LMFDB - Embedded newform 162.5.f.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(45.7302 + 8.06347i) q^{5} +(-14.1135 + 11.8427i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})$	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(45.7302 + 8.06347i) q^{5} +(-14.1135 + 11.8427i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-65.6700 + 113.744i) q^{10} +(-26.2774 + 4.63341i) q^{11} +(264.299 - 96.1968i) q^{13} +(-17.8229 - 48.9681i) q^{14} +(11.1135 + 63.0277i) q^{16} +(198.275 + 114.474i) q^{17} +(-296.757 - 513.998i) q^{19} +(-238.786 - 284.574i) q^{20} +(13.1053 - 74.3237i) q^{22} +(35.9381 - 42.8294i) q^{23} +(1438.93 + 523.726i) q^{25} +795.525i q^{26} +147.391 q^{28} +(-275.398 + 756.649i) q^{29} +(1191.27 + 999.596i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-496.063 + 416.246i) q^{34} +(-740.909 + 427.764i) q^{35} +(-341.738 + 591.907i) q^{37} +(1653.21 - 291.505i) q^{38} +(987.354 - 359.367i) q^{40} +(645.848 + 1774.45i) q^{41} +(13.4427 + 76.2371i) q^{43} +(184.864 + 106.731i) q^{44} +(79.0684 + 136.951i) q^{46} +(-650.504 - 775.240i) q^{47} +(-357.986 + 2030.24i) q^{49} +(-2783.97 + 3317.81i) q^{50} +(-2114.39 - 769.574i) q^{52} -875.975i q^{53} -1239.03 q^{55} +(-142.583 + 391.745i) q^{56} +(-1744.65 - 1463.93i) q^{58} +(-554.966 - 97.8554i) q^{59} +(2577.69 - 2162.94i) q^{61} +(-3809.19 + 2199.24i) q^{62} +(256.000 - 443.405i) q^{64} +(12862.1 - 2267.94i) q^{65} +(179.020 - 65.1580i) q^{67} +(-626.440 - 1721.13i) q^{68} +(-420.194 - 2383.04i) q^{70} +(-1111.68 - 641.827i) q^{71} +(-1587.66 - 2749.92i) q^{73} +(-1242.61 - 1480.89i) q^{74} +(-824.501 + 4675.98i) q^{76} +(315.995 - 376.588i) q^{77} +(3735.10 + 1359.47i) q^{79} +2971.88i q^{80} -5341.01 q^{82} +(913.049 - 2508.58i) q^{83} +(8144.11 + 6833.72i) q^{85} +(-215.631 - 38.0216i) q^{86} +(-462.508 + 388.091i) q^{88} +(3034.04 - 1751.71i) q^{89} +(-2590.96 + 4487.68i) q^{91} +(-440.483 + 77.6691i) q^{92} +(2689.76 - 978.992i) q^{94} +(-9426.16 - 25898.2i) q^{95} +(-1155.73 - 6554.45i) q^{97} +(-5049.77 - 2915.48i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	45.7302	+	8.06347i	1.82921	+	0.322539i	0.978993	−	0.203895i	$-0.0653600\pi$
$5$	45.7302	+	8.06347i	1.82921	+	0.322539i	0.850216	+	0.526434i	$0.176471\pi$
$6$		0			0
$7$	−14.1135	+	11.8427i	−0.288032	+	0.241687i	−0.775342	−	0.631542i	$-0.782422\pi$
$7$	−14.1135	+	11.8427i	−0.288032	+	0.241687i	0.487310	+	0.873229i	$0.337978\pi$
$8$	19.5959	−	11.3137i	0.306186	−	0.176777i
$9$		0			0
$10$	−65.6700	+	113.744i	−0.656700	+	1.13744i
$11$	−26.2774	+	4.63341i	−0.217168	+	0.0382927i	−0.281174	−	0.959657i	$-0.590724\pi$
$11$	−26.2774	+	4.63341i	−0.217168	+	0.0382927i	0.0640052	+	0.997950i	$0.479613\pi$
$12$		0			0
$13$	264.299	−	96.1968i	1.56390	−	0.569212i	0.592272	−	0.805738i	$-0.298231\pi$
$13$	264.299	−	96.1968i	1.56390	−	0.569212i	0.971625	+	0.236526i	$0.0760090\pi$
$14$	−17.8229	−	48.9681i	−0.0909333	−	0.249837i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	198.275	+	114.474i	0.686074	+	0.396105i	0.802139	−	0.597137i	$-0.203695\pi$
$17$	198.275	+	114.474i	0.686074	+	0.396105i	−0.116066	+	0.993242i	$0.537028\pi$
$18$		0			0
$19$	−296.757	−	513.998i	−0.822042	−	1.42382i	−0.904159	−	0.427196i	$-0.859502\pi$
$19$	−296.757	−	513.998i	−0.822042	−	1.42382i	0.0821174	−	0.996623i	$-0.473832\pi$
$20$	−238.786	−	284.574i	−0.596966	−	0.711436i
$21$		0			0
$22$	13.1053	−	74.3237i	0.0270770	−	0.153561i
$23$	35.9381	−	42.8294i	0.0679360	−	0.0809630i	−0.731006	−	0.682371i	$-0.760949\pi$
$23$	35.9381	−	42.8294i	0.0679360	−	0.0809630i	0.798942	+	0.601408i	$0.205393\pi$
$24$		0			0
$25$	1438.93	+	523.726i	2.30228	+	0.837962i
$26$			795.525i			1.17681i
$27$		0			0
$28$	147.391			0.187999
$29$	−275.398	+	756.649i	−0.327465	+	0.899701i	0.661287	+	0.750133i	$0.270011\pi$
$29$	−275.398	+	756.649i	−0.327465	+	0.899701i	−0.988751	+	0.149568i	$0.952212\pi$
$30$		0			0
$31$	1191.27	+	999.596i	1.23962	+	1.04016i	0.997554	+	0.0699016i	$0.0222685\pi$
$31$	1191.27	+	999.596i	1.23962	+	1.04016i	0.242063	+	0.970261i	$0.422176\pi$
$32$	−178.269	−	31.4337i	−0.174091	−	0.0306970i
$33$		0			0
$34$	−496.063	+	416.246i	−0.429120	+	0.360075i
$35$	−740.909	+	427.764i	−0.604823	+	0.349195i
$36$		0			0
$37$	−341.738	+	591.907i	−0.249626	+	0.432365i	−0.963422	−	0.267989i	$-0.913641\pi$
$37$	−341.738	+	591.907i	−0.249626	+	0.432365i	0.713796	+	0.700354i	$0.246974\pi$
$38$	1653.21	−	291.505i	1.14488	−	0.201873i
$39$		0			0
$40$	987.354	−	359.367i	0.617096	−	0.224605i
$41$	645.848	+	1774.45i	0.384205	+	1.05559i	0.969568	+	0.244823i	$0.0787297\pi$
$41$	645.848	+	1774.45i	0.384205	+	1.05559i	−0.585363	+	0.810771i	$0.699048\pi$
$42$		0			0
$43$	13.4427	+	76.2371i	0.00727023	+	0.0412315i	0.988227	−	0.152994i	$-0.0488916\pi$
$43$	13.4427	+	76.2371i	0.00727023	+	0.0412315i	−0.980957	+	0.194226i	$0.937781\pi$
$44$	184.864	+	106.731i	0.0954874	+	0.0551296i
$45$		0			0
$46$	79.0684	+	136.951i	0.0373669	+	0.0647214i
$47$	−650.504	−	775.240i	−0.294479	−	0.350946i	0.598437	−	0.801170i	$-0.295789\pi$
$47$	−650.504	−	775.240i	−0.294479	−	0.350946i	−0.892916	+	0.450224i	$0.851344\pi$
$48$		0			0
$49$	−357.986	+	2030.24i	−0.149099	+	0.845581i
$50$	−2783.97	+	3317.81i	−1.11359	+	1.32712i
$51$		0			0
$52$	−2114.39	−	769.574i	−0.781948	−	0.284606i
$53$		−	875.975i		−	0.311846i	−0.987769	−	0.155923i	$-0.950165\pi$
$53$		−	875.975i		−	0.311846i	0.987769	−	0.155923i	$-0.0498351\pi$
$54$		0			0
$55$	−1239.03			−0.409597
$56$	−142.583	+	391.745i	−0.0454666	+	0.124919i
$57$		0			0
$58$	−1744.65	−	1463.93i	−0.518623	−	0.435176i
$59$	−554.966	−	97.8554i	−0.159427	−	0.0281113i	0.0933648	−	0.995632i	$-0.470238\pi$
$59$	−554.966	−	97.8554i	−0.159427	−	0.0281113i	−0.252792	+	0.967521i	$0.581349\pi$
$60$		0			0
$61$	2577.69	−	2162.94i	0.692741	−	0.581279i	−0.226957	−	0.973905i	$-0.572878\pi$
$61$	2577.69	−	2162.94i	0.692741	−	0.581279i	0.919698	+	0.392626i	$0.128433\pi$
$62$	−3809.19	+	2199.24i	−0.990944	+	0.572122i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	12862.1	−	2267.94i	3.04429	−	0.536790i
$66$		0			0
$67$	179.020	−	65.1580i	0.0398797	−	0.0145150i	−0.322003	−	0.946739i	$-0.604356\pi$
$67$	179.020	−	65.1580i	0.0398797	−	0.0145150i	0.361883	+	0.932224i	$0.382134\pi$
$68$	−626.440	−	1721.13i	−0.135476	−	0.372217i
$69$		0			0
$70$	−420.194	−	2383.04i	−0.0857538	−	0.486334i
$71$	−1111.68	−	641.827i	−0.220527	−	0.127321i	0.385667	−	0.922638i	$-0.373971\pi$
$71$	−1111.68	−	641.827i	−0.220527	−	0.127321i	−0.606194	+	0.795317i	$0.707305\pi$
$72$		0			0
$73$	−1587.66	−	2749.92i	−0.297929	−	0.516029i	0.677733	−	0.735308i	$-0.262963\pi$
$73$	−1587.66	−	2749.92i	−0.297929	−	0.516029i	−0.975662	+	0.219280i	$0.929629\pi$
$74$	−1242.61	−	1480.89i	−0.226920	−	0.270432i
$75$		0			0
$76$	−824.501	+	4675.98i	−0.142746	+	0.809553i
$77$	315.995	−	376.588i	0.0532965	−	0.0635163i
$78$		0			0
$79$	3735.10	+	1359.47i	0.598478	+	0.217828i	0.623454	−	0.781860i	$-0.285729\pi$
$79$	3735.10	+	1359.47i	0.598478	+	0.217828i	−0.0249763	+	0.999688i	$0.507951\pi$
$80$			2971.88i			0.464357i
$81$		0			0
$82$	−5341.01			−0.794321
$83$	913.049	−	2508.58i	0.132537	−	0.364143i	−0.855617	−	0.517610i	$-0.826822\pi$
$83$	913.049	−	2508.58i	0.132537	−	0.364143i	0.988154	+	0.153467i	$0.0490439\pi$
$84$		0			0
$85$	8144.11	+	6833.72i	1.12721	+	0.945844i
$86$	−215.631	−	38.0216i	−0.0291551	−	0.00514083i
