LMFDB - Embedded newform 324.5.d.f.163.16

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			163.16
Character	$\chi$	$=$	324.163
Dual form			324.5.d.f.163.15

$q$-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	$-0.646080\pi$
$5$	−22.1491			−0.885964			−0.442982	+	0.896530i	$0.646080\pi$
$6$		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	$-0.971195\pi$
$11$		−	21.8693i		−	0.180738i	0.995908	−	0.0903689i	$-0.0288046\pi$
$12$		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	$-0.663411\pi$
$17$	−283.865			−0.982232			−0.491116	+	0.871094i	$0.663411\pi$
$18$		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	$-0.930513\pi$
$23$		−	229.131i		−	0.433139i	0.976267	−	0.216570i	$-0.0694868\pi$
$24$		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	$-0.244522\pi$
$29$	1209.64			1.43834			0.719170	+	0.694835i	$0.244522\pi$
$30$		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	$-0.468816\pi$
$41$	328.837			0.195620			0.0978099	+	0.995205i	$0.468816\pi$
$42$		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	$-0.910435\pi$
$47$		−	1226.78i		−	0.555356i	0.960674	−	0.277678i	$-0.0895648\pi$
$48$		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	$-0.668323\pi$
$53$	−2834.27			−1.00900			−0.504499	+	0.863412i	$0.668323\pi$
$54$		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	$-0.932006\pi$
$59$		−	1475.86i		−	0.423975i	0.977272	−	0.211988i	$-0.0679937\pi$
$60$		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	$-0.859456\pi$
$71$		−	4308.28i		−	0.854648i	0.904099	−	0.427324i	$-0.140544\pi$
$72$		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	$0.0775225\pi$
$83$			3322.48i			0.482287i	−0.970489	+	0.241144i	$0.922477\pi$
$84$		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	$-0.531191\pi$
$89$	−1549.85			−0.195664			−0.0978318	+	0.995203i	$0.531191\pi$
$90$		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	$-0.586869\pi$
$101$	−5499.00			−0.539065			−0.269532	+	0.962991i	$0.586869\pi$
$102$		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	$0.124285\pi$
$107$			8715.17i			0.761217i	−0.924736	+	0.380608i	$0.875715\pi$
$108$		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	$-0.796062\pi$
$113$	−20473.4			−1.60337			−0.801684	+	0.597748i	$0.796062\pi$
$114$		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	$0.157264\pi$
$131$			16275.6i			0.948406i	−0.880416	+	0.474203i	$0.842736\pi$
$132$		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	$-0.271821\pi$
$137$	24662.9			1.31402			0.657011	+	0.753881i	$0.271821\pi$
$138$		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	$-0.264977\pi$
$149$	29885.5			1.34613			0.673066	+	0.739583i	$0.264977\pi$
$150$		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	$-0.704877\pi$
$167$		−	44617.8i		−	1.59983i	0.600111	−	0.799917i	$-0.295123\pi$
$168$		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	$-0.844842\pi$
$173$	−52886.6			−1.76707			−0.883534	+	0.468367i	$0.844842\pi$
$174$		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	$0.171274\pi$
$179$			32840.8i			1.02496i	−0.858698	+	0.512482i	$0.828726\pi$
$180$		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	$0.288949\pi$
$191$			57503.3i			1.57625i	−0.615513	+	0.788127i	$0.711051\pi$
$192$		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	$-0.694419\pi$
$197$	−44514.7			−1.14702			−0.573510	+	0.819198i	$0.694419\pi$
$198$		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	$0.0185656\pi$
$227$			6007.51i			0.116585i	−0.998300	+	0.0582925i	$0.981434\pi$
$228$		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	$-0.612022\pi$
$233$	−37427.6			−0.689414			−0.344707	+	0.938710i	$0.612022\pi$
$234$		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	$-0.927922\pi$
$239$		−	25648.6i		−	0.449022i	0.974472	−	0.224511i	$-0.0720785\pi$
$240$		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	$-0.822604\pi$
$251$		−	66642.6i		−	1.05780i	0.848683	−	0.528902i	$-0.177396\pi$
$252$		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	$-0.351472\pi$
$257$	59426.4			0.899732			0.449866	+	0.893096i	$0.351472\pi$
$258$		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	$-0.941830\pi$
$263$		−	25140.3i		−	0.363462i	0.983348	−	0.181731i	$-0.0581700\pi$
$264$		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	$-0.494383\pi$
