LMFDB - Embedded newform 588.2.x.a.55.11

Newspace parameters

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			55.11
Character	$\chi$	$=$	588.55
Dual form			588.2.x.a.139.11

$q$-expansion

$f(q)$	$=$	$q+(-0.537130 - 1.30824i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-1.42298 + 1.40539i) q^{4} +(-1.35460 + 2.81286i) q^{5} +(-0.0836867 + 1.41174i) q^{6} +(2.57260 - 0.617858i) q^{7} +(2.60291 + 1.10673i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-0.537130 - 1.30824i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-1.42298 + 1.40539i) q^{4} +(-1.35460 + 2.81286i) q^{5} +(-0.0836867 + 1.41174i) q^{6} +(2.57260 - 0.617858i) q^{7} +(2.60291 + 1.10673i) q^{8} +(0.623490 + 0.781831i) q^{9} +(4.40750 + 0.261274i) q^{10} +(-1.76527 - 1.40775i) q^{11} +(1.89184 - 0.648803i) q^{12} +(-3.29095 - 2.62444i) q^{13} +(-2.19013 - 3.03370i) q^{14} +(2.44091 - 1.94656i) q^{15} +(0.0497615 - 3.99969i) q^{16} +(-0.732085 - 0.167094i) q^{17} +(0.687928 - 1.23562i) q^{18} -2.18601 q^{19} +(-2.02559 - 5.90641i) q^{20} +(-2.58591 - 0.559536i) q^{21} +(-0.893502 + 3.06554i) q^{22} +(-6.10010 + 1.39231i) q^{23} +(-1.86495 - 2.12649i) q^{24} +(-2.95981 - 3.71148i) q^{25} +(-1.66574 + 5.71502i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-2.79243 + 4.49470i) q^{28} +(0.287151 - 1.25809i) q^{29} +(-3.85766 - 2.14774i) q^{30} +0.402929 q^{31} +(-5.25928 + 2.08325i) q^{32} +(0.979650 + 2.03426i) q^{33} +(0.174626 + 1.04749i) q^{34} +(-1.74690 + 8.07332i) q^{35} +(-1.98599 - 0.236287i) q^{36} +(0.433292 - 1.89838i) q^{37} +(1.17417 + 2.85983i) q^{38} +(1.82634 + 3.79243i) q^{39} +(-6.63899 + 5.82247i) q^{40} +(-0.368199 + 0.764573i) q^{41} +(0.656960 + 3.68353i) q^{42} +(-5.46538 - 11.3490i) q^{43} +(4.49039 - 0.477678i) q^{44} +(-3.04377 + 0.694720i) q^{45} +(5.09802 + 7.23254i) q^{46} +(-7.96580 + 9.98879i) q^{47} +(-1.78023 + 3.58201i) q^{48} +(6.23650 - 3.17900i) q^{49} +(-3.26571 + 5.86568i) q^{50} +(0.587087 + 0.468186i) q^{51} +(8.37133 - 0.890525i) q^{52} +(-1.85688 - 8.13550i) q^{53} +(-1.15592 + 0.814774i) q^{54} +(6.35106 - 3.05851i) q^{55} +(7.38004 + 1.23893i) q^{56} +(1.96953 + 0.948475i) q^{57} +(-1.80012 + 0.300095i) q^{58} +(-8.17303 + 3.93592i) q^{59} +(-0.737699 + 6.20036i) q^{60} +(-9.90217 - 2.26011i) q^{61} +(-0.216425 - 0.527128i) q^{62} +(2.08705 + 1.62611i) q^{63} +(5.55031 + 5.76143i) q^{64} +(11.8401 - 5.70191i) q^{65} +(2.13511 - 2.37428i) q^{66} -1.76525i q^{67} +(1.27658 - 0.791093i) q^{68} +(6.10010 + 1.39231i) q^{69} +(11.5001 - 2.05106i) q^{70} +(9.16755 - 2.09243i) q^{71} +(0.757616 + 2.72507i) q^{72} +(5.14288 - 4.10131i) q^{73} +(-2.71627 + 0.452825i) q^{74} +(1.05634 + 4.62814i) q^{75} +(3.11066 - 3.07220i) q^{76} +(-5.41111 - 2.53090i) q^{77} +(3.98043 - 4.42632i) q^{78} +5.36375i q^{79} +(11.1832 + 5.55797i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(1.19802 + 0.0710176i) q^{82} +(-4.49133 - 5.63195i) q^{83} +(4.46607 - 2.83800i) q^{84} +(1.46170 - 1.83291i) q^{85} +(-11.9116 + 13.2459i) q^{86} +(-0.804578 + 1.00891i) q^{87} +(-3.03684 - 5.61793i) q^{88} +(-12.4429 + 9.92291i) q^{89} +(2.54376 + 3.60882i) q^{90} +(-10.0878 - 4.71829i) q^{91} +(6.72360 - 10.5542i) q^{92} +(-0.363026 - 0.174824i) q^{93} +(17.3464 + 5.05589i) q^{94} +(2.96118 - 6.14895i) q^{95} +(5.64234 + 0.404971i) q^{96} -0.150995i q^{97} +(-7.50871 - 6.45130i) q^{98} -2.25786i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−0.537130	−	1.30824i	−0.379808	−	0.925065i
$2$	−0.537130	−	1.30824i	−0.379808	−	0.925065i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	−1.42298	+	1.40539i	−0.711492	+	0.702695i
$5$	−1.35460	+	2.81286i	−0.605797	+	1.25795i	0.342186	+	0.939632i	$0.388833\pi$
$5$	−1.35460	+	2.81286i	−0.605797	+	1.25795i	−0.947984	+	0.318319i	$0.896882\pi$
$6$	−0.0836867	+	1.41174i	−0.0341650	+	0.576339i
$7$	2.57260	−	0.617858i	0.972350	−	0.233529i
$7$	2.57260	−	0.617858i	0.972350	−	0.233529i
$8$	2.60291	+	1.10673i	0.920269	+	0.391287i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	4.40750	+	0.261274i	1.39377	+	0.0826220i
$11$	−1.76527	−	1.40775i	−0.532248	−	0.424454i	0.320135	−	0.947372i	$-0.396272\pi$
$11$	−1.76527	−	1.40775i	−0.532248	−	0.424454i	−0.852383	+	0.522918i	$0.824843\pi$
$12$	1.89184	−	0.648803i	0.546127	−	0.187293i
$13$	−3.29095	−	2.62444i	−0.912745	−	0.727890i	0.0498721	−	0.998756i	$-0.484119\pi$
$13$	−3.29095	−	2.62444i	−0.912745	−	0.727890i	−0.962617	+	0.270866i	$0.912690\pi$
$14$	−2.19013	−	3.03370i	−0.585336	−	0.810791i
$15$	2.44091	−	1.94656i	0.630241	−	0.502600i
$16$	0.0497615	−	3.99969i	0.0124404	−	0.999923i
$17$	−0.732085	−	0.167094i	−0.177557	−	0.0405262i	0.132818	−	0.991140i	$-0.457597\pi$
$17$	−0.732085	−	0.167094i	−0.177557	−	0.0405262i	−0.310375	+	0.950614i	$0.600455\pi$
$18$	0.687928	−	1.23562i	0.162146	−	0.291238i
$19$	−2.18601			−0.501505			−0.250753	−	0.968051i	$-0.580678\pi$
$19$	−2.18601			−0.501505			−0.250753	+	0.968051i	$0.580678\pi$
$20$	−2.02559	−	5.90641i	−0.452936	−	1.32071i
$21$	−2.58591	−	0.559536i	−0.564291	−	0.122101i
$22$	−0.893502	+	3.06554i	−0.190495	+	0.653575i
$23$	−6.10010	+	1.39231i	−1.27196	+	0.290316i	−0.804635	−	0.593770i	$-0.797639\pi$
$23$	−6.10010	+	1.39231i	−1.27196	+	0.290316i	−0.467324	+	0.884086i	$0.654782\pi$
$24$	−1.86495	−	2.12649i	−0.380682	−	0.434068i
$25$	−2.95981	−	3.71148i	−0.591961	−	0.742296i
$26$	−1.66574	+	5.71502i	−0.326678	+	1.12081i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	−2.79243	+	4.49470i	−0.527719	+	0.849419i
$29$	0.287151	−	1.25809i	0.0533225	−	0.233621i	−0.941244	−	0.337729i	$-0.890341\pi$
$29$	0.287151	−	1.25809i	0.0533225	−	0.233621i	0.994566	+	0.104107i	$0.0331985\pi$
$30$	−3.85766	−	2.14774i	−0.704309	−	0.392122i
$31$	0.402929			0.0723682			0.0361841	−	0.999345i	$-0.488480\pi$
$31$	0.402929			0.0723682			0.0361841	+	0.999345i	$0.488480\pi$
$32$	−5.25928	+	2.08325i	−0.929719	+	0.368271i
$33$	0.979650	+	2.03426i	0.170535	+	0.354120i
$34$	0.174626	+	1.04749i	0.0299481	+	0.179644i
$35$	−1.74690	+	8.07332i	−0.295280	+	1.36464i
$36$	−1.98599	−	0.236287i	−0.330999	−	0.0393812i
$37$	0.433292	−	1.89838i	0.0712328	−	0.312091i	−0.926742	−	0.375698i	$-0.877403\pi$
$37$	0.433292	−	1.89838i	0.0712328	−	0.312091i	0.997975	+	0.0636065i	$0.0202603\pi$
$38$	1.17417	+	2.85983i	0.190476	+	0.463925i
$39$	1.82634	+	3.79243i	0.292448	+	0.607275i
$40$	−6.63899	+	5.82247i	−1.04972	+	0.920613i
$41$	−0.368199	+	0.764573i	−0.0575030	+	0.119406i	−0.927740	−	0.373227i	$-0.878251\pi$
$41$	−0.368199	+	0.764573i	−0.0575030	+	0.119406i	0.870237	+	0.492633i	$0.163966\pi$
$42$	0.656960	+	3.68353i	0.101371	+	0.568381i
$43$	−5.46538	−	11.3490i	−0.833462	−	1.73070i	−0.667555	−	0.744561i	$-0.732659\pi$
$43$	−5.46538	−	11.3490i	−0.833462	−	1.73070i	−0.165907	−	0.986141i	$-0.553055\pi$
$44$	4.49039	−	0.477678i	0.676952	−	0.0720127i
$45$	−3.04377	+	0.694720i	−0.453738	+	0.103563i
$46$	5.09802	+	7.23254i	0.751662	+	1.06638i
$47$	−7.96580	+	9.98879i	−1.16193	+	1.45702i	−0.297175	+	0.954823i	$0.596044\pi$
$47$	−7.96580	+	9.98879i	−1.16193	+	1.45702i	−0.864756	+	0.502192i	$0.832527\pi$
$48$	−1.78023	+	3.58201i	−0.256955	+	0.517018i
$49$	6.23650	−	3.17900i	0.890929	−	0.454143i
$50$	−3.26571	+	5.86568i	−0.461841	+	0.829533i
$51$	0.587087	+	0.468186i	0.0822086	+	0.0655592i
$52$	8.37133	−	0.890525i	1.16089	−	0.123494i
