LMFDB - Embedded newform 162.5.f.a.35.7

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			35.7
Character	$\chi$	$=$	162.35
Dual form			162.5.f.a.125.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81808 - 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-14.9830 + 41.1655i) q^{5} +(12.4750 - 70.7490i) q^{7} +(-19.5959 - 11.3137i) q^{8} +O(q^{10})$	\(q+(1.81808 - 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-14.9830 + 41.1655i) q^{5} +(12.4750 - 70.7490i) q^{7} +(-19.5959 - 11.3137i) q^{8} +(61.9530 + 107.306i) q^{10} +(5.45082 + 14.9760i) q^{11} +(-34.8751 + 29.2636i) q^{13} +(-130.611 - 155.657i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(-413.470 + 238.717i) q^{17} +(-344.267 + 596.287i) q^{19} +(345.135 + 60.8566i) q^{20} +(42.3585 + 15.4172i) q^{22} +(-346.359 + 61.0724i) q^{23} +(-991.328 - 831.823i) q^{25} +128.767i q^{26} -574.723 q^{28} +(18.9983 - 22.6413i) q^{29} +(155.830 + 883.753i) q^{31} +(-61.9123 + 170.103i) q^{32} +(-234.492 + 1329.87i) q^{34} +(2725.50 + 1573.57i) q^{35} +(-268.374 - 464.837i) q^{37} +(666.073 + 1830.02i) q^{38} +(759.340 - 637.162i) q^{40} +(-94.4822 - 112.599i) q^{41} +(1366.62 - 497.411i) q^{43} +(110.416 - 63.7485i) q^{44} +(-497.382 + 861.491i) q^{46} +(-1375.04 - 242.456i) q^{47} +(-2593.59 - 943.991i) q^{49} +(-3604.62 + 635.592i) q^{50} +(279.000 + 234.109i) q^{52} -3259.92i q^{53} -698.164 q^{55} +(-1044.89 + 1245.25i) q^{56} +(-14.5165 - 82.3272i) q^{58} +(-461.271 + 1267.33i) q^{59} +(396.659 - 2249.57i) q^{61} +(2198.14 + 1269.10i) q^{62} +(256.000 + 443.405i) q^{64} +(-682.119 - 1874.11i) q^{65} +(-2245.35 + 1884.08i) q^{67} +(2455.11 + 2925.89i) q^{68} +(8364.63 - 3044.48i) q^{70} +(1309.89 - 756.267i) q^{71} +(-3471.25 + 6012.38i) q^{73} +(-1495.09 - 263.624i) q^{74} +(5176.08 + 1883.94i) q^{76} +(1127.54 - 198.815i) q^{77} +(5233.12 + 4391.11i) q^{79} -2803.67i q^{80} -415.745 q^{82} +(3446.90 - 4107.86i) q^{83} +(-3631.88 - 20597.4i) q^{85} +(1406.89 - 3865.40i) q^{86} +(62.6203 - 355.138i) q^{88} +(6651.93 + 3840.49i) q^{89} +(1635.31 + 2832.44i) q^{91} +(962.314 + 2643.94i) q^{92} +(-3025.25 + 2538.49i) q^{94} +(-19388.3 - 23106.1i) q^{95} +(-2809.87 + 1022.71i) q^{97} +(-6760.70 + 3903.29i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−14.9830	+	41.1655i	−0.599320	+	1.64662i	0.153312	+	0.988178i	$0.451006\pi$
$5$	−14.9830	+	41.1655i	−0.599320	+	1.64662i	−0.752632	+	0.658441i	$0.771216\pi$
$6$		0			0
$7$	12.4750	−	70.7490i	0.254591	−	1.44386i	−0.542529	−	0.840037i	$-0.682533\pi$
$7$	12.4750	−	70.7490i	0.254591	−	1.44386i	0.797120	−	0.603820i	$-0.206356\pi$
$8$	−19.5959	−	11.3137i	−0.306186	−	0.176777i
$9$		0			0
$10$	61.9530	+	107.306i	0.619530	+	1.07306i
$11$	5.45082	+	14.9760i	0.0450481	+	0.123769i	0.960177	−	0.279393i	$-0.0901333\pi$
$11$	5.45082	+	14.9760i	0.0450481	+	0.123769i	−0.915129	+	0.403162i	$0.867911\pi$
$12$		0			0
$13$	−34.8751	+	29.2636i	−0.206361	+	0.173158i	−0.740111	−	0.672485i	$-0.765227\pi$
$13$	−34.8751	+	29.2636i	−0.206361	+	0.173158i	0.533750	+	0.845643i	$0.320783\pi$
$14$	−130.611	−	155.657i	−0.666385	−	0.794167i
$15$		0			0
$16$	−60.1403	+	21.8893i	−0.234923	+	0.0855050i
$17$	−413.470	+	238.717i	−1.43069	+	0.826011i	−0.997173	−	0.0751340i	$-0.976062\pi$
$17$	−413.470	+	238.717i	−1.43069	+	0.826011i	−0.433519	+	0.901145i	$0.642728\pi$
$18$		0			0
$19$	−344.267	+	596.287i	−0.953647	+	1.65177i	−0.216214	+	0.976346i	$0.569371\pi$
$19$	−344.267	+	596.287i	−0.953647	+	1.65177i	−0.737433	+	0.675420i	$0.763962\pi$
$20$	345.135	+	60.8566i	0.862837	+	0.152141i
$21$		0			0
$22$	42.3585	+	15.4172i	0.0875176	+	0.0318538i
$23$	−346.359	+	61.0724i	−0.654743	+	0.115449i	−0.491144	−	0.871078i	$-0.663421\pi$
$23$	−346.359	+	61.0724i	−0.654743	+	0.115449i	−0.163599	+	0.986527i	$0.552310\pi$
$24$		0			0
$25$	−991.328	−	831.823i	−1.58613	−	1.33092i
$26$			128.767i			0.190484i
$27$		0			0
$28$	−574.723			−0.733065
$29$	18.9983	−	22.6413i	0.0225901	−	0.0269219i	−0.754631	−	0.656149i	$-0.772184\pi$
$29$	18.9983	−	22.6413i	0.0225901	−	0.0269219i	0.777221	+	0.629227i	$0.216629\pi$
$30$		0			0
$31$	155.830	+	883.753i	0.162154	+	0.919619i	0.951951	+	0.306251i	$0.0990746\pi$
$31$	155.830	+	883.753i	0.162154	+	0.919619i	−0.789797	+	0.613368i	$0.789814\pi$
$32$	−61.9123	+	170.103i	−0.0604612	+	0.166116i
$33$		0			0
$34$	−234.492	+	1329.87i	−0.202848	+	1.15041i
$35$	2725.50	+	1573.57i	2.22490	+	1.28455i
$36$		0			0
$37$	−268.374	−	464.837i	−0.196036	−	0.339545i	0.751203	−	0.660071i	$-0.229474\pi$
$37$	−268.374	−	464.837i	−0.196036	−	0.339545i	−0.947240	+	0.320526i	$0.896140\pi$
$38$	666.073	+	1830.02i	0.461269	+	1.26733i
$39$		0			0
$40$	759.340	−	637.162i	0.474588	−	0.398226i
$41$	−94.4822	−	112.599i	−0.0562059	−	0.0669836i	0.737209	−	0.675665i	$-0.236143\pi$
$41$	−94.4822	−	112.599i	−0.0562059	−	0.0669836i	−0.793415	+	0.608681i	$0.791699\pi$
$42$		0			0
$43$	1366.62	−	497.411i	0.739116	−	0.269016i	0.0550974	−	0.998481i	$-0.482453\pi$
$43$	1366.62	−	497.411i	0.739116	−	0.269016i	0.684018	+	0.729465i	$0.260231\pi$
$44$	110.416	−	63.7485i	0.0570329	−	0.0329280i
$45$		0			0
$46$	−497.382	+	861.491i	−0.235058	+	0.407132i
$47$	−1375.04	−	242.456i	−0.622469	−	0.109758i	−0.146487	−	0.989213i	$-0.546797\pi$
$47$	−1375.04	−	242.456i	−0.622469	−	0.109758i	−0.475983	+	0.879454i	$0.657908\pi$
$48$		0			0
$49$	−2593.59	−	943.991i	−1.08021	−	0.393166i
$50$	−3604.62	+	635.592i	−1.44185	+	0.254237i
$51$		0			0
$52$	279.000	+	234.109i	0.103181	+	0.0865788i
$53$		−	3259.92i		−	1.16053i	−0.814429	−	0.580264i	$-0.802949\pi$
$53$		−	3259.92i		−	1.16053i	0.814429	−	0.580264i	$-0.197051\pi$
$54$		0			0
$55$	−698.164			−0.230798
$56$	−1044.89	+	1245.25i	−0.333193	+	0.397083i
$57$		0			0
$58$	−14.5165	−	82.3272i	−0.00431525	−	0.0244730i
$59$	−461.271	+	1267.33i	−0.132511	+	0.364071i	−0.988148	−	0.153506i	$-0.950944\pi$
$59$	−461.271	+	1267.33i	−0.132511	+	0.364071i	0.855637	+	0.517577i	$0.173166\pi$
$60$		0			0
$61$	396.659	−	2249.57i	0.106600	−	0.604560i	−0.883969	−	0.467546i	$-0.845138\pi$
$61$	396.659	−	2249.57i	0.106600	−	0.604560i	0.990569	−	0.137014i	$-0.0437505\pi$
$62$	2198.14	+	1269.10i	0.571837	+	0.330150i
$63$		0			0
$64$	256.000	+	443.405i	0.0625000	+	0.108253i
$65$	−682.119	−	1874.11i	−0.161448	−	0.443575i
$66$		0			0
$67$	−2245.35	+	1884.08i	−0.500190	+	0.419709i	−0.857661	−	0.514215i	$-0.828083\pi$
$67$	−2245.35	+	1884.08i	−0.500190	+	0.419709i	0.357471	+	0.933924i	$0.383639\pi$
$68$	2455.11	+	2925.89i	0.530949	+	0.632761i
$69$		0			0
$70$	8364.63	−	3044.48i	1.70707	−	0.621322i
$71$	1309.89	−	756.267i	0.259848	−	0.150023i	−0.364417	−	0.931236i	$-0.618732\pi$
$71$	1309.89	−	756.267i	0.259848	−	0.150023i	0.624265	+	0.781213i	$0.285399\pi$
$72$		0			0
$73$	−3471.25	+	6012.38i	−0.651389	+	1.12824i	0.331397	+	0.943491i	$0.392480\pi$
$73$	−3471.25	+	6012.38i	−0.651389	+	1.12824i	−0.982786	+	0.184747i	$0.940853\pi$
$74$	−1495.09	−	263.624i	−0.273025	−	0.0481417i
$75$		0			0
$76$	5176.08	+	1883.94i	0.896135	+	0.326167i
$77$	1127.54	−	198.815i	0.190173	−	0.0335326i
$78$		0			0
$79$	5233.12	+	4391.11i	0.838507	+	0.703591i	0.957227	−	0.289337i	$-0.0934348\pi$
$79$	5233.12	+	4391.11i	0.838507	+	0.703591i	−0.118721	+	0.992928i	$0.537879\pi$
$80$		−	2803.67i		−	0.438074i
$81$		0			0
$82$	−415.745			−0.0618301
$83$	3446.90	−	4107.86i	0.500349	−	0.596293i	−0.455469	−	0.890252i	$-0.650528\pi$
