LMFDB - Embedded newform 81.3.f.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,3,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	81.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:	$2.20709014132$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	81.17
Dual form			81.3.f.a.62.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.898786 + 2.46939i) q^{2} +(-2.22591 - 1.86776i) q^{4} +(-6.15614 - 1.08549i) q^{5} +(-6.21846 + 5.21791i) q^{7} +(-2.49037 + 1.43782i) q^{8} +O(q^{10})$	\(q+(-0.898786 + 2.46939i) q^{2} +(-2.22591 - 1.86776i) q^{4} +(-6.15614 - 1.08549i) q^{5} +(-6.21846 + 5.21791i) q^{7} +(-2.49037 + 1.43782i) q^{8} +(8.21356 - 14.2263i) q^{10} +(7.99059 - 1.40896i) q^{11} +(-9.12402 + 3.32087i) q^{13} +(-7.29600 - 20.0456i) q^{14} +(-3.33052 - 18.8883i) q^{16} +(13.0143 + 7.51380i) q^{17} +(8.93226 + 15.4711i) q^{19} +(11.6756 + 13.9144i) q^{20} +(-3.70256 + 20.9983i) q^{22} +(-16.9268 + 20.1726i) q^{23} +(13.2275 + 4.81440i) q^{25} -25.5156i q^{26} +23.5875 q^{28} +(-5.18906 + 14.2568i) q^{29} +(25.0755 + 21.0408i) q^{31} +(38.3082 + 6.75478i) q^{32} +(-30.2516 + 25.3841i) q^{34} +(43.9457 - 25.3721i) q^{35} +(-15.8096 + 27.3831i) q^{37} +(-46.2325 + 8.15204i) q^{38} +(16.8918 - 6.14813i) q^{40} +(-5.65018 - 15.5238i) q^{41} +(-14.5559 - 82.5505i) q^{43} +(-20.4179 - 11.7883i) q^{44} +(-34.6005 - 59.9298i) q^{46} +(-8.46562 - 10.0889i) q^{47} +(2.93393 - 16.6391i) q^{49} +(-23.7773 + 28.3367i) q^{50} +(26.5118 + 9.64952i) q^{52} +25.7140i q^{53} -50.7206 q^{55} +(7.98389 - 21.9356i) q^{56} +(-30.5419 - 25.6277i) q^{58} +(22.3660 + 3.94373i) q^{59} +(26.1131 - 21.9115i) q^{61} +(-74.4955 + 43.0100i) q^{62} +(-12.7517 + 22.0867i) q^{64} +(59.7736 - 10.5397i) q^{65} +(-7.61567 + 2.77188i) q^{67} +(-14.9346 - 41.0326i) q^{68} +(23.1558 + 131.323i) q^{70} +(-35.7557 - 20.6436i) q^{71} +(40.4046 + 69.9827i) q^{73} +(-53.4101 - 63.6517i) q^{74} +(9.01395 - 51.1206i) q^{76} +(-42.3374 + 50.4557i) q^{77} +(25.9652 + 9.45057i) q^{79} +119.894i q^{80} +43.4126 q^{82} +(6.01607 - 16.5290i) q^{83} +(-71.9616 - 60.3830i) q^{85} +(216.932 + 38.2510i) q^{86} +(-17.8737 + 14.9978i) q^{88} +(-24.4986 + 14.1443i) q^{89} +(39.4094 - 68.2590i) q^{91} +(75.3552 - 13.2871i) q^{92} +(32.5223 - 11.8372i) q^{94} +(-38.1945 - 104.938i) q^{95} +(29.2825 + 166.069i) q^{97} +(38.4516 + 22.2000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) $ 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8	$ 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29} + 39 q^{31} + 360 q^{32} + 54 q^{34} + 252 q^{35} - 3 q^{37} + 84 q^{38} - 33 q^{40} - 228 q^{41} - 96 q^{43} - 639 q^{44} - 3 q^{46} - 399 q^{47} - 78 q^{49} - 303 q^{50} - 9 q^{52} - 12 q^{55} + 393 q^{56} + 129 q^{58} + 474 q^{59} + 138 q^{61} + 900 q^{62} - 51 q^{64} + 411 q^{65} + 354 q^{67} - 99 q^{68} + 489 q^{70} - 315 q^{71} - 66 q^{73} - 321 q^{74} + 258 q^{76} - 201 q^{77} + 30 q^{79} - 12 q^{82} + 33 q^{83} - 261 q^{85} + 258 q^{86} - 642 q^{88} - 72 q^{89} + 96 q^{91} + 3 q^{92} - 861 q^{94} - 681 q^{95} - 582 q^{97} - 882 q^{98}+O(q^{100}) $ 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.898786	+	2.46939i	−0.449393	+	1.23470i	0.483755	+	0.875203i	$0.339273\pi$
$2$	−0.898786	+	2.46939i	−0.449393	+	1.23470i	−0.933148	+	0.359493i	$0.882950\pi$
$3$		0			0
$3$		0			0
$4$	−2.22591	−	1.86776i	−0.556477	−	0.466940i
$5$	−6.15614	−	1.08549i	−1.23123	−	0.217099i	−0.480076	−	0.877227i	$-0.659391\pi$
$5$	−6.15614	−	1.08549i	−1.23123	−	0.217099i	−0.751153	+	0.660128i	$0.770502\pi$
$6$		0			0
$7$	−6.21846	+	5.21791i	−0.888352	+	0.745415i	−0.967879	−	0.251417i	$-0.919103\pi$
$7$	−6.21846	+	5.21791i	−0.888352	+	0.745415i	0.0795272	+	0.996833i	$0.474659\pi$
$8$	−2.49037	+	1.43782i	−0.311297	+	0.179727i
$9$		0			0
$10$	8.21356	−	14.2263i	0.821356	−	1.42263i
$11$	7.99059	−	1.40896i	0.726417	−	0.128087i	0.201802	−	0.979426i	$-0.435320\pi$
$11$	7.99059	−	1.40896i	0.726417	−	0.128087i	0.524615	+	0.851339i	$0.324209\pi$
$12$		0			0
$13$	−9.12402	+	3.32087i	−0.701848	+	0.255452i	−0.668200	−	0.743982i	$-0.732935\pi$
$13$	−9.12402	+	3.32087i	−0.701848	+	0.255452i	−0.0336483	+	0.999434i	$0.510713\pi$
$14$	−7.29600	−	20.0456i	−0.521143	−	1.43183i
$15$		0			0
$16$	−3.33052	−	18.8883i	−0.208157	−	1.18052i
$17$	13.0143	+	7.51380i	0.765546	+	0.441988i	0.831284	−	0.555849i	$-0.187607\pi$
$17$	13.0143	+	7.51380i	0.765546	+	0.441988i	−0.0657372	+	0.997837i	$0.520940\pi$
$18$		0			0
$19$	8.93226	+	15.4711i	0.470119	+	0.814270i	0.999416	−	0.0341664i	$-0.0108776\pi$
$19$	8.93226	+	15.4711i	0.470119	+	0.814270i	−0.529297	+	0.848437i	$0.677544\pi$
$20$	11.6756	+	13.9144i	0.583778	+	0.695720i
$21$		0			0
$22$	−3.70256	+	20.9983i	−0.168298	+	0.954466i
$23$	−16.9268	+	20.1726i	−0.735949	+	0.877070i	−0.996076	−	0.0885045i	$-0.971791\pi$
$23$	−16.9268	+	20.1726i	−0.735949	+	0.877070i	0.260127	+	0.965575i	$0.416236\pi$
$24$		0			0
$25$	13.2275	+	4.81440i	0.529099	+	0.192576i
$26$		−	25.5156i		−	0.981367i
$27$		0			0
$28$	23.5875			0.842411
$29$	−5.18906	+	14.2568i	−0.178933	+	0.491615i	−0.996440	−	0.0843038i	$-0.973133\pi$
$29$	−5.18906	+	14.2568i	−0.178933	+	0.491615i	0.817507	+	0.575919i	$0.195356\pi$
$30$		0			0
$31$	25.0755	+	21.0408i	0.808886	+	0.678736i	0.950342	−	0.311209i	$-0.100734\pi$
$31$	25.0755	+	21.0408i	0.808886	+	0.678736i	−0.141456	+	0.989945i	$0.545178\pi$
$32$	38.3082	+	6.75478i	1.19713	+	0.211087i
$33$		0			0
$34$	−30.2516	+	25.3841i	−0.889752	+	0.746591i
$35$	43.9457	−	25.3721i	1.25559	−	0.724917i
$36$		0			0
$37$	−15.8096	+	27.3831i	−0.427287	+	0.740083i	−0.996631	−	0.0820163i	$-0.973864\pi$
$37$	−15.8096	+	27.3831i	−0.427287	+	0.740083i	0.569344	+	0.822100i	$0.307197\pi$
$38$	−46.2325	+	8.15204i	−1.21664	+	0.214527i
$39$		0			0
$40$	16.8918	−	6.14813i	0.422296	−	0.153703i
$41$	−5.65018	−	15.5238i	−0.137809	−	0.378628i	0.851520	−	0.524321i	$-0.175681\pi$
$41$	−5.65018	−	15.5238i	−0.137809	−	0.378628i	−0.989330	+	0.145693i	$0.953459\pi$
$42$		0			0
$43$	−14.5559	−	82.5505i	−0.338509	−	1.91978i	−0.389385	−	0.921075i	$-0.627312\pi$
$43$	−14.5559	−	82.5505i	−0.338509	−	1.91978i	0.0508761	−	0.998705i	$-0.483799\pi$
$44$	−20.4179	−	11.7883i	−0.464044	−	0.267916i
$45$		0			0
$46$	−34.6005	−	59.9298i	−0.752185	−	1.30282i
$47$	−8.46562	−	10.0889i	−0.180120	−	0.214658i	0.668429	−	0.743776i	$-0.266967\pi$
$47$	−8.46562	−	10.0889i	−0.180120	−	0.214658i	−0.848548	+	0.529118i	$0.822523\pi$
$48$		0			0
$49$	2.93393	−	16.6391i	0.0598761	−	0.339574i
$50$	−23.7773	+	28.3367i	−0.475546	+	0.566734i
$51$		0			0
$52$	26.5118	+	9.64952i	0.509843	+	0.185568i
$53$			25.7140i			0.485169i	0.970130	+	0.242585i	$0.0779952\pi$
$53$			25.7140i			0.485169i	−0.970130	+	0.242585i	$0.922005\pi$
$54$		0			0
$55$	−50.7206			−0.922193
$56$	7.98389	−	21.9356i	0.142569	−	0.391706i
$57$		0			0
$58$	−30.5419	−	25.6277i	−0.526584	−	0.441856i
$59$	22.3660	+	3.94373i	0.379085	+	0.0668428i	0.359944	−	0.932974i	$-0.382796\pi$
$59$	22.3660	+	3.94373i	0.379085	+	0.0668428i	0.0191407	+	0.999817i	$0.493907\pi$
$60$		0			0
$61$	26.1131	−	21.9115i	0.428084	−	0.359205i	−0.403144	−	0.915137i	$-0.632083\pi$
$61$	26.1131	−	21.9115i	0.428084	−	0.359205i	0.831228	+	0.555931i	$0.187638\pi$
$62$	−74.4955	+	43.0100i	−1.20154	+	0.693710i
$63$		0			0
$64$	−12.7517	+	22.0867i	−0.199246	+	0.345104i
$65$	59.7736	−	10.5397i	0.919593	−	0.162149i
$66$		0			0
$67$	−7.61567	+	2.77188i	−0.113667	+	0.0413713i	−0.398227	−	0.917287i	$-0.630375\pi$
$67$	−7.61567	+	2.77188i	−0.113667	+	0.0413713i	0.284561	+	0.958658i	$0.408152\pi$
$68$	−14.9346	−	41.0326i	−0.219627	−	0.603420i
$69$		0			0
$70$	23.1558	+	131.323i	0.330798	+	1.87605i
$71$	−35.7557	−	20.6436i	−0.503601	−	0.290754i	0.226598	−	0.973988i	$-0.427240\pi$
$71$	−35.7557	−	20.6436i	−0.503601	−	0.290754i	−0.730199	+	0.683234i	$0.760573\pi$
