LMFDB - Embedded newform 144.2.u.a.59.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,2,Mod(11,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.u (of order $12$, degree $4$, 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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.19
Character	$\chi$	$=$	144.59
Dual form			144.2.u.a.83.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19684 - 0.753382i) q^{2} +(-0.256373 - 1.71297i) q^{3} +(0.864831 - 1.80335i) q^{4} +(0.546024 + 2.03779i) q^{5} +(-1.59736 - 1.85700i) q^{6} +(-0.0638076 - 0.110518i) q^{7} +(-0.323550 - 2.80986i) q^{8} +(-2.86855 + 0.878321i) q^{9} +(2.18873 + 2.02753i) q^{10} +(-0.181856 + 0.678695i) q^{11} +(-3.31081 - 1.01910i) q^{12} +(0.493860 + 1.84311i) q^{13} +(-0.159630 - 0.0842004i) q^{14} +(3.35069 - 1.45776i) q^{15} +(-2.50413 - 3.11918i) q^{16} +4.32243i q^{17} +(-2.77147 + 3.21232i) q^{18} +(-3.97707 - 3.97707i) q^{19} +(4.14706 + 0.777671i) q^{20} +(-0.172956 + 0.137635i) q^{21} +(0.293665 + 0.949293i) q^{22} +(6.81589 + 3.93516i) q^{23} +(-4.73026 + 1.27461i) q^{24} +(0.475689 - 0.274639i) q^{25} +(1.97963 + 1.83383i) q^{26} +(2.23996 + 4.68856i) q^{27} +(-0.254485 + 0.0194880i) q^{28} +(-0.248377 + 0.926957i) q^{29} +(2.91197 - 4.26904i) q^{30} +(4.91353 + 2.83683i) q^{31} +(-5.34697 - 1.84658i) q^{32} +(1.20921 + 0.137514i) q^{33} +(3.25644 + 5.17324i) q^{34} +(0.190372 - 0.190372i) q^{35} +(-0.896888 + 5.93259i) q^{36} +(-6.64358 - 6.64358i) q^{37} +(-7.75614 - 1.76364i) q^{38} +(3.03058 - 1.31849i) q^{39} +(5.54923 - 2.19358i) q^{40} +(-4.61325 + 7.99038i) q^{41} +(-0.103308 + 0.295028i) q^{42} +(-10.8712 - 2.91294i) q^{43} +(1.06665 + 0.914906i) q^{44} +(-3.35613 - 5.36590i) q^{45} +(11.1222 - 0.425234i) q^{46} +(-5.92267 - 10.2584i) q^{47} +(-4.70108 + 5.08919i) q^{48} +(3.49186 - 6.04807i) q^{49} +(0.362413 - 0.687073i) q^{50} +(7.40421 - 1.10816i) q^{51} +(3.75087 + 0.703377i) q^{52} +(-0.00259022 + 0.00259022i) q^{53} +(6.21314 + 3.92389i) q^{54} -1.48233 q^{55} +(-0.289895 + 0.215049i) q^{56} +(-5.79299 + 7.83221i) q^{57} +(0.401086 + 1.29654i) q^{58} +(-4.09587 + 1.09748i) q^{59} +(0.268933 - 7.30317i) q^{60} +(4.44908 + 1.19213i) q^{61} +(8.01790 - 0.306548i) q^{62} +(0.280105 + 0.260982i) q^{63} +(-7.79063 + 1.81826i) q^{64} +(-3.48621 + 2.01276i) q^{65} +(1.55082 - 0.746413i) q^{66} +(2.01106 - 0.538862i) q^{67} +(7.79486 + 3.73818i) q^{68} +(4.99340 - 12.6843i) q^{69} +(0.0844211 - 0.371267i) q^{70} -3.80683i q^{71} +(3.39608 + 7.77603i) q^{72} -1.87674i q^{73} +(-12.9564 - 2.94612i) q^{74} +(-0.592403 - 0.744431i) q^{75} +(-10.6115 + 3.73255i) q^{76} +(0.0866118 - 0.0232076i) q^{77} +(2.63378 - 3.86120i) q^{78} +(-3.00919 + 1.73736i) q^{79} +(4.98892 - 6.80604i) q^{80} +(7.45710 - 5.03901i) q^{81} +(0.498509 + 13.0387i) q^{82} +(-1.47149 - 0.394284i) q^{83} +(0.0986256 + 0.430930i) q^{84} +(-8.80821 + 2.36015i) q^{85} +(-15.2056 + 4.70388i) q^{86} +(1.65153 + 0.187816i) q^{87} +(1.96588 + 0.291398i) q^{88} +10.5967 q^{89} +(-8.05931 - 3.89366i) q^{90} +(0.172185 - 0.172185i) q^{91} +(12.9911 - 8.88818i) q^{92} +(3.59971 - 9.14402i) q^{93} +(-14.8169 - 7.81555i) q^{94} +(5.93284 - 10.2760i) q^{95} +(-1.79232 + 9.63263i) q^{96} +(3.31795 + 5.74685i) q^{97} +(-0.377331 - 9.86925i) q^{98} +(-0.0744506 - 2.10659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27}+ \cdots + 46 q^{99}+O(q^{100}) $ 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.19684	−	0.753382i	0.846291	−	0.532722i
$2$	1.19684	−	0.753382i	0.846291	−	0.532722i
$3$	−0.256373	−	1.71297i	−0.148017	−	0.988985i
$3$	−0.256373	−	1.71297i	−0.148017	−	0.988985i
$4$	0.864831	−	1.80335i	0.432416	−	0.901674i
$5$	0.546024	+	2.03779i	0.244189	+	0.911327i	0.973789	+	0.227452i	$0.0730396\pi$
$5$	0.546024	+	2.03779i	0.244189	+	0.911327i	−0.729600	+	0.683874i	$0.760294\pi$
$6$	−1.59736	−	1.85700i	−0.652119	−	0.758117i
$7$	−0.0638076	−	0.110518i	−0.0241170	−	0.0417719i	0.853715	−	0.520741i	$-0.174344\pi$
$7$	−0.0638076	−	0.110518i	−0.0241170	−	0.0417719i	−0.877832	+	0.478969i	$0.841011\pi$
$8$	−0.323550	−	2.80986i	−0.114392	−	0.993436i
$9$	−2.86855	+	0.878321i	−0.956182	+	0.292774i
$10$	2.18873	+	2.02753i	0.692138	+	0.641162i
$11$	−0.181856	+	0.678695i	−0.0548316	+	0.204634i	−0.987907	−	0.155046i	$-0.950447\pi$
$11$	−0.181856	+	0.678695i	−0.0548316	+	0.204634i	0.933076	+	0.359680i	$0.117114\pi$
$12$	−3.31081	−	1.01910i	−0.955747	−	0.294189i
$13$	0.493860	+	1.84311i	0.136972	+	0.511187i	0.999982	+	0.00599967i	$0.00190977\pi$
$13$	0.493860	+	1.84311i	0.136972	+	0.511187i	−0.863010	+	0.505187i	$0.831424\pi$
$14$	−0.159630	−	0.0842004i	−0.0426628	−	0.0225035i
$15$	3.35069	−	1.45776i	0.865144	−	0.376391i
$16$	−2.50413	−	3.11918i	−0.626034	−	0.779796i
$17$			4.32243i			1.04834i	0.851612	+	0.524172i	$0.175625\pi$
$17$			4.32243i			1.04834i	−0.851612	+	0.524172i	$0.824375\pi$
$18$	−2.77147	+	3.21232i	−0.653241	+	0.757150i
$19$	−3.97707	−	3.97707i	−0.912401	−	0.912401i	0.0840594	−	0.996461i	$-0.473211\pi$
$19$	−3.97707	−	3.97707i	−0.912401	−	0.912401i	−0.996461	+	0.0840594i	$0.973211\pi$
$20$	4.14706	+	0.777671i	0.927311	+	0.173893i
$21$	−0.172956	+	0.137635i	−0.0377420	+	0.0300343i
$22$	0.293665	+	0.949293i	0.0626096	+	0.202390i
$23$	6.81589	+	3.93516i	1.42121	+	0.820537i	0.996403	−	0.0847463i	$-0.0270080\pi$
$23$	6.81589	+	3.93516i	1.42121	+	0.820537i	0.424809	+	0.905283i	$0.360341\pi$
$24$	−4.73026	+	1.27461i	−0.965561	+	0.260178i
$25$	0.475689	−	0.274639i	0.0951377	−	0.0549278i
$26$	1.97963	+	1.83383i	0.388238	+	0.359644i
$27$	2.23996	+	4.68856i	0.431080	+	0.902314i
$28$	−0.254485	+	0.0194880i	−0.0480932	+	0.00368288i
$29$	−0.248377	+	0.926957i	−0.0461225	+	0.172132i	−0.985145	−	0.171724i	$-0.945066\pi$
$29$	−0.248377	+	0.926957i	−0.0461225	+	0.172132i	0.939023	+	0.343855i	$0.111733\pi$
$30$	2.91197	−	4.26904i	0.531651	−	0.779417i
$31$	4.91353	+	2.83683i	0.882496	+	0.509509i	0.871480	−	0.490430i	$-0.163160\pi$
$31$	4.91353	+	2.83683i	0.882496	+	0.509509i	0.0110152	+	0.999939i	$0.496494\pi$
$32$	−5.34697	−	1.84658i	−0.945220	−	0.326433i
$33$	1.20921	+	0.137514i	0.210496	+	0.0239382i
$34$	3.25644	+	5.17324i	0.558476	+	0.887204i
$35$	0.190372	−	0.190372i	0.0321787	−	0.0321787i
$36$	−0.896888	+	5.93259i	−0.149481	+	0.988765i
$37$	−6.64358	−	6.64358i	−1.09220	−	1.09220i	−0.995294	−	0.0969037i	$-0.969106\pi$
$37$	−6.64358	−	6.64358i	−1.09220	−	1.09220i	−0.0969037	−	0.995294i	$-0.530894\pi$
$38$	−7.75614	−	1.76364i	−1.25821	−	0.286101i
$39$	3.03058	−	1.31849i	0.485281	−	0.211128i
$40$	5.54923	−	2.19358i	0.877411	−	0.346835i
$41$	−4.61325	+	7.99038i	−0.720469	+	1.24789i	0.240344	+	0.970688i	$0.422740\pi$
$41$	−4.61325	+	7.99038i	−0.720469	+	1.24789i	−0.960812	+	0.277200i	$0.910593\pi$
$42$	−0.103308	+	0.295028i	−0.0159408	+	0.0455238i
$43$	−10.8712	−	2.91294i	−1.65785	−	0.444219i	−0.696053	−	0.717991i	$-0.745062\pi$
$43$	−10.8712	−	2.91294i	−1.65785	−	0.444219i	−0.961795	+	0.273772i	$0.911729\pi$
$44$	1.06665	+	0.914906i	0.160803	+	0.137927i
$45$	−3.35613	−	5.36590i	−0.500302	−	0.799902i
$46$	11.1222	−	0.425234i	1.63988	−	0.0626973i
$47$	−5.92267	−	10.2584i	−0.863910	−	1.49634i	−0.868125	−	0.496345i	$-0.834675\pi$
$47$	−5.92267	−	10.2584i	−0.863910	−	1.49634i	0.00421475	−	0.999991i	$-0.498658\pi$
$48$	−4.70108	+	5.08919i	−0.678543	+	0.734561i
$49$	3.49186	−	6.04807i	0.498837	−	0.864011i
$50$	0.362413	−	0.687073i	0.0512530	−	0.0971668i
$51$	7.40421	−	1.10816i	1.03680	−	0.155173i
$52$	3.75087	+	0.703377i	0.520153	+	0.0975408i
$53$	−0.00259022	+	0.00259022i	−0.000355794	+	0.000355794i	−0.707285	−	0.706929i	$-0.750080\pi$
$53$	−0.00259022	+	0.00259022i	−0.000355794	+	0.000355794i	0.706929	+	0.707285i	$0.250080\pi$
$54$	6.21314	+	3.92389i	0.845501	+	0.533974i
$55$	−1.48233			−0.199878
$56$	−0.289895	+	0.215049i	−0.0387389	+	0.0287371i
$57$	−5.79299	+	7.83221i	−0.767300	+	1.03740i
$58$	0.401086	+	1.29654i	0.0526651	+	0.170244i
$59$	−4.09587	+	1.09748i	−0.533237	+	0.142880i	−0.515382	−	0.856960i	$-0.672350\pi$
$59$	−4.09587	+	1.09748i	−0.533237	+	0.142880i	−0.0178541	+	0.999841i	$0.505683\pi$
$60$	0.268933	−	7.30317i	0.0347191	−	0.942836i
$61$	4.44908	+	1.19213i	0.569646	+	0.152636i	0.532134	−	0.846660i	$-0.321390\pi$
$61$	4.44908	+	1.19213i	0.569646	+	0.152636i	0.0375117	+	0.999296i	$0.488057\pi$
$62$	8.01790	−	0.306548i	1.01827	−	0.0389317i
$63$	0.280105	+	0.260982i	0.0352900	+	0.0328807i
$64$	−7.79063	+	1.81826i	−0.973829	+	0.227282i
$65$	−3.48621	+	2.01276i	−0.432411	+	0.249652i
$66$	1.55082	−	0.746413i	0.190893	−	0.0918771i
$67$	2.01106	−	0.538862i	0.245690	−	0.0658325i	−0.133872	−	0.990999i	$-0.542741\pi$
$67$	2.01106	−	0.538862i	0.245690	−	0.0658325i	0.379563	+	0.925166i	$0.376075\pi$
$68$	7.79486	+	3.73818i	0.945265	+	0.453320i
$69$	4.99340	−	12.6843i	0.601134	−	1.52701i
$70$	0.0844211	−	0.371267i	0.0100903	−	0.0443748i
$71$		−	3.80683i		−	0.451788i	−0.974152	−	0.225894i	$-0.927470\pi$
$71$		−	3.80683i		−	0.451788i	0.974152	−	0.225894i	$-0.0725303\pi$
$72$	3.39608	+	7.77603i	0.400232	+	0.916414i
$73$		−	1.87674i		−	0.219656i	−0.993951	−	0.109828i	$-0.964970\pi$
$73$		−	1.87674i		−	0.219656i	0.993951	−	0.109828i	$-0.0350300\pi$
$74$	−12.9564	−	2.94612i	−1.50615	−	0.342479i
$75$	−0.592403	−	0.744431i	−0.0684048	−	0.0859595i
$76$	−10.6115	+	3.73255i	−1.21723	+	0.428152i
$77$	0.0866118	−	0.0232076i	0.00987033	−	0.00264475i
