LMFDB - Embedded newform 288.2.v.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	288.109
Dual form			288.2.v.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -2.00000 q^{4} +(3.12132 - 1.29289i) q^{5} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q-1.41421i q^{2} -2.00000 q^{4} +(3.12132 - 1.29289i) q^{5} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.82843 - 4.41421i) q^{10} +(-0.121320 - 0.292893i) q^{11} +(1.70711 + 0.707107i) q^{13} +(-1.41421 - 1.41421i) q^{14} +4.00000 q^{16} -2.82843i q^{17} +(-5.53553 - 2.29289i) q^{19} +(-6.24264 + 2.58579i) q^{20} +(-0.414214 + 0.171573i) q^{22} +(-0.171573 - 0.171573i) q^{23} +(4.53553 - 4.53553i) q^{25} +(1.00000 - 2.41421i) q^{26} +(-2.00000 + 2.00000i) q^{28} +(-1.12132 + 2.70711i) q^{29} -4.00000 q^{31} -5.65685i q^{32} -4.00000 q^{34} +(1.82843 - 4.41421i) q^{35} +(1.70711 - 0.707107i) q^{37} +(-3.24264 + 7.82843i) q^{38} +(3.65685 + 8.82843i) q^{40} +(5.82843 + 5.82843i) q^{41} +(3.29289 + 7.94975i) q^{43} +(0.242641 + 0.585786i) q^{44} +(-0.242641 + 0.242641i) q^{46} +11.6569i q^{47} +5.00000i q^{49} +(-6.41421 - 6.41421i) q^{50} +(-3.41421 - 1.41421i) q^{52} +(-3.12132 - 7.53553i) q^{53} +(-0.757359 - 0.757359i) q^{55} +(2.82843 + 2.82843i) q^{56} +(3.82843 + 1.58579i) q^{58} +(6.12132 - 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +5.65685i q^{62} -8.00000 q^{64} +6.24264 q^{65} +(1.53553 - 3.70711i) q^{67} +5.65685i q^{68} +(-6.24264 - 2.58579i) q^{70} +(0.171573 - 0.171573i) q^{71} +(7.00000 + 7.00000i) q^{73} +(-1.00000 - 2.41421i) q^{74} +(11.0711 + 4.58579i) q^{76} +(-0.414214 - 0.171573i) q^{77} +6.00000i q^{79} +(12.4853 - 5.17157i) q^{80} +(8.24264 - 8.24264i) q^{82} +(-6.12132 - 2.53553i) q^{83} +(-3.65685 - 8.82843i) q^{85} +(11.2426 - 4.65685i) q^{86} +(0.828427 - 0.343146i) q^{88} +(2.65685 - 2.65685i) q^{89} +(2.41421 - 1.00000i) q^{91} +(0.343146 + 0.343146i) q^{92} +16.4853 q^{94} -20.2426 q^{95} -1.51472 q^{97} +7.07107 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) $ 4 * q - 8 * q^4 + 4 * q^5 + 4 * q^7	$ 4 q - 8 q^{4} + 4 q^{5} + 4 q^{7} + 4 q^{10} + 8 q^{11} + 4 q^{13} + 16 q^{16} - 8 q^{19} - 8 q^{20} + 4 q^{22} - 12 q^{23} + 4 q^{25} + 4 q^{26} - 8 q^{28} + 4 q^{29} - 16 q^{31} - 16 q^{34} - 4 q^{35} + 4 q^{37} + 4 q^{38} - 8 q^{40} + 12 q^{41} + 16 q^{43} - 16 q^{44} + 16 q^{46} - 20 q^{50} - 8 q^{52} - 4 q^{53} - 20 q^{55} + 4 q^{58} + 16 q^{59} + 4 q^{61} - 32 q^{64} + 8 q^{65} - 8 q^{67} - 8 q^{70} + 12 q^{71} + 28 q^{73} - 4 q^{74} + 16 q^{76} + 4 q^{77} + 16 q^{80} + 16 q^{82} - 16 q^{83} + 8 q^{85} + 28 q^{86} - 8 q^{88} - 12 q^{89} + 4 q^{91} + 24 q^{92} + 32 q^{94} - 64 q^{95} - 40 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 + 4 * q^5 + 4 * q^7 + 4 * q^10 + 8 * q^11 + 4 * q^13 + 16 * q^16 - 8 * q^19 - 8 * q^20 + 4 * q^22 - 12 * q^23 + 4 * q^25 + 4 * q^26 - 8 * q^28 + 4 * q^29 - 16 * q^31 - 16 * q^34 - 4 * q^35 + 4 * q^37 + 4 * q^38 - 8 * q^40 + 12 * q^41 + 16 * q^43 - 16 * q^44 + 16 * q^46 - 20 * q^50 - 8 * q^52 - 4 * q^53 - 20 * q^55 + 4 * q^58 + 16 * q^59 + 4 * q^61 - 32 * q^64 + 8 * q^65 - 8 * q^67 - 8 * q^70 + 12 * q^71 + 28 * q^73 - 4 * q^74 + 16 * q^76 + 4 * q^77 + 16 * q^80 + 16 * q^82 - 16 * q^83 + 8 * q^85 + 28 * q^86 - 8 * q^88 - 12 * q^89 + 4 * q^91 + 24 * q^92 + 32 * q^94 - 64 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$		−	1.41421i		−	1.00000i
$2$		−	1.41421i		−	1.00000i
$3$		0			0
$3$		0			0
$4$	−2.00000			−1.00000
$5$	3.12132	−	1.29289i	1.39590	−	0.578199i	0.447214	−	0.894427i	$-0.352416\pi$
$5$	3.12132	−	1.29289i	1.39590	−	0.578199i	0.948683	+	0.316228i	$0.102416\pi$
$6$		0			0
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$			2.82843i			1.00000i
$9$		0			0
$10$	−1.82843	−	4.41421i	−0.578199	−	1.39590i
$11$	−0.121320	−	0.292893i	−0.0365795	−	0.0883106i	0.904534	−	0.426401i	$-0.140219\pi$
$11$	−0.121320	−	0.292893i	−0.0365795	−	0.0883106i	−0.941113	+	0.338091i	$0.890219\pi$
$12$		0			0
$13$	1.70711	+	0.707107i	0.473466	+	0.196116i	0.606640	−	0.794977i	$-0.292517\pi$
$13$	1.70711	+	0.707107i	0.473466	+	0.196116i	−0.133174	+	0.991093i	$0.542517\pi$
$14$	−1.41421	−	1.41421i	−0.377964	−	0.377964i
$15$		0			0
$16$	4.00000			1.00000
$17$		−	2.82843i		−	0.685994i	−0.939336	−	0.342997i	$-0.888558\pi$
$17$		−	2.82843i		−	0.685994i	0.939336	−	0.342997i	$-0.111442\pi$
$18$		0			0
$19$	−5.53553	−	2.29289i	−1.26994	−	0.526026i	−0.356993	−	0.934107i	$-0.616198\pi$
$19$	−5.53553	−	2.29289i	−1.26994	−	0.526026i	−0.912946	+	0.408081i	$0.866198\pi$
$20$	−6.24264	+	2.58579i	−1.39590	+	0.578199i
$21$		0			0
$22$	−0.414214	+	0.171573i	−0.0883106	+	0.0365795i
$23$	−0.171573	−	0.171573i	−0.0357754	−	0.0357754i	0.688993	−	0.724768i	$-0.258053\pi$
$23$	−0.171573	−	0.171573i	−0.0357754	−	0.0357754i	−0.724768	+	0.688993i	$0.758053\pi$
$24$		0			0
$25$	4.53553	−	4.53553i	0.907107	−	0.907107i
$26$	1.00000	−	2.41421i	0.196116	−	0.473466i
$27$		0			0
$28$	−2.00000	+	2.00000i	−0.377964	+	0.377964i
$29$	−1.12132	+	2.70711i	−0.208224	+	0.502697i	−0.993144	−	0.116900i	$-0.962704\pi$
$29$	−1.12132	+	2.70711i	−0.208224	+	0.502697i	0.784920	+	0.619598i	$0.212704\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		−	5.65685i		−	1.00000i
$33$		0			0
$34$	−4.00000			−0.685994
$35$	1.82843	−	4.41421i	0.309061	−	0.746138i
$36$		0			0
$37$	1.70711	−	0.707107i	0.280647	−	0.116248i	−0.237920	−	0.971285i	$-0.576466\pi$
$37$	1.70711	−	0.707107i	0.280647	−	0.116248i	0.518567	+	0.855037i	$0.326466\pi$
$38$	−3.24264	+	7.82843i	−0.526026	+	1.26994i
$39$		0			0
$40$	3.65685	+	8.82843i	0.578199	+	1.39590i
$41$	5.82843	+	5.82843i	0.910247	+	0.910247i	0.996291	−	0.0860440i	$-0.0274225\pi$
$41$	5.82843	+	5.82843i	0.910247	+	0.910247i	−0.0860440	+	0.996291i	$0.527423\pi$
$42$		0			0
$43$	3.29289	+	7.94975i	0.502162	+	1.21233i	0.948304	+	0.317363i	$0.102797\pi$
$43$	3.29289	+	7.94975i	0.502162	+	1.21233i	−0.446143	+	0.894962i	$0.647203\pi$
$44$	0.242641	+	0.585786i	0.0365795	+	0.0883106i
$45$		0			0
$46$	−0.242641	+	0.242641i	−0.0357754	+	0.0357754i
$47$			11.6569i			1.70033i	0.526519	+	0.850163i	$0.323497\pi$
$47$			11.6569i			1.70033i	−0.526519	+	0.850163i	$0.676503\pi$
$48$		0			0
$49$			5.00000i			0.714286i
$50$	−6.41421	−	6.41421i	−0.907107	−	0.907107i
$51$		0			0
$52$	−3.41421	−	1.41421i	−0.473466	−	0.196116i
$53$	−3.12132	−	7.53553i	−0.428746	−	1.03509i	−0.979686	−	0.200540i	$-0.935730\pi$
$53$	−3.12132	−	7.53553i	−0.428746	−	1.03509i	0.550939	−	0.834545i	$-0.314270\pi$
$54$		0			0
$55$	−0.757359	−	0.757359i	−0.102122	−	0.102122i
$56$	2.82843	+	2.82843i	0.377964	+	0.377964i
$57$		0			0
$58$	3.82843	+	1.58579i	0.502697	+	0.208224i
$59$	6.12132	−	2.53553i	0.796928	−	0.330098i	0.0532027	−	0.998584i	$-0.483057\pi$
$59$	6.12132	−	2.53553i	0.796928	−	0.330098i	0.743725	+	0.668485i	$0.233057\pi$
$60$		0			0
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	−0.904019	−	0.427492i	$-0.859397\pi$
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	0.941520	+	0.336956i	$0.109397\pi$
$62$			5.65685i			0.718421i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	6.24264			0.774304
$66$		0			0
$67$	1.53553	−	3.70711i	0.187595	−	0.452895i	−0.801900	−	0.597458i	$-0.796178\pi$
$67$	1.53553	−	3.70711i	0.187595	−	0.452895i	0.989496	+	0.144563i	$0.0461775\pi$
$68$			5.65685i			0.685994i
$69$		0			0
$70$	−6.24264	−	2.58579i	−0.746138	−	0.309061i
$71$	0.171573	−	0.171573i	0.0203620	−	0.0203620i	−0.696853	−	0.717214i	$-0.745417\pi$
$71$	0.171573	−	0.171573i	0.0203620	−	0.0203620i	0.717214	+	0.696853i	$0.245417\pi$
