LMFDB - Embedded newform 288.2.bc.a.277.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 21, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			277.43
Character	$\chi$	$=$	288.277
Dual form			288.2.bc.a.157.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37247 + 0.341058i) q^{2} +(-1.38971 - 1.03379i) q^{3} +(1.76736 + 0.936186i) q^{4} +(-0.375467 + 0.0494312i) q^{5} +(-1.55475 - 1.89282i) q^{6} +(1.86379 - 0.499402i) q^{7} +(2.10636 + 1.88766i) q^{8} +(0.862562 + 2.87332i) q^{9} +O(q^{10})$	\(q+(1.37247 + 0.341058i) q^{2} +(-1.38971 - 1.03379i) q^{3} +(1.76736 + 0.936186i) q^{4} +(-0.375467 + 0.0494312i) q^{5} +(-1.55475 - 1.89282i) q^{6} +(1.86379 - 0.499402i) q^{7} +(2.10636 + 1.88766i) q^{8} +(0.862562 + 2.87332i) q^{9} +(-0.532177 - 0.0602133i) q^{10} +(2.38296 - 1.82851i) q^{11} +(-1.48829 - 3.12810i) q^{12} +(2.91857 - 3.80355i) q^{13} +(2.72833 - 0.0497528i) q^{14} +(0.572891 + 0.319459i) q^{15} +(2.24711 + 3.30915i) q^{16} +3.75523i q^{17} +(0.203871 + 4.23774i) q^{18} +(-1.46737 - 3.54254i) q^{19} +(-0.709862 - 0.264145i) q^{20} +(-3.10640 - 1.23275i) q^{21} +(3.89417 - 1.69685i) q^{22} +(-6.16625 - 1.65224i) q^{23} +(-0.975770 - 4.80082i) q^{24} +(-4.69110 + 1.25698i) q^{25} +(5.30289 - 4.22487i) q^{26} +(1.77170 - 4.88478i) q^{27} +(3.76152 + 0.862235i) q^{28} +(-0.992961 + 7.54229i) q^{29} +(0.677322 + 0.633838i) q^{30} +(1.20555 + 2.08807i) q^{31} +(1.95548 + 5.30812i) q^{32} +(-5.20190 + 0.0776120i) q^{33} +(-1.28075 + 5.15395i) q^{34} +(-0.675107 + 0.279639i) q^{35} +(-1.16551 + 5.88571i) q^{36} +(-2.52174 + 6.08802i) q^{37} +(-0.805709 - 5.36250i) q^{38} +(-7.98802 + 2.26863i) q^{39} +(-0.884177 - 0.604636i) q^{40} +(-4.10842 - 1.10085i) q^{41} +(-3.84300 - 2.75137i) q^{42} +(5.64414 - 4.33090i) q^{43} +(5.92336 - 1.00074i) q^{44} +(-0.465896 - 1.03620i) q^{45} +(-7.89949 - 4.37070i) q^{46} +(0.200164 + 0.115565i) q^{47} +(0.298142 - 6.92179i) q^{48} +(-2.83786 + 1.63844i) q^{49} +(-6.86710 + 0.125226i) q^{50} +(3.88212 - 5.21867i) q^{51} +(8.71899 - 3.98992i) q^{52} +(-3.10539 - 1.28630i) q^{53} +(4.09761 - 6.09997i) q^{54} +(-0.804337 + 0.804337i) q^{55} +(4.86851 + 2.46629i) q^{56} +(-1.62303 + 6.44004i) q^{57} +(-3.93517 + 10.0129i) q^{58} +(-11.5626 + 1.52225i) q^{59} +(0.713430 + 1.10093i) q^{60} +(1.04865 - 7.96531i) q^{61} +(0.942426 + 3.27698i) q^{62} +(3.04258 + 4.92451i) q^{63} +(0.873469 + 7.95217i) q^{64} +(-0.907813 + 1.57238i) q^{65} +(-7.16593 - 1.66763i) q^{66} +(-5.64017 - 4.32785i) q^{67} +(-3.51560 + 6.63684i) q^{68} +(6.86120 + 8.67073i) q^{69} +(-1.02194 + 0.153545i) q^{70} +(3.00945 + 3.00945i) q^{71} +(-3.60700 + 7.68047i) q^{72} +(8.14413 - 8.14413i) q^{73} +(-5.53739 + 7.49558i) q^{74} +(7.81869 + 3.10278i) q^{75} +(0.723112 - 7.63468i) q^{76} +(3.52818 - 4.59801i) q^{77} +(-11.7371 + 0.389255i) q^{78} +(3.20972 + 1.85313i) q^{79} +(-1.00729 - 1.13140i) q^{80} +(-7.51197 + 4.95684i) q^{81} +(-5.26324 - 2.91209i) q^{82} +(-7.77292 - 1.02332i) q^{83} +(-4.33604 - 5.08687i) q^{84} +(-0.185626 - 1.40997i) q^{85} +(9.22351 - 4.01906i) q^{86} +(9.17706 - 9.45505i) q^{87} +(8.47095 + 0.646729i) q^{88} +(1.17489 + 1.17489i) q^{89} +(-0.286023 - 1.58106i) q^{90} +(3.54011 - 8.54657i) q^{91} +(-9.35116 - 8.69286i) q^{92} +(0.483267 - 4.14808i) q^{93} +(0.235305 + 0.226877i) q^{94} +(0.726062 + 1.25758i) q^{95} +(2.76992 - 9.39827i) q^{96} +(6.28300 - 10.8825i) q^{97} +(-4.45369 + 1.28084i) q^{98} +(7.30934 + 5.26980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.37247	+	0.341058i	0.970484	+	0.241165i
$2$	1.37247	+	0.341058i	0.970484	+	0.241165i
$3$	−1.38971	−	1.03379i	−0.802347	−	0.596858i
$3$	−1.38971	−	1.03379i	−0.802347	−	0.596858i
$4$	1.76736	+	0.936186i	0.883679	+	0.468093i
$5$	−0.375467	+	0.0494312i	−0.167914	+	0.0221063i	−0.214014	−	0.976831i	$-0.568654\pi$
$5$	−0.375467	+	0.0494312i	−0.167914	+	0.0221063i	0.0461003	+	0.998937i	$0.485321\pi$
$6$	−1.55475	−	1.89282i	−0.634724	−	0.772739i
$7$	1.86379	−	0.499402i	0.704447	−	0.188756i	0.111225	−	0.993795i	$-0.464522\pi$
$7$	1.86379	−	0.499402i	0.704447	−	0.188756i	0.593222	+	0.805039i	$0.297856\pi$
$8$	2.10636	+	1.88766i	0.744709	+	0.667389i
$9$	0.862562	+	2.87332i	0.287521	+	0.957774i
$10$	−0.532177	−	0.0602133i	−0.168289	−	0.0190411i
$11$	2.38296	−	1.82851i	0.718488	−	0.551315i	−0.183530	−	0.983014i	$-0.558752\pi$
$11$	2.38296	−	1.82851i	0.718488	−	0.551315i	0.902018	+	0.431699i	$0.142086\pi$
$12$	−1.48829	−	3.12810i	−0.429632	−	0.903004i
$13$	2.91857	−	3.80355i	0.809465	−	1.05492i	−0.187887	−	0.982191i	$-0.560164\pi$
$13$	2.91857	−	3.80355i	0.809465	−	1.05492i	0.997352	−	0.0727252i	$-0.0231696\pi$
$14$	2.72833	−	0.0497528i	0.729176	−	0.0132970i
$15$	0.572891	+	0.319459i	0.147920	+	0.0824840i
$16$	2.24711	+	3.30915i	0.561778	+	0.827288i
$17$			3.75523i			0.910778i	0.890293	+	0.455389i	$0.150500\pi$
$17$			3.75523i			0.910778i	−0.890293	+	0.455389i	$0.849500\pi$
$18$	0.203871	+	4.23774i	0.0480528	+	0.998845i
$19$	−1.46737	−	3.54254i	−0.336638	−	0.812715i	−0.998034	−	0.0626784i	$-0.980036\pi$
$19$	−1.46737	−	3.54254i	−0.336638	−	0.812715i	0.661396	−	0.750037i	$-0.269964\pi$
$20$	−0.709862	−	0.264145i	−0.158730	−	0.0590645i
$21$	−3.10640	−	1.23275i	−0.677871	−	0.269007i
$22$	3.89417	−	1.69685i	0.830239	−	0.361769i
$23$	−6.16625	−	1.65224i	−1.28575	−	0.344516i	−0.449706	−	0.893177i	$-0.648471\pi$
$23$	−6.16625	−	1.65224i	−1.28575	−	0.344516i	−0.836045	+	0.548660i	$0.815138\pi$
$24$	−0.975770	−	4.80082i	−0.199178	−	0.979963i
$25$	−4.69110	+	1.25698i	−0.938219	+	0.251395i
$26$	5.30289	−	4.22487i	1.03998	−	0.828565i
$27$	1.77170	−	4.88478i	0.340964	−	0.940076i
$28$	3.76152	+	0.862235i	0.710861	+	0.162947i
$29$	−0.992961	+	7.54229i	−0.184388	+	1.40057i	0.609636	+	0.792682i	$0.291316\pi$
$29$	−0.992961	+	7.54229i	−0.184388	+	1.40057i	−0.794024	+	0.607886i	$0.792018\pi$
$30$	0.677322	+	0.633838i	0.123662	+	0.115722i
$31$	1.20555	+	2.08807i	0.216523	+	0.375028i	0.953743	−	0.300625i	$-0.0971951\pi$
$31$	1.20555	+	2.08807i	0.216523	+	0.375028i	−0.737220	+	0.675653i	$0.763862\pi$
$32$	1.95548	+	5.30812i	0.345684	+	0.938351i
$33$	−5.20190	+	0.0776120i	−0.905534	+	0.0135105i
$34$	−1.28075	+	5.15395i	−0.219647	+	0.883895i
$35$	−0.675107	+	0.279639i	−0.114114	+	0.0472675i
$36$	−1.16551	+	5.88571i	−0.194252	+	0.980952i
$37$	−2.52174	+	6.08802i	−0.414572	+	1.00086i	0.569323	+	0.822114i	$0.307205\pi$
$37$	−2.52174	+	6.08802i	−0.414572	+	1.00086i	−0.983894	+	0.178750i	$0.942795\pi$
$38$	−0.805709	−	5.36250i	−0.130703	−	0.869912i
$39$	−7.98802	+	2.26863i	−1.27911	+	0.363272i
$40$	−0.884177	−	0.604636i	−0.139801	−	0.0956013i
$41$	−4.10842	−	1.10085i	−0.641627	−	0.171923i	−0.0766868	−	0.997055i	$-0.524434\pi$
$41$	−4.10842	−	1.10085i	−0.641627	−	0.171923i	−0.564940	+	0.825132i	$0.691101\pi$
$42$	−3.84300	−	2.75137i	−0.592988	−	0.424546i
$43$	5.64414	−	4.33090i	0.860723	−	0.660456i	−0.0810480	−	0.996710i	$-0.525827\pi$
$43$	5.64414	−	4.33090i	0.860723	−	0.660456i	0.941771	+	0.336254i	$0.109160\pi$
$44$	5.92336	−	1.00074i	0.892980	−	0.150867i
$45$	−0.465896	−	1.03620i	−0.0694516	−	0.154468i
$46$	−7.89949	−	4.37070i	−1.16472	−	0.644425i
$47$	0.200164	+	0.115565i	0.0291969	+	0.0168568i	0.514527	−	0.857474i	$-0.327967\pi$
$47$	0.200164	+	0.115565i	0.0291969	+	0.0168568i	−0.485331	+	0.874331i	$0.661301\pi$
$48$	0.298142	−	6.92179i	0.0430331	−	0.999074i
$49$	−2.83786	+	1.63844i	−0.405408	+	0.234063i
$50$	−6.86710	+	0.125226i	−0.971155	+	0.0177096i
$51$	3.88212	−	5.21867i	0.543605	−	0.730759i
$52$	8.71899	−	3.98992i	1.20911	−	0.553302i
$53$	−3.10539	−	1.28630i	−0.426559	−	0.176686i	0.159067	−	0.987268i	$-0.449151\pi$
$53$	−3.10539	−	1.28630i	−0.426559	−	0.176686i	−0.585626	+	0.810581i	$0.699151\pi$
$54$	4.09761	−	6.09997i	0.557614	−	0.830101i
$55$	−0.804337	+	0.804337i	−0.108457	+	0.108457i
$56$	4.86851	+	2.46629i	0.650582	+	0.329572i
$57$	−1.62303	+	6.44004i	−0.214976	+	0.853004i
$58$	−3.93517	+	10.0129i	−0.516713	+	1.31476i
$59$	−11.5626	+	1.52225i	−1.50533	+	0.198180i	−0.837623	−	0.546248i	$-0.816056\pi$
$59$	−11.5626	+	1.52225i	−1.50533	+	0.198180i	−0.667703	+	0.744428i	$0.732722\pi$
$60$	0.713430	+	1.10093i	0.0921034	+	0.142130i
$61$	1.04865	−	7.96531i	0.134266	−	1.01985i	−0.783124	−	0.621865i	$-0.786375\pi$
$61$	1.04865	−	7.96531i	0.134266	−	1.01985i	0.917391	−	0.397988i	$-0.130291\pi$
$62$	0.942426	+	3.27698i	0.119688	+	0.416177i
$63$	3.04258	+	4.92451i	0.383329	+	0.620430i
$64$	0.873469	+	7.95217i	0.109184	+	0.994022i
$65$	−0.907813	+	1.57238i	−0.112600	+	0.195030i
$66$	−7.16593	−	1.66763i	−0.882065	−	0.205271i
$67$	−5.64017	−	4.32785i	−0.689056	−	0.528731i	0.203834	−	0.979005i	$-0.434660\pi$
$67$	−5.64017	−	4.32785i	−0.689056	−	0.528731i	−0.892890	+	0.450274i	$0.851326\pi$
$68$	−3.51560	+	6.63684i	−0.426329	+	0.804835i
$69$	6.86120	+	8.67073i	0.825991	+	1.04383i
$70$	−1.02194	+	0.153545i	−0.122145	+	0.0183522i
$71$	3.00945	+	3.00945i	0.357156	+	0.357156i	0.862764	−	0.505608i	$-0.168732\pi$
$71$	3.00945	+	3.00945i	0.357156	+	0.357156i	−0.505608	+	0.862764i	$0.668732\pi$
$72$	−3.60700	+	7.68047i	−0.425089	+	0.905152i
$73$	8.14413	−	8.14413i	0.953198	−	0.953198i	−0.0457543	−	0.998953i	$-0.514569\pi$
$73$	8.14413	−	8.14413i	0.953198	−	0.953198i	0.998953	+	0.0457543i	$0.0145691\pi$
$74$	−5.53739	+	7.49558i	−0.643708	+	0.871343i
$75$	7.81869	+	3.10278i	0.902824	+	0.358278i
