LMFDB - Embedded newform 162.5.f.a.17.8

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			17.8
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(33.5989 + 5.92440i) q^{5} +(-63.3453 + 53.1530i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})$	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(33.5989 + 5.92440i) q^{5} +(-63.3453 + 53.1530i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(48.2491 - 83.5699i) q^{10} +(-47.4215 + 8.36169i) q^{11} +(-245.240 + 89.2600i) q^{13} +(79.9940 + 219.782i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-271.708 - 156.871i) q^{17} +(-99.4947 - 172.330i) q^{19} +(-175.441 - 209.083i) q^{20} +(-23.6504 + 134.128i) q^{22} +(-264.654 + 315.403i) q^{23} +(506.482 + 184.345i) q^{25} +738.160i q^{26} +661.532 q^{28} +(33.7127 - 92.6248i) q^{29} +(768.107 + 644.519i) q^{31} +(178.269 + 31.4337i) q^{32} +(-679.784 + 570.407i) q^{34} +(-2443.24 + 1410.60i) q^{35} +(-714.533 + 1237.61i) q^{37} +(-554.276 + 97.7339i) q^{38} +(-725.429 + 264.035i) q^{40} +(-547.896 - 1505.33i) q^{41} +(431.574 + 2447.58i) q^{43} +(333.614 + 192.612i) q^{44} +(582.273 + 1008.53i) q^{46} +(2188.92 + 2608.65i) q^{47} +(770.456 - 4369.47i) q^{49} +(979.921 - 1167.82i) q^{50} +(1961.92 + 714.080i) q^{52} -1849.34i q^{53} -1642.85 q^{55} +(639.952 - 1758.25i) q^{56} +(-213.570 - 179.207i) q^{58} +(3737.00 + 658.935i) q^{59} +(4465.31 - 3746.84i) q^{61} +(2456.09 - 1418.02i) q^{62} +(256.000 - 443.405i) q^{64} +(-8768.61 + 1546.14i) q^{65} +(-7493.63 + 2727.46i) q^{67} +(858.447 + 2358.56i) q^{68} +(1385.64 + 7858.35i) q^{70} +(-3123.69 - 1803.47i) q^{71} +(-1193.15 - 2066.60i) q^{73} +(2598.15 + 3096.36i) q^{74} +(-276.433 + 1567.73i) q^{76} +(2559.48 - 3050.27i) q^{77} +(-632.967 - 230.381i) q^{79} +2183.50i q^{80} -4530.97 q^{82} +(347.677 - 955.235i) q^{83} +(-8199.74 - 6880.40i) q^{85} +(6922.79 + 1220.67i) q^{86} +(834.666 - 700.368i) q^{88} +(-5725.77 + 3305.78i) q^{89} +(10790.4 - 18689.5i) q^{91} +(3243.79 - 571.968i) q^{92} +(9050.93 - 3294.27i) q^{94} +(-2321.97 - 6379.55i) q^{95} +(-510.260 - 2893.83i) q^{97} +(-10868.1 - 6274.69i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	33.5989	+	5.92440i	1.34396	+	0.236976i	0.798921	−	0.601436i	$-0.205405\pi$
$5$	33.5989	+	5.92440i	1.34396	+	0.236976i	0.545037	+	0.838412i	$0.316516\pi$
$6$		0			0
$7$	−63.3453	+	53.1530i	−1.29276	+	1.08476i	−0.301414	+	0.953493i	$0.597459\pi$
$7$	−63.3453	+	53.1530i	−1.29276	+	1.08476i	−0.991348	+	0.131263i	$0.958097\pi$
$8$	−19.5959	+	11.3137i	−0.306186	+	0.176777i
$9$		0			0
$10$	48.2491	−	83.5699i	0.482491	−	0.835699i
$11$	−47.4215	+	8.36169i	−0.391913	+	0.0691049i	−0.366132	−	0.930563i	$-0.619318\pi$
$11$	−47.4215	+	8.36169i	−0.391913	+	0.0691049i	−0.0257808	+	0.999668i	$0.508207\pi$
$12$		0			0
$13$	−245.240	+	89.2600i	−1.45112	+	0.528166i	−0.942905	−	0.333062i	$-0.891918\pi$
$13$	−245.240	+	89.2600i	−1.45112	+	0.528166i	−0.508219	+	0.861228i	$0.669696\pi$
$14$	79.9940	+	219.782i	0.408133	+	1.12134i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	−271.708	−	156.871i	−0.940167	−	0.542805i	−0.0501540	−	0.998741i	$-0.515971\pi$
$17$	−271.708	−	156.871i	−0.940167	−	0.542805i	−0.890013	+	0.455936i	$0.849305\pi$
$18$		0			0
$19$	−99.4947	−	172.330i	−0.275609	−	0.477368i	0.694680	−	0.719319i	$-0.255546\pi$
$19$	−99.4947	−	172.330i	−0.275609	−	0.477368i	−0.970288	+	0.241951i	$0.922213\pi$
$20$	−175.441	−	209.083i	−0.438603	−	0.522707i
$21$		0			0
$22$	−23.6504	+	134.128i	−0.0488645	+	0.277124i
$23$	−264.654	+	315.403i	−0.500292	+	0.596225i	−0.955804	−	0.294005i	$-0.905012\pi$
$23$	−264.654	+	315.403i	−0.500292	+	0.596225i	0.455512	+	0.890230i	$0.349456\pi$
$24$		0			0
$25$	506.482	+	184.345i	0.810372	+	0.294951i
$26$			738.160i			1.09195i
$27$		0			0
$28$	661.532			0.843790
$29$	33.7127	−	92.6248i	0.0400864	−	0.110136i	−0.918034	−	0.396501i	$-0.870224\pi$
$29$	33.7127	−	92.6248i	0.0400864	−	0.110136i	0.958121	+	0.286364i	$0.0924467\pi$
$30$		0			0
$31$	768.107	+	644.519i	0.799279	+	0.670675i	0.948023	−	0.318201i	$-0.103079\pi$
$31$	768.107	+	644.519i	0.799279	+	0.670675i	−0.148744	+	0.988876i	$0.547523\pi$
$32$	178.269	+	31.4337i	0.174091	+	0.0306970i
$33$		0			0
$34$	−679.784	+	570.407i	−0.588048	+	0.493431i
$35$	−2443.24	+	1410.60i	−1.99448	+	1.15151i
$36$		0			0
$37$	−714.533	+	1237.61i	−0.521938	+	0.904023i	0.477736	+	0.878503i	$0.341457\pi$
$37$	−714.533	+	1237.61i	−0.521938	+	0.904023i	−0.999674	+	0.0255196i	$0.991876\pi$
$38$	−554.276	+	97.7339i	−0.383848	+	0.0676827i
$39$		0			0
$40$	−725.429	+	264.035i	−0.453393	+	0.165022i
$41$	−547.896	−	1505.33i	−0.325935	−	0.895498i	−0.989129	−	0.147051i	$-0.953022\pi$
$41$	−547.896	−	1505.33i	−0.325935	−	0.895498i	0.663194	−	0.748447i	$-0.269200\pi$
$42$		0			0
$43$	431.574	+	2447.58i	0.233409	+	1.32373i	0.845938	+	0.533281i	$0.179041\pi$
$43$	431.574	+	2447.58i	0.233409	+	1.32373i	−0.612529	+	0.790448i	$0.709848\pi$
$44$	333.614	+	192.612i	0.172321	+	0.0994898i
$45$		0			0
$46$	582.273	+	1008.53i	0.275176	+	0.476619i
$47$	2188.92	+	2608.65i	0.990910	+	1.18092i	0.983493	+	0.180948i	$0.0579165\pi$
$47$	2188.92	+	2608.65i	0.990910	+	1.18092i	0.00741696	+	0.999972i	$0.497639\pi$
$48$		0			0
$49$	770.456	−	4369.47i	0.320889	−	1.81985i
$50$	979.921	−	1167.82i	0.391968	−	0.467130i
$51$		0			0
$52$	1961.92	+	714.080i	0.725562	+	0.264083i
$53$		−	1849.34i		−	0.658362i	−0.944267	−	0.329181i	$-0.893227\pi$
$53$		−	1849.34i		−	0.658362i	0.944267	−	0.329181i	$-0.106773\pi$
$54$		0			0
$55$	−1642.85			−0.543091
$56$	639.952	−	1758.25i	0.204066	−	0.560668i
$57$		0			0
$58$	−213.570	−	179.207i	−0.0634869	−	0.0532719i
$59$	3737.00	+	658.935i	1.07354	+	0.189295i	0.682359	−	0.731017i	$-0.260954\pi$
$59$	3737.00	+	658.935i	1.07354	+	0.189295i	0.391185	+	0.920312i	$0.372065\pi$
$60$		0			0
$61$	4465.31	−	3746.84i	1.20003	−	1.00694i	0.200400	−	0.979714i	$-0.435776\pi$
$61$	4465.31	−	3746.84i	1.20003	−	1.00694i	0.999629	−	0.0272302i	$-0.00866873\pi$
$62$	2456.09	−	1418.02i	0.638940	−	0.368892i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−8768.61	+	1546.14i	−2.07541	+	0.365951i
$66$		0			0
$67$	−7493.63	+	2727.46i	−1.66933	+	0.607587i	−0.991788	−	0.127894i	$-0.959178\pi$
$67$	−7493.63	+	2727.46i	−1.66933	+	0.607587i	−0.677545	+	0.735482i	$0.736956\pi$
$68$	858.447	+	2358.56i	0.185650	+	0.510070i
$69$		0			0
$70$	1385.64	+	7858.35i	0.282783	+	1.60374i
$71$	−3123.69	−	1803.47i	−0.619658	−	0.357759i	0.157078	−	0.987586i	$-0.449793\pi$
$71$	−3123.69	−	1803.47i	−0.619658	−	0.357759i	−0.776736	+	0.629827i	$0.783126\pi$
$72$		0			0
$73$	−1193.15	−	2066.60i	−0.223898	−	0.387802i	0.732090	−	0.681208i	$-0.238545\pi$
$73$	−1193.15	−	2066.60i	−0.223898	−	0.387802i	−0.955988	+	0.293405i	$0.905212\pi$
$74$	2598.15	+	3096.36i	0.474462	+	0.565442i
$75$		0			0
$76$	−276.433	+	1567.73i	−0.0478589	+	0.271421i
$77$	2559.48	−	3050.27i	0.431689	−	0.514466i
$78$		0			0
$79$	−632.967	−	230.381i	−0.101421	−	0.0369141i	0.290811	−	0.956780i	$-0.406075\pi$
$79$	−632.967	−	230.381i	−0.101421	−	0.0369141i	−0.392232	+	0.919866i	$0.628297\pi$
$80$			2183.50i			0.341173i
$81$		0			0
$82$	−4530.97			−0.673851
$83$	347.677	−	955.235i	0.0504685	−	0.138661i	−0.911897	−	0.410418i	$-0.865383\pi$
$83$	347.677	−	955.235i	0.0504685	−	0.138661i	0.962366	+	0.271758i	$0.0876049\pi$
$84$		0			0
$85$	−8199.74	−	6880.40i	−1.13491	−	0.952304i
