−	0.332862i
$327$		0			0
$328$	−19420.8	+	8108.51i	−0.180518	+	0.0753691i
$329$	−117275.			−1.08346
$330$		0			0
$331$		−	184521.i		−	1.68418i	−0.539335	−	0.842091i	$-0.681324\pi$
$331$		−	184521.i		−	1.68418i	0.539335	−	0.842091i	$-0.318676\pi$
$332$	51374.0	+	13662.3i	0.466087	+	0.123950i
$333$		0			0
$334$	141489.	−	108779.i	1.26832	−	0.975108i
$335$		−	5490.12i		−	0.0489207i
$336$		0			0
$337$	65626.1			0.577852			0.288926	−	0.957351i	$-0.406702\pi$
$337$	65626.1			0.577852			0.288926	+	0.957351i	$0.406702\pi$
$338$	30788.2	+	40046.0i	0.269495	+	0.350531i
$339$		0			0
$340$	−25854.1	+	97218.6i	−0.223652	+	0.840992i
$341$	18145.5			0.156049
$342$		0			0
$343$		−	414560.i		−	3.52370i
$344$	−5106.19	−	12229.9i	−0.0431499	−	0.103349i
$345$		0			0
$346$	−128939.	−	167710.i	−1.07704	−	1.40090i
$347$			104869.i			0.870941i	0.900203	+	0.435470i	$0.143418\pi$
$347$			104869.i			0.870941i	−0.900203	+	0.435470i	$0.856582\pi$
$348$		0			0
$349$	87343.9			0.717104			0.358552	−	0.933510i	$-0.383271\pi$
$349$	87343.9			0.717104			0.358552	+	0.933510i	$0.383271\pi$
$350$	−40748.1	+	31327.9i	−0.332637	+	0.255738i
$351$		0			0
$352$	−22188.6	+	3027.20i	−0.179079	+	0.0244318i
$353$	48708.6			0.390892			0.195446	−	0.980715i	$-0.437385\pi$
$353$	48708.6			0.390892			0.195446	+	0.980715i	$0.437385\pi$
$354$		0			0
$355$			95424.6i			0.757187i
$356$	−6373.12	+	23964.7i	−0.0502866	+	0.189091i
$357$		0			0
$358$	−104142.	+	80066.8i	−0.812572	+	0.624721i
$359$		−	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
$362$	55486.0	+	72170.4i	0.423415	+	0.550734i
$363$		0			0
$364$	−186580.	−	49618.7i	−1.40819	−	0.374492i
$365$	66685.4			0.500547
$366$		0			0
$367$			1284.97i			0.00954031i	0.999989	+	0.00477015i	$0.00151839\pi$
$367$			1284.97i			0.00954031i	−0.999989	+	0.00477015i	$0.998482\pi$
$368$	29137.8	−	50908.6i	0.215160	−	0.375920i
$369$		0			0
$370$	17207.1	+	22381.2i	0.125691	+	0.163486i
$371$			270945.i			1.96849i
$372$		0			0
$373$	−73554.3			−0.528677			−0.264339	−	0.964430i	$-0.585154\pi$
$373$	−73554.3			−0.528677			−0.264339	+	0.964430i	$0.585154\pi$
$374$	19686.1	−	15135.1i	0.140740	−	0.108203i
$375$		0			0
$376$	30250.2	+	72452.5i	0.213970	+	0.512481i
$377$	−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	$0.839152\pi$
$380$	−110871.	−	29484.9i	−0.767807	−	0.204189i
$381$		0			0
$382$	−182350.	+	140194.i	−1.24963	+	0.960736i
$383$		−	103923.i		−	0.708461i	−0.935158	−	0.354230i	$-0.884743\pi$
$383$		−	103923.i		−	0.708461i	0.935158	−	0.354230i	$-0.115257\pi$
$384$		0			0
$385$	−46305.2			−0.312398
$386$	109569.	+	142515.i	0.735380	+	0.956505i
$387$		0			0
$388$	−24003.7	+	90260.7i	−0.159447	+	0.599563i
$389$	100082.			0.661388			0.330694	−	0.943738i	$-0.392717\pi$
$389$	100082.			0.661388			0.330694	+	0.943738i	$0.392717\pi$
$390$		0			0
$391$			65042.1i			0.425443i
$392$	−397915.	+	166136.i	−2.58952	+	1.08117i
$393$		0			0
$394$	−108528.	−	141162.i	−0.699116	−	0.909337i
$395$			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	$0.325370\pi$
$398$	60463.4	−	46485.5i	0.381704	−	0.293461i
$399$		0			0
$400$	29865.0	+	17093.4i	0.186656	+	0.106833i
$401$	156453.			0.972961			0.486481	−	0.873691i	$-0.338280\pi$
$401$	156453.			0.972961			0.486481	+	0.873691i	$0.338280\pi$
$402$		0			0
$403$		−	104732.i		−	0.644866i
$404$	−22612.3	+	85028.6i	−0.138542	+	0.520958i
$405$		0			0
$406$	−366699.	+	281926.i	−2.22463	+	1.71034i
$407$		−	6968.64i		−	0.0420687i
$408$		0			0
$409$	270702.			1.61825			0.809125	−	0.587637i	$-0.199942\pi$
$409$	270702.			1.61825			0.809125	+	0.587637i	$0.199942\pi$
$410$	17757.2	+	23096.7i	0.105635	+	0.137399i
$411$		0			0
$412$	−277294.	−	73743.1i	−1.63360	−	0.434437i
$413$	−141086.			−0.827149
$414$		0			0
$415$		−	73589.9i		−	0.427290i
$416$	17472.3	+	128068.i	0.100963	+	0.740036i
