LMFDB - Embedded newform 162.5.f.a.17.4

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			17.4
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(20.4117 + 3.59913i) q^{5} +(-31.5466 + 26.4708i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})$	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(20.4117 + 3.59913i) q^{5} +(-31.5466 + 26.4708i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-29.3118 + 50.7695i) q^{10} +(75.0698 - 13.2368i) q^{11} +(-76.2312 + 27.7459i) q^{13} +(-39.8379 - 109.454i) q^{14} +(11.1135 + 63.0277i) q^{16} +(9.50385 + 5.48705i) q^{17} +(332.610 + 576.097i) q^{19} +(-106.582 - 127.020i) q^{20} +(-37.4394 + 212.329i) q^{22} +(-222.606 + 265.291i) q^{23} +(-183.625 - 66.8340i) q^{25} -229.452i q^{26} +329.450 q^{28} +(-386.043 + 1060.64i) q^{29} +(-563.887 - 473.157i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-23.7776 + 19.9518i) q^{34} +(-739.192 + 426.773i) q^{35} +(-1218.40 + 2110.33i) q^{37} +(-1852.94 + 326.723i) q^{38} +(440.705 - 160.404i) q^{40} +(-98.9929 - 271.981i) q^{41} +(-50.8333 - 288.290i) q^{43} +(-528.122 - 304.911i) q^{44} +(-489.761 - 848.291i) q^{46} +(-2021.13 - 2408.68i) q^{47} +(-122.441 + 694.395i) q^{49} +(355.270 - 423.394i) q^{50} +(609.850 + 221.967i) q^{52} +113.642i q^{53} +1579.94 q^{55} +(-318.703 + 875.629i) q^{56} +(-2445.59 - 2052.09i) q^{58} +(3366.31 + 593.572i) q^{59} +(-3604.93 + 3024.90i) q^{61} +(1803.07 - 1041.00i) q^{62} +(256.000 - 443.405i) q^{64} +(-1655.87 + 291.974i) q^{65} +(469.094 - 170.736i) q^{67} +(-30.0269 - 82.4982i) q^{68} +(-419.220 - 2377.51i) q^{70} +(6673.19 + 3852.77i) q^{71} +(4417.91 + 7652.04i) q^{73} +(-4430.30 - 5279.82i) q^{74} +(924.113 - 5240.91i) q^{76} +(-2017.81 + 2404.73i) q^{77} +(-1024.07 - 372.732i) q^{79} +1326.50i q^{80} +818.648 q^{82} +(-259.814 + 713.833i) q^{83} +(174.241 + 146.206i) q^{85} +(815.407 + 143.778i) q^{86} +(1321.30 - 1108.71i) q^{88} +(10666.3 - 6158.20i) q^{89} +(1670.38 - 2893.19i) q^{91} +(2728.42 - 481.094i) q^{92} +(8357.12 - 3041.74i) q^{94} +(4715.68 + 12956.2i) q^{95} +(-1137.76 - 6452.54i) q^{97} +(-1727.15 - 997.172i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	20.4117	+	3.59913i	0.816467	+	0.143965i	0.566260	−	0.824227i	$-0.308390\pi$
$5$	20.4117	+	3.59913i	0.816467	+	0.143965i	0.250208	+	0.968192i	$0.419501\pi$
$6$		0			0
$7$	−31.5466	+	26.4708i	−0.643809	+	0.540220i	−0.905185	−	0.425017i	$-0.860268\pi$
$7$	−31.5466	+	26.4708i	−0.643809	+	0.540220i	0.261376	+	0.965237i	$0.415824\pi$
$8$	19.5959	−	11.3137i	0.306186	−	0.176777i
$9$		0			0
$10$	−29.3118	+	50.7695i	−0.293118	+	0.507695i
$11$	75.0698	−	13.2368i	0.620411	−	0.109395i	0.145397	−	0.989373i	$-0.453554\pi$
$11$	75.0698	−	13.2368i	0.620411	−	0.109395i	0.475014	+	0.879978i	$0.342443\pi$
$12$		0			0
$13$	−76.2312	+	27.7459i	−0.451072	+	0.164177i	−0.557559	−	0.830137i	$-0.688262\pi$
$13$	−76.2312	+	27.7459i	−0.451072	+	0.164177i	0.106487	+	0.994314i	$0.466040\pi$
$14$	−39.8379	−	109.454i	−0.203254	−	0.558437i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	9.50385	+	5.48705i	0.0328853	+	0.0189863i	0.516353	−	0.856376i	$-0.327289\pi$
$17$	9.50385	+	5.48705i	0.0328853	+	0.0189863i	−0.483467	+	0.875362i	$0.660623\pi$
$18$		0			0
$19$	332.610	+	576.097i	0.921357	+	1.59584i	0.797318	+	0.603559i	$0.206251\pi$
$19$	332.610	+	576.097i	0.921357	+	1.59584i	0.124038	+	0.992277i	$0.460415\pi$
$20$	−106.582	−	127.020i	−0.266456	−	0.317549i
$21$		0			0
$22$	−37.4394	+	212.329i	−0.0773541	+	0.438697i
$23$	−222.606	+	265.291i	−0.420805	+	0.501496i	−0.934246	−	0.356629i	$-0.883926\pi$
$23$	−222.606	+	265.291i	−0.420805	+	0.501496i	0.513441	+	0.858125i	$0.328371\pi$
$24$		0			0
$25$	−183.625	−	66.8340i	−0.293800	−	0.106934i
$26$		−	229.452i		−	0.339426i
$27$		0			0
$28$	329.450			0.420217
$29$	−386.043	+	1060.64i	−0.459029	+	1.26117i	0.467181	+	0.884162i	$0.345270\pi$
$29$	−386.043	+	1060.64i	−0.459029	+	1.26117i	−0.926209	+	0.377009i	$0.876952\pi$
$30$		0			0
$31$	−563.887	−	473.157i	−0.586771	−	0.492359i	0.300392	−	0.953816i	$-0.402882\pi$
$31$	−563.887	−	473.157i	−0.586771	−	0.492359i	−0.887163	+	0.461457i	$0.847327\pi$
$32$	−178.269	−	31.4337i	−0.174091	−	0.0306970i
$33$		0			0
$34$	−23.7776	+	19.9518i	−0.0205688	+	0.0172593i
$35$	−739.192	+	426.773i	−0.603422	+	0.348386i
$36$		0			0
$37$	−1218.40	+	2110.33i	−0.889994	+	1.54151i	−0.0501124	+	0.998744i	$0.515958\pi$
$37$	−1218.40	+	2110.33i	−0.889994	+	1.54151i	−0.839881	+	0.542770i	$0.817375\pi$
$38$	−1852.94	+	326.723i	−1.28320	+	0.226263i
$39$		0			0
$40$	440.705	−	160.404i	0.275441	−	0.100252i
$41$	−98.9929	−	271.981i	−0.0588893	−	0.161797i	0.906759	−	0.421649i	$-0.138549\pi$
$41$	−98.9929	−	271.981i	−0.0588893	−	0.161797i	−0.965649	+	0.259852i	$0.916326\pi$
$42$		0			0
$43$	−50.8333	−	288.290i	−0.0274923	−	0.155917i	0.967971	−	0.251062i	$-0.0807797\pi$
$43$	−50.8333	−	288.290i	−0.0274923	−	0.155917i	−0.995463	+	0.0951450i	$0.969669\pi$
$44$	−528.122	−	304.911i	−0.272790	−	0.157496i
$45$		0			0
$46$	−489.761	−	848.291i	−0.231456	−	0.400894i
$47$	−2021.13	−	2408.68i	−0.914951	−	1.09040i	−0.995605	−	0.0936534i	$-0.970145\pi$
$47$	−2021.13	−	2408.68i	−0.914951	−	1.09040i	0.0806543	−	0.996742i	$-0.474299\pi$
$48$		0			0
$49$	−122.441	+	694.395i	−0.0509956	+	0.289211i
$50$	355.270	−	423.394i	0.142108	−	0.169358i
$51$		0			0
$52$	609.850	+	221.967i	0.225536	+	0.0820884i
$53$			113.642i			0.0404563i	0.999795	+	0.0202281i	$0.00643925\pi$
$53$			113.642i			0.0404563i	−0.999795	+	0.0202281i	$0.993561\pi$
$54$		0			0
$55$	1579.94			0.522295
$56$	−318.703	+	875.629i	−0.101627	+	0.279218i
$57$		0			0
$58$	−2445.59	−	2052.09i	−0.726988	−	0.610015i
$59$	3366.31	+	593.572i	0.967054	+	0.170518i	0.634804	−	0.772674i	$-0.281081\pi$
$59$	3366.31	+	593.572i	0.967054	+	0.170518i	0.332250	+	0.943191i	$0.392192\pi$
$60$		0			0
$61$	−3604.93	+	3024.90i	−0.968807	+	0.812925i	−0.982363	−	0.186983i	$-0.940129\pi$
$61$	−3604.93	+	3024.90i	−0.968807	+	0.812925i	0.0135565	+	0.999908i	$0.495685\pi$
$62$	1803.07	−	1041.00i	0.469062	−	0.270813i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−1655.87	+	291.974i	−0.391922	+	0.0691064i
$66$		0			0
$67$	469.094	−	170.736i	0.104498	−	0.0380343i	−0.289242	−	0.957256i	$-0.593403\pi$
$67$	469.094	−	170.736i	0.104498	−	0.0380343i	0.393740	+	0.919222i	$0.371181\pi$
$68$	−30.0269	−	82.4982i	−0.00649371	−	0.0178413i
$69$		0			0
$70$	−419.220	−	2377.51i	−0.0855551	−	0.485207i
$71$	6673.19	+	3852.77i	1.32378	+	0.764286i	0.984330	−	0.176337i	$-0.0564248\pi$
$71$	6673.19	+	3852.77i	1.32378	+	0.764286i	0.339453	+	0.940623i	$0.389758\pi$
$72$		0			0
$73$	4417.91	+	7652.04i	0.829031	+	1.43592i	0.898799	+	0.438361i	$0.144441\pi$
$73$	4417.91	+	7652.04i	0.829031	+	1.43592i	−0.0697677	+	0.997563i	$0.522226\pi$
$74$	−4430.30	−	5279.82i	−0.809039	−	0.964175i
$75$		0			0
$76$	924.113	−	5240.91i	0.159992	−	0.907359i
$77$	−2017.81	+	2404.73i	−0.340329	+	0.405588i
$78$		0			0
$79$	−1024.07	−	372.732i	−0.164088	−	0.0597232i	0.258670	−	0.965966i	$-0.416716\pi$
$79$	−1024.07	−	372.732i	−0.164088	−	0.0597232i	−0.422758	+	0.906243i	$0.638938\pi$
$80$			1326.50i			0.207266i
$81$		0			0
$82$	818.648			0.121750
$83$	−259.814	+	713.833i	−0.0377143	+	0.103619i	−0.957120	−	0.289690i	$-0.906448\pi$
$83$	−259.814	+	713.833i	−0.0377143	+	0.103619i	0.919406	+	0.393309i	$0.128670\pi$
$84$		0			0
$85$	174.241	+	146.206i	0.0241164	+	0.0202361i
