LMFDB - Embedded newform 162.5.f.a.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,5,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7459340196$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.1
Character	$\chi$	$=$	162.35
Dual form			162.5.f.a.125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-4.26691 + 11.7232i) q^{5} +(3.24231 - 18.3880i) q^{7} +(19.5959 + 11.3137i) q^{8} +O(q^{10})$	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-4.26691 + 11.7232i) q^{5} +(3.24231 - 18.3880i) q^{7} +(19.5959 + 11.3137i) q^{8} +(-17.6432 - 30.5589i) q^{10} +(-15.9790 - 43.9018i) q^{11} +(15.9561 - 13.3888i) q^{13} +(33.9466 + 40.4560i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(121.836 - 70.3422i) q^{17} +(37.0626 - 64.1942i) q^{19} +(98.2887 + 17.3309i) q^{20} +(124.173 + 45.1953i) q^{22} +(234.653 - 41.3756i) q^{23} +(359.550 + 301.698i) q^{25} +58.9139i q^{26} -149.374 q^{28} +(1074.63 - 1280.70i) q^{29} +(206.238 + 1169.63i) q^{31} +(61.9123 - 170.103i) q^{32} +(-69.0973 + 391.870i) q^{34} +(201.733 + 116.471i) q^{35} +(436.819 + 756.593i) q^{37} +(71.7071 + 197.014i) q^{38} +(-216.247 + 181.453i) q^{40} +(819.867 + 977.079i) q^{41} +(496.648 - 180.765i) q^{43} +(-323.681 + 186.877i) q^{44} +(-336.968 + 583.646i) q^{46} +(2772.95 + 488.946i) q^{47} +(1928.59 + 701.951i) q^{49} +(-1307.38 + 230.526i) q^{50} +(-127.649 - 107.110i) q^{52} +2967.28i q^{53} +582.853 q^{55} +(271.573 - 323.648i) q^{56} +(821.122 + 4656.82i) q^{58} +(-484.627 + 1331.50i) q^{59} +(1022.11 - 5796.68i) q^{61} +(-2909.20 - 1679.63i) q^{62} +(256.000 + 443.405i) q^{64} +(88.8764 + 244.186i) q^{65} +(-1529.77 + 1283.63i) q^{67} +(-723.442 - 862.164i) q^{68} +(-619.123 + 225.342i) q^{70} +(-628.278 + 362.737i) q^{71} +(4295.09 - 7439.31i) q^{73} +(-2433.48 - 429.089i) q^{74} +(-557.239 - 202.818i) q^{76} +(-859.078 + 151.479i) q^{77} +(-7686.73 - 6449.93i) q^{79} -798.440i q^{80} -3607.62 q^{82} +(7627.68 - 9090.32i) q^{83} +(304.774 + 1728.46i) q^{85} +(-511.281 + 1404.73i) q^{86} +(183.570 - 1041.08i) q^{88} +(-5702.61 - 3292.40i) q^{89} +(-194.458 - 336.812i) q^{91} +(-651.952 - 1791.22i) q^{92} +(-6100.84 + 5119.21i) q^{94} +(594.422 + 708.405i) q^{95} +(-9822.34 + 3575.04i) q^{97} +(-5027.25 + 2902.49i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{5}+O(q^{10}) $ 72 * q + 18 * q^5	$ 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) $ 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.81808	+	2.16670i	−0.454519	+	0.541675i
$2$	−1.81808	+	2.16670i	−0.454519	+	0.541675i
$3$		0			0
$3$		0			0
$4$	−1.38919	−	7.87846i	−0.0868241	−	0.492404i
$5$	−4.26691	+	11.7232i	−0.170677	+	0.468930i	−0.995310	−	0.0967376i	$-0.969159\pi$
$5$	−4.26691	+	11.7232i	−0.170677	+	0.468930i	0.824633	+	0.565668i	$0.191381\pi$
$6$		0			0
$7$	3.24231	−	18.3880i	0.0661696	−	0.375266i	−0.933683	−	0.358100i	$-0.883425\pi$
$7$	3.24231	−	18.3880i	0.0661696	−	0.375266i	0.999853	−	0.0171659i	$-0.00546433\pi$
$8$	19.5959	+	11.3137i	0.306186	+	0.176777i
$9$		0			0
$10$	−17.6432	−	30.5589i	−0.176432	−	0.305589i
$11$	−15.9790	−	43.9018i	−0.132058	−	0.362825i	0.855986	−	0.516999i	$-0.172951\pi$
$11$	−15.9790	−	43.9018i	−0.132058	−	0.362825i	−0.988044	+	0.154173i	$0.950729\pi$
$12$		0			0
$13$	15.9561	−	13.3888i	0.0944147	−	0.0792234i	−0.594359	−	0.804200i	$-0.702594\pi$
$13$	15.9561	−	13.3888i	0.0944147	−	0.0792234i	0.688773	+	0.724977i	$0.258150\pi$
$14$	33.9466	+	40.4560i	0.173197	+	0.206408i
$15$		0			0
$16$	−60.1403	+	21.8893i	−0.234923	+	0.0855050i
$17$	121.836	−	70.3422i	0.421579	−	0.243399i	−0.274174	−	0.961680i	$-0.588404\pi$
$17$	121.836	−	70.3422i	0.421579	−	0.243399i	0.695753	+	0.718281i	$0.255071\pi$
$18$		0			0
$19$	37.0626	−	64.1942i	0.102666	−	0.177823i	−0.810116	−	0.586270i	$-0.800596\pi$
$19$	37.0626	−	64.1942i	0.102666	−	0.177823i	0.912782	+	0.408446i	$0.133929\pi$
$20$	98.2887	+	17.3309i	0.245722	+	0.0433274i
$21$		0			0
$22$	124.173	+	45.1953i	0.256556	+	0.0933788i
$23$	234.653	−	41.3756i	0.443578	−	0.0782148i	0.0526018	−	0.998616i	$-0.483249\pi$
$23$	234.653	−	41.3756i	0.443578	−	0.0782148i	0.390976	+	0.920401i	$0.372137\pi$
$24$		0			0
$25$	359.550	+	301.698i	0.575280	+	0.482717i
$26$			58.9139i			0.0871507i
$27$		0			0
$28$	−149.374			−0.190528
$29$	1074.63	−	1280.70i	1.27780	−	1.52283i	0.554797	−	0.831986i	$-0.312796\pi$
$29$	1074.63	−	1280.70i	1.27780	−	1.52283i	0.723007	−	0.690841i	$-0.242759\pi$
$30$		0			0
$31$	206.238	+	1169.63i	0.214608	+	1.21710i	0.881586	+	0.472024i	$0.156476\pi$
$31$	206.238	+	1169.63i	0.214608	+	1.21710i	−0.666978	+	0.745077i	$0.732413\pi$
$32$	61.9123	−	170.103i	0.0604612	−	0.166116i
$33$		0			0
$34$	−69.0973	+	391.870i	−0.0597728	+	0.338988i
$35$	201.733	+	116.471i	0.164680	+	0.0950780i
$36$		0			0
$37$	436.819	+	756.593i	0.319079	+	0.552661i	0.980296	−	0.197534i	$-0.0632931\pi$
$37$	436.819	+	756.593i	0.319079	+	0.552661i	−0.661217	+	0.750195i	$0.729960\pi$
$38$	71.7071	+	197.014i	0.0496587	+	0.136436i
$39$		0			0
$40$	−216.247	+	181.453i	−0.135155	+	0.113408i
$41$	819.867	+	977.079i	0.487726	+	0.581249i	0.952638	−	0.304108i	$-0.0983584\pi$
$41$	819.867	+	977.079i	0.487726	+	0.581249i	−0.464912	+	0.885357i	$0.653914\pi$
$42$		0			0
$43$	496.648	−	180.765i	0.268604	−	0.0977638i	−0.204207	−	0.978928i	$-0.565462\pi$
$43$	496.648	−	180.765i	0.268604	−	0.0977638i	0.472811	+	0.881164i	$0.343239\pi$
$44$	−323.681	+	186.877i	−0.167191	+	0.0965276i
$45$		0			0
$46$	−336.968	+	583.646i	−0.159248	+	0.275825i
$47$	2772.95	+	488.946i	1.25530	+	0.221343i	0.761460	−	0.648212i	$-0.224483\pi$
$47$	2772.95	+	488.946i	1.25530	+	0.221343i	0.493837	+	0.869554i	$0.335594\pi$
$48$		0			0
$49$	1928.59	+	701.951i	0.803246	+	0.292358i
$50$	−1307.38	+	230.526i	−0.522952	+	0.0922105i
$51$		0			0
$52$	−127.649	−	107.110i	−0.0472074	−	0.0396117i
$53$			2967.28i			1.05635i	0.849137	+	0.528173i	$0.177123\pi$
$53$			2967.28i			1.05635i	−0.849137	+	0.528173i	$0.822877\pi$
$54$		0			0
$55$	582.853			0.192679
$56$	271.573	−	323.648i	0.0865985	−	0.103204i
$57$		0			0
$58$	821.122	+	4656.82i	0.244091	+	1.38431i
$59$	−484.627	+	1331.50i	−0.139221	+	0.382506i	−0.989635	−	0.143609i	$-0.954129\pi$
$59$	−484.627	+	1331.50i	−0.139221	+	0.382506i	0.850414	+	0.526114i	$0.176352\pi$
$60$		0			0
$61$	1022.11	−	5796.68i	0.274687	−	1.55783i	−0.465266	−	0.885171i	$-0.654041\pi$
$61$	1022.11	−	5796.68i	0.274687	−	1.55783i	0.739953	−	0.672658i	$-0.234847\pi$
$62$	−2909.20	−	1679.63i	−0.756817	−	0.436948i
$63$		0			0
$64$	256.000	+	443.405i	0.0625000	+	0.108253i
$65$	88.8764	+	244.186i	0.0210358	+	0.0577955i
$66$		0			0
$67$	−1529.77	+	1283.63i	−0.340783	+	0.285950i	−0.797076	−	0.603879i	$-0.793621\pi$
$67$	−1529.77	+	1283.63i	−0.340783	+	0.285950i	0.456294	+	0.889829i	$0.349177\pi$
$68$	−723.442	−	862.164i	−0.156454	−	0.186454i
$69$		0			0
$70$	−619.123	+	225.342i	−0.126352	+	0.0459882i
$71$	−628.278	+	362.737i	−0.124634	+	0.0719573i	−0.561021	−	0.827802i	$-0.689591\pi$
$71$	−628.278	+	362.737i	−0.124634	+	0.0719573i	0.436387	+	0.899759i	$0.356258\pi$
$72$		0			0
$73$	4295.09	−	7439.31i	0.805984	−	1.39601i	−0.109641	−	0.993971i	$-0.534970\pi$
$73$	4295.09	−	7439.31i	0.805984	−	1.39601i	0.915625	−	0.402034i	$-0.131697\pi$
$74$	−2433.48	−	429.089i	−0.444390	−	0.0783580i
$75$		0			0
$76$	−557.239	−	202.818i	−0.0964748	−	0.0351140i
$77$	−859.078	+	151.479i	−0.144894	+	0.0255488i
$78$		0			0
$79$	−7686.73	−	6449.93i	−1.23165	−	1.03348i	−0.998130	−	0.0611253i	$-0.980531\pi$
