LMFDB - Embedded newform 288.2.bf.a.11.45

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(11,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 15, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.45
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.45

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39742 + 0.217290i) q^{2} +(-1.47060 - 0.915056i) q^{3} +(1.90557 + 0.607292i) q^{4} +(0.279615 + 2.12388i) q^{5} +(-1.85622 - 1.59827i) q^{6} +(0.262694 + 0.980387i) q^{7} +(2.53092 + 1.26270i) q^{8} +(1.32535 + 2.69137i) q^{9} +(-0.0707598 + 3.02872i) q^{10} +(3.41279 - 2.61873i) q^{11} +(-2.24663 - 2.63679i) q^{12} +(-0.912029 + 1.18858i) q^{13} +(0.154065 + 1.42709i) q^{14} +(1.53227 - 3.37925i) q^{15} +(3.26239 + 2.31447i) q^{16} -5.39882 q^{17} +(1.26726 + 4.04896i) q^{18} +(6.75131 - 2.79649i) q^{19} +(-0.756992 + 4.21702i) q^{20} +(0.510790 - 1.68214i) q^{21} +(5.33813 - 2.91790i) q^{22} +(-2.26322 - 0.606428i) q^{23} +(-2.56654 - 4.17287i) q^{24} +(0.396933 - 0.106358i) q^{25} +(-1.53275 + 1.46277i) q^{26} +(0.513691 - 5.17070i) q^{27} +(-0.0947992 + 2.02773i) q^{28} +(-4.40149 - 0.579467i) q^{29} +(2.87550 - 4.38929i) q^{30} +(-8.30037 + 4.79222i) q^{31} +(4.05602 + 3.94318i) q^{32} +(-7.41515 + 0.728215i) q^{33} +(-7.54443 - 1.17311i) q^{34} +(-2.00877 + 0.832061i) q^{35} +(0.891096 + 5.93346i) q^{36} +(2.47820 - 5.98289i) q^{37} +(10.0421 - 2.44087i) q^{38} +(2.42885 - 0.913371i) q^{39} +(-1.97415 + 5.72846i) q^{40} +(-1.03703 + 3.87025i) q^{41} +(1.07930 - 2.23967i) q^{42} +(-5.15179 - 6.71394i) q^{43} +(8.09365 - 2.91761i) q^{44} +(-5.34556 + 3.56743i) q^{45} +(-3.03090 - 1.33921i) q^{46} +(-7.46917 - 4.31233i) q^{47} +(-2.67981 - 6.38894i) q^{48} +(5.17003 - 2.98492i) q^{49} +(0.577793 - 0.0623770i) q^{50} +(7.93952 + 4.94022i) q^{51} +(-2.45975 + 1.71105i) q^{52} +(-1.62188 + 3.91557i) q^{53} +(1.84139 - 7.11402i) q^{54} +(6.51614 + 6.51614i) q^{55} +(-0.573080 + 2.81299i) q^{56} +(-12.4874 - 2.06531i) q^{57} +(-6.02482 - 1.76616i) q^{58} +(-2.91589 + 0.383885i) q^{59} +(4.97204 - 5.50887i) q^{60} +(0.0439705 - 0.333989i) q^{61} +(-12.6404 + 4.89316i) q^{62} +(-2.29042 + 2.00636i) q^{63} +(4.81116 + 6.39162i) q^{64} +(-2.77942 - 1.60470i) q^{65} +(-10.5203 - 0.593616i) q^{66} +(3.21736 - 4.19294i) q^{67} +(-10.2878 - 3.27866i) q^{68} +(2.77338 + 2.96279i) q^{69} +(-2.98790 + 0.726253i) q^{70} +(-2.98357 - 2.98357i) q^{71} +(-0.0440464 + 8.48517i) q^{72} +(-1.45130 + 1.45130i) q^{73} +(4.76311 - 7.82213i) q^{74} +(-0.681054 - 0.206805i) q^{75} +(14.5634 - 1.22888i) q^{76} +(3.46389 + 2.65793i) q^{77} +(3.59259 - 0.748599i) q^{78} +(4.91023 - 8.50477i) q^{79} +(-4.00346 + 7.57610i) q^{80} +(-5.48691 + 7.13399i) q^{81} +(-2.29014 + 5.18303i) q^{82} +(2.17172 + 0.285913i) q^{83} +(1.99489 - 2.89524i) q^{84} +(-1.50959 - 11.4665i) q^{85} +(-5.74034 - 10.5016i) q^{86} +(5.94260 + 4.87978i) q^{87} +(11.9442 - 2.31846i) q^{88} +(2.17841 - 2.17841i) q^{89} +(-8.24517 + 3.82366i) q^{90} +(-1.40485 - 0.581909i) q^{91} +(-3.94444 - 2.53002i) q^{92} +(16.5917 + 0.547845i) q^{93} +(-9.50055 - 7.64911i) q^{94} +(7.82717 + 13.5571i) q^{95} +(-2.35657 - 9.51034i) q^{96} +(4.24778 - 7.35737i) q^{97} +(7.87330 - 3.04779i) q^{98} +(11.5711 + 5.71436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.39742	+	0.217290i	0.988126	+	0.153647i
$2$	1.39742	+	0.217290i	0.988126	+	0.153647i
$3$	−1.47060	−	0.915056i	−0.849053	−	0.528308i
$3$	−1.47060	−	0.915056i	−0.849053	−	0.528308i
$4$	1.90557	+	0.607292i	0.952785	+	0.303646i
$5$	0.279615	+	2.12388i	0.125047	+	0.949830i	0.932822	+	0.360338i	$0.117339\pi$
$5$	0.279615	+	2.12388i	0.125047	+	0.949830i	−0.807774	+	0.589492i	$0.799328\pi$
$6$	−1.85622	−	1.59827i	−0.757798	−	0.652489i
$7$	0.262694	+	0.980387i	0.0992889	+	0.370551i	0.997635	−	0.0687376i	$-0.0218971\pi$
$7$	0.262694	+	0.980387i	0.0992889	+	0.370551i	−0.898346	+	0.439289i	$0.855230\pi$
$8$	2.53092	+	1.26270i	0.894817	+	0.446433i
$9$	1.32535	+	2.69137i	0.441782	+	0.897122i
$10$	−0.0707598	+	3.02872i	−0.0223762	+	0.957764i
$11$	3.41279	−	2.61873i	1.02900	−	0.789576i	0.0511053	−	0.998693i	$-0.483726\pi$
$11$	3.41279	−	2.61873i	1.02900	−	0.789576i	0.977891	+	0.209117i	$0.0670589\pi$
$12$	−2.24663	−	2.63679i	−0.648547	−	0.761175i
$13$	−0.912029	+	1.18858i	−0.252951	+	0.329653i	−0.902518	−	0.430652i	$-0.858284\pi$
$13$	−0.912029	+	1.18858i	−0.252951	+	0.329653i	0.649567	+	0.760305i	$0.274950\pi$
$14$	0.154065	+	1.42709i	0.0411757	+	0.381407i
$15$	1.53227	−	3.37925i	0.395630	−	0.872519i
$16$	3.26239	+	2.31447i	0.815598	+	0.578618i
$17$	−5.39882			−1.30941			−0.654703	−	0.755886i	$-0.727206\pi$
$17$	−5.39882			−1.30941			−0.654703	+	0.755886i	$0.727206\pi$
$18$	1.26726	+	4.04896i	0.298696	+	0.954348i
$19$	6.75131	−	2.79649i	1.54886	−	0.641558i	0.565748	−	0.824578i	$-0.308587\pi$
$19$	6.75131	−	2.79649i	1.54886	−	0.641558i	0.983109	+	0.183020i	$0.0585874\pi$
$20$	−0.756992	+	4.21702i	−0.169268	+	0.942953i
$21$	0.510790	−	1.68214i	0.111463	−	0.367073i
$22$	5.33813	−	2.91790i	1.13809	−	0.622098i
$23$	−2.26322	−	0.606428i	−0.471914	−	0.126449i	0.0150211	−	0.999887i	$-0.495218\pi$
$23$	−2.26322	−	0.606428i	−0.471914	−	0.126449i	−0.486935	+	0.873438i	$0.661885\pi$
$24$	−2.56654	−	4.17287i	−0.523893	−	0.851784i
$25$	0.396933	−	0.106358i	0.0793865	−	0.0212716i
$26$	−1.53275	+	1.46277i	−0.300598	+	0.286873i
$27$	0.513691	−	5.17070i	0.0988600	−	0.995101i
$28$	−0.0947992	+	2.02773i	−0.0179154	+	0.383204i
$29$	−4.40149	−	0.579467i	−0.817337	−	0.107604i	−0.289746	−	0.957103i	$-0.593571\pi$
$29$	−4.40149	−	0.579467i	−0.817337	−	0.107604i	−0.527590	+	0.849499i	$0.676904\pi$
$30$	2.87550	−	4.38929i	0.524993	−	0.801371i
$31$	−8.30037	+	4.79222i	−1.49079	+	0.860708i	−0.999944	−	0.0105382i	$-0.996646\pi$
$31$	−8.30037	+	4.79222i	−1.49079	+	0.860708i	−0.490846	+	0.871246i	$0.663312\pi$
$32$	4.05602	+	3.94318i	0.717011	+	0.697062i
$33$	−7.41515	+	0.728215i	−1.29081	+	0.126766i
$34$	−7.54443	−	1.17311i	−1.29386	−	0.201187i
$35$	−2.00877	+	0.832061i	−0.339545	+	0.140644i
$36$	0.891096	+	5.93346i	0.148516	+	0.988910i
$37$	2.47820	−	5.98289i	0.407413	−	0.983582i	−0.578403	−	0.815751i	$-0.696324\pi$
$37$	2.47820	−	5.98289i	0.407413	−	0.983582i	0.985816	−	0.167831i	$-0.0536762\pi$
$38$	10.0421	−	2.44087i	1.62904	−	0.395962i
$39$	2.42885	−	0.913371i	0.388927	−	0.146256i
$40$	−1.97415	+	5.72846i	−0.312141	+	0.905749i
$41$	−1.03703	+	3.87025i	−0.161957	+	0.604432i	0.836452	+	0.548040i	$0.184626\pi$
$41$	−1.03703	+	3.87025i	−0.161957	+	0.604432i	−0.998409	+	0.0563911i	$0.982041\pi$
$42$	1.07930	−	2.23967i	0.166540	−	0.345588i
$43$	−5.15179	−	6.71394i	−0.785640	−	1.02387i	−0.998901	−	0.0468706i	$-0.985075\pi$
$43$	−5.15179	−	6.71394i	−0.785640	−	1.02387i	0.213261	−	0.976995i	$-0.431592\pi$
$44$	8.09365	−	2.91761i	1.22016	−	0.439846i
$45$	−5.34556	+	3.56743i	−0.796870	+	0.531801i
$46$	−3.03090	−	1.33921i	−0.446882	−	0.197456i
$47$	−7.46917	−	4.31233i	−1.08949	−	0.629018i	−0.156050	−	0.987749i	$-0.549876\pi$
$47$	−7.46917	−	4.31233i	−1.08949	−	0.629018i	−0.933441	+	0.358732i	$0.883209\pi$
$48$	−2.67981	−	6.38894i	−0.386798	−	0.922165i
$49$	5.17003	−	2.98492i	0.738575	−	0.426417i
$50$	0.577793	−	0.0623770i	0.0817122	−	0.00882144i
$51$	7.93952	+	4.94022i	1.11176	+	0.691769i
$52$	−2.45975	+	1.71105i	−0.341106	+	0.237280i
$53$	−1.62188	+	3.91557i	−0.222783	+	0.537845i	−0.995266	−	0.0971903i	$-0.969014\pi$
$53$	−1.62188	+	3.91557i	−0.222783	+	0.537845i	0.772483	+	0.635035i	$0.219014\pi$
$54$	1.84139	−	7.11402i	0.250581	−	0.968096i
$55$	6.51614	+	6.51614i	0.878636	+	0.878636i
$56$	−0.573080	+	2.81299i	−0.0765810	+	0.375901i
$57$	−12.4874	−	2.06531i	−1.65400	−	0.273557i
$58$	−6.02482	−	1.76616i	−0.791098	−	0.231908i
$59$	−2.91589	+	0.383885i	−0.379617	+	0.0499775i	−0.317920	−	0.948117i	$-0.602984\pi$
$59$	−2.91589	+	0.383885i	−0.379617	+	0.0499775i	−0.0616966	+	0.998095i	$0.519651\pi$
$60$	4.97204	−	5.50887i	0.641887	−	0.711192i
$61$	0.0439705	−	0.333989i	0.00562984	−	0.0427629i	−0.988399	−	0.151877i	$-0.951468\pi$
$61$	0.0439705	−	0.333989i	0.00562984	−	0.0427629i	0.994029	+	0.109114i	$0.0348015\pi$
$62$	−12.6404	+	4.89316i	−1.60533	+	0.621432i
$63$	−2.29042	+	2.00636i	−0.288566	+	0.252777i
$64$	4.81116	+	6.39162i	0.601395	+	0.798952i
$65$	−2.77942	−	1.60470i	−0.344745	−	0.199038i
$66$	−10.5203	−	0.593616i	−1.29496	−	0.0730691i
$67$	3.21736	−	4.19294i	0.393063	−	0.512250i	−0.554341	−	0.832290i	$-0.687030\pi$
$67$	3.21736	−	4.19294i	0.393063	−	0.512250i	0.947404	+	0.320040i	$0.103696\pi$
$68$	−10.2878	−	3.27866i	−1.24758	−	0.397596i
$69$	2.77338	+	2.96279i	0.333876	+	0.356677i
$70$	−2.98790	+	0.726253i	−0.357123	+	0.0868038i
$71$	−2.98357	−	2.98357i	−0.354085	−	0.354085i	0.507542	−	0.861627i	$-0.330554\pi$
$71$	−2.98357	−	2.98357i	−0.354085	−	0.354085i	−0.861627	+	0.507542i	$0.830554\pi$
$72$	−0.0440464	+	8.48517i	−0.00519092	+	0.999987i
$73$	−1.45130	+	1.45130i	−0.169862	+	0.169862i	−0.786919	−	0.617057i	$-0.788325\pi$
$73$	−1.45130	+	1.45130i	−0.169862	+	0.169862i	0.617057	+	0.786919i	$0.288325\pi$
$74$	4.76311	−	7.82213i	0.553700	−	0.909305i
$75$	−0.681054	−	0.206805i	−0.0786413	−	0.0238798i
$76$	14.5634	−	1.22888i	1.67053	−	0.140962i
$77$	3.46389	+	2.65793i	0.394746	+	0.302900i
$78$	3.59259	−	0.748599i	0.406781	−	0.0847621i
