LMFDB - Embedded newform 1274.2.n.d.753.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(753,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("1274.753");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.n (of order $6$, degree $2$, not 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:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			753.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1274.753
Dual form			1274.2.n.d.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} +1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} +1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(2.00000 - 3.00000i) q^{13} -3.00000i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.73205 - 1.00000i) q^{18} +(5.19615 - 3.00000i) q^{19} -3.00000i q^{20} +(3.00000 + 5.19615i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.232051 + 3.59808i) q^{26} +5.00000 q^{27} +(1.50000 + 2.59808i) q^{30} +(0.866025 + 0.500000i) q^{32} -3.00000i q^{34} +2.00000 q^{36} +(-2.59808 + 1.50000i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-1.59808 - 3.23205i) q^{39} +(1.50000 + 2.59808i) q^{40} -1.00000 q^{43} +(5.19615 + 3.00000i) q^{45} +(-5.19615 - 3.00000i) q^{46} +(-2.59808 + 1.50000i) q^{47} -1.00000 q^{48} +4.00000i q^{50} +(1.50000 + 2.59808i) q^{51} +(-1.59808 - 3.23205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-4.33013 + 2.50000i) q^{54} -6.00000i q^{57} +(-5.19615 - 3.00000i) q^{59} +(-2.59808 - 1.50000i) q^{60} +(4.00000 + 6.92820i) q^{61} -1.00000 q^{64} +(0.696152 - 10.7942i) q^{65} +(-10.3923 - 6.00000i) q^{67} +(1.50000 + 2.59808i) q^{68} +6.00000 q^{69} -15.0000i q^{71} +(-1.73205 + 1.00000i) q^{72} +(5.19615 + 3.00000i) q^{73} +(1.50000 - 2.59808i) q^{74} +(-2.00000 - 3.46410i) q^{75} -6.00000i q^{76} +(3.00000 + 2.00000i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(-2.59808 - 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} -6.00000i q^{83} +9.00000i q^{85} +(0.866025 - 0.500000i) q^{86} +(5.19615 - 3.00000i) q^{89} -6.00000 q^{90} +6.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(9.00000 - 15.5885i) q^{95} +(0.866025 - 0.500000i) q^{96} +12.0000i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9} - 6 q^{10} - 2 q^{12} + 8 q^{13} - 2 q^{16} - 6 q^{17} + 12 q^{23} + 8 q^{25} + 6 q^{26} + 20 q^{27} + 6 q^{30} + 8 q^{36} - 12 q^{38} + 4 q^{39} + 6 q^{40} - 4 q^{43} - 4 q^{48} + 6 q^{51} + 4 q^{52} + 12 q^{53} + 16 q^{61} - 4 q^{64} - 18 q^{65} + 6 q^{68} + 24 q^{69} + 6 q^{74} - 8 q^{75} + 12 q^{78} - 20 q^{79} - 2 q^{81} - 24 q^{90} + 24 q^{92} + 6 q^{94} + 36 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9 - 6 * q^10 - 2 * q^12 + 8 * q^13 - 2 * q^16 - 6 * q^17 + 12 * q^23 + 8 * q^25 + 6 * q^26 + 20 * q^27 + 6 * q^30 + 8 * q^36 - 12 * q^38 + 4 * q^39 + 6 * q^40 - 4 * q^43 - 4 * q^48 + 6 * q^51 + 4 * q^52 + 12 * q^53 + 16 * q^61 - 4 * q^64 - 18 * q^65 + 6 * q^68 + 24 * q^69 + 6 * q^74 - 8 * q^75 + 12 * q^78 - 20 * q^79 - 2 * q^81 - 24 * q^90 + 24 * q^92 + 6 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.59808	−	1.50000i	1.16190	−	0.670820i	0.210138	−	0.977672i	$-0.432609\pi$
$5$	2.59808	−	1.50000i	1.16190	−	0.670820i	0.951757	+	0.306851i	$0.0992755\pi$
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$		0			0
$15$		−	3.00000i		−	0.774597i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−1.73205	−	1.00000i	−0.408248	−	0.235702i
$19$	5.19615	−	3.00000i	1.19208	−	0.688247i	0.233301	−	0.972404i	$-0.425047\pi$
$19$	5.19615	−	3.00000i	1.19208	−	0.688247i	0.958778	+	0.284157i	$0.0917138\pi$
$20$		−	3.00000i		−	0.670820i
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−0.232051	+	3.59808i	−0.0455089	+	0.705641i
$27$	5.00000			0.962250
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	3.00000i		−	0.514496i
$35$		0			0
$36$	2.00000			0.333333
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	−0.698119	−	0.715981i	$-0.745980\pi$
$37$	−2.59808	+	1.50000i	−0.427121	+	0.246598i	0.270998	+	0.962580i	$0.412646\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$	−1.59808	−	3.23205i	−0.255897	−	0.517542i
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$	5.19615	+	3.00000i	0.774597	+	0.447214i
$46$	−5.19615	−	3.00000i	−0.766131	−	0.442326i
$47$	−2.59808	+	1.50000i	−0.378968	+	0.218797i	−0.677369	−	0.735643i	$-0.736880\pi$
$47$	−2.59808	+	1.50000i	−0.378968	+	0.218797i	0.298401	+	0.954441i	$0.403547\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$			4.00000i			0.565685i
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$	−1.59808	−	3.23205i	−0.221613	−	0.448205i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$	−4.33013	+	2.50000i	−0.589256	+	0.340207i
$55$		0			0
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$		0			0
$59$	−5.19615	−	3.00000i	−0.676481	−	0.390567i	0.122047	−	0.992524i	$-0.461054\pi$
$59$	−5.19615	−	3.00000i	−0.676481	−	0.390567i	−0.798528	+	0.601958i	$0.794388\pi$
$60$	−2.59808	−	1.50000i	−0.335410	−	0.193649i
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.696152	−	10.7942i	0.0863471	−	1.33886i
$66$		0			0
$67$	−10.3923	−	6.00000i	−1.26962	−	0.733017i	−0.294706	−	0.955588i	$-0.595222\pi$
$67$	−10.3923	−	6.00000i	−1.26962	−	0.733017i	−0.974916	+	0.222571i	$0.928555\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	6.00000			0.722315
$70$		0			0
$71$		−	15.0000i		−	1.78017i	−0.455792	−	0.890086i	$-0.650644\pi$
$71$		−	15.0000i		−	1.78017i	0.455792	−	0.890086i	$-0.349356\pi$
$72$	−1.73205	+	1.00000i	−0.204124	+	0.117851i
$73$	5.19615	+	3.00000i	0.608164	+	0.351123i	0.772246	−	0.635323i	$-0.219133\pi$
$73$	5.19615	+	3.00000i	0.608164	+	0.351123i	−0.164083	+	0.986447i	$0.552466\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$		−	6.00000i		−	0.688247i
$77$		0			0
$78$	3.00000	+	2.00000i	0.339683	+	0.226455i
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	−2.59808	−	1.50000i	−0.290474	−	0.167705i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$			9.00000i			0.976187i
$86$	0.866025	−	0.500000i	0.0933859	−	0.0539164i
$87$		0			0
$88$		0			0
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	−0.198650	−	0.980071i	$-0.563656\pi$
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	0.749441	+	0.662071i	$0.230322\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$	6.00000			0.625543
$93$		0			0