$79$	−7686.73	−	6449.93i	−1.23165	−	1.03348i	−0.233520	−	0.972352i	$-0.575024\pi$
$80$		−	798.440i		−	0.124756i
$81$		0			0
$82$	−3607.62			−0.536529
$83$	7627.68	−	9090.32i	1.10723	−	1.31954i	0.164349	−	0.986402i	$-0.447448\pi$
$83$	7627.68	−	9090.32i	1.10723	−	1.31954i	0.942878	−	0.333139i	$-0.108108\pi$
$84$		0			0
$85$	304.774	+	1728.46i	0.0421833	+	0.239233i
$86$	−511.281	+	1404.73i	−0.0691294	+	0.189932i
$87$		0			0
$88$	183.570	−	1041.08i	0.0237048	−	0.134437i
$89$	−5702.61	−	3292.40i	−0.719935	−	0.415655i	0.0947936	−	0.995497i	$-0.469781\pi$
$89$	−5702.61	−	3292.40i	−0.719935	−	0.415655i	−0.814729	+	0.579842i	$0.803114\pi$
$90$		0			0
$91$	−194.458	−	336.812i	−0.0234825	−	0.0406728i
$92$	−651.952	−	1791.22i	−0.0770265	−	0.211629i
$93$		0			0
$94$	−6100.84	+	5119.21i	−0.690453	+	0.579359i
$95$	594.422	+	708.405i	0.0658640	+	0.0784936i
$96$		0			0
$97$	−9822.34	+	3575.04i	−1.04393	+	0.379960i	−0.806369	−	0.591413i	$-0.798570\pi$
$97$	−9822.34	+	3575.04i	−1.04393	+	0.379960i	−0.237562	+	0.971372i	$0.576348\pi$
$98$	−5027.25	+	2902.49i	−0.523454	+	0.302216i
$99$		0			0
$100$	1877.44	−	3251.81i	0.187744	−	0.325181i
$101$	−3343.15	−	589.488i	−0.327728	−	0.0577873i	0.00736352	−	0.999973i	$-0.497656\pi$
$101$	−3343.15	−	589.488i	−0.327728	−	0.0577873i	−0.335091	+	0.942186i	$0.608767\pi$
$102$		0			0
$103$	−9463.75	−	3444.52i	−0.892049	−	0.324679i	−0.144987	−	0.989434i	$-0.546314\pi$
$103$	−9463.75	−	3444.52i	−0.892049	−	0.324679i	−0.747062	+	0.664754i	$0.768536\pi$
$104$	464.151	−	81.8423i	0.0429133	−	0.00756678i
$105$		0			0
$106$	−6429.20	−	5394.74i	−0.572196	−	0.480130i
$107$		−	7072.88i		−	0.617773i	−0.951099	−	0.308886i	$-0.900044\pi$
$107$		−	7072.88i		−	0.617773i	0.951099	−	0.308886i	$-0.0999563\pi$
$108$		0			0
$109$	15724.8			1.32352			0.661761	−	0.749715i	$-0.269809\pi$
$109$	15724.8			1.32352			0.661761	+	0.749715i	$0.269809\pi$
$110$	−1059.67	+	1262.87i	−0.0875762	+	0.104369i
$111$		0			0
$112$	207.508	+	1176.83i	0.0165424	+	0.0938166i
$113$	−7728.46	+	21233.8i	−0.605252	+	1.66292i	0.135209	+	0.990817i	$0.456829\pi$
$113$	−7728.46	+	21233.8i	−0.605252	+	1.66292i	−0.740461	+	0.672099i	$0.765393\pi$
$114$		0			0
$115$	−516.186	+	2927.44i	−0.0390311	+	0.221356i
$116$	−11582.8	−	6687.33i	−0.860790	−	0.496977i
$117$		0			0
$118$	−2003.88	−	3470.82i	−0.143915	−	0.249269i
$119$	−898.425	−	2468.40i	−0.0634436	−	0.174310i
$120$		0			0
$121$	9543.61	−	8008.04i	0.651842	−	0.546960i
$122$	10701.4	+	12753.4i	0.718987	+	0.856855i
$123$		0			0
$124$	8928.41	−	3249.68i	0.580672	−	0.211347i
$125$	−11823.7	+	6826.40i	−0.756715	+	0.436890i
$126$		0			0
$127$	6435.07	−	11145.9i	0.398975	−	0.691046i	−0.594624	−	0.804004i	$-0.702699\pi$
$127$	6435.07	−	11145.9i	0.398975	−	0.691046i	0.993600	+	0.112958i	$0.0360326\pi$
$128$	−1426.15	−	251.469i	−0.0870455	−	0.0153485i
$129$		0			0
$130$	−690.662	−	251.380i	−0.0408676	−	0.0148746i
$131$	−986.852	+	174.009i	−0.0575055	+	0.0101398i	−0.202327	−	0.979318i	$-0.564850\pi$
$131$	−986.852	+	174.009i	−0.0575055	+	0.0101398i	0.144821	+	0.989458i	$0.453739\pi$
$132$		0			0
$133$	−1060.24	−	889.646i	−0.0599377	−	0.0502937i
$134$		−	5648.30i		−	0.314564i
$135$		0			0
$136$	3183.33			0.172109
$137$	13955.2	−	16631.2i	0.743526	−	0.886100i	−0.253161	−	0.967424i	$-0.581470\pi$
$137$	13955.2	−	16631.2i	0.743526	−	0.886100i	0.996688	+	0.0813239i	$0.0259148\pi$
$138$		0			0
$139$	2984.68	+	16927.0i	0.154479	+	0.876092i	0.959261	+	0.282522i	$0.0911710\pi$
$139$	2984.68	+	16927.0i	0.154479	+	0.876092i	−0.804782	+	0.593570i	$0.797718\pi$
$140$	637.365	−	1751.14i	0.0325186	−	0.0893441i
$141$		0			0
$142$	356.317	−	2020.77i	0.0176710	−	0.100217i
$143$	−842.752	−	486.563i	−0.0412124	−	0.0237940i
$144$		0			0
$145$	10428.6	+	18062.8i	0.496008	+	0.859111i
$146$	8309.96	+	22831.4i	0.389846	+	1.07109i
$147$		0			0
$148$	5353.97	−	4492.51i	0.244429	−	0.205100i
$149$	13822.9	+	16473.5i	0.622626	+	0.742017i	0.981520	−	0.191362i	$-0.0612903\pi$
$149$	13822.9	+	16473.5i	0.622626	+	0.742017i	−0.358894	+	0.933378i	$0.616846\pi$
$150$		0			0
$151$	−25243.2	+	9187.77i	−1.10711	+	0.402955i	−0.829932	−	0.557864i	$-0.811621\pi$
$151$	−25243.2	+	9187.77i	−1.10711	+	0.402955i	−0.277177	+	0.960819i	$0.589399\pi$
$152$	1452.55	−	838.630i	0.0628701	−	0.0362980i
$153$		0			0
$154$	1233.66	−	2136.76i	0.0520181	−	0.0900980i
$155$	−14591.9	−	2572.95i	−0.607363	−	0.107095i
$156$		0			0
$157$	−8028.49	−	2922.13i	−0.325713	−	0.118550i	0.173988	−	0.984748i	$-0.444335\pi$
$157$	−8028.49	−	2922.13i	−0.325713	−	0.118550i	−0.499701	+	0.866198i	$0.666557\pi$
$158$	27950.1	−	4928.36i	1.11962	−	0.197419i
$159$		0			0
$160$	1729.98	+	1451.63i	0.0675773	+	0.0567041i
$161$		−	4448.96i		−	0.171635i
$162$		0			0
$163$	20365.8			0.766526			0.383263	−	0.923639i	$-0.374800\pi$
$163$	20365.8			0.766526			0.383263	+	0.923639i	$0.374800\pi$
$164$	6558.94	−	7816.63i	0.243863	−	0.290624i
$165$		0			0
$166$	5828.28	+	33053.8i	0.211507	+	1.19951i
$167$	2603.44	−	7152.90i	0.0933501	−	0.256477i	−0.884226	−	0.467059i	$-0.845314\pi$
$167$	2603.44	−	7152.90i	0.0933501	−	0.256477i	0.977576	+	0.210582i	$0.0675358\pi$
$168$		0			0
$169$	−4884.23	+	27699.8i	−0.171010	+	0.969848i
$170$	−4299.16	−	2482.12i	−0.148760	−	0.0858866i
$171$		0			0
$172$	−2114.09	−	3661.71i	−0.0714605	−	0.123773i
$173$	4530.87	+	12448.5i	0.151387	+	0.415933i	0.992084	−	0.125572i	$-0.0400767\pi$
$173$	4530.87	+	12448.5i	0.151387	+	0.415933i	−0.840697	+	0.541506i	$0.817854\pi$
$174$		0			0
$175$	6713.41	−	5633.22i	0.219213	−	0.183942i
$176$	1921.96	+	2290.50i	0.0620467	+	0.0739444i
$177$		0			0
$178$	17501.4	−	6370.00i	0.552374	−	0.201048i
$179$	9616.37	−	5552.01i	0.300127	−	0.173278i	−0.342373	−	0.939564i	$-0.611231\pi$
$179$	9616.37	−	5552.01i	0.300127	−	0.173278i	0.642500	+	0.766286i	$0.277897\pi$
$180$		0			0
$181$	−12694.3	+	21987.1i	−0.387481	+	0.671136i	−0.992110	−	0.125371i	$-0.959988\pi$
$181$	−12694.3	+	21987.1i	−0.387481	+	0.671136i	0.604629	+	0.796507i	$0.293321\pi$
$182$	1083.31	+	191.017i	0.0327047	+	0.00576672i
$183$		0			0
$184$	5066.35	+	1844.00i	0.149644	+	0.0544660i
$185$	−10733.6	+	1892.62i	−0.313619	+	0.0552994i
$186$		0			0
$187$	−5034.97	−	4224.84i	−0.143984	−	0.120817i
$188$		−	22525.8i		−	0.637331i
$189$		0			0
$190$	−2615.61			−0.0724545
$191$	22654.1	−	26998.1i	0.620983	−	0.740059i	−0.360256	−	0.932853i	$-0.617311\pi$
$191$	22654.1	−	26998.1i	0.620983	−	0.740059i	0.981239	+	0.192795i	$0.0617551\pi$
$192$		0			0
$193$	2890.49	+	16392.8i	0.0775992	+	0.440087i	0.998710	+	0.0507855i	$0.0161725\pi$
$193$	2890.49	+	16392.8i	0.0775992	+	0.440087i	−0.921110	+	0.389302i	$0.872716\pi$
$194$	10111.7	−	27781.8i	0.268672	−	0.738170i
$195$		0			0
$196$	2851.12	−	16169.5i	0.0742170	−	0.420905i
$197$	41665.6	+	24055.7i	1.07361	+	0.619848i	0.929165	−	0.369666i	$-0.120528\pi$
$197$	41665.6	+	24055.7i	1.07361	+	0.619848i	0.144443	+	0.989513i	$0.453861\pi$
$198$		0			0
$199$	8495.30	+	14714.3i	0.214522	+	0.371563i	0.953125	−	0.302578i	$-0.0978472\pi$
$199$	8495.30	+	14714.3i	0.214522	+	0.371563i	−0.738602	+	0.674141i	$0.764514\pi$
$200$	3632.38	+	9979.89i	0.0908096	+	0.249497i
$201$		0			0
$202$	7355.36	−	6171.88i	0.180261	−	0.151257i
$203$	−20065.2	−	23912.8i	−0.486914	−	0.580281i
$204$		0			0
$205$	−14952.8	+	5442.39i	−0.355808	+	0.129504i
$206$	24669.1	−	14242.7i	0.581324	−	0.335628i
$207$		0			0
$208$	−666.534	+	1154.47i	−0.0154062	+	0.0266843i
$209$	−3410.47	−	601.357i	−0.0780767	−	0.0137670i