$76$	0.723112	−	7.63468i	0.0829466	−	0.875757i
$77$	3.52818	−	4.59801i	0.402073	−	0.523992i
$78$	−11.7371	+	0.389255i	−1.32896	+	0.0440745i
$79$	3.20972	+	1.85313i	0.361122	+	0.208494i	0.669573	−	0.742747i	$-0.266477\pi$
$79$	3.20972	+	1.85313i	0.361122	+	0.208494i	−0.308451	+	0.951240i	$0.599811\pi$
$80$	−1.00729	−	1.13140i	−0.112619	−	0.126495i
$81$	−7.51197	+	4.95684i	−0.834664	+	0.550760i
$82$	−5.26324	−	2.91209i	−0.581227	−	0.321587i
$83$	−7.77292	−	1.02332i	−0.853188	−	0.112324i	−0.308769	−	0.951137i	$-0.599917\pi$
$83$	−7.77292	−	1.02332i	−0.853188	−	0.112324i	−0.544420	+	0.838813i	$0.683250\pi$
$84$	−4.33604	−	5.08687i	−0.473100	−	0.555023i
$85$	−0.185626	−	1.40997i	−0.0201339	−	0.152932i
$86$	9.22351	−	4.01906i	0.994597	−	0.433386i
$87$	9.17706	−	9.45505i	0.983884	−	1.01369i
$88$	8.47095	+	0.646729i	0.903007	+	0.0689416i
$89$	1.17489	+	1.17489i	0.124538	+	0.124538i	0.766629	−	0.642090i	$-0.221933\pi$
$89$	1.17489	+	1.17489i	0.124538	+	0.124538i	−0.642090	+	0.766629i	$0.721933\pi$
$90$	−0.286023	−	1.58106i	−0.0301495	−	0.166658i
$91$	3.54011	−	8.54657i	0.371104	−	0.895924i
$92$	−9.35116	−	8.69286i	−0.974926	−	0.906293i
$93$	0.483267	−	4.14808i	0.0501125	−	0.430136i
$94$	0.235305	+	0.226877i	0.0242698	+	0.0234005i
$95$	0.726062	+	1.25758i	0.0744924	+	0.129025i
$96$	2.76992	−	9.39827i	0.282704	−	0.959207i
$97$	6.28300	−	10.8825i	0.637942	−	1.10495i	−0.347942	−	0.937516i	$-0.613119\pi$
$97$	6.28300	−	10.8825i	0.637942	−	1.10495i	0.985884	−	0.167431i	$-0.0535472\pi$
$98$	−4.45369	+	1.28084i	−0.449890	+	0.129384i
$99$	7.30934	+	5.26980i	0.734616	+	0.529635i
$100$	−9.46761	−	2.17021i	−0.946761	−	0.217021i
$101$	9.83664	+	12.8194i	0.978782	+	1.27557i	0.961236	+	0.275728i	$0.0889189\pi$
$101$	9.83664	+	12.8194i	0.978782	+	1.27557i	0.0175468	+	0.999846i	$0.494414\pi$
$102$	7.10797	−	5.83844i	0.703794	−	0.578092i
$103$	−3.11818	+	11.6372i	−0.307243	+	1.14665i	0.623753	+	0.781621i	$0.285607\pi$
$103$	−3.11818	+	11.6372i	−0.307243	+	1.14665i	−0.930997	+	0.365027i	$0.881060\pi$
$104$	13.3274	−	2.50237i	1.30686	−	0.245377i
$105$	1.22729	+	0.309303i	0.119771	+	0.0301849i
$106$	−3.82336	−	2.82453i	−0.371358	−	0.274342i
$107$	3.77097	+	1.56199i	0.364553	+	0.151003i	0.557438	−	0.830219i	$-0.311784\pi$
$107$	3.77097	+	1.56199i	0.364553	+	0.151003i	−0.192885	+	0.981221i	$0.561784\pi$
$108$	7.70430	−	6.97451i	0.741346	−	0.671123i
$109$	−5.92568	−	14.3059i	−0.567577	−	1.37025i	−0.903591	−	0.428396i	$-0.859079\pi$
$109$	−5.92568	−	14.3059i	−0.567577	−	1.37025i	0.336014	−	0.941857i	$-0.390921\pi$
$110$	−1.37826	+	0.829604i	−0.131412	+	0.0790997i
$111$	9.79820	−	5.85361i	0.930004	−	0.555600i
$112$	5.84074	+	5.04536i	0.551898	+	0.476742i
$113$	0.486718	−	0.281007i	0.0457866	−	0.0264349i	−0.476932	−	0.878940i	$-0.658251\pi$
$113$	0.486718	−	0.281007i	0.0457866	−	0.0264349i	0.522719	+	0.852505i	$0.324918\pi$
$114$	−4.42399	+	8.28523i	−0.414345	+	0.775983i
$115$	2.39690	+	0.315558i	0.223512	+	0.0294259i
$116$	−8.81590	+	12.4003i	−0.818536	+	1.15134i
$117$	13.4463	+	5.10519i	1.24311	+	0.471975i
$118$	−16.3886	−	1.85429i	−1.50869	−	0.170701i
$119$	1.87537	+	6.99897i	0.171915	+	0.641595i
$120$	0.603680	+	1.75432i	0.0551082	+	0.160147i
$121$	−0.511966	+	1.91068i	−0.0465424	+	0.173699i
$122$	4.15588	−	10.5745i	0.376256	−	0.957371i
$123$	4.57145	+	5.77709i	0.412193	+	0.520903i
$124$	0.175813	+	4.81898i	0.0157885	+	0.432757i
$125$	3.44862	−	1.42847i	0.308454	−	0.127766i
$126$	2.49631	+	7.79645i	0.222389	+	0.694563i
$127$	10.1924			0.904434			0.452217	−	0.891908i	$-0.350633\pi$
$127$	10.1924			0.904434			0.452217	+	0.891908i	$0.350633\pi$
$128$	−1.51334	+	11.2120i	−0.133762	+	0.991013i
$129$	−12.3209	+	0.183828i	−1.08480	+	0.0161851i
$130$	−1.78222	+	1.84843i	−0.156311	+	0.162118i
$131$	−15.3454	−	11.7749i	−1.34073	−	1.02878i	−0.995932	−	0.0901045i	$-0.971280\pi$
$131$	−15.3454	−	11.7749i	−1.34073	−	1.02878i	−0.344800	−	0.938676i	$-0.612053\pi$
$132$	−9.26627	−	4.73277i	−0.806526	−	0.411935i
$133$	−4.50402	−	5.86976i	−0.390548	−	0.508973i
$134$	−6.26492	−	7.86348i	−0.541207	−	0.679301i
$135$	−0.423756	+	1.92165i	−0.0364711	+	0.165390i
$136$	−7.08861	+	7.90986i	−0.607843	+	0.678264i
$137$	−0.257228	−	0.959989i	−0.0219765	−	0.0820174i	0.954067	−	0.299594i	$-0.0968513\pi$
$137$	−0.257228	−	0.959989i	−0.0219765	−	0.0820174i	−0.976043	+	0.217577i	$0.930185\pi$
$138$	6.45958	+	14.2404i	0.549876	+	1.21222i
$139$	0.582729	+	4.42626i	0.0494264	+	0.375431i	0.998225	+	0.0595501i	$0.0189666\pi$
$139$	0.582729	+	4.42626i	0.0494264	+	0.375431i	−0.948799	+	0.315881i	$0.897700\pi$
$140$	−1.45495	−	0.137804i	−0.122966	−	0.0116466i
$141$	−0.158699	−	0.367528i	−0.0133649	−	0.0309514i
$142$	3.10399	+	5.15678i	0.260481	+	0.432748i
$143$		−	14.4003i		−	1.20422i
$144$	−7.56999	+	9.31103i	−0.630833	+	0.775919i
$145$		−	2.88097i		−	0.239251i
$146$	13.9552	−	8.39997i	1.15494	−	0.695186i
$147$	5.63759	+	0.656800i	0.464980	+	0.0541719i
$148$	−10.1563	+	8.39890i	−0.834846	+	0.690385i
$149$	1.88577	+	14.3239i	0.154489	+	1.17346i	0.876439	+	0.481513i	$0.159913\pi$
$149$	1.88577	+	14.3239i	0.154489	+	1.17346i	−0.721950	+	0.691945i	$0.756754\pi$
$150$	9.67270	+	6.92510i	0.789773	+	0.565432i
$151$	3.88017	+	14.4810i	0.315764	+	1.17845i	0.923276	+	0.384137i	$0.125501\pi$
$151$	3.88017	+	14.4810i	0.315764	+	1.17845i	−0.607512	+	0.794311i	$0.707832\pi$
$152$	3.59632	−	10.2318i	0.291700	−	0.829905i
$153$	−10.7900	+	3.23912i	−0.872320	+	0.261867i
$154$	6.41051	−	5.10732i	0.516574	−	0.411560i
$155$	−0.555860	−	0.724410i	−0.0446477	−	0.0581860i
$156$	−16.2416	−	3.46878i	−1.30037	−	0.277725i
$157$	7.16778	+	5.50003i	0.572051	+	0.438950i	0.853847	−	0.520524i	$-0.174263\pi$
$157$	7.16778	+	5.50003i	0.572051	+	0.438950i	−0.281796	+	0.959474i	$0.590930\pi$
$158$	3.77322	+	3.63807i	0.300182	+	0.289430i
$159$	2.98582	+	4.99789i	0.236791	+	0.396359i
$160$	−0.996607	−	1.89636i	−0.0787887	−	0.149921i
$161$	−12.3177			−0.970773
$162$	−12.0005	+	4.24110i	−0.942852	+	0.333212i
$163$	−17.7395	+	7.34794i	−1.38946	+	0.575535i	−0.946995	−	0.321248i	$-0.895898\pi$
$163$	−17.7395	+	7.34794i	−1.38946	+	0.575535i	−0.442470	+	0.896783i	$0.645898\pi$
$164$	−6.23045	−	5.79184i	−0.486516	−	0.452266i
$165$	1.94931	−	0.286277i	0.151753	−	0.0222866i
$166$	−10.3191	−	4.05550i	−0.800917	−	0.314768i
$167$	1.85783	−	6.93352i	0.143763	−	0.536532i	−0.856044	−	0.516903i	$-0.827085\pi$
$167$	1.85783	−	6.93352i	0.143763	−	0.536532i	0.999807	−	0.0196289i	$-0.00624848\pi$
$168$	−4.21617	−	8.46043i	−0.325285	−	0.652736i
$169$	−2.58433	−	9.64483i	−0.198794	−	0.741910i
$170$	0.226115	−	1.99845i	0.0173422	−	0.153274i
$171$	8.91318	−	7.27189i	0.681608	−	0.556095i
$172$	14.0297	−	2.37029i	1.06976	−	0.180733i
$173$	15.8790	+	2.09051i	1.20726	+	0.158939i	0.707175	−	0.707039i	$-0.249969\pi$
$173$	15.8790	+	2.09051i	1.20726	+	0.158939i	0.500083	+	0.865977i	$0.333303\pi$
$174$	15.8200	−	9.84688i	1.19931	−	0.746490i
$175$	−8.11549	+	4.68548i	−0.613474	+	0.354189i
$176$	11.4056	+	3.77671i	0.859727	+	0.284680i
$177$	17.6423	+	9.83784i	1.32608	+	0.739457i
$178$	1.21180	+	2.01321i	0.0908283	+	0.150897i
$179$	−4.60120	−	11.1083i	−0.343910	−	0.830272i	−0.997313	−	0.0732614i	$-0.976659\pi$
$179$	−4.60120	−	11.1083i	−0.343910	−	0.830272i	0.653403	−	0.757010i	$-0.273341\pi$
$180$	0.146673	−	2.26751i	0.0109324	−	0.169010i
$181$	12.9235	+	5.35310i	0.960599	+	0.397893i	0.807204	−	0.590272i	$-0.200980\pi$
$181$	12.9235	+	5.35310i	0.960599	+	0.397893i	0.153394	+	0.988165i	$0.450980\pi$
$182$	7.77357	−	10.5225i	0.576216	−	0.779983i
$183$	−9.69177	+	9.98535i	−0.716436	+	0.738138i
$184$	−9.86944	−	15.1200i	−0.727585	−	1.11466i
$185$	0.645893	−	2.41051i	0.0474870	−	0.177224i
$186$	2.07801	−	5.52830i	0.152367	−	0.405355i
$187$	6.86647	+	8.94855i	0.502126	+	0.654383i
$188$	0.245571	+	0.391634i	0.0179101	+	0.0285629i
$189$	0.862620	−	9.98900i	0.0627463	−	0.726593i
$190$	0.567593	+	1.97362i	0.0411775	+	0.143181i
$191$	−1.71412	+	2.96894i	−0.124029	+	0.214825i	−0.921353	−	0.388727i	$-0.872915\pi$
$191$	−1.71412	+	2.96894i	−0.124029	+	0.214825i	0.797324	+	0.603552i	$0.206248\pi$
$192$	7.00700	−	11.9542i	0.505687	−	0.862717i
$193$	9.42320	+	16.3215i	0.678297	+	1.17484i	0.975493	+	0.220028i	$0.0706150\pi$
$193$	9.42320	+	16.3215i	0.678297	+	1.17484i	−0.297197	+	0.954816i	$0.596052\pi$
$194$	12.3348	−	12.7930i	0.885586	−	0.918485i
$195$	2.88710	−	1.24666i	0.206750	−	0.0892749i
$196$	−6.54940	+	0.238944i	−0.467814	+	0.0170674i
$197$	7.87141	−	19.0033i	0.560815	−	1.35393i	−0.348301	−	0.937383i	$-0.613241\pi$
$197$	7.87141	−	19.0033i	0.560815	−	1.35393i	0.909116	−	0.416544i	$-0.136759\pi$
$198$	8.23455	+	9.72557i	0.585204	+	0.691166i
$199$	−5.79184	−	5.79184i	−0.410572	−	0.410572i	0.471366	−	0.881938i	$-0.343761\pi$
$199$	−5.79184	−	5.79184i	−0.410572	−	0.410572i	−0.881938	+	0.471366i	$0.843761\pi$
$200$	−12.2539	−	6.20756i	−0.866479	−	0.438941i
$201$	3.36408	+	11.8452i	0.237284	+	0.835495i
$202$	9.12836	+	20.9491i	0.642269	+	1.47397i
$203$	1.91596	+	14.5531i	0.134474	+	1.02143i
$204$	11.7467	−	5.58887i	0.822436	−	0.391299i
$205$	1.59699	+	0.210248i	0.111539	+	0.0146844i
$206$	−8.24858	+	14.9083i	−0.574706	+	1.03871i
$207$	−0.571345	−	19.1428i	−0.0397113	−	1.33052i
$208$	19.1449	+	1.11098i	1.32746	+	0.0770328i
$209$	−9.97424	−	5.75863i	−0.689933	−	0.398333i
$210$	1.57893	+	0.843086i	0.108956	+	0.0581785i
