LMFDB - Embedded newform 162.4.e.a.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			91.1
Character	$\chi$	$=$	162.91
Dual form			162.4.e.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.347296 - 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-5.41266 - 4.54176i) q^{5} +(-4.71753 - 1.71704i) q^{7} +(4.00000 + 6.92820i) q^{8} +O(q^{10})$	\(q+(-0.347296 - 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-5.41266 - 4.54176i) q^{5} +(-4.71753 - 1.71704i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-7.06572 + 12.2382i) q^{10} +(-12.3335 + 10.3490i) q^{11} +(-3.15057 + 17.8677i) q^{13} +(-1.74353 + 9.88804i) q^{14} +(12.2567 - 10.2846i) q^{16} +(-42.7502 + 74.0455i) q^{17} +(55.6054 + 96.3114i) q^{19} +(26.5584 + 9.66648i) q^{20} +(24.6670 + 20.6981i) q^{22} +(-168.375 + 61.2834i) q^{23} +(-13.0367 - 73.9350i) q^{25} +36.2868 q^{26} +20.0812 q^{28} +(27.8427 + 157.904i) q^{29} +(116.644 - 42.4549i) q^{31} +(-24.5134 - 20.5692i) q^{32} +(160.688 + 58.4857i) q^{34} +(17.7360 + 30.7196i) q^{35} +(-120.363 + 208.475i) q^{37} +(170.385 - 142.970i) q^{38} +(9.81560 - 55.6670i) q^{40} +(28.3724 - 160.908i) q^{41} +(-150.236 + 126.063i) q^{43} +(32.2005 - 55.7729i) q^{44} +(179.181 + 310.350i) q^{46} +(242.602 + 88.2999i) q^{47} +(-243.446 - 204.276i) q^{49} +(-141.096 + 51.3547i) q^{50} +(-12.6023 - 71.4710i) q^{52} +170.862 q^{53} +113.760 q^{55} +(-6.97411 - 39.5522i) q^{56} +(301.340 - 109.679i) q^{58} +(-448.948 - 376.712i) q^{59} +(-745.428 - 271.314i) q^{61} +(-124.130 - 214.999i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(98.2040 - 82.4029i) q^{65} +(61.1386 - 346.734i) q^{67} +(59.3879 - 336.806i) q^{68} +(54.3462 - 45.6019i) q^{70} +(-474.203 + 821.343i) q^{71} +(-133.887 - 231.898i) q^{73} +(452.416 + 164.666i) q^{74} +(-340.770 - 285.940i) q^{76} +(75.9534 - 27.6448i) q^{77} +(-191.813 - 1087.83i) q^{79} -113.052 q^{80} -326.780 q^{82} +(-165.513 - 938.668i) q^{83} +(567.689 - 206.622i) q^{85} +(300.471 + 252.125i) q^{86} +(-121.034 - 44.0529i) q^{88} +(299.794 + 519.258i) q^{89} +(45.5425 - 78.8820i) q^{91} +(549.041 - 460.700i) q^{92} +(89.6621 - 508.499i) q^{94} +(136.450 - 773.847i) q^{95} +(-1399.05 + 1173.94i) q^{97} +(-317.797 + 550.440i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.347296	−	1.96962i	−0.122788	−	0.696364i
$2$	−0.347296	−	1.96962i	−0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−3.75877	+	1.36808i	−0.469846	+	0.171010i
$5$	−5.41266	−	4.54176i	−0.484123	−	0.406227i	0.367792	−	0.929908i	$-0.380114\pi$
$5$	−5.41266	−	4.54176i	−0.484123	−	0.406227i	−0.851915	+	0.523681i	$0.824558\pi$
$6$		0			0
$7$	−4.71753	−	1.71704i	−0.254723	−	0.0927115i	0.211503	−	0.977377i	$-0.432164\pi$
$7$	−4.71753	−	1.71704i	−0.254723	−	0.0927115i	−0.466226	+	0.884666i	$0.654386\pi$
$8$	4.00000	+	6.92820i	0.176777	+	0.306186i
$9$		0			0
$10$	−7.06572	+	12.2382i	−0.223438	+	0.387006i
$11$	−12.3335	+	10.3490i	−0.338063	+	0.283668i	−0.795976	−	0.605329i	$-0.793042\pi$
$11$	−12.3335	+	10.3490i	−0.338063	+	0.283668i	0.457913	+	0.888997i	$0.348597\pi$
$12$		0			0
$13$	−3.15057	+	17.8677i	−0.0672161	+	0.381202i	0.932579	+	0.360966i	$0.117553\pi$
$13$	−3.15057	+	17.8677i	−0.0672161	+	0.381202i	−0.999795	+	0.0202360i	$0.993558\pi$
$14$	−1.74353	+	9.88804i	−0.0332841	+	0.188764i
$15$		0			0
$16$	12.2567	−	10.2846i	0.191511	−	0.160697i
$17$	−42.7502	+	74.0455i	−0.609908	+	1.05639i	0.381347	+	0.924432i	$0.375460\pi$
$17$	−42.7502	+	74.0455i	−0.609908	+	1.05639i	−0.991255	+	0.131960i	$0.957873\pi$
$18$		0			0
$19$	55.6054	+	96.3114i	0.671408	+	1.16291i	0.977505	+	0.210913i	$0.0676436\pi$
$19$	55.6054	+	96.3114i	0.671408	+	1.16291i	−0.306097	+	0.952000i	$0.599023\pi$
$20$	26.5584	+	9.66648i	0.296932	+	0.108075i
$21$		0			0
$22$	24.6670	+	20.6981i	0.239047	+	0.200584i
$23$	−168.375	+	61.2834i	−1.52646	+	0.555586i	−0.962751	−	0.270389i	$-0.912848\pi$
$23$	−168.375	+	61.2834i	−1.52646	+	0.555586i	−0.563708	+	0.825974i	$0.690626\pi$
$24$		0			0
$25$	−13.0367	−	73.9350i	−0.104294	−	0.591480i
$26$	36.2868			0.273709
$27$		0			0
$28$	20.0812			0.135535
$29$	27.8427	+	157.904i	0.178285	+	1.01110i	0.934284	+	0.356530i	$0.116040\pi$
$29$	27.8427	+	157.904i	0.178285	+	1.01110i	−0.755999	+	0.654573i	$0.772849\pi$
$30$		0			0
$31$	116.644	−	42.4549i	0.675802	−	0.245972i	0.0187582	−	0.999824i	$-0.494029\pi$
$31$	116.644	−	42.4549i	0.675802	−	0.245972i	0.657044	+	0.753852i	$0.271807\pi$
$32$	−24.5134	−	20.5692i	−0.135419	−	0.113630i
$33$		0			0
$34$	160.688	+	58.4857i	0.810523	+	0.295006i
$35$	17.7360	+	30.7196i	0.0856552	+	0.148359i
$36$		0			0
$37$	−120.363	+	208.475i	−0.534798	+	0.926297i	0.464375	+	0.885639i	$0.346279\pi$
$37$	−120.363	+	208.475i	−0.534798	+	0.926297i	−0.999173	+	0.0406588i	$0.987054\pi$
$38$	170.385	−	142.970i	0.727370	−	0.610336i
$39$		0			0
$40$	9.81560	−	55.6670i	0.0387996	−	0.220043i
$41$	28.3724	−	160.908i	0.108074	−	0.612917i	−0.881874	−	0.471485i	$-0.843718\pi$
$41$	28.3724	−	160.908i	0.108074	−	0.612917i	0.989948	−	0.141432i	$-0.0451706\pi$
$42$		0			0
$43$	−150.236	+	126.063i	−0.532807	+	0.447078i	−0.869069	−	0.494690i	$-0.835282\pi$
$43$	−150.236	+	126.063i	−0.532807	+	0.447078i	0.336262	+	0.941768i	$0.390837\pi$
$44$	32.2005	−	55.7729i	0.110327	−	0.191093i
$45$		0			0
$46$	179.181	+	310.350i	0.574320	+	0.994752i
$47$	242.602	+	88.2999i	0.752918	+	0.274040i	0.689833	−	0.723968i	$-0.257684\pi$
$47$	242.602	+	88.2999i	0.752918	+	0.274040i	0.0630850	+	0.998008i	$0.479906\pi$
$48$		0			0
$49$	−243.446	−	204.276i	−0.709756	−	0.595556i
$50$	−141.096	+	51.3547i	−0.399079	+	0.145253i
$51$		0			0
$52$	−12.6023	−	71.4710i	−0.0336081	−	0.190601i
$53$	170.862			0.442826			0.221413	−	0.975180i	$-0.428933\pi$
$53$	170.862			0.442826			0.221413	+	0.975180i	$0.428933\pi$
$54$		0			0
$55$	113.760			0.278898
$56$	−6.97411	−	39.5522i	−0.0166421	−	0.0943818i
$57$		0			0
$58$	301.340	−	109.679i	0.682205	−	0.248302i
$59$	−448.948	−	376.712i	−0.990644	−	0.831249i	−0.00498347	−	0.999988i	$-0.501586\pi$
$59$	−448.948	−	376.712i	−0.990644	−	0.831249i	−0.985661	+	0.168738i	$0.946031\pi$
$60$		0			0
$61$	−745.428	−	271.314i	−1.56463	−	0.569478i	−0.592837	−	0.805322i	$-0.701992\pi$
$61$	−745.428	−	271.314i	−1.56463	−	0.569478i	−0.971791	+	0.235844i	$0.924215\pi$
$62$	−124.130	−	214.999i	−0.254266	−	0.440402i
$63$		0			0
$64$	−32.0000	+	55.4256i	−0.0625000	+	0.108253i
$65$	98.2040	−	82.4029i	0.187395	−	0.157243i
$66$		0			0
$67$	61.1386	−	346.734i	0.111482	−	0.632244i	−0.876951	−	0.480581i	$-0.840426\pi$
$67$	61.1386	−	346.734i	0.111482	−	0.632244i	0.988432	−	0.151663i	$-0.0484630\pi$
$68$	59.3879	−	336.806i	0.105909	−	0.600643i
$69$		0			0
$70$	54.3462	−	45.6019i	0.0927945	−	0.0778639i
$71$	−474.203	+	821.343i	−0.792641	+	1.37289i	0.131685	+	0.991292i	$0.457961\pi$
$71$	−474.203	+	821.343i	−0.792641	+	1.37289i	−0.924326	+	0.381603i	$0.875372\pi$
$72$		0			0
$73$	−133.887	−	231.898i	−0.214661	−	0.371804i	0.738507	−	0.674246i	$-0.235531\pi$
$73$	−133.887	−	231.898i	−0.214661	−	0.371804i	−0.953168	+	0.302443i	$0.902198\pi$
$74$	452.416	+	164.666i	0.710707	+	0.258676i
$75$		0			0
$76$	−340.770	−	285.940i	−0.514329	−	0.431573i
$77$	75.9534	−	27.6448i	0.112412	−	0.0409145i
$78$		0			0
$79$	−191.813	−	1087.83i	−0.273173	−	1.54924i	−0.744707	−	0.667391i	$-0.767411\pi$
$79$	−191.813	−	1087.83i	−0.273173	−	1.54924i	0.471534	−	0.881848i	$-0.343700\pi$
$80$	−113.052			−0.157994