$72$		0			0
$73$	40.4046	+	69.9827i	0.553487	+	0.958668i	0.998020	+	0.0629050i	$0.0200365\pi$
$73$	40.4046	+	69.9827i	0.553487	+	0.958668i	−0.444532	+	0.895763i	$0.646630\pi$
$74$	−53.4101	−	63.6517i	−0.721758	−	0.860158i
$75$		0			0
$76$	9.01395	−	51.1206i	0.118605	−	0.672640i
$77$	−42.3374	+	50.4557i	−0.549836	+	0.655269i
$78$		0			0
$79$	25.9652	+	9.45057i	0.328674	+	0.119627i	0.501086	−	0.865397i	$-0.332934\pi$
$79$	25.9652	+	9.45057i	0.328674	+	0.119627i	−0.172412	+	0.985025i	$0.555156\pi$
$80$			119.894i			1.49868i
$81$		0			0
$82$	43.4126			0.529421
$83$	6.01607	−	16.5290i	0.0724827	−	0.199145i	−0.898161	−	0.439667i	$-0.855096\pi$
$83$	6.01607	−	16.5290i	0.0724827	−	0.199145i	0.970644	+	0.240522i	$0.0773187\pi$
$84$		0			0
$85$	−71.9616	−	60.3830i	−0.846607	−	0.710388i
$86$	216.932	+	38.2510i	2.52247	+	0.444779i
$87$		0			0
$88$	−17.8737	+	14.9978i	−0.203111	+	0.170430i
$89$	−24.4986	+	14.1443i	−0.275265	+	0.158924i	−0.631278	−	0.775557i	$-0.717469\pi$
$89$	−24.4986	+	14.1443i	−0.275265	+	0.158924i	0.356013	+	0.934481i	$0.384136\pi$
$90$		0			0
$91$	39.4094	−	68.2590i	0.433070	−	0.750099i
$92$	75.3552	−	13.2871i	0.819078	−	0.144426i
$93$		0			0
$94$	32.5223	−	11.8372i	0.345982	−	0.125927i
$95$	−38.1945	−	104.938i	−0.402047	−	1.10461i
$96$		0			0
$97$	29.2825	+	166.069i	0.301881	+	1.71205i	0.637834	+	0.770174i	$0.279831\pi$
$97$	29.2825	+	166.069i	0.301881	+	1.71205i	−0.335953	+	0.941879i	$0.609058\pi$
$98$	38.4516	+	22.2000i	0.392363	+	0.226531i
$99$		0			0
$100$	−20.4510	−	35.4221i	−0.204510	−	0.354221i
$101$	44.8847	+	53.4915i	0.444403	+	0.529619i	0.941020	−	0.338351i	$-0.109869\pi$
$101$	44.8847	+	53.4915i	0.444403	+	0.529619i	−0.496617	+	0.867970i	$0.665425\pi$
$102$		0			0
$103$	12.1315	−	68.8014i	0.117782	−	0.667974i	−0.867553	−	0.497344i	$-0.834309\pi$
$103$	12.1315	−	68.8014i	0.117782	−	0.667974i	0.985335	−	0.170630i	$-0.0545803\pi$
$104$	17.9474	−	21.3889i	0.172571	−	0.205662i
$105$		0			0
$106$	−63.4979	−	23.1113i	−0.599037	−	0.218031i
$107$		−	121.432i		−	1.13488i	−0.823416	−	0.567438i	$-0.807935\pi$
$107$		−	121.432i		−	1.13488i	0.823416	−	0.567438i	$-0.192065\pi$
$108$		0			0
$109$	−119.633			−1.09755			−0.548777	−	0.835969i	$-0.684907\pi$
$109$	−119.633			−1.09755			−0.548777	+	0.835969i	$0.684907\pi$
$110$	45.5870	−	125.249i	0.414427	−	1.13863i
$111$		0			0
$112$	119.268	+	100.078i	1.06489	+	0.893552i
$113$	−122.474	−	21.5955i	−1.08384	−	0.191111i	−0.396929	−	0.917849i	$-0.629924\pi$
$113$	−122.474	−	21.5955i	−1.08384	−	0.191111i	−0.686914	+	0.726738i	$0.741035\pi$
$114$		0			0
$115$	126.101	−	105.811i	1.09653	−	0.920100i
$116$	38.1787	−	22.0425i	0.329127	−	0.190021i
$117$		0			0
$118$	−29.8408	+	51.6859i	−0.252889	+	0.438016i
$119$	−120.135	+	21.1831i	−1.00954	+	0.178009i
$120$		0			0
$121$	−51.8384	+	18.8676i	−0.428417	+	0.155931i
$122$	30.6381	+	84.1774i	0.251132	+	0.689979i
$123$		0			0
$124$	−16.5165	−	93.6699i	−0.133198	−	0.755402i
$125$	59.1363	+	34.1424i	0.473091	+	0.273139i
$126$		0			0
$127$	58.7300	+	101.723i	0.462441	+	0.800971i	0.999082	−	0.0428396i	$-0.0136404\pi$
$127$	58.7300	+	101.723i	0.462441	+	0.800971i	−0.536641	+	0.843811i	$0.680307\pi$
$128$	56.9361	+	67.8538i	0.444814	+	0.530108i
$129$		0			0
$130$	−27.6970	+	157.077i	−0.213054	+	1.20829i
$131$	−3.02933	+	3.61022i	−0.0231247	+	0.0275589i	−0.777483	−	0.628904i	$-0.783504\pi$
$131$	−3.02933	+	3.61022i	−0.0231247	+	0.0275589i	0.754358	+	0.656463i	$0.227948\pi$
$132$		0			0
$133$	−136.272	−	49.5989i	−1.02460	−	0.372924i
$134$		−	21.2974i		−	0.158936i
$135$		0			0
$136$	−43.2139			−0.317749
$137$	−75.5147	+	207.475i	−0.551202	+	1.51442i	0.280869	+	0.959746i	$0.409377\pi$
$137$	−75.5147	+	207.475i	−0.551202	+	1.51442i	−0.832071	+	0.554669i	$0.812845\pi$
$138$		0			0
$139$	−27.3980	−	22.9896i	−0.197108	−	0.165393i	0.538892	−	0.842375i	$-0.318843\pi$
$139$	−27.3980	−	22.9896i	−0.197108	−	0.165393i	−0.736000	+	0.676982i	$0.763288\pi$
$140$	−145.208	−	25.6041i	−1.03720	−	0.182886i
$141$		0			0
$142$	83.1137	−	69.7407i	0.585308	−	0.491132i
$143$	−68.2274	+	39.3911i	−0.477114	+	0.275462i
$144$		0			0
$145$	47.4203	−	82.1344i	0.327037	−	0.566444i
$146$	−209.130	+	36.8753i	−1.43240	+	0.252570i
$147$		0			0
$148$	86.3358	−	31.4237i	0.583350	−	0.212322i
$149$	57.3691	+	157.620i	0.385028	+	1.05786i	0.969211	+	0.246233i	$0.0791929\pi$
$149$	57.3691	+	157.620i	0.385028	+	1.05786i	−0.584183	+	0.811622i	$0.698585\pi$
$150$		0			0
$151$	−14.5375	−	82.4463i	−0.0962748	−	0.546002i	−0.994349	−	0.106158i	$-0.966145\pi$
$151$	−14.5375	−	82.4463i	−0.0962748	−	0.546002i	0.898074	−	0.439844i	$-0.144966\pi$
$152$	−44.4893	−	25.6859i	−0.292693	−	0.168986i
$153$		0			0
$154$	−86.5428	−	149.896i	−0.561966	−	0.973354i
$155$	−131.528	−	156.750i	−0.848571	−	1.01129i
$156$		0			0
$157$	−12.9271	+	73.3133i	−0.0823383	+	0.466963i	0.915561	+	0.402179i	$0.131747\pi$
$157$	−12.9271	+	73.3133i	−0.0823383	+	0.466963i	−0.997899	+	0.0647844i	$0.979364\pi$
$158$	−46.6744	+	55.6243i	−0.295407	+	0.352053i
$159$		0			0
$160$	−228.499	−	83.1667i	−1.42812	−	0.519792i
$161$		−	213.765i		−	1.32773i
$162$		0			0
$163$	254.830			1.56337			0.781687	−	0.623670i	$-0.214359\pi$
$163$	254.830			1.56337			0.781687	+	0.623670i	$0.214359\pi$
$164$	−16.4178	+	45.1076i	−0.100109	+	0.275047i
$165$		0			0
$166$	35.4095	+	29.7121i	0.213310	+	0.178988i
$167$	156.190	+	27.5405i	0.935269	+	0.164913i	0.620457	−	0.784241i	$-0.286947\pi$
$167$	156.190	+	27.5405i	0.935269	+	0.164913i	0.314813	+	0.949154i	$0.398058\pi$
$168$		0			0
$169$	−57.2419	+	48.0317i	−0.338710	+	0.284211i
$170$	213.787	−	123.430i	1.25757	−	0.726060i
$171$		0			0
$172$	−121.784	+	210.937i	−0.708049	+	1.22638i
$173$	293.553	−	51.7613i	1.69684	−	0.299198i	0.760249	−	0.649632i	$-0.225077\pi$
$173$	293.553	−	51.7613i	1.69684	−	0.299198i	0.936587	+	0.350434i	$0.113966\pi$
$174$		0			0
$175$	−107.376	+	39.0815i	−0.613575	+	0.223323i
$176$	−53.2256	−	146.236i	−0.302418	−	0.830887i
$177$		0			0
$178$	−12.9088	−	73.2093i	−0.0725212	−	0.411288i
$179$	−25.3997	−	14.6645i	−0.141898	−	0.0819248i	0.427370	−	0.904077i	$-0.359440\pi$
$179$	−25.3997	−	14.6645i	−0.141898	−	0.0819248i	−0.569268	+	0.822152i	$0.692773\pi$
$180$		0			0
$181$	−41.7019	−	72.2299i	−0.230397	−	0.399060i	0.727528	−	0.686078i	$-0.240669\pi$
$181$	−41.7019	−	72.2299i	−0.230397	−	0.399060i	−0.957925	+	0.287018i	$0.907336\pi$
$182$	133.138	+	158.667i	0.731526	+	0.871799i
$183$		0			0
$184$	13.1496	−	74.5750i	0.0714652	−	0.405299i
$185$	127.050	−	151.413i	0.686759	−	0.818448i
$186$		0			0
$187$	114.578	+	41.7031i	0.612719	+	0.223011i
$188$			38.2688i			0.203557i
$189$		0			0
$190$	293.463			1.54454
$191$	−53.6797	+	147.484i	−0.281046	+	0.772166i	0.716193	+	0.697902i	$0.245883\pi$
$191$	−53.6797	+	147.484i	−0.281046	+	0.772166i	−0.997239	+	0.0742641i	$0.976339\pi$
$192$		0			0
$193$	−31.7673	−	26.6559i	−0.164598	−	0.138114i	0.556769	−	0.830668i	$-0.312041\pi$
$193$	−31.7673	−	26.6559i	−0.164598	−	0.138114i	−0.721366	+	0.692554i	$0.756485\pi$
$194$	−436.409	−	76.9506i	−2.24953	−	0.396653i
$195$		0			0
$196$	−37.6086	+	31.5573i	−0.191880	+	0.161007i
$197$	182.437	−	105.330i	0.926074	−	0.534669i	0.0405063	−	0.999179i	$-0.487103\pi$
$197$	182.437	−	105.330i	0.926074	−	0.534669i	0.885568	+	0.464510i	$0.153770\pi$
$198$		0			0
$199$	87.7654	−	152.014i	0.441032	−	0.763890i	−0.556734	−	0.830691i	$-0.687946\pi$
$199$	87.7654	−	152.014i	0.441032	−	0.763890i	0.997766	+	0.0668004i	$0.0212791\pi$
$200$	−39.8636	+	7.02902i	−0.199318	+	0.0351451i
$201$		0			0
$202$	−172.433	+	62.7606i	−0.853631	+	0.310696i
$203$	−42.1229	−	115.732i	−0.207502	−	0.570107i
$204$		0			0
$205$	17.9324	+	101.700i	0.0874751	+	0.496096i
$206$	158.994	+	91.7952i	0.771815	+	0.445608i
$207$		0			0
$208$	93.1133	+	161.277i	0.447660	+	0.775370i
