LMFDB - Embedded newform 483.2.bf.a.10.22

Newspace parameters

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bf (of order $66$, degree $20$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$32$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			10.22
Character	$\chi$	$=$	483.10
Dual form			483.2.bf.a.145.22

$q$-expansion

$f(q)$	$=$	$q+(0.369500 - 1.06760i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(0.568868 + 0.447363i) q^{4} +(3.97561 - 0.379625i) q^{5} +(-1.11823 + 0.160778i) q^{6} +(-2.62638 + 0.319547i) q^{7} +(2.58859 - 1.66358i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(0.369500 - 1.06760i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(0.568868 + 0.447363i) q^{4} +(3.97561 - 0.379625i) q^{5} +(-1.11823 + 0.160778i) q^{6} +(-2.62638 + 0.319547i) q^{7} +(2.58859 - 1.66358i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(1.06370 - 4.38463i) q^{10} +(0.579905 - 0.200707i) q^{11} +(0.136961 - 0.710623i) q^{12} +(-0.0130536 - 0.0444565i) q^{13} +(-0.629300 + 2.92200i) q^{14} +(-2.15915 - 3.35971i) q^{15} +(-0.478320 - 1.97166i) q^{16} +(2.93114 + 1.17345i) q^{17} +(0.655310 + 0.920254i) q^{18} +(0.106407 - 0.0425988i) q^{19} +(2.43143 + 1.56258i) q^{20} +(1.48750 + 2.18800i) q^{21} -0.693267i q^{22} +(-3.88694 + 2.80922i) q^{23} +(-2.66481 - 1.53853i) q^{24} +(10.7517 - 2.07222i) q^{25} +(-0.0522850 - 0.00249064i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-1.63702 - 0.993166i) q^{28} +(-0.704571 - 4.90040i) q^{29} +(-4.38463 + 1.06370i) q^{30} +(-0.899627 + 0.0428545i) q^{31} +(3.84456 + 0.367111i) q^{32} +(-0.444123 - 0.423471i) q^{33} +(2.33583 - 2.69569i) q^{34} +(-10.3202 + 2.26743i) q^{35} +(-0.694387 + 0.203890i) q^{36} +(-6.97719 - 4.96843i) q^{37} +(-0.00616122 - 0.129340i) q^{38} +(-0.0335330 + 0.0319737i) q^{39} +(9.65967 - 7.59645i) q^{40} +(-2.62914 - 1.20069i) q^{41} +(2.88554 - 0.779593i) q^{42} +(-3.51134 + 5.46375i) q^{43} +(0.419678 + 0.145252i) q^{44} +(-1.99685 + 3.45864i) q^{45} +(1.56290 + 5.18770i) q^{46} +(-11.8139 + 6.82078i) q^{47} +(-1.53330 + 1.32862i) q^{48} +(6.79578 - 1.67850i) q^{49} +(1.76045 - 12.2442i) q^{50} +(-0.300121 - 3.14301i) q^{51} +(0.0124624 - 0.0311296i) q^{52} +(-6.16614 - 6.46686i) q^{53} +(0.517674 - 1.00415i) q^{54} +(2.22928 - 1.01808i) q^{55} +(-6.26703 + 5.19638i) q^{56} +(-0.0866217 - 0.0750581i) q^{57} +(-5.49200 - 1.05850i) q^{58} +(5.96573 + 1.44727i) q^{59} +(0.274735 - 2.87716i) q^{60} +(3.58765 + 1.84956i) q^{61} +(-0.286661 + 0.976276i) q^{62} +(1.26316 - 2.32474i) q^{63} +(3.49813 - 7.65983i) q^{64} +(-0.0687728 - 0.171786i) q^{65} +(-0.616200 + 0.317673i) q^{66} +(1.38928 + 7.20828i) q^{67} +(1.14247 + 1.97882i) q^{68} +(4.27803 + 2.16759i) q^{69} +(-1.39259 + 11.8556i) q^{70} +(-2.10992 - 2.43498i) q^{71} +(-0.146412 + 3.07357i) q^{72} +(0.180264 - 0.229224i) q^{73} +(-7.88237 + 5.61301i) q^{74} +(-6.76859 - 8.60696i) q^{75} +(0.0795884 + 0.0233693i) q^{76} +(-1.45892 + 0.712440i) q^{77} +(0.0217446 + 0.0476141i) q^{78} +(7.96425 - 8.35267i) q^{79} +(-2.65011 - 7.65698i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-2.25332 + 2.36321i) q^{82} +(5.02032 + 10.9930i) q^{83} +(-0.132636 + 1.91013i) q^{84} +(12.0985 + 3.55245i) q^{85} +(4.53565 + 5.76755i) q^{86} +(-4.03280 + 2.87174i) q^{87} +(1.16724 - 1.48427i) q^{88} +(-0.699789 + 14.6904i) q^{89} +(2.95461 + 3.40980i) q^{90} +(0.0484897 + 0.112589i) q^{91} +(-3.46789 - 0.140795i) q^{92} +(0.450324 + 0.779983i) q^{93} +(2.91661 + 15.1328i) q^{94} +(0.406860 - 0.209751i) q^{95} +(-1.43538 - 3.58540i) q^{96} +(-1.42557 + 3.12156i) q^{97} +(0.719069 - 7.87538i) q^{98} +(-0.172887 + 0.588798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.369500	−	1.06760i	0.261276	−	0.754907i	−0.735708	−	0.677299i	$-0.763151\pi$
$2$	0.369500	−	1.06760i	0.261276	−	0.754907i	0.996984	−	0.0776081i	$-0.0247283\pi$
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$4$	0.568868	+	0.447363i	0.284434	+	0.223681i
$5$	3.97561	−	0.379625i	1.77795	−	0.169773i	0.846196	−	0.532871i	$-0.178887\pi$
$5$	3.97561	−	0.379625i	1.77795	−	0.169773i	0.931751	+	0.363098i	$0.118281\pi$
$6$	−1.11823	+	0.160778i	−0.456517	+	0.0656373i
$7$	−2.62638	+	0.319547i	−0.992680	+	0.120777i
$7$	−2.62638	+	0.319547i	−0.992680	+	0.120777i
$8$	2.58859	−	1.66358i	0.915203	−	0.588165i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	1.06370	−	4.38463i	0.336371	−	1.38654i
$11$	0.579905	−	0.200707i	0.174848	−	0.0605154i	−0.238241	−	0.971206i	$-0.576571\pi$
$11$	0.579905	−	0.200707i	0.174848	−	0.0605154i	0.413089	+	0.910691i	$0.364450\pi$
$12$	0.136961	−	0.710623i	0.0395374	−	0.205139i
$13$	−0.0130536	−	0.0444565i	−0.00362042	−	0.0123300i	0.957663	−	0.287892i	$-0.0929543\pi$
$13$	−0.0130536	−	0.0444565i	−0.00362042	−	0.0123300i	−0.961283	+	0.275562i	$0.911136\pi$
$14$	−0.629300	+	2.92200i	−0.168188	+	0.780937i
$15$	−2.15915	−	3.35971i	−0.557491	−	0.867473i
$16$	−0.478320	−	1.97166i	−0.119580	−	0.492916i
$17$	2.93114	+	1.17345i	0.710905	+	0.284604i	0.698794	−	0.715323i	$-0.253720\pi$
$17$	2.93114	+	1.17345i	0.710905	+	0.284604i	0.0121116	+	0.999927i	$0.496145\pi$
$18$	0.655310	+	0.920254i	0.154458	+	0.216906i
$19$	0.106407	−	0.0425988i	0.0244114	−	0.00977284i	−0.359425	−	0.933174i	$-0.617027\pi$
$19$	0.106407	−	0.0425988i	0.0244114	−	0.00977284i	0.383836	+	0.923401i	$0.374603\pi$
$20$	2.43143	+	1.56258i	0.543684	+	0.349404i
$21$	1.48750	+	2.18800i	0.324600	+	0.477460i
$22$		−	0.693267i		−	0.147805i
$23$	−3.88694	+	2.80922i	−0.810482	+	0.585763i
$23$	−3.88694	+	2.80922i	−0.810482	+	0.585763i
$24$	−2.66481	−	1.53853i	−0.543952	−	0.314051i
$25$	10.7517	−	2.07222i	2.15034	−	0.414445i
$26$	−0.0522850	−	0.00249064i	−0.0102539	−	0.000488455i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	−1.63702	−	0.993166i	−0.309367	−	0.187691i
$29$	−0.704571	−	4.90040i	−0.130836	−	0.909982i	−0.944468	−	0.328602i	$-0.893422\pi$
$29$	−0.704571	−	4.90040i	−0.130836	−	0.909982i	0.813633	−	0.581379i	$-0.197487\pi$
$30$	−4.38463	+	1.06370i	−0.800520	+	0.194204i
$31$	−0.899627	+	0.0428545i	−0.161578	+	0.00769690i	−0.128215	−	0.991746i	$-0.540925\pi$
$31$	−0.899627	+	0.0428545i	−0.161578	+	0.00769690i	−0.0333629	+	0.999443i	$0.510622\pi$
$32$	3.84456	+	0.367111i	0.679629	+	0.0648967i
$33$	−0.444123	−	0.423471i	−0.0773119	−	0.0737168i
$34$	2.33583	−	2.69569i	0.400592	−	0.462307i
$35$	−10.3202	+	2.26743i	−1.74443	+	0.383266i
$36$	−0.694387	+	0.203890i	−0.115731	+	0.0339817i
$37$	−6.97719	−	4.96843i	−1.14704	−	0.816806i	−0.161607	−	0.986855i	$-0.551668\pi$
$37$	−6.97719	−	4.96843i	−1.14704	−	0.816806i	−0.985436	+	0.170050i	$0.945607\pi$
$38$	−0.00616122	−	0.129340i	−0.000999482	−	0.0209817i
$39$	−0.0335330	+	0.0319737i	−0.00536958	+	0.00511988i
$40$	9.65967	−	7.59645i	1.52733	−	1.20110i
$41$	−2.62914	−	1.20069i	−0.410602	−	0.187516i	0.199395	−	0.979919i	$-0.436102\pi$
$41$	−2.62914	−	1.20069i	−0.410602	−	0.187516i	−0.609997	+	0.792403i	$0.708830\pi$
$42$	2.88554	−	0.779593i	0.445248	−	0.120294i
$43$	−3.51134	+	5.46375i	−0.535474	+	0.833213i	−0.998590	−	0.0530841i	$-0.983095\pi$
$43$	−3.51134	+	5.46375i	−0.535474	+	0.833213i	0.463116	+	0.886298i	$0.346731\pi$
$44$	0.419678	+	0.145252i	0.0632688	+	0.0218976i
$45$	−1.99685	+	3.45864i	−0.297672	+	0.515584i
$46$	1.56290	+	5.18770i	0.230437	+	0.764884i
$47$	−11.8139	+	6.82078i	−1.72324	+	0.994913i	−0.811251	+	0.584698i	$0.801213\pi$
$47$	−11.8139	+	6.82078i	−1.72324	+	0.994913i	−0.911989	+	0.410216i	$0.865453\pi$
$48$	−1.53330	+	1.32862i	−0.221313	+	0.191769i
$49$	6.79578	−	1.67850i	0.970826	−	0.239786i