$81$		0			0
$82$	−326.780			−0.440083
$83$	−165.513	−	938.668i	−0.218884	−	1.24135i	−0.874038	−	0.485857i	$-0.838508\pi$
$83$	−165.513	−	938.668i	−0.218884	−	1.24135i	0.655155	−	0.755495i	$-0.272604\pi$
$84$		0			0
$85$	567.689	−	206.622i	0.724406	−	0.263662i
$86$	300.471	+	252.125i	0.376751	+	0.316132i
$87$		0			0
$88$	−121.034	−	44.0529i	−0.146617	−	0.0533642i
$89$	299.794	+	519.258i	0.357057	+	0.618441i	0.987468	−	0.157821i	$-0.0504468\pi$
$89$	299.794	+	519.258i	0.357057	+	0.618441i	−0.630411	+	0.776262i	$0.717113\pi$
$90$		0			0
$91$	45.5425	−	78.8820i	0.0524632	−	0.0908690i
$92$	549.041	−	460.700i	0.622190	−	0.522080i
$93$		0			0
$94$	89.6621	−	508.499i	0.0983823	−	0.557954i
$95$	136.450	−	773.847i	0.147363	−	0.835737i
$96$		0			0
$97$	−1399.05	+	1173.94i	−1.46445	+	1.22882i	−0.543345	+	0.839509i	$0.682843\pi$
$97$	−1399.05	+	1173.94i	−1.46445	+	1.22882i	−0.921106	+	0.389311i	$0.872713\pi$
$98$	−317.797	+	550.440i	−0.327575	+	0.567376i
$99$		0			0
$100$	150.151	+	260.069i	0.150151	+	0.260069i
$101$	−367.236	−	133.663i	−0.361796	−	0.131683i	0.154725	−	0.987958i	$-0.450551\pi$
$101$	−367.236	−	133.663i	−0.361796	−	0.131683i	−0.516521	+	0.856275i	$0.672773\pi$
$102$		0			0
$103$	1470.79	+	1234.14i	1.40700	+	1.18061i	0.957889	+	0.287138i	$0.0927039\pi$
$103$	1470.79	+	1234.14i	1.40700	+	1.18061i	0.449112	+	0.893476i	$0.351741\pi$
$104$	−136.394	+	49.6432i	−0.128601	+	0.0468069i
$105$		0			0
$106$	−59.3399	−	336.533i	−0.0543736	−	0.308368i
$107$	1237.08			1.11769			0.558846	−	0.829272i	$-0.311244\pi$
$107$	1237.08			1.11769			0.558846	+	0.829272i	$0.311244\pi$
$108$		0			0
$109$	709.963			0.623873			0.311936	−	0.950103i	$-0.399022\pi$
$109$	709.963			0.623873			0.311936	+	0.950103i	$0.399022\pi$
$110$	−39.5084	−	224.063i	−0.0342453	−	0.194214i
$111$		0			0
$112$	−75.4805	+	27.4726i	−0.0636807	+	0.0231779i
$113$	−761.835	−	639.256i	−0.634225	−	0.532178i	0.268013	−	0.963415i	$-0.413633\pi$
$113$	−761.835	−	639.256i	−0.634225	−	0.532178i	−0.902239	+	0.431237i	$0.858077\pi$
$114$		0			0
$115$	1189.69	+	433.011i	0.964688	+	0.351118i
$116$	−320.679	−	555.433i	−0.256675	−	0.444575i
$117$		0			0
$118$	−586.060	+	1015.09i	−0.457213	+	0.791917i
$119$	328.814	−	275.908i	0.253297	−	0.212542i
$120$		0			0
$121$	−186.113	+	1055.50i	−0.139829	+	0.793012i
$122$	−275.499	+	1562.43i	−0.204447	+	1.15948i
$123$		0			0
$124$	−380.356	+	319.157i	−0.275460	+	0.231138i
$125$	−706.839	+	1224.28i	−0.505773	+	0.876025i
$126$		0			0
$127$	78.7351	+	136.373i	0.0550127	+	0.0952848i	0.892220	−	0.451600i	$-0.149147\pi$
$127$	78.7351	+	136.373i	0.0550127	+	0.0952848i	−0.837208	+	0.546885i	$0.815813\pi$
$128$	120.281	+	43.7786i	0.0830579	+	0.0302306i
$129$		0			0
$130$	−196.408	−	164.806i	−0.132509	−	0.111188i
$131$	1639.68	−	596.793i	1.09358	−	0.398031i	0.268635	−	0.963242i	$-0.413427\pi$
$131$	1639.68	−	596.793i	1.09358	−	0.398031i	0.824946	+	0.565211i	$0.191205\pi$
$132$		0			0
$133$	−96.9496	−	549.829i	−0.0632075	−	0.358468i
$134$	−704.167			−0.453961
$135$		0			0
$136$	−684.003			−0.431270
$137$	277.955	+	1576.36i	0.173338	+	0.983050i	0.940045	+	0.341052i	$0.110783\pi$
$137$	277.955	+	1576.36i	0.173338	+	0.983050i	−0.766706	+	0.641998i	$0.778106\pi$
$138$		0			0
$139$	959.717	−	349.308i	0.585627	−	0.213151i	−0.0321781	−	0.999482i	$-0.510244\pi$
$139$	959.717	−	349.308i	0.585627	−	0.213151i	0.617805	+	0.786331i	$0.288022\pi$
$140$	−108.692	−	91.2038i	−0.0656157	−	0.0550581i
$141$		0			0
$142$	1782.42	+	648.748i	1.05336	+	0.383392i
$143$	−146.056	−	252.977i	−0.0854116	−	0.147937i
$144$		0			0
$145$	566.458	−	981.134i	0.324426	−	0.561922i
$146$	−410.252	+	344.243i	−0.232553	+	0.195135i
$147$		0			0
$148$	167.206	−	948.274i	0.0928667	−	0.526673i
$149$	−196.111	+	1112.20i	−0.107826	+	0.611510i	0.882228	+	0.470822i	$0.156043\pi$
$149$	−196.111	+	1112.20i	−0.107826	+	0.611510i	−0.990054	+	0.140688i	$0.955069\pi$
$150$		0			0
$151$	−1508.83	+	1266.06i	−0.813159	+	0.682321i	−0.951359	−	0.308083i	$-0.900312\pi$
$151$	−1508.83	+	1266.06i	−0.813159	+	0.682321i	0.138201	+	0.990404i	$0.455868\pi$
$152$	−444.843	+	770.491i	−0.237379	+	0.411152i
$153$		0			0
$154$	−80.8279	−	139.998i	−0.0422942	−	0.0732556i
$155$	−824.174	−	299.975i	−0.427092	−	0.155449i
$156$		0			0
$157$	411.983	+	345.695i	0.209426	+	0.175729i	0.741467	−	0.670989i	$-0.234130\pi$
$157$	411.983	+	345.695i	0.209426	+	0.175729i	−0.532041	+	0.846718i	$0.678575\pi$
$158$	−2075.98	+	755.595i	−1.04529	+	0.380455i
$159$		0			0
$160$	39.2624	+	222.668i	0.0193998	+	0.110022i
$161$	899.539			0.440333
$162$		0			0
$163$	1030.50			0.495183			0.247592	−	0.968864i	$-0.420361\pi$
$163$	1030.50			0.495183			0.247592	+	0.968864i	$0.420361\pi$
$164$	113.490	+	643.631i	0.0540369	+	0.306458i
$165$		0			0
$166$	−1791.33	+	651.992i	−0.837557	+	0.304846i
$167$	560.836	+	470.598i	0.259873	+	0.218060i	0.763410	−	0.645914i	$-0.223524\pi$
$167$	560.836	+	470.598i	0.259873	+	0.218060i	−0.503537	+	0.863974i	$0.667968\pi$
$168$		0			0
$169$	1755.17	+	638.831i	0.798896	+	0.290774i
$170$	−604.122	−	1046.37i	−0.272553	−	0.472076i
$171$		0			0
$172$	392.237	−	679.375i	0.173883	−	0.301173i
$173$	−2891.32	+	2426.10i	−1.27065	+	1.06620i	−0.276190	+	0.961103i	$0.589072\pi$
$173$	−2891.32	+	2426.10i	−1.27065	+	1.06620i	−0.994462	+	0.105100i	$0.966484\pi$
$174$		0			0
$175$	−65.4482	+	371.175i	−0.0282710	+	0.160333i
$176$	−44.7325	+	253.690i	−0.0191582	+	0.108651i
$177$		0			0
$178$	918.622	−	770.815i	0.386818	−	0.324579i
$179$	1197.85	−	2074.74i	0.500177	−	0.866332i	−0.499823	−	0.866128i	$-0.666602\pi$
$179$	1197.85	−	2074.74i	0.500177	−	0.866332i	1.00000		0.000204660i	$-6.51454e-5\pi$
$180$		0			0
$181$	−445.760	−	772.079i	−0.183056	−	0.317062i	0.759864	−	0.650082i	$-0.225266\pi$
$181$	−445.760	−	772.079i	−0.183056	−	0.317062i	−0.942920	+	0.333020i	$0.891932\pi$
$182$	−171.184	−	62.3059i	−0.0697198	−	0.0253759i
$183$		0			0
$184$	−1098.08	−	921.401i	−0.439955	−	0.369166i
$185$	1598.32	−	581.743i	0.635195	−	0.231192i
$186$		0			0
$187$	−239.040	−	1355.66i	−0.0934778	−	0.530139i
$188$	−1032.69			−0.400619
$189$		0			0
$190$	−1571.57			−0.600072
$191$	−93.6707	−	531.233i	−0.0354857	−	0.201250i	0.961911	−	0.273364i	$-0.0881364\pi$
$191$	−93.6707	−	531.233i	−0.0354857	−	0.201250i	−0.997396	+	0.0721145i	$0.977025\pi$
$192$		0			0
$193$	−4119.65	+	1499.43i	−1.53647	+	0.559230i	−0.965196	−	0.261528i	$-0.915774\pi$
$193$	−4119.65	+	1499.43i	−1.53647	+	0.559230i	−0.571276	+	0.820758i	$0.693551\pi$
$194$	2798.10	+	2347.88i	1.03552	+	0.868907i
$195$		0			0
$196$	1194.52	+	434.771i	0.435322	+	0.158444i
$197$	−857.768	−	1485.70i	−0.310221	−	0.537318i	0.668189	−	0.743991i	$-0.267070\pi$
$197$	−857.768	−	1485.70i	−0.310221	−	0.537318i	−0.978410	+	0.206673i	$0.933736\pi$
$198$		0			0
$199$	983.316	−	1703.15i	0.350278	−	0.606700i	−0.636020	−	0.771673i	$-0.719420\pi$
$199$	983.316	−	1703.15i	0.350278	−	0.606700i	0.986298	+	0.164973i	$0.0527537\pi$
$200$	460.090	−	386.061i	0.162666	−	0.136493i
$201$		0			0
$202$	−135.725	+	769.735i	−0.0472752	+	0.268111i
$203$	139.778	−	792.723i	0.0483277	−	0.274080i
$204$		0			0
$205$	−884.375	+	742.079i	−0.301305	+	0.252825i
$206$	1919.98	−	3325.50i	0.649375	−	1.12475i
$207$		0			0
$208$	145.147	+	251.402i	0.0483853	+	0.0838058i
$209$	−1682.54	−	612.395i	−0.556860	−	0.202680i
$210$		0			0
$211$	−660.684	−	554.380i	−0.215561	−	0.180877i	0.528613	−	0.848863i	$-0.322712\pi$