$209$	93.1722	+	111.038i	0.445800	+	0.531284i
$210$		0			0
$211$	−45.2968	+	256.891i	−0.214677	+	1.21749i	0.666789	+	0.745246i	$0.267668\pi$
$211$	−45.2968	+	256.891i	−0.214677	+	1.21749i	−0.881466	+	0.472247i	$0.843443\pi$
$212$	48.0275	−	57.2369i	0.226545	−	0.269985i
$213$		0			0
$214$	299.862	+	109.141i	1.40123	+	0.510005i
$215$			523.993i			2.43718i
$216$		0			0
$217$	−265.720			−1.22452
$218$	107.525	−	295.422i	0.493233	−	1.35515i
$219$		0			0
$220$	112.899	+	94.7339i	0.513179	+	0.430609i
$221$	−143.695	−	25.3373i	−0.650204	−	0.114648i
$222$		0			0
$223$	−298.157	+	250.184i	−1.33703	+	1.12190i	−0.354650	+	0.934999i	$0.615400\pi$
$223$	−298.157	+	250.184i	−1.33703	+	1.12190i	−0.982379	+	0.186901i	$0.940156\pi$
$224$	−273.464	+	157.885i	−1.22082	+	0.704842i
$225$		0			0
$226$	163.406	−	283.027i	0.723035	−	1.25233i
$227$	343.139	−	60.5046i	1.51162	−	0.266540i	0.644489	−	0.764614i	$-0.277070\pi$
$227$	343.139	−	60.5046i	1.51162	−	0.266540i	0.867135	+	0.498074i	$0.165959\pi$
$228$		0			0
$229$	342.540	−	124.675i	1.49581	−	0.544430i	0.540838	−	0.841127i	$-0.318107\pi$
$229$	342.540	−	124.675i	1.49581	−	0.544430i	0.954972	+	0.296696i	$0.0958849\pi$
$230$	147.952	+	406.495i	0.643270	+	1.76737i
$231$		0			0
$232$	−7.57603	−	42.9658i	−0.0326553	−	0.185197i
$233$	−164.260	−	94.8353i	−0.704976	−	0.407018i	0.104222	−	0.994554i	$-0.466765\pi$
$233$	−164.260	−	94.8353i	−0.704976	−	0.407018i	−0.809198	+	0.587536i	$0.800098\pi$
$234$		0			0
$235$	41.1641	+	71.2983i	0.175166	+	0.303397i
$236$	−42.4187	−	50.5527i	−0.179740	−	0.214206i
$237$		0			0
$238$	55.6664	−	315.700i	0.233893	−	1.32647i
$239$	196.756	−	234.485i	0.823249	−	0.981110i	−0.176746	−	0.984256i	$-0.556557\pi$
$239$	196.756	−	234.485i	0.823249	−	0.981110i	0.999995	+	0.00314661i	$0.00100160\pi$
$240$		0			0
$241$	277.120	+	100.864i	1.14988	+	0.418521i	0.845471	−	0.534021i	$-0.179320\pi$
$241$	277.120	+	100.864i	1.14988	+	0.418521i	0.304406	+	0.952542i	$0.401542\pi$
$242$		−	144.967i		−	0.599039i
$243$		0			0
$244$	−99.0509			−0.405946
$245$	−36.1234	+	99.2481i	−0.147442	+	0.405094i
$246$		0			0
$247$	−132.876	−	111.496i	−0.537959	−	0.451401i
$248$	−92.7002	−	16.3455i	−0.373791	−	0.0659094i
$249$		0			0
$250$	−137.462	+	115.344i	−0.549847	+	0.461377i
$251$	−158.404	+	91.4547i	−0.631092	+	0.364361i	−0.781175	−	0.624312i	$-0.785379\pi$
$251$	−158.404	+	91.4547i	−0.631092	+	0.364361i	0.150083	+	0.988673i	$0.452046\pi$
$252$		0			0
$253$	−106.833	+	185.040i	−0.422265	+	0.731384i
$254$	−303.980	+	53.6000i	−1.19677	+	0.211023i
$255$		0			0
$256$	−314.593	+	114.502i	−1.22888	+	0.447275i
$257$	91.7859	+	252.180i	0.357144	+	0.981244i	0.980016	+	0.198920i	$0.0637435\pi$
$257$	91.7859	+	252.180i	0.357144	+	0.981244i	−0.622872	+	0.782324i	$0.714034\pi$
$258$		0			0
$259$	−44.5708	−	252.774i	−0.172088	−	0.975961i
$260$	−152.736	−	88.1822i	−0.587447	−	0.339162i
$261$		0			0
$262$	−6.19233	−	10.7254i	−0.0236348	−	0.0409368i
$263$	−226.246	−	269.629i	−0.860250	−	1.02521i	−0.999390	−	0.0349337i	$-0.988878\pi$
$263$	−226.246	−	269.629i	−0.860250	−	1.02521i	0.139139	−	0.990273i	$-0.455566\pi$
$264$		0			0
$265$	27.9123	−	158.299i	0.105330	−	0.597354i
$266$	244.958	−	291.930i	0.920896	−	1.09748i
$267$		0			0
$268$	22.1290	+	8.05429i	0.0825708	+	0.0300533i
$269$		−	164.243i		−	0.610570i	−0.952261	−	0.305285i	$-0.901248\pi$
$269$		−	164.243i		−	0.610570i	0.952261	−	0.305285i	$-0.0987518\pi$
$270$		0			0
$271$	−128.850			−0.475462			−0.237731	−	0.971331i	$-0.576404\pi$
$271$	−128.850			−0.475462			−0.237731	+	0.971331i	$0.576404\pi$
$272$	98.5786	−	270.843i	0.362421	−	0.995745i
$273$		0			0
$274$	−444.466	−	372.951i	−1.62214	−	1.36113i
$275$	112.479	+	19.8330i	0.409013	+	0.0721200i
$276$		0			0
$277$	115.074	−	96.5583i	0.415428	−	0.348586i	−0.410992	−	0.911639i	$-0.634818\pi$
$277$	115.074	−	96.5583i	0.415428	−	0.348586i	0.826421	+	0.563053i	$0.190373\pi$
$278$	81.3953	−	46.9936i	0.292789	−	0.169042i
$279$		0			0
$280$	−72.9609	+	126.372i	−0.260575	+	0.451328i
$281$	−453.995	+	80.0516i	−1.61564	+	0.284881i	−0.907140	−	0.420828i	$-0.861739\pi$
$281$	−453.995	+	80.0516i	−1.61564	+	0.284881i	−0.708501	+	0.705710i	$0.750628\pi$
$282$		0			0
$283$	64.7049	−	23.5506i	0.228639	−	0.0832178i	−0.225160	−	0.974322i	$-0.572291\pi$
$283$	64.7049	−	23.5506i	0.228639	−	0.0832178i	0.453799	+	0.891104i	$0.350068\pi$
$284$	41.0317	+	112.734i	0.144478	+	0.396949i
$285$		0			0
$286$	−35.9503	−	203.884i	−0.125700	−	0.712882i
$287$	116.137	+	67.0517i	0.404658	+	0.233630i
$288$		0			0
$289$	−31.5856	−	54.7078i	−0.109293	−	0.189300i
$290$	160.201	+	190.921i	0.552419	+	0.658347i
$291$		0			0
$292$	40.7741	−	231.241i	0.139637	−	0.791922i
$293$	−328.314	+	391.270i	−1.12053	+	1.33539i	−0.184755	+	0.982785i	$0.559149\pi$
$293$	−328.314	+	391.270i	−1.12053	+	1.33539i	−0.935772	+	0.352607i	$0.885295\pi$
$294$		0			0
$295$	−133.407	−	48.5563i	−0.452228	−	0.164598i
$296$		−	90.9255i		−	0.307181i
$297$		0			0
$298$	−440.789			−1.47916
$299$	87.4501	−	240.267i	0.292475	−	0.803569i
$300$		0			0
$301$	521.256	+	437.386i	1.73175	+	1.45311i
$302$	216.658	+	38.2027i	0.717412	+	0.126499i
$303$		0			0
$304$	262.474	−	220.242i	0.863402	−	0.724480i
$305$	−184.541	+	106.545i	−0.605053	+	0.349327i
$306$		0			0
$307$	−26.3017	+	45.5559i	−0.0856734	+	0.148391i	−0.905678	−	0.423966i	$-0.860637\pi$
$307$	−26.3017	+	45.5559i	−0.0856734	+	0.148391i	0.820005	+	0.572357i	$0.193971\pi$
$308$	188.478	−	33.2338i	0.611942	−	0.107902i
$309$		0			0
$310$	505.292	−	183.911i	1.62997	−	0.593262i
$311$	121.357	+	333.427i	0.390217	+	1.07211i	0.966903	+	0.255146i	$0.0821234\pi$
$311$	121.357	+	333.427i	0.390217	+	1.07211i	−0.576686	+	0.816966i	$0.695654\pi$
$312$		0			0
$313$	29.2161	+	165.693i	0.0933421	+	0.529369i	0.995243	+	0.0974258i	$0.0310609\pi$
$313$	29.2161	+	165.693i	0.0933421	+	0.529369i	−0.901901	+	0.431943i	$0.857828\pi$
$314$	−169.421	−	97.8150i	−0.539556	−	0.311513i
$315$		0			0
$316$	−40.1448	−	69.5329i	−0.127041	−	0.220041i
$317$	−327.814	−	390.674i	−1.03411	−	1.23241i	−0.972157	−	0.234330i	$-0.924710\pi$
$317$	−327.814	−	390.674i	−1.03411	−	1.23241i	−0.0619572	−	0.998079i	$-0.519734\pi$
$318$		0			0
$319$	−21.3764	+	121.232i	−0.0670107	+	0.380037i
$320$	102.476	−	122.127i	0.320239	−	0.381646i
$321$		0			0
$322$	527.870	+	192.129i	1.63935	+	0.596674i
$323$			268.461i			0.831149i
$324$		0			0
$325$	−136.676			−0.420541
$326$	−229.038	+	629.276i	−0.702569	+	1.93029i
$327$		0			0
$328$	36.3914	+	30.5360i	0.110949	+	0.0930976i
$329$	105.286	+	18.5648i	0.320019	+	0.0564280i
$330$		0			0
$331$	−259.951	+	218.125i	−0.785350	+	0.658987i	−0.944590	−	0.328253i	$-0.893540\pi$
$331$	−259.951	+	218.125i	−0.785350	+	0.658987i	0.159240	+	0.987240i	$0.449096\pi$
$332$	−44.2634	+	25.5555i	−0.133324	+	0.0769744i
$333$		0			0
$334$	−208.390	+	360.941i	−0.623921	+	1.08066i
$335$	49.8920	−	8.79731i	0.148931	−	0.0262606i
$336$		0			0
$337$	64.1227	−	23.3388i	0.190275	−	0.0692545i	−0.245125	−	0.969491i	$-0.578829\pi$
$337$	64.1227	−	23.3388i	0.190275	−	0.0692545i	0.435400	+	0.900237i	$0.356607\pi$
$338$	−67.1609	−	184.523i	−0.198701	−	0.545926i
$339$		0			0
$340$	47.3991	+	268.814i	0.139409	+	0.790629i
$341$	230.013	+	132.798i	0.674526	+	0.389438i
$342$		0			0
$343$	−130.305	−	225.695i	−0.379897	−	0.658002i
$344$	154.942	+	184.653i	0.450414	+	0.536782i
$345$		0			0
$346$	−136.022	+	771.419i	−0.393127	+	2.22954i
$347$	111.265	−	132.600i	0.320648	−	0.382134i	−0.581510	−	0.813539i	$-0.697538\pi$
$347$	111.265	−	132.600i	0.320648	−	0.382134i	0.902158	+	0.431406i	$0.141982\pi$
$348$		0			0
$349$	−431.866	−	157.186i	−1.23744	−	0.450390i	−0.361299	−	0.932450i	$-0.617667\pi$
$349$	−431.866	−	157.186i	−1.23744	−	0.450390i	−0.876138	+	0.482060i	$0.839889\pi$
$350$		−	300.278i		−	0.857939i
$351$		0			0