$50$	1.76045	−	12.2442i	0.248966	−	1.73159i
$51$	−0.300121	−	3.14301i	−0.0420253	−	0.440109i
$52$	0.0124624	−	0.0311296i	0.00172822	−	0.00431689i
$53$	−6.16614	−	6.46686i	−0.846984	−	0.888291i	0.147932	−	0.988997i	$-0.452738\pi$
$53$	−6.16614	−	6.46686i	−0.846984	−	0.888291i	−0.994916	+	0.100706i	$0.967890\pi$
$54$	0.517674	−	1.00415i	0.0704465	−	0.136647i
$55$	2.22928	−	1.01808i	0.300596	−	0.137278i
$56$	−6.26703	+	5.19638i	−0.837467	+	0.694396i
$57$	−0.0866217	−	0.0750581i	−0.0114733	−	0.00994169i
$58$	−5.49200	−	1.05850i	−0.721135	−	0.138987i
$59$	5.96573	+	1.44727i	0.776672	+	0.188419i	0.604454	−	0.796640i	$-0.293391\pi$
$59$	5.96573	+	1.44727i	0.776672	+	0.188419i	0.172218	+	0.985059i	$0.444907\pi$
$60$	0.274735	−	2.87716i	0.0354681	−	0.371439i
$61$	3.58765	+	1.84956i	0.459351	+	0.236812i	0.672340	−	0.740243i	$-0.265289\pi$
$61$	3.58765	+	1.84956i	0.459351	+	0.236812i	−0.212988	+	0.977055i	$0.568320\pi$
$62$	−0.286661	+	0.976276i	−0.0364059	+	0.123987i
$63$	1.26316	−	2.32474i	0.159143	−	0.292890i
$64$	3.49813	−	7.65983i	0.437266	−	0.957478i
$65$	−0.0687728	−	0.171786i	−0.00853022	−	0.0213075i
$66$	−0.616200	+	0.317673i	−0.0758490	+	0.0391029i
$67$	1.38928	+	7.20828i	0.169728	+	0.880632i	0.962535	+	0.271159i	$0.0874068\pi$
$67$	1.38928	+	7.20828i	0.169728	+	0.880632i	−0.792807	+	0.609473i	$0.791381\pi$
$68$	1.14247	+	1.97882i	0.138545	+	0.239967i
$69$	4.27803	+	2.16759i	0.515015	+	0.260947i
$70$	−1.39259	+	11.8556i	−0.166446	+	1.41702i
$71$	−2.10992	−	2.43498i	−0.250402	−	0.288979i	0.616608	−	0.787270i	$-0.288506\pi$
$71$	−2.10992	−	2.43498i	−0.250402	−	0.288979i	−0.867010	+	0.498291i	$0.833961\pi$
$72$	−0.146412	+	3.07357i	−0.0172549	+	0.362224i
$73$	0.180264	−	0.229224i	0.0210983	−	0.0268287i	−0.775389	−	0.631483i	$-0.782446\pi$
$73$	0.180264	−	0.229224i	0.0210983	−	0.0268287i	0.796488	+	0.604655i	$0.206689\pi$
$74$	−7.88237	+	5.61301i	−0.916307	+	0.652499i
$75$	−6.76859	−	8.60696i	−0.781570	−	0.993847i
$76$	0.0795884	+	0.0233693i	0.00912942	+	0.00268064i
$77$	−1.45892	+	0.712440i	−0.166259	+	0.0811901i
$78$	0.0217446	+	0.0476141i	0.00246209	+	0.00539123i
$79$	7.96425	−	8.35267i	0.896049	−	0.939749i	−0.102438	−	0.994739i	$-0.532664\pi$
$79$	7.96425	−	8.35267i	0.896049	−	0.939749i	0.998487	+	0.0549906i	$0.0175129\pi$
$80$	−2.65011	−	7.65698i	−0.296291	−	0.856077i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	−2.25332	+	2.36321i	−0.248837	+	0.260973i
$83$	5.02032	+	10.9930i	0.551051	+	1.20663i	0.956289	+	0.292423i	$0.0944615\pi$
$83$	5.02032	+	10.9930i	0.551051	+	1.20663i	−0.405238	+	0.914211i	$0.632811\pi$
$84$	−0.132636	+	1.91013i	−0.0144718	+	0.208413i
$85$	12.0985	+	3.55245i	1.31227	+	0.385317i
$86$	4.53565	+	5.76755i	0.489092	+	0.621931i
$87$	−4.03280	+	2.87174i	−0.432361	+	0.307883i
$88$	1.16724	−	1.48427i	0.124428	−	0.158223i
$89$	−0.699789	+	14.6904i	−0.0741775	+	1.55718i	0.588639	+	0.808396i	$0.299664\pi$
$89$	−0.699789	+	14.6904i	−0.0741775	+	1.55718i	−0.662817	+	0.748782i	$0.730639\pi$
$90$	2.95461	+	3.40980i	0.311443	+	0.359424i
$91$	0.0484897	+	0.112589i	0.00508310	+	0.0118025i
$92$	−3.46789	−	0.140795i	−0.361553	−	0.0146789i
$93$	0.450324	+	0.779983i	0.0466964	+	0.0808805i
$94$	2.91661	+	15.1328i	0.300826	+	1.56083i
$95$	0.406860	−	0.209751i	0.0417429	−	0.0215200i
$96$	−1.43538	−	3.58540i	−0.146498	−	0.365934i
$97$	−1.42557	+	3.12156i	−0.144744	+	0.316946i	−0.968093	−	0.250589i	$-0.919376\pi$
$97$	−1.42557	+	3.12156i	−0.144744	+	0.316946i	0.823349	+	0.567535i	$0.192103\pi$
$98$	0.719069	−	7.87538i	0.0726369	−	0.795533i
$99$	−0.172887	+	0.588798i	−0.0173758	+	0.0591764i
$100$	7.04335	+	3.63110i	0.704335	+	0.363110i
$101$	−1.72272	+	18.0411i	−0.171417	+	1.79516i	0.344774	+	0.938686i	$0.387956\pi$
$101$	−1.72272	+	18.0411i	−0.171417	+	1.79516i	−0.516190	+	0.856474i	$0.672650\pi$
$102$	−3.46637	−	0.840931i	−0.343221	−	0.0832646i
$103$	−15.3984	−	2.96779i	−1.51725	−	0.292425i	−0.638466	−	0.769650i	$-0.720431\pi$
$103$	−15.3984	−	2.96779i	−1.51725	−	0.292425i	−0.878781	+	0.477224i	$0.841643\pi$
$104$	−0.107747	−	0.0933637i	−0.0105655	−	0.00915506i
$105$	6.74435	+	8.13394i	0.658181	+	0.793791i
$106$	−9.18240	+	4.19346i	−0.891873	+	0.407305i
$107$	−2.22097	+	4.30808i	−0.214709	+	0.416478i	−0.971452	−	0.237234i	$-0.923759\pi$
$107$	−2.22097	+	4.30808i	−0.214709	+	0.416478i	0.756743	+	0.653712i	$0.226789\pi$
$108$	0.499411	+	0.523767i	0.0480559	+	0.0503995i
$109$	−0.0235768	+	0.0588920i	−0.00225825	+	0.00564084i	−0.929493	−	0.368840i	$-0.879755\pi$
$109$	−0.0235768	+	0.0588920i	−0.00225825	+	0.00564084i	0.927235	+	0.374481i	$0.122179\pi$
$110$	−0.263181	−	2.75616i	−0.0250934	−	0.262790i
$111$	−1.21899	+	8.47824i	−0.115701	+	0.804719i
$112$	1.88629	+	5.02550i	0.178238	+	0.474865i
$113$	5.29534	−	4.58844i	0.498144	−	0.431644i	−0.369202	−	0.929349i	$-0.620369\pi$
$113$	5.29534	−	4.58844i	0.498144	−	0.431644i	0.867347	+	0.497705i	$0.165824\pi$
$114$	−0.112139	+	0.0647433i	−0.0105027	+	0.00606377i
$115$	−14.3865	+	12.6439i	−1.34155	+	1.17905i
$116$	1.79145	−	3.10288i	0.166332	−	0.288095i
$117$	0.0437850	+	0.0151541i	0.00404793	+	0.00140100i
$118$	3.74944	−	5.83424i	0.345164	−	0.537086i
$119$	−8.07327	−	2.14530i	−0.740075	−	0.196659i
$120$	−11.1783	−	5.10496i	−1.02044	−	0.466017i
$121$	−8.35058	+	6.56697i	−0.759143	+	0.596997i
$122$	3.30023	−	3.14676i	0.298788	−	0.284894i
$123$	0.137528	+	2.88706i	0.0124004	+	0.260317i
$124$	−0.530941	−	0.378081i	−0.0476799	−	0.0339527i
$125$	22.7984	−	6.69421i	2.03915	−	0.598749i
$126$	−2.01516	−	2.20754i	−0.179525	−	0.196663i
$127$	8.14098	−	9.39519i	0.722395	−	0.833688i	−0.269198	−	0.963085i	$-0.586759\pi$
$127$	8.14098	−	9.39519i	0.722395	−	0.833688i	0.991593	+	0.129397i	$0.0413041\pi$
$128$	−1.29487	−	1.23466i	−0.114452	−	0.109129i
$129$	6.46536	+	0.617367i	0.569243	+	0.0543561i
$130$	−0.208810	+	0.00994687i	−0.0183139	+	0.000872398i
$131$	13.8468	−	3.35919i	1.20980	−	0.293494i	0.420380	−	0.907348i	$-0.361897\pi$
$131$	13.8468	−	3.35919i	1.20980	−	0.293494i	0.789419	+	0.613854i	$0.210382\pi$
$132$	−0.0632025	−	0.439583i	−0.00550107	−	0.0382608i
$133$	−0.265852	+	0.145883i	−0.0230523	+	0.0126496i
$134$	8.20890	+	1.18026i	0.709141	+	0.101959i
$135$	3.98917	+	0.190028i	0.343333	+	0.0163550i
$136$	9.53964	−	1.83861i	0.818017	−	0.157660i
$137$	−1.13982	−	0.658078i	−0.0973818	−	0.0562234i	0.450518	−	0.892767i	$-0.351239\pi$
$137$	−1.13982	−	0.658078i	−0.0973818	−	0.0562234i	−0.547900	+	0.836544i	$0.684573\pi$
$138$	3.89485	−	3.76630i	0.331551	−	0.320609i
$139$			1.67284i			0.141888i	0.997480	+	0.0709442i	$0.0226012\pi$
$139$			1.67284i			0.141888i	−0.997480	+	0.0709442i	$0.977399\pi$
$140$	−6.88518	−	3.32699i	−0.581904	−	0.281182i
$141$	11.4760	+	7.37518i	0.966454	+	0.621103i
$142$	−3.37920	+	1.35283i	−0.283576	+	0.113527i
$143$	−0.0164926	−	0.0231606i	−0.00137918	−	0.00193679i
$144$	1.88352	+	0.754048i	0.156960	+	0.0628374i
$145$	−4.66141	−	19.2146i	−0.387109	−	1.59569i
$146$	−0.178112	−	0.277148i	−0.0147407	−	0.0229369i
$147$	−4.60592	−	5.27119i	−0.379890	−	0.434761i
$148$	−1.74641	−	5.94772i	−0.143554	−	0.488899i
$149$	−1.12355	+	5.82955i	−0.0920452	+	0.477576i	0.906429	+	0.422358i	$0.138797\pi$
$149$	−1.12355	+	5.82955i	−0.0920452	+	0.477576i	−0.998474	+	0.0552178i	$0.982415\pi$
$150$	−11.6898	+	4.04587i	−0.954467	+	0.330344i
$151$	0.855463	−	3.52627i	0.0696166	−	0.286964i	−0.926353	−	0.376657i	$-0.877074\pi$
$151$	0.855463	−	3.52627i	0.0696166	−	0.286964i	0.995969	+	0.0896934i	$0.0285887\pi$
$152$	0.204576	−	0.287287i	0.0165933	−	0.0233020i
$153$	−2.65609	+	1.70697i	−0.214732	+	0.138000i
