LMFDB - Embedded newform 1014.2.g.a.437.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.959512576.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 81 $ x^8 + 7*x^4 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.2
Root			$0.819051 - 1.52616i$ of defining polynomial
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.a.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.52616 - 0.819051i) q^{6} +(2.34521 - 2.34521i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.52616 - 0.819051i) q^{6} +(2.34521 - 2.34521i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.50000 + 1.65831i) q^{9} -1.00000i q^{10} +(-2.82843 - 2.82843i) q^{11} +(1.65831 - 0.500000i) q^{12} +3.31662i q^{14} +(-1.52616 - 0.819051i) q^{15} -1.00000 q^{16} -3.31662 q^{17} +(0.595163 - 2.94037i) q^{18} +(-4.69042 - 4.69042i) q^{19} +(0.707107 + 0.707107i) q^{20} +(5.06169 + 2.71648i) q^{21} +4.00000 q^{22} -6.63325 q^{23} +(-0.819051 + 1.52616i) q^{24} +4.00000i q^{25} +(-4.00000 - 3.31662i) q^{27} +(-2.34521 - 2.34521i) q^{28} +(1.65831 - 0.500000i) q^{30} +(-4.69042 - 4.69042i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.27620 - 6.10463i) q^{33} +(2.34521 - 2.34521i) q^{34} +3.31662i q^{35} +(1.65831 + 2.50000i) q^{36} +(-7.03562 + 7.03562i) q^{37} +6.63325 q^{38} -1.00000 q^{40} +(-5.50000 + 1.65831i) q^{42} +7.00000i q^{43} +(-2.82843 + 2.82843i) q^{44} +(0.595163 - 2.94037i) q^{45} +(4.69042 - 4.69042i) q^{46} +(-6.36396 - 6.36396i) q^{47} +(-0.500000 - 1.65831i) q^{48} -4.00000i q^{49} +(-2.82843 - 2.82843i) q^{50} +(-1.65831 - 5.50000i) q^{51} -6.63325i q^{53} +(5.17364 - 0.483219i) q^{54} +4.00000 q^{55} +3.31662 q^{56} +(5.43297 - 10.1234i) q^{57} +(9.89949 + 9.89949i) q^{59} +(-0.819051 + 1.52616i) q^{60} -4.00000 q^{61} +6.63325 q^{62} +(-1.97393 + 9.75211i) q^{63} +1.00000i q^{64} +(2.00000 + 6.63325i) q^{66} +3.31662i q^{68} +(-3.31662 - 11.0000i) q^{69} +(-2.34521 - 2.34521i) q^{70} +(2.12132 - 2.12132i) q^{71} +(-2.94037 - 0.595163i) q^{72} +(4.69042 - 4.69042i) q^{73} -9.94987i q^{74} +(-6.63325 + 2.00000i) q^{75} +(-4.69042 + 4.69042i) q^{76} -13.2665 q^{77} +14.0000 q^{79} +(0.707107 - 0.707107i) q^{80} +(3.50000 - 8.29156i) q^{81} +(-4.24264 + 4.24264i) q^{83} +(2.71648 - 5.06169i) q^{84} +(2.34521 - 2.34521i) q^{85} +(-4.94975 - 4.94975i) q^{86} -4.00000i q^{88} +(1.41421 + 1.41421i) q^{89} +(1.65831 + 2.50000i) q^{90} +6.63325i q^{92} +(5.43297 - 10.1234i) q^{93} +9.00000 q^{94} +6.63325 q^{95} +(1.52616 + 0.819051i) q^{96} +(2.82843 + 2.82843i) q^{98} +(11.7615 + 2.38065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 20 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 20 * q^9	$ 8 q + 4 q^{3} - 20 q^{9} - 8 q^{16} + 32 q^{22} - 32 q^{27} - 8 q^{40} - 44 q^{42} - 4 q^{48} + 32 q^{55} - 32 q^{61} + 16 q^{66} + 112 q^{79} + 28 q^{81} + 72 q^{94}+O(q^{100}) $ 8 * q + 4 * q^3 - 20 * q^9 - 8 * q^16 + 32 * q^22 - 32 * q^27 - 8 * q^40 - 44 * q^42 - 4 * q^48 + 32 * q^55 - 32 * q^61 + 16 * q^66 + 112 * q^79 + 28 * q^81 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	−0.847316	−	0.531089i	$-0.821783\pi$
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i	0.531089	+	0.847316i	$0.321783\pi$
$6$	−1.52616	−	0.819051i	−0.623051	−	0.334376i
$7$	2.34521	−	2.34521i	0.886405	−	0.886405i	−0.107771	−	0.994176i	$-0.534371\pi$
$7$	2.34521	−	2.34521i	0.886405	−	0.886405i	0.994176	+	0.107771i	$0.0343712\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.50000	+	1.65831i	−0.833333	+	0.552771i
$10$		−	1.00000i		−	0.316228i
$11$	−2.82843	−	2.82843i	−0.852803	−	0.852803i	0.137675	−	0.990478i	$-0.456037\pi$
$11$	−2.82843	−	2.82843i	−0.852803	−	0.852803i	−0.990478	+	0.137675i	$0.956037\pi$
$12$	1.65831	−	0.500000i	0.478714	−	0.144338i
$13$		0			0
$13$		0			0
$14$			3.31662i			0.886405i
$15$	−1.52616	−	0.819051i	−0.394052	−	0.211478i
$16$	−1.00000			−0.250000
$17$	−3.31662			−0.804400			−0.402200	−	0.915552i	$-0.631754\pi$
$17$	−3.31662			−0.804400			−0.402200	+	0.915552i	$0.631754\pi$
$18$	0.595163	−	2.94037i	0.140281	−	0.693052i
$19$	−4.69042	−	4.69042i	−1.07606	−	1.07606i	−0.996859	−	0.0791961i	$-0.974765\pi$
$19$	−4.69042	−	4.69042i	−1.07606	−	1.07606i	−0.0791961	−	0.996859i	$-0.525235\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	5.06169	+	2.71648i	1.10455	+	0.592785i
$22$	4.00000			0.852803
$23$	−6.63325			−1.38313			−0.691564	−	0.722315i	$-0.743078\pi$
$23$	−6.63325			−1.38313			−0.691564	+	0.722315i	$0.743078\pi$
$24$	−0.819051	+	1.52616i	−0.167188	+	0.311526i
$25$			4.00000i			0.800000i
$26$		0			0
$27$	−4.00000	−	3.31662i	−0.769800	−	0.638285i
$28$	−2.34521	−	2.34521i	−0.443203	−	0.443203i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	1.65831	−	0.500000i	0.302765	−	0.0912871i
$31$	−4.69042	−	4.69042i	−0.842424	−	0.842424i	0.146750	−	0.989174i	$-0.453119\pi$
$31$	−4.69042	−	4.69042i	−0.842424	−	0.842424i	−0.989174	+	0.146750i	$0.953119\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.27620	−	6.10463i	0.570314	−	1.06268i
$34$	2.34521	−	2.34521i	0.402200	−	0.402200i
$35$			3.31662i			0.560612i
$36$	1.65831	+	2.50000i	0.276385	+	0.416667i
$37$	−7.03562	+	7.03562i	−1.15665	+	1.15665i	−0.171458	+	0.985191i	$0.554848\pi$
$37$	−7.03562	+	7.03562i	−1.15665	+	1.15665i	−0.985191	+	0.171458i	$0.945152\pi$
$38$	6.63325			1.07606
$39$		0			0
$40$	−1.00000			−0.158114
$41$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$41$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$42$	−5.50000	+	1.65831i	−0.848668	+	0.255883i
$43$			7.00000i			1.06749i	0.845645	+	0.533745i	$0.179216\pi$
$43$			7.00000i			1.06749i	−0.845645	+	0.533745i	$0.820784\pi$
$44$	−2.82843	+	2.82843i	−0.426401	+	0.426401i
$45$	0.595163	−	2.94037i	0.0887217	−	0.438325i
$46$	4.69042	−	4.69042i	0.691564	−	0.691564i
$47$	−6.36396	−	6.36396i	−0.928279	−	0.928279i	0.0693157	−	0.997595i	$-0.477918\pi$
$47$	−6.36396	−	6.36396i	−0.928279	−	0.928279i	−0.997595	+	0.0693157i	$0.977918\pi$
$48$	−0.500000	−	1.65831i	−0.0721688	−	0.239357i
$49$		−	4.00000i		−	0.571429i
$50$	−2.82843	−	2.82843i	−0.400000	−	0.400000i
$51$	−1.65831	−	5.50000i	−0.232210	−	0.770154i
$52$		0			0
$53$		−	6.63325i		−	0.911147i	−0.890198	−	0.455573i	$-0.849434\pi$
$53$		−	6.63325i		−	0.911147i	0.890198	−	0.455573i	$-0.150566\pi$
$54$	5.17364	−	0.483219i	0.704043	−	0.0657578i
$55$	4.00000			0.539360
$56$	3.31662			0.443203
$57$	5.43297	−	10.1234i	0.719614	−	1.34087i
$58$		0			0
$59$	9.89949	+	9.89949i	1.28880	+	1.28880i	0.935513	+	0.353291i	$0.114937\pi$
$59$	9.89949	+	9.89949i	1.28880	+	1.28880i	0.353291	+	0.935513i	$0.385063\pi$
$60$	−0.819051	+	1.52616i	−0.105739	+	0.197026i
$61$	−4.00000			−0.512148			−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000			−0.512148			−0.256074	+	0.966657i	$0.582429\pi$
$62$	6.63325			0.842424
$63$	−1.97393	+	9.75211i	−0.248692	+	1.22865i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	2.00000	+	6.63325i	0.246183	+	0.816497i
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$			3.31662i			0.402200i
$69$	−3.31662	−	11.0000i	−0.399275	−	1.32424i
$70$	−2.34521	−	2.34521i	−0.280306	−	0.280306i
$71$	2.12132	−	2.12132i	0.251754	−	0.251754i	−0.569935	−	0.821690i	$-0.693032\pi$
$71$	2.12132	−	2.12132i	0.251754	−	0.251754i	0.821690	+	0.569935i	$0.193032\pi$
$72$	−2.94037	−	0.595163i	−0.346526	−	0.0701406i
$73$	4.69042	−	4.69042i	0.548972	−	0.548972i	−0.377172	−	0.926143i	$-0.623103\pi$
$73$	4.69042	−	4.69042i	0.548972	−	0.548972i	0.926143	+	0.377172i	$0.123103\pi$
