LMFDB - Embedded newform 162.5.f.a.35.6

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			35.6
Character	$\chi$	$=$	162.35
Dual form			162.5.f.a.125.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(12.4033 - 34.0778i) q^{5} +(-2.97171 + 16.8534i) q^{7} +(19.5959 + 11.3137i) q^{8} +O(q^{10})$	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(12.4033 - 34.0778i) q^{5} +(-2.97171 + 16.8534i) q^{7} +(19.5959 + 11.3137i) q^{8} +(51.2862 + 88.8303i) q^{10} +(-35.2977 - 96.9796i) q^{11} +(109.012 - 91.4718i) q^{13} +(-31.1135 - 37.0796i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(-342.265 + 197.607i) q^{17} +(-153.738 + 266.282i) q^{19} +(-285.711 - 50.3786i) q^{20} +(274.300 + 99.8370i) q^{22} +(-724.657 + 127.777i) q^{23} +(-528.676 - 443.612i) q^{25} +402.499i q^{26} +136.907 q^{28} +(627.540 - 747.873i) q^{29} +(-243.722 - 1382.22i) q^{31} +(61.9123 - 170.103i) q^{32} +(194.109 - 1100.85i) q^{34} +(537.467 + 310.307i) q^{35} +(-569.723 - 986.789i) q^{37} +(-297.446 - 817.226i) q^{38} +(628.600 - 527.458i) q^{40} +(-45.9410 - 54.7504i) q^{41} +(-19.2565 + 7.00879i) q^{43} +(-715.015 + 412.814i) q^{44} +(1040.63 - 1802.42i) q^{46} +(-3830.71 - 675.458i) q^{47} +(1981.00 + 721.024i) q^{49} +(1922.35 - 338.962i) q^{50} +(-872.095 - 731.775i) q^{52} -4515.82i q^{53} -3742.66 q^{55} +(-248.908 + 296.637i) q^{56} +(479.501 + 2719.38i) q^{58} +(-606.606 + 1666.64i) q^{59} +(-741.802 + 4206.97i) q^{61} +(3437.96 + 1984.91i) q^{62} +(256.000 + 443.405i) q^{64} +(-1765.05 - 4849.44i) q^{65} +(942.455 - 790.814i) q^{67} +(2032.30 + 2422.01i) q^{68} +(-1649.50 + 600.369i) q^{70} +(-5834.63 + 3368.63i) q^{71} +(2430.52 - 4209.78i) q^{73} +(3173.88 + 559.640i) q^{74} +(2311.46 + 841.304i) q^{76} +(1739.33 - 306.691i) q^{77} +(-3310.58 - 2777.91i) q^{79} +2320.95i q^{80} +202.152 q^{82} +(2812.47 - 3351.77i) q^{83} +(2488.78 + 14114.6i) q^{85} +(19.8239 - 54.4656i) q^{86} +(405.508 - 2299.75i) q^{88} +(7203.27 + 4158.81i) q^{89} +(1217.66 + 2109.05i) q^{91} +(2013.37 + 5531.68i) q^{92} +(8428.05 - 7071.97i) q^{94} +(7167.44 + 8541.82i) q^{95} +(-14810.8 + 5390.70i) q^{97} +(-5163.85 + 2981.35i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	12.4033	−	34.0778i	0.496132	−	1.36311i	−0.398853	−	0.917015i	$-0.630592\pi$
$5$	12.4033	−	34.0778i	0.496132	−	1.36311i	0.894985	−	0.446096i	$-0.147186\pi$
$6$		0			0
$7$	−2.97171	+	16.8534i	−0.0606471	+	0.343947i	0.939352	+	0.342953i	$0.111427\pi$
$7$	−2.97171	+	16.8534i	−0.0606471	+	0.343947i	−1.00000		0.000993371i	$0.999684\pi$
$8$	19.5959	+	11.3137i	0.306186	+	0.176777i
$9$		0			0
$10$	51.2862	+	88.8303i	0.512862	+	0.888303i
$11$	−35.2977	−	96.9796i	−0.291717	−	0.801485i	−0.995816	−	0.0913830i	$-0.970871\pi$
$11$	−35.2977	−	96.9796i	−0.291717	−	0.801485i	0.704099	−	0.710102i	$-0.251351\pi$
$12$		0			0
$13$	109.012	−	91.4718i	0.645041	−	0.541253i	−0.260521	−	0.965468i	$-0.583894\pi$
$13$	109.012	−	91.4718i	0.645041	−	0.541253i	0.905562	+	0.424215i	$0.139450\pi$
$14$	−31.1135	−	37.0796i	−0.158742	−	0.189182i
$15$		0			0
$16$	−60.1403	+	21.8893i	−0.234923	+	0.0855050i
$17$	−342.265	+	197.607i	−1.18431	+	0.683760i	−0.957007	−	0.290065i	$-0.906323\pi$
$17$	−342.265	+	197.607i	−1.18431	+	0.683760i	−0.227300	+	0.973825i	$0.572990\pi$
$18$		0			0
$19$	−153.738	+	266.282i	−0.425867	+	0.737623i	−0.996501	−	0.0835813i	$-0.973364\pi$
$19$	−153.738	+	266.282i	−0.425867	+	0.737623i	0.570634	+	0.821204i	$0.306697\pi$
$20$	−285.711	−	50.3786i	−0.714278	−	0.125946i
$21$		0			0
$22$	274.300	+	99.8370i	0.566735	+	0.206275i
$23$	−724.657	+	127.777i	−1.36986	+	0.241544i	−0.809702	−	0.586841i	$-0.800371\pi$
$23$	−724.657	+	127.777i	−1.36986	+	0.241544i	−0.560160	+	0.828385i	$0.689260\pi$
$24$		0			0
$25$	−528.676	−	443.612i	−0.845881	−	0.709779i
$26$			402.499i			0.595413i
$27$		0			0
$28$	136.907			0.174626
$29$	627.540	−	747.873i	0.746183	−	0.889266i	−0.250708	−	0.968063i	$-0.580663\pi$
$29$	627.540	−	747.873i	0.746183	−	0.889266i	0.996891	+	0.0787966i	$0.0251077\pi$
$30$		0			0
$31$	−243.722	−	1382.22i	−0.253613	−	1.43831i	−0.799607	−	0.600523i	$-0.794959\pi$
$31$	−243.722	−	1382.22i	−0.253613	−	1.43831i	0.545994	−	0.837789i	$-0.316152\pi$
$32$	61.9123	−	170.103i	0.0604612	−	0.166116i
$33$		0			0
$34$	194.109	−	1100.85i	0.167915	−	0.952292i
$35$	537.467	+	310.307i	0.438749	+	0.253312i
$36$		0			0
$37$	−569.723	−	986.789i	−0.416160	−	0.720810i	0.579389	−	0.815051i	$-0.303291\pi$
$37$	−569.723	−	986.789i	−0.416160	−	0.720810i	−0.995549	+	0.0942406i	$0.969958\pi$
$38$	−297.446	−	817.226i	−0.205987	−	0.565946i
$39$		0			0
$40$	628.600	−	527.458i	0.392875	−	0.329661i
$41$	−45.9410	−	54.7504i	−0.0273296	−	0.0325701i	0.752207	−	0.658927i	$-0.228990\pi$
$41$	−45.9410	−	54.7504i	−0.0273296	−	0.0325701i	−0.779536	+	0.626357i	$0.784545\pi$
$42$		0			0
$43$	−19.2565	+	7.00879i	−0.0104145	+	0.00379059i	−0.347222	−	0.937783i	$-0.612875\pi$
$43$	−19.2565	+	7.00879i	−0.0104145	+	0.00379059i	0.336808	+	0.941573i	$0.390653\pi$
$44$	−715.015	+	412.814i	−0.369326	+	0.213231i
$45$		0			0
$46$	1040.63	−	1802.42i	0.491791	−	0.851807i
$47$	−3830.71	−	675.458i	−1.73414	−	0.305775i	−0.784734	−	0.619832i	$-0.787201\pi$
$47$	−3830.71	−	675.458i	−1.73414	−	0.305775i	−0.949404	+	0.314057i	$0.898312\pi$
$48$		0			0
$49$	1981.00	+	721.024i	0.825071	+	0.300301i
$50$	1922.35	−	338.962i	0.768939	−	0.135585i
$51$		0			0
$52$	−872.095	−	731.775i	−0.322520	−	0.270627i
$53$		−	4515.82i		−	1.60762i	−0.594883	−	0.803812i	$-0.702802\pi$
$53$		−	4515.82i		−	1.60762i	0.594883	−	0.803812i	$-0.297198\pi$
$54$		0			0
$55$	−3742.66			−1.23724
$56$	−248.908	+	296.637i	−0.0793711	+	0.0945908i
$57$		0			0
$58$	479.501	+	2719.38i	0.142539	+	0.808378i
$59$	−606.606	+	1666.64i	−0.174262	+	0.478781i	−0.995819	−	0.0913450i	$-0.970883\pi$
$59$	−606.606	+	1666.64i	−0.174262	+	0.478781i	0.821557	+	0.570126i	$0.193106\pi$
$60$		0			0
$61$	−741.802	+	4206.97i	−0.199356	+	1.13060i	0.706723	+	0.707491i	$0.250173\pi$
$61$	−741.802	+	4206.97i	−0.199356	+	1.13060i	−0.906078	+	0.423111i	$0.860938\pi$
$62$	3437.96	+	1984.91i	0.894370	+	0.516365i
$63$		0			0
$64$	256.000	+	443.405i	0.0625000	+	0.108253i
$65$	−1765.05	−	4849.44i	−0.417763	−	1.14780i
$66$		0			0
$67$	942.455	−	790.814i	0.209948	−	0.176167i	−0.531750	−	0.846901i	$-0.678465\pi$
$67$	942.455	−	790.814i	0.209948	−	0.176167i	0.741698	+	0.670734i	$0.234021\pi$
$68$	2032.30	+	2422.01i	0.439512	+	0.523790i
$69$		0			0
$70$	−1649.50	+	600.369i	−0.336633	+	0.122524i
$71$	−5834.63	+	3368.63i	−1.15744	+	0.668246i	−0.950688	−	0.310148i	$-0.899621\pi$
$71$	−5834.63	+	3368.63i	−1.15744	+	0.668246i	−0.206748	+	0.978394i	$0.566288\pi$
$72$		0			0
$73$	2430.52	−	4209.78i	0.456092	−	0.789975i	−0.542658	−	0.839954i	$-0.682582\pi$
$73$	2430.52	−	4209.78i	0.456092	−	0.789975i	0.998750	+	0.0499789i	$0.0159154\pi$
$74$	3173.88	+	559.640i	0.579598	+	0.102199i
$75$		0			0
$76$	2311.46	+	841.304i	0.400184	+	0.145655i
$77$	1739.33	−	306.691i	0.293360	−	0.0517272i
$78$		0			0
$79$	−3310.58	−	2777.91i	−0.530457	−	0.445106i	0.337802	−	0.941217i	$-0.390316\pi$
$79$	−3310.58	−	2777.91i	−0.530457	−	0.445106i	−0.868259	+	0.496111i	$0.834761\pi$
$80$			2320.95i			0.362648i
$81$		0			0
$82$	202.152			0.0300643
$83$	2812.47	−	3351.77i	0.408255	−	0.486539i	−0.522264	−	0.852784i	$-0.674912\pi$
$83$	2812.47	−	3351.77i	0.408255	−	0.486539i	0.930519	+	0.366245i	$0.119357\pi$