$417$		0			0
$418$	17260.5	+	22450.7i	0.0987874	+	0.128492i
$419$		−	57003.2i		−	0.324692i	−0.986734	−	0.162346i	$-0.948094\pi$
$419$		−	57003.2i		−	0.324692i	0.986734	−	0.162346i	$-0.0519060\pi$
$420$		0			0
$421$	233625.			1.31812			0.659059	−	0.752091i	$-0.270955\pi$
$421$	233625.			1.31812			0.659059	+	0.752091i	$0.270955\pi$
$422$	3021.82	−	2323.24i	0.0169685	−	0.0130457i
$423$		0			0
$424$	167390.	−	69888.0i	0.931101	−	0.388750i
$425$	−38156.3			−0.211246
$426$		0			0
$427$		−	178990.i		−	0.981687i
$428$	134759.	+	35837.5i	0.735647	+	0.195637i
$429$		0			0
$430$	−14544.7	+	11182.3i	−0.0786627	+	0.0604774i
$431$		−	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	$0.694719\pi$
$434$	−193380.	−	251529.i	−1.02667	−	1.33539i
$435$		0			0
$436$	50011.6	−	188057.i	0.263086	−	0.989275i
$437$	−74176.2			−0.388420
$438$		0			0
$439$		−	31238.4i		−	0.162091i	−0.996710	−	0.0810455i	$-0.974174\pi$
$439$		−	31238.4i		−	0.162091i	0.996710	−	0.0810455i	$-0.0258259\pi$
$440$	11944.0	+	28607.3i	0.0616944	+	0.147765i
$441$		0			0
$442$	−87356.3	−	113624.i	−0.447146	−	0.581601i
$443$		−	213422.i		−	1.08751i	−0.839245	−	0.543754i	$-0.817003\pi$
$443$		−	213422.i		−	1.08751i	0.839245	−	0.543754i	$-0.182997\pi$
$444$		0			0
$445$	34327.8			0.173351
$446$	137444.	−	105669.i	0.690963	−	0.531226i
$447$		0			0
$448$	278430.	+	275312.i	1.38727	+	1.37173i
$449$	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
$452$	−84188.3	+	316571.i	−0.412074	+	1.54951i
$453$		0			0
$454$	−19050.6	+	14646.5i	−0.0924265	+	0.0710593i
$455$			267264.i			1.29097i
$456$		0			0
$457$	−72357.5			−0.346458			−0.173229	−	0.984882i	$-0.555420\pi$
$457$	−72357.5			−0.346458			−0.173229	+	0.984882i	$0.555420\pi$
$458$	9938.23	+	12926.6i	0.0473782	+	0.0616246i
$459$		0			0
$460$	−78473.1	−	20869.0i	−0.370856	−	0.0986246i
$461$	−58191.8			−0.273817			−0.136908	−	0.990584i	$-0.543717\pi$
$461$	−58191.8			−0.273817			−0.136908	+	0.990584i	$0.543717\pi$
$462$		0			0
$463$		−	74734.1i		−	0.348623i	−0.984691	−	0.174312i	$-0.944230\pi$
$463$		−	74734.1i		−	0.348623i	0.984691	−	0.174312i	$-0.0557700\pi$
$464$	268760.	+	153826.i	1.24833	+	0.714487i
$465$		0			0
$466$	−91249.4	−	118688.i	−0.420202	−	0.546555i
$467$			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
$470$	86166.2	−	66246.2i	0.390069	−	0.299892i
$471$		0			0
$472$	36391.9	+	87162.8i	0.163351	+	0.391244i
$473$	4528.67			0.0202418
$474$		0			0
$475$		−	43514.7i		−	0.192863i
$476$	−419597.	−	111587.i	−1.85191	−	0.492492i
$477$		0			0
$478$	81334.9	−	62531.9i	0.355976	−	0.273682i
$479$		−	279681.i		−	1.21897i	−0.792799	−	0.609483i	$-0.791377\pi$
$479$		−	279681.i		−	1.21897i	0.792799	−	0.609483i	$-0.208623\pi$
$480$		0			0
$481$	−40221.4			−0.173847
$482$	−186757.	−	242913.i	−0.803863	−	1.04558i
$483$		0			0
$484$	−58238.3	+	218992.i	−0.248610	+	0.934841i
$485$	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	$0.957932\pi$
$488$	−110580.	+	46168.9i	−0.464340	+	0.193870i
$489$		0			0
$490$	363830.	+	473232.i	1.51533	+	1.97098i
$491$		−	336874.i		−	1.39735i	−0.715440	−	0.698674i	$-0.753774\pi$
$491$		−	336874.i		−	1.39735i	0.715440	−	0.698674i	$-0.246226\pi$
$492$		0			0
$493$	−343375.			−1.41278
$494$	129580.	−	99624.0i	0.530989	−	0.408235i
$495$		0			0
$496$	−105514.	+	184350.i	−0.428889	+	0.749342i
$497$	−411854.			−1.66736
$498$		0			0
$499$		−	319430.i		−	1.28285i	−0.767187	−	0.641424i	$-0.778344\pi$
$499$		−	319430.i		−	1.28285i	0.767187	−	0.641424i	$-0.221656\pi$
$500$	69166.9	−	260087.i	0.276668	−	1.04035i
$501$		0			0
$502$	211332.	−	162476.i	0.838607	−	0.644737i
$503$			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
$506$	12216.7	+	15890.3i	0.0477149	+	0.0620626i
$507$		0			0
$508$	125717.	+	33433.0i	0.487155	+	0.129553i
$509$	−94557.1			−0.364971			−0.182486	−	0.983209i	$-0.558414\pi$
