LMFDB - Embedded newform 1134.2.l.e.269.4

Newspace parameters

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.l (of order $6$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.4
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1134.269
Dual form			1134.2.l.e.215.2

$q$-expansion

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +(-3.67423 + 2.12132i) q^{11} +(-0.621320 + 0.358719i) q^{13} +(2.09077 - 1.62132i) q^{14} +1.00000 q^{16} +(1.22474 - 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} +(-1.22474 + 2.12132i) q^{20} +(-2.12132 - 3.67423i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.358719 - 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} +(1.52192 + 0.878680i) q^{29} +9.08052i q^{31} +1.00000i q^{32} +(2.12132 + 1.22474i) q^{34} +(-6.42090 + 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} +(-2.44949 - 4.24264i) q^{38} +(-2.12132 - 1.22474i) q^{40} +(-1.22474 - 2.12132i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(3.67423 - 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} -12.8418 q^{47} +(-1.74264 + 6.77962i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.621320 - 0.358719i) q^{52} +(-12.5446 - 7.24264i) q^{53} +10.3923i q^{55} +(-2.09077 + 1.62132i) q^{56} +(-0.878680 + 1.52192i) q^{58} +2.44949 q^{59} +4.18154i q^{61} -9.08052 q^{62} -1.00000 q^{64} +1.75736i q^{65} +13.4853 q^{67} +(-1.22474 + 2.12132i) q^{68} +(-0.878680 - 6.42090i) q^{70} -12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} +(4.54026 - 2.62132i) q^{74} +(4.24264 - 2.44949i) q^{76} +(10.3923 + 4.24264i) q^{77} +0.757359 q^{79} +(1.22474 - 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} +(7.64564 - 13.2426i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(-6.06218 - 3.50000i) q^{86} +(2.12132 + 3.67423i) q^{88} +(1.52192 + 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} +(5.19615 + 3.00000i) q^{92} -12.8418i q^{94} +12.0000i q^{95} +(-2.74264 - 1.58346i) q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 + 4 * q^7	$ 8 q - 8 q^{4} + 4 q^{7} + 12 q^{13} + 8 q^{16} - 4 q^{25} - 4 q^{28} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} - 12 q^{52} - 24 q^{58} - 8 q^{64} + 40 q^{67} - 24 q^{70} - 72 q^{73} + 40 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^13 + 8 * q^16 - 4 * q^25 - 4 * q^28 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 - 12 * q^52 - 24 * q^58 - 8 * q^64 + 40 * q^67 - 24 * q^70 - 72 * q^73 + 40 * q^79 - 24 * q^85 + 48 * q^91 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	−0.450708	−	0.892672i	$-0.648828\pi$
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	0.998430	−	0.0560116i	$-0.0178384\pi$
$6$		0			0
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.12132	+	1.22474i	0.670820	+	0.387298i
$11$	−3.67423	+	2.12132i	−1.10782	+	0.639602i	−0.938265	−	0.345918i	$-0.887568\pi$
$11$	−3.67423	+	2.12132i	−1.10782	+	0.639602i	−0.169559	+	0.985520i	$0.554234\pi$
$12$		0			0
$13$	−0.621320	+	0.358719i	−0.172323	+	0.0994909i	−0.583681	−	0.811983i	$-0.698388\pi$
$13$	−0.621320	+	0.358719i	−0.172323	+	0.0994909i	0.411358	+	0.911474i	$0.365055\pi$
$14$	2.09077	−	1.62132i	0.558782	−	0.433316i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.22474	−	2.12132i	0.297044	−	0.514496i	−0.678414	−	0.734680i	$-0.737332\pi$
$17$	1.22474	−	2.12132i	0.297044	−	0.514496i	0.975458	+	0.220184i	$0.0706658\pi$
$18$		0			0
$19$	−4.24264	+	2.44949i	−0.973329	+	0.561951i	−0.900249	−	0.435375i	$-0.856616\pi$
$19$	−4.24264	+	2.44949i	−0.973329	+	0.561951i	−0.0730792	+	0.997326i	$0.523283\pi$
$20$	−1.22474	+	2.12132i	−0.273861	+	0.474342i
$21$		0			0
$22$	−2.12132	−	3.67423i	−0.452267	−	0.783349i
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.151642	−	0.988436i	$-0.548456\pi$
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.931831	+	0.362892i	$0.881789\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.358719	−	0.621320i	−0.0703507	−	0.121851i
$27$		0			0
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	1.52192	+	0.878680i	0.282613	+	0.163167i	0.634606	−	0.772836i	$-0.281162\pi$
$29$	1.52192	+	0.878680i	0.282613	+	0.163167i	−0.351993	+	0.936003i	$0.614496\pi$
$30$		0			0
$31$			9.08052i			1.63091i	0.578821	+	0.815455i	$0.303513\pi$
$31$			9.08052i			1.63091i	−0.578821	+	0.815455i	$0.696487\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	2.12132	+	1.22474i	0.363803	+	0.210042i
$35$	−6.42090	+	0.878680i	−1.08533	+	0.148524i
$36$		0			0
$37$	−2.62132	−	4.54026i	−0.430942	−	0.746414i	0.566012	−	0.824397i	$-0.308485\pi$
$37$	−2.62132	−	4.54026i	−0.430942	−	0.746414i	−0.996955	+	0.0779826i	$0.975152\pi$
$38$	−2.44949	−	4.24264i	−0.397360	−	0.688247i
$39$		0			0
$40$	−2.12132	−	1.22474i	−0.335410	−	0.193649i
$41$	−1.22474	−	2.12132i	−0.191273	−	0.331295i	0.754399	−	0.656416i	$-0.227928\pi$
$41$	−1.22474	−	2.12132i	−0.191273	−	0.331295i	−0.945672	+	0.325121i	$0.894595\pi$
$42$		0			0
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	0.465478	+	0.885059i	$0.345882\pi$
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	−0.999223	+	0.0394140i	$0.987451\pi$
$44$	3.67423	−	2.12132i	0.553912	−	0.319801i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−12.8418			−1.87317			−0.936584	−	0.350443i	$-0.886031\pi$
$47$	−12.8418			−1.87317			−0.936584	+	0.350443i	$0.886031\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$	0.621320	−	0.358719i	0.0861616	−	0.0497454i
$53$	−12.5446	−	7.24264i	−1.72314	−	0.994853i	−0.912231	−	0.409675i	$-0.865642\pi$
$53$	−12.5446	−	7.24264i	−1.72314	−	0.994853i	−0.810905	−	0.585178i	$-0.801025\pi$
$54$		0			0
$55$			10.3923i			1.40130i
$56$	−2.09077	+	1.62132i	−0.279391	+	0.216658i
