LMFDB - Embedded newform 588.2.b.b.391.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(391,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("588.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.b (of order $2$, degree $1$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.5
Root			$0.0777157 + 1.41208i$ of defining polynomial
Character	$\chi$	$=$	588.391
Dual form			588.2.b.b.391.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0777157 - 1.41208i) q^{2} +1.00000 q^{3} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.0777157 - 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.0777157 - 1.41208i) q^{2} +1.00000 q^{3} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.0777157 - 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +1.00000 q^{9} +(-0.619848 + 0.0341142i) q^{10} -2.11598i q^{11} +(-1.98792 + 0.219481i) q^{12} -3.84803i q^{13} -0.438962i q^{15} +(3.90366 - 0.872621i) q^{16} -5.64831i q^{17} +(-0.0777157 - 1.41208i) q^{18} -2.97584 q^{19} +(0.0963438 + 0.872621i) q^{20} +(-2.98792 + 0.164445i) q^{22} -4.77038i q^{23} +(0.464416 + 2.79004i) q^{24} +4.80731 q^{25} +(-5.43371 + 0.299052i) q^{26} +1.00000 q^{27} +7.02285 q^{29} +(-0.619848 + 0.0341142i) q^{30} -7.42528 q^{31} +(-1.53558 - 5.44445i) q^{32} -2.11598i q^{33} +(-7.97584 + 0.438962i) q^{34} +(-1.98792 + 0.219481i) q^{36} -5.28670 q^{37} +(0.231269 + 4.20212i) q^{38} -3.84803i q^{39} +(1.22472 - 0.203861i) q^{40} +6.81813i q^{41} +4.38646i q^{43} +(0.464416 + 4.20639i) q^{44} -0.438962i q^{45} +(-6.73615 + 0.370733i) q^{46} -1.68914 q^{47} +(3.90366 - 0.872621i) q^{48} +(-0.373604 - 6.78829i) q^{50} -5.64831i q^{51} +(0.844569 + 7.64957i) q^{52} +10.7120 q^{53} +(-0.0777157 - 1.41208i) q^{54} -0.928833 q^{55} -2.97584 q^{57} +(-0.545785 - 9.91680i) q^{58} +8.11818 q^{59} +(0.0963438 + 0.872621i) q^{60} -6.18674i q^{61} +(0.577061 + 10.4851i) q^{62} +(-7.56863 + 2.59148i) q^{64} -1.68914 q^{65} +(-2.98792 + 0.164445i) q^{66} +7.85056i q^{67} +(1.23970 + 11.2284i) q^{68} -4.77038i q^{69} -1.16982i q^{71} +(0.464416 + 2.79004i) q^{72} -10.0348i q^{73} +(0.410860 + 7.46523i) q^{74} +4.80731 q^{75} +(5.91574 - 0.653140i) q^{76} +(-5.43371 + 0.299052i) q^{78} +15.5836i q^{79} +(-0.383048 - 1.71356i) q^{80} +1.00000 q^{81} +(9.62772 - 0.529876i) q^{82} -5.49645 q^{83} -2.47939 q^{85} +(6.19401 - 0.340896i) q^{86} +7.02285 q^{87} +(5.90366 - 0.982694i) q^{88} +10.4187i q^{89} +(-0.619848 + 0.0341142i) q^{90} +(1.04701 + 9.48314i) q^{92} -7.42528 q^{93} +(0.131272 + 2.38519i) q^{94} +1.30628i q^{95} +(-1.53558 - 5.44445i) q^{96} +2.22605i q^{97} -2.11598i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} + 2 q^{12} + 10 q^{16} - 2 q^{18} + 12 q^{19} + 22 q^{20} - 6 q^{22} + 4 q^{24} - 4 q^{25} - 6 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 12 q^{31} - 12 q^{32} - 28 q^{34} + 2 q^{36} - 12 q^{37} - 2 q^{38} + 4 q^{40} + 4 q^{44} - 12 q^{46} - 8 q^{47} + 10 q^{48} + 2 q^{50} + 4 q^{52} + 8 q^{53} - 2 q^{54} - 8 q^{55} + 12 q^{57} - 14 q^{58} + 28 q^{59} + 22 q^{60} - 48 q^{62} + 2 q^{64} - 8 q^{65} - 6 q^{66} + 16 q^{68} + 4 q^{72} + 38 q^{74} - 4 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{80} + 8 q^{81} - 4 q^{82} + 4 q^{83} - 32 q^{85} + 6 q^{86} - 16 q^{87} + 26 q^{88} - 8 q^{90} - 28 q^{92} - 12 q^{93} - 32 q^{94} - 12 q^{96}+O(q^{100}) $ 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 + 2 * q^12 + 10 * q^16 - 2 * q^18 + 12 * q^19 + 22 * q^20 - 6 * q^22 + 4 * q^24 - 4 * q^25 - 6 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 12 * q^31 - 12 * q^32 - 28 * q^34 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 4 * q^40 + 4 * q^44 - 12 * q^46 - 8 * q^47 + 10 * q^48 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 2 * q^54 - 8 * q^55 + 12 * q^57 - 14 * q^58 + 28 * q^59 + 22 * q^60 - 48 * q^62 + 2 * q^64 - 8 * q^65 - 6 * q^66 + 16 * q^68 + 4 * q^72 + 38 * q^74 - 4 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^80 + 8 * q^81 - 4 * q^82 + 4 * q^83 - 32 * q^85 + 6 * q^86 - 16 * q^87 + 26 * q^88 - 8 * q^90 - 28 * q^92 - 12 * q^93 - 32 * q^94 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.0777157	−	1.41208i	−0.0549533	−	0.998489i
$2$	−0.0777157	−	1.41208i	−0.0549533	−	0.998489i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.98792	+	0.219481i	−0.993960	+	0.109740i
$5$		−	0.438962i		−	0.196310i	−0.995171	−	0.0981549i	$-0.968706\pi$
$5$		−	0.438962i		−	0.196310i	0.995171	−	0.0981549i	$-0.0312941\pi$
$6$	−0.0777157	−	1.41208i	−0.0317273	−	0.576478i
$7$		0			0
$7$		0			0
$8$	0.464416	+	2.79004i	0.164196	+	0.986428i
$9$	1.00000			0.333333
$10$	−0.619848	+	0.0341142i	−0.196013	+	0.0107879i
$11$		−	2.11598i		−	0.637991i	−0.947756	−	0.318995i	$-0.896655\pi$
$11$		−	2.11598i		−	0.637991i	0.947756	−	0.318995i	$-0.103345\pi$
$12$	−1.98792	+	0.219481i	−0.573863	+	0.0633587i
$13$		−	3.84803i		−	1.06725i	−0.845721	−	0.533625i	$-0.820829\pi$
$13$		−	3.84803i		−	1.06725i	0.845721	−	0.533625i	$-0.179171\pi$
$14$		0			0
$15$		−	0.438962i		−	0.113339i
$16$	3.90366	−	0.872621i	0.975914	−	0.218155i
$17$		−	5.64831i		−	1.36992i	−0.728583	−	0.684958i	$-0.759821\pi$
$17$		−	5.64831i		−	1.36992i	0.728583	−	0.684958i	$-0.240179\pi$
$18$	−0.0777157	−	1.41208i	−0.0183178	−	0.332830i
$19$	−2.97584			−0.682705			−0.341352	−	0.939935i	$-0.610885\pi$
$19$	−2.97584			−0.682705			−0.341352	+	0.939935i	$0.610885\pi$
$20$	0.0963438	+	0.872621i	0.0215431	+	0.195124i
$21$		0			0
$22$	−2.98792	+	0.164445i	−0.637027	+	0.0350597i
$23$		−	4.77038i		−	0.994694i	−0.867552	−	0.497347i	$-0.834308\pi$
$23$		−	4.77038i		−	0.994694i	0.867552	−	0.497347i	$-0.165692\pi$
$24$	0.464416	+	2.79004i	0.0947986	+	0.569514i
$25$	4.80731			0.961462
$26$	−5.43371	+	0.299052i	−1.06564	+	0.0586489i
$27$	1.00000			0.192450
$28$		0			0
$29$	7.02285			1.30411			0.652055	−	0.758172i	$-0.273907\pi$
$29$	7.02285			1.30411			0.652055	+	0.758172i	$0.273907\pi$
$30$	−0.619848	+	0.0341142i	−0.113168	+	0.00622838i
$31$	−7.42528			−1.33362			−0.666810	−	0.745228i	$-0.732341\pi$
$31$	−7.42528			−1.33362			−0.666810	+	0.745228i	$0.732341\pi$
$32$	−1.53558	−	5.44445i	−0.271455	−	0.962451i
$33$		−	2.11598i		−	0.368344i
$34$	−7.97584	+	0.438962i	−1.36785	+	0.0752813i
$35$		0			0
$36$	−1.98792	+	0.219481i	−0.331320	+	0.0365802i
$37$	−5.28670			−0.869129			−0.434564	−	0.900641i	$-0.643098\pi$
$37$	−5.28670			−0.869129			−0.434564	+	0.900641i	$0.643098\pi$
$38$	0.231269	+	4.20212i	0.0375169	+	0.681673i
$39$		−	3.84803i		−	0.616177i
$40$	1.22472	−	0.203861i	0.193645	−	0.0322333i
$41$			6.81813i			1.06481i	0.846489	+	0.532407i	$0.178712\pi$
$41$			6.81813i			1.06481i	−0.846489	+	0.532407i	$0.821288\pi$
$42$		0			0
$43$			4.38646i			0.668928i	0.942408	+	0.334464i	$0.108555\pi$
$43$			4.38646i			0.668928i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	0.464416	+	4.20639i	0.0700134	+	0.634138i
$45$		−	0.438962i		−	0.0654366i
$46$	−6.73615	+	0.370733i	−0.993190	+	0.0546617i
$47$	−1.68914			−0.246386			−0.123193	−	0.992383i	$-0.539313\pi$
$47$	−1.68914			−0.246386			−0.123193	+	0.992383i	$0.539313\pi$
$48$	3.90366	−	0.872621i	0.563444	−	0.125952i
$49$		0			0
$50$	−0.373604	−	6.78829i	−0.0528355	−	0.960010i
$51$		−	5.64831i		−	0.790921i
$52$	0.844569	+	7.64957i	0.117121	+	1.06080i
$53$	10.7120			1.47140			0.735702	−	0.677305i	$-0.236852\pi$
$53$	10.7120			1.47140			0.735702	+	0.677305i	$0.236852\pi$
$54$	−0.0777157	−	1.41208i	−0.0105758	−	0.192159i
$55$	−0.928833			−0.125244
$56$		0			0
$57$	−2.97584			−0.394160
$58$	−0.545785	−	9.91680i	−0.0716651	−	1.30214i
$59$	8.11818			1.05690			0.528448	−	0.848966i	$-0.322774\pi$
$59$	8.11818			1.05690			0.528448	+	0.848966i	$0.322774\pi$
$60$	0.0963438	+	0.872621i	0.0124379	+	0.112655i
