LMFDB - Embedded newform 1014.2.g.a.437.3

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			437.3
Root			$1.52616 - 0.819051i$ of defining polynomial
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.a.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.500000 - 1.65831i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.819051 - 1.52616i) q^{6} +(2.34521 - 2.34521i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.500000 - 1.65831i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.819051 - 1.52616i) 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} +(-0.819051 - 1.52616i) q^{15} -1.00000 q^{16} +3.31662 q^{17} +(-2.94037 + 0.595163i) q^{18} +(-4.69042 - 4.69042i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-2.71648 - 5.06169i) q^{21} +4.00000 q^{22} +6.63325 q^{23} +(-1.52616 + 0.819051i) 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} +(6.10463 - 3.27620i) 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} +(-2.94037 + 0.595163i) 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} +(-0.483219 + 5.17364i) q^{54} +4.00000 q^{55} -3.31662 q^{56} +(-10.1234 + 5.43297i) q^{57} +(-9.89949 - 9.89949i) q^{59} +(-1.52616 + 0.819051i) q^{60} -4.00000 q^{61} -6.63325 q^{62} +(-9.75211 + 1.97393i) 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} +(0.595163 + 2.94037i) 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} +(-5.06169 + 2.71648i) 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} +(-10.1234 + 5.43297i) q^{93} +9.00000 q^{94} -6.63325 q^{95} +(0.819051 + 1.52616i) q^{96} +(-2.82843 - 2.82843i) q^{98} +(-2.38065 - 11.7615i) 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	−0.531089	−	0.847316i	$-0.678217\pi$
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i	0.847316	+	0.531089i	$0.178217\pi$
$6$	−0.819051	−	1.52616i	−0.334376	−	0.623051i
$7$	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	0.990478	−	0.137675i	$-0.0439628\pi$
$11$	2.82843	+	2.82843i	0.852803	+	0.852803i	−0.137675	+	0.990478i	$0.543963\pi$
$12$	−1.65831	−	0.500000i	−0.478714	−	0.144338i
$13$		0			0
$13$		0			0
$14$		−	3.31662i		−	0.886405i
$15$	−0.819051	−	1.52616i	−0.211478	−	0.394052i
$16$	−1.00000			−0.250000
$17$	3.31662			0.804400			0.402200	−	0.915552i	$-0.368246\pi$
$17$	3.31662			0.804400			0.402200	+	0.915552i	$0.368246\pi$
$18$	−2.94037	+	0.595163i	−0.693052	+	0.140281i
$19$	−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
$21$	−2.71648	−	5.06169i	−0.592785	−	1.10455i
$22$	4.00000			0.852803
$23$	6.63325			1.38313			0.691564	−	0.722315i	$-0.256922\pi$
$23$	6.63325			1.38313			0.691564	+	0.722315i	$0.256922\pi$
$24$	−1.52616	+	0.819051i	−0.311526	+	0.167188i
$25$			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
$33$	6.10463	−	3.27620i	1.06268	−	0.570314i
$34$	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
$45$	−2.94037	+	0.595163i	−0.438325	+	0.0887217i
$46$	4.69042	−	4.69042i	0.691564	−	0.691564i
$47$	6.36396	+	6.36396i	0.928279	+	0.928279i	0.997595	−	0.0693157i	$-0.0220816\pi$
$47$	6.36396	+	6.36396i	0.928279	+	0.928279i	−0.0693157	+	0.997595i	$0.522082\pi$
$48$	−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	$0.150566\pi$
$53$			6.63325i			0.911147i	−0.890198	+	0.455573i	$0.849434\pi$
$54$	−0.483219	+	5.17364i	−0.0657578	+	0.704043i
$55$	4.00000			0.539360
$56$	−3.31662			−0.443203
$57$	−10.1234	+	5.43297i	−1.34087	+	0.719614i
$58$		0			0
$59$	−9.89949	−	9.89949i	−1.28880	−	1.28880i	−0.935513	−	0.353291i	$-0.885063\pi$
$59$	−9.89949	−	9.89949i	−1.28880	−	1.28880i	−0.353291	−	0.935513i	$-0.614937\pi$
$60$	−1.52616	+	0.819051i	−0.197026	+	0.105739i
$61$	−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
$63$	−9.75211	+	1.97393i	−1.22865	+	0.248692i
$64$			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	−0.821690	−	0.569935i	$-0.806968\pi$