$53$	−1.85688	−	8.13550i	−0.255061	−	1.11750i	−0.926458	−	0.376399i	$-0.877162\pi$
$53$	−1.85688	−	8.13550i	−0.255061	−	1.11750i	0.671396	−	0.741098i	$-0.265695\pi$
$54$	−1.15592	+	0.814774i	−0.157300	+	0.110877i
$55$	6.35106	−	3.05851i	0.856377	−	0.412409i
$56$	7.38004	+	1.23893i	0.986200	+	0.165559i
$57$	1.96953	+	0.948475i	0.260870	+	0.125629i
$58$	−1.80012	+	0.300095i	−0.236367	+	0.0394044i
$59$	−8.17303	+	3.93592i	−1.06404	+	0.512414i	−0.882181	−	0.470911i	$-0.843925\pi$
$59$	−8.17303	+	3.93592i	−1.06404	+	0.512414i	−0.181858	+	0.983325i	$0.558211\pi$
$60$	−0.737699	+	6.20036i	−0.0952365	+	0.800463i
$61$	−9.90217	−	2.26011i	−1.26784	−	0.289377i	−0.464863	−	0.885383i	$-0.653896\pi$
$61$	−9.90217	−	2.26011i	−1.26784	−	0.289377i	−0.802980	+	0.596006i	$0.796754\pi$
$62$	−0.216425	−	0.527128i	−0.0274860	−	0.0669453i
$63$	2.08705	+	1.62611i	0.262943	+	0.204870i
$64$	5.55031	+	5.76143i	0.693789	+	0.720178i
$65$	11.8401	−	5.70191i	1.46859	−	0.707235i
$66$	2.13511	−	2.37428i	0.262813	−	0.292254i
$67$		−	1.76525i		−	0.215659i	−0.994169	−	0.107830i	$-0.965610\pi$
$67$		−	1.76525i		−	0.215659i	0.994169	−	0.107830i	$-0.0343901\pi$
$68$	1.27658	−	0.791093i	0.154808	−	0.0959342i
$69$	6.10010	+	1.39231i	0.734366	+	0.167614i
$70$	11.5001	−	2.05106i	1.37453	−	0.245149i
$71$	9.16755	−	2.09243i	1.08799	−	0.248326i	0.359335	−	0.933209i	$-0.383004\pi$
$71$	9.16755	−	2.09243i	1.08799	−	0.248326i	0.728653	+	0.684883i	$0.240146\pi$
$72$	0.757616	+	2.72507i	0.0892859	+	0.321153i
$73$	5.14288	−	4.10131i	0.601928	−	0.480022i	−0.274479	−	0.961593i	$-0.588505\pi$
$73$	5.14288	−	4.10131i	0.601928	−	0.480022i	0.876407	+	0.481572i	$0.159934\pi$
$74$	−2.71627	+	0.452825i	−0.315760	+	0.0526398i
$75$	1.05634	+	4.62814i	0.121976	+	0.534412i
$76$	3.11066	−	3.07220i	0.356817	−	0.352405i
$77$	−5.41111	−	2.53090i	−0.616654	−	0.288423i
$78$	3.98043	−	4.42632i	0.450695	−	0.501182i
$79$			5.36375i			0.603469i	0.953392	+	0.301735i	$0.0975657\pi$
$79$			5.36375i			0.603469i	−0.953392	+	0.301735i	$0.902434\pi$
$80$	11.1832	+	5.55797i	1.25032	+	0.621400i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	1.19802	+	0.0710176i	0.132299	+	0.00784258i
$83$	−4.49133	−	5.63195i	−0.492987	−	0.618187i	0.471644	−	0.881789i	$-0.343661\pi$
$83$	−4.49133	−	5.63195i	−0.492987	−	0.618187i	−0.964631	+	0.263602i	$0.915089\pi$
$84$	4.46607	−	2.83800i	0.487288	−	0.309651i
$85$	1.46170	−	1.83291i	0.158543	−	0.198807i
$86$	−11.9116	+	13.2459i	−1.28446	+	1.42834i
$87$	−0.804578	+	1.00891i	−0.0862598	+	0.108166i
$88$	−3.03684	−	5.61793i	−0.323728	−	0.598873i
$89$	−12.4429	+	9.92291i	−1.31895	+	1.05183i	−0.324580	+	0.945858i	$0.605223\pi$
$89$	−12.4429	+	9.92291i	−1.31895	+	1.05183i	−0.994369	+	0.105968i	$0.966206\pi$
$90$	2.54376	+	3.60882i	0.268136	+	0.380403i
$91$	−10.0878	−	4.71829i	−1.05749	−	0.494612i
$92$	6.72360	−	10.5542i	0.700984	−	1.10036i
$93$	−0.363026	−	0.174824i	−0.0376441	−	0.0181284i
$94$	17.3464	+	5.05589i	1.78914	+	0.521476i
$95$	2.96118	−	6.14895i	0.303811	−	0.630869i
$96$	5.64234	+	0.404971i	0.575869	+	0.0413322i
$97$		−	0.150995i		−	0.0153312i	−0.999971	−	0.00766559i	$-0.997560\pi$
$97$		−	0.150995i		−	0.0153312i	0.999971	−	0.00766559i	$-0.00244006\pi$
$98$	−7.50871	−	6.45130i	−0.758494	−	0.651680i
$99$		−	2.25786i		−	0.226924i
$100$	9.42783	+	1.12169i	0.942783	+	0.112169i
$101$	−1.32602	+	2.75352i	−0.131944	+	0.273985i	−0.956465	−	0.291846i	$-0.905730\pi$
$101$	−1.32602	+	2.75352i	−0.131944	+	0.273985i	0.824521	+	0.565832i	$0.191445\pi$
$102$	0.297158	−	1.01953i	0.0294230	−	0.100948i
$103$	3.22255	+	1.55190i	0.317527	+	0.152913i	0.585858	−	0.810414i	$-0.300758\pi$
$103$	3.22255	+	1.55190i	0.317527	+	0.152913i	−0.268331	+	0.963327i	$0.586472\pi$
$104$	−5.66151	−	10.4734i	−0.555157	−	1.02700i
$105$	5.07678	−	6.51586i	0.495443	−	0.635883i
$106$	−9.64580	+	6.79906i	−0.936883	+	0.660383i
$107$	−9.16516	+	7.30897i	−0.886029	+	0.706585i	−0.956750	−	0.290912i	$-0.906041\pi$
$107$	−9.16516	+	7.30897i	−0.886029	+	0.706585i	0.0707209	+	0.997496i	$0.477470\pi$
$108$	1.68680	+	1.07458i	0.162312	+	0.103401i
$109$	−12.1163	+	15.1933i	−1.16053	+	1.45526i	−0.294227	+	0.955736i	$0.595062\pi$
$109$	−12.1163	+	15.1933i	−1.16053	+	1.45526i	−0.866302	+	0.499521i	$0.833509\pi$
$110$	−7.41261	−	6.66590i	−0.706765	−	0.635568i
$111$	−1.21406	+	1.52238i	−0.115233	+	0.144498i
$112$	−2.34323	−	10.3203i	−0.221414	−	0.975180i
$113$	−12.1396	−	15.2226i	−1.14200	−	1.43202i	−0.884988	−	0.465614i	$-0.845834\pi$
$113$	−12.1396	−	15.2226i	−1.14200	−	1.43202i	−0.257011	−	0.966408i	$-0.582738\pi$
$114$	0.182940	−	3.08607i	0.0171339	−	0.289037i
$115$	4.34685	−	19.0448i	0.405346	−	1.77594i
$116$	1.35949	+	2.19380i	0.126226	+	0.203689i
$117$		−	4.20928i		−	0.389148i
$118$	9.53911	+	8.57818i	0.878147	+	0.789686i
$119$	−1.98660	+	0.0224605i	−0.182111	+	0.00205895i
$120$	8.50780	−	2.36531i	0.776652	−	0.215922i
$121$	−1.31333	−	5.75408i	−0.119394	−	0.523098i
$122$	2.36199	+	14.1684i	0.213845	+	1.28275i
$123$	0.663471	−	0.529101i	0.0598232	−	0.0477074i
$124$	−0.573361	+	0.566272i	−0.0514894	+	0.0508527i
$125$	−0.769582	+	0.175652i	−0.0688335	+	0.0157108i
$126$	1.00632	−	3.60379i	0.0896504	−	0.321051i
$127$	9.73846	+	2.22274i	0.864148	+	0.197236i	0.631549	−	0.775336i	$-0.282420\pi$
$127$	9.73846	+	2.22274i	0.864148	+	0.197236i	0.232600	+	0.972573i	$0.425277\pi$
$128$	4.55609	−	10.3558i	0.402705	−	0.915330i
$129$			12.5964i			1.10905i
$130$	−13.8192	−	12.4271i	−1.21202	−	1.08993i
$131$	15.7276	−	7.57402i	1.37413	−	0.661745i	0.406389	−	0.913700i	$-0.366788\pi$
$131$	15.7276	−	7.57402i	1.37413	−	0.661745i	0.967739	+	0.251955i	$0.0810734\pi$
$132$	−4.25296	−	1.51793i	−0.370172	−	0.132119i
$133$	−5.62372	+	1.35065i	−0.487639	+	0.117116i
$134$	−2.30937	+	0.948166i	−0.199499	+	0.0819091i
$135$	3.04377	+	0.694720i	0.261966	+	0.0597920i
$136$	−1.72063	−	1.24515i	−0.147543	−	0.106771i
$137$	18.3012	−	8.81338i	1.56357	−	0.752977i	0.566122	−	0.824321i	$-0.308443\pi$
$137$	18.3012	−	8.81338i	1.56357	−	0.752977i	0.997452	+	0.0713439i	$0.0227288\pi$
$138$	−1.45507	−	8.72824i	−0.123864	−	0.742997i
$139$	8.96026	+	4.31503i	0.759999	+	0.365996i	0.773404	−	0.633914i	$-0.218553\pi$
$139$	8.96026	+	4.31503i	0.759999	+	0.365996i	−0.0134043	+	0.999910i	$0.504267\pi$
$140$	−8.86035	−	13.9433i	−0.748836	−	1.17842i
$141$	11.5109	−	5.54336i	0.969393	−	0.466835i
$142$	−7.66157	−	10.8694i	−0.642945	−	0.912144i
$143$	2.11483	+	9.26569i	0.176851	+	0.774836i
$144$	3.15811	−	2.45486i	0.263176	−	0.204572i
$145$	3.14986	+	2.51193i	0.261582	+	0.208604i
$146$	−8.12788	−	4.52518i	−0.672668	−	0.374507i
$147$	−6.99821	+	0.158264i	−0.577203	+	0.0130534i
$148$	2.05139	+	3.31030i	0.168623	+	0.272105i
$149$	10.4176	−	13.0633i	0.853443	−	1.07018i	−0.143311	−	0.989678i	$-0.545775\pi$
$149$	10.4176	−	13.0633i	0.853443	−	1.07018i	0.996754	−	0.0805058i	$-0.0256535\pi$
$150$	5.48732	−	3.86786i	0.448038	−	0.315810i
$151$	−2.98349	+	0.680962i	−0.242793	+	0.0554159i	−0.342186	−	0.939632i	$-0.611167\pi$
$151$	−2.98349	+	0.680962i	−0.242793	+	0.0554159i	0.0993926	+	0.995048i	$0.468310\pi$
$152$	−5.69000	−	2.41932i	−0.461520	−	0.196232i
$153$	−0.325809	−	0.676548i	−0.0263401	−	0.0546957i
$154$	−0.404550	+	8.43846i	−0.0325995	+	0.679990i
$155$	−0.545809	+	1.13338i	−0.0438405	+	0.0910357i
$156$	−7.92869	−	2.82985i	−0.634803	−	0.226569i
