LMFDB - Embedded newform 162.5.f.a.17.9

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			17.9
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-5.05113 - 0.890650i) q^{5} +(14.8841 - 12.4892i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})$	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-5.05113 - 0.890650i) q^{5} +(14.8841 - 12.4892i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-7.25357 + 12.5636i) q^{10} +(-189.030 + 33.3311i) q^{11} +(40.7236 - 14.8222i) q^{13} +(-18.7959 - 51.6414i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-81.7214 - 47.1819i) q^{17} +(30.4781 + 52.7896i) q^{19} +(26.3751 + 31.4326i) q^{20} +(-94.2747 + 534.659i) q^{22} +(-653.526 + 778.842i) q^{23} +(-562.587 - 204.765i) q^{25} -122.576i q^{26} -155.438 q^{28} +(-218.912 + 601.454i) q^{29} +(683.468 + 573.498i) q^{31} +(178.269 + 31.4337i) q^{32} +(-204.458 + 171.561i) q^{34} +(-86.3048 + 49.8281i) q^{35} +(-428.478 + 742.145i) q^{37} +(169.791 - 29.9387i) q^{38} +(109.058 - 39.6939i) q^{40} +(-384.538 - 1056.51i) q^{41} +(-125.410 - 711.234i) q^{43} +(1329.84 + 767.786i) q^{44} +(1437.84 + 2490.41i) q^{46} +(-691.787 - 824.440i) q^{47} +(-351.374 + 1992.74i) q^{49} +(-1088.47 + 1297.19i) q^{50} +(-325.789 - 118.578i) q^{52} -89.7780i q^{53} +984.503 q^{55} +(-150.368 + 413.131i) q^{56} +(1386.81 + 1163.67i) q^{58} +(-4976.00 - 877.402i) q^{59} +(1135.19 - 952.539i) q^{61} +(2185.45 - 1261.77i) q^{62} +(256.000 - 443.405i) q^{64} +(-218.902 + 38.5983i) q^{65} +(4070.77 - 1481.64i) q^{67} +(258.194 + 709.383i) q^{68} +(48.9463 + 277.588i) q^{70} +(3149.55 + 1818.39i) q^{71} +(-1734.14 - 3003.62i) q^{73} +(1558.01 + 1856.77i) q^{74} +(84.6795 - 480.241i) q^{76} +(-2397.26 + 2856.94i) q^{77} +(-11221.9 - 4084.44i) q^{79} -328.259i q^{80} -3180.04 q^{82} +(2967.38 - 8152.82i) q^{83} +(370.763 + 311.107i) q^{85} +(-2011.67 - 354.712i) q^{86} +(3327.12 - 2791.79i) q^{88} +(6125.54 - 3536.58i) q^{89} +(421.016 - 729.220i) q^{91} +(8010.07 - 1412.39i) q^{92} +(-2860.46 + 1041.12i) q^{94} +(-106.932 - 293.793i) q^{95} +(-2526.36 - 14327.7i) q^{97} +(4956.50 + 2861.64i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	−5.05113	−	0.890650i	−0.202045	−	0.0356260i	0.0717096	−	0.997426i	$-0.477155\pi$
$5$	−5.05113	−	0.890650i	−0.202045	−	0.0356260i	−0.273755	+	0.961800i	$0.588266\pi$
$6$		0			0
$7$	14.8841	−	12.4892i	0.303756	−	0.254882i	−0.478149	−	0.878279i	$-0.658692\pi$
$7$	14.8841	−	12.4892i	0.303756	−	0.254882i	0.781906	+	0.623397i	$0.214248\pi$
$8$	−19.5959	+	11.3137i	−0.306186	+	0.176777i
$9$		0			0
$10$	−7.25357	+	12.5636i	−0.0725357	+	0.125636i
$11$	−189.030	+	33.3311i	−1.56223	+	0.275464i	−0.886870	−	0.462020i	$-0.847125\pi$
$11$	−189.030	+	33.3311i	−1.56223	+	0.275464i	−0.675365	+	0.737484i	$0.736014\pi$
$12$		0			0
$13$	40.7236	−	14.8222i	0.240968	−	0.0877053i	−0.218713	−	0.975789i	$-0.570186\pi$
$13$	40.7236	−	14.8222i	0.240968	−	0.0877053i	0.459681	+	0.888084i	$0.347964\pi$
$14$	−18.7959	−	51.6414i	−0.0958977	−	0.263477i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	−81.7214	−	47.1819i	−0.282773	−	0.163259i	0.351905	−	0.936036i	$-0.385534\pi$
$17$	−81.7214	−	47.1819i	−0.282773	−	0.163259i	−0.634678	+	0.772777i	$0.718867\pi$
$18$		0			0
$19$	30.4781	+	52.7896i	0.0844269	+	0.146232i	0.905147	−	0.425099i	$-0.139761\pi$
$19$	30.4781	+	52.7896i	0.0844269	+	0.146232i	−0.820720	+	0.571331i	$0.806427\pi$
$20$	26.3751	+	31.4326i	0.0659378	+	0.0785816i
$21$		0			0
$22$	−94.2747	+	534.659i	−0.194782	+	1.10467i
$23$	−653.526	+	778.842i	−1.23540	+	1.47229i	−0.405769	+	0.913976i	$0.632996\pi$
$23$	−653.526	+	778.842i	−1.23540	+	1.47229i	−0.829629	+	0.558314i	$0.811448\pi$
$24$		0			0
$25$	−562.587	−	204.765i	−0.900140	−	0.327624i
$26$		−	122.576i		−	0.181326i
$27$		0			0
$28$	−155.438			−0.198263
$29$	−218.912	+	601.454i	−0.260299	+	0.715166i	0.738848	+	0.673872i	$0.235370\pi$
$29$	−218.912	+	601.454i	−0.260299	+	0.715166i	−0.999147	+	0.0412937i	$0.986852\pi$
$30$		0			0
$31$	683.468	+	573.498i	0.711205	+	0.596772i	0.924937	−	0.380120i	$-0.124117\pi$
$31$	683.468	+	573.498i	0.711205	+	0.596772i	−0.213732	+	0.976892i	$0.568562\pi$
$32$	178.269	+	31.4337i	0.174091	+	0.0306970i
$33$		0			0
$34$	−204.458	+	171.561i	−0.176867	+	0.148409i
$35$	−86.3048	+	49.8281i	−0.0704529	+	0.0406760i
$36$		0			0
$37$	−428.478	+	742.145i	−0.312986	+	0.542108i	−0.979007	−	0.203825i	$-0.934663\pi$
$37$	−428.478	+	742.145i	−0.312986	+	0.542108i	0.666021	+	0.745933i	$0.267996\pi$
$38$	169.791	−	29.9387i	0.117584	−	0.0207332i
$39$		0			0
$40$	109.058	−	39.6939i	0.0681613	−	0.0248087i
$41$	−384.538	−	1056.51i	−0.228756	−	0.628501i	0.771212	−	0.636579i	$-0.219651\pi$
$41$	−384.538	−	1056.51i	−0.228756	−	0.628501i	−0.999967	+	0.00807769i	$0.997429\pi$
$42$		0			0
$43$	−125.410	−	711.234i	−0.0678257	−	0.384659i	−0.999757	−	0.0220249i	$-0.992989\pi$
$43$	−125.410	−	711.234i	−0.0678257	−	0.384659i	0.931932	−	0.362634i	$-0.118122\pi$
$44$	1329.84	+	767.786i	0.686903	+	0.396584i
$45$		0			0
$46$	1437.84	+	2490.41i	0.679508	+	1.17694i
$47$	−691.787	−	824.440i	−0.313168	−	0.373219i	0.586384	−	0.810033i	$-0.300551\pi$
$47$	−691.787	−	824.440i	−0.313168	−	0.373219i	−0.899552	+	0.436815i	$0.856107\pi$
$48$		0			0
$49$	−351.374	+	1992.74i	−0.146345	+	0.829964i
$50$	−1088.47	+	1297.19i	−0.435388	+	0.518875i
$51$		0			0
$52$	−325.789	−	118.578i	−0.120484	−	0.0438526i
$53$		−	89.7780i		−	0.0319608i	−0.999872	−	0.0159804i	$-0.994913\pi$
$53$		−	89.7780i		−	0.0319608i	0.999872	−	0.0159804i	$-0.00508694\pi$
$54$		0			0
$55$	984.503			0.325455
$56$	−150.368	+	413.131i	−0.0479488	+	0.131738i
$57$		0			0
$58$	1386.81	+	1163.67i	0.412249	+	0.345918i
$59$	−4976.00	−	877.402i	−1.42947	−	0.252055i	−0.595276	−	0.803521i	$-0.702957\pi$
$59$	−4976.00	−	877.402i	−1.42947	−	0.252055i	−0.834197	+	0.551466i	$0.814068\pi$
$60$		0			0
$61$	1135.19	−	952.539i	0.305077	−	0.255990i	−0.477377	−	0.878699i	$-0.658412\pi$
$61$	1135.19	−	952.539i	0.305077	−	0.255990i	0.782454	+	0.622709i	$0.213968\pi$
$62$	2185.45	−	1261.77i	0.568534	−	0.328243i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−218.902	+	38.5983i	−0.0518110	+	0.00913569i
$66$		0			0
$67$	4070.77	−	1481.64i	0.906832	−	0.330060i	0.153845	−	0.988095i	$-0.450834\pi$
$67$	4070.77	−	1481.64i	0.906832	−	0.330060i	0.752987	+	0.658035i	$0.228612\pi$
$68$	258.194	+	709.383i	0.0558379	+	0.153413i
$69$		0			0
$70$	48.9463	+	277.588i	0.00998903	+	0.0566506i
$71$	3149.55	+	1818.39i	0.624787	+	0.360721i	0.778730	−	0.627359i	$-0.215864\pi$
$71$	3149.55	+	1818.39i	0.624787	+	0.360721i	−0.153943	+	0.988080i	$0.549197\pi$
$72$		0			0
$73$	−1734.14	−	3003.62i	−0.325416	−	0.563637i	0.656180	−	0.754604i	$-0.272171\pi$
$73$	−1734.14	−	3003.62i	−0.325416	−	0.563637i	−0.981596	+	0.190967i	$0.938838\pi$
$74$	1558.01	+	1856.77i	0.284516	+	0.339073i
$75$		0			0
$76$	84.6795	−	480.241i	0.0146606	−	0.0831443i
$77$	−2397.26	+	2856.94i	−0.404328	+	0.481859i
$78$		0			0
$79$	−11221.9	−	4084.44i	−1.79809	−	0.654452i	−0.998549	−	0.0538429i	$-0.982853\pi$
$79$	−11221.9	−	4084.44i	−1.79809	−	0.654452i	−0.799543	−	0.600609i	$-0.794925\pi$
$80$		−	328.259i		−	0.0512905i
$81$		0			0
$82$	−3180.04			−0.472939
$83$	2967.38	−	8152.82i	0.430742	−	1.18345i	−0.514616	−	0.857421i	$-0.672065\pi$
$83$	2967.38	−	8152.82i	0.430742	−	1.18345i	0.945358	−	0.326034i	$-0.105712\pi$
$84$		0			0