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	9.00000	−	15.5885i	0.923381	−	1.59934i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$			12.0000i			1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$			12.0000i			1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$	−2.59808	−	1.50000i	−0.257248	−	0.148522i
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$	3.00000	+	2.00000i	0.294174	+	0.196116i
$105$		0			0
$106$			6.00000i			0.582772i
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	7.79423	+	4.50000i	0.746552	+	0.431022i	0.824447	−	0.565940i	$-0.191487\pi$
$109$	7.79423	+	4.50000i	0.746552	+	0.431022i	−0.0778949	+	0.996962i	$0.524820\pi$
$110$		0			0
$111$			3.00000i			0.284747i
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	15.5885	+	9.00000i	1.45363	+	0.839254i
$116$		0			0
$117$	7.19615	+	0.464102i	0.665285	+	0.0429062i
$118$	6.00000			0.552345
$119$		0			0
$120$	3.00000			0.273861
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	−6.92820	−	4.00000i	−0.627250	−	0.362143i
$123$		0			0
$124$		0			0
$125$			3.00000i			0.268328i
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.500000	+	0.866025i	−0.0440225	+	0.0762493i
$130$	4.79423	+	9.69615i	0.420482	+	0.850409i
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	0.924084	−	0.382190i	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$		0			0
$133$		0			0
$134$	12.0000			1.03664
$135$	12.9904	−	7.50000i	1.11803	−	0.645497i
$136$	−2.59808	−	1.50000i	−0.222783	−	0.128624i
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.985577	−	0.169226i	$-0.0541268\pi$
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.346235	+	0.938148i	$0.387460\pi$
$138$	−5.19615	+	3.00000i	−0.442326	+	0.255377i
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$		0			0
$141$			3.00000i			0.252646i
$142$	7.50000	+	12.9904i	0.629386	+	1.09013i
$143$		0			0
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$		0			0
$146$	−6.00000			−0.496564
$147$		0			0
$148$			3.00000i			0.246598i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$	3.46410	+	2.00000i	0.282843	+	0.163299i
$151$	−12.9904	−	7.50000i	−1.05714	−	0.610341i	−0.132502	−	0.991183i	$-0.542301\pi$
$151$	−12.9904	−	7.50000i	−1.05714	−	0.610341i	−0.924640	+	0.380841i	$0.875634\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	−3.59808	−	0.232051i	−0.288077	−	0.0185789i
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.853646	−	0.520854i	$-0.174386\pi$
$158$	8.66025	+	5.00000i	0.688973	+	0.397779i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	3.00000			0.237171
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−5.19615	+	3.00000i	−0.406994	+	0.234978i	−0.689497	−	0.724288i	$-0.742169\pi$
$163$	−5.19615	+	3.00000i	−0.406994	+	0.234978i	0.282503	+	0.959266i	$0.408835\pi$
$164$		0			0
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−4.50000	−	7.79423i	−0.345134	−	0.597790i
$171$	10.3923	+	6.00000i	0.794719	+	0.458831i
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.19615	+	3.00000i	−0.390567	+	0.225494i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	−0.997446	+	0.0714220i	$0.977246\pi$
$180$	5.19615	−	3.00000i	0.387298	−	0.223607i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$	−5.19615	+	3.00000i	−0.383065	+	0.221163i
$185$	−4.50000	+	7.79423i	−0.330847	+	0.573043i
$186$		0			0
$187$		0			0
$188$			3.00000i			0.218797i
$189$		0			0
$190$			18.0000i			1.30586i
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	5.19615	+	3.00000i	0.374027	+	0.215945i	0.675216	−	0.737620i	$-0.264050\pi$
$193$	5.19615	+	3.00000i	0.374027	+	0.215945i	−0.301189	+	0.953564i	$0.597384\pi$
$194$	−6.00000	−	10.3923i	−0.430775	−	0.746124i
$195$	−9.00000	−	6.00000i	−0.644503	−	0.429669i
$196$		0			0
$197$		−	3.00000i		−	0.213741i	−0.994273	−	0.106871i	$-0.965917\pi$
$197$		−	3.00000i		−	0.213741i	0.994273	−	0.106871i	$-0.0340831\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	3.46410	+	2.00000i	0.244949	+	0.141421i
$201$	−10.3923	+	6.00000i	−0.733017	+	0.423207i
$202$		−	12.0000i		−	0.844317i
$203$		0			0
$204$	3.00000			0.210042
$205$		0			0
$206$	12.1244	+	7.00000i	0.844744	+	0.487713i
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$	−3.59808	−	0.232051i	−0.249482	−	0.0160898i
$209$		0			0
$210$		0			0
$211$	−23.0000			−1.58339			−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000			−1.58339			−0.791693	+	0.610920i	$0.790800\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	−12.9904	−	7.50000i	−0.890086	−	0.513892i
$214$	−10.3923	−	6.00000i	−0.710403	−	0.410152i
$215$	−2.59808	+	1.50000i	−0.177187	+	0.102299i
$216$			5.00000i			0.340207i
$217$		0			0
$218$	−9.00000			−0.609557
$219$	5.19615	−	3.00000i	0.351123	−	0.202721i
$220$		0			0
$221$	4.79423	+	9.69615i	0.322495	+	0.652234i
$222$	−1.50000	−	2.59808i	−0.100673	−	0.174371i
$223$			9.00000i			0.602685i	0.953516	+	0.301342i	$0.0974347\pi$
$223$			9.00000i			0.602685i	−0.953516	+	0.301342i	$0.902565\pi$
$224$		0			0
$225$	8.00000			0.533333
$226$	5.19615	−	3.00000i	0.345643	−	0.199557i
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	0.113761	−	0.993508i	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$	−5.19615	−	3.00000i	−0.344124	−	0.198680i
$229$	−7.79423	+	4.50000i	−0.515057	+	0.297368i	−0.734910	−	0.678165i	$-0.762776\pi$
$229$	−7.79423	+	4.50000i	−0.515057	+	0.297368i	0.219853	+	0.975533i	$0.429442\pi$
$230$	−18.0000			−1.18688
$231$		0			0
$232$		0			0
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$	−6.46410	+	3.19615i	−0.422572	+	0.208939i
$235$	−4.50000	+	7.79423i	−0.293548	+	0.508439i
$236$	−5.19615	+	3.00000i	−0.338241	+	0.195283i
$237$	−10.0000			−0.649570
$238$		0			0
$239$		−	9.00000i		−	0.582162i	−0.956698	−	0.291081i	$-0.905985\pi$
$239$		−	9.00000i		−	0.582162i	0.956698	−	0.291081i	$-0.0940149\pi$
$240$	−2.59808	+	1.50000i	−0.167705	+	0.0968246i
$241$	−25.9808	−	15.0000i	−1.67357	−	0.966235i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−25.9808	−	15.0000i	−1.67357	−	0.966235i	−0.707953	−	0.706260i	$-0.750381\pi$
$242$	9.52628	+	5.50000i	0.612372	+	0.353553i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	8.00000			0.512148
$245$		0			0
$246$		0			0
$247$	1.39230	−	21.5885i	0.0885902	−	1.37364i
$248$		0			0
$249$	−5.19615	−	3.00000i	−0.329293	−	0.190117i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		0			0
$254$	1.73205	−	1.00000i	0.108679	−	0.0627456i