$86$	815.407	+	143.778i	0.110250	+	0.0194400i
$87$		0			0
$88$	1321.30	−	1108.71i	0.170623	−	0.143170i
$89$	10666.3	−	6158.20i	1.34659	−	0.777453i	0.358823	−	0.933406i	$-0.383178\pi$
$89$	10666.3	−	6158.20i	1.34659	−	0.777453i	0.987764	+	0.155953i	$0.0498448\pi$
$90$		0			0
$91$	1670.38	−	2893.19i	0.201713	−	0.349377i
$92$	2728.42	−	481.094i	0.322356	−	0.0568400i
$93$		0			0
$94$	8357.12	−	3041.74i	0.945804	−	0.344244i
$95$	4715.68	+	12956.2i	0.522513	+	1.43559i
$96$		0			0
$97$	−1137.76	−	6452.54i	−0.120922	−	0.685784i	−0.983647	−	0.180110i	$-0.942355\pi$
$97$	−1137.76	−	6452.54i	−0.120922	−	0.685784i	0.862724	−	0.505675i	$-0.168756\pi$
$98$	−1727.15	−	997.172i	−0.179837	−	0.103829i
$99$		0			0
$100$	781.638	+	1353.84i	0.0781638	+	0.135384i
$101$	2738.78	+	3263.94i	0.268481	+	0.319963i	0.883393	−	0.468632i	$-0.155253\pi$
$101$	2738.78	+	3263.94i	0.268481	+	0.319963i	−0.614912	+	0.788595i	$0.710809\pi$
$102$		0			0
$103$	2782.11	−	15778.1i	0.262240	−	1.48724i	−0.514539	−	0.857467i	$-0.672037\pi$
$103$	2782.11	−	15778.1i	0.262240	−	1.48724i	0.776780	−	0.629772i	$-0.216852\pi$
$104$	−1179.91	+	1406.16i	−0.109089	+	0.130008i
$105$		0			0
$106$	−302.043	−	109.935i	−0.0268817	−	0.00978413i
$107$		−	19563.9i		−	1.70878i	−0.519630	−	0.854391i	$-0.673930\pi$
$107$		−	19563.9i		−	1.70878i	0.519630	−	0.854391i	$-0.326070\pi$
$108$		0			0
$109$	17284.9			1.45484			0.727418	−	0.686194i	$-0.240720\pi$
$109$	17284.9			1.45484			0.727418	+	0.686194i	$0.240720\pi$
$110$	−1528.40	+	4199.25i	−0.126314	+	0.347046i
$111$		0			0
$112$	−2018.99	−	1694.13i	−0.160952	−	0.135055i
$113$	21401.7	+	3773.70i	1.67607	+	0.295536i	0.929238	−	0.369481i	$-0.120465\pi$
$113$	21401.7	+	3773.70i	1.67607	+	0.295536i	0.746828	+	0.665017i	$0.231576\pi$
$114$		0			0
$115$	−5498.58	+	4613.86i	−0.415772	+	0.348874i
$116$	7819.97	−	4514.86i	0.581151	−	0.335528i
$117$		0			0
$118$	−4834.13	+	8372.96i	−0.347180	+	0.601333i
$119$	−445.061	+	78.4763i	−0.0314286	+	0.00554172i
$120$		0			0
$121$	−8297.78	+	3020.15i	−0.566750	+	0.206280i
$122$	−4552.39	−	12507.6i	−0.305858	−	0.840338i
$123$		0			0
$124$	1022.58	+	5799.35i	0.0665050	+	0.377169i
$125$	−14726.1	−	8502.14i	−0.942472	−	0.544137i
$126$		0			0
$127$	−5929.81	−	10270.7i	−0.367649	−	0.636786i	0.621549	−	0.783375i	$-0.286504\pi$
$127$	−5929.81	−	10270.7i	−0.367649	−	0.636786i	−0.989197	+	0.146589i	$0.953170\pi$
$128$	930.856	+	1109.35i	0.0568149	+	0.0677094i
$129$		0			0
$130$	825.828	−	4683.50i	0.0488656	−	0.277130i
$131$	−20069.8	+	23918.3i	−1.16950	+	1.39376i	−0.266659	+	0.963791i	$0.585920\pi$
$131$	−20069.8	+	23918.3i	−1.16950	+	1.39376i	−0.902844	+	0.429969i	$0.858525\pi$
$132$		0			0
$133$	−25742.5	−	9369.49i	−1.45528	−	0.529679i
$134$			1411.95i			0.0786338i
$135$		0			0
$136$	248.316			0.0134254
$137$	1550.08	−	4258.80i	0.0825870	−	0.226906i	−0.891525	−	0.452971i	$-0.850364\pi$
$137$	1550.08	−	4258.80i	0.0825870	−	0.226906i	0.974112	+	0.226065i	$0.0725862\pi$
$138$		0			0
$139$	12058.8	+	10118.6i	0.624131	+	0.523708i	0.899099	−	0.437745i	$-0.144223\pi$
$139$	12058.8	+	10118.6i	0.624131	+	0.523708i	−0.274968	+	0.961453i	$0.588667\pi$
$140$	6724.62	+	1185.73i	0.343093	+	0.0604966i
$141$		0			0
$142$	−16695.6	+	14009.3i	−0.827990	+	0.694766i
$143$	−5355.39	+	3091.94i	−0.261890	+	0.151202i
$144$		0			0
$145$	−11697.2	+	20260.1i	−0.556347	+	0.963621i
$146$	−24611.8	+	4339.72i	−1.15462	+	0.203590i
$147$		0			0
$148$	18318.8	−	6667.48i	0.836320	−	0.304396i
$149$	1571.50	+	4317.65i	0.0707849	+	0.194480i	0.970040	−	0.242944i	$-0.0781131\pi$
$149$	1571.50	+	4317.65i	0.0707849	+	0.194480i	−0.899255	+	0.437424i	$0.855891\pi$
$150$		0			0
$151$	65.3853	+	370.818i	0.00286765	+	0.0162632i	0.986208	−	0.165511i	$-0.0529272\pi$
$151$	65.3853	+	370.818i	0.00286765	+	0.0162632i	−0.983340	+	0.181774i	$0.941816\pi$
$152$	13035.6	+	7526.10i	0.564213	+	0.325749i
$153$		0			0
$154$	−4439.44	−	7689.33i	−0.187192	−	0.324225i
$155$	−9806.92	−	11687.4i	−0.408196	−	0.486470i
$156$		0			0
$157$	1365.66	−	7745.06i	0.0554044	−	0.314214i	−0.944493	−	0.328531i	$-0.893446\pi$
$157$	1365.66	−	7745.06i	0.0554044	−	0.314214i	0.999898	+	0.0143173i	$0.00455750\pi$
$158$	1981.34	−	2361.26i	0.0793677	−	0.0945867i
$159$		0			0
$160$	−3525.64	−	1283.23i	−0.137720	−	0.0501261i
$161$		−	14261.6i		−	0.550195i
$162$		0			0
$163$	42762.2			1.60948			0.804739	−	0.593629i	$-0.202305\pi$
$163$	42762.2			1.60948			0.804739	+	0.593629i	$0.202305\pi$
$164$	−791.943	+	2175.85i	−0.0294447	+	0.0808985i
$165$		0			0
$166$	−1645.92	−	1381.09i	−0.0597301	−	0.0501195i
$167$	−10611.9	−	1871.16i	−0.380504	−	0.0670931i	−0.0198750	−	0.999802i	$-0.506327\pi$
$167$	−10611.9	−	1871.16i	−0.380504	−	0.0670931i	−0.360629	+	0.932709i	$0.617438\pi$
$168$		0			0
$169$	−16837.6	+	14128.4i	−0.589532	+	0.494676i
$170$	−557.150	+	321.671i	−0.0192785	+	0.0111305i
$171$		0			0
$172$	−1170.95	+	2028.14i	−0.0395805	+	0.0685554i
$173$	−15933.7	+	2809.54i	−0.532384	+	0.0938737i	−0.433376	−	0.901213i	$-0.642678\pi$
$173$	−15933.7	+	2809.54i	−0.532384	+	0.0938737i	−0.0990076	+	0.995087i	$0.531567\pi$
$174$		0			0
$175$	7561.89	−	2752.30i	0.246919	−	0.0898712i
$176$	1668.57	+	4584.37i	0.0538666	+	0.147997i
$177$		0			0
$178$	6049.22	+	34306.8i	0.190923	+	1.08278i
$179$	−27468.2	−	15858.8i	−0.857282	−	0.494952i	0.00581897	−	0.999983i	$-0.498148\pi$
$179$	−27468.2	−	15858.8i	−0.857282	−	0.494952i	−0.863101	+	0.505031i	$0.831481\pi$
$180$		0			0
$181$	−5433.41	−	9410.94i	−0.165850	−	0.287261i	0.771107	−	0.636706i	$-0.219703\pi$
$181$	−5433.41	−	9410.94i	−0.165850	−	0.287261i	−0.936957	+	0.349445i	$0.886370\pi$
$182$	6073.78	+	7238.44i	0.183365	+	0.218526i
$183$		0			0
$184$	−1360.74	+	7717.13i	−0.0401919	+	0.227940i
$185$	−32465.0	+	38690.3i	−0.948575	+	1.13047i
$186$		0			0
$187$	786.083	+	286.111i	0.0224794	+	0.00818184i
$188$			25154.5i			0.711705i
$189$		0			0
$190$	−38997.5			−1.08026
$191$	20965.6	−	57602.6i	0.574700	−	1.57898i	−0.222289	−	0.974981i	$-0.571353\pi$
$191$	20965.6	−	57602.6i	0.574700	−	1.57898i	0.796989	−	0.603994i	$-0.206425\pi$
$192$		0			0
$193$	4016.86	+	3370.55i	0.107838	+	0.0904869i	0.695112	−	0.718901i	$-0.255355\pi$
$193$	4016.86	+	3370.55i	0.107838	+	0.0904869i	−0.587274	+	0.809388i	$0.699799\pi$
$194$	18250.6	+	3218.06i	0.484923	+	0.0855050i
$195$		0			0
$196$	4321.15	−	3625.87i	0.112483	−	0.0943844i
$197$	−27400.0	+	15819.4i	−0.706021	+	0.407622i	−0.809586	−	0.587001i	$-0.800308\pi$
$197$	−27400.0	+	15819.4i	−0.706021	+	0.407622i	0.103565	+	0.994623i	$0.466975\pi$
$198$		0			0
$199$	−4038.58	+	6995.02i	−0.101982	+	0.176637i	−0.912501	−	0.409074i	$-0.865852\pi$
$199$	−4038.58	+	6995.02i	−0.101982	+	0.176637i	0.810519	+	0.585712i	$0.199185\pi$
$200$	−4354.44	+	767.805i	−0.108861	+	0.0191951i
$201$		0			0
$202$	−11324.5	+	4121.79i	−0.277534	+	0.101014i
$203$	−15897.7	−	43678.7i	−0.385783	−	1.05993i
$204$		0			0
$205$	−1041.72	−	5907.88i	−0.0247880	−	0.140580i
$206$	39244.6	+	22657.9i	0.924794	+	0.533930i
$207$		0			0
$208$	−2595.95	−	4496.32i	−0.0600026	−	0.103928i
$209$	32594.6	+	38844.8i	0.746197	+	0.889283i
$210$		0			0
$211$	−13503.3	+	76581.0i	−0.303302	+	1.72011i	0.328090	+	0.944647i	$0.393595\pi$
$211$	−13503.3	+	76581.0i	−0.303302	+	1.72011i	−0.631392	+	0.775464i	$0.717516\pi$
$212$	584.379	−	696.436i	0.0130024	−	0.0154956i
$213$		0			0
$214$	51997.8	+	18925.7i	1.13542	+	0.413260i