$211$	−660.684	−	554.380i	−0.215561	−	0.180877i	−0.744174	+	0.667986i	$0.767157\pi$
$212$	−642.233	+	233.754i	−0.208060	+	0.0757277i
$213$		0			0
$214$	−429.633	−	2436.57i	−0.137239	−	0.778320i
$215$	1385.72			0.439559
$216$		0			0
$217$	−623.168			−0.194947
$218$	−246.568	−	1398.35i	−0.0766040	−	0.434443i
$219$		0			0
$220$	−427.597	+	155.633i	−0.131039	+	0.0476943i
$221$	−1188.34	−	997.135i	−0.361703	−	0.303505i
$222$		0			0
$223$	5587.94	+	2033.84i	1.67801	+	0.610745i	0.993035	−	0.117822i	$-0.0375913\pi$
$223$	5587.94	+	2033.84i	1.67801	+	0.610745i	0.684974	+	0.728567i	$0.259813\pi$
$224$	80.3247	+	139.126i	0.0239594	+	0.0414990i
$225$		0			0
$226$	−994.506	+	1722.53i	−0.292715	+	0.506997i
$227$	673.754	−	565.347i	0.196998	−	0.165301i	−0.538953	−	0.842336i	$-0.681180\pi$
$227$	673.754	−	565.347i	0.196998	−	0.165301i	0.735951	+	0.677035i	$0.236735\pi$
$228$		0			0
$229$	−312.864	+	1774.34i	−0.0902822	+	0.512016i	0.905809	+	0.423686i	$0.139264\pi$
$229$	−312.864	+	1774.34i	−0.0902822	+	0.512016i	−0.996091	+	0.0883298i	$0.971847\pi$
$230$	439.691	−	2493.61i	0.126054	−	0.714887i
$231$		0			0
$232$	−982.618	+	824.515i	−0.278069	+	0.233328i
$233$	2348.08	−	4067.00i	0.660206	−	1.14351i	−0.320355	−	0.947298i	$-0.603802\pi$
$233$	2348.08	−	4067.00i	0.660206	−	1.14351i	0.980561	−	0.196213i	$-0.0628644\pi$
$234$		0			0
$235$	−912.085	−	1579.78i	−0.253182	−	0.438525i
$236$	2202.86	+	801.777i	0.607603	+	0.221149i
$237$		0			0
$238$	−657.629	−	551.816i	−0.179108	−	0.150290i
$239$	2792.76	−	1016.48i	0.755853	−	0.275108i	0.0647864	−	0.997899i	$-0.479363\pi$
$239$	2792.76	−	1016.48i	0.755853	−	0.275108i	0.691066	+	0.722791i	$0.257141\pi$
$240$		0			0
$241$	−1107.27	−	6279.63i	−0.295956	−	1.67845i	−0.663291	−	0.748361i	$-0.730841\pi$
$241$	−1107.27	−	6279.63i	−0.295956	−	1.67845i	0.367335	−	0.930089i	$-0.380270\pi$
$242$	2143.56			0.569395
$243$		0			0
$244$	3173.07			0.832521
$245$	389.921	+	2211.35i	0.101678	+	0.576645i
$246$		0			0
$247$	−1896.06	+	690.108i	−0.488434	+	0.177775i
$248$	760.712	+	638.313i	0.194779	+	0.163439i
$249$		0			0
$250$	2656.85	+	967.013i	0.672135	+	0.244637i
$251$	−285.906	−	495.204i	−0.0718974	−	0.124530i	0.827835	−	0.560971i	$-0.189572\pi$
$251$	−285.906	−	495.204i	−0.0718974	−	0.124530i	−0.899733	+	0.436441i	$0.856239\pi$
$252$		0			0
$253$	1442.43	−	2498.36i	0.358437	−	0.620831i
$254$	241.258	−	202.440i	0.0595980	−	0.0500087i
$255$		0			0
$256$	44.4539	−	252.111i	0.0108530	−	0.0615505i
$257$	−620.353	+	3518.20i	−0.150570	+	0.853927i	0.812154	+	0.583443i	$0.198295\pi$
$257$	−620.353	+	3518.20i	−0.150570	+	0.853927i	−0.962725	+	0.270484i	$0.912816\pi$
$258$		0			0
$259$	925.775	−	776.817i	0.222104	−	0.186367i
$260$	−256.392	+	444.085i	−0.0611568	+	0.105927i
$261$		0			0
$262$	−1744.91	−	3022.27i	−0.411453	−	0.712658i
$263$	−2015.97	−	733.753i	−0.472662	−	0.172035i	0.0946959	−	0.995506i	$-0.469812\pi$
$263$	−2015.97	−	733.753i	−0.472662	−	0.172035i	−0.567358	+	0.823471i	$0.692034\pi$
$264$		0			0
$265$	−924.820	−	776.016i	−0.214382	−	0.179888i
$266$	−1049.28	+	381.907i	−0.241863	+	0.0880309i
$267$		0			0
$268$	244.555	+	1386.94i	0.0557408	+	0.316122i
$269$	−1022.08			−0.231663			−0.115831	−	0.993269i	$-0.536953\pi$
$269$	−1022.08			−0.231663			−0.115831	+	0.993269i	$0.536953\pi$
$270$		0			0
$271$	−5880.19			−1.31807			−0.659033	−	0.752114i	$-0.729034\pi$
$271$	−5880.19			−1.31807			−0.659033	+	0.752114i	$0.729034\pi$
$272$	237.552	+	1347.22i	0.0529547	+	0.300321i
$273$		0			0
$274$	3008.30	−	1094.93i	0.663277	−	0.241413i
$275$	925.944	+	776.960i	0.203042	+	0.170372i
$276$		0			0
$277$	−489.348	−	178.108i	−0.106145	−	0.0386335i	0.288402	−	0.957509i	$-0.406876\pi$
$277$	−489.348	−	178.108i	−0.106145	−	0.0386335i	−0.394547	+	0.918876i	$0.629098\pi$
$278$	−1021.31	−	1768.96i	−0.220338	−	0.381637i
$279$		0			0
$280$	−141.888	+	245.757i	−0.0302837	+	0.0524529i
$281$	−1948.18	+	1634.71i	−0.413589	+	0.347042i	−0.825718	−	0.564083i	$-0.809230\pi$
$281$	−1948.18	+	1634.71i	−0.413589	+	0.347042i	0.412129	+	0.911125i	$0.364785\pi$
$282$		0			0
$283$	328.746	−	1864.41i	0.0690528	−	0.391618i	−0.930619	−	0.365990i	$-0.880730\pi$
$283$	328.746	−	1864.41i	0.0690528	−	0.391618i	0.999672	−	0.0256279i	$-0.00815851\pi$
$284$	658.756	−	3735.99i	0.137641	−	0.780599i
$285$		0			0
$286$	−447.543	+	375.533i	−0.0925307	+	0.0776425i
$287$	−410.133	+	710.371i	−0.0843532	+	0.146104i
$288$		0			0
$289$	−1198.66	−	2076.14i	−0.243977	−	0.422580i
$290$	−2129.19	−	774.960i	−0.431138	−	0.156921i
$291$		0			0
$292$	820.505	+	688.485i	0.164440	+	0.137981i
$293$	−6387.89	+	2325.00i	−1.27367	+	0.463577i	−0.888333	−	0.459200i	$-0.848136\pi$
$293$	−6387.89	+	2325.00i	−1.27367	+	0.463577i	−0.385334	+	0.922777i	$0.625914\pi$
$294$		0			0
$295$	719.066	+	4078.03i	0.141917	+	0.804854i
$296$	−1925.81			−0.378159
$297$		0			0
$298$	2258.72			0.439073
$299$	−564.520	−	3201.55i	−0.109187	−	0.619233i
$300$		0			0
$301$	925.195	−	336.743i	0.177167	−	0.0644836i
$302$	3017.66	+	2532.12i	0.574990	+	0.482474i
$303$		0			0
$304$	1672.06	+	608.582i	0.315459	+	0.114818i
$305$	2802.51	+	4854.09i	0.526135	+	0.911292i
$306$		0			0
$307$	−830.528	+	1438.52i	−0.154400	+	0.267428i	−0.932840	−	0.360290i	$-0.882678\pi$
$307$	−830.528	+	1438.52i	−0.154400	+	0.267428i	0.778441	+	0.627718i	$0.216011\pi$
$308$	−247.671	+	207.821i	−0.0458194	+	0.0384470i
$309$		0			0
$310$	−304.602	+	1727.49i	−0.0558073	+	0.316499i
$311$	−919.158	+	5212.80i	−0.167591	+	0.950453i	0.778763	+	0.627319i	$0.215848\pi$
$311$	−919.158	+	5212.80i	−0.167591	+	0.950453i	−0.946353	+	0.323134i	$0.895263\pi$
$312$		0			0
$313$	−7027.32	+	5896.62i	−1.26903	+	1.06485i	−0.274376	+	0.961622i	$0.588471\pi$
$313$	−7027.32	+	5896.62i	−1.26903	+	1.06485i	−0.994658	+	0.103224i	$0.967084\pi$
$314$	537.806	−	931.507i	0.0966565	−	0.167414i
$315$		0			0
$316$	2209.21	+	3826.47i	0.393285	+	0.681189i
$317$	4171.37	+	1518.25i	0.739077	+	0.269002i	0.684002	−	0.729480i	$-0.260238\pi$
$317$	4171.37	+	1518.25i	0.739077	+	0.269002i	0.0550749	+	0.998482i	$0.482460\pi$
$318$		0			0
$319$	−1977.55	−	1659.36i	−0.347089	−	0.291243i
$320$	424.935	−	154.664i	0.0742331	−	0.0270186i
$321$		0			0
$322$	−312.407	−	1771.75i	−0.0540675	−	0.306632i
$323$	−9508.57			−1.63799
$324$		0			0
$325$	1362.12			0.232483
$326$	−357.888	−	2029.69i	−0.0608025	−	0.344828i
$327$		0			0
$328$	1228.29	−	447.062i	0.206772	−	0.0752587i
$329$	−992.868	−	833.115i	−0.166379	−	0.139608i
$330$		0			0
$331$	3814.55	+	1388.38i	0.633434	+	0.230551i	0.638725	−	0.769435i	$-0.279462\pi$
$331$	3814.55	+	1388.38i	0.633434	+	0.230551i	−0.00529144	+	0.999986i	$0.501684\pi$
$332$	1906.30	+	3301.80i	0.315125	+	0.545813i
$333$		0			0
$334$	732.120	−	1268.07i	0.119940	−	0.207741i
$335$	−1905.71	+	1599.08i	−0.310806	+	0.260797i
$336$		0			0
$337$	−1552.19	+	8802.92i	−0.250900	+	1.42292i	0.555482	+	0.831529i	$0.312534\pi$
$337$	−1552.19	+	8802.92i	−0.250900	+	1.42292i	−0.806382	+	0.591396i	$0.798577\pi$
$338$	648.686	−	3678.88i	0.104390	−	0.592026i
$339$		0			0
$340$	−1851.14	+	1553.29i	−0.295271	+	0.247762i
$341$	−999.261	+	1730.77i	−0.158689	+	0.274858i
$342$		0			0
$343$	1658.70	+	2872.95i	0.261111	+	0.452258i
$344$	−1474.33	−	536.612i	−0.231077	−	0.0841052i
$345$		0			0
$346$	5782.63	+	4852.20i	0.898486	+	0.753919i
$347$	8502.38	−	3094.61i	1.31536	−	0.478754i	0.413395	−	0.910552i	$-0.364343\pi$
$347$	8502.38	−	3094.61i	1.31536	−	0.478754i	0.901970	+	0.431798i	$0.142121\pi$