$74$		−	9.94987i		−	1.15665i
$75$	−6.63325	+	2.00000i	−0.765942	+	0.230940i
$76$	−4.69042	+	4.69042i	−0.538028	+	0.538028i
$77$	−13.2665			−1.51186
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$		0			0
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$84$	2.71648	−	5.06169i	0.296393	−	0.552276i
$85$	2.34521	−	2.34521i	0.254374	−	0.254374i
$86$	−4.94975	−	4.94975i	−0.533745	−	0.533745i
$87$		0			0
$88$		−	4.00000i		−	0.426401i
$89$	1.41421	+	1.41421i	0.149906	+	0.149906i	0.778076	−	0.628170i	$-0.216196\pi$
$89$	1.41421	+	1.41421i	0.149906	+	0.149906i	−0.628170	+	0.778076i	$0.716196\pi$
$90$	1.65831	+	2.50000i	0.174801	+	0.263523i
$91$		0			0
$92$			6.63325i			0.691564i
$93$	5.43297	−	10.1234i	0.563372	−	1.04975i
$94$	9.00000			0.928279
$95$	6.63325			0.680557
$96$	1.52616	+	0.819051i	0.155763	+	0.0835940i
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	2.82843	+	2.82843i	0.285714	+	0.285714i
$99$	11.7615	+	2.38065i	1.18207	+	0.239265i
$100$	4.00000			0.400000
$101$	13.2665			1.32007			0.660033	−	0.751237i	$-0.270542\pi$
$101$	13.2665			1.32007			0.660033	+	0.751237i	$0.270542\pi$
$102$	5.06169	+	2.71648i	0.501182	+	0.268972i
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$		0			0
$105$	−5.50000	+	1.65831i	−0.536745	+	0.161835i
$106$	4.69042	+	4.69042i	0.455573	+	0.455573i
$107$		−	6.63325i		−	0.641260i	−0.947204	−	0.320630i	$-0.896105\pi$
$107$		−	6.63325i		−	0.641260i	0.947204	−	0.320630i	$-0.103895\pi$
$108$	−3.31662	+	4.00000i	−0.319142	+	0.384900i
$109$	2.34521	+	2.34521i	0.224630	+	0.224630i	0.810445	−	0.585815i	$-0.199225\pi$
$109$	2.34521	+	2.34521i	0.224630	+	0.224630i	−0.585815	+	0.810445i	$0.699225\pi$
$110$	−2.82843	+	2.82843i	−0.269680	+	0.269680i
$111$	−15.1851	−	8.14945i	−1.44130	−	0.773512i
$112$	−2.34521	+	2.34521i	−0.221601	+	0.221601i
$113$			13.2665i			1.24801i	0.781421	+	0.624004i	$0.214495\pi$
$113$			13.2665i			1.24801i	−0.781421	+	0.624004i	$0.785505\pi$
$114$	3.31662	+	11.0000i	0.310630	+	1.03024i
$115$	4.69042	−	4.69042i	0.437384	−	0.437384i
$116$		0			0
$117$		0			0
$118$	−14.0000			−1.28880
$119$	−7.77817	+	7.77817i	−0.713024	+	0.713024i
$120$	−0.500000	−	1.65831i	−0.0456435	−	0.151383i
$121$			5.00000i			0.454545i
$122$	2.82843	−	2.82843i	0.256074	−	0.256074i
$123$		0			0
$124$	−4.69042	+	4.69042i	−0.421212	+	0.421212i
$125$	−6.36396	−	6.36396i	−0.569210	−	0.569210i
$126$	−5.50000	−	8.29156i	−0.489979	−	0.738671i
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−11.6082	+	3.50000i	−1.02204	+	0.308158i
$130$		0			0
$131$		−	16.5831i		−	1.44887i	−0.689341	−	0.724437i	$-0.742100\pi$
$131$		−	16.5831i		−	1.44887i	0.689341	−	0.724437i	$-0.257900\pi$
$132$	−6.10463	−	3.27620i	−0.531340	−	0.285157i
$133$	−22.0000			−1.90764
$134$		0			0
$135$	5.17364	−	0.483219i	0.445276	−	0.0415889i
$136$	−2.34521	−	2.34521i	−0.201100	−	0.201100i
$137$	4.24264	+	4.24264i	0.362473	+	0.362473i	0.864723	−	0.502249i	$-0.167494\pi$
$137$	4.24264	+	4.24264i	0.362473	+	0.362473i	−0.502249	+	0.864723i	$0.667494\pi$
$138$	10.1234	+	5.43297i	0.861760	+	0.462485i
$139$	13.0000			1.10265			0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000			1.10265			0.551323	+	0.834292i	$0.314123\pi$
$140$	3.31662			0.280306
$141$	7.37145	−	13.7354i	0.620788	−	1.15673i
$142$			3.00000i			0.251754i
$143$		0			0
$144$	2.50000	−	1.65831i	0.208333	−	0.138193i
$145$		0			0
$146$			6.63325i			0.548972i
$147$	6.63325	−	2.00000i	0.547101	−	0.164957i
$148$	7.03562	+	7.03562i	0.578325	+	0.578325i
$149$	−4.24264	+	4.24264i	−0.347571	+	0.347571i	−0.859204	−	0.511633i	$-0.829041\pi$
$149$	−4.24264	+	4.24264i	−0.347571	+	0.347571i	0.511633	+	0.859204i	$0.329041\pi$
$150$	3.27620	−	6.10463i	0.267501	−	0.498441i
$151$	−7.03562	+	7.03562i	−0.572551	+	0.572551i	−0.932841	−	0.360290i	$-0.882678\pi$
$151$	−7.03562	+	7.03562i	−0.572551	+	0.572551i	0.360290	+	0.932841i	$0.382678\pi$
$152$		−	6.63325i		−	0.538028i
$153$	8.29156	−	5.50000i	0.670333	−	0.444649i
$154$	9.38083	−	9.38083i	0.755929	−	0.755929i
$155$	6.63325			0.532795
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	−9.89949	+	9.89949i	−0.787562	+	0.787562i
$159$	11.0000	−	3.31662i	0.872357	−	0.263025i
$160$			1.00000i			0.0790569i
$161$	−15.5563	+	15.5563i	−1.22601	+	1.22601i
$162$	3.38815	+	8.33789i	0.266198	+	0.655087i
$163$	−4.69042	+	4.69042i	−0.367382	+	0.367382i	−0.866521	−	0.499140i	$-0.833649\pi$
$163$	−4.69042	+	4.69042i	−0.367382	+	0.367382i	0.499140	+	0.866521i	$0.333649\pi$
$164$		0			0
$165$	2.00000	+	6.63325i	0.155700	+	0.516398i
$166$		−	6.00000i		−	0.465690i
$167$	−8.48528	−	8.48528i	−0.656611	−	0.656611i	0.297966	−	0.954577i	$-0.403692\pi$
$167$	−8.48528	−	8.48528i	−0.656611	−	0.656611i	−0.954577	+	0.297966i	$0.903692\pi$
$168$	1.65831	+	5.50000i	0.127942	+	0.424334i
$169$		0			0
$170$			3.31662i			0.254374i
$171$	19.5042	+	3.94786i	1.49152	+	0.301901i
$172$	7.00000			0.533745
$173$	−6.63325			−0.504317			−0.252158	−	0.967686i	$-0.581140\pi$
$173$	−6.63325			−0.504317			−0.252158	+	0.967686i	$0.581140\pi$
$174$		0			0
$175$	9.38083	+	9.38083i	0.709124	+	0.709124i
$176$	2.82843	+	2.82843i	0.213201	+	0.213201i
$177$	−11.4667	+	21.3662i	−0.861891	+	1.60598i
$178$	−2.00000			−0.149906
$179$	−23.2164			−1.73527			−0.867637	−	0.497199i	$-0.834362\pi$
$179$	−23.2164			−1.73527			−0.867637	+	0.497199i	$0.834362\pi$
$180$	−2.94037	−	0.595163i	−0.219162	−	0.0443608i
$181$		−	10.0000i		−	0.743294i	−0.928374	−	0.371647i	$-0.878793\pi$
$181$		−	10.0000i		−	0.743294i	0.928374	−	0.371647i	$-0.121207\pi$
$182$		0			0
$183$	−2.00000	−	6.63325i	−0.147844	−	0.490344i
$184$	−4.69042	−	4.69042i	−0.345782	−	0.345782i
$185$		−	9.94987i		−	0.731529i
$186$	3.31662	+	11.0000i	0.243187	+	0.806559i
$187$	9.38083	+	9.38083i	0.685994	+	0.685994i
$188$	−6.36396	+	6.36396i	−0.464140	+	0.464140i
$189$	−17.1590	+	1.60266i	−1.24813	+	0.116576i
$190$	−4.69042	+	4.69042i	−0.340279	+	0.340279i
$191$		−	13.2665i		−	0.959930i	−0.877288	−	0.479965i	$-0.840649\pi$
$191$		−	13.2665i		−	0.959930i	0.877288	−	0.479965i	$-0.159351\pi$
$192$	−1.65831	+	0.500000i	−0.119678	+	0.0360844i
$193$	14.0712	−	14.0712i	1.01287	−	1.01287i	0.0129545	−	0.999916i	$-0.495876\pi$
$193$	14.0712	−	14.0712i	1.01287	−	1.01287i	0.999916	−	0.0129545i	$-0.00412365\pi$
$194$		0			0
$195$		0			0
$196$	−4.00000			−0.285714
$197$	−16.2635	+	16.2635i	−1.15872	+	1.15872i	−0.173973	+	0.984750i	$0.555660\pi$
$197$	−16.2635	+	16.2635i	−1.15872	+	1.15872i	−0.984750	+	0.173973i	$0.944340\pi$
$198$	−10.0000	+	6.63325i	−0.710669	+	0.471405i
$199$		−	4.00000i		−	0.283552i	−0.989899	−	0.141776i	$-0.954719\pi$
$199$		−	4.00000i		−	0.283552i	0.989899	−	0.141776i	$-0.0452813\pi$
$200$	−2.82843	+	2.82843i	−0.200000	+	0.200000i
$201$		0			0
$202$	−9.38083	+	9.38083i	−0.660033	+	0.660033i
$203$		0			0
$204$	−5.50000	+	1.65831i	−0.385077	+	0.116105i
$205$		0			0
$206$	4.24264	+	4.24264i	0.295599	+	0.295599i
$207$	16.5831	−	11.0000i	1.15261	−	0.764553i
$208$		0			0
$209$			26.5330i			1.83533i
$210$	2.71648	−	5.06169i	0.187455	−	0.349290i
$211$	1.00000			0.0688428			0.0344214	−	0.999407i	$-0.489041\pi$
$211$	1.00000			0.0688428			0.0344214	+	0.999407i	$0.489041\pi$
$212$	−6.63325			−0.455573
$213$	4.57847	+	2.45715i	0.313712	+	0.168361i
$214$	4.69042	+	4.69042i	0.320630	+	0.320630i
$215$	−4.94975	−	4.94975i	−0.337570	−	0.337570i
$216$	−0.483219	−	5.17364i	−0.0328789	−	0.352021i
$217$	−22.0000			−1.49346
$218$	−3.31662			−0.224630