$215$		−	6067.44i		−	0.131259i
$216$		0			0
$217$	30313.6			0.643750
$218$	−16721.1	+	45940.7i	−0.351845	+	0.966685i
$219$		0			0
$220$	−9682.44	−	8124.53i	−0.200050	−	0.167862i
$221$	−876.733	−	154.592i	−0.0179508	−	0.00316520i
$222$		0			0
$223$	59826.2	−	50200.1i	1.20304	−	1.00947i	0.203506	−	0.979074i	$-0.434766\pi$
$223$	59826.2	−	50200.1i	1.20304	−	1.00947i	0.999538	−	0.0303996i	$-0.00967798\pi$
$224$	6455.87	−	3727.30i	0.128665	−	0.0742845i
$225$		0			0
$226$	−30733.5	+	53231.9i	−0.601721	+	1.04221i
$227$	26865.0	−	4737.03i	0.521357	−	0.0919293i	0.0932243	−	0.995645i	$-0.470283\pi$
$227$	26865.0	−	4737.03i	0.521357	−	0.0919293i	0.428133	+	0.903716i	$0.359172\pi$
$228$		0			0
$229$	−47027.4	+	17116.6i	−0.896768	+	0.326397i	−0.748957	−	0.662619i	$-0.769445\pi$
$229$	−47027.4	+	17116.6i	−0.896768	+	0.326397i	−0.147811	+	0.989016i	$0.547223\pi$
$230$	−6943.74	−	19077.8i	−0.131262	−	0.360638i
$231$		0			0
$232$	4434.96	+	25151.9i	0.0823974	+	0.467299i
$233$	−11831.4	−	6830.88i	−0.217934	−	0.125824i	0.387059	−	0.922055i	$-0.373491\pi$
$233$	−11831.4	−	6830.88i	−0.217934	−	0.125824i	−0.604993	+	0.796230i	$0.706824\pi$
$234$		0			0
$235$	−32585.4	−	56439.6i	−0.590048	−	1.02199i
$236$	−17577.6	−	20948.2i	−0.315600	−	0.376117i
$237$		0			0
$238$	221.964	−	1258.82i	0.00391859	−	0.0222234i
$239$	45371.2	−	54071.2i	0.794299	−	0.946609i	−0.205185	−	0.978723i	$-0.565780\pi$
$239$	45371.2	−	54071.2i	0.794299	−	0.946609i	0.999484	+	0.0321143i	$0.0102240\pi$
$240$		0			0
$241$	−29540.0	−	10751.7i	−0.508600	−	0.185115i	0.0749581	−	0.997187i	$-0.476118\pi$
$241$	−29540.0	−	10751.7i	−0.508600	−	0.185115i	−0.583558	+	0.812071i	$0.698340\pi$
$242$		−	24975.9i		−	0.426472i
$243$		0			0
$244$	37647.2			0.632344
$245$	−4998.43	+	13733.1i	−0.0832725	+	0.228789i
$246$		0			0
$247$	−41339.6	−	34688.0i	−0.677598	−	0.568572i
$248$	−16403.0	−	2892.30i	−0.266699	−	0.0470262i
$249$		0			0
$250$	36843.2	−	30915.1i	0.589491	−	0.494641i
$251$	23115.6	−	13345.8i	0.366908	−	0.211834i	−0.305199	−	0.952289i	$-0.598723\pi$
$251$	23115.6	−	13345.8i	0.366908	−	0.211834i	0.672107	+	0.740454i	$0.265390\pi$
$252$		0			0
$253$	−13199.4	+	22862.0i	−0.206211	+	0.357168i
$254$	33034.4	−	5824.86i	0.512035	−	0.0902855i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	−969.468	−	2663.59i	−0.0146780	−	0.0403275i	0.932137	−	0.362105i	$-0.117942\pi$
$257$	−969.468	−	2663.59i	−0.0146780	−	0.0403275i	−0.946815	+	0.321778i	$0.895720\pi$
$258$		0			0
$259$	−17425.7	−	98825.9i	−0.259771	−	1.47323i
$260$	11649.2	+	6725.65i	0.172325	+	0.0994919i
$261$		0			0
$262$	−44156.2	−	76480.7i	−0.643264	−	1.11417i
$263$	15916.3	+	18968.3i	0.230107	+	0.274231i	0.868727	−	0.495292i	$-0.164939\pi$
$263$	15916.3	+	18968.3i	0.230107	+	0.274231i	−0.638620	+	0.769522i	$0.720494\pi$
$264$		0			0
$265$	−409.011	+	2319.62i	−0.00582429	+	0.0330312i
$266$	49805.4	−	59355.8i	0.703904	−	0.838880i
$267$		0			0
$268$	−3752.75	−	1365.89i	−0.0522492	−	0.0190172i
$269$			116840.i			1.61468i	0.590086	+	0.807340i	$0.299094\pi$
$269$			116840.i			1.61468i	−0.590086	+	0.807340i	$0.700906\pi$
$270$		0			0
$271$	78496.3			1.06883			0.534417	−	0.845221i	$-0.320531\pi$
$271$	78496.3			1.06883			0.534417	+	0.845221i	$0.320531\pi$
$272$	−240.215	+	659.986i	−0.00324685	+	0.00892066i
$273$		0			0
$274$	9819.75	+	8239.75i	0.130797	+	0.109752i
$275$	−14669.3	−	2586.60i	−0.193975	−	0.0342030i
$276$		0			0
$277$	99675.3	−	83637.5i	1.29906	−	1.09004i	0.308749	−	0.951143i	$-0.400090\pi$
$277$	99675.3	−	83637.5i	1.29906	−	1.09004i	0.990307	−	0.138894i	$-0.0443548\pi$
$278$	−38559.1	+	22262.1i	−0.498927	+	0.288056i
$279$		0			0
$280$	−9656.76	+	16726.0i	−0.123173	+	0.213342i
$281$	85986.2	−	15161.7i	1.08897	−	0.192015i	0.399792	−	0.916606i	$-0.369082\pi$
$281$	85986.2	−	15161.7i	1.08897	−	0.192015i	0.689179	+	0.724591i	$0.257971\pi$
$282$		0			0
$283$	25744.5	−	9370.22i	0.321448	−	0.116998i	−0.176256	−	0.984344i	$-0.556399\pi$
$283$	25744.5	−	9370.22i	0.321448	−	0.116998i	0.497704	+	0.867347i	$0.334176\pi$
$284$	−21083.6	−	57926.7i	−0.261401	−	0.718194i
$285$		0			0
$286$	−3037.22	−	17224.9i	−0.0371316	−	0.210584i
$287$	10322.4	+	5959.66i	0.125319	+	0.0723532i
$288$		0			0
$289$	−41700.3	−	72227.0i	−0.499279	−	0.864777i
$290$	−42532.8	−	50688.6i	−0.505741	−	0.602719i
$291$		0			0
$292$	12274.6	−	69612.6i	0.143960	−	0.816436i
$293$	−29429.4	+	35072.6i	−0.342804	+	0.408538i	−0.909710	−	0.415245i	$-0.863696\pi$
$293$	−29429.4	+	35072.6i	−0.342804	+	0.408538i	0.566906	+	0.823783i	$0.308140\pi$
$294$		0			0
$295$	66575.8	+	24231.6i	0.765019	+	0.278444i
$296$			55138.5i			0.629320i
$297$		0			0
$298$	−12995.9			−0.146344
$299$	9608.78	−	26399.9i	0.107480	−	0.295298i
$300$		0			0
$301$	9234.87	+	7748.98i	0.101929	+	0.0855286i
$302$	−1048.83	−	184.937i	−0.0114999	−	0.00202773i
$303$		0			0
$304$	−32613.6	+	27366.1i	−0.352900	+	0.296118i
$305$	−84469.7	+	48768.6i	−0.908032	+	0.524253i
$306$		0			0
$307$	4644.53	−	8044.56i	0.0492793	−	0.0853543i	−0.840334	−	0.542070i	$-0.817641\pi$
$307$	4644.53	−	8044.56i	0.0492793	−	0.0853543i	0.889613	+	0.456715i	$0.150974\pi$
$308$	24731.7	−	4360.87i	0.260707	−	0.0459697i
$309$		0			0
$310$	40550.5	−	14759.2i	0.421961	−	0.153581i
$311$	−23164.6	−	63644.2i	−0.239499	−	0.658019i	−0.999963	−	0.00863788i	$-0.997250\pi$
$311$	−23164.6	−	63644.2i	−0.239499	−	0.658019i	0.760464	−	0.649381i	$-0.224972\pi$
$312$		0			0
$313$	13354.0	+	75734.1i	0.136308	+	0.773042i	0.973940	+	0.226806i	$0.0728284\pi$
$313$	13354.0	+	75734.1i	0.136308	+	0.773042i	−0.837632	+	0.546235i	$0.816060\pi$
$314$	19264.1	+	11122.1i	0.195384	+	0.112805i
$315$		0			0
$316$	4359.19	+	7550.33i	0.0436547	+	0.0756122i
$317$	63228.2	+	75352.4i	0.629205	+	0.749858i	0.982624	−	0.185608i	$-0.0594254\pi$
$317$	63228.2	+	75352.4i	0.629205	+	0.749858i	−0.353419	+	0.935465i	$0.614981\pi$
$318$		0			0
$319$	−14940.6	+	84732.4i	−0.146820	+	0.832660i
$320$	6821.26	−	8129.27i	0.0666139	−	0.0793874i
$321$		0			0
$322$	37905.3	+	13796.4i	0.365584	+	0.133062i
$323$			7300.18i			0.0699727i
$324$		0			0
$325$	15852.3			0.150081
$326$	−41367.3	+	113656.i	−0.389244	+	1.06944i
$327$		0			0
$328$	−5016.97	−	4209.74i	−0.0466330	−	0.0391298i
$329$	127519.	+	22485.1i	1.17811	+	0.207732i
$330$		0			0
$331$	−93154.4	+	78165.8i	−0.850251	+	0.713446i	−0.959845	−	0.280531i	$-0.909490\pi$
$331$	−93154.4	+	78165.8i	−0.850251	+	0.713446i	0.109594	+	0.993976i	$0.465045\pi$
$332$	5262.97	−	3038.58i	0.0477480	−	0.0275673i
$333$		0			0
$334$	15239.0	−	26394.7i	0.136604	−	0.236605i
$335$	10189.5	−	1796.68i	0.0907952	−	0.0160096i
$336$		0			0
$337$	−145331.	+	52896.3i	−1.27968	+	0.465764i	−0.890325	−	0.455326i	$-0.849523\pi$
$337$	−145331.	+	52896.3i	−1.27968	+	0.465764i	−0.389351	+	0.921090i	$0.627301\pi$
$338$	−21263.0	−	58419.5i	−0.186119	−	0.511357i
$339$		0			0
$340$	−315.978	−	1792.00i	−0.00273337	−	0.0155017i
$341$	−48593.9	−	28055.7i	−0.417901	−	0.241275i
$342$		0			0
$343$	−63956.6	−	110776.i	−0.543622	−	0.941582i
$344$	−4257.75	−	5074.19i	−0.0359802	−	0.0428795i
$345$		0			0
$346$	7946.59	−	45067.4i	0.0663787	−	0.376452i
$347$	89451.7	−	106604.i	0.742898	−	0.885352i	−0.253740	−	0.967272i	$-0.581661\pi$
$347$	89451.7	−	106604.i	0.742898	−	0.885352i	0.996639	+	0.0819205i	$0.0261054\pi$
$348$		0			0
$349$	73288.8	+	26674.9i	0.601709	+	0.219004i	0.624872	−	0.780727i	$-0.285151\pi$
