LMFDB - Embedded newform 216.2.t.a.157.17

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			157.17
Character	$\chi$	$=$	216.157
Dual form			216.2.t.a.205.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.301188 - 1.38177i) q^{2} +(1.40645 + 1.01088i) q^{3} +(-1.81857 + 0.832346i) q^{4} +(-1.34230 - 3.68793i) q^{5} +(0.973201 - 2.24786i) q^{6} +(-0.499959 - 2.83541i) q^{7} +(1.69784 + 2.26215i) q^{8} +(0.956226 + 2.84352i) q^{9} +(-4.69159 + 2.96551i) q^{10} +(0.996019 - 2.73654i) q^{11} +(-3.39914 - 0.667709i) q^{12} +(-2.55767 + 3.04812i) q^{13} +(-3.76729 + 1.54482i) q^{14} +(1.84019 - 6.54382i) q^{15} +(2.61440 - 3.02736i) q^{16} +(2.48745 - 4.30839i) q^{17} +(3.64109 - 2.17772i) q^{18} +(1.78004 - 1.02771i) q^{19} +(5.51070 + 5.58951i) q^{20} +(2.16310 - 4.49327i) q^{21} +(-4.08125 - 0.552054i) q^{22} +(0.165146 - 0.936587i) q^{23} +(0.101163 + 4.89793i) 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} +(-9.59629 - 0.571800i) q^{30} +(0.331534 - 1.88022i) q^{31} +(-4.97054 - 2.70069i) q^{32} +(4.16718 - 2.84196i) q^{33} +(-6.70240 - 2.13945i) q^{34} +(-9.78570 + 5.64977i) q^{35} +(-4.10576 - 4.37524i) q^{36} +(8.31066 + 4.79816i) q^{37} +(-1.95618 - 2.15007i) q^{38} +(-6.67855 + 1.70152i) q^{39} +(6.06366 - 9.29801i) q^{40} +(0.581151 + 0.487644i) q^{41} +(-6.86016 - 1.63558i) q^{42} +(-2.14125 + 5.88303i) q^{43} +(0.466416 + 5.80562i) q^{44} +(9.20319 - 7.34336i) q^{45} +(-1.34389 + 0.0538962i) q^{46} +(0.932102 + 5.28621i) q^{47} +(6.73735 - 1.61498i) q^{48} +(-1.21172 + 0.441031i) q^{49} +(11.6396 + 8.99718i) q^{50} +(7.85378 - 3.54503i) q^{51} +(2.11423 - 7.67209i) q^{52} +3.54207i q^{53} +(7.32245 + 0.617856i) q^{54} -11.4291 q^{55} +(5.56527 - 5.94505i) q^{56} +(3.54244 + 0.353992i) q^{57} +(6.97656 - 9.02551i) q^{58} +(-2.13303 - 5.86045i) q^{59} +(2.10020 + 13.4321i) q^{60} +(-3.22446 + 0.568559i) q^{61} +(-2.69789 + 0.108198i) q^{62} +(7.58447 - 4.13293i) q^{63} +(-2.23467 + 7.68155i) q^{64} +(14.6744 + 5.34105i) q^{65} +(-5.18203 - 4.90211i) q^{66} +(4.40861 - 5.25398i) q^{67} +(-0.937536 + 9.90554i) q^{68} +(1.17905 - 1.15032i) q^{69} +(10.7540 + 11.8199i) q^{70} +(3.83709 - 6.64603i) q^{71} +(-4.80896 + 6.99098i) q^{72} +(3.46824 + 6.00718i) q^{73} +(4.12688 - 12.9286i) q^{74} +(-17.9673 + 1.34890i) q^{75} +(-2.38172 + 3.35057i) q^{76} +(-8.25717 - 1.45596i) q^{77} +(4.36261 + 8.71573i) 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} +(-0.193796 + 9.97178i) q^{84} +(-19.2280 - 3.39041i) q^{85} +(8.77391 + 1.18681i) q^{86} +(1.04596 + 13.9321i) q^{87} +(7.88155 - 2.39307i) q^{88} +(-4.11349 - 7.12477i) q^{89} +(-12.9187 - 10.5049i) q^{90} +(9.92138 + 5.72811i) q^{91} +(0.479235 + 1.84071i) q^{92} +(2.36698 - 2.30931i) q^{93} +(7.02358 - 2.88009i) q^{94} +(-6.17946 - 5.18518i) q^{95} +(-4.26075 - 8.82304i) q^{96} +(5.06123 + 1.84214i) q^{97} +(0.974360 + 1.54149i) 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 $

$2$	−0.301188	−	1.38177i	−0.212972	−	0.977058i
$2$	−0.301188	−	1.38177i	−0.212972	−	0.977058i
$3$	1.40645	+	1.01088i	0.812017	+	0.583634i
$3$	1.40645	+	1.01088i	0.812017	+	0.583634i
$4$	−1.81857	+	0.832346i	−0.909286	+	0.416173i
$5$	−1.34230	−	3.68793i	−0.600294	−	1.64929i	−0.750679	−	0.660667i	$-0.770274\pi$
$5$	−1.34230	−	3.68793i	−0.600294	−	1.64929i	0.150386	−	0.988627i	$-0.451948\pi$
$6$	0.973201	−	2.24786i	0.397308	−	0.917686i
$7$	−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	$-0.238687\pi$
$8$	1.69784	+	2.26215i	0.600278	+	0.799792i
$9$	0.956226	+	2.84352i	0.318742	+	0.947841i
$10$	−4.69159	+	2.96551i	−1.48361	+	0.937776i
$11$	0.996019	−	2.73654i	0.300311	−	0.825098i	−0.694135	−	0.719845i	$-0.744213\pi$
$11$	0.996019	−	2.73654i	0.300311	−	0.825098i	0.994446	−	0.105252i	$-0.0335650\pi$
$12$	−3.39914	−	0.667709i	−0.981248	−	0.192751i
$13$	−2.55767	+	3.04812i	−0.709371	+	0.845396i	−0.993552	−	0.113375i	$-0.963834\pi$
$13$	−2.55767	+	3.04812i	−0.709371	+	0.845396i	0.284181	+	0.958771i	$0.408278\pi$
$14$	−3.76729	+	1.54482i	−1.00685	+	0.412870i
$15$	1.84019	−	6.54382i	0.475136	−	1.68961i
$16$	2.61440	−	3.02736i	0.653600	−	0.756840i
$17$	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	$-0.0394795\pi$
$18$	3.64109	−	2.17772i	0.858213	−	0.513294i
$19$	1.78004	−	1.02771i	0.408369	−	0.235772i	−0.281720	−	0.959497i	$-0.590905\pi$
$19$	1.78004	−	1.02771i	0.408369	−	0.235772i	0.690089	+	0.723725i	$0.257571\pi$
$20$	5.51070	+	5.58951i	1.23223	+	1.24985i
$21$	2.16310	−	4.49327i	0.472027	−	0.980512i
$22$	−4.08125	−	0.552054i	−0.870126	−	0.117698i
$23$	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	$0.0239424\pi$
$24$	0.101163	+	4.89793i	0.0206498	+	0.999787i
$25$	−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	$0.0472157\pi$
$29$	5.18495	+	6.17919i	0.962821	+	1.14745i	−0.0261974	+	0.999657i	$0.508340\pi$
$30$	−9.59629	−	0.571800i	−1.75203	−	0.104396i
$31$	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	$0.000709125\pi$
$32$	−4.97054	−	2.70069i	−0.878675	−	0.477420i
$33$	4.16718	−	2.84196i	0.725413	−	0.494721i
$34$	−6.70240	−	2.13945i	−1.14945	−	0.366912i
$35$	−9.78570	+	5.64977i	−1.65408	+	0.954986i
$36$	−4.10576	−	4.37524i	−0.684293	−	0.729207i
$37$	8.31066	+	4.79816i	1.36626	+	0.788813i	0.990449	−	0.137881i	$-0.0440293\pi$
$37$	8.31066	+	4.79816i	1.36626	+	0.788813i	0.375816	+	0.926694i	$0.377363\pi$
$38$	−1.95618	−	2.15007i	−0.317334	−	0.348788i
$39$	−6.67855	+	1.70152i	−1.06942	+	0.272462i
$40$	6.06366	−	9.29801i	0.958748	−	1.47014i
$41$	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	$0.703355\pi$
$42$	−6.86016	−	1.63558i	−1.05855	−	0.252376i
$43$	−2.14125	+	5.88303i	−0.326537	+	0.897154i	0.662444	+	0.749112i	$0.269519\pi$
$43$	−2.14125	+	5.88303i	−0.326537	+	0.897154i	−0.988981	+	0.148042i	$0.952703\pi$
$44$	0.466416	+	5.80562i	0.0703148	+	0.875231i
$45$	9.20319	−	7.34336i	1.37193	−	1.09468i
$46$	−1.34389	+	0.0538962i	−0.198145	+	0.00794656i
$47$	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	$0.816406\pi$
$48$	6.73735	−	1.61498i	0.972452	−	0.233103i
$49$	−1.21172	+	0.441031i	−0.173103	+	0.0630044i
$50$	11.6396	+	8.99718i	1.64608	+	1.27239i
$51$	7.85378	−	3.54503i	1.09975	−	0.496404i
$52$	2.11423	−	7.67209i	0.293190	−	1.06393i
$53$			3.54207i			0.486541i	0.969959	+	0.243270i	$0.0782202\pi$
$53$			3.54207i			0.486541i	−0.969959	+	0.243270i	$0.921780\pi$
$54$	7.32245	+	0.617856i	0.996459	+	0.0840796i
$55$	−11.4291			−1.54110
$56$	5.56527	−	5.94505i	0.743691	−	0.794441i
$57$	3.54244	+	0.353992i	0.469207	+	0.0468874i
$58$	6.97656	−	9.02551i	0.916067	−	1.18511i
$59$	−2.13303	−	5.86045i	−0.277697	−	0.762966i	−0.997623	−	0.0689146i	$-0.978046\pi$
$59$	−2.13303	−	5.86045i	−0.277697	−	0.762966i	0.719926	−	0.694051i	$-0.244176\pi$
$60$	2.10020	+	13.4321i	0.271134	+	1.73407i
$61$	−3.22446	+	0.568559i	−0.412849	+	0.0727965i	−0.376215	−	0.926532i	$-0.622775\pi$
$61$	−3.22446	+	0.568559i	−0.412849	+	0.0727965i	−0.0366341	+	0.999329i	$0.511664\pi$
$62$	−2.69789	+	0.108198i	−0.342632	+	0.0137412i
$63$	7.58447	−	4.13293i	0.955554	−	0.520701i
$64$	−2.23467	+	7.68155i	−0.279333	+	0.960194i
$65$	14.6744	+	5.34105i	1.82014	+	0.662476i
$66$	−5.18203	−	4.90211i	−0.637864	−	0.603409i
$67$	4.40861	−	5.25398i	0.538598	−	0.641876i	−0.426275	−	0.904594i	$-0.640174\pi$
$67$	4.40861	−	5.25398i	0.538598	−	0.641876i	0.964873	+	0.262718i	$0.0846188\pi$
$68$	−0.937536	+	9.90554i	−0.113693	+	1.20122i
$69$	1.17905	−	1.15032i	0.141941	−	0.138483i
$70$	10.7540	+	11.8199i	1.28535	+	1.41275i
$71$	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	$0.0161707\pi$
$72$	−4.80896	+	6.99098i	−0.566742	+	0.823895i
$73$	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	$0.700282\pi$
$74$	4.12688	−	12.9286i	0.479740	−	1.50292i
$75$	−17.9673	+	1.34890i	−2.07468	+	0.155757i
$76$	−2.38172	+	3.35057i	−0.273202	+	0.384336i
$77$	−8.25717	−	1.45596i	−0.940992	−	0.165922i
$78$	4.36261	+	8.71573i	0.493969	+	0.986862i