$255$	7.79423	+	4.50000i	0.488094	+	0.281801i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$		−	1.00000i		−	0.0622573i
$259$		0			0
$260$	−9.00000	−	6.00000i	−0.558156	−	0.372104i
$261$		0			0
$262$	−2.59808	−	1.50000i	−0.160510	−	0.0926703i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$		−	18.0000i		−	1.10573i
$266$		0			0
$267$		−	6.00000i		−	0.367194i
$268$	−10.3923	+	6.00000i	−0.634811	+	0.366508i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	−7.50000	+	12.9904i	−0.456435	+	0.790569i
$271$	−12.9904	+	7.50000i	−0.789109	+	0.455593i	−0.839649	−	0.543130i	$-0.817239\pi$
$271$	−12.9904	+	7.50000i	−0.789109	+	0.455593i	0.0505395	+	0.998722i	$0.483906\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	−18.0000			−1.08742
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−4.33013	+	2.50000i	−0.259704	+	0.149940i
$279$		0			0
$280$		0			0
$281$			30.0000i			1.78965i	0.446417	+	0.894825i	$0.352700\pi$
$281$			30.0000i			1.78965i	−0.446417	+	0.894825i	$0.647300\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−12.9904	−	7.50000i	−0.770837	−	0.445043i
$285$	−9.00000	−	15.5885i	−0.533114	−	0.923381i
$286$		0			0
$287$		0			0
$288$			2.00000i			0.117851i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	10.3923	+	6.00000i	0.609208	+	0.351726i
$292$	5.19615	−	3.00000i	0.304082	−	0.175562i
$293$			9.00000i			0.525786i	0.964825	+	0.262893i	$0.0846766\pi$
$293$			9.00000i			0.525786i	−0.964825	+	0.262893i	$0.915323\pi$
$294$		0			0
$295$	−18.0000			−1.04800
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$		0			0
$298$	−3.00000	+	5.19615i	−0.173785	+	0.301005i
$299$	21.5885	+	1.39230i	1.24849	+	0.0805191i
$300$	−4.00000			−0.230940
$301$		0			0
$302$	15.0000			0.863153
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$	−5.19615	−	3.00000i	−0.298020	−	0.172062i
$305$	20.7846	+	12.0000i	1.19012	+	0.687118i
$306$	5.19615	−	3.00000i	0.297044	−	0.171499i
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$		0			0
$309$	−14.0000			−0.796432
$310$		0			0
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$	3.23205	−	1.59808i	0.182979	−	0.0904732i
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$			22.0000i			1.24153i
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−15.5885	+	9.00000i	−0.875535	+	0.505490i	−0.869184	−	0.494489i	$-0.835355\pi$
$317$	−15.5885	+	9.00000i	−0.875535	+	0.505490i	−0.00635137	+	0.999980i	$0.502022\pi$
$318$	5.19615	+	3.00000i	0.291386	+	0.168232i
$319$		0			0
$320$	−2.59808	+	1.50000i	−0.145237	+	0.0838525i
$321$	12.0000			0.669775
$322$		0			0
$323$			18.0000i			1.00155i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−6.39230	−	12.9282i	−0.354581	−	0.717128i
$326$	3.00000	−	5.19615i	0.166155	−	0.287788i
$327$	7.79423	−	4.50000i	0.431022	−	0.248851i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−25.9808	+	15.0000i	−1.42803	+	0.824475i	−0.996965	−	0.0778456i	$-0.975196\pi$
$331$	−25.9808	+	15.0000i	−1.42803	+	0.824475i	−0.431066	+	0.902320i	$0.641863\pi$
$332$	−5.19615	−	3.00000i	−0.285176	−	0.164646i
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	−36.0000			−1.96689
$336$		0			0
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	10.3301	+	7.89230i	0.561885	+	0.429285i
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$	7.79423	+	4.50000i	0.422701	+	0.244047i
$341$		0			0
$342$	−12.0000			−0.648886
$343$		0			0
$344$		−	1.00000i		−	0.0539164i
$345$	15.5885	−	9.00000i	0.839254	−	0.484544i
$346$	−5.19615	−	3.00000i	−0.279347	−	0.161281i
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.0409337	+	0.999162i	$0.513033\pi$
$347$	−16.5000	+	28.5788i	−0.885766	+	1.53419i	−0.844833	+	0.535031i	$0.820300\pi$
$348$		0			0
$349$			21.0000i			1.12410i	0.827102	+	0.562052i	$0.189988\pi$
$349$			21.0000i			1.12410i	−0.827102	+	0.562052i	$0.810012\pi$
$350$		0			0
$351$	10.0000	−	15.0000i	0.533761	−	0.800641i
$352$		0			0
$353$	5.19615	+	3.00000i	0.276563	+	0.159674i	0.631867	−	0.775077i	$-0.282289\pi$
$353$	5.19615	+	3.00000i	0.276563	+	0.159674i	−0.355303	+	0.934751i	$0.615622\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$	−22.5000	−	38.9711i	−1.19418	−	2.06837i
$356$		−	6.00000i		−	0.317999i
$357$		0			0
$358$		−	15.0000i		−	0.792775i
$359$	−20.7846	+	12.0000i	−1.09697	+	0.633336i	−0.935423	−	0.353529i	$-0.884981\pi$
$359$	−20.7846	+	12.0000i	−1.09697	+	0.633336i	−0.161546	+	0.986865i	$0.551648\pi$
$360$	−3.00000	+	5.19615i	−0.158114	+	0.273861i
$361$	8.50000	−	14.7224i	0.447368	−	0.774865i
$362$	−1.73205	+	1.00000i	−0.0910346	+	0.0525588i
$363$	−11.0000			−0.577350
$364$		0			0
$365$	18.0000			0.942163
$366$	−6.92820	+	4.00000i	−0.362143	+	0.209083i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$		0			0
$370$		−	9.00000i		−	0.467888i
$371$		0			0
$372$		0			0
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$		0			0
$375$	2.59808	+	1.50000i	0.134164	+	0.0774597i
$376$	−1.50000	−	2.59808i	−0.0773566	−	0.133986i
$377$		0			0
$378$		0			0
$379$			6.00000i			0.308199i	0.988055	+	0.154100i	$0.0492477\pi$
$379$			6.00000i			0.308199i	−0.988055	+	0.154100i	$0.950752\pi$
$380$	−9.00000	−	15.5885i	−0.461690	−	0.799671i
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$	10.3923	+	6.00000i	0.531717	+	0.306987i
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	−0.287469	−	0.957790i	$-0.592814\pi$
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	0.685736	+	0.727851i	$0.259481\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$	−6.00000			−0.305392
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	10.3923	+	6.00000i	0.527589	+	0.304604i
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$	10.7942	+	0.696152i	0.546587	+	0.0352510i
$391$	−18.0000			−0.910299
$392$		0			0
$393$	3.00000			0.151330
$394$	1.50000	+	2.59808i	0.0755689	+	0.130889i
$395$	−25.9808	−	15.0000i	−1.30723	−	0.754732i
$396$		0			0
$397$	−15.5885	+	9.00000i	−0.782362	+	0.451697i	−0.837267	−	0.546795i	$-0.815848\pi$
$397$	−15.5885	+	9.00000i	−0.782362	+	0.451697i	0.0549046	+	0.998492i	$0.482515\pi$
$398$			20.0000i			1.00251i
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−25.9808	+	15.0000i	−1.29742	+	0.749064i	−0.979957	−	0.199207i	$-0.936163\pi$
$401$	−25.9808	+	15.0000i	−1.29742	+	0.749064i	−0.317460	+	0.948272i	$0.602830\pi$
$402$	6.00000	−	10.3923i	0.299253	−	0.518321i
$403$		0			0
$404$	6.00000	+	10.3923i	0.298511	+	0.517036i
$405$			3.00000i			0.149071i
$406$		0			0
$407$		0			0