$219$	10.1234	+	5.43297i	0.684075	+	0.367126i
$220$		−	4.00000i		−	0.269680i
$221$		0			0
$222$	16.5000	−	4.97494i	1.10741	−	0.333896i
$223$	−7.03562	−	7.03562i	−0.471140	−	0.471140i	0.431143	−	0.902283i	$-0.358110\pi$
$223$	−7.03562	−	7.03562i	−0.471140	−	0.471140i	−0.902283	+	0.431143i	$0.858110\pi$
$224$		−	3.31662i		−	0.221601i
$225$	−6.63325	−	10.0000i	−0.442217	−	0.666667i
$226$	−9.38083	−	9.38083i	−0.624004	−	0.624004i
$227$	−14.1421	+	14.1421i	−0.938647	+	0.938647i	−0.998224	−	0.0595772i	$-0.981025\pi$
$227$	−14.1421	+	14.1421i	−0.938647	+	0.938647i	0.0595772	+	0.998224i	$0.481025\pi$
$228$	−10.1234	−	5.43297i	−0.670437	−	0.359807i
$229$	−2.34521	+	2.34521i	−0.154976	+	0.154976i	−0.780336	−	0.625360i	$-0.784952\pi$
$229$	−2.34521	+	2.34521i	−0.154976	+	0.154976i	0.625360	+	0.780336i	$0.284952\pi$
$230$			6.63325i			0.437384i
$231$	−6.63325	−	22.0000i	−0.436436	−	1.44749i
$232$		0			0
$233$	−3.31662			−0.217279			−0.108640	−	0.994081i	$-0.534649\pi$
$233$	−3.31662			−0.217279			−0.108640	+	0.994081i	$0.534649\pi$
$234$		0			0
$235$	9.00000			0.587095
$236$	9.89949	−	9.89949i	0.644402	−	0.644402i
$237$	7.00000	+	23.2164i	0.454699	+	1.50807i
$238$		−	11.0000i		−	0.713024i
$239$	9.19239	−	9.19239i	0.594606	−	0.594606i	−0.344266	−	0.938872i	$-0.611872\pi$
$239$	9.19239	−	9.19239i	0.594606	−	0.594606i	0.938872	+	0.344266i	$0.111872\pi$
$240$	1.52616	+	0.819051i	0.0985130	+	0.0528695i
$241$	−14.0712	+	14.0712i	−0.906409	+	0.906409i	−0.995980	−	0.0895717i	$-0.971450\pi$
$241$	−14.0712	+	14.0712i	−0.906409	+	0.906409i	0.0895717	+	0.995980i	$0.471450\pi$
$242$	−3.53553	−	3.53553i	−0.227273	−	0.227273i
$243$	15.5000	+	1.65831i	0.994325	+	0.106381i
$244$			4.00000i			0.256074i
$245$	2.82843	+	2.82843i	0.180702	+	0.180702i
$246$		0			0
$247$		0			0
$248$		−	6.63325i		−	0.421212i
$249$	−9.15694	−	4.91430i	−0.580298	−	0.311431i
$250$	9.00000			0.569210
$251$	6.63325			0.418687			0.209344	−	0.977842i	$-0.432867\pi$
$251$	6.63325			0.418687			0.209344	+	0.977842i	$0.432867\pi$
$252$	9.75211	+	1.97393i	0.614325	+	0.124346i
$253$	18.7617	+	18.7617i	1.17954	+	1.17954i
$254$	−4.24264	−	4.24264i	−0.266207	−	0.266207i
$255$	5.06169	+	2.71648i	0.316975	+	0.170113i
$256$	1.00000			0.0625000
$257$	3.31662			0.206885			0.103443	−	0.994635i	$-0.467014\pi$
$257$	3.31662			0.206885			0.103443	+	0.994635i	$0.467014\pi$
$258$	5.73335	−	10.6831i	0.356943	−	0.665101i
$259$			33.0000i			2.05052i
$260$		0			0
$261$		0			0
$262$	11.7260	+	11.7260i	0.724437	+	0.724437i
$263$			13.2665i			0.818047i	0.912524	+	0.409024i	$0.134131\pi$
$263$			13.2665i			0.818047i	−0.912524	+	0.409024i	$0.865869\pi$
$264$	6.63325	−	2.00000i	0.408248	−	0.123091i
$265$	4.69042	+	4.69042i	0.288130	+	0.288130i
$266$	15.5563	−	15.5563i	0.953821	−	0.953821i
$267$	−1.63810	+	3.05231i	−0.100250	+	0.186799i
$268$		0			0
$269$			13.2665i			0.808873i	0.914566	+	0.404436i	$0.132532\pi$
$269$			13.2665i			0.808873i	−0.914566	+	0.404436i	$0.867468\pi$
$270$	−3.31662	+	4.00000i	−0.201843	+	0.243432i
$271$	7.03562	−	7.03562i	0.427384	−	0.427384i	−0.460353	−	0.887736i	$-0.652277\pi$
$271$	7.03562	−	7.03562i	0.427384	−	0.427384i	0.887736	+	0.460353i	$0.152277\pi$
$272$	3.31662			0.201100
$273$		0			0
$274$	−6.00000			−0.362473
$275$	11.3137	−	11.3137i	0.682242	−	0.682242i
$276$	−11.0000	+	3.31662i	−0.662122	+	0.199637i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	−9.19239	+	9.19239i	−0.551323	+	0.551323i
$279$	19.5042	+	3.94786i	1.16769	+	0.236352i
$280$	−2.34521	+	2.34521i	−0.140153	+	0.140153i
$281$	−12.7279	−	12.7279i	−0.759284	−	0.759284i	0.216908	−	0.976192i	$-0.430403\pi$
$281$	−12.7279	−	12.7279i	−0.759284	−	0.759284i	−0.976192	+	0.216908i	$0.930403\pi$
$282$	4.50000	+	14.9248i	0.267971	+	0.888760i
$283$			28.0000i			1.66443i	0.554455	+	0.832214i	$0.312927\pi$
$283$			28.0000i			1.66443i	−0.554455	+	0.832214i	$0.687073\pi$
$284$	−2.12132	−	2.12132i	−0.125877	−	0.125877i
$285$	3.31662	+	11.0000i	0.196460	+	0.651584i
$286$		0			0
$287$		0			0
$288$	−0.595163	+	2.94037i	−0.0350703	+	0.173263i
$289$	−6.00000			−0.352941
$290$		0			0
$291$		0			0
$292$	−4.69042	−	4.69042i	−0.274486	−	0.274486i
$293$	13.4350	+	13.4350i	0.784883	+	0.784883i	0.980650	−	0.195768i	$-0.0627198\pi$
$293$	13.4350	+	13.4350i	0.784883	+	0.784883i	−0.195768	+	0.980650i	$0.562720\pi$
$294$	−3.27620	+	6.10463i	−0.191072	+	0.356029i
$295$	−14.0000			−0.815112
$296$	−9.94987			−0.578325
$297$	1.93288	+	20.6945i	0.112157	+	1.20082i
$298$		−	6.00000i		−	0.347571i
$299$		0			0
$300$	2.00000	+	6.63325i	0.115470	+	0.382971i
$301$	16.4165	+	16.4165i	0.946229	+	0.946229i
$302$		−	9.94987i		−	0.572551i
$303$	6.63325	+	22.0000i	0.381070	+	1.26387i
$304$	4.69042	+	4.69042i	0.269014	+	0.269014i
$305$	2.82843	−	2.82843i	0.161955	−	0.161955i
$306$	−1.97393	+	9.75211i	−0.112842	+	0.557491i
$307$	−4.69042	+	4.69042i	−0.267696	+	0.267696i	−0.828171	−	0.560475i	$-0.810619\pi$
$307$	−4.69042	+	4.69042i	−0.267696	+	0.267696i	0.560475	+	0.828171i	$0.310619\pi$
$308$			13.2665i			0.755929i
$309$	9.94987	−	3.00000i	0.566029	−	0.170664i
$310$	−4.69042	+	4.69042i	−0.266398	+	0.266398i
$311$	19.8997			1.12841			0.564206	−	0.825634i	$-0.309183\pi$
$311$	19.8997			1.12841			0.564206	+	0.825634i	$0.309183\pi$
$312$		0			0
$313$	−21.0000			−1.18699			−0.593495	−	0.804838i	$-0.702252\pi$
$313$	−21.0000			−1.18699			−0.593495	+	0.804838i	$0.702252\pi$
$314$	−1.41421	+	1.41421i	−0.0798087	+	0.0798087i
$315$	−5.50000	−	8.29156i	−0.309890	−	0.467177i
$316$		−	14.0000i		−	0.787562i
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	−0.666276	−	0.745706i	$-0.732113\pi$
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	0.745706	+	0.666276i	$0.232113\pi$
$318$	−5.43297	+	10.1234i	−0.304666	+	0.567691i
$319$		0			0
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	11.0000	−	3.31662i	0.613960	−	0.185116i
$322$		−	22.0000i		−	1.22601i
$323$	15.5563	+	15.5563i	0.865578	+	0.865578i
$324$	−8.29156	−	3.50000i	−0.460642	−	0.194444i
$325$		0			0
$326$		−	6.63325i		−	0.367382i
$327$	−2.71648	+	5.06169i	−0.150222	+	0.279912i
$328$		0			0
$329$	−29.8496			−1.64566
$330$	−6.10463	−	3.27620i	−0.336049	−	0.180349i
$331$	−4.69042	−	4.69042i	−0.257809	−	0.257809i	0.566354	−	0.824162i	$-0.308354\pi$
$331$	−4.69042	−	4.69042i	−0.257809	−	0.257809i	−0.824162	+	0.566354i	$0.808354\pi$
$332$	4.24264	+	4.24264i	0.232845	+	0.232845i
$333$	5.92180	−	29.2563i	0.324512	−	1.60324i
$334$	12.0000			0.656611
$335$		0			0
$336$	−5.06169	−	2.71648i	−0.276138	−	0.148196i
$337$		−	13.0000i		−	0.708155i	−0.935216	−	0.354078i	$-0.884795\pi$
$337$		−	13.0000i		−	0.708155i	0.935216	−	0.354078i	$-0.115205\pi$
$338$		0			0
$339$	−22.0000	+	6.63325i	−1.19488	+	0.360269i
$340$	−2.34521	−	2.34521i	−0.127187	−	0.127187i
$341$			26.5330i			1.43684i
$342$	−16.5831	+	11.0000i	−0.896713	+	0.594812i
$343$	7.03562	+	7.03562i	0.379888	+	0.379888i
$344$	−4.94975	+	4.94975i	−0.266872	+	0.266872i
$345$	10.1234	+	5.43297i	0.545025	+	0.292501i
$346$	4.69042	−	4.69042i	0.252158	−	0.252158i
$347$		−	23.2164i		−	1.24632i	−0.782094	−	0.623160i	$-0.785848\pi$
$347$		−	23.2164i		−	1.24632i	0.782094	−	0.623160i	$-0.214152\pi$
$348$		0			0
$349$	−11.7260	+	11.7260i	−0.627680	+	0.627680i	−0.947484	−	0.319803i	$-0.896383\pi$
$349$	−11.7260	+	11.7260i	−0.627680	+	0.627680i	0.319803	+	0.947484i	$0.396383\pi$
$350$	−13.2665			−0.709124
$351$		0			0
$352$	−4.00000			−0.213201
$353$	9.89949	−	9.89949i	0.526897	−	0.526897i	−0.392749	−	0.919646i	$-0.628476\pi$