$84$		0			0
$85$	2488.78	+	14114.6i	0.344468	+	1.95358i
$86$	19.8239	−	54.4656i	0.00268035	−	0.00736420i
$87$		0			0
$88$	405.508	−	2299.75i	0.0523642	−	0.296972i
$89$	7203.27	+	4158.81i	0.909390	+	0.525036i	0.880235	−	0.474539i	$-0.157385\pi$
$89$	7203.27	+	4158.81i	0.909390	+	0.525036i	0.0291549	+	0.999575i	$0.490718\pi$
$90$		0			0
$91$	1217.66	+	2109.05i	0.147043	+	0.254685i
$92$	2013.37	+	5531.68i	0.237874	+	0.653554i
$93$		0			0
$94$	8428.05	−	7071.97i	0.953831	−	0.800359i
$95$	7167.44	+	8541.82i	0.794176	+	0.946462i
$96$		0			0
$97$	−14810.8	+	5390.70i	−1.57411	+	0.572930i	−0.973913	−	0.226921i	$-0.927134\pi$
$97$	−14810.8	+	5390.70i	−1.57411	+	0.572930i	−0.600198	+	0.799851i	$0.704912\pi$
$98$	−5163.85	+	2981.35i	−0.537677	+	0.310428i
$99$		0			0
$100$	−2760.55	+	4781.41i	−0.276055	+	0.478141i
$101$	−8136.53	−	1434.69i	−0.797621	−	0.140642i	−0.240038	−	0.970763i	$-0.577160\pi$
$101$	−8136.53	−	1434.69i	−0.797621	−	0.140642i	−0.557583	+	0.830121i	$0.688271\pi$
$102$		0			0
$103$	−542.740	−	197.541i	−0.0511585	−	0.0186202i	0.316314	−	0.948654i	$-0.397555\pi$
$103$	−542.740	−	197.541i	−0.0511585	−	0.0186202i	−0.367473	+	0.930034i	$0.619777\pi$
$104$	3171.07	−	559.146i	0.293184	−	0.0516962i
$105$		0			0
$106$	9784.43	+	8210.11i	0.870810	+	0.730697i
$107$			20451.4i			1.78630i	0.449757	+	0.893151i	$0.351511\pi$
$107$			20451.4i			1.78630i	−0.449757	+	0.893151i	$0.648489\pi$
$108$		0			0
$109$	1607.19			0.135274			0.0676370	−	0.997710i	$-0.478454\pi$
$109$	1607.19			0.135274			0.0676370	+	0.997710i	$0.478454\pi$
$110$	6804.45	−	8109.22i	0.562351	−	0.670184i
$111$		0			0
$112$	−190.189	−	1078.62i	−0.0151618	−	0.0859867i
$113$	3457.61	−	9499.69i	0.270781	−	0.743965i	−0.727541	−	0.686064i	$-0.759337\pi$
$113$	3457.61	−	9499.69i	0.270781	−	0.743965i	0.998322	−	0.0579012i	$-0.0184408\pi$
$114$		0			0
$115$	−4633.80	+	26279.6i	−0.350381	+	1.98711i
$116$	−6763.86	−	3905.12i	−0.502665	−	0.290214i
$117$		0			0
$118$	−2508.25	−	4344.41i	−0.180138	−	0.312009i
$119$	−2313.23	−	6355.55i	−0.163352	−	0.448807i
$120$		0			0
$121$	3056.54	−	2564.74i	0.208765	−	0.175175i
$122$	−7766.59	−	9255.86i	−0.521808	−	0.621866i
$123$		0			0
$124$	−10551.2	+	3840.31i	−0.686211	+	0.249760i
$125$	−2045.71	+	1181.09i	−0.130926	+	0.0755900i
$126$		0			0
$127$	10227.1	−	17713.8i	0.634081	−	1.09826i	−0.352628	−	0.935763i	$-0.614712\pi$
$127$	10227.1	−	17713.8i	0.634081	−	1.09826i	0.986709	−	0.162497i	$-0.0519546\pi$
$128$	−1426.15	−	251.469i	−0.0870455	−	0.0153485i
$129$		0			0
$130$	13716.3	+	4992.32i	0.811614	+	0.295403i
$131$	32525.5	−	5735.13i	1.89532	−	0.334195i	0.900413	−	0.435036i	$-0.143264\pi$
$131$	32525.5	−	5735.13i	1.89532	−	0.334195i	0.994903	+	0.100840i	$0.0321532\pi$
$132$		0			0
$133$	−4030.89	−	3382.32i	−0.227876	−	0.191210i
$134$			3479.78i			0.193795i
$135$		0			0
$136$	−8942.65			−0.483491
$137$	10381.9	−	12372.7i	0.553140	−	0.659207i	−0.414939	−	0.909849i	$-0.636197\pi$
$137$	10381.9	−	12372.7i	0.553140	−	0.659207i	0.968080	+	0.250642i	$0.0806417\pi$
$138$		0			0
$139$	85.3048	+	483.788i	0.00441514	+	0.0250395i	0.986936	−	0.161114i	$-0.0515088\pi$
$139$	85.3048	+	483.788i	0.00441514	+	0.0250395i	−0.982521	+	0.186154i	$0.940398\pi$
$140$	1698.10	−	4665.49i	0.0866377	−	0.238035i
$141$		0			0
$142$	3309.01	−	18766.3i	0.164105	−	0.930685i
$143$	−12718.8	−	7343.19i	−0.621975	−	0.359098i
$144$		0			0
$145$	−17702.3	−	30661.3i	−0.841964	−	1.45832i
$146$	4702.46	+	12919.9i	0.220607	+	0.606113i
$147$		0			0
$148$	−6982.93	+	5859.37i	−0.318797	+	0.267502i
$149$	5678.25	+	6767.07i	0.255765	+	0.304809i	0.878614	−	0.477533i	$-0.158469\pi$
$149$	5678.25	+	6767.07i	0.255765	+	0.304809i	−0.622848	+	0.782343i	$0.714025\pi$
$150$		0			0
$151$	32784.2	−	11932.5i	1.43784	−	0.523331i	0.498672	−	0.866791i	$-0.333821\pi$
$151$	32784.2	−	11932.5i	1.43784	−	0.523331i	0.939167	+	0.343460i	$0.111599\pi$
$152$	−6025.27	+	3478.69i	−0.260789	+	0.150567i
$153$		0			0
$154$	−2497.73	+	4326.20i	−0.105318	+	0.182417i
$155$	−50125.9	−	8838.55i	−2.08641	−	0.367890i
$156$		0			0
$157$	−31264.9	−	11379.5i	−1.26840	−	0.461661i	−0.381823	−	0.924235i	$-0.624704\pi$
$157$	−31264.9	−	11379.5i	−1.26840	−	0.461661i	−0.886580	+	0.462574i	$0.846926\pi$
$158$	12037.8	−	2122.59i	0.482206	−	0.0850259i
$159$		0			0
$160$	−5028.80	−	4219.67i	−0.196438	−	0.164831i
$161$		−	12592.6i		−	0.485809i
$162$		0			0
$163$	25522.8			0.960623			0.480311	−	0.877098i	$-0.340524\pi$
$163$	25522.8			0.960623			0.480311	+	0.877098i	$0.340524\pi$
$164$	−367.528	+	438.003i	−0.0136648	+	0.0162851i
$165$		0			0
$166$	2148.99	+	12187.6i	0.0779864	+	0.442283i
$167$	−4657.50	+	12796.4i	−0.167001	+	0.458833i	−0.994758	−	0.102254i	$-0.967394\pi$
$167$	−4657.50	+	12796.4i	−0.167001	+	0.458833i	0.827757	+	0.561087i	$0.189617\pi$
$168$		0			0
$169$	−1443.07	+	8184.06i	−0.0505259	+	0.286547i
$170$	−35106.9	−	20269.0i	−1.21477	−	0.701349i
$171$		0			0
$172$	81.9694	+	141.975i	0.00277073	+	0.00479905i
$173$	7010.51	+	19261.2i	0.234238	+	0.643564i	1.00000		0.000439656i	$0.000139947\pi$
$173$	7010.51	+	19261.2i	0.234238	+	0.643564i	−0.765762	+	0.643124i	$0.777638\pi$
$174$		0			0
$175$	9047.43	−	7591.70i	0.295426	−	0.247892i
$176$	4245.63	+	5059.75i	0.137062	+	0.163344i
$177$		0			0
$178$	−22107.0	+	8046.30i	−0.697734	+	0.253955i
$179$	16329.4	−	9427.78i	0.509641	−	0.294241i	−0.223045	−	0.974808i	$-0.571600\pi$
$179$	16329.4	−	9427.78i	0.509641	−	0.294241i	0.732686	+	0.680567i	$0.238266\pi$
$180$		0			0
$181$	26414.0	−	45750.3i	0.806262	−	1.39649i	−0.109174	−	0.994023i	$-0.534820\pi$
$181$	26414.0	−	45750.3i	0.806262	−	1.39649i	0.915436	−	0.402464i	$-0.131846\pi$
$182$	−6783.48	−	1196.11i	−0.204790	−	0.0361101i
$183$		0			0
$184$	−15645.9	−	5694.66i	−0.462132	−	0.168202i
$185$	−40694.0	+	7175.46i	−1.18901	+	0.209655i
$186$		0			0
$187$	31245.0	+	26217.6i	0.893505	+	0.749739i
$188$			31118.5i			0.880445i
$189$		0			0
$190$	−31538.5			−0.873644
$191$	−10274.5	+	12244.7i	−0.281641	+	0.335647i	−0.888256	−	0.459349i	$-0.848083\pi$
$191$	−10274.5	+	12244.7i	−0.281641	+	0.335647i	0.606615	+	0.794996i	$0.292527\pi$
$192$		0			0
$193$	2773.71	+	15730.5i	0.0744639	+	0.422306i	0.999137	+	0.0415431i	$0.0132274\pi$
$193$	2773.71	+	15730.5i	0.0744639	+	0.422306i	−0.924673	+	0.380763i	$0.875661\pi$
$194$	15247.2	−	41891.3i	0.405123	−	1.11306i
$195$		0			0
$196$	2928.59	−	16608.8i	0.0762335	−	0.432342i
$197$	−15749.9	−	9093.20i	−0.405831	−	0.234306i	0.283166	−	0.959071i	$-0.408615\pi$
$197$	−15749.9	−	9093.20i	−0.405831	−	0.234306i	−0.688997	+	0.724764i	$0.741949\pi$
$198$		0			0
$199$	−4062.90	−	7037.14i	−0.102596	−	0.177701i	0.810158	−	0.586212i	$-0.199381\pi$
$199$	−4062.90	−	7037.14i	−0.102596	−	0.177701i	−0.912753	+	0.408511i	$0.866048\pi$
$200$	−5340.99	−	14674.3i	−0.133525	−	0.366856i
$201$		0			0
$202$	17901.4	−	15021.0i	0.438716	−	0.368127i
$203$	10739.3	+	12798.6i	0.260606	+	0.310579i
$204$		0			0
$205$	−2435.59	+	886.483i	−0.0579558	+	0.0210942i
$206$	1414.76	−	816.810i	0.0333386	−	0.0192481i
$207$		0			0
$208$	−4553.76	+	7887.34i	−0.105255	+	0.182307i
$209$	31250.5	+	5510.31i	0.715426	+	0.126149i
$210$		0			0
$211$	−32893.7	−	11972.3i	−0.738836	−	0.268914i	−0.0549358	−	0.998490i	$-0.517495\pi$
$211$	−32893.7	−	11972.3i	−0.738836	−	0.268914i	−0.683900	+	0.729576i	$0.739718\pi$
$212$	−35577.7	+	6273.31i	−0.791601	+	0.139581i
$213$		0			0