$83$	3446.90	−	4107.86i	0.500349	−	0.596293i	0.955818	+	0.293959i	$0.0949729\pi$
$84$		0			0
$85$	−3631.88	−	20597.4i	−0.502682	−	2.85085i
$86$	1406.89	−	3865.40i	0.190223	−	0.522634i
$87$		0			0
$88$	62.6203	−	355.138i	0.00808630	−	0.0458597i
$89$	6651.93	+	3840.49i	0.839784	+	0.484850i	0.857191	−	0.514999i	$-0.172208\pi$
$89$	6651.93	+	3840.49i	0.839784	+	0.484850i	−0.0174067	+	0.999848i	$0.505541\pi$
$90$		0			0
$91$	1635.31	+	2832.44i	0.197477	+	0.342041i
$92$	962.314	+	2643.94i	0.113695	+	0.312374i
$93$		0			0
$94$	−3025.25	+	2538.49i	−0.342378	+	0.287289i
$95$	−19388.3	−	23106.1i	−2.14829	−	2.56023i
$96$		0			0
$97$	−2809.87	+	1022.71i	−0.298636	+	0.108695i	−0.486993	−	0.873406i	$-0.661906\pi$
$97$	−2809.87	+	1022.71i	−0.298636	+	0.108695i	0.188356	+	0.982101i	$0.439684\pi$
$98$	−6760.70	+	3903.29i	−0.703947	+	0.406424i
$99$		0			0
$100$	−5176.35	+	8965.70i	−0.517635	+	0.896570i
$101$	68.9346	+	12.1550i	0.00675763	+	0.00119155i	0.177026	−	0.984206i	$-0.443352\pi$
$101$	68.9346	+	12.1550i	0.00675763	+	0.00119155i	−0.170268	+	0.985398i	$0.554463\pi$
$102$		0			0
$103$	1653.08	+	601.673i	0.155819	+	0.0567135i	0.418752	−	0.908101i	$-0.362468\pi$
$103$	1653.08	+	601.673i	0.155819	+	0.0567135i	−0.262933	+	0.964814i	$0.584690\pi$
$104$	1014.49	−	178.882i	0.0937952	−	0.0165386i
$105$		0			0
$106$	−7063.28	−	5926.79i	−0.628629	−	0.527482i
$107$		−	16938.9i		−	1.47951i	−0.672877	−	0.739754i	$-0.734942\pi$
$107$		−	16938.9i		−	1.47951i	0.672877	−	0.739754i	$-0.265058\pi$
$108$		0			0
$109$	1735.99			0.146115			0.0730574	−	0.997328i	$-0.476724\pi$
$109$	1735.99			0.146115			0.0730574	+	0.997328i	$0.476724\pi$
$110$	−1269.32	+	1512.71i	−0.104902	+	0.125018i
$111$		0			0
$112$	798.397	+	4527.94i	0.0636477	+	0.360964i
$113$	656.985	−	1805.05i	0.0514516	−	0.141362i	−0.911305	−	0.411732i	$-0.864924\pi$
$113$	656.985	−	1805.05i	0.0514516	−	0.141362i	0.962756	+	0.270370i	$0.0871461\pi$
$114$		0			0
$115$	2675.42	−	15173.1i	0.202301	−	1.14730i
$116$	−204.771	−	118.224i	−0.0152178	−	0.00878600i
$117$		0			0
$118$	1907.30	+	3303.54i	0.136979	+	0.237255i
$119$	11731.0	+	32230.6i	0.828400	+	2.27601i
$120$		0			0
$121$	11021.1	−	9247.79i	0.752755	−	0.631637i
$122$	−4152.98	−	4949.33i	−0.279023	−	0.332527i
$123$		0			0
$124$	6746.14	−	2455.39i	0.438745	−	0.159690i
$125$	25384.0	−	14655.5i	1.62458	−	0.937951i
$126$		0			0
$127$	3561.66	−	6168.98i	0.220823	−	0.382477i	−0.734235	−	0.678896i	$-0.762459\pi$
$127$	3561.66	−	6168.98i	0.220823	−	0.382477i	0.955058	+	0.296418i	$0.0957922\pi$
$128$	1426.15	+	251.469i	0.0870455	+	0.0153485i
$129$		0			0
$130$	−5300.77	−	1929.32i	−0.313655	−	0.114161i
$131$	−22834.1	+	4026.27i	−1.33058	+	0.234617i	−0.793324	−	0.608800i	$-0.791651\pi$
$131$	−22834.1	+	4026.27i	−1.33058	+	0.234617i	−0.537258	+	0.843418i	$0.680540\pi$
$132$		0			0
$133$	37892.0	+	31795.2i	2.14212	+	1.79746i
$134$			8290.41i			0.461707i
$135$		0			0
$136$	10803.1			0.584078
$137$	−8157.47	+	9721.69i	−0.434625	+	0.517965i	−0.938251	−	0.345956i	$-0.887555\pi$
$137$	−8157.47	+	9721.69i	−0.434625	+	0.517965i	0.503626	+	0.863922i	$0.331999\pi$
$138$		0			0
$139$	−1915.91	−	10865.7i	−0.0991621	−	0.562376i	−0.993392	−	0.114769i	$-0.963387\pi$
$139$	−1915.91	−	10865.7i	−0.0991621	−	0.562376i	0.894230	−	0.447608i	$-0.147724\pi$
$140$	8611.08	−	23658.8i	0.439341	−	1.20708i
$141$		0			0
$142$	742.883	−	4213.10i	0.0368420	−	0.208941i
$143$	−628.350	−	362.778i	−0.0307277	−	0.0177406i
$144$		0			0
$145$	647.388	+	1121.31i	0.0307913	+	0.0533321i
$146$	6716.03	+	18452.1i	0.315070	+	0.865648i
$147$		0			0
$148$	−3289.38	+	2760.12i	−0.150173	+	0.126010i
$149$	26833.6	+	31979.0i	1.20867	+	1.44043i	0.865319	+	0.501222i	$0.167116\pi$
$149$	26833.6	+	31979.0i	1.20867	+	1.44043i	0.343346	+	0.939209i	$0.388439\pi$
$150$		0			0
$151$	−19830.8	+	7217.84i	−0.869736	+	0.316558i	−0.738060	−	0.674735i	$-0.764258\pi$
$151$	−19830.8	+	7217.84i	−0.869736	+	0.316558i	−0.131675	+	0.991293i	$0.542036\pi$
$152$	13492.4	−	7789.87i	0.583987	−	0.337165i
$153$		0			0
$154$	1619.18	−	2804.49i	0.0682736	−	0.118253i
$155$	−38714.9	−	6826.49i	−1.61144	−	0.284141i
$156$		0			0
$157$	−36279.7	−	13204.7i	−1.47185	−	0.535711i	−0.523250	−	0.852179i	$-0.675280\pi$
$157$	−36279.7	−	13204.7i	−1.47185	−	0.535711i	−0.948603	+	0.316469i	$0.897503\pi$
$158$	19028.4	−	3355.23i	0.762235	−	0.134403i
$159$		0			0
$160$	−6074.72	−	5097.30i	−0.237294	−	0.199113i
$161$			25266.4i			0.974748i
$162$		0			0
$163$	4517.94			0.170046			0.0850228	−	0.996379i	$-0.472904\pi$
$163$	4517.94			0.170046			0.0850228	+	0.996379i	$0.472904\pi$
$164$	−755.857	+	900.796i	−0.0281030	+	0.0334918i
$165$		0			0
$166$	−2633.76	−	14936.8i	−0.0955786	−	0.542053i
$167$	−14666.7	+	40296.5i	−0.525897	+	1.44489i	0.337965	+	0.941159i	$0.390262\pi$
$167$	−14666.7	+	40296.5i	−0.525897	+	1.44489i	−0.863861	+	0.503730i	$0.831961\pi$
$168$		0			0
$169$	−4599.66	+	26086.0i	−0.161047	+	0.913342i
$170$	−51231.4	−	29578.5i	−1.77271	−	1.02348i
$171$		0			0
$172$	−5817.33	−	10075.9i	−0.196638	−	0.340586i
$173$	−4048.78	−	11123.9i	−0.135280	−	0.371677i	0.853493	−	0.521104i	$-0.174480\pi$
$173$	−4048.78	−	11123.9i	−0.135280	−	0.371677i	−0.988773	+	0.149426i	$0.952257\pi$
$174$		0			0
$175$	−71217.4	+	59758.5i	−2.32547	+	1.95130i
$176$	−655.628	−	781.347i	−0.0211657	−	0.0252243i
$177$		0			0
$178$	20414.9	−	7430.43i	0.644329	−	0.234517i
$179$	21139.9	−	12205.1i	0.659778	−	0.380923i	−0.132415	−	0.991194i	$-0.542273\pi$
$179$	21139.9	−	12205.1i	0.659778	−	0.380923i	0.792192	+	0.610272i	$0.208940\pi$
$180$		0			0
$181$	−6051.66	+	10481.8i	−0.184721	+	0.319947i	−0.943483	−	0.331422i	$-0.892472\pi$
$181$	−6051.66	+	10481.8i	−0.184721	+	0.319947i	0.758761	+	0.651369i	$0.225805\pi$
$182$	9110.17	+	1606.37i	0.275032	+	0.0484956i
$183$		0			0
$184$	7478.18	+	2721.83i	0.220882	+	0.0803945i
$185$	23156.3	−	4083.08i	0.676590	−	0.119301i
$186$		0			0
$187$	−5828.78	−	4890.93i	−0.166684	−	0.139865i
$188$			11170.0i			0.316036i
$189$		0			0
$190$	−85313.4			−2.36325
$191$	7689.14	−	9163.55i	0.210771	−	0.251187i	−0.650293	−	0.759683i	$-0.725354\pi$
$191$	7689.14	−	9163.55i	0.210771	−	0.251187i	0.861064	+	0.508496i	$0.169798\pi$
$192$		0			0
$193$	−6311.78	−	35795.9i	−0.169448	−	0.960989i	−0.944359	−	0.328918i	$-0.893316\pi$
$193$	−6311.78	−	35795.9i	−0.169448	−	0.960989i	0.774910	−	0.632071i	$-0.217795\pi$
$194$	−2892.66	+	7947.51i	−0.0768588	+	0.211168i
$195$		0			0
$196$	−3834.21	+	21744.9i	−0.0998078	+	0.566038i
$197$	592.415	+	342.031i	0.0152649	+	0.00881319i	0.507613	−	0.861585i	$-0.330528\pi$
$197$	592.415	+	342.031i	0.0152649	+	0.00881319i	−0.492348	+	0.870398i	$0.663861\pi$
$198$		0			0
$199$	18076.1	+	31308.8i	0.456457	+	0.790607i	0.998771	−	0.0495695i	$-0.0157849\pi$
$199$	18076.1	+	31308.8i	0.456457	+	0.790607i	−0.542314	+	0.840176i	$0.682452\pi$
$200$	10015.0	+	27515.9i	0.250375	+	0.687898i
$201$		0			0
$202$	151.665	−	127.262i	0.00371691	−	0.00311886i
$203$	−1364.84	−	1626.56i	−0.0331201	−	0.0394710i
$204$		0			0
$205$	6050.84	−	2202.33i	0.143982	−	0.0524051i
$206$	4309.08	−	2487.85i	0.101543	−	0.0586259i
$207$		0			0
$208$	1456.84	−	2523.32i	0.0336732	−	0.0583237i
$209$	−10806.5	−	1905.48i	−0.247397	−	0.0436227i
$210$		0			0
$211$	77261.4	+	28120.8i	1.73539	+	0.631631i	0.998991	−	0.0449140i	$-0.0143014\pi$
$211$	77261.4	+	28120.8i	1.73539	+	0.631631i	0.736401	+	0.676545i	$0.236524\pi$
$212$	−25683.2	+	4528.64i	−0.571448	+	0.100762i