$78$	2.63378	−	3.86120i	0.298217	−	0.437195i
$79$	−3.00919	+	1.73736i	−0.338560	+	0.195468i	−0.659635	−	0.751586i	$-0.729289\pi$
$79$	−3.00919	+	1.73736i	−0.338560	+	0.195468i	0.321075	+	0.947054i	$0.395956\pi$
$80$	4.98892	−	6.80604i	0.557778	−	0.760939i
$81$	7.45710	−	5.03901i	0.828567	−	0.559890i
$82$	0.498509	+	13.0387i	0.0550511	+	1.43989i
$83$	−1.47149	−	0.394284i	−0.161517	−	0.0432783i	0.177155	−	0.984183i	$-0.443311\pi$
$83$	−1.47149	−	0.394284i	−0.161517	−	0.0432783i	−0.338671	+	0.940905i	$0.609977\pi$
$84$	0.0986256	+	0.430930i	0.0107609	+	0.0470183i
$85$	−8.80821	+	2.36015i	−0.955384	+	0.255994i
$86$	−15.2056	+	4.70388i	−1.63967	+	0.507233i
$87$	1.65153	+	0.187816i	0.177062	+	0.0201360i
$88$	1.96588	+	0.291398i	0.209563	+	0.0310631i
$89$	10.5967			1.12325			0.561624	−	0.827392i	$-0.310177\pi$
$89$	10.5967			1.12325			0.561624	+	0.827392i	$0.310177\pi$
$90$	−8.05931	−	3.89366i	−0.849525	−	0.410428i
$91$	0.172185	−	0.172185i	0.0180499	−	0.0180499i
$92$	12.9911	−	8.88818i	1.35441	−	0.926657i
$93$	3.59971	−	9.14402i	0.373272	−	0.948191i
$94$	−14.8169	−	7.81555i	−1.52825	−	0.806112i
$95$	5.93284	−	10.2760i	0.608697	−	1.05429i
$96$	−1.79232	+	9.63263i	−0.182928	+	0.983126i
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	0.983845	−	0.179021i	$-0.0572928\pi$
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	−0.646959	+	0.762525i	$0.723960\pi$
$98$	−0.377331	−	9.86925i	−0.0381162	−	0.996945i
$99$	−0.0744506	−	2.10659i	−0.00748257	−	0.211721i
$100$	−0.0838795	−	1.09535i	−0.00838795	−	0.109535i
$101$	12.0922	+	3.24008i	1.20321	+	0.322400i	0.804096	−	0.594499i	$-0.202650\pi$
$101$	12.0922	+	3.24008i	1.20321	+	0.322400i	0.399118	+	0.916899i	$0.369316\pi$
$102$	8.02676	−	6.90448i	0.794767	−	0.683645i
$103$	−4.21850	+	7.30665i	−0.415661	+	0.719946i	−0.995498	−	0.0947868i	$-0.969783\pi$
$103$	−4.21850	+	7.30665i	−0.415661	+	0.719946i	0.579837	+	0.814733i	$0.303116\pi$
$104$	5.01909	−	1.98401i	0.492162	−	0.194549i
$105$	−0.374908	−	0.277295i	−0.0365873	−	0.0270613i
$106$	−0.00114864	+	0.00505149i	−0.000111566	+	0.000490644i
$107$	−7.25071	−	7.25071i	−0.700953	−	0.700953i	0.263662	−	0.964615i	$-0.415070\pi$
$107$	−7.25071	−	7.25071i	−0.700953	−	0.700953i	−0.964615	+	0.263662i	$0.915070\pi$
$108$	10.3923	+	0.0153855i	0.999999	+	0.00148048i
$109$	10.2850	−	10.2850i	0.985128	−	0.985128i	−0.0147630	−	0.999891i	$-0.504699\pi$
$109$	10.2850	−	10.2850i	0.985128	−	0.985128i	0.999891	+	0.0147630i	$0.00469937\pi$
$110$	−1.77411	+	1.11676i	−0.169155	+	0.106479i
$111$	−9.67702	+	13.0835i	−0.918503	+	1.24183i
$112$	−0.184943	+	0.475780i	−0.0174755	+	0.0449570i
$113$	−18.2964	−	10.5634i	−1.72118	−	0.993722i	−0.916526	−	0.399976i	$-0.869019\pi$
$113$	−18.2964	−	10.5634i	−1.72118	−	0.993722i	−0.804652	−	0.593747i	$-0.797648\pi$
$114$	−1.03260	+	13.7382i	−0.0967122	+	1.28670i
$115$	−4.29738	+	16.0380i	−0.400732	+	1.49555i
$116$	1.45682	+	1.24957i	0.135263	+	0.116020i
$117$	−3.03550	−	4.85328i	−0.280632	−	0.448685i
$118$	−4.07526	+	4.39926i	−0.375158	+	0.404985i
$119$	0.477707	−	0.275804i	0.0437913	−	0.0252829i
$120$	−5.18021	−	8.94331i	−0.472886	−	0.816409i
$121$	9.09872	+	5.25315i	0.827157	+	0.477559i
$122$	6.22294	−	1.92507i	0.563399	−	0.174288i
$123$	14.8700	+	5.85384i	1.34078	+	0.527823i
$124$	9.36516	−	6.40743i	0.841016	−	0.575404i
$125$	8.27822	+	8.27822i	0.740426	+	0.740426i
$126$	0.531860	+	0.101327i	0.0473818	+	0.00902690i
$127$			13.1109i			1.16340i	0.813403	+	0.581700i	$0.197612\pi$
$127$			13.1109i			1.16340i	−0.813403	+	0.581700i	$0.802388\pi$
$128$	−7.95426	+	8.04548i	−0.703064	+	0.711127i
$129$	−2.20269	+	19.3689i	−0.193936	+	1.70534i
$130$	−2.65604	+	5.03539i	−0.232950	+	0.441633i
$131$	1.27247	+	4.74891i	0.111176	+	0.414914i	0.998972	−	0.0453222i	$-0.0144315\pi$
$131$	1.27247	+	4.74891i	0.111176	+	0.414914i	−0.887797	+	0.460236i	$0.847765\pi$
$132$	1.29375	−	2.06170i	0.112606	−	0.179448i
$133$	−0.185770	+	0.693305i	−0.0161083	+	0.0601171i
$134$	2.00094	−	2.16003i	0.172855	−	0.186598i
$135$	−8.33122	+	7.12462i	−0.717037	+	0.613190i
$136$	12.1454	−	1.39852i	1.04146	−	0.119922i
$137$	−3.41217	−	5.91005i	−0.291521	−	0.504930i	0.682648	−	0.730747i	$-0.260828\pi$
$137$	−3.41217	−	5.91005i	−0.291521	−	0.504930i	−0.974170	+	0.225817i	$0.927495\pi$
$138$	−3.57984	−	18.9430i	−0.304737	−	1.61253i
$139$	−2.77132	−	10.3427i	−0.235061	−	0.877258i	−0.978121	−	0.208035i	$-0.933293\pi$
$139$	−2.77132	−	10.3427i	−0.235061	−	0.877258i	0.743061	−	0.669224i	$-0.233373\pi$
$140$	−0.178667	−	0.507946i	−0.0151002	−	0.0429293i
$141$	−16.0539	+	12.7753i	−1.35198	+	1.07588i
$142$	−2.86800	−	4.55615i	−0.240677	−	0.382344i
$143$	−1.34072			−0.112117
$144$	9.92287	+	6.74809i	0.826906	+	0.562341i
$145$	−2.02456			−0.168131
$146$	−1.41390	−	2.24615i	−0.117016	−	0.185893i
$147$	−11.2554	−	4.43089i	−0.928330	−	0.365453i
$148$	−17.7263	+	6.23512i	−1.45709	+	0.512523i
$149$	−0.0546714	−	0.204036i	−0.00447885	−	0.0167153i	0.963650	−	0.267167i	$-0.0860875\pi$
$149$	−0.0546714	−	0.204036i	−0.00447885	−	0.0167153i	−0.968129	+	0.250452i	$0.919421\pi$
$150$	−1.26985	−	0.444656i	−0.103683	−	0.0363060i
$151$	1.14798	+	1.98835i	0.0934210	+	0.161810i	0.908949	−	0.416908i	$-0.136886\pi$
$151$	1.14798	+	1.98835i	0.0934210	+	0.161810i	−0.815528	+	0.578718i	$0.803553\pi$
$152$	−9.88822	+	12.4618i	−0.802040	+	1.01078i
$153$	−3.79649	−	12.3991i	−0.306928	−	1.00241i
$154$	0.0861759	−	0.0930274i	0.00694425	−	0.00749636i
$155$	−3.09795	+	11.5617i	−0.248833	+	0.928658i
$156$	0.243240	−	6.60547i	0.0194748	−	0.528861i
$157$	4.34480	+	16.2150i	0.346753	+	1.29410i	0.890551	+	0.454883i	$0.150319\pi$
$157$	4.34480	+	16.2150i	0.346753	+	1.29410i	−0.543799	+	0.839216i	$0.683015\pi$
$158$	−2.29261	+	4.34640i	−0.182390	+	0.345781i
$159$	0.00510103	+	0.00377291i	0.000404538	+	0.000299211i
$160$	0.843367	−	11.9043i	0.0666740	−	0.941116i
$161$		−	1.00437i		−	0.0791556i
$162$	5.12863	−	11.6489i	0.402943	−	0.915225i
$163$	0.490399	+	0.490399i	0.0384110	+	0.0384110i	0.726051	−	0.687640i	$-0.241353\pi$
$163$	0.490399	+	0.490399i	0.0384110	+	0.0384110i	−0.687640	+	0.726051i	$0.741353\pi$
$164$	10.4198	+	15.2296i	0.813647	+	1.18923i
$165$	0.380031	+	2.53920i	0.0295854	+	0.197676i
$166$	−2.05817	+	0.636699i	−0.159745	+	0.0494174i
$167$	9.34175	+	5.39346i	0.722887	+	0.417359i	0.815814	−	0.578314i	$-0.196289\pi$
$167$	9.34175	+	5.39346i	0.722887	+	0.417359i	−0.0929276	+	0.995673i	$0.529622\pi$
$168$	0.442694	+	0.441450i	0.0341546	+	0.0340586i
$169$	8.10518	−	4.67953i	0.623475	−	0.359963i
$170$	−8.76388	+	9.46066i	−0.672159	+	0.725599i
$171$	14.9015	+	7.91525i	1.13955	+	0.605294i
$172$	−14.6548	+	17.0854i	−1.11742	+	1.30275i
$173$	1.23685	−	4.61598i	0.0940358	−	0.350946i	−0.902836	−	0.429986i	$-0.858519\pi$
$173$	1.23685	−	4.61598i	0.0940358	−	0.350946i	0.996871	+	0.0790394i	$0.0251853\pi$
$174$	2.11811	−	1.01945i	0.160573	−	0.0772841i
$175$	−0.0607051	−	0.0350481i	−0.00458888	−	0.00264939i
$176$	2.57236	−	1.13230i	0.193899	−	0.0853504i
$177$	2.93003	+	6.73474i	0.220235	+	0.506214i
$178$	12.6825	−	7.98337i	0.950595	−	0.598379i
$179$	−3.52882	+	3.52882i	−0.263756	+	0.263756i	−0.826578	−	0.562822i	$-0.809716\pi$
$179$	−3.52882	+	3.52882i	−0.263756	+	0.263756i	0.562822	+	0.826578i	$0.309716\pi$
$180$	−12.5791	+	1.41167i	−0.937589	+	0.105219i
$181$	7.34860	+	7.34860i	0.546217	+	0.546217i	0.925344	−	0.379127i	$-0.123776\pi$
$181$	7.34860	+	7.34860i	0.546217	+	0.546217i	−0.379127	+	0.925344i	$0.623776\pi$
$182$	0.0763560	−	0.335798i	0.00565988	−	0.0248910i
$183$	0.901454	−	7.92677i	0.0666374	−	0.585964i
$184$	8.85196	−	20.4249i	0.652575	−	1.50575i
$185$	9.91065	−	17.1658i	0.728646	−	1.26205i
$186$	−2.58069	−	13.6558i	−0.189225	−	1.00130i
$187$	−2.93361	−	0.786059i	−0.214527	−	0.0574824i
$188$	−23.6215	+	1.80889i	−1.72278	+	0.131927i
$189$	0.375244	−	0.546722i	0.0272950	−	0.0397681i
$190$	−0.641105	−	16.7684i	−0.0465106	−	1.21651i
$191$	2.58888	+	4.48407i	0.187325	+	0.324456i	0.944357	−	0.328921i	$-0.106685\pi$
$191$	2.58888	+	4.48407i	0.187325	+	0.324456i	−0.757033	+	0.653377i	$0.773352\pi$
$192$	5.11194	+	12.8790i	0.368922	+	0.929460i
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.209003	−	0.977915i	$-0.432978\pi$
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.742398	−	0.669960i	$-0.233689\pi$
$194$	8.30061	+	4.37836i	0.595949	+	0.314348i
$195$	4.34158	+	5.45576i	0.310907	+	0.390695i
$196$	−7.88692	−	11.5276i	−0.563351	−	0.823400i
$197$	−5.14652	+	5.14652i	−0.366674	+	0.366674i	−0.866263	−	0.499588i	$-0.833485\pi$
$197$	−5.14652	+	5.14652i	−0.366674	+	0.366674i	0.499588	+	0.866263i	$0.333485\pi$
$198$	−1.67618	−	2.46516i	−0.119121	−	0.175191i
$199$	−1.37436			−0.0974261			−0.0487130	−	0.998813i	$-0.515512\pi$
$199$	−1.37436			−0.0974261			−0.0487130	+	0.998813i	$0.515512\pi$
$200$	−0.925606	−	1.24776i	−0.0654502	−	0.0882299i
$201$	−1.43864	−	3.30674i	−0.101474	−	0.233240i
$202$	16.9133	−	5.23217i	1.19002	−	0.368134i
$203$	0.118294	−	0.0316967i	0.00830260	−	0.00222468i
$204$	4.40500	−	14.3107i	0.308411	−	1.00195i
$205$	−18.8017	−	5.03789i	−1.31316	−	0.351861i
$206$	0.455852	+	11.9230i	0.0317607	+	0.830715i
$207$	−23.0080	−	5.30163i	−1.59917	−	0.368489i
$208$	4.51231	−	6.15583i	0.312872	−	0.426830i
$209$	3.42246	−	1.97596i	0.236737	−	0.136680i
$210$	−0.657613	−	0.0494281i	−0.0453796	−	0.00341086i
$211$	11.1381	−	2.98444i	0.766776	−	0.205457i	0.145829	−	0.989310i	$-0.453415\pi$