$57$		0			0
$58$	−0.878680	+	1.52192i	−0.115376	+	0.199838i
$59$	2.44949			0.318896			0.159448	−	0.987206i	$-0.449029\pi$
$59$	2.44949			0.318896			0.159448	+	0.987206i	$0.449029\pi$
$60$		0			0
$61$			4.18154i			0.535391i	0.963504	+	0.267696i	$0.0862622\pi$
$61$			4.18154i			0.535391i	−0.963504	+	0.267696i	$0.913738\pi$
$62$	−9.08052			−1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$			1.75736i			0.217974i
$66$		0			0
$67$	13.4853			1.64749			0.823745	−	0.566961i	$-0.191881\pi$
$67$	13.4853			1.64749			0.823745	+	0.566961i	$0.191881\pi$
$68$	−1.22474	+	2.12132i	−0.148522	+	0.257248i
$69$		0			0
$70$	−0.878680	−	6.42090i	−0.105022	−	0.767444i
$71$		−	12.7279i		−	1.51053i	−0.655422	−	0.755263i	$-0.727509\pi$
$71$		−	12.7279i		−	1.51053i	0.655422	−	0.755263i	$-0.272491\pi$
$72$		0			0
$73$	−4.75736	−	2.74666i	−0.556807	−	0.321473i	0.195056	−	0.980792i	$-0.437511\pi$
$73$	−4.75736	−	2.74666i	−0.556807	−	0.321473i	−0.751863	+	0.659320i	$0.770844\pi$
$74$	4.54026	−	2.62132i	0.527795	−	0.304722i
$75$		0			0
$76$	4.24264	−	2.44949i	0.486664	−	0.280976i
$77$	10.3923	+	4.24264i	1.18431	+	0.483494i
$78$		0			0
$79$	0.757359			0.0852096			0.0426048	−	0.999092i	$-0.486434\pi$
$79$	0.757359			0.0852096			0.0426048	+	0.999092i	$0.486434\pi$
$80$	1.22474	−	2.12132i	0.136931	−	0.237171i
$81$		0			0
$82$	2.12132	−	1.22474i	0.234261	−	0.135250i
$83$	7.64564	−	13.2426i	0.839218	−	1.45357i	−0.0513309	−	0.998682i	$-0.516346\pi$
$83$	7.64564	−	13.2426i	0.839218	−	1.45357i	0.890549	−	0.454887i	$-0.150320\pi$
$84$		0			0
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$	−6.06218	−	3.50000i	−0.653701	−	0.377415i
$87$		0			0
$88$	2.12132	+	3.67423i	0.226134	+	0.391675i
$89$	1.52192	+	2.63604i	0.161323	+	0.279420i	0.935343	−	0.353741i	$-0.115091\pi$
$89$	1.52192	+	2.63604i	0.161323	+	0.279420i	−0.774020	+	0.633161i	$0.781757\pi$
$90$		0			0
$91$	1.75736	+	0.717439i	0.184221	+	0.0752080i
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$		0			0
$94$		−	12.8418i		−	1.32453i
$95$			12.0000i			1.23117i
$96$		0			0
$97$	−2.74264	−	1.58346i	−0.278473	−	0.160776i	0.354259	−	0.935147i	$-0.384733\pi$
$97$	−2.74264	−	1.58346i	−0.278473	−	0.160776i	−0.632732	+	0.774371i	$0.718066\pi$
$98$	−6.77962	−	1.74264i	−0.684845	−	0.176033i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.67423	+	6.36396i	0.365600	+	0.633238i	0.988872	−	0.148767i	$-0.0475305\pi$
$101$	3.67423	+	6.36396i	0.365600	+	0.633238i	−0.623272	+	0.782005i	$0.714197\pi$
$102$		0			0
$103$	−9.62132	−	5.55487i	−0.948017	−	0.547338i	−0.0555525	−	0.998456i	$-0.517692\pi$
$103$	−9.62132	−	5.55487i	−0.948017	−	0.547338i	−0.892464	+	0.451118i	$0.851025\pi$
$104$	0.358719	+	0.621320i	0.0351753	+	0.0609255i
$105$		0			0
$106$	7.24264	−	12.5446i	0.703467	−	1.21844i
$107$	−2.15232	+	1.24264i	−0.208072	+	0.120131i	−0.600415	−	0.799688i	$-0.704998\pi$
$107$	−2.15232	+	1.24264i	−0.208072	+	0.120131i	0.392343	+	0.919819i	$0.371665\pi$
$108$		0			0
$109$	8.86396	−	15.3528i	0.849013	−	1.47053i	−0.0330761	−	0.999453i	$-0.510530\pi$
$109$	8.86396	−	15.3528i	0.849013	−	1.47053i	0.882090	−	0.471082i	$-0.156136\pi$
$110$	−10.3923			−0.990867
$111$		0			0
$112$	−1.62132	−	2.09077i	−0.153200	−	0.197559i
$113$	8.87039	−	5.12132i	0.834456	−	0.481773i	−0.0209200	−	0.999781i	$-0.506660\pi$
$113$	8.87039	−	5.12132i	0.834456	−	0.481773i	0.855376	+	0.518008i	$0.173326\pi$
$114$		0			0
$115$	−12.7279	+	7.34847i	−1.18688	+	0.685248i
$116$	−1.52192	−	0.878680i	−0.141307	−	0.0815834i
$117$		0			0
$118$			2.44949i			0.225494i
$119$	−6.42090	+	0.878680i	−0.588603	+	0.0805484i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−4.18154			−0.378579
$123$		0			0
$124$		−	9.08052i		−	0.815455i
$125$	9.79796			0.876356
$126$		0			0
$127$	−7.72792			−0.685742			−0.342871	−	0.939382i	$-0.611399\pi$
$127$	−7.72792			−0.685742			−0.342871	+	0.939382i	$0.611399\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−1.75736			−0.154131
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	12.0000	+	4.89898i	1.04053	+	0.424795i
$134$			13.4853i			1.16495i
$135$		0			0
$136$	−2.12132	−	1.22474i	−0.181902	−	0.105021i
$137$	5.19615	−	3.00000i	0.443937	−	0.256307i	−0.261329	−	0.965250i	$-0.584161\pi$
$137$	5.19615	−	3.00000i	0.443937	−	0.256307i	0.705266	+	0.708942i	$0.250827\pi$
$138$		0			0
$139$	6.98528	−	4.03295i	0.592484	−	0.342071i	−0.173595	−	0.984817i	$-0.555538\pi$
$139$	6.98528	−	4.03295i	0.592484	−	0.342071i	0.766079	+	0.642746i	$0.222205\pi$
$140$	6.42090	−	0.878680i	0.542665	−	0.0742620i
$141$		0			0
$142$	12.7279			1.06810
$143$	1.52192	−	2.63604i	0.127269	−	0.220437i
$144$		0			0
$145$	3.72792	−	2.15232i	0.309587	−	0.178740i
$146$	2.74666	−	4.75736i	0.227315	−	0.393722i
$147$		0			0
$148$	2.62132	+	4.54026i	0.215471	+	0.373207i
$149$	−14.0665	−	8.12132i	−1.15238	−	0.665324i	−0.202911	−	0.979197i	$-0.565040\pi$
$149$	−14.0665	−	8.12132i	−1.15238	−	0.665324i	−0.949465	+	0.313873i	$0.898373\pi$
$150$		0			0
$151$	−4.37868	−	7.58410i	−0.356332	−	0.617185i	0.631013	−	0.775772i	$-0.282639\pi$
$151$	−4.37868	−	7.58410i	−0.356332	−	0.617185i	−0.987345	+	0.158587i	$0.949306\pi$
$152$	2.44949	+	4.24264i	0.198680	+	0.344124i
$153$		0			0
$154$	−4.24264	+	10.3923i	−0.341882	+	0.837436i
$155$	19.2627	+	11.1213i	1.54722	+	0.893286i
$156$		0			0
$157$			10.3923i			0.829396i	0.909959	+	0.414698i	$0.136113\pi$
$157$			10.3923i			0.829396i	−0.909959	+	0.414698i	$0.863887\pi$
$158$			0.757359i			0.0602523i
$159$		0			0
$160$	2.12132	+	1.22474i	0.167705	+	0.0968246i
$161$	2.15232	+	15.7279i	0.169626	+	1.23953i
$162$		0			0
$163$	4.74264	+	8.21449i	0.371472	+	0.643409i	0.989792	−	0.142518i	$-0.0455197\pi$