$213$		0			0
$214$	−36701.5	−	30796.2i	−0.801413	−	0.672466i
$215$			63710.5i			1.37827i
$216$		0			0
$217$	64468.6			1.36908
$218$	3156.16	−	3761.37i	0.0664120	−	0.0791468i
$219$		0			0
$220$	969.879	+	5500.46i	0.0200388	+	0.113646i
$221$	7434.06	−	20424.9i	0.152209	−	0.418192i
$222$		0			0
$223$	−8253.12	+	46805.8i	−0.165962	+	0.941217i	0.782105	+	0.623146i	$0.214146\pi$
$223$	−8253.12	+	46805.8i	−0.165962	+	0.941217i	−0.948067	+	0.318070i	$0.896965\pi$
$224$	11262.2	+	6502.25i	0.224455	+	0.129589i
$225$		0			0
$226$	−2716.56	−	4705.21i	−0.0531866	−	0.0921218i
$227$	−6423.60	−	17648.7i	−0.124660	−	0.342500i	0.861627	−	0.507543i	$-0.169446\pi$
$227$	−6423.60	−	17648.7i	−0.124660	−	0.342500i	−0.986286	+	0.165043i	$0.947224\pi$
$228$		0			0
$229$	26346.7	−	22107.5i	0.502407	−	0.421569i	−0.356041	−	0.934470i	$-0.615874\pi$
$229$	26346.7	−	22107.5i	0.502407	−	0.421569i	0.858448	+	0.512901i	$0.171429\pi$
$230$	−28011.4	−	33382.7i	−0.529516	−	0.631053i
$231$		0			0
$232$	−628.446	+	228.736i	−0.0116759	+	0.00424969i
$233$	−83376.3	+	48137.3i	−1.53579	+	0.886687i	−0.536708	+	0.843768i	$0.680332\pi$
$233$	−83376.3	+	48137.3i	−1.53579	+	0.886687i	−0.999079	+	0.0429188i	$0.986334\pi$
$234$		0			0
$235$	30583.0	−	52971.3i	0.553789	−	0.959190i
$236$	10625.4	+	1873.55i	0.190775	+	0.0336388i
$237$		0			0
$238$	91161.8	+	33180.2i	1.60938	+	0.585767i
$239$	−56693.5	+	9996.59i	−0.992516	+	0.175007i	−0.646247	−	0.763128i	$-0.723663\pi$
$239$	−56693.5	+	9996.59i	−0.992516	+	0.175007i	−0.346269	+	0.938135i	$0.612551\pi$
$240$		0			0
$241$	−62828.1	−	52719.0i	−1.08173	−	0.907681i	−0.0856690	−	0.996324i	$-0.527303\pi$
$241$	−62828.1	−	52719.0i	−1.08173	−	0.907681i	−0.996064	+	0.0886423i	$0.971747\pi$
$242$		−	40692.6i		−	0.694840i
$243$		0			0
$244$	−18274.2			−0.306943
$245$	77719.7	−	92622.7i	1.29479	−	1.54307i
$246$		0			0
$247$	−5443.22	−	30870.1i	−0.0892200	−	0.505992i
$248$	6944.91	−	19081.0i	0.112918	−	0.310240i
$249$		0			0
$250$	14396.1	−	81644.4i	0.230338	−	1.30631i
$251$	37657.4	+	21741.5i	0.597727	+	0.345098i	0.768147	−	0.640274i	$-0.221179\pi$
$251$	37657.4	+	21741.5i	0.597727	+	0.345098i	−0.170420	+	0.985372i	$0.554512\pi$
$252$		0			0
$253$	−2802.56	−	4854.18i	−0.0437839	−	0.0758359i
$254$	−6890.95	−	18932.7i	−0.106810	−	0.293458i
$255$		0			0
$256$	3137.72	−	2632.86i	0.0478778	−	0.0401742i
$257$	28921.7	+	34467.5i	0.437882	+	0.521847i	0.939179	−	0.343428i	$-0.111588\pi$
$257$	28921.7	+	34467.5i	0.437882	+	0.521847i	−0.501297	+	0.865275i	$0.667144\pi$
$258$		0			0
$259$	−36234.7	+	13188.4i	−0.540163	+	0.196603i
$260$	−13817.5	+	7977.53i	−0.204401	+	0.118011i
$261$		0			0
$262$	−32790.5	+	56794.8i	−0.477689	+	0.827381i
$263$	−28767.3	−	5072.44i	−0.415898	−	0.0733341i	−0.0382163	−	0.999269i	$-0.512168\pi$
$263$	−28767.3	−	5072.44i	−0.415898	−	0.0733341i	−0.377682	+	0.925935i	$0.623279\pi$
$264$		0			0
$265$	134196.	+	48843.4i	1.91095	+	0.695528i
$266$	137781.	−	24294.6i	1.94727	−	0.343357i
$267$		0			0
$268$	17962.8	+	15072.6i	0.250095	+	0.209855i
$269$		−	16725.8i		−	0.231143i	−0.993299	−	0.115572i	$-0.963130\pi$
$269$		−	16725.8i		−	0.231143i	0.993299	−	0.115572i	$-0.0368700\pi$
$270$		0			0
$271$	−30699.3			−0.418013			−0.209006	−	0.977914i	$-0.567023\pi$
$271$	−30699.3			−0.418013			−0.209006	+	0.977914i	$0.567023\pi$
$272$	19640.9	−	23407.1i	0.265475	−	0.316380i
$273$		0			0
$274$	6233.09	+	35349.6i	0.0830237	+	0.470851i
$275$	7053.84	−	19380.3i	0.0932739	−	0.256268i
$276$		0			0
$277$	4053.85	−	22990.5i	0.0528333	−	0.299632i	−0.946929	−	0.321443i	$-0.895832\pi$
$277$	4053.85	−	22990.5i	0.0528333	−	0.299632i	0.999762	+	0.0218108i	$0.00694315\pi$
$278$	−27025.9	−	15603.4i	−0.349696	−	0.201897i
$279$		0			0
$280$	−35605.8	−	61671.1i	−0.454156	−	0.786621i
$281$	−44937.7	−	123465.i	−0.569113	−	1.56363i	−0.805892	−	0.592062i	$-0.798314\pi$
$281$	−44937.7	−	123465.i	−0.569113	−	1.56363i	0.236779	−	0.971564i	$-0.423908\pi$
$282$		0			0
$283$	−59708.3	+	50101.2i	−0.745525	+	0.625569i	−0.934315	−	0.356448i	$-0.883988\pi$
$283$	−59708.3	+	50101.2i	−0.745525	+	0.625569i	0.188791	+	0.982017i	$0.439543\pi$
$284$	−7777.90	−	9269.34i	−0.0964330	−	0.114924i
$285$		0			0
$286$	−1928.42	+	701.888i	−0.0235760	+	0.00858096i
$287$	−9144.96	+	5279.85i	−0.111024	+	0.0640999i
$288$		0			0
$289$	72211.2	−	125073.i	0.864587	−	1.49751i
$290$	3606.54	+	635.930i	0.0428840	+	0.00756160i
$291$		0			0
$292$	52190.6	+	18995.8i	0.612105	+	0.222788i
$293$	−37331.2	+	6582.50i	−0.434847	+	0.0766753i	−0.386787	−	0.922169i	$-0.626415\pi$
$293$	−37331.2	+	6582.50i	−0.434847	+	0.0766753i	−0.0480604	+	0.998844i	$0.515304\pi$
$294$		0			0
$295$	−45259.1	−	37976.9i	−0.520070	−	0.436390i
$296$			12145.2i			0.138619i
$297$		0			0
$298$	118074.			1.32961
$299$	10292.1	−	12265.6i	0.115123	−	0.137198i
$300$		0			0
$301$	−18142.7	−	102893.i	−0.200249	−	1.13567i
$302$	−20415.1	+	56090.1i	−0.223840	+	0.614996i
$303$		0			0
$304$	7652.00	−	43396.7i	0.0827996	−	0.469580i
$305$	86661.3	+	50033.9i	0.931592	+	0.537855i
$306$		0			0
$307$	1849.44	+	3203.32i	0.0196229	+	0.0339879i	0.875670	−	0.482910i	$-0.160420\pi$
$307$	1849.44	+	3203.32i	0.0196229	+	0.0339879i	−0.856047	+	0.516898i	$0.827087\pi$
$308$	−3132.71	−	8607.06i	−0.0330232	−	0.0907305i
$309$		0			0
$310$	−85177.7	+	71472.6i	−0.886345	+	0.743731i
$311$	111411.	+	132774.i	1.15188	+	1.37275i	0.916101	+	0.400947i	$0.131319\pi$
$311$	111411.	+	132774.i	1.15188	+	1.37275i	0.235777	+	0.971807i	$0.424237\pi$
$312$		0			0
$313$	69188.7	−	25182.6i	0.706231	−	0.257047i	0.0361619	−	0.999346i	$-0.488487\pi$
$313$	69188.7	−	25182.6i	0.706231	−	0.257047i	0.670069	+	0.742299i	$0.266265\pi$
$314$	−94570.0	+	54600.0i	−0.959167	+	0.553775i
$315$		0			0
$316$	27325.4	−	47329.0i	0.273648	−	0.473973i
$317$	95682.6	+	16871.4i	0.952170	+	0.167893i	0.628094	−	0.778138i	$-0.283835\pi$
$317$	95682.6	+	16871.4i	0.952170	+	0.167893i	0.324076	+	0.946031i	$0.394947\pi$
$318$		0			0
$319$	442.632	+	161.105i	0.00434972	+	0.00158317i
$320$	−22088.6	+	3894.82i	−0.215709	+	0.0380354i
$321$		0			0
$322$	54744.8	+	45936.3i	0.527997	+	0.443042i
$323$		−	328729.i		−	3.15089i
$324$		0			0
$325$	58914.8			0.557773
$326$	8213.97	−	9789.02i	0.0772890	−	0.0921095i
$327$		0			0
$328$	577.547	+	3275.43i	0.00536834	+	0.0304454i
$329$	−34307.0	+	94257.7i	−0.316950	+	0.870814i
$330$		0			0
$331$	−21153.2	+	119966.i	−0.193072	+	1.09497i	0.722065	+	0.691826i	$0.243193\pi$
$331$	−21153.2	+	119966.i	−0.193072	+	1.09497i	−0.915137	+	0.403143i	$0.867918\pi$
$332$	−37152.0	−	21449.7i	−0.337059	−	0.194601i
$333$		0			0
$334$	60645.2	+	105041.i	0.543630	+	0.941595i
$335$	−43916.7	−	120660.i	−0.391327	−	1.07516i
$336$		0			0
$337$	−151836.	+	127405.i	−1.33695	+	1.12183i	−0.354546	+	0.935039i	$0.615365\pi$
$337$	−151836.	+	127405.i	−1.33695	+	1.12183i	−0.982399	+	0.186792i	$0.940191\pi$
$338$	48157.9	+	57392.4i	0.421536	+	0.502367i
$339$		0			0
$340$	−157230.	+	57227.2i	−1.36012	+	0.495045i
$341$	−12385.7	+	7150.89i	−0.106515	+	0.0614966i
$342$		0			0
$343$	−12897.0	+	22338.2i	−0.109622	+	0.189872i
$344$	−32407.8	−	5714.37i	−0.273863	−	0.0482894i
$345$		0			0
$346$	−31463.2	−	11451.7i	−0.262816	−	0.0956571i
$347$	59276.8	−	10452.1i	0.492295	−	0.0868049i	0.0780110	−	0.996952i	$-0.475143\pi$
$347$	59276.8	−	10452.1i	0.492295	−	0.0868049i	0.414284	+	0.910148i	$0.364032\pi$
$348$		0			0
