LMFDB - Embedded newform 1274.2.n.j.961.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(753,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,0,4,0,0,0,0,4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			961.3
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1274.961
Dual form			1274.2.n.j.753.3

$q$-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} +(-0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} -1.41421i q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.707107 - 1.22474i) q^{10} +(3.46410 - 2.00000i) q^{11} +(0.707107 - 1.22474i) q^{12} +(-3.53553 - 0.707107i) q^{13} +2.00000i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.67423 - 2.12132i) q^{19} -1.41421i q^{20} +4.00000 q^{22} +(1.22474 - 0.707107i) q^{24} +(-1.50000 - 2.59808i) q^{25} +(-2.70831 - 2.38014i) q^{26} -5.65685 q^{27} -2.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(7.34847 - 4.24264i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.89898 - 2.82843i) q^{33} +2.82843i q^{34} +1.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(-2.12132 - 3.67423i) q^{38} +(1.63397 + 4.83013i) q^{39} +(0.707107 - 1.22474i) q^{40} -5.65685i q^{41} -8.00000 q^{43} +(3.46410 + 2.00000i) q^{44} +(-1.22474 + 0.707107i) q^{45} +(-2.44949 - 1.41421i) q^{47} +1.41421 q^{48} -3.00000i q^{50} +(2.00000 - 3.46410i) q^{51} +(-1.15539 - 3.41542i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(-4.89898 - 2.82843i) q^{54} -5.65685 q^{55} +6.00000i q^{57} +(-1.73205 - 1.00000i) q^{58} +(6.12372 - 3.53553i) q^{59} +(-1.73205 + 1.00000i) q^{60} +(0.707107 - 1.22474i) q^{61} +8.48528 q^{62} -1.00000 q^{64} +(3.83013 + 3.36603i) q^{65} +(-2.82843 - 4.89898i) q^{66} +(-3.46410 + 2.00000i) q^{67} +(-1.41421 + 2.44949i) q^{68} -8.00000i q^{71} +(0.866025 + 0.500000i) q^{72} +(12.2474 - 7.07107i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.12132 + 3.67423i) q^{75} -4.24264i q^{76} +(-1.00000 + 5.00000i) q^{78} +(1.00000 - 1.73205i) q^{79} +(1.22474 - 0.707107i) q^{80} +(2.50000 + 4.33013i) q^{81} +(2.82843 - 4.89898i) q^{82} +1.41421i q^{83} -4.00000i q^{85} +(-6.92820 - 4.00000i) q^{86} +(1.41421 + 2.44949i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-7.34847 - 4.24264i) q^{89} -1.41421 q^{90} +(-10.3923 - 6.00000i) q^{93} +(-1.41421 - 2.44949i) q^{94} +(3.00000 + 5.19615i) q^{95} +(1.22474 + 0.707107i) q^{96} -5.65685i q^{97} -4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{9} - 4 q^{16} + 32 q^{22} - 12 q^{25} - 16 q^{29} - 8 q^{30} + 8 q^{36} + 20 q^{39} - 64 q^{43} + 16 q^{51} - 40 q^{53} - 8 q^{64} - 4 q^{65} - 8 q^{74} - 8 q^{78} + 8 q^{79} + 20 q^{81}+ \cdots + 24 q^{95}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^9 - 4 * q^16 + 32 * q^22 - 12 * q^25 - 16 * q^29 - 8 * q^30 + 8 * q^36 + 20 * q^39 - 64 * q^43 + 16 * q^51 - 40 * q^53 - 8 * q^64 - 4 * q^65 - 8 * q^74 - 8 * q^78 + 8 * q^79 + 20 * q^81 + 16 * q^88 + 24 * q^95

Character values

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

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

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
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	0.586445	−	0.809989i	$-0.300527\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	−0.994694	+	0.102882i	$0.967194\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	0.200480	−	0.979698i	$-0.435750\pi$
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	−0.748203	+	0.663470i	$0.769083\pi$
$6$		−	1.41421i		−	0.577350i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.707107	−	1.22474i	−0.223607	−	0.387298i
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.123371	−	0.992361i	$-0.460630\pi$
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.921095	+	0.389338i	$0.127296\pi$
$12$	0.707107	−	1.22474i	0.204124	−	0.353553i
$13$	−3.53553	−	0.707107i	−0.980581	−	0.196116i
$13$	−3.53553	−	0.707107i	−0.980581	−	0.196116i
$14$		0			0
$15$			2.00000i			0.516398i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	0.984988	−	0.172624i	$-0.0552245\pi$
$17$	1.41421	+	2.44949i	0.342997	+	0.594089i	−0.641991	+	0.766712i	$0.721891\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−3.67423	−	2.12132i	−0.842927	−	0.486664i	0.0153309	−	0.999882i	$-0.495120\pi$
$19$	−3.67423	−	2.12132i	−0.842927	−	0.486664i	−0.858258	+	0.513218i	$0.828453\pi$
$20$		−	1.41421i		−	0.316228i
$21$		0			0
$22$	4.00000			0.852803
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.22474	−	0.707107i	0.250000	−	0.144338i
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$	−2.70831	−	2.38014i	−0.531143	−	0.466784i
$27$	−5.65685			−1.08866
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	7.34847	−	4.24264i	1.31982	−	0.762001i	0.336124	−	0.941818i	$-0.390884\pi$
$31$	7.34847	−	4.24264i	1.31982	−	0.762001i	0.983700	+	0.179817i	$0.0575506\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.89898	−	2.82843i	−0.852803	−	0.492366i
$34$			2.82843i			0.485071i
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	0.350823	−	0.936442i	$-0.385902\pi$
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	−0.635571	+	0.772043i	$0.719235\pi$
$38$	−2.12132	−	3.67423i	−0.344124	−	0.596040i
$39$	1.63397	+	4.83013i	0.261645	+	0.773439i
$40$	0.707107	−	1.22474i	0.111803	−	0.193649i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	3.46410	+	2.00000i	0.522233	+	0.301511i
$45$	−1.22474	+	0.707107i	−0.182574	+	0.105409i
$46$		0			0
$47$	−2.44949	−	1.41421i	−0.357295	−	0.206284i	0.310599	−	0.950541i	$-0.399470\pi$
$47$	−2.44949	−	1.41421i	−0.357295	−	0.206284i	−0.667893	+	0.744257i	$0.732804\pi$
$48$	1.41421			0.204124
$49$		0			0
$50$		−	3.00000i		−	0.424264i
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	−1.15539	−	3.41542i	−0.160224	−	0.473633i
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	−0.972867	−	0.231367i	$-0.925680\pi$
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	0.286064	−	0.958211i	$-0.407653\pi$
$54$	−4.89898	−	2.82843i	−0.666667	−	0.384900i
$55$	−5.65685			−0.762770
$56$		0			0
$57$			6.00000i			0.794719i
$58$	−1.73205	−	1.00000i	−0.227429	−	0.131306i
$59$	6.12372	−	3.53553i	0.797241	−	0.460287i	−0.0452645	−	0.998975i	$-0.514413\pi$
$59$	6.12372	−	3.53553i	0.797241	−	0.460287i	0.842506	+	0.538688i	$0.181080\pi$
$60$	−1.73205	+	1.00000i	−0.223607	+	0.129099i
$61$	0.707107	−	1.22474i	0.0905357	−	0.156813i	−0.817201	−	0.576353i	$-0.804475\pi$
$61$	0.707107	−	1.22474i	0.0905357	−	0.156813i	0.907737	+	0.419540i	$0.137809\pi$
$62$	8.48528			1.07763
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.83013	+	3.36603i	0.475069	+	0.417504i
$66$	−2.82843	−	4.89898i	−0.348155	−	0.603023i
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$	−1.41421	+	2.44949i	−0.171499	+	0.297044i
$69$		0			0
$70$		0			0
$71$		−	8.00000i		−	0.949425i	−0.880141	−	0.474713i	$-0.842552\pi$
$71$		−	8.00000i		−	0.949425i	0.880141	−	0.474713i	$-0.157448\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	12.2474	−	7.07107i	1.43346	−	0.827606i	0.436073	−	0.899911i	$-0.356369\pi$
$73$	12.2474	−	7.07107i	1.43346	−	0.827606i	0.997383	+	0.0723054i	$0.0230356\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−2.12132	+	3.67423i	−0.244949	+	0.424264i
$76$		−	4.24264i		−	0.486664i
$77$		0			0
$78$	−1.00000	+	5.00000i	−0.113228	+	0.566139i