$87$		0			0
$88$	−462.508	+	388.091i	−0.0597247	+	0.0501150i
$89$	3034.04	−	1751.71i	0.383038	−	0.221147i	−0.296101	−	0.955157i	$-0.595687\pi$
$89$	3034.04	−	1751.71i	0.383038	−	0.221147i	0.679139	+	0.734009i	$0.262353\pi$
$90$		0			0
$91$	−2590.96	+	4487.68i	−0.312880	+	0.541925i
$92$	−440.483	+	77.6691i	−0.0520420	+	0.00917641i
$93$		0			0
$94$	2689.76	−	978.992i	0.304409	−	0.110796i
$95$	−9426.16	−	25898.2i	−1.04445	−	2.86960i
$96$		0			0
$97$	−1155.73	−	6554.45i	−0.122832	−	0.696615i	−0.982572	−	0.185883i	$-0.940486\pi$
$97$	−1155.73	−	6554.45i	−0.122832	−	0.696615i	0.859740	−	0.510732i	$-0.170626\pi$
$98$	−5049.77	−	2915.48i	−0.525798	−	0.303570i
$99$		0			0
$100$	−6125.09	−	10609.0i	−0.612509	−	1.06090i
$101$	−9029.17	−	10760.5i	−0.885126	−	1.05485i	−0.998122	−	0.0612563i	$-0.980489\pi$
$101$	−9029.17	−	10760.5i	−0.885126	−	1.05485i	0.112996	−	0.993595i	$-0.463955\pi$
$102$		0			0
$103$	2925.17	−	16589.5i	0.275726	−	1.56372i	−0.460922	−	0.887441i	$-0.652481\pi$
$103$	2925.17	−	16589.5i	0.275726	−	1.56372i	0.736647	−	0.676277i	$-0.236408\pi$
$104$	4090.83	−	4875.26i	0.378220	−	0.450745i
$105$		0			0
$106$	2328.21	+	847.400i	0.207210	+	0.0754183i
$107$			16203.9i			1.41531i	0.706556	+	0.707657i	$0.250248\pi$
$107$			16203.9i			1.41531i	−0.706556	+	0.707657i	$0.749752\pi$
$108$		0			0
$109$	−16906.9			−1.42302			−0.711508	−	0.702678i	$-0.751987\pi$
$109$	−16906.9			−1.42302			−0.711508	+	0.702678i	$0.751987\pi$
$110$	1198.61	−	3293.16i	0.0990590	−	0.272162i
$111$		0			0
$112$	−903.267	−	757.931i	−0.0720079	−	0.0604218i
$113$	−8991.58	−	1585.46i	−0.704173	−	0.124165i	−0.189915	−	0.981801i	$-0.560821\pi$
$113$	−8991.58	−	1585.46i	−0.704173	−	0.124165i	−0.514257	+	0.857636i	$0.671932\pi$
$114$		0			0
$115$	1988.81	−	1668.81i	0.150383	−	0.126186i
$116$	5578.65	−	3220.84i	0.414585	−	0.239361i
$117$		0			0
$118$	796.948	−	1380.35i	0.0572355	−	0.0991348i
$119$	−4154.05	+	732.471i	−0.293344	+	0.0517245i
$120$		0			0
$121$	−13089.0	+	4764.01i	−0.893997	+	0.325388i
$122$	3255.17	+	8943.50i	0.218702	+	0.600880i
$123$		0			0
$124$	−2160.32	−	12251.8i	−0.140499	−	0.796810i
$125$	36445.3	+	21041.7i	2.33250	+	1.34667i
$126$		0			0
$127$	−2509.06	−	4345.82i	−0.155562	−	0.269442i	0.777701	−	0.628634i	$-0.216386\pi$
$127$	−2509.06	−	4345.82i	−0.155562	−	0.269442i	−0.933264	+	0.359192i	$0.883052\pi$
$128$	930.856	+	1109.35i	0.0568149	+	0.0677094i
$129$		0			0
$130$	−6414.70	+	36379.5i	−0.379568	+	2.15264i
$131$	−13504.5	+	16094.1i	−0.786931	+	0.937828i	−0.999224	−	0.0393779i	$-0.987462\pi$
$131$	−13504.5	+	16094.1i	−0.786931	+	0.937828i	0.212293	+	0.977206i	$0.431907\pi$
$132$		0			0
$133$	10275.4	+	3739.94i	0.580893	+	0.211428i
$134$			538.842i			0.0300090i
$135$		0			0
$136$	5180.51			0.280088
$137$	4294.69	−	11799.6i	0.228818	−	0.628673i	−0.771150	−	0.636654i	$-0.780318\pi$
$137$	4294.69	−	11799.6i	0.228818	−	0.628673i	0.999968	+	0.00798061i	$0.00254033\pi$
$138$		0			0
$139$	4449.78	+	3733.81i	0.230308	+	0.193251i	0.750638	−	0.660714i	$-0.229746\pi$
$139$	4449.78	+	3733.81i	0.230308	+	0.193251i	−0.520330	+	0.853965i	$0.674191\pi$
$140$	6740.24	+	1188.49i	0.343890	+	0.0606371i
$141$		0			0
$142$	2781.29	−	2333.78i	0.137934	−	0.115740i
$143$	−6499.35	+	3752.40i	−0.317832	+	0.183501i
$144$		0			0
$145$	−18695.2	+	32381.1i	−0.889190	+	1.54012i
$146$	8844.74	−	1559.57i	0.414934	−	0.0731641i
$147$		0			0
$148$	5138.06	−	1870.10i	0.234572	−	0.0853771i
$149$	−7759.33	−	21318.6i	−0.349504	−	0.960253i	−0.982527	−	0.186120i	$-0.940409\pi$
$149$	−7759.33	−	21318.6i	−0.349504	−	0.960253i	0.633023	−	0.774133i	$-0.281814\pi$
$150$		0			0
$151$	−4232.78	−	24005.3i	−0.185640	−	1.05282i	−0.925130	−	0.379650i	$-0.876044\pi$
$151$	−4232.78	−	24005.3i	−0.185640	−	1.05282i	0.739490	−	0.673168i	$-0.235067\pi$
$152$	−11630.5	−	6714.85i	−0.503396	−	0.290636i
$153$		0			0
$154$	695.229	+	1204.17i	0.0293148	+	0.0507747i
$155$	46416.9	+	55317.5i	1.93203	+	2.30250i
$156$		0			0
$157$	−2585.16	+	14661.1i	−0.104879	+	0.594797i	0.886390	+	0.462939i	$0.153205\pi$
$157$	−2585.16	+	14661.1i	−0.104879	+	0.594797i	−0.991269	+	0.131857i	$0.957906\pi$
$158$	−7226.52	+	8612.23i	−0.289477	+	0.344986i
$159$		0			0
$160$	−7898.83	−	2874.94i	−0.308548	−	0.112302i
$161$			1030.08i			0.0397392i
$162$		0			0
$163$	49558.1			1.86526			0.932631	−	0.360832i	$-0.117507\pi$
$163$	49558.1			1.86526			0.932631	+	0.360832i	$0.117507\pi$
$164$	5166.79	−	14195.6i	0.192102	−	0.527797i
$165$		0			0
$166$	5784.17	+	4853.50i	0.209906	+	0.176132i
$167$	−7147.93	−	1260.37i	−0.256299	−	0.0451925i	0.0440221	−	0.999031i	$-0.485983\pi$
$167$	−7147.93	−	1260.37i	−0.256299	−	0.0451925i	−0.300321	+	0.953838i	$0.597094\pi$
$168$		0			0
$169$	38720.9	−	32490.7i	1.35573	−	1.13759i
$170$	−26041.5	+	15035.0i	−0.901089	+	0.520244i
$171$		0			0
$172$	309.653	−	536.334i	0.0104669	−	0.0181292i
$173$	−52433.7	+	9245.47i	−1.75194	+	0.308913i	−0.955320	−	0.295573i	$-0.904489\pi$
$173$	−52433.7	+	9245.47i	−1.75194	+	0.308913i	−0.796615	+	0.604487i	$0.793378\pi$
$174$		0			0
$175$	−26510.7	+	9649.09i	−0.865655	+	0.315072i
$176$	−584.066	−	1604.71i	−0.0188555	−	0.0518049i
$177$		0			0
$178$	1720.71	+	9758.60i	0.0543083	+	0.307998i
$179$	−30319.5	−	17505.0i	−0.946271	−	0.546330i	−0.0543505	−	0.998522i	$-0.517309\pi$
$179$	−30319.5	−	17505.0i	−0.946271	−	0.546330i	−0.891921	+	0.452192i	$0.850642\pi$
$180$		0			0
$181$	−16016.8	−	27742.0i	−0.488900	−	0.846799i	0.511019	−	0.859570i	$-0.329268\pi$
$181$	−16016.8	−	27742.0i	−0.488900	−	0.846799i	−0.999918	+	0.0127706i	$0.995935\pi$
$182$	−9421.15	−	11227.7i	−0.284421	−	0.338959i
$183$		0			0
$184$	219.681	−	1245.88i	0.00648870	−	0.0367992i
$185$	−20400.6	+	24312.5i	−0.596073	+	0.710372i
$186$		0			0
$187$	−5740.56	−	2089.39i	−0.164161	−	0.0597499i
$188$			8096.03i			0.229064i
$189$		0			0
$190$	77952.1			2.15934
$191$	−1369.87	+	3763.68i	−0.0375502	+	0.103168i	−0.957051	−	0.289920i	$-0.906371\pi$
$191$	−1369.87	+	3763.68i	−0.0375502	+	0.103168i	0.919501	+	0.393089i	$0.128593\pi$
$192$		0			0
$193$	13912.6	+	11674.1i	0.373503	+	0.313406i	0.810146	−	0.586229i	$-0.199388\pi$
$193$	13912.6	+	11674.1i	0.373503	+	0.313406i	−0.436642	+	0.899635i	$0.643832\pi$
$194$	18538.8	+	3268.89i	0.492581	+	0.0868553i
$195$		0			0
$196$	12634.0	−	10601.2i	0.328872	−	0.275957i
$197$	35548.3	−	20523.8i	0.915980	−	0.528841i	0.0336297	−	0.999434i	$-0.489293\pi$
$197$	35548.3	−	20523.8i	0.915980	−	0.528841i	0.882350	+	0.470593i	$0.155960\pi$
$198$		0			0
$199$	−24097.7	+	41738.4i	−0.608512	+	1.05397i	0.382974	+	0.923759i	$0.374900\pi$
$199$	−24097.7	+	41738.4i	−0.608512	+	1.05397i	−0.991486	+	0.130214i	$0.958434\pi$
$200$	34122.4	−	6016.69i	0.853059	−	0.150417i
$201$		0			0
$202$	37334.6	−	13588.7i	0.914973	−	0.333023i
$203$	−5073.91	−	13940.4i	−0.123126	−	0.338286i
$204$		0			0
$205$	15226.5	+	86353.9i	0.362321	+	2.05482i
$206$	41262.6	+	23823.0i	0.972350	+	0.561386i
$207$		0			0
$208$	9000.34	+	15589.0i	0.208033	+	0.360324i
$209$	10179.6	+	12131.5i	0.233043	+	0.277730i
$210$		0			0
$211$	9719.41	−	55121.5i	0.218311	−	1.23810i	−0.656758	−	0.754102i	$-0.728073\pi$
$211$	9719.41	−	55121.5i	0.218311	−	1.23810i	0.875068	−	0.483999i	$-0.160816\pi$
$212$	−4504.53	+	5368.28i	−0.100225	+	0.119444i
$213$		0			0
$214$	−43067.7	−	15675.3i	−0.940424	−	0.342286i
$215$			3594.73i			0.0777660i
$216$		0			0
$217$	−28651.0			−0.608443