$349$	58140.8	+	48785.9i	0.477342	+	0.400538i	0.849464	−	0.527646i	$-0.176925\pi$
$349$	58140.8	+	48785.9i	0.477342	+	0.400538i	−0.372122	+	0.928184i	$0.621370\pi$
$350$			262953.i			2.14655i
$351$		0			0
$352$	−2884.93			−0.0232836
$353$	−53884.4	+	64216.9i	−0.432428	+	0.515347i	−0.937621	−	0.347659i	$-0.886977\pi$
$353$	−53884.4	+	64216.9i	−0.432428	+	0.515347i	0.505193	+	0.863006i	$0.331421\pi$
$354$		0			0
$355$	11506.0	+	65253.5i	0.0912990	+	0.517782i
$356$	21016.4	−	57742.1i	0.165828	−	0.455610i
$357$		0			0
$358$	11989.1	−	67993.8i	0.0935453	−	0.530522i
$359$	20901.9	+	12067.7i	0.162180	+	0.0936347i	0.578893	−	0.815403i	$-0.303485\pi$
$359$	20901.9	+	12067.7i	0.162180	+	0.0936347i	−0.416713	+	0.909038i	$0.636818\pi$
$360$		0			0
$361$	−171879.	−	297703.i	−1.31889	−	2.28438i
$362$	11708.5	+	32168.8i	0.0893478	+	0.245481i
$363$		0			0
$364$	20043.5	−	16818.5i	0.151276	−	0.126936i
$365$	−195493.	−	232979.i	−1.46739	−	1.74877i
$366$		0			0
$367$	−191468.	+	69688.8i	−1.42156	+	0.517405i	−0.934500	−	0.355964i	$-0.884153\pi$
$367$	−191468.	+	69688.8i	−1.42156	+	0.517405i	−0.487059	+	0.873369i	$0.661930\pi$
$368$	19493.3	−	11254.5i	0.143943	−	0.0831054i
$369$		0			0
$370$	33253.1	−	57596.1i	0.242901	−	0.420717i
$371$	−230636.	−	40667.4i	−1.67564	−	0.295460i
$372$		0			0
$373$	132075.	+	48071.5i	0.949301	+	0.345517i	0.769832	−	0.638246i	$-0.220340\pi$
$373$	132075.	+	48071.5i	0.949301	+	0.345517i	0.179469	+	0.983764i	$0.442562\pi$
$374$	−21194.3	+	3737.14i	−0.151522	+	0.0267175i
$375$		0			0
$376$	24202.0	+	20307.9i	0.171189	+	0.143645i
$377$			1345.58i			0.00946728i
$378$		0			0
$379$	−186672.			−1.29957			−0.649787	−	0.760117i	$-0.725142\pi$
$379$	−186672.			−1.29957			−0.649787	+	0.760117i	$0.725142\pi$
$380$	−155106.	+	184849.i	−1.07414	+	1.28012i
$381$		0			0
$382$	−5875.23	−	33320.1i	−0.0402623	−	0.228339i
$383$	−23561.1	+	64733.7i	−0.160620	+	0.441299i	−0.993730	−	0.111808i	$-0.964336\pi$
$383$	−23561.1	+	64733.7i	−0.160620	+	0.441299i	0.833110	+	0.553107i	$0.186558\pi$
$384$		0			0
$385$	−8709.57	+	49394.4i	−0.0587591	+	0.333239i
$386$	−89034.2	−	51403.9i	−0.597561	−	0.345002i
$387$		0			0
$388$	11960.8	+	20716.7i	0.0794505	+	0.137612i
$389$	56737.4	+	155885.i	0.374947	+	1.03016i	0.973422	+	0.229018i	$0.0735515\pi$
$389$	56737.4	+	155885.i	0.374947	+	1.03016i	−0.598475	+	0.801142i	$0.704226\pi$
$390$		0			0
$391$	128630.	−	107933.i	0.841374	−	0.705996i
$392$	40143.8	+	47841.5i	0.261244	+	0.311339i
$393$		0			0
$394$	1818.14	−	661.747i	0.0117121	−	0.00426285i
$395$	−259170.	+	149632.i	−1.66108	+	0.959025i
$396$		0			0
$397$	−121583.	+	210588.i	−0.771421	+	1.33614i	0.165363	+	0.986233i	$0.447121\pi$
$397$	−121583.	+	210588.i	−0.771421	+	1.33614i	−0.936784	+	0.349908i	$0.886213\pi$
$398$	100701.	+	17756.2i	0.635720	+	0.112095i
$399$		0			0
$400$	77826.8	+	28326.6i	0.486418	+	0.177042i
$401$	267371.	−	47144.7i	1.66274	−	0.293187i	0.738291	−	0.674483i	$-0.235633\pi$
$401$	267371.	−	47144.7i	1.66274	−	0.293187i	0.924453	+	0.381296i	$0.124522\pi$
$402$		0			0
$403$	−31296.4	−	26260.8i	−0.192701	−	0.161696i
$404$		−	559.984i		−	0.00343094i
$405$		0			0
$406$	−6005.66			−0.0364342
$407$	5498.54	−	6552.91i	0.0331939	−	0.0395590i
$408$		0			0
$409$	−42487.9	−	240961.i	−0.253991	−	1.44045i	−0.798650	−	0.601796i	$-0.794452\pi$
$409$	−42487.9	−	240961.i	−0.253991	−	1.44045i	0.544659	−	0.838658i	$-0.316659\pi$
$410$	6229.12	−	17114.4i	0.0370560	−	0.101811i
$411$		0			0
$412$	2443.82	−	13859.6i	0.0143971	−	0.0816500i
$413$	83908.0	+	48444.3i	0.491930	+	0.284016i
$414$		0			0
$415$	117457.	+	203442.i	0.681997	+	1.18125i
$416$	−2818.63	−	7744.11i	−0.0162874	−	0.0447492i
$417$		0			0
$418$	−23775.7	+	19950.2i	−0.136076	+	0.114181i
$419$	80916.8	+	96432.9i	0.460904	+	0.549284i	0.945572	−	0.325414i	$-0.105504\pi$
$419$	80916.8	+	96432.9i	0.460904	+	0.549284i	−0.484667	+	0.874699i	$0.661059\pi$
$420$		0			0
$421$	−109311.	+	39785.9i	−0.616736	+	0.224473i	−0.631448	−	0.775418i	$-0.717539\pi$
$421$	−109311.	+	39785.9i	−0.616736	+	0.224473i	0.0147122	+	0.999892i	$0.495317\pi$
$422$	201397.	−	116276.i	1.13091	−	0.652930i
$423$		0			0
$424$	−36881.8	+	63881.2i	−0.205154	+	0.355338i
$425$	608455.	+	107287.i	3.36861	+	0.593977i
$426$		0			0
$427$	−154206.	−	56126.5i	−0.845758	−	0.307831i
$428$	−133452.	+	23531.3i	−0.728516	+	0.128457i
$429$		0			0
$430$	138042.	+	115831.i	0.746574	+	0.626450i
$431$			236314.i			1.27214i	0.771631	+	0.636070i	$0.219441\pi$
$431$			236314.i			1.27214i	−0.771631	+	0.636070i	$0.780559\pi$
$432$		0			0
$433$	321843.			1.71660			0.858299	−	0.513150i	$-0.171522\pi$
$433$	321843.			1.71660			0.858299	+	0.513150i	$0.171522\pi$
$434$	117209.	−	139684.i	0.622274	−	0.741597i
$435$		0			0
$436$	−2411.61	−	13676.9i	−0.0126863	−	0.0719475i
$437$	82823.2	−	227555.i	0.433700	−	1.19158i
$438$		0			0
$439$	21480.4	−	121821.i	0.111458	−	0.632112i	−0.876985	−	0.480518i	$-0.840449\pi$
$439$	21480.4	−	121821.i	0.111458	−	0.632112i	0.988443	−	0.151593i	$-0.0484404\pi$
$440$	13681.2	+	7898.82i	0.0706672	+	0.0407997i
$441$		0			0
$442$	−30739.0	−	53241.5i	−0.157342	−	0.272524i
$443$	30850.7	+	84761.5i	0.157202	+	0.431908i	0.993142	−	0.116912i	$-0.0372995\pi$
$443$	30850.7	+	84761.5i	0.157202	+	0.431908i	−0.835941	+	0.548820i	$0.815077\pi$
$444$		0			0
$445$	−257762.	+	216288.i	−1.30166	+	1.09222i
$446$	86409.3	+	102979.i	0.434401	+	0.517699i
$447$		0			0
$448$	34564.0	−	12580.3i	0.172214	−	0.0626808i
$449$	10347.0	−	5973.85i	0.0513242	−	0.0296321i	−0.474118	−	0.880461i	$-0.657233\pi$
$449$	10347.0	−	5973.85i	0.0513242	−	0.0296321i	0.525443	+	0.850829i	$0.323900\pi$
$450$		0			0
$451$	1171.29	−	2028.73i	0.00575850	−	0.00997402i
$452$	−15133.7	−	2668.48i	−0.0740744	−	0.0130613i
$453$		0			0
$454$	−49918.0	−	18168.7i	−0.242184	−	0.0881478i
$455$	−141101.	+	24879.8i	−0.681563	+	0.120178i
$456$		0			0
$457$	−245134.	−	205692.i	−1.17374	−	0.984882i	−1.00000		9.03114e-5i	$-0.999971\pi$
$457$	−245134.	−	205692.i	−1.17374	−	0.984882i	−0.173737	−	0.984792i	$-0.555584\pi$
$458$		−	97278.6i		−	0.463753i
$459$		0			0
$460$	−123257.			−0.582501
$461$	−259207.	+	308911.i	−1.21968	+	1.45356i	−0.367727	+	0.929934i	$0.619864\pi$
$461$	−259207.	+	308911.i	−1.21968	+	1.45356i	−0.851951	+	0.523622i	$0.824580\pi$
$462$		0			0
$463$	−41153.4	−	233392.i	−0.191974	−	1.08874i	−0.916662	−	0.399663i	$-0.869127\pi$
$463$	−41153.4	−	233392.i	−0.191974	−	1.08874i	0.724688	−	0.689078i	$-0.241984\pi$
$464$	−646.962	+	1777.51i	−0.00300499	+	0.00825614i
$465$		0			0
$466$	−47285.4	+	268169.i	−0.217749	+	1.23491i
$467$	−180410.	−	104160.i	−0.827230	−	0.477601i	0.0256736	−	0.999670i	$-0.491827\pi$
$467$	−180410.	−	104160.i	−0.827230	−	0.477601i	−0.852903	+	0.522069i	$0.825160\pi$
$468$		0			0
$469$	105286.	+	182360.i	0.478656	+	0.829057i
$470$	−59170.7	−	162570.i	−0.267862	−	0.735944i
$471$		0			0
$472$	23377.2	−	19615.8i	0.104932	−	0.0880486i
$473$	14898.5	+	17755.3i	0.0665915	+	0.0793607i
$474$		0			0
$475$	837287.	−	304748.i	3.71097	−	1.35068i
$476$	237631.	−	137196.i	1.04879	−	0.605520i
$477$		0			0
$478$	−81413.6	+	141012.i	−0.356321	+	0.617166i
$479$	−259756.	−	45802.0i	−1.13213	−	0.199624i	−0.423967	−	0.905678i	$-0.639363\pi$
$479$	−259756.	−	45802.0i	−1.13213	−	0.199624i	−0.708158	+	0.706054i	$0.750474\pi$
$480$		0			0
$481$	22962.4	+	8357.62i	0.0992491	+	0.0361237i
$482$	−228453.	+	40282.4i	−0.983337	+	0.173389i
$483$		0			0
$484$	−88168.7	−	73982.3i	−0.376378	−	0.315818i