$509$	−94557.1			−0.364971			−0.182486	+	0.983209i	$0.558414\pi$
$510$		0			0
$511$			287815.i			1.10223i
$512$	98268.5	−	243028.i	0.374865	−	0.927080i
$513$		0			0
$514$	144883.	+	188449.i	0.548392	+	0.713291i
$515$			397206.i			1.49762i
$516$		0			0
$517$	−26828.8			−0.100374
$518$	−96597.6	+	74266.1i	−0.360003	+	0.276778i
$519$		0			0
$520$	165115.	−	68938.4i	0.610633	−	0.254950i
$521$	−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	$-0.0380670\pi$
$524$	251662.	+	66926.6i	0.916549	+	0.243745i
$525$		0			0
$526$	79723.1	−	61292.6i	0.288146	−	0.221532i
$527$		−	235530.i		−	0.848058i
$528$		0			0
$529$	227340.			0.812391
$530$	−153051.	−	199073.i	−0.544859	−	0.708696i
$531$		0			0
$532$	127257.	−	478523.i	0.449634	−	1.69075i
$533$	−41507.3			−0.146107
$534$		0			0
$535$		−	193033.i		−	0.674411i
$536$	−6112.04	−	14639.0i	−0.0212744	−	0.0509545i
$537$		0			0
$538$	6225.39	+	8097.33i	0.0215081	+	0.0279755i
$539$		−	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	$0.402789\pi$
$542$	−14660.5	+	11271.2i	−0.0499055	+	0.0383684i
$543$		0			0
$544$	39293.3	+	288010.i	0.132776	+	0.973216i
$545$	−269380.			−0.906926
$546$		0			0
$547$		−	273097.i		−	0.912730i	−0.889793	−	0.456365i	$-0.849151\pi$
$547$		−	273097.i		−	0.912730i	0.889793	−	0.456365i	$-0.150849\pi$
$548$	101416.	−	381351.i	0.337710	−	1.26988i
$549$		0			0
$550$	−9321.85	+	7166.82i	−0.0308160	+	0.0236920i
$551$		−	391597.i		−	1.28984i
$552$		0			0
$553$	−687519.			−2.24820
$554$	24025.2	+	31249.5i	0.0782794	+	0.101818i
$555$		0			0
$556$	−304923.	−	81090.6i	−0.986372	−	0.262314i
$557$	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
$560$	269258.	−	470439.i	0.858604	−	1.50013i
$561$		0			0
$562$	−118042.	−	153537.i	−0.373736	−	0.486117i
$563$		−	32046.7i		−	0.101104i	−0.998721	−	0.0505518i	$-0.983902\pi$
$563$		−	32046.7i		−	0.101104i	0.998721	−	0.0505518i	$-0.0160980\pi$
$564$		0			0
$565$	453468.			1.42053
$566$	−419318.	+	322380.i	−1.30891	+	1.00632i
$567$		0			0
$568$	106234.	+	254443.i	0.329282	+	0.788667i
$569$	277128.			0.855964			0.427982	−	0.903787i	$-0.359225\pi$
$569$	277128.			0.855964			0.427982	+	0.903787i	$0.359225\pi$
$570$		0			0
$571$			642532.i			1.97071i	0.170515	+	0.985355i	$0.445457\pi$
$571$			642532.i			1.97071i	−0.170515	+	0.985355i	$0.554543\pi$
$572$	−42683.5	−	11351.2i	−0.130457	−	0.0346935i
$573$		0			0
$574$	−99685.8	+	76640.4i	−0.302559	+	0.232613i
$575$		−	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	$0.263140\pi$
$578$	7171.81	+	9328.34i	0.0214671	+	0.0279221i
$579$		0			0
$580$	110173.	−	414281.i	0.327506	−	1.23151i
$581$	317615.			0.940913
$582$		0			0
$583$			61983.5i			0.182364i
$584$	177812.	−	74239.5i	0.521357	−	0.217675i
$585$		0			0
$586$	−218250.	−	283876.i	−0.635563	−	0.826674i
$587$		−	378466.i		−	1.09838i	−0.835699	−	0.549188i	$-0.814937\pi$
$587$		−	378466.i		−	1.09838i	0.835699	−	0.549188i	$-0.185063\pi$
$588$		0			0
$589$	268607.			0.774259
$590$	103661.	−	79696.4i	0.297790	−	0.228947i
$591$		0			0
$592$	70798.0	+	40521.6i	0.202012	+	0.115623i
$593$	−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
$596$	122891.	−	462106.i	0.345963	−	1.30091i
$597$		0			0
$598$	91715.1	−	70512.4i	0.256471	−	0.197180i
$599$			208851.i			0.582080i	0.956711	+	0.291040i	$0.0940013\pi$
$599$			208851.i			0.582080i	−0.956711	+	0.291040i	$0.905999\pi$
$600$		0			0
$601$	360007.			0.996695			0.498348	−	0.866977i	$-0.333940\pi$
$601$	360007.			0.996695			0.498348	+	0.866977i	$0.333940\pi$
$602$	−48262.9	−	62775.3i	−0.133174	−	0.173219i
$603$		0			0
$604$	−92203.3	−	24520.4i	−0.252739	−	0.0672130i
$605$	313692.			0.857023
$606$		0			0
$607$			322980.i			0.876593i	0.898830	+	0.438297i	$0.144418\pi$
$607$			322980.i			0.876593i	−0.898830	+	0.438297i	$0.855582\pi$
