LMFDB - Embedded newform 171.4.u.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(28,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	171.73
Dual form			171.4.u.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.98693 - 2.50633i) q^{2} +(1.25086 + 7.09397i) q^{4} +(-2.58856 + 14.6804i) q^{5} +(5.35146 + 9.26900i) q^{7} +(-1.55302 + 2.68992i) q^{8} +O(q^{10})$	\(q+(-2.98693 - 2.50633i) q^{2} +(1.25086 + 7.09397i) q^{4} +(-2.58856 + 14.6804i) q^{5} +(5.35146 + 9.26900i) q^{7} +(-1.55302 + 2.68992i) q^{8} +(44.5258 - 37.3616i) q^{10} +(14.6256 - 25.3323i) q^{11} +(-76.4727 - 27.8338i) q^{13} +(7.24674 - 41.0983i) q^{14} +(65.5325 - 23.8519i) q^{16} +(-61.3408 - 51.4710i) q^{17} +(81.6408 - 13.9203i) q^{19} -107.380 q^{20} +(-107.177 + 39.0091i) q^{22} +(-11.6670 - 66.1669i) q^{23} +(-91.3527 - 33.2497i) q^{25} +(158.658 + 274.803i) q^{26} +(-59.0601 + 49.5573i) q^{28} +(-1.78142 + 1.49479i) q^{29} +(-68.9182 - 119.370i) q^{31} +(-232.171 - 84.5035i) q^{32} +(54.2171 + 307.480i) q^{34} +(-149.925 + 54.5684i) q^{35} -305.379 q^{37} +(-278.744 - 163.040i) q^{38} +(-35.4690 - 29.7621i) q^{40} +(-213.997 + 77.8884i) q^{41} +(-29.9719 + 169.979i) q^{43} +(198.001 + 72.0665i) q^{44} +(-130.987 + 226.877i) q^{46} +(324.048 - 271.908i) q^{47} +(114.224 - 197.841i) q^{49} +(189.529 + 328.274i) q^{50} +(101.796 - 577.311i) q^{52} +(28.7445 + 163.018i) q^{53} +(334.030 + 280.284i) q^{55} -33.2438 q^{56} +9.06741 q^{58} +(-355.251 - 298.091i) q^{59} +(-106.337 - 603.067i) q^{61} +(-93.3264 + 529.280i) q^{62} +(202.732 + 351.143i) q^{64} +(606.566 - 1050.60i) q^{65} +(166.222 - 139.477i) q^{67} +(288.405 - 499.533i) q^{68} +(584.582 + 212.771i) q^{70} +(9.51311 - 53.9515i) q^{71} +(130.528 - 47.5085i) q^{73} +(912.146 + 765.381i) q^{74} +(200.872 + 561.745i) q^{76} +313.073 q^{77} +(-436.266 + 158.788i) q^{79} +(180.521 + 1023.79i) q^{80} +(834.406 + 303.699i) q^{82} +(-43.2845 - 74.9710i) q^{83} +(914.401 - 767.273i) q^{85} +(515.548 - 432.596i) q^{86} +(45.4278 + 78.6833i) q^{88} +(443.288 + 161.344i) q^{89} +(-151.249 - 857.777i) q^{91} +(454.792 - 165.531i) q^{92} -1649.40 q^{94} +(-6.97532 + 1234.56i) q^{95} +(-326.817 - 274.232i) q^{97} +(-837.033 + 304.655i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	$ 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) $ 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−2.98693	−	2.50633i	−1.05604	−	0.886121i	−0.0623221	−	0.998056i	$-0.519851\pi$
$2$	−2.98693	−	2.50633i	−1.05604	−	0.886121i	−0.993715	+	0.111935i	$0.964295\pi$
$3$		0			0
$3$		0			0
$4$	1.25086	+	7.09397i	0.156357	+	0.886746i
$5$	−2.58856	+	14.6804i	−0.231527	+	1.31306i	0.618277	+	0.785960i	$0.287831\pi$
$5$	−2.58856	+	14.6804i	−0.231527	+	1.31306i	−0.849805	+	0.527097i	$0.823280\pi$
$6$		0			0
$7$	5.35146	+	9.26900i	0.288952	+	0.500479i	0.973560	−	0.228432i	$-0.0733600\pi$
$7$	5.35146	+	9.26900i	0.288952	+	0.500479i	−0.684608	+	0.728911i	$0.740027\pi$
$8$	−1.55302	+	2.68992i	−0.0686346	+	0.118879i
$9$		0			0
$10$	44.5258	−	37.3616i	1.40803	−	1.18148i
$11$	14.6256	−	25.3323i	0.400890	−	0.694361i	−0.592944	−	0.805244i	$-0.702034\pi$
$11$	14.6256	−	25.3323i	0.400890	−	0.694361i	0.993834	+	0.110883i	$0.0353677\pi$
$12$		0			0
$13$	−76.4727	−	27.8338i	−1.63152	−	0.593823i	−0.645990	−	0.763346i	$-0.723555\pi$
$13$	−76.4727	−	27.8338i	−1.63152	−	0.593823i	−0.985526	+	0.169522i	$0.945778\pi$
$14$	7.24674	−	41.0983i	0.138341	−	0.784571i
$15$		0			0
$16$	65.5325	−	23.8519i	1.02394	−	0.372685i
$17$	−61.3408	−	51.4710i	−0.875137	−	0.734327i	0.0900365	−	0.995938i	$-0.471302\pi$
$17$	−61.3408	−	51.4710i	−0.875137	−	0.734327i	−0.965173	+	0.261612i	$0.915746\pi$
$18$		0			0
$19$	81.6408	−	13.9203i	0.985773	−	0.168081i
$19$	81.6408	−	13.9203i	0.985773	−	0.168081i
$20$	−107.380			−1.20055
$21$		0			0
$22$	−107.177	+	39.0091i	−1.03864	+	0.378035i
$23$	−11.6670	−	66.1669i	−0.105771	−	0.599858i	−0.990909	−	0.134530i	$-0.957047\pi$
$23$	−11.6670	−	66.1669i	−0.105771	−	0.599858i	0.885138	−	0.465328i	$-0.154064\pi$
$24$		0			0
$25$	−91.3527	−	33.2497i	−0.730822	−	0.265997i
$26$	158.658	+	274.803i	1.19674	+	2.07282i
$27$		0			0
$28$	−59.0601	+	49.5573i	−0.398618	+	0.334480i
$29$	−1.78142	+	1.49479i	−0.0114070	+	0.00957158i	−0.648473	−	0.761237i	$-0.724592\pi$
$29$	−1.78142	+	1.49479i	−0.0114070	+	0.00957158i	0.637066	+	0.770809i	$0.280148\pi$
$30$		0			0
$31$	−68.9182	−	119.370i	−0.399292	−	0.691595i	0.594346	−	0.804209i	$-0.297411\pi$
$31$	−68.9182	−	119.370i	−0.399292	−	0.691595i	−0.993639	+	0.112614i	$0.964078\pi$
$32$	−232.171	−	84.5035i	−1.28258	−	0.466820i
$33$		0			0
$34$	54.2171	+	307.480i	0.273475	+	1.55095i
$35$	−149.925	+	54.5684i	−0.724058	+	0.263536i
$36$		0			0
$37$	−305.379			−1.35687			−0.678433	−	0.734662i	$-0.737341\pi$
$37$	−305.379			−1.35687			−0.678433	+	0.734662i	$0.737341\pi$
$38$	−278.744	−	163.040i	−1.18995	−	0.696014i
$39$		0			0
$40$	−35.4690	−	29.7621i	−0.140204	−	0.117645i
$41$	−213.997	+	77.8884i	−0.815138	+	0.296686i	−0.715744	−	0.698362i	$-0.753912\pi$
$41$	−213.997	+	77.8884i	−0.815138	+	0.296686i	−0.0993934	+	0.995048i	$0.531690\pi$
$42$		0			0
$43$	−29.9719	+	169.979i	−0.106295	+	0.602828i	0.884400	+	0.466729i	$0.154568\pi$
$43$	−29.9719	+	169.979i	−0.106295	+	0.602828i	−0.990695	+	0.136099i	$0.956544\pi$
$44$	198.001	+	72.0665i	0.678404	+	0.246919i
$45$		0			0
$46$	−130.987	+	226.877i	−0.419849	+	0.727199i
$47$	324.048	−	271.908i	1.00569	−	0.843870i	0.0179234	−	0.999839i	$-0.494294\pi$
$47$	324.048	−	271.908i	1.00569	−	0.843870i	0.987762	+	0.155969i	$0.0498501\pi$
$48$		0			0
$49$	114.224	−	197.841i	0.333014	−	0.576797i
$50$	189.529	+	328.274i	0.536070	+	0.928500i
$51$		0			0
$52$	101.796	−	577.311i	0.271471	−	1.53959i
$53$	28.7445	+	163.018i	0.0744973	+	0.422495i	0.999133	+	0.0416416i	$0.0132588\pi$
$53$	28.7445	+	163.018i	0.0744973	+	0.422495i	−0.924635	+	0.380854i	$0.875630\pi$
$54$		0			0
$55$	334.030	+	280.284i	0.818919	+	0.687155i
$56$	−33.2438			−0.0793284
$57$		0			0
$58$	9.06741			0.0205278
$59$	−355.251	−	298.091i	−0.783894	−	0.657765i	0.160332	−	0.987063i	$-0.448743\pi$
$59$	−355.251	−	298.091i	−0.783894	−	0.657765i	−0.944226	+	0.329298i	$0.893188\pi$
$60$		0			0
$61$	−106.337	−	603.067i	−0.223198	−	1.26582i	−0.866101	−	0.499870i	$-0.833381\pi$
$61$	−106.337	−	603.067i	−0.223198	−	1.26582i	0.642903	−	0.765948i	$-0.277730\pi$
$62$	−93.3264	+	529.280i	−0.191169	+	1.08417i
$63$		0			0
$64$	202.732	+	351.143i	0.395962	+	0.685826i
$65$	606.566	−	1050.60i	1.15747	−	2.00479i
$66$		0			0
$67$	166.222	−	139.477i	0.303093	−	0.254325i	−0.478537	−	0.878067i	$-0.658833\pi$
$67$	166.222	−	139.477i	0.303093	−	0.254325i	0.781630	+	0.623742i	$0.214388\pi$
$68$	288.405	−	499.533i	0.514328	−	0.890841i
$69$		0			0
$70$	584.582	+	212.771i	0.998157	+	0.363299i
$71$	9.51311	−	53.9515i	0.0159014	−	0.0901812i	−0.975824	−	0.218557i	$-0.929865\pi$
$71$	9.51311	−	53.9515i	0.0159014	−	0.0901812i	0.991726	+	0.128375i	$0.0409763\pi$
$72$		0			0
$73$	130.528	−	47.5085i	0.209277	−	0.0761705i	−0.235255	−	0.971934i	$-0.575592\pi$
$73$	130.528	−	47.5085i	0.209277	−	0.0761705i	0.444531	+	0.895763i	$0.353370\pi$
$74$	912.146	+	765.381i	1.43290	+	1.20235i
$75$		0			0
$76$	200.872	+	561.745i	0.303178	+	0.847850i
$77$	313.073			0.463351
$78$		0			0
$79$	−436.266	+	158.788i	−0.621313	+	0.226140i	−0.633446	−	0.773787i	$-0.718360\pi$
$79$	−436.266	+	158.788i	−0.621313	+	0.226140i	0.0121327	+	0.999926i	$0.496138\pi$
$80$	180.521	+	1023.79i	0.252286	+	1.43079i
$81$		0			0
$82$	834.406	+	303.699i	1.12372	+	0.408999i
$83$	−43.2845	−	74.9710i	−0.0572421	−	0.0991462i	0.835984	−	0.548753i	$-0.184897\pi$