$85$	370.763	+	311.107i	0.0513166	+	0.0430598i
$86$	−2011.67	−	354.712i	−0.271995	−	0.0479600i
$87$		0			0
$88$	3327.12	−	2791.79i	0.429639	−	0.360510i
$89$	6125.54	−	3536.58i	0.773329	−	0.446482i	−0.0607317	−	0.998154i	$-0.519343\pi$
$89$	6125.54	−	3536.58i	0.773329	−	0.446482i	0.834061	+	0.551672i	$0.186010\pi$
$90$		0			0
$91$	421.016	−	729.220i	0.0508412	−	0.0880595i
$92$	8010.07	−	1412.39i	0.946370	−	0.166871i
$93$		0			0
$94$	−2860.46	+	1041.12i	−0.323728	+	0.117827i
$95$	−106.932	−	293.793i	−0.0118484	−	0.0325532i
$96$		0			0
$97$	−2526.36	−	14327.7i	−0.268504	−	1.52276i	−0.758867	−	0.651245i	$-0.774247\pi$
$97$	−2526.36	−	14327.7i	−0.268504	−	1.52276i	0.490363	−	0.871518i	$-0.336864\pi$
$98$	4956.50	+	2861.64i	0.516088	+	0.297963i
$99$		0			0
$100$	2394.77	+	4147.87i	0.239477	+	0.414787i
$101$	−11066.1	−	13188.1i	−1.08481	−	1.29282i	−0.953471	−	0.301483i	$-0.902518\pi$
$101$	−11066.1	−	13188.1i	−1.08481	−	1.29282i	−0.131335	−	0.991338i	$-0.541926\pi$
$102$		0			0
$103$	2077.68	−	11783.1i	0.195842	−	1.11067i	−0.715373	−	0.698742i	$-0.753743\pi$
$103$	2077.68	−	11783.1i	0.195842	−	1.11067i	0.911215	−	0.411931i	$-0.135146\pi$
$104$	−630.323	+	751.190i	−0.0582769	+	0.0694517i
$105$		0			0
$106$	−238.617	−	86.8494i	−0.0212368	−	0.00772956i
$107$			12927.3i			1.12912i	0.825392	+	0.564560i	$0.190954\pi$
$107$			12927.3i			1.12912i	−0.825392	+	0.564560i	$0.809046\pi$
$108$		0			0
$109$	−16523.4			−1.39074			−0.695370	−	0.718652i	$-0.744760\pi$
$109$	−16523.4			−1.39074			−0.695370	+	0.718652i	$0.744760\pi$
$110$	952.387	−	2616.66i	0.0787097	−	0.216253i
$111$		0			0
$112$	952.580	+	799.309i	0.0759391	+	0.0637205i
$113$	14173.4	+	2499.15i	1.10999	+	0.195720i	0.698440	−	0.715669i	$-0.253878\pi$
$113$	14173.4	+	2499.15i	1.10999	+	0.195720i	0.411546	+	0.911389i	$0.364989\pi$
$114$		0			0
$115$	3994.72	−	3351.97i	0.302058	−	0.253457i
$116$	4434.43	−	2560.22i	0.329550	−	0.190266i
$117$		0			0
$118$	−7145.68	+	12376.7i	−0.513192	+	0.888874i
$119$	−1805.61	+	318.378i	−0.127506	+	0.0224827i
$120$		0			0
$121$	20863.5	−	7593.68i	1.42500	−	0.518658i
$122$	−1433.55	−	3938.64i	−0.0963146	−	0.264622i
$123$		0			0
$124$	−1239.44	−	7029.20i	−0.0806086	−	0.457154i
$125$	5435.51	+	3138.19i	0.347872	+	0.200844i
$126$		0			0
$127$	6724.74	+	11647.6i	0.416935	+	0.722152i	0.995629	−	0.0933921i	$-0.0297710\pi$
$127$	6724.74	+	11647.6i	0.416935	+	0.722152i	−0.578695	+	0.815544i	$0.696438\pi$
$128$	−930.856	−	1109.35i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	−109.172	+	619.147i	−0.00645991	+	0.0366359i
$131$	−16647.4	+	19839.6i	−0.970072	+	1.15609i	0.0176471	+	0.999844i	$0.494382\pi$
$131$	−16647.4	+	19839.6i	−0.970072	+	1.15609i	−0.987719	+	0.156242i	$0.950062\pi$
$132$		0			0
$133$	1112.94	+	405.077i	0.0629170	+	0.0228999i
$134$		−	12252.8i		−	0.682379i
$135$		0			0
$136$	2135.21			0.115442
$137$	8654.72	−	23778.6i	0.461118	−	1.26691i	−0.463528	−	0.886082i	$-0.653417\pi$
$137$	8654.72	−	23778.6i	0.461118	−	1.26691i	0.924646	−	0.380828i	$-0.124361\pi$
$138$		0			0
$139$	26198.3	+	21983.0i	1.35595	+	1.13778i	0.977210	+	0.212275i	$0.0680874\pi$
$139$	26198.3	+	21983.0i	1.35595	+	1.13778i	0.378741	+	0.925503i	$0.376357\pi$
$140$	785.138	+	138.441i	0.0400580	+	0.00706331i
$141$		0			0
$142$	7879.84	−	6611.97i	0.390787	−	0.327910i
$143$	−7203.96	+	4159.21i	−0.352289	+	0.203394i
$144$		0			0
$145$	1641.44	−	2843.05i	0.0780707	−	0.135222i
$146$	−9660.75	+	1703.45i	−0.453216	+	0.0799142i
$147$		0			0
$148$	6442.20	−	2344.77i	0.294111	−	0.107047i
$149$	−4494.89	−	12349.6i	−0.202464	−	0.556264i	0.796357	−	0.604827i	$-0.206758\pi$
$149$	−4494.89	−	12349.6i	−0.202464	−	0.556264i	−0.998820	+	0.0485634i	$0.984536\pi$
$150$		0			0
$151$	5012.65	+	28428.1i	0.219843	+	1.24679i	0.872301	+	0.488969i	$0.162627\pi$
$151$	5012.65	+	28428.1i	0.219843	+	1.24679i	−0.652458	+	0.757825i	$0.726262\pi$
$152$	−1194.49	−	689.641i	−0.0517007	−	0.0298494i
$153$		0			0
$154$	5274.27	+	9135.31i	0.222393	+	0.385196i
$155$	−2941.50	−	3505.54i	−0.122435	−	0.145912i
$156$		0			0
$157$	−1270.57	+	7205.76i	−0.0515465	+	0.292335i	−0.999673	−	0.0255575i	$-0.991864\pi$
$157$	−1270.57	+	7205.76i	−0.0515465	+	0.292335i	0.948127	+	0.317892i	$0.102975\pi$
$158$	−21711.6	+	25874.9i	−0.869718	+	1.03649i
$159$		0			0
$160$	−872.464	−	317.551i	−0.0340806	−	0.0124043i
$161$			19754.3i			0.762098i
$162$		0			0
$163$	−52617.9			−1.98042			−0.990212	−	0.139569i	$-0.955428\pi$
$163$	−52617.9			−1.98042			−0.990212	+	0.139569i	$0.955428\pi$
$164$	−3076.31	+	8452.08i	−0.114378	+	0.314251i
$165$		0			0
$166$	−18798.4	−	15773.7i	−0.682189	−	0.572425i
$167$	41405.7	+	7300.95i	1.48466	+	0.261786i	0.856439	−	0.516247i	$-0.172672\pi$
$167$	41405.7	+	7300.95i	1.48466	+	0.261786i	0.628223	+	0.778033i	$0.283783\pi$
$168$		0			0
$169$	−20440.3	+	17151.4i	−0.715671	+	0.600519i
$170$	1185.54	−	684.474i	0.0410223	−	0.0236842i
$171$		0			0
$172$	−2888.82	+	5003.59i	−0.0976482	+	0.169132i
$173$	−18571.5	+	3274.65i	−0.620518	+	0.109414i	−0.475064	−	0.879951i	$-0.657575\pi$
$173$	−18571.5	+	3274.65i	−0.620518	+	0.109414i	−0.145453	+	0.989365i	$0.546464\pi$
$174$		0			0
$175$	−10930.9	+	3978.53i	−0.356928	+	0.129911i
$176$	−4201.57	−	11543.7i	−0.135640	−	0.372667i
$177$		0			0
$178$	−3473.99	−	19702.0i	−0.109645	−	0.621828i
$179$	14984.3	+	8651.18i	0.467660	+	0.270004i	0.715260	−	0.698859i	$-0.246308\pi$
$179$	14984.3	+	8651.18i	0.467660	+	0.270004i	−0.247600	+	0.968862i	$0.579642\pi$
$180$		0			0
$181$	18983.5	+	32880.4i	0.579454	+	1.00364i	0.995542	+	0.0943190i	$0.0300674\pi$
$181$	18983.5	+	32880.4i	0.579454	+	1.00364i	−0.416088	+	0.909324i	$0.636599\pi$
$182$	−1530.88	−	1824.43i	−0.0462166	−	0.0550788i
$183$		0			0
$184$	3994.85	−	22655.9i	0.117995	−	0.669185i
$185$	2825.29	−	3367.05i	0.0825504	−	0.0983798i
$186$		0			0
$187$	17020.4	+	6194.94i	0.486730	+	0.177155i
$188$			8609.84i			0.243601i
$189$		0			0
$190$	−884.301			−0.0244959
$191$	−1933.88	+	5313.30i	−0.0530107	+	0.145646i	−0.963372	−	0.268169i	$-0.913582\pi$
$191$	−1933.88	+	5313.30i	−0.0530107	+	0.145646i	0.910361	+	0.413814i	$0.135804\pi$
$192$		0			0
$193$	−8102.16	−	6798.52i	−0.217514	−	0.182516i	0.527520	−	0.849543i	$-0.323122\pi$
$193$	−8102.16	−	6798.52i	−0.217514	−	0.182516i	−0.745033	+	0.667027i	$0.767566\pi$
$194$	−40524.8	−	7145.62i	−1.07676	−	0.189861i
$195$		0			0
$196$	12400.6	−	10405.4i	0.322799	−	0.270860i
$197$	−38607.4	+	22290.0i	−0.994806	+	0.574351i	−0.906707	−	0.421760i	$-0.861412\pi$
$197$	−38607.4	+	22290.0i	−0.994806	+	0.574351i	−0.0880985	+	0.996112i	$0.528079\pi$
$198$		0			0
$199$	15060.1	−	26084.8i	0.380296	−	0.658691i	−0.610809	−	0.791778i	$-0.709156\pi$
$199$	15060.1	−	26084.8i	0.380296	−	0.658691i	0.991104	+	0.133087i	$0.0424889\pi$
$200$	13341.1	−	2352.39i	0.333527	−	0.0588097i
$201$		0			0
$202$	−45757.1	+	16654.2i	−1.12139	+	0.408151i
$203$	4253.40	+	11686.1i	0.103215	+	0.283582i
$204$		0			0
$205$	1001.37	+	5679.06i	0.0238280	+	0.135135i
$206$	−29307.9	−	16920.9i	−0.690638	−	0.398740i
$207$		0			0
$208$	1386.79	+	2401.99i	0.0320541	+	0.0555194i
$209$	−7520.83	−	8962.97i	−0.172176	−	0.205192i
$210$		0			0
$211$	−8324.85	+	47212.6i	−0.186987	+	1.06046i	0.736389	+	0.676559i	$0.236530\pi$
$211$	−8324.85	+	47212.6i	−0.186987	+	1.06046i	−0.923376	+	0.383898i	$0.874582\pi$
$212$	−461.666	+	550.192i	−0.0102720	+	0.0122417i
$213$		0			0
$214$	34358.8	+	12505.6i	0.750258	+	0.273072i