$353$	9.89949	−	9.89949i	0.526897	−	0.526897i	0.919646	+	0.392749i	$0.128476\pi$
$354$	−7.00000	−	23.2164i	−0.372046	−	1.23394i
$355$			3.00000i			0.159223i
$356$	1.41421	−	1.41421i	0.0749532	−	0.0749532i
$357$	−16.7877	−	9.00956i	−0.888501	−	0.476836i
$358$	16.4165	−	16.4165i	0.867637	−	0.867637i
$359$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$359$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$360$	2.50000	−	1.65831i	0.131762	−	0.0874007i
$361$			25.0000i			1.31579i
$362$	7.07107	+	7.07107i	0.371647	+	0.371647i
$363$	−8.29156	+	2.50000i	−0.435194	+	0.131216i
$364$		0			0
$365$			6.63325i			0.347200i
$366$	6.10463	+	3.27620i	0.319094	+	0.171250i
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$	6.63325			0.345782
$369$		0			0
$370$	7.03562	+	7.03562i	0.365765	+	0.365765i
$371$	−15.5563	−	15.5563i	−0.807645	−	0.807645i
$372$	−10.1234	−	5.43297i	−0.524873	−	0.281686i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	−13.2665			−0.685994
$375$	7.37145	−	13.7354i	0.380660	−	0.709294i
$376$		−	9.00000i		−	0.464140i
$377$		0			0
$378$	11.0000	−	13.2665i	0.565779	−	0.682355i
$379$	−4.69042	−	4.69042i	−0.240930	−	0.240930i	0.576305	−	0.817235i	$-0.304494\pi$
$379$	−4.69042	−	4.69042i	−0.240930	−	0.240930i	−0.817235	+	0.576305i	$0.804494\pi$
$380$		−	6.63325i		−	0.340279i
$381$	−9.94987	+	3.00000i	−0.509748	+	0.153695i
$382$	9.38083	+	9.38083i	0.479965	+	0.479965i
$383$	14.8492	−	14.8492i	0.758761	−	0.758761i	−0.217336	−	0.976097i	$-0.569737\pi$
$383$	14.8492	−	14.8492i	0.758761	−	0.758761i	0.976097	+	0.217336i	$0.0697367\pi$
$384$	0.819051	−	1.52616i	0.0417970	−	0.0778814i
$385$	9.38083	−	9.38083i	0.478091	−	0.478091i
$386$			19.8997i			1.01287i
$387$	−11.6082	−	17.5000i	−0.590077	−	0.889575i
$388$		0			0
$389$	6.63325			0.336319			0.168160	−	0.985760i	$-0.446218\pi$
$389$	6.63325			0.336319			0.168160	+	0.985760i	$0.446218\pi$
$390$		0			0
$391$	22.0000			1.11259
$392$	2.82843	−	2.82843i	0.142857	−	0.142857i
$393$	27.5000	−	8.29156i	1.38719	−	0.418254i
$394$		−	23.0000i		−	1.15872i
$395$	−9.89949	+	9.89949i	−0.498098	+	0.498098i
$396$	2.38065	−	11.7615i	0.119632	−	0.591037i
$397$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$397$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$398$	2.82843	+	2.82843i	0.141776	+	0.141776i
$399$	−11.0000	−	36.4829i	−0.550689	−	1.82643i
$400$		−	4.00000i		−	0.200000i
$401$	−24.0416	−	24.0416i	−1.20058	−	1.20058i	−0.973990	−	0.226592i	$-0.927242\pi$
$401$	−24.0416	−	24.0416i	−1.20058	−	1.20058i	−0.226592	−	0.973990i	$-0.572758\pi$
$402$		0			0
$403$		0			0
$404$		−	13.2665i		−	0.660033i
$405$	3.38815	+	8.33789i	0.168358	+	0.414313i
$406$		0			0
$407$	39.7995			1.97279
$408$	2.71648	−	5.06169i	0.134486	−	0.250591i
$409$	−23.4521	−	23.4521i	−1.15963	−	1.15963i	−0.984555	−	0.175076i	$-0.943983\pi$
$409$	−23.4521	−	23.4521i	−1.15963	−	1.15963i	−0.175076	−	0.984555i	$-0.556017\pi$
$410$		0			0
$411$	−4.91430	+	9.15694i	−0.242405	+	0.451679i
$412$	−6.00000			−0.295599
$413$	46.4327			2.28481
$414$	−3.94786	+	19.5042i	−0.194027	+	0.958580i
$415$		−	6.00000i		−	0.294528i
$416$		0			0
$417$	6.50000	+	21.5581i	0.318306	+	1.05570i
$418$	−18.7617	−	18.7617i	−0.917663	−	0.917663i
$419$		−	3.31662i		−	0.162028i	−0.996713	−	0.0810139i	$-0.974184\pi$
$419$		−	3.31662i		−	0.162028i	0.996713	−	0.0810139i	$-0.0258158\pi$
$420$	1.65831	+	5.50000i	0.0809174	+	0.268373i
$421$	−21.1069	−	21.1069i	−1.02869	−	1.02869i	−0.999576	−	0.0291097i	$-0.990733\pi$
$421$	−21.1069	−	21.1069i	−1.02869	−	1.02869i	−0.0291097	−	0.999576i	$-0.509267\pi$
$422$	−0.707107	+	0.707107i	−0.0344214	+	0.0344214i
$423$	26.4633	+	5.35647i	1.28669	+	0.260440i
$424$	4.69042	−	4.69042i	0.227787	−	0.227787i
$425$		−	13.2665i		−	0.643520i
$426$	−4.97494	+	1.50000i	−0.241036	+	0.0726752i
$427$	−9.38083	+	9.38083i	−0.453970	+	0.453970i
$428$	−6.63325			−0.320630
$429$		0			0
$430$	7.00000			0.337570
$431$	2.12132	−	2.12132i	0.102180	−	0.102180i	−0.654168	−	0.756349i	$-0.726981\pi$
$431$	2.12132	−	2.12132i	0.102180	−	0.102180i	0.756349	+	0.654168i	$0.226981\pi$
$432$	4.00000	+	3.31662i	0.192450	+	0.159571i
$433$			5.00000i			0.240285i	0.992757	+	0.120142i	$0.0383351\pi$
$433$			5.00000i			0.240285i	−0.992757	+	0.120142i	$0.961665\pi$
$434$	15.5563	−	15.5563i	0.746729	−	0.746729i
$435$		0			0
$436$	2.34521	−	2.34521i	0.112315	−	0.112315i
$437$	31.1127	+	31.1127i	1.48832	+	1.48832i
$438$	−11.0000	+	3.31662i	−0.525600	+	0.158474i
$439$		−	26.0000i		−	1.24091i	−0.784241	−	0.620456i	$-0.786947\pi$
$439$		−	26.0000i		−	1.24091i	0.784241	−	0.620456i	$-0.213053\pi$
$440$	2.82843	+	2.82843i	0.134840	+	0.134840i
$441$	6.63325	+	10.0000i	0.315869	+	0.476190i
$442$		0			0
$443$		−	16.5831i		−	0.787888i	−0.919134	−	0.393944i	$-0.871110\pi$
$443$		−	16.5831i		−	0.787888i	0.919134	−	0.393944i	$-0.128890\pi$
$444$	−8.14945	+	15.1851i	−0.386756	+	0.720652i
$445$	−2.00000			−0.0948091
$446$	9.94987			0.471140
$447$	−9.15694	−	4.91430i	−0.433109	−	0.232439i
$448$	2.34521	+	2.34521i	0.110801	+	0.110801i
$449$	−22.6274	−	22.6274i	−1.06785	−	1.06785i	−0.997524	−	0.0703301i	$-0.977595\pi$
$449$	−22.6274	−	22.6274i	−1.06785	−	1.06785i	−0.0703301	−	0.997524i	$-0.522405\pi$
$450$	11.7615	+	2.38065i	0.554442	+	0.112225i
$451$		0			0
$452$	13.2665			0.624004
$453$	−15.1851	−	8.14945i	−0.713457	−	0.382895i
$454$		−	20.0000i		−	0.938647i
$455$		0			0
$456$	11.0000	−	3.31662i	0.515122	−	0.155315i
$457$	−4.69042	−	4.69042i	−0.219408	−	0.219408i	0.588841	−	0.808249i	$-0.299585\pi$
$457$	−4.69042	−	4.69042i	−0.219408	−	0.219408i	−0.808249	+	0.588841i	$0.799585\pi$
$458$		−	3.31662i		−	0.154976i
$459$	13.2665	+	11.0000i	0.619227	+	0.513436i
$460$	−4.69042	−	4.69042i	−0.218692	−	0.218692i
$461$	7.77817	−	7.77817i	0.362266	−	0.362266i	−0.502381	−	0.864646i	$-0.667542\pi$
$461$	7.77817	−	7.77817i	0.362266	−	0.362266i	0.864646	+	0.502381i	$0.167542\pi$
$462$	20.2468	+	10.8659i	0.941965	+	0.505529i
$463$	14.0712	−	14.0712i	0.653946	−	0.653946i	−0.299995	−	0.953941i	$-0.596985\pi$
$463$	14.0712	−	14.0712i	0.653946	−	0.653946i	0.953941	+	0.299995i	$0.0969849\pi$
$464$		0			0
$465$	3.31662	+	11.0000i	0.153805	+	0.510113i
$466$	2.34521	−	2.34521i	0.108640	−	0.108640i
$467$	−6.63325			−0.306950			−0.153475	−	0.988153i	$-0.549046\pi$
$467$	−6.63325			−0.306950			−0.153475	+	0.988153i	$0.549046\pi$
$468$		0			0
$469$		0			0
$470$	−6.36396	+	6.36396i	−0.293548	+	0.293548i
$471$	1.00000	+	3.31662i	0.0460776	+	0.152822i
$472$			14.0000i			0.644402i
$473$	19.7990	−	19.7990i	0.910359	−	0.910359i
$474$	−21.3662	−	11.4667i	−0.981382	−	0.526683i
$475$	18.7617	−	18.7617i	0.860844	−	0.860844i
$476$	7.77817	+	7.77817i	0.356512	+	0.356512i
$477$	11.0000	+	16.5831i	0.503655	+	0.759289i
$478$			13.0000i			0.594606i
$479$	−3.53553	−	3.53553i	−0.161543	−	0.161543i	0.621707	−	0.783250i	$-0.286439\pi$
$479$	−3.53553	−	3.53553i	−0.161543	−	0.161543i	−0.783250	+	0.621707i	$0.786439\pi$
$480$	−1.65831	+	0.500000i	−0.0756913	+	0.0228218i
$481$		0			0
$482$		−	19.8997i		−	0.906409i
$483$	−33.5755	−	18.0191i	−1.52774	−	0.819898i
$484$	5.00000			0.227273
$485$		0			0
$486$	−12.1328	+	9.78755i	−0.550353	+	0.443972i
$487$	−23.4521	−	23.4521i	−1.06272	−	1.06272i	−0.997897	−	0.0648180i	$-0.979353\pi$
$487$	−23.4521	−	23.4521i	−1.06272	−	1.06272i	−0.0648180	−	0.997897i	$-0.520647\pi$
$488$	−2.82843	−	2.82843i	−0.128037	−	0.128037i
$489$	−10.1234	−	5.43297i	−0.457795	−	0.245687i
