LMFDB - Embedded newform 216.2.t.a.157.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			157.31
Character	$\chi$	$=$	216.157
Dual form			216.2.t.a.205.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30848 + 0.536554i) q^{2} +(-1.40645 - 1.01088i) q^{3} +(1.42422 + 1.40414i) q^{4} +(1.34230 + 3.68793i) q^{5} +(-1.29792 - 2.07736i) q^{6} +(-0.499959 - 2.83541i) q^{7} +(1.11016 + 2.60145i) q^{8} +(0.956226 + 2.84352i) q^{9} +(-0.222412 + 5.54579i) q^{10} +(-0.996019 + 2.73654i) q^{11} +(-0.583678 - 3.41457i) q^{12} +(2.55767 - 3.04812i) q^{13} +(0.867166 - 3.97832i) q^{14} +(1.84019 - 6.54382i) q^{15} +(0.0567986 + 3.99960i) q^{16} +(2.48745 - 4.30839i) q^{17} +(-0.274506 + 4.23375i) q^{18} +(-1.78004 + 1.02771i) q^{19} +(-3.26664 + 7.13719i) q^{20} +(-2.16310 + 4.49327i) q^{21} +(-2.77157 + 3.04628i) q^{22} +(0.165146 - 0.936587i) q^{23} +(1.06838 - 4.78106i) q^{24} +(-7.96887 + 6.68667i) q^{25} +(4.98214 - 2.61606i) q^{26} +(1.52959 - 4.96592i) q^{27} +(3.26925 - 4.74025i) q^{28} +(-5.18495 - 6.17919i) q^{29} +(5.91896 - 7.57506i) q^{30} +(0.331534 - 1.88022i) q^{31} +(-2.07168 + 5.26385i) q^{32} +(4.16718 - 2.84196i) q^{33} +(5.56646 - 4.30278i) q^{34} +(9.78570 - 5.64977i) q^{35} +(-2.63082 + 5.39247i) q^{36} +(-8.31066 - 4.79816i) q^{37} +(-2.88056 + 0.389641i) q^{38} +(-6.67855 + 1.70152i) q^{39} +(-8.10381 + 7.58612i) q^{40} +(0.581151 + 0.487644i) q^{41} +(-5.24125 + 4.71871i) q^{42} +(2.14125 - 5.88303i) q^{43} +(-5.26103 + 2.49888i) q^{44} +(-9.20319 + 7.34336i) q^{45} +(0.718619 - 1.13689i) q^{46} +(0.932102 + 5.28621i) q^{47} +(3.96324 - 5.68267i) q^{48} +(-1.21172 + 0.441031i) q^{49} +(-14.0148 + 4.47362i) q^{50} +(-7.85378 + 3.54503i) q^{51} +(7.92266 - 0.749861i) q^{52} -3.54207i q^{53} +(4.66591 - 5.67708i) q^{54} -11.4291 q^{55} +(6.82113 - 4.44837i) q^{56} +(3.54244 + 0.353992i) q^{57} +(-3.46892 - 10.8673i) q^{58} +(2.13303 + 5.86045i) q^{59} +(11.8093 - 6.73594i) q^{60} +(3.22446 - 0.568559i) q^{61} +(1.44265 - 2.28234i) q^{62} +(7.58447 - 4.13293i) q^{63} +(-5.53509 + 5.77605i) q^{64} +(14.6744 + 5.34105i) q^{65} +(6.97752 - 1.48271i) q^{66} +(-4.40861 + 5.25398i) q^{67} +(9.59225 - 2.64337i) q^{68} +(-1.17905 + 1.15032i) q^{69} +(15.8358 - 2.14204i) q^{70} +(3.83709 - 6.64603i) q^{71} +(-6.33572 + 5.64434i) q^{72} +(3.46824 + 6.00718i) q^{73} +(-8.29983 - 10.7374i) q^{74} +(17.9673 - 1.34890i) q^{75} +(-3.97821 - 1.03574i) q^{76} +(8.25717 + 1.45596i) q^{77} +(-9.65168 - 1.35700i) q^{78} +(0.205269 - 0.172241i) q^{79} +(-14.6740 + 5.57812i) q^{80} +(-7.17126 + 5.43811i) q^{81} +(0.498775 + 0.949889i) q^{82} +(7.91149 + 9.42855i) q^{83} +(-9.38989 + 3.36211i) q^{84} +(19.2280 + 3.39041i) q^{85} +(5.95834 - 6.54891i) q^{86} +(1.04596 + 13.9321i) q^{87} +(-8.22471 + 0.446904i) q^{88} +(-4.11349 - 7.12477i) q^{89} +(-15.9823 + 4.67059i) q^{90} +(-9.92138 - 5.72811i) q^{91} +(1.55030 - 1.10202i) q^{92} +(-2.36698 + 2.30931i) q^{93} +(-1.61671 + 7.41700i) q^{94} +(-6.17946 - 5.18518i) q^{95} +(8.23487 - 5.30914i) q^{96} +(5.06123 + 1.84214i) q^{97} +(-1.82215 - 0.0730766i) q^{98} +(-8.73384 - 0.215453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	1.30848	+	0.536554i	0.925232	+	0.379401i
$2$	1.30848	+	0.536554i	0.925232	+	0.379401i
$3$	−1.40645	−	1.01088i	−0.812017	−	0.583634i
$3$	−1.40645	−	1.01088i	−0.812017	−	0.583634i
$4$	1.42422	+	1.40414i	0.712109	+	0.702069i
$5$	1.34230	+	3.68793i	0.600294	+	1.64929i	0.750679	+	0.660667i	$0.229726\pi$
$5$	1.34230	+	3.68793i	0.600294	+	1.64929i	−0.150386	+	0.988627i	$0.548052\pi$
$6$	−1.29792	−	2.07736i	−0.529872	−	0.848077i
$7$	−0.499959	−	2.83541i	−0.188967	−	1.07168i	−0.920752	−	0.390148i	$-0.872424\pi$
$7$	−0.499959	−	2.83541i	−0.188967	−	1.07168i	0.731786	−	0.681535i	$-0.238687\pi$
$8$	1.11016	+	2.60145i	0.392501	+	0.919752i
$9$	0.956226	+	2.84352i	0.318742	+	0.947841i
$10$	−0.222412	+	5.54579i	−0.0703329	+	1.75373i
$11$	−0.996019	+	2.73654i	−0.300311	+	0.825098i	0.694135	+	0.719845i	$0.255787\pi$
$11$	−0.996019	+	2.73654i	−0.300311	+	0.825098i	−0.994446	+	0.105252i	$0.966435\pi$
$12$	−0.583678	−	3.41457i	−0.168493	−	0.985703i
$13$	2.55767	−	3.04812i	0.709371	−	0.845396i	−0.284181	−	0.958771i	$-0.591722\pi$
$13$	2.55767	−	3.04812i	0.709371	−	0.845396i	0.993552	+	0.113375i	$0.0361661\pi$
$14$	0.867166	−	3.97832i	0.231760	−	1.06325i
$15$	1.84019	−	6.54382i	0.475136	−	1.68961i
$16$	0.0567986	+	3.99960i	0.0141996	+	0.999899i
$17$	2.48745	−	4.30839i	0.603296	−	1.04494i	−0.389022	−	0.921228i	$-0.627187\pi$
$17$	2.48745	−	4.30839i	0.603296	−	1.04494i	0.992318	−	0.123711i	$-0.0394795\pi$
$18$	−0.274506	+	4.23375i	−0.0647018	+	0.997905i
$19$	−1.78004	+	1.02771i	−0.408369	+	0.235772i	−0.690089	−	0.723725i	$-0.742429\pi$
$19$	−1.78004	+	1.02771i	−0.408369	+	0.235772i	0.281720	+	0.959497i	$0.409095\pi$
$20$	−3.26664	+	7.13719i	−0.730442	+	1.59593i
$21$	−2.16310	+	4.49327i	−0.472027	+	0.980512i
$22$	−2.77157	+	3.04628i	−0.590900	+	0.649469i
$23$	0.165146	−	0.936587i	0.0344352	−	0.195292i	−0.962737	−	0.270438i	$-0.912831\pi$
$23$	0.165146	−	0.936587i	0.0344352	−	0.195292i	0.997173	+	0.0751465i	$0.0239424\pi$
$24$	1.06838	−	4.78106i	0.218081	−	0.975931i
$25$	−7.96887	+	6.68667i	−1.59377	+	1.33733i
$26$	4.98214	−	2.61606i	0.977077	−	0.513051i
$27$	1.52959	−	4.96592i	0.294369	−	0.955692i
$28$	3.26925	−	4.74025i	0.617830	−	0.895823i
$29$	−5.18495	−	6.17919i	−0.962821	−	1.14745i	−0.989019	−	0.147789i	$-0.952784\pi$
$29$	−5.18495	−	6.17919i	−0.962821	−	1.14745i	0.0261974	−	0.999657i	$-0.491660\pi$
$30$	5.91896	−	7.57506i	1.08065	−	1.38301i
$31$	0.331534	−	1.88022i	0.0595453	−	0.337698i	−0.940452	−	0.339926i	$-0.889598\pi$
$31$	0.331534	−	1.88022i	0.0595453	−	0.337698i	0.999998	+	0.00222778i	$0.000709125\pi$
$32$	−2.07168	+	5.26385i	−0.366225	+	0.930526i
$33$	4.16718	−	2.84196i	0.725413	−	0.494721i
$34$	5.56646	−	4.30278i	0.954640	−	0.737920i
$35$	9.78570	−	5.64977i	1.65408	−	0.954986i
$36$	−2.63082	+	5.39247i	−0.438470	+	0.898746i
$37$	−8.31066	−	4.79816i	−1.36626	−	0.788813i	−0.375816	−	0.926694i	$-0.622637\pi$
$37$	−8.31066	−	4.79816i	−1.36626	−	0.788813i	−0.990449	+	0.137881i	$0.955971\pi$
$38$	−2.88056	+	0.389641i	−0.467289	+	0.0632082i
$39$	−6.67855	+	1.70152i	−1.06942	+	0.272462i
$40$	−8.10381	+	7.58612i	−1.28132	+	1.19947i
$41$	0.581151	+	0.487644i	0.0907605	+	0.0761571i	0.687039	−	0.726621i	$-0.258910\pi$
$41$	0.581151	+	0.487644i	0.0907605	+	0.0761571i	−0.596278	+	0.802778i	$0.703355\pi$
$42$	−5.24125	+	4.71871i	−0.808742	+	0.728114i
$43$	2.14125	−	5.88303i	0.326537	−	0.897154i	−0.662444	−	0.749112i	$-0.730481\pi$
$43$	2.14125	−	5.88303i	0.326537	−	0.897154i	0.988981	−	0.148042i	$-0.0472972\pi$
$44$	−5.26103	+	2.49888i	−0.793129	+	0.376721i
$45$	−9.20319	+	7.34336i	−1.37193	+	1.09468i
$46$	0.718619	−	1.13689i	0.105955	−	0.167626i
$47$	0.932102	+	5.28621i	0.135961	+	0.771073i	0.974186	+	0.225748i	$0.0724826\pi$
$47$	0.932102	+	5.28621i	0.135961	+	0.771073i	−0.838225	+	0.545325i	$0.816406\pi$
$48$	3.96324	−	5.68267i	0.572045	−	0.820222i
$49$	−1.21172	+	0.441031i	−0.173103	+	0.0630044i
$50$	−14.0148	+	4.47362i	−1.98200	+	0.632666i
$51$	−7.85378	+	3.54503i	−1.09975	+	0.496404i
$52$	7.92266	−	0.749861i	1.09868	−	0.103987i
$53$		−	3.54207i		−	0.486541i	−0.969959	−	0.243270i	$-0.921780\pi$
$53$		−	3.54207i		−	0.486541i	0.969959	−	0.243270i	$-0.0782202\pi$
$54$	4.66591	−	5.67708i	0.634950	−	0.772553i
$55$	−11.4291			−1.54110
$56$	6.82113	−	4.44837i	0.911513	−	0.594439i
$57$	3.54244	+	0.353992i	0.469207	+	0.0468874i
$58$	−3.46892	−	10.8673i	−0.455491	−	1.42695i
$59$	2.13303	+	5.86045i	0.277697	+	0.762966i	0.997623	+	0.0689146i	$0.0219536\pi$
$59$	2.13303	+	5.86045i	0.277697	+	0.762966i	−0.719926	+	0.694051i	$0.755824\pi$
$60$	11.8093	−	6.73594i	1.52457	−	0.869607i
$61$	3.22446	−	0.568559i	0.412849	−	0.0727965i	0.0366341	−	0.999329i	$-0.488336\pi$
$61$	3.22446	−	0.568559i	0.412849	−	0.0727965i	0.376215	+	0.926532i	$0.377225\pi$
$62$	1.44265	−	2.28234i	0.183216	−	0.289858i
$63$	7.58447	−	4.13293i	0.955554	−	0.520701i
$64$	−5.53509	+	5.77605i	−0.691886	+	0.722007i
$65$	14.6744	+	5.34105i	1.82014	+	0.662476i
$66$	6.97752	−	1.48271i	0.858873	−	0.182510i
$67$	−4.40861	+	5.25398i	−0.538598	+	0.641876i	−0.964873	−	0.262718i	$-0.915381\pi$
$67$	−4.40861	+	5.25398i	−0.538598	+	0.641876i	0.426275	+	0.904594i	$0.359826\pi$
$68$	9.59225	−	2.64337i	1.16323	−	0.320556i
$69$	−1.17905	+	1.15032i	−0.141941	+	0.138483i
$70$	15.8358	−	2.14204i	1.89274	−	0.256022i
$71$	3.83709	−	6.64603i	0.455378	−	0.788738i	−0.543332	−	0.839518i	$-0.682837\pi$
$71$	3.83709	−	6.64603i	0.455378	−	0.788738i	0.998710	+	0.0507798i	$0.0161707\pi$
$72$	−6.33572	+	5.64434i	−0.746672	+	0.665192i
$73$	3.46824	+	6.00718i	0.405927	+	0.703087i	0.994429	−	0.105409i	$-0.0336153\pi$
$73$	3.46824	+	6.00718i	0.405927	+	0.703087i	−0.588502	+	0.808496i	$0.700282\pi$
$74$	−8.29983	−	10.7374i	−0.964835	−	1.24820i
$75$	17.9673	−	1.34890i	2.07468	−	0.155757i
$76$	−3.97821	−	1.03574i	−0.456332	−	0.118808i
$77$	8.25717	+	1.45596i	0.940992	+	0.165922i
$78$	−9.65168	−	1.35700i	−1.09284	−	0.153650i
$79$	0.205269	−	0.172241i	0.0230945	−	0.0193786i	−0.631167	−	0.775647i	$-0.717424\pi$
$79$	0.205269	−	0.172241i	0.0230945	−	0.0193786i	0.654262	+	0.756268i	$0.272979\pi$