$79$	4.91023	−	8.50477i	0.552444	−	0.956861i	−0.445653	−	0.895206i	$-0.647029\pi$
$79$	4.91023	−	8.50477i	0.552444	−	0.956861i	0.998097	−	0.0616558i	$-0.0196381\pi$
$80$	−4.00346	+	7.57610i	−0.447600	+	0.847034i
$81$	−5.48691	+	7.13399i	−0.609657	+	0.792665i
$82$	−2.29014	+	5.18303i	−0.252903	+	0.572370i
$83$	2.17172	+	0.285913i	0.238378	+	0.0313830i	0.248768	−	0.968563i	$-0.419974\pi$
$83$	2.17172	+	0.285913i	0.238378	+	0.0313830i	−0.0103908	+	0.999946i	$0.503308\pi$
$84$	1.99489	−	2.89524i	0.217661	−	0.315896i
$85$	−1.50959	−	11.4665i	−0.163738	−	1.24371i
$86$	−5.74034	−	10.5016i	−0.618997	−	1.13242i
$87$	5.94260	+	4.87978i	0.637114	+	0.523167i
$88$	11.9442	−	2.31846i	1.27326	−	0.247148i
$89$	2.17841	−	2.17841i	0.230911	−	0.230911i	−0.582162	−	0.813073i	$-0.697793\pi$
$89$	2.17841	−	2.17841i	0.230911	−	0.230911i	0.813073	+	0.582162i	$0.197793\pi$
$90$	−8.24517	+	3.82366i	−0.869117	+	0.403049i
$91$	−1.40485	−	0.581909i	−0.147268	−	0.0610006i
$92$	−3.94444	−	2.53002i	−0.411237	−	0.263773i
$93$	16.5917	+	0.547845i	1.72048	+	0.0568089i
$94$	−9.50055	−	7.64911i	−0.979907	−	0.788946i
$95$	7.82717	+	13.5571i	0.803051	+	1.39093i
$96$	−2.35657	−	9.51034i	−0.240517	−	0.970645i
$97$	4.24778	−	7.35737i	0.431297	−	0.747028i	−0.565689	−	0.824619i	$-0.691390\pi$
$97$	4.24778	−	7.35737i	0.431297	−	0.747028i	0.996985	+	0.0775912i	$0.0247229\pi$
$98$	7.87330	−	3.04779i	0.795323	−	0.307873i
$99$	11.5711	+	5.71436i	1.16294	+	0.574314i
$100$	0.820973	+	0.0383817i	0.0820973	+	0.00383817i
$101$	7.98538	−	6.12739i	0.794575	−	0.609698i	−0.129645	−	0.991560i	$-0.541384\pi$
$101$	7.98538	−	6.12739i	0.794575	−	0.609698i	0.924219	+	0.381862i	$0.124717\pi$
$102$	10.0214	+	8.62875i	0.992266	+	0.854373i
$103$	16.1860	+	4.33702i	1.59485	+	0.427339i	0.943482	−	0.331423i	$-0.107529\pi$
$103$	16.1860	+	4.33702i	1.59485	+	0.427339i	0.651368	+	0.758762i	$0.274195\pi$
$104$	−3.80910	+	1.85658i	−0.373513	+	0.182053i
$105$	3.71549	+	0.614508i	0.362595	+	0.0599698i
$106$	−3.11727	+	5.11928i	−0.302776	+	0.497228i
$107$	−8.79307	−	3.64221i	−0.850058	−	0.352106i	−0.0852469	−	0.996360i	$-0.527168\pi$
$107$	−8.79307	−	3.64221i	−0.850058	−	0.352106i	−0.764811	+	0.644254i	$0.777168\pi$
$108$	4.11900	−	9.54117i	0.396351	−	0.918099i
$109$	2.67483	+	6.45762i	0.256203	+	0.618528i	0.998681	−	0.0513420i	$-0.0163499\pi$
$109$	2.67483	+	6.45762i	0.256203	+	0.618528i	−0.742479	+	0.669870i	$0.766350\pi$
$110$	7.68990	+	10.5217i	0.733203	+	1.00320i
$111$	−9.11912	+	6.53078i	−0.865549	+	0.619874i
$112$	−1.41207	+	3.80641i	−0.133428	+	0.359671i
$113$	3.88868	+	6.73539i	0.365816	+	0.633612i	0.988907	−	0.148537i	$-0.0474565\pi$
$113$	3.88868	+	6.73539i	0.365816	+	0.633612i	−0.623091	+	0.782150i	$0.714123\pi$
$114$	−17.0014	−	5.59950i	−1.59233	−	0.524441i
$115$	0.655153	−	4.97638i	0.0610933	−	0.464050i
$116$	−8.03545	−	3.77721i	−0.746072	−	0.350705i
$117$	−4.40766	−	0.879325i	−0.407488	−	0.0812936i
$118$	−4.15814	−	0.0971466i	−0.382788	−	0.00894307i
$119$	−1.41824	−	5.29293i	−0.130010	−	0.485202i
$120$	8.14505	−	6.61783i	0.743538	−	0.604123i
$121$	1.94241	−	7.24917i	0.176583	−	0.659016i
$122$	0.134018	−	0.457169i	0.0121334	−	0.0413901i
$123$	5.06655	−	4.74266i	0.456836	−	0.427631i
$124$	−18.7272	+	4.09117i	−1.68175	+	0.367398i
$125$	4.43582	+	10.7090i	0.396752	+	0.957844i
$126$	−3.63664	+	2.30604i	−0.323978	+	0.205438i
$127$			16.4140i			1.45650i	0.685309	+	0.728252i	$0.259667\pi$
$127$			16.4140i			1.45650i	−0.685309	+	0.728252i	$0.740333\pi$
$128$	5.33438	+	9.97719i	0.471497	+	0.881868i
$129$	1.43261	+	14.5877i	0.126134	+	1.28438i
$130$	−3.53533	−	2.84638i	−0.310069	−	0.249644i
$131$	−13.9074	−	10.6715i	−1.21509	−	0.932372i	−0.216060	−	0.976380i	$-0.569321\pi$
$131$	−13.9074	−	10.6715i	−1.21509	−	0.932372i	−0.999031	+	0.0440080i	$0.985987\pi$
$132$	−14.5723	−	3.11549i	−1.26836	−	0.271169i
$133$	4.51517	+	5.88428i	0.391514	+	0.510232i
$134$	5.40709	−	5.16021i	0.467101	−	0.445774i
$135$	11.1256	−	0.354782i	0.957539	−	0.0305347i
$136$	−13.6640	−	6.81711i	−1.17168	−	0.584562i
$137$	−20.2591	+	5.42840i	−1.73085	+	0.463780i	−0.980378	−	0.197125i	$-0.936840\pi$
$137$	−20.2591	+	5.42840i	−1.73085	+	0.463780i	−0.750470	+	0.660904i	$0.770173\pi$
$138$	3.23180	+	4.74289i	0.275109	+	0.403741i
$139$	2.66709	−	0.351130i	0.226220	−	0.0297824i	−0.0165640	−	0.999863i	$-0.505273\pi$
$139$	2.66709	−	0.351130i	0.226220	−	0.0297824i	0.242784	+	0.970080i	$0.421939\pi$
$140$	−4.33316	+	0.365640i	−0.366219	+	0.0309022i
$141$	7.03817	+	13.1764i	0.592720	+	1.10966i
$142$	−3.52101	−	4.81761i	−0.295476	−	0.404285i
$143$			6.44473i			0.538935i
$144$	−1.90529	+	11.8478i	−0.158775	+	0.987315i
$145$		−	9.51028i		−	0.789786i
$146$	−2.34343	+	1.71272i	−0.193944	+	0.141746i
$147$	−10.3344	−	0.341235i	−0.852369	−	0.0281446i
$148$	8.35574	−	9.89584i	0.686837	−	0.813433i
$149$	16.7129	−	2.20030i	1.36918	−	0.180256i	0.590174	−	0.807276i	$-0.299059\pi$
$149$	16.7129	−	2.20030i	1.36918	−	0.180256i	0.779003	+	0.627020i	$0.215726\pi$
$150$	−0.906782	−	0.436980i	−0.0740384	−	0.0356793i
$151$	−11.5109	+	3.08432i	−0.936740	+	0.250999i	−0.694726	−	0.719274i	$-0.744475\pi$
$151$	−11.5109	+	3.08432i	−0.936740	+	0.250999i	−0.242014	+	0.970273i	$0.577808\pi$
$152$	20.6182	+	1.44721i	1.67236	+	0.117385i
$153$	−7.15531	−	14.5302i	−0.578473	−	1.17470i
$154$	4.26296	+	4.46692i	0.343519	+	0.359955i
$155$	−12.4990	−	16.2890i	−1.00395	−	1.30837i
$156$	5.18302	−	0.265473i	0.414974	−	0.0212549i
$157$	−11.7454	−	9.01257i	−0.937385	−	0.719281i	0.0224786	−	0.999747i	$-0.492844\pi$
$157$	−11.7454	−	9.01257i	−0.937385	−	0.719281i	−0.959864	+	0.280466i	$0.909511\pi$
$158$	8.70966	−	10.8178i	0.692904	−	0.860618i
$159$	5.96811	−	4.27414i	0.473302	−	0.338961i
$160$	−7.24073	+	9.71709i	−0.572430	+	0.768204i
$161$		−	2.37813i		−	0.187423i
$162$	−9.21767	+	8.77693i	−0.724209	+	0.689581i
$163$	1.16595	+	2.81484i	0.0913240	+	0.220476i	0.962941	−	0.269712i	$-0.0869284\pi$
$163$	1.16595	+	2.81484i	0.0913240	+	0.220476i	−0.871617	+	0.490187i	$0.836928\pi$
$164$	−4.32650	+	6.74525i	−0.337843	+	0.526716i
$165$	−3.62003	−	15.5453i	−0.281819	−	1.21020i
$166$	2.97268	+	0.871435i	0.230725	+	0.0676364i
$167$	0.941472	−	3.51362i	0.0728533	−	0.271892i	−0.919885	−	0.392189i	$-0.871718\pi$
$167$	0.941472	−	3.51362i	0.0728533	−	0.271892i	0.992738	+	0.120297i	$0.0383846\pi$
$168$	3.41681	−	3.61239i	0.263613	−	0.278702i
$169$	2.78372	+	10.3890i	0.214133	+	0.799154i
$170$	0.382020	−	16.3515i	0.0292996	−	1.25410i
$171$	16.4742	+	14.4639i	1.25981	+	1.10609i
$172$	−5.73977	−	15.9225i	−0.437653	−	1.21408i
$173$	−2.46882	+	18.7526i	−0.187701	+	1.42573i	0.595196	+	0.803581i	$0.297075\pi$
$173$	−2.46882	+	18.7526i	−0.187701	+	1.42573i	−0.782897	+	0.622152i	$0.786259\pi$
$174$	7.24399	+	8.11037i	0.549165	+	0.614846i
$175$	0.208544	+	0.361208i	0.0157644	+	0.0273048i
$176$	17.1949	−	0.644504i	1.29611	−	0.0485813i
$177$	4.63940	+	2.10366i	0.348718	+	0.158121i
$178$	3.51750	−	2.57080i	0.263648	−	0.192690i
$179$	2.08061	+	5.02303i	0.155512	+	0.375439i	0.982363	−	0.186981i	$-0.0598704\pi$
$179$	2.08061	+	5.02303i	0.155512	+	0.375439i	−0.826852	+	0.562420i	$0.809870\pi$
$180$	−12.3528	+	3.55167i	−0.920724	+	0.264726i
$181$	−1.19920	−	0.496727i	−0.0891362	−	0.0369214i	0.337670	−	0.941265i	$-0.390361\pi$
$181$	−1.19920	−	0.496727i	−0.0891362	−	0.0369214i	−0.426806	+	0.904343i	$0.640361\pi$
$182$	−1.83673	−	1.11843i	−0.136147	−	0.0829037i
$183$	−0.370281	+	0.450930i	−0.0273720	+	0.0333337i
$184$	−4.96230	−	4.39260i	−0.365825	−	0.323827i
$185$	13.3999	+	3.59050i	0.985181	+	0.263978i
$186$	23.0665	+	4.37078i	1.69132	+	0.320481i
$187$	−18.4251	+	14.1380i	−1.34737	+	1.03388i
$188$	−11.6142	−	12.7534i	−0.847052	−	0.930138i
$189$	5.20423	−	0.854694i	0.378552	−	0.0621699i
$190$	7.99204	+	20.6457i	0.579804	+	1.49780i
$191$	9.67208	−	16.7525i	0.699847	−	1.21217i	−0.268672	−	0.963232i	$-0.586585\pi$
$191$	9.67208	−	16.7525i	0.699847	−	1.21217i	0.968519	−	0.248939i	$-0.0800819\pi$
$192$	−1.22662	−	13.8020i	−0.0885238	−	0.996074i
$193$	7.28617	+	12.6200i	0.524470	+	0.908408i	0.999594	+	0.0284897i	$0.00906978\pi$
$193$	7.28617	+	12.6200i	0.524470	+	0.908408i	−0.475124	+	0.879919i	$0.657597\pi$
$194$	7.53462	−	9.35834i	0.540954	−	0.671890i
$195$	2.61903	+	4.90320i	0.187553	+	0.351125i
$196$	11.6646	−	2.54825i	0.833183	−	0.182018i
$197$	9.24225	+	3.82826i	0.658483	+	0.272753i	0.686800	−	0.726846i	$-0.259015\pi$
$197$	9.24225	+	3.82826i	0.658483	+	0.272753i	−0.0283171	+	0.999599i	$0.509015\pi$
$198$	14.9280	+	10.4996i	1.06089	+	0.746177i
$199$	−18.4609	+	18.4609i	−1.30866	+	1.30866i	−0.386276	+	0.922383i	$0.626239\pi$
$199$	−18.4609	+	18.4609i	−1.30866	+	1.30866i	−0.922383	+	0.386276i	$0.873761\pi$
$200$	1.13891	+	0.232025i	0.0805328	+	0.0164066i
$201$	−8.56823	+	3.22209i	−0.604357	+	0.227269i
$202$	12.4904	−	6.82740i	0.878818	−	0.480374i
$203$	−0.588143	−	4.46739i	−0.0412795	−	0.313549i
$204$	12.1292	+	14.2355i	0.849211	+	0.996687i
$205$	−8.50993	−	1.12035i	−0.594359	−	0.0782489i
$206$	21.6762	+	9.57769i	1.51025	+	0.667309i
$207$	−1.36743	−	6.89488i	−0.0950430	−	0.479227i
$208$	−5.72633	+	1.76675i	−0.397050	+	0.122502i
$209$	15.7176	−	27.2237i	1.08721	−	1.88310i
$210$	5.05858	+	1.66607i	0.349075	+	0.114969i
$211$	6.11216	+	4.69003i	0.420779	+	0.322875i	0.797355	−	0.603511i	$-0.206232\pi$
