LMFDB - Embedded newform 1395.2.c.g.559.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1395,2,Mod(559,1395)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1395.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1395, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1395 = 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1395.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-12,0,0,0,0,0,18,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$11.1391310820$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 16 x^{14} - 14 x^{13} + 113 x^{12} - 170 x^{11} + 292 x^{10} - 394 x^{9} + 493 x^{8} + \cdots + 1576 $ x^16 + 16x^14 - 14x^13 + 113x^12 - 170x^11 + 292x^10 - 394x^9 + 493x^8 + 704x^7 - 372x^6 + 160x^5 - 788x^4 + 2448x^3 + 432x^2 - 1168x + 1576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.15
Root			$0.429493 + 0.667773i$ of defining polynomial
Character	$\chi$	$=$	1395.559
Dual form			1395.2.c.g.559.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.72869i q^{2} -5.44577 q^{4} +(-2.12679 - 0.690483i) q^{5} -0.363635i q^{7} -9.40246i q^{8} +(1.88412 - 5.80336i) q^{10} +5.69456 q^{11} +2.16431i q^{13} +0.992249 q^{14} +14.7649 q^{16} +1.91527i q^{17} -1.10511 q^{19} +(11.5820 + 3.76021i) q^{20} +15.5387i q^{22} -7.73467i q^{23} +(4.04647 + 2.93702i) q^{25} -5.90573 q^{26} +1.98027i q^{28} +6.52907 q^{29} -1.00000 q^{31} +21.4840i q^{32} -5.22619 q^{34} +(-0.251084 + 0.773375i) q^{35} +5.51041i q^{37} -3.01552i q^{38} +(-6.49224 + 19.9971i) q^{40} -8.62833 q^{41} +9.99008i q^{43} -31.0113 q^{44} +21.1056 q^{46} -4.18224i q^{47} +6.86777 q^{49} +(-8.01424 + 11.0416i) q^{50} -11.7863i q^{52} +5.03921i q^{53} +(-12.1111 - 3.93200i) q^{55} -3.41906 q^{56} +17.8158i q^{58} -7.34671 q^{59} +1.24112 q^{61} -2.72869i q^{62} -29.0934 q^{64} +(1.49442 - 4.60302i) q^{65} +1.06897i q^{67} -10.4301i q^{68} +(-2.11030 - 0.685131i) q^{70} +11.7215 q^{71} +11.7863i q^{73} -15.0362 q^{74} +6.01820 q^{76} -2.07074i q^{77} -0.773812 q^{79} +(-31.4018 - 10.1949i) q^{80} -23.5441i q^{82} -8.37479i q^{83} +(1.32246 - 4.07338i) q^{85} -27.2599 q^{86} -53.5429i q^{88} +5.48339 q^{89} +0.787018 q^{91} +42.1213i q^{92} +11.4121 q^{94} +(2.35034 + 0.763062i) q^{95} -7.34931i q^{97} +18.7400i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} + 18 q^{10} + 44 q^{16} + 36 q^{25} - 16 q^{31} - 24 q^{34} + 88 q^{46} - 16 q^{49} - 28 q^{55} + 64 q^{61} - 176 q^{64} + 38 q^{70} - 12 q^{76} - 72 q^{79} + 72 q^{85} - 16 q^{91} + 8 q^{94}+O(q^{100}) $ 16 * q - 12 * q^4 + 18 * q^10 + 44 * q^16 + 36 * q^25 - 16 * q^31 - 24 * q^34 + 88 * q^46 - 16 * q^49 - 28 * q^55 + 64 * q^61 - 176 * q^64 + 38 * q^70 - 12 * q^76 - 72 * q^79 + 72 * q^85 - 16 * q^91 + 8 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1395\mathbb{Z}\right)^\times$.

$n$	$406$	$776$	$1117$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			2.72869i			1.92948i	0.263208	+	0.964739i	$0.415219\pi$
$2$			2.72869i			1.92948i	−0.263208	+	0.964739i	$0.584781\pi$
$3$		0			0
$3$		0			0
$4$	−5.44577			−2.72289
$5$	−2.12679	−	0.690483i	−0.951129	−	0.308793i
$5$	−2.12679	−	0.690483i	−0.951129	−	0.308793i
$6$		0			0
$7$		−	0.363635i		−	0.137441i	−0.997636	−	0.0687206i	$-0.978108\pi$
$7$		−	0.363635i		−	0.137441i	0.997636	−	0.0687206i	$-0.0218917\pi$
$8$		−	9.40246i		−	3.32427i
$9$		0			0
$10$	1.88412	−	5.80336i	0.595810	−	1.83518i
$11$	5.69456			1.71697			0.858487	−	0.512835i	$-0.171405\pi$
$11$	5.69456			1.71697			0.858487	+	0.512835i	$0.171405\pi$
$12$		0			0
$13$			2.16431i			0.600271i	0.953897	+	0.300135i	$0.0970318\pi$
$13$			2.16431i			0.600271i	−0.953897	+	0.300135i	$0.902968\pi$
$14$	0.992249			0.265190
$15$		0			0
$16$	14.7649			3.69122
$17$			1.91527i			0.464521i	0.972654	+	0.232261i	$0.0746122\pi$
$17$			1.91527i			0.464521i	−0.972654	+	0.232261i	$0.925388\pi$
$18$		0			0
$19$	−1.10511			−0.253530			−0.126765	−	0.991933i	$-0.540459\pi$
$19$	−1.10511			−0.253530			−0.126765	+	0.991933i	$0.540459\pi$
$20$	11.5820	+	3.76021i	2.58982	+	0.840809i
$21$		0			0
$22$			15.5387i			3.31286i
$23$		−	7.73467i		−	1.61279i	−0.591377	−	0.806395i	$-0.701416\pi$
$23$		−	7.73467i		−	1.61279i	0.591377	−	0.806395i	$-0.298584\pi$
$24$		0			0
$25$	4.04647	+	2.93702i	0.809293	+	0.587405i
$26$	−5.90573			−1.15821
$27$		0			0
$28$			1.98027i			0.374237i
$29$	6.52907			1.21242			0.606209	−	0.795305i	$-0.292689\pi$
$29$	6.52907			1.21242			0.606209	+	0.795305i	$0.292689\pi$
$30$		0			0
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$			21.4840i			3.79786i
$33$		0			0
$34$	−5.22619			−0.896284
$35$	−0.251084	+	0.773375i	−0.0424409	+	0.130724i
$36$		0			0
$37$			5.51041i			0.905906i	0.891534	+	0.452953i	$0.149630\pi$
$37$			5.51041i			0.905906i	−0.891534	+	0.452953i	$0.850370\pi$
$38$		−	3.01552i		−	0.489181i
$39$		0			0
$40$	−6.49224	+	19.9971i	−1.02651	+	3.16181i
$41$	−8.62833			−1.34752			−0.673760	−	0.738950i	$-0.735322\pi$
$41$	−8.62833			−1.34752			−0.673760	+	0.738950i	$0.735322\pi$
$42$		0			0
$43$			9.99008i			1.52347i	0.647887	+	0.761736i	$0.275653\pi$
$43$			9.99008i			1.52347i	−0.647887	+	0.761736i	$0.724347\pi$
$44$	−31.0113			−4.67513
$45$		0			0
$46$	21.1056			3.11184
$47$		−	4.18224i		−	0.610042i	−0.952346	−	0.305021i	$-0.901336\pi$
$47$		−	4.18224i		−	0.610042i	0.952346	−	0.305021i	$-0.0986635\pi$
$48$		0			0
$49$	6.86777			0.981110
$50$	−8.01424	+	11.0416i	−1.13338	+	1.56151i
$51$		0			0
$52$		−	11.7863i		−	1.63447i
$53$			5.03921i			0.692189i	0.938200	+	0.346095i	$0.112492\pi$
$53$			5.03921i			0.692189i	−0.938200	+	0.346095i	$0.887508\pi$
$54$		0			0
$55$	−12.1111	−	3.93200i	−1.63306	−	0.530190i
$56$	−3.41906			−0.456892
$57$		0			0
$58$			17.8158i			2.33934i
$59$	−7.34671			−0.956460			−0.478230	−	0.878235i	$-0.658722\pi$
$59$	−7.34671			−0.956460			−0.478230	+	0.878235i	$0.658722\pi$
$60$		0			0
$61$	1.24112			0.158910			0.0794548	−	0.996838i	$-0.474682\pi$
$61$	1.24112			0.158910			0.0794548	+	0.996838i	$0.474682\pi$
$62$		−	2.72869i		−	0.346545i