$211$	11.1381	−	2.98444i	0.766776	−	0.205457i	0.620947	+	0.783853i	$0.286748\pi$
$212$	0.00243097	+	0.00691117i	0.000166959	+	0.000474661i
$213$	−6.52100	+	0.975971i	−0.446811	+	0.0668724i
$214$	−14.1405	−	3.21536i	−0.966623	−	0.219797i
$215$		−	23.7438i		−	1.61931i
$216$	12.4495	−	7.81095i	0.847078	−	0.531468i
$217$		−	0.724045i		−	0.0491514i
$218$	4.56094	−	20.0581i	0.308906	−	1.35850i
$219$	−3.21481	+	0.481147i	−0.217237	+	0.0325129i
$220$	−1.28197	+	2.67316i	−0.0864303	+	0.180225i
$221$	−7.96672	+	2.13468i	−0.535900	+	0.143594i
$222$	−1.72494	+	22.9493i	−0.115770	+	1.54026i
$223$	17.9819	−	10.3819i	1.20416	−	0.695220i	0.242680	−	0.970106i	$-0.421974\pi$
$223$	17.9819	−	10.3819i	1.20416	−	0.695220i	0.961477	+	0.274886i	$0.0886402\pi$
$224$	0.137097	+	0.708763i	0.00916019	+	0.0473562i
$225$	−1.12331	+	1.20562i	−0.0748876	+	0.0803748i
$226$	−29.8560	+	1.14149i	−1.98599	+	0.0759305i
$227$	7.65406	+	2.05090i	0.508018	+	0.136123i	0.503718	−	0.863868i	$-0.331965\pi$
$227$	7.65406	+	2.05090i	0.508018	+	0.136123i	0.00429906	+	0.999991i	$0.498632\pi$
$228$	9.11426	+	17.2203i	0.603607	+	1.14044i
$229$	0.448692	−	0.120227i	0.0296504	−	0.00794481i	−0.243963	−	0.969784i	$-0.578448\pi$
$229$	0.448692	−	0.120227i	0.0296504	−	0.00794481i	0.273614	+	0.961840i	$0.411781\pi$
$230$	6.93951	+	22.4325i	0.457578	+	1.47915i
$231$	−0.0619589	−	0.142414i	−0.00407659	−	0.00937014i
$232$	2.68498	+	0.397989i	0.176278	+	0.0261293i
$233$	−9.13737			−0.598609			−0.299305	−	0.954158i	$-0.596755\pi$
$233$	−9.13737			−0.598609			−0.299305	+	0.954158i	$0.596755\pi$
$234$	−7.28937	−	3.52168i	−0.476521	−	0.230219i
$235$	17.6705	−	17.6705i	1.15269	−	1.15269i
$236$	−1.56309	+	8.33542i	−0.101748	+	0.542589i
$237$	3.74752	+	4.70925i	0.243428	+	0.305898i
$238$	0.363951	−	0.689988i	0.0235914	−	0.0447253i
$239$	3.65824	−	6.33626i	0.236632	−	0.409859i	−0.723114	−	0.690729i	$-0.757290\pi$
$239$	3.65824	−	6.33626i	0.236632	−	0.409859i	0.959746	+	0.280870i	$0.0906231\pi$
$240$	−12.9376	−	6.80099i	−0.835118	−	0.439002i
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	0.823006	−	0.568033i	$-0.192295\pi$
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	−0.903434	+	0.428727i	$0.858962\pi$
$242$	14.8473	−	0.567657i	0.954421	−	0.0364904i
$243$	−10.5435	−	11.4819i	−0.676365	−	0.736567i
$244$	5.99752	−	6.99225i	0.383952	−	0.447633i
$245$	14.2313	+	3.81327i	0.909206	+	0.243621i
$246$	22.2071	−	4.19671i	1.41588	−	0.267573i
$247$	5.36605	−	9.29428i	0.341434	−	0.591381i
$248$	6.38132	−	14.7242i	0.405214	−	0.934986i
$249$	−0.298147	+	2.62170i	−0.0188943	+	0.166144i
$250$	16.1443	+	3.67100i	1.02106	+	0.232175i
$251$	2.77626	+	2.77626i	0.175236	+	0.175236i	0.789275	−	0.614039i	$-0.210456\pi$
$251$	2.77626	+	2.77626i	0.175236	+	0.175236i	−0.614039	+	0.789275i	$0.710456\pi$
$252$	0.712886	−	0.279422i	0.0449076	−	0.0176019i
$253$	−3.91028	+	3.91028i	−0.245837	+	0.245837i
$254$	9.87749	+	15.6915i	0.619769	+	0.984575i
$255$	6.30106	+	14.4831i	0.394588	+	0.906969i
$256$	−3.45862	+	15.6217i	−0.216164	+	0.976357i
$257$	−9.61957	−	5.55386i	−0.600052	−	0.346440i	0.169010	−	0.985614i	$-0.445943\pi$
$257$	−9.61957	−	5.55386i	−0.600052	−	0.346440i	−0.769062	+	0.639174i	$0.779276\pi$
$258$	11.9559	+	24.8409i	0.744344	+	1.54653i
$259$	−0.310324	+	1.15815i	−0.0192826	+	0.0719637i
$260$	0.614733	+	8.02755i	0.0381241	+	0.497847i
$261$	−0.101684	−	2.87717i	−0.00629409	−	0.178093i
$262$	5.10067	+	4.72501i	0.315121	+	0.291912i
$263$	−16.6320	+	9.60247i	−1.02557	+	0.592114i	−0.915713	−	0.401834i	$-0.868373\pi$
$263$	−16.6320	+	9.60247i	−1.02557	+	0.592114i	−0.109858	+	0.993947i	$0.535040\pi$
$264$	−0.00484285	−	3.44220i	−0.000298057	−	0.211853i
$265$	−0.00669264	−	0.00386400i	−0.000411125	−	0.000237363i
$266$	0.299987	+	0.969728i	0.0183934	+	0.0594578i
$267$	−2.71671	−	18.1519i	−0.166260	−	1.11088i
$268$	0.767472	−	4.09267i	0.0468808	−	0.250000i
$269$	−7.66476	−	7.66476i	−0.467329	−	0.467329i	0.433719	−	0.901048i	$-0.357201\pi$
$269$	−7.66476	−	7.66476i	−0.467329	−	0.467329i	−0.901048	+	0.433719i	$0.857201\pi$
$270$	−4.60354	+	14.8036i	−0.280162	+	0.900918i
$271$			12.9801i			0.788486i	0.919006	+	0.394243i	$0.128993\pi$
$271$			12.9801i			0.788486i	−0.919006	+	0.394243i	$0.871007\pi$
$272$	13.4825	−	10.8240i	0.817495	−	0.656299i
$273$	−0.339091	−	0.250804i	−0.0205227	−	0.0151794i
$274$	−8.53633	−	4.50269i	−0.515699	−	0.272018i
$275$	0.0998893	+	0.372792i	0.00602355	+	0.0224802i
$276$	−18.5558	−	19.9746i	−1.11693	−	1.20233i
$277$	−6.42631	+	23.9833i	−0.386119	+	1.44102i	0.450276	+	0.892890i	$0.351326\pi$
$277$	−6.42631	+	23.9833i	−0.386119	+	1.44102i	−0.836395	+	0.548127i	$0.815341\pi$
$278$	−11.1088	−	10.2907i	−0.666264	−	0.617194i
$279$	−16.5863	−	3.82191i	−0.992997	−	0.228812i
$280$	−0.596513	−	0.473324i	−0.0356485	−	0.0282865i
$281$	−3.69120	−	6.39334i	−0.220198	−	0.381395i	0.734670	−	0.678425i	$-0.237337\pi$
$281$	−3.69120	−	6.39334i	−0.220198	−	0.381395i	−0.954868	+	0.297030i	$0.904004\pi$
$282$	−9.58914	+	27.3847i	−0.571025	+	1.63073i
$283$	1.60691	+	5.99708i	0.0955211	+	0.356490i	0.997098	−	0.0761294i	$-0.0242562\pi$
$283$	1.60691	+	5.99708i	0.0955211	+	0.356490i	−0.901577	+	0.432619i	$0.857590\pi$
$284$	−6.86505	−	3.29227i	−0.407366	−	0.195360i
$285$	−19.1235	−	7.52830i	−1.13278	−	0.445938i
$286$	−1.60462	+	1.01007i	−0.0948832	+	0.0597269i
$287$	1.17744			0.0695022
$288$	16.9599	+	0.600642i	0.999373	+	0.0353932i
$289$	−1.68344			−0.0990261
$290$	−2.42307	+	1.52527i	−0.142287	+	0.0895668i
$291$	8.99356	−	7.15689i	0.527212	−	0.419544i
$292$	−3.38442	−	1.62307i	−0.198058	−	0.0949827i
$293$	6.43453	+	24.0140i	0.375909	+	1.40291i	0.852012	+	0.523522i	$0.175382\pi$
$293$	6.43453	+	24.0140i	0.375909	+	1.40291i	−0.476103	+	0.879390i	$0.657951\pi$
$294$	−16.8090	+	3.17657i	−0.980322	+	0.185261i
$295$	−4.47288	−	7.74726i	−0.260421	−	0.451063i
$296$	−16.5180	+	20.8171i	−0.960089	+	1.20997i
$297$	−3.58945	+	0.667607i	−0.208281	+	0.0387385i
$298$	−0.219150	−	0.203009i	−0.0126950	−	0.0117600i
$299$	−3.88683	+	14.5058i	−0.224781	+	0.838895i
$300$	−1.85480	+	0.424502i	−0.107087	+	0.0245086i
$301$	0.371735	+	1.38734i	0.0214265	+	0.0799647i
$302$	2.87193	+	1.51487i	0.165261	+	0.0871708i
$303$	2.45006	−	21.5442i	0.140753	−	1.23768i
$304$	−2.44609	+	22.3643i	−0.140293	+	1.28268i
$305$			9.71720i			0.556406i
$306$	−13.8850	−	11.9795i	−0.793754	−	0.684821i
$307$	−17.3773	−	17.3773i	−0.991773	−	0.991773i	0.00819381	−	0.999966i	$-0.497392\pi$
$307$	−17.3773	−	17.3773i	−0.991773	−	0.991773i	−0.999966	+	0.00819381i	$0.997392\pi$
$308$	0.0330532	−	0.176262i	0.00188338	−	0.0100435i
$309$	13.5976	+	5.35294i	0.773541	+	0.304518i
$310$	5.00264	+	16.1714i	0.284131	+	0.918474i
$311$	−11.9437	−	6.89568i	−0.677264	−	0.391018i	0.121560	−	0.992584i	$-0.461210\pi$
$311$	−11.9437	−	6.89568i	−0.677264	−	0.391018i	−0.798823	+	0.601566i	$0.794544\pi$
$312$	−4.68532	−	8.08891i	−0.265254	−	0.457945i
$313$	−17.6368	+	10.1826i	−0.996890	+	0.575555i	−0.907327	−	0.420426i	$-0.861881\pi$
$313$	−17.6368	+	10.1826i	−0.996890	+	0.575555i	−0.0895635	+	0.995981i	$0.528547\pi$
$314$	17.4161	+	16.1334i	0.982848	+	0.910461i
$315$	−0.378883	+	0.713298i	−0.0213476	+	0.0401898i
$316$	0.530619	+	6.92914i	0.0298497	+	0.389795i
$317$	5.44301	−	20.3136i	0.305710	−	1.14092i	−0.626623	−	0.779322i	$-0.715563\pi$
$317$	5.44301	−	20.3136i	0.305710	−	1.14092i	0.932333	−	0.361601i	$-0.117770\pi$
$318$	0.00894754		0.000672523i	0.000501753		3.77132e-5i
$319$	−0.583952	−	0.337145i	−0.0326950	−	0.0188765i
$320$	−7.95910	−	14.8828i	−0.444927	−	0.831976i
$321$	−10.5614	+	14.2792i	−0.589479	+	0.796985i
$322$	−0.756676	−	1.20207i	−0.0421679	−	0.0669886i
$323$	17.1906	−	17.1906i	0.956511	−	0.956511i
$324$	−2.63795	−	17.8057i	−0.146553	−	0.989203i
$325$	0.741113	+	0.741113i	0.0411096	+	0.0411096i
$326$	0.956385	+	0.217469i	0.0529693	+	0.0120445i
$327$	−20.2548	−	14.9812i	−1.12009	−	0.828461i
$328$	23.9445	+	10.3773i	1.32211	+	0.572991i
$329$	−0.755823	+	1.30912i	−0.0416699	+	0.0721743i
$330$	2.36782	+	2.75269i	0.130344	+	0.151531i
$331$	17.0629	+	4.57199i	0.937862	+	0.251299i	0.695204	−	0.718813i	$-0.255314\pi$
$331$	17.0629	+	4.57199i	0.937862	+	0.251299i	0.242658	+	0.970112i	$0.421981\pi$
$332$	−1.98362	+	2.31262i	−0.108865	+	0.126921i
$333$	24.8926	+	13.2222i	1.36411	+	0.724573i
$334$	15.2439	−	0.582819i	0.834108	−	0.0318904i
$335$	2.19618	+	3.80389i	0.119990	+	0.207829i
$336$	0.862412	+	0.194825i	0.0470484	+	0.0106286i
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	−0.966999	−	0.254778i	$-0.917997\pi$
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	0.704144	+	0.710057i	$0.251331\pi$
$338$	6.17509	−	11.7069i	0.335881	−	0.636772i
$339$	−13.4041	+	34.0493i	−0.728012	+	1.84931i
$340$	−3.36143	+	17.9254i	−0.182299	+	0.972141i
$341$	−2.81889	+	2.81889i	−0.152652	+	0.152652i
$342$	23.7979	−	1.75329i	1.28684	−	0.0948071i
$343$	−1.78454			−0.0963558
$344$	−4.66756	+	31.4891i	−0.251658	+	1.69778i
$345$	28.5744	+	3.24956i	1.53840	+	0.174950i
$346$	−1.99729	−	6.45638i	−0.107375	−	0.347097i
$347$	18.4037	−	4.93125i	0.987960	−	0.264723i	0.271567	−	0.962420i	$-0.412458\pi$
$347$	18.4037	−	4.93125i	0.987960	−	0.264723i	0.716393	+	0.697696i	$0.245792\pi$
$348$	1.76699	−	2.81585i	0.0947207	−	0.150946i
$349$	−17.4744	−	4.68226i	−0.935385	−	0.250636i	−0.241236	−	0.970467i	$-0.577553\pi$