$210$		0			0
$211$	−77029.1	−	28036.3i	−1.73017	−	0.629732i	−0.731531	−	0.681808i	$-0.761194\pi$
$211$	−77029.1	−	28036.3i	−1.73017	−	0.629732i	−0.998643	+	0.0520759i	$0.983416\pi$
$212$	23377.6	−	4122.10i	0.520149	−	0.0917163i
$213$		0			0
$214$	15324.8	+	12859.0i	0.334632	+	0.280790i
$215$			6593.64i			0.142642i
$216$		0			0
$217$	22176.0			0.470937
$218$	−28588.8	+	34070.9i	−0.601567	+	0.716919i
$219$		0			0
$220$	−809.691	−	4591.98i	−0.0167291	−	0.0948757i
$221$	1002.24	−	2753.62i	0.0205204	−	0.0563793i
$222$		0			0
$223$	3297.79	−	18702.7i	0.0663152	−	0.376092i	−0.933530	−	0.358499i	$-0.883289\pi$
$223$	3297.79	−	18702.7i	0.0663152	−	0.376092i	0.999845	−	0.0175929i	$-0.00560028\pi$
$224$	−2927.11	−	1689.97i	−0.0583369	−	0.0336809i
$225$		0			0
$226$	−31956.3	−	55349.9i	−0.625662	−	1.08368i
$227$	−7048.52	−	19365.7i	−0.136787	−	0.375820i	0.852319	−	0.523022i	$-0.175196\pi$
$227$	−7048.52	−	19365.7i	−0.136787	−	0.375820i	−0.989106	+	0.147202i	$0.952973\pi$
$228$		0			0
$229$	56533.2	−	47437.0i	1.07803	−	0.904578i	0.0822781	−	0.996609i	$-0.473780\pi$
$229$	56533.2	−	47437.0i	1.07803	−	0.904578i	0.995756	+	0.0920313i	$0.0293360\pi$
$230$	−5404.42	−	6440.73i	−0.102163	−	0.121753i
$231$		0			0
$232$	35547.9	−	12938.4i	0.660446	−	0.240383i
$233$	−28468.2	+	16436.1i	−0.524383	+	0.302753i	−0.738726	−	0.674006i	$-0.764572\pi$
$233$	−28468.2	+	16436.1i	−0.524383	+	0.302753i	0.214343	+	0.976758i	$0.431239\pi$
$234$		0			0
$235$	−17564.0	+	30421.7i	−0.318044	+	0.550868i
$236$	11163.4	+	1968.41i	0.200435	+	0.0353421i
$237$		0			0
$238$	6981.70	+	2541.13i	0.123256	+	0.0448614i
$239$	−88560.4	+	15615.6i	−1.55040	+	0.273377i	−0.882298	−	0.470692i	$-0.844004\pi$
$239$	−88560.4	+	15615.6i	−1.55040	+	0.273377i	−0.668102	+	0.744069i	$0.732893\pi$
$240$		0			0
$241$	40278.7	+	33797.8i	0.693491	+	0.581908i	0.919914	−	0.392121i	$-0.128259\pi$
$241$	40278.7	+	33797.8i	0.693491	+	0.581908i	−0.226422	+	0.974029i	$0.572703\pi$
$242$			35237.4i			0.601690i
$243$		0			0
$244$	−47088.8			−0.790930
$245$	−16458.3	+	19614.2i	−0.274191	+	0.326768i
$246$		0			0
$247$	−268.107	−	1520.51i	−0.00439455	−	0.0249227i
$248$	−9191.47	+	25253.4i	−0.149445	+	0.410597i
$249$		0			0
$250$	6705.59	−	38029.3i	0.107289	−	0.608469i
$251$	47667.0	+	27520.5i	0.756606	+	0.436827i	0.828076	−	0.560616i	$-0.189436\pi$
$251$	47667.0	+	27520.5i	0.756606	+	0.436827i	−0.0714696	+	0.997443i	$0.522769\pi$
$252$		0			0
$253$	−5565.97	−	9640.55i	−0.0869561	−	0.150612i
$254$	12450.3	+	34206.9i	0.192980	+	0.530209i
$255$		0			0
$256$	3137.72	−	2632.86i	0.0478778	−	0.0401742i
$257$	−44630.0	−	53187.9i	−0.675710	−	0.805280i	0.313839	−	0.949476i	$-0.398385\pi$
$257$	−44630.0	−	53187.9i	−0.675710	−	0.805280i	−0.989549	+	0.144197i	$0.953940\pi$
$258$		0			0
$259$	15328.6	−	5579.14i	0.228508	−	0.0831702i
$260$	1800.34	−	1039.43i	0.0266323	−	0.0153762i
$261$		0			0
$262$	1417.15	−	2454.57i	0.0206449	−	0.0357580i
$263$	−91782.2	−	16183.7i	−1.32693	−	0.233973i	−0.535136	−	0.844766i	$-0.679740\pi$
$263$	−91782.2	−	16183.7i	−1.32693	−	0.233973i	−0.791790	+	0.610793i	$0.790851\pi$
$264$		0			0
$265$	−34786.1	−	12661.1i	−0.495352	−	0.180293i
$266$	3855.19	−	679.774i	0.0544857	−	0.00960730i
$267$		0			0
$268$	12238.2	+	10269.1i	0.170391	+	0.142975i
$269$			65717.5i			0.908189i	0.890954	+	0.454094i	$0.150037\pi$
$269$			65717.5i			0.908189i	−0.890954	+	0.454094i	$0.849963\pi$
$270$		0			0
$271$	−98809.8			−1.34543			−0.672716	−	0.739901i	$-0.734872\pi$
$271$	−98809.8			−1.34543			−0.672716	+	0.739901i	$0.734872\pi$
$272$	−5787.53	+	6897.31i	−0.0782268	+	0.0932271i
$273$		0			0
$274$	10663.1	+	60473.7i	0.142031	+	0.805500i
$275$	7499.87	−	20605.7i	0.0991718	−	0.272472i
$276$		0			0
$277$	−9561.22	+	54224.4i	−0.124610	+	0.706700i	0.856928	+	0.515436i	$0.172370\pi$
$277$	−9561.22	+	54224.4i	−0.124610	+	0.706700i	−0.981539	+	0.191264i	$0.938741\pi$
$278$	−42102.1	−	24307.7i	−0.544771	−	0.314524i
$279$		0			0
$280$	2635.43	+	4564.70i	0.0336152	+	0.0582232i
$281$	969.620	+	2664.01i	0.0122797	+	0.0337383i	0.945681	−	0.325096i	$-0.105397\pi$
$281$	969.620	+	2664.01i	0.0122797	+	0.0337383i	−0.933401	+	0.358834i	$0.883174\pi$
$282$		0			0
$283$	95586.0	−	80206.1i	1.19350	−	1.00146i	0.193705	−	0.981060i	$-0.437950\pi$
$283$	95586.0	−	80206.1i	1.19350	−	1.00146i	0.999792	−	0.0204029i	$-0.00649489\pi$
$284$	3730.60	+	4445.96i	0.0462532	+	0.0551225i
$285$		0			0
$286$	2586.43	−	941.382i	0.0316205	−	0.0115089i
$287$	20624.8	−	11907.8i	0.250396	−	0.144566i
$288$		0			0
$289$	−31864.4	+	55190.8i	−0.381514	+	0.660802i
$290$	−58096.7	−	10244.0i	−0.690804	−	0.121807i
$291$		0			0
$292$	−64577.0	−	23504.1i	−0.757377	−	0.275663i
$293$	−17720.1	+	3124.52i	−0.206410	+	0.0363956i	−0.275897	−	0.961187i	$-0.588975\pi$
$293$	−17720.1	+	3124.52i	−0.206410	+	0.0363956i	0.0694872	+	0.997583i	$0.477864\pi$
$294$		0			0
$295$	−13541.7	−	11362.8i	−0.155607	−	0.130569i
$296$			19768.2i			0.225623i
$297$		0			0
$298$	−60824.3			−0.684928
$299$	3190.17	−	3801.90i	0.0356839	−	0.0425264i
$300$		0			0
$301$	−1713.63	−	9718.49i	−0.0189140	−	0.107267i
$302$	25986.9	−	71398.5i	0.284932	−	0.782844i
$303$		0			0
$304$	−823.788	+	4671.94i	−0.00891392	+	0.0505533i
$305$	63594.7	+	36716.4i	0.683630	+	0.394694i
$306$		0			0
$307$	−48970.5	−	84819.3i	−0.519586	−	0.899949i	−0.999741	−	0.0227656i	$-0.992753\pi$
$307$	−48970.5	−	84819.3i	−0.519586	−	0.899949i	0.480155	−	0.877184i	$-0.340580\pi$
$308$	2386.84	+	6557.78i	0.0251606	+	0.0691282i
$309$		0			0
$310$	32104.0	−	26938.5i	0.334069	−	0.280317i
$311$	−65269.9	−	77785.7i	−0.674827	−	0.804227i	0.314606	−	0.949222i	$-0.398128\pi$
$311$	−65269.9	−	77785.7i	−0.674827	−	0.804227i	−0.989432	+	0.144995i	$0.953683\pi$
$312$		0			0
$313$	59245.7	−	21563.7i	0.604740	−	0.220107i	−0.0214604	−	0.999770i	$-0.506832\pi$
$313$	59245.7	−	21563.7i	0.604740	−	0.220107i	0.626200	+	0.779663i	$0.284609\pi$
$314$	20927.8	−	12082.7i	0.212258	−	0.122547i
$315$		0			0
$316$	−40137.2	+	69519.8i	−0.401951	+	0.696200i
$317$	104755.	+	18471.1i	1.04245	+	0.183812i	0.668559	−	0.743659i	$-0.266911\pi$
$317$	104755.	+	18471.1i	1.04245	+	0.183812i	0.373893	+	0.927472i	$0.378023\pi$
$318$		0			0
$319$	−73396.5	−	26714.1i	−0.721263	−	0.262518i
$320$	−6290.48	+	1109.18i	−0.0614304	+	0.0108318i
$321$		0			0
$322$	9639.56	+	8088.55i	0.0929706	+	0.0780116i
$323$		−	10428.3i		−	0.0999555i
$324$		0			0
$325$	9776.37			0.0925573
$326$	−37026.7	+	44126.7i	−0.348401	+	0.415208i
$327$		0			0
$328$	5011.65	+	28422.5i	0.0465836	+	0.264189i
$329$	17981.5	−	49403.8i	0.166125	−	0.456425i
$330$		0			0
$331$	−3415.13	+	19368.2i	−0.0311710	+	0.176780i	−0.996419	−	0.0845575i	$-0.973052\pi$
$331$	−3415.13	+	19368.2i	−0.0311710	+	0.176780i	0.965248	+	0.261337i	$0.0841634\pi$
$332$	−82214.0	−	47466.3i	−0.745881	−	0.430635i
$333$		0			0
$334$	10764.9	+	18645.4i	0.0964980	+	0.167139i
$335$	−8520.92	−	23411.0i	−0.0759272	−	0.208608i
$336$		0			0
$337$	141124.	−	118417.i	1.24263	−	1.04269i	0.245312	−	0.969444i	$-0.421109\pi$
$337$	141124.	−	118417.i	1.24263	−	1.04269i	0.997314	−	0.0732434i	$-0.0233350\pi$
$338$	−51137.3	−	60943.1i	−0.447615	−	0.533447i
$339$		0			0
$340$	13194.2	−	4802.31i	0.114137	−	0.0415424i
$341$	48053.6	−	27743.8i	0.413254	−	0.238592i
$342$		0			0
$343$	41576.0	−	72011.7i	0.353390	−	0.612090i
$344$	11777.4	+	2076.67i	0.0995251	+	0.0175490i
$345$		0			0
$346$	−35209.6	−	12815.2i	−0.294109	−	0.107047i