$61$		−	6.18674i		−	0.792130i	−0.918222	−	0.396065i	$-0.870375\pi$
$61$		−	6.18674i		−	0.792130i	0.918222	−	0.396065i	$-0.129625\pi$
$62$	0.577061	+	10.4851i	0.0732868	+	1.33160i
$63$		0			0
$64$	−7.56863	+	2.59148i	−0.946079	+	0.323935i
$65$	−1.68914			−0.209512
$66$	−2.98792	+	0.164445i	−0.367788	+	0.0202417i
$67$			7.85056i			0.959098i	0.877515	+	0.479549i	$0.159200\pi$
$67$			7.85056i			0.959098i	−0.877515	+	0.479549i	$0.840800\pi$
$68$	1.23970	+	11.2284i	0.150335	+	1.36164i
$69$		−	4.77038i		−	0.574287i
$70$		0			0
$71$		−	1.16982i		−	0.138833i	−0.997588	−	0.0694163i	$-0.977886\pi$
$71$		−	1.16982i		−	0.138833i	0.997588	−	0.0694163i	$-0.0221137\pi$
$72$	0.464416	+	2.79004i	0.0547320	+	0.328809i
$73$		−	10.0348i		−	1.17448i	−0.809413	−	0.587240i	$-0.800214\pi$
$73$		−	10.0348i		−	1.17448i	0.809413	−	0.587240i	$-0.199786\pi$
$74$	0.410860	+	7.46523i	0.0477615	+	0.867815i
$75$	4.80731			0.555101
$76$	5.91574	−	0.653140i	0.678581	−	0.0749203i
$77$		0			0
$78$	−5.43371	+	0.299052i	−0.615246	+	0.0338610i
$79$			15.5836i			1.75329i	0.481136	+	0.876646i	$0.340224\pi$
$79$			15.5836i			1.75329i	−0.481136	+	0.876646i	$0.659776\pi$
$80$	−0.383048	−	1.71356i	−0.0428260	−	0.191581i
$81$	1.00000			0.111111
$82$	9.62772	−	0.529876i	1.06320	−	0.0585150i
$83$	−5.49645			−0.603314			−0.301657	−	0.953417i	$-0.597540\pi$
$83$	−5.49645			−0.603314			−0.301657	+	0.953417i	$0.597540\pi$
$84$		0			0
$85$	−2.47939			−0.268928
$86$	6.19401	−	0.340896i	0.667918	−	0.0367598i
$87$	7.02285			0.752928
$88$	5.90366	−	0.982694i	0.629332	−	0.104756i
$89$			10.4187i			1.10438i	0.833719	+	0.552189i	$0.186207\pi$
$89$			10.4187i			1.10438i	−0.833719	+	0.552189i	$0.813793\pi$
$90$	−0.619848	+	0.0341142i	−0.0653377	+	0.00359595i
$91$		0			0
$92$	1.04701	+	9.48314i	0.109158	+	0.988686i
$93$	−7.42528			−0.769966
$94$	0.131272	+	2.38519i	0.0135397	+	0.246014i
$95$			1.30628i			0.134022i
$96$	−1.53558	−	5.44445i	−0.156725	−	0.555671i
$97$			2.22605i			0.226021i	0.993594	+	0.113011i	$0.0360494\pi$
$97$			2.22605i			0.226021i	−0.993594	+	0.113011i	$0.963951\pi$
$98$		0			0
$99$		−	2.11598i		−	0.212664i
$100$	−9.55656	+	1.05511i	−0.955656	+	0.105511i
$101$		−	0.767851i		−	0.0764040i	−0.999270	−	0.0382020i	$-0.987837\pi$
$101$		−	0.767851i		−	0.0764040i	0.999270	−	0.0382020i	$-0.0121630\pi$
$102$	−7.97584	+	0.438962i	−0.789726	+	0.0434637i
$103$	−8.63878			−0.851205			−0.425602	−	0.904910i	$-0.639938\pi$
$103$	−8.63878			−0.851205			−0.425602	+	0.904910i	$0.639938\pi$
$104$	10.7361	−	1.78709i	1.05277	−	0.175238i
$105$		0			0
$106$	−0.832489	−	15.1261i	−0.0808585	−	1.46918i
$107$			2.54433i			0.245970i	0.992409	+	0.122985i	$0.0392467\pi$
$107$			2.54433i			0.245970i	−0.992409	+	0.122985i	$0.960753\pi$
$108$	−1.98792	+	0.219481i	−0.191288	+	0.0211196i
$109$	−6.80731			−0.652022			−0.326011	−	0.945366i	$-0.605705\pi$
$109$	−6.80731			−0.652022			−0.326011	+	0.945366i	$0.605705\pi$
$110$	0.0721849	+	1.31158i	0.00688256	+	0.125055i
$111$	−5.28670			−0.501792
$112$		0			0
$113$	13.6408			1.28322			0.641610	−	0.767031i	$-0.278267\pi$
$113$	13.6408			1.28322			0.641610	+	0.767031i	$0.278267\pi$
$114$	0.231269	+	4.20212i	0.0216604	+	0.393564i
$115$	−2.09402			−0.195268
$116$	−13.9609	+	1.54138i	−1.29623	+	0.143114i
$117$		−	3.84803i		−	0.355750i
$118$	−0.630909	−	11.4635i	−0.0580799	−	1.05530i
$119$		0			0
$120$	1.22472	−	0.203861i	0.111801	−	0.0186099i
$121$	6.52264			0.592968
$122$	−8.73615	+	0.480806i	−0.790933	+	0.0435302i
$123$			6.81813i			0.614770i
$124$	14.7609	−	1.62971i	1.32557	−	0.146352i
$125$		−	4.30504i		−	0.385054i
$126$		0			0
$127$		−	3.51914i		−	0.312273i	−0.987735	−	0.156137i	$-0.950096\pi$
$127$		−	3.51914i		−	0.312273i	0.987735	−	0.156137i	$-0.0499040\pi$
$128$	4.24757	+	10.4861i	0.375436	+	0.926848i
$129$			4.38646i			0.386206i
$130$	0.131272	+	2.38519i	0.0115134	+	0.209195i
$131$	19.6167			1.71392			0.856958	−	0.515387i	$-0.172352\pi$
$131$	19.6167			1.71392			0.856958	+	0.515387i	$0.172352\pi$
$132$	0.464416	+	4.20639i	0.0404223	+	0.366119i
$133$		0			0
$134$	11.0856	−	0.610111i	0.957649	−	0.0527056i
$135$		−	0.438962i		−	0.0377798i
$136$	15.7590	−	2.62317i	1.35132	−	0.224935i
$137$	−3.37827			−0.288625			−0.144313	−	0.989532i	$-0.546097\pi$
$137$	−3.37827			−0.288625			−0.144313	+	0.989532i	$0.546097\pi$
$138$	−6.73615	+	0.370733i	−0.573419	+	0.0315589i
$139$	16.4481			1.39511			0.697556	−	0.716530i	$-0.254271\pi$
$139$	16.4481			1.39511			0.697556	+	0.716530i	$0.254271\pi$
$140$		0			0
$141$	−1.68914			−0.142251
$142$	−1.65188	+	0.0909137i	−0.138623	+	0.00762930i
$143$	−8.14233			−0.680896
$144$	3.90366	−	0.872621i	0.325305	−	0.0727185i
$145$		−	3.08276i		−	0.256010i
$146$	−14.1699	+	0.779858i	−1.17271	+	0.0645415i
$147$		0			0
$148$	10.5095	−	1.16033i	0.863879	−	0.0953786i
$149$	6.47939			0.530812			0.265406	−	0.964137i	$-0.414494\pi$
$149$	6.47939			0.530812			0.265406	+	0.964137i	$0.414494\pi$
$150$	−0.373604	−	6.78829i	−0.0305046	−	0.554262i
$151$		−	7.76914i		−	0.632244i	−0.948719	−	0.316122i	$-0.897619\pi$
$151$		−	7.76914i		−	0.632244i	0.948719	−	0.316122i	$-0.102381\pi$
$152$	−1.38203	−	8.30271i	−0.112097	−	0.673439i
$153$		−	5.64831i		−	0.456639i
$154$		0			0
$155$			3.25942i			0.261803i
$156$	0.844569	+	7.64957i	0.0676196	+	0.612456i
$157$			8.46391i			0.675493i	0.941237	+	0.337747i	$0.109665\pi$
$157$			8.46391i			0.675493i	−0.941237	+	0.337747i	$0.890335\pi$
$158$	22.0052	−	1.21109i	1.75064	−	0.0963492i
$159$	10.7120			0.849516
$160$	−2.38990	+	0.674063i	−0.188939	+	0.0532893i
$161$		0			0
$162$	−0.0777157	−	1.41208i	−0.00610592	−	0.110943i
$163$			6.95459i			0.544725i	0.962195	+	0.272363i	$0.0878050\pi$
$163$			6.95459i			0.544725i	−0.962195	+	0.272363i	$0.912195\pi$
$164$	−1.49645	−	13.5539i	−0.116853	−	1.05838i
$165$	−0.928833			−0.0723096
$166$	0.427160	+	7.76141i	0.0331541	+	0.602402i
$167$	8.12021			0.628361			0.314180	−	0.949363i	$-0.398270\pi$
$167$	8.12021			0.628361			0.314180	+	0.949363i	$0.398270\pi$
$168$		0			0
$169$	−1.80731			−0.139024
$170$	0.192688	+	3.50109i	0.0147785	+	0.268521i
$171$	−2.97584			−0.227568
$172$	−0.962744	−	8.71993i	−0.0734085	−	0.664888i
$173$			1.41635i			0.107683i	0.998549	+	0.0538417i	$0.0171466\pi$
$173$			1.41635i			0.107683i	−0.998549	+	0.0538417i	$0.982853\pi$
$174$	−0.545785	−	9.91680i	−0.0413759	−	0.751791i
$175$		0			0
$176$	−1.84645	−	8.26004i	−0.139181	−	0.622624i
$177$	8.11818			0.610199
$178$	14.7120	−	0.809695i	1.10271	−	0.0606892i
$179$			10.7318i			0.802132i	0.916049	+	0.401066i	$0.131360\pi$
$179$			10.7318i			0.802132i	−0.916049	+	0.401066i	$0.868640\pi$
$180$	0.0963438	+	0.872621i	0.00718104	+	0.0650414i
$181$			1.21426i			0.0902549i	0.998981	+	0.0451275i	$0.0143694\pi$
$181$			1.21426i			0.0902549i	−0.998981	+	0.0451275i	$0.985631\pi$
$182$		0			0
$183$		−	6.18674i		−	0.457337i
$184$	13.3096	−	2.21544i	0.981193	−	0.163325i
$185$			2.32066i			0.170618i
$186$	0.577061	+	10.4851i	0.0423122	+	0.768802i
$187$	−11.9517			−0.873994
$188$	3.35787	−	0.370733i	0.244898	−	0.0270385i
$189$		0			0
$190$	1.84457	−	0.101518i	0.133819	−	0.00736493i
$191$		−	6.55261i		−	0.474131i	−0.971494	−	0.237065i	$-0.923814\pi$
$191$		−	6.55261i		−	0.474131i	0.971494	−	0.237065i	$-0.0761855\pi$
$192$	−7.56863	+	2.59148i	−0.546219	+	0.187024i
$193$	−3.23635			−0.232958			−0.116479	−	0.993193i	$-0.537161\pi$
$193$	−3.23635			−0.232958			−0.116479	+	0.993193i	$0.537161\pi$
$194$	3.14335	−	0.172999i	0.225680	−	0.0124206i
$195$	−1.68914			−0.120962
$196$		0			0
$197$	−19.2554			−1.37189			−0.685947	−	0.727652i	$-0.740612\pi$
$197$	−19.2554			−1.37189			−0.685947	+	0.727652i	$0.740612\pi$
$198$	−2.98792	+	0.164445i	−0.212342	+	0.0116866i