$215$			3704.23i			0.0801348i
$216$		0			0
$217$	17335.3			0.368140
$218$	−15984.4	+	43916.7i	−0.336343	+	0.924095i
$219$		0			0
$220$	−6033.38	−	5062.61i	−0.124657	−	0.104599i
$221$	−4027.33	−	710.127i	−0.0824580	−	0.0145396i
$222$		0			0
$223$	−61595.1	+	51684.4i	−1.23861	+	1.03932i	−0.240983	+	0.970529i	$0.577470\pi$
$223$	−61595.1	+	51684.4i	−1.23861	+	1.03932i	−0.997631	+	0.0687916i	$0.978086\pi$
$224$	3045.95	−	1758.58i	0.0607054	−	0.0350483i
$225$		0			0
$226$	20353.4	−	35253.2i	0.398493	−	0.690210i
$227$	5901.07	−	1040.52i	0.114519	−	0.0201928i	−0.116095	−	0.993238i	$-0.537038\pi$
$227$	5901.07	−	1040.52i	0.114519	−	0.0201928i	0.230614	+	0.973045i	$0.425927\pi$
$228$		0			0
$229$	56374.2	−	20518.5i	1.07500	−	0.391269i	0.256958	−	0.966423i	$-0.417280\pi$
$229$	56374.2	−	20518.5i	1.07500	−	0.391269i	0.818046	+	0.575153i	$0.195058\pi$
$230$	−5044.62	−	13860.0i	−0.0953615	−	0.262004i
$231$		0			0
$232$	−2514.91	−	14262.8i	−0.0467247	−	0.264989i
$233$	−17362.4	−	10024.2i	−0.319814	−	0.184645i	0.331495	−	0.943457i	$-0.392447\pi$
$233$	−17362.4	−	10024.2i	−0.319814	−	0.184645i	−0.651310	+	0.758812i	$0.725780\pi$
$234$		0			0
$235$	2760.02	+	4780.49i	0.0499777	+	0.0865639i
$236$	25982.8	+	30965.1i	0.466511	+	0.555966i
$237$		0			0
$238$	−900.508	+	5107.04i	−0.0158977	+	0.0901602i
$239$	40024.8	−	47699.7i	0.700701	−	0.835063i	−0.291904	−	0.956448i	$-0.594289\pi$
$239$	40024.8	−	47699.7i	0.700701	−	0.835063i	0.992606	+	0.121384i	$0.0387333\pi$
$240$		0			0
$241$	−14083.9	−	5126.12i	−0.242487	−	0.0882581i	0.217918	−	0.975967i	$-0.430074\pi$
$241$	−14083.9	−	5126.12i	−0.242487	−	0.0882581i	−0.460405	+	0.887709i	$0.652296\pi$
$242$		−	62798.0i		−	1.07230i
$243$		0			0
$244$	−11855.1			−0.199125
$245$	3549.67	−	9752.65i	0.0591366	−	0.162476i
$246$		0			0
$247$	2023.64	+	1698.03i	0.0331695	+	0.0278325i
$248$	−19881.6	−	3505.66i	−0.323257	−	0.0569989i
$249$		0			0
$250$	13599.0	−	11411.0i	0.217585	−	0.182575i
$251$	14479.0	−	8359.45i	0.229822	−	0.132688i	−0.380668	−	0.924712i	$-0.624306\pi$
$251$	14479.0	−	8359.45i	0.229822	−	0.132688i	0.610490	+	0.792024i	$0.290973\pi$
$252$		0			0
$253$	97576.5	−	169007.i	1.52442	−	2.64037i
$254$	37463.0	−	6605.73i	0.580677	−	0.102389i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	−6547.79	−	17989.9i	−0.0991353	−	0.272372i	0.880204	−	0.474595i	$-0.157406\pi$
$257$	−6547.79	−	17989.9i	−0.0991353	−	0.272372i	−0.979339	+	0.202223i	$0.935183\pi$
$258$		0			0
$259$	2891.32	+	16397.5i	0.0431019	+	0.244443i
$260$	1539.99	+	889.114i	0.0227809	+	0.0131526i
$261$		0			0
$262$	36626.4	+	63438.7i	0.533570	+	0.924170i
$263$	81090.1	+	96639.4i	1.17235	+	1.39715i	0.900526	+	0.434802i	$0.143182\pi$
$263$	81090.1	+	96639.4i	1.17235	+	1.39715i	0.271822	+	0.962348i	$0.412374\pi$
$264$		0			0
$265$	−79.9608	+	453.480i	−0.00113864	+	0.00645753i
$266$	2153.27	−	2566.16i	0.0304323	−	0.0362678i
$267$		0			0
$268$	−32566.1	−	11853.1i	−0.453416	−	0.165030i
$269$		−	42480.3i		−	0.587061i	−0.955950	−	0.293530i	$-0.905170\pi$
$269$		−	42480.3i		−	0.587061i	0.955950	−	0.293530i	$-0.0948302\pi$
$270$		0			0
$271$	−30849.7			−0.420061			−0.210030	−	0.977695i	$-0.567356\pi$
$271$	−30849.7			−0.420061			−0.210030	+	0.977695i	$0.567356\pi$
$272$	2065.56	−	5675.07i	0.0279189	−	0.0767067i
$273$		0			0
$274$	−54827.7	−	46005.9i	−0.730296	−	0.612791i
$275$	113171.	+	19955.1i	1.49648	+	0.263869i
$276$		0			0
$277$	59458.8	−	49891.9i	0.774920	−	0.650235i	−0.167044	−	0.985949i	$-0.553422\pi$
$277$	59458.8	−	49891.9i	0.774920	−	0.650235i	0.941964	+	0.335715i	$0.108978\pi$
$278$	83771.3	−	48365.4i	1.08394	−	0.625814i
$279$		0			0
$280$	1127.48	−	1952.85i	0.0143811	−	0.0249089i
$281$	−46919.7	+	8273.21i	−0.594214	+	0.104776i	−0.462664	−	0.886534i	$-0.653106\pi$
$281$	−46919.7	+	8273.21i	−0.594214	+	0.104776i	−0.131550	+	0.991310i	$0.541995\pi$
$282$		0			0
$283$	−118630.	+	43177.6i	−1.48122	+	0.539121i	−0.951122	−	0.308815i	$-0.900068\pi$
$283$	−118630.	+	43177.6i	−1.48122	+	0.539121i	−0.530100	+	0.847935i	$0.677845\pi$
$284$	−9950.84	−	27339.7i	−0.123374	−	0.338967i
$285$		0			0
$286$	4085.60	+	23170.6i	0.0499487	+	0.283273i
$287$	−18918.5	−	10922.6i	−0.229679	−	0.132606i
$288$		0			0
$289$	−37308.2	−	64619.8i	−0.446693	−	0.773695i
$290$	−5968.52	−	7113.00i	−0.0709693	−	0.0845779i
$291$		0			0
$292$	−4818.09	+	27324.7i	−0.0565079	+	0.320472i
$293$	68264.2	−	81354.1i	0.795166	−	0.947642i	−0.204346	−	0.978899i	$-0.565507\pi$
$293$	68264.2	−	81354.1i	0.795166	−	0.947642i	0.999511	+	0.0312571i	$0.00995107\pi$
$294$		0			0
$295$	24352.9	+	8863.74i	0.279838	+	0.101853i
$296$		−	19390.7i		−	0.221314i
$297$		0			0
$298$	−37171.7			−0.418582
$299$	−15069.8	+	41403.9i	−0.168564	+	0.463126i
$300$		0			0
$301$	−10749.4	−	9019.78i	−0.118645	−	0.0995550i
$302$	80406.9	+	14177.9i	0.881616	+	0.155453i
$303$		0			0
$304$	−2988.49	+	2507.64i	−0.0323374	+	0.0271343i
$305$	−6582.38	+	3800.34i	−0.0707592	+	0.0408529i
$306$		0			0
$307$	36118.3	−	62558.7i	0.383222	−	0.663759i	−0.608299	−	0.793708i	$-0.708148\pi$
$307$	36118.3	−	62558.7i	0.383222	−	0.663759i	0.991521	+	0.129948i	$0.0414812\pi$
$308$	29382.5	−	5180.93i	0.309733	−	0.0546143i
$309$		0			0
$310$	−12162.8	+	4426.88i	−0.126564	+	0.0460654i
$311$	−17413.8	−	47844.0i	−0.180041	−	0.494660i	0.816539	−	0.577291i	$-0.195890\pi$
$311$	−17413.8	−	47844.0i	−0.180041	−	0.494660i	−0.996580	+	0.0826308i	$0.973668\pi$
$312$		0			0
$313$	−200.530	−	1137.26i	−0.00204688	−	0.0116084i	0.983767	−	0.179449i	$-0.0574316\pi$
$313$	−200.530	−	1137.26i	−0.00204688	−	0.0116084i	−0.985814	+	0.167841i	$0.946320\pi$
$314$	17922.7	+	10347.7i	0.181779	+	0.104950i
$315$		0			0
$316$	47768.4	+	82737.2i	0.478372	+	0.828565i
$317$	−33975.0	−	40489.8i	−0.338097	−	0.402928i	0.570030	−	0.821624i	$-0.306932\pi$
$317$	−33975.0	−	40489.8i	−0.338097	−	0.402928i	−0.908126	+	0.418696i	$0.862487\pi$
$318$		0			0
$319$	21333.8	−	120990.i	0.209646	−	1.18896i
$320$	−1688.01	+	2011.69i	−0.0164844	+	0.0196454i
$321$		0			0
$322$	52504.1	+	19109.9i	0.506386	+	0.184309i
$323$		−	5752.06i		−	0.0551338i
$324$		0			0
$325$	−25945.7			−0.245639
$326$	−50901.5	+	139851.i	−0.478955	+	1.31592i
$327$		0			0
$328$	19488.4	+	16352.7i	0.181146	+	0.152000i
$329$	−20593.2	−	3631.14i	−0.190253	−	0.0335468i
$330$		0			0
$331$	−77485.3	+	65017.9i	−0.707235	+	0.593440i	−0.923822	−	0.382823i	$-0.874952\pi$
$331$	−77485.3	+	65017.9i	−0.707235	+	0.593440i	0.216587	+	0.976263i	$0.430507\pi$
$332$	−60109.4	+	34704.2i	−0.545339	+	0.314852i
$333$		0			0
$334$	59459.9	−	102988.i	0.533005	−	0.923192i
$335$	−21881.6	+	3858.31i	−0.194980	+	0.0343802i
$336$		0			0
$337$	−36057.9	+	13124.0i	−0.317498	+	0.115560i	−0.495853	−	0.868406i	$-0.665145\pi$
$337$	−36057.9	+	13124.0i	−0.317498	+	0.115560i	0.178355	+	0.983966i	$0.442922\pi$
$338$	25812.5	+	70919.2i	0.225942	+	0.620769i
$339$		0			0
$340$	−672.361	−	3813.15i	−0.00581627	−	0.0329857i
$341$	−148312.	−	85627.7i	−1.27546	−	0.736386i
$342$		0			0
$343$	42983.3	+	74449.3i	0.365352	+	0.632809i
$344$	10504.2	+	12518.4i	0.0887660	+	0.105787i
$345$		0			0
$346$	−9262.12	+	52528.1i	−0.0773674	+	0.438772i
$347$	−75783.0	+	90314.6i	−0.629379	+	0.750065i	−0.982653	−	0.185455i	$-0.940624\pi$
$347$	−75783.0	+	90314.6i	−0.629379	+	0.750065i	0.353273	+	0.935520i	$0.385069\pi$
$348$		0			0
$349$	−18625.5	−	6779.12i	−0.152917	−	0.0556573i	0.264427	−	0.964406i	$-0.414817\pi$