$349$	73288.8	+	26674.9i	0.601709	+	0.219004i	−0.0231624	+	0.999732i	$0.507373\pi$
$350$			22760.9i			0.185803i
$351$		0			0
$352$	−13798.7			−0.111366
$353$	31592.5	−	86799.7i	0.253533	−	0.696576i	−0.745998	−	0.665948i	$-0.768027\pi$
$353$	31592.5	−	86799.7i	0.253533	−	0.696576i	0.999531	−	0.0306278i	$-0.00975066\pi$
$354$		0			0
$355$	122344.	+	102659.i	0.970795	+	0.814593i
$356$	−97034.3	−	17109.8i	−0.765641	−	0.135003i
$357$		0			0
$358$	68722.4	−	57664.9i	0.536207	−	0.449931i
$359$	58663.7	−	33869.5i	0.455177	−	0.262797i	−0.254837	−	0.966984i	$-0.582022\pi$
$359$	58663.7	−	33869.5i	0.455177	−	0.262797i	0.710014	+	0.704187i	$0.248689\pi$
$360$		0			0
$361$	−156098.	+	270370.i	−1.19780	+	2.07464i
$362$	30269.1	−	5337.25i	0.230984	−	0.0407287i
$363$		0			0
$364$	−25114.4	+	9140.88i	−0.189548	+	0.0689899i
$365$	62636.2	+	172092.i	0.470154	+	1.29174i
$366$		0			0
$367$	3762.39	+	21337.6i	0.0279339	+	0.158421i	0.995584	−	0.0938750i	$-0.0299254\pi$
$367$	3762.39	+	21337.6i	0.0279339	+	0.158421i	−0.967650	+	0.252296i	$0.918814\pi$
$368$	−19194.6	−	11082.0i	−0.141737	−	0.0818321i
$369$		0			0
$370$	−71427.0	−	123715.i	−0.521746	−	0.903691i
$371$	−3008.18	−	3585.01i	−0.0218553	−	0.0260461i
$372$		0			0
$373$	−35210.4	+	199688.i	−0.253077	+	1.43527i	0.547883	+	0.836555i	$0.315434\pi$
$373$	−35210.4	+	199688.i	−0.253077	+	1.43527i	−0.800960	+	0.598718i	$0.795677\pi$
$374$	−1520.88	+	1812.51i	−0.0108731	+	0.0129580i
$375$		0			0
$376$	−66857.0	−	24333.9i	−0.472902	−	0.172122i
$377$		−	91565.4i		−	0.644241i
$378$		0			0
$379$	139468.			0.970950			0.485475	−	0.874251i	$-0.338647\pi$
$379$	139468.			0.970950			0.485475	+	0.874251i	$0.338647\pi$
$380$	37725.4	−	103650.i	0.261256	−	0.717796i
$381$		0			0
$382$	132817.	+	111447.i	0.910183	+	0.763734i
$383$	−286495.	−	50516.7i	−1.95307	−	0.344380i	−0.998995	−	0.0448272i	$-0.985726\pi$
$383$	−286495.	−	50516.7i	−1.95307	−	0.344380i	−0.954080	−	0.299553i	$-0.903163\pi$
$384$		0			0
$385$	−49841.9	+	41822.3i	−0.336258	+	0.282154i
$386$	−12844.2	+	7415.63i	−0.0862053	+	0.0497706i
$387$		0			0
$388$	−26208.3	+	45394.2i	−0.174091	+	0.301534i
$389$	22690.9	−	4001.01i	0.149952	−	0.0264406i	−0.0981682	−	0.995170i	$-0.531298\pi$
$389$	22690.9	−	4001.01i	0.149952	−	0.0264406i	0.248120	+	0.968729i	$0.420187\pi$
$390$		0			0
$391$	−3571.28	+	1299.84i	−0.0233599	+	0.00850230i
$392$	5456.84	+	14992.6i	0.0355115	+	0.0975671i
$393$		0			0
$394$	−15539.4	−	88128.4i	−0.100102	−	0.567706i
$395$	−19561.6	−	11293.9i	−0.125375	−	0.0723850i
$396$		0			0
$397$	−61334.4	−	106234.i	−0.389156	−	0.674037i	0.603181	−	0.797605i	$-0.293900\pi$
$397$	−61334.4	−	106234.i	−0.389156	−	0.674037i	−0.992336	+	0.123567i	$0.960566\pi$
$398$	−14684.9	−	17500.8i	−0.0927053	−	0.110482i
$399$		0			0
$400$	2171.68	−	12316.2i	0.0135730	−	0.0769763i
$401$	−75142.5	+	89551.3i	−0.467301	+	0.556908i	−0.947294	−	0.320364i	$-0.896195\pi$
$401$	−75142.5	+	89551.3i	−0.467301	+	0.556908i	0.479993	+	0.877272i	$0.340639\pi$
$402$		0			0
$403$	56113.9	+	20423.8i	0.345510	+	0.125755i
$404$		−	34086.2i		−	0.208841i
$405$		0			0
$406$	131471.			0.797584
$407$	−63531.0	+	174550.i	−0.383528	+	1.05373i
$408$		0			0
$409$	−102196.	−	85753.0i	−0.610927	−	0.512628i	0.284010	−	0.958821i	$-0.408335\pi$
$409$	−102196.	−	85753.0i	−0.610927	−	0.512628i	−0.894937	+	0.446193i	$0.852780\pi$
$410$	16710.0	+	2946.42i	0.0994051	+	0.0175278i
$411$		0			0
$412$	−98185.6	+	82387.5i	−0.578433	+	0.485363i
$413$	−121908.	+	70383.8i	−0.714715	+	0.412641i
$414$		0			0
$415$	−7872.41	+	13635.4i	−0.0457101	+	0.0791721i
$416$	14461.8	−	2550.01i	0.0835674	−	0.0147352i
$417$		0			0
$418$	−134775.	+	49054.1i	−0.771359	+	0.280752i
$419$	52240.3	+	143529.i	0.297562	+	0.817546i	0.994906	+	0.100809i	$0.0321430\pi$
$419$	52240.3	+	143529.i	0.297562	+	0.817546i	−0.697344	+	0.716737i	$0.745635\pi$
$420$		0			0
$421$	10623.6	+	60249.6i	0.0599389	+	0.339930i	0.999999	−	0.00107738i	$-0.000342941\pi$
$421$	10623.6	+	60249.6i	0.0599389	+	0.339930i	−0.940061	+	0.341008i	$0.889232\pi$
$422$	−190478.	−	109973.i	−1.06960	−	0.617533i
$423$		0			0
$424$	1285.71	+	2226.91i	0.00715172	+	0.0123871i
$425$	−1378.42	−	1642.74i	−0.00763140	−	0.00909474i
$426$		0			0
$427$	33652.1	−	190851.i	0.184568	−	1.04674i
$428$	−100603.	+	119894.i	−0.549192	+	0.654502i
$429$		0			0
$430$	16126.3	+	5869.51i	0.0872166	+	0.0317442i
$431$		−	26698.2i		−	0.143723i	−0.997415	−	0.0718616i	$-0.977106\pi$
$431$		−	26698.2i		−	0.143723i	0.997415	−	0.0718616i	$-0.0228940\pi$
$432$		0			0
$433$	17869.1			0.0953074			0.0476537	−	0.998864i	$-0.484826\pi$
$433$	17869.1			0.0953074			0.0476537	+	0.998864i	$0.484826\pi$
$434$	−29324.7	+	80569.0i	−0.155688	+	0.427748i
$435$		0			0
$436$	−105928.	−	88884.2i	−0.557235	−	0.467575i
$437$	−226875.	−	40004.1i	−1.18802	−	0.209480i
$438$		0			0
$439$	−145671.	+	122233.i	−0.755867	+	0.634248i	−0.937047	−	0.349202i	$-0.886453\pi$
$439$	−145671.	+	122233.i	−0.755867	+	0.634248i	0.181181	+	0.983450i	$0.442008\pi$
$440$	30960.4	−	17875.0i	0.159919	−	0.0923295i
$441$		0			0
$442$	1259.02	−	2180.68i	0.00644446	−	0.0111621i
$443$	−294959.	+	52009.3i	−1.50298	+	0.265017i	−0.863721	−	0.503971i	$-0.831872\pi$
$443$	−294959.	+	52009.3i	−1.50298	+	0.265017i	−0.639264	+	0.768987i	$0.720761\pi$
$444$		0			0
$445$	239882.	−	87309.8i	1.21137	−	0.440903i
$446$	75549.9	+	207572.i	0.379808	+	1.04351i
$447$		0			0
$448$	3661.33	+	20764.5i	0.0182425	+	0.103458i
$449$	168655.	+	97373.3i	0.836581	+	0.483000i	0.856100	−	0.516809i	$-0.172880\pi$
$449$	168655.	+	97373.3i	0.836581	+	0.483000i	−0.0195199	+	0.999809i	$0.506214\pi$
$450$		0			0
$451$	−11031.5	−	19107.2i	−0.0542354	−	0.0939385i
$452$	−111752.	−	133181.i	−0.546987	−	0.651874i
$453$		0			0
$454$	−13398.3	+	75985.7i	−0.0650039	+	0.368655i
$455$	44508.3	−	53042.9i	0.214990	−	0.256215i
$456$		0			0
$457$	−170822.	−	62174.3i	−0.817923	−	0.297700i	−0.101031	−	0.994883i	$-0.532214\pi$
$457$	−170822.	−	62174.3i	−0.817923	−	0.297700i	−0.716893	+	0.697184i	$0.754436\pi$
$458$		−	141550.i		−	0.674806i
$459$		0			0
$460$	57423.1			0.271376
$461$	93280.4	−	256286.i	0.438923	−	1.20593i	−0.501270	−	0.865291i	$-0.667134\pi$
$461$	93280.4	−	256286.i	0.438923	−	1.20593i	0.940194	−	0.340641i	$-0.110644\pi$
$462$		0			0
$463$	14637.1	+	12282.0i	0.0682799	+	0.0572937i	0.676289	−	0.736636i	$-0.263587\pi$
$463$	14637.1	+	12282.0i	0.0682799	+	0.0572937i	−0.608009	+	0.793930i	$0.708032\pi$
$464$	−71140.3	−	12544.0i	−0.330430	−	0.0582638i
$465$		0			0
$466$	29601.0	−	24838.2i	0.136312	−	0.114379i
$467$	29014.0	−	16751.2i	0.133037	−	0.0768092i	−0.432004	−	0.901872i	$-0.642193\pi$
$467$	29014.0	−	16751.2i	0.133037	−	0.0768092i	0.565042	+	0.825062i	$0.308860\pi$
$468$		0			0
$469$	−10278.8	+	17803.4i	−0.0467302	+	0.0809390i
$470$	181531.	−	32008.7i	0.821777	−	0.144901i
$471$		0			0
$472$	72681.5	−	26453.9i	0.326242	−	0.118742i
$473$	−7632.08	−	20969.0i	−0.0341131	−	0.0937249i
$474$		0			0
$475$	−22572.6	−	128015.i	−0.100045	−	0.567381i
$476$	3131.04	+	1807.71i	0.0138189	+	0.00797837i
$477$		0			0
$478$	99822.3	+	172897.i	0.436890	+	0.756715i
$479$	167364.	+	199457.i	0.729442	+	0.869315i	0.995512	−	0.0946384i	$-0.0301695\pi$
$479$	167364.	+	199457.i	0.729442	+	0.869315i	−0.266069	+	0.963954i	$0.585725\pi$
$480$		0			0
$481$	34327.1	−	194679.i	0.148370	−	0.841451i
$482$	57152.7	−	68112.0i	0.246004	−	0.293177i
$483$		0			0
$484$	66382.3	+	24161.2i	0.283375	+	0.103140i