$199$	−8.62173			−0.611178			−0.305589	−	0.952164i	$-0.598853\pi$
$199$	−8.62173			−0.611178			−0.305589	+	0.952164i	$0.598853\pi$
$200$	2.23260	+	13.4126i	0.157868	+	0.948413i
$201$			7.85056i			0.553736i
$202$	−1.08426	+	0.0596741i	−0.0762886	+	0.00419865i
$203$		0			0
$204$	1.23970	+	11.2284i	0.0867961	+	0.786144i
$205$	2.99290			0.209033
$206$	0.671369	+	12.1986i	0.0467765	+	0.849918i
$207$		−	4.77038i		−	0.331565i
$208$	−3.35787	−	15.0214i	−0.232826	−	1.04154i
$209$			6.29681i			0.435559i
$210$		0			0
$211$			6.09787i			0.419795i	0.977723	+	0.209897i	$0.0673130\pi$
$211$			6.09787i			0.419795i	−0.977723	+	0.209897i	$0.932687\pi$
$212$	−21.2946	+	2.35108i	−1.46252	+	0.161473i
$213$		−	1.16982i		−	0.0801550i
$214$	3.59279	−	0.197735i	0.245598	−	0.0135169i
$215$	1.92549			0.131317
$216$	0.464416	+	2.79004i	0.0315995	+	0.189838i
$217$		0			0
$218$	0.529035	+	9.61245i	0.0358308	+	0.651037i
$219$		−	10.0348i		−	0.678086i
$220$	1.84645	−	0.203861i	0.124487	−	0.0137443i
$221$	−21.7348			−1.46204
$222$	0.410860	+	7.46523i	0.0275751	+	0.501033i
$223$	2.44944			0.164027			0.0820134	−	0.996631i	$-0.473865\pi$
$223$	2.44944			0.164027			0.0820134	+	0.996631i	$0.473865\pi$
$224$		0			0
$225$	4.80731			0.320487
$226$	−1.06011	−	19.2619i	−0.0705172	−	1.28128i
$227$	23.2796			1.54512			0.772561	−	0.634941i	$-0.218976\pi$
$227$	23.2796			1.54512			0.772561	+	0.634941i	$0.218976\pi$
$228$	5.91574	−	0.653140i	0.391779	−	0.0432553i
$229$			11.7069i			0.773615i	0.922160	+	0.386808i	$0.126422\pi$
$229$			11.7069i			0.773615i	−0.922160	+	0.386808i	$0.873578\pi$
$230$	0.162738	+	2.95691i	0.0107306	+	0.194973i
$231$		0			0
$232$	3.26153	+	19.5940i	0.214130	+	1.28641i
$233$	−8.16853			−0.535138			−0.267569	−	0.963539i	$-0.586220\pi$
$233$	−8.16853			−0.535138			−0.267569	+	0.963539i	$0.586220\pi$
$234$	−5.43371	+	0.299052i	−0.355213	+	0.0195496i
$235$			0.741467i			0.0483680i
$236$	−16.1383	+	1.78178i	−1.05051	+	0.115984i
$237$			15.5836i			1.01226i
$238$		0			0
$239$		−	18.1984i		−	1.17716i	−0.808439	−	0.588579i	$-0.799687\pi$
$239$		−	18.1984i		−	1.17716i	0.808439	−	0.588579i	$-0.200313\pi$
$240$	−0.383048	−	1.71356i	−0.0247256	−	0.110610i
$241$			28.9148i			1.86256i	0.364299	+	0.931282i	$0.381309\pi$
$241$			28.9148i			1.86256i	−0.364299	+	0.931282i	$0.618691\pi$
$242$	−0.506912	−	9.21047i	−0.0325855	−	0.592072i
$243$	1.00000			0.0641500
$244$	1.35787	+	12.2987i	0.0869288	+	0.787346i
$245$		0			0
$246$	9.62772	−	0.529876i	0.613841	−	0.0337836i
$247$			11.4511i			0.728617i
$248$	−3.44842	−	20.7168i	−0.218975	−	1.31552i
$249$	−5.49645			−0.348323
$250$	−6.07904	+	0.334569i	−0.384472	+	0.0211600i
$251$	−20.3586			−1.28502			−0.642512	−	0.766276i	$-0.722108\pi$
$251$	−20.3586			−1.28502			−0.642512	+	0.766276i	$0.722108\pi$
$252$		0			0
$253$	−10.0940			−0.634605
$254$	−4.96929	+	0.273492i	−0.311801	+	0.0171604i
$255$	−2.47939			−0.155266
$256$	14.4771	−	6.81283i	0.904816	−	0.425802i
$257$		−	21.2869i		−	1.32784i	−0.747802	−	0.663922i	$-0.768891\pi$
$257$		−	21.2869i		−	1.32784i	0.747802	−	0.663922i	$-0.231109\pi$
$258$	6.19401	−	0.340896i	0.385622	−	0.0212233i
$259$		0			0
$260$	3.35787	−	0.370733i	0.208246	−	0.0229919i
$261$	7.02285			0.434703
$262$	−1.52452	−	27.7002i	−0.0941853	−	1.71133i
$263$		−	20.1796i		−	1.24433i	−0.782887	−	0.622164i	$-0.786254\pi$
$263$		−	20.1796i		−	1.24433i	0.782887	−	0.622164i	$-0.213746\pi$
$264$	5.90366	−	0.982694i	0.363345	−	0.0604807i
$265$		−	4.70215i		−	0.288851i
$266$		0			0
$267$			10.4187i			0.637613i
$268$	−1.72305	−	15.6063i	−0.105252	−	0.953306i
$269$			16.3695i			0.998066i	0.866583	+	0.499033i	$0.166311\pi$
$269$			16.3695i			0.998066i	−0.866583	+	0.499033i	$0.833689\pi$
$270$	−0.619848	+	0.0341142i	−0.0377227	+	0.00207613i
$271$	−13.4539			−0.817268			−0.408634	−	0.912698i	$-0.633995\pi$
$271$	−13.4539			−0.817268			−0.408634	+	0.912698i	$0.633995\pi$
$272$	−4.92883	−	22.0490i	−0.298854	−	1.33692i
$273$		0			0
$274$	0.262545	+	4.77038i	0.0158609	+	0.288189i
$275$		−	10.1722i		−	0.613404i
$276$	1.04701	+	9.48314i	0.0630225	+	0.570818i
$277$	2.80731			0.168675			0.0843375	−	0.996437i	$-0.473123\pi$
$277$	2.80731			0.168675			0.0843375	+	0.996437i	$0.473123\pi$
$278$	−1.27828	−	23.2260i	−0.0766660	−	1.39300i
$279$	−7.42528			−0.444540
$280$		0			0
$281$	−25.4502			−1.51823			−0.759115	−	0.650957i	$-0.774368\pi$
$281$	−25.4502			−1.51823			−0.759115	+	0.650957i	$0.774368\pi$
$282$	0.131272	+	2.38519i	0.00781716	+	0.142036i
$283$	4.73949			0.281733			0.140867	−	0.990029i	$-0.455011\pi$
$283$	4.73949			0.281733			0.140867	+	0.990029i	$0.455011\pi$
$284$	0.256754	+	2.32552i	0.0152356	+	0.137994i
$285$			1.30628i			0.0773774i
$286$	0.632787	+	11.4976i	0.0374175	+	0.679867i
$287$		0			0
$288$	−1.53558	−	5.44445i	−0.0904851	−	0.320817i
$289$	−14.9034			−0.876668
$290$	−4.35310	+	0.239579i	−0.255623	+	0.0140686i
$291$			2.22605i			0.130493i
$292$	2.20244	+	19.9483i	0.128888	+	1.16739i
$293$			3.22818i			0.188592i	0.995544	+	0.0942960i	$0.0300600\pi$
$293$			3.22818i			0.188592i	−0.995544	+	0.0942960i	$0.969940\pi$
$294$		0			0
$295$		−	3.56357i		−	0.207479i
$296$	−2.45523	−	14.7501i	−0.142707	−	0.857333i
$297$		−	2.11598i		−	0.122781i
$298$	−0.503550	−	9.14940i	−0.0291699	−	0.530010i
$299$	−18.3566			−1.06159
$300$	−9.55656	+	1.05511i	−0.551748	+	0.0609170i
$301$		0			0
$302$	−10.9706	+	0.603784i	−0.631288	+	0.0347439i
$303$		−	0.767851i		−	0.0441119i
$304$	−11.6167	+	2.59678i	−0.666261	+	0.148936i
$305$	−2.71574			−0.155503
$306$	−7.97584	+	0.438962i	−0.455948	+	0.0250938i
$307$	5.45523			0.311347			0.155673	−	0.987809i	$-0.450245\pi$
$307$	5.45523			0.311347			0.155673	+	0.987809i	$0.450245\pi$
$308$		0			0
$309$	−8.63878			−0.491443
$310$	4.60255	−	0.253308i	0.261407	−	0.0143869i
$311$	−30.5251			−1.73092			−0.865460	−	0.500979i	$-0.832973\pi$
$311$	−30.5251			−1.73092			−0.865460	+	0.500979i	$0.832973\pi$
$312$	10.7361	−	1.78709i	0.607815	−	0.101174i
$313$			18.8324i			1.06447i	0.846596	+	0.532235i	$0.178648\pi$
$313$			18.8324i			1.06447i	−0.846596	+	0.532235i	$0.821352\pi$
$314$	11.9517	−	0.657778i	0.674472	−	0.0371206i
$315$		0			0
$316$	−3.42030	−	30.9790i	−0.192407	−	1.74270i
$317$	17.1652			0.964093			0.482046	−	0.876146i	$-0.339894\pi$
$317$	17.1652			0.964093			0.482046	+	0.876146i	$0.339894\pi$
$318$	−0.832489	−	15.1261i	−0.0466837	−	0.848232i
$319$		−	14.8602i		−	0.832010i
$320$	1.13756	+	3.32234i	0.0635916	+	0.185725i
$321$			2.54433i			0.142011i
$322$		0			0
$323$			16.8085i			0.935248i
$324$	−1.98792	+	0.219481i	−0.110440	+	0.0121934i
$325$		−	18.4987i		−	1.02612i
$326$	9.82041	−	0.540480i	0.543902	−	0.0299344i
$327$	−6.80731			−0.376445
$328$	−19.0228	+	3.16645i	−1.05036	+	0.174838i
$329$		0			0
$330$	0.0721849	+	1.31158i	0.00397365	+	0.0722003i
$331$		−	21.4868i		−	1.18102i	−0.807029	−	0.590511i	$-0.798926\pi$
$331$		−	21.4868i		−	1.18102i	0.807029	−	0.590511i	$-0.201074\pi$
$332$	10.9265	−	1.20637i	0.599670	−	0.0662079i
$333$	−5.28670			−0.289710
$334$	−0.631068	−	11.4664i	−0.0345305	−	0.627411i
$335$	3.44610			0.188280
$336$		0			0
$337$	5.91046			0.321964			0.160982	−	0.986957i	$-0.448534\pi$
$337$	5.91046			0.321964			0.160982	+	0.986957i	$0.448534\pi$
$338$	0.140456	+	2.55206i	0.00763983	+	0.138814i
$339$	13.6408			0.740868
$340$	4.92883	−	0.544179i	0.267303	−	0.0295123i
$341$			15.7117i			0.850837i
$342$	0.231269	+	4.20212i	0.0125056	+	0.227224i
$343$		0			0
$344$	−12.2384	+	2.03714i	−0.659850	+	0.109835i
$345$	−2.09402			−0.112738
$346$	2.00000	−	0.110073i	0.107521	−	0.00591755i
$347$		−	2.81560i		−	0.151149i	−0.997140	−	0.0755746i	$-0.975921\pi$
$347$		−	2.81560i		−	0.151149i	0.997140	−	0.0755746i	$-0.0240791\pi$
