LMFDB - Embedded newform 432.3.x.a.125.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(125,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 10]))

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

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

chi := DirichletCharacter("432.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.x (of order $12$, degree $4$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.18
Character	$\chi$	$=$	432.125
Dual form			432.3.x.a.197.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.897969 - 1.78708i) q^{2} +(-2.38730 + 3.20948i) q^{4} +(3.11886 - 0.835695i) q^{5} +(-0.108974 + 0.0629164i) q^{7} +(7.87933 + 1.38428i) q^{8} +O(q^{10})$	\(q+(-0.897969 - 1.78708i) q^{2} +(-2.38730 + 3.20948i) q^{4} +(3.11886 - 0.835695i) q^{5} +(-0.108974 + 0.0629164i) q^{7} +(7.87933 + 1.38428i) q^{8} +(-4.29409 - 4.82321i) q^{10} +(-4.38767 + 16.3750i) q^{11} +(-23.2011 + 6.21671i) q^{13} +(0.210292 + 0.138249i) q^{14} +(-4.60157 - 15.3240i) q^{16} -26.4707i q^{17} +(-12.4559 - 12.4559i) q^{19} +(-4.76350 + 12.0050i) q^{20} +(33.2034 - 6.86314i) q^{22} +(11.0176 - 19.0831i) q^{23} +(-12.6218 + 7.28718i) q^{25} +(31.9436 + 35.8798i) q^{26} +(0.0582258 - 0.499952i) q^{28} +(-34.3012 - 9.19097i) q^{29} +(-2.65318 + 4.59544i) q^{31} +(-23.2532 + 21.9839i) q^{32} +(-47.3052 + 23.7698i) q^{34} +(-0.287297 + 0.287297i) q^{35} +(-22.6051 + 22.6051i) q^{37} +(-11.0746 + 33.4446i) q^{38} +(25.7313 - 2.26734i) q^{40} +(-13.0140 + 22.5410i) q^{41} +(-21.3428 - 5.71880i) q^{43} +(-42.0806 - 53.1742i) q^{44} +(-43.9965 - 2.55335i) q^{46} +(-13.6253 + 7.86657i) q^{47} +(-24.4921 + 42.4215i) q^{49} +(24.3567 + 16.0124i) q^{50} +(35.4356 - 89.3047i) q^{52} +(19.5741 + 19.5741i) q^{53} +54.7380i q^{55} +(-0.945739 + 0.344888i) q^{56} +(14.3764 + 69.5521i) q^{58} +(53.8883 - 14.4393i) q^{59} +(-19.8523 + 74.0899i) q^{61} +(10.5949 + 0.614877i) q^{62} +(60.1675 + 21.8144i) q^{64} +(-67.1656 + 38.7781i) q^{65} +(54.1848 - 14.5188i) q^{67} +(84.9572 + 63.1935i) q^{68} +(0.771405 + 0.255438i) q^{70} -10.7106 q^{71} -98.0523i q^{73} +(60.6957 + 20.0984i) q^{74} +(69.7129 - 10.2410i) q^{76} +(-0.552113 - 2.06051i) q^{77} +(1.02359 + 1.77291i) q^{79} +(-27.1578 - 43.9479i) q^{80} +(51.9687 + 3.01601i) q^{82} +(-86.3114 - 23.1271i) q^{83} +(-22.1214 - 82.5582i) q^{85} +(8.94527 + 43.2767i) q^{86} +(-57.2395 + 122.950i) q^{88} -76.9719 q^{89} +(2.13719 - 2.13719i) q^{91} +(34.9445 + 80.9181i) q^{92} +(26.2933 + 17.2855i) q^{94} +(-49.2574 - 28.4388i) q^{95} +(19.6709 + 34.0710i) q^{97} +(97.8038 + 5.67606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.897969	−	1.78708i	−0.448985	−	0.893540i
$2$	−0.897969	−	1.78708i	−0.448985	−	0.893540i
$3$		0			0
$3$		0			0
$4$	−2.38730	+	3.20948i	−0.596826	+	0.802371i
$5$	3.11886	−	0.835695i	0.623771	−	0.167139i	0.0669296	−	0.997758i	$-0.478680\pi$
$5$	3.11886	−	0.835695i	0.623771	−	0.167139i	0.556842	+	0.830619i	$0.312013\pi$
$6$		0			0
$7$	−0.108974	+	0.0629164i	−0.0155678	+	0.00898806i	−0.507764	−	0.861496i	$-0.669528\pi$
$7$	−0.108974	+	0.0629164i	−0.0155678	+	0.00898806i	0.492196	+	0.870484i	$0.336194\pi$
$8$	7.87933	+	1.38428i	0.984916	+	0.173035i
$9$		0			0
$10$	−4.29409	−	4.82321i	−0.429409	−	0.482321i
$11$	−4.38767	+	16.3750i	−0.398879	+	1.48864i	0.416193	+	0.909276i	$0.363364\pi$
$11$	−4.38767	+	16.3750i	−0.398879	+	1.48864i	−0.815072	+	0.579360i	$0.803303\pi$
$12$		0			0
$13$	−23.2011	+	6.21671i	−1.78470	+	0.478209i	−0.991427	−	0.130659i	$-0.958291\pi$
$13$	−23.2011	+	6.21671i	−1.78470	+	0.478209i	−0.793272	+	0.608867i	$0.791624\pi$
$14$	0.210292	+	0.138249i	0.0150209	+	0.00987492i
$15$		0			0
$16$	−4.60157	−	15.3240i	−0.287598	−	0.957751i
$17$		−	26.4707i		−	1.55710i	−0.627584	−	0.778549i	$-0.715956\pi$
$17$		−	26.4707i		−	1.55710i	0.627584	−	0.778549i	$-0.284044\pi$
$18$		0			0
$19$	−12.4559	−	12.4559i	−0.655573	−	0.655573i	0.298757	−	0.954329i	$-0.403428\pi$
$19$	−12.4559	−	12.4559i	−0.655573	−	0.655573i	−0.954329	+	0.298757i	$0.903428\pi$
$20$	−4.76350	+	12.0050i	−0.238175	+	0.600249i
$21$		0			0
$22$	33.2034	−	6.86314i	1.50925	−	0.311961i
$23$	11.0176	−	19.0831i	0.479028	−	0.829700i	−0.520683	−	0.853750i	$-0.674323\pi$
$23$	11.0176	−	19.0831i	0.479028	−	0.829700i	0.999711	+	0.0240499i	$0.00765606\pi$
$24$		0			0
$25$	−12.6218	+	7.28718i	−0.504870	+	0.291487i
$26$	31.9436	+	35.8798i	1.22860	+	1.37999i
$27$		0			0
$28$	0.0582258	−	0.499952i	0.00207949	−	0.0178554i
$29$	−34.3012	−	9.19097i	−1.18280	−	0.316930i	−0.386763	−	0.922179i	$-0.626407\pi$
$29$	−34.3012	−	9.19097i	−1.18280	−	0.316930i	−0.796036	+	0.605249i	$0.793073\pi$
$30$		0			0
$31$	−2.65318	+	4.59544i	−0.0855865	+	0.148240i	−0.905641	−	0.424045i	$-0.860610\pi$
$31$	−2.65318	+	4.59544i	−0.0855865	+	0.148240i	0.820054	+	0.572285i	$0.193943\pi$
$32$	−23.2532	+	21.9839i	−0.726661	+	0.686996i
$33$		0			0
$34$	−47.3052	+	23.7698i	−1.39133	+	0.699113i
$35$	−0.287297	+	0.287297i	−0.00820848	+	0.00820848i
$36$		0			0
$37$	−22.6051	+	22.6051i	−0.610948	+	0.610948i	−0.943193	−	0.332245i	$-0.892194\pi$
$37$	−22.6051	+	22.6051i	−0.610948	+	0.610948i	0.332245	+	0.943193i	$0.392194\pi$
$38$	−11.0746	+	33.4446i	−0.291438	+	0.880122i
$39$		0			0
$40$	25.7313	−	2.26734i	0.643283	−	0.0566834i
$41$	−13.0140	+	22.5410i	−0.317416	+	0.549780i	−0.979948	−	0.199253i	$-0.936148\pi$
$41$	−13.0140	+	22.5410i	−0.317416	+	0.549780i	0.662532	+	0.749033i	$0.269482\pi$
$42$		0			0
$43$	−21.3428	−	5.71880i	−0.496345	−	0.132995i	0.00195805	−	0.999998i	$-0.499377\pi$
$43$	−21.3428	−	5.71880i	−0.496345	−	0.132995i	−0.498303	+	0.867003i	$0.666043\pi$
$44$	−42.0806	−	53.1742i	−0.956377	−	1.20851i
$45$		0			0
$46$	−43.9965	−	2.55335i	−0.956446	−	0.0555075i
$47$	−13.6253	+	7.86657i	−0.289900	+	0.167374i	−0.637897	−	0.770122i	$-0.720195\pi$
$47$	−13.6253	+	7.86657i	−0.289900	+	0.167374i	0.347997	+	0.937496i	$0.386862\pi$
$48$		0			0
$49$	−24.4921	+	42.4215i	−0.499838	+	0.865746i
$50$	24.3567	+	16.0124i	0.487134	+	0.320248i
$51$		0			0
$52$	35.4356	−	89.3047i	0.681454	−	1.71740i
$53$	19.5741	+	19.5741i	0.369322	+	0.369322i	0.867230	−	0.497908i	$-0.165898\pi$
$53$	19.5741	+	19.5741i	0.369322	+	0.369322i	−0.497908	+	0.867230i	$0.665898\pi$
$54$		0			0
$55$			54.7380i			0.995237i
$56$	−0.945739	+	0.344888i	−0.0168882	+	0.00615871i
$57$		0			0
$58$	14.3764	+	69.5521i	0.247869	+	1.19917i
$59$	53.8883	−	14.4393i	0.913361	−	0.244734i	0.228616	−	0.973517i	$-0.426580\pi$
$59$	53.8883	−	14.4393i	0.913361	−	0.244734i	0.684745	+	0.728782i	$0.259913\pi$
$60$		0			0
$61$	−19.8523	+	74.0899i	−0.325448	+	1.21459i	0.588413	+	0.808560i	$0.299753\pi$
$61$	−19.8523	+	74.0899i	−0.325448	+	1.21459i	−0.913861	+	0.406027i	$0.866914\pi$
$62$	10.5949	+	0.614877i	0.170885	+	0.00991737i
$63$		0			0
$64$	60.1675	+	21.8144i	0.940118	+	0.340850i
$65$	−67.1656	+	38.7781i	−1.03332	+	0.596586i
$66$		0			0
$67$	54.1848	−	14.5188i	0.808729	−	0.216698i	0.169316	−	0.985562i	$-0.445844\pi$
$67$	54.1848	−	14.5188i	0.808729	−	0.216698i	0.639413	+	0.768863i	$0.279177\pi$
$68$	84.9572	+	63.1935i	1.24937	+	0.929316i
$69$		0			0
$70$	0.771405	+	0.255438i	0.0110201	+	0.00364912i
$71$	−10.7106			−0.150854			−0.0754270	−	0.997151i	$-0.524032\pi$
$71$	−10.7106			−0.150854			−0.0754270	+	0.997151i	$0.524032\pi$
$72$		0			0
$73$		−	98.0523i		−	1.34318i	−0.740922	−	0.671591i	$-0.765611\pi$
$73$		−	98.0523i		−	1.34318i	0.740922	−	0.671591i	$-0.234389\pi$
$74$	60.6957	+	20.0984i	0.820212	+	0.271600i
$75$		0			0
$76$	69.7129	−	10.2410i	0.917275	−	0.134750i