$157$	7.66058	+	15.9073i	0.611381	+	1.26954i	0.945072	+	0.326862i	$0.105991\pi$
$157$	7.66058	+	15.9073i	0.611381	+	1.26954i	−0.333691	+	0.942682i	$0.608294\pi$
$158$	7.01707	−	2.88103i	0.558248	−	0.229203i
$159$	−1.85688	+	8.13550i	−0.147260	+	0.645187i
$160$	1.26434	−	17.6156i	0.0999547	−	1.39264i
$161$	−14.8328	+	7.35084i	−1.16899	+	0.579328i
$162$	1.39496	−	0.232552i	0.109599	−	0.0182710i
$163$	6.84045	+	14.2043i	0.535785	+	1.11257i	0.976618	+	0.214980i	$0.0689687\pi$
$163$	6.84045	+	14.2043i	0.535785	+	1.11257i	−0.440833	+	0.897589i	$0.645317\pi$
$164$	−0.550582	−	1.60544i	−0.0429932	−	0.125364i
$165$	−7.04915			−0.548775
$166$	−4.95551	+	8.90082i	−0.384622	+	0.690838i
$167$	0.0438096	−	0.191942i	0.00339009	−	0.0148530i	−0.973205	−	0.229941i	$-0.926147\pi$
$167$	0.0438096	−	0.191942i	0.00339009	−	0.0148530i	0.976595	+	0.215088i	$0.0690038\pi$
$168$	−6.11164	−	4.31832i	−0.471523	−	0.333165i
$169$	1.04987	+	4.59976i	0.0807589	+	0.353828i
$170$	−3.18301	−	0.927740i	−0.244126	−	0.0711544i
$171$	−1.36296	−	1.70909i	−0.104228	−	0.130698i
$172$	23.7269	+	8.46841i	1.80916	+	0.645710i
$173$	23.6429	−	5.39634i	1.79754	−	0.410276i	0.812549	−	0.582893i	$-0.198079\pi$
$173$	23.6429	−	5.39634i	1.79754	−	0.410276i	0.984989	+	0.172616i	$0.0552220\pi$
$174$	1.75206	+	0.510666i	0.132823	+	0.0387135i
$175$	−9.90756	−	7.71940i	−0.748941	−	0.583532i
$176$	−5.71842	+	6.99047i	−0.431042	+	0.526927i
$177$	9.07138			0.681847
$178$	19.6650	+	10.9485i	1.47396	+	0.820622i
$179$	9.00212	+	2.05468i	0.672850	+	0.153574i	0.545278	−	0.838256i	$-0.316424\pi$
$179$	9.00212	+	2.05468i	0.672850	+	0.153574i	0.127573	+	0.991829i	$0.459281\pi$
$180$	3.35488	−	5.26625i	0.250058	−	0.392523i
$181$	−3.24137	+	2.58490i	−0.240929	+	0.192134i	−0.736509	−	0.676428i	$-0.763527\pi$
$181$	−3.24137	+	2.58490i	−0.240929	+	0.192134i	0.495580	+	0.868562i	$0.334956\pi$
$182$	−0.754193	+	15.7316i	−0.0559045	+	1.16611i
$183$	7.94093	+	6.33268i	0.587010	+	0.468125i
$184$	−17.4189	−	3.12709i	−1.28414	−	0.230532i
$185$	4.75294	+	3.79034i	0.349443	+	0.278671i
$186$	−0.0337198	+	0.568829i	−0.00247246	+	0.0417086i
$187$	1.05710	+	1.32556i	0.0773028	+	0.0969346i
$188$	−2.70295	−	25.4089i	−0.197133	−	1.85314i
$189$	−1.17482	−	2.37061i	−0.0854559	−	0.172436i
$190$	−9.63484	−	0.571147i	−0.698985	−	0.0414354i
$191$	−3.74677	+	7.78026i	−0.271107	+	0.562960i	−0.991424	−	0.130686i	$-0.958282\pi$
$191$	−3.74677	+	7.78026i	−0.271107	+	0.562960i	0.720317	+	0.693645i	$0.243996\pi$
$192$	−2.50087	−	7.59906i	−0.180485	−	0.548415i
$193$	−7.82112	−	3.76645i	−0.562977	−	0.271115i	0.130676	−	0.991425i	$-0.458285\pi$
$193$	−7.82112	−	3.76645i	−0.562977	−	0.271115i	−0.693652	+	0.720310i	$0.744000\pi$
$194$	−0.197537	+	0.0811037i	−0.0141823	+	0.00582290i
$195$	−13.1416			−0.941087
$196$	−4.40670	+	13.2884i	−0.314764	+	0.949170i
$197$	8.77346			0.625083			0.312542	−	0.949904i	$-0.398820\pi$
$197$	8.77346			0.625083			0.312542	+	0.949904i	$0.398820\pi$
$198$	−2.95383	+	1.21277i	−0.209919	+	0.0861875i
$199$	3.67429	+	1.76944i	0.260463	+	0.125433i	0.559559	−	0.828791i	$-0.310971\pi$
$199$	3.67429	+	1.76944i	0.260463	+	0.125433i	−0.299095	+	0.954223i	$0.596685\pi$
$200$	−3.59653	−	12.9364i	−0.254313	−	0.914739i
$201$	−0.765912	+	1.59043i	−0.0540232	+	0.112180i
$202$	4.31451	+	0.255761i	0.303568	+	0.0179953i
$203$	−0.0385984	−	3.41397i	−0.00270908	−	0.239614i
$204$	−1.49340	+	0.158865i	−0.104559	+	0.0111227i
$205$	−1.65188	−	2.07139i	−0.115372	−	0.144672i
$206$	0.299327	−	5.04944i	0.0208551	−	0.351811i
$207$	−4.89190	−	3.90116i	−0.340011	−	0.271149i
$208$	−10.6607	+	13.0322i	−0.739188	+	0.903619i
$209$	3.85890	+	3.07737i	0.266925	+	0.212866i
$210$	−11.2512	−	3.14179i	−0.776406	−	0.216804i
$211$	11.1768	−	8.91320i	0.769442	−	0.613610i	−0.158059	−	0.987430i	$-0.550524\pi$
$211$	11.1768	−	8.91320i	0.769442	−	0.613610i	0.927501	+	0.373820i	$0.121952\pi$
$212$	14.0758	+	8.96705i	0.966733	+	0.615859i
$213$	−9.16755	−	2.09243i	−0.628150	−	0.143371i
$214$	14.4848	+	8.06436i	0.990158	+	0.551268i
$215$	39.3265			2.68205
$216$	0.499776	−	2.78392i	0.0340054	−	0.189422i
$217$	1.03657	−	0.248953i	0.0703672	−	0.0169000i
$218$	26.3845	+	7.69020i	1.78699	+	0.520846i
$219$	−6.41306	+	1.46374i	−0.433354	+	0.0989103i
$220$	−4.73906	+	13.2779i	−0.319507	+	0.895197i
$221$	1.97073	+	2.47121i	0.132565	+	0.166232i
$222$	2.64374	+	0.770563i	0.177437	+	0.0517168i
$223$	−3.37774	−	14.7988i	−0.226190	−	0.991004i	−0.952715	−	0.303864i	$-0.901723\pi$
$223$	−3.37774	−	14.7988i	−0.226190	−	0.991004i	0.726525	−	0.687140i	$-0.241134\pi$
$224$	−12.2429	+	8.60886i	−0.818010	+	0.575204i
$225$	1.05634	−	4.62814i	0.0704229	−	0.308543i
$226$	−13.3943	+	24.0580i	−0.890973	+	1.60032i
$227$	−6.77591			−0.449733			−0.224866	−	0.974390i	$-0.572195\pi$
$227$	−6.77591			−0.449733			−0.224866	+	0.974390i	$0.572195\pi$
$228$	−4.13558	+	1.41829i	−0.273886	+	0.0939286i
$229$	1.69166	+	3.51276i	0.111788	+	0.232130i	0.949356	−	0.314204i	$-0.101737\pi$
$229$	1.69166	+	3.51276i	0.111788	+	0.232130i	−0.837568	+	0.546333i	$0.816023\pi$
$230$	−27.2500	+	4.54280i	−1.79681	+	0.299543i
$231$	3.77713	+	4.62805i	0.248517	+	0.304504i
$232$	2.13979	−	2.95690i	0.140484	−	0.194130i
$233$	−1.98352	+	8.69038i	−0.129945	+	0.569326i	0.867471	+	0.497487i	$0.165744\pi$
$233$	−1.98352	+	8.69038i	−0.129945	+	0.569326i	−0.997416	+	0.0718386i	$0.977113\pi$
$234$	−5.50675	+	2.26093i	−0.359988	+	0.147802i
$235$	−17.3066	−	35.9376i	−1.12896	−	2.34431i
$236$	6.09858	−	17.0870i	0.396984	−	1.11227i
$237$	2.32724	−	4.83257i	0.151171	−	0.313909i
$238$	1.09645	+	2.58688i	0.0710720	+	0.167683i
$239$	−0.305326	−	0.634016i	−0.0197499	−	0.0410111i	0.890861	−	0.454277i	$-0.150102\pi$
$239$	−0.305326	−	0.634016i	−0.0197499	−	0.0410111i	−0.910610	+	0.413266i	$0.864388\pi$
$240$	−7.66419	−	9.85976i	−0.494721	−	0.636445i
$241$	−20.4870	+	4.67602i	−1.31968	+	0.301209i	−0.823652	−	0.567096i	$-0.808067\pi$
$241$	−20.4870	+	4.67602i	−1.31968	+	0.301209i	−0.496031	+	0.868305i	$0.665210\pi$
$242$	−6.82229	+	4.80884i	−0.438553	+	0.309124i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	17.2670	−	10.7003i	1.10540	−	0.685018i
$245$	0.494107	+	21.8487i	0.0315674	+	1.39586i
$246$	−1.04856	−	0.583784i	−0.0668538	−	0.0372207i
$247$	7.19405	+	5.73706i	0.457746	+	0.365041i
$248$	1.04879	+	0.445932i	0.0665982	+	0.0283167i
$249$	1.60294	+	7.02292i	0.101582	+	0.445060i
$250$	0.643161	+	0.912450i	0.0406770	+	0.0577084i
$251$	−22.2284	+	10.7047i	−1.40305	+	0.675672i	−0.973777	−	0.227504i	$-0.926943\pi$
$251$	−22.2284	+	10.7047i	−1.40305	+	0.675672i	−0.429270	+	0.903176i	$0.641229\pi$
$252$	−5.25515	+	0.619192i	−0.331043	+	0.0390054i
$253$	12.7283	+	6.12964i	0.800224	+	0.385367i
$254$	−2.32294	−	13.9341i	−0.145754	−	0.874306i
$255$	−2.11221	+	1.01719i	−0.132272	+	0.0636988i
$256$	−15.9950	−	0.398061i	−0.999690	−	0.0248788i
$257$	−11.3538	−	2.59143i	−0.708229	−	0.161649i	−0.146791	−	0.989167i	$-0.546895\pi$
$257$	−11.3538	−	2.59143i	−0.708229	−	0.161649i	−0.561438	+	0.827519i	$0.689752\pi$
$258$	16.4791	−	6.76591i	1.02595	−	0.421227i
$259$	−0.0582426	−	5.15147i	−0.00361902	−	0.320097i
$260$	−8.83491	+	24.7537i	−0.547918	+	1.53516i
$261$	1.16265	−	0.559902i	0.0719662	−	0.0346571i
$262$	−18.3564	−	16.5073i	−1.13406	−	1.01982i
$263$		−	16.5696i		−	1.02173i	−0.859661	−	0.510864i	$-0.829326\pi$