$63$		0			0
$64$	−29.0934			−3.63667
$65$	1.49442	−	4.60302i	0.185360	−	0.570935i
$66$		0			0
$67$			1.06897i			0.130596i	0.997866	+	0.0652978i	$0.0207997\pi$
$67$			1.06897i			0.130596i	−0.997866	+	0.0652978i	$0.979200\pi$
$68$		−	10.4301i		−	1.26484i
$69$		0			0
$70$	−2.11030	−	0.685131i	−0.252230	−	0.0818888i
$71$	11.7215			1.39108			0.695541	−	0.718486i	$-0.255165\pi$
$71$	11.7215			1.39108			0.695541	+	0.718486i	$0.255165\pi$
$72$		0			0
$73$			11.7863i			1.37948i	0.724055	+	0.689742i	$0.242276\pi$
$73$			11.7863i			1.37948i	−0.724055	+	0.689742i	$0.757724\pi$
$74$	−15.0362			−1.74793
$75$		0			0
$76$	6.01820			0.690335
$77$		−	2.07074i		−	0.235983i
$78$		0			0
$79$	−0.773812			−0.0870607			−0.0435304	−	0.999052i	$-0.513861\pi$
$79$	−0.773812			−0.0870607			−0.0435304	+	0.999052i	$0.513861\pi$
$80$	−31.4018	−	10.1949i	−3.51083	−	1.13983i
$81$		0			0
$82$		−	23.5441i		−	2.60001i
$83$		−	8.37479i		−	0.919253i	−0.888112	−	0.459626i	$-0.847983\pi$
$83$		−	8.37479i		−	0.919253i	0.888112	−	0.459626i	$-0.152017\pi$
$84$		0			0
$85$	1.32246	−	4.07338i	0.143441	−	0.441820i
$86$	−27.2599			−2.93951
$87$		0			0
$88$		−	53.5429i		−	5.70769i
$89$	5.48339			0.581238			0.290619	−	0.956839i	$-0.406139\pi$
$89$	5.48339			0.581238			0.290619	+	0.956839i	$0.406139\pi$
$90$		0			0
$91$	0.787018			0.0825019
$92$			42.1213i			4.39144i
$93$		0			0
$94$	11.4121			1.17706
$95$	2.35034	+	0.763062i	0.241140	+	0.0782885i
$96$		0			0
$97$		−	7.34931i		−	0.746209i	−0.927789	−	0.373105i	$-0.878293\pi$
$97$		−	7.34931i		−	0.746209i	0.927789	−	0.373105i	$-0.121707\pi$
$98$			18.7400i			1.89303i
$99$		0			0
$100$	−22.0361	−	15.9944i	−2.20361	−	1.59944i
$101$	15.3686			1.52923			0.764615	−	0.644487i	$-0.222929\pi$
$101$	15.3686			1.52923			0.764615	+	0.644487i	$0.222929\pi$
$102$		0			0
$103$			9.98565i			0.983915i	0.870619	+	0.491958i	$0.163718\pi$
$103$			9.98565i			0.983915i	−0.870619	+	0.491958i	$0.836282\pi$
$104$	20.3498			1.99546
$105$		0			0
$106$	−13.7505			−1.33556
$107$			17.7428i			1.71526i	0.514265	+	0.857632i	$0.328065\pi$
$107$			17.7428i			1.71526i	−0.514265	+	0.857632i	$0.671935\pi$
$108$		0			0
$109$	0.0115945			0.00111055			0.000555277	−	1.00000i	$-0.499823\pi$
$109$	0.0115945			0.00111055			0.000555277		1.00000i	$0.499823\pi$
$110$	10.7292	−	33.0476i	1.02299	−	3.15096i
$111$		0			0
$112$		−	5.36903i		−	0.507326i
$113$			9.89582i			0.930921i	0.885069	+	0.465460i	$0.154111\pi$
$113$			9.89582i			0.930921i	−0.885069	+	0.465460i	$0.845889\pi$
$114$		0			0
$115$	−5.34066	+	16.4500i	−0.498019	+	1.53397i
$116$	−35.5559			−3.30128
$117$		0			0
$118$		−	20.0469i		−	1.84547i
$119$	0.696460			0.0638443
$120$		0			0
$121$	21.4280			1.94800
$122$			3.38665i			0.306613i
$123$		0			0
$124$	5.44577			0.489045
$125$	−6.57802	−	9.04045i	−0.588356	−	0.808602i
$126$		0			0
$127$			5.91670i			0.525022i	0.964929	+	0.262511i	$0.0845506\pi$
$127$			5.91670i			0.525022i	−0.964929	+	0.262511i	$0.915449\pi$
$128$		−	36.4190i		−	3.21901i
$129$		0			0
$130$	12.5602	+	4.07781i	1.10161	+	0.357647i
$131$	18.7876			1.64148			0.820742	−	0.571299i	$-0.193560\pi$
$131$	18.7876			1.64148			0.820742	+	0.571299i	$0.193560\pi$
$132$		0			0
$133$			0.401858i			0.0348455i
$134$	−2.91690			−0.251981
$135$		0			0
$136$	18.0083			1.54419
$137$			13.8322i			1.18176i	0.806758	+	0.590881i	$0.201220\pi$
$137$			13.8322i			1.18176i	−0.806758	+	0.590881i	$0.798780\pi$
$138$		0			0
$139$	−15.4402			−1.30962			−0.654810	−	0.755793i	$-0.727251\pi$
$139$	−15.4402			−1.30962			−0.654810	+	0.755793i	$0.727251\pi$
$140$	1.36735	−	4.21163i	0.115562	−	0.355947i
$141$		0			0
$142$			31.9843i			2.68406i
$143$			12.3248i			1.03065i
$144$		0			0
$145$	−13.8860	−	4.50822i	−1.15317	−	0.374387i
$146$	−32.1613			−2.66168
$147$		0			0
$148$		−	30.0085i		−	2.46668i
$149$	13.7546			1.12682			0.563411	−	0.826177i	$-0.309489\pi$
$149$	13.7546			1.12682			0.563411	+	0.826177i	$0.309489\pi$
$150$		0			0
$151$	7.97186			0.648741			0.324370	−	0.945930i	$-0.394848\pi$
$151$	7.97186			0.648741			0.324370	+	0.945930i	$0.394848\pi$
$152$			10.3908i			0.842804i
$153$		0			0
$154$	5.65042			0.455324
$155$	2.12679	+	0.690483i	0.170828	+	0.0554609i
$156$		0			0
$157$			11.9800i			0.956110i	0.878330	+	0.478055i	$0.158658\pi$
$157$			11.9800i			0.956110i	−0.878330	+	0.478055i	$0.841342\pi$
$158$		−	2.11150i		−	0.167982i
$159$		0			0
$160$	14.8343	−	45.6919i	1.17276	−	3.61226i
$161$	−2.81260			−0.221664
$162$		0			0
$163$			12.6691i			0.992318i	0.868232	+	0.496159i	$0.165257\pi$
$163$			12.6691i			0.992318i	−0.868232	+	0.496159i	$0.834743\pi$
$164$	46.9879			3.66914
$165$		0			0
$166$	22.8522			1.77368
$167$		−	20.3020i		−	1.57102i	−0.618851	−	0.785509i	$-0.712401\pi$
$167$		−	20.3020i		−	1.57102i	0.618851	−	0.785509i	$-0.287599\pi$
$168$		0			0
$169$	8.31578			0.639675
$170$	11.1150	+	3.60859i	0.852482	+	0.276767i
$171$		0			0
$172$		−	54.4037i		−	4.14824i
$173$			20.2355i			1.53848i	0.638960	+	0.769240i	$0.279365\pi$
$173$			20.2355i			1.53848i	−0.638960	+	0.769240i	$0.720635\pi$
$174$		0			0
$175$	1.06800	−	1.47144i	0.0807336	−	0.111230i
$176$	84.0796			6.33774
$177$		0			0
$178$			14.9625i			1.12149i
$179$	−9.62221			−0.719198			−0.359599	−	0.933107i	$-0.617086\pi$
$179$	−9.62221			−0.719198			−0.359599	+	0.933107i	$0.617086\pi$
$180$		0			0
$181$	5.66158			0.420822			0.210411	−	0.977613i	$-0.432520\pi$
$181$	5.66158			0.420822			0.210411	+	0.977613i	$0.432520\pi$
$182$			2.14753i			0.159186i
$183$		0			0
$184$	−72.7249			−5.36135
$185$	3.80485	−	11.7195i	0.279738	−	0.861634i
$186$		0			0
$187$			10.9066i			0.797571i
$188$			22.7755i			1.66108i
$189$		0			0
$190$	−2.08216	+	6.41337i	−0.151056	+	0.465275i
$191$	10.7827			0.780205			0.390103	−	0.920771i	$-0.372439\pi$
$191$	10.7827			0.780205			0.390103	+	0.920771i	$0.372439\pi$
$192$		0			0
$193$		−	10.0239i		−	0.721534i	−0.932656	−	0.360767i	$-0.882515\pi$
$193$		−	10.0239i		−	0.721534i	0.932656	−	0.360767i	$-0.117485\pi$
$194$	20.0540			1.43979
$195$		0			0