$485$		−	130993.i		−	0.556883i
$486$		0			0
$487$	−211624.			−0.892291			−0.446146	−	0.894960i	$-0.647204\pi$
$487$	−211624.			−0.892291			−0.446146	+	0.894960i	$0.647204\pi$
$488$	−33223.8	+	39594.6i	−0.139512	+	0.166263i
$489$		0			0
$490$	−59385.3	−	336791.i	−0.247336	−	1.40271i
$491$	33120.2	−	90996.9i	0.137382	−	0.377454i	−0.851855	−	0.523778i	$-0.824522\pi$
$491$	33120.2	−	90996.9i	0.137382	−	0.377454i	0.989237	+	0.146324i	$0.0467443\pi$
$492$		0			0
$493$	−2450.36	+	13896.7i	−0.0100818	+	0.0571766i
$494$	−76782.4	−	44330.3i	−0.314636	−	0.181655i
$495$		0			0
$496$	−28716.4	−	49738.2i	−0.116726	−	0.202175i
$497$	−37164.3	−	102108.i	−0.150457	−	0.413377i
$498$		0			0
$499$	−250197.	+	209940.i	−1.00480	+	0.843131i	−0.987643	−	0.156722i	$-0.949907\pi$
$499$	−250197.	+	209940.i	−1.00480	+	0.843131i	−0.0171612	+	0.999853i	$0.505463\pi$
$500$	−150726.	−	179628.i	−0.602903	−	0.718512i
$501$		0			0
$502$	115571.	−	42064.6i	0.458610	−	0.166920i
$503$	214064.	−	123590.i	0.846073	−	0.488481i	−0.0132507	−	0.999912i	$-0.504218\pi$
$503$	214064.	−	123590.i	0.846073	−	0.488481i	0.859324	+	0.511432i	$0.170885\pi$
$504$		0			0
$505$	−1533.22	+	2655.61i	−0.00601202	+	0.0104131i
$506$	−15612.8	−	2752.96i	−0.0609791	−	0.0107523i
$507$		0			0
$508$	−53549.9	−	19490.6i	−0.207506	−	0.0755261i
$509$	−122402.	+	21582.7i	−0.472445	+	0.0833048i	−0.404801	−	0.914405i	$-0.632659\pi$
$509$	−122402.	+	21582.7i	−0.472445	+	0.0833048i	−0.0676439	+	0.997710i	$0.521548\pi$
$510$		0			0
$511$	382066.	+	320592.i	1.46318	+	1.22775i
$512$		−	11585.2i		−	0.0441942i
$513$		0			0
$514$	127263.			0.481697
$515$	−49536.3	+	59035.1i	−0.186771	+	0.222585i
$516$		0			0
$517$	−3864.05	−	21914.1i	−0.0144564	−	0.0819866i
$518$	−37302.3	+	102487.i	−0.139020	+	0.381953i
$519$		0			0
$520$	−7836.34	+	44442.1i	−0.0289806	+	0.164357i
$521$	−146942.	−	84836.9i	−0.541340	−	0.312543i	0.204282	−	0.978912i	$-0.434514\pi$
$521$	−146942.	−	84836.9i	−0.541340	−	0.312543i	−0.745622	+	0.666369i	$0.767847\pi$
$522$		0			0
$523$	−73793.7	−	127814.i	−0.269784	−	0.467279i	0.699022	−	0.715100i	$-0.253619\pi$
$523$	−73793.7	−	127814.i	−0.269784	−	0.467279i	−0.968806	+	0.247821i	$0.920286\pi$
$524$	63441.6	+	174304.i	0.231053	+	0.634813i
$525$		0			0
$526$	−63291.6	+	53107.9i	−0.228757	+	0.191950i
$527$	−275398.	−	328206.i	−0.991607	−	1.18175i
$528$		0			0
$529$	−146730.	+	53405.3i	−0.524333	+	0.190841i
$530$	349808.	−	201962.i	1.24531	−	0.718982i
$531$		0			0
$532$	197858.	−	342700.i	0.699086	−	1.21085i
$533$	6590.14	+	1162.02i	0.0231975	+	0.00409034i
$534$		0			0
$535$	697298.	+	253796.i	2.43619	+	0.886700i
$536$	65315.6	−	11516.9i	0.227346	−	0.0400873i
$537$		0			0
$538$	−36239.7	−	30408.7i	−0.125205	−	0.105059i
$539$		−	43987.2i		−	0.151408i
$540$		0			0
$541$	416315.			1.42242			0.711209	−	0.702980i	$-0.248148\pi$
$541$	416315.			1.42242			0.711209	+	0.702980i	$0.248148\pi$
$542$	−55813.7	+	66516.1i	−0.189995	+	0.226427i
$543$		0			0
$544$	−15007.5	−	85111.8i	−0.0507120	−	0.287602i
$545$	−26010.3	+	71462.8i	−0.0875696	+	0.240595i
$546$		0			0
$547$	34899.8	−	197927.i	0.116640	−	0.661499i	−0.869285	−	0.494311i	$-0.835420\pi$
$547$	34899.8	−	197927.i	0.116640	−	0.661499i	0.985925	−	0.167188i	$-0.0534687\pi$
$548$	87924.2	+	50763.1i	0.292784	+	0.169039i
$549$		0			0
$550$	−29166.8	−	50518.4i	−0.0964192	−	0.167003i
$551$	6960.23	+	19123.1i	0.0229256	+	0.0629875i
$552$		0			0
$553$	375950.	−	315459.i	1.22936	−	1.03156i
$554$	−42443.3	−	50582.0i	−0.138290	−	0.164807i
$555$		0			0
$556$	−82943.2	+	30188.9i	−0.268307	+	0.0976556i
$557$	310672.	−	179367.i	1.00136	−	0.578138i	0.0927129	−	0.995693i	$-0.470446\pi$
$557$	310672.	−	179367.i	1.00136	−	0.578138i	0.908652	+	0.417555i	$0.137113\pi$
$558$		0			0
$559$	−33105.1	+	57339.7i	−0.105943	+	0.183498i
$560$	−198357.	−	34975.7i	−0.632516	−	0.111530i
$561$		0			0
$562$	−349213.	−	127103.i	−1.10565	−	0.402424i
$563$	253601.	−	44716.7i	0.800082	−	0.141076i	0.241365	−	0.970434i	$-0.422405\pi$
$563$	253601.	−	44716.7i	0.800082	−	0.141076i	0.558717	+	0.829358i	$0.311294\pi$
$564$		0			0
$565$	64462.2	+	54090.2i	0.201933	+	0.169442i
$566$			220458.i			0.688166i
$567$		0			0
$568$	−34224.7			−0.106082
$569$	−213406.	+	254327.i	−0.659146	+	0.785540i	−0.987263	−	0.159098i	$-0.949142\pi$
$569$	−213406.	+	254327.i	−0.659146	+	0.785540i	0.328117	+	0.944637i	$0.393586\pi$
$570$		0			0
$571$	60638.1	+	343896.i	0.185983	+	1.05476i	0.924686	+	0.380731i	$0.124328\pi$
$571$	60638.1	+	343896.i	0.185983	+	1.05476i	−0.738703	+	0.674031i	$0.764561\pi$
$572$	−1985.24	+	5454.40i	−0.00606765	+	0.0166707i
$573$		0			0
$574$	−5186.41	+	29413.6i	−0.0157414	+	0.0892738i
$575$	394157.	+	227567.i	1.19216	+	0.688292i
$576$		0			0
$577$	73223.7	+	126827.i	0.219938	+	0.380944i	0.954789	−	0.297285i	$-0.0960812\pi$
$577$	73223.7	+	126827.i	0.219938	+	0.380944i	−0.734851	+	0.678229i	$0.762748\pi$
$578$	−139711.	−	383853.i	−0.418192	−	1.14897i
$579$		0			0
$580$	7934.84	−	6658.12i	0.0235875	−	0.0197923i
$581$	−247627.	−	295110.i	−0.733577	−	0.874243i
$582$		0			0
$583$	48820.6	−	17769.3i	0.143637	−	0.0522796i
$584$	136045.	−	78545.5i	0.398893	−	0.230301i
$585$		0			0
$586$	−53608.7	+	92853.1i	−0.156113	+	0.270396i
$587$	126022.	+	22221.0i	0.365737	+	0.0644893i	0.353497	−	0.935436i	$-0.384993\pi$
$587$	126022.	+	22221.0i	0.365737	+	0.0644893i	0.0122403	+	0.999925i	$0.496104\pi$
$588$		0			0
$589$	−580618.	−	211328.i	−1.67363	−	0.609152i
$590$	−164569.	+	29017.9i	−0.472763	+	0.0833610i
$591$		0			0
$592$	26315.0	+	22080.9i	0.0750863	+	0.0630049i
$593$		−	232435.i		−	0.660984i	−0.943809	−	0.330492i	$-0.892785\pi$
$593$		−	232435.i		−	0.660984i	0.943809	−	0.330492i	$-0.107215\pi$
$594$		0			0
$595$	−1.50255e6			−4.24420
$596$	214669.	−	255832.i	0.604333	−	0.720215i
$597$		0			0
$598$	−7864.14	−	44599.8i	−0.0219912	−	0.124718i
$599$	−61729.5	+	169600.i	−0.172044	+	0.472687i	−0.995508	−	0.0946823i	$-0.969816\pi$
$599$	−61729.5	+	169600.i	−0.172044	+	0.472687i	0.823464	+	0.567369i	$0.192039\pi$
$600$		0			0
$601$	42494.5	−	240998.i	0.117648	−	0.667214i	−0.867757	−	0.496988i	$-0.834439\pi$
$601$	42494.5	−	240998.i	0.117648	−	0.667214i	0.985405	−	0.170226i	$-0.0544497\pi$
$602$	−255922.	−	147757.i	−0.706179	−	0.407713i
$603$		0			0
$604$	84414.2	+	146210.i	0.231388	+	0.400776i
$605$	215561.	+	592248.i	0.588923	+	1.61805i
$606$		0			0
$607$	270710.	−	227153.i	0.734729	−	0.616511i	−0.196688	−	0.980466i	$-0.563018\pi$
$607$	270710.	−	227153.i	0.734729	−	0.616511i	0.931416	+	0.363956i	$0.118574\pi$
$608$	−80115.7	−	95478.1i	−0.216726	−	0.258284i
$609$		0			0
$610$	265966.	−	96803.6i	0.714769	−	0.260155i
$611$	55049.6	−	31782.9i	0.147459	−	0.0851355i
$612$		0			0
$613$	−307250.	+	532173.i	−0.817658	+	1.41622i	0.0897457	+	0.995965i	$0.471395\pi$
$613$	−307250.	+	532173.i	−0.817658	+	1.41622i	−0.907404	+	0.420260i	$0.861939\pi$
$614$	10303.1	+	1816.71i	0.0273294	+	0.00481891i
$615$		0			0
$616$	−24344.4	−	8860.65i	−0.0641562	−	0.0233509i
$617$	−497782.	+	87772.4i	−1.30758	+	0.230562i	−0.783652	−	0.621200i	$-0.786645\pi$
$617$	−497782.	+	87772.4i	−1.30758	+	0.230562i	−0.523929	+	0.851762i	$0.675534\pi$
$618$		0			0
$619$	−123451.	−	103588.i	−0.322192	−	0.270351i	0.467317	−	0.884090i	$-0.345221\pi$
$619$	−123451.	−	103588.i	−0.322192	−	0.270351i	−0.789509	+	0.613738i	$0.789665\pi$
$620$			314497.i			0.818151i
$621$		0			0