$77$	−0.552113	−	2.06051i	−0.00717030	−	0.0267599i
$78$		0			0
$79$	1.02359	+	1.77291i	0.0129569	+	0.0224419i	0.872431	−	0.488737i	$-0.162542\pi$
$79$	1.02359	+	1.77291i	0.0129569	+	0.0224419i	−0.859474	+	0.511179i	$0.829209\pi$
$80$	−27.1578	−	43.9479i	−0.339473	−	0.549349i
$81$		0			0
$82$	51.9687	+	3.01601i	0.633765	+	0.0367807i
$83$	−86.3114	−	23.1271i	−1.03990	−	0.278639i	−0.301826	−	0.953363i	$-0.597596\pi$
$83$	−86.3114	−	23.1271i	−1.03990	−	0.278639i	−0.738070	+	0.674724i	$0.764263\pi$
$84$		0			0
$85$	−22.1214	−	82.5582i	−0.260252	−	0.971273i
$86$	8.94527	+	43.2767i	0.104015	+	0.503217i
$87$		0			0
$88$	−57.2395	+	122.950i	−0.650449	+	1.39716i
$89$	−76.9719			−0.864853			−0.432427	−	0.901669i	$-0.642343\pi$
$89$	−76.9719			−0.864853			−0.432427	+	0.901669i	$0.642343\pi$
$90$		0			0
$91$	2.13719	−	2.13719i	0.0234856	−	0.0234856i
$92$	34.9445	+	80.9181i	0.379831	+	0.879544i
$93$		0			0
$94$	26.2933	+	17.2855i	0.279716	+	0.183889i
$95$	−49.2574	−	28.4388i	−0.518499	−	0.299356i
$96$		0			0
$97$	19.6709	+	34.0710i	0.202793	+	0.351247i	0.949427	−	0.313987i	$-0.101665\pi$
$97$	19.6709	+	34.0710i	0.202793	+	0.351247i	−0.746635	+	0.665234i	$0.768332\pi$
$98$	97.8038	+	5.67606i	0.997998	+	0.0579190i
$99$		0			0
$100$	6.74389	−	57.9060i	0.0674389	−	0.579060i
$101$	35.9552	−	134.186i	0.355992	−	1.32858i	−0.523240	−	0.852185i	$-0.675277\pi$
$101$	35.9552	−	134.186i	0.355992	−	1.32858i	0.879232	−	0.476394i	$-0.158056\pi$
$102$		0			0
$103$	−39.0917	−	22.5696i	−0.379531	−	0.219122i	0.298083	−	0.954540i	$-0.403653\pi$
$103$	−39.0917	−	22.5696i	−0.379531	−	0.219122i	−0.677614	+	0.735418i	$0.736986\pi$
$104$	−191.415	+	16.8667i	−1.84053	+	0.162180i
$105$		0			0
$106$	17.4035	−	52.5573i	0.164184	−	0.495824i
$107$	73.8367	+	73.8367i	0.690063	+	0.690063i	0.962246	−	0.272183i	$-0.0877455\pi$
$107$	73.8367	+	73.8367i	0.690063	+	0.690063i	−0.272183	+	0.962246i	$0.587746\pi$
$108$		0			0
$109$	13.8650	+	13.8650i	0.127202	+	0.127202i	0.767842	−	0.640640i	$-0.221331\pi$
$109$	13.8650	+	13.8650i	0.127202	+	0.127202i	−0.640640	+	0.767842i	$0.721331\pi$
$110$	97.8212	−	49.1531i	0.889283	−	0.446846i
$111$		0			0
$112$	1.46559	+	1.38041i	0.0130856	+	0.0123251i
$113$	49.6608	+	28.6717i	0.439476	+	0.253731i	0.703375	−	0.710819i	$-0.251675\pi$
$113$	49.6608	+	28.6717i	0.439476	+	0.253731i	−0.263899	+	0.964550i	$0.585009\pi$
$114$		0			0
$115$	18.4148	−	68.7248i	0.160128	−	0.597607i
$116$	111.385	−	88.1474i	0.960220	−	0.759891i
$117$		0			0
$118$	−74.1942	−	83.3366i	−0.628765	−	0.706242i
$119$	1.66544	+	2.88463i	0.0139953	+	0.0242406i
$120$		0			0
$121$	−144.100	−	83.1962i	−1.19091	−	0.687572i
$122$	150.231	−	31.0527i	1.23140	−	0.254531i
$123$		0			0
$124$	−8.41506	−	19.4861i	−0.0678634	−	0.157146i
$125$	−90.3546	+	90.3546i	−0.722837	+	0.722837i
$126$		0			0
$127$	93.1714			0.733633			0.366816	−	0.930293i	$-0.380448\pi$
$127$	93.1714			0.733633			0.366816	+	0.930293i	$0.380448\pi$
$128$	−15.0445	−	127.113i	−0.117535	−	0.993069i
$129$		0			0
$130$	129.612	+	85.2087i	0.997016	+	0.655452i
$131$	6.20834	+	23.1698i	0.0473919	+	0.176869i	0.985565	−	0.169298i	$-0.0541499\pi$
$131$	6.20834	+	23.1698i	0.0473919	+	0.176869i	−0.938173	+	0.346167i	$0.887483\pi$
$132$		0			0
$133$	2.14105	+	0.573693i	0.0160981	+	0.00431348i
$134$	−74.6025	−	83.7952i	−0.556735	−	0.625337i
$135$		0			0
$136$	36.6429	−	208.571i	0.269433	−	1.53361i
$137$	31.3293	+	54.2639i	0.228681	+	0.396087i	0.957417	−	0.288707i	$-0.0932254\pi$
$137$	31.3293	+	54.2639i	0.228681	+	0.396087i	−0.728736	+	0.684794i	$0.759892\pi$
$138$		0			0
$139$	2.78647	+	10.3992i	0.0200465	+	0.0748147i	0.975224	−	0.221218i	$-0.0710031\pi$
$139$	2.78647	+	10.3992i	0.0200465	+	0.0748147i	−0.955178	+	0.296032i	$0.904336\pi$
$140$	−0.236210	−	1.60794i	−0.00168721	−	0.0114853i
$141$		0			0
$142$	9.61781	+	19.1407i	0.0677311	+	0.134794i
$143$		−	407.195i		−	2.84752i
$144$		0			0
$145$	−114.661			−0.790767
$146$	−175.227	+	88.0479i	−1.20019	+	0.603068i
$147$		0			0
$148$	−18.5855	−	126.516i	−0.125577	−	0.854836i
$149$	−34.5886	+	9.26799i	−0.232138	+	0.0622013i	−0.373013	−	0.927826i	$-0.621675\pi$
$149$	−34.5886	+	9.26799i	−0.232138	+	0.0622013i	0.140875	+	0.990027i	$0.455009\pi$
$150$		0			0
$151$	−58.7226	+	33.9035i	−0.388891	+	0.224526i	−0.681680	−	0.731651i	$-0.738750\pi$
$151$	−58.7226	+	33.9035i	−0.388891	+	0.224526i	0.292788	+	0.956177i	$0.405417\pi$
$152$	−80.9015	−	115.386i	−0.532247	−	0.759121i
$153$		0			0
$154$	−3.18652	+	2.83695i	−0.0206917	+	0.0184217i
$155$	−4.43450	+	16.5498i	−0.0286097	+	0.106773i
$156$		0			0
$157$	−251.958	+	67.5119i	−1.60483	+	0.430012i	−0.946496	−	0.322716i	$-0.895404\pi$
$157$	−251.958	+	67.5119i	−1.60483	+	0.430012i	−0.658331	+	0.752728i	$0.728737\pi$
$158$	2.24918	−	3.42126i	0.0142353	−	0.0216535i
$159$		0			0
$160$	−54.1515	+	87.9971i	−0.338447	+	0.549982i
$161$			2.77276i			0.0172221i
$162$		0			0
$163$	139.682	+	139.682i	0.856947	+	0.856947i	0.990977	−	0.134030i	$-0.0427920\pi$
$163$	139.682	+	139.682i	0.856947	+	0.856947i	−0.134030	+	0.990977i	$0.542792\pi$
$164$	−41.2765	−	95.5805i	−0.251686	−	0.582808i
$165$		0			0
$166$	36.1751	+	175.013i	0.217922	+	1.05429i
$167$	146.617	−	253.948i	0.877946	−	1.52065i	0.0243553	−	0.999703i	$-0.492247\pi$
$167$	146.617	−	253.948i	0.877946	−	1.52065i	0.853591	−	0.520944i	$-0.174420\pi$
$168$		0			0
$169$	353.285	−	203.969i	2.09044	−	1.20692i
$170$	−127.674	+	113.667i	−0.751022	+	0.668632i
$171$		0			0
$172$	69.3062	−	54.8470i	0.402943	−	0.318878i
$173$	−283.735	−	76.0266i	−1.64009	−	0.439460i	−0.683274	−	0.730162i	$-0.739445\pi$
$173$	−283.735	−	76.0266i	−1.64009	−	0.439460i	−0.956814	+	0.290702i	$0.906111\pi$
$174$		0			0
$175$	0.916966	−	1.58823i	0.00523981	−	0.00907561i
$176$	271.121	−	8.11401i	1.54046	−	0.0461024i
$177$		0			0
$178$	69.1184	+	137.555i	0.388306	+	0.772780i
$179$	92.1924	−	92.1924i	0.515042	−	0.515042i	−0.401025	−	0.916067i	$-0.631346\pi$
$179$	92.1924	−	92.1924i	0.515042	−	0.515042i	0.916067	+	0.401025i	$0.131346\pi$
$180$		0			0
$181$	−114.860	+	114.860i	−0.634587	+	0.634587i	−0.949215	−	0.314628i	$-0.898120\pi$
$181$	−114.860	+	114.860i	−0.634587	+	0.634587i	0.314628	+	0.949215i	$0.398120\pi$
$182$	−5.73847	−	1.90020i	−0.0315300	−	0.0104407i
$183$		0			0
$184$	113.228	−	135.110i	0.615369	−	0.734296i
$185$	−51.6110	+	89.3929i	−0.278978	+	0.483205i
$186$		0			0
$187$	433.457	+	116.145i	2.31795	+	0.621094i
$188$	7.28008	−	62.5100i	0.0387239	−	0.332500i
$189$		0			0
$190$	−6.59071	+	113.564i	−0.0346879	+	0.597705i
$191$	21.1407	−	12.2056i	0.110684	−	0.0639036i	−0.443636	−	0.896207i	$-0.646312\pi$
$191$	21.1407	−	12.2056i	0.110684	−	0.0639036i	0.554320	+	0.832304i	$0.312978\pi$
$192$		0			0
$193$	114.683	−	198.637i	0.594212	−	1.02921i	−0.399446	−	0.916757i	$-0.630797\pi$
$193$	114.683	−	198.637i	0.594212	−	1.02921i	0.993658	−	0.112449i	$-0.0358693\pi$
$194$	43.2236	−	65.7481i	0.222802	−	0.338908i
$195$		0			0
$196$	−77.6812	−	179.880i	−0.396333	−	0.917755i
$197$	−21.4131	−	21.4131i	−0.108696	−	0.108696i	0.650667	−	0.759363i	$-0.274489\pi$
$197$	−21.4131	−	21.4131i	−0.108696	−	0.108696i	−0.759363	+	0.650667i	$0.774489\pi$
$198$		0			0
$199$			154.622i			0.776995i	0.921450	+	0.388498i	$0.127006\pi$
$199$			154.622i			0.776995i	−0.921450	+	0.388498i	$0.872994\pi$
$200$	−109.538	+	39.9460i	−0.547692	+	0.199730i
$201$		0			0
$202$	−272.088	+	56.2406i	−1.34697	+	0.278419i
$203$	4.31621	−	1.15653i	0.0212621	−	0.00569717i
$204$		0			0
$205$	−21.7515	+	81.1778i	−0.106105	+	0.395989i
$206$	−5.23052	+	90.1267i	−0.0253909	+	0.437508i