$349$	−18625.5	−	6779.12i	−0.152917	−	0.0556573i	−0.417345	+	0.908748i	$0.637039\pi$
$350$			32901.6i			0.268584i
$351$		0			0
$352$	−34746.0			−0.280427
$353$	−4271.08	+	11734.7i	−0.0342759	+	0.0941722i	−0.955650	−	0.294504i	$-0.904845\pi$
$353$	−4271.08	+	11734.7i	−0.0342759	+	0.0941722i	0.921374	+	0.388677i	$0.127068\pi$
$354$		0			0
$355$	−14289.2	−	11990.1i	−0.113384	−	0.0951406i
$356$	−55725.7	−	9825.94i	−0.439699	−	0.0775308i
$357$		0			0
$358$	37489.1	−	31457.1i	0.292508	−	0.245444i
$359$	−97479.4	+	56279.7i	−0.756352	+	0.436680i	−0.827984	−	0.560751i	$-0.810512\pi$
$359$	−97479.4	+	56279.7i	−0.756352	+	0.436680i	0.0716326	+	0.997431i	$0.477179\pi$
$360$		0			0
$361$	63302.7	−	109643.i	0.485744	−	0.841334i
$362$	105755.	−	18647.5i	0.807022	−	0.142300i
$363$		0			0
$364$	−6330.00	+	2303.93i	−0.0477751	+	0.0173887i
$365$	6084.20	+	16716.2i	0.0456686	+	0.125473i
$366$		0			0
$367$	25811.4	+	146384.i	0.191637	+	1.08683i	0.917127	+	0.398595i	$0.130502\pi$
$367$	25811.4	+	146384.i	0.191637	+	1.08683i	−0.725490	+	0.688232i	$0.758387\pi$
$368$	−56351.5	−	32534.6i	−0.416112	−	0.240242i
$369$		0			0
$370$	−6215.99	−	10766.4i	−0.0454053	−	0.0786443i
$371$	−1121.26	−	1336.26i	−0.00814624	−	0.00970831i
$372$		0			0
$373$	−10264.1	+	58210.6i	−0.0737740	+	0.418393i	0.925445	+	0.378882i	$0.123691\pi$
$373$	−10264.1	+	58210.6i	−0.0737740	+	0.418393i	−0.999219	+	0.0395114i	$0.987420\pi$
$374$	32930.4	−	39245.0i	0.235426	−	0.280570i
$375$		0			0
$376$	22883.7	+	8328.98i	0.161864	+	0.0589137i
$377$			27738.2i			0.195162i
$378$		0			0
$379$	−209594.			−1.45915			−0.729576	−	0.683900i	$-0.760282\pi$
$379$	−209594.			−1.45915			−0.729576	+	0.683900i	$0.760282\pi$
$380$	−855.454	+	2350.34i	−0.00592420	+	0.0162766i
$381$		0			0
$382$	12251.2	+	10279.9i	0.0839558	+	0.0704473i
$383$	−161840.	−	28536.8i	−1.10329	−	0.194540i	−0.407796	−	0.913073i	$-0.633703\pi$
$383$	−161840.	−	28536.8i	−1.10329	−	0.194540i	−0.695493	+	0.718533i	$0.744814\pi$
$384$		0			0
$385$	14653.4	−	12295.7i	0.0988592	−	0.0829527i
$386$	−25907.3	+	14957.6i	−0.173879	+	0.100389i
$387$		0			0
$388$	−58194.8	+	100796.i	−0.386564	+	0.669548i
$389$	−175561.	+	30956.1i	−1.16019	+	0.204572i	−0.720419	−	0.693540i	$-0.756050\pi$
$389$	−175561.	+	30956.1i	−1.16019	+	0.204572i	−0.439768	+	0.898112i	$0.644939\pi$
$390$		0			0
$391$	90154.2	−	32813.5i	0.589702	−	0.214634i
$392$	−15659.8	−	43025.0i	−0.101909	−	0.279994i
$393$		0			0
$394$	21895.5	+	124176.i	0.141047	+	0.799916i
$395$	53045.4	+	30625.8i	0.339980	+	0.196288i
$396$		0			0
$397$	120672.	+	209010.i	0.765642	+	1.32613i	0.939907	+	0.341432i	$0.110912\pi$
$397$	120672.	+	209010.i	0.765642	+	1.32613i	−0.174265	+	0.984699i	$0.555755\pi$
$398$	−54760.8	−	65261.4i	−0.345704	−	0.411993i
$399$		0			0
$400$	6653.56	−	37734.2i	0.0415848	−	0.235839i
$401$	107640.	−	128280.i	0.669399	−	0.797759i	−0.319303	−	0.947653i	$-0.603449\pi$
$401$	107640.	−	128280.i	0.669399	−	0.797759i	0.988702	+	0.149894i	$0.0478933\pi$
$402$		0			0
$403$	36333.8	+	13224.4i	0.223718	+	0.0814267i
$404$			137726.i			0.843829i
$405$		0			0
$406$	35174.6			0.213392
$407$	56258.7	−	154570.i	0.339626	−	0.933115i
$408$		0			0
$409$	−73785.3	−	61913.3i	−0.441086	−	0.370115i	0.395029	−	0.918668i	$-0.370734\pi$
$409$	−73785.3	−	61913.3i	−0.441086	−	0.370115i	−0.836116	+	0.548553i	$0.815179\pi$
$410$	16062.8	+	2832.31i	0.0955550	+	0.0168489i
$411$		0			0
$412$	−73325.2	+	61527.2i	−0.431975	+	0.362470i
$413$	−85021.1	+	49087.0i	−0.498456	+	0.287784i
$414$		0			0
$415$	−22250.0	+	38538.0i	−0.129191	+	0.223766i
$416$	7725.69	−	1362.25i	0.0446427	−	0.00787171i
$417$		0			0
$418$	−31097.7	+	11318.7i	−0.177982	+	0.0647802i
$419$	83738.8	+	230070.i	0.476978	+	1.31049i	0.912046	+	0.410089i	$0.134502\pi$
$419$	83738.8	+	230070.i	0.476978	+	1.31049i	−0.435067	+	0.900398i	$0.643275\pi$
$420$		0			0
$421$	1058.47	+	6002.86i	0.00597191	+	0.0338684i	0.987648	−	0.156688i	$-0.0500818\pi$
$421$	1058.47	+	6002.86i	0.00597191	+	0.0338684i	−0.981676	+	0.190557i	$0.938971\pi$
$422$	117431.	+	67798.7i	0.659412	+	0.380712i
$423$		0			0
$424$	1015.72	+	1759.28i	0.00564993	+	0.00978597i
$425$	36314.2	+	43277.6i	0.201048	+	0.239599i
$426$		0			0
$427$	4999.80	−	28355.3i	0.0274219	−	0.155517i
$428$	66476.0	−	79223.0i	0.362892	−	0.432478i
$429$		0			0
$430$	9845.30	+	3583.40i	0.0532466	+	0.0193802i
$431$			72233.2i			0.388850i	0.980917	+	0.194425i	$0.0622841\pi$
$431$			72233.2i			0.388850i	−0.980917	+	0.194425i	$0.937716\pi$
$432$		0			0
$433$	−160967.			−0.858542			−0.429271	−	0.903176i	$-0.641229\pi$
$433$	−160967.			−0.858542			−0.429271	+	0.903176i	$0.641229\pi$
$434$	16769.8	−	46074.7i	0.0890326	−	0.244615i
$435$		0			0
$436$	101261.	+	84968.2i	0.532684	+	0.446975i
$437$	−61033.0	−	10761.8i	−0.319596	−	0.0563535i
$438$		0			0
$439$	178670.	−	149922.i	0.927093	−	0.777924i	−0.0482000	−	0.998838i	$-0.515348\pi$
$439$	178670.	−	149922.i	0.927093	−	0.777924i	0.975293	+	0.220914i	$0.0709040\pi$
$440$	−19292.2	+	11138.4i	−0.0996500	+	0.0575329i
$441$		0			0
$442$	−5783.37	+	10017.1i	−0.0296030	+	0.0512740i
$443$	−34326.5	+	6052.68i	−0.174913	+	0.0308418i	−0.260418	−	0.965496i	$-0.583861\pi$
$443$	−34326.5	+	6052.68i	−0.174913	+	0.0308418i	0.0855057	+	0.996338i	$0.472749\pi$
$444$		0			0
$445$	−34090.8	+	12408.0i	−0.172154	+	0.0626588i
$446$	77783.7	+	213709.i	0.391038	+	1.07437i
$447$		0			0
$448$	−1727.46	−	9796.90i	−0.00860700	−	0.0488127i
$449$	119602.	+	69052.5i	0.593263	+	0.342521i	0.766387	−	0.642379i	$-0.222053\pi$
$449$	119602.	+	69052.5i	0.593263	+	0.342521i	−0.173123	+	0.984900i	$0.555386\pi$
$450$		0			0
$451$	107904.	+	186895.i	0.530499	+	0.918852i
$452$	−74008.3	−	88199.6i	−0.362246	−	0.431708i
$453$		0			0
$454$	2943.03	−	16690.7i	0.0142785	−	0.0809774i
$455$	−2776.08	+	3308.41i	−0.0134094	+	0.0159807i
$456$		0			0
$457$	−53409.5	−	19439.5i	−0.255733	−	0.0930790i	0.210973	−	0.977492i	$-0.432337\pi$
$457$	−53409.5	−	19439.5i	−0.255733	−	0.0930790i	−0.466705	+	0.884413i	$0.654559\pi$
$458$		−	169684.i		−	0.808926i
$459$		0			0
$460$	−41717.9			−0.197154
$461$	89999.7	−	247272.i	0.423486	−	1.16352i	−0.526212	−	0.850353i	$-0.676388\pi$
$461$	89999.7	−	247272.i	0.423486	−	1.16352i	0.949698	−	0.313166i	$-0.101390\pi$
$462$		0			0
$463$	63765.2	+	53505.3i	0.297455	+	0.249595i	0.779284	−	0.626671i	$-0.215583\pi$
$463$	63765.2	+	53505.3i	0.297455	+	0.249595i	−0.481829	+	0.876265i	$0.660027\pi$
$464$	−40341.2	−	7113.24i	−0.187375	−	0.0330393i
$465$		0			0
$466$	−43438.8	+	36449.5i	−0.200035	+	0.167849i
$467$	151774.	−	87626.6i	0.695926	−	0.401793i	−0.109902	−	0.993942i	$-0.535054\pi$
$467$	151774.	−	87626.6i	0.695926	−	0.401793i	0.805828	+	0.592150i	$0.201721\pi$
$468$		0			0
$469$	42085.1	−	72893.4i	0.191330	−	0.331393i
$470$	15375.8	−	2711.17i	0.0696054	−	0.0122733i
$471$		0			0
$472$	107436.	−	39103.5i	0.482242	−	0.175522i
$473$	47412.5	+	130265.i	0.211919	+	0.582244i
$474$		0			0
$475$	−6337.13	−	35939.6i	−0.0280870	−	0.159289i
$476$	12702.6	+	7333.86i	0.0560634	+	0.0323682i
$477$		0			0
$478$	−88059.5	−	152524.i	−0.385408	−	0.667546i
$479$	139259.	+	165962.i	0.606949	+	0.723334i	0.978768	−	0.204971i	$-0.0657101\pi$
$479$	139259.	+	165962.i	0.606949	+	0.723334i	−0.371819	+	0.928305i	$0.621266\pi$
$480$		0			0
$481$	−6448.95	+	36573.8i	−0.0278740	+	0.158081i
$482$	−27248.9	+	32474.0i	−0.117289	+	0.139779i
$483$		0			0
$484$	−166908.	−	60749.4i	−0.712501	−	0.259329i
