LMFDB - Embedded newform 546.2.bu.a.197.11

Newspace parameters

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.11
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.a.449.11

$q$-expansion

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.264812 - 1.71169i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.429580 - 0.429580i) q^{5} +(-1.72190 - 0.187229i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.85975 + 0.906550i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.264812 - 1.71169i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.429580 - 0.429580i) q^{5} +(-1.72190 - 0.187229i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.85975 + 0.906550i) q^{9} +(-0.526126 + 0.303759i) q^{10} +(-1.44890 - 0.388232i) q^{11} +(-0.626510 + 1.61477i) q^{12} +(-1.82271 - 3.11091i) q^{13} +1.00000i q^{14} +(-0.621549 + 0.849065i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.50234 + 4.33419i) q^{17} +(0.135502 + 2.99694i) q^{18} +(0.744411 + 2.77818i) q^{19} +(0.157237 + 0.586817i) q^{20} +(0.698806 + 1.58483i) q^{21} +(-0.750007 + 1.29905i) q^{22} +(-2.87235 - 4.97505i) q^{23} +(1.39760 + 1.02310i) q^{24} -4.63092i q^{25} +(-3.47666 + 0.955436i) q^{26} +(2.30902 + 4.65493i) q^{27} +(0.965926 + 0.258819i) q^{28} +(-5.53687 + 3.19672i) q^{29} +(0.659265 + 0.820125i) q^{30} +(2.86572 - 2.86572i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.280846 + 2.58288i) q^{33} +(3.53885 + 3.53885i) q^{34} +(0.526126 + 0.303759i) q^{35} +(2.92989 + 0.644780i) q^{36} +(2.29499 - 8.56502i) q^{37} +2.87618 q^{38} +(-4.84223 + 3.94371i) q^{39} +0.607518 q^{40} +(-0.973141 + 3.63181i) q^{41} +(1.71169 - 0.264812i) q^{42} +(9.35271 + 5.39979i) q^{43} +(1.06067 + 1.06067i) q^{44} +(1.61793 + 0.839056i) q^{45} +(-5.54895 + 1.48684i) q^{46} +(-7.10501 + 7.10501i) q^{47} +(1.34996 - 1.08518i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-4.47313 - 1.19857i) q^{50} +(8.08143 + 3.13549i) q^{51} +(0.0230552 + 3.60548i) q^{52} -7.88465i q^{53} +(5.09394 - 1.02556i) q^{54} +(0.455643 + 0.789196i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.55825 - 2.00989i) q^{57} +(1.65474 + 6.17558i) q^{58} +(-3.35057 - 12.5045i) q^{59} +(0.962810 - 0.424537i) q^{60} +(-0.879168 + 1.52276i) q^{61} +(-2.02637 - 3.50978i) q^{62} +(2.52767 - 1.61582i) q^{63} -1.00000i q^{64} +(-0.553386 + 2.11938i) q^{65} +(2.42218 + 0.939774i) q^{66} +(-10.7168 - 2.87155i) q^{67} +(4.33419 - 2.50234i) q^{68} +(-7.75510 + 6.23401i) q^{69} +(0.429580 - 0.429580i) q^{70} +(5.54815 - 1.48662i) q^{71} +(1.38112 - 2.66318i) q^{72} +(-10.8592 - 10.8592i) q^{73} +(-7.67919 - 4.43358i) q^{74} +(-7.92669 + 1.22632i) q^{75} +(0.744411 - 2.77818i) q^{76} +1.50001 q^{77} +(2.55607 + 5.69794i) q^{78} +3.68438 q^{79} +(0.157237 - 0.586817i) q^{80} +(7.35634 - 5.18501i) q^{81} +(3.25619 + 1.87996i) q^{82} +(5.15594 + 5.15594i) q^{83} +(0.187229 - 1.72190i) q^{84} +(2.93684 - 0.786923i) q^{85} +(7.63646 - 7.63646i) q^{86} +(6.93801 + 8.63087i) q^{87} +(1.29905 - 0.750007i) q^{88} +(-6.57035 - 1.76052i) q^{89} +(1.22922 - 1.34563i) q^{90} +(2.56576 + 2.53316i) q^{91} +5.74469i q^{92} +(-5.66410 - 4.14635i) q^{93} +(5.02400 + 8.70183i) q^{94} +(0.873667 - 1.51324i) q^{95} +(-0.698806 - 1.58483i) q^{96} +(-0.785006 - 2.92968i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(4.49545 - 0.203255i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−0.264812	−	1.71169i	−0.152889	−	0.988243i
$3$	−0.264812	−	1.71169i	−0.152889	−	0.988243i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.429580	−	0.429580i	−0.192114	−	0.192114i	0.604495	−	0.796609i	$-0.293375\pi$
$5$	−0.429580	−	0.429580i	−0.192114	−	0.192114i	−0.796609	+	0.604495i	$0.793375\pi$
$6$	−1.72190	−	0.187229i	−0.702963	−	0.0764359i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.85975	+	0.906550i	−0.953250	+	0.302183i
$10$	−0.526126	+	0.303759i	−0.166376	+	0.0960570i
$11$	−1.44890	−	0.388232i	−0.436860	−	0.117056i	0.0336843	−	0.999433i	$-0.489276\pi$
$11$	−1.44890	−	0.388232i	−0.436860	−	0.117056i	−0.470545	+	0.882376i	$0.655943\pi$
$12$	−0.626510	+	1.61477i	−0.180858	+	0.466144i
$13$	−1.82271	−	3.11091i	−0.505527	−	0.862811i
$13$	−1.82271	−	3.11091i	−0.505527	−	0.862811i
$14$			1.00000i			0.267261i
$15$	−0.621549	+	0.849065i	−0.160483	+	0.219228i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.50234	+	4.33419i	−0.606908	+	1.05119i	0.384839	+	0.922984i	$0.374257\pi$
$17$	−2.50234	+	4.33419i	−0.606908	+	1.05119i	−0.991747	+	0.128211i	$0.959076\pi$
$18$	0.135502	+	2.99694i	0.0319381	+	0.706385i
$19$	0.744411	+	2.77818i	0.170780	+	0.637358i	0.997232	+	0.0743518i	$0.0236888\pi$
$19$	0.744411	+	2.77818i	0.170780	+	0.637358i	−0.826452	+	0.563007i	$0.809645\pi$
$20$	0.157237	+	0.586817i	0.0351593	+	0.131216i
$21$	0.698806	+	1.58483i	0.152492	+	0.345837i
$22$	−0.750007	+	1.29905i	−0.159902	+	0.276958i
$23$	−2.87235	−	4.97505i	−0.598925	−	1.03737i	−0.992980	−	0.118282i	$-0.962261\pi$
$23$	−2.87235	−	4.97505i	−0.598925	−	1.03737i	0.394055	−	0.919087i	$-0.371072\pi$
$24$	1.39760	+	1.02310i	0.285283	+	0.208839i
$25$		−	4.63092i		−	0.926184i
$26$	−3.47666	+	0.955436i	−0.681828	+	0.187376i
$27$	2.30902	+	4.65493i	0.444372	+	0.895842i
$28$	0.965926	+	0.258819i	0.182543	+	0.0489122i
$29$	−5.53687	+	3.19672i	−1.02817	+	0.593615i	−0.916460	−	0.400125i	$-0.868967\pi$
$29$	−5.53687	+	3.19672i	−1.02817	+	0.593615i	−0.111711	+	0.993741i	$0.535633\pi$
$30$	0.659265	+	0.820125i	0.120365	+	0.149734i
$31$	2.86572	−	2.86572i	0.514699	−	0.514699i	−0.401263	−	0.915963i	$-0.631429\pi$
$31$	2.86572	−	2.86572i	0.514699	−	0.514699i	0.915963	+	0.401263i	$0.131429\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.280846	+	2.58288i	−0.0488890	+	0.449621i
$34$	3.53885	+	3.53885i	0.606908	+	0.606908i
$35$	0.526126	+	0.303759i	0.0889315	+	0.0513446i
$36$	2.92989	+	0.644780i	0.488315	+	0.107463i
$37$	2.29499	−	8.56502i	0.377294	−	1.40808i	−0.472670	−	0.881240i	$-0.656710\pi$
$37$	2.29499	−	8.56502i	0.377294	−	1.40808i	0.849964	−	0.526841i	$-0.176624\pi$
$38$	2.87618			0.466579
$39$	−4.84223	+	3.94371i	−0.775377	+	0.631498i
$40$	0.607518			0.0960570
$41$	−0.973141	+	3.63181i	−0.151979	+	0.567194i	0.847366	+	0.531009i	$0.178187\pi$
$41$	−0.973141	+	3.63181i	−0.151979	+	0.567194i	−0.999345	+	0.0361844i	$0.988480\pi$
$42$	1.71169	−	0.264812i	0.264119	−	0.0408613i
$43$	9.35271	+	5.39979i	1.42628	+	0.823460i	0.996824	−	0.0796301i	$-0.0253739\pi$
$43$	9.35271	+	5.39979i	1.42628	+	0.823460i	0.429451	+	0.903090i	$0.358707\pi$
$44$	1.06067	+	1.06067i	0.159902	+	0.159902i
$45$	1.61793	+	0.839056i	0.241186	+	0.125079i
$46$	−5.54895	+	1.48684i	−0.818147	+	0.219222i
$47$	−7.10501	+	7.10501i	−1.03637	+	1.03637i	−0.0370599	+	0.999313i	$0.511799\pi$
$47$	−7.10501	+	7.10501i	−1.03637	+	1.03637i	−0.999313	+	0.0370599i	$0.988201\pi$
$48$	1.34996	−	1.08518i	0.194850	−	0.156632i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	−4.47313	−	1.19857i	−0.632596	−	0.169504i
$51$	8.08143	+	3.13549i	1.13163	+	0.439056i
$52$	0.0230552	+	3.60548i	0.00319718	+	0.499990i
$53$		−	7.88465i		−	1.08304i	−0.840688	−	0.541520i	$-0.817849\pi$
$53$		−	7.88465i		−	1.08304i	0.840688	−	0.541520i	$-0.182151\pi$
$54$	5.09394	−	1.02556i	0.693197	−	0.139561i