$490$	−4.00000			−0.180702
$491$	9.94987			0.449032			0.224516	−	0.974470i	$-0.427920\pi$
$491$	9.94987			0.449032			0.224516	+	0.974470i	$0.427920\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−10.0000	+	6.63325i	−0.449467	+	0.298142i
$496$	4.69042	+	4.69042i	0.210606	+	0.210606i
$497$		−	9.94987i		−	0.446313i
$498$	9.94987	−	3.00000i	0.445865	−	0.134433i
$499$	−28.1425	−	28.1425i	−1.25983	−	1.25983i	−0.951173	−	0.308658i	$-0.900120\pi$
$499$	−28.1425	−	28.1425i	−1.25983	−	1.25983i	−0.308658	−	0.951173i	$-0.599880\pi$
$500$	−6.36396	+	6.36396i	−0.284605	+	0.284605i
$501$	9.82861	−	18.3139i	0.439110	−	0.818204i
$502$	−4.69042	+	4.69042i	−0.209344	+	0.209344i
$503$		−	33.1662i		−	1.47881i	−0.673261	−	0.739405i	$-0.735107\pi$
$503$		−	33.1662i		−	1.47881i	0.673261	−	0.739405i	$-0.264893\pi$
$504$	−8.29156	+	5.50000i	−0.369336	+	0.244989i
$505$	−9.38083	+	9.38083i	−0.417442	+	0.417442i
$506$	−26.5330			−1.17954
$507$		0			0
$508$	6.00000			0.266207
$509$	12.7279	−	12.7279i	0.564155	−	0.564155i	−0.366330	−	0.930485i	$-0.619386\pi$
$509$	12.7279	−	12.7279i	0.564155	−	0.564155i	0.930485	+	0.366330i	$0.119386\pi$
$510$	−5.50000	+	1.65831i	−0.243544	+	0.0734313i
$511$		−	22.0000i		−	0.973223i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.20531	+	34.3180i	0.141518	+	1.51518i
$514$	−2.34521	+	2.34521i	−0.103443	+	0.103443i
$515$	4.24264	+	4.24264i	0.186953	+	0.186953i
$516$	3.50000	+	11.6082i	0.154079	+	0.511022i
$517$			36.0000i			1.58328i
$518$	−23.3345	−	23.3345i	−1.02526	−	1.02526i
$519$	−3.31662	−	11.0000i	−0.145584	−	0.482846i
$520$		0			0
$521$			29.8496i			1.30774i	0.756609	+	0.653868i	$0.226855\pi$
$521$			29.8496i			1.30774i	−0.756609	+	0.653868i	$0.773145\pi$
$522$		0			0
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$	−16.5831			−0.724437
$525$	−10.8659	+	20.2468i	−0.474228	+	0.883641i
$526$	−9.38083	−	9.38083i	−0.409024	−	0.409024i
$527$	15.5563	+	15.5563i	0.677645	+	0.677645i
$528$	−3.27620	+	6.10463i	−0.142578	+	0.265670i
$529$	21.0000			0.913043
$530$	−6.63325			−0.288130
$531$	−41.1652	−	8.33228i	−1.78642	−	0.361590i
$532$			22.0000i			0.953821i
$533$		0			0
$534$	−1.00000	−	3.31662i	−0.0432742	−	0.143524i
$535$	4.69042	+	4.69042i	0.202784	+	0.202784i
$536$		0			0
$537$	−11.6082	−	38.5000i	−0.500930	−	1.66140i
$538$	−9.38083	−	9.38083i	−0.404436	−	0.404436i
$539$	−11.3137	+	11.3137i	−0.487316	+	0.487316i
$540$	−0.483219	−	5.17364i	−0.0207944	−	0.222638i
$541$	−21.1069	+	21.1069i	−0.907455	+	0.907455i	−0.996066	−	0.0886110i	$-0.971757\pi$
$541$	−21.1069	+	21.1069i	−0.907455	+	0.907455i	0.0886110	+	0.996066i	$0.471757\pi$
$542$			9.94987i			0.427384i
$543$	16.5831	−	5.00000i	0.711650	−	0.214571i
$544$	−2.34521	+	2.34521i	−0.100550	+	0.100550i
$545$	−3.31662			−0.142069
$546$		0			0
$547$	−27.0000			−1.15444			−0.577218	−	0.816590i	$-0.695862\pi$
$547$	−27.0000			−1.15444			−0.577218	+	0.816590i	$0.695862\pi$
$548$	4.24264	−	4.24264i	0.181237	−	0.181237i
$549$	10.0000	−	6.63325i	0.426790	−	0.283100i
$550$			16.0000i			0.682242i
$551$		0			0
$552$	5.43297	−	10.1234i	0.231242	−	0.430880i
$553$	32.8329	−	32.8329i	1.39620	−	1.39620i
$554$		0			0
$555$	16.5000	−	4.97494i	0.700386	−	0.211174i
$556$		−	13.0000i		−	0.551323i
$557$	21.9203	+	21.9203i	0.928793	+	0.928793i	0.997628	−	0.0688347i	$-0.0219281\pi$
$557$	21.9203	+	21.9203i	0.928793	+	0.928793i	−0.0688347	+	0.997628i	$0.521928\pi$
$558$	−16.5831	+	11.0000i	−0.702020	+	0.465667i
$559$		0			0
$560$		−	3.31662i		−	0.140153i
$561$	−10.8659	+	20.2468i	−0.458760	+	0.854819i
$562$	18.0000			0.759284
$563$	23.2164			0.978453			0.489227	−	0.872157i	$-0.337279\pi$
$563$	23.2164			0.978453			0.489227	+	0.872157i	$0.337279\pi$
$564$	−13.7354	−	7.37145i	−0.578365	−	0.310394i
$565$	−9.38083	−	9.38083i	−0.394655	−	0.394655i
$566$	−19.7990	−	19.7990i	−0.832214	−	0.832214i
$567$	−11.2372	−	27.6537i	−0.471918	−	1.16134i
$568$	3.00000			0.125877
$569$	−23.2164			−0.973281			−0.486641	−	0.873602i	$-0.661778\pi$
$569$	−23.2164			−0.973281			−0.486641	+	0.873602i	$0.661778\pi$
$570$	−10.1234	−	5.43297i	−0.424022	−	0.227562i
$571$			33.0000i			1.38101i	0.723329	+	0.690504i	$0.242611\pi$
$571$			33.0000i			1.38101i	−0.723329	+	0.690504i	$0.757389\pi$
$572$		0			0
$573$	22.0000	−	6.63325i	0.919063	−	0.277108i
$574$		0			0
$575$		−	26.5330i		−	1.10650i
$576$	−1.65831	−	2.50000i	−0.0690963	−	0.104167i
$577$	4.69042	+	4.69042i	0.195265	+	0.195265i	0.797966	−	0.602702i	$-0.205909\pi$
$577$	4.69042	+	4.69042i	0.195265	+	0.195265i	−0.602702	+	0.797966i	$0.705909\pi$
$578$	4.24264	−	4.24264i	0.176471	−	0.176471i
$579$	30.3701	+	16.2989i	1.26214	+	0.677359i
$580$		0			0
$581$			19.8997i			0.825581i
$582$		0			0
$583$	−18.7617	+	18.7617i	−0.777029	+	0.777029i
$584$	6.63325			0.274486
$585$		0			0
$586$	−19.0000			−0.784883
$587$	−12.7279	+	12.7279i	−0.525338	+	0.525338i	−0.919179	−	0.393841i	$-0.871146\pi$
$587$	−12.7279	+	12.7279i	−0.525338	+	0.525338i	0.393841	+	0.919179i	$0.371146\pi$
$588$	−2.00000	−	6.63325i	−0.0824786	−	0.273551i
$589$			44.0000i			1.81299i
$590$	9.89949	−	9.89949i	0.407556	−	0.407556i
$591$	−35.1016	−	18.8382i	−1.44389	−	0.774898i
$592$	7.03562	−	7.03562i	0.289162	−	0.289162i
$593$	22.6274	+	22.6274i	0.929197	+	0.929197i	0.997654	−	0.0684574i	$-0.0218077\pi$
$593$	22.6274	+	22.6274i	0.929197	+	0.929197i	−0.0684574	+	0.997654i	$0.521808\pi$
$594$	−16.0000	−	13.2665i	−0.656488	−	0.544331i
$595$		−	11.0000i		−	0.450956i
$596$	4.24264	+	4.24264i	0.173785	+	0.173785i
$597$	6.63325	−	2.00000i	0.271481	−	0.0818546i
$598$		0			0
$599$			33.1662i			1.35514i	0.735460	+	0.677568i	$0.236966\pi$
$599$			33.1662i			1.35514i	−0.735460	+	0.677568i	$0.763034\pi$
$600$	−6.10463	−	3.27620i	−0.249220	−	0.133750i
$601$	−19.0000			−0.775026			−0.387513	−	0.921864i	$-0.626666\pi$
$601$	−19.0000			−0.775026			−0.387513	+	0.921864i	$0.626666\pi$
$602$	−23.2164			−0.946229
$603$		0			0
$604$	7.03562	+	7.03562i	0.286275	+	0.286275i
$605$	−3.53553	−	3.53553i	−0.143740	−	0.143740i
$606$	−20.2468	−	10.8659i	−0.822469	−	0.441398i
$607$	10.0000			0.405887			0.202944	−	0.979190i	$-0.434949\pi$
$607$	10.0000			0.405887			0.202944	+	0.979190i	$0.434949\pi$
$608$	−6.63325			−0.269014
$609$		0			0
$610$			4.00000i			0.161955i
$611$		0			0
$612$	−5.50000	−	8.29156i	−0.222324	−	0.335167i
$613$	−28.1425	−	28.1425i	−1.13666	−	1.13666i	−0.989044	−	0.147621i	$-0.952839\pi$
$613$	−28.1425	−	28.1425i	−1.13666	−	1.13666i	−0.147621	−	0.989044i	$-0.547161\pi$
$614$		−	6.63325i		−	0.267696i
$615$		0			0
$616$	−9.38083	−	9.38083i	−0.377964	−	0.377964i
$617$	28.2843	−	28.2843i	1.13868	−	1.13868i	0.149995	−	0.988687i	$-0.452074\pi$
$617$	28.2843	−	28.2843i	1.13868	−	1.13868i	0.988687	−	0.149995i	$-0.0479258\pi$
$618$	−4.91430	+	9.15694i	−0.197682	+	0.368346i
$619$	9.38083	−	9.38083i	0.377047	−	0.377047i	−0.492988	−	0.870036i	$-0.664096\pi$
$619$	9.38083	−	9.38083i	0.377047	−	0.377047i	0.870036	+	0.492988i	$0.164096\pi$
$620$		−	6.63325i		−	0.266398i
$621$	26.5330	+	22.0000i	1.06473	+	0.882830i
$622$	−14.0712	+	14.0712i	−0.564206	+	0.564206i
$623$	6.63325			0.265756
$624$		0			0
$625$	−11.0000			−0.440000
$626$	14.8492	−	14.8492i	0.593495	−	0.593495i
$627$	−44.0000	+	13.2665i	−1.75719	+	0.529813i
$628$		−	2.00000i		−	0.0798087i
$629$	23.3345	−	23.3345i	0.930408	−	0.930408i
$630$	9.75211	+	1.97393i	0.388533	+	0.0786433i
$631$	−7.03562	+	7.03562i	−0.280084	+	0.280084i	−0.833142	−	0.553059i	$-0.813461\pi$