$86$	6922.79	+	1220.67i	0.936018	+	0.165045i
$87$		0			0
$88$	834.666	−	700.368i	0.107782	−	0.0904401i
$89$	−5725.77	+	3305.78i	−0.722860	+	0.417343i	−0.815804	−	0.578328i	$-0.803705\pi$
$89$	−5725.77	+	3305.78i	−0.722860	+	0.417343i	0.0929444	+	0.995671i	$0.470372\pi$
$90$		0			0
$91$	10790.4	−	18689.5i	1.30303	−	2.25691i
$92$	3243.79	−	571.968i	0.383246	−	0.0675766i
$93$		0			0
$94$	9050.93	−	3294.27i	1.02432	−	0.372823i
$95$	−2321.97	−	6379.55i	−0.257281	−	0.706875i
$96$		0			0
$97$	−510.260	−	2893.83i	−0.0542310	−	0.307559i	0.945612	−	0.325298i	$-0.105465\pi$
$97$	−510.260	−	2893.83i	−0.0542310	−	0.307559i	−0.999843	+	0.0177383i	$0.994353\pi$
$98$	−10868.1	−	6274.69i	−1.13162	−	0.653341i
$99$		0			0
$100$	−2155.95	−	3734.21i	−0.215595	−	0.373421i
$101$	3592.73	+	4281.65i	0.352194	+	0.419728i	0.912834	−	0.408332i	$-0.133889\pi$
$101$	3592.73	+	4281.65i	0.352194	+	0.419728i	−0.560640	+	0.828060i	$0.689445\pi$
$102$		0			0
$103$	−467.871	+	2653.43i	−0.0441014	+	0.250111i	−0.998886	−	0.0471868i	$-0.984974\pi$
$103$	−467.871	+	2653.43i	−0.0441014	+	0.250111i	0.954785	+	0.297298i	$0.0960855\pi$
$104$	3795.84	−	4523.70i	0.350947	−	0.418242i
$105$		0			0
$106$	−4915.27	−	1789.01i	−0.437457	−	0.159221i
$107$		−	14410.8i		−	1.25869i	−0.777125	−	0.629347i	$-0.783322\pi$
$107$		−	14410.8i		−	1.25869i	0.777125	−	0.629347i	$-0.216678\pi$
$108$		0			0
$109$	8548.62			0.719520			0.359760	−	0.933045i	$-0.382859\pi$
$109$	8548.62			0.719520			0.359760	+	0.933045i	$0.382859\pi$
$110$	−1589.26	+	4366.45i	−0.131344	+	0.360864i
$111$		0			0
$112$	−4054.10	−	3401.79i	−0.323190	−	0.271189i
$113$	7187.19	+	1267.30i	0.562863	+	0.0992478i	0.447838	−	0.894115i	$-0.352194\pi$
$113$	7187.19	+	1267.30i	0.562863	+	0.0992478i	0.115025	+	0.993363i	$0.463305\pi$
$114$		0			0
$115$	−10760.7	+	9029.28i	−0.813662	+	0.682744i
$116$	−682.908	+	394.277i	−0.0507512	+	0.0293012i
$117$		0			0
$118$	5366.45	−	9294.97i	0.385410	−	0.667550i
$119$	25549.6	−	4505.08i	1.80422	−	0.318133i
$120$		0			0
$121$	−11579.2	+	4214.47i	−0.790872	+	0.287854i
$122$	−5638.90	−	15492.7i	−0.378856	−	1.04090i
$123$		0			0
$124$	−1392.93	−	7899.68i	−0.0905910	−	0.513767i
$125$	−2541.37	−	1467.26i	−0.162648	−	0.0939046i
$126$		0			0
$127$	5041.71	+	8732.50i	0.312587	+	0.541416i	0.978922	−	0.204237i	$-0.0654712\pi$
$127$	5041.71	+	8732.50i	0.312587	+	0.541416i	−0.666335	+	0.745653i	$0.732138\pi$
$128$	−930.856	−	1109.35i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	−4373.15	+	24801.4i	−0.258766	+	1.46754i
$131$	−5147.86	+	6134.98i	−0.299975	+	0.357496i	−0.894885	−	0.446296i	$-0.852743\pi$
$131$	−5147.86	+	6134.98i	−0.299975	+	0.357496i	0.594911	+	0.803792i	$0.297187\pi$
$132$		0			0
$133$	15462.4	+	5627.85i	0.874124	+	0.318155i
$134$			22555.5i			1.25615i
$135$		0			0
$136$	7099.16			0.383821
$137$	−8823.36	+	24242.0i	−0.470103	+	1.29160i	0.447566	+	0.894251i	$0.352291\pi$
$137$	−8823.36	+	24242.0i	−0.470103	+	1.29160i	−0.917669	+	0.397346i	$0.869931\pi$
$138$		0			0
$139$	−11971.6	−	10045.4i	−0.619618	−	0.519921i	0.278065	−	0.960562i	$-0.410307\pi$
$139$	−11971.6	−	10045.4i	−0.619618	−	0.519921i	−0.897684	+	0.440641i	$0.854751\pi$
$140$	22226.8	+	3919.18i	1.13402	+	0.199958i
$141$		0			0
$142$	−7815.14	+	6557.68i	−0.387579	+	0.325217i
$143$	10883.3	−	6283.46i	0.532216	−	0.307275i
$144$		0			0
$145$	1681.46	−	2912.37i	0.0799741	−	0.138519i
$146$	−6646.94	+	1172.04i	−0.311829	+	0.0549838i
$147$		0			0
$148$	10743.1	−	3910.15i	0.490461	−	0.178513i
$149$	−7084.87	−	19465.5i	−0.319124	−	0.876785i	−0.990726	−	0.135874i	$-0.956616\pi$
$149$	−7084.87	−	19465.5i	−0.319124	−	0.876785i	0.671602	−	0.740912i	$-0.265606\pi$
$150$		0			0
$151$	5786.17	+	32815.0i	0.253768	+	1.43919i	0.799215	+	0.601046i	$0.205249\pi$
$151$	5786.17	+	32815.0i	0.253768	+	1.43919i	−0.545446	+	0.838146i	$0.683640\pi$
$152$	3899.38	+	2251.31i	0.168775	+	0.0974423i
$153$		0			0
$154$	−5631.18	−	9753.49i	−0.237442	−	0.411262i
$155$	21989.2	+	26205.7i	0.915264	+	1.09077i
$156$		0			0
$157$	−266.509	+	1511.45i	−0.0108122	+	0.0613189i	−0.989736	−	0.142905i	$-0.954356\pi$
$157$	−266.509	+	1511.45i	−0.0108122	+	0.0613189i	0.978924	+	0.204223i	$0.0654669\pi$
$158$	−1224.64	+	1459.47i	−0.0490562	+	0.0584629i
$159$		0			0
$160$	5803.43	+	2112.28i	0.226697	+	0.0825108i
$161$		−	34046.5i		−	1.31347i
$162$		0			0
$163$	−1663.58			−0.0626136			−0.0313068	−	0.999510i	$-0.509967\pi$
$163$	−1663.58			−0.0626136			−0.0313068	+	0.999510i	$0.509967\pi$
$164$	−4383.17	+	12042.7i	−0.162967	+	0.447749i
$165$		0			0
$166$	−2202.54	−	1848.15i	−0.0799295	−	0.0670688i
$167$	−30464.4	−	5371.69i	−1.09234	−	0.192610i	−0.401676	−	0.915782i	$-0.631572\pi$
$167$	−30464.4	−	5371.69i	−1.09234	−	0.192610i	−0.690668	+	0.723172i	$0.742683\pi$
$168$		0			0
$169$	30296.3	−	25421.6i	1.06076	−	0.890080i
$170$	−26219.3	+	15137.7i	−0.907244	+	0.523797i
$171$		0			0
$172$	9941.33	−	17218.9i	0.336038	−	0.582034i
$173$	−23943.5	+	4221.88i	−0.800010	+	0.141063i	−0.558684	−	0.829381i	$-0.688693\pi$
$173$	−23943.5	+	4221.88i	−0.800010	+	0.141063i	−0.241326	+	0.970444i	$0.577582\pi$
$174$		0			0
$175$	−41881.8	+	15243.7i	−1.36757	+	0.497754i
$176$	−1054.04	−	2895.94i	−0.0340275	−	0.0934898i
$177$		0			0
$178$	3247.27	+	18416.2i	0.102489	+	0.581246i
$179$	2216.85	+	1279.90i	0.0691880	+	0.0399457i	0.534195	−	0.845361i	$-0.320615\pi$
$179$	2216.85	+	1279.90i	0.0691880	+	0.0399457i	−0.465007	+	0.885307i	$0.653948\pi$
$180$		0			0
$181$	27321.8	+	47322.7i	0.833973	+	1.44448i	0.894864	+	0.446339i	$0.147272\pi$
$181$	27321.8	+	47322.7i	0.833973	+	1.44448i	−0.0608915	+	0.998144i	$0.519394\pi$
$182$	−39235.4	−	46759.0i	−1.18450	−	1.41163i
$183$		0			0
$184$	1617.77	−	9174.83i	0.0477839	−	0.270996i
$185$	−31339.6	+	37349.1i	−0.915694	+	1.09128i
$186$		0			0
$187$	14196.5	+	5167.11i	0.405974	+	0.147763i
$188$		−	27242.8i		−	0.770791i
$189$		0			0
$190$	−19202.1			−0.531914
$191$	−20668.2	+	56785.3i	−0.566546	+	1.55657i	0.243314	+	0.969948i	$0.421765\pi$
$191$	−20668.2	+	56785.3i	−0.566546	+	1.55657i	−0.809860	+	0.586624i	$0.800457\pi$
$192$		0			0
$193$	36497.9	+	30625.4i	0.979835	+	0.822179i	0.984065	−	0.177812i	$-0.0569018\pi$
$193$	36497.9	+	30625.4i	0.979835	+	0.822179i	−0.00422920	+	0.999991i	$0.501346\pi$
$194$	−8184.98	−	1443.23i	−0.217477	−	0.0383471i
$195$		0			0
$196$	−27190.8	+	22815.8i	−0.707798	+	0.593913i
$197$	20228.9	−	11679.2i	0.521242	−	0.300939i	−0.216201	−	0.976349i	$-0.569367\pi$
$197$	20228.9	−	11679.2i	0.521242	−	0.300939i	0.737443	+	0.675410i	$0.236033\pi$
$198$		0			0
$199$	−3465.94	+	6003.19i	−0.0875216	+	0.151592i	−0.906463	−	0.422285i	$-0.861228\pi$
$199$	−3465.94	+	6003.19i	−0.0875216	+	0.151592i	0.818941	+	0.573877i	$0.194561\pi$
$200$	−12010.6	+	2117.79i	−0.300265	+	0.0529449i
$201$		0			0
$202$	14855.5	−	5406.97i	0.364070	−	0.132511i
$203$	2787.75	+	7659.28i	0.0676490	+	0.185864i
$204$		0			0
$205$	−9490.54	−	53823.5i	−0.225831	−	1.28075i
$206$	6599.82	+	3810.41i	0.155524	+	0.0897918i
$207$		0			0
$208$	−8351.32	−	14464.9i	−0.193032	−	0.334341i
$209$	6159.16	+	7340.20i	0.141003	+	0.168041i
$210$		0			0
$211$	−744.875	+	4224.39i	−0.0167309	+	0.0948854i	−0.992030	−	0.126004i	$-0.959785\pi$
$211$	−744.875	+	4224.39i	−0.0167309	+	0.0948854i	0.975299	+	0.220889i	$0.0708959\pi$
$212$	−9509.86	+	11333.4i	−0.211594	+	0.252167i
$213$		0			0