$347$	83165.4	−	14664.3i	0.690691	−	0.121788i	0.182724	−	0.983164i	$-0.441508\pi$
$347$	83165.4	−	14664.3i	0.690691	−	0.121788i	0.507967	+	0.861377i	$0.330397\pi$
$348$		0			0
$349$	16766.8	+	14069.0i	0.137657	+	0.115508i	0.709016	−	0.705192i	$-0.249139\pi$
$349$	16766.8	+	14069.0i	0.137657	+	0.115508i	−0.571359	+	0.820700i	$0.693584\pi$
$350$			24787.6i			0.202348i
$351$		0			0
$352$	−8457.11			−0.0682553
$353$	−88723.1	+	105736.i	−0.712012	+	0.848543i	−0.993829	−	0.110925i	$-0.964619\pi$
$353$	−88723.1	+	105736.i	−0.712012	+	0.848543i	0.281817	+	0.959468i	$0.409063\pi$
$354$		0			0
$355$	−1571.64	−	8913.23i	−0.0124709	−	0.0707259i
$356$	−18017.1	+	49501.5i	−0.142162	+	0.390588i
$357$		0			0
$358$	−5453.76	+	30929.8i	−0.0425529	+	0.241330i
$359$	113805.	+	65705.5i	0.883025	+	0.509815i	0.871655	−	0.490120i	$-0.163047\pi$
$359$	113805.	+	65705.5i	0.883025	+	0.509815i	0.0113707	+	0.999935i	$0.496381\pi$
$360$		0			0
$361$	62413.2	+	108103.i	0.478919	+	0.829512i
$362$	−24560.3	−	67478.9i	−0.187420	−	0.514933i
$363$		0			0
$364$	−2383.42	+	1999.93i	−0.0179886	+	0.0150942i
$365$	68886.1	+	82095.3i	0.517066	+	0.616215i
$366$		0			0
$367$	58174.4	−	21173.8i	0.431917	−	0.157205i	−0.116907	−	0.993143i	$-0.537298\pi$
$367$	58174.4	−	21173.8i	0.431917	−	0.157205i	0.548824	+	0.835938i	$0.315076\pi$
$368$	−13206.4	+	7624.72i	−0.0975190	+	0.0563026i
$369$		0			0
$370$	15413.8	−	26697.4i	0.112591	−	0.195014i
$371$	54562.4	+	9620.83i	0.396411	+	0.0698980i
$372$		0			0
$373$	−117615.	−	42808.3i	−0.845366	−	0.307688i	−0.117216	−	0.993106i	$-0.537397\pi$
$373$	−117615.	−	42808.3i	−0.845366	−	0.307688i	−0.728149	+	0.685418i	$0.759619\pi$
$374$	18307.9	−	3228.18i	0.130887	−	0.0230789i
$375$		0			0
$376$	48806.7	+	40953.7i	0.345226	+	0.289679i
$377$		−	34822.9i		−	0.245009i
$378$		0			0
$379$	−69801.2			−0.485942			−0.242971	−	0.970034i	$-0.578122\pi$
$379$	−69801.2			−0.485942			−0.242971	+	0.970034i	$0.578122\pi$
$380$	4755.38	−	5667.24i	0.0329320	−	0.0392468i
$381$		0			0
$382$	17309.9	+	98169.2i	0.118623	+	0.672742i
$383$	−8712.88	+	23938.4i	−0.0593969	+	0.163192i	−0.965842	−	0.259132i	$-0.916563\pi$
$383$	−8712.88	+	23938.4i	−0.0593969	+	0.163192i	0.906445	+	0.422324i	$0.138786\pi$
$384$		0			0
$385$	1889.79	−	10717.5i	0.0127495	−	0.0723058i
$386$	−40773.4	−	23540.6i	−0.273655	−	0.157995i
$387$		0			0
$388$	41810.9	+	72418.6i	0.277732	+	0.481046i
$389$	33910.7	+	93169.0i	0.224098	+	0.615704i	0.999883	−	0.0152931i	$-0.00486813\pi$
$389$	33910.7	+	93169.0i	0.224098	+	0.615704i	−0.775785	+	0.630997i	$0.782646\pi$
$390$		0			0
$391$	25678.8	−	21547.0i	0.167966	−	0.140940i
$392$	29850.9	+	35574.9i	0.194261	+	0.231511i
$393$		0			0
$394$	−127873.	+	46541.9i	−0.823732	+	0.299814i
$395$	108413.	−	62592.1i	0.694842	−	0.401167i
$396$		0			0
$397$	36155.3	−	62622.9i	0.229399	−	0.397331i	−0.728231	−	0.685332i	$-0.759657\pi$
$397$	36155.3	−	62622.9i	0.229399	−	0.397331i	0.957630	+	0.288001i	$0.0929906\pi$
$398$	−47326.6	−	8344.95i	−0.298771	−	0.0526814i
$399$		0			0
$400$	−28227.4	−	10273.9i	−0.176421	−	0.0642121i
$401$	120066.	−	21170.9i	0.746677	−	0.131659i	0.212652	−	0.977128i	$-0.431790\pi$
$401$	120066.	−	21170.9i	0.746677	−	0.131659i	0.534025	+	0.845469i	$0.320679\pi$
$402$		0			0
$403$	18950.7	+	15901.5i	0.116685	+	0.0979103i
$404$			27157.8i			0.166392i
$405$		0			0
$406$	88292.1			0.535636
$407$	26235.9	−	31266.7i	0.158383	−	0.188753i
$408$		0			0
$409$	44810.4	+	254133.i	0.267875	+	1.51920i	0.760721	+	0.649079i	$0.224846\pi$
$409$	44810.4	+	254133.i	0.267875	+	1.51920i	−0.492845	+	0.870117i	$0.664043\pi$
$410$	15393.4	−	42293.0i	0.0915729	−	0.251594i
$411$		0			0
$412$	−13990.6	+	79344.9i	−0.0824220	+	0.467438i
$413$	22912.4	+	13228.5i	0.134329	+	0.0775551i
$414$		0			0
$415$	74021.4	+	128209.i	0.429795	+	0.744426i
$416$	−1289.58	−	3543.10i	−0.00745182	−	0.0204737i
$417$		0			0
$418$	7503.45	−	6296.15i	0.0429446	−	0.0360348i
$419$	120380.	+	143464.i	0.685689	+	0.817173i	0.990827	−	0.135135i	$-0.0431470\pi$
$419$	120380.	+	143464.i	0.685689	+	0.817173i	−0.305138	+	0.952308i	$0.598703\pi$
$420$		0			0
$421$	−76987.3	+	28021.1i	−0.434365	+	0.158096i	−0.549942	−	0.835203i	$-0.685350\pi$
$421$	−76987.3	+	28021.1i	−0.434365	+	0.158096i	0.115577	+	0.993298i	$0.463128\pi$
$422$	200791.	−	115927.i	1.12751	−	0.650967i
$423$		0			0
$424$	−33570.9	+	58146.5i	−0.186737	+	0.323439i
$425$	65028.3	+	11466.3i	0.360018	+	0.0634810i
$426$		0			0
$427$	−103276.	−	37589.3i	−0.566425	−	0.206162i
$428$	−55723.4	+	9825.54i	−0.304194	+	0.0536375i
$429$		0			0
$430$	−14286.4	−	11987.8i	−0.0772658	−	0.0648337i
$431$		−	345117.i		−	1.85786i	−0.370262	−	0.928928i	$-0.620732\pi$
$431$		−	345117.i		−	1.85786i	0.370262	−	0.928928i	$-0.379268\pi$
$432$		0			0
$433$	346295.			1.84702			0.923508	−	0.383579i	$-0.125309\pi$
$433$	346295.			1.84702			0.923508	+	0.383579i	$0.125309\pi$
$434$	−40317.6	+	48048.7i	−0.214050	+	0.255095i
$435$		0			0
$436$	−21844.6	−	123887.i	−0.114914	−	0.651707i
$437$	6040.76	−	16596.8i	0.0316321	−	0.0869086i
$438$		0			0
$439$	−29142.3	+	165274.i	−0.151215	+	0.857584i	0.810950	+	0.585116i	$0.198951\pi$
$439$	−29142.3	+	165274.i	−0.151215	+	0.857584i	−0.962165	+	0.272468i	$0.912160\pi$
$440$	11421.5	+	6594.23i	0.0589955	+	0.0340611i
$441$		0			0
$442$	4144.13	+	7177.85i	0.0212124	+	0.0367409i
$443$	−96877.9	−	266170.i	−0.493648	−	1.35629i	−0.897319	−	0.441382i	$-0.854488\pi$
$443$	−96877.9	−	266170.i	−0.493648	−	1.35629i	0.403671	−	0.914904i	$-0.367734\pi$
$444$		0			0
$445$	62930.2	−	52804.7i	0.317789	−	0.266657i
$446$	34527.5	+	41148.2i	0.173578	+	0.206862i
$447$		0			0
$448$	8983.38	−	3269.68i	0.0447594	−	0.0162911i
$449$	−303439.	+	175191.i	−1.50515	+	0.868996i	−0.505164	+	0.863024i	$0.668568\pi$
$449$	−303439.	+	175191.i	−1.50515	+	0.868996i	−0.999982	+	0.00597279i	$0.998099\pi$
$450$		0			0
$451$	29795.0	−	51606.4i	0.146484	−	0.253717i
$452$	178026.	+	31390.7i	0.871377	+	0.153647i
$453$		0			0
$454$	54774.3	+	19936.2i	0.265745	+	0.0967233i
$455$	4778.27	−	842.537i	0.0230806	−	0.00406974i
$456$		0			0
$457$	−55643.2	−	46690.2i	−0.266428	−	0.223560i	0.499780	−	0.866153i	$-0.333414\pi$
$457$	−55643.2	−	46690.2i	−0.266428	−	0.223560i	−0.766208	+	0.642593i	$0.777859\pi$
$458$			208735.i			0.995093i
$459$		0			0
$460$	23780.8			0.112386
$461$	−161300.	+	192230.i	−0.758983	+	0.904520i	−0.997783	−	0.0665483i	$-0.978801\pi$
$461$	−161300.	+	192230.i	−0.758983	+	0.904520i	0.238801	+	0.971069i	$0.423246\pi$
$462$		0			0
$463$	55436.3	+	314395.i	0.258602	+	1.46661i	0.786654	+	0.617395i	$0.211812\pi$
$463$	55436.3	+	314395.i	0.258602	+	1.46661i	−0.528051	+	0.849213i	$0.677077\pi$
$464$	−36595.2	+	100545.i	−0.169976	+	0.467006i
$465$		0			0
$466$	16145.3	−	91564.3i	0.0743486	−	0.421652i
$467$	−57221.9	−	33037.1i	−0.262379	−	0.151485i	0.363040	−	0.931773i	$-0.381739\pi$
$467$	−57221.9	−	33037.1i	−0.262379	−	0.151485i	−0.625419	+	0.780289i	$0.715072\pi$
$468$		0			0
$469$	18643.5	+	32291.5i	0.0847581	+	0.146805i
$470$	−33982.1	−	93364.9i	−0.153835	−	0.422657i
$471$		0			0
$472$	−24560.9	+	20609.1i	−0.110246	+	0.0925070i
$473$	−15871.8	−	18915.3i	−0.0709423	−	0.0845457i
$474$		0			0
$475$	32693.1	−	11899.3i	0.144900	−	0.0527394i
$476$	−18199.1	+	10507.3i	−0.0803225	+	0.0463742i
$477$		0			0
$478$	127175.	−	220274.i	0.556605	−	0.964069i
$479$	118668.	+	20924.3i	0.517204	+	0.0911970i	0.426156	−	0.904650i	$-0.359867\pi$
$479$	118668.	+	20924.3i	0.517204	+	0.0911970i	0.0910476	+	0.995847i	$0.470978\pi$