$348$	−13.9609	+	1.54138i	−0.748381	+	0.0826267i
$349$			9.54077i			0.510705i	0.966848	+	0.255353i	$0.0821916\pi$
$349$			9.54077i			0.510705i	−0.966848	+	0.255353i	$0.917808\pi$
$350$		0			0
$351$		−	3.84803i		−	0.205392i
$352$	−11.5203	+	3.24926i	−0.614035	+	0.173186i
$353$			9.96912i			0.530603i	0.964166	+	0.265301i	$0.0854715\pi$
$353$			9.96912i			0.530603i	−0.964166	+	0.265301i	$0.914529\pi$
$354$	−0.630909	−	11.4635i	−0.0335325	−	0.609277i
$355$	−0.513508			−0.0272542
$356$	−2.28670	−	20.7115i	−0.121195	−	1.09771i
$357$		0			0
$358$	15.1541	−	0.834029i	0.800920	−	0.0440798i
$359$		−	6.92820i		−	0.365657i	−0.983145	−	0.182828i	$-0.941475\pi$
$359$		−	6.92820i		−	0.365657i	0.983145	−	0.182828i	$-0.0585252\pi$
$360$	1.22472	−	0.203861i	0.0645485	−	0.0107444i
$361$	−10.1444			−0.533914
$362$	1.71462	−	0.0943667i	0.0901185	−	0.00495980i
$363$	6.52264			0.342350
$364$		0			0
$365$	−4.40488			−0.230562
$366$	−8.73615	+	0.480806i	−0.456646	+	0.0251322i
$367$	−17.9047			−0.934616			−0.467308	−	0.884094i	$-0.654776\pi$
$367$	−17.9047			−0.934616			−0.467308	+	0.884094i	$0.654776\pi$
$368$	−4.16274	−	18.6219i	−0.216998	−	0.970735i
$369$			6.81813i			0.354938i
$370$	3.27695	−	0.180352i	0.170361	−	0.00937604i
$371$		0			0
$372$	14.7609	−	1.62971i	0.765316	−	0.0844964i
$373$	14.4743			0.749452			0.374726	−	0.927136i	$-0.377737\pi$
$373$	14.4743			0.749452			0.374726	+	0.927136i	$0.377737\pi$
$374$	0.928833	+	16.8767i	0.0480288	+	0.872673i
$375$		−	4.30504i		−	0.222311i
$376$	−0.784463	−	4.71276i	−0.0404556	−	0.243042i
$377$		−	27.0241i		−	1.39181i
$378$		0			0
$379$			21.5969i			1.10936i	0.832064	+	0.554679i	$0.187159\pi$
$379$			21.5969i			1.10936i	−0.832064	+	0.554679i	$0.812841\pi$
$380$	−0.286704	−	2.59678i	−0.0147076	−	0.133212i
$381$		−	3.51914i		−	0.180291i
$382$	−9.25279	+	0.509241i	−0.473414	+	0.0260550i
$383$	0.636338			0.0325154			0.0162577	−	0.999868i	$-0.494825\pi$
$383$	0.636338			0.0325154			0.0162577	+	0.999868i	$0.494825\pi$
$384$	4.24757	+	10.4861i	0.216758	+	0.535116i
$385$		0			0
$386$	0.251515	+	4.56997i	0.0128018	+	0.232606i
$387$			4.38646i			0.222976i
$388$	−0.488575	−	4.42521i	−0.0248037	−	0.224656i
$389$	−1.01909			−0.0516701			−0.0258351	−	0.999666i	$-0.508224\pi$
$389$	−1.01909			−0.0516701			−0.0258351	+	0.999666i	$0.508224\pi$
$390$	0.131272	+	2.38519i	0.00664724	+	0.120779i
$391$	−26.9446			−1.36265
$392$		0			0
$393$	19.6167			0.989530
$394$	1.49645	+	27.1902i	0.0753900	+	1.36982i
$395$	6.84061			0.344188
$396$	0.464416	+	4.20639i	0.0233378	+	0.211379i
$397$		−	29.7953i		−	1.49538i	−0.664047	−	0.747691i	$-0.731162\pi$
$397$		−	29.7953i		−	1.49538i	0.664047	−	0.747691i	$-0.268838\pi$
$398$	0.670043	+	12.1745i	0.0335862	+	0.610254i
$399$		0			0
$400$	18.7661	−	4.19496i	0.938305	−	0.209748i
$401$	−6.79025			−0.339089			−0.169545	−	0.985523i	$-0.554230\pi$
$401$	−6.79025			−0.339089			−0.169545	+	0.985523i	$0.554230\pi$
$402$	11.0856	−	0.610111i	0.552899	−	0.0304296i
$403$			28.5727i			1.42331i
$404$	0.168529	+	1.52643i	0.00838461	+	0.0759426i
$405$		−	0.438962i		−	0.0218122i
$406$		0			0
$407$			11.1865i			0.554496i
$408$	15.7590	−	2.62317i	0.780186	−	0.129866i
$409$			3.71322i			0.183607i	0.995777	+	0.0918034i	$0.0292631\pi$
$409$			3.71322i			0.183607i	−0.995777	+	0.0918034i	$0.970737\pi$
$410$	−0.232595	−	4.22620i	−0.0114871	−	0.208717i
$411$	−3.37827			−0.166638
$412$	17.1732	−	1.89605i	0.846064	−	0.0934116i
$413$		0			0
$414$	−6.73615	+	0.370733i	−0.331063	+	0.0182206i
$415$			2.41273i			0.118436i
$416$	−20.9504	+	5.90897i	−1.02718	+	0.289711i
$417$	16.4481			0.805468
$418$	8.89158	−	0.489361i	0.434901	−	0.0239354i
$419$	20.7082			1.01166			0.505832	−	0.862632i	$-0.331186\pi$
$419$	20.7082			1.01166			0.505832	+	0.862632i	$0.331186\pi$
$420$		0			0
$421$	15.6579			0.763118			0.381559	−	0.924344i	$-0.375387\pi$
$421$	15.6579			0.763118			0.381559	+	0.924344i	$0.375387\pi$
$422$	8.61066	−	0.473900i	0.419161	−	0.0230691i
$423$	−1.68914			−0.0821287
$424$	4.97482	+	29.8869i	0.241599	+	1.45143i
$425$		−	27.1532i		−	1.31712i
$426$	−1.65188	+	0.0909137i	−0.0800339	+	0.00440478i
$427$		0			0
$428$	−0.558433	−	5.05793i	−0.0269929	−	0.244484i
$429$	−8.14233			−0.393116
$430$	−0.149641	−	2.71894i	−0.00721631	−	0.131119i
$431$			11.8614i			0.571345i	0.958327	+	0.285672i	$0.0922169\pi$
$431$			11.8614i			0.571345i	−0.958327	+	0.285672i	$0.907783\pi$
$432$	3.90366	−	0.872621i	0.187815	−	0.0419840i
$433$			16.9269i			0.813454i	0.913550	+	0.406727i	$0.133330\pi$
$433$			16.9269i			0.813454i	−0.913550	+	0.406727i	$0.866670\pi$
$434$		0			0
$435$		−	3.08276i		−	0.147807i
$436$	13.5324	−	1.49408i	0.648084	−	0.0715532i
$437$			14.1959i			0.679082i
$438$	−14.1699	+	0.779858i	−0.677062	+	0.0372631i
$439$	2.35281			0.112293			0.0561467	−	0.998423i	$-0.482119\pi$
$439$	2.35281			0.112293			0.0561467	+	0.998423i	$0.482119\pi$
$440$	−0.431365	−	2.59148i	−0.0205645	−	0.123544i
$441$		0			0
$442$	1.68914	+	30.6913i	0.0803441	+	1.45983i
$443$			1.60393i			0.0762050i	0.999274	+	0.0381025i	$0.0121313\pi$
$443$			1.60393i			0.0762050i	−0.999274	+	0.0381025i	$0.987869\pi$
$444$	10.5095	−	1.16033i	0.498761	−	0.0550669i
$445$	4.57341			0.216800
$446$	−0.190360	−	3.45880i	−0.00901381	−	0.163779i
$447$	6.47939			0.306465
$448$		0			0
$449$	1.35208			0.0638086			0.0319043	−	0.999491i	$-0.489843\pi$
$449$	1.35208			0.0638086			0.0319043	+	0.999491i	$0.489843\pi$
$450$	−0.373604	−	6.78829i	−0.0176118	−	0.320003i
$451$	14.4270			0.679341
$452$	−27.1169	+	2.99390i	−1.27547	+	0.140821i
$453$		−	7.76914i		−	0.365026i
$454$	−1.80919	−	32.8726i	−0.0849095	−	1.54279i
$455$		0			0
$456$	−1.38203	−	8.30271i	−0.0647195	−	0.388810i
$457$	22.1468			1.03598			0.517992	−	0.855385i	$-0.326680\pi$
$457$	22.1468			1.03598			0.517992	+	0.855385i	$0.326680\pi$
$458$	16.5311	−	0.909811i	0.772446	−	0.0425127i
$459$		−	5.64831i		−	0.263640i
$460$	4.16274	−	0.459597i	0.194089	−	0.0214288i
$461$		−	30.7842i		−	1.43376i	−0.697195	−	0.716882i	$-0.745569\pi$
$461$		−	30.7842i		−	1.43376i	0.697195	−	0.716882i	$-0.254431\pi$
$462$		0			0
$463$		−	13.8120i		−	0.641897i	−0.947097	−	0.320948i	$-0.895998\pi$
$463$		−	13.8120i		−	0.641897i	0.947097	−	0.320948i	$-0.104002\pi$
$464$	27.4148	−	6.12829i	1.27270	−	0.284499i
$465$			3.25942i			0.151152i
$466$	0.634823	+	11.5346i	0.0294076	+	0.534329i
$467$	17.0266			0.787897			0.393949	−	0.919132i	$-0.371109\pi$
$467$	17.0266			0.787897			0.393949	+	0.919132i	$0.371109\pi$
$468$	0.844569	+	7.64957i	0.0390402	+	0.353602i
$469$		0			0
$470$	1.04701	−	0.0576236i	0.0482949	−	0.00265798i
$471$			8.46391i			0.389996i
$472$	3.77021	+	22.6500i	0.173538	+	1.04255i
$473$	9.28164			0.426770
$474$	22.0052	−	1.21109i	1.01073	−	0.0556272i
$475$	−14.3058			−0.656395
$476$		0			0
$477$	10.7120			0.490468
$478$	−25.6976	+	1.41430i	−1.17538	+	0.0646887i
$479$	31.7805			1.45209			0.726045	−	0.687647i	$-0.241356\pi$
$479$	31.7805			1.45209			0.726045	+	0.687647i	$0.241356\pi$
$480$	−2.38990	+	0.674063i	−0.109084	+	0.0307666i
$481$			20.3434i			0.927578i
$482$	40.8299	−	2.24713i	1.85975	−	0.102354i
$483$		0			0
$484$	−12.9665	+	1.43160i	−0.589386	+	0.0650726i
$485$	0.977151			0.0443701
$486$	−0.0777157	−	1.41208i	−0.00352525	−	0.0640531i
$487$		−	5.76992i		−	0.261460i	−0.991418	−	0.130730i	$-0.958268\pi$
$487$		−	5.76992i		−	0.261460i	0.991418	−	0.130730i	$-0.0417321\pi$
$488$	17.2612	−	2.87322i	0.781379	−	0.130065i
$489$			6.95459i			0.314497i
$490$		0			0
$491$		−	22.6443i		−	1.02192i	−0.859603	−	0.510962i	$-0.829289\pi$
$491$		−	22.6443i		−	1.02192i	0.859603	−	0.510962i	$-0.170711\pi$
$492$	−1.49645	−	13.5539i	−0.0674652	−	0.611057i
$493$		−	39.6672i		−	1.78652i
$494$	16.1699	−	0.889931i	0.727516	−	0.0400399i