$408$	−2.59808	+	1.50000i	−0.128624	+	0.0742611i
$409$	−5.19615	−	3.00000i	−0.256933	−	0.148340i	0.366002	−	0.930614i	$-0.380726\pi$
$409$	−5.19615	−	3.00000i	−0.256933	−	0.148340i	−0.622935	+	0.782274i	$0.714060\pi$
$410$		0			0
$411$	15.5885	−	9.00000i	0.768922	−	0.443937i
$412$	−14.0000			−0.689730
$413$		0			0
$414$		−	12.0000i		−	0.589768i
$415$	−9.00000	−	15.5885i	−0.441793	−	0.765207i
$416$	3.23205	−	1.59808i	0.158464	−	0.0783521i
$417$	2.50000	−	4.33013i	0.122426	−	0.212047i
$418$		0			0
$419$	15.0000			0.732798			0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000			0.732798			0.366399	+	0.930458i	$0.380591\pi$
$420$		0			0
$421$			15.0000i			0.731055i	0.930800	+	0.365528i	$0.119111\pi$
$421$			15.0000i			0.731055i	−0.930800	+	0.365528i	$0.880889\pi$
$422$	19.9186	−	11.5000i	0.969622	−	0.559811i
$423$	−5.19615	−	3.00000i	−0.252646	−	0.145865i
$424$	5.19615	+	3.00000i	0.252347	+	0.145693i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	15.0000			0.726752
$427$		0			0
$428$	12.0000			0.580042
$429$		0			0
$430$	1.50000	−	2.59808i	0.0723364	−	0.125290i
$431$	−12.9904	−	7.50000i	−0.625725	−	0.361262i	0.153370	−	0.988169i	$-0.450987\pi$
$431$	−12.9904	−	7.50000i	−0.625725	−	0.361262i	−0.779094	+	0.626907i	$0.784321\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$		0			0
$435$		0			0
$436$	7.79423	−	4.50000i	0.373276	−	0.215511i
$437$	31.1769	+	18.0000i	1.49139	+	0.861057i
$438$	−3.00000	+	5.19615i	−0.143346	+	0.248282i
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$		0			0
$441$		0			0
$442$	−9.00000	−	6.00000i	−0.428086	−	0.285391i
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	0.999999	−	0.00130426i	$-0.000415158\pi$
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	−0.501129	+	0.865373i	$0.667082\pi$
$444$	2.59808	+	1.50000i	0.123299	+	0.0711868i
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−4.50000	−	7.79423i	−0.213081	−	0.369067i
$447$		−	6.00000i		−	0.283790i
$448$		0			0
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$	−6.92820	+	4.00000i	−0.326599	+	0.188562i
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−12.9904	+	7.50000i	−0.610341	+	0.352381i
$454$	12.0000			0.563188
$455$		0			0
$456$	6.00000			0.280976
$457$	−15.5885	+	9.00000i	−0.729197	+	0.421002i	−0.818128	−	0.575036i	$-0.804988\pi$
$457$	−15.5885	+	9.00000i	−0.729197	+	0.421002i	0.0889312	+	0.996038i	$0.471655\pi$
$458$	4.50000	−	7.79423i	0.210271	−	0.364200i
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$	15.5885	−	9.00000i	0.726816	−	0.419627i
$461$			15.0000i			0.698620i	0.937007	+	0.349310i	$0.113584\pi$
$461$			15.0000i			0.698620i	−0.937007	+	0.349310i	$0.886416\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$		0			0
$465$		0			0
$466$	−18.1865	−	10.5000i	−0.842475	−	0.486403i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$	4.00000	−	6.00000i	0.184900	−	0.277350i
$469$		0			0
$470$		−	9.00000i		−	0.415139i
$471$	−11.0000	−	19.0526i	−0.506853	−	0.877896i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$		0			0
$474$	8.66025	−	5.00000i	0.397779	−	0.229658i
$475$		−	24.0000i		−	1.10120i
$476$		0			0
$477$	12.0000			0.549442
$478$	4.50000	+	7.79423i	0.205825	+	0.356500i
$479$	33.7750	+	19.5000i	1.54322	+	0.890978i	0.998633	+	0.0522726i	$0.0166465\pi$
$479$	33.7750	+	19.5000i	1.54322	+	0.890978i	0.544586	+	0.838705i	$0.316687\pi$
$480$	1.50000	−	2.59808i	0.0684653	−	0.118585i
$481$	−0.696152	+	10.7942i	−0.0317418	+	0.492174i
$482$	30.0000			1.36646
$483$		0			0
$484$	−11.0000			−0.500000
$485$	18.0000	+	31.1769i	0.817338	+	1.41567i
$486$	−13.8564	−	8.00000i	−0.628539	−	0.362887i
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	0.245705	−	0.969345i	$-0.420981\pi$
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	−0.716625	+	0.697459i	$0.754314\pi$
$488$	−6.92820	+	4.00000i	−0.313625	+	0.181071i
$489$			6.00000i			0.271329i
$490$		0			0
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$		0			0
$493$		0			0
$494$	9.58846	+	19.3923i	0.431405	+	0.872501i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	6.00000			0.268866
$499$	31.1769	−	18.0000i	1.39567	−	0.805791i	0.401735	−	0.915756i	$-0.368407\pi$
$499$	31.1769	−	18.0000i	1.39567	−	0.805791i	0.993935	+	0.109965i	$0.0350740\pi$
$500$	2.59808	+	1.50000i	0.116190	+	0.0670820i
$501$	10.3923	+	6.00000i	0.464294	+	0.268060i
$502$	−10.3923	+	6.00000i	−0.463831	+	0.267793i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$			36.0000i			1.60198i
$506$		0			0
$507$	−12.8923	−	1.66987i	−0.572567	−	0.0741617i
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	−0.380402	−	0.924821i	$-0.624214\pi$
$509$	5.19615	−	3.00000i	0.230315	−	0.132973i	0.610718	+	0.791849i	$0.290881\pi$
$510$	−9.00000			−0.398527
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	25.9808	−	15.0000i	1.14708	−	0.662266i
$514$	2.59808	+	1.50000i	0.114596	+	0.0661622i
$515$	−36.3731	−	21.0000i	−1.60279	−	0.925371i
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$		0			0
$518$		0			0
$519$	6.00000			0.263371
$520$	10.7942	+	0.696152i	0.473358	+	0.0305283i
$521$	−13.5000	+	23.3827i	−0.591446	+	1.02441i	0.402592	+	0.915379i	$0.368109\pi$
$521$	−13.5000	+	23.3827i	−0.591446	+	1.02441i	−0.994038	+	0.109035i	$0.965224\pi$
$522$		0			0
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	0.986216	−	0.165460i	$-0.0529109\pi$
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	−0.636401	+	0.771358i	$0.719578\pi$
$524$	3.00000			0.131056
$525$		0			0
$526$		−	24.0000i		−	1.04645i
$527$		0			0
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	9.00000	+	15.5885i	0.390935	+	0.677119i
$531$		−	12.0000i		−	0.520756i
$532$		0			0
$533$		0			0
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$	31.1769	+	18.0000i	1.34790	+	0.778208i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	7.50000	+	12.9904i	0.323649	+	0.560576i
$538$		0			0
$539$		0			0
$540$		−	15.0000i		−	0.645497i
$541$	12.9904	−	7.50000i	0.558500	−	0.322450i	−0.194043	−	0.980993i	$-0.562160\pi$
$541$	12.9904	−	7.50000i	0.558500	−	0.322450i	0.752543	+	0.658543i	$0.228827\pi$
$542$	7.50000	−	12.9904i	0.322153	−	0.557985i
$543$	1.00000	−	1.73205i	0.0429141	−	0.0743294i
$544$	−2.59808	+	1.50000i	−0.111392	+	0.0643120i
$545$	27.0000			1.15655
$546$		0			0
$547$	−37.0000			−1.58201			−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000			−1.58201			−0.791003	+	0.611812i	$0.790441\pi$
