LMFDB - Embedded newform 152.2.o.b.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(27,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("152.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			107.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	152.107
Dual form			152.2.o.b.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.224745 - 0.389270i) q^{6} -2.82843i q^{8} +(-1.44949 + 2.51059i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.224745 - 0.389270i) q^{6} -2.82843i q^{8} +(-1.44949 + 2.51059i) q^{9} -0.550510 q^{11} -0.635674i q^{12} +(-2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +4.09978i q^{18} +(-3.17423 - 2.98735i) q^{19} +(-0.674235 + 0.389270i) q^{22} +(-0.449490 - 0.778539i) q^{24} +(-2.50000 + 4.33013i) q^{25} +1.87492i q^{27} +(-4.89898 - 2.82843i) q^{32} +(-0.151531 + 0.0874863i) q^{33} +(7.34847 + 4.24264i) q^{34} +(2.89898 + 5.02118i) q^{36} +(-6.00000 - 1.41421i) q^{38} +(0.398979 - 0.230351i) q^{41} +(-5.00000 - 8.66025i) q^{43} +(-0.550510 + 0.953512i) q^{44} +(-1.10102 - 0.635674i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(1.65153 + 0.953512i) q^{51} +(1.32577 + 2.29629i) q^{54} +(-1.34847 - 0.317837i) q^{57} +(10.6237 - 6.13361i) q^{59} -8.00000 q^{64} +(-0.123724 + 0.214297i) q^{66} +(-6.82577 - 3.94086i) q^{67} +12.0000 q^{68} +(7.10102 + 4.09978i) q^{72} +(-7.84847 - 13.5939i) q^{73} +1.58919i q^{75} +(-8.34847 + 2.51059i) q^{76} +(-4.05051 - 7.01569i) q^{81} +(0.325765 - 0.564242i) q^{82} +6.55051 q^{83} +(-12.2474 - 7.07107i) q^{86} +1.55708i q^{88} +(4.89898 + 2.82843i) q^{89} -1.79796 q^{96} +(14.8485 - 8.57277i) q^{97} +(8.57321 - 4.94975i) q^{98} +(0.797959 - 1.38211i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^9	$ 4 q + 6 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{11} - 8 q^{16} + 12 q^{17} + 2 q^{19} + 12 q^{22} + 8 q^{24} - 10 q^{25} - 30 q^{33} - 8 q^{36} - 24 q^{38} - 18 q^{41} - 20 q^{43} - 12 q^{44} - 24 q^{48} + 28 q^{49} + 36 q^{51} + 20 q^{54} + 24 q^{57} + 18 q^{59} - 32 q^{64} + 24 q^{66} - 42 q^{67} + 48 q^{68} + 48 q^{72} - 2 q^{73} - 4 q^{76} - 26 q^{81} + 16 q^{82} + 36 q^{83} + 32 q^{96} + 30 q^{97} - 36 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^11 - 8 * q^16 + 12 * q^17 + 2 * q^19 + 12 * q^22 + 8 * q^24 - 10 * q^25 - 30 * q^33 - 8 * q^36 - 24 * q^38 - 18 * q^41 - 20 * q^43 - 12 * q^44 - 24 * q^48 + 28 * q^49 + 36 * q^51 + 20 * q^54 + 24 * q^57 + 18 * q^59 - 32 * q^64 + 24 * q^66 - 42 * q^67 + 48 * q^68 + 48 * q^72 - 2 * q^73 - 4 * q^76 - 26 * q^81 + 16 * q^82 + 36 * q^83 + 32 * q^96 + 30 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$3$	0.275255	−	0.158919i	0.158919	−	0.0917517i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	0.275255	−	0.158919i	0.158919	−	0.0917517i	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$	0.224745	−	0.389270i	0.0917517	−	0.158919i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$		−	2.82843i		−	1.00000i
$9$	−1.44949	+	2.51059i	−0.483163	+	0.836863i
$10$		0			0
$11$	−0.550510			−0.165985			−0.0829925	−	0.996550i	$-0.526448\pi$
$11$	−0.550510			−0.165985			−0.0829925	+	0.996550i	$0.526448\pi$
$12$		−	0.635674i		−	0.183503i
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$			4.09978i			0.966326i
$19$	−3.17423	−	2.98735i	−0.728219	−	0.685344i
$19$	−3.17423	−	2.98735i	−0.728219	−	0.685344i
$20$		0			0
$21$		0			0
$22$	−0.674235	+	0.389270i	−0.143747	+	0.0829925i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	−0.449490	−	0.778539i	−0.0917517	−	0.158919i
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$		0			0
$27$			1.87492i			0.360828i
$28$		0			0
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−4.89898	−	2.82843i	−0.866025	−	0.500000i
$33$	−0.151531	+	0.0874863i	−0.0263781	+	0.0152294i
$34$	7.34847	+	4.24264i	1.26025	+	0.727607i
$35$		0			0
$36$	2.89898	+	5.02118i	0.483163	+	0.836863i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	−6.00000	−	1.41421i	−0.973329	−	0.229416i
$39$		0			0
$40$		0			0
$41$	0.398979	−	0.230351i	0.0623101	−	0.0359748i	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	0.398979	−	0.230351i	0.0623101	−	0.0359748i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	0.179069	−	0.983836i	$-0.442691\pi$
$44$	−0.550510	+	0.953512i	−0.0829925	+	0.143747i
$45$		0			0
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−1.10102	−	0.635674i	−0.158919	−	0.0917517i
$49$	7.00000			1.00000
$50$			7.07107i			1.00000i
$51$	1.65153	+	0.953512i	0.231261	+	0.133518i
$52$		0			0
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$	1.32577	+	2.29629i	0.180414	+	0.312486i
$55$		0			0
$56$		0			0
$57$	−1.34847	−	0.317837i	−0.178609	−	0.0420986i
$58$		0			0
$59$	10.6237	−	6.13361i	1.38309	−	0.798528i	0.390567	−	0.920575i	$-0.372279\pi$
$59$	10.6237	−	6.13361i	1.38309	−	0.798528i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$		0			0