$214$	−44312.0	−	37182.2i	−0.967596	−	0.811909i
$215$			743.151i			0.0160768i
$216$		0			0
$217$	24019.3			0.510084
$218$	−2922.00	+	3482.30i	−0.0614847	+	0.0732746i
$219$		0			0
$220$	5199.25	+	29486.4i	0.107422	+	0.609223i
$221$	−19235.5	+	52849.0i	−0.393839	+	1.08206i
$222$		0			0
$223$	−1885.50	+	10693.2i	−0.0379155	+	0.215030i	−0.997879	−	0.0650954i	$-0.979265\pi$
$223$	−1885.50	+	10693.2i	−0.0379155	+	0.215030i	0.959964	+	0.280125i	$0.0903759\pi$
$224$	2682.82	+	1548.93i	0.0534682	+	0.0308699i
$225$		0			0
$226$	14296.8	+	24762.8i	0.279912	+	0.484822i
$227$	2484.94	+	6827.32i	0.0482241	+	0.132495i	0.961467	−	0.274922i	$-0.0886520\pi$
$227$	2484.94	+	6827.32i	0.0482241	+	0.132495i	−0.913242	+	0.407417i	$0.866430\pi$
$228$		0			0
$229$	75486.7	−	63340.8i	1.43946	−	1.20785i	0.499614	−	0.866248i	$-0.333475\pi$
$229$	75486.7	−	63340.8i	1.43946	−	1.20785i	0.939845	−	0.341601i	$-0.110969\pi$
$230$	−48515.3	−	57818.3i	−0.917114	−	1.09297i
$231$		0			0
$232$	20758.4	−	7555.45i	0.385673	−	0.140373i
$233$	77030.9	−	44473.8i	1.41890	−	0.819205i	0.422702	−	0.906269i	$-0.361082\pi$
$233$	77030.9	−	44473.8i	1.41890	−	0.819205i	0.996203	+	0.0870642i	$0.0277485\pi$
$234$		0			0
$235$	−70531.6	+	122164.i	−1.27717	+	2.21212i
$236$	13973.2	+	2463.86i	0.250884	+	0.0442376i
$237$		0			0
$238$	17976.2	+	6542.80i	0.317354	+	0.115507i
$239$	−51879.2	+	9147.71i	−0.908234	+	0.160146i	−0.608201	−	0.793783i	$-0.708109\pi$
$239$	−51879.2	+	9147.71i	−0.908234	+	0.160146i	−0.300033	+	0.953929i	$0.596998\pi$
$240$		0			0
$241$	−18664.0	−	15661.0i	−0.321345	−	0.269640i	0.467817	−	0.883825i	$-0.345041\pi$
$241$	−18664.0	−	15661.0i	−0.321345	−	0.269640i	−0.789162	+	0.614185i	$0.789485\pi$
$242$			11285.5i			0.192704i
$243$		0			0
$244$	34174.9			0.574021
$245$	49141.8	−	58564.9i	0.818688	−	0.975675i
$246$		0			0
$247$	7598.03	+	43090.6i	0.124540	+	0.706299i
$248$	10862.0	−	29843.2i	0.176607	−	0.485224i
$249$		0			0
$250$	1160.19	−	6579.77i	0.0185630	−	0.105276i
$251$	99346.8	+	57357.9i	1.57691	+	0.910428i	0.995288	+	0.0969677i	$0.0309144\pi$
$251$	99346.8	+	57357.9i	1.57691	+	0.910428i	0.581620	+	0.813460i	$0.302419\pi$
$252$		0			0
$253$	37970.5	+	65766.8i	0.593205	+	1.02746i
$254$	19786.9	+	54364.2i	0.306698	+	0.842646i
$255$		0			0
$256$	3137.72	−	2632.86i	0.0478778	−	0.0401742i
$257$	−12315.0	−	14676.5i	−0.186453	−	0.222206i	0.664718	−	0.747094i	$-0.268552\pi$
$257$	−12315.0	−	14676.5i	−0.186453	−	0.222206i	−0.851171	+	0.524888i	$0.824107\pi$
$258$		0			0
$259$	18323.8	−	6669.32i	0.273159	−	0.0994218i
$260$	−35754.1	+	20642.6i	−0.528907	+	0.305365i
$261$		0			0
$262$	−46707.6	+	80900.0i	−0.680433	+	1.17854i
$263$	8254.28	+	1455.45i	0.119335	+	0.0210420i	0.232997	−	0.972478i	$-0.425147\pi$
$263$	8254.28	+	1455.45i	0.119335	+	0.0210420i	−0.113662	+	0.993520i	$0.536258\pi$
$264$		0			0
$265$	−153889.	−	56011.0i	−2.19137	−	0.797594i
$266$	14656.9	−	2584.41i	0.207148	−	0.0365257i
$267$		0			0
$268$	−7539.64	−	6326.51i	−0.104974	−	0.0880835i
$269$		−	105762.i		−	1.46158i	−0.682601	−	0.730791i	$-0.739151\pi$
$269$		−	105762.i		−	1.46158i	0.682601	−	0.730791i	$-0.260849\pi$
$270$		0			0
$271$	19400.8			0.264169			0.132084	−	0.991238i	$-0.457833\pi$
$271$	19400.8			0.264169			0.132084	+	0.991238i	$0.457833\pi$
$272$	16258.4	−	19376.1i	0.219756	−	0.261895i
$273$		0			0
$274$	7932.76	+	44988.9i	0.105663	+	0.599245i
$275$	−24360.3	+	66929.2i	−0.322119	+	0.885015i
$276$		0			0
$277$	11616.1	−	65878.3i	0.151392	−	0.858584i	−0.810619	−	0.585573i	$-0.800869\pi$
$277$	11616.1	−	65878.3i	0.151392	−	0.858584i	0.962011	−	0.273011i	$-0.0880195\pi$
$278$	−1203.31	−	694.734i	−0.0155700	−	0.00898936i
$279$		0			0
$280$	7021.44	+	12161.5i	0.0895592	+	0.155121i
$281$	15952.1	+	43828.0i	0.202025	+	0.555059i	0.998787	−	0.0492341i	$-0.0156780\pi$
$281$	15952.1	+	43828.0i	0.202025	+	0.555059i	−0.796762	+	0.604293i	$0.793456\pi$
$282$		0			0
$283$	−6790.92	+	5698.26i	−0.0847921	+	0.0711490i	−0.684199	−	0.729296i	$-0.739848\pi$
$283$	−6790.92	+	5698.26i	−0.0847921	+	0.0711490i	0.599406	+	0.800445i	$0.295403\pi$
$284$	34645.0	+	41288.3i	0.429540	+	0.511906i
$285$		0			0
$286$	39034.2	−	14207.3i	0.477214	−	0.173692i
$287$	1059.25	−	611.560i	0.0128599	−	0.00742464i
$288$		0			0
$289$	36336.2	−	62936.2i	0.435055	−	0.753537i
$290$	98617.9	+	17389.0i	1.17263	+	0.206766i
$291$		0			0
$292$	−36543.0	−	13300.6i	−0.428586	−	0.155993i
$293$	57637.7	−	10163.1i	0.671385	−	0.118383i	0.172444	−	0.985019i	$-0.444834\pi$
$293$	57637.7	−	10163.1i	0.671385	−	0.118383i	0.498941	+	0.866636i	$0.333722\pi$
$294$		0			0
$295$	49271.4	+	41343.6i	0.566175	+	0.475077i
$296$		−	25782.7i		−	0.294270i
$297$		0			0
$298$	−24985.7			−0.281358
$299$	−67308.3	+	80214.9i	−0.752881	+	0.897248i
$300$		0			0
$301$	−60.8973	−	345.365i	−0.000672148	−	0.00381194i
$302$	−33750.1	+	92727.6i	−0.370051	+	1.01671i
$303$		0			0
$304$	3417.13	−	19379.5i	0.0369755	−	0.209699i
$305$	134163.	+	77459.2i	1.44223	+	0.832671i
$306$		0			0
$307$	26378.7	+	45689.2i	0.279883	+	0.484771i	0.971355	−	0.237632i	$-0.0763711\pi$
$307$	26378.7	+	45689.2i	0.279883	+	0.484771i	−0.691473	+	0.722403i	$0.743038\pi$
$308$	−4832.50	−	13277.2i	−0.0509414	−	0.139960i
$309$		0			0
$310$	110283.	−	92538.6i	1.14759	−	0.962941i
$311$	12624.0	+	15044.7i	0.130519	+	0.155547i	0.827346	−	0.561693i	$-0.189850\pi$
$311$	12624.0	+	15044.7i	0.130519	+	0.155547i	−0.696827	+	0.717240i	$0.745405\pi$
$312$		0			0
$313$	20881.0	−	7600.06i	0.213139	−	0.0775761i	−0.233244	−	0.972418i	$-0.574934\pi$
$313$	20881.0	−	7600.06i	0.213139	−	0.0775761i	0.446383	+	0.894842i	$0.352712\pi$
$314$	81497.9	−	47052.8i	0.826584	−	0.477229i
$315$		0			0
$316$	−17286.6	+	29941.3i	−0.173116	+	0.299845i
$317$	−102373.	−	18051.2i	−1.01875	−	0.179633i	−0.360760	−	0.932659i	$-0.617483\pi$
$317$	−102373.	−	18051.2i	−1.01875	−	0.179633i	−0.657992	+	0.753025i	$0.728594\pi$
$318$		0			0
$319$	−94679.2	−	34460.4i	−0.930407	−	0.338640i
$320$	18285.5	−	3224.23i	0.178569	−	0.0314866i
$321$		0			0
$322$	27284.5	+	22894.4i	0.263151	+	0.220809i
$323$		−	121519.i		−	1.16476i
$324$		0			0
$325$	−98209.9			−0.929798
$326$	−46402.4	+	55300.3i	−0.436622	+	0.520346i
$327$		0			0
$328$	−280.827	−	1592.65i	−0.00261030	−	0.0148038i
$329$	22767.5	−	62553.2i	0.210341	−	0.577907i
$330$		0			0
$331$	3952.33	−	22414.8i	0.0360742	−	0.204587i	−0.961444	−	0.275002i	$-0.911321\pi$
$331$	3952.33	−	22414.8i	0.0360742	−	0.204587i	0.997518	+	0.0704154i	$0.0224325\pi$
$332$	−30313.8	−	17501.7i	−0.275020	−	0.158783i
$333$		0			0
$334$	−19258.2	−	33356.3i	−0.172633	−	0.299009i
$335$	−15259.6	−	41925.5i	−0.135973	−	0.373584i
$336$		0			0
$337$	−130012.	+	109093.i	−1.14478	+	0.960586i	−0.999585	−	0.0288163i	$-0.990826\pi$
$337$	−130012.	+	109093.i	−1.14478	+	0.960586i	−0.145198	+	0.989403i	$0.546382\pi$
$338$	−15108.8	−	18006.0i	−0.132250	−	0.157610i
$339$		0			0
$340$	107744.	−	39215.6i	0.932041	−	0.339235i
$341$	−125444.	+	72425.2i	−1.07880	+	0.622847i
$342$		0			0
$343$	−38583.3	+	66828.2i	−0.327952	+	0.568030i
$344$	−456.644	−	80.5187i	−0.00385888	−	0.000680424i
$345$		0			0
$346$	−54479.0	−	19828.7i	−0.455068	−	0.165631i
$347$	−139485.	+	24595.0i	−1.15843	+	0.204262i	−0.719652	−	0.694335i	$-0.755699\pi$
$347$	−139485.	+	24595.0i	−1.15843	+	0.204262i	−0.438775	+	0.898597i	$0.644587\pi$
$348$		0			0
$349$	110984.	+	93126.8i	0.911192	+	0.764581i	0.972345	−	0.233547i	$-0.0750333\pi$