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$	1.22474	−	0.707107i	0.136931	−	0.0790569i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	2.82843	−	4.89898i	0.312348	−	0.541002i
$83$			1.41421i			0.155230i	0.996983	+	0.0776151i	$0.0247305\pi$
$83$			1.41421i			0.155230i	−0.996983	+	0.0776151i	$0.975269\pi$
$84$		0			0
$85$		−	4.00000i		−	0.433861i
$86$	−6.92820	−	4.00000i	−0.747087	−	0.431331i
$87$	1.41421	+	2.44949i	0.151620	+	0.262613i
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	−7.34847	−	4.24264i	−0.778936	−	0.449719i	0.0571170	−	0.998367i	$-0.481809\pi$
$89$	−7.34847	−	4.24264i	−0.778936	−	0.449719i	−0.836053	+	0.548648i	$0.815143\pi$
$90$	−1.41421			−0.149071
$91$		0			0
$92$		0			0
$93$	−10.3923	−	6.00000i	−1.07763	−	0.622171i
$94$	−1.41421	−	2.44949i	−0.145865	−	0.252646i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	1.22474	+	0.707107i	0.125000	+	0.0721688i
$97$		−	5.65685i		−	0.574367i	−0.957876	−	0.287183i	$-0.907281\pi$
$97$		−	5.65685i		−	0.574367i	0.957876	−	0.287183i	$-0.0927189\pi$
$98$		0			0
$99$		−	4.00000i		−	0.402015i
$100$	1.50000	−	2.59808i	0.150000	−	0.259808i
$101$	7.77817	+	13.4722i	0.773957	+	1.34053i	0.935379	+	0.353648i	$0.115059\pi$
$101$	7.77817	+	13.4722i	0.773957	+	1.34053i	−0.161421	+	0.986886i	$0.551608\pi$
$102$	3.46410	−	2.00000i	0.342997	−	0.198030i
$103$	−9.89949	+	17.1464i	−0.975426	+	1.68949i	−0.296905	+	0.954907i	$0.595954\pi$
$103$	−9.89949	+	17.1464i	−0.975426	+	1.68949i	−0.678521	+	0.734581i	$0.737379\pi$
$104$	0.707107	−	3.53553i	0.0693375	−	0.346688i
$105$		0			0
$106$		−	10.0000i		−	0.971286i
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	−0.992003	−	0.126217i	$-0.959717\pi$
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	0.605308	+	0.795991i	$0.293050\pi$
$108$	−2.82843	−	4.89898i	−0.272166	−	0.471405i
$109$	−8.66025	+	5.00000i	−0.829502	+	0.478913i	−0.853682	−	0.520794i	$-0.825636\pi$
$109$	−8.66025	+	5.00000i	−0.829502	+	0.478913i	0.0241802	+	0.999708i	$0.492302\pi$
$110$	−4.89898	−	2.82843i	−0.467099	−	0.269680i
$111$			2.82843i			0.268462i
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$		0			0
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	−2.38014	+	2.70831i	−0.220044	+	0.250383i
$118$	7.07107			0.650945
$119$		0			0
$120$	−2.00000			−0.182574
$121$	2.50000	−	4.33013i	0.227273	−	0.393648i
$122$	1.22474	−	0.707107i	0.110883	−	0.0640184i
$123$	−6.92820	+	4.00000i	−0.624695	+	0.360668i
$124$	7.34847	+	4.24264i	0.659912	+	0.381000i
$125$			11.3137i			1.01193i
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	5.65685	+	9.79796i	0.498058	+	0.862662i
$130$	1.63397	+	4.83013i	0.143309	+	0.423630i
$131$	2.12132	−	3.67423i	0.185341	−	0.321019i	−0.758351	−	0.651847i	$-0.773994\pi$
$131$	2.12132	−	3.67423i	0.185341	−	0.321019i	0.943691	+	0.330827i	$0.107328\pi$
$132$		−	5.65685i		−	0.492366i
$133$		0			0
$134$	−4.00000			−0.345547
$135$	6.92820	+	4.00000i	0.596285	+	0.344265i
$136$	−2.44949	+	1.41421i	−0.210042	+	0.121268i
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.873247	−	0.487278i	$-0.837990\pi$
$137$	−10.3923	+	6.00000i	−0.887875	+	0.512615i	−0.0146279	+	0.999893i	$0.504656\pi$
$138$		0			0
$139$	−4.24264			−0.359856			−0.179928	−	0.983680i	$-0.557586\pi$
$139$	−4.24264			−0.359856			−0.179928	+	0.983680i	$0.557586\pi$
$140$		0			0
$141$			4.00000i			0.336861i
$142$	4.00000	−	6.92820i	0.335673	−	0.581402i
$143$	−13.6617	+	4.62158i	−1.14245	+	0.386476i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	2.44949	+	1.41421i	0.203419	+	0.117444i
$146$	14.1421			1.17041
$147$		0			0
$148$		−	2.00000i		−	0.164399i
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	0.697507	−	0.716578i	$-0.254293\pi$
$149$	5.19615	+	3.00000i	0.425685	+	0.245770i	−0.271821	+	0.962348i	$0.587626\pi$
$150$	−3.67423	+	2.12132i	−0.300000	+	0.173205i
$151$	19.0526	−	11.0000i	1.55048	−	0.895167i	0.552372	−	0.833597i	$-0.313723\pi$
$151$	19.0526	−	11.0000i	1.55048	−	0.895167i	0.998103	−	0.0615699i	$-0.0196107\pi$
$152$	2.12132	−	3.67423i	0.172062	−	0.298020i
$153$	2.82843			0.228665
$154$		0			0
$155$	−12.0000			−0.963863
$156$	−3.36603	+	3.83013i	−0.269498	+	0.306656i
$157$	0.707107	+	1.22474i	0.0564333	+	0.0977453i	0.892862	−	0.450331i	$-0.148694\pi$
$157$	0.707107	+	1.22474i	0.0564333	+	0.0977453i	−0.836429	+	0.548076i	$0.815361\pi$
$158$	1.73205	−	1.00000i	0.137795	−	0.0795557i
$159$	−7.07107	+	12.2474i	−0.560772	+	0.971286i
$160$	1.41421			0.111803
$161$		0			0
$162$			5.00000i			0.392837i
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.932326	−	0.361619i	$-0.117776\pi$
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.152992	+	0.988227i	$0.451109\pi$
$164$	4.89898	−	2.82843i	0.382546	−	0.220863i
$165$	4.00000	+	6.92820i	0.311400	+	0.539360i
$166$	−0.707107	+	1.22474i	−0.0548821	+	0.0950586i
$167$		−	14.1421i		−	1.09435i	−0.837018	−	0.547176i	$-0.815703\pi$
$167$		−	14.1421i		−	1.09435i	0.837018	−	0.547176i	$-0.184297\pi$
$168$		0			0
$169$	12.0000	+	5.00000i	0.923077	+	0.384615i
$170$	2.00000	−	3.46410i	0.153393	−	0.265684i
$171$	−3.67423	+	2.12132i	−0.280976	+	0.162221i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	6.36396	−	11.0227i	0.483843	−	0.838041i	−0.515985	−	0.856598i	$-0.672574\pi$
$173$	6.36396	−	11.0227i	0.483843	−	0.838041i	0.999828	+	0.0185571i	$0.00590724\pi$
$174$			2.82843i			0.214423i
$175$		0			0
$176$			4.00000i			0.301511i
$177$	−8.66025	−	5.00000i	−0.650945	−	0.375823i
$178$	−4.24264	−	7.34847i	−0.317999	−	0.550791i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	−1.22474	−	0.707107i	−0.0912871	−	0.0527046i
$181$	18.3848			1.36653			0.683265	−	0.730171i	$-0.260559\pi$
$181$	18.3848			1.36653			0.683265	+	0.730171i	$0.260559\pi$
$182$		0			0
$183$	−2.00000			−0.147844
$184$		0			0
$185$	1.41421	+	2.44949i	0.103975	+	0.180090i
$186$	−6.00000	−	10.3923i	−0.439941	−	0.762001i
$187$	9.79796	+	5.65685i	0.716498	+	0.413670i
$188$		−	2.82843i		−	0.206284i
$189$		0			0
$190$			6.00000i			0.435286i
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	0.126314	+	0.991990i	$0.459685\pi$
$191$	−11.0000	+	19.0526i	−0.795932	+	1.37859i	−0.922246	+	0.386604i	$0.873648\pi$
$192$	0.707107	+	1.22474i	0.0510310	+	0.0883883i
$193$	22.5167	−	13.0000i	1.62078	−	0.935760i	0.634074	−	0.773272i	$-0.281381\pi$
$193$	22.5167	−	13.0000i	1.62078	−	0.935760i	0.986710	−	0.162488i	$-0.0519520\pi$
$194$	2.82843	−	4.89898i	0.203069	−	0.351726i
$195$	1.41421	−	7.07107i	0.101274	−	0.506370i
$196$		0			0
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	4.24264	+	7.34847i	0.300753	+	0.520919i	0.976307	−	0.216391i	$-0.0694287\pi$
$199$	4.24264	+	7.34847i	0.300753	+	0.520919i	−0.675554	+	0.737311i	$0.736095\pi$
$200$	2.59808	−	1.50000i	0.183712	−	0.106066i
$201$	4.89898	+	2.82843i	0.345547	+	0.199502i
$202$			15.5563i			1.09454i
$203$		0			0
$204$	4.00000			0.280056
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$	−17.1464	+	9.89949i	−1.19465	+	0.689730i
$207$		0			0
$208$	2.38014	−	2.70831i	0.165033	−	0.187787i
$209$	−16.9706			−1.17388
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	5.00000	−	8.66025i	0.343401	−	0.594789i
$213$	−9.79796	+	5.65685i	−0.671345	+	0.387601i
$214$	−6.92820	+	4.00000i	−0.473602	+	0.273434i
$215$	9.79796	+	5.65685i	0.668215	+	0.385794i
$216$		−	5.65685i		−	0.384900i
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−17.3205	−	10.0000i	−1.17041	−	0.675737i
$220$	−2.82843	−	4.89898i	−0.190693	−	0.330289i