$83$	−43.2845	−	74.9710i	−0.0572421	−	0.0991462i	−0.893226	+	0.449607i	$0.851564\pi$
$84$		0			0
$85$	914.401	−	767.273i	1.16683	−	0.979088i
$86$	515.548	−	432.596i	0.646429	−	0.542419i
$87$		0			0
$88$	45.4278	+	78.6833i	0.0550298	+	0.0953145i
$89$	443.288	+	161.344i	0.527960	+	0.192162i	0.592227	−	0.805771i	$-0.298249\pi$
$89$	443.288	+	161.344i	0.527960	+	0.192162i	−0.0642673	+	0.997933i	$0.520471\pi$
$90$		0			0
$91$	−151.249	−	857.777i	−0.174233	−	0.988126i
$92$	454.792	−	165.531i	0.515384	−	0.187584i
$93$		0			0
$94$	−1649.40			−1.80981
$95$	−6.97532	+	1234.56i	−0.00753319	+	1.33329i
$96$		0			0
$97$	−326.817	−	274.232i	−0.342095	−	0.287052i	0.455512	−	0.890230i	$-0.349456\pi$
$97$	−326.817	−	274.232i	−0.342095	−	0.287052i	−0.797606	+	0.603178i	$0.793901\pi$
$98$	−837.033	+	304.655i	−0.862787	+	0.314029i
$99$		0			0
$100$	121.603	−	689.644i	0.121603	−	0.689644i
$101$	−738.716	−	268.871i	−0.727772	−	0.264887i	−0.0485505	−	0.998821i	$-0.515460\pi$
$101$	−738.716	−	268.871i	−0.727772	−	0.264887i	−0.679221	+	0.733933i	$0.737682\pi$
$102$		0			0
$103$	−787.352	+	1363.73i	−0.753205	+	1.30459i	0.193057	+	0.981187i	$0.438160\pi$
$103$	−787.352	+	1363.73i	−0.753205	+	1.30459i	−0.946262	+	0.323401i	$0.895174\pi$
$104$	193.635	−	162.479i	0.182571	−	0.153196i
$105$		0			0
$106$	322.719	−	558.966i	0.295710	−	0.512185i
$107$	−545.898	−	945.523i	−0.493214	−	0.854272i	0.506755	−	0.862090i	$-0.330845\pi$
$107$	−545.898	−	945.523i	−0.493214	−	0.854272i	−0.999969	+	0.00781778i	$0.997511\pi$
$108$		0			0
$109$	22.6313	−	128.348i	0.0198870	−	0.112785i	−0.973248	−	0.229756i	$-0.926207\pi$
$109$	22.6313	−	128.348i	0.0198870	−	0.112785i	0.993135	+	0.116971i	$0.0373184\pi$
$110$	−295.238	−	1674.38i	−0.255907	−	1.45132i
$111$		0			0
$112$	571.777	+	479.778i	0.482392	+	0.404775i
$113$	−384.818			−0.320360			−0.160180	−	0.987088i	$-0.551207\pi$
$113$	−384.818			−0.320360			−0.160180	+	0.987088i	$0.551207\pi$
$114$		0			0
$115$	1001.56			0.812137
$116$	−12.8323	−	10.7676i	−0.0102711	−	0.00861849i
$117$		0			0
$118$	313.994	+	1780.75i	0.244962	+	1.38925i
$119$	148.822	−	844.013i	0.114643	−	0.650173i
$120$		0			0
$121$	237.683	+	411.679i	0.178575	+	0.309301i
$122$	−1193.86	+	2067.83i	−0.885962	+	1.53453i
$123$		0			0
$124$	760.598	−	638.218i	0.550837	−	0.462207i
$125$	−207.090	+	358.690i	−0.148181	+	0.256658i
$126$		0			0
$127$	−1654.45	−	602.171i	−1.15598	−	0.420741i	−0.308317	−	0.951284i	$-0.599766\pi$
$127$	−1654.45	−	602.171i	−1.15598	−	0.420741i	−0.847658	+	0.530543i	$0.821988\pi$
$128$	−68.6958	+	389.593i	−0.0474368	+	0.269027i
$129$		0			0
$130$	−4444.92	+	1617.82i	−2.99881	+	1.09148i
$131$	1859.76	+	1560.52i	1.24036	+	1.04079i	0.997496	+	0.0707287i	$0.0225325\pi$
$131$	1859.76	+	1560.52i	1.24036	+	1.04079i	0.242867	+	0.970059i	$0.421912\pi$
$132$		0			0
$133$	565.925	+	682.235i	0.368962	+	0.444791i
$134$	−846.067			−0.545441
$135$		0			0
$136$	233.717	−	85.0659i	0.147360	−	0.0536348i
$137$	−494.457	−	2804.20i	−0.308353	−	1.74875i	−0.607289	−	0.794481i	$-0.707743\pi$
$137$	−494.457	−	2804.20i	−0.308353	−	1.74875i	0.298936	−	0.954273i	$-0.403368\pi$
$138$		0			0
$139$	−1403.68	−	510.896i	−0.856534	−	0.311753i	−0.123833	−	0.992303i	$-0.539519\pi$
$139$	−1403.68	−	510.896i	−0.856534	−	0.311753i	−0.732702	+	0.680550i	$0.761741\pi$
$140$	−574.642	−	995.309i	−0.346901	−	0.600850i
$141$		0			0
$142$	−163.635	+	137.306i	−0.0967039	+	0.0811442i
$143$	−1823.55	+	1530.14i	−1.06639	+	0.894804i
$144$		0			0
$145$	−17.3329	−	30.0214i	−0.00992700	−	0.0171941i
$146$	−508.951	−	185.243i	−0.288500	−	0.105006i
$147$		0			0
$148$	−381.986	−	2166.35i	−0.212156	−	1.20320i
$149$	−2523.37	+	918.430i	−1.38740	+	0.504971i	−0.924412	−	0.381395i	$-0.875444\pi$
$149$	−2523.37	+	918.430i	−1.38740	+	0.504971i	−0.462985	+	0.886366i	$0.653222\pi$
$150$		0			0
$151$	1148.04			0.618716			0.309358	−	0.950946i	$-0.399886\pi$
$151$	1148.04			0.618716			0.309358	+	0.950946i	$0.399886\pi$
$152$	−89.3456	+	241.226i	−0.0476769	+	0.128724i
$153$		0			0
$154$	−935.127	−	784.665i	−0.489316	−	0.410585i
$155$	1930.80	−	702.753i	1.00055	−	0.364171i
$156$		0			0
$157$	−454.023	+	2574.89i	−0.230796	+	1.30891i	0.620493	+	0.784212i	$0.286933\pi$
$157$	−454.023	+	2574.89i	−0.230796	+	1.30891i	−0.851289	+	0.524697i	$0.824179\pi$
$158$	1701.07	+	619.138i	0.856517	+	0.311747i
$159$		0			0
$160$	1841.54	−	3189.63i	0.909914	−	1.57602i
$161$	550.865	−	462.231i	0.269654	−	0.226266i
$162$		0			0
$163$	437.063	−	757.016i	0.210021	−	0.363767i	−0.741700	−	0.670732i	$-0.765980\pi$
$163$	437.063	−	757.016i	0.210021	−	0.363767i	0.951721	+	0.306965i	$0.0993134\pi$
$164$	−820.217	−	1420.66i	−0.390538	−	0.676431i
$165$		0			0
$166$	−58.6143	+	332.418i	−0.0274057	+	0.155426i
$167$	−66.8343	−	379.036i	−0.0309688	−	0.175633i	0.965400	−	0.260773i	$-0.0839774\pi$
$167$	−66.8343	−	379.036i	−0.0309688	−	0.175633i	−0.996369	+	0.0851399i	$0.972866\pi$
$168$		0			0
$169$	3390.36	+	2844.85i	1.54318	+	1.29488i
$170$	−4654.29			−2.09981
$171$		0			0
$172$	−1243.32			−0.551175
$173$	2598.46	+	2180.37i	1.14195	+	0.958209i	0.999501	−	0.0315931i	$-0.0100581\pi$
$173$	2598.46	+	2180.37i	1.14195	+	0.958209i	0.142448	+	0.989802i	$0.454503\pi$
$174$		0			0
$175$	−180.679	−	1024.68i	−0.0780461	−	0.442621i
$176$	354.230	−	2008.94i	0.151711	−	0.860393i
$177$		0			0
$178$	−919.688	−	1592.95i	−0.387267	−	0.670766i
$179$	251.009	−	434.760i	0.104812	−	0.181539i	−0.808850	−	0.588016i	$-0.799909\pi$
$179$	251.009	−	434.760i	0.104812	−	0.181539i	0.913661	+	0.406477i	$0.133243\pi$
$180$		0			0
$181$	1364.18	−	1144.68i	0.560214	−	0.470075i	−0.318168	−	0.948034i	$-0.603068\pi$
$181$	1364.18	−	1144.68i	0.560214	−	0.470075i	0.878382	+	0.477959i	$0.158623\pi$
$182$	−1698.10	+	2941.20i	−0.691602	+	1.19789i
$183$		0			0
$184$	196.103	+	71.3755i	0.0785699	+	0.0285971i
$185$	790.492	−	4483.10i	0.314152	−	1.78164i
$186$		0			0
$187$	−2201.03	+	801.108i	−0.860722	+	0.313277i
$188$	2334.25	+	1958.67i	0.905545	+	0.759842i
$189$		0			0
$190$	3115.04	−	3670.04i	1.18941	−	1.40133i
$191$	112.666			0.0426817			0.0213408	−	0.999772i	$-0.493206\pi$
$191$	112.666			0.0426817			0.0213408	+	0.999772i	$0.493206\pi$
$192$		0			0
$193$	117.904	−	42.9135i	0.0439737	−	0.0160051i	−0.319940	−	0.947438i	$-0.603663\pi$
$193$	117.904	−	42.9135i	0.0439737	−	0.0160051i	0.363913	+	0.931433i	$0.381440\pi$
$194$	288.862	+	1638.22i	0.106903	+	0.606275i
$195$		0			0
$196$	1546.36	+	562.828i	0.563542	+	0.205112i
$197$	46.0978	+	79.8437i	0.0166717	+	0.0288763i	0.874241	−	0.485492i	$-0.161360\pi$
$197$	46.0978	+	79.8437i	0.0166717	+	0.0288763i	−0.857569	+	0.514369i	$0.828026\pi$
$198$		0			0
$199$	6.42587	−	5.39195i	0.00228904	−	0.00192073i	−0.641642	−	0.767004i	$-0.721747\pi$
$199$	6.42587	−	5.39195i	0.00228904	−	0.00192073i	0.643931	+	0.765083i	$0.277302\pi$
$200$	231.312	−	194.094i	0.0817811	−	0.0686225i
$201$		0			0
$202$	1532.61	+	2654.56i	0.533832	+	0.924625i
$203$	−23.3884	−	8.51269i	−0.00808643	−	0.00294322i
$204$		0			0
$205$	−589.493	−	3343.18i	−0.200839	−	1.13901i
$206$	5769.72	−	2100.01i	1.95144	−	0.710265i
$207$		0			0
$208$	−5675.33			−1.89189
$209$	841.413	−	2271.74i	0.278477	−	0.751865i
$210$		0			0
$211$	3749.45	+	3146.16i	1.22333	+	1.02650i	0.998644	+	0.0520651i	$0.0165803\pi$
$211$	3749.45	+	3146.16i	1.22333	+	1.02650i	0.224687	+	0.974431i	$0.427864\pi$
$212$	−1120.49	+	407.825i	−0.362998	+	0.132120i
$213$		0			0
$214$	−739.234	+	4192.40i	−0.236136	+	1.33919i
$215$	−2417.78	−	880.001i	−0.766937	−	0.279142i
$216$		0			0
$217$	737.626	−	1277.60i	0.230752	−	0.399675i
$218$	−389.281	+	326.645i	−0.120942	+	0.101483i
$219$		0			0
$220$	−1570.50	+	2720.19i	−0.481288	+	0.833615i