$495$	−0.928833			−0.0417479
$496$	−28.9858	+	6.47946i	−1.30150	+	0.290936i
$497$		0			0
$498$	0.427160	+	7.76141i	0.0191415	+	0.347797i
$499$			19.4432i			0.870396i	0.900335	+	0.435198i	$0.143322\pi$
$499$			19.4432i			0.870396i	−0.900335	+	0.435198i	$0.856678\pi$
$500$	0.944874	+	8.55807i	0.0422560	+	0.382729i
$501$	8.12021			0.362784
$502$	1.58218	+	28.7479i	0.0706162	+	1.28308i
$503$	−11.7570			−0.524217			−0.262108	−	0.965038i	$-0.584418\pi$
$503$	−11.7570			−0.524217			−0.262108	+	0.965038i	$0.584418\pi$
$504$		0			0
$505$	−0.337057			−0.0149989
$506$	0.784463	+	14.2535i	0.0348736	+	0.633646i
$507$	−1.80731			−0.0802656
$508$	0.772384	+	6.99577i	0.0342690	+	0.310387i
$509$			20.1467i			0.892987i	0.894787	+	0.446494i	$0.147327\pi$
$509$			20.1467i			0.892987i	−0.894787	+	0.446494i	$0.852673\pi$
$510$	0.192688	+	3.50109i	0.00853235	+	0.155031i
$511$		0			0
$512$	−10.7453	−	19.9133i	−0.474881	−	0.880050i
$513$	−2.97584			−0.131387
$514$	−30.0588	+	1.65433i	−1.32584	+	0.0729693i
$515$			3.79210i			0.167100i
$516$	−0.962744	−	8.71993i	−0.0423824	−	0.383873i
$517$			3.57417i			0.157192i
$518$		0			0
$519$			1.41635i			0.0621710i
$520$	−0.784463	−	4.71276i	−0.0344010	−	0.206668i
$521$		−	35.9071i		−	1.57312i	−0.617515	−	0.786559i	$-0.711860\pi$
$521$		−	35.9071i		−	1.57312i	0.617515	−	0.786559i	$-0.288140\pi$
$522$	−0.545785	−	9.91680i	−0.0238884	−	0.434047i
$523$	45.2961			1.98066			0.990330	−	0.138735i	$-0.0443035\pi$
$523$	45.2961			1.98066			0.990330	+	0.138735i	$0.0443035\pi$
$524$	−38.9964	+	4.30548i	−1.70356	+	0.188086i
$525$		0			0
$526$	−28.4951	+	1.56827i	−1.24245	+	0.0683799i
$527$			41.9403i			1.82695i
$528$	−1.84645	−	8.26004i	−0.0803563	−	0.359472i
$529$	0.243451			0.0105848
$530$	−6.63980	+	0.365431i	−0.288415	+	0.0158733i
$531$	8.11818			0.352299
$532$		0			0
$533$	26.2364			1.13642
$534$	14.7120	−	0.809695i	0.636650	−	0.0350389i
$535$	1.11687			0.0482863
$536$	−21.9034	+	3.64593i	−0.946081	+	0.157480i
$537$			10.7318i			0.463111i
$538$	23.1150	−	1.27217i	0.996558	−	0.0548470i
$539$		0			0
$540$	0.0963438	+	0.872621i	0.00414598	+	0.0375516i
$541$	−33.8983			−1.45740			−0.728701	−	0.684832i	$-0.759876\pi$
$541$	−33.8983			−1.45740			−0.728701	+	0.684832i	$0.759876\pi$
$542$	1.04558	+	18.9980i	0.0449115	+	0.816033i
$543$			1.21426i			0.0521087i
$544$	−30.7519	+	8.67345i	−1.31848	+	0.371871i
$545$			2.98815i			0.127998i
$546$		0			0
$547$		−	7.83251i		−	0.334894i	−0.985881	−	0.167447i	$-0.946448\pi$
$547$		−	7.83251i		−	0.334894i	0.985881	−	0.167447i	$-0.0535523\pi$
$548$	6.71574	−	0.741467i	0.286882	−	0.0316739i
$549$		−	6.18674i		−	0.264043i
$550$	−14.3639	+	0.790536i	−0.612477	+	0.0337086i
$551$	−20.8989			−0.890322
$552$	13.3096	−	2.21544i	0.566492	−	0.0942956i
$553$		0			0
$554$	−0.218172	−	3.96414i	−0.00926925	−	0.168420i
$555$			2.32066i			0.0985066i
$556$	−32.6976	+	3.61005i	−1.38669	+	0.153100i
$557$	15.3940			0.652266			0.326133	−	0.945324i	$-0.394254\pi$
$557$	15.3940			0.652266			0.326133	+	0.945324i	$0.394254\pi$
$558$	0.577061	+	10.4851i	0.0244289	+	0.443868i
$559$	16.8792			0.713914
$560$		0			0
$561$	−11.9517			−0.504600
$562$	1.97788	+	35.9376i	0.0834317	+	1.51594i
$563$	−16.4410			−0.692907			−0.346453	−	0.938067i	$-0.612614\pi$
$563$	−16.4410			−0.692907			−0.346453	+	0.938067i	$0.612614\pi$
$564$	3.35787	−	0.370733i	0.141392	−	0.0156107i
$565$		−	5.98780i		−	0.251909i
$566$	−0.368333	−	6.69252i	−0.0154822	−	0.281308i
$567$		0			0
$568$	3.26385	−	0.543286i	0.136948	−	0.0227958i
$569$	−37.2292			−1.56073			−0.780366	−	0.625323i	$-0.784967\pi$
$569$	−37.2292			−1.56073			−0.780366	+	0.625323i	$0.784967\pi$
$570$	1.84457	−	0.101518i	0.0772605	−	0.00425214i
$571$			20.7454i			0.868166i	0.900873	+	0.434083i	$0.142928\pi$
$571$			20.7454i			0.868166i	−0.900873	+	0.434083i	$0.857072\pi$
$572$	16.1863	−	1.78709i	0.676784	−	0.0747219i
$573$		−	6.55261i		−	0.273739i
$574$		0			0
$575$		−	22.9327i		−	0.956361i
$576$	−7.56863	+	2.59148i	−0.315360	+	0.107978i
$577$		−	15.4211i		−	0.641988i	−0.947081	−	0.320994i	$-0.895983\pi$
$577$		−	15.4211i		−	0.641988i	0.947081	−	0.320994i	$-0.104017\pi$
$578$	1.15822	+	21.0447i	0.0481758	+	0.875344i
$579$	−3.23635			−0.134498
$580$	0.676608	+	6.12829i	0.0280946	+	0.254463i
$581$		0			0
$582$	3.14335	−	0.172999i	0.130296	−	0.00717104i
$583$		−	22.6663i		−	0.938743i
$584$	27.9974	−	4.66031i	1.15854	−	0.192845i
$585$	−1.68914			−0.0698372
$586$	4.55843	−	0.250880i	0.188307	−	0.0103638i
$587$	34.0410			1.40502			0.702512	−	0.711672i	$-0.252062\pi$
$587$	34.0410			1.40502			0.702512	+	0.711672i	$0.252062\pi$
$588$		0			0
$589$	22.0965			0.910469
$590$	−5.03203	+	0.276945i	−0.207166	+	0.0114017i
$591$	−19.2554			−0.792063
$592$	−20.6375	+	4.61329i	−0.848195	+	0.189605i
$593$		−	31.8347i		−	1.30729i	−0.756800	−	0.653647i	$-0.773238\pi$
$593$		−	31.8347i		−	1.30729i	0.756800	−	0.653647i	$-0.226762\pi$
$594$	−2.98792	+	0.164445i	−0.122596	+	0.00674724i
$595$		0			0
$596$	−12.8805	+	1.42210i	−0.527606	+	0.0582516i
$597$	−8.62173			−0.352864
$598$	1.42659	+	25.9209i	0.0583377	+	1.05998i
$599$		−	20.7846i		−	0.849236i	−0.905373	−	0.424618i	$-0.860408\pi$
$599$		−	20.7846i		−	0.849236i	0.905373	−	0.424618i	$-0.139592\pi$
$600$	2.23260	+	13.4126i	0.0911453	+	0.547567i
$601$		−	15.8614i		−	0.646999i	−0.946228	−	0.323499i	$-0.895141\pi$
$601$		−	15.8614i		−	0.646999i	0.946228	−	0.323499i	$-0.104859\pi$
$602$		0			0
$603$			7.85056i			0.319699i
$604$	1.70518	+	15.4444i	0.0693827	+	0.628425i
$605$		−	2.86319i		−	0.116405i
$606$	−1.08426	+	0.0596741i	−0.0440452	+	0.00242409i
$607$	43.4302			1.76278			0.881388	−	0.472393i	$-0.156610\pi$
$607$	43.4302			1.76278			0.881388	+	0.472393i	$0.156610\pi$
$608$	4.56965	+	16.2018i	0.185324	+	0.657070i
$609$		0			0
$610$	0.211056	+	3.83484i	0.00854539	+	0.155268i
$611$			6.49985i			0.262956i
$612$	1.23970	+	11.2284i	0.0501117	+	0.453881i
$613$	15.5206			0.626871			0.313436	−	0.949609i	$-0.398520\pi$
$613$	15.5206			0.626871			0.313436	+	0.949609i	$0.398520\pi$
$614$	−0.423957	−	7.70321i	−0.0171095	−	0.310876i
$615$	2.99290			0.120685
$616$		0			0
$617$	−19.8053			−0.797330			−0.398665	−	0.917097i	$-0.630526\pi$
$617$	−19.8053			−0.797330			−0.398665	+	0.917097i	$0.630526\pi$
$618$	0.671369	+	12.1986i	0.0270064	+	0.490701i
$619$	16.3133			0.655687			0.327844	−	0.944732i	$-0.393678\pi$
$619$	16.3133			0.655687			0.327844	+	0.944732i	$0.393678\pi$
$620$	−0.715380	−	6.47946i	−0.0287303	−	0.260221i
$621$		−	4.77038i		−	0.191429i
$622$	2.37228	+	43.1038i	0.0951197	+	1.72830i
$623$		0			0
$624$	−3.35787	−	15.0214i	−0.134422	−	0.601336i
$625$	22.1468			0.885873
$626$	26.5928	−	1.46357i	1.06286	−	0.0584962i
$627$			6.29681i			0.251470i
$628$	−1.85767	−	16.8256i	−0.0741289	−	0.671413i
$629$			29.8609i			1.19063i
$630$		0			0
$631$		−	27.3095i		−	1.08717i	−0.839353	−	0.543587i	$-0.817066\pi$
$631$		−	27.3095i		−	1.08717i	0.839353	−	0.543587i	$-0.182934\pi$
$632$	−43.4789	+	7.23728i	−1.72950	+	0.287884i
$633$			6.09787i			0.242369i
$634$	−1.33400	−	24.2386i	−0.0529801	−	0.962636i
$635$	−1.54477			−0.0613022
$636$	−21.2946	+	2.35108i	−0.844385	+	0.0932263i
$637$		0			0
$638$	−20.9837	+	1.15487i	−0.830753	+	0.0457217i
$639$		−	1.16982i		−	0.0462775i
$640$	4.60300	−	1.86452i	0.181949	−	0.0737017i
$641$	9.79066			0.386708			0.193354	−	0.981129i	$-0.438063\pi$
$641$	9.79066			0.386708			0.193354	+	0.981129i	$0.438063\pi$
$642$	3.59279	−	0.197735i	0.141796	−	0.00780396i
$643$	−7.26458			−0.286487			−0.143244	−	0.989687i	$-0.545753\pi$
$643$	−7.26458			−0.286487			−0.143244	+	0.989687i	$0.545753\pi$
$644$		0			0
$645$	1.92549			0.0758160
$646$	23.7348	−	1.30628i	0.933835	−	0.0513949i