$71$	−2.12132	+	2.12132i	−0.251754	+	0.251754i	0.569935	+	0.821690i	$0.306968\pi$
$72$	0.595163	+	2.94037i	0.0701406	+	0.346526i
$73$	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	−0.434825	−	0.900515i	$-0.643190\pi$
$83$	4.24264	−	4.24264i	0.465690	−	0.465690i	0.900515	+	0.434825i	$0.143190\pi$
$84$	−5.06169	+	2.71648i	−0.552276	+	0.296393i
$85$	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	0.628170	−	0.778076i	$-0.283804\pi$
$89$	−1.41421	−	1.41421i	−0.149906	−	0.149906i	−0.778076	+	0.628170i	$0.783804\pi$
$90$	−1.65831	+	2.50000i	−0.174801	+	0.263523i
$91$		0			0
$92$		−	6.63325i		−	0.691564i
$93$	−10.1234	+	5.43297i	−1.04975	+	0.563372i
$94$	9.00000			0.928279
$95$	−6.63325			−0.680557
$96$	0.819051	+	1.52616i	0.0835940	+	0.155763i
$97$		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
$99$	−2.38065	−	11.7615i	−0.239265	−	1.18207i
$100$	4.00000			0.400000
$101$	−13.2665			−1.32007			−0.660033	−	0.751237i	$-0.729458\pi$
$101$	−13.2665			−1.32007			−0.660033	+	0.751237i	$0.729458\pi$
$102$	−2.71648	−	5.06169i	−0.268972	−	0.501182i
$103$		−	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	$0.103895\pi$
$107$			6.63325i			0.641260i	−0.947204	+	0.320630i	$0.896105\pi$
$108$	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
$111$	8.14945	+	15.1851i	0.773512	+	1.44130i
$112$	−2.34521	+	2.34521i	−0.221601	+	0.221601i
$113$		−	13.2665i		−	1.24801i	−0.781421	−	0.624004i	$-0.785505\pi$
$113$		−	13.2665i		−	1.24801i	0.781421	−	0.624004i	$-0.214495\pi$
$114$	−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	$0.257900\pi$
$131$			16.5831i			1.44887i	−0.689341	+	0.724437i	$0.742100\pi$
$132$	−3.27620	−	6.10463i	−0.285157	−	0.531340i
$133$	−22.0000			−1.90764
$134$		0			0
$135$	−0.483219	+	5.17364i	−0.0415889	+	0.445276i
$136$	−2.34521	−	2.34521i	−0.201100	−	0.201100i
$137$	−4.24264	−	4.24264i	−0.362473	−	0.362473i	0.502249	−	0.864723i	$-0.332506\pi$
$137$	−4.24264	−	4.24264i	−0.362473	−	0.362473i	−0.864723	+	0.502249i	$0.832506\pi$
$138$	−5.43297	−	10.1234i	−0.462485	−	0.861760i
$139$	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
$141$	13.7354	−	7.37145i	1.15673	−	0.620788i
$142$			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	−0.511633	−	0.859204i	$-0.670959\pi$
$149$	4.24264	−	4.24264i	0.347571	−	0.347571i	0.859204	+	0.511633i	$0.170959\pi$
$150$	6.10463	−	3.27620i	0.498441	−	0.267501i
$151$	−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
$162$	8.33789	+	3.38815i	0.655087	+	0.266198i
$163$	−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	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$	−1.65831	+	5.50000i	−0.127942	+	0.424334i
$169$		0			0
$170$		−	3.31662i		−	0.254374i
$171$	3.94786	+	19.5042i	0.301901	+	1.49152i
$172$	7.00000			0.533745
$173$	6.63325			0.504317			0.252158	−	0.967686i	$-0.418860\pi$
$173$	6.63325			0.504317			0.252158	+	0.967686i	$0.418860\pi$
$174$		0			0
$175$	9.38083	+	9.38083i	0.709124	+	0.709124i
$176$	−2.82843	−	2.82843i	−0.213201	−	0.213201i
$177$	−21.3662	+	11.4667i	−1.60598	+	0.861891i
$178$	−2.00000			−0.149906
$179$	23.2164			1.73527			0.867637	−	0.497199i	$-0.165638\pi$
$179$	23.2164			1.73527			0.867637	+	0.497199i	$0.165638\pi$
$180$	0.595163	+	2.94037i	0.0443608	+	0.219162i
$181$		−	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
$189$	−1.60266	+	17.1590i	−0.116576	+	1.24813i
$190$	−4.69042	+	4.69042i	−0.340279	+	0.340279i
$191$			13.2665i			0.959930i	0.877288	+	0.479965i	$0.159351\pi$
$191$			13.2665i			0.959930i	−0.877288	+	0.479965i	$0.840649\pi$
$192$	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	$-0.444340\pi$
$197$	16.2635	−	16.2635i	1.15872	−	1.15872i	0.984750	−	0.173973i	$-0.0556605\pi$
$198$	−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
$210$	−5.06169	+	2.71648i	−0.349290	+	0.187455i