$80$	−14.6740	+	5.57812i	−1.64060	+	0.623653i
$81$	−7.17126	+	5.43811i	−0.796807	+	0.604234i
$82$	0.498775	+	0.949889i	0.0550805	+	0.104898i
$83$	7.91149	+	9.42855i	0.868399	+	1.03492i	0.999054	+	0.0434896i	$0.0138475\pi$
$83$	7.91149	+	9.42855i	0.868399	+	1.03492i	−0.130655	+	0.991428i	$0.541708\pi$
$84$	−9.38989	+	3.36211i	−1.02452	+	0.366836i
$85$	19.2280	+	3.39041i	2.08557	+	0.367742i
$86$	5.95834	−	6.54891i	0.642504	−	0.706187i
$87$	1.04596	+	13.9321i	0.112138	+	1.49368i
$88$	−8.22471	+	0.446904i	−0.876757	+	0.0476401i
$89$	−4.11349	−	7.12477i	−0.436029	−	0.755224i	0.561350	−	0.827578i	$-0.310282\pi$
$89$	−4.11349	−	7.12477i	−0.436029	−	0.755224i	−0.997379	+	0.0723541i	$0.976949\pi$
$90$	−15.9823	+	4.67059i	−1.68468	+	0.492324i
$91$	−9.92138	−	5.72811i	−1.04004	−	0.600469i
$92$	1.55030	−	1.10202i	0.161630	−	0.114893i
$93$	−2.36698	+	2.30931i	−0.245444	+	0.239464i
$94$	−1.61671	+	7.41700i	−0.166751	+	0.765005i
$95$	−6.17946	−	5.18518i	−0.633999	−	0.531988i
$96$	8.23487	−	5.30914i	0.840468	−	0.541861i
$97$	5.06123	+	1.84214i	0.513891	+	0.187041i	0.585931	−	0.810361i	$-0.300729\pi$
$97$	5.06123	+	1.84214i	0.513891	+	0.187041i	−0.0720406	+	0.997402i	$0.522951\pi$
$98$	−1.82215	−	0.0730766i	−0.184065	−	0.00738186i
$99$	−8.73384	−	0.215453i	−0.877784	−	0.0216539i
$100$	−20.7384	−	1.66609i	−2.07384	−	0.166609i
$101$	3.98336	−	0.702375i	0.396360	−	0.0698889i	0.0280840	−	0.999606i	$-0.491059\pi$
$101$	3.98336	−	0.702375i	0.396360	−	0.0698889i	0.368276	+	0.929717i	$0.379948\pi$
$102$	−12.1786	+	0.424612i	−1.20586	+	0.0420428i
$103$	1.07241	−	0.390325i	0.105668	−	0.0384599i	−0.288645	−	0.957436i	$-0.593205\pi$
$103$	1.07241	−	0.390325i	0.105668	−	0.0384599i	0.394313	+	0.918976i	$0.370983\pi$
$104$	10.7690	+	3.26976i	1.05598	+	0.320627i
$105$	−19.4744	−	1.94606i	−1.90051	−	0.189916i
$106$	1.90051	−	4.63471i	0.184594	−	0.450163i
$107$			4.87553i			0.471335i	0.971834	+	0.235667i	$0.0757276\pi$
$107$			4.87553i			0.471335i	−0.971834	+	0.235667i	$0.924272\pi$
$108$	9.15130	−	4.92481i	0.880584	−	0.473890i
$109$			2.52010i			0.241382i	0.992690	+	0.120691i	$0.0385111\pi$
$109$			2.52010i			0.241382i	−0.992690	+	0.120691i	$0.961489\pi$
$110$	−14.9547	−	6.13235i	−1.42588	−	0.584697i
$111$	6.83818	+	15.1495i	0.649051	+	1.43793i
$112$	11.3121	−	2.16068i	1.06889	−	0.204165i
$113$	−6.79620	+	2.47361i	−0.639332	+	0.232698i	−0.641288	−	0.767300i	$-0.721600\pi$
$113$	−6.79620	+	2.47361i	−0.639332	+	0.232698i	0.00195583	+	0.999998i	$0.499377\pi$
$114$	4.44526	+	2.36390i	0.416337	+	0.221400i
$115$	3.67575	−	0.648133i	0.342765	−	0.0604387i
$116$	1.29192	−	16.0809i	0.119951	−	1.49307i
$117$	11.1131	+	4.35812i	1.02741	+	0.402908i
$118$	−0.353432	+	8.81275i	−0.0325361	+	0.811279i
$119$	−13.4597	−	4.89892i	−1.23385	−	0.449083i
$120$	19.0663	−	2.47751i	1.74051	−	0.226165i
$121$	1.92989	+	1.61937i	0.175445	+	0.147216i
$122$	4.52419	+	0.986151i	0.409601	+	0.0892819i
$123$	−0.324411	−	1.27332i	−0.0292511	−	0.114812i
$124$	3.11227	−	2.21233i	0.279490	−	0.198673i
$125$	−18.3625	−	10.6016i	−1.64239	−	0.948236i
$126$	12.1416	−	1.33836i	1.08166	−	0.119231i
$127$	−2.38507	−	4.13106i	−0.211641	−	0.366573i	0.740587	−	0.671960i	$-0.234547\pi$
$127$	−2.38507	−	4.13106i	−0.211641	−	0.366573i	−0.952228	+	0.305387i	$0.901214\pi$
$128$	−10.3417	+	4.58795i	−0.914086	+	0.405522i
$129$	−8.95864	+	6.10966i	−0.788764	+	0.537926i
$130$	16.3354	+	14.8623i	1.43271	+	1.30351i
$131$	3.45051	+	0.608417i	0.301472	+	0.0531577i	0.322338	−	0.946625i	$-0.395531\pi$
$131$	3.45051	+	0.608417i	0.301472	+	0.0531577i	−0.0208660	+	0.999782i	$0.506642\pi$
$132$	9.92547	+	1.80372i	0.863902	+	0.156994i
$133$	3.80391	+	4.53333i	0.329841	+	0.393089i
$134$	−8.58761	+	4.50925i	−0.741857	+	0.389540i
$135$	20.3671	−	1.02473i	1.75292	−	0.0881951i
$136$	13.9695	+	1.68798i	1.19788	+	0.144743i
$137$	−12.6574	+	10.6208i	−1.08140	+	0.907400i	−0.996036	−	0.0889501i	$-0.971649\pi$
$137$	−12.6574	+	10.6208i	−1.08140	+	0.907400i	−0.0853611	+	0.996350i	$0.527204\pi$
$138$	−2.15997	+	0.872546i	−0.183869	+	0.0742761i
$139$	−19.5648	−	3.44981i	−1.65947	−	0.292609i	−0.736199	−	0.676765i	$-0.763381\pi$
$139$	−19.5648	−	3.44981i	−1.65947	−	0.292609i	−0.923268	+	0.384157i	$0.874492\pi$
$140$	21.8700	+	5.69394i	1.84836	+	0.481226i
$141$	4.03279	−	8.37706i	0.339622	−	0.705476i
$142$	8.58669	−	6.63736i	0.720579	−	0.556995i
$143$	5.79380	+	10.0352i	0.484502	+	0.839182i
$144$	−11.3186	+	3.98603i	−0.943220	+	0.332169i
$145$	15.8287	−	27.4161i	1.31450	−	2.27678i
$146$	1.31494	+	9.72115i	0.108825	+	0.804528i
$147$	2.15006	+	0.604622i	0.177334	+	0.0498683i
$148$	−5.09892	−	18.5029i	−0.419129	−	1.52093i
$149$	−7.39950	+	8.81838i	−0.606190	+	0.722429i	−0.978630	−	0.205627i	$-0.934077\pi$
$149$	−7.39950	+	8.81838i	−0.606190	+	0.722429i	0.372440	+	0.928056i	$0.378521\pi$
$150$	24.2335	+	7.87543i	1.97866	+	0.643026i
$151$	−3.42462	−	1.24646i	−0.278692	−	0.101436i	0.198893	−	0.980021i	$-0.436265\pi$
$151$	−3.42462	−	1.24646i	−0.278692	−	0.101436i	−0.477585	+	0.878586i	$0.658488\pi$
$152$	−4.64966	−	3.48977i	−0.377137	−	0.283058i
$153$	14.6296	+	2.95333i	1.18273	+	0.238763i
$154$	10.0231	+	6.33551i	0.807685	+	0.510530i
$155$	7.37916	−	1.30114i	0.592708	−	0.104510i
$156$	−11.9009	−	6.95425i	−0.952833	−	0.556786i
$157$	−5.00630	−	13.7547i	−0.399546	−	1.09774i	−0.962506	−	0.271259i	$-0.912560\pi$
$157$	−5.00630	−	13.7547i	−0.399546	−	1.09774i	0.562960	−	0.826484i	$-0.309662\pi$
$158$	0.361005	−	0.115235i	0.0287201	−	0.00916762i
$159$	−3.58062	+	4.98176i	−0.283962	+	0.395079i
$160$	−22.1935	−	0.574566i	−1.75455	−	0.0454234i
$161$	−2.73817			−0.215798
$162$	−12.3013	+	3.26786i	−0.966479	+	0.256747i
$163$		−	5.93891i		−	0.465171i	−0.972576	−	0.232586i	$-0.925281\pi$
$163$		−	5.93891i		−	0.465171i	0.972576	−	0.232586i	$-0.0747186\pi$
$164$	0.142968	+	1.51053i	0.0111639	+	0.117952i
$165$	16.0745	+	11.5535i	1.25140	+	0.899441i
$166$	5.29307	+	16.5820i	0.410822	+	1.28701i
$167$	−18.7096	+	6.80974i	−1.44779	+	0.526953i	−0.941974	−	0.335687i	$-0.891032\pi$
$167$	−18.7096	+	6.80974i	−1.44779	+	0.526953i	−0.505818	+	0.862640i	$0.668809\pi$
$168$	−14.0904	−	0.638945i	−1.08710	−	0.0492957i
$169$	−0.491897	−	2.78968i	−0.0378382	−	0.214591i
$170$	23.3402	+	14.7531i	1.79011	+	1.13151i
$171$	−4.62443	−	4.07887i	−0.353639	−	0.311919i
$172$	11.3102	−	5.37212i	0.862394	−	0.409620i
$173$	−3.76876	+	10.3546i	−0.286534	+	0.787245i	0.710011	+	0.704190i	$0.248690\pi$
$173$	−3.76876	+	10.3546i	−0.286534	+	0.787245i	−0.996545	+	0.0830547i	$0.973532\pi$
$174$	−6.10674	+	18.7911i	−0.462950	+	1.42455i
$175$	22.9435	+	19.2519i	1.73437	+	1.45531i
$176$	−11.0016	−	3.82824i	−0.829279	−	0.288565i
$177$	2.92423	−	10.3987i	0.219799	−	0.781614i
$178$	−1.55957	−	11.5297i	−0.116895	−	0.864188i
$179$	−3.66363	−	2.11520i	−0.273832	−	0.158097i	0.356796	−	0.934182i	$-0.383869\pi$
$179$	−3.66363	−	2.11520i	−0.273832	−	0.158097i	−0.630628	+	0.776085i	$0.717203\pi$
$180$	−23.4184	−	2.46399i	−1.74551	−	0.183655i
$181$	16.4676	−	9.50759i	1.22403	−	0.706694i	0.258255	−	0.966077i	$-0.416853\pi$
$181$	16.4676	−	9.50759i	1.22403	−	0.706694i	0.965775	+	0.259383i	$0.0835192\pi$
$182$	−9.90845	−	12.8185i	−0.734463	−	0.950168i
$183$	−5.10980	−	2.45990i	−0.377727	−	0.181841i
$184$	2.61982	−	0.610144i	0.193136	−	0.0449804i
$185$	6.53992	−	37.0897i	0.480825	−	2.72689i
$186$	−4.33620	+	1.75166i	−0.317946	+	0.128438i
$187$	9.31254	+	11.0983i	0.681000	+	0.811585i
$188$	−6.09505	+	8.83752i	−0.444527	+	0.644542i
$189$	−14.8451	−	1.85424i	−1.07982	−	0.134876i
$190$	−5.30354	−	10.1003i	−0.384759	−	0.732753i
$191$	6.22796	−	5.22588i	0.450639	−	0.378131i	−0.389034	−	0.921224i	$-0.627191\pi$
$191$	6.22796	−	5.22588i	0.450639	−	0.378131i	0.839673	+	0.543092i	$0.182747\pi$
$192$	13.6238	−	2.52842i	0.983211	−	0.182473i
$193$	−2.29037	+	12.9893i	−0.164864	+	0.934993i	0.784340	+	0.620332i	$0.213002\pi$
$193$	−2.29037	+	12.9893i	−0.164864	+	0.934993i	−0.949204	+	0.314661i	$0.898109\pi$
$194$	5.63410	+	5.12602i	0.404505	+	0.368027i
$195$	−15.2397	−	22.3461i	−1.09134	−	1.60024i
$196$	−2.34503	−	1.07330i	−0.167502	−	0.0766643i
$197$	5.35211	−	3.09004i	0.381322	−	0.220156i	−0.297071	−	0.954855i	$-0.596010\pi$
$197$	5.35211	−	3.09004i	0.381322	−	0.220156i	0.678393	+	0.734699i	$0.262677\pi$
$198$	−11.3124	−	4.96809i	−0.803938	−	0.353067i
$199$	4.43708	−	7.68525i	0.314537	−	0.544793i	−0.664802	−	0.747019i	$-0.731484\pi$
$199$	4.43708	−	7.68525i	0.314537	−	0.544793i	0.979339	+	0.202226i	$0.0648176\pi$
$200$	−26.2418	−	13.3073i	−1.85557	−	0.940971i
$201$	11.5117	−	2.93289i	0.811971	−	0.206870i
$202$	5.58900	+	1.21825i	0.393241	+	0.0857159i
$203$	−14.9282	+	17.7908i	−1.04776	+	1.24867i
$204$	−16.1632	−	5.97888i	−1.13165	−	0.418605i
$205$	−1.01832	+	2.79781i	−0.0711225	+	0.195407i
$206$	1.61265	+	0.0646749i	0.112359	+	0.00450612i
$207$	2.82113	−	0.425994i	0.196082	−	0.0296086i
$208$	12.3365	+	10.0565i	0.855383	+	0.697295i
$209$	−1.03941	−	5.89477i	−0.0718972	−	0.407750i
$210$	−24.4376	−	12.9954i	−1.68636	−	0.896771i
$211$	6.04444	+	16.6070i	0.416116	+	1.14327i	0.953884	+	0.300177i	$0.0970457\pi$
$211$	6.04444	+	16.6070i	0.416116	+	1.14327i	−0.537767	+	0.843093i	$0.680732\pi$