$66$	−0.123724	+	0.214297i	−0.0152294	+	0.0263781i
$67$	−6.82577	−	3.94086i	−0.833900	−	0.481452i	0.0212861	−	0.999773i	$-0.493224\pi$
$67$	−6.82577	−	3.94086i	−0.833900	−	0.481452i	−0.855186	+	0.518321i	$0.826557\pi$
$68$	12.0000			1.45521
$69$		0			0
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	7.10102	+	4.09978i	0.836863	+	0.483163i
$73$	−7.84847	−	13.5939i	−0.918594	−	1.59105i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	−7.84847	−	13.5939i	−0.918594	−	1.59105i	−0.117041	−	0.993127i	$-0.537341\pi$
$74$		0			0
$75$			1.58919i			0.183503i
$76$	−8.34847	+	2.51059i	−0.957635	+	0.287984i
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$		0			0
$81$	−4.05051	−	7.01569i	−0.450057	−	0.779521i
$82$	0.325765	−	0.564242i	0.0359748	−	0.0623101i
$83$	6.55051			0.719012			0.359506	−	0.933143i	$-0.382945\pi$
$83$	6.55051			0.719012			0.359506	+	0.933143i	$0.382945\pi$
$84$		0			0
$85$		0			0
$86$	−12.2474	−	7.07107i	−1.32068	−	0.762493i
$87$		0			0
$88$			1.55708i			0.165985i
$89$	4.89898	+	2.82843i	0.519291	+	0.299813i	0.736644	−	0.676280i	$-0.236409\pi$
$89$	4.89898	+	2.82843i	0.519291	+	0.299813i	−0.217354	+	0.976093i	$0.569742\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.79796			−0.183503
$97$	14.8485	−	8.57277i	1.50763	−	0.870433i	0.507673	−	0.861550i	$-0.330506\pi$
$97$	14.8485	−	8.57277i	1.50763	−	0.870433i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	8.57321	−	4.94975i	0.866025	−	0.500000i
$99$	0.797959	−	1.38211i	0.0801979	−	0.138907i
$100$	5.00000	+	8.66025i	0.500000	+	0.866025i
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$	2.69694			0.267037
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			19.7990i			1.91404i	0.290021	+	0.957020i	$0.406338\pi$
$107$			19.7990i			1.91404i	−0.290021	+	0.957020i	$0.593662\pi$
$108$	3.24745	+	1.87492i	0.312486	+	0.180414i
$109$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$109$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	9.93160i		−	0.934287i	−0.884182	−	0.467143i	$-0.845283\pi$
$113$		−	9.93160i		−	0.934287i	0.884182	−	0.467143i	$-0.154717\pi$
$114$	−1.87628	+	0.564242i	−0.175729	+	0.0528461i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	8.67423	−	15.0242i	0.798528	−	1.38309i
$119$		0			0
$120$		0			0
$121$	−10.6969			−0.972449
$122$		0			0
$123$	0.0732141	−	0.126811i	0.00660149	−	0.0114341i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$127$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$	−2.75255	−	1.58919i	−0.242349	−	0.139920i
$130$		0			0
$131$	10.6237	+	18.4008i	0.928199	+	1.60769i	0.786334	+	0.617802i	$0.211977\pi$
$131$	10.6237	+	18.4008i	0.928199	+	1.60769i	0.141865	+	0.989886i	$0.454690\pi$
$132$			0.349945i			0.0304588i
$133$		0			0
$134$	−11.1464			−0.962905
$135$		0			0
$136$	14.6969	−	8.48528i	1.26025	−	0.727607i
$137$	−11.2980	+	19.5686i	−0.965250	+	1.67186i	−0.256307	+	0.966595i	$0.582506\pi$
$137$	−11.2980	+	19.5686i	−0.965250	+	1.67186i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−9.17423	+	15.8902i	−0.778148	+	1.34779i	0.154859	+	0.987937i	$0.450508\pi$
$139$	−9.17423	+	15.8902i	−0.778148	+	1.34779i	−0.933008	+	0.359856i	$0.882826\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	11.5959			0.966326
$145$		0			0
$146$	−19.2247	−	11.0994i	−1.59105	−	0.918594i
$147$	1.92679	−	1.11243i	0.158919	−	0.0917517i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	1.12372	+	1.94635i	0.0917517	+	0.158919i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−8.44949	+	8.97809i	−0.685344	+	0.728219i
$153$	−17.3939			−1.40621
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−9.92168	−	5.72829i	−0.779521	−	0.450057i
$163$	−23.0454			−1.80506			−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−23.0454			−1.80506			−0.902528	+	0.430632i	$0.858291\pi$
$164$		−	0.921404i		−	0.0719495i
$165$		0			0
$166$	8.02270	−	4.63191i	0.622683	−	0.359506i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$		0			0
$171$	12.1010	−	3.63907i	0.925388	−	0.278287i
$172$	−20.0000			−1.52499
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$		0			0
$176$	1.10102	+	1.90702i	0.0829925	+	0.143747i
$177$	1.94949	−	3.37662i	0.146533	−	0.253802i
$178$	8.00000			0.599625
$179$			25.4880i			1.90506i	0.304446	+	0.952529i	$0.401529\pi$
$179$			25.4880i			1.90506i	−0.304446	+	0.952529i	$0.598471\pi$
$180$		0			0
$181$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$181$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.65153	−	2.86054i	−0.120772	−	0.209183i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−2.20204	+	1.27135i	−0.158919	+	0.0917517i
$193$	14.6969	−	8.48528i	1.05791	−	0.610784i	0.133056	−	0.991109i	$-0.457521\pi$
$193$	14.6969	−	8.48528i	1.05791	−	0.610784i	0.924853	+	0.380325i	$0.124188\pi$
$194$	12.1237	−	20.9989i	0.870433	−	1.50763i
$195$		0			0
$196$	7.00000	−	12.1244i	0.500000	−	0.866025i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		−	2.25697i		−	0.160396i