$211$	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
$213$	2.45715	+	4.57847i	0.168361	+	0.313712i
$214$	4.69042	+	4.69042i	0.320630	+	0.320630i
$215$	4.94975	+	4.94975i	0.337570	+	0.337570i
$216$	5.17364	+	0.483219i	0.352021	+	0.0328789i
$217$	−22.0000			−1.49346
$218$	3.31662			0.224630
$219$	−5.43297	−	10.1234i	−0.367126	−	0.684075i
$220$		−	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	−0.0595772	−	0.998224i	$-0.518975\pi$
$227$	14.1421	−	14.1421i	0.938647	−	0.938647i	0.998224	+	0.0595772i	$0.0189752\pi$
$228$	5.43297	+	10.1234i	0.359807	+	0.670437i
$229$	−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	$-0.465351\pi$
$233$	3.31662			0.217279			0.108640	+	0.994081i	$0.465351\pi$
$234$		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	−0.938872	−	0.344266i	$-0.888128\pi$
$239$	−9.19239	+	9.19239i	−0.594606	+	0.594606i	0.344266	+	0.938872i	$0.388128\pi$
$240$	0.819051	+	1.52616i	0.0528695	+	0.0985130i
$241$	−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
$249$	−4.91430	−	9.15694i	−0.311431	−	0.580298i
$250$	9.00000			0.569210
$251$	−6.63325			−0.418687			−0.209344	−	0.977842i	$-0.567133\pi$
$251$	−6.63325			−0.418687			−0.209344	+	0.977842i	$0.567133\pi$
$252$	1.97393	+	9.75211i	0.124346	+	0.614325i
$253$	18.7617	+	18.7617i	1.17954	+	1.17954i
$254$	4.24264	+	4.24264i	0.266207	+	0.266207i
$255$	−2.71648	−	5.06169i	−0.170113	−	0.316975i
$256$	1.00000			0.0625000
$257$	−3.31662			−0.206885			−0.103443	−	0.994635i	$-0.532986\pi$
$257$	−3.31662			−0.206885			−0.103443	+	0.994635i	$0.532986\pi$
$258$	10.6831	−	5.73335i	0.665101	−	0.356943i
$259$			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	$-0.865869\pi$
$263$		−	13.2665i		−	0.818047i	0.912524	−	0.409024i	$-0.134131\pi$
$264$	−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
$267$	−3.05231	+	1.63810i	−0.186799	+	0.100250i
$268$		0			0
$269$		−	13.2665i		−	0.808873i	−0.914566	−	0.404436i	$-0.867468\pi$
$269$		−	13.2665i		−	0.808873i	0.914566	−	0.404436i	$-0.132532\pi$
$270$	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
$279$	3.94786	+	19.5042i	0.236352	+	1.16769i
$280$	−2.34521	+	2.34521i	−0.140153	+	0.140153i
$281$	12.7279	+	12.7279i	0.759284	+	0.759284i	0.976192	−	0.216908i	$-0.0695971\pi$
$281$	12.7279	+	12.7279i	0.759284	+	0.759284i	−0.216908	+	0.976192i	$0.569597\pi$
$282$	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
$288$	2.94037	−	0.595163i	0.173263	−	0.0350703i
$289$	−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	0.195768	−	0.980650i	$-0.437280\pi$
$293$	−13.4350	−	13.4350i	−0.784883	−	0.784883i	−0.980650	+	0.195768i	$0.937280\pi$
$294$	−6.10463	+	3.27620i	−0.356029	+	0.191072i
$295$	−14.0000			−0.815112
$296$	9.94987			0.578325
$297$	−20.6945	−	1.93288i	−1.20082	−	0.112157i
$298$		−	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
$306$	−9.75211	+	1.97393i	−0.557491	+	0.112842i
$307$	−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	$-0.690817\pi$
$311$	−19.8997			−1.12841			−0.564206	+	0.825634i	$0.690817\pi$
$312$		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	−0.745706	−	0.666276i	$-0.767887\pi$
$317$	−1.41421	+	1.41421i	−0.0794301	+	0.0794301i	0.666276	+	0.745706i	$0.267887\pi$
$318$	10.1234	−	5.43297i	0.567691	−	0.304666i
$319$		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
$327$	5.06169	−	2.71648i	0.279912	−	0.150222i
$328$		0			0
$329$	29.8496			1.64566
$330$	−3.27620	−	6.10463i	−0.180349	−	0.336049i
$331$	−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
$333$	29.2563	−	5.92180i	1.60324	−	0.324512i
$334$	12.0000			0.656611
$335$		0			0
$336$	2.71648	+	5.06169i	0.148196	+	0.276138i
$337$		−	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
$345$	−5.43297	−	10.1234i	−0.292501	−	0.545025i
$346$	4.69042	−	4.69042i	0.252158	−	0.252158i