$218$	16355.3	−	44935.9i	0.344149	−	0.945542i
$219$		0			0
$220$	7593.23	+	6371.47i	0.156885	+	0.131642i
$221$	63415.9	+	11181.9i	1.29842	+	0.228946i
$222$		0			0
$223$	−38810.2	+	32565.6i	−0.780435	+	0.654862i	−0.943358	−	0.331776i	$-0.892352\pi$
$223$	−38810.2	+	32565.6i	−0.780435	+	0.654862i	0.162924	+	0.986639i	$0.447908\pi$
$224$	2888.27	−	1667.54i	0.0575628	−	0.0332339i
$225$		0			0
$226$	12912.2	−	22364.5i	0.252803	−	0.437868i
$227$	−85898.1	+	15146.1i	−1.66699	+	0.293934i	−0.925982	−	0.377567i	$-0.876761\pi$
$227$	−85898.1	+	15146.1i	−1.66699	+	0.293934i	−0.741003	+	0.671502i	$0.765650\pi$
$228$		0			0
$229$	35369.5	−	12873.4i	0.674462	−	0.245484i	0.0179942	−	0.999838i	$-0.494272\pi$
$229$	35369.5	−	12873.4i	0.674462	−	0.245484i	0.656468	+	0.754354i	$0.272050\pi$
$230$	2511.52	+	6900.34i	0.0474768	+	0.130441i
$231$		0			0
$232$	3163.83	+	17943.0i	0.0587811	+	0.333364i
$233$	11351.1	+	6553.56i	0.209086	+	0.120716i	0.600887	−	0.799334i	$-0.294814\pi$
$233$	11351.1	+	6553.56i	0.209086	+	0.120716i	−0.391800	+	0.920050i	$0.628148\pi$
$234$		0			0
$235$	−23496.6	−	40697.2i	−0.425469	−	0.736935i
$236$	2897.83	+	3453.49i	0.0520293	+	0.0620061i
$237$		0			0
$238$	2071.74	−	11749.4i	0.0365748	−	0.207426i
$239$	56473.4	−	67302.4i	0.988663	−	1.17824i	0.00467838	−	0.999989i	$-0.498511\pi$
$239$	56473.4	−	67302.4i	0.988663	−	1.17824i	0.983985	−	0.178254i	$-0.0570447\pi$
$240$		0			0
$241$	36639.4	+	13335.6i	0.630832	+	0.229604i	0.637594	−	0.770373i	$-0.279930\pi$
$241$	36639.4	+	13335.6i	0.630832	+	0.229604i	−0.00676125	+	0.999977i	$0.502152\pi$
$242$		−	39397.2i		−	0.672721i
$243$		0			0
$244$	−26919.5			−0.452155
$245$	−32741.6	+	89956.7i	−0.545465	+	1.49865i
$246$		0			0
$247$	−127877.	−	107302.i	−2.09604	−	1.75879i
$248$	34653.2	+	6110.29i	0.563430	+	0.0993479i
$249$		0			0
$250$	−91182.2	+	76510.9i	−1.45891	+	1.22417i
$251$	−33768.4	+	19496.2i	−0.535998	+	0.309458i	−0.743455	−	0.668786i	$-0.766814\pi$
$251$	−33768.4	+	19496.2i	−0.535998	+	0.309458i	0.207458	+	0.978244i	$0.433481\pi$
$252$		0			0
$253$	−745.914	+	1291.96i	−0.0116533	+	0.0201840i
$254$	13977.8	−	2464.66i	0.216656	−	0.0382023i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	9435.52	+	25923.9i	0.142856	+	0.392495i	0.990400	−	0.138231i	$-0.0441417\pi$
$257$	9435.52	+	25923.9i	0.142856	+	0.392495i	−0.847544	+	0.530726i	$0.821919\pi$
$258$		0			0
$259$	−2186.63	−	12401.0i	−0.0325969	−	0.184866i
$260$	−90486.0	−	52242.1i	−1.33855	−	0.772813i
$261$		0			0
$262$	−29711.7	−	51462.1i	−0.432837	−	0.749696i
$263$	−58936.8	−	70238.1i	−0.852069	−	1.01546i	−0.999651	−	0.0264069i	$-0.991593\pi$
$263$	−58936.8	−	70238.1i	−0.852069	−	1.01546i	0.147582	−	0.989050i	$-0.452851\pi$
$264$		0			0
$265$	7063.40	−	40058.5i	0.100582	−	0.570431i
$266$	−19880.4	+	23692.6i	−0.280972	+	0.334849i
$267$		0			0
$268$	−1432.16	−	521.264i	−0.0199399	−	0.00725752i
$269$		−	86292.9i		−	1.19253i	−0.802786	−	0.596267i	$-0.796650\pi$
$269$		−	86292.9i		−	1.19253i	0.802786	−	0.596267i	$-0.203350\pi$
$270$		0			0
$271$	−11670.3			−0.158907			−0.0794533	−	0.996839i	$-0.525317\pi$
$271$	−11670.3			−0.158907			−0.0794533	+	0.996839i	$0.525317\pi$
$272$	−5011.52	+	13769.0i	−0.0677379	+	0.186108i
$273$		0			0
$274$	27206.9	+	22829.3i	0.362391	+	0.304083i
$275$	−40237.8	−	7095.02i	−0.532071	−	0.0938184i
$276$		0			0
$277$	−10746.3	+	9017.25i	−0.140056	+	0.117521i	−0.710124	−	0.704077i	$-0.751361\pi$
$277$	−10746.3	+	9017.25i	−0.140056	+	0.117521i	0.570068	+	0.821597i	$0.306917\pi$
$278$	−14228.5	+	8214.84i	−0.184107	+	0.106294i
$279$		0			0
$280$	−9679.19	+	16764.9i	−0.123459	+	0.213837i
$281$	101355.	−	17871.6i	1.28361	−	0.226335i	0.510096	−	0.860117i	$-0.329610\pi$
$281$	101355.	−	17871.6i	1.28361	−	0.226335i	0.773511	+	0.633783i	$0.218499\pi$
$282$		0			0
$283$	38738.6	−	14099.7i	0.483695	−	0.176051i	−0.0886511	−	0.996063i	$-0.528256\pi$
$283$	38738.6	−	14099.7i	0.483695	−	0.176051i	0.572346	+	0.820012i	$0.306033\pi$
$284$	3512.28	+	9649.92i	0.0435465	+	0.119643i
$285$		0			0
$286$	−3686.00	−	20904.3i	−0.0450633	−	0.255567i
$287$	−30129.5	−	17395.3i	−0.365787	−	0.211187i
$288$		0			0
$289$	−15551.8	−	26936.5i	−0.186202	−	0.322511i
$290$	−67978.7	−	81013.9i	−0.808308	−	0.963304i
$291$		0			0
$292$	−4411.12	+	25016.7i	−0.0517349	+	0.293403i
$293$	−36220.5	+	43165.9i	−0.421909	+	0.502812i	−0.934570	−	0.355780i	$-0.884215\pi$
$293$	−36220.5	+	43165.9i	−0.421909	+	0.502812i	0.512661	+	0.858591i	$0.328660\pi$
$294$		0			0
$295$	−24589.7	−	8949.90i	−0.282559	−	0.102843i
$296$			15465.3i			0.176512i
$297$		0			0
$298$	64167.8			0.722578
$299$	5378.35	−	14776.9i	0.0601598	−	0.165288i
$300$		0			0
$301$	−1092.57	−	916.779i	−0.0120592	−	0.0101189i
$302$	67897.2	+	11972.1i	0.744455	+	0.131267i
$303$		0			0
$304$	29098.1	−	24416.2i	0.314860	−	0.264199i
$305$	135319.	−	78126.5i	1.45465	−	0.839845i
$306$		0			0
$307$	−60176.2	+	104228.i	−0.638481	+	1.10588i	0.347285	+	0.937760i	$0.387104\pi$
$307$	−60176.2	+	104228.i	−0.638481	+	1.10588i	−0.985766	+	0.168123i	$0.946230\pi$
$308$	−3873.06	+	682.925i	−0.0408275	+	0.00719899i
$309$		0			0
$310$	−191929.	+	69856.3i	−1.99718	+	0.726912i
$311$	31942.8	+	87762.1i	0.330257	+	0.907374i	0.988044	+	0.154170i	$0.0492704\pi$
$311$	31942.8	+	87762.1i	0.330257	+	0.907374i	−0.657787	+	0.753204i	$0.728507\pi$
$312$		0			0
$313$	12725.9	+	72172.3i	0.129897	+	0.736685i	0.978278	+	0.207298i	$0.0664669\pi$
$313$	12725.9	+	72172.3i	0.129897	+	0.736685i	−0.848381	+	0.529387i	$0.822422\pi$
$314$	−36466.3	−	21053.8i	−0.369856	−	0.213537i
$315$		0			0
$316$	−15899.2	−	27538.3i	−0.159222	−	0.275780i
$317$	5187.13	+	6181.78i	0.0516188	+	0.0615169i	0.791236	−	0.611511i	$-0.209438\pi$
$317$	5187.13	+	6181.78i	0.0516188	+	0.0615169i	−0.739617	+	0.673028i	$0.764993\pi$
$318$		0			0
$319$	3730.86	−	21158.8i	0.0366630	−	0.207926i
$320$	15282.3	−	18212.8i	0.149241	−	0.177859i
$321$		0			0
$322$	−2737.80	−	996.476i	−0.0264052	−	0.00961071i
$323$		−	135884.i		−	1.30246i
$324$		0			0
$325$	430687.			4.07751
$326$	−47941.5	+	131718.i	−0.451104	+	1.23940i
$327$		0			0
$328$	32731.6	+	27465.1i	0.304243	+	0.255290i
$329$	18361.8	+	3237.69i	0.169638	+	0.0299118i
$330$		0			0
$331$	−77897.2	+	65363.5i	−0.710994	+	0.596595i	−0.924878	−	0.380264i	$-0.875833\pi$
$331$	−77897.2	+	65363.5i	−0.710994	+	0.596595i	0.213884	+	0.976859i	$0.431389\pi$
$332$	−18495.4	+	10678.3i	−0.167798	+	0.0968782i
$333$		0			0
$334$	10264.6	−	17778.9i	0.0920133	−	0.159372i
$335$	8712.03	−	1536.17i	0.0776301	−	0.0136883i
$336$		0			0
$337$	66204.6	−	24096.5i	0.582946	−	0.212175i	−0.0336781	−	0.999433i	$-0.510722\pi$
$337$	66204.6	−	24096.5i	0.582946	−	0.212175i	0.616624	+	0.787258i	$0.288500\pi$
$338$	48897.7	+	134345.i	0.428011	+	1.17595i
$339$		0			0
$340$	−14769.0	−	83759.0i	−0.127759	−	0.724558i
$341$	−35935.0	−	20747.1i	−0.309036	−	0.178422i
$342$		0			0
$343$	−41108.9	−	71202.8i	−0.349420	−	0.605213i
$344$	1125.95	+	1341.85i	0.00951482	+	0.0113393i
$345$		0			0
$346$	26150.1	−	148305.i	0.218435	−	1.23881i
$347$	9724.37	−	11589.0i	0.0807611	−	0.0962474i	−0.724151	−	0.689642i	$-0.757768\pi$
$347$	9724.37	−	11589.0i	0.0807611	−	0.0962474i	0.804912	+	0.593394i	$0.202213\pi$
$348$		0			0
$349$	−112243.	−	40853.2i	−0.921529	−	0.335409i	−0.162682	−	0.986679i	$-0.552015\pi$
$349$	−112243.	−	40853.2i	−0.921529	−	0.335409i	−0.758847	+	0.651269i	$0.774237\pi$