$263$		−	16.5696i		−	1.02173i	0.859661	−	0.510864i	$-0.170674\pi$
$264$	0.298569	+	6.37922i	0.0183757	+	0.392614i
$265$	25.3994	+	5.79725i	1.56027	+	0.356122i
$266$	4.78764	+	6.63171i	0.293549	+	0.406616i
$267$	15.5161	−	3.54145i	0.949570	−	0.216733i
$268$	2.48086	+	2.51192i	0.151543	+	0.153440i
$269$	6.90235	−	5.50444i	0.420844	−	0.335612i	−0.390062	−	0.920789i	$-0.627546\pi$
$269$	6.90235	−	5.50444i	0.420844	−	0.335612i	0.810906	+	0.585177i	$0.198975\pi$
$270$	−0.726038	−	4.35513i	−0.0441853	−	0.265045i
$271$	2.77844	+	12.1731i	0.168778	+	0.739466i	0.986488	+	0.163835i	$0.0523864\pi$
$271$	2.77844	+	12.1731i	0.168778	+	0.739466i	−0.817710	+	0.575631i	$0.804756\pi$
$272$	−0.704753	+	2.91980i	−0.0427319	+	0.177039i
$273$	7.04162	+	8.62798i	0.426178	+	0.522189i
$274$	−21.3601	−	19.2084i	−1.29041	−	1.16042i
$275$			10.7184i			0.646346i
$276$	−10.6371	+	6.59178i	−0.640277	+	0.396779i
$277$	−5.33018	+	23.3530i	−0.320259	+	1.40315i	0.516833	+	0.856086i	$0.327111\pi$
$277$	−5.33018	+	23.3530i	−0.320259	+	1.40315i	−0.837092	+	0.547062i	$0.815746\pi$
$278$	0.832276	−	14.0399i	0.0499166	−	0.842058i
$279$	0.251222	+	0.315023i	0.0150403	+	0.0188599i
$280$	−13.4820	+	19.0808i	−0.805702	+	1.14030i
$281$	−13.2980	+	16.6751i	−0.793290	+	0.994755i	0.206576	+	0.978430i	$0.433768\pi$
$281$	−13.2980	+	16.6751i	−0.793290	+	0.994755i	−0.999867	+	0.0163241i	$0.994804\pi$
$282$	−13.4349	−	12.0815i	−0.800037	−	0.719444i
$283$	−0.223316	+	0.280030i	−0.0132748	+	0.0166460i	−0.788425	−	0.615131i	$-0.789103\pi$
$283$	−0.223316	+	0.280030i	−0.0132748	+	0.0166460i	0.775150	+	0.631777i	$0.217674\pi$
$284$	−10.1046	+	15.8615i	−0.599597	+	0.941206i
$285$	−5.33586	+	4.25521i	−0.316069	+	0.252057i
$286$	10.9858	−	7.74359i	0.649605	−	0.457888i
$287$	−0.474829	+	2.19443i	−0.0280283	+	0.129533i
$288$	−4.90786	−	2.81299i	−0.289199	−	0.165757i
$289$	−14.8084	−	7.13137i	−0.871085	−	0.419492i
$290$	1.59432	−	5.47000i	0.0936218	−	0.321210i
$291$	−0.0655141	+	0.136041i	−0.00384050	+	0.00797489i
$292$	−1.55429	+	13.0638i	−0.0909581	+	0.764503i
$293$			23.2621i			1.35899i	0.733682	+	0.679493i	$0.237800\pi$
$293$			23.2621i			1.35899i	−0.733682	+	0.679493i	$0.762200\pi$
$294$	3.96600	+	9.07033i	0.231302	+	0.528992i
$295$		−	28.3213i		−	1.64893i
$296$	3.22881	−	4.46177i	0.187670	−	0.259335i
$297$	−0.979650	+	2.03426i	−0.0568450	+	0.118040i
$298$	−22.6855	−	6.61205i	−1.31413	−	0.383026i
$299$	23.7291	+	11.4274i	1.37229	+	0.660861i
$300$	−8.00750	−	5.10119i	−0.462313	−	0.294517i
$301$	−21.0723	−	25.8195i	−1.21459	−	1.48821i
$302$	2.49338	+	3.53736i	0.143478	+	0.203552i
$303$	2.38941	−	1.90549i	0.137268	−	0.109468i
$304$	−0.108779	+	8.74337i	−0.00623892	+	0.501467i
$305$	19.7709	−	24.7919i	1.13208	−	1.41958i
$306$	−0.710086	+	0.789630i	−0.0405929	+	0.0451402i
$307$	−18.9069	+	23.7086i	−1.07908	+	1.35312i	−0.147712	+	0.989030i	$0.547191\pi$
$307$	−18.9069	+	23.7086i	−1.07908	+	1.35312i	−0.931364	+	0.364088i	$0.881381\pi$
$308$	11.2568	−	4.00330i	0.641417	−	0.228109i
$309$	−2.23007	−	2.79642i	−0.126864	−	0.159083i
$310$	1.77591	+	0.105275i	0.100865	+	0.00597920i
$311$	−1.27455	+	5.58416i	−0.0722730	+	0.316649i	−0.998123	−	0.0612427i	$-0.980494\pi$
$311$	−1.27455	+	5.58416i	−0.0722730	+	0.316649i	0.925850	+	0.377892i	$0.123351\pi$
$312$	0.556616	+	11.8926i	0.0315122	+	0.673287i
$313$		−	11.4620i		−	0.647870i	−0.946079	−	0.323935i	$-0.894994\pi$
$313$		−	11.4620i		−	0.647870i	0.946079	−	0.323935i	$-0.105006\pi$
$314$	16.6959	−	18.5662i	0.942204	−	1.04775i
$315$	−7.40115	+	3.66785i	−0.417007	+	0.206660i
$316$	−7.53816	−	7.63253i	−0.424055	−	0.429363i
$317$	1.24478	+	5.45372i	0.0699136	+	0.306312i	0.997780	−	0.0666022i	$-0.0212158\pi$
$317$	1.24478	+	5.45372i	0.0699136	+	0.306312i	−0.927866	+	0.372914i	$0.878359\pi$
$318$	11.6406	−	1.94058i	0.652771	−	0.108822i
$319$	−2.27798	+	1.81663i	−0.127542	+	0.101712i
$320$	−23.7246	+	7.80783i	−1.32624	+	0.436471i
$321$	11.4288	−	2.60854i	0.637891	−	0.145595i
$322$	17.5838	+	15.4566i	0.979909	+	0.861360i
$323$	1.60035	+	0.365269i	0.0890457	+	0.0203241i
$324$	−1.05351	−	1.70003i	−0.0585283	−	0.0944464i
$325$			19.9821i			1.10841i
$326$	14.9085	−	16.5785i	0.825704	−	0.918199i
$327$	17.5085	−	8.43166i	0.968224	−	0.466272i
$328$	−1.80456	+	1.58262i	−0.0996403	+	0.0873856i
$329$	−14.3211	+	30.6189i	−0.789549	+	1.68807i
$330$	3.78631	+	9.22198i	0.208429	+	0.507653i
$331$	−23.5793	−	5.38182i	−1.29603	−	0.295811i	−0.481766	−	0.876300i	$-0.660004\pi$
$331$	−23.5793	−	5.38182i	−1.29603	−	0.295811i	−0.814268	+	0.580488i	$0.802862\pi$
$332$	14.3062	+	1.70210i	0.785153	+	0.0934149i
$333$	1.75436	−	0.844857i	0.0961385	−	0.0462979i
$334$	−0.274638	+	0.0457845i	−0.0150275	+	0.00250522i
$335$	4.96540	+	2.39121i	0.271289	+	0.130646i
$336$	−2.36665	+	10.3150i	−0.129111	+	0.562729i
$337$	7.55735	−	3.63943i	0.411675	−	0.198252i	−0.216571	−	0.976267i	$-0.569487\pi$
$337$	7.55735	−	3.63943i	0.411675	−	0.198252i	0.628246	+	0.778014i	$0.283773\pi$
$338$	5.45368	−	3.84414i	0.296641	−	0.209094i
$339$	4.33258	+	18.9823i	0.235313	+	1.03098i
$340$	0.495982	+	4.66246i	0.0268984	+	0.252857i
$341$	−0.711278	−	0.567225i	−0.0385178	−	0.0307170i
$342$	−1.50382	+	2.70108i	−0.0813172	+	0.146058i
$343$	14.0798	−	12.0316i	0.760239	−	0.649643i
$344$	−1.66569	−	35.5891i	−0.0898081	−	1.91883i
$345$	−12.1796	+	15.2727i	−0.655727	+	0.822256i
$346$	−19.7590	−	28.0321i	−1.06225	−	1.50701i
$347$	0.152163	−	0.0347302i	0.00816854	−	0.00186442i	−0.218435	−	0.975852i	$-0.570095\pi$
$347$	0.152163	−	0.0347302i	0.00816854	−	0.00186442i	0.226603	+	0.973987i	$0.427238\pi$
$348$	−0.273009	−	2.56641i	−0.0146348	−	0.137574i
$349$	12.7426	+	26.4603i	0.682096	+	1.41639i	0.898010	+	0.439975i	$0.145013\pi$
$349$	12.7426	+	26.4603i	0.682096	+	1.41639i	−0.215914	+	0.976412i	$0.569273\pi$
$350$	−4.77718	+	17.1078i	−0.255351	+	0.914449i
$351$	−1.82634	+	3.79243i	−0.0974828	+	0.202425i
$352$	12.2168	+	3.72628i	0.651155	+	0.198611i
$353$	−0.125093	−	0.259758i	−0.00665802	−	0.0138255i	0.897613	−	0.440784i	$-0.145299\pi$
$353$	−0.125093	−	0.259758i	−0.00665802	−	0.0138255i	−0.904271	+	0.426958i	$0.859585\pi$
$354$	−4.87251	−	11.8675i	−0.258971	−	0.630753i
$355$	−6.53267	+	28.6215i	−0.346718	+	1.51907i
$356$	3.76054	−	31.6073i	0.199308	−	1.67518i
$357$	1.79961	+	0.841717i	0.0952455	+	0.0445484i
$358$	−2.14730	−	12.8806i	−0.113488	−	0.680759i
$359$	−5.48979	−	11.3997i	−0.289740	−	0.601651i	0.704394	−	0.709809i	$-0.251219\pi$
$359$	−5.48979	−	11.3997i	−0.289740	−	0.601651i	−0.994134	+	0.108158i	$0.965505\pi$
$360$	−8.69153	−	1.56032i	−0.458084	−	0.0822362i
$361$	−14.2214			−0.748492
$362$	5.12271	+	2.85206i	0.269244	+	0.149901i
$363$	−1.31333	+	5.75408i	−0.0689320	+	0.302011i
$364$	20.9858	−	7.46326i	1.09996	−	0.391181i
$365$	4.56986	+	20.0219i	0.239197	+	1.04799i
$366$	4.01935	−	13.7901i	0.210095	−	0.720820i
$367$	3.11165	+	3.90189i	0.162427	+	0.203677i	0.856384	−	0.516340i	$-0.172706\pi$
$367$	3.11165	+	3.90189i	0.162427	+	0.203677i	−0.693957	+	0.720016i	$0.744134\pi$
$368$	5.26525	+	24.4678i	0.274470	+	1.27547i
$369$	−0.827335	+	0.188834i	−0.0430694	+	0.00983030i
$370$	2.40573	−	8.25389i	0.125068	−	0.429099i
$371$	−9.80358	−	19.7821i	−0.508976	−	1.02703i
$372$	0.762277	−	0.261421i	0.0395222	−	0.0135541i
$373$	−24.4494			−1.26594			−0.632970	−	0.774176i	$-0.718164\pi$
$373$	−24.4494			−1.26594			−0.632970	+	0.774176i	$0.718164\pi$