$548$	15.5885	−	9.00000i	0.665906	−	0.384461i
$549$	−8.00000	+	13.8564i	−0.341432	+	0.591377i
$550$		0			0
$551$		0			0
$552$			6.00000i			0.255377i
$553$		0			0
$554$		−	8.00000i		−	0.339887i
$555$	4.50000	+	7.79423i	0.191014	+	0.330847i
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	−23.3827	−	13.5000i	−0.990756	−	0.572013i	−0.0852559	−	0.996359i	$-0.527171\pi$
$557$	−23.3827	−	13.5000i	−0.990756	−	0.572013i	−0.905500	+	0.424346i	$0.860504\pi$
$558$		0			0
$559$	−2.00000	+	3.00000i	−0.0845910	+	0.126886i
$560$		0			0
$561$		0			0
$562$	−15.0000	−	25.9808i	−0.632737	−	1.09593i
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	0.0824933	+	0.996592i	$0.473712\pi$
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	−0.904320	+	0.426855i	$0.859622\pi$
$564$	2.59808	+	1.50000i	0.109399	+	0.0631614i
$565$	−15.5885	+	9.00000i	−0.655811	+	0.378633i
$566$		−	4.00000i		−	0.168133i
$567$		0			0
$568$	15.0000			0.629386
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.759220	−	0.650835i	$-0.774419\pi$
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.184030	−	0.982921i	$-0.558914\pi$
$570$	15.5885	+	9.00000i	0.652929	+	0.376969i
$571$	11.5000	−	19.9186i	0.481260	−	0.833567i	−0.518509	−	0.855072i	$-0.673513\pi$
$571$	11.5000	−	19.9186i	0.481260	−	0.833567i	0.999769	+	0.0215055i	$0.00684595\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$	24.0000			1.00087
$576$	−1.00000	−	1.73205i	−0.0416667	−	0.0721688i
$577$	−36.3731	−	21.0000i	−1.51423	−	0.874241i	−0.999861	−	0.0166728i	$-0.994693\pi$
$577$	−36.3731	−	21.0000i	−1.51423	−	0.874241i	−0.514370	−	0.857569i	$-0.671974\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$	5.19615	−	3.00000i	0.215945	−	0.124676i
$580$		0			0
$581$		0			0
$582$	−12.0000			−0.497416
$583$		0			0
$584$	−3.00000	+	5.19615i	−0.124141	+	0.215018i
$585$	19.3923	−	9.58846i	0.801773	−	0.396434i
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$		−	18.0000i		−	0.742940i	−0.928445	−	0.371470i	$-0.878854\pi$
$587$		−	18.0000i		−	0.742940i	0.928445	−	0.371470i	$-0.121146\pi$
$588$		0			0
$589$		0			0
$590$	15.5885	−	9.00000i	0.641767	−	0.370524i
$591$	−2.59808	−	1.50000i	−0.106871	−	0.0617018i
$592$	2.59808	+	1.50000i	0.106780	+	0.0616496i
$593$	−31.1769	+	18.0000i	−1.28028	+	0.739171i	−0.976900	−	0.213697i	$-0.931449\pi$
$593$	−31.1769	+	18.0000i	−1.28028	+	0.739171i	−0.303383	+	0.952869i	$0.598116\pi$
$594$		0			0
$595$		0			0
$596$		−	6.00000i		−	0.245770i
$597$	−10.0000	−	17.3205i	−0.409273	−	0.708881i
$598$	−19.3923	+	9.58846i	−0.793010	+	0.392101i
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$	3.46410	−	2.00000i	0.141421	−	0.0816497i
$601$	37.0000			1.50926			0.754631	−	0.656150i	$-0.227816\pi$
$601$	37.0000			1.50926			0.754631	+	0.656150i	$0.227816\pi$
$602$		0			0
$603$		−	24.0000i		−	0.977356i
$604$	−12.9904	+	7.50000i	−0.528571	+	0.305171i
$605$	−28.5788	−	16.5000i	−1.16190	−	0.670820i
$606$	−10.3923	−	6.00000i	−0.422159	−	0.243733i
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−24.0000			−0.971732
$611$	−0.696152	+	10.7942i	−0.0281633	+	0.436688i
$612$	−3.00000	+	5.19615i	−0.121268	+	0.210042i
$613$	5.19615	+	3.00000i	0.209871	+	0.121169i	0.601251	−	0.799060i	$-0.294669\pi$
$613$	5.19615	+	3.00000i	0.209871	+	0.121169i	−0.391381	+	0.920229i	$0.628002\pi$
$614$	9.00000	+	15.5885i	0.363210	+	0.629099i
$615$		0			0
$616$		0			0
$617$			12.0000i			0.483102i	0.970388	+	0.241551i	$0.0776561\pi$
$617$			12.0000i			0.483102i	−0.970388	+	0.241551i	$0.922344\pi$
$618$	12.1244	−	7.00000i	0.487713	−	0.281581i
$619$	20.7846	+	12.0000i	0.835404	+	0.482321i	0.855699	−	0.517473i	$-0.173127\pi$
$619$	20.7846	+	12.0000i	0.835404	+	0.482321i	−0.0202954	+	0.999794i	$0.506461\pi$
$620$		0			0
$621$	15.0000	+	25.9808i	0.601929	+	1.04257i
$622$			18.0000i			0.721734i
$623$		0			0
$624$	−2.00000	+	3.00000i	−0.0800641	+	0.120096i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	16.4545	+	9.50000i	0.657653	+	0.379696i
$627$		0			0
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$		−	9.00000i		−	0.358854i
$630$		0			0
$631$			15.0000i			0.597141i	0.954388	+	0.298570i	$0.0965097\pi$
$631$			15.0000i			0.597141i	−0.954388	+	0.298570i	$0.903490\pi$
$632$	8.66025	−	5.00000i	0.344486	−	0.198889i
$633$	−11.5000	+	19.9186i	−0.457084	+	0.791693i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	−5.19615	+	3.00000i	−0.206203	+	0.119051i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		0			0
$639$	25.9808	−	15.0000i	1.02778	−	0.593391i
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	−10.3923	+	6.00000i	−0.410152	+	0.236801i
$643$		−	36.0000i		−	1.41970i	−0.704352	−	0.709851i	$-0.748762\pi$
$643$		−	36.0000i		−	1.41970i	0.704352	−	0.709851i	$-0.251238\pi$
$644$		0			0
$645$			3.00000i			0.118125i
$646$	−9.00000	−	15.5885i	−0.354100	−	0.613320i
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	−0.0758684	−	0.997118i	$-0.524173\pi$
$647$	21.0000	−	36.3731i	0.825595	−	1.42997i	0.901464	−	0.432855i	$-0.142494\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$		0			0
$650$	12.0000	+	8.00000i	0.470679	+	0.313786i
$651$		0			0
$652$			6.00000i			0.234978i
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	0.966910	+	0.255119i	$0.0821147\pi$
$653$	18.0000	+	31.1769i	0.704394	+	1.22005i	−0.262515	+	0.964928i	$0.584552\pi$
$654$	−4.50000	+	7.79423i	−0.175964	+	0.304778i
$655$	7.79423	+	4.50000i	0.304546	+	0.175830i
$656$		0			0
$657$			12.0000i			0.468165i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	25.9808	+	15.0000i	1.01053	+	0.583432i	0.911348	−	0.411636i	$-0.135043\pi$
$661$	25.9808	+	15.0000i	1.01053	+	0.583432i	0.0991864	+	0.995069i	$0.468376\pi$
$662$	15.0000	−	25.9808i	0.582992	−	1.00977i
$663$	10.7942	+	0.696152i	0.419213	+	0.0270363i
$664$	6.00000			0.232845
$665$		0			0
$666$	6.00000			0.232495
$667$		0			0
$668$	10.3923	+	6.00000i	0.402090	+	0.232147i
$669$	7.79423	+	4.50000i	0.301342	+	0.173980i
$670$	31.1769	−	18.0000i	1.20447	−	0.695401i
$671$		0			0
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	−11.2583	+	6.50000i	−0.433655	+	0.250371i
$675$	10.0000	−	17.3205i	0.384900	−	0.666667i
$676$	−12.8923	−	1.66987i	−0.495858	−	0.0642259i
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$		−	6.00000i		−	0.230429i
$679$		0			0
$680$	−9.00000			−0.345134
$681$	−10.3923	+	6.00000i	−0.398234	+	0.229920i
$682$		0			0