$212$	4.97355	−	5.04468i	0.341585	−	0.346470i
$213$	−12.1151	+	5.46848i	−0.830110	+	0.374694i
$214$	−2.61598	+	6.37951i	−0.178825	+	0.436094i
$215$	24.5704			1.67569
$216$	14.6167	−	1.53383i	0.994539	−	0.104364i
$217$	−5.49695			−0.373157
$218$	−1.35217	+	3.29750i	−0.0915807	+	0.223335i
$219$	1.19463	−	11.9548i	0.0807258	−	0.807831i
$220$	−16.2776	−	16.0481i	−1.09743	−	1.08196i
$221$	−6.77040	−	18.6015i	−0.455426	−	1.25127i
$222$	0.819054	+	23.4918i	0.0549713	+	1.57667i
$223$	−4.05080	−	22.9732i	−0.271262	−	1.53840i	−0.750592	−	0.660767i	$-0.770231\pi$
$223$	−4.05080	−	22.9732i	−0.271262	−	1.53840i	0.479330	−	0.877635i	$-0.340880\pi$
$224$	15.9609	+	3.24235i	1.06643	+	0.216639i
$225$	−26.6338	−	16.2657i	−1.77558	−	1.08438i
$226$	−10.2199	−	0.409865i	−0.679817	−	0.0272638i
$227$	8.48739	−	23.3189i	0.563328	−	1.54773i	−0.251398	−	0.967884i	$-0.580890\pi$
$227$	8.48739	−	23.3189i	0.563328	−	1.54773i	0.814726	−	0.579846i	$-0.196887\pi$
$228$	4.54815	+	5.47823i	0.301209	+	0.362805i
$229$	−3.58229	+	4.26921i	−0.236724	+	0.282117i	−0.871307	−	0.490738i	$-0.836727\pi$
$229$	−3.58229	+	4.26921i	−0.236724	+	0.282117i	0.634583	+	0.772855i	$0.281172\pi$
$230$	5.15738	+	1.12417i	0.340068	+	0.0741256i
$231$	−10.1415	−	10.3948i	−0.667263	−	0.683927i
$232$	10.3187	−	20.3483i	0.677457	−	1.33593i
$233$	−3.32571	+	5.76031i	−0.217875	+	0.377370i	−0.954158	−	0.299303i	$-0.903246\pi$
$233$	−3.32571	+	5.76031i	−0.217875	+	0.377370i	0.736283	+	0.676673i	$0.236579\pi$
$234$	12.2029	+	11.6653i	0.797727	+	0.762583i
$235$	−18.2440	+	10.5332i	−1.19011	+	0.687110i
$236$	−5.19097	+	11.3416i	−0.337904	+	0.738277i
$237$	−0.462816	+	0.0347460i	−0.0300631	+	0.00225699i
$238$	−14.9831	−	13.6320i	−0.971211	−	0.883629i
$239$	−4.54329	+	25.7663i	−0.293881	+	1.66668i	0.377836	+	0.925872i	$0.376668\pi$
$239$	−4.54329	+	25.7663i	−0.293881	+	1.66668i	−0.671717	+	0.740808i	$0.734443\pi$
$240$	26.2771	+	6.98835i	1.69618	+	0.451096i
$241$	−19.2391	+	16.1435i	−1.23930	+	1.03989i	−0.241718	+	0.970347i	$0.577711\pi$
$241$	−19.2391	+	16.1435i	−1.23930	+	1.03989i	−0.997579	+	0.0695464i	$0.977845\pi$
$242$	1.65634	+	3.15440i	0.106473	+	0.202773i
$243$	15.5833	−	0.399129i	0.999672	−	0.0256041i
$244$	5.39067	+	3.71783i	0.345102	+	0.238010i
$245$	−3.25299	−	3.87676i	−0.207826	−	0.247677i
$246$	0.258724	−	1.84018i	0.0164956	−	0.117326i
$247$	−1.42019	+	8.05431i	−0.0903647	+	0.512484i
$248$	5.25936	−	1.22488i	0.333970	−	0.0777799i
$249$	−1.59598	−	21.2584i	−0.101141	−	1.34720i
$250$	−18.3386	−	23.7244i	−1.15983	−	1.50046i
$251$	−25.2441	+	14.5747i	−1.59339	+	0.919945i	−0.600672	+	0.799495i	$0.705100\pi$
$251$	−25.2441	+	14.5747i	−1.59339	+	0.919945i	−0.992719	+	0.120450i	$0.961566\pi$
$252$	16.6052	+	4.76344i	1.04603	+	0.300068i
$253$	2.39852	+	1.38479i	0.150794	+	0.0870608i
$254$	−0.904268	−	6.68512i	−0.0567388	−	0.419462i
$255$	−23.6159	−	24.2057i	−1.47889	−	1.51582i
$256$	−15.9935	+	0.454343i	−0.999597	+	0.0283964i
$257$	−5.42626	−	4.55318i	−0.338481	−	0.284019i	0.457664	−	0.889125i	$-0.348686\pi$
$257$	−5.42626	−	4.55318i	−0.338481	−	0.284019i	−0.796145	+	0.605106i	$0.793131\pi$
$258$	−15.0003	+	3.18755i	−0.933879	+	0.198448i
$259$	−9.44975	+	25.9630i	−0.587179	+	1.61326i
$260$	13.4000	+	28.2117i	0.831034	+	1.74962i
$261$	12.6127	−	20.6522i	0.780705	−	1.27834i
$262$	4.18845	+	2.64748i	0.258764	+	0.163562i
$263$	1.99223	+	11.2985i	0.122846	+	0.696695i	0.982564	+	0.185926i	$0.0595283\pi$
$263$	1.99223	+	11.2985i	0.122846	+	0.696695i	−0.859718	+	0.510770i	$0.829361\pi$
$264$	12.0194	+	7.68568i	0.739746	+	0.473021i
$265$	13.0629	−	4.75451i	0.802449	−	0.292067i
$266$	2.54495	+	7.97276i	0.156041	+	0.488841i
$267$	−1.41689	+	14.1789i	−0.0867120	+	0.867736i
$268$	−13.6561	+	1.29252i	−0.834182	+	0.0789533i
$269$		−	15.1820i		−	0.925661i	−0.886447	−	0.462831i	$-0.846834\pi$
$269$		−	15.1820i		−	0.925661i	0.886447	−	0.462831i	$-0.153166\pi$
$270$	27.1997	+	9.58724i	1.65532	+	0.583461i
$271$	13.2808			0.806753			0.403376	−	0.915034i	$-0.367837\pi$
$271$	13.2808			0.806753			0.403376	+	0.915034i	$0.367837\pi$
$272$	17.3731	+	9.70410i	1.05340	+	0.588397i
$273$	8.16351	+	18.0857i	0.494078	+	1.09460i
$274$	−22.2606	+	7.10572i	−1.34481	+	0.429272i
$275$	−10.3612	−	28.4672i	−0.624804	−	1.71664i
$276$	−3.29444	−	0.0172362i	−0.198302	−	0.00103749i
$277$	−2.53413	+	0.446836i	−0.152261	+	0.0268478i	−0.249259	−	0.968437i	$-0.580187\pi$
$277$	−2.53413	+	0.446836i	−0.152261	+	0.0268478i	0.0969979	+	0.995285i	$0.469076\pi$
$278$	−23.7491	−	15.0116i	−1.42438	−	0.900335i
$279$	5.66348	−	0.855194i	0.339064	−	0.0511991i
$280$	25.5613	+	19.1848i	1.52758	+	1.14651i
$281$	25.4277	+	9.25491i	1.51689	+	0.552102i	0.960368	−	0.278734i	$-0.0899147\pi$
$281$	25.4277	+	9.25491i	1.51689	+	0.552102i	0.556518	+	0.830835i	$0.312137\pi$
$282$	9.77156	−	8.79737i	0.581888	−	0.523876i
$283$	17.1845	−	20.4797i	1.02151	−	1.21739i	0.0456626	−	0.998957i	$-0.485460\pi$
$283$	17.1845	−	20.4797i	1.02151	−	1.21739i	0.975851	−	0.218436i	$-0.0700955\pi$
$284$	14.7968	−	4.07760i	0.878028	−	0.241961i
$285$	3.44951	+	13.5394i	0.204331	+	0.802007i
$286$	2.19664	+	16.2395i	0.129890	+	0.960259i
$287$	1.09212	−	1.89160i	0.0644656	−	0.111658i
$288$	−16.9489	−	0.857444i	−0.998723	−	0.0505254i
$289$	−3.87484	−	6.71142i	−0.227932	−	0.394789i
$290$	35.4217	−	27.3803i	2.08003	−	1.60783i
$291$	−5.25621	−	7.70721i	−0.308124	−	0.451804i
$292$	−3.49536	+	13.4254i	−0.204550	+	0.785663i
$293$	17.3330	+	3.05628i	1.01261	+	0.178550i	0.655245	−	0.755416i	$-0.272565\pi$
$293$	17.3330	+	3.05628i	1.01261	+	0.178550i	0.357361	+	0.933966i	$0.383677\pi$
$294$	2.48889	+	1.94476i	0.145155	+	0.113421i
$295$	−18.7498	+	15.7329i	−1.09166	+	0.916007i
$296$	3.25602	−	26.9465i	0.189252	−	1.56623i
$297$	12.0659	+	9.13192i	0.700137	+	0.529888i
$298$	−14.4136	+	7.56840i	−0.834957	+	0.438426i
$299$	−2.43244	−	2.89887i	−0.140672	−	0.167646i
$300$	27.4834	+	23.3074i	1.58675	+	1.34565i
$301$	−17.7513	−	3.13004i	−1.02317	−	0.180412i
$302$	−3.81224	−	3.46846i	−0.219370	−	0.199587i
$303$	−6.31244	−	3.03886i	−0.362640	−	0.174578i
$304$	−4.21152	−	7.06107i	−0.241547	−	0.404980i
$305$	6.42499	+	11.1284i	0.367894	+	0.637211i
$306$	17.5578	+	11.7139i	1.00372	+	0.669641i
$307$	10.1962	+	5.88676i	0.581926	+	0.335975i	0.761898	−	0.647696i	$-0.224268\pi$
$307$	10.1962	+	5.88676i	0.581926	+	0.335975i	−0.179972	+	0.983672i	$0.557601\pi$
$308$	9.71565	+	13.6678i	0.553600	+	0.778796i
$309$	−1.90287	−	0.535107i	−0.108250	−	0.0304412i
$310$	10.3536	+	2.25680i	0.588044	+	0.128178i
$311$	26.0496	+	21.8582i	1.47714	+	1.23947i	0.909175	+	0.416414i	$0.136713\pi$
$311$	26.0496	+	21.8582i	1.47714	+	1.23947i	0.567965	+	0.823053i	$0.307731\pi$
$312$	−11.8407	−	15.4849i	−0.670347	−	0.876662i
$313$	6.64081	+	2.41706i	0.375361	+	0.136620i	0.522809	−	0.852450i	$-0.324884\pi$
$313$	6.64081	+	2.41706i	0.375361	+	0.136620i	−0.147449	+	0.989070i	$0.547106\pi$
$314$	0.829518	−	20.6838i	0.0468124	−	1.16726i
$315$	25.4226	+	22.4234i	1.43240	+	1.26342i
$316$	0.534197	+	0.0429166i	0.0300509	+	0.00241425i
$317$	−5.34112	+	0.941783i	−0.299987	+	0.0528958i	−0.321616	−	0.946870i	$-0.604226\pi$
$317$	−5.34112	+	0.941783i	−0.299987	+	0.0528958i	0.0216287	+	0.999766i	$0.493115\pi$
$318$	−7.35814	+	4.59731i	−0.412624	+	0.257805i
$319$	22.0739	−	8.03424i	1.23590	−	0.449831i
$320$	−28.7314	−	12.6599i	−1.60614	−	0.707707i
$321$	4.92859	−	6.85720i	0.275087	−	0.382732i
$322$	−3.58283	−	1.46918i	−0.199663	−	0.0818741i
$323$			10.2255i			0.568961i
$324$	−17.8493	−	2.32438i	−0.991627	−	0.129132i
$325$			41.3924i			2.29604i
$326$	3.18655	−	7.77092i	0.176486	−	0.430391i
$327$	2.54753	−	3.54441i	0.140879	−	0.196006i
$328$	−0.623410	+	2.05320i	−0.0344220	+	0.113369i
$329$	14.5225	−	5.28577i	0.800654	−	0.291414i
$330$	14.8341	+	23.7424i	0.816588	+	1.30698i
$331$	−5.34260	+	0.942044i	−0.293656	+	0.0517794i	−0.318535	−	0.947911i	$-0.603191\pi$
$331$	−5.34260	+	0.942044i	−0.293656	+	0.0517794i	0.0248795	+	0.999690i	$0.492080\pi$
$332$	−1.97128	+	24.5371i	−0.108188	+	1.34665i
$333$	5.69682	−	28.2197i	0.312184	−	1.54643i
$334$	−28.1348	−	1.12834i	−1.53947	−	0.0617400i
$335$	−25.2940	−	9.20627i	−1.38196	−	0.502992i
$336$	−18.0941	−	8.39631i	−0.987116	−	0.458056i
$337$	−22.3325	−	18.7392i	−1.21653	−	1.02079i	−0.998999	−	0.0447328i	$-0.985756\pi$
$337$	−22.3325	−	18.7392i	−1.21653	−	1.02079i	−0.217528	−	0.976054i	$-0.569799\pi$
$338$	0.853182	−	3.91416i	0.0464070	−	0.212902i
$339$	12.0591	+	3.39114i	0.654959	+	0.184182i
$340$	22.6242	+	31.8274i	1.22697	+	1.72608i
$341$	4.81509	+	2.77999i	0.260752	+	0.150545i
$342$	−3.86242	−	7.81836i	−0.208856	−	0.422768i
$343$	−8.22070	−	14.2387i	−0.443876	−	0.768816i
$344$	17.6816	−	0.960757i	0.953325	−	0.0518006i
$345$	−5.82496	−	2.80418i	−0.313605	−	0.150972i
$346$	−10.4871	+	11.5266i	−0.563792	+	0.619673i
$347$	17.1238	+	3.01939i	0.919255	+	0.162089i	0.613203	−	0.789925i	$-0.289881\pi$
$347$	17.1238	+	3.01939i	0.919255	+	0.162089i	0.306052	+	0.952015i	$0.400992\pi$
$348$	−18.0729	+	21.3111i	−0.968812	+	1.14239i
$349$	−3.38478	−	4.03383i	−0.181183	−	0.215926i	0.667807	−	0.744335i	$-0.267233\pi$
$349$	−3.38478	−	4.03383i	−0.181183	−	0.215926i	−0.848990	+	0.528409i	$0.822789\pi$
$350$	19.6914	+	37.5011i	1.05255	+	2.00452i