$211$	6.11216	+	4.69003i	0.420779	+	0.322875i	−0.376576	+	0.926386i	$0.622899\pi$
$212$	−5.46850	+	6.47644i	−0.375578	+	0.444804i
$213$	1.65752	+	7.11779i	0.113571	+	0.487703i
$214$	−11.4962	−	7.00035i	−0.785864	−	0.478534i
$215$	12.8191	−	12.8191i	0.874256	−	0.874256i
$216$	7.82917	−	12.4380i	0.532708	−	0.846299i
$217$	−6.87868	−	6.87868i	−0.466956	−	0.466956i
$218$	2.33469	+	9.60523i	0.158125	+	0.650548i
$219$	3.46231	−	0.806266i	0.233961	−	0.0544824i
$220$	8.45976	+	16.3742i	0.570357	+	1.10395i
$221$	4.92388	−	6.41693i	0.331216	−	0.431649i
$222$	−14.1623	+	7.14475i	−0.950513	+	0.479524i
$223$	−15.0037	−	8.66241i	−1.00472	−	0.580078i	−0.0950816	−	0.995469i	$-0.530311\pi$
$223$	−15.0037	−	8.66241i	−1.00472	−	0.580078i	−0.909643	+	0.415392i	$0.863645\pi$
$224$	−2.80035	+	5.01232i	−0.187106	+	0.334900i
$225$	0.812321	+	0.927331i	0.0541548	+	0.0618220i
$226$	3.97059	+	10.2571i	0.264120	+	0.682295i
$227$	−3.35498	+	25.4836i	−0.222678	+	1.69140i	0.406108	+	0.913825i	$0.366886\pi$
$227$	−3.35498	+	25.4836i	−0.222678	+	1.69140i	−0.628785	+	0.777579i	$0.716448\pi$
$228$	−22.5415	−	11.5191i	−1.49284	−	0.762871i
$229$	3.10447	−	0.408711i	0.205149	−	0.0270084i	−0.0272513	−	0.999629i	$-0.508675\pi$
$229$	3.10447	−	0.408711i	0.205149	−	0.0270084i	0.232400	+	0.972620i	$0.425342\pi$
$230$	1.99684	−	6.81174i	0.131668	−	0.449153i
$231$	−2.66184	−	7.07841i	−0.175137	−	0.465725i
$232$	−10.4081	−	7.02437i	−0.683329	−	0.461172i
$233$	−20.9855	−	20.9855i	−1.37481	−	1.37481i	−0.853163	−	0.521645i	$-0.825319\pi$
$233$	−20.9855	−	20.9855i	−1.37481	−	1.37481i	−0.521645	−	0.853163i	$-0.674681\pi$
$234$	−5.96828	−	2.18653i	−0.390159	−	0.142938i
$235$	7.07039	−	17.0694i	0.461222	−	1.11349i
$236$	−5.78957	−	1.03928i	−0.376869	−	0.0676513i
$237$	−15.0033	+	8.01401i	−0.974572	+	0.520566i
$238$	−0.831772	−	7.70462i	−0.0539157	−	0.499417i
$239$	−3.78438	+	2.18491i	−0.244791	+	0.141330i	−0.617377	−	0.786667i	$-0.711805\pi$
$239$	−3.78438	+	2.18491i	−0.244791	+	0.141330i	0.372586	+	0.927998i	$0.378471\pi$
$240$	12.8201	−	7.47805i	0.827531	−	0.482706i
$241$	−6.71220	−	3.87529i	−0.432371	−	0.249629i	0.267985	−	0.963423i	$-0.413642\pi$
$241$	−6.71220	−	3.87529i	−0.432371	−	0.249629i	−0.700356	+	0.713794i	$0.746975\pi$
$242$	4.28954	−	9.70808i	0.275742	−	0.624059i
$243$	14.5971	−	5.47044i	0.936402	−	0.350929i
$244$	0.286617	−	0.609736i	0.0183488	−	0.0390344i
$245$	7.78523	+	10.1459i	0.497380	+	0.648198i
$246$	8.11064	−	5.52658i	0.517116	−	0.352362i
$247$	−2.83355	+	10.5749i	−0.180294	+	0.672868i
$248$	−27.0588	+	1.64784i	−1.71823	+	0.104638i
$249$	−2.93212	−	2.40771i	−0.185815	−	0.152583i
$250$	3.87174	+	15.9289i	0.244871	+	1.00743i
$251$	2.35690	−	5.69006i	0.148766	−	0.359153i	−0.831876	−	0.554961i	$-0.812733\pi$
$251$	2.35690	−	5.69006i	0.148766	−	0.359153i	0.980642	+	0.195808i	$0.0627330\pi$
$252$	−5.58300	+	2.43230i	−0.351696	+	0.153221i
$253$	−9.31197	+	3.85714i	−0.585438	+	0.242497i
$254$	−3.56660	+	22.9372i	−0.223788	+	1.43921i
$255$	−8.27245	+	18.2440i	−0.518041	+	1.14248i
$256$	5.28643	+	15.1014i	0.330402	+	0.943840i
$257$	13.5420	−	7.81847i	0.844726	−	0.487703i	−0.0141420	−	0.999900i	$-0.504502\pi$
$257$	13.5420	−	7.81847i	0.844726	−	0.487703i	0.858868	+	0.512197i	$0.171168\pi$
$258$	−1.16781	+	20.6965i	−0.0727048	+	1.28851i
$259$	6.51656	+	0.857921i	0.404919	+	0.0533086i
$260$	−4.32186	−	4.74578i	−0.268030	−	0.294321i
$261$	−4.27394	−	12.6140i	−0.264550	−	0.780789i
$262$	−17.1156	−	17.9345i	−1.05741	−	1.10800i
$263$	4.92734	−	1.32028i	0.303833	−	0.0814117i	−0.103682	−	0.994611i	$-0.533062\pi$
$263$	4.92734	−	1.32028i	0.303833	−	0.0814117i	0.407514	+	0.913199i	$0.366396\pi$
$264$	−19.6867	−	7.52008i	−1.21163	−	0.462829i
$265$	−8.76972	−	2.34984i	−0.538719	−	0.144349i
$266$	5.03099	+	9.20391i	0.308470	+	0.564328i
$267$	−5.19693	+	1.21021i	−0.318047	+	0.0740635i
$268$	8.67724	−	6.03607i	0.530047	−	0.368712i
$269$	−1.56831	+	0.649614i	−0.0956214	+	0.0396077i	−0.429981	−	0.902838i	$-0.641480\pi$
$269$	−1.56831	+	0.649614i	−0.0956214	+	0.0396077i	0.334360	+	0.942445i	$0.391480\pi$
$270$	15.6242	+	1.92170i	0.950860	+	0.116951i
$271$	−1.58685			−0.0963942			−0.0481971	−	0.998838i	$-0.515348\pi$
$271$	−1.58685			−0.0963942			−0.0481971	+	0.998838i	$0.515348\pi$
$272$	−17.6131	−	12.4954i	−1.06795	−	0.757647i
$273$	1.53350	+	2.14127i	0.0928117	+	0.129596i
$274$	−29.4900	+	3.18366i	−1.78155	+	0.192332i
$275$	1.07613	−	1.40244i	0.0648929	−	0.0845701i
$276$	3.48560	+	7.33005i	0.209808	+	0.441217i
$277$	10.3814	−	7.96596i	0.623760	−	0.478628i	−0.247869	−	0.968793i	$-0.579730\pi$
$277$	10.3814	−	7.96596i	0.623760	−	0.478628i	0.871629	+	0.490166i	$0.163064\pi$
$278$	3.80335	+	0.0888576i	0.228110	+	0.00532932i
$279$	−23.8985	−	15.9880i	−1.43077	−	0.957176i
$280$	−6.13470	−	0.430601i	−0.366619	−	0.0257334i
$281$	0.699325	+	2.60992i	0.0417182	+	0.155695i	0.983643	−	0.180130i	$-0.0576518\pi$
$281$	0.699325	+	2.60992i	0.0417182	+	0.155695i	−0.941925	+	0.335824i	$0.890985\pi$
$282$	6.97217	+	19.9423i	0.415187	+	1.18755i
$283$	−0.786331	−	5.97277i	−0.0467425	−	0.355045i	−0.998794	−	0.0491055i	$-0.984363\pi$
$283$	−0.786331	−	5.97277i	−0.0467425	−	0.355045i	0.952051	−	0.305939i	$-0.0989704\pi$
$284$	−3.87351	−	7.49731i	−0.229850	−	0.444883i
$285$	0.894800	−	27.0994i	0.0530034	−	1.60523i
$286$	−1.40038	+	9.00600i	−0.0828060	+	0.532536i
$287$	−4.06676			−0.240053
$288$	−5.23690	+	16.1423i	−0.308588	+	0.951196i
$289$	12.1473			0.714545
$290$	2.06649	−	13.2899i	0.121349	−	0.780408i
$291$	−12.9792	+	6.93282i	−0.760854	+	0.406409i
$292$	−3.64692	+	1.88419i	−0.213420	+	0.110264i
$293$	−1.14284	−	8.68074i	−0.0667655	−	0.507134i	−0.991854	−	0.127382i	$-0.959343\pi$
$293$	−1.14284	−	8.68074i	−0.0667655	−	0.507134i	0.925088	−	0.379752i	$-0.123991\pi$
$294$	−14.3674	−	2.72242i	−0.837923	−	0.158775i
$295$	−1.63065	−	6.08568i	−0.0949403	−	0.354322i
$296$	13.8268	−	12.0130i	0.803664	−	0.698243i
$297$	−11.7875	−	18.9917i	−0.683982	−	1.10201i
$298$	23.8331	+	0.556812i	1.38062	+	0.0322553i
$299$	2.78491	−	2.13694i	0.161055	−	0.123582i
$300$	−1.17220	−	0.807680i	−0.0676773	−	0.0466314i
$301$	5.22891	−	6.81445i	0.301389	−	0.392778i
$302$	−16.7557	+	1.80890i	−0.964182	+	0.104091i
$303$	−17.3502	+	1.70390i	−0.996744	+	0.0978866i
$304$	28.4978	+	6.50250i	1.63446	+	0.372944i
$305$	0.721648			0.0413214
$306$	−6.84171	−	21.8596i	−0.391114	−	1.24963i
$307$	−25.8866	+	10.7226i	−1.47742	+	0.611969i	−0.968538	−	0.248865i	$-0.919942\pi$
$307$	−25.8866	+	10.7226i	−1.47742	+	0.611969i	−0.508886	+	0.860834i	$0.669942\pi$
$308$	4.98654	+	7.16847i	0.284134	+	0.408461i
$309$	−19.8345	−	21.1891i	−1.12835	−	1.20541i
$310$	−13.9269	−	25.4786i	−0.790997	−	1.44709i
$311$	0.827596	+	0.221754i	0.0469287	+	0.0125745i	0.282207	−	0.959354i	$-0.408934\pi$
$311$	0.827596	+	0.221754i	0.0469287	+	0.0125745i	−0.235278	+	0.971928i	$0.575600\pi$
$312$	7.30055	+	0.755242i	0.413312	+	0.0427572i
$313$	17.6037	−	4.71691i	0.995022	−	0.266615i	0.275663	−	0.961254i	$-0.411102\pi$
$313$	17.6037	−	4.71691i	0.995022	−	0.266615i	0.719359	+	0.694639i	$0.244436\pi$
$314$	−14.4549	−	15.1465i	−0.815739	−	0.854767i
$315$	−4.90170	−	4.30358i	−0.276180	−	0.242479i
$316$	14.5217	−	13.2245i	0.816908	−	0.743936i
$317$	−11.9153	−	1.56867i	−0.669227	−	0.0881055i	−0.211746	−	0.977325i	$-0.567915\pi$
$317$	−11.9153	−	1.56867i	−0.669227	−	0.0881055i	−0.457481	+	0.889219i	$0.651248\pi$
$318$	9.26869	−	4.67596i	0.519762	−	0.262215i
$319$	−16.5389	+	9.54871i	−0.925998	+	0.534625i
$320$	−12.2298	+	12.0055i	−0.683665	+	0.671129i
$321$	9.59829	+	13.4024i	0.535725	+	0.748049i
$322$	0.516745	−	3.32325i	0.0287971	−	0.185198i
$323$	−36.4491	+	15.0977i	−2.02808	+	0.840060i
$324$	−14.7881	+	10.2622i	−0.821562	+	0.570120i
$325$	−0.235599	+	0.568787i	−0.0130687	+	0.0315506i
$326$	1.01768	+	4.18687i	0.0563641	+	0.231889i
$327$	1.97546	−	11.9442i	0.109243	−	0.660517i
$328$	−7.51163	+	8.48585i	−0.414760	+	0.468553i
$329$	2.26564	−	8.45550i	0.124909	−	0.466167i
$330$	−1.68086	−	22.5099i	−0.0925283	−	1.23913i
$331$	9.82898	+	12.8094i	0.540249	+	0.704067i	0.981097	−	0.193515i	$-0.0619888\pi$
$331$	9.82898	+	12.8094i	0.540249	+	0.704067i	−0.440848	+	0.897582i	$0.645322\pi$
$332$	3.96474	+	1.86370i	0.217593	+	0.102284i
$333$	19.3866	−	1.25967i	1.06238	−	0.0690297i
$334$	2.07911	−	4.70544i	0.113764	−	0.257470i
$335$	9.80494	+	5.66089i	0.535701	+	0.309287i
$336$	5.55966	−	4.30559i	0.303305	−	0.234889i
$337$	−11.5406	+	6.66299i	−0.628658	+	0.362956i	−0.780232	−	0.625490i	$-0.784899\pi$
$337$	−11.5406	+	6.66299i	−0.628658	+	0.362956i	0.151574	+	0.988446i	$0.451566\pi$
$338$	1.63261	+	15.1227i	0.0888021	+	0.822565i
$339$	0.444553	−	13.4634i	0.0241448	−	0.731234i
$340$	4.08686	−	22.7669i	0.221641	−	1.23471i
$341$	−15.7779	+	38.0913i	−0.854422	+	2.06276i
$342$	19.8785	+	23.7919i	1.07491	+	1.28652i
$343$	9.30836	+	9.30836i	0.502604	+	0.502604i
$344$	−4.56107	−	23.4976i	−0.245916	−	1.26691i
$345$	−5.51713	+	6.71878i	−0.297032	+	0.361727i
$346$	−7.52474	+	25.6688i	−0.404532	+	1.37996i
$347$	−5.41397	+	0.712763i	−0.290637	+	0.0382631i	−0.274435	−	0.961606i	$-0.588491\pi$
$347$	−5.41397	+	0.712763i	−0.290637	+	0.0382631i	−0.0162021	+	0.999869i	$0.505158\pi$
$348$	8.36060	+	12.9076i	0.448175	+	0.691923i