$196$	−37.4003			−2.67145
$197$		−	14.5562i		−	1.03709i	−0.855051	−	0.518543i	$-0.826475\pi$
$197$		−	14.5562i		−	1.03709i	0.855051	−	0.518543i	$-0.173525\pi$
$198$		0			0
$199$	3.35886			0.238103			0.119051	−	0.992888i	$-0.462015\pi$
$199$	3.35886			0.238103			0.119051	+	0.992888i	$0.462015\pi$
$200$	27.6152	−	38.0467i	1.95269	−	2.69031i
$201$		0			0
$202$			41.9362i			2.95062i
$203$		−	2.37420i		−	0.166636i
$204$		0			0
$205$	18.3507	+	5.95772i	1.28167	+	0.416105i
$206$	−27.2478			−1.89844
$207$		0			0
$208$			31.9557i			2.21573i
$209$	−6.29314			−0.435305
$210$		0			0
$211$	−10.9845			−0.756203			−0.378101	−	0.925764i	$-0.623423\pi$
$211$	−10.9845			−0.756203			−0.378101	+	0.925764i	$0.623423\pi$
$212$		−	27.4424i		−	1.88475i
$213$		0			0
$214$	−48.4147			−3.30956
$215$	6.89798	−	21.2468i	0.470438	−	1.44902i
$216$		0			0
$217$			0.363635i			0.0246852i
$218$			0.0316379i			0.00214279i
$219$		0			0
$220$	65.9545	+	21.4128i	4.44665	+	1.44365i
$221$	−4.14523			−0.278838
$222$		0			0
$223$		−	20.1694i		−	1.35064i	−0.737523	−	0.675322i	$-0.764004\pi$
$223$		−	20.1694i		−	1.35064i	0.737523	−	0.675322i	$-0.235996\pi$
$224$	7.81232			0.521983
$225$		0			0
$226$	−27.0027			−1.79619
$227$		−	20.6209i		−	1.36866i	−0.729174	−	0.684328i	$-0.760096\pi$
$227$		−	20.6209i		−	1.36866i	0.729174	−	0.684328i	$-0.239904\pi$
$228$		0			0
$229$	1.19805			0.0791691			0.0395846	−	0.999216i	$-0.487397\pi$
$229$	1.19805			0.0791691			0.0395846	+	0.999216i	$0.487397\pi$
$230$	−44.8871	−	14.5730i	−2.95977	−	0.960917i
$231$		0			0
$232$		−	61.3894i		−	4.03041i
$233$		−	12.2854i		−	0.804845i	−0.915454	−	0.402423i	$-0.868168\pi$
$233$		−	12.2854i		−	0.804845i	0.915454	−	0.402423i	$-0.131832\pi$
$234$		0			0
$235$	−2.88777	+	8.89474i	−0.188377	+	0.580229i
$236$	40.0085			2.60433
$237$		0			0
$238$			1.90043i			0.123186i
$239$	−6.59202			−0.426403			−0.213201	−	0.977008i	$-0.568389\pi$
$239$	−6.59202			−0.426403			−0.213201	+	0.977008i	$0.568389\pi$
$240$		0			0
$241$	−3.65042			−0.235144			−0.117572	−	0.993064i	$-0.537511\pi$
$241$	−3.65042			−0.235144			−0.117572	+	0.993064i	$0.537511\pi$
$242$			58.4705i			3.75863i
$243$		0			0
$244$	−6.75888			−0.432693
$245$	−14.6063	−	4.74208i	−0.933162	−	0.302960i
$246$		0			0
$247$		−	2.39180i		−	0.152187i
$248$			9.40246i			0.597057i
$249$		0			0
$250$	24.6686	−	17.9494i	1.56018	−	1.13522i
$251$	9.82696			0.620272			0.310136	−	0.950692i	$-0.399625\pi$
$251$	9.82696			0.620272			0.310136	+	0.950692i	$0.399625\pi$
$252$		0			0
$253$		−	44.0455i		−	2.76912i
$254$	−16.1449			−1.01302
$255$		0			0
$256$	41.1896			2.57435
$257$		−	28.4788i		−	1.77646i	−0.459401	−	0.888229i	$-0.651936\pi$
$257$		−	28.4788i		−	1.77646i	0.459401	−	0.888229i	$-0.348064\pi$
$258$		0			0
$259$	2.00378			0.124509
$260$	−8.13825	+	25.0670i	−0.504713	+	1.55459i
$261$		0			0
$262$			51.2657i			3.16721i
$263$			23.2395i			1.43301i	0.697581	+	0.716506i	$0.254260\pi$
$263$			23.2395i			1.43301i	−0.697581	+	0.716506i	$0.745740\pi$
$264$		0			0
$265$	3.47949	−	10.7173i	0.213743	−	0.658361i
$266$	−1.09655			−0.0672337
$267$		0			0
$268$		−	5.82138i		−	0.355597i
$269$	5.41403			0.330099			0.165049	−	0.986285i	$-0.447222\pi$
$269$	5.41403			0.330099			0.165049	+	0.986285i	$0.447222\pi$
$270$		0			0
$271$	2.30650			0.140110			0.0700550	−	0.997543i	$-0.477683\pi$
$271$	2.30650			0.140110			0.0700550	+	0.997543i	$0.477683\pi$
$272$			28.2788i			1.71465i
$273$		0			0
$274$	−37.7438			−2.28019
$275$	23.0428	+	16.7251i	1.38954	+	1.00856i
$276$		0			0
$277$		−	16.7851i		−	1.00852i	−0.863552	−	0.504259i	$-0.831766\pi$
$277$		−	16.7851i		−	1.00852i	0.863552	−	0.504259i	$-0.168234\pi$
$278$		−	42.1316i		−	2.52688i
$279$		0			0
$280$	7.27163	+	2.36081i	0.434563	+	0.141085i
$281$	−28.7008			−1.71215			−0.856075	−	0.516852i	$-0.827104\pi$
$281$	−28.7008			−1.71215			−0.856075	+	0.516852i	$0.827104\pi$
$282$		0			0
$283$			7.82577i			0.465194i	0.972573	+	0.232597i	$0.0747223\pi$
$283$			7.82577i			0.465194i	−0.972573	+	0.232597i	$0.925278\pi$
$284$	−63.8324			−3.78776
$285$		0			0
$286$	−33.6305			−1.98862
$287$			3.13757i			0.185205i
$288$		0			0
$289$	13.3317			0.784220
$290$	12.3015	−	37.8906i	0.722371	−	2.22501i
$291$		0			0
$292$		−	64.1856i		−	3.75618i
$293$			20.2763i			1.18455i	0.805734	+	0.592277i	$0.201771\pi$
$293$			20.2763i			1.18455i	−0.805734	+	0.592277i	$0.798229\pi$
$294$		0			0
$295$	15.6249	+	5.07278i	0.909717	+	0.295349i
$296$	51.8114			3.01148
$297$		0			0
$298$			37.5321i			2.17418i
$299$	16.7402			0.968111
$300$		0			0
$301$	3.63274			0.209388
$302$			21.7528i			1.25173i
$303$		0			0
$304$	−16.3169			−0.935837
$305$	−2.63961	−	0.856975i	−0.151144	−	0.0490702i
$306$		0			0
$307$			5.83583i			0.333068i	0.986036	+	0.166534i	$0.0532576\pi$
$307$			5.83583i			0.333068i	−0.986036	+	0.166534i	$0.946742\pi$
$308$			11.2768i			0.642555i
$309$		0			0
$310$	−1.88412	+	5.80336i	−0.107011	+	0.329609i
$311$	−19.5768			−1.11010			−0.555048	−	0.831818i	$-0.687300\pi$
$311$	−19.5768			−1.11010			−0.555048	+	0.831818i	$0.687300\pi$
$312$		0			0
$313$			30.9264i			1.74806i	0.485870	+	0.874031i	$0.338503\pi$
$313$			30.9264i			1.74806i	−0.485870	+	0.874031i	$0.661497\pi$
$314$	−32.6898			−1.84479
$315$		0			0
$316$	4.21401			0.237056
$317$			11.3161i			0.635577i	0.948162	+	0.317789i	$0.102940\pi$
$317$			11.3161i			0.635577i	−0.948162	+	0.317789i	$0.897060\pi$
$318$		0			0
$319$	37.1802			2.08169
$320$	61.8755	+	20.0885i	3.45894	+	1.12298i
$321$		0			0
$322$		−	7.67472i		−	0.427695i
$323$		−	2.11659i		−	0.117770i
$324$		0			0
$325$	−6.35662	+	8.75779i	−0.352602	+	0.485795i
$326$	−34.5700			−1.91466
$327$		0			0
$328$			81.1276i			4.47952i
$329$	−1.52081			−0.0838449
$330$		0			0
$331$	9.87111			0.542565			0.271283	−	0.962500i	$-0.412552\pi$
$331$	9.87111			0.542565			0.271283	+	0.962500i	$0.412552\pi$
$332$			45.6072i			2.50302i
$333$		0			0
$334$	55.3980			3.03124
$335$	0.738107	−	2.27348i	0.0403271	−	0.124213i
$336$		0			0
$337$			23.2517i			1.26660i	0.773907	+	0.633299i	$0.218300\pi$