$163$	4.74264	+	8.21449i	0.371472	+	0.643409i	−0.618320	+	0.785926i	$0.712186\pi$
$164$	1.22474	+	2.12132i	0.0956365	+	0.165647i
$165$		0			0
$166$	13.2426	+	7.64564i	1.02783	+	0.593417i
$167$	−0.297173	−	0.514719i	−0.0229959	−	0.0398301i	0.854298	−	0.519783i	$-0.173987\pi$
$167$	−0.297173	−	0.514719i	−0.0229959	−	0.0398301i	−0.877294	+	0.479953i	$0.840654\pi$
$168$		0			0
$169$	−6.24264	+	10.8126i	−0.480203	+	0.831736i
$170$	5.19615	−	3.00000i	0.398527	−	0.230089i
$171$		0			0
$172$	3.50000	−	6.06218i	0.266872	−	0.462237i
$173$	−20.7846			−1.58022			−0.790112	−	0.612962i	$-0.789978\pi$
$173$	−20.7846			−1.58022			−0.790112	+	0.612962i	$0.789978\pi$
$174$		0			0
$175$	−1.00000	+	2.44949i	−0.0755929	+	0.185164i
$176$	−3.67423	+	2.12132i	−0.276956	+	0.159901i
$177$		0			0
$178$	−2.63604	+	1.52192i	−0.197579	+	0.114073i
$179$	5.82655	+	3.36396i	0.435497	+	0.251434i	0.701686	−	0.712487i	$-0.252431\pi$
$179$	5.82655	+	3.36396i	0.435497	+	0.251434i	−0.266189	+	0.963921i	$0.585764\pi$
$180$		0			0
$181$		−	9.79796i		−	0.728277i	−0.931345	−	0.364138i	$-0.881364\pi$
$181$		−	9.79796i		−	0.728277i	0.931345	−	0.364138i	$-0.118636\pi$
$182$	−0.717439	+	1.75736i	−0.0531801	+	0.130264i
$183$		0			0
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−12.8418			−0.944148
$186$		0			0
$187$			10.3923i			0.759961i
$188$	12.8418			0.936584
$189$		0			0
$190$	−12.0000			−0.870572
$191$			21.2132i			1.53493i	0.641089	+	0.767467i	$0.278483\pi$
$191$			21.2132i			1.53493i	−0.641089	+	0.767467i	$0.721517\pi$
$192$		0			0
$193$	−1.48528			−0.106913			−0.0534564	−	0.998570i	$-0.517024\pi$
$193$	−1.48528			−0.106913			−0.0534564	+	0.998570i	$0.517024\pi$
$194$	1.58346	−	2.74264i	0.113686	−	0.196910i
$195$		0			0
$196$	1.74264	−	6.77962i	0.124474	−	0.484258i
$197$			16.9706i			1.20910i	0.796566	+	0.604551i	$0.206648\pi$
$197$			16.9706i			1.20910i	−0.796566	+	0.604551i	$0.793352\pi$
$198$		0			0
$199$	−18.1066	−	10.4539i	−1.28354	−	0.741054i	−0.306049	−	0.952016i	$-0.599007\pi$
$199$	−18.1066	−	10.4539i	−1.28354	−	0.741054i	−0.977494	+	0.210962i	$0.932340\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$		0			0
$202$	−6.36396	+	3.67423i	−0.447767	+	0.258518i
$203$	−0.630399	−	4.60660i	−0.0442453	−	0.323320i
$204$		0			0
$205$	−6.00000			−0.419058
$206$	5.55487	−	9.62132i	0.387026	−	0.670349i
$207$		0			0
$208$	−0.621320	+	0.358719i	−0.0430808	+	0.0248727i
$209$	10.3923	−	18.0000i	0.718851	−	1.24509i
$210$		0			0
$211$	−1.74264	−	3.01834i	−0.119968	−	0.207791i	0.799787	−	0.600284i	$-0.204946\pi$
$211$	−1.74264	−	3.01834i	−0.119968	−	0.207791i	−0.919755	+	0.392493i	$0.871613\pi$
$212$	12.5446	+	7.24264i	0.861568	+	0.497427i
$213$		0			0
$214$	−1.24264	−	2.15232i	−0.0849452	−	0.147129i
$215$	8.57321	+	14.8492i	0.584688	+	1.01271i
$216$		0			0
$217$	18.9853	−	14.7224i	1.28880	−	0.999424i
$218$	15.3528	+	8.86396i	1.03982	+	0.600343i
$219$		0			0
$220$		−	10.3923i		−	0.700649i
$221$			1.75736i			0.118213i
$222$		0			0
$223$	9.00000	+	5.19615i	0.602685	+	0.347960i	0.770097	−	0.637927i	$-0.220208\pi$
$223$	9.00000	+	5.19615i	0.602685	+	0.347960i	−0.167412	+	0.985887i	$0.553541\pi$
$224$	2.09077	−	1.62132i	0.139695	−	0.108329i
$225$		0			0
$226$	5.12132	+	8.87039i	0.340665	+	0.590049i
$227$	−12.5446	−	21.7279i	−0.832616	−	1.44213i	−0.895957	−	0.444141i	$-0.853509\pi$
$227$	−12.5446	−	21.7279i	−0.832616	−	1.44213i	0.0633412	−	0.997992i	$-0.479824\pi$
$228$		0			0
$229$	4.86396	+	2.80821i	0.321420	+	0.185572i	0.652025	−	0.758197i	$-0.273920\pi$
$229$	4.86396	+	2.80821i	0.321420	+	0.185572i	−0.330606	+	0.943769i	$0.607253\pi$
$230$	−7.34847	−	12.7279i	−0.484544	−	0.839254i
$231$		0			0
$232$	0.878680	−	1.52192i	0.0576881	−	0.0999188i
$233$	17.7408	−	10.2426i	1.16224	−	0.671018i	0.210398	−	0.977616i	$-0.432524\pi$
$233$	17.7408	−	10.2426i	1.16224	−	0.671018i	0.951839	+	0.306598i	$0.0991908\pi$
$234$		0			0
$235$	−15.7279	+	27.2416i	−1.02598	+	1.77704i
$236$	−2.44949			−0.159448
$237$		0			0
$238$	−0.878680	−	6.42090i	−0.0569563	−	0.416205i
$239$	14.0665	−	8.12132i	0.909889	−	0.525325i	0.0294934	−	0.999565i	$-0.490611\pi$
$239$	14.0665	−	8.12132i	0.909889	−	0.525325i	0.880395	+	0.474240i	$0.157277\pi$
$240$		0			0
$241$	0.985281	−	0.568852i	0.0634676	−	0.0366430i	−0.467930	−	0.883765i	$-0.655000\pi$
$241$	0.985281	−	0.568852i	0.0634676	−	0.0366430i	0.531398	+	0.847122i	$0.321667\pi$
$242$	6.06218	+	3.50000i	0.389692	+	0.224989i
$243$		0			0
$244$		−	4.18154i		−	0.267696i
$245$	12.2474	+	12.0000i	0.782461	+	0.766652i
$246$		0			0
$247$	1.75736	−	3.04384i	0.111818	−	0.193675i
$248$	9.08052			0.576614
$249$		0			0
$250$			9.79796i			0.619677i
$251$	15.2913			0.965177			0.482589	−	0.875847i	$-0.339697\pi$
$251$	15.2913			0.965177			0.482589	+	0.875847i	$0.339697\pi$
$252$		0			0
$253$	25.4558			1.60040
$254$		−	7.72792i		−	0.484893i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.5446	+	21.7279i	−0.782512	+	1.35535i	0.147962	+	0.988993i	$0.452729\pi$
$257$	−12.5446	+	21.7279i	−0.782512	+	1.35535i	−0.930474	+	0.366358i	$0.880605\pi$
$258$		0			0
$259$	−5.24264	+	12.8418i	−0.325762	+	0.797950i
$260$		−	1.75736i		−	0.108987i
$261$		0			0
$262$		0			0
$263$	5.82655	−	3.36396i	0.359281	−	0.207431i	−0.309485	−	0.950904i	$-0.600157\pi$
$263$	5.82655	−	3.36396i	0.359281	−	0.207431i	0.668765	+	0.743474i	$0.266823\pi$
$264$		0			0
$265$	−30.7279	+	17.7408i	−1.88760	+	1.08981i
$266$	−4.89898	+	12.0000i	−0.300376	+	0.735767i
$267$		0			0
$268$	−13.4853			−0.823745
$269$	−4.89898	+	8.48528i	−0.298696	+	0.517357i	−0.975838	−	0.218496i	$-0.929885\pi$
$269$	−4.89898	+	8.48528i	−0.298696	+	0.517357i	0.677142	+	0.735853i	$0.263218\pi$
$270$		0			0