$221$	−3.26795	−	9.66025i	−0.219826	−	0.649819i
$222$	−1.41421	+	2.44949i	−0.0949158	+	0.164399i
$223$			22.6274i			1.51524i	0.652694	+	0.757622i	$0.273639\pi$
$223$			22.6274i			1.51524i	−0.652694	+	0.757622i	$0.726361\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$	10.3923	+	6.00000i	0.691286	+	0.399114i
$227$	−18.3712	+	10.6066i	−1.21934	+	0.703985i	−0.964776	−	0.263072i	$-0.915264\pi$
$227$	−18.3712	+	10.6066i	−1.21934	+	0.703985i	−0.254561	+	0.967057i	$0.581931\pi$
$228$	−5.19615	+	3.00000i	−0.344124	+	0.198680i
$229$	23.2702	+	13.4350i	1.53773	+	0.887812i	0.998971	+	0.0453550i	$0.0144419\pi$
$229$	23.2702	+	13.4350i	1.53773	+	0.887812i	0.538764	+	0.842457i	$0.318891\pi$
$230$		0			0
$231$		0			0
$232$		−	2.00000i		−	0.131306i
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$	−3.41542	+	1.15539i	−0.223273	+	0.0755305i
$235$	2.00000	+	3.46410i	0.130466	+	0.225973i
$236$	6.12372	+	3.53553i	0.398621	+	0.230144i
$237$	−2.82843			−0.183726
$238$		0			0
$239$			18.0000i			1.16432i	0.813073	+	0.582162i	$0.197793\pi$
$239$			18.0000i			1.16432i	−0.813073	+	0.582162i	$0.802207\pi$
$240$	−1.73205	−	1.00000i	−0.111803	−	0.0645497i
$241$	19.5959	−	11.3137i	1.26228	−	0.728780i	0.288768	−	0.957399i	$-0.406754\pi$
$241$	19.5959	−	11.3137i	1.26228	−	0.728780i	0.973516	+	0.228619i	$0.0734210\pi$
$242$	4.33013	−	2.50000i	0.278351	−	0.160706i
$243$	−4.94975	+	8.57321i	−0.317526	+	0.549972i
$244$	1.41421			0.0905357
$245$		0			0
$246$	−8.00000			−0.510061
$247$	11.4904	+	10.0981i	0.731115	+	0.642525i
$248$	4.24264	+	7.34847i	0.269408	+	0.466628i
$249$	1.73205	−	1.00000i	0.109764	−	0.0633724i
$250$	−5.65685	+	9.79796i	−0.357771	+	0.619677i
$251$	−15.5563			−0.981908			−0.490954	−	0.871185i	$-0.663352\pi$
$251$	−15.5563			−0.981908			−0.490954	+	0.871185i	$0.663352\pi$
$252$		0			0
$253$		0			0
$254$	6.92820	+	4.00000i	0.434714	+	0.250982i
$255$	−4.89898	+	2.82843i	−0.306786	+	0.177123i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.48528	−	14.6969i	0.529297	−	0.916770i	−0.470119	−	0.882603i	$-0.655789\pi$
$257$	8.48528	−	14.6969i	0.529297	−	0.916770i	0.999416	−	0.0341667i	$-0.0108777\pi$
$258$			11.3137i			0.704361i
$259$		0			0
$260$	−1.00000	+	5.00000i	−0.0620174	+	0.310087i
$261$	−1.00000	+	1.73205i	−0.0618984	+	0.107211i
$262$	3.67423	−	2.12132i	0.226995	−	0.131056i
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	0.895209	−	0.445647i	$-0.147026\pi$
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	−0.833546	+	0.552450i	$0.813693\pi$
$264$	2.82843	−	4.89898i	0.174078	−	0.301511i
$265$			14.1421i			0.868744i
$266$		0			0
$267$			12.0000i			0.734388i
$268$	−3.46410	−	2.00000i	−0.211604	−	0.122169i
$269$	7.77817	+	13.4722i	0.474244	+	0.821414i	0.999565	−	0.0294897i	$-0.00938824\pi$
$269$	7.77817	+	13.4722i	0.474244	+	0.821414i	−0.525321	+	0.850904i	$0.676055\pi$
$270$	4.00000	+	6.92820i	0.243432	+	0.421637i
$271$	9.79796	+	5.65685i	0.595184	+	0.343629i	0.767144	−	0.641474i	$-0.221677\pi$
$271$	9.79796	+	5.65685i	0.595184	+	0.343629i	−0.171961	+	0.985104i	$0.555010\pi$
$272$	−2.82843			−0.171499
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−10.3923	−	6.00000i	−0.626680	−	0.361814i
$276$		0			0
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	0.575408	−	0.817867i	$-0.304843\pi$
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	−0.995997	+	0.0893846i	$0.971510\pi$
$278$	−3.67423	−	2.12132i	−0.220366	−	0.127228i
$279$		−	8.48528i		−	0.508001i
$280$		0			0
$281$		−	24.0000i		−	1.43172i	−0.698244	−	0.715860i	$-0.746035\pi$
$281$		−	24.0000i		−	1.43172i	0.698244	−	0.715860i	$-0.253965\pi$
$282$	−2.00000	+	3.46410i	−0.119098	+	0.206284i
$283$	−12.0208	−	20.8207i	−0.714563	−	1.23766i	−0.963128	−	0.269045i	$-0.913292\pi$
$283$	−12.0208	−	20.8207i	−0.714563	−	1.23766i	0.248564	−	0.968615i	$-0.420041\pi$
$284$	6.92820	−	4.00000i	0.411113	−	0.237356i
$285$	4.24264	−	7.34847i	0.251312	−	0.435286i
$286$	−14.1421	−	2.82843i	−0.836242	−	0.167248i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	4.50000	−	7.79423i	0.264706	−	0.458484i
$290$	1.41421	+	2.44949i	0.0830455	+	0.143839i
$291$	−6.92820	+	4.00000i	−0.406138	+	0.234484i
$292$	12.2474	+	7.07107i	0.716728	+	0.413803i
$293$			9.89949i			0.578335i	0.957279	+	0.289167i	$0.0933784\pi$
$293$			9.89949i			0.578335i	−0.957279	+	0.289167i	$0.906622\pi$
$294$		0			0
$295$	−10.0000			−0.582223
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−19.5959	+	11.3137i	−1.13707	+	0.656488i
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$		0			0
$300$	−4.24264			−0.244949
$301$		0			0
$302$	22.0000			1.26596
$303$	11.0000	−	19.0526i	0.631933	−	1.09454i
$304$	3.67423	−	2.12132i	0.210732	−	0.121666i
$305$	−1.73205	+	1.00000i	−0.0991769	+	0.0572598i
$306$	2.44949	+	1.41421i	0.140028	+	0.0808452i
$307$			24.0416i			1.37213i	0.727541	+	0.686064i	$0.240663\pi$
$307$			24.0416i			1.37213i	−0.727541	+	0.686064i	$0.759337\pi$
$308$		0			0
$309$	28.0000			1.59286
$310$	−10.3923	−	6.00000i	−0.590243	−	0.340777i
$311$	−2.82843	−	4.89898i	−0.160385	−	0.277796i	0.774622	−	0.632425i	$-0.217940\pi$
$311$	−2.82843	−	4.89898i	−0.160385	−	0.277796i	−0.935007	+	0.354629i	$0.884607\pi$
$312$	−4.83013	+	1.63397i	−0.273452	+	0.0925056i
$313$	9.89949	−	17.1464i	0.559553	−	0.969173i	−0.437981	−	0.898984i	$-0.644306\pi$
$313$	9.89949	−	17.1464i	0.559553	−	0.969173i	0.997534	−	0.0701893i	$-0.0223603\pi$
$314$			1.41421i			0.0798087i
$315$		0			0
$316$	2.00000			0.112509
$317$	29.4449	+	17.0000i	1.65379	+	0.954815i	0.975494	+	0.220024i	$0.0706137\pi$
$317$	29.4449	+	17.0000i	1.65379	+	0.954815i	0.678294	+	0.734791i	$0.262720\pi$
$318$	−12.2474	+	7.07107i	−0.686803	+	0.396526i
$319$	−6.92820	+	4.00000i	−0.387905	+	0.223957i
$320$	1.22474	+	0.707107i	0.0684653	+	0.0395285i
$321$	11.3137			0.631470
$322$		0			0
$323$		−	12.0000i		−	0.667698i
$324$	−2.50000	+	4.33013i	−0.138889	+	0.240563i
$325$	3.46618	+	10.2462i	0.192269	+	0.568360i
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$	12.2474	+	7.07107i	0.677285	+	0.391031i
$328$	5.65685			0.312348
$329$		0			0
$330$			8.00000i			0.440386i
$331$	−13.8564	−	8.00000i	−0.761617	−	0.439720i	0.0682590	−	0.997668i	$-0.478256\pi$
$331$	−13.8564	−	8.00000i	−0.761617	−	0.439720i	−0.829876	+	0.557948i	$0.811589\pi$
$332$	−1.22474	+	0.707107i	−0.0672166	+	0.0388075i
$333$	−1.73205	+	1.00000i	−0.0949158	+	0.0547997i
$334$	7.07107	−	12.2474i	0.386912	−	0.670151i
$335$	5.65685			0.309067
$336$		0			0
$337$	−20.0000			−1.08947			−0.544735	−	0.838608i	$-0.683370\pi$
$337$	−20.0000			−1.08947			−0.544735	+	0.838608i	$0.683370\pi$
$338$	7.89230	+	10.3301i	0.429285	+	0.561885i
$339$	−8.48528	−	14.6969i	−0.460857	−	0.798228i
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	16.9706	−	29.3939i	0.919007	−	1.59177i
$342$	−4.24264			−0.229416
$343$		0			0
$344$		−	8.00000i		−	0.431331i
$345$		0			0
$346$	11.0227	−	6.36396i	0.592584	−	0.342129i
$347$	16.0000	+	27.7128i	0.858925	+	1.48770i	0.872955	+	0.487800i	$0.162201\pi$
$347$	16.0000	+	27.7128i	0.858925	+	1.48770i	−0.0140303	+	0.999902i	$0.504466\pi$
$348$	−1.41421	+	2.44949i	−0.0758098	+	0.131306i
$349$			4.24264i			0.227103i	0.993532	+	0.113552i	$0.0362227\pi$
$349$			4.24264i			0.227103i	−0.993532	+	0.113552i	$0.963777\pi$
$350$		0			0
$351$	20.0000	+	4.00000i	1.06752	+	0.213504i
$352$	−2.00000	+	3.46410i	−0.106600	+	0.184637i