$72$		0			0
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	0.986005	−	0.166717i	$-0.0533166\pi$
$73$	7.00000	+	7.00000i	0.819288	+	0.819288i	−0.166717	+	0.986005i	$0.553317\pi$
$74$	−1.00000	−	2.41421i	−0.116248	−	0.280647i
$75$		0			0
$76$	11.0711	+	4.58579i	1.26994	+	0.526026i
$77$	−0.414214	−	0.171573i	−0.0472040	−	0.0195525i
$78$		0			0
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$	12.4853	−	5.17157i	1.39590	−	0.578199i
$81$		0			0
$82$	8.24264	−	8.24264i	0.910247	−	0.910247i
$83$	−6.12132	−	2.53553i	−0.671902	−	0.278311i	0.0205350	−	0.999789i	$-0.493463\pi$
$83$	−6.12132	−	2.53553i	−0.671902	−	0.278311i	−0.692437	+	0.721478i	$0.743463\pi$
$84$		0			0
$85$	−3.65685	−	8.82843i	−0.396642	−	0.957577i
$86$	11.2426	−	4.65685i	1.21233	−	0.502162i
$87$		0			0
$88$	0.828427	−	0.343146i	0.0883106	−	0.0365795i
$89$	2.65685	−	2.65685i	0.281626	−	0.281626i	−0.552131	−	0.833757i	$-0.686185\pi$
$89$	2.65685	−	2.65685i	0.281626	−	0.281626i	0.833757	+	0.552131i	$0.186185\pi$
$90$		0			0
$91$	2.41421	−	1.00000i	0.253078	−	0.104828i
$92$	0.343146	+	0.343146i	0.0357754	+	0.0357754i
$93$		0			0
$94$	16.4853			1.70033
$95$	−20.2426			−2.07685
$96$		0			0
$97$	−1.51472			−0.153796			−0.0768982	−	0.997039i	$-0.524502\pi$
$97$	−1.51472			−0.153796			−0.0768982	+	0.997039i	$0.524502\pi$
$98$	7.07107			0.714286
$99$		0			0
$100$	−9.07107	+	9.07107i	−0.907107	+	0.907107i
$101$	−11.3640	+	4.70711i	−1.13076	+	0.468375i	−0.868038	−	0.496498i	$-0.834619\pi$
$101$	−11.3640	+	4.70711i	−1.13076	+	0.468375i	−0.262718	+	0.964873i	$0.584619\pi$
$102$		0			0
$103$	−7.48528	+	7.48528i	−0.737547	+	0.737547i	−0.972103	−	0.234556i	$-0.924636\pi$
$103$	−7.48528	+	7.48528i	−0.737547	+	0.737547i	0.234556	+	0.972103i	$0.424636\pi$
$104$	−2.00000	+	4.82843i	−0.196116	+	0.473466i
$105$		0			0
$106$	−10.6569	+	4.41421i	−1.03509	+	0.428746i
$107$	−0.121320	−	0.292893i	−0.0117285	−	0.0283151i	0.917907	−	0.396796i	$-0.129878\pi$
$107$	−0.121320	−	0.292893i	−0.0117285	−	0.0283151i	−0.929635	+	0.368481i	$0.879878\pi$
$108$		0			0
$109$	−4.29289	−	1.77817i	−0.411185	−	0.170318i	0.167496	−	0.985873i	$-0.446432\pi$
$109$	−4.29289	−	1.77817i	−0.411185	−	0.170318i	−0.578680	+	0.815555i	$0.696432\pi$
$110$	−1.07107	+	1.07107i	−0.102122	+	0.102122i
$111$		0			0
$112$	4.00000	−	4.00000i	0.377964	−	0.377964i
$113$			17.6569i			1.66102i	0.557006	+	0.830509i	$0.311950\pi$
$113$			17.6569i			1.66102i	−0.557006	+	0.830509i	$0.688050\pi$
$114$		0			0
$115$	−0.757359	−	0.313708i	−0.0706241	−	0.0292535i
$116$	2.24264	−	5.41421i	0.208224	−	0.502697i
$117$		0			0
$118$	−3.58579	−	8.65685i	−0.330098	−	0.796928i
$119$	−2.82843	−	2.82843i	−0.259281	−	0.259281i
$120$		0			0
$121$	7.70711	−	7.70711i	0.700646	−	0.700646i
$122$	−1.00000	−	0.414214i	−0.0905357	−	0.0375011i
$123$		0			0
$124$	8.00000			0.718421
$125$	1.82843	−	4.41421i	0.163539	−	0.394819i
$126$		0			0
$127$	−20.9706			−1.86084			−0.930418	−	0.366499i	$-0.880556\pi$
$127$	−20.9706			−1.86084			−0.930418	+	0.366499i	$0.880556\pi$
$128$			11.3137i			1.00000i
$129$		0			0
$130$		−	8.82843i		−	0.774304i
$131$	3.63604	−	8.77817i	0.317682	−	0.766953i	−0.681694	−	0.731637i	$-0.738756\pi$
$131$	3.63604	−	8.77817i	0.317682	−	0.766953i	0.999376	−	0.0353153i	$-0.0112435\pi$
$132$		0			0
$133$	−7.82843	+	3.24264i	−0.678811	+	0.281173i
$134$	−5.24264	−	2.17157i	−0.452895	−	0.187595i
$135$		0			0
$136$	8.00000			0.685994
$137$	−2.65685	−	2.65685i	−0.226990	−	0.226990i	0.584444	−	0.811434i	$-0.301313\pi$
$137$	−2.65685	−	2.65685i	−0.226990	−	0.226990i	−0.811434	+	0.584444i	$0.801313\pi$
$138$		0			0
$139$	−5.19239	−	12.5355i	−0.440413	−	1.06325i	−0.975804	−	0.218646i	$-0.929836\pi$
$139$	−5.19239	−	12.5355i	−0.440413	−	1.06325i	0.535392	−	0.844604i	$-0.320164\pi$
$140$	−3.65685	+	8.82843i	−0.309061	+	0.746138i
$141$		0			0
$142$	−0.242641	−	0.242641i	−0.0203620	−	0.0203620i
$143$		−	0.585786i		−	0.0489859i
$144$		0			0
$145$			9.89949i			0.822108i
$146$	9.89949	−	9.89949i	0.819288	−	0.819288i
$147$		0			0
$148$	−3.41421	+	1.41421i	−0.280647	+	0.116248i
$149$	−5.60660	−	13.5355i	−0.459311	−	1.10887i	−0.968677	−	0.248324i	$-0.920120\pi$
$149$	−5.60660	−	13.5355i	−0.459311	−	1.10887i	0.509366	−	0.860550i	$-0.329880\pi$
$150$		0			0
$151$	15.4853	+	15.4853i	1.26017	+	1.26017i	0.951008	+	0.309166i	$0.100050\pi$
$151$	15.4853	+	15.4853i	1.26017	+	1.26017i	0.309166	+	0.951008i	$0.399950\pi$
$152$	6.48528	−	15.6569i	0.526026	−	1.26994i
$153$		0			0
$154$	−0.242641	+	0.585786i	−0.0195525	+	0.0472040i
$155$	−12.4853	+	5.17157i	−1.00284	+	0.415391i
$156$		0			0
$157$	0.292893	−	0.707107i	0.0233754	−	0.0564333i	−0.911761	−	0.410722i	$-0.865277\pi$
$157$	0.292893	−	0.707107i	0.0233754	−	0.0564333i	0.935136	+	0.354288i	$0.115277\pi$
$158$	8.48528			0.675053
$159$		0			0
$160$	−7.31371	−	17.6569i	−0.578199	−	1.39590i
$161$	−0.343146			−0.0270437
$162$		0			0
$163$	7.53553	−	18.1924i	0.590229	−	1.42494i	−0.293054	−	0.956096i	$-0.594671\pi$
$163$	7.53553	−	18.1924i	0.590229	−	1.42494i	0.883282	−	0.468842i	$-0.155329\pi$
$164$	−11.6569	−	11.6569i	−0.910247	−	0.910247i
$165$		0			0
$166$	−3.58579	+	8.65685i	−0.278311	+	0.671902i
$167$	−3.34315	+	3.34315i	−0.258700	+	0.258700i	−0.824525	−	0.565825i	$-0.808558\pi$
$167$	−3.34315	+	3.34315i	−0.258700	+	0.258700i	0.565825	+	0.824525i	$0.308558\pi$
$168$		0			0
$169$	−6.77817	−	6.77817i	−0.521398	−	0.521398i
$170$	−12.4853	+	5.17157i	−0.957577	+	0.396642i
$171$		0			0
$172$	−6.58579	−	15.8995i	−0.502162	−	1.21233i
$173$	1.12132	+	0.464466i	0.0852524	+	0.0353127i	0.424902	−	0.905239i	$-0.360309\pi$
$173$	1.12132	+	0.464466i	0.0852524	+	0.0353127i	−0.339650	+	0.940552i	$0.610309\pi$
$174$		0			0
$175$		−	9.07107i		−	0.685708i
$176$	−0.485281	−	1.17157i	−0.0365795	−	0.0883106i
$177$		0			0
$178$	−3.75736	−	3.75736i	−0.281626	−	0.281626i
$179$	14.3640	+	5.94975i	1.07361	+	0.444705i	0.848264	−	0.529573i	$-0.177648\pi$
$179$	14.3640	+	5.94975i	1.07361	+	0.444705i	0.225349	+	0.974278i	$0.427648\pi$
$180$		0			0
$181$	−2.19239	−	5.29289i	−0.162959	−	0.393418i	0.821216	−	0.570618i	$-0.193296\pi$
$181$	−2.19239	−	5.29289i	−0.162959	−	0.393418i	−0.984175	+	0.177200i	$0.943296\pi$
$182$	−1.41421	−	3.41421i	−0.104828	−	0.253078i
$183$		0			0
$184$	0.485281	−	0.485281i	0.0357754	−	0.0357754i
$185$	4.41421	−	4.41421i	0.324539	−	0.324539i
$186$		0			0
$187$	−0.828427	+	0.343146i	−0.0605806	+	0.0250933i
$188$		−	23.3137i		−	1.70033i
$189$		0			0
$190$			28.6274i			2.07685i
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		0			0
$193$	−18.4853			−1.33060			−0.665300	−	0.746576i	$-0.731696\pi$
$193$	−18.4853			−1.33060			−0.665300	+	0.746576i	$0.731696\pi$
$194$			2.14214i			0.153796i
$195$		0			0
$196$		−	10.0000i		−	0.714286i
$197$	−17.3640	+	7.19239i	−1.23713	+	0.512436i	−0.902817	−	0.430025i	$-0.858505\pi$
$197$	−17.3640	+	7.19239i	−1.23713	+	0.512436i	−0.334314	+	0.942462i	$0.608505\pi$
$198$		0			0
$199$	17.9706	−	17.9706i	1.27390	−	1.27390i	0.329875	−	0.944025i	$-0.392994\pi$
$199$	17.9706	−	17.9706i	1.27390	−	1.27390i	0.944025	−	0.329875i	$-0.107006\pi$
$200$	12.8284	+	12.8284i	0.907107	+	0.907107i
$201$		0			0
$202$	6.65685	+	16.0711i	0.468375	+	1.13076i
$203$	1.58579	+	3.82843i	0.111300	+	0.268703i
$204$		0			0
$205$	25.7279	+	10.6569i	1.79692	+	0.744307i
$206$	10.5858	+	10.5858i	0.737547	+	0.737547i
$207$		0			0
$208$	6.82843	+	2.82843i	0.473466	+	0.196116i
$209$			1.89949i			0.131391i
$210$		0			0
$211$	0.464466	+	0.192388i	0.0319752	+	0.0132445i	0.398614	−	0.917119i	$-0.369491\pi$