$485$			74621.1i			0.317233i
$486$		0			0
$487$	−129523.			−0.546122			−0.273061	−	0.961997i	$-0.588036\pi$
$487$	−129523.			−0.546122			−0.273061	+	0.961997i	$0.588036\pi$
$488$	−11468.4	+	31509.1i	−0.0481573	+	0.132311i
$489$		0			0
$490$	−22487.2	−	18869.0i	−0.0936577	−	0.0785882i
$491$	−346984.	−	61182.7i	−1.43928	−	0.253785i	−0.601101	−	0.799173i	$-0.705271\pi$
$491$	−346984.	−	61182.7i	−1.43928	−	0.253785i	−0.838184	+	0.545388i	$0.816382\pi$
$492$		0			0
$493$	46267.5	−	38823.0i	0.190363	−	0.159733i
$494$	6470.75	−	3735.89i	0.0265155	−	0.0153088i
$495$		0			0
$496$	−28550.5	+	49451.0i	−0.116052	+	0.201007i
$497$	69588.4	−	12270.3i	0.281724	−	0.0496756i
$498$		0			0
$499$	219353.	−	79838.1i	0.880934	−	0.320634i	0.138347	−	0.990384i	$-0.455821\pi$
$499$	219353.	−	79838.1i	0.880934	−	0.320634i	0.742587	+	0.669750i	$0.233599\pi$
$500$	−17173.2	−	47183.0i	−0.0686928	−	0.188732i
$501$		0			0
$502$	−8211.51	−	46569.8i	−0.0325848	−	0.184798i
$503$	−5161.57	−	2980.04i	−0.0204008	−	0.0117784i	0.489765	−	0.871855i	$-0.337083\pi$
$503$	−5161.57	−	2980.04i	−0.0204008	−	0.0117784i	−0.510166	+	0.860076i	$0.670416\pi$
$504$		0			0
$505$	44150.4	+	76470.7i	0.173122	+	0.299856i
$506$	−354803.	−	422838.i	−1.38576	−	1.65148i
$507$		0			0
$508$	18683.8	−	105961.i	0.0724000	−	0.410601i
$509$	−30884.6	+	36806.9i	−0.119208	+	0.142067i	−0.822348	−	0.568985i	$-0.807336\pi$
$509$	−30884.6	+	36806.9i	−0.119208	+	0.142067i	0.703140	+	0.711052i	$0.251781\pi$
$510$		0			0
$511$	−63323.9	−	23048.0i	−0.242508	−	0.0882657i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	−54148.7			−0.204956
$515$	−20989.3	+	57667.6i	−0.0791377	+	0.217429i
$516$		0			0
$517$	158248.	+	132786.i	0.592050	+	0.496789i
$518$	46379.1	+	8177.88i	0.172847	+	0.0304776i
$519$		0			0
$520$	3852.89	−	3232.96i	0.0142489	−	0.0119562i
$521$	288557.	−	166598.i	1.06305	−	0.613755i	0.136779	−	0.990602i	$-0.456325\pi$
$521$	288557.	−	166598.i	1.06305	−	0.613755i	0.926276	+	0.376847i	$0.122992\pi$
$522$		0			0
$523$	−127621.	+	221045.i	−0.466571	+	0.808124i	−0.999271	−	0.0381799i	$-0.987844\pi$
$523$	−127621.	+	221045.i	−0.466571	+	0.808124i	0.532700	+	0.846304i	$0.321177\pi$
$524$	204042.	−	35978.2i	0.743118	−	0.131032i
$525$		0			0
$526$	335298.	−	122039.i	1.21188	−	0.441088i
$527$	−28795.3	−	79114.4i	−0.103681	−	0.284862i
$528$		0			0
$529$	−130904.	−	742396.i	−0.467782	−	2.65292i
$530$	1127.93	+	651.211i	0.00401542	+	0.00231830i
$531$		0			0
$532$	−4737.46	−	8205.52i	−0.0167387	−	0.0289923i
$533$	−31319.6	−	37325.2i	−0.110246	−	0.131386i
$534$		0			0
$535$	11513.7	−	65297.4i	0.0402260	−	0.228133i
$536$	−63007.6	+	75089.5i	−0.219312	+	0.261366i
$537$		0			0
$538$	−112906.	−	41094.6i	−0.390080	−	0.141978i
$539$		−	388401.i		−	1.33691i
$540$		0			0
$541$	34518.5			0.117939			0.0589695	−	0.998260i	$-0.481219\pi$
$541$	34518.5			0.117939			0.0589695	+	0.998260i	$0.481219\pi$
$542$	−29843.3	+	81993.8i	−0.101589	+	0.279115i
$543$		0			0
$544$	−13085.3	−	10979.9i	−0.0442167	−	0.0371022i
$545$	83461.7	+	14716.6i	0.280992	+	0.0495465i
$546$		0			0
$547$	180274.	−	151268.i	0.602501	−	0.505559i	−0.289747	−	0.957103i	$-0.593571\pi$
$547$	180274.	−	151268.i	0.602501	−	0.505559i	0.892249	+	0.451544i	$0.149127\pi$
$548$	−175316.	+	101219.i	−0.583796	+	0.337055i
$549$		0			0
$550$	162517.	−	281488.i	0.537247	−	0.930539i
$551$	−38422.6	+	6774.94i	−0.126556	+	0.0223153i
$552$		0			0
$553$	−218039.	+	79359.6i	−0.712990	+	0.259507i
$554$	−75086.0	−	206297.i	−0.244647	−	0.672161i
$555$		0			0
$556$	−47509.4	−	269439.i	−0.153685	−	0.871589i
$557$	416788.	+	240633.i	1.34340	+	0.775612i	0.987305	−	0.158838i	$-0.0507747\pi$
$557$	416788.	+	240633.i	1.34340	+	0.775612i	0.356095	+	0.934450i	$0.384108\pi$
$558$		0			0
$559$	−15649.2	−	27105.2i	−0.0500804	−	0.0867419i
$560$	−4099.70	−	4885.83i	−0.0130730	−	0.0155798i
$561$		0			0
$562$	−23400.2	+	132709.i	−0.0740877	+	0.420172i
$563$	−240474.	+	286585.i	−0.758666	+	0.904143i	−0.997763	−	0.0668529i	$-0.978704\pi$
$563$	−240474.	+	286585.i	−0.758666	+	0.904143i	0.239097	+	0.970996i	$0.423149\pi$
$564$		0			0
$565$	−69365.8	−	25247.1i	−0.217294	−	0.0790887i
$566$			357069.i			1.11460i
$567$		0			0
$568$	−82291.2			−0.255068
$569$	151449.	−	416102.i	0.467779	−	1.28521i	−0.451733	−	0.892153i	$-0.649194\pi$
$569$	151449.	−	416102.i	0.467779	−	1.28521i	0.919513	−	0.393060i	$-0.128584\pi$
$570$		0			0
$571$	−199526.	−	167422.i	−0.611967	−	0.513501i	0.283300	−	0.959031i	$-0.408571\pi$
$571$	−199526.	−	167422.i	−0.611967	−	0.513501i	−0.895267	+	0.445530i	$0.853015\pi$
$572$	65536.3	+	11555.8i	0.200304	+	0.0353190i
$573$		0			0
$574$	−47331.9	+	39716.2i	−0.143658	+	0.120544i
$575$	527145.	−	304347.i	1.59439	−	0.920521i
$576$		0			0
$577$	−247397.	+	428504.i	−0.743093	+	1.28707i	0.207988	+	0.978131i	$0.433309\pi$
$577$	−247397.	+	428504.i	−0.743093	+	1.28707i	−0.951081	+	0.308943i	$0.900025\pi$
$578$	−207841.	+	36648.0i	−0.622122	+	0.109697i
$579$		0			0
$580$	−24679.1	+	8982.47i	−0.0733624	+	0.0267017i
$581$	−57655.6	−	158407.i	−0.170800	−	0.469270i
$582$		0			0
$583$	2992.40	+	16970.8i	0.00880406	+	0.0499303i
$584$	67964.2	+	39239.1i	0.199276	+	0.115052i
$585$		0			0
$586$	−150190.	−	260136.i	−0.437366	−	0.757540i
$587$	354984.	+	423054.i	1.03023	+	1.22778i	0.973333	+	0.229396i	$0.0736751\pi$
$587$	354984.	+	423054.i	1.03023	+	1.22778i	0.0568935	+	0.998380i	$0.481880\pi$
$588$		0			0
$589$	−9443.93	+	53559.2i	−0.0272221	+	0.154384i
$590$	47117.0	−	56151.9i	0.135355	−	0.161310i
$591$		0			0
$592$	−51537.6	−	18758.1i	−0.147055	−	0.0535237i
$593$			328016.i			0.932795i	0.884575	+	0.466398i	$0.154448\pi$
$593$			328016.i			0.932795i	−0.884575	+	0.466398i	$0.845552\pi$
$594$		0			0
$595$	9403.93			0.0265629
$596$	−35959.1	+	98796.9i	−0.101232	+	0.278132i
$597$		0			0
$598$	95467.3	+	80106.6i	0.266964	+	0.224009i
$599$	−57137.5	−	10074.9i	−0.159246	−	0.0280793i	0.0934568	−	0.995623i	$-0.470208\pi$
$599$	−57137.5	−	10074.9i	−0.159246	−	0.0280793i	−0.252703	+	0.967544i	$0.581319\pi$
$600$		0			0
$601$	−389939.	+	327197.i	−1.07956	+	0.905860i	−0.995884	−	0.0906334i	$-0.971111\pi$
$601$	−389939.	+	327197.i	−1.07956	+	0.905860i	−0.0836770	+	0.996493i	$0.526666\pi$
$602$	−34371.9	+	19844.7i	−0.0948443	+	0.0547584i
$603$		0			0
$604$	115467.	−	199994.i	0.316507	−	0.548206i
$605$	−112147.	+	19774.6i	−0.306393	+	0.0540253i
$606$		0			0
$607$	341371.	−	124249.i	0.926508	−	0.337221i	0.165683	−	0.986179i	$-0.447017\pi$
$607$	341371.	−	124249.i	0.926508	−	0.337221i	0.760825	+	0.648958i	$0.224795\pi$
$608$	3773.94	+	10368.8i	0.0102091	+	0.0280493i
$609$		0			0
$610$	3733.08	+	21171.4i	0.0100325	+	0.0568969i
$611$	−40392.1	−	23320.4i	−0.108197	−	0.0624674i
$612$		0			0
$613$	239790.	+	415328.i	0.638130	+	1.10527i	0.985843	+	0.167673i	$0.0536252\pi$
$613$	239790.	+	415328.i	0.638130	+	1.10527i	−0.347712	+	0.937601i	$0.613041\pi$
$614$	−131332.	−	156515.i	−0.348363	−	0.415163i
$615$		0			0
$616$	14653.9	−	83106.3i	0.0386181	−	0.219014i
$617$	−150790.	+	179704.i	−0.396097	+	0.472049i	−0.926826	−	0.375492i	$-0.877474\pi$
$617$	−150790.	+	179704.i	−0.396097	+	0.472049i	0.530729	+	0.847542i	$0.321918\pi$
$618$		0			0
$619$	−16381.6	−	5962.41i	−0.0427538	−	0.0155611i	0.320555	−	0.947230i	$-0.396131\pi$
$619$	−16381.6	−	5962.41i	−0.0427538	−	0.0155611i	−0.363309	+	0.931669i	$0.618353\pi$
$620$			36609.3i			0.0952375i
$621$		0			0