$79$	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	$-0.986152\pi$
$83$	−7.91149	−	9.42855i	−0.868399	−	1.03492i	0.130655	−	0.991428i	$-0.458292\pi$
$84$	−0.193796	+	9.97178i	−0.0211448	+	1.08801i
$85$	−19.2280	−	3.39041i	−2.08557	−	0.367742i
$86$	8.77391	+	1.18681i	0.946115	+	0.127977i
$87$	1.04596	+	13.9321i	0.112138	+	1.49368i
$88$	7.88155	−	2.39307i	0.840176	−	0.255102i
$89$	−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	$0.976949\pi$
$90$	−12.9187	−	10.5049i	−1.36175	−	1.10732i
$91$	9.92138	+	5.72811i	1.04004	+	0.600469i
$92$	0.479235	+	1.84071i	0.0499637	+	0.191907i
$93$	2.36698	−	2.30931i	0.245444	−	0.239464i
$94$	7.02358	−	2.88009i	0.724427	−	0.297059i
$95$	−6.17946	−	5.18518i	−0.633999	−	0.531988i
$96$	−4.26075	−	8.82304i	−0.434861	−	0.900498i
$97$	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	$0.522951\pi$
$98$	0.974360	+	1.54149i	0.0984252	+	0.155714i
$99$	8.73384	+	0.215453i	0.877784	+	0.0216539i
$100$	8.92633	−	18.7930i	0.892633	−	1.87930i
$101$	−3.98336	+	0.702375i	−0.396360	+	0.0698889i	−0.368276	−	0.929717i	$-0.620052\pi$
$101$	−3.98336	+	0.702375i	−0.396360	+	0.0698889i	−0.0280840	+	0.999606i	$0.508941\pi$
$102$	−7.26388	−	9.78438i	−0.719231	−	0.968798i
$103$	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	$0.370983\pi$
$104$	−11.2378	−	0.610627i	−1.10196	−	0.0598769i
$105$	−19.4744	−	1.94606i	−1.90051	−	0.189916i
$106$	4.89432	−	1.06683i	0.475379	−	0.103620i
$107$		−	4.87553i		−	0.471335i	−0.971834	−	0.235667i	$-0.924272\pi$
$107$		−	4.87553i		−	0.471335i	0.971834	−	0.235667i	$-0.0757276\pi$
$108$	−1.35170	−	10.3040i	−0.130068	−	0.991505i
$109$		−	2.52010i		−	0.241382i	−0.992690	−	0.120691i	$-0.961489\pi$
$109$		−	2.52010i		−	0.241382i	0.992690	−	0.120691i	$-0.0385111\pi$
$110$	3.44232	+	15.7924i	0.328212	+	1.50575i
$111$	6.83818	+	15.1495i	0.649051	+	1.43793i
$112$	−9.89089	−	5.89934i	−0.934601	−	0.557435i
$113$	−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	$0.499377\pi$
$114$	−0.577806	−	5.00145i	−0.0541165	−	0.468429i
$115$	−3.67575	+	0.648133i	−0.342765	+	0.0604387i
$116$	−14.5724	−	6.92162i	−1.35302	−	0.642656i
$117$	−11.1131	−	4.35812i	−1.02741	−	0.402908i
$118$	−7.45535	+	4.71245i	−0.686320	+	0.433817i
$119$	−13.4597	−	4.89892i	−1.23385	−	0.449083i
$120$	17.9275	−	6.94757i	1.63655	−	0.634223i
$121$	1.92989	+	1.61937i	0.175445	+	0.147216i
$122$	1.75679	+	4.28421i	0.159052	+	0.387874i
$123$	0.324411	+	1.27332i	0.0292511	+	0.114812i
$124$	0.962077	+	3.69527i	0.0863971	+	0.331845i
$125$	18.3625	+	10.6016i	1.64239	+	0.948236i
$126$	−7.99512	−	9.23520i	−0.712262	−	0.822737i
$127$	−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	$0.901214\pi$
$128$	11.2872	+	0.774196i	0.997656	+	0.0684299i
$129$	−8.95864	+	6.10966i	−0.788764	+	0.537926i
$130$	2.96033	−	21.8853i	0.259638	−	1.91947i
$131$	−3.45051	−	0.608417i	−0.301472	−	0.0531577i	0.0208660	−	0.999782i	$-0.493358\pi$
$131$	−3.45051	−	0.608417i	−0.301472	−	0.0531577i	−0.322338	+	0.946625i	$0.604469\pi$
$132$	−5.21282	+	8.63683i	−0.453718	+	0.751740i
$133$	−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	$0.527204\pi$
$138$	−1.94460	−	1.28271i	−0.165535	−	0.109192i
$139$	19.5648	+	3.44981i	1.65947	+	0.292609i	0.923268	−	0.384157i	$-0.125508\pi$
$139$	19.5648	+	3.44981i	1.65947	+	0.292609i	0.736199	+	0.676765i	$0.236619\pi$
$140$	13.0934	−	18.4196i	1.10660	−	1.55674i
$141$	−4.03279	+	8.37706i	−0.339622	+	0.705476i
$142$	−10.3390	−	3.30026i	−0.867626	−	0.276952i
$143$	5.79380	+	10.0352i	0.484502	+	0.839182i
$144$	11.1083	+	4.53927i	0.925694	+	0.378273i
$145$	15.8287	−	27.4161i	1.31450	−	2.27678i
$146$	7.25593	−	6.60160i	0.600505	−	0.546353i
$147$	−2.15006	−	0.604622i	−0.177334	−	0.0498683i
$148$	−19.1073	−	1.80846i	−1.57061	−	0.148654i
$149$	7.39950	−	8.81838i	0.606190	−	0.722429i	−0.372440	−	0.928056i	$-0.621479\pi$
$149$	7.39950	−	8.81838i	0.606190	−	0.722429i	0.978630	+	0.205627i	$0.0659233\pi$
$150$	7.27541	+	24.4204i	0.594034	+	1.99392i
$151$	−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	$0.658488\pi$
$152$	5.34706	+	2.28184i	0.433704	+	0.185082i
$153$	14.6296	+	2.95333i	1.18273	+	0.238763i
$154$	0.475161	+	11.8480i	0.0382896	+	0.954741i
$155$	−7.37916	+	1.30114i	−0.592708	+	0.104510i
$156$	10.7292	−	8.65320i	0.859020	−	0.692811i
$157$	5.00630	+	13.7547i	0.399546	+	1.09774i	0.962506	+	0.271259i	$0.0874402\pi$
$157$	5.00630	+	13.7547i	0.399546	+	1.09774i	−0.562960	+	0.826484i	$0.690338\pi$
$158$	−0.299821	−	0.231757i	−0.0238525	−	0.0184376i
$159$	−3.58062	+	4.98176i	−0.283962	+	0.395079i
$160$	−3.28803	+	21.9562i	−0.259942	+	1.73579i
$161$	−2.73817			−0.215798
$162$	9.67411	+	8.27113i	0.760070	+	0.649842i
$163$			5.93891i			0.465171i	0.972576	+	0.232586i	$0.0747186\pi$
$163$			5.93891i			0.465171i	−0.972576	+	0.232586i	$0.925281\pi$
$164$	−1.46275	−	0.403096i	−0.114222	−	0.0314765i
$165$	−16.0745	−	11.5535i	−1.25140	−	0.899441i
$166$	−10.6452	+	13.7716i	−0.826230	+	1.06889i
$167$	−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	$0.668809\pi$
$168$	13.8371	−	2.73560i	1.06755	−	0.211056i
$169$	−0.491897	−	2.78968i	−0.0378382	−	0.214591i
$170$	1.10648	+	27.5898i	0.0848631	+	2.11604i
$171$	4.62443	+	4.07887i	0.353639	+	0.311919i
$172$	−1.00270	−	12.4810i	−0.0764555	−	0.951665i
$173$	3.76876	−	10.3546i	0.286534	−	0.787245i	−0.710011	−	0.704190i	$-0.751310\pi$
$173$	3.76876	−	10.3546i	0.286534	−	0.787245i	0.996545	−	0.0830547i	$-0.0264676\pi$
$174$	18.9360	−	5.64147i	1.43553	−	0.427678i
$175$	22.9435	+	19.2519i	1.73437	+	1.45531i
$176$	−5.68050	−	10.1697i	−0.428183	−	0.766571i
$177$	2.92423	−	10.3987i	0.219799	−	0.781614i
$178$	−8.60585	+	7.82979i	−0.645036	+	0.586868i
$179$	3.66363	+	2.11520i	0.273832	+	0.158097i	0.630628	−	0.776085i	$-0.282797\pi$
$179$	3.66363	+	2.11520i	0.273832	+	0.158097i	−0.356796	+	0.934182i	$0.616131\pi$
$180$	−10.6244	+	21.0146i	−0.791899	+	1.56634i
$181$	−16.4676	+	9.50759i	−1.22403	+	0.706694i	−0.965775	−	0.259383i	$-0.916481\pi$
$181$	−16.4676	+	9.50759i	−1.22403	+	0.706694i	−0.258255	+	0.966077i	$0.583147\pi$
$182$	4.92672	−	15.4343i	0.365193	−	1.14407i
$183$	−5.10980	−	2.45990i	−0.377727	−	0.181841i
$184$	2.39909	−	1.21659i	0.176864	−	0.0896884i
$185$	6.53992	−	37.0897i	0.480825	−	2.72689i
$186$	−3.90383	−	2.57508i	−0.286243	−	0.188814i
$187$	−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	$0.182747\pi$
$192$	−10.9081	+	8.54476i	−0.787225	+	0.616665i
$193$	−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	$0.898109\pi$
$194$	1.02102	−	7.54829i	0.0733053	−	0.541936i
$195$	15.2397	+	22.3461i	1.09134	+	1.60024i
$196$	1.83651	−	1.81062i	0.131180	−	0.129330i
$197$	−5.35211	+	3.09004i	−0.381322	+	0.220156i	−0.678393	−	0.734699i	$-0.737323\pi$
$197$	−5.35211	+	3.09004i	−0.381322	+	0.220156i	0.297071	+	0.954855i	$0.403990\pi$
$198$	−2.33282	−	12.1330i	−0.165787	−	0.862257i
$199$	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	$0.0648176\pi$
$200$	−28.6561	−	6.67388i	−2.02630	−	0.471914i
$201$	11.5117	−	2.93289i	0.811971	−	0.206870i
$202$	2.17026	+	5.29254i	0.152699	+	0.372382i
$203$	14.9282	−	17.7908i	1.04776	−	1.24867i
$204$	−11.3320	+	12.9839i	−0.793396	+	0.909058i
$205$	1.01832	−	2.79781i	0.0711225	−	0.195407i
$206$	−0.862336	−	1.36426i	−0.0600818	−	0.0950526i
$207$	2.82113	−	0.425994i	0.196082	−	0.0296086i
$208$	2.54096	+	15.7120i	0.176184	+	1.08943i
$209$	−1.03941	−	5.89477i	−0.0718972	−	0.407750i
$210$	3.17646	+	27.4953i	0.219197	+	1.89735i
$211$	−6.04444	−	16.6070i	−0.416116	−	1.14327i	−0.953884	−	0.300177i	$-0.902954\pi$
$211$	−6.04444	−	16.6070i	−0.416116	−	1.14327i	0.537767	−	0.843093i	$-0.319268\pi$
$212$	−2.94823	−	6.44151i	−0.202485	−	0.442405i
$213$	12.1151	−	5.46848i	0.830110	−	0.374694i
$214$	−6.73685	+	1.46845i	−0.460522	+	0.100381i
$215$	24.5704			1.67569
$216$	−13.8307	+	4.97119i	−0.941057	+	0.338247i
$217$	−5.49695			−0.373157
$218$	−3.48220	+	0.759026i	−0.235844	+	0.0514077i