$154$	0.221531	+	1.82079i	0.0178515	+	0.146723i
$155$	−3.56030	+	0.511894i	−0.285970	+	0.0411163i
$156$	−0.0333797	+	0.00318737i	−0.00267251	+	0.000255194i
$157$	−7.35293	−	5.78241i	−0.586828	−	0.461486i	0.280065	−	0.959981i	$-0.409644\pi$
$157$	−7.35293	−	5.78241i	−0.586828	−	0.461486i	−0.866893	+	0.498495i	$0.833886\pi$
$158$	−5.97451	−	11.5889i	−0.475307	−	0.921967i
$159$	−2.92249	+	8.44397i	−0.231768	+	0.669650i
$160$	15.4239			1.21936
$161$	9.31091	−	8.62015i	0.733803	−	0.679363i
$162$	−1.12973			−0.0887603
$163$	2.47855	−	7.16131i	0.194135	−	0.560917i	−0.805357	−	0.592790i	$-0.798026\pi$
$163$	2.47855	−	7.16131i	0.194135	−	0.560917i	0.999492	+	0.0318737i	$0.0101474\pi$
$164$	−0.958489	−	1.85921i	−0.0748455	−	0.145180i
$165$	−1.92642	−	1.51495i	−0.149972	−	0.117939i
$166$	13.5911	−	1.29779i	1.05487	−	0.100728i
$167$	3.58201	−	0.515015i	0.277184	−	0.0398531i	−0.00232072	−	0.999997i	$-0.500739\pi$
$167$	3.58201	−	0.515015i	0.277184	−	0.0398531i	0.279505	+	0.960144i	$0.409830\pi$
$168$	7.49044	+	3.18924i	0.577900	+	0.246055i
$169$	10.9345	−	7.02717i	0.841115	−	0.540552i
$170$	8.26300	−	11.6038i	0.633743	−	0.889968i
$171$	−0.0270220	+	0.111386i	−0.00206642	+	0.00851790i
$172$	−4.44176	+	1.53731i	−0.338681	+	0.117219i
$173$	−3.88190	+	20.1412i	−0.295135	+	1.53131i	0.467216	+	0.884143i	$0.345257\pi$
$173$	−3.88190	+	20.1412i	−0.295135	+	1.53131i	−0.762351	+	0.647164i	$0.775955\pi$
$174$	1.57575	+	5.36652i	0.119457	+	0.406835i
$175$	−27.5760	+	8.87813i	−2.08455	+	0.671124i
$176$	−0.673107	−	1.04737i	−0.0507373	−	0.0789488i
$177$	−1.44727	−	5.96573i	−0.108783	−	0.448412i
$178$	15.4249	+	6.17519i	1.15614	+	0.462850i
$179$	−15.2596	−	21.4291i	−1.14055	−	1.60168i	−0.719225	−	0.694777i	$-0.755503\pi$
$179$	−15.2596	−	21.4291i	−1.14055	−	1.60168i	−0.421329	−	0.906908i	$-0.638436\pi$
$180$	−2.68321	+	1.07419i	−0.199995	+	0.0800658i
$181$	9.90417	+	6.36502i	0.736171	+	0.473108i	0.854228	−	0.519898i	$-0.174030\pi$
$181$	9.90417	+	6.36502i	0.736171	+	0.473108i	−0.118057	+	0.993007i	$0.537667\pi$
$182$	0.138116	−	0.0101661i	0.0102379	−	0.000753563i
$183$		−	4.03635i		−	0.298375i
$184$	−5.38830	+	13.7382i	−0.397231	+	1.01279i
$185$	−29.6247	−	17.1038i	−2.17805	−	1.25750i
$186$	0.999104	−	0.192562i	0.0732579	−	0.0141193i
$187$	1.93530	+	0.0921897i	0.141523	+	0.00674158i
$188$	−9.77193	−	1.40499i	−0.712691	−	0.102470i
$189$	−2.64513	−	0.0574792i	−0.192405	−	0.00418099i
$190$	−0.0735953	−	0.511866i	−0.00533916	−	0.0371347i
$191$	−21.7550	+	5.27770i	−1.57414	+	0.381881i	−0.925357	−	0.379097i	$-0.876235\pi$
$191$	−21.7550	+	5.27770i	−1.57414	+	0.381881i	−0.648778	+	0.760978i	$0.724720\pi$
$192$	−8.41126	+	0.400678i	−0.607030	+	0.0289164i
$193$	−22.6257	−	2.16050i	−1.62864	−	0.155516i	−0.759643	−	0.650340i	$-0.774626\pi$
$193$	−22.6257	−	2.16050i	−1.62864	−	0.155516i	−0.868993	+	0.494824i	$0.835232\pi$
$194$	2.80582	+	2.67535i	0.201446	+	0.192079i
$195$	−0.121176	+	0.139845i	−0.00867761	+	0.0100145i
$196$	4.61680	+	2.08533i	0.329771	+	0.148952i
$197$	11.7035	−	3.43646i	0.833839	−	0.244837i	0.163174	−	0.986597i	$-0.447827\pi$
$197$	11.7035	−	3.43646i	0.833839	−	0.244837i	0.670665	+	0.741760i	$0.266009\pi$
$198$	0.564719	+	0.402134i	0.0401328	+	0.0285784i
$199$	−0.492608	−	10.3411i	−0.0349200	−	0.733061i	−0.946648	−	0.322268i	$-0.895555\pi$
$199$	−0.492608	−	10.3411i	−0.0349200	−	0.733061i	0.911728	−	0.410793i	$-0.134748\pi$
$200$	24.3844	−	23.2505i	1.72424	−	1.64406i
$201$	5.77037	−	4.53787i	0.407011	−	0.320077i
$202$	18.6242	+	8.50537i	1.31039	+	0.598436i
$203$	3.41638	+	12.6452i	0.239783	+	0.887518i
$204$	1.23533	−	1.92222i	0.0864907	−	0.134582i
$205$	−10.9082	−	3.77538i	−0.761864	−	0.263684i
$206$	−8.85811	+	15.3427i	−0.617174	+	1.06898i
$207$	−0.0336788	−	4.79571i	−0.00234084	−	0.333325i
$208$	−0.0814094	+	0.0470017i	−0.00564473	+	0.00325898i
$209$	0.0531558	−	0.0460598i	0.00367687	−	0.00318602i
$210$	11.1758	−	4.19478i	0.771205	−	0.289467i
$211$	−1.05331	+	7.32590i	−0.0725125	+	0.504336i	0.920905	+	0.389787i	$0.127451\pi$
$211$	−1.05331	+	7.32590i	−0.0725125	+	0.504336i	−0.993418	+	0.114549i	$0.963458\pi$
$212$	−0.614686	−	6.43729i	−0.0422168	−	0.442115i
$213$	−1.19747	+	2.99115i	−0.0820496	+	0.204950i
$214$	3.77866	+	3.96294i	0.258304	+	0.270901i
$215$	−11.8855	+	23.0547i	−0.810587	+	1.57232i
$216$	2.79899	−	1.27826i	0.190447	−	0.0869743i
$217$	2.34907	−	0.400025i	0.159465	−	0.0271555i
$218$	0.0541615	+	0.0469312i	0.00366828	+	0.00317858i
$219$	−0.286344	−	0.0551884i	−0.0193494	−	0.00372928i
$220$	1.72362	+	0.418145i	0.116206	+	0.0281913i
$221$	0.0139056	−	0.145626i	0.000935391	−	0.00979586i
$222$	8.60095	+	4.43410i	0.577258	+	0.297597i
$223$	3.48642	−	11.8736i	0.233468	−	0.795118i	−0.756521	−	0.653970i	$-0.773102\pi$
$223$	3.48642	−	11.8736i	0.233468	−	0.795118i	0.989988	−	0.141148i	$-0.0450794\pi$
$224$	−10.2146	+	0.264343i	−0.682492	+	0.0176621i
$225$	−4.54863	+	9.96010i	−0.303242	+	0.664007i
$226$	−2.94199	−	7.34873i	−0.195698	−	0.488831i
$227$	16.0954	−	8.29774i	1.06829	−	0.550740i	0.167889	−	0.985806i	$-0.446305\pi$
$227$	16.0954	−	8.29774i	1.06829	−	0.550740i	0.900399	+	0.435066i	$0.143275\pi$
$228$	−0.0156981	−	0.0814494i	−0.00103963	−	0.00539412i
$229$	2.70976	+	4.69344i	0.179066	+	0.310151i	0.941561	−	0.336843i	$-0.109359\pi$
$229$	2.70976	+	4.69344i	0.179066	+	0.310151i	−0.762495	+	0.646994i	$0.776026\pi$
$230$	8.18286	+	20.0310i	0.539562	+	1.32080i
$231$	1.30176	+	0.970278i	0.0856493	+	0.0638396i
$232$	−9.97607	−	11.5130i	−0.654961	−	0.755865i
$233$	−0.216059	+	4.53563i	−0.0141545	+	0.297139i	0.980679	+	0.195622i	$0.0626726\pi$
$233$	−0.216059	+	4.53563i	−0.0141545	+	0.297139i	−0.994834	+	0.101517i	$0.967630\pi$
$234$	0.0323571	−	0.0411454i	0.00211525	−	0.00268976i
$235$	−44.3783	+	31.6016i	−2.89492	+	2.06146i
$236$	2.74626	+	3.49215i	0.178766	+	0.227320i
$237$	−11.0736	−	3.25150i	−0.719306	−	0.211207i
$238$	−5.27339	+	7.82633i	−0.341823	+	0.507305i
$239$	−3.10404	−	6.79691i	−0.200784	−	0.439655i	0.782278	−	0.622930i	$-0.214058\pi$
$239$	−3.10404	−	6.79691i	−0.200784	−	0.439655i	−0.983062	+	0.183274i	$0.941330\pi$
$240$	−5.59145	+	5.86414i	−0.360926	+	0.378529i
$241$	6.85251	+	19.7990i	0.441409	+	1.27537i	0.918118	+	0.396306i	$0.129708\pi$
$241$	6.85251	+	19.7990i	0.441409	+	1.27537i	−0.476710	+	0.879061i	$0.658171\pi$
$242$	3.92535	+	11.3416i	0.252331	+	0.729063i
$243$	−0.690079	+	0.723734i	−0.0442686	+	0.0464276i
$244$	1.21347	+	2.65714i	0.0776847	+	0.170106i
$245$	26.3802	−	9.25293i	1.68537	−	0.591148i
$246$	3.13304	+	0.919943i	0.199755	+	0.0586534i
$247$	−0.00328278	−	0.00417440i	−0.000208879	−	0.000265611i
$248$	−2.25747	+	1.60754i	−0.143349	+	0.102079i
$249$	7.47049	−	9.49950i	0.473423	−	0.602006i
$250$	1.27726	−	26.8131i	0.0807812	−	1.69581i
$251$	1.99912	+	2.30711i	0.126184	+	0.145624i	0.815326	−	0.579003i	$-0.196558\pi$
$251$	1.99912	+	2.30711i	0.126184	+	0.145624i	−0.689142	+	0.724626i	$0.742012\pi$
$252$	1.75857	−	0.757383i	0.110780	−	0.0477106i
$253$	−1.69022	+	2.40922i	−0.106263	+	0.151466i
$254$	−7.02221	−	12.1628i	−0.440612	−	0.763163i
$255$	−2.38633	−	12.3814i	−0.149438	−	0.775356i
$256$	13.1728	−	6.79107i	0.823302	−	0.424442i
$257$	−9.94391	−	24.8387i	−0.620284	−	1.54940i	−0.821719	−	0.569893i	$-0.806984\pi$
$257$	−9.94391	−	24.8387i	−0.620284	−	1.54940i	0.201434	−	0.979502i	$-0.435440\pi$
$258$	3.04805	−	6.67430i	0.189763	−	0.415523i
$259$	19.9124	+	10.8195i	1.23730	+	0.672290i
$260$	0.0377281	−	0.128490i	0.00233980	−	0.00796862i
$261$	4.40044	+	2.26858i	0.272380	+	0.140422i
$262$	1.53011	−	16.0240i	0.0945305	−	0.989968i