$211$	0.464466	+	0.192388i	0.0319752	+	0.0132445i	−0.366639	+	0.930363i	$0.619491\pi$
$212$	6.24264	+	15.0711i	0.428746	+	1.03509i
$213$		0			0
$214$	−0.414214	+	0.171573i	−0.0283151	+	0.0117285i
$215$	20.5563	+	20.5563i	1.40193	+	1.40193i
$216$		0			0
$217$	−4.00000	+	4.00000i	−0.271538	+	0.271538i
$218$	−2.51472	+	6.07107i	−0.170318	+	0.411185i
$219$		0			0
$220$	1.51472	+	1.51472i	0.102122	+	0.102122i
$221$	2.00000	−	4.82843i	0.134535	−	0.324795i
$222$		0			0
$223$	12.9706			0.868573			0.434287	−	0.900775i	$-0.357001\pi$
$223$	12.9706			0.868573			0.434287	+	0.900775i	$0.357001\pi$
$224$	−5.65685	−	5.65685i	−0.377964	−	0.377964i
$225$		0			0
$226$	24.9706			1.66102
$227$	2.60660	−	6.29289i	0.173006	−	0.417674i	−0.813464	−	0.581616i	$-0.802421\pi$
$227$	2.60660	−	6.29289i	0.173006	−	0.417674i	0.986470	+	0.163942i	$0.0524208\pi$
$228$		0			0
$229$	−24.7782	+	10.2635i	−1.63739	+	0.678228i	−0.996030	−	0.0890139i	$-0.971628\pi$
$229$	−24.7782	+	10.2635i	−1.63739	+	0.678228i	−0.641357	+	0.767242i	$0.721628\pi$
$230$	−0.443651	+	1.07107i	−0.0292535	+	0.0706241i
$231$		0			0
$232$	−7.65685	−	3.17157i	−0.502697	−	0.208224i
$233$	−8.65685	−	8.65685i	−0.567129	−	0.567129i	0.364194	−	0.931323i	$-0.381345\pi$
$233$	−8.65685	−	8.65685i	−0.567129	−	0.567129i	−0.931323	+	0.364194i	$0.881345\pi$
$234$		0			0
$235$	15.0711	+	36.3848i	0.983128	+	2.37348i
$236$	−12.2426	+	5.07107i	−0.796928	+	0.330098i
$237$		0			0
$238$	−4.00000	+	4.00000i	−0.259281	+	0.259281i
$239$		−	17.3137i		−	1.11993i	−0.828516	−	0.559965i	$-0.810814\pi$
$239$		−	17.3137i		−	1.11993i	0.828516	−	0.559965i	$-0.189186\pi$
$240$		0			0
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$	−10.8995	−	10.8995i	−0.700646	−	0.700646i
$243$		0			0
$244$	−0.585786	+	1.41421i	−0.0375011	+	0.0905357i
$245$	6.46447	+	15.6066i	0.413000	+	0.997069i
$246$		0			0
$247$	−7.82843	−	7.82843i	−0.498111	−	0.498111i
$248$		−	11.3137i		−	0.718421i
$249$		0			0
$250$	−6.24264	−	2.58579i	−0.394819	−	0.163539i
$251$	14.6066	−	6.05025i	0.921961	−	0.381889i	0.129338	−	0.991601i	$-0.458715\pi$
$251$	14.6066	−	6.05025i	0.921961	−	0.381889i	0.792623	+	0.609712i	$0.208715\pi$
$252$		0			0
$253$	−0.0294373	+	0.0710678i	−0.00185070	+	0.00446800i
$254$			29.6569i			1.86084i
$255$		0			0
$256$	16.0000			1.00000
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		0			0
$259$	1.00000	−	2.41421i	0.0621370	−	0.150012i
$260$	−12.4853			−0.774304
$261$		0			0
$262$	−12.4142	−	5.14214i	−0.766953	−	0.317682i
$263$	0.171573	−	0.171573i	0.0105796	−	0.0105796i	−0.701797	−	0.712377i	$-0.747619\pi$
$263$	0.171573	−	0.171573i	0.0105796	−	0.0105796i	0.712377	+	0.701797i	$0.247619\pi$
$264$		0			0
$265$	−19.4853	−	19.4853i	−1.19697	−	1.19697i
$266$	4.58579	+	11.0711i	0.281173	+	0.678811i
$267$		0			0
$268$	−3.07107	+	7.41421i	−0.187595	+	0.452895i
$269$	−4.87868	−	2.02082i	−0.297458	−	0.123211i	0.228963	−	0.973435i	$-0.426467\pi$
$269$	−4.87868	−	2.02082i	−0.297458	−	0.123211i	−0.526421	+	0.850224i	$0.676467\pi$
$270$		0			0
$271$			18.0000i			1.09342i	0.837321	+	0.546711i	$0.184120\pi$
$271$			18.0000i			1.09342i	−0.837321	+	0.546711i	$0.815880\pi$
$272$		−	11.3137i		−	0.685994i
$273$		0			0
$274$	−3.75736	+	3.75736i	−0.226990	+	0.226990i
$275$	−1.87868	−	0.778175i	−0.113289	−	0.0469257i
$276$		0			0
$277$	0.292893	+	0.707107i	0.0175982	+	0.0424859i	0.932434	−	0.361339i	$-0.117680\pi$
$277$	0.292893	+	0.707107i	0.0175982	+	0.0424859i	−0.914836	+	0.403825i	$0.867680\pi$
$278$	−17.7279	+	7.34315i	−1.06325	+	0.440413i
$279$		0			0
$280$	12.4853	+	5.17157i	0.746138	+	0.309061i
$281$	6.17157	−	6.17157i	0.368165	−	0.368165i	−0.498643	−	0.866808i	$-0.666168\pi$
$281$	6.17157	−	6.17157i	0.368165	−	0.368165i	0.866808	+	0.498643i	$0.166168\pi$
$282$		0			0
$283$	−9.77817	+	4.05025i	−0.581252	+	0.240763i	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−9.77817	+	4.05025i	−0.581252	+	0.240763i	0.0726300	+	0.997359i	$0.476861\pi$
$284$	−0.343146	+	0.343146i	−0.0203620	+	0.0203620i
$285$		0			0
$286$	−0.828427			−0.0489859
$287$	11.6569			0.688082
$288$		0			0
$289$	9.00000			0.529412
$290$	14.0000			0.822108
$291$		0			0
$292$	−14.0000	−	14.0000i	−0.819288	−	0.819288i
$293$	11.6066	−	4.80761i	0.678065	−	0.280864i	−0.0169528	−	0.999856i	$-0.505397\pi$
$293$	11.6066	−	4.80761i	0.678065	−	0.280864i	0.695018	+	0.718993i	$0.255397\pi$
$294$		0			0
$295$	15.8284	−	15.8284i	0.921567	−	0.921567i
$296$	2.00000	+	4.82843i	0.116248	+	0.280647i
$297$		0			0
$298$	−19.1421	+	7.92893i	−1.10887	+	0.459311i
$299$	−0.171573	−	0.414214i	−0.00992232	−	0.0239546i
$300$		0			0
$301$	11.2426	+	4.65685i	0.648015	+	0.268417i
$302$	21.8995	−	21.8995i	1.26017	−	1.26017i
$303$		0			0
$304$	−22.1421	−	9.17157i	−1.26994	−	0.526026i
$305$		−	2.58579i		−	0.148062i
$306$		0			0
$307$	2.94975	+	1.22183i	0.168351	+	0.0697333i	0.465267	−	0.885170i	$-0.345958\pi$
$307$	2.94975	+	1.22183i	0.168351	+	0.0697333i	−0.296916	+	0.954904i	$0.595958\pi$
$308$	0.828427	+	0.343146i	0.0472040	+	0.0195525i
$309$		0			0
$310$	7.31371	+	17.6569i	0.415391	+	1.00284i
$311$	−8.65685	−	8.65685i	−0.490885	−	0.490885i	0.417700	−	0.908585i	$-0.362836\pi$
$311$	−8.65685	−	8.65685i	−0.490885	−	0.490885i	−0.908585	+	0.417700i	$0.862836\pi$
$312$		0			0
$313$	9.48528	−	9.48528i	0.536140	−	0.536140i	−0.386253	−	0.922393i	$-0.626231\pi$
$313$	9.48528	−	9.48528i	0.536140	−	0.536140i	0.922393	+	0.386253i	$0.126231\pi$
$314$	−1.00000	−	0.414214i	−0.0564333	−	0.0233754i
$315$		0			0
$316$		−	12.0000i		−	0.675053i
$317$	−4.63604	+	11.1924i	−0.260386	+	0.628627i	−0.998962	−	0.0455425i	$-0.985498\pi$
$317$	−4.63604	+	11.1924i	−0.260386	+	0.628627i	0.738577	+	0.674170i	$0.235498\pi$
$318$		0			0
$319$	0.928932			0.0520102
$320$	−24.9706	+	10.3431i	−1.39590	+	0.578199i
$321$		0			0
$322$			0.485281i			0.0270437i
$323$	−6.48528	+	15.6569i	−0.360851	+	0.871171i
$324$		0			0
$325$	10.9497	−	4.53553i	0.607383	−	0.251586i
$326$	−25.7279	−	10.6569i	−1.42494	−	0.590229i
$327$		0			0
$328$	−16.4853	+	16.4853i	−0.910247	+	0.910247i
$329$	11.6569	+	11.6569i	0.642663	+	0.642663i
$330$		0			0
$331$	−2.70711	−	6.53553i	−0.148796	−	0.359225i	0.831854	−	0.554995i	$-0.187280\pi$
$331$	−2.70711	−	6.53553i	−0.148796	−	0.359225i	−0.980650	+	0.195769i	$0.937280\pi$
$332$	12.2426	+	5.07107i	0.671902	+	0.278311i
$333$		0			0
$334$	4.72792	+	4.72792i	0.258700	+	0.258700i
$335$		−	13.5563i		−	0.740662i
$336$		0			0
$337$			16.9706i			0.924445i	0.886764	+	0.462223i	$0.152948\pi$
$337$			16.9706i			0.924445i	−0.886764	+	0.462223i	$0.847052\pi$
$338$	−9.58579	+	9.58579i	−0.521398	+	0.521398i
$339$		0			0
$340$	7.31371	+	17.6569i	0.396642	+	0.957577i
$341$	0.485281	+	1.17157i	0.0262795	+	0.0634442i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$	−22.4853	+	9.31371i	−1.21233	+	0.502162i
$345$		0			0
$346$	0.656854	−	1.58579i	0.0353127	−	0.0852524i
$347$	−14.3640	+	5.94975i	−0.771098	+	0.319399i	−0.733317	−	0.679887i	$-0.762029\pi$
$347$	−14.3640	+	5.94975i	−0.771098	+	0.319399i	−0.0377808	+	0.999286i	$0.512029\pi$
$348$		0			0
$349$	−10.6777	+	25.7782i	−0.571563	+	1.37987i	0.328662	+	0.944448i	$0.393402\pi$
$349$	−10.6777	+	25.7782i	−0.571563	+	1.37987i	−0.900224	+	0.435426i	$0.856598\pi$
$350$	−12.8284			−0.685708
$351$		0			0
$352$	−1.65685	+	0.686292i	−0.0883106	+	0.0365795i
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	0.313708	−	0.757359i	0.0166499	−	0.0401965i
$356$	−5.31371	+	5.31371i	−0.281626	+	0.281626i
$357$		0			0
$358$	8.41421	−	20.3137i	0.444705	−	1.07361i