$608$	−328456.	+	44811.4i	−0.888525	+	0.121222i
$609$		0			0
$610$	101108.	+	131510.i	0.271721	+	0.353427i
$611$			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	$0.674939\pi$
$614$	198915.	−	152930.i	0.527632	−	0.405654i
$615$		0			0
$616$	−123470.	+	51550.7i	−0.325386	+	0.135854i
$617$	−384203.			−1.00923			−0.504616	−	0.863344i	$-0.668366\pi$
$617$	−384203.			−1.00923			−0.504616	+	0.863344i	$0.668366\pi$
$618$		0			0
$619$			695791.i			1.81592i	0.419052	+	0.907962i	$0.362362\pi$
$619$			695791.i			1.81592i	−0.419052	+	0.907962i	$0.637638\pi$
$620$	284166.	+	75570.6i	0.739247	+	0.196594i
$621$		0			0
$622$	389360.	−	299347.i	1.00640	−	0.773739i
$623$			148159.i			0.381727i
$624$		0			0
$625$	−288546.			−0.738679
$626$	118461.	+	154082.i	0.302293	+	0.393191i
$627$		0			0
$628$	143869.	−	540989.i	0.364795	−	1.37173i
$629$	−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	$0.906420\pi$
$632$	177340.	+	424749.i	0.443989	+	1.06340i
$633$		0			0
$634$	−268508.	−	349247.i	−0.668004	−	0.868869i
$635$		−	180082.i		−	0.446603i
$636$		0			0
$637$	−850449.			−2.09590
$638$	−83889.0	+	64495.5i	−0.206093	+	0.158449i
$639$		0			0
$640$	−360090.	−	45001.6i	−0.879126	−	0.109867i
$641$	−518941.			−1.26300			−0.631498	−	0.775377i	$-0.717560\pi$
$641$	−518941.			−1.26300			−0.631498	+	0.775377i	$0.717560\pi$
$642$		0			0
$643$		−	225212.i		−	0.544716i	−0.962196	−	0.272358i	$-0.912197\pi$
$643$		−	225212.i		−	0.544716i	0.962196	−	0.272358i	$-0.0878035\pi$
$644$	90070.8	−	338691.i	0.217176	−	0.816643i
$645$		0			0
$646$	291412.	−	224043.i	0.698300	−	0.536867i
$647$			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
$650$	41365.3	+	53803.7i	0.0979061	+	0.127346i
$651$		0			0
$652$	−224359.	−	59665.5i	−0.527774	−	0.140355i
$653$	−72240.7			−0.169416			−0.0847082	−	0.996406i	$-0.526996\pi$
$653$	−72240.7			−0.169416			−0.0847082	+	0.996406i	$0.526996\pi$
$654$		0			0
$655$		−	360490.i		−	0.840254i
$656$	73061.5	+	41817.1i	0.169778	+	0.0971731i
$657$		0			0
$658$	285920.	+	371895.i	0.660378	+	0.858950i
$659$			234586.i			0.540171i	0.962836	+	0.270086i	$0.0870520\pi$
$659$			234586.i			0.540171i	−0.962836	+	0.270086i	$0.912948\pi$
$660$		0			0
$661$	597947.			1.36855			0.684274	−	0.729225i	$-0.260119\pi$
$661$	597947.			1.36855			0.684274	+	0.729225i	$0.260119\pi$
$662$	−585138.	+	449866.i	−1.33519	+	1.02652i
$663$		0			0
$664$	−81926.2	−	196223.i	−0.185817	−	0.445054i
$665$	−685452.			−1.55001
$666$		0			0
$667$		−	277166.i		−	0.623001i
$668$	−689905.	−	183472.i	−1.54610	−	0.411166i
$669$		0			0
$670$	−17409.9	+	13385.0i	−0.0387834	+	0.0298174i
$671$		−	40947.2i		−	0.0909450i
$672$		0			0
$673$	−751705.			−1.65965			−0.829826	−	0.558022i	$-0.811561\pi$
$673$	−751705.			−1.65965			−0.829826	+	0.558022i	$0.811561\pi$
$674$	−159998.	−	208109.i	−0.352204	−	0.458111i
$675$		0			0
$676$	51928.7	−	195266.i	0.113636	−	0.427301i
$677$	84647.6			0.184687			0.0923437	−	0.995727i	$-0.470564\pi$
$677$	84647.6			0.184687			0.0923437	+	0.995727i	$0.470564\pi$
$678$		0			0
$679$			558029.i			1.21037i
$680$	371326.	−	155035.i	0.803040	−	0.335283i
$681$		0			0
$682$	−44239.2	−	57541.8i	−0.0951128	−	0.123713i
$683$		−	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
$686$	−1.31462e6	+	1.01071e6i	−2.79352	+	2.14771i
$687$		0			0
$688$	−26333.5	+	46009.1i	−0.0556330	+	0.0972002i
$689$	357755.			0.753612
$690$		0			0
$691$			444378.i			0.930672i	0.885134	+	0.465336i	$0.154067\pi$
$691$			444378.i			0.930672i	−0.885134	+	0.465336i	$0.845933\pi$
$692$	−217474.	+	817762.i	−0.454145	+	1.70771i
$693$		0			0
$694$	332553.	−	255673.i	0.690466	−	0.530844i
$695$			436782.i			0.904264i
$696$		0			0
$697$	−93345.3			−0.192144
$698$	−212947.	−	276979.i	−0.437079	−	0.568506i
$699$		0			0
$700$	198690.	+	52839.1i	0.405489	+	0.107835i