$349$	110984.	+	93126.8i	0.911192	+	0.764581i	−0.0611530	+	0.998128i	$0.519478\pi$
$350$			33405.4i			0.272697i
$351$		0			0
$352$	−18681.8			−0.150777
$353$	−34204.6	+	40763.4i	−0.274495	+	0.327131i	−0.885626	−	0.464399i	$-0.846270\pi$
$353$	−34204.6	+	40763.4i	−0.274495	+	0.327131i	0.611131	+	0.791529i	$0.290715\pi$
$354$		0			0
$355$	42426.7	+	240614.i	0.336653	+	1.90925i
$356$	22758.4	−	62528.1i	0.179573	−	0.493373i
$357$		0			0
$358$	−9260.93	+	52521.3i	−0.0722584	+	0.409798i
$359$	−96156.0	−	55515.7i	−0.746084	−	0.430752i	0.0781934	−	0.996938i	$-0.475085\pi$
$359$	−96156.0	−	55515.7i	−0.746084	−	0.430752i	−0.824277	+	0.566187i	$0.808418\pi$
$360$		0			0
$361$	17889.8	+	30986.0i	0.137275	+	0.237767i
$362$	51104.6	+	140409.i	0.389981	+	1.07146i
$363$		0			0
$364$	14924.5	−	12523.1i	0.112641	−	0.0945171i
$365$	−113313.	−	135042.i	−0.850542	−	1.01364i
$366$		0			0
$367$	−71354.4	+	25970.9i	−0.529772	+	0.192821i	−0.593036	−	0.805176i	$-0.702071\pi$
$367$	−71354.4	+	25970.9i	−0.529772	+	0.192821i	0.0632647	+	0.997997i	$0.479849\pi$
$368$	40784.2	−	23546.8i	0.301159	−	0.173874i
$369$		0			0
$370$	58437.9	−	101217.i	0.426865	−	0.739352i
$371$	76106.9	+	13419.7i	0.552937	+	0.0974978i
$372$		0			0
$373$	−99354.3	−	36162.0i	−0.714116	−	0.259917i	−0.0406902	−	0.999172i	$-0.512956\pi$
$373$	−99354.3	−	36162.0i	−0.714116	−	0.259917i	−0.673426	+	0.739255i	$0.735178\pi$
$374$	−113612.	+	20032.8i	−0.812231	+	0.143218i
$375$		0			0
$376$	−67424.4	−	56575.8i	−0.476915	−	0.400180i
$377$		−	138929.i		−	0.977487i
$378$		0			0
$379$	176955.			1.23192			0.615962	−	0.787776i	$-0.288768\pi$
$379$	176955.			1.23192			0.615962	+	0.787776i	$0.288768\pi$
$380$	57339.5	−	68334.6i	0.397088	−	0.473231i
$381$		0			0
$382$	−7850.74	−	44523.8i	−0.0538002	−	0.305116i
$383$	−3838.07	+	10545.0i	−0.0261647	+	0.0718868i	−0.952087	−	0.305826i	$-0.901067\pi$
$383$	−3838.07	+	10545.0i	−0.0261647	+	0.0718868i	0.925923	+	0.377713i	$0.123289\pi$
$384$		0			0
$385$	11122.1	−	63076.5i	0.0750352	−	0.425546i
$386$	−39126.0	−	22589.4i	−0.262598	−	0.151611i
$387$		0			0
$388$	63045.4	+	109198.i	0.418784	+	0.725355i
$389$	−56092.9	−	154114.i	−0.370688	−	1.01846i	−0.975096	−	0.221782i	$-0.928813\pi$
$389$	−56092.9	−	154114.i	−0.370688	−	1.01846i	0.604408	−	0.796675i	$-0.293410\pi$
$390$		0			0
$391$	222775.	−	186930.i	1.45718	−	1.22272i
$392$	30662.0	+	36541.5i	0.199539	+	0.237802i
$393$		0			0
$394$	48336.8	−	17593.1i	0.311376	−	0.113332i
$395$	−135727.	+	78362.0i	−0.869906	+	0.502240i
$396$		0			0
$397$	114070.	−	197574.i	0.723750	−	1.25357i	−0.235736	−	0.971817i	$-0.575750\pi$
$397$	114070.	−	197574.i	0.723750	−	1.25357i	0.959486	−	0.281755i	$-0.0909165\pi$
$398$	22634.0	+	3990.99i	0.142888	+	0.0251950i
$399$		0			0
$400$	41505.1	+	15106.6i	0.259407	+	0.0944163i
$401$	−9808.76	+	1729.55i	−0.0609994	+	0.0107558i	−0.204065	−	0.978957i	$-0.565415\pi$
$401$	−9808.76	+	1729.55i	−0.0609994	+	0.0107558i	0.143065	+	0.989713i	$0.454304\pi$
$402$		0			0
$403$	−153003.	−	128384.i	−0.942082	−	0.790501i
$404$			66096.4i			0.404963i
$405$		0			0
$406$	−47255.8			−0.286683
$407$	−75588.5	+	90082.9i	−0.456318	+	0.543818i
$408$		0			0
$409$	−41711.1	−	236555.i	−0.249347	−	1.41412i	−0.810175	−	0.586187i	$-0.800628\pi$
$409$	−41711.1	−	236555.i	−0.249347	−	1.41412i	0.560828	−	0.827932i	$-0.310483\pi$
$410$	2507.35	−	6888.89i	0.0149158	−	0.0409809i
$411$		0			0
$412$	−802.355	+	4550.38i	−0.00472685	+	0.0268073i
$413$	−26285.8	−	15176.1i	−0.154107	−	0.0889735i
$414$		0			0
$415$	−79337.0	−	137416.i	−0.460659	−	0.797884i
$416$	−8810.42	−	24206.4i	−0.0509108	−	0.139876i
$417$		0			0
$418$	−68755.1	+	57692.4i	−0.393507	+	0.330191i
$419$	26095.1	+	31098.9i	0.148638	+	0.177140i	0.835226	−	0.549907i	$-0.185337\pi$
$419$	26095.1	+	31098.9i	0.148638	+	0.177140i	−0.686588	+	0.727047i	$0.740892\pi$
$420$		0			0
$421$	−256038.	+	93190.0i	−1.44457	+	0.525782i	−0.941070	−	0.338212i	$-0.890178\pi$
$421$	−256038.	+	93190.0i	−1.44457	+	0.525782i	−0.503503	+	0.863994i	$0.667956\pi$
$422$	85743.8	−	49504.2i	0.481480	−	0.277982i
$423$		0			0
$424$	51090.6	−	88491.6i	0.284191	−	0.492233i
$425$	268608.	+	47362.8i	1.48710	+	0.262216i
$426$		0			0
$427$	−68697.3	−	25003.8i	−0.376776	−	0.137135i
$428$	161125.	−	28410.7i	0.879582	−	0.155094i
$429$		0			0
$430$	−1610.19	−	1351.11i	−0.00870842	−	0.00730723i
$431$		−	48623.1i		−	0.261751i	−0.991399	−	0.130875i	$-0.958221\pi$
$431$		−	48623.1i		−	0.261751i	0.991399	−	0.130875i	$-0.0417788\pi$
$432$		0			0
$433$	−248366.			−1.32470			−0.662348	−	0.749196i	$-0.730440\pi$
$433$	−248366.			−1.32470			−0.662348	+	0.749196i	$0.730440\pi$
$434$	−43669.0	+	52042.7i	−0.231843	+	0.276300i
$435$		0			0
$436$	−2232.69	−	12662.2i	−0.0117450	−	0.0666095i
$437$	77382.7	−	212607.i	0.405211	−	1.11331i
$438$		0			0
$439$	28260.6	−	160274.i	0.146640	−	0.831638i	−0.819395	−	0.573229i	$-0.805691\pi$
$439$	28260.6	−	160274.i	0.146640	−	0.831638i	0.966036	−	0.258409i	$-0.0831983\pi$
$440$	−73340.8	−	42343.3i	−0.378827	−	0.218716i
$441$		0			0
$442$	−79536.5	−	137761.i	−0.407119	−	0.705151i
$443$	570.063	+	1566.23i	0.00290479	+	0.00798085i	0.941137	−	0.338027i	$-0.109759\pi$
$443$	570.063	+	1566.23i	0.00290479	+	0.00798085i	−0.938232	+	0.346007i	$0.887537\pi$
$444$		0			0
$445$	231067.	−	193889.i	1.16686	−	0.979112i
$446$	−19741.0	−	23526.4i	−0.0992429	−	0.118273i
$447$		0			0
$448$	−8233.64	+	2996.80i	−0.0410238	+	0.0149314i
$449$	−104576.	+	60377.2i	−0.518729	+	0.299489i	−0.736415	−	0.676530i	$-0.763483\pi$
$449$	−104576.	+	60377.2i	−0.518729	+	0.299489i	0.217685	+	0.976019i	$0.430149\pi$
$450$		0			0
$451$	−3688.06	+	6387.91i	−0.0181320	+	0.0314055i
$452$	−79646.2	−	14043.8i	−0.389842	−	0.0687396i
$453$		0			0
$454$	−19310.6	−	7028.48i	−0.0936879	−	0.0340996i
$455$	86974.7	−	15336.0i	0.420117	−	0.0740779i
$456$		0			0
$457$	84715.6	+	71084.8i	0.405631	+	0.340365i	0.822665	−	0.568526i	$-0.192486\pi$
$457$	84715.6	+	71084.8i	0.405631	+	0.340365i	−0.417035	+	0.908891i	$0.636931\pi$
$458$			278716.i			1.32871i
$459$		0			0
$460$	213480.			1.00888
$461$	−7370.89	+	8784.29i	−0.0346831	+	0.0413337i	−0.783107	−	0.621887i	$-0.786366\pi$
$461$	−7370.89	+	8784.29i	−0.0346831	+	0.0413337i	0.748424	+	0.663221i	$0.230811\pi$
$462$		0			0
$463$	68029.5	+	385815.i	0.317348	+	1.79977i	0.558742	+	0.829342i	$0.311284\pi$
$463$	68029.5	+	385815.i	0.317348	+	1.79977i	−0.241394	+	0.970427i	$0.577605\pi$
$464$	−21370.0	+	58713.7i	−0.0992589	+	0.272712i
$465$		0			0
$466$	−43686.7	+	247760.i	−0.201177	+	1.14093i
$467$	−28697.3	−	16568.4i	−0.131585	−	0.0759709i	0.432762	−	0.901508i	$-0.357539\pi$
$467$	−28697.3	−	16568.4i	−0.131585	−	0.0759709i	−0.564348	+	0.825537i	$0.690872\pi$
$468$		0			0
$469$	10527.2	+	18233.6i	0.0478594	+	0.0828948i
$470$	−136462.	−	374925.i	−0.617753	−	1.69726i
$471$		0			0
$472$	−30742.8	+	25796.3i	−0.137994	+	0.115791i
$473$	1359.42	+	1620.09i	0.00607619	+	0.00724132i
$474$		0			0
$475$	199403.	−	72576.9i	0.883782	−	0.321670i
$476$	−46858.4	+	27053.7i	−0.206811	+	0.119402i
$477$		0			0
$478$	74500.1	−	129038.i	0.326063	−	0.564757i
$479$	95908.0	+	16911.2i	0.418007	+	0.0737059i	0.378696	−	0.925521i	$-0.376373\pi$
$479$	95908.0	+	16911.2i	0.418007	+	0.0737059i	0.0393110	+	0.999227i	$0.487484\pi$
$480$		0			0
$481$	−152370.	−	55458.1i	−0.658581	−	0.239704i
$482$	67865.3	−	11966.5i	0.292115	−	0.0515078i
$483$		0			0