$359$	12.1716	−	12.1716i	0.642391	−	0.642391i	−0.308752	−	0.951143i	$-0.599911\pi$
$359$	12.1716	−	12.1716i	0.642391	−	0.642391i	0.951143	+	0.308752i	$0.0999112\pi$
$360$		0			0
$361$	11.9497	+	11.9497i	0.628934	+	0.628934i
$362$	−7.48528	+	3.10051i	−0.393418	+	0.162959i
$363$		0			0
$364$	−4.82843	+	2.00000i	−0.253078	+	0.104828i
$365$	30.8995	+	12.7990i	1.61735	+	0.669930i
$366$		0			0
$367$		−	6.00000i		−	0.313197i	−0.987662	−	0.156599i	$-0.949947\pi$
$367$		−	6.00000i		−	0.313197i	0.987662	−	0.156599i	$-0.0500529\pi$
$368$	−0.686292	−	0.686292i	−0.0357754	−	0.0357754i
$369$		0			0
$370$	−6.24264	−	6.24264i	−0.324539	−	0.324539i
$371$	−10.6569	−	4.41421i	−0.553276	−	0.229175i
$372$		0			0
$373$	−11.7071	−	28.2635i	−0.606171	−	1.46343i	−0.867133	−	0.498077i	$-0.834040\pi$
$373$	−11.7071	−	28.2635i	−0.606171	−	1.46343i	0.260962	−	0.965349i	$-0.415960\pi$
$374$	0.485281	+	1.17157i	0.0250933	+	0.0605806i
$375$		0			0
$376$	−32.9706			−1.70033
$377$	−3.82843	+	3.82843i	−0.197174	+	0.197174i
$378$		0			0
$379$	21.6777	−	8.97918i	1.11351	−	0.461230i	0.251363	−	0.967893i	$-0.419121\pi$
$379$	21.6777	−	8.97918i	1.11351	−	0.461230i	0.862144	+	0.506663i	$0.169121\pi$
$380$	40.4853			2.07685
$381$		0			0
$382$		−	16.9706i		−	0.868290i
$383$	−16.9706			−0.867155			−0.433578	−	0.901116i	$-0.642749\pi$
$383$	−16.9706			−0.867155			−0.433578	+	0.901116i	$0.642749\pi$
$384$		0			0
$385$	−1.51472			−0.0771972
$386$			26.1421i			1.33060i
$387$		0			0
$388$	3.02944			0.153796
$389$	29.6066	−	12.2635i	1.50111	−	0.621782i	0.527413	−	0.849609i	$-0.323162\pi$
$389$	29.6066	−	12.2635i	1.50111	−	0.621782i	0.973702	+	0.227827i	$0.0731622\pi$
$390$		0			0
$391$	−0.485281	+	0.485281i	−0.0245417	+	0.0245417i
$392$	−14.1421			−0.714286
$393$		0			0
$394$	10.1716	+	24.5563i	0.512436	+	1.23713i
$395$	7.75736	+	18.7279i	0.390315	+	0.942304i
$396$		0			0
$397$	−24.7782	−	10.2635i	−1.24358	−	0.515108i	−0.338749	−	0.940877i	$-0.610004\pi$
$397$	−24.7782	−	10.2635i	−1.24358	−	0.515108i	−0.904832	+	0.425769i	$0.860004\pi$
$398$	−25.4142	−	25.4142i	−1.27390	−	1.27390i
$399$		0			0
$400$	18.1421	−	18.1421i	0.907107	−	0.907107i
$401$		−	2.82843i		−	0.141245i	−0.997503	−	0.0706225i	$-0.977501\pi$
$401$		−	2.82843i		−	0.141245i	0.997503	−	0.0706225i	$-0.0224986\pi$
$402$		0			0
$403$	−6.82843	−	2.82843i	−0.340148	−	0.140894i
$404$	22.7279	−	9.41421i	1.13076	−	0.468375i
$405$		0			0
$406$	5.41421	−	2.24264i	0.268703	−	0.111300i
$407$	−0.414214	−	0.414214i	−0.0205318	−	0.0205318i
$408$		0			0
$409$	4.51472	−	4.51472i	0.223238	−	0.223238i	−0.586622	−	0.809861i	$-0.699543\pi$
$409$	4.51472	−	4.51472i	0.223238	−	0.223238i	0.809861	+	0.586622i	$0.199543\pi$
$410$	15.0711	−	36.3848i	0.744307	−	1.79692i
$411$		0			0
$412$	14.9706	−	14.9706i	0.737547	−	0.737547i
$413$	3.58579	−	8.65685i	0.176445	−	0.425976i
$414$		0			0
$415$	−22.3848			−1.09883
$416$	4.00000	−	9.65685i	0.196116	−	0.473466i
$417$		0			0
$418$	2.68629			0.131391
$419$	8.60660	−	20.7782i	0.420460	−	1.01508i	−0.561752	−	0.827306i	$-0.689873\pi$
$419$	8.60660	−	20.7782i	0.420460	−	1.01508i	0.982212	−	0.187775i	$-0.0601275\pi$
$420$		0			0
$421$	7.70711	−	3.19239i	0.375621	−	0.155587i	−0.186882	−	0.982382i	$-0.559838\pi$
$421$	7.70711	−	3.19239i	0.375621	−	0.155587i	0.562504	+	0.826795i	$0.309838\pi$
$422$	0.272078	−	0.656854i	0.0132445	−	0.0319752i
$423$		0			0
$424$	21.3137	−	8.82843i	1.03509	−	0.428746i
$425$	−12.8284	−	12.8284i	−0.622270	−	0.622270i
$426$		0			0
$427$	−0.414214	−	1.00000i	−0.0200452	−	0.0483934i
$428$	0.242641	+	0.585786i	0.0117285	+	0.0283151i
$429$		0			0
$430$	29.0711	−	29.0711i	1.40193	−	1.40193i
$431$			23.6569i			1.13951i	0.821814	+	0.569755i	$0.192962\pi$
$431$			23.6569i			1.13951i	−0.821814	+	0.569755i	$0.807038\pi$
$432$		0			0
$433$		−	32.4853i		−	1.56114i	−0.625067	−	0.780571i	$-0.714928\pi$
$433$		−	32.4853i		−	1.56114i	0.625067	−	0.780571i	$-0.285072\pi$
$434$	5.65685	+	5.65685i	0.271538	+	0.271538i
$435$		0			0
$436$	8.58579	+	3.55635i	0.411185	+	0.170318i
$437$	0.556349	+	1.34315i	0.0266138	+	0.0642514i
$438$		0			0
$439$	−17.0000	−	17.0000i	−0.811366	−	0.811366i	0.173473	−	0.984839i	$-0.444501\pi$
$439$	−17.0000	−	17.0000i	−0.811366	−	0.811366i	−0.984839	+	0.173473i	$0.944501\pi$
$440$	2.14214	−	2.14214i	0.102122	−	0.102122i
$441$		0			0
$442$	−6.82843	−	2.82843i	−0.324795	−	0.134535i
$443$	20.6066	−	8.53553i	0.979049	−	0.405535i	0.164976	−	0.986298i	$-0.447245\pi$
$443$	20.6066	−	8.53553i	0.979049	−	0.405535i	0.814073	+	0.580762i	$0.197245\pi$
$444$		0			0
$445$	4.85786	−	11.7279i	0.230285	−	0.555957i
$446$		−	18.3431i		−	0.868573i
$447$		0			0
$448$	−8.00000	+	8.00000i	−0.377964	+	0.377964i
$449$	−31.4558			−1.48449			−0.742247	−	0.670127i	$-0.766240\pi$
$449$	−31.4558			−1.48449			−0.742247	+	0.670127i	$0.766240\pi$
$450$		0			0
$451$	1.00000	−	2.41421i	0.0470882	−	0.113681i
$452$		−	35.3137i		−	1.66102i
$453$		0			0
$454$	−8.89949	−	3.68629i	−0.417674	−	0.173006i
$455$	6.24264	−	6.24264i	0.292660	−	0.292660i
$456$		0			0
$457$	9.48528	+	9.48528i	0.443703	+	0.443703i	0.893254	−	0.449552i	$-0.148416\pi$
$457$	9.48528	+	9.48528i	0.443703	+	0.443703i	−0.449552	+	0.893254i	$0.648416\pi$
$458$	14.5147	+	35.0416i	0.678228	+	1.63739i
$459$		0			0
$460$	1.51472	+	0.627417i	0.0706241	+	0.0292535i
$461$	−13.3640	−	5.53553i	−0.622422	−	0.257816i	0.0491076	−	0.998793i	$-0.484362\pi$
$461$	−13.3640	−	5.53553i	−0.622422	−	0.257816i	−0.671529	+	0.740978i	$0.734362\pi$
$462$		0			0
$463$		−	10.9706i		−	0.509845i	−0.966961	−	0.254923i	$-0.917950\pi$
$463$		−	10.9706i		−	0.509845i	0.966961	−	0.254923i	$-0.0820500\pi$
$464$	−4.48528	+	10.8284i	−0.208224	+	0.502697i
$465$		0			0
$466$	−12.2426	+	12.2426i	−0.567129	+	0.567129i
$467$	−29.0919	−	12.0503i	−1.34621	−	0.557619i	−0.410977	−	0.911646i	$-0.634812\pi$
$467$	−29.0919	−	12.0503i	−1.34621	−	0.557619i	−0.935235	+	0.354027i	$0.884812\pi$
$468$		0			0
$469$	−2.17157	−	5.24264i	−0.100274	−	0.242083i
$470$	51.4558	−	21.3137i	2.37348	−	0.983128i
$471$		0			0
$472$	7.17157	+	17.3137i	0.330098	+	0.796928i
$473$	1.92893	−	1.92893i	0.0886924	−	0.0886924i
$474$		0			0
$475$	−35.5061	+	14.7071i	−1.62913	+	0.674808i
$476$	5.65685	+	5.65685i	0.259281	+	0.259281i
$477$		0			0
$478$	−24.4853			−1.11993
$479$	4.97056			0.227111			0.113555	−	0.993532i	$-0.463776\pi$
$479$	4.97056			0.227111			0.113555	+	0.993532i	$0.463776\pi$
$480$		0			0
$481$	3.41421			0.155675
$482$	12.0000			0.546585
$483$		0			0
$484$	−15.4142	+	15.4142i	−0.700646	+	0.700646i
$485$	−4.72792	+	1.95837i	−0.214684	+	0.0889250i
$486$		0			0
$487$	−11.0000	+	11.0000i	−0.498458	+	0.498458i	−0.910958	−	0.412500i	$-0.864656\pi$
$487$	−11.0000	+	11.0000i	−0.498458	+	0.498458i	0.412500	+	0.910958i	$0.364656\pi$
$488$	2.00000	+	0.828427i	0.0905357	+	0.0375011i
$489$		0			0
$490$	22.0711	−	9.14214i	0.997069	−	0.413000i
$491$	7.33452	+	17.7071i	0.331002	+	0.799111i	0.998513	+	0.0545104i	$0.0173598\pi$
$491$	7.33452	+	17.7071i	0.331002	+	0.799111i	−0.667511	+	0.744600i	$0.732640\pi$
$492$		0			0
$493$	7.65685	+	3.17157i	0.344847	+	0.142840i
$494$	−11.0711	+	11.0711i	−0.498111	+	0.498111i
$495$		0			0
$496$	−16.0000			−0.718421
$497$		−	0.343146i		−	0.0153922i
$498$		0			0
$499$	8.94975	+	3.70711i	0.400646	+	0.165953i	0.573902	−	0.818924i	$-0.305429\pi$
$499$	8.94975	+	3.70711i	0.400646	+	0.165953i	−0.173256	+	0.984877i	$0.555429\pi$
$500$	−3.65685	+	8.82843i	−0.163539	+	0.394819i
$501$		0			0
$502$	−8.55635	−	20.6569i	−0.381889	−	0.921961i