$349$	−17.4744	−	4.68226i	−0.935385	−	0.250636i	−0.694150	+	0.719831i	$0.744219\pi$
$350$	−0.0990587	+	0.00378731i	−0.00529491	+	0.000202440i
$351$	−7.53530	+	6.44398i	−0.402205	+	0.343954i
$352$	2.22564	−	3.29315i	0.118627	−	0.175526i
$353$	5.65589	−	3.26543i	0.301033	−	0.173801i	−0.341874	−	0.939746i	$-0.611062\pi$
$353$	5.65589	−	3.26543i	0.301033	−	0.173801i	0.642907	+	0.765944i	$0.277728\pi$
$354$	8.58060	+	5.85294i	0.456054	+	0.311080i
$355$	7.75752	−	2.07862i	0.411726	−	0.110322i
$356$	9.16436	−	19.1096i	0.485710	−	1.01280i
$357$	−0.594916	−	0.747590i	−0.0314863	−	0.0395667i
$358$	−1.56487	+	6.88196i	−0.0827058	+	0.363723i
$359$			22.8075i			1.20373i	0.798597	+	0.601866i	$0.205576\pi$
$359$			22.8075i			1.20373i	−0.798597	+	0.601866i	$0.794424\pi$
$360$	−13.9916	+	11.1664i	−0.737420	+	0.588520i
$361$			12.6341i			0.664952i
$362$	14.3314	+	3.25876i	0.753240	+	0.171277i
$363$	6.66583	−	16.9326i	0.349865	−	0.888732i
$364$	−0.161599	−	0.459420i	−0.00847006	−	0.0240802i
$365$	3.82440	−	1.02475i	0.200178	−	0.0536377i
$366$	−4.89300	−	10.1662i	−0.255761	−	0.531395i
$367$	20.7702	−	11.9917i	1.08419	−	0.625959i	0.152169	−	0.988355i	$-0.451374\pi$
$367$	20.7702	−	11.9917i	1.08419	−	0.625959i	0.932025	+	0.362395i	$0.118041\pi$
$368$	−4.79343	−	31.1142i	−0.249875	−	1.62194i
$369$	6.21519	−	26.9727i	0.323550	−	1.40414i
$370$	−1.07095	−	28.0111i	−0.0556759	−	1.45623i
$371$	0.000451542	0	0.000120990i	2.34429e−5	0	6.28150e-6i
$372$	−13.3767	−	14.3996i	−0.693551	−	0.746582i
$373$	−23.1710	+	6.20866i	−1.19975	+	0.321472i	−0.802733	−	0.596338i	$-0.796622\pi$
$373$	−23.1710	+	6.20866i	−1.19975	+	0.321472i	−0.397018	+	0.917811i	$0.629955\pi$
$374$	−4.10326	+	1.26935i	−0.212174	+	0.0656364i
$375$	12.0580	−	16.3027i	0.622674	−	0.841866i
$376$	−26.9083	+	19.9610i	−1.38769	+	1.02941i
$377$	−1.83115			−0.0943089
$378$	0.0372151	−	0.937038i	0.00191414	−	0.0481960i
$379$	9.96634	−	9.96634i	0.511936	−	0.511936i	−0.403183	−	0.915119i	$-0.632096\pi$
$379$	9.96634	−	9.96634i	0.511936	−	0.511936i	0.915119	+	0.403183i	$0.132096\pi$
$380$	−13.4003	−	19.5860i	−0.687420	−	1.00474i
$381$	22.4585	−	3.36128i	1.15059	−	0.172203i
$382$	6.47668	+	3.41628i	0.331376	+	0.174792i
$383$	−2.30770	+	3.99705i	−0.117918	+	0.204240i	−0.918942	−	0.394392i	$-0.870955\pi$
$383$	−2.30770	+	3.99705i	−0.117918	+	0.204240i	0.801024	+	0.598632i	$0.204289\pi$
$384$	15.8209	+	11.5628i	0.807359	+	0.590061i
$385$	0.0945842	+	0.163825i	0.00482046	+	0.00834927i
$386$	−1.42826	−	37.3568i	−0.0726967	−	1.90141i
$387$	33.7431	−	1.19254i	1.71526	−	0.0606202i
$388$	13.2330	−	1.01336i	0.671806	−	0.0514455i
$389$	−12.3565	−	3.31091i	−0.626498	−	0.167870i	−0.0684178	−	0.997657i	$-0.521795\pi$
$389$	−12.3565	−	3.31091i	−0.626498	−	0.167870i	−0.558080	+	0.829787i	$0.688462\pi$
$390$	9.30642	+	3.25878i	0.471249	+	0.165015i
$391$	−17.0095	+	29.4612i	−0.860205	+	1.48992i
$392$	−18.1240	−	7.85478i	−0.915402	−	0.396726i
$393$	7.80852	−	3.39719i	0.393887	−	0.171366i
$394$	−2.28224	+	10.0368i	−0.114978	+	0.505649i
$395$	−5.18345	−	5.18345i	−0.260808	−	0.260808i
$396$	−3.86331	−	1.68759i	−0.194139	−	0.0848045i
$397$	−3.70313	+	3.70313i	−0.185855	+	0.185855i	−0.793901	−	0.608047i	$-0.791953\pi$
$397$	−3.70313	+	3.70313i	−0.185855	+	0.185855i	0.608047	+	0.793901i	$0.291953\pi$
$398$	−1.64489	+	1.03542i	−0.0824508	+	0.0519010i
$399$	1.23524	+	0.140475i	0.0618392	+	0.00703252i
$400$	−2.04784	−	0.796028i	−0.102392	−	0.0398014i
$401$	11.5871	+	6.68983i	0.578633	+	0.334074i	0.760590	−	0.649232i	$-0.224910\pi$
$401$	11.5871	+	6.68983i	0.578633	+	0.334074i	−0.181957	+	0.983307i	$0.558243\pi$
$402$	−4.21306	−	2.87378i	−0.210128	−	0.143331i
$403$	−2.80199	+	10.4572i	−0.139577	+	0.520908i
$404$	16.3007	−	19.0043i	0.810989	−	0.945497i
$405$	14.3402	+	12.4446i	0.712570	+	0.618376i
$406$	0.117699	−	0.127056i	0.00584128	−	0.00630570i
$407$	5.71713	−	3.30079i	0.283388	−	0.163614i
$408$	−5.50940	−	20.4463i	−0.272756	−	1.01224i
$409$	−24.1053	−	13.9172i	−1.19193	−	0.688161i	−0.233185	−	0.972432i	$-0.574915\pi$
$409$	−24.1053	−	13.9172i	−1.19193	−	0.688161i	−0.958744	+	0.284272i	$0.908248\pi$
$410$	−26.2979	+	8.13530i	−1.29876	+	0.401774i
$411$	−9.24896	+	7.36013i	−0.456217	+	0.363048i
$412$	9.52816	+	13.9264i	0.469419	+	0.686107i
$413$	0.382639	+	0.382639i	0.0188285	+	0.0188285i
$414$	−31.5310	+	10.9886i	−1.54966	+	0.540062i
$415$		−	3.21387i		−	0.157763i
$416$	0.762797	−	10.7670i	0.0373992	−	0.527896i
$417$	−17.0063	+	7.39880i	−0.832802	+	0.362321i
$418$	2.60747	−	4.94332i	0.127536	−	0.241786i
$419$	2.67387	+	9.97902i	0.130627	+	0.487507i	0.999978	−	0.00668892i	$-0.00212917\pi$
$419$	2.67387	+	9.97902i	0.130627	+	0.487507i	−0.869350	+	0.494196i	$0.835462\pi$
$420$	−0.824292	+	0.436276i	−0.0402214	+	0.0212881i
$421$	7.99904	−	29.8528i	0.389849	−	1.45494i	−0.440529	−	0.897738i	$-0.645209\pi$
$421$	7.99904	−	29.8528i	0.389849	−	1.45494i	0.830379	−	0.557199i	$-0.188124\pi$
$422$	11.0820	−	11.9631i	0.539464	−	0.582354i
$423$	25.9996	+	24.2246i	1.26414	+	1.17784i
$424$	0.00811622	+	0.00644009i	0.000394158	+	0.000312758i
$425$	1.18711	+	2.05613i	0.0575833	+	0.0997371i
$426$	−7.06928	+	6.08088i	−0.342508	+	0.294620i
$427$	−0.152134	−	0.567770i	−0.00736226	−	0.0274763i
$428$	−19.3462	+	6.80492i	−0.935134	+	0.328928i
$429$	0.343725	+	2.29662i	0.0165952	+	0.110882i
$430$	−17.8882	−	28.4174i	−0.862643	−	1.37041i
$431$	−14.8449			−0.715053			−0.357526	−	0.933903i	$-0.616380\pi$
$431$	−14.8449			−0.715053			−0.357526	+	0.933903i	$0.616380\pi$
$432$	9.01532	−	18.7276i	0.433750	−	0.901033i
$433$	−32.1617			−1.54559			−0.772796	−	0.634654i	$-0.781143\pi$
$433$	−32.1617			−1.54559			−0.772796	+	0.634654i	$0.781143\pi$
$434$	−0.545482	−	0.866562i	−0.0261840	−	0.0415963i
$435$	0.519044	+	3.46802i	0.0248863	+	0.166279i
$436$	−9.65269	−	27.4423i	−0.462280	−	1.31425i
$437$	−11.4569	−	42.7576i	−0.548056	−	2.04537i
$438$	−3.48511	+	2.99783i	−0.166525	+	0.143242i
$439$	−0.140035	−	0.242548i	−0.00668352	−	0.0115762i	0.862664	−	0.505777i	$-0.168794\pi$
$439$	−0.140035	−	0.242548i	−0.00668352	−	0.0115762i	−0.869348	+	0.494201i	$0.835461\pi$
$440$	0.479609	+	4.16515i	0.0228644	+	0.198566i
$441$	−4.70440	+	20.4161i	−0.224019	+	0.972197i
$442$	−7.92663	+	8.55684i	−0.377031	+	0.407007i
$443$	−6.50011	+	24.2588i	−0.308830	+	1.15257i	0.620768	+	0.783994i	$0.286821\pi$
$443$	−6.50011	+	24.2588i	−0.308830	+	1.15257i	−0.929598	+	0.368574i	$0.879846\pi$
$444$	15.2251	+	28.7661i	0.722552	+	1.36518i
$445$	5.78605	+	21.5938i	0.274285	+	1.02365i
$446$	13.6999	−	25.9726i	0.648708	−	1.22984i
$447$	−0.335492	+	0.145960i	−0.0158682	+	0.00690367i
$448$	0.698052	+	0.744986i	0.0329799	+	0.0351973i
$449$			14.2885i			0.674318i	0.941448	+	0.337159i	$0.109466\pi$
$449$			14.2885i			0.674318i	−0.941448	+	0.337159i	$0.890534\pi$
$450$	−0.436128	+	2.28922i	−0.0205593	+	0.107915i
$451$	−4.58408	−	4.58408i	−0.215856	−	0.215856i
$452$	−34.8728	+	23.8592i	−1.64028	+	1.12224i
$453$	3.11168	−	2.47621i	0.146200	−	0.116343i
$454$	10.7058	−	3.31184i	0.502446	−	0.155432i
$455$	0.444893	+	0.256859i	0.0208569	+	0.0120417i
$456$	23.8818	+	13.7434i	1.11837	+	0.643592i
$457$	24.1097	−	13.9198i	1.12781	−	0.651139i	0.184424	−	0.982847i	$-0.440958\pi$
$457$	24.1097	−	13.9198i	1.12781	−	0.651139i	0.943382	+	0.331708i	$0.107625\pi$
$458$	0.446434	−	0.481928i	0.0208605	−	0.0225190i
$459$	−20.2660	+	9.68207i	−0.945935	+	0.451921i
$460$	25.2057	+	21.6199i	1.17522	+	1.00803i
$461$	4.33776	−	16.1887i	0.202030	−	0.753985i	−0.788305	−	0.615285i	$-0.789041\pi$
$461$	4.33776	−	16.1887i	0.202030	−	0.753985i	0.990334	−	0.138700i	$-0.0442923\pi$
$462$	−0.181447	−	0.123767i	−0.00844166	−	0.00575817i
$463$	−26.1951	−	15.1238i	−1.21739	−	0.702861i	−0.253032	−	0.967458i	$-0.581428\pi$
$463$	−26.1951	−	15.1238i	−1.21739	−	0.702861i	−0.964359	+	0.264597i	$0.914761\pi$
$464$	3.51332	−	1.54649i	0.163102	−	0.0717940i
$465$	20.5991	+	2.34259i	0.955261	+	0.108635i
$466$	−10.9359	+	6.88393i	−0.506597	+	0.318892i
$467$	−15.9369	+	15.9369i	−0.737469	+	0.737469i	−0.972088	−	0.234618i	$-0.924616\pi$
$467$	−15.9369	+	15.9369i	−0.737469	+	0.737469i	0.234618	+	0.972088i	$0.424616\pi$
$468$	−11.3773	+	1.27680i	−0.525918	+	0.0590202i
$469$	−0.187875	−	0.187875i	−0.00867527	−	0.00867527i
$470$	7.83603	−	34.4612i	0.361449	−	1.58958i
$471$	26.6620	−	11.5996i	1.22852	−	0.534482i
$472$	4.40900	+	11.1537i	0.202940	+	0.513392i
$473$	3.95399	−	6.84851i	0.181805	−	0.314895i
$474$	8.03303	+	2.81288i	0.368969	+	0.129200i
$475$	−2.98410	−	0.799588i	−0.136920	−	0.0366876i
$476$	−0.0842354	−	1.10000i	−0.00386092	−	0.0504183i
$477$	0.00515511	−	0.00970520i	0.000236036	−	0.000444371i
$478$	−0.395311	−	10.3395i	−0.0180811	−	0.472919i
$479$	14.8100	+	25.6516i	0.676684	+	1.17205i	0.975973	+	0.217889i	$0.0699172\pi$
$479$	14.8100	+	25.6516i	0.676684	+	1.17205i	−0.299289	+	0.954163i	$0.596749\pi$
$480$	−20.6079	+	1.60728i	−0.940618	+	0.0733618i
$481$	8.96385	−	15.5258i	0.408716	−	0.707917i
$482$	−3.12361	−	1.64763i	−0.142277	−	0.0750473i
$483$	−1.72046	+	0.257494i	−0.0782837	+	0.0117164i
$484$	17.3421	−	11.8651i	0.788278	−	0.539322i
$485$	−9.89919	+	9.89919i	−0.449499	+	0.449499i
$486$	−21.2691	−	5.79873i	−0.964786	−	0.263036i
$487$	25.6320			1.16150			0.580749	−	0.814083i	$-0.302760\pi$
$487$	25.6320			1.16150			0.580749	+	0.814083i	$0.302760\pi$
$488$	1.91021	−	12.8870i	0.0864712	−	0.583367i