$484$	−24452.3	−	20517.9i	−0.104383	−	0.0875875i
$485$			571582.i			2.42994i
$486$		0			0
$487$	−89694.8			−0.378190			−0.189095	−	0.981959i	$-0.560555\pi$
$487$	−89694.8			−0.378190			−0.189095	+	0.981959i	$0.560555\pi$
$488$	−62132.7	+	74046.9i	−0.260904	+	0.310933i
$489$		0			0
$490$	37549.0	+	212951.i	0.156389	+	0.886926i
$491$	−14887.5	+	40903.2i	−0.0617533	+	0.169666i	−0.966732	−	0.255791i	$-0.917664\pi$
$491$	−14887.5	+	40903.2i	−0.0617533	+	0.169666i	0.904979	+	0.425456i	$0.139886\pi$
$492$		0			0
$493$	−67000.1	+	379976.i	−0.275665	+	1.56337i
$494$	−107178.	−	61879.4i	−0.439190	−	0.253567i
$495$		0			0
$496$	44913.3	+	77792.1i	0.182563	+	0.316208i
$497$	−39434.0	−	108344.i	−0.159646	−	0.438624i
$498$		0			0
$499$	55528.2	−	46593.7i	0.223004	−	0.187122i	−0.524440	−	0.851447i	$-0.675725\pi$
$499$	55528.2	−	46593.7i	0.223004	−	0.187122i	0.747444	+	0.664325i	$0.231281\pi$
$500$	12147.1	+	14476.3i	0.0485883	+	0.0579053i
$501$		0			0
$502$	−304898.	+	110974.i	−1.20989	+	0.440365i
$503$	211049.	−	121849.i	0.834155	−	0.481599i	−0.0211184	−	0.999777i	$-0.506723\pi$
$503$	211049.	−	121849.i	0.834155	−	0.481599i	0.855273	+	0.518178i	$0.173389\pi$
$504$		0			0
$505$	−149811.	+	259480.i	−0.587436	+	1.01747i
$506$	−211530.	−	37298.5i	−0.826173	−	0.145677i
$507$		0			0
$508$	−153765.	−	55965.9i	−0.595841	−	0.216868i
$509$	361209.	−	63690.9i	1.39419	−	0.245834i	0.574438	−	0.818548i	$-0.305220\pi$
$509$	361209.	−	63690.9i	1.39419	−	0.245834i	0.819755	+	0.572714i	$0.194109\pi$
$510$		0			0
$511$	63726.2	+	53472.7i	0.244049	+	0.204781i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	54189.2			0.205110
$515$	−13463.5	+	16045.2i	−0.0507627	+	0.0604967i
$516$		0			0
$517$	69709.7	+	395343.i	0.260803	+	1.47909i
$518$	−18863.7	+	51827.5i	−0.0703019	+	0.193153i
$519$		0			0
$520$	20277.3	−	114998.i	0.0749901	−	0.425290i
$521$	−96183.1	−	55531.4i	−0.354343	−	0.204580i	0.312254	−	0.949999i	$-0.398916\pi$
$521$	−96183.1	−	55531.4i	−0.354343	−	0.204580i	−0.666596	+	0.745419i	$0.732249\pi$
$522$		0			0
$523$	−207845.	−	359999.i	−0.759866	−	1.31613i	−0.942919	−	0.333023i	$-0.891931\pi$
$523$	−207845.	−	359999.i	−0.759866	−	1.31613i	0.183053	−	0.983103i	$-0.441402\pi$
$524$	−90367.9	−	248284.i	−0.329118	−	0.904245i
$525$		0			0
$526$	−18160.4	+	15238.4i	−0.0656379	+	0.0550768i
$527$	356553.	+	424923.i	1.28382	+	1.52999i
$528$		0			0
$529$	245837.	−	89477.2i	0.878486	−	0.319743i
$530$	401141.	−	231599.i	1.42806	−	0.824490i
$531$		0			0
$532$	−21047.8	+	36455.9i	−0.0743676	+	0.128808i
$533$	−10016.2	−	1766.13i	−0.0352574	−	0.00621683i
$534$		0			0
$535$	696937.	+	253664.i	2.43493	+	0.886242i
$536$	27415.3	−	4834.06i	0.0954253	−	0.0168261i
$537$		0			0
$538$	229154.	+	192283.i	0.791703	+	0.664317i
$539$		−	217567.i		−	0.748885i
$540$		0			0
$541$	174752.			0.597074			0.298537	−	0.954398i	$-0.403501\pi$
$541$	174752.			0.597074			0.298537	+	0.954398i	$0.403501\pi$
$542$	−35272.2	+	42035.8i	−0.120070	+	0.143094i
$543$		0			0
$544$	12423.0	+	70454.3i	0.0419787	+	0.238073i
$545$	19934.5	−	54769.5i	0.0671138	−	0.184394i
$546$		0			0
$547$	−41418.5	+	234896.i	−0.138427	+	0.785057i	0.833985	+	0.551787i	$0.186054\pi$
$547$	−41418.5	+	234896.i	−0.138427	+	0.785057i	−0.972412	+	0.233270i	$0.925057\pi$
$548$	−111900.	−	64605.4i	−0.372622	−	0.215133i
$549$		0			0
$550$	−100727.	−	174464.i	−0.332981	−	0.576740i
$551$	102668.	+	282079.i	0.338169	+	0.929111i
$552$		0			0
$553$	56655.2	−	47539.4i	0.185263	−	0.155455i
$554$	121620.	+	144941.i	0.396263	+	0.472248i
$555$		0			0
$556$	3693.00	−	1344.14i	0.0119462	−	0.00434806i
$557$	−455479.	+	262971.i	−1.46811	+	0.847613i	−0.999362	−	0.0357196i	$-0.988628\pi$
$557$	−455479.	+	262971.i	−1.46811	+	0.847613i	−0.468747	+	0.883333i	$0.655294\pi$
$558$		0			0
$559$	−1458.08	+	2525.47i	−0.00466614	+	0.00808199i
$560$	−39115.9	−	6897.18i	−0.124732	−	0.0219936i
$561$		0			0
$562$	−123964.	−	45119.3i	−0.392486	−	0.142853i
$563$	136561.	−	24079.3i	0.430833	−	0.0759674i	0.0459733	−	0.998943i	$-0.485361\pi$
$563$	136561.	−	24079.3i	0.430833	−	0.0759674i	0.384859	+	0.922975i	$0.374250\pi$
$564$		0			0
$565$	−280843.	−	235655.i	−0.879764	−	0.738210i
$566$		−	25073.8i		−	0.0782684i
$567$		0			0
$568$	−152447.			−0.472521
$569$	309776.	−	369176.i	0.956804	−	1.14027i	−0.0332304	−	0.999448i	$-0.510580\pi$
$569$	309776.	−	369176.i	0.956804	−	1.14027i	0.990034	−	0.140827i	$-0.0449760\pi$
$570$		0			0
$571$	−31702.6	−	179794.i	−0.0972349	−	0.551447i	−0.994040	−	0.109020i	$-0.965229\pi$
$571$	−31702.6	−	179794.i	−0.0972349	−	0.551447i	0.896805	−	0.442427i	$-0.145882\pi$
$572$	−40184.3	+	110405.i	−0.122819	+	0.337441i
$573$		0			0
$574$	−600.737	+	3406.95i	−0.00182331	+	0.0103405i
$575$	439792.	+	253914.i	1.33018	+	0.767982i
$576$		0			0
$577$	308907.	+	535043.i	0.927848	+	1.60708i	0.786916	+	0.617060i	$0.211676\pi$
$577$	308907.	+	535043.i	0.927848	+	1.60708i	0.140931	+	0.990019i	$0.454990\pi$
$578$	70301.8	+	193153.i	0.210431	+	0.578156i
$579$		0			0
$580$	−216972.	+	182061.i	−0.644982	+	0.541204i
$581$	48130.8	+	57360.1i	0.142584	+	0.169925i
$582$		0			0
$583$	−437942.	+	159398.i	−1.28849	+	0.468971i
$584$	95256.3	−	54996.3i	0.279298	−	0.161253i
$585$		0			0
$586$	−82769.5	+	143361.i	−0.241032	+	0.417480i
$587$	−413037.	−	72829.5i	−1.19871	−	0.211364i	−0.461567	−	0.887105i	$-0.652713\pi$
$587$	−413037.	−	72829.5i	−1.19871	−	0.211364i	−0.737139	+	0.675741i	$0.763824\pi$
$588$		0			0
$589$	405529.	+	147601.i	1.16894	+	0.425459i
$590$	−179158.	+	31590.4i	−0.514675	+	0.0907511i
$591$		0			0
$592$	55863.4	+	46875.0i	0.159399	+	0.133751i
$593$			348464.i			0.990943i	0.868624	+	0.495471i	$0.165005\pi$
$593$			348464.i			0.990943i	−0.868624	+	0.495471i	$0.834995\pi$
$594$		0			0
$595$	−245275.			−0.692818
$596$	45426.0	−	54136.6i	0.127883	−	0.152405i
$597$		0			0
$598$	−51430.0	−	291674.i	−0.143818	−	0.815634i
$599$	13641.0	−	37478.3i	0.0380183	−	0.104454i	−0.919231	−	0.393719i	$-0.871188\pi$
$599$	13641.0	−	37478.3i	0.0380183	−	0.104454i	0.957249	+	0.289264i	$0.0934106\pi$
$600$		0			0
$601$	−3380.73	+	19173.1i	−0.00935969	+	0.0530815i	−0.989130	−	0.147044i	$-0.953024\pi$
$601$	−3380.73	+	19173.1i	−0.00935969	+	0.0530815i	0.979770	+	0.200126i	$0.0641351\pi$
$602$	859.020	+	495.955i	0.00237034	+	0.00136851i
$603$		0			0
$604$	−139553.	−	241712.i	−0.382529	−	0.662560i
$605$	−49489.5	−	135971.i	−0.135208	−	0.371481i
$606$		0			0
$607$	75676.2	−	63499.9i	0.205391	−	0.172344i	−0.534290	−	0.845301i	$-0.679421\pi$
$607$	75676.2	−	63499.9i	0.205391	−	0.172344i	0.739681	+	0.672958i	$0.234976\pi$
$608$	35777.0	+	42637.3i	0.0967824	+	0.115341i
$609$		0			0
$610$	−411750.	+	149865.i	−1.10656	+	0.402754i
$611$	−479379.	+	276769.i	−1.28409	+	0.741371i
$612$		0			0
$613$	270027.	−	467701.i	0.718599	−	1.24465i	−0.242955	−	0.970037i	$-0.578117\pi$
$613$	270027.	−	467701.i	0.718599	−	1.24465i	0.961555	−	0.274613i	$-0.0885498\pi$
$614$	−146953.	−	25911.8i	−0.389801	−	0.0687324i
$615$		0			0
$616$	37553.6	+	13668.4i	0.0989669	+	0.0360210i
$617$	−228282.	+	40252.3i	−0.599655	+	0.105735i	−0.465232	−	0.885189i	$-0.654029\pi$
$617$	−228282.	+	40252.3i	−0.599655	+	0.105735i	−0.134423	+	0.990924i	$0.542918\pi$
$618$		0			0
$619$	−570053.	−	478331.i	−1.48776	−	1.24838i	−0.897380	−	0.441258i	$-0.854533\pi$
$619$	−570053.	−	478331.i	−1.48776	−	1.24838i	−0.590382	−	0.807124i	$-0.701023\pi$
$620$			407193.i			1.05930i