$353$	−17.1464	+	9.89949i	−0.912612	+	0.526897i	−0.881271	−	0.472612i	$-0.843311\pi$
$353$	−17.1464	+	9.89949i	−0.912612	+	0.526897i	−0.0313416	+	0.999509i	$0.509978\pi$
$354$	−5.00000	−	8.66025i	−0.265747	−	0.460287i
$355$	−5.65685	+	9.79796i	−0.300235	+	0.520022i
$356$		−	8.48528i		−	0.449719i
$357$		0			0
$358$		−	4.00000i		−	0.211407i
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	0.0286287	−	0.999590i	$-0.490886\pi$
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	−0.851356	+	0.524588i	$0.824219\pi$
$360$	−0.707107	−	1.22474i	−0.0372678	−	0.0645497i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	15.9217	+	9.19239i	0.836825	+	0.483141i
$363$	−7.07107			−0.371135
$364$		0			0
$365$	−20.0000			−1.04685
$366$	−1.73205	−	1.00000i	−0.0905357	−	0.0522708i
$367$	−5.65685	−	9.79796i	−0.295285	−	0.511449i	0.679766	−	0.733429i	$-0.262081\pi$
$367$	−5.65685	−	9.79796i	−0.295285	−	0.511449i	−0.975051	+	0.221980i	$0.928748\pi$
$368$		0			0
$369$	−4.89898	−	2.82843i	−0.255031	−	0.147242i
$370$			2.82843i			0.147043i
$371$		0			0
$372$		−	12.0000i		−	0.622171i
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$	5.65685	+	9.79796i	0.292509	+	0.506640i
$375$	13.8564	−	8.00000i	0.715542	−	0.413118i
$376$	1.41421	−	2.44949i	0.0729325	−	0.126323i
$377$	7.07107	+	1.41421i	0.364179	+	0.0728357i
$378$		0			0
$379$		−	16.0000i		−	0.821865i	−0.911666	−	0.410932i	$-0.865203\pi$
$379$		−	16.0000i		−	0.821865i	0.911666	−	0.410932i	$-0.134797\pi$
$380$	−3.00000	+	5.19615i	−0.153897	+	0.266557i
$381$	−5.65685	−	9.79796i	−0.289809	−	0.501965i
$382$	−19.0526	+	11.0000i	−0.974814	+	0.562809i
$383$	−17.1464	−	9.89949i	−0.876142	−	0.505841i	−0.00675728	−	0.999977i	$-0.502151\pi$
$383$	−17.1464	−	9.89949i	−0.876142	−	0.505841i	−0.869384	+	0.494137i	$0.835484\pi$
$384$			1.41421i			0.0721688i
$385$		0			0
$386$	26.0000			1.32337
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	4.89898	−	2.82843i	0.248708	−	0.143592i
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$	4.76028	−	5.41662i	0.241046	−	0.274281i
$391$		0			0
$392$		0			0
$393$	−6.00000			−0.302660
$394$	1.00000	−	1.73205i	0.0503793	−	0.0872595i
$395$	−2.44949	+	1.41421i	−0.123247	+	0.0711568i
$396$	3.46410	−	2.00000i	0.174078	−	0.100504i
$397$	11.0227	+	6.36396i	0.553214	+	0.319398i	0.750417	−	0.660965i	$-0.229853\pi$
$397$	11.0227	+	6.36396i	0.553214	+	0.319398i	−0.197203	+	0.980363i	$0.563186\pi$
$398$			8.48528i			0.425329i
$399$		0			0
$400$	3.00000			0.150000
$401$	−32.9090	−	19.0000i	−1.64340	−	0.948815i	−0.979614	−	0.200888i	$-0.935617\pi$
$401$	−32.9090	−	19.0000i	−1.64340	−	0.948815i	−0.663781	−	0.747927i	$-0.731049\pi$
$402$	2.82843	+	4.89898i	0.141069	+	0.244339i
$403$	−28.9808	+	9.80385i	−1.44363	+	0.488364i
$404$	−7.77817	+	13.4722i	−0.386979	+	0.670267i
$405$		−	7.07107i		−	0.351364i
$406$		0			0
$407$	−8.00000			−0.396545
$408$	3.46410	+	2.00000i	0.171499	+	0.0990148i
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$	−6.92820	+	4.00000i	−0.342160	+	0.197546i
$411$	14.6969	+	8.48528i	0.724947	+	0.418548i
$412$	−19.7990			−0.975426
$413$		0			0
$414$		0			0
$415$	1.00000	−	1.73205i	0.0490881	−	0.0850230i
$416$	3.41542	−	1.15539i	0.167455	−	0.0566479i
$417$	3.00000	+	5.19615i	0.146911	+	0.254457i
$418$	−14.6969	−	8.48528i	−0.718851	−	0.415029i
$419$	−24.0416			−1.17451			−0.587255	−	0.809402i	$-0.699792\pi$
$419$	−24.0416			−1.17451			−0.587255	+	0.809402i	$0.699792\pi$
$420$		0			0
$421$			6.00000i			0.292422i	0.989253	+	0.146211i	$0.0467079\pi$
$421$			6.00000i			0.292422i	−0.989253	+	0.146211i	$0.953292\pi$
$422$		0			0
$423$	−2.44949	+	1.41421i	−0.119098	+	0.0687614i
$424$	8.66025	−	5.00000i	0.420579	−	0.242821i
$425$	4.24264	−	7.34847i	0.205798	−	0.356453i
$426$	−11.3137			−0.548151
$427$		0			0
$428$	−8.00000			−0.386695
$429$	15.3205	+	13.4641i	0.739681	+	0.650053i
$430$	5.65685	+	9.79796i	0.272798	+	0.472500i
$431$	8.66025	−	5.00000i	0.417150	−	0.240842i	−0.276707	−	0.960954i	$-0.589243\pi$
$431$	8.66025	−	5.00000i	0.417150	−	0.240842i	0.693857	+	0.720113i	$0.255910\pi$
$432$	2.82843	−	4.89898i	0.136083	−	0.235702i
$433$	25.4558			1.22333			0.611665	−	0.791117i	$-0.290500\pi$
$433$	25.4558			1.22333			0.611665	+	0.791117i	$0.290500\pi$
$434$		0			0
$435$		−	4.00000i		−	0.191785i
$436$	−8.66025	−	5.00000i	−0.414751	−	0.239457i
$437$		0			0
$438$	−10.0000	−	17.3205i	−0.477818	−	0.827606i
$439$	−11.3137	+	19.5959i	−0.539974	+	0.935262i	0.458931	+	0.888472i	$0.348233\pi$
$439$	−11.3137	+	19.5959i	−0.539974	+	0.935262i	−0.998905	+	0.0467902i	$0.985101\pi$
$440$		−	5.65685i		−	0.269680i
$441$		0			0
$442$	2.00000	−	10.0000i	0.0951303	−	0.475651i
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$	−2.44949	+	1.41421i	−0.116248	+	0.0671156i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	−11.3137	+	19.5959i	−0.535720	+	0.927894i
$447$		−	8.48528i		−	0.401340i
$448$		0			0
$449$			4.00000i			0.188772i	0.995536	+	0.0943858i	$0.0300887\pi$
$449$			4.00000i			0.188772i	−0.995536	+	0.0943858i	$0.969911\pi$
$450$	−2.59808	−	1.50000i	−0.122474	−	0.0707107i
$451$	−11.3137	−	19.5959i	−0.532742	−	0.922736i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	−26.9444	−	15.5563i	−1.26596	−	0.730901i
$454$	−21.2132			−0.995585
$455$		0			0
$456$	−6.00000			−0.280976
$457$	8.66025	+	5.00000i	0.405110	+	0.233890i	0.688686	−	0.725059i	$-0.258188\pi$
$457$	8.66025	+	5.00000i	0.405110	+	0.233890i	−0.283577	+	0.958950i	$0.591521\pi$
$458$	13.4350	+	23.2702i	0.627778	+	1.08734i
$459$	−8.00000	−	13.8564i	−0.373408	−	0.646762i
$460$		0			0
$461$		−	32.5269i		−	1.51493i	−0.652876	−	0.757465i	$-0.726438\pi$
$461$		−	32.5269i		−	1.51493i	0.652876	−	0.757465i	$-0.273562\pi$
$462$		0			0
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$	8.48528	+	14.6969i	0.393496	+	0.681554i
$466$	15.5885	−	9.00000i	0.722121	−	0.416917i
$467$	−2.12132	+	3.67423i	−0.0981630	+	0.170023i	−0.910924	−	0.412574i	$-0.864630\pi$
$467$	−2.12132	+	3.67423i	−0.0981630	+	0.170023i	0.812761	+	0.582597i	$0.197963\pi$
$468$	−3.53553	−	0.707107i	−0.163430	−	0.0326860i
$469$		0			0
$470$			4.00000i			0.184506i
$471$	1.00000	−	1.73205i	0.0460776	−	0.0798087i
$472$	3.53553	+	6.12372i	0.162736	+	0.281867i
$473$	−27.7128	+	16.0000i	−1.27424	+	0.735681i
$474$	−2.44949	−	1.41421i	−0.112509	−	0.0649570i
$475$			12.7279i			0.583997i
$476$		0			0
$477$	−10.0000			−0.457869
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	12.2474	−	7.07107i	0.559600	−	0.323085i	−0.193385	−	0.981123i	$-0.561947\pi$
$479$	12.2474	−	7.07107i	0.559600	−	0.323085i	0.752985	+	0.658038i	$0.228613\pi$
$480$	−1.00000	−	1.73205i	−0.0456435	−	0.0790569i
$481$	5.41662	+	4.76028i	0.246977	+	0.217050i
$482$	22.6274			1.03065
$483$		0			0
$484$	5.00000			0.227273
$485$	−4.00000	+	6.92820i	−0.181631	+	0.314594i
$486$	−8.57321	+	4.94975i	−0.388889	+	0.224525i
$487$	−15.5885	+	9.00000i	−0.706380	+	0.407829i	−0.809719	−	0.586817i	$-0.800381\pi$
$487$	−15.5885	+	9.00000i	−0.706380	+	0.407829i	0.103339	+	0.994646i	$0.467047\pi$
$488$	1.22474	+	0.707107i	0.0554416	+	0.0320092i
$489$		−	22.6274i		−	1.02325i
$490$		0			0
$491$	4.00000			0.180517			0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000			0.180517			0.0902587	+	0.995918i	$0.471231\pi$
$492$	−6.92820	−	4.00000i	−0.312348	−	0.180334i
$493$	−2.82843	−	4.89898i	−0.127386	−	0.220639i