$631$	−7.03562	+	7.03562i	−0.280084	+	0.280084i	0.553059	+	0.833142i	$0.313461\pi$
$632$	9.89949	+	9.89949i	0.393781	+	0.393781i
$633$	0.500000	+	1.65831i	0.0198732	+	0.0659120i
$634$			2.00000i			0.0794301i
$635$	−4.24264	−	4.24264i	−0.168364	−	0.168364i
$636$	−3.31662	−	11.0000i	−0.131513	−	0.436178i
$637$		0			0
$638$		0			0
$639$	−1.78549	+	8.82111i	−0.0706329	+	0.348958i
$640$	1.00000			0.0395285
$641$	−39.7995			−1.57199			−0.785993	−	0.618236i	$-0.787848\pi$
$641$	−39.7995			−1.57199			−0.785993	+	0.618236i	$0.787848\pi$
$642$	−5.43297	+	10.1234i	−0.214422	+	0.399538i
$643$	28.1425	+	28.1425i	1.10983	+	1.10983i	0.993172	+	0.116660i	$0.0372187\pi$
$643$	28.1425	+	28.1425i	1.10983	+	1.10983i	0.116660	+	0.993172i	$0.462781\pi$
$644$	15.5563	+	15.5563i	0.613006	+	0.613006i
$645$	5.73335	−	10.6831i	0.225751	−	0.420647i
$646$	−22.0000			−0.865578
$647$	−6.63325			−0.260780			−0.130390	−	0.991463i	$-0.541623\pi$
$647$	−6.63325			−0.260780			−0.130390	+	0.991463i	$0.541623\pi$
$648$	8.33789	−	3.38815i	0.327543	−	0.133099i
$649$		−	56.0000i		−	2.19819i
$650$		0			0
$651$	−11.0000	−	36.4829i	−0.431124	−	1.42988i
$652$	4.69042	+	4.69042i	0.183691	+	0.183691i
$653$			39.7995i			1.55747i	0.627350	+	0.778737i	$0.284140\pi$
$653$			39.7995i			1.55747i	−0.627350	+	0.778737i	$0.715860\pi$
$654$	−1.65831	−	5.50000i	−0.0648451	−	0.215067i
$655$	11.7260	+	11.7260i	0.458174	+	0.458174i
$656$		0			0
$657$	−3.94786	+	19.5042i	−0.154021	+	0.760932i
$658$	21.1069	−	21.1069i	0.822831	−	0.822831i
$659$			19.8997i			0.775184i	0.921831	+	0.387592i	$0.126693\pi$
$659$			19.8997i			0.775184i	−0.921831	+	0.387592i	$0.873307\pi$
$660$	6.63325	−	2.00000i	0.258199	−	0.0778499i
$661$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$661$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$662$	6.63325			0.257809
$663$		0			0
$664$	−6.00000			−0.232845
$665$	15.5563	−	15.5563i	0.603249	−	0.603249i
$666$	16.5000	+	24.8747i	0.639362	+	0.963875i
$667$		0			0
$668$	−8.48528	+	8.48528i	−0.328305	+	0.328305i
$669$	8.14945	−	15.1851i	0.315076	−	0.587089i
$670$		0			0
$671$	11.3137	+	11.3137i	0.436761	+	0.436761i
$672$	5.50000	−	1.65831i	0.212167	−	0.0639708i
$673$		−	41.0000i		−	1.58043i	−0.612827	−	0.790217i	$-0.709968\pi$
$673$		−	41.0000i		−	1.58043i	0.612827	−	0.790217i	$-0.290032\pi$
$674$	9.19239	+	9.19239i	0.354078	+	0.354078i
$675$	13.2665	−	16.0000i	0.510628	−	0.615840i
$676$		0			0
$677$		−	19.8997i		−	0.764809i	−0.923995	−	0.382405i	$-0.875096\pi$
$677$		−	19.8997i		−	0.764809i	0.923995	−	0.382405i	$-0.124904\pi$
$678$	10.8659	−	20.2468i	0.417304	−	0.777572i
$679$		0			0
$680$	3.31662			0.127187
$681$	−30.5231	−	16.3810i	−1.16965	−	0.627722i
$682$	−18.7617	−	18.7617i	−0.718421	−	0.718421i
$683$	−18.3848	−	18.3848i	−0.703474	−	0.703474i	0.261681	−	0.965155i	$-0.415723\pi$
$683$	−18.3848	−	18.3848i	−0.703474	−	0.703474i	−0.965155	+	0.261681i	$0.915723\pi$
$684$	3.94786	−	19.5042i	0.150950	−	0.745762i
$685$	−6.00000			−0.229248
$686$	−9.94987			−0.379888
$687$	−5.06169	−	2.71648i	−0.193116	−	0.103640i
$688$		−	7.00000i		−	0.266872i
$689$		0			0
$690$	−11.0000	+	3.31662i	−0.418763	+	0.126262i
$691$	28.1425	+	28.1425i	1.07059	+	1.07059i	0.997311	+	0.0732795i	$0.0233465\pi$
$691$	28.1425	+	28.1425i	1.07059	+	1.07059i	0.0732795	+	0.997311i	$0.476653\pi$
$692$			6.63325i			0.252158i
$693$	33.1662	−	22.0000i	1.25988	−	0.835711i
$694$	16.4165	+	16.4165i	0.623160	+	0.623160i
$695$	−9.19239	+	9.19239i	−0.348687	+	0.348687i
$696$		0			0
$697$		0			0
$698$		−	16.5831i		−	0.627680i
$699$	−1.65831	−	5.50000i	−0.0627231	−	0.208029i
$700$	9.38083	−	9.38083i	0.354562	−	0.354562i
$701$	33.1662			1.25267			0.626336	−	0.779553i	$-0.284554\pi$
$701$	33.1662			1.25267			0.626336	+	0.779553i	$0.284554\pi$
$702$		0			0
$703$	66.0000			2.48924
$704$	2.82843	−	2.82843i	0.106600	−	0.106600i
$705$	4.50000	+	14.9248i	0.169480	+	0.562101i
$706$			14.0000i			0.526897i
$707$	31.1127	−	31.1127i	1.17011	−	1.17011i
$708$	21.3662	+	11.4667i	0.802991	+	0.430945i
$709$	−9.38083	+	9.38083i	−0.352305	+	0.352305i	−0.860966	−	0.508662i	$-0.830140\pi$
$709$	−9.38083	+	9.38083i	−0.352305	+	0.352305i	0.508662	+	0.860966i	$0.330140\pi$
$710$	−2.12132	−	2.12132i	−0.0796117	−	0.0796117i
$711$	−35.0000	+	23.2164i	−1.31260	+	0.870682i
$712$			2.00000i			0.0749532i
$713$	31.1127	+	31.1127i	1.16518	+	1.16518i
$714$	18.2414	−	5.50000i	0.682669	−	0.205832i
$715$		0			0
$716$			23.2164i			0.867637i
$717$	19.8400	+	10.6477i	0.740940	+	0.397644i
$718$		0			0
$719$	−13.2665			−0.494757			−0.247378	−	0.968919i	$-0.579569\pi$
$719$	−13.2665			−0.494757			−0.247378	+	0.968919i	$0.579569\pi$
$720$	−0.595163	+	2.94037i	−0.0221804	+	0.109581i
$721$	−14.0712	−	14.0712i	−0.524041	−	0.524041i
$722$	−17.6777	−	17.6777i	−0.657895	−	0.657895i
$723$	−30.3701	−	16.2989i	−1.12948	−	0.606163i
$724$	−10.0000			−0.371647
$725$		0			0
$726$	4.09525	−	7.63079i	0.151989	−	0.283205i
$727$			40.0000i			1.48352i	0.670667	+	0.741759i	$0.266008\pi$
$727$			40.0000i			1.48352i	−0.670667	+	0.741759i	$0.733992\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$	−4.69042	−	4.69042i	−0.173600	−	0.173600i
$731$		−	23.2164i		−	0.858689i
$732$	−6.63325	+	2.00000i	−0.245172	+	0.0739221i
$733$	16.4165	+	16.4165i	0.606356	+	0.606356i	0.941992	−	0.335636i	$-0.108951\pi$
$733$	16.4165	+	16.4165i	0.606356	+	0.606356i	−0.335636	+	0.941992i	$0.608951\pi$
$734$	5.65685	−	5.65685i	0.208798	−	0.208798i
$735$	−3.27620	+	6.10463i	−0.120845	+	0.225173i
$736$	−4.69042	+	4.69042i	−0.172891	+	0.172891i
$737$		0			0
$738$		0			0
$739$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$739$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$740$	−9.94987			−0.365765
$741$		0			0
$742$	22.0000			0.807645
$743$	20.5061	−	20.5061i	0.752296	−	0.752296i	−0.222612	−	0.974907i	$-0.571458\pi$
$743$	20.5061	−	20.5061i	0.752296	−	0.752296i	0.974907	+	0.222612i	$0.0714581\pi$
$744$	11.0000	−	3.31662i	0.403280	−	0.121593i
$745$		−	6.00000i		−	0.219823i
$746$	2.82843	−	2.82843i	0.103556	−	0.103556i
$747$	3.57098	−	17.6422i	0.130655	−	0.645495i
$748$	9.38083	−	9.38083i	0.342997	−	0.342997i
$749$	−15.5563	−	15.5563i	−0.568417	−	0.568417i
$750$	4.50000	+	14.9248i	0.164317	+	0.544977i
$751$		−	4.00000i		−	0.145962i	−0.997333	−	0.0729810i	$-0.976749\pi$
$751$		−	4.00000i		−	0.145962i	0.997333	−	0.0729810i	$-0.0232513\pi$
$752$	6.36396	+	6.36396i	0.232070	+	0.232070i
$753$	3.31662	+	11.0000i	0.120865	+	0.400862i
$754$		0			0
$755$		−	9.94987i		−	0.362113i
$756$	1.60266	+	17.1590i	0.0582881	+	0.624067i
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	6.63325			0.240930
$759$	−21.7319	+	40.4935i	−0.788817	+	1.46982i
$760$	4.69042	+	4.69042i	0.170139	+	0.170139i
$761$	9.89949	+	9.89949i	0.358856	+	0.358856i	0.863391	−	0.504535i	$-0.168336\pi$
$761$	9.89949	+	9.89949i	0.358856	+	0.358856i	−0.504535	+	0.863391i	$0.668336\pi$
$762$	4.91430	−	9.15694i	0.178026	−	0.331721i
$763$	11.0000			0.398227
$764$	−13.2665			−0.479965
$765$	−1.97393	+	9.75211i	−0.0713677	+	0.352588i
$766$			21.0000i			0.758761i
$767$		0			0
$768$	0.500000	+	1.65831i	0.0180422	+	0.0598392i
$769$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$769$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$770$			13.2665i			0.478091i
$771$	1.65831	+	5.50000i	0.0597227	+	0.198078i
$772$	−14.0712	−	14.0712i	−0.506435	−	0.506435i
$773$	−21.9203	+	21.9203i	−0.788419	+	0.788419i	−0.981235	−	0.192816i	$-0.938238\pi$