$263$	22.8456	+	5.54228i	1.40872	+	0.341752i	0.866790	−	0.498673i	$-0.166179\pi$
$263$	22.8456	+	5.54228i	1.40872	+	0.341752i	0.541929	+	0.840424i	$0.317694\pi$
$264$	−1.85413	−	0.357354i	−0.114114	−	0.0219936i
$265$	−26.9691	−	23.3689i	−1.65670	−	1.43554i
$266$	0.0575119	+	0.337727i	0.00352628	+	0.0207074i
$267$	13.3780	−	6.10953i	0.818720	−	0.373897i
$268$	−2.43440	+	4.72207i	−0.148705	+	0.288447i
$269$	−10.9301	−	11.4632i	−0.666422	−	0.698923i	0.300562	−	0.953762i	$-0.402826\pi$
$269$	−10.9301	−	11.4632i	−0.666422	−	0.698923i	−0.966983	+	0.254840i	$0.917977\pi$
$270$	1.67687	−	4.18862i	0.102051	−	0.254911i
$271$	−2.60885	−	27.3211i	−0.158476	−	1.65964i	−0.629114	−	0.777313i	$-0.716582\pi$
$271$	−2.60885	−	27.3211i	−0.158476	−	1.65964i	0.470637	−	0.882327i	$-0.344024\pi$
$272$	0.911627	−	6.34050i	0.0552755	−	0.384449i
$273$	0.0778534	−	0.0946904i	0.00471190	−	0.00573093i
$274$	−1.12373	+	0.973716i	−0.0678869	+	0.0588244i
$275$	5.81907	−	3.35964i	0.350903	−	0.202594i
$276$	1.46394	+	3.14690i	0.0881187	+	0.189421i
$277$	11.7516	−	20.3543i	0.706084	−	1.22297i	−0.260215	−	0.965551i	$-0.583794\pi$
$277$	11.7516	−	20.3543i	0.706084	−	1.22297i	0.966299	−	0.257422i	$-0.0828731\pi$
$278$	1.78592	+	0.618113i	0.107112	+	0.0370720i
$279$	0.486927	−	0.757673i	0.0291515	−	0.0453607i
$280$	−22.9426	+	23.0379i	−1.37108	+	1.37678i
$281$	−0.363126	−	0.165834i	−0.0216623	−	0.00989283i	0.404554	−	0.914514i	$-0.367427\pi$
$281$	−0.363126	−	0.165834i	−0.0216623	−	0.00989283i	−0.426217	+	0.904621i	$0.640154\pi$
$282$	12.1141	−	9.52665i	0.721386	−	0.567304i
$283$	−2.93315	+	2.79675i	−0.174358	+	0.166250i	−0.772233	−	0.635339i	$-0.780860\pi$
$283$	−2.93315	+	2.79675i	−0.174358	+	0.166250i	0.597875	+	0.801589i	$0.296012\pi$
$284$	−0.110948	−	2.32908i	−0.00658355	−	0.138206i
$285$	−0.372868	−	0.265518i	−0.0220868	−	0.0157279i
$286$	−0.0308202	+	0.00904963i	−0.00182244	+	0.000535116i
$287$	7.28880	+	2.31333i	0.430244	+	0.136552i
$288$	−2.52911	+	2.91874i	−0.149029	+	0.171989i
$289$	−5.08889	−	4.85225i	−0.299347	−	0.285426i
$290$	−22.2359	−	2.12327i	−1.30574	−	0.124683i
$291$	3.42778	−	0.163285i	0.200940	−	0.00957196i
$292$	0.205093	−	0.0497550i	0.0120021	−	0.00291169i
$293$	1.63567	+	11.3763i	0.0955567	+	0.664611i	0.980151	+	0.198251i	$0.0635260\pi$
$293$	1.63567	+	11.3763i	0.0955567	+	0.664611i	−0.884595	+	0.466361i	$0.845565\pi$
$294$	−7.32941	+	2.96957i	−0.427460	+	0.173189i
$295$	24.2668	+	3.48904i	1.41287	+	0.203140i
$296$	−26.3265	−	1.25408i	−1.53019	−	0.0728921i
$297$	0.602566	−	0.116135i	0.0349644	−	0.00673884i
$298$	5.80847	+	3.35352i	0.336476	+	0.194264i
$299$	0.175627	+	0.136129i	0.0101568	+	0.00787255i
$300$		−	7.92424i		−	0.457506i
$301$	7.47619	−	15.4719i	0.430921	−	0.891787i
$302$	−3.44855	−	2.21625i	−0.198442	−	0.127531i
$303$	16.8250	−	6.73571i	0.966571	−	0.386956i
$304$	−0.134887	−	0.189422i	−0.00773630	−	0.0108641i
$305$	14.9652	+	5.99118i	0.856907	+	0.343054i
$306$	0.840931	+	3.46637i	0.0480728	+	0.198159i
$307$	−11.5672	−	17.9988i	−0.660172	−	1.02725i	−0.996343	−	0.0854472i	$-0.972768\pi$
$307$	−11.5672	−	17.9988i	−0.660172	−	1.02725i	0.336170	−	0.941801i	$-0.390868\pi$
$308$	−1.14865	−	0.247381i	−0.0654504	−	0.0140958i
$309$	4.41807	+	15.0465i	0.251335	+	0.855968i
$310$	−0.769032	+	3.99012i	−0.0436781	+	0.226623i
$311$	26.9803	−	9.33797i	1.52991	−	0.529508i	0.572917	−	0.819613i	$-0.305812\pi$
$311$	26.9803	−	9.33797i	1.52991	−	0.529508i	0.956995	+	0.290105i	$0.0936904\pi$
$312$	−0.0336122	+	0.138551i	−0.00190292	+	0.00784393i
$313$	−13.7579	+	19.3202i	−0.777640	+	1.09204i	0.215659	+	0.976469i	$0.430810\pi$
$313$	−13.7579	+	19.3202i	−0.777640	+	1.09204i	−0.993299	+	0.115573i	$0.963129\pi$
$314$	−8.89020	+	5.71338i	−0.501703	+	0.322425i
$315$	4.13929	−	9.72180i	0.233223	−	0.547762i
$316$	8.26728	−	1.18866i	0.465071	−	0.0668671i
$317$	3.42140	−	0.326704i	0.192165	−	0.0183495i	0.00147035	−	0.999999i	$-0.499532\pi$
$317$	3.42140	−	0.326704i	0.192165	−	0.0183495i	0.190695	+	0.981649i	$0.438926\pi$
$318$	7.93492	+	6.24009i	0.444968	+	0.349927i
$319$	−1.39213	−	2.70035i	−0.0779442	−	0.151191i
$320$	10.9993	−	31.7805i	0.614881	−	1.77658i
$321$	4.84689			0.270527
$322$	−5.76249	−	13.1255i	−0.321131	−	0.731454i
$323$	0.361880			0.0201356
$324$	0.236700	−	0.683899i	0.0131500	−	0.0379944i
$325$	−0.232473	−	0.450934i	−0.0128953	−	0.0250133i
$326$	−6.72958	−	5.29220i	−0.372717	−	0.293108i
$327$	0.0631489	−	0.00602999i	0.00349214	−	0.000333459i
$328$	−8.80319	+	1.26571i	−0.486075	+	0.0698870i
$329$	28.8484	−	21.6891i	1.59046	−	1.19576i
$330$	−2.32918	+	1.49687i	−0.128217	+	0.0824000i
$331$	2.18659	−	3.07063i	0.120186	−	0.168777i	−0.750100	−	0.661324i	$-0.769995\pi$
$331$	2.18659	−	3.07063i	0.120186	−	0.168777i	0.870286	+	0.492547i	$0.163934\pi$
$332$	−2.06194	+	8.49944i	−0.113164	+	0.466468i
$333$	8.09433	−	2.80148i	0.443567	−	0.153520i
$334$	0.773722	−	4.01445i	0.0423362	−	0.219661i
$335$	8.25969	+	28.1299i	0.451275	+	1.53690i
$336$	3.60249	−	3.97942i	0.196532	−	0.217095i
$337$	−11.6998	−	18.2053i	−0.637331	−	0.991706i	−0.998251	−	0.0591098i	$-0.981174\pi$
$337$	−11.6998	−	18.2053i	−0.637331	−	0.991706i	0.360921	−	0.932597i	$-0.382463\pi$
$338$	−3.46191	−	14.2702i	−0.188303	−	0.776196i
$339$	−6.50484	−	2.60414i	−0.353294	−	0.141438i
$340$	5.29323	+	7.43331i	0.287066	+	0.403128i
$341$	−0.513097	+	0.205413i	−0.0277858	+	0.0111237i
$342$	0.108931	+	0.0700057i	0.00589032	+	0.00378548i
$343$	−17.3120	+	6.57996i	−0.934758	+	0.355285i
$344$			19.9848i			1.07751i
$345$	17.8307	+	6.99344i	0.959971	+	0.376514i
$346$	20.0684	+	11.5865i	1.07888	+	0.622893i
$347$	−14.0437	+	2.70671i	−0.753907	+	0.145304i	−0.551704	−	0.834040i	$-0.686022\pi$
$347$	−14.0437	+	2.70671i	−0.753907	+	0.145304i	−0.202203	+	0.979344i	$0.564810\pi$
$348$	−3.57884	−	0.170481i	−0.191846	−	0.00913874i
$349$	−25.7931	−	3.70849i	−1.38067	−	0.198511i	−0.588347	−	0.808608i	$-0.700221\pi$
$349$	−25.7931	−	3.70849i	−1.38067	−	0.198511i	−0.792326	+	0.610097i	$0.791130\pi$
$350$	−0.711025	+	32.7206i	−0.0380059	+	1.74899i
$351$	−0.00659392	−	0.0458617i	−0.000351957	−	0.00244792i
$352$	2.30316	−	0.558741i	0.122759	−	0.0297810i
$353$	3.41322	−	0.162591i	0.181667	−	0.00865387i	0.0434488	−	0.999056i	$-0.486165\pi$
$353$	3.41322	−	0.162591i	0.181667	−	0.00865387i	0.138218	+	0.990402i	$0.455862\pi$
$354$	−6.90377	−	0.659231i	−0.366931	−	0.0350377i
$355$	−9.31261	−	8.87956i	−0.494262	−	0.471278i
$356$	−6.97002	+	8.04383i	−0.369410	+	0.426322i
$357$	1.79257	+	8.15884i	0.0948728	+	0.431811i
$358$	−28.5161	+	8.37308i	−1.50712	+	0.442531i
$359$	19.4983	+	13.8847i	1.02908	+	0.732805i	0.964224	−	0.265089i	$-0.0854015\pi$
$359$	19.4983	+	13.8847i	1.02908	+	0.732805i	0.0648570	+	0.997895i	$0.479341\pi$
$360$	0.584726	+	12.2749i	0.0308178	+	0.646945i
$361$	−13.7414	+	13.1024i	−0.723234	+	0.689602i
$362$	10.4549	−	8.22181i	0.549496	−	0.432129i
$363$	9.66341	+	4.41313i	0.507197	+	0.231629i
$364$	−0.0227837	+	0.0857405i	−0.00119419	+	0.00449402i
$365$	0.629640	−	0.979739i	0.0329569	−	0.0512819i
$366$	−4.30920	−	1.49143i	−0.225246	−	0.0779583i
$367$	14.8447	−	25.7118i	0.774888	−	1.34214i	−0.159970	−	0.987122i	$-0.551140\pi$
$367$	14.8447	−	25.7118i	0.774888	−	1.34214i	0.934858	−	0.355023i	$-0.115527\pi$
$368$	7.39804	+	6.32002i	0.385649	+	0.329454i
$369$	2.50310	−	1.44517i	0.130306	−	0.0752323i
$370$	−29.2064	+	25.3075i	−1.51837	+	1.31567i
$371$	18.2611	+	15.0141i	0.948069	+	0.779492i
$372$	−0.0927608	+	0.645166i	−0.00480942	+	0.0334503i
$373$	−1.04172	−	10.9094i	−0.0539383	−	0.564867i	−0.981535	−	0.191284i	$-0.938735\pi$