$219$	−1.19463	+	11.9548i	−0.0807258	+	0.807831i
$220$	20.7847	−	9.51299i	1.40130	−	0.641365i
$221$	6.77040	+	18.6015i	0.455426	+	1.25127i
$222$	18.8735	−	14.0116i	1.26671	−	0.940400i
$223$	−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	$-0.340880\pi$
$224$	−5.17250	+	15.4437i	−0.345602	+	1.03188i
$225$	−26.6338	−	16.2657i	−1.77558	−	1.08438i
$226$	5.46490	+	8.64575i	0.363520	+	0.575107i
$227$	−8.48739	+	23.3189i	−0.563328	+	1.54773i	0.251398	+	0.967884i	$0.419110\pi$
$227$	−8.48739	+	23.3189i	−0.563328	+	1.54773i	−0.814726	+	0.579846i	$0.803113\pi$
$228$	−6.73682	+	2.30477i	−0.446157	+	0.152637i
$229$	3.58229	−	4.26921i	0.236724	−	0.282117i	−0.634583	−	0.772855i	$-0.718828\pi$
$229$	3.58229	−	4.26921i	0.236724	−	0.282117i	0.871307	+	0.490738i	$0.163273\pi$
$230$	2.00266	+	4.88382i	0.132052	+	0.322030i
$231$	−10.1415	−	10.3948i	−0.667263	−	0.683927i
$232$	−5.17503	+	22.2204i	−0.339757	+	1.45884i
$233$	−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	$0.236579\pi$
$234$	−2.67477	+	16.6684i	−0.174855	+	1.08965i
$235$	18.2440	−	10.5332i	1.19011	−	0.687110i
$236$	8.75699	+	8.88223i	0.570031	+	0.578184i
$237$	0.462816	−	0.0347460i	0.0300631	−	0.00225699i
$238$	−2.71528	+	20.0737i	−0.176005	+	1.30118i
$239$	−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	$0.734443\pi$
$240$	−14.9995	−	22.6791i	−0.968212	−	1.46393i
$241$	−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
$246$	1.66173	−	0.831772i	0.105948	−	0.0530318i
$247$	−1.42019	+	8.05431i	−0.0903647	+	0.512484i
$248$	4.81624	−	2.44234i	0.305832	−	0.155089i
$249$	−1.59598	−	21.2584i	−0.101141	−	1.34720i
$250$	9.11839	−	28.5658i	0.576697	−	1.80666i
$251$	25.2441	−	14.5747i	1.59339	−	0.919945i	0.600672	−	0.799495i	$-0.294900\pi$
$251$	25.2441	−	14.5747i	1.59339	−	0.919945i	0.992719	−	0.120450i	$-0.0384337\pi$
$252$	−10.3529	+	13.8289i	−0.652170	+	0.871141i
$253$	−2.39852	−	1.38479i	−0.150794	−	0.0870608i
$254$	−4.98982	+	4.53985i	−0.313089	+	0.284855i
$255$	−23.6159	−	24.2057i	−1.47889	−	1.51582i
$256$	−2.32981	−	15.8295i	−0.145613	−	0.989342i
$257$	−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	$0.793131\pi$
$258$	11.1404	+	10.5386i	0.693570	+	0.656105i
$259$	9.44975	−	25.9630i	0.587179	−	1.61326i
$260$	−31.1321	+	2.50111i	−1.93073	+	0.155112i
$261$	−12.6127	+	20.6522i	−0.780705	+	1.27834i
$262$	0.198560	+	4.95105i	0.0122671	+	0.305877i
$263$	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	$0.829361\pi$
$264$	13.5042	+	4.60160i	0.831123	+	0.283209i
$265$	13.0629	−	4.75451i	0.802449	−	0.292067i
$266$	−5.11832	+	6.62151i	−0.313824	+	0.405991i
$267$	1.41689	−	14.1789i	0.0867120	−	0.867736i
$268$	−3.64425	+	13.2242i	−0.222608	+	0.807798i
$269$			15.1820i			0.925661i	0.886447	+	0.462831i	$0.153166\pi$
$269$			15.1820i			0.925661i	−0.886447	+	0.462831i	$0.846834\pi$
$270$	−7.55030	−	27.8341i	−0.459496	−	1.69393i
$271$	13.2808			0.806753			0.403376	−	0.915034i	$-0.367837\pi$
$271$	13.2808			0.806753			0.403376	+	0.915034i	$0.367837\pi$
$272$	−6.53986	−	18.7943i	−0.396537	−	1.13957i
$273$	8.16351	+	18.0857i	0.494078	+	1.09460i
$274$	18.4878	+	14.2908i	1.11689	+	0.863337i
$275$	10.3612	+	28.4672i	0.624804	+	1.71664i
$276$	−1.18672	+	3.07332i	−0.0714322	+	0.184992i
$277$	2.53413	−	0.446836i	0.152261	−	0.0268478i	−0.0969979	−	0.995285i	$-0.530924\pi$
$277$	2.53413	−	0.446836i	0.152261	−	0.0268478i	0.249259	+	0.968437i	$0.419813\pi$
$278$	−1.12586	−	28.0731i	−0.0675248	−	1.68371i
$279$	5.66348	−	0.855194i	0.339064	−	0.0511991i
$280$	−29.3952	−	12.5443i	−1.75670	−	0.749666i
$281$	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	$0.312137\pi$
$282$	12.7898	+	3.04931i	0.761621	+	0.181584i
$283$	−17.1845	+	20.4797i	−1.02151	+	1.21739i	−0.0456626	+	0.998957i	$0.514540\pi$
$283$	−17.1845	+	20.4797i	−1.02151	+	1.21739i	−0.975851	+	0.218436i	$0.929905\pi$
$284$	−1.44622	+	15.2801i	−0.0858174	+	0.906705i
$285$	−3.44951	−	13.5394i	−0.204331	−	0.802007i
$286$	12.1212	−	11.0282i	0.716744	−	0.652109i
$287$	1.09212	−	1.89160i	0.0644656	−	0.111658i
$288$	2.92653	−	16.7163i	0.172447	−	0.985019i
$289$	−3.87484	−	6.71142i	−0.227932	−	0.394789i
$290$	−42.6501	−	13.6142i	−2.50450	−	0.799452i
$291$	5.25621	+	7.70721i	0.308124	+	0.451804i
$292$	−11.3073	−	8.03770i	−0.661709	−	0.470371i
$293$	−17.3330	−	3.05628i	−1.01261	−	0.178550i	−0.357361	−	0.933966i	$-0.616323\pi$
$293$	−17.3330	−	3.05628i	−1.01261	−	0.178550i	−0.655245	+	0.755416i	$0.727435\pi$
$294$	−0.187873	+	3.15300i	−0.0109570	+	0.183886i
$295$	−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
$300$	31.5521	−	17.4081i	1.82166	−	1.00506i
$301$	17.7513	+	3.13004i	1.02317	+	0.180412i
$302$	−0.690864	+	5.10746i	−0.0397547	+	0.293901i
$303$	−6.31244	−	3.03886i	−0.362640	−	0.174578i
$304$	1.54250	−	8.07566i	0.0884686	−	0.463171i
$305$	6.42499	+	11.1284i	0.367894	+	0.637211i
$306$	−0.325440	−	21.1042i	−0.0186042	−	1.20645i
$307$	−10.1962	−	5.88676i	−0.581926	−	0.335975i	0.179972	−	0.983672i	$-0.442399\pi$
$307$	−10.1962	−	5.88676i	−0.581926	−	0.335975i	−0.761898	+	0.647696i	$0.775732\pi$
$308$	16.2281	−	4.22505i	0.924683	−	0.240745i
$309$	1.90287	+	0.535107i	0.108250	+	0.0304412i
$310$	4.02040	+	9.80440i	0.228343	+	0.556852i
$311$	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	$0.307731\pi$
$312$	−15.1882	−	12.2190i	−0.859864	−	0.691763i
$313$	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	$0.547106\pi$
$314$	17.4980	−	11.0603i	0.987467	−	0.624169i
$315$	−25.4226	−	22.4234i	−1.43240	−	1.26342i
$316$	−0.229932	+	0.484086i	−0.0129347	+	0.0272320i
$317$	5.34112	−	0.941783i	0.299987	−	0.0528958i	−0.0216287	−	0.999766i	$-0.506885\pi$
$317$	5.34112	−	0.941783i	0.299987	−	0.0528958i	0.321616	+	0.946870i	$0.395774\pi$
$318$	7.96208	+	3.44715i	0.446491	+	0.193306i
$319$	22.0739	−	8.03424i	1.23590	−	0.449831i
$320$	31.3286	−	2.06964i	1.75132	−	0.115696i
$321$	4.92859	−	6.85720i	0.275087	−	0.382732i
$322$	0.824706	+	3.78352i	0.0459590	+	0.210847i
$323$		−	10.2255i		−	0.568961i
$324$	8.51507	−	15.8586i	0.473059	−	0.881031i
$325$		−	41.3924i		−	2.29604i
$326$	8.20620	−	1.78873i	0.454499	−	0.0990686i
$327$	2.54753	−	3.54441i	0.140879	−	0.196006i
$328$	−0.116421	+	2.14259i	−0.00642830	+	0.118305i
$329$	14.5225	−	5.28577i	0.800654	−	0.291414i
$330$	−11.1228	+	25.6911i	−0.612292	+	1.41425i
$331$	5.34260	−	0.942044i	0.293656	−	0.0517794i	−0.0248795	−	0.999690i	$-0.507920\pi$
$331$	5.34260	−	0.942044i	0.293656	−	0.0517794i	0.318535	+	0.947911i	$0.396809\pi$
$332$	22.2354	+	10.5614i	1.22033	+	0.579632i
$333$	−5.69682	+	28.2197i	−0.312184	+	1.54643i
$334$	15.0446	+	23.8013i	0.823204	+	1.30235i
$335$	−25.2940	−	9.20627i	−1.38196	−	0.502992i
$336$	−7.94753	−	18.2957i	−0.433573	−	0.998112i
$337$	−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	$-0.569799\pi$
$338$	−3.70654	+	1.51991i	−0.201609	+	0.0826721i
$339$	−12.0591	−	3.39114i	−0.654959	−	0.184182i
$340$	37.7894	−	9.83862i	2.04942	−	0.533574i
$341$	−4.81509	−	2.77999i	−0.260752	−	0.150545i
$342$	4.24323	−	7.61840i	0.229448	−	0.411956i
$343$	−8.22070	−	14.2387i	−0.443876	−	0.768816i
$344$	−16.9438	+	5.14463i	−0.913550	+	0.277380i
$345$	−5.82496	−	2.80418i	−0.313605	−	0.150972i
$346$	−15.4428	−	2.08888i	−0.830208	−	0.112299i
$347$	−17.1238	−	3.01939i	−0.919255	−	0.162089i	−0.306052	−	0.952015i	$-0.599008\pi$
$347$	−17.1238	−	3.01939i	−0.919255	−	0.162089i	−0.613203	+	0.789925i	$0.710119\pi$
$348$	−13.4985	−	24.4660i	−0.723595	−	1.31151i
$349$	3.38478	+	4.03383i	0.181183	+	0.215926i	0.848990	−	0.528409i	$-0.177211\pi$
$349$	3.38478	+	4.03383i	0.181183	+	0.215926i	−0.667807	+	0.744335i	$0.732767\pi$
$350$	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	$0.358482\pi$
$354$	−15.2493	−	0.908640i	−0.810494	−	0.0482937i
$355$	−29.6606	−	5.22997i	−1.57422	−	0.277578i
$356$	13.4109	+	9.53306i	0.710779	+	0.505251i
$357$	−13.9782	−	20.4963i	−0.739803	−	1.08478i
$358$	1.81927	−	5.69936i	0.0961515	−	0.301221i