$773$	−21.9203	+	21.9203i	−0.788419	+	0.788419i	0.192816	+	0.981235i	$0.438238\pi$
$774$	20.5826	+	4.16614i	0.739826	+	0.149749i
$775$	18.7617	−	18.7617i	0.673939	−	0.673939i
$776$		0			0
$777$	−54.7243	+	16.5000i	−1.96322	+	0.591934i
$778$	−4.69042	+	4.69042i	−0.168160	+	0.168160i
$779$		0			0
$780$		0			0
$781$	−12.0000			−0.429394
$782$	−15.5563	+	15.5563i	−0.556294	+	0.556294i
$783$		0			0
$784$			4.00000i			0.142857i
$785$	−1.41421	+	1.41421i	−0.0504754	+	0.0504754i
$786$	−13.5824	+	25.3085i	−0.484469	+	0.902723i
$787$	−28.1425	+	28.1425i	−1.00317	+	1.00317i	−0.00317664	+	0.999995i	$0.501011\pi$
$787$	−28.1425	+	28.1425i	−1.00317	+	1.00317i	−0.999995	+	0.00317664i	$0.998989\pi$
$788$	16.2635	+	16.2635i	0.579362	+	0.579362i
$789$	−22.0000	+	6.63325i	−0.783221	+	0.236150i
$790$		−	14.0000i		−	0.498098i
$791$	31.1127	+	31.1127i	1.10624	+	1.10624i
$792$	6.63325	+	10.0000i	0.235702	+	0.355335i
$793$		0			0
$794$		0			0
$795$	−5.43297	+	10.1234i	−0.192687	+	0.359039i
$796$	−4.00000			−0.141776
$797$	33.1662			1.17481			0.587404	−	0.809294i	$-0.300150\pi$
$797$	33.1662			1.17481			0.587404	+	0.809294i	$0.300150\pi$
$798$	33.5755	+	18.0191i	1.18856	+	0.637870i
$799$	21.1069	+	21.1069i	0.746707	+	0.746707i
$800$	2.82843	+	2.82843i	0.100000	+	0.100000i
$801$	−5.88074	−	1.19033i	−0.207786	−	0.0420581i
$802$	34.0000			1.20058
$803$	−26.5330			−0.936329
$804$		0			0
$805$		−	22.0000i		−	0.775398i
$806$		0			0
$807$	−22.0000	+	6.63325i	−0.774437	+	0.233501i
$808$	9.38083	+	9.38083i	0.330017	+	0.330017i
$809$		−	16.5831i		−	0.583032i	−0.956566	−	0.291516i	$-0.905840\pi$
$809$		−	16.5831i		−	0.583032i	0.956566	−	0.291516i	$-0.0941596\pi$
$810$	−8.29156	−	3.50000i	−0.291336	−	0.122977i
$811$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$811$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$812$		0			0
$813$	15.1851	+	8.14945i	0.532564	+	0.285814i
$814$	−28.1425	+	28.1425i	−0.986394	+	0.986394i
$815$		−	6.63325i		−	0.232353i
$816$	1.65831	+	5.50000i	0.0580525	+	0.192539i
$817$	32.8329	−	32.8329i	1.14868	−	1.14868i
$818$	33.1662			1.15963
$819$		0			0
$820$		0			0
$821$	6.36396	−	6.36396i	0.222104	−	0.222104i	−0.587280	−	0.809384i	$-0.699801\pi$
$821$	6.36396	−	6.36396i	0.222104	−	0.222104i	0.809384	+	0.587280i	$0.199801\pi$
$822$	−3.00000	−	9.94987i	−0.104637	−	0.347042i
$823$		−	34.0000i		−	1.18517i	−0.805510	−	0.592583i	$-0.798108\pi$
$823$		−	34.0000i		−	1.18517i	0.805510	−	0.592583i	$-0.201892\pi$
$824$	4.24264	−	4.24264i	0.147799	−	0.147799i
$825$	24.4185	+	13.1048i	0.850144	+	0.456251i
$826$	−32.8329	+	32.8329i	−1.14240	+	1.14240i
$827$	−9.89949	−	9.89949i	−0.344239	−	0.344239i	0.513719	−	0.857958i	$-0.328267\pi$
$827$	−9.89949	−	9.89949i	−0.344239	−	0.344239i	−0.857958	+	0.513719i	$0.828267\pi$
$828$	−11.0000	−	16.5831i	−0.382276	−	0.576303i
$829$		−	36.0000i		−	1.25033i	−0.780492	−	0.625166i	$-0.785031\pi$
$829$		−	36.0000i		−	1.25033i	0.780492	−	0.625166i	$-0.214969\pi$
$830$	4.24264	+	4.24264i	0.147264	+	0.147264i
$831$		0			0
$832$		0			0
$833$			13.2665i			0.459657i
$834$	−19.8400	−	10.6477i	−0.687005	−	0.368698i
$835$	12.0000			0.415277
$836$	26.5330			0.917663
$837$	3.20531	+	34.3180i	0.110792	+	1.18620i
$838$	2.34521	+	2.34521i	0.0810139	+	0.0810139i
$839$	−16.9706	−	16.9706i	−0.585889	−	0.585889i	0.350626	−	0.936515i	$-0.385969\pi$
$839$	−16.9706	−	16.9706i	−0.585889	−	0.585889i	−0.936515	+	0.350626i	$0.885969\pi$
$840$	−5.06169	−	2.71648i	−0.174645	−	0.0937276i
$841$	29.0000			1.00000
$842$	29.8496			1.02869
$843$	14.7429	−	27.4708i	0.507773	−	0.946146i
$844$		−	1.00000i		−	0.0344214i
$845$		0			0
$846$	−22.5000	+	14.9248i	−0.773566	+	0.513126i
$847$	11.7260	+	11.7260i	0.402911	+	0.402911i
$848$			6.63325i			0.227787i
$849$	−46.4327	+	14.0000i	−1.59357	+	0.480479i
$850$	9.38083	+	9.38083i	0.321760	+	0.321760i
$851$	46.6690	−	46.6690i	1.59979	−	1.59979i
$852$	2.45715	−	4.57847i	0.0841806	−	0.156856i
$853$	2.34521	−	2.34521i	0.0802984	−	0.0802984i	−0.665817	−	0.746115i	$-0.731917\pi$
$853$	2.34521	−	2.34521i	0.0802984	−	0.0802984i	0.746115	+	0.665817i	$0.231917\pi$
$854$		−	13.2665i		−	0.453970i
$855$	−16.5831	+	11.0000i	−0.567131	+	0.376192i
$856$	4.69042	−	4.69042i	0.160315	−	0.160315i
$857$	−39.7995			−1.35952			−0.679762	−	0.733432i	$-0.737917\pi$
$857$	−39.7995			−1.35952			−0.679762	+	0.733432i	$0.737917\pi$
$858$		0			0
$859$	−8.00000			−0.272956			−0.136478	−	0.990643i	$-0.543578\pi$
$859$	−8.00000			−0.272956			−0.136478	+	0.990643i	$0.543578\pi$
$860$	−4.94975	+	4.94975i	−0.168785	+	0.168785i
$861$		0			0
$862$			3.00000i			0.102180i
$863$	−19.0919	+	19.0919i	−0.649895	+	0.649895i	−0.952968	−	0.303072i	$-0.901988\pi$
$863$	−19.0919	+	19.0919i	−0.649895	+	0.649895i	0.303072	+	0.952968i	$0.401988\pi$
$864$	−5.17364	+	0.483219i	−0.176011	+	0.0164395i
$865$	4.69042	−	4.69042i	0.159479	−	0.159479i
$866$	−3.53553	−	3.53553i	−0.120142	−	0.120142i
$867$	−3.00000	−	9.94987i	−0.101885	−	0.337915i
$868$			22.0000i			0.746729i
$869$	−39.5980	−	39.5980i	−1.34327	−	1.34327i
$870$		0			0
$871$		0			0
$872$			3.31662i			0.112315i
$873$		0			0
$874$	−44.0000			−1.48832
$875$	−29.8496			−1.00910
$876$	5.43297	−	10.1234i	0.183563	−	0.342037i
$877$	25.7973	+	25.7973i	0.871112	+	0.871112i	0.992594	−	0.121481i	$-0.0387644\pi$
$877$	25.7973	+	25.7973i	0.871112	+	0.871112i	−0.121481	+	0.992594i	$0.538764\pi$
$878$	18.3848	+	18.3848i	0.620456	+	0.620456i
$879$	−15.5620	+	28.9970i	−0.524892	+	0.978044i
$880$	−4.00000			−0.134840
$881$	−16.5831			−0.558700			−0.279350	−	0.960189i	$-0.590119\pi$
$881$	−16.5831			−0.558700			−0.279350	+	0.960189i	$0.590119\pi$
$882$	−11.7615	−	2.38065i	−0.396030	−	0.0801607i
$883$			29.0000i			0.975928i	0.872864	+	0.487964i	$0.162260\pi$
$883$			29.0000i			0.975928i	−0.872864	+	0.487964i	$0.837740\pi$
$884$		0			0
$885$	−7.00000	−	23.2164i	−0.235302	−	0.780410i
$886$	11.7260	+	11.7260i	0.393944	+	0.393944i
$887$			26.5330i			0.890891i	0.895309	+	0.445445i	$0.146955\pi$
$887$			26.5330i			0.890891i	−0.895309	+	0.445445i	$0.853045\pi$
$888$	−4.97494	−	16.5000i	−0.166948	−	0.553704i
$889$	14.0712	+	14.0712i	0.471934	+	0.471934i
$890$	1.41421	−	1.41421i	0.0474045	−	0.0474045i
$891$	−33.3516	+	13.5526i	−1.11732	+	0.454029i
$892$	−7.03562	+	7.03562i	−0.235570	+	0.235570i
$893$			59.6992i			1.99776i
$894$	9.94987	−	3.00000i	0.332774	−	0.100335i
$895$	16.4165	−	16.4165i	0.548742	−	0.548742i
$896$	−3.31662			−0.110801
$897$		0			0
$898$	32.0000			1.06785
$899$		0			0
$900$	−10.0000	+	6.63325i	−0.333333	+	0.221108i
$901$			22.0000i			0.732926i
$902$		0			0
$903$	−19.0154	+	35.4318i	−0.632792	+	1.17910i
$904$	−9.38083	+	9.38083i	−0.312002	+	0.312002i
$905$	7.07107	+	7.07107i	0.235050	+	0.235050i
$906$	16.5000	−	4.97494i	0.548176	−	0.165281i
$907$			17.0000i			0.564476i	0.959344	+	0.282238i	$0.0910767\pi$
$907$			17.0000i			0.564476i	−0.959344	+	0.282238i	$0.908923\pi$
$908$	14.1421	+	14.1421i	0.469323	+	0.469323i
$909$	−33.1662	+	22.0000i	−1.10006	+	0.729694i
$910$		0			0
$911$		−	53.0660i		−	1.75815i	−0.476679	−	0.879077i	$-0.658160\pi$
$911$		−	53.0660i		−	1.75815i	0.476679	−	0.879077i	$-0.341840\pi$
$912$	−5.43297	+	10.1234i	−0.179904	+	0.335219i
$913$	24.0000			0.794284
$914$	6.63325			0.219408
$915$	6.10463	+	3.27620i	0.201813	+	0.108308i
$916$	2.34521	+	2.34521i	0.0774878	+	0.0774878i
$917$	−38.8909	−	38.8909i	−1.28429	−	1.28429i
$918$	−17.1590	+	1.60266i	−0.566332	+	0.0528956i
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$	6.63325			0.218692