$503$	−17.1421	−	17.1421i	−0.764330	−	0.764330i	0.212772	−	0.977102i	$-0.431751\pi$
$503$	−17.1421	−	17.1421i	−0.764330	−	0.764330i	−0.977102	+	0.212772i	$0.931751\pi$
$504$		0			0
$505$	−29.3848	+	29.3848i	−1.30761	+	1.30761i
$506$	0.100505	+	0.0416306i	0.00446800	+	0.00185070i
$507$		0			0
$508$	41.9411			1.86084
$509$	−12.0919	+	29.1924i	−0.535963	+	1.29393i	0.391556	+	0.920154i	$0.371937\pi$
$509$	−12.0919	+	29.1924i	−0.535963	+	1.29393i	−0.927519	+	0.373776i	$0.878063\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$			8.48528i			0.374270i
$515$	−13.6863	+	33.0416i	−0.603090	+	1.45599i
$516$		0			0
$517$	3.41421	−	1.41421i	0.150157	−	0.0621970i
$518$	−3.41421	−	1.41421i	−0.150012	−	0.0621370i
$519$		0			0
$520$			17.6569i			0.774304i
$521$	−14.6569	−	14.6569i	−0.642128	−	0.642128i	0.308950	−	0.951078i	$-0.400022\pi$
$521$	−14.6569	−	14.6569i	−0.642128	−	0.642128i	−0.951078	+	0.308950i	$0.900022\pi$
$522$		0			0
$523$	0.807612	+	1.94975i	0.0353144	+	0.0852565i	0.940553	−	0.339648i	$-0.110308\pi$
$523$	0.807612	+	1.94975i	0.0353144	+	0.0852565i	−0.905238	+	0.424904i	$0.860308\pi$
$524$	−7.27208	+	17.5563i	−0.317682	+	0.766953i
$525$		0			0
$526$	−0.242641	−	0.242641i	−0.0105796	−	0.0105796i
$527$			11.3137i			0.492833i
$528$		0			0
$529$		−	22.9411i		−	0.997440i
$530$	−27.5563	+	27.5563i	−1.19697	+	1.19697i
$531$		0			0
$532$	15.6569	−	6.48528i	0.678811	−	0.281173i
$533$	5.82843	+	14.0711i	0.252457	+	0.609486i
$534$		0			0
$535$	−0.757359	−	0.757359i	−0.0327435	−	0.0327435i
$536$	10.4853	+	4.34315i	0.452895	+	0.187595i
$537$		0			0
$538$	−2.85786	+	6.89949i	−0.123211	+	0.297458i
$539$	1.46447	−	0.606602i	0.0630790	−	0.0261282i
$540$		0			0
$541$	5.26346	−	12.7071i	0.226294	−	0.546321i	−0.769427	−	0.638735i	$-0.779458\pi$
$541$	5.26346	−	12.7071i	0.226294	−	0.546321i	0.995721	+	0.0924135i	$0.0294582\pi$
$542$	25.4558			1.09342
$543$		0			0
$544$	−16.0000			−0.685994
$545$	−15.6985			−0.672449
$546$		0			0
$547$	−10.4645	+	25.2635i	−0.447428	+	1.08019i	0.525854	+	0.850575i	$0.323746\pi$
$547$	−10.4645	+	25.2635i	−0.447428	+	1.08019i	−0.973282	+	0.229612i	$0.926254\pi$
$548$	5.31371	+	5.31371i	0.226990	+	0.226990i
$549$		0			0
$550$	−1.10051	+	2.65685i	−0.0469257	+	0.113289i
$551$	12.4142	−	12.4142i	0.528863	−	0.528863i
$552$		0			0
$553$	6.00000	+	6.00000i	0.255146	+	0.255146i
$554$	1.00000	−	0.414214i	0.0424859	−	0.0175982i
$555$		0			0
$556$	10.3848	+	25.0711i	0.440413	+	1.06325i
$557$	−10.8787	−	4.50610i	−0.460944	−	0.190929i	0.140113	−	0.990136i	$-0.455254\pi$
$557$	−10.8787	−	4.50610i	−0.460944	−	0.190929i	−0.601057	+	0.799206i	$0.705254\pi$
$558$		0			0
$559$			15.8995i			0.672477i
$560$	7.31371	−	17.6569i	0.309061	−	0.746138i
$561$		0			0
$562$	−8.72792	−	8.72792i	−0.368165	−	0.368165i
$563$	−12.1213	−	5.02082i	−0.510853	−	0.211602i	0.112341	−	0.993670i	$-0.464165\pi$
$563$	−12.1213	−	5.02082i	−0.510853	−	0.211602i	−0.623194	+	0.782068i	$0.714165\pi$
$564$		0			0
$565$	22.8284	+	55.1127i	0.960399	+	2.31861i
$566$	5.72792	+	13.8284i	0.240763	+	0.581252i
$567$		0			0
$568$	0.485281	+	0.485281i	0.0203620	+	0.0203620i
$569$	−3.34315	+	3.34315i	−0.140152	+	0.140152i	−0.773702	−	0.633550i	$-0.781597\pi$
$569$	−3.34315	+	3.34315i	−0.140152	+	0.140152i	0.633550	+	0.773702i	$0.281597\pi$
$570$		0			0
$571$	−1.29289	+	0.535534i	−0.0541059	+	0.0224114i	−0.409572	−	0.912278i	$-0.634322\pi$
$571$	−1.29289	+	0.535534i	−0.0541059	+	0.0224114i	0.355466	+	0.934689i	$0.384322\pi$
$572$			1.17157i			0.0489859i
$573$		0			0
$574$		−	16.4853i		−	0.688082i
$575$	−1.55635			−0.0649042
$576$		0			0
$577$	−14.9706			−0.623233			−0.311616	−	0.950208i	$-0.600870\pi$
$577$	−14.9706			−0.623233			−0.311616	+	0.950208i	$0.600870\pi$
$578$		−	12.7279i		−	0.529412i
$579$		0			0
$580$		−	19.7990i		−	0.822108i
$581$	−8.65685	+	3.58579i	−0.359147	+	0.148763i
$582$		0			0
$583$	−1.82843	+	1.82843i	−0.0757257	+	0.0757257i
$584$	−19.7990	+	19.7990i	−0.819288	+	0.819288i
$585$		0			0
$586$	−6.79899	−	16.4142i	−0.280864	−	0.678065i
$587$	−8.60660	−	20.7782i	−0.355232	−	0.857607i	−0.995957	−	0.0898359i	$-0.971366\pi$
$587$	−8.60660	−	20.7782i	−0.355232	−	0.857607i	0.640724	−	0.767771i	$-0.278634\pi$
$588$		0			0
$589$	22.1421	+	9.17157i	0.912351	+	0.377908i
$590$	−22.3848	−	22.3848i	−0.921567	−	0.921567i
$591$		0			0
$592$	6.82843	−	2.82843i	0.280647	−	0.116248i
$593$		−	28.2843i		−	1.16150i	−0.814083	−	0.580748i	$-0.802760\pi$
$593$		−	28.2843i		−	1.16150i	0.814083	−	0.580748i	$-0.197240\pi$
$594$		0			0
$595$	−12.4853	−	5.17157i	−0.511847	−	0.212014i
$596$	11.2132	+	27.0711i	0.459311	+	1.10887i
$597$		0			0
$598$	−0.585786	+	0.242641i	−0.0239546	+	0.00992232i
$599$	15.3431	+	15.3431i	0.626904	+	0.626904i	0.947288	−	0.320384i	$-0.103812\pi$
$599$	15.3431	+	15.3431i	0.626904	+	0.626904i	−0.320384	+	0.947288i	$0.603812\pi$
$600$		0			0
$601$	11.9706	−	11.9706i	0.488289	−	0.488289i	−0.419477	−	0.907766i	$-0.637786\pi$
$601$	11.9706	−	11.9706i	0.488289	−	0.488289i	0.907766	+	0.419477i	$0.137786\pi$
$602$	6.58579	−	15.8995i	0.268417	−	0.648015i
$603$		0			0
$604$	−30.9706	−	30.9706i	−1.26017	−	1.26017i
$605$	14.0919	−	34.0208i	0.572917	−	1.38314i
$606$		0			0
$607$	0.970563			0.0393939			0.0196970	−	0.999806i	$-0.493730\pi$
$607$	0.970563			0.0393939			0.0196970	+	0.999806i	$0.493730\pi$
$608$	−12.9706	+	31.3137i	−0.526026	+	1.26994i
$609$		0			0
$610$	−3.65685			−0.148062
$611$	−8.24264	+	19.8995i	−0.333462	+	0.805047i
$612$		0			0
$613$	36.6777	−	15.1924i	1.48140	−	0.613615i	0.511972	−	0.859002i	$-0.328915\pi$
$613$	36.6777	−	15.1924i	1.48140	−	0.613615i	0.969425	+	0.245387i	$0.0789151\pi$
$614$	1.72792	−	4.17157i	0.0697333	−	0.168351i
$615$		0			0
$616$	0.485281	−	1.17157i	0.0195525	−	0.0472040i
$617$	16.7990	+	16.7990i	0.676302	+	0.676302i	0.959161	−	0.282859i	$-0.0912830\pi$
$617$	16.7990	+	16.7990i	0.676302	+	0.676302i	−0.282859	+	0.959161i	$0.591283\pi$
$618$		0			0
$619$	−6.22183	−	15.0208i	−0.250076	−	0.603738i	0.748133	−	0.663548i	$-0.230950\pi$
$619$	−6.22183	−	15.0208i	−0.250076	−	0.603738i	−0.998210	+	0.0598107i	$0.980950\pi$
$620$	24.9706	−	10.3431i	1.00284	−	0.415391i
$621$		0			0
$622$	−12.2426	+	12.2426i	−0.490885	+	0.490885i
$623$		−	5.31371i		−	0.212889i
$624$		0			0
$625$			15.9289i			0.637157i
$626$	−13.4142	−	13.4142i	−0.536140	−	0.536140i
$627$		0			0
$628$	−0.585786	+	1.41421i	−0.0233754	+	0.0564333i
$629$	−2.00000	−	4.82843i	−0.0797452	−	0.192522i
$630$		0			0
$631$	−18.4558	−	18.4558i	−0.734716	−	0.734716i	0.236834	−	0.971550i	$-0.423890\pi$
$631$	−18.4558	−	18.4558i	−0.734716	−	0.734716i	−0.971550	+	0.236834i	$0.923890\pi$
$632$	−16.9706			−0.675053
$633$		0			0
$634$	15.8284	+	6.55635i	0.628627	+	0.260386i
$635$	−65.4558	+	27.1127i	−2.59754	+	1.07593i
$636$		0			0
$637$	−3.53553	+	8.53553i	−0.140083	+	0.338190i
$638$		−	1.31371i		−	0.0520102i
$639$		0			0
$640$	14.6274	+	35.3137i	0.578199	+	1.39590i
$641$	43.4558			1.71640			0.858201	−	0.513313i	$-0.171582\pi$
$641$	43.4558			1.71640			0.858201	+	0.513313i	$0.171582\pi$
$642$		0			0
$643$	−15.4350	+	37.2635i	−0.608698	+	1.46953i	0.255719	+	0.966751i	$0.417688\pi$
$643$	−15.4350	+	37.2635i	−0.608698	+	1.46953i	−0.864417	+	0.502776i	$0.832312\pi$
$644$	0.686292			0.0270437
$645$		0			0
$646$	22.1421	+	9.17157i	0.871171	+	0.360851i
$647$	−11.8284	+	11.8284i	−0.465023	+	0.465023i	−0.900298	−	0.435274i	$-0.856651\pi$
$647$	−11.8284	+	11.8284i	−0.465023	+	0.465023i	0.435274	+	0.900298i	$0.356651\pi$
$648$		0			0
$649$	−1.48528	−	1.48528i	−0.0583024	−	0.0583024i