$647$	−46.0839			−1.81174			−0.905872	−	0.423551i	$-0.860783\pi$
$647$	−46.0839			−1.81174			−0.905872	+	0.423551i	$0.860783\pi$
$648$	0.464416	+	2.79004i	0.0182440	+	0.109603i
$649$		−	17.1779i		−	0.674290i
$650$	−26.1215	+	1.43764i	−1.02457	+	0.0563887i
$651$		0			0
$652$	−1.52640	−	13.8252i	−0.0597784	−	0.541435i
$653$	−6.77981			−0.265314			−0.132657	−	0.991162i	$-0.542351\pi$
$653$	−6.77981			−0.265314			−0.132657	+	0.991162i	$0.542351\pi$
$654$	0.529035	+	9.61245i	0.0206869	+	0.375876i
$655$		−	8.61097i		−	0.336458i
$656$	5.94965	+	26.6156i	0.232295	+	1.03917i
$657$		−	10.0348i		−	0.391493i
$658$		0			0
$659$			29.3184i			1.14208i	0.820921	+	0.571041i	$0.193460\pi$
$659$			29.3184i			1.14208i	−0.820921	+	0.571041i	$0.806540\pi$
$660$	1.84645	−	0.203861i	0.0718728	−	0.00793528i
$661$			30.5780i			1.18935i	0.803967	+	0.594674i	$0.202719\pi$
$661$			30.5780i			1.18935i	−0.803967	+	0.594674i	$0.797281\pi$
$662$	−30.3410	+	1.66986i	−1.17924	+	0.0649011i
$663$	−21.7348			−0.844111
$664$	−2.55264	−	15.3353i	−0.0990617	−	0.595125i
$665$		0			0
$666$	0.410860	+	7.46523i	0.0159205	+	0.289272i
$667$		−	33.5017i		−	1.29719i
$668$	−16.1423	+	1.78223i	−0.624566	+	0.0689566i
$669$	2.44944			0.0947009
$670$	−0.267816	−	4.86615i	−0.0103466	−	0.187996i
$671$	−13.0910			−0.505372
$672$		0			0
$673$	−6.37827			−0.245864			−0.122932	−	0.992415i	$-0.539230\pi$
$673$	−6.37827			−0.245864			−0.122932	+	0.992415i	$0.539230\pi$
$674$	−0.459336	−	8.34603i	−0.0176930	−	0.321477i
$675$	4.80731			0.185034
$676$	3.59279	−	0.396671i	0.138184	−	0.0152566i
$677$			12.4960i			0.480261i	0.970741	+	0.240131i	$0.0771903\pi$
$677$			12.4960i			0.480261i	−0.970741	+	0.240131i	$0.922810\pi$
$678$	−1.06011	−	19.2619i	−0.0407131	−	0.739748i
$679$		0			0
$680$	−1.15147	−	6.91760i	−0.0441569	−	0.265278i
$681$	23.2796			0.892076
$682$	22.1862	−	1.22105i	0.849552	−	0.0467563i
$683$			45.2547i			1.73162i	0.500371	+	0.865811i	$0.333197\pi$
$683$			45.2547i			1.73162i	−0.500371	+	0.865811i	$0.666803\pi$
$684$	5.91574	−	0.653140i	0.226194	−	0.0249734i
$685$			1.48293i			0.0566600i
$686$		0			0
$687$			11.7069i			0.446647i
$688$	3.82772	+	17.1232i	0.145930	+	0.652817i
$689$		−	41.2200i		−	1.57036i
$690$	0.162738	+	2.95691i	0.00619532	+	0.112568i
$691$	10.5931			0.402980			0.201490	−	0.979491i	$-0.435422\pi$
$691$	10.5931			0.402980			0.201490	+	0.979491i	$0.435422\pi$
$692$	−0.310863	−	2.81560i	−0.0118172	−	0.107033i
$693$		0			0
$694$	−3.97584	+	0.218816i	−0.150921	+	0.00830615i
$695$		−	7.22010i		−	0.273874i
$696$	3.26153	+	19.5940i	0.123628	+	0.742710i
$697$	38.5109			1.45870
$698$	13.4723	−	0.741467i	0.509934	−	0.0280649i
$699$	−8.16853			−0.308962
$700$		0			0
$701$	29.6566			1.12011			0.560057	−	0.828454i	$-0.310779\pi$
$701$	29.6566			1.12011			0.560057	+	0.828454i	$0.310779\pi$
$702$	−5.43371	+	0.299052i	−0.205082	+	0.0112870i
$703$	15.7324			0.593358
$704$	5.48351	+	16.0151i	0.206668	+	0.603590i
$705$			0.741467i			0.0279253i
$706$	14.0772	−	0.774757i	0.529801	−	0.0291584i
$707$		0			0
$708$	−16.1383	+	1.78178i	−0.606514	+	0.0669636i
$709$	−35.7011			−1.34078			−0.670392	−	0.742007i	$-0.733874\pi$
$709$	−35.7011			−1.34078			−0.670392	+	0.742007i	$0.733874\pi$
$710$	0.0399076	+	0.725113i	0.00149771	+	0.0272130i
$711$			15.5836i			0.584431i
$712$	−29.0685	+	4.83861i	−1.08939	+	0.181335i
$713$			35.4214i			1.32654i
$714$		0			0
$715$			3.57417i			0.133667i
$716$	−2.35543	−	21.3340i	−0.0880264	−	0.797288i
$717$		−	18.1984i		−	0.679633i
$718$	−9.78315	+	0.538430i	−0.365104	+	0.0200940i
$719$	12.8089			0.477693			0.238846	−	0.971057i	$-0.423231\pi$
$719$	12.8089			0.477693			0.238846	+	0.971057i	$0.423231\pi$
$720$	−0.383048	−	1.71356i	−0.0142753	−	0.0638605i
$721$		0			0
$722$	0.788376	+	14.3246i	0.0293403	+	0.533107i
$723$			28.9148i			1.07535i
$724$	−0.266506	−	2.41384i	−0.00990462	−	0.0897098i
$725$	33.7610			1.25385
$726$	−0.506912	−	9.21047i	−0.0188133	−	0.341833i
$727$	19.3286			0.716860			0.358430	−	0.933557i	$-0.383312\pi$
$727$	19.3286			0.716860			0.358430	+	0.933557i	$0.383312\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	0.342328	+	6.22003i	0.0126701	+	0.230214i
$731$	24.7761			0.916375
$732$	1.35787	+	12.2987i	0.0501883	+	0.454575i
$733$			37.6903i			1.39212i	0.717983	+	0.696061i	$0.245066\pi$
$733$			37.6903i			1.39212i	−0.717983	+	0.696061i	$0.754934\pi$
$734$	1.39147	+	25.2828i	0.0513602	+	0.933204i
$735$		0			0
$736$	−25.9721	+	7.32532i	−0.957344	+	0.270015i
$737$	16.6116			0.611896
$738$	9.62772	−	0.529876i	0.354401	−	0.0195050i
$739$		−	13.8647i		−	0.510023i	−0.966938	−	0.255011i	$-0.917921\pi$
$739$		−	13.8647i		−	0.510023i	0.966938	−	0.255011i	$-0.0820792\pi$
$740$	−0.509341	−	4.61329i	−0.0187237	−	0.169588i
$741$			11.4511i			0.420667i
$742$		0			0
$743$			18.9927i			0.696773i	0.937351	+	0.348387i	$0.113270\pi$
$743$			18.9927i			0.696773i	−0.937351	+	0.348387i	$0.886730\pi$
$744$	−3.44842	−	20.7168i	−0.126425	−	0.759516i
$745$		−	2.84421i		−	0.104204i
$746$	−1.12488	−	20.4389i	−0.0411849	−	0.748320i
$747$	−5.49645			−0.201105
$748$	23.7590	−	2.62317i	0.868715	−	0.0959125i
$749$		0			0
$750$	−6.07904	+	0.334569i	−0.221975	+	0.0122167i
$751$		−	29.1987i		−	1.06547i	−0.846281	−	0.532737i	$-0.821164\pi$
$751$		−	29.1987i		−	1.06547i	0.846281	−	0.532737i	$-0.178836\pi$
$752$	−6.59381	+	1.47398i	−0.240452	+	0.0537504i
$753$	−20.3586			−0.741909
$754$	−38.1601	+	2.10020i	−1.38971	+	0.0764847i
$755$	−3.41036			−0.124116
$756$		0			0
$757$	−10.8022			−0.392614			−0.196307	−	0.980542i	$-0.562895\pi$
$757$	−10.8022			−0.392614			−0.196307	+	0.980542i	$0.562895\pi$
$758$	30.4965	−	1.67842i	1.10768	−	0.0609628i
$759$	−10.0940			−0.366390
$760$	−3.64457	+	0.606658i	−0.132203	+	0.0220058i
$761$			0.234595i			0.00850407i	0.999991	+	0.00425204i	$0.00135347\pi$
$761$			0.234595i			0.00850407i	−0.999991	+	0.00425204i	$0.998647\pi$
$762$	−4.96929	+	0.273492i	−0.180018	+	0.00990758i
$763$		0			0
$764$	1.43817	+	13.0261i	0.0520313	+	0.471267i
$765$	−2.47939			−0.0896426
$766$	−0.0494535	−	0.898559i	−0.00178683	−	0.0324662i
$767$		−	31.2390i		−	1.12797i
$768$	14.4771	−	6.81283i	0.522396	−	0.245837i
$769$		−	34.8540i		−	1.25687i	−0.777863	−	0.628434i	$-0.783696\pi$
$769$		−	34.8540i		−	1.25687i	0.777863	−	0.628434i	$-0.216304\pi$
$770$		0			0
$771$		−	21.2869i		−	0.766631i
$772$	6.43361	−	0.710317i	0.231551	−	0.0255649i
$773$			19.6717i			0.707540i	0.935332	+	0.353770i	$0.115100\pi$
$773$			19.6717i			0.707540i	−0.935332	+	0.353770i	$0.884900\pi$
$774$	6.19401	−	0.340896i	0.222639	−	0.0122533i
$775$	−35.6957			−1.28223
$776$	−6.21076	+	1.03381i	−0.222953	+	0.0371118i
$777$		0			0
$778$	0.0791996	+	1.43904i	0.00283944	+	0.0515920i
$779$		−	20.2897i		−	0.726953i
$780$	3.35787	−	0.370733i	0.120231	−	0.0132744i
$781$	−2.47532			−0.0885739
$782$	2.09402	+	38.0478i	0.0748819	+	1.36059i
$783$	7.02285			0.250976
$784$		0			0
$785$	3.71533			0.132606
$786$	−1.52452	−	27.7002i	−0.0543779	−	0.988034i
$787$	38.9562			1.38864			0.694319	−	0.719668i	$-0.255706\pi$
$787$	38.9562			1.38864			0.694319	+	0.719668i	$0.255706\pi$
$788$	38.2783	−	4.22620i	1.36361	−	0.150552i
$789$		−	20.1796i		−	0.718413i
$790$	−0.531622	−	9.65946i	−0.0189143	−	0.343668i
$791$		0			0
$792$	5.90366	−	0.982694i	0.209777	−	0.0349185i
$793$	−23.8067			−0.845402
$794$	−42.0732	+	2.31556i	−1.49312	+	0.0821762i
$795$		−	4.70215i		−	0.166768i
$796$	17.1393	−	1.89230i	0.607487	−	0.0670710i
$797$		−	20.4557i		−	0.724579i	−0.932066	−	0.362289i	$-0.881995\pi$
$797$		−	20.4557i		−	0.724579i	0.932066	−	0.362289i	$-0.118005\pi$
$798$		0			0
$799$			9.54077i			0.337528i
$800$	−7.38203	−	26.1731i	−0.260994	−	0.925361i
$801$			10.4187i			0.368126i