$701$	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
$704$	63695.9	+	62982.4i	0.128519	+	0.127079i
$705$		0			0
$706$	−118753.	−	154461.i	−0.238251	−	0.309892i
$707$			525682.i			1.05168i
$708$		0			0
$709$	185631.			0.369282			0.184641	−	0.982806i	$-0.440888\pi$
$709$	185631.			0.369282			0.184641	+	0.982806i	$0.440888\pi$
$710$	302603.	−	232647.i	0.600284	−	0.461510i
$711$		0			0
$712$	91532.8	−	38216.5i	0.180558	−	0.0753860i
$713$	190116.			0.373972
$714$		0			0
$715$			61141.4i			0.119598i
$716$	507804.	+	135044.i	0.990535	+	0.263421i
$717$		0			0
$718$	−346948.	+	266741.i	−0.673001	+	0.517416i
$719$		−	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
$722$	−62219.6	−	80928.7i	−0.119358	−	0.155249i
$723$		0			0
$724$	93585.2	−	351906.i	0.178538	−	0.671351i
$725$	162597.			0.309340
$726$		0			0
$727$			240082.i			0.454246i	0.973866	+	0.227123i	$0.0729320\pi$
$727$			240082.i			0.454246i	−0.973866	+	0.227123i	$0.927068\pi$
$728$	297539.	+	712640.i	0.561412	+	1.34465i
$729$		0			0
$730$	−162581.	−	211468.i	−0.305086	−	0.396825i
$731$		−	58782.5i		−	0.110005i
$732$		0			0
$733$	−55680.1			−0.103632			−0.0518158	−	0.998657i	$-0.516501\pi$
$733$	−55680.1			−0.103632			−0.0518158	+	0.998657i	$0.516501\pi$
$734$	4074.82	−	3132.80i	0.00756338	−	0.00581487i
$735$		0			0
$736$	−232476.	+	31716.8i	−0.429163	+	0.0585509i
$737$	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	$-0.0970435\pi$
$740$	29022.3	−	109132.i	0.0529990	−	0.199291i
$741$		0			0
$742$	859201.	−	660571.i	1.56058	−	1.19981i
$743$		−	12875.8i		−	0.0233237i	−0.999932	−	0.0116618i	$-0.996288\pi$
$743$		−	12875.8i		−	0.0233237i	0.999932	−	0.0116618i	$-0.00371217\pi$
$744$		0			0
$745$	−661936.			−1.19262
$746$	179327.	+	233250.i	0.322232	+	0.419126i
$747$		0			0
$748$	−95990.4	−	25527.5i	−0.171563	−	0.0456252i
$749$	833135.			1.48509
$750$		0			0
$751$		−	531658.i		−	0.942655i	−0.881958	−	0.471328i	$-0.843775\pi$
$751$		−	531658.i		−	0.942655i	0.881958	−	0.471328i	$-0.156225\pi$
$752$	156006.	−	272568.i	0.275870	−	0.481991i
$753$		0			0
$754$	372254.	+	484189.i	0.654782	+	0.851672i
$755$			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	$0.319858\pi$
$758$	441008.	−	339055.i	0.767552	−	0.590109i
$759$		0			0
$760$	176807.	+	423472.i	0.306106	+	0.733158i
$761$	820697.			1.41714			0.708571	−	0.705639i	$-0.249340\pi$
$761$	820697.			1.41714			0.708571	+	0.705639i	$0.249340\pi$
$762$		0			0
$763$		−	1.16265e6i		−	1.99710i
$764$	889149.	+	236458.i	1.52331	+	0.405105i
$765$		0			0
$766$	−329554.	+	253368.i	−0.561654	+	0.431811i
$767$			186290.i			0.316664i
$768$		0			0
$769$	−131443.			−0.222273			−0.111136	−	0.993805i	$-0.535449\pi$
$769$	−131443.			−0.222273			−0.111136	+	0.993805i	$0.535449\pi$
$770$	112893.	+	146840.i	0.190409	+	0.247664i
$771$		0			0
$772$	184803.	−	694912.i	0.310081	−	1.16599i
$773$	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
$776$	344750.	−	143939.i	0.572507	−	0.239031i
$777$		0			0
$778$	−244002.	−	317372.i	−0.403120	−	0.524336i
$779$		−	106454.i		−	0.175423i
$780$		0			0
$781$	−94219.0			−0.154467
$782$	206257.	−	158574.i	0.337283	−	0.259310i
$783$		0			0
$784$	1.49697e6	+	856796.i	2.43545	+	1.39394i
$785$	−774931.			−1.25755
$786$		0			0
$787$			479245.i			0.773763i	0.922130	+	0.386881i	$0.126448\pi$
$787$			479245.i			0.773763i	−0.922130	+	0.386881i	$0.873552\pi$
$788$	−183048.	+	688311.i	−0.294790	+	1.10849i
$789$		0			0
$790$	505144.	−	388365.i	0.809396	−	0.622279i
$791$			1.95717e6i			3.12807i
$792$		0			0
$793$	−236338.			−0.375826
$794$	−400783.	−	521296.i	−0.635723	−	0.826882i
$795$		0			0
$796$	−294823.	−	78404.5i	−0.465302	−	0.123741i
$797$	688016.			1.08313			0.541567	−	0.840658i	$-0.317831\pi$
$797$	688016.			1.08313			0.541567	+	0.840658i	$0.317831\pi$
$798$		0			0
$799$			348240.i			0.545488i