$489$	0.714315	−	0.965765i	0.0323024	−	0.0436734i
$490$	19.9054	−	6.15777i	0.899235	−	0.278180i
$491$	−5.25069	+	1.40692i	−0.236960	+	0.0634933i	−0.375345	−	0.926885i	$-0.622476\pi$
$491$	−5.25069	+	1.40692i	−0.236960	+	0.0634933i	0.138385	+	0.990379i	$0.455809\pi$
$492$	23.4166	−	21.7532i	1.05570	−	0.980712i
$493$	−4.00671	−	1.07360i	−0.180453	−	0.0483523i
$494$	−0.579857	−	15.1664i	−0.0260890	−	0.682369i
$495$	4.25214	−	1.30196i	0.191119	−	0.0585190i
$496$	−3.45555	−	22.4300i	−0.155159	−	1.00714i
$497$	−0.420724	+	0.242905i	−0.0188720	+	0.0108958i
$498$	1.61831	+	3.36236i	0.0725182	+	0.150671i
$499$	−21.5779	+	5.78179i	−0.965961	+	0.258829i	−0.707122	−	0.707092i	$-0.750007\pi$
$499$	−21.5779	+	5.78179i	−0.965961	+	0.258829i	−0.258840	+	0.965920i	$0.583340\pi$
$500$	22.0878	−	7.76925i	0.987795	−	0.347452i
$501$	6.84387	−	17.3849i	0.305762	−	0.776700i
$502$	5.41432	+	1.23114i	0.241653	+	0.0549487i
$503$			24.7337i			1.10282i	0.834235	+	0.551410i	$0.185910\pi$
$503$			24.7337i			1.10282i	−0.834235	+	0.551410i	$0.814090\pi$
$504$	0.642696	−	0.871498i	0.0286280	−	0.0388196i
$505$			26.4104i			1.17525i
$506$	−1.73403	+	7.62589i	−0.0770869	+	0.339012i
$507$	−10.0938	−	12.6842i	−0.448284	−	0.563327i
$508$	23.6435	+	11.3387i	1.04901	+	0.503073i
$509$	−8.62284	+	2.31048i	−0.382201	+	0.102410i	−0.444804	−	0.895628i	$-0.646726\pi$
$509$	−8.62284	+	2.31048i	−0.382201	+	0.102410i	0.0626029	+	0.998039i	$0.480060\pi$
$510$	18.4527	+	12.5868i	0.817098	+	0.557354i
$511$	−0.207414	+	0.119751i	−0.00917545	+	0.00529745i
$512$	7.62971	+	21.3023i	0.337189	+	0.941437i
$513$	9.73824	−	27.5552i	0.429954	−	1.21659i
$514$	−15.6972	+	0.600152i	−0.692375	+	0.0264716i
$515$	−17.1928	−	4.60680i	−0.757606	−	0.203000i
$516$	33.0240	+	20.7231i	1.45380	+	0.912282i
$517$	8.03937	−	2.15414i	0.353571	−	0.0947391i
$518$	0.501119	+	1.61990i	0.0220179	+	0.0711745i
$519$	−8.22413	−	0.935271i	−0.360999	−	0.0410538i
$520$	6.78354	+	9.14453i	0.297478	+	0.401014i
$521$	−14.1129			−0.618299			−0.309149	−	0.951013i	$-0.600044\pi$
$521$	−14.1129			−0.618299			−0.309149	+	0.951013i	$0.600044\pi$
$522$	−2.28931	−	3.36690i	−0.100200	−	0.147365i
$523$	−27.5776	+	27.5776i	−1.20588	+	1.20588i	−0.233534	+	0.972349i	$0.575029\pi$
$523$	−27.5776	+	27.5776i	−1.20588	+	1.20588i	−0.972349	+	0.233534i	$0.924971\pi$
$524$	9.66440	+	1.81230i	0.422191	+	0.0791708i
$525$	−0.0444733	+	0.112972i	−0.00194097	+	0.00493048i
$526$	−12.6714	+	24.0228i	−0.552499	+	1.04744i
$527$	−12.2620	+	21.2384i	−0.534141	+	0.925159i
$528$	−2.59909	−	4.11610i	−0.113111	−	0.179130i
$529$	19.4709	+	33.7246i	0.846561	+	1.46629i
$530$	−0.0109211		0.000417544i	−0.000474380		1.81370e-5i
$531$	10.7852	−	6.74567i	0.468039	−	0.292737i
$532$	1.08961	+	0.934600i	0.0472406	+	0.0405201i
$533$	−17.0054	−	4.55660i	−0.736588	−	0.197368i
$534$	−16.9267	−	19.6781i	−0.732492	−	0.851553i
$535$	10.8164	−	18.7345i	0.467632	−	0.809962i
$536$	−2.16481	−	5.47646i	−0.0935054	−	0.236547i
$537$	6.94946	+	5.14007i	0.299891	+	0.221810i
$538$	−14.9479	−	3.39896i	−0.644452	−	0.146540i
$539$	3.46978	+	3.46978i	0.149454	+	0.149454i
$540$	5.64309	+	21.1857i	0.242840	+	0.911687i
$541$	7.82995	−	7.82995i	0.336636	−	0.336636i	−0.518464	−	0.855100i	$-0.673496\pi$
$541$	7.82995	−	7.82995i	0.336636	−	0.336636i	0.855100	+	0.518464i	$0.173496\pi$
$542$	9.77898	+	15.5351i	0.420043	+	0.667288i
$543$	10.7040	−	14.4719i	0.459351	−	0.621050i
$544$	7.98173	−	23.1119i	0.342214	−	0.990917i
$545$	26.5746	+	15.3429i	1.13833	+	0.657216i
$546$	−0.594788	−	0.0447060i	−0.0254546	−	0.00191324i
$547$	5.82566	−	21.7416i	0.249087	−	0.929606i	−0.722198	−	0.691686i	$-0.756868\pi$
$547$	5.82566	−	21.7416i	0.249087	−	0.929606i	0.971285	−	0.237919i	$-0.0764653\pi$
$548$	−13.6088	+	1.04214i	−0.581340	+	0.0445178i
$549$	−13.8094	+	0.488049i	−0.589373	+	0.0208294i
$550$	0.400406	+	0.370916i	0.0170734	+	0.0158159i
$551$	4.67438	−	2.69876i	0.199135	−	0.114971i
$552$	−37.2567	−	9.92675i	−1.58575	−	0.422511i
$553$	0.384019	+	0.221713i	0.0163301	+	0.00942821i
$554$	10.3774	+	33.5455i	0.440892	+	1.42521i
$555$	−31.9453	−	12.5758i	−1.35600	−	0.533814i
$556$	−21.0483	−	3.94705i	−0.892645	−	0.167392i
$557$	25.5918	+	25.5918i	1.08436	+	1.08436i	0.996097	+	0.0882628i	$0.0281315\pi$
$557$	25.5918	+	25.5918i	1.08436	+	1.08436i	0.0882628	+	0.996097i	$0.471868\pi$
$558$	−22.7305	+	7.92164i	−0.962257	+	0.335350i
$559$		−	21.4755i		−	0.908315i
$560$	−1.07052	−	0.117088i	−0.0452378	−	0.00494788i
$561$	−0.594397	+	5.22672i	−0.0250955	+	0.220672i
$562$	−9.23439	−	4.87090i	−0.389529	−	0.205466i
$563$	3.04735	+	11.3728i	0.128430	+	0.479308i	0.999939	−	0.0110721i	$-0.00352444\pi$
$563$	3.04735	+	11.3728i	0.128430	+	0.479308i	−0.871508	+	0.490381i	$0.836858\pi$
$564$	9.15450	+	39.9993i	0.385474	+	1.68427i
$565$	11.5357	−	43.0520i	0.485313	−	1.81121i
$566$	6.44131	+	5.96690i	0.270748	+	0.250808i
$567$	−1.03272	−	0.502617i	−0.0433702	−	0.0211079i
$568$	−10.6967	+	1.23170i	−0.448822	+	0.0516810i
$569$	−0.819418	−	1.41927i	−0.0343518	−	0.0594990i	0.848338	−	0.529454i	$-0.177603\pi$
$569$	−0.819418	−	1.41927i	−0.0343518	−	0.0594990i	−0.882690	+	0.469955i	$0.844270\pi$
$570$	−28.5594	+	5.39716i	−1.19622	+	0.226062i
$571$	8.76233	+	32.7015i	0.366692	+	1.36851i	0.865112	+	0.501578i	$0.167247\pi$
$571$	8.76233	+	32.7015i	0.366692	+	1.36851i	−0.498420	+	0.866936i	$0.666086\pi$
$572$	−1.15950	+	2.41779i	−0.0484810	+	0.101093i
$573$	7.01737	−	5.58427i	0.293155	−	0.233286i
$574$	1.40920	−	0.887064i	0.0588191	−	0.0370253i
$575$	4.32299			0.180281
$576$	20.7508	−	12.0584i	0.864615	−	0.502435i
$577$	−16.0429			−0.667873			−0.333936	−	0.942596i	$-0.608377\pi$
$577$	−16.0429			−0.667873			−0.333936	+	0.942596i	$0.608377\pi$
$578$	−2.01481	+	1.26828i	−0.0838049	+	0.0527533i
$579$	−42.6036	−	16.7717i	−1.77055	−	0.697007i
$580$	−1.75090	+	3.65099i	−0.0727023	+	0.151599i
$581$	0.0503166	+	0.187784i	0.00208749	+	0.00779060i
$582$	5.37194	−	15.3412i	0.222674	−	0.635913i
$583$	−0.00128692	−	0.00222901i	−5.32988e−5	−	9.23163e-5i
$584$	−5.27339	+	0.607220i	−0.218214	+	0.0251269i
$585$	8.23249	−	8.83571i	0.340372	−	0.365312i
$586$	25.7928	+	23.8931i	1.06549	+	0.987016i
$587$	9.90974	−	36.9837i	0.409019	−	1.52648i	−0.387502	−	0.921869i	$-0.626662\pi$
$587$	9.90974	−	36.9837i	0.409019	−	1.52648i	0.796521	−	0.604611i	$-0.206671\pi$
$588$	−17.7245	+	16.4654i	−0.730944	+	0.679023i
$589$	−8.25918	−	30.8237i	−0.340313	−	1.27007i
$590$	−11.1899	−	5.90241i	−0.460683	−	0.242998i
$591$	10.1353	+	7.49641i	0.416910	+	0.308361i
$592$	−4.08613	+	37.3590i	−0.167939	+	1.53544i
$593$		−	32.2597i		−	1.32475i	−0.749173	−	0.662374i	$-0.769549\pi$
$593$		−	32.2597i		−	1.32475i	0.749173	−	0.662374i	$-0.230451\pi$
$594$	−3.79302	+	3.50324i	−0.155629	+	0.143740i
$595$	0.822870	+	0.822870i	0.0337344	+	0.0337344i
$596$	−0.415230	−	0.0778654i	−0.0170085	−	0.00318949i
$597$	0.352351	+	2.35425i	0.0144207	+	0.0963529i
$598$	6.27655	+	20.2894i	0.256667	+	0.829694i
$599$	11.7417	+	6.77905i	0.479751	+	0.276984i	0.720313	−	0.693649i	$-0.243998\pi$
$599$	11.7417	+	6.77905i	0.479751	+	0.276984i	−0.240562	+	0.970634i	$0.577332\pi$
$600$	−1.90008	+	1.90543i	−0.0775703	+	0.0777889i
$601$	0.496416	−	0.286606i	0.0202492	−	0.0116909i	−0.489841	−	0.871812i	$-0.662945\pi$
$601$	0.496416	−	0.286606i	0.0202492	−	0.0116909i	0.510090	+	0.860121i	$0.329612\pi$
$602$	1.49010	+	1.38035i	0.0607319	+	0.0562590i
$603$	−5.29553	+	3.31211i	−0.215651	+	0.134880i
$604$	4.57850	−	0.350612i	0.186297	−	0.0142662i
$605$	−5.73669	+	21.4096i	−0.233230	+	0.870425i
$606$	−13.2987	−	27.6307i	−0.540222	−	1.12242i
$607$	−29.1103	−	16.8068i	−1.18155	−	0.682168i	−0.225178	−	0.974318i	$-0.572296\pi$
$607$	−29.1103	−	16.8068i	−1.18155	−	0.682168i	−0.956373	+	0.292149i	$0.905630\pi$
$608$	13.9213	+	28.6092i	0.564583	+	1.16026i
$609$	−0.0846230	−	0.194508i	−0.00342910	−	0.00788185i
$610$	7.32077	+	11.6299i	0.296409	+	0.470881i
$611$	15.9823	−	15.9823i	0.646576	−	0.646576i
$612$	−25.6432	−	3.87674i	−1.03657	−	0.156708i
$613$	26.5621	+	26.5621i	1.07283	+	1.07283i	0.997130	+	0.0757042i	$0.0241205\pi$
$613$	26.5621	+	26.5621i	1.07283	+	1.07283i	0.0757042	+	0.997130i	$0.475880\pi$
$614$	−33.8894	−	7.70601i	−1.36767	−	0.310989i
$615$	−3.80951	+	33.4983i	−0.153614	+	1.35078i
$616$	−0.0932332	−	0.235858i	−0.00375647	−	0.00950300i
$617$	−11.8730	+	20.5647i	−0.477991	+	0.827904i	−0.999682	−	0.0252305i	$-0.991968\pi$
$617$	−11.8730	+	20.5647i	−0.477991	+	0.827904i	0.521691	+	0.853134i	$0.325301\pi$
$618$	20.3069	−	3.83760i	0.816863	−	0.154371i
$619$	−17.1798	−	4.60330i	−0.690513	−	0.185022i	−0.103535	−	0.994626i	$-0.533016\pi$
$619$	−17.1798	−	4.60330i	−0.690513	−	0.185022i	−0.586977	+	0.809603i	$0.699682\pi$
$620$	18.1706	+	15.5856i	0.729748	+	0.625933i
$621$	−3.18290	+	40.7713i	−0.127725	+	1.63610i
$622$	−19.4897	+	0.745149i	−0.781466	+	0.0298778i
$623$	−0.676151	−	1.17113i	−0.0270894	−	0.0469202i
$624$	−11.7016	−	6.15126i	−0.468439	−	0.246248i
$625$	−10.9760	+	19.0109i	−0.439038	+	0.760436i
$626$	−13.4369	+	25.4741i	−0.537048	+	1.01815i
$627$	−4.26219	−	5.35600i	−0.170216	−	0.213898i
$628$	32.9988	+	6.18806i	1.31680	+	0.246930i
$629$	28.7164	−	28.7164i	1.14500	−	1.14500i
$630$	0.0839255	+	1.13914i	0.00334367	+	0.0453846i
$631$	16.0572			0.639228			0.319614	−	0.947548i	$-0.396447\pi$
$631$	16.0572			0.639228			0.319614	+	0.947548i	$0.396447\pi$