$55$	0.455643	+	0.789196i	0.0614389	+	0.106415i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	4.55825	−	2.00989i	0.603755	−	0.266217i
$58$	1.65474	+	6.17558i	0.217278	+	0.810894i
$59$	−3.35057	−	12.5045i	−0.436207	−	1.62795i	−0.738161	−	0.674625i	$-0.764305\pi$
$59$	−3.35057	−	12.5045i	−0.436207	−	1.62795i	0.301954	−	0.953323i	$-0.402361\pi$
$60$	0.962810	−	0.424537i	0.124298	−	0.0548075i
$61$	−0.879168	+	1.52276i	−0.112566	+	0.194970i	−0.916804	−	0.399337i	$-0.869240\pi$
$61$	−0.879168	+	1.52276i	−0.112566	+	0.194970i	0.804238	+	0.594307i	$0.202574\pi$
$62$	−2.02637	−	3.50978i	−0.257350	−	0.445743i
$63$	2.52767	−	1.61582i	0.318457	−	0.203574i
$64$		−	1.00000i		−	0.125000i
$65$	−0.553386	+	2.11938i	−0.0686391	+	0.262877i
$66$	2.42218	+	0.939774i	0.298150	+	0.115678i
$67$	−10.7168	−	2.87155i	−1.30926	−	0.350815i	−0.464316	−	0.885670i	$-0.653700\pi$
$67$	−10.7168	−	2.87155i	−1.30926	−	0.350815i	−0.844944	+	0.534855i	$0.820366\pi$
$68$	4.33419	−	2.50234i	0.525597	−	0.303454i
$69$	−7.75510	+	6.23401i	−0.933604	+	0.750486i
$70$	0.429580	−	0.429580i	0.0513446	−	0.0513446i
$71$	5.54815	−	1.48662i	0.658444	−	0.176430i	0.0859005	−	0.996304i	$-0.472623\pi$
$71$	5.54815	−	1.48662i	0.658444	−	0.176430i	0.572544	+	0.819874i	$0.305957\pi$
$72$	1.38112	−	2.66318i	0.162767	−	0.313858i
$73$	−10.8592	−	10.8592i	−1.27097	−	1.27097i	−0.945580	−	0.325388i	$-0.894505\pi$
$73$	−10.8592	−	10.8592i	−1.27097	−	1.27097i	−0.325388	−	0.945580i	$-0.605495\pi$
$74$	−7.67919	−	4.43358i	−0.892687	−	0.515393i
$75$	−7.92669	+	1.22632i	−0.915296	+	0.141603i
$76$	0.744411	−	2.77818i	0.0853898	−	0.318679i
$77$	1.50001			0.170942
$78$	2.55607	+	5.69794i	0.289418	+	0.645165i
$79$	3.68438			0.414525			0.207262	−	0.978285i	$-0.433545\pi$
$79$	3.68438			0.414525			0.207262	+	0.978285i	$0.433545\pi$
$80$	0.157237	−	0.586817i	0.0175797	−	0.0656082i
$81$	7.35634	−	5.18501i	0.817371	−	0.576112i
$82$	3.25619	+	1.87996i	0.359586	+	0.207607i
$83$	5.15594	+	5.15594i	0.565938	+	0.565938i	0.930988	−	0.365050i	$-0.118948\pi$
$83$	5.15594	+	5.15594i	0.565938	+	0.565938i	−0.365050	+	0.930988i	$0.618948\pi$
$84$	0.187229	−	1.72190i	0.0204284	−	0.187875i
$85$	2.93684	−	0.786923i	0.318545	−	0.0853538i
$86$	7.63646	−	7.63646i	0.823460	−	0.823460i
$87$	6.93801	+	8.63087i	0.743833	+	0.925327i
$88$	1.29905	−	0.750007i	0.138479	−	0.0799510i
$89$	−6.57035	−	1.76052i	−0.696455	−	0.186615i	−0.106813	−	0.994279i	$-0.534065\pi$
$89$	−6.57035	−	1.76052i	−0.696455	−	0.186615i	−0.589642	+	0.807664i	$0.700731\pi$
$90$	1.22922	−	1.34563i	0.129571	−	0.141842i
$91$	2.56576	+	2.53316i	0.268965	+	0.265547i
$92$			5.74469i			0.598925i
$93$	−5.66410	−	4.14635i	−0.587340	−	0.429956i
$94$	5.02400	+	8.70183i	0.518186	+	0.897525i
$95$	0.873667	−	1.51324i	0.0896363	−	0.155255i
$96$	−0.698806	−	1.58483i	−0.0713216	−	0.161751i
$97$	−0.785006	−	2.92968i	−0.0797053	−	0.297464i	0.914554	−	0.404464i	$-0.132542\pi$
$97$	−0.785006	−	2.92968i	−0.0797053	−	0.297464i	−0.994259	+	0.107000i	$0.965875\pi$
$98$	−0.258819	−	0.965926i	−0.0261447	−	0.0975732i
$99$	4.49545	−	0.203255i	0.451810	−	0.0204279i
$100$	−2.31546	+	4.01050i	−0.231546	+	0.401050i
$101$	−2.55267	−	4.42136i	−0.254001	−	0.439942i	0.710623	−	0.703573i	$-0.248413\pi$
$101$	−2.55267	−	4.42136i	−0.254001	−	0.439942i	−0.964624	+	0.263631i	$0.915080\pi$
$102$	5.12028	−	6.99453i	0.506983	−	0.692562i
$103$		−	5.89303i		−	0.580658i	−0.956927	−	0.290329i	$-0.906235\pi$
$103$		−	5.89303i		−	0.580658i	0.956927	−	0.290329i	$-0.0937647\pi$
$104$	3.48859	+	0.910897i	0.342084	+	0.0893208i
$105$	0.380616	−	0.981002i	0.0371443	−	0.0957360i
$106$	−7.61599	−	2.04070i	−0.739730	−	0.198210i
$107$	9.22495	−	5.32603i	0.891810	−	0.514886i	0.0172756	−	0.999851i	$-0.494501\pi$
$107$	9.22495	−	5.32603i	0.891810	−	0.514886i	0.874534	+	0.484964i	$0.161167\pi$
$108$	0.327793	−	5.18580i	0.0315419	−	0.499004i
$109$	−0.363108	+	0.363108i	−0.0347794	+	0.0347794i	−0.724283	−	0.689503i	$-0.757829\pi$
$109$	−0.363108	+	0.363108i	−0.0347794	+	0.0347794i	0.689503	+	0.724283i	$0.257829\pi$
$110$	0.880234	−	0.235858i	0.0839270	−	0.0224882i
$111$	−15.2684	−	1.66019i	−1.44921	−	0.157578i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−13.3023	−	7.68008i	−1.25137	−	0.722481i	−0.279992	−	0.960002i	$-0.590332\pi$
$113$	−13.3023	−	7.68008i	−1.25137	−	0.722481i	−0.971382	+	0.237521i	$0.923665\pi$
$114$	−0.761647	−	4.92313i	−0.0713348	−	0.461093i
$115$	−0.903279	+	3.37108i	−0.0842312	+	0.314355i
$116$	6.39343			0.593615
$117$	8.03267	+	7.24404i	0.742621	+	0.669712i
$118$	−12.9456			−1.19174
$119$	1.29531	−	4.83416i	0.118741	−	0.443147i
$120$	−0.160878	−	1.03988i	−0.0146861	−	0.0949277i
$121$	−7.57769	−	4.37498i	−0.688881	−	0.397725i
$122$	1.24333	+	1.24333i	0.112566	+	0.112566i
$123$	6.47423	+	0.703967i	0.583761	+	0.0634746i
$124$	−3.91465	+	1.04893i	−0.351546	+	0.0941965i
$125$	−4.13725	+	4.13725i	−0.370047	+	0.370047i
$126$	−0.906550	−	2.85975i	−0.0807619	−	0.254767i
$127$	9.14243	−	5.27839i	0.811260	−	0.468381i	−0.0361335	−	0.999347i	$-0.511504\pi$
$127$	9.14243	−	5.27839i	0.811260	−	0.468381i	0.847393	+	0.530966i	$0.178171\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	6.76605	−	17.4388i	0.595717	−	1.53540i
$130$	1.90394	+	1.08307i	0.166986	+	0.0949912i
$131$			12.2294i			1.06848i	0.845331	+	0.534242i	$0.179403\pi$
$131$			12.2294i			1.06848i	−0.845331	+	0.534242i	$0.820597\pi$
$132$	1.53466	−	2.09641i	0.133575	−	0.182469i
$133$	−1.43809	−	2.49085i	−0.124698	−	0.215984i
$134$	−5.54740	+	9.60838i	−0.479222	+	0.830037i
$135$	1.00776	−	2.99158i	0.0867338	−	0.257474i
$136$	−1.29531	−	4.83416i	−0.111072	−	0.414526i
$137$	−4.39879	−	16.4165i	−0.375814	−	1.40256i	−0.852151	−	0.523295i	$-0.824703\pi$
$137$	−4.39879	−	16.4165i	−0.375814	−	1.40256i	0.476337	−	0.879263i	$-0.341964\pi$
$138$	4.01442	+	9.10433i	0.341730	+	0.775012i
$139$	−3.35001	+	5.80239i	−0.284144	+	0.492152i	−0.972401	−	0.233315i	$-0.925043\pi$
$139$	−3.35001	+	5.80239i	−0.284144	+	0.492152i	0.688257	+	0.725467i	$0.258376\pi$
$140$	−0.303759	−	0.526126i	−0.0256723	−	0.0444658i
$141$	14.0431	+	10.2801i	1.18264	+	0.865739i
$142$		−	5.74387i		−	0.482015i
$143$	1.43317	+	5.21503i	0.119847	+	0.436103i
$144$	−2.21497	−	2.02334i	−0.184581	−	0.168612i
$145$	3.75178	+	1.00529i	0.311568	+	0.0834844i
$146$	−13.2997	+	7.67859i	−1.10069	+	0.635484i
$147$	−1.08518	−	1.34996i	−0.0895039	−	0.111343i
$148$	−6.27003	+	6.27003i	−0.515393	+	0.515393i
$149$	20.1156	−	5.38997i	1.64794	−	0.441564i	0.688904	−	0.724853i	$-0.258092\pi$
$149$	20.1156	−	5.38997i	1.64794	−	0.441564i	0.959034	+	0.283289i	$0.0914257\pi$
$150$	−0.867043	+	7.97399i	−0.0707938	+	0.651074i
$151$	1.83850	+	1.83850i	0.149615	+	0.149615i	0.777946	−	0.628331i	$-0.216262\pi$
$151$	1.83850	+	1.83850i	0.149615	+	0.149615i	−0.628331	+	0.777946i	$0.716262\pi$
$152$	−2.49085	−	1.43809i	−0.202034	−	0.116645i
$153$	3.22692	−	14.6632i	0.260881	−	1.18545i
$154$	0.388232	−	1.44890i	0.0312846	−	0.116756i
$155$	−2.46212			−0.197762
$156$	6.16535	−	0.994236i	0.493623	−	0.0796026i
$157$	20.5606			1.64092			0.820459	−	0.571706i	$-0.193718\pi$
$157$	20.5606			1.64092			0.820459	+	0.571706i	$0.193718\pi$
$158$	0.953587	−	3.55883i	0.0758633	−	0.283126i