$269$	2553.46			0.0352877			0.0176439	+	0.999844i	$0.494383\pi$
$270$		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	$-0.599188\pi$
$281$	−48417.2			−0.613178			−0.306589	+	0.951842i	$0.599188\pi$
$282$		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	$-0.674581\pi$
$293$	−89519.1			−1.04275			−0.521375	+	0.853327i	$0.674581\pi$
$294$		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	$-0.781113\pi$
$311$		−	122783.i		−	1.26945i	0.772737	−	0.634726i	$-0.218887\pi$
$312$		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	$-0.684606\pi$
$317$	−110133.			−1.09598			−0.547988	+	0.836486i	$0.684606\pi$
$318$		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	$-0.856582\pi$
$347$		−	104869.i		−	0.870941i	0.900203	−	0.435470i	$-0.143418\pi$
$348$		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	$-0.562615\pi$
$353$	−48708.6			−0.390892			−0.195446	+	0.980715i	$0.562615\pi$
$354$		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	$0.139535\pi$
$359$			109409.i			0.848911i	−0.905449	+	0.424456i	$0.860465\pi$
$360$		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	$0.115257\pi$
$383$			103923.i			0.708461i	−0.935158	+	0.354230i	$0.884743\pi$
$384$		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	$-0.607283\pi$
$389$	−100082.			−0.661388			−0.330694	+	0.943738i	$0.607283\pi$
$390$		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	$-0.661720\pi$
$401$	−156453.			−0.972961			−0.486481	+	0.873691i	$0.661720\pi$
$402$		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	$0.0519060\pi$
$419$			57003.2i			0.324692i	−0.986734	+	0.162346i	$0.948094\pi$
$420$		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	$0.354113\pi$
$431$			333180.i			1.79360i	−0.442439	+	0.896798i	$0.645887\pi$
$432$		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	$0.182997\pi$
$443$			213422.i			1.08751i	−0.839245	+	0.543754i	$0.817003\pi$
$444$		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	$-0.928429\pi$
$449$	−393053.			−1.94966			−0.974828	+	0.222956i	$0.928429\pi$
$450$		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	$-0.456283\pi$
$461$	58191.8			0.273817			0.136908	+	0.990584i	$0.456283\pi$
$462$		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	$-0.792735\pi$
$467$		−	264366.i		−	1.21219i	0.795392	−	0.606096i	$-0.207265\pi$
$468$		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	$0.208623\pi$
$479$			279681.i			1.21897i	−0.792799	+	0.609483i	$0.791377\pi$
$480$		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	$0.246226\pi$
$491$			336874.i			1.39735i	−0.715440	+	0.698674i	$0.753774\pi$
$492$		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	$-0.982196\pi$
$503$		−	28287.7i		−	0.111805i	0.998436	−	0.0559025i	$-0.0178036\pi$
$504$		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	$-0.441586\pi$
$509$	94557.1			0.364971			0.182486	+	0.983209i	$0.441586\pi$
$510$		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	$-0.261362\pi$
$521$	369932.			1.36285			0.681423	+	0.731890i	$0.261362\pi$
$522$		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	$-0.761511\pi$
$557$	−454335.			−1.46442			−0.732211	+	0.681078i	$0.761511\pi$
$558$		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	$0.0160980\pi$
$563$			32046.7i			0.101104i	−0.998721	+	0.0505518i	$0.983902\pi$
$564$		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	$-0.640775\pi$
$569$	−277128.			−0.855964			−0.427982	+	0.903787i	$0.640775\pi$
$570$		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	$0.185063\pi$
$587$			378466.i			1.09838i	−0.835699	+	0.549188i	$0.814937\pi$
$588$		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	$-0.437150\pi$
$593$	137966.			0.392339			0.196170	+	0.980570i	$0.437150\pi$
$594$		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	$-0.905999\pi$
$599$		−	208851.i		−	0.582080i	0.956711	−	0.291040i	$-0.0940013\pi$
$600$		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	$-0.331634\pi$
$617$	384203.			1.00923			0.504616	+	0.863344i	$0.331634\pi$
$618$		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	$-0.282440\pi$
$641$	518941.			1.26300			0.631498	+	0.775377i	$0.282440\pi$
$642$		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	$-0.941305\pi$
$647$		−	153505.i		−	0.366703i	0.983047	−	0.183352i	$-0.0586947\pi$