$349$	−4.32405	+	32.8444i	−0.231461	+	1.75812i	0.342763	+	0.939422i	$0.388637\pi$
$349$	−4.32405	+	32.8444i	−0.231461	+	1.75812i	−0.574224	+	0.818698i	$0.694696\pi$
$350$	0.212936	+	0.550074i	0.0113819	+	0.0294027i
$351$	5.67728	+	5.32639i	0.303031	+	0.284302i
$352$	24.1685	+	2.83563i	1.28818	+	0.151140i
$353$	29.4504	+	17.0032i	1.56748	+	0.904988i	0.996461	+	0.0840537i	$0.0267867\pi$
$353$	29.4504	+	17.0032i	1.56748	+	0.904988i	0.571023	+	0.820934i	$0.306547\pi$
$354$	6.02609	+	3.94780i	0.320283	+	0.209823i
$355$	5.50251	−	7.17101i	0.292043	−	0.380598i
$356$	5.47403	−	2.82818i	0.290123	−	0.149893i
$357$	−2.75766	+	9.08157i	−0.145951	+	0.480648i
$358$	1.81603	+	7.47138i	0.0959801	+	0.394875i
$359$	13.1660	+	13.1660i	0.694877	+	0.694877i	0.963301	−	0.268424i	$-0.0865027\pi$
$359$	13.1660	+	13.1660i	0.694877	+	0.694877i	−0.268424	+	0.963301i	$0.586503\pi$
$360$	−18.0338	+	2.27903i	−0.950466	+	0.120115i
$361$	24.3249	−	24.3249i	1.28026	−	1.28026i
$362$	−1.56786	−	0.954712i	−0.0824049	−	0.0501785i
$363$	−9.48991	+	8.88324i	−0.498091	+	0.466249i
$364$	−2.32365	−	1.96202i	−0.121793	−	0.102838i
$365$	−3.48820	−	2.67659i	−0.182581	−	0.140099i
$366$	−0.615422	+	0.549680i	−0.0321686	+	0.0287322i
$367$	−0.868465	+	1.50423i	−0.0453335	+	0.0785199i	−0.887802	−	0.460226i	$-0.847768\pi$
$367$	−0.868465	+	1.50423i	−0.0453335	+	0.0785199i	0.842468	+	0.538746i	$0.181102\pi$
$368$	−5.97995	−	7.21657i	−0.311726	−	0.376189i
$369$	−11.7907	+	2.33839i	−0.613799	+	0.121732i
$370$	17.9451	+	7.92910i	0.932923	+	0.412214i
$371$	−4.26483	−	0.561476i	−0.221419	−	0.0291504i
$372$	31.2839	+	11.1200i	1.62200	+	0.576543i
$373$	−4.10050	−	31.1464i	−0.212316	−	1.61270i	−0.683015	−	0.730404i	$-0.739332\pi$
$373$	−4.10050	−	31.1464i	−0.212316	−	1.61270i	0.470699	−	0.882294i	$-0.344002\pi$
$374$	−28.8196	+	15.7532i	−1.49023	+	0.814579i
$375$	3.27602	−	19.8077i	0.169173	−	1.02287i
$376$	−13.4587	−	20.3455i	−0.694080	−	1.04924i
$377$	4.70303	−	4.70303i	0.242218	−	0.242218i
$378$	7.45821	−	0.0635400i	0.383609	−	0.00326814i
$379$	−24.9141	−	10.3198i	−1.27975	−	0.530091i	−0.363837	−	0.931462i	$-0.618534\pi$
$379$	−24.9141	−	10.3198i	−1.27975	−	0.530091i	−0.915915	+	0.401372i	$0.868534\pi$
$380$	6.68214	+	30.5873i	0.342786	+	1.56910i
$381$	15.0197	−	24.1384i	0.769482	−	1.23665i
$382$	17.1561	−	21.3087i	0.877784	−	1.09025i
$383$	5.45733	+	9.45238i	0.278857	+	0.482994i	0.971101	−	0.238669i	$-0.0767112\pi$
$383$	5.45733	+	9.45238i	0.278857	+	0.482994i	−0.692244	+	0.721663i	$0.743378\pi$
$384$	1.28493	−	19.5537i	0.0655715	−	0.997848i
$385$	−4.67659	+	8.10009i	−0.238341	+	0.412819i
$386$	7.43964	+	19.2187i	0.378668	+	0.978205i
$387$	11.2418	−	22.7636i	0.571451	−	1.15714i
$388$	12.5625	−	11.4403i	0.637765	−	0.580795i
$389$	−2.46155	+	1.88881i	−0.124805	+	0.0957665i	−0.669278	−	0.743012i	$-0.733396\pi$
$389$	−2.46155	+	1.88881i	−0.124805	+	0.0957665i	0.544473	+	0.838779i	$0.316730\pi$
$390$	2.59448	+	7.42092i	0.131376	+	0.375773i
$391$	12.2187	+	3.27399i	0.617927	+	0.165573i
$392$	16.8540	−	1.02639i	0.851256	−	0.0518404i
$393$	10.6872	+	28.4195i	0.539098	+	1.43358i
$394$	12.0835	+	7.35795i	0.608756	+	0.370688i
$395$	19.4361	+	8.05070i	0.977937	+	0.405075i
$396$	18.5792	+	17.9161i	0.933642	+	0.900320i
$397$	−9.05217	−	21.8539i	−0.454316	−	1.09681i	−0.970665	−	0.240437i	$-0.922709\pi$
$397$	−9.05217	−	21.8539i	−0.454316	−	1.09681i	0.516349	−	0.856378i	$-0.327291\pi$
$398$	−29.8090	+	21.7863i	−1.49419	+	1.09205i
$399$	−1.25557	−	12.7851i	−0.0628574	−	0.640054i
$400$	1.54111	+	0.571709i	0.0770557	+	0.0285855i
$401$	7.88970	+	13.6654i	0.393993	+	0.682416i	0.992972	−	0.118349i	$-0.0377601\pi$
$401$	7.88970	+	13.6654i	0.393993	+	0.682416i	−0.598979	+	0.800765i	$0.704427\pi$
$402$	−12.6736	+	2.64083i	−0.632100	+	0.131713i
$403$	1.87424	−	14.2363i	0.0933627	−	0.709160i
$404$	18.9378	−	6.82673i	0.942191	−	0.339642i
$405$	−16.6860	−	9.65880i	−0.829133	−	0.479949i
$406$	0.148837	−	6.37062i	0.00738663	−	0.316168i
$407$	−7.21001	−	26.9081i	−0.357387	−	1.33379i
$408$	13.8563	+	22.5286i	0.685989	+	1.11533i
$409$	−6.88466	+	25.6939i	−0.340425	+	1.27048i	0.557443	+	0.830215i	$0.311783\pi$
$409$	−6.88466	+	25.6939i	−0.340425	+	1.27048i	−0.897867	+	0.440266i	$0.854884\pi$
$410$	−11.6485	−	3.41473i	−0.575279	−	0.168641i
$411$	34.7603	+	10.5551i	1.71460	+	0.520647i
$412$	28.2097	+	18.0941i	1.38979	+	0.891432i
$413$	−1.14234	−	2.75786i	−0.0562110	−	0.135705i
$414$	−0.412686	−	9.93218i	−0.0202824	−	0.488140i
$415$			4.69243i			0.230342i
$416$	−8.38599	+	1.22461i	−0.411157	+	0.0600416i
$417$	−4.24354	−	1.92417i	−0.207807	−	0.0942269i
$418$	27.8795	−	34.6277i	1.36363	−	1.69369i
$419$	14.1183	+	10.8334i	0.689725	+	0.529245i	0.893101	−	0.449856i	$-0.148525\pi$
$419$	14.1183	+	10.8334i	0.689725	+	0.529245i	−0.203376	+	0.979101i	$0.565191\pi$
$420$	6.70694	+	3.42737i	0.327265	+	0.167239i
$421$	−6.35570	−	8.28291i	−0.309758	−	0.403684i	0.612369	−	0.790572i	$-0.290217\pi$
$421$	−6.35570	−	8.28291i	−0.309758	−	0.403684i	−0.922127	+	0.386888i	$0.873550\pi$
$422$	7.52217	+	7.88206i	0.366173	+	0.383692i
$423$	1.70682	−	25.8176i	0.0829882	−	1.25530i
$424$	−9.04907	+	7.86206i	−0.439462	+	0.381815i
$425$	−2.14297	+	0.574207i	−0.103949	+	0.0278531i
$426$	0.769623	+	10.3067i	0.0372884	+	0.499361i
$427$	0.338989	−	0.0446287i	0.0164048	−	0.00215974i
$428$	−14.5439	−	12.2804i	−0.703007	−	0.593598i
$429$	5.89729	−	9.47764i	0.284724	−	0.457585i
$430$	20.6992	−	15.1282i	0.998202	−	0.729548i
$431$			33.1788i			1.59817i	0.601220	+	0.799084i	$0.294682\pi$
$431$			33.1788i			1.59817i	−0.601220	+	0.799084i	$0.705318\pi$
$432$	13.6433	−	15.6799i	0.656414	−	0.754401i
$433$		−	12.9633i		−	0.622976i	−0.950250	−	0.311488i	$-0.899173\pi$
$433$		−	12.9633i		−	0.622976i	0.950250	−	0.311488i	$-0.100827\pi$
$434$	−8.11775	−	11.1071i	−0.389664	−	0.533157i
$435$	−8.70244	+	13.9859i	−0.417250	+	0.670570i
$436$	1.17542	+	13.9299i	0.0562926	+	0.667119i
$437$	−16.9756	+	2.23488i	−0.812051	+	0.106909i
$438$	5.01349	−	0.374368i	0.239554	−	0.0178880i
$439$	12.2184	−	3.27390i	0.583151	−	0.156255i	0.0448299	−	0.998995i	$-0.485725\pi$
$439$	12.2184	−	3.27390i	0.583151	−	0.156255i	0.538321	+	0.842740i	$0.319059\pi$
$440$	8.26391	+	24.7198i	0.393966	+	1.17847i
$441$	14.8856	+	9.95839i	0.708837	+	0.474209i
$442$	8.27507	−	7.89724i	0.393605	−	0.375633i
$443$	5.21798	+	6.80020i	0.247914	+	0.323087i	0.900689	−	0.434464i	$-0.143062\pi$
$443$	5.21798	+	6.80020i	0.247914	+	0.323087i	−0.652776	+	0.757551i	$0.726396\pi$
$444$	−21.3432	+	6.90688i	−1.01290	+	0.327786i
$445$	5.23580	+	4.01757i	0.248201	+	0.190451i
$446$	−19.0843	−	15.3652i	−0.903667	−	0.727563i
$447$	−26.5915	−	12.0575i	−1.25773	−	0.570300i
$448$	−5.00239	+	6.39583i	−0.236341	+	0.302175i
$449$		−	14.4515i		−	0.682010i	−0.940061	−	0.341005i	$-0.889233\pi$
$449$		−	14.4515i		−	0.682010i	0.940061	−	0.341005i	$-0.110767\pi$
$450$	0.933655	+	1.47238i	0.0440129	+	0.0694087i
$451$	6.59596	+	15.9241i	0.310592	+	0.749835i
$452$	3.31981	+	15.1963i	0.156150	+	0.714775i
$453$	19.7502	+	5.99725i	0.927946	+	0.281776i
$454$	−10.2256	+	34.8823i	−0.479913	+	1.63711i
$455$	0.843089	−	3.14645i	0.0395246	−	0.147508i
$456$	−28.9969	−	20.9951i	−1.35790	−	0.983184i
$457$	10.8555	+	40.5132i	0.507797	+	1.89513i	0.441349	+	0.897335i	$0.354500\pi$
$457$	10.8555	+	40.5132i	0.507797	+	1.89513i	0.0664480	+	0.997790i	$0.478833\pi$
$458$	4.42706	+	0.103429i	0.206863	+	0.00483293i
$459$	−2.77333	+	27.9157i	−0.129448	+	1.30299i
$460$	4.27055	−	9.08497i	0.199116	−	0.423589i
$461$	4.86953	−	36.9877i	0.226796	−	1.72269i	−0.377568	−	0.925982i	$-0.623239\pi$
$461$	4.86953	−	36.9877i	0.226796	−	1.72269i	0.604364	−	0.796708i	$-0.293427\pi$
$462$	−2.18165	−	10.4699i	−0.101499	−	0.487105i
$463$	−3.54843	−	6.14606i	−0.164910	−	0.285632i	0.771714	−	0.635970i	$-0.219400\pi$
$463$	−3.54843	−	6.14606i	−0.164910	−	0.285632i	−0.936623	+	0.350339i	$0.886067\pi$
$464$	−13.0182	−	12.0776i	−0.604357	−	0.560688i
$465$	3.47572	+	35.3920i	0.161183	+	1.64127i
$466$	−24.7657	−	33.8856i	−1.14725	−	1.56972i
$467$	4.76497	+	11.5037i	0.220497	+	0.532326i	0.994958	−	0.100296i	$-0.0319789\pi$
$467$	4.76497	+	11.5037i	0.220497	+	0.532326i	−0.774461	+	0.632622i	$0.781979\pi$
$468$	−7.86509	−	4.35235i	−0.363564	−	0.201187i
$469$	4.95589	+	2.05280i	0.228842	+	0.0947893i
$470$	13.5893	−	22.3169i	0.626829	−	1.02940i
$471$	9.02583	+	24.0016i	0.415888	+	1.10594i
$472$	−7.86464	−	2.71033i	−0.361999	−	0.124753i
$473$	−35.1640	−	9.42215i	−1.61684	−	0.433231i
$474$	−22.7073	+	7.93886i	−1.04298	+	0.364644i
$475$	2.38239	−	1.82807i	0.109312	−	0.0838777i
$476$	0.511804	−	10.9473i	0.0234585	−	0.501770i
$477$	−12.6878	+	0.824407i	−0.580934	+	0.0377470i
$478$	−5.76314	+	2.23094i	−0.263600	+	0.102041i
$479$	17.9620	−	31.1111i	0.820706	−	1.42150i	−0.0844520	−	0.996428i	$-0.526914\pi$
$479$	17.9620	−	31.1111i	0.820706	−	1.42150i	0.905158	−	0.425076i	$-0.139753\pi$
$480$	19.5399	−	7.66432i	0.891871	−	0.349827i
$481$	4.85096	+	8.40210i	0.221185	+	0.383103i
$482$	−8.53770	−	6.87391i	−0.388882	−	0.313098i
$483$	−2.17612	+	3.49729i	−0.0990171	+	0.159132i
$484$	8.10376	−	12.6342i	0.368353	−	0.574282i
$485$	16.8139	+	6.96456i	0.763482	+	0.316244i
$486$	21.5869	−	4.47270i	0.979202	−	0.202886i
$487$	1.72336	−	1.72336i	0.0780927	−	0.0780927i	−0.666982	−	0.745074i	$-0.732414\pi$