$214$	−38301.7	−	13940.7i	−0.836355	−	0.304408i
$215$			84792.8i			1.83435i
$216$		0			0
$217$	−82914.1			−1.76080
$218$	8269.75	−	22721.0i	0.174012	−	0.478095i
$219$		0			0
$220$	10068.0	+	8448.03i	0.208016	+	0.174546i
$221$	80636.0	+	14218.3i	1.65099	+	0.291114i
$222$		0			0
$223$	−11635.9	+	9763.65i	−0.233986	+	0.196337i	−0.752240	−	0.658889i	$-0.771027\pi$
$223$	−11635.9	+	9763.65i	−0.233986	+	0.196337i	0.518254	+	0.855227i	$0.326582\pi$
$224$	−12963.3	+	7484.38i	−0.258357	+	0.149162i
$225$		0			0
$226$	10321.0	−	17876.5i	0.202072	−	0.349999i
$227$	80682.7	−	14226.5i	1.56577	−	0.276088i	0.677542	−	0.735484i	$-0.263045\pi$
$227$	80682.7	−	14226.5i	1.56577	−	0.276088i	0.888232	+	0.459396i	$0.151934\pi$
$228$		0			0
$229$	33273.7	−	12110.7i	0.634499	−	0.230939i	−0.00468952	−	0.999989i	$-0.501493\pi$
$229$	33273.7	−	12110.7i	0.634499	−	0.230939i	0.639188	+	0.769050i	$0.279271\pi$
$230$	13588.8	+	37335.0i	0.256878	+	0.705766i
$231$		0			0
$232$	387.299	+	2196.48i	0.00719566	+	0.0408086i
$233$	−40318.4	−	23277.8i	−0.742662	−	0.428776i	0.0803741	−	0.996765i	$-0.474389\pi$
$233$	−40318.4	−	23277.8i	−0.742662	−	0.428776i	−0.823037	+	0.567988i	$0.807722\pi$
$234$		0			0
$235$	58090.7	+	100616.i	1.05189	+	1.82193i
$236$	−19513.3	−	23255.0i	−0.350353	−	0.417534i
$237$		0			0
$238$	12742.3	−	72265.2i	0.224954	−	1.27578i
$239$	8679.94	−	10344.3i	0.151957	−	0.181095i	−0.684696	−	0.728829i	$-0.740065\pi$
$239$	8679.94	−	10344.3i	0.151957	−	0.181095i	0.836653	+	0.547734i	$0.184509\pi$
$240$		0			0
$241$	−51817.6	−	18860.1i	−0.892160	−	0.324720i	−0.145054	−	0.989424i	$-0.546335\pi$
$241$	−51817.6	−	18860.1i	−0.892160	−	0.324720i	−0.747107	+	0.664704i	$0.768558\pi$
$242$			34852.7i			0.595121i
$243$		0			0
$244$	−46632.4			−0.783264
$245$	51773.0	−	142245.i	0.862524	−	2.36976i
$246$		0			0
$247$	39782.2	+	33381.3i	0.652072	+	0.547153i
$248$	−22343.7	−	3939.79i	−0.363288	−	0.0640575i
$249$		0			0
$250$	−6358.22	+	5335.18i	−0.101732	+	0.0853629i
$251$	10629.7	−	6137.08i	0.168723	−	0.0974125i	−0.413260	−	0.910613i	$-0.635610\pi$
$251$	10629.7	−	6137.08i	0.168723	−	0.0974125i	0.581984	+	0.813200i	$0.302277\pi$
$252$		0			0
$253$	9913.01	−	17169.8i	0.154869	−	0.268241i
$254$	28086.9	−	4952.49i	0.435348	−	0.0767637i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	−23061.0	−	63359.7i	−0.349150	−	0.959283i	−0.982639	−	0.185530i	$-0.940600\pi$
$257$	−23061.0	−	63359.7i	−0.349150	−	0.959283i	0.633488	−	0.773752i	$-0.281623\pi$
$258$		0			0
$259$	−20520.3	−	116376.i	−0.305903	−	1.73486i
$260$	61687.9	+	35615.5i	0.912543	+	0.526857i
$261$		0			0
$262$	11325.9	+	19617.1i	0.164995	+	0.285780i
$263$	−51641.2	−	61543.6i	−0.746595	−	0.889757i	0.250327	−	0.968161i	$-0.419462\pi$
$263$	−51641.2	−	61543.6i	−0.746595	−	0.889757i	−0.996922	+	0.0784046i	$0.975017\pi$
$264$		0			0
$265$	10956.2	−	62135.8i	0.156016	−	0.884811i
$266$	29916.0	−	35652.5i	0.422805	−	0.503879i
$267$		0			0
$268$	59949.1	+	21819.7i	0.834666	+	0.303794i
$269$		−	71741.4i		−	0.991437i	−0.868483	−	0.495718i	$-0.834905\pi$
$269$		−	71741.4i		−	0.991437i	0.868483	−	0.495718i	$-0.165095\pi$
$270$		0			0
$271$	−56388.7			−0.767810			−0.383905	−	0.923373i	$-0.625421\pi$
$271$	−56388.7			−0.767810			−0.383905	+	0.923373i	$0.625421\pi$
$272$	6867.58	−	18868.5i	0.0928252	−	0.255035i
$273$		0			0
$274$	55896.1	+	46902.4i	0.744527	+	0.624732i
$275$	−25559.6	−	4506.84i	−0.337978	−	0.0595946i
$276$		0			0
$277$	38715.8	−	32486.4i	0.504578	−	0.423391i	−0.354638	−	0.935003i	$-0.615396\pi$
$277$	38715.8	−	32486.4i	0.504578	−	0.423391i	0.859216	+	0.511612i	$0.170952\pi$
$278$	−38280.3	+	22101.1i	−0.495320	+	0.285973i
$279$		0			0
$280$	31918.3	−	55284.1i	0.407121	−	0.705155i
$281$	−58441.3	+	10304.8i	−0.740129	+	0.130505i	−0.530986	−	0.847381i	$-0.678178\pi$
$281$	−58441.3	+	10304.8i	−0.740129	+	0.130505i	−0.209143	+	0.977885i	$0.567067\pi$
$282$		0			0
$283$	−19047.3	+	6932.64i	−0.237826	+	0.0865618i	−0.458184	−	0.888857i	$-0.651500\pi$
$283$	−19047.3	+	6932.64i	−0.237826	+	0.0865618i	0.220357	+	0.975419i	$0.429278\pi$
$284$	9869.14	+	27115.3i	0.122361	+	0.336184i
$285$		0			0
$286$	−6172.26	−	35004.6i	−0.0754592	−	0.427950i
$287$	114720.	+	66233.4i	1.39275	+	0.804106i
$288$		0			0
$289$	7456.37	+	12914.8i	0.0892754	+	0.154630i
$290$	−6114.04	−	7286.43i	−0.0726996	−	0.0866400i
$291$		0			0
$292$	−3315.02	+	18800.4i	−0.0388795	+	0.220496i
$293$	−82662.8	+	98513.7i	−0.962886	+	1.14752i	0.0261217	+	0.999659i	$0.491684\pi$
$293$	−82662.8	+	98513.7i	−0.962886	+	1.14752i	−0.989008	+	0.147864i	$0.952760\pi$
$294$		0			0
$295$	121656.	+	44279.0i	1.39794	+	0.508808i
$296$		−	32336.1i		−	0.369066i
$297$		0			0
$298$	−58590.2			−0.659770
$299$	36751.0	−	100972.i	0.411080	−	1.12943i
$300$		0			0
$301$	−157434.	−	132103.i	−1.73767	−	1.45807i
$302$	92814.8	+	16365.8i	1.01766	+	0.179441i
$303$		0			0
$304$	9755.82	−	8186.11i	0.105564	−	0.0885789i
$305$	172227.	−	99435.6i	1.85141	−	1.06891i
$306$		0			0
$307$	6747.60	−	11687.2i	0.0715933	−	0.124003i	−0.828006	−	0.560719i	$-0.810525\pi$
$307$	6747.60	−	11687.2i	0.0715933	−	0.124003i	0.899600	+	0.436715i	$0.143858\pi$
$308$	−31370.8	+	5531.52i	−0.330693	+	0.0583100i
$309$		0			0
$310$	90922.8	−	33093.2i	0.946127	−	0.344362i
$311$	49034.8	+	134722.i	0.506971	+	1.39289i	0.884346	+	0.466831i	$0.154605\pi$
$311$	49034.8	+	134722.i	0.506971	+	1.39289i	−0.377375	+	0.926060i	$0.623173\pi$
$312$		0			0
$313$	12129.1	+	68787.8i	0.123806	+	0.702138i	0.982010	+	0.188829i	$0.0604693\pi$
$313$	12129.1	+	68787.8i	0.123806	+	0.702138i	−0.858204	+	0.513309i	$0.828420\pi$
$314$	3759.39	+	2170.49i	0.0381293	+	0.0220140i
$315$		0			0
$316$	2694.36	+	4666.76i	0.0269824	+	0.0467349i
$317$	88290.2	+	105220.i	0.878606	+	1.04708i	0.998525	+	0.0542982i	$0.0172921\pi$
$317$	88290.2	+	105220.i	0.878606	+	1.04708i	−0.119919	+	0.992784i	$0.538263\pi$
$318$		0			0
$319$	−824.205	+	4674.30i	−0.00809942	+	0.0459341i
$320$	11228.2	−	13381.3i	0.109651	−	0.130677i
$321$		0			0
$322$	−90490.5	−	32935.9i	−0.872753	−	0.317656i
$323$			62431.2i			0.598407i
$324$		0			0
$325$	−140664.			−1.33173
$326$	−1609.31	+	4421.55i	−0.0151428	+	0.0416044i
$327$		0			0
$328$	27767.4	+	23299.6i	0.258100	+	0.216572i
$329$	−277316.	−	48898.2i	−2.56202	−	0.451753i
$330$		0			0
$331$	−10267.8	+	8615.68i	−0.0937173	+	0.0786382i	−0.688443	−	0.725291i	$-0.741705\pi$
$331$	−10267.8	+	8615.68i	−0.0937173	+	0.0786382i	0.594725	+	0.803929i	$0.297261\pi$
$332$	−7042.80	+	4066.16i	−0.0638953	+	0.0368900i
$333$		0			0
$334$	−43747.8	+	75773.3i	−0.392160	+	0.679240i
$335$	−267937.	+	47244.5i	−2.38750	+	0.420980i
$336$		0			0
$337$	203677.	−	74132.4i	1.79342	−	0.652752i	0.794453	−	0.607326i	$-0.207758\pi$
$337$	203677.	−	74132.4i	1.79342	−	0.652752i	0.998968	−	0.0454256i	$-0.0144644\pi$
$338$	−38258.8	−	105115.i	−0.334887	−	0.920095i
$339$		0			0
$340$	14869.8	+	84331.1i	0.128632	+	0.729507i
$341$	−41814.1	−	24141.4i	−0.359595	−	0.207612i
$342$		0			0
$343$	84174.8	+	145795.i	0.715474	+	1.23924i
$344$	−36148.2	−	43079.8i	−0.305471	−	0.364046i
$345$		0			0
$346$	−11941.3	+	67722.4i	−0.0997468	+	0.565692i
$347$	28057.6	−	33437.7i	0.233019	−	0.277701i	−0.636846	−	0.770991i	$-0.719761\pi$
$347$	28057.6	−	33437.7i	0.233019	−	0.277701i	0.869865	+	0.493290i	$0.164206\pi$
$348$		0			0
$349$	−154719.	−	56313.2i	−1.27026	−	0.462337i	−0.383062	−	0.923723i	$-0.625130\pi$