$221$	3258.26	+	5643.48i	0.991740	+	1.71774i
$222$		0			0
$223$	616.247	−	3494.91i	0.185054	−	1.04949i	−0.740833	−	0.671690i	$-0.765569\pi$
$223$	616.247	−	3494.91i	0.185054	−	1.04949i	0.925886	−	0.377802i	$-0.123320\pi$
$224$	−459.193	−	2604.21i	−0.136969	−	0.776792i
$225$		0			0
$226$	1149.42	+	964.480i	0.338312	+	0.283877i
$227$	−2211.89			−0.646733			−0.323366	−	0.946274i	$-0.604815\pi$
$227$	−2211.89			−0.646733			−0.323366	+	0.946274i	$0.604815\pi$
$228$		0			0
$229$	356.283			0.102812			0.0514058	−	0.998678i	$-0.483630\pi$
$229$	356.283			0.102812			0.0514058	+	0.998678i	$0.483630\pi$
$230$	−2991.58	−	2510.23i	−0.857648	−	0.719652i
$231$		0			0
$232$	−1.25427	−	7.11333i	−0.000354944	−	0.00201299i
$233$	−961.539	+	5453.16i	−0.270354	+	1.53326i	0.482988	+	0.875627i	$0.339551\pi$
$233$	−961.539	+	5453.16i	−0.270354	+	1.53326i	−0.753343	+	0.657628i	$0.771560\pi$
$234$		0			0
$235$	3152.91	+	5461.01i	0.875206	+	1.51590i
$236$	1670.28	−	2893.01i	0.460703	−	0.797961i
$237$		0			0
$238$	−2559.89	+	2148.01i	−0.697199	+	0.585019i
$239$	−1006.55	+	1743.40i	−0.272421	+	0.471847i	−0.969481	−	0.245166i	$-0.921158\pi$
$239$	−1006.55	+	1743.40i	−0.272421	+	0.471847i	0.697060	+	0.717013i	$0.254491\pi$
$240$		0			0
$241$	−218.000	−	79.3455i	−0.0582681	−	0.0212078i	0.312722	−	0.949845i	$-0.398759\pi$
$241$	−218.000	−	79.3455i	−0.0582681	−	0.0212078i	−0.370990	+	0.928637i	$0.620982\pi$
$242$	321.862	−	1825.37i	0.0854961	−	0.484872i
$243$		0			0
$244$	4145.13	−	1508.70i	1.08756	−	0.395839i
$245$	2608.72	+	2188.98i	0.680266	+	0.570811i
$246$		0			0
$247$	−6630.75	−	1207.85i	−1.70812	−	0.311148i
$248$	428.126			0.109621
$249$		0			0
$250$	1517.56	−	552.346i	0.383915	−	0.139734i
$251$	−491.638	−	2788.22i	−0.123633	−	0.701158i	−0.982110	−	0.188306i	$-0.939700\pi$
$251$	−491.638	−	2788.22i	−0.123633	−	0.701158i	0.858477	−	0.512852i	$-0.171411\pi$
$252$		0			0
$253$	−1846.80	−	672.179i	−0.458921	−	0.167034i
$254$	3432.49	+	5945.24i	0.847926	+	1.46865i
$255$		0			0
$256$	3666.47	−	3076.53i	0.895134	−	0.751107i
$257$	2406.27	−	2019.10i	0.584044	−	0.490071i	−0.302229	−	0.953235i	$-0.597731\pi$
$257$	2406.27	−	2019.10i	0.584044	−	0.490071i	0.886272	+	0.463165i	$0.153286\pi$
$258$		0			0
$259$	−1634.23	−	2830.56i	−0.392069	−	0.679083i
$260$	8211.67	+	2988.80i	1.95872	+	0.712914i
$261$		0			0
$262$	−1643.78	−	9322.31i	−0.387606	−	2.19822i
$263$	−3422.16	+	1245.56i	−0.802355	+	0.292033i	−0.710462	−	0.703735i	$-0.751514\pi$
$263$	−3422.16	+	1245.56i	−0.802355	+	0.292033i	−0.0918931	+	0.995769i	$0.529292\pi$
$264$		0			0
$265$	−2467.58			−0.572009
$266$	19.5276	−	3456.18i	0.00450119	−	0.796661i
$267$		0			0
$268$	1197.36	+	1004.71i	0.272913	+	0.229001i
$269$	−1799.26	+	654.876i	−0.407816	+	0.148433i	−0.537779	−	0.843086i	$-0.680737\pi$
$269$	−1799.26	+	654.876i	−0.407816	+	0.148433i	0.129963	+	0.991519i	$0.458514\pi$
$270$		0			0
$271$	−974.560	+	5527.00i	−0.218451	+	1.23890i	0.656365	+	0.754444i	$0.272093\pi$
$271$	−974.560	+	5527.00i	−0.218451	+	1.23890i	−0.874816	+	0.484455i	$0.839018\pi$
$272$	−5247.49	−	1909.93i	−1.16976	−	0.425760i
$273$		0			0
$274$	−5551.35	+	9615.22i	−1.22398	+	2.11999i
$275$	−2178.38	+	1827.88i	−0.477677	+	0.400819i
$276$		0			0
$277$	−2730.76	+	4729.81i	−0.592330	+	1.02595i	0.401588	+	0.915821i	$0.368458\pi$
$277$	−2730.76	+	4729.81i	−0.592330	+	1.02595i	−0.993918	+	0.110125i	$0.964875\pi$
$278$	2912.20	+	5044.08i	0.628282	+	1.08822i
$279$		0			0
$280$	86.0534	−	488.033i	0.0183667	−	0.104163i
$281$	33.9875	+	192.753i	0.00721539	+	0.0409205i	0.988203	−	0.153150i	$-0.0489419\pi$
$281$	33.9875	+	192.753i	0.00721539	+	0.0409205i	−0.980987	+	0.194071i	$0.937831\pi$
$282$		0			0
$283$	−4422.46	−	3710.88i	−0.928932	−	0.779467i	0.0466933	−	0.998909i	$-0.485132\pi$
$283$	−4422.46	−	3710.88i	−0.928932	−	0.779467i	−0.975625	+	0.219443i	$0.929576\pi$
$284$	394.630			0.0824541
$285$		0			0
$286$	9281.86			1.91905
$287$	−1867.14	−	1566.72i	−0.384020	−	0.322231i
$288$		0			0
$289$	260.291	+	1476.19i	0.0529801	+	0.300465i
$290$	−23.4715	+	133.113i	−0.00475274	+	0.0269541i
$291$		0			0
$292$	500.296	+	866.539i	0.100266	+	0.173666i
$293$	2058.64	−	3565.68i	0.410469	−	0.710952i	−0.584472	−	0.811414i	$-0.698698\pi$
$293$	2058.64	−	3565.68i	0.410469	−	0.710952i	0.994941	+	0.100461i	$0.0320318\pi$
$294$		0			0
$295$	5295.69	−	4443.61i	1.04518	−	0.877007i
$296$	474.262	−	821.445i	0.0931281	−	0.161303i
$297$		0			0
$298$	9838.99	+	3581.10i	1.91261	+	0.696133i
$299$	−949.467	+	5384.70i	−0.183643	+	1.04149i
$300$		0			0
$301$	−1735.93	+	631.827i	−0.332417	+	0.120990i
$302$	−3429.11	−	2877.37i	−0.653388	−	0.548257i
$303$		0			0
$304$	5018.10	−	2859.52i	0.946736	−	0.539489i
$305$	9128.54			1.71377
$306$		0			0
$307$	−8283.81	+	3015.06i	−1.54001	+	0.560517i	−0.966047	−	0.258366i	$-0.916816\pi$
$307$	−8283.81	+	3015.06i	−1.54001	+	0.560517i	−0.573960	+	0.818883i	$0.694594\pi$
$308$	391.610	+	2220.93i	0.0724483	+	0.410875i
$309$		0			0
$310$	−7528.48	−	2740.14i	−1.37932	−	0.502031i
$311$	−1447.09	−	2506.43i	−0.263848	−	0.456998i	0.703413	−	0.710781i	$-0.251658\pi$
$311$	−1447.09	−	2506.43i	−0.263848	−	0.456998i	−0.967261	+	0.253783i	$0.918325\pi$
$312$		0			0
$313$	2808.83	−	2356.89i	0.507235	−	0.425621i	−0.352920	−	0.935654i	$-0.614811\pi$
$313$	2808.83	−	2356.89i	0.507235	−	0.425621i	0.860155	+	0.510033i	$0.170367\pi$
$314$	7809.66	−	6553.08i	1.40358	−	1.17774i
$315$		0			0
$316$	−1672.14	−	2896.24i	−0.297675	−	0.515589i
$317$	−201.198	−	73.2302i	−0.0356480	−	0.0129748i	0.324135	−	0.946011i	$-0.394927\pi$
$317$	−201.198	−	73.2302i	−0.0356480	−	0.0129748i	−0.359783	+	0.933036i	$0.617149\pi$
$318$		0			0
$319$	11.8121	+	66.9897i	0.00207320	+	0.0117577i
$320$	−5679.71	+	2067.25i	−0.992205	+	0.361133i
$321$		0			0
$322$	−2803.90			−0.485264
$323$	−5724.41	−	3348.25i	−0.986113	−	0.576786i
$324$		0			0
$325$	6060.53	+	5085.39i	1.03439	+	0.867959i
$326$	−3202.81	+	1165.73i	−0.544132	+	0.198048i
$327$		0			0
$328$	122.829	−	696.596i	0.0206771	−	0.117265i
$329$	4254.45	+	1548.49i	0.712934	+	0.259487i
$330$		0			0
$331$	4757.36	−	8240.00i	0.789995	−	1.36831i	−0.135974	−	0.990712i	$-0.543416\pi$
$331$	4757.36	−	8240.00i	0.789995	−	1.36831i	0.925969	−	0.377599i	$-0.123250\pi$
$332$	477.699	−	400.837i	0.0789673	−	0.0662615i
$333$		0			0
$334$	−750.360	+	1299.66i	−0.122928	+	0.212917i
$335$	1617.30	+	2801.25i	0.263769	+	0.456862i
$336$		0			0
$337$	604.235	−	3426.79i	0.0976700	−	0.553914i	−0.896226	−	0.443597i	$-0.853702\pi$
$337$	604.235	−	3426.79i	0.0976700	−	0.553914i	0.993896	−	0.110317i	$-0.0351866\pi$
$338$	−2996.62	−	16994.7i	−0.482233	−	2.73488i
$339$		0			0
$340$	6586.80	+	5526.98i	1.05064	+	0.881596i
$341$	−4031.88			−0.640289
$342$		0			0
$343$	6116.16			0.962803
$344$	−410.683	−	344.604i	−0.0643678	−	0.0540110i
$345$		0			0
$346$	−2296.69	−	13025.2i	−0.356852	−	2.02381i
$347$	−672.915	+	3816.29i	−0.104104	+	0.590401i	0.887471	+	0.460864i	$0.152460\pi$
$347$	−672.915	+	3816.29i	−0.104104	+	0.590401i	−0.991575	+	0.129538i	$0.958651\pi$
$348$		0			0
$349$	−4270.73	−	7397.12i	−0.655034	−	1.13455i	−0.981885	−	0.189476i	$-0.939321\pi$
$349$	−4270.73	−	7397.12i	−0.655034	−	1.13455i	0.326851	−	0.945076i	$-0.394012\pi$
$350$	−2028.52	+	3513.49i	−0.309796	+	0.536583i
$351$		0			0
$352$	−5536.31	+	4645.52i	−0.838314	+	0.703429i
$353$	−401.051	+	694.641i	−0.0604697	+	0.104737i	−0.894675	−	0.446717i	$-0.852593\pi$
$353$	−401.051	+	694.641i	−0.0604697	+	0.104737i	0.834206	+	0.551453i	$0.185927\pi$
$354$		0			0
$355$	767.406	+	279.313i	0.114732	+	0.0417589i
$356$	−590.076	+	3346.49i	−0.0878483	+	0.498212i
$357$		0			0
$358$	−1839.40	+	669.485i	−0.271551	+	0.0988363i