$800$	−18606.3	−	136380.i	−0.0290724	−	0.213093i
$801$		0			0
$802$	−381436.	−	496133.i	−0.593026	−	0.771346i
$803$			65842.9i			0.102112i
$804$		0			0
$805$	−485153.			−0.748664
$806$	−332118.	+	255339.i	−0.511238	+	0.393050i
$807$		0			0
$808$	324766.	−	135595.i	0.497448	−	0.207693i
$809$	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	$0.937283\pi$
$812$	1.78804e6	+	475509.i	2.71185	+	0.721185i
$813$		0			0
$814$	−22098.4	+	16989.7i	−0.0333513	+	0.0256411i
$815$			321379.i			0.483841i
$816$		0			0
$817$	67037.5			0.100432
$818$	−659979.	−	858432.i	−0.986333	−	1.28292i
$819$		0			0
$820$	29950.1	−	112621.i	0.0445421	−	0.167491i
$821$	878068.			1.30269			0.651347	−	0.758780i	$-0.274204\pi$
$821$	878068.			1.30269			0.651347	+	0.758780i	$0.274204\pi$
$822$		0			0
$823$			659598.i			0.973822i	0.873452	+	0.486911i	$0.161876\pi$
$823$			659598.i			0.973822i	−0.873452	+	0.486911i	$0.838124\pi$
$824$	442201.	+	1.05912e6i	0.651277	+	1.55988i
$825$		0			0
$826$	343971.	+	447402.i	0.504152	+	0.655749i
$827$		−	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	$0.370972\pi$
$830$	−233363.	+	179414.i	−0.338747	+	0.260435i
$831$		0			0
$832$	363521.	−	367639.i	0.525149	−	0.531098i
$833$	−1.91256e6			−2.75630
$834$		0			0
$835$			988244.i			1.41740i
$836$	29112.4	−	109471.i	0.0416548	−	0.156634i
$837$		0			0
$838$	−180764.	+	138975.i	−0.257410	+	0.197901i
$839$			1.17490e6i			1.66908i	0.550947	+	0.834540i	$0.314267\pi$
$839$			1.17490e6i			1.66908i	−0.550947	+	0.834540i	$0.685733\pi$
$840$		0			0
$841$	755956.			1.06882
$842$	−569582.	−	740853.i	−0.803401	−	1.04498i
$843$		0			0
$844$	−14734.6	−	3918.48i	−0.0206848	−	0.00550088i
$845$	−279706.			−0.391732
$846$		0			0
$847$			1.35390e6i			1.88721i
$848$	−629724.	−	360425.i	−0.875706	−	0.501214i
$849$		0			0
$850$	93025.9	+	120998.i	0.128756	+	0.167472i
$851$		−	73012.3i		−	0.100818i
$852$		0			0
$853$	1.17515e6			1.61508			0.807541	−	0.589812i	$-0.200798\pi$
$853$	1.17515e6			1.61508			0.807541	+	0.589812i	$0.200798\pi$
$854$	−567600.	+	436382.i	−0.778263	+	0.598344i
$855$		0			0
$856$	−214900.	−	514710.i	−0.293284	−	0.702449i
$857$	−895397.			−1.21914			−0.609570	−	0.792732i	$-0.708658\pi$
$857$	−895397.			−1.21914			−0.609570	+	0.792732i	$0.708658\pi$
$858$		0			0
$859$			1.06038e6i			1.43707i	0.695493	+	0.718533i	$0.255186\pi$
$859$			1.06038e6i			1.43707i	−0.695493	+	0.718533i	$0.744814\pi$
$860$	70920.8	+	18860.5i	0.0958908	+	0.0255010i
$861$		0			0
$862$	−1.05656e6	+	812301.i	−1.42193	+	1.09321i
$863$			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
$866$	525012.	+	682881.i	0.700057	+	0.910561i
$867$		0			0
$868$	−326164.	+	1.22647e6i	−0.432909	+	1.62786i
$869$	−157282.			−0.208277
$870$		0			0
$871$		−	31287.5i		−	0.0412414i
$872$	−718283.	+	299895.i	−0.944631	+	0.394399i
$873$		0			0
$874$	180843.	+	235222.i	0.236744	+	0.307932i
$875$		−	1.60796e6i		−	2.10020i
$876$		0			0
$877$	−1.17774e6			−1.53126			−0.765632	−	0.643279i	$-0.777574\pi$
$877$	−1.17774e6			−1.53126			−0.765632	+	0.643279i	$0.777574\pi$
$878$	−99060.8	+	76159.8i	−0.128503	+	0.0987955i
$879$		0			0
$880$	61597.6	−	107621.i	0.0795424	−	0.138974i
$881$	−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	$-0.0224516\pi$
$884$	−147339.	+	554036.i	−0.188544	+	0.708979i
$885$		0			0
$886$	−676789.	+	520329.i	−0.862156	+	0.662842i
$887$			988937.i			1.25696i	0.777826	+	0.628480i	$0.216323\pi$
$887$			988937.i			1.25696i	−0.777826	+	0.628480i	$0.783677\pi$
$888$		0			0
$889$	777235.			0.983442
$890$	−83692.1	−	108858.i	−0.105658	−	0.137429i
$891$		0			0
$892$	−670181.	−	178227.i	−0.842292	−	0.223997i
$893$	−397145.			−0.498019
$894$		0			0
$895$		−	727395.i		−	0.908081i
$896$	194228.	−	1.55415e6i	0.241933	−	1.93588i
$897$		0			0
$898$	−958272.	−	1.24642e6i	−1.18833	−	1.54565i