$485$		−	135802.i		−	0.577329i
$486$		0			0
$487$	129818.			0.547364			0.273682	−	0.961820i	$-0.411758\pi$
$487$	129818.			0.547364			0.273682	+	0.961820i	$0.411758\pi$
$488$	−36419.1	+	100061.i	−0.152929	+	0.420169i
$489$		0			0
$490$	−31665.1	−	26570.2i	−0.131883	−	0.110663i
$491$	247730.	+	43681.4i	1.02758	+	0.181190i	0.661932	−	0.749564i	$-0.269737\pi$
$491$	247730.	+	43681.4i	1.02758	+	0.181190i	0.365647	+	0.930754i	$0.380848\pi$
$492$		0			0
$493$	−9488.71	+	7961.97i	−0.0390403	+	0.0327587i
$494$	132187.	−	76318.0i	0.541669	−	0.312733i
$495$		0			0
$496$	23555.3	−	40798.9i	0.0957468	−	0.165838i
$497$	−312502.	+	55102.6i	−1.26515	+	0.223079i
$498$		0			0
$499$	380789.	−	138596.i	1.52927	−	0.556608i	0.565825	−	0.824525i	$-0.308558\pi$
$499$	380789.	−	138596.i	1.52927	−	0.556608i	0.963442	+	0.267917i	$0.0863354\pi$
$500$	46526.4	+	127830.i	0.186106	+	0.511321i
$501$		0			0
$502$	13109.6	+	74348.1i	0.0520213	+	0.295028i
$503$	155352.	+	89692.5i	0.614018	+	0.354503i	0.774536	−	0.632530i	$-0.217983\pi$
$503$	155352.	+	89692.5i	0.614018	+	0.354503i	−0.160519	+	0.987033i	$0.551317\pi$
$504$		0			0
$505$	44155.6	+	76479.8i	0.173142	+	0.299891i
$506$	−47994.9	−	57198.1i	−0.187454	−	0.223399i
$507$		0			0
$508$	−16475.2	+	93435.5i	−0.0638415	+	0.362063i
$509$	109012.	−	129916.i	0.420765	−	0.501449i	−0.513469	−	0.858108i	$-0.671640\pi$
$509$	109012.	−	129916.i	0.420765	−	0.501449i	0.934234	+	0.356659i	$0.116084\pi$
$510$		0			0
$511$	−341926.	−	124451.i	−1.30945	−	0.476602i
$512$		−	11585.2i		−	0.0441942i
$513$		0			0
$514$	8017.28			0.0303459
$515$	113575.	−	312045.i	0.428221	−	1.17653i
$516$		0			0
$517$	−183609.	−	154066.i	−0.686930	−	0.576403i
$518$	279522.	+	49287.3i	1.04173	+	0.183686i
$519$		0			0
$520$	−29145.0	+	24455.5i	−0.107785	+	0.0904420i
$521$	394066.	−	227514.i	1.45176	−	0.838171i	0.453174	−	0.891422i	$-0.350292\pi$
$521$	394066.	−	227514.i	1.45176	−	0.838171i	0.998581	+	0.0532507i	$0.0169583\pi$
$522$		0			0
$523$	−25794.6	+	44677.6i	−0.0943031	+	0.163338i	−0.909318	−	0.416103i	$-0.863396\pi$
$523$	−25794.6	+	44677.6i	−0.0943031	+	0.163338i	0.815014	+	0.579441i	$0.196729\pi$
$524$	245990.	−	43374.7i	0.895891	−	0.157970i
$525$		0			0
$526$	−65811.9	+	23953.6i	−0.237866	+	0.0865763i
$527$	−2762.86	−	7590.89i	−0.00994803	−	0.0273320i
$528$		0			0
$529$	27767.7	+	157479.i	0.0992268	+	0.562743i
$530$	−5769.53	−	3331.04i	−0.0205394	−	0.0118585i
$531$		0			0
$532$	109578.	+	189795.i	0.387169	+	0.670597i
$533$	15092.7	+	17986.8i	0.0531267	+	0.0633139i
$534$		0			0
$535$	70412.9	−	399331.i	0.246005	−	1.39517i
$536$	7260.66	−	8652.92i	0.0252724	−	0.0301185i
$537$		0			0
$538$	−310543.	−	113028.i	−1.07290	−	0.390502i
$539$			53748.8i			0.185008i
$540$		0			0
$541$	−71764.2			−0.245196			−0.122598	−	0.992456i	$-0.539123\pi$
$541$	−71764.2			−0.245196			−0.122598	+	0.992456i	$0.539123\pi$
$542$	−75935.6	+	208631.i	−0.258492	+	0.710201i
$543$		0			0
$544$	−1521.77	−	1276.91i	−0.00514221	−	0.00431483i
$545$	352814.	+	62210.6i	1.18783	+	0.209446i
$546$		0			0
$547$	−41984.3	+	35229.0i	−0.140318	+	0.117740i	−0.710245	−	0.703955i	$-0.751416\pi$
$547$	−41984.3	+	35229.0i	−0.140318	+	0.117740i	0.569927	+	0.821695i	$0.306971\pi$
$548$	−31399.4	+	18128.5i	−0.104559	+	0.0603671i
$549$		0			0
$550$	21065.6	−	36486.7i	0.0696384	−	0.120617i
$551$	−739436.	+	130383.i	−2.43555	+	0.429454i
$552$		0			0
$553$	42172.6	−	15349.6i	0.137905	−	0.0501933i
$554$	125872.	+	345831.i	0.410120	+	1.12679i
$555$		0			0
$556$	−21868.1	−	124020.i	−0.0707395	−	0.401184i
$557$	−43774.5	−	25273.2i	−0.141095	−	0.0814610i	0.427791	−	0.903878i	$-0.359292\pi$
$557$	−43774.5	−	25273.2i	−0.141095	−	0.0814610i	−0.568886	+	0.822417i	$0.692625\pi$
$558$		0			0
$559$	11873.9	+	20566.3i	0.0379989	+	0.0658161i
$560$	−35113.5	−	41846.6i	−0.111969	−	0.133440i
$561$		0			0
$562$	−42883.7	+	243206.i	−0.135775	+	0.770019i
$563$	283965.	−	338416.i	0.895876	−	1.06766i	−0.101468	−	0.994839i	$-0.532354\pi$
$563$	283965.	−	338416.i	0.895876	−	1.06766i	0.997345	−	0.0728250i	$-0.0232015\pi$
$564$		0			0
$565$	423263.	+	154055.i	1.32591	+	0.482591i
$566$			77489.6i			0.241886i
$567$		0			0
$568$	174356.			0.540432
$569$	26106.6	−	71727.3i	0.0806354	−	0.221544i	−0.892823	−	0.450407i	$-0.851279\pi$
$569$	26106.6	−	71727.3i	0.0806354	−	0.221544i	0.973459	+	0.228864i	$0.0735009\pi$
$570$		0			0
$571$	14412.4	+	12093.4i	0.0442041	+	0.0370917i	0.664622	−	0.747180i	$-0.268593\pi$
$571$	14412.4	+	12093.4i	0.0442041	+	0.0370917i	−0.620418	+	0.784271i	$0.713037\pi$
$572$	48719.4	+	8590.55i	0.148905	+	0.0262560i
$573$		0			0
$574$	−25825.6	+	21670.3i	−0.0783839	+	0.0657719i
$575$	58606.5	−	33836.5i	0.177260	−	0.102341i
$576$		0			0
$577$	−37223.8	+	64473.6i	−0.111807	+	0.193656i	−0.916499	−	0.400037i	$-0.868997\pi$
$577$	−37223.8	+	64473.6i	−0.111807	+	0.193656i	0.804692	+	0.593693i	$0.202331\pi$
$578$	232309.	−	40962.3i	0.695360	−	0.122611i
$579$		0			0
$580$	175868.	−	64010.8i	0.522795	−	0.190282i
$581$	−10699.5	−	29396.5i	−0.0316963	−	0.0870850i
$582$		0			0
$583$	1504.25	+	8531.05i	0.00442572	+	0.0250995i
$584$	173146.	+	99965.8i	0.507676	+	0.293107i
$585$		0			0
$586$	−64748.3	−	112147.i	−0.188553	−	0.326583i
$587$	−62083.0	−	73987.6i	−0.180176	−	0.214725i	0.668396	−	0.743806i	$-0.266981\pi$
$587$	−62083.0	−	73987.6i	−0.180176	−	0.214725i	−0.848571	+	0.529081i	$0.822537\pi$
$588$		0			0
$589$	85030.1	−	482230.i	0.245099	−	1.39003i
$590$	−128808.	+	153507.i	−0.370032	+	0.440987i
$591$		0			0
$592$	−146550.	−	53339.9i	−0.418160	−	0.152198i
$593$		−	57718.2i		−	0.164136i	−0.996627	−	0.0820679i	$-0.973848\pi$
$593$		−	57718.2i		−	0.164136i	0.996627	−	0.0820679i	$-0.0261524\pi$
$594$		0			0
$595$	−9366.89			−0.0264583
$596$	12572.0	−	34541.2i	0.0353925	−	0.0972400i
$597$		0			0
$598$	60871.7	+	51077.4i	0.170221	+	0.142832i
$599$	−132729.	−	23403.7i	−0.369924	−	0.0652276i	−0.0144041	−	0.999896i	$-0.504585\pi$
$599$	−132729.	−	23403.7i	−0.369924	−	0.0652276i	−0.355520	+	0.934669i	$0.615696\pi$
$600$		0			0
$601$	506731.	−	425198.i	1.40291	−	1.17718i	0.443116	−	0.896464i	$-0.353873\pi$
$601$	506731.	−	425198.i	1.40291	−	1.17718i	0.959791	−	0.280714i	$-0.0905714\pi$
$602$	−29529.3	+	17048.7i	−0.0814816	+	0.0470434i
$603$		0			0
$604$	1506.15	−	2608.74i	0.00412853	−	0.00715083i
$605$	−180242.	+	31781.5i	−0.492430	+	0.0868287i
$606$		0			0
$607$	−71120.6	+	25885.8i	−0.193027	+	0.0702561i	−0.436725	−	0.899595i	$-0.643862\pi$
$607$	−71120.6	+	25885.8i	−0.193027	+	0.0702561i	0.243698	+	0.969851i	$0.421639\pi$
$608$	−41185.2	−	113156.i	−0.111413	−	0.306104i
$609$		0			0
$610$	−47905.5	−	271686.i	−0.128744	−	0.730141i
$611$	220904.	+	127539.i	0.591727	+	0.341634i
$612$		0			0
$613$	229035.	+	396700.i	0.609510	+	1.05570i	0.991321	+	0.131462i	$0.0419671\pi$
$613$	229035.	+	396700.i	0.609510	+	1.05570i	−0.381811	+	0.924240i	$0.624700\pi$
$614$	16888.2	+	20126.6i	0.0447968	+	0.0533868i
$615$		0			0
$616$	−12334.4	+	69951.9i	−0.0325055	+	0.184348i
$617$	−255604.	+	304618.i	−0.671426	+	0.800174i	−0.988977	−	0.148067i	$-0.952695\pi$
$617$	−255604.	+	304618.i	−0.671426	+	0.800174i	0.317552	+	0.948241i	$0.397139\pi$
$618$		0			0
$619$	157809.	+	57437.7i	0.411860	+	0.149905i	0.539637	−	0.841898i	$-0.318562\pi$
$619$	157809.	+	57437.7i	0.411860	+	0.149905i	−0.127776	+	0.991803i	$0.540784\pi$
$620$			122055.i			0.317520i
$621$		0			0
$622$	191566.			0.495151