$359$	−5348.84	−	4488.21i	−0.786354	−	0.659830i	0.158486	−	0.987361i	$-0.449339\pi$
$359$	−5348.84	−	4488.21i	−0.786354	−	0.659830i	−0.944840	+	0.327532i	$0.893783\pi$
$360$		0			0
$361$	6471.45	−	2272.94i	0.943497	−	0.331380i
$362$	−6943.66			−1.00815
$363$		0			0
$364$	5895.85	−	2145.91i	0.848974	−	0.309001i
$365$	359.565	+	2039.19i	0.0515629	+	0.292428i
$366$		0			0
$367$	−8503.07	−	3094.86i	−1.20942	−	0.440192i	−0.342916	−	0.939366i	$-0.611415\pi$
$367$	−8503.07	−	3094.86i	−1.20942	−	0.440192i	−0.866502	+	0.499174i	$0.833637\pi$
$368$	−2342.77	−	4057.80i	−0.331862	−	0.574803i
$369$		0			0
$370$	−13597.3	+	11409.5i	−1.91051	+	1.60311i
$371$	−1357.19	+	1138.82i	−0.189924	+	0.159365i
$372$		0			0
$373$	2885.86	+	4998.45i	0.400601	+	0.693861i	0.993798	−	0.111196i	$-0.0354681\pi$
$373$	2885.86	+	4998.45i	0.400601	+	0.693861i	−0.593198	+	0.805057i	$0.702135\pi$
$374$	8582.14	+	3123.64i	1.18656	+	0.431871i
$375$		0			0
$376$	228.157	+	1293.94i	0.0312933	+	0.177473i
$377$	177.836	−	64.7270i	0.0242945	−	0.00884246i
$378$		0			0
$379$	−2255.18			−0.305648			−0.152824	−	0.988253i	$-0.548837\pi$
$379$	−2255.18			−0.305648			−0.152824	+	0.988253i	$0.548837\pi$
$380$	−8766.62	+	1494.77i	−1.18347	+	0.201790i
$381$		0			0
$382$	−336.524	−	282.377i	−0.0450735	−	0.0378211i
$383$	−579.774	+	211.020i	−0.0773500	+	0.0281531i	−0.380405	−	0.924820i	$-0.624216\pi$
$383$	−579.774	+	211.020i	−0.0773500	+	0.0281531i	0.303055	+	0.952973i	$0.401993\pi$
$384$		0			0
$385$	−810.408	+	4596.05i	−0.107278	+	0.608406i
$386$	−459.726	−	167.327i	−0.0606203	−	0.0220640i
$387$		0			0
$388$	1536.59	−	2661.45i	0.201053	−	0.348234i
$389$	−5378.15	+	4512.80i	−0.700984	+	0.588196i	−0.922054	−	0.387062i	$-0.873490\pi$
$389$	−5378.15	+	4512.80i	−0.700984	+	0.588196i	0.221069	+	0.975258i	$0.429045\pi$
$390$		0			0
$391$	−2690.01	+	4659.24i	−0.347928	+	0.602629i
$392$	354.785	+	614.505i	0.0457126	+	0.0791765i
$393$		0			0
$394$	62.4239	−	354.023i	0.00798190	−	0.0452676i
$395$	−1201.77	−	6815.60i	−0.153083	−	0.868178i
$396$		0			0
$397$	1889.67	+	1585.62i	0.238891	+	0.200453i	0.754371	−	0.656448i	$-0.227942\pi$
$397$	1889.67	+	1585.62i	0.238891	+	0.200453i	−0.515480	+	0.856901i	$0.672386\pi$
$398$	−32.7076			−0.00411931
$399$		0			0
$400$	−6779.64			−0.847455
$401$	5939.65	+	4983.96i	0.739681	+	0.620666i	0.932752	−	0.360519i	$-0.117400\pi$
$401$	5939.65	+	4983.96i	0.739681	+	0.620666i	−0.193071	+	0.981185i	$0.561845\pi$
$402$		0			0
$403$	1947.85	+	11046.8i	0.240767	+	1.36546i
$404$	983.331	−	5576.75i	0.121095	−	0.686766i
$405$		0			0
$406$	48.5239	+	84.0459i	0.00593153	+	0.0102737i
$407$	−4466.36	+	7735.96i	−0.543954	+	0.942156i
$408$		0			0
$409$	558.667	−	468.777i	0.0675411	−	0.0566737i	−0.608392	−	0.793637i	$-0.708185\pi$
$409$	558.667	−	468.777i	0.0675411	−	0.0566737i	0.675933	+	0.736963i	$0.263741\pi$
$410$	−6618.33	+	11463.3i	−0.797210	+	1.38081i
$411$		0			0
$412$	−10659.1	−	3879.61i	−1.27461	−	0.463919i
$413$	861.894	−	4888.04i	0.102690	−	0.582385i
$414$		0			0
$415$	1212.65	−	441.369i	0.143438	−	0.0522071i
$416$	15402.7	+	12924.4i	1.81534	+	1.52325i
$417$		0			0
$418$	−8206.97	+	4676.67i	−0.960325	+	0.547233i
$419$	−2807.54			−0.327344			−0.163672	−	0.986515i	$-0.552334\pi$
$419$	−2807.54			−0.327344			−0.163672	+	0.986515i	$0.552334\pi$
$420$		0			0
$421$	−10367.0	+	3773.26i	−1.20013	+	0.436812i	−0.863270	−	0.504743i	$-0.831587\pi$
$421$	−10367.0	+	3773.26i	−1.20013	+	0.436812i	−0.336860	+	0.941555i	$0.609365\pi$
$422$	−3314.01	−	18794.7i	−0.382283	−	2.16804i
$423$		0			0
$424$	−483.146	−	175.851i	−0.0553388	−	0.0201417i
$425$	3892.25	+	6741.58i	0.444240	+	0.769446i
$426$		0			0
$427$	5020.77	−	4212.93i	0.569022	−	0.477466i
$428$	6024.67	−	5055.30i	0.680405	−	0.570928i
$429$		0			0
$430$	5016.17	+	8688.26i	0.562561	+	0.974384i
$431$	−2580.70	−	939.297i	−0.288417	−	0.104975i	0.193760	−	0.981049i	$-0.437932\pi$
$431$	−2580.70	−	939.297i	−0.288417	−	0.104975i	−0.482177	+	0.876074i	$0.660154\pi$
$432$		0			0
$433$	−2064.25	−	11706.9i	−0.229103	−	1.29931i	−0.854685	−	0.519147i	$-0.826250\pi$
$433$	−2064.25	−	11706.9i	−0.229103	−	1.29931i	0.625582	−	0.780158i	$-0.284862\pi$
$434$	−5405.33	+	1967.38i	−0.597844	+	0.217597i
$435$		0			0
$436$	938.807			0.103121
$437$	−1873.57	−	5239.51i	−0.205091	−	0.573546i
$438$		0			0
$439$	−6394.86	−	5365.92i	−0.695239	−	0.583375i	0.225176	−	0.974318i	$-0.427704\pi$
$439$	−6394.86	−	5365.92i	−0.695239	−	0.583375i	−0.920415	+	0.390943i	$0.872149\pi$
$440$	−1272.70	+	463.224i	−0.137894	+	0.0501894i
$441$		0			0
$442$	4412.22	−	25022.9i	0.474814	−	2.69280i
$443$	13040.2	+	4746.23i	1.39855	+	0.509030i	0.927747	−	0.373210i	$-0.121743\pi$
$443$	13040.2	+	4746.23i	1.39855	+	0.509030i	0.470801	+	0.882240i	$0.343965\pi$
$444$		0			0
$445$	−3516.07	+	6090.01i	−0.374557	+	0.648751i
$446$	−10600.1	+	8894.53i	−1.12540	+	0.944323i
$447$		0			0
$448$	−2169.83	+	3758.25i	−0.228828	+	0.396341i
$449$	−3893.89	−	6744.42i	−0.409275	−	0.708884i	0.585534	−	0.810648i	$-0.300885\pi$
$449$	−3893.89	−	6744.42i	−0.409275	−	0.708884i	−0.994809	+	0.101764i	$0.967551\pi$
$450$		0			0
$451$	−1156.74	+	6560.19i	−0.120773	+	0.684938i
$452$	−481.353	−	2729.89i	−0.0500906	−	0.284078i
$453$		0			0
$454$	6606.75	+	5543.72i	0.682974	+	0.573083i
$455$	12984.1			1.33781
$456$		0			0
$457$	3130.91			0.320476			0.160238	−	0.987078i	$-0.448774\pi$
$457$	3130.91			0.320476			0.160238	+	0.987078i	$0.448774\pi$
$458$	−1064.19	−	892.962i	−0.108573	−	0.0911034i
$459$		0			0
$460$	1252.81	+	7105.02i	0.126984	+	0.720160i
$461$	2165.88	−	12283.3i	0.218818	−	1.24098i	−0.655338	−	0.755336i	$-0.727474\pi$
$461$	2165.88	−	12283.3i	0.218818	−	1.24098i	0.874156	−	0.485645i	$-0.161415\pi$
$462$		0			0
$463$	4248.56	+	7358.72i	0.426452	+	0.738637i	0.996555	−	0.0829368i	$-0.0264300\pi$
$463$	4248.56	+	7358.72i	0.426452	+	0.738637i	−0.570103	+	0.821573i	$0.693097\pi$
$464$	−81.0875	+	140.448i	−0.00811291	+	0.0140520i
$465$		0			0
$466$	16539.5	−	13878.3i	1.64415	−	1.37961i
$467$	−9910.20	+	17165.0i	−0.981990	+	1.70086i	−0.327376	+	0.944894i	$0.606164\pi$
$467$	−9910.20	+	17165.0i	−0.981990	+	1.70086i	−0.654614	+	0.755963i	$0.727169\pi$
$468$		0			0
$469$	2182.34	+	794.307i	0.214864	+	0.0782040i
$470$	4269.56	−	24213.9i	0.419021	−	2.37639i
$471$		0			0
$472$	1353.55	−	492.653i	0.131996	−	0.0480428i
$473$	3867.61	+	3245.31i	0.375968	+	0.315474i
$474$		0			0
$475$	−7920.96	−	1442.87i	−0.765134	−	0.139376i
$476$	6173.56			0.594463
$477$		0			0
$478$	7376.05	−	2684.66i	0.705800	−	0.256890i
$479$	1053.81	+	5976.45i	0.100521	+	0.570086i	0.992915	+	0.118827i	$0.0379135\pi$
$479$	1053.81	+	5976.45i	0.100521	+	0.570086i	−0.892393	+	0.451258i	$0.850975\pi$
$480$		0			0
$481$	23353.2	+	8499.87i	2.21375	+	0.805739i
$482$	452.284	+	783.378i	0.0427406	+	0.0740288i
$483$		0			0
$484$	−2623.13	+	2201.07i	−0.246350	+	0.206712i
$485$	4871.82	−	4087.94i	0.456120	−	0.382730i
$486$		0			0
$487$	3060.83	+	5301.51i	0.284803	+	0.493294i	0.972561	−	0.232646i	$-0.0747383\pi$
$487$	3060.83	+	5301.51i	0.284803	+	0.493294i	−0.687758	+	0.725940i	$0.741405\pi$
$488$	1787.34	+	650.540i	0.165798	+	0.0603454i
$489$		0			0
$490$	−2305.76	−	13076.6i	−0.212579	−	1.20559i
$491$	18238.2	−	6638.15i	1.67633	−	0.610134i	0.683529	−	0.729923i	$-0.260444\pi$
$491$	18238.2	−	6638.15i	1.67633	−	0.610134i	0.992799	+	0.119790i	$0.0382221\pi$
$492$		0			0
$493$	186.212			0.0170113
$494$	16778.3	+	20226.6i	1.52812	+	1.84218i
$495$		0			0
$496$	−7363.57	−	6178.77i	−0.666601	−	0.559344i
$497$	550.986	−	200.542i	0.0497285	−	0.0180997i
$498$		0			0
$499$	−1002.85	+	5687.46i	−0.0899676	+	0.510232i	0.906206	+	0.422836i	$0.138965\pi$