$352$	315.623			0.896655
$353$	137.578	−	377.991i	0.389738	−	1.07080i	−0.577381	−	0.816475i	$-0.695925\pi$
$353$	137.578	−	377.991i	0.389738	−	1.07080i	0.967119	−	0.254322i	$-0.0818524\pi$
$354$		0			0
$355$	197.709	+	165.897i	0.556926	+	0.467316i
$356$	80.9497	+	14.2736i	0.227387	+	0.0400944i
$357$		0			0
$358$	59.0414	−	49.5416i	0.164920	−	0.138384i
$359$	197.249	−	113.882i	0.549439	−	0.317219i	−0.199457	−	0.979907i	$-0.563918\pi$
$359$	197.249	−	113.882i	0.549439	−	0.317219i	0.748896	+	0.662688i	$0.230584\pi$
$360$		0			0
$361$	20.9294	−	36.2507i	0.0579761	−	0.100418i
$362$	215.845	−	38.0593i	0.596257	−	0.105136i
$363$		0			0
$364$	−215.213	+	78.3312i	−0.591245	+	0.215195i
$365$	−172.770	−	474.683i	−0.473343	−	1.30050i
$366$		0			0
$367$	−40.8884	−	231.890i	−0.111413	−	0.631852i	−0.988464	−	0.151456i	$-0.951604\pi$
$367$	−40.8884	−	231.890i	−0.111413	−	0.631852i	0.877052	−	0.480396i	$-0.159507\pi$
$368$	437.401	+	252.534i	1.18859	+	0.686233i
$369$		0			0
$370$	259.707	+	449.825i	0.701910	+	1.21574i
$371$	−134.173	−	159.901i	−0.361653	−	0.431001i
$372$		0			0
$373$	113.349	−	642.835i	0.303885	−	1.72342i	−0.324822	−	0.945775i	$-0.605304\pi$
$373$	113.349	−	642.835i	0.303885	−	1.72342i	0.628707	−	0.777642i	$-0.283585\pi$
$374$	−205.963	+	245.457i	−0.550703	+	0.656302i
$375$		0			0
$376$	35.5886	+	12.9532i	0.0946506	+	0.0344500i
$377$		−	147.312i		−	0.390748i
$378$		0			0
$379$	625.053			1.64922			0.824608	−	0.565705i	$-0.191396\pi$
$379$	625.053			1.64922			0.824608	+	0.565705i	$0.191396\pi$
$380$	−110.982	+	304.921i	−0.292059	+	0.802425i
$381$		0			0
$382$	−315.949	−	265.113i	−0.827091	−	0.694012i
$383$	−104.921	−	18.5004i	−0.273945	−	0.0483039i	0.0349879	−	0.999388i	$-0.488861\pi$
$383$	−104.921	−	18.5004i	−0.273945	−	0.0483039i	−0.308933	+	0.951084i	$0.599972\pi$
$384$		0			0
$385$	315.404	−	264.656i	0.819232	−	0.687417i
$386$	94.3760	−	54.4880i	0.244497	−	0.141161i
$387$		0			0
$388$	244.997	−	424.347i	0.631436	−	1.09368i
$389$	584.613	−	103.083i	1.50286	−	0.264995i	0.639190	−	0.769049i	$-0.279270\pi$
$389$	584.613	−	103.083i	1.50286	−	0.264995i	0.863672	+	0.504054i	$0.168159\pi$
$390$		0			0
$391$	−371.864	+	135.347i	−0.951058	+	0.346157i
$392$	16.6175	+	45.6561i	0.0423915	+	0.116470i
$393$		0			0
$394$	96.1293	+	545.177i	0.243983	+	1.38370i
$395$	−149.587	−	86.3642i	−0.378702	−	0.218643i
$396$		0			0
$397$	−187.410	−	324.603i	−0.472064	−	0.817640i	0.527425	−	0.849602i	$-0.323158\pi$
$397$	−187.410	−	324.603i	−0.472064	−	0.817640i	−0.999489	+	0.0319623i	$0.989824\pi$
$398$	296.500	+	353.355i	0.744976	+	0.887828i
$399$		0			0
$400$	46.8816	−	265.879i	0.117204	−	0.664697i
$401$	176.385	−	210.207i	0.439862	−	0.524207i	−0.499879	−	0.866095i	$-0.666622\pi$
$401$	176.385	−	210.207i	0.439862	−	0.524207i	0.939741	+	0.341889i	$0.111067\pi$
$402$		0			0
$403$	−298.663	−	108.704i	−0.741099	−	0.269738i
$404$		−	202.901i		−	0.502231i
$405$		0			0
$406$	323.646			0.797158
$407$	−87.7467	+	241.082i	−0.215594	+	0.592339i
$408$		0			0
$409$	−422.454	−	354.481i	−1.03289	−	0.866701i	−0.0417017	−	0.999130i	$-0.513278\pi$
$409$	−422.454	−	354.481i	−1.03289	−	0.866701i	−0.991193	+	0.132429i	$0.957722\pi$
$410$	−267.254	−	47.1241i	−0.651839	−	0.114937i
$411$		0			0
$412$	−155.508	+	130.487i	−0.377447	+	0.316715i
$413$	−159.660	+	92.1798i	−0.386586	+	0.223196i
$414$		0			0
$415$	−54.9779	+	95.2245i	−0.132477	+	0.229457i
$416$	−371.957	+	65.5861i	−0.894128	+	0.157659i
$417$		0			0
$418$	−357.939	+	130.279i	−0.856314	+	0.311673i
$419$	29.9567	+	82.3055i	0.0714958	+	0.196433i	0.970294	−	0.241930i	$-0.0777805\pi$
$419$	29.9567	+	82.3055i	0.0714958	+	0.196433i	−0.898798	+	0.438363i	$0.855558\pi$
$420$		0			0
$421$	51.4449	+	291.759i	0.122197	+	0.693013i	0.982933	+	0.183962i	$0.0588924\pi$
$421$	51.4449	+	291.759i	0.122197	+	0.693013i	−0.860736	+	0.509051i	$0.829996\pi$
$422$	−593.653	−	342.746i	−1.40676	−	0.812194i
$423$		0			0
$424$	−36.9720	−	64.0374i	−0.0871981	−	0.151032i
$425$	135.972	+	162.045i	0.319933	+	0.381281i
$426$		0			0
$427$	−48.0512	+	272.512i	−0.112532	+	0.638201i
$428$	−226.805	+	270.296i	−0.529918	+	0.631532i
$429$		0			0
$430$	−1293.95	−	470.957i	−3.00917	−	1.09525i
$431$			586.175i			1.36003i	0.733196	+	0.680017i	$0.238028\pi$
$431$			586.175i			1.36003i	−0.733196	+	0.680017i	$0.761972\pi$
$432$		0			0
$433$	415.367			0.959277			0.479639	−	0.877466i	$-0.340768\pi$
$433$	415.367			0.959277			0.479639	+	0.877466i	$0.340768\pi$
$434$	238.825	−	656.167i	0.550288	−	1.51190i
$435$		0			0
$436$	266.293	+	223.446i	0.610764	+	0.512492i
$437$	−463.288	−	81.6902i	−1.06016	−	0.186934i
$438$		0			0
$439$	256.133	−	214.921i	0.583447	−	0.489570i	−0.302630	−	0.953108i	$-0.597865\pi$
$439$	256.133	−	214.921i	0.583447	−	0.489570i	0.886077	+	0.463538i	$0.153420\pi$
$440$	126.313	−	72.9270i	0.287076	−	0.165743i
$441$		0			0
$442$	191.719	−	332.067i	0.433753	−	0.751282i
$443$	−444.780	+	78.4268i	−1.00402	+	0.177036i	−0.651402	−	0.758732i	$-0.725819\pi$
$443$	−444.780	+	78.4268i	−1.00402	+	0.177036i	−0.352616	+	0.935768i	$0.614708\pi$
$444$		0			0
$445$	166.170	−	60.4810i	0.373416	−	0.135912i
$446$	−349.823	−	961.129i	−0.784355	−	2.15500i
$447$		0			0
$448$	−35.9500	−	203.883i	−0.0802455	−	0.455095i
$449$	165.422	+	95.5067i	0.368424	+	0.212710i	0.672770	−	0.739852i	$-0.265104\pi$
$449$	165.422	+	95.5067i	0.368424	+	0.212710i	−0.304346	+	0.952562i	$0.598438\pi$
$450$		0			0
$451$	−67.0206	−	116.083i	−0.148604	−	0.257390i
$452$	232.281	+	276.822i	0.513897	+	0.612438i
$453$		0			0
$454$	−158.998	+	901.725i	−0.350217	+	1.98618i
$455$	−316.704	+	377.434i	−0.696054	+	0.829525i
$456$		0			0
$457$	362.489	+	131.935i	0.793192	+	0.288698i	0.706662	−	0.707551i	$-0.250200\pi$
$457$	362.489	+	131.935i	0.793192	+	0.288698i	0.0865297	+	0.996249i	$0.472422\pi$
$458$			957.923i			2.09153i
$459$		0			0
$460$	−478.320			−1.03983
$461$	−148.113	+	406.937i	−0.321286	+	0.882727i	0.668947	+	0.743310i	$0.266745\pi$
$461$	−148.113	+	406.937i	−0.321286	+	0.882727i	−0.990234	+	0.139417i	$0.955477\pi$
$462$		0			0
$463$	423.513	+	355.369i	0.914714	+	0.767536i	0.973010	−	0.230763i	$-0.0741223\pi$
$463$	423.513	+	355.369i	0.914714	+	0.767536i	−0.0582960	+	0.998299i	$0.518567\pi$
$464$	286.570	+	50.5299i	0.617607	+	0.108901i
$465$		0			0
$466$	381.820	−	320.385i	0.819355	−	0.687521i
$467$	186.467	−	107.657i	0.399286	−	0.230528i	−0.286890	−	0.957964i	$-0.592621\pi$
$467$	186.467	−	107.657i	0.399286	−	0.230528i	0.686176	+	0.727436i	$0.259288\pi$
$468$		0			0
$469$	32.8943	−	56.9747i	0.0701372	−	0.121481i
$470$	−213.061	+	37.5684i	−0.453322	+	0.0799329i
$471$		0			0
$472$	−61.3700	+	22.3369i	−0.130021	+	0.0473239i
$473$	−232.620	−	639.119i	−0.491798	−	1.35120i
$474$		0			0
$475$	43.6669	+	247.647i	0.0919304	+	0.521363i
$476$	306.975	+	177.232i	0.644905	+	0.372336i
$477$		0			0
$478$	402.194	+	696.621i	0.841411	+	1.45737i
$479$	145.585	+	173.501i	0.303935	+	0.362216i	0.896295	−	0.443457i	$-0.146248\pi$
$479$	145.585	+	173.501i	0.303935	+	0.362216i	−0.592360	+	0.805673i	$0.701804\pi$
$480$		0			0
$481$	53.3117	−	302.346i	0.110835	−	0.628577i
$482$	−498.144	+	593.664i	−1.03349	+	1.23167i
$483$		0			0
$484$	150.628	+	54.8241i	0.311215	+	0.113273i
$485$		−	1054.13i		−	2.17347i
$486$		0			0
$487$	−443.130			−0.909919			−0.454959	−	0.890512i	$-0.650346\pi$
$487$	−443.130			−0.909919			−0.454959	+	0.890512i	$0.650346\pi$
$488$	−33.5267	+	92.1138i	−0.0687023	+	0.188758i
$489$		0			0
$490$	−212.615	−	178.406i	−0.433909	−	0.364093i
$491$	657.316	+	115.902i	1.33873	+	0.236054i	0.796735	−	0.604329i	$-0.206559\pi$
$491$	657.316	+	115.902i	1.33873	+	0.236054i	0.541993	+	0.840383i	$0.317670\pi$
$492$		0			0
$493$	−174.655	+	146.553i	−0.354270	+	0.297268i
$494$	394.754	−	227.912i	0.799098	−	0.461360i
$495$		0			0