$349$	−154719.	−	56313.2i	−1.27026	−	0.462337i	−0.887200	+	0.461385i	$0.847353\pi$
$350$			126062.i			1.02908i
$351$		0			0
$352$	−8716.63			−0.0703499
$353$	9703.43	−	26659.9i	0.0778710	−	0.213949i	−0.894648	−	0.446771i	$-0.852574\pi$
$353$	9703.43	−	26659.9i	0.0778710	−	0.213949i	0.972519	+	0.232822i	$0.0747961\pi$
$354$		0			0
$355$	−94268.4	−	79100.5i	−0.748013	−	0.627658i
$356$	52088.9	+	9184.67i	0.411003	+	0.0724709i
$357$		0			0
$358$	5546.33	−	4653.92i	0.0432752	−	0.0363122i
$359$	−67668.5	+	39068.4i	−0.525046	+	0.303135i	−0.738997	−	0.673709i	$-0.764700\pi$
$359$	−67668.5	+	39068.4i	−0.525046	+	0.303135i	0.213951	+	0.976844i	$0.431367\pi$
$360$		0			0
$361$	45362.1	−	78569.5i	0.348080	−	0.602892i
$362$	152207.	−	26838.2i	1.16150	−	0.204803i
$363$		0			0
$364$	−162234.	+	59048.3i	−1.22444	+	0.445661i
$365$	−27845.3	−	76504.2i	−0.209009	−	0.574248i
$366$		0			0
$367$	−22415.1	−	127123.i	−0.166421	−	0.943823i	−0.947587	−	0.319499i	$-0.896486\pi$
$367$	−22415.1	−	127123.i	−0.166421	−	0.943823i	0.781165	−	0.624324i	$-0.214626\pi$
$368$	−22820.3	−	13175.3i	−0.168510	−	0.0972895i
$369$		0			0
$370$	68951.1	+	119427.i	0.503660	+	0.872366i
$371$	98298.0	+	117147.i	0.714162	+	0.851105i
$372$		0			0
$373$	−14641.7	+	83037.1i	−0.105238	+	0.596835i	0.885887	+	0.463902i	$0.153551\pi$
$373$	−14641.7	+	83037.1i	−0.105238	+	0.596835i	−0.991125	+	0.132934i	$0.957560\pi$
$374$	27466.8	−	32733.7i	0.196365	−	0.234019i
$375$		0			0
$376$	−72407.4	−	26354.1i	−0.512162	−	0.186412i
$377$			25724.5i			0.180994i
$378$		0			0
$379$	−64876.3			−0.451656			−0.225828	−	0.974167i	$-0.572509\pi$
$379$	−64876.3			−0.451656			−0.225828	+	0.974167i	$0.572509\pi$
$380$	−18575.7	+	51036.4i	−0.128641	+	0.353438i
$381$		0			0
$382$	130933.	+	109866.i	0.897268	+	0.752897i
$383$	−65262.4	−	11507.5i	−0.444903	−	0.0784485i	−0.0532916	−	0.998579i	$-0.516971\pi$
$383$	−65262.4	−	11507.5i	−0.444903	−	0.0784485i	−0.391612	+	0.920131i	$0.628082\pi$
$384$		0			0
$385$	104067.	−	87322.5i	0.702087	−	0.589121i
$386$	116705.	−	67379.7i	0.783276	−	0.452225i
$387$		0			0
$388$	−11753.9	+	20358.3i	−0.0780760	+	0.135232i
$389$	112167.	−	19778.0i	0.741249	−	0.130702i	0.209743	−	0.977757i	$-0.432737\pi$
$389$	112167.	−	19778.0i	0.741249	−	0.130702i	0.531506	+	0.847054i	$0.321626\pi$
$390$		0			0
$391$	121386.	−	44181.0i	0.793992	−	0.288989i
$392$	34337.1	+	94340.5i	0.223456	+	0.613940i
$393$		0			0
$394$	−11472.5	−	65063.6i	−0.0739034	−	0.419127i
$395$	−19902.1	−	11490.5i	−0.127557	−	0.0736453i
$396$		0			0
$397$	−14912.2	−	25828.7i	−0.0946153	−	0.163879i	0.814833	−	0.579696i	$-0.196829\pi$
$397$	−14912.2	−	25828.7i	−0.0946153	−	0.163879i	−0.909448	+	0.415818i	$0.863495\pi$
$398$	12602.7	+	15019.3i	0.0795606	+	0.0948166i
$399$		0			0
$400$	−5990.03	+	33971.1i	−0.0374377	+	0.212320i
$401$	−120826.	+	143995.i	−0.751400	+	0.895483i	−0.997272	−	0.0738191i	$-0.976481\pi$
$401$	−120826.	+	143995.i	−0.751400	+	0.895483i	0.245872	+	0.969302i	$0.420926\pi$
$402$		0			0
$403$	−245900.	−	89500.4i	−1.51408	−	0.551080i
$404$		−	44714.3i		−	0.273958i
$405$		0			0
$406$	23054.0			0.139860
$407$	23535.7	−	64663.9i	0.142082	−	0.390367i
$408$		0			0
$409$	170169.	+	142789.i	1.01727	+	0.853588i	0.989282	−	0.146020i	$-0.0466463\pi$
$409$	170169.	+	142789.i	1.01727	+	0.853588i	0.0279855	+	0.999608i	$0.491091\pi$
$410$	−152236.	−	26843.3i	−0.905627	−	0.159686i
$411$		0			0
$412$	16512.0	−	13855.2i	0.0972760	−	0.0816243i
$413$	−271746.	+	156893.i	−1.59317	+	0.919820i
$414$		0			0
$415$	17340.8	−	30035.1i	0.100687	−	0.174395i
$416$	−46524.5	+	8203.53i	−0.268841	+	0.0474039i
$417$		0			0
$418$	25467.4	−	9269.37i	0.145758	−	0.0530515i
$419$	109913.	+	301982.i	0.626065	+	1.72010i	0.691631	+	0.722251i	$0.256893\pi$
$419$	109913.	+	301982.i	0.626065	+	1.72010i	−0.0655657	+	0.997848i	$0.520885\pi$
$420$		0			0
$421$	55418.6	+	314294.i	0.312674	+	1.77326i	0.584978	+	0.811049i	$0.301103\pi$
$421$	55418.6	+	314294.i	0.312674	+	1.77326i	−0.272304	+	0.962211i	$0.587786\pi$
$422$	10507.2	+	6066.36i	0.0590016	+	0.0340646i
$423$		0			0
$424$	20922.9	+	36239.5i	0.116383	+	0.201581i
$425$	−108697.	−	129540.i	−0.601783	−	0.717177i
$426$		0			0
$427$	−83700.6	+	474690.i	−0.459063	+	2.60348i
$428$	−74104.6	+	88314.4i	−0.404536	+	0.482108i
$429$		0			0
$430$	225367.	+	82026.7i	1.21886	+	0.443628i
$431$		−	227477.i		−	1.22457i	−0.790639	−	0.612283i	$-0.790251\pi$
$431$		−	227477.i		−	1.22457i	0.790639	−	0.612283i	$-0.209749\pi$
$432$		0			0
$433$	144002.			0.768056			0.384028	−	0.923321i	$-0.374537\pi$
$433$	144002.			0.768056			0.384028	+	0.923321i	$0.374537\pi$
$434$	−80209.4	+	220374.i	−0.425839	+	1.16998i
$435$		0			0
$436$	−52389.0	−	43959.6i	−0.275592	−	0.231249i
$437$	80685.0	+	14226.9i	0.422503	+	0.0744987i
$438$		0			0
$439$	−136049.	+	114159.i	−0.705938	+	0.592352i	−0.923456	−	0.383704i	$-0.874648\pi$
$439$	−136049.	+	114159.i	−0.705938	+	0.592352i	0.217518	+	0.976056i	$0.430204\pi$
$440$	32193.2	−	18586.7i	0.166287	−	0.0960058i
$441$		0			0
$442$	115796.	−	200564.i	0.592718	−	1.02662i
$443$	−205817.	+	36291.1i	−1.04875	+	0.184924i	−0.671362	−	0.741130i	$-0.734290\pi$
$443$	−205817.	+	36291.1i	−1.04875	+	0.184924i	−0.377392	+	0.926053i	$0.623179\pi$
$444$		0			0
$445$	−211965.	+	77148.8i	−1.07039	+	0.389591i
$446$	14694.1	+	40371.6i	0.0738706	+	0.202958i
$447$		0			0
$448$	7351.92	+	41694.8i	0.0366307	+	0.207743i
$449$	−53558.0	−	30921.7i	−0.265663	−	0.153381i	0.361252	−	0.932468i	$-0.382349\pi$
$449$	−53558.0	−	30921.7i	−0.265663	−	0.153381i	−0.626915	+	0.779088i	$0.715683\pi$
$450$		0			0
$451$	38569.2	+	66803.8i	0.189621	+	0.328434i
$452$	−37528.8	−	44725.1i	−0.183691	−	0.218915i
$453$		0			0
$454$	40238.7	−	228205.i	0.195224	−	1.10717i
$455$	473268.	−	564019.i	2.28605	−	2.72440i
$456$		0			0
$457$	207024.	+	75350.6i	0.991262	+	0.360790i	0.786209	−	0.617961i	$-0.212041\pi$
$457$	207024.	+	75350.6i	0.991262	+	0.360790i	0.205053	+	0.978751i	$0.434263\pi$
$458$		−	100152.i		−	0.477452i
$459$		0			0
$460$	112377.			0.531080
$461$	−106322.	+	292117.i	−0.500289	+	1.37453i	0.390705	+	0.920516i	$0.372231\pi$
$461$	−106322.	+	292117.i	−0.500289	+	1.37453i	−0.890994	+	0.454016i	$0.849991\pi$
$462$		0			0
$463$	105623.	+	88628.1i	0.492715	+	0.413437i	0.854998	−	0.518631i	$-0.173558\pi$
$463$	105623.	+	88628.1i	0.492715	+	0.413437i	−0.362283	+	0.932068i	$0.618003\pi$
$464$	6212.59	+	1095.45i	0.0288561	+	0.00508810i
$465$		0			0
$466$	−100872.	+	84641.9i	−0.464515	+	0.389774i
$467$	33199.5	−	19167.8i	0.152229	−	0.0878896i	−0.421950	−	0.906619i	$-0.638654\pi$
$467$	33199.5	−	19167.8i	0.152229	−	0.0878896i	0.574180	+	0.818729i	$0.305321\pi$
$468$		0			0
$469$	329714.	−	571081.i	1.49897	−	2.59628i
$470$	323618.	−	57062.6i	1.46500	−	0.258319i
$471$		0			0
$472$	−80685.0	+	29367.0i	−0.362167	+	0.131818i
$473$	−40931.7	−	112459.i	−0.182952	−	0.502657i
$474$		0			0
$475$	−18624.2	−	105623.i	−0.0825451	−	0.468137i
$476$	−179744.	−	103775.i	−0.793303	−	0.458014i
$477$		0			0
$478$	−19097.0	−	33076.9i	−0.0835811	−	0.144767i
$479$	3129.53	+	3729.62i	0.0136398	+	0.0162553i	0.772821	−	0.634624i	$-0.218845\pi$
$479$	3129.53	+	3729.62i	0.0136398	+	0.0162553i	−0.759181	+	0.650879i	$0.774400\pi$
$480$		0			0
$481$	64763.1	−	367290.i	0.279922	−	1.58752i
$482$	−100254.	+	119479.i	−0.431529	+	0.514276i
$483$		0			0
$484$	92633.3	+	33715.8i	0.395436	+	0.143927i