$359$	−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	$0.974381\pi$
$360$	32.2373	+	8.35116i	1.69906	+	0.440145i
$361$	−7.38764	+	12.7958i	−0.388823	+	0.673461i
$362$	18.0972	+	19.8909i	0.951165	+	1.04544i
$363$	1.07731	+	4.22847i	0.0565440	+	0.221937i
$364$	−22.8105	−	2.15896i	−1.19560	−	0.113160i
$365$	17.4986	−	20.8541i	0.915921	−	1.09155i
$366$	−1.86000	+	7.80146i	−0.0972239	+	0.407789i
$367$	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	$0.502654\pi$
$368$	−2.40363	−	2.94857i	−0.125298	−	0.153705i
$369$	−0.830915	+	2.11881i	−0.0432557	+	0.110301i
$370$	−53.2192	+	2.13434i	−2.76673	+	0.110959i
$371$	10.0432	−	1.77089i	0.521417	−	0.0919400i
$372$	−2.38237	+	6.16978i	−0.123520	+	0.319888i
$373$	−2.16442	−	5.94669i	−0.112069	−	0.307908i	0.870961	−	0.491353i	$-0.163497\pi$
$373$	−2.16442	−	5.94669i	−0.112069	−	0.307908i	−0.983030	+	0.183445i	$0.941275\pi$
$374$	−12.5304	+	16.2104i	−0.647931	+	0.838222i
$375$	15.1090	+	33.4730i	0.780227	+	1.72854i
$376$	−10.3757	+	11.0837i	−0.535083	+	0.571598i
$377$	−32.0963			−1.65304
$378$	−1.90905	−	21.0710i	−0.0981908	−	1.08378i
$379$			28.5066i			1.46428i	0.681152	+	0.732142i	$0.261479\pi$
$379$			28.5066i			1.46428i	−0.681152	+	0.732142i	$0.738521\pi$
$380$	15.5536	+	4.28618i	0.797885	+	0.219876i
$381$	0.821535	−	8.22118i	0.0420885	−	0.421184i
$382$	−9.09675	−	7.03163i	−0.465430	−	0.359769i
$383$	−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	$0.685747\pi$
$384$	15.0923	+	12.4989i	0.770175	+	0.637832i
$385$	5.71409	+	32.4062i	0.291217	+	1.65157i
$386$	18.6381	−	0.747475i	0.948654	−	0.0380455i
$387$	−18.7761	−	0.463183i	−0.954441	−	0.0235449i
$388$	−10.7375	+	0.862636i	−0.545115	+	0.0437937i
$389$	1.34416	−	3.69306i	0.0681518	−	0.187246i	−0.900941	−	0.433941i	$-0.857123\pi$
$389$	1.34416	−	3.69306i	0.0681518	−	0.187246i	0.969093	+	0.246696i	$0.0793448\pi$
$390$	26.2871	−	27.7881i	1.33110	−	1.40711i
$391$	−3.62440	−	3.04123i	−0.183294	−	0.153802i
$392$	−3.05499	−	1.99230i	−0.154300	−	0.100626i
$393$	−4.23794	−	4.34377i	−0.213776	−	0.219114i
$394$	5.88171	+	6.46469i	0.296316	+	0.325686i
$395$	−0.910744	−	0.525818i	−0.0458245	−	0.0264568i
$396$	−16.0624	+	6.87775i	−0.807168	+	0.345620i
$397$	17.9961	−	10.3901i	0.903200	−	0.521463i	0.0249629	−	0.999688i	$-0.492053\pi$
$397$	17.9961	−	10.3901i	0.903200	−	0.521463i	0.878237	+	0.478226i	$0.158720\pi$
$398$	−11.9556	−	3.81631i	−0.599282	−	0.191295i
$399$	−0.767360	−	10.2212i	−0.0384161	−	0.511702i
$400$	−0.590854	+	41.6063i	−0.0295427	+	2.08031i
$401$	−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	$0.859166\pi$
$402$	−7.51976	−	15.0231i	−0.375051	−	0.749286i
$403$	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
$408$	21.3539	+	11.7475i	1.05717	+	0.581589i
$409$	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	$-0.201215\pi$
$410$	−4.17263	−	0.564414i	−0.206072	−	0.0278744i
$411$	−28.5385	+	2.14253i	−1.40770	+	0.105683i
$412$	−1.62537	+	1.60245i	−0.0800761	+	0.0789470i
$413$	−15.5503	+	8.97799i	−0.765182	+	0.441778i
$414$	−1.43832	−	3.76984i	−0.0706893	−	0.185278i
$415$	−24.1523	+	41.8330i	−1.18559	+	2.05350i
$416$	20.9451	−	8.24329i	1.02692	−	0.404161i
$417$	24.0297	+	24.6298i	1.17674	+	1.20612i
$418$	−7.83215	+	3.21165i	−0.383083	+	0.157087i
$419$	8.33906	−	9.93810i	0.407390	−	0.485508i	−0.522869	−	0.852413i	$-0.675138\pi$
$419$	8.33906	−	9.93810i	0.407390	−	0.485508i	0.930258	+	0.366905i	$0.119583\pi$
$420$	37.0354	−	12.6704i	1.80714	−	0.618252i
$421$	−1.49536	+	4.10848i	−0.0728795	+	0.200235i	−0.970784	−	0.239956i	$-0.922867\pi$
$421$	−1.49536	+	4.10848i	−0.0728795	+	0.200235i	0.897904	+	0.440191i	$0.145089\pi$
$422$	−21.1265	+	13.3538i	−1.02842	+	0.650055i
$423$	−14.1402	+	7.70527i	−0.687519	+	0.374643i
$424$	−8.01270	+	6.01388i	−0.389131	+	0.292060i
$425$	8.98665	+	50.9658i	0.435916	+	2.47220i
$426$	−11.2051	−	15.0932i	−0.542889	−	0.731266i
$427$	3.22419	+	8.85839i	0.156030	+	0.428688i
$428$	4.05812	+	8.86649i	0.196157	+	0.428578i
$429$	−1.99567	+	19.9709i	−0.0963517	+	0.964202i
$430$	−7.40033	−	33.9507i	−0.356876	−	1.63725i
$431$	1.15854			0.0558051			0.0279025	−	0.999611i	$-0.491117\pi$
$431$	1.15854			0.0558051			0.0279025	+	0.999611i	$0.491117\pi$
$432$	11.0347	+	17.6135i	0.530906	+	0.847431i
$433$	37.7498			1.81414			0.907069	−	0.420982i	$-0.138314\pi$
$433$	37.7498			1.81414			0.907069	+	0.420982i	$0.138314\pi$
$434$	1.65562	+	7.59552i	0.0794722	+	0.364596i
$435$	49.9768	−	22.5585i	2.39620	−	1.08160i
$436$	2.09760	+	4.58299i	0.100457	+	0.219485i
$437$	−0.668571	−	1.83688i	−0.0319821	−	0.0878701i
$438$	16.8786	−	1.94994i	0.806490	−	0.0931720i
$439$	−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	$-0.279052\pi$
$440$	−19.4049	−	25.8544i	−0.925090	−	1.23256i
$441$	−2.41276	−	3.02384i	−0.114894	−	0.143992i
$442$	23.6638	−	14.9577i	1.12557	−	0.711465i
$443$	−10.3614	+	28.4677i	−0.492285	+	1.35254i	0.406299	+	0.913740i	$0.366819\pi$
$443$	−10.3614	+	28.4677i	−0.492285	+	1.35254i	−0.898584	+	0.438802i	$0.855403\pi$
$444$	−25.0453	−	21.8587i	−1.18860	−	1.03737i
$445$	−20.7542	+	24.7338i	−0.983841	+	1.17250i
$446$	−30.5236	+	12.5165i	−1.44534	+	0.592675i
$447$	19.3214	−	4.92261i	0.913871	−	0.232831i
$448$	22.8976	+	2.49573i	1.08181	+	0.117912i
$449$	−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	$0.192297\pi$
$450$	−14.4537	+	41.7007i	−0.681352	+	1.96579i
$451$	1.91329	−	1.10464i	0.0900934	−	0.0520155i
$452$	10.3005	−	10.1552i	0.484493	−	0.477662i
$453$	−3.55655	−	5.21499i	−0.167101	−	0.245021i
$454$	34.7776	+	4.70422i	1.63220	+	0.220780i
$455$	7.80745	−	44.2782i	0.366019	−	2.07580i
$456$	5.21371	+	8.61456i	0.244155	+	0.403414i
$457$	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	$-0.966120\pi$
$461$	−19.8885	−	23.7021i	−0.926298	−	1.10392i	0.0680433	−	0.997682i	$-0.478324\pi$
$462$	−11.3087	+	17.1440i	−0.526128	+	0.797612i
$463$	−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	$0.861908\pi$
$464$	32.2622	+	0.458157i	1.49773	+	0.0212694i
$465$	−11.6938	−	5.62947i	−0.542285	−	0.261061i
$466$	8.96108	+	2.86043i	0.415114	+	0.132507i
$467$	−0.849394	+	0.490398i	−0.0393052	+	0.0226929i	−0.519524	−	0.854456i	$-0.673891\pi$
$467$	−0.849394	+	0.490398i	−0.0393052	+	0.0226929i	0.480219	+	0.877149i	$0.340557\pi$
$468$	23.8374	−	1.32440i	1.10189	−	0.0612204i
$469$	−17.1013	−	9.87344i	−0.789665	−	0.455913i
$470$	−20.0493	−	22.0366i	−0.924807	−	1.01647i
$471$	−6.86327	+	24.4061i	−0.316243	+	1.12457i
$472$	9.63568	−	14.7754i	0.443518	−	0.680091i
$473$	13.9664	+	11.7192i	0.642177	+	0.538851i
$474$	−0.187406	−	0.629040i	−0.00860783	−	0.0288928i
$475$	−7.31297	+	20.0922i	−0.335542	+	0.921894i
$476$	28.5550	−	2.29407i	1.30881	−	0.105148i
$477$	−10.0720	+	3.38702i	−0.461164	+	0.155081i
$478$	36.9714	−	1.48273i	1.69103	−	0.0678183i
$479$	−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	$0.997492\pi$
$480$	−26.8196	+	27.5565i	−1.22414	+	1.25778i
$481$	−35.8813	+	13.0597i	−1.63605	+	0.595473i
$482$	28.1011	+	21.7217i	1.27997	+	0.989396i
$483$	−3.85111	−	2.76797i	−0.175232	−	0.125947i
$484$	−4.85753	−	1.33861i	−0.220797	−	0.0608458i
$485$		−	21.1382i		−	0.959836i
$486$	5.24503	+	21.4124i	0.237919	+	0.971285i
$487$	0.153837			0.00697103			0.00348552	−	0.999994i	$-0.498891\pi$
$487$	0.153837			0.00697103			0.00348552	+	0.999994i	$0.498891\pi$
$488$	−6.76079	−	6.32889i	−0.306046	−	0.286495i
$489$	−6.00355	+	8.35280i	−0.271490	+	0.377727i
$490$	4.37702	−	5.66251i	0.197734	−	0.255806i
$491$	7.10851	+	19.5305i	0.320802	+	0.881398i	0.990345	+	0.138624i	$0.0442679\pi$
$491$	7.10851	+	19.5305i	0.320802	+	0.881398i	−0.669543	+	0.742774i	$0.733510\pi$
$492$	−1.64981	−	2.04561i	−0.0743792	−	0.0922232i
$493$	39.5197	−	6.96839i	1.77988	−	0.313840i
$494$	11.5569	−	0.463488i	0.519971	−	0.0208533i
$495$	−10.9288	−	32.4990i	−0.491215	−	1.46072i
$496$	−4.82535	−	5.91933i	−0.216665	−	0.265786i
$497$	−20.7626	−	7.55696i	−0.931329	−	0.338976i