$351$	−11.2245	−	17.3636i	−0.599121	−	0.926799i
$352$	−12.3413	−	10.9121i	−0.657794	−	0.581619i
$353$	−7.22029	+	6.05854i	−0.384297	+	0.322463i	−0.814387	−	0.580323i	$-0.802926\pi$
$353$	−7.22029	+	6.05854i	−0.384297	+	0.322463i	0.430090	+	0.902786i	$0.358482\pi$
$354$	9.40575	−	12.0374i	0.499910	−	0.639783i
$355$	29.6606	+	5.22997i	1.57422	+	0.277578i
$356$	4.14565	−	15.9231i	0.219719	−	0.843925i
$357$	13.9782	+	20.4963i	0.739803	+	1.08478i
$358$	−3.65885	−	4.73342i	−0.193376	−	0.250169i
$359$	−8.12377	−	14.0708i	−0.428756	−	0.742628i	0.568007	−	0.823024i	$-0.307715\pi$
$359$	−8.12377	−	14.0708i	−0.428756	−	0.742628i	−0.996763	+	0.0803962i	$0.974381\pi$
$360$	−29.3204	−	15.7893i	−1.54532	−	0.832171i
$361$	−7.38764	+	12.7958i	−0.388823	+	0.673461i
$362$	26.6488	−	3.60468i	1.40063	−	0.189458i
$363$	−1.07731	−	4.22847i	−0.0565440	−	0.221937i
$364$	−6.08717	−	22.0891i	−0.319054	−	1.15778i
$365$	−17.4986	+	20.8541i	−0.915921	+	1.09155i
$366$	−5.36618	−	5.96041i	−0.280495	−	0.311555i
$367$	12.0315	+	4.37912i	0.628042	+	0.228588i	0.636379	−	0.771377i	$-0.280432\pi$
$367$	12.0315	+	4.37912i	0.628042	+	0.228588i	−0.00833711	+	0.999965i	$0.502654\pi$
$368$	3.75535	+	0.607319i	0.195761	+	0.0316587i
$369$	−0.830915	+	2.11881i	−0.0432557	+	0.110301i
$370$	28.4580	−	45.0220i	1.47946	−	2.34058i
$371$	−10.0432	+	1.77089i	−0.521417	+	0.0919400i
$372$	−6.61367	−	0.0346020i	−0.342903	−	0.00179403i
$373$	2.16442	+	5.94669i	0.112069	+	0.307908i	0.983030	−	0.183445i	$-0.0587248\pi$
$373$	2.16442	+	5.94669i	0.112069	+	0.307908i	−0.870961	+	0.491353i	$0.836503\pi$
$374$	6.23042	+	19.5185i	0.322167	+	1.00928i
$375$	15.1090	+	33.4730i	0.780227	+	1.72854i
$376$	−12.7170	+	8.29336i	−0.655831	+	0.427697i
$377$	−32.0963			−1.65304
$378$	−18.4296	−	10.3915i	−0.947916	−	0.534479i
$379$		−	28.5066i		−	1.46428i	−0.681152	−	0.732142i	$-0.738521\pi$
$379$		−	28.5066i		−	1.46428i	0.681152	−	0.732142i	$-0.261479\pi$
$380$	−1.52020	−	16.0616i	−0.0779844	−	0.823945i
$381$	−0.821535	+	8.22118i	−0.0420885	+	0.421184i
$382$	10.9531	−	3.49630i	0.560410	−	0.178886i
$383$	−29.5410	+	10.7521i	−1.50948	+	0.549405i	−0.958494	−	0.285112i	$-0.907969\pi$
$383$	−29.5410	+	10.7521i	−1.50948	+	0.549405i	−0.550983	+	0.834517i	$0.685747\pi$
$384$	19.1830	+	4.00151i	0.978929	+	0.204201i
$385$	5.71409	+	32.4062i	0.291217	+	1.65157i
$386$	−9.96638	+	15.7673i	−0.507275	+	0.802536i
$387$	18.7761	+	0.463183i	0.954441	+	0.0235449i
$388$	4.62169	+	9.73028i	0.234631	+	0.493980i
$389$	−1.34416	+	3.69306i	−0.0681518	+	0.187246i	−0.969093	−	0.246696i	$-0.920655\pi$
$389$	−1.34416	+	3.69306i	−0.0681518	+	0.187246i	0.900941	+	0.433941i	$0.142877\pi$
$390$	−7.95091	−	37.4162i	−0.402610	−	1.89464i
$391$	−3.62440	−	3.04123i	−0.183294	−	0.153802i
$392$	−2.49253	−	2.66262i	−0.125892	−	0.134483i
$393$	−4.23794	−	4.34377i	−0.213776	−	0.219114i
$394$	8.66108	−	1.17155i	0.436339	−	0.0590217i
$395$	0.910744	+	0.525818i	0.0458245	+	0.0264568i
$396$	−12.1364	−	12.5704i	−0.609875	−	0.631684i
$397$	−17.9961	+	10.3901i	−0.903200	+	0.521463i	−0.878237	−	0.478226i	$-0.841280\pi$
$397$	−17.9961	+	10.3901i	−0.903200	+	0.521463i	−0.0249629	+	0.999688i	$0.507947\pi$
$398$	9.92937	−	7.67523i	0.497715	−	0.384725i
$399$	−0.767360	−	10.2212i	−0.0384161	−	0.511702i
$400$	−27.1966	−	31.4925i	−1.35983	−	1.57462i
$401$	−4.02373	+	22.8197i	−0.200935	+	1.13956i	0.702774	+	0.711413i	$0.251945\pi$
$401$	−4.02373	+	22.8197i	−0.200935	+	1.13956i	−0.903709	+	0.428147i	$0.859166\pi$
$402$	16.6364	+	2.33903i	0.829749	+	0.116660i
$403$	−4.88319	−	5.81955i	−0.243249	−	0.289893i
$404$	6.65941	+	4.59285i	0.331318	+	0.228503i
$405$	−29.6813	−	19.1476i	−1.47488	−	0.951451i
$406$	−29.0790	+	15.2690i	−1.44316	+	0.757788i
$407$	21.4079	−	17.9634i	1.06115	−	0.890412i
$408$	−17.9412	−	16.4957i	−0.888220	−	0.816656i
$409$	5.07096	−	28.7589i	0.250743	−	1.42203i	−0.556025	−	0.831165i	$-0.687674\pi$
$409$	5.07096	−	28.7589i	0.250743	−	1.42203i	0.806768	−	0.590868i	$-0.201215\pi$
$410$	−2.83362	+	3.11448i	−0.139943	+	0.153813i
$411$	28.5385	−	2.14253i	1.40770	−	0.105683i
$412$	2.07542	+	0.949901i	0.102248	+	0.0467983i
$413$	15.5503	−	8.97799i	0.765182	−	0.441778i
$414$	3.91994	+	0.956285i	0.192655	+	0.0469988i
$415$	−24.1523	+	41.8330i	−1.18559	+	2.05350i
$416$	10.7462	+	19.7779i	0.526873	+	0.969694i
$417$	24.0297	+	24.6298i	1.17674	+	1.20612i
$418$	1.80282	−	8.27086i	0.0881790	−	0.404541i
$419$	−8.33906	+	9.93810i	−0.407390	+	0.485508i	−0.930258	−	0.366905i	$-0.880417\pi$
$419$	−8.33906	+	9.93810i	−0.407390	+	0.485508i	0.522869	+	0.852413i	$0.324862\pi$
$420$	−25.0033	−	30.1163i	−1.22004	−	1.46953i
$421$	1.49536	−	4.10848i	0.0728795	−	0.200235i	−0.897904	−	0.440191i	$-0.854911\pi$
$421$	1.49536	−	4.10848i	0.0728795	−	0.200235i	0.970784	+	0.239956i	$0.0771330\pi$
$422$	−1.00153	+	24.9730i	−0.0487539	+	1.21567i
$423$	−14.1402	+	7.70527i	−0.687519	+	0.374643i
$424$	9.21452	−	3.93227i	0.447497	−	0.190968i
$425$	8.98665	+	50.9658i	0.435916	+	2.47220i
$426$	−18.7864	+	0.654996i	−0.910204	+	0.0317347i
$427$	−3.22419	−	8.85839i	−0.156030	−	0.428688i
$428$	−6.84591	+	6.94382i	−0.330909	+	0.335642i
$429$	1.99567	−	19.9709i	0.0963517	−	0.964202i
$430$	32.1498	+	13.1834i	1.55040	+	0.635759i
$431$	1.15854			0.0558051			0.0279025	−	0.999611i	$-0.491117\pi$
$431$	1.15854			0.0558051			0.0279025	+	0.999611i	$0.491117\pi$
$432$	19.9486	+	5.83567i	0.959775	+	0.280769i
$433$	37.7498			1.81414			0.907069	−	0.420982i	$-0.138314\pi$
$433$	37.7498			1.81414			0.907069	+	0.420982i	$0.138314\pi$
$434$	−7.19263	−	2.94941i	−0.345257	−	0.141576i
$435$	−49.9768	+	22.5585i	−2.39620	+	1.08160i
$436$	−3.53857	+	3.58918i	−0.169467	+	0.171891i
$437$	0.668571	+	1.83688i	0.0319821	+	0.0878701i
$438$	7.97755	−	15.0016i	0.381182	−	0.716804i
$439$	−4.69964	−	26.6530i	−0.224301	−	1.27208i	−0.864016	−	0.503464i	$-0.832059\pi$
$439$	−4.69964	−	26.6530i	−0.224301	−	1.27208i	0.639715	−	0.768612i	$-0.279052\pi$
$440$	−12.6882	−	29.7323i	−0.604885	−	1.41743i
$441$	−2.41276	−	3.02384i	−0.114894	−	0.143992i
$442$	1.12182	−	27.9723i	0.0533596	−	1.33051i
$443$	10.3614	−	28.4677i	0.492285	−	1.35254i	−0.406299	−	0.913740i	$-0.633181\pi$
$443$	10.3614	−	28.4677i	0.492285	−	1.35254i	0.898584	−	0.438802i	$-0.144597\pi$
$444$	−11.5329	+	31.1780i	−0.547329	+	1.47964i
$445$	20.7542	−	24.7338i	0.983841	−	1.17250i
$446$	7.02601	−	32.2334i	0.332691	−	1.52630i
$447$	19.3214	−	4.92261i	0.913871	−	0.232831i
$448$	19.1448	+	12.8064i	0.904506	+	0.605047i
$449$	−1.70434	+	2.95201i	−0.0804330	+	0.139314i	−0.903436	−	0.428723i	$-0.858964\pi$
$449$	−1.70434	+	2.95201i	−0.0804330	+	0.139314i	0.823003	+	0.568037i	$0.192297\pi$
$450$	−26.1222	−	35.5737i	−1.23141	−	1.67696i
$451$	−1.91329	+	1.10464i	−0.0900934	+	0.0520155i
$452$	−13.1526	−	6.01982i	−0.618644	−	0.283149i
$453$	3.55655	+	5.21499i	0.167101	+	0.245021i
$454$	23.6174	−	25.9583i	1.10842	−	1.21828i
$455$	7.80745	−	44.2782i	0.366019	−	2.07580i
$456$	3.01178	+	9.60846i	0.141040	+	0.449958i
$457$	7.27754	−	6.10658i	0.340429	−	0.285654i	−0.456504	−	0.889721i	$-0.650899\pi$
$457$	7.27754	−	6.10658i	0.340429	−	0.285654i	0.796933	+	0.604068i	$0.206454\pi$
$458$	−6.97800	+	3.66406i	−0.326060	+	0.171210i
$459$	−17.5904	−	18.9425i	−0.821048	−	0.884162i
$460$	6.14514	+	4.23817i	0.286518	+	0.197606i
$461$	19.8885	+	23.7021i	0.926298	+	1.10392i	0.994341	+	0.106236i	$0.0338799\pi$
$461$	19.8885	+	23.7021i	0.926298	+	1.10392i	−0.0680433	+	0.997682i	$0.521676\pi$
$462$	−7.69257	−	19.0428i	−0.357891	−	0.885952i
$463$	−4.27095	+	24.2217i	−0.198488	+	1.12568i	0.708876	+	0.705333i	$0.249203\pi$
$463$	−4.27095	+	24.2217i	−0.198488	+	1.12568i	−0.907364	+	0.420347i	$0.861908\pi$
$464$	24.4198	−	21.0887i	1.13366	−	0.979018i
$465$	−11.6938	−	5.62947i	−0.542285	−	0.261061i
$466$	−7.44233	+	5.75280i	−0.344759	+	0.266493i
$467$	0.849394	−	0.490398i	0.0393052	−	0.0226929i	−0.480219	−	0.877149i	$-0.659443\pi$
$467$	0.849394	−	0.490398i	0.0393052	−	0.0226929i	0.519524	+	0.854456i	$0.326109\pi$
$468$	9.70811	+	21.8112i	0.448757	+	1.00823i
$469$	17.1013	+	9.87344i	0.789665	+	0.455913i
$470$	−29.5235	+	3.99352i	−1.36182	+	0.184207i
$471$	−6.86327	+	24.4061i	−0.316243	+	1.12457i
$472$	−12.8777	+	12.0550i	−0.592743	+	0.554877i
$473$	13.9664	+	11.7192i	0.642177	+	0.538851i
$474$	−0.624227	−	0.202862i	−0.0286717	−	0.00931775i
$475$	7.31297	−	20.0922i	0.335542	−	0.921894i
$476$	−12.2908	−	25.8764i	−0.563346	−	1.18604i
$477$	10.0720	−	3.38702i	0.461164	−	0.155081i
$478$	−19.7698	+	31.2768i	−0.904248	+	1.43057i
$479$	−1.26087	−	7.15074i	−0.0576105	−	0.326726i	0.942358	−	0.334605i	$-0.108603\pi$
$479$	−1.26087	−	7.15074i	−0.0576105	−	0.326726i	−0.999969	+	0.00787960i	$0.997492\pi$
$480$	30.6334	+	23.2432i	1.39822	+	1.06090i
$481$	−35.8813	+	13.0597i	−1.63605	+	0.595473i
$482$	−33.8357	+	10.8006i	−1.54117	+	0.491952i
$483$	3.85111	+	2.76797i	0.175232	+	0.125947i
$484$	0.474769	+	5.01618i	0.0215804	+	0.228008i
$485$			21.1382i			0.959836i
$486$	20.6046	+	7.83906i	0.934643	+	0.355587i
$487$	0.153837			0.00697103			0.00348552	−	0.999994i	$-0.498891\pi$
$487$	0.153837			0.00697103			0.00348552	+	0.999994i	$0.498891\pi$
$488$	5.05874	+	7.75707i	0.228999	+	0.351146i
$489$	−6.00355	+	8.35280i	−0.271490	+	0.377727i