$485$		−	100252.i		−	0.426198i
$486$		0			0
$487$	−238377.			−1.00509			−0.502546	−	0.864550i	$-0.667603\pi$
$487$	−238377.			−1.00509			−0.502546	+	0.864550i	$0.667603\pi$
$488$	−45111.2	+	123942.i	−0.189428	+	0.520450i
$489$		0			0
$490$	−327982.	−	275210.i	−1.36602	−	1.14623i
$491$	139273.	+	24557.6i	0.577703	+	0.101865i	0.454862	−	0.890562i	$-0.349688\pi$
$491$	139273.	+	24557.6i	0.577703	+	0.101865i	0.122841	+	0.992426i	$0.460800\pi$
$492$		0			0
$493$	−23690.1	+	19878.4i	−0.0974706	+	0.0817875i
$494$	127207.	−	73443.0i	0.521263	−	0.300951i
$495$		0			0
$496$	−32086.2	+	55574.9i	−0.130423	+	0.225899i
$497$	293731.	−	51792.7i	1.18915	−	0.209679i
$498$		0			0
$499$	−389386.	+	141725.i	−1.56379	+	0.569174i	−0.971601	−	0.236624i	$-0.923959\pi$
$499$	−389386.	+	141725.i	−1.56379	+	0.569174i	−0.592191	+	0.805798i	$0.701737\pi$
$500$	8029.32	+	22060.4i	0.0321173	+	0.0882414i
$501$		0			0
$502$	−6028.47	−	34189.2i	−0.0239221	−	0.135669i
$503$	286319.	+	165307.i	1.13166	+	0.653362i	0.944351	−	0.328939i	$-0.106691\pi$
$503$	286319.	+	165307.i	1.13166	+	0.653362i	0.187306	+	0.982302i	$0.440024\pi$
$504$		0			0
$505$	95345.7	+	165144.i	0.373868	+	0.647558i
$506$	−36045.2	−	42957.0i	−0.140782	−	0.167777i
$507$		0			0
$508$	14007.7	−	79441.9i	0.0542801	−	0.307838i
$509$	182042.	−	216949.i	0.702645	−	0.837380i	−0.290178	−	0.956973i	$-0.593715\pi$
$509$	182042.	−	216949.i	0.702645	−	0.837380i	0.992823	+	0.119593i	$0.0381590\pi$
$510$		0			0
$511$	185427.	+	67489.8i	0.710118	+	0.258462i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	−190709.			−0.721848
$515$	−31440.0	+	86380.6i	−0.118541	+	0.325688i
$516$		0			0
$517$	−125615.	−	105403.i	−0.469958	−	0.394342i
$518$	−329162.	−	58040.1i	−1.22673	−	0.216306i
$519$		0			0
$520$	154336.	−	129504.i	0.570771	−	0.478934i
$521$	−181454.	+	104763.i	−0.668485	+	0.385950i	−0.795502	−	0.605950i	$-0.792793\pi$
$521$	−181454.	+	104763.i	−0.668485	+	0.385950i	0.127017	+	0.991901i	$0.459460\pi$
$522$		0			0
$523$	6455.38	−	11181.0i	0.0236003	−	0.0408770i	−0.853984	−	0.520299i	$-0.825820\pi$
$523$	6455.38	−	11181.0i	0.0236003	−	0.0408770i	0.877584	+	0.479422i	$0.159154\pi$
$524$	63095.9	−	11125.5i	0.229794	−	0.0405189i
$525$		0			0
$526$	−213530.	+	77718.7i	−0.771770	+	0.280901i
$527$	−107595.	−	295615.i	−0.387410	−	1.06440i
$528$		0			0
$529$	19156.9	+	108644.i	0.0684563	+	0.388235i
$530$	−154549.	−	89228.9i	−0.550192	−	0.317654i
$531$		0			0
$532$	−65818.9	−	114002.i	−0.232556	−	0.402799i
$533$	268732.	+	320262.i	0.945943	+	1.12733i
$534$		0			0
$535$	85375.2	−	484187.i	0.298280	−	1.69163i
$536$	115987.	−	138228.i	0.403719	−	0.481134i
$537$		0			0
$538$	−190678.	−	69401.1i	−0.658773	−	0.239774i
$539$			213649.i			0.735400i
$540$		0			0
$541$	−378251.			−1.29237			−0.646183	−	0.763182i	$-0.723636\pi$
$541$	−378251.			−1.29237			−0.646183	+	0.763182i	$0.723636\pi$
$542$	−54549.2	+	149873.i	−0.185691	+	0.510181i
$543$		0			0
$544$	−43506.2	−	36506.0i	−0.147012	−	0.123358i
$545$	287225.	+	50645.4i	0.967005	+	0.170509i
$546$		0			0
$547$	−138792.	+	116461.i	−0.463864	+	0.389228i	−0.844550	−	0.535476i	$-0.820132\pi$
$547$	−138792.	+	116461.i	−0.463864	+	0.389228i	0.380686	+	0.924704i	$0.375688\pi$
$548$	178732.	−	103191.i	0.595171	−	0.343622i
$549$		0			0
$550$	−36704.3	+	63573.8i	−0.121337	+	0.210161i
$551$	−19316.2	+	3405.98i	−0.0636238	+	0.0112186i
$552$		0			0
$553$	52341.0	−	19050.6i	0.171156	−	0.0622956i
$554$	−48891.2	−	134327.i	−0.159298	−	0.437668i
$555$		0			0
$556$	21710.0	+	123124.i	0.0702280	+	0.398283i
$557$	−147198.	−	84985.1i	−0.474453	−	0.273925i	0.243649	−	0.969863i	$-0.421655\pi$
$557$	−147198.	−	84985.1i	−0.474453	−	0.273925i	−0.718102	+	0.695938i	$0.754989\pi$
$558$		0			0
$559$	−324310.	−	561721.i	−1.03785	−	1.79762i
$560$	−116060.	−	138315.i	−0.370089	−	0.441055i
$561$		0			0
$562$	−29146.3	+	165297.i	−0.0922807	+	0.523350i
$563$	−71855.5	+	85634.1i	−0.226696	+	0.270165i	−0.867388	−	0.497632i	$-0.834203\pi$
$563$	−71855.5	+	85634.1i	−0.226696	+	0.270165i	0.640692	+	0.767798i	$0.278647\pi$
$564$		0			0
$565$	233974.	+	85159.6i	0.732944	+	0.266770i
$566$			57331.4i			0.178961i
$567$		0			0
$568$	81615.5			0.252974
$569$	168487.	−	462914.i	0.520405	−	1.42980i	−0.349666	−	0.936874i	$-0.613705\pi$
$569$	168487.	−	462914.i	0.520405	−	1.42980i	0.870071	−	0.492926i	$-0.164073\pi$
$570$		0			0
$571$	304126.	+	255192.i	0.932783	+	0.782698i	0.976315	−	0.216354i	$-0.0694165\pi$
$571$	304126.	+	255192.i	0.932783	+	0.782698i	−0.0435317	+	0.999052i	$0.513861\pi$
$572$	−99008.1	−	17457.8i	−0.302607	−	0.0533577i
$573$		0			0
$574$	287016.	−	240835.i	0.871129	−	0.730964i
$575$	−192186.	+	110958.i	−0.581280	+	0.335602i
$576$		0			0
$577$	−273003.	+	472856.i	−0.820004	+	1.42029i	0.0856737	+	0.996323i	$0.472696\pi$
$577$	−273003.	+	472856.i	−0.820004	+	1.42029i	−0.905678	+	0.423966i	$0.860638\pi$
$578$	41538.8	−	7324.41i	0.124336	−	0.0219239i
$579$		0			0
$580$	−25280.8	+	9201.47i	−0.0751511	+	0.0273528i
$581$	28749.9	+	78989.8i	0.0851696	+	0.234002i
$582$		0			0
$583$	15463.6	+	87698.4i	0.0454960	+	0.258021i
$584$	46761.8	+	26997.9i	0.137109	+	0.0791598i
$585$		0			0
$586$	181869.	+	315006.i	0.529618	+	0.917325i
$587$	88176.9	+	105085.i	0.255905	+	0.304976i	0.878666	−	0.477436i	$-0.158434\pi$
$587$	88176.9	+	105085.i	0.255905	+	0.304976i	−0.622762	+	0.782412i	$0.713989\pi$
$588$		0			0
$589$	34647.2	−	196494.i	0.0998706	−	0.566394i
$590$	235374.	−	280508.i	0.676168	−	0.805826i
$591$		0			0
$592$	−85944.5	−	31281.2i	−0.245231	−	0.0892566i
$593$			352773.i			1.00320i	0.865101	+	0.501598i	$0.167254\pi$
$593$			352773.i			1.00320i	−0.865101	+	0.501598i	$0.832746\pi$
$594$		0			0
$595$	885129.			2.50019
$596$	−56678.9	+	155724.i	−0.159562	+	0.438393i
$597$		0			0
$598$	−232818.	−	195357.i	−0.651049	−	0.546295i
$599$	569370.	+	100395.i	1.58687	+	0.279808i	0.896296	−	0.443456i	$-0.146248\pi$
$599$	569370.	+	100395.i	1.58687	+	0.279808i	0.690572	+	0.723263i	$0.257359\pi$
$600$		0			0
$601$	−141992.	+	119145.i	−0.393111	+	0.329859i	−0.817824	−	0.575469i	$-0.804820\pi$
$601$	−141992.	+	119145.i	−0.393111	+	0.329859i	0.424713	+	0.905328i	$0.360375\pi$
$602$	−503409.	+	290643.i	−1.38908	+	0.801987i
$603$		0			0
$604$	133285.	−	230856.i	0.365348	−	0.632802i
$605$	−414016.	+	73002.1i	−1.13111	+	0.199446i
$606$		0			0
$607$	279219.	−	101627.i	0.757822	−	0.275824i	0.0659284	−	0.997824i	$-0.478999\pi$
$607$	279219.	−	101627.i	0.757822	−	0.275824i	0.691893	+	0.722000i	$0.256777\pi$
$608$	−12319.9	−	33848.6i	−0.0333272	−	0.0915658i
$609$		0			0
$610$	−97675.8	−	553947.i	−0.262499	−	1.48870i
$611$	−769659.	−	444363.i	−2.06165	−	1.19030i
$612$		0			0
$613$	−176079.	−	304978.i	−0.468584	−	0.811612i	0.530771	−	0.847515i	$-0.321902\pi$
$613$	−176079.	−	304978.i	−0.468584	−	0.811612i	−0.999355	+	0.0359037i	$0.988569\pi$
$614$	−24535.3	−	29240.1i	−0.0650811	−	0.0775607i
$615$		0			0
$616$	−15645.5	+	88730.1i	−0.0412314	+	0.233835i
$617$	−18861.9	+	22478.8i	−0.0495469	+	0.0590477i	−0.790249	−	0.612786i	$-0.790049\pi$
$617$	−18861.9	+	22478.8i	−0.0495469	+	0.0590477i	0.740702	+	0.671834i	$0.234493\pi$
$618$		0			0
$619$	242949.	+	88426.4i	0.634066	+	0.230781i	0.639000	−	0.769207i	$-0.279348\pi$
$619$	242949.	+	88426.4i	0.634066	+	0.230781i	−0.00493391	+	0.999988i	$0.501571\pi$
$620$		−	273673.i		−	0.711949i
$621$		0			0