$207$		0			0
$208$	202.027	+	326.927i	0.971281	+	1.57177i
$209$	258.617	−	149.313i	1.23740	−	0.714415i
$210$		0			0
$211$	−125.154	+	33.5348i	−0.593146	+	0.158933i	−0.542890	−	0.839804i	$-0.682670\pi$
$211$	−125.154	+	33.5348i	−0.593146	+	0.158933i	−0.0502551	+	0.998736i	$0.516003\pi$
$212$	−109.552	+	16.0934i	−0.516754	+	0.0759124i
$213$		0			0
$214$	65.6490	−	198.255i	0.306771	−	0.926426i
$215$	−71.3444			−0.331835
$216$		0			0
$217$		−	0.667715i		−	0.00307703i
$218$	12.3275	−	37.2282i	0.0565483	−	0.170772i
$219$		0			0
$220$	−175.681	−	130.676i	−0.798549	−	0.593983i
$221$	164.561	+	614.148i	0.744618	+	2.77895i
$222$		0			0
$223$	−131.634	−	227.996i	−0.590286	−	1.02241i	−0.994194	−	0.107605i	$-0.965682\pi$
$223$	−131.634	−	227.996i	−0.590286	−	1.02241i	0.403908	−	0.914800i	$-0.367652\pi$
$224$	1.15085	−	3.85869i	0.00513774	−	0.0172263i
$225$		0			0
$226$	6.64468	−	114.494i	0.0294012	−	0.506610i
$227$	320.488	+	85.8746i	1.41184	+	0.378302i	0.882583	−	0.470157i	$-0.155803\pi$
$227$	320.488	+	85.8746i	1.41184	+	0.378302i	0.529260	+	0.848459i	$0.322469\pi$
$228$		0			0
$229$	−31.2680	−	116.694i	−0.136542	−	0.509580i	−0.999987	−	0.00513753i	$-0.998365\pi$
$229$	−31.2680	−	116.694i	−0.136542	−	0.509580i	0.863445	−	0.504443i	$-0.168302\pi$
$230$	−139.353	+	28.8041i	−0.605881	+	0.125235i
$231$		0			0
$232$	−257.547	−	119.901i	−1.11012	−	0.516815i
$233$	289.513			1.24254			0.621272	−	0.783595i	$-0.286616\pi$
$233$	289.513			1.24254			0.621272	+	0.783595i	$0.286616\pi$
$234$		0			0
$235$	−35.9213	+	35.9213i	−0.152857	+	0.152857i
$236$	−82.3049	+	207.425i	−0.348750	+	0.878918i
$237$		0			0
$238$	3.65954	−	5.56658i	0.0153762	−	0.0233890i
$239$	0.616801	+	0.356110i	0.00258076	+	0.00149000i	0.501290	−	0.865279i	$-0.332859\pi$
$239$	0.616801	+	0.356110i	0.00258076	+	0.00149000i	−0.498709	+	0.866769i	$0.666192\pi$
$240$		0			0
$241$	−14.9538	−	25.9007i	−0.0620488	−	0.107472i	0.833332	−	0.552772i	$-0.186430\pi$
$241$	−14.9538	−	25.9007i	−0.0620488	−	0.107472i	−0.895381	+	0.445301i	$0.853097\pi$
$242$	−19.2808	+	332.226i	−0.0796726	+	1.37283i
$243$		0			0
$244$	−190.397	−	240.591i	−0.780314	−	0.986027i
$245$	−40.9358	+	152.775i	−0.167085	+	0.623570i
$246$		0			0
$247$	366.425	+	211.555i	1.48350	+	0.856500i
$248$	−27.2667	+	32.5362i	−0.109946	+	0.131195i
$249$		0			0
$250$	242.606	+	80.3352i	0.970426	+	0.321341i
$251$	128.737	+	128.737i	0.512896	+	0.512896i	0.915413	−	0.402516i	$-0.131864\pi$
$251$	128.737	+	128.737i	0.512896	+	0.512896i	−0.402516	+	0.915413i	$0.631864\pi$
$252$		0			0
$253$	264.144	+	264.144i	1.04405	+	1.04405i
$254$	−83.6650	−	166.505i	−0.329390	−	0.655530i
$255$		0			0
$256$	−213.651	+	141.029i	−0.834575	+	0.550895i
$257$	−158.342	−	91.4186i	−0.616115	−	0.355714i	0.159240	−	0.987240i	$-0.449096\pi$
$257$	−158.342	−	91.4186i	−0.616115	−	0.355714i	−0.775355	+	0.631526i	$0.782429\pi$
$258$		0			0
$259$	1.04114	−	3.88561i	0.00401986	−	0.0150023i
$260$	35.8870	−	308.142i	0.138027	−	1.18516i
$261$		0			0
$262$	35.8314	−	31.9006i	0.136761	−	0.121758i
$263$	167.300	+	289.773i	0.636123	+	1.10180i	0.986276	+	0.165105i	$0.0527963\pi$
$263$	167.300	+	289.773i	0.636123	+	1.10180i	−0.350153	+	0.936693i	$0.613870\pi$
$264$		0			0
$265$	77.4067	+	44.6908i	0.292101	+	0.168644i
$266$	−0.897364	−	4.34139i	−0.00337355	−	0.0163210i
$267$		0			0
$268$	−82.7578	+	208.566i	−0.308798	+	0.778232i
$269$	−87.1516	+	87.1516i	−0.323984	+	0.323984i	−0.850293	−	0.526309i	$-0.823575\pi$
$269$	−87.1516	+	87.1516i	−0.323984	+	0.323984i	0.526309	+	0.850293i	$0.323575\pi$
$270$		0			0
$271$	−479.619			−1.76981			−0.884907	−	0.465769i	$-0.845778\pi$
$271$	−479.619			−1.76981			−0.884907	+	0.465769i	$0.845778\pi$
$272$	−405.637	+	121.807i	−1.49131	+	0.447819i
$273$		0			0
$274$	68.8412	−	104.715i	0.251245	−	0.382173i
$275$	−63.9474	−	238.655i	−0.232536	−	0.867837i
$276$		0			0
$277$	−306.096	−	82.0181i	−1.10504	−	0.296094i	−0.340224	−	0.940344i	$-0.610503\pi$
$277$	−306.096	−	82.0181i	−1.10504	−	0.296094i	−0.764815	+	0.644250i	$0.777170\pi$
$278$	16.0821	−	14.3178i	0.0578493	−	0.0515030i
$279$		0			0
$280$	−2.66140	+	1.86600i	−0.00950501	+	0.00666430i
$281$	−33.8559	−	58.6402i	−0.120484	−	0.208684i	0.799475	−	0.600700i	$-0.205111\pi$
$281$	−33.8559	−	58.6402i	−0.120484	−	0.208684i	−0.919959	+	0.392016i	$0.871778\pi$
$282$		0			0
$283$	−77.1937	−	288.091i	−0.272769	−	1.01799i	−0.957322	−	0.289025i	$-0.906669\pi$
$283$	−77.1937	−	288.091i	−0.272769	−	1.01799i	0.684552	−	0.728964i	$-0.259998\pi$
$284$	25.5695	−	34.3756i	0.0900335	−	0.121041i
$285$		0			0
$286$	−727.689	+	365.648i	−2.54437	+	1.27849i
$287$		−	3.27519i		−	0.0114118i
$288$		0			0
$289$	−411.696			−1.42455
$290$	102.962	+	204.909i	0.355042	+	0.706581i
$291$		0			0
$292$	314.697	+	234.080i	1.07773	+	0.801645i
$293$	−255.960	+	68.5842i	−0.873582	+	0.234076i	−0.667636	−	0.744488i	$-0.732694\pi$
$293$	−255.960	+	68.5842i	−0.873582	+	0.234076i	−0.205946	+	0.978563i	$0.566027\pi$
$294$		0			0
$295$	156.003	−	90.0683i	0.528824	−	0.305316i
$296$	−209.405	+	146.821i	−0.707448	+	0.496017i
$297$		0			0
$298$	47.6221	+	53.4902i	0.159806	+	0.179497i
$299$	−136.987	+	511.242i	−0.458150	+	1.70984i
$300$		0			0
$301$	2.68563	−	0.719613i	0.00892236	−	0.00239074i
$302$	113.319	+	74.4976i	0.375229	+	0.246681i
$303$		0			0
$304$	−133.558	+	248.191i	−0.439334	+	0.816417i
$305$			247.666i			0.812020i
$306$		0			0
$307$	314.665	+	314.665i	1.02497	+	1.02497i	0.999680	+	0.0252880i	$0.00805028\pi$
$307$	314.665	+	314.665i	1.02497	+	1.02497i	0.0252880	+	0.999680i	$0.491950\pi$
$308$	7.93124	+	3.14707i	0.0257508	+	0.0102178i
$309$		0			0
$310$	33.5578	−	6.93639i	0.108251	−	0.0223754i
$311$	−191.301	+	331.343i	−0.615115	+	1.06541i	0.375249	+	0.926924i	$0.377557\pi$
$311$	−191.301	+	331.343i	−0.615115	+	1.06541i	−0.990364	+	0.138486i	$0.955776\pi$
$312$		0			0
$313$	−7.19769	+	4.15559i	−0.0229958	+	0.0132766i	−0.511454	−	0.859311i	$-0.670893\pi$
$313$	−7.19769	+	4.15559i	−0.0229958	+	0.0132766i	0.488458	+	0.872587i	$0.337560\pi$
$314$	346.899	+	389.645i	1.10478	+	1.24091i
$315$		0			0
$316$	−8.13376	−	0.947279i	−0.0257397	−	0.00299772i
$317$	−56.0396	−	15.0158i	−0.176781	−	0.0473684i	0.169343	−	0.985557i	$-0.445836\pi$
$317$	−56.0396	−	15.0158i	−0.176781	−	0.0473684i	−0.346124	+	0.938189i	$0.612502\pi$
$318$		0			0
$319$	301.004	−	521.355i	0.943587	−	1.63434i
$320$	205.884	+	17.7543i	0.643388	+	0.0554822i
$321$		0			0
$322$	4.95514	−	2.48985i	0.0153886	−	0.00773246i
$323$	−329.715	+	329.715i	−1.02079	+	1.02079i
$324$		0			0
$325$	247.536	−	247.536i	0.761650	−	0.761650i
$326$	124.193	−	375.054i	0.380960	−	1.15047i
$327$		0			0
$328$	−133.745	+	159.593i	−0.407759	+	0.486563i
$329$	0.989873	−	1.71451i	0.00300873	−	0.00521128i
$330$		0			0
$331$	432.052	+	115.768i	1.30529	+	0.349752i	0.843450	−	0.537208i	$-0.180521\pi$
$331$	432.052	+	115.768i	1.30529	+	0.349752i	0.461844	+	0.886961i	$0.347188\pi$
$332$	280.277	−	221.804i	0.844209	−	0.668083i
$333$		0			0
$334$	−585.483	−	33.9786i	−1.75294	−	0.101732i
$335$	156.861	−	90.5640i	0.468243	−	0.270340i
$336$		0			0
$337$	−58.1836	+	100.777i	−0.172651	+	0.299041i	−0.939346	−	0.342971i	$-0.888567\pi$
$337$	−58.1836	+	100.777i	−0.172651	+	0.299041i	0.766695	+	0.642012i	$0.221900\pi$
$338$	−681.748	−	448.190i	−2.01701	−	1.32601i
$339$		0			0
$340$	317.780	+	126.093i	0.934646	+	0.370862i
$341$	−63.6091	−	63.6091i	−0.186537	−	0.186537i
$342$		0			0
$343$		−	12.3296i		−	0.0359464i
$344$	−160.251	−	74.6048i	−0.465845	−	0.216874i
$345$		0			0
$346$	118.920	+	575.327i	0.343699	+	1.66279i