$899$			1.00367e6i			1.24186i
$900$		0			0
$901$	804551.			0.991070
$902$	−22804.9	+	17532.9i	−0.0280295	+	0.0215496i
$903$		0			0
$904$	1.20914e6	−	504836.i	1.47958	−	0.617751i
$905$	−504082.			−0.615467
$906$		0			0
$907$			514619.i			0.625563i	0.949825	+	0.312781i	$0.101261\pi$
$907$			514619.i			0.625563i	−0.949825	+	0.312781i	$0.898739\pi$
$908$	92891.5	+	24703.4i	0.112669	+	0.0299630i
$909$		0			0
$910$	847527.	−	651595.i	1.02346	−	0.786856i
$911$			1.14551e6i			1.38026i	0.723684	+	0.690131i	$0.242447\pi$
$911$			1.14551e6i			1.38026i	−0.723684	+	0.690131i	$0.757553\pi$
$912$		0			0
$913$	72660.2			0.0871676
$914$	176409.	+	229455.i	0.211168	+	0.274666i
$915$		0			0
$916$	16762.3	−	63030.8i	0.0199775	−	0.0751211i
$917$	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	$-0.0624913\pi$
$920$	125141.	+	299727.i	0.147851	+	0.354120i
$921$		0			0
$922$	141873.	+	184533.i	0.166893	+	0.217077i
$923$			543811.i			0.638329i
$924$		0			0
$925$	42831.9			0.0500592
$926$	−236991.	+	182203.i	−0.276382	+	0.212488i
$927$		0			0
$928$	−167442.	−	1.22731e6i	−0.194432	−	1.42514i
$929$	907069.			1.05101			0.525507	−	0.850789i	$-0.323876\pi$
$929$	907069.			1.05101			0.525507	+	0.850789i	$0.323876\pi$
$930$		0			0
$931$		−	2.18115e6i		−	2.51644i
$932$	−153905.	+	578727.i	−0.177183	+	0.666257i
$933$		0			0
$934$	838337.	−	644530.i	0.961003	−	0.738838i
$935$			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	$0.235359\pi$
$938$	−57770.1	−	75141.3i	−0.0656595	−	0.0854030i
$939$		0			0
$940$	−420150.	−	111734.i	−0.475498	−	0.126453i
$941$	−109957.			−0.124178			−0.0620888	−	0.998071i	$-0.519776\pi$
$941$	−109957.			−0.124178			−0.0620888	+	0.998071i	$0.519776\pi$
$942$		0			0
$943$		−	75346.6i		−	0.0847306i
$944$	187680.	−	327908.i	0.210608	−	0.367967i
$945$		0			0
$946$	−11041.0	−	14361.0i	−0.0123375	−	0.0160473i
$947$		−	550631.i		−	0.613989i	−0.951711	−	0.306995i	$-0.900677\pi$
$947$		−	550631.i		−	0.613989i	0.951711	−	0.306995i	$-0.0993234\pi$
$948$		0			0
$949$	380031.			0.421975
$950$	−137991.	+	106090.i	−0.152898	+	0.117551i
$951$		0			0
$952$	669132.	+	1.60265e6i	0.738309	+	1.76833i
$953$	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
$956$	−396593.	−	105469.i	−0.433939	−	0.115401i
$957$		0			0
$958$	−886904.	+	681869.i	−0.966374	+	0.742967i
$959$		−	2.35767e6i		−	2.56357i
$960$		0			0
$961$	235074.			0.254541
$962$	98060.8	+	127547.i	0.105961	+	0.137823i
$963$		0			0
$964$	−314992.	+	1.18446e6i	−0.338958	+	1.27458i
$965$	−995416.			−1.06893
$966$		0			0
$967$		−	954387.i		−	1.02064i	−0.859985	−	0.510319i	$-0.829527\pi$
$967$		−	954387.i		−	1.02064i	0.859985	−	0.510319i	$-0.170473\pi$
$968$	836438.	−	349227.i	0.892654	−	0.372698i
$969$		0			0
$970$	−315218.	−	410003.i	−0.335018	−	0.435756i
$971$		−	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
$974$	198215.	−	152392.i	0.208939	−	0.160636i
$975$		0			0
$976$	416004.	+	238102.i	0.436715	+	0.249956i
$977$	623105.			0.652788			0.326394	−	0.945234i	$-0.394166\pi$
$977$	623105.			0.652788			0.326394	+	0.945234i	$0.394166\pi$
$978$		0			0
$979$			33894.1i			0.0353638i
$980$	613652.	−	2.30750e6i	0.638954	−	2.40264i
$981$		0			0
$982$	−1.06827e6	+	821307.i	−1.10779	+	0.851692i
$983$		−	1.73566e6i		−	1.79621i	−0.439781	−	0.898105i	$-0.644944\pi$
$983$		−	1.73566e6i		−	1.79621i	0.439781	−	0.898105i	$-0.355056\pi$
$984$		0			0
$985$	985961.			1.01622
$986$	837157.	+	1.08889e6i	0.861099	+	1.12003i
$987$		0			0
$988$	−631841.	−	168030.i	−0.647282	−	0.172137i
$989$	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	$0.982772\pi$
$992$	841842.	−	114853.i	0.855475	−	0.116713i
$993$		0			0
$994$	1.00411e6	+	1.30604e6i	1.01627	+	1.32186i
$995$			422314.i			0.426569i
$996$		0			0
$997$	−1.53009e6			−1.53931			−0.769656	−	0.638459i	$-0.779572\pi$