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	12.2474	+	7.07107i	0.866025	+	0.500000i
$201$	−2.50510			−0.176696
$202$		0			0
$203$		0			0
$204$	3.30306	−	1.90702i	0.231261	−	0.133518i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.74745	+	1.64456i	0.120874	+	0.113757i
$210$		0			0
$211$	22.0454	−	12.7279i	1.51767	−	0.876226i	0.517884	−	0.855451i	$-0.326720\pi$
$211$	22.0454	−	12.7279i	1.51767	−	0.876226i	0.999784	−	0.0207756i	$-0.00661356\pi$
$212$		0			0
$213$		0			0
$214$	14.0000	+	24.2487i	0.957020	+	1.65761i
$215$		0			0
$216$	5.30306			0.360828
$217$		0			0
$218$		0			0
$219$	−4.32066	−	2.49454i	−0.291963	−	0.168565i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$223$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$224$		0			0
$225$	−7.24745	−	12.5529i	−0.483163	−	0.836863i
$226$	−7.02270	−	12.1637i	−0.467143	−	0.809116i
$227$		−	24.5665i		−	1.63054i	−0.579082	−	0.815270i	$-0.696589\pi$
$227$		−	24.5665i		−	1.63054i	0.579082	−	0.815270i	$-0.303411\pi$
$228$	−1.89898	+	2.01778i	−0.125763	+	0.133631i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.94949	−	17.2330i	−0.651813	−	1.12897i	−0.982683	−	0.185296i	$-0.940675\pi$
$233$	−9.94949	−	17.2330i	−0.651813	−	1.12897i	0.330870	−	0.943676i	$-0.392658\pi$
$234$		0			0
$235$		0			0
$236$		−	24.5344i		−	1.59706i
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	26.8485	+	15.5010i	1.72946	+	0.998505i	0.892058	+	0.451920i	$0.149261\pi$
$241$	26.8485	+	15.5010i	1.72946	+	0.998505i	0.837404	+	0.546585i	$0.184072\pi$
$242$	−13.1010	+	7.56388i	−0.842165	+	0.486224i
$243$	−7.10102	−	4.09978i	−0.455531	−	0.263001i
$244$		0			0
$245$		0			0
$246$		−	0.207081i		−	0.0132030i
$247$		0			0
$248$		0			0
$249$	1.80306	−	1.04100i	0.114264	−	0.0659706i
$250$		0			0
$251$	11.9722	−	20.7364i	0.755678	−	1.30887i	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	11.9722	−	20.7364i	0.755678	−	1.30887i	0.945036	−	0.326965i	$-0.106026\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	27.3990	+	15.8188i	1.70910	+	0.986750i	0.935674	+	0.352865i	$0.114792\pi$
$257$	27.3990	+	15.8188i	1.70910	+	0.986750i	0.773427	+	0.633885i	$0.218541\pi$
$258$	−4.49490			−0.279840
$259$		0			0
$260$		0			0
$261$		0			0
$262$	26.0227	+	15.0242i	1.60769	+	0.928199i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$	0.247449	+	0.428594i	0.0152294	+	0.0263781i
$265$		0			0
$266$		0			0
$267$	1.79796			0.110033
$268$	−13.6515	+	7.88171i	−0.833900	+	0.481452i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$	12.0000	−	20.7846i	0.727607	−	1.26025i
$273$		0			0
$274$			31.9555i			1.93050i
$275$	1.37628	−	2.38378i	0.0829925	−	0.143747i
$276$		0			0
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$			25.9487i			1.55630i
$279$		0			0
$280$		0			0
$281$	−25.7474	−	14.8653i	−1.53596	−	0.886789i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−25.7474	−	14.8653i	−1.53596	−	0.886789i	−0.536895	−	0.843649i	$-0.680403\pi$
$282$		0			0
$283$	−16.5227	−	28.6182i	−0.982173	−	1.70117i	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−16.5227	−	28.6182i	−0.982173	−	1.70117i	−0.328291	−	0.944577i	$-0.606473\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	14.2020	−	8.19955i	0.836863	−	0.483163i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	2.72474	−	4.71940i	0.159727	−	0.276656i
$292$	−31.3939			−1.83719
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	1.57321	−	2.72489i	0.0917517	−	0.158919i
$295$		0			0
$296$		0			0
$297$		−	1.03216i		−	0.0598920i
$298$		0			0
$299$		0			0
$300$	2.75255	+	1.58919i	0.158919	+	0.0917517i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−4.00000	+	16.9706i	−0.229416	+	0.973329i
$305$		0			0
$306$	−21.3031	+	12.2993i	−1.21781	+	0.703106i
$307$	−29.1742	+	16.8438i	−1.66506	+	0.961324i	−0.694820	+	0.719183i	$0.744516\pi$
$307$	−29.1742	+	16.8438i	−1.66506	+	0.961324i	−0.970241	+	0.242140i	$0.922151\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	−12.1969	+	21.1257i	−0.689412	+	1.19410i	0.282617	+	0.959233i	$0.408798\pi$
$313$	−12.1969	+	21.1257i	−0.689412	+	1.19410i	−0.972028	+	0.234863i	$0.924536\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	3.14643	+	5.44977i	0.175616	+	0.304177i
$322$		0			0
$323$	6.00000	−	25.4558i	0.333849	−	1.41640i
$324$	−16.2020			−0.900113
$325$		0			0
$326$	−28.2247	+	16.2956i	−1.56322	+	0.902528i
$327$		0			0
$328$	−0.651531	−	1.12848i	−0.0359748	−	0.0623101i
$329$		0			0
$330$		0			0
$331$			35.2446i			1.93722i	0.248590	+	0.968609i	$0.420033\pi$
$331$			35.2446i			1.93722i	−0.248590	+	0.968609i	$0.579967\pi$
$332$	6.55051	−	11.3458i	0.359506	−	0.622683i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	25.1969	−	14.5475i	1.37256	−	0.792451i	0.381314	−	0.924445i	$-0.375472\pi$
$337$	25.1969	−	14.5475i	1.37256	−	0.792451i	0.991250	+	0.131995i	$0.0421382\pi$
$338$	15.9217	+	9.19239i	0.866025	+	0.500000i