$494$	4.90192	+	14.4904i	0.220548	+	0.651953i
$495$	−2.82843	+	4.89898i	−0.127128	+	0.220193i
$496$			8.48528i			0.381000i
$497$		0			0
$498$	2.00000			0.0896221
$499$	27.7128	+	16.0000i	1.24060	+	0.716258i	0.969216	−	0.246214i	$-0.0791865\pi$
$499$	27.7128	+	16.0000i	1.24060	+	0.716258i	0.271380	+	0.962472i	$0.412520\pi$
$500$	−9.79796	+	5.65685i	−0.438178	+	0.252982i
$501$	−17.3205	+	10.0000i	−0.773823	+	0.446767i
$502$	−13.4722	−	7.77817i	−0.601293	−	0.347157i
$503$	22.6274			1.00891			0.504453	−	0.863439i	$-0.331694\pi$
$503$	22.6274			1.00891			0.504453	+	0.863439i	$0.331694\pi$
$504$		0			0
$505$		−	22.0000i		−	0.978987i
$506$		0			0
$507$	−2.36156	−	18.2325i	−0.104880	−	0.809733i
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	−8.57321	−	4.94975i	−0.380001	−	0.219394i	0.297818	−	0.954623i	$-0.403741\pi$
$509$	−8.57321	−	4.94975i	−0.380001	−	0.219394i	−0.677819	+	0.735229i	$0.737075\pi$
$510$	−5.65685			−0.250490
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	20.7846	+	12.0000i	0.917663	+	0.529813i
$514$	14.6969	−	8.48528i	0.648254	−	0.374270i
$515$	24.2487	−	14.0000i	1.06853	−	0.616914i
$516$	−5.65685	+	9.79796i	−0.249029	+	0.431331i
$517$	−11.3137			−0.497576
$518$		0			0
$519$	−18.0000			−0.790112
$520$	−3.36603	+	3.83013i	−0.147610	+	0.167962i
$521$	−1.41421	−	2.44949i	−0.0619578	−	0.107314i	0.833383	−	0.552696i	$-0.186401\pi$
$521$	−1.41421	−	2.44949i	−0.0619578	−	0.107314i	−0.895340	+	0.445382i	$0.853068\pi$
$522$	−1.73205	+	1.00000i	−0.0758098	+	0.0437688i
$523$	10.6066	−	18.3712i	0.463794	−	0.803315i	−0.535352	−	0.844629i	$-0.679821\pi$
$523$	10.6066	−	18.3712i	0.463794	−	0.803315i	0.999146	+	0.0413138i	$0.0131543\pi$
$524$	4.24264			0.185341
$525$		0			0
$526$			2.00000i			0.0872041i
$527$	20.7846	+	12.0000i	0.905392	+	0.522728i
$528$	4.89898	−	2.82843i	0.213201	−	0.123091i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−7.07107	+	12.2474i	−0.307148	+	0.531995i
$531$		−	7.07107i		−	0.306858i
$532$		0			0
$533$	−4.00000	+	20.0000i	−0.173259	+	0.866296i
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$	9.79796	−	5.65685i	0.423603	−	0.244567i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−2.82843	+	4.89898i	−0.122056	+	0.211407i
$538$			15.5563i			0.670682i
$539$		0			0
$540$			8.00000i			0.344265i
$541$	−39.8372	−	23.0000i	−1.71273	−	0.988847i	−0.930834	−	0.365444i	$-0.880917\pi$
$541$	−39.8372	−	23.0000i	−1.71273	−	0.988847i	−0.781900	−	0.623404i	$-0.785749\pi$
$542$	5.65685	+	9.79796i	0.242983	+	0.420858i
$543$	−13.0000	−	22.5167i	−0.557883	−	0.966282i
$544$	−2.44949	−	1.41421i	−0.105021	−	0.0606339i
$545$	14.1421			0.605783
$546$		0			0
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	−10.3923	−	6.00000i	−0.443937	−	0.256307i
$549$	−0.707107	−	1.22474i	−0.0301786	−	0.0522708i
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	7.34847	+	4.24264i	0.313055	+	0.180743i
$552$		0			0
$553$		0			0
$554$		−	14.0000i		−	0.594803i
$555$	2.00000	−	3.46410i	0.0848953	−	0.147043i
$556$	−2.12132	−	3.67423i	−0.0899640	−	0.155822i
$557$	22.5167	−	13.0000i	0.954062	−	0.550828i	0.0597213	−	0.998215i	$-0.480979\pi$
$557$	22.5167	−	13.0000i	0.954062	−	0.550828i	0.894340	+	0.447387i	$0.147645\pi$
$558$	4.24264	−	7.34847i	0.179605	−	0.311086i
$559$	28.2843	+	5.65685i	1.19630	+	0.239259i
$560$		0			0
$561$		−	16.0000i		−	0.675521i
$562$	12.0000	−	20.7846i	0.506189	−	0.876746i
$563$	−10.6066	−	18.3712i	−0.447015	−	0.774253i	0.551175	−	0.834390i	$-0.314180\pi$
$563$	−10.6066	−	18.3712i	−0.447015	−	0.774253i	−0.998190	+	0.0601369i	$0.980846\pi$
$564$	−3.46410	+	2.00000i	−0.145865	+	0.0842152i
$565$	−14.6969	−	8.48528i	−0.618305	−	0.356978i
$566$		−	24.0416i		−	1.01055i
$567$		0			0
$568$	8.00000			0.335673
$569$	20.0000	−	34.6410i	0.838444	−	1.45223i	−0.0527519	−	0.998608i	$-0.516799\pi$
$569$	20.0000	−	34.6410i	0.838444	−	1.45223i	0.891196	−	0.453619i	$-0.149867\pi$
$570$	7.34847	−	4.24264i	0.307794	−	0.177705i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−10.8332	−	9.52056i	−0.452960	−	0.398075i
$573$	31.1127			1.29975
$574$		0			0
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	22.0454	−	12.7279i	0.917762	−	0.529870i	0.0348418	−	0.999393i	$-0.488907\pi$
$577$	22.0454	−	12.7279i	0.917762	−	0.529870i	0.882921	+	0.469523i	$0.155574\pi$
$578$	7.79423	−	4.50000i	0.324197	−	0.187175i
$579$	−31.8434	−	18.3848i	−1.32337	−	0.764045i
$580$			2.82843i			0.117444i
$581$		0			0
$582$	−8.00000			−0.331611
$583$	−34.6410	−	20.0000i	−1.43468	−	0.828315i
$584$	7.07107	+	12.2474i	0.292603	+	0.506803i
$585$	4.83013	−	1.63397i	0.199701	−	0.0675565i
$586$	−4.94975	+	8.57321i	−0.204472	+	0.354156i
$587$		−	38.1838i		−	1.57601i	−0.615667	−	0.788006i	$-0.711113\pi$
$587$		−	38.1838i		−	1.57601i	0.615667	−	0.788006i	$-0.288887\pi$
$588$		0			0
$589$	−36.0000			−1.48335
$590$	−8.66025	−	5.00000i	−0.356537	−	0.205847i
$591$	−2.44949	+	1.41421i	−0.100759	+	0.0581730i
$592$	1.73205	−	1.00000i	0.0711868	−	0.0410997i
$593$	−31.8434	−	18.3848i	−1.30765	−	0.754972i	−0.325947	−	0.945388i	$-0.605683\pi$
$593$	−31.8434	−	18.3848i	−1.30765	−	0.754972i	−0.981704	+	0.190416i	$0.939016\pi$
$594$	−22.6274			−0.928414
$595$		0			0
$596$			6.00000i			0.245770i
$597$	6.00000	−	10.3923i	0.245564	−	0.425329i
$598$		0			0
$599$	−17.0000	−	29.4449i	−0.694601	−	1.20308i	−0.970315	−	0.241845i	$-0.922248\pi$
$599$	−17.0000	−	29.4449i	−0.694601	−	1.20308i	0.275714	−	0.961240i	$-0.411086\pi$
$600$	−3.67423	−	2.12132i	−0.150000	−	0.0866025i
$601$	16.9706			0.692244			0.346122	−	0.938190i	$-0.387498\pi$
$601$	16.9706			0.692244			0.346122	+	0.938190i	$0.387498\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$	19.0526	+	11.0000i	0.775238	+	0.447584i
$605$	−6.12372	+	3.53553i	−0.248965	+	0.143740i
$606$	19.0526	−	11.0000i	0.773957	−	0.446844i
$607$	−16.9706	+	29.3939i	−0.688814	+	1.19306i	0.283408	+	0.958999i	$0.408535\pi$
$607$	−16.9706	+	29.3939i	−0.688814	+	1.19306i	−0.972222	+	0.234061i	$0.924798\pi$
$608$	4.24264			0.172062
$609$		0			0
$610$	−2.00000			−0.0809776
$611$	7.66025	+	6.73205i	0.309901	+	0.272350i
$612$	1.41421	+	2.44949i	0.0571662	+	0.0990148i
$613$	25.9808	−	15.0000i	1.04935	−	0.605844i	0.126885	−	0.991917i	$-0.459502\pi$
$613$	25.9808	−	15.0000i	1.04935	−	0.605844i	0.922468	+	0.386073i	$0.126169\pi$
$614$	−12.0208	+	20.8207i	−0.485121	+	0.840254i
$615$	11.3137			0.456213
$616$		0			0
$617$			42.0000i			1.69086i	0.534089	+	0.845428i	$0.320655\pi$
$617$			42.0000i			1.69086i	−0.534089	+	0.845428i	$0.679345\pi$
$618$	24.2487	+	14.0000i	0.975426	+	0.563163i
$619$	18.3712	−	10.6066i	0.738400	−	0.426315i	−0.0830874	−	0.996542i	$-0.526478\pi$
$619$	18.3712	−	10.6066i	0.738400	−	0.426315i	0.821487	+	0.570227i	$0.193145\pi$
$620$	−6.00000	−	10.3923i	−0.240966	−	0.417365i
$621$		0			0
$622$		−	5.65685i		−	0.226819i
$623$		0			0
$624$	−5.00000	−	1.00000i	−0.200160	−	0.0400320i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	17.1464	−	9.89949i	0.685309	−	0.395663i
$627$	12.0000	+	20.7846i	0.479234	+	0.830057i
$628$	−0.707107	+	1.22474i	−0.0282166	+	0.0488726i
$629$		−	5.65685i		−	0.225554i
$630$		0			0
$631$			40.0000i			1.59237i	0.605050	+	0.796187i	$0.293153\pi$
$631$			40.0000i			1.59237i	−0.605050	+	0.796187i	$0.706847\pi$
$632$	1.73205	+	1.00000i	0.0688973	+	0.0397779i
$633$		0			0
$634$	17.0000	+	29.4449i	0.675156	+	1.16940i
$635$	−9.79796	−	5.65685i	−0.388820	−	0.224485i