$490$	−2.17636	−	6.81805i	−0.0983181	−	0.308008i
$491$	−7.10851	−	19.5305i	−0.320802	−	0.881398i	−0.990345	−	0.138624i	$-0.955732\pi$
$491$	−7.10851	−	19.5305i	−0.320802	−	0.881398i	0.669543	−	0.742774i	$-0.266490\pi$
$492$	1.32589	−	2.26901i	0.0597757	−	0.102295i
$493$	−39.5197	+	6.96839i	−1.77988	+	0.313840i
$494$	−6.17986	+	9.77686i	−0.278045	+	0.439882i
$495$	−10.9288	−	32.4990i	−0.491215	−	1.46072i
$496$	7.53897	+	1.21921i	0.338510	+	0.0547441i
$497$	−20.7626	−	7.55696i	−0.931329	−	0.338976i
$498$	9.31800	−	28.6725i	0.417549	−	1.28484i
$499$	−12.0312	+	14.3382i	−0.538588	+	0.641865i	−0.964871	−	0.262726i	$-0.915379\pi$
$499$	−12.0312	+	14.3382i	−0.538588	+	0.641865i	0.426282	+	0.904590i	$0.359823\pi$
$500$	−11.2661	−	40.8825i	−0.503837	−	1.82832i
$501$	33.1980	+	9.33565i	1.48318	+	0.417086i
$502$	−40.8514	+	5.52579i	−1.82329	+	0.246628i
$503$	15.2553	−	26.4230i	0.680200	−	1.17814i	−0.294719	−	0.955584i	$-0.595226\pi$
$503$	15.2553	−	26.4230i	0.680200	−	1.17814i	0.974919	−	0.222558i	$-0.0714406\pi$
$504$	19.1716	+	15.1424i	0.853971	+	0.674497i
$505$	7.93717	+	13.7476i	0.353200	+	0.611760i
$506$	2.39539	+	3.09890i	0.106488	+	0.137763i
$507$	−2.12822	+	4.42081i	−0.0945175	+	0.196335i
$508$	2.40372	−	9.23250i	0.106648	−	0.409626i
$509$	−25.1247	−	4.43017i	−1.11363	−	0.196364i	−0.413590	−	0.910463i	$-0.635725\pi$
$509$	−25.1247	−	4.43017i	−1.11363	−	0.196364i	−0.700044	+	0.714099i	$0.746836\pi$
$510$	−17.9132	−	44.3438i	−0.793211	−	1.96358i
$511$	15.2988	−	12.8372i	0.676779	−	0.567885i
$512$	−21.1710	−	7.98691i	−0.935633	−	0.352975i
$513$	2.38079	+	10.4115i	0.105114	+	0.459679i
$514$	−4.65711	−	8.86921i	−0.205416	−	0.391204i
$515$	2.87899	+	3.43104i	0.126863	+	0.151190i
$516$	−21.3379	−	3.87766i	−0.939347	−	0.170704i
$517$	−15.3943	−	2.71443i	−0.677041	−	0.119381i
$518$	−26.2953	+	28.9016i	−1.15535	+	1.26987i
$519$	15.7679	−	10.7535i	0.692133	−	0.472025i
$520$	2.39648	+	44.1042i	0.105092	+	1.93410i
$521$	−8.58140	−	14.8634i	−0.375958	−	0.651178i	0.614512	−	0.788908i	$-0.289353\pi$
$521$	−8.58140	−	14.8634i	−0.375958	−	0.651178i	−0.990470	+	0.137729i	$0.956020\pi$
$522$	27.5844	−	20.2556i	1.20734	−	0.886562i
$523$	35.9656	+	20.7647i	1.57266	+	0.907978i	0.995841	+	0.0911099i	$0.0290415\pi$
$523$	35.9656	+	20.7647i	1.57266	+	0.907978i	0.576824	+	0.816869i	$0.304292\pi$
$524$	4.05997	+	5.71150i	0.177361	+	0.249508i
$525$	−12.8076	−	50.2702i	−0.558969	−	2.19397i
$526$	−3.45547	+	15.8528i	−0.150666	+	0.691213i
$527$	−7.27607	−	6.10535i	−0.316950	−	0.265953i
$528$	11.6034	+	16.5056i	0.504972	+	0.718315i
$529$	20.7630	+	7.55712i	0.902739	+	0.328570i
$530$	19.6436	+	0.787799i	0.853262	+	0.0342198i
$531$	−14.6247	+	11.6692i	−0.634657	+	0.506402i
$532$	−0.947808	+	11.7977i	−0.0410927	+	0.511494i
$533$	2.97279	−	0.524183i	0.128766	−	0.0227049i
$534$	−9.46173	+	17.7925i	−0.409449	+	0.769959i
$535$	−17.9806	+	6.54441i	−0.777370	+	0.282939i
$536$	−18.5622	−	5.63603i	−0.801767	−	0.243439i
$537$	3.01451	+	6.67843i	0.130086	+	0.288196i
$538$	8.14595	−	19.8652i	0.351197	−	0.856452i
$539$		−	3.75520i		−	0.161748i
$540$	30.4461	+	27.1388i	1.31019	+	1.16787i
$541$			11.2309i			0.482852i	0.970419	+	0.241426i	$0.0776152\pi$
$541$			11.2309i			0.482852i	−0.970419	+	0.241426i	$0.922385\pi$
$542$	17.3776	+	7.12589i	0.746434	+	0.306083i
$543$	−32.7720	−	3.27488i	−1.40638	−	0.140538i
$544$	17.5255	+	22.0192i	0.751401	+	0.944065i
$545$	−9.29398	+	3.38273i	−0.398110	+	0.144900i
$546$	0.977798	+	28.0449i	0.0418459	+	1.20021i
$547$	19.8704	−	3.50369i	0.849599	−	0.149807i	0.268137	−	0.963381i	$-0.413592\pi$
$547$	19.8704	−	3.50369i	0.849599	−	0.149807i	0.581462	+	0.813574i	$0.302481\pi$
$548$	−32.9401	−	2.64636i	−1.40713	−	0.113047i
$549$	4.70002	+	8.62515i	0.200592	+	0.368113i
$550$	1.71680	−	42.8080i	0.0732046	−	1.82534i
$551$	15.5798	+	5.67059i	0.663722	+	0.241575i
$552$	−4.30145	−	1.79020i	−0.183082	−	0.0761959i
$553$	−0.590998	−	0.495906i	−0.0251318	−	0.0210881i
$554$	−3.55560	−	0.775026i	−0.151063	−	0.0329277i
$555$	−46.6915	+	45.5539i	−1.98194	+	1.93366i
$556$	−23.0206	−	32.3850i	−0.976290	−	1.37343i
$557$	26.7781	+	15.4604i	1.13463	+	0.655076i	0.945094	−	0.326798i	$-0.105970\pi$
$557$	26.7781	+	15.4604i	1.13463	+	0.655076i	0.189532	+	0.981875i	$0.439303\pi$
$558$	7.86939	+	1.91977i	0.333138	+	0.0812702i
$559$	−12.4556	−	21.5737i	−0.526814	−	0.912469i
$560$	23.1526	+	38.8179i	0.978377	+	1.64036i
$561$	−1.87861	−	25.0231i	−0.0793150	−	1.05648i
$562$	28.3057	+	25.7531i	1.19400	+	1.08633i
$563$	−20.3052	−	3.58035i	−0.855761	−	0.150894i	−0.271479	−	0.962444i	$-0.587513\pi$
$563$	−20.3052	−	3.58035i	−0.855761	−	0.150894i	−0.584282	+	0.811551i	$0.698624\pi$
$564$	17.5061	−	6.26818i	0.737140	−	0.263938i
$565$	−18.2450	−	21.7436i	−0.767575	−	0.914760i
$566$	33.4740	−	17.5768i	1.40702	−	0.738808i
$567$	19.0046	+	17.6146i	0.798117	+	0.739744i
$568$	21.5491	+	2.60383i	0.904180	+	0.109254i
$569$	−3.82688	+	3.21114i	−0.160431	+	0.134618i	−0.719469	−	0.694524i	$-0.755615\pi$
$569$	−3.82688	+	3.21114i	−0.160431	+	0.134618i	0.559038	+	0.829142i	$0.311171\pi$
$570$	−2.75105	+	19.5669i	−0.115229	+	0.819566i
$571$	7.54047	+	1.32959i	0.315559	+	0.0556415i	0.329184	−	0.944266i	$-0.393226\pi$
$571$	7.54047	+	1.32959i	0.315559	+	0.0556415i	−0.0136257	+	0.999907i	$0.504337\pi$
$572$	−5.83910	+	22.4276i	−0.244145	+	0.937743i
$573$	−14.0421	+	1.05421i	−0.586617	+	0.0440404i
$574$	2.44395	−	1.88913i	0.102009	−	0.0788509i
$575$	4.94663	+	8.56781i	0.206289	+	0.357303i
$576$	−21.7171	−	10.2159i	−0.904881	−	0.425664i
$577$	6.53703	−	11.3225i	0.272140	−	0.471361i	−0.697269	−	0.716809i	$-0.745602\pi$
$577$	6.53703	−	11.3225i	0.272140	−	0.471361i	0.969410	+	0.245449i	$0.0789352\pi$
$578$	−1.46909	−	10.8608i	−0.0611062	−	0.451749i
$579$	16.3520	−	15.9536i	0.679567	−	0.663009i
$580$	61.0394	−	16.8209i	2.53452	−	0.698448i
$581$	22.7783	−	27.1462i	0.945005	−	1.12621i
$582$	−2.74228	−	12.9049i	−0.113671	−	0.534927i
$583$	9.69302	+	3.52797i	0.401444	+	0.146114i
$584$	−11.7771	+	15.6914i	−0.487338	+	0.649314i
$585$	−1.15535	+	46.8343i	−0.0477677	+	1.93636i
$586$	21.0400	+	13.2992i	0.869154	+	0.549384i
$587$	20.2706	−	3.57425i	0.836657	−	0.147525i	0.261126	−	0.965305i	$-0.415906\pi$
$587$	20.2706	−	3.57425i	0.836657	−	0.147525i	0.575532	+	0.817780i	$0.304795\pi$
$588$	2.21319	+	3.88010i	0.0912704	+	0.160013i
$589$	1.34217	+	3.68759i	0.0553033	+	0.151945i
$590$	−32.9752	+	10.5259i	−1.35757	+	0.433344i
$591$	−10.6512	−	1.06436i	−0.438130	−	0.0437819i
$592$	18.7187	−	33.5118i	0.769333	−	1.37733i
$593$	35.4674			1.45647			0.728237	−	0.685326i	$-0.240340\pi$
$593$	35.4674			1.45647			0.728237	+	0.685326i	$0.240340\pi$
$594$	10.8882	+	18.4229i	0.446749	+	0.755902i
$595$		−	56.2142i		−	2.30456i
$596$	−22.9207	+	2.16939i	−0.938869	+	0.0888617i
$597$	−14.0095	+	6.32358i	−0.573369	+	0.258807i
$598$	−1.62739	−	5.09824i	−0.0665489	−	0.208482i
$599$	4.95171	−	1.80227i	0.202321	−	0.0736389i	−0.238872	−	0.971051i	$-0.576778\pi$
$599$	4.95171	−	1.80227i	0.202321	−	0.0736389i	0.441193	+	0.897412i	$0.354555\pi$
$600$	23.4557	+	45.2435i	0.957574	+	1.84706i
$601$	−6.16086	−	34.9400i	−0.251307	−	1.42523i	−0.805378	−	0.592762i	$-0.798038\pi$
$601$	−6.16086	−	34.9400i	−0.251307	−	1.42523i	0.554071	−	0.832469i	$-0.313074\pi$
$602$	−21.5478	−	13.6201i	−0.878221	−	0.555115i
$603$	−19.1555	−	7.51201i	−0.780071	−	0.305913i
$604$	−3.12721	−	6.58387i	−0.127244	−	0.267894i
$605$	−3.38165	+	9.29100i	−0.137484	+	0.377733i
$606$	−6.62916	−	7.36325i	−0.269291	−	0.299111i
$607$	−6.68660	−	5.61072i	−0.271401	−	0.227732i	0.496922	−	0.867795i	$-0.334464\pi$
$607$	−6.68660	−	5.61072i	−0.271401	−	0.227732i	−0.768322	+	0.640063i	$0.778908\pi$
$608$	−1.72202	−	11.4990i	−0.0698371	−	0.466344i
$609$	38.9803	−	9.93120i	1.57956	−	0.402432i
$610$	2.43595	+	18.0086i	0.0986287	+	0.729147i
$611$	18.4970	+	10.6793i	0.748309	+	0.432036i
$612$	16.6889	+	24.7481i	0.674607	+	1.00038i
$613$	28.4795	−	16.4426i	1.15028	−	0.664112i	0.201321	−	0.979525i	$-0.435477\pi$
$613$	28.4795	−	16.4426i	1.15028	−	0.664112i	0.948954	+	0.315414i	$0.102143\pi$
$614$	10.1829	+	13.1735i	0.410947	+	0.531639i
$615$	4.26048	−	2.90559i	0.171799	−	0.117165i
$616$	5.37917	+	23.0970i	0.216733	+	0.930603i
$617$	5.77150	−	32.7318i	0.232352	−	1.31773i	−0.615767	−	0.787928i	$-0.711154\pi$
$617$	5.77150	−	32.7318i	0.232352	−	1.31773i	0.848119	−	0.529805i	$-0.177735\pi$
$618$	−2.20274	−	1.72117i	−0.0886073	−	0.0692355i
$619$	22.6481	+	26.9910i	0.910305	+	1.08486i	0.996072	+	0.0885446i	$0.0282216\pi$
$619$	22.6481	+	26.9910i	0.910305	+	1.08486i	−0.0857667	+	0.996315i	$0.527334\pi$
$620$	12.3365	+	8.50823i	0.495446	+	0.341699i
$621$	−4.39841	−	2.25269i	−0.176502	−	0.0903974i
$622$	22.3572	+	42.5780i	0.896442	+	1.70722i
$623$	−18.1451	+	15.2255i	−0.726966	+	0.609997i
$624$	−7.18474	−	26.6148i	−0.287620	−	1.06545i
$625$	5.41806	−	30.7273i	0.216722	−	1.22909i
$626$	7.39246	+	6.72582i	0.295462	+	0.268818i
$627$	−4.49705	+	9.34144i	−0.179595	+	0.373061i
$628$	12.1834	−	26.6192i	0.486171	−	1.06222i
$629$	−41.3448	+	23.8704i	−1.64852	+	0.951775i
$630$	21.2335	+	42.9811i	0.845963	+	1.71241i
$631$	−20.3613	+	35.2667i	−0.810569	+	1.40395i	0.101898	+	0.994795i	$0.467509\pi$