$802$	0.527709	+	9.58836i	0.0186341	+	0.338577i
$803$	−21.2333			−0.749308
$804$	−1.72305	−	15.6063i	−0.0607672	−	0.550391i
$805$		0			0
$806$	40.3468	−	2.22055i	1.42116	−	0.0782154i
$807$			16.3695i			0.576234i
$808$	2.14233	−	0.356603i	0.0753670	−	0.0125452i
$809$	−48.9300			−1.72029			−0.860143	−	0.510053i	$-0.829626\pi$
$809$	−48.9300			−1.72029			−0.860143	+	0.510053i	$0.829626\pi$
$810$	−0.619848	+	0.0341142i	−0.0217792	+	0.00119865i
$811$	−51.9424			−1.82394			−0.911972	−	0.410253i	$-0.865440\pi$
$811$	−51.9424			−1.82394			−0.911972	+	0.410253i	$0.865440\pi$
$812$		0			0
$813$	−13.4539			−0.471850
$814$	15.7963	−	0.869369i	0.553658	−	0.0304714i
$815$	3.05280			0.106935
$816$	−4.92883	−	22.0490i	−0.172544	−	0.771871i
$817$		−	13.0534i		−	0.456681i
$818$	5.24335	−	0.288575i	0.183329	−	0.0100898i
$819$		0			0
$820$	−5.94965	+	0.656884i	−0.207771	+	0.0229394i
$821$	31.4645			1.09812			0.549059	−	0.835784i	$-0.314986\pi$
$821$	31.4645			1.09812			0.549059	+	0.835784i	$0.314986\pi$
$822$	0.262545	+	4.77038i	0.00915730	+	0.166386i
$823$		−	41.5119i		−	1.44701i	−0.690317	−	0.723507i	$-0.742529\pi$
$823$		−	41.5119i		−	1.44701i	0.690317	−	0.723507i	$-0.257471\pi$
$824$	−4.01199	−	24.1025i	−0.139764	−	0.839652i
$825$		−	10.1722i		−	0.354149i
$826$		0			0
$827$			38.6850i			1.34521i	0.740003	+	0.672604i	$0.234824\pi$
$827$			38.6850i			1.34521i	−0.740003	+	0.672604i	$0.765176\pi$
$828$	1.04701	+	9.48314i	0.0363860	+	0.329562i
$829$			10.3289i			0.358737i	0.983782	+	0.179369i	$0.0574054\pi$
$829$			10.3289i			0.358737i	−0.983782	+	0.179369i	$0.942595\pi$
$830$	3.40696	−	0.187507i	0.118257	−	0.00650847i
$831$	2.80731			0.0973846
$832$	9.97209	+	29.1243i	0.345720	+	1.00970i
$833$		0			0
$834$	−1.27828	−	23.2260i	−0.0442631	−	0.804251i
$835$		−	3.56446i		−	0.123353i
$836$	−1.38203	−	12.5176i	−0.0477985	−	0.432929i
$837$	−7.42528			−0.256655
$838$	−1.60935	−	29.2416i	−0.0555942	−	1.01013i
$839$	−10.4794			−0.361789			−0.180894	−	0.983503i	$-0.557899\pi$
$839$	−10.4794			−0.361789			−0.180894	+	0.983503i	$0.557899\pi$
$840$		0			0
$841$	20.3204			0.700704
$842$	−1.21686	−	22.1101i	−0.0419359	−	0.761965i
$843$	−25.4502			−0.876550
$844$	−1.33837	−	12.1221i	−0.0460685	−	0.417259i
$845$			0.793341i			0.0272918i
$846$	0.131272	+	2.38519i	0.00451324	+	0.0820046i
$847$		0			0
$848$	41.8159	−	9.34751i	1.43596	−	0.320995i
$849$	4.73949			0.162659
$850$	−38.3424	+	2.11023i	−1.31513	+	0.0723802i
$851$			25.2196i			0.864517i
$852$	0.256754	+	2.32552i	0.00879625	+	0.0796709i
$853$		−	25.5157i		−	0.873642i	−0.899548	−	0.436821i	$-0.856104\pi$
$853$		−	25.5157i		−	0.873642i	0.899548	−	0.436821i	$-0.143896\pi$
$854$		0			0
$855$			1.30628i			0.0446739i
$856$	−7.09879	+	1.18163i	−0.242632	+	0.0403873i
$857$		−	11.5450i		−	0.394370i	−0.980366	−	0.197185i	$-0.936820\pi$
$857$		−	11.5450i		−	0.394370i	0.980366	−	0.197185i	$-0.0631800\pi$
$858$	0.632787	+	11.4976i	0.0216030	+	0.392522i
$859$	−32.9105			−1.12289			−0.561445	−	0.827514i	$-0.689754\pi$
$859$	−32.9105			−1.12289			−0.561445	+	0.827514i	$0.689754\pi$
$860$	−3.82772	+	0.422608i	−0.130524	+	0.0144108i
$861$		0			0
$862$	16.7492	−	0.921819i	0.570481	−	0.0313973i
$863$			57.2818i			1.94990i	0.222432	+	0.974948i	$0.428600\pi$
$863$			57.2818i			1.94990i	−0.222432	+	0.974948i	$0.571400\pi$
$864$	−1.53558	−	5.44445i	−0.0522416	−	0.185224i
$865$	0.621725			0.0211393
$866$	23.9020	−	1.31548i	0.812224	−	0.0447019i
$867$	−14.9034			−0.506145
$868$		0			0
$869$	32.9745			1.11858
$870$	−4.35310	+	0.239579i	−0.147584	+	0.00812249i
$871$	30.2092			1.02360
$872$	−3.16143	−	18.9927i	−0.107059	−	0.643173i
$873$			2.22605i			0.0753403i
$874$	20.0457	−	1.10324i	0.678056	−	0.0373178i
$875$		0			0
$876$	2.20244	+	19.9483i	0.0744135	+	0.673991i
$877$	34.0431			1.14955			0.574777	−	0.818310i	$-0.305089\pi$
$877$	34.0431			1.14955			0.574777	+	0.818310i	$0.305089\pi$
$878$	−0.182850	−	3.32234i	−0.00617089	−	0.112124i
$879$			3.22818i			0.108884i
$880$	−3.62584	+	0.810520i	−0.122227	+	0.0273226i
$881$			23.4638i			0.790514i	0.918571	+	0.395257i	$0.129344\pi$
$881$			23.4638i			0.790514i	−0.918571	+	0.395257i	$0.870656\pi$
$882$		0			0
$883$		−	8.14468i		−	0.274090i	−0.990565	−	0.137045i	$-0.956239\pi$
$883$		−	8.14468i		−	0.274090i	0.990565	−	0.137045i	$-0.0437606\pi$
$884$	43.2071	−	4.77038i	1.45321	−	0.160445i
$885$		−	3.56357i		−	0.119788i
$886$	2.26487	−	0.124651i	0.0760899	−	0.00418772i
$887$	−29.2217			−0.981170			−0.490585	−	0.871393i	$-0.663217\pi$
$887$	−29.2217			−0.981170			−0.490585	+	0.871393i	$0.663217\pi$
$888$	−2.45523	−	14.7501i	−0.0823922	−	0.494981i
$889$		0			0
$890$	−0.355425	−	6.45800i	−0.0119139	−	0.216473i
$891$		−	2.11598i		−	0.0708879i
$892$	−4.86930	+	0.537606i	−0.163036	+	0.0180004i
$893$	5.02660			0.168209
$894$	−0.503550	−	9.14940i	−0.0168412	−	0.306002i
$895$	4.71085			0.157466
$896$		0			0
$897$	−18.3566			−0.612908
$898$	−0.105078	−	1.90924i	−0.00350649	−	0.0637122i
$899$	−52.1466			−1.73919
$900$	−9.55656	+	1.05511i	−0.318552	+	0.0351705i
$901$		−	60.5046i		−	2.01570i
$902$	−1.12120	−	20.3720i	−0.0373320	−	0.678314i
$903$		0			0
$904$	6.33502	+	38.0584i	0.210700	+	1.26580i
$905$	0.533012			0.0177179
$906$	−10.9706	+	0.603784i	−0.364474	+	0.0200594i
$907$		−	56.1181i		−	1.86337i	−0.363265	−	0.931686i	$-0.618338\pi$
$907$		−	56.1181i		−	1.86337i	0.363265	−	0.931686i	$-0.381662\pi$
$908$	−46.2780	+	5.10943i	−1.53579	+	0.169562i
$909$		−	0.767851i		−	0.0254680i
$910$		0			0
$911$		−	43.1536i		−	1.42974i	−0.699256	−	0.714871i	$-0.746485\pi$
$911$		−	43.1536i		−	1.42974i	0.699256	−	0.714871i	$-0.253515\pi$
$912$	−11.6167	+	2.59678i	−0.384666	+	0.0859881i
$913$			11.6304i			0.384909i
$914$	−1.72115	−	31.2730i	−0.0569307	−	1.03442i
$915$	−2.71574			−0.0897796
$916$	−2.56945	−	23.2724i	−0.0848969	−	0.768943i
$917$		0			0
$918$	−7.97584	+	0.438962i	−0.263242	+	0.0144879i
$919$		−	38.5228i		−	1.27075i	−0.772203	−	0.635375i	$-0.780845\pi$
$919$		−	38.5228i		−	1.27075i	0.772203	−	0.635375i	$-0.219155\pi$
$920$	−0.972496	−	5.84239i	−0.0320622	−	0.192618i
$921$	5.45523			0.179756
$922$	−43.4697	+	2.39242i	−1.43160	+	0.0787900i
$923$	−4.50151			−0.148169
$924$		0			0
$925$	−25.4148			−0.835635
$926$	−19.5036	+	1.07341i	−0.640927	+	0.0352743i
$927$	−8.63878			−0.283735
$928$	−10.7842	−	38.2355i	−0.354008	−	1.25514i
$929$			47.6930i			1.56476i	0.622803	+	0.782379i	$0.285994\pi$
$929$			47.6930i			1.56476i	−0.622803	+	0.782379i	$0.714006\pi$
$930$	4.60255	−	0.253308i	0.150923	−	0.00830629i
$931$		0			0
$932$	16.2384	−	1.79284i	0.531906	−	0.0587263i
$933$	−30.5251			−0.999347
$934$	−1.32323	−	24.0429i	−0.0432975	−	0.786707i
$935$			5.24633i			0.171573i
$936$	10.7361	−	1.78709i	0.350922	−	0.0584128i
$937$			6.18932i			0.202196i	0.994876	+	0.101098i	$0.0322356\pi$
$937$			6.18932i			0.202196i	−0.994876	+	0.101098i	$0.967764\pi$
$938$		0			0
$939$			18.8324i			0.614573i
$940$	−0.162738	−	1.47398i	−0.00530792	−	0.0480758i
$941$		−	7.30986i		−	0.238295i	−0.992877	−	0.119147i	$-0.961984\pi$
$941$		−	7.30986i		−	0.238295i	0.992877	−	0.119147i	$-0.0380161\pi$
$942$	11.9517	−	0.657778i	0.389407	−	0.0214316i
$943$	32.5251			1.05916
$944$	31.6906	−	7.08409i	1.03144	−	0.230568i
$945$		0			0
$946$	−0.721329	−	13.1064i	−0.0234524	−	0.426125i
$947$		−	15.2196i		−	0.494569i	−0.968943	−	0.247285i	$-0.920462\pi$
$947$		−	15.2196i		−	0.494569i	0.968943	−	0.247285i	$-0.0795382\pi$
$948$	−3.42030	−	30.9790i	−0.111086	−	1.00615i
$949$	−38.6140			−1.25346
$950$	1.11178	+	20.2009i	0.0360711	+	0.655403i
$951$	17.1652			0.556619
$952$		0			0
$953$	17.5899			0.569792			0.284896	−	0.958558i	$-0.408041\pi$
$953$	17.5899			0.569792			0.284896	+	0.958558i	$0.408041\pi$