$159$	−13.4961	+	2.08795i	−1.07031	+	0.165585i
$160$	−0.526126	−	0.303759i	−0.0415939	−	0.0240143i
$161$	4.06211	+	4.06211i	0.320139	+	0.320139i
$162$	−3.10437	−	8.44765i	−0.243903	−	0.663710i
$163$	−6.48922	+	1.73878i	−0.508275	+	0.136192i	−0.503838	−	0.863798i	$-0.668079\pi$
$163$	−6.48922	+	1.73878i	−0.508275	+	0.136192i	−0.00443696	+	0.999990i	$0.501412\pi$
$164$	2.65867	−	2.65867i	0.207607	−	0.207607i
$165$	1.23020	−	0.988907i	0.0957708	−	0.0769863i
$166$	6.31471	−	3.64580i	0.490116	−	0.282969i
$167$	6.75418	+	1.80978i	0.522654	+	0.140045i	0.510494	−	0.859881i	$-0.329463\pi$
$167$	6.75418	+	1.80978i	0.522654	+	0.140045i	0.0121601	+	0.999926i	$0.496129\pi$
$168$	−1.61477	−	0.626510i	−0.124582	−	0.0483363i
$169$	−6.35549	+	11.3405i	−0.488884	+	0.872349i
$170$		−	3.04044i		−	0.233191i
$171$	−4.64739	−	7.27006i	−0.355395	−	0.555955i
$172$	−5.39979	−	9.35271i	−0.411730	−	0.713138i
$173$	−4.19368	+	7.26366i	−0.318839	+	0.552246i	−0.980246	−	0.197781i	$-0.936626\pi$
$173$	−4.19368	+	7.26366i	−0.318839	+	0.552246i	0.661407	+	0.750027i	$0.269960\pi$
$174$	10.1325	−	4.46777i	0.768141	−	0.338701i
$175$	1.19857	+	4.47313i	0.0906034	+	0.338137i
$176$	−0.388232	−	1.44890i	−0.0292641	−	0.109215i
$177$	−20.5165	+	9.04647i	−1.54212	+	0.679974i
$178$	−3.40106	+	5.89081i	−0.254920	+	0.441535i
$179$	8.32290	+	14.4157i	0.622083	+	1.07748i	0.989097	+	0.147264i	$0.0470465\pi$
$179$	8.32290	+	14.4157i	0.622083	+	1.07748i	−0.367015	+	0.930215i	$0.619620\pi$
$180$	−0.981638	−	1.53561i	−0.0731670	−	0.114457i
$181$			4.99273i			0.371106i	0.982634	+	0.185553i	$0.0594077\pi$
$181$			4.99273i			0.371106i	−0.982634	+	0.185553i	$0.940592\pi$
$182$	3.11091	−	1.82271i	0.230596	−	0.135108i
$183$	2.83931	+	1.10162i	0.209888	+	0.0814338i
$184$	5.54895	+	1.48684i	0.409074	+	0.109611i
$185$	−4.66524	+	2.69348i	−0.342996	+	0.198029i
$186$	−5.47104	+	4.39795i	−0.401156	+	0.322473i
$187$	5.30832	−	5.30832i	0.388183	−	0.388183i
$188$	9.70563	−	2.60062i	0.707856	−	0.189669i
$189$	−3.43513	−	3.89870i	−0.249869	−	0.283589i
$190$	−1.23555	−	1.23555i	−0.0896363	−	0.0896363i
$191$	−0.216953	−	0.125258i	−0.0156981	−	0.00906332i	0.492130	−	0.870521i	$-0.336218\pi$
$191$	−0.216953	−	0.125258i	−0.0156981	−	0.00906332i	−0.507829	+	0.861458i	$0.669552\pi$
$192$	−1.71169	+	0.264812i	−0.123530	+	0.0191111i
$193$	2.68125	−	10.0066i	0.193001	−	0.720288i	−0.799775	−	0.600300i	$-0.795048\pi$
$193$	2.68125	−	10.0066i	0.193001	−	0.720288i	0.992775	−	0.119988i	$-0.0382856\pi$
$194$	−3.03303			−0.217759
$195$	3.77426	+	0.385987i	0.270281	+	0.0276411i
$196$	−1.00000			−0.0714286
$197$	2.69377	−	10.0533i	0.191923	−	0.716267i	−0.801119	−	0.598505i	$-0.795762\pi$
$197$	2.69377	−	10.0533i	0.191923	−	0.716267i	0.993042	−	0.117761i	$-0.0375718\pi$
$198$	0.967179	−	4.39488i	0.0687344	−	0.312330i
$199$	−2.17443	−	1.25541i	−0.154141	−	0.0889936i	0.420945	−	0.907086i	$-0.361698\pi$
$199$	−2.17443	−	1.25541i	−0.154141	−	0.0889936i	−0.575087	+	0.818092i	$0.695032\pi$
$200$	3.27456	+	3.27456i	0.231546	+	0.231546i
$201$	−2.07727	+	19.1042i	−0.146519	+	1.34750i
$202$	−4.93139	+	1.32136i	−0.346971	+	0.0929706i
$203$	4.52084	−	4.52084i	0.317301	−	0.317301i
$204$	−5.43098	−	6.75613i	−0.380244	−	0.473023i
$205$	1.97820	−	1.14211i	0.138163	−	0.0797685i
$206$	−5.69223	−	1.52523i	−0.396597	−	0.106268i
$207$	12.7243	+	11.6235i	0.884401	+	0.807887i
$208$	1.78277	−	3.13396i	0.123613	−	0.217301i
$209$		−	4.31432i		−	0.298428i
$210$	−0.849065	−	0.621549i	−0.0585910	−	0.0428910i
$211$	11.0701	+	19.1740i	0.762097	+	1.31999i	0.941768	+	0.336263i	$0.109163\pi$
$211$	11.0701	+	19.1740i	0.762097	+	1.31999i	−0.179671	+	0.983727i	$0.557503\pi$
$212$	−3.94233	+	6.82831i	−0.270760	+	0.468970i
$213$	−4.01385	−	9.10303i	−0.275024	−	0.623729i
$214$	−2.75695	−	10.2891i	−0.188462	−	0.703348i
$215$	−1.69810	−	6.33738i	−0.115809	−	0.432206i
$216$	−4.92426	−	1.65881i	−0.335054	−	0.112868i
$217$	−2.02637	+	3.50978i	−0.137559	+	0.238259i
$218$	0.256756	+	0.444715i	0.0173897	+	0.0301199i
$219$	−15.7119	+	21.4631i	−1.06171	+	1.45034i
$220$		−	0.911286i		−	0.0614389i
$221$	18.0443	−	0.115384i	1.21379	−	0.00776156i
$222$	−5.55537	+	14.3184i	−0.372852	+	0.960990i
$223$	9.49542	+	2.54429i	0.635860	+	0.170378i	0.562328	−	0.826914i	$-0.309906\pi$
$223$	9.49542	+	2.54429i	0.635860	+	0.170378i	0.0735328	+	0.997293i	$0.476573\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	4.19816	+	13.2433i	0.279877	+	0.882885i
$226$	−10.8613	+	10.8613i	−0.722481	+	0.722481i
$227$	−5.59370	+	1.49883i	−0.371267	+	0.0994807i	−0.439628	−	0.898180i	$-0.644890\pi$
$227$	−5.59370	+	1.49883i	−0.371267	+	0.0994807i	0.0683609	+	0.997661i	$0.478223\pi$
$228$	−4.95251	−	0.538505i	−0.327988	−	0.0356634i
$229$	1.44073	+	1.44073i	0.0952059	+	0.0952059i	0.753106	−	0.657900i	$-0.228555\pi$
$229$	1.44073	+	1.44073i	0.0952059	+	0.0952059i	−0.657900	+	0.753106i	$0.728555\pi$
$230$	3.02243	+	1.74500i	0.199293	+	0.115062i
$231$	−0.397221	−	2.56756i	−0.0261352	−	0.168933i
$232$	1.65474	−	6.17558i	0.108639	−	0.405447i
$233$	12.7341			0.834241			0.417120	−	0.908851i	$-0.363039\pi$
$233$	12.7341			0.834241			0.417120	+	0.908851i	$0.363039\pi$
$234$	9.07622	−	5.88407i	0.593331	−	0.384654i
$235$	6.10435			0.398204
$236$	−3.35057	+	12.5045i	−0.218104	+	0.813974i
$237$	−0.975666	−	6.30650i	−0.0633763	−	0.409651i
$238$	−4.33419	−	2.50234i	−0.280944	−	0.162203i
$239$	−13.2419	−	13.2419i	−0.856548	−	0.856548i	0.134382	−	0.990930i	$-0.457095\pi$
$239$	−13.2419	−	13.2419i	−0.856548	−	0.856548i	−0.990930	+	0.134382i	$0.957095\pi$
$240$	−1.04609	−	0.113745i	−0.0675246	−	0.00734221i
$241$	−15.6813	+	4.20178i	−1.01012	+	0.270661i	−0.725679	−	0.688033i	$-0.758474\pi$
$241$	−15.6813	+	4.20178i	−1.01012	+	0.270661i	−0.284440	+	0.958694i	$0.591808\pi$
$242$	−6.18715	+	6.18715i	−0.397725	+	0.397725i
$243$	−10.8232	−	11.2187i	−0.694306	−	0.719680i
$244$	1.52276	−	0.879168i	0.0974850	−	0.0562830i
$245$	−0.586817	−	0.157237i	−0.0374904	−	0.0100455i
$246$	2.35563	−	6.07142i	0.150190	−	0.387100i
$247$	7.28582	−	7.37960i	0.463586	−	0.469553i
$248$			4.05275i			0.257350i
$249$	7.46000	−	10.1907i	0.472758	−	0.645810i
$250$	2.92548	+	5.06708i	0.185024	+	0.320470i
$251$	−0.537453	+	0.930896i	−0.0339237	+	0.0587576i	−0.882489	−	0.470333i	$-0.844134\pi$
$251$	−0.537453	+	0.930896i	−0.0339237	+	0.0587576i	0.848565	+	0.529091i	$0.177467\pi$
$252$	−2.99694	+	0.135502i	−0.188789	+	0.00853582i
$253$	2.23027	+	8.32350i	0.140216	+	0.523294i
$254$	−2.73229	−	10.1971i	−0.171439	−	0.639820i
$255$	−2.12468	−	4.81856i	−0.133052	−	0.301750i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.8936	+	18.8683i	0.679524	+	1.17697i	0.975125	+	0.221658i	$0.0711468\pi$
$257$	10.8936	+	18.8683i	0.679524	+	1.17697i	−0.295601	+	0.955312i	$0.595520\pi$
$258$	−15.0935	−	11.0490i	−0.939677	−	0.687881i
$259$			8.86716i			0.550978i
$260$	1.53894	−	1.55875i	0.0954408	−	0.0966693i
$261$	12.9361	−	14.1613i	0.800724	−	0.876560i
$262$	11.8127	+	3.16519i	0.729789	+	0.195546i
$263$	−7.39268	+	4.26816i	−0.455852	+	0.263186i	−0.710298	−	0.703901i	$-0.751440\pi$
$263$	−7.39268	+	4.26816i	−0.455852	+	0.263186i	0.254447	+	0.967087i	$0.418107\pi$
$264$	−1.62778	−	2.02496i	−0.100183	−	0.124628i
$265$	−3.38709	+	3.38709i	−0.208067	+	0.208067i