$621$		0			0
$622$	−55548.6			−0.143580
$623$	−91496.1	+	109041.i	−0.235736	+	0.280940i
$624$		0			0
$625$	−60025.2	−	340420.i	−0.153665	−	0.871475i
$626$	−21496.2	+	59060.3i	−0.0548546	+	0.150712i
$627$		0			0
$628$	−46220.1	+	262127.i	−0.117196	+	0.664650i
$629$	389992.	+	225162.i	0.985722	+	0.569107i
$630$		0			0
$631$	2758.42	+	4777.73i	0.00692791	+	0.0119995i	0.869469	−	0.493988i	$-0.164461\pi$
$631$	2758.42	+	4777.73i	0.00692791	+	0.0119995i	−0.862541	+	0.505988i	$0.831128\pi$
$632$	−33445.4	−	91890.6i	−0.0837342	−	0.230058i
$633$		0			0
$634$	225234.	−	188994.i	0.560345	−	0.470186i
$635$	−476799.	−	568226.i	−1.18246	−	1.40920i
$636$		0			0
$637$	281906.	−	102605.i	0.694744	−	0.252866i
$638$	246799.	−	142490.i	0.606321	−	0.350060i
$639$		0			0
$640$	−26258.5	+	45481.1i	−0.0641077	+	0.111038i
$641$	435177.	+	76733.4i	1.05913	+	0.186753i	0.675971	−	0.736929i	$-0.263725\pi$
$641$	435177.	+	76733.4i	1.05913	+	0.186753i	0.383160	+	0.923682i	$0.374836\pi$
$642$		0			0
$643$	482956.	+	175782.i	1.16811	+	0.425159i	0.851990	−	0.523559i	$-0.175396\pi$
$643$	482956.	+	175782.i	1.16811	+	0.425159i	0.316125	+	0.948718i	$0.397618\pi$
$644$	−99210.7	+	17493.5i	−0.239214	+	0.0421799i
$645$		0			0
$646$	263294.	+	220930.i	0.630923	+	0.529407i
$647$		−	484526.i		−	1.15747i	−0.815517	−	0.578733i	$-0.803547\pi$
$647$		−	484526.i		−	1.15747i	0.815517	−	0.578733i	$-0.196453\pi$
$648$		0			0
$649$	183042.			0.434571
$650$	178553.	−	212791.i	0.422611	−	0.503649i
$651$		0			0
$652$	−35455.9	−	201080.i	−0.0834052	−	0.473014i
$653$	33553.9	−	92188.5i	0.0786894	−	0.216197i	−0.894110	−	0.447848i	$-0.852190\pi$
$653$	33553.9	−	92188.5i	0.0786894	−	0.216197i	0.972799	+	0.231651i	$0.0744127\pi$
$654$		0			0
$655$	207983.	−	1.17953e6i	0.484781	−	2.74933i
$656$	3961.36	+	2287.09i	0.00920526	+	0.00531466i
$657$		0			0
$658$	94141.0	+	163057.i	0.217434	+	0.376607i
$659$	−219465.	−	602976.i	−0.505353	−	1.38845i	−0.885983	−	0.463718i	$-0.846515\pi$
$659$	−219465.	−	602976.i	−0.505353	−	1.38845i	0.380630	−	0.924727i	$-0.375707\pi$
$660$		0			0
$661$	−175363.	+	147147.i	−0.401362	+	0.336783i	−0.821020	−	0.570900i	$-0.806594\pi$
$661$	−175363.	+	147147.i	−0.401362	+	0.336783i	0.419658	+	0.907682i	$0.362150\pi$
$662$	41380.4	+	49315.3i	0.0944233	+	0.112529i
$663$		0			0
$664$	93033.8	−	33861.5i	0.211011	−	0.0768017i
$665$	−165258.	+	95411.9i	−0.373697	+	0.215754i
$666$		0			0
$667$	−359191.	+	622136.i	−0.807371	+	1.39841i
$668$	107286.	+	18917.4i	0.240431	+	0.0423944i
$669$		0			0
$670$	118583.	+	43160.7i	0.264164	+	0.0961478i
$671$	434174.	−	76556.6i	0.964315	−	0.170035i
$672$		0			0
$673$	−59071.7	−	49567.0i	−0.130422	−	0.109437i	0.575244	−	0.817982i	$-0.304907\pi$
$673$	−59071.7	−	49567.0i	−0.130422	−	0.109437i	−0.705665	+	0.708545i	$0.749352\pi$
$674$		−	480036.i		−	1.05671i
$675$		0			0
$676$	66482.5			0.145484
$677$	128312.	−	152917.i	0.279957	−	0.333639i	−0.607682	−	0.794181i	$-0.707900\pi$
$677$	128312.	−	152917.i	0.279957	−	0.333639i	0.887638	+	0.460541i	$0.152345\pi$
$678$		0			0
$679$	−46838.1	−	265632.i	−0.101592	−	0.576157i
$680$	−110918.	+	304746.i	−0.239875	+	0.659052i
$681$		0			0
$682$	71143.5	−	403475.i	0.152956	−	0.867456i
$683$	92263.0	+	53268.1i	0.197782	+	0.114189i	0.595620	−	0.803266i	$-0.296906\pi$
$683$	92263.0	+	53268.1i	0.197782	+	0.114189i	−0.397839	+	0.917455i	$0.630240\pi$
$684$		0			0
$685$	−292863.	−	507254.i	−0.624142	−	1.08105i
$686$	−74649.3	−	205097.i	−0.158627	−	0.435824i
$687$		0			0
$688$	1004.67	−	843.022i	0.00212250	−	0.00178099i
$689$	−413070.	−	492278.i	−0.870132	−	1.03698i
$690$		0			0
$691$	−287038.	+	104473.i	−0.601150	+	0.218801i	−0.624626	−	0.780924i	$-0.714749\pi$
$691$	−287038.	+	104473.i	−0.601150	+	0.218801i	0.0234765	+	0.999724i	$0.492527\pi$
$692$	142010.	−	81989.5i	0.296556	−	0.171217i
$693$		0			0
$694$	200305.	−	346938.i	0.415884	−	0.720332i
$695$	17544.5	+	3093.56i	0.0363221	+	0.00640456i
$696$		0			0
$697$	26543.0	+	9660.87i	0.0546367	+	0.0198861i
$698$	−403556.	+	71157.8i	−0.828309	+	0.146053i
$699$		0			0
$700$	−72379.4	−	60733.6i	−0.147713	−	0.123946i
$701$		−	352610.i		−	0.717562i	−0.933422	−	0.358781i	$-0.883193\pi$
$701$		−	352610.i		−	0.717562i	0.933422	−	0.358781i	$-0.116807\pi$
$702$		0			0
$703$	350352.			0.708915
$704$	33965.0	−	40478.0i	0.0685310	−	0.0816720i
$705$		0			0
$706$	−26135.6	−	148222.i	−0.0524351	−	0.297374i
$707$	48358.8	−	132865.i	0.0967468	−	0.265810i
$708$		0			0
$709$	−127720.	+	724334.i	−0.254077	+	1.44094i	0.544354	+	0.838856i	$0.316775\pi$
$709$	−127720.	+	724334.i	−0.254077	+	1.44094i	−0.798431	+	0.602087i	$0.794336\pi$
$710$	−598472.	−	345528.i	−1.18721	−	0.685436i
$711$		0			0
$712$	94103.2	+	162992.i	0.185628	+	0.321518i
$713$	353230.	+	970492.i	0.694830	+	1.90903i
$714$		0			0
$715$	−407994.	+	342348.i	−0.798072	+	0.669662i
$716$	−96961.0	−	115554.i	−0.189135	−	0.225402i
$717$		0			0
$718$	295105.	−	107409.i	0.572437	−	0.208350i
$719$	−274995.	+	158768.i	−0.531946	+	0.307119i	−0.741808	−	0.670612i	$-0.766032\pi$
$719$	−274995.	+	158768.i	−0.531946	+	0.307119i	0.209863	+	0.977731i	$0.432698\pi$
$720$		0			0
$721$	4942.11	−	8559.98i	0.00950696	−	0.0164665i
$722$	−99662.4	−	17573.2i	−0.191186	−	0.0337113i
$723$		0			0
$724$	−397136.	−	144546.i	−0.757638	−	0.275758i
$725$	−663530.	+	116998.i	−1.26236	+	0.222589i
$726$		0			0
$727$	23554.5	+	19764.6i	0.0445662	+	0.0373954i	0.664799	−	0.747023i	$-0.268517\pi$
$727$	23554.5	+	19764.6i	0.0445662	+	0.0373954i	−0.620233	+	0.784418i	$0.712962\pi$
$728$			55105.0i			0.103975i
$729$		0			0
$730$	498608.			0.935649
$731$	5205.84	−	6204.07i	0.00974217	−	0.0116103i
$732$		0			0
$733$	−30961.9	−	175594.i	−0.0576261	−	0.326814i	0.942343	−	0.334648i	$-0.108617\pi$
$733$	−30961.9	−	175594.i	−0.0576261	−	0.326814i	−0.999969	+	0.00783406i	$0.997506\pi$
$734$	73456.8	−	201821.i	0.136345	−	0.374605i
$735$		0			0
$736$	−23130.0	+	131177.i	−0.0426993	+	0.242160i
$737$	−109959.	−	63485.0i	−0.202440	−	0.116879i
$738$		0			0
$739$	−92846.0	−	160814.i	−0.170010	−	0.294466i	0.768413	−	0.639954i	$-0.221047\pi$
$739$	−92846.0	−	160814.i	−0.170010	−	0.294466i	−0.938423	+	0.345488i	$0.887713\pi$
$740$	113063.	+	310638.i	0.206470	+	0.567272i
$741$		0			0
$742$	−167445.	+	140503.i	−0.304133	+	0.255198i
$743$	330085.	+	393380.i	0.597927	+	0.712581i	0.977109	−	0.212741i	$-0.0682391\pi$
$743$	330085.	+	393380.i	0.597927	+	0.712581i	−0.379182	+	0.925322i	$0.623795\pi$
$744$		0			0
$745$	301036.	−	109568.i	0.542382	−	0.197411i
$746$	258986.	−	149526.i	0.465370	−	0.268682i
$747$		0			0
$748$	163150.	−	282583.i	0.291597	−	0.505061i
$749$	−344675.	−	60775.5i	−0.614393	−	0.108334i
$750$		0			0
$751$	−771463.	−	280790.i	−1.36784	−	0.497853i	−0.449370	−	0.893346i	$-0.648352\pi$
$751$	−771463.	−	280790.i	−1.36784	−	0.497853i	−0.918469	+	0.395493i	$0.870574\pi$
$752$	245166.	−	43229.3i	0.433535	−	0.0764439i
$753$		0			0
$754$	301018.	+	252584.i	0.529481	+	0.444287i
$755$		−	1.26521e6i		−	2.21958i
$756$		0			0
$757$	−193283.			−0.337289			−0.168645	−	0.985677i	$-0.553939\pi$
$757$	−193283.			−0.337289			−0.168645	+	0.985677i	$0.553939\pi$
$758$	−321717.	+	383408.i	−0.559933	+	0.667302i
$759$		0			0
$760$	43812.9	+	248475.i	0.0758533	+	0.430186i
$761$	−161459.	+	443606.i	−0.278801	+	0.765999i	0.718698	+	0.695322i	$0.244738\pi$
$761$	−161459.	+	443606.i	−0.278801	+	0.765999i	−0.997499	+	0.0706771i	$0.977484\pi$