$623$	−173474.	+	476616.i	−0.446950	+	1.22798i
$624$		0			0
$625$	−176427.	−	148040.i	−0.451653	−	0.378982i
$626$	−214208.	−	37770.7i	−0.546623	−	0.0963844i
$627$		0			0
$628$	−48196.7	+	40441.8i	−0.122208	+	0.102544i
$629$	−23159.0	+	13370.9i	−0.0585354	+	0.0337954i
$630$		0			0
$631$	−23547.4	+	40785.3i	−0.0591404	+	0.102434i	−0.894080	−	0.447908i	$-0.852169\pi$
$631$	−23547.4	+	40785.3i	−0.0591404	+	0.102434i	0.834939	+	0.550342i	$0.185503\pi$
$632$	−24284.7	+	4282.04i	−0.0607992	+	0.0107205i
$633$		0			0
$634$	−261441.	+	95156.8i	−0.650423	+	0.236734i
$635$	−84071.6	−	230985.i	−0.208498	−	0.572844i
$636$		0			0
$637$	−9932.81	−	56331.8i	−0.0244790	−	0.138827i
$638$	−210753.	−	121678.i	−0.517764	−	0.298931i
$639$		0			0
$640$	15007.6	+	25994.0i	0.0366397	+	0.0634619i
$641$	−405500.	−	483256.i	−0.986904	−	1.17615i	−0.984363	−	0.176150i	$-0.943636\pi$
$641$	−405500.	−	483256.i	−0.986904	−	1.17615i	−0.00254102	−	0.999997i	$-0.500809\pi$
$642$		0			0
$643$	−21079.2	+	119546.i	−0.0509837	+	0.289143i	−0.999630	−	0.0271953i	$-0.991342\pi$
$643$	−21079.2	+	119546.i	−0.0509837	+	0.289143i	0.948646	+	0.316338i	$0.102453\pi$
$644$	−73337.5	+	87400.2i	−0.176829	+	0.210737i
$645$		0			0
$646$	−19402.8	−	7062.05i	−0.0464943	−	0.0169225i
$647$		−	21227.2i		−	0.0507090i	−0.999679	−	0.0253545i	$-0.991929\pi$
$647$		−	21227.2i		−	0.0507090i	0.999679	−	0.0253545i	$-0.00807145\pi$
$648$		0			0
$649$	260565.			0.618625
$650$	−15335.2	+	42133.1i	−0.0362963	+	0.0997233i
$651$		0			0
$652$	−262062.	−	219896.i	−0.616466	−	0.517276i
$653$	−122654.	−	21627.2i	−0.287644	−	0.0507194i	0.0279645	−	0.999609i	$-0.491097\pi$
$653$	−122654.	−	21627.2i	−0.287644	−	0.0507194i	−0.315608	+	0.948890i	$0.602209\pi$
$654$		0			0
$655$	−495744.	+	415979.i	−1.15551	+	0.969591i
$656$	16042.2	−	9261.95i	0.0372782	−	0.0215226i
$657$		0			0
$658$	−183122.	+	317176.i	−0.422949	+	0.732570i
$659$	18809.9	−	3316.70i	0.0433128	−	0.00763722i	−0.151950	−	0.988388i	$-0.548555\pi$
$659$	18809.9	−	3316.70i	0.0433128	−	0.00763722i	0.195263	+	0.980751i	$0.437444\pi$
$660$		0			0
$661$	−722285.	+	262890.i	−1.65313	+	0.601689i	−0.989260	−	0.146164i	$-0.953307\pi$
$661$	−722285.	+	262890.i	−1.65313	+	0.601689i	−0.663865	+	0.747852i	$0.731085\pi$
$662$	−117638.	−	323207.i	−0.268429	−	0.737504i
$663$		0			0
$664$	2984.80	+	16927.7i	0.00676986	+	0.0383938i
$665$	−491725.	−	283897.i	−1.11193	−	0.641975i
$666$		0			0
$667$	−195445.	−	338520.i	−0.439311	−	0.760909i
$668$	55411.3	+	66036.6i	0.124178	+	0.147990i
$669$		0			0
$670$	−5081.79	+	28820.2i	−0.0113205	+	0.0642019i
$671$	−230581.	+	274796.i	−0.512128	+	0.610331i
$672$		0			0
$673$	−313581.	−	114134.i	−0.692341	−	0.251992i	−0.0282038	−	0.999602i	$-0.508979\pi$
$673$	−313581.	−	114134.i	−0.692341	−	0.251992i	−0.664137	+	0.747611i	$0.731201\pi$
$674$		−	437440.i		−	0.962939i
$675$		0			0
$676$	175840.			0.384790
$677$	51912.4	−	142628.i	0.113265	−	0.311192i	−0.870089	−	0.492895i	$-0.835939\pi$
$677$	51912.4	−	142628.i	0.113265	−	0.311192i	0.983353	+	0.181703i	$0.0581609\pi$
$678$		0			0
$679$	206696.	+	173439.i	0.448325	+	0.376190i
$680$	5068.54	+	893.720i	0.0109614	+	0.00193279i
$681$		0			0
$682$	121577.	−	102015.i	0.261386	−	0.219329i
$683$	89028.7	−	51400.7i	0.190848	−	0.110186i	−0.401531	−	0.915845i	$-0.631522\pi$
$683$	89028.7	−	51400.7i	0.190848	−	0.110186i	0.592380	+	0.805659i	$0.298189\pi$
$684$		0			0
$685$	46967.6	−	81350.3i	0.100096	−	0.173372i
$686$	356297.	−	62824.8i	0.757118	−	0.133500i
$687$		0			0
$688$	17605.3	−	6407.81i	0.0371935	−	0.0135373i
$689$	−3153.09	−	8663.04i	−0.00664198	−	0.0182487i
$690$		0			0
$691$	120276.	+	682121.i	0.251898	+	1.42858i	0.803913	+	0.594748i	$0.202748\pi$
$691$	120276.	+	682121.i	0.251898	+	1.42858i	−0.552015	+	0.833834i	$0.686141\pi$
$692$	112095.	+	64718.1i	0.234085	+	0.135149i
$693$		0			0
$694$	196805.	+	340876.i	0.408617	+	0.707746i
$695$	209723.	+	249938.i	0.434187	+	0.517444i
$696$		0			0
$697$	551.558	−	3128.04i	0.00113534	−	0.00643883i
$698$	−141796.	+	168986.i	−0.291041	+	0.346849i
$699$		0			0
$700$	−60495.1	−	22018.4i	−0.123459	−	0.0449356i
$701$			734340.i			1.49438i	0.664611	+	0.747190i	$0.268597\pi$
$701$			734340.i			1.49438i	−0.664611	+	0.747190i	$0.731403\pi$
$702$		0			0
$703$	−1.62101e6			−3.28001
$704$	13348.6	−	36674.9i	0.0269333	−	0.0739987i
$705$		0			0
$706$	200139.	+	167936.i	0.401533	+	0.336927i
$707$	−172798.	−	30469.0i	−0.345701	−	0.0609564i
$708$		0			0
$709$	454607.	−	381461.i	0.904366	−	0.758853i	−0.0666730	−	0.997775i	$-0.521238\pi$
$709$	454607.	−	381461.i	0.904366	−	0.758853i	0.971039	+	0.238922i	$0.0767940\pi$
$710$	−391206.	+	225863.i	−0.776049	+	0.448052i
$711$		0			0
$712$	139344.	−	241351.i	0.274871	−	0.476091i
$713$	251049.	−	44266.7i	0.493832	−	0.0870760i
$714$		0			0
$715$	−120441.	+	43836.9i	−0.235593	+	0.0857487i
$716$	86784.3	+	238438.i	0.169284	+	0.465103i
$717$		0			0
$718$	33270.1	+	188684.i	0.0645364	+	0.366004i
$719$	801342.	+	462655.i	1.55010	+	0.894951i	0.998132	+	0.0610867i	$0.0194566\pi$
$719$	801342.	+	462655.i	1.55010	+	0.894951i	0.551969	+	0.833865i	$0.313877\pi$
$720$		0			0
$721$	329893.	+	571391.i	0.634604	+	1.09917i
$722$	−567596.	−	676435.i	−1.08884	−	1.29763i
$723$		0			0
$724$	−15096.0	+	85613.8i	−0.0287995	+	0.163330i
$725$	141774.	−	168960.i	0.269725	−	0.321446i
$726$		0			0
$727$	91933.8	+	33461.2i	0.173943	+	0.0633100i	0.427523	−	0.904004i	$-0.359386\pi$
$727$	91933.8	+	33461.2i	0.173943	+	0.0633100i	−0.253581	+	0.967314i	$0.581608\pi$
$728$		−	75592.9i		−	0.142633i
$729$		0			0
$730$	−517987.			−0.972016
$731$	1098.75	−	3018.79i	0.00205619	−	0.00564934i
$732$		0			0
$733$	220094.	+	184681.i	0.409639	+	0.343728i	0.824205	−	0.566291i	$-0.191622\pi$
$733$	220094.	+	184681.i	0.409639	+	0.343728i	−0.414566	+	0.910019i	$0.636067\pi$
$734$	−60351.8	−	10641.7i	−0.112021	−	0.0197523i
$735$		0			0
$736$	48022.9	−	40296.0i	0.0886528	−	0.0743886i
$737$	32954.8	−	19026.4i	0.0606713	−	0.0350286i
$738$		0			0
$739$	429465.	−	743855.i	0.786392	−	1.36207i	−0.141772	−	0.989899i	$-0.545280\pi$
$739$	429465.	−	743855.i	0.786392	−	1.36207i	0.928164	−	0.372171i	$-0.121387\pi$
$740$	397914.	−	70163.0i	0.726651	−	0.128128i
$741$		0			0
$742$	12438.5	−	4527.24i	0.0225923	−	0.00822291i
$743$	−206615.	−	567669.i	−0.374269	−	1.02829i	−0.973693	−	0.227863i	$-0.926826\pi$
$743$	−206615.	−	567669.i	−0.374269	−	1.02829i	0.599424	−	0.800431i	$-0.295396\pi$
$744$		0			0
$745$	16537.1	+	93786.6i	0.0297952	+	0.168977i
$746$	−496680.	−	286758.i	−0.892481	−	0.515274i
$747$		0			0
$748$	−3346.13	−	5795.66i	−0.00598052	−	0.0103586i
$749$	517870.	+	617174.i	0.923119	+	1.10013i
$750$		0			0
$751$	−154629.	+	876945.i	−0.274164	+	1.55486i	0.467439	+	0.884025i	$0.345177\pi$
$751$	−154629.	+	876945.i	−0.274164	+	1.55486i	−0.741604	+	0.670838i	$0.765934\pi$
$752$	129352.	−	154156.i	0.228738	−	0.272599i
$753$		0			0
$754$	243367.	+	88578.4i	0.428075	+	0.155806i
$755$			7804.35i			0.0136912i
$756$		0			0
$757$	−761196.			−1.32833			−0.664164	−	0.747587i	$-0.731212\pi$
$757$	−761196.			−1.32833			−0.664164	+	0.747587i	$0.731212\pi$
$758$	−134919.	+	370686.i	−0.234819	+	0.645160i
$759$		0			0
$760$	238991.	+	200537.i	0.413765	+	0.347190i
$761$	130355.	+	22985.1i	0.225091	+	0.0396896i	0.285056	−	0.958511i	$-0.407988\pi$
$761$	130355.	+	22985.1i	0.225091	+	0.0396896i	−0.0599650	+	0.998200i	$0.519099\pi$
$762$		0			0