$480$		0			0
$481$	17099.8	+	6223.80i	0.0739094	+	0.0269008i
$482$	−146460.	+	25824.8i	−0.630411	+	0.111158i
$483$		0			0
$484$	−76348.9	−	64064.3i	−0.325921	−	0.273480i
$485$		−	130404.i		−	0.554380i
$486$		0			0
$487$	−256600.			−1.08193			−0.540965	−	0.841045i	$-0.681941\pi$
$487$	−256600.			−1.08193			−0.540965	+	0.841045i	$0.681941\pi$
$488$	85611.2	−	102027.i	0.359493	−	0.428427i
$489$		0			0
$490$	−12575.7	−	71320.4i	−0.0523770	−	0.297044i
$491$	−33700.7	+	92591.9i	−0.139790	+	0.384070i	−0.989756	−	0.142767i	$-0.954400\pi$
$491$	−33700.7	+	92591.9i	−0.139790	+	0.384070i	0.849966	+	0.526837i	$0.176622\pi$
$492$		0			0
$493$	40842.2	−	231628.i	0.168041	−	0.953007i
$494$	3781.93	+	2183.50i	0.0154974	+	0.00894745i
$495$		0			0
$496$	−38005.7	−	65827.8i	−0.154485	−	0.267575i
$497$	4632.95	+	12728.9i	0.0187562	+	0.0515322i
$498$		0			0
$499$	−212563.	+	178362.i	−0.853663	+	0.716309i	−0.960593	−	0.277958i	$-0.910342\pi$
$499$	−212563.	+	178362.i	−0.853663	+	0.716309i	0.106930	+	0.994267i	$0.465898\pi$
$500$	70206.8	+	83669.2i	0.280827	+	0.334677i
$501$		0			0
$502$	−146291.	+	53245.6i	−0.580511	+	0.211289i
$503$	−436426.	+	251971.i	−1.72494	+	0.995896i	−0.817220	+	0.576326i	$0.804486\pi$
$503$	−436426.	+	251971.i	−1.72494	+	0.995896i	−0.907723	+	0.419570i	$0.862181\pi$
$504$		0			0
$505$	21175.7	−	36677.3i	0.0830336	−	0.143818i
$506$	31007.6	+	5467.47i	0.121106	+	0.0213543i
$507$		0			0
$508$	−96751.9	−	35214.8i	−0.374914	−	0.136458i
$509$	74928.6	−	13211.9i	0.289209	−	0.0509954i	−0.0271613	−	0.999631i	$-0.508647\pi$
$509$	74928.6	−	13211.9i	0.289209	−	0.0509954i	0.316371	+	0.948636i	$0.397536\pi$
$510$		0			0
$511$	−122868.	−	103099.i	−0.470542	−	0.394832i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	196383.			0.743323
$515$	80762.0	−	96248.4i	0.304504	−	0.362893i
$516$		0			0
$517$	−22843.2	−	129551.i	−0.0854627	−	0.484683i
$518$	−15780.2	+	43355.7i	−0.0588102	+	0.161580i
$519$		0			0
$520$	−1021.03	+	5790.57i	−0.00377601	+	0.0214148i
$521$	−392109.	−	226384.i	−1.44455	−	0.834009i	−0.446397	−	0.894835i	$-0.647293\pi$
$521$	−392109.	−	226384.i	−1.44455	−	0.834009i	−0.998148	+	0.0608259i	$0.980627\pi$
$522$		0			0
$523$	−217955.	−	377510.i	−0.796827	−	1.38014i	−0.921673	−	0.387968i	$-0.873177\pi$
$523$	−217955.	−	377510.i	−0.796827	−	1.38014i	0.124846	−	0.992176i	$-0.460156\pi$
$524$	2741.84	+	7533.14i	0.00998572	+	0.0274355i
$525$		0			0
$526$	201932.	−	169441.i	0.729851	−	0.612418i
$527$	107402.	+	127997.i	0.386715	+	0.460869i
$528$		0			0
$529$	−209615.	+	76293.5i	−0.749049	+	0.272631i
$530$	90676.7	−	52352.2i	0.322808	−	0.186373i
$531$		0			0
$532$	−5536.17	+	9588.93i	−0.0195608	+	0.0338803i
$533$	26163.7	+	4613.37i	0.0920970	+	0.0162392i
$534$		0			0
$535$	82917.1	+	30179.4i	0.289692	+	0.105439i
$536$	−44499.9	+	7846.54i	−0.154892	+	0.0273117i
$537$		0			0
$538$	−142390.	−	119479.i	−0.491943	−	0.412790i
$539$		−	95885.3i		−	0.330046i
$540$		0			0
$541$	−107007.			−0.365608			−0.182804	−	0.983149i	$-0.558517\pi$
$541$	−107007.			−0.365608			−0.182804	+	0.983149i	$0.558517\pi$
$542$	179644.	−	214091.i	0.611525	−	0.728787i
$543$		0			0
$544$	−4422.23	−	25079.7i	−0.0149432	−	0.0847471i
$545$	−67096.2	+	184345.i	−0.225894	+	0.620639i
$546$		0			0
$547$	94727.3	−	537225.i	0.316593	−	1.79549i	−0.246555	−	0.969129i	$-0.579298\pi$
$547$	94727.3	−	537225.i	0.316593	−	1.79549i	0.563147	−	0.826357i	$-0.309590\pi$
$548$	−150415.	−	86842.0i	−0.500875	−	0.289180i
$549$		0			0
$550$	31011.1	+	53712.8i	0.102516	+	0.177563i
$551$	−42384.8	−	116451.i	−0.139607	−	0.383566i
$552$		0			0
$553$	−143524.	+	120431.i	−0.469327	+	0.393812i
$554$	−100105.	−	119300.i	−0.326164	−	0.388707i
$555$		0			0
$556$	129212.	−	47029.4i	0.417979	−	0.152132i
$557$	−339902.	+	196242.i	−1.09558	+	0.632532i	−0.935056	−	0.354501i	$-0.884651\pi$
$557$	−339902.	+	196242.i	−1.09558	+	0.632532i	−0.160521	+	0.987032i	$0.551318\pi$
$558$		0			0
$559$	5504.35	−	9533.81i	0.0176150	−	0.0305100i
$560$	−14681.7	−	2588.79i	−0.0468168	−	0.00825506i
$561$		0			0
$562$	−7534.96	−	2742.50i	−0.0238566	−	0.00868309i
$563$	−172303.	+	30381.6i	−0.543595	+	0.0958504i	−0.438701	−	0.898633i	$-0.644561\pi$
$563$	−172303.	+	30381.6i	−0.543595	+	0.0958504i	−0.104894	+	0.994483i	$0.533450\pi$
$564$		0			0
$565$	−215952.	−	181205.i	−0.676489	−	0.567641i
$566$			352927.i			1.10167i
$567$		0			0
$568$	−16415.6			−0.0508815
$569$	147041.	−	175236.i	0.454164	−	0.541251i	−0.489567	−	0.871966i	$-0.662845\pi$
$569$	147041.	−	175236.i	0.454164	−	0.541251i	0.943731	+	0.330714i	$0.107290\pi$
$570$		0			0
$571$	82946.8	+	470415.i	0.254406	+	1.44281i	0.797593	+	0.603196i	$0.206106\pi$
$571$	82946.8	+	470415.i	0.254406	+	1.44281i	−0.543187	+	0.839612i	$0.682782\pi$
$572$	−2662.63	+	7315.52i	−0.00813802	+	0.0223590i
$573$		0			0
$574$	−11697.0	+	66337.1i	−0.0355019	+	0.201341i
$575$	96852.3	+	55917.7i	0.292937	+	0.169127i
$576$		0			0
$577$	−109111.	−	188985.i	−0.327730	−	0.567644i	0.654331	−	0.756208i	$-0.272950\pi$
$577$	−109111.	−	188985.i	−0.327730	−	0.567644i	−0.982061	+	0.188564i	$0.939617\pi$
$578$	−61650.0	−	169382.i	−0.184534	−	0.507004i
$579$		0			0
$580$	127820.	−	107254.i	0.379964	−	0.318828i
$581$	−142422.	−	169732.i	−0.421915	−	0.502818i
$582$		0			0
$583$	130269.	−	47414.0i	0.383269	−	0.139498i
$584$	168332.	−	97186.8i	0.493562	−	0.284958i
$585$		0			0
$586$	25446.5	−	44074.7i	0.0741026	−	0.128349i
$587$	−147416.	−	25993.4i	−0.427827	−	0.0754375i	−0.0444114	−	0.999013i	$-0.514141\pi$
$587$	−147416.	−	25993.4i	−0.427827	−	0.0754375i	−0.383416	+	0.923576i	$0.625252\pi$
$588$		0			0
$589$	82727.5	+	30110.3i	0.238462	+	0.0867931i
$590$	49239.6	−	8682.27i	0.141453	−	0.0249419i
$591$		0			0
$592$	−42831.7	−	35940.1i	−0.122214	−	0.102550i
$593$		−	455765.i		−	1.29608i	−0.761607	−	0.648040i	$-0.775589\pi$
$593$		−	455765.i		−	1.29608i	0.761607	−	0.648040i	$-0.224411\pi$
$594$		0			0
$595$	32771.2			0.0925675
$596$	110583.	−	131788.i	0.311313	−	0.371008i
$597$		0			0
$598$	2437.60	+	13824.3i	0.00681647	+	0.0386581i
$599$	−80021.0	+	219856.i	−0.223023	+	0.612752i	−0.999856	−	0.0169552i	$-0.994603\pi$
$599$	−80021.0	+	219856.i	−0.223023	+	0.612752i	0.776833	+	0.629707i	$0.216825\pi$
$600$		0			0
$601$	−10721.0	+	60801.6i	−0.0296815	+	0.168332i	−0.996045	−	0.0888469i	$-0.971682\pi$
$601$	−10721.0	+	60801.6i	−0.0296815	+	0.168332i	0.966364	+	0.257179i	$0.0827929\pi$
$602$	24172.6	+	13956.0i	0.0667006	+	0.0385096i
$603$		0			0
$604$	107453.	+	186114.i	0.294540	+	0.510159i
$605$	53158.5	+	146052.i	0.145232	+	0.399021i
$606$		0			0
$607$	−345045.	+	289527.i	−0.936479	+	0.785799i	−0.976969	−	0.213381i	$-0.931552\pi$
$607$	−345045.	+	289527.i	−0.936479	+	0.785799i	0.0404904	+	0.999180i	$0.487108\pi$
$608$	−8624.98	−	10278.8i	−0.0233319	−	0.0278059i
$609$		0			0
$610$	−195174.	+	71037.3i	−0.524519	+	0.190909i
$611$	50791.8	−	29324.7i	0.136054	−	0.0785509i
$612$		0			0
$613$	−191843.	+	332281.i	−0.510533	+	0.884270i	0.489392	+	0.872064i	$0.337219\pi$
$613$	−191843.	+	332281.i	−0.510533	+	0.884270i	−0.999926	+	0.0122060i	$0.996115\pi$
$614$	272810.	+	48103.8i	0.723642	+	0.127598i
$615$		0			0
$616$	−18548.2	−	6750.99i	−0.0488810	−	0.0177912i
$617$	156366.	−	27571.5i	0.410745	−	0.0724254i	0.0355420	−	0.999368i	$-0.488684\pi$
$617$	156366.	−	27571.5i	0.410745	−	0.0724254i	0.375203	+	0.926943i	$0.377573\pi$
$618$		0			0
$619$	385709.	+	323648.i	1.00665	+	0.844680i	0.987892	−	0.155144i	$-0.0495843\pi$