$997$	−1.53009e6			−1.53931			−0.769656	+	0.638459i	$0.779572\pi$
$998$	−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	324.5.d.e.163.7		22
3.2	odd	2		324.5.d.f.163.16		22
4.3	odd	2	inner	324.5.d.e.163.8		22
9.2	odd	6		36.5.f.a.31.15	yes	44
9.4	even	3		108.5.f.a.19.22		44
9.5	odd	6		36.5.f.a.7.1	✓	44
9.7	even	3		108.5.f.a.91.8		44
12.11	even	2		324.5.d.f.163.15		22
36.7	odd	6		108.5.f.a.91.22		44
36.11	even	6		36.5.f.a.31.1	yes	44
36.23	even	6		36.5.f.a.7.15	yes	44
36.31	odd	6		108.5.f.a.19.8		44

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

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43802 - 3.17113i) q^{2} +(-4.11208 + 15.4626i) q^{4} +22.1491 q^{5} +95.5959i q^{7} +(59.0591 - 24.6582i) q^{8} +O(q^{10})\)	\(q+(-2.43802 - 3.17113i) q^{2} +(-4.11208 + 15.4626i) q^{4} +22.1491 q^{5} +95.5959i q^{7} +(59.0591 - 24.6582i) q^{8} +(-54.0000 - 70.2376i) q^{10} +21.8693i q^{11} +126.225 q^{13} +(303.147 - 233.065i) q^{14} +(-222.182 - 127.167i) q^{16} +283.865 q^{17} +323.729i q^{19} +(-91.0790 + 342.482i) q^{20} +(69.3502 - 53.3178i) q^{22} +229.131i q^{23} -134.417 q^{25} +(-307.739 - 400.274i) q^{26} +(-1478.16 - 393.098i) q^{28} -1209.64 q^{29} -829.727i q^{31} +(138.422 + 1014.60i) q^{32} +(-692.070 - 900.172i) q^{34} +2117.36i q^{35} -318.650 q^{37} +(1026.59 - 789.259i) q^{38} +(1308.11 - 546.156i) q^{40} -328.837 q^{41} -207.079i q^{43} +(-338.155 - 89.9283i) q^{44} +(726.602 - 558.626i) q^{46} +1226.78i q^{47} -6737.58 q^{49} +(327.712 + 426.253i) q^{50} +(-519.046 + 1951.76i) q^{52} +2834.27 q^{53} +484.385i q^{55} +(2357.22 + 5645.81i) q^{56} +(2949.14 + 3835.93i) q^{58} +1475.86i q^{59} -1872.36 q^{61} +(-2631.17 + 2022.89i) q^{62} +(2879.95 - 2912.58i) q^{64} +2795.76 q^{65} -247.871i q^{67} +(-1167.28 + 4389.28i) q^{68} +(6714.43 - 5162.18i) q^{70} +4308.28i q^{71} +3010.75 q^{73} +(776.875 + 1010.48i) q^{74} +(-5005.68 - 1331.20i) q^{76} -2090.61 q^{77} +7191.93i q^{79} +(-4921.12 - 2816.63i) q^{80} +(801.712 + 1042.78i) q^{82} -3322.48i q^{83} +6287.36 q^{85} +(-656.674 + 504.863i) q^{86} +(539.256 + 1291.58i) q^{88} +1549.85 q^{89} +12066.6i q^{91} +(-3542.95 - 942.204i) q^{92} +(3890.28 - 2990.92i) q^{94} +7170.31i q^{95} +5837.37 q^{97} +(16426.4 + 21365.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8}+O(q^{10}) \) 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8	\( 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8} + 14 q^{10} + 2 q^{13} + 252 q^{14} + q^{16} + 28 q^{17} - 140 q^{20} + 33 q^{22} + 1752 q^{25} - 548 q^{26} - 258 q^{28} + 526 q^{29} - 121 q^{32} - 385 q^{34} - 4 q^{37} + 1395 q^{38} + 2276 q^{40} - 2762 q^{41} - 3357 q^{44} + 1788 q^{46} - 3428 q^{49} + 6375 q^{50} - 1438 q^{52} + 5044 q^{53} - 7506 q^{56} + 4064 q^{58} + 2 q^{61} + 9162 q^{62} + 4513 q^{64} - 2014 q^{65} - 11405 q^{68} - 3666 q^{70} - 1708 q^{73} + 14620 q^{74} - 1581 q^{76} - 3942 q^{77} - 22760 q^{80} - 4243 q^{82} + 1252 q^{85} + 22113 q^{86} - 1995 q^{88} - 6524 q^{89} - 30294 q^{92} - 7524 q^{94} - 5638 q^{97} + 46469 q^{98}+O(q^{100}) \) 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8 + 14 * q^10 + 2 * q^13 + 252 * q^14 + q^16 + 28 * q^17 - 140 * q^20 + 33 * q^22 + 1752 * q^25 - 548 * q^26 - 258 * q^28 + 526 * q^29 - 121 * q^32 - 385 * q^34 - 4 * q^37 + 1395 * q^38 + 2276 * q^40 - 2762 * q^41 - 3357 * q^44 + 1788 * q^46 - 3428 * q^49 + 6375 * q^50 - 1438 * q^52 + 5044 * q^53 - 7506 * q^56 + 4064 * q^58 + 2 * q^61 + 9162 * q^62 + 4513 * q^64 - 2014 * q^65 - 11405 * q^68 - 3666 * q^70 - 1708 * q^73 + 14620 * q^74 - 1581 * q^76 - 3942 * q^77 - 22760 * q^80 - 4243 * q^82 + 1252 * q^85 + 22113 * q^86 - 1995 * q^88 - 6524 * q^89 - 30294 * q^92 - 7524 * q^94 - 5638 * q^97 + 46469 * q^98

Introduction

L-functions

Modular forms

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