$337$			23.2517i			1.26660i	−0.773907	+	0.633299i	$0.781700\pi$
$338$			22.6912i			1.23424i
$339$		0			0
$340$	−7.20183	+	22.1827i	−0.390574	+	1.20302i
$341$	−5.69456			−0.308378
$342$		0			0
$343$		−	5.04281i		−	0.272286i
$344$	93.9313			5.06444
$345$		0			0
$346$	−55.2166			−2.96846
$347$		−	22.1077i		−	1.18680i	−0.804907	−	0.593401i	$-0.797785\pi$
$347$		−	22.1077i		−	1.18680i	0.804907	−	0.593401i	$-0.202215\pi$
$348$		0			0
$349$	4.31475			0.230964			0.115482	−	0.993310i	$-0.463159\pi$
$349$	4.31475			0.230964			0.115482	+	0.993310i	$0.463159\pi$
$350$	4.01510	+	2.91426i	0.214616	+	0.155774i
$351$		0			0
$352$			122.342i			6.52083i
$353$		−	3.37872i		−	0.179831i	−0.995949	−	0.0899157i	$-0.971340\pi$
$353$		−	3.37872i		−	0.179831i	0.995949	−	0.0899157i	$-0.0286598\pi$
$354$		0			0
$355$	−24.9291	−	8.09347i	−1.32310	−	0.429557i
$356$	−29.8613			−1.58265
$357$		0			0
$358$		−	26.2561i		−	1.38768i
$359$	2.37338			0.125262			0.0626311	−	0.998037i	$-0.480051\pi$
$359$	2.37338			0.125262			0.0626311	+	0.998037i	$0.480051\pi$
$360$		0			0
$361$	−17.7787			−0.935722
$362$			15.4487i			0.811966i
$363$		0			0
$364$	−4.28592			−0.224643
$365$	8.13825	−	25.0670i	0.425976	−	1.31207i
$366$		0			0
$367$		−	11.7481i		−	0.613246i	−0.951831	−	0.306623i	$-0.900801\pi$
$367$		−	11.7481i		−	0.613246i	0.951831	−	0.306623i	$-0.0991990\pi$
$368$		−	114.202i		−	5.95317i
$369$		0			0
$370$	31.9789	+	10.3823i	1.66250	+	0.539748i
$371$	1.83244			0.0951353
$372$		0			0
$373$		−	7.01763i		−	0.363359i	−0.983358	−	0.181679i	$-0.941847\pi$
$373$		−	7.01763i		−	0.363359i	0.983358	−	0.181679i	$-0.0581533\pi$
$374$	−29.7608			−1.53890
$375$		0			0
$376$	−39.3233			−2.02795
$377$			14.1309i			0.727779i
$378$		0			0
$379$	10.3561			0.531957			0.265979	−	0.963979i	$-0.414305\pi$
$379$	10.3561			0.531957			0.265979	+	0.963979i	$0.414305\pi$
$380$	−12.7994	−	4.15546i	−0.656597	−	0.213171i
$381$		0			0
$382$			29.4226i			1.50539i
$383$			13.7657i			0.703395i	0.936114	+	0.351697i	$0.114395\pi$
$383$			13.7657i			0.703395i	−0.936114	+	0.351697i	$0.885605\pi$
$384$		0			0
$385$	−1.42981	+	4.40403i	−0.0728700	+	0.224450i
$386$	27.3521			1.39218
$387$		0			0
$388$			40.0227i			2.03184i
$389$	11.7765			0.597094			0.298547	−	0.954395i	$-0.403498\pi$
$389$	11.7765			0.597094			0.298547	+	0.954395i	$0.403498\pi$
$390$		0			0
$391$	14.8140			0.749175
$392$		−	64.5739i		−	3.26148i
$393$		0			0
$394$	39.7194			2.00104
$395$	1.64574	+	0.534304i	0.0828060	+	0.0268838i
$396$		0			0
$397$		−	14.7131i		−	0.738427i	−0.929345	−	0.369214i	$-0.879627\pi$
$397$		−	14.7131i		−	0.738427i	0.929345	−	0.369214i	$-0.120373\pi$
$398$			9.16529i			0.459415i
$399$		0			0
$400$	59.7456	+	43.3648i	2.98728	+	2.16824i
$401$	−14.2081			−0.709520			−0.354760	−	0.934957i	$-0.615437\pi$
$401$	−14.2081			−0.709520			−0.354760	+	0.934957i	$0.615437\pi$
$402$		0			0
$403$		−	2.16431i		−	0.107812i
$404$	−83.6938			−4.16392
$405$		0			0
$406$	6.47847			0.321521
$407$			31.3794i			1.55542i
$408$		0			0
$409$	−33.1914			−1.64121			−0.820604	−	0.571498i	$-0.806363\pi$
$409$	−33.1914			−1.64121			−0.820604	+	0.571498i	$0.806363\pi$
$410$	−16.2568	+	50.0733i	−0.802866	+	2.47294i
$411$		0			0
$412$		−	54.3796i		−	2.67909i
$413$			2.67152i			0.131457i
$414$		0			0
$415$	−5.78265	+	17.8114i	−0.283859	+	0.874328i
$416$	−46.4979			−2.27975
$417$		0			0
$418$		−	17.1720i		−	0.839912i
$419$	−17.0350			−0.832216			−0.416108	−	0.909315i	$-0.636606\pi$
$419$	−17.0350			−0.832216			−0.416108	+	0.909315i	$0.636606\pi$
$420$		0			0
$421$	−21.6984			−1.05752			−0.528758	−	0.848773i	$-0.677342\pi$
$421$	−21.6984			−1.05752			−0.528758	+	0.848773i	$0.677342\pi$
$422$		−	29.9733i		−	1.45908i
$423$		0			0
$424$	47.3810			2.30103
$425$	−5.62520	+	7.75008i	−0.272862	+	0.375934i
$426$		0			0
$427$		−	0.451316i		−	0.0218407i
$428$		−	96.6234i		−	4.67047i
$429$		0			0
$430$	57.9760	+	18.8225i	2.79585	+	0.907700i
$431$	11.5438			0.556043			0.278022	−	0.960575i	$-0.410321\pi$
$431$	11.5438			0.556043			0.278022	+	0.960575i	$0.410321\pi$
$432$		0			0
$433$			5.14235i			0.247125i	0.992337	+	0.123563i	$0.0394320\pi$
$433$			5.14235i			0.247125i	−0.992337	+	0.123563i	$0.960568\pi$
$434$	−0.992249			−0.0476295
$435$		0			0
$436$	−0.0631411			−0.00302391
$437$			8.54769i			0.408891i
$438$		0			0
$439$	18.5498			0.885333			0.442666	−	0.896686i	$-0.354033\pi$
$439$	18.5498			0.885333			0.442666	+	0.896686i	$0.354033\pi$
$440$	−36.9704	+	113.874i	−1.76250	+	5.42875i
$441$		0			0
$442$		−	11.3111i		−	0.538013i
$443$		−	0.829840i		−	0.0394269i	−0.999806	−	0.0197135i	$-0.993725\pi$
$443$		−	0.829840i		−	0.0394269i	0.999806	−	0.0197135i	$-0.00627539\pi$
$444$		0			0
$445$	−11.6620	−	3.78619i	−0.552833	−	0.179483i
$446$	55.0362			2.60604
$447$		0			0
$448$			10.5794i			0.499828i
$449$	19.9721			0.942540			0.471270	−	0.881989i	$-0.343796\pi$
$449$	19.9721			0.942540			0.471270	+	0.881989i	$0.343796\pi$
$450$		0			0
$451$	−49.1346			−2.31366
$452$		−	53.8904i		−	2.53479i
$453$		0			0
$454$	56.2681			2.64079
$455$	−1.67382	−	0.543422i	−0.0784699	−	0.0254760i
$456$		0			0
$457$			14.8949i			0.696754i	0.937354	+	0.348377i	$0.113267\pi$
$457$			14.8949i			0.696754i	−0.937354	+	0.348377i	$0.886733\pi$
$458$			3.26910i			0.152755i
$459$		0			0
$460$	29.0840	−	89.5830i	1.35605	−	4.17683i
$461$	10.0510			0.468120			0.234060	−	0.972222i	$-0.424799\pi$
$461$	10.0510			0.468120			0.234060	+	0.972222i	$0.424799\pi$
$462$		0			0
$463$		−	34.0072i		−	1.58045i	−0.612817	−	0.790225i	$-0.709964\pi$
$463$		−	34.0072i		−	1.58045i	0.612817	−	0.790225i	$-0.290036\pi$
$464$	96.4011			4.47531
$465$		0			0
$466$	33.5232			1.55293
$467$		−	36.3361i		−	1.68143i	−0.541474	−	0.840717i	$-0.682134\pi$
$467$		−	36.3361i		−	1.68143i	0.541474	−	0.840717i	$-0.317866\pi$
$468$		0			0
$469$	0.388716			0.0179492
$470$	−24.2710	−	7.87983i	−1.11954	−	0.363469i
$471$		0			0
$472$			69.0772i			3.17953i
$473$			56.8891i			2.61576i
$474$		0			0
$475$	−4.47180	−	3.24575i	−0.205180	−	0.148925i