$487$	1.72336	−	1.72336i	0.0780927	−	0.0780927i	0.745074	+	0.666982i	$0.232414\pi$
$488$	0.533015	−	0.789779i	0.0241284	−	0.0357516i
$489$	0.861094	−	5.20642i	0.0389400	−	0.235443i
$490$	8.67464	+	15.8698i	0.391880	+	0.716923i
$491$	−0.937781	−	7.12316i	−0.0423215	−	0.321464i	−0.999490	−	0.0319323i	$-0.989834\pi$
$491$	−0.937781	−	7.12316i	−0.0423215	−	0.321464i	0.957169	−	0.289531i	$-0.0934994\pi$
$492$	12.5349	−	5.96060i	0.565115	−	0.268724i
$493$	23.7629	+	3.12844i	1.07023	+	0.140898i
$494$	−6.25749	+	14.1619i	−0.281538	+	0.637176i
$495$	−8.90118	+	26.1735i	−0.400078	+	1.17641i
$496$	−38.1705	−	3.57687i	−1.71391	−	0.160606i
$497$	2.14129	−	3.70882i	0.0960499	−	0.166363i
$498$	−3.57423	−	4.00171i	−0.160165	−	0.179321i
$499$	28.0851	+	21.5504i	1.25726	+	0.964730i	0.999999	−	0.00161157i	$-0.000512980\pi$
$499$	28.0851	+	21.5504i	1.25726	+	0.964730i	0.257262	+	0.966342i	$0.417180\pi$
$500$	1.94927	+	23.1006i	0.0871740	+	1.03309i
$501$	−4.59969	+	4.30564i	−0.205499	+	0.192362i
$502$	4.52997	−	7.43927i	0.202183	−	0.332031i
$503$	−14.0204	+	14.0204i	−0.625137	+	0.625137i	−0.946840	−	0.321704i	$-0.895745\pi$
$503$	−14.0204	+	14.0204i	−0.625137	+	0.625137i	0.321704	+	0.946840i	$0.395745\pi$
$504$	−8.33032	+	2.18582i	−0.371062	+	0.0973641i
$505$	15.2467	+	15.2467i	0.678469	+	0.678469i
$506$	−13.8509	+	3.36665i	−0.615746	+	0.149666i
$507$	5.41276	−	17.8254i	0.240389	−	0.791652i
$508$	−9.96807	+	31.2780i	−0.442262	+	1.38774i
$509$	−18.9980	+	24.7587i	−0.842072	+	1.09741i	0.151967	+	0.988386i	$0.451439\pi$
$509$	−18.9980	+	24.7587i	−0.842072	+	1.09741i	−0.994039	+	0.109025i	$0.965227\pi$
$510$	−15.5243	+	23.6970i	−0.687429	+	1.04932i
$511$	−1.80408	−	1.04159i	−0.0798079	−	0.0460771i
$512$	4.10596	+	22.2518i	0.181460	+	0.983398i
$513$	−10.9917	−	36.3455i	−0.485295	−	1.60469i
$514$	20.6227	−	7.98315i	0.909629	−	0.352122i
$515$	−4.68549	+	35.5898i	−0.206467	+	1.56827i
$516$	−6.12906	+	28.6679i	−0.269817	+	1.26203i
$517$	−36.7836	+	4.84265i	−1.61774	+	0.212979i
$518$	8.91995	+	2.61486i	0.391920	+	0.114890i
$519$	20.7903	−	25.3185i	0.912594	−	1.11136i
$520$	−5.00824	−	7.57096i	−0.219626	−	0.332008i
$521$	−6.89274	−	6.89274i	−0.301977	−	0.301977i	0.539810	−	0.841787i	$-0.318496\pi$
$521$	−6.89274	−	6.89274i	−0.301977	−	0.301977i	−0.841787	+	0.539810i	$0.818496\pi$
$522$	−3.23159	−	18.5558i	−0.141443	−	0.812165i
$523$	−0.948159	+	2.28906i	−0.0414601	+	0.100094i	−0.943253	−	0.332075i	$-0.892251\pi$
$523$	−0.948159	+	2.28906i	−0.0414601	+	0.100094i	0.901793	+	0.432168i	$0.142251\pi$
$524$	−20.0207	−	28.7811i	−0.874610	−	1.25731i
$525$	0.0238406	−	0.722023i	0.00104049	−	0.0315116i
$526$	7.17244	−	0.774319i	0.312733	−	0.0337619i
$527$	44.8122	−	25.8723i	1.95205	−	1.12702i
$528$	−25.8766	−	14.7864i	−1.12613	−	0.643497i
$529$	−15.1642	−	8.75504i	−0.659312	−	0.380654i
$530$	−11.7444	−	5.18929i	−0.510144	−	0.225408i
$531$	−4.89774	−	7.33896i	−0.212544	−	0.318484i
$532$	5.03049	+	13.9549i	0.218099	+	0.605023i
$533$	−3.65430	−	4.76237i	−0.158285	−	0.206281i
$534$	−7.52527	+	0.561927i	−0.325650	+	0.0243170i
$535$	5.27696	−	19.6939i	0.228143	−	0.851440i
$536$	13.4373	−	6.54945i	0.580405	−	0.282893i
$537$	1.53660	−	9.29075i	0.0663093	−	0.400925i
$538$	−2.33274	+	0.567006i	−0.100572	+	0.0244454i
$539$	9.82755	−	23.7258i	0.423303	−	1.02194i
$540$	21.4161	+	6.08042i	0.921600	+	0.261660i
$541$	−33.1384	+	13.7264i	−1.42473	+	0.590142i	−0.956044	−	0.293223i	$-0.905272\pi$
$541$	−33.1384	+	13.7264i	−1.42473	+	0.590142i	−0.468685	+	0.883365i	$0.655272\pi$
$542$	−2.21749	−	0.344807i	−0.0952496	−	0.0148107i
$543$	1.30902	+	1.82783i	0.0561755	+	0.0784396i
$544$	−21.8978	−	21.2885i	−0.938858	−	0.912738i
$545$	−12.9673	+	7.48668i	−0.555459	+	0.320694i
$546$	1.67767	+	3.32547i	0.0717975	+	0.142317i
$547$	22.4101	+	2.95034i	0.958186	+	0.126148i	0.593368	−	0.804931i	$-0.297798\pi$
$547$	22.4101	+	2.95034i	0.958186	+	0.126148i	0.364818	+	0.931079i	$0.381131\pi$
$548$	−41.9017	−	1.95897i	−1.78995	−	0.0836828i
$549$	0.957163	−	0.324310i	0.0408507	−	0.0138412i
$550$	1.80854	−	1.72596i	0.0771163	−	0.0735953i
$551$	−31.3363	+	8.39654i	−1.33497	+	0.357705i
$552$	3.27810	+	11.0005i	0.139525	+	0.468214i
$553$	9.62785	+	2.57977i	0.409418	+	0.109703i
$554$	16.2382	−	8.87601i	0.689893	−	0.377106i
$555$	−16.4204	−	17.5419i	−0.697009	−	0.744610i
$556$	5.29557	+	0.950602i	0.224582	+	0.0403145i
$557$	27.8912	−	11.5529i	1.18179	−	0.489513i	0.296716	−	0.954966i	$-0.404108\pi$
$557$	27.8912	−	11.5529i	1.18179	−	0.489513i	0.885073	+	0.465453i	$0.154108\pi$
$558$	−29.9222	−	27.5349i	−1.26671	−	1.16564i
$559$	12.6786			0.536249
$560$	−8.47920	−	1.93474i	−0.358311	−	0.0817578i
$561$	40.0331	−	3.93150i	1.69020	−	0.165988i
$562$	0.410142	+	3.79911i	0.0173008	+	0.160256i
$563$	14.0095	−	18.2575i	0.590429	−	0.769462i	−0.398609	−	0.917121i	$-0.630507\pi$
$563$	14.0095	−	18.2575i	0.590429	−	0.769462i	0.989038	+	0.147659i	$0.0471738\pi$
$564$	5.40978	+	29.3828i	0.227793	+	1.23724i
$565$	−13.2179	+	10.1424i	−0.556079	+	0.426695i
$566$	0.198990	−	8.51734i	0.00836419	−	0.358011i
$567$	−8.43544	−	3.50524i	−0.354255	−	0.147206i
$568$	−3.78383	−	11.3186i	−0.158766	−	0.474917i
$569$	8.67494	+	32.3753i	0.363673	+	1.35724i	0.869211	+	0.494441i	$0.164627\pi$
$569$	8.67494	+	32.3753i	0.363673	+	1.35724i	−0.505539	+	0.862804i	$0.668706\pi$
$570$	7.13884	−	37.6748i	0.299013	−	1.57802i
$571$	0.282974	+	2.14940i	0.0118421	+	0.0899495i	0.996345	−	0.0854171i	$-0.0272223\pi$
$571$	0.282974	+	2.14940i	0.0118421	+	0.0899495i	−0.984503	+	0.175367i	$0.943889\pi$
$572$	−3.91383	+	12.2809i	−0.163646	+	0.513490i
$573$	−29.5533	+	15.7858i	−1.23461	+	0.659463i
$574$	−5.68298	−	0.883668i	−0.237203	−	0.0368836i
$575$	−0.962844			−0.0401534
$576$	−10.8257	+	21.4197i	−0.451072	+	0.892488i
$577$	26.0027			1.08251			0.541254	−	0.840859i	$-0.317950\pi$
$577$	26.0027			1.08251			0.541254	+	0.840859i	$0.317950\pi$
$578$	16.9748	+	2.63948i	0.706061	+	0.109788i
$579$	0.832952	−	25.2263i	0.0346163	−	1.04837i
$580$	5.77552	−	18.1225i	0.239815	−	0.752496i
$581$	0.290193	+	2.20424i	0.0120392	+	0.0914471i
$582$	−19.6438	+	6.86781i	−0.814263	+	0.284680i
$583$	4.71867	+	17.6103i	0.195427	+	0.729344i
$584$	−5.50569	+	1.84057i	−0.227827	+	0.0761633i
$585$	0.635139	−	9.60722i	0.0262597	−	0.397210i
$586$	0.289210	−	12.3790i	0.0119471	−	0.511371i
$587$	−2.40040	+	1.84189i	−0.0990750	+	0.0760229i	−0.657111	−	0.753794i	$-0.728222\pi$
$587$	−2.40040	+	1.84189i	−0.0990750	+	0.0760229i	0.558036	+	0.829817i	$0.311555\pi$
$588$	−19.4857	−	6.92626i	−0.803578	−	0.285634i
$589$	−42.6370	+	55.5656i	−1.75683	+	2.28954i
$590$	−0.956350	−	8.85858i	−0.0393723	−	0.364702i
$591$	−10.0886	−	14.0870i	−0.414990	−	0.579463i
$592$	21.9321	−	13.7828i	0.901404	−	0.566471i
$593$	11.5374			0.473783			0.236891	−	0.971536i	$-0.423871\pi$
$593$	11.5374			0.473783			0.236891	+	0.971536i	$0.423871\pi$
$594$	−12.3454	−	29.1008i	−0.506539	−	1.19402i
$595$	10.8450	−	4.49215i	0.444602	−	0.184160i
$596$	33.1839	+	5.95680i	1.35927	+	0.244000i
$597$	44.0414	−	10.2559i	1.80250	−	0.419747i
$598$	4.35602	−	2.38106i	0.178131	−	0.0973690i
$599$	41.6644	+	11.1639i	1.70236	+	0.456146i	0.973532	−	0.228551i	$-0.0733987\pi$
$599$	41.6644	+	11.1639i	1.70236	+	0.456146i	0.728828	+	0.684697i	$0.240065\pi$
$600$	−1.46256	−	1.38338i	−0.0597088	−	0.0564762i
$601$	31.8874	−	8.54420i	1.30071	−	0.348525i	0.458994	−	0.888440i	$-0.348210\pi$
$601$	31.8874	−	8.54420i	1.30071	−	0.348525i	0.841720	+	0.539914i	$0.181543\pi$
$602$	8.78770	−	8.38646i	0.358160	−	0.341807i
$603$	15.5489	+	3.10199i	0.633199	+	0.126323i
$604$	−23.8078	−	1.11305i	−0.968726	−	0.0452894i
$605$	15.9395	+	2.09848i	0.648034	+	0.0853153i
$606$	−24.6158	−	1.38896i	−0.999949	−	0.0564228i
$607$	18.3285	−	10.5819i	0.743929	−	0.429508i	−0.0795670	−	0.996830i	$-0.525354\pi$
$607$	18.3285	−	10.5819i	0.743929	−	0.429508i	0.823496	+	0.567322i	$0.192020\pi$
$608$	38.4105	+	15.2790i	1.55775	+	0.619646i
$609$	−3.22298	+	7.10794i	−0.130602	+	0.288028i
$610$	1.00845	+	0.156807i	0.0408308	+	0.00634893i
$611$	11.9376	−	4.94473i	0.482945	−	0.200042i
$612$	−4.81087	−	32.0337i	−0.194468	−	1.29489i
$613$	−7.04864	+	17.0169i	−0.284692	+	0.687307i	−0.999933	−	0.0115710i	$-0.996317\pi$
$613$	−7.04864	+	17.0169i	−0.284692	+	0.687307i	0.715241	+	0.698878i	$0.246317\pi$
$614$	−38.5043	+	9.35904i	−1.55391	+	0.377700i
$615$	11.4895	+	9.43465i	0.463303	+	0.380442i
$616$	5.41065	+	11.1009i	0.218001	+	0.447268i
$617$	−3.78551	+	14.1277i	−0.152399	+	0.568760i	0.846915	+	0.531728i	$0.178457\pi$
$617$	−3.78551	+	14.1277i	−0.152399	+	0.568760i	−0.999314	+	0.0370322i	$0.988210\pi$
$618$	−23.1130	−	33.9199i	−0.929741	−	1.36446i
$619$	−21.5005	−	28.0199i	−0.864176	−	1.12622i	−0.990943	−	0.134284i	$-0.957127\pi$
$619$	−21.5005	−	28.0199i	−0.864176	−	1.12622i	0.126767	−	0.991933i	$-0.459540\pi$
$620$	−13.9256	−	38.6305i	−0.559264	−	1.55144i
$621$	−4.29825	+	11.3909i	−0.172483	+	0.457101i
$622$	1.10831	+	0.489712i	0.0444394	+	0.0196356i
$623$	2.70793	+	1.56343i	0.108491	+	0.0626374i
$624$	10.0378	+	2.64173i	0.401835	+	0.105754i
$625$	−19.7250	+	11.3882i	−0.789000	+	0.455529i
$626$	25.6248	−	2.76639i	1.02417	−	0.110567i
$627$	−48.0255	+	25.6528i	−1.91796	+	1.02447i
$628$	−16.9084	−	24.3070i	−0.674720	−	0.969953i
$629$	−13.3793	+	32.3006i	−0.533469	+	1.28791i