$271$	−16.3492	+	9.43924i	−0.993146	+	0.573393i	−0.906213	−	0.422821i	$-0.861040\pi$
$271$	−16.3492	+	9.43924i	−0.993146	+	0.573393i	−0.0869326	+	0.996214i	$0.527706\pi$
$272$	1.22474	−	2.12132i	0.0742611	−	0.128624i
$273$		0			0
$274$	3.00000	+	5.19615i	0.181237	+	0.313911i
$275$	3.67423	+	2.12132i	0.221565	+	0.127920i
$276$		0			0
$277$	−11.8640	−	20.5490i	−0.712836	−	1.23467i	−0.963788	−	0.266669i	$-0.914077\pi$
$277$	−11.8640	−	20.5490i	−0.712836	−	1.23467i	0.250952	−	0.968000i	$-0.419256\pi$
$278$	4.03295	+	6.98528i	0.241881	+	0.418949i
$279$		0			0
$280$	0.878680	+	6.42090i	0.0525112	+	0.383722i
$281$	11.9142	+	6.87868i	0.710743	+	0.410348i	0.811336	−	0.584580i	$-0.198741\pi$
$281$	11.9142	+	6.87868i	0.710743	+	0.410348i	−0.100593	+	0.994928i	$0.532074\pi$
$282$		0			0
$283$		−	6.03668i		−	0.358844i	−0.983772	−	0.179422i	$-0.942577\pi$
$283$		−	6.03668i		−	0.358844i	0.983772	−	0.179422i	$-0.0574227\pi$
$284$			12.7279i			0.755263i
$285$		0			0
$286$	2.63604	+	1.52192i	0.155872	+	0.0899929i
$287$	−2.44949	+	6.00000i	−0.144589	+	0.354169i
$288$		0			0
$289$	5.50000	+	9.52628i	0.323529	+	0.560369i
$290$	2.15232	+	3.72792i	0.126388	+	0.218911i
$291$		0			0
$292$	4.75736	+	2.74666i	0.278403	+	0.160736i
$293$	−6.42090	−	11.1213i	−0.375113	−	0.649714i	0.615231	−	0.788347i	$-0.289063\pi$
$293$	−6.42090	−	11.1213i	−0.375113	−	0.649714i	−0.990344	+	0.138632i	$0.955729\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$	−4.54026	+	2.62132i	−0.263897	+	0.152361i
$297$		0			0
$298$	8.12132	−	14.0665i	0.470455	−	0.814853i
$299$	4.30463			0.248943
$300$		0			0
$301$	18.3492	−	2.51104i	1.05763	−	0.144734i
$302$	7.58410	−	4.37868i	0.436416	−	0.251965i
$303$		0			0
$304$	−4.24264	+	2.44949i	−0.243332	+	0.140488i
$305$	8.87039	+	5.12132i	0.507917	+	0.293246i
$306$		0			0
$307$			26.8213i			1.53077i	0.643571	+	0.765386i	$0.277452\pi$
$307$			26.8213i			1.53077i	−0.643571	+	0.765386i	$0.722548\pi$
$308$	−10.3923	−	4.24264i	−0.592157	−	0.241747i
$309$		0			0
$310$	−11.1213	+	19.2627i	−0.631649	+	1.09405i
$311$	−17.1464			−0.972285			−0.486142	−	0.873880i	$-0.661596\pi$
$311$	−17.1464			−0.972285			−0.486142	+	0.873880i	$0.661596\pi$
$312$		0			0
$313$		−	20.1903i		−	1.14122i	−0.821221	−	0.570611i	$-0.806707\pi$
$313$		−	20.1903i		−	1.14122i	0.821221	−	0.570611i	$-0.193293\pi$
$314$	−10.3923			−0.586472
$315$		0			0
$316$	−0.757359			−0.0426048
$317$		−	22.2426i		−	1.24927i	−0.780916	−	0.624636i	$-0.785248\pi$
$317$		−	22.2426i		−	1.24927i	0.780916	−	0.624636i	$-0.214752\pi$
$318$		0			0
$319$	−7.45584			−0.417447
$320$	−1.22474	+	2.12132i	−0.0684653	+	0.118585i
$321$		0			0
$322$	−15.7279	+	2.15232i	−0.876483	+	0.119944i
$323$			12.0000i			0.667698i
$324$		0			0
$325$	0.621320	+	0.358719i	0.0344647	+	0.0198982i
$326$	−8.21449	+	4.74264i	−0.454959	+	0.262671i
$327$		0			0
$328$	−2.12132	+	1.22474i	−0.117130	+	0.0676252i
$329$	20.8207	+	26.8492i	1.14788	+	1.48025i
$330$		0			0
$331$	10.0000			0.549650			0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000			0.549650			0.274825	+	0.961494i	$0.411380\pi$
$332$	−7.64564	+	13.2426i	−0.419609	+	0.726784i
$333$		0			0
$334$	0.514719	−	0.297173i	0.0281642	−	0.0162606i
$335$	16.5160	−	28.6066i	0.902367	−	1.56295i
$336$		0			0
$337$	10.7279	+	18.5813i	0.584387	+	1.01219i	0.994952	+	0.100357i	$0.0319984\pi$
$337$	10.7279	+	18.5813i	0.584387	+	1.01219i	−0.410564	+	0.911832i	$0.634668\pi$
$338$	−10.8126	−	6.24264i	−0.588126	−	0.339555i
$339$		0			0
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	−19.2627	−	33.3640i	−1.04313	−	1.80676i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	6.06218	+	3.50000i	0.326851	+	0.188707i
$345$		0			0
$346$		−	20.7846i		−	1.11739i
$347$			4.97056i			0.266834i	0.991060	+	0.133417i	$0.0425949\pi$
$347$			4.97056i			0.266834i	−0.991060	+	0.133417i	$0.957405\pi$
$348$		0			0
$349$	0.106602	+	0.0615465i	0.00570626	+	0.00329451i	0.502850	−	0.864373i	$-0.332285\pi$
$349$	0.106602	+	0.0615465i	0.00570626	+	0.00329451i	−0.497144	+	0.867668i	$0.665618\pi$
$350$	−2.44949	−	1.00000i	−0.130931	−	0.0534522i
$351$		0			0
$352$	−2.12132	−	3.67423i	−0.113067	−	0.195837i
$353$	−5.49333	−	9.51472i	−0.292380	−	0.506417i	0.681992	−	0.731360i	$-0.261114\pi$
$353$	−5.49333	−	9.51472i	−0.292380	−	0.506417i	−0.974372	+	0.224942i	$0.927781\pi$
$354$		0			0
$355$	−27.0000	−	15.5885i	−1.43301	−	0.827349i
$356$	−1.52192	−	2.63604i	−0.0806615	−	0.139710i
$357$		0			0
$358$	−3.36396	+	5.82655i	−0.177791	+	0.307943i
$359$	−12.5446	+	7.24264i	−0.662080	+	0.382252i	−0.793069	−	0.609132i	$-0.791518\pi$
$359$	−12.5446	+	7.24264i	−0.662080	+	0.382252i	0.130989	+	0.991384i	$0.458185\pi$
$360$		0			0
$361$	2.50000	−	4.33013i	0.131579	−	0.227901i
$362$	9.79796			0.514969
$363$		0			0
$364$	−1.75736	−	0.717439i	−0.0921107	−	0.0376040i
$365$	−11.6531	+	6.72792i	−0.609951	+	0.352156i
$366$		0			0
$367$	25.9706	−	14.9941i	1.35565	−	0.782686i	0.366618	−	0.930372i	$-0.380516\pi$
$367$	25.9706	−	14.9941i	1.35565	−	0.782686i	0.989034	+	0.147685i	$0.0471823\pi$
$368$	−5.19615	−	3.00000i	−0.270868	−	0.156386i
$369$		0			0
$370$		−	12.8418i		−	0.667613i
$371$	5.19615	+	37.9706i	0.269771	+	1.97133i
$372$		0			0
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	−0.427051	−	0.904227i	$-0.640448\pi$
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	0.996610	−	0.0822766i	$-0.0262191\pi$
$374$	−10.3923			−0.537373
$375$		0			0
$376$			12.8418i			0.662265i
$377$	−1.26080			−0.0649344
$378$		0			0
$379$	−7.48528			−0.384493			−0.192247	−	0.981347i	$-0.561577\pi$
$379$	−7.48528			−0.384493			−0.192247	+	0.981347i	$0.561577\pi$
$380$		−	12.0000i		−	0.615587i
$381$		0			0