$347$			23.2164i			1.24632i	0.782094	+	0.623160i	$0.214152\pi$
$347$			23.2164i			1.24632i	−0.782094	+	0.623160i	$0.785848\pi$
$348$		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	−0.919646	−	0.392749i	$-0.871524\pi$
$353$	−9.89949	+	9.89949i	−0.526897	+	0.526897i	0.392749	+	0.919646i	$0.371524\pi$
$354$	−7.00000	+	23.2164i	−0.372046	+	1.23394i
$355$			3.00000i			0.159223i
$356$	−1.41421	+	1.41421i	−0.0749532	+	0.0749532i
$357$	−9.00956	−	16.7877i	−0.476836	−	0.888501i
$358$	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
$366$	3.27620	+	6.10463i	0.171250	+	0.319094i
$367$	−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
$372$	5.43297	+	10.1234i	0.281686	+	0.524873i
$373$	−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
$375$	13.7354	−	7.37145i	0.709294	−	0.380660i
$376$		−	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	−0.976097	−	0.217336i	$-0.930263\pi$
$383$	−14.8492	+	14.8492i	−0.758761	+	0.758761i	0.217336	+	0.976097i	$0.430263\pi$
$384$	1.52616	−	0.819051i	0.0778814	−	0.0417970i
$385$	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	$-0.553782\pi$
$389$	−6.63325			−0.336319			−0.168160	+	0.985760i	$0.553782\pi$
$390$		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
$396$	−11.7615	+	2.38065i	−0.591037	+	0.119632i
$397$		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	$0.0727584\pi$
$401$	24.0416	+	24.0416i	1.20058	+	1.20058i	0.226592	+	0.973990i	$0.427242\pi$
$402$		0			0
$403$		0			0
$404$			13.2665i			0.660033i
$405$	8.33789	+	3.38815i	0.414313	+	0.168358i
$406$		0			0
$407$	−39.7995			−1.97279
$408$	−5.06169	+	2.71648i	−0.250591	+	0.134486i
$409$	−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
$411$	−9.15694	+	4.91430i	−0.451679	+	0.242405i
$412$	−6.00000			−0.295599
$413$	−46.4327			−2.28481
$414$	−19.5042	+	3.94786i	−0.958580	+	0.194027i
$415$		−	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	$0.0258158\pi$
$419$			3.31662i			0.162028i	−0.996713	+	0.0810139i	$0.974184\pi$
$420$	−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
$423$	−5.35647	−	26.4633i	−0.260440	−	1.28669i
$424$	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	−0.756349	−	0.654168i	$-0.773019\pi$
$431$	−2.12132	+	2.12132i	−0.102180	+	0.102180i	0.654168	+	0.756349i	$0.273019\pi$
$432$	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	$0.128890\pi$
$443$			16.5831i			0.787888i	−0.919134	+	0.393944i	$0.871110\pi$
$444$	15.1851	−	8.14945i	0.720652	−	0.386756i
$445$	−2.00000			−0.0948091
$446$	−9.94987			−0.471140
$447$	−4.91430	−	9.15694i	−0.232439	−	0.433109i
$448$	2.34521	+	2.34521i	0.110801	+	0.110801i
$449$	22.6274	+	22.6274i	1.06785	+	1.06785i	0.997524	+	0.0703301i	$0.0224052\pi$
$449$	22.6274	+	22.6274i	1.06785	+	1.06785i	0.0703301	+	0.997524i	$0.477595\pi$
$450$	−2.38065	−	11.7615i	−0.112225	−	0.554442i
$451$		0			0
$452$	−13.2665			−0.624004
$453$	8.14945	+	15.1851i	0.382895	+	0.713457i
$454$		−	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	−0.864646	−	0.502381i	$-0.832458\pi$
$461$	−7.77817	+	7.77817i	−0.362266	+	0.362266i	0.502381	+	0.864646i	$0.332458\pi$
$462$	−10.8659	−	20.2468i	−0.505529	−	0.941965i
$463$	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	$-0.450954\pi$
$467$	6.63325			0.306950			0.153475	+	0.988153i	$0.450954\pi$
$468$		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
$474$	−11.4667	−	21.3662i	−0.526683	−	0.981382i
$475$	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	0.783250	−	0.621707i	$-0.213561\pi$
$479$	3.53553	+	3.53553i	0.161543	+	0.161543i	−0.621707	+	0.783250i	$0.713561\pi$
$480$	1.65831	+	0.500000i	0.0756913	+	0.0228218i
$481$		0			0
$482$			19.8997i			0.906409i
$483$	−18.0191	−	33.5755i	−0.819898	−	1.52774i
$484$	5.00000			0.227273
$485$		0			0
$486$	9.78755	−	12.1328i	0.443972	−	0.550353i