$476$	−3.79276			−0.173841
$477$		0			0
$478$		−	17.9876i		−	0.822735i
$479$	37.1451			1.69720			0.848600	−	0.529034i	$-0.177446\pi$
$479$	37.1451			1.69720			0.848600	+	0.529034i	$0.177446\pi$
$480$		0			0
$481$	−11.9262			−0.543789
$482$		−	9.96088i		−	0.453706i
$483$		0			0
$484$	−116.692			−5.30419
$485$	−5.07457	+	15.6304i	−0.230424	+	0.709741i
$486$		0			0
$487$		−	10.0458i		−	0.455219i	−0.973753	−	0.227609i	$-0.926909\pi$
$487$		−	10.0458i		−	0.455219i	0.973753	−	0.227609i	$-0.0730909\pi$
$488$		−	11.6696i		−	0.528259i
$489$		0			0
$490$	12.9397	−	39.8561i	0.584555	−	1.80052i
$491$	21.7701			0.982469			0.491235	−	0.871027i	$-0.336546\pi$
$491$	21.7701			0.982469			0.491235	+	0.871027i	$0.336546\pi$
$492$		0			0
$493$			12.5049i			0.563194i
$494$	6.52650			0.293641
$495$		0			0
$496$	−14.7649			−0.662963
$497$		−	4.26234i		−	0.191192i
$498$		0			0
$499$	−26.8960			−1.20403			−0.602016	−	0.798484i	$-0.705635\pi$
$499$	−26.8960			−1.20403			−0.602016	+	0.798484i	$0.705635\pi$
$500$	35.8224	+	49.2322i	1.60203	+	2.20173i
$501$		0			0
$502$			26.8148i			1.19680i
$503$		−	23.8273i		−	1.06241i	−0.847244	−	0.531204i	$-0.821740\pi$
$503$		−	23.8273i		−	1.06241i	0.847244	−	0.531204i	$-0.178260\pi$
$504$		0			0
$505$	−32.6857	−	10.6117i	−1.45450	−	0.472216i
$506$	120.187			5.34296
$507$		0			0
$508$		−	32.2210i		−	1.42958i
$509$	−14.6305			−0.648484			−0.324242	−	0.945974i	$-0.605109\pi$
$509$	−14.6305			−0.648484			−0.324242	+	0.945974i	$0.605109\pi$
$510$		0			0
$511$	4.28592			0.189598
$512$			39.5557i			1.74813i
$513$		0			0
$514$	77.7099			3.42764
$515$	6.89492	−	21.2374i	0.303826	−	0.935830i
$516$		0			0
$517$		−	23.8160i		−	1.04743i
$518$			5.46770i			0.240237i
$519$		0			0
$520$	−43.2797	−	14.0512i	−1.89794	−	0.616186i
$521$	3.72289			0.163103			0.0815514	−	0.996669i	$-0.474013\pi$
$521$	3.72289			0.163103			0.0815514	+	0.996669i	$0.474013\pi$
$522$		0			0
$523$		−	39.2901i		−	1.71804i	−0.511944	−	0.859019i	$-0.671074\pi$
$523$		−	39.2901i		−	1.71804i	0.511944	−	0.859019i	$-0.328926\pi$
$524$	−102.313			−4.46957
$525$		0			0
$526$	−63.4136			−2.76497
$527$		−	1.91527i		−	0.0834305i
$528$		0			0
$529$	−36.8251			−1.60109
$530$	29.2444	+	9.49447i	1.27029	+	0.412413i
$531$		0			0
$532$		−	2.18843i		−	0.0948804i
$533$		−	18.6744i		−	0.808876i
$534$		0			0
$535$	12.2511	−	37.7352i	0.529662	−	1.63144i
$536$	10.0510			0.434135
$537$		0			0
$538$			14.7732i			0.636919i
$539$	39.1089			1.68454
$540$		0			0
$541$	40.5855			1.74491			0.872453	−	0.488698i	$-0.162528\pi$
$541$	40.5855			1.74491			0.872453	+	0.488698i	$0.162528\pi$
$542$			6.29374i			0.270339i
$543$		0			0
$544$	−41.1476			−1.76419
$545$	−0.0246591	−	0.00800582i	−0.00105628	−	0.000342931i
$546$		0			0
$547$		−	22.1212i		−	0.945832i	−0.881107	−	0.472916i	$-0.843201\pi$
$547$		−	22.1212i		−	0.945832i	0.881107	−	0.472916i	$-0.156799\pi$
$548$		−	75.3269i		−	3.21781i
$549$		0			0
$550$	−45.6376	+	62.8769i	−1.94599	+	2.68108i
$551$	−7.21537			−0.307385
$552$		0			0
$553$			0.281385i			0.0119657i
$554$	45.8014			1.94592
$555$		0			0
$556$	84.0838			3.56595
$557$		−	4.74048i		−	0.200861i	−0.994944	−	0.100430i	$-0.967978\pi$
$557$		−	4.74048i		−	0.200861i	0.994944	−	0.100430i	$-0.0320219\pi$
$558$		0			0
$559$	−21.6216			−0.914496
$560$	−3.70723	+	11.4188i	−0.156659	+	0.482532i
$561$		0			0
$562$		−	78.3158i		−	3.30355i
$563$			34.7932i			1.46636i	0.680036	+	0.733178i	$0.261964\pi$
$563$			34.7932i			1.46636i	−0.680036	+	0.733178i	$0.738036\pi$
$564$		0			0
$565$	6.83290	−	21.0463i	0.287462	−	0.885426i
$566$	−21.3541			−0.897581
$567$		0			0
$568$		−	110.211i		−	4.62433i
$569$	−30.7307			−1.28830			−0.644150	−	0.764899i	$-0.722789\pi$
$569$	−30.7307			−1.28830			−0.644150	+	0.764899i	$0.722789\pi$
$570$		0			0
$571$	38.4989			1.61113			0.805564	−	0.592509i	$-0.201862\pi$
$571$	38.4989			1.61113			0.805564	+	0.592509i	$0.201862\pi$
$572$		−	67.1179i		−	2.80634i
$573$		0			0
$574$	−8.56146			−0.357348
$575$	22.7169	−	31.2981i	0.947361	−	1.30522i
$576$		0			0
$577$		−	20.7281i		−	0.862924i	−0.902131	−	0.431462i	$-0.857998\pi$
$577$		−	20.7281i		−	0.862924i	0.902131	−	0.431462i	$-0.142002\pi$
$578$			36.3782i			1.51314i
$579$		0			0
$580$	75.6198	+	24.5507i	3.13994	+	1.01941i
$581$	−3.04537			−0.126343
$582$		0			0
$583$			28.6961i			1.18847i
$584$	110.820			4.58578
$585$		0			0
$586$	−55.3278			−2.28557
$587$			15.6299i			0.645115i	0.946550	+	0.322558i	$0.104543\pi$
$587$			15.6299i			0.645115i	−0.946550	+	0.322558i	$0.895457\pi$
$588$		0			0
$589$	1.10511			0.0455354
$590$	−13.8421	+	42.6356i	−0.569869	+	1.75528i
$591$		0			0
$592$			81.3607i			3.34390i
$593$		−	9.50337i		−	0.390257i	−0.980778	−	0.195128i	$-0.937488\pi$
$593$		−	9.50337i		−	0.390257i	0.980778	−	0.195128i	$-0.0625123\pi$
$594$		0			0
$595$	−1.48122	−	0.480893i	−0.0607242	−	0.0197147i
$596$	−74.9045			−3.06821
$597$		0			0
$598$			45.6789i			1.86795i
$599$	27.8631			1.13845			0.569227	−	0.822180i	$-0.307242\pi$
$599$	27.8631			1.13845			0.569227	+	0.822180i	$0.307242\pi$
$600$		0			0
$601$	−12.6250			−0.514986			−0.257493	−	0.966280i	$-0.582896\pi$
$601$	−12.6250			−0.514986			−0.257493	+	0.966280i	$0.582896\pi$
$602$			9.91264i			0.404009i
$603$		0			0
$604$	−43.4129			−1.76645
$605$	−45.5729	−	14.7957i	−1.85280	−	0.601530i
$606$		0			0
$607$			39.0820i			1.58629i	0.609034	+	0.793144i	$0.291557\pi$
$607$			39.0820i			1.58629i	−0.609034	+	0.793144i	$0.708443\pi$
$608$		−	23.7422i		−	0.962874i
$609$		0			0
$610$	2.33842	−	7.20268i	0.0946799	−	0.291628i
$611$	9.05165			0.366190
$612$		0			0
$613$			19.4039i			0.783718i	0.920025	+	0.391859i	$0.128168\pi$
$613$			19.4039i			0.783718i	−0.920025	+	0.391859i	$0.871832\pi$
$614$	−15.9242			−0.642648
$615$		0			0
$616$	−19.4701			−0.784471
$617$		−	14.9950i		−	0.603676i	−0.953359	−	0.301838i	$-0.902400\pi$
$617$		−	14.9950i		−	0.603676i	0.953359	−	0.301838i	$-0.0976002\pi$
$618$		0			0
$619$	40.7680			1.63860			0.819302	−	0.573362i	$-0.194361\pi$