$382$	−21.2132			−1.08536
$383$	−2.74666	+	4.75736i	−0.140348	+	0.243090i	−0.927628	−	0.373506i	$-0.878155\pi$
$383$	−2.74666	+	4.75736i	−0.140348	+	0.243090i	0.787280	+	0.616596i	$0.211489\pi$
$384$		0			0
$385$	21.7279	−	16.8493i	1.10736	−	0.858718i
$386$		−	1.48528i		−	0.0755988i
$387$		0			0
$388$	2.74264	+	1.58346i	0.139236	+	0.0803882i
$389$	−13.4361	+	7.75736i	−0.681239	+	0.393314i	−0.800322	−	0.599571i	$-0.795338\pi$
$389$	−13.4361	+	7.75736i	−0.681239	+	0.393314i	0.119082	+	0.992884i	$0.462005\pi$
$390$		0			0
$391$	−12.7279	+	7.34847i	−0.643679	+	0.371628i
$392$	6.77962	+	1.74264i	0.342422	+	0.0880166i
$393$		0			0
$394$	−16.9706			−0.854965
$395$	0.927572	−	1.60660i	0.0466712	−	0.0808369i
$396$		0			0
$397$	−13.1360	+	7.58410i	−0.659279	+	0.380635i	−0.792002	−	0.610518i	$-0.790961\pi$
$397$	−13.1360	+	7.58410i	−0.659279	+	0.380635i	0.132723	+	0.991153i	$0.457628\pi$
$398$	10.4539	−	18.1066i	0.524004	−	0.907602i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	17.1104	+	9.87868i	0.854451	+	0.493318i	0.862150	−	0.506653i	$-0.169117\pi$
$401$	17.1104	+	9.87868i	0.854451	+	0.493318i	−0.00769892	+	0.999970i	$0.502451\pi$
$402$		0			0
$403$	−3.25736	−	5.64191i	−0.162261	−	0.281044i
$404$	−3.67423	−	6.36396i	−0.182800	−	0.316619i
$405$		0			0
$406$	4.60660	−	0.630399i	0.228622	−	0.0312862i
$407$	19.2627	+	11.1213i	0.954816	+	0.551263i
$408$		0			0
$409$			3.76127i			0.185983i	0.995667	+	0.0929915i	$0.0296430\pi$
$409$			3.76127i			0.185983i	−0.995667	+	0.0929915i	$0.970357\pi$
$410$		−	6.00000i		−	0.296319i
$411$		0			0
$412$	9.62132	+	5.55487i	0.474008	+	0.273669i
$413$	−3.97141	−	5.12132i	−0.195420	−	0.252004i
$414$		0			0
$415$	−18.7279	−	32.4377i	−0.919318	−	1.59230i
$416$	−0.358719	−	0.621320i	−0.0175877	−	0.0304627i
$417$		0			0
$418$	18.0000	+	10.3923i	0.880409	+	0.508304i
$419$	−3.97141	−	6.87868i	−0.194016	−	0.336045i	0.752562	−	0.658522i	$-0.228818\pi$
$419$	−3.97141	−	6.87868i	−0.194016	−	0.336045i	−0.946577	+	0.322476i	$0.895485\pi$
$420$		0			0
$421$	11.7279	−	20.3134i	0.571584	−	0.990012i	−0.424820	−	0.905278i	$-0.639662\pi$
$421$	11.7279	−	20.3134i	0.571584	−	0.990012i	0.996404	−	0.0847344i	$-0.0270042\pi$
$422$	3.01834	−	1.74264i	0.146931	−	0.0848304i
$423$		0			0
$424$	−7.24264	+	12.5446i	−0.351734	+	0.609221i
$425$	−2.44949			−0.118818
$426$		0			0
$427$	8.74264	−	6.77962i	0.423086	−	0.328089i
$428$	2.15232	−	1.24264i	0.104036	−	0.0600653i
$429$		0			0
$430$	−14.8492	+	8.57321i	−0.716094	+	0.413437i
$431$	1.52192	+	0.878680i	0.0733082	+	0.0423245i	0.536206	−	0.844087i	$-0.319857\pi$
$431$	1.52192	+	0.878680i	0.0733082	+	0.0423245i	−0.462898	+	0.886412i	$0.653190\pi$
$432$		0			0
$433$			2.57258i			0.123630i	0.998088	+	0.0618152i	$0.0196889\pi$
$433$			2.57258i			0.123630i	−0.998088	+	0.0618152i	$0.980311\pi$
$434$	14.7224	+	18.9853i	0.706699	+	0.911323i
$435$		0			0
$436$	−8.86396	+	15.3528i	−0.424507	+	0.735267i
$437$	29.3939			1.40610
$438$		0			0
$439$			4.30463i			0.205449i	0.994710	+	0.102724i	$0.0327560\pi$
$439$			4.30463i			0.205449i	−0.994710	+	0.102724i	$0.967244\pi$
$440$	10.3923			0.495434
$441$		0			0
$442$	−1.75736			−0.0835891
$443$		−	25.4558i		−	1.20944i	−0.796437	−	0.604722i	$-0.793284\pi$
$443$		−	25.4558i		−	1.20944i	0.796437	−	0.604722i	$-0.206716\pi$
$444$		0			0
$445$	7.45584			0.353441
$446$	−5.19615	+	9.00000i	−0.246045	+	0.426162i
$447$		0			0
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$			5.27208i			0.248805i	0.992232	+	0.124402i	$0.0397014\pi$
$449$			5.27208i			0.248805i	−0.992232	+	0.124402i	$0.960299\pi$
$450$		0			0
$451$	9.00000	+	5.19615i	0.423793	+	0.244677i
$452$	−8.87039	+	5.12132i	−0.417228	+	0.240887i
$453$		0			0
$454$	21.7279	−	12.5446i	1.01974	−	0.588748i
$455$	3.67423	−	2.84924i	0.172251	−	0.133575i
$456$		0			0
$457$	−23.0000			−1.07589			−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000			−1.07589			−0.537947	+	0.842978i	$0.680800\pi$
$458$	−2.80821	+	4.86396i	−0.131219	+	0.227278i
$459$		0			0
$460$	12.7279	−	7.34847i	0.593442	−	0.342624i
$461$	−10.7255	+	18.5772i	−0.499538	+	0.865225i	−1.00000		0.000533648i	$-0.999830\pi$
$461$	−10.7255	+	18.5772i	−0.499538	+	0.865225i	0.500462	+	0.865758i	$0.333163\pi$
$462$		0			0
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	0.999916	+	0.0129968i	$0.00413714\pi$
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	−0.488702	+	0.872451i	$0.662530\pi$
$464$	1.52192	+	0.878680i	0.0706533	+	0.0407917i
$465$		0			0
$466$	10.2426	+	17.7408i	0.474481	+	0.821825i
$467$	−8.87039	−	15.3640i	−0.410473	−	0.710959i	0.584469	−	0.811416i	$-0.301303\pi$
$467$	−8.87039	−	15.3640i	−0.410473	−	0.710959i	−0.994941	+	0.100457i	$0.967970\pi$
$468$		0			0
$469$	−21.8640	−	28.1946i	−1.00958	−	1.30191i
$470$	−27.2416	−	15.7279i	−1.25656	−	0.725475i
$471$		0			0
$472$		−	2.44949i		−	0.112747i
$473$		−	29.6985i		−	1.36554i
$474$		0			0
$475$	4.24264	+	2.44949i	0.194666	+	0.112390i
$476$	6.42090	−	0.878680i	0.294301	−	0.0402742i
$477$		0			0
$478$	8.12132	+	14.0665i	0.371461	+	0.643389i
$479$	−1.22474	−	2.12132i	−0.0559600	−	0.0969256i	0.836688	−	0.547679i	$-0.184489\pi$
$479$	−1.22474	−	2.12132i	−0.0559600	−	0.0969256i	−0.892648	+	0.450754i	$0.851155\pi$
$480$		0			0
$481$	3.25736	+	1.88064i	0.148523	+	0.0857497i
$482$	0.568852	+	0.985281i	0.0259105	+	0.0448783i
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	−6.71807	+	3.87868i	−0.305052	+	0.176122i
$486$		0			0
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	−0.999998	−	0.00178012i	$-0.999433\pi$
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	0.501541	+	0.865134i	$0.332767\pi$
$488$	4.18154			0.189289
$489$		0			0