$266$	−2.77818	+	0.744411i	−0.170341	+	0.0456428i
$267$	−1.27355	+	11.7126i	−0.0779403	+	0.716799i
$268$	7.84521	+	7.84521i	0.479222	+	0.479222i
$269$	−13.8882	−	8.01838i	−0.846782	−	0.488890i	0.0127821	−	0.999918i	$-0.495931\pi$
$269$	−13.8882	−	8.01838i	−0.846782	−	0.488890i	−0.859564	+	0.511029i	$0.829265\pi$
$270$	−2.62882	−	1.74769i	−0.159985	−	0.106361i
$271$	−2.03506	+	7.59496i	−0.123621	+	0.461361i	−0.999787	−	0.0206495i	$-0.993427\pi$
$271$	−2.03506	+	7.59496i	−0.123621	+	0.461361i	0.876165	+	0.482010i	$0.160093\pi$
$272$	−5.00469			−0.303454
$273$	3.65653	−	5.06259i	0.221303	−	0.306402i
$274$	−16.9956			−1.02674
$275$	−1.79787	+	6.70975i	−0.108416	+	0.404613i
$276$	9.83312	−	1.52126i	0.591884	−	0.0915691i
$277$	16.7024	+	9.64316i	1.00355	+	0.579401i	0.909297	−	0.416147i	$-0.136620\pi$
$277$	16.7024	+	9.64316i	1.00355	+	0.579401i	0.0942548	+	0.995548i	$0.469953\pi$
$278$	4.73763	+	4.73763i	0.284144	+	0.284144i
$279$	−5.59733	+	10.7932i	−0.335104	+	0.646170i
$280$	−0.586817	+	0.157237i	−0.0350690	+	0.00939672i
$281$	−16.0700	+	16.0700i	−0.958654	+	0.958654i	−0.999179	−	0.0405247i	$-0.987097\pi$
$281$	−16.0700	+	16.0700i	−0.958654	+	0.958654i	0.0405247	+	0.999179i	$0.487097\pi$
$282$	13.5644	−	10.9039i	0.807748	−	0.649316i
$283$	−12.6510	+	7.30408i	−0.752026	+	0.434182i	−0.826426	−	0.563046i	$-0.809629\pi$
$283$	−12.6510	+	7.30408i	−0.752026	+	0.434182i	0.0743994	+	0.997229i	$0.476296\pi$
$284$	−5.54815	−	1.48662i	−0.329222	−	0.0882148i
$285$	−2.82154	−	1.09472i	−0.167134	−	0.0648458i
$286$	5.40827	−	0.0345831i	0.319798	−	0.00204494i
$287$		−	3.75993i		−	0.221941i
$288$	−2.52767	+	1.61582i	−0.148945	+	0.0952129i
$289$	−4.02345	−	6.96883i	−0.236674	−	0.409931i
$290$	1.94206	−	3.36375i	0.114042	−	0.197526i
$291$	−4.80682	+	2.11950i	−0.281781	+	0.124247i
$292$	3.97473	+	14.8339i	0.232603	+	0.868088i
$293$	−2.19074	−	8.17594i	−0.127984	−	0.477643i	0.871944	−	0.489605i	$-0.162859\pi$
$293$	−2.19074	−	8.17594i	−0.127984	−	0.477643i	−0.999928	+	0.0119617i	$0.996192\pi$
$294$	−1.58483	+	0.698806i	−0.0924289	+	0.0407552i
$295$	−3.93235	+	6.81102i	−0.228950	+	0.396553i
$296$	4.43358	+	7.67919i	0.257697	+	0.446344i
$297$	−1.53836	−	7.64098i	−0.0892645	−	0.443375i
$298$		−	20.8253i		−	1.20637i
$299$	−10.2415	+	18.0036i	−0.592280	+	1.04118i
$300$	7.47788	+	2.90132i	0.431735	+	0.167508i
$301$	−10.4316	−	2.79514i	−0.601267	−	0.161109i
$302$	2.25169	−	1.30001i	0.129570	−	0.0748073i
$303$	−6.89201	+	5.54021i	−0.395936	+	0.318277i
$304$	−2.03377	+	2.03377i	−0.116645	+	0.116645i
$305$	1.03182	−	0.276476i	0.0590820	−	0.0158310i
$306$	−13.3284	−	6.91208i	−0.761932	−	0.395137i
$307$	5.74908	+	5.74908i	0.328117	+	0.328117i	0.851870	−	0.523753i	$-0.175469\pi$
$307$	5.74908	+	5.74908i	0.328117	+	0.328117i	−0.523753	+	0.851870i	$0.675469\pi$
$308$	−1.29905	−	0.750007i	−0.0740203	−	0.0427356i
$309$	−10.0870	+	1.56054i	−0.573831	+	0.0887762i
$310$	−0.637243	+	2.37822i	−0.0361929	+	0.135074i
$311$	26.7307			1.51576			0.757879	−	0.652395i	$-0.226236\pi$
$311$	26.7307			1.51576			0.757879	+	0.652395i	$0.226236\pi$
$312$	0.635351	−	6.21259i	0.0359697	−	0.351719i
$313$	16.9273			0.956789			0.478395	−	0.878145i	$-0.341219\pi$
$313$	16.9273			0.956789			0.478395	+	0.878145i	$0.341219\pi$
$314$	5.32148	−	19.8601i	0.300309	−	1.12077i
$315$	−1.77996	−	0.391715i	−0.100289	−	0.0220707i
$316$	−3.19076	−	1.84219i	−0.179494	−	0.103631i
$317$	5.59592	+	5.59592i	0.314298	+	0.314298i	0.846572	−	0.532274i	$-0.178662\pi$
$317$	5.59592	+	5.59592i	0.314298	+	0.314298i	−0.532274	+	0.846572i	$0.678662\pi$
$318$	−1.47624	+	13.5766i	−0.0827832	+	0.761338i
$319$	9.26346	−	2.48214i	0.518654	−	0.138973i
$320$	−0.429580	+	0.429580i	−0.0240143	+	0.0240143i
$321$	−11.5594	−	14.3798i	−0.645181	−	0.802604i
$322$	4.97505	−	2.87235i	0.277249	−	0.160070i
$323$	−13.9039	−	3.72555i	−0.773635	−	0.207295i
$324$	−8.96328	+	0.812182i	−0.497960	+	0.0451212i
$325$	−14.4064	+	8.44081i	−0.799122	+	0.468212i
$326$			6.71813i			0.372083i
$327$	0.717683	+	0.525372i	0.0396879	+	0.0290532i
$328$	−1.87996	−	3.25619i	−0.103804	−	0.179793i
$329$	5.02400	−	8.70183i	0.276982	−	0.479747i
$330$	−0.636812	−	1.44423i	−0.0350553	−	0.0795021i
$331$	−5.58301	−	20.8361i	−0.306870	−	1.14525i	−0.931324	−	0.364193i	$-0.881345\pi$
$331$	−5.58301	−	20.8361i	−0.306870	−	1.14525i	0.624454	−	0.781062i	$-0.285322\pi$
$332$	−1.88720	−	7.04314i	−0.103574	−	0.386543i
$333$	1.20152	+	26.5743i	0.0658428	+	1.45626i
$334$	3.49622	−	6.05563i	0.191305	−	0.331349i
$335$	3.37015	+	5.83726i	0.184131	+	0.318924i
$336$	−1.02310	+	1.39760i	−0.0558145	+	0.0762451i
$337$		−	26.6748i		−	1.45307i	−0.687129	−	0.726535i	$-0.741129\pi$
$337$		−	26.6748i		−	1.45307i	0.687129	−	0.726535i	$-0.258871\pi$
$338$	9.30919	+	9.07408i	0.506353	+	0.493565i
$339$	−9.62330	+	24.8031i	−0.522666	+	1.34712i
$340$	−2.93684	−	0.786923i	−0.159272	−	0.0426769i
$341$	−5.26472	+	3.03959i	−0.285101	+	0.164603i
$342$	−8.22517	+	2.60740i	−0.444766	+	0.140992i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−10.4316	+	2.79514i	−0.562434	+	0.150704i
$345$	6.00944	+	0.653430i	0.323537	+	0.0351795i
$346$	5.93075	+	5.93075i	0.318839	+	0.318839i
$347$	11.0636	+	6.38760i	0.593928	+	0.342904i	0.766649	−	0.642066i	$-0.221923\pi$
$347$	11.0636	+	6.38760i	0.593928	+	0.342904i	−0.172721	+	0.984971i	$0.555256\pi$
$348$	−1.69306	−	10.9436i	−0.0907573	−	0.586636i
$349$	−7.64398	+	28.5277i	−0.409173	+	1.52705i	0.387054	+	0.922057i	$0.373493\pi$
$349$	−7.64398	+	28.5277i	−0.409173	+	1.52705i	−0.796227	+	0.604997i	$0.793174\pi$
$350$	4.63092			0.247533
$351$	10.2724	−	15.6677i	0.548300	−	0.836282i
$352$	−1.50001			−0.0799510
$353$	−5.52047	+	20.6027i	−0.293825	+	1.09657i	0.648321	+	0.761367i	$0.275472\pi$
$353$	−5.52047	+	20.6027i	−0.293825	+	1.09657i	−0.942146	+	0.335203i	$0.891195\pi$
$354$	3.42815	+	22.1588i	0.182204	+	1.17773i
$355$	−3.02200	−	1.74475i	−0.160391	−	0.0926018i
$356$	4.80983	+	4.80983i	0.254920	+	0.254920i
$357$	−8.61758	−	0.937023i	−0.456091	−	0.0495925i
$358$	16.0786	−	4.30825i	0.849781	−	0.227698i
$359$	−6.63087	+	6.63087i	−0.349964	+	0.349964i	−0.860096	−	0.510132i	$-0.829597\pi$
$359$	−6.63087	+	6.63087i	−0.349964	+	0.349964i	0.510132	+	0.860096i	$0.329597\pi$
$360$	−1.73735	+	0.550745i	−0.0915664	+	0.0290268i
$361$	9.29034	−	5.36378i	0.488965	−	0.282304i
$362$	4.82260	+	1.29221i	0.253470	+	0.0679172i
$363$	−5.48194	+	14.1292i	−0.287727	+	0.741589i
$364$	−0.955436	−	3.47666i	−0.0500784	−	0.182226i
$365$			9.32976i			0.488342i
$366$	1.79895	−	2.45744i	0.0940325	−	0.128453i
$367$	2.21303	+	3.83308i	0.115519	+	0.200085i	0.917987	−	0.396610i	$-0.129814\pi$
$367$	2.21303	+	3.83308i	0.115519	+	0.200085i	−0.802468	+	0.596695i	$0.796480\pi$
$368$	2.87235	−	4.97505i	0.149731	−	0.259342i
$369$	−0.509477	−	11.2683i	−0.0265223	−	0.586603i
$370$	1.39425	+	5.20340i	0.0724835	+	0.270512i
$371$	2.04070	+	7.61599i	0.105948	+	0.395403i
$372$	2.83208	+	6.42289i	0.146837	+	0.333012i
$373$	9.33873	−	16.1752i	0.483541	−	0.837518i	−0.516280	−	0.856420i	$-0.672684\pi$
$373$	9.33873	−	16.1752i	0.483541	−	0.837518i	0.999821	+	0.0189019i	$0.00601701\pi$
$374$	−3.75355	−	6.50134i	−0.194092	−	0.336176i
$375$	8.17728	+	5.98609i	0.422273	+	0.309120i
$376$		−	10.0480i		−	0.518186i