$650$	−6.41421	−	15.4853i	−0.251586	−	0.607383i
$651$		0			0
$652$	−15.0711	+	36.3848i	−0.590229	+	1.42494i
$653$	36.0919	+	14.9497i	1.41238	+	0.585029i	0.952935	−	0.303175i	$-0.0980467\pi$
$653$	36.0919	+	14.9497i	1.41238	+	0.585029i	0.459450	+	0.888204i	$0.348047\pi$
$654$		0			0
$655$		−	32.1005i		−	1.25427i
$656$	23.3137	+	23.3137i	0.910247	+	0.910247i
$657$		0			0
$658$	16.4853	−	16.4853i	0.642663	−	0.642663i
$659$	5.87868	+	2.43503i	0.229001	+	0.0948553i	0.494234	−	0.869329i	$-0.335449\pi$
$659$	5.87868	+	2.43503i	0.229001	+	0.0948553i	−0.265233	+	0.964184i	$0.585449\pi$
$660$		0			0
$661$	7.74874	+	18.7071i	0.301391	+	0.727622i	0.999927	+	0.0120477i	$0.00383499\pi$
$661$	7.74874	+	18.7071i	0.301391	+	0.727622i	−0.698536	+	0.715574i	$0.746165\pi$
$662$	−9.24264	+	3.82843i	−0.359225	+	0.148796i
$663$		0			0
$664$	7.17157	−	17.3137i	0.278311	−	0.671902i
$665$	−20.2426	+	20.2426i	−0.784976	+	0.784976i
$666$		0			0
$667$	0.656854	−	0.272078i	0.0254335	−	0.0105349i
$668$	6.68629	−	6.68629i	0.258700	−	0.258700i
$669$		0			0
$670$	−19.1716			−0.740662
$671$	−0.242641			−0.00936704
$672$		0			0
$673$	5.51472			0.212577			0.106288	−	0.994335i	$-0.466103\pi$
$673$	5.51472			0.212577			0.106288	+	0.994335i	$0.466103\pi$
$674$	24.0000			0.924445
$675$		0			0
$676$	13.5563	+	13.5563i	0.521398	+	0.521398i
$677$	5.60660	−	2.32233i	0.215479	−	0.0892544i	−0.272333	−	0.962203i	$-0.587795\pi$
$677$	5.60660	−	2.32233i	0.215479	−	0.0892544i	0.487812	+	0.872949i	$0.337795\pi$
$678$		0			0
$679$	−1.51472	+	1.51472i	−0.0581296	+	0.0581296i
$680$	24.9706	−	10.3431i	0.957577	−	0.396642i
$681$		0			0
$682$	1.65685	−	0.686292i	0.0634442	−	0.0262795i
$683$	5.87868	+	14.1924i	0.224941	+	0.543057i	0.995548	−	0.0942543i	$-0.0300467\pi$
$683$	5.87868	+	14.1924i	0.224941	+	0.543057i	−0.770607	+	0.637311i	$0.780047\pi$
$684$		0			0
$685$	−11.7279	−	4.85786i	−0.448101	−	0.185609i
$686$	16.9706	−	16.9706i	0.647939	−	0.647939i
$687$		0			0
$688$	13.1716	+	31.7990i	0.502162	+	1.21233i
$689$		−	15.0711i		−	0.574162i
$690$		0			0
$691$	−28.5061	−	11.8076i	−1.08442	−	0.449183i	−0.232364	−	0.972629i	$-0.574646\pi$
$691$	−28.5061	−	11.8076i	−1.08442	−	0.449183i	−0.852059	+	0.523446i	$0.824646\pi$
$692$	−2.24264	−	0.928932i	−0.0852524	−	0.0353127i
$693$		0			0
$694$	8.41421	+	20.3137i	0.319399	+	0.771098i
$695$	−32.4142	−	32.4142i	−1.22954	−	1.22954i
$696$		0			0
$697$	16.4853	−	16.4853i	0.624425	−	0.624425i
$698$	36.4558	+	15.1005i	1.37987	+	0.571563i
$699$		0			0
$700$			18.1421i			0.685708i
$701$	−7.12132	+	17.1924i	−0.268969	+	0.649348i	−0.999435	−	0.0336007i	$-0.989303\pi$
$701$	−7.12132	+	17.1924i	−0.268969	+	0.649348i	0.730467	+	0.682948i	$0.239303\pi$
$702$		0			0
$703$	−11.0711			−0.417553
$704$	0.970563	+	2.34315i	0.0365795	+	0.0883106i
$705$		0			0
$706$			8.48528i			0.319348i
$707$	−6.65685	+	16.0711i	−0.250357	+	0.604415i
$708$		0			0
$709$	−6.77817	+	2.80761i	−0.254560	+	0.105442i	−0.506314	−	0.862349i	$-0.668992\pi$
$709$	−6.77817	+	2.80761i	−0.254560	+	0.105442i	0.251755	+	0.967791i	$0.418992\pi$
$710$	−1.07107	−	0.443651i	−0.0401965	−	0.0166499i
$711$		0			0
$712$	7.51472	+	7.51472i	0.281626	+	0.281626i
$713$	0.686292	+	0.686292i	0.0257018	+	0.0257018i
$714$		0			0
$715$	−0.757359	−	1.82843i	−0.0283236	−	0.0683793i
$716$	−28.7279	−	11.8995i	−1.07361	−	0.444705i
$717$		0			0
$718$	−17.2132	−	17.2132i	−0.642391	−	0.642391i
$719$		−	24.3431i		−	0.907846i	−0.891041	−	0.453923i	$-0.850024\pi$
$719$		−	24.3431i		−	0.907846i	0.891041	−	0.453923i	$-0.149976\pi$
$720$		0			0
$721$			14.9706i			0.557533i
$722$	16.8995	−	16.8995i	0.628934	−	0.628934i
$723$		0			0
$724$	4.38478	+	10.5858i	0.162959	+	0.393418i
$725$	7.19239	+	17.3640i	0.267119	+	0.644881i
$726$		0			0
$727$	23.9706	+	23.9706i	0.889019	+	0.889019i	0.994429	−	0.105410i	$-0.0336155\pi$
$727$	23.9706	+	23.9706i	0.889019	+	0.889019i	−0.105410	+	0.994429i	$0.533615\pi$
$728$	2.82843	+	6.82843i	0.104828	+	0.253078i
$729$		0			0
$730$	18.1005	−	43.6985i	0.669930	−	1.61735i
$731$	22.4853	−	9.31371i	0.831648	−	0.344480i
$732$		0			0
$733$	−0.736544	+	1.77817i	−0.0272049	+	0.0656784i	−0.936898	−	0.349602i	$-0.886317\pi$
$733$	−0.736544	+	1.77817i	−0.0272049	+	0.0656784i	0.909693	+	0.415281i	$0.136317\pi$
$734$	−8.48528			−0.313197
$735$		0			0
$736$	−0.970563	+	0.970563i	−0.0357754	+	0.0357754i
$737$	−1.27208			−0.0468576
$738$		0			0
$739$	7.53553	−	18.1924i	0.277199	−	0.669218i	−0.722557	−	0.691312i	$-0.757033\pi$
$739$	7.53553	−	18.1924i	0.277199	−	0.669218i	0.999756	+	0.0220937i	$0.00703323\pi$
$740$	−8.82843	+	8.82843i	−0.324539	+	0.324539i
$741$		0			0
$742$	−6.24264	+	15.0711i	−0.229175	+	0.553276i
$743$	13.6274	−	13.6274i	0.499941	−	0.499941i	−0.411478	−	0.911420i	$-0.634987\pi$
$743$	13.6274	−	13.6274i	0.499941	−	0.499941i	0.911420	+	0.411478i	$0.134987\pi$
$744$		0			0
$745$	−35.0000	−	35.0000i	−1.28230	−	1.28230i
$746$	−39.9706	+	16.5563i	−1.46343	+	0.606171i
$747$		0			0
$748$	1.65685	−	0.686292i	0.0605806	−	0.0250933i
$749$	−0.414214	−	0.171573i	−0.0151350	−	0.00626914i
$750$		0			0
$751$			22.9706i			0.838208i	0.907938	+	0.419104i	$0.137656\pi$
$751$			22.9706i			0.838208i	−0.907938	+	0.419104i	$0.862344\pi$
$752$			46.6274i			1.70033i
$753$		0			0
$754$	5.41421	+	5.41421i	0.197174	+	0.197174i
$755$	68.3553	+	28.3137i	2.48771	+	1.03044i
$756$		0			0
$757$	−0.736544	−	1.77817i	−0.0267701	−	0.0646289i	0.909929	−	0.414764i	$-0.136136\pi$
$757$	−0.736544	−	1.77817i	−0.0267701	−	0.0646289i	−0.936699	+	0.350135i	$0.886136\pi$
$758$	−12.6985	−	30.6569i	−0.461230	−	1.11351i
$759$		0			0
$760$		−	57.2548i		−	2.07685i
$761$	24.1716	−	24.1716i	0.876219	−	0.876219i	−0.116922	−	0.993141i	$-0.537303\pi$
$761$	24.1716	−	24.1716i	0.876219	−	0.876219i	0.993141	+	0.116922i	$0.0373028\pi$
$762$		0			0
$763$	−6.07107	+	2.51472i	−0.219787	+	0.0910389i
$764$	−24.0000			−0.868290
$765$		0			0
$766$			24.0000i			0.867155i
$767$	12.2426			0.442056
$768$		0			0
$769$	22.4853			0.810840			0.405420	−	0.914131i	$-0.367125\pi$
$769$	22.4853			0.810840			0.405420	+	0.914131i	$0.367125\pi$
$770$			2.14214i			0.0771972i
$771$		0			0
$772$	36.9706			1.33060
$773$	26.0919	−	10.8076i	0.938460	−	0.388723i	0.139578	−	0.990211i	$-0.455425\pi$
$773$	26.0919	−	10.8076i	0.938460	−	0.388723i	0.798882	+	0.601488i	$0.205425\pi$
$774$		0			0
$775$	−18.1421	+	18.1421i	−0.651685	+	0.651685i
$776$		−	4.28427i		−	0.153796i
$777$		0			0
$778$	−17.3431	−	41.8701i	−0.621782	−	1.50111i
$779$	−18.8995	−	45.6274i	−0.677145	−	1.63477i
$780$		0			0
$781$	−0.0710678	−	0.0294373i	−0.00254301	−	0.00105335i
$782$	0.686292	+	0.686292i	0.0245417	+	0.0245417i
$783$		0			0
$784$			20.0000i			0.714286i
$785$		−	2.58579i		−	0.0922907i
$786$		0			0
$787$	8.94975	+	3.70711i	0.319024	+	0.132144i	0.536448	−	0.843933i	$-0.319766\pi$
$787$	8.94975	+	3.70711i	0.319024	+	0.132144i	−0.217424	+	0.976077i	$0.569766\pi$
$788$	34.7279	−	14.3848i	1.23713	−	0.512436i
$789$		0			0
$790$	26.4853	−	10.9706i	0.942304	−	0.390315i
$791$	17.6569	+	17.6569i	0.627805	+	0.627805i
$792$		0			0
$793$	1.00000	−	1.00000i	0.0355110	−	0.0355110i
$794$	−14.5147	+	35.0416i	−0.515108	+	1.24358i
$795$		0			0
$796$	−35.9411	+	35.9411i	−1.27390	+	1.27390i
$797$	−12.0919	+	29.1924i	−0.428316	+	1.03405i	0.551505	+	0.834172i	$0.314054\pi$
$797$	−12.0919	+	29.1924i	−0.428316	+	1.03405i	−0.979821	+	0.199876i	$0.935946\pi$
$798$		0			0
$799$	32.9706			1.16641
$800$	−25.6569	−	25.6569i	−0.907107	−	0.907107i
$801$		0			0
$802$	−4.00000			−0.141245