$499$	−1002.85	+	5687.46i	−0.0899676	+	0.510232i	−0.996174	+	0.0873953i	$0.972146\pi$
$500$	−2803.58	−	1020.42i	−0.250760	−	0.0912690i
$501$		0			0
$502$	−5519.70	+	9560.40i	−0.490749	+	0.850003i
$503$	−2.94155	+	2.46825i	−0.000260750	+	0.000218795i	−0.642918	−	0.765935i	$-0.722276\pi$
$503$	−2.94155	+	2.46825i	−0.000260750	+	0.000218795i	0.642657	+	0.766154i	$0.277832\pi$
$504$		0			0
$505$	5859.34	−	10148.7i	0.516311	−	0.894278i
$506$	3831.54	+	6636.42i	0.336626	+	0.583053i
$507$		0			0
$508$	2202.30	−	12489.9i	0.192345	−	1.09084i
$509$	−1532.11	−	8689.04i	−0.133418	−	0.756650i	−0.975948	−	0.218002i	$-0.930046\pi$
$509$	−1532.11	−	8689.04i	−0.133418	−	0.756650i	0.842530	−	0.538649i	$-0.181065\pi$
$510$		0			0
$511$	1138.87	+	955.629i	0.0985926	+	0.0827290i
$512$	−15497.4			−1.33769
$513$		0			0
$514$	−12247.9			−1.05103
$515$	−17982.1	−	15088.8i	−1.53861	−	1.29105i
$516$		0			0
$517$	−2148.67	−	12185.7i	−0.182782	−	1.03661i
$518$	−2213.01	+	12550.6i	−0.187710	+	1.06456i
$519$		0			0
$520$	1884.02	+	3263.22i	0.158884	+	0.275196i
$521$	2368.71	−	4102.73i	0.199185	−	0.344998i	−0.749080	−	0.662480i	$-0.769504\pi$
$521$	2368.71	−	4102.73i	0.199185	−	0.344998i	0.948264	+	0.317482i	$0.102837\pi$
$522$		0			0
$523$	−5623.82	+	4718.95i	−0.470196	+	0.394542i	−0.846866	−	0.531806i	$-0.821514\pi$
$523$	−5623.82	+	4718.95i	−0.470196	+	0.394542i	0.376670	+	0.926348i	$0.377069\pi$
$524$	−8743.99	+	15145.0i	−0.728975	+	1.26262i
$525$		0			0
$526$	13343.5	+	4856.65i	1.10609	+	0.402585i
$527$	−1916.59	+	10869.5i	−0.158421	+	0.898451i
$528$		0			0
$529$	7191.31	−	2617.42i	0.591050	−	0.215125i
$530$	7370.48	+	6184.57i	0.604063	+	0.506869i
$531$		0			0
$532$	−4131.86	+	4868.03i	−0.336727	+	0.396722i
$533$	18532.8			1.50609
$534$		0			0
$535$	15293.8	−	5566.47i	1.23590	−	0.449831i
$536$	117.034	+	663.734i	0.00943117	+	0.0534868i
$537$		0			0
$538$	7015.58	+	2553.46i	0.562199	+	0.204624i
$539$	−3341.18	−	5787.10i	−0.267004	−	0.462464i
$540$		0			0
$541$	−5575.95	+	4678.78i	−0.443122	+	0.371823i	−0.836876	−	0.547393i	$-0.815620\pi$
$541$	−5575.95	+	4678.78i	−0.443122	+	0.371823i	0.393754	+	0.919216i	$0.371176\pi$
$542$	16763.4	−	14066.2i	1.32851	−	1.11475i
$543$		0			0
$544$	9892.09	+	17133.6i	0.779632	+	1.35036i
$545$	1825.62	+	664.473i	0.143488	+	0.0522255i
$546$		0			0
$547$	3892.10	+	22073.2i	0.304230	+	1.72538i	0.627105	+	0.778935i	$0.284240\pi$
$547$	3892.10	+	22073.2i	0.304230	+	1.72538i	−0.322875	+	0.946442i	$0.604649\pi$
$548$	19274.4	−	7015.32i	1.50249	−	0.546861i
$549$		0			0
$550$	11087.9			0.859619
$551$	−124.629	+	146.834i	−0.00963587	+	0.0113527i
$552$		0			0
$553$	−3806.46	−	3194.00i	−0.292708	−	0.245611i
$554$	20011.0	−	7283.42i	1.53463	−	0.558561i
$555$		0			0
$556$	1868.48	−	10596.7i	0.142520	−	0.808273i
$557$	5218.93	+	1899.53i	0.397007	+	0.144499i	0.532806	−	0.846238i	$-0.321138\pi$
$557$	5218.93	+	1899.53i	0.397007	+	0.144499i	−0.135798	+	0.990737i	$0.543360\pi$
$558$		0			0
$559$	7023.20	−	12164.5i	0.531395	−	0.920403i
$560$	−8523.43	+	7152.00i	−0.643179	+	0.539692i
$561$		0			0
$562$	381.583	−	660.922i	0.0286408	−	0.0496073i
$563$	−2190.35	−	3793.79i	−0.163965	−	0.283995i	0.772323	−	0.635231i	$-0.219095\pi$
$563$	−2190.35	−	3793.79i	−0.163965	−	0.283995i	−0.936287	+	0.351236i	$0.885762\pi$
$564$		0			0
$565$	996.123	−	5649.29i	0.0741721	−	0.420651i
$566$	3908.86	+	22168.3i	0.290286	+	1.64629i
$567$		0			0
$568$	130.351	+	109.377i	0.00962924	+	0.00807989i
$569$	−13999.8			−1.03146			−0.515731	−	0.856750i	$-0.672480\pi$
$569$	−13999.8			−1.03146			−0.515731	+	0.856750i	$0.672480\pi$
$570$		0			0
$571$	−22551.7			−1.65282			−0.826410	−	0.563069i	$-0.809620\pi$
$571$	−22551.7			−1.65282			−0.826410	+	0.563069i	$0.809620\pi$
$572$	−13135.8	−	11022.2i	−0.960201	−	0.805705i
$573$		0			0
$574$	1650.30	+	9359.34i	0.120004	+	0.680577i
$575$	−1134.21	+	6432.45i	−0.0822609	+	0.466525i
$576$		0			0
$577$	−6663.86	−	11542.1i	−0.480798	−	0.832766i	0.518960	−	0.854799i	$-0.326319\pi$
$577$	−6663.86	−	11542.1i	−0.480798	−	0.832766i	−0.999757	+	0.0220329i	$0.992986\pi$
$578$	2922.34	−	5061.63i	0.210300	−	0.364249i
$579$		0			0
$580$	191.290	−	160.511i	0.0136946	−	0.0114912i
$581$	463.271	−	802.409i	0.0330804	−	0.0572969i
$582$		0			0
$583$	4550.03	+	1656.07i	0.323230	+	0.117646i
$584$	−74.9200	+	424.893i	−0.00530858	+	0.0301065i
$585$		0			0
$586$	−15085.8	+	5490.77i	−1.06346	+	0.387068i
$587$	−13531.2	−	11354.0i	−0.951433	−	0.798347i	0.0281053	−	0.999605i	$-0.491053\pi$
$587$	−13531.2	−	11354.0i	−0.951433	−	0.798347i	−0.979538	+	0.201258i	$0.935497\pi$
$588$		0			0
$589$	−7288.20	−	8786.08i	−0.509856	−	0.614642i
$590$	−26955.0			−1.88088
$591$		0			0
$592$	−20012.3	+	7283.87i	−1.38936	+	0.505685i
$593$	−1982.53	−	11243.5i	−0.137289	−	0.778607i	−0.973238	−	0.229799i	$-0.926193\pi$
$593$	−1982.53	−	11243.5i	−0.137289	−	0.778607i	0.835949	−	0.548808i	$-0.184918\pi$
$594$		0			0
$595$	12005.2	+	4369.55i	0.827171	+	0.301066i
$596$	−9671.69	−	16751.9i	−0.664711	−	1.15131i
$597$		0			0
$598$	16331.8	−	13704.0i	1.11682	−	0.937122i
$599$	−411.117	+	344.968i	−0.0280431	+	0.0235309i	−0.656701	−	0.754151i	$-0.728049\pi$
$599$	−411.117	+	344.968i	−0.0280431	+	0.0235309i	0.628658	+	0.777682i	$0.283604\pi$
$600$		0			0
$601$	−3598.36	−	6232.54i	−0.244226	−	0.423013i	0.717687	−	0.696365i	$-0.245201\pi$
$601$	−3598.36	−	6232.54i	−0.244226	−	0.423013i	−0.961914	+	0.273353i	$0.911867\pi$
$602$	6768.66	+	2463.59i	0.458256	+	0.166792i
$603$		0			0
$604$	1436.04	+	8144.16i	0.0967408	+	0.548644i
$605$	−6658.89	+	2423.64i	−0.447475	+	0.162867i
$606$		0			0
$607$	−2891.61			−0.193355			−0.0966776	−	0.995316i	$-0.530822\pi$
$607$	−2891.61			−0.193355			−0.0966776	+	0.995316i	$0.530822\pi$
$608$	−20131.0	−	3667.03i	−1.34279	−	0.244601i
$609$		0			0
$610$	−27266.3	−	22879.1i	−1.80980	−	1.51860i
$611$	−32349.0	+	11774.1i	−2.14190	+	0.779589i
$612$		0			0
$613$	−2187.88	+	12408.1i	−0.144156	+	0.817548i	0.823885	+	0.566757i	$0.191802\pi$
$613$	−2187.88	+	12408.1i	−0.144156	+	0.817548i	−0.968041	+	0.250792i	$0.919309\pi$
$614$	32299.9	+	11756.2i	2.12299	+	0.772706i
$615$		0			0
$616$	−486.211	+	842.142i	−0.0318019	+	0.0550825i
$617$	12640.1	−	10606.3i	0.824749	−	0.692046i	−0.129330	−	0.991602i	$-0.541283\pi$
$617$	12640.1	−	10606.3i	0.824749	−	0.692046i	0.954079	+	0.299555i	$0.0968383\pi$
$618$		0			0
$619$	6741.60	−	11676.8i	0.437751	−	0.758207i	−0.559765	−	0.828652i	$-0.689109\pi$
$619$	6741.60	−	11676.8i	0.437751	−	0.758207i	0.997516	+	0.0704448i	$0.0224419\pi$
$620$	7400.46	+	12818.0i	0.479370	+	0.830294i
$621$		0			0
$622$	−1959.59	+	11113.4i	−0.126322	+	0.716409i
$623$	876.744	+	4972.26i	0.0563820	+	0.319758i
$624$		0			0
$625$	−14038.6	−	11779.8i	−0.898470	−	0.753906i
$626$	−14296.9			−0.912811
$627$		0			0
$628$	−18834.1			−1.19676
$629$	18732.2	+	15718.2i	1.18744	+	0.996384i
$630$		0			0
$631$	−2419.97	−	13724.4i	−0.152675	−	0.865860i	−0.960881	−	0.276961i	$-0.910673\pi$
$631$	−2419.97	−	13724.4i	−0.152675	−	0.865860i	0.808207	−	0.588899i	$-0.200438\pi$
$632$	250.406	−	1420.12i	0.0157604	−	0.0893819i
$633$		0			0
$634$	417.425	+	723.002i	0.0261484	+	0.0452903i
$635$	13122.8	−	22729.3i	0.820097	−	1.42045i
$636$		0			0
$637$	−14241.7	+	11950.2i	−0.885833	+	0.743302i
$638$	132.616	−	229.698i	0.00822936	−	0.0142537i
$639$		0			0
$640$	−5541.57	−	2016.97i	−0.342265	−	0.124574i
$641$	953.113	−	5405.37i	0.0587297	−	0.333072i	−0.941260	−	0.337684i	$-0.890357\pi$
$641$	953.113	−	5405.37i	0.0587297	−	0.333072i	0.999989	+	0.00461105i	$0.00146775\pi$
$642$		0			0
$643$	15966.1	−	5811.17i	0.979222	−	0.356408i	0.197684	−	0.980266i	$-0.436658\pi$