$348$		0			0
$349$	−1058.41	−	6002.53i	−0.162336	−	0.920653i	−0.951769	−	0.306816i	$-0.900736\pi$
$349$	−1058.41	−	6002.53i	−0.162336	−	0.920653i	0.789433	−	0.613837i	$-0.210375\pi$
$350$	753.802			0.115121
$351$		0			0
$352$	515.208			0.0780133
$353$	225.606	+	1279.48i	0.0340164	+	0.192917i	0.997081	−	0.0763548i	$-0.0243282\pi$
$353$	225.606	+	1279.48i	0.0340164	+	0.192917i	−0.963064	+	0.269272i	$0.913217\pi$
$354$		0			0
$355$	6297.04	−	2291.94i	0.941443	−	0.342657i
$356$	−1837.24	−	1541.63i	−0.273522	−	0.229512i
$357$		0			0
$358$	−4502.45	−	1638.76i	−0.664699	−	0.241930i
$359$	1338.22	+	2317.86i	0.196737	+	0.340758i	0.947468	−	0.319849i	$-0.103632\pi$
$359$	1338.22	+	2317.86i	0.196737	+	0.340758i	−0.750732	+	0.660607i	$0.770299\pi$
$360$		0			0
$361$	−2754.43	+	4770.80i	−0.401578	+	0.695554i
$362$	−1365.89	+	1146.12i	−0.198313	+	0.166405i
$363$		0			0
$364$	−63.2670	+	358.805i	−0.00911015	+	0.0516662i
$365$	−328.544	+	1863.27i	−0.0471145	+	0.267200i
$366$		0			0
$367$	−1872.68	+	1571.37i	−0.266358	+	0.223501i	−0.766178	−	0.642629i	$-0.777844\pi$
$367$	−1872.68	+	1571.37i	−0.266358	+	0.223501i	0.499820	+	0.866129i	$0.333399\pi$
$368$	−1433.44	+	2482.80i	−0.203053	+	0.351698i
$369$		0			0
$370$	−1700.90	−	2946.05i	−0.238988	−	0.413940i
$371$	−806.049	−	293.378i	−0.112798	−	0.0410550i
$372$		0			0
$373$	−510.566	−	428.415i	−0.0708742	−	0.0594705i	0.606662	−	0.794960i	$-0.292508\pi$
$373$	−510.566	−	428.415i	−0.0708742	−	0.0594705i	−0.677537	+	0.735489i	$0.736952\pi$
$374$	−2587.12	+	941.634i	−0.357692	+	0.130189i
$375$		0			0
$376$	358.648	+	2034.00i	0.0491912	+	0.278977i
$377$	−2909.10			−0.397418
$378$		0			0
$379$	6612.13			0.896154			0.448077	−	0.893995i	$-0.352109\pi$
$379$	6612.13			0.896154			0.448077	+	0.893995i	$0.352109\pi$
$380$	545.801	+	3095.39i	0.0736815	+	0.417869i
$381$		0			0
$382$	−1013.79	+	368.991i	−0.135786	+	0.0494220i
$383$	−3100.20	−	2601.38i	−0.413610	−	0.347060i	0.412116	−	0.911131i	$-0.364790\pi$
$383$	−3100.20	−	2601.38i	−0.413610	−	0.347060i	−0.825726	+	0.564071i	$0.809234\pi$
$384$		0			0
$385$	−536.666	−	195.330i	−0.0710416	−	0.0258570i
$386$	4384.04	+	7593.38i	0.578088	+	1.00128i
$387$		0			0
$388$	3652.65	−	6326.58i	0.477926	−	0.827793i
$389$	8917.85	−	7482.96i	1.16235	−	0.975325i	0.162412	−	0.986723i	$-0.448073\pi$
$389$	8917.85	−	7482.96i	1.16235	−	0.975325i	0.999935	+	0.0113984i	$0.00362831\pi$
$390$		0			0
$391$	2660.29	−	15087.3i	0.344084	−	1.95140i
$392$	441.479	−	2503.75i	0.0568827	−	0.322598i
$393$		0			0
$394$	−2628.35	+	2205.45i	−0.336078	+	0.282003i
$395$	−3902.42	+	6759.19i	−0.497094	+	0.860992i
$396$		0			0
$397$	5127.44	+	8880.98i	0.648208	+	1.12273i	0.983550	+	0.180633i	$0.0578148\pi$
$397$	5127.44	+	8880.98i	0.648208	+	1.12273i	−0.335342	+	0.942096i	$0.608852\pi$
$398$	−3696.06	−	1345.25i	−0.465494	−	0.169426i
$399$		0			0
$400$	−920.179	−	772.122i	−0.115022	−	0.0965153i
$401$	5003.12	−	1820.99i	0.623052	−	0.226772i	−0.0111526	−	0.999938i	$-0.503550\pi$
$401$	5003.12	−	1820.99i	0.623052	−	0.226772i	0.634204	+	0.773166i	$0.281328\pi$
$402$		0			0
$403$	391.079	+	2217.92i	0.0483401	+	0.274150i
$404$	1563.22			0.192508
$405$		0			0
$406$	−1609.90			−0.196794
$407$	−673.016	−	3816.86i	−0.0819660	−	0.464852i
$408$		0			0
$409$	9547.64	−	3475.06i	1.15428	−	0.420123i	0.307229	−	0.951636i	$-0.400598\pi$
$409$	9547.64	−	3475.06i	1.15428	−	0.420123i	0.847050	+	0.531512i	$0.178376\pi$
$410$	1768.75	+	1484.16i	0.213054	+	0.178774i
$411$		0			0
$412$	−7216.76	−	2626.68i	−0.862971	−	0.314096i
$413$	1471.09	+	2548.01i	0.175273	+	0.303582i
$414$		0			0
$415$	−3367.34	+	5832.41i	−0.398304	+	0.689883i
$416$	444.756	−	373.195i	0.0524182	−	0.0439841i
$417$		0			0
$418$	−621.842	+	3526.64i	−0.0727638	+	0.412664i
$419$	−1392.74	+	7898.60i	−0.162386	+	0.920935i	0.789333	+	0.613965i	$0.210426\pi$
$419$	−1392.74	+	7898.60i	−0.162386	+	0.920935i	−0.951719	+	0.306970i	$0.900685\pi$
$420$		0			0
$421$	5501.92	−	4616.66i	0.636929	−	0.534447i	−0.266144	−	0.963933i	$-0.585750\pi$
$421$	5501.92	−	4616.66i	0.636929	−	0.534447i	0.903073	+	0.429486i	$0.141305\pi$
$422$	−862.462	+	1493.83i	−0.0994881	+	0.172319i
$423$		0			0
$424$	683.450	+	1183.77i	0.0782813	+	0.135587i
$425$	6031.87	+	2195.42i	0.688444	+	0.250573i
$426$		0			0
$427$	3050.72	+	2559.86i	0.345749	+	0.290118i
$428$	−4649.90	+	1692.42i	−0.525143	+	0.191136i
$429$		0			0
$430$	−481.255	−	2729.33i	−0.0539725	−	0.306094i
$431$	−6739.13			−0.753161			−0.376580	−	0.926384i	$-0.622900\pi$
$431$	−6739.13			−0.753161			−0.376580	+	0.926384i	$0.622900\pi$
$432$		0			0
$433$	−1081.70			−0.120054			−0.0600269	−	0.998197i	$-0.519119\pi$
$433$	−1081.70			−0.120054			−0.0600269	+	0.998197i	$0.519119\pi$
$434$	216.424	+	1227.40i	0.0239371	+	0.135754i
$435$		0			0
$436$	−2668.59	+	971.287i	−0.293124	+	0.106689i
$437$	−15264.8	−	12808.7i	−1.67098	−	1.40211i
$438$		0			0
$439$	−4487.05	−	1633.15i	−0.487825	−	0.177554i	0.0863850	−	0.996262i	$-0.472468\pi$
$439$	−4487.05	−	1633.15i	−0.487825	−	0.177554i	−0.574210	+	0.818708i	$0.694691\pi$
$440$	455.040	+	788.152i	0.0493026	+	0.0853947i
$441$		0			0
$442$	−1551.27	+	2686.87i	−0.166937	+	0.289144i
$443$	12514.3	−	10500.8i	1.34215	−	1.12620i	0.361084	−	0.932533i	$-0.382407\pi$
$443$	12514.3	−	10500.8i	1.34215	−	1.12620i	0.981068	−	0.193666i	$-0.0620378\pi$
$444$		0			0
$445$	735.664	−	4172.16i	0.0783682	−	0.444448i
$446$	2065.22	−	11712.4i	0.219262	−	1.24350i
$447$		0			0
$448$	246.129	−	206.527i	0.0259565	−	0.0217801i
$449$	7786.23	−	13486.1i	0.818385	−	1.41748i	−0.0884868	−	0.996077i	$-0.528203\pi$
$449$	7786.23	−	13486.1i	0.818385	−	1.41748i	0.906872	−	0.421407i	$-0.138464\pi$
$450$		0			0
$451$	1315.31	+	2278.18i	0.137329	+	0.237861i
$452$	3738.12	+	1360.56i	0.388996	+	0.141583i
$453$		0			0
$454$	−1347.51	−	1130.69i	−0.139299	−	0.116886i
$455$	−604.769	+	220.118i	−0.0623121	+	0.0226798i
$456$		0			0
$457$	287.550	+	1630.78i	0.0294333	+	0.166925i	0.995981	−	0.0895610i	$-0.0285464\pi$
$457$	287.550	+	1630.78i	0.0294333	+	0.166925i	−0.966548	+	0.256486i	$0.917435\pi$
$458$	3603.42			0.367635
$459$		0			0
$460$	−5064.16			−0.513300
$461$	572.945	+	3249.34i	0.0578844	+	0.328279i	0.999975	−	0.00707977i	$-0.00225358\pi$
$461$	572.945	+	3249.34i	0.0578844	+	0.328279i	−0.942090	+	0.335359i	$0.891142\pi$
$462$		0			0
$463$	−6415.28	+	2334.97i	−0.643938	+	0.234374i	−0.643287	−	0.765625i	$-0.722430\pi$
$463$	−6415.28	+	2334.97i	−0.643938	+	0.234374i	−0.000651627		1.00000i	$0.500207\pi$
$464$	1965.24	+	1649.03i	0.196625	+	0.164988i
$465$		0			0
$466$	−8825.91	−	3212.37i	−0.877365	−	0.319335i
$467$	−3985.48	−	6903.06i	−0.394917	−	0.684016i	0.598174	−	0.801366i	$-0.295893\pi$
$467$	−3985.48	−	6903.06i	−0.394917	−	0.684016i	−0.993091	+	0.117351i	$0.962560\pi$
$468$		0			0
$469$	−883.780	+	1530.75i	−0.0870132	+	0.150711i
$470$	−2794.79	+	2345.11i	−0.274285	+	0.230153i
$471$		0			0
$472$	814.146	−	4617.25i	0.0793942	−	0.450267i
$473$	548.304	−	3109.59i	0.0533003	−	0.302281i
$474$		0			0
$475$	6395.87	−	5366.77i	0.617816	−	0.518409i
$476$	−858.474	+	1486.92i	−0.0826640	+	0.143178i
$477$		0			0
$478$	−2972.00	−	5147.65i	−0.284385	−	0.492569i
$479$	14528.9	+	5288.08i	1.38589	+	0.504423i	0.923959	−	0.382492i	$-0.124934\pi$
$479$	14528.9	+	5288.08i	1.38589	+	0.504423i	0.461932	+	0.886915i	$0.347156\pi$
$480$		0			0
$481$	−3345.76	−	2807.43i	−0.317159	−	0.266128i