$622$	405506.			1.04813
$623$	186989.	−	513748.i	0.481770	−	1.32365i
$624$		0			0
$625$	−334750.	−	280888.i	−0.856959	−	0.719074i
$626$	194561.	+	34306.4i	0.496487	+	0.0875440i
$627$		0			0
$628$	9405.59	−	7892.23i	0.0238488	−	0.0200115i
$629$	388289.	−	224179.i	0.981417	−	0.566621i
$630$		0			0
$631$	327446.	−	567153.i	0.822395	−	1.42443i	−0.0814983	−	0.996673i	$-0.525971\pi$
$631$	327446.	−	567153.i	0.822395	−	1.42443i	0.903894	−	0.427757i	$-0.140696\pi$
$632$	15010.0	−	2646.67i	0.0375792	−	0.00662623i
$633$		0			0
$634$	365070.	−	132875.i	0.908233	−	0.330570i
$635$	117661.	+	323272.i	0.291801	+	0.801716i
$636$		0			0
$637$	201073.	+	1.14034e6i	0.495535	+	2.81032i
$638$	11626.3	+	6712.44i	0.0285627	+	0.0164907i
$639$		0			0
$640$	−24703.5	−	42787.8i	−0.0603114	−	0.104462i
$641$	−68734.9	−	81915.1i	−0.167287	−	0.199365i	0.675888	−	0.737005i	$-0.263760\pi$
$641$	−68734.9	−	81915.1i	−0.167287	−	0.199365i	−0.843174	+	0.537640i	$0.819316\pi$
$642$		0			0
$643$	−74157.1	+	420566.i	−0.179362	+	1.01721i	0.753625	+	0.657304i	$0.228303\pi$
$643$	−74157.1	+	420566.i	−0.179362	+	1.01721i	−0.932987	+	0.359909i	$0.882808\pi$
$644$	−175077.	+	208649.i	−0.422142	+	0.503089i
$645$		0			0
$646$	165933.	+	60394.7i	0.397620	+	0.144722i
$647$			44983.4i			0.107459i	0.998556	+	0.0537296i	$0.0171109\pi$
$647$			44983.4i			0.107459i	−0.998556	+	0.0537296i	$0.982889\pi$
$648$		0			0
$649$	−182724.			−0.433817
$650$	−136076.	+	373865.i	−0.322073	+	0.884887i
$651$		0			0
$652$	10195.0	+	8554.63i	0.0239824	+	0.0201236i
$653$	151331.	+	26683.8i	0.354897	+	0.0625779i	0.348255	−	0.937400i	$-0.386774\pi$
$653$	151331.	+	26683.8i	0.354897	+	0.0625779i	0.00664253	+	0.999978i	$0.497886\pi$
$654$		0			0
$655$	−209309.	+	175631.i	−0.487871	+	0.409372i
$656$	88788.6	−	51262.1i	0.206324	−	0.119121i
$657$		0			0
$658$	−398234.	+	689761.i	−0.919785	+	1.59311i
$659$	−532395.	+	93875.7i	−1.22592	+	0.216163i	−0.748874	−	0.662713i	$-0.769405\pi$
$659$	−532395.	+	93875.7i	−1.22592	+	0.216163i	−0.477050	+	0.878876i	$0.658294\pi$
$660$		0			0
$661$	−193876.	+	70565.1i	−0.443733	+	0.161505i	−0.554217	−	0.832372i	$-0.686982\pi$
$661$	−193876.	+	70565.1i	−0.443733	+	0.161505i	0.110484	+	0.993878i	$0.464760\pi$
$662$	12966.4	+	35624.8i	0.0295871	+	0.0812899i
$663$		0			0
$664$	3994.20	+	22652.2i	0.00905928	+	0.0513777i
$665$	486178.	+	280695.i	1.09939	+	0.634733i
$666$		0			0
$667$	20291.9	+	35146.6i	0.0456112	+	0.0790009i
$668$	159074.	+	189577.i	0.356488	+	0.424846i
$669$		0			0
$670$	−133628.	+	757839.i	−0.297678	+	1.68821i
$671$	−180422.	+	215018.i	−0.400723	+	0.477563i
$672$		0			0
$673$	−313357.	−	114053.i	−0.691846	−	0.251812i	−0.0279208	−	0.999610i	$-0.508889\pi$
$673$	−313357.	−	114053.i	−0.691846	−	0.251812i	−0.663926	+	0.747799i	$0.731111\pi$
$674$		−	613057.i		−	1.34953i
$675$		0			0
$676$	−316392.			−0.692360
$677$	−28454.7	+	78178.5i	−0.0620835	+	0.170573i	−0.966856	−	0.255322i	$-0.917818\pi$
$677$	−28454.7	+	78178.5i	−0.0620835	+	0.170573i	0.904773	+	0.425895i	$0.140041\pi$
$678$		0			0
$679$	186138.	+	156189.i	0.403735	+	0.338774i
$680$	238524.	+	42058.3i	0.515840	+	0.0909565i
$681$		0			0
$682$	−104614.	+	87781.8i	−0.224917	+	0.188728i
$683$	−209637.	+	121034.i	−0.449393	+	0.259457i	−0.707574	−	0.706640i	$-0.750210\pi$
$683$	−209637.	+	121034.i	−0.449393	+	0.259457i	0.258181	+	0.966097i	$0.416877\pi$
$684$		0			0
$685$	−440075.	+	762232.i	−0.937876	+	1.62445i
$686$	468931.	−	82685.1i	0.996461	−	0.175703i
$687$		0			0
$688$	−149469.	+	54402.2i	−0.315772	+	0.114932i
$689$	165072.	+	453532.i	0.347724	+	0.955365i
$690$		0			0
$691$	−127434.	−	722714.i	−0.266888	−	1.51360i	−0.763604	−	0.645685i	$-0.776572\pi$
$691$	−127434.	−	722714.i	−0.266888	−	1.51360i	0.496716	−	0.867913i	$-0.334539\pi$
$692$	168444.	+	97251.4i	0.351758	+	0.203088i
$693$		0			0
$694$	−61730.2	−	106920.i	−0.128168	−	0.221993i
$695$	−342722.	−	408440.i	−0.709532	−	0.845587i
$696$		0			0
$697$	−87274.8	+	494960.i	−0.179648	+	1.01884i
$698$	−299344.	+	356744.i	−0.614412	+	0.732228i
$699$		0			0
$700$	335054.	+	121950.i	0.683784	+	0.248877i
$701$		−	140875.i		−	0.286680i	−0.989674	−	0.143340i	$-0.954216\pi$
$701$		−	140875.i		−	0.286680i	0.989674	−	0.143340i	$-0.0457842\pi$
$702$		0			0
$703$	284369.			0.575402
$704$	−8432.29	+	23167.5i	−0.0170138	+	0.0467449i
$705$		0			0
$706$	−61471.3	−	51580.5i	−0.123328	−	0.103485i
$707$	−455165.	−	80257.9i	−0.910605	−	0.160564i
$708$		0			0
$709$	239465.	−	200935.i	0.476375	−	0.399726i	−0.372739	−	0.927936i	$-0.621581\pi$
$709$	239465.	−	200935.i	0.476375	−	0.399726i	0.849114	+	0.528210i	$0.177137\pi$
$710$	−301431.	+	174031.i	−0.597958	+	0.345231i
$711$		0			0
$712$	74801.2	−	129559.i	0.147553	−	0.255570i
$713$	−406566.	+	71688.6i	−0.799746	+	0.141017i
$714$		0			0
$715$	402892.	−	146641.i	0.788092	−	0.286842i
$716$	−7004.03	−	19243.4i	−0.0136622	−	0.0375367i
$717$		0			0
$718$	38377.0	+	217647.i	0.0744427	+	0.422185i
$719$	413454.	+	238708.i	0.799778	+	0.461752i	0.843394	−	0.537296i	$-0.180554\pi$
$719$	413454.	+	238708.i	0.799778	+	0.461752i	−0.0436155	+	0.999048i	$0.513888\pi$
$720$		0			0
$721$	−111400.	−	192951.i	−0.214297	−	0.371174i
$722$	−164944.	−	196572.i	−0.316418	−	0.377092i
$723$		0			0
$724$	75910.0	−	430507.i	0.144818	−	0.821303i
$725$	34149.7	−	40698.1i	0.0649698	−	0.0774280i
$726$		0			0
$727$	−429800.	−	156434.i	−0.813201	−	0.295981i	−0.0982555	−	0.995161i	$-0.531326\pi$
$727$	−429800.	−	156434.i	−0.813201	−	0.295981i	−0.714945	+	0.699180i	$0.753548\pi$
$728$			488316.i			0.921379i
$729$		0			0
$730$	−230274.			−0.432115
$731$	266691.	−	732728.i	0.499084	−	1.37122i
$732$		0			0
$733$	529216.	+	444065.i	0.984975	+	0.826492i	0.984832	−	0.173508i	$-0.0555102\pi$
$733$	529216.	+	444065.i	0.984975	+	0.826492i	0.000142490		1.00000i	$0.499955\pi$
$734$	−359557.	−	63399.6i	−0.667383	−	0.117678i
$735$		0			0
$736$	−57094.0	+	47907.6i	−0.105399	+	0.0884400i
$737$	332553.	−	192000.i	0.612246	−	0.353481i
$738$		0			0
$739$	−1943.66	+	3366.53i	−0.00355904	+	0.00616443i	−0.867799	−	0.496915i	$-0.834466\pi$
$739$	−1943.66	+	3366.53i	−0.00355904	+	0.00616443i	0.864240	+	0.503079i	$0.167800\pi$
$740$	384121.	−	67730.9i	0.701462	−	0.123687i
$741$		0			0
$742$	406451.	−	147936.i	0.738245	−	0.268699i
$743$	−267134.	−	733946.i	−0.483896	−	1.32949i	−0.906127	−	0.423006i	$-0.860975\pi$
$743$	−267134.	−	733946.i	−0.483896	−	1.32949i	0.422231	−	0.906488i	$-0.361247\pi$
$744$		0			0
$745$	−122723.	−	695994.i	−0.221112	−	1.25399i
$746$	206536.	+	119244.i	0.371124	+	0.214268i
$747$		0			0
$748$	−60430.4	−	104669.i	−0.108007	−	0.187074i
$749$	765977.	+	912856.i	1.36538	+	1.62719i
$750$		0			0
$751$	−24144.2	+	136928.i	−0.0428087	+	0.242780i	−0.998702	−	0.0509337i	$-0.983780\pi$
$751$	−24144.2	+	136928.i	−0.0428087	+	0.242780i	0.955893	+	0.293714i	$0.0948914\pi$
$752$	−140091.	+	166954.i	−0.247727	+	0.295230i
$753$		0			0
$754$	68371.9	+	24885.3i	0.120264	+	0.0437724i
$755$			1.13683e6i			1.99435i
$756$		0			0
$757$	365800.			0.638339			0.319170	−	0.947698i	$-0.396596\pi$
$757$	365800.			0.638339			0.319170	+	0.947698i	$0.396596\pi$
$758$	−62759.9	+	172431.i	−0.109231	+	0.300108i
$759$		0			0
$760$	117677.	+	98743.0i	0.203735	+	0.170954i
$761$	−701026.	−	123610.i	−1.21050	−	0.213444i	−0.468267	−	0.883587i	$-0.655122\pi$
$761$	−701026.	−	123610.i	−1.21050	−	0.213444i	−0.742232	+	0.670143i	$0.766233\pi$