$762$		0			0
$763$	−4776.10	+	27086.6i	−0.00820398	+	0.0465271i
$764$	110743.	+	63937.4i	0.189727	+	0.109539i
$765$		0			0
$766$	−15870.0	−	27487.6i	−0.0270470	−	0.0468467i
$767$	86323.0	+	237171.i	0.146736	+	0.403153i
$768$		0			0
$769$	−472750.	+	396684.i	−0.799427	+	0.670799i	−0.948059	−	0.318094i	$-0.896957\pi$
$769$	−472750.	+	396684.i	−0.799427	+	0.670799i	0.148632	+	0.988893i	$0.452513\pi$
$770$	116447.	+	138776.i	0.196403	+	0.234063i
$771$		0			0
$772$	120079.	−	43705.1i	0.201480	−	0.0733326i
$773$	−723051.	+	417454.i	−1.21007	+	0.698633i	−0.962774	−	0.270307i	$-0.912875\pi$
$773$	−723051.	+	417454.i	−1.21007	+	0.698633i	−0.247294	+	0.968941i	$0.579541\pi$
$774$		0			0
$775$	−484318.	+	838863.i	−0.806356	+	1.39665i
$776$	−351220.	−	61929.6i	−0.583252	−	0.102843i
$777$		0			0
$778$	435900.	+	158655.i	0.720157	+	0.262116i
$779$	21641.9	−	3816.05i	0.0356632	−	0.00628839i
$780$		0			0
$781$	532637.	+	446936.i	0.873232	+	0.732729i
$782$			822541.i			1.34507i
$783$		0			0
$784$	−134920.			−0.219506
$785$	−775575.	+	924295.i	−1.25859	+	1.49993i
$786$		0			0
$787$	−115675.	−	656026.i	−0.186763	−	1.05918i	−0.923670	−	0.383190i	$-0.874826\pi$
$787$	−115675.	−	656026.i	−0.186763	−	1.05918i	0.736907	−	0.675994i	$-0.236286\pi$
$788$	−49760.9	+	136717.i	−0.0801375	+	0.220176i
$789$		0			0
$790$	76975.2	−	436548.i	0.123338	−	0.699484i
$791$	149827.	+	86502.7i	0.239462	+	0.138254i
$792$		0			0
$793$	303954.	+	526464.i	0.483350	+	0.837186i
$794$	220697.	+	606360.i	0.350070	+	0.961810i
$795$		0			0
$796$	−49797.7	+	41785.3i	−0.0785929	+	0.0659473i
$797$	−106764.	−	127236.i	−0.168076	−	0.200305i	0.675431	−	0.737423i	$-0.263958\pi$
$797$	−106764.	−	127236.i	−0.168076	−	0.200305i	−0.843507	+	0.537118i	$0.819513\pi$
$798$		0			0
$799$	1.44459e6	−	525789.i	2.26283	−	0.823602i
$800$	−108191.	+	62464.1i	−0.169048	+	0.0976001i
$801$		0			0
$802$	14085.7	−	24397.1i	0.0218992	−	0.0379306i
$803$	−494054.	−	87115.1i	−0.766202	−	0.135102i
$804$		0			0
$805$	−429129.	−	156190.i	−0.662211	−	0.241025i
$806$	556342.	−	98098.0i	0.856390	−	0.151005i
$807$		0			0
$808$	−143211.	−	120168.i	−0.219358	−	0.184063i
$809$		−	710247.i		−	1.08521i	−0.839989	−	0.542603i	$-0.817439\pi$
$809$		−	710247.i		−	1.08521i	0.839989	−	0.542603i	$-0.182561\pi$
$810$		0			0
$811$	−997435.			−1.51650			−0.758251	−	0.651963i	$-0.773946\pi$
$811$	−997435.			−1.51650			−0.758251	+	0.651963i	$0.773946\pi$
$812$	85914.7	−	102389.i	0.130303	−	0.155289i
$813$		0			0
$814$	−57756.9	−	327556.i	−0.0871676	−	0.494352i
$815$	316567.	−	869760.i	0.476596	−	1.30944i
$816$		0			0
$817$	1094.14	−	6205.18i	0.00163919	−	0.00929630i
$818$	588379.	+	339701.i	0.879327	+	0.507680i
$819$		0			0
$820$	10367.6	+	17957.2i	0.0154188	+	0.0267062i
$821$	354876.	+	975014.i	0.526491	+	1.44652i	0.863176	+	0.504904i	$0.168472\pi$
$821$	354876.	+	975014.i	0.526491	+	1.44652i	−0.336685	+	0.941617i	$0.609306\pi$
$822$		0			0
$823$	−445728.	+	374010.i	−0.658068	+	0.552184i	−0.909507	−	0.415689i	$-0.863541\pi$
$823$	−445728.	+	374010.i	−0.658068	+	0.552184i	0.251439	+	0.967873i	$0.419096\pi$
$824$	−8400.57	−	10011.4i	−0.0123724	−	0.0147449i
$825$		0			0
$826$	80671.8	−	29362.1i	0.118239	−	0.0430356i
$827$	1.06628e6	−	615618.i	1.55905	−	0.900120i	0.561705	−	0.827338i	$-0.310146\pi$
$827$	1.06628e6	−	615618.i	1.55905	−	0.900120i	0.997348	−	0.0727821i	$-0.0231878\pi$
$828$		0			0
$829$	518398.	−	897892.i	0.754317	−	1.30652i	−0.191395	−	0.981513i	$-0.561301\pi$
$829$	518398.	−	897892.i	0.754317	−	1.30652i	0.945713	−	0.325003i	$-0.105365\pi$
$830$	441979.	+	77932.9i	0.641573	+	0.113127i
$831$		0			0
$832$	68466.1	+	24919.6i	0.0989075	+	0.0359994i
$833$	−820504.	+	144677.i	−1.18247	+	0.208502i
$834$		0			0
$835$	378304.	+	317435.i	0.542585	+	0.455283i
$836$		−	253861.i		−	0.363231i
$837$		0			0
$838$	−114825.			−0.163511
$839$	677324.	−	807204.i	0.962217	−	1.14673i	−0.0269070	−	0.999638i	$-0.508566\pi$
$839$	677324.	−	807204.i	0.962217	−	1.14673i	0.989124	−	0.147087i	$-0.0469898\pi$
$840$		0			0
$841$	−42689.5	−	242104.i	−0.0603573	−	0.342303i
$842$	263581.	−	724183.i	0.371784	−	1.02147i
$843$		0			0
$844$	−48628.1	+	275784.i	−0.0682657	+	0.387154i
$845$	260996.	+	150686.i	0.365527	+	0.211037i
$846$		0			0
$847$	34141.4	+	59134.7i	0.0475899	+	0.0824281i
$848$	98848.0	+	271583.i	0.137460	+	0.377668i
$849$		0			0
$850$	−590970.	+	495883.i	−0.817952	+	0.686343i
$851$	538942.	+	642287.i	0.744189	+	0.886890i
$852$		0			0
$853$	−953730.	+	347129.i	−1.31077	+	0.477082i	−0.900490	−	0.434876i	$-0.856792\pi$
$853$	−953730.	+	347129.i	−1.31077	+	0.477082i	−0.410282	+	0.911959i	$0.634570\pi$
$854$	179073.	−	103388.i	0.245535	−	0.141760i
$855$		0			0
$856$	−231381.	+	400763.i	−0.315777	+	0.546941i
$857$	805804.	+	142085.i	1.09715	+	0.193458i	0.692789	−	0.721140i	$-0.256382\pi$
$857$	805804.	+	142085.i	1.09715	+	0.193458i	0.404365	+	0.914598i	$0.367493\pi$
$858$		0			0
$859$	799728.	+	291077.i	1.08382	+	0.394477i	0.821327	−	0.570457i	$-0.193234\pi$
$859$	799728.	+	291077.i	1.08382	+	0.394477i	0.262490	+	0.964935i	$0.415456\pi$
$860$	5854.89	−	1032.37i	0.00791629	−	0.00139586i
$861$		0			0
$862$	105352.	+	88400.5i	0.141784	+	0.118971i
$863$			16791.3i			0.0225457i	0.999936	+	0.0112729i	$0.00358834\pi$
$863$			16791.3i			0.0225457i	−0.999936	+	0.0112729i	$0.996412\pi$
$864$		0			0
$865$	743333.			0.993462
$866$	451549.	−	538135.i	0.602100	−	0.717555i
$867$		0			0
$868$	−33367.3	−	189235.i	−0.0442876	−	0.251167i
$869$	−152544.	+	419113.i	−0.202003	+	0.554998i
$870$		0			0
$871$	30401.6	−	172416.i	0.0400738	−	0.227270i
$872$	31494.4	+	18183.3i	0.0414190	+	0.0239133i
$873$		0			0
$874$	319968.	+	554202.i	0.418875	+	0.725513i
$875$	−13826.2	−	37987.1i	−0.0180587	−	0.0496158i
$876$		0			0
$877$	−469556.	+	394004.i	−0.610504	+	0.512273i	−0.894802	−	0.446462i	$-0.852684\pi$
$877$	−469556.	+	394004.i	−0.610504	+	0.512273i	0.284299	+	0.958736i	$0.408239\pi$
$878$	295886.	+	352623.i	0.383827	+	0.457427i
$879$		0			0
$880$	225085.	−	81924.1i	0.290657	−	0.105790i
$881$	26492.8	−	15295.7i	0.0341332	−	0.0197068i	−0.482836	−	0.875711i	$-0.660393\pi$
$881$	26492.8	−	15295.7i	0.0341332	−	0.0197068i	0.516969	+	0.856004i	$0.327060\pi$
$882$		0			0
$883$	−282975.	+	490127.i	−0.362933	+	0.628619i	−0.988442	−	0.151598i	$-0.951558\pi$
$883$	−282975.	+	490127.i	−0.362933	+	0.628619i	0.625509	+	0.780217i	$0.284891\pi$
$884$	443091.	+	78128.9i	0.567007	+	0.0999786i
$885$		0			0
$886$	−4429.98	−	1612.38i	−0.00564331	−	0.00205400i
$887$	−249963.	+	44075.3i	−0.317709	+	0.0560206i	−0.330229	−	0.943901i	$-0.607126\pi$
$887$	−249963.	+	44075.3i	−0.317709	+	0.0560206i	0.0125199	+	0.999922i	$0.496015\pi$
$888$		0			0
$889$	268146.	+	225001.i	0.339288	+	0.284696i
$890$			853159.i			1.07708i
$891$		0			0
$892$	86865.3			0.109173
$893$	768788.	−	916206.i	0.964059	−	1.14892i
$894$		0			0
$895$	−118739.	−	673405.i	−0.148234	−	0.840679i
$896$	8476.23	−	23288.2i	0.0105581	−	0.0290082i
$897$		0			0
$898$	59308.7	−	336356.i	0.0735471	−	0.417106i
$899$	−1.18667e6	−	685124.i	−1.46828	−	0.847714i
$900$		0			0
$901$	892355.	+	1.54560e6i	1.09923	+	1.90392i
$902$	−7135.50	−	19604.6i	−0.00877024	−	0.0240960i
$903$		0			0
$904$	175232.	−	147037.i	0.214425	−	0.179924i
$905$	−1.23145e6	−	1.46758e6i	−1.50355	−	1.79187i
$906$		0			0
$907$	202497.	−	73702.8i	0.246152	−	0.0895921i	−0.215998	−	0.976394i	$-0.569300\pi$