$490$	−12.0000	+	12.2474i	−0.542105	+	0.553283i
$491$	30.2854	−	17.4853i	1.36676	−	0.789100i	0.376248	−	0.926519i	$-0.377214\pi$
$491$	30.2854	−	17.4853i	1.36676	−	0.789100i	0.990513	+	0.137419i	$0.0438808\pi$
$492$		0			0
$493$	3.72792	−	2.15232i	0.167897	−	0.0969355i
$494$	3.04384	+	1.75736i	0.136949	+	0.0790673i
$495$		0			0
$496$			9.08052i			0.407727i
$497$	−26.6112	+	20.6360i	−1.19367	+	0.925653i
$498$		0			0
$499$	12.2279	−	21.1794i	0.547397	−	0.948119i	−0.451055	−	0.892496i	$-0.648952\pi$
$499$	12.2279	−	21.1794i	0.547397	−	0.948119i	0.998452	−	0.0556231i	$-0.0177145\pi$
$500$	−9.79796			−0.438178
$501$		0			0
$502$			15.2913i			0.682483i
$503$	−0.594346			−0.0265006			−0.0132503	−	0.999912i	$-0.504218\pi$
$503$	−0.594346			−0.0265006			−0.0132503	+	0.999912i	$0.504218\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$			25.4558i			1.13165i
$507$		0			0
$508$	7.72792			0.342871
$509$	4.60181	−	7.97056i	0.203971	−	0.353289i	−0.745833	−	0.666133i	$-0.767948\pi$
$509$	4.60181	−	7.97056i	0.203971	−	0.353289i	0.949805	+	0.312844i	$0.101282\pi$
$510$		0			0
$511$	1.97056	+	14.3998i	0.0871726	+	0.637008i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−21.7279	−	12.5446i	−0.958378	−	0.553320i
$515$	−23.5673	+	13.6066i	−1.03850	+	0.599579i
$516$		0			0
$517$	47.1838	−	27.2416i	2.07514	−	1.19808i
$518$	−12.8418	−	5.24264i	−0.564236	−	0.230348i
$519$		0			0
$520$	1.75736			0.0770653
$521$	14.9941	−	25.9706i	0.656904	−	1.13779i	−0.324509	−	0.945883i	$-0.605199\pi$
$521$	14.9941	−	25.9706i	0.656904	−	1.13779i	0.981413	−	0.191908i	$-0.0614676\pi$
$522$		0			0
$523$	23.7426	−	13.7078i	1.03819	−	0.599401i	0.118872	−	0.992910i	$-0.462072\pi$
$523$	23.7426	−	13.7078i	1.03819	−	0.599401i	0.919321	+	0.393508i	$0.128739\pi$
$524$		0			0
$525$		0			0
$526$	3.36396	+	5.82655i	0.146676	+	0.254050i
$527$	19.2627	+	11.1213i	0.839096	+	0.484452i
$528$		0			0
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$	−17.7408	−	30.7279i	−0.770610	−	1.33474i
$531$		0			0
$532$	−12.0000	−	4.89898i	−0.520266	−	0.212398i
$533$	1.52192	+	0.878680i	0.0659216	+	0.0380598i
$534$		0			0
$535$			6.08767i			0.263193i
$536$		−	13.4853i		−	0.582475i
$537$		0			0
$538$	−8.48528	−	4.89898i	−0.365826	−	0.211210i
$539$	−7.97887	−	28.6066i	−0.343674	−	1.23217i
$540$		0			0
$541$	2.72792	+	4.72490i	0.117283	+	0.203139i	0.918690	−	0.394980i	$-0.129248\pi$
$541$	2.72792	+	4.72490i	0.117283	+	0.203139i	−0.801407	+	0.598119i	$0.795915\pi$
$542$	−9.43924	−	16.3492i	−0.405450	−	0.702260i
$543$		0			0
$544$	2.12132	+	1.22474i	0.0909509	+	0.0525105i
$545$	−21.7122	−	37.6066i	−0.930048	−	1.61089i
$546$		0			0
$547$	−19.9853	+	34.6155i	−0.854509	+	1.48005i	0.0225909	+	0.999745i	$0.492808\pi$
$547$	−19.9853	+	34.6155i	−0.854509	+	1.48005i	−0.877100	+	0.480308i	$0.840525\pi$
$548$	−5.19615	+	3.00000i	−0.221969	+	0.128154i
$549$		0			0
$550$	−2.12132	+	3.67423i	−0.0904534	+	0.156670i
$551$	−8.60927			−0.366767
$552$		0			0
$553$	−1.22792	−	1.58346i	−0.0522166	−	0.0673358i
$554$	20.5490	−	11.8640i	0.873043	−	0.504051i
$555$		0			0
$556$	−6.98528	+	4.03295i	−0.296242	+	0.171035i
$557$	−18.3712	−	10.6066i	−0.778412	−	0.449416i	0.0574555	−	0.998348i	$-0.481701\pi$
$557$	−18.3712	−	10.6066i	−0.778412	−	0.449416i	−0.835867	+	0.548932i	$0.815035\pi$
$558$		0			0
$559$		−	5.02207i		−	0.212411i
$560$	−6.42090	+	0.878680i	−0.271332	+	0.0371310i
$561$		0			0
$562$	−6.87868	+	11.9142i	−0.290160	+	0.502571i
$563$	−45.8739			−1.93335			−0.966676	−	0.256002i	$-0.917595\pi$
$563$	−45.8739			−1.93335			−0.966676	+	0.256002i	$0.917595\pi$
$564$		0			0
$565$		−	25.0892i		−	1.05551i
$566$	6.03668			0.253741
$567$		0			0
$568$	−12.7279			−0.534052
$569$		−	10.2426i		−	0.429394i	−0.976681	−	0.214697i	$-0.931124\pi$
$569$		−	10.2426i		−	0.429394i	0.976681	−	0.214697i	$-0.0688764\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	−1.52192	+	2.63604i	−0.0636346	+	0.110218i
$573$		0			0
$574$	−6.00000	−	2.44949i	−0.250435	−	0.102240i
$575$			6.00000i			0.250217i
$576$		0			0
$577$	23.7426	+	13.7078i	0.988419	+	0.570664i	0.904801	−	0.425834i	$-0.140019\pi$
$577$	23.7426	+	13.7078i	0.988419	+	0.570664i	0.0836177	+	0.996498i	$0.473353\pi$
$578$	−9.52628	+	5.50000i	−0.396241	+	0.228770i
$579$		0			0
$580$	−3.72792	+	2.15232i	−0.154794	+	0.0893701i
$581$	−40.0834	+	5.48528i	−1.66294	+	0.227568i
$582$		0			0
$583$	61.4558			2.54524
$584$	−2.74666	+	4.75736i	−0.113658	+	0.196861i
$585$		0			0
$586$	11.1213	−	6.42090i	0.459418	−	0.265245i
$587$	−16.2189	+	28.0919i	−0.669424	+	1.15948i	0.308642	+	0.951178i	$0.400126\pi$
$587$	−16.2189	+	28.0919i	−0.669424	+	1.15948i	−0.978065	+	0.208298i	$0.933208\pi$
$588$		0			0
$589$	−22.2426	−	38.5254i	−0.916492	−	1.58741i
$590$	5.19615	+	3.00000i	0.213922	+	0.123508i
$591$		0			0
$592$	−2.62132	−	4.54026i	−0.107736	−	0.186604i
$593$	0.927572	+	1.60660i	0.0380908	+	0.0659752i	0.884442	−	0.466650i	$-0.154539\pi$
$593$	0.927572	+	1.60660i	0.0380908	+	0.0659752i	−0.846352	+	0.532625i	$0.821206\pi$
$594$		0			0
$595$	−6.00000	+	14.6969i	−0.245976	+	0.602516i
$596$	14.0665	+	8.12132i	0.576188	+	0.332662i
$597$		0			0
$598$			4.30463i			0.176030i
$599$		−	3.51472i		−	0.143608i	−0.997419	−	0.0718038i	$-0.977124\pi$
$599$		−	3.51472i		−	0.143608i	0.997419	−	0.0718038i	$-0.0228755\pi$
$600$		0			0
$601$	−35.9558	−	20.7591i	−1.46667	−	0.846782i	−0.467365	−	0.884065i	$-0.654796\pi$
$601$	−35.9558	−	20.7591i	−1.46667	−	0.846782i	−0.999305	+	0.0372826i	$0.988130\pi$
$602$	2.51104	+	18.3492i	0.102342	+	0.747859i
$603$		0			0
$604$	4.37868	+	7.58410i	0.178166	+	0.308592i
$605$	−8.57321	−	14.8492i	−0.348551	−	0.603708i
$606$		0			0