$374$	1.16635	−	2.09494i	0.0603106	−	0.108327i
$375$	0.769582	+	0.175652i	0.0397410	+	0.00907063i
$376$	−31.7891	+	17.1840i	−1.63940	+	0.886197i
$377$	−4.24678	+	3.38670i	−0.218720	+	0.174424i
$378$	−2.47029	+	2.81028i	−0.127058	+	0.144545i
$379$	18.1646	+	14.4858i	0.933051	+	0.744083i	0.966850	−	0.255345i	$-0.0821891\pi$
$379$	18.1646	+	14.4858i	0.933051	+	0.744083i	−0.0337988	+	0.999429i	$0.510761\pi$
$380$	4.42797	+	12.9115i	0.227150	+	0.662344i
$381$	−7.80964	−	6.22798i	−0.400100	−	0.319069i
$382$	12.1909	+	0.722671i	0.623743	+	0.0369751i
$383$	−9.17187	−	11.5012i	−0.468660	−	0.587682i	0.490182	−	0.871620i	$-0.336930\pi$
$383$	−9.17187	−	11.5012i	−0.468660	−	0.587682i	−0.958842	+	0.283938i	$0.908359\pi$
$384$	−8.59810	+	7.35342i	−0.438770	+	0.375253i
$385$	14.4490	−	11.7924i	0.736389	−	0.600995i
$386$	−0.726467	+	12.2550i	−0.0369762	+	0.623762i
$387$	5.46538	−	11.3490i	0.277821	−	0.576901i
$388$	0.212206	+	0.214863i	0.0107731	+	0.0109080i
$389$	−15.3648	−	7.39929i	−0.779025	−	0.375159i	0.00172788	−	0.999999i	$-0.499450\pi$
$389$	−15.3648	−	7.39929i	−0.779025	−	0.375159i	−0.780753	+	0.624840i	$0.785164\pi$
$390$	7.05873	+	17.1923i	0.357432	+	0.870567i
$391$	4.69844			0.237610
$392$	19.7514	−	1.37256i	0.997594	−	0.0693248i
$393$	−17.4563			−0.880556
$394$	−4.71249	−	11.4778i	−0.237412	−	0.578243i
$395$	−15.0875	−	7.26576i	−0.759135	−	0.365580i
$396$	3.17318	+	3.21290i	0.159458	+	0.161454i
$397$	16.6744	−	34.6248i	0.836866	−	1.73777i	0.180139	−	0.983641i	$-0.442345\pi$
$397$	16.6744	−	34.6248i	0.836866	−	1.73777i	0.656727	−	0.754128i	$-0.271940\pi$
$398$	0.341287	−	5.75727i	0.0171072	−	0.288586i
$399$	5.65282	+	1.22315i	0.282995	+	0.0612342i
$400$	−14.9921	+	11.6536i	−0.749603	+	0.582681i
$401$	12.4272	+	15.5832i	0.620586	+	0.778190i	0.988427	−	0.151699i	$-0.0484743\pi$
$401$	12.4272	+	15.5832i	0.620586	+	0.778190i	−0.367841	+	0.929889i	$0.619903\pi$
$402$	2.49206	+	0.147728i	0.124293	+	0.00736799i
$403$	−1.32602	−	1.05746i	−0.0660537	−	0.0526761i
$404$	−1.98285	−	5.78179i	−0.0986507	−	0.287655i
$405$	−2.44091	−	1.94656i	−0.121290	−	0.0967255i
$406$	−4.44556	+	1.88424i	−0.220630	+	0.0935134i
$407$	−3.43732	+	2.74117i	−0.170382	+	0.135875i
$408$	1.00998	+	1.86839i	0.0500016	+	0.0924992i
$409$	12.1359	+	2.76994i	0.600082	+	0.136965i	0.511762	−	0.859127i	$-0.328993\pi$
$409$	12.1359	+	2.76994i	0.600082	+	0.136965i	0.0883204	+	0.996092i	$0.471850\pi$
$410$	−1.82260	+	3.27365i	−0.0900118	+	0.161674i
$411$	−20.3128			−1.00195
$412$	−6.76665	+	2.32061i	−0.333369	+	0.114328i
$413$	−18.5941	+	15.1753i	−0.914954	+	0.746729i
$414$	−2.47607	+	8.49521i	−0.121692	+	0.417517i
$415$	21.9259	−	5.00444i	1.07630	−	0.245658i
$416$	22.7754	+	6.94681i	1.11666	+	0.340596i
$417$	−6.20069	−	7.77542i	−0.303649	−	0.380764i
$418$	1.95321	−	6.70131i	0.0955344	−	0.327772i
$419$	−2.95873	−	12.9630i	−0.144543	−	0.633286i	−0.994346	−	0.106185i	$-0.966136\pi$
$419$	−2.95873	−	12.9630i	−0.144543	−	0.633286i	0.849803	−	0.527100i	$-0.176721\pi$
$420$	1.93314	+	16.4068i	0.0943278	+	0.800570i
$421$	0.265489	−	1.16318i	0.0129392	−	0.0566901i	−0.968046	−	0.250772i	$-0.919316\pi$
$421$	0.265489	−	1.16318i	0.0129392	−	0.0566901i	0.980985	+	0.194082i	$0.0621727\pi$
$422$	−17.6640	−	9.83439i	−0.859870	−	0.478730i
$423$	−12.7761			−0.621197
$424$	4.17049	−	23.2311i	0.202537	−	1.12820i
$425$	1.54667	+	3.21168i	0.0750243	+	0.155790i
$426$	2.18676	+	13.1173i	0.105949	+	0.635534i
$427$	−26.8707	+	0.303801i	−1.30037	+	0.0147020i
$428$	2.76992	−	23.2812i	0.133889	−	1.12534i
$429$	2.11483	−	9.26569i	0.102105	−	0.447352i
$430$	−21.1235	−	51.4486i	−1.01866	−	2.48107i
$431$	−6.88673	−	14.3004i	−0.331722	−	0.688828i	0.666679	−	0.745345i	$-0.267715\pi$
$431$	−6.88673	−	14.3004i	−0.331722	−	0.688828i	−0.998402	+	0.0565163i	$0.982001\pi$
$432$	−3.91048	+	0.841501i	−0.188143	+	0.0404867i
$433$	−6.92016	+	14.3699i	−0.332562	+	0.690571i	−0.998460	−	0.0554708i	$-0.982334\pi$
$433$	−6.92016	+	14.3699i	−0.332562	+	0.690571i	0.665899	+	0.746042i	$0.268048\pi$
$434$	−0.882465	−	1.22237i	−0.0423597	−	0.0586755i
$435$	−1.74804	−	3.62984i	−0.0838121	−	0.174038i
$436$	−4.11129	−	38.6479i	−0.196895	−	1.85090i
$437$	13.3349	−	3.04360i	0.637894	−	0.145595i
$438$	5.35957	+	7.60360i	0.256090	+	0.363314i
$439$	−10.0216	+	12.5666i	−0.478303	+	0.599773i	−0.961182	−	0.275914i	$-0.911020\pi$
$439$	−10.0216	+	12.5666i	−0.478303	+	0.599773i	0.482879	+	0.875687i	$0.339591\pi$
$440$	19.9162	−	0.932147i	0.949467	−	0.0444384i
$441$	6.37384	+	2.89382i	0.303516	+	0.137801i
$442$	2.17440	−	3.90555i	0.103426	−	0.185768i
$443$	6.44100	+	5.13653i	0.306021	+	0.244044i	0.764444	−	0.644691i	$-0.223014\pi$
$443$	6.44100	+	5.13653i	0.306021	+	0.244044i	−0.458422	+	0.888735i	$0.651585\pi$
$444$	−0.411953	−	3.87254i	−0.0195504	−	0.183783i
$445$	−11.0566	−	48.4419i	−0.524131	−	2.29637i
$446$	−17.5461	+	12.3678i	−0.830834	+	0.585632i
$447$	−15.0539	+	7.24956i	−0.712023	+	0.342892i
$448$	17.8385	+	11.3925i	0.842788	+	0.538246i
$449$	−5.20166	−	2.50499i	−0.245482	−	0.118218i	0.307098	−	0.951678i	$-0.400642\pi$
$449$	−5.20166	−	2.50499i	−0.245482	−	0.118218i	−0.552579	+	0.833460i	$0.686356\pi$
$450$	−6.62211	+	1.10396i	−0.312169	+	0.0520413i
$451$	1.72630	−	0.831342i	0.0812883	−	0.0391464i
$452$	38.6682	+	4.60061i	1.81880	+	0.216395i
$453$	2.98349	+	0.680962i	0.140177	+	0.0319944i
$454$	3.63954	+	8.86451i	0.170812	+	0.416032i
$455$	26.9369	−	21.9842i	1.26282	−	1.03064i
$456$	4.07681	+	4.64853i	0.190914	+	0.217687i
$457$	22.2625	−	10.7211i	1.04140	−	0.501510i	0.166612	−	0.986023i	$-0.446717\pi$
$457$	22.2625	−	10.7211i	1.04140	−	0.501510i	0.874784	+	0.484513i	$0.161003\pi$
$458$	3.68690	−	4.09990i	0.172277	−	0.191576i
$459$			0.750912i			0.0350496i
$460$	20.5798	+	33.2094i	0.959540	+	1.54840i
$461$	8.13931	+	1.85774i	0.379086	+	0.0865238i	0.407818	−	0.913063i	$-0.366290\pi$
$461$	8.13931	+	1.85774i	0.379086	+	0.0865238i	−0.0287322	+	0.999587i	$0.509147\pi$
$462$	4.02580	−	7.42726i	0.187297	−	0.345547i
$463$	28.8224	−	6.57852i	1.33949	−	0.305730i	0.508042	−	0.861332i	$-0.330369\pi$
$463$	28.8224	−	6.57852i	1.33949	−	0.305730i	0.831448	+	0.555602i	$0.187512\pi$
$464$	−5.01768	−	1.21112i	−0.232940	−	0.0562247i
$465$	0.983515	−	0.784327i	0.0456094	−	0.0363723i
$466$	12.4345	−	2.07294i	0.576017	−	0.0960270i
$467$	−3.83599	−	16.8066i	−0.177509	−	0.777716i	−0.982775	−	0.184804i	$-0.940835\pi$
$467$	−3.83599	−	16.8066i	−0.177509	−	0.777716i	0.805267	−	0.592913i	$-0.202022\pi$
$468$	5.91568	+	5.98974i	0.273452	+	0.276876i
$469$	−1.09067	−	4.54127i	−0.0503626	−	0.209696i
$470$	−37.7191	+	41.9444i	−1.73985	+	1.93475i
$471$		−	17.6558i		−	0.813538i
$472$	−25.6297	+	1.19956i	−1.17970	+	0.0552141i
$473$	−6.32871	+	27.7279i	−0.290994	+	1.27493i
$474$	−7.57220	−	0.448875i	−0.347803	−	0.0206175i
$475$	6.47017	+	8.11334i	0.296872	+	0.372265i
$476$	2.79533	−	2.82391i	0.128124	−	0.129434i
$477$	5.20285	−	6.52417i	0.238222	−	0.298721i
$478$	−0.665445	+	0.739988i	−0.0304368	+	0.0338463i
$479$	−4.88805	+	6.12943i	−0.223341	+	0.280061i	−0.880860	−	0.473378i	$-0.843035\pi$
$479$	−4.88805	+	6.12943i	−0.223341	+	0.280061i	0.657519	+	0.753438i	$0.271606\pi$
$480$	−8.78227	+	15.3226i	−0.400854	+	0.699376i
$481$	−6.40813	+	5.11031i	−0.292185	+	0.233010i
$482$	17.1215	+	24.2903i	0.779864	+	1.10639i
$483$	16.5533	−	0.187152i	0.753203	−	0.00851573i