$373$	−1.04172	−	10.9094i	−0.0539383	−	0.564867i	0.927596	−	0.373584i	$-0.121871\pi$
$374$	0.813515	−	2.03206i	0.0420658	−	0.105075i
$375$	−16.3969	−	17.1966i	−0.846731	−	0.888026i
$376$	−19.2345	+	37.3096i	−0.991941	+	1.92410i
$377$	−0.208657	+	0.0952907i	−0.0107464	+	0.00490772i
$378$	−1.03874	+	2.80270i	−0.0534269	+	0.144155i
$379$	20.3592	+	17.6414i	1.04578	+	0.906177i	0.995706	−	0.0925688i	$-0.0295078\pi$
$379$	20.3592	+	17.6414i	1.04578	+	0.906177i	0.0500772	+	0.998745i	$0.484053\pi$
$380$	0.325284	+	0.0626934i	0.0166867	+	0.00321610i
$381$	−12.0812	−	2.93086i	−0.618938	−	0.150153i
$382$	−2.40399	+	25.1757i	−0.122999	+	1.28810i
$383$	−1.88655	−	0.972586i	−0.0963984	−	0.0496968i	0.409353	−	0.912376i	$-0.365754\pi$
$383$	−1.88655	−	0.972586i	−0.0963984	−	0.0496968i	−0.505751	+	0.862679i	$0.668785\pi$
$384$	−0.504063	+	1.71668i	−0.0257229	+	0.0876040i
$385$	−5.52963	+	3.38623i	−0.281816	+	0.172578i
$386$	−10.6667	+	23.3569i	−0.542923	+	1.18884i
$387$	−2.41386	−	6.02953i	−0.122703	−	0.306498i
$388$	−2.20743	+	1.13801i	−0.112065	+	0.0577736i
$389$	5.61320	+	29.1241i	0.284601	+	1.47665i	0.789649	+	0.613558i	$0.210262\pi$
$389$	5.61320	+	29.1241i	0.284601	+	1.47665i	−0.505049	+	0.863091i	$0.668525\pi$
$390$	0.104524	+	0.181040i	0.00529276	+	0.00916733i
$391$	−14.6896	+	3.67308i	−0.742887	+	0.185756i
$392$	14.7991	−	15.6503i	0.747469	−	0.790459i
$393$	−9.33073	−	10.7682i	−0.470673	−	0.543186i
$394$	0.655680	−	13.7644i	0.0330327	−	0.693441i
$395$	28.4919	−	36.2304i	1.43358	−	1.82295i
$396$	−0.361756	+	0.257605i	−0.0181789	+	0.0129451i
$397$	9.40916	+	11.9647i	0.472232	+	0.600492i	0.962568	−	0.271042i	$-0.0873682\pi$
$397$	9.40916	+	11.9647i	0.472232	+	0.600492i	−0.490336	+	0.871534i	$0.663126\pi$
$398$	−11.2222	−	3.29513i	−0.562517	−	0.165170i
$399$	0.251486	+	0.169452i	0.0125901	+	0.00848320i
$400$	−9.22850	−	20.2076i	−0.461425	−	1.01038i
$401$	−23.5225	+	24.6696i	−1.17466	+	1.23194i	−0.207367	+	0.978263i	$0.566489\pi$
$401$	−23.5225	+	24.6696i	−1.17466	+	1.23194i	−0.967288	+	0.253680i	$0.918359\pi$
$402$	−2.71248	−	7.83719i	−0.135286	−	0.390883i
$403$	0.0136485	+	0.0394349i	0.000679882	+	0.00196439i
$404$	−9.05093	+	9.49234i	−0.450300	+	0.472262i
$405$	−1.65904	−	3.63279i	−0.0824384	−	0.180515i
$406$	14.7623	+	1.02507i	0.732643	+	0.0508732i
$407$	−5.04330	−	1.48085i	−0.249987	−	0.0734029i
$408$	−6.00554	−	7.63666i	−0.297319	−	0.378071i
$409$	26.4038	−	18.8020i	1.30558	−	0.929701i	0.305833	−	0.952085i	$-0.401065\pi$
$409$	26.4038	−	18.8020i	1.30558	−	0.929701i	0.999749	+	0.0223837i	$0.00712556\pi$
$410$	−8.06118	+	10.2506i	−0.398113	+	0.506242i
$411$	−0.0626252	+	1.31467i	−0.00308908	+	0.0648477i
$412$	−7.43196	−	8.57694i	−0.366147	−	0.422556i
$413$	−16.1308	−	1.89476i	−0.793743	−	0.0932349i
$414$	−5.13234	−	1.73606i	−0.252241	−	0.0853227i
$415$	24.1320	+	41.7979i	1.18459	+	2.05178i
$416$	−0.0338649	−	0.175708i	−0.00166036	−	0.00861479i
$417$	1.48688	−	0.766539i	0.0728127	−	0.0375376i
$418$	−0.0295323	−	0.0737682i	−0.00144447	−	0.00360812i
$419$	7.31135	−	16.0096i	0.357183	−	0.782121i	−0.642689	−	0.766127i	$-0.722181\pi$
$419$	7.31135	−	16.0096i	0.357183	−	0.782121i	0.999872	−	0.0159943i	$-0.00509136\pi$
$420$	0.197826	+	7.64431i	0.00965292	+	0.373004i
$421$	7.44134	−	25.3429i	0.362669	−	1.23514i	−0.552993	−	0.833186i	$-0.686514\pi$
$421$	7.44134	−	25.3429i	0.362669	−	1.23514i	0.915662	−	0.401950i	$-0.131667\pi$
$422$	7.43193	+	3.83143i	0.361781	+	0.186511i
$423$	1.29671	−	13.5798i	0.0630483	−	0.660272i
$424$	−26.7197	−	6.48214i	−1.29762	−	0.314800i
$425$	33.9464	+	6.54264i	1.64664	+	0.317365i
$426$	2.75088	+	2.38365i	0.133281	+	0.115488i
$427$	−10.0136	−	3.71124i	−0.484590	−	0.179599i
$428$	−3.19072	+	1.45715i	−0.154229	+	0.0704340i
$429$	−0.0130286	+	0.0252720i	−0.000629027	+	0.00122014i
$430$	20.2215	+	21.2077i	0.975167	+	1.02273i
$431$	9.49371	−	23.7141i	0.457296	−	1.14227i	−0.503248	−	0.864142i	$-0.667862\pi$
$431$	9.49371	−	23.7141i	0.457296	−	1.14227i	0.960544	−	0.278128i	$-0.0897140\pi$
$432$	−0.192855	−	2.01967i	−0.00927873	−	0.0971712i
$433$	0.953042	−	6.62855i	0.0458003	−	0.318548i	−0.954023	−	0.299734i	$-0.903102\pi$
$433$	0.953042	−	6.62855i	0.0458003	−	0.318548i	0.999823	−	0.0188137i	$-0.00598893\pi$
$434$	0.440915	−	2.65568i	0.0211646	−	0.127477i
$435$	−14.9426	+	12.9479i	−0.716445	+	0.620803i
$436$	−0.0397582	+	0.0229544i	−0.00190407	+	0.00109932i
$437$	−0.293927	+	0.464499i	−0.0140604	+	0.0222200i
$438$	−0.164723	+	0.285309i	−0.00787078	+	0.0136326i
$439$	22.6072	+	7.82443i	1.07898	+	0.373440i	0.808023	−	0.589151i	$-0.200538\pi$
$439$	22.6072	+	7.82443i	1.07898	+	0.373440i	0.270960	+	0.962591i	$0.412659\pi$
$440$	4.07703	−	6.34398i	0.194365	−	0.302437i
$441$	−2.57467	+	6.50931i	−0.122603	+	0.309967i
$442$	−0.150332	−	0.0686543i	−0.00715056	−	0.00326555i
$443$	−25.8768	+	20.3497i	−1.22944	+	0.966845i	−0.999979	−	0.00647221i	$-0.997940\pi$
$443$	−25.8768	+	20.3497i	−1.22944	+	0.966845i	−0.229464	+	0.973317i	$0.573697\pi$
$444$	−4.48629	+	4.27767i	−0.212910	+	0.203009i
$445$	2.79474	+	58.6689i	0.132484	+	2.78117i
$446$	−11.3881	−	8.10940i	−0.539240	−	0.383991i
$447$	5.69636	−	1.67260i	0.269428	−	0.0791113i
$448$	−6.73975	+	21.2355i	−0.318423	+	1.00328i
$449$	21.8865	−	25.2584i	1.03289	−	1.19202i	0.0517585	−	0.998660i	$-0.483517\pi$
$449$	21.8865	−	25.2584i	1.03289	−	1.19202i	0.981129	−	0.193356i	$-0.0619372\pi$
$450$	8.95268	+	8.53637i	0.422034	+	0.402408i
$451$	−1.76564	−	0.168598i	−0.0831405	−	0.00793896i
$452$	5.06505	−	0.241278i	0.238240	−	0.0113488i
$453$	−3.52627	+	0.855463i	−0.165678	+	0.0401932i
$454$	−2.91143	−	20.2494i	−0.136640	−	0.950352i
$455$	0.235518	+	0.429200i	0.0110412	+	0.0201212i
$456$	−0.349093	−	0.0501920i	−0.0163478	−	0.00235046i
$457$	24.4241	+	1.16346i	1.14251	+	0.0544246i	0.610289	−	0.792179i	$-0.291054\pi$
$457$	24.4241	+	1.16346i	1.14251	+	0.0544246i	0.532224	+	0.846604i	$0.321357\pi$
$458$	6.01197	−	1.15871i	0.280921	−	0.0541430i
$459$	2.73430	+	1.57865i	0.127626	+	0.0736851i
$460$	−13.8404	+	0.756752i	−0.645314	+	0.0352837i
$461$		−	11.7671i		−	0.548048i	−0.961723	−	0.274024i	$-0.911645\pi$
$461$		−	11.7671i		−	0.548048i	0.961723	−	0.274024i	$-0.0883547\pi$
$462$	1.51687	−	1.03124i	0.0705710	−	0.0479775i
$463$	−5.90873	−	3.79731i	−0.274602	−	0.176476i	0.396090	−	0.918211i	$-0.370367\pi$
$463$	−5.90873	−	3.79731i	−0.274602	−	0.176476i	−0.670693	+	0.741735i	$0.734003\pi$
$464$	−9.32493	+	3.73314i	−0.432899	+	0.173307i
$465$	2.08641	+	2.92996i	0.0967551	+	0.135873i
$466$	4.76240	+	1.90658i	0.220614	+	0.0883205i
$467$	−1.23792	−	5.10276i	−0.0572839	−	0.236128i	0.935971	−	0.352076i	$-0.114524\pi$
$467$	−1.23792	−	5.10276i	−0.0572839	−	0.236128i	−0.993255	+	0.115949i	$0.963009\pi$
$468$	0.0181285	+	0.0282085i	0.000837990	+	0.00130394i
$469$	−5.95217	−	18.4878i	−0.274846	−	0.853686i
$470$	17.3401	+	59.0550i	0.799840	+	2.72401i
$471$	−1.77030	+	9.18520i	−0.0815712	+	0.423232i
$472$	17.8505	−	6.17810i	0.821634	−	0.284370i
$473$	−0.939629	+	3.87320i	−0.0432042	+	0.178090i
$474$	−7.56298	+	10.6207i	−0.347379	+	0.487826i
$475$	1.05578	−	0.678509i	0.0484425	−	0.0311321i
$476$	−3.63290	−	4.83207i	−0.166514	−	0.221477i
$477$	8.84446	−	1.27164i	0.404960	−	0.0582244i
$478$	−8.40332	+	0.802420i	−0.384359	+	0.0367018i
$479$	−31.2983	−	24.6132i	−1.43005	−	1.12461i	−0.971806	−	0.235783i	$-0.924234\pi$
$479$	−31.2983	−	24.6132i	−1.43005	−	1.12461i	−0.458249	−	0.888824i	$-0.651523\pi$
$480$	−7.06762	−	13.7093i	−0.322591	−	0.625740i
$481$	−0.129802	+	0.375037i	−0.00591845	+	0.0171002i
$482$	23.6694			1.07811
$483$	−11.9284	−	4.32589i	−0.542761	−	0.196835i