$643$	15966.1	−	5811.17i	0.979222	−	0.356408i	0.781538	+	0.623858i	$0.214436\pi$
$644$	3968.10	+	3329.64i	0.242803	+	0.203736i
$645$		0			0
$646$	8706.55	+	24348.2i	0.530271	+	1.48292i
$647$	−28250.5			−1.71660			−0.858300	−	0.513148i	$-0.828479\pi$
$647$	−28250.5			−1.71660			−0.858300	+	0.513148i	$0.828479\pi$
$648$		0			0
$649$	−12747.1	+	4639.56i	−0.770982	+	0.280614i
$650$	−5356.70	−	30379.3i	−0.323242	−	1.83319i
$651$		0			0
$652$	5916.95	+	2153.59i	0.355408	+	0.129358i
$653$	15120.2	+	26188.9i	0.906123	+	1.56945i	0.819402	+	0.573219i	$0.194306\pi$
$653$	15120.2	+	26188.9i	0.906123	+	1.56945i	0.0867214	+	0.996233i	$0.472361\pi$
$654$		0			0
$655$	−27723.2	+	23262.5i	−1.65379	+	1.38770i
$656$	−12165.9	+	10208.4i	−0.724086	+	0.607580i
$657$		0			0
$658$	−8826.69	−	15288.3i	−0.522948	−	0.905773i
$659$	25603.4	+	9318.87i	1.51345	+	0.550852i	0.959503	−	0.281697i	$-0.0908973\pi$
$659$	25603.4	+	9318.87i	1.51345	+	0.550852i	0.553951	+	0.832549i	$0.313120\pi$
$660$		0			0
$661$	5474.40	+	31046.9i	0.322132	+	1.82690i	0.529105	+	0.848556i	$0.322528\pi$
$661$	5474.40	+	31046.9i	0.322132	+	1.82690i	−0.206973	+	0.978347i	$0.566361\pi$
$662$	−34862.0	+	12688.7i	−2.04675	+	0.744958i
$663$		0			0
$664$	268.888			0.0157152
$665$	−11480.4	+	6542.02i	−0.669461	+	0.381487i
$666$		0			0
$667$	119.689	+	100.431i	0.00694812	+	0.00583016i
$668$	2605.27	−	948.241i	0.150900	−	0.0549230i
$669$		0			0
$670$	2190.09	−	12420.6i	0.126284	−	0.716195i
$671$	−16832.3	−	6126.46i	−0.968412	−	0.352473i
$672$		0			0
$673$	10009.4	−	17336.8i	0.573306	−	0.992995i	−0.422917	−	0.906168i	$-0.638994\pi$
$673$	10009.4	−	17336.8i	0.573306	−	0.992995i	0.996223	−	0.0868269i	$-0.0276727\pi$
$674$	−10393.5	+	8721.15i	−0.593978	+	0.498406i
$675$		0			0
$676$	−15940.4	+	27609.6i	−0.906941	+	1.57087i
$677$	−14206.1	−	24605.7i	−0.806478	−	1.39686i	−0.915289	−	0.402799i	$-0.868038\pi$
$677$	−14206.1	−	24605.7i	−0.806478	−	1.39686i	0.108811	−	0.994063i	$-0.465296\pi$
$678$		0			0
$679$	792.908	−	4496.80i	0.0448144	−	0.254155i
$680$	643.815	+	3651.26i	0.0363076	+	0.205911i
$681$		0			0
$682$	12042.9	+	10105.2i	0.676169	+	0.567373i
$683$	−13697.9			−0.767401			−0.383701	−	0.923458i	$-0.625351\pi$
$683$	−13697.9			−0.767401			−0.383701	+	0.923458i	$0.625351\pi$
$684$		0			0
$685$	42446.8			2.36761
$686$	−18268.5	−	15329.1i	−1.01676	−	0.853160i
$687$		0			0
$688$	2090.19	+	11854.0i	0.115825	+	0.656877i
$689$	2339.24	−	13266.5i	0.129344	−	0.733547i
$690$		0			0
$691$	−1262.06	−	2185.96i	−0.0694807	−	0.120344i	0.829192	−	0.558964i	$-0.188801\pi$
$691$	−1262.06	−	2185.96i	−0.0694807	−	0.120344i	−0.898673	+	0.438620i	$0.855468\pi$
$692$	−12217.1	+	21160.7i	−0.671136	+	1.16244i
$693$		0			0
$694$	11574.8	−	9712.43i	0.633104	−	0.531238i
$695$	11133.7	−	19284.1i	0.607661	−	1.05250i
$696$		0			0
$697$	17135.7	+	6236.89i	0.931222	+	0.338937i
$698$	−5783.26	+	32798.5i	−0.313610	+	1.77857i
$699$		0			0
$700$	7043.06	−	2563.47i	0.380290	−	0.138414i
$701$	9868.96	+	8281.04i	0.531734	+	0.446178i	0.868700	−	0.495339i	$-0.164956\pi$
$701$	9868.96	+	8281.04i	0.531734	+	0.446178i	−0.336966	+	0.941517i	$0.609401\pi$
$702$		0			0
$703$	−24931.4	+	4250.98i	−1.33756	+	0.228064i
$704$	11860.3			0.634948
$705$		0			0
$706$	2938.91	−	1069.67i	0.156667	−	0.0570223i
$707$	−1461.05	−	8286.01i	−0.0777204	−	0.440774i
$708$		0			0
$709$	−14312.0	−	5209.16i	−0.758110	−	0.275929i	−0.0660957	−	0.997813i	$-0.521054\pi$
$709$	−14312.0	−	5209.16i	−0.758110	−	0.275929i	−0.692014	+	0.721884i	$0.743276\pi$
$710$	−1592.13	−	2757.66i	−0.0841574	−	0.145765i
$711$		0			0
$712$	−1122.44	+	941.837i	−0.0590803	+	0.0495742i
$713$	−7094.25	+	5952.79i	−0.372625	+	0.312670i
$714$		0			0
$715$	−17742.8	−	30731.4i	−0.928032	−	1.60740i
$716$	3398.15	+	1236.83i	0.177367	+	0.0645563i
$717$		0			0
$718$	4727.66	+	26811.9i	0.245731	+	1.39361i
$719$	30780.6	−	11203.2i	1.59655	−	0.581098i	0.617837	−	0.786307i	$-0.288009\pi$
$719$	30780.6	−	11203.2i	1.59655	−	0.581098i	0.978718	+	0.205208i	$0.0657871\pi$
$720$		0			0
$721$	−16853.9			−0.870559
$722$	−25026.5	−	9430.48i	−1.29001	−	0.486103i
$723$		0			0
$724$	9826.75	+	8245.62i	0.504431	+	0.423268i
$725$	212.439	−	77.3215i	0.0108825	−	0.00396090i
$726$		0			0
$727$	5486.88	−	31117.7i	0.279914	−	1.58747i	−0.442994	−	0.896524i	$-0.646084\pi$
$727$	5486.88	−	31117.7i	0.279914	−	1.58747i	0.722908	−	0.690944i	$-0.242805\pi$
$728$	2542.24	+	925.301i	0.129426	+	0.0471070i
$729$		0			0
$730$	4036.89	−	6992.10i	0.204674	−	0.354506i
$731$	10587.5	−	8883.97i	0.535695	−	0.449502i
$732$		0			0
$733$	2103.22	−	3642.88i	0.105981	−	0.183565i	−0.808158	−	0.588966i	$-0.799535\pi$
$733$	2103.22	−	3642.88i	0.105981	−	0.183565i	0.914139	+	0.405402i	$0.132868\pi$
$734$	17641.3	+	30555.6i	0.887127	+	1.53655i
$735$		0			0
$736$	−2882.59	+	16348.0i	−0.144366	+	0.818741i
$737$	−1102.17	−	6250.71i	−0.0550868	−	0.312413i
$738$		0			0
$739$	3074.72	+	2580.00i	0.153052	+	0.128426i	0.716098	−	0.698000i	$-0.245926\pi$
$739$	3074.72	+	2580.00i	0.153052	+	0.128426i	−0.563046	+	0.826425i	$0.690371\pi$
$740$	32791.8			1.62899
$741$		0			0
$742$	6908.08			0.341784
$743$	−20561.9	−	17253.5i	−1.01527	−	0.851909i	−0.0262409	−	0.999656i	$-0.508354\pi$
$743$	−20561.9	−	17253.5i	−1.01527	−	0.851909i	−0.989025	+	0.147746i	$0.952798\pi$
$744$		0			0
$745$	−6951.07	−	39421.5i	−0.341836	−	1.93865i
$746$	3907.92	−	22162.9i	0.191795	−	1.08772i
$747$		0			0
$748$	−8436.20	−	14611.9i	−0.412377	−	0.714258i
$749$	5842.70	−	10119.9i	0.285030	−	0.493687i
$750$		0			0
$751$	27339.8	−	22940.8i	1.32842	−	1.11468i	0.343977	−	0.938978i	$-0.388226\pi$
$751$	27339.8	−	22940.8i	1.32842	−	1.11468i	0.984444	−	0.175700i	$-0.0562188\pi$
$752$	14750.1	−	25548.0i	0.715268	−	1.23888i
$753$		0			0
$754$	−693.410	−	252.380i	−0.0334914	−	0.0121899i
$755$	−2971.77	+	16853.7i	−0.143250	+	0.812410i
$756$		0			0
$757$	35587.0	−	12952.6i	1.70863	−	0.621889i	0.711866	−	0.702315i	$-0.247850\pi$
$757$	35587.0	−	12952.6i	1.70863	−	0.621889i	0.996761	+	0.0804257i	$0.0256280\pi$
$758$	6736.04	+	5652.21i	0.322776	+	0.270841i
$759$		0			0
$760$	−3310.02	−	1936.06i	−0.157983	−	0.0924055i
$761$	7828.30			0.372898			0.186449	−	0.982465i	$-0.440302\pi$
$761$	7828.30			0.372898			0.186449	+	0.982465i	$0.440302\pi$
$762$		0			0
$763$	1310.77	−	477.081i	0.0621928	−	0.0226363i
$764$	140.929	+	799.247i	0.00667359	+	0.0378478i
$765$		0			0
$766$	2260.63	+	822.801i	0.106632	+	0.0388107i
$767$	18870.0	+	32683.8i	0.888340	+	1.53865i
$768$		0			0
$769$	4423.14	−	3711.46i	0.207416	−	0.174042i	−0.533162	−	0.846013i	$-0.678996\pi$
$769$	4423.14	−	3711.46i	0.207416	−	0.174042i	0.740578	+	0.671971i	$0.234552\pi$
$770$	13939.8	−	11696.9i	0.652412	−	0.547438i
$771$		0			0
$772$	451.909	+	782.729i	0.0210681	+	0.0364910i
$773$	8939.45	+	3253.69i	0.415950	+	0.151394i	0.541513	−	0.840692i	$-0.317852\pi$
$773$	8939.45	+	3253.69i	0.415950	+	0.151394i	−0.125563	+	0.992086i	$0.540074\pi$
$774$		0			0
$775$	2326.86	+	13196.3i	0.107849	+	0.611643i
$776$	1245.21	−	453.221i	0.0576039	−	0.0209661i
$777$		0			0
$778$	27374.7			1.26148
$779$	−16386.6	+	9337.78i	−0.753674	+	0.429474i
$780$		0			0
$781$	−1227.58	−	1030.06i	−0.0562437	−	0.0471940i
$782$	19712.5	−	7174.75i	0.901427	−	0.328093i
$783$		0			0
$784$	2766.48	−	15689.5i	0.126024	−	0.714718i
$785$	−36625.2	−	13330.5i	−1.66524	−	0.606097i
$786$		0			0
$787$	4208.20	−	7288.81i	0.190605	−	0.330137i	−0.754846	−	0.655902i	$-0.772288\pi$
$787$	4208.20	−	7288.81i	0.190605	−	0.330137i	0.945451	+	0.325765i	$0.105622\pi$
$788$	−508.747	+	426.889i	−0.0229992	+	0.0192986i
$789$		0			0
$790$	−13492.5	+	23369.7i	−0.607649	+	1.05248i