$350$		−	79795.8i		−	0.651394i
$351$		0			0
$352$	4830.09			0.0389825
$353$	5526.54	−	15184.0i	0.0443510	−	0.121853i	−0.915540	−	0.402227i	$-0.868236\pi$
$353$	5526.54	−	15184.0i	0.0443510	−	0.121853i	0.959891	+	0.280374i	$0.0904584\pi$
$354$		0			0
$355$	−45661.9	−	38314.9i	−0.362324	−	0.304026i
$356$	−27601.5	−	4866.89i	−0.217787	−	0.0384018i
$357$		0			0
$358$	75856.0	−	63650.7i	0.591867	−	0.496635i
$359$	4568.71	−	2637.75i	0.0354491	−	0.0204665i	−0.482171	−	0.876077i	$-0.660152\pi$
$359$	4568.71	−	2637.75i	0.0354491	−	0.0204665i	0.517620	+	0.855611i	$0.326818\pi$
$360$		0			0
$361$	−110969.	+	192204.i	−0.851506	+	1.47485i
$362$	89228.4	−	15733.4i	0.680904	−	0.120062i
$363$		0			0
$364$	38955.3	−	14178.6i	0.294011	−	0.107011i
$365$	−50430.4	−	138556.i	−0.378536	−	1.04002i
$366$		0			0
$367$	−9079.02	−	51489.7i	−0.0674073	−	0.382286i	−0.999784	−	0.0207970i	$-0.993380\pi$
$367$	−9079.02	−	51489.7i	−0.0674073	−	0.382286i	0.932376	−	0.361489i	$-0.117731\pi$
$368$	3098.84	+	1789.11i	0.0228825	+	0.0132112i
$369$		0			0
$370$	−44883.8	−	77741.1i	−0.327859	−	0.567868i
$371$	10373.9	+	12363.1i	0.0753691	+	0.0898214i
$372$		0			0
$373$	−16402.8	+	93024.7i	−0.117896	+	0.668622i	0.867379	+	0.497648i	$0.165803\pi$
$373$	−16402.8	+	93024.7i	−0.117896	+	0.668622i	−0.985275	+	0.170975i	$0.945308\pi$
$374$	11106.6	−	13236.3i	0.0794032	−	0.0946290i
$375$		0			0
$376$	−21518.1	−	7831.93i	−0.152204	−	0.0553979i
$377$			226474.i			1.59344i
$378$		0			0
$379$	127147.			0.885169			0.442584	−	0.896727i	$-0.354062\pi$
$379$	127147.			0.885169			0.442584	+	0.896727i	$0.354062\pi$
$380$	−75409.3	+	207185.i	−0.522225	+	1.43480i
$381$		0			0
$382$	−8678.12	−	7281.81i	−0.0594702	−	0.0499014i
$383$	−10087.7	−	1778.72i	−0.0687690	−	0.0121258i	0.139158	−	0.990270i	$-0.455560\pi$
$383$	−10087.7	−	1778.72i	−0.0687690	−	0.0121258i	−0.207927	+	0.978144i	$0.566672\pi$
$384$		0			0
$385$	17487.1	−	14673.4i	0.117977	−	0.0989944i
$386$	−44486.7	+	25684.4i	−0.298577	+	0.172383i
$387$		0			0
$388$	−26622.2	+	46111.1i	−0.176840	+	0.306296i
$389$	−104884.	+	18493.8i	−0.693121	+	0.122216i	−0.509101	−	0.860707i	$-0.670022\pi$
$389$	−104884.	+	18493.8i	−0.693121	+	0.122216i	−0.184020	+	0.982923i	$0.558911\pi$
$390$		0			0
$391$	12028.5	−	4378.02i	0.0786789	−	0.0286368i
$392$	15954.5	+	43834.5i	0.103827	+	0.285262i
$393$		0			0
$394$	20160.6	+	114336.i	0.129871	+	0.736532i
$395$	159845.	+	92286.5i	1.02448	+	0.591486i
$396$		0			0
$397$	39511.4	+	68435.8i	0.250693	+	0.434213i	0.963717	−	0.266927i	$-0.0860083\pi$
$397$	39511.4	+	68435.8i	0.250693	+	0.434213i	−0.713024	+	0.701140i	$0.752675\pi$
$398$	−87622.9	−	104425.i	−0.553161	−	0.659231i
$399$		0			0
$400$	−17017.8	+	96512.6i	−0.106361	+	0.603204i
$401$	183328.	−	218482.i	1.14009	−	1.35871i	0.216067	−	0.976378i	$-0.430677\pi$
$401$	183328.	−	218482.i	1.14009	−	1.35871i	0.924025	−	0.382331i	$-0.124879\pi$
$402$		0			0
$403$	411009.	+	149595.i	2.53071	+	0.921102i
$404$			112375.i			0.688506i
$405$		0			0
$406$	41960.0			0.254556
$407$	6237.43	−	17137.2i	0.0376545	−	0.103455i
$408$		0			0
$409$	−46231.0	−	38792.4i	−0.276367	−	0.231900i	0.494060	−	0.869428i	$-0.335512\pi$
$409$	−46231.0	−	38792.4i	−0.276367	−	0.231900i	−0.770427	+	0.637528i	$0.779957\pi$
$410$	−244246.	−	43067.1i	−1.45298	−	0.256199i
$411$		0			0
$412$	−103235.	+	86624.1i	−0.608178	+	0.510322i
$413$	8991.41	−	5191.19i	0.0527142	−	0.0304345i
$414$		0			0
$415$	61981.8	−	107356.i	0.359889	−	0.623345i
$416$	−50140.1	+	8841.06i	−0.289734	+	0.0510878i
$417$		0			0
$418$	−42091.3	+	15320.0i	−0.240902	+	0.0876811i
$419$	45770.9	+	125755.i	0.260712	+	0.716301i	0.999120	+	0.0419466i	$0.0133559\pi$
$419$	45770.9	+	125755.i	0.260712	+	0.716301i	−0.738407	+	0.674355i	$0.764422\pi$
$420$		0			0
$421$	39866.3	+	226093.i	0.224927	+	1.27562i	0.862825	+	0.505503i	$0.168693\pi$
$421$	39866.3	+	226093.i	0.224927	+	1.27562i	−0.637898	+	0.770121i	$0.720196\pi$
$422$	137102.	+	79156.1i	0.769875	+	0.444488i
$423$		0			0
$424$	−9910.52	−	17165.5i	−0.0551271	−	0.0954829i
$425$	225350.	+	268562.i	1.24761	+	1.48685i
$426$		0			0
$427$	−10765.4	+	61053.5i	−0.0590437	+	0.334853i
$428$	83325.5	−	99303.5i	0.454873	−	0.542097i
$429$		0			0
$430$	−9554.27	−	3477.47i	−0.0516727	−	0.0188073i
$431$			141782.i			0.763248i	0.924318	+	0.381624i	$0.124635\pi$
$431$			141782.i			0.763248i	−0.924318	+	0.381624i	$0.875365\pi$
$432$		0			0
$433$	−213202.			−1.13714			−0.568572	−	0.822634i	$-0.692504\pi$
$433$	−213202.			−1.13714			−0.568572	+	0.822634i	$0.692504\pi$
$434$	27716.3	−	76150.0i	0.147149	−	0.404288i
$435$		0			0
$436$	103611.	+	86940.1i	0.545047	+	0.457349i
$437$	−32679.1	−	5762.21i	−0.171123	−	0.0301736i
$438$		0			0
$439$	166560.	−	139760.i	0.864252	−	0.725194i	−0.0986275	−	0.995124i	$-0.531445\pi$
$439$	166560.	−	139760.i	0.864252	−	0.725194i	0.962880	+	0.269931i	$0.0870008\pi$
$440$	−24280.0	+	14018.0i	−0.125413	+	0.0724073i
$441$		0			0
$442$	−91067.2	+	157733.i	−0.466141	+	0.807380i
$443$	−351498.	+	61978.6i	−1.79108	+	0.315816i	−0.967782	−	0.251792i	$-0.918980\pi$
$443$	−351498.	+	61978.6i	−1.79108	+	0.315816i	−0.823299	+	0.567607i	$0.807869\pi$
$444$		0			0
$445$	152872.	−	55641.0i	0.771985	−	0.280980i
$446$	−49010.5	−	134655.i	−0.246388	−	0.676945i
$447$		0			0
$448$	1638.03	+	9289.74i	0.00816143	+	0.0462858i
$449$	44891.6	+	25918.2i	0.222676	+	0.128562i	0.607189	−	0.794558i	$-0.292297\pi$
$449$	44891.6	+	25918.2i	0.222676	+	0.128562i	−0.384513	+	0.923120i	$0.625631\pi$
$450$		0			0
$451$	−25193.0	−	43635.5i	−0.123859	−	0.214529i
$452$	46950.7	+	55953.7i	0.229808	+	0.273875i
$453$		0			0
$454$	42839.8	−	242956.i	0.207843	−	1.17874i
$455$	−154672.	+	184330.i	−0.747116	+	0.890378i
$456$		0			0
$457$	−274027.	−	99737.8i	−1.31208	−	0.477559i	−0.411170	−	0.911559i	$-0.634880\pi$
$457$	−274027.	−	99737.8i	−1.31208	−	0.477559i	−0.900913	+	0.434000i	$0.857102\pi$
$458$			106460.i			0.507524i
$459$		0			0
$460$	−20769.7			−0.0981554
$461$	40377.4	−	110936.i	0.189992	−	0.522000i	−0.807723	−	0.589563i	$-0.799300\pi$
$461$	40377.4	−	110936.i	0.189992	−	0.522000i	0.997715	+	0.0675630i	$0.0215224\pi$
$462$		0			0
$463$	277410.	+	232775.i	1.29408	+	1.08586i	0.991136	+	0.132853i	$0.0424138\pi$
$463$	277410.	+	232775.i	1.29408	+	1.08586i	0.302943	+	0.953009i	$0.402031\pi$
$464$	−50750.5	−	8948.68i	−0.235724	−	0.0415645i
$465$		0			0
$466$	−28399.2	+	23829.8i	−0.130778	+	0.109736i
$467$	−292386.	+	168809.i	−1.34067	+	0.774037i	−0.986906	−	0.161296i	$-0.948432\pi$
$467$	−292386.	+	168809.i	−1.34067	+	0.774037i	−0.353766	+	0.935334i	$0.615099\pi$
$468$		0			0
$469$	−1754.96	+	3039.69i	−0.00797853	+	0.0138192i
$470$	130897.	−	23080.7i	0.592563	−	0.104485i
$471$		0			0
$472$	−11982.2	+	4361.15i	−0.0537838	+	0.0195757i
$473$	−706.476	−	1941.03i	−0.00315773	−	0.00867579i
$474$		0			0
$475$	−157817.	−	895025.i	−0.699466	−	3.96687i
$476$	29224.1	+	16872.5i	0.128981	+	0.0744674i
$477$		0			0
$478$	124249.	+	215205.i	0.543796	+	0.941882i
$479$	−66282.3	−	78992.1i	−0.288886	−	0.344281i	0.602010	−	0.798489i	$-0.294367\pi$
$479$	−66282.3	−	78992.1i	−0.288886	−	0.344281i	−0.890896	+	0.454208i	$0.849922\pi$
$480$		0			0
$481$	−33381.2	+	189314.i	−0.144282	+	0.818264i
$482$	−70888.3	+	84481.4i	−0.305127	+	0.363636i
$483$		0			0
$484$	104712.	+	38112.1i	0.446998	+	0.162694i
$485$		−	309056.i		−	1.31387i
$486$		0			0