$630$	−5.91462	−	7.07900i	−0.235644	−	0.282034i
$631$	−18.2865	−	18.2865i	−0.727975	−	0.727975i	0.242241	−	0.970216i	$-0.422117\pi$
$631$	−18.2865	−	18.2865i	−0.727975	−	0.727975i	−0.970216	+	0.242241i	$0.922117\pi$
$632$	23.1664	−	15.3248i	0.921511	−	0.609586i
$633$	−4.69693	−	12.4901i	−0.186686	−	0.496438i
$634$	−16.3098	−	4.78116i	−0.647744	−	0.189884i
$635$	−34.8614	+	4.58959i	−1.38343	+	0.182132i
$636$	13.9683	−	4.52028i	0.553879	−	0.179241i
$637$	−1.16740	+	8.86732i	−0.0462543	+	0.351336i
$638$	−25.1866	+	9.74984i	−0.997146	+	0.386000i
$639$	4.07562	−	11.9842i	0.161229	−	0.474086i
$640$	−19.6988	+	14.1194i	−0.778665	+	0.558117i
$641$	−26.6775	−	15.4023i	−1.05370	−	0.608352i	−0.130015	−	0.991512i	$-0.541503\pi$
$641$	−26.6775	−	15.4023i	−1.05370	−	0.608352i	−0.923682	+	0.383160i	$0.874836\pi$
$642$	10.5006	+	20.8144i	0.414428	+	0.821479i
$643$	8.78636	−	11.4506i	0.346500	−	0.451568i	−0.587296	−	0.809372i	$-0.699808\pi$
$643$	8.78636	−	11.4506i	0.346500	−	0.451568i	0.933797	+	0.357804i	$0.116474\pi$
$644$	1.44422	−	4.53170i	0.0569103	−	0.178574i
$645$	−30.5820	+	7.12162i	−1.20417	+	0.280414i
$646$	−54.2154	+	13.1778i	−2.13308	+	0.518475i
$647$	−24.9147	−	24.9147i	−0.979498	−	0.979498i	0.0202960	−	0.999794i	$-0.493539\pi$
$647$	−24.9147	−	24.9147i	−0.979498	−	0.979498i	−0.999794	+	0.0202960i	$0.993539\pi$
$648$	−22.8951	+	11.1272i	−0.899403	+	0.437119i
$649$	−8.94605	+	8.94605i	−0.351163	+	0.351163i
$650$	−0.452823	+	0.743642i	−0.0177612	+	0.0291680i
$651$	3.82144	+	16.4102i	0.149774	+	0.643166i
$652$	0.512362	+	6.07195i	0.0200656	+	0.237796i
$653$	−0.207119	−	0.158928i	−0.00810520	−	0.00621934i	0.604701	−	0.796453i	$-0.293293\pi$
$653$	−0.207119	−	0.158928i	−0.00810520	−	0.00621934i	−0.612806	+	0.790233i	$0.709959\pi$
$654$	5.35591	−	16.2619i	0.209433	−	0.635889i
$655$	18.7763	−	32.5215i	0.733651	−	1.27072i
$656$	−12.3408	+	10.2261i	−0.481827	+	0.399262i
$657$	−5.82946	−	1.98251i	−0.227429	−	0.0773449i
$658$	5.00335	−	11.3236i	0.195051	−	0.441439i
$659$	9.44652	+	1.24366i	0.367984	+	0.0484460i	0.312251	−	0.950000i	$-0.398917\pi$
$659$	9.44652	+	1.24366i	0.367984	+	0.0484460i	0.0557332	+	0.998446i	$0.482250\pi$
$660$	2.54231	−	31.8210i	0.0989593	−	1.23863i
$661$	−0.965154	−	7.33107i	−0.0375402	−	0.285146i	−0.999910	−	0.0134033i	$-0.995733\pi$
$661$	−0.965154	−	7.33107i	−0.0375402	−	0.285146i	0.962370	−	0.271742i	$-0.0875999\pi$
$662$	10.9519	+	20.0358i	0.425656	+	0.778714i
$663$	−13.1129	+	4.93113i	−0.509264	+	0.191509i
$664$	5.13544	+	3.46587i	0.199294	+	0.134502i
$665$	−11.2350	+	11.2350i	−0.435675	+	0.435675i
$666$	27.3650	+	2.45223i	1.06037	+	0.0950220i
$667$	9.61014	+	3.98065i	0.372106	+	0.154131i
$668$	3.92783	−	6.12370i	0.151972	−	0.236933i
$669$	14.1380	+	26.4682i	0.546605	+	1.02332i
$670$	12.4716	+	10.0412i	0.481819	+	0.387924i
$671$	−0.724564	−	1.25498i	−0.0279715	−	0.0484480i
$672$	8.70475	−	4.80866i	0.335793	−	0.185498i
$673$	−2.66322	+	4.61284i	−0.102660	+	0.177812i	−0.912780	−	0.408452i	$-0.866069\pi$
$673$	−2.66322	+	4.61284i	−0.102660	+	0.177812i	0.810120	+	0.586264i	$0.199402\pi$
$674$	−17.5749	+	6.80333i	−0.676961	+	0.262054i
$675$	−0.346043	−	2.10705i	−0.0133192	−	0.0811006i
$676$	−1.00457	+	21.4875i	−0.0386374	+	0.826442i
$677$	−15.5474	+	11.9299i	−0.597534	+	0.458504i	−0.862712	−	0.505696i	$-0.831236\pi$
$677$	−15.5474	+	11.9299i	−0.597534	+	0.458504i	0.265178	+	0.964199i	$0.414569\pi$
$678$	3.54670	−	18.7175i	0.136210	−	0.718841i
$679$	8.32893	+	2.23173i	0.319635	+	0.0856460i
$680$	10.6581	−	30.9269i	0.408719	−	1.18599i
$681$	28.2527	−	34.4062i	1.08265	−	1.31845i
$682$	−30.3253	+	49.8012i	−1.16121	+	1.90698i
$683$	−19.9067	−	8.24564i	−0.761710	−	0.315510i	−0.0322004	−	0.999481i	$-0.510251\pi$
$683$	−19.9067	−	8.24564i	−0.761710	−	0.315510i	−0.729509	+	0.683971i	$0.760251\pi$
$684$	22.6089	+	37.5667i	0.864473	+	1.43640i
$685$	−17.1940	−	41.5100i	−0.656950	−	1.58602i
$686$	10.9851	+	15.0303i	0.419412	+	0.573860i
$687$	−4.93943	−	2.23971i	−0.188451	−	0.0854502i
$688$	−1.26792	−	33.8272i	−0.0483391	−	1.28965i
$689$	−3.17476	−	5.49885i	−0.120949	−	0.209489i
$690$	−9.16968	+	8.19014i	−0.349084	+	0.311793i
$691$	3.76739	−	28.6162i	0.143318	−	1.08861i	−0.757011	−	0.653402i	$-0.773341\pi$
$691$	3.76739	−	28.6162i	0.143318	−	1.08861i	0.900329	−	0.435209i	$-0.143326\pi$
$692$	−16.0928	+	34.2351i	−0.611757	+	1.30142i
$693$	−2.56262	+	12.8453i	−0.0973460	+	0.487952i
$694$	−7.72047	−	0.180373i	−0.293065	−	0.00684687i
$695$	1.49152	+	5.56642i	0.0565765	+	0.211146i
$696$	8.87857	+	19.8541i	0.336541	+	0.752567i
$697$	5.59874	−	20.8948i	0.212067	−	0.791447i
$698$	−13.1793	+	44.9579i	−0.498843	+	1.70168i
$699$	11.6585	+	50.0643i	0.440963	+	1.89361i
$700$	0.178036	+	0.814954i	0.00672912	+	0.0308024i
$701$	−17.0186	−	41.0865i	−0.642784	−	1.55182i	−0.822909	−	0.568174i	$-0.807650\pi$
$701$	−17.0186	−	41.0865i	−0.642784	−	1.55182i	0.180125	−	0.983644i	$-0.442350\pi$
$702$	6.77618	+	8.67682i	0.255750	+	0.327486i
$703$		−	47.3226i		−	1.78481i
$704$	33.1574	+	9.21414i	1.24967	+	0.347271i
$705$	−26.0172	+	18.6326i	−0.979865	+	0.701743i
$706$	37.4599	+	30.1599i	1.40982	+	1.13508i
$707$	8.10492	+	6.21913i	0.304817	+	0.233894i
$708$	7.56316	+	6.82614i	0.284241	+	0.256542i
$709$	7.89339	+	10.2869i	0.296443	+	0.386331i	0.917699	−	0.397276i	$-0.130044\pi$
$709$	7.89339	+	10.2869i	0.296443	+	0.386331i	−0.621257	+	0.783607i	$0.713378\pi$
$710$	9.24751	−	8.82528i	0.347053	−	0.331207i
$711$	29.3972	+	1.94347i	1.10248	+	0.0728857i
$712$	8.26406	−	2.76270i	0.309709	−	0.103537i
$713$	21.6917	−	5.81227i	0.812360	−	0.217671i
$714$	−5.82695	+	12.0916i	−0.218068	+	0.452515i
$715$	−13.6879	+	1.80204i	−0.511897	+	0.0673925i
$716$	0.914298	+	10.8353i	0.0341689	+	0.404933i
$717$	7.56464	+	0.249779i	0.282507	+	0.00932816i
$718$	15.5377	+	21.2594i	0.579860	+	0.793392i
$719$		−	18.1643i		−	0.677416i	−0.940892	−	0.338708i	$-0.890010\pi$
$719$		−	18.1643i		−	0.677416i	0.940892	−	0.338708i	$-0.109990\pi$
$720$	−25.6960	−	0.733813i	−0.957635	−	0.0273476i
$721$			17.0078i			0.633404i
$722$	39.2776	−	28.7065i	1.46176	−	1.06835i
$723$	6.32487	+	11.8410i	0.235225	+	0.440373i
$724$	−1.98351	−	1.67481i	−0.0737166	−	0.0622440i
$725$	−1.80873	+	0.238123i	−0.0671744	+	0.00884368i
$726$	−15.1916	+	10.3516i	−0.563815	+	0.384183i
$727$	−39.7845	+	10.6602i	−1.47552	+	0.395366i	−0.904822	−	0.425791i	$-0.859996\pi$
$727$	−39.7845	+	10.6602i	−1.47552	+	0.395366i	−0.570703	+	0.821157i	$0.693329\pi$
$728$	−2.82080	−	3.24668i	−0.104546	−	0.120330i
$729$	−26.4722	−	5.31229i	−0.980453	−	0.196751i
$730$	−4.29288	−	4.49827i	−0.158887	−	0.166488i
$731$	27.8136	+	36.2473i	1.02872	+	1.34066i
$732$	−0.979443	+	0.634409i	−0.0362013	+	0.0234484i
$733$	22.1966	+	17.0320i	0.819849	+	0.629092i	0.931126	−	0.364697i	$-0.118827\pi$
$733$	22.1966	+	17.0320i	0.819849	+	0.629092i	−0.111277	+	0.993789i	$0.535494\pi$
$734$	−1.54046	+	1.91333i	−0.0568596	+	0.0706222i
$735$	−2.16491	−	22.0445i	−0.0798540	−	0.813125i
$736$	−6.78842	−	11.3840i	−0.250224	−	0.419618i
$737$		−	22.7350i		−	0.837456i
$738$	−16.9847	+	0.705719i	−0.625214	+	0.0259779i
$739$	−10.8083	−	26.0935i	−0.397590	−	0.959866i	−0.988236	−	0.152936i	$-0.951127\pi$
$739$	−10.8083	−	26.0935i	−0.397590	−	0.959866i	0.590646	−	0.806931i	$-0.298873\pi$
$740$	23.3540	+	14.9796i	0.858510	+	0.550661i
$741$	13.8437	−	12.9587i	0.508561	−	0.476050i
$742$	−5.83776	−	1.71132i	−0.214311	−	0.0628247i
$743$	−5.41476	+	20.2082i	−0.198648	+	0.741366i	0.792644	+	0.609685i	$0.208704\pi$
$743$	−5.41476	+	20.2082i	−0.198648	+	0.741366i	−0.991292	+	0.131681i	$0.957963\pi$
$744$	41.3006	+	22.3370i	1.51415	+	0.818912i
$745$	9.34636	+	34.8811i	0.342424	+	1.27794i
$746$	1.03768	−	44.4156i	0.0379922	−	1.62617i
$747$	2.10879	+	6.22384i	0.0771566	+	0.227718i
$748$	−43.6962	+	15.7517i	−1.59769	+	0.575937i
$749$	1.26089	−	9.57740i	0.0460719	−	0.349950i
$750$	8.88200	−	26.9679i	0.324325	−	0.984729i
$751$	−5.34187	−	9.25238i	−0.194927	−	0.337624i	0.751949	−	0.659221i	$-0.229114\pi$
$751$	−5.34187	−	9.25238i	−0.194927	−	0.337624i	−0.946877	+	0.321597i	$0.895780\pi$
$752$	−14.3866	−	31.3557i	−0.524626	−	1.14343i
$753$	−8.67278	+	6.21112i	−0.316054	+	0.226346i
$754$	7.59404	−	5.55019i	0.276558	−	0.202126i
$755$	−9.76935	−	23.5853i	−0.355543	−	0.858356i
$756$	10.4361	+	1.53180i	0.379556	+	0.0557112i
$757$	8.88251	+	3.67926i	0.322840	+	0.133725i	0.538217	−	0.842806i	$-0.319098\pi$
$757$	8.88251	+	3.67926i	0.322840	+	0.133725i	−0.215377	+	0.976531i	$0.569098\pi$
$758$	−32.5731	−	19.8347i	−1.18311	−	0.720427i
$759$	17.2237	+	2.84864i	0.625181	+	0.103399i
$760$	2.69143	+	44.1953i	0.0976286	+	1.60313i
$761$	12.6843	+	3.39875i	0.459805	+	0.123204i	0.481284	−	0.876565i	$-0.340171\pi$
$761$	12.6843	+	3.39875i	0.459805	+	0.123204i	−0.0214785	+	0.999769i	$0.506837\pi$
$762$	26.2339	−	30.4679i	0.950353	−	1.10374i
$763$	−5.62830	+	4.31875i	−0.203758	+	0.156349i
$764$	28.6045	−	26.0494i	1.03487	−	0.942433i
$765$	28.8597	−	19.2599i	1.04343	−	0.696343i
$766$	5.57228	+	14.3948i	0.201335	+	0.520104i
$767$	2.20310	−	3.81588i	0.0795494	−	0.137784i
$768$	6.04443	−	27.0456i	0.218110	−	0.975924i
$769$	−10.0871	−	17.4713i	−0.363750	−	0.630033i	0.624825	−	0.780765i	$-0.285170\pi$
$769$	−10.0871	−	17.4713i	−0.363750	−	0.630033i	−0.988575	+	0.150732i	$0.951837\pi$