$211$	6.54054	−	8.52380i	0.450270	−	0.586803i	−0.511971	−	0.859003i	$-0.671085\pi$
$211$	6.54054	−	8.52380i	0.450270	−	0.586803i	0.962241	+	0.272200i	$0.0877512\pi$
$212$	−4.28413	−	5.18057i	−0.294235	−	0.355803i
$213$	−1.07111	−	7.29338i	−0.0733914	−	0.499734i
$214$	4.64282	+	3.42990i	0.317376	+	0.234463i
$215$	−1.90511	+	1.90511i	−0.129927	+	0.129927i
$216$	12.9526	−	6.94471i	0.881316	−	0.472527i
$217$	3.28967	+	3.28967i	0.223318	+	0.223318i
$218$	−3.25370	−	21.6554i	−0.220368	−	1.46669i
$219$	−19.7373	+	2.89863i	−1.33372	+	0.195871i
$220$	−2.17456	+	0.668543i	−0.146609	+	0.0450731i
$221$	14.2832	+	10.9599i	0.960794	+	0.737243i
$222$	15.4442	−	4.69215i	1.03655	−	0.314917i
$223$	−2.98799	+	5.17534i	−0.200090	+	0.346567i	−0.948557	−	0.316605i	$-0.897457\pi$
$223$	−2.98799	+	5.17534i	−0.200090	+	0.346567i	0.748467	+	0.663172i	$0.230790\pi$
$224$	6.29549	+	8.91665i	0.420635	+	0.595769i
$225$	−7.65806	−	12.3948i	−0.510537	−	0.826321i
$226$	0.763847	−	0.219675i	0.0508103	−	0.0146125i
$227$	2.34054	−	17.7782i	0.155347	−	1.17998i	−0.719116	−	0.694890i	$-0.755453\pi$
$227$	2.34054	−	17.7782i	0.155347	−	1.17998i	0.874464	−	0.485091i	$-0.161214\pi$
$228$	−8.89755	+	9.86240i	−0.589255	+	0.653154i
$229$	−23.0080	+	3.02906i	−1.52041	+	0.200166i	−0.843995	−	0.536351i	$-0.819802\pi$
$229$	−23.0080	+	3.02906i	−1.52041	+	0.200166i	−0.676418	+	0.736518i	$0.736469\pi$
$230$	3.18205	+	1.25058i	0.209818	+	0.0824605i
$231$	−9.65649	+	2.74249i	−0.635351	+	0.180442i
$232$	−16.3288	+	14.0124i	−1.07204	+	0.919957i
$233$	18.3811	−	18.3811i	1.20419	−	1.20419i	0.231305	−	0.972881i	$-0.425700\pi$
$233$	18.3811	−	18.3811i	1.20419	−	1.20419i	0.972881	−	0.231305i	$-0.0742997\pi$
$234$	16.7135	+	11.5927i	1.09259	+	0.757839i
$235$	−0.0808675	−	0.0334964i	−0.00527521	−	0.00218506i
$236$	−21.8604	−	8.13441i	−1.42299	−	0.529505i
$237$	−2.54482	−	5.89348i	−0.165304	−	0.382823i
$238$	0.186833	+	10.2455i	0.0121106	+	0.664117i
$239$	4.27335	−	2.46722i	0.276420	−	0.159591i	−0.355382	−	0.934721i	$-0.615649\pi$
$239$	4.27335	−	2.46722i	0.276420	−	0.159591i	0.631802	+	0.775130i	$0.282316\pi$
$240$	0.230210	+	2.61364i	0.0148600	+	0.168710i
$241$	−20.6147	−	11.9019i	−1.32791	−	0.766668i	−0.342932	−	0.939360i	$-0.611420\pi$
$241$	−20.6147	−	11.9019i	−1.32791	−	0.766668i	−0.984976	+	0.172692i	$0.944753\pi$
$242$	−1.35431	+	2.44775i	−0.0870586	+	0.157347i
$243$	15.5638	+	0.877253i	0.998415	+	0.0562758i
$244$	9.31036	−	13.0958i	0.596035	−	0.838374i
$245$	0.984534	−	0.755459i	0.0628996	−	0.0482645i
$246$	4.30386	+	9.48802i	0.274404	+	0.604934i
$247$	−17.7569	−	4.75794i	−1.12984	−	0.302740i
$248$	−1.40226	+	6.67388i	−0.0890434	+	0.423792i
$249$	9.74416	+	9.45767i	0.617511	+	0.599356i
$250$	5.22032	−	0.784348i	0.330162	−	0.0496065i
$251$	−8.58619	+	20.7289i	−0.541956	+	1.30840i	0.381386	+	0.924416i	$0.375447\pi$
$251$	−8.58619	+	20.7289i	−0.541956	+	1.30840i	−0.923341	+	0.383980i	$0.874553\pi$
$252$	0.767065	+	11.5518i	0.0483206	+	0.727695i
$253$	−17.7150	+	7.33781i	−1.11373	+	0.461324i
$254$	13.9888	+	3.47622i	0.877738	+	0.218117i
$255$	−1.19964	+	2.15134i	−0.0751246	+	0.134722i
$256$	−5.90098	+	14.8721i	−0.368811	+	0.929504i
$257$	−12.9639	−	22.4541i	−0.808663	−	1.40065i	−0.913790	−	0.406187i	$-0.866858\pi$
$257$	−12.9639	−	22.4541i	−0.808663	−	1.40065i	0.105127	−	0.994459i	$-0.466475\pi$
$258$	−16.9728	−	3.94986i	−1.05668	−	0.245907i
$259$	−1.65963	+	12.6062i	−0.103125	+	0.783309i
$260$	−3.07647	+	1.92907i	−0.190795	+	0.119636i
$261$	−22.5279	+	3.65259i	−1.39444	+	0.226090i
$262$	−17.0452	−	21.3944i	−1.05305	−	1.32175i
$263$	27.5086	−	7.37091i	1.69625	−	0.454510i	0.724262	−	0.689525i	$-0.242181\pi$
$263$	27.5086	−	7.37091i	1.69625	−	0.454510i	0.971992	+	0.235015i	$0.0755140\pi$
$264$	−11.1035	−	9.65594i	−0.683376	−	0.594282i
$265$	1.22956	+	0.329459i	0.0755311	+	0.0202385i
$266$	−4.17972	−	9.59221i	−0.256275	−	0.588136i
$267$	−0.418164	−	2.84735i	−0.0255912	−	0.174255i
$268$	−5.91652	−	12.9291i	−0.361409	−	0.789771i
$269$	−5.05869	−	12.2128i	−0.308434	−	0.744625i	−0.999756	−	0.0220784i	$-0.992972\pi$
$269$	−5.05869	−	12.2128i	−0.308434	−	0.744625i	0.691323	−	0.722546i	$-0.257028\pi$
$270$	−1.23699	+	2.49289i	−0.0752808	+	0.151712i
$271$			22.9324i			1.39304i	0.717535	+	0.696522i	$0.245270\pi$
$271$			22.9324i			1.39304i	−0.717535	+	0.696522i	$0.754730\pi$
$272$	−12.4266	+	8.43843i	−0.753476	+	0.511655i
$273$	−13.7551	+	8.21749i	−0.832494	+	0.497345i
$274$	−0.0256263	−	1.40529i	−0.00154814	−	0.0848966i
$275$	−8.88029	+	11.5730i	−0.535502	+	0.697879i
$276$	4.00878	+	21.7476i	0.241300	+	1.30905i
$277$	−9.26782	+	7.11145i	−0.556849	+	0.427285i	−0.848466	−	0.529250i	$-0.822473\pi$
$277$	−9.26782	+	7.11145i	−0.556849	+	0.427285i	0.291617	+	0.956535i	$0.405807\pi$
$278$	−0.709836	+	6.27367i	−0.0425731	+	0.376270i
$279$	−4.95984	+	5.26502i	−0.296938	+	0.315208i
$280$	−1.94988	−	0.685356i	−0.116528	−	0.0409578i
$281$	11.2321	−	3.00963i	0.670051	−	0.179540i	0.0922733	−	0.995734i	$-0.470587\pi$
$281$	11.2321	−	3.00963i	0.670051	−	0.179540i	0.577778	+	0.816194i	$0.303920\pi$
$282$	−0.0924618	−	0.558547i	−0.00550602	−	0.0332610i
$283$	3.63137	−	0.478079i	0.215863	−	0.0284188i	−0.0218192	−	0.999762i	$-0.506946\pi$
$283$	3.63137	−	0.478079i	0.215863	−	0.0284188i	0.237682	+	0.971343i	$0.423612\pi$
$284$	2.50137	+	8.13618i	0.148429	+	0.482793i
$285$	0.291056	−	2.49825i	0.0172407	−	0.147984i
$286$	4.91135	−	19.7640i	0.290414	−	1.16867i
$287$	−8.20700			−0.484444
$288$	−13.5652	+	10.1973i	−0.799337	+	0.600882i
$289$	2.89823			0.170484
$290$	0.982578	−	3.95405i	0.0576990	−	0.232190i
$291$	−19.9817	+	8.62813i	−1.17135	+	0.505790i
$292$	22.0180	−	6.76918i	1.28851	−	0.396136i
$293$	−2.07925	+	0.273739i	−0.121471	+	0.0159920i	−0.191017	−	0.981587i	$-0.561178\pi$
$293$	−2.07925	+	0.273739i	−0.121471	+	0.0159920i	0.0695454	+	0.997579i	$0.477845\pi$
$294$	7.51342	+	2.82419i	0.438192	+	0.164710i
$295$	4.26614	−	1.14311i	0.248385	−	0.0665544i
$296$	−16.8038	+	8.06334i	−0.976701	+	0.468672i
$297$	−4.70996	−	14.8798i	−0.273300	−	0.863413i
$298$	−2.29711	+	20.3023i	−0.133068	+	1.17608i
$299$	−24.2810	+	18.6315i	−1.40421	+	1.07749i
$300$	10.9136	+	12.8035i	0.630100	+	0.739209i
$301$	8.35665	−	10.8906i	0.481669	−	0.627723i
$302$	0.386562	+	21.1981i	0.0222441	+	1.21982i
$303$	−0.417522	−	27.9841i	−0.0239860	−	1.60765i
$304$	8.42547	−	12.8162i	0.483234	−	0.735062i
$305$			3.04255i			0.174216i
$306$	−15.9137	+	0.765582i	−0.909726	+	0.0437654i
$307$	−6.58844	−	15.9059i	−0.376022	−	0.907798i	−0.992703	−	0.120584i	$-0.961523\pi$
$307$	−6.58844	−	15.9059i	−0.376022	−	0.907798i	0.616681	−	0.787213i	$-0.288477\pi$
$308$	10.5401	−	4.82330i	0.600580	−	0.274833i
$309$	16.3638	−	12.9487i	0.930902	−	0.736629i
$310$	−0.515835	−	1.18381i	−0.0292975	−	0.0672361i
$311$	−16.0157	−	4.29138i	−0.908165	−	0.243342i	−0.225645	−	0.974209i	$-0.572449\pi$
$311$	−16.0157	−	4.29138i	−0.908165	−	0.243342i	−0.682519	+	0.730867i	$0.739116\pi$
$312$	−21.1080	−	10.3001i	−1.19501	−	0.583130i
$313$	9.71400	−	2.60286i	0.549068	−	0.147122i	0.0263887	−	0.999652i	$-0.491599\pi$
$313$	9.71400	−	2.60286i	0.549068	−	0.147122i	0.522679	+	0.852529i	$0.324933\pi$
$314$	7.96175	+	9.99327i	0.449308	+	0.563953i
$315$	−1.38581	−	1.69860i	−0.0780817	−	0.0957050i
$316$	3.93785	+	6.28004i	0.221521	+	0.353280i
$317$	−1.48796	+	11.3022i	−0.0835720	+	0.634792i	0.897481	+	0.441053i	$0.145395\pi$
$317$	−1.48796	+	11.3022i	−0.0835720	+	0.634792i	−0.981053	+	0.193739i	$0.937938\pi$
$318$	2.39339	+	7.87781i	0.134214	+	0.441766i
$319$	11.4249	+	19.7886i	0.639674	+	1.10795i
$320$	−0.721045	−	2.94261i	−0.0403076	−	0.164497i
$321$	−3.62577	−	6.06908i	−0.202371	−	0.338743i
$322$	−16.9057	−	4.20107i	−0.942120	−	0.234116i
$323$	13.3031	−	5.51031i	0.740203	−	0.306602i
$324$	−17.9169	+	1.72790i	−0.995382	+	0.0959945i
$325$	−8.91032	+	21.5114i	−0.494255	+	1.19324i
$326$	−26.8530	+	4.03464i	−1.48725	+	0.223458i
$327$	−6.55429	+	26.0068i	−0.362453	+	1.43818i
$328$	−6.57576	−	10.0741i	−0.363086	−	0.556248i
$329$	0.430777	+	0.115426i	0.0237495	+	0.00636366i
$330$	2.77301	+	0.271920i	0.152649	+	0.0149687i
$331$	−18.9754	+	14.5603i	−1.04298	+	0.800309i	−0.980258	−	0.197722i	$-0.936646\pi$
$331$	−18.9754	+	14.5603i	−1.04298	+	0.800309i	−0.0627245	+	0.998031i	$0.519979\pi$
$332$	−12.7795	−	9.08548i	−0.701367	−	0.498630i
$333$	−19.6680	−	1.99448i	−1.07780	−	0.109297i
$334$	4.91455	−	8.88243i	0.268912	−	0.486025i
$335$	2.33163	+	1.34617i	0.127391	+	0.0735490i
$336$	−2.90108	−	13.0497i	−0.158267	−	0.711917i
$337$	23.6773	−	13.6701i	1.28979	−	0.744659i	0.311171	−	0.950354i	$-0.399279\pi$
$337$	23.6773	−	13.6701i	1.28979	−	0.744659i	0.978616	+	0.205695i	$0.0659454\pi$
$338$	−0.257463	−	14.1187i	−0.0140041	−	0.767954i
$339$	−0.966897	−	0.112647i	−0.0525146	−	0.00611815i
$340$	0.991925	−	2.66570i	0.0537947	−	0.144568i
$341$	6.69081	+	2.77143i	0.362328	+	0.150081i
$342$	14.7132	−	6.94055i	0.795600	−	0.375302i
$343$	−14.0217	+	14.0217i	−0.757099	+	0.757099i
$344$	20.0638	+	1.53181i	1.08177	+	0.0825895i
$345$	−3.00476	−	2.91642i	−0.161771	−	0.157015i
$346$	21.0805	+	8.28484i	1.13329	+	0.445395i
$347$	26.3755	−	3.47240i	1.41591	−	0.186408i	0.616576	−	0.787296i	$-0.288519\pi$
$347$	26.3755	−	3.47240i	1.41591	−	0.186408i	0.799334	+	0.600888i	$0.205186\pi$
$348$	25.0708	−	8.11902i	1.34394	−	0.435225i