$487$	6688.37			0.0282008			0.0141004	−	0.999901i	$-0.495512\pi$
$487$	6688.37			0.0282008			0.0141004	+	0.999901i	$0.495512\pi$
$488$	26041.3	−	71548.0i	0.109351	−	0.300440i
$489$		0			0
$490$	−207418.	−	174044.i	−0.863882	−	0.724883i
$491$	−16750.4	−	2953.55i	−0.0694804	−	0.0122513i	0.138800	−	0.990320i	$-0.455676\pi$
$491$	−16750.4	−	2953.55i	−0.0694804	−	0.0122513i	−0.208280	+	0.978069i	$0.566787\pi$
$492$		0			0
$493$	−141221.	+	118499.i	−0.581041	+	0.487551i
$494$	408899.	−	236078.i	1.67557	−	0.967389i
$495$		0			0
$496$	−49763.0	+	86192.1i	−0.202276	+	0.350352i
$497$	23290.7	−	4106.77i	0.0942907	−	0.0166260i
$498$		0			0
$499$	−445147.	+	162020.i	−1.78773	+	0.650682i	−0.788363	+	0.615210i	$0.789071\pi$
$499$	−445147.	+	162020.i	−1.78773	+	0.650682i	−0.999371	+	0.0354716i	$0.988707\pi$
$500$	−115147.	−	316364.i	−0.460588	−	1.26546i
$501$		0			0
$502$	−19151.2	−	108612.i	−0.0759954	−	0.430992i
$503$	−133046.	−	76814.4i	−0.525856	−	0.303603i	0.213471	−	0.976949i	$-0.431523\pi$
$503$	−133046.	−	76814.4i	−0.525856	−	0.303603i	−0.739327	+	0.673346i	$0.764856\pi$
$504$		0			0
$505$	−326139.	−	564888.i	−1.27885	−	2.21503i
$506$	−2712.26	−	3232.34i	−0.0105933	−	0.0126246i
$507$		0			0
$508$	−6971.10	+	39535.1i	−0.0270131	+	0.153199i
$509$	119577.	−	142507.i	0.461544	−	0.550047i	−0.484201	−	0.874957i	$-0.660890\pi$
$509$	119577.	−	142507.i	0.461544	−	0.550047i	0.945745	+	0.324910i	$0.105334\pi$
$510$		0			0
$511$	54973.9	+	20008.9i	0.210531	+	0.0766268i
$512$		−	11585.2i		−	0.0441942i
$513$		0			0
$514$	−78029.5			−0.295347
$515$	267538.	−	735054.i	1.00872	−	2.77143i
$516$		0			0
$517$	20685.5	+	17357.2i	0.0773902	+	0.0649381i
$518$	35075.3	+	6184.73i	0.130720	+	0.0230495i
$519$		0			0
$520$	226386.	−	189961.i	0.837227	−	0.702517i
$521$	−162417.	+	93771.3i	−0.598350	+	0.345457i	−0.768392	−	0.639979i	$-0.778943\pi$
$521$	−162417.	+	93771.3i	−0.598350	+	0.345457i	0.170042	+	0.985437i	$0.445610\pi$
$522$		0			0
$523$	−47956.7	+	83063.5i	−0.175326	+	0.303673i	−0.940274	−	0.340419i	$-0.889431\pi$
$523$	−47956.7	+	83063.5i	−0.175326	+	0.303673i	0.764948	+	0.644092i	$0.222765\pi$
$524$	165521.	−	29185.8i	0.602824	−	0.106294i
$525$		0			0
$526$	243697.	−	88698.4i	0.880802	−	0.320586i
$527$	121772.	+	334565.i	0.438455	+	1.20465i
$528$		0			0
$529$	48051.1	+	272511.i	0.171708	+	0.973807i
$530$	99636.6	+	57525.2i	0.354705	+	0.204789i
$531$		0			0
$532$	−43739.5	−	75759.0i	−0.154543	−	0.267677i
$533$	341394.	+	406857.i	1.20171	+	1.43215i
$534$		0			0
$535$	−130660.	+	741009.i	−0.456494	+	2.58891i
$536$	2770.89	−	3302.21i	0.00964471	−	0.0114941i
$537$		0			0
$538$	229354.	+	83478.0i	0.792395	+	0.288408i
$539$		−	55008.1i		−	0.189343i
$540$		0			0
$541$	−243345.			−0.831435			−0.415718	−	0.909494i	$-0.636470\pi$
$541$	−243345.			−0.831435			−0.415718	+	0.909494i	$0.636470\pi$
$542$	11289.6	−	31017.8i	0.0384307	−	0.105588i
$543$		0			0
$544$	−31748.0	−	26639.8i	−0.107280	−	0.0900187i
$545$	−773154.	−	136328.i	−2.60299	−	0.458978i
$546$		0			0
$547$	160978.	−	135077.i	0.538013	−	0.451447i	−0.332845	−	0.942982i	$-0.608008\pi$
$547$	160978.	−	135077.i	0.538013	−	0.451447i	0.870858	+	0.491535i	$0.163564\pi$
$548$	−86996.3	+	50227.3i	−0.289694	+	0.167255i
$549$		0			0
$550$	57782.8	−	100083.i	0.191017	−	0.330852i
$551$	470643.	−	82987.0i	1.55020	−	0.273342i
$552$		0			0
$553$	−68815.2	+	25046.7i	−0.225027	+	0.0819031i
$554$	−13570.7	−	37285.3i	−0.0442164	−	0.121484i
$555$		0			0
$556$	−8069.46	−	45764.2i	−0.0261033	−	0.148039i
$557$	−179589.	−	103686.i	−0.578856	−	0.334202i	0.181823	−	0.983331i	$-0.441800\pi$
$557$	−179589.	−	103686.i	−0.578856	−	0.334202i	−0.760678	+	0.649129i	$0.775134\pi$
$558$		0			0
$559$	10886.6	+	18856.2i	0.0348394	+	0.0603436i
$560$	−35195.0	−	41943.8i	−0.112229	−	0.133749i
$561$		0			0
$562$	−50548.5	+	286675.i	−0.160043	+	0.907647i
$563$	−64386.1	+	76732.4i	−0.203131	+	0.242082i	−0.857987	−	0.513672i	$-0.828285\pi$
$563$	−64386.1	+	76732.4i	−0.203131	+	0.242082i	0.654856	+	0.755754i	$0.272729\pi$
$564$		0			0
$565$	−398403.	−	145007.i	−1.24803	−	0.454246i
$566$			116601.i			0.363974i
$567$		0			0
$568$	−29045.8			−0.0900298
$569$	212491.	−	583813.i	0.656319	−	1.80322i	0.0633581	−	0.997991i	$-0.479819\pi$
$569$	212491.	−	583813.i	0.656319	−	1.80322i	0.592961	−	0.805231i	$-0.297959\pi$
$570$		0			0
$571$	−88757.5	−	74476.4i	−0.272228	−	0.228426i	0.496445	−	0.868068i	$-0.334638\pi$
$571$	−88757.5	−	74476.4i	−0.272228	−	0.228426i	−0.768673	+	0.639642i	$0.779083\pi$
$572$	59126.3	+	10425.6i	0.180713	+	0.0318645i
$573$		0			0
$574$	75380.7	−	63251.9i	0.228790	−	0.191977i
$575$	74143.2	−	42806.6i	0.224252	−	0.129472i
$576$		0			0
$577$	151275.	−	262016.i	0.454377	−	0.787003i	−0.544275	−	0.838907i	$-0.683195\pi$
$577$	151275.	−	262016.i	0.454377	−	0.787003i	0.998652	+	0.0519031i	$0.0165287\pi$
$578$	86637.6	−	15276.5i	0.259329	−	0.0457267i
$579$		0			0
$580$	281084.	−	102306.i	0.835565	−	0.304121i
$581$	16821.9	+	46217.9i	0.0498338	+	0.136917i
$582$		0			0
$583$	4058.75	+	23018.3i	0.0119414	+	0.0677230i
$584$	−62223.5	−	35924.8i	−0.182444	−	0.105334i
$585$		0			0
$586$	−79689.6	−	138026.i	−0.232063	−	0.401945i
$587$	−197108.	−	234904.i	−0.572041	−	0.681732i	0.400007	−	0.916512i	$-0.369008\pi$
$587$	−197108.	−	234904.i	−0.572041	−	0.681732i	−0.972049	+	0.234780i	$0.924563\pi$
$588$		0			0
$589$	160272.	−	908949.i	0.461985	−	2.62005i
$590$	47575.0	−	56697.7i	0.136671	−	0.162878i
$591$		0			0
$592$	−41104.5	−	14960.8i	−0.117286	−	0.0426886i
$593$			543893.i			1.54669i	0.633984	+	0.773346i	$0.281419\pi$
$593$			543893.i			1.54669i	−0.633984	+	0.773346i	$0.718581\pi$
$594$		0			0
$595$	−195872.			−0.553271
$596$	−62074.6	+	170549.i	−0.174752	+	0.480127i
$597$		0			0
$598$	34071.9	+	28589.7i	0.0952782	+	0.0799479i
$599$	211814.	+	37348.4i	0.590337	+	0.104092i	0.460834	−	0.887487i	$-0.347551\pi$
$599$	211814.	+	37348.4i	0.590337	+	0.104092i	0.129504	+	0.991579i	$0.458662\pi$
$600$		0			0
$601$	323056.	−	271076.i	0.894394	−	0.750485i	−0.0746928	−	0.997207i	$-0.523798\pi$
$601$	323056.	−	271076.i	0.894394	−	0.750485i	0.969087	+	0.246721i	$0.0793532\pi$
$602$	3493.60	−	2017.03i	0.00964006	−	0.00556569i
$603$		0			0
$604$	−97502.5	+	168879.i	−0.267265	+	0.462916i
$605$	−636978.	+	112316.i	−1.74026	+	0.306854i
$606$		0			0
$607$	197556.	−	71904.6i	0.536183	−	0.195155i	−0.0597138	−	0.998216i	$-0.519019\pi$
$607$	197556.	−	71904.6i	0.536183	−	0.195155i	0.595897	+	0.803061i	$0.296797\pi$
$608$	36745.8	+	100958.i	0.0994033	+	0.273108i
$609$		0			0
$610$	76743.9	+	435236.i	0.206245	+	1.16968i
$611$	−246503.	−	142318.i	−0.660297	−	0.381223i
$612$		0			0
$613$	71524.6	+	123884.i	0.190342	+	0.329682i	0.945364	−	0.326018i	$-0.105707\pi$
$613$	71524.6	+	123884.i	0.190342	+	0.329682i	−0.755022	+	0.655700i	$0.772374\pi$
$614$	−218810.	−	260768.i	−0.580405	−	0.691699i
$615$		0			0
$616$	1931.60	−	10954.7i	0.00509046	−	0.0288694i
$617$	−79441.0	+	94674.1i	−0.208677	+	0.248691i	−0.860223	−	0.509917i	$-0.829676\pi$
$617$	−79441.0	+	94674.1i	−0.208677	+	0.248691i	0.651547	+	0.758609i	$0.274120\pi$
$618$		0			0
$619$	−381088.	−	138705.i	−0.994589	−	0.362001i	−0.207093	−	0.978321i	$-0.566400\pi$
$619$	−381088.	−	138705.i	−0.994589	−	0.362001i	−0.787495	+	0.616320i	$0.788623\pi$
$620$		−	577695.i		−	1.50285i
$621$		0			0
$622$	−264159.			−0.682787
$623$	−22076.2	+	60654.0i	−0.0568786	+	0.156273i