$339$	−1.57832	−	2.73372i	−0.0857224	−	0.148476i
$340$		0			0
$341$		0			0
$342$	12.2474	−	13.0137i	0.662266	−	0.703698i
$343$		0			0
$344$	−24.4949	+	14.1421i	−1.32068	+	0.762493i
$345$		0			0
$346$		0			0
$347$	−14.4217	−	24.9791i	−0.774197	−	1.34095i	−0.935245	−	0.354001i	$-0.884821\pi$
$347$	−14.4217	−	24.9791i	−0.774197	−	1.34095i	0.161048	−	0.986947i	$-0.448512\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$	2.69694	+	1.55708i	0.143747	+	0.0829925i
$353$	4.59592			0.244616			0.122308	−	0.992492i	$-0.460970\pi$
$353$	4.59592			0.244616			0.122308	+	0.992492i	$0.460970\pi$
$354$		−	5.51399i		−	0.293065i
$355$		0			0
$356$	9.79796	−	5.65685i	0.519291	−	0.299813i
$357$		0			0
$358$	18.0227	+	31.2162i	0.952529	+	1.64983i
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$		0			0
$361$	1.15153	+	18.9651i	0.0606069	+	0.998162i
$362$		0			0
$363$	−2.94439	+	1.69994i	−0.154540	+	0.0892239i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$		0			0
$369$			1.33557i			0.0695267i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$	−4.04541	−	2.33562i	−0.209183	−	0.120772i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	8.48528i		−	0.435860i	−0.975964	−	0.217930i	$-0.930070\pi$
$379$		−	8.48528i		−	0.435860i	0.975964	−	0.217930i	$-0.0699304\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$	−1.79796	+	3.11416i	−0.0917517	+	0.158919i
$385$		0			0
$386$	12.0000	−	20.7846i	0.610784	−	1.05791i
$387$	28.9898			1.47363
$388$		−	34.2911i		−	1.74087i
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$		−	19.7990i		−	1.00000i
$393$	5.84847	+	3.37662i	0.295016	+	0.170328i
$394$		0			0
$395$		0			0
$396$	−1.59592	−	2.76421i	−0.0801979	−	0.138907i
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$		0			0
$399$		0			0
$400$	20.0000			1.00000
$401$	−12.6464	+	7.30142i	−0.631532	+	0.364615i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	−12.6464	+	7.30142i	−0.631532	+	0.364615i	0.149813	+	0.988714i	$0.452133\pi$
$402$	−3.06811	+	1.77138i	−0.153023	+	0.0883482i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	2.69694	−	4.67123i	0.133518	−	0.231261i
$409$	31.1969	+	18.0116i	1.54259	+	0.890614i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	31.1969	+	18.0116i	1.54259	+	0.890614i	0.543915	+	0.839140i	$0.316941\pi$
$410$		0			0
$411$			7.18182i			0.354253i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$			5.83183i			0.285586i
$418$	3.30306	+	0.778539i	0.161558	+	0.0380796i
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$		0			0
$421$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$421$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$422$	18.0000	−	31.1769i	0.876226	−	1.51767i
$423$		0			0
$424$		0			0
$425$	−30.0000			−1.45521
$426$		0			0
$427$		0			0
$428$	34.2929	+	19.7990i	1.65761	+	0.957020i
$429$		0			0
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	6.49490	−	3.74983i	0.312486	−	0.180414i
$433$	−14.6969	−	8.48528i	−0.706290	−	0.407777i	0.103396	−	0.994640i	$-0.467029\pi$
$433$	−14.6969	−	8.48528i	−0.706290	−	0.407777i	−0.809686	+	0.586864i	$0.800362\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−7.05561			−0.337130
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	−10.1464	+	17.5741i	−0.483163	+	0.836863i
$442$		0			0
$443$	−9.27526	+	16.0652i	−0.440681	+	0.763281i	−0.997740	−	0.0671913i	$-0.978596\pi$
$443$	−9.27526	+	16.0652i	−0.440681	+	0.763281i	0.557059	+	0.830473i	$0.311930\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	33.5446i		−	1.58307i	−0.611124	−	0.791535i	$-0.709282\pi$
$449$		−	33.5446i		−	1.58307i	0.611124	−	0.791535i	$-0.290718\pi$
$450$	−17.7526	−	10.2494i	−0.836863	−	0.483163i
$451$	−0.219642	+	0.126811i	−0.0103426	+	0.00597128i
$452$	−17.2020	−	9.93160i	−0.809116	−	0.467143i
$453$		0			0
$454$	−17.3712	−	30.0878i	−0.815270	−	1.41209i
$455$		0			0
$456$	−0.898979	+	3.81405i	−0.0420986	+	0.178609i
$457$	16.3939			0.766873			0.383437	−	0.923567i	$-0.374740\pi$
$457$	16.3939			0.766873			0.383437	+	0.923567i	$0.374740\pi$
$458$		0			0
$459$	−9.74235	+	5.62475i	−0.454734	+	0.262541i
$460$		0			0
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$	−24.3712	−	14.0707i	−1.12897	−	0.651813i
$467$	−41.9444			−1.94095			−0.970477	−	0.241192i	$-0.922462\pi$
$467$	−41.9444			−1.94095			−0.970477	+	0.241192i	$0.922462\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−17.3485	−	30.0484i	−0.798528	−	1.38309i
$473$	2.75255	+	4.76756i	0.126562	+	0.219213i
$474$		0			0
$475$	20.8712	−	6.27647i	0.957635	−	0.287984i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$		0			0
$482$	43.8434			1.99701
$483$		0			0
$484$	−10.6969	+	18.5276i	−0.486224	+	0.842165i
$485$		0			0
$486$	−11.5959			−0.526002
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$		0			0
$489$	−6.34337	+	3.66234i	−0.286857	+	0.165617i
$490$		0			0
$491$	21.0000	+	36.3731i	0.947717	+	1.64149i	0.750218	+	0.661190i	$0.229948\pi$