$482$	−11983.9	+	4361.78i	−1.13247	+	0.412186i
$483$		0			0
$484$	−744.452	−	4222.00i	−0.0699147	−	0.396506i
$485$	12904.3			1.20816
$486$		0			0
$487$	−16078.0			−1.49603			−0.748014	−	0.663683i	$-0.768992\pi$
$487$	−16078.0			−1.49603			−0.748014	+	0.663683i	$0.768992\pi$
$488$	−1102.00	−	6249.73i	−0.102223	−	0.579738i
$489$		0			0
$490$	4220.09	−	1535.99i	0.389070	−	0.141610i
$491$	−2442.53	−	2049.52i	−0.224500	−	0.188378i	0.523599	−	0.851965i	$-0.324589\pi$
$491$	−2442.53	−	2049.52i	−0.224500	−	0.188378i	−0.748099	+	0.663587i	$0.769033\pi$
$492$		0			0
$493$	−12882.3	−	4688.79i	−1.17686	−	0.428342i
$494$	2017.74	+	3494.83i	0.183770	+	0.318299i
$495$		0			0
$496$	993.039	−	1719.99i	0.0898967	−	0.155706i
$497$	3647.35	−	3060.49i	0.329187	−	0.276220i
$498$		0			0
$499$	2673.81	−	15163.9i	0.239872	−	1.36038i	−0.592234	−	0.805766i	$-0.701754\pi$
$499$	2673.81	−	15163.9i	0.239872	−	1.36038i	0.832106	−	0.554617i	$-0.187135\pi$
$500$	981.931	−	5568.81i	0.0878266	−	0.498089i
$501$		0			0
$502$	−876.067	+	735.108i	−0.0778900	+	0.0653575i
$503$	−4941.68	+	8559.23i	−0.438049	+	0.758722i	−0.997539	−	0.0701145i	$-0.977664\pi$
$503$	−4941.68	+	8559.23i	−0.438049	+	0.758722i	0.559490	+	0.828837i	$0.310997\pi$
$504$		0			0
$505$	1380.66	+	2391.37i	0.121661	+	0.210722i
$506$	−5421.75	−	1973.36i	−0.476336	−	0.173372i
$507$		0			0
$508$	−482.517	−	404.880i	−0.0421422	−	0.0353615i
$509$	1313.34	−	478.018i	0.114367	−	0.0416263i	−0.284203	−	0.958764i	$-0.591729\pi$
$509$	1313.34	−	478.018i	0.114367	−	0.0416263i	0.398570	+	0.917138i	$0.369507\pi$
$510$		0			0
$511$	233.435	+	1323.88i	0.0202085	+	0.114608i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	7144.94			0.613132
$515$	−2355.72	−	13359.9i	−0.201564	−	1.14312i
$516$		0			0
$517$	−3905.95	+	1421.65i	−0.332270	+	0.120936i
$518$	−1851.55	−	1553.63i	−0.157051	−	0.131781i
$519$		0			0
$520$	963.720	+	350.765i	0.0812729	+	0.0295809i
$521$	−6942.87	−	12025.4i	−0.583825	−	1.01121i	−0.995021	−	0.0996670i	$-0.968222\pi$
$521$	−6942.87	−	12025.4i	−0.583825	−	1.01121i	0.411196	−	0.911547i	$-0.365111\pi$
$522$		0			0
$523$	−9988.09	+	17299.9i	−0.835084	+	1.44641i	0.0588786	+	0.998265i	$0.481248\pi$
$523$	−9988.09	+	17299.9i	−0.835084	+	1.44641i	−0.893962	+	0.448142i	$0.852086\pi$
$524$	−5346.70	+	4486.42i	−0.445748	+	0.374027i
$525$		0			0
$526$	−745.073	+	4225.52i	−0.0617618	+	0.350269i
$527$	−1842.95	+	10451.9i	−0.152335	+	0.863933i
$528$		0			0
$529$	15273.9	−	12816.3i	1.25536	−	1.05337i
$530$	−1207.27	+	2091.05i	−0.0989440	+	0.171376i
$531$		0			0
$532$	1116.62	+	1934.05i	0.0909994	+	0.157616i
$533$	2785.67	+	1013.90i	0.226381	+	0.0823958i
$534$		0			0
$535$	−6695.89	−	5618.52i	−0.541100	−	0.454037i
$536$	2646.80	−	963.357i	0.213292	−	0.0776319i
$537$		0			0
$538$	354.964	+	2013.10i	0.0284453	+	0.161322i
$539$	5116.60			0.408883
$540$		0			0
$541$	21492.9			1.70804			0.854021	−	0.520238i	$-0.174157\pi$
$541$	21492.9			1.70804			0.854021	+	0.520238i	$0.174157\pi$
$542$	2042.17	+	11581.7i	0.161842	+	0.917854i
$543$		0			0
$544$	2571.01	−	935.771i	0.202631	−	0.0737516i
$545$	−3842.79	−	3224.48i	−0.302031	−	0.253434i
$546$		0			0
$547$	7661.46	+	2788.54i	0.598867	+	0.217970i	0.623625	−	0.781724i	$-0.285659\pi$
$547$	7661.46	+	2788.54i	0.598867	+	0.217970i	−0.0247578	+	0.999693i	$0.507881\pi$
$548$	−3201.36	−	5544.92i	−0.249554	−	0.432240i
$549$		0			0
$550$	1208.73	−	2093.59i	0.0937102	−	0.162311i
$551$	−13659.7	+	11461.9i	−1.05612	+	0.886193i
$552$		0			0
$553$	−962.957	+	5461.20i	−0.0740490	+	0.419953i
$554$	−180.856	+	1025.68i	−0.0138697	+	0.0786591i
$555$		0			0
$556$	−3129.47	+	2625.94i	−0.238704	+	0.200296i
$557$	607.095	−	1051.52i	0.0461822	−	0.0799898i	−0.842010	−	0.539461i	$-0.818628\pi$
$557$	607.095	−	1051.52i	0.0461822	−	0.0799898i	0.888192	+	0.459472i	$0.151961\pi$
$558$		0			0
$559$	−1779.13	−	3081.54i	−0.134614	−	0.233158i
$560$	533.324	+	194.114i	0.0402448	+	0.0146479i
$561$		0			0
$562$	3896.35	+	3269.43i	0.292451	+	0.245396i
$563$	−325.846	+	118.598i	−0.0243921	+	0.00887802i	−0.354187	−	0.935174i	$-0.615243\pi$
$563$	−325.846	+	118.598i	−0.0243921	+	0.00887802i	0.329795	+	0.944052i	$0.393020\pi$
$564$		0			0
$565$	1220.21	+	6920.15i	0.0908576	+	0.515279i
$566$	−3786.35			−0.281188
$567$		0			0
$568$	−7587.24			−0.560482
$569$	2947.40	+	16715.5i	0.217155	+	1.23155i	0.877127	+	0.480259i	$0.159457\pi$
$569$	2947.40	+	16715.5i	0.217155	+	1.23155i	−0.659971	+	0.751291i	$0.729432\pi$
$570$		0			0
$571$	−10658.6	+	3879.41i	−0.781169	+	0.284322i	−0.701660	−	0.712512i	$-0.747557\pi$
$571$	−10658.6	+	3879.41i	−0.781169	+	0.284322i	−0.0795091	+	0.996834i	$0.525335\pi$
$572$	895.086	+	751.066i	0.0654291	+	0.0549015i
$573$		0			0
$574$	1541.60	+	561.095i	0.112099	+	0.0408008i
$575$	6726.04	+	11649.8i	0.487818	+	0.844925i
$576$		0			0
$577$	12539.8	−	21719.6i	0.904749	−	1.56707i	0.0834946	−	0.996508i	$-0.473392\pi$
$577$	12539.8	−	21719.6i	0.904749	−	1.56707i	0.821254	−	0.570563i	$-0.193275\pi$
$578$	−3672.90	+	3081.93i	−0.264312	+	0.221784i
$579$		0			0
$580$	−786.915	+	4462.82i	−0.0563360	+	0.319497i
$581$	−830.921	+	4712.39i	−0.0593329	+	0.336494i
$582$		0			0
$583$	−2107.33	+	1768.26i	−0.149703	+	0.125616i
$584$	1071.09	−	1855.19i	0.0758941	−	0.131452i
$585$		0			0
$586$	6797.85	+	11774.2i	0.479209	+	0.830014i
$587$	−5829.20	−	2121.66i	−0.409876	−	0.149183i	0.128849	−	0.991664i	$-0.458872\pi$
$587$	−5829.20	−	2121.66i	−0.409876	−	0.149183i	−0.538725	+	0.842482i	$0.681094\pi$
$588$		0			0
$589$	10574.9	+	8873.42i	0.739783	+	0.620752i
$590$	7782.41	−	2832.57i	0.543046	−	0.197652i
$591$		0			0
$592$	668.825	+	3793.10i	0.0464334	+	0.263337i
$593$	6986.06			0.483783			0.241891	−	0.970303i	$-0.422232\pi$
$593$	6986.06			0.483783			0.241891	+	0.970303i	$0.422232\pi$
$594$		0			0
$595$	−3032.87			−0.208967
$596$	−784.444	−	4448.80i	−0.0539129	−	0.305755i
$597$		0			0
$598$	−6109.77	+	2223.78i	−0.417805	+	0.152069i
$599$	19819.3	+	16630.4i	1.35191	+	1.13439i	0.978390	+	0.206769i	$0.0662948\pi$
$599$	19819.3	+	16630.4i	1.35191	+	1.13439i	0.373523	+	0.927621i	$0.378150\pi$
$600$		0			0
$601$	3098.27	+	1127.68i	0.210284	+	0.0765372i	0.445015	−	0.895523i	$-0.353198\pi$
$601$	3098.27	+	1127.68i	0.210284	+	0.0765372i	−0.234730	+	0.972061i	$0.575421\pi$
$602$	−984.572	−	1705.33i	−0.0666581	−	0.115455i
$603$		0			0
$604$	3939.28	−	6823.03i	0.265376	−	0.459644i
$605$	5801.19	−	4867.78i	0.389838	−	0.327113i
$606$		0			0
$607$	−2520.41	+	14293.9i	−0.168534	+	0.955805i	0.776811	+	0.629734i	$0.216836\pi$
$607$	−2520.41	+	14293.9i	−0.168534	+	0.955805i	−0.945345	+	0.326071i	$0.894275\pi$
$608$	617.970	−	3504.68i	0.0412204	−	0.233772i
$609$		0			0
$610$	8587.38	−	7205.67i	0.569988	−	0.478277i
$611$	−2342.05	+	4056.56i	−0.155073	+	0.268594i
$612$		0			0
$613$	89.7207	+	155.401i	0.00591156	+	0.0102391i	0.868966	−	0.494872i	$-0.164785\pi$
$613$	89.7207	+	155.401i	0.00591156	+	0.0102391i	−0.863054	+	0.505111i	$0.831452\pi$
$614$	3121.76	+	1136.23i	0.205186	+	0.0746816i
$615$		0			0
$616$	495.342	+	415.641i	0.0323992	+	0.0271862i
$617$	−8743.94	+	3182.53i	−0.570531	+	0.207656i	−0.611145	−	0.791519i	$-0.709291\pi$
$617$	−8743.94	+	3182.53i	−0.570531	+	0.207656i	0.0406141	+	0.999175i	$0.487069\pi$
$618$		0			0
$619$	4250.26	+	24104.4i	0.275981	+	1.56517i	0.735827	+	0.677170i	$0.236794\pi$
$619$	4250.26	+	24104.4i	0.275981	+	1.56517i	−0.459845	+	0.887999i	$0.652095\pi$