$484$	9.95557	+	6.34222i	0.452526	+	0.288283i
$485$	0.424727	+	0.204538i	0.0192859	+	0.00928758i
$486$	−1.35772	−	0.395729i	−0.0615873	−	0.0179506i
$487$	0.641610	−	1.33232i	0.0290741	−	0.0603731i	−0.885926	−	0.463827i	$-0.846476\pi$
$487$	0.641610	−	1.33232i	0.0290741	−	0.0603731i	0.915000	+	0.403454i	$0.132190\pi$
$488$	−23.2732	−	16.8419i	−1.05353	−	0.762395i
$489$		−	15.7656i		−	0.712946i
$490$	28.3180	−	12.3820i	1.27928	−	0.559362i
$491$			11.9603i			0.539761i	0.962894	+	0.269880i	$0.0869841\pi$
$491$			11.9603i			0.539761i	−0.962894	+	0.269880i	$0.913016\pi$
$492$	−0.200516	+	1.68534i	−0.00903996	+	0.0759809i
$493$	−0.420437	+	0.873047i	−0.0189356	+	0.0393201i
$494$	3.64132	−	12.4931i	0.163831	−	0.562091i
$495$	6.35106	+	3.05851i	0.285459	+	0.137470i
$496$	0.0200504	−	1.61159i	0.000900288	−	0.0723626i
$497$	22.2916	−	11.0472i	0.999914	−	0.495536i
$498$	8.32668	−	5.86925i	0.373128	−	0.263007i
$499$	−28.2478	+	22.5269i	−1.26455	+	1.00844i	−0.265530	+	0.964103i	$0.585547\pi$
$499$	−28.2478	+	22.5269i	−1.26455	+	1.00844i	−0.999017	+	0.0443397i	$0.985882\pi$
$500$	0.848243	−	1.33151i	0.0379346	−	0.0595470i
$501$	−0.122752	+	0.153926i	−0.00548415	+	0.00687690i
$502$	25.9438	+	23.3303i	1.15793	+	1.04128i
$503$	13.9354	−	17.4744i	0.621347	−	0.779144i	−0.367186	−	0.930147i	$-0.619679\pi$
$503$	13.9354	−	17.4744i	0.621347	−	0.779144i	0.988533	+	0.151003i	$0.0482503\pi$
$504$	3.63275	+	6.54241i	0.161816	+	0.291422i
$505$	−5.94904	−	7.45985i	−0.264729	−	0.331959i
$506$	1.18228	−	19.9441i	0.0525585	−	0.886625i
$507$	1.04987	−	4.59976i	0.0466261	−	0.204283i
$508$	−16.9815	+	10.5234i	−0.753431	+	0.466901i
$509$		−	39.3395i		−	1.74369i	−0.489778	−	0.871847i	$-0.662922\pi$
$509$		−	39.3395i		−	1.74369i	0.489778	−	0.871847i	$-0.337078\pi$
$510$	2.46526	+	2.21692i	0.109164	+	0.0981669i
$511$	10.6965	−	13.7286i	0.473186	−	0.607316i
$512$	8.07066	+	21.1392i	0.356676	+	0.934228i
$513$	0.486433	+	2.13120i	0.0214766	+	0.0940949i
$514$	2.70825	+	16.2454i	0.119456	+	0.716554i
$515$	−8.73055	+	6.96238i	−0.384714	+	0.306799i
$516$	−17.7029	−	17.9245i	−0.779325	−	0.789081i
$517$	28.1235	−	6.41901i	1.23687	−	0.282308i
$518$	−6.70807	+	2.84320i	−0.294736	+	0.124923i
$519$	−23.6429	−	5.39634i	−1.03781	−	0.236873i
$520$	37.1293	−	1.73778i	1.62823	−	0.0762067i
$521$		−	33.0548i		−	1.44816i	−0.689718	−	0.724078i	$-0.742266\pi$
$521$		−	33.0548i		−	1.44816i	0.689718	−	0.724078i	$-0.257734\pi$
$522$	−1.35698	−	1.22028i	−0.0593934	−	0.0534104i
$523$	29.3529	−	14.1356i	1.28351	−	0.618107i	0.337222	−	0.941425i	$-0.390513\pi$
$523$	29.3529	−	14.1356i	1.28351	−	0.618107i	0.946290	+	0.323318i	$0.104798\pi$
$524$	−11.7357	+	32.8811i	−0.512676	+	1.43642i
$525$	5.57708	+	11.2537i	0.243404	+	0.491150i
$526$	−21.6771	+	8.90005i	−0.945165	+	0.388061i
$527$	−0.294978	−	0.0673269i	−0.0128495	−	0.00293281i
$528$	8.18517	−	3.81707i	0.356214	−	0.166117i
$529$	14.5504	−	7.00711i	0.632627	−	0.304657i
$530$	−6.05859	−	36.3424i	−0.263168	−	1.57861i
$531$	−8.17303	−	3.93592i	−0.354679	−	0.170805i
$532$	6.10428	−	9.82547i	0.264654	−	0.425988i
$533$	3.21830	−	1.54985i	0.139400	−	0.0671316i
$534$	−12.9672	−	18.3966i	−0.561146	−	0.796097i
$535$	−8.14398	−	35.6811i	−0.352095	−	1.54263i
$536$	1.95364	−	4.59478i	0.0843846	−	0.198464i
$537$	−7.21914	−	5.75707i	−0.311529	−	0.248436i
$538$	−10.9086	−	6.07333i	−0.470303	−	0.261840i
$539$	−15.4843	−	3.16767i	−0.666958	−	0.136441i
$540$	−5.30758	+	3.28910i	−0.228402	+	0.141541i
$541$	−22.5653	+	28.2959i	−0.970156	+	1.21654i	0.00611428	+	0.999981i	$0.498054\pi$
$541$	−22.5653	+	28.2959i	−0.970156	+	1.21654i	−0.976270	+	0.216556i	$0.930518\pi$
$542$	14.4330	−	10.1734i	0.619951	−	0.436986i
$543$	4.04192	−	0.922541i	0.173455	−	0.0395900i
$544$	4.19834	−	0.646326i	0.180002	−	0.0277110i
$545$	−26.3240	−	54.6624i	−1.12760	−	2.34148i
$546$	7.50520	−	13.8465i	0.321193	−	0.592574i
$547$	−19.0714	+	39.6022i	−0.815435	+	1.69327i	−0.0995684	+	0.995031i	$0.531746\pi$
$547$	−19.0714	+	39.6022i	−0.815435	+	1.69327i	−0.715866	+	0.698237i	$0.753968\pi$
$548$	−13.6560	+	38.2615i	−0.583356	+	1.63445i
$549$	−4.40688	−	9.15098i	−0.188081	−	0.390554i
$550$	14.0223	−	5.75719i	0.597912	−	0.245488i
$551$	−0.627714	+	2.75020i	−0.0267415	+	0.117162i
$552$	14.3371	+	10.3752i	0.610229	+	0.441598i
$553$	3.31404	+	13.7988i	0.140927	+	0.586783i
$554$	33.4144	−	5.57046i	1.41964	−	0.236666i
$555$	−2.63768	−	5.47720i	−0.111963	−	0.232494i
$556$	−18.8146	+	6.45243i	−0.797917	+	0.273644i
$557$	8.18944			0.346998			0.173499	−	0.984834i	$-0.444493\pi$
$557$	8.18944			0.346998			0.173499	+	0.984834i	$0.444493\pi$
$558$	0.277186	−	0.497867i	0.0117342	−	0.0210764i
$559$	−11.7985	+	51.6925i	−0.499022	+	2.18636i
$560$	32.2038	+	7.38879i	1.36086	+	0.312233i
$561$	−0.377275	−	1.65295i	−0.0159285	−	0.0697875i
$562$	28.9578	+	8.44023i	1.22151	+	0.356029i
$563$	8.93422	+	11.2032i	0.376533	+	0.472157i	0.933603	−	0.358308i	$-0.116646\pi$
$563$	8.93422	+	11.2032i	0.376533	+	0.472157i	−0.557071	+	0.830465i	$0.688075\pi$
$564$	−8.58925	+	24.0654i	−0.361673	+	1.01334i
$565$	59.2635	−	13.5265i	2.49323	−	0.569064i
$566$	0.486296	+	0.141739i	0.0204405	+	0.00595773i
$567$	0.0299110	+	2.64558i	0.00125614	+	0.111104i
$568$	26.1781	+	4.69955i	1.09841	+	0.197189i
$569$	−2.68987			−0.112765			−0.0563826	−	0.998409i	$-0.517957\pi$
$569$	−2.68987			−0.112765			−0.0563826	+	0.998409i	$0.517957\pi$
$570$	8.43288	+	4.69499i	0.353215	+	0.196651i
$571$	8.17051	+	1.86487i	0.341925	+	0.0780422i	0.390035	−	0.920800i	$-0.372463\pi$
$571$	8.17051	+	1.86487i	0.341925	+	0.0780422i	−0.0481102	+	0.998842i	$0.515320\pi$
$572$	−16.0313	−	10.2128i	−0.670302	−	0.427017i
$573$	6.75145	−	5.38411i	0.282046	−	0.224924i
$574$	3.12589	−	0.557504i	0.130472	−	0.0232698i
$575$	23.2226	+	18.5194i	0.968451	+	0.772314i
$576$	−1.04390	+	7.93160i	−0.0434959	+	0.330483i
$577$	−28.7603	−	22.9356i	−1.19731	−	0.954821i	−0.197631	−	0.980276i	$-0.563325\pi$
$577$	−28.7603	−	22.9356i	−1.19731	−	0.954821i	−0.999676	+	0.0254557i	$0.991896\pi$
$578$	−1.37549	+	23.2035i	−0.0572127	+	0.965137i
$579$	5.41238	+	6.78691i	0.224931	+	0.282055i
$580$	−8.01243	+	0.852346i	−0.332698	+	0.0353918i
$581$	−15.0341	−	11.7137i	−0.623721	−	0.485967i
$582$	0.213164	+	0.0126362i	0.00883594	+	0.000523789i
$583$	−8.17491	+	16.9754i	−0.338570	+	0.703048i
$584$	17.9255	−	4.98359i	0.741762	−	0.206222i
$585$	11.8401	+	5.70191i	0.489530	+	0.235745i
$586$	30.4324	−	12.4948i	1.25715	−	0.516154i
$587$	−17.7570			−0.732910			−0.366455	−	0.930436i	$-0.619429\pi$
$587$	−17.7570			−0.732910			−0.366455	+	0.930436i	$0.619429\pi$
$588$	9.73591	−	10.0604i	0.401502	−	0.414885i
$589$	−0.880807			−0.0362930
$590$	−37.0510	+	15.2122i	−1.52537	+	0.626276i
$591$	−7.90462	−	3.80666i	−0.325152	−	0.156585i
$592$	−7.57136	−	1.82750i	−0.311181	−	0.0751098i
$593$	8.09174	−	16.8027i	0.332288	−	0.690003i	−0.666153	−	0.745815i	$-0.732060\pi$
$593$	8.09174	−	16.8027i	0.332288	−	0.690003i	0.998441	+	0.0558118i	$0.0177747\pi$
$594$	3.18750	+	0.188953i	0.130785	+	0.00775284i
$595$	2.62788	−	5.61846i	0.107733	−	0.230334i
$596$	3.53489	+	33.2296i	0.144795	+	1.36114i
$597$	−2.54269	−	3.18843i	−0.104065	−	0.130494i
$598$	2.20409	−	37.1814i	0.0901319	−	1.52046i
$599$	15.6722	+	12.4981i	0.640348	+	0.510661i	0.888985	−	0.457936i	$-0.151411\pi$