$636$	−14.1421			−0.560772
$637$		0			0
$638$	−8.00000			−0.316723
$639$	−6.92820	−	4.00000i	−0.274075	−	0.158238i
$640$	0.707107	+	1.22474i	0.0279508	+	0.0484123i
$641$	16.0000	+	27.7128i	0.631962	+	1.09459i	0.987150	+	0.159795i	$0.0510835\pi$
$641$	16.0000	+	27.7128i	0.631962	+	1.09459i	−0.355188	+	0.934795i	$0.615583\pi$
$642$	9.79796	+	5.65685i	0.386695	+	0.223258i
$643$			29.6985i			1.17119i	0.810602	+	0.585597i	$0.199140\pi$
$643$			29.6985i			1.17119i	−0.810602	+	0.585597i	$0.800860\pi$
$644$		0			0
$645$		−	16.0000i		−	0.629999i
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	−21.2132	−	36.7423i	−0.833977	−	1.44449i	−0.894861	−	0.446346i	$-0.852725\pi$
$647$	−21.2132	−	36.7423i	−0.833977	−	1.44449i	0.0608835	−	0.998145i	$-0.480608\pi$
$648$	−4.33013	+	2.50000i	−0.170103	+	0.0982093i
$649$	14.1421	−	24.4949i	0.555127	−	0.961509i
$650$	−2.12132	+	10.6066i	−0.0832050	+	0.416025i
$651$		0			0
$652$			16.0000i			0.626608i
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$	7.07107	+	12.2474i	0.276501	+	0.478913i
$655$	−5.19615	+	3.00000i	−0.203030	+	0.117220i
$656$	4.89898	+	2.82843i	0.191273	+	0.110432i
$657$		−	14.1421i		−	0.551737i
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	−4.00000	+	6.92820i	−0.155700	+	0.269680i
$661$	35.5176	−	20.5061i	1.38147	−	0.797595i	0.389140	−	0.921178i	$-0.372772\pi$
$661$	35.5176	−	20.5061i	1.38147	−	0.797595i	0.992334	+	0.123584i	$0.0394387\pi$
$662$	−8.00000	−	13.8564i	−0.310929	−	0.538545i
$663$	−9.52056	+	10.8332i	−0.369748	+	0.420728i
$664$	−1.41421			−0.0548821
$665$		0			0
$666$	−2.00000			−0.0774984
$667$		0			0
$668$	12.2474	−	7.07107i	0.473868	−	0.273588i
$669$	27.7128	−	16.0000i	1.07144	−	0.618596i
$670$	4.89898	+	2.82843i	0.189264	+	0.109272i
$671$		−	5.65685i		−	0.218380i
$672$		0			0
$673$	30.0000			1.15642			0.578208	−	0.815890i	$-0.303752\pi$
$673$	30.0000			1.15642			0.578208	+	0.815890i	$0.303752\pi$
$674$	−17.3205	−	10.0000i	−0.667161	−	0.385186i
$675$	8.48528	+	14.6969i	0.326599	+	0.565685i
$676$	1.66987	+	12.8923i	0.0642259	+	0.495858i
$677$	−2.12132	+	3.67423i	−0.0815290	+	0.141212i	−0.903907	−	0.427729i	$-0.859314\pi$
$677$	−2.12132	+	3.67423i	−0.0815290	+	0.141212i	0.822378	+	0.568942i	$0.192647\pi$
$678$		−	16.9706i		−	0.651751i
$679$		0			0
$680$	4.00000			0.153393
$681$	25.9808	+	15.0000i	0.995585	+	0.574801i
$682$	29.3939	−	16.9706i	1.12555	−	0.649836i
$683$	−6.92820	+	4.00000i	−0.265100	+	0.153056i	−0.626659	−	0.779294i	$-0.715578\pi$
$683$	−6.92820	+	4.00000i	−0.265100	+	0.153056i	0.361559	+	0.932349i	$0.382245\pi$
$684$	−3.67423	−	2.12132i	−0.140488	−	0.0811107i
$685$	16.9706			0.648412
$686$		0			0
$687$		−	38.0000i		−	1.44979i
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	11.5539	+	34.1542i	0.440170	+	1.30117i
$690$		0			0
$691$	−1.22474	−	0.707107i	−0.0465915	−	0.0268996i	0.476523	−	0.879162i	$-0.341897\pi$
$691$	−1.22474	−	0.707107i	−0.0465915	−	0.0268996i	−0.523115	+	0.852262i	$0.675230\pi$
$692$	12.7279			0.483843
$693$		0			0
$694$			32.0000i			1.21470i
$695$	5.19615	+	3.00000i	0.197101	+	0.113796i
$696$	−2.44949	+	1.41421i	−0.0928477	+	0.0536056i
$697$	13.8564	−	8.00000i	0.524849	−	0.303022i
$698$	−2.12132	+	3.67423i	−0.0802932	+	0.139072i
$699$	−25.4558			−0.962828
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	15.3205	+	13.4641i	0.578235	+	0.508170i
$703$	4.24264	+	7.34847i	0.160014	+	0.277153i
$704$	−3.46410	+	2.00000i	−0.130558	+	0.0753778i
$705$	2.82843	−	4.89898i	0.106525	−	0.184506i
$706$	−19.7990			−0.745145
$707$		0			0
$708$		−	10.0000i		−	0.375823i
$709$	29.4449	+	17.0000i	1.10583	+	0.638448i	0.937745	−	0.347325i	$-0.112910\pi$
$709$	29.4449	+	17.0000i	1.10583	+	0.638448i	0.168080	+	0.985773i	$0.446243\pi$
$710$	−9.79796	+	5.65685i	−0.367711	+	0.212298i
$711$	−1.00000	−	1.73205i	−0.0375029	−	0.0649570i
$712$	4.24264	−	7.34847i	0.159000	−	0.275396i
$713$		0			0
$714$		0			0
$715$	20.0000	+	4.00000i	0.747958	+	0.149592i
$716$	2.00000	−	3.46410i	0.0747435	−	0.129460i
$717$	22.0454	−	12.7279i	0.823301	−	0.475333i
$718$	−9.00000	−	15.5885i	−0.335877	−	0.581756i
$719$	−18.3848	+	31.8434i	−0.685636	+	1.18756i	0.287600	+	0.957751i	$0.407143\pi$
$719$	−18.3848	+	31.8434i	−0.685636	+	1.18756i	−0.973236	+	0.229807i	$0.926191\pi$
$720$		−	1.41421i		−	0.0527046i
$721$		0			0
$722$		−	1.00000i		−	0.0372161i
$723$	−27.7128	−	16.0000i	−1.03065	−	0.595046i
$724$	9.19239	+	15.9217i	0.341632	+	0.591725i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	−6.12372	−	3.53553i	−0.227273	−	0.131216i
$727$	8.48528			0.314702			0.157351	−	0.987543i	$-0.449705\pi$
$727$	8.48528			0.314702			0.157351	+	0.987543i	$0.449705\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−17.3205	−	10.0000i	−0.641061	−	0.370117i
$731$	−11.3137	−	19.5959i	−0.418453	−	0.724781i
$732$	−1.00000	−	1.73205i	−0.0369611	−	0.0640184i
$733$	−25.7196	−	14.8492i	−0.949977	−	0.548469i	−0.0569030	−	0.998380i	$-0.518123\pi$
$733$	−25.7196	−	14.8492i	−0.949977	−	0.548469i	−0.893074	+	0.449910i	$0.851456\pi$
$734$		−	11.3137i		−	0.417597i
$735$		0			0
$736$		0			0
$737$	−8.00000	+	13.8564i	−0.294684	+	0.510407i
$738$	−2.82843	−	4.89898i	−0.104116	−	0.180334i
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	−1.41421	+	2.44949i	−0.0519875	+	0.0900450i
$741$	4.24264	−	21.2132i	0.155857	−	0.779287i
$742$		0			0
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$	6.00000	−	10.3923i	0.219971	−	0.381000i
$745$	−4.24264	−	7.34847i	−0.155438	−	0.269227i
$746$	−22.5167	+	13.0000i	−0.824394	+	0.475964i
$747$	1.22474	+	0.707107i	0.0448111	+	0.0258717i
$748$			11.3137i			0.413670i
$749$		0			0
$750$	16.0000			0.584237
$751$	−12.0000	+	20.7846i	−0.437886	+	0.758441i	−0.997526	−	0.0702946i	$-0.977606\pi$
$751$	−12.0000	+	20.7846i	−0.437886	+	0.758441i	0.559640	+	0.828736i	$0.310939\pi$
$752$	2.44949	−	1.41421i	0.0893237	−	0.0515711i
$753$	11.0000	+	19.0526i	0.400862	+	0.694314i
$754$	5.41662	+	4.76028i	0.197262	+	0.173359i
$755$	−31.1127			−1.13231
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$		0			0
$760$	−5.19615	+	3.00000i	−0.188484	+	0.108821i
$761$	−9.79796	−	5.65685i	−0.355176	−	0.205061i	0.311787	−	0.950152i	$-0.399073\pi$
$761$	−9.79796	−	5.65685i	−0.355176	−	0.205061i	−0.666962	+	0.745091i	$0.732406\pi$
$762$		−	11.3137i		−	0.409852i
$763$		0			0
$764$	−22.0000			−0.795932
$765$	−3.46410	−	2.00000i	−0.125245	−	0.0723102i
$766$	−9.89949	−	17.1464i	−0.357683	−	0.619526i
$767$	−24.1506	+	8.16987i	−0.872029	+	0.294997i
$768$	−0.707107	+	1.22474i	−0.0255155	+	0.0441942i
$769$			39.5980i			1.42794i	0.700176	+	0.713970i	$0.253105\pi$
$769$			39.5980i			1.42794i	−0.700176	+	0.713970i	$0.746895\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$	22.5167	+	13.0000i	0.810392	+	0.467880i
$773$	28.1691	−	16.2635i	1.01317	−	0.584956i	0.101054	−	0.994881i	$-0.467778\pi$
$773$	28.1691	−	16.2635i	1.01317	−	0.584956i	0.912119	+	0.409925i	$0.134445\pi$
$774$	−6.92820	+	4.00000i	−0.249029	+	0.143777i
$775$	−22.0454	−	12.7279i	−0.791894	−	0.457200i
$776$	5.65685			0.203069
$777$		0			0
$778$		−	18.0000i		−	0.645331i
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$	6.83083	−	2.31079i	0.244583	−	0.0827395i
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$		0			0
$783$	11.3137			0.404319
$784$		0			0
$785$		−	2.00000i		−	0.0713831i
$786$	−5.19615	−	3.00000i	−0.185341	−	0.107006i