$770$	−8.29523	+	10.3031i	−0.298939	+	0.371296i
$771$	−27.0692	−	0.893805i	−0.974874	−	0.0321896i
$772$	6.22027	+	28.4731i	0.223873	+	1.02477i
$773$	29.7330	+	12.3158i	1.06942	+	0.442969i	0.846786	−	0.531933i	$-0.178534\pi$
$773$	29.7330	+	12.3158i	1.06942	+	0.442969i	0.222635	+	0.974902i	$0.428534\pi$
$774$	20.6558	−	29.3677i	0.742457	−	1.05560i
$775$	−2.78500	+	2.78500i	−0.100040	+	0.100040i
$776$	20.0410	−	13.2573i	0.719430	−	0.475908i
$777$	−8.79822	−	7.22467i	−0.315634	−	0.259184i
$778$	−3.85024	+	2.10459i	−0.138038	+	0.0754533i
$779$	3.82178	+	29.0293i	0.136930	+	1.04008i
$780$	2.01308	+	10.9339i	0.0720799	+	0.391497i
$781$	−17.9955	−	2.36915i	−0.643929	−	0.0847749i
$782$	16.3633	+	7.23015i	0.585150	+	0.258550i
$783$	−5.25726	+	22.4611i	−0.187879	+	0.802695i
$784$	23.7752	+	2.22792i	0.849113	+	0.0795685i
$785$	15.8575	−	27.4659i	0.565977	−	0.980300i
$786$	8.75922	+	42.0363i	0.312431	+	1.49938i
$787$	−16.4390	−	12.6141i	−0.585988	−	0.449644i	0.272732	−	0.962090i	$-0.412073\pi$
$787$	−16.4390	−	12.6141i	−0.585988	−	0.449644i	−0.858720	+	0.512446i	$0.828740\pi$
$788$	15.2869	+	12.9078i	0.544572	+	0.459820i
$789$	−8.45428	−	2.56718i	−0.300980	−	0.0913942i
$790$	25.4111	+	15.4735i	0.904086	+	0.550522i
$791$	−5.58176	+	5.58176i	−0.198464	+	0.198464i
$792$	22.0700	+	29.0735i	0.784224	+	1.03308i
$793$	0.356870	+	0.356870i	0.0126728	+	0.0126728i
$794$	−7.90106	−	32.5060i	−0.280398	−	1.15360i
$795$	10.7465	+	11.4805i	0.381140	+	0.407170i
$796$	−46.3897	+	23.9674i	−1.64424	+	0.849502i
$797$	15.5862	−	20.3123i	0.552090	−	0.719497i	−0.431055	−	0.902326i	$-0.641859\pi$
$797$	15.5862	−	20.3123i	0.552090	−	0.719497i	0.983145	+	0.182828i	$0.0585252\pi$
$798$	1.02350	−	18.1389i	0.0362316	−	0.642111i
$799$	40.3247	+	23.2815i	1.42659	+	0.823640i
$800$	2.02936	+	1.13379i	0.0717486	+	0.0400854i
$801$	8.75003	+	2.97575i	0.309167	+	0.105143i
$802$	8.05588	+	20.8106i	0.284463	+	0.734849i
$803$	−1.15243	+	8.75355i	−0.0406682	+	0.308906i
$804$	−18.2841	+	0.936508i	−0.644831	+	0.0330281i
$805$	5.05088	−	0.664961i	0.178020	−	0.0234368i
$806$	5.71251	−	19.4868i	0.201215	−	0.686394i
$807$	2.90079	+	0.479764i	0.102113	+	0.0168885i
$808$	27.9475	−	5.42481i	0.983188	−	0.190844i
$809$	−10.6460	−	10.6460i	−0.374293	−	0.374293i	0.494745	−	0.869038i	$-0.335261\pi$
$809$	−10.6460	−	10.6460i	−0.374293	−	0.374293i	−0.869038	+	0.494745i	$0.835261\pi$
$810$	−21.2186	−	17.1231i	−0.745545	−	0.601644i
$811$	−4.07895	+	9.84747i	−0.143231	+	0.345791i	−0.979173	−	0.203027i	$-0.934922\pi$
$811$	−4.07895	+	9.84747i	−0.143231	+	0.345791i	0.835942	+	0.548818i	$0.184922\pi$
$812$	1.59226	−	8.87009i	0.0558774	−	0.311279i
$813$	2.33362	+	1.45205i	0.0818438	+	0.0509258i
$814$	−4.22854	−	39.1686i	−0.148210	−	1.37286i
$815$	−5.65239	+	3.26341i	−0.197994	+	0.114312i
$816$	14.4678	+	34.4928i	0.506476	+	1.20749i
$817$	−53.5567	−	30.9210i	−1.87371	−	1.08179i
$818$	−15.2038	+	34.4092i	−0.531588	+	1.20309i
$819$	−0.295786	−	4.55220i	−0.0103356	−	0.159067i
$820$	−15.5359	−	7.30292i	−0.542537	−	0.255029i
$821$	−19.0390	−	24.8121i	−0.664466	−	0.865948i	0.332555	−	0.943084i	$-0.392089\pi$
$821$	−19.0390	−	24.8121i	−0.664466	−	0.865948i	−0.997021	+	0.0771355i	$0.975423\pi$
$822$	46.2813	+	22.3031i	1.61425	+	0.777909i
$823$	−1.34997	+	5.03815i	−0.0470569	+	0.175619i	−0.985455	−	0.169938i	$-0.945643\pi$
$823$	−1.34997	+	5.03815i	−0.0470569	+	0.175619i	0.938398	+	0.345557i	$0.112310\pi$
$824$	35.4891	+	31.4147i	1.23632	+	1.09438i
$825$	−2.86586	+	1.07771i	−0.0997765	+	0.0375211i
$826$	−0.997078	−	4.10211i	−0.0346928	−	0.142731i
$827$	7.61758	−	18.3905i	0.264889	−	0.639499i	−0.734339	−	0.678783i	$-0.762508\pi$
$827$	7.61758	−	18.3905i	0.264889	−	0.639499i	0.999228	+	0.0392837i	$0.0125076\pi$
$828$	1.58147	−	13.9691i	0.0549598	−	0.485460i
$829$	39.0063	−	16.1569i	1.35475	−	0.561154i	0.417136	−	0.908844i	$-0.363034\pi$
$829$	39.0063	−	16.1569i	1.35475	−	0.561154i	0.937609	+	0.347690i	$0.113034\pi$
$830$	−1.01962	+	6.55730i	−0.0353915	+	0.227607i
$831$	−22.5563	+	2.21517i	−0.782468	+	0.0768433i
$832$	−11.9849	−	0.110895i	−0.415500	−	0.00384458i
$833$	−27.9121	+	16.1150i	−0.967095	+	0.558353i
$834$	−5.51191	−	3.61095i	−0.190862	−	0.125037i
$835$	7.72577	+	1.01712i	0.267361	+	0.0351988i
$836$	46.4837	−	42.3315i	1.60767	−	1.46406i
$837$	20.5153	+	45.3804i	0.709112	+	1.56858i
$838$	17.3752	+	18.2065i	0.600218	+	0.628935i
$839$	−19.1062	+	5.11950i	−0.659620	+	0.176745i	−0.573075	−	0.819503i	$-0.694250\pi$
$839$	−19.1062	+	5.11950i	−0.659620	+	0.176745i	−0.0865457	+	0.996248i	$0.527583\pi$
$840$	8.62769	+	6.24684i	0.297684	+	0.215536i
$841$	−8.97450	−	2.40471i	−0.309465	−	0.0829210i
$842$	−7.08179	−	12.9557i	−0.244055	−	0.446484i
$843$	1.35979	−	4.47807i	0.0468336	−	0.154233i
$844$	8.79894	+	12.6490i	0.302872	+	0.435398i
$845$	−21.2867	+	8.81722i	−0.732283	+	0.303322i
$846$	7.99505	−	35.7072i	0.274876	−	1.22764i
$847$	7.61725			0.261732
$848$	−14.3537	+	9.02033i	−0.492908	+	0.309759i
$849$	−4.30904	+	9.50312i	−0.147886	+	0.326146i
$850$	−3.11940	+	0.336762i	−0.106994	+	0.0115509i
$851$	−9.23689	+	12.0378i	−0.316637	+	0.412649i
$852$	−1.16406	+	14.5700i	−0.0398800	+	0.499161i
$853$	30.0905	−	23.0892i	1.03028	−	0.790560i	0.0521653	−	0.998638i	$-0.483388\pi$
$853$	30.0905	−	23.0892i	1.03028	−	0.790560i	0.978112	+	0.208079i	$0.0667210\pi$
$854$	0.483408	+	0.0112938i	0.0165419	+	0.000386467i
$855$	−26.1133	+	39.0336i	−0.893057	+	1.33492i
$856$	−17.6556	−	20.3212i	−0.603455	−	0.694564i
$857$	−7.25866	−	27.0897i	−0.247951	−	0.925366i	−0.971877	−	0.235488i	$-0.924331\pi$
$857$	−7.25866	−	27.0897i	−0.247951	−	0.925366i	0.723926	−	0.689878i	$-0.242336\pi$
$858$	10.3004	−	11.9628i	0.351650	−	0.408404i
$859$	−4.33846	−	32.9539i	−0.148027	−	1.12437i	−0.890658	−	0.454673i	$-0.849756\pi$
$859$	−4.33846	−	32.9539i	−0.148027	−	1.12437i	0.742632	−	0.669700i	$-0.233577\pi$
$860$	32.2126	−	16.6428i	1.09844	−	0.567514i
$861$	5.98059	+	3.72131i	0.203818	+	0.126822i
$862$	−7.20943	+	46.3648i	−0.245554	+	1.57919i
$863$	33.6814			1.14653			0.573264	−	0.819371i	$-0.305677\pi$
$863$	33.6814			1.14653			0.573264	+	0.819371i	$0.305677\pi$
$864$	22.4725	−	18.9469i	0.764531	−	0.644587i
$865$	−40.5186			−1.37767
$866$	2.81679	−	18.1152i	0.0957186	−	0.615578i
$867$	−17.8638	−	11.1154i	−0.606687	−	0.377500i
$868$	−8.93045	−	17.2852i	−0.303119	−	0.586697i
$869$	−5.51408	−	41.8836i	−0.187052	−	1.42080i
$870$	−15.2000	+	17.6532i	−0.515327	+	0.598498i
$871$	2.04932	+	7.64817i	0.0694386	+	0.259148i
$872$	−1.38426	+	19.7213i	−0.0468769	+	0.667847i
$873$	25.4312	+	1.68127i	0.860714	+	0.0569023i
$874$	−24.2076	−	0.565562i	−0.818835	−	0.0191304i
$875$	−9.33372	+	7.16201i	−0.315537	+	0.242120i
$876$	7.08730	+	0.566233i	0.239458	+	0.0191312i
$877$	−19.4658	+	25.3684i	−0.657314	+	0.856628i	−0.996457	−	0.0841066i	$-0.973196\pi$
$877$	−19.4658	+	25.3684i	−0.657314	+	0.856628i	0.339143	+	0.940735i	$0.389863\pi$
$878$	17.7856	−	1.92009i	0.600235	−	0.0647998i
$879$	−6.26269	+	13.8117i	−0.211235	+	0.465856i
$880$	6.17678	+	36.3397i	0.208219	+	1.22501i
$881$	1.81478			0.0611416			0.0305708	−	0.999533i	$-0.490267\pi$
$881$	1.81478			0.0611416			0.0305708	+	0.999533i	$0.490267\pi$
$882$	18.6376	+	17.1506i	0.627560	+	0.577489i
$883$	−40.2761	+	16.6829i	−1.35540	+	0.561425i	−0.937791	−	0.347201i	$-0.887132\pi$
$883$	−40.2761	+	16.6829i	−1.35540	+	0.561425i	−0.417610	+	0.908627i	$0.637132\pi$
$884$	13.2797	−	9.23767i	0.446646	−	0.310696i
$885$	−3.17069	+	10.4418i	−0.106582	+	0.350996i
$886$	5.81409	+	10.6366i	0.195328	+	0.357342i
$887$	−11.4271	−	3.06187i	−0.383683	−	0.102808i	0.0618215	−	0.998087i	$-0.480309\pi$
$887$	−11.4271	−	3.06187i	−0.383683	−	0.102808i	−0.445505	+	0.895280i	$0.646976\pi$
$888$	−31.3262	+	5.01415i	−1.05124	+	0.168264i
$889$	−16.0920	+	4.31185i	−0.539710	+	0.144615i
$890$	6.44363	+	6.75192i	0.215991	+	0.226325i
$891$	−0.0437198	+	38.7156i	−0.00146467	+	1.29702i
$892$	−23.3301	−	25.6185i	−0.781148	−	0.857770i
$893$	−62.4861	−	8.22645i	−2.09102	−	0.275288i
$894$	−34.5395	−	22.6275i	−1.15517	−	0.756776i
$895$	−10.0866	+	5.82348i	−0.337156	+	0.194657i
$896$	−8.38020	+	7.85070i	−0.279963	+	0.262273i
$897$	−6.05091	+	0.594238i	−0.202034	+	0.0198410i
$898$	3.14018	−	20.1949i	0.104789	−	0.673912i
$899$	39.3109	−	16.2831i	1.31109	−	0.543073i
$900$	0.984775	+	2.26041i	0.0328258	+	0.0753470i
$901$	8.75625	−	21.1395i	0.291713	−	0.704258i
$902$	5.75719	+	23.6859i	0.191694	+	0.788653i
$903$	−13.9253	+	5.23661i	−0.463404	+	0.174263i
$904$	1.33715	+	21.9570i	0.0444730	+	0.730280i
$905$	0.719675	−	2.68586i	0.0239228	−	0.0892811i
$906$	26.2962	+	12.6722i	0.873634	+	0.421006i
$907$	−4.23830	−	5.52346i	−0.140730	−	0.183403i	0.717671	−	0.696383i	$-0.245208\pi$
$907$	−4.23830	−	5.52346i	−0.140730	−	0.183403i	−0.858401	+	0.512979i	$0.828542\pi$
$908$	−21.8691	+	46.5233i	−0.725752	+	1.54393i
$909$	27.0745	+	13.3707i	0.898003	+	0.443477i
$910$	1.86184	−	4.21372i	0.0617195	−	0.139683i
$911$	4.22132	+	2.43718i	0.139859	+	0.0807474i	0.568297	−	0.822824i	$-0.307603\pi$
$911$	4.22132	+	2.43718i	0.139859	+	0.0807474i	−0.428438	+	0.903571i	$0.640936\pi$
$912$	−35.9589	−	35.6397i	−1.19072	−	1.18015i
$913$	8.16037	−	4.71139i	0.270069	−	0.155924i
$914$	6.36654	+	58.9727i	0.210587	+	1.95064i
$915$	−1.06126	−	0.660348i	−0.0350841	−	0.0218304i