$491$	21.0000	+	36.3731i	0.947717	+	1.64149i	0.197499	+	0.980303i	$0.436718\pi$
$492$	−0.146428	−	0.253621i	−0.00660149	−	0.0114341i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.47219	−	2.54991i	0.0659706	−	0.114264i
$499$	14.8712	+	25.7576i	0.665725	+	1.15307i	0.979088	+	0.203436i	$0.0652110\pi$
$499$	14.8712	+	25.7576i	0.665725	+	1.15307i	−0.313363	+	0.949633i	$0.601456\pi$
$500$		0			0
$501$		0			0
$502$		−	33.8625i		−	1.51136i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.57832	+	2.06594i	0.158919	+	0.0917517i
$508$		0			0
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			1.00000i
$513$	5.60102	−	5.95142i	0.247291	−	0.262762i
$514$	44.7423			1.97350
$515$		0			0
$516$	−5.50510	+	3.17837i	−0.242349	+	0.139920i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	27.8236i		−	1.21897i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$		−	27.8236i		−	1.21897i	0.792797	−	0.609486i	$-0.208624\pi$
$522$		0			0
$523$	−22.0454	−	12.7279i	−0.963978	−	0.556553i	−0.0665832	−	0.997781i	$-0.521210\pi$
$523$	−22.0454	−	12.7279i	−0.963978	−	0.556553i	−0.897395	+	0.441228i	$0.854543\pi$
$524$	42.4949			1.85640
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.606123	+	0.349945i	0.0263781	+	0.0152294i
$529$	−11.5000	−	19.9186i	−0.500000	−	0.866025i
$530$		0			0
$531$			35.5624i			1.54328i
$532$		0			0
$533$		0			0
$534$	2.20204	−	1.27135i	0.0952916	−	0.0550167i
$535$		0			0
$536$	−11.1464	+	19.3062i	−0.481452	+	0.833900i
$537$	4.05051	+	7.01569i	0.174792	+	0.302749i
$538$		0			0
$539$	−3.85357			−0.165985
$540$		0			0
$541$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$541$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$		0			0
$544$		−	33.9411i		−	1.45521i
$545$		0			0
$546$		0			0
$547$	7.34847	+	4.24264i	0.314198	+	0.181402i	0.648803	−	0.760956i	$-0.275270\pi$
$547$	7.34847	+	4.24264i	0.314198	+	0.181402i	−0.334606	+	0.942358i	$0.608603\pi$
$548$	22.5959	+	39.1373i	0.965250	+	1.67186i
$549$		0			0
$550$		−	3.89270i		−	0.165985i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	18.3485	+	31.7805i	0.778148	+	1.34779i
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.909185	−	0.524918i	−0.0383858	−	0.0221621i
$562$	−42.0454			−1.77358
$563$			7.59599i			0.320133i	0.987106	+	0.160066i	$0.0511708\pi$
$563$			7.59599i			0.320133i	−0.987106	+	0.160066i	$0.948829\pi$
$564$		0			0
$565$		0			0
$566$	−40.4722	−	23.3666i	−1.70117	−	0.982173i
$567$		0			0
$568$		0			0
$569$		−	22.6274i		−	0.948591i	−0.880366	−	0.474295i	$-0.842703\pi$
$569$		−	22.6274i		−	0.948591i	0.880366	−	0.474295i	$-0.157297\pi$
$570$		0			0
$571$	25.7423			1.07728			0.538642	−	0.842535i	$-0.318938\pi$
$571$	25.7423			1.07728			0.538642	+	0.842535i	$0.318938\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	11.5959	−	20.0847i	0.483163	−	0.836863i
$577$	−12.3939			−0.515964			−0.257982	−	0.966150i	$-0.583058\pi$
$577$	−12.3939			−0.515964			−0.257982	+	0.966150i	$0.583058\pi$
$578$			26.8701i			1.11765i
$579$	2.69694	−	4.67123i	0.112081	−	0.194130i
$580$		0			0
$581$		0			0
$582$		−	7.70674i		−	0.319455i
$583$		0			0
$584$	−38.4495	+	22.1988i	−1.59105	+	0.918594i
$585$		0			0
$586$		0			0
$587$	3.00000	+	5.19615i	0.123823	+	0.214468i	0.921272	−	0.388918i	$-0.127151\pi$
$587$	3.00000	+	5.19615i	0.123823	+	0.214468i	−0.797449	+	0.603386i	$0.793818\pi$
$588$		−	4.44972i		−	0.183503i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−24.0959	+	41.7354i	−0.989501	+	1.71387i	−0.369586	+	0.929197i	$0.620500\pi$
$593$	−24.0959	+	41.7354i	−0.989501	+	1.71387i	−0.619915	+	0.784669i	$0.712833\pi$
$594$	−0.729847	−	1.26413i	−0.0299460	−	0.0518680i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	4.49490			0.183503
$601$		−	31.3519i		−	1.27887i	−0.768845	−	0.639435i	$-0.779168\pi$
$601$		−	31.3519i		−	1.27887i	0.768845	−	0.639435i	$-0.220832\pi$
$602$		0			0
$603$	19.7878	−	11.4245i	0.805820	−	0.465240i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	7.10102	+	23.6130i	0.287984	+	0.957635i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−17.3939	+	30.1271i	−0.703106	+	1.21781i
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	−23.8207	+	41.2586i	−0.961324	+	1.66506i
$615$		0			0
$616$		0			0
$617$	24.6464	−	42.6889i	0.992228	−	1.71859i	0.388351	−	0.921512i	$-0.373045\pi$
$617$	24.6464	−	42.6889i	0.992228	−	1.71859i	0.603877	−	0.797077i	$-0.293622\pi$
$618$		0			0
$619$	−26.0000			−1.04503			−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000			−1.04503			−0.522514	+	0.852631i	$0.675006\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$			34.4982i			1.37882i
$627$	0.742346	+	0.174973i	0.0296464	+	0.00698774i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$631$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$632$		0			0