$632$	5.85535	+	7.89328i	0.232913	+	0.313978i
$633$	−7.96776	−	18.3141i	−0.316690	−	0.727919i
$634$	−8.78950	−	28.4127i	−0.349076	−	1.12841i
$635$	−26.7172	+	7.15884i	−1.06024	+	0.284090i
$636$	0.0112154	−	0.00593602i	0.000444720	−	0.000235378i
$637$	12.8717	+	3.44897i	0.509997	+	0.136653i
$638$	−0.952893	+	0.0364320i	−0.0377254	+	0.00144235i
$639$	3.34362	+	10.9201i	0.132272	+	0.431991i
$640$	−20.7382	−	11.8161i	−0.819749	−	0.467071i
$641$	35.3930	−	20.4342i	1.39794	−	0.807102i	0.403764	−	0.914863i	$-0.367702\pi$
$641$	35.3930	−	20.4342i	1.39794	−	0.807102i	0.994177	+	0.107761i	$0.0343683\pi$
$642$	−1.88257	+	25.0466i	−0.0742992	+	0.988509i
$643$	33.2700	−	8.91467i	1.31204	−	0.351560i	0.466050	−	0.884758i	$-0.345677\pi$
$643$	33.2700	−	8.91467i	1.31204	−	0.351560i	0.845991	+	0.533198i	$0.179010\pi$
$644$	−1.81123	−	0.868612i	−0.0713726	−	0.0342281i
$645$	−40.6725	+	6.08728i	−1.60148	+	0.239686i
$646$	7.62324	−	33.5254i	0.299932	−	1.31904i
$647$		−	28.1696i		−	1.10746i	−0.832696	−	0.553730i	$-0.813204\pi$
$647$		−	28.1696i		−	1.10746i	0.832696	−	0.553730i	$-0.186796\pi$
$648$	−16.5717	−	19.3231i	−0.650996	−	0.759081i
$649$		−	2.97943i		−	0.116953i
$650$	1.44533	+	0.328649i	0.0566906	+	0.0128907i
$651$	−1.24027	+	0.185626i	−0.0486099	+	0.00727525i
$652$	1.30847	−	0.460248i	0.0512438	−	0.0180247i
$653$	8.11558	−	2.17456i	0.317587	−	0.0850972i	−0.0965042	−	0.995333i	$-0.530766\pi$
$653$	8.11558	−	2.17456i	0.317587	−	0.0850972i	0.414091	+	0.910235i	$0.364099\pi$
$654$	−35.5282	−	2.67040i	−1.38926	−	0.104421i
$655$	−8.98247	+	5.18603i	−0.350974	+	0.202635i
$656$	36.4757	−	5.61941i	1.42414	−	0.219401i
$657$	1.64838	+	5.38352i	0.0643096	+	0.210031i
$658$	0.0816744	+	2.13623i	0.00318400	+	0.0832789i
$659$	−24.7356	−	6.62788i	−0.963562	−	0.258186i	−0.257455	−	0.966290i	$-0.582884\pi$
$659$	−24.7356	−	6.62788i	−0.963562	−	0.258186i	−0.706107	+	0.708105i	$0.749550\pi$
$660$	4.90772	+	1.51065i	0.191033	+	0.0588018i
$661$	20.3200	−	5.44473i	0.790357	−	0.211775i	0.159011	−	0.987277i	$-0.449170\pi$
$661$	20.3200	−	5.44473i	0.790357	−	0.211775i	0.631346	+	0.775501i	$0.282503\pi$
$662$	23.8659	−	7.38296i	0.927576	−	0.286947i
$663$	5.69910	+	13.0995i	0.221335	+	0.508742i
$664$	−0.631783	+	4.26224i	−0.0245179	+	0.165407i
$665$	−1.51424			−0.0587198
$666$	39.7537	−	2.92882i	1.54043	−	0.113490i
$667$	−5.34063	+	5.34063i	−0.206790	+	0.206790i
$668$	17.8053	−	12.1820i	0.688909	−	0.471336i
$669$	−22.3939	−	28.1408i	−0.865798	−	1.08799i
$670$	5.49424	+	2.89807i	0.212261	+	0.111962i
$671$	−1.61818	+	2.80277i	−0.0624691	+	0.108200i
$672$	1.17894	−	0.416552i	0.0454787	−	0.0160688i
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	0.517110	−	0.855919i	$-0.327008\pi$
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	−0.999803	+	0.0198709i	$0.993674\pi$
$674$	0.521432	+	13.6383i	0.0200848	+	0.525327i
$675$	2.35318	+	1.61511i	0.0905741	+	0.0621658i
$676$	−1.42921	−	18.6635i	−0.0549696	−	0.717825i
$677$	−18.3334	−	4.91241i	−0.704608	−	0.188799i	−0.111314	−	0.993785i	$-0.535506\pi$
$677$	−18.3334	−	4.91241i	−0.704608	−	0.188799i	−0.593294	+	0.804986i	$0.702173\pi$
$678$	9.60963	+	50.8499i	0.369056	+	1.95288i
$679$	0.423420	−	0.733386i	0.0162494	−	0.0281448i
$680$	9.48159	+	23.9862i	0.363602	+	0.919829i
$681$	1.55083	−	13.6370i	0.0594281	−	0.522570i
$682$	−1.25005	+	5.49745i	−0.0478668	+	0.210508i
$683$	−3.70253	−	3.70253i	−0.141673	−	0.141673i	0.632713	−	0.774386i	$-0.281941\pi$
$683$	−3.70253	−	3.70253i	−0.141673	−	0.141673i	−0.774386	+	0.632713i	$0.781941\pi$
$684$	27.1613	−	20.0273i	1.03854	−	0.765763i
$685$	10.1803	−	10.1803i	0.388969	−	0.388969i
$686$	−2.13580	+	1.34444i	−0.0815450	+	0.0513308i
$687$	−0.320978	−	0.737774i	−0.0122461	−	0.0281478i
$688$	18.1370	+	41.2038i	0.691468	+	1.57088i
$689$	−0.00605326	−	0.00349485i	−0.000230611	−	0.000133143i
$690$	36.6471	−	17.6383i	1.39513	−	0.671477i
$691$	−2.19392	+	8.18783i	−0.0834607	+	0.311480i	−0.995018	−	0.0996929i	$-0.968214\pi$
$691$	−2.19392	+	8.18783i	−0.0834607	+	0.311480i	0.911558	+	0.411173i	$0.134881\pi$
$692$	−7.25455	−	6.22251i	−0.275777	−	0.236544i
$693$	−0.228066	+	0.142645i	−0.00866352	+	0.00541863i
$694$	18.3110	−	19.7669i	0.695078	−	0.750340i
$695$	19.5631	−	11.2947i	0.742070	−	0.428434i
$696$	−0.00661434	−	4.70133i	−0.000250716	−	0.178204i
$697$	−34.5379	−	19.9405i	−1.30822	−	0.755299i
$698$	−24.4416	+	7.56103i	−0.925127	+	0.286189i
$699$	2.34258	+	15.6521i	0.0886045	+	0.592015i
$700$	−0.115704	+	0.0791618i	−0.00437319	+	0.00299204i
$701$	−16.2977	−	16.2977i	−0.615557	−	0.615557i	0.328831	−	0.944389i	$-0.393345\pi$
$701$	−16.2977	−	16.2977i	−0.615557	−	0.615557i	−0.944389	+	0.328831i	$0.893345\pi$
$702$	−4.16374	+	13.3893i	−0.157150	+	0.505348i
$703$			52.8439i			1.99304i
$704$	0.182727	−	5.61812i	0.00688680	−	0.211741i
$705$	−34.7992	−	25.7388i	−1.31062	−	0.969378i
$706$	4.30906	−	8.16923i	0.162173	−	0.307453i
$707$	−0.413484	−	1.54314i	−0.0155507	−	0.0580359i
$708$	14.6791	+	0.540543i	0.551673	+	0.0203149i
$709$	4.99557	−	18.6437i	0.187613	−	0.700180i	−0.806443	−	0.591311i	$-0.798610\pi$
$709$	4.99557	−	18.6437i	0.187613	−	0.700180i	0.994056	−	0.108869i	$-0.0347229\pi$
$710$	7.71848	−	8.33214i	0.289669	−	0.312700i
$711$	7.10604	−	7.62672i	0.266497	−	0.286024i
$712$	−3.42856	−	29.7753i	−0.128491	−	1.11588i
$713$	22.3267	+	38.6710i	0.836142	+	1.44824i
$714$	−1.27524	−	0.446543i	−0.0477246	−	0.0167114i
$715$	−0.732065	−	2.73210i	−0.0273777	−	0.102175i
$716$	3.31186	+	9.41552i	0.123770	+	0.351875i
$717$	−11.7917	−	4.64202i	−0.440370	−	0.173359i
$718$	17.1827	+	27.2968i	0.641254	+	1.01871i
$719$	24.2401			0.904003			0.452002	−	0.892017i	$-0.350710\pi$
$719$	24.2401			0.904003			0.452002	+	0.892017i	$0.350710\pi$
$720$	−8.33305	+	23.9053i	−0.310555	+	0.890899i
$721$	1.07669			0.0400980
$722$	9.51830	+	15.1209i	0.354234	+	0.562743i
$723$	−3.38438	+	2.69322i	−0.125866	+	0.100162i
$724$	19.6074	−	6.89679i	0.728703	−	0.256317i
$725$	0.136428	+	0.509157i	0.00506682	+	0.0189096i
$726$	−4.77884	−	25.2875i	−0.177359	−	0.938507i
$727$	−8.10074	−	14.0309i	−0.300440	−	0.520377i	0.675796	−	0.737089i	$-0.263800\pi$
$727$	−8.10074	−	14.0309i	−0.300440	−	0.520377i	−0.976236	+	0.216712i	$0.930467\pi$
$728$	−0.539526	−	0.428105i	−0.0199962	−	0.0158666i
$729$	−16.9652	+	21.0044i	−0.628340	+	0.777939i
$730$	3.80516	−	4.10769i	0.140835	−	0.152032i
$731$	12.5910	−	46.9902i	0.465694	−	1.73800i
$732$	−13.5151	−	8.48096i	−0.499534	−	0.313465i
$733$	−2.15479	−	8.04180i	−0.0795891	−	0.297031i	0.914646	−	0.404257i	$-0.132470\pi$
$733$	−2.15479	−	8.04180i	−0.0795891	−	0.297031i	−0.994235	+	0.107226i	$0.965803\pi$
$734$	15.8242	−	29.9999i	0.584081	−	1.10732i
$735$	2.88349	−	25.3555i	0.106359	−	0.935251i
$736$	−29.1778	−	33.6273i	−1.07551	−	1.23952i
$737$			1.46289i			0.0538863i
$738$	−12.8822	−	36.9643i	−0.474199	−	1.36067i
$739$	22.8405	+	22.8405i	0.840203	+	0.840203i	0.988885	−	0.148682i	$-0.0475030\pi$
$739$	22.8405	+	22.8405i	0.840203	+	0.840203i	−0.148682	+	0.988885i	$0.547503\pi$
$740$	−22.3848	−	32.7178i	−0.822882	−	1.20273i
$741$	−17.2966	−	6.80909i	−0.635405	−	0.250138i
$742$	0.000631573	0	0.000195378i	2.31858e−5	0	7.17255e-6i
$743$	−7.19608	−	4.15466i	−0.263999	−	0.152420i	0.362159	−	0.932116i	$-0.382040\pi$
$743$	−7.19608	−	4.15466i	−0.263999	−	0.152420i	−0.626157	+	0.779697i	$0.715373\pi$
$744$	−26.8581	−	7.15612i	−0.984666	−	0.262356i
$745$	0.385931	−	0.222817i	0.0141394	−	0.00816339i
$746$	−23.0544	+	24.8874i	−0.844083	+	0.911192i
$747$	4.56734	−	0.161417i	0.167110	−	0.00590595i
$748$	−3.95462	+	4.61052i	−0.144595	+	0.168577i
$749$	−0.338684	+	1.26399i	−0.0123752	+	0.0461850i
$750$	2.14935	−	28.5959i	0.0784832	−	1.04418i
$751$	−28.0215	−	16.1782i	−1.02252	−	0.590352i	−0.107687	−	0.994185i	$-0.534344\pi$
$751$	−28.0215	−	16.1782i	−1.02252	−	0.590352i	−0.914833	+	0.403833i	$0.867678\pi$
$752$	−17.1666	+	44.1622i	−0.626001	+	1.61043i
$753$	4.04390	−	5.46742i	0.147368	−	0.199244i
$754$	−2.19158	+	1.37955i	−0.0798127	+	0.0502404i
$755$	−3.42502	+	3.42502i	−0.124649	+	0.124649i
$756$	−0.661407	−	1.14952i	−0.0240551	−	0.0418076i
$757$	3.76265	+	3.76265i	0.136756	+	0.136756i	0.772171	−	0.635415i	$-0.219171\pi$
$757$	3.76265	+	3.76265i	0.136756	+	0.136756i	−0.635415	+	0.772171i	$0.719171\pi$
$758$	4.41961	−	19.4365i	0.160527	−	0.705967i
$759$	7.70069	+	5.69570i	0.279517	+	0.206741i
$760$	−30.7937	−	13.3457i	−1.11700	−	0.484098i
$761$	−13.1168	+	22.7190i	−0.475485	+	0.823564i	−0.999606	−	0.0280801i	$-0.991061\pi$
$761$	−13.1168	+	22.7190i	−0.475485	+	0.823564i	0.524121	+	0.851644i	$0.324394\pi$
$762$	24.3469	−	20.9428i	0.881993	−	0.758676i
$763$	−1.79295	−	0.480419i	−0.0649090	−	0.0173923i
$764$	10.3253	−	0.790689i	0.373556	−	0.0286061i
$765$	23.1938	−	14.5066i	0.838572	−	0.524489i
$766$	0.249371	+	6.52239i	0.00901012	+	0.235664i
$767$	−4.04557	−	7.00713i	−0.146077	−	0.253013i
$768$	27.6463	+	1.91953i	0.997598	+	0.0692651i
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	−0.983665	−	0.180009i	$-0.942387\pi$
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	0.647725	+	0.761874i	$0.275721\pi$
$770$	0.236624	+	0.124813i	0.00852734	+	0.00449795i
$771$	−7.04741	+	17.9019i	−0.253806	+	0.644722i
$772$	−29.8534	−	43.6340i	−1.07445	−	1.57042i
$773$	4.69430	−	4.69430i	0.168842	−	0.168842i	−0.617628	−	0.786470i	$-0.711906\pi$