$620$	3508.27			0.227251
$621$		0			0
$622$	10586.4			0.682440
$623$	−522.699	−	2964.38i	−0.0336140	−	0.190634i
$624$		0			0
$625$	567.782	−	206.656i	0.0363380	−	0.0132260i
$626$	14054.6	+	11793.2i	0.897343	+	0.752960i
$627$		0			0
$628$	−2021.49	−	735.762i	−0.128449	−	0.0467517i
$629$	−10291.1	−	17824.7i	−0.652356	−	1.12991i
$630$		0			0
$631$	−7740.52	+	13407.0i	−0.488344	+	0.845837i	−0.999910	−	0.0134072i	$-0.995732\pi$
$631$	−7740.52	+	13407.0i	−0.488344	+	0.845837i	0.511566	+	0.859244i	$0.329066\pi$
$632$	6769.42	−	5680.22i	0.426065	−	0.357511i
$633$		0			0
$634$	1541.67	−	8743.27i	0.0965737	−	0.547697i
$635$	193.208	−	1095.74i	0.0120744	−	0.0684772i
$636$		0			0
$637$	4416.94	−	3706.25i	0.274734	−	0.230529i
$638$	−2581.51	+	4471.30i	−0.160193	+	0.277462i
$639$		0			0
$640$	−452.206	−	783.244i	−0.0279297	−	0.0483757i
$641$	−28724.1	−	10454.7i	−1.76995	−	0.644208i	−0.999981	−	0.00612154i	$-0.998051\pi$
$641$	−28724.1	−	10454.7i	−1.76995	−	0.644208i	−0.769965	−	0.638086i	$-0.779726\pi$
$642$		0			0
$643$	−7557.72	−	6341.68i	−0.463526	−	0.388945i	0.380900	−	0.924616i	$-0.375614\pi$
$643$	−7557.72	−	6341.68i	−0.463526	−	0.388945i	−0.844426	+	0.535672i	$0.820059\pi$
$644$	−3381.16	+	1230.64i	−0.206889	+	0.0753014i
$645$		0			0
$646$	3302.29	+	18728.2i	0.201125	+	1.14064i
$647$	−17561.5			−1.06710			−0.533550	−	0.845768i	$-0.679142\pi$
$647$	−17561.5			−1.06710			−0.533550	+	0.845768i	$0.679142\pi$
$648$		0			0
$649$	9435.70			0.570699
$650$	−473.061	−	2682.86i	−0.0285461	−	0.161893i
$651$		0			0
$652$	−3873.41	+	1409.81i	−0.232660	+	0.0846813i
$653$	3624.57	+	3041.37i	0.217213	+	0.182264i	0.744901	−	0.667175i	$-0.232497\pi$
$653$	3624.57	+	3041.37i	0.217213	+	0.182264i	−0.527688	+	0.849438i	$0.676941\pi$
$654$		0			0
$655$	−11585.5	−	4216.78i	−0.691119	−	0.251547i
$656$	−1307.12	−	2264.00i	−0.0777965	−	0.134747i
$657$		0			0
$658$	−1296.10	+	2244.91i	−0.0767890	+	0.133002i
$659$	−16591.1	+	13921.6i	−0.980723	+	0.822924i	−0.984198	−	0.177070i	$-0.943338\pi$
$659$	−16591.1	+	13921.6i	−0.980723	+	0.822924i	0.00347564	+	0.999994i	$0.498894\pi$
$660$		0			0
$661$	−3278.57	+	18593.7i	−0.192922	+	1.09412i	0.722424	+	0.691450i	$0.243028\pi$
$661$	−3278.57	+	18593.7i	−0.192922	+	1.09412i	−0.915347	+	0.402667i	$0.868083\pi$
$662$	1409.80	−	7995.37i	0.0827695	−	0.469409i
$663$		0			0
$664$	5841.23	−	4901.38i	0.341391	−	0.286461i
$665$	−1972.43	+	3416.36i	−0.115019	+	0.199219i
$666$		0			0
$667$	−14364.9	−	24880.7i	−0.833899	−	1.44435i
$668$	−2751.87	−	1001.60i	−0.159391	−	0.0580135i
$669$		0			0
$670$	3811.41	+	3198.16i	0.219773	+	0.184411i
$671$	12001.6	−	4368.22i	0.690486	−	0.251316i
$672$		0			0
$673$	4313.94	+	24465.5i	0.247088	+	1.40130i	0.815594	+	0.578625i	$0.196410\pi$
$673$	4313.94	+	24465.5i	0.247088	+	1.40130i	−0.568506	+	0.822679i	$0.692478\pi$
$674$	17877.4			1.02168
$675$		0			0
$676$	−7471.27			−0.425084
$677$	2922.94	+	16576.8i	0.165935	+	0.941062i	0.948096	+	0.317985i	$0.103006\pi$
$677$	2922.94	+	16576.8i	0.165935	+	0.941062i	−0.782161	+	0.623076i	$0.785883\pi$
$678$		0			0
$679$	8615.75	−	3135.88i	0.486955	−	0.177237i
$680$	3702.28	+	3106.58i	0.208788	+	0.175194i
$681$		0			0
$682$	3755.99	+	1367.07i	0.210886	+	0.0767563i
$683$	−2956.52	−	5120.84i	−0.165634	−	0.286886i	0.771246	−	0.636537i	$-0.219634\pi$
$683$	−2956.52	−	5120.84i	−0.165634	−	0.286886i	−0.936880	+	0.349650i	$0.886300\pi$
$684$		0			0
$685$	5654.99	−	9794.72i	0.315425	−	0.546332i
$686$	5082.54	−	4264.76i	0.282875	−	0.237360i
$687$		0			0
$688$	−544.890	+	3090.22i	−0.0301944	+	0.171241i
$689$	−538.313	+	3052.93i	−0.0297650	+	0.168806i
$690$		0			0
$691$	15603.6	−	13093.0i	0.859030	−	0.720812i	−0.102729	−	0.994709i	$-0.532757\pi$
$691$	15603.6	−	13093.0i	0.859030	−	0.720812i	0.961759	+	0.273897i	$0.0883129\pi$
$692$	7548.69	−	13074.7i	0.414679	−	0.718246i
$693$		0			0
$694$	−9048.04	−	15671.7i	−0.494898	−	0.857188i
$695$	−6781.10	−	2468.12i	−0.370103	−	0.134706i
$696$		0			0
$697$	10701.6	+	8979.69i	0.581565	+	0.487991i
$698$	−11455.1	+	4169.31i	−0.621177	+	0.226090i
$699$		0			0
$700$	−261.793	−	1484.70i	−0.0141355	−	0.0801663i
$701$	6737.52			0.363014			0.181507	−	0.983390i	$-0.441903\pi$
$701$	6737.52			0.363014			0.181507	+	0.983390i	$0.441903\pi$
$702$		0			0
$703$	−26771.3			−1.43627
$704$	−178.930	−	1014.76i	−0.00957908	−	0.0543257i
$705$		0			0
$706$	2441.72	−	888.715i	0.130164	−	0.0473757i
$707$	1502.94	+	1261.12i	0.0799491	+	0.0670853i
$708$		0			0
$709$	−24797.6	−	9025.59i	−1.31353	−	0.478086i	−0.412152	−	0.911115i	$-0.635223\pi$
$709$	−24797.6	−	9025.59i	−1.31353	−	0.478086i	−0.901380	+	0.433029i	$0.857445\pi$
$710$	−6701.17	−	11606.8i	−0.354212	−	0.613513i
$711$		0			0
$712$	−2398.35	+	4154.07i	−0.126239	+	0.218652i
$713$	−17038.1	+	14296.7i	−0.894926	+	0.750932i
$714$		0			0
$715$	−358.408	+	2032.63i	−0.0187464	+	0.106316i
$716$	−1664.04	+	9437.24i	−0.0868549	+	0.492578i
$717$		0			0
$718$	4100.54	−	3440.76i	0.213135	−	0.178841i
$719$	−9945.46	+	17226.0i	−0.515859	+	0.893495i	0.483971	+	0.875084i	$0.339194\pi$
$719$	−9945.46	+	17226.0i	−0.515859	+	0.893495i	−0.999831	+	0.0184107i	$0.994139\pi$
$720$		0			0
$721$	−4819.42	−	8347.49i	−0.248939	−	0.431174i
$722$	10353.3	+	3768.28i	0.533668	+	0.194239i
$723$		0			0
$724$	2731.77	+	2292.23i	0.140229	+	0.117666i
$725$	11311.6	−	4117.10i	0.579453	−	0.210904i
$726$		0			0
$727$	924.306	+	5242.00i	0.0471535	+	0.267421i	0.999265	−	0.0383297i	$-0.0122037\pi$
$727$	924.306	+	5242.00i	0.0471535	+	0.267421i	−0.952112	+	0.305751i	$0.901093\pi$
$728$	728.681			0.0370971
$729$		0			0
$730$	3784.02			0.191853
$731$	−2911.77	−	16513.5i	−0.147326	−	0.835530i
$732$		0			0
$733$	−24374.8	+	8871.69i	−1.22824	+	0.447044i	−0.872996	−	0.487728i	$-0.837826\pi$
$733$	−24374.8	+	8871.69i	−1.22824	+	0.447044i	−0.355248	+	0.934772i	$0.615604\pi$
$734$	3745.37	+	3142.74i	0.188343	+	0.158039i
$735$		0			0
$736$	5387.99	+	1961.07i	0.269842	+	0.0982146i
$737$	2834.31	+	4909.18i	0.141660	+	0.245362i
$738$		0			0
$739$	17509.0	−	30326.5i	0.871556	−	1.50958i	0.0111699	−	0.999938i	$-0.496444\pi$
$739$	17509.0	−	30326.5i	0.871556	−	1.50958i	0.860386	−	0.509642i	$-0.170222\pi$
$740$	−5211.86	+	4373.27i	−0.258908	+	0.217250i
$741$		0			0
$742$	−297.904	+	1689.50i	−0.0147391	+	0.0835894i
$743$	−4418.50	+	25058.5i	−0.218168	+	1.23729i	0.657156	+	0.753755i	$0.271759\pi$
$743$	−4418.50	+	25058.5i	−0.218168	+	1.23729i	−0.875324	+	0.483538i	$0.839352\pi$
$744$		0			0
$745$	6112.83	−	5129.27i	0.300613	−	0.252244i
$746$	−666.496	+	1154.41i	−0.0327107	+	0.0566565i
$747$		0			0
$748$	2753.15	+	4768.60i	0.134579	+	0.233098i
$749$	−5835.96	−	2124.12i	−0.284701	−	0.103623i
$750$		0			0
$751$	−12687.3	−	10645.9i	−0.616468	−	0.517278i	0.280223	−	0.959935i	$-0.409592\pi$
$751$	−12687.3	−	10645.9i	−0.616468	−	0.517278i	−0.896691	+	0.442657i	$0.854036\pi$
$752$	3881.63	−	1412.80i	0.188230	−	0.0685099i
$753$		0			0
$754$	1010.32	+	5729.82i	0.0487981	+	0.276748i
$755$	13916.9			0.670846
$756$		0			0
$757$	−4077.47			−0.195771			−0.0978853	−	0.995198i	$-0.531208\pi$
$757$	−4077.47			−0.195771			−0.0978853	+	0.995198i	$0.531208\pi$
$758$	−2296.37	−	13023.4i	−0.110037	−	0.624050i
$759$		0			0
$760$	5907.17	−	2150.03i	0.281942	−	0.102618i
$761$	−11550.4	−	9691.95i	−0.550200	−	0.461673i	0.324809	−	0.945780i	$-0.394700\pi$
$761$	−11550.4	−	9691.95i	−0.550200	−	0.461673i	−0.875009	+	0.484107i	$0.839145\pi$