$633$	4.04541	−	7.00685i	0.160791	−	0.278497i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−43.7474	+	25.2576i	−1.72792	+	0.997615i	−0.829450	+	0.558581i	$0.811346\pi$
$641$	−43.7474	+	25.2576i	−1.72792	+	0.997615i	−0.898470	+	0.439034i	$0.855321\pi$
$642$	7.70714	+	4.44972i	0.304177	+	0.175616i
$643$	8.82577	+	15.2867i	0.348054	+	0.602848i	0.985904	−	0.167313i	$-0.0535092\pi$
$643$	8.82577	+	15.2867i	0.348054	+	0.602848i	−0.637850	+	0.770161i	$0.720176\pi$
$644$		0			0
$645$		0			0
$646$	−10.6515	−	35.4196i	−0.419079	−	1.39356i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−19.8434	+	11.4566i	−0.779521	+	0.450057i
$649$	−5.84847	+	3.37662i	−0.229572	+	0.132544i
$650$		0			0
$651$		0			0
$652$	−23.0454	+	39.9158i	−0.902528	+	1.56322i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	−1.59592	−	0.921404i	−0.0623101	−	0.0359748i
$657$	45.5051			1.77532
$658$		0			0
$659$	−41.6413	−	24.0416i	−1.62212	−	0.936529i	−0.986353	−	0.164644i	$-0.947352\pi$
$659$	−41.6413	−	24.0416i	−1.62212	−	0.936529i	−0.635763	−	0.771885i	$-0.719314\pi$
$660$		0			0
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	24.9217	+	43.1656i	0.968609	+	1.67768i
$663$		0			0
$664$		−	18.5276i		−	0.719012i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		−	50.9117i		−	1.96250i	−0.192736	−	0.981251i	$-0.561736\pi$
$673$		−	50.9117i		−	1.96250i	0.192736	−	0.981251i	$-0.438264\pi$
$674$	20.5732	−	35.6339i	0.792451	−	1.37256i
$675$	−8.11862	−	4.68729i	−0.312486	−	0.180414i
$676$	26.0000			1.00000
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$	−3.86607	−	2.23208i	−0.148476	−	0.0857224i
$679$		0			0
$680$		0			0
$681$	−3.90408	−	6.76207i	−0.149605	−	0.259123i
$682$		0			0
$683$			31.1127i			1.19049i	0.803543	+	0.595247i	$0.202946\pi$
$683$			31.1127i			1.19049i	−0.803543	+	0.595247i	$0.797054\pi$
$684$	5.79796	−	24.5987i	0.221691	−	0.940553i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−20.0000	+	34.6410i	−0.762493	+	1.32068i
$689$		0			0
$690$		0			0
$691$	46.0000			1.74992			0.874961	−	0.484193i	$-0.160887\pi$
$691$	46.0000			1.74992			0.874961	+	0.484193i	$0.160887\pi$
$692$		0			0
$693$		0			0
$694$	−35.3258	−	20.3953i	−1.34095	−	0.774197i
$695$		0			0
$696$		0			0
$697$	2.39388	+	1.38211i	0.0906746	+	0.0523510i
$698$		0			0
$699$	−5.47730	−	3.16232i	−0.207170	−	0.119610i
$700$		0			0
$701$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$701$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$702$		0			0
$703$		0			0
$704$	4.40408			0.165985
$705$		0			0
$706$	5.62883	−	3.24980i	0.211844	−	0.122308i
$707$		0			0
$708$	−3.89898	−	6.75323i	−0.146533	−	0.253802i
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	8.00000	−	13.8564i	0.299813	−	0.519291i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	44.1464	+	25.4880i	1.64983	+	0.952529i
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$		0			0
$721$		0			0
$722$	14.8207	+	22.4131i	0.551568	+	0.834130i
$723$	9.85357			0.366458
$724$		0			0
$725$		0			0
$726$	−2.40408	+	4.16399i	−0.0892239	+	0.154540i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$		0			0
$729$	21.6969			0.803590
$730$		0			0
$731$	30.0000	−	51.9615i	1.10959	−	1.92187i
$732$		0			0
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.75765	+	2.16948i	0.138415	+	0.0799139i
$738$	0.944387	+	1.63573i	0.0347634	+	0.0602119i
$739$	−26.8712	−	46.5422i	−0.988472	−	1.71208i	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−26.8712	−	46.5422i	−0.988472	−	1.71208i	−0.363117	−	0.931744i	$-0.618287\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$743$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.49490	+	16.4456i	−0.347400	+	0.601715i
$748$	−6.60612			−0.241544
$749$		0			0
$750$		0			0
$751$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$751$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$752$		0			0
$753$		−	7.61042i		−	0.277339i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$757$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$758$	−6.00000	−	10.3923i	−0.217930	−	0.377466i
$759$		0			0
$760$		0			0
$761$	17.2020			0.623574			0.311787	−	0.950152i	$-0.399073\pi$
$761$	17.2020			0.623574			0.311787	+	0.950152i	$0.399073\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$			5.08540i			0.183503i
$769$	−11.0000	+	19.0526i	−0.396670	+	0.687053i	−0.993313	−	0.115454i	$-0.963168\pi$
$769$	−11.0000	+	19.0526i	−0.396670	+	0.687053i	0.596643	+	0.802507i	$0.296501\pi$
$770$		0			0
$771$	10.0556			0.362144
$772$		−	33.9411i		−	1.22157i
$773$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$773$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$774$	35.5051	−	20.4989i	1.27620	−	0.736817i
$775$		0			0
$776$	−24.2474	−	41.9978i	−0.870433	−	1.50763i
$777$		0			0
$778$		0			0
$779$	−1.95459	−	0.460702i	−0.0700305	−	0.0165064i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−14.0000	−	24.2487i	−0.500000	−	0.866025i
$785$		0			0
$786$	9.55051			0.340655