$487$	−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
$489$	5.43297	+	10.1234i	0.245687	+	0.457795i
$490$	−4.00000			−0.180702
$491$	−9.94987			−0.449032			−0.224516	−	0.974470i	$-0.572080\pi$
$491$	−9.94987			−0.449032			−0.224516	+	0.974470i	$0.572080\pi$
$492$		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
$501$	18.3139	−	9.82861i	0.818204	−	0.439110i
$502$	−4.69042	+	4.69042i	−0.209344	+	0.209344i
$503$			33.1662i			1.47881i	0.673261	+	0.739405i	$0.264893\pi$
$503$			33.1662i			1.47881i	−0.673261	+	0.739405i	$0.735107\pi$
$504$	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	−0.930485	−	0.366330i	$-0.880614\pi$
$509$	−12.7279	+	12.7279i	−0.564155	+	0.564155i	0.366330	+	0.930485i	$0.380614\pi$
$510$	−5.50000	−	1.65831i	−0.243544	−	0.0734313i
$511$		−	22.0000i		−	0.973223i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	34.3180	+	3.20531i	1.51518	+	0.141518i
$514$	−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	$-0.773145\pi$
$521$		−	29.8496i		−	1.30774i	0.756609	−	0.653868i	$-0.226855\pi$
$522$		0			0
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$	16.5831			0.724437
$525$	20.2468	−	10.8659i	0.883641	−	0.474228i
$526$	−9.38083	−	9.38083i	−0.409024	−	0.409024i
$527$	−15.5563	−	15.5563i	−0.677645	−	0.677645i
$528$	−6.10463	+	3.27620i	−0.265670	+	0.142578i
$529$	21.0000			0.913043
$530$	6.63325			0.288130
$531$	8.33228	+	41.1652i	0.361590	+	1.78642i
$532$			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
$540$	5.17364	+	0.483219i	0.222638	+	0.0207944i
$541$	−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
$552$	−10.1234	+	5.43297i	−0.430880	+	0.231242i
$553$	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	0.0688347	−	0.997628i	$-0.478072\pi$
$557$	−21.9203	−	21.9203i	−0.928793	−	0.928793i	−0.997628	+	0.0688347i	$0.978072\pi$
$558$	16.5831	+	11.0000i	0.702020	+	0.465667i
$559$		0			0
$560$			3.31662i			0.140153i
$561$	20.2468	−	10.8659i	0.854819	−	0.458760i
$562$	18.0000			0.759284
$563$	−23.2164			−0.978453			−0.489227	−	0.872157i	$-0.662721\pi$
$563$	−23.2164			−0.978453			−0.489227	+	0.872157i	$0.662721\pi$
$564$	−7.37145	−	13.7354i	−0.310394	−	0.578365i
$565$	−9.38083	−	9.38083i	−0.394655	−	0.394655i
$566$	19.7990	+	19.7990i	0.832214	+	0.832214i
$567$	27.6537	+	11.2372i	1.16134	+	0.471918i
$568$	3.00000			0.125877
$569$	23.2164			0.973281			0.486641	−	0.873602i	$-0.338222\pi$
$569$	23.2164			0.973281			0.486641	+	0.873602i	$0.338222\pi$
$570$	5.43297	+	10.1234i	0.227562	+	0.424022i
$571$			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
$579$	−16.2989	−	30.3701i	−0.677359	−	1.26214i
$580$		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	−0.393841	−	0.919179i	$-0.628854\pi$
$587$	12.7279	−	12.7279i	0.525338	−	0.525338i	0.919179	+	0.393841i	$0.128854\pi$
$588$	−2.00000	+	6.63325i	−0.0824786	+	0.273551i
$589$			44.0000i			1.81299i
$590$	−9.89949	+	9.89949i	−0.407556	+	0.407556i
$591$	−18.8382	−	35.1016i	−0.774898	−	1.44389i
$592$	7.03562	−	7.03562i	0.289162	−	0.289162i
$593$	−22.6274	−	22.6274i	−0.929197	−	0.929197i	0.0684574	−	0.997654i	$-0.478192\pi$
$593$	−22.6274	−	22.6274i	−0.929197	−	0.929197i	−0.997654	+	0.0684574i	$0.978192\pi$
$594$	−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	$-0.763034\pi$
$599$		−	33.1662i		−	1.35514i	0.735460	−	0.677568i	$-0.236966\pi$
$600$	−3.27620	−	6.10463i	−0.133750	−	0.249220i
$601$	−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
$606$	10.8659	+	20.2468i	0.441398	+	0.822469i
$607$	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	$0.547926\pi$
$617$	−28.2843	+	28.2843i	−1.13868	+	1.13868i	−0.988687	+	0.149995i	$0.952074\pi$
$618$	−9.15694	+	4.91430i	−0.368346	+	0.197682i
$619$	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
$630$	1.97393	+	9.75211i	0.0786433	+	0.388533i