$607$	−31.2426	−	18.0379i	−1.26810	−	0.732138i	−0.293471	−	0.955968i	$-0.594811\pi$
$607$	−31.2426	−	18.0379i	−1.26810	−	0.732138i	−0.974628	+	0.223830i	$0.928144\pi$
$608$	−2.44949	−	4.24264i	−0.0993399	−	0.172062i
$609$		0			0
$610$	−5.12132	+	8.87039i	−0.207356	+	0.359151i
$611$	7.97887	−	4.60660i	0.322790	−	0.186363i
$612$		0			0
$613$	14.1066	−	24.4334i	0.569760	−	0.986854i	−0.426829	−	0.904332i	$-0.640369\pi$
$613$	14.1066	−	24.4334i	0.569760	−	0.986854i	0.996589	−	0.0825214i	$-0.0262973\pi$
$614$	−26.8213			−1.08242
$615$		0			0
$616$	4.24264	−	10.3923i	0.170941	−	0.418718i
$617$	3.67423	−	2.12132i	0.147919	−	0.0854011i	−0.424214	−	0.905562i	$-0.639449\pi$
$617$	3.67423	−	2.12132i	0.147919	−	0.0854011i	0.572133	+	0.820161i	$0.306116\pi$
$618$		0			0
$619$	11.0147	−	6.35935i	0.442719	−	0.255604i	−0.262031	−	0.965059i	$-0.584392\pi$
$619$	11.0147	−	6.35935i	0.442719	−	0.255604i	0.704750	+	0.709455i	$0.251059\pi$
$620$	−19.2627	−	11.1213i	−0.773608	−	0.446643i
$621$		0			0
$622$		−	17.1464i		−	0.687509i
$623$	3.04384	−	7.45584i	0.121949	−	0.298712i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	20.1903			0.806965
$627$		0			0
$628$		−	10.3923i		−	0.414698i
$629$	−12.8418			−0.512036
$630$		0			0
$631$	−14.7574			−0.587481			−0.293741	−	0.955885i	$-0.594900\pi$
$631$	−14.7574			−0.587481			−0.293741	+	0.955885i	$0.594900\pi$
$632$		−	0.757359i		−	0.0301261i
$633$		0			0
$634$	22.2426			0.883368
$635$	−9.46473	+	16.3934i	−0.375596	+	0.650552i
$636$		0			0
$637$	−1.34924	−	4.83743i	−0.0534589	−	0.191666i
$638$		−	7.45584i		−	0.295180i
$639$		0			0
$640$	−2.12132	−	1.22474i	−0.0838525	−	0.0484123i
$641$	−28.7635	+	16.6066i	−1.13609	+	0.655921i	−0.945459	−	0.325741i	$-0.894386\pi$
$641$	−28.7635	+	16.6066i	−1.13609	+	0.655921i	−0.190630	+	0.981662i	$0.561053\pi$
$642$		0			0
$643$	−1.50000	+	0.866025i	−0.0591542	+	0.0341527i	−0.529285	−	0.848444i	$-0.677540\pi$
$643$	−1.50000	+	0.866025i	−0.0591542	+	0.0341527i	0.470131	+	0.882597i	$0.344207\pi$
$644$	−2.15232	−	15.7279i	−0.0848132	−	0.619767i
$645$		0			0
$646$	−12.0000			−0.472134
$647$	−10.3923	+	18.0000i	−0.408564	+	0.707653i	−0.994729	−	0.102538i	$-0.967304\pi$
$647$	−10.3923	+	18.0000i	−0.408564	+	0.707653i	0.586165	+	0.810191i	$0.300637\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$	−0.358719	+	0.621320i	−0.0140701	+	0.0243702i
$651$		0			0
$652$	−4.74264	−	8.21449i	−0.185736	−	0.321704i
$653$	2.15232	+	1.24264i	0.0842267	+	0.0486283i	0.541522	−	0.840687i	$-0.317848\pi$
$653$	2.15232	+	1.24264i	0.0842267	+	0.0486283i	−0.457295	+	0.889315i	$0.651182\pi$
$654$		0			0
$655$		0			0
$656$	−1.22474	−	2.12132i	−0.0478183	−	0.0828236i
$657$		0			0
$658$	−26.8492	+	20.8207i	−1.04669	+	0.811674i
$659$	−19.2627	−	11.1213i	−0.750368	−	0.433225i	0.0754589	−	0.997149i	$-0.475958\pi$
$659$	−19.2627	−	11.1213i	−0.750368	−	0.433225i	−0.825827	+	0.563924i	$0.809291\pi$
$660$		0			0
$661$			4.89898i			0.190548i	0.995451	+	0.0952741i	$0.0303728\pi$
$661$			4.89898i			0.190548i	−0.995451	+	0.0952741i	$0.969627\pi$
$662$			10.0000i			0.388661i
$663$		0			0
$664$	−13.2426	−	7.64564i	−0.513914	−	0.296708i
$665$	25.0892	−	19.4558i	0.972919	−	0.754465i
$666$		0			0
$667$	−5.27208	−	9.13151i	−0.204136	−	0.353573i
$668$	0.297173	+	0.514719i	0.0114980	+	0.0199151i
$669$		0			0
$670$	28.6066	+	16.5160i	1.10517	+	0.638070i
$671$	−8.87039	−	15.3640i	−0.342437	−	0.593119i
$672$		0			0
$673$	22.7279	−	39.3659i	0.876097	−	1.51744i	0.0205075	−	0.999790i	$-0.493472\pi$
$673$	22.7279	−	39.3659i	0.876097	−	1.51744i	0.855590	−	0.517655i	$-0.173195\pi$
$674$	−18.5813	+	10.7279i	−0.715725	+	0.413224i
$675$		0			0
$676$	6.24264	−	10.8126i	0.240102	−	0.415868i
$677$	−14.6969			−0.564849			−0.282425	−	0.959289i	$-0.591139\pi$
$677$	−14.6969			−0.564849			−0.282425	+	0.959289i	$0.591139\pi$
$678$		0			0
$679$	1.13604	+	8.30153i	0.0435972	+	0.318584i
$680$	−5.19615	+	3.00000i	−0.199263	+	0.115045i
$681$		0			0
$682$	33.3640	−	19.2627i	1.27757	−	0.737607i
$683$	8.87039	+	5.12132i	0.339416	+	0.195962i	0.660014	−	0.751254i	$-0.270550\pi$
$683$	8.87039	+	5.12132i	0.339416	+	0.195962i	−0.320598	+	0.947215i	$0.603884\pi$
$684$		0			0
$685$		−	14.6969i		−	0.561541i
$686$	7.34847	+	17.0000i	0.280566	+	0.649063i
$687$		0			0
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	10.3923			0.395915
$690$		0			0
$691$			2.57258i			0.0978657i	0.998802	+	0.0489328i	$0.0155820\pi$
$691$			2.57258i			0.0978657i	−0.998802	+	0.0489328i	$0.984418\pi$
$692$	20.7846			0.790112
$693$		0			0
$694$	−4.97056			−0.188680
$695$		−	19.7574i		−	0.749439i
$696$		0			0
$697$	−6.00000			−0.227266
$698$	−0.0615465	+	0.106602i	−0.00232957	+	0.00403493i
$699$		0			0
$700$	1.00000	−	2.44949i	0.0377964	−	0.0925820i
$701$			20.4853i			0.773718i	0.922139	+	0.386859i	$0.126440\pi$
$701$			20.4853i			0.773718i	−0.922139	+	0.386859i	$0.873560\pi$
$702$		0			0
$703$	22.2426	+	12.8418i	0.838897	+	0.484337i
$704$	3.67423	−	2.12132i	0.138478	−	0.0799503i
$705$		0			0
$706$	9.51472	−	5.49333i	0.358091	−	0.206744i
$707$	7.34847	−	18.0000i	0.276368	−	0.676960i
$708$		0			0
$709$	16.2132			0.608900			0.304450	−	0.952528i	$-0.401527\pi$
$709$	16.2132			0.608900			0.304450	+	0.952528i	$0.401527\pi$
$710$	15.5885	−	27.0000i	0.585024	−	1.01329i
$711$		0			0
$712$	2.63604	−	1.52192i	0.0987897	−	0.0570363i
$713$	27.2416	−	47.1838i	1.02020	−	1.76705i
$714$		0			0
$715$	−3.72792	−	6.45695i	−0.139416	−	0.241476i
$716$	−5.82655	−	3.36396i	−0.217748	−	0.125717i
$717$		0			0
$718$	−7.24264	−	12.5446i	−0.270293	−	0.468161i
$719$	−26.3140	−	45.5772i	−0.981346	−	1.69974i	−0.657166	−	0.753746i	$-0.728245\pi$
$719$	−26.3140	−	45.5772i	−0.981346	−	1.69974i	−0.324181	−	0.945995i	$-0.605089\pi$