$498$	−28.8935	+	8.60806i	−1.29475	+	0.385737i
$499$	12.0312	−	14.3382i	0.538588	−	0.641865i	−0.426282	−	0.904590i	$-0.640177\pi$
$499$	12.0312	−	14.3382i	0.538588	−	0.641865i	0.964871	+	0.262726i	$0.0846214\pi$
$500$	−42.2177	−	3.99581i	−1.88803	−	0.178698i
$501$	−33.1980	−	9.33565i	−1.48318	−	0.417086i
$502$	−27.7421	−	30.4918i	−1.23819	−	1.36091i
$503$	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	$-0.0714406\pi$
$504$	22.2266	+	10.1402i	0.990050	+	0.451679i
$505$	7.93717	+	13.7476i	0.353200	+	0.611760i
$506$	−1.19105	+	3.73128i	−0.0529485	+	0.165876i
$507$	2.12822	−	4.42081i	0.0945175	−	0.196335i
$508$	7.77589	+	5.52743i	0.344999	+	0.245240i
$509$	25.1247	+	4.43017i	1.11363	+	0.196364i	0.700044	−	0.714099i	$-0.253164\pi$
$509$	25.1247	+	4.43017i	1.11363	+	0.196364i	0.413590	+	0.910463i	$0.364275\pi$
$510$	−26.3338	+	39.9223i	−1.16608	+	1.76779i
$511$	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
$516$	11.2066	−	18.5675i	0.493341	−	0.817390i
$517$	15.3943	+	2.71443i	0.677041	+	0.119381i
$518$	−38.7210	−	5.23763i	−1.70130	−	0.230128i
$519$	15.7679	−	10.7535i	0.692133	−	0.472025i
$520$	12.8326	+	42.2640i	0.562745	+	1.85340i
$521$	−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	$0.956020\pi$
$522$	32.3354	+	11.2076i	1.41528	+	0.490543i
$523$	−35.9656	−	20.7647i	−1.57266	−	0.907978i	−0.995841	−	0.0911099i	$-0.970959\pi$
$523$	−35.9656	−	20.7647i	−1.57266	−	0.907978i	−0.576824	−	0.816869i	$-0.695708\pi$
$524$	6.78140	−	1.76556i	0.296247	−	0.0771290i
$525$	12.8076	+	50.2702i	0.558969	+	2.19397i
$526$	15.0119	−	6.15578i	0.654549	−	0.268405i
$527$	−7.27607	−	6.10535i	−0.316950	−	0.265953i
$528$	2.29105	−	20.0456i	0.0997053	−	0.872371i
$529$	20.7630	+	7.55712i	0.902739	+	0.328570i
$530$	−10.5040	−	16.6179i	−0.456266	−	0.721837i
$531$	14.6247	−	11.6692i	0.634657	−	0.506402i
$532$	10.6910	+	5.07801i	0.463513	+	0.220160i
$533$	−2.97279	+	0.524183i	−0.128766	+	0.0227049i
$534$	−20.0188	+	2.31272i	−0.866296	+	0.100081i
$535$	−17.9806	+	6.54441i	−0.777370	+	0.282939i
$536$	19.3704	+	1.05253i	0.836675	+	0.0454622i
$537$	3.01451	+	6.67843i	0.130086	+	0.288196i
$538$	20.9780	−	4.57263i	0.904425	−	0.197140i
$539$			3.75520i			0.161748i
$540$	−36.1862	+	18.8161i	−1.55720	+	0.809714i
$541$		−	11.2309i		−	0.482852i	−0.970419	−	0.241426i	$-0.922385\pi$
$541$		−	11.2309i		−	0.482852i	0.970419	−	0.241426i	$-0.0776152\pi$
$542$	−4.00003	−	18.3510i	−0.171816	−	0.788244i
$543$	−32.7720	−	3.27488i	−1.40638	−	0.140538i
$544$	−23.9996	+	14.6972i	−1.02898	+	0.630137i
$545$	−9.29398	+	3.38273i	−0.398110	+	0.144900i
$546$	22.5315	−	16.7273i	0.964259	−	0.715862i
$547$	−19.8704	+	3.50369i	−0.849599	+	0.149807i	−0.581462	−	0.813574i	$-0.697519\pi$
$547$	−19.8704	+	3.50369i	−0.849599	+	0.149807i	−0.268137	+	0.963381i	$0.586408\pi$
$548$	14.1782	−	29.8501i	0.605664	−	1.27513i
$549$	−4.70002	−	8.62515i	−0.200592	−	0.368113i
$550$	36.2144	−	22.8908i	1.54419	−	0.976066i
$551$	15.5798	+	5.67059i	0.663722	+	0.241575i
$552$	4.60405	+	0.714125i	0.195961	+	0.0303952i
$553$	−0.590998	−	0.495906i	−0.0251318	−	0.0210881i
$554$	−1.38068	−	3.36700i	−0.0586593	−	0.143050i
$555$	46.6915	−	45.5539i	1.98194	−	1.93366i
$556$	−38.4515	+	10.0110i	−1.63070	+	0.424560i
$557$	−26.7781	−	15.4604i	−1.13463	−	0.655076i	−0.189532	−	0.981875i	$-0.560697\pi$
$557$	−26.7781	−	15.4604i	−1.13463	−	0.655076i	−0.945094	+	0.326798i	$0.894030\pi$
$558$	−2.88746	−	7.56805i	−0.122236	−	0.320381i
$559$	−12.4556	−	21.5737i	−0.526814	−	0.912469i
$560$	−8.47984	+	44.3956i	−0.358339	+	1.87606i
$561$	−1.87861	−	25.0231i	−0.0793150	−	1.05648i
$562$	5.12963	−	37.9226i	0.216380	−	1.59967i
$563$	20.3052	+	3.58035i	0.855761	+	0.150894i	0.584282	−	0.811551i	$-0.301376\pi$
$563$	20.3052	+	3.58035i	0.855761	+	0.150894i	0.271479	+	0.962444i	$0.412487\pi$
$564$	0.361304	−	18.5910i	0.0152137	−	0.782820i
$565$	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	$0.311171\pi$
$570$	−17.6694	+	8.84434i	−0.740091	+	0.370449i
$571$	−7.54047	−	1.32959i	−0.315559	−	0.0556415i	0.0136257	−	0.999907i	$-0.495663\pi$
$571$	−7.54047	−	1.32959i	−0.315559	−	0.0556415i	−0.329184	+	0.944266i	$0.606774\pi$
$572$	−18.8892	−	13.4272i	−0.789796	−	0.561420i
$573$	14.0421	−	1.05421i	0.586617	−	0.0440404i
$574$	−2.94269	−	0.939324i	−0.122825	−	0.0392066i
$575$	4.94663	+	8.56781i	0.206289	+	0.357303i
$576$	−23.9795	+	0.990978i	−0.999147	+	0.0412907i
$577$	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	$0.0789352\pi$
$578$	−8.10657	+	7.37553i	−0.337189	+	0.306782i
$579$	−16.3520	+	15.9536i	−0.679567	+	0.663009i
$580$	−5.96592	+	63.0330i	−0.247722	+	2.61730i
$581$	−22.7783	+	27.1462i	−0.945005	+	1.12621i
$582$	9.06647	−	9.58418i	0.375817	−	0.397277i
$583$	9.69302	+	3.52797i	0.401444	+	0.146114i
$584$	−7.70061	+	18.0449i	−0.318654	+	0.746705i
$585$	−1.15535	+	46.8343i	−0.0477677	+	1.93636i
$586$	0.997434	+	24.8708i	0.0412036	+	1.02740i
$587$	−20.2706	+	3.57425i	−0.836657	+	0.147525i	−0.575532	−	0.817780i	$-0.695205\pi$
$587$	−20.2706	+	3.57425i	−0.836657	+	0.147525i	−0.261126	+	0.965305i	$0.584094\pi$
$588$	4.41330	−	0.690049i	0.182001	−	0.0284571i
$589$	−1.34217	−	3.68759i	−0.0553033	−	0.151945i
$590$	27.3865	+	21.1693i	1.12748	+	0.871526i
$591$	−10.6512	−	1.06436i	−0.438130	−	0.0437819i
$592$	36.2532	−	12.6150i	1.49000	−	0.518475i
$593$	35.4674			1.45647			0.728237	−	0.685326i	$-0.240340\pi$
$593$	35.4674			1.45647			0.728237	+	0.685326i	$0.240340\pi$
$594$	8.98409	−	19.4228i	0.368621	−	0.796926i
$595$			56.2142i			2.30456i
$596$	−6.11657	+	22.1958i	−0.250545	+	0.909175i
$597$	14.0095	−	6.32358i	0.573369	−	0.258807i
$598$	3.27294	−	4.23418i	0.133841	−	0.173148i
$599$	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	$0.354555\pi$
$600$	−33.5570	−	38.3545i	−1.36996	−	1.56582i
$601$	−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	$-0.313074\pi$
$602$	−1.02151	−	25.4710i	−0.0416334	−	1.03812i
$603$	19.1555	+	7.51201i	0.780071	+	0.305913i
$604$	7.26540	−	0.583692i	0.295625	−	0.0237501i
$605$	3.38165	−	9.29100i	0.137484	−	0.377733i
$606$	−2.29777	+	9.63760i	−0.0933406	+	0.391501i
$607$	−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	$0.778908\pi$
$608$	−11.6233	+	0.300914i	−0.471386	+	0.0122037i
$609$	38.9803	−	9.93120i	1.57956	−	0.402432i
$610$	13.4418	−	12.2296i	0.544241	−	0.495162i
$611$	−18.4970	−	10.6793i	−0.748309	−	0.432036i
$612$	−29.0631	+	6.80603i	−1.17481	+	0.275118i
$613$	−28.4795	+	16.4426i	−1.15028	+	0.664112i	−0.948954	−	0.315414i	$-0.897857\pi$
$613$	−28.4795	+	16.4426i	−1.15028	+	0.664112i	−0.201321	+	0.979525i	$0.564523\pi$
$614$	−5.06318	+	15.8618i	−0.204333	+	0.640129i
$615$	4.26048	−	2.90559i	0.171799	−	0.117165i
$616$	−10.7258	−	21.1510i	−0.432153	−	0.852197i
$617$	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	$-0.177735\pi$
$618$	0.166273	−	2.79049i	0.00668848	−	0.112250i
$619$	−22.6481	−	26.9910i	−0.910305	−	1.08486i	−0.996072	−	0.0885446i	$-0.971778\pi$
$619$	−22.6481	−	26.9910i	−0.910305	−	1.08486i	0.0857667	−	0.996315i	$-0.472666\pi$
$620$	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
$624$	−12.3093	+	24.6668i	−0.492765	+	0.987463i
$625$	5.41806	−	30.7273i	0.216722	−	1.22909i
$626$	1.33968	−	9.90405i	0.0535444	−	0.395846i
$627$	4.49705	−	9.34144i	0.179595	−	0.373061i
$628$	−20.5530	−	20.8469i	−0.820152	−	0.831882i
$629$	41.3448	−	23.8704i	1.64852	−	0.951775i
$630$	−23.3270	+	41.8818i	−0.929369	+	1.66861i
$631$	−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	$0.865825\pi$
$632$	0.738148	+	0.171911i	0.0293620	+	0.00683826i
$633$	8.28649	−	29.4672i	0.329358	−	1.17121i
$634$	−2.91001	−	7.09654i	−0.115571	−	0.281840i
$635$	−12.0336	+	14.3411i	−0.477539	+	0.569109i
$636$	2.36507	−	12.0400i	0.0937812	−	0.477417i
$637$	1.75488	−	4.82149i	0.0695308	−	0.191034i
$638$	−17.7499	−	28.0812i	−0.702724	−	1.11175i
$639$	22.5673	+	4.55574i	0.892747	+	0.180222i
$640$	−12.2956	−	42.6656i	−0.486026	−	1.68651i