$791$	−2059.34	−	3566.88i	−0.0925685	−	0.160333i
$792$		0			0
$793$	−8653.77	+	49078.0i	−0.387521	+	2.19774i
$794$	−1670.21	−	9472.24i	−0.0746519	−	0.423372i
$795$		0			0
$796$	46.2882	+	38.8404i	0.00206111	+	0.00172947i
$797$	7985.39			0.354902			0.177451	−	0.984130i	$-0.443215\pi$
$797$	7985.39			0.354902			0.177451	+	0.984130i	$0.443215\pi$
$798$		0			0
$799$	−33872.7			−1.49979
$800$	18399.8	+	15439.2i	0.813163	+	0.682325i
$801$		0			0
$802$	−5249.86	−	29773.4i	−0.231146	−	1.31089i
$803$	705.559	−	4001.43i	0.0310070	−	0.175850i
$804$		0			0
$805$	5359.80	+	9283.45i	0.234668	+	0.406458i
$806$	21868.8	−	37877.9i	0.955701	−	1.65532i
$807$		0			0
$808$	1870.48	−	1569.52i	0.0814398	−	0.0683361i
$809$	−4510.81	+	7812.96i	−0.196034	+	0.339541i	−0.947239	−	0.320528i	$-0.896140\pi$
$809$	−4510.81	+	7812.96i	−0.196034	+	0.339541i	0.751205	+	0.660069i	$0.229473\pi$
$810$		0			0
$811$	−12106.6	−	4406.46i	−0.524195	−	0.190791i	0.0663497	−	0.997796i	$-0.478865\pi$
$811$	−12106.6	−	4406.46i	−0.524195	−	0.190791i	−0.590544	+	0.807005i	$0.701087\pi$
$812$	31.1332	−	176.565i	0.00134552	−	0.00763081i
$813$		0			0
$814$	32729.5	−	11912.6i	1.40930	−	0.512943i
$815$	9981.96	+	8375.85i	0.429022	+	0.359992i
$816$		0			0
$817$	−80.7646	+	14294.5i	−0.00345850	+	0.612118i
$818$	−2843.61			−0.121546
$819$		0			0
$820$	22979.0	−	8363.69i	0.978613	−	0.356186i
$821$	5826.23	+	33042.2i	0.247670	+	1.40460i	0.814210	+	0.580570i	$0.197170\pi$
$821$	5826.23	+	33042.2i	0.247670	+	1.40460i	−0.566540	+	0.824034i	$0.691718\pi$
$822$		0			0
$823$	−61.4922	−	22.3813i	−0.00260448	−	0.000947952i	0.340718	−	0.940166i	$-0.389330\pi$
$823$	−61.4922	−	22.3813i	−0.00260448	−	0.000947952i	−0.343322	+	0.939218i	$0.611552\pi$
$824$	−2445.55	−	4235.82i	−0.103392	−	0.179080i
$825$		0			0
$826$	−14825.5	+	12440.0i	−0.624508	+	0.524024i
$827$	18699.7	−	15690.9i	0.786277	−	0.659765i	−0.158544	−	0.987352i	$-0.550680\pi$
$827$	18699.7	−	15690.9i	0.786277	−	0.659765i	0.944821	+	0.327587i	$0.106236\pi$
$828$		0			0
$829$	23601.0	+	40878.2i	0.988779	+	1.71262i	0.623762	+	0.781614i	$0.285603\pi$
$829$	23601.0	+	40878.2i	0.988779	+	1.71262i	0.365017	+	0.931001i	$0.381063\pi$
$830$	−4728.31	−	1720.97i	−0.197738	−	0.0719706i
$831$		0			0
$832$	−5729.86	−	32495.7i	−0.238759	−	1.35407i
$833$	−17189.7	+	6256.53i	−0.714990	+	0.260235i
$834$		0			0
$835$	5737.42			0.237786
$836$	17168.2	+	3127.33i	0.710255	+	0.129379i
$837$		0			0
$838$	8385.91	+	7036.61i	0.345688	+	0.290067i
$839$	25520.9	−	9288.84i	1.05015	−	0.382225i	0.241433	−	0.970418i	$-0.422383\pi$
$839$	25520.9	−	9288.84i	1.05015	−	0.382225i	0.808721	+	0.588193i	$0.200160\pi$
$840$		0			0
$841$	−4234.17	+	24013.2i	−0.173610	+	0.984589i
$842$	40422.4	+	14712.5i	1.65445	+	0.602171i
$843$		0			0
$844$	−17628.7	+	30533.9i	−0.718965	+	1.24528i
$845$	−50539.7	+	42407.8i	−2.05754	+	1.72648i
$846$		0			0
$847$	−2543.90	+	4406.17i	−0.103199	+	0.178746i
$848$	5771.98	+	9997.37i	0.233739	+	0.404848i
$849$		0			0
$850$	5270.74	−	29891.9i	0.212688	−	1.20621i
$851$	3562.86	+	20206.0i	0.143517	+	0.813928i
$852$		0			0
$853$	−27343.5	−	22943.9i	−1.09756	−	0.920965i	−0.100305	−	0.994957i	$-0.531982\pi$
$853$	−27343.5	−	22943.9i	−1.09756	−	0.920965i	−0.997259	+	0.0739913i	$0.976426\pi$
$854$	−25555.7			−1.02400
$855$		0			0
$856$	3391.17			0.135406
$857$	−15636.9	−	13120.9i	−0.623273	−	0.522988i	0.275557	−	0.961285i	$-0.411138\pi$
$857$	−15636.9	−	13120.9i	−0.623273	−	0.522988i	−0.898830	+	0.438296i	$0.855582\pi$
$858$		0			0
$859$	1104.57	+	6264.30i	0.0438734	+	0.248819i	0.998855	−	0.0478477i	$-0.0152362\pi$
$859$	1104.57	+	6264.30i	0.0438734	+	0.248819i	−0.954981	+	0.296666i	$0.904125\pi$
$860$	3218.40	−	18252.4i	0.127612	−	0.723724i
$861$		0			0
$862$	5354.16	+	9273.68i	0.211559	+	0.366430i
$863$	2674.86	−	4633.00i	0.105508	−	0.182745i	−0.808438	−	0.588582i	$-0.799686\pi$
$863$	2674.86	−	4633.00i	0.105508	−	0.182745i	0.913946	+	0.405837i	$0.133020\pi$
$864$		0			0
$865$	−38735.0	+	32502.5i	−1.52258	+	1.27759i
$866$	−23175.7	+	40141.4i	−0.909401	+	1.57513i
$867$		0			0
$868$	9985.95	+	3634.59i	0.390490	+	0.142127i
$869$	−2358.19	+	13374.0i	−0.0920555	+	0.522073i
$870$		0			0
$871$	−16593.6	+	6039.58i	−0.645526	+	0.234952i
$872$	310.099	+	260.204i	0.0120428	+	0.0101051i
$873$		0			0
$874$	−7535.72	+	20345.8i	−0.291647	+	0.787422i
$875$	−4432.93			−0.171269
$876$		0			0
$877$	−2904.07	+	1057.00i	−0.111817	+	0.0406981i	−0.397323	−	0.917679i	$-0.630061\pi$
$877$	−2904.07	+	1057.00i	−0.111817	+	0.0406981i	0.285506	+	0.958377i	$0.407838\pi$
$878$	5652.20	+	32055.2i	0.217258	+	1.23213i
$879$		0			0
$880$	28575.1	+	10400.5i	1.09462	+	0.398409i
$881$	−16387.7	−	28384.4i	−0.626694	−	1.08547i	−0.988211	−	0.153100i	$-0.951074\pi$
$881$	−16387.7	−	28384.4i	−0.626694	−	1.08547i	0.361517	−	0.932366i	$-0.382259\pi$
$882$		0			0
$883$	−6598.40	+	5536.71i	−0.251476	+	0.211014i	−0.759808	−	0.650148i	$-0.774707\pi$
$883$	−6598.40	+	5536.71i	−0.251476	+	0.211014i	0.508331	+	0.861162i	$0.330263\pi$
$884$	−35959.0	+	30173.2i	−1.36814	+	1.14800i
$885$		0			0
$886$	−27054.4	−	46859.6i	−1.02586	−	1.77684i
$887$	−2859.19	−	1040.66i	−0.108232	−	0.0393934i	0.287336	−	0.957830i	$-0.407230\pi$
$887$	−2859.19	−	1040.66i	−0.108232	−	0.0393934i	−0.395569	+	0.918436i	$0.629453\pi$
$888$		0			0
$889$	−3272.21	−	18557.6i	−0.123449	−	0.700115i
$890$	25765.8	−	9377.98i	0.970418	−	0.353203i
$891$		0			0
$892$	25563.6			0.959567
$893$	22670.5	−	26709.7i	0.849539	−	1.00090i
$894$		0			0
$895$	5732.71	+	4810.32i	0.214104	+	0.179655i
$896$	−3978.76	+	1448.15i	−0.148349	+	0.0539948i
$897$		0			0
$898$	−5272.96	+	29904.5i	−0.195948	+	1.11128i
$899$	301.205	+	109.630i	0.0111744	+	0.00406714i
$900$		0			0
$901$	6627.50	−	11479.2i	0.245054	−	0.424447i
$902$	19897.1	−	16695.6i	0.734479	−	0.616301i
$903$		0			0
$904$	597.632	−	1035.13i	0.0219878	−	0.0380839i
$905$	13273.2	+	22989.8i	0.487531	+	0.844429i
$906$		0			0
$907$	−634.730	+	3599.73i	−0.0232369	+	0.131783i	−0.994219	−	0.107368i	$-0.965758\pi$
$907$	−634.730	+	3599.73i	−0.0232369	+	0.131783i	0.970983	+	0.239151i	$0.0768689\pi$
$908$	−2766.76	−	15691.1i	−0.101121	−	0.573488i
$909$		0			0
$910$	−38782.4	−	32542.3i	−1.41277	−	1.18546i
$911$	35581.3			1.29403			0.647015	−	0.762477i	$-0.276017\pi$
$911$	35581.3			1.29403			0.647015	+	0.762477i	$0.276017\pi$
$912$		0			0
$913$	−2532.25			−0.0917911
$914$	−9351.78	−	7847.08i	−0.338435	−	0.283981i
$915$		0			0
$916$	445.659	+	2527.46i	0.0160753	+	0.0911677i
$917$	−4512.05	+	25589.1i	−0.162488	+	0.921513i
$918$		0			0
$919$	13785.8	+	23877.8i	0.494835	+	0.857079i	0.999982	−	0.00595408i	$-0.00189526\pi$
$919$	13785.8	+	23877.8i	0.494835	+	0.857079i	−0.505148	+	0.863033i	$0.668562\pi$
$920$	−1555.44	+	2694.11i	−0.0557408	+	0.0965458i
$921$		0			0
$922$	−37255.4	+	31261.0i	−1.33074	+	1.11662i
$923$	−2229.17	+	3861.03i	−0.0794951	+	0.137690i
$924$		0			0
$925$	27897.3	+	10153.8i	0.991628	+	0.360923i
$926$	5753.24	−	32628.2i	0.204172	−	1.15792i
$927$		0			0
$928$	539.910	−	196.511i	0.0190985	−	0.00695129i
$929$	−21431.8	−	17983.4i	−0.756895	−	0.635110i	0.180422	−	0.983589i	$-0.442254\pi$
$929$	−21431.8	−	17983.4i	−0.756895	−	0.635110i	−0.937317	+	0.348479i	$0.886698\pi$
$930$		0			0
$931$	6571.30	−	17742.0i	0.231327	−	0.624564i
$932$	−39887.3			−1.40188
$933$		0			0
$934$	72622.1	−	26432.3i	2.54418	−	0.926007i
$935$	−6063.13	−	34385.7i	−0.212070	−	1.20271i
$936$		0			0
$937$	12379.7	+	4505.84i	0.431619	+	0.157096i	0.548688	−	0.836027i	$-0.315128\pi$
$937$	12379.7	+	4505.84i	0.431619	+	0.157096i	−0.117069	+	0.993124i	$0.537350\pi$
$938$	−4527.69	−	7842.20i	−0.157606	−	0.272982i
$939$		0			0