$496$	313.911	−	543.710i	0.632885	−	1.09619i
$497$	330.061	−	58.1987i	0.664108	−	0.117100i
$498$		0			0
$499$	54.0177	−	19.6608i	0.108252	−	0.0394005i	−0.287326	−	0.957833i	$-0.592766\pi$
$499$	54.0177	−	19.6608i	0.108252	−	0.0394005i	0.395578	+	0.918432i	$0.370544\pi$
$500$	−67.8624	−	186.450i	−0.135725	−	0.372901i
$501$		0			0
$502$	−83.4662	−	473.360i	−0.166267	−	0.942949i
$503$	−423.202	−	244.336i	−0.841356	−	0.485757i	0.0163686	−	0.999866i	$-0.494789\pi$
$503$	−423.202	−	244.336i	−0.841356	−	0.485757i	−0.857725	+	0.514109i	$0.828123\pi$
$504$		0			0
$505$	−218.252	−	378.024i	−0.432182	−	0.748562i
$506$	−360.917	−	430.124i	−0.713275	−	0.850048i
$507$		0			0
$508$	59.2671	−	336.120i	0.116667	−	0.661654i
$509$	−182.714	+	217.750i	−0.358966	+	0.427799i	−0.915058	−	0.403322i	$-0.867856\pi$
$509$	−182.714	+	217.750i	−0.358966	+	0.427799i	0.556093	+	0.831120i	$0.312300\pi$
$510$		0			0
$511$	−616.418	−	224.358i	−1.20630	−	0.439056i
$512$		−	525.459i		−	1.02629i
$513$		0			0
$514$	−705.227			−1.37204
$515$	−149.367	+	410.382i	−0.290033	+	0.796859i
$516$		0			0
$517$	−81.8602	−	68.6889i	−0.158337	−	0.132860i
$518$	664.258	+	117.127i	1.28235	+	0.226113i
$519$		0			0
$520$	−133.704	+	112.191i	−0.257124	+	0.215752i
$521$	−35.1966	+	20.3207i	−0.0675558	+	0.0390033i	−0.533397	−	0.845865i	$-0.679085\pi$
$521$	−35.1966	+	20.3207i	−0.0675558	+	0.0390033i	0.465842	+	0.884868i	$0.345752\pi$
$522$		0			0
$523$	−174.951	+	303.024i	−0.334514	+	0.579395i	−0.983391	−	0.181498i	$-0.941905\pi$
$523$	−174.951	+	303.024i	−0.334514	+	0.579395i	0.648877	+	0.760893i	$0.275239\pi$
$524$	13.4860	−	2.37795i	0.0257367	−	0.00453808i
$525$		0			0
$526$	869.167	−	316.351i	1.65241	−	0.601428i
$527$	168.243	+	462.243i	0.319246	+	0.877122i
$528$		0			0
$529$	−28.5567	−	161.953i	−0.0539825	−	0.306150i
$530$	365.815	+	211.203i	0.690216	+	0.398497i
$531$		0			0
$532$	210.690	+	364.926i	0.396034	+	0.685951i
$533$	103.105	+	122.876i	0.193442	+	0.230536i
$534$		0			0
$535$	−131.813	+	747.550i	−0.246380	+	1.39729i
$536$	14.9804	−	17.8530i	0.0279485	−	0.0333078i
$537$		0			0
$538$	405.582	+	147.620i	0.753869	+	0.274386i
$539$		−	137.090i		−	0.254342i
$540$		0			0
$541$	145.531			0.269003			0.134501	−	0.990913i	$-0.457057\pi$
$541$	145.531			0.269003			0.134501	+	0.990913i	$0.457057\pi$
$542$	115.809	−	318.182i	0.213669	−	0.587051i
$543$		0			0
$544$	447.800	+	375.749i	0.823163	+	0.690715i
$545$	736.481	+	129.861i	1.35134	+	0.238278i
$546$		0			0
$547$	372.320	−	312.413i	0.680657	−	0.571139i	−0.235541	−	0.971864i	$-0.575686\pi$
$547$	372.320	−	312.413i	0.680657	−	0.571139i	0.916198	+	0.400725i	$0.131242\pi$
$548$	555.602	−	320.777i	1.01387	−	0.585359i
$549$		0			0
$550$	−150.070	+	259.928i	−0.272854	+	0.472597i
$551$	−266.919	+	47.0651i	−0.484427	+	0.0854176i
$552$		0			0
$553$	−210.776	+	76.7162i	−0.381150	+	0.138727i
$554$	135.014	+	370.947i	0.243707	+	0.669580i
$555$		0			0
$556$	18.0463	+	102.346i	0.0324574	+	0.184075i
$557$	−2.82805	−	1.63278i	−0.00507730	−	0.00293138i	0.497459	−	0.867487i	$-0.334266\pi$
$557$	−2.82805	−	1.63278i	−0.00507730	−	0.00293138i	−0.502537	+	0.864556i	$0.667600\pi$
$558$		0			0
$559$	406.948	+	704.855i	0.727993	+	1.26092i
$560$	−625.597	−	745.558i	−1.11714	−	1.33135i
$561$		0			0
$562$	210.365	−	1193.04i	0.374316	−	2.12285i
$563$	427.292	−	509.227i	0.758956	−	0.904489i	−0.238825	−	0.971063i	$-0.576762\pi$
$563$	427.292	−	509.227i	0.758956	−	0.904489i	0.997781	+	0.0665739i	$0.0212068\pi$
$564$		0			0
$565$	730.527	+	265.890i	1.29297	+	0.470602i
$566$			180.949i			0.319697i
$567$		0			0
$568$	118.727			0.209026
$569$	−25.9713	+	71.3556i	−0.0456438	+	0.125405i	−0.960420	−	0.278555i	$-0.910144\pi$
$569$	−25.9713	+	71.3556i	−0.0456438	+	0.125405i	0.914776	+	0.403960i	$0.132367\pi$
$570$		0			0
$571$	−225.287	−	189.038i	−0.394548	−	0.331065i	0.423834	−	0.905740i	$-0.360684\pi$
$571$	−225.287	−	189.038i	−0.394548	−	0.331065i	−0.818382	+	0.574675i	$0.805129\pi$
$572$	225.441	+	39.7513i	0.394128	+	0.0694953i
$573$		0			0
$574$	−269.959	+	226.523i	−0.470312	+	0.394639i
$575$	−321.018	+	185.340i	−0.558292	+	0.322330i
$576$		0			0
$577$	−529.296	+	916.768i	−0.917325	+	1.58885i	−0.113864	+	0.993496i	$0.536323\pi$
$577$	−529.296	+	916.768i	−0.917325	+	1.58885i	−0.803461	+	0.595357i	$0.797011\pi$
$578$	163.484	−	28.8266i	0.282844	−	0.0498730i
$579$		0			0
$580$	−258.961	+	94.2539i	−0.446484	+	0.162507i
$581$	48.8362	+	134.176i	0.0840554	+	0.230940i
$582$		0			0
$583$	36.2299	+	205.470i	0.0621438	+	0.352435i
$584$	−201.245	−	116.189i	−0.344597	−	0.198953i
$585$		0			0
$586$	−671.115	−	1162.40i	−1.14525	−	1.98363i
$587$	−89.2844	−	106.405i	−0.152103	−	0.181269i	0.684612	−	0.728907i	$-0.259971\pi$
$587$	−89.2844	−	106.405i	−0.152103	−	0.181269i	−0.836715	+	0.547638i	$0.815527\pi$
$588$		0			0
$589$	−101.545	+	575.888i	−0.172402	+	0.977738i
$590$	239.809	−	285.793i	0.406456	−	0.484396i
$591$		0			0
$592$	569.874	+	207.417i	0.962625	+	0.350367i
$593$			145.309i			0.245040i	0.992466	+	0.122520i	$0.0390975\pi$
$593$			145.309i			0.245040i	−0.992466	+	0.122520i	$0.960902\pi$
$594$		0			0
$595$	762.563			1.28162
$596$	166.698	−	458.000i	0.279695	−	0.768457i
$597$		0			0
$598$	514.715	+	431.897i	0.860728	+	0.722236i
$599$	22.6235	+	3.98914i	0.0377688	+	0.00665966i	0.192501	−	0.981297i	$-0.438340\pi$
$599$	22.6235	+	3.98914i	0.0377688	+	0.00665966i	−0.154732	+	0.987957i	$0.549451\pi$
$600$		0			0
$601$	−710.406	+	596.102i	−1.18204	+	0.991849i	−0.182077	+	0.983284i	$0.558282\pi$
$601$	−710.406	+	596.102i	−1.18204	+	0.991849i	−0.999963	+	0.00856516i	$0.997274\pi$
$602$	−1548.58	+	894.071i	−2.57238	+	1.48517i
$603$		0			0
$604$	−121.631	+	210.670i	−0.201375	+	0.348792i
$605$	339.605	−	59.8816i	0.561331	−	0.0989779i
$606$		0			0
$607$	−492.373	+	179.209i	−0.811158	+	0.295237i	−0.714102	−	0.700042i	$-0.753165\pi$
$607$	−492.373	+	179.209i	−0.811158	+	0.295237i	−0.0970557	+	0.995279i	$0.530943\pi$
$608$	237.675	+	653.007i	0.390913	+	1.07403i
$609$		0			0
$610$	−97.2382	−	551.465i	−0.159407	−	0.904041i
$611$	110.745	+	63.9384i	0.181251	+	0.104646i
$612$		0			0
$613$	−35.0848	−	60.7687i	−0.0572346	−	0.0991333i	0.835988	−	0.548747i	$-0.184895\pi$
$613$	−35.0848	−	60.7687i	−0.0572346	−	0.0991333i	−0.893223	+	0.449614i	$0.851562\pi$
$614$	−88.8559	−	105.894i	−0.144716	−	0.172466i
$615$		0			0
$616$	32.8897	−	186.527i	0.0533924	−	0.302804i
$617$	−427.172	+	509.083i	−0.692337	+	0.825095i	−0.991636	−	0.129064i	$-0.958803\pi$
$617$	−427.172	+	509.083i	−0.692337	+	0.825095i	0.299299	+	0.954159i	$0.403247\pi$
$618$		0			0
$619$	912.210	+	332.017i	1.47368	+	0.536377i	0.949098	−	0.314981i	$-0.101998\pi$
$619$	912.210	+	332.017i	1.47368	+	0.536377i	0.524585	+	0.851358i	$0.324220\pi$
$620$			594.574i			0.958990i
$621$		0			0
$622$	−932.436			−1.49909
$623$	78.5400	−	215.787i	0.126067	−	0.346367i
$624$		0			0
$625$	−596.569	−	500.581i	−0.954510	−	0.800929i
$626$	−435.419	−	76.7761i	−0.695558	−	0.122646i
$627$		0			0
$628$	165.706	−	139.044i	0.263863	−	0.221408i
$629$	−411.502	+	237.581i	−0.654216	+	0.377712i
$630$		0			0
$631$	94.6588	−	163.954i	0.150014	−	0.259832i	−0.781218	−	0.624258i	$-0.785401\pi$
$631$	94.6588	−	163.954i	0.150014	−	0.259832i	0.931232	+	0.364426i	$0.118735\pi$
$632$	−78.2513	+	13.7978i	−0.123815	+	0.0218320i
$633$		0			0
$634$	1259.36	−	458.370i	1.98637	−	0.722981i
$635$	−251.130	−	689.974i	−0.395480	−	1.08657i
$636$		0			0
$637$	28.4872	+	161.559i	0.0447209	+	0.253625i
$638$	−280.156	−	161.748i	−0.439116	−	0.253524i
$639$		0			0
$640$	−276.852	−	479.522i	−0.432581	−	0.749253i
$641$	445.262	+	530.643i	0.694637	+	0.827836i	0.991908	−	0.126957i	$-0.0405210\pi$
$641$	445.262	+	530.643i	0.694637	+	0.827836i	−0.297271	+	0.954793i	$0.596077\pi$
$642$		0			0
$643$	184.867	−	1048.43i	0.287506	−	1.63053i	−0.408687	−	0.912675i	$-0.634013\pi$