$349$	1.29671	−	9.84945i	0.0694110	−	0.527229i	−0.921051	−	0.389442i	$-0.872668\pi$
$349$	1.29671	−	9.84945i	0.0694110	−	0.527229i	0.990462	−	0.137787i	$-0.0439989\pi$
$350$	−12.7363	+	3.66284i	−0.680784	+	0.195787i
$351$	−13.4087	−	20.9953i	−0.715702	−	1.12065i
$352$	14.3658	+	9.07339i	0.765697	+	0.483613i
$353$	−11.1398	+	19.2947i	−0.592912	+	1.02695i	0.400926	+	0.916110i	$0.368688\pi$
$353$	−11.1398	+	19.2947i	−0.592912	+	1.02695i	−0.993838	+	0.110843i	$0.964645\pi$
$354$	20.8583	+	19.5192i	1.10861	+	1.03743i
$355$	−1.27871	−	0.981190i	−0.0678669	−	0.0520761i
$356$	0.976538	+	3.17637i	0.0517564	+	0.168348i
$357$	4.62925	−	11.6652i	0.245006	−	0.617390i
$358$	−2.52645	−	16.8151i	−0.133527	−	0.888704i
$359$	6.82729	+	6.82729i	0.360331	+	0.360331i	0.863935	−	0.503604i	$-0.167993\pi$
$359$	6.82729	+	6.82729i	0.360331	+	0.360331i	−0.503604	+	0.863935i	$0.667993\pi$
$360$	0.974656	−	3.06206i	0.0513689	−	0.161385i
$361$	3.03859	−	3.03859i	0.159926	−	0.159926i
$362$	15.9115	+	11.7547i	0.836288	+	0.617811i
$363$	2.68673	−	2.12602i	0.141017	−	0.111587i
$364$	14.2578	−	11.7907i	0.747313	−	0.617998i
$365$	−2.65528	+	3.46043i	−0.138984	+	0.181127i
$366$	−16.7073	+	10.3992i	−0.873303	+	0.543572i
$367$	15.0563	+	8.69276i	0.785933	+	0.453759i	0.838529	−	0.544857i	$-0.183416\pi$
$367$	15.0563	+	8.69276i	0.785933	+	0.453759i	−0.0525959	+	0.998616i	$0.516750\pi$
$368$	−8.38873	−	24.1178i	−0.437293	−	1.25723i
$369$	−0.380673	−	12.7544i	−0.0198171	−	0.663966i
$370$	1.70859	−	3.08807i	0.0888256	−	0.160541i
$371$	−6.43019	−	0.846550i	−0.333839	−	0.0439507i
$372$	4.73748	−	6.87872i	0.245627	−	0.356645i
$373$	−2.88148	−	21.8870i	−0.149198	−	1.13327i	−0.888164	−	0.459526i	$-0.848019\pi$
$373$	−2.88148	−	21.8870i	−0.149198	−	1.13327i	0.738967	−	0.673742i	$-0.235314\pi$
$374$	6.37205	+	14.6235i	0.329491	+	0.756163i
$375$	−6.26930	−	1.58000i	−0.323745	−	0.0815908i
$376$	0.203469	+	0.621261i	0.0104931	+	0.0320391i
$377$	25.7895	+	25.7895i	1.32823	+	1.32823i
$378$	4.59075	−	13.4154i	0.236123	−	0.690015i
$379$	11.7800	−	28.4394i	0.605097	−	1.46083i	−0.263177	−	0.964748i	$-0.584770\pi$
$379$	11.7800	−	28.4394i	0.605097	−	1.46083i	0.868274	−	0.496085i	$-0.165230\pi$
$380$	0.105886	+	2.90232i	0.00543186	+	0.148886i
$381$	−14.1645	−	10.5368i	−0.725669	−	0.539819i
$382$	−3.36516	+	3.49017i	−0.172176	+	0.178572i
$383$	−6.87223	−	11.9031i	−0.351155	−	0.608217i	0.635298	−	0.772267i	$-0.280877\pi$
$383$	−6.87223	−	11.9031i	−0.351155	−	0.608217i	−0.986452	+	0.164050i	$0.947544\pi$
$384$	13.6940	−	14.0170i	0.698818	−	0.715299i
$385$	−1.09743	+	1.90080i	−0.0559302	+	0.0968739i
$386$	7.36651	+	25.6146i	0.374945	+	1.30375i
$387$	17.3125	+	12.4818i	0.880044	+	0.634484i
$388$	21.2923	−	13.3512i	1.08095	−	0.677803i
$389$	−16.3364	−	21.2901i	−0.828290	−	1.07945i	−0.995615	−	0.0935469i	$-0.970180\pi$
$389$	−16.3364	−	21.2901i	−0.828290	−	1.07945i	0.167325	−	0.985902i	$-0.446487\pi$
$390$	4.38765	−	0.726331i	0.222177	−	0.0367792i
$391$	6.20455	−	23.1557i	0.313778	−	1.17103i
$392$	−9.07036	−	1.90578i	−0.458122	−	0.0962566i
$393$	9.15278	+	32.2276i	0.461696	+	1.62567i
$394$	17.2845	−	23.3968i	0.870781	−	1.17872i
$395$	−1.29675	−	0.537130i	−0.0652465	−	0.0270260i
$396$	7.98470	+	16.1565i	0.401246	+	0.811896i
$397$	−1.42375	−	3.43724i	−0.0714560	−	0.172510i	0.884116	−	0.467267i	$-0.154761\pi$
$397$	−1.42375	−	3.43724i	−0.0714560	−	0.172510i	−0.955572	+	0.294757i	$0.904761\pi$
$398$	−5.97378	−	9.92449i	−0.299438	−	0.497470i
$399$	0.191176	+	12.8134i	0.00957076	+	0.641474i
$400$	−14.7009	−	12.6990i	−0.735047	−	0.634950i
$401$	2.99858	−	1.73123i	0.149742	−	0.0864535i	−0.423257	−	0.906010i	$-0.639113\pi$
$401$	2.99858	−	1.73123i	0.149742	−	0.0864535i	0.572999	+	0.819556i	$0.305780\pi$
$402$	0.577214	+	17.4045i	0.0287888	+	0.868059i
$403$	11.4606	+	1.50881i	0.570891	+	0.0751592i
$404$	5.38356	+	31.8653i	0.267842	+	1.58536i
$405$	2.57548	−	2.23246i	0.127977	−	0.110932i
$406$	−2.33387	+	20.6272i	−0.115828	+	1.02371i
$407$	5.12279	+	19.1185i	0.253927	+	0.947669i
$408$	18.0282	−	3.66424i	0.892529	−	0.181407i
$409$	5.81522	−	21.7027i	0.287544	−	1.07313i	−0.659416	−	0.751778i	$-0.729196\pi$
$409$	5.81522	−	21.7027i	0.287544	−	1.07313i	0.946960	−	0.321351i	$-0.104137\pi$
$410$	2.12012	+	0.833228i	0.104705	+	0.0411502i
$411$	−0.634954	+	1.60002i	−0.0313200	+	0.0789233i
$412$	−16.4055	+	17.6479i	−0.808243	+	0.869451i
$413$	−20.7901	+	8.61155i	−1.02301	+	0.423747i
$414$	5.74465	−	26.4678i	0.282334	−	1.30082i
$415$	2.96906			0.145745
$416$	25.8969	+	8.05432i	1.26970	+	0.394895i
$417$	3.76600	−	6.75362i	0.184422	−	0.330726i
$418$	−11.7253	−	11.3054i	−0.573505	−	0.552963i
$419$	22.5687	+	17.3176i	1.10255	+	0.846018i	0.989059	−	0.147520i	$-0.0471292\pi$
$419$	22.5687	+	17.3176i	1.10255	+	0.846018i	0.113494	+	0.993539i	$0.463796\pi$
$420$	1.87949	+	1.69562i	0.0917098	+	0.0827377i
$421$	7.80358	+	10.1698i	0.380323	+	0.495647i	0.943815	−	0.330475i	$-0.107209\pi$
$421$	7.80358	+	10.1698i	0.380323	+	0.495647i	−0.563492	+	0.826122i	$0.690542\pi$
$422$	11.8838	−	9.46797i	0.578496	−	0.460894i
$423$	−0.159401	+	0.674817i	−0.00775033	+	0.0328107i
$424$	−4.11297	−	8.57133i	−0.199744	−	0.416260i
$425$	−4.72024	−	17.6162i	−0.228965	−	0.854509i
$426$	1.01740	−	10.3753i	0.0492930	−	0.502684i
$427$	−2.02342	−	15.3694i	−0.0979200	−	0.743776i
$428$	5.20234	+	6.29091i	0.251465	+	0.304083i
$429$	−14.8869	+	20.0122i	−0.718746	+	0.966198i
$430$	−3.26446	+	1.96496i	−0.157426	+	0.0947586i
$431$		−	34.0824i		−	1.64169i	−0.571151	−	0.820845i	$-0.693503\pi$
$431$		−	34.0824i		−	1.64169i	0.571151	−	0.820845i	$-0.306497\pi$
$432$	20.1457	−	5.11381i	0.969260	−	0.246038i
$433$			27.5984i			1.32630i	0.748489	+	0.663148i	$0.230780\pi$
$433$			27.5984i			1.32630i	−0.748489	+	0.663148i	$0.769220\pi$
$434$	3.39301	+	5.63696i	0.162870	+	0.270583i
$435$	−2.97831	+	4.00370i	−0.142799	+	0.191963i
$436$	2.92014	−	30.8311i	0.139850	−	1.47654i
$437$	3.19503	+	24.2686i	0.152839	+	1.16093i
$438$	−28.0774	−	2.75327i	−1.34159	−	0.131556i
$439$	−0.115872	−	0.432440i	−0.00553027	−	0.0206392i	0.963106	−	0.269124i	$-0.0867341\pi$
$439$	−0.115872	−	0.432440i	−0.00553027	−	0.0206392i	−0.968636	+	0.248485i	$0.920067\pi$
$440$	−3.21254	+	0.175904i	−0.153152	+	0.00838589i
$441$	−7.15559	−	6.74083i	−0.340743	−	0.320992i
$442$	15.8654	+	19.9136i	0.754638	+	0.947192i
$443$	−5.65020	−	7.36349i	−0.268449	−	0.349850i	0.639604	−	0.768705i	$-0.279098\pi$
$443$	−5.65020	−	7.36349i	−0.268449	−	0.349850i	−0.908053	+	0.418855i	$0.862432\pi$
$444$	22.7970	−	1.17248i	1.08190	−	0.0556435i
$445$	−0.499210	−	0.383058i	−0.0236648	−	0.0181587i
$446$	−5.86602	+	6.08394i	−0.277764	+	0.288083i
$447$	12.1872	−	21.8555i	0.576434	−	1.03373i
$448$	5.59929	+	14.3850i	0.264542	+	0.679627i
$449$	2.70594			0.127701			0.0638505	−	0.997959i	$-0.479662\pi$
$449$	2.70594			0.127701			0.0638505	+	0.997959i	$0.479662\pi$
$450$	−6.28311	−	19.6234i	−0.296189	−	0.925055i
$451$	−11.8031	+	4.88900i	−0.555786	+	0.230214i
$452$	1.12328	−	0.0409811i	0.0528347	−	0.00192759i
$453$	9.57800	−	24.1356i	0.450014	−	1.13399i
$454$	9.27574	−	23.6018i	0.435332	−	1.10769i
$455$	−0.906727	+	3.38395i	−0.0425080	+	0.158642i
$456$	−15.5753	+	10.5013i	−0.729380	+	0.491768i
$457$	7.35456	+	27.4476i	0.344032	+	1.28394i	0.893739	+	0.448587i	$0.148073\pi$
$457$	7.35456	+	27.4476i	0.344032	+	1.28394i	−0.549707	+	0.835357i	$0.685261\pi$
$458$	−32.6110	−	3.68977i	−1.52381	−	0.172412i
$459$	18.3435	+	6.65316i	0.856200	+	0.310543i
$460$	3.94076	+	2.80165i	0.183739	+	0.130627i
$461$	21.0010	+	2.76483i	0.978113	+	0.128771i	0.602598	−	0.798045i	$-0.294132\pi$
$461$	21.0010	+	2.76483i	0.978113	+	0.128771i	0.375515	+	0.926816i	$0.377466\pi$
$462$	−14.1886	+	0.470560i	−0.660114	+	0.0218924i
$463$	−23.7829	+	13.7311i	−1.10529	+	0.638137i	−0.937604	−	0.347704i	$-0.886961\pi$
$463$	−23.7829	+	13.7311i	−1.10529	+	0.638137i	−0.167681	+	0.985841i	$0.553628\pi$
$464$	−27.1899	+	13.6625i	−1.26226	+	0.634266i
$465$	0.0235938	+	1.58136i	0.00109413	+	0.0733337i
$466$	31.4966	−	18.9585i	1.45905	−	0.878237i
$467$	4.71882	+	11.3922i	0.218361	+	0.527170i	0.994661	−	0.103193i	$-0.0329059\pi$
$467$	4.71882	+	11.3922i	0.218361	+	0.527170i	−0.776300	+	0.630363i	$0.782906\pi$
$468$	18.9850	+	21.6109i	0.877582	+	0.998966i
$469$	−12.6734	−	5.24951i	−0.585205	−	0.242400i
$470$	−0.0995641	−	0.0735534i	−0.00459255	−	0.00339276i
$471$	−4.27523	−	15.0534i	−0.196992	−	0.693624i
$472$	−27.2285	−	18.6199i	−1.25329	−	0.857052i
$473$	5.53066	−	20.6407i	0.254300	−	0.949060i
$474$	−1.48267	−	8.95657i	−0.0681012	−	0.411389i
$475$	11.3365	+	14.7740i	0.520153	+	0.677876i
$476$	−3.23789	+	14.1254i	−0.148408	+	0.647436i
$477$	1.01735	−	10.0323i	0.0465813	−	0.459348i
$478$	6.70652	−	1.92873i	0.306749	−	0.0882180i
$479$	−3.93035	+	6.80757i	−0.179582	+	0.311046i	−0.941738	−	0.336349i	$-0.890808\pi$
$479$	−3.93035	+	6.80757i	−0.179582	+	0.311046i	0.762155	+	0.647394i	$0.224141\pi$
$480$	−0.575448	+	3.66567i	−0.0262655	+	0.167314i
$481$	15.7962	+	27.3599i	0.720246	+	1.24750i
$482$	−24.2338	−	23.3658i	−1.10382	−	1.06428i
$483$	17.1180	+	12.7339i	0.778897	+	0.579414i
$484$	−2.69358	+	2.89757i	−0.122436	+	0.131708i
$485$	−1.82113	+	4.39659i	−0.0826931	+	0.199639i
$486$	21.0616	+	6.51215i	0.955375	+	0.295397i
$487$	8.35844	+	8.35844i	0.378757	+	0.378757i	0.870654	−	0.491897i	$-0.163696\pi$