$641$	−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	$-0.531725\pi$
$642$	−10.9595	−	4.74487i	−0.432537	−	0.187265i
$643$	15.1261	+	41.5587i	0.596517	+	1.63892i	0.758162	+	0.652067i	$0.226098\pi$
$643$	15.1261	+	41.5587i	0.596517	+	1.63892i	−0.161645	+	0.986849i	$0.551680\pi$
$644$	4.97956	−	2.27911i	0.196222	−	0.0898093i
$645$	34.5572	+	24.8379i	1.36069	+	0.977990i
$646$	−14.1293	+	3.07980i	−0.555908	+	0.121173i
$647$	2.96214			0.116454			0.0582268	−	0.998303i	$-0.481455\pi$
$647$	2.96214			0.116454			0.0582268	+	0.998303i	$0.481455\pi$
$648$	−24.4775	−	6.98944i	−0.961567	−	0.274571i
$649$	−18.1619			−0.712917
$650$	−57.1947	+	12.4669i	−2.24336	+	0.488992i
$651$	−7.73121	−	5.55678i	−0.303010	−	0.217787i
$652$	−4.94322	−	10.8003i	−0.193592	−	0.422973i
$653$	−0.829258	−	2.27837i	−0.0324514	−	0.0891594i	0.922409	−	0.386215i	$-0.126218\pi$
$653$	−0.829258	−	2.27837i	−0.0324514	−	0.0891594i	−0.954860	+	0.297055i	$0.903995\pi$
$654$	−5.66485	−	2.45257i	−0.221513	−	0.0959030i
$655$	2.38780	+	13.5419i	0.0932992	+	0.529126i
$656$	2.99563	−	0.484457i	0.116960	−	0.0189149i
$657$	−13.7651	+	15.6063i	−0.537029	+	0.608858i
$658$	−11.6777	−	18.4748i	−0.455246	−	0.720222i
$659$	14.7728	−	40.5879i	0.575466	−	1.58108i	−0.220272	−	0.975438i	$-0.570695\pi$
$659$	14.7728	−	40.5879i	0.575466	−	1.58108i	0.795738	−	0.605641i	$-0.207083\pi$
$660$	38.8492	+	7.63133i	1.51220	+	0.297049i
$661$	11.3612	−	13.5398i	0.441901	−	0.526637i	−0.498415	−	0.866938i	$-0.666085\pi$
$661$	11.3612	−	13.5398i	0.441901	−	0.526637i	0.940317	+	0.340301i	$0.110529\pi$
$662$	−2.91082	−	7.09850i	−0.113132	−	0.275891i
$663$	−9.28173	+	33.0063i	−0.360472	+	1.28186i
$664$	7.89635	−	33.9052i	0.306438	−	1.31578i
$665$	−11.6126	+	20.1137i	−0.450318	+	0.779974i
$666$	40.7089	−	0.627756i	1.57744	−	0.0243251i
$667$	6.64362	−	3.83570i	0.257242	−	0.148519i
$668$	28.3567	−	27.9568i	1.09715	−	1.08168i
$669$	17.5260	−	36.4057i	0.677595	−	1.40753i
$670$	−5.10267	+	37.7233i	−0.197133	+	1.45738i
$671$	−1.65574	+	9.39015i	−0.0639190	+	0.362503i
$672$	−22.8867	+	16.4921i	−0.882874	+	0.636197i
$673$	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	0.844118	−	0.536158i	$-0.180125\pi$
$677$	4.41092	+	5.25673i	0.169526	+	0.202033i	−0.674592	+	0.738191i	$0.735680\pi$
$678$	−1.05372	+	17.6842i	−0.0404680	+	0.679159i
$679$	2.69280	−	15.2717i	0.103340	−	0.586072i
$680$	−24.9764	−	49.2530i	−0.957803	−	1.88877i
$681$	−35.5098	+	24.2172i	−1.36074	+	0.928005i
$682$	−2.39106	+	7.49065i	−0.0915584	+	0.286832i
$683$	−4.11971	+	2.37852i	−0.157636	+	0.0910113i	−0.576743	−	0.816926i	$-0.695677\pi$
$683$	−4.11971	+	2.37852i	−0.157636	+	0.0910113i	0.419107	+	0.907937i	$0.362343\pi$
$684$	−11.8049	−	3.56859i	−0.451371	−	0.136448i
$685$	56.1590	+	32.4234i	2.14573	+	1.23884i
$686$	−17.1986	+	15.6476i	−0.656645	+	0.597429i
$687$	9.35400	−	2.38316i	0.356877	−	0.0909233i
$688$	12.2120	+	21.8629i	0.465577	+	0.833517i
$689$	−10.7966	−	9.05946i	−0.411320	−	0.345138i
$690$	−2.12033	+	8.89333i	−0.0807194	+	0.338563i
$691$	−4.35017	+	11.9520i	−0.165488	+	0.454675i	−0.994523	−	0.104523i	$-0.966669\pi$
$691$	−4.35017	+	11.9520i	−0.165488	+	0.454675i	0.829034	+	0.559198i	$0.188891\pi$
$692$	1.76484	+	21.9675i	0.0670890	+	0.835078i
$693$	−3.75566	−	24.8717i	−0.142666	−	0.944798i
$694$	0.985395	+	24.5706i	0.0374051	+	0.932686i
$695$	−13.5392	−	76.7844i	−0.513570	−	2.91260i
$696$	−29.7407	+	26.0207i	−1.12732	+	0.986311i
$697$	3.54655	−	1.29084i	0.134335	−	0.0488939i
$698$	4.55436	−	5.89193i	0.172385	−	0.223013i
$699$	−10.5005	+	4.73969i	−0.397164	+	0.179272i
$700$	−57.7487	−	15.9140i	−2.18270	−	0.601493i
$701$			12.2688i			0.463386i	0.972789	+	0.231693i	$0.0744265\pi$
$701$			12.2688i			0.463386i	−0.972789	+	0.231693i	$0.925573\pi$
$702$	−20.6117	+	20.7394i	−0.777940	+	0.782759i
$703$	19.7244			0.743921
$704$	18.7951	+	13.7662i	0.708367	+	0.518834i
$705$	36.3072	+	3.62815i	1.36741	+	0.136644i
$706$	10.5462	+	8.15200i	0.396910	+	0.306805i
$707$	3.98304	+	10.9433i	0.149797	+	0.411565i
$708$	3.33740	+	21.3447i	0.125427	+	0.802185i
$709$	25.9792	−	4.58083i	0.975668	−	0.172037i	0.336988	−	0.941509i	$-0.390592\pi$
$709$	25.9792	−	4.58083i	0.975668	−	0.172037i	0.638680	+	0.769473i	$0.279481\pi$
$710$	1.70683	+	42.5593i	0.0640561	+	1.59722i
$711$	0.686054	+	0.418985i	0.0257290	+	0.0157132i
$712$	9.13326	−	21.4021i	0.342284	−	0.802077i
$713$	−1.70624	−	0.621021i	−0.0638993	−	0.0232574i
$714$	−24.1111	+	25.4878i	−0.902334	+	0.953859i
$715$	29.2320	−	34.8373i	1.09321	−	1.30284i
$716$	−8.42314	−	0.797231i	−0.314788	−	0.0297939i
$717$	−32.4366	+	31.6463i	−1.21137	+	1.18185i
$718$	−16.9958	+	15.4631i	−0.634277	+	0.577079i
$719$	−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	$0.964016\pi$
$720$	1.82985	−	47.0598i	0.0681945	−	1.75382i
$721$	−1.64289	−	2.84557i	−0.0611845	−	0.105975i
$722$	19.9059	+	6.35407i	0.740819	+	0.236474i
$723$	−43.3780	+	3.25661i	−1.61325	+	0.121115i
$724$	22.0340	−	30.9970i	0.818886	−	1.15199i
$725$	−82.6364	−	14.5710i	−3.06904	−	0.541154i
$726$	5.51830	−	2.76216i	0.204803	−	0.102513i
$727$	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
$732$	11.3400	+	0.220387i	0.419139	+	0.00814572i
$733$	0.103428	+	0.0182371i	0.00382018	+	0.000673601i	0.175558	−	0.984469i	$-0.443827\pi$
$733$	0.103428	+	0.0182371i	0.00382018	+	0.000673601i	−0.171738	+	0.985143i	$0.554938\pi$
$734$	2.42718	−	17.9438i	0.0895887	−	0.662316i
$735$	0.656222	+	8.74087i	0.0242051	+	0.322412i
$736$	−3.35030	+	4.20934i	−0.123494	+	0.155158i
$737$	−9.98667	−	17.2974i	−0.367864	−	0.637158i
$738$	3.17797	+	0.509970i	0.116983	+	0.0187722i
$739$	−26.3545	−	15.2158i	−0.969466	−	0.559722i	−0.0703928	−	0.997519i	$-0.522425\pi$
$739$	−26.3545	−	15.2158i	−0.969466	−	0.559722i	−0.899074	+	0.437798i	$0.855759\pi$
$740$	18.9782	+	72.8938i	0.697651	+	2.67963i
$741$	−10.1394	+	9.89237i	−0.372481	+	0.363405i
$742$	−5.47186	−	13.3440i	−0.200878	−	0.489875i
$743$	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	$0.622116\pi$
$744$	9.24275	+	1.43362i	0.338856	+	0.0525592i
$745$	−42.4539	−	15.4520i	−1.55539	−	0.566116i
$746$	−7.56506	+	4.78180i	−0.276976	+	0.175074i
$747$	19.2451	−	31.5123i	0.704143	−	1.15298i
$748$	26.1731	+	12.4317i	0.956983	+	0.454548i
$749$	−13.8241	+	2.43756i	−0.505122	+	0.0890666i
$750$	41.7013	−	30.9589i	1.52272	−	1.13046i
$751$	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	$0.296855\pi$
$752$	18.4401	+	10.9985i	0.672443	+	0.401073i
$753$	50.2379	+	5.02023i	1.83077	+	0.182947i
$754$	9.66704	+	44.3497i	0.352053	+	1.61512i
$755$			14.3029i			0.520536i
$756$	−28.5403	+	8.98421i	−1.03800	+	0.326753i
$757$			27.3201i			0.992967i	0.868046	+	0.496484i	$0.165376\pi$
$757$			27.3201i			0.992967i	−0.868046	+	0.496484i	$0.834624\pi$
$758$	39.3895	−	8.58585i	1.43069	−	0.311852i
$759$	−1.97355	−	4.37226i	−0.0716353	−	0.158703i
$760$	1.23793	−	22.7825i	0.0449043	−	0.826408i
$761$	−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	$0.477083\pi$
$762$	−11.6072	+	1.34095i	−0.420485	+	0.0485776i
$763$	−7.14552	+	1.25995i	−0.258685	+	0.0456132i
$764$	−6.97625	+	14.6874i	−0.252392	+	0.531373i
$765$	−8.74558	−	57.9172i	−0.316197	−	2.09400i
$766$	23.7543	+	37.5805i	0.858277	+	1.35784i
$767$	23.3189	+	8.48740i	0.841998	+	0.306462i
$768$	12.7250	−	24.6186i	0.459173	−	0.888347i
$769$	−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	$0.808846\pi$
$770$	43.0569	−	17.6559i	1.55166	−	0.636276i
$771$	−3.02906	−	11.8892i	−0.109089	−	0.428178i
$772$	−6.64642	−	25.5284i	−0.239210	−	0.918788i
$773$	−27.9615	−	16.1436i	−1.00571	−	0.580644i	−0.0957742	−	0.995403i	$-0.530533\pi$
$773$	−27.9615	−	16.1436i	−1.00571	−	0.580644i	−0.909931	+	0.414759i	$0.863866\pi$
$774$	5.01512	+	26.0837i	0.180265	+	0.937559i
$775$	9.93049	+	17.2001i	0.356714	+	0.617846i
$776$	4.42598	+	14.5769i	0.158883	+	0.523282i
$777$	39.5362	−	26.9631i	1.41835	−	0.967297i
$778$	−5.50780	−	0.745017i	−0.197464	−	0.0267102i