$347$	453.760	−	121.585i	1.30767	−	0.350388i	0.463322	−	0.886190i	$-0.346657\pi$
$347$	453.760	−	121.585i	1.30767	−	0.350388i	0.844343	+	0.535802i	$0.179991\pi$
$348$		0			0
$349$	123.585	−	461.226i	0.354112	−	1.32157i	−0.527486	−	0.849564i	$-0.676865\pi$
$349$	123.585	−	461.226i	0.354112	−	1.32157i	0.881598	−	0.472001i	$-0.156468\pi$
$350$	−3.66170	−	0.212508i	−0.0104620	−	0.000607165i
$351$		0			0
$352$	−257.959	−	477.229i	−0.732837	−	1.35576i
$353$	166.903	−	96.3615i	0.472813	−	0.272979i	−0.244604	−	0.969623i	$-0.578658\pi$
$353$	166.903	−	96.3615i	0.472813	−	0.272979i	0.717417	+	0.696644i	$0.245324\pi$
$354$		0			0
$355$	−33.4049	+	8.95082i	−0.0940983	+	0.0252136i
$356$	183.755	−	247.040i	0.516167	−	0.693933i
$357$		0			0
$358$	−247.541	−	81.9692i	−0.691456	−	0.228964i
$359$	−351.048			−0.977851			−0.488925	−	0.872326i	$-0.662611\pi$
$359$	−351.048			−0.977851			−0.488925	+	0.872326i	$0.662611\pi$
$360$		0			0
$361$		−	50.7021i		−	0.140449i
$362$	308.405	+	102.123i	0.851948	+	0.282109i
$363$		0			0
$364$	1.75716	+	11.9614i	0.00482736	+	0.0328610i
$365$	−81.9418	−	305.811i	−0.224498	−	0.837838i
$366$		0			0
$367$	−227.733	−	394.445i	−0.620526	−	1.07478i	−0.989388	−	0.145298i	$-0.953586\pi$
$367$	−227.733	−	394.445i	−0.620526	−	1.07478i	0.368862	−	0.929484i	$-0.379747\pi$
$368$	−343.128	−	81.0222i	−0.932414	−	0.220169i
$369$		0			0
$370$	206.097	+	11.9609i	0.557020	+	0.0323267i
$371$	−3.36460	−	0.901543i	−0.00906901	−	0.00243004i
$372$		0			0
$373$	152.354	+	568.591i	0.408455	+	1.52437i	0.797594	+	0.603195i	$0.206106\pi$
$373$	152.354	+	568.591i	0.408455	+	1.52437i	−0.389139	+	0.921179i	$0.627227\pi$
$374$	−181.672	−	878.917i	−0.485754	−	2.35004i
$375$		0			0
$376$	−118.248	+	43.1220i	−0.314489	+	0.114686i
$377$	852.962			2.26250
$378$		0			0
$379$	−185.274	+	185.274i	−0.488851	+	0.488851i	−0.907943	−	0.419093i	$-0.862348\pi$
$379$	−185.274	+	185.274i	−0.488851	+	0.488851i	0.419093	+	0.907943i	$0.362348\pi$
$380$	208.866	−	90.1989i	0.549648	−	0.237365i
$381$		0			0
$382$	−40.7960	−	26.8198i	−0.106796	−	0.0702090i
$383$	277.854	+	160.419i	0.725467	+	0.418848i	0.816761	−	0.576976i	$-0.195767\pi$
$383$	277.854	+	160.419i	0.725467	+	0.418848i	−0.0912948	+	0.995824i	$0.529101\pi$
$384$		0			0
$385$	−3.44392	−	5.96505i	−0.00894525	−	0.0154936i
$386$	−457.961	−	26.5779i	−1.18643	−	0.0688546i
$387$		0			0
$388$	−156.311	−	18.2043i	−0.402862	−	0.0469184i
$389$	104.704	−	390.762i	0.269163	−	1.00453i	−0.690490	−	0.723342i	$-0.742605\pi$
$389$	104.704	−	390.762i	0.269163	−	1.00453i	0.959653	−	0.281188i	$-0.0907284\pi$
$390$		0			0
$391$	−505.142	−	291.644i	−1.29192	−	0.745893i
$392$	−251.704	+	300.349i	−0.642103	+	0.766197i
$393$		0			0
$394$	−19.0386	+	57.4953i	−0.0483214	+	0.145927i
$395$	4.67405	+	4.67405i	0.0118330	+	0.0118330i
$396$		0			0
$397$	314.667	+	314.667i	0.792612	+	0.792612i	0.981918	−	0.189306i	$-0.0606239\pi$
$397$	314.667	+	314.667i	0.792612	+	0.792612i	−0.189306	+	0.981918i	$0.560624\pi$
$398$	276.322	−	138.846i	0.694276	−	0.348859i
$399$		0			0
$400$	169.749	+	159.884i	0.424372	+	0.399709i
$401$	−147.995	−	85.4451i	−0.369065	−	0.213080i	0.303985	−	0.952677i	$-0.401683\pi$
$401$	−147.995	−	85.4451i	−0.369065	−	0.213080i	−0.673050	+	0.739597i	$0.735016\pi$
$402$		0			0
$403$	32.9881	−	123.113i	0.0818564	−	0.305492i
$404$	344.833	+	435.741i	0.853548	+	1.07857i
$405$		0			0
$406$	−5.94263	−	6.67489i	−0.0146370	−	0.0164406i
$407$	−270.975	−	469.342i	−0.665785	−	1.15317i
$408$		0			0
$409$	263.338	+	152.038i	0.643858	+	0.371732i	0.786099	−	0.618100i	$-0.212098\pi$
$409$	263.338	+	152.038i	0.643858	+	0.371732i	−0.142241	+	0.989832i	$0.545431\pi$
$410$	164.603	−	34.0235i	0.401472	−	0.0829841i
$411$		0			0
$412$	165.760	−	71.5837i	0.402331	−	0.173747i
$413$	−4.96398	+	4.96398i	−0.0120193	+	0.0120193i
$414$		0			0
$415$	−288.520			−0.695229
$416$	402.831	−	654.608i	0.968345	−	1.57358i
$417$		0			0
$418$	−499.064	−	328.091i	−1.19393	−	0.784907i
$419$	−92.4334	−	344.966i	−0.220605	−	0.823308i	−0.984118	−	0.177516i	$-0.943194\pi$
$419$	−92.4334	−	344.966i	−0.220605	−	0.823308i	0.763513	−	0.645792i	$-0.223473\pi$
$420$		0			0
$421$	454.736	+	121.846i	1.08013	+	0.289421i	0.754651	−	0.656127i	$-0.227806\pi$
$421$	454.736	+	121.846i	1.08013	+	0.289421i	0.325483	+	0.945548i	$0.394473\pi$
$422$	172.314	+	193.546i	0.408326	+	0.458641i
$423$		0			0
$424$	127.134	+	181.327i	0.299845	+	0.427657i
$425$	192.896	+	334.106i	0.453874	+	0.786133i
$426$		0			0
$427$	−2.49807	−	9.32294i	−0.00585029	−	0.0218336i
$428$	−413.248	+	60.7071i	−0.965533	+	0.141839i
$429$		0			0
$430$	64.0651	+	127.498i	0.148989	+	0.296507i
$431$			5.42582i			0.0125889i	0.999980	+	0.00629445i	$0.00200360\pi$
$431$			5.42582i			0.0125889i	−0.999980	+	0.00629445i	$0.997996\pi$
$432$		0			0
$433$	229.597			0.530246			0.265123	−	0.964215i	$-0.414587\pi$
$433$	229.597			0.530246			0.265123	+	0.964215i	$0.414587\pi$
$434$	−1.19326	+	0.599587i	−0.00274944	+	0.00138154i
$435$		0			0
$436$	−77.5996	+	11.3996i	−0.177981	+	0.0261458i
$437$	−374.931	+	100.462i	−0.857966	+	0.229891i
$438$		0			0
$439$	−586.491	+	338.611i	−1.33597	+	0.771323i	−0.986207	−	0.165515i	$-0.947071\pi$
$439$	−586.491	+	338.611i	−1.33597	+	0.771323i	−0.349763	+	0.936838i	$0.613738\pi$
$440$	−75.7728	+	431.299i	−0.172211	+	0.980224i
$441$		0			0
$442$	949.762	−	845.569i	2.14878	−	1.91305i
$443$	−86.2050	+	321.722i	−0.194594	+	0.726234i	0.797778	+	0.602951i	$0.206009\pi$
$443$	−86.2050	+	321.722i	−0.194594	+	0.726234i	−0.992372	+	0.123282i	$0.960658\pi$
$444$		0			0
$445$	−240.064	+	64.3250i	−0.539470	+	0.144551i
$446$	−289.244	+	439.974i	−0.648530	+	0.986488i
$447$		0			0
$448$	−7.92921	+	1.40831i	−0.0176991	+	0.00314356i
$449$		−	456.248i		−	1.01614i	−0.861315	−	0.508072i	$-0.830358\pi$
$449$		−	456.248i		−	1.01614i	0.861315	−	0.508072i	$-0.169642\pi$
$450$		0			0
$451$	−312.007	−	312.007i	−0.691812	−	0.691812i
$452$	−210.576	+	90.9375i	−0.465877	+	0.201189i
$453$		0			0
$454$	−134.324	−	649.851i	−0.295868	−	1.43139i
$455$	4.87956	−	8.45164i	0.0107243	−	0.0185750i
$456$		0			0
$457$	−221.668	+	127.980i	−0.485051	+	0.280044i	−0.722519	−	0.691351i	$-0.757016\pi$
$457$	−221.668	+	127.980i	−0.485051	+	0.280044i	0.237468	+	0.971395i	$0.423683\pi$
$458$	−180.463	+	160.666i	−0.394025	+	0.350799i
$459$		0			0
$460$	176.610	+	223.169i	0.383934	+	0.485150i
$461$	211.964	+	56.7956i	0.459792	+	0.123201i	0.481278	−	0.876568i	$-0.340173\pi$
$461$	211.964	+	56.7956i	0.459792	+	0.123201i	−0.0214855	+	0.999769i	$0.506840\pi$
$462$		0			0
$463$	−364.839	+	631.920i	−0.787990	+	1.36484i	0.139207	+	0.990263i	$0.455545\pi$
$463$	−364.839	+	631.920i	−0.787990	+	1.36484i	−0.927197	+	0.374575i	$0.877789\pi$
$464$	16.9966	+	567.924i	0.0366307	+	1.22397i
$465$		0			0
$466$	−259.973	−	517.382i	−0.557883	−	1.11026i
$467$	−368.129	+	368.129i	−0.788285	+	0.788285i	−0.981213	−	0.192928i	$-0.938202\pi$
$467$	−368.129	+	368.129i	−0.788285	+	0.788285i	0.192928	+	0.981213i	$0.438202\pi$
$468$		0			0
$469$	−4.99129	+	4.99129i	−0.0106424	+	0.0106424i
$470$	96.4504	+	31.9380i	0.205214	+	0.0679531i
$471$		0			0
$472$	444.591	−	39.1756i	0.941931	−	0.0829991i
$473$	187.291	−	324.397i	0.395963	−	0.685829i
$474$		0			0
$475$	247.983	+	66.4469i	0.522070	+	0.139888i
$476$	−13.2341	−	1.54127i	−0.0278027	−	0.00323797i
$477$		0			0
$478$	0.0825289	−	1.42205i	0.000172655	−	0.00297500i
$479$	341.192	−	196.987i	0.712300	−	0.411247i	−0.0996121	−	0.995026i	$-0.531760\pi$
$479$	341.192	−	196.987i	0.712300	−	0.411247i	0.811912	+	0.583780i	$0.198427\pi$