$619$	40.7680			1.63860			0.819302	+	0.573362i	$0.194361\pi$
$620$	−11.5820	−	3.76021i	−0.465145	−	0.151014i
$621$		0			0
$622$		−	53.4190i		−	2.14191i
$623$		−	1.99395i		−	0.0798860i
$624$		0			0
$625$	7.74778	+	23.7691i	0.309911	+	0.950766i
$626$	−84.3886			−3.37285
$627$		0			0
$628$		−	65.2405i		−	2.60338i
$629$	−10.5539			−0.420813
$630$		0			0
$631$	15.1448			0.602907			0.301453	−	0.953481i	$-0.402528\pi$
$631$	15.1448			0.602907			0.301453	+	0.953481i	$0.402528\pi$
$632$			7.27574i			0.289413i
$633$		0			0
$634$	−30.8783			−1.22633
$635$	4.08538	−	12.5836i	0.162123	−	0.499364i
$636$		0			0
$637$			14.8640i			0.588931i
$638$			101.453i			4.01658i
$639$		0			0
$640$	−25.1467	+	77.4555i	−0.994011	+	3.06170i
$641$	−14.1668			−0.559554			−0.279777	−	0.960065i	$-0.590261\pi$
$641$	−14.1668			−0.559554			−0.279777	+	0.960065i	$0.590261\pi$
$642$		0			0
$643$		−	27.7195i		−	1.09315i	−0.837411	−	0.546574i	$-0.815932\pi$
$643$		−	27.7195i		−	1.09315i	0.837411	−	0.546574i	$-0.184068\pi$
$644$	15.3168			0.603565
$645$		0			0
$646$	5.77553			0.227235
$647$			29.0621i			1.14255i	0.820758	+	0.571275i	$0.193551\pi$
$647$			29.0621i			1.14255i	−0.820758	+	0.571275i	$0.806449\pi$
$648$		0			0
$649$	−41.8363			−1.64222
$650$	−23.8973	−	17.3453i	−0.937331	−	0.680337i
$651$		0			0
$652$		−	68.9929i		−	2.70197i
$653$			9.36152i			0.366345i	0.983081	+	0.183172i	$0.0586366\pi$
$653$			9.36152i			0.366345i	−0.983081	+	0.183172i	$0.941363\pi$
$654$		0			0
$655$	−39.9574	−	12.9725i	−1.56126	−	0.506879i
$656$	−127.396			−4.97400
$657$		0			0
$658$		−	4.14982i		−	0.161777i
$659$	−30.5155			−1.18872			−0.594358	−	0.804201i	$-0.702594\pi$
$659$	−30.5155			−1.18872			−0.594358	+	0.804201i	$0.702594\pi$
$660$		0			0
$661$	21.9723			0.854623			0.427312	−	0.904104i	$-0.359461\pi$
$661$	21.9723			0.854623			0.427312	+	0.904104i	$0.359461\pi$
$662$			26.9352i			1.04687i
$663$		0			0
$664$	−78.7436			−3.05585
$665$	0.277476	−	0.854667i	0.0107601	−	0.0331426i
$666$		0			0
$667$		−	50.5002i		−	1.95538i
$668$			110.560i			4.27770i
$669$		0			0
$670$	6.20362	+	2.01407i	0.239667	+	0.0778102i
$671$	7.06765			0.272844
$672$		0			0
$673$			20.6046i			0.794250i	0.917765	+	0.397125i	$0.129992\pi$
$673$			20.6046i			0.794250i	−0.917765	+	0.397125i	$0.870008\pi$
$674$	−63.4467			−2.44387
$675$		0			0
$676$	−45.2858			−1.74176
$677$		−	17.4511i		−	0.670700i	−0.942094	−	0.335350i	$-0.891145\pi$
$677$		−	17.4511i		−	0.670700i	0.942094	−	0.335350i	$-0.108855\pi$
$678$		0			0
$679$	−2.67247			−0.102560
$680$	−38.2998	−	12.4344i	−1.46873	−	0.476837i
$681$		0			0
$682$		−	15.5387i		−	0.595008i
$683$			6.69829i			0.256303i	0.991755	+	0.128151i	$0.0409044\pi$
$683$			6.69829i			0.256303i	−0.991755	+	0.128151i	$0.959096\pi$
$684$		0			0
$685$	9.55089	−	29.4181i	0.364921	−	1.12401i
$686$	13.7603			0.525370
$687$		0			0
$688$			147.502i			5.62348i
$689$	−10.9064			−0.415501
$690$		0			0
$691$	20.2732			0.771227			0.385614	−	0.922660i	$-0.373990\pi$
$691$	20.2732			0.771227			0.385614	+	0.922660i	$0.373990\pi$
$692$		−	110.198i		−	4.18910i
$693$		0			0
$694$	60.3251			2.28991
$695$	32.8380	+	10.6612i	1.24562	+	0.404402i
$696$		0			0
$697$		−	16.5256i		−	0.625952i
$698$			11.7736i			0.445639i
$699$		0			0
$700$	−5.81611	+	8.01311i	−0.219828	+	0.302867i
$701$	−9.05067			−0.341839			−0.170920	−	0.985285i	$-0.554674\pi$
$701$	−9.05067			−0.341839			−0.170920	+	0.985285i	$0.554674\pi$
$702$		0			0
$703$		−	6.08963i		−	0.229675i
$704$	−165.674			−6.24407
$705$		0			0
$706$	9.21950			0.346981
$707$		−	5.58855i		−	0.210179i
$708$		0			0
$709$	−37.3240			−1.40173			−0.700867	−	0.713292i	$-0.747203\pi$
$709$	−37.3240			−1.40173			−0.700867	+	0.713292i	$0.747203\pi$
$710$	22.0846	−	68.0239i	0.828821	−	2.55289i
$711$		0			0
$712$		−	51.5574i		−	1.93219i
$713$			7.73467i			0.289666i
$714$		0			0
$715$	8.51005	−	26.2122i	0.318258	−	0.980280i
$716$	52.4003			1.95829
$717$		0			0
$718$			6.47623i			0.241691i
$719$	−11.7669			−0.438830			−0.219415	−	0.975632i	$-0.570415\pi$
$719$	−11.7669			−0.438830			−0.219415	+	0.975632i	$0.570415\pi$
$720$		0			0
$721$	3.63113			0.135230
$722$		−	48.5127i		−	1.80546i
$723$		0			0
$724$	−30.8317			−1.14585
$725$	26.4197	+	19.1760i	0.981202	+	0.712181i
$726$		0			0
$727$			13.1618i			0.488145i	0.969757	+	0.244073i	$0.0784835\pi$
$727$			13.1618i			0.488145i	−0.969757	+	0.244073i	$0.921517\pi$
$728$		−	7.39990i		−	0.274259i
$729$		0			0
$730$	68.4002	+	22.2068i	2.53161	+	0.821911i
$731$	−19.1337			−0.707685
$732$		0			0
$733$			49.0781i			1.81274i	0.422483	+	0.906371i	$0.361159\pi$
$733$			49.0781i			1.81274i	−0.422483	+	0.906371i	$0.638841\pi$
$734$	32.0570			1.18324
$735$		0			0
$736$	166.171			6.12516
$737$			6.08732i			0.224229i
$738$		0			0
$739$	−30.4019			−1.11835			−0.559176	−	0.829049i	$-0.688883\pi$
$739$	−30.4019			−1.11835			−0.559176	+	0.829049i	$0.688883\pi$
$740$	−20.7203	+	63.8217i	−0.761694	+	2.34613i
$741$		0			0
$742$			5.00016i			0.183561i
$743$		−	18.4888i		−	0.678287i	−0.940735	−	0.339143i	$-0.889863\pi$
$743$		−	18.4888i		−	0.678287i	0.940735	−	0.339143i	$-0.110137\pi$
$744$		0			0
$745$	−29.2532	−	9.49732i	−1.07175	−	0.347955i
$746$	19.1490			0.701093
$747$		0			0
$748$		−	59.3950i		−	2.17170i
$749$	6.45191			0.235748
$750$		0			0
$751$	−28.8407			−1.05241			−0.526205	−	0.850358i	$-0.676386\pi$
$751$	−28.8407			−1.05241			−0.526205	+	0.850358i	$0.676386\pi$
$752$		−	61.7503i		−	2.25180i
$753$		0			0
$754$	−38.5590			−1.40423
$755$	−16.9545	−	5.50443i	−0.617036	−	0.200327i
$756$		0			0
$757$		−	4.12046i		−	0.149761i	−0.997193	−	0.0748803i	$-0.976143\pi$
$757$		−	4.12046i		−	0.149761i	0.997193	−	0.0748803i	$-0.0238575\pi$
$758$			28.2586i			1.02640i
$759$		0			0
$760$	7.17466	−	22.0990i	0.260252	−	0.801615i
$761$	8.64846			0.313506			0.156753	−	0.987638i	$-0.449897\pi$
$761$	8.64846			0.313506			0.156753	+	0.987638i	$0.449897\pi$
$762$		0			0
$763$		−	0.00421617i		−	0.000152636i
$764$	−58.7199			−2.12441
$765$		0			0
$766$	−37.5624			−1.35718