$631$	−20.3613	+	35.2667i	−0.810569	+	1.40395i	−0.912466	+	0.409152i	$0.865825\pi$
$632$	0.675957	+	0.342781i	0.0268881	+	0.0136351i
$633$	8.28649	−	29.4672i	0.329358	−	1.17121i
$634$	−7.49404	−	1.63350i	−0.297626	−	0.0648746i
$635$	12.0336	−	14.3411i	0.477539	−	0.569109i
$636$	−12.0947	+	2.06743i	−0.479585	+	0.0819789i
$637$	−1.75488	+	4.82149i	−0.0695308	+	0.191034i
$638$	33.1940	+	1.33123i	1.31416	+	0.0527040i
$639$	22.5673	+	4.55574i	0.892747	+	0.180222i
$640$	−30.8017	−	31.9811i	−1.21754	−	1.26416i
$641$	−8.76821	−	49.7270i	−0.346323	−	1.96410i	−0.246823	−	0.969061i	$-0.579387\pi$
$641$	−8.76821	−	49.7270i	−0.346323	−	1.96410i	−0.0995006	−	0.995038i	$-0.531725\pi$
$642$	10.1282	−	6.32803i	0.399728	−	0.249747i
$643$	−15.1261	−	41.5587i	−0.596517	−	1.63892i	−0.758162	−	0.652067i	$-0.773902\pi$
$643$	−15.1261	−	41.5587i	−0.596517	−	1.63892i	0.161645	−	0.986849i	$-0.448320\pi$
$644$	−3.89976	−	3.84477i	−0.153672	−	0.151505i
$645$	−34.5572	−	24.8379i	−1.36069	−	0.977990i
$646$	−5.48653	+	13.3798i	−0.215865	+	0.526421i
$647$	2.96214			0.116454			0.0582268	−	0.998303i	$-0.481455\pi$
$647$	2.96214			0.116454			0.0582268	+	0.998303i	$0.481455\pi$
$648$	−22.1082	−	12.6185i	−0.868493	−	0.495702i
$649$	−18.1619			−0.712917
$650$	−22.2093	+	54.1609i	−0.871119	+	2.12437i
$651$	7.73121	+	5.55678i	0.303010	+	0.217787i
$652$	8.33904	−	8.45830i	0.326582	−	0.331253i
$653$	0.829258	+	2.27837i	0.0324514	+	0.0891594i	0.954860	−	0.297055i	$-0.0960046\pi$
$653$	0.829258	+	2.27837i	0.0324514	+	0.0891594i	−0.922409	+	0.386215i	$0.873782\pi$
$654$	5.23516	−	3.27089i	0.204711	−	0.127902i
$655$	2.38780	+	13.5419i	0.0932992	+	0.529126i
$656$	−1.91737	+	2.35207i	−0.0748607	+	0.0918328i
$657$	−13.7651	+	15.6063i	−0.537029	+	0.608858i
$658$	21.8385	+	0.875826i	0.851354	+	0.0341433i
$659$	−14.7728	+	40.5879i	−0.575466	+	1.58108i	0.220272	+	0.975438i	$0.429305\pi$
$659$	−14.7728	+	40.5879i	−0.575466	+	1.58108i	−0.795738	+	0.605641i	$0.792917\pi$
$660$	6.67094	+	39.0256i	0.259666	+	1.51907i
$661$	−11.3612	+	13.5398i	−0.441901	+	0.526637i	−0.940317	−	0.340301i	$-0.889471\pi$
$661$	−11.3612	+	13.5398i	−0.441901	+	0.526637i	0.498415	+	0.866938i	$0.333915\pi$
$662$	−7.49612	−	1.63395i	−0.291345	−	0.0635053i
$663$	−9.28173	+	33.0063i	−0.360472	+	1.28186i
$664$	−15.7449	+	31.0485i	−0.611020	+	1.20492i
$665$	−11.6126	+	20.1137i	−0.450318	+	0.779974i
$666$	22.5956	−	33.8681i	0.875560	−	1.31236i
$667$	−6.64362	+	3.83570i	−0.257242	+	0.148519i
$668$	−36.2084	−	16.5723i	−1.40094	−	0.641201i
$669$	−17.5260	+	36.4057i	−0.677595	+	1.40753i
$670$	−28.1569	−	25.6178i	−1.08780	−	0.989702i
$671$	−1.65574	+	9.39015i	−0.0639190	+	0.362503i
$672$	−19.1707	−	20.6949i	−0.739524	−	0.798321i
$673$	1.22568	−	1.02847i	0.0472465	−	0.0396445i	−0.618859	−	0.785502i	$-0.712405\pi$
$673$	1.22568	−	1.02847i	0.0472465	−	0.0396445i	0.666105	+	0.745858i	$0.267960\pi$
$674$	−19.1669	−	36.5023i	−0.738282	−	1.40602i
$675$	21.0164	+	49.8006i	0.808923	+	1.91683i
$676$	3.21653	−	4.66381i	0.123713	−	0.179377i
$677$	−4.41092	−	5.25673i	−0.169526	−	0.202033i	0.674592	−	0.738191i	$-0.264320\pi$
$677$	−4.41092	−	5.25673i	−0.169526	−	0.202033i	−0.844118	+	0.536158i	$0.819875\pi$
$678$	13.9595	+	10.9076i	0.536110	+	0.418903i
$679$	2.69280	−	15.2717i	0.103340	−	0.586072i
$680$	12.5261	+	53.7845i	0.480356	+	2.06254i
$681$	−35.5098	+	24.2172i	−1.36074	+	0.928005i
$682$	4.80881	+	6.22111i	0.184139	+	0.238219i
$683$	4.11971	−	2.37852i	0.157636	−	0.0910113i	−0.419107	−	0.907937i	$-0.637657\pi$
$683$	4.11971	−	2.37852i	0.157636	−	0.0910113i	0.576743	+	0.816926i	$0.304323\pi$
$684$	−0.858912	−	12.3025i	−0.0328413	−	0.470399i
$685$	−56.1590	−	32.4234i	−2.14573	−	1.23884i
$686$	−3.11677	−	23.0418i	−0.118999	−	0.879741i
$687$	9.35400	−	2.38316i	0.356877	−	0.0909233i
$688$	23.6514	+	8.22999i	0.901701	+	0.313765i
$689$	−10.7966	−	9.05946i	−0.411320	−	0.345138i
$690$	−6.11722	−	6.79461i	−0.232879	−	0.258667i
$691$	4.35017	−	11.9520i	0.165488	−	0.454675i	−0.829034	−	0.559198i	$-0.811109\pi$
$691$	4.35017	−	11.9520i	0.165488	−	0.454675i	0.994523	+	0.104523i	$0.0333315\pi$
$692$	−19.9068	+	9.45535i	−0.756743	+	0.359438i
$693$	3.75566	+	24.8717i	0.142666	+	0.944798i
$694$	20.7860	+	13.1387i	0.789027	+	0.498737i
$695$	−13.5392	−	76.7844i	−0.513570	−	2.91260i
$696$	−35.0826	+	18.1879i	−1.32980	+	0.689410i
$697$	3.54655	−	1.29084i	0.134335	−	0.0488939i
$698$	−2.26454	−	7.09429i	−0.0857141	−	0.268523i
$699$	10.5005	−	4.73969i	0.397164	−	0.179272i
$700$	5.64429	+	59.6348i	0.213334	+	2.25398i
$701$		−	12.2688i		−	0.463386i	−0.972789	−	0.231693i	$-0.925573\pi$
$701$		−	12.2688i		−	0.463386i	0.972789	−	0.231693i	$-0.0744265\pi$
$702$	−5.37053	−	28.7424i	−0.202698	−	1.08481i
$703$	19.7244			0.743921
$704$	−10.2933	−	20.9000i	−0.387945	−	0.787700i
$705$	36.3072	+	3.62815i	1.36741	+	0.136644i
$706$	−12.6983	+	4.05338i	−0.477907	+	0.152551i
$707$	−3.98304	−	10.9433i	−0.149797	−	0.411565i
$708$	18.7659	−	10.7040i	0.705267	−	0.402281i
$709$	−25.9792	+	4.58083i	−0.975668	+	0.172037i	−0.638680	−	0.769473i	$-0.720519\pi$
$709$	−25.9792	+	4.58083i	−0.975668	+	0.172037i	−0.336988	+	0.941509i	$0.609408\pi$
$710$	36.0041	+	22.7578i	1.35121	+	0.854086i
$711$	0.686054	+	0.418985i	0.0257290	+	0.0157132i
$712$	13.9681	−	18.6107i	0.523477	−	0.697465i
$713$	−1.70624	−	0.621021i	−0.0638993	−	0.0232574i
$714$	7.29273	+	34.3189i	0.272924	+	1.28435i
$715$	−29.2320	+	34.8373i	−1.09321	+	1.30284i
$716$	−2.24778	−	8.15674i	−0.0840036	−	0.304832i
$717$	32.4366	−	31.6463i	1.21137	−	1.18185i
$718$	−3.08002	−	22.7701i	−0.114945	−	0.849774i
$719$	−15.9411	+	27.6108i	−0.594502	+	1.02971i	0.399115	+	0.916901i	$0.369317\pi$
$719$	−15.9411	+	27.6108i	−0.594502	+	1.02971i	−0.993617	+	0.112807i	$0.964016\pi$
$720$	−29.8932	−	36.3920i	−1.11405	−	1.35625i
$721$	−1.64289	−	2.84557i	−0.0611845	−	0.105975i
$722$	−16.5322	+	12.7791i	−0.615264	+	0.475588i
$723$	43.3780	−	3.25661i	1.61325	−	0.121115i
$724$	36.8035	+	9.58192i	1.36779	+	0.356109i
$725$	82.6364	+	14.5710i	3.06904	+	0.541154i
$726$	0.859174	−	6.11089i	0.0318869	−	0.226796i
$727$	30.8679	−	25.9013i	1.14483	−	0.960625i	0.145243	−	0.989396i	$-0.453604\pi$
$727$	30.8679	−	25.9013i	1.14483	−	0.960625i	0.999586	+	0.0287706i	$0.00915924\pi$
$728$	3.88708	−	32.1691i	0.144065	−	1.19227i
$729$	−22.3207	−	15.1916i	−0.826694	−	0.562652i
$730$	−34.0859	+	17.8981i	−1.26158	+	0.662438i
$731$	−20.0202	−	23.8591i	−0.740473	−	0.882461i
$732$	−3.82343	−	10.6783i	−0.141318	−	0.394681i
$733$	−0.103428	−	0.0182371i	−0.00382018	−	0.000673601i	0.171738	−	0.985143i	$-0.445062\pi$
$733$	−0.103428	−	0.0182371i	−0.00382018	−	0.000673601i	−0.175558	+	0.984469i	$0.556173\pi$
$734$	13.3934	+	12.1856i	0.494358	+	0.449777i
$735$	0.656222	+	8.74087i	0.0242051	+	0.322412i
$736$	4.58793	+	2.80961i	0.169113	+	0.103564i
$737$	−9.98667	−	17.2974i	−0.367864	−	0.637158i
$738$	−2.22409	+	2.32659i	−0.0818699	+	0.0856428i
$739$	26.3545	+	15.2158i	0.969466	+	0.559722i	0.899074	−	0.437798i	$-0.144241\pi$
$739$	26.3545	+	15.2158i	0.969466	+	0.559722i	0.0703928	+	0.997519i	$0.477575\pi$
$740$	61.3933	−	43.6410i	2.25686	−	1.60427i
$741$	10.1394	−	9.89237i	0.372481	−	0.363405i
$742$	−14.0915	−	3.07156i	−0.517314	−	0.112761i
$743$	12.9183	+	10.8397i	0.473926	+	0.397671i	0.848224	−	0.529637i	$-0.177672\pi$
$743$	12.9183	+	10.8397i	0.473926	+	0.397671i	−0.374298	+	0.927308i	$0.622116\pi$
$744$	−8.63527	−	3.59387i	−0.316584	−	0.131758i
$745$	−42.4539	−	15.4520i	−1.55539	−	0.566116i
$746$	−0.358633	+	8.94243i	−0.0131305	+	0.327406i
$747$	−19.2451	+	31.5123i	−0.704143	+	1.15298i
$748$	−2.32037	+	28.8824i	−0.0848412	+	1.05605i
$749$	13.8241	−	2.43756i	0.505122	−	0.0890666i
$750$	1.80971	+	51.9055i	0.0660812	+	1.89532i
$751$	14.6848	−	5.34482i	0.535855	−	0.195035i	−0.0598958	−	0.998205i	$-0.519077\pi$
$751$	14.6848	−	5.34482i	0.535855	−	0.195035i	0.595751	+	0.803169i	$0.296855\pi$
$752$	−21.0898	+	4.02828i	−0.769065	+	0.146896i
$753$	50.2379	+	5.02023i	1.83077	+	0.182947i
$754$	−41.9972	−	17.2214i	−1.52945	−	0.627167i
$755$		−	14.3029i		−	0.520536i
$756$	−18.5391	−	23.4854i	−0.674261	−	0.854157i
$757$		−	27.3201i		−	0.992967i	−0.868046	−	0.496484i	$-0.834624\pi$
$757$		−	27.3201i		−	0.992967i	0.868046	−	0.496484i	$-0.165376\pi$
$758$	15.2953	−	37.3002i	0.555551	−	1.35480i
$759$	−1.97355	−	4.37226i	−0.0716353	−	0.158703i
$760$	6.62880	−	21.8319i	0.240452	−	0.791928i
$761$	−14.1817	+	5.16172i	−0.514086	+	0.187112i	−0.586019	−	0.810297i	$-0.699306\pi$
$761$	−14.1817	+	5.16172i	−0.514086	+	0.187112i	0.0719327	+	0.997409i	$0.477083\pi$
$762$	−5.48607	+	10.3164i	−0.198739	+	0.373725i
$763$	7.14552	−	1.25995i	0.258685	−	0.0456132i
$764$	16.2078	+	1.30211i	0.586379	+	0.0471088i
$765$	8.74558	+	57.9172i	0.316197	+	2.09400i
$766$	−44.4228	−	1.78156i	−1.60506	−	0.0643705i
$767$	23.3189	+	8.48740i	0.841998	+	0.306462i
$768$	22.9535	+	15.5286i	0.828262	+	0.560341i
$769$	−11.4199	−	9.58242i	−0.411811	−	0.345551i	0.413226	−	0.910628i	$-0.364402\pi$
$769$	−11.4199	−	9.58242i	−0.411811	−	0.345551i	−0.825038	+	0.565077i	$0.808846\pi$
$770$	−9.91095	+	45.4687i	−0.357166	+	1.63858i
$771$	3.02906	+	11.8892i	0.109089	+	0.428178i
$772$	−21.5008	+	15.2837i	−0.773831	+	0.550071i