$377$	20.0368	+	11.3980i	1.03195	+	0.587029i
$378$	−4.65493	+	2.30902i	−0.239424	+	0.118763i
$379$	−28.2454	−	7.56834i	−1.45087	−	0.388759i	−0.554544	−	0.832154i	$-0.687107\pi$
$379$	−28.2454	−	7.56834i	−1.45087	−	0.388759i	−0.896326	+	0.443395i	$0.853774\pi$
$380$	−1.51324	+	0.873667i	−0.0776273	+	0.0448182i
$381$	−11.4560	−	14.2512i	−0.586907	−	0.730112i
$382$	−0.177141	+	0.177141i	−0.00906332	+	0.00906332i
$383$	22.1048	−	5.92296i	1.12950	−	0.302649i	0.354779	−	0.934950i	$-0.384556\pi$
$383$	22.1048	−	5.92296i	1.12950	−	0.302649i	0.774723	+	0.632301i	$0.217889\pi$
$384$	−0.187229	+	1.72190i	−0.00955449	+	0.0878704i
$385$	−0.644376	−	0.644376i	−0.0328405	−	0.0328405i
$386$	−8.97164	−	5.17978i	−0.456645	−	0.263644i
$387$	−31.6416	−	6.96335i	−1.60843	−	0.353967i
$388$	−0.785006	+	2.92968i	−0.0398526	+	0.148732i
$389$	−6.65640			−0.337493			−0.168746	−	0.985659i	$-0.553972\pi$
$389$	−6.65640			−0.337493			−0.168746	+	0.985659i	$0.553972\pi$
$390$	1.34969	−	3.54576i	0.0683440	−	0.179546i
$391$	28.7504			1.45397
$392$	−0.258819	+	0.965926i	−0.0130723	+	0.0487866i
$393$	20.9329	−	3.23848i	1.05592	−	0.163360i
$394$	−9.01352	−	5.20396i	−0.454095	−	0.262172i
$395$	−1.58273	−	1.58273i	−0.0796360	−	0.0796360i
$396$	−3.99480	−	2.07170i	−0.200746	−	0.104107i
$397$	−20.0004	+	5.35909i	−1.00379	+	0.268965i	−0.723033	−	0.690814i	$-0.757253\pi$
$397$	−20.0004	+	5.35909i	−1.00379	+	0.268965i	−0.280758	+	0.959779i	$0.590586\pi$
$398$	−1.77542	+	1.77542i	−0.0889936	+	0.0889936i
$399$	−3.88273	+	3.12117i	−0.194380	+	0.156254i
$400$	4.01050	−	2.31546i	0.200525	−	0.115773i
$401$	−22.2943	−	5.97375i	−1.11333	−	0.298315i	−0.345146	−	0.938549i	$-0.612171\pi$
$401$	−22.2943	−	5.97375i	−1.11333	−	0.298315i	−0.768180	+	0.640234i	$0.778837\pi$
$402$	17.9156	+	6.95101i	0.893547	+	0.346685i
$403$	−14.1384	−	3.69163i	−0.704283	−	0.183893i
$404$			5.10535i			0.254001i
$405$	−5.38751	−	0.932759i	−0.267708	−	0.0463491i
$406$	−3.19672	−	5.53687i	−0.158650	−	0.274790i
$407$	−6.65043	+	11.5189i	−0.329650	+	0.570970i
$408$	−7.93156	+	3.49731i	−0.392671	+	0.173142i
$409$	−6.78397	−	25.3181i	−0.335446	−	1.25190i	−0.903385	−	0.428830i	$-0.858926\pi$
$409$	−6.78397	−	25.3181i	−0.335446	−	1.25190i	0.567940	−	0.823070i	$-0.307741\pi$
$410$	−0.591201	−	2.20639i	−0.0291973	−	0.108966i
$411$	−26.9351	+	11.8766i	−1.32861	+	0.585832i
$412$	−2.94652	+	5.10352i	−0.145164	+	0.251432i
$413$	6.47281	+	11.2112i	0.318506	+	0.551669i
$414$	14.5207	−	9.28237i	0.713654	−	0.456204i
$415$		−	4.42978i		−	0.217449i
$416$	−2.56576	−	2.53316i	−0.125797	−	0.124198i
$417$	10.8190	+	4.19763i	0.529808	+	0.205559i
$418$	−4.16731	−	1.11663i	−0.203830	−	0.0546160i
$419$	16.6593	−	9.61826i	0.813860	−	0.469883i	−0.0344342	−	0.999407i	$-0.510963\pi$
$419$	16.6593	−	9.61826i	0.813860	−	0.469883i	0.848295	+	0.529524i	$0.177630\pi$
$420$	−0.820125	+	0.659265i	−0.0400180	+	0.0321688i
$421$	6.20540	−	6.20540i	0.302433	−	0.302433i	−0.539532	−	0.841965i	$-0.681399\pi$
$421$	6.20540	−	6.20540i	0.302433	−	0.302433i	0.841965	+	0.539532i	$0.181399\pi$
$422$	21.3858	−	5.73030i	1.04104	−	0.278947i
$423$	13.8775	−	26.7596i	0.674748	−	1.30110i
$424$	5.57529	+	5.57529i	0.270760	+	0.270760i
$425$	20.0713	+	11.5882i	0.973600	+	0.562108i
$426$	−9.83171	+	1.52104i	−0.476348	+	0.0736948i
$427$	0.455091	−	1.69842i	0.0220234	−	0.0821924i
$428$	−10.6521			−0.514886
$429$	8.54699	−	3.83414i	0.412653	−	0.185114i
$430$	−6.56094			−0.316397
$431$	1.96096	−	7.31839i	0.0944559	−	0.352514i	−0.902480	−	0.430731i	$-0.858256\pi$
$431$	1.96096	−	7.31839i	0.0944559	−	0.352514i	0.996936	+	0.0782165i	$0.0249225\pi$
$432$	−2.87678	+	4.32714i	−0.138409	+	0.208190i
$433$	3.29167	+	1.90044i	0.158187	+	0.0913295i	0.577004	−	0.816741i	$-0.304222\pi$
$433$	3.29167	+	1.90044i	0.158187	+	0.0913295i	−0.418817	+	0.908071i	$0.637555\pi$
$434$	2.86572	+	2.86572i	0.137559	+	0.137559i
$435$	0.727221	−	6.68808i	0.0348676	−	0.320669i
$436$	0.496015	−	0.132907i	0.0237548	−	0.00636508i
$437$	11.6834	−	11.6834i	0.558892	−	0.558892i
$438$	16.6653	+	20.7316i	0.796297	+	0.990592i
$439$	3.83310	−	2.21304i	0.182944	−	0.105623i	−0.405731	−	0.913992i	$-0.632983\pi$
$439$	3.83310	−	2.21304i	0.182944	−	0.105623i	0.588675	+	0.808370i	$0.299650\pi$
$440$	−0.880234	−	0.235858i	−0.0419635	−	0.0112441i
$441$	−2.02334	+	2.21497i	−0.0963496	+	0.105475i
$442$	4.55875	−	17.4593i	0.216838	−	0.830455i
$443$			0.744366i			0.0353659i	0.999844	+	0.0176829i	$0.00562895\pi$
$443$			0.744366i			0.0353659i	−0.999844	+	0.0176829i	$0.994371\pi$
$444$	12.3927	+	9.07195i	0.588132	+	0.430536i
$445$	2.06621	+	3.57877i	0.0979476	+	0.169650i
$446$	4.91519	−	8.51336i	0.232741	−	0.403119i
$447$	−14.5528	−	33.0044i	−0.688324	−	1.56105i
$448$	0.258819	+	0.965926i	0.0122281	+	0.0456357i
$449$	−3.55603	−	13.2713i	−0.167819	−	0.626310i	−0.997664	−	0.0683153i	$-0.978238\pi$
$449$	−3.55603	−	13.2713i	−0.167819	−	0.626310i	0.829845	−	0.557995i	$-0.188429\pi$
$450$	13.8786	−	0.627499i	0.654243	−	0.0295806i
$451$	2.81997	−	4.88433i	0.132787	−	0.229994i
$452$	7.68008	+	13.3023i	0.361241	+	0.625687i
$453$	2.66008	−	3.63379i	0.124981	−	0.170730i
$454$			5.79103i			0.271786i
$455$	−0.0140064	−	2.19039i	−0.000656631	−	0.102687i
$456$	−1.80196	+	4.64438i	−0.0843845	+	0.217493i
$457$	13.1858	+	3.53312i	0.616805	+	0.165272i	0.553675	−	0.832733i	$-0.313225\pi$
$457$	13.1858	+	3.53312i	0.616805	+	0.165272i	0.0631300	+	0.998005i	$0.479892\pi$
$458$	1.76452	−	1.01875i	0.0824507	−	0.0476029i
$459$	−25.9533	−	1.64050i	−1.21140	−	0.0765720i
$460$	2.46780	−	2.46780i	0.115062	−	0.115062i
$461$	18.9023	−	5.06487i	0.880370	−	0.235894i	0.209803	−	0.977744i	$-0.432718\pi$
$461$	18.9023	−	5.06487i	0.880370	−	0.235894i	0.670567	+	0.741849i	$0.266051\pi$
$462$	−2.58288	−	0.280846i	−0.120166	−	0.0130661i
$463$	1.12387	+	1.12387i	0.0522307	+	0.0522307i	0.732740	−	0.680509i	$-0.238241\pi$
$463$	1.12387	+	1.12387i	0.0522307	+	0.0522307i	−0.680509	+	0.732740i	$0.738241\pi$
$464$	−5.53687	−	3.19672i	−0.257043	−	0.148404i
$465$	0.651997	+	4.21437i	0.0302356	+	0.195437i
$466$	3.29584	−	12.3002i	0.152677	−	0.569797i
$467$	27.6183			1.27802			0.639011	−	0.769198i	$-0.279344\pi$
$467$	27.6183			1.27802			0.639011	+	0.769198i	$0.279344\pi$
$468$	−3.33448	−	10.2899i	−0.154136	−	0.475649i
$469$	11.0948			0.512310
$470$	1.57992	−	5.89635i	0.0728763	−	0.271978i
$471$	−5.44470	−	35.1934i	−0.250878	−	1.62163i
$472$	11.2112	+	6.47281i	0.516039	+	0.297935i
$473$	−11.4548	−	11.4548i	−0.526692	−	0.526692i
$474$	−6.34413	−	0.689822i	−0.291396	−	0.0316846i
$475$	12.8655	−	3.44731i	0.590311	−	0.158173i
$476$	−3.53885	+	3.53885i	−0.162203	+	0.162203i
$477$	7.14783	+	22.5481i	0.327277	+	1.03241i
$478$	−16.2180	+	9.36344i	−0.741792	+	0.428274i
$479$	−39.4326	−	10.5659i	−1.80172	−	0.482770i	−0.807476	−	0.589901i	$-0.799167\pi$
$479$	−39.4326	−	10.5659i	−1.80172	−	0.482770i	−0.994245	+	0.107131i	$0.965833\pi$
$480$	−0.380616	+	0.981002i	−0.0173727	+	0.0447764i
$481$	−30.8281	+	8.47200i	−1.40564	+	0.386290i
$482$			16.2344i			0.739459i
$483$	5.87737	−	8.02876i	0.267430	−	0.365321i
$484$	4.37498	+	7.57769i	0.198863	+	0.344440i
$485$	−0.921310	+	1.59576i	−0.0418345	+	0.0724595i
$486$	−13.6377	+	7.55076i	−0.618617	+	0.342509i