$622$	−144008.			−0.372225
$623$	47003.8	−	129142.i	0.121104	−	0.332729i
$624$		0			0
$625$	261980.	+	219828.i	0.670670	+	0.562759i
$626$	−3216.67	−	567.186i	−0.00820839	−	0.00144736i
$627$		0			0
$628$	44840.7	−	37625.8i	0.113698	−	0.0954039i
$629$	70031.6	−	40432.8i	0.177008	−	0.102196i
$630$		0			0
$631$	651.357	−	1128.18i	0.00163591	−	0.00283348i	−0.865206	−	0.501416i	$-0.832813\pi$
$631$	651.357	−	1128.18i	0.00163591	−	0.00283348i	0.866842	+	0.498583i	$0.166146\pi$
$632$	266113.	−	46923.0i	0.666243	−	0.117477i
$633$		0			0
$634$	−140483.	+	51131.5i	−0.349498	+	0.127207i
$635$	−23593.6	−	64822.9i	−0.0585122	−	0.160761i
$636$		0			0
$637$	15227.6	+	86359.9i	0.0375277	+	0.212830i
$638$	−300935.	−	173745.i	−0.739318	−	0.426845i
$639$		0			0
$640$	3713.83	+	6432.54i	0.00906697	+	0.0157044i
$641$	215844.	+	257233.i	0.525321	+	0.626053i	0.961830	−	0.273647i	$-0.0882300\pi$
$641$	215844.	+	257233.i	0.525321	+	0.626053i	−0.436510	+	0.899700i	$0.643786\pi$
$642$		0			0
$643$	−56802.7	+	322144.i	−0.137387	+	0.779162i	0.835780	+	0.549064i	$0.185016\pi$
$643$	−56802.7	+	322144.i	−0.137387	+	0.779162i	−0.973167	+	0.230098i	$0.926095\pi$
$644$	101583.	−	121062.i	0.244934	−	0.291900i
$645$		0			0
$646$	−15288.1	−	5564.42i	−0.0366344	−	0.0133338i
$647$		−	752100.i		−	1.79666i	−0.439317	−	0.898332i	$-0.644779\pi$
$647$		−	752100.i		−	1.79666i	0.439317	−	0.898332i	$-0.355221\pi$
$648$		0			0
$649$	969859.			2.30260
$650$	−25099.3	+	68959.7i	−0.0594066	+	0.163218i
$651$		0			0
$652$	322461.	+	270577.i	0.758547	+	0.636496i
$653$	−222492.	−	39231.3i	−0.521781	−	0.0920040i	−0.0934464	−	0.995624i	$-0.529788\pi$
$653$	−222492.	−	39231.3i	−0.521781	−	0.0920040i	−0.428334	+	0.903620i	$0.640899\pi$
$654$		0			0
$655$	101758.	−	85385.3i	0.237185	−	0.199022i
$656$	62315.9	−	35978.1i	0.144807	−	0.0836046i
$657$		0			0
$658$	−29572.5	+	51221.0i	−0.0683024	+	0.118303i
$659$	264436.	−	46627.3i	0.608906	−	0.107367i	0.139311	−	0.990249i	$-0.455511\pi$
$659$	264436.	−	46627.3i	0.608906	−	0.107367i	0.469595	+	0.882882i	$0.344400\pi$
$660$		0			0
$661$	−616713.	+	224465.i	−1.41150	+	0.513743i	−0.931569	−	0.363565i	$-0.881559\pi$
$661$	−616713.	+	224465.i	−1.41150	+	0.513743i	−0.479928	+	0.877308i	$0.659337\pi$
$662$	97850.3	+	268842.i	0.223278	+	0.613452i
$663$		0			0
$664$	34090.0	+	193334.i	0.0773199	+	0.438503i
$665$	−5260.82	−	3037.33i	−0.0118962	−	0.00686830i
$666$		0			0
$667$	−325373.	−	563563.i	−0.731359	−	1.26675i
$668$	−216205.	−	257664.i	−0.484522	−	0.577431i
$669$		0			0
$670$	−10913.0	+	61890.5i	−0.0243104	+	0.137871i
$671$	−182836.	+	217896.i	−0.406086	+	0.483954i
$672$		0			0
$673$	174713.	+	63590.5i	0.385741	+	0.140398i	0.527609	−	0.849487i	$-0.323089\pi$
$673$	174713.	+	63590.5i	0.385741	+	0.140398i	−0.141868	+	0.989886i	$0.545311\pi$
$674$			108532.i			0.238913i
$675$		0			0
$676$	213463.			0.467121
$677$	−148682.	+	408499.i	−0.324399	+	0.891279i	0.665102	+	0.746753i	$0.268388\pi$
$677$	−148682.	+	408499.i	−0.324399	+	0.891279i	−0.989501	+	0.144526i	$0.953834\pi$
$678$		0			0
$679$	−216544.	−	181702.i	−0.469685	−	0.394112i
$680$	−10785.2	−	1901.72i	−0.0233244	−	0.00411272i
$681$		0			0
$682$	−371059.	+	311356.i	−0.797765	+	0.669404i
$683$	−566595.	+	327124.i	−1.21460	+	0.701247i	−0.963757	−	0.266782i	$-0.914040\pi$
$683$	−566595.	+	327124.i	−1.21460	+	0.701247i	−0.250838	+	0.968029i	$0.580706\pi$
$684$		0			0
$685$	−64894.6	+	112401.i	−0.138302	+	0.239545i
$686$	239456.	−	42222.6i	0.508837	−	0.0897216i
$687$		0			0
$688$	43433.7	−	15808.6i	0.0917593	−	0.0333976i
$689$	−1330.71	−	3656.09i	−0.00280313	−	0.00770155i
$690$		0			0
$691$	39018.0	+	221282.i	0.0817163	+	0.463436i	0.998017	+	0.0629453i	$0.0200494\pi$
$691$	39018.0	+	221282.i	0.0817163	+	0.463436i	−0.916301	+	0.400491i	$0.868840\pi$
$692$	130652.	+	75431.9i	0.272837	+	0.157523i
$693$		0			0
$694$	166732.	+	288788.i	0.346178	+	0.599599i
$695$	−112752.	−	134373.i	−0.233429	−	0.278190i
$696$		0			0
$697$	−18423.1	+	104483.i	−0.0379226	+	0.215070i
$698$	−36035.8	+	42945.8i	−0.0739645	+	0.0881474i
$699$		0			0
$700$	87447.5	+	31828.3i	0.178464	+	0.0649557i
$701$			603832.i			1.22880i	0.788996	+	0.614399i	$0.210601\pi$
$701$			603832.i			1.22880i	−0.788996	+	0.614399i	$0.789399\pi$
$702$		0			0
$703$	−52236.8			−0.105698
$704$	−33612.6	+	92349.8i	−0.0678198	+	0.186333i
$705$		0			0
$706$	27057.4	+	22703.8i	0.0542845	+	0.0455501i
$707$	−329417.	−	58085.1i	−0.659033	−	0.116205i
$708$		0			0
$709$	354385.	−	297365.i	0.704991	−	0.591557i	−0.218198	−	0.975905i	$-0.570018\pi$
$709$	354385.	−	297365.i	0.704991	−	0.591557i	0.923189	+	0.384347i	$0.125573\pi$
$710$	−45691.0	+	26379.7i	−0.0906388	+	0.0523303i
$711$		0			0
$712$	−80023.7	+	138605.i	−0.157855	+	0.273413i
$713$	−893328.	+	157518.i	−1.75724	+	0.309849i
$714$		0			0
$715$	40092.5	−	14592.5i	0.0784244	−	0.0285442i
$716$	−47342.1	−	130071.i	−0.0923467	−	0.253720i
$717$		0			0
$718$	55283.7	+	313530.i	0.107238	+	0.608176i
$719$	−328988.	−	189941.i	−0.636389	−	0.367419i	0.146833	−	0.989161i	$-0.453092\pi$
$719$	−328988.	−	189941.i	−0.636389	−	0.367419i	−0.783222	+	0.621742i	$0.786425\pi$
$720$		0			0
$721$	−116238.	−	201330.i	−0.223602	−	0.387291i
$722$	−230178.	−	274316.i	−0.441560	−	0.526231i
$723$		0			0
$724$	52743.2	−	299121.i	0.100621	−	0.570650i
$725$	246314.	−	293545.i	0.468611	−	0.558469i
$726$		0			0
$727$	846871.	+	308236.i	1.60232	+	0.583195i	0.979900	−	0.199491i	$-0.0639288\pi$
$727$	846871.	+	308236.i	1.60232	+	0.583195i	0.622416	+	0.782686i	$0.286151\pi$
$728$			19053.0i			0.0359501i
$729$		0			0
$730$	50314.9			0.0944171
$731$	−23308.7	+	64040.1i	−0.0436197	+	0.119844i
$732$		0			0
$733$	−218418.	−	183275.i	−0.406519	−	0.341110i	0.416488	−	0.909141i	$-0.363261\pi$
$733$	−218418.	−	183275.i	−0.406519	−	0.341110i	−0.823007	+	0.568031i	$0.807705\pi$
$734$	414036.	+	73005.6i	0.768503	+	0.135508i
$735$		0			0
$736$	−140985.	+	118301.i	−0.260267	+	0.218390i
$737$	−720114.	+	415758.i	−1.32576	+	0.765430i
$738$		0			0
$739$	−274476.	+	475407.i	−0.502593	+	0.870516i	0.497403	+	0.867520i	$0.334287\pi$
$739$	−274476.	+	475407.i	−0.502593	+	0.870516i	−0.999996	+	0.00299630i	$0.999046\pi$
$740$	−34628.7	+	6105.98i	−0.0632373	+	0.0111504i
$741$		0			0
$742$	−4636.26	+	1687.46i	−0.00842094	+	0.00306497i
$743$	−109924.	−	302013.i	−0.199120	−	0.547077i	0.799439	−	0.600747i	$-0.205130\pi$
$743$	−109924.	−	302013.i	−0.199120	−	0.547077i	−0.998559	+	0.0536701i	$0.982908\pi$
$744$		0			0
$745$	11705.1	+	66382.9i	0.0210893	+	0.119603i
$746$	144786.	+	83592.2i	0.260165	+	0.150206i
$747$		0			0
$748$	−72451.1	−	125489.i	−0.129492	−	0.224286i
$749$	161452.	+	192410.i	0.287792	+	0.342977i
$750$		0			0
$751$	78371.5	−	444467.i	0.138956	−	0.788060i	−0.833066	−	0.553173i	$-0.813417\pi$
$751$	78371.5	−	444467.i	0.138956	−	0.788060i	0.972023	−	0.234887i	$-0.0754721\pi$
$752$	44274.4	−	52764.2i	0.0782919	−	0.0933047i
$753$		0			0
$754$	73723.9	+	26833.3i	0.129678	+	0.0471989i
$755$		−	148059.i		−	0.259741i
$756$		0			0
$757$	374377.			0.653307			0.326654	−	0.945144i	$-0.394079\pi$
$757$	374377.			0.653307			0.326654	+	0.945144i	$0.394079\pi$
$758$	−202757.	+	557070.i	−0.352888	+	0.969552i
$759$		0			0
$760$	5419.31	+	4547.34i	0.00938246	+	0.00787282i
$761$	731243.	+	128938.i	1.26268	+	0.222644i	0.764609	−	0.644494i	$-0.222932\pi$
$761$	731243.	+	128938.i	1.26268	+	0.222644i	0.498068	+	0.867138i	$0.334043\pi$