$624$		0			0
$625$	763843.	+	640941.i	1.95544	+	1.64081i
$626$	−204134.	−	35994.3i	−0.520915	−	0.0918513i
$627$		0			0
$628$	91234.8	−	76555.1i	0.231335	−	0.194113i
$629$	−135516.	+	78240.4i	−0.342524	+	0.197756i
$630$		0			0
$631$	−187097.	+	324062.i	−0.469903	+	0.813896i	−0.999408	−	0.0344109i	$-0.989045\pi$
$631$	−187097.	+	324062.i	−0.469903	+	0.813896i	0.529505	+	0.848307i	$0.322378\pi$
$632$	88573.3	−	15617.9i	0.221753	−	0.0391010i
$633$		0			0
$634$	−21448.2	+	7806.49i	−0.0533595	+	0.0194213i
$635$	−79697.5	−	218967.i	−0.197650	−	0.543040i
$636$		0			0
$637$	100687.	+	571026.i	0.248140	+	1.40727i
$638$	52627.8	+	30384.6i	0.129293	+	0.0746471i
$639$		0			0
$640$	33623.0	+	58236.8i	0.0820875	+	0.142180i
$641$	13322.7	+	15877.3i	0.0324246	+	0.0386422i	0.782013	−	0.623262i	$-0.214193\pi$
$641$	13322.7	+	15877.3i	0.0324246	+	0.0386422i	−0.749588	+	0.661904i	$0.769749\pi$
$642$		0			0
$643$	91377.5	−	518228.i	0.221013	−	1.25343i	−0.649150	−	0.760661i	$-0.724875\pi$
$643$	91377.5	−	518228.i	0.221013	−	1.25343i	0.870162	−	0.492765i	$-0.164014\pi$
$644$	5296.97	−	6312.69i	0.0127719	−	0.0152210i
$645$		0			0
$646$	361160.	+	131452.i	0.865436	+	0.314993i
$647$			758688.i			1.81240i	0.422846	+	0.906201i	$0.361031\pi$
$647$			758688.i			1.81240i	−0.422846	+	0.906201i	$0.638969\pi$
$648$		0			0
$649$	15036.5			0.0356990
$650$	−416637.	+	1.14470e6i	−0.986124	+	2.70935i
$651$		0			0
$652$	−303710.	−	254843.i	−0.714437	−	0.599484i
$653$	729204.	+	128578.i	1.71010	+	0.301537i	0.941206	−	0.337834i	$-0.109694\pi$
$653$	729204.	+	128578.i	1.71010	+	0.301537i	0.768898	+	0.639371i	$0.220805\pi$
$654$		0			0
$655$	−747339.	+	627092.i	−1.74195	+	1.46167i
$656$	−104662.	+	60426.7i	−0.243210	+	0.140417i
$657$		0			0
$658$	−26368.1	+	45671.0i	−0.0609015	+	0.105484i
$659$	509089.	−	89766.1i	1.17226	−	0.206701i	0.446585	−	0.894741i	$-0.352640\pi$
$659$	509089.	−	89766.1i	1.17226	−	0.206701i	0.725672	+	0.688041i	$0.241529\pi$
$660$		0			0
$661$	15658.2	−	5699.12i	0.0358376	−	0.0130438i	−0.324039	−	0.946044i	$-0.605041\pi$
$661$	15658.2	−	5699.12i	0.0358376	−	0.0130438i	0.359877	+	0.933000i	$0.382819\pi$
$662$	−98370.5	−	270271.i	−0.224465	−	0.616713i
$663$		0			0
$664$	−10489.3	−	59487.9i	−0.0237909	−	0.134925i
$665$	439740.	+	253884.i	0.994380	+	0.574106i
$666$		0			0
$667$	22509.5	+	38987.7i	0.0505959	+	0.0876346i
$668$	37323.8	+	44480.8i	0.0836437	+	0.0996827i
$669$		0			0
$670$	−4344.94	+	24641.4i	−0.00967907	+	0.0548927i
$671$	−57713.1	+	68779.9i	−0.128183	+	0.152762i
$672$		0			0
$673$	−194007.	−	70612.7i	−0.428338	−	0.155902i	0.118849	−	0.992912i	$-0.462079\pi$
$673$	−194007.	−	70612.7i	−0.428338	−	0.155902i	−0.547188	+	0.837010i	$0.684302\pi$
$674$			199272.i			0.438659i
$675$		0			0
$676$	−404372.			−0.884888
$677$	−125737.	+	345459.i	−0.274337	+	0.753736i	0.723641	+	0.690177i	$0.242467\pi$
$677$	−125737.	+	345459.i	−0.274337	+	0.753736i	−0.997978	+	0.0635590i	$0.979755\pi$
$678$		0			0
$679$	93933.6	+	78819.6i	0.203742	+	0.170960i
$680$	236906.	+	41772.9i	0.512340	+	0.0903394i
$681$		0			0
$682$	89905.5	−	75439.7i	0.193294	−	0.162193i
$683$	−190719.	+	110112.i	−0.408840	+	0.236044i	−0.690291	−	0.723532i	$-0.742518\pi$
$683$	−190719.	+	110112.i	−0.408840	+	0.236044i	0.281451	+	0.959576i	$0.409184\pi$
$684$		0			0
$685$	291543.	−	504967.i	0.621328	−	1.07617i
$686$	229014.	−	40381.4i	0.486647	−	0.0858091i
$687$		0			0
$688$	−4655.65	+	1694.52i	−0.00983567	+	0.00357989i
$689$	−84266.0	−	231519.i	−0.177506	−	0.487695i
$690$		0			0
$691$	43000.7	+	243869.i	0.0900575	+	0.510741i	0.996150	+	0.0876623i	$0.0279396\pi$
$691$	43000.7	+	243869.i	0.0900575	+	0.510741i	−0.906093	+	0.423079i	$0.860949\pi$
$692$	368875.	+	212970.i	0.770313	+	0.444740i
$693$		0			0
$694$	21394.8	+	37056.9i	0.0444212	+	0.0769397i
$695$	173382.	+	206628.i	0.358950	+	0.427780i
$696$		0			0
$697$	−75073.6	+	425763.i	−0.154533	+	0.876401i
$698$	217163.	−	258805.i	0.445734	−	0.531205i
$699$		0			0
$700$	212085.	+	77192.8i	0.432827	+	0.157536i
$701$		−	252180.i		−	0.513185i	−0.966520	−	0.256593i	$-0.917400\pi$
$701$		−	252180.i		−	0.513185i	0.966520	−	0.256593i	$-0.0825998\pi$
$702$		0			0
$703$	405653.			0.820812
$704$	−4672.53	+	12837.7i	−0.00942773	+	0.0259025i
$705$		0			0
$706$	35010.7	+	29377.4i	0.0702411	+	0.0589392i
$707$	254867.	+	44940.0i	0.509888	+	0.0899071i
$708$		0			0
$709$	−12945.2	+	10862.3i	−0.0257524	+	0.0216088i	−0.655573	−	0.755132i	$-0.727573\pi$
$709$	−12945.2	+	10862.3i	−0.0257524	+	0.0216088i	0.629821	+	0.776741i	$0.283128\pi$
$710$	146008.	−	84297.5i	0.289640	−	0.167224i
$711$		0			0
$712$	39636.6	−	68652.6i	0.0781873	−	0.135424i
$713$	85624.2	−	15097.9i	0.168429	−	0.0296986i
$714$		0			0
$715$	−327474.	+	119191.i	−0.640568	+	0.233148i
$716$	95792.8	+	263188.i	0.186856	+	0.513382i
$717$		0			0
$718$	2591.07	+	14694.7i	0.00502608	+	0.0285043i
$719$	−24722.9	−	14273.8i	−0.0478235	−	0.0276109i	0.475898	−	0.879501i	$-0.342123\pi$
$719$	−24722.9	−	14273.8i	−0.0478235	−	0.0276109i	−0.523721	+	0.851890i	$0.675457\pi$
$720$		0			0
$721$	155179.	+	268778.i	0.298513	+	0.517039i
$722$	−403501.	−	480873.i	−0.774052	−	0.922479i
$723$		0			0
$724$	−44500.7	+	252376.i	−0.0848965	+	0.481472i
$725$	−792554.	+	944529.i	−1.50783	+	1.79696i
$726$		0			0
$727$	978911.	+	356295.i	1.85214	+	0.674125i	0.984095	+	0.177646i	$0.0568480\pi$
$727$	978911.	+	356295.i	1.85214	+	0.674125i	0.868049	+	0.496479i	$0.165374\pi$
$728$			117254.i			0.221240i
$729$		0			0
$730$	417048.			0.782600
$731$	−6061.84	+	16654.8i	−0.0113441	+	0.0311676i
$732$		0			0
$733$	−293387.	−	246181.i	−0.546052	−	0.458192i	0.327550	−	0.944834i	$-0.393777\pi$
$733$	−293387.	−	246181.i	−0.546052	−	0.458192i	−0.873601	+	0.486642i	$0.838222\pi$
$734$	145635.	+	25679.4i	0.270317	+	0.0476642i
$735$		0			0
$736$	−7752.95	+	6505.50i	−0.0143124	+	0.0120095i
$737$	−4402.28	+	2541.66i	−0.00810480	+	0.00467931i
$738$		0			0
$739$	303987.	−	526522.i	0.556630	−	0.964112i	−0.441144	−	0.897436i	$-0.645427\pi$
$739$	303987.	−	526522.i	0.556630	−	0.964112i	0.997775	−	0.0666758i	$-0.0212393\pi$
$740$	250044.	−	44089.5i	0.456618	−	0.0805141i
$741$		0			0
$742$	−42894.8	+	15612.4i	−0.0779106	+	0.0283572i
$743$	138783.	+	381303.i	0.251396	+	0.690705i	0.999628	+	0.0272680i	$0.00868076\pi$
$743$	138783.	+	381303.i	0.251396	+	0.690705i	−0.748232	+	0.663437i	$0.769097\pi$
$744$		0			0
$745$	−182934.	−	1.03747e6i	−0.329596	−	1.86923i
$746$	−231378.	−	133586.i	−0.415762	−	0.240040i
$747$		0			0
$748$	24435.9	+	42324.2i	0.0436742	+	0.0756460i
$749$	−191898.	−	228695.i	−0.342063	−	0.407655i
$750$		0			0
$751$	5136.66	−	29131.4i	0.00910753	−	0.0516514i	−0.979915	−	0.199414i	$-0.936096\pi$
$751$	5136.66	−	29131.4i	0.00910753	−	0.0516514i	0.989023	+	0.147763i	$0.0472072\pi$
$752$	41632.2	−	49615.4i	0.0736197	−	0.0877365i
$753$		0			0
$754$	−601933.	−	219086.i	−1.05878	−	0.385364i
$755$		−	1.13190e6i		−	1.98570i
$756$		0			0
$757$	43535.1			0.0759710			0.0379855	−	0.999278i	$-0.487906\pi$
$757$	43535.1			0.0759710			0.0379855	+	0.999278i	$0.487906\pi$
$758$	−122999.	+	337937.i	−0.214073	+	0.588162i
$759$		0			0
$760$	−477718.	−	400853.i	−0.827075	−	0.693998i
$761$	−439599.	−	77513.2i	−0.759080	−	0.133846i	−0.219306	−	0.975656i	$-0.570379\pi$
$761$	−439599.	−	77513.2i	−0.759080	−	0.133846i	−0.539774	+	0.841810i	$0.681490\pi$
$762$		0			0