$622$	490235.			1.26714
$623$	354694.	−	422707.i	0.913855	−	1.08909i
$624$		0			0
$625$	82523.2	+	468012.i	0.211259	+	1.19811i
$626$	71227.2	−	195695.i	0.181760	−	0.499381i
$627$		0			0
$628$	−53633.7	+	304172.i	−0.135994	+	0.771259i
$629$	221929.	+	128131.i	0.560935	+	0.323856i
$630$		0			0
$631$	336469.	+	582781.i	0.845057	+	1.46368i	0.885571	+	0.464503i	$0.153767\pi$
$631$	336469.	+	582781.i	0.845057	+	1.46368i	−0.0405139	+	0.999179i	$0.512900\pi$
$632$	−52868.1	−	145254.i	−0.132361	−	0.363658i
$633$		0			0
$634$	210514.	−	176642.i	0.523724	−	0.439456i
$635$	200585.	+	239047.i	0.497451	+	0.592839i
$636$		0			0
$637$	118076.	−	42976.3i	0.290994	−	0.105913i
$638$	1153.81	−	666.150i	0.00283460	−	0.00163656i
$639$		0			0
$640$	−31719.9	+	54940.5i	−0.0774413	+	0.134132i
$641$	123358.	+	21751.3i	0.300228	+	0.0529382i	0.321733	−	0.946831i	$-0.395735\pi$
$641$	123358.	+	21751.3i	0.300228	+	0.0529382i	−0.0215052	+	0.999769i	$0.506846\pi$
$642$		0			0
$643$	−49154.5	−	17890.8i	−0.118889	−	0.0432721i	0.281891	−	0.959447i	$-0.409038\pi$
$643$	−49154.5	−	17890.8i	−0.118889	−	0.0432721i	−0.400780	+	0.916174i	$0.631261\pi$
$644$	199061.	−	35099.8i	0.479969	−	0.0846316i
$645$		0			0
$646$	−712258.	−	597656.i	−1.70676	−	1.43214i
$647$		−	301665.i		−	0.720637i	−0.932829	−	0.360318i	$-0.882668\pi$
$647$		−	301665.i		−	0.720637i	0.932829	−	0.360318i	$-0.117332\pi$
$648$		0			0
$649$	−21493.9			−0.0510299
$650$	107112.	−	127651.i	0.253519	−	0.302132i
$651$		0			0
$652$	−6276.26	−	35594.4i	−0.0147640	−	0.0837311i
$653$	100561.	−	276290.i	0.235833	−	0.647947i	−0.764162	−	0.645024i	$-0.776847\pi$
$653$	100561.	−	276290.i	0.235833	−	0.647947i	0.999996	−	0.00292299i	$-0.000930419\pi$
$654$		0			0
$655$	176380.	−	1.00030e6i	0.411119	−	2.33157i
$656$	8146.91	+	4703.62i	0.0189315	+	0.0109301i
$657$		0			0
$658$	141855.	+	245701.i	0.327638	+	0.567486i
$659$	112506.	+	309107.i	0.259062	+	0.711767i	0.999226	+	0.0393405i	$0.0125257\pi$
$659$	112506.	+	309107.i	0.259062	+	0.711767i	−0.740164	+	0.672427i	$0.765252\pi$
$660$		0			0
$661$	380771.	−	319505.i	0.871487	−	0.731264i	−0.0929240	−	0.995673i	$-0.529621\pi$
$661$	380771.	−	319505.i	0.871487	−	0.731264i	0.964411	+	0.264409i	$0.0851769\pi$
$662$	221472.	+	263940.i	0.505362	+	0.602267i
$663$		0			0
$664$	−114020.	+	41500.0i	−0.258611	+	0.0941265i
$665$	−1.87660e6	+	1.08346e6i	−4.24354	+	2.45001i
$666$		0			0
$667$	−5197.47	+	9002.28i	−0.0116826	+	0.0202349i
$668$	337849.	+	59571.9i	0.757129	+	0.133502i
$669$		0			0
$670$	−341278.	−	124215.i	−0.760255	−	0.276710i
$671$	35851.6	−	6321.61i	0.0796277	−	0.0140405i
$672$		0			0
$673$	515756.	+	432771.i	1.13871	+	0.955494i	0.999396	−	0.0347536i	$-0.0110646\pi$
$673$	515756.	+	432771.i	1.13871	+	0.955494i	0.139318	+	0.990248i	$0.455509\pi$
$674$			560615.i			1.23408i
$675$		0			0
$676$	211907.			0.463716
$677$	50714.2	−	60438.8i	0.110650	−	0.131868i	−0.707877	−	0.706336i	$-0.750347\pi$
$677$	50714.2	−	60438.8i	0.110650	−	0.131868i	0.818527	+	0.574468i	$0.194791\pi$
$678$		0			0
$679$	37302.6	+	211554.i	0.0809095	+	0.458861i
$680$	−161863.	+	444715.i	−0.350050	+	0.961753i
$681$		0			0
$682$	−7024.33	+	39837.0i	−0.0151021	+	0.0856481i
$683$	674444.	+	389390.i	1.44579	+	0.834726i	0.998227	−	0.0595276i	$-0.0189594\pi$
$683$	674444.	+	389390.i	1.44579	+	0.834726i	0.447561	+	0.894253i	$0.352293\pi$
$684$		0			0
$685$	−277975.	−	481466.i	−0.592412	−	1.02609i
$686$	24952.5	+	68556.5i	0.0530233	+	0.145680i
$687$		0			0
$688$	−71301.3	+	59828.9i	−0.150633	+	0.126396i
$689$	95397.2	+	113690.i	0.200954	+	0.239488i
$690$		0			0
$691$	−546962.	+	199078.i	−1.14552	+	0.416934i	−0.843902	−	0.536497i	$-0.819747\pi$
$691$	−546962.	+	199078.i	−1.14552	+	0.416934i	−0.301613	+	0.953430i	$0.597525\pi$
$692$	−82015.0	+	47351.4i	−0.171270	+	0.0988827i
$693$		0			0
$694$	85123.2	−	147438.i	0.176738	−	0.306119i
$695$	475997.	+	83931.1i	0.985450	+	0.173761i
$696$		0			0
$697$	65945.0	+	24002.0i	0.135743	+	0.0494063i
$698$	211409.	−	37277.1i	0.433923	−	0.0765123i
$699$		0			0
$700$	569739.	+	478068.i	1.16273	+	0.975649i
$701$		−	447426.i		−	0.910512i	−0.890361	−	0.455256i	$-0.849548\pi$
$701$		−	447426.i		−	0.910512i	0.890361	−	0.455256i	$-0.150452\pi$
$702$		0			0
$703$	369569.			0.747798
$704$	−5245.03	+	6250.78i	−0.0105828	+	0.0126121i
$705$		0			0
$706$	41172.8	+	233503.i	0.0826040	+	0.468471i
$707$	1719.91	−	4725.42i	0.00344086	−	0.00945370i
$708$		0			0
$709$	−94351.7	+	535095.i	−0.187697	+	1.06448i	0.734744	+	0.678345i	$0.237302\pi$
$709$	−94351.7	+	535095.i	−0.187697	+	1.06448i	−0.922441	+	0.386138i	$0.873809\pi$
$710$	162304.	+	93706.0i	0.321967	+	0.185888i
$711$		0			0
$712$	−86900.5	−	150516.i	−0.171420	−	0.296909i
$713$	−107946.	−	296579.i	−0.212338	−	0.583393i
$714$		0			0
$715$	24348.5	−	20430.8i	0.0476278	−	0.0399645i
$716$	−125525.	−	149595.i	−0.244852	−	0.291804i
$717$		0			0
$718$	64148.5	−	23348.2i	0.124434	−	0.0452901i
$719$	−162085.	+	93579.8i	−0.313534	+	0.181019i	−0.648507	−	0.761209i	$-0.724606\pi$
$719$	−162085.	+	93579.8i	−0.313534	+	0.181019i	0.334973	+	0.942228i	$0.391273\pi$
$720$		0			0
$721$	63189.9	−	109448.i	0.121556	−	0.210542i
$722$	−957521.	−	168837.i	−1.83685	−	0.323886i
$723$		0			0
$724$	90987.2	+	33116.6i	0.173581	+	0.0631784i
$725$	−37667.1	+	6641.72i	−0.0716615	+	0.0126359i
$726$		0			0
$727$	23995.6	+	20134.7i	0.0454007	+	0.0380957i	0.665206	−	0.746660i	$-0.268344\pi$
$727$	23995.6	+	20134.7i	0.0454007	+	0.0380957i	−0.619805	+	0.784756i	$0.712788\pi$
$728$		−	74005.6i		−	0.139637i
$729$		0			0
$730$	−860218.			−1.61422
$731$	−446318.	+	531901.i	−0.835237	+	0.995396i
$732$		0			0
$733$	−94514.5	−	536018.i	−0.175910	−	0.997635i	−0.937088	−	0.349093i	$-0.886490\pi$
$733$	−94514.5	−	536018.i	−0.175910	−	0.997635i	0.761178	−	0.648543i	$-0.224621\pi$
$734$	−197110.	+	541554.i	−0.365861	+	1.00519i
$735$		0			0
$736$	11055.3	−	62697.7i	0.0204087	−	0.115743i
$737$	−40454.9	−	23356.7i	−0.0744795	−	0.0430007i
$738$		0			0
$739$	−420101.	−	727636.i	−0.769245	−	1.33237i	−0.937973	−	0.346709i	$-0.887299\pi$
$739$	−420101.	−	727636.i	−0.769245	−	1.33237i	0.168728	−	0.985663i	$-0.446034\pi$
$740$	−64336.7	−	176764.i	−0.117489	−	0.322797i
$741$		0			0
$742$	−507429.	+	425783.i	−0.921653	+	0.773358i
$743$	598053.	+	712732.i	1.08333	+	1.29107i	0.954112	+	0.299451i	$0.0968034\pi$
$743$	598053.	+	712732.i	1.08333	+	1.29107i	0.129222	+	0.991616i	$0.458752\pi$
$744$		0			0
$745$	−1.71848e6	+	625475.i	−3.09622	+	1.12693i
$746$	344280.	−	198770.i	0.618634	−	0.357168i
$747$		0			0
$748$	−30435.7	+	52716.2i	−0.0543977	+	0.0942195i
$749$	−1.19841e6	−	211312.i	−2.13620	−	0.376670i
$750$		0			0
$751$	−96285.8	−	35045.2i	−0.170719	−	0.0621367i	0.255247	−	0.966876i	$-0.417843\pi$
$751$	−96285.8	−	35045.2i	−0.170719	−	0.0621367i	−0.425966	+	0.904739i	$0.640066\pi$
$752$	88002.2	−	15517.2i	0.155617	−	0.0274395i
$753$		0			0
$754$	2915.46	+	2446.36i	0.00512819	+	0.00430306i
$755$		−	924491.i		−	1.62184i
$756$		0			0
$757$	233507.			0.407482			0.203741	−	0.979025i	$-0.434690\pi$
$757$	233507.			0.407482			0.203741	+	0.979025i	$0.434690\pi$
$758$	−339384.	+	404462.i	−0.590681	+	0.703947i
$759$		0			0
$760$	118516.	+	672139.i	0.205187	+	1.16367i
$761$	298313.	−	819608.i	0.515113	−	1.41526i	−0.360732	−	0.932669i	$-0.617473\pi$
$761$	298313.	−	819608.i	0.515113	−	1.41526i	0.875845	−	0.482592i	$-0.160305\pi$
$762$		0			0
$763$	21656.4	−	122820.i	0.0371995	−	0.210969i