$683$	5.19615	+	3.00000i	0.198825	+	0.114792i	0.596107	−	0.802905i	$-0.296713\pi$
$683$	5.19615	+	3.00000i	0.198825	+	0.114792i	−0.397282	+	0.917697i	$0.630047\pi$
$684$	10.3923	−	6.00000i	0.397360	−	0.229416i
$685$	54.0000			2.06323
$686$		0			0
$687$			9.00000i			0.343371i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−9.58846	−	19.3923i	−0.365291	−	0.738788i
$690$	−9.00000	+	15.5885i	−0.342624	+	0.593442i
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$		−	33.0000i		−	1.25266i
$695$	12.9904	−	7.50000i	0.492753	−	0.284491i
$696$		0			0
$697$		0			0
$698$	−10.5000	−	18.1865i	−0.397431	−	0.688370i
$699$	21.0000			0.794293
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	−1.16025	+	17.9904i	−0.0437910	+	0.679003i
$703$	−9.00000	+	15.5885i	−0.339441	+	0.587930i
$704$		0			0
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$	−6.00000			−0.225813
$707$		0			0
$708$			6.00000i			0.225494i
$709$	5.19615	−	3.00000i	0.195146	−	0.112667i	−0.399244	−	0.916845i	$-0.630727\pi$
$709$	5.19615	−	3.00000i	0.195146	−	0.112667i	0.594389	+	0.804178i	$0.297394\pi$
$710$	38.9711	+	22.5000i	1.46256	+	0.844410i
$711$	10.0000	−	17.3205i	0.375029	−	0.649570i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	7.50000	+	12.9904i	0.280288	+	0.485473i
$717$	−7.79423	−	4.50000i	−0.291081	−	0.168056i
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		−	6.00000i		−	0.223607i
$721$		0			0
$722$			17.0000i			0.632674i
$723$	−25.9808	+	15.0000i	−0.966235	+	0.557856i
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$		0			0
$726$	9.52628	−	5.50000i	0.353553	−	0.204124i
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−15.5885	+	9.00000i	−0.576955	+	0.333105i
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$	4.00000	−	6.92820i	0.147844	−	0.256074i
$733$	7.79423	−	4.50000i	0.287886	−	0.166211i	−0.349102	−	0.937085i	$-0.613513\pi$
$733$	7.79423	−	4.50000i	0.287886	−	0.166211i	0.636988	+	0.770873i	$0.280180\pi$
$734$		−	8.00000i		−	0.295285i
$735$		0			0
$736$			6.00000i			0.221163i
$737$		0			0
$738$		0			0
$739$	−31.1769	−	18.0000i	−1.14686	−	0.662141i	−0.198741	−	0.980052i	$-0.563685\pi$
$739$	−31.1769	−	18.0000i	−1.14686	−	0.662141i	−0.948120	+	0.317911i	$0.897019\pi$
$740$	4.50000	+	7.79423i	0.165423	+	0.286522i
$741$	−18.0000	−	12.0000i	−0.661247	−	0.440831i
$742$		0			0
$743$			39.0000i			1.43077i	0.698730	+	0.715386i	$0.253749\pi$
$743$			39.0000i			1.43077i	−0.698730	+	0.715386i	$0.746251\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	3.46410	+	2.00000i	0.126830	+	0.0732252i
$747$	10.3923	−	6.00000i	0.380235	−	0.219529i
$748$		0			0
$749$		0			0
$750$	−3.00000			−0.109545
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$	2.59808	+	1.50000i	0.0947421	+	0.0546994i
$753$	6.00000	−	10.3923i	0.218652	−	0.378717i
$754$		0			0
$755$	−45.0000			−1.63772
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$		0			0
$760$	15.5885	+	9.00000i	0.565453	+	0.326464i
$761$	25.9808	−	15.0000i	0.941802	−	0.543750i	0.0512772	−	0.998684i	$-0.483671\pi$
$761$	25.9808	−	15.0000i	0.941802	−	0.543750i	0.890525	+	0.454935i	$0.150337\pi$
$762$		−	2.00000i		−	0.0724524i
$763$		0			0
$764$	−12.0000			−0.434145
$765$	−15.5885	+	9.00000i	−0.563602	+	0.325396i
$766$	−4.50000	+	7.79423i	−0.162592	+	0.281617i
$767$	−19.3923	+	9.58846i	−0.700216	+	0.346219i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$		−	24.0000i		−	0.865462i	−0.901523	−	0.432731i	$-0.857550\pi$
$769$		−	24.0000i		−	0.865462i	0.901523	−	0.432731i	$-0.142450\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$	5.19615	−	3.00000i	0.187014	−	0.107972i
$773$	18.1865	+	10.5000i	0.654124	+	0.377659i	0.790034	−	0.613062i	$-0.210063\pi$
$773$	18.1865	+	10.5000i	0.654124	+	0.377659i	−0.135910	+	0.990721i	$0.543396\pi$
$774$	1.73205	+	1.00000i	0.0622573	+	0.0359443i
$775$		0			0
$776$	−12.0000			−0.430775
$777$		0			0
$778$			30.0000i			1.07555i
$779$		0			0
$780$	−9.69615	+	4.79423i	−0.347178	+	0.171661i
$781$		0			0
$782$	15.5885	−	9.00000i	0.557442	−	0.321839i
$783$		0			0
$784$		0			0
$785$		−	66.0000i		−	2.35564i
$786$	−2.59808	+	1.50000i	−0.0926703	+	0.0535032i
$787$	−10.3923	−	6.00000i	−0.370446	−	0.213877i	0.303207	−	0.952925i	$-0.401942\pi$
$787$	−10.3923	−	6.00000i	−0.370446	−	0.213877i	−0.673653	+	0.739048i	$0.735276\pi$
$788$	−2.59808	−	1.50000i	−0.0925526	−	0.0534353i
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$	30.0000			1.06735
$791$		0			0
$792$		0			0
$793$	28.7846	+	1.85641i	1.02217	+	0.0659229i
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$	−15.5885	−	9.00000i	−0.552866	−	0.319197i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$		−	9.00000i		−	0.318397i
$800$	3.46410	−	2.00000i	0.122474	−	0.0707107i
$801$	10.3923	+	6.00000i	0.367194	+	0.212000i
$802$	15.0000	−	25.9808i	0.529668	−	0.917413i
$803$		0			0
$804$			12.0000i			0.423207i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−10.3923	−	6.00000i	−0.365600	−	0.211079i
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	−0.967219	−	0.253946i	$-0.918272\pi$
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	0.703533	+	0.710663i	$0.251605\pi$
$810$	−1.50000	−	2.59808i	−0.0527046	−	0.0912871i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$			15.0000i			0.526073i
$814$		0			0
$815$	−9.00000	+	15.5885i	−0.315256	+	0.546040i
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$	−5.19615	+	3.00000i	−0.181790	+	0.104957i
$818$	6.00000			0.209785
$819$		0			0
$820$		0			0
$821$	−38.9711	+	22.5000i	−1.36010	+	0.785255i	−0.989637	−	0.143591i	$-0.954135\pi$
$821$	−38.9711	+	22.5000i	−1.36010	+	0.785255i	−0.370465	+	0.928846i	$0.620802\pi$
$822$	−9.00000	+	15.5885i	−0.313911	+	0.543710i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	12.1244	−	7.00000i	0.422372	−	0.243857i
$825$		0			0
$826$		0			0
$827$		−	18.0000i		−	0.625921i	−0.949766	−	0.312961i	$-0.898679\pi$
$827$		−	18.0000i		−	0.625921i	0.949766	−	0.312961i	$-0.101321\pi$
$828$	6.00000	+	10.3923i	0.208514	+	0.361158i
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$	15.5885	+	9.00000i	0.541083	+	0.312395i
$831$	4.00000	+	6.92820i	0.138758	+	0.240337i
$832$	−2.00000	+	3.00000i	−0.0693375	+	0.104006i
$833$		0			0
$834$			5.00000i			0.173136i
$835$	18.0000	+	31.1769i	0.622916	+	1.07892i
$836$		0			0
$837$		0			0
$838$	−12.9904	+	7.50000i	−0.448745	+	0.259083i
$839$		−	24.0000i		−	0.828572i	−0.910147	−	0.414286i	$-0.864031\pi$