$480$		0			0
$481$	383.933	−	664.992i	0.798198	−	1.38252i
$482$	−32.8585	+	49.9816i	−0.0681712	+	0.103696i
$483$		0			0
$484$	611.027	−	263.872i	1.26245	−	0.545190i
$485$	89.8235	+	89.8235i	0.185203	+	0.185203i
$486$		0			0
$487$		−	549.648i		−	1.12864i	−0.825556	−	0.564320i	$-0.809138\pi$
$487$		−	549.648i		−	1.12864i	0.825556	−	0.564320i	$-0.190862\pi$
$488$	−258.984	+	556.297i	−0.530705	+	1.13995i
$489$		0			0
$490$	309.779	−	64.0313i	0.632203	−	0.130676i
$491$	−300.675	+	80.5657i	−0.612374	+	0.164085i	−0.551658	−	0.834070i	$-0.686005\pi$
$491$	−300.675	+	80.5657i	−0.612374	+	0.164085i	−0.0607152	+	0.998155i	$0.519338\pi$
$492$		0			0
$493$	−243.291	+	907.974i	−0.493491	+	1.84173i
$494$	49.0281	−	844.800i	0.0992472	−	1.71012i
$495$		0			0
$496$	82.6295	+	19.5111i	0.166592	+	0.0393370i
$497$	1.16718	−	0.673874i	0.00234846	−	0.00135588i
$498$		0			0
$499$	−70.7474	+	18.9567i	−0.141778	+	0.0379894i	−0.329010	−	0.944326i	$-0.606715\pi$
$499$	−70.7474	+	18.9567i	−0.141778	+	0.0379894i	0.187232	+	0.982316i	$0.440048\pi$
$500$	−74.2878	−	505.695i	−0.148576	−	1.01139i
$501$		0			0
$502$	114.461	−	345.665i	0.228011	−	0.688576i
$503$	−444.742			−0.884178			−0.442089	−	0.896971i	$-0.645763\pi$
$503$	−444.742			−0.884178			−0.442089	+	0.896971i	$0.645763\pi$
$504$		0			0
$505$		−	448.556i		−	0.888229i
$506$	234.853	−	709.240i	0.464137	−	1.40166i
$507$		0			0
$508$	−222.428	+	299.032i	−0.437851	+	0.588646i
$509$	−170.434	−	636.068i	−0.334841	−	1.24964i	−0.904042	−	0.427444i	$-0.859414\pi$
$509$	−170.434	−	636.068i	−0.334841	−	1.24964i	0.569201	−	0.822199i	$-0.307253\pi$
$510$		0			0
$511$	6.16910	+	10.6852i	0.0120726	+	0.0209104i
$512$	443.882	+	255.172i	0.866958	+	0.498382i
$513$		0			0
$514$	−21.1863	+	365.060i	−0.0412185	+	0.710234i
$515$	−140.783	−	37.7226i	−0.273364	−	0.0732478i
$516$		0			0
$517$	−69.0318	−	257.630i	−0.133524	−	0.498317i
$518$	−7.87880	+	1.62855i	−0.0152100	+	0.00314391i
$519$		0			0
$520$	−582.899	+	212.569i	−1.12096	+	0.408786i
$521$	297.577			0.571164			0.285582	−	0.958354i	$-0.407813\pi$
$521$	297.577			0.571164			0.285582	+	0.958354i	$0.407813\pi$
$522$		0			0
$523$	694.715	−	694.715i	1.32833	−	1.32833i	0.421496	−	0.906830i	$-0.361505\pi$
$523$	694.715	−	694.715i	1.32833	−	1.32833i	0.906830	−	0.421496i	$-0.138495\pi$
$524$	−89.1844	−	35.3879i	−0.170199	−	0.0675341i
$525$		0			0
$526$	367.616	−	559.186i	0.698890	−	1.06309i
$527$	121.644	+	70.2315i	0.230824	+	0.133267i
$528$		0			0
$529$	21.7235	+	37.6262i	0.0410652	+	0.0711271i
$530$	10.3571	−	178.463i	0.0195417	−	0.336722i
$531$		0			0
$532$	−6.95260	+	5.50209i	−0.0130688	+	0.0103423i
$533$	161.809	−	603.880i	0.303582	−	1.13298i
$534$		0			0
$535$	291.991	+	168.581i	0.545778	+	0.315105i
$536$	447.038	−	39.3912i	0.834026	−	0.0734910i
$537$		0			0
$538$	234.006	+	77.4874i	0.434956	+	0.144029i
$539$	−587.190	−	587.190i	−1.08941	−	1.08941i
$540$		0			0
$541$	84.7467	+	84.7467i	0.156648	+	0.156648i	0.781080	−	0.624431i	$-0.214669\pi$
$541$	84.7467	+	84.7467i	0.156648	+	0.156648i	−0.624431	+	0.781080i	$0.714669\pi$
$542$	430.683	+	857.118i	0.794619	+	1.58140i
$543$		0			0
$544$	581.928	+	615.527i	1.06972	+	1.13148i
$545$	54.8299	+	31.6561i	0.100605	+	0.0580845i
$546$		0			0
$547$	−216.534	+	808.116i	−0.395858	+	1.47736i	0.424457	+	0.905448i	$0.360465\pi$
$547$	−216.534	+	808.116i	−0.395858	+	1.47736i	−0.820315	+	0.571912i	$0.806202\pi$
$548$	−248.952	−	28.9936i	−0.454291	−	0.0529080i
$549$		0			0
$550$	−369.073	+	328.584i	−0.671041	+	0.597425i
$551$	312.769	+	541.733i	0.567640	+	0.983181i
$552$		0			0
$553$	−0.223091	−	0.128801i	−0.000403419	−	0.000232914i
$554$	128.292	+	620.667i	0.231573	+	1.12034i
$555$		0			0
$556$	−40.0284	−	15.8830i	−0.0719935	−	0.0285666i
$557$	−223.985	+	223.985i	−0.402127	+	0.402127i	−0.878982	−	0.476855i	$-0.841777\pi$
$557$	−223.985	+	223.985i	−0.402127	+	0.402127i	0.476855	+	0.878982i	$0.341777\pi$
$558$		0			0
$559$	530.730			0.949427
$560$	5.72455	+	3.08052i	0.0102224	+	0.00550093i
$561$		0			0
$562$	−74.3931	+	113.160i	−0.132372	+	0.201353i
$563$	160.017	+	597.193i	0.284223	+	1.06073i	0.949406	+	0.314053i	$0.101687\pi$
$563$	160.017	+	597.193i	0.284223	+	1.06073i	−0.665183	+	0.746680i	$0.731646\pi$
$564$		0			0
$565$	178.845	+	47.9215i	0.316541	+	0.0848168i
$566$	−445.523	+	396.648i	−0.787144	+	0.700791i
$567$		0			0
$568$	−84.3925	−	14.8265i	−0.148578	−	0.0261030i
$569$	−538.550	−	932.795i	−0.946485	−	1.63936i	−0.752751	−	0.658305i	$-0.771274\pi$
$569$	−538.550	−	932.795i	−0.946485	−	1.63936i	−0.193733	−	0.981054i	$-0.562060\pi$
$570$		0			0
$571$	13.8381	+	51.6444i	0.0242348	+	0.0904455i	0.976984	−	0.213313i	$-0.0684252\pi$
$571$	13.8381	+	51.6444i	0.0242348	+	0.0904455i	−0.952749	+	0.303758i	$0.901759\pi$
$572$	1306.89	+	972.097i	2.28476	+	1.69947i
$573$		0			0
$574$	−5.85302	+	2.94102i	−0.0101969	+	0.00512372i
$575$			321.150i			0.558521i
$576$		0			0
$577$	−404.152			−0.700436			−0.350218	−	0.936668i	$-0.613893\pi$
$577$	−404.152			−0.700436			−0.350218	+	0.936668i	$0.613893\pi$
$578$	369.691	+	735.734i	0.639603	+	1.27290i
$579$		0			0
$580$	273.731	−	368.003i	0.471950	−	0.634488i
$581$	10.8608	−	2.91014i	0.0186933	−	0.00500885i
$582$		0			0
$583$	−406.410	+	234.641i	−0.697101	+	0.402472i
$584$	135.732	−	772.586i	0.232418	−	1.32292i
$585$		0			0
$586$	352.409	+	395.833i	0.601381	+	0.675484i
$587$	131.537	−	490.901i	0.224083	−	0.836289i	−0.758687	−	0.651455i	$-0.774159\pi$
$587$	131.537	−	490.901i	0.224083	−	0.836289i	0.982770	−	0.184833i	$-0.0591746\pi$
$588$		0			0
$589$	90.2880	−	24.1926i	0.153290	−	0.0410740i
$590$	−301.045	−	197.911i	−0.510246	−	0.335442i
$591$		0			0
$592$	450.419	+	242.382i	0.760844	+	0.409429i
$593$		−	384.676i		−	0.648695i	−0.945938	−	0.324347i	$-0.894855\pi$
$593$		−	384.676i		−	0.648695i	0.945938	−	0.324347i	$-0.105145\pi$
$594$		0			0
$595$	7.60493	+	7.60493i	0.0127814	+	0.0127814i
$596$	52.8280	−	133.137i	0.0886376	−	0.223384i
$597$		0			0
$598$	1036.64	−	214.273i	1.73351	−	0.358317i
$599$	326.242	−	565.067i	0.544644	−	0.943351i	−0.453985	−	0.891009i	$-0.649998\pi$
$599$	326.242	−	565.067i	0.544644	−	0.943351i	0.998629	−	0.0523418i	$-0.0166685\pi$
$600$		0			0
$601$	31.4347	−	18.1488i	0.0523040	−	0.0301977i	−0.473620	−	0.880729i	$-0.657053\pi$
$601$	31.4347	−	18.1488i	0.0523040	−	0.0301977i	0.525924	+	0.850532i	$0.323720\pi$
$602$	−3.69762	−	4.15325i	−0.00614222	−	0.00689908i
$603$		0			0
$604$	31.3758	−	269.407i	0.0519468	−	0.446038i
$605$	−518.954	−	139.053i	−0.857775	−	0.229840i
$606$		0			0
$607$	−411.210	+	712.236i	−0.677446	+	1.17337i	0.298302	+	0.954472i	$0.403580\pi$
$607$	−411.210	+	712.236i	−0.677446	+	1.17337i	−0.975748	+	0.218899i	$0.929754\pi$
$608$	563.467	+	15.8102i	0.926755	+	0.0260036i
$609$		0			0
$610$	442.599	−	222.396i	0.725572	−	0.364584i
$611$	267.218	−	267.218i	0.437345	−	0.437345i
$612$		0			0
$613$	−346.639	+	346.639i	−0.565479	+	0.565479i	−0.930859	−	0.365380i	$-0.880939\pi$
$613$	−346.639	+	346.639i	−0.565479	+	0.565479i	0.365380	+	0.930859i	$0.380939\pi$
$614$	279.772	−	844.891i	0.455655	−	1.37604i
$615$		0			0
$616$	−1.49795	−	16.9997i	−0.00243173	−	0.0275970i
$617$	−280.986	+	486.683i	−0.455407	+	0.788789i	−0.998712	−	0.0507474i	$-0.983840\pi$
$617$	−280.986	+	486.683i	−0.455407	+	0.788789i	0.543304	+	0.839536i	$0.317173\pi$
$618$		0			0
$619$	−340.821	−	91.3227i	−0.550599	−	0.147533i	−0.0272153	−	0.999630i	$-0.508664\pi$
$619$	−340.821	−	91.3227i	−0.550599	−	0.147533i	−0.523384	+	0.852097i	$0.675331\pi$