$773$	4.69430	−	4.69430i	0.168842	−	0.168842i	0.786470	+	0.617628i	$0.211906\pi$
$774$	39.4865	−	26.8487i	1.41931	−	0.965058i
$775$	3.11641			0.111945
$776$	15.0743	−	11.1824i	0.541137	−	0.401423i
$777$	2.06343	+	0.234659i	0.0740252	+	0.00841834i
$778$	−17.2830	+	5.34653i	−0.619627	+	0.191682i
$779$	50.1255	−	13.4311i	1.79593	−	0.481218i
$780$	13.5934	−	3.11107i	0.486720	−	0.111394i
$781$	2.58368	+	0.692294i	0.0924512	+	0.0247722i
$782$	1.83805	+	48.0749i	0.0657284	+	1.71915i
$783$	−4.90245	+	0.911813i	−0.175199	+	0.0325855i
$784$	−27.6091	+	4.25344i	−0.986041	+	0.151909i
$785$	−30.6704	+	17.7076i	−1.09467	+	0.632010i
$786$	6.78613	−	9.94867i	0.242053	−	0.354857i
$787$	43.7964	−	11.7352i	1.56117	−	0.418315i	0.628139	−	0.778101i	$-0.283817\pi$
$787$	43.7964	−	11.7352i	1.56117	−	0.418315i	0.933035	+	0.359786i	$0.117150\pi$
$788$	4.83010	+	13.7318i	0.172065	+	0.489177i
$789$	20.7128	+	26.0283i	0.737394	+	0.926631i
$790$	−10.1089	−	2.29862i	−0.359657	−	0.0817813i
$791$			2.69611i			0.0958625i
$792$	−5.89515	+	0.890784i	−0.209475	+	0.0316526i
$793$			8.78888i			0.312102i
$794$	−1.64217	+	7.22191i	−0.0582783	+	0.256296i
$795$	−0.00490310	+	0.0124549i	−0.000173895	+	0.000441731i
$796$	−1.18859	+	2.47846i	−0.0421286	+	0.0878466i
$797$	−36.4751	+	9.77347i	−1.29201	+	0.346194i	−0.838425	−	0.545017i	$-0.816523\pi$
$797$	−36.4751	+	9.77347i	−1.29201	+	0.346194i	−0.453589	+	0.891211i	$0.649857\pi$
$798$	1.58421	−	0.762481i	0.0560803	−	0.0269915i
$799$	44.3411	−	25.6004i	1.56868	−	0.905676i
$800$	−3.05064	+	0.590090i	−0.107856	+	0.0208628i
$801$	−30.3971	+	9.30731i	−1.07403	+	0.328858i
$802$	18.9079	−	0.722905i	0.667660	−	0.0255266i
$803$	1.27374	+	0.341296i	0.0449492	+	0.0120441i
$804$	−7.20739	−	0.265406i	−0.254185	−	0.00936014i
$805$	2.04670	−	0.548411i	0.0721366	−	0.0193289i
$806$	4.52472	+	14.6265i	0.159376	+	0.515196i
$807$	−11.1645	+	15.0946i	−0.393008	+	0.531353i
$808$	5.19177	−	35.0256i	0.182646	−	1.23220i
$809$	24.0071			0.844045			0.422023	−	0.906585i	$-0.361320\pi$
$809$	24.0071			0.844045			0.422023	+	0.906585i	$0.361320\pi$
$810$	26.5384	+	4.09048i	0.932463	+	0.143725i
$811$	−0.243845	+	0.243845i	−0.00856256	+	0.00856256i	−0.711375	−	0.702813i	$-0.751927\pi$
$811$	−0.243845	+	0.243845i	−0.00856256	+	0.00856256i	0.702813	+	0.711375i	$0.251927\pi$
$812$	0.0451439	−	0.240737i	0.00158424	−	0.00844823i
$813$	22.2346	−	3.32776i	0.779800	−	0.116710i
$814$	4.35571	−	8.25769i	0.152668	−	0.289432i
$815$	−0.731560	+	1.26710i	−0.0256254	+	0.0443846i
$816$	−21.9977	−	20.3201i	−0.770073	−	0.711346i
$817$	31.6507	+	54.8205i	1.10732	+	1.91793i
$818$	−39.3350	+	1.50389i	−1.37532	+	0.0525824i
$819$	−0.342686	+	0.645154i	−0.0119744	+	0.0225435i
$820$	−25.3453	+	29.5490i	−0.885097	+	1.03190i
$821$	−46.3025	−	12.4067i	−1.61597	−	0.432998i	−0.666156	−	0.745813i	$-0.732061\pi$
$821$	−46.3025	−	12.4067i	−1.61597	−	0.432998i	−0.949814	+	0.312815i	$0.898728\pi$
$822$	−5.52449	+	15.7769i	−0.192689	+	0.550281i
$823$	−0.737958	+	1.27818i	−0.0257236	+	0.0445546i	−0.878601	−	0.477557i	$-0.841522\pi$
$823$	−0.737958	+	1.27818i	−0.0257236	+	0.0445546i	0.852877	+	0.522112i	$0.174856\pi$
$824$	21.8956	+	9.48933i	0.762768	+	0.330576i
$825$	0.612973	−	0.266682i	0.0213410	−	0.00928466i
$826$	0.746230	+	0.169683i	0.0259647	+	0.00590402i
$827$	11.5464	+	11.5464i	0.401509	+	0.401509i	0.878764	−	0.477256i	$-0.158368\pi$
$827$	11.5464	+	11.5464i	0.401509	+	0.401509i	−0.477256	+	0.878764i	$0.658368\pi$
$828$	−29.4587	+	36.9065i	−1.02376	+	1.28259i
$829$	34.7961	−	34.7961i	1.20852	−	1.20852i	0.237010	−	0.971507i	$-0.423833\pi$
$829$	34.7961	−	34.7961i	1.20852	−	1.20852i	0.971507	−	0.237010i	$-0.0761675\pi$
$830$	−2.42127	−	3.84647i	−0.0840435	−	0.133513i
$831$	42.7303	+	4.85940i	1.48230	+	0.168571i
$832$	−7.19873	−	13.4610i	−0.249571	−	0.466677i
$833$	26.1424	+	15.0933i	0.905781	+	0.522953i
$834$	−14.7796	+	21.6674i	−0.511777	+	0.750280i
$835$	−5.88992	+	21.9815i	−0.203829	+	0.760700i
$836$	−0.603493	−	7.88077i	−0.0208722	−	0.272562i
$837$	−2.29453	+	29.3917i	−0.0793106	+	1.01593i
$838$	10.7182	+	9.92880i	0.370254	+	0.342985i
$839$	−41.3065	+	23.8483i	−1.42606	+	0.823335i	−0.996807	−	0.0798497i	$-0.974556\pi$
$839$	−41.3065	+	23.8483i	−1.42606	+	0.823335i	−0.429252	+	0.903185i	$0.641223\pi$
$840$	−0.657860	+	1.14316i	−0.0226983	+	0.0394427i
$841$	24.3172	+	14.0395i	0.838523	+	0.484122i
$842$	−12.9170	−	41.7553i	−0.445151	−	1.43898i
$843$	−10.0053	+	7.96200i	−0.344601	+	0.274226i
$844$	4.25057	−	22.6668i	0.146311	−	0.780225i
$845$	13.9615	+	13.9615i	0.480290	+	0.480290i
$846$	49.3676	+	9.40522i	1.69729	+	0.323358i
$847$		−	1.34076i		−	0.0460692i
$848$	0.0145656	+	0.00159311i	0.000500186	+	5.47078e-5i
$849$	9.86087	−	4.29009i	0.338424	−	0.147236i
$850$	2.96983	+	1.56651i	0.101864	+	0.0537308i
$851$	−19.1384	−	71.4254i	−0.656055	−	2.44843i
$852$	−3.87955	+	12.6037i	−0.132911	+	0.431795i
$853$	−11.3911	+	42.5120i	−0.390023	+	1.45558i	0.440072	+	0.897962i	$0.354953\pi$
$853$	−11.3911	+	42.5120i	−0.390023	+	1.45558i	−0.830095	+	0.557622i	$0.811714\pi$
$854$	−0.609827	−	0.564913i	−0.0208678	−	0.0193309i
$855$	−7.99302	+	34.6881i	−0.273355	+	1.18631i
$856$	−18.0275	+	22.7195i	−0.616168	+	0.776535i
$857$	−4.36756	−	7.56483i	−0.149193	−	0.258410i	0.781736	−	0.623609i	$-0.214334\pi$
$857$	−4.36756	−	7.56483i	−0.149193	−	0.258410i	−0.930929	+	0.365199i	$0.881001\pi$
$858$	2.14161	+	2.48971i	0.0731134	+	0.0849975i
$859$	12.9902	+	48.4800i	0.443219	+	1.65411i	0.720597	+	0.693354i	$0.243868\pi$
$859$	12.9902	+	48.4800i	0.443219	+	1.65411i	−0.277378	+	0.960761i	$0.589466\pi$
$860$	−42.8184	−	20.5344i	−1.46009	−	0.700217i
$861$	−0.301865	−	2.01693i	−0.0102875	−	0.0687366i
$862$	−17.7669	+	11.1839i	−0.605142	+	0.380924i
$863$	3.87853			0.132027			0.0660134	−	0.997819i	$-0.478972\pi$
$863$	3.87853			0.132027			0.0660134	+	0.997819i	$0.478972\pi$
$864$	−3.31919	−	29.2059i	−0.112921	−	0.993604i
$865$	10.0817			0.342789
$866$	−38.4923	+	24.2300i	−1.30802	+	0.823370i
$867$	0.431590	+	2.88369i	0.0146576	+	0.0979353i
$868$	−1.30571	−	0.626176i	−0.0443185	−	0.0212538i
$869$	−0.631896	−	2.35827i	−0.0214356	−	0.0799988i
$870$	3.23395	+	3.75961i	0.109641	+	0.127463i
$871$	1.98636	+	3.44049i	0.0673054	+	0.116576i
$872$	−32.2272	−	25.5718i	−1.09135	−	0.865970i
$873$	−14.5653	−	13.5709i	−0.492959	−	0.459305i
$874$	−45.9248	−	42.5424i	−1.55343	−	1.43902i
$875$	0.386679	−	1.44311i	0.0130721	−	0.0487859i
$876$	−1.91259	+	6.21353i	−0.0646204	+	0.209936i
$877$	5.43592	+	20.2871i	0.183558	+	0.685047i	0.994935	+	0.100524i	$0.0320519\pi$
$877$	5.43592	+	20.2871i	0.183558	+	0.685047i	−0.811377	+	0.584524i	$0.801281\pi$
$878$	−0.350331	−	0.184790i	−0.0118231	−	0.00623637i
$879$	39.4856	−	17.1787i	1.33182	−	0.579424i
$880$	3.71196	+	4.62367i	0.125130	+	0.155864i
$881$		−	7.45496i		−	0.251164i	−0.992083	−	0.125582i	$-0.959920\pi$
$881$		−	7.45496i		−	0.251164i	0.992083	−	0.125582i	$-0.0400798\pi$
$882$	9.75076	+	27.9790i	0.328325	+	0.942101i
$883$	−9.55597	−	9.55597i	−0.321584	−	0.321584i	0.527791	−	0.849375i	$-0.323021\pi$
$883$	−9.55597	−	9.55597i	−0.321584	−	0.321584i	−0.849375	+	0.527791i	$0.823021\pi$
$884$	−3.04030	+	16.2129i	−0.102256	+	0.545299i
$885$	−12.1241	+	9.64811i	−0.407547	+	0.324318i
$886$	10.4965	+	33.9308i	0.352638	+	1.13993i
$887$	−41.0581	−	23.7049i	−1.37860	−	0.795934i	−0.386607	−	0.922245i	$-0.626353\pi$
$887$	−41.0581	−	23.7049i	−1.37860	−	0.795934i	−0.991991	+	0.126311i	$0.959686\pi$
$888$	39.8938	+	22.9579i	1.33875	+	0.770418i
$889$	1.44899	−	0.836573i	0.0485975	−	0.0280578i
$890$	23.1934	+	21.4852i	0.777444	+	0.720185i
$891$	2.06383	+	5.97747i	0.0691409	+	0.200253i
$892$	−3.17080	−	41.4062i	−0.106166	−	1.38638i
$893$	−17.2433	+	64.3530i	−0.577027	+	2.15349i
$894$	−0.291565	+	0.427444i	−0.00975140	+	0.0142959i
$895$	−9.11780	−	5.26416i	−0.304774	−	0.175962i
$896$	1.39671	+	0.365726i	0.0466609	+	0.0122181i
$897$	25.8446	+	2.93912i	0.862926	+	0.0981342i
$898$	10.7647	+	17.1010i	0.359224	+	0.570669i
$899$	−3.85003	+	3.85003i	−0.128406	+	0.128406i
$900$	1.20268	+	3.06839i	0.0400893	+	0.102280i
$901$	−0.0111960	−	0.0111960i	−0.000372994	−	0.000372994i
$902$	−8.93996	−	2.03283i	−0.297668	−	0.0676858i
$903$	2.28116	−	0.992448i	0.0759124	−	0.0330266i
$904$	−23.7619	+	54.8280i	−0.790310	+	1.82355i
$905$	−10.9624	+	18.9874i	−0.364402	+	0.631162i
$906$	1.85864	−	5.30790i	0.0617491	−	0.176343i
$907$	13.6705	+	3.66301i	0.453923	+	0.121628i	0.478534	−	0.878069i	$-0.341168\pi$
$907$	13.6705	+	3.66301i	0.453923	+	0.121628i	−0.0246114	+	0.999697i	$0.507835\pi$
$908$	10.3180	−	12.0293i	0.342413	−	0.399205i
$909$	−37.5327	+	1.32647i	−1.24488	+	0.0439963i
$910$	0.725977	−	0.0277563i	0.0240659	−	0.000920111i
$911$	−20.0062	−	34.6517i	−0.662834	−	1.14806i	−0.979868	−	0.199648i	$-0.936020\pi$
$911$	−20.0062	−	34.6517i	−0.662834	−	1.14806i	0.317034	−	0.948414i	$-0.397313\pi$
$912$	38.9365	−	1.54352i	1.28932	−	0.0511112i
$913$	0.535197	−	0.926988i	0.0177124	−	0.0306788i
$914$	18.3685	−	34.8235i	0.607576	−	1.15186i
$915$	16.6453	−	2.49123i	0.550277	−	0.0823576i
$916$	0.171232	−	0.913125i	0.00565767	−	0.0301705i
$917$	0.443647	−	0.443647i	0.0146505	−	0.0146505i
$918$	−16.9608	+	26.8559i	−0.559789	+	0.886376i
$919$	−18.6876			−0.616446			−0.308223	−	0.951314i	$-0.599734\pi$
$919$	−18.6876			−0.616446			−0.308223	+	0.951314i	$0.599734\pi$
$920$	46.4550	+	6.88593i	1.53158	+	0.227022i