$940$	−34796.4	+	29197.6i	−1.20737	+	1.01311i
$941$	−8136.78	+	6827.57i	−0.281882	+	0.236527i	−0.772756	−	0.634704i	$-0.781122\pi$
$941$	−8136.78	+	6827.57i	−0.281882	+	0.236527i	0.490873	+	0.871231i	$0.336678\pi$
$942$		0			0
$943$	7650.33	+	13250.8i	0.264188	+	0.457586i
$944$	−30390.5	−	11061.2i	−1.04780	−	0.381369i
$945$		0			0
$946$	−3418.45	−	19387.0i	−0.117488	−	0.666306i
$947$	34283.1	−	12478.0i	1.17640	−	0.428174i	0.321470	−	0.946920i	$-0.395823\pi$
$947$	34283.1	−	12478.0i	1.17640	−	0.428174i	0.854929	+	0.518746i	$0.173601\pi$
$948$		0			0
$949$	−11304.2			−0.386670
$950$	20043.0	+	24162.3i	0.684506	+	0.825187i
$951$		0			0
$952$	2039.20	+	1711.09i	0.0694232	+	0.0582530i
$953$	30465.5	−	11088.5i	1.03555	−	0.376908i	0.232356	−	0.972631i	$-0.425357\pi$
$953$	30465.5	−	11088.5i	1.03555	−	0.376908i	0.803190	+	0.595723i	$0.203134\pi$
$954$		0			0
$955$	−291.641	+	1653.98i	−0.00988198	+	0.0560435i
$956$	−13626.7	−	4959.72i	−0.461003	−	0.167792i
$957$		0			0
$958$	11831.3	−	20492.4i	0.399010	−	0.691106i
$959$	23346.1	−	19589.7i	0.786116	−	0.659629i
$960$		0			0
$961$	5396.08	−	9346.28i	0.181131	−	0.313728i
$962$	−48450.8	−	83919.3i	−1.62382	−	2.81254i
$963$		0			0
$964$	290.187	−	1645.73i	0.00969534	−	0.0549850i
$965$	324.788	+	1841.97i	0.0108345	+	0.0614456i
$966$		0			0
$967$	−8794.89	−	7379.79i	−0.292476	−	0.245417i	0.484728	−	0.874665i	$-0.338919\pi$
$967$	−8794.89	−	7379.79i	−0.292476	−	0.245417i	−0.777205	+	0.629248i	$0.783363\pi$
$968$	−1476.51			−0.0490257
$969$		0			0
$970$	−24797.5			−0.820824
$971$	16707.1	+	14019.0i	0.552171	+	0.463326i	0.875675	−	0.482900i	$-0.160417\pi$
$971$	16707.1	+	14019.0i	0.552171	+	0.463326i	−0.323504	+	0.946227i	$0.604861\pi$
$972$		0			0
$973$	−2776.22	−	15744.7i	−0.0914712	−	0.518759i
$974$	4144.85	−	23506.6i	0.136355	−	0.773307i
$975$		0			0
$976$	−21352.8	−	36984.2i	−0.700294	−	1.21294i
$977$	−16129.9	+	27937.7i	−0.528188	+	0.914848i	0.471272	+	0.881988i	$0.343795\pi$
$977$	−16129.9	+	27937.7i	−0.528188	+	0.914848i	−0.999460	+	0.0328605i	$0.989538\pi$
$978$		0			0
$979$	10570.6	−	8869.75i	0.345083	−	0.289559i
$980$	−12265.4	+	21244.3i	−0.399800	+	0.692473i
$981$		0			0
$982$	−71113.4	−	25883.2i	−2.31092	−	0.841105i
$983$	−7844.15	+	44486.4i	−0.254516	+	1.44343i	0.542795	+	0.839865i	$0.317366\pi$
$983$	−7844.15	+	44486.4i	−0.254516	+	1.44343i	−0.797312	+	0.603568i	$0.793745\pi$
$984$		0			0
$985$	−1291.47	+	470.055i	−0.0417762	+	0.0152053i
$986$	−556.202	−	466.709i	−0.0179646	−	0.0150741i
$987$		0			0
$988$	274.306	−	48549.2i	0.00883283	−	1.56332i
$989$	11596.7			0.372854
$990$		0			0
$991$	16564.2	−	6028.87i	0.530958	−	0.193253i	−0.0626083	−	0.998038i	$-0.519942\pi$
$991$	16564.2	−	6028.87i	0.530958	−	0.193253i	0.593566	+	0.804785i	$0.297720\pi$
$992$	5913.67	+	33538.1i	0.189273	+	1.07342i
$993$		0			0
$994$	−2148.38	−	781.946i	−0.0685537	−	0.0249515i
$995$	62.5224	+	108.292i	0.00199205	+	0.00345034i
$996$		0			0
$997$	35562.2	−	29840.2i	1.12965	−	0.947893i	0.130603	−	0.991435i	$-0.458309\pi$
$997$	35562.2	−	29840.2i	1.12965	−	0.947893i	0.999052	+	0.0435420i	$0.0138642\pi$
$998$	17250.1	−	14474.5i	0.547136	−	0.459102i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.u.b.73.1		24
3.2	odd	2		19.4.e.a.16.4	yes	24
19.6	even	9	inner	171.4.u.b.82.1		24
57.5	odd	18		361.4.a.n.1.10		12
57.14	even	18		361.4.a.m.1.3		12
57.44	odd	18		19.4.e.a.6.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.6.4	✓	24	57.44	odd	18
19.4.e.a.16.4	yes	24	3.2	odd	2
171.4.u.b.73.1		24	1.1	even	1	trivial
171.4.u.b.82.1		24	19.6	even	9	inner
361.4.a.m.1.3		12	57.14	even	18
361.4.a.n.1.10		12	57.5	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.98693 - 2.50633i) q^{2} +(1.25086 + 7.09397i) q^{4} +(-2.58856 + 14.6804i) q^{5} +(5.35146 + 9.26900i) q^{7} +(-1.55302 + 2.68992i) q^{8} +O(q^{10})\)	\(q+(-2.98693 - 2.50633i) q^{2} +(1.25086 + 7.09397i) q^{4} +(-2.58856 + 14.6804i) q^{5} +(5.35146 + 9.26900i) q^{7} +(-1.55302 + 2.68992i) q^{8} +(44.5258 - 37.3616i) q^{10} +(14.6256 - 25.3323i) q^{11} +(-76.4727 - 27.8338i) q^{13} +(7.24674 - 41.0983i) q^{14} +(65.5325 - 23.8519i) q^{16} +(-61.3408 - 51.4710i) q^{17} +(81.6408 - 13.9203i) q^{19} -107.380 q^{20} +(-107.177 + 39.0091i) q^{22} +(-11.6670 - 66.1669i) q^{23} +(-91.3527 - 33.2497i) q^{25} +(158.658 + 274.803i) q^{26} +(-59.0601 + 49.5573i) q^{28} +(-1.78142 + 1.49479i) q^{29} +(-68.9182 - 119.370i) q^{31} +(-232.171 - 84.5035i) q^{32} +(54.2171 + 307.480i) q^{34} +(-149.925 + 54.5684i) q^{35} -305.379 q^{37} +(-278.744 - 163.040i) q^{38} +(-35.4690 - 29.7621i) q^{40} +(-213.997 + 77.8884i) q^{41} +(-29.9719 + 169.979i) q^{43} +(198.001 + 72.0665i) q^{44} +(-130.987 + 226.877i) q^{46} +(324.048 - 271.908i) q^{47} +(114.224 - 197.841i) q^{49} +(189.529 + 328.274i) q^{50} +(101.796 - 577.311i) q^{52} +(28.7445 + 163.018i) q^{53} +(334.030 + 280.284i) q^{55} -33.2438 q^{56} +9.06741 q^{58} +(-355.251 - 298.091i) q^{59} +(-106.337 - 603.067i) q^{61} +(-93.3264 + 529.280i) q^{62} +(202.732 + 351.143i) q^{64} +(606.566 - 1050.60i) q^{65} +(166.222 - 139.477i) q^{67} +(288.405 - 499.533i) q^{68} +(584.582 + 212.771i) q^{70} +(9.51311 - 53.9515i) q^{71} +(130.528 - 47.5085i) q^{73} +(912.146 + 765.381i) q^{74} +(200.872 + 561.745i) q^{76} +313.073 q^{77} +(-436.266 + 158.788i) q^{79} +(180.521 + 1023.79i) q^{80} +(834.406 + 303.699i) q^{82} +(-43.2845 - 74.9710i) q^{83} +(914.401 - 767.273i) q^{85} +(515.548 - 432.596i) q^{86} +(45.4278 + 78.6833i) q^{88} +(443.288 + 161.344i) q^{89} +(-151.249 - 857.777i) q^{91} +(454.792 - 165.531i) q^{92} -1649.40 q^{94} +(-6.97532 + 1234.56i) q^{95} +(-326.817 - 274.232i) q^{97} +(-837.033 + 304.655i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8}+O(q^{10}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8	\( 24 q + 6 q^{2} - 24 q^{4} + 6 q^{5} + 3 q^{7} + 75 q^{8} + 75 q^{10} - 39 q^{11} - 156 q^{13} - 93 q^{14} + 504 q^{16} - 12 q^{17} + 546 q^{19} + 198 q^{20} - 6 q^{22} - 6 q^{23} - 498 q^{25} + 639 q^{26} - 1368 q^{28} + 630 q^{29} - 591 q^{31} - 147 q^{32} - 408 q^{34} - 2001 q^{35} - 72 q^{37} - 2934 q^{38} + 2886 q^{40} + 477 q^{41} + 588 q^{43} + 3423 q^{44} - 1728 q^{46} + 1242 q^{47} - 639 q^{49} + 1788 q^{50} + 2733 q^{52} + 300 q^{53} + 315 q^{55} - 4638 q^{56} - 2820 q^{58} - 2097 q^{59} - 2316 q^{61} + 1320 q^{62} - 1785 q^{64} + 2433 q^{65} + 57 q^{67} + 438 q^{68} - 213 q^{70} + 792 q^{71} + 4068 q^{73} - 4287 q^{74} + 5538 q^{76} - 3786 q^{77} + 1824 q^{79} + 2739 q^{80} + 2205 q^{82} - 1071 q^{83} - 2394 q^{85} + 5256 q^{86} + 1101 q^{88} + 3006 q^{89} - 3285 q^{91} + 1452 q^{92} - 1086 q^{94} + 3078 q^{95} - 2535 q^{97} + 2403 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 24 * q^4 + 6 * q^5 + 3 * q^7 + 75 * q^8 + 75 * q^10 - 39 * q^11 - 156 * q^13 - 93 * q^14 + 504 * q^16 - 12 * q^17 + 546 * q^19 + 198 * q^20 - 6 * q^22 - 6 * q^23 - 498 * q^25 + 639 * q^26 - 1368 * q^28 + 630 * q^29 - 591 * q^31 - 147 * q^32 - 408 * q^34 - 2001 * q^35 - 72 * q^37 - 2934 * q^38 + 2886 * q^40 + 477 * q^41 + 588 * q^43 + 3423 * q^44 - 1728 * q^46 + 1242 * q^47 - 639 * q^49 + 1788 * q^50 + 2733 * q^52 + 300 * q^53 + 315 * q^55 - 4638 * q^56 - 2820 * q^58 - 2097 * q^59 - 2316 * q^61 + 1320 * q^62 - 1785 * q^64 + 2433 * q^65 + 57 * q^67 + 438 * q^68 - 213 * q^70 + 792 * q^71 + 4068 * q^73 - 4287 * q^74 + 5538 * q^76 - 3786 * q^77 + 1824 * q^79 + 2739 * q^80 + 2205 * q^82 - 1071 * q^83 - 2394 * q^85 + 5256 * q^86 + 1101 * q^88 + 3006 * q^89 - 3285 * q^91 + 1452 * q^92 - 1086 * q^94 + 3078 * q^95 - 2535 * q^97 + 2403 * q^98

Introduction

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