$763$	238616.	−	200222.i	0.409874	−	0.343925i
$764$	27749.0	−	16020.9i	0.0475402	−	0.0274473i
$765$		0			0
$766$	14486.2	−	25090.8i	0.0246886	−	0.0427619i
$767$	−156090.	+	27522.9i	−0.265329	+	0.0467846i
$768$		0			0
$769$	236860.	−	86210.0i	0.400534	−	0.145782i	−0.133896	−	0.990995i	$-0.542749\pi$
$769$	236860.	−	86210.0i	0.400534	−	0.145782i	0.534430	+	0.845213i	$0.320526\pi$
$770$	22083.2	+	60673.0i	0.0372460	+	0.102333i
$771$		0			0
$772$	−25229.9	−	143086.i	−0.0423331	−	0.240083i
$773$	−567905.	−	327880.i	−0.950423	−	0.548727i	−0.0572108	−	0.998362i	$-0.518221\pi$
$773$	−567905.	−	327880.i	−0.950423	−	0.548727i	−0.893212	+	0.449635i	$0.851554\pi$
$774$		0			0
$775$	1.19064e6	+	2.06224e6i	1.98233	+	3.43350i
$776$	−96802.6	−	115365.i	−0.160755	−	0.191580i
$777$		0			0
$778$	52308.5	−	296656.i	0.0864197	−	0.490111i
$779$	720406.	−	858547.i	1.18714	−	1.41478i
$780$		0			0
$781$	32185.8	+	11714.7i	0.0527670	+	0.0192056i
$782$			36205.2i			0.0592049i
$783$		0			0
$784$	−131940.			−0.214656
$785$	−236439.	+	649612.i	−0.383690	+	1.05418i
$786$		0			0
$787$	−203084.	−	170408.i	−0.327889	−	0.275131i	0.463950	−	0.885861i	$-0.346432\pi$
$787$	−203084.	−	170408.i	−0.327889	−	0.275131i	−0.791839	+	0.610730i	$0.790876\pi$
$788$	−323392.	−	57022.7i	−0.520807	−	0.0918323i
$789$		0			0
$790$	−399915.	+	335568.i	−0.640786	+	0.537683i
$791$	145679.	−	84107.9i	0.232833	−	0.134426i
$792$		0			0
$793$	473212.	−	819627.i	0.752505	−	1.30338i
$794$	−220115.	+	38812.2i	−0.349147	+	0.0615640i
$795$		0			0
$796$	362310.	−	131870.i	0.571814	−	0.208123i
$797$	−97569.8	−	268071.i	−0.153603	−	0.422020i	0.838894	−	0.544296i	$-0.183203\pi$
$797$	−97569.8	−	268071.i	−0.153603	−	0.422020i	−0.992496	+	0.122276i	$0.960981\pi$
$798$		0			0
$799$	−40233.7	−	228177.i	−0.0630227	−	0.357419i
$800$	−240054.	−	138595.i	−0.375084	−	0.216555i
$801$		0			0
$802$	403345.	+	698614.i	0.627087	+	1.08615i
$803$	54461.2	+	64904.3i	0.0844609	+	0.100657i
$804$		0			0
$805$	−8306.01	+	47105.7i	−0.0128174	+	0.0726912i
$806$	−795204.	+	947687.i	−1.22408	+	1.45880i
$807$		0			0
$808$	−298676.	−	108709.i	−0.457486	−	0.166511i
$809$		−	1.23892e6i		−	1.89298i	−0.322735	−	0.946489i	$-0.604602\pi$
$809$		−	1.23892e6i		−	1.89298i	0.322735	−	0.946489i	$-0.395398\pi$
$810$		0			0
$811$	692598.			1.05303			0.526514	−	0.850167i	$-0.323499\pi$
$811$	692598.			1.05303			0.526514	+	0.850167i	$0.323499\pi$
$812$	−40591.3	+	111524.i	−0.0615631	+	0.169143i
$813$		0			0
$814$	39514.2	+	33156.3i	0.0596354	+	0.0500400i
$815$	2.26631e6	+	399611.i	3.41195	+	0.601620i
$816$		0			0
$817$	35196.5	−	29533.4i	0.0527298	−	0.0442455i
$818$	147827.	−	85348.2i	0.220927	−	0.127552i
$819$		0			0
$820$	350744.	−	607507.i	0.521630	−	0.903490i
$821$	−941753.	+	166056.i	−1.39717	+	0.246360i	−0.820982	−	0.570954i	$-0.806573\pi$
$821$	−941753.	+	166056.i	−1.39717	+	0.246360i	−0.576193	+	0.817314i	$0.695462\pi$
$822$		0			0
$823$	−850201.	+	309448.i	−1.25523	+	0.456865i	−0.882164	−	0.470942i	$-0.843914\pi$
$823$	−850201.	+	309448.i	−1.25523	+	0.456865i	−0.373062	+	0.927807i	$0.621692\pi$
$824$	−130367.	−	358181.i	−0.192005	−	0.527531i
$825$		0			0
$826$	5099.32	+	28919.7i	0.00747398	+	0.0423871i
$827$	180555.	+	104244.i	0.263997	+	0.152419i	0.626157	−	0.779697i	$-0.284627\pi$
$827$	180555.	+	104244.i	0.263997	+	0.152419i	−0.362159	+	0.932116i	$0.617960\pi$
$828$		0			0
$829$	−216679.	−	375298.i	−0.315288	−	0.546094i	0.664211	−	0.747545i	$-0.268768\pi$
$829$	−216679.	−	375298.i	−0.315288	−	0.546094i	−0.979499	+	0.201451i	$0.935434\pi$
$830$	225376.	+	268592.i	0.327153	+	0.389885i
$831$		0			0
$832$	25006.3	−	141818.i	0.0361246	−	0.204873i
$833$	−303390.	+	361566.i	−0.437231	+	0.521072i
$834$		0			0
$835$	−316713.	−	115274.i	−0.454248	−	0.165333i
$836$		−	126693.i		−	0.181276i
$837$		0			0
$838$	−378515.			−0.539008
$839$	206734.	−	567998.i	0.293690	−	0.806906i	−0.701829	−	0.712345i	$-0.747633\pi$
$839$	206734.	−	567998.i	0.293690	−	0.806906i	0.995519	−	0.0945610i	$-0.0301447\pi$
$840$		0			0
$841$	45135.0	+	37872.7i	0.0638148	+	0.0535469i
$842$	−639487.	−	112759.i	−0.902002	−	0.159047i
$843$		0			0
$844$	−343015.	+	287824.i	−0.481536	+	0.404057i
$845$	2.03270e6	−	1.17358e6i	2.84682	−	1.64361i
$846$		0			0
$847$	128314.	−	222246.i	0.178857	−	0.309790i
$848$	55210.7	−	9735.13i	0.0767770	−	0.0135379i
$849$		0			0
$850$	−931797.	+	339146.i	−1.28968	+	0.469407i
$851$	13069.6	+	35908.5i	0.0180470	+	0.0495836i
$852$		0			0
$853$	144424.	+	819067.i	0.198491	+	1.12570i	0.907359	+	0.420356i	$0.138095\pi$
$853$	144424.	+	819067.i	0.198491	+	1.12570i	−0.708869	+	0.705340i	$0.750794\pi$
$854$	−151857.	−	87674.6i	−0.208218	−	0.120215i
$855$		0			0
$856$	183327.	+	317531.i	0.250195	+	0.433350i
$857$	−283419.	−	337766.i	−0.385893	−	0.459890i	0.537772	−	0.843090i	$-0.319266\pi$
$857$	−283419.	−	337766.i	−0.385893	−	0.459890i	−0.923665	+	0.383201i	$0.874822\pi$
$858$		0			0
$859$	11437.9	−	64867.5i	0.0155010	−	0.0879104i	−0.976076	−	0.217430i	$-0.930233\pi$
$859$	11437.9	−	64867.5i	0.0155010	−	0.0879104i	0.991577	+	0.129520i	$0.0413436\pi$
$860$	18485.2	−	22029.8i	0.0249935	−	0.0297861i
$861$		0			0
$862$	−376835.	−	137157.i	−0.507150	−	0.184587i
$863$			835541.i			1.12188i	0.827857	+	0.560939i	$0.189560\pi$
$863$			835541.i			1.12188i	−0.827857	+	0.560939i	$0.810440\pi$
$864$		0			0
$865$	−2.47235e6			−3.30429
$866$	206247.	−	566659.i	0.275012	−	0.755590i
$867$		0			0
$868$	175583.	+	147332.i	0.233047	+	0.195550i
$869$	−104448.	−	18416.9i	−0.138312	−	0.0243881i
$870$		0			0
$871$	41046.8	−	34442.3i	0.0541057	−	0.0454001i
$872$	−331305.	+	191279.i	−0.435708	+	0.251556i
$873$		0			0
$874$	46928.2	−	81282.1i	0.0614344	−	0.106407i
$875$	−763563.	+	134637.i	−0.997306	+	0.175852i
$876$		0			0
$877$	−62159.8	+	22624.3i	−0.0808184	+	0.0294155i	−0.382113	−	0.924116i	$-0.624803\pi$
$877$	−62159.8	+	22624.3i	−0.0808184	+	0.0294155i	0.301295	+	0.953531i	$0.402581\pi$
$878$	210335.	+	577892.i	0.272850	+	0.749648i
$879$		0			0
$880$	−13770.0	−	78093.3i	−0.0177815	−	0.100844i
$881$	234845.	+	135588.i	0.302572	+	0.174690i	0.643598	−	0.765364i	$-0.277441\pi$
$881$	234845.	+	135588.i	0.302572	+	0.174690i	−0.341026	+	0.940054i	$0.610774\pi$
$882$		0			0
$883$	226502.	+	392314.i	0.290504	+	0.503167i	0.973929	−	0.226853i	$-0.0728438\pi$
$883$	226502.	+	392314.i	0.290504	+	0.503167i	−0.683425	+	0.730020i	$0.739510\pi$
$884$	−331134.	−	394631.i	−0.423740	−	0.504994i
$885$		0			0
$886$	175302.	−	994186.i	0.223316	−	1.26649i
$887$	908242.	−	1.08240e6i	1.15440	−	1.37575i	0.240079	−	0.970753i	$-0.422827\pi$
$887$	908242.	−	1.08240e6i	1.15440	−	1.37575i	0.914316	−	0.405001i	$-0.132729\pi$
$888$		0			0
$889$	86877.9	+	31621.0i	0.109927	+	0.0400103i
$890$			460138.i			0.580909i
$891$		0			0
$892$	405305.			0.509392
$893$	−205431.	+	564416.i	−0.257610	+	0.707777i
$894$		0			0
$895$	−1.24537e6	−	1.04499e6i	−1.55472	−	1.30456i
$896$	−26275.4	−	4633.05i	−0.0327290	−	0.00577100i
$897$		0			0
$898$	−112314.	+	94242.6i	−0.139278	+	0.116868i
$899$	−1.08442e6	+	626088.i	−1.34177	+	0.774669i
$900$		0			0
$901$	100277.	−	173684.i	0.123524	−	0.213949i
$902$	140348.	−	24747.1i	0.172501	−	0.0304167i
$903$		0			0
$904$	−194136.	+	70659.6i	−0.237557	+	0.0864638i
$905$	−508757.	−	1.39780e6i	−0.621174	−	1.70666i
$906$		0			0
$907$	41856.3	+	237379.i	0.0508799	+	0.288554i	0.999622	−	0.0274975i	$-0.00875384\pi$