$631$	−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
$639$	8.82111	−	1.78549i	0.348958	−	0.0706329i
$640$	1.00000			0.0395285
$641$	39.7995			1.57199			0.785993	−	0.618236i	$-0.212152\pi$
$641$	39.7995			1.57199			0.785993	+	0.618236i	$0.212152\pi$
$642$	10.1234	−	5.43297i	0.399538	−	0.214422i
$643$	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
$645$	10.6831	−	5.73335i	0.420647	−	0.225751i
$646$	−22.0000			−0.865578
$647$	6.63325			0.260780			0.130390	−	0.991463i	$-0.458377\pi$
$647$	6.63325			0.260780			0.130390	+	0.991463i	$0.458377\pi$
$648$	3.38815	−	8.33789i	0.133099	−	0.327543i
$649$		−	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	$-0.715860\pi$
$653$		−	39.7995i		−	1.55747i	0.627350	−	0.778737i	$-0.284140\pi$
$654$	1.65831	−	5.50000i	0.0648451	−	0.215067i
$655$	11.7260	+	11.7260i	0.458174	+	0.458174i
$656$		0			0
$657$	−19.5042	+	3.94786i	−0.760932	+	0.154021i
$658$	21.1069	−	21.1069i	0.822831	−	0.822831i
$659$		−	19.8997i		−	0.775184i	−0.921831	−	0.387592i	$-0.873307\pi$
$659$		−	19.8997i		−	0.775184i	0.921831	−	0.387592i	$-0.126693\pi$
$660$	−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
$669$	−15.1851	+	8.14945i	−0.587089	+	0.315076i
$670$		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	$0.124904\pi$
$677$			19.8997i			0.764809i	−0.923995	+	0.382405i	$0.875096\pi$
$678$	−20.2468	+	10.8659i	−0.777572	+	0.417304i
$679$		0			0
$680$	−3.31662			−0.127187
$681$	−16.3810	−	30.5231i	−0.627722	−	1.16965i
$682$	−18.7617	−	18.7617i	−0.718421	−	0.718421i
$683$	18.3848	+	18.3848i	0.703474	+	0.703474i	0.965155	−	0.261681i	$-0.0842767\pi$
$683$	18.3848	+	18.3848i	0.703474	+	0.703474i	−0.261681	+	0.965155i	$0.584277\pi$
$684$	19.5042	−	3.94786i	0.745762	−	0.150950i
$685$	−6.00000			−0.229248
$686$	9.94987			0.379888
$687$	2.71648	+	5.06169i	0.103640	+	0.193116i
$688$		−	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	$-0.715446\pi$
$701$	−33.1662			−1.25267			−0.626336	+	0.779553i	$0.715446\pi$
$702$		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
$708$	11.4667	+	21.3662i	0.430945	+	0.802991i
$709$	−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
$717$	10.6477	+	19.8400i	0.397644	+	0.740940i
$718$		0			0
$719$	13.2665			0.494757			0.247378	−	0.968919i	$-0.420431\pi$
$719$	13.2665			0.494757			0.247378	+	0.968919i	$0.420431\pi$
$720$	2.94037	−	0.595163i	0.109581	−	0.0221804i
$721$	−14.0712	−	14.0712i	−0.524041	−	0.524041i
$722$	17.6777	+	17.6777i	0.657895	+	0.657895i
$723$	16.2989	+	30.3701i	0.606163	+	1.12948i
$724$	−10.0000			−0.371647
$725$		0			0
$726$	7.63079	−	4.09525i	0.283205	−	0.151989i
$727$			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
$735$	−6.10463	+	3.27620i	−0.225173	+	0.120845i
$736$	−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	−0.974907	−	0.222612i	$-0.928542\pi$
$743$	−20.5061	+	20.5061i	−0.752296	+	0.752296i	0.222612	+	0.974907i	$0.428542\pi$
$744$	11.0000	+	3.31662i	0.403280	+	0.121593i
$745$		−	6.00000i		−	0.219823i
$746$	−2.82843	+	2.82843i	−0.103556	+	0.103556i
$747$	−17.6422	+	3.57098i	−0.645495	+	0.130655i
$748$	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
$756$	17.1590	+	1.60266i	0.624067	+	0.0582881i
$757$	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
$759$	40.4935	−	21.7319i	1.46982	−	0.788817i
$760$	4.69042	+	4.69042i	0.170139	+	0.170139i
$761$	−9.89949	−	9.89949i	−0.358856	−	0.358856i	0.504535	−	0.863391i	$-0.331664\pi$
$761$	−9.89949	−	9.89949i	−0.358856	−	0.358856i	−0.863391	+	0.504535i	$0.831664\pi$
$762$	9.15694	−	4.91430i	0.331721	−	0.178026i
$763$	11.0000			0.398227
$764$	13.2665			0.479965
$765$	−9.75211	+	1.97393i	−0.352588	+	0.0713677i
$766$			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	−0.192816	−	0.981235i	$-0.561762\pi$
$773$	21.9203	−	21.9203i	0.788419	−	0.788419i	0.981235	+	0.192816i	$0.0617621\pi$