$620$	−42.5297	−	53.7418i	−0.0685964	−	0.0866803i
$621$		0			0
$622$	763.918	+	44.3341i	1.22816	+	0.0712767i
$623$	8.38797	−	4.84280i	0.0134638	−	0.00777335i
$624$		0			0
$625$	−24.1147	+	41.7679i	−0.0385835	+	0.0668286i
$626$	13.8897	+	9.13125i	0.0221880	+	0.0145867i
$627$		0			0
$628$	384.821	−	969.826i	0.612773	−	1.54431i
$629$	598.371	+	598.371i	0.951306	+	0.951306i
$630$		0			0
$631$		−	645.121i		−	1.02238i	−0.859468	−	0.511189i	$-0.829205\pi$
$631$		−	645.121i		−	1.02238i	0.859468	−	0.511189i	$-0.170795\pi$
$632$	5.61100	+	15.3863i	0.00887817	+	0.0243454i
$633$		0			0
$634$	23.4875	+	113.631i	0.0370465	+	0.179229i
$635$	290.588	−	77.8629i	0.457619	−	0.122619i
$636$		0			0
$637$	304.521	−	1136.49i	0.478054	−	1.78412i
$638$	−1201.99	−	69.7580i	−1.88400	−	0.109338i
$639$		0			0
$640$	−153.149	−	383.874i	−0.239296	−	0.599803i
$641$	−81.9269	+	47.3005i	−0.127811	+	0.0737917i	−0.562542	−	0.826768i	$-0.690177\pi$
$641$	−81.9269	+	47.3005i	−0.127811	+	0.0737917i	0.434731	+	0.900560i	$0.356843\pi$
$642$		0			0
$643$	−1223.98	+	327.964i	−1.90354	+	0.510053i	−0.907628	+	0.419776i	$0.862109\pi$
$643$	−1223.98	+	327.964i	−1.90354	+	0.510053i	−0.995917	+	0.0902770i	$0.971225\pi$
$644$	−8.89913	−	6.61942i	−0.0138185	−	0.0102786i
$645$		0			0
$646$	885.302	+	293.153i	1.37044	+	0.453798i
$647$	−778.698			−1.20355			−0.601776	−	0.798665i	$-0.705540\pi$
$647$	−778.698			−1.20355			−0.601776	+	0.798665i	$0.705540\pi$
$648$		0			0
$649$			945.776i			1.45728i
$650$	−664.647	−	220.087i	−1.02253	−	0.338595i
$651$		0			0
$652$	−781.772	+	114.844i	−1.19904	+	0.176141i
$653$	134.110	+	500.507i	0.205376	+	0.766473i	0.989335	+	0.145660i	$0.0465306\pi$
$653$	134.110	+	500.507i	0.205376	+	0.766473i	−0.783959	+	0.620813i	$0.786803\pi$
$654$		0			0
$655$	38.7258	+	67.0751i	0.0591234	+	0.102405i
$656$	405.303	+	95.7035i	0.617841	+	0.145889i
$657$		0			0
$658$	−3.95284	−	0.229404i	−0.00600736	−	0.000348638i
$659$	−1081.28	−	289.729i	−1.64079	−	0.439649i	−0.683779	−	0.729689i	$-0.739665\pi$
$659$	−1081.28	−	289.729i	−1.64079	−	0.439649i	−0.957015	+	0.290039i	$0.906332\pi$
$660$		0			0
$661$	−22.6527	−	84.5409i	−0.0342703	−	0.127899i	0.946671	−	0.322200i	$-0.104423\pi$
$661$	−22.6527	−	84.5409i	−0.0342703	−	0.127899i	−0.980942	+	0.194302i	$0.937756\pi$
$662$	−181.083	−	876.068i	−0.273539	−	1.32337i
$663$		0			0
$664$	−648.061	−	301.705i	−0.975995	−	0.454375i
$665$	7.15706			0.0107625
$666$		0			0
$667$	−553.310	+	553.310i	−0.829550	+	0.829550i
$668$	465.023	+	1076.82i	0.696142	+	1.61200i
$669$		0			0
$670$	−302.702	−	199.000i	−0.451794	−	0.297015i
$671$	−1126.12	−	650.163i	−1.67827	−	0.968947i
$672$		0			0
$673$	285.489	+	494.482i	0.424204	+	0.734743i	0.996346	−	0.0854120i	$-0.0272206\pi$
$673$	285.489	+	494.482i	0.424204	+	0.734743i	−0.572142	+	0.820155i	$0.693887\pi$
$674$	232.343	+	13.4841i	0.344723	+	0.0200061i
$675$		0			0
$676$	−188.762	+	1620.80i	−0.279234	+	2.39763i
$677$	0.624464	−	2.33053i	0.000922398	−	0.00344244i	−0.965463	−	0.260540i	$-0.916099\pi$
$677$	0.624464	−	2.33053i	0.000922398	−	0.00344244i	0.966385	+	0.257097i	$0.0827661\pi$
$678$		0			0
$679$	−4.28725	−	2.47524i	−0.00631406	−	0.00364542i
$680$	−60.0179	−	681.125i	−0.0882617	−	1.00165i
$681$		0			0
$682$	−56.5555	+	170.794i	−0.0829260	+	0.250430i
$683$	696.716	+	696.716i	1.02008	+	1.02008i	0.999794	+	0.0202881i	$0.00645833\pi$
$683$	696.716	+	696.716i	1.02008	+	1.02008i	0.0202881	+	0.999794i	$0.493542\pi$
$684$		0			0
$685$	143.060	+	143.060i	0.208846	+	0.208846i
$686$	−22.0340	+	11.0716i	−0.0321196	+	0.0161394i
$687$		0			0
$688$	10.5756	+	353.374i	0.0153716	+	0.513624i
$689$	−575.826	−	332.453i	−0.835742	−	0.482516i
$690$		0			0
$691$	69.5177	−	259.444i	0.100605	−	0.375461i	−0.897205	−	0.441614i	$-0.854406\pi$
$691$	69.5177	−	259.444i	0.100605	−	0.375461i	0.997809	+	0.0661532i	$0.0210726\pi$
$692$	921.368	−	729.145i	1.33146	−	1.05368i
$693$		0			0
$694$	−624.744	−	701.726i	−0.900207	−	1.01113i
$695$	17.3812	+	30.1051i	0.0250089	+	0.0433167i
$696$		0			0
$697$	596.675	+	344.490i	0.856062	+	0.494247i
$698$	−935.223	+	193.310i	−1.33986	+	0.276949i
$699$		0			0
$700$	2.90833	+	6.73458i	0.00415476	+	0.00962083i
$701$	491.487	−	491.487i	0.701123	−	0.701123i	−0.263529	−	0.964652i	$-0.584886\pi$
$701$	491.487	−	491.487i	0.701123	−	0.701123i	0.964652	+	0.263529i	$0.0848864\pi$
$702$		0			0
$703$	563.132			0.801041
$704$	−621.206	+	889.529i	−0.882395	+	1.26354i
$705$		0			0
$706$	−322.079	−	211.739i	−0.456203	−	0.299914i
$707$	4.52434	+	16.8851i	0.00639935	+	0.0238827i
$708$		0			0
$709$	−1353.47	−	362.662i	−1.90899	−	0.511512i	−0.994196	−	0.107588i	$-0.965687\pi$
$709$	−1353.47	−	362.662i	−1.90899	−	0.511512i	−0.914793	−	0.403924i	$-0.867646\pi$
$710$	45.9924	+	51.6596i	0.0647780	+	0.0727601i
$711$		0			0
$712$	−606.487	−	106.551i	−0.851807	−	0.149650i
$713$	58.4635	+	101.262i	0.0819966	+	0.142022i
$714$		0			0
$715$	−340.291	−	1269.98i	−0.475931	−	1.77620i
$716$	75.7989	+	515.981i	0.105864	+	0.720644i
$717$		0			0
$718$	315.231	+	627.351i	0.439040	+	0.873748i
$719$			30.3572i			0.0422215i	0.999777	+	0.0211107i	$0.00672025\pi$
$719$			30.3572i			0.0422215i	−0.999777	+	0.0211107i	$0.993280\pi$
$720$		0			0
$721$	5.67999			0.00787794
$722$	−90.6087	+	45.5289i	−0.125497	+	0.0630595i
$723$		0			0
$724$	−94.4358	−	642.848i	−0.130436	−	0.887912i
$725$	499.917	−	133.952i	0.689541	−	0.184762i
$726$		0			0
$727$	−80.1769	+	46.2902i	−0.110285	+	0.0636729i	−0.554128	−	0.832432i	$-0.686948\pi$
$727$	−80.1769	+	46.2902i	−0.110285	+	0.0636729i	0.443843	+	0.896105i	$0.353615\pi$
$728$	19.7981	−	13.8812i	0.0271952	−	0.0190675i
$729$		0			0
$730$	−472.927	+	421.045i	−0.647845	+	0.576774i
$731$	−151.380	+	564.959i	−0.207087	+	0.772858i
$732$		0			0
$733$	478.189	−	128.130i	0.652373	−	0.174803i	0.0825713	−	0.996585i	$-0.473687\pi$
$733$	478.189	−	128.130i	0.652373	−	0.174803i	0.569801	+	0.821782i	$0.307020\pi$
$734$	−500.407	+	761.176i	−0.681754	+	1.03703i
$735$		0			0
$736$	163.326	+	685.953i	0.221910	+	0.932001i
$737$			950.981i			1.29034i
$738$		0			0
$739$	−736.411	−	736.411i	−0.996497	−	0.996497i	0.00349738	−	0.999994i	$-0.498887\pi$
$739$	−736.411	−	736.411i	−0.996497	−	0.996497i	−0.999994	+	0.00349738i	$0.998887\pi$
$740$	−163.694	−	379.053i	−0.221208	−	0.512233i
$741$		0			0
$742$	1.41018	+	6.82237i	0.00190052	+	0.00919457i
$743$	182.739	−	316.514i	0.245948	−	0.425995i	−0.716450	−	0.697639i	$-0.754234\pi$
$743$	182.739	−	316.514i	0.245948	−	0.425995i	0.962398	+	0.271644i	$0.0875674\pi$
$744$		0			0
$745$	−100.132	+	57.8110i	−0.134405	+	0.0775987i
$746$	879.309	−	782.846i	1.17870	−	1.04939i
$747$		0			0
$748$	−1407.56	+	1113.90i	−1.88176	+	1.48917i
$749$	−12.6919	−	3.40077i	−0.0169451	−	0.00454042i
$750$		0			0
$751$	−4.41811	+	7.65240i	−0.00588297	+	0.0101896i	−0.868952	−	0.494897i	$-0.835206\pi$
$751$	−4.41811	+	7.65240i	−0.00588297	+	0.0101896i	0.863069	+	0.505086i	$0.168539\pi$
$752$	183.245	+	172.596i	0.243677	+	0.229516i
$753$		0			0
$754$	−765.933	−	1524.31i	−1.01583	−	2.02163i
$755$	−154.814	+	154.814i	−0.205052	+	0.205052i
$756$		0			0
$757$	308.653	−	308.653i	0.407732	−	0.407732i	−0.473215	−	0.880947i	$-0.656907\pi$
$757$	308.653	−	308.653i	0.407732	−	0.407732i	0.880947	+	0.473215i	$0.156907\pi$
$758$	497.471	+	164.729i	0.656294	+	0.217321i
$759$		0			0
$760$	−348.748	−	292.264i	−0.458879	−	0.384559i
$761$	−71.5261	+	123.887i	−0.0939896	+	0.162795i	−0.909186	−	0.416389i	$-0.863295\pi$
$761$	−71.5261	+	123.887i	−0.0939896	+	0.162795i	0.815197	+	0.579184i	$0.196629\pi$
$762$		0			0