$787$	−1.22474	+	0.707107i	−0.0436574	+	0.0252056i	−0.521670	−	0.853147i	$-0.674691\pi$
$787$	−1.22474	+	0.707107i	−0.0436574	+	0.0252056i	0.478012	+	0.878353i	$0.341357\pi$
$788$	1.73205	−	1.00000i	0.0617018	−	0.0356235i
$789$	1.41421	−	2.44949i	0.0503473	−	0.0872041i
$790$	−2.82843			−0.100631
$791$		0			0
$792$	4.00000			0.142134
$793$	−3.36603	+	3.83013i	−0.119531	+	0.136012i
$794$	6.36396	+	11.0227i	0.225849	+	0.391181i
$795$	17.3205	−	10.0000i	0.614295	−	0.354663i
$796$	−4.24264	+	7.34847i	−0.150376	+	0.260460i
$797$	−4.24264			−0.150282			−0.0751410	−	0.997173i	$-0.523941\pi$
$797$	−4.24264			−0.150282			−0.0751410	+	0.997173i	$0.523941\pi$
$798$		0			0
$799$		−	8.00000i		−	0.283020i
$800$	2.59808	+	1.50000i	0.0918559	+	0.0530330i
$801$	−7.34847	+	4.24264i	−0.259645	+	0.149906i
$802$	−19.0000	−	32.9090i	−0.670913	−	1.16206i
$803$	28.2843	−	48.9898i	0.998130	−	1.72881i
$804$			5.65685i			0.199502i
$805$		0			0
$806$	−30.0000	−	6.00000i	−1.05670	−	0.211341i
$807$	11.0000	−	19.0526i	0.387218	−	0.670682i
$808$	−13.4722	+	7.77817i	−0.473950	+	0.273635i
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	0.996125	−	0.0879478i	$-0.0280309\pi$
$809$	12.0000	+	20.7846i	0.421898	+	0.730748i	−0.574228	+	0.818696i	$0.694698\pi$
$810$	3.53553	−	6.12372i	0.124226	−	0.215166i
$811$		−	24.0416i		−	0.844216i	−0.906546	−	0.422108i	$-0.861290\pi$
$811$		−	24.0416i		−	0.844216i	0.906546	−	0.422108i	$-0.138710\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$	−6.92820	−	4.00000i	−0.242833	−	0.140200i
$815$	−11.3137	−	19.5959i	−0.396302	−	0.686415i
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	29.3939	+	16.9706i	1.02836	+	0.593725i
$818$		0			0
$819$		0			0
$820$	−8.00000			−0.279372
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.0273557	−	0.999626i	$-0.508709\pi$
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.879379	+	0.476122i	$0.842042\pi$
$822$	8.48528	+	14.6969i	0.295958	+	0.512615i
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	0.998580	−	0.0532760i	$-0.0169663\pi$
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	−0.545428	+	0.838157i	$0.683633\pi$
$824$	−17.1464	−	9.89949i	−0.597324	−	0.344865i
$825$			16.9706i			0.590839i
$826$		0			0
$827$		−	8.00000i		−	0.278187i	−0.990279	−	0.139094i	$-0.955581\pi$
$827$		−	8.00000i		−	0.278187i	0.990279	−	0.139094i	$-0.0444189\pi$
$828$		0			0
$829$	−10.6066	−	18.3712i	−0.368383	−	0.638057i	0.620930	−	0.783866i	$-0.286755\pi$
$829$	−10.6066	−	18.3712i	−0.368383	−	0.638057i	−0.989313	+	0.145809i	$0.953422\pi$
$830$	1.73205	−	1.00000i	0.0601204	−	0.0347105i
$831$	−9.89949	+	17.1464i	−0.343410	+	0.594803i
$832$	3.53553	+	0.707107i	0.122573	+	0.0245145i
$833$		0			0
$834$			6.00000i			0.207763i
$835$	−10.0000	+	17.3205i	−0.346064	+	0.599401i
$836$	−8.48528	−	14.6969i	−0.293470	−	0.508304i
$837$	−41.5692	+	24.0000i	−1.43684	+	0.829561i
$838$	−20.8207	−	12.0208i	−0.719238	−	0.415252i
$839$		−	31.1127i		−	1.07413i	−0.843541	−	0.537065i	$-0.819533\pi$
$839$		−	31.1127i		−	1.07413i	0.843541	−	0.537065i	$-0.180467\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−3.00000	+	5.19615i	−0.103387	+	0.179071i
$843$	−29.3939	+	16.9706i	−1.01238	+	0.584497i
$844$		0			0
$845$	−11.1614	−	14.6090i	−0.383964	−	0.502565i
$846$	−2.82843			−0.0972433
$847$		0			0
$848$	10.0000			0.343401
$849$	−17.0000	+	29.4449i	−0.583438	+	1.01055i
$850$	7.34847	−	4.24264i	0.252050	−	0.145521i
$851$		0			0
$852$	−9.79796	−	5.65685i	−0.335673	−	0.193801i
$853$		−	1.41421i		−	0.0484218i	−0.999707	−	0.0242109i	$-0.992293\pi$
$853$		−	1.41421i		−	0.0484218i	0.999707	−	0.0242109i	$-0.00770731\pi$
$854$		0			0
$855$	6.00000			0.205196
$856$	−6.92820	−	4.00000i	−0.236801	−	0.136717i
$857$	−18.3848	−	31.8434i	−0.628012	−	1.08775i	−0.987950	−	0.154773i	$-0.950536\pi$
$857$	−18.3848	−	31.8434i	−0.628012	−	1.08775i	0.359938	−	0.932976i	$-0.382798\pi$
$858$	6.53590	+	19.3205i	0.223132	+	0.659591i
$859$	−12.0208	+	20.8207i	−0.410145	+	0.710392i	−0.994905	−	0.100814i	$-0.967855\pi$
$859$	−12.0208	+	20.8207i	−0.410145	+	0.710392i	0.584760	+	0.811206i	$0.301189\pi$
$860$			11.3137i			0.385794i
$861$		0			0
$862$	10.0000			0.340601
$863$	27.7128	+	16.0000i	0.943355	+	0.544646i	0.891010	−	0.453983i	$-0.149997\pi$
$863$	27.7128	+	16.0000i	0.943355	+	0.544646i	0.0523446	+	0.998629i	$0.483331\pi$
$864$	4.89898	−	2.82843i	0.166667	−	0.0962250i
$865$	−15.5885	+	9.00000i	−0.530023	+	0.306009i
$866$	22.0454	+	12.7279i	0.749133	+	0.432512i
$867$	−12.7279			−0.432263
$868$		0			0
$869$		−	8.00000i		−	0.271381i
$870$	2.00000	−	3.46410i	0.0678064	−	0.117444i
$871$	13.6617	−	4.62158i	0.462908	−	0.156596i
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$	−4.89898	−	2.82843i	−0.165805	−	0.0957278i
$874$		0			0
$875$		0			0
$876$		−	20.0000i		−	0.675737i
$877$	−22.5167	−	13.0000i	−0.760334	−	0.438979i	0.0690819	−	0.997611i	$-0.477993\pi$
$877$	−22.5167	−	13.0000i	−0.760334	−	0.438979i	−0.829416	+	0.558632i	$0.811326\pi$
$878$	−19.5959	+	11.3137i	−0.661330	+	0.381819i
$879$	12.1244	−	7.00000i	0.408944	−	0.236104i
$880$	2.82843	−	4.89898i	0.0953463	−	0.165145i
$881$	−33.9411			−1.14351			−0.571753	−	0.820426i	$-0.693736\pi$
$881$	−33.9411			−1.14351			−0.571753	+	0.820426i	$0.693736\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$	6.73205	−	7.66025i	0.226423	−	0.257642i
$885$	7.07107	+	12.2474i	0.237691	+	0.411693i
$886$	20.7846	−	12.0000i	0.698273	−	0.403148i
$887$	−1.41421	+	2.44949i	−0.0474846	+	0.0822458i	−0.888791	−	0.458313i	$-0.848454\pi$
$887$	−1.41421	+	2.44949i	−0.0474846	+	0.0822458i	0.841306	+	0.540559i	$0.181787\pi$
$888$	−2.82843			−0.0949158
$889$		0			0
$890$			12.0000i			0.402241i
$891$	17.3205	+	10.0000i	0.580259	+	0.335013i
$892$	−19.5959	+	11.3137i	−0.656120	+	0.378811i
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$	4.24264	−	7.34847i	0.141895	−	0.245770i
$895$			5.65685i			0.189088i
$896$		0			0
$897$		0			0
$898$	−2.00000	+	3.46410i	−0.0667409	+	0.115599i
$899$	−14.6969	+	8.48528i	−0.490170	+	0.283000i
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	14.1421	−	24.4949i	0.471143	−	0.816043i
$902$		−	22.6274i		−	0.753411i
$903$		0			0
$904$			12.0000i			0.399114i
$905$	−22.5167	−	13.0000i	−0.748479	−	0.432135i
$906$	−15.5563	−	26.9444i	−0.516825	−	0.895167i
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$	−18.3712	−	10.6066i	−0.609669	−	0.351992i
$909$	15.5563			0.515972
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	−5.19615	−	3.00000i	−0.172062	−	0.0993399i
$913$	2.82843	+	4.89898i	0.0936073	+	0.162133i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$	2.44949	+	1.41421i	0.0809776	+	0.0467525i
$916$			26.8701i			0.887812i
$917$		0			0
$918$		−	16.0000i		−	0.528079i
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	−0.625573	−	0.780165i	$-0.715135\pi$
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	0.988430	+	0.151680i	$0.0484682\pi$
$920$		0			0
$921$	29.4449	−	17.0000i	0.970241	−	0.560169i
$922$	16.2635	−	28.1691i	0.535608	−	0.927701i
$923$	−5.65685	+	28.2843i	−0.186198	+	0.930988i
$924$		0			0
$925$			6.00000i			0.197279i
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	9.89949	+	17.1464i	0.325142	+	0.563163i
$928$	1.73205	−	1.00000i	0.0568574	−	0.0328266i
$929$	39.1918	+	22.6274i	1.28584	+	0.742381i	0.977910	−	0.209027i	$-0.0670296\pi$
$929$	39.1918	+	22.6274i	1.28584	+	0.742381i	0.307932	+	0.951408i	$0.400363\pi$