$954$	−0.832489	−	15.1261i	−0.0269528	−	0.489727i
$955$	−2.87635			−0.0930764
$956$	3.99421	+	36.1770i	0.129182	+	1.17005i
$957$		−	14.8602i		−	0.480361i
$958$	−2.46985	−	44.8765i	−0.0797971	−	1.44990i
$959$		0			0
$960$	1.13756	+	3.32234i	0.0367146	+	0.107228i
$961$	24.1348			0.778543
$962$	28.7264	−	1.58100i	0.926177	−	0.0509735i
$963$			2.54433i			0.0819900i
$964$	−6.34624	−	57.4803i	−0.204399	−	1.85131i
$965$			1.42063i			0.0457318i
$966$		0			0
$967$			15.0905i			0.485279i	0.970117	+	0.242640i	$0.0780132\pi$
$967$			15.0905i			0.485279i	−0.970117	+	0.242640i	$0.921987\pi$
$968$	3.02922	+	18.1984i	0.0973629	+	0.584920i
$969$			16.8085i			0.539966i
$970$	−0.0759399	−	1.37981i	−0.00243828	−	0.0443031i
$971$	−44.9320			−1.44194			−0.720968	−	0.692968i	$-0.756303\pi$
$971$	−44.9320			−1.44194			−0.720968	+	0.692968i	$0.756303\pi$
$972$	−1.98792	+	0.219481i	−0.0637626	+	0.00703985i
$973$		0			0
$974$	−8.14757	+	0.448413i	−0.261065	+	0.0143681i
$975$		−	18.4987i		−	0.592432i
$976$	−5.39868	−	24.1509i	−0.172807	−	0.773051i
$977$	12.0824			0.386551			0.193276	−	0.981144i	$-0.438089\pi$
$977$	12.0824			0.386551			0.193276	+	0.981144i	$0.438089\pi$
$978$	9.82041	−	0.540480i	0.314022	−	0.0172827i
$979$	22.0457			0.704584
$980$		0			0
$981$	−6.80731			−0.217341
$982$	−31.9755	+	1.75982i	−1.02038	+	0.0561581i
$983$	17.3495			0.553362			0.276681	−	0.960962i	$-0.410765\pi$
$983$	17.3495			0.553362			0.276681	+	0.960962i	$0.410765\pi$
$984$	−19.0228	+	3.16645i	−0.606426	+	0.100943i
$985$			8.45241i			0.269316i
$986$	−56.0131	+	3.08276i	−1.78382	+	0.0981752i
$987$		0			0
$988$	−2.51330	−	22.7639i	−0.0799588	−	0.724216i
$989$	20.9251			0.665379
$990$	0.0721849	+	1.31158i	0.00229419	+	0.0416849i
$991$			49.0905i			1.55941i	0.626147	+	0.779705i	$0.284631\pi$
$991$			49.0905i			1.55941i	−0.626147	+	0.779705i	$0.715369\pi$
$992$	11.4021	+	40.4265i	0.362018	+	1.28354i
$993$		−	21.4868i		−	0.681864i
$994$		0			0
$995$			3.78461i			0.119980i
$996$	10.9265	−	1.20637i	0.346220	−	0.0382252i
$997$			9.09953i			0.288185i	0.989564	+	0.144093i	$0.0460263\pi$
$997$			9.09953i			0.288185i	−0.989564	+	0.144093i	$0.953974\pi$
$998$	27.4552	−	1.51104i	0.869081	−	0.0478311i
$999$	−5.28670			−0.167264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.b.b.391.5		8
3.2	odd	2		1764.2.b.i.1567.4		8
4.3	odd	2		588.2.b.a.391.6		8
7.2	even	3		588.2.o.b.31.1		8
7.3	odd	6		588.2.o.d.19.4		8
7.4	even	3		84.2.o.a.19.4	✓	8
7.5	odd	6		84.2.o.b.31.1	yes	8
7.6	odd	2		588.2.b.a.391.5		8
12.11	even	2		1764.2.b.j.1567.3		8
21.5	even	6		252.2.bf.f.199.4		8
21.11	odd	6		252.2.bf.g.19.1		8
21.20	even	2		1764.2.b.j.1567.4		8
28.3	even	6		588.2.o.b.19.1		8
28.11	odd	6		84.2.o.b.19.1	yes	8
28.19	even	6		84.2.o.a.31.4	yes	8
28.23	odd	6		588.2.o.d.31.4		8
28.27	even	2	inner	588.2.b.b.391.6		8
56.5	odd	6		1344.2.bl.i.703.3		8
56.11	odd	6		1344.2.bl.i.1279.3		8
56.19	even	6		1344.2.bl.j.703.3		8
56.53	even	6		1344.2.bl.j.1279.3		8
84.11	even	6		252.2.bf.f.19.4		8
84.47	odd	6		252.2.bf.g.199.1		8
84.83	odd	2		1764.2.b.i.1567.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.4	✓	8	7.4	even	3
84.2.o.a.31.4	yes	8	28.19	even	6
84.2.o.b.19.1	yes	8	28.11	odd	6
84.2.o.b.31.1	yes	8	7.5	odd	6
252.2.bf.f.19.4		8	84.11	even	6
252.2.bf.f.199.4		8	21.5	even	6
252.2.bf.g.19.1		8	21.11	odd	6
252.2.bf.g.199.1		8	84.47	odd	6
588.2.b.a.391.5		8	7.6	odd	2
588.2.b.a.391.6		8	4.3	odd	2
588.2.b.b.391.5		8	1.1	even	1	trivial
588.2.b.b.391.6		8	28.27	even	2	inner
588.2.o.b.19.1		8	28.3	even	6
588.2.o.b.31.1		8	7.2	even	3
588.2.o.d.19.4		8	7.3	odd	6
588.2.o.d.31.4		8	28.23	odd	6
1344.2.bl.i.703.3		8	56.5	odd	6
1344.2.bl.i.1279.3		8	56.11	odd	6
1344.2.bl.j.703.3		8	56.19	even	6
1344.2.bl.j.1279.3		8	56.53	even	6
1764.2.b.i.1567.3		8	84.83	odd	2
1764.2.b.i.1567.4		8	3.2	odd	2
1764.2.b.j.1567.3		8	12.11	even	2
1764.2.b.j.1567.4		8	21.20	even	2

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0777157 - 1.41208i) q^{2} +1.00000 q^{3} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.0777157 - 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.0777157 - 1.41208i) q^{2} +1.00000 q^{3} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.0777157 - 1.41208i) q^{6} +(0.464416 + 2.79004i) q^{8} +1.00000 q^{9} +(-0.619848 + 0.0341142i) q^{10} -2.11598i q^{11} +(-1.98792 + 0.219481i) q^{12} -3.84803i q^{13} -0.438962i q^{15} +(3.90366 - 0.872621i) q^{16} -5.64831i q^{17} +(-0.0777157 - 1.41208i) q^{18} -2.97584 q^{19} +(0.0963438 + 0.872621i) q^{20} +(-2.98792 + 0.164445i) q^{22} -4.77038i q^{23} +(0.464416 + 2.79004i) q^{24} +4.80731 q^{25} +(-5.43371 + 0.299052i) q^{26} +1.00000 q^{27} +7.02285 q^{29} +(-0.619848 + 0.0341142i) q^{30} -7.42528 q^{31} +(-1.53558 - 5.44445i) q^{32} -2.11598i q^{33} +(-7.97584 + 0.438962i) q^{34} +(-1.98792 + 0.219481i) q^{36} -5.28670 q^{37} +(0.231269 + 4.20212i) q^{38} -3.84803i q^{39} +(1.22472 - 0.203861i) q^{40} +6.81813i q^{41} +4.38646i q^{43} +(0.464416 + 4.20639i) q^{44} -0.438962i q^{45} +(-6.73615 + 0.370733i) q^{46} -1.68914 q^{47} +(3.90366 - 0.872621i) q^{48} +(-0.373604 - 6.78829i) q^{50} -5.64831i q^{51} +(0.844569 + 7.64957i) q^{52} +10.7120 q^{53} +(-0.0777157 - 1.41208i) q^{54} -0.928833 q^{55} -2.97584 q^{57} +(-0.545785 - 9.91680i) q^{58} +8.11818 q^{59} +(0.0963438 + 0.872621i) q^{60} -6.18674i q^{61} +(0.577061 + 10.4851i) q^{62} +(-7.56863 + 2.59148i) q^{64} -1.68914 q^{65} +(-2.98792 + 0.164445i) q^{66} +7.85056i q^{67} +(1.23970 + 11.2284i) q^{68} -4.77038i q^{69} -1.16982i q^{71} +(0.464416 + 2.79004i) q^{72} -10.0348i q^{73} +(0.410860 + 7.46523i) q^{74} +4.80731 q^{75} +(5.91574 - 0.653140i) q^{76} +(-5.43371 + 0.299052i) q^{78} +15.5836i q^{79} +(-0.383048 - 1.71356i) q^{80} +1.00000 q^{81} +(9.62772 - 0.529876i) q^{82} -5.49645 q^{83} -2.47939 q^{85} +(6.19401 - 0.340896i) q^{86} +7.02285 q^{87} +(5.90366 - 0.982694i) q^{88} +10.4187i q^{89} +(-0.619848 + 0.0341142i) q^{90} +(1.04701 + 9.48314i) q^{92} -7.42528 q^{93} +(0.131272 + 2.38519i) q^{94} +1.30628i q^{95} +(-1.53558 - 5.44445i) q^{96} +2.22605i q^{97} -2.11598i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 2 q^{4} - 2 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} + 2 q^{12} + 10 q^{16} - 2 q^{18} + 12 q^{19} + 22 q^{20} - 6 q^{22} + 4 q^{24} - 4 q^{25} - 6 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 12 q^{31} - 12 q^{32} - 28 q^{34} + 2 q^{36} - 12 q^{37} - 2 q^{38} + 4 q^{40} + 4 q^{44} - 12 q^{46} - 8 q^{47} + 10 q^{48} + 2 q^{50} + 4 q^{52} + 8 q^{53} - 2 q^{54} - 8 q^{55} + 12 q^{57} - 14 q^{58} + 28 q^{59} + 22 q^{60} - 48 q^{62} + 2 q^{64} - 8 q^{65} - 6 q^{66} + 16 q^{68} + 4 q^{72} + 38 q^{74} - 4 q^{75} + 44 q^{76} - 6 q^{78} + 6 q^{80} + 8 q^{81} - 4 q^{82} + 4 q^{83} - 32 q^{85} + 6 q^{86} - 16 q^{87} + 26 q^{88} - 8 q^{90} - 28 q^{92} - 12 q^{93} - 32 q^{94} - 12 q^{96}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 2 * q^4 - 2 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 + 2 * q^12 + 10 * q^16 - 2 * q^18 + 12 * q^19 + 22 * q^20 - 6 * q^22 + 4 * q^24 - 4 * q^25 - 6 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 12 * q^31 - 12 * q^32 - 28 * q^34 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 4 * q^40 + 4 * q^44 - 12 * q^46 - 8 * q^47 + 10 * q^48 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 2 * q^54 - 8 * q^55 + 12 * q^57 - 14 * q^58 + 28 * q^59 + 22 * q^60 - 48 * q^62 + 2 * q^64 - 8 * q^65 - 6 * q^66 + 16 * q^68 + 4 * q^72 + 38 * q^74 - 4 * q^75 + 44 * q^76 - 6 * q^78 + 6 * q^80 + 8 * q^81 - 4 * q^82 + 4 * q^83 - 32 * q^85 + 6 * q^86 - 16 * q^87 + 26 * q^88 - 8 * q^90 - 28 * q^92 - 12 * q^93 - 32 * q^94 - 12 * q^96

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