$643$	184.867	−	1048.43i	0.287506	−	1.63053i	0.696193	−	0.717854i	$-0.254876\pi$
$644$	−399.262	+	475.822i	−0.619972	+	0.738854i
$645$		0			0
$646$	−662.936	−	241.289i	−1.02622	−	0.373512i
$647$			352.755i			0.545217i	0.962125	+	0.272608i	$0.0878863\pi$
$647$			352.755i			0.545217i	−0.962125	+	0.272608i	$0.912114\pi$
$648$		0			0
$649$	184.274			0.283935
$650$	122.842	−	337.506i	0.188988	−	0.519240i
$651$		0			0
$652$	−567.229	−	475.961i	−0.869982	−	0.730002i
$653$	−461.316	−	81.3425i	−0.706457	−	0.124567i	−0.191135	−	0.981564i	$-0.561217\pi$
$653$	−461.316	−	81.3425i	−0.706457	−	0.124567i	−0.515322	+	0.856996i	$0.672328\pi$
$654$		0			0
$655$	22.5679	−	18.9367i	0.0344548	−	0.0289110i
$656$	−274.399	+	158.424i	−0.418291	+	0.241501i
$657$		0			0
$658$	−140.474	+	243.307i	−0.213486	+	0.369768i
$659$	84.6349	−	14.9234i	0.128429	−	0.0226455i	−0.109064	−	0.994035i	$-0.534785\pi$
$659$	84.6349	−	14.9234i	0.128429	−	0.0226455i	0.237493	+	0.971389i	$0.423674\pi$
$660$		0			0
$661$	−115.687	+	42.1068i	−0.175019	+	0.0637016i	−0.428043	−	0.903758i	$-0.640797\pi$
$661$	−115.687	+	42.1068i	−0.175019	+	0.0637016i	0.253024	+	0.967460i	$0.418575\pi$
$662$	−304.996	−	837.968i	−0.460718	−	1.26581i
$663$		0			0
$664$	8.78345	+	49.8134i	0.0132281	+	0.0750202i
$665$	785.070	+	453.260i	1.18056	+	0.681594i
$666$		0			0
$667$	−199.763	−	346.000i	−0.299495	−	0.518741i
$668$	−296.226	−	353.028i	−0.443452	−	0.528485i
$669$		0			0
$670$	−23.1182	+	131.110i	−0.0345048	+	0.195686i
$671$	177.787	−	211.878i	0.264958	−	0.315765i
$672$		0			0
$673$	598.221	+	217.735i	0.888887	+	0.323528i	0.745791	−	0.666180i	$-0.232072\pi$
$673$	598.221	+	217.735i	0.888887	+	0.323528i	0.143096	+	0.989709i	$0.454294\pi$
$674$			179.321i			0.266054i
$675$		0			0
$676$	217.127			0.321194
$677$	−56.5391	+	155.340i	−0.0835141	+	0.229453i	−0.974420	−	0.224735i	$-0.927848\pi$
$677$	−56.5391	+	155.340i	−0.0835141	+	0.229453i	0.890906	+	0.454188i	$0.150071\pi$
$678$		0			0
$679$	−1048.63	−	879.901i	−1.54437	−	1.29588i
$680$	266.031	+	46.9084i	0.391222	+	0.0689830i
$681$		0			0
$682$	−534.664	+	448.636i	−0.783965	+	0.657824i
$683$	1129.58	−	652.163i	1.65385	−	0.954851i	0.678383	−	0.734709i	$-0.262681\pi$
$683$	1129.58	−	652.163i	1.65385	−	0.954851i	0.975468	−	0.220142i	$-0.0706522\pi$
$684$		0			0
$685$	690.092	−	1195.27i	1.00743	−	1.74493i
$686$	674.445	−	118.923i	0.983155	−	0.173357i
$687$		0			0
$688$	−1510.76	+	549.872i	−2.19587	+	0.799232i
$689$	−85.3928	−	234.615i	−0.123937	−	0.340515i
$690$		0			0
$691$	−62.8288	−	356.320i	−0.0909245	−	0.515658i	−0.995920	−	0.0902378i	$-0.971237\pi$
$691$	−62.8288	−	356.320i	−0.0909245	−	0.515658i	0.904996	−	0.425421i	$-0.139874\pi$
$692$	−750.099	−	433.070i	−1.08396	−	0.625824i
$693$		0			0
$694$	227.439	+	393.936i	0.327722	+	0.567632i
$695$	143.711	+	171.268i	0.206778	+	0.246428i
$696$		0			0
$697$	43.1093	−	244.485i	0.0618498	−	0.350767i
$698$	776.309	−	925.169i	1.11219	−	1.32546i
$699$		0			0
$700$	312.003	+	113.560i	0.445719	+	0.162228i
$701$		−	893.344i		−	1.27438i	−0.770705	−	0.637192i	$-0.780096\pi$
$701$		−	893.344i		−	1.27438i	0.770705	−	0.637192i	$-0.219904\pi$
$702$		0			0
$703$	−564.863			−0.803504
$704$	−70.7748	+	194.452i	−0.100532	+	0.276210i
$705$		0			0
$706$	809.756	+	679.466i	1.14696	+	0.962417i
$707$	−558.228	−	98.4307i	−0.789573	−	0.139223i
$708$		0			0
$709$	−529.040	+	443.917i	−0.746178	+	0.626118i	−0.934489	−	0.355992i	$-0.884143\pi$
$709$	−529.040	+	443.917i	−0.746178	+	0.626118i	0.188311	+	0.982109i	$0.439699\pi$
$710$	−587.363	+	339.114i	−0.827272	+	0.477626i
$711$		0			0
$712$	40.6737	−	70.4490i	0.0571260	−	0.0989452i
$713$	−848.896	+	149.683i	−1.19060	+	0.209935i
$714$		0			0
$715$	462.776	−	168.437i	0.647239	−	0.235576i
$716$	29.1476	+	80.0825i	0.0407090	+	0.111847i
$717$		0			0
$718$	103.934	+	589.439i	0.144755	+	0.820946i
$719$	−417.508	−	241.049i	−0.580679	−	0.335255i	0.180724	−	0.983534i	$-0.442156\pi$
$719$	−417.508	−	241.049i	−0.580679	−	0.335255i	−0.761403	+	0.648279i	$0.775489\pi$
$720$		0			0
$721$	283.560	+	491.140i	0.393287	+	0.681192i
$722$	70.7063	+	84.2645i	0.0979312	+	0.116710i
$723$		0			0
$724$	−42.0833	+	238.666i	−0.0581261	+	0.329650i
$725$	−137.276	+	163.600i	−0.189347	+	0.225655i
$726$		0			0
$727$	−324.225	−	118.008i	−0.445977	−	0.162322i	0.109263	−	0.994013i	$-0.465151\pi$
$727$	−324.225	−	118.008i	−0.445977	−	0.162322i	−0.555239	+	0.831691i	$0.687373\pi$
$728$			226.654i			0.311338i
$729$		0			0
$730$	1327.46			1.81844
$731$	430.834	−	1183.71i	0.589376	−	1.61930i
$732$		0			0
$733$	413.108	+	346.639i	0.563585	+	0.472904i	0.879510	−	0.475880i	$-0.157870\pi$
$733$	413.108	+	346.639i	0.563585	+	0.472904i	−0.315925	+	0.948784i	$0.602315\pi$
$734$	609.376	+	107.450i	0.830213	+	0.146389i
$735$		0			0
$736$	−784.699	+	658.440i	−1.06617	+	0.894620i
$737$	−56.9482	+	32.8791i	−0.0772704	+	0.0446121i
$738$		0			0
$739$	−368.737	+	638.671i	−0.498968	+	0.864237i	−0.999999	−	0.00119161i	$-0.999621\pi$
$739$	−368.737	+	638.671i	−0.498968	+	0.864237i	0.501032	+	0.865429i	$0.332954\pi$
$740$	−565.606	+	99.7315i	−0.764332	+	0.134772i
$741$		0			0
$742$	515.452	−	187.609i	0.694679	−	0.252842i
$743$	356.128	+	978.454i	0.479311	+	1.31690i	0.910079	+	0.414434i	$0.136020\pi$
$743$	356.128	+	978.454i	0.479311	+	1.31690i	−0.430768	+	0.902463i	$0.641757\pi$
$744$		0			0
$745$	−182.077	−	1032.61i	−0.244398	−	1.38605i
$746$	1485.54	+	857.674i	1.99133	+	1.14970i
$747$		0			0
$748$	−177.150	−	306.832i	−0.236831	−	0.410204i
$749$	633.619	+	755.118i	0.845953	+	1.00817i
$750$		0			0
$751$	41.8554	−	237.374i	0.0557329	−	0.316077i	−0.944178	−	0.329436i	$-0.893141\pi$
$751$	41.8554	−	237.374i	0.0557329	−	0.316077i	0.999911	+	0.0133592i	$0.00425248\pi$
$752$	−162.368	+	193.503i	−0.215915	+	0.257317i
$753$		0			0
$754$	363.771	+	132.402i	0.482455	+	0.175599i
$755$			523.331i			0.693154i
$756$		0			0
$757$	32.7615			0.0432781			0.0216391	−	0.999766i	$-0.493112\pi$
$757$	32.7615			0.0432781			0.0216391	+	0.999766i	$0.493112\pi$
$758$	−561.788	+	1543.50i	−0.741145	+	2.03628i
$759$		0			0
$760$	246.001	+	206.419i	0.323685	+	0.271604i
$761$	−314.502	−	55.4551i	−0.413274	−	0.0728714i	−0.0368545	−	0.999321i	$-0.511734\pi$
$761$	−314.502	−	55.4551i	−0.413274	−	0.0728714i	−0.376420	+	0.926449i	$0.622845\pi$
$762$		0			0
$763$	743.936	−	624.236i	0.975014	−	0.818134i
$764$	394.950	−	228.025i	0.516951	−	0.298462i
$765$		0			0
$766$	139.986	−	242.463i	0.182750	−	0.316531i
$767$	−217.164	+	38.2920i	−0.283135	+	0.0499243i
$768$		0			0
$769$	447.488	−	162.872i	0.581910	−	0.211798i	−0.0342578	−	0.999413i	$-0.510907\pi$
$769$	447.488	−	162.872i	0.581910	−	0.211798i	0.616167	+	0.787615i	$0.288685\pi$
$770$	370.058	+	1016.73i	0.480595	+	1.32042i
$771$		0			0
$772$	20.9243	+	118.667i	0.0271040	+	0.153714i
$773$	−1122.62	−	648.147i	−1.45229	−	0.838482i	−0.453682	−	0.891164i	$-0.649890\pi$
$773$	−1122.62	−	648.147i	−1.45229	−	0.838482i	−0.998611	+	0.0526817i	$0.983223\pi$
$774$		0			0
$775$	230.386	+	399.040i	0.297272	+	0.514890i
$776$	−311.701	−	371.471i	−0.401677	−	0.478700i
$777$		0			0
$778$	−270.889	+	1536.29i	−0.348187	+	1.97467i
$779$	189.701	−	226.077i	0.243519	−	0.290214i
$780$		0			0
$781$	−314.795	−	114.576i	−0.403066	−	0.146704i
$782$		−	1039.93i		−	1.32983i
$783$		0			0
$784$	−324.056			−0.413337
$785$	159.162	−	437.295i	0.202754	−	0.557063i
$786$		0			0
$787$	659.528	+	553.410i	0.838028	+	0.703189i	0.957119	−	0.289694i	$-0.0935535\pi$
$787$	659.528	+	553.410i	0.838028	+	0.703189i	−0.119091	+	0.992883i	$0.537998\pi$
$788$	−602.818	−	106.293i	−0.764997	−	0.134890i
$789$		0			0
$790$	347.714	−	291.766i	0.440144	−	0.369325i
$791$	874.285	−	504.769i	1.10529	−	0.638140i
$792$		0			0
$793$	−165.492	+	286.640i	−0.208690	+	0.361462i