$762$		0			0
$763$	−3349.27	−	1219.04i	−0.158915	−	0.0578402i
$764$	1078.86	+	1868.63i	0.0510886	+	0.0884880i
$765$		0			0
$766$	−4047.02	+	7009.65i	−0.190894	+	0.330638i
$767$	8145.43	−	6834.83i	0.383461	−	0.321762i
$768$		0			0
$769$	2032.09	−	11524.6i	0.0952915	−	0.540425i	−0.899366	−	0.437196i	$-0.855971\pi$
$769$	2032.09	−	11524.6i	0.0952915	−	0.540425i	0.994658	−	0.103229i	$-0.0329174\pi$
$770$	−198.344	+	1124.86i	−0.00928287	+	0.0526458i
$771$		0			0
$772$	13433.5	−	11272.0i	0.626272	−	0.525504i
$773$	13963.6	−	24185.6i	0.649721	−	1.12535i	−0.333468	−	0.942761i	$-0.608219\pi$
$773$	13963.6	−	24185.6i	0.649721	−	1.12535i	0.983189	−	0.182589i	$-0.0584476\pi$
$774$		0			0
$775$	−4659.56	−	8070.59i	−0.215969	−	0.374070i
$776$	−13729.5	−	4997.13i	−0.635129	−	0.231168i
$777$		0			0
$778$	−17835.7	−	14965.9i	−0.821903	−	0.689659i
$779$	17074.9	−	6214.76i	0.785331	−	0.285837i
$780$		0			0
$781$	−2651.53	−	15037.6i	−0.121484	−	0.688972i
$782$	−30640.0			−1.40113
$783$		0			0
$784$	−5084.75			−0.231630
$785$	−659.861	−	3742.26i	−0.0300018	−	0.170149i
$786$		0			0
$787$	24110.0	−	8775.32i	1.09203	−	0.397467i	0.267658	−	0.963514i	$-0.413750\pi$
$787$	24110.0	−	8775.32i	1.09203	−	0.397467i	0.824373	+	0.566047i	$0.191528\pi$
$788$	5256.71	+	4410.90i	0.237643	+	0.199406i
$789$		0			0
$790$	14668.3	+	5338.83i	0.660601	+	0.240439i
$791$	2496.35	+	4323.81i	0.112213	+	0.194358i
$792$		0			0
$793$	7196.29	−	12464.3i	0.322254	−	0.558161i
$794$	15711.4	−	13183.4i	0.702237	−	0.589247i
$795$		0			0
$796$	−1366.01	+	7747.01i	−0.0608252	+	0.344957i
$797$	3744.20	−	21234.4i	0.166407	−	0.943741i	−0.781195	−	0.624287i	$-0.785389\pi$
$797$	3744.20	−	21234.4i	0.166407	−	0.943741i	0.947602	−	0.319454i	$-0.103499\pi$
$798$		0			0
$799$	−16909.5	+	14188.8i	−0.748705	+	0.628238i
$800$	−1201.21	+	2080.55i	−0.0530864	+	0.0919484i
$801$		0			0
$802$	−5324.21	−	9221.80i	−0.234419	−	0.406026i
$803$	4051.22	+	1474.52i	0.178038	+	0.0648005i
$804$		0			0
$805$	−4868.90	−	4085.49i	−0.213175	−	0.178875i
$806$	4232.63	−	1540.55i	0.184973	−	0.0673246i
$807$		0			0
$808$	−542.900	−	3078.94i	−0.0236376	−	0.134055i
$809$	25132.8			1.09224			0.546120	−	0.837707i	$-0.316104\pi$
$809$	25132.8			1.09224			0.546120	+	0.837707i	$0.316104\pi$
$810$		0			0
$811$	−14270.4			−0.617880			−0.308940	−	0.951082i	$-0.599974\pi$
$811$	−14270.4			−0.617880			−0.308940	+	0.951082i	$0.599974\pi$
$812$	559.114	+	3170.89i	0.0241638	+	0.137040i
$813$		0			0
$814$	−7284.01	+	2651.16i	−0.313642	+	0.114156i
$815$	−5577.74	−	4680.28i	−0.239730	−	0.201157i
$816$		0			0
$817$	−20495.2	−	7459.63i	−0.877644	−	0.319436i
$818$	−10160.4	−	17598.3i	−0.434290	−	0.752213i
$819$		0			0
$820$	2308.94	−	3999.20i	0.0983313	−	0.170315i
$821$	−4374.67	+	3670.79i	−0.185965	+	0.156043i	−0.731017	−	0.682359i	$-0.760954\pi$
$821$	−4374.67	+	3670.79i	−0.185965	+	0.156043i	0.545053	+	0.838402i	$0.316510\pi$
$822$		0			0
$823$	−4130.20	+	23423.5i	−0.174933	+	0.992093i	0.763289	+	0.646057i	$0.223583\pi$
$823$	−4130.20	+	23423.5i	−0.174933	+	0.992093i	−0.938222	+	0.346035i	$0.887528\pi$
$824$	−2667.21	+	15126.5i	−0.112763	+	0.639509i
$825$		0			0
$826$	4507.70	−	3782.41i	0.189882	−	0.159330i
$827$	6748.71	−	11689.1i	0.283767	−	0.491499i	−0.688542	−	0.725196i	$-0.741749\pi$
$827$	6748.71	−	11689.1i	0.283767	−	0.491499i	0.972309	+	0.233697i	$0.0750824\pi$
$828$		0			0
$829$	5467.47	+	9469.93i	0.229063	+	0.396748i	0.957531	−	0.288332i	$-0.0931006\pi$
$829$	5467.47	+	9469.93i	0.229063	+	0.396748i	−0.728468	+	0.685080i	$0.759767\pi$
$830$	12657.1	+	4606.80i	0.529317	+	0.192656i
$831$		0			0
$832$	−889.513	−	746.390i	−0.0370653	−	0.0311015i
$833$	25533.1	−	9293.28i	1.06203	−	0.386546i
$834$		0			0
$835$	−898.275	−	5094.37i	−0.0372288	−	0.211135i
$836$	7162.09			0.296299
$837$		0			0
$838$	16040.9			0.661245
$839$	−1713.32	−	9716.70i	−0.0705009	−	0.399831i	−0.999553	−	0.0298827i	$-0.990487\pi$
$839$	−1713.32	−	9716.70i	−0.0705009	−	0.399831i	0.929052	−	0.369948i	$-0.120624\pi$
$840$		0			0
$841$	−1240.21	+	451.401i	−0.0508513	+	0.0185084i
$842$	−11003.8	−	9233.31i	−0.450377	−	0.377911i
$843$		0			0
$844$	3241.80	+	1179.92i	0.132212	+	0.0481214i
$845$	−6598.74	−	11429.4i	−0.268643	−	0.465304i
$846$		0			0
$847$	2690.33	−	4659.79i	0.109139	−	0.189034i
$848$	2094.21	−	1757.25i	0.0848060	−	0.0711607i
$849$		0			0
$850$	2229.29	−	12642.9i	0.0899577	−	0.510175i
$851$	7490.03	−	42478.1i	0.301710	−	1.71108i
$852$		0			0
$853$	−9164.27	+	7689.74i	−0.367853	+	0.308665i	−0.807912	−	0.589304i	$-0.799402\pi$
$853$	−9164.27	+	7689.74i	−0.367853	+	0.308665i	0.440059	+	0.897969i	$0.354958\pi$
$854$	3982.44	−	6897.78i	0.159574	−	0.276390i
$855$		0			0
$856$	4948.32	+	8570.74i	0.197582	+	0.342222i
$857$	11611.2	+	4226.14i	0.462815	+	0.168451i	0.562895	−	0.826529i	$-0.309688\pi$
$857$	11611.2	+	4226.14i	0.462815	+	0.168451i	−0.100080	+	0.994979i	$0.531910\pi$
$858$		0			0
$859$	15563.7	+	13059.5i	0.618193	+	0.518725i	0.897235	−	0.441554i	$-0.145573\pi$
$859$	15563.7	+	13059.5i	0.618193	+	0.518725i	−0.279042	+	0.960279i	$0.590017\pi$
$860$	−5208.60	+	1895.78i	−0.206525	+	0.0751691i
$861$		0			0
$862$	2340.47	+	13273.5i	0.0924790	+	0.524474i
$863$	602.707			0.0237733			0.0118867	−	0.999929i	$-0.496216\pi$
$863$	602.707			0.0237733			0.0118867	+	0.999929i	$0.496216\pi$
$864$		0			0
$865$	26668.5			1.04827
$866$	375.671	+	2130.54i	0.0147411	+	0.0836012i
$867$		0			0
$868$	2342.35	−	852.544i	0.0915949	−	0.0333378i
$869$	13623.7	+	11431.6i	0.531820	+	0.446250i
$870$		0			0
$871$	6002.74	+	2184.82i	0.233519	+	0.0849940i
$872$	2839.85	+	4918.77i	0.110286	+	0.191021i
$873$		0			0
$874$	−19926.8	+	34514.3i	−0.771207	+	1.33577i
$875$	5436.68	−	4561.91i	0.210049	−	0.176252i
$876$		0			0
$877$	−2450.81	+	13899.3i	−0.0943650	+	0.535171i	0.900575	+	0.434701i	$0.143146\pi$
$877$	−2450.81	+	13899.3i	−0.0943650	+	0.535171i	−0.994940	+	0.100470i	$0.967965\pi$
$878$	−1658.35	+	9404.95i	−0.0637431	+	0.361505i
$879$		0			0
$880$	1394.32	−	1169.98i	0.0534120	−	0.0448180i
$881$	−7955.12	+	13778.7i	−0.304217	+	0.526919i	−0.977087	−	0.212842i	$-0.931728\pi$
$881$	−7955.12	+	13778.7i	−0.304217	+	0.526919i	0.672870	+	0.739761i	$0.265061\pi$
$882$		0			0
$883$	20174.8	+	34943.8i	0.768898	+	1.33177i	0.938161	+	0.346200i	$0.112528\pi$
$883$	20174.8	+	34943.8i	0.768898	+	1.33177i	−0.169262	+	0.985571i	$0.554138\pi$
$884$	5830.85	+	2122.26i	0.221847	+	0.0807457i
$885$		0			0
$886$	−25028.6	−	21001.5i	−0.949045	−	0.796343i
$887$	−15956.2	+	5807.60i	−0.604011	+	0.219842i	−0.625881	−	0.779919i	$-0.715260\pi$
$887$	−15956.2	+	5807.60i	−0.604011	+	0.219842i	0.0218694	+	0.999761i	$0.493038\pi$
$888$		0			0
$889$	−137.277	−	778.536i	−0.00517899	−	0.0293715i
$890$	−8473.05			−0.319120
$891$		0			0
$892$	−23786.2			−0.892850
$893$	4985.70	+	28275.3i	0.186831	+	1.05957i
$894$		0			0
$895$	−15906.5	+	5789.51i	−0.594075	+	0.216226i
$896$	−492.258	−	413.054i	−0.0183540	−	0.0154008i
$897$		0			0
$898$	−29266.6	−	10652.2i	−1.08757	−	0.395844i
$899$	9951.47	+	17236.5i	0.369188	+	0.639453i
$900$		0			0
$901$	−7304.40	+	12651.6i	−0.270083	+	0.467798i
$902$	4030.35	−	3381.86i	0.148776	−	0.124838i
$903$		0			0
$904$	1381.55	−	7835.17i	0.0508294	−	0.288268i
$905$	−1093.85	+	6203.53i	−0.0401777	+	0.227859i
$906$		0			0
$907$	26603.8	−	22323.3i	0.973942	−	0.817235i	−0.00922222	−	0.999957i	$-0.502936\pi$
$907$	26603.8	−	22323.3i	0.973942	−	0.817235i	0.983164	+	0.182723i	$0.0584911\pi$