$619$	385709.	+	323648.i	1.00665	+	0.844680i	0.0187582	+	0.999824i	$0.494029\pi$
$620$			118536.i			0.308367i
$621$		0			0
$622$	287204.			0.742352
$623$	−79030.4	+	94184.8i	−0.203619	+	0.242664i
$624$		0			0
$625$	21362.6	+	121153.i	0.0546882	+	0.310152i
$626$	−60991.3	+	167572.i	−0.155639	+	0.427615i
$627$		0			0
$628$	−11868.8	+	67311.6i	−0.0300946	+	0.170675i
$629$	106441.	+	61453.7i	0.269034	+	0.155327i
$630$		0			0
$631$	−55266.3	−	95724.0i	−0.138804	−	0.240415i	0.788240	−	0.615368i	$-0.210992\pi$
$631$	−55266.3	−	95724.0i	−0.138804	−	0.240415i	−0.927044	+	0.374952i	$0.877659\pi$
$632$	−77655.9	−	213358.i	−0.194420	−	0.534164i
$633$		0			0
$634$	−230474.	+	193391.i	−0.573382	+	0.481124i
$635$	103208.	+	122998.i	0.255956	+	0.305037i
$636$		0			0
$637$	40171.1	−	14621.1i	0.0989999	−	0.0360330i
$638$	191322.	−	110460.i	0.470028	−	0.271371i
$639$		0			0
$640$	9033.31	−	15646.2i	0.0220540	−	0.0381986i
$641$	180419.	+	31812.7i	0.439102	+	0.0774255i	0.388829	−	0.921310i	$-0.372880\pi$
$641$	180419.	+	31812.7i	0.439102	+	0.0774255i	0.0502730	+	0.998736i	$0.483991\pi$
$642$		0			0
$643$	370867.	+	134984.i	0.897007	+	0.326484i	0.749053	−	0.662510i	$-0.230509\pi$
$643$	370867.	+	134984.i	0.897007	+	0.326484i	0.147954	+	0.988994i	$0.452731\pi$
$644$	−35050.9	+	6180.43i	−0.0845139	+	0.0149021i
$645$		0			0
$646$	22594.9	+	18959.4i	0.0541434	+	0.0454317i
$647$			402827.i			0.962300i	0.876638	+	0.481150i	$0.159781\pi$
$647$			402827.i			0.962300i	−0.876638	+	0.481150i	$0.840219\pi$
$648$		0			0
$649$	66199.2			0.157168
$650$	−17774.2	+	21182.5i	−0.0420691	+	0.0501360i
$651$		0			0
$652$	−28291.9	−	160451.i	−0.0665529	−	0.377440i
$653$	207398.	−	569820.i	0.486382	−	1.33632i	−0.417553	−	0.908653i	$-0.637112\pi$
$653$	207398.	−	569820.i	0.486382	−	1.33632i	0.903935	−	0.427671i	$-0.140666\pi$
$654$		0			0
$655$	2170.86	−	12311.6i	0.00506000	−	0.0286967i
$656$	−70694.6	−	40815.6i	−0.164278	−	0.0948458i
$657$		0			0
$658$	74351.5	+	128781.i	0.171727	+	0.297440i
$659$	141491.	+	388742.i	0.325804	+	0.895140i	0.989161	+	0.146836i	$0.0469091\pi$
$659$	141491.	+	388742.i	0.325804	+	0.895140i	−0.663357	+	0.748304i	$0.730869\pi$
$660$		0			0
$661$	4556.49	−	3823.35i	0.0104286	−	0.00875067i	−0.637558	−	0.770402i	$-0.720056\pi$
$661$	4556.49	−	3823.35i	0.0104286	−	0.00875067i	0.647987	+	0.761651i	$0.275611\pi$
$662$	−35756.0	−	42612.4i	−0.0815893	−	0.0972343i
$663$		0			0
$664$	252317.	−	91835.8i	0.572282	−	0.208294i
$665$	14953.5	−	8633.40i	0.0338142	−	0.0195226i
$666$		0			0
$667$	199176.	−	344983.i	0.447698	−	0.775436i
$668$	−59970.5	−	10574.4i	−0.134396	−	0.0236976i
$669$		0			0
$670$	66216.4	+	24100.8i	0.147508	+	0.0536886i
$671$	−270817.	+	47752.4i	−0.601494	+	0.106060i
$672$		0			0
$673$	−303850.	−	254961.i	−0.670857	−	0.562916i	0.242462	−	0.970161i	$-0.422045\pi$
$673$	−303850.	−	254961.i	−0.670857	−	0.562916i	−0.913319	+	0.407245i	$0.866489\pi$
$674$			521064.i			1.14702i
$675$		0			0
$676$	225017.			0.492405
$677$	−54554.6	+	65015.6i	−0.119029	+	0.141854i	−0.822269	−	0.569100i	$-0.807292\pi$
$677$	−54554.6	+	65015.6i	−0.119029	+	0.141854i	0.703239	+	0.710953i	$0.251736\pi$
$678$		0			0
$679$	33890.9	+	192205.i	0.0735096	+	0.416894i
$680$	−13583.0	+	37318.9i	−0.0293749	+	0.0807070i
$681$		0			0
$682$	−27252.8	+	154558.i	−0.0585925	+	0.332294i
$683$	457840.	+	264334.i	0.981460	+	0.566646i	0.902711	−	0.430248i	$-0.141574\pi$
$683$	457840.	+	264334.i	0.981460	+	0.566646i	0.0787494	+	0.996894i	$0.474907\pi$
$684$		0			0
$685$	135426.	+	234565.i	0.288616	+	0.499898i
$686$	80439.5	+	221006.i	0.170931	+	0.469629i
$687$		0			0
$688$	−25911.8	+	21742.6i	−0.0547419	+	0.0459339i
$689$	39728.1	+	47346.1i	0.0836873	+	0.0997346i
$690$		0			0
$691$	507599.	−	184751.i	1.06308	−	0.386929i	0.249494	−	0.968376i	$-0.419736\pi$
$691$	507599.	−	184751.i	1.06308	−	0.386929i	0.813584	+	0.581448i	$0.197513\pi$
$692$	91780.5	−	52989.5i	0.191663	−	0.110657i
$693$		0			0
$694$	−119428.	+	206855.i	−0.247963	+	0.429485i
$695$	−211175.	−	37235.8i	−0.437192	−	0.0770887i
$696$		0			0
$697$	168619.	+	61372.5i	0.347090	+	0.126330i
$698$	−60966.8	+	10750.1i	−0.125136	+	0.0220648i
$699$		0			0
$700$	−53707.3	−	45065.8i	−0.109607	−	0.0919709i
$701$		−	475075.i		−	0.966777i	−0.875406	−	0.483388i	$-0.839406\pi$
$701$		−	475075.i		−	0.966777i	0.875406	−	0.483388i	$-0.160594\pi$
$702$		0			0
$703$	64758.6			0.131035
$704$	15375.7	−	18324.0i	0.0310234	−	0.0369722i
$705$		0			0
$706$	−67793.0	−	384473.i	−0.136011	−	0.771359i
$707$	−21679.1	+	59562.7i	−0.0433712	+	0.119161i
$708$		0			0
$709$	−103837.	+	588890.i	−0.206567	+	1.17150i	0.688388	+	0.725342i	$0.258319\pi$
$709$	−103837.	+	588890.i	−0.206567	+	1.17150i	−0.894955	+	0.446156i	$0.852793\pi$
$710$	22169.7	+	12799.7i	0.0439787	+	0.0253911i
$711$		0			0
$712$	−74498.5	−	129035.i	−0.146956	−	0.254536i
$713$	96788.6	+	265925.i	0.190391	+	0.523094i
$714$		0			0
$715$	9300.05	−	7803.67i	0.0181917	−	0.0152647i
$716$	−57100.2	−	68049.4i	−0.111381	−	0.132739i
$717$		0			0
$718$	−349271.	+	127124.i	−0.677506	+	0.246592i
$719$	216647.	−	125081.i	0.419078	−	0.241955i	−0.275605	−	0.961271i	$-0.588878\pi$
$719$	216647.	−	125081.i	0.419078	−	0.241955i	0.694683	+	0.719316i	$0.255545\pi$
$720$		0			0
$721$	−94022.4	+	162852.i	−0.180868	+	0.313272i
$722$	−347699.	−	61308.7i	−0.667004	−	0.117611i
$723$		0			0
$724$	190859.	+	69467.0i	0.364113	+	0.132526i
$725$	772768.	−	136260.i	1.47019	−	0.259234i
$726$		0			0
$727$	673687.	+	565290.i	1.27464	+	1.06955i	0.993959	+	0.109754i	$0.0350063\pi$
$727$	673687.	+	565290.i	1.27464	+	1.06955i	0.280686	+	0.959800i	$0.409438\pi$
$728$		−	8800.18i		−	0.0166046i
$729$		0			0
$730$	−303116.			−0.568805
$731$	47794.4	−	56959.1i	0.0894421	−	0.106593i
$732$		0			0
$733$	−176921.	−	1.00337e6i	−0.329285	−	1.86747i	−0.477670	−	0.878539i	$-0.658519\pi$
$733$	−176921.	−	1.00337e6i	−0.329285	−	1.86747i	0.148385	−	0.988930i	$-0.452593\pi$
$734$	−59888.4	+	164542.i	−0.111161	+	0.305411i
$735$		0			0
$736$	7489.79	−	42476.7i	0.0138265	−	0.0784142i
$737$	80798.0	+	46648.7i	0.148753	+	0.0858825i
$738$		0			0
$739$	73080.3	+	126579.i	0.133817	+	0.231778i	0.925145	−	0.379614i	$-0.123943\pi$
$739$	73080.3	+	126579.i	0.133817	+	0.231778i	−0.791328	+	0.611392i	$0.790610\pi$
$740$	29821.9	+	81935.0i	0.0544593	+	0.149626i
$741$		0			0
$742$	−120044.	+	100729.i	−0.218039	+	0.182956i
$743$	137289.	+	163615.i	0.248690	+	0.296377i	0.875919	−	0.482457i	$-0.160256\pi$
$743$	137289.	+	163615.i	0.248690	+	0.296377i	−0.627230	+	0.778834i	$0.715811\pi$
$744$		0			0
$745$	−252104.	+	91758.5i	−0.454222	+	0.165323i
$746$	306586.	−	177007.i	0.550902	−	0.318063i
$747$		0			0
$748$	−26290.7	+	45536.9i	−0.0469894	+	0.0813880i
$749$	−130056.	−	22932.5i	−0.231829	−	0.0408777i
$750$		0			0
$751$	545586.	+	198577.i	0.967350	+	0.352087i	0.776909	−	0.629612i	$-0.216786\pi$
$751$	545586.	+	198577.i	0.967350	+	0.352087i	0.190440	+	0.981699i	$0.439008\pi$
$752$	−177469.	+	31292.6i	−0.313824	+	0.0553357i
$753$		0			0
$754$	75450.8	+	63310.8i	0.132715	+	0.111361i
$755$		−	335136.i		−	0.587932i
$756$		0			0
$757$	−169286.			−0.295413			−0.147707	−	0.989031i	$-0.547189\pi$
$757$	−169286.			−0.295413			−0.147707	+	0.989031i	$0.547189\pi$
$758$	126904.	−	151238.i	0.220870	−	0.263223i
$759$		0			0
$760$	3633.56	+	20607.0i	0.00629080	+	0.0356769i
$761$	324203.	−	890741.i	0.559819	−	1.53809i	−0.260082	−	0.965587i	$-0.583750\pi$