$774$	−4.16614	−	20.5826i	−0.149749	−	0.739826i
$775$	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
$786$	25.3085	−	13.5824i	0.902723	−	0.484469i
$787$	−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
$795$	10.1234	−	5.43297i	0.359039	−	0.192687i
$796$	−4.00000			−0.141776
$797$	−33.1662			−1.17481			−0.587404	−	0.809294i	$-0.699850\pi$
$797$	−33.1662			−1.17481			−0.587404	+	0.809294i	$0.699850\pi$
$798$	18.0191	+	33.5755i	0.637870	+	1.18856i
$799$	21.1069	+	21.1069i	0.746707	+	0.746707i
$800$	−2.82843	−	2.82843i	−0.100000	−	0.100000i
$801$	1.19033	+	5.88074i	0.0420581	+	0.207786i
$802$	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	$0.0941596\pi$
$809$			16.5831i			0.583032i	−0.956566	+	0.291516i	$0.905840\pi$
$810$	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
$813$	−8.14945	−	15.1851i	−0.285814	−	0.532564i
$814$	−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	−0.809384	−	0.587280i	$-0.800199\pi$
$821$	−6.36396	+	6.36396i	−0.222104	+	0.222104i	0.587280	+	0.809384i	$0.300199\pi$
$822$	−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
$825$	13.1048	+	24.4185i	0.456251	+	0.850144i
$826$	−32.8329	+	32.8329i	−1.14240	+	1.14240i
$827$	9.89949	+	9.89949i	0.344239	+	0.344239i	0.857958	−	0.513719i	$-0.171733\pi$
$827$	9.89949	+	9.89949i	0.344239	+	0.344239i	−0.513719	+	0.857958i	$0.671733\pi$
$828$	−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
$834$	−10.6477	−	19.8400i	−0.368698	−	0.687005i
$835$	12.0000			0.415277
$836$	−26.5330			−0.917663
$837$	34.3180	+	3.20531i	1.18620	+	0.110792i
$838$	2.34521	+	2.34521i	0.0810139	+	0.0810139i
$839$	16.9706	+	16.9706i	0.585889	+	0.585889i	0.936515	−	0.350626i	$-0.114031\pi$
$839$	16.9706	+	16.9706i	0.585889	+	0.585889i	−0.350626	+	0.936515i	$0.614031\pi$
$840$	2.71648	+	5.06169i	0.0937276	+	0.174645i
$841$	29.0000			1.00000
$842$	−29.8496			−1.02869
$843$	27.4708	−	14.7429i	0.946146	−	0.507773i
$844$		−	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
$852$	4.57847	−	2.45715i	0.156856	−	0.0841806i
$853$	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	$-0.262083\pi$
$857$	39.7995			1.35952			0.679762	+	0.733432i	$0.262083\pi$
$858$		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	−0.303072	−	0.952968i	$-0.598012\pi$
$863$	19.0919	−	19.0919i	0.649895	−	0.649895i	0.952968	+	0.303072i	$0.0980124\pi$
$864$	0.483219	−	5.17364i	0.0164395	−	0.176011i
$865$	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
$876$	−10.1234	+	5.43297i	−0.342037	+	0.183563i
$877$	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
$879$	−28.9970	+	15.5620i	−0.978044	+	0.524892i
$880$	−4.00000			−0.134840
$881$	16.5831			0.558700			0.279350	−	0.960189i	$-0.409881\pi$
$881$	16.5831			0.558700			0.279350	+	0.960189i	$0.409881\pi$
$882$	2.38065	+	11.7615i	0.0801607	+	0.396030i
$883$			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	$-0.853045\pi$
$887$		−	26.5330i		−	0.890891i	0.895309	−	0.445445i	$-0.146955\pi$
$888$	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
$891$	−13.5526	+	33.3516i	−0.454029	+	1.11732i
$892$	−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
$903$	35.4318	−	19.0154i	1.17910	−	0.632792i
$904$	−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	$0.341840\pi$
$911$			53.0660i			1.75815i	−0.476679	+	0.879077i	$0.658160\pi$
$912$	10.1234	−	5.43297i	0.335219	−	0.179904i
$913$	24.0000			0.794284
$914$	−6.63325			−0.219408
$915$	3.27620	+	6.10463i	0.108308	+	0.201813i
$916$	2.34521	+	2.34521i	0.0774878	+	0.0774878i
$917$	38.8909	+	38.8909i	1.28429	+	1.28429i
$918$	−1.60266	+	17.1590i	−0.0528956	+	0.566332i
$919$	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
$921$	5.43297	+	10.1234i	0.179022	+	0.333577i
$922$			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	$-0.379280\pi$