$921$	−25.3117	+	34.2218i	−0.834049	+	1.12765i
$922$	−7.00472	−	22.6432i	−0.230688	−	0.745716i
$923$	7.01641	−	1.88004i	0.230948	−	0.0618823i
$924$	−0.310406	−	0.0114304i	−0.0102116	−	0.000376033i
$925$	−4.98486	−	1.33569i	−0.163901	−	0.0439172i
$926$	−42.7452	+	1.63428i	−1.40470	+	0.0537057i
$927$	5.68337	−	24.6647i	0.186666	−	0.810094i
$928$	3.03977	−	4.49777i	0.0997853	−	0.147646i
$929$	−8.76538	+	5.06070i	−0.287583	+	0.166036i	−0.636851	−	0.770987i	$-0.719763\pi$
$929$	−8.76538	+	5.06070i	−0.287583	+	0.166036i	0.349268	+	0.937023i	$0.386430\pi$
$930$	26.4186	−	12.7153i	0.866300	−	0.416951i
$931$	−37.9409	+	10.1662i	−1.24346	+	0.333185i
$932$	−7.90228	+	16.4779i	−0.258848	+	0.539750i
$933$	−8.75007	+	22.2270i	−0.286464	+	0.727681i
$934$	−7.06725	+	31.0803i	−0.231248	+	1.01698i
$935$		−	6.40729i		−	0.209541i
$936$	−12.6549	+	10.0996i	−0.413638	+	0.330116i
$937$		−	19.1375i		−	0.625194i	−0.949886	−	0.312597i	$-0.898801\pi$
$937$		−	19.1375i		−	0.625194i	0.949886	−	0.312597i	$-0.101199\pi$
$938$	−0.366397	−	0.0833139i	−0.0119633	−	0.00272030i
$939$	21.9641	+	27.6008i	0.716772	+	0.900717i
$940$	−16.5840	−	47.1480i	−0.540912	−	1.53780i
$941$	41.4559	−	11.1081i	1.35142	−	0.362113i	0.490764	−	0.871292i	$-0.336718\pi$
$941$	41.4559	−	11.1081i	1.35142	−	0.362113i	0.860660	+	0.509179i	$0.170051\pi$
$942$	23.1710	−	33.9695i	0.754953	−	1.10679i
$943$	−62.8868	+	36.3077i	−2.04788	+	1.18234i
$944$	13.6799	+	10.0275i	0.445241	+	0.326368i
$945$	1.31899	+	0.466145i	0.0429069	+	0.0151637i
$946$	−0.427269	−	11.1754i	−0.0138917	−	0.363344i
$947$	45.0535	+	12.0721i	1.46404	+	0.392289i	0.900884	−	0.434060i	$-0.142919\pi$
$947$	45.0535	+	12.0721i	1.46404	+	0.392289i	0.563159	+	0.826349i	$0.309586\pi$
$948$	11.7334	−	2.68538i	0.381083	−	0.0872172i
$949$	3.45904	−	0.926848i	0.112285	−	0.0300867i
$950$	−4.17387	+	1.29119i	−0.135418	+	0.0418919i
$951$	−36.1920	−	4.11585i	−1.17361	−	0.133466i
$952$	−0.929534	−	1.25305i	−0.0301264	−	0.0406117i
$953$	20.2249			0.655149			0.327575	−	0.944825i	$-0.393769\pi$
$953$	20.2249			0.655149			0.327575	+	0.944825i	$0.393769\pi$
$954$	−0.00114190	−	0.0154993i	−3.69703e−5	−	0.000501808i
$955$	−7.72399	+	7.72399i	−0.249943	+	0.249943i
$956$	−8.26273	−	12.0769i	−0.267236	−	0.390594i
$957$	−0.427810	+	1.08673i	−0.0138291	+	0.0351289i
$958$	37.0506	+	19.5432i	1.19705	+	0.631412i
$959$	−0.435445	+	0.754212i	−0.0140612	+	0.0243548i
$960$	−23.4534	+	17.4493i	−0.756955	+	0.563173i
$961$	0.595170	+	1.03087i	0.0191990	+	0.0332537i
$962$	−0.968635	−	25.3351i	−0.0312301	−	0.816836i
$963$	27.1675	+	14.4305i	0.875459	+	0.465018i
$964$	−4.97974	+	0.381338i	−0.160387	+	0.0122821i
$965$	53.8680	+	14.4339i	1.73407	+	0.464644i
$966$	−1.86512	+	1.60434i	−0.0600092	+	0.0516189i
$967$	15.9815	−	27.6807i	0.513930	−	0.890152i	−0.485940	−	0.873992i	$-0.661523\pi$
$967$	15.9815	−	27.6807i	0.513930	−	0.890152i	0.999869	−	0.0161601i	$-0.00514413\pi$
$968$	11.8167	−	27.2658i	0.379804	−	0.876356i
$969$	−33.8542	−	25.0398i	−1.08755	−	0.804395i
$970$	−4.38983	+	19.3056i	−0.140949	+	0.619864i
$971$	−4.69660	−	4.69660i	−0.150721	−	0.150721i	0.627719	−	0.778440i	$-0.283989\pi$
$971$	−4.69660	−	4.69660i	−0.150721	−	0.150721i	−0.778440	+	0.627719i	$0.783989\pi$
$972$	−29.8243	+	9.08364i	−0.956614	+	0.291358i
$973$	−0.966226	+	0.966226i	−0.0309758	+	0.0309758i
$974$	30.6773	−	19.3107i	0.982964	−	0.618755i
$975$	1.07950	−	1.45951i	0.0345718	−	0.0467417i
$976$	−7.42262	−	16.8627i	−0.237592	−	0.539763i
$977$	−22.7888	−	13.1571i	−0.729079	−	0.420934i	0.0890064	−	0.996031i	$-0.471631\pi$
$977$	−22.7888	−	13.1571i	−0.729079	−	0.420934i	−0.818085	+	0.575097i	$0.804964\pi$
$978$	0.127327	−	1.69401i	0.00407147	−	0.0541686i
$979$	−1.92707	+	7.19193i	−0.0615895	+	0.229855i
$980$	19.1844	−	22.3662i	0.612822	−	0.714463i
$981$	−20.4695	+	38.5367i	−0.653542	+	1.23038i
$982$	−5.22426	+	5.63962i	−0.166713	+	0.179968i
$983$	19.6448	−	11.3420i	0.626573	−	0.361752i	−0.152851	−	0.988249i	$-0.548845\pi$
$983$	19.6448	−	11.3420i	0.626573	−	0.361752i	0.779424	+	0.626497i	$0.215512\pi$
$984$	11.6373	−	43.6767i	0.370983	−	1.39236i
$985$	−13.2976	−	7.67740i	−0.423698	−	0.244622i
$986$	−5.60420	+	1.73367i	−0.178474	+	0.0552112i
$987$	2.43627	+	0.959079i	0.0775472	+	0.0305278i
$988$	−12.1201	−	17.7148i	−0.385592	−	0.563584i
$989$	−62.6343	−	62.6343i	−1.99165	−	1.99165i
$990$	4.10824	−	4.76172i	0.130568	−	0.151338i
$991$		−	13.0577i		−	0.414793i	−0.978257	−	0.207396i	$-0.933501\pi$
$991$		−	13.0577i		−	0.414793i	0.978257	−	0.207396i	$-0.0664990\pi$
$992$	−21.0341	−	24.2417i	−0.667833	−	0.769674i
$993$	3.45722	−	30.4004i	0.109711	−	0.964728i
$994$	−0.320537	+	0.607683i	−0.0101668	+	0.0192745i
$995$	−0.750435	−	2.80066i	−0.0237904	−	0.0887870i
$996$	4.46999	+	2.80499i	0.141637	+	0.0888795i
$997$	−2.05844	+	7.68222i	−0.0651916	+	0.243298i	−0.990831	−	0.135109i	$-0.956861\pi$
$997$	−2.05844	+	7.68222i	−0.0651916	+	0.243298i	0.925639	+	0.378407i	$0.123528\pi$
$998$	−21.4694	+	23.1763i	−0.679601	+	0.733633i
$999$	16.2675	−	46.0301i	0.514680	−	1.45633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.u.a.59.19	yes	88
3.2	odd	2		432.2.v.a.395.4		88
4.3	odd	2		576.2.y.a.527.11		88
9.2	odd	6	inner	144.2.u.a.11.19	✓	88
9.7	even	3		432.2.v.a.251.4		88
12.11	even	2		1728.2.z.a.719.5		88
16.3	odd	4	inner	144.2.u.a.131.19	yes	88
16.13	even	4		576.2.y.a.239.22		88
36.7	odd	6		1728.2.z.a.143.5		88
36.11	even	6		576.2.y.a.335.22		88
48.29	odd	4		1728.2.z.a.1583.5		88
48.35	even	4		432.2.v.a.179.4		88
144.29	odd	12		576.2.y.a.47.11		88
144.61	even	12		1728.2.z.a.1007.5		88
144.83	even	12	inner	144.2.u.a.83.19	yes	88
144.115	odd	12		432.2.v.a.35.4		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.19	✓	88	9.2	odd	6	inner
144.2.u.a.59.19	yes	88	1.1	even	1	trivial
144.2.u.a.83.19	yes	88	144.83	even	12	inner
144.2.u.a.131.19	yes	88	16.3	odd	4	inner
432.2.v.a.35.4		88	144.115	odd	12
432.2.v.a.179.4		88	48.35	even	4
432.2.v.a.251.4		88	9.7	even	3
432.2.v.a.395.4		88	3.2	odd	2
576.2.y.a.47.11		88	144.29	odd	12
576.2.y.a.239.22		88	16.13	even	4
576.2.y.a.335.22		88	36.11	even	6
576.2.y.a.527.11		88	4.3	odd	2
1728.2.z.a.143.5		88	36.7	odd	6
1728.2.z.a.719.5		88	12.11	even	2
1728.2.z.a.1007.5		88	144.61	even	12
1728.2.z.a.1583.5		88	48.29	odd	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19684 - 0.753382i) q^{2} +(-0.256373 - 1.71297i) q^{3} +(0.864831 - 1.80335i) q^{4} +(0.546024 + 2.03779i) q^{5} +(-1.59736 - 1.85700i) q^{6} +(-0.0638076 - 0.110518i) q^{7} +(-0.323550 - 2.80986i) q^{8} +(-2.86855 + 0.878321i) q^{9} +(2.18873 + 2.02753i) q^{10} +(-0.181856 + 0.678695i) q^{11} +(-3.31081 - 1.01910i) q^{12} +(0.493860 + 1.84311i) q^{13} +(-0.159630 - 0.0842004i) q^{14} +(3.35069 - 1.45776i) q^{15} +(-2.50413 - 3.11918i) q^{16} +4.32243i q^{17} +(-2.77147 + 3.21232i) q^{18} +(-3.97707 - 3.97707i) q^{19} +(4.14706 + 0.777671i) q^{20} +(-0.172956 + 0.137635i) q^{21} +(0.293665 + 0.949293i) q^{22} +(6.81589 + 3.93516i) q^{23} +(-4.73026 + 1.27461i) q^{24} +(0.475689 - 0.274639i) q^{25} +(1.97963 + 1.83383i) q^{26} +(2.23996 + 4.68856i) q^{27} +(-0.254485 + 0.0194880i) q^{28} +(-0.248377 + 0.926957i) q^{29} +(2.91197 - 4.26904i) q^{30} +(4.91353 + 2.83683i) q^{31} +(-5.34697 - 1.84658i) q^{32} +(1.20921 + 0.137514i) q^{33} +(3.25644 + 5.17324i) q^{34} +(0.190372 - 0.190372i) q^{35} +(-0.896888 + 5.93259i) q^{36} +(-6.64358 - 6.64358i) q^{37} +(-7.75614 - 1.76364i) q^{38} +(3.03058 - 1.31849i) q^{39} +(5.54923 - 2.19358i) q^{40} +(-4.61325 + 7.99038i) q^{41} +(-0.103308 + 0.295028i) q^{42} +(-10.8712 - 2.91294i) q^{43} +(1.06665 + 0.914906i) q^{44} +(-3.35613 - 5.36590i) q^{45} +(11.1222 - 0.425234i) q^{46} +(-5.92267 - 10.2584i) q^{47} +(-4.70108 + 5.08919i) q^{48} +(3.49186 - 6.04807i) q^{49} +(0.362413 - 0.687073i) q^{50} +(7.40421 - 1.10816i) q^{51} +(3.75087 + 0.703377i) q^{52} +(-0.00259022 + 0.00259022i) q^{53} +(6.21314 + 3.92389i) q^{54} -1.48233 q^{55} +(-0.289895 + 0.215049i) q^{56} +(-5.79299 + 7.83221i) q^{57} +(0.401086 + 1.29654i) q^{58} +(-4.09587 + 1.09748i) q^{59} +(0.268933 - 7.30317i) q^{60} +(4.44908 + 1.19213i) q^{61} +(8.01790 - 0.306548i) q^{62} +(0.280105 + 0.260982i) q^{63} +(-7.79063 + 1.81826i) q^{64} +(-3.48621 + 2.01276i) q^{65} +(1.55082 - 0.746413i) q^{66} +(2.01106 - 0.538862i) q^{67} +(7.79486 + 3.73818i) q^{68} +(4.99340 - 12.6843i) q^{69} +(0.0844211 - 0.371267i) q^{70} -3.80683i q^{71} +(3.39608 + 7.77603i) q^{72} -1.87674i q^{73} +(-12.9564 - 2.94612i) q^{74} +(-0.592403 - 0.744431i) q^{75} +(-10.6115 + 3.73255i) q^{76} +(0.0866118 - 0.0232076i) q^{77} +(2.63378 - 3.86120i) q^{78} +(-3.00919 + 1.73736i) q^{79} +(4.98892 - 6.80604i) q^{80} +(7.45710 - 5.03901i) q^{81} +(0.498509 + 13.0387i) q^{82} +(-1.47149 - 0.394284i) q^{83} +(0.0986256 + 0.430930i) q^{84} +(-8.80821 + 2.36015i) q^{85} +(-15.2056 + 4.70388i) q^{86} +(1.65153 + 0.187816i) q^{87} +(1.96588 + 0.291398i) q^{88} +10.5967 q^{89} +(-8.05931 - 3.89366i) q^{90} +(0.172185 - 0.172185i) q^{91} +(12.9911 - 8.88818i) q^{92} +(3.59971 - 9.14402i) q^{93} +(-14.8169 - 7.81555i) q^{94} +(5.93284 - 10.2760i) q^{95} +(-1.79232 + 9.63263i) q^{96} +(3.31795 + 5.74685i) q^{97} +(-0.377331 - 9.86925i) q^{98} +(-0.0744506 - 2.10659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27}+ \cdots + 46 q^{99}+O(q^{100}) \) 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more