$599$	15.6722	+	12.4981i	0.640348	+	0.510661i	−0.248637	+	0.968597i	$0.579983\pi$
$600$	−2.37252	+	13.2157i	−0.0968576	+	0.539530i
$601$	−29.9587	−	23.8913i	−1.22204	−	0.974546i	−0.222043	−	0.975037i	$-0.571272\pi$
$601$	−29.9587	−	23.8913i	−1.22204	−	0.974546i	−1.00000		0.000490558i	$0.999844\pi$
$602$	−22.4595	+	41.4360i	−0.915383	+	1.68881i
$603$	1.38012	−	1.10061i	0.0562030	−	0.0448204i
$604$	3.28844	−	5.16196i	0.133805	−	0.210037i
$605$	17.9645	+	4.10028i	0.730361	+	0.166700i
$606$	−3.77627	−	2.10243i	−0.153400	−	0.0854053i
$607$	−12.5819			−0.510682			−0.255341	−	0.966851i	$-0.582188\pi$
$607$	−12.5819			−0.510682			−0.255341	+	0.966851i	$0.582188\pi$
$608$	11.4969	−	4.55401i	0.466259	−	0.184690i
$609$	−1.44649	+	3.09263i	−0.0586148	+	0.125320i
$610$	−43.0533	−	12.5486i	−1.74318	−	0.508078i
$611$	52.4301	−	11.9668i	2.12109	−	0.484126i
$612$	1.41443	+	0.504829i	0.0571751	+	0.0204065i
$613$	5.77642	+	7.24340i	0.233307	+	0.292558i	0.884679	−	0.466201i	$-0.154378\pi$
$613$	5.77642	+	7.24340i	0.233307	+	0.292558i	−0.651372	+	0.758759i	$0.725806\pi$
$614$	41.1720	+	12.0002i	1.66156	+	0.484290i
$615$	0.589548	+	2.58298i	0.0237729	+	0.104156i
$616$	−11.2836	−	12.5763i	−0.454631	−	0.506715i
$617$	3.90667	−	17.1162i	0.157277	−	0.689073i	−0.833381	−	0.552699i	$-0.813598\pi$
$617$	3.90667	−	17.1162i	0.157277	−	0.689073i	0.990657	−	0.136374i	$-0.0435450\pi$
$618$	−2.46055	+	4.41951i	−0.0989779	+	0.177779i
$619$	−19.2221			−0.772600			−0.386300	−	0.922373i	$-0.626247\pi$
$619$	−19.2221			−0.772600			−0.386300	+	0.922373i	$0.626247\pi$
$620$	−0.816170	−	2.37986i	−0.0327782	−	0.0955776i
$621$	2.71480	+	5.63734i	0.108941	+	0.226219i
$622$	7.99002	−	1.33201i	0.320371	−	0.0534085i
$623$	−25.8797	+	33.2156i	−1.03685	+	1.33076i
$624$	15.2594	−	7.11607i	0.610866	−	0.284871i
$625$	5.83011	−	25.5434i	0.233204	−	1.02173i
$626$	−14.9950	+	6.15658i	−0.599322	+	0.246066i
$627$	−2.14153	−	4.44692i	−0.0855243	−	0.177593i
$628$	−33.2569	−	11.8698i	−1.32709	−	0.473656i
$629$	−0.634413	+	1.31737i	−0.0252957	+	0.0525271i
$630$	8.77381	+	7.71236i	0.349557	+	0.307268i
$631$	7.16902	+	14.8866i	0.285394	+	0.592627i	0.993546	−	0.113433i	$-0.0361848\pi$
$631$	7.16902	+	14.8866i	0.285394	+	0.592627i	−0.708151	+	0.706061i	$0.750471\pi$
$632$	−5.93621	+	13.9614i	−0.236130	+	0.555354i
$633$	−13.9372	+	3.18108i	−0.553956	+	0.126437i
$634$	6.46617	−	4.55782i	0.256804	−	0.181014i
$635$	−19.4440	+	24.3820i	−0.771612	+	0.967571i
$636$	−8.79125	−	14.1863i	−0.348596	−	0.562524i
$637$	−28.8671	−	5.90542i	−1.14376	−	0.233981i
$638$	3.60015	+	2.00438i	0.142531	+	0.0793541i
$639$	7.35181	+	5.86287i	0.290833	+	0.231932i
$640$	22.9577	+	26.8436i	0.907483	+	1.06109i
$641$	−3.60571	−	15.7976i	−0.142417	−	0.623969i	−0.994870	−	0.101165i	$-0.967743\pi$
$641$	−3.60571	−	15.7976i	−0.142417	−	0.623969i	0.852453	−	0.522804i	$-0.175114\pi$
$642$	−9.55133	−	13.5504i	−0.376961	−	0.534793i
$643$	14.2270	−	6.85134i	0.561057	−	0.270191i	−0.131788	−	0.991278i	$-0.542072\pi$
$643$	14.2270	−	6.85134i	0.561057	−	0.270191i	0.692844	+	0.721087i	$0.256357\pi$
$644$	10.7761	−	31.3060i	0.424637	−	1.23363i
$645$	−35.4320	−	17.0631i	−1.39513	−	0.671861i
$646$	−0.381735	−	2.28983i	−0.0150192	−	0.0900923i
$647$	26.0269	−	12.5339i	1.02322	−	0.492758i	0.154466	−	0.987998i	$-0.450634\pi$
$647$	26.0269	−	12.5339i	1.02322	−	0.492758i	0.868756	+	0.495240i	$0.164920\pi$
$648$	−1.65818	+	2.29138i	−0.0651395	+	0.0900140i
$649$	19.9684	+	4.55766i	0.783829	+	0.178904i
$650$	26.1414	−	10.7330i	1.02535	−	0.420983i
$651$	−1.04194	−	0.225453i	−0.0408367	−	0.00883622i
$652$	−29.6965	−	10.5990i	−1.16300	−	0.415090i
$653$	15.7832	−	7.60080i	0.617645	−	0.297442i	−0.0987766	−	0.995110i	$-0.531493\pi$
$653$	15.7832	−	7.60080i	0.617645	−	0.297442i	0.716422	+	0.697667i	$0.245779\pi$
$654$	−20.4350	−	18.3765i	−0.799071	−	0.718576i
$655$			54.4995i			2.12947i
$656$	3.03973	+	1.51073i	0.118682	+	0.0589840i
$657$	6.41306	+	1.46374i	0.250197	+	0.0571059i
$658$	47.7491	+	2.28915i	1.86145	+	0.0892403i
$659$	−29.7658	+	6.79385i	−1.15951	+	0.264651i	−0.758656	−	0.651491i	$-0.774144\pi$
$659$	−29.7658	+	6.79385i	−1.15951	+	0.264651i	−0.400854	+	0.916142i	$0.631287\pi$
$660$	10.0308	−	9.90680i	0.390449	−	0.385622i
$661$	12.3670	−	9.86231i	0.481019	−	0.383600i	−0.352746	−	0.935719i	$-0.614752\pi$
$661$	12.3670	−	9.86231i	0.481019	−	0.383600i	0.833765	+	0.552119i	$0.186181\pi$
$662$	5.62443	+	33.7381i	0.218600	+	1.31127i
$663$	−0.703344	−	3.08155i	−0.0273156	−	0.119678i
$664$	−5.45751	−	19.6301i	−0.211793	−	0.761797i
$665$	3.81874	−	17.6484i	0.148084	−	0.684374i
$666$	−2.04760	−	1.84133i	−0.0793428	−	0.0713501i
$667$			8.07427i			0.312637i
$668$	0.207414	+	0.334700i	0.00802507	+	0.0129500i
$669$	−3.37774	+	14.7988i	−0.130591	+	0.572156i
$670$	0.461212	−	7.78032i	0.0178182	−	0.300580i
$671$	14.2983	+	17.9295i	0.551980	+	0.692161i
$672$	14.7657	−	2.44434i	0.569598	−	0.0942925i
$673$	−15.1530	+	19.0013i	−0.584105	+	0.732445i	−0.982807	−	0.184636i	$-0.940889\pi$
$673$	−15.1530	+	19.0013i	−0.584105	+	0.732445i	0.398702	+	0.917081i	$0.369461\pi$
$674$	−8.82053	−	7.93198i	−0.339754	−	0.305529i
$675$	−2.95981	+	3.71148i	−0.113923	+	0.142855i
$676$	−7.95839	−	5.06991i	−0.306092	−	0.194997i
$677$	4.81249	−	3.83783i	0.184959	−	0.147500i	−0.526633	−	0.850093i	$-0.676546\pi$
$677$	4.81249	−	3.83783i	0.184959	−	0.147500i	0.711592	+	0.702593i	$0.247974\pi$
$678$	22.5062	−	15.8640i	0.864346	−	0.609253i
$679$	−0.0932932	−	0.388448i	−0.00358027	−	0.0149073i
$680$	5.83320	−	3.15321i	0.223693	−	0.120920i
$681$	6.10488	+	2.93996i	0.233940	+	0.112659i
$682$	−0.360018	+	1.23520i	−0.0137858	+	0.0472981i
$683$	19.2024	−	39.8742i	0.734760	−	1.52574i	−0.111964	−	0.993712i	$-0.535714\pi$
$683$	19.2024	−	39.8742i	0.734760	−	1.52574i	0.846724	−	0.532032i	$-0.178571\pi$
$684$	4.34140	+	0.516526i	0.165998	+	0.0197499i
$685$			63.4173i			2.42305i
$686$	−23.3029	−	11.9573i	−0.889707	−	0.456531i
$687$		−	3.89887i		−	0.148751i
$688$	−45.6643	+	21.2951i	−1.74094	+	0.811867i
$689$	−15.2403	+	31.6468i	−0.580609	+	1.20565i
$690$	26.5224	+	7.73039i	1.00969	+	0.294291i
$691$	−33.6567	−	16.2082i	−1.28036	−	0.616589i	−0.334877	−	0.942262i	$-0.608695\pi$
$691$	−33.6567	−	16.2082i	−1.28036	−	0.616589i	−0.945482	+	0.325673i	$0.894409\pi$
$692$	−26.0595	+	40.9064i	−0.990634	+	1.55503i
$693$	−1.39504	−	5.80857i	−0.0529932	−	0.220649i
$694$	−0.127167	−	0.180411i	−0.00482719	−	0.00684832i
$695$	−24.2752	+	19.3588i	−0.920811	+	0.734323i
$696$	−3.21083	+	1.73565i	−0.121706	+	0.0657898i
$697$	0.397308	−	0.498209i	0.0150491	−	0.0188710i
$698$	27.7720	−	30.8830i	1.05118	−	1.16894i
$699$	5.55771	−	6.96914i	0.210212	−	0.263597i
$700$	24.9470	−	2.93940i	0.942910	−	0.111099i
$701$	8.08209	+	10.1346i	0.305256	+	0.382779i	0.910672	−	0.413130i	$-0.135565\pi$
$701$	8.08209	+	10.1346i	0.305256	+	0.382779i	−0.605416	+	0.795910i	$0.706993\pi$
$702$	5.94239	+	0.352261i	0.224281	+	0.0132952i
$703$	−0.947181	+	4.14987i	−0.0357236	+	0.156515i
$704$	−1.68712	−	17.9839i	−0.0635856	−	0.677795i
$705$			39.8877i			1.50226i
$706$	−0.272634	+	0.303175i	−0.0102607	+	0.0114101i
$707$	−1.71004	+	7.90299i	−0.0643127	+	0.297222i
$708$	−12.9084	+	12.7488i	−0.485128	+	0.479130i
$709$	−6.05826	−	26.5430i	−0.227523	−	0.996842i	−0.951652	−	0.307178i	$-0.900615\pi$
$709$	−6.05826	−	26.5430i	−0.227523	−	0.996842i	0.724129	−	0.689664i	$-0.242242\pi$