$794$	970.013	−	171.039i	1.22168	−	0.215415i
$795$		0			0
$796$	−479.284	+	174.445i	−0.602115	+	0.219152i
$797$	198.415	+	545.140i	0.248952	+	0.683990i	0.999725	+	0.0234300i	$0.00745867\pi$
$797$	198.415	+	545.140i	0.248952	+	0.683990i	−0.750774	+	0.660560i	$0.770319\pi$
$798$		0			0
$799$	−34.3678	−	194.909i	−0.0430135	−	0.243942i
$800$	474.201	+	273.780i	0.592751	+	0.342225i
$801$		0			0
$802$	360.552	+	624.494i	0.449566	+	0.778671i
$803$	421.459	+	502.275i	0.524855	+	0.625498i
$804$		0			0
$805$	−232.041	+	1315.97i	−0.288249	+	1.63474i
$806$	536.868	−	639.814i	0.666089	−	0.793814i
$807$		0			0
$808$	−188.691	−	68.6779i	−0.233528	−	0.0849974i
$809$			661.323i			0.817457i	0.912656	+	0.408729i	$0.134028\pi$
$809$			661.323i			0.817457i	−0.912656	+	0.408729i	$0.865972\pi$
$810$		0			0
$811$	−168.725			−0.208045			−0.104023	−	0.994575i	$-0.533171\pi$
$811$	−168.725			−0.208045			−0.104023	+	0.994575i	$0.533171\pi$
$812$	−122.397	+	336.283i	−0.150735	+	0.414142i
$813$		0			0
$814$	−516.461	−	433.362i	−0.634473	−	0.532386i
$815$	−1568.77	−	276.617i	−1.92487	−	0.339407i
$816$		0			0
$817$	1147.13	−	962.559i	1.40408	−	1.17816i
$818$	1255.05	−	724.602i	1.53429	−	0.885822i
$819$		0			0
$820$	150.035	−	259.868i	0.182969	−	0.316912i
$821$	−149.275	+	26.3213i	−0.181822	+	0.0320600i	−0.263817	−	0.964573i	$-0.584982\pi$
$821$	−149.275	+	26.3213i	−0.181822	+	0.0320600i	0.0819959	+	0.996633i	$0.473871\pi$
$822$		0			0
$823$	−211.263	+	76.8935i	−0.256699	+	0.0934307i	−0.467164	−	0.884171i	$-0.654724\pi$
$823$	−211.263	+	76.8935i	−0.256699	+	0.0934307i	0.210465	+	0.977601i	$0.432502\pi$
$824$	68.7118	+	188.784i	0.0833881	+	0.229107i
$825$		0			0
$826$	−84.1280	−	477.113i	−0.101850	−	0.577619i
$827$	−292.855	−	169.080i	−0.354117	−	0.204449i	0.312380	−	0.949957i	$-0.398874\pi$
$827$	−292.855	−	169.080i	−0.354117	−	0.204449i	−0.666497	+	0.745508i	$0.732207\pi$
$828$		0			0
$829$	401.806	+	695.949i	0.484688	+	0.839504i	0.999845	−	0.0175917i	$-0.00559990\pi$
$829$	401.806	+	695.949i	0.484688	+	0.839504i	−0.515157	+	0.857096i	$0.672267\pi$
$830$	−185.733	−	221.348i	−0.223775	−	0.266685i
$831$		0			0
$832$	43.0002	−	243.866i	0.0516829	−	0.293108i
$833$	163.206	−	194.502i	0.195926	−	0.233495i
$834$		0			0
$835$	−931.633	−	339.087i	−1.11573	−	0.406092i
$836$		−	421.184i		−	0.503809i
$837$		0			0
$838$	−230.169			−0.274665
$839$	−292.066	+	802.443i	−0.348111	+	0.956428i	0.634853	+	0.772633i	$0.281061\pi$
$839$	−292.066	+	802.443i	−0.348111	+	0.956428i	−0.982965	+	0.183795i	$0.941162\pi$
$840$		0			0
$841$	467.912	+	392.625i	0.556376	+	0.466855i
$842$	−766.705	−	135.191i	−0.910576	−	0.160559i
$843$		0			0
$844$	580.637	−	487.213i	0.687959	−	0.577266i
$845$	404.527	−	233.554i	0.478731	−	0.276395i
$846$		0			0
$847$	223.906	−	387.816i	0.264351	−	0.457870i
$848$	485.693	−	85.6407i	0.572751	−	0.100991i
$849$		0			0
$850$	−522.361	+	190.124i	−0.614542	+	0.223675i
$851$	−284.781	−	782.430i	−0.334643	−	0.919424i
$852$		0			0
$853$	−138.765	−	786.975i	−0.162679	−	0.922596i	−0.951426	−	0.307878i	$-0.900381\pi$
$853$	−138.765	−	786.975i	−0.162679	−	0.922596i	0.788747	−	0.614718i	$-0.210730\pi$
$854$	−629.751	−	363.587i	−0.737414	−	0.425746i
$855$		0			0
$856$	174.597	+	302.410i	0.203968	+	0.353283i
$857$	−998.416	−	1189.87i	−1.16501	−	1.38841i	−0.906397	−	0.422427i	$-0.861178\pi$
$857$	−998.416	−	1189.87i	−1.16501	−	1.38841i	−0.258616	−	0.965980i	$-0.583266\pi$
$858$		0			0
$859$	−4.90592	+	27.8228i	−0.00571119	+	0.0323898i	−0.987530	−	0.157430i	$-0.949679\pi$
$859$	−4.90592	+	27.8228i	−0.00571119	+	0.0323898i	0.981819	+	0.189820i	$0.0607903\pi$
$860$	978.693	−	1166.36i	1.13802	−	1.35623i
$861$		0			0
$862$	−1447.50	−	526.846i	−1.67923	−	0.611190i
$863$		−	951.550i		−	1.10261i	−0.834305	−	0.551304i	$-0.814131\pi$
$863$		−	951.550i		−	1.10261i	0.834305	−	0.551304i	$-0.185869\pi$
$864$		0			0
$865$	−1863.34			−2.15415
$866$	−373.326	+	1025.70i	−0.431092	+	1.18442i
$867$		0			0
$868$	591.468	+	496.301i	0.681415	+	0.571775i
$869$	220.793	+	38.9318i	0.254077	+	0.0448006i
$870$		0			0
$871$	60.2805	−	50.5813i	0.0692084	−	0.0580727i
$872$	297.932	−	172.011i	0.341665	−	0.197260i
$873$		0			0
$874$	618.122	−	1070.62i	0.707233	−	1.22496i
$875$	−545.889	+	96.2549i	−0.623873	+	0.110006i
$876$		0			0
$877$	214.431	−	78.0465i	0.244505	−	0.0889926i	−0.216861	−	0.976203i	$-0.569582\pi$
$877$	214.431	−	78.0465i	0.244505	−	0.0889926i	0.461366	+	0.887210i	$0.347360\pi$
$878$	300.516	+	825.662i	0.342274	+	0.940390i
$879$		0			0
$880$	168.926	+	958.026i	0.191961	+	1.08867i
$881$	1343.36	+	775.592i	1.52482	+	0.880354i	0.999568	+	0.0294054i	$0.00936139\pi$
$881$	1343.36	+	775.592i	1.52482	+	0.880354i	0.525250	+	0.850948i	$0.323972\pi$
$882$		0			0
$883$	−781.794	−	1354.11i	−0.885384	−	1.53353i	−0.845272	−	0.534336i	$-0.820562\pi$
$883$	−781.794	−	1354.11i	−0.885384	−	1.53353i	−0.0401121	−	0.999195i	$-0.512772\pi$
$884$	272.528	+	324.786i	0.308290	+	0.367405i
$885$		0			0
$886$	206.096	−	1168.83i	0.232614	−	1.31922i
$887$	−451.340	+	537.886i	−0.508839	+	0.606411i	−0.957904	−	0.287088i	$-0.907313\pi$
$887$	−451.340	+	537.886i	−0.508839	+	0.606411i	0.449065	+	0.893499i	$0.351757\pi$
$888$		0			0
$889$	−895.993	−	326.115i	−1.00787	−	0.366833i
$890$			464.699i			0.522134i
$891$		0			0
$892$	1130.95			1.26789
$893$	80.4701	−	221.090i	0.0901121	−	0.247581i
$894$		0			0
$895$	140.446	+	117.848i	0.156923	+	0.131674i
$896$	−708.110	−	124.859i	−0.790302	−	0.139352i
$897$		0			0
$898$	−384.523	+	322.653i	−0.428199	+	0.359302i
$899$	−430.094	+	248.315i	−0.478413	+	0.276212i
$900$		0			0
$901$	−193.210	+	334.649i	−0.214439	+	0.371419i
$902$	346.892	−	61.1664i	0.384581	−	0.0678120i
$903$		0			0
$904$	336.057	−	122.315i	0.371745	−	0.135304i
$905$	178.318	+	489.924i	0.197036	+	0.541353i
$906$		0			0
$907$	280.357	+	1589.99i	0.309104	+	1.75302i	0.603528	+	0.797341i	$0.293761\pi$
$907$	280.357	+	1589.99i	0.309104	+	1.75302i	−0.294424	+	0.955675i	$0.595128\pi$
$908$	−876.803	−	506.222i	−0.965642	−	0.557514i
$909$		0			0
$910$	−647.383	−	1121.30i	−0.711410	−	1.23220i
$911$	394.005	+	469.556i	0.432497	+	0.515430i	0.937641	−	0.347605i	$-0.113005\pi$
$911$	394.005	+	469.556i	0.432497	+	0.515430i	−0.505144	+	0.863035i	$0.668561\pi$
$912$		0			0
$913$	24.7833	−	140.553i	0.0271449	−	0.153946i
$914$	−651.599	+	776.546i	−0.712910	+	0.849613i
$915$		0			0
$916$	−995.326	−	362.269i	−1.08660	−	0.395490i
$917$		−	38.2568i		−	0.0417195i
$918$		0			0
$919$	628.091			0.683451			0.341725	−	0.939800i	$-0.388989\pi$
$919$	628.091			0.683451			0.341725	+	0.939800i	$0.388989\pi$
$920$	−161.901	+	444.821i	−0.175980	+	0.483501i
$921$		0			0
$922$	−871.766	−	731.499i	−0.945516	−	0.793382i
$923$	394.790	+	69.6122i	0.427725	+	0.0754195i
$924$		0			0
$925$	−340.955	+	286.095i	−0.368600	+	0.309292i
$926$	−1258.19	+	726.418i	−1.35874	+	0.784469i
$927$		0			0
$928$	−295.086	+	511.103i	−0.317980	+	0.550758i
$929$	−1234.51	+	217.678i	−1.32886	+	0.234314i	−0.792603	−	0.609738i	$-0.791274\pi$
$929$	−1234.51	+	217.678i	−1.32886	+	0.234314i	−0.536260	+	0.844053i	$0.680163\pi$
$930$		0			0
$931$	283.633	−	103.234i	0.304654	−	0.110885i
$932$	188.497	+	517.892i	0.202250	+	0.555678i
$933$		0			0
$934$	98.2529	+	557.220i	0.105196	+	0.596595i
$935$	−660.093	−	381.105i	−0.705981	−	0.407599i
$936$		0			0
$937$	460.132	+	796.972i	0.491070	+	0.850557i	0.999947	−	0.0102815i	$-0.00327275\pi$
$937$	460.132	+	796.972i	0.491070	+	0.850557i	−0.508878	+	0.860839i	$0.669939\pi$
$938$	111.128	+	132.437i	0.118473	+	0.141191i
$939$		0			0
$940$	41.5405	−	235.588i	0.0441921	−	0.250626i
$941$	439.314	−	523.554i	0.466859	−	0.556381i	−0.480317	−	0.877095i	$-0.659478\pi$
$941$	439.314	−	523.554i	0.466859	−	0.556381i	0.947176	+	0.320714i	$0.103923\pi$
$942$		0			0
$943$	408.794	+	148.789i	0.433504	+	0.157783i