$930$			16.9706i			0.556487i
$931$		0			0
$932$	18.0000			0.589610
$933$	−4.00000	+	6.92820i	−0.130954	+	0.226819i
$934$	−3.67423	+	2.12132i	−0.120225	+	0.0694117i
$935$	−8.00000	−	13.8564i	−0.261628	−	0.453153i
$936$	−2.70831	−	2.38014i	−0.0885238	−	0.0777973i
$937$	11.3137			0.369603			0.184801	−	0.982776i	$-0.440836\pi$
$937$	11.3137			0.369603			0.184801	+	0.982776i	$0.440836\pi$
$938$		0			0
$939$	−28.0000			−0.913745
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$	−15.9217	+	9.19239i	−0.519032	+	0.299663i	−0.736539	−	0.676396i	$-0.763541\pi$
$941$	−15.9217	+	9.19239i	−0.519032	+	0.299663i	0.217506	+	0.976059i	$0.430208\pi$
$942$	1.73205	−	1.00000i	0.0564333	−	0.0325818i
$943$		0			0
$944$			7.07107i			0.230144i
$945$		0			0
$946$	−32.0000			−1.04041
$947$	−31.1769	−	18.0000i	−1.01311	−	0.584921i	−0.101012	−	0.994885i	$-0.532208\pi$
$947$	−31.1769	−	18.0000i	−1.01311	−	0.584921i	−0.912102	+	0.409964i	$0.865541\pi$
$948$	−1.41421	−	2.44949i	−0.0459315	−	0.0795557i
$949$	−48.3013	+	16.3397i	−1.56793	+	0.530411i
$950$	−6.36396	+	11.0227i	−0.206474	+	0.357624i
$951$		−	48.0833i		−	1.55921i
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−8.66025	−	5.00000i	−0.280386	−	0.161881i
$955$	26.9444	−	15.5563i	0.871900	−	0.503392i
$956$	−15.5885	+	9.00000i	−0.504167	+	0.291081i
$957$	9.79796	+	5.65685i	0.316723	+	0.182860i
$958$	14.1421			0.456912
$959$		0			0
$960$		−	2.00000i		−	0.0645497i
$961$	20.5000	−	35.5070i	0.661290	−	1.14539i
$962$	2.31079	+	6.83083i	0.0745028	+	0.220235i
$963$	4.00000	+	6.92820i	0.128898	+	0.223258i
$964$	19.5959	+	11.3137i	0.631142	+	0.364390i
$965$	−36.7696			−1.18365
$966$		0			0
$967$		−	6.00000i		−	0.192947i	−0.995336	−	0.0964735i	$-0.969244\pi$
$967$		−	6.00000i		−	0.192947i	0.995336	−	0.0964735i	$-0.0307563\pi$
$968$	4.33013	+	2.50000i	0.139176	+	0.0803530i
$969$	−14.6969	+	8.48528i	−0.472134	+	0.272587i
$970$	−6.92820	+	4.00000i	−0.222451	+	0.128432i
$971$	21.9203	−	37.9671i	0.703456	−	1.21842i	−0.263790	−	0.964580i	$-0.584972\pi$
$971$	21.9203	−	37.9671i	0.703456	−	1.21842i	0.967246	−	0.253842i	$-0.0816942\pi$
$972$	−9.89949			−0.317526
$973$		0			0
$974$	−18.0000			−0.576757
$975$	10.0981	−	11.4904i	0.323397	−	0.367987i
$976$	0.707107	+	1.22474i	0.0226339	+	0.0392031i
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	−0.324462	−	0.945899i	$-0.605183\pi$
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	0.656941	+	0.753942i	$0.271850\pi$
$978$	11.3137	−	19.5959i	0.361773	−	0.626608i
$979$	−33.9411			−1.08476
$980$		0			0
$981$			10.0000i			0.319275i
$982$	3.46410	+	2.00000i	0.110544	+	0.0638226i
$983$	−41.6413	+	24.0416i	−1.32815	+	0.766809i	−0.985014	−	0.172476i	$-0.944823\pi$
$983$	−41.6413	+	24.0416i	−1.32815	+	0.766809i	−0.343138	+	0.939285i	$0.611490\pi$
$984$	−4.00000	−	6.92820i	−0.127515	−	0.220863i
$985$	−1.41421	+	2.44949i	−0.0450606	+	0.0780472i
$986$		−	5.65685i		−	0.180151i
$987$		0			0
$988$	−3.00000	+	15.0000i	−0.0954427	+	0.477214i
$989$		0			0
$990$	−4.89898	+	2.82843i	−0.155700	+	0.0898933i
$991$	7.00000	+	12.1244i	0.222362	+	0.385143i	0.955525	−	0.294911i	$-0.0952899\pi$
$991$	7.00000	+	12.1244i	0.222362	+	0.385143i	−0.733163	+	0.680053i	$0.761957\pi$
$992$	−4.24264	+	7.34847i	−0.134704	+	0.233314i
$993$			22.6274i			0.718059i
$994$		0			0
$995$		−	12.0000i		−	0.380426i
$996$	1.73205	+	1.00000i	0.0548821	+	0.0316862i
$997$	19.0919	+	33.0681i	0.604646	+	1.04728i	0.992107	+	0.125392i	$0.0400187\pi$
$997$	19.0919	+	33.0681i	0.604646	+	1.04728i	−0.387461	+	0.921886i	$0.626648\pi$
$998$	16.0000	+	27.7128i	0.506471	+	0.877234i
$999$	9.79796	+	5.65685i	0.309994	+	0.178975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.n.j.961.3		8
7.2	even	3		1274.2.d.h.883.2	yes	4
7.3	odd	6	inner	1274.2.n.j.753.2		8
7.4	even	3	inner	1274.2.n.j.753.1		8
7.5	odd	6		1274.2.d.h.883.1	✓	4
7.6	odd	2	inner	1274.2.n.j.961.4		8
13.12	even	2	inner	1274.2.n.j.961.1		8
91.12	odd	6		1274.2.d.h.883.3	yes	4
91.25	even	6	inner	1274.2.n.j.753.3		8
91.38	odd	6	inner	1274.2.n.j.753.4		8
91.51	even	6		1274.2.d.h.883.4	yes	4
91.90	odd	2	inner	1274.2.n.j.961.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1274.2.d.h.883.1	✓	4	7.5	odd	6
1274.2.d.h.883.2	yes	4	7.2	even	3
1274.2.d.h.883.3	yes	4	91.12	odd	6
1274.2.d.h.883.4	yes	4	91.51	even	6
1274.2.n.j.753.1		8	7.4	even	3	inner
1274.2.n.j.753.2		8	7.3	odd	6	inner
1274.2.n.j.753.3		8	91.25	even	6	inner
1274.2.n.j.753.4		8	91.38	odd	6	inner
1274.2.n.j.961.1		8	13.12	even	2	inner
1274.2.n.j.961.2		8	91.90	odd	2	inner
1274.2.n.j.961.3		8	1.1	even	1	trivial
1274.2.n.j.961.4		8	7.6	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 $\F_{q}$
Belyi maps

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} +(-0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} -1.41421i q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.707107 - 1.22474i) q^{10} +(3.46410 - 2.00000i) q^{11} +(0.707107 - 1.22474i) q^{12} +(-3.53553 - 0.707107i) q^{13} +2.00000i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.67423 - 2.12132i) q^{19} -1.41421i q^{20} +4.00000 q^{22} +(1.22474 - 0.707107i) q^{24} +(-1.50000 - 2.59808i) q^{25} +(-2.70831 - 2.38014i) q^{26} -5.65685 q^{27} -2.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(7.34847 - 4.24264i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.89898 - 2.82843i) q^{33} +2.82843i q^{34} +1.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(-2.12132 - 3.67423i) q^{38} +(1.63397 + 4.83013i) q^{39} +(0.707107 - 1.22474i) q^{40} -5.65685i q^{41} -8.00000 q^{43} +(3.46410 + 2.00000i) q^{44} +(-1.22474 + 0.707107i) q^{45} +(-2.44949 - 1.41421i) q^{47} +1.41421 q^{48} -3.00000i q^{50} +(2.00000 - 3.46410i) q^{51} +(-1.15539 - 3.41542i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(-4.89898 - 2.82843i) q^{54} -5.65685 q^{55} +6.00000i q^{57} +(-1.73205 - 1.00000i) q^{58} +(6.12372 - 3.53553i) q^{59} +(-1.73205 + 1.00000i) q^{60} +(0.707107 - 1.22474i) q^{61} +8.48528 q^{62} -1.00000 q^{64} +(3.83013 + 3.36603i) q^{65} +(-2.82843 - 4.89898i) q^{66} +(-3.46410 + 2.00000i) q^{67} +(-1.41421 + 2.44949i) q^{68} -8.00000i q^{71} +(0.866025 + 0.500000i) q^{72} +(12.2474 - 7.07107i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.12132 + 3.67423i) q^{75} -4.24264i q^{76} +(-1.00000 + 5.00000i) q^{78} +(1.00000 - 1.73205i) q^{79} +(1.22474 - 0.707107i) q^{80} +(2.50000 + 4.33013i) q^{81} +(2.82843 - 4.89898i) q^{82} +1.41421i q^{83} -4.00000i q^{85} +(-6.92820 - 4.00000i) q^{86} +(1.41421 + 2.44949i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-7.34847 - 4.24264i) q^{89} -1.41421 q^{90} +(-10.3923 - 6.00000i) q^{93} +(-1.41421 - 2.44949i) q^{94} +(3.00000 + 5.19615i) q^{95} +(1.22474 + 0.707107i) q^{96} -5.65685i q^{97} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{9} - 4 q^{16} + 32 q^{22} - 12 q^{25} - 16 q^{29} - 8 q^{30} + 8 q^{36} + 20 q^{39} - 64 q^{43} + 16 q^{51} - 40 q^{53} - 8 q^{64} - 4 q^{65} - 8 q^{74} - 8 q^{78} + 8 q^{79} + 20 q^{81}+ \cdots + 24 q^{95}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^9 - 4 * q^16 + 32 * q^22 - 12 * q^25 - 16 * q^29 - 8 * q^30 + 8 * q^36 + 20 * q^39 - 64 * q^43 + 16 * q^51 - 40 * q^53 - 8 * q^64 - 4 * q^65 - 8 * q^74 - 8 * q^78 + 8 * q^79 + 20 * q^81 + 16 * q^88 + 24 * q^95

Introduction

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