$487$	8.35844	+	8.35844i	0.378757	+	0.378757i	−0.491897	+	0.870654i	$0.663696\pi$
$488$	17.2446	−	14.7983i	0.780628	−	0.669886i
$489$	32.2489	+	8.12742i	1.45835	+	0.367535i
$490$	1.60890	−	0.701063i	0.0726827	−	0.0316708i
$491$	0.786307	+	5.97260i	0.0354856	+	0.269540i	0.999985	+	0.00545513i	$0.00173643\pi$
$491$	0.786307	+	5.97260i	0.0354856	+	0.269540i	−0.964500	+	0.264084i	$0.914930\pi$
$492$	2.67095	+	14.4899i	0.120416	+	0.653256i
$493$	−28.3231	−	3.72880i	−1.27561	−	0.167937i
$494$	−22.7481	−	12.5863i	−1.02348	−	0.566283i
$495$	−3.00491	−	1.61733i	−0.135061	−	0.0726936i
$496$	−4.20074	+	8.68146i	−0.188619	+	0.389809i
$497$	7.11191	+	4.10606i	0.319013	+	0.184182i
$498$	10.1480	+	16.3037i	0.454741	+	0.730587i
$499$	−6.42641	+	8.37506i	−0.287686	+	0.374919i	−0.914731	−	0.404064i	$-0.867597\pi$
$499$	−6.42641	+	8.37506i	−0.287686	+	0.374919i	0.627045	+	0.778983i	$0.284264\pi$
$500$	7.43226	+	0.703940i	0.332381	+	0.0314812i
$501$	−9.74963	+	7.71494i	−0.435581	+	0.344678i
$502$	−18.8541	+	25.5214i	−0.841498	+	1.13908i
$503$	23.9705	−	23.9705i	1.06879	−	1.06879i	0.0713393	−	0.997452i	$-0.477273\pi$
$503$	23.9705	−	23.9705i	1.06879	−	1.06879i	0.997452	−	0.0713393i	$-0.0227273\pi$
$504$	−2.88706	+	16.1161i	−0.128600	+	0.717870i
$505$	−4.32702	−	4.32702i	−0.192550	−	0.192550i
$506$	−26.8160	+	4.02907i	−1.19212	+	0.179114i
$507$	−6.37927	+	16.0751i	−0.283313	+	0.713921i
$508$	18.0137	+	9.54203i	0.799229	+	0.423359i
$509$	13.6115	+	10.4445i	0.603318	+	0.462942i	0.864697	−	0.502294i	$-0.167510\pi$
$509$	13.6115	+	10.4445i	0.603318	+	0.462942i	−0.261379	+	0.965236i	$0.584177\pi$
$510$	−2.38021	+	2.54350i	−0.105397	+	0.112628i
$511$	11.1118	−	19.2462i	0.491556	−	0.851400i
$512$	−13.1712	+	18.3989i	−0.582089	+	0.813125i
$513$	−19.9043	+	0.891441i	−0.878796	+	0.0393581i
$514$	−10.1344	−	35.2390i	−0.447008	−	1.55433i
$515$	0.595534	−	4.52353i	0.0262424	−	0.199330i
$516$	−21.9476	−	11.2098i	−0.966189	−	0.493484i
$517$	0.688292	−	0.0906153i	0.0302710	−	0.00398526i
$518$	−6.57724	+	16.7356i	−0.288987	+	0.735319i
$519$	−19.9060	−	19.3207i	−0.873776	−	0.848086i
$520$	−4.88030	+	1.59834i	−0.214015	+	0.0700921i
$521$	1.65153	−	1.65153i	0.0723550	−	0.0723550i	−0.670003	−	0.742358i	$-0.733707\pi$
$521$	1.65153	−	1.65153i	0.0723550	−	0.0723550i	0.742358	+	0.670003i	$0.233707\pi$
$522$	−32.1647	−	2.67026i	−1.40781	−	0.116874i
$523$	40.4596	+	16.7589i	1.76917	+	0.732816i	0.995004	+	0.0998391i	$0.0318328\pi$
$523$	40.4596	+	16.7589i	1.76917	+	0.732816i	0.774171	+	0.632977i	$0.218167\pi$
$524$	−16.0973	−	35.1767i	−0.703213	−	1.53670i
$525$	16.1219	+	1.87827i	0.703619	+	0.0819743i
$526$	40.2687	−	0.734325i	1.75580	−	0.0320181i
$527$	−7.84119	+	4.52711i	−0.341567	+	0.197204i
$528$	−11.9461	−	17.0395i	−0.519886	−	0.741548i
$529$	15.3741	+	8.87625i	0.668440	+	0.385924i
$530$	1.57517	+	0.871524i	0.0684209	+	0.0378566i
$531$	−14.3474	−	31.9101i	−0.622624	−	1.38478i
$532$	−2.46504	−	14.5906i	−0.106873	−	0.632581i
$533$	−16.1778	+	12.4137i	−0.700740	+	0.537697i
$534$	0.397193	−	4.05052i	0.0171882	−	0.175283i
$535$	−1.49309	−	0.400071i	−0.0645517	−	0.0172966i
$536$	−3.71068	−	19.7627i	−0.160277	−	0.853620i
$537$	−5.08930	+	20.1939i	−0.219620	+	0.871431i
$538$	−2.77765	−	18.4870i	−0.119753	−	0.797030i
$539$	−3.76660	+	9.09337i	−0.162239	+	0.391679i
$540$	−2.54795	+	2.99953i	−0.109646	+	0.129079i
$541$	−3.88648	+	1.60983i	−0.167093	+	0.0692120i	−0.464662	−	0.885488i	$-0.653824\pi$
$541$	−3.88648	+	1.60983i	−0.167093	+	0.0692120i	0.297569	+	0.954700i	$0.403824\pi$
$542$	−7.82129	+	31.4741i	−0.335953	+	1.35193i
$543$	−12.4259	−	20.7994i	−0.533248	−	0.892589i
$544$	−19.9332	+	7.34329i	−0.854629	+	0.314841i
$545$	2.93206	+	5.07847i	0.125596	+	0.217538i
$546$	−21.6811	+	6.58700i	−0.927864	+	0.281898i
$547$	4.51534	−	34.2974i	0.193062	−	1.46645i	−0.570809	−	0.821083i	$-0.693370\pi$
$547$	4.51534	−	34.2974i	0.193062	−	1.46645i	0.763871	−	0.645369i	$-0.223296\pi$
$548$	0.444114	−	1.93746i	0.0189716	−	0.0827641i
$549$	23.7914	−	3.85745i	1.01539	−	0.164632i
$550$	−16.1350	+	12.8549i	−0.688000	+	0.548137i
$551$	28.1759	−	7.54972i	1.20034	−	0.321629i
$552$	−1.91527	+	31.2153i	−0.0815193	+	1.32861i
$553$	6.90771	+	1.85091i	0.293746	+	0.0787089i
$554$	−15.1452	+	6.59939i	−0.643459	+	0.280381i
$555$	−3.38956	+	2.68218i	−0.143879	+	0.113852i
$556$	−3.11392	+	8.36834i	−0.132059	+	0.354897i
$557$	6.56962	+	15.8605i	0.278364	+	0.672029i	0.999791	−	0.0204613i	$-0.00651350\pi$
$557$	6.56962	+	15.8605i	0.278364	+	0.672029i	−0.721427	+	0.692490i	$0.756513\pi$
$558$	−8.60292	+	5.53449i	−0.364191	+	0.234294i
$559$		−	34.1078i		−	1.44261i
$560$	−2.44241	−	1.60565i	−0.103211	−	0.0678513i
$561$	−0.291451	−	19.5343i	−0.0123051	−	0.824740i
$562$	16.4422	−	0.299834i	0.693573	−	0.0126477i
$563$	−7.16341	+	9.33554i	−0.301902	+	0.393446i	−0.919527	−	0.393026i	$-0.871428\pi$
$563$	−7.16341	+	9.33554i	−0.301902	+	0.393446i	0.617625	+	0.786472i	$0.288095\pi$
$564$	0.0635959	−	0.798125i	0.00267787	−	0.0336071i
$565$	−0.168856	+	0.129568i	−0.00710384	+	0.00545097i
$566$	5.14701	+	0.582359i	0.216345	+	0.0244784i
$567$	−11.5253	+	12.9900i	−0.484017	+	0.545529i
$568$	0.658149	+	12.0198i	0.0276153	+	0.504339i
$569$	14.6973	−	3.93812i	0.616141	−	0.165095i	0.0627683	−	0.998028i	$-0.480007\pi$
$569$	14.6973	−	3.93812i	0.616141	−	0.165095i	0.553373	+	0.832934i	$0.313340\pi$
$570$	1.25152	−	3.32952i	0.0524203	−	0.139458i
$571$	4.49158	−	0.591328i	0.187967	−	0.0247463i	−0.0359551	−	0.999353i	$-0.511447\pi$
$571$	4.49158	−	0.591328i	0.187967	−	0.0247463i	0.223922	+	0.974607i	$0.428114\pi$
$572$	13.4814	−	25.4505i	0.563685	−	1.06414i
$573$	5.45137	−	2.35391i	0.227734	−	0.0983361i
$574$	−11.2639	−	2.79907i	−0.470145	−	0.116831i
$575$	31.0033			1.29293
$576$	−22.0957	+	9.36900i	−0.920656	+	0.390375i
$577$	36.8652			1.53472			0.767360	−	0.641217i	$-0.221570\pi$
$577$	36.8652			1.53472			0.767360	+	0.641217i	$0.221570\pi$
$578$	3.97774	+	0.988465i	0.165452	+	0.0411147i
$579$	3.77747	−	32.4236i	0.156986	−	1.34748i
$580$	2.69712	−	5.09170i	0.111992	−	0.211421i
$581$	−14.9981	+	1.97454i	−0.622228	+	0.0819179i
$582$	−30.3670	+	5.02695i	−1.25875	+	0.208374i
$583$	−9.75202	+	2.61304i	−0.403887	+	0.108221i
$584$	32.5278	−	1.78107i	1.34601	−	0.0737014i
$585$	−5.30100	−	1.25217i	−0.219169	−	0.0517708i
$586$	−2.94708	−	0.333448i	−0.121743	−	0.0137746i
$587$	14.4757	−	11.1076i	0.597476	−	0.458459i	−0.265216	−	0.964189i	$-0.585443\pi$
$587$	14.4757	−	11.1076i	0.597476	−	0.458459i	0.862692	+	0.505730i	$0.168777\pi$
$588$	9.34875	+	6.43863i	0.385536	+	0.265525i
$589$	5.62809	−	7.33467i	0.231902	−	0.302220i
$590$	6.24503	−	0.113882i	0.257104	−	0.00468845i
$591$	−30.5843	+	18.2716i	−1.25807	+	0.751592i
$592$	−25.8128	+	5.33564i	−1.06090	+	0.219293i
$593$		−	20.9154i		−	0.858893i	−0.903092	−	0.429447i	$-0.858709\pi$
$593$		−	20.9154i		−	0.858893i	0.903092	−	0.429447i	$-0.141291\pi$
$594$	−1.38941	−	22.0285i	−0.0570083	−	0.903839i
$595$	−1.05011	−	2.53518i	−0.0430502	−	0.103932i
$596$	−10.0770	+	27.0809i	−0.412769	+	1.10928i
$597$	2.06141	+	14.0365i	0.0843679	+	0.574475i
$598$	−39.6794	+	17.2899i	−1.62261	+	0.707038i
$599$	9.56655	+	2.56335i	0.390879	+	0.104736i	0.448905	−	0.893579i	$-0.351814\pi$
$599$	9.56655	+	2.56335i	0.390879	+	0.104736i	−0.0580265	+	0.998315i	$0.518481\pi$
$600$	10.6119	+	21.2946i	0.433231	+	0.869348i
$601$	−27.4696	+	7.36046i	−1.12051	+	0.300239i	−0.771089	−	0.636727i	$-0.780288\pi$
$601$	−27.4696	+	7.36046i	−1.12051	+	0.300239i	−0.349420	+	0.936966i	$0.613621\pi$
$602$	15.1836	−	12.0969i	0.618837	−	0.493034i
$603$	7.57033	−	19.9391i	0.308288	−	0.811981i
$604$	−6.69926	+	29.2257i	−0.272589	+	1.18918i
$605$	0.0977792	−	0.742707i	0.00397529	−	0.0301953i
$606$	8.97119	−	38.5499i	0.364430	−	1.56598i
$607$	−5.03047	−	8.71302i	−0.204180	−	0.353651i	0.745691	−	0.666292i	$-0.232120\pi$
$607$	−5.03047	−	8.71302i	−0.204180	−	0.353651i	−0.949871	+	0.312641i	$0.898786\pi$
$608$	15.9348	−	14.7164i	0.646242	−	0.596827i
$609$	12.3823	−	22.2053i	0.501755	−	0.899803i
$610$	−1.03769	+	4.17582i	−0.0420147	+	0.169074i
$611$	1.02375	−	0.424050i	0.0414164	−	0.0171552i
$612$	−22.1022	−	4.37676i	−0.893429	−	0.176920i
$613$	−17.9837	+	43.4164i	−0.726353	+	1.75357i	−0.0719718	+	0.997407i	$0.522929\pi$
$613$	−17.9837	+	43.4164i	−0.726353	+	1.75357i	−0.654381	+	0.756165i	$0.727071\pi$
$614$	−3.61761	−	24.0774i	−0.145995	−	0.971687i
$615$	−2.00200	−	1.94314i	−0.0807284	−	0.0783548i
$616$	16.1111	−	3.02504i	0.649134	−	0.121882i
$617$	−25.7113	−	6.88933i	−1.03510	−	0.277354i	−0.299018	−	0.954248i	$-0.596659\pi$
$617$	−25.7113	−	6.88933i	−1.03510	−	0.277354i	−0.736081	+	0.676894i	$0.763326\pi$
$618$	26.8751	−	12.1908i	1.08107	−	0.490386i
$619$	−25.1356	+	19.2872i	−1.01029	+	0.775220i	−0.974557	−	0.224142i	$-0.928042\pi$
$619$	−25.1356	+	19.2872i	−1.01029	+	0.775220i	−0.0357296	+	0.999361i	$0.511376\pi$
$620$	−0.304220	−	1.80068i	−0.0122178	−	0.0723171i
$621$	−18.9956	+	27.1935i	−0.762267	+	1.09124i
$622$	−20.5174	−	11.3521i	−0.822674	−	0.455177i
$623$	2.77650	+	1.60301i	0.111238	+	0.0642233i
$624$	−25.4572	−	21.3357i	−1.01910	−	0.854112i
$625$	19.8054	−	11.4346i	0.792215	−	0.457386i
$626$	14.2199	−	0.259309i	0.568342	−	0.0103641i
$627$	7.90805	+	18.3141i	0.315817	+	0.731393i
$628$	7.51899	+	16.4309i	0.300040	+	0.655665i
$629$	−22.8619	−	9.46972i	−0.911565	−	0.377583i
$630$	−1.32267	−	2.80392i	−0.0526964	−	0.111711i