$761$	324203.	−	890741.i	0.559819	−	1.53809i	0.819901	−	0.572505i	$-0.194028\pi$
$762$		0			0
$763$	50984.5	−	289148.i	0.0875769	−	0.496673i
$764$	−244174.	−	140974.i	−0.418324	−	0.241520i
$765$		0			0
$766$	−36026.7	−	62400.1i	−0.0613999	−	0.106348i
$767$	10094.4	+	27734.1i	0.0171589	+	0.0471437i
$768$		0			0
$769$	−71726.4	+	60185.6i	−0.121290	+	0.101775i	−0.701415	−	0.712753i	$-0.747448\pi$
$769$	−71726.4	+	60185.6i	−0.121290	+	0.101775i	0.580125	+	0.814528i	$0.303004\pi$
$770$	19785.9	+	23579.9i	0.0333714	+	0.0397705i
$771$		0			0
$772$	125135.	−	45545.3i	0.209963	−	0.0764203i
$773$	113073.	−	65283.0i	0.189235	−	0.109255i	−0.402389	−	0.915469i	$-0.631820\pi$
$773$	113073.	−	65283.0i	0.189235	−	0.109255i	0.591624	+	0.806214i	$0.298487\pi$
$774$		0			0
$775$	−278723.	+	482763.i	−0.464056	+	0.803768i
$776$	−232925.	−	41070.9i	−0.386805	−	0.0682042i
$777$		0			0
$778$	−263522.	−	95914.0i	−0.435369	−	0.158461i
$779$	93109.2	−	16417.7i	0.153433	−	0.0270543i
$780$		0			0
$781$	25964.0	+	21786.4i	0.0425667	+	0.0357177i
$782$			94812.4i			0.155043i
$783$		0			0
$784$	−131351.			−0.213699
$785$	68513.8	−	81651.5i	0.111183	−	0.132503i
$786$		0			0
$787$	−178670.	−	1.01329e6i	−0.288470	−	1.63600i	−0.692620	−	0.721303i	$-0.743544\pi$
$787$	−178670.	−	1.01329e6i	−0.288470	−	1.63600i	0.404149	−	0.914693i	$-0.367568\pi$
$788$	131640.	−	361679.i	0.212000	−	0.582466i
$789$		0			0
$790$	−61484.4	+	348695.i	−0.0985169	+	0.558717i
$791$	365390.	+	210958.i	0.583987	+	0.337165i
$792$		0			0
$793$	−61301.4	−	106177.i	−0.0974819	−	0.168844i
$794$	69951.8	+	192191.i	0.110958	+	0.304854i
$795$		0			0
$796$	104124.	−	87370.7i	0.164334	−	0.137892i
$797$	−299631.	−	357087.i	−0.471705	−	0.562156i	0.476762	−	0.879032i	$-0.341810\pi$
$797$	−299631.	−	357087.i	−0.471705	−	0.562156i	−0.948467	+	0.316876i	$0.897366\pi$
$798$		0			0
$799$	372240.	−	135484.i	0.583081	−	0.212224i
$800$	73580.2	−	42481.5i	0.114969	−	0.0663774i
$801$		0			0
$802$	−172419.	+	298638.i	−0.268062	+	0.464298i
$803$	−395231.	−	69689.8i	−0.612942	−	0.108078i
$804$		0			0
$805$	52156.2	+	18983.3i	0.0804849	+	0.0292941i
$806$	−68907.7	+	12150.3i	−0.106071	+	0.0187032i
$807$		0			0
$808$	−58842.8	−	49375.0i	−0.0901303	−	0.0756283i
$809$		−	187743.i		−	0.286858i	−0.989661	−	0.143429i	$-0.954187\pi$
$809$		−	187743.i		−	0.286858i	0.989661	−	0.143429i	$-0.0458129\pi$
$810$		0			0
$811$	−509709.			−0.774962			−0.387481	−	0.921878i	$-0.626655\pi$
$811$	−509709.			−0.774962			−0.387481	+	0.921878i	$0.626655\pi$
$812$	−160522.	+	191303.i	−0.243457	+	0.290141i
$813$		0			0
$814$	20046.7	+	113691.i	0.0302548	+	0.171584i
$815$	−86899.2	+	238754.i	−0.130828	+	0.359447i
$816$		0			0
$817$	6802.97	−	38581.6i	0.0101919	−	0.0578011i
$818$	−632098.	−	364942.i	−0.944666	−	0.545403i
$819$		0			0
$820$	63649.9	+	110245.i	0.0946608	+	0.163957i
$821$	130657.	+	358977.i	0.193841	+	0.532574i	0.998094	−	0.0617133i	$-0.0196564\pi$
$821$	130657.	+	358977.i	0.193841	+	0.532574i	−0.804253	+	0.594287i	$0.797434\pi$
$822$		0			0
$823$	−246531.	+	206864.i	−0.363975	+	0.305411i	−0.806373	−	0.591408i	$-0.798572\pi$
$823$	−246531.	+	206864.i	−0.363975	+	0.305411i	0.442398	+	0.896819i	$0.354128\pi$
$824$	−146481.	−	174569.i	−0.215737	−	0.257106i
$825$		0			0
$826$	−70318.7	+	25593.9i	−0.103065	+	0.0375126i
$827$	230081.	−	132838.i	0.336411	−	0.194227i	−0.322273	−	0.946647i	$-0.604447\pi$
$827$	230081.	−	132838.i	0.336411	−	0.194227i	0.658684	+	0.752420i	$0.271113\pi$
$828$		0			0
$829$	32209.9	−	55789.2i	0.0468685	−	0.0811786i	−0.841639	−	0.540040i	$-0.818409\pi$
$829$	32209.9	−	55789.2i	0.0468685	−	0.0811786i	0.888508	+	0.458861i	$0.151743\pi$
$830$	−412367.	−	72711.4i	−0.598587	−	0.105547i
$831$		0			0
$832$	10021.4	+	3647.49i	0.0144771	+	0.00526923i
$833$	284350.	−	50138.5i	0.409791	−	0.0722572i
$834$		0			0
$835$	72746.5	+	61041.6i	0.104337	+	0.0875493i
$836$			27704.6i			0.0396406i
$837$		0			0
$838$	−529704.			−0.754301
$839$	−437727.	+	521662.i	−0.621840	+	0.741081i	−0.981386	−	0.192047i	$-0.938487\pi$
$839$	−437727.	+	521662.i	−0.621840	+	0.741081i	0.359545	+	0.933128i	$0.382932\pi$
$840$		0			0
$841$	−362532.	−	2.05602e6i	−0.512572	−	2.90694i
$842$	79255.6	−	217753.i	0.111791	−	0.307142i
$843$		0			0
$844$	−113875.	+	645818.i	−0.159862	+	0.906620i
$845$	−303891.	−	175452.i	−0.425603	−	0.245722i
$846$		0			0
$847$	−116309.	−	201453.i	−0.162124	−	0.280806i
$848$	−64951.6	−	178453.i	−0.0903229	−	0.248160i
$849$		0			0
$850$	−143071.	+	120050.i	−0.198021	+	0.166160i
$851$	133805.	+	159463.i	0.184763	+	0.220192i
$852$		0			0
$853$	−517043.	+	188188.i	−0.710606	+	0.258639i	−0.671932	−	0.740612i	$-0.734535\pi$
$853$	−517043.	+	188188.i	−0.710606	+	0.258639i	−0.0386736	+	0.999252i	$0.512313\pi$
$854$	269208.	−	155427.i	0.369124	−	0.213114i
$855$		0			0
$856$	80020.5	−	138600.i	0.109208	−	0.189153i
$857$	−244740.	−	43154.3i	−0.333230	−	0.0587574i	0.00453003	−	0.999990i	$-0.498558\pi$
$857$	−244740.	−	43154.3i	−0.333230	−	0.0587574i	−0.337760	+	0.941232i	$0.609669\pi$
$858$		0			0
$859$	106046.	+	38597.6i	0.143717	+	0.0523087i	0.412877	−	0.910787i	$-0.364524\pi$
$859$	106046.	+	38597.6i	0.143717	+	0.0523087i	−0.269160	+	0.963095i	$0.586746\pi$
$860$	51947.7	−	9159.79i	0.0702376	−	0.0123848i
$861$		0			0
$862$	747765.	+	627450.i	1.00635	+	0.844431i
$863$			434460.i			0.583348i	0.956518	+	0.291674i	$0.0942123\pi$
$863$			434460.i			0.583348i	−0.956518	+	0.291674i	$0.905788\pi$
$864$		0			0
$865$	−165269.			−0.220882
$866$	−629592.	+	750318.i	−0.839505	+	1.00048i
$867$		0			0
$868$	−30806.5	−	174713.i	−0.0408887	−	0.231891i
$869$	−160338.	+	440525.i	−0.212323	+	0.583352i
$870$		0			0
$871$	−7222.97	+	40963.5i	−0.00952093	+	0.0539959i
$872$	308141.	+	177905.i	0.405244	+	0.233968i
$873$		0			0
$874$	24977.8	+	43262.9i	0.0326988	+	0.0566360i
$875$	87188.2	+	239548.i	0.113878	+	0.312879i
$876$		0			0
$877$	223312.	−	187381.i	0.290345	−	0.243628i	−0.485967	−	0.873977i	$-0.661533\pi$
$877$	223312.	−	187381.i	0.290345	−	0.243628i	0.776312	+	0.630349i	$0.217088\pi$
$878$	−305117.	−	363625.i	−0.395802	−	0.471698i
$879$		0			0
$880$	−35053.0	+	12758.2i	−0.0452647	+	0.0164750i
$881$	−919789.	+	531040.i	−1.18505	+	0.684189i	−0.957177	−	0.289503i	$-0.906510\pi$
$881$	−919789.	+	531040.i	−1.18505	+	0.684189i	−0.227872	+	0.973691i	$0.573177\pi$
$882$		0			0
$883$	661671.	−	1.14605e6i	0.848634	−	1.46988i	−0.0337936	−	0.999429i	$-0.510759\pi$
$883$	661671.	−	1.14605e6i	0.848634	−	1.46988i	0.882428	−	0.470448i	$-0.155908\pi$
$884$	−23086.6	−	4070.79i	−0.0295431	−	0.00520924i
$885$		0			0
$886$	752842.	+	274012.i	0.959039	+	0.349062i
$887$	−1.35025e6	+	238086.i	−1.71620	+	0.302613i	−0.943307	−	0.331921i	$-0.892303\pi$
$887$	−1.35025e6	+	238086.i	−1.71620	+	0.302613i	−0.772895	+	0.634534i	$0.781192\pi$
$888$		0			0
$889$	−184086.	−	154467.i	−0.232926	−	0.195448i
$890$			232354.i			0.293339i
$891$		0			0
$892$	−151930.			−0.190947
$893$	134160.	−	159886.i	0.168237	−	0.200497i
$894$		0			0
$895$	24055.4	+	136425.i	0.0300308	+	0.170313i
$896$	−9248.06	+	25408.8i	−0.0115195	+	0.0316496i
$897$		0			0
$898$	172090.	−	975971.i	0.213404	−	1.21028i
$899$	1.71958e6	+	992798.i	2.12766	+	1.22841i
$900$		0			0
$901$	208725.	+	361522.i	0.257113	+	0.445333i
$902$	57646.0	+	158381.i	0.0708527	+	0.194666i
$903$		0			0
$904$	−391679.	+	328658.i	−0.479285	+	0.402168i
$905$	−203595.	−	242635.i	−0.248582	−	0.296248i
$906$		0			0
$907$	445396.	−	162111.i	0.541417	−	0.197060i	−0.0568117	−	0.998385i	$-0.518093\pi$