$484$	−7.68819			−0.349463
$485$	−4.48248	+	12.9513i	−0.203539	+	0.588087i
$486$	0.517674	+	1.00415i	0.0234822	+	0.0455491i
$487$	−10.5015	−	8.25847i	−0.475868	−	0.374227i	0.351225	−	0.936291i	$-0.385765\pi$
$487$	−10.5015	−	8.25847i	−0.475868	−	0.374227i	−0.827094	+	0.562064i	$0.810007\pi$
$488$	12.3638	−	1.18060i	0.559685	−	0.0534434i
$489$	−7.50096	+	1.07848i	−0.339205	+	0.0487703i
$490$	−0.130951	−	31.5824i	−0.00591576	−	1.42675i
$491$	−11.8119	+	7.59106i	−0.533065	+	0.342580i	−0.779321	−	0.626625i	$-0.784436\pi$
$491$	−11.8119	+	7.59106i	−0.533065	+	0.342580i	0.246256	+	0.969205i	$0.420800\pi$
$492$	−1.21333	+	1.70388i	−0.0547010	+	0.0768168i
$493$	3.68518	−	15.1905i	0.165972	−	0.684147i
$494$	−0.00566957	+	0.00196226i	−0.000255086	+	8.82862e-5i
$495$	−0.463808	+	2.40646i	−0.0208466	+	0.108162i
$496$	0.514805	+	1.75326i	0.0231154	+	0.0787238i
$497$	6.31956	+	5.72097i	0.283471	+	0.256621i
$498$	−7.38132	−	11.4856i	−0.330765	−	0.514680i
$499$	−2.80196	−	11.5498i	−0.125433	−	0.517041i	−0.999511	−	0.0312566i	$-0.990049\pi$
$499$	−2.80196	−	11.5498i	−0.125433	−	0.517041i	0.874079	−	0.485785i	$-0.161466\pi$
$500$	15.9640	+	6.39103i	0.713932	+	0.285815i
$501$	−2.09914	−	2.94782i	−0.0937825	−	0.131699i
$502$	3.20175	−	1.28179i	0.142901	−	0.0572089i
$503$	22.7929	+	14.6481i	1.01629	+	0.653127i	0.939013	−	0.343883i	$-0.111742\pi$
$503$	22.7929	+	14.6481i	1.01629	+	0.653127i	0.0772730	+	0.997010i	$0.475379\pi$
$504$	−0.597615	−	8.11917i	−0.0266199	−	0.361656i
$505$			72.3785i			3.22080i
$506$	1.94754	+	2.69469i	0.0865787	+	0.119793i
$507$	−11.2565	−	6.49893i	−0.499917	−	0.288627i
$508$	8.83419	−	1.70265i	0.391954	−	0.0755429i
$509$	15.5308	+	0.739824i	0.688391	+	0.0327921i	0.388863	−	0.921295i	$-0.372868\pi$
$509$	15.5308	+	0.739824i	0.688391	+	0.0327921i	0.299528	+	0.954088i	$0.403171\pi$
$510$	−14.1002	−	2.02730i	−0.624366	−	0.0897702i
$511$	−0.400195	+	0.659634i	−0.0177036	+	0.0291805i
$512$	−2.89203	−	20.1145i	−0.127811	−	0.888943i
$513$	0.111386	−	0.0270220i	0.00491781	−	0.00119305i
$514$	−30.1921	+	1.43822i	−1.33171	+	0.0634374i
$515$	−62.3446	−	5.95319i	−2.74723	−	0.262329i
$516$	3.40175	+	3.24356i	0.149754	+	0.142790i
$517$	−5.48198	+	6.32654i	−0.241097	+	0.278241i
$518$	18.9085	−	17.2607i	0.830792	−	0.758391i
$519$	19.6810	−	5.77886i	0.863900	−	0.253664i
$520$	−0.463805	−	0.330274i	−0.0203392	−	0.0144835i
$521$	0.965263	+	20.2634i	0.0422889	+	0.887754i	0.915968	+	0.401251i	$0.131425\pi$
$521$	0.965263	+	20.2634i	0.0422889	+	0.887754i	−0.873679	+	0.486503i	$0.838272\pi$
$522$	4.04790	−	3.85967i	0.177172	−	0.168933i
$523$	11.5408	−	9.07576i	0.504643	−	0.396855i	−0.333125	−	0.942883i	$-0.608103\pi$
$523$	11.5408	−	9.07576i	0.504643	−	0.396855i	0.837767	+	0.546027i	$0.183861\pi$
$524$	9.37977	+	4.28360i	0.409757	+	0.187130i
$525$	20.5272	+	20.4423i	0.895882	+	0.892175i
$526$	14.3584	−	22.3421i	0.626055	−	0.974160i
$527$	−2.68722	−	0.930056i	−0.117057	−	0.0405139i
$528$	−0.622508	+	1.07822i	−0.0270912	+	0.0469233i
$529$	7.21656	−	21.8385i	0.313763	−	0.949501i
$530$	−34.9137	+	20.1574i	−1.51655	+	0.875583i
$531$	−4.63937	+	4.02004i	−0.201332	+	0.174455i
$532$	−0.216497	−	0.0359445i	−0.00938635	−	0.00155839i
$533$	−0.0190586	+	0.132556i	−0.000825520	+	0.00574162i
$534$	−1.57936	−	16.5398i	−0.0683456	−	0.715748i
$535$	−7.19426	+	17.9704i	−0.311035	+	0.776928i
$536$	15.5879	+	16.3481i	0.673293	+	0.706129i
$537$	−12.0546	+	23.3826i	−0.520194	+	1.00903i
$538$	−16.2768	+	7.43335i	−0.701741	+	0.320475i
$539$	3.60402	−	2.33733i	0.155236	−	0.100676i
$540$	2.18430	+	1.89271i	0.0939973	+	0.0814491i
$541$	−15.3356	−	2.95570i	−0.659331	−	0.127076i	−0.151399	−	0.988473i	$-0.548378\pi$
$541$	−15.3356	−	2.95570i	−0.659331	−	0.127076i	−0.507932	+	0.861397i	$0.669590\pi$
$542$	−30.1320	−	7.30994i	−1.29428	−	0.313989i
$543$	1.11910	−	11.7198i	0.0480254	−	0.502945i
$544$	10.8382	+	5.58746i	0.464682	+	0.239560i
$545$	−0.0713754	+	0.243082i	−0.00305739	+	0.0104125i
$546$	−0.0723246	−	0.118104i	−0.00309521	−	0.00505440i
$547$	−10.9530	+	23.9837i	−0.468316	+	1.02547i	0.517196	+	0.855867i	$0.326976\pi$
$547$	−10.9530	+	23.9837i	−0.468316	+	1.02547i	−0.985512	+	0.169603i	$0.945751\pi$
$548$	−0.354010	−	0.884274i	−0.0151226	−	0.0377743i
$549$	−3.58765	+	1.84956i	−0.153117	+	0.0789374i
$550$	−1.43661	−	7.45382i	−0.0612571	−	0.317832i
$551$	−0.283722	−	0.491421i	−0.0120870	−	0.0209353i
$552$	14.6800	−	1.50587i	0.624823	−	0.0640943i
$553$	−18.2481	+	24.4823i	−0.775989	+	1.04109i
$554$	−17.3881	−	20.0669i	−0.738748	−	0.852560i
$555$	−1.62767	+	34.1690i	−0.0690906	+	1.45039i
$556$	−0.748365	+	0.951624i	−0.0317378	+	0.0403579i
$557$	4.36851	−	3.11081i	0.185100	−	0.131809i	−0.483751	−	0.875206i	$-0.660726\pi$
$557$	4.36851	−	3.11081i	0.185100	−	0.131809i	0.668851	+	0.743397i	$0.266787\pi$
$558$	−0.628972	−	0.799803i	−0.0266265	−	0.0338583i
$559$	0.288735	+	0.0847801i	0.0122122	+	0.00358582i
$560$	9.40696	+	19.2633i	0.397517	+	0.814025i
$561$	−0.804865	−	1.76241i	−0.0339814	−	0.0744089i
$562$	−0.311219	+	0.326397i	−0.0131280	+	0.0137682i
$563$	4.76189	+	13.7586i	0.200690	+	0.579855i	0.999772	−	0.0213672i	$-0.00680190\pi$
$563$	4.76189	+	13.7586i	0.200690	+	0.579855i	−0.799082	+	0.601222i	$0.794681\pi$
$564$	3.22895	+	9.32944i	0.135963	+	0.392840i
$565$	19.3103	−	20.2521i	0.812392	−	0.852012i
$566$	1.90201	+	4.16483i	0.0799476	+	0.175061i
$567$	1.16098	+	2.37742i	0.0487565	+	0.0998423i
$568$	−9.51251	−	2.79312i	−0.399136	−	0.117197i
$569$	5.19356	+	6.60414i	0.217725	+	0.276860i	0.882630	−	0.470068i	$-0.155771\pi$
$569$	5.19356	+	6.60414i	0.217725	+	0.276860i	−0.664905	+	0.746928i	$0.731528\pi$
$570$	−0.421242	+	0.299965i	−0.0176439	+	0.0125641i
$571$	0.315772	−	0.401536i	0.0132146	−	0.0168038i	−0.779401	−	0.626526i	$-0.784476\pi$
$571$	0.315772	−	0.401536i	0.0132146	−	0.0168038i	0.792616	+	0.609722i	$0.208719\pi$
$572$	0.000979083	−	0.0205535i	4.09375e−5	−	0.000859384i
$573$	14.6597	+	16.9182i	0.612418	+	0.706769i
$574$	5.16292	−	6.92674i	0.215496	−	0.289117i
$575$	−35.9699	+	38.2586i	−1.50005	+	1.59549i
$576$	4.21040	+	7.29262i	0.175433	+	0.303859i
$577$	−3.81545	−	19.7965i	−0.158839	−	0.824137i	−0.970702	−	0.240288i	$-0.922758\pi$
$577$	−3.81545	−	19.7965i	−0.158839	−	0.824137i	0.811862	−	0.583849i	$-0.198454\pi$
$578$	−7.06060	+	3.63999i	−0.293682	+	0.151404i
$579$	8.44739	+	21.1006i	0.351061	+	0.876909i
$580$	5.94417	−	13.0159i	0.246818	−	0.540457i
$581$	−16.6980	−	27.2675i	−0.692752	−	1.13125i
$582$	1.09224	−	3.71983i	0.0452748	−	0.154192i
$583$	−4.87371	−	2.51257i	−0.201849	−	0.104060i
$584$	0.0852951	−	0.893251i	0.00352954	−	0.0369630i
$585$	0.179825	+	0.0436251i	0.00743485	+	0.00180368i
$586$	12.7497	+	2.45731i	0.526686	+	0.101510i
$587$	−22.4152	−	19.4229i	−0.925174	−	0.801668i	0.0552691	−	0.998471i	$-0.482398\pi$
$587$	−22.4152	−	19.4229i	−0.925174	−	0.801668i	−0.980443	+	0.196804i	$0.936944\pi$
$588$	−0.262025	−	5.05913i	−0.0108057	−	0.208635i
$589$	−0.0939008	+	0.0428830i	−0.00386911	+	0.00176697i
$590$	12.6915	−	24.6181i	0.522500	−	1.01351i
$591$	−8.41729	−	8.82780i	−0.346241	−	0.363127i
$592$	−6.45875	+	16.1332i	−0.265453	+	0.663069i
$593$	1.71637	+	17.9746i	0.0704828	+	0.738129i	0.959771	+	0.280783i	$0.0905940\pi$
$593$	1.71637	+	17.9746i	0.0704828	+	0.738129i	−0.889289	+	0.457347i	$0.848800\pi$
$594$	0.0986622	−	0.686211i	0.00404816	−	0.0281556i
$595$	−32.9106	−	5.46405i	−1.34920	−	0.224004i
$596$	−3.24708	+	2.81361i	−0.133006	+	0.115250i
$597$	−8.96581	+	5.17642i	−0.366946	+	0.211857i
$598$	0.210225	−	0.137199i	0.00859675	−	0.00561049i
$599$	−8.61659	+	14.9244i	−0.352064	+	0.609793i	−0.986611	−	0.163091i	$-0.947853\pi$