$720$		0			0
$721$	3.98528	+	29.1222i	0.148420	+	1.08457i
$722$	4.33013	+	2.50000i	0.161151	+	0.0930404i
$723$		0			0
$724$			9.79796i			0.364138i
$725$		−	1.75736i		−	0.0652667i
$726$		0			0
$727$	24.3198	+	14.0410i	0.901972	+	0.520754i	0.877839	−	0.478955i	$-0.158984\pi$
$727$	24.3198	+	14.0410i	0.901972	+	0.520754i	0.0241323	+	0.999709i	$0.492318\pi$
$728$	0.717439	−	1.75736i	0.0265901	−	0.0651321i
$729$		0			0
$730$	−6.72792	−	11.6531i	−0.249012	−	0.431301i
$731$	8.57321	+	14.8492i	0.317092	+	0.549219i
$732$		0			0
$733$	−1.13604	−	0.655892i	−0.0419606	−	0.0242259i	0.478873	−	0.877884i	$-0.341045\pi$
$733$	−1.13604	−	0.655892i	−0.0419606	−	0.0242259i	−0.520834	+	0.853658i	$0.674379\pi$
$734$	14.9941	+	25.9706i	0.553443	+	0.958591i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−49.5481	+	28.6066i	−1.82513	+	1.05374i
$738$		0			0
$739$	4.22792	−	7.32298i	0.155527	−	0.269380i	−0.777724	−	0.628606i	$-0.783626\pi$
$739$	4.22792	−	7.32298i	0.155527	−	0.269380i	0.933251	+	0.359226i	$0.116959\pi$
$740$	12.8418			0.472074
$741$		0			0
$742$	−37.9706	+	5.19615i	−1.39394	+	0.190757i
$743$	16.2189	−	9.36396i	0.595012	−	0.343530i	−0.172065	−	0.985086i	$-0.555044\pi$
$743$	16.2189	−	9.36396i	0.595012	−	0.343530i	0.767077	+	0.641555i	$0.221710\pi$
$744$		0			0
$745$	−34.4558	+	19.8931i	−1.26236	+	0.728826i
$746$	19.0526	+	11.0000i	0.697564	+	0.402739i
$747$		0			0
$748$		−	10.3923i		−	0.379980i
$749$	6.08767	+	2.48528i	0.222439	+	0.0908102i
$750$		0			0
$751$	−26.7279	+	46.2941i	−0.975316	+	1.68930i	−0.296427	+	0.955056i	$0.595795\pi$
$751$	−26.7279	+	46.2941i	−0.975316	+	1.68930i	−0.678889	+	0.734241i	$0.737538\pi$
$752$	−12.8418			−0.468292
$753$		0			0
$754$		−	1.26080i		−	0.0459156i
$755$	−21.4511			−0.780684
$756$		0			0
$757$	32.7574			1.19059			0.595293	−	0.803509i	$-0.297036\pi$
$757$	32.7574			1.19059			0.595293	+	0.803509i	$0.297036\pi$
$758$		−	7.48528i		−	0.271878i
$759$		0			0
$760$	12.0000			0.435286
$761$	−12.2474	+	21.2132i	−0.443970	+	0.768978i	−0.997980	−	0.0635319i	$-0.979764\pi$
$761$	−12.2474	+	21.2132i	−0.443970	+	0.768978i	0.554010	+	0.832510i	$0.313097\pi$
$762$		0			0
$763$	−46.4706	+	6.35935i	−1.68235	+	0.230224i
$764$		−	21.2132i		−	0.767467i
$765$		0			0
$766$	−4.75736	−	2.74666i	−0.171890	−	0.0992410i
$767$	−1.52192	+	0.878680i	−0.0549533	+	0.0317273i
$768$		0			0
$769$	−34.9706	+	20.1903i	−1.26107	+	0.728080i	−0.973282	−	0.229614i	$-0.926254\pi$
$769$	−34.9706	+	20.1903i	−1.26107	+	0.728080i	−0.287789	+	0.957694i	$0.592920\pi$
$770$	16.8493	+	21.7279i	0.607205	+	0.783020i
$771$		0			0
$772$	1.48528			0.0534564
$773$	4.89898	−	8.48528i	0.176204	−	0.305194i	−0.764373	−	0.644774i	$-0.776951\pi$
$773$	4.89898	−	8.48528i	0.176204	−	0.305194i	0.940577	+	0.339580i	$0.110285\pi$
$774$		0			0
$775$	7.86396	−	4.54026i	0.282482	−	0.163091i
$776$	−1.58346	+	2.74264i	−0.0568431	+	0.0984551i
$777$		0			0
$778$	−7.75736	−	13.4361i	−0.278115	−	0.481709i
$779$	10.3923	+	6.00000i	0.372343	+	0.214972i
$780$		0			0
$781$	27.0000	+	46.7654i	0.966136	+	1.67340i
$782$	−7.34847	−	12.7279i	−0.262781	−	0.455150i
$783$		0			0
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$	22.0454	+	12.7279i	0.786834	+	0.454279i
$786$		0			0
$787$			28.2562i			1.00722i	0.863930	+	0.503612i	$0.167996\pi$
$787$			28.2562i			1.00722i	−0.863930	+	0.503612i	$0.832004\pi$
$788$		−	16.9706i

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +(-3.67423 + 2.12132i) q^{11} +(-0.621320 + 0.358719i) q^{13} +(2.09077 - 1.62132i) q^{14} +1.00000 q^{16} +(1.22474 - 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} +(-1.22474 + 2.12132i) q^{20} +(-2.12132 - 3.67423i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.358719 - 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} +(1.52192 + 0.878680i) q^{29} +9.08052i q^{31} +1.00000i q^{32} +(2.12132 + 1.22474i) q^{34} +(-6.42090 + 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} +(-2.44949 - 4.24264i) q^{38} +(-2.12132 - 1.22474i) q^{40} +(-1.22474 - 2.12132i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(3.67423 - 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} -12.8418 q^{47} +(-1.74264 + 6.77962i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.621320 - 0.358719i) q^{52} +(-12.5446 - 7.24264i) q^{53} +10.3923i q^{55} +(-2.09077 + 1.62132i) q^{56} +(-0.878680 + 1.52192i) q^{58} +2.44949 q^{59} +4.18154i q^{61} -9.08052 q^{62} -1.00000 q^{64} +1.75736i q^{65} +13.4853 q^{67} +(-1.22474 + 2.12132i) q^{68} +(-0.878680 - 6.42090i) q^{70} -12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} +(4.54026 - 2.62132i) q^{74} +(4.24264 - 2.44949i) q^{76} +(10.3923 + 4.24264i) q^{77} +0.757359 q^{79} +(1.22474 - 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} +(7.64564 - 13.2426i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(-6.06218 - 3.50000i) q^{86} +(2.12132 + 3.67423i) q^{88} +(1.52192 + 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} +(5.19615 + 3.00000i) q^{92} -12.8418i q^{94} +12.0000i q^{95} +(-2.74264 - 1.58346i) q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 + 4 * q^7	\( 8 q - 8 q^{4} + 4 q^{7} + 12 q^{13} + 8 q^{16} - 4 q^{25} - 4 q^{28} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} - 12 q^{52} - 24 q^{58} - 8 q^{64} + 40 q^{67} - 24 q^{70} - 72 q^{73} + 40 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^13 + 8 * q^16 - 4 * q^25 - 4 * q^28 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 - 12 * q^52 - 24 * q^58 - 8 * q^64 + 40 * q^67 - 24 * q^70 - 72 * q^73 + 40 * q^79 - 24 * q^85 + 48 * q^91 + 12 * q^97

Introduction

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