$767$		−	15.9005i		−	0.574135i
$768$		0			0
$769$	15.9750			0.576075			0.288037	−	0.957619i	$-0.406997\pi$
$769$	15.9750			0.576075			0.288037	+	0.957619i	$0.406997\pi$
$770$	−12.0173	−	3.90152i	−0.433072	−	0.140601i
$771$		0			0
$772$			54.5877i			1.96466i
$773$			42.3024i			1.52151i	0.649037	+	0.760757i	$0.275172\pi$
$773$			42.3024i			1.52151i	−0.649037	+	0.760757i	$0.724828\pi$
$774$		0			0
$775$	−4.04647	−	2.93702i	−0.145353	−	0.105501i
$776$	−69.1016			−2.48060
$777$		0			0
$778$			32.1345i			1.15208i
$779$	9.53529			0.341637
$780$		0			0
$781$	66.7486			2.38845
$782$			40.4228i			1.44552i
$783$		0			0
$784$	101.402			3.62150
$785$	8.27200	−	25.4790i	0.295240	−	0.909384i
$786$		0			0
$787$			31.5495i			1.12462i	0.826928	+	0.562308i	$0.190087\pi$
$787$			31.5495i			1.12462i	−0.826928	+	0.562308i	$0.809913\pi$
$788$			79.2698i			2.82387i
$789$		0			0
$790$	−1.45795	+	4.49071i	−0.0518717	+	0.159772i
$791$	3.59847			0.127947
$792$		0			0
$793$			2.68617i			0.0953887i
$794$	40.1475			1.42478
$795$		0			0
$796$	−18.2916			−0.648327
$797$		−	24.5171i		−	0.868440i	−0.900807	−	0.434220i	$-0.857024\pi$
$797$		−	24.5171i		−	0.868440i	0.900807	−	0.434220i	$-0.142976\pi$
$798$		0			0
$799$	8.01012			0.283378
$800$	−63.0989	+	86.9341i	−2.23088	+	3.07359i
$801$		0			0
$802$		−	38.7696i		−	1.36900i
$803$			67.1179i			2.36854i
$804$		0			0
$805$	5.98180	+	1.94205i	0.210831	+	0.0684483i
$806$	5.90573			0.208020
$807$		0			0
$808$		−	144.502i		−	5.08358i
$809$	−10.5514			−0.370966			−0.185483	−	0.982647i	$-0.559385\pi$
$809$	−10.5514			−0.370966			−0.185483	+	0.982647i	$0.559385\pi$
$810$		0			0
$811$	−2.45238			−0.0861145			−0.0430573	−	0.999073i	$-0.513710\pi$
$811$	−2.45238			−0.0861145			−0.0430573	+	0.999073i	$0.513710\pi$
$812$			12.9294i			0.453731i
$813$		0			0
$814$	−85.6247			−3.00115
$815$	8.74778	−	26.9444i	0.306421	−	0.943823i
$816$		0			0
$817$		−	11.0402i		−	0.386247i
$818$		−	90.5691i		−	3.16667i
$819$		0			0
$820$	−99.9335	−	32.4444i	−3.48983	−	1.13301i
$821$	−32.9646			−1.15047			−0.575236	−	0.817987i	$-0.695090\pi$
$821$	−32.9646			−1.15047			−0.575236	+	0.817987i	$0.695090\pi$
$822$		0			0
$823$		−	21.3701i		−	0.744915i	−0.928049	−	0.372458i	$-0.878515\pi$
$823$		−	21.3701i		−	0.744915i	0.928049	−	0.372458i	$-0.121485\pi$
$824$	93.8897			3.27080
$825$		0			0
$826$	−7.28977			−0.253643
$827$		−	25.5351i		−	0.887941i	−0.896041	−	0.443971i	$-0.853569\pi$
$827$		−	25.5351i		−	0.887941i	0.896041	−	0.443971i	$-0.146431\pi$
$828$		0			0
$829$	50.1867			1.74306			0.871529	−	0.490344i	$-0.163129\pi$
$829$	50.1867			1.74306			0.871529	+	0.490344i	$0.163129\pi$
$830$	−48.6019	−	15.7791i	−1.68700	−	0.547700i
$831$		0			0
$832$		−	62.9670i		−	2.18299i
$833$			13.1536i			0.455746i
$834$		0			0
$835$	−14.0182	+	43.1781i	−0.485120	+	1.49424i
$836$	34.2710			1.18529
$837$		0			0
$838$		−	46.4834i		−	1.60574i
$839$	−32.7185			−1.12957			−0.564784	−	0.825239i	$-0.691040\pi$
$839$	−32.7185			−1.12957			−0.564784	+	0.825239i	$0.691040\pi$
$840$		0			0
$841$	13.6288			0.469959
$842$		−	59.2083i		−	2.04045i
$843$		0			0
$844$	59.8190			2.05905
$845$	−17.6859	−	5.74190i	−0.608414	−	0.197528i
$846$		0			0
$847$		−	7.79198i		−	0.267736i
$848$			74.4035i			2.55503i
$849$		0			0
$850$	−21.1476	−	15.3494i	−0.725356	−	0.526481i
$851$	42.6212			1.46104
$852$		0			0
$853$		−	56.5855i		−	1.93745i	−0.248136	−	0.968725i	$-0.579818\pi$
$853$		−	56.5855i		−	1.93745i	0.248136	−	0.968725i	$-0.420182\pi$
$854$	1.23150			0.0421412
$855$		0			0
$856$	166.826			5.70200
$857$			9.30014i			0.317687i	0.987304	+	0.158843i	$0.0507765\pi$
$857$			9.30014i			0.317687i	−0.987304	+	0.158843i	$0.949224\pi$
$858$		0			0
$859$	−29.5054			−1.00671			−0.503356	−	0.864079i	$-0.667902\pi$
$859$	−29.5054			−1.00671			−0.503356	+	0.864079i	$0.667902\pi$
$860$	−37.5648	+	115.705i	−1.28095	+	3.94551i
$861$		0			0
$862$			31.4994i			1.07287i
$863$			12.2429i			0.416753i	0.978049	+	0.208376i	$0.0668179\pi$
$863$			12.2429i			0.416753i	−0.978049	+	0.208376i	$0.933182\pi$
$864$		0			0
$865$	13.9723	−	43.0367i	0.475072	−	1.46329i
$866$	−14.0319			−0.476823
$867$		0			0
$868$		−	1.98027i		−	0.0672149i
$869$	−4.40652			−0.149481
$870$		0			0
$871$	−2.31358			−0.0783927
$872$		−	0.109017i		−	0.00369178i
$873$		0			0
$874$	−23.3240			−0.788947
$875$	−3.28742	+	2.39200i	−0.111135	+	0.0808643i
$876$		0			0
$877$		−	25.6754i		−	0.866997i	−0.901154	−	0.433499i	$-0.857279\pi$
$877$		−	25.6754i		−	0.866997i	0.901154	−	0.433499i	$-0.142721\pi$
$878$			50.6167i			1.70823i
$879$		0			0
$880$	−178.820	−	58.0555i	−6.02801	−	1.95705i
$881$	−51.6637			−1.74059			−0.870297	−	0.492527i	$-0.836073\pi$
$881$	−51.6637			−1.74059			−0.870297	+	0.492527i	$0.836073\pi$
$882$		0			0
$883$		−	1.40767i		−	0.0473719i	−0.999719	−	0.0236860i	$-0.992460\pi$
$883$		−	1.40767i		−	0.0473719i	0.999719	−	0.0236860i	$-0.00754018\pi$
$884$	22.5740			0.759245
$885$		0			0
$886$	2.26438			0.0760734
$887$		−	9.06740i		−	0.304453i	−0.988346	−	0.152227i	$-0.951356\pi$
$887$		−	9.06740i		−	0.304453i	0.988346	−	0.152227i	$-0.0486444\pi$
$888$		0			0
$889$	2.15152			0.0721597
$890$	10.3313	−	31.8221i	0.346308	−	1.06668i
$891$		0			0
$892$			109.838i			3.67765i
$893$			4.62185i			0.154664i
$894$		0			0
$895$	20.4644	+	6.64397i	0.684050	+	0.222083i
$896$	−13.2432			−0.442425
$897$		0			0
$898$			54.4976i			1.81861i
$899$	−6.52907			−0.217757
$900$		0			0
$901$	−9.65146			−0.321537
$902$		−	134.073i		−	4.46415i
$903$		0			0
$904$	93.0451			3.09463
$905$	−12.0410	−	3.90922i	−0.400256	−	0.129947i
$906$		0			0
$907$		−	34.2737i		−	1.13804i	−0.822324	−	0.569020i	$-0.807323\pi$
$907$		−	34.2737i		−	1.13804i	0.822324	−	0.569020i	$-0.192677\pi$
$908$			112.297i			3.72669i
$909$		0			0
$910$	1.48283	−	4.56735i	0.0491555	−	0.151406i
$911$	−44.0662			−1.45998			−0.729989	−	0.683459i	$-0.760475\pi$
$911$	−44.0662			−1.45998			−0.729989	+	0.683459i	$0.760475\pi$
$912$		0			0
$913$		−	47.6908i		−	1.57833i
$914$	−40.6436			−1.34437