$907$	41856.3	+	237379.i	0.0508799	+	0.288554i	−0.948742	+	0.316052i	$0.897643\pi$
$908$	604300.	+	348893.i	0.732961	+	0.423175i
$909$		0			0
$910$	−340297.	−	589412.i	−0.410937	−	0.711764i
$911$	950117.	+	1.13230e6i	1.14483	+	1.36435i	0.920924	+	0.389741i	$0.127436\pi$
$911$	950117.	+	1.13230e6i	1.14483	+	1.36435i	0.223903	+	0.974611i	$0.428120\pi$
$912$		0			0
$913$	−12369.2	+	70149.5i	−0.0148389	+	0.0841556i
$914$	530176.	−	631840.i	0.634641	−	0.756335i
$915$		0			0
$916$	−282956.	−	102987.i	−0.337231	−	0.122742i
$917$		−	387074.i		−	0.460315i
$918$		0			0
$919$	−443058.			−0.524601			−0.262301	−	0.964986i	$-0.584481\pi$
$919$	−443058.			−0.524601			−0.262301	+	0.964986i	$0.584481\pi$
$920$	20092.2	−	55202.8i	0.0237384	−	0.0652206i
$921$		0			0
$922$	255791.	+	214634.i	0.300901	+	0.252486i
$923$	−355556.	−	62694.2i	−0.417354	−	0.0735908i
$924$		0			0
$925$	−801733.	+	672734.i	−0.937015	+	0.786249i
$926$	−887043.	+	512134.i	−1.03448	+	0.597258i
$927$		0			0
$928$	72879.2	−	126230.i	0.0846267	−	0.146578i
$929$	−1.07887e6	+	190233.i	−1.25008	+	0.220422i	−0.759229	−	0.650824i	$-0.774424\pi$
$929$	−1.07887e6	+	190233.i	−1.25008	+	0.220422i	−0.490847	+	0.871246i	$0.663313\pi$
$930$		0			0
$931$	1.14977e6	−	418484.i	1.32652	−	0.482813i
$932$	−35863.2	−	98533.3i	−0.0412873	−	0.113436i
$933$		0			0
$934$	−165822.	−	940421.i	−0.190085	−	1.07802i
$935$	−245669.	−	141837.i	−0.281014	−	0.162243i
$936$		0			0
$937$	−537812.	−	931517.i	−0.612563	−	1.06099i	−0.990807	−	0.135285i	$-0.956805\pi$
$937$	−537812.	−	931517.i	−0.612563	−	1.06099i	0.378243	−	0.925706i	$-0.376528\pi$
$938$	−6381.33	−	7604.97i	−0.00725279	−	0.00864354i
$939$		0			0
$940$	−65282.1	+	370233.i	−0.0738820	+	0.419006i
$941$	317242.	−	378074.i	0.358270	−	0.426970i	−0.556561	−	0.830807i	$-0.687879\pi$
$941$	317242.	−	378074.i	0.358270	−	0.426970i	0.914831	+	0.403837i	$0.132324\pi$
$942$		0			0
$943$	99209.4	+	36109.3i	0.111565	+	0.0406065i
$944$		−	36065.7i		−	0.0404716i
$945$		0			0
$946$	5842.39			0.00652842
$947$	286735.	−	787798.i	0.319728	−	0.878446i	−0.670862	−	0.741583i	$-0.734076\pi$
$947$	286735.	−	787798.i	0.319728	−	0.878446i	0.990590	−	0.136864i	$-0.0437022\pi$
$948$		0			0
$949$	−684151.	−	574071.i	−0.759660	−	0.637431i
$950$	2.53151e6	+	446374.i	2.80500	+	0.494597i
$951$		0			0
$952$	−73115.4	+	61351.1i	−0.0806743	+	0.0676938i
$953$	148002.	−	85449.2i	0.162961	−	0.0940854i	−0.416302	−	0.909227i	$-0.636674\pi$
$953$	148002.	−	85449.2i	0.162961	−	0.0940854i	0.579262	+	0.815141i	$0.303341\pi$
$954$		0			0
$955$	−92992.7	+	161068.i	−0.101963	+	0.176605i
$956$	−692178.	+	122050.i	−0.757360	+	0.133543i
$957$		0			0
$958$	274069.	−	99753.1i	0.298627	−	0.108691i
$959$	79125.1	+	217394.i	0.0860353	+	0.236380i
$960$		0			0
$961$	259569.	+	1.47209e6i	0.281065	+	1.59400i
$962$	−470877.	−	271861.i	−0.508812	−	0.293763i
$963$		0			0
$964$	−155963.	−	270136.i	−0.167829	−	0.290689i
$965$	542094.	+	646042.i	0.582129	+	0.693755i
$966$		0			0
$967$	40510.3	−	229746.i	0.0433225	−	0.245694i	−0.955454	−	0.295139i	$-0.904634\pi$
$967$	40510.3	−	229746.i	0.0433225	−	0.245694i	0.998777	+	0.0494449i	$0.0157452\pi$
$968$	−202593.	+	241440.i	−0.216208	+	0.257667i
$969$		0			0
$970$	821424.	+	298974.i	0.873020	+	0.317753i
$971$		−	806491.i		−	0.855384i	−0.903925	−	0.427692i	$-0.859327\pi$
$971$		−	806491.i		−	0.855384i	0.903925	−	0.427692i	$-0.140673\pi$
$972$		0			0
$973$	−107020.			−0.113042
$974$	−6470.19	+	17776.7i	−0.00682023	+	0.0187384i
$975$		0			0
$976$	164972.	+	138428.i	0.173185	+	0.145320i
$977$	−1.01302e6	−	178622.i	−1.06127	−	0.187131i	−0.384352	−	0.923187i	$-0.625575\pi$
$977$	−1.01302e6	−	178622.i	−1.06127	−	0.187131i	−0.676921	+	0.736056i	$0.736686\pi$
$978$		0			0
$979$	−71610.4	+	60088.2i	−0.0747155	+	0.0626937i
$980$	663236.	−	382920.i	0.690583	−	0.398708i
$981$		0			0
$982$	24054.1	−	41662.9i	0.0249440	−	0.0432043i
$983$	−1.16869e6	+	206071.i	−1.20946	+	0.213260i	−0.741784	−	0.670639i	$-0.766020\pi$
$983$	−1.16869e6	+	206071.i	−1.20946	+	0.213260i	−0.467677	+	0.883900i	$0.654909\pi$
$984$		0			0
$985$	1.79112e6	−	651916.i	1.84609	−	0.671922i
$986$	−178338.	−	489979.i	−0.183438	−	0.503992i
$987$		0			0
$988$	231900.	+	1.31517e6i	0.237567	+	1.34731i
$989$	3748.29	+	2164.08i	0.00383214	+	0.00221249i
$990$		0			0
$991$	583016.	+	1.00981e6i	0.593653	+	1.02824i	0.993735	+	0.111759i	$0.0356483\pi$
$991$	583016.	+	1.00981e6i	0.593653	+	1.02824i	−0.400082	+	0.916479i	$0.631018\pi$
$992$	−180946.	−	215643.i	−0.183876	−	0.219135i
$993$		0			0
$994$	−11615.7	+	65875.9i	−0.0117564	+	0.0666736i
$995$	−1.43855e6	+	1.71440e6i	−1.45304	+	1.73167i
$996$		0			0
$997$	−383175.	−	139464.i	−0.385484	−	0.140305i	0.142006	−	0.989866i	$-0.454645\pi$
$997$	−383175.	−	139464.i	−0.385484	−	0.140305i	−0.527490	+	0.849561i	$0.676867\pi$
$998$		−	1.33987e6i		−	1.34525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.1		72
3.2	odd	2		54.5.f.a.23.11	✓	72
27.7	even	9		54.5.f.a.47.11	yes	72
27.20	odd	18	inner	162.5.f.a.143.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.11	✓	72	3.2	odd	2
54.5.f.a.47.11	yes	72	27.7	even	9
162.5.f.a.17.1		72	1.1	even	1	trivial
162.5.f.a.143.1		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)

\(f(q)\)	\(=\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(45.7302 + 8.06347i) q^{5} +(-14.1135 + 11.8427i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(45.7302 + 8.06347i) q^{5} +(-14.1135 + 11.8427i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-65.6700 + 113.744i) q^{10} +(-26.2774 + 4.63341i) q^{11} +(264.299 - 96.1968i) q^{13} +(-17.8229 - 48.9681i) q^{14} +(11.1135 + 63.0277i) q^{16} +(198.275 + 114.474i) q^{17} +(-296.757 - 513.998i) q^{19} +(-238.786 - 284.574i) q^{20} +(13.1053 - 74.3237i) q^{22} +(35.9381 - 42.8294i) q^{23} +(1438.93 + 523.726i) q^{25} +795.525i q^{26} +147.391 q^{28} +(-275.398 + 756.649i) q^{29} +(1191.27 + 999.596i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-496.063 + 416.246i) q^{34} +(-740.909 + 427.764i) q^{35} +(-341.738 + 591.907i) q^{37} +(1653.21 - 291.505i) q^{38} +(987.354 - 359.367i) q^{40} +(645.848 + 1774.45i) q^{41} +(13.4427 + 76.2371i) q^{43} +(184.864 + 106.731i) q^{44} +(79.0684 + 136.951i) q^{46} +(-650.504 - 775.240i) q^{47} +(-357.986 + 2030.24i) q^{49} +(-2783.97 + 3317.81i) q^{50} +(-2114.39 - 769.574i) q^{52} -875.975i q^{53} -1239.03 q^{55} +(-142.583 + 391.745i) q^{56} +(-1744.65 - 1463.93i) q^{58} +(-554.966 - 97.8554i) q^{59} +(2577.69 - 2162.94i) q^{61} +(-3809.19 + 2199.24i) q^{62} +(256.000 - 443.405i) q^{64} +(12862.1 - 2267.94i) q^{65} +(179.020 - 65.1580i) q^{67} +(-626.440 - 1721.13i) q^{68} +(-420.194 - 2383.04i) q^{70} +(-1111.68 - 641.827i) q^{71} +(-1587.66 - 2749.92i) q^{73} +(-1242.61 - 1480.89i) q^{74} +(-824.501 + 4675.98i) q^{76} +(315.995 - 376.588i) q^{77} +(3735.10 + 1359.47i) q^{79} +2971.88i q^{80} -5341.01 q^{82} +(913.049 - 2508.58i) q^{83} +(8144.11 + 6833.72i) q^{85} +(-215.631 - 38.0216i) q^{86} +(-462.508 + 388.091i) q^{88} +(3034.04 - 1751.71i) q^{89} +(-2590.96 + 4487.68i) q^{91} +(-440.483 + 77.6691i) q^{92} +(2689.76 - 978.992i) q^{94} +(-9426.16 - 25898.2i) q^{95} +(-1155.73 - 6554.45i) q^{97} +(-5049.77 - 2915.48i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 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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