$944$		−	435.590i		−	0.461430i
$945$		0			0
$946$	1787.31			1.88934
$947$	287.907	−	791.018i	0.304020	−	0.835288i	−0.689771	−	0.724027i	$-0.742289\pi$
$947$	287.907	−	791.018i	0.304020	−	0.835288i	0.993791	−	0.111261i	$-0.0354889\pi$
$948$		0			0
$949$	−601.056	−	504.346i	−0.633357	−	0.531450i
$950$	−650.786	−	114.751i	−0.685038	−	0.120791i
$951$		0			0
$952$	268.724	−	225.486i	0.282273	−	0.236855i
$953$	−1277.52	+	737.576i	−1.34052	+	0.773952i	−0.986884	−	0.161430i	$-0.948390\pi$
$953$	−1277.52	+	737.576i	−1.34052	+	0.773952i	−0.353640	+	0.935382i	$0.615056\pi$
$954$		0			0
$955$	490.553	−	849.662i	0.513668	−	0.889698i
$956$	−875.924	+	154.449i	−0.916238	+	0.161558i
$957$		0			0
$958$	−559.293	+	203.566i	−0.583813	+	0.212490i
$959$	−613.000	−	1684.20i	−0.639207	−	1.75621i
$960$		0			0
$961$	19.1872	+	108.816i	0.0199659	+	0.113232i
$962$	698.694	+	403.391i	0.726294	+	0.419326i
$963$		0			0
$964$	−428.456	−	742.107i	−0.444456	−	0.769821i
$965$	166.629	+	198.581i	0.172673	+	0.205783i
$966$		0			0
$967$	56.3919	−	319.814i	0.0583163	−	0.330728i	−0.941667	−	0.336547i	$-0.890741\pi$
$967$	56.3919	−	319.814i	0.0583163	−	0.330728i	0.999983	+	0.00581841i	$0.00185207\pi$
$968$	101.969	−	121.522i	0.105340	−	0.125539i
$969$		0			0
$970$	2603.06	+	947.438i	2.68357	+	0.976740i
$971$			1203.37i			1.23931i	0.784873	+	0.619657i	$0.212728\pi$
$971$			1203.37i			1.23931i	−0.784873	+	0.619657i	$0.787272\pi$
$972$		0			0
$973$	290.331			0.298387
$974$	398.279	−	1094.26i	0.408911	−	1.12347i
$975$		0			0
$976$	−500.842	−	420.256i	−0.513157	−	0.430590i
$977$	−186.452	−	32.8765i	−0.190841	−	0.0336505i	0.0774104	−	0.996999i	$-0.475335\pi$
$977$	−186.452	−	32.8765i	−0.190841	−	0.0336505i	−0.268252	+	0.963349i	$0.586446\pi$
$978$		0			0
$979$	−175.829	+	147.538i	−0.179601	+	0.150703i
$980$	265.779	−	153.448i	0.271203	−	0.156579i
$981$		0			0
$982$	−876.994	+	1519.00i	−0.893070	+	1.54684i
$983$	1245.48	−	219.613i	1.26702	−	0.223411i	0.500562	−	0.865701i	$-0.333127\pi$
$983$	1245.48	−	219.613i	1.26702	−	0.223411i	0.766462	+	0.642290i	$0.222016\pi$
$984$		0			0
$985$	−1237.44	+	450.391i	−1.25628	+	0.457250i
$986$	−204.919	−	563.012i	−0.207829	−	0.571006i
$987$		0			0
$988$	87.5217	+	496.360i	0.0885847	+	0.502389i
$989$	1911.64	+	1103.69i	1.93291	+	1.11596i
$990$		0			0
$991$	697.271	+	1207.71i	0.703604	+	1.21868i	0.967193	+	0.254043i	$0.0817603\pi$
$991$	697.271	+	1207.71i	0.703604	+	1.21868i	−0.263589	+	0.964635i	$0.584906\pi$
$992$	818.471	+	975.416i	0.825072	+	0.983282i
$993$		0			0
$994$	−152.939	+	867.360i	−0.153862	+	0.872595i
$995$	−705.307	+	840.552i	−0.708851	+	0.844776i
$996$		0			0
$997$	−947.882	−	345.001i	−0.950734	−	0.346039i	−0.180338	−	0.983605i	$-0.557719\pi$
$997$	−947.882	−	345.001i	−0.950734	−	0.346039i	−0.770396	+	0.637566i	$0.779941\pi$
$998$			151.062i			0.151365i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.3.f.a.17.1		30
3.2	odd	2		27.3.f.a.23.5	yes	30
9.2	odd	6		243.3.f.d.215.1		30
9.4	even	3		243.3.f.b.134.1		30
9.5	odd	6		243.3.f.c.134.5		30
9.7	even	3		243.3.f.a.215.5		30
12.11	even	2		432.3.bc.a.401.5		30
27.2	odd	18		243.3.f.b.107.1		30
27.7	even	9		27.3.f.a.20.5	✓	30
27.11	odd	18		243.3.f.a.26.5		30
27.13	even	9		729.3.b.a.728.5		30
27.14	odd	18		729.3.b.a.728.26		30
27.16	even	9		243.3.f.d.26.1		30
27.20	odd	18	inner	81.3.f.a.62.1		30
27.25	even	9		243.3.f.c.107.5		30
108.7	odd	18		432.3.bc.a.209.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.5	✓	30	27.7	even	9
27.3.f.a.23.5	yes	30	3.2	odd	2
81.3.f.a.17.1		30	1.1	even	1	trivial
81.3.f.a.62.1		30	27.20	odd	18	inner
243.3.f.a.26.5		30	27.11	odd	18
243.3.f.a.215.5		30	9.7	even	3
243.3.f.b.107.1		30	27.2	odd	18
243.3.f.b.134.1		30	9.4	even	3
243.3.f.c.107.5		30	27.25	even	9
243.3.f.c.134.5		30	9.5	odd	6
243.3.f.d.26.1		30	27.16	even	9
243.3.f.d.215.1		30	9.2	odd	6
432.3.bc.a.209.5		30	108.7	odd	18
432.3.bc.a.401.5		30	12.11	even	2
729.3.b.a.728.5		30	27.13	even	9
729.3.b.a.728.26		30	27.14	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.898786 + 2.46939i) q^{2} +(-2.22591 - 1.86776i) q^{4} +(-6.15614 - 1.08549i) q^{5} +(-6.21846 + 5.21791i) q^{7} +(-2.49037 + 1.43782i) q^{8} +O(q^{10})\)	\(q+(-0.898786 + 2.46939i) q^{2} +(-2.22591 - 1.86776i) q^{4} +(-6.15614 - 1.08549i) q^{5} +(-6.21846 + 5.21791i) q^{7} +(-2.49037 + 1.43782i) q^{8} +(8.21356 - 14.2263i) q^{10} +(7.99059 - 1.40896i) q^{11} +(-9.12402 + 3.32087i) q^{13} +(-7.29600 - 20.0456i) q^{14} +(-3.33052 - 18.8883i) q^{16} +(13.0143 + 7.51380i) q^{17} +(8.93226 + 15.4711i) q^{19} +(11.6756 + 13.9144i) q^{20} +(-3.70256 + 20.9983i) q^{22} +(-16.9268 + 20.1726i) q^{23} +(13.2275 + 4.81440i) q^{25} -25.5156i q^{26} +23.5875 q^{28} +(-5.18906 + 14.2568i) q^{29} +(25.0755 + 21.0408i) q^{31} +(38.3082 + 6.75478i) q^{32} +(-30.2516 + 25.3841i) q^{34} +(43.9457 - 25.3721i) q^{35} +(-15.8096 + 27.3831i) q^{37} +(-46.2325 + 8.15204i) q^{38} +(16.8918 - 6.14813i) q^{40} +(-5.65018 - 15.5238i) q^{41} +(-14.5559 - 82.5505i) q^{43} +(-20.4179 - 11.7883i) q^{44} +(-34.6005 - 59.9298i) q^{46} +(-8.46562 - 10.0889i) q^{47} +(2.93393 - 16.6391i) q^{49} +(-23.7773 + 28.3367i) q^{50} +(26.5118 + 9.64952i) q^{52} +25.7140i q^{53} -50.7206 q^{55} +(7.98389 - 21.9356i) q^{56} +(-30.5419 - 25.6277i) q^{58} +(22.3660 + 3.94373i) q^{59} +(26.1131 - 21.9115i) q^{61} +(-74.4955 + 43.0100i) q^{62} +(-12.7517 + 22.0867i) q^{64} +(59.7736 - 10.5397i) q^{65} +(-7.61567 + 2.77188i) q^{67} +(-14.9346 - 41.0326i) q^{68} +(23.1558 + 131.323i) q^{70} +(-35.7557 - 20.6436i) q^{71} +(40.4046 + 69.9827i) q^{73} +(-53.4101 - 63.6517i) q^{74} +(9.01395 - 51.1206i) q^{76} +(-42.3374 + 50.4557i) q^{77} +(25.9652 + 9.45057i) q^{79} +119.894i q^{80} +43.4126 q^{82} +(6.01607 - 16.5290i) q^{83} +(-71.9616 - 60.3830i) q^{85} +(216.932 + 38.2510i) q^{86} +(-17.8737 + 14.9978i) q^{88} +(-24.4986 + 14.1443i) q^{89} +(39.4094 - 68.2590i) q^{91} +(75.3552 - 13.2871i) q^{92} +(32.5223 - 11.8372i) q^{94} +(-38.1945 - 104.938i) q^{95} +(29.2825 + 166.069i) q^{97} +(38.4516 + 22.2000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) \) 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8	\( 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 6 q^{11} - 6 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} - 3 q^{19} - 213 q^{20} - 42 q^{22} - 120 q^{23} - 15 q^{25} - 12 q^{28} + 168 q^{29} + 39 q^{31} + 360 q^{32} + 54 q^{34} + 252 q^{35} - 3 q^{37} + 84 q^{38} - 33 q^{40} - 228 q^{41} - 96 q^{43} - 639 q^{44} - 3 q^{46} - 399 q^{47} - 78 q^{49} - 303 q^{50} - 9 q^{52} - 12 q^{55} + 393 q^{56} + 129 q^{58} + 474 q^{59} + 138 q^{61} + 900 q^{62} - 51 q^{64} + 411 q^{65} + 354 q^{67} - 99 q^{68} + 489 q^{70} - 315 q^{71} - 66 q^{73} - 321 q^{74} + 258 q^{76} - 201 q^{77} + 30 q^{79} - 12 q^{82} + 33 q^{83} - 261 q^{85} + 258 q^{86} - 642 q^{88} - 72 q^{89} + 96 q^{91} + 3 q^{92} - 861 q^{94} - 681 q^{95} - 582 q^{97} - 882 q^{98}+O(q^{100}) \) 30 * q + 6 * q^2 - 6 * q^4 + 15 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 6 * q^11 - 6 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 - 3 * q^19 - 213 * q^20 - 42 * q^22 - 120 * q^23 - 15 * q^25 - 12 * q^28 + 168 * q^29 + 39 * q^31 + 360 * q^32 + 54 * q^34 + 252 * q^35 - 3 * q^37 + 84 * q^38 - 33 * q^40 - 228 * q^41 - 96 * q^43 - 639 * q^44 - 3 * q^46 - 399 * q^47 - 78 * q^49 - 303 * q^50 - 9 * q^52 - 12 * q^55 + 393 * q^56 + 129 * q^58 + 474 * q^59 + 138 * q^61 + 900 * q^62 - 51 * q^64 + 411 * q^65 + 354 * q^67 - 99 * q^68 + 489 * q^70 - 315 * q^71 - 66 * q^73 - 321 * q^74 + 258 * q^76 - 201 * q^77 + 30 * q^79 - 12 * q^82 + 33 * q^83 - 261 * q^85 + 258 * q^86 - 642 * q^88 - 72 * q^89 + 96 * q^91 + 3 * q^92 - 861 * q^94 - 681 * q^95 - 582 * q^97 - 882 * q^98

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