$763$	−545281.	+	457545.i	−0.936637	+	0.785932i
$764$	−424695.	+	245198.i	−0.727596	+	0.420078i
$765$		0			0
$766$	411415.	−	712591.i	0.701168	−	1.21446i
$767$	−273087.	+	48152.7i	−0.464206	+	0.0818521i
$768$		0			0
$769$	713591.	−	259726.i	1.20669	−	0.439200i	0.341137	−	0.940013i	$-0.389188\pi$
$769$	713591.	−	259726.i	1.20669	−	0.439200i	0.865555	+	0.500813i	$0.166966\pi$
$770$	−62941.5	−	172930.i	−0.106159	−	0.291669i
$771$		0			0
$772$	−7284.39	−	41311.8i	−0.0122225	−	0.0693170i
$773$	−979526.	−	565529.i	−1.63929	−	0.946447i	−0.981077	−	0.193619i	$-0.937977\pi$
$773$	−979526.	−	565529.i	−1.63929	−	0.946447i	−0.658217	−	0.752828i	$-0.728689\pi$
$774$		0			0
$775$	71920.6	+	124570.i	0.119743	+	0.207401i
$776$	−95297.6	−	113571.i	−0.158255	−	0.188601i
$777$		0			0
$778$	−11316.6	+	64179.5i	−0.0186963	+	0.106032i
$779$	123761.	−	147493.i	0.203944	−	0.243050i
$780$		0			0
$781$	551953.	+	200894.i	0.904899	+	0.329356i
$782$		−	10749.4i		−	0.0175780i
$783$		0			0
$784$	−45126.8			−0.0734180
$785$	55751.0	−	153174.i	0.0904717	−	0.248569i
$786$		0			0
$787$	919199.	+	771299.i	1.48409	+	1.24530i	0.901681	+	0.432402i	$0.142334\pi$
$787$	919199.	+	771299.i	1.48409	+	1.24530i	0.582408	+	0.812896i	$0.302111\pi$
$788$	249265.	+	43952.1i	0.401429	+	0.0707827i
$789$		0			0
$790$	48940.9	−	41066.3i	0.0784183	−	0.0658008i
$791$	−775044.	+	447472.i	−1.23872	+	0.715176i
$792$		0			0
$793$	190880.	−	330613.i	0.303538	−	0.525744i
$794$	341689.	−	60248.9i	0.541988	−	0.0955671i
$795$		0			0
$796$	60720.3	−	22100.4i	0.0958314	−	0.0348798i
$797$	60023.6	+	164914.i	0.0944943	+	0.259621i	0.977930	−	0.208931i	$-0.0669983\pi$
$797$	60023.6	+	164914.i	0.0944943	+	0.259621i	−0.883436	+	0.468551i	$0.844776\pi$
$798$		0			0
$799$	−5991.91	−	33981.8i	−0.00938580	−	0.0532295i
$800$	30633.8	+	17686.4i	0.0478653	+	0.0276351i
$801$		0			0
$802$	−165323.	−	286348.i	−0.257030	−	0.445190i
$803$	432940.	+	515958.i	0.671424	+	0.800172i
$804$		0			0
$805$	51329.4	−	291103.i	0.0792090	−	0.449216i
$806$	−108567.	+	129385.i	−0.167120	+	0.199165i
$807$		0			0
$808$	90596.1	+	32974.3i	0.138767	+	0.0505071i
$809$		−	29152.9i		−	0.0445436i	−0.999752	−	0.0222718i	$-0.992910\pi$
$809$		−	29152.9i		−	0.0445436i	0.999752	−	0.0222718i	$-0.00708992\pi$
$810$		0			0
$811$	561677.			0.853975			0.426987	−	0.904258i	$-0.359575\pi$
$811$	561677.			0.853975			0.426987	+	0.904258i	$0.359575\pi$
$812$	−127182.	+	349429.i	−0.192891	+	0.529965i
$813$		0			0
$814$	−402469.	−	337712.i	−0.607413	−	0.509680i
$815$	872849.	+	153907.i	1.31409	+	0.231709i
$816$		0			0
$817$	149175.	−	125173.i	0.223487	−	0.187528i
$818$	326782.	−	188667.i	0.488372	−	0.281962i
$819$		0			0
$820$	−23996.1	+	41562.4i	−0.0356872	+	0.0618120i
$821$	728254.	−	128411.i	1.08043	−	0.190509i	0.395025	−	0.918671i	$-0.370736\pi$
$821$	728254.	−	128411.i	1.08043	−	0.190509i	0.685406	+	0.728162i	$0.259625\pi$
$822$		0			0
$823$	−562630.	+	204781.i	−0.830660	+	0.302335i	−0.722130	−	0.691758i	$-0.756837\pi$
$823$	−562630.	+	204781.i	−0.830660	+	0.302335i	−0.108530	+	0.994093i	$0.534614\pi$
$824$	−123991.	−	340663.i	−0.182615	−	0.501730i
$825$		0			0
$826$	−69138.1	−	392102.i	−0.101335	−	0.574697i
$827$	729576.	+	421221.i	1.06674	+	0.615884i	0.927290	−	0.374345i	$-0.122132\pi$
$827$	729576.	+	421221.i	1.06674	+	0.615884i	0.139453	+	0.990229i	$0.455466\pi$
$828$		0			0
$829$	−355494.	−	615734.i	−0.517277	−	0.895950i	−0.999799	−	0.0200662i	$-0.993612\pi$
$829$	−355494.	−	615734.i	−0.517277	−	0.895950i	0.482521	−	0.875884i	$-0.339721\pi$
$830$	−28625.3	−	34114.3i	−0.0415522	−	0.0495200i
$831$		0			0
$832$	−7212.52	+	40904.3i	−0.0104193	+	0.0590911i
$833$	−4973.83	+	5927.58i	−0.00716805	+	0.00854255i
$834$		0			0
$835$	−209872.	−	76387.1i	−0.301010	−	0.109559i
$836$		−	405666.i		−	0.580438i
$837$		0			0
$838$	−432015.			−0.615193
$839$	117286.	−	322242.i	0.166619	−	0.457781i	−0.828080	−	0.560609i	$-0.810567\pi$
$839$	117286.	−	322242.i	0.166619	−	0.457781i	0.994699	+	0.102828i	$0.0327892\pi$
$840$		0			0
$841$	−434130.	−	364278.i	−0.613801	−	0.515040i
$842$	−170411.	−	30048.1i	−0.240367	−	0.0423832i
$843$		0			0
$844$	476556.	−	399878.i	0.669004	−	0.561361i
$845$	−394535.	+	227785.i	−0.552550	+	0.319015i
$846$		0			0
$847$	181822.	−	314924.i	0.253442	−	0.438975i
$848$	−7162.57	+	1262.95i	−0.00996041	+	0.00175629i
$849$		0			0
$850$	5699.61	−	2074.49i	0.00788873	−	0.00287126i
$851$	−288630.	−	793004.i	−0.398549	−	1.09501i
$852$		0			0
$853$	−96974.5	−	549970.i	−0.133278	−	0.755859i	−0.976043	−	0.217577i	$-0.930185\pi$
$853$	−96974.5	−	549970.i	−0.133278	−	0.755859i	0.842765	−	0.538282i	$-0.180926\pi$
$854$	474698.	+	274067.i	0.650882	+	0.375787i
$855$		0			0
$856$	−221340.	−	383372.i	−0.302073	−	0.523206i
$857$	863808.	+	1.02945e6i	1.17613	+	1.40166i	0.897360	+	0.441300i	$0.145483\pi$
$857$	863808.	+	1.02945e6i	1.17613	+	1.40166i	0.278771	+	0.960358i	$0.410073\pi$
$858$		0			0
$859$	−166658.	+	945165.i	−0.225861	+	1.28092i	0.635173	+	0.772370i	$0.280929\pi$
$859$	−166658.	+	945165.i	−0.225861	+	1.28092i	−0.861033	+	0.508549i	$0.830182\pi$
$860$	−31200.6	+	37183.4i	−0.0421857	+	0.0502750i
$861$		0			0
$862$	70959.8	+	25827.3i	0.0954988	+	0.0347587i
$863$			787753.i			1.05771i	0.848711	+	0.528857i	$0.177379\pi$
$863$			787753.i			1.05771i	−0.848711	+	0.528857i	$0.822621\pi$
$864$		0			0
$865$	−335346.			−0.448189
$866$	−17286.2	+	47493.4i	−0.0230496	+	0.0633282i
$867$		0			0
$868$	−185772.	−	155881.i	−0.246571	−	0.206897i
$869$	−81810.8	−	14425.4i	−0.108336	−	0.0191025i
$870$		0			0
$871$	−31022.4	+	26030.9i	−0.0408920	+	0.0343125i
$872$	338714.	−	195556.i	0.445451	−	0.257181i
$873$		0			0
$874$	325799.	−	564300.i	0.426507	−	0.738732i
$875$	689618.	−	121598.i	0.900726	−	0.158822i
$876$		0			0
$877$	683058.	−	248613.i	0.888093	−	0.323239i	0.142622	−	0.989777i	$-0.454447\pi$
$877$	683058.	−	248613.i	0.888093	−	0.323239i	0.745471	+	0.666538i	$0.232225\pi$
$878$	−183957.	−	505419.i	−0.238632	−	0.655635i
$879$		0			0
$880$	17558.7	+	99580.1i	0.0226739	+	0.128590i
$881$	−622184.	−	359218.i	−0.801617	−	0.462814i	0.0424190	−	0.999100i	$-0.486494\pi$
$881$	−622184.	−	359218.i	−0.801617	−	0.462814i	−0.844036	+	0.536286i	$0.819827\pi$
$882$		0			0
$883$	140768.	+	243817.i	0.180543	+	0.312710i	0.942066	−	0.335428i	$-0.108881\pi$
$883$	140768.	+	243817.i	0.180543	+	0.312710i	−0.761522	+	0.648139i	$0.775548\pi$
$884$	4577.98	+	5455.82i	0.00585826	+	0.00698161i
$885$		0			0
$886$	147104.	−	834271.i	0.187395	−	1.06277i
$887$	−766760.	+	913788.i	−0.974568	+	1.16144i	0.0123019	+	0.999924i	$0.496084\pi$
$887$	−766760.	+	913788.i	−0.974568	+	1.16144i	−0.986869	+	0.161520i	$0.948360\pi$
$888$		0			0
$889$	458940.	+	167040.i	0.580700	+	0.211358i
$890$			722032.i			0.911541i
$891$		0			0
$892$	−624780.			−0.785231
$893$	715389.	−	1.96552e6i	0.897097	−	2.46475i
$894$		0			0
$895$	−503594.	−	422566.i	−0.628687	−	0.527531i
$896$	−58730.8	−	10355.8i	−0.0731559	−	0.0128994i
$897$		0			0
$898$	−421958.	+	354064.i	−0.523258	+	0.439066i
$899$	719536.	−	415424.i	0.890294	−	0.514011i
$900$		0			0
$901$	−623.557	+	1080.03i	−0.000768116	+	0.00133042i
$902$	61455.8	−	10836.3i	0.0755352	−	0.0133189i
$903$		0			0
$904$	462080.	−	168183.i	0.565432	−	0.205801i
$905$	−77033.8	−	211649.i	−0.0940555	−	0.258415i
$906$		0			0
$907$	−101379.	−	574951.i	−0.123235	−	0.698902i	−0.982340	−	0.187103i	$-0.940090\pi$