$599$	−8.61659	+	14.9244i	−0.352064	+	0.609793i	0.634547	+	0.772884i	$0.281187\pi$
$600$	−31.8395	−	11.0198i	−1.29984	−	0.449879i
$601$	9.30228	−	14.4746i	0.379448	−	0.590433i	−0.598029	−	0.801474i	$-0.704049\pi$
$601$	9.30228	−	14.4746i	0.379448	−	0.590433i	0.977477	+	0.211042i	$0.0676856\pi$
$602$	−13.7554	−	13.6985i	−0.560627	−	0.558307i
$603$	−6.67756	−	3.04954i	−0.271931	−	0.124187i
$604$	2.06417	−	1.62328i	0.0839897	−	0.0660502i
$605$	−30.7057	+	29.2778i	−1.24836	+	1.19031i
$606$	−0.974211	−	20.4512i	−0.0395746	−	0.830773i
$607$	5.70534	+	4.06275i	0.231572	+	0.164902i	0.689953	−	0.723854i	$-0.257631\pi$
$607$	5.70534	+	4.06275i	0.231572	+	0.164902i	−0.458381	+	0.888756i	$0.651570\pi$
$608$	0.424726	−	0.124711i	0.0172249	−	0.00505769i
$609$	9.67401	−	8.83096i	0.392011	−	0.357849i
$610$	11.9258	−	13.7631i	0.482863	−	0.557253i
$611$	0.457442	+	0.436170i	0.0185061	+	0.0176456i
$612$	−2.27460	−	0.217198i	−0.0919452	−	0.00877970i
$613$	3.20416	−	0.152633i	0.129415	−	0.00616479i	0.0172255	−	0.999852i	$-0.494517\pi$
$613$	3.20416	−	0.152633i	0.129415	−	0.00616479i	0.112189	+	0.993687i	$0.464214\pi$
$614$	−23.4896	+	5.69852i	−0.947964	+	0.229974i
$615$	1.64275	+	11.4256i	0.0662423	+	0.460725i
$616$	−2.59133	+	4.27124i	−0.104408	+	0.172093i
$617$	−13.9555	−	2.00650i	−0.561827	−	0.0807785i	−0.144450	−	0.989512i	$-0.546141\pi$
$617$	−13.9555	−	2.00650i	−0.561827	−	0.0807785i	−0.417377	+	0.908734i	$0.637050\pi$
$618$	17.6962	+	0.842972i	0.711844	+	0.0339093i
$619$	36.9657	−	7.12455i	1.48578	−	0.286360i	0.619132	−	0.785287i	$-0.287484\pi$
$619$	36.9657	−	7.12455i	1.48578	−	0.286360i	0.866644	+	0.498927i	$0.166272\pi$
$620$	−2.25434	−	1.30154i	−0.0905365	−	0.0522713i
$621$	−4.24717	+	2.22746i	−0.170433	+	0.0893848i
$622$		−	32.2545i		−	1.29329i
$623$	−2.85635	−	38.8062i	−0.114437	−	1.55474i
$624$	0.0790808	+	0.0508221i	0.00316576	+	0.00203451i
$625$	37.2700	−	14.9206i	1.49080	−	0.596826i
$626$	15.5427	+	21.8267i	0.621212	+	0.872370i
$627$	−0.0652970	−	0.0261410i	−0.00260771	−	0.00104397i
$628$	−1.59601	−	6.57885i	−0.0636878	−	0.262525i
$629$	−14.6209	−	22.7506i	−0.582973	−	0.907124i
$630$	−8.84952	−	8.01131i	−0.352574	−	0.319178i
$631$	12.5107	+	42.6075i	0.498042	+	1.69618i	0.697768	+	0.716324i	$0.254177\pi$
$631$	12.5107	+	42.6075i	0.498042	+	1.69618i	−0.199725	+	0.979852i	$0.564005\pi$
$632$	6.72080	−	34.8708i	0.267339	−	1.38709i
$633$	6.99417	−	2.42071i	0.277993	−	0.0962145i
$634$	0.915418	−	3.77341i	0.0363559	−	0.149861i
$635$	28.7987	−	40.4421i	1.14284	−	1.60490i
$636$	−5.44002	+	3.49609i	−0.215711	+	0.138629i
$637$	−0.163330	−	0.280206i	−0.00647136	−	0.0111022i
$638$	−3.39729	+	0.488456i	−0.134500	+	0.0193382i
$639$	3.20735	−	0.306265i	0.126881	−	0.0121157i
$640$	−5.61661	−	4.41695i	−0.222016	−	0.174595i
$641$	7.92467	+	15.3717i	0.313005	+	0.607146i	0.991890	−	0.127099i	$-0.0405666\pi$
$641$	7.92467	+	15.3717i	0.313005	+	0.607146i	−0.678885	+	0.734245i	$0.737536\pi$
$642$	1.79092	−	5.17453i	0.0706821	−	0.204222i
$643$	−9.60052			−0.378608			−0.189304	−	0.981919i	$-0.560623\pi$
$643$	−9.60052			−0.378608			−0.189304	+	0.981919i	$0.560623\pi$
$644$	9.15301	−	0.738372i	0.360679	−	0.0290959i
$645$	25.9381			1.02131
$646$	0.133715	−	0.386343i	0.00526093	−	0.0152005i
$647$	−6.90744	−	13.3986i	−0.271559	−	0.526752i	0.713138	−	0.701023i	$-0.247273\pi$
$647$	−6.90744	−	13.3986i	−0.271559	−	0.526752i	−0.984698	+	0.174272i	$0.944243\pi$
$648$	−2.41873	−	1.90211i	−0.0950167	−	0.0747220i
$649$	3.75003	−	0.358085i	0.147202	−	0.0140560i
$650$	−0.567315	+	0.0815676i	−0.0222519	+	0.00319935i
$651$	−1.43196	−	1.90464i	−0.0561231	−	0.0746486i
$652$	4.61367	−	2.96503i	0.180685	−	0.116119i
$653$	23.5214	−	33.0311i	0.920462	−	1.29261i	−0.0355765	−	0.999367i	$-0.511327\pi$
$653$	23.5214	−	33.0311i	0.920462	−	1.29261i	0.956039	−	0.293241i	$-0.0947339\pi$
$654$	0.0168959	−	0.0696458i	0.000660681	−	0.00272336i
$655$	53.7742	−	18.6114i	2.10113	−	0.727209i
$656$	−1.10978	+	5.75809i	−0.0433296	+	0.224815i
$657$	0.0821572	+	0.279802i	0.00320526	+	0.0109161i
$658$	−12.4958	−	38.8126i	−0.487137	−	1.51307i
$659$	−23.7478	−	36.9522i	−0.925081	−	1.43945i	−0.898087	−	0.439819i	$-0.855043\pi$
$659$	−23.7478	−	36.9522i	−0.925081	−	1.43945i	−0.0269944	−	0.999636i	$-0.508594\pi$
$660$	−0.418145	−	1.72362i	−0.0162763	−	0.0670917i
$661$	−6.73992	−	2.69826i	−0.262152	−	0.104950i	0.236863	−	0.971543i	$-0.423881\pi$
$661$	−6.73992	−	2.69826i	−0.262152	−	0.104950i	−0.499016	+	0.866593i	$0.666305\pi$
$662$	−2.47026	−	3.46900i	−0.0960095	−	0.134826i
$663$	−0.135809	+	0.0543699i	−0.00527440	+	0.00211155i
$664$	31.2832	+	20.1045i	1.21402	+	0.780206i
$665$	−1.00154	+	0.680897i	−0.0388382	+	0.0264041i
$666$		−	9.67665i		−	0.374963i
$667$	16.5049	+	17.0683i	0.639073	+	0.660885i
$668$	2.26809	+	1.30948i	0.0877550	+	0.0506654i
$669$	−12.1513	+	2.34197i	−0.469796	+	0.0905457i
$670$	33.0834	+	1.57596i	1.27812	+	0.0608846i
$671$	2.45171	+	0.352503i	0.0946474	+	0.0136082i
$672$	4.91556	+	8.95798i	0.189622	+	0.345561i
$673$	1.20865	+	8.40638i	0.0465902	+	0.324042i	0.999766	+	0.0216257i	$0.00688422\pi$
$673$	1.20865	+	8.40638i	0.0465902	+	0.324042i	−0.953176	+	0.302416i	$0.902207\pi$
$674$	−23.7591	+	5.76389i	−0.915165	+	0.222017i
$675$	10.9372	−	0.521003i	0.420973	−	0.0200534i
$676$	9.36397	+	0.894151i	0.360153	+	0.0343904i
$677$	−3.10883	−	2.96427i	−0.119482	−	0.113926i	0.627983	−	0.778227i	$-0.283881\pi$
$677$	−3.10883	−	2.96427i	−0.119482	−	0.113926i	−0.747465	+	0.664301i	$0.768729\pi$
$678$	−5.18372	+	5.98233i	−0.199080	+	0.229750i
$679$	2.74660	−	8.65394i	0.105405	−	0.332108i
$680$	37.2279	−	10.9311i	1.42762	−	0.419188i
$681$	−14.7507	−	10.5039i	−0.565246	−	0.402510i
$682$	0.0297096	+	0.623682i	0.00113764	+	0.0238820i
$683$	−1.14555	+	1.09228i	−0.0438331	+	0.0417948i	−0.711679	−	0.702505i	$-0.752065\pi$
$683$	−1.14555	+	1.09228i	−0.0438331	+	0.0417948i	0.667846	+	0.744299i	$0.267216\pi$
$684$	−0.0652019	+	0.0512753i	−0.00249306	+	0.00196056i
$685$	−4.78132	−	2.18356i	−0.182685	−	0.0834294i
$686$	0.628000	+	20.9135i	0.0239772	+	0.798483i
$687$	2.93001	−	4.55919i	0.111787	−	0.173944i
$688$	12.4522	+	4.30975i	0.474736	+	0.164308i
$689$	−0.207004	+	0.358541i	−0.00788621	+	0.0136593i
$690$	14.0546	−	16.4519i	0.535050	−	0.626314i
$691$	−30.7780	+	17.7697i	−1.17085	+	0.675991i	−0.953880	−	0.300187i	$-0.902951\pi$
$691$	−30.7780	+	17.7697i	−1.17085	+	0.675991i	−0.216971	+	0.976178i	$0.569618\pi$
$692$	−11.2187	+	9.72106i	−0.426471	+	0.369539i
$693$	0.265918	−	1.60165i	0.0101014	−	0.0608418i
$694$	−2.29948	+	15.9932i	−0.0872869	+	0.607094i
$695$	0.635051	+	6.65056i	0.0240889	+	0.252270i
$696$	−5.66186	+	14.1426i	−0.214612	+	0.536075i
$697$	−6.29742	−	6.60454i	−0.238532	−	0.250165i
$698$	−13.4897	+	26.1664i	−0.510594	+	0.990414i
$699$	4.13043	−	1.88630i	0.156227	−	0.0713466i
$700$	−19.6588	−	7.28598i	−0.743034	−	0.275384i
$701$	24.1623	+	20.9368i	0.912598	+	0.790770i	0.978327	−	0.207067i	$-0.0663919\pi$
$701$	24.1623	+	20.9368i	0.912598	+	0.790770i	−0.0657292	+	0.997838i	$0.520937\pi$
$702$	−0.0513984	−	0.00990623i	−0.00193991	−	0.000373886i
$703$	−0.954069	−	0.231455i	−0.0359834	−	0.00872948i
$704$	0.491199	−	5.14407i	0.0185128	−	0.193874i
$705$	48.4240	+	24.9643i	1.82375	+	0.940209i
$706$	1.08760	−	3.70402i	0.0409324	−	0.139403i
$707$	−1.24046	−	47.9334i	−0.0466524	−	1.80272i
$708$	1.84554	−	4.04117i	0.0693596	−	0.151876i
$709$	−6.93625	−	17.3259i	−0.260497	−	0.650689i	0.739245	−	0.673437i	$-0.235183\pi$
$709$	−6.93625	−	17.3259i	−0.260497	−	0.650689i	−0.999741	+	0.0227480i	$0.992758\pi$