$487$	−0.944238	−	3.52394i	−0.0427875	−	0.159685i	0.941227	−	0.337776i	$-0.109675\pi$
$487$	−0.944238	−	3.52394i	−0.0427875	−	0.159685i	−0.984014	+	0.178091i	$0.943008\pi$
$488$	−0.455091	−	1.69842i	−0.0206010	−	0.0768840i
$489$	4.69467	+	10.6471i	0.212300	+	0.481477i
$490$	−0.303759	+	0.526126i	−0.0137224	+	0.0237680i
$491$	12.1442	+	21.0344i	0.548061	+	0.949269i	0.998407	+	0.0564153i	$0.0179671\pi$
$491$	12.1442	+	21.0344i	0.548061	+	0.949269i	−0.450347	+	0.892854i	$0.648700\pi$
$492$	−5.25486	−	3.84677i	−0.236907	−	0.173426i
$493$		−	31.9971i		−	1.44108i
$494$	−5.24244	−	8.94754i	−0.235868	−	0.402569i
$495$	−2.01847	−	1.84384i	−0.0907235	−	0.0828745i
$496$	3.91465	+	1.04893i	0.175773	+	0.0470983i
$497$	−4.97434	+	2.87193i	−0.223129	+	0.128824i
$498$	−7.91267	−	9.84336i	−0.354575	−	0.441091i
$499$	−6.04184	+	6.04184i	−0.270470	+	0.270470i	−0.829289	−	0.558819i	$-0.811254\pi$
$499$	−6.04184	+	6.04184i	−0.270470	+	0.270470i	0.558819	+	0.829289i	$0.311254\pi$
$500$	5.65159	−	1.51434i	0.252747	−	0.0677233i
$501$	1.30919	−	12.0403i	0.0584902	−	0.537921i
$502$	0.760073	+	0.760073i	0.0339237	+	0.0339237i
$503$	−16.7473	−	9.66904i	−0.746724	−	0.431121i	0.0777852	−	0.996970i	$-0.475215\pi$
$503$	−16.7473	−	9.66904i	−0.746724	−	0.431121i	−0.824509	+	0.565849i	$0.808548\pi$
$504$	−0.644780	+	2.92989i	−0.0287208	+	0.130508i
$505$	−0.802751	+	2.99591i	−0.0357219	+	0.133316i
$506$	8.61712			0.383078
$507$	21.0945	+	7.87551i	0.936838	+	0.349764i
$508$	−10.5568			−0.468381
$509$	9.82494	−	36.6672i	0.435483	−	1.62524i	−0.304426	−	0.952536i	$-0.598465\pi$
$509$	9.82494	−	36.6672i	0.435483	−	1.62524i	0.739908	−	0.672708i	$-0.234869\pi$
$510$	−5.20428	+	0.805143i	−0.230449	+	0.0356523i
$511$	13.2997	+	7.67859i	0.588344	+	0.339681i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−11.2134	+	9.88007i	−0.495083	+	0.436216i
$514$	21.0448	−	5.63894i	0.928246	−	0.248723i
$515$	−2.53153	+	2.53153i	−0.111553	+	0.111553i
$516$	−14.5790	+	11.7195i	−0.641804	+	0.515920i
$517$	13.0529	−	7.53608i	0.574064	−	0.331436i
$518$	8.56502	+	2.29499i	0.376325	+	0.100836i
$519$	13.5437	+	5.25476i	0.594500	+	0.230658i
$520$	−1.10733	−	1.88993i	−0.0485595	−	0.0828790i
$521$			13.5471i			0.593507i	0.954954	+	0.296754i	$0.0959040\pi$
$521$			13.5471i			0.593507i	−0.954954	+	0.296754i	$0.904096\pi$
$522$	−10.3306	−	16.1605i	−0.452159	−	0.707326i
$523$	−21.9843	−	38.0779i	−0.961305	−	1.66503i	−0.719231	−	0.694771i	$-0.755506\pi$
$523$	−21.9843	−	38.0779i	−0.961305	−	1.66503i	−0.242074	−	0.970258i	$-0.577828\pi$
$524$	6.11468	−	10.5909i	0.267121	−	0.462667i
$525$	7.33920	−	3.23611i	0.320309	−	0.141236i
$526$	2.20936	+	8.24546i	0.0963328	+	0.359519i
$527$	5.24956	+	19.5916i	0.228674	+	0.853424i
$528$	−2.37726	+	1.04822i	−0.103457	+	0.0456179i
$529$	−5.00074	+	8.66153i	−0.217423	+	0.376588i
$530$	2.39503	+	4.14832i	0.104034	+	0.180192i
$531$	20.9177	+	32.7223i	0.907753	+	1.42003i
$532$			2.87618i			0.124698i
$533$	13.0720	−	3.59237i	0.566210	−	0.155603i
$534$	10.9839	+	4.26160i	0.475319	+	0.184417i
$535$	−6.25081	−	1.67490i	−0.270246	−	0.0724122i
$536$	9.60838	−	5.54740i	0.415019	−	0.239611i
$537$	22.4711	−	18.0636i	0.969702	−	0.779504i
$538$	−11.3397	+	11.3397i	−0.488890	+	0.488890i
$539$	−1.44890	+	0.388232i	−0.0624086	+	0.0167223i
$540$	−2.36853	+	2.08690i	−0.101925	+	0.0898061i
$541$	−20.4730	−	20.4730i	−0.880204	−	0.880204i	0.113351	−	0.993555i	$-0.463841\pi$
$541$	−20.4730	−	20.4730i	−0.880204	−	0.880204i	−0.993555	+	0.113351i	$0.963841\pi$
$542$	6.80945	+	3.93144i	0.292491	+	0.168870i
$543$	8.54599	−	1.32213i	0.366743	−	0.0567381i
$544$	−1.29531	+	4.83416i	−0.0555359	+	0.207263i
$545$	0.311968			0.0133632
$546$	−3.94371	−	4.84223i	−0.168775	−	0.207228i
$547$	−14.9014			−0.637139			−0.318569	−	0.947900i	$-0.603202\pi$
$547$	−14.9014			−0.637139			−0.318569	+	0.947900i	$0.603202\pi$
$548$	−4.39879	+	16.4165i	−0.187907	+	0.701279i
$549$	1.13374	−	5.15173i	0.0483868	−	0.219871i
$550$	6.01580	+	3.47322i	0.256515	+	0.148099i
$551$	−13.0028	−	13.0028i	−0.553936	−	0.553936i
$552$	1.07557	−	9.89179i	0.0457794	−	0.421023i
$553$	−3.55883	+	0.953587i	−0.151337	+	0.0405506i
$554$	13.6375	−	13.6375i	0.579401	−	0.579401i
$555$	5.84581	+	7.27218i	0.248141	+	0.308687i
$556$	5.80239	−	3.35001i	0.246076	−	0.142072i
$557$	5.20313	+	1.39418i	0.220464	+	0.0590731i	0.367360	−	0.930079i	$-0.380262\pi$
$557$	5.20313	+	1.39418i	0.220464	+	0.0590731i	−0.146896	+	0.989152i	$0.546928\pi$
$558$	8.97671	+	8.20009i	0.380014	+	0.347137i
$559$	−0.248986	−	38.9376i	−0.0105310	−	1.64689i
$560$			0.607518i			0.0256723i
$561$	−10.4919	−	7.68049i	−0.442968	−	0.324270i
$562$	11.3632	+	19.6816i	0.479327	+	0.830219i
$563$	20.4692	−	35.4536i	0.862672	−	1.49419i	−0.00666798	−	0.999978i	$-0.502123\pi$
$563$	20.4692	−	35.4536i	0.862672	−	1.49419i	0.869340	−	0.494214i	$-0.164544\pi$
$564$	−7.02161	−	15.9243i	−0.295663	−	0.670535i
$565$	2.41519	+	9.01361i	0.101608	+	0.379205i
$566$	3.78087	+	14.1104i	0.158922	+	0.593104i
$567$	−5.76370	+	6.91229i	−0.242052	+	0.290289i
$568$	−2.87193	+	4.97434i	−0.120504	+	0.208718i
$569$	−18.8139	−	32.5867i	−0.788722	−	1.36611i	−0.926750	−	0.375678i	$-0.877410\pi$
$569$	−18.8139	−	32.5867i	−0.788722	−	1.36611i	0.138029	−	0.990428i	$-0.455923\pi$
$570$	−1.78769	+	2.44207i	−0.0748781	+	0.102287i
$571$			46.6107i			1.95060i	0.220892	+	0.975298i	$0.429103\pi$
$571$			46.6107i			1.95060i	−0.220892	+	0.975298i	$0.570897\pi$
$572$	1.36636	−	5.23294i	0.0571303	−	0.218800i
$573$	−0.156950	+	0.404525i	−0.00655670	+	0.0168993i
$574$	−3.63181	−	0.973141i	−0.151589	−	0.0406181i
$575$	−23.0391	+	13.3016i	−0.960795	+	0.554715i
$576$	0.906550	+	2.85975i	0.0377729	+	0.119156i
$577$	−19.7783	+	19.7783i	−0.823382	+	0.823382i	−0.986591	−	0.163210i	$-0.947815\pi$
$577$	−19.7783	+	19.7783i	−0.823382	+	0.823382i	0.163210	+	0.986591i	$0.447815\pi$
$578$	−7.77272	+	2.08269i	−0.323302	+	0.0866286i
$579$	−17.8381	−	1.93961i	−0.741328	−	0.0806074i
$580$	−2.74649	−	2.74649i	−0.114042	−	0.114042i
$581$	−6.31471	−	3.64580i	−0.261978	−	0.151253i
$582$	0.803181	+	5.19160i	0.0332929	+	0.215199i
$583$	−3.06108	+	11.4241i	−0.126777	+	0.473138i
$584$	15.3572			0.635484
$585$	−0.338779	−	6.56257i	−0.0140068	−	0.271329i
$586$	−8.46435			−0.349659
$587$	4.80513	−	17.9330i	0.198329	−	0.740174i	−0.793051	−	0.609156i	$-0.791509\pi$
$587$	4.80513	−	17.9330i	0.198329	−	0.740174i	0.991380	−	0.131019i	$-0.0418248\pi$
$588$	0.264812	+	1.71169i	0.0109206	+	0.0705888i
$589$	10.0948	+	5.82822i	0.415948	+	0.240148i
$590$	5.56118	+	5.56118i	0.228950	+	0.228950i
$591$	−17.9214	−	1.94866i	−0.737189	−	0.0801574i
$592$	8.56502	−	2.29499i	0.352020	−	0.0943235i
$593$	23.0341	−	23.0341i	0.945899	−	0.945899i	−0.0527111	−	0.998610i	$-0.516786\pi$
$593$	23.0341	−	23.0341i	0.945899	−	0.945899i	0.998610	+	0.0527111i	$0.0167862\pi$
$594$	−7.77878	−	0.491694i	−0.319167	−	0.0201744i
$595$	−2.63310	+	1.52022i	−0.107946	+	0.0623229i
$596$	−20.1156	−	5.38997i	−0.823969	−	0.220782i
$597$	−1.57305	+	4.05439i	−0.0643808	+	0.165935i
$598$	14.7395	+	14.5522i	0.602743	+	0.595083i
$599$		−	18.7978i		−	0.768058i	−0.923321	−	0.384029i	$-0.874536\pi$
$599$		−	18.7978i		−	0.768058i	0.923321	−	0.384029i	$-0.125464\pi$
$600$	4.73788	−	6.47216i	0.193423	−	0.264225i