$762$		0			0
$763$	−541515.	+	454385.i	−0.930168	+	0.780504i
$764$	418669.	−	241719.i	0.717272	−	0.414117i
$765$		0			0
$766$	−93718.8	+	162326.i	−0.159724	+	0.276649i
$767$	−975279.	+	171968.i	−1.65782	+	0.292319i
$768$		0			0
$769$	355029.	−	129220.i	0.600358	−	0.218513i	−0.0239208	−	0.999714i	$-0.507615\pi$
$769$	355029.	−	129220.i	0.600358	−	0.218513i	0.624279	+	0.781201i	$0.285393\pi$
$770$	−131418.	−	361068.i	−0.221653	−	0.608987i
$771$		0			0
$772$	−66187.2	−	375366.i	−0.111055	−	0.629826i
$773$	−610512.	−	352480.i	−1.02173	−	0.589895i	−0.107124	−	0.994246i	$-0.534164\pi$
$773$	−610512.	−	352480.i	−1.02173	−	0.589895i	−0.914604	+	0.404350i	$0.867498\pi$
$774$		0			0
$775$	270219.	+	468034.i	0.449897	+	0.779244i
$776$	42738.9	+	50934.3i	0.0709741	+	0.0845837i
$777$		0			0
$778$	55940.6	−	317255.i	0.0924204	−	0.524142i
$779$	−204901.	+	244191.i	−0.337652	+	0.402398i
$780$		0			0
$781$	163210.	+	59403.7i	0.267575	+	0.0973893i
$782$		−	365366.i		−	0.597469i
$783$		0			0
$784$	283960.			0.461982
$785$	−17908.9	+	49204.2i	−0.0290622	+	0.0798478i
$786$		0			0
$787$	−502128.	−	421336.i	−0.810709	−	0.680266i	0.140068	−	0.990142i	$-0.455268\pi$
$787$	−502128.	−	421336.i	−0.810709	−	0.680266i	−0.950777	+	0.309876i	$0.899712\pi$
$788$	−184028.	−	32449.0i	−0.296367	−	0.0522576i
$789$		0			0
$790$	−49793.0	+	41781.3i	−0.0797837	+	0.0669465i
$791$	−522636.	+	301744.i	−0.835307	+	0.482265i
$792$		0			0
$793$	−760629.	+	1.31745e6i	−1.20956	+	2.09502i
$794$	−83074.7	+	14648.3i	−0.131773	+	0.0232352i
$795$		0			0
$796$	52110.8	−	18966.8i	0.0822434	−	0.0299342i
$797$	−268671.	−	738167.i	−0.422964	−	1.16208i	−0.950002	−	0.312243i	$-0.898920\pi$
$797$	−268671.	−	738167.i	−0.422964	−	1.16208i	0.527038	−	0.849842i	$-0.323303\pi$
$798$		0			0
$799$	−185526.	−	1.05217e6i	−0.290610	−	1.64813i
$800$	84495.6	+	48783.6i	0.132024	+	0.0762243i
$801$		0			0
$802$	265832.	+	460434.i	0.413293	+	0.715845i
$803$	73861.3	+	88024.5i	0.114548	+	0.136512i
$804$		0			0
$805$	201705.	−	1.14393e6i	0.311261	−	1.76525i
$806$	−475758.	+	566986.i	−0.732345	+	0.872775i
$807$		0			0
$808$	−118844.	−	43255.7i	−0.182035	−	0.0662553i
$809$		−	305958.i		−	0.467481i	−0.972299	−	0.233741i	$-0.924903\pi$
$809$		−	305958.i		−	0.467481i	0.972299	−	0.233741i	$-0.0750966\pi$
$810$		0			0
$811$	97769.0			0.148648			0.0743240	−	0.997234i	$-0.476320\pi$
$811$	97769.0			0.148648			0.0743240	+	0.997234i	$0.476320\pi$
$812$	22302.0	−	61274.2i	0.0338245	−	0.0929321i
$813$		0			0
$814$	−149099.	−	125109.i	−0.225023	−	0.188816i
$815$	−55894.6	−	9855.72i	−0.0841500	−	0.0148379i
$816$		0			0
$817$	378851.	−	317894.i	0.567577	−	0.476253i
$818$	544131.	−	314154.i	0.813199	−	0.469500i
$819$		0			0
$820$	−218615.	+	378653.i	−0.325127	+	0.563136i
$821$	490652.	−	86515.2i	0.727926	−	0.128353i	0.202609	−	0.979260i	$-0.435058\pi$
$821$	490652.	−	86515.2i	0.727926	−	0.128353i	0.525317	+	0.850907i	$0.323947\pi$
$822$		0			0
$823$	−518419.	+	188689.i	−0.765388	+	0.278578i	−0.695066	−	0.718946i	$-0.744625\pi$
$823$	−518419.	+	188689.i	−0.765388	+	0.278578i	−0.0703219	+	0.997524i	$0.522403\pi$
$824$	−20851.8	−	57289.8i	−0.0307106	−	0.0843767i
$825$		0			0
$826$	154116.	+	874036.i	0.225885	+	1.28106i
$827$	532755.	+	307586.i	0.778963	+	0.449734i	0.836063	−	0.548634i	$-0.184852\pi$
$827$	532755.	+	307586.i	0.778963	+	0.449734i	−0.0570999	+	0.998368i	$0.518185\pi$
$828$		0			0
$829$	−521305.	−	902927.i	−0.758547	−	1.31384i	−0.943591	−	0.331112i	$-0.892576\pi$
$829$	−521305.	−	902927.i	−0.758547	−	1.31384i	0.185044	−	0.982730i	$-0.440757\pi$
$830$	−63053.8	−	75144.6i	−0.0915282	−	0.109079i
$831$		0			0
$832$	−23203.1	+	131591.i	−0.0335196	+	0.190099i
$833$	−894781.	+	1.06636e6i	−1.28952	+	1.53679i
$834$		0			0
$835$	−991747.	−	360966.i	−1.42242	−	0.517718i
$836$		−	76655.6i		−	0.109681i
$837$		0			0
$838$	908952.			1.29435
$839$	151839.	−	417173.i	0.215704	−	0.592642i	−0.783897	−	0.620891i	$-0.786771\pi$
$839$	151839.	−	417173.i	0.215704	−	0.592642i	0.999601	+	0.0282489i	$0.00899311\pi$
$840$		0			0
$841$	534366.	+	448386.i	0.755521	+	0.633958i
$842$	888959.	+	156747.i	1.25388	+	0.221094i
$843$		0			0
$844$	26288.0	−	22058.2i	0.0369039	−	0.0309660i
$845$	1.16853e6	−	674651.i	1.63654	−	0.944856i
$846$		0			0
$847$	509474.	−	882434.i	0.710158	−	1.23003i
$848$	116560.	−	20552.6i	0.162090	−	0.0285808i
$849$		0			0
$850$	−449450.	+	163586.i	−0.622076	+	0.226417i
$851$	−201241.	−	552904.i	−0.277879	−	0.763468i
$852$		0			0
$853$	74628.3	+	423238.i	0.102566	+	0.581683i	0.992164	+	0.124939i	$0.0398735\pi$
$853$	74628.3	+	423238.i	0.102566	+	0.581683i	−0.889598	+	0.456744i	$0.849015\pi$
$854$	1.18068e6	+	681669.i	1.61889	+	0.934668i
$855$		0			0
$856$	163039.	+	282393.i	0.222508	+	0.385395i
$857$	−21433.0	−	25542.9i	−0.0291825	−	0.0347783i	0.751256	−	0.660011i	$-0.229448\pi$
$857$	−21433.0	−	25542.9i	−0.0291825	−	0.0347783i	−0.780438	+	0.625233i	$0.785004\pi$
$858$		0			0
$859$	−40739.5	+	231045.i	−0.0552115	+	0.313120i	−0.999889	−	0.0148798i	$-0.995263\pi$
$859$	−40739.5	+	231045.i	−0.0552115	+	0.313120i	0.944678	+	0.328000i	$0.106375\pi$
$860$	436030.	−	519640.i	0.589548	−	0.702596i
$861$		0			0
$862$	−604599.	−	220056.i	−0.813679	−	0.296155i
$863$		−	978275.i		−	1.31353i	−0.754096	−	0.656764i	$-0.771925\pi$
$863$		−	978275.i		−	1.31353i	0.754096	−	0.656764i	$-0.228075\pi$
$864$		0			0
$865$	−829488.			−1.10861
$866$	139305.	−	382736.i	0.185750	−	0.510345i
$867$		0			0
$868$	508127.	+	426369.i	0.674424	+	0.565909i
$869$	31942.6	+	5632.35i	0.0422991	+	0.00745847i
$870$		0			0
$871$	1.59429e6	−	1.33776e6i	2.10150	−	1.76337i
$872$	−167518.	+	96716.6i	−0.220307	+	0.127194i
$873$		0			0
$874$	115866.	−	200686.i	0.151682	−	0.262721i
$875$	238973.	−	42137.4i	0.312128	−	0.0550366i
$876$		0			0
$877$	747588.	−	272100.i	0.971993	−	0.353777i	0.193271	−	0.981145i	$-0.438090\pi$
$877$	747588.	−	272100.i	0.971993	−	0.353777i	0.778722	+	0.627369i	$0.215868\pi$
$878$	171806.	+	472033.i	0.222869	+	0.612327i
$879$		0			0
$880$	−18257.8	−	103545.i	−0.0235767	−	0.133710i
$881$	174297.	+	100630.i	0.224563	+	0.129651i	0.608061	−	0.793890i	$-0.291948\pi$
$881$	174297.	+	100630.i	0.224563	+	0.129651i	−0.383499	+	0.923541i	$0.625281\pi$
$882$		0			0
$883$	−643571.	−	1.11470e6i	−0.825420	−	1.42967i	−0.901598	−	0.432576i	$-0.857605\pi$
$883$	−643571.	−	1.11470e6i	−0.825420	−	1.42967i	0.0761772	−	0.997094i	$-0.475729\pi$
$884$	−421051.	−	501789.i	−0.538803	−	0.642121i
$885$		0			0
$886$	−102647.	+	582138.i	−0.130761	+	0.741581i
$887$	509641.	−	607366.i	0.647764	−	0.771975i	−0.337811	−	0.941214i	$-0.609686\pi$
$887$	509641.	−	607366.i	0.647764	−	0.771975i	0.985575	+	0.169239i	$0.0541309\pi$
$888$		0			0
$889$	−783528.	−	285181.i	−0.991405	−	0.360842i
$890$			638003.i			0.805458i
$891$		0			0
$892$	121516.			0.152723
$893$	231763.	−	636763.i	0.290630	−	0.798500i
$894$		0			0
$895$	66901.3	+	56136.8i	0.0835196	+	0.0700813i
$896$	117931.	+	20794.4i	0.146896	+	0.0259018i
$897$		0			0
$898$	−133996.	+	112436.i	−0.166165	+	0.139429i
$899$	85593.4	−	49417.3i	0.105906	−	0.0611449i
$900$		0			0
$901$	−290107.	+	502481.i	−0.357363	+	0.618970i
$902$	214866.	−	37886.6i	0.264091	−	0.0465664i
$903$		0			0
$904$	−155177.	+	56480.0i	−0.189885	+	0.0691127i
$905$	637624.	+	1.75186e6i	0.778516	+	2.13896i
$906$		0			0