$803$	1.20101	−	2.89949i	0.0423827	−	0.102321i
$804$		0			0
$805$	−1.07107	+	0.443651i	−0.0377502	+	0.0156366i
$806$	−4.00000	+	9.65685i	−0.140894	+	0.340148i
$807$		0			0
$808$	−13.3137	−	32.1421i	−0.468375	−	1.13076i
$809$	0.857864	+	0.857864i	0.0301609	+	0.0301609i	0.722026	−	0.691865i	$-0.243211\pi$
$809$	0.857864	+	0.857864i	0.0301609	+	0.0301609i	−0.691865	+	0.722026i	$0.743211\pi$
$810$		0			0
$811$	−9.73654	−	23.5061i	−0.341896	−	0.825411i	−0.997524	−	0.0703264i	$-0.977596\pi$
$811$	−9.73654	−	23.5061i	−0.341896	−	0.825411i	0.655628	−	0.755084i	$-0.272404\pi$
$812$	−3.17157	−	7.65685i	−0.111300	−	0.268703i
$813$		0			0
$814$	−0.585786	+	0.585786i	−0.0205318	+	0.0205318i
$815$		−	66.5269i		−	2.33034i
$816$		0			0
$817$		−	51.5563i		−	1.80373i
$818$	−6.38478	−	6.38478i	−0.223238	−	0.223238i
$819$		0			0
$820$	−51.4558	−	21.3137i	−1.79692	−	0.744307i
$821$	0.393398	+	0.949747i	0.0137297	+	0.0331464i	0.930596	−	0.366049i	$-0.119290\pi$
$821$	0.393398	+	0.949747i	0.0137297	+	0.0331464i	−0.916866	+	0.399195i	$0.869290\pi$
$822$		0			0
$823$	2.02944	+	2.02944i	0.0707417	+	0.0707417i	0.741592	−	0.670851i	$-0.234071\pi$
$823$	2.02944	+	2.02944i	0.0707417	+	0.0707417i	−0.670851	+	0.741592i	$0.734071\pi$
$824$	−21.1716	−	21.1716i	−0.737547	−	0.737547i
$825$		0			0
$826$	−12.2426	−	5.07107i	−0.425976	−	0.176445i
$827$	−11.8787	+	4.92031i	−0.413062	+	0.171096i	−0.579530	−	0.814951i	$-0.696764\pi$
$827$	−11.8787	+	4.92031i	−0.413062	+	0.171096i	0.166468	+	0.986047i	$0.446764\pi$
$828$		0			0
$829$	15.8076	−	38.1630i	0.549021	−	1.32545i	−0.369187	−	0.929355i	$-0.620364\pi$
$829$	15.8076	−	38.1630i	0.549021	−	1.32545i	0.918208	−	0.396099i	$-0.129636\pi$
$830$			31.6569i			1.09883i
$831$		0			0
$832$	−13.6569	−	5.65685i	−0.473466	−	0.196116i
$833$	14.1421			0.489996
$834$		0			0
$835$	−6.11270	+	14.7574i	−0.211539	+	0.510699i
$836$		−	3.79899i		−	0.131391i
$837$		0			0
$838$	−29.3848	−	12.1716i	−1.01508	−	0.420460i
$839$	−32.3137	+	32.3137i	−1.11559	+	1.11559i	−0.123213	+	0.992380i	$0.539320\pi$
$839$	−32.3137	+	32.3137i	−1.11559	+	1.11559i	−0.992380	+	0.123213i	$0.960680\pi$
$840$		0			0
$841$	14.4350	+	14.4350i	0.497760	+	0.497760i
$842$	−4.51472	−	10.8995i	−0.155587	−	0.375621i
$843$		0			0
$844$	−0.928932	−	0.384776i	−0.0319752	−	0.0132445i
$845$	−29.9203	−	12.3934i	−1.02929	−	0.426346i
$846$		0			0
$847$		−	15.4142i		−	0.529639i
$848$	−12.4853	−	30.1421i	−0.428746	−	1.03509i
$849$		0			0
$850$	−18.1421	+	18.1421i	−0.622270	+	0.622270i
$851$	−0.414214	−	0.171573i	−0.0141991	−	0.00588144i
$852$		0			0
$853$	−1.16295	−	2.80761i	−0.0398187	−	0.0961308i	0.902719	−	0.430231i	$-0.141568\pi$
$853$	−1.16295	−	2.80761i	−0.0398187	−	0.0961308i	−0.942538	+	0.334100i	$0.891568\pi$
$854$	−1.41421	+	0.585786i	−0.0483934	+	0.0200452i
$855$		0			0
$856$	0.828427	−	0.343146i	0.0283151	−	0.0117285i
$857$	−32.3137	+	32.3137i	−1.10382	+	1.10382i	−0.109869	+	0.993946i	$0.535043\pi$
$857$	−32.3137	+	32.3137i	−1.10382	+	1.10382i	−0.993946	+	0.109869i	$0.964957\pi$
$858$		0			0
$859$	33.6777	−	13.9497i	1.14907	−	0.475959i	0.274847	−	0.961488i	$-0.411373\pi$
$859$	33.6777	−	13.9497i	1.14907	−	0.475959i	0.874221	+	0.485529i	$0.161373\pi$
$860$	−41.1127	−	41.1127i	−1.40193	−	1.40193i
$861$		0			0
$862$	33.4558			1.13951
$863$	45.9411			1.56385			0.781927	−	0.623370i	$-0.214237\pi$
$863$	45.9411			1.56385			0.781927	+	0.623370i	$0.214237\pi$
$864$		0			0
$865$	4.10051			0.139421
$866$	−45.9411			−1.56114
$867$		0			0
$868$	8.00000	−	8.00000i	0.271538	−	0.271538i
$869$	1.75736	−	0.727922i	0.0596143	−	0.0246931i
$870$		0			0
$871$	5.24264	−	5.24264i	0.177640	−	0.177640i
$872$	5.02944	−	12.1421i	0.170318	−	0.411185i
$873$		0			0
$874$	1.89949	−	0.786797i	0.0642514	−	0.0266138i
$875$	−2.58579	−	6.24264i	−0.0874155	−	0.211040i
$876$		0			0
$877$	−33.2635	−	13.7782i	−1.12323	−	0.465256i	−0.257754	−	0.966211i	$-0.582982\pi$
$877$	−33.2635	−	13.7782i	−1.12323	−	0.465256i	−0.865473	+	0.500955i	$0.832982\pi$
$878$	−24.0416	+	24.0416i	−0.811366	+	0.811366i
$879$		0			0
$880$	−3.02944	−	3.02944i	−0.102122	−	0.102122i
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$		0			0
$883$	47.4350	+	19.6482i	1.59632	+	0.661216i	0.990888	−	0.134685i	$-0.0430022\pi$
$883$	47.4350	+	19.6482i	1.59632	+	0.661216i	0.605427	+	0.795901i	$0.293002\pi$
$884$	−4.00000	+	9.65685i	−0.134535	+	0.324795i
$885$		0			0
$886$	−12.0711	−	29.1421i	−0.405535	−	0.979049i
$887$	20.3137	+	20.3137i	0.682068	+	0.682068i	0.960466	−	0.278398i	$-0.0898035\pi$
$887$	20.3137	+	20.3137i	0.682068	+	0.682068i	−0.278398	+	0.960466i	$0.589803\pi$
$888$		0			0
$889$	−20.9706	+	20.9706i	−0.703330	+	0.703330i
$890$	−16.5858	−	6.87006i	−0.555957	−	0.230285i
$891$		0			0
$892$	−25.9411			−0.868573
$893$	26.7279	−	64.5269i	0.894416	−	2.15931i
$894$		0			0
$895$	52.5269			1.75578
$896$	11.3137	+	11.3137i	0.377964	+	0.377964i
$897$		0			0
$898$			44.4853i			1.48449i
$899$	4.48528	−	10.8284i	0.149593	−	0.361148i
$900$		0			0
$901$	−21.3137	+	8.82843i	−0.710063	+	0.294118i
$902$	−3.41421	−	1.41421i	−0.113681	−	0.0470882i
$903$		0			0
$904$	−49.9411			−1.66102
$905$	−13.6863	−	13.6863i	−0.454948	−	0.454948i
$906$		0			0
$907$	−0.221825	−	0.535534i	−0.00736559	−	0.0177821i	0.920154	−	0.391557i	$-0.128063\pi$
$907$	−0.221825	−	0.535534i	−0.00736559	−	0.0177821i	−0.927520	+	0.373775i	$0.878063\pi$
$908$	−5.21320	+	12.5858i	−0.173006	+	0.417674i
$909$		0			0
$910$	−8.82843	−	8.82843i	−0.292660	−	0.292660i
$911$			45.5980i			1.51073i	0.655305	+	0.755364i	$0.272540\pi$
$911$			45.5980i			1.51073i	−0.655305	+	0.755364i	$0.727460\pi$
$912$		0			0
$913$			2.10051i			0.0695166i
$914$	13.4142	−	13.4142i	0.443703	−	0.443703i
$915$		0			0
$916$	49.5563	−	20.5269i	1.63739	−	0.678228i
$917$	−5.14214	−	12.4142i	−0.169808	−	0.409953i
$918$		0			0
$919$	−25.4853	−	25.4853i	−0.840682	−	0.840682i	0.148266	−	0.988948i	$-0.452631\pi$
$919$	−25.4853	−	25.4853i	−0.840682	−	0.840682i	−0.988948	+	0.148266i	$0.952631\pi$
$920$	0.887302	−	2.14214i	0.0292535	−	0.0706241i
$921$		0			0
$922$	−7.82843	+	18.8995i	−0.257816	+	0.622422i
$923$	0.414214	−	0.171573i	0.0136340	−	0.00564739i
$924$		0			0
$925$	4.53553	−	10.9497i	0.149127	−	0.360025i
$926$	−15.5147			−0.509845
$927$		0			0
$928$	15.3137	+	6.34315i	0.502697	+	0.208224i
$929$	26.4853			0.868954			0.434477	−	0.900683i	$-0.356933\pi$
$929$	26.4853			0.868954			0.434477	+	0.900683i	$0.356933\pi$
$930$		0			0
$931$	11.4645	−	27.6777i	0.375733	−	0.907099i
$932$	17.3137	+	17.3137i	0.567129	+	0.567129i
$933$		0			0
$934$	−17.0416	+	41.1421i	−0.557619	+	1.34621i
$935$	−2.14214	+	2.14214i	−0.0700553	+	0.0700553i
$936$		0			0
$937$	19.0000	+	19.0000i	0.620703	+	0.620703i	0.945711	−	0.325008i	$-0.105367\pi$
$937$	19.0000	+	19.0000i	0.620703	+	0.620703i	−0.325008	+	0.945711i	$0.605367\pi$
$938$	−7.41421	+	3.07107i	−0.242083	+	0.100274i
$939$		0			0
$940$	−30.1421	−	72.7696i	−0.983128	−	2.37348i
$941$	−13.3640	−	5.53553i	−0.435653	−	0.180453i	0.154068	−	0.988060i	$-0.450762\pi$
$941$	−13.3640	−	5.53553i	−0.435653	−	0.180453i	−0.589721	+	0.807607i	$0.700762\pi$
$942$		0			0
$943$		−	2.00000i		−	0.0651290i
$944$	24.4853	−	10.1421i	0.796928	−	0.330098i
$945$		0			0
$946$	−2.72792	−	2.72792i	−0.0886924	−	0.0886924i
$947$	37.3345	+	15.4645i	1.21321	+	0.502528i	0.895245	−	0.445575i	$-0.147001\pi$
$947$	37.3345	+	15.4645i	1.21321	+	0.502528i	0.317964	+	0.948103i	$0.397001\pi$
$948$		0			0
$949$	7.00000	+	16.8995i	0.227230	+	0.548581i
$950$	20.7990	+	50.2132i	0.674808	+	1.62913i
$951$		0			0