$601$	3.42337	+	5.92945i	0.139642	+	0.241867i	0.927361	−	0.374167i	$-0.122071\pi$
$601$	3.42337	+	5.92945i	0.139642	+	0.241867i	−0.787719	+	0.616035i	$0.788738\pi$
$602$	−5.39979	+	9.35271i	−0.220079	+	0.381188i
$603$	33.2504	−	1.50337i	1.35406	−	0.0612218i
$604$	−0.672936	−	2.51143i	−0.0273814	−	0.102189i
$605$	1.37582	+	5.13463i	0.0559350	+	0.208752i
$606$	3.56765	+	8.09108i	0.144926	+	0.328678i
$607$	22.9741	−	39.7924i	0.932491	−	1.61512i	0.153443	−	0.988157i	$-0.450964\pi$
$607$	22.9741	−	39.7924i	0.932491	−	1.61512i	0.779048	−	0.626964i	$-0.215703\pi$
$608$	1.43809	+	2.49085i	0.0583223	+	0.101017i
$609$	−8.93544	−	6.54109i	−0.362082	−	0.265059i
$610$		−	1.06822i		−	0.0432510i
$611$	35.0534	+	9.15270i	1.41811	+	0.370279i
$612$	−10.1262	+	11.0852i	−0.409327	+	0.448094i
$613$	−16.8630	−	4.51842i	−0.681089	−	0.182497i	−0.0983444	−	0.995152i	$-0.531355\pi$
$613$	−16.8630	−	4.51842i	−0.681089	−	0.182497i	−0.582745	+	0.812655i	$0.698021\pi$
$614$	7.04115	−	4.06521i	0.284158	−	0.164059i
$615$	−2.47879	−	3.08361i	−0.0999544	−	0.124343i
$616$	−1.06067	+	1.06067i	−0.0427356	+	0.0427356i
$617$	17.9619	−	4.81288i	0.723119	−	0.193759i	0.121556	−	0.992585i	$-0.461212\pi$
$617$	17.9619	−	4.81288i	0.723119	−	0.193759i	0.601563	+	0.798825i	$0.294545\pi$
$618$	−1.10335	+	10.1472i	−0.0443831	+	0.408181i
$619$	14.2267	+	14.2267i	0.571818	+	0.571818i	0.932636	−	0.360818i	$-0.117502\pi$
$619$	14.2267	+	14.2267i	0.571818	+	0.571818i	−0.360818	+	0.932636i	$0.617502\pi$
$620$	2.13226	+	1.23106i	0.0856334	+	0.0494405i
$621$	16.5262	−	24.8581i	0.663174	−	0.997521i
$622$	6.91841	−	25.8199i	0.277403	−	1.03528i
$623$	6.80212			0.272521
$624$	−5.83646	−	2.22164i	−0.233646	−	0.0889368i
$625$	−19.6000			−0.784002
$626$	4.38112	−	16.3505i	0.175105	−	0.653499i
$627$	−7.38476	+	1.14248i	−0.294919	+	0.0456263i
$628$	−17.8060	−	10.2803i	−0.710538	−	0.410229i
$629$	31.3795	+	31.3795i	1.25118	+	1.25118i
$630$	−0.839056	+	1.61793i	−0.0334288	+	0.0644598i
$631$	18.0970	−	4.84907i	0.720430	−	0.193039i	0.120066	−	0.992766i	$-0.461689\pi$
$631$	18.0970	−	4.84907i	0.720430	−	0.193039i	0.600363	+	0.799727i	$0.295023\pi$
$632$	−2.60525	+	2.60525i	−0.103631	+	0.103631i
$633$	29.8883	−	24.0260i	1.18796	−	0.954949i
$634$	6.85358	−	3.95692i	0.272190	−	0.157149i
$635$	−6.19490	−	1.65992i	−0.245837	−	0.0658718i
$636$	12.7319	+	4.93982i	0.504853	+	0.195876i
$637$	−3.13396	−	1.78277i	−0.124172	−	0.0706360i
$638$		−	9.59024i		−	0.379681i
$639$	−14.5186	+	9.28104i	−0.574348	+	0.367152i
$640$	0.303759	+	0.526126i	0.0120071	+	0.0207970i
$641$	−12.0969	+	20.9525i	−0.477799	+	0.827573i	−0.999676	−	0.0254482i	$-0.991899\pi$
$641$	−12.0969	+	20.9525i	−0.477799	+	0.827573i	0.521877	+	0.853021i	$0.325232\pi$
$642$	−16.8816	+	7.44372i	−0.666265	+	0.293780i
$643$	−2.06922	−	7.72242i	−0.0816020	−	0.304543i	0.913047	−	0.407854i	$-0.133723\pi$
$643$	−2.06922	−	7.72242i	−0.0816020	−	0.304543i	−0.994649	+	0.103311i	$0.967056\pi$
$644$	−1.48684	−	5.54895i	−0.0585895	−	0.218659i
$645$	−10.3979	+	4.58482i	−0.409419	+	0.180527i
$646$	−7.19720	+	12.4659i	−0.283170	+	0.490465i
$647$	12.4194	+	21.5110i	0.488256	+	0.845684i	0.999909	−	0.0135085i	$-0.00430002\pi$
$647$	12.4194	+	21.5110i	0.488256	+	0.845684i	−0.511653	+	0.859192i	$0.670967\pi$
$648$	−1.53536	+	8.86807i	−0.0603146	+	0.348371i
$649$			19.4186i			0.762247i
$650$	4.42455	+	16.1001i	0.173545	+	0.631499i
$651$	6.54426	+	2.53909i	0.256490	+	0.0995147i
$652$	6.48922	+	1.73878i	0.254137	+	0.0680959i
$653$	−31.1279	+	17.9717i	−1.21813	+	0.703287i	−0.964517	−	0.264019i	$-0.914952\pi$
$653$	−31.1279	+	17.9717i	−1.21813	+	0.703287i	−0.253611	+	0.967306i	$0.581618\pi$
$654$	0.693221	−	0.557252i	0.0271071	−	0.0217903i
$655$	5.25349	−	5.25349i	0.205271	−	0.205271i
$656$	−3.63181	+	0.973141i	−0.141798	+	0.0379948i
$657$	40.8989	+	21.2101i	1.59562	+	0.827485i
$658$	−7.10501	−	7.10501i	−0.276982	−	0.276982i
$659$	−18.0111	−	10.3987i	−0.701611	−	0.405075i	0.106336	−	0.994330i	$-0.466088\pi$
$659$	−18.0111	−	10.3987i	−0.701611	−	0.405075i	−0.807947	+	0.589255i	$0.799421\pi$
$660$	−1.55984	+	0.241319i	−0.0607165	+	0.00939333i
$661$	−8.51046	+	31.7615i	−0.331018	+	1.23538i	0.577103	+	0.816671i	$0.304183\pi$
$661$	−8.51046	+	31.7615i	−0.331018	+	1.23538i	−0.908122	+	0.418706i	$0.862484\pi$
$662$	−21.5711			−0.838384
$663$	−4.97584	−	30.8556i	−0.193246	−	1.19833i
$664$	−7.29160			−0.282969
$665$	−0.452243	+	1.68779i	−0.0175372	+	0.0654499i
$666$	25.9798	+	5.71737i	1.00670	+	0.221543i
$667$	31.8076	+	18.3641i	1.23160	+	0.711063i
$668$	−4.94440	−	4.94440i	−0.191305	−	0.191305i
$669$	1.84053	−	16.9270i	0.0711591	−	0.654434i
$670$	6.51062	−	1.74452i	0.251527	−	0.0673965i
$671$	1.86502	−	1.86502i	0.0719981	−	0.0719981i
$672$	1.08518	+	1.34996i	0.0418616	+	0.0520758i
$673$	−27.0469	+	15.6155i	−1.04258	+	0.601934i	−0.920563	−	0.390594i	$-0.872270\pi$
$673$	−27.0469	+	15.6155i	−1.04258	+	0.601934i	−0.122017	+	0.992528i	$0.538936\pi$
$674$	−25.7659	−	6.90396i	−0.992466	−	0.265930i
$675$	21.5566	−	10.6929i	0.829715	−	0.411570i
$676$	11.1743	−	6.64344i	0.429780	−	0.255517i
$677$		−	2.63720i		−	0.101356i	−0.998715	−	0.0506778i	$-0.983862\pi$
$677$		−	2.63720i		−	0.101356i	0.998715	−	0.0506778i	$-0.0161382\pi$
$678$	21.4673	+	15.7149i	0.824447	+	0.603528i
$679$	1.51651	+	2.62668i	0.0581985	+	0.100803i
$680$	−1.52022	+	2.63310i	−0.0582977	+	0.100975i
$681$	4.04680	+	9.17777i	0.155074	+	0.351693i
$682$	1.57341	+	5.87203i	0.0602489	+	0.224852i
$683$	−10.8450	−	40.4741i	−0.414972	−	1.54870i	−0.784891	−	0.619633i	$-0.787281\pi$
$683$	−10.8450	−	40.4741i	−0.414972	−	1.54870i	0.369919	−	0.929064i	$-0.379385\pi$
$684$	0.389729	+	8.61975i	0.0149016	+	0.329584i
$685$	−5.16258	+	8.94184i	−0.197252	+	0.341650i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	2.08455	−	2.84759i	0.0795306	−	0.108643i
$688$			10.7996i			0.411730i
$689$	−24.5284	+	14.3714i	−0.934459	+	0.547507i
$690$	2.18652	−	5.63556i	0.0832395	−	0.214542i
$691$	16.2923	+	4.36550i	0.619788	+	0.166072i	0.555031	−	0.831829i	$-0.312706\pi$
$691$	16.2923	+	4.36550i	0.619788	+	0.166072i	0.0647564	+	0.997901i	$0.479373\pi$
$692$	7.26366	−	4.19368i	0.276123	−	0.159420i
$693$	−4.28966	+	1.35984i	−0.162951	+	0.0516559i
$694$	9.03343	−	9.03343i	0.342904	−	0.342904i
$695$	3.93169	−	1.05349i	0.149137	−	0.0399612i
$696$	−11.0089	−	1.19704i	−0.417290	−	0.0453735i
$697$	−13.3058	−	13.3058i	−0.503994	−	0.503994i
$698$	25.5773	+	14.7670i	0.968114	+	0.558941i
$699$	−3.37215	−	21.7969i	−0.127546	−	0.824433i
$700$	1.19857	−	4.47313i	0.0453017	−	0.169068i
$701$	−29.1790			−1.10208			−0.551038	−	0.834480i	$-0.685768\pi$
$701$	−29.1790			−1.10208			−0.551038	+	0.834480i	$0.685768\pi$
$702$	−12.4752	−	13.9775i	−0.470845	−	0.527546i
$703$	25.5036			0.961886
$704$	−0.388232	+	1.44890i	−0.0146321	+	0.0546076i
$705$	−1.61650	−	10.4487i	−0.0608810	−	0.393522i
$706$	18.4719	+	10.6647i	0.695198	+	0.401372i
$707$	3.61003	+	3.61003i	0.135769	+	0.135769i
$708$	22.2911	+	2.42379i	0.837750	+	0.0910918i
$709$	12.3313	−	3.30417i	0.463112	−	0.124091i	−0.0197161	−	0.999806i	$-0.506276\pi$
$709$	12.3313	−	3.30417i	0.463112	−	0.124091i	0.482828	+	0.875715i	$0.339610\pi$
$710$	−2.46745	+	2.46745i	−0.0926018	+	0.0926018i