$762$		0			0
$763$	−245935.	+	206364.i	−0.422446	+	0.354474i
$764$	39174.1	−	22617.2i	0.0671139	−	0.0387482i
$765$		0			0
$766$	−232408.	+	402542.i	−0.396089	+	0.686046i
$767$	−215646.	+	38024.2i	−0.366564	+	0.0646352i
$768$		0			0
$769$	−321031.	+	116846.i	−0.542868	+	0.197588i	−0.598875	−	0.800843i	$-0.704385\pi$
$769$	−321031.	+	116846.i	−0.542868	+	0.197588i	0.0560069	+	0.998430i	$0.482163\pi$
$770$	−18504.7	−	50841.1i	−0.0312104	−	0.0857499i
$771$		0			0
$772$	14692.9	+	83327.5i	0.0246532	+	0.139815i
$773$	−535928.	−	309418.i	−0.896908	−	0.517830i	−0.0207121	−	0.999785i	$-0.506593\pi$
$773$	−535928.	−	309418.i	−0.896908	−	0.517830i	−0.876196	+	0.481956i	$0.839927\pi$
$774$		0			0
$775$	−267078.	−	462593.i	−0.444667	−	0.770186i
$776$	211605.	+	252182.i	0.351401	+	0.418784i
$777$		0			0
$778$	−87557.0	+	496560.i	−0.144654	+	0.820375i
$779$	44052.8	−	52500.1i	0.0725936	−	0.0865137i
$780$		0			0
$781$	−655970.	−	238754.i	−1.07543	−	0.391424i
$782$		−	271360.i		−	0.443743i
$783$		0			0
$784$	−129503.			−0.210692
$785$	12835.6	−	35265.6i	0.0208294	−	0.0572284i
$786$		0			0
$787$	−617155.	−	517854.i	−0.996425	−	0.836100i	−0.00993977	−	0.999951i	$-0.503164\pi$
$787$	−617155.	−	517854.i	−0.996425	−	0.836100i	−0.986485	+	0.163851i	$0.947608\pi$
$788$	351222.	+	61929.9i	0.565626	+	0.0997351i
$789$		0			0
$790$	132714.	−	111360.i	0.212648	−	0.178433i
$791$	242170.	−	139817.i	0.387051	−	0.223464i
$792$		0			0
$793$	32110.4	−	55616.9i	0.0510622	−	0.0884423i
$794$	672254.	−	118536.i	1.06633	−	0.188023i
$795$		0			0
$796$	−226430.	+	82413.7i	−0.357361	+	0.130069i
$797$	52138.6	+	143250.i	0.0820810	+	0.225516i	0.973943	−	0.226791i	$-0.0728235\pi$
$797$	52138.6	+	143250.i	0.0820810	+	0.225516i	−0.891862	+	0.452307i	$0.850601\pi$
$798$		0			0
$799$	17635.2	+	100014.i	0.0276240	+	0.156664i
$800$	−93855.5	−	54187.5i	−0.146649	−	0.0846680i
$801$		0			0
$802$	−236822.	−	410187.i	−0.368190	−	0.637725i
$803$	427920.	+	509975.i	0.663638	+	0.790893i
$804$		0			0
$805$	17594.2	−	99781.7i	0.0271505	−	0.153978i
$806$	70297.1	−	83776.9i	0.108210	−	0.128960i
$807$		0			0
$808$	366057.	+	133234.i	0.560693	+	0.204076i
$809$			30402.2i			0.0464524i	0.999730	+	0.0232262i	$0.00739379\pi$
$809$			30402.2i			0.0464524i	−0.999730	+	0.0232262i	$0.992606\pi$
$810$		0			0
$811$	87579.6			0.133156			0.0665781	−	0.997781i	$-0.478792\pi$
$811$	87579.6			0.133156			0.0665781	+	0.997781i	$0.478792\pi$
$812$	34027.2	−	93488.9i	0.0516076	−	0.141791i
$813$		0			0
$814$	−356400.	−	299055.i	−0.537884	−	0.451338i
$815$	265780.	+	46864.1i	0.400135	+	0.0705546i
$816$		0			0
$817$	33723.5	−	28297.4i	0.0505230	−	0.0423938i
$818$	−235935.	+	136217.i	−0.352602	+	0.203575i
$819$		0			0
$820$	23066.7	−	39952.6i	0.0343050	−	0.0594180i
$821$	−409876.	+	72272.2i	−0.608088	+	0.107222i	−0.469209	−	0.883087i	$-0.655461\pi$
$821$	−409876.	+	72272.2i	−0.608088	+	0.107222i	−0.138879	+	0.990309i	$0.544350\pi$
$822$		0			0
$823$	336875.	−	122612.i	0.497357	−	0.181023i	−0.0811476	−	0.996702i	$-0.525859\pi$
$823$	336875.	−	122612.i	0.497357	−	0.181023i	0.578505	+	0.815679i	$0.303636\pi$
$824$	92596.8	+	254408.i	0.136377	+	0.374693i
$825$		0			0
$826$	48218.2	+	273459.i	0.0706726	+	0.400804i
$827$	−110271.	−	63665.1i	−0.161232	−	0.0930873i	0.417213	−	0.908809i	$-0.363007\pi$
$827$	−110271.	−	63665.1i	−0.161232	−	0.0930873i	−0.578445	+	0.815721i	$0.696340\pi$
$828$		0			0
$829$	−588999.	−	1.02018e6i	−0.857049	−	1.48445i	−0.874731	−	0.484608i	$-0.838962\pi$
$829$	−588999.	−	1.02018e6i	−0.857049	−	1.48445i	0.0176826	−	0.999844i	$-0.494371\pi$
$830$	80904.3	+	96418.0i	0.117440	+	0.139959i
$831$		0			0
$832$	3853.02	−	21851.5i	0.00556614	−	0.0315672i
$833$	122736.	−	146271.i	0.176882	−	0.210799i
$834$		0			0
$835$	−202643.	−	73756.1i	−0.290642	−	0.105785i
$836$			93602.6i			0.133929i
$837$		0			0
$838$	692500.			0.986125
$839$	216016.	−	593500.i	0.306876	−	0.843135i	−0.686385	−	0.727238i	$-0.740804\pi$
$839$	216016.	−	593500.i	0.306876	−	0.843135i	0.993261	−	0.115897i	$-0.0369742\pi$
$840$		0			0
$841$	227983.	+	191301.i	0.322338	+	0.270474i
$842$	16978.7	+	2993.80i	0.0239486	+	0.00422278i
$843$		0			0
$844$	293799.	−	246527.i	0.412444	−	0.346082i
$845$	118522.	−	68428.9i	0.165992	−	0.0958355i
$846$		0			0
$847$	215694.	−	373593.i	0.300657	−	0.520753i
$848$	5658.50	−	997.747i	0.00786882	−	0.00138749i
$849$		0			0
$850$	150155.	−	54652.0i	0.207827	−	0.0756429i
$851$	−297992.	−	818727.i	−0.411477	−	1.13052i
$852$		0			0
$853$	96556.7	+	547600.i	0.132704	+	0.752602i	0.976431	+	0.215830i	$0.0692456\pi$
$853$	96556.7	+	547600.i	0.132704	+	0.752602i	−0.843727	+	0.536773i	$0.819643\pi$
$854$	−70527.5	−	40719.1i	−0.0967036	−	0.0558318i
$855$		0			0
$856$	−146256.	−	253322.i	−0.199602	−	0.345721i
$857$	−313067.	−	373098.i	−0.426260	−	0.507997i	0.509579	−	0.860424i	$-0.329801\pi$
$857$	−313067.	−	373098.i	−0.426260	−	0.507997i	−0.935840	+	0.352426i	$0.885357\pi$
$858$		0			0
$859$	239511.	−	1.35834e6i	0.324593	−	1.84086i	−0.187923	−	0.982184i	$-0.560176\pi$
$859$	239511.	−	1.35834e6i	0.324593	−	1.84086i	0.512517	−	0.858677i	$-0.328713\pi$
$860$	19048.3	−	22700.8i	0.0257548	−	0.0306934i
$861$		0			0
$862$	191985.	+	69876.9i	0.258377	+	0.0940414i
$863$		−	1.17778e6i		−	1.58140i	−0.612203	−	0.790701i	$-0.709716\pi$
$863$		−	1.17778e6i		−	1.58140i	0.612203	−	0.790701i	$-0.290284\pi$
$864$		0			0
$865$	96723.5			0.129271
$866$	−155716.	+	427827.i	−0.207634	+	0.570469i
$867$		0			0
$868$	−106237.	−	89143.4i	−0.141006	−	0.118318i
$869$	2.25742e6	+	398044.i	2.98932	+	0.527098i
$870$		0			0
$871$	143815.	−	120675.i	0.189570	−	0.159068i
$872$	323791.	−	186941.i	0.425825	−	0.245850i
$873$		0			0
$874$	−87645.2	+	151806.i	−0.114737	+	0.198731i
$875$	120096.	−	21176.2i	0.156860	−	0.0276586i
$876$		0			0
$877$	−324912.	+	118258.i	−0.422442	+	0.153756i	−0.544489	−	0.838768i	$-0.683276\pi$
$877$	−324912.	+	118258.i	−0.422442	+	0.153756i	0.122047	+	0.992524i	$0.461054\pi$
$878$	−225629.	−	619911.i	−0.292689	−	0.804156i
$879$		0			0
$880$	10941.3	+	62050.9i	0.0141287	+	0.0801278i
$881$	−222148.	−	128257.i	−0.286214	−	0.165245i	0.350019	−	0.936742i	$-0.386175\pi$
$881$	−222148.	−	128257.i	−0.286214	−	0.165245i	−0.636233	+	0.771497i	$0.719508\pi$
$882$		0			0
$883$	−74906.9	−	129742.i	−0.0960727	−	0.166403i	0.813983	−	0.580889i	$-0.197295\pi$
$883$	−74906.9	−	129742.i	−0.0960727	−	0.166403i	−0.910056	+	0.414486i	$0.863961\pi$
$884$	21029.2	+	25061.7i	0.0269103	+	0.0320705i
$885$		0			0
$886$	−17119.6	+	97089.9i	−0.0218085	+	0.123682i
$887$	−80550.3	+	95996.1i	−0.102381	+	0.122013i	−0.814802	−	0.579739i	$-0.803154\pi$
$887$	−80550.3	+	95996.1i	−0.102381	+	0.122013i	0.712421	+	0.701753i	$0.247599\pi$
$888$		0			0
$889$	245561.	+	89376.8i	0.310710	+	0.113089i
$890$			102611.i			0.129544i
$891$		0			0
$892$	643253.			0.808448
$893$	22437.5	−	61646.6i	0.0281366	−	0.0773047i
$894$		0			0
$895$	−67982.4	−	57044.0i	−0.0848692	−	0.0712138i
$896$	−27709.8	−	4885.99i	−0.0345158	−	0.00608607i
$897$		0			0
$898$	299232.	−	251086.i	0.371070	−	0.311365i
$899$	−494552.	+	285530.i	−0.611917	+	0.353291i
$900$		0			0
$901$	−4235.89	+	7336.78i	−0.00521790	+	0.00903766i
$902$	601124.	−	105994.i	0.738842	−	0.130278i
$903$		0			0
$904$	−306016.	+	111381.i	−0.374461	+	0.136293i
$905$	−66603.1	−	182991.i	−0.0813200	−	0.223425i
$906$		0			0
$907$	105824.	+	600156.i	0.128638	+	0.729540i	0.979081	+	0.203473i	$0.0652229\pi$