$916$	6.16399	+	1.10649i	0.203664	+	0.0365594i
$917$	6.80881	−	16.4379i	0.224847	−	0.542828i
$918$	−9.94131	+	38.4073i	−0.328112	+	1.26763i
$919$	23.9876	+	23.9876i	0.791278	+	0.791278i	0.981702	−	0.190424i	$-0.0609862\pi$
$919$	23.9876	+	23.9876i	0.791278	+	0.791278i	−0.190424	+	0.981702i	$0.560986\pi$
$920$	7.94183	−	11.7676i	0.261835	−	0.387965i
$921$	47.8806	+	7.91900i	1.57772	+	0.260940i
$922$	14.8418	−	50.6293i	0.488790	−	1.66739i
$923$	6.26732	−	0.825108i	0.206291	−	0.0271588i
$924$	−0.773670	−	15.1049i	−0.0254519	−	0.496916i
$925$	0.347350	−	2.63838i	0.0114208	−	0.0867495i
$926$	−3.62317	−	9.35967i	−0.119065	−	0.307578i
$927$	9.77951	+	49.3104i	0.321201	+	1.61957i
$928$	−15.5676	−	19.7062i	−0.511032	−	0.646888i
$929$	0.758151	+	0.437718i	0.0248741	+	0.0143611i	0.512385	−	0.858756i	$-0.328762\pi$
$929$	0.758151	+	0.437718i	0.0248741	+	0.0143611i	−0.487511	+	0.873117i	$0.662095\pi$
$930$	−2.83329	+	50.2128i	−0.0929073	+	1.64654i
$931$	26.5572	−	34.6100i	0.870377	−	1.13430i
$932$	−27.2451	−	52.7337i	−0.892441	−	1.72735i
$933$	−1.01415	−	1.08341i	−0.0332017	−	0.0354692i
$934$	4.15904	+	17.1108i	0.136088	+	0.559884i
$935$	−35.1795	−	35.1795i	−1.15049	−	1.15049i
$936$	−10.0451	−	7.79107i	−0.328335	−	0.254659i
$937$	24.9448	−	24.9448i	0.814909	−	0.814909i	−0.170456	−	0.985365i	$-0.554524\pi$
$937$	24.9448	−	24.9448i	0.814909	−	0.814909i	0.985365	+	0.170456i	$0.0545240\pi$
$938$	6.47941	+	3.94548i	0.211560	+	0.128825i
$939$	−30.2043	−	9.17170i	−0.985682	−	0.299307i
$940$	23.8393	−	28.2332i	0.777551	−	0.920866i
$941$	−38.1406	−	29.2663i	−1.24335	−	0.954055i	−0.243475	−	0.969907i	$-0.578287\pi$
$941$	−38.1406	−	29.2663i	−1.24335	−	0.954055i	−0.999874	+	0.0158517i	$0.994954\pi$
$942$	7.39757	+	35.5016i	0.241026	+	1.15670i
$943$	4.69405	−	8.13034i	0.152859	−	0.264760i
$944$	−10.4013	−	5.49638i	−0.338533	−	0.178892i
$945$	3.27045	+	10.8142i	0.106388	+	0.351786i
$946$	−47.0915	−	20.8075i	−1.53108	−	0.676510i
$947$	−7.34384	−	0.966835i	−0.238643	−	0.0314179i	0.0102560	−	0.999947i	$-0.496735\pi$
$947$	−7.34384	−	0.966835i	−0.238643	−	0.0314179i	−0.248899	+	0.968529i	$0.580069\pi$
$948$	−33.4568	+	6.15985i	−1.08662	+	0.200063i
$949$	−0.401357	−	3.04861i	−0.0130286	−	0.0989621i
$950$	3.72642	−	2.03692i	0.120901	−	0.0660863i
$951$	16.0872	+	13.2100i	0.521663	+	0.428364i
$952$	3.09395	−	15.1868i	0.100276	−	0.492208i
$953$	−20.7163	+	20.7163i	−0.671065	+	0.671065i	−0.957962	−	0.286896i	$-0.907377\pi$
$953$	−20.7163	+	20.7163i	−0.671065	+	0.671065i	0.286896	+	0.957962i	$0.407377\pi$
$954$	−17.9093	−	1.60489i	−0.579836	−	0.0519602i
$955$	38.2849	+	15.8581i	1.23887	+	0.513157i
$956$	−8.53829	+	1.86528i	−0.276148	+	0.0603276i
$957$	33.0597	+	1.09161i	1.06867	+	0.0352866i
$958$	31.8606	−	39.5724i	1.02937	−	1.27853i
$959$	−10.6439	−	18.4357i	−0.343708	−	0.595320i
$960$	28.9709	−	6.46444i	0.935031	−	0.208639i
$961$	30.4308	−	52.7076i	0.981637	−	1.70025i
$962$	4.95313	+	12.7953i	0.159695	+	0.412538i
$963$	−1.85135	−	28.4926i	−0.0596588	−	0.918160i
$964$	−10.4371	−	11.4609i	−0.336157	−	0.369131i
$965$	−24.7661	+	19.0037i	−0.797250	+	0.611751i
$966$	−3.80089	+	4.41434i	−0.122292	+	0.142029i
$967$	−16.9520	−	4.54228i	−0.545140	−	0.146070i	−0.0242696	−	0.999705i	$-0.507726\pi$
$967$	−16.9520	−	4.54228i	−0.545140	−	0.146070i	−0.520871	+	0.853635i	$0.674393\pi$
$968$	14.0697	−	15.8944i	0.452216	−	0.510866i
$969$	67.4175	+	11.1502i	2.16576	+	0.358197i
$970$	21.9828	+	13.3859i	0.705826	+	0.429796i
$971$	28.6212	+	11.8553i	0.918497	+	0.380454i	0.791303	−	0.611424i	$-0.209403\pi$
$971$	28.6212	+	11.8553i	0.918497	+	0.380454i	0.127194	+	0.991878i	$0.459403\pi$
$972$	31.1379	−	1.55962i	0.998748	−	0.0500249i
$973$	1.04487	+	2.52254i	0.0334971	+	0.0808691i
$974$	2.78272	−	2.03379i	0.0891642	−	0.0651667i
$975$	0.866945	−	0.620874i	0.0277645	−	0.0198839i
$976$	0.916457	−	0.987835i	0.0293351	−	0.0316198i
$977$	−2.69148	−	4.66178i	−0.0861081	−	0.149144i	0.819755	−	0.572715i	$-0.194110\pi$
$977$	−2.69148	−	4.66178i	−0.0861081	−	0.149144i	−0.905863	+	0.423571i	$0.860776\pi$
$978$	2.33462	−	7.08846i	0.0746528	−	0.226664i
$979$	1.72980	−	13.1391i	0.0552845	−	0.419928i
$980$	8.67378	+	24.0616i	0.277074	+	0.768621i
$981$	−13.8347	+	15.7575i	−0.441709	+	0.503100i
$982$	0.237317	−	10.1578i	0.00757308	−	0.324149i
$983$	9.25791	+	34.5510i	0.295281	+	1.10200i	0.940994	+	0.338424i	$0.109894\pi$
$983$	9.25791	+	34.5510i	0.295281	+	1.10200i	−0.645712	+	0.763581i	$0.723439\pi$
$984$	18.8116	−	5.60576i	0.599693	−	0.178705i
$985$	−5.54652	+	20.6999i	−0.176727	+	0.659554i
$986$	32.5270	+	9.53519i	1.03587	+	0.303662i
$987$	−11.0691	+	10.3615i	−0.352334	+	0.329810i
$988$	−11.8216	+	18.4305i	−0.376095	+	0.586353i
$989$	7.58810	+	18.3193i	0.241288	+	0.582520i
$990$	−18.1259	+	34.6412i	−0.576080	+	1.10097i
$991$		−	24.3967i		−	0.774986i	−0.921873	−	0.387493i	$-0.873341\pi$
$991$		−	24.3967i		−	0.774986i	0.921873	−	0.387493i	$-0.126659\pi$
$992$	−52.5631	−	13.2925i	−1.66888	−	0.422037i
$993$	−2.73324	−	27.8316i	−0.0867366	−	0.883208i
$994$	3.79817	−	4.71750i	0.120471	−	0.149630i
$995$	−44.3708	−	34.0469i	−1.40665	−	1.07936i
$996$	−4.12517	−	6.36871i	−0.130711	−	0.201800i
$997$	−23.5073	−	30.6353i	−0.744484	−	0.970230i	−0.999994	−	0.00342389i	$-0.998910\pi$
$997$	−23.5073	−	30.6353i	−0.744484	−	0.970230i	0.255510	−	0.966806i	$-0.417757\pi$
$998$	34.5640	+	36.2176i	1.09410	+	1.14645i
$999$	−29.6627	−	15.8874i	−0.938487	−	0.502654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.45	✓	368
3.2	odd	2		864.2.bn.a.683.2		368
9.4	even	3		864.2.bn.a.395.13		368
9.5	odd	6	inner	288.2.bf.a.203.34	yes	368
32.3	odd	8	inner	288.2.bf.a.227.34	yes	368
96.35	even	8		864.2.bn.a.35.13		368
288.67	odd	24		864.2.bn.a.611.2		368
288.131	even	24	inner	288.2.bf.a.131.45	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.45	✓	368	1.1	even	1	trivial
288.2.bf.a.131.45	yes	368	288.131	even	24	inner
288.2.bf.a.203.34	yes	368	9.5	odd	6	inner
288.2.bf.a.227.34	yes	368	32.3	odd	8	inner
864.2.bn.a.35.13		368	96.35	even	8
864.2.bn.a.395.13		368	9.4	even	3
864.2.bn.a.611.2		368	288.67	odd	24
864.2.bn.a.683.2		368	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39742 + 0.217290i) q^{2} +(-1.47060 - 0.915056i) q^{3} +(1.90557 + 0.607292i) q^{4} +(0.279615 + 2.12388i) q^{5} +(-1.85622 - 1.59827i) q^{6} +(0.262694 + 0.980387i) q^{7} +(2.53092 + 1.26270i) q^{8} +(1.32535 + 2.69137i) q^{9} +(-0.0707598 + 3.02872i) q^{10} +(3.41279 - 2.61873i) q^{11} +(-2.24663 - 2.63679i) q^{12} +(-0.912029 + 1.18858i) q^{13} +(0.154065 + 1.42709i) q^{14} +(1.53227 - 3.37925i) q^{15} +(3.26239 + 2.31447i) q^{16} -5.39882 q^{17} +(1.26726 + 4.04896i) q^{18} +(6.75131 - 2.79649i) q^{19} +(-0.756992 + 4.21702i) q^{20} +(0.510790 - 1.68214i) q^{21} +(5.33813 - 2.91790i) q^{22} +(-2.26322 - 0.606428i) q^{23} +(-2.56654 - 4.17287i) q^{24} +(0.396933 - 0.106358i) q^{25} +(-1.53275 + 1.46277i) q^{26} +(0.513691 - 5.17070i) q^{27} +(-0.0947992 + 2.02773i) q^{28} +(-4.40149 - 0.579467i) q^{29} +(2.87550 - 4.38929i) q^{30} +(-8.30037 + 4.79222i) q^{31} +(4.05602 + 3.94318i) q^{32} +(-7.41515 + 0.728215i) q^{33} +(-7.54443 - 1.17311i) q^{34} +(-2.00877 + 0.832061i) q^{35} +(0.891096 + 5.93346i) q^{36} +(2.47820 - 5.98289i) q^{37} +(10.0421 - 2.44087i) q^{38} +(2.42885 - 0.913371i) q^{39} +(-1.97415 + 5.72846i) q^{40} +(-1.03703 + 3.87025i) q^{41} +(1.07930 - 2.23967i) q^{42} +(-5.15179 - 6.71394i) q^{43} +(8.09365 - 2.91761i) q^{44} +(-5.34556 + 3.56743i) q^{45} +(-3.03090 - 1.33921i) q^{46} +(-7.46917 - 4.31233i) q^{47} +(-2.67981 - 6.38894i) q^{48} +(5.17003 - 2.98492i) q^{49} +(0.577793 - 0.0623770i) q^{50} +(7.93952 + 4.94022i) q^{51} +(-2.45975 + 1.71105i) q^{52} +(-1.62188 + 3.91557i) q^{53} +(1.84139 - 7.11402i) q^{54} +(6.51614 + 6.51614i) q^{55} +(-0.573080 + 2.81299i) q^{56} +(-12.4874 - 2.06531i) q^{57} +(-6.02482 - 1.76616i) q^{58} +(-2.91589 + 0.383885i) q^{59} +(4.97204 - 5.50887i) q^{60} +(0.0439705 - 0.333989i) q^{61} +(-12.6404 + 4.89316i) q^{62} +(-2.29042 + 2.00636i) q^{63} +(4.81116 + 6.39162i) q^{64} +(-2.77942 - 1.60470i) q^{65} +(-10.5203 - 0.593616i) q^{66} +(3.21736 - 4.19294i) q^{67} +(-10.2878 - 3.27866i) q^{68} +(2.77338 + 2.96279i) q^{69} +(-2.98790 + 0.726253i) q^{70} +(-2.98357 - 2.98357i) q^{71} +(-0.0440464 + 8.48517i) q^{72} +(-1.45130 + 1.45130i) q^{73} +(4.76311 - 7.82213i) q^{74} +(-0.681054 - 0.206805i) q^{75} +(14.5634 - 1.22888i) q^{76} +(3.46389 + 2.65793i) q^{77} +(3.59259 - 0.748599i) q^{78} +(4.91023 - 8.50477i) q^{79} +(-4.00346 + 7.57610i) q^{80} +(-5.48691 + 7.13399i) q^{81} +(-2.29014 + 5.18303i) q^{82} +(2.17172 + 0.285913i) q^{83} +(1.99489 - 2.89524i) q^{84} +(-1.50959 - 11.4665i) q^{85} +(-5.74034 - 10.5016i) q^{86} +(5.94260 + 4.87978i) q^{87} +(11.9442 - 2.31846i) q^{88} +(2.17841 - 2.17841i) q^{89} +(-8.24517 + 3.82366i) q^{90} +(-1.40485 - 0.581909i) q^{91} +(-3.94444 - 2.53002i) q^{92} +(16.5917 + 0.547845i) q^{93} +(-9.50055 - 7.64911i) q^{94} +(7.82717 + 13.5571i) q^{95} +(-2.35657 - 9.51034i) q^{96} +(4.24778 - 7.35737i) q^{97} +(7.87330 - 3.04779i) q^{98} +(11.5711 + 5.71436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21}+ \cdots - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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