$711$	−10.5364	+	3.34007i	−0.395146	+	0.125262i
$712$	5.89081	−	3.40106i	0.220768	−	0.127460i
$713$	−22.4885	−	6.02577i	−0.842200	−	0.225667i
$714$	−3.13549	+	8.08143i	−0.117343	+	0.302440i
$715$	1.62461	−	2.85593i	0.0607571	−	0.106806i
$716$		−	16.6458i		−	0.622083i
$717$	−19.1594	+	26.1726i	−0.715521	+	0.977434i
$718$	4.68874	+	8.12113i	0.174982	+	0.303078i
$719$	18.6879	−	32.3684i	0.696942	−	1.20714i	−0.272580	−	0.962133i	$-0.587877\pi$
$719$	18.6879	−	32.3684i	0.696942	−	1.20714i	0.969522	−	0.245006i	$-0.0787899\pi$
$720$	0.0823199	+	1.82069i	0.00306788	+	0.0678533i
$721$	1.52523	+	5.69223i	0.0568025	+	0.211990i
$722$	−2.77650	−	10.3620i	−0.103331	−	0.385635i
$723$	11.3447	+	25.7288i	0.421915	+	0.956863i
$724$	2.49636	−	4.32383i	0.0927766	−	0.160694i
$725$	14.8037	+	25.6408i	0.549797	+	0.952277i
$726$	12.2289	+	8.95205i	0.453857	+	0.332242i
$727$		−	5.06432i		−	0.187825i	−0.995580	−	0.0939126i	$-0.970063\pi$
$727$		−	5.06432i		−	0.187825i	0.995580	−	0.0939126i	$-0.0299374\pi$
$728$	−3.60548	+	0.0230552i	−0.133628	+	0.000854481i
$729$	−16.3368	+	21.4967i	−0.605067	+	0.796175i
$730$	9.01186	+	2.41472i	0.333544	+	0.0893728i
$731$	−46.8074	+	27.0243i	−1.73123	+	0.999529i
$732$	−1.90811	−	2.37368i	−0.0705257	−	0.0877338i
$733$	−31.5628	+	31.5628i	−1.16580	+	1.16580i	−0.182613	+	0.983185i	$0.558455\pi$
$733$	−31.5628	+	31.5628i	−1.16580	+	1.16580i	−0.983185	+	0.182613i	$0.941545\pi$
$734$	4.27524	−	1.14555i	0.157802	−	0.0422829i
$735$	−0.113745	+	1.04609i	−0.00419555	+	0.0385855i
$736$	−4.06211	−	4.06211i	−0.149731	−	0.149731i
$737$	14.4127	+	8.32118i	0.530899	+	0.306515i
$738$	−11.0162	−	2.42433i	−0.405511	−	0.0892407i
$739$	−6.71344	+	25.0549i	−0.246958	+	0.921659i	0.725431	+	0.688294i	$0.241640\pi$
$739$	−6.71344	+	25.0549i	−0.246958	+	0.921659i	−0.972389	+	0.233365i	$0.925026\pi$
$740$	5.38696			0.198029
$741$	−14.5609	−	10.5168i	−0.534909	−	0.386346i
$742$	7.88465			0.289455
$743$	−1.54626	+	5.77071i	−0.0567267	+	0.211707i	−0.988472	−	0.151407i	$-0.951620\pi$
$743$	−1.54626	+	5.77071i	−0.0567267	+	0.211707i	0.931745	+	0.363114i	$0.118286\pi$
$744$	6.93704	−	1.07321i	0.254324	−	0.0393459i
$745$	−10.9567	−	6.32586i	−0.401423	−	0.231761i
$746$	−13.2070	−	13.2070i	−0.483541	−	0.483541i
$747$	−19.4188	−	10.0706i	−0.710497	−	0.368463i
$748$	−7.25131	+	1.94298i	−0.265134	+	0.0710424i
$749$	−7.53214	+	7.53214i	−0.275218	+	0.275218i
$750$	7.89856	−	6.34933i	0.288414	−	0.231845i
$751$	7.90712	−	4.56518i	0.288535	−	0.166586i	−0.348746	−	0.937217i	$-0.613392\pi$
$751$	7.90712	−	4.56518i	0.288535	−	0.166586i	0.637281	+	0.770632i	$0.280059\pi$
$752$	−9.70563	−	2.60062i	−0.353928	−	0.0948347i
$753$	1.73573	+	0.673440i	0.0632534	+	0.0245415i
$754$	16.1956	−	16.4040i	0.589807	−	0.597399i
$755$		−	1.57956i		−	0.0574862i
$756$	1.02556	+	5.09394i	0.0372993	+	0.185265i
$757$	18.4318	+	31.9247i	0.669913	+	1.16032i	0.977928	+	0.208942i	$0.0670021\pi$
$757$	18.4318	+	31.9247i	0.669913	+	1.16032i	−0.308015	+	0.951382i	$0.599665\pi$
$758$	−14.6209	+	25.3242i	−0.531055	+	0.919815i
$759$	13.6566	−	6.02169i	0.495704	−	0.218574i
$760$	0.452243	+	1.68779i	0.0164046	+	0.0612227i
$761$	−5.30708	−	19.8063i	−0.192382	−	0.717978i	−0.992929	−	0.118708i	$-0.962125\pi$
$761$	−5.30708	−	19.8063i	−0.192382	−	0.717978i	0.800548	−	0.599269i	$-0.204542\pi$
$762$	−16.7306	+	7.37713i	−0.606087	+	0.267245i
$763$	0.256756	−	0.444715i	0.00929519	−	0.0160997i
$764$	0.125258	+	0.216953i	0.00453166	+	0.00784907i
$765$	−7.68524	+	4.91279i	−0.277860	+	0.177622i
$766$		−	22.8846i		−	0.826853i
$767$	−32.7932	+	33.2153i	−1.18410	+	1.19934i
$768$	1.61477	+	0.626510i	0.0582680	+	0.0226072i
$769$	−35.5339	−	9.52129i	−1.28139	−	0.343347i	−0.447004	−	0.894532i	$-0.647509\pi$
$769$	−35.5339	−	9.52129i	−1.28139	−	0.343347i	−0.834383	+	0.551185i	$0.814176\pi$
$770$	−0.789196	+	0.455643i	−0.0284407	+	0.0164202i
$771$	29.4118	−	23.6430i	1.05924	−	0.851480i
$772$	−7.32531	+	7.32531i	−0.263644	+	0.263644i

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.264812 - 1.71169i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.429580 - 0.429580i) q^{5} +(-1.72190 - 0.187229i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.85975 + 0.906550i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.264812 - 1.71169i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.429580 - 0.429580i) q^{5} +(-1.72190 - 0.187229i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.85975 + 0.906550i) q^{9} +(-0.526126 + 0.303759i) q^{10} +(-1.44890 - 0.388232i) q^{11} +(-0.626510 + 1.61477i) q^{12} +(-1.82271 - 3.11091i) q^{13} +1.00000i q^{14} +(-0.621549 + 0.849065i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.50234 + 4.33419i) q^{17} +(0.135502 + 2.99694i) q^{18} +(0.744411 + 2.77818i) q^{19} +(0.157237 + 0.586817i) q^{20} +(0.698806 + 1.58483i) q^{21} +(-0.750007 + 1.29905i) q^{22} +(-2.87235 - 4.97505i) q^{23} +(1.39760 + 1.02310i) q^{24} -4.63092i q^{25} +(-3.47666 + 0.955436i) q^{26} +(2.30902 + 4.65493i) q^{27} +(0.965926 + 0.258819i) q^{28} +(-5.53687 + 3.19672i) q^{29} +(0.659265 + 0.820125i) q^{30} +(2.86572 - 2.86572i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.280846 + 2.58288i) q^{33} +(3.53885 + 3.53885i) q^{34} +(0.526126 + 0.303759i) q^{35} +(2.92989 + 0.644780i) q^{36} +(2.29499 - 8.56502i) q^{37} +2.87618 q^{38} +(-4.84223 + 3.94371i) q^{39} +0.607518 q^{40} +(-0.973141 + 3.63181i) q^{41} +(1.71169 - 0.264812i) q^{42} +(9.35271 + 5.39979i) q^{43} +(1.06067 + 1.06067i) q^{44} +(1.61793 + 0.839056i) q^{45} +(-5.54895 + 1.48684i) q^{46} +(-7.10501 + 7.10501i) q^{47} +(1.34996 - 1.08518i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-4.47313 - 1.19857i) q^{50} +(8.08143 + 3.13549i) q^{51} +(0.0230552 + 3.60548i) q^{52} -7.88465i q^{53} +(5.09394 - 1.02556i) q^{54} +(0.455643 + 0.789196i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.55825 - 2.00989i) q^{57} +(1.65474 + 6.17558i) q^{58} +(-3.35057 - 12.5045i) q^{59} +(0.962810 - 0.424537i) q^{60} +(-0.879168 + 1.52276i) q^{61} +(-2.02637 - 3.50978i) q^{62} +(2.52767 - 1.61582i) q^{63} -1.00000i q^{64} +(-0.553386 + 2.11938i) q^{65} +(2.42218 + 0.939774i) q^{66} +(-10.7168 - 2.87155i) q^{67} +(4.33419 - 2.50234i) q^{68} +(-7.75510 + 6.23401i) q^{69} +(0.429580 - 0.429580i) q^{70} +(5.54815 - 1.48662i) q^{71} +(1.38112 - 2.66318i) q^{72} +(-10.8592 - 10.8592i) q^{73} +(-7.67919 - 4.43358i) q^{74} +(-7.92669 + 1.22632i) q^{75} +(0.744411 - 2.77818i) q^{76} +1.50001 q^{77} +(2.55607 + 5.69794i) q^{78} +3.68438 q^{79} +(0.157237 - 0.586817i) q^{80} +(7.35634 - 5.18501i) q^{81} +(3.25619 + 1.87996i) q^{82} +(5.15594 + 5.15594i) q^{83} +(0.187229 - 1.72190i) q^{84} +(2.93684 - 0.786923i) q^{85} +(7.63646 - 7.63646i) q^{86} +(6.93801 + 8.63087i) q^{87} +(1.29905 - 0.750007i) q^{88} +(-6.57035 - 1.76052i) q^{89} +(1.22922 - 1.34563i) q^{90} +(2.56576 + 2.53316i) q^{91} +5.74469i q^{92} +(-5.66410 - 4.14635i) q^{93} +(5.02400 + 8.70183i) q^{94} +(0.873667 - 1.51324i) q^{95} +(-0.698806 - 1.58483i) q^{96} +(-0.785006 - 2.92968i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(4.49545 - 0.203255i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

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