$631$	28.8464	−	28.8464i	1.14836	−	1.14836i	0.161481	−	0.986876i	$-0.448373\pi$
$631$	28.8464	−	28.8464i	1.14836	−	1.14836i	0.986876	−	0.161481i	$-0.0516270\pi$
$632$	3.26272	+	9.96222i	0.129784	+	0.396276i
$633$	−17.9012	+	5.08403i	−0.711510	+	0.202072i
$634$	−5.89687	+	15.0044i	−0.234195	+	0.595901i
$635$	−3.82693	+	0.503825i	−0.151867	+	0.0199937i
$636$	0.598062	+	11.6284i	0.0237147	+	0.461094i
$637$	−2.05060	+	15.5758i	−0.0812477	+	0.617138i
$638$	8.93135	+	31.0558i	0.353596	+	1.22951i
$639$	−6.05129	+	11.2430i	−0.239385	+	0.444765i
$640$	0.0139866	−	4.28456i	0.000552869	−	0.169362i
$641$	−9.90198	+	17.1507i	−0.391105	+	0.677413i	−0.992596	−	0.121466i	$-0.961240\pi$
$641$	−9.90198	+	17.1507i	−0.391105	+	0.677413i	0.601491	+	0.798880i	$0.294574\pi$
$642$	−2.90635	−	9.56624i	−0.114705	−	0.377549i
$643$	−4.74013	−	3.63723i	−0.186933	−	0.143438i	0.511056	−	0.859548i	$-0.329255\pi$
$643$	−4.74013	−	3.63723i	−0.186933	−	0.143438i	−0.697988	+	0.716109i	$0.745921\pi$
$644$	−21.7699	−	11.5317i	−0.857852	−	0.454412i
$645$	4.61702	−	0.678060i	0.181795	−	0.0266986i
$646$	20.1374	−	3.02563i	0.792297	−	0.119042i
$647$	7.04874	+	7.04874i	0.277115	+	0.277115i	0.831956	−	0.554842i	$-0.187221\pi$
$647$	7.04874	+	7.04874i	0.277115	+	0.277115i	−0.554842	+	0.831956i	$0.687221\pi$
$648$	−25.1797	−	3.73920i	−0.989153	−	0.146890i
$649$	−24.7698	+	24.7698i	−0.972299	+	0.972299i
$650$	−19.5658	+	26.4849i	−0.767434	+	1.03882i
$651$	−1.17085	−	7.97251i	−0.0458892	−	0.312467i
$652$	−38.2311	−	3.62103i	−1.49725	−	0.141810i
$653$	−17.3055	+	22.5530i	−0.677218	+	0.882568i	−0.997910	−	0.0646154i	$-0.979418\pi$
$653$	−17.3055	+	22.5530i	−0.677218	+	0.882568i	0.320692	+	0.947184i	$0.396085\pi$
$654$	−17.8654	+	33.4583i	−0.698593	+	1.30832i
$655$	6.34374	+	3.66256i	0.247871	+	0.143108i
$656$	−5.58920	−	16.0691i	−0.218222	−	0.627393i
$657$	30.4255	+	16.3759i	1.18701	+	0.638885i
$658$	0.551862	+	0.305339i	0.0215138	+	0.0119034i
$659$	−10.1311	−	1.33378i	−0.394650	−	0.0519567i	−0.0694102	−	0.997588i	$-0.522112\pi$
$659$	−10.1311	−	1.33378i	−0.394650	−	0.0519567i	−0.325240	+	0.945632i	$0.605445\pi$
$660$	3.71313	+	1.31896i	0.144533	+	0.0513404i
$661$	4.70903	+	35.7687i	0.183160	+	1.39124i	0.798033	+	0.602613i	$0.205874\pi$
$661$	4.70903	+	35.7687i	0.183160	+	1.39124i	−0.614873	+	0.788626i	$0.710793\pi$
$662$	−31.0091	+	13.5119i	−1.20520	+	0.525156i
$663$	−8.51925	−	29.9969i	−0.330860	−	1.16498i
$664$	−14.4408	−	16.8281i	−0.560413	−	0.653058i
$665$	1.98126	+	1.98126i	0.0768301	+	0.0768301i
$666$	−26.3136	−	9.44531i	−1.01963	−	0.365998i
$667$	18.5845	−	44.8670i	0.719596	−	1.73726i
$668$	9.77452	−	10.5147i	0.378187	−	0.406827i
$669$	9.50263	−	4.10326i	0.367393	−	0.158641i
$670$	2.74098	+	2.64280i	0.105893	+	0.102100i
$671$	−12.0657	−	20.8984i	−0.465792	−	0.806776i
$672$	0.469051	−	18.8997i	0.0180941	−	0.729073i
$673$	−1.86343	+	3.22756i	−0.0718301	+	0.124413i	−0.899703	−	0.436502i	$-0.856217\pi$
$673$	−1.86343	+	3.22756i	−0.0718301	+	0.124413i	0.827873	+	0.560915i	$0.189551\pi$
$674$	37.1588	−	10.6865i	1.43130	−	0.411629i
$675$	−2.17118	+	25.1420i	−0.0835688	+	0.967714i
$676$	4.46193	−	19.4653i	0.171613	−	0.748665i
$677$	−14.3327	−	18.6787i	−0.550850	−	0.717882i	0.432085	−	0.901833i	$-0.357778\pi$
$677$	−14.3327	−	18.6787i	−0.550850	−	0.717882i	−0.982935	+	0.183951i	$0.941111\pi$
$678$	−1.28862	−	0.484373i	−0.0494891	−	0.0186022i
$679$	6.27548	−	23.4204i	0.240831	−	0.898792i
$680$	2.27055	−	3.32029i	0.0870715	−	0.127327i
$681$	−21.6316	+	22.2868i	−0.828924	+	0.854033i
$682$	8.23774	+	6.08566i	0.315439	+	0.233032i
$683$	−29.5763	−	12.2509i	−1.13170	−	0.468767i	−0.263344	−	0.964702i	$-0.584826\pi$
$683$	−29.5763	−	12.2509i	−1.13170	−	0.468767i	−0.868360	+	0.495935i	$0.834826\pi$
$684$	22.5606	−	4.50764i	0.862627	−	0.172354i
$685$	0.144034	+	0.347730i	0.00550327	+	0.0132861i
$686$	−24.0266	+	14.4621i	−0.917338	+	0.552167i
$687$	35.1058	+	19.5759i	1.33937	+	0.746868i
$688$	27.0146	+	8.94530i	1.02992	+	0.341037i
$689$	−13.9558	+	8.05739i	−0.531674	+	0.306962i
$690$	−3.12928	−	5.02750i	−0.119130	−	0.191394i
$691$	−12.8011	−	1.68530i	−0.486977	−	0.0641117i	−0.116960	−	0.993137i	$-0.537315\pi$
$691$	−12.8011	−	1.68530i	−0.486977	−	0.0641117i	−0.370017	+	0.929025i	$0.620648\pi$
$692$	26.1068	+	18.5604i	0.992431	+	0.705560i
$693$	16.2548	+	6.17152i	0.617470	+	0.234437i
$694$	37.3839	+	4.22981i	1.41907	+	0.160561i
$695$	−0.437591	−	1.63311i	−0.0165988	−	0.0619475i
$696$	37.1781	−	2.59252i	1.40923	−	0.0982690i
$697$	4.13394	−	15.4281i	0.156584	−	0.584380i
$698$	5.13893	−	13.0758i	0.194511	−	0.494928i
$699$	−44.5465	+	6.54214i	−1.68490	+	0.247447i
$700$	−18.7295	+	0.683315i	−0.707907	+	0.0258269i
$701$	18.2158	−	7.54525i	0.688003	−	0.284980i	−0.0111650	−	0.999938i	$-0.503554\pi$
$701$	18.2158	−	7.54525i	0.688003	−	0.284980i	0.699168	+	0.714958i	$0.253554\pi$
$702$	−11.2424	−	33.3886i	−0.424317	−	1.26017i
$703$	25.2674			0.952978
$704$	16.6220	+	17.3525i	0.626467	+	0.653998i
$705$	0.0777537	+	0.130150i	0.00292837	+	0.00490173i
$706$	−21.8697	+	22.6821i	−0.823076	+	0.853653i
$707$	24.7355	+	18.9802i	0.930273	+	0.713823i
$708$	21.9703	+	33.9035i	0.825693	+	1.27417i
$709$	0.809796	+	1.05535i	0.0304125	+	0.0396344i	0.808312	−	0.588754i	$-0.200381\pi$
$709$	0.809796	+	1.05535i	0.0304125	+	0.0396344i	−0.777900	+	0.628389i	$0.783715\pi$
$710$	−1.42035	−	1.78277i	−0.0533049	−	0.0669062i
$711$	−2.55607	+	10.8210i	−0.0958600	+	0.405819i
$712$	0.256942	+	4.69254i	0.00962932	+	0.175860i
$713$	−3.98371	−	14.8674i	−0.149191	−	0.556789i
$714$	10.3320	−	14.4314i	0.386667	−	0.540081i
$715$	0.711826	+	5.40685i	0.0266208	+	0.202205i
$716$	2.26745	−	23.9399i	0.0847385	−	0.894676i
$717$	−8.48928	−	0.989033i	−0.317038	−	0.0369361i
$718$	7.04176	+	11.6988i	0.262796	+	0.436594i
$719$			18.7893i			0.700723i	0.936615	+	0.350362i	$0.113941\pi$
$719$			18.7893i			0.700723i	−0.936615	+	0.350362i	$0.886059\pi$
$720$	2.38203	−	3.87018i	0.0887730	−	0.144233i
$721$			23.2466i			0.865747i
$722$	5.20671	−	3.13404i	0.193774	−	0.116637i
$723$	16.3443	+	37.8513i	0.607850	+	1.40771i
$724$	17.8290	+	21.5597i	0.662610	+	0.801259i
$725$	−4.82240	−	36.6297i	−0.179099	−	1.36039i
$726$	4.41255	−	2.00158i	0.163765	−	0.0742854i
$727$	−11.3116	−	42.2153i	−0.419522	−	1.56568i	−0.775601	−	0.631223i	$-0.782553\pi$
$727$	−11.3116	−	42.2153i	−0.419522	−	1.56568i	0.356079	−	0.934456i	$-0.384113\pi$
$728$	23.5898	−	11.3196i	0.874294	−	0.419532i
$729$	−20.7221	−	17.3088i	−0.767487	−	0.641065i
$730$	−4.82451	+	3.84374i	−0.178563	+	0.142263i
$731$	16.2635	+	21.1951i	0.601529	+	0.783928i
$732$	−26.4770	+	8.57439i	−0.978617	+	0.316919i
$733$	0.00684455	+	0.00525201i	0.000252809	+	0.000193987i	0.608888	−	0.793256i	$-0.291616\pi$
$733$	0.00684455	+	0.00525201i	0.000252809	+	0.000193987i	−0.608635	+	0.793450i	$0.708283\pi$
$734$	17.6996	+	17.0657i	0.653305	+	0.629905i
$735$	−2.14920	+	0.0320659i	−0.0792743	+	0.00118277i
$736$	−3.28771	−	35.9621i	−0.121186	−	1.32558i
$737$	−21.3538			−0.786576
$738$	3.82752	−	17.6348i	0.140893	−	0.649147i
$739$	−26.6657	+	11.0453i	−0.980914	+	0.406308i	−0.814764	−	0.579793i	$-0.803134\pi$
$739$	−26.6657	+	11.0453i	−0.980914	+	0.406308i	−0.166150	+	0.986101i	$0.553134\pi$
$740$	3.39821	−	3.65555i	0.124921	−	0.134381i
$741$	19.7581	+	24.9690i	0.725833	+	0.917259i
$742$	−8.53653	−	3.35493i	−0.313386	−	0.123164i
$743$	11.7844	−	43.9801i	0.432329	−	1.61347i	−0.315049	−	0.949076i	$-0.602021\pi$
$743$	11.7844	−	43.9801i	0.432329	−	1.61347i	0.747378	−	0.664399i	$-0.231312\pi$
$744$	8.84811	−	7.82509i	0.324387	−	0.286882i
$745$	−1.41609	−	5.28493i	−0.0518817	−	0.193625i
$746$	3.51000	−	31.0221i	0.128510	−	1.13580i
$747$	−3.76428	−	23.2168i	−0.137728	−	0.849458i
$748$	3.75800	+	22.2436i	0.137406	+	0.813306i
$749$	7.80835	+	1.02799i	0.285311	+	0.0375619i
$750$	−8.06556	−	4.30670i	−0.294513	−	0.157258i
$751$	−37.2676	+	21.5164i	−1.35991	+	0.785146i	−0.989612	−	0.143766i	$-0.954079\pi$
$751$	−37.2676	+	21.5164i	−1.35991	+	0.785146i	−0.370301	+	0.928912i	$0.620745\pi$
$752$	0.0673693	+	0.922059i	0.00245671	+	0.0336240i
$753$	33.3616	−	19.9308i	1.21576	−	0.726317i
$754$	26.5996	+	44.1910i	0.968701	+	1.60934i
$755$	−2.17269	−	5.24535i	−0.0790724	−	0.190898i
$756$	10.8761	−	16.8466i	0.395561	−	0.612704i
$757$	30.1307	+	12.4805i	1.09512	+	0.453613i	0.855789	−	0.517325i	$-0.173072\pi$
$757$	30.1307	+	12.4805i	1.09512	+	0.453613i	0.239330	+	0.970938i	$0.423072\pi$
$758$	25.8672	−	35.0146i	0.939538	−	1.27179i
$759$	32.2044	+	8.11621i	1.16895	+	0.294600i
$760$	−0.844533	+	4.01946i	−0.0306344	+	0.145801i
$761$	5.29400	−	19.7575i	0.191907	−	0.716208i	−0.801138	−	0.598479i	$-0.795772\pi$
$761$	5.29400	−	19.7575i	0.191907	−	0.716208i	0.993046	−	0.117729i	$-0.0375615\pi$
$762$	−15.8467	−	19.2924i	−0.574065	−	0.698891i
$763$	−18.1886	−	23.7039i	−0.658472	−	0.858137i
$764$	−5.80893	+	3.64244i	−0.210160	+	0.131779i
$765$	3.89118	−	1.74955i	0.140686	−	0.0632550i
$766$	−5.37231	−	18.6804i	−0.194109	−	0.674951i
$767$	−27.9564	+	48.4219i	−1.00945	+	1.74841i
$768$	23.5752	−	14.5674i	0.850697	−	0.525657i
$769$	−6.87367	−	11.9056i	−0.247871	−	0.429325i	0.715064	−	0.699059i	$-0.246398\pi$
$769$	−6.87367	−	11.9056i	−0.247871	−	0.429325i	−0.962935	+	0.269734i	$0.913064\pi$
$770$	−2.15448	+	2.23451i	−0.0776420	+	0.0805262i
$771$	−5.19681	+	44.6064i	−0.187159	+	1.60646i