$839$		−	24.0000i		−	0.828572i	0.910147	−	0.414286i	$-0.135969\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−7.50000	−	12.9904i	−0.258467	−	0.447678i
$843$	25.9808	+	15.0000i	0.894825	+	0.516627i
$844$	−11.5000	+	19.9186i	−0.395846	+	0.685626i
$845$	−30.9904	−	23.6769i	−1.06610	−	0.814511i
$846$	6.00000			0.206284
$847$		0			0
$848$	−6.00000			−0.206041
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$	−10.3923	−	6.00000i	−0.356453	−	0.205798i
$851$	−15.5885	−	9.00000i	−0.534365	−	0.308516i
$852$	−12.9904	+	7.50000i	−0.445043	+	0.256946i
$853$			39.0000i			1.33533i	0.744460	+	0.667667i	$0.232707\pi$
$853$			39.0000i			1.33533i	−0.744460	+	0.667667i	$0.767293\pi$
$854$		0			0
$855$	36.0000			1.23117
$856$	−10.3923	+	6.00000i	−0.355202	+	0.205076i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$			3.00000i			0.102299i
$861$		0			0
$862$	15.0000			0.510902
$863$	33.7750	−	19.5000i	1.14971	−	0.663788i	0.200897	−	0.979612i	$-0.435615\pi$
$863$	33.7750	−	19.5000i	1.14971	−	0.663788i	0.948818	+	0.315825i	$0.102281\pi$
$864$	4.33013	+	2.50000i	0.147314	+	0.0850517i
$865$	15.5885	+	9.00000i	0.530023	+	0.306009i
$866$	9.52628	−	5.50000i	0.323716	−	0.186898i
$867$	8.00000			0.271694
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−38.7846	+	19.1769i	−1.31417	+	0.649785i
$872$	−4.50000	+	7.79423i	−0.152389	+	0.263946i
$873$	−20.7846	+	12.0000i	−0.703452	+	0.406138i
$874$	−36.0000			−1.21772
$875$		0			0
$876$		−	6.00000i		−	0.202721i
$877$	−2.59808	+	1.50000i	−0.0877308	+	0.0506514i	−0.543224	−	0.839588i	$-0.682796\pi$
$877$	−2.59808	+	1.50000i	−0.0877308	+	0.0506514i	0.455493	+	0.890239i	$0.349463\pi$
$878$	−8.66025	−	5.00000i	−0.292269	−	0.168742i
$879$	7.79423	+	4.50000i	0.262893	+	0.151781i
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	−11.0000			−0.370179			−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000			−0.370179			−0.185090	+	0.982722i	$0.559258\pi$
$884$	10.7942	+	0.696152i	0.363049	+	0.0234141i
$885$	−9.00000	+	15.5885i	−0.302532	+	0.524000i
$886$	−18.1865	−	10.5000i	−0.610989	−	0.352754i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$	−3.00000			−0.100673
$889$		0			0
$890$			18.0000i			0.603361i
$891$		0			0
$892$	7.79423	+	4.50000i	0.260970	+	0.150671i
$893$	−9.00000	+	15.5885i	−0.301174	+	0.521648i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$			45.0000i			1.50418i
$896$		0			0
$897$	12.0000	−	18.0000i	0.400668	−	0.601003i
$898$	12.0000	+	20.7846i	0.400445	+	0.693591i
$899$		0			0
$900$	4.00000	−	6.92820i	0.133333	−	0.230940i
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$		0			0
$904$		−	6.00000i		−	0.199557i
$905$	5.19615	−	3.00000i	0.172726	−	0.0997234i
$906$	7.50000	−	12.9904i	0.249171	−	0.431577i
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$	−10.3923	+	6.00000i	−0.344881	+	0.199117i
$909$	−24.0000			−0.796030
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−5.19615	+	3.00000i	−0.172062	+	0.0993399i
$913$		0			0
$914$	9.00000	−	15.5885i	0.297694	−	0.515620i
$915$	20.7846	−	12.0000i	0.687118	−	0.396708i
$916$			9.00000i			0.297368i
$917$		0			0
$918$		−	15.0000i		−	0.495074i
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	0.982486	−	0.186338i	$-0.0596619\pi$
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	−0.652616	+	0.757689i	$0.726329\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$	−15.5885	−	9.00000i	−0.513657	−	0.296560i
$922$	−7.50000	−	12.9904i	−0.246999	−	0.427815i
$923$	−45.0000	−	30.0000i	−1.48119	−	0.987462i
$924$		0			0
$925$			12.0000i			0.394558i
$926$	−12.0000	−	20.7846i	−0.394344	−	0.683025i
$927$	14.0000	−	24.2487i	0.459820	−	0.796432i
$928$		0			0
$929$	31.1769	−	18.0000i	1.02288	−	0.590561i	0.107944	−	0.994157i	$-0.465573\pi$
$929$	31.1769	−	18.0000i	1.02288	−	0.590561i	0.914937	+	0.403596i	$0.132240\pi$
$930$		0			0
$931$		0			0
$932$	21.0000			0.687878
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$	−10.3923	−	6.00000i	−0.340047	−	0.196326i
$935$		0			0
$936$	−0.464102	+	7.19615i	−0.0151696	+	0.235214i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	−19.0000			−0.620042
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$	−38.9711	−	22.5000i	−1.27042	−	0.733479i	−0.295355	−	0.955387i	$-0.595438\pi$
$941$	−38.9711	−	22.5000i	−1.27042	−	0.733479i	−0.975068	+	0.221908i	$0.928771\pi$
$942$	19.0526	+	11.0000i	0.620766	+	0.358399i
$943$		0			0
$944$			6.00000i			0.195283i
$945$		0			0
$946$		0			0
$947$	−41.5692	+	24.0000i	−1.35082	+	0.779895i	−0.988364	−	0.152106i	$-0.951394\pi$
$947$	−41.5692	+	24.0000i	−1.35082	+	0.779895i	−0.362454	+	0.932002i	$0.618061\pi$
$948$	−5.00000	+	8.66025i	−0.162392	+	0.281272i
$949$	19.3923	−	9.58846i	0.629501	−	0.311254i
$950$	12.0000	+	20.7846i	0.389331	+	0.674342i
$951$			18.0000i			0.583690i
$952$		0			0
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$	−10.3923	+	6.00000i	−0.336463	+	0.194257i
$955$	−31.1769	−	18.0000i	−1.00886	−	0.582466i
$956$	−7.79423	−	4.50000i	−0.252083	−	0.145540i
$957$		0			0
$958$	−39.0000			−1.26003
$959$		0			0
$960$			3.00000i			0.0968246i
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$	−4.79423	−	9.69615i	−0.154572	−	0.312617i
$963$	−12.0000	+	20.7846i	−0.386695	+	0.669775i
$964$	−25.9808	+	15.0000i	−0.836784	+	0.483117i
$965$	18.0000			0.579441
$966$		0			0
$967$		−	3.00000i		−	0.0964735i	−0.998836	−	0.0482367i	$-0.984640\pi$
$967$		−	3.00000i		−	0.0964735i	0.998836	−	0.0482367i	$-0.0153602\pi$
$968$	9.52628	−	5.50000i	0.306186	−	0.176777i
$969$	15.5885	+	9.00000i	0.500773	+	0.289122i
$970$	−31.1769	−	18.0000i	−1.00103	−	0.577945i
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	0.563914	−	0.825833i	$-0.309295\pi$
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	−0.997150	+	0.0754473i	$0.975962\pi$
$972$	16.0000			0.513200
$973$		0			0
$974$	12.0000			0.384505
$975$	−14.3923	−	0.928203i	−0.460923	−	0.0297263i
$976$	4.00000	−	6.92820i	0.128037	−	0.221766i
$977$	−10.3923	−	6.00000i	−0.332479	−	0.191957i	0.324462	−	0.945899i	$-0.394817\pi$
$977$	−10.3923	−	6.00000i	−0.332479	−	0.191957i	−0.656941	+	0.753942i	$0.728150\pi$
$978$	−3.00000	−	5.19615i	−0.0959294	−	0.166155i
$979$		0			0
$980$		0			0
$981$			18.0000i			0.574696i
$982$	−23.3827	+	13.5000i	−0.746171	+	0.430802i
$983$	−7.79423	−	4.50000i	−0.248597	−	0.143528i	0.370525	−	0.928823i	$-0.379178\pi$
$983$	−7.79423	−	4.50000i	−0.248597	−	0.143528i	−0.619122	+	0.785295i	$0.712511\pi$