$779$	1.53563	+	0.270772i	0.0550195	+	0.00970143i
$780$	−46.3142	−	27.9532i	−1.65831	−	1.00089i
$781$	−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
$786$	−4.72567	+	7.16415i	−0.168559	+	0.255537i
$787$	39.6718	+	6.99522i	1.41415	+	0.249353i	0.827944	−	0.560811i	$-0.189510\pi$
$787$	39.6718	+	6.99522i	1.41415	+	0.249353i	0.586204	+	0.810163i	$0.300622\pi$
$788$	7.16120	−	10.0743i	0.255107	−	0.358881i
$789$	−8.61949	+	17.9047i	−0.306862	+	0.637425i
$790$	−0.452254	+	1.41681i	−0.0160905	+	0.0504078i
$791$	10.4115	+	18.0333i	0.370191	+	0.641189i
$792$	14.3413	+	20.1231i	0.509595	+	0.715042i
$793$	6.51408	−	11.2827i	0.231322	−	0.400661i
$794$	−19.7769	−	21.7371i	−0.701856	−	0.771422i
$795$	23.1787	+	6.51809i	0.822062	+	0.231173i
$796$	−1.67236	+	17.6694i	−0.0592754	+	0.626274i
$797$	2.35451	−	2.80599i	0.0834009	−	0.0993934i	−0.722730	−	0.691130i	$-0.757113\pi$
$797$	2.35451	−	2.80599i	0.0834009	−	0.0993934i	0.806131	+	0.591737i	$0.201558\pi$
$798$	−13.8923	+	4.13883i	−0.491781	+	0.146513i
$799$	25.0936	+	9.13334i	0.887749	+	0.323114i
$800$	57.6682	−	11.7149i	2.03888	−	0.414184i
$801$	16.3260	−	18.5097i	0.576852	−	0.654008i
$802$	32.7434	−	1.31316i	1.15621	−	0.0463695i
$803$	19.8933	−	3.50773i	0.702020	−	0.123785i
$804$	−18.4936	+	14.9154i	−0.652220	+	0.526024i
$805$	3.67544	+	10.0982i	0.129542	+	0.355915i
$806$	6.57052	−	8.50022i	0.231437	−	0.299407i
$807$	−15.3472	+	21.3527i	−0.540248	+	0.751652i
$808$	−8.35200	−	7.81846i	−0.293822	−	0.275052i
$809$	−41.2691			−1.45094			−0.725472	−	0.688252i	$-0.758378\pi$
$809$	−41.2691			−1.45094			−0.725472	+	0.688252i	$0.758378\pi$
$810$	17.5179	−	46.7798i	0.615515	−	1.64367i
$811$		−	25.6578i		−	0.900966i	−0.892785	−	0.450483i	$-0.851252\pi$
$811$		−	25.6578i		−	0.900966i	0.892785	−	0.450483i	$-0.148748\pi$
$812$	−12.3400	+	44.7793i	−0.433049	+	1.57144i
$813$	18.6789	+	13.4254i	0.655097	+	0.470849i
$814$	−31.2691	−	24.1705i	−1.09598	−	0.847174i
$815$	21.9023	−	7.97178i	0.767204	−	0.279239i
$816$	9.80084	−	33.0443i	0.343098	−	1.15678i
$817$	2.23452	+	12.6726i	0.0781761	+	0.443359i
$818$	−41.2654	+	1.65494i	−1.44281	+	0.0578635i
$819$	−6.80094	+	33.6891i	−0.237644	+	1.17719i
$820$	0.476858	+	5.93561i	0.0166526	+	0.207280i
$821$	−8.61194	+	23.6611i	−0.300559	+	0.825778i	0.693844	+	0.720125i	$0.255916\pi$
$821$	−8.61194	+	23.6611i	−0.300559	+	0.825778i	−0.994403	+	0.105653i	$0.966307\pi$
$822$	11.5560	+	38.7884i	0.403061	+	1.35290i
$823$	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	$0.646246\pi$
$824$	2.70376	+	1.76324i	0.0941898	+	0.0614255i
$825$	−14.2045	+	50.5117i	−0.494536	+	1.75859i
$826$	17.0891	+	18.7829i	0.594605	+	0.653541i
$827$	9.62668	+	5.55796i	0.334752	+	0.193269i	0.657949	−	0.753062i	$-0.271424\pi$
$827$	9.62668	+	5.55796i	0.334752	+	0.193269i	−0.323197	+	0.946332i	$0.604758\pi$
$828$	−4.77584	+	3.12285i	−0.165972	+	0.108527i
$829$	−26.4493	+	15.2705i	−0.918621	+	0.530366i	−0.883195	−	0.469006i	$-0.844612\pi$
$829$	−26.4493	+	15.2705i	−0.918621	+	0.530366i	−0.0354262	+	0.999372i	$0.511279\pi$
$830$	65.0779	+	20.7733i	2.25889	+	0.721050i
$831$	4.01584	+	1.93326i	0.139308	+	0.0670640i
$832$	−17.6987	−	26.4584i	−0.613593	−	0.917281i
$833$	−1.11397	+	6.31762i	−0.0385967	+	0.218893i
$834$	26.7952	−	40.6217i	0.927841	−	1.40661i
$835$	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	$0.304148\pi$
$840$	−28.6622	−	47.3582i	−0.988939	−	1.63401i
$841$	−6.26281	+	35.5181i	−0.215959	+	1.22476i
$842$	6.12735	+	0.828821i	0.211162	+	0.0285631i
$843$	26.4072	+	38.7210i	0.909512	+	1.33362i
$844$	24.8150	+	25.1699i	0.854167	+	0.866383i
$845$	−9.62790	+	5.55867i	−0.331210	+	0.191224i
$846$	14.9058	+	17.2177i	0.512470	+	0.591957i
$847$	3.62672	−	6.28165i	0.124615	−	0.215840i
$848$	10.7231	+	9.26039i	0.368233	+	0.318003i
$849$	−44.8719	+	11.4322i	−1.54000	+	0.392353i
$850$	67.7163	−	27.7678i	2.32265	−	0.952427i
$851$	5.86637	−	6.99127i	0.201097	−	0.239657i
$852$	−17.4804	+	20.0287i	−0.598869	+	0.686173i
$853$	7.52367	−	20.6711i	0.257605	−	0.707765i	−0.741708	−	0.670723i	$-0.765984\pi$
$853$	7.52367	−	20.6711i	0.257605	−	0.707765i	0.999314	−	0.0370424i	$-0.0117937\pi$
$854$	11.2692	−	7.12313i	0.385623	−	0.243749i
$855$	8.83523	−	22.5296i	0.302159	−	0.770498i
$856$	11.0292	−	8.27787i	0.376970	−	0.282932i
$857$	−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	$0.993021\pi$
$858$	28.1962	−	3.25744i	0.962602	−	0.111207i
$859$	−7.12897	−	19.5867i	−0.243237	−	0.668289i	−0.999895	−	0.0144780i	$-0.995391\pi$
$859$	−7.12897	−	19.5867i	−0.243237	−	0.668289i	0.756658	−	0.653811i	$-0.226831\pi$
$860$	−44.6831	+	20.4511i	−1.52368	+	0.697377i
$861$	3.44820	−	1.55645i	0.117514	−	0.0530436i
$862$	−0.348940	−	1.60084i	−0.0118849	−	0.0545248i
$863$	−21.4666			−0.730731			−0.365365	−	0.930864i	$-0.619056\pi$
$863$	−21.4666			−0.730731			−0.365365	+	0.930864i	$0.619056\pi$
$864$	21.0143	−	20.5524i	0.714921	−	0.699205i
$865$	−43.2459			−1.47040
$866$	−11.3698	−	52.1615i	−0.386361	−	1.77252i
$867$	1.33468	−	13.3563i	0.0453282	−	0.453604i
$868$	9.99660	−	4.57536i	0.339307	−	0.155298i
$869$	−0.266892	−	0.733280i	−0.00905370	−	0.0248748i
$870$	−46.2230	−	62.2620i	−1.56711	−	2.11088i
$871$	4.73896	+	26.8760i	0.160573	+	0.910657i
$872$	5.70086	−	4.27874i	0.193055	−	0.144896i
$873$	−0.398481	+	16.1532i	−0.0134866	+	0.546705i
$874$	−2.33678	+	1.47706i	−0.0790429	+	0.0499623i
$875$	20.8794	−	57.3655i	0.705851	−	1.93931i
$876$	−7.77801	−	22.7350i	−0.262795	−	0.768145i
$877$	0.176559	−	0.210415i	0.00596198	−	0.00710521i	−0.763055	−	0.646333i	$-0.776302\pi$
$877$	0.176559	−	0.210415i	0.00596198	−	0.00710521i	0.769017	+	0.639228i	$0.220746\pi$
$878$	−35.4128	+	14.5214i	−1.19512	+	0.490073i
$879$	−21.2886	−	21.8202i	−0.718045	−	0.735977i
$880$	−29.8803	+	34.6001i	−1.00727	+	1.16637i
$881$	−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	$0.298269\pi$
$882$	−3.45155	+	4.24463i	−0.116220	+	0.142924i
$883$	4.93626	−	2.84995i	0.166118	−	0.0959085i	−0.414636	−	0.909987i	$-0.636091\pi$
$883$	4.93626	−	2.84995i	0.166118	−	0.0959085i	0.580754	+	0.814079i	$0.302758\pi$
$884$	−27.7953	−	28.1929i	−0.934859	−	0.948229i
$885$	−42.2749	+	3.17379i	−1.42106	+	0.106686i
$886$	42.4566	+	5.74292i	1.42636	+	0.192937i
$887$	−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	$0.962519\pi$
$888$	−22.6604	+	41.1905i	−0.760432	+	1.38226i
$889$	−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
$894$	−12.6213	−	25.2151i	−0.422119	−	0.843319i
$895$	2.88302	−	16.3504i	0.0963689	−	0.546535i
$896$	−3.44797	−	32.3908i	−0.115188	−	1.08210i
$897$	0.490694	+	6.53604i	0.0163838	+	0.218232i
$898$	4.59232	+	1.46590i	0.153248	+	0.0489177i
$899$	13.3372	−	7.70026i	0.444822	−	0.256818i
$900$	61.9741	+	7.41183i	2.06580	+	0.247061i
$901$	15.2606	+	8.81073i	0.508405	+	0.293528i
$902$	−2.10262	−	2.31102i	−0.0700096	−	0.0769487i
$903$	21.8023	+	22.3468i	0.725536	+	0.743655i
$904$	−17.1346	−	11.1742i	−0.569887	−	0.371649i
$905$	57.1678	+	47.9695i	1.90032	+	1.59456i
$906$	−6.13471	+	6.48502i	−0.203812	+	0.215450i
$907$	−14.9621	+	41.1081i	−0.496809	+	1.36497i	0.397533	+	0.917588i	$0.369866\pi$
$907$	−14.9621	+	41.1081i	−0.496809	+	1.36497i	−0.894342	+	0.447383i	$0.852356\pi$
$908$	−3.97447	−	49.4715i	−0.131897	−	1.64177i
$909$	−5.80622	−	10.6552i	−0.192580	−	0.353410i
$910$	−63.5338	+	2.54800i	−2.10613	+	0.0844655i
$911$	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	$0.930828\pi$
$912$	10.3330	−	9.79875i	0.342160	−	0.324469i
$913$	−33.6816	+	12.2591i	−1.11470	+	0.405717i
$914$	−10.6298	−	8.21664i	−0.351602	−	0.271782i
$915$	−2.21308	+	22.1465i	−0.0731622	+	0.732141i
$916$	−2.96119	+	10.7456i	−0.0978405	+	0.355043i
$917$			10.0878i			0.333127i
$918$	20.8762	−	30.0111i	0.689018	−	0.990514i
$919$	−59.9068			−1.97614			−0.988071	−	0.153998i	$-0.950785\pi$
$919$	−59.9068			−1.97614			−0.988071	+	0.153998i	$0.950785\pi$
$920$	−7.70701	−	7.21467i	−0.254093	−	0.237861i
$921$	−8.38961	−	18.5866i	−0.276447	−	0.612449i