$772$	1.37425	+	37.6677i	0.0494602	+	1.35569i
$773$	6.80001	−	16.4167i	0.244579	−	0.590467i	−0.753148	−	0.657852i	$-0.771465\pi$
$773$	6.80001	−	16.4167i	0.244579	−	0.590467i	0.997727	+	0.0673845i	$0.0214654\pi$
$774$	19.5039	+	23.0355i	0.701053	+	0.827992i
$775$	−8.27999	−	8.27999i	−0.297426	−	0.297426i
$776$	33.7766	−	11.0622i	1.21251	−	0.397109i
$777$	15.3385	−	15.8031i	0.550266	−	0.566935i
$778$	−15.1601	−	34.7917i	−0.543518	−	1.24734i
$779$	2.12877	+	16.1696i	0.0762710	+	0.579336i
$780$	6.26964	+	0.499575i	0.224489	+	0.0178877i
$781$	12.6742	+	1.66859i	0.453518	+	0.0597068i
$782$	16.4130	−	29.6644i	0.586928	−	1.06080i
$783$	35.0832	+	18.2131i	1.25377	+	0.650883i
$784$	−11.7988	−	5.70915i	−0.421387	−	0.203898i
$785$	−2.96314	−	1.71077i	−0.105759	−	0.0610600i
$786$	1.57045	+	47.3531i	0.0560159	+	1.68903i
$787$	−15.8591	+	20.6679i	−0.565315	+	0.736732i	−0.985307	−	0.170795i	$-0.945366\pi$
$787$	−15.8591	+	20.6679i	−0.565315	+	0.736732i	0.419992	+	0.907528i	$0.362033\pi$
$788$	31.7022	−	26.2165i	1.12934	−	0.933923i
$789$	−45.8488	−	18.1947i	−1.63226	−	0.647748i
$790$	−1.59656	−	1.17946i	−0.0568029	−	0.0419634i
$791$	0.766806	−	0.766806i	0.0272645	−	0.0272645i
$792$	5.44846	+	24.8976i	0.193603	+	0.884699i
$793$	−27.2359	−	27.2359i	−0.967176	−	0.967176i
$794$	−0.781759	−	5.20309i	−0.0277436	−	0.184651i
$795$	−1.36813	−	1.72895i	−0.0485226	−	0.0613197i
$796$	−4.81401	−	15.6585i	−0.170628	−	0.555000i
$797$	−33.6721	−	25.8375i	−1.19273	−	0.915211i	−0.194881	−	0.980827i	$-0.562432\pi$
$797$	−33.6721	−	25.8375i	−1.19273	−	0.915211i	−0.997845	+	0.0656159i	$0.979099\pi$
$798$	−4.10775	+	17.6513i	−0.145413	+	0.624849i
$799$	−0.433972	+	0.751661i	−0.0153528	+	0.0265919i
$800$	−15.8455	−	22.4429i	−0.560224	−	0.793476i
$801$	−2.36243	+	4.38926i	−0.0834723	+	0.155087i
$802$	4.70591	−	1.35337i	0.166172	−	0.0477893i
$803$	4.51551	−	34.2987i	0.159349	−	1.21037i
$804$	−5.14375	+	24.0841i	−0.181406	+	0.849380i
$805$	4.62491	−	0.608881i	0.163007	−	0.0214602i
$806$	15.2147	+	5.97952i	0.535915	+	0.210620i
$807$	−5.59532	+	22.2017i	−0.196965	+	0.781538i
$808$	−3.47915	+	45.5704i	−0.122396	+	1.60316i
$809$	−16.6760	+	16.6760i	−0.586296	+	0.586296i	−0.936626	−	0.350331i	$-0.886069\pi$
$809$	−16.6760	+	16.6760i	−0.586296	+	0.586296i	0.350331	+	0.936626i	$0.386069\pi$
$810$	4.29617	−	2.18560i	0.150952	−	0.0767940i
$811$	−15.0855	−	6.24861i	−0.529723	−	0.219419i	0.101759	−	0.994809i	$-0.467553\pi$
$811$	−15.0855	−	6.24861i	−0.529723	−	0.219419i	−0.631482	+	0.775391i	$0.717553\pi$
$812$	−10.2383	+	27.5143i	−0.359293	+	0.965563i
$813$	23.7073	−	31.8693i	0.831450	−	1.11770i
$814$	0.510357	+	27.9868i	0.0178880	+	0.980936i
$815$	6.29739	−	3.63580i	0.220588	−	0.127356i
$816$	25.9929	+	1.11959i	0.909934	+	0.0391936i
$817$	−23.6244	−	13.6396i	−0.826515	−	0.477189i
$818$	15.3831	−	27.8030i	0.537858	−	0.972109i
$819$	27.6106	+	2.79992i	0.964793	+	0.0978373i
$820$	2.62563	+	1.86667i	0.0916909	+	0.0651868i
$821$	15.5581	−	11.9382i	0.542983	−	0.416645i	−0.300516	−	0.953777i	$-0.597159\pi$
$821$	15.5581	−	11.9382i	0.542983	−	0.416645i	0.843498	+	0.537132i	$0.180492\pi$
$822$	−1.41716	+	1.97943i	−0.0494291	+	0.0690405i
$823$	18.8514	+	5.05122i	0.657119	+	0.176075i	0.571946	−	0.820292i	$-0.306189\pi$
$823$	18.8514	+	5.05122i	0.657119	+	0.176075i	0.0851737	+	0.996366i	$0.472855\pi$
$824$	−28.5351	+	18.6260i	−0.994067	+	0.648868i
$825$	24.3050	−	6.90274i	0.846193	−	0.240323i
$826$	−31.4709	+	4.72847i	−1.09501	+	0.164524i
$827$	−8.15125	+	19.6789i	−0.283447	+	0.684301i	−0.999911	−	0.0133224i	$-0.995759\pi$
$827$	−8.15125	+	19.6789i	−0.283447	+	0.684301i	0.716464	+	0.697624i	$0.245759\pi$
$828$	16.9114	−	34.3670i	0.587713	−	1.19434i
$829$	3.57589	−	1.48118i	0.124196	−	0.0514436i	−0.319720	−	0.947512i	$-0.603589\pi$
$829$	3.57589	−	1.48118i	0.124196	−	0.0514436i	0.443916	+	0.896068i	$0.353589\pi$
$830$	4.07495	+	1.01262i	0.141444	+	0.0351487i
$831$	20.2313	−	0.301849i	0.701815	−	0.0104710i
$832$	32.7958	+	19.8867i	1.13699	+	0.689447i
$833$	−6.15272	−	10.6568i	−0.213179	−	0.369237i
$834$	7.47211	−	7.98473i	0.258738	−	0.276489i
$835$	−0.354823	+	2.69515i	−0.0122791	+	0.0932693i
$836$	−12.2369	−	19.5153i	−0.423222	−	0.674951i
$837$	12.3356	−	2.18939i	0.426382	−	0.0756765i
$838$	25.0686	+	31.4651i	0.865980	+	1.08694i
$839$	−27.2624	+	7.30494i	−0.941202	+	0.252194i	−0.696625	−	0.717435i	$-0.745316\pi$
$839$	−27.2624	+	7.30494i	−0.941202	+	0.252194i	−0.244577	+	0.969630i	$0.578649\pi$
$840$	2.00124	+	2.96820i	0.0690495	+	0.102413i
$841$	−27.8883	−	7.47265i	−0.961666	−	0.257678i
$842$	7.24169	+	16.6193i	0.249565	+	0.572738i
$843$	−18.7206	−	7.42912i	−0.644773	−	0.255872i
$844$	19.5393	−	8.94145i	0.672572	−	0.307777i
$845$	1.44709	+	3.49357i	0.0497813	+	0.120183i
$846$	−0.448925	+	0.871802i	−0.0154344	+	0.0299732i
$847$			3.81679i			0.131147i
$848$	−2.72161	−	13.1667i	−0.0934606	−	0.452145i
$849$	−5.54077	−	3.08968i	−0.190159	−	0.106038i
$850$	−0.470252	−	25.7876i	−0.0161295	−	0.884506i
$851$	25.6086	−	33.3737i	0.877850	−	1.14404i
$852$	4.93492	−	13.8928i	0.169068	−	0.475959i
$853$	−11.7047	+	8.98132i	−0.400761	+	0.307515i	−0.789404	−	0.613874i	$-0.789610\pi$
$853$	−11.7047	+	8.98132i	−0.400761	+	0.307515i	0.388644	+	0.921388i	$0.372944\pi$
$854$	2.46477	−	21.7841i	0.0843428	−	0.745438i
$855$	−2.98715	+	3.17095i	−0.102158	+	0.108444i
$856$	4.99450	+	10.4084i	0.170708	+	0.355752i
$857$	−41.6515	+	11.1605i	−1.42279	+	0.381235i	−0.886472	−	0.462783i	$-0.846851\pi$
$857$	−41.6515	+	11.1605i	−1.42279	+	0.381235i	−0.536315	+	0.844018i	$0.680184\pi$
$858$	−27.2572	+	22.3889i	−0.930544	+	0.764344i
$859$	−5.16211	+	0.679605i	−0.176129	+	0.0231878i	−0.218075	−	0.975932i	$-0.569978\pi$
$859$	−5.16211	+	0.679605i	−0.176129	+	0.0231878i	0.0419457	+	0.999120i	$0.486644\pi$
$860$	−5.15055	+	1.58347i	−0.175632	+	0.0539960i
$861$	11.4053	+	8.48431i	0.388692	+	0.289144i
$862$	11.6241	−	46.7771i	0.395918	−	1.59323i
$863$	−44.0023			−1.49785			−0.748927	−	0.662652i	$-0.769431\pi$
$863$	−44.0023			−1.49785			−0.748927	+	0.662652i	$0.769431\pi$
$864$	29.3935	−	0.147700i	0.999987	−	0.00502484i
$865$	−6.06539			−0.206229
$866$	−9.41267	+	37.8781i	−0.319856	+	1.28715i
$867$	−4.02768	−	2.99616i	−0.136787	−	0.101755i
$868$	2.73429	+	8.89378i	0.0928077	+	0.301875i
$869$	11.0371	−	1.45306i	0.374407	−	0.0492917i
$870$	−5.45314	+	4.47918i	−0.184879	+	0.151858i
$871$	−32.9224	+	8.82154i	−1.11553	+	0.298906i
$872$	14.5230	−	41.3189i	0.491812	−	1.39923i
$873$	36.6883	+	8.66628i	1.24171	+	0.293309i
$874$	−3.89194	+	34.3977i	−0.131647	+	1.16352i
$875$	5.71413	−	4.38461i	0.193173	−	0.148227i
$876$	−37.5965	−	13.3548i	−1.27027	−	0.451218i
$877$	−2.69327	+	3.50994i	−0.0909454	+	0.118522i	−0.836610	−	0.547800i	$-0.815466\pi$
$877$	−2.69327	+	3.50994i	−0.0909454	+	0.118522i	0.745664	+	0.666322i	$0.232132\pi$
$878$	−0.0115437	−	0.633031i	−0.000389582	−	0.0213638i
$879$	3.17254	+	1.76909i	0.107007	+	0.0596700i
$880$	−4.46911	−	0.854239i	−0.150654	−	0.0287964i
$881$			56.1131i			1.89050i	0.326351	+	0.945249i	$0.394181\pi$
$881$			56.1131i			1.89050i	−0.326351	+	0.945249i	$0.605819\pi$
$882$	−7.52183	−	11.6921i	−0.253273	−	0.393693i
$883$	8.92105	+	21.5373i	0.300217	+	0.724788i	0.999946	+	0.0103800i	$0.00330412\pi$
$883$	8.92105	+	21.5373i	0.300217	+	0.724788i	−0.699729	+	0.714408i	$0.746696\pi$
$884$	14.9831	+	32.7418i	0.503935	+	1.10123i
$885$	−7.11042	−	2.82171i	−0.239014	−	0.0948506i
$886$	−5.24336	−	12.0332i	−0.176154	−	0.404264i
$887$	17.4486	+	4.67535i	0.585868	+	0.156983i	0.539564	−	0.841945i	$-0.318589\pi$
$887$	17.4486	+	4.67535i	0.585868	+	0.156983i	0.0463039	+	0.998927i	$0.485256\pi$
$888$	31.6881	+	6.16591i	1.06338	+	0.206914i
$889$	18.9966	−	5.09012i	0.637126	−	0.170717i
$890$	−0.554507	−	0.695996i	−0.0185871	−	0.0233298i
$891$	−8.83710	+	25.5476i	−0.296054	+	0.855877i
$892$	−10.1259	+	6.34938i	−0.339041	+	0.212593i
$893$	0.115678	−	0.878665i	0.00387103	−	0.0294034i
$894$	24.1806	−	25.8395i	0.808719	−	0.864201i
$895$	2.27670	+	3.94335i	0.0761016	+	0.131812i
$896$	2.77875	+	21.6527i	0.0928315	+	0.723365i
$897$	53.0044	−	0.790823i	1.76977	−	0.0264048i
$898$	3.71382	+	0.922882i	0.123932	+	0.0307970i
$899$	−16.9459	+	7.01922i	−0.565177	+	0.234104i
$900$	−1.93067	−	29.0755i	−0.0643558	−	0.969182i
$901$	4.83034	−	11.6615i	0.160922	−	0.388500i
$902$	−17.8668	+	2.68447i	−0.594901	+	0.0893831i
$903$	−22.8718	+	6.49571i	−0.761127	+	0.216164i
$904$	1.55565	+	0.326859i	0.0517401	+	0.0108712i
$905$	−5.11698	−	1.37109i	−0.170094	−	0.0455766i
$906$	21.3772	−	29.8588i	0.710210	−	0.991992i
$907$	46.9571	−	36.0314i	1.55918	−	1.19640i	0.666701	−	0.745326i	$-0.267706\pi$
$907$	46.9571	−	36.0314i	1.55918	−	1.19640i	0.892484	−	0.451079i	$-0.148961\pi$
$908$	20.7803	−	29.2293i	0.689618	−	0.970007i
$909$	−28.3495	+	39.3213i	−0.940292	+	1.30421i
$910$	−2.39858	+	4.33513i	−0.0795122	+	0.143708i
$911$	4.66680	+	2.69438i	0.154618	+	0.0892688i	0.575313	−	0.817933i	$-0.304880\pi$
$911$	4.66680	+	2.69438i	0.154618	+	0.0892688i	−0.420695	+	0.907202i	$0.638214\pi$
$912$	−24.9582	+	9.10064i	−0.826449	+	0.301352i
$913$	−20.3937	+	11.7743i	−0.674932	+	0.389672i
$914$	0.732697	+	40.1794i	0.0242355	+	1.32902i
$915$	3.14535	−	4.22825i	0.103982	−	0.139782i
$916$	−43.4992	−	16.1864i	−1.43725	−	0.534812i
$917$	−34.4810	−	14.2825i	−1.13866	−	0.471650i
$918$	22.9068	+	15.3875i	0.756037	+	0.507862i