$764$	−82876.3	−	47848.7i	−0.141985	−	0.0819753i
$765$		0			0
$766$	97422.5	+	168741.i	0.166036	+	0.287582i
$767$	−20999.9	−	57696.7i	−0.0356965	−	0.0980754i
$768$		0			0
$769$	−394451.	+	330984.i	−0.667022	+	0.559698i	−0.912182	−	0.409784i	$-0.865604\pi$
$769$	−394451.	+	330984.i	−0.667022	+	0.559698i	0.245160	+	0.969483i	$0.421159\pi$
$770$	91188.2	+	108674.i	0.153800	+	0.183292i
$771$		0			0
$772$	−273248.	+	99454.2i	−0.458482	+	0.166874i
$773$	−180710.	+	104333.i	−0.302428	+	0.174607i	−0.643533	−	0.765418i	$-0.722532\pi$
$773$	−180710.	+	104333.i	−0.302428	+	0.174607i	0.341105	+	0.940025i	$0.389199\pi$
$774$		0			0
$775$	580648.	−	1.00571e6i	0.966740	−	1.67444i
$776$	66632.6	+	11749.1i	0.110653	+	0.0195111i
$777$		0			0
$778$	440909.	+	160478.i	0.728433	+	0.265128i
$779$	99668.7	−	17574.3i	0.164242	−	0.0289603i
$780$		0			0
$781$	18465.8	+	15494.7i	0.0302738	+	0.0254027i
$782$		−	474934.i		−	0.776640i
$783$		0			0
$784$	176643.			0.287385
$785$	1.08716e6	−	1.29562e6i	1.76422	−	2.10252i
$786$		0			0
$787$	182469.	+	1.03483e6i	0.294604	+	1.67078i	0.668808	+	0.743435i	$0.266805\pi$
$787$	182469.	+	1.03483e6i	0.294604	+	1.67078i	−0.374204	+	0.927346i	$0.622084\pi$
$788$	1871.70	−	5142.46i	0.00301429	−	0.00828169i
$789$		0			0
$790$	−146984.	+	833586.i	−0.235513	+	1.33566i
$791$	−119510.	−	68999.0i	−0.191007	−	0.110278i
$792$		0			0
$793$	51997.0	+	90061.5i	0.0826860	+	0.143216i
$794$	235234.	+	646299.i	0.373128	+	1.02516i
$795$		0			0
$796$	221554.	−	185906.i	0.349666	−	0.293405i
$797$	26453.1	+	31525.5i	0.0416447	+	0.0496302i	0.786465	−	0.617635i	$-0.211909\pi$
$797$	26453.1	+	31525.5i	0.0416447	+	0.0496302i	−0.744820	+	0.667265i	$0.767465\pi$
$798$		0			0
$799$	626414.	−	227996.i	0.981224	−	0.357136i
$800$	202871.	−	117127.i	0.316985	−	0.183012i
$801$		0			0
$802$	383953.	−	665025.i	0.596937	−	1.03393i
$803$	−108963.	−	19213.1i	−0.168984	−	0.0297965i
$804$		0			0
$805$	−1.04010e6	−	378567.i	−1.60504	−	0.584186i
$806$	−113799.	+	20065.8i	−0.175173	+	0.0308877i
$807$		0			0
$808$	−1213.32	−	1018.10i	−0.00185846	−	0.00155943i
$809$			556748.i			0.850672i	0.905036	+	0.425336i	$0.139844\pi$
$809$			556748.i			0.850672i	−0.905036	+	0.425336i	$0.860156\pi$
$810$		0			0
$811$	1.04776e6			1.59301			0.796505	−	0.604631i	$-0.206680\pi$
$811$	1.04776e6			1.59301			0.796505	+	0.604631i	$0.206680\pi$
$812$	−10918.8	+	13012.5i	−0.0165600	+	0.0197355i
$813$		0			0
$814$	−4201.41	−	23827.4i	−0.00634084	−	0.0359607i
$815$	−67692.3	+	185983.i	−0.101912	+	0.280000i
$816$		0			0
$817$	−173884.	+	986143.i	−0.260504	+	1.47739i
$818$	−599336.	−	346027.i	−0.895702	−	0.517134i
$819$		0			0
$820$	−25756.7	−	44611.9i	−0.0383056	−	0.0663472i
$821$	294142.	+	808148.i	0.436386	+	1.19896i	0.941827	+	0.336098i	$0.109107\pi$
$821$	294142.	+	808148.i	0.436386	+	1.19896i	−0.505441	+	0.862861i	$0.668670\pi$
$822$		0			0
$823$	−448065.	+	375971.i	−0.661517	+	0.555079i	−0.910541	−	0.413418i	$-0.864335\pi$
$823$	−448065.	+	375971.i	−0.661517	+	0.555079i	0.249024	+	0.968497i	$0.419890\pi$
$824$	−25586.5	−	30492.9i	−0.0376840	−	0.0449101i
$825$		0			0
$826$	257516.	−	93728.1i	0.377436	−	0.137376i
$827$	506796.	−	292599.i	0.741007	−	0.427821i	−0.0814284	−	0.996679i	$-0.525948\pi$
$827$	506796.	−	292599.i	0.741007	−	0.427821i	0.822435	+	0.568859i	$0.192615\pi$
$828$		0			0
$829$	−53706.8	+	93022.9i	−0.0781484	+	0.135357i	−0.902451	−	0.430792i	$-0.858234\pi$
$829$	−53706.8	+	93022.9i	−0.0781484	+	0.135357i	0.824303	+	0.566149i	$0.191567\pi$
$830$	654343.	+	115378.i	0.949837	+	0.167482i
$831$		0			0
$832$	−21903.7	−	7972.28i	−0.0316424	−	0.0115169i
$833$	1.29772e6	−	228823.i	1.87021	−	0.329769i
$834$		0			0
$835$	−1.43907e6	−	1.20753e6i	−2.06400	−	1.73190i
$836$			87786.0i			0.125607i
$837$		0			0
$838$	356054.			0.507024
$839$	−166314.	+	198205.i	−0.236268	+	0.281573i	−0.871130	−	0.491052i	$-0.836612\pi$
$839$	−166314.	+	198205.i	−0.236268	+	0.281573i	0.634862	+	0.772625i	$0.281057\pi$
$840$		0			0
$841$	122666.	+	695676.i	0.173434	+	0.983591i
$842$	−112531.	+	309178.i	−0.158727	+	0.436098i
$843$		0			0
$844$	114219.	−	647766.i	0.160344	−	0.909355i
$845$	−1.00492e6	−	580193.i	−1.40741	−	0.812567i
$846$		0			0
$847$	−516784.	−	895097.i	−0.720348	−	1.24768i
$848$	71357.4	+	196053.i	0.0992310	+	0.272635i
$849$		0			0
$850$	1.33868e6	−	1.12328e6i	1.85284	−	1.55472i
$851$	121342.	+	144610.i	0.167553	+	0.199682i
$852$		0			0
$853$	1.17343e6	−	427094.i	1.61272	−	0.586983i	0.630746	−	0.775989i	$-0.282749\pi$
$853$	1.17343e6	−	427094.i	1.61272	−	0.586983i	0.981976	+	0.189006i	$0.0605266\pi$
$854$	−401968.	+	232077.i	−0.551158	+	0.318211i
$855$		0			0
$856$	−191642.	+	331933.i	−0.261543	+	0.453005i
$857$	−536460.	−	94592.4i	−0.730426	−	0.128794i	−0.203947	−	0.978982i	$-0.565377\pi$
$857$	−536460.	−	94592.4i	−0.730426	−	0.128794i	−0.526479	+	0.850188i	$0.676488\pi$
$858$		0			0
$859$	−460710.	−	167685.i	−0.624369	−	0.227252i	0.0104095	−	0.999946i	$-0.496686\pi$
$859$	−460710.	−	167685.i	−0.624369	−	0.227252i	−0.634779	+	0.772694i	$0.718909\pi$
$860$	501941.	−	88505.7i	0.678665	−	0.119667i
$861$		0			0
$862$	512022.	+	429638.i	0.689087	+	0.578213i
$863$		−	265152.i		−	0.356020i	−0.984029	−	0.178010i	$-0.943034\pi$
$863$		−	265152.i		−	0.356020i	0.984029	−	0.178010i	$-0.0569659\pi$
$864$		0			0
$865$	518585.			0.693087
$866$	585136.	−	697338.i	0.780227	−	0.929839i
$867$		0			0
$868$	−89558.9	−	507914.i	−0.118869	−	0.674141i
$869$	−37236.5	+	102306.i	−0.0493093	+	0.135476i
$870$		0			0
$871$	23171.9	−	131414.i	0.0305440	−	0.173224i
$872$	−34018.3	−	19640.5i	−0.0447383	−	0.0258297i
$873$		0			0
$874$	−342464.	−	593165.i	−0.448324	−	0.776520i
$875$	−720196.	−	1.97872e6i	−0.940664	−	2.58445i
$876$		0			0
$877$	1.15119e6	−	965964.i	1.49675	−	1.25592i	0.611106	−	0.791549i	$-0.290725\pi$
$877$	1.15119e6	−	965964.i	1.49675	−	1.25592i	0.885641	−	0.464371i	$-0.153720\pi$
$878$	−224897.	−	268022.i	−0.291739	−	0.347681i
$879$		0			0
$880$	41987.8	−	15282.3i	0.0542198	−	0.0197344i
$881$	−406935.	+	234944.i	−0.524292	+	0.302700i	−0.738689	−	0.674047i	$-0.764555\pi$
$881$	−406935.	+	234944.i	−0.524292	+	0.302700i	0.214397	+	0.976747i	$0.431221\pi$
$882$		0			0
$883$	429892.	−	744596.i	0.551364	−	0.954991i	−0.446812	−	0.894628i	$-0.647441\pi$
$883$	429892.	−	744596.i	0.551364	−	0.954991i	0.998176	−	0.0603629i	$-0.0192258\pi$
$884$	−171244.	−	30195.0i	−0.219135	−	0.0386394i
$885$		0			0
$886$	239742.	+	87258.9i	0.305405	+	0.111158i
$887$	123829.	−	21834.4i	0.157389	−	0.0277519i	−0.0943984	−	0.995535i	$-0.530093\pi$
$887$	123829.	−	21834.4i	0.157389	−	0.0277519i	0.251787	+	0.967783i	$0.418982\pi$
$888$		0			0
$889$	−392017.	−	328942.i	−0.496023	−	0.416213i
$890$			951721.i			1.20152i
$891$		0			0
$892$	380223.			0.477868
$893$	617952.	−	736447.i	0.774911	−	0.923503i
$894$		0			0
$895$	185691.	+	1.05311e6i	0.231817	+	1.31470i
$896$	35582.4	−	97761.9i	0.0443220	−	0.121774i
$897$		0			0
$898$	5868.13	−	33279.8i	0.00727691	−	0.0412694i
$899$	22969.8	+	13261.6i	0.0284209	+	0.0164088i
$900$		0			0
$901$	778199.	+	1.34788e6i	0.958608	+	1.66036i
$902$	−2266.15	−	6226.20i	−0.00278533	−	0.00765262i
$903$		0			0
$904$	−33296.0	+	27938.7i	−0.0407433	+	0.0341877i
$905$	−340815.	−	406168.i	−0.416123	−	0.495916i
$906$		0			0
$907$	70897.4	−	25804.6i	0.0861819	−	0.0313676i	−0.298569	−	0.954388i	$-0.596509\pi$