$773$	27.9615	+	16.1436i	1.00571	+	0.580644i	0.909931	−	0.414759i	$-0.136134\pi$
$773$	27.9615	+	16.1436i	1.00571	+	0.580644i	0.0957742	+	0.995403i	$0.469467\pi$
$774$	24.3195	+	10.6804i	0.874147	+	0.383901i
$775$	9.93049	+	17.2001i	0.356714	+	0.617846i
$776$	0.826549	+	15.2116i	0.0296714	+	0.546065i
$777$	39.5362	−	26.9631i	1.41835	−	0.967297i
$778$	−3.74033	+	4.11106i	−0.134097	+	0.147389i
$779$	−1.53563	−	0.270772i	−0.0550195	−	0.00970143i
$780$	9.67227	−	53.2243i	0.346323	−	1.90574i
$781$	14.3653	+	17.1199i	0.514031	+	0.612598i
$782$	−3.11065	−	5.92406i	−0.111237	−	0.211844i
$783$	−38.6162	+	16.2965i	−1.38003	+	0.582388i
$784$	−1.83277	−	4.82135i	−0.0654561	−	0.172191i
$785$	44.0064	−	36.9258i	1.57066	−	1.31794i
$786$	−3.21457	−	7.95761i	−0.114660	−	0.283838i
$787$	−39.6718	−	6.99522i	−1.41415	−	0.249353i	−0.586204	−	0.810163i	$-0.699378\pi$
$787$	−39.6718	−	6.99522i	−1.41415	−	0.249353i	−0.827944	+	0.560811i	$0.810490\pi$
$788$	11.9614	+	3.11420i	0.426108	+	0.110939i
$789$	8.61949	−	17.9047i	0.306862	−	0.637425i
$790$	0.909556	+	1.17668i	0.0323606	+	0.0418645i
$791$	10.4115	+	18.0333i	0.370191	+	0.641189i
$792$	−9.13547	−	22.9598i	−0.324615	−	0.815842i
$793$	6.51408	−	11.2827i	0.231322	−	0.400661i
$794$	−29.1223	+	3.93926i	−1.03351	+	0.139799i
$795$	−23.1787	−	6.51809i	−0.822062	−	0.231173i
$796$	17.1105	−	4.71521i	0.606467	−	0.167126i
$797$	−2.35451	+	2.80599i	−0.0834009	+	0.0993934i	−0.806131	−	0.591737i	$-0.798442\pi$
$797$	−2.35451	+	2.80599i	−0.0834009	+	0.0993934i	0.722730	+	0.691130i	$0.242887\pi$
$798$	4.48017	−	13.7860i	0.158596	−	0.488018i
$799$	25.0936	+	9.13334i	0.887749	+	0.323114i
$800$	−18.6887	−	55.7996i	−0.660745	−	1.97281i
$801$	16.3260	−	18.5097i	0.576852	−	0.654008i
$802$	−17.5090	+	27.7001i	−0.618263	+	0.978123i
$803$	−19.8933	+	3.50773i	−0.702020	+	0.123785i
$804$	20.5133	+	11.9869i	0.723449	+	0.422746i
$805$	−3.67544	−	10.0982i	−0.129542	−	0.355915i
$806$	−3.26702	−	10.2348i	−0.115076	−	0.360507i
$807$	−15.3472	+	21.3527i	−0.540248	+	0.751652i
$808$	6.24937	+	9.58278i	0.219852	+	0.337121i
$809$	−41.2691			−1.45094			−0.725472	−	0.688252i	$-0.758378\pi$
$809$	−41.2691			−1.45094			−0.725472	+	0.688252i	$0.758378\pi$
$810$	−28.5636	−	40.9798i	−1.00362	−	1.43988i
$811$			25.6578i			0.900966i	0.892785	+	0.450483i	$0.148748\pi$
$811$			25.6578i			0.900966i	−0.892785	+	0.450483i	$0.851252\pi$
$812$	−46.2418	+	4.37668i	−1.62277	+	0.153591i
$813$	−18.6789	−	13.4254i	−0.655097	−	0.470849i
$814$	37.6501	−	12.0181i	1.31964	−	0.421236i
$815$	21.9023	−	7.97178i	0.767204	−	0.279239i
$816$	−14.6248	−	31.2106i	−0.511970	−	1.09259i
$817$	2.23452	+	12.6726i	0.0781761	+	0.443359i
$818$	22.0659	−	34.9094i	0.771517	−	1.22058i
$819$	6.80094	−	33.6891i	0.237644	−	1.17719i
$820$	−5.37882	+	2.55483i	−0.187836	+	0.0892186i
$821$	8.61194	−	23.6611i	0.300559	−	0.825778i	−0.693844	−	0.720125i	$-0.744084\pi$
$821$	8.61194	−	23.6611i	0.300559	−	0.825778i	0.994403	−	0.105653i	$-0.0336933\pi$
$822$	38.4916	+	12.5090i	1.34255	+	0.436302i
$823$	10.3916	+	8.71956i	0.362227	+	0.303945i	0.805678	−	0.592354i	$-0.201801\pi$
$823$	10.3916	+	8.71956i	0.362227	+	0.303945i	−0.443450	+	0.896299i	$0.646246\pi$
$824$	2.20596	+	2.35650i	0.0768482	+	0.0820924i
$825$	−14.2045	+	50.5117i	−0.494536	+	1.75859i
$826$	25.1644	−	3.40388i	0.875582	−	0.118436i
$827$	−9.62668	−	5.55796i	−0.334752	−	0.193269i	0.323197	−	0.946332i	$-0.395242\pi$
$827$	−9.62668	−	5.55796i	−0.334752	−	0.193269i	−0.657949	+	0.753062i	$0.728576\pi$
$828$	4.61605	+	3.35454i	0.160419	+	0.116578i
$829$	26.4493	−	15.2705i	0.918621	−	0.530366i	0.0354262	−	0.999372i	$-0.488721\pi$
$829$	26.4493	−	15.2705i	0.918621	−	0.530366i	0.883195	+	0.469006i	$0.155388\pi$
$830$	−54.0483	+	41.7784i	−1.87605	+	1.45015i
$831$	4.01584	+	1.93326i	0.139308	+	0.0670640i
$832$	3.44914	+	31.6449i	0.119577	+	1.09709i
$833$	−1.11397	+	6.31762i	−0.0385967	+	0.218893i
$834$	18.2270	+	45.1207i	0.631151	+	1.56240i
$835$	−50.2277	−	59.8590i	−1.73820	−	2.07151i
$836$	6.79672	−	9.85491i	0.235069	−	0.340839i
$837$	−8.82993	−	4.52233i	−0.305207	−	0.156315i
$838$	−16.2438	+	8.52941i	−0.561132	+	0.294644i
$839$	−3.67221	+	3.08135i	−0.126779	+	0.106380i	−0.703972	−	0.710227i	$-0.748592\pi$
$839$	−3.67221	+	3.08135i	−0.126779	+	0.106380i	0.577194	+	0.816607i	$0.304148\pi$
$840$	−16.5571	−	52.8221i	−0.571275	−	1.82254i
$841$	−6.26281	+	35.5181i	−0.215959	+	1.22476i
$842$	4.16107	−	4.57350i	0.143400	−	0.157613i
$843$	−26.4072	−	38.7210i	−0.909512	−	1.33362i
$844$	−14.7098	+	32.1392i	−0.506334	+	1.10628i
$845$	9.62790	−	5.55867i	0.331210	−	0.191224i
$846$	−22.6364	+	2.49519i	−0.778254	+	0.0857863i
$847$	3.62672	−	6.28165i	0.124615	−	0.215840i
$848$	14.1669	−	0.201185i	0.486492	−	0.00690870i
$849$	−44.8719	+	11.4322i	−1.54000	+	0.392353i
$850$	−15.5871	+	71.5093i	−0.534634	+	2.45275i
$851$	−5.86637	+	6.99127i	−0.201097	+	0.239657i
$852$	−24.9330	−	9.22287i	−0.854190	−	0.315970i
$853$	−7.52367	+	20.6711i	−0.257605	+	0.707765i	0.741708	+	0.670723i	$0.234016\pi$
$853$	−7.52367	+	20.6711i	−0.257605	+	0.707765i	−0.999314	+	0.0370424i	$0.988206\pi$
$854$	0.534232	−	13.3209i	0.0182811	−	0.455833i
$855$	8.83523	−	22.5296i	0.302159	−	0.770498i
$856$	−12.6834	+	5.41262i	−0.433511	+	0.184999i
$857$	−1.54554	−	8.76520i	−0.0527947	−	0.299414i	0.946965	−	0.321337i	$-0.104132\pi$
$857$	−1.54554	−	8.76520i	−0.0527947	−	0.299414i	−0.999760	+	0.0219232i	$0.993021\pi$
$858$	13.3267	−	25.0606i	0.454967	−	0.855555i
$859$	7.12897	+	19.5867i	0.243237	+	0.668289i	0.999895	+	0.0144780i	$0.00460866\pi$
$859$	7.12897	+	19.5867i	0.243237	+	0.668289i	−0.756658	+	0.653811i	$0.773169\pi$
$860$	34.9937	+	34.5003i	1.19327	+	1.17645i
$861$	−3.44820	+	1.55645i	−0.117514	+	0.0530436i
$862$	1.51593	+	0.621621i	0.0516326	+	0.0211725i
$863$	−21.4666			−0.730731			−0.365365	−	0.930864i	$-0.619056\pi$
$863$	−21.4666			−0.730731			−0.365365	+	0.930864i	$0.619056\pi$
$864$	22.9711	+	18.3393i	0.781491	+	0.623916i
$865$	−43.2459			−1.47040
$866$	49.3947	+	20.2548i	1.67850	+	0.688286i
$867$	−1.33468	+	13.3563i	−0.0453282	+	0.453604i
$868$	−7.82886	−	7.71847i	−0.265729	−	0.261982i
$869$	0.266892	+	0.733280i	0.00905370	+	0.0248748i
$870$	−77.4973	+	2.70198i	−2.62740	+	0.0916057i
$871$	4.73896	+	26.8760i	0.160573	+	0.910657i
$872$	−6.55593	+	2.79772i	−0.222012	+	0.0947428i
$873$	−0.398481	+	16.1532i	−0.0134866	+	0.546705i
$874$	−0.110779	+	2.76224i	−0.00374715	+	0.0934343i
$875$	−20.8794	+	57.3655i	−0.705851	+	1.93931i
$876$	18.4876	−	15.3488i	0.624638	−	0.518589i
$877$	−0.176559	+	0.210415i	−0.00596198	+	0.00710521i	−0.769017	−	0.639228i	$-0.779254\pi$
$877$	−0.176559	+	0.210415i	−0.00596198	+	0.00710521i	0.763055	+	0.646333i	$0.223698\pi$
$878$	8.15140	−	37.3964i	0.275096	−	1.26207i
$879$	−21.2886	−	21.8202i	−0.718045	−	0.735977i
$880$	−0.649158	−	45.7119i	−0.0218831	−	1.54095i
$881$	−11.9250	+	20.6547i	−0.401763	+	0.695873i	−0.993939	−	0.109935i	$-0.964936\pi$
$881$	−11.9250	+	20.6547i	−0.401763	+	0.695873i	0.592176	+	0.805809i	$0.298269\pi$
$882$	−1.53459	−	5.25120i	−0.0516723	−	0.176817i
$883$	−4.93626	+	2.84995i	−0.166118	+	0.0959085i	−0.580754	−	0.814079i	$-0.697242\pi$
$883$	−4.93626	+	2.84995i	−0.166118	+	0.0959085i	0.414636	+	0.909987i	$0.363909\pi$
$884$	16.4765	−	35.9992i	0.554166	−	1.21078i
$885$	42.2749	−	3.17379i	1.42106	−	0.106686i
$886$	28.8321	−	31.6899i	0.968634	−	1.06464i
$887$	−2.98032	+	16.9022i	−0.100069	+	0.567521i	0.893006	+	0.450044i	$0.148592\pi$
$887$	−2.98032	+	16.9022i	−0.100069	+	0.567521i	−0.993076	+	0.117477i	$0.962519\pi$
$888$	−31.8192	+	34.6076i	−1.06778	+	1.16135i
$889$	−10.5208	+	8.82801i	−0.352857	+	0.296082i
$890$	40.4274	−	21.2279i	1.35513	−	0.711561i
$891$	−7.73888	−	25.0409i	−0.259262	−	0.838902i
$892$	26.4883	−	38.4068i	0.886895	−	1.28595i
$893$	−7.09185	−	8.45174i	−0.237320	−	0.282827i
$894$	27.9228	+	3.92587i	0.933880	+	0.131301i
$895$	2.88302	−	16.3504i	0.0963689	−	0.546535i
$896$	18.1791	+	27.0291i	0.607322	+	0.902980i
$897$	0.490694	+	6.53604i	0.0163838	+	0.218232i
$898$	−3.81401	+	2.94816i	−0.127275	+	0.0983814i
$899$	−13.3372	+	7.70026i	−0.444822	+	0.256818i
$900$	−15.0930	−	60.5634i	−0.503101	−	2.01878i
$901$	−15.2606	−	8.81073i	−0.508405	−	0.293528i
$902$	−3.09620	+	0.418810i	−0.103092	+	0.0139448i
$903$	21.8023	+	22.3468i	0.725536	+	0.743655i
$904$	−13.9798	−	14.9339i	−0.464963	−	0.496693i
$905$	57.1678	+	47.9695i	1.90032	+	1.59456i
$906$	1.85553	+	8.73196i	0.0616459	+	0.290100i
$907$	14.9621	−	41.1081i	0.496809	−	1.36497i	−0.397533	−	0.917588i	$-0.630134\pi$
$907$	14.9621	−	41.1081i	0.496809	−	1.36497i	0.894342	−	0.447383i	$-0.147644\pi$
$908$	44.8308	−	21.2938i	1.48776	−	0.706658i
$909$	5.80622	+	10.6552i	0.192580	+	0.353410i
$910$	33.9735	−	53.7479i	1.12621	−	1.78173i
$911$	0.448255	+	2.54218i	0.0148514	+	0.0842262i	0.991333	−	0.131376i	$-0.0419396\pi$
$911$	0.448255	+	2.54218i	0.0148514	+	0.0842262i	−0.976481	+	0.215602i	$0.930828\pi$
$912$	−1.21462	+	14.1884i	−0.0402201	+	0.469826i
$913$	−33.6816	+	12.2591i	−1.11470	+	0.405717i
$914$	12.7990	−	4.08552i	0.423353	−	0.135137i
$915$	2.21308	−	22.1465i	0.0731622	−	0.732141i
$916$	−11.0965	+	1.05026i	−0.366639	+	0.0347015i
$917$		−	10.0878i		−	0.333127i
$918$	−12.8529	−	34.2241i	−0.424208	−	1.12956i