$710$	40.9527	−	6.82716i	1.53693	−	0.256219i
$711$	−4.19355	+	3.34424i	−0.157270	+	0.125419i
$712$	−43.3698	+	12.0575i	−1.62535	+	0.451876i
$713$	−2.45791	+	0.561001i	−0.0920493	+	0.0210097i
$714$	0.134544	−	2.80643i	0.00503517	−	0.105028i
$715$	−28.9279	−	6.60261i	−1.08184	−	0.246923i
$716$	−15.6975	+	9.72772i	−0.586643	+	0.363542i
$717$			0.703705i			0.0262803i
$718$	−11.9648	+	13.3051i	−0.446521	+	0.496540i
$719$	21.7925	−	10.4947i	0.812724	−	0.391387i	0.0191165	−	0.999817i	$-0.493915\pi$
$719$	21.7925	−	10.4947i	0.812724	−	0.391387i	0.793608	+	0.608430i	$0.208200\pi$
$720$	2.62720	+	12.2087i	0.0979101	+	0.454991i
$721$	9.24917	+	2.00133i	0.344457	+	0.0745333i
$722$	7.63871	+	18.6049i	0.284284	+	0.692404i
$723$	20.4870	+	4.67602i	0.761919	+	0.173903i
$724$	0.979614	−	8.23365i	0.0364070	−	0.306001i
$725$	−5.51928	+	2.65795i	−0.204981	+	0.0987137i
$726$	8.23315	−	1.37254i	0.305561	−	0.0509396i
$727$	−5.90979	−	2.84601i	−0.219182	−	0.105552i	0.321071	−	0.947055i	$-0.395957\pi$
$727$	−5.90979	−	2.84601i	−0.219182	−	0.105552i	−0.540253	+	0.841503i	$0.681671\pi$
$728$	−21.0358	−	23.4458i	−0.779640	−	0.868958i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	23.7388	−	16.7328i	0.878612	−	0.619309i
$731$	2.10478	+	9.22164i	0.0778481	+	0.341075i
$732$	−20.1997	+	2.14880i	−0.746602	+	0.0794220i
$733$	−7.72035	−	6.15677i	−0.285158	−	0.227406i	0.470456	−	0.882424i	$-0.344090\pi$
$733$	−7.72035	−	6.15677i	−0.285158	−	0.227406i	−0.755613	+	0.655018i	$0.772661\pi$
$734$	3.43324	−	6.16660i	0.126723	−	0.227613i
$735$	9.03463	−	19.8994i	0.333247	−	0.734001i
$736$	29.1816	−	20.0306i	1.07565	−	0.738337i
$737$	−2.48503	+	3.11613i	−0.0915374	+	0.114784i
$738$	0.691427	+	0.980925i	0.0254518	+	0.0361083i
$739$	33.7183	−	7.69597i	1.24035	−	0.283101i	0.448478	−	0.893794i	$-0.351966\pi$
$739$	33.7183	−	7.69597i	1.24035	−	0.283101i	0.791868	+	0.610693i	$0.209109\pi$
$740$	−12.0903	+	1.28614i	−0.444447	+	0.0472793i
$741$	−3.99240	−	8.29030i	−0.146664	−	0.304552i
$742$	−20.6139	+	23.4510i	−0.756760	+	0.860912i
$743$	18.4038	−	38.2158i	0.675169	−	1.40200i	−0.228403	−	0.973567i	$-0.573350\pi$
$743$	18.4038	−	38.2158i	0.675169	−	1.40200i	0.903572	−	0.428436i	$-0.140935\pi$
$744$	−0.751444	−	0.856824i	−0.0275493	−	0.0314127i
$745$	22.6334	+	46.9988i	0.829225	+	1.72190i
$746$	13.1325	+	31.9856i	0.480814	+	1.17108i
$747$	1.60294	−	7.02292i	0.0586484	−	0.256955i
$748$	−3.36716	−	0.400614i	−0.123116	−	0.0146479i
$749$	−19.0623	+	24.4658i	−0.696523	+	0.893961i
$750$	−0.183570	−	1.10115i	−0.00670304	−	0.0402082i
$751$	11.0550	+	22.9560i	0.403404	+	0.837677i	0.999398	+	0.0346883i	$0.0110439\pi$
$751$	11.0550	+	22.9560i	0.403404	+	0.837677i	−0.595994	+	0.802989i	$0.703242\pi$
$752$	39.5557	+	32.3578i	1.44245	+	1.17997i
$753$	24.6717			0.899087
$754$	6.71168	+	3.73671i	0.244425	+	0.136083i
$755$	2.12599	−	9.31459i	0.0773728	−	0.338993i
$756$	5.00338	+	1.72225i	0.181971	+	0.0626377i
$757$	−7.73434	−	33.8864i	−0.281109	−	1.23162i	−0.896374	−	0.443300i	$-0.853808\pi$
$757$	−7.73434	−	33.8864i	−0.281109	−	1.23162i	0.615264	−	0.788321i	$-0.289049\pi$
$758$	9.19412	−	31.5443i	0.333945	−	1.14574i
$759$	−8.80828	−	11.0452i	−0.319720	−	0.400917i
$760$	14.5129	−	12.7280i	0.526438	−	0.461692i
$761$	−42.2373	+	9.64038i	−1.53110	+	0.349464i	−0.903334	−	0.428938i	$-0.858888\pi$
$761$	−42.2373	+	9.64038i	−1.53110	+	0.349464i	−0.627766	+	0.778402i	$0.716031\pi$
$762$	−3.95290	+	13.5621i	−0.143198	+	0.491303i
$763$	−21.7830	+	46.5724i	−0.788596	+	1.68604i
$764$	−5.60269	−	16.3369i	−0.202698	−	0.591047i
$765$	2.34438			0.0847613
$766$	−10.1198	+	18.1766i	−0.365643	+	0.656748i
$767$	37.2266	+	8.49674i	1.34418	+	0.306799i
$768$	14.2383	+	7.29863i	0.513781	+	0.263367i
$769$	17.3956	−	13.8726i	0.627303	−	0.500257i	−0.257466	−	0.966287i	$-0.582888\pi$
$769$	17.3956	−	13.8726i	0.627303	−	0.500257i	0.884769	+	0.466030i	$0.154316\pi$
$770$	−23.1882	−	12.5687i	−0.835646	−	0.452945i
$771$	9.10503	+	7.26102i	0.327909	+	0.261499i

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537130 - 1.30824i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-1.42298 + 1.40539i) q^{4} +(-1.35460 + 2.81286i) q^{5} +(-0.0836867 + 1.41174i) q^{6} +(2.57260 - 0.617858i) q^{7} +(2.60291 + 1.10673i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.537130 - 1.30824i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-1.42298 + 1.40539i) q^{4} +(-1.35460 + 2.81286i) q^{5} +(-0.0836867 + 1.41174i) q^{6} +(2.57260 - 0.617858i) q^{7} +(2.60291 + 1.10673i) q^{8} +(0.623490 + 0.781831i) q^{9} +(4.40750 + 0.261274i) q^{10} +(-1.76527 - 1.40775i) q^{11} +(1.89184 - 0.648803i) q^{12} +(-3.29095 - 2.62444i) q^{13} +(-2.19013 - 3.03370i) q^{14} +(2.44091 - 1.94656i) q^{15} +(0.0497615 - 3.99969i) q^{16} +(-0.732085 - 0.167094i) q^{17} +(0.687928 - 1.23562i) q^{18} -2.18601 q^{19} +(-2.02559 - 5.90641i) q^{20} +(-2.58591 - 0.559536i) q^{21} +(-0.893502 + 3.06554i) q^{22} +(-6.10010 + 1.39231i) q^{23} +(-1.86495 - 2.12649i) q^{24} +(-2.95981 - 3.71148i) q^{25} +(-1.66574 + 5.71502i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-2.79243 + 4.49470i) q^{28} +(0.287151 - 1.25809i) q^{29} +(-3.85766 - 2.14774i) q^{30} +0.402929 q^{31} +(-5.25928 + 2.08325i) q^{32} +(0.979650 + 2.03426i) q^{33} +(0.174626 + 1.04749i) q^{34} +(-1.74690 + 8.07332i) q^{35} +(-1.98599 - 0.236287i) q^{36} +(0.433292 - 1.89838i) q^{37} +(1.17417 + 2.85983i) q^{38} +(1.82634 + 3.79243i) q^{39} +(-6.63899 + 5.82247i) q^{40} +(-0.368199 + 0.764573i) q^{41} +(0.656960 + 3.68353i) q^{42} +(-5.46538 - 11.3490i) q^{43} +(4.49039 - 0.477678i) q^{44} +(-3.04377 + 0.694720i) q^{45} +(5.09802 + 7.23254i) q^{46} +(-7.96580 + 9.98879i) q^{47} +(-1.78023 + 3.58201i) q^{48} +(6.23650 - 3.17900i) q^{49} +(-3.26571 + 5.86568i) q^{50} +(0.587087 + 0.468186i) q^{51} +(8.37133 - 0.890525i) q^{52} +(-1.85688 - 8.13550i) q^{53} +(-1.15592 + 0.814774i) q^{54} +(6.35106 - 3.05851i) q^{55} +(7.38004 + 1.23893i) q^{56} +(1.96953 + 0.948475i) q^{57} +(-1.80012 + 0.300095i) q^{58} +(-8.17303 + 3.93592i) q^{59} +(-0.737699 + 6.20036i) q^{60} +(-9.90217 - 2.26011i) q^{61} +(-0.216425 - 0.527128i) q^{62} +(2.08705 + 1.62611i) q^{63} +(5.55031 + 5.76143i) q^{64} +(11.8401 - 5.70191i) q^{65} +(2.13511 - 2.37428i) q^{66} -1.76525i q^{67} +(1.27658 - 0.791093i) q^{68} +(6.10010 + 1.39231i) q^{69} +(11.5001 - 2.05106i) q^{70} +(9.16755 - 2.09243i) q^{71} +(0.757616 + 2.72507i) q^{72} +(5.14288 - 4.10131i) q^{73} +(-2.71627 + 0.452825i) q^{74} +(1.05634 + 4.62814i) q^{75} +(3.11066 - 3.07220i) q^{76} +(-5.41111 - 2.53090i) q^{77} +(3.98043 - 4.42632i) q^{78} +5.36375i q^{79} +(11.1832 + 5.55797i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(1.19802 + 0.0710176i) q^{82} +(-4.49133 - 5.63195i) q^{83} +(4.46607 - 2.83800i) q^{84} +(1.46170 - 1.83291i) q^{85} +(-11.9116 + 13.2459i) q^{86} +(-0.804578 + 1.00891i) q^{87} +(-3.03684 - 5.61793i) q^{88} +(-12.4429 + 9.92291i) q^{89} +(2.54376 + 3.60882i) q^{90} +(-10.0878 - 4.71829i) q^{91} +(6.72360 - 10.5542i) q^{92} +(-0.363026 - 0.174824i) q^{93} +(17.3464 + 5.05589i) q^{94} +(2.96118 - 6.14895i) q^{95} +(5.64234 + 0.404971i) q^{96} -0.150995i q^{97} +(-7.50871 - 6.45130i) q^{98} -2.25786i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

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