$907$	202497.	−	73702.8i	0.246152	−	0.0895921i	0.462150	+	0.886802i	$0.347078\pi$
$908$	50336.7	−	29061.9i	0.0610539	−	0.0352495i
$909$		0			0
$910$	−124898.	+	216330.i	−0.150825	+	0.261237i
$911$	−240915.	−	42479.9i	−0.290287	−	0.0511854i	0.0266084	−	0.999646i	$-0.491529\pi$
$911$	−240915.	−	42479.9i	−0.290287	−	0.0511854i	−0.316895	+	0.948461i	$0.602640\pi$
$912$		0			0
$913$	−424327.	−	154442.i	−0.509048	−	0.185278i
$914$	−308039.	+	54315.6i	−0.368734	+	0.0650178i
$915$		0			0
$916$	−603893.	−	506727.i	−0.719729	−	0.603925i
$917$			565208.i			0.672156i
$918$		0			0
$919$	−160579.			−0.190133			−0.0950665	−	0.995471i	$-0.530306\pi$
$919$	−160579.			−0.190133			−0.0950665	+	0.995471i	$0.530306\pi$
$920$	−388123.	+	462547.i	−0.458557	+	0.546487i
$921$		0			0
$922$	−5632.07	−	31941.0i	−0.00662531	−	0.0375740i
$923$	−327910.	+	900925.i	−0.384903	+	1.05751i
$924$		0			0
$925$	−136552.	+	774427.i	−0.159594	+	0.905101i
$926$	−959628.	−	554041.i	−1.11913	−	0.646131i
$927$		0			0
$928$	−88362.7	−	153049.i	−0.102606	−	0.177719i
$929$	205566.	+	564788.i	0.238188	+	0.654417i	0.999978	+	0.00659270i	$0.00209854\pi$
$929$	205566.	+	564788.i	0.238188	+	0.654417i	−0.761790	+	0.647824i	$0.775679\pi$
$930$		0			0
$931$	−496550.	+	416655.i	−0.572880	+	0.480703i
$932$	−457395.	−	545103.i	−0.526575	−	0.627547i
$933$		0			0
$934$	88072.8	−	32055.9i	0.100960	−	0.0367463i
$935$	1.28098e6	−	739574.i	1.46527	−	0.845977i
$936$		0			0
$937$	78489.9	−	135948.i	0.0893993	−	0.154844i	−0.817858	−	0.575420i	$-0.804839\pi$
$937$	78489.9	−	135948.i	0.0893993	−	0.154844i	0.907257	+	0.420576i	$0.138172\pi$
$938$	−58646.1	−	10340.9i	−0.0666551	−	0.0117531i
$939$		0			0
$940$	1.06045e6	+	385972.i	1.20014	+	0.436817i
$941$	847701.	−	149473.i	0.957334	−	0.168804i	0.326910	−	0.945055i	$-0.393992\pi$
$941$	847701.	−	149473.i	0.957334	−	0.168804i	0.630423	+	0.776252i	$0.282881\pi$
$942$		0			0
$943$	40287.3	+	33805.1i	0.0453049	+	0.0380153i
$944$		−	113510.i		−	0.127377i
$945$		0			0
$946$	−5981.79			−0.00668419
$947$	−459377.	+	547464.i	−0.512235	+	0.610457i	−0.958726	−	0.284330i	$-0.908229\pi$
$947$	−459377.	+	547464.i	−0.512235	+	0.610457i	0.446492	+	0.894788i	$0.352673\pi$
$948$		0			0
$949$	−120121.	−	681239.i	−0.133379	−	0.756427i
$950$	−205278.	+	563998.i	−0.227455	+	0.624928i
$951$		0			0
$952$	26575.0	−	150714.i	0.0293223	−	0.166295i
$953$	1.02302e6	+	590641.i	1.12641	+	0.650336i	0.943031	−	0.332706i	$-0.107962\pi$
$953$	1.02302e6	+	590641.i	1.12641	+	0.650336i	0.183384	+	0.983041i	$0.441295\pi$
$954$		0			0
$955$	289835.	+	502009.i	0.317793	+	0.550433i
$956$	144140.	+	396021.i	0.157713	+	0.433313i
$957$		0			0
$958$	−211010.	+	177058.i	−0.229917	+	0.192923i
$959$	177669.	+	211738.i	0.193186	+	0.230230i
$960$		0			0
$961$	−983300.	+	357892.i	−1.06473	+	0.387530i
$962$	397182.	−	229313.i	0.429180	−	0.247787i
$963$		0			0
$964$	−97456.7	+	168800.i	−0.104871	+	0.181643i
$965$	570463.	+	100588.i	0.612594	+	0.108017i
$966$		0			0
$967$	766640.	+	279034.i	0.819858	+	0.298404i	0.717689	−	0.696363i	$-0.245200\pi$
$967$	766640.	+	279034.i	0.819858	+	0.298404i	0.102168	+	0.994767i	$0.467422\pi$
$968$	88912.3	−	15677.6i	0.0948880	−	0.0167313i
$969$		0			0
$970$	−1.23845e6	−	1.03918e6i	−1.31624	−	1.10445i
$971$			890566.i			0.944556i	0.881450	+	0.472278i	$0.156568\pi$
$971$			890566.i			0.944556i	−0.881450	+	0.472278i	$0.843432\pi$
$972$		0			0
$973$	−8406.97			−0.00888001
$974$	163072.	−	194342.i	0.171895	−	0.204856i
$975$		0			0
$976$	−47475.3	−	269246.i	−0.0498389	−	0.282650i
$977$	−271992.	+	747292.i	−0.284949	+	0.782891i	0.711805	+	0.702378i	$0.247878\pi$
$977$	−271992.	+	747292.i	−0.284949	+	0.782891i	−0.996754	+	0.0805133i	$0.974344\pi$
$978$		0			0
$979$	149061.	−	845367.i	0.155525	−	0.882023i
$980$	−529668.	−	305804.i	−0.551508	−	0.318413i
$981$		0			0
$982$	−61558.2	−	106622.i	−0.0638356	−	0.110567i
$983$	−117075.	−	321662.i	−0.121160	−	0.332884i	0.864255	−	0.503054i	$-0.167790\pi$
$983$	−117075.	−	321662.i	−0.121160	−	0.332884i	−0.985415	+	0.170170i	$0.945568\pi$
$984$		0			0
$985$	−505227.	+	423935.i	−0.520731	+	0.436946i
$986$	−701484.	−	835996.i	−0.721546	−	0.859905i
$987$		0			0
$988$	328933.	−	119722.i	0.336971	−	0.122648i
$989$	13058.8	−	7539.50i	0.0133509	−	0.00770815i
$990$		0			0
$991$	389087.	−	673919.i	0.396187	−	0.686215i	−0.597065	−	0.802193i	$-0.703667\pi$
$991$	389087.	−	673919.i	0.396187	−	0.686215i	0.993252	+	0.115977i	$0.0370000\pi$
$992$	−250208.	−	44118.5i	−0.254260	−	0.0448329i
$993$		0			0
$994$	306443.	+	111536.i	0.310154	+	0.112887i
$995$	−290203.	+	51170.7i	−0.293127	+	0.0516863i
$996$		0			0
$997$	93503.6	+	78458.8i	0.0940672	+	0.0789317i	0.688608	−	0.725133i	$-0.258222\pi$
$997$	93503.6	+	78458.8i	0.0940672	+	0.0789317i	−0.594541	+	0.804065i	$0.702666\pi$
$998$			205024.i			0.205846i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.35.6		72
3.2	odd	2		54.5.f.a.11.11	yes	72
27.5	odd	18	inner	162.5.f.a.125.6		72
27.22	even	9		54.5.f.a.5.11	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.5.11	✓	72	27.22	even	9
54.5.f.a.11.11	yes	72	3.2	odd	2
162.5.f.a.35.6		72	1.1	even	1	trivial
162.5.f.a.125.6		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)

\(f(q)\)	\(=\)	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(12.4033 - 34.0778i) q^{5} +(-2.97171 + 16.8534i) q^{7} +(19.5959 + 11.3137i) q^{8} +O(q^{10})\)	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(12.4033 - 34.0778i) q^{5} +(-2.97171 + 16.8534i) q^{7} +(19.5959 + 11.3137i) q^{8} +(51.2862 + 88.8303i) q^{10} +(-35.2977 - 96.9796i) q^{11} +(109.012 - 91.4718i) q^{13} +(-31.1135 - 37.0796i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(-342.265 + 197.607i) q^{17} +(-153.738 + 266.282i) q^{19} +(-285.711 - 50.3786i) q^{20} +(274.300 + 99.8370i) q^{22} +(-724.657 + 127.777i) q^{23} +(-528.676 - 443.612i) q^{25} +402.499i q^{26} +136.907 q^{28} +(627.540 - 747.873i) q^{29} +(-243.722 - 1382.22i) q^{31} +(61.9123 - 170.103i) q^{32} +(194.109 - 1100.85i) q^{34} +(537.467 + 310.307i) q^{35} +(-569.723 - 986.789i) q^{37} +(-297.446 - 817.226i) q^{38} +(628.600 - 527.458i) q^{40} +(-45.9410 - 54.7504i) q^{41} +(-19.2565 + 7.00879i) q^{43} +(-715.015 + 412.814i) q^{44} +(1040.63 - 1802.42i) q^{46} +(-3830.71 - 675.458i) q^{47} +(1981.00 + 721.024i) q^{49} +(1922.35 - 338.962i) q^{50} +(-872.095 - 731.775i) q^{52} -4515.82i q^{53} -3742.66 q^{55} +(-248.908 + 296.637i) q^{56} +(479.501 + 2719.38i) q^{58} +(-606.606 + 1666.64i) q^{59} +(-741.802 + 4206.97i) q^{61} +(3437.96 + 1984.91i) q^{62} +(256.000 + 443.405i) q^{64} +(-1765.05 - 4849.44i) q^{65} +(942.455 - 790.814i) q^{67} +(2032.30 + 2422.01i) q^{68} +(-1649.50 + 600.369i) q^{70} +(-5834.63 + 3368.63i) q^{71} +(2430.52 - 4209.78i) q^{73} +(3173.88 + 559.640i) q^{74} +(2311.46 + 841.304i) q^{76} +(1739.33 - 306.691i) q^{77} +(-3310.58 - 2777.91i) q^{79} +2320.95i q^{80} +202.152 q^{82} +(2812.47 - 3351.77i) q^{83} +(2488.78 + 14114.6i) q^{85} +(19.8239 - 54.4656i) q^{86} +(405.508 - 2299.75i) q^{88} +(7203.27 + 4158.81i) q^{89} +(1217.66 + 2109.05i) q^{91} +(2013.37 + 5531.68i) q^{92} +(8428.05 - 7071.97i) q^{94} +(7167.44 + 8541.82i) q^{95} +(-14810.8 + 5390.70i) q^{97} +(-5163.85 + 2981.35i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 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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