$763$	−2.38327	−	0.638595i	−0.00312355	−	0.000836953i
$764$	−11.2956	+	96.9891i	−0.0147848	+	0.126949i
$765$		0			0
$766$	37.1772	−	640.598i	0.0485342	−	0.836290i
$767$	−1160.50	+	670.016i	−1.51304	+	0.873554i
$768$		0			0
$769$	−66.1593	+	114.591i	−0.0860329	+	0.149013i	−0.905831	−	0.423639i	$-0.860752\pi$
$769$	−66.1593	+	114.591i	−0.0860329	+	0.149013i	0.819798	+	0.572653i	$0.194086\pi$
$770$	−7.56747	+	11.5110i	−0.00982789	+	0.0149493i
$771$		0			0
$772$	363.738	+	842.279i	0.471164	+	1.09103i
$773$	218.705	+	218.705i	0.282930	+	0.282930i	0.834276	−	0.551346i	$-0.185886\pi$
$773$	218.705	+	218.705i	0.282930	+	0.282930i	−0.551346	+	0.834276i	$0.685886\pi$
$774$		0			0
$775$		−	77.3368i		−	0.0997894i
$776$	107.829	+	295.686i	0.138955	+	0.381039i
$777$		0			0
$778$	−792.344	+	163.777i	−1.01844	+	0.210511i
$779$	442.869	−	118.666i	0.568510	−	0.152332i
$780$		0			0
$781$	46.9947	−	175.387i	0.0601725	−	0.224567i
$782$	−67.5888	+	1164.62i	−0.0864306	+	1.48928i
$783$		0			0
$784$	762.770	+	180.111i	0.972921	+	0.229734i
$785$	−729.401	+	421.120i	−0.929173	+	0.536458i
$786$		0			0
$787$	324.462	−	86.9393i	0.412277	−	0.110469i	−0.0467182	−	0.998908i	$-0.514876\pi$
$787$	324.462	−	86.9393i	0.412277	−	0.110469i	0.458995	+	0.888439i	$0.348210\pi$
$788$	119.845	−	17.6055i	0.152087	−	0.0223420i
$789$		0			0
$790$	4.15574	−	12.5500i	0.00526043	−	0.0158861i
$791$	−7.21567			−0.00912221
$792$		0			0
$793$		−	1842.38i		−	2.32331i
$794$	279.773	−	844.896i	0.352359	−	1.06410i
$795$		0			0
$796$	−496.257	−	369.130i	−0.623439	−	0.463731i
$797$	−134.777	−	502.994i	−0.169105	−	0.631109i	−0.997481	−	0.0709360i	$-0.977401\pi$
$797$	−134.777	−	502.994i	−0.169105	−	0.631109i	0.828376	−	0.560173i	$-0.189265\pi$
$798$		0			0
$799$	208.233	+	360.671i	0.260617	+	0.451403i
$800$	133.296	−	446.925i	0.166619	−	0.558656i
$801$		0			0
$802$	−19.8020	+	341.206i	−0.0246907	+	0.425444i
$803$	1605.61	+	430.221i	1.99951	+	0.535767i
$804$		0			0
$805$	2.31718	+	8.64784i	0.00287849	+	0.0107427i
$806$	−249.636	+	51.5996i	−0.309722	+	0.0640194i
$807$		0			0
$808$	469.054	−	1007.53i	0.580513	−	1.24694i
$809$	−148.860			−0.184005			−0.0920024	−	0.995759i	$-0.529327\pi$
$809$	−148.860			−0.184005			−0.0920024	+	0.995759i	$0.529327\pi$
$810$		0			0
$811$	−1134.76	+	1134.76i	−1.39921	+	1.39921i	−0.596879	+	0.802331i	$0.703593\pi$
$811$	−1134.76	+	1134.76i	−1.39921	+	1.39921i	−0.802331	+	0.596879i	$0.796407\pi$
$812$	−6.59225	+	16.6138i	−0.00811854	+	0.0204603i
$813$		0			0
$814$	−595.424	+	905.707i	−0.731479	+	1.11266i
$815$	552.381	+	318.917i	0.677768	+	0.391310i
$816$		0			0
$817$	194.611	+	337.077i	0.238202	+	0.412578i
$818$	35.2350	−	607.131i	0.0430745	−	0.742214i
$819$		0			0
$820$	−208.611	−	263.607i	−0.254404	−	0.321472i
$821$	−312.062	+	1164.63i	−0.380100	+	1.41855i	0.465647	+	0.884970i	$0.345822\pi$
$821$	−312.062	+	1164.63i	−0.380100	+	1.41855i	−0.845748	+	0.533583i	$0.820845\pi$
$822$		0			0
$823$	572.726	+	330.664i	0.695900	+	0.401778i	0.805819	−	0.592162i	$-0.201726\pi$
$823$	572.726	+	330.664i	0.695900	+	0.401778i	−0.109918	+	0.993941i	$0.535059\pi$
$824$	−276.773	−	231.947i	−0.335890	−	0.281489i
$825$		0			0
$826$	13.3285	+	4.41352i	0.0161362	+	0.00534324i
$827$	−1138.25	−	1138.25i	−1.37636	−	1.37636i	−0.850689	−	0.525670i	$-0.823815\pi$
$827$	−1138.25	−	1138.25i	−1.37636	−	1.37636i	−0.525670	−	0.850689i	$-0.676185\pi$
$828$		0			0
$829$	265.912	+	265.912i	0.320762	+	0.320762i	0.849059	−	0.528298i	$-0.177169\pi$
$829$	265.912	+	265.912i	0.320762	+	0.320762i	−0.528298	+	0.849059i	$0.677169\pi$
$830$	259.082	+	515.608i	0.312147	+	0.621214i
$831$		0			0
$832$	−1531.57	−	132.074i	−1.84083	−	0.158742i
$833$	1122.93	+	648.322i	1.34805	+	0.778298i
$834$		0			0
$835$	245.054	−	914.555i	0.293478	−	1.09527i
$836$	−138.181	+	1186.48i	−0.165288	+	1.41924i
$837$		0			0
$838$	−533.479	+	474.955i	−0.636610	+	0.566772i
$839$	240.766	+	417.019i	0.286968	+	0.497043i	0.973085	−	0.230448i	$-0.0740193\pi$
$839$	240.766	+	417.019i	0.286968	+	0.497043i	−0.686116	+	0.727492i	$0.740686\pi$
$840$		0			0
$841$	363.768	+	210.021i	0.432542	+	0.249728i
$842$	−190.590	−	922.064i	−0.226354	−	1.09509i
$843$		0			0
$844$	191.150	−	481.737i	0.226481	−	0.570778i
$845$	931.389	−	931.389i	1.10224	−	1.10224i
$846$		0			0
$847$	20.9376			0.0247197
$848$	209.882	−	390.025i	0.247502	−	0.459935i
$849$		0			0
$850$	423.860	−	644.738i	0.498658	−	0.758516i
$851$	182.320	+	680.429i	0.214243	+	0.799564i
$852$		0			0
$853$	−1188.11	−	318.353i	−1.39286	−	0.373216i	−0.517085	−	0.855934i	$-0.672983\pi$
$853$	−1188.11	−	318.353i	−1.39286	−	0.373216i	−0.875776	+	0.482718i	$0.839650\pi$
$854$	−14.4176	+	12.8360i	−0.0168825	+	0.0150304i
$855$		0			0
$856$	479.573	+	683.994i	0.560248	+	0.799059i
$857$	−74.3855	−	128.839i	−0.0867975	−	0.150338i	0.819358	−	0.573282i	$-0.194330\pi$
$857$	−74.3855	−	128.839i	−0.0867975	−	0.150338i	−0.906156	+	0.422944i	$0.860997\pi$
$858$		0			0
$859$	363.774	+	1357.62i	0.423485	+	1.58047i	0.767208	+	0.641398i	$0.221645\pi$
$859$	363.774	+	1357.62i	0.423485	+	1.58047i	−0.343723	+	0.939071i	$0.611688\pi$
$860$	170.321	−	228.979i	0.198047	−	0.266254i
$861$		0			0
$862$	9.69637	−	4.87222i	0.0112487	−	0.00565223i
$863$		−	109.514i		−	0.126899i	−0.997985	−	0.0634493i	$-0.979790\pi$
$863$		−	109.514i		−	0.126899i	0.997985	−	0.0634493i	$-0.0202101\pi$
$864$		0			0
$865$	−948.464			−1.09649
$866$	−206.171	−	410.307i	−0.238072	−	0.473796i
$867$		0			0
$868$	2.14302	+	1.59404i	0.00246892	+	0.00183645i
$869$	−33.5226	+	8.98236i	−0.0385761	+	0.0103364i
$870$		0			0
$871$	−1166.89	+	673.703i	−1.33971	+	0.773483i
$872$	90.0539	+	128.440i	0.103273	+	0.147294i
$873$		0			0
$874$	516.211	+	579.819i	0.590630	+	0.663409i
$875$	4.16155	−	15.5311i	0.00475606	−	0.0177499i
$876$		0			0
$877$	−941.126	+	252.174i	−1.07312	+	0.287541i	−0.751774	−	0.659421i	$-0.770802\pi$
$877$	−941.126	+	252.174i	−1.07312	+	0.287541i	−0.321345	+	0.946962i	$0.604135\pi$
$878$	1131.77	+	744.044i	1.28904	+	0.847430i
$879$		0			0
$880$	838.806	−	251.881i	0.953189	−	0.286228i
$881$		−	468.501i		−	0.531783i	−0.964003	−	0.265892i	$-0.914334\pi$
$881$		−	468.501i		−	0.531783i	0.964003	−	0.265892i	$-0.0856663\pi$
$882$		0			0
$883$	1159.62	+	1159.62i	1.31327	+	1.31327i	0.918990	+	0.394280i	$0.129006\pi$
$883$	1159.62	+	1159.62i	1.31327	+	1.31327i	0.394280	+	0.918990i	$0.370994\pi$
$884$	−2363.96	−	938.004i	−2.67416	−	1.06109i
$885$		0			0
$886$	652.351	−	134.841i	0.736288	−	0.152191i
$887$	−132.286	+	229.126i	−0.149138	+	0.258315i	−0.930909	−	0.365251i	$-0.880983\pi$
$887$	−132.286	+	229.126i	−0.149138	+	0.258315i	0.781771	+	0.623566i	$0.214317\pi$
$888$		0			0
$889$	−10.1533	+	5.86201i	−0.0114210	+	0.00659394i
$890$	330.524	+	371.252i	0.371376	+	0.417137i
$891$		0			0
$892$	1046.00	+	121.820i	1.17265	+	0.136569i
$893$	267.700	+	71.7300i	0.299776	+	0.0803248i
$894$		0			0
$895$	210.490	−	364.580i	0.235185	−	0.407352i
$896$	9.63695	+	12.9055i	0.0107555	+	0.0144035i
$897$		0			0
$898$	−815.352	+	409.697i	−0.907964	+	0.456233i
$899$	133.244	−	133.244i	0.148213	−	0.148213i
$900$		0			0
$901$	518.139	−	518.139i	0.575071	−	0.575071i
$902$	−277.409	+	837.755i	−0.307549	+	0.928775i
$903$		0			0
$904$	351.604	+	294.658i	0.388942	+	0.325949i
$905$	−262.244	+	454.220i	−0.289773	+	0.501901i
$906$		0			0
$907$	456.307	+	122.267i	0.503095	+	0.134804i	0.501436	−	0.865195i	$-0.332805\pi$
$907$	456.307	+	122.267i	0.503095	+	0.134804i	0.00165906	+	0.999999i	$0.499472\pi$
$908$	−1040.72	+	823.594i	−1.14616	+	0.907041i
$909$		0			0