$907$	445396.	−	162111.i	0.541417	−	0.197060i	0.598229	+	0.801325i	$0.295871\pi$
$908$	−142780.	+	82434.0i	−0.173179	+	0.0999849i
$909$		0			0
$910$	−6861.73	+	11884.9i	−0.00828612	+	0.0143520i
$911$	−1.44422e6	−	254655.i	−1.74019	−	0.306842i	−0.788757	−	0.614705i	$-0.789275\pi$
$911$	−1.44422e6	−	254655.i	−1.74019	−	0.306842i	−0.951431	+	0.307862i	$0.900386\pi$
$912$		0			0
$913$	−520964.	−	189615.i	−0.624980	−	0.227474i
$914$	202327.	−	35675.8i	0.242193	−	0.0427052i
$915$		0			0
$916$	−452266.	−	379496.i	−0.539017	−	0.452289i
$917$			18710.5i			0.0222508i
$918$		0			0
$919$	53623.4			0.0634927			0.0317463	−	0.999496i	$-0.489893\pi$
$919$	53623.4			0.0634927			0.0317463	+	0.999496i	$0.489893\pi$
$920$	−43235.3	+	51525.9i	−0.0510814	+	0.0608765i
$921$		0			0
$922$	−123248.	−	698977.i	−0.144984	−	0.822244i
$923$	−5168.28	+	14199.7i	−0.00606656	+	0.0166677i
$924$		0			0
$925$	−71204.4	+	403820.i	−0.0832192	+	0.471960i
$926$	−781988.	−	451481.i	−0.911965	−	0.526523i
$927$		0			0
$928$	−151317.	−	262089.i	−0.175708	−	0.304335i
$929$	204382.	+	561535.i	0.236816	+	0.650647i	0.999990	+	0.00445401i	$0.00141776\pi$
$929$	204382.	+	561535.i	0.236816	+	0.650647i	−0.763174	+	0.646193i	$0.776360\pi$
$930$		0			0
$931$	116540.	−	97788.6i	0.134454	−	0.112821i
$932$	169039.	+	201453.i	0.194606	+	0.231922i
$933$		0			0
$934$	175615.	−	63918.8i	0.201312	−	0.0732715i
$935$	71012.6	−	40999.2i	0.0812293	−	0.0468977i
$936$		0			0
$937$	−261262.	+	452519.i	−0.297576	+	0.515416i	−0.975581	−	0.219641i	$-0.929511\pi$
$937$	−261262.	+	452519.i	−0.297576	+	0.515416i	0.678005	+	0.735057i	$0.262845\pi$
$938$	−103861.	−	18313.5i	−0.118045	−	0.0208145i
$939$		0			0
$940$	264076.	+	96115.8i	0.298864	+	0.108777i
$941$	−139233.	+	24550.5i	−0.157240	+	0.0277257i	−0.251714	−	0.967802i	$-0.580994\pi$
$941$	−139233.	+	24550.5i	−0.157240	+	0.0277257i	0.0944739	+	0.995527i	$0.469883\pi$
$942$		0			0
$943$	232811.	+	195352.i	0.261807	+	0.219682i
$944$		−	90685.1i		−	0.101764i
$945$		0			0
$946$	69840.1			0.0780410
$947$	386835.	−	461012.i	0.431346	−	0.514058i	−0.505964	−	0.862555i	$-0.668863\pi$
$947$	386835.	−	461012.i	0.431346	−	0.514058i	0.937310	+	0.348496i	$0.113308\pi$
$948$		0			0
$949$	−31070.3	−	176208.i	−0.0344995	−	0.195656i
$950$	−33656.4	+	92470.1i	−0.0372924	+	0.102460i
$951$		0			0
$952$	10321.3	−	58535.1i	0.0113884	−	0.0645867i
$953$	325633.	+	188004.i	0.358544	+	0.207006i	0.668442	−	0.743764i	$-0.266961\pi$
$953$	325633.	+	188004.i	0.358544	+	0.207006i	−0.309898	+	0.950770i	$0.600295\pi$
$954$		0			0
$955$	219842.	+	380778.i	0.241048	+	0.417508i
$956$	246054.	+	676027.i	0.269224	+	0.739687i
$957$		0			0
$958$	−261084.	+	219076.i	−0.284478	+	0.238706i
$959$	−260568.	−	310533.i	−0.283325	−	0.337653i
$960$		0			0
$961$	−457683.	+	166583.i	−0.495585	+	0.180378i
$962$	−44573.8	+	25734.7i	−0.0481648	+	0.0278080i
$963$		0			0
$964$	210320.	−	364285.i	0.226322	−	0.392001i
$965$	−204510.	−	36060.7i	−0.219614	−	0.0387239i
$966$		0			0
$967$	250410.	+	91141.6i	0.267792	+	0.0974684i	0.472426	−	0.881370i	$-0.343378\pi$
$967$	250410.	+	91141.6i	0.267792	+	0.0974684i	−0.204634	+	0.978839i	$0.565600\pi$
$968$	277617.	−	48951.3i	0.296275	−	0.0522412i
$969$		0			0
$970$	282547.	+	237085.i	0.300294	+	0.251977i
$971$		−	572961.i		−	0.607697i	−0.952720	−	0.303848i	$-0.901728\pi$
$971$		−	572961.i		−	0.607697i	0.952720	−	0.303848i	$-0.0982716\pi$
$972$		0			0
$973$	320931.			0.338990
$974$	466519.	−	555976.i	0.491758	−	0.586054i
$975$		0			0
$976$	65415.1	+	370988.i	0.0686718	+	0.389457i
$977$	163736.	−	449861.i	0.171536	−	0.471291i	−0.823899	−	0.566737i	$-0.808206\pi$
$977$	163736.	−	449861.i	0.171536	−	0.471291i	0.995435	+	0.0954461i	$0.0304278\pi$
$978$		0			0
$979$	−53420.7	+	302964.i	−0.0557371	+	0.316101i
$980$	177394.	+	102418.i	0.184708	+	0.106641i
$981$		0			0
$982$	−139348.	−	241359.i	−0.144504	−	0.250288i
$983$	−425666.	−	1.16951e6i	−0.440517	−	1.21031i	−0.939153	−	0.343498i	$-0.888388\pi$
$983$	−425666.	−	1.16951e6i	−0.440517	−	1.21031i	0.498637	−	0.866811i	$-0.333834\pi$
$984$		0			0
$985$	−459794.	+	385813.i	−0.473905	+	0.397653i
$986$	427613.	+	509610.i	0.439843	+	0.524184i
$987$		0			0
$988$	−11606.8	+	4224.54i	−0.0118905	+	0.00432779i
$989$	109061.	−	62966.2i	0.111500	−	0.0643746i
$990$		0			0
$991$	−552970.	+	957772.i	−0.563059	+	0.975247i	0.434168	+	0.900832i	$0.357042\pi$
$991$	−552970.	+	957772.i	−0.563059	+	0.975247i	−0.997227	+	0.0744154i	$0.976291\pi$
$992$	211726.	+	37333.1i	0.215155	+	0.0379376i
$993$		0			0
$994$	−36002.8	−	13103.9i	−0.0364388	−	0.0132626i
$995$	−208748.	+	36807.9i	−0.210851	+	0.0371787i
$996$		0			0
$997$	176706.	+	148274.i	0.177771	+	0.149167i	0.727331	−	0.686287i	$-0.240760\pi$
$997$	176706.	+	148274.i	0.177771	+	0.149167i	−0.549561	+	0.835454i	$0.685205\pi$
$998$		−	784836.i		−	0.787985i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.35.1		72
3.2	odd	2		54.5.f.a.11.12	yes	72
27.5	odd	18	inner	162.5.f.a.125.1		72
27.22	even	9		54.5.f.a.5.12	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.5.12	✓	72	27.22	even	9
54.5.f.a.11.12	yes	72	3.2	odd	2
162.5.f.a.35.1		72	1.1	even	1	trivial
162.5.f.a.125.1		72	27.5	odd	18	inner

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-4.26691 + 11.7232i) q^{5} +(3.24231 - 18.3880i) q^{7} +(19.5959 + 11.3137i) q^{8} +O(q^{10})\)	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-4.26691 + 11.7232i) q^{5} +(3.24231 - 18.3880i) q^{7} +(19.5959 + 11.3137i) q^{8} +(-17.6432 - 30.5589i) q^{10} +(-15.9790 - 43.9018i) q^{11} +(15.9561 - 13.3888i) q^{13} +(33.9466 + 40.4560i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(121.836 - 70.3422i) q^{17} +(37.0626 - 64.1942i) q^{19} +(98.2887 + 17.3309i) q^{20} +(124.173 + 45.1953i) q^{22} +(234.653 - 41.3756i) q^{23} +(359.550 + 301.698i) q^{25} +58.9139i q^{26} -149.374 q^{28} +(1074.63 - 1280.70i) q^{29} +(206.238 + 1169.63i) q^{31} +(61.9123 - 170.103i) q^{32} +(-69.0973 + 391.870i) q^{34} +(201.733 + 116.471i) q^{35} +(436.819 + 756.593i) q^{37} +(71.7071 + 197.014i) q^{38} +(-216.247 + 181.453i) q^{40} +(819.867 + 977.079i) q^{41} +(496.648 - 180.765i) q^{43} +(-323.681 + 186.877i) q^{44} +(-336.968 + 583.646i) q^{46} +(2772.95 + 488.946i) q^{47} +(1928.59 + 701.951i) q^{49} +(-1307.38 + 230.526i) q^{50} +(-127.649 - 107.110i) q^{52} +2967.28i q^{53} +582.853 q^{55} +(271.573 - 323.648i) q^{56} +(821.122 + 4656.82i) q^{58} +(-484.627 + 1331.50i) q^{59} +(1022.11 - 5796.68i) q^{61} +(-2909.20 - 1679.63i) q^{62} +(256.000 + 443.405i) q^{64} +(88.8764 + 244.186i) q^{65} +(-1529.77 + 1283.63i) q^{67} +(-723.442 - 862.164i) q^{68} +(-619.123 + 225.342i) q^{70} +(-628.278 + 362.737i) q^{71} +(4295.09 - 7439.31i) q^{73} +(-2433.48 - 429.089i) q^{74} +(-557.239 - 202.818i) q^{76} +(-859.078 + 151.479i) q^{77} +(-7686.73 - 6449.93i) q^{79} -798.440i q^{80} -3607.62 q^{82} +(7627.68 - 9090.32i) q^{83} +(304.774 + 1728.46i) q^{85} +(-511.281 + 1404.73i) q^{86} +(183.570 - 1041.08i) q^{88} +(-5702.61 - 3292.40i) q^{89} +(-194.458 - 336.812i) q^{91} +(-651.952 - 1791.22i) q^{92} +(-6100.84 + 5119.21i) q^{94} +(594.422 + 708.405i) q^{95} +(-9822.34 + 3575.04i) q^{97} +(-5027.25 + 2902.49i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 72 * q + 18 * q^5	\( 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) \) 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Introduction

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