$984$		0			0
$985$	−4.50000	−	7.79423i	−0.143382	−	0.248345i
$986$		0			0
$987$		0			0
$988$	−18.0000	−	12.0000i	−0.572656	−	0.381771i
$989$	−3.00000	−	5.19615i	−0.0953945	−	0.165228i
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$		0			0
$993$			30.0000i			0.952021i
$994$		0			0
$995$		−	60.0000i		−	1.90213i
$996$	−5.19615	+	3.00000i	−0.164646	+	0.0950586i
$997$	−4.00000	+	6.92820i	−0.126681	+	0.219418i	−0.922389	−	0.386263i	$-0.873766\pi$
$997$	−4.00000	+	6.92820i	−0.126681	+	0.219418i	0.795708	+	0.605681i	$0.207099\pi$
$998$	−18.0000	+	31.1769i	−0.569780	+	0.986888i
$999$	−12.9904	+	7.50000i	−0.410997	+	0.237289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.n.d.753.1		4
7.2	even	3	inner	1274.2.n.d.961.2		4
7.3	odd	6		1274.2.d.c.883.1		2
7.4	even	3		26.2.b.a.25.1	✓	2
7.5	odd	6		1274.2.n.c.961.2		4
7.6	odd	2		1274.2.n.c.753.1		4
13.12	even	2	inner	1274.2.n.d.753.2		4
21.11	odd	6		234.2.b.b.181.2		2
28.11	odd	6		208.2.f.a.129.2		2
35.4	even	6		650.2.d.b.51.2		2
35.18	odd	12		650.2.c.a.649.1		2
35.32	odd	12		650.2.c.d.649.2		2
56.11	odd	6		832.2.f.b.129.1		2
56.53	even	6		832.2.f.d.129.1		2
84.11	even	6		1872.2.c.f.1585.1		2
91.4	even	6		338.2.e.c.23.2		4
91.11	odd	12		338.2.c.b.191.1		2
91.12	odd	6		1274.2.n.c.961.1		4
91.18	odd	12		338.2.a.b.1.1		1
91.25	even	6		26.2.b.a.25.2	yes	2
91.32	odd	12		338.2.c.f.315.1		2
91.38	odd	6		1274.2.d.c.883.2		2
91.46	odd	12		338.2.c.b.315.1		2
91.51	even	6	inner	1274.2.n.d.961.1		4
91.60	odd	12		338.2.a.d.1.1		1
91.67	odd	12		338.2.c.f.191.1		2
91.74	even	3		338.2.e.c.23.1		4
91.81	even	3		338.2.e.c.147.2		4
91.88	even	6		338.2.e.c.147.1		4
91.90	odd	2		1274.2.n.c.753.2		4
273.116	odd	6		234.2.b.b.181.1		2
273.200	even	12		3042.2.a.j.1.1		1
273.242	even	12		3042.2.a.g.1.1		1
364.151	even	12		2704.2.a.j.1.1		1
364.207	odd	6		208.2.f.a.129.1		2
364.291	even	12		2704.2.a.k.1.1		1
455.109	odd	12		8450.2.a.u.1.1		1
455.207	odd	12		650.2.c.a.649.2		2
455.298	odd	12		650.2.c.d.649.1		2
455.389	even	6		650.2.d.b.51.1		2
455.424	odd	12		8450.2.a.h.1.1		1
728.389	even	6		832.2.f.d.129.2		2
728.571	odd	6		832.2.f.b.129.2		2
1092.935	even	6		1872.2.c.f.1585.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.b.a.25.1	✓	2	7.4	even	3
26.2.b.a.25.2	yes	2	91.25	even	6
208.2.f.a.129.1		2	364.207	odd	6
208.2.f.a.129.2		2	28.11	odd	6
234.2.b.b.181.1		2	273.116	odd	6
234.2.b.b.181.2		2	21.11	odd	6
338.2.a.b.1.1		1	91.18	odd	12
338.2.a.d.1.1		1	91.60	odd	12
338.2.c.b.191.1		2	91.11	odd	12
338.2.c.b.315.1		2	91.46	odd	12
338.2.c.f.191.1		2	91.67	odd	12
338.2.c.f.315.1		2	91.32	odd	12
338.2.e.c.23.1		4	91.74	even	3
338.2.e.c.23.2		4	91.4	even	6
338.2.e.c.147.1		4	91.88	even	6
338.2.e.c.147.2		4	91.81	even	3
650.2.c.a.649.1		2	35.18	odd	12
650.2.c.a.649.2		2	455.207	odd	12
650.2.c.d.649.1		2	455.298	odd	12
650.2.c.d.649.2		2	35.32	odd	12
650.2.d.b.51.1		2	455.389	even	6
650.2.d.b.51.2		2	35.4	even	6
832.2.f.b.129.1		2	56.11	odd	6
832.2.f.b.129.2		2	728.571	odd	6
832.2.f.d.129.1		2	56.53	even	6
832.2.f.d.129.2		2	728.389	even	6
1274.2.d.c.883.1		2	7.3	odd	6
1274.2.d.c.883.2		2	91.38	odd	6
1274.2.n.c.753.1		4	7.6	odd	2
1274.2.n.c.753.2		4	91.90	odd	2
1274.2.n.c.961.1		4	91.12	odd	6
1274.2.n.c.961.2		4	7.5	odd	6
1274.2.n.d.753.1		4	1.1	even	1	trivial
1274.2.n.d.753.2		4	13.12	even	2	inner
1274.2.n.d.961.1		4	91.51	even	6	inner
1274.2.n.d.961.2		4	7.2	even	3	inner
1872.2.c.f.1585.1		2	84.11	even	6
1872.2.c.f.1585.2		2	1092.935	even	6
2704.2.a.j.1.1		1	364.151	even	12
2704.2.a.k.1.1		1	364.291	even	12
3042.2.a.g.1.1		1	273.242	even	12
3042.2.a.j.1.1		1	273.200	even	12
8450.2.a.h.1.1		1	455.424	odd	12
8450.2.a.u.1.1		1	455.109	odd	12

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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} +1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.59808 - 1.50000i) q^{5} +1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(2.00000 - 3.00000i) q^{13} -3.00000i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.73205 - 1.00000i) q^{18} +(5.19615 - 3.00000i) q^{19} -3.00000i q^{20} +(3.00000 + 5.19615i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.232051 + 3.59808i) q^{26} +5.00000 q^{27} +(1.50000 + 2.59808i) q^{30} +(0.866025 + 0.500000i) q^{32} -3.00000i q^{34} +2.00000 q^{36} +(-2.59808 + 1.50000i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-1.59808 - 3.23205i) q^{39} +(1.50000 + 2.59808i) q^{40} -1.00000 q^{43} +(5.19615 + 3.00000i) q^{45} +(-5.19615 - 3.00000i) q^{46} +(-2.59808 + 1.50000i) q^{47} -1.00000 q^{48} +4.00000i q^{50} +(1.50000 + 2.59808i) q^{51} +(-1.59808 - 3.23205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-4.33013 + 2.50000i) q^{54} -6.00000i q^{57} +(-5.19615 - 3.00000i) q^{59} +(-2.59808 - 1.50000i) q^{60} +(4.00000 + 6.92820i) q^{61} -1.00000 q^{64} +(0.696152 - 10.7942i) q^{65} +(-10.3923 - 6.00000i) q^{67} +(1.50000 + 2.59808i) q^{68} +6.00000 q^{69} -15.0000i q^{71} +(-1.73205 + 1.00000i) q^{72} +(5.19615 + 3.00000i) q^{73} +(1.50000 - 2.59808i) q^{74} +(-2.00000 - 3.46410i) q^{75} -6.00000i q^{76} +(3.00000 + 2.00000i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(-2.59808 - 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} -6.00000i q^{83} +9.00000i q^{85} +(0.866025 - 0.500000i) q^{86} +(5.19615 - 3.00000i) q^{89} -6.00000 q^{90} +6.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(9.00000 - 15.5885i) q^{95} +(0.866025 - 0.500000i) q^{96} +12.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{9} - 6 q^{10} - 2 q^{12} + 8 q^{13} - 2 q^{16} - 6 q^{17} + 12 q^{23} + 8 q^{25} + 6 q^{26} + 20 q^{27} + 6 q^{30} + 8 q^{36} - 12 q^{38} + 4 q^{39} + 6 q^{40} - 4 q^{43} - 4 q^{48} + 6 q^{51} + 4 q^{52} + 12 q^{53} + 16 q^{61} - 4 q^{64} - 18 q^{65} + 6 q^{68} + 24 q^{69} + 6 q^{74} - 8 q^{75} + 12 q^{78} - 20 q^{79} - 2 q^{81} - 24 q^{90} + 24 q^{92} + 6 q^{94} + 36 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^9 - 6 * q^10 - 2 * q^12 + 8 * q^13 - 2 * q^16 - 6 * q^17 + 12 * q^23 + 8 * q^25 + 6 * q^26 + 20 * q^27 + 6 * q^30 + 8 * q^36 - 12 * q^38 + 4 * q^39 + 6 * q^40 - 4 * q^43 - 4 * q^48 + 6 * q^51 + 4 * q^52 + 12 * q^53 + 16 * q^61 - 4 * q^64 - 18 * q^65 + 6 * q^68 + 24 * q^69 + 6 * q^74 - 8 * q^75 + 12 * q^78 - 20 * q^79 - 2 * q^81 - 24 * q^90 + 24 * q^92 + 6 * q^94 + 36 * q^95

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