$929$	39.5980	−	39.5980i	1.29917	−	1.29917i	0.928942	−	0.370226i	$-0.120720\pi$
$930$	5.43297	+	10.1234i	0.178154	+	0.331959i
$931$	−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	−0.858530	−	0.512764i	$-0.828622\pi$
$941$	−10.6066	+	10.6066i	−0.345765	+	0.345765i	0.512764	+	0.858530i	$0.328622\pi$
$942$	−1.63810	−	3.05231i	−0.0533722	−	0.0994498i
$943$		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	0.793019	−	0.609196i	$-0.208508\pi$
$947$	5.65685	+	5.65685i	0.183823	+	0.183823i	−0.609196	+	0.793019i	$0.708508\pi$
$948$	−23.2164	−	7.00000i	−0.754033	−	0.227349i
$949$		0			0
$950$		−	26.5330i		−	0.860844i
$951$	1.63810	+	3.05231i	0.0531191	+	0.0989781i
$952$	−11.0000			−0.356512
$953$	−9.94987			−0.322308			−0.161154	−	0.986929i	$-0.551522\pi$
$953$	−9.94987			−0.322308			−0.161154	+	0.986929i	$0.551522\pi$
$954$	−3.94786	−	19.5042i	−0.127817	−	0.631472i
$955$	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
$960$	1.52616	−	0.819051i	0.0492565	−	0.0264347i
$961$			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
$969$	−33.5755	+	18.0191i	−1.07860	+	0.578857i
$970$		0			0
$971$		−	9.94987i		−	0.319307i	−0.987173	−	0.159653i	$-0.948962\pi$
$971$		−	9.94987i		−	0.319307i	0.987173	−	0.159653i	$-0.0510376\pi$
$972$	−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	−0.315500	−	0.948926i	$-0.602172\pi$
$977$	19.7990	−	19.7990i	0.633426	−	0.633426i	0.948926	+	0.315500i	$0.102172\pi$
$978$	11.0000	+	3.31662i	0.351741	+	0.106054i
$979$		−	8.00000i		−	0.255681i
$980$	−2.82843	+	2.82843i	−0.0903508	+	0.0903508i
$981$	−1.97393	−	9.75211i	−0.0630228	−	0.311361i
$982$	−7.03562	+	7.03562i	−0.224516	+	0.224516i
$983$	−43.1335	−	43.1335i	−1.37575	−	1.37575i	−0.851675	−	0.524071i	$-0.824413\pi$
$983$	−43.1335	−	43.1335i	−1.37575	−	1.37575i	−0.524071	−	0.851675i	$-0.675587\pi$
$984$		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
$990$	−11.7615	+	2.38065i	−0.373804	+	0.0756621i
$991$	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
$993$	−10.1234	+	5.43297i	−0.321256	+	0.172410i
$994$	7.03562	+	7.03562i	0.223156	+	0.223156i
$995$	−2.82843	−	2.82843i	−0.0896672	−	0.0896672i
$996$	−9.15694	+	4.91430i	−0.290149	+	0.155716i
$997$	−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
$999$	4.80797	−	51.4770i	0.152117	−	1.62866i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.500000 - 1.65831i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.819051 - 1.52616i) q^{6} +(2.34521 - 2.34521i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.500000 - 1.65831i) q^{3} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.819051 - 1.52616i) 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} +(-0.819051 - 1.52616i) q^{15} -1.00000 q^{16} +3.31662 q^{17} +(-2.94037 + 0.595163i) q^{18} +(-4.69042 - 4.69042i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-2.71648 - 5.06169i) q^{21} +4.00000 q^{22} +6.63325 q^{23} +(-1.52616 + 0.819051i) 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} +(6.10463 - 3.27620i) 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} +(-2.94037 + 0.595163i) 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} +(-0.483219 + 5.17364i) q^{54} +4.00000 q^{55} -3.31662 q^{56} +(-10.1234 + 5.43297i) q^{57} +(-9.89949 - 9.89949i) q^{59} +(-1.52616 + 0.819051i) q^{60} -4.00000 q^{61} -6.63325 q^{62} +(-9.75211 + 1.97393i) 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} +(0.595163 + 2.94037i) 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} +(-5.06169 + 2.71648i) 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} +(-10.1234 + 5.43297i) q^{93} +9.00000 q^{94} -6.63325 q^{95} +(0.819051 + 1.52616i) q^{96} +(-2.82843 - 2.82843i) q^{98} +(-2.38065 - 11.7615i) 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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