$952$	8.00000	−	8.00000i	0.259281	−	0.259281i
$953$	−3.34315	+	3.34315i	−0.108295	+	0.108295i	−0.759178	−	0.650883i	$-0.774399\pi$
$953$	−3.34315	+	3.34315i	−0.108295	+	0.108295i	0.650883	+	0.759178i	$0.274399\pi$
$954$		0			0
$955$	37.4558	−	15.5147i	1.21204	−	0.502045i
$956$			34.6274i			1.11993i
$957$		0			0
$958$		−	7.02944i		−	0.227111i
$959$	−5.31371			−0.171589
$960$		0			0
$961$	−15.0000			−0.483871
$962$		−	4.82843i		−	0.155675i
$963$		0			0
$964$		−	16.9706i		−	0.546585i
$965$	−57.6985	+	23.8995i	−1.85738	+	0.769352i
$966$		0			0
$967$	−39.9706	+	39.9706i	−1.28537	+	1.28537i	−0.347797	+	0.937570i	$0.613070\pi$
$967$	−39.9706	+	39.9706i	−1.28537	+	1.28537i	−0.937570	+	0.347797i	$0.886930\pi$
$968$	21.7990	+	21.7990i	0.700646	+	0.700646i
$969$		0			0
$970$	2.76955	+	6.68629i	0.0889250	+	0.214684i
$971$	−9.63604	−	23.2635i	−0.309235	−	0.746560i	−0.999730	−	0.0232228i	$-0.992607\pi$
$971$	−9.63604	−	23.2635i	−0.309235	−	0.746560i	0.690495	−	0.723337i	$-0.257393\pi$
$972$		0			0
$973$	−17.7279	−	7.34315i	−0.568331	−	0.235410i
$974$	15.5563	+	15.5563i	0.498458	+	0.498458i
$975$		0			0
$976$	1.17157	−	2.82843i	0.0375011	−	0.0905357i
$977$			14.1421i			0.452447i	0.974075	+	0.226224i	$0.0726380\pi$
$977$			14.1421i			0.452447i	−0.974075	+	0.226224i	$0.927362\pi$
$978$		0			0
$979$	−1.10051	−	0.455844i	−0.0351723	−	0.0145688i
$980$	−12.9289	−	31.2132i	−0.413000	−	0.997069i
$981$		0			0
$982$	25.0416	−	10.3726i	0.799111	−	0.331002i
$983$	−25.6274	−	25.6274i	−0.817388	−	0.817388i	0.168341	−	0.985729i	$-0.446159\pi$
$983$	−25.6274	−	25.6274i	−0.817388	−	0.817388i	−0.985729	+	0.168341i	$0.946159\pi$
$984$		0			0
$985$	−44.8995	+	44.8995i	−1.43062	+	1.43062i
$986$	4.48528	−	10.8284i	0.142840	−	0.344847i
$987$		0			0
$988$	15.6569	+	15.6569i	0.498111	+	0.498111i
$989$	0.798990	−	1.92893i	0.0254064	−	0.0613365i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$			22.6274i			0.718421i
$993$		0			0
$994$	−0.485281			−0.0153922
$995$	32.8579	−	79.3259i	1.04166	−	2.51480i
$996$		0			0
$997$	−1.80761	+	0.748737i	−0.0572476	+	0.0237127i	−0.411124	−	0.911580i	$-0.634864\pi$
$997$	−1.80761	+	0.748737i	−0.0572476	+	0.0237127i	0.353876	+	0.935292i	$0.384864\pi$
$998$	5.24264	−	12.6569i	0.165953	−	0.400646i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.a.109.1		4
3.2	odd	2		32.2.g.a.13.1	yes	4
4.3	odd	2		1152.2.v.a.145.1		4
12.11	even	2		128.2.g.a.17.1		4
15.2	even	4		800.2.ba.a.749.1		4
15.8	even	4		800.2.ba.b.749.1		4
15.14	odd	2		800.2.y.a.301.1		4
24.5	odd	2		256.2.g.b.33.1		4
24.11	even	2		256.2.g.a.33.1		4
32.5	even	8	inner	288.2.v.a.37.1		4
32.27	odd	8		1152.2.v.a.1009.1		4
48.5	odd	4		512.2.g.a.321.1		4
48.11	even	4		512.2.g.c.321.1		4
48.29	odd	4		512.2.g.d.321.1		4
48.35	even	4		512.2.g.b.321.1		4
96.5	odd	8		32.2.g.a.5.1	✓	4
96.11	even	8		256.2.g.a.225.1		4
96.29	odd	8		512.2.g.d.193.1		4
96.35	even	8		512.2.g.b.193.1		4
96.53	odd	8		256.2.g.b.225.1		4
96.59	even	8		128.2.g.a.113.1		4
96.77	odd	8		512.2.g.a.193.1		4
96.83	even	8		512.2.g.c.193.1		4
192.5	odd	16		4096.2.a.e.1.4		4
192.59	even	16		4096.2.a.f.1.1		4
192.101	odd	16		4096.2.a.e.1.1		4
192.155	even	16		4096.2.a.f.1.4		4
480.197	even	8		800.2.ba.b.549.1		4
480.293	even	8		800.2.ba.a.549.1		4
480.389	odd	8		800.2.y.a.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.5.1	✓	4	96.5	odd	8
32.2.g.a.13.1	yes	4	3.2	odd	2
128.2.g.a.17.1		4	12.11	even	2
128.2.g.a.113.1		4	96.59	even	8
256.2.g.a.33.1		4	24.11	even	2
256.2.g.a.225.1		4	96.11	even	8
256.2.g.b.33.1		4	24.5	odd	2
256.2.g.b.225.1		4	96.53	odd	8
288.2.v.a.37.1		4	32.5	even	8	inner
288.2.v.a.109.1		4	1.1	even	1	trivial
512.2.g.a.193.1		4	96.77	odd	8
512.2.g.a.321.1		4	48.5	odd	4
512.2.g.b.193.1		4	96.35	even	8
512.2.g.b.321.1		4	48.35	even	4
512.2.g.c.193.1		4	96.83	even	8
512.2.g.c.321.1		4	48.11	even	4
512.2.g.d.193.1		4	96.29	odd	8
512.2.g.d.321.1		4	48.29	odd	4
800.2.y.a.101.1		4	480.389	odd	8
800.2.y.a.301.1		4	15.14	odd	2
800.2.ba.a.549.1		4	480.293	even	8
800.2.ba.a.749.1		4	15.2	even	4
800.2.ba.b.549.1		4	480.197	even	8
800.2.ba.b.749.1		4	15.8	even	4
1152.2.v.a.145.1		4	4.3	odd	2
1152.2.v.a.1009.1		4	32.27	odd	8
4096.2.a.e.1.1		4	192.101	odd	16
4096.2.a.e.1.4		4	192.5	odd	16
4096.2.a.f.1.1		4	192.59	even	16
4096.2.a.f.1.4		4	192.155	even	16

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(3.12132 - 1.29289i) q^{5} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(3.12132 - 1.29289i) q^{5} +(1.00000 - 1.00000i) q^{7} +2.82843i q^{8} +(-1.82843 - 4.41421i) q^{10} +(-0.121320 - 0.292893i) q^{11} +(1.70711 + 0.707107i) q^{13} +(-1.41421 - 1.41421i) q^{14} +4.00000 q^{16} -2.82843i q^{17} +(-5.53553 - 2.29289i) q^{19} +(-6.24264 + 2.58579i) q^{20} +(-0.414214 + 0.171573i) q^{22} +(-0.171573 - 0.171573i) q^{23} +(4.53553 - 4.53553i) q^{25} +(1.00000 - 2.41421i) q^{26} +(-2.00000 + 2.00000i) q^{28} +(-1.12132 + 2.70711i) q^{29} -4.00000 q^{31} -5.65685i q^{32} -4.00000 q^{34} +(1.82843 - 4.41421i) q^{35} +(1.70711 - 0.707107i) q^{37} +(-3.24264 + 7.82843i) q^{38} +(3.65685 + 8.82843i) q^{40} +(5.82843 + 5.82843i) q^{41} +(3.29289 + 7.94975i) q^{43} +(0.242641 + 0.585786i) q^{44} +(-0.242641 + 0.242641i) q^{46} +11.6569i q^{47} +5.00000i q^{49} +(-6.41421 - 6.41421i) q^{50} +(-3.41421 - 1.41421i) q^{52} +(-3.12132 - 7.53553i) q^{53} +(-0.757359 - 0.757359i) q^{55} +(2.82843 + 2.82843i) q^{56} +(3.82843 + 1.58579i) q^{58} +(6.12132 - 2.53553i) q^{59} +(0.292893 - 0.707107i) q^{61} +5.65685i q^{62} -8.00000 q^{64} +6.24264 q^{65} +(1.53553 - 3.70711i) q^{67} +5.65685i q^{68} +(-6.24264 - 2.58579i) q^{70} +(0.171573 - 0.171573i) q^{71} +(7.00000 + 7.00000i) q^{73} +(-1.00000 - 2.41421i) q^{74} +(11.0711 + 4.58579i) q^{76} +(-0.414214 - 0.171573i) q^{77} +6.00000i q^{79} +(12.4853 - 5.17157i) q^{80} +(8.24264 - 8.24264i) q^{82} +(-6.12132 - 2.53553i) q^{83} +(-3.65685 - 8.82843i) q^{85} +(11.2426 - 4.65685i) q^{86} +(0.828427 - 0.343146i) q^{88} +(2.65685 - 2.65685i) q^{89} +(2.41421 - 1.00000i) q^{91} +(0.343146 + 0.343146i) q^{92} +16.4853 q^{94} -20.2426 q^{95} -1.51472 q^{97} +7.07107 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 4 q^{5} + 4 q^{7}+O(q^{10}) \) 4 * q - 8 * q^4 + 4 * q^5 + 4 * q^7	\( 4 q - 8 q^{4} + 4 q^{5} + 4 q^{7} + 4 q^{10} + 8 q^{11} + 4 q^{13} + 16 q^{16} - 8 q^{19} - 8 q^{20} + 4 q^{22} - 12 q^{23} + 4 q^{25} + 4 q^{26} - 8 q^{28} + 4 q^{29} - 16 q^{31} - 16 q^{34} - 4 q^{35} + 4 q^{37} + 4 q^{38} - 8 q^{40} + 12 q^{41} + 16 q^{43} - 16 q^{44} + 16 q^{46} - 20 q^{50} - 8 q^{52} - 4 q^{53} - 20 q^{55} + 4 q^{58} + 16 q^{59} + 4 q^{61} - 32 q^{64} + 8 q^{65} - 8 q^{67} - 8 q^{70} + 12 q^{71} + 28 q^{73} - 4 q^{74} + 16 q^{76} + 4 q^{77} + 16 q^{80} + 16 q^{82} - 16 q^{83} + 8 q^{85} + 28 q^{86} - 8 q^{88} - 12 q^{89} + 4 q^{91} + 24 q^{92} + 32 q^{94} - 64 q^{95} - 40 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 + 4 * q^5 + 4 * q^7 + 4 * q^10 + 8 * q^11 + 4 * q^13 + 16 * q^16 - 8 * q^19 - 8 * q^20 + 4 * q^22 - 12 * q^23 + 4 * q^25 + 4 * q^26 - 8 * q^28 + 4 * q^29 - 16 * q^31 - 16 * q^34 - 4 * q^35 + 4 * q^37 + 4 * q^38 - 8 * q^40 + 12 * q^41 + 16 * q^43 - 16 * q^44 + 16 * q^46 - 20 * q^50 - 8 * q^52 - 4 * q^53 - 20 * q^55 + 4 * q^58 + 16 * q^59 + 4 * q^61 - 32 * q^64 + 8 * q^65 - 8 * q^67 - 8 * q^70 + 12 * q^71 + 28 * q^73 - 4 * q^74 + 16 * q^76 + 4 * q^77 + 16 * q^80 + 16 * q^82 - 16 * q^83 + 8 * q^85 + 28 * q^86 - 8 * q^88 - 12 * q^89 + 4 * q^91 + 24 * q^92 + 32 * q^94 - 64 * q^95 - 40 * q^97

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