$907$	−101379.	−	574951.i	−0.123235	−	0.698902i	0.859105	−	0.511799i	$-0.171021\pi$
$908$	−188998.	−	109118.i	−0.229237	−	0.132350i
$909$		0			0
$910$	97923.9	+	169609.i	0.118251	+	0.204817i
$911$	−79228.8	−	94421.2i	−0.0954655	−	0.113771i	0.716197	−	0.697899i	$-0.245881\pi$
$911$	−79228.8	−	94421.2i	−0.0954655	−	0.113771i	−0.811662	+	0.584127i	$0.801437\pi$
$912$		0			0
$913$	−10055.3	+	57026.4i	−0.0120629	+	0.0684123i
$914$	330500.	−	393875.i	0.395621	−	0.471483i
$915$		0			0
$916$	376219.	+	136933.i	0.448384	+	0.163198i
$917$		−	1.28581e6i		−	1.52910i
$918$		0			0
$919$	−360954.			−0.427386			−0.213693	−	0.976901i	$-0.568549\pi$
$919$	−360954.			−0.427386			−0.213693	+	0.976901i	$0.568549\pi$
$920$	−55549.9	+	152622.i	−0.0656308	+	0.180319i
$921$		0			0
$922$	590932.	+	495851.i	0.695146	+	0.583296i
$923$	−615604.	−	108548.i	−0.722600	−	0.127414i
$924$		0			0
$925$	364771.	−	306079.i	0.426321	−	0.357725i
$926$	−46803.3	+	27021.9i	−0.0545827	+	0.0315133i
$927$		0			0
$928$	102160.	−	176946.i	0.118627	−	0.205468i
$929$	237180.	−	41821.1i	0.274818	−	0.0484579i	−0.0345404	−	0.999403i	$-0.510997\pi$
$929$	237180.	−	41821.1i	0.274818	−	0.0484579i	0.309359	+	0.950945i	$0.399886\pi$
$930$		0			0
$931$	−440764.	+	160425.i	−0.508518	+	0.185085i
$932$	37380.8	+	102703.i	0.0430345	+	0.118236i
$933$		0			0
$934$	16454.8	+	93319.7i	0.0188625	+	0.106974i
$935$	15015.5	+	8669.22i	0.0171758	+	0.00991646i
$936$		0			0
$937$	714604.	+	1.23773e6i	0.813929	+	1.40977i	0.910094	+	0.414401i	$0.136009\pi$
$937$	714604.	+	1.23773e6i	0.813929	+	1.40977i	−0.0961654	+	0.995365i	$0.530658\pi$
$938$	−37375.4	−	44542.2i	−0.0424795	−	0.0506251i
$939$		0			0
$940$	−90534.4	+	513446.i	−0.102461	+	0.581084i
$941$	161421.	−	192374.i	0.182298	−	0.217254i	−0.667155	−	0.744919i	$-0.732488\pi$
$941$	161421.	−	192374.i	0.182298	−	0.217254i	0.849452	+	0.527665i	$0.176932\pi$
$942$		0			0
$943$	94190.6	+	34282.6i	0.105922	+	0.0385523i
$944$			218768.i			0.245493i
$945$		0			0
$946$	63115.6			0.0705268
$947$	−162773.	+	447216.i	−0.181503	+	0.498674i	−0.996761	−	0.0804234i	$-0.974373\pi$
$947$	−162773.	+	447216.i	−0.181503	+	0.498674i	0.815258	+	0.579098i	$0.196595\pi$
$948$		0			0
$949$	−549095.	−	460746.i	−0.609699	−	0.511598i
$950$	362082.	+	63844.8i	0.401199	+	0.0707422i
$951$		0			0
$952$	−7833.52	+	6573.11i	−0.00864337	+	0.00725265i
$953$	−458155.	+	264516.i	−0.504460	+	0.291250i	−0.730553	−	0.682856i	$-0.760738\pi$
$953$	−458155.	+	264516.i	−0.504460	+	0.291250i	0.226094	+	0.974106i	$0.427404\pi$
$954$		0			0
$955$	635263.	−	1.10031e6i	0.696541	−	1.20645i
$956$	−556101.	+	98055.7i	−0.608469	+	0.107289i
$957$		0			0
$958$	−692031.	+	251879.i	−0.754040	+	0.274448i
$959$	63834.0	+	175383.i	0.0694089	+	0.190699i
$960$		0			0
$961$	−66277.2	−	375877.i	−0.0717658	−	0.407004i
$962$	484220.	+	279565.i	0.523230	+	0.302087i
$963$		0			0
$964$	125743.	+	217794.i	0.135310	+	0.234364i
$965$	69859.9	+	83255.7i	0.0750193	+	0.0894045i
$966$		0			0
$967$	−51037.4	+	289448.i	−0.0545803	+	0.309540i	−0.999860	−	0.0167202i	$-0.994678\pi$
$967$	−51037.4	+	289448.i	−0.0545803	+	0.309540i	0.945280	+	0.326260i	$0.105789\pi$
$968$	−128434.	+	153061.i	−0.137065	+	0.163348i
$969$		0			0
$970$	360942.	+	131372.i	0.383614	+	0.139624i
$971$			93759.7i			0.0994438i	0.998763	+	0.0497219i	$0.0158335\pi$
$971$			93759.7i			0.0994438i	−0.998763	+	0.0497219i	$0.984166\pi$
$972$		0			0
$973$	−648262.			−0.684739
$974$	−125583.	+	345036.i	−0.132377	+	0.363703i
$975$		0			0
$976$	−230715.	−	193593.i	−0.242202	−	0.203231i
$977$	411581.	+	72572.8i	0.431187	+	0.0760299i	0.385030	−	0.922904i	$-0.374191\pi$
$977$	411581.	+	72572.8i	0.431187	+	0.0760299i	0.0461576	+	0.998934i	$0.485302\pi$
$978$		0			0
$979$	719203.	−	603483.i	0.750388	−	0.629651i
$980$	101252.	−	58457.8i	0.105427	−	0.0608682i
$981$		0			0
$982$	−355747.	+	616173.i	−0.368909	+	0.638968i
$983$	−1.27737e6	+	225235.i	−1.32193	+	0.233092i	−0.789693	−	0.613502i	$-0.789760\pi$
$983$	−1.27737e6	+	225235.i	−1.32193	+	0.233092i	−0.532239	+	0.846594i	$0.678649\pi$
$984$		0			0
$985$	−616216.	+	224284.i	−0.635127	+	0.231167i
$986$	−11982.6	−	32921.8i	−0.0123253	−	0.0338634i
$987$		0			0
$988$	74967.4	+	425161.i	0.0767995	+	0.435552i
$989$	87796.6	+	50689.4i	0.0897605	+	0.0518232i
$990$		0			0
$991$	−106592.	−	184623.i	−0.108537	−	0.187992i	0.806641	−	0.591042i	$-0.201283\pi$
$991$	−106592.	−	184623.i	−0.108537	−	0.187992i	−0.915178	+	0.403050i	$0.867950\pi$
$992$	85650.6	+	102074.i	0.0870376	+	0.103727i
$993$		0			0
$994$	155854.	−	883890.i	0.157741	−	0.894593i
$995$	−107610.	+	128245.i	−0.108694	+	0.129537i
$996$		0			0
$997$	44229.6	+	16098.2i	0.0444961	+	0.0161953i	0.364172	−	0.931332i	$-0.381352\pi$
$997$	44229.6	+	16098.2i	0.0444961	+	0.0161953i	−0.319676	+	0.947527i	$0.603574\pi$
$998$			1.14616e6i			1.15075i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.4		72
3.2	odd	2		54.5.f.a.23.9	✓	72
27.7	even	9		54.5.f.a.47.9	yes	72
27.20	odd	18	inner	162.5.f.a.143.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.9	✓	72	3.2	odd	2
54.5.f.a.47.9	yes	72	27.7	even	9
162.5.f.a.17.4		72	1.1	even	1	trivial
162.5.f.a.143.4		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)

\(f(q)\)	\(=\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(20.4117 + 3.59913i) q^{5} +(-31.5466 + 26.4708i) q^{7} +(19.5959 - 11.3137i) q^{8} +O(q^{10})\)	\(q+(-0.967379 + 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(20.4117 + 3.59913i) q^{5} +(-31.5466 + 26.4708i) q^{7} +(19.5959 - 11.3137i) q^{8} +(-29.3118 + 50.7695i) q^{10} +(75.0698 - 13.2368i) q^{11} +(-76.2312 + 27.7459i) q^{13} +(-39.8379 - 109.454i) q^{14} +(11.1135 + 63.0277i) q^{16} +(9.50385 + 5.48705i) q^{17} +(332.610 + 576.097i) q^{19} +(-106.582 - 127.020i) q^{20} +(-37.4394 + 212.329i) q^{22} +(-222.606 + 265.291i) q^{23} +(-183.625 - 66.8340i) q^{25} -229.452i q^{26} +329.450 q^{28} +(-386.043 + 1060.64i) q^{29} +(-563.887 - 473.157i) q^{31} +(-178.269 - 31.4337i) q^{32} +(-23.7776 + 19.9518i) q^{34} +(-739.192 + 426.773i) q^{35} +(-1218.40 + 2110.33i) q^{37} +(-1852.94 + 326.723i) q^{38} +(440.705 - 160.404i) q^{40} +(-98.9929 - 271.981i) q^{41} +(-50.8333 - 288.290i) q^{43} +(-528.122 - 304.911i) q^{44} +(-489.761 - 848.291i) q^{46} +(-2021.13 - 2408.68i) q^{47} +(-122.441 + 694.395i) q^{49} +(355.270 - 423.394i) q^{50} +(609.850 + 221.967i) q^{52} +113.642i q^{53} +1579.94 q^{55} +(-318.703 + 875.629i) q^{56} +(-2445.59 - 2052.09i) q^{58} +(3366.31 + 593.572i) q^{59} +(-3604.93 + 3024.90i) q^{61} +(1803.07 - 1041.00i) q^{62} +(256.000 - 443.405i) q^{64} +(-1655.87 + 291.974i) q^{65} +(469.094 - 170.736i) q^{67} +(-30.0269 - 82.4982i) q^{68} +(-419.220 - 2377.51i) q^{70} +(6673.19 + 3852.77i) q^{71} +(4417.91 + 7652.04i) q^{73} +(-4430.30 - 5279.82i) q^{74} +(924.113 - 5240.91i) q^{76} +(-2017.81 + 2404.73i) q^{77} +(-1024.07 - 372.732i) q^{79} +1326.50i q^{80} +818.648 q^{82} +(-259.814 + 713.833i) q^{83} +(174.241 + 146.206i) q^{85} +(815.407 + 143.778i) q^{86} +(1321.30 - 1108.71i) q^{88} +(10666.3 - 6158.20i) q^{89} +(1670.38 - 2893.19i) q^{91} +(2728.42 - 481.094i) q^{92} +(8357.12 - 3041.74i) q^{94} +(4715.68 + 12956.2i) q^{95} +(-1137.76 - 6452.54i) q^{97} +(-1727.15 - 997.172i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 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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