$907$	−44048.9	−	249814.i	−0.0535452	−	0.303670i	0.946260	−	0.323407i	$-0.104828\pi$
$907$	−44048.9	−	249814.i	−0.0535452	−	0.303670i	−0.999805	+	0.0197370i	$0.993717\pi$
$908$	−567610.	−	327710.i	−0.688459	−	0.397482i
$909$		0			0
$910$	−1.04125e6	−	1.80350e6i	−1.25740	−	2.17787i
$911$	−810462.	−	965871.i	−0.976553	−	1.16381i	−0.986484	−	0.163860i	$-0.947605\pi$
$911$	−810462.	−	965871.i	−0.976553	−	1.16381i	0.00993026	−	0.999951i	$-0.496839\pi$
$912$		0			0
$913$	−8499.99	+	48205.9i	−0.0101971	+	0.0578307i
$914$	400542.	−	477347.i	0.479463	−	0.571402i
$915$		0			0
$916$	−266190.	−	96885.2i	−0.317249	−	0.115469i
$917$		−	662247.i		−	0.787556i
$918$		0			0
$919$	1.32867e6			1.57321			0.786604	−	0.617458i	$-0.211838\pi$
$919$	1.32867e6			1.57321			0.786604	+	0.617458i	$0.211838\pi$
$920$	108711.	−	298680.i	0.128439	−	0.352883i
$921$		0			0
$922$	673550.	+	565175.i	0.792333	+	0.664847i
$923$	927032.	+	163461.i	1.08816	+	0.191871i
$924$		0			0
$925$	−590044.	+	495106.i	−0.689606	+	0.578648i
$926$	337738.	−	194993.i	0.393874	−	0.227403i
$927$		0			0
$928$	8921.47	−	15452.4i	0.0103595	−	0.0179432i
$929$	1.21080e6	−	213497.i	1.40295	−	0.247378i	0.579596	−	0.814904i	$-0.303210\pi$
$929$	1.21080e6	−	213497.i	1.40295	−	0.247378i	0.823355	+	0.567526i	$0.192099\pi$
$930$		0			0
$931$	−829647.	+	301967.i	−0.957180	+	0.348385i
$932$	127384.	+	349984.i	0.146650	+	0.402918i
$933$		0			0
$934$	−18828.5	−	106782.i	−0.0215835	−	0.122406i
$935$	446376.	+	257715.i	0.510596	+	0.294793i
$936$		0			0
$937$	135753.	+	235132.i	0.154622	+	0.267813i	0.932921	−	0.360080i	$-0.117251\pi$
$937$	135753.	+	235132.i	0.154622	+	0.267813i	−0.778299	+	0.627894i	$0.783917\pi$
$938$	−1.19889e6	−	1.42878e6i	−1.36262	−	1.62390i
$939$		0			0
$940$	161397.	−	915330.i	0.182659	−	1.03591i
$941$	−1.12104e6	+	1.33600e6i	−1.26602	+	1.50879i	−0.499923	+	0.866070i	$0.666639\pi$
$941$	−1.12104e6	+	1.33600e6i	−1.26602	+	1.50879i	−0.766101	+	0.642720i	$0.777806\pi$
$942$		0			0
$943$	619789.	+	225585.i	0.696981	+	0.253680i
$944$			242858.i			0.272526i
$945$		0			0
$946$	−338496.			−0.378243
$947$	−328755.	+	903246.i	−0.366583	+	1.00718i	0.610069	+	0.792348i	$0.291142\pi$
$947$	−328755.	+	903246.i	−0.366583	+	1.00718i	−0.976652	+	0.214829i	$0.931081\pi$
$948$		0			0
$949$	477073.	+	400312.i	0.529727	+	0.444494i
$950$	−298748.	−	52677.3i	−0.331023	−	0.0583682i
$951$		0			0
$952$	−449699.	+	377342.i	−0.496190	+	0.416353i
$953$	116399.	−	67202.9i	0.128163	−	0.0739950i	−0.434548	−	0.900649i	$-0.643092\pi$
$953$	116399.	−	67202.9i	0.128163	−	0.0739950i	0.562711	+	0.826654i	$0.309758\pi$
$954$		0			0
$955$	−1.03085e6	+	1.78548e6i	−1.13028	+	1.95771i
$956$	−106387.	+	18759.0i	−0.116406	+	0.0205255i
$957$		0			0
$958$	12940.2	−	4709.86i	0.0140997	−	0.00513188i
$959$	−729617.	−	2.00461e6i	−0.793337	−	2.17967i
$960$		0			0
$961$	14217.0	+	80628.4i	0.0153943	+	0.0873054i
$962$	−913552.	−	527439.i	−0.987150	−	0.569931i
$963$		0			0
$964$	220572.	+	382043.i	0.237354	+	0.411110i
$965$	1.04485e6	+	1.24521e6i	1.12202	+	1.33717i
$966$		0			0
$967$	180384.	−	1.02301e6i	0.192906	−	1.09402i	−0.722463	−	0.691409i	$-0.756990\pi$
$967$	180384.	−	1.02301e6i	0.192906	−	1.09402i	0.915369	−	0.402615i	$-0.131899\pi$
$968$	179223.	−	213590.i	0.191268	−	0.227945i
$969$		0			0
$970$	−266456.	−	96982.2i	−0.283193	−	0.103074i
$971$			500363.i			0.530697i	0.964153	+	0.265349i	$0.0854870\pi$
$971$			500363.i			0.530697i	−0.964153	+	0.265349i	$0.914513\pi$
$972$		0			0
$973$	1.29229e6			1.36501
$974$	−230601.	+	633570.i	−0.243076	+	0.667847i
$975$		0			0
$976$	285780.	+	239798.i	0.300007	+	0.251736i
$977$	−116833.	−	20600.8i	−0.122398	−	0.0215822i	0.112113	−	0.993695i	$-0.464238\pi$
$977$	−116833.	−	20600.8i	−0.122398	−	0.0215822i	−0.234512	+	0.972113i	$0.575349\pi$
$978$		0			0
$979$	243883.	−	204642.i	0.254458	−	0.213516i
$980$	−1.04875e6	+	605496.i	−1.09199	+	0.630463i
$981$		0			0
$982$	200001.	−	346411.i	0.207400	−	0.359227i
$983$	1.05555e6	−	186121.i	1.09237	−	0.192614i	0.401691	−	0.915775i	$-0.368423\pi$
$983$	1.05555e6	−	186121.i	1.09237	−	0.192614i	0.690680	+	0.723161i	$0.257311\pi$
$984$		0			0
$985$	748861.	−	272563.i	0.771843	−	0.280928i
$986$	29916.5	+	82194.8i	0.0307720	+	0.0845455i
$987$		0			0
$988$	−72143.2	−	409144.i	−0.0739063	−	0.419144i
$989$	−886190.	−	511642.i	−0.906013	−	0.523087i
$990$		0			0
$991$	490464.	+	849508.i	0.499413	+	0.865008i	1.00000		0.000678131i	$-0.000215856\pi$
$991$	490464.	+	849508.i	0.499413	+	0.865008i	−0.500587	+	0.865686i	$0.666883\pi$
$992$	116670.	+	139042.i	0.118560	+	0.141294i
$993$		0			0
$994$	146492.	−	830797.i	0.148266	−	0.840857i
$995$	−152017.	+	181167.i	−0.153549	+	0.182993i
$996$		0			0
$997$	327927.	+	119356.i	0.329904	+	0.120075i	0.501661	−	0.865064i	$-0.332722\pi$
$997$	327927.	+	119356.i	0.329904	+	0.120075i	−0.171758	+	0.985139i	$0.554945\pi$
$998$			1.17203e6i			1.17673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.8		72
3.2	odd	2		54.5.f.a.23.6	✓	72
27.7	even	9		54.5.f.a.47.6	yes	72
27.20	odd	18	inner	162.5.f.a.143.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.6	✓	72	3.2	odd	2
54.5.f.a.47.6	yes	72	27.7	even	9
162.5.f.a.17.8		72	1.1	even	1	trivial
162.5.f.a.143.8		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)

\(f(q)\)	\(=\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(33.5989 + 5.92440i) q^{5} +(-63.3453 + 53.1530i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(33.5989 + 5.92440i) q^{5} +(-63.3453 + 53.1530i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(48.2491 - 83.5699i) q^{10} +(-47.4215 + 8.36169i) q^{11} +(-245.240 + 89.2600i) q^{13} +(79.9940 + 219.782i) q^{14} +(11.1135 + 63.0277i) q^{16} +(-271.708 - 156.871i) q^{17} +(-99.4947 - 172.330i) q^{19} +(-175.441 - 209.083i) q^{20} +(-23.6504 + 134.128i) q^{22} +(-264.654 + 315.403i) q^{23} +(506.482 + 184.345i) q^{25} +738.160i q^{26} +661.532 q^{28} +(33.7127 - 92.6248i) q^{29} +(768.107 + 644.519i) q^{31} +(178.269 + 31.4337i) q^{32} +(-679.784 + 570.407i) q^{34} +(-2443.24 + 1410.60i) q^{35} +(-714.533 + 1237.61i) q^{37} +(-554.276 + 97.7339i) q^{38} +(-725.429 + 264.035i) q^{40} +(-547.896 - 1505.33i) q^{41} +(431.574 + 2447.58i) q^{43} +(333.614 + 192.612i) q^{44} +(582.273 + 1008.53i) q^{46} +(2188.92 + 2608.65i) q^{47} +(770.456 - 4369.47i) q^{49} +(979.921 - 1167.82i) q^{50} +(1961.92 + 714.080i) q^{52} -1849.34i q^{53} -1642.85 q^{55} +(639.952 - 1758.25i) q^{56} +(-213.570 - 179.207i) q^{58} +(3737.00 + 658.935i) q^{59} +(4465.31 - 3746.84i) q^{61} +(2456.09 - 1418.02i) q^{62} +(256.000 - 443.405i) q^{64} +(-8768.61 + 1546.14i) q^{65} +(-7493.63 + 2727.46i) q^{67} +(858.447 + 2358.56i) q^{68} +(1385.64 + 7858.35i) q^{70} +(-3123.69 - 1803.47i) q^{71} +(-1193.15 - 2066.60i) q^{73} +(2598.15 + 3096.36i) q^{74} +(-276.433 + 1567.73i) q^{76} +(2559.48 - 3050.27i) q^{77} +(-632.967 - 230.381i) q^{79} +2183.50i q^{80} -4530.97 q^{82} +(347.677 - 955.235i) q^{83} +(-8199.74 - 6880.40i) q^{85} +(6922.79 + 1220.67i) q^{86} +(834.666 - 700.368i) q^{88} +(-5725.77 + 3305.78i) q^{89} +(10790.4 - 18689.5i) q^{91} +(3243.79 - 571.968i) q^{92} +(9050.93 - 3294.27i) q^{94} +(-2321.97 - 6379.55i) q^{95} +(-510.260 - 2893.83i) q^{97} +(-10868.1 - 6274.69i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 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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