$908$	−1759.05	+	3046.76i	−0.0642908	+	0.111355i
$909$		0			0
$910$	643.582	+	1114.72i	0.0234445	+	0.0406071i
$911$	−16657.2	−	6062.74i	−0.605794	−	0.220491i	0.0208677	−	0.999782i	$-0.493357\pi$
$911$	−16657.2	−	6062.74i	−0.605794	−	0.220491i	−0.626662	+	0.779291i	$0.715579\pi$
$912$		0			0
$913$	11755.7	+	9864.17i	0.426129	+	0.357565i
$914$	3112.14	−	1132.73i	0.112626	−	0.0409927i
$915$		0			0
$916$	−1251.46	−	7097.36i	−0.0451411	−	0.256008i
$917$	−8759.94			−0.315462
$918$		0			0
$919$	35753.7			1.28336			0.641680	−	0.766973i	$-0.278238\pi$
$919$	35753.7			1.28336			0.641680	+	0.766973i	$0.278238\pi$
$920$	1758.77	+	9974.45i	0.0630269	+	0.357444i
$921$		0			0
$922$	6200.96	−	2256.96i	0.221494	−	0.0806173i
$923$	−13181.5	−	11060.6i	−0.470071	−	0.394437i
$924$		0			0
$925$	16982.7	+	6181.20i	0.603662	+	0.219715i
$926$	6827.00	+	11824.7i	0.242278	+	0.419637i
$927$		0			0
$928$	2565.43	−	4443.46i	0.0907484	−	0.157181i
$929$	182.467	−	153.108i	0.00644409	−	0.00540723i	−0.639560	−	0.768741i	$-0.720883\pi$
$929$	182.467	−	153.108i	0.00644409	−	0.00540723i	0.646004	+	0.763334i	$0.276439\pi$
$930$		0			0
$931$	6137.15	−	34805.5i	0.216044	−	1.22525i
$932$	−3261.92	+	18499.3i	−0.114644	+	0.650176i
$933$		0			0
$934$	−12212.2	+	10247.3i	−0.427833	+	0.358995i
$935$	−4863.26	+	8423.41i	−0.170102	+	0.294626i
$936$		0			0
$937$	−11740.1	−	20334.5i	−0.409321	−	0.708964i	0.585493	−	0.810677i	$-0.300901\pi$
$937$	−11740.1	−	20334.5i	−0.409321	−	0.708964i	−0.994814	+	0.101713i	$0.967568\pi$
$938$	3321.93	+	1209.08i	0.115634	+	0.0420874i
$939$		0			0
$940$	5589.58	+	4690.22i	0.193949	+	0.162743i
$941$	−48312.6	+	17584.4i	−1.67370	+	0.609175i	−0.992424	−	0.122856i	$-0.960795\pi$
$941$	−48312.6	+	17584.4i	−1.67370	+	0.609175i	−0.681271	+	0.732032i	$0.738572\pi$
$942$		0			0
$943$	5083.78	+	28831.6i	0.175558	+	0.995636i
$944$	−9376.95			−0.323299
$945$		0			0
$946$	−6315.11			−0.217042
$947$	−2367.31	−	13425.7i	−0.0812324	−	0.460692i	−0.998106	−	0.0615147i	$-0.980407\pi$
$947$	−2367.31	−	13425.7i	−0.0812324	−	0.460692i	0.916874	−	0.399177i	$-0.130704\pi$
$948$		0			0
$949$	4565.32	−	1661.64i	0.156161	−	0.0568379i
$950$	−12791.7	−	10733.5i	−0.436862	−	0.366571i
$951$		0			0
$952$	3226.80	+	1174.46i	0.109854	+	0.0399837i
$953$	19230.3	+	33307.9i	0.653653	+	1.13216i	0.982230	+	0.187683i	$0.0600978\pi$
$953$	19230.3	+	33307.9i	0.653653	+	1.13216i	−0.328577	+	0.944477i	$0.606569\pi$
$954$		0			0
$955$	−1905.73	+	3300.81i	−0.0645737	+	0.111845i
$956$	−9106.73	+	7641.45i	−0.308088	+	0.258517i
$957$		0			0
$958$	5369.66	−	30452.9i	0.181092	−	1.02702i
$959$	1395.42	−	7913.80i	0.0469868	−	0.266476i
$960$		0			0
$961$	−11017.8	+	9245.06i	−0.369838	+	0.310331i
$962$	−4367.58	+	7564.87i	−0.146379	+	0.253536i
$963$		0			0
$964$	12753.0	+	22088.9i	0.426086	+	0.738002i
$965$	29108.3	+	10594.6i	0.971016	+	0.353421i
$966$		0			0
$967$	7063.35	+	5926.85i	0.234893	+	0.197099i	0.752635	−	0.658438i	$-0.228783\pi$
$967$	7063.35	+	5926.85i	0.234893	+	0.197099i	−0.517741	+	0.855537i	$0.673227\pi$
$968$	−8057.17	+	2932.57i	−0.267528	+	0.0973722i
$969$		0			0
$970$	−4481.63	−	25416.6i	−0.148347	−	0.841316i
$971$	−23062.0			−0.762200			−0.381100	−	0.924534i	$-0.624455\pi$
$971$	−23062.0			−0.762200			−0.381100	+	0.924534i	$0.624455\pi$
$972$		0			0
$973$	−5127.27			−0.168934
$974$	5583.84	+	31667.6i	0.183694	+	1.04178i
$975$		0			0
$976$	−11926.9	+	4341.02i	−0.391157	+	0.142370i
$977$	−36514.6	−	30639.4i	−1.19571	−	1.00332i	−0.999742	−	0.0227057i	$-0.992772\pi$
$977$	−36514.6	−	30639.4i	−1.19571	−	1.00332i	−0.195964	−	0.980611i	$-0.562784\pi$
$978$		0			0
$979$	−9071.33	−	3301.70i	−0.296140	−	0.107786i
$980$	−4490.93	−	7778.51i	−0.146385	−	0.253546i
$981$		0			0
$982$	−3188.49	+	5522.63i	−0.103614	+	0.179465i
$983$	−33035.7	+	27720.3i	−1.07190	+	0.899430i	−0.995223	−	0.0976263i	$-0.968875\pi$
$983$	−33035.7	+	27720.3i	−1.07190	+	0.899430i	−0.0766755	+	0.997056i	$0.524431\pi$
$984$		0			0
$985$	−2104.88	+	11937.4i	−0.0680883	+	0.386148i
$986$	−4761.12	+	27001.7i	−0.153778	+	0.872118i
$987$		0			0
$988$	6182.72	−	5187.92i	0.199087	−	0.167054i
$989$	17570.3	−	30432.7i	0.564918	−	0.978466i
$990$		0			0
$991$	19166.5	+	33197.3i	0.614373	+	1.06412i	0.990494	+	0.137555i	$0.0439242\pi$
$991$	19166.5	+	33197.3i	0.614373	+	1.06412i	−0.376121	+	0.926570i	$0.622742\pi$
$992$	−3732.61	−	1358.56i	−0.119466	−	0.0434821i
$993$		0			0
$994$	−7294.69	−	6120.97i	−0.232770	−	0.195317i
$995$	−13057.7	+	4752.60i	−0.416036	+	0.151425i
$996$		0			0
$997$	−9495.94	−	53854.2i	−0.301645	−	1.71071i	−0.638893	−	0.769295i	$-0.720607\pi$
$997$	−9495.94	−	53854.2i	−0.301645	−	1.71071i	0.337249	−	0.941416i	$-0.390504\pi$
$998$	−30795.7			−0.976776
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.91.1		24
3.2	odd	2		54.4.e.a.13.3	✓	24
27.2	odd	18		54.4.e.a.25.3	yes	24
27.5	odd	18		1458.4.a.h.1.10		12
27.22	even	9		1458.4.a.e.1.3		12
27.25	even	9	inner	162.4.e.a.73.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.13.3	✓	24	3.2	odd	2
54.4.e.a.25.3	yes	24	27.2	odd	18
162.4.e.a.73.1		24	27.25	even	9	inner
162.4.e.a.91.1		24	1.1	even	1	trivial
1458.4.a.e.1.3		12	27.22	even	9
1458.4.a.h.1.10		12	27.5	odd	18

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.347296 - 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-5.41266 - 4.54176i) q^{5} +(-4.71753 - 1.71704i) q^{7} +(4.00000 + 6.92820i) q^{8} +O(q^{10})\)	\(q+(-0.347296 - 1.96962i) q^{2} +(-3.75877 + 1.36808i) q^{4} +(-5.41266 - 4.54176i) q^{5} +(-4.71753 - 1.71704i) q^{7} +(4.00000 + 6.92820i) q^{8} +(-7.06572 + 12.2382i) q^{10} +(-12.3335 + 10.3490i) q^{11} +(-3.15057 + 17.8677i) q^{13} +(-1.74353 + 9.88804i) q^{14} +(12.2567 - 10.2846i) q^{16} +(-42.7502 + 74.0455i) q^{17} +(55.6054 + 96.3114i) q^{19} +(26.5584 + 9.66648i) q^{20} +(24.6670 + 20.6981i) q^{22} +(-168.375 + 61.2834i) q^{23} +(-13.0367 - 73.9350i) q^{25} +36.2868 q^{26} +20.0812 q^{28} +(27.8427 + 157.904i) q^{29} +(116.644 - 42.4549i) q^{31} +(-24.5134 - 20.5692i) q^{32} +(160.688 + 58.4857i) q^{34} +(17.7360 + 30.7196i) q^{35} +(-120.363 + 208.475i) q^{37} +(170.385 - 142.970i) q^{38} +(9.81560 - 55.6670i) q^{40} +(28.3724 - 160.908i) q^{41} +(-150.236 + 126.063i) q^{43} +(32.2005 - 55.7729i) q^{44} +(179.181 + 310.350i) q^{46} +(242.602 + 88.2999i) q^{47} +(-243.446 - 204.276i) q^{49} +(-141.096 + 51.3547i) q^{50} +(-12.6023 - 71.4710i) q^{52} +170.862 q^{53} +113.760 q^{55} +(-6.97411 - 39.5522i) q^{56} +(301.340 - 109.679i) q^{58} +(-448.948 - 376.712i) q^{59} +(-745.428 - 271.314i) q^{61} +(-124.130 - 214.999i) q^{62} +(-32.0000 + 55.4256i) q^{64} +(98.2040 - 82.4029i) q^{65} +(61.1386 - 346.734i) q^{67} +(59.3879 - 336.806i) q^{68} +(54.3462 - 45.6019i) q^{70} +(-474.203 + 821.343i) q^{71} +(-133.887 - 231.898i) q^{73} +(452.416 + 164.666i) q^{74} +(-340.770 - 285.940i) q^{76} +(75.9534 - 27.6448i) q^{77} +(-191.813 - 1087.83i) q^{79} -113.052 q^{80} -326.780 q^{82} +(-165.513 - 938.668i) q^{83} +(567.689 - 206.622i) q^{85} +(300.471 + 252.125i) q^{86} +(-121.034 - 44.0529i) q^{88} +(299.794 + 519.258i) q^{89} +(45.5425 - 78.8820i) q^{91} +(549.041 - 460.700i) q^{92} +(89.6621 - 508.499i) q^{94} +(136.450 - 773.847i) q^{95} +(-1399.05 + 1173.94i) q^{97} +(-317.797 + 550.440i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Introduction

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