$910$	−19.4854	−	1.13084i	−0.0214126	−	0.00124268i
$911$	296.353	−	171.099i	0.325305	−	0.187815i	−0.328450	−	0.944521i	$-0.606526\pi$
$911$	296.353	−	171.099i	0.325305	−	0.187815i	0.653755	+	0.756707i	$0.273193\pi$
$912$		0			0
$913$	757.411	−	1311.87i	0.829585	−	1.43688i
$914$	427.762	+	281.217i	0.468011	+	0.307677i
$915$		0			0
$916$	449.173	+	178.229i	0.490364	+	0.194574i
$917$	−2.13431	−	2.13431i	−0.00232750	−	0.00232750i
$918$		0			0
$919$		−	1099.02i		−	1.19589i	−0.801538	−	0.597944i	$-0.795985\pi$
$919$		−	1099.02i		−	1.19589i	0.801538	−	0.597944i	$-0.204015\pi$
$920$	240.230	−	516.014i	0.261120	−	0.560885i
$921$		0			0
$922$	−88.8390	−	429.797i	−0.0963547	−	0.466158i
$923$	248.498	−	66.5849i	0.269229	−	0.0721397i
$924$		0			0
$925$	120.589	−	450.043i	0.130366	−	0.486533i
$926$	1456.91	+	84.5518i	1.57333	+	0.0913086i
$927$		0			0
$928$	999.663	−	540.353i	1.07722	−	0.582277i
$929$	123.120	−	71.0831i	0.132529	−	0.0765158i	−0.432270	−	0.901744i	$-0.642287\pi$
$929$	123.120	−	71.0831i	0.132529	−	0.0765158i	0.564799	+	0.825229i	$0.308954\pi$
$930$		0			0
$931$	833.468	−	223.327i	0.895239	−	0.239879i
$932$	−691.154	+	929.186i	−0.741582	+	0.996981i
$933$		0			0
$934$	988.444	+	327.307i	1.05829	+	0.350436i
$935$	1448.95			1.54968
$936$		0			0
$937$			825.181i			0.880662i	0.897835	+	0.440331i	$0.145139\pi$
$937$			825.181i			0.880662i	−0.897835	+	0.440331i	$0.854861\pi$
$938$	13.4019	+	4.43781i	0.0142877	+	0.00473114i
$939$		0			0
$940$	−29.5338	−	201.044i	−0.0314189	−	0.213876i
$941$	116.128	+	433.397i	0.123410	+	0.460571i	0.999778	−	0.0210704i	$-0.00670741\pi$
$941$	116.128	+	433.397i	0.123410	+	0.460571i	−0.876368	+	0.481641i	$0.840041\pi$
$942$		0			0
$943$	286.768	+	496.697i	0.304102	+	0.526720i
$944$	−469.239	−	759.342i	−0.497076	−	0.804387i
$945$		0			0
$946$	−747.904	−	43.4048i	−0.790596	−	0.0458824i
$947$	62.4257	+	16.7269i	0.0659195	+	0.0176631i	0.291628	−	0.956532i	$-0.405803\pi$
$947$	62.4257	+	16.7269i	0.0659195	+	0.0176631i	−0.225709	+	0.974195i	$0.572470\pi$
$948$		0			0
$949$	609.563	+	2274.92i	0.642321	+	2.39718i
$950$	−103.935	−	502.833i	−0.109406	−	0.529298i
$951$		0			0
$952$	9.12941	+	25.0343i	0.00958971	+	0.0262966i
$953$	−1766.55			−1.85367			−0.926835	−	0.375468i	$-0.877482\pi$
$953$	−1766.55			−1.85367			−0.926835	+	0.375468i	$0.877482\pi$
$954$		0			0
$955$	55.7346	−	55.7346i	0.0583608	−	0.0583608i
$956$	−2.61542	+	1.12947i	−0.00273580	+	0.00118145i
$957$		0			0
$958$	−658.411	−	432.848i	−0.687277	−	0.451825i
$959$	−6.82819	−	3.94225i	−0.00712011	−	0.00411080i
$960$		0			0
$961$	466.421	+	807.865i	0.485350	+	0.840651i
$962$	−1533.15	−	88.9768i	−1.59371	−	0.0924915i
$963$		0			0
$964$	118.827	+	13.8389i	0.123264	+	0.0143557i
$965$	191.680	−	715.359i	0.198632	−	0.741305i
$966$		0			0
$967$	1320.48	+	762.380i	1.36554	+	0.788397i	0.990355	−	0.138551i	$-0.0442444\pi$
$967$	1320.48	+	762.380i	1.36554	+	0.788397i	0.375189	+	0.926948i	$0.377578\pi$
$968$	−1020.24	−	855.005i	−1.05397	−	0.883269i
$969$		0			0
$970$	79.8630	−	241.181i	0.0823330	−	0.248640i
$971$	−155.539	−	155.539i	−0.160184	−	0.160184i	0.622464	−	0.782648i	$-0.286132\pi$
$971$	−155.539	−	155.539i	−0.160184	−	0.160184i	−0.782648	+	0.622464i	$0.786132\pi$
$972$		0			0
$973$	−0.957938	−	0.957938i	−0.000984520	−	0.000984520i
$974$	−982.265	+	493.567i	−1.00849	+	0.506742i
$975$		0			0
$976$	1226.71	−	36.7124i	1.25687	−	0.0376152i
$977$	180.963	+	104.479i	0.185223	+	0.106938i	0.589744	−	0.807590i	$-0.299229\pi$
$977$	180.963	+	104.479i	0.185223	+	0.106938i	−0.404522	+	0.914528i	$0.632562\pi$
$978$		0			0
$979$	337.727	−	1260.42i	0.344972	−	1.28745i
$980$	−392.601	−	496.102i	−0.400613	−	0.506226i
$981$		0			0
$982$	413.975	+	464.985i	0.421563	+	0.473508i
$983$	−481.713	−	834.351i	−0.490043	−	0.848780i	0.509891	−	0.860239i	$-0.329686\pi$
$983$	−481.713	−	834.351i	−0.490043	−	0.848780i	−0.999934	+	0.0114591i	$0.996352\pi$
$984$		0			0
$985$	−84.6794	−	48.8897i	−0.0859689	−	0.0496342i
$986$	1841.09	−	380.553i	1.86723	−	0.385956i
$987$		0			0
$988$	−1553.75	+	670.987i	−1.57262	+	0.679137i
$989$	−344.280	+	344.280i	−0.348109	+	0.348109i
$990$		0			0
$991$	599.362			0.604805			0.302403	−	0.953180i	$-0.402211\pi$
$991$	599.362			0.604805			0.302403	+	0.953180i	$0.402211\pi$
$992$	−39.3308	−	165.186i	−0.0396480	−	0.166518i
$993$		0			0
$994$	−2.25236	−	1.48073i	−0.00226596	−	0.00148967i
$995$	129.217	+	482.244i	0.129866	+	0.484667i
$996$		0			0
$997$	1483.24	+	397.434i	1.48771	+	0.398630i	0.908962	−	0.416880i	$-0.136876\pi$
$997$	1483.24	+	397.434i	1.48771	+	0.398630i	0.578744	+	0.815509i	$0.303543\pi$
$998$	97.4062	+	109.409i	0.0976014	+	0.109628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.x.a.125.18		184
3.2	odd	2		144.3.w.a.77.29	yes	184
9.2	odd	6	inner	432.3.x.a.413.32		184
9.7	even	3		144.3.w.a.29.15	yes	184
16.5	even	4	inner	432.3.x.a.341.32		184
48.5	odd	4		144.3.w.a.5.15	✓	184
144.101	odd	12	inner	432.3.x.a.197.18		184
144.133	even	12		144.3.w.a.101.29	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.15	✓	184	48.5	odd	4
144.3.w.a.29.15	yes	184	9.7	even	3
144.3.w.a.77.29	yes	184	3.2	odd	2
144.3.w.a.101.29	yes	184	144.133	even	12
432.3.x.a.125.18		184	1.1	even	1	trivial
432.3.x.a.197.18		184	144.101	odd	12	inner
432.3.x.a.341.32		184	16.5	even	4	inner
432.3.x.a.413.32		184	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.897969 - 1.78708i) q^{2} +(-2.38730 + 3.20948i) q^{4} +(3.11886 - 0.835695i) q^{5} +(-0.108974 + 0.0629164i) q^{7} +(7.87933 + 1.38428i) q^{8} +O(q^{10})\)	\(q+(-0.897969 - 1.78708i) q^{2} +(-2.38730 + 3.20948i) q^{4} +(3.11886 - 0.835695i) q^{5} +(-0.108974 + 0.0629164i) q^{7} +(7.87933 + 1.38428i) q^{8} +(-4.29409 - 4.82321i) q^{10} +(-4.38767 + 16.3750i) q^{11} +(-23.2011 + 6.21671i) q^{13} +(0.210292 + 0.138249i) q^{14} +(-4.60157 - 15.3240i) q^{16} -26.4707i q^{17} +(-12.4559 - 12.4559i) q^{19} +(-4.76350 + 12.0050i) q^{20} +(33.2034 - 6.86314i) q^{22} +(11.0176 - 19.0831i) q^{23} +(-12.6218 + 7.28718i) q^{25} +(31.9436 + 35.8798i) q^{26} +(0.0582258 - 0.499952i) q^{28} +(-34.3012 - 9.19097i) q^{29} +(-2.65318 + 4.59544i) q^{31} +(-23.2532 + 21.9839i) q^{32} +(-47.3052 + 23.7698i) q^{34} +(-0.287297 + 0.287297i) q^{35} +(-22.6051 + 22.6051i) q^{37} +(-11.0746 + 33.4446i) q^{38} +(25.7313 - 2.26734i) q^{40} +(-13.0140 + 22.5410i) q^{41} +(-21.3428 - 5.71880i) q^{43} +(-42.0806 - 53.1742i) q^{44} +(-43.9965 - 2.55335i) q^{46} +(-13.6253 + 7.86657i) q^{47} +(-24.4921 + 42.4215i) q^{49} +(24.3567 + 16.0124i) q^{50} +(35.4356 - 89.3047i) q^{52} +(19.5741 + 19.5741i) q^{53} +54.7380i q^{55} +(-0.945739 + 0.344888i) q^{56} +(14.3764 + 69.5521i) q^{58} +(53.8883 - 14.4393i) q^{59} +(-19.8523 + 74.0899i) q^{61} +(10.5949 + 0.614877i) q^{62} +(60.1675 + 21.8144i) q^{64} +(-67.1656 + 38.7781i) q^{65} +(54.1848 - 14.5188i) q^{67} +(84.9572 + 63.1935i) q^{68} +(0.771405 + 0.255438i) q^{70} -10.7106 q^{71} -98.0523i q^{73} +(60.6957 + 20.0984i) q^{74} +(69.7129 - 10.2410i) q^{76} +(-0.552113 - 2.06051i) q^{77} +(1.02359 + 1.77291i) q^{79} +(-27.1578 - 43.9479i) q^{80} +(51.9687 + 3.01601i) q^{82} +(-86.3114 - 23.1271i) q^{83} +(-22.1214 - 82.5582i) q^{85} +(8.94527 + 43.2767i) q^{86} +(-57.2395 + 122.950i) q^{88} -76.9719 q^{89} +(2.13719 - 2.13719i) q^{91} +(34.9445 + 80.9181i) q^{92} +(26.2933 + 17.2855i) q^{94} +(-49.2574 - 28.4388i) q^{95} +(19.6709 + 34.0710i) q^{97} +(97.8038 + 5.67606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

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