$907$	105824.	+	600156.i	0.128638	+	0.729540i	−0.850443	+	0.526067i	$0.823666\pi$
$908$	−41514.5	−	23968.4i	−0.0503533	−	0.0290715i
$909$		0			0
$910$	6107.73	+	10578.9i	0.00737560	+	0.0127749i
$911$	127258.	+	151660.i	0.153337	+	0.182740i	0.837245	−	0.546829i	$-0.184165\pi$
$911$	127258.	+	151660.i	0.153337	+	0.182740i	−0.683907	+	0.729569i	$0.739721\pi$
$912$		0			0
$913$	−289183.	+	1.64004e6i	−0.346921	+	1.96749i
$914$	−103334.	+	123149.i	−0.123695	+	0.147414i
$915$		0			0
$916$	−450994.	−	164148.i	−0.537502	−	0.195635i
$917$			503207.i			0.598422i
$918$		0			0
$919$	863627.			1.02258			0.511288	−	0.859410i	$-0.329169\pi$
$919$	863627.			1.02258			0.511288	+	0.859410i	$0.329169\pi$
$920$	−40357.0	+	110880.i	−0.0476807	+	0.131002i
$921$		0			0
$922$	−570149.	−	478412.i	−0.670698	−	0.562782i
$923$	155214.	+	27368.4i	0.182191	+	0.0321252i
$924$		0			0
$925$	393022.	−	329784.i	0.459339	−	0.385431i
$926$	203894.	−	117718.i	0.237784	−	0.137285i
$927$		0			0
$928$	−57931.1	+	100340.i	−0.0672692	+	0.116514i
$929$	322288.	−	56828.1i	0.373433	−	0.0658464i	0.0162181	−	0.999868i	$-0.494837\pi$
$929$	322288.	−	56828.1i	0.373433	−	0.0658464i	0.357215	+	0.934022i	$0.383726\pi$
$930$		0			0
$931$	−115905.	+	42186.1i	−0.133722	+	0.0486710i
$932$	54855.6	+	150715.i	0.0631523	+	0.173509i
$933$		0			0
$934$	−86075.8	−	488160.i	−0.0986705	−	0.559588i
$935$	−80454.9	−	46450.7i	−0.0920300	−	0.0531336i
$936$		0			0
$937$	−50931.2	−	88215.4i	−0.0580102	−	0.100477i	0.835562	−	0.549396i	$-0.185142\pi$
$937$	−50931.2	−	88215.4i	−0.0580102	−	0.100477i	−0.893572	+	0.448920i	$0.851809\pi$
$938$	−153028.	−	182371.i	−0.173926	−	0.207277i
$939$		0			0
$940$	7668.36	−	43489.4i	0.00867854	−	0.0492184i
$941$	488850.	−	582589.i	0.552073	−	0.657935i	−0.415776	−	0.909467i	$-0.636490\pi$
$941$	488850.	−	582589.i	0.552073	−	0.657935i	0.967849	+	0.251532i	$0.0809345\pi$
$942$		0			0
$943$	1.07416e6	+	390962.i	1.20794	+	0.439654i
$944$		−	323377.i		−	0.362881i
$945$		0			0
$946$	392090.			0.438131
$947$	63701.5	−	175018.i	0.0710313	−	0.195157i	−0.899097	−	0.437750i	$-0.855776\pi$
$947$	63701.5	−	175018.i	0.0710313	−	0.195157i	0.970128	+	0.242593i	$0.0779979\pi$
$948$		0			0
$949$	−115141.	−	96614.6i	−0.127849	−	0.107278i
$950$	−101653.	−	17924.1i	−0.112634	−	0.0198605i
$951$		0			0
$952$	31780.6	−	26667.1i	0.0350661	−	0.0294240i
$953$	108706.	−	62761.3i	0.119692	−	0.0691044i	−0.438959	−	0.898507i	$-0.644653\pi$
$953$	108706.	−	62761.3i	0.119692	−	0.0691044i	0.558651	+	0.829403i	$0.311319\pi$
$954$		0			0
$955$	14500.6	−	25115.7i	0.0158993	−	0.0275384i
$956$	−490572.	+	86501.1i	−0.536768	+	0.0946468i
$957$		0			0
$958$	575820.	−	209581.i	0.627416	−	0.228361i
$959$	−168159.	−	462013.i	−0.182845	−	0.502363i
$960$		0			0
$961$	−22138.7	−	125555.i	−0.0239721	−	0.135953i
$962$	90969.3	+	52521.1i	0.0982980	+	0.0567524i
$963$		0			0
$964$	59951.1	+	103838.i	0.0645124	+	0.111739i
$965$	34869.9	+	41556.4i	0.0374452	+	0.0446255i
$966$		0			0
$967$	144529.	−	819663.i	0.154561	−	0.876562i	−0.804624	−	0.593784i	$-0.797633\pi$
$967$	144529.	−	819663.i	0.154561	−	0.876562i	0.959186	−	0.282777i	$-0.0912557\pi$
$968$	−322926.	+	384848.i	−0.344629	+	0.410713i
$969$		0			0
$970$	198332.	+	72186.8i	0.210789	+	0.0767211i
$971$			1.10420e6i			1.17114i	0.810623	+	0.585569i	$0.199129\pi$
$971$			1.10420e6i			1.17114i	−0.810623	+	0.585569i	$0.800871\pi$
$972$		0			0
$973$	664488.			0.701878
$974$	−125298.	+	344253.i	−0.132077	+	0.362878i
$975$		0			0
$976$	72652.3	+	60962.5i	0.0762693	+	0.0639975i
$977$	−890467.	−	157013.i	−0.932886	−	0.164493i	−0.313508	−	0.949586i	$-0.601504\pi$
$977$	−890467.	−	157013.i	−0.932886	−	0.164493i	−0.619378	+	0.785093i	$0.712615\pi$
$978$		0			0
$979$	−1.04003e6	+	872693.i	−1.08513	+	0.910534i
$980$	−71904.7	+	41514.2i	−0.0748696	+	0.0432260i
$981$		0			0
$982$	−498280.	+	863046.i	−0.516714	+	0.894975i
$983$	−154152.	+	27181.2i	−0.159530	+	0.0281295i	−0.252843	−	0.967507i	$-0.581366\pi$
$983$	−154152.	+	27181.2i	−0.159530	+	0.0281295i	0.0933126	+	0.995637i	$0.470254\pi$
$984$		0			0
$985$	214864.	−	78204.0i	0.221458	−	0.0806040i
$986$	−58427.7	−	160529.i	−0.0600987	−	0.165120i
$987$		0			0
$988$	−3669.77	−	20812.3i	−0.00375946	−	0.0213209i
$989$	635897.	+	367135.i	0.650121	+	0.375348i
$990$		0			0
$991$	−667891.	−	1.15682e6i	−0.680077	−	1.17793i	−0.974957	−	0.222394i	$-0.928613\pi$
$991$	−667891.	−	1.15682e6i	−0.680077	−	1.17793i	0.294880	−	0.955534i	$-0.404720\pi$
$992$	103814.	+	123721.i	0.105495	+	0.125725i
$993$		0			0
$994$	34705.7	−	196826.i	0.0351260	−	0.199209i
$995$	−99302.9	+	118345.i	−0.100303	+	0.119537i
$996$		0			0
$997$	−1.56730e6	−	570450.i	−1.57675	−	0.573888i	−0.602253	−	0.798306i	$-0.705730\pi$
$997$	−1.56730e6	−	570450.i	−1.57675	−	0.573888i	−0.974493	+	0.224417i	$0.927952\pi$
$998$		−	660243.i		−	0.662891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.9		72
3.2	odd	2		54.5.f.a.23.1	✓	72
27.7	even	9		54.5.f.a.47.1	yes	72
27.20	odd	18	inner	162.5.f.a.143.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.1	✓	72	3.2	odd	2
54.5.f.a.47.1	yes	72	27.7	even	9
162.5.f.a.17.9		72	1.1	even	1	trivial
162.5.f.a.143.9		72	27.20	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)

\(f(q)\)	\(=\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-5.05113 - 0.890650i) q^{5} +(14.8841 - 12.4892i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-5.05113 - 0.890650i) q^{5} +(14.8841 - 12.4892i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-7.25357 + 12.5636i) q^{10} +(-189.030 + 33.3311i) q^{11} +(40.7236 - 14.8222i) q^{13} +(-18.7959 - 51.6414i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-81.7214 - 47.1819i) q^{17} +(30.4781 + 52.7896i) q^{19} +(26.3751 + 31.4326i) q^{20} +(-94.2747 + 534.659i) q^{22} +(-653.526 + 778.842i) q^{23} +(-562.587 - 204.765i) q^{25} -122.576i q^{26} -155.438 q^{28} +(-218.912 + 601.454i) q^{29} +(683.468 + 573.498i) q^{31} +(178.269 + 31.4337i) q^{32} +(-204.458 + 171.561i) q^{34} +(-86.3048 + 49.8281i) q^{35} +(-428.478 + 742.145i) q^{37} +(169.791 - 29.9387i) q^{38} +(109.058 - 39.6939i) q^{40} +(-384.538 - 1056.51i) q^{41} +(-125.410 - 711.234i) q^{43} +(1329.84 + 767.786i) q^{44} +(1437.84 + 2490.41i) q^{46} +(-691.787 - 824.440i) q^{47} +(-351.374 + 1992.74i) q^{49} +(-1088.47 + 1297.19i) q^{50} +(-325.789 - 118.578i) q^{52} -89.7780i q^{53} +984.503 q^{55} +(-150.368 + 413.131i) q^{56} +(1386.81 + 1163.67i) q^{58} +(-4976.00 - 877.402i) q^{59} +(1135.19 - 952.539i) q^{61} +(2185.45 - 1261.77i) q^{62} +(256.000 - 443.405i) q^{64} +(-218.902 + 38.5983i) q^{65} +(4070.77 - 1481.64i) q^{67} +(258.194 + 709.383i) q^{68} +(48.9463 + 277.588i) q^{70} +(3149.55 + 1818.39i) q^{71} +(-1734.14 - 3003.62i) q^{73} +(1558.01 + 1856.77i) q^{74} +(84.6795 - 480.241i) q^{76} +(-2397.26 + 2856.94i) q^{77} +(-11221.9 - 4084.44i) q^{79} -328.259i q^{80} -3180.04 q^{82} +(2967.38 - 8152.82i) q^{83} +(370.763 + 311.107i) q^{85} +(-2011.67 - 354.712i) q^{86} +(3327.12 - 2791.79i) q^{88} +(6125.54 - 3536.58i) q^{89} +(421.016 - 729.220i) q^{91} +(8010.07 - 1412.39i) q^{92} +(-2860.46 + 1041.12i) q^{94} +(-106.932 - 293.793i) q^{95} +(-2526.36 - 14327.7i) q^{97} +(4956.50 + 2861.64i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 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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