$921$	−10.1234	−	5.43297i	−0.333577	−	0.179022i
$922$			11.0000i			0.362266i
$923$		0			0
$924$	−22.0000	+	6.63325i	−0.723747	+	0.218218i
$925$	−28.1425	−	28.1425i	−0.925320	−	0.925320i
$926$			19.8997i			0.653946i
$927$	9.94987	+	15.0000i	0.326797	+	0.492665i
$928$		0			0
$929$	−39.5980	+	39.5980i	−1.29917	+	1.29917i	−0.370226	+	0.928942i	$0.620720\pi$
$929$	−39.5980	+	39.5980i	−1.29917	+	1.29917i	−0.928942	+	0.370226i	$0.879280\pi$
$930$	−10.1234	−	5.43297i	−0.331959	−	0.178154i
$931$	−18.7617	+	18.7617i	−0.614889	+	0.614889i
$932$			3.31662i			0.108640i
$933$	9.94987	+	33.0000i	0.325744	+	1.08037i
$934$	4.69042	−	4.69042i	0.153475	−	0.153475i
$935$	−13.2665			−0.433861
$936$		0			0
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$		0			0
$939$	−10.5000	−	34.8246i	−0.342655	−	1.13646i
$940$		−	9.00000i		−	0.293548i
$941$	10.6066	−	10.6066i	0.345765	−	0.345765i	−0.512764	−	0.858530i	$-0.671378\pi$
$941$	10.6066	−	10.6066i	0.345765	−	0.345765i	0.858530	+	0.512764i	$0.171378\pi$
$942$	−3.05231	−	1.63810i	−0.0994498	−	0.0533722i
$943$		0			0
$944$	−9.89949	−	9.89949i	−0.322201	−	0.322201i
$945$	11.0000	−	13.2665i	0.357830	−	0.431559i
$946$			28.0000i			0.910359i
$947$	−5.65685	−	5.65685i	−0.183823	−	0.183823i	0.609196	−	0.793019i	$-0.291492\pi$
$947$	−5.65685	−	5.65685i	−0.183823	−	0.183823i	−0.793019	+	0.609196i	$0.791492\pi$
$948$	23.2164	−	7.00000i	0.754033	−	0.227349i
$949$		0			0
$950$			26.5330i			0.860844i
$951$	3.05231	+	1.63810i	0.0989781	+	0.0531191i
$952$	−11.0000			−0.356512
$953$	9.94987			0.322308			0.161154	−	0.986929i	$-0.448478\pi$
$953$	9.94987			0.322308			0.161154	+	0.986929i	$0.448478\pi$
$954$	−19.5042	−	3.94786i	−0.631472	−	0.127817i
$955$	9.38083	+	9.38083i	0.303557	+	0.303557i
$956$	−9.19239	−	9.19239i	−0.297303	−	0.297303i
$957$		0			0
$958$	5.00000			0.161543
$959$	19.8997			0.642596
$960$	0.819051	−	1.52616i	0.0264347	−	0.0492565i
$961$			13.0000i			0.419355i
$962$		0			0
$963$	11.0000	+	16.5831i	0.354470	+	0.534384i
$964$	14.0712	+	14.0712i	0.453204	+	0.453204i
$965$			19.8997i			0.640596i
$966$	36.4829	−	11.0000i	1.17382	−	0.353919i
$967$	−2.34521	−	2.34521i	−0.0754168	−	0.0754168i	0.668392	−	0.743809i	$-0.266983\pi$
$967$	−2.34521	−	2.34521i	−0.0754168	−	0.0754168i	−0.743809	+	0.668392i	$0.766983\pi$
$968$	−3.53553	+	3.53553i	−0.113636	+	0.113636i
$969$	−18.0191	+	33.5755i	−0.578857	+	1.07860i
$970$		0			0
$971$			9.94987i			0.319307i	0.987173	+	0.159653i	$0.0510376\pi$
$971$			9.94987i			0.319307i	−0.987173	+	0.159653i	$0.948962\pi$
$972$	1.65831	−	15.5000i	0.0531904	−	0.497163i
$973$	30.4877	−	30.4877i	0.977391	−	0.977391i
$974$	33.1662			1.06272
$975$		0			0
$976$	4.00000			0.128037
$977$	−19.7990	+	19.7990i	−0.633426	+	0.633426i	−0.948926	−	0.315500i	$-0.897828\pi$
$977$	−19.7990	+	19.7990i	−0.633426	+	0.633426i	0.315500	+	0.948926i	$0.397828\pi$
$978$	11.0000	−	3.31662i	0.351741	−	0.106054i
$979$		−	8.00000i		−	0.255681i
$980$	2.82843	−	2.82843i	0.0903508	−	0.0903508i
$981$	−9.75211	−	1.97393i	−0.311361	−	0.0630228i
$982$	−7.03562	+	7.03562i	−0.224516	+	0.224516i
$983$	43.1335	+	43.1335i	1.37575	+	1.37575i	0.851675	+	0.524071i	$0.175587\pi$
$983$	43.1335	+	43.1335i	1.37575	+	1.37575i	0.524071	+	0.851675i	$0.324413\pi$
$984$		0			0
$985$		−	23.0000i		−	0.732841i
$986$		0			0
$987$	−14.9248	−	49.5000i	−0.475062	−	1.57560i
$988$		0			0
$989$		−	46.4327i		−	1.47648i
$990$	2.38065	−	11.7615i	0.0756621	−	0.373804i
$991$	58.0000			1.84243			0.921215	−	0.389053i	$-0.127198\pi$
$991$	58.0000			1.84243			0.921215	+	0.389053i	$0.127198\pi$
$992$	−6.63325			−0.210606
$993$	5.43297	−	10.1234i	0.172410	−	0.321256i
$994$	7.03562	+	7.03562i	0.223156	+	0.223156i
$995$	2.82843	+	2.82843i	0.0896672	+	0.0896672i
$996$	−4.91430	+	9.15694i	−0.155716	+	0.290149i
$997$	−52.0000			−1.64686			−0.823428	−	0.567420i	$-0.807941\pi$
$997$	−52.0000			−1.64686			−0.823428	+	0.567420i	$0.807941\pi$
$998$	39.7995			1.25983
$999$	51.4770	−	4.80797i	1.62866	−	0.152117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.a.437.2	yes	8
3.2	odd	2	inner	1014.2.g.a.437.3	yes	8
13.5	odd	4	inner	1014.2.g.a.239.4	yes	8
13.8	odd	4	inner	1014.2.g.a.239.2	yes	8
13.12	even	2	inner	1014.2.g.a.437.4	yes	8
39.5	even	4	inner	1014.2.g.a.239.1	✓	8
39.8	even	4	inner	1014.2.g.a.239.3	yes	8
39.38	odd	2	inner	1014.2.g.a.437.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.g.a.239.1	✓	8	39.5	even	4	inner
1014.2.g.a.239.2	yes	8	13.8	odd	4	inner
1014.2.g.a.239.3	yes	8	39.8	even	4	inner
1014.2.g.a.239.4	yes	8	13.5	odd	4	inner
1014.2.g.a.437.1	yes	8	39.38	odd	2	inner
1014.2.g.a.437.2	yes	8	1.1	even	1	trivial
1014.2.g.a.437.3	yes	8	3.2	odd	2	inner
1014.2.g.a.437.4	yes	8	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.52616 - 0.819051i) q^{6} +(2.34521 - 2.34521i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.52616 - 0.819051i) q^{6} +(2.34521 - 2.34521i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.50000 + 1.65831i) q^{9} -1.00000i q^{10} +(-2.82843 - 2.82843i) q^{11} +(1.65831 - 0.500000i) q^{12} +3.31662i q^{14} +(-1.52616 - 0.819051i) q^{15} -1.00000 q^{16} -3.31662 q^{17} +(0.595163 - 2.94037i) q^{18} +(-4.69042 - 4.69042i) q^{19} +(0.707107 + 0.707107i) q^{20} +(5.06169 + 2.71648i) q^{21} +4.00000 q^{22} -6.63325 q^{23} +(-0.819051 + 1.52616i) q^{24} +4.00000i q^{25} +(-4.00000 - 3.31662i) q^{27} +(-2.34521 - 2.34521i) q^{28} +(1.65831 - 0.500000i) q^{30} +(-4.69042 - 4.69042i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.27620 - 6.10463i) q^{33} +(2.34521 - 2.34521i) q^{34} +3.31662i q^{35} +(1.65831 + 2.50000i) q^{36} +(-7.03562 + 7.03562i) q^{37} +6.63325 q^{38} -1.00000 q^{40} +(-5.50000 + 1.65831i) q^{42} +7.00000i q^{43} +(-2.82843 + 2.82843i) q^{44} +(0.595163 - 2.94037i) q^{45} +(4.69042 - 4.69042i) q^{46} +(-6.36396 - 6.36396i) q^{47} +(-0.500000 - 1.65831i) q^{48} -4.00000i q^{49} +(-2.82843 - 2.82843i) q^{50} +(-1.65831 - 5.50000i) q^{51} -6.63325i q^{53} +(5.17364 - 0.483219i) q^{54} +4.00000 q^{55} +3.31662 q^{56} +(5.43297 - 10.1234i) q^{57} +(9.89949 + 9.89949i) q^{59} +(-0.819051 + 1.52616i) q^{60} -4.00000 q^{61} +6.63325 q^{62} +(-1.97393 + 9.75211i) q^{63} +1.00000i q^{64} +(2.00000 + 6.63325i) q^{66} +3.31662i q^{68} +(-3.31662 - 11.0000i) q^{69} +(-2.34521 - 2.34521i) q^{70} +(2.12132 - 2.12132i) q^{71} +(-2.94037 - 0.595163i) q^{72} +(4.69042 - 4.69042i) q^{73} -9.94987i q^{74} +(-6.63325 + 2.00000i) q^{75} +(-4.69042 + 4.69042i) q^{76} -13.2665 q^{77} +14.0000 q^{79} +(0.707107 - 0.707107i) q^{80} +(3.50000 - 8.29156i) q^{81} +(-4.24264 + 4.24264i) q^{83} +(2.71648 - 5.06169i) q^{84} +(2.34521 - 2.34521i) q^{85} +(-4.94975 - 4.94975i) q^{86} -4.00000i q^{88} +(1.41421 + 1.41421i) q^{89} +(1.65831 + 2.50000i) q^{90} +6.63325i q^{92} +(5.43297 - 10.1234i) q^{93} +9.00000 q^{94} +6.63325 q^{95} +(1.52616 + 0.819051i) q^{96} +(2.82843 + 2.82843i) q^{98} +(11.7615 + 2.38065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 20 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 20 * q^9	\( 8 q + 4 q^{3} - 20 q^{9} - 8 q^{16} + 32 q^{22} - 32 q^{27} - 8 q^{40} - 44 q^{42} - 4 q^{48} + 32 q^{55} - 32 q^{61} + 16 q^{66} + 112 q^{79} + 28 q^{81} + 72 q^{94}+O(q^{100}) \) 8 * q + 4 * q^3 - 20 * q^9 - 8 * q^16 + 32 * q^22 - 32 * q^27 - 8 * q^40 - 44 * q^42 - 4 * q^48 + 32 * q^55 - 32 * q^61 + 16 * q^66 + 112 * q^79 + 28 * q^81 + 72 * q^94

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