$648$		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	$-0.473004\pi$
$653$	72240.7			0.169416			0.0847082	+	0.996406i	$0.473004\pi$
$654$		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	$-0.912948\pi$
$659$		−	234586.i		−	0.540171i	0.962836	−	0.270086i	$-0.0870520\pi$
$660$		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	$-0.529436\pi$
$677$	−84647.6			−0.184687			−0.0923437	+	0.995727i	$0.529436\pi$
$678$		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	$0.238524\pi$
$683$			635506.i			1.36232i	−0.732136	+	0.681159i	$0.761476\pi$
$684$		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	$-0.624482\pi$
$701$	−374624.			−0.762359			−0.381179	+	0.924501i	$0.624482\pi$
$702$		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	$0.216863\pi$
$719$			651163.i			1.25960i	−0.776759	+	0.629799i	$0.783137\pi$
$720$		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	$0.00371217\pi$
$743$			12875.8i			0.0233237i	−0.999932	+	0.0116618i	$0.996288\pi$
$744$		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	$-0.750660\pi$
$761$	−820697.			−1.41714			−0.708571	+	0.705639i	$0.750660\pi$
$762$		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	$-0.500168\pi$
$773$	−629.598			−0.00105367			−0.000526834		1.00000i	$0.500168\pi$
$774$		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	$-0.682169\pi$
$797$	−688016.			−1.08313			−0.541567	+	0.840658i	$0.682169\pi$
$798$		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	$-0.604978\pi$
$809$	−423910.			−0.647703			−0.323852	+	0.946108i	$0.604978\pi$
$810$		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	$-0.725796\pi$
$821$	−878068.			−1.30269			−0.651347	+	0.758780i	$0.725796\pi$
$822$		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	$0.214522\pi$
$827$			853638.i			1.24814i	−0.781369	+	0.624069i	$0.785478\pi$
$828$		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	$-0.685733\pi$
$839$		−	1.17490e6i		−	1.66908i	0.550947	−	0.834540i	$-0.314267\pi$
$840$		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	$-0.291342\pi$
$857$	895397.			1.21914			0.609570	+	0.792732i	$0.291342\pi$
$858$		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	$-0.967845\pi$
$863$		−	150213.i		−	0.201691i	0.994902	−	0.100845i	$-0.0321547\pi$
$864$		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	$-0.234018\pi$
$881$	1.15136e6			1.48341			0.741703	+	0.670728i	$0.234018\pi$
$882$		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	$-0.783677\pi$
$887$		−	988937.i		−	1.25696i	0.777826	−	0.628480i	$-0.216323\pi$
$888$		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	$-0.757553\pi$
$911$		−	1.14551e6i		−	1.38026i	0.723684	−	0.690131i	$-0.242447\pi$
$912$		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	$-0.676124\pi$
$929$	−907069.			−1.05101			−0.525507	+	0.850789i	$0.676124\pi$
$930$		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	$-0.480224\pi$
$941$	109957.			0.124178			0.0620888	+	0.998071i	$0.480224\pi$
$942$		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	$0.0993234\pi$
$947$			550631.i			0.613989i	−0.951711	+	0.306995i	$0.900677\pi$
$948$		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	$-0.645749\pi$
$953$	−802951.			−0.884104			−0.442052	+	0.896989i	$0.645749\pi$
$954$		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	$0.122652\pi$
$971$			708749.i			0.751716i	−0.926677	+	0.375858i	$0.877348\pi$
$972$		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	$-0.605834\pi$
$977$	−623105.			−0.652788			−0.326394	+	0.945234i	$0.605834\pi$
$978$		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	$0.355056\pi$
$983$			1.73566e6i			1.79621i	−0.439781	+	0.898105i	$0.644944\pi$
$984$		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.f.163.16		22
3.2	odd	2		324.5.d.e.163.7		22
4.3	odd	2	inner	324.5.d.f.163.15		22
9.2	odd	6		108.5.f.a.91.8		44
9.4	even	3		36.5.f.a.7.1	✓	44
9.5	odd	6		108.5.f.a.19.22		44
9.7	even	3		36.5.f.a.31.15	yes	44
12.11	even	2		324.5.d.e.163.8		22
36.7	odd	6		36.5.f.a.31.1	yes	44
36.11	even	6		108.5.f.a.91.22		44
36.23	even	6		108.5.f.a.19.8		44
36.31	odd	6		36.5.f.a.7.15	yes	44

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

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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Database

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