$922$	−26.7607	+	34.6201i	−0.881317	+	1.14015i
$923$	10.4439	+	28.6943i	0.343764	+	0.944483i
$924$	27.0951	+	10.4624i	0.891364	+	0.344188i
$925$	−98.3103	+	17.3348i	−3.23242	+	0.569963i
$926$	34.7552	−	1.39385i	1.14213	−	0.0458047i
$927$	2.13537	+	2.67618i	0.0701346	+	0.0878974i
$928$	−9.08392	−	44.7168i	−0.298194	−	1.46790i
$929$	−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	$0.787629\pi$
$930$	−4.25661	+	17.8536i	−0.139580	+	0.585442i
$931$	−1.70366	+	2.03035i	−0.0558354	+	0.0665420i
$932$	1.25348	−	13.2437i	0.0410592	−	0.433811i
$933$	14.5415	+	57.0758i	0.476066	+	1.86858i
$934$	0.933444	+	1.02596i	0.0305432	+	0.0335706i
$935$	−28.4294	+	49.2412i	−0.929741	+	1.61036i
$936$	−9.00958	−	32.5390i	−0.294487	−	1.06357i
$937$	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	$0.744754\pi$
$938$	−8.49210	+	26.6038i	−0.277277	+	0.868645i
$939$	6.89663	+	10.1126i	0.225063	+	0.330011i
$940$	−24.4108	+	34.3407i	−0.796193	+	1.12007i
$941$	−20.4427	−	3.60459i	−0.666412	−	0.117506i	−0.169799	−	0.985479i	$-0.554312\pi$
$941$	−20.4427	−	3.60459i	−0.666412	−	0.117506i	−0.496613	+	0.867972i	$0.665423\pi$
$942$	35.7908	+	2.13261i	1.16613	+	0.0694842i
$943$	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	0.539702	−	0.841856i	$-0.318537\pi$
$947$	−11.7887	−	14.0493i	−0.383082	−	0.456540i	−0.922785	+	0.385316i	$0.874092\pi$
$948$	−0.812743	+	0.448411i	−0.0263967	+	0.0145637i
$949$	−27.1812	−	4.79278i	−0.882340	−	0.155580i
$950$	29.9654	+	4.05329i	0.972205	+	0.131506i
$951$	8.46407	+	4.07468i	0.274466	+	0.132130i
$952$	−11.7703	−	38.7654i	−0.381477	−	1.25639i
$953$	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	$0.815431\pi$
$954$	7.71364	+	12.8970i	0.249738	+	0.417556i
$955$	−27.6325	−	15.9536i	−0.894166	−	0.516247i
$956$	−13.1841	−	50.6393i	−0.426406	−	1.63779i
$957$	39.1676	+	11.0144i	1.26611	+	0.356044i
$958$	−9.50091	+	3.89595i	−0.306960	+	0.125872i
$959$	36.4426	+	30.5790i	1.17679	+	0.987447i
$960$	46.1545	+	28.7588i	1.48963	+	0.928186i
$961$	25.7051	+	9.35591i	0.829198	+	0.301803i
$962$	28.8526	+	45.6463i	0.930245	+	1.47169i
$963$	13.8637	−	4.66211i	0.446751	−	0.150234i
$964$	21.5506	−	45.3716i	0.694099	−	1.46132i
$965$	50.9782	−	8.98883i	1.64105	−	0.289361i
$966$	−2.66479	+	6.15503i	−0.0857382	+	0.198035i
$967$	−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	$0.554502\pi$
$968$	−0.386614	+	7.11516i	−0.0124262	+	0.228690i
$969$	10.3368	−	14.3817i	0.332065	−	0.462006i
$970$	−29.2081	+	6.36658i	−0.937816	+	0.204419i
$971$		−	0.278968i		−	0.00895249i	−0.999990	−	0.00447625i	$-0.998575\pi$
$971$		−	0.278968i		−	0.00895249i	0.999990	−	0.00447625i	$-0.00142484\pi$
$972$	28.0072	−	13.6966i	0.898332	−	0.439318i
$973$		−	57.1990i		−	1.83372i
$974$	−0.0463340	−	0.212568i	−0.00148464	−	0.00681110i
$975$	41.8429	−	58.2165i	1.34005	−	1.86442i
$976$	−6.70879	+	11.2480i	−0.214743	+	0.360041i
$977$	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	$0.277591\pi$
$978$	13.3498	+	5.77975i	0.426881	+	0.184816i
$979$	−23.5943	+	4.16032i	−0.754078	+	0.132964i
$980$	−9.14259	−	4.34255i	−0.292049	−	0.138718i
$981$	7.16598	−	2.40979i	0.228792	−	0.0769387i
$982$	24.8456	−	15.7047i	0.792855	−	0.501156i
$983$	−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	$0.641027\pi$
$984$	−2.32966	+	2.89577i	−0.0742667	+	0.0923138i
$985$	18.5800	+	15.5905i	0.592008	+	0.496753i
$986$	−21.5316	−	52.5083i	−0.685705	−	1.67220i
$987$	25.7686	+	7.24641i	0.820223	+	0.230656i
$988$	−4.12125	−	15.8294i	−0.131114	−	0.503601i
$989$	5.15636	+	2.97702i	0.163963	+	0.0946639i
$990$	−41.6145	+	24.8894i	−1.32260	+	0.791039i
$991$	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	$0.645044\pi$
$992$	−6.72581	+	8.45035i	−0.213545	+	0.268299i
$993$	8.46642	+	4.07581i	0.268674	+	0.129342i
$994$	−4.18853	+	30.9652i	−0.132852	+	0.982155i
$995$	−34.2986	−	6.04777i	−1.08734	−	0.191727i
$996$	20.5968	+	37.3315i	0.652633	+	1.18290i
$997$	16.1819	+	19.2848i	0.512485	+	0.610756i	0.958787	−	0.284127i	$-0.0917036\pi$
$997$	16.1819	+	19.2848i	0.512485	+	0.610756i	−0.446302	+	0.894883i	$0.647259\pi$
$998$	−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.157.17	✓	204
3.2	odd	2		648.2.t.a.37.18		204
4.3	odd	2		864.2.bf.a.49.7		204
8.3	odd	2		864.2.bf.a.49.28		204
8.5	even	2	inner	216.2.t.a.157.31	yes	204
24.5	odd	2		648.2.t.a.37.4		204
27.11	odd	18		648.2.t.a.613.4		204
27.16	even	9	inner	216.2.t.a.205.31	yes	204
108.43	odd	18		864.2.bf.a.529.28		204
216.43	odd	18		864.2.bf.a.529.7		204
216.173	odd	18		648.2.t.a.613.18		204
216.205	even	18	inner	216.2.t.a.205.17	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.17	✓	204	1.1	even	1	trivial
216.2.t.a.157.31	yes	204	8.5	even	2	inner
216.2.t.a.205.17	yes	204	216.205	even	18	inner
216.2.t.a.205.31	yes	204	27.16	even	9	inner
648.2.t.a.37.4		204	24.5	odd	2
648.2.t.a.37.18		204	3.2	odd	2
648.2.t.a.613.4		204	27.11	odd	18
648.2.t.a.613.18		204	216.173	odd	18
864.2.bf.a.49.7		204	4.3	odd	2
864.2.bf.a.49.28		204	8.3	odd	2
864.2.bf.a.529.7		204	216.43	odd	18
864.2.bf.a.529.28		204	108.43	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+(-0.301188 - 1.38177i) q^{2} +(1.40645 + 1.01088i) q^{3} +(-1.81857 + 0.832346i) q^{4} +(-1.34230 - 3.68793i) q^{5} +(0.973201 - 2.24786i) q^{6} +(-0.499959 - 2.83541i) q^{7} +(1.69784 + 2.26215i) q^{8} +(0.956226 + 2.84352i) q^{9} +(-4.69159 + 2.96551i) q^{10} +(0.996019 - 2.73654i) q^{11} +(-3.39914 - 0.667709i) q^{12} +(-2.55767 + 3.04812i) q^{13} +(-3.76729 + 1.54482i) q^{14} +(1.84019 - 6.54382i) q^{15} +(2.61440 - 3.02736i) q^{16} +(2.48745 - 4.30839i) q^{17} +(3.64109 - 2.17772i) q^{18} +(1.78004 - 1.02771i) q^{19} +(5.51070 + 5.58951i) q^{20} +(2.16310 - 4.49327i) q^{21} +(-4.08125 - 0.552054i) q^{22} +(0.165146 - 0.936587i) q^{23} +(0.101163 + 4.89793i) 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} +(-9.59629 - 0.571800i) q^{30} +(0.331534 - 1.88022i) q^{31} +(-4.97054 - 2.70069i) q^{32} +(4.16718 - 2.84196i) q^{33} +(-6.70240 - 2.13945i) q^{34} +(-9.78570 + 5.64977i) q^{35} +(-4.10576 - 4.37524i) q^{36} +(8.31066 + 4.79816i) q^{37} +(-1.95618 - 2.15007i) q^{38} +(-6.67855 + 1.70152i) q^{39} +(6.06366 - 9.29801i) q^{40} +(0.581151 + 0.487644i) q^{41} +(-6.86016 - 1.63558i) q^{42} +(-2.14125 + 5.88303i) q^{43} +(0.466416 + 5.80562i) q^{44} +(9.20319 - 7.34336i) q^{45} +(-1.34389 + 0.0538962i) q^{46} +(0.932102 + 5.28621i) q^{47} +(6.73735 - 1.61498i) q^{48} +(-1.21172 + 0.441031i) q^{49} +(11.6396 + 8.99718i) q^{50} +(7.85378 - 3.54503i) q^{51} +(2.11423 - 7.67209i) q^{52} +3.54207i q^{53} +(7.32245 + 0.617856i) q^{54} -11.4291 q^{55} +(5.56527 - 5.94505i) q^{56} +(3.54244 + 0.353992i) q^{57} +(6.97656 - 9.02551i) q^{58} +(-2.13303 - 5.86045i) q^{59} +(2.10020 + 13.4321i) q^{60} +(-3.22446 + 0.568559i) q^{61} +(-2.69789 + 0.108198i) q^{62} +(7.58447 - 4.13293i) q^{63} +(-2.23467 + 7.68155i) q^{64} +(14.6744 + 5.34105i) q^{65} +(-5.18203 - 4.90211i) q^{66} +(4.40861 - 5.25398i) q^{67} +(-0.937536 + 9.90554i) q^{68} +(1.17905 - 1.15032i) q^{69} +(10.7540 + 11.8199i) q^{70} +(3.83709 - 6.64603i) q^{71} +(-4.80896 + 6.99098i) q^{72} +(3.46824 + 6.00718i) q^{73} +(4.12688 - 12.9286i) q^{74} +(-17.9673 + 1.34890i) q^{75} +(-2.38172 + 3.35057i) q^{76} +(-8.25717 - 1.45596i) q^{77} +(4.36261 + 8.71573i) 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} +(-0.193796 + 9.97178i) q^{84} +(-19.2280 - 3.39041i) q^{85} +(8.77391 + 1.18681i) q^{86} +(1.04596 + 13.9321i) q^{87} +(7.88155 - 2.39307i) q^{88} +(-4.11349 - 7.12477i) q^{89} +(-12.9187 - 10.5049i) q^{90} +(9.92138 + 5.72811i) q^{91} +(0.479235 + 1.84071i) q^{92} +(2.36698 - 2.30931i) q^{93} +(7.02358 - 2.88009i) q^{94} +(-6.17946 - 5.18518i) q^{95} +(-4.26075 - 8.82304i) q^{96} +(5.06123 + 1.84214i) q^{97} +(0.974360 + 1.54149i) 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

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