$907$	70897.4	−	25804.6i	0.0861819	−	0.0313676i	0.384751	+	0.923020i	$0.374287\pi$
$908$	−130121.	+	75125.4i	−0.157825	+	0.0911202i
$909$		0			0
$910$	−202625.	+	350956.i	−0.244686	+	0.423809i
$911$	−356031.	−	62777.9i	−0.428994	−	0.0756433i	−0.0450179	−	0.998986i	$-0.514334\pi$
$911$	−356031.	−	62777.9i	−0.428994	−	0.0756433i	−0.383976	+	0.923343i	$0.625446\pi$
$912$		0			0
$913$	80307.8	+	29229.6i	0.0963421	+	0.0350656i
$914$	−891345.	+	157168.i	−1.06697	+	0.188136i
$915$		0			0
$916$	−210774.	−	176860.i	−0.251203	−	0.210785i
$917$			1.66572e6i			1.98090i
$918$		0			0
$919$	−144794.			−0.171443			−0.0857213	−	0.996319i	$-0.527319\pi$
$919$	−144794.			−0.171443			−0.0857213	+	0.996319i	$0.527319\pi$
$920$	−224091.	+	267062.i	−0.264758	+	0.315526i
$921$		0			0
$922$	198059.	+	1.12325e6i	0.232988	+	1.32134i
$923$	−23551.4	+	64707.1i	−0.0276448	+	0.0759536i
$924$		0			0
$925$	−120616.	+	684046.i	−0.140968	+	0.799469i
$926$	−580511.	−	335158.i	−0.677000	−	0.390866i
$927$		0			0
$928$	2675.11	+	4633.43i	0.00310632	+	0.00538030i
$929$	−319957.	−	879074.i	−0.370732	−	1.01858i	−0.975079	−	0.221857i	$-0.928788\pi$
$929$	−319957.	−	879074.i	−0.370732	−	1.01858i	0.604347	−	0.796721i	$-0.293434\pi$
$930$		0			0
$931$	1.45578e6	−	1.22154e6i	1.67956	−	1.40932i
$932$	495073.	+	590005.i	0.569951	+	0.679242i
$933$		0			0
$934$	−553681.	+	201524.i	−0.634697	+	0.231011i
$935$	288670.	−	166664.i	0.330201	−	0.190642i
$936$		0			0
$937$	17048.1	−	29528.2i	0.0194176	−	0.0336323i	−0.856153	−	0.516722i	$-0.827152\pi$
$937$	17048.1	−	29528.2i	0.0194176	−	0.0336323i	0.875571	+	0.483090i	$0.160485\pi$
$938$	586538.	+	103422.i	0.666638	+	0.117546i
$939$		0			0
$940$	−459817.	−	167360.i	−0.520391	−	0.189407i
$941$	329635.	−	58123.6i	0.372267	−	0.0656407i	0.0156150	−	0.999878i	$-0.495029\pi$
$941$	329635.	−	58123.6i	0.372267	−	0.0656407i	0.356652	+	0.934237i	$0.383918\pi$
$942$		0			0
$943$	39601.5	+	33229.6i	0.0445336	+	0.0373682i
$944$		−	86314.6i		−	0.0968590i
$945$		0			0
$946$	65556.9			0.0732548
$947$	673338.	−	802454.i	0.750816	−	0.894788i	−0.246414	−	0.969165i	$-0.579252\pi$
$947$	673338.	−	802454.i	0.750816	−	0.894788i	0.997230	+	0.0743770i	$0.0236968\pi$
$948$		0			0
$949$	−54884.2	−	311264.i	−0.0609417	−	0.345618i
$950$	861956.	−	2.36821e6i	0.955076	−	2.62405i
$951$		0			0
$952$	134768.	−	764309.i	0.148701	−	0.843325i
$953$	−142318.	−	82167.4i	−0.156702	−	0.0904719i	0.419599	−	0.907710i	$-0.362171\pi$
$953$	−142318.	−	82167.4i	−0.156702	−	0.0904719i	−0.576300	+	0.817238i	$0.695504\pi$
$954$		0			0
$955$	262016.	+	453825.i	0.287290	+	0.497601i
$956$	157516.	+	432770.i	0.172349	+	0.473524i
$957$		0			0
$958$	−571496.	+	479542.i	−0.622704	+	0.522511i
$959$	586036.	+	698411.i	0.637217	+	0.759405i
$960$		0			0
$961$	111089.	−	40432.9i	0.120288	−	0.0437813i
$962$	59855.9	−	34557.8i	0.0646780	−	0.0373419i
$963$		0			0
$964$	−328065.	+	568225.i	−0.353025	+	0.611458i
$965$	1.56812e6	+	276502.i	1.68394	+	0.296923i
$966$		0			0
$967$	894751.	+	325663.i	0.956862	+	0.348269i	0.772803	−	0.634646i	$-0.218854\pi$
$967$	894751.	+	325663.i	0.956862	+	0.348269i	0.184059	+	0.982915i	$0.441076\pi$
$968$	−320595.	+	56529.6i	−0.342142	+	0.0603288i
$969$		0			0
$970$	−283822.	−	238155.i	−0.301650	−	0.253114i
$971$		−	790669.i		−	0.838602i	−0.907847	−	0.419301i	$-0.862275\pi$
$971$		−	790669.i		−	0.838602i	0.907847	−	0.419301i	$-0.137725\pi$
$972$		0			0
$973$	−792636.			−0.837237
$974$	−384748.	+	458525.i	−0.405564	+	0.483332i
$975$		0			0
$976$	25386.2	+	143972.i	0.0266500	+	0.151140i
$977$	−352151.	+	967527.i	−0.368927	+	1.01362i	0.606844	+	0.794821i	$0.292435\pi$
$977$	−352151.	+	967527.i	−0.368927	+	1.01362i	−0.975771	+	0.218796i	$0.929787\pi$
$978$		0			0
$979$	−21256.8	+	120553.i	−0.0221785	+	0.125781i
$980$	−837692.	−	483641.i	−0.872232	−	0.503583i
$981$		0			0
$982$	−136948.	−	237201.i	−0.142015	−	0.245976i
$983$	395010.	+	1.08528e6i	0.408790	+	1.12314i	0.957827	+	0.287344i	$0.0927724\pi$
$983$	395010.	+	1.08528e6i	0.408790	+	1.12314i	−0.549037	+	0.835798i	$0.685005\pi$
$984$		0			0
$985$	−22956.0	+	19262.4i	−0.0236605	+	0.0198535i
$986$	25655.1	+	30574.5i	0.0263888	+	0.0314489i
$987$		0			0
$988$	−235647.	+	85768.5i	−0.241406	+	0.0878646i
$989$	−442965.	+	255746.i	−0.452873	+	0.261466i
$990$		0			0
$991$	−466765.	+	808461.i	−0.475282	+	0.823212i	−0.999599	−	0.0283106i	$-0.990987\pi$
$991$	−466765.	+	808461.i	−0.475282	+	0.823212i	0.524317	+	0.851523i	$0.324321\pi$
$992$	−159976.	−	28208.2i	−0.162567	−	0.0286650i
$993$		0			0
$994$	−288805.	−	105116.i	−0.292302	−	0.106389i
$995$	−1.55968e6	+	275013.i	−1.57539	+	0.277784i
$996$		0			0
$997$	116358.	+	97636.2i	0.117060	+	0.0982247i	0.699438	−	0.714693i	$-0.253434\pi$
$997$	116358.	+	97636.2i	0.117060	+	0.0982247i	−0.582379	+	0.812918i	$0.697878\pi$
$998$			923790.i			0.927497i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.35.7		72
3.2	odd	2		54.5.f.a.11.5	yes	72
27.5	odd	18	inner	162.5.f.a.125.7		72
27.22	even	9		54.5.f.a.5.5	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.5.5	✓	72	27.22	even	9
54.5.f.a.11.5	yes	72	3.2	odd	2
162.5.f.a.35.7		72	1.1	even	1	trivial
162.5.f.a.125.7		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)

\(f(q)\)	\(=\)	\(q+(1.81808 - 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-14.9830 + 41.1655i) q^{5} +(12.4750 - 70.7490i) q^{7} +(-19.5959 - 11.3137i) q^{8} +O(q^{10})\)	\(q+(1.81808 - 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-14.9830 + 41.1655i) q^{5} +(12.4750 - 70.7490i) q^{7} +(-19.5959 - 11.3137i) q^{8} +(61.9530 + 107.306i) q^{10} +(5.45082 + 14.9760i) q^{11} +(-34.8751 + 29.2636i) q^{13} +(-130.611 - 155.657i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(-413.470 + 238.717i) q^{17} +(-344.267 + 596.287i) q^{19} +(345.135 + 60.8566i) q^{20} +(42.3585 + 15.4172i) q^{22} +(-346.359 + 61.0724i) q^{23} +(-991.328 - 831.823i) q^{25} +128.767i q^{26} -574.723 q^{28} +(18.9983 - 22.6413i) q^{29} +(155.830 + 883.753i) q^{31} +(-61.9123 + 170.103i) q^{32} +(-234.492 + 1329.87i) q^{34} +(2725.50 + 1573.57i) q^{35} +(-268.374 - 464.837i) q^{37} +(666.073 + 1830.02i) q^{38} +(759.340 - 637.162i) q^{40} +(-94.4822 - 112.599i) q^{41} +(1366.62 - 497.411i) q^{43} +(110.416 - 63.7485i) q^{44} +(-497.382 + 861.491i) q^{46} +(-1375.04 - 242.456i) q^{47} +(-2593.59 - 943.991i) q^{49} +(-3604.62 + 635.592i) q^{50} +(279.000 + 234.109i) q^{52} -3259.92i q^{53} -698.164 q^{55} +(-1044.89 + 1245.25i) q^{56} +(-14.5165 - 82.3272i) q^{58} +(-461.271 + 1267.33i) q^{59} +(396.659 - 2249.57i) q^{61} +(2198.14 + 1269.10i) q^{62} +(256.000 + 443.405i) q^{64} +(-682.119 - 1874.11i) q^{65} +(-2245.35 + 1884.08i) q^{67} +(2455.11 + 2925.89i) q^{68} +(8364.63 - 3044.48i) q^{70} +(1309.89 - 756.267i) q^{71} +(-3471.25 + 6012.38i) q^{73} +(-1495.09 - 263.624i) q^{74} +(5176.08 + 1883.94i) q^{76} +(1127.54 - 198.815i) q^{77} +(5233.12 + 4391.11i) q^{79} -2803.67i q^{80} -415.745 q^{82} +(3446.90 - 4107.86i) q^{83} +(-3631.88 - 20597.4i) q^{85} +(1406.89 - 3865.40i) q^{86} +(62.6203 - 355.138i) q^{88} +(6651.93 + 3840.49i) q^{89} +(1635.31 + 2832.44i) q^{91} +(962.314 + 2643.94i) q^{92} +(-3025.25 + 2538.49i) q^{94} +(-19388.3 - 23106.1i) q^{95} +(-2809.87 + 1022.71i) q^{97} +(-6760.70 + 3903.29i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 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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