$787$		−	30.5733i		−	1.08982i	−0.838494	−	0.544911i	$-0.816563\pi$
$787$		−	30.5733i		−	1.08982i	0.838494	−	0.544911i	$-0.183437\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−3.90918	−	2.25697i	−0.138907	−	0.0801979i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$	24.4949	−	14.1421i	0.866025	−	0.500000i
$801$	−14.2020	+	8.19955i	−0.501804	+	0.289717i
$802$	−10.3258	+	17.8848i	−0.364615	+	0.631532i
$803$	4.32066	+	7.48361i	0.152473	+	0.264091i
$804$	−2.50510	+	4.33896i	−0.0883482	+	0.153023i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	45.9898			1.61692			0.808458	−	0.588555i	$-0.200303\pi$
$809$	45.9898			1.61692			0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	36.7423	+	21.2132i	1.29020	+	0.744896i	0.978689	−	0.205347i	$-0.0658323\pi$
$811$	36.7423	+	21.2132i	1.29020	+	0.744896i	0.311509	+	0.950243i	$0.399166\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		−	7.62809i		−	0.267037i
$817$	−10.0000	+	42.4264i	−0.349856	+	1.48431i
$818$	50.9444			1.78123
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	5.07832	+	8.79590i	0.177127	+	0.306792i
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		−	0.874863i		−	0.0304588i
$826$		0			0
$827$	−49.0732	−	28.3324i	−1.70644	−	0.985215i	−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−49.0732	−	28.3324i	−1.70644	−	0.985215i	−0.767561	−	0.640976i	$-0.778530\pi$
$828$		0			0
$829$		0			0			−	1.00000i	$-0.5\pi$
$829$		0			0				1.00000i	$0.5\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	21.0000	+	36.3731i	0.727607	+	1.26025i
$834$	4.12372	+	7.14250i	0.142793	+	0.247325i
$835$		0			0
$836$	4.59592	−	1.38211i	0.158953	−	0.0478011i
$837$		0			0
$838$	22.0454	−	12.7279i	0.761546	−	0.439679i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$		0			0
$843$	−9.44949			−0.325458
$844$		−	50.9117i		−	1.75245i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−9.09592	−	5.25153i	−0.312171	−	0.180232i
$850$	−36.7423	+	21.2132i	−1.26025	+	0.727607i
$851$		0			0
$852$		0			0
$853$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$853$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$854$		0			0
$855$		0			0
$856$	56.0000			1.91404
$857$	−30.7020	+	17.7258i	−1.04876	+	0.605503i	−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−30.7020	+	17.7258i	−1.04876	+	0.605503i	−0.126459	+	0.991972i	$0.540361\pi$
$858$		0			0
$859$	18.1742	−	31.4787i	0.620097	−	1.07404i	−0.369370	−	0.929282i	$-0.620427\pi$
$859$	18.1742	−	31.4787i	0.620097	−	1.07404i	0.989467	−	0.144757i	$-0.0462401\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	5.30306	−	9.18517i	0.180414	−	0.312486i
$865$		0			0
$866$	−24.0000			−0.815553
$867$			6.03891i			0.205092i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$			49.7046i			1.68224i
$874$		0			0
$875$		0			0
$876$	−8.64133	+	4.98907i	−0.291963	+	0.168565i
$877$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$877$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−39.9898			−1.34729			−0.673645	−	0.739055i	$-0.735272\pi$
$881$	−39.9898			−1.34729			−0.673645	+	0.739055i	$0.735272\pi$
$882$			28.6984i			0.966326i
$883$	−26.2196	+	45.4138i	−0.882361	+	1.52829i	−0.0336527	+	0.999434i	$0.510714\pi$
$883$	−26.2196	+	45.4138i	−0.882361	+	1.52829i	−0.848709	+	0.528861i	$0.822619\pi$
$884$		0			0
$885$		0			0
$886$			26.2344i			0.881361i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.22985	+	3.86221i	0.0747027	+	0.129389i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−23.7196	−	41.0836i	−0.791535	−	1.37098i
$899$		0			0
$900$	−28.9898			−0.966326
$901$		0			0
$902$	−0.179337	+	0.310621i	−0.00597128	+	0.0103426i
$903$		0			0
$904$	−28.0908			−0.934287
$905$		0			0
$906$		0			0
$907$	−33.2196	+	19.1794i	−1.10304	+	0.636841i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−33.2196	+	19.1794i	−1.10304	+	0.636841i	−0.166022	+	0.986122i	$0.553092\pi$
$908$	−42.5505	−	24.5665i	−1.41209	−	0.815270i
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	1.59592	+	5.30691i	0.0528461	+	0.175729i
$913$	−3.60612			−0.119345
$914$	20.0783	−	11.5922i	0.664132	−	0.383437i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−7.95459	+	13.7778i	−0.262541	+	0.454734i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−5.35357	+	9.27266i	−0.176406	+	0.305544i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.7474	+	44.5959i	0.844746	+	1.46314i	0.885841	+	0.463988i	$0.153582\pi$
$929$	25.7474	+	44.5959i	0.844746	+	1.46314i	−0.0410949	+	0.999155i	$0.513085\pi$
$930$		0			0
$931$	−22.2196	−	20.9114i	−0.728219	−	0.685344i
$932$	−39.7980			−1.30363
$933$		0			0
$934$	−51.3712	+	29.6592i	−1.68092	+	0.970477i
$935$		0			0
$936$		0			0
$937$	−13.5454	+	23.4613i	−0.442509	+	0.766448i	−0.997875	−	0.0651578i	$-0.979245\pi$
$937$	−13.5454	+	23.4613i	−0.442509	+	0.766448i	0.555366	+	0.831606i	$0.312578\pi$
$938$		0			0
$939$			7.75328i			0.253019i
$940$		0			0