$919$	−59.9068			−1.97614			−0.988071	−	0.153998i	$-0.950785\pi$
$919$	−59.9068			−1.97614			−0.988071	+	0.153998i	$0.950785\pi$
$920$	5.76675	+	8.84274i	0.190124	+	0.291537i
$921$	−8.38961	−	18.5866i	−0.276447	−	0.612449i
$922$	13.3061	+	41.6849i	0.438212	+	1.37282i
$923$	−10.4439	−	28.6943i	−0.343764	−	0.944483i
$924$	0.151958	−	29.0445i	0.00499905	−	0.955495i
$925$	98.3103	−	17.3348i	3.23242	−	0.569963i
$926$	−18.5847	+	29.4020i	−0.610732	+	0.966209i
$927$	2.13537	+	2.67618i	0.0701346	+	0.0878974i
$928$	43.2679	−	14.4915i	1.42034	−	0.475707i
$929$	−30.1626	−	10.9783i	−0.989604	−	0.360186i	−0.204037	−	0.978963i	$-0.565406\pi$
$929$	−30.1626	−	10.9783i	−0.989604	−	0.360186i	−0.785567	+	0.618777i	$0.787629\pi$
$930$	−12.2805	−	13.6404i	−0.402693	−	0.447285i
$931$	1.70366	−	2.03035i	0.0558354	−	0.0665420i
$932$	−12.8248	+	3.53418i	−0.420090	+	0.115766i
$933$	−14.5415	−	57.0758i	−0.476066	−	1.86858i
$934$	1.37454	−	0.185928i	0.0449762	−	0.00608374i
$935$	−28.4294	+	49.2412i	−0.929741	+	1.61036i
$936$	0.999904	+	33.7484i	0.0326829	+	1.10310i
$937$	8.40875	+	14.5644i	0.274702	+	0.475797i	0.970060	−	0.242866i	$-0.0780875\pi$
$937$	8.40875	+	14.5644i	0.274702	+	0.475797i	−0.695358	+	0.718663i	$0.744754\pi$
$938$	17.0790	+	22.0949i	0.557649	+	0.721425i
$939$	−6.89663	−	10.1126i	−0.225063	−	0.330011i
$940$	−40.7736	−	10.6155i	−1.32989	−	0.346241i
$941$	20.4427	+	3.60459i	0.666412	+	0.117506i	0.496613	−	0.867972i	$-0.334577\pi$
$941$	20.4427	+	3.60459i	0.666412	+	0.117506i	0.169799	+	0.985479i	$0.445688\pi$
$942$	−22.0756	+	28.2523i	−0.719263	+	0.920510i
$943$	0.552695	−	0.463766i	0.0179982	−	0.0151023i
$944$	−23.3183	+	8.86412i	−0.758946	+	0.288503i
$945$	−13.0883	−	57.2368i	−0.425761	−	1.86191i
$946$	11.9867	+	22.8281i	0.389722	+	0.742205i
$947$	11.7887	+	14.0493i	0.383082	+	0.456540i	0.922785	−	0.385316i	$-0.125908\pi$
$947$	11.7887	+	14.0493i	0.383082	+	0.456540i	−0.539702	+	0.841856i	$0.681463\pi$
$948$	−0.707940	−	0.600371i	−0.0229928	−	0.0194992i
$949$	27.1812	+	4.79278i	0.882340	+	0.155580i
$950$	20.3494	−	22.3664i	0.660222	−	0.725661i
$951$	8.46407	+	4.07468i	0.274466	+	0.132130i
$952$	−2.19810	−	40.4533i	−0.0712407	−	1.31110i
$953$	1.73534	+	3.00570i	0.0562133	+	0.0973643i	0.892763	−	0.450527i	$-0.148764\pi$
$953$	1.73534	+	3.00570i	0.0562133	+	0.0973643i	−0.836549	+	0.547892i	$0.815431\pi$
$954$	14.9962	+	0.972321i	0.485521	+	0.0314801i
$955$	27.6325	+	15.9536i	0.894166	+	0.516247i
$956$	−42.6500	+	30.3174i	−1.37940	+	0.980534i
$957$	−39.1676	−	11.0144i	−1.26611	−	0.356044i
$958$	2.18694	−	10.0331i	0.0706570	−	0.324154i
$959$	36.4426	+	30.5790i	1.17679	+	0.987447i
$960$	27.6118	+	46.8497i	0.891167	+	1.51207i
$961$	25.7051	+	9.35591i	0.829198	+	0.301803i
$962$	−53.9571	−	2.16393i	−1.73965	−	0.0697680i
$963$	−13.8637	+	4.66211i	−0.446751	+	0.150234i
$964$	−50.0683	−	4.02241i	−1.61259	−	0.129553i
$965$	−50.9782	+	8.98883i	−1.64105	+	0.289361i
$966$	3.55392	+	5.68816i	0.114346	+	0.183014i
$967$	−29.0536	+	10.5747i	−0.934301	+	0.340058i	−0.763913	−	0.645319i	$-0.776724\pi$
$967$	−29.0536	+	10.5747i	−0.934301	+	0.340058i	−0.170388	+	0.985377i	$0.554502\pi$
$968$	−2.07023	+	6.81829i	−0.0665396	+	0.219148i
$969$	10.3368	−	14.3817i	0.332065	−	0.462006i
$970$	−11.3418	+	27.6588i	−0.364163	+	0.888071i
$971$			0.278968i			0.00895249i	0.999990	+	0.00447625i	$0.00142484\pi$
$971$			0.278968i			0.00895249i	−0.999990	+	0.00447625i	$0.998575\pi$
$972$	22.7545	+	21.3127i	0.729852	+	0.683605i
$973$			57.1990i			1.83372i
$974$	0.201292	+	0.0825420i	0.00644982	+	0.00264482i
$975$	41.8429	−	58.2165i	1.34005	−	1.86442i
$976$	2.45715	+	12.8642i	0.0786515	+	0.411774i
$977$	20.1241	−	7.32457i	0.643827	−	0.234334i	0.000588326	−	1.00000i	$-0.499813\pi$
$977$	20.1241	−	7.32457i	0.643827	−	0.234334i	0.643238	+	0.765666i	$0.277591\pi$
$978$	−12.3372	+	7.70821i	−0.394501	+	0.246481i
$979$	23.5943	−	4.16032i	0.754078	−	0.132964i
$980$	0.810535	−	10.0890i	0.0258916	−	0.322281i
$981$	−7.16598	+	2.40979i	−0.228792	+	0.0769387i
$982$	1.17784	−	29.3692i	0.0375865	−	0.937210i
$983$	−5.52983	−	2.01269i	−0.176374	−	0.0641950i	0.252324	−	0.967643i	$-0.418805\pi$
$983$	−5.52983	−	2.01269i	−0.176374	−	0.0641950i	−0.428698	+	0.903448i	$0.641027\pi$
$984$	2.95234	−	2.25753i	0.0941172	−	0.0719675i
$985$	18.5800	+	15.5905i	0.592008	+	0.496753i
$986$	−55.4495	−	12.0865i	−1.76587	−	0.384912i
$987$	−25.7686	−	7.24641i	−0.820223	−	0.230656i
$988$	−13.3320	+	9.47696i	−0.424148	+	0.301502i
$989$	−5.15636	−	2.97702i	−0.163963	−	0.0946639i
$990$	3.13737	−	48.3881i	0.0997121	−	1.53787i
$991$	17.5543	+	30.4049i	0.557631	+	0.965845i	0.997694	+	0.0678778i	$0.0216228\pi$
$991$	17.5543	+	30.4049i	0.557631	+	0.965845i	−0.440063	+	0.897967i	$0.645044\pi$
$992$	9.21038	+	5.64037i	0.292430	+	0.179082i
$993$	8.46642	+	4.07581i	0.268674	+	0.129342i
$994$	−23.1126	−	21.0284i	−0.733088	−	0.666979i
$995$	34.2986	+	6.04777i	1.08734	+	0.191727i
$996$	27.5767	−	32.5176i	0.873802	−	1.03036i
$997$	−16.1819	−	19.2848i	−0.512485	−	0.610756i	0.446302	−	0.894883i	$-0.352741\pi$
$997$	−16.1819	−	19.2848i	−0.512485	−	0.610756i	−0.958787	+	0.284127i	$0.908296\pi$
$998$	−23.4357	+	12.3058i	−0.741844	+	0.389533i
$999$	−36.5392	+	33.9309i	−1.15605	+	1.07353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.157.31	yes	204
3.2	odd	2		648.2.t.a.37.4		204
4.3	odd	2		864.2.bf.a.49.28		204
8.3	odd	2		864.2.bf.a.49.7		204
8.5	even	2	inner	216.2.t.a.157.17	✓	204
24.5	odd	2		648.2.t.a.37.18		204
27.11	odd	18		648.2.t.a.613.18		204
27.16	even	9	inner	216.2.t.a.205.17	yes	204
108.43	odd	18		864.2.bf.a.529.7		204
216.43	odd	18		864.2.bf.a.529.28		204
216.173	odd	18		648.2.t.a.613.4		204
216.205	even	18	inner	216.2.t.a.205.31	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.17	✓	204	8.5	even	2	inner
216.2.t.a.157.31	yes	204	1.1	even	1	trivial
216.2.t.a.205.17	yes	204	27.16	even	9	inner
216.2.t.a.205.31	yes	204	216.205	even	18	inner
648.2.t.a.37.4		204	3.2	odd	2
648.2.t.a.37.18		204	24.5	odd	2
648.2.t.a.613.4		204	216.173	odd	18
648.2.t.a.613.18		204	27.11	odd	18
864.2.bf.a.49.7		204	8.3	odd	2
864.2.bf.a.49.28		204	4.3	odd	2
864.2.bf.a.529.7		204	108.43	odd	18
864.2.bf.a.529.28		204	216.43	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30848 + 0.536554i) q^{2} +(-1.40645 - 1.01088i) q^{3} +(1.42422 + 1.40414i) q^{4} +(1.34230 + 3.68793i) q^{5} +(-1.29792 - 2.07736i) q^{6} +(-0.499959 - 2.83541i) q^{7} +(1.11016 + 2.60145i) q^{8} +(0.956226 + 2.84352i) q^{9} +(-0.222412 + 5.54579i) q^{10} +(-0.996019 + 2.73654i) q^{11} +(-0.583678 - 3.41457i) q^{12} +(2.55767 - 3.04812i) q^{13} +(0.867166 - 3.97832i) q^{14} +(1.84019 - 6.54382i) q^{15} +(0.0567986 + 3.99960i) q^{16} +(2.48745 - 4.30839i) q^{17} +(-0.274506 + 4.23375i) q^{18} +(-1.78004 + 1.02771i) q^{19} +(-3.26664 + 7.13719i) q^{20} +(-2.16310 + 4.49327i) q^{21} +(-2.77157 + 3.04628i) q^{22} +(0.165146 - 0.936587i) q^{23} +(1.06838 - 4.78106i) q^{24} +(-7.96887 + 6.68667i) q^{25} +(4.98214 - 2.61606i) q^{26} +(1.52959 - 4.96592i) q^{27} +(3.26925 - 4.74025i) q^{28} +(-5.18495 - 6.17919i) q^{29} +(5.91896 - 7.57506i) q^{30} +(0.331534 - 1.88022i) q^{31} +(-2.07168 + 5.26385i) q^{32} +(4.16718 - 2.84196i) q^{33} +(5.56646 - 4.30278i) q^{34} +(9.78570 - 5.64977i) q^{35} +(-2.63082 + 5.39247i) q^{36} +(-8.31066 - 4.79816i) q^{37} +(-2.88056 + 0.389641i) q^{38} +(-6.67855 + 1.70152i) q^{39} +(-8.10381 + 7.58612i) q^{40} +(0.581151 + 0.487644i) q^{41} +(-5.24125 + 4.71871i) q^{42} +(2.14125 - 5.88303i) q^{43} +(-5.26103 + 2.49888i) q^{44} +(-9.20319 + 7.34336i) q^{45} +(0.718619 - 1.13689i) q^{46} +(0.932102 + 5.28621i) q^{47} +(3.96324 - 5.68267i) q^{48} +(-1.21172 + 0.441031i) q^{49} +(-14.0148 + 4.47362i) q^{50} +(-7.85378 + 3.54503i) q^{51} +(7.92266 - 0.749861i) q^{52} -3.54207i q^{53} +(4.66591 - 5.67708i) q^{54} -11.4291 q^{55} +(6.82113 - 4.44837i) q^{56} +(3.54244 + 0.353992i) q^{57} +(-3.46892 - 10.8673i) q^{58} +(2.13303 + 5.86045i) q^{59} +(11.8093 - 6.73594i) q^{60} +(3.22446 - 0.568559i) q^{61} +(1.44265 - 2.28234i) q^{62} +(7.58447 - 4.13293i) q^{63} +(-5.53509 + 5.77605i) q^{64} +(14.6744 + 5.34105i) q^{65} +(6.97752 - 1.48271i) q^{66} +(-4.40861 + 5.25398i) q^{67} +(9.59225 - 2.64337i) q^{68} +(-1.17905 + 1.15032i) q^{69} +(15.8358 - 2.14204i) q^{70} +(3.83709 - 6.64603i) q^{71} +(-6.33572 + 5.64434i) q^{72} +(3.46824 + 6.00718i) q^{73} +(-8.29983 - 10.7374i) q^{74} +(17.9673 - 1.34890i) q^{75} +(-3.97821 - 1.03574i) q^{76} +(8.25717 + 1.45596i) q^{77} +(-9.65168 - 1.35700i) q^{78} +(0.205269 - 0.172241i) q^{79} +(-14.6740 + 5.57812i) q^{80} +(-7.17126 + 5.43811i) q^{81} +(0.498775 + 0.949889i) q^{82} +(7.91149 + 9.42855i) q^{83} +(-9.38989 + 3.36211i) q^{84} +(19.2280 + 3.39041i) q^{85} +(5.95834 - 6.54891i) q^{86} +(1.04596 + 13.9321i) q^{87} +(-8.22471 + 0.446904i) q^{88} +(-4.11349 - 7.12477i) q^{89} +(-15.9823 + 4.67059i) q^{90} +(-9.92138 - 5.72811i) q^{91} +(1.55030 - 1.10202i) q^{92} +(-2.36698 + 2.30931i) q^{93} +(-1.61671 + 7.41700i) q^{94} +(-6.17946 - 5.18518i) q^{95} +(8.23487 - 5.30914i) q^{96} +(5.06123 + 1.84214i) q^{97} +(-1.82215 - 0.0730766i) q^{98} +(-8.73384 - 0.215453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more