$919$	3.23612	−	3.23612i	0.106750	−	0.106750i	−0.651715	−	0.758464i	$-0.725950\pi$
$919$	3.23612	−	3.23612i	0.106750	−	0.106750i	0.758464	+	0.651715i	$0.225950\pi$
$920$	4.45305	+	5.18921i	0.146813	+	0.171083i
$921$	−7.28735	+	28.9156i	−0.240126	+	0.952800i
$922$	27.8803	+	10.9572i	0.918188	+	0.360857i
$923$	20.2299	−	2.66332i	0.665875	−	0.0876641i
$924$	−19.6340	−	4.19332i	−0.645910	−	0.137950i
$925$	4.17724	−	31.7293i	0.137347	−	1.04325i
$926$	−37.3245	+	10.7341i	−1.22656	+	0.352746i
$927$	−36.1271	+	1.07827i	−1.18657	+	0.0354150i
$928$	−41.9771	+	9.47807i	−1.37796	+	0.311133i
$929$	8.38548	−	14.5241i	0.275119	−	0.476520i	−0.695046	−	0.718965i	$-0.744616\pi$
$929$	8.38548	−	14.5241i	0.275119	−	0.476520i	0.970165	+	0.242445i	$0.0779495\pi$
$930$	−0.506954	+	2.17842i	−0.0166237	+	0.0714331i
$931$	9.96843	+	7.64904i	0.326702	+	0.250687i
$932$	49.6942	−	15.2779i	1.62779	−	0.500443i
$933$	17.8207	+	22.5206i	0.583422	+	0.737290i
$934$	2.59103	+	17.2449i	0.0847811	+	0.564271i
$935$	−3.02047	−	3.02047i	−0.0987800	−	0.0987800i
$936$	18.6858	+	36.1354i	0.610764	+	1.18112i
$937$	−14.2564	+	14.2564i	−0.465736	+	0.465736i	−0.900530	−	0.434794i	$-0.856821\pi$
$937$	−14.2564	+	14.2564i	−0.465736	+	0.465736i	0.434794	+	0.900530i	$0.356821\pi$
$938$	−15.6035	−	11.5272i	−0.509474	−	0.376376i
$939$	−16.1904	−	6.42502i	−0.528354	−	0.209673i
$940$	−0.111563	−	0.134907i	−0.00363878	−	0.00440019i
$941$	−17.8410	+	23.2508i	−0.581599	+	0.757954i	−0.987783	−	0.155837i	$-0.950192\pi$
$941$	−17.8410	+	23.2508i	−0.581599	+	0.757954i	0.406184	+	0.913791i	$0.366859\pi$
$942$	−0.733550	−	22.1185i	−0.0239004	−	0.720659i
$943$	23.5147	+	13.5762i	0.765743	+	0.442102i
$944$	−31.0199	−	34.8418i	−1.00961	−	1.13401i
$945$	0.169883	+	3.79319i	0.00552630	+	0.123392i
$946$	14.6304	−	26.4425i	0.475674	−	0.859720i
$947$	−16.0851	−	2.11765i	−0.522696	−	0.0688142i	−0.135438	−	0.990786i	$-0.543244\pi$
$947$	−16.0851	−	2.11765i	−0.522696	−	0.0688142i	−0.387258	+	0.921972i	$0.626578\pi$
$948$	1.01979	−	12.7983i	0.0331213	−	0.415670i
$949$	−7.20743	−	54.7458i	−0.233963	−	1.77713i
$950$	10.5202	+	24.1433i	0.341320	+	0.783311i
$951$	13.7519	−	14.1684i	0.445935	−	0.459443i
$952$	−9.26150	+	18.2824i	−0.300167	+	0.592536i
$953$	−11.1939	−	11.1939i	−0.362604	−	0.362604i	0.502167	−	0.864771i	$-0.332536\pi$
$953$	−11.1939	−	11.1939i	−0.362604	−	0.362604i	−0.864771	+	0.502167i	$0.832536\pi$
$954$	4.81789	−	13.4221i	0.155985	−	0.434556i
$955$	0.496837	−	1.19947i	0.0160773	−	0.0388139i
$956$	9.86232	−	0.359811i	0.318970	−	0.0116371i
$957$	4.57991	−	39.3113i	0.148047	−	1.27075i
$958$	−7.71607	+	8.00272i	−0.249295	+	0.258556i
$959$	−0.958840	−	1.66076i	−0.0309626	−	0.0536287i
$960$	−2.03999	+	4.83476i	−0.0658405	+	0.156041i
$961$	12.5933	−	21.8123i	0.406236	−	0.703621i
$962$	12.3486	+	42.9381i	0.398134	+	1.38438i
$963$	−1.23540	+	12.1825i	−0.0398102	+	0.392576i
$964$	−25.2911	−	40.3341i	−0.814573	−	1.29907i
$965$	−4.34490	−	5.66238i	−0.139867	−	0.182278i
$966$	19.1510	+	23.3152i	0.616173	+	0.750155i
$967$	8.23836	−	30.7460i	0.264928	−	0.988723i	−0.697367	−	0.716714i	$-0.745645\pi$
$967$	8.23836	−	30.7460i	0.264928	−	0.988723i	0.962295	−	0.272009i	$-0.0876881\pi$
$968$	−4.68511	+	3.05816i	−0.150585	+	0.0982930i
$969$	−24.1839	−	6.09486i	−0.776897	−	0.195795i
$970$	−3.99894	+	5.41308i	−0.128398	+	0.173804i
$971$	−15.5619	−	6.44594i	−0.499405	−	0.206860i	0.118739	−	0.992926i	$-0.462115\pi$
$971$	−15.5619	−	6.44594i	−0.499405	−	0.206860i	−0.618143	+	0.786065i	$0.712115\pi$
$972$	26.6855	+	16.1210i	0.855936	+	0.517081i
$973$	3.29657	+	7.95862i	0.105683	+	0.255142i
$974$	8.62100	+	14.3224i	0.276235	+	0.458920i
$975$	34.6210	−	20.6831i	1.10876	−	0.662390i
$976$	28.7149	−	14.4288i	0.919140	−	0.461854i
$977$	33.6160	−	19.4082i	1.07547	−	0.620923i	0.145799	−	0.989314i	$-0.453425\pi$
$977$	33.6160	−	19.4082i	1.07547	−	0.620923i	0.929671	+	0.368391i	$0.120091\pi$
$978$	41.4888	+	22.1534i	1.32666	+	0.708388i
$979$	4.94802	+	0.651419i	0.158139	+	0.0208194i
$980$	2.44727	−	0.413461i	0.0781753	−	0.0132075i
$981$	35.9941	−	29.3661i	1.14920	−	0.937587i
$982$	−0.957820	+	8.46540i	−0.0305653	+	0.270142i
$983$	3.66715	+	13.6860i	0.116964	+	0.436515i	0.999426	−	0.0338676i	$-0.0107825\pi$
$983$	3.66715	+	13.6860i	0.116964	+	0.436515i	−0.882462	+	0.470383i	$0.844116\pi$
$984$	−1.27610	+	20.7980i	−0.0406805	+	0.663014i
$985$	−2.01610	+	7.52420i	−0.0642384	+	0.239741i
$986$	−37.6009	−	14.7775i	−1.19746	−	0.470611i
$987$	−0.479326	−	0.605741i	−0.0152571	−	0.0192809i
$988$	−26.9284	−	25.0327i	−0.856708	−	0.796397i
$989$	−41.9589	+	17.3799i	−1.33421	+	0.552650i
$990$	−3.57255	−	3.24459i	−0.113543	−	0.103120i
$991$	4.46196			0.141739			0.0708694	−	0.997486i	$-0.477423\pi$
$991$	4.46196			0.141739			0.0708694	+	0.997486i	$0.477423\pi$
$992$	−8.72628	+	10.4824i	−0.277060	+	0.332816i
$993$	41.4225	−	0.618022i	1.31450	−	0.0196123i
$994$	8.36049	+	8.06103i	0.265179	+	0.255680i
$995$	2.46094	+	1.88835i	0.0780171	+	0.0598647i
$996$	8.36729	+	25.8374i	0.265128	+	0.818691i
$997$	−17.6224	−	22.9659i	−0.558106	−	0.727338i	0.426039	−	0.904705i	$-0.359909\pi$
$997$	−17.6224	−	22.9659i	−0.558106	−	0.727338i	−0.984145	+	0.177367i	$0.943242\pi$
$998$	−11.6765	+	9.30275i	−0.369612	+	0.294474i
$999$	25.2709	+	23.1043i	0.799535	+	0.730988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.277.43	yes	368
3.2	odd	2		864.2.bk.a.181.4		368
9.4	even	3	inner	288.2.bc.a.85.12	yes	368
9.5	odd	6		864.2.bk.a.469.35		368
32.29	even	8	inner	288.2.bc.a.61.12	✓	368
96.29	odd	8		864.2.bk.a.829.35		368
288.157	even	24	inner	288.2.bc.a.157.43	yes	368
288.221	odd	24		864.2.bk.a.253.4		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.61.12	✓	368	32.29	even	8	inner
288.2.bc.a.85.12	yes	368	9.4	even	3	inner
288.2.bc.a.157.43	yes	368	288.157	even	24	inner
288.2.bc.a.277.43	yes	368	1.1	even	1	trivial
864.2.bk.a.181.4		368	3.2	odd	2
864.2.bk.a.253.4		368	288.221	odd	24
864.2.bk.a.469.35		368	9.5	odd	6
864.2.bk.a.829.35		368	96.29	odd	8

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

\(f(q)\)	\(=\)	\(q+(1.37247 + 0.341058i) q^{2} +(-1.38971 - 1.03379i) q^{3} +(1.76736 + 0.936186i) q^{4} +(-0.375467 + 0.0494312i) q^{5} +(-1.55475 - 1.89282i) q^{6} +(1.86379 - 0.499402i) q^{7} +(2.10636 + 1.88766i) q^{8} +(0.862562 + 2.87332i) q^{9} +O(q^{10})\)	\(q+(1.37247 + 0.341058i) q^{2} +(-1.38971 - 1.03379i) q^{3} +(1.76736 + 0.936186i) q^{4} +(-0.375467 + 0.0494312i) q^{5} +(-1.55475 - 1.89282i) q^{6} +(1.86379 - 0.499402i) q^{7} +(2.10636 + 1.88766i) q^{8} +(0.862562 + 2.87332i) q^{9} +(-0.532177 - 0.0602133i) q^{10} +(2.38296 - 1.82851i) q^{11} +(-1.48829 - 3.12810i) q^{12} +(2.91857 - 3.80355i) q^{13} +(2.72833 - 0.0497528i) q^{14} +(0.572891 + 0.319459i) q^{15} +(2.24711 + 3.30915i) q^{16} +3.75523i q^{17} +(0.203871 + 4.23774i) q^{18} +(-1.46737 - 3.54254i) q^{19} +(-0.709862 - 0.264145i) q^{20} +(-3.10640 - 1.23275i) q^{21} +(3.89417 - 1.69685i) q^{22} +(-6.16625 - 1.65224i) q^{23} +(-0.975770 - 4.80082i) q^{24} +(-4.69110 + 1.25698i) q^{25} +(5.30289 - 4.22487i) q^{26} +(1.77170 - 4.88478i) q^{27} +(3.76152 + 0.862235i) q^{28} +(-0.992961 + 7.54229i) q^{29} +(0.677322 + 0.633838i) q^{30} +(1.20555 + 2.08807i) q^{31} +(1.95548 + 5.30812i) q^{32} +(-5.20190 + 0.0776120i) q^{33} +(-1.28075 + 5.15395i) q^{34} +(-0.675107 + 0.279639i) q^{35} +(-1.16551 + 5.88571i) q^{36} +(-2.52174 + 6.08802i) q^{37} +(-0.805709 - 5.36250i) q^{38} +(-7.98802 + 2.26863i) q^{39} +(-0.884177 - 0.604636i) q^{40} +(-4.10842 - 1.10085i) q^{41} +(-3.84300 - 2.75137i) q^{42} +(5.64414 - 4.33090i) q^{43} +(5.92336 - 1.00074i) q^{44} +(-0.465896 - 1.03620i) q^{45} +(-7.89949 - 4.37070i) q^{46} +(0.200164 + 0.115565i) q^{47} +(0.298142 - 6.92179i) q^{48} +(-2.83786 + 1.63844i) q^{49} +(-6.86710 + 0.125226i) q^{50} +(3.88212 - 5.21867i) q^{51} +(8.71899 - 3.98992i) q^{52} +(-3.10539 - 1.28630i) q^{53} +(4.09761 - 6.09997i) q^{54} +(-0.804337 + 0.804337i) q^{55} +(4.86851 + 2.46629i) q^{56} +(-1.62303 + 6.44004i) q^{57} +(-3.93517 + 10.0129i) q^{58} +(-11.5626 + 1.52225i) q^{59} +(0.713430 + 1.10093i) q^{60} +(1.04865 - 7.96531i) q^{61} +(0.942426 + 3.27698i) q^{62} +(3.04258 + 4.92451i) q^{63} +(0.873469 + 7.95217i) q^{64} +(-0.907813 + 1.57238i) q^{65} +(-7.16593 - 1.66763i) q^{66} +(-5.64017 - 4.32785i) q^{67} +(-3.51560 + 6.63684i) q^{68} +(6.86120 + 8.67073i) q^{69} +(-1.02194 + 0.153545i) q^{70} +(3.00945 + 3.00945i) q^{71} +(-3.60700 + 7.68047i) q^{72} +(8.14413 - 8.14413i) q^{73} +(-5.53739 + 7.49558i) q^{74} +(7.81869 + 3.10278i) q^{75} +(0.723112 - 7.63468i) q^{76} +(3.52818 - 4.59801i) q^{77} +(-11.7371 + 0.389255i) q^{78} +(3.20972 + 1.85313i) q^{79} +(-1.00729 - 1.13140i) q^{80} +(-7.51197 + 4.95684i) q^{81} +(-5.26324 - 2.91209i) q^{82} +(-7.77292 - 1.02332i) q^{83} +(-4.33604 - 5.08687i) q^{84} +(-0.185626 - 1.40997i) q^{85} +(9.22351 - 4.01906i) q^{86} +(9.17706 - 9.45505i) q^{87} +(8.47095 + 0.646729i) q^{88} +(1.17489 + 1.17489i) q^{89} +(-0.286023 - 1.58106i) q^{90} +(3.54011 - 8.54657i) q^{91} +(-9.35116 - 8.69286i) q^{92} +(0.483267 - 4.14808i) q^{93} +(0.235305 + 0.226877i) q^{94} +(0.726062 + 1.25758i) q^{95} +(2.76992 - 9.39827i) q^{96} +(6.28300 - 10.8825i) q^{97} +(-4.45369 + 1.28084i) q^{98} +(7.30934 + 5.26980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more