$710$	−12.9208	+	6.66114i	−0.484910	+	0.249988i
$711$	2.18416	+	11.3325i	0.0819125	+	0.425002i
$712$	22.6272	+	39.1915i	0.847991	+	1.46876i
$713$	3.37641	−	2.69382i	0.126447	−	0.100885i
$714$	9.37272	+	1.10094i	0.350765	+	0.0412017i
$715$	−0.0743604	−	0.0858165i	−0.00278092	−	0.00320935i
$716$	0.905886	−	19.0169i	0.0338545	−	0.710694i
$717$	−4.61898	+	5.87351i	−0.172499	+	0.219350i
$718$	22.0279	−	15.6860i	0.822073	−	0.585396i
$719$	−26.2077	−	33.3258i	−0.977383	−	1.24284i	−0.970059	−	0.242870i	$-0.921911\pi$
$719$	−26.2077	−	33.3258i	−0.977383	−	1.24284i	−0.00732433	−	0.999973i	$-0.502331\pi$
$720$	7.77441	+	2.28277i	0.289735	+	0.0850739i
$721$	41.3904	+	2.87407i	1.54146	+	0.107036i
$722$	8.91069	+	19.5117i	0.331622	+	0.726150i
$723$	14.4581	−	15.1632i	0.537701	−	0.563925i
$724$	2.78669	+	8.05161i	0.103566	+	0.299236i
$725$	−17.7301	−	51.2277i	−0.658479	−	1.90255i
$726$	8.28208	−	8.68600i	0.307377	−	0.322368i
$727$	8.45869	+	18.5220i	0.313716	+	0.686941i	0.999151	−	0.0411919i	$-0.0131155\pi$
$727$	8.45869	+	18.5220i	0.313716	+	0.686941i	−0.685436	+	0.728133i	$0.740388\pi$
$728$	0.312820	+	0.210779i	0.0115939	+	0.00781197i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−0.813317	−	1.03422i	−0.0301022	−	0.0382781i
$731$	−16.7036	+	11.8946i	−0.617807	+	0.439938i
$732$	1.80571	−	2.29615i	0.0667410	−	0.0848681i
$733$	−0.00165928	+	0.0348326i	−6.12870e−5	+	0.00128657i	−0.998898	−	0.0469386i	$-0.985053\pi$
$733$	−0.00165928	+	0.0348326i	−6.12870e−5	+	0.00128657i	0.998836	+	0.0482252i	$0.0153565\pi$
$734$	−21.9648	−	25.3487i	−0.810735	−	0.935638i
$735$	−20.3124	−	19.2077i	−0.749235	−	0.708487i
$736$	−15.9749	+	9.37329i	−0.588842	+	0.345504i
$737$	2.25240	+	3.90128i	0.0829684	+	0.143705i
$738$	−0.617963	−	3.20630i	−0.0227475	−	0.118025i
$739$	5.11971	−	2.63940i	0.188332	−	0.0970917i	−0.361482	−	0.932379i	$-0.617729\pi$
$739$	5.11971	−	2.63940i	0.188332	−	0.0970917i	0.549814	+	0.835287i	$0.314699\pi$
$740$	−9.20094	−	22.9828i	−0.338233	−	0.844866i
$741$	−0.00220610	+	0.00483068i	−8.10429e−5	+	0.000177459i
$742$	22.7765	−	13.9478i	0.836151	−	0.512041i
$743$	−0.159725	+	0.543973i	−0.00585974	+	0.0199565i	−0.962371	−	0.271739i	$-0.912401\pi$
$743$	−0.159725	+	0.543973i	−0.00585974	+	0.0199565i	0.956511	+	0.291696i	$0.0942194\pi$
$744$	2.46327	+	1.26990i	0.0903078	+	0.0465569i
$745$	−2.25377	+	23.6026i	−0.0825718	+	0.864731i
$746$	−12.0318	−	2.91888i	−0.440515	−	0.106868i
$747$	−11.8667	−	2.28711i	−0.434179	−	0.0836811i
$748$	1.05969	+	0.918225i	0.0387460	+	0.0335736i
$749$	4.45649	−	12.0244i	0.162837	−	0.439361i
$750$	−24.4177	+	11.1512i	−0.891607	+	0.407183i
$751$	9.92862	−	19.2588i	0.362301	−	0.702765i	−0.635280	−	0.772282i	$-0.719115\pi$
$751$	9.92862	−	19.2588i	0.362301	−	0.702765i	0.997581	+	0.0695166i	$0.0221457\pi$
$752$	19.0991	+	20.0306i	0.696473	+	0.730440i
$753$	1.13459	−	2.83407i	0.0413468	−	0.103279i
$754$	0.0246334	+	0.257972i	0.000897095	+	0.00939480i
$755$	2.06233	−	14.3438i	0.0750559	−	0.522025i
$756$	−1.47901	−	1.21603i	−0.0537912	−	0.0442265i
$757$	31.3505	−	27.1654i	1.13946	−	0.987343i	0.139459	−	0.990228i	$-0.455464\pi$
$757$	31.3505	−	27.1654i	1.13946	−	0.987343i	0.999996	+	0.00288443i	$0.000918143\pi$
$758$	26.3567	−	15.2170i	0.957317	−	0.552707i
$759$	2.91590	+	0.398364i	0.105841	+	0.0144597i
$760$	0.704254	−	1.21980i	0.0255460	−	0.0442469i
$761$	20.1163	+	6.96231i	0.729215	+	0.252384i	0.666351	−	0.745638i	$-0.267855\pi$
$761$	20.1163	+	6.96231i	0.729215	+	0.252384i	0.0628640	+	0.998022i	$0.479977\pi$
$762$	−7.59298	+	11.8149i	−0.275065	+	0.428009i
$763$	0.0431030	−	0.162207i	0.00156043	−	0.00587229i
$764$	−14.7368	−	6.73005i	−0.533157	−	0.243485i
$765$	−9.91158	+	7.79455i	−0.358354	+	0.281813i
$766$	−1.73541	+	1.65471i	−0.0627030	+	0.0597872i
$767$	−0.0135337	−	0.284107i	−0.000488674	−	0.0102585i
$768$	−12.0723	−	8.59663i	−0.435621	−	0.310204i
$769$	27.4633	−	8.06394i	0.990351	−	0.290793i	0.253860	−	0.967241i	$-0.418300\pi$
$769$	27.4633	−	8.06394i	0.990351	−	0.290793i	0.736491	+	0.676448i	$0.236482\pi$
$770$	1.57194	+	7.15463i	0.0566487	+	0.257835i

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.369500 - 1.06760i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(0.568868 + 0.447363i) q^{4} +(3.97561 - 0.379625i) q^{5} +(-1.11823 + 0.160778i) q^{6} +(-2.62638 + 0.319547i) q^{7} +(2.58859 - 1.66358i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.369500 - 1.06760i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(0.568868 + 0.447363i) q^{4} +(3.97561 - 0.379625i) q^{5} +(-1.11823 + 0.160778i) q^{6} +(-2.62638 + 0.319547i) q^{7} +(2.58859 - 1.66358i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(1.06370 - 4.38463i) q^{10} +(0.579905 - 0.200707i) q^{11} +(0.136961 - 0.710623i) q^{12} +(-0.0130536 - 0.0444565i) q^{13} +(-0.629300 + 2.92200i) q^{14} +(-2.15915 - 3.35971i) q^{15} +(-0.478320 - 1.97166i) q^{16} +(2.93114 + 1.17345i) q^{17} +(0.655310 + 0.920254i) q^{18} +(0.106407 - 0.0425988i) q^{19} +(2.43143 + 1.56258i) q^{20} +(1.48750 + 2.18800i) q^{21} -0.693267i q^{22} +(-3.88694 + 2.80922i) q^{23} +(-2.66481 - 1.53853i) q^{24} +(10.7517 - 2.07222i) q^{25} +(-0.0522850 - 0.00249064i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-1.63702 - 0.993166i) q^{28} +(-0.704571 - 4.90040i) q^{29} +(-4.38463 + 1.06370i) q^{30} +(-0.899627 + 0.0428545i) q^{31} +(3.84456 + 0.367111i) q^{32} +(-0.444123 - 0.423471i) q^{33} +(2.33583 - 2.69569i) q^{34} +(-10.3202 + 2.26743i) q^{35} +(-0.694387 + 0.203890i) q^{36} +(-6.97719 - 4.96843i) q^{37} +(-0.00616122 - 0.129340i) q^{38} +(-0.0335330 + 0.0319737i) q^{39} +(9.65967 - 7.59645i) q^{40} +(-2.62914 - 1.20069i) q^{41} +(2.88554 - 0.779593i) q^{42} +(-3.51134 + 5.46375i) q^{43} +(0.419678 + 0.145252i) q^{44} +(-1.99685 + 3.45864i) q^{45} +(1.56290 + 5.18770i) q^{46} +(-11.8139 + 6.82078i) q^{47} +(-1.53330 + 1.32862i) q^{48} +(6.79578 - 1.67850i) q^{49} +(1.76045 - 12.2442i) q^{50} +(-0.300121 - 3.14301i) q^{51} +(0.0124624 - 0.0311296i) q^{52} +(-6.16614 - 6.46686i) q^{53} +(0.517674 - 1.00415i) q^{54} +(2.22928 - 1.01808i) q^{55} +(-6.26703 + 5.19638i) q^{56} +(-0.0866217 - 0.0750581i) q^{57} +(-5.49200 - 1.05850i) q^{58} +(5.96573 + 1.44727i) q^{59} +(0.274735 - 2.87716i) q^{60} +(3.58765 + 1.84956i) q^{61} +(-0.286661 + 0.976276i) q^{62} +(1.26316 - 2.32474i) q^{63} +(3.49813 - 7.65983i) q^{64} +(-0.0687728 - 0.171786i) q^{65} +(-0.616200 + 0.317673i) q^{66} +(1.38928 + 7.20828i) q^{67} +(1.14247 + 1.97882i) q^{68} +(4.27803 + 2.16759i) q^{69} +(-1.39259 + 11.8556i) q^{70} +(-2.10992 - 2.43498i) q^{71} +(-0.146412 + 3.07357i) q^{72} +(0.180264 - 0.229224i) q^{73} +(-7.88237 + 5.61301i) q^{74} +(-6.76859 - 8.60696i) q^{75} +(0.0795884 + 0.0233693i) q^{76} +(-1.45892 + 0.712440i) q^{77} +(0.0217446 + 0.0476141i) q^{78} +(7.96425 - 8.35267i) q^{79} +(-2.65011 - 7.65698i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-2.25332 + 2.36321i) q^{82} +(5.02032 + 10.9930i) q^{83} +(-0.132636 + 1.91013i) q^{84} +(12.0985 + 3.55245i) q^{85} +(4.53565 + 5.76755i) q^{86} +(-4.03280 + 2.87174i) q^{87} +(1.16724 - 1.48427i) q^{88} +(-0.699789 + 14.6904i) q^{89} +(2.95461 + 3.40980i) q^{90} +(0.0484897 + 0.112589i) q^{91} +(-3.46789 - 0.140795i) q^{92} +(0.450324 + 0.779983i) q^{93} +(2.91661 + 15.1328i) q^{94} +(0.406860 - 0.209751i) q^{95} +(-1.43538 - 3.58540i) q^{96} +(-1.42557 + 3.12156i) q^{97} +(0.719069 - 7.87538i) q^{98} +(-0.172887 + 0.588798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

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