$915$		0			0
$916$	−6.52429			−0.215569
$917$		−	6.83185i		−	0.225607i
$918$		0			0
$919$	3.21793			0.106150			0.0530749	−	0.998591i	$-0.483098\pi$
$919$	3.21793			0.106150			0.0530749	+	0.998591i	$0.483098\pi$
$920$	154.671	+	50.2153i	5.09934	+	1.65555i
$921$		0			0
$922$			27.4260i			0.903227i
$923$			25.3688i			0.835026i
$924$		0			0
$925$	−16.1842	+	22.2977i	−0.532134	+	0.733144i
$926$	92.7953			3.04944
$927$		0			0
$928$			140.270i			4.60460i
$929$	−40.7022			−1.33540			−0.667698	−	0.744433i	$-0.732720\pi$
$929$	−40.7022			−1.33540			−0.667698	+	0.744433i	$0.732720\pi$
$930$		0			0
$931$	−7.58967			−0.248741
$932$			66.9037i			2.19150i
$933$		0			0
$934$	99.1501			3.24429
$935$	7.53084	−	23.1961i	0.246285	−	0.758593i
$936$		0			0
$937$		−	5.49291i		−	0.179446i	−0.995967	−	0.0897228i	$-0.971402\pi$
$937$		−	5.49291i		−	0.179446i	0.995967	−	0.0897228i	$-0.0285981\pi$
$938$			1.06069i			0.0346326i
$939$		0			0
$940$	15.7261	−	48.4387i	0.512929	−	1.57990i
$941$	25.9336			0.845413			0.422706	−	0.906267i	$-0.361080\pi$
$941$	25.9336			0.845413			0.422706	+	0.906267i	$0.361080\pi$
$942$		0			0
$943$			66.7373i			2.17327i
$944$	−108.473			−3.53051
$945$		0			0
$946$	−155.233			−5.04706
$947$		−	32.9687i		−	1.07134i	−0.844428	−	0.535669i	$-0.820060\pi$
$947$		−	32.9687i		−	1.07134i	0.844428	−	0.535669i	$-0.179940\pi$
$948$		0			0
$949$	−25.5092			−0.828064
$950$	8.85665	−	12.2022i	0.287348	−	0.395891i
$951$		0			0
$952$		−	6.54843i		−	0.212236i
$953$		−	6.46663i		−	0.209475i	−0.994500	−	0.104737i	$-0.966600\pi$
$953$		−	6.46663i		−	0.209475i	0.994500	−	0.104737i	$-0.0334002\pi$
$954$		0			0
$955$	−22.9324	−	7.44524i	−0.742076	−	0.240922i
$956$	35.8987			1.16105
$957$		0			0
$958$			101.358i			3.27471i
$959$	5.02987			0.162423
$960$		0			0
$961$	1.00000			0.0322581
$962$		−	32.5430i		−	1.04923i
$963$		0			0
$964$	19.8794			0.640271
$965$	−6.92131	+	21.3187i	−0.222805	+	0.686272i
$966$		0			0
$967$			20.1694i			0.648605i	0.945953	+	0.324303i	$0.105130\pi$
$967$			20.1694i			0.648605i	−0.945953	+	0.324303i	$0.894870\pi$
$968$		−	201.476i		−	6.47568i
$969$		0			0
$970$	−42.6507	−	13.8470i	−1.36943	−	0.444599i
$971$	−27.2911			−0.875811			−0.437906	−	0.899021i	$-0.644280\pi$
$971$	−27.2911			−0.875811			−0.437906	+	0.899021i	$0.644280\pi$
$972$		0			0
$973$			5.61460i			0.179996i
$974$	27.4119			0.878335
$975$		0			0
$976$	18.3251			0.586571
$977$			30.9195i			0.989202i	0.869120	+	0.494601i	$0.164686\pi$
$977$			30.9195i			0.989202i	−0.869120	+	0.494601i	$0.835314\pi$
$978$		0			0
$979$	31.2255			0.997971
$980$	79.5426	+	25.8243i	2.54089	+	0.824926i
$981$		0			0
$982$			59.4038i			1.89565i
$983$		−	10.0088i		−	0.319230i	−0.987179	−	0.159615i	$-0.948975\pi$
$983$		−	10.0088i		−	0.319230i	0.987179	−	0.159615i	$-0.0510252\pi$
$984$		0			0
$985$	−10.0508	+	30.9580i	−0.320245	+	0.986403i
$986$	−34.1222			−1.08667
$987$		0			0
$988$			13.0252i			0.414387i
$989$	77.2700			2.45704
$990$		0			0
$991$	11.6459			0.369946			0.184973	−	0.982744i	$-0.440780\pi$
$991$	11.6459			0.369946			0.184973	+	0.982744i	$0.440780\pi$
$992$		−	21.4840i		−	0.682116i
$993$		0			0
$994$	11.6306			0.368901
$995$	−7.14358	−	2.31923i	−0.226467	−	0.0735246i
$996$		0			0
$997$			8.93602i			0.283007i	0.989938	+	0.141503i	$0.0451936\pi$
$997$			8.93602i			0.283007i	−0.989938	+	0.141503i	$0.954806\pi$
$998$		−	73.3910i		−	2.32315i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1395.2.c.g.559.15	yes	16
3.2	odd	2	inner	1395.2.c.g.559.2	yes	16
5.2	odd	4		6975.2.a.ck.1.2		16
5.3	odd	4		6975.2.a.ck.1.15		16
5.4	even	2	inner	1395.2.c.g.559.1	✓	16
15.2	even	4		6975.2.a.ck.1.16		16
15.8	even	4		6975.2.a.ck.1.1		16
15.14	odd	2	inner	1395.2.c.g.559.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1395.2.c.g.559.1	✓	16	5.4	even	2	inner
1395.2.c.g.559.2	yes	16	3.2	odd	2	inner
1395.2.c.g.559.15	yes	16	1.1	even	1	trivial
1395.2.c.g.559.16	yes	16	15.14	odd	2	inner
6975.2.a.ck.1.1		16	15.8	even	4
6975.2.a.ck.1.2		16	5.2	odd	4
6975.2.a.ck.1.15		16	5.3	odd	4
6975.2.a.ck.1.16		16	15.2	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1395 = 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1395.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.72869i q^{2} -5.44577 q^{4} +(-2.12679 - 0.690483i) q^{5} -0.363635i q^{7} -9.40246i q^{8} +(1.88412 - 5.80336i) q^{10} +5.69456 q^{11} +2.16431i q^{13} +0.992249 q^{14} +14.7649 q^{16} +1.91527i q^{17} -1.10511 q^{19} +(11.5820 + 3.76021i) q^{20} +15.5387i q^{22} -7.73467i q^{23} +(4.04647 + 2.93702i) q^{25} -5.90573 q^{26} +1.98027i q^{28} +6.52907 q^{29} -1.00000 q^{31} +21.4840i q^{32} -5.22619 q^{34} +(-0.251084 + 0.773375i) q^{35} +5.51041i q^{37} -3.01552i q^{38} +(-6.49224 + 19.9971i) q^{40} -8.62833 q^{41} +9.99008i q^{43} -31.0113 q^{44} +21.1056 q^{46} -4.18224i q^{47} +6.86777 q^{49} +(-8.01424 + 11.0416i) q^{50} -11.7863i q^{52} +5.03921i q^{53} +(-12.1111 - 3.93200i) q^{55} -3.41906 q^{56} +17.8158i q^{58} -7.34671 q^{59} +1.24112 q^{61} -2.72869i q^{62} -29.0934 q^{64} +(1.49442 - 4.60302i) q^{65} +1.06897i q^{67} -10.4301i q^{68} +(-2.11030 - 0.685131i) q^{70} +11.7215 q^{71} +11.7863i q^{73} -15.0362 q^{74} +6.01820 q^{76} -2.07074i q^{77} -0.773812 q^{79} +(-31.4018 - 10.1949i) q^{80} -23.5441i q^{82} -8.37479i q^{83} +(1.32246 - 4.07338i) q^{85} -27.2599 q^{86} -53.5429i q^{88} +5.48339 q^{89} +0.787018 q^{91} +42.1213i q^{92} +11.4121 q^{94} +(2.35034 + 0.763062i) q^{95} -7.34931i q^{97} +18.7400i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 18 q^{10} + 44 q^{16} + 36 q^{25} - 16 q^{31} - 24 q^{34} + 88 q^{46} - 16 q^{49} - 28 q^{55} + 64 q^{61} - 176 q^{64} + 38 q^{70} - 12 q^{76} - 72 q^{79} + 72 q^{85} - 16 q^{91} + 8 q^{94}+O(q^{100}) \) 16 * q - 12 * q^4 + 18 * q^10 + 44 * q^16 + 36 * q^25 - 16 * q^31 - 24 * q^34 + 88 * q^46 - 16 * q^49 - 28 * q^55 + 64 * q^61 - 176 * q^64 + 38 * q^70 - 12 * q^76 - 72 * q^79 + 72 * q^85 - 16 * q^91 + 8 * q^94

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