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$		0			0
$944$	−42.4949	−	24.5344i	−1.38309	−	0.798528i
$945$		0			0
$946$	6.74235	+	3.89270i	0.219213	+	0.126562i
$947$	15.0000	+	25.9808i	0.487435	+	0.844261i	0.999896	−	0.0144491i	$-0.00459946\pi$
$947$	15.0000	+	25.9808i	0.487435	+	0.844261i	−0.512461	+	0.858710i	$0.671266\pi$
$948$		0			0
$949$		0			0
$950$	21.1237	−	22.4452i	0.685344	−	0.728219i
$951$		0			0
$952$		0			0
$953$	51.0959	−	29.5002i	1.65516	−	0.955607i	0.680257	−	0.732974i	$-0.261868\pi$
$953$	51.0959	−	29.5002i	1.65516	−	0.955607i	0.974902	−	0.222633i	$-0.0714650\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$	−49.7071	−	28.6984i	−1.60179	−	0.924794i
$964$	53.6969	−	31.0019i	1.72946	−	0.998505i
$965$		0			0
$966$		0			0
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$			30.2555i			0.972449i
$969$	−2.39388	−	7.96036i	−0.0769024	−	0.255724i
$970$		0			0
$971$	−53.9722	+	31.1609i	−1.73205	+	1.00000i	−0.865579	+	0.500773i	$0.833049\pi$
$971$	−53.9722	+	31.1609i	−1.73205	+	1.00000i	−0.866471	+	0.499227i	$0.833617\pi$
$972$	−14.2020	+	8.19955i	−0.455531	+	0.263001i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$			25.9165i			0.829144i	0.910017	+	0.414572i	$0.136069\pi$
$977$			25.9165i			0.829144i	−0.910017	+	0.414572i	$0.863931\pi$
$978$	−5.17934	+	8.97088i	−0.165617	+	0.286857i
$979$	−2.69694	−	1.55708i	−0.0861945	−	0.0497644i
$980$		0			0
$981$		0			0
$982$	51.4393	+	29.6985i	1.64149	+	0.947717i
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$	−0.358674	−	0.207081i	−0.0114341	−	0.00660149i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$	5.60102	+	9.70125i	0.177743	+	0.307860i
$994$		0			0
$995$		0			0
$996$		−	4.16399i		−	0.131941i
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$	36.4268	+	21.0310i	1.15307	+	0.665725i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.b.107.2	yes	4
4.3	odd	2		608.2.s.a.335.2		4
8.3	odd	2	CM	152.2.o.b.107.2	yes	4
8.5	even	2		608.2.s.a.335.2		4
19.8	odd	6	inner	152.2.o.b.27.2	✓	4
76.27	even	6		608.2.s.a.559.2		4
152.27	even	6	inner	152.2.o.b.27.2	✓	4
152.141	odd	6		608.2.s.a.559.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.b.27.2	✓	4	19.8	odd	6	inner
152.2.o.b.27.2	✓	4	152.27	even	6	inner
152.2.o.b.107.2	yes	4	1.1	even	1	trivial
152.2.o.b.107.2	yes	4	8.3	odd	2	CM
608.2.s.a.335.2		4	4.3	odd	2
608.2.s.a.335.2		4	8.5	even	2
608.2.s.a.559.2		4	76.27	even	6
608.2.s.a.559.2		4	152.141	odd	6

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.224745 - 0.389270i) q^{6} -2.82843i q^{8} +(-1.44949 + 2.51059i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.275255 - 0.158919i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.224745 - 0.389270i) q^{6} -2.82843i q^{8} +(-1.44949 + 2.51059i) q^{9} -0.550510 q^{11} -0.635674i q^{12} +(-2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +4.09978i q^{18} +(-3.17423 - 2.98735i) q^{19} +(-0.674235 + 0.389270i) q^{22} +(-0.449490 - 0.778539i) q^{24} +(-2.50000 + 4.33013i) q^{25} +1.87492i q^{27} +(-4.89898 - 2.82843i) q^{32} +(-0.151531 + 0.0874863i) q^{33} +(7.34847 + 4.24264i) q^{34} +(2.89898 + 5.02118i) q^{36} +(-6.00000 - 1.41421i) q^{38} +(0.398979 - 0.230351i) q^{41} +(-5.00000 - 8.66025i) q^{43} +(-0.550510 + 0.953512i) q^{44} +(-1.10102 - 0.635674i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(1.65153 + 0.953512i) q^{51} +(1.32577 + 2.29629i) q^{54} +(-1.34847 - 0.317837i) q^{57} +(10.6237 - 6.13361i) q^{59} -8.00000 q^{64} +(-0.123724 + 0.214297i) q^{66} +(-6.82577 - 3.94086i) q^{67} +12.0000 q^{68} +(7.10102 + 4.09978i) q^{72} +(-7.84847 - 13.5939i) q^{73} +1.58919i q^{75} +(-8.34847 + 2.51059i) q^{76} +(-4.05051 - 7.01569i) q^{81} +(0.325765 - 0.564242i) q^{82} +6.55051 q^{83} +(-12.2474 - 7.07107i) q^{86} +1.55708i q^{88} +(4.89898 + 2.82843i) q^{89} -1.79796 q^{96} +(14.8485 - 8.57277i) q^{97} +(8.57321 - 4.94975i) q^{98} +(0.797959 - 1.38211i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^9	\( 4 q + 6 q^{3} + 4 q^{4} - 4 q^{6} + 4 q^{9} - 12 q^{11} - 8 q^{16} + 12 q^{17} + 2 q^{19} + 12 q^{22} + 8 q^{24} - 10 q^{25} - 30 q^{33} - 8 q^{36} - 24 q^{38} - 18 q^{41} - 20 q^{43} - 12 q^{44} - 24 q^{48} + 28 q^{49} + 36 q^{51} + 20 q^{54} + 24 q^{57} + 18 q^{59} - 32 q^{64} + 24 q^{66} - 42 q^{67} + 48 q^{68} + 48 q^{72} - 2 q^{73} - 4 q^{76} - 26 q^{81} + 16 q^{82} + 36 q^{83} + 32 q^{96} + 30 q^{97} - 36 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 + 4 * q^4 - 4 * q^6 + 4 * q^9 - 12 * q^11 - 8 * q^16 + 12 * q^17 + 2 * q^19 + 12 * q^22 + 8 * q^24 - 10 * q^25 - 30 * q^33 - 8 * q^36 - 24 * q^38 - 18 * q^41 - 20 * q^43 - 12 * q^44 - 24 * q^48 + 28 * q^49 + 36 * q^51 + 20 * q^54 + 24 * q^57 + 18 * q^59 - 32 * q^64 + 24 * q^66 - 42 * q^67 + 48 * q^68 + 48 * q^72 - 2 * q^73 - 4 * q^76 - 26 * q^81 + 16 * q^82 + 36 * q^83 + 32 * q^96 + 30 * q^97 - 36 * q^99

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