LMFDB - Embedded newform 216.2.t.a.205.17

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			205.17
Character	$\chi$	$=$	216.205
Dual form			216.2.t.a.157.17

$q$-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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{9}\right)$

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	0.150386	+	0.988627i	$0.451948\pi$
$5$	−1.34230	+	3.68793i	−0.600294	+	1.64929i	−0.750679	+	0.660667i	$0.770274\pi$
$6$	0.973201	+	2.24786i	0.397308	+	0.917686i
$7$	−0.499959	+	2.83541i	−0.188967	+	1.07168i	0.731786	+	0.681535i	$0.238687\pi$
$7$	−0.499959	+	2.83541i	−0.188967	+	1.07168i	−0.920752	+	0.390148i	$0.872424\pi$
$8$	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	0.994446	+	0.105252i	$0.0335650\pi$
$11$	0.996019	+	2.73654i	0.300311	+	0.825098i	−0.694135	+	0.719845i	$0.744213\pi$
$12$	−3.39914	+	0.667709i	−0.981248	+	0.192751i
$13$	−2.55767	−	3.04812i	−0.709371	−	0.845396i	0.284181	−	0.958771i	$-0.408278\pi$
$13$	−2.55767	−	3.04812i	−0.709371	−	0.845396i	−0.993552	+	0.113375i	$0.963834\pi$
$14$	−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	0.992318	+	0.123711i	$0.0394795\pi$
$17$	2.48745	+	4.30839i	0.603296	+	1.04494i	−0.389022	+	0.921228i	$0.627187\pi$
$18$	3.64109	+	2.17772i	0.858213	+	0.513294i
$19$	1.78004	+	1.02771i	0.408369	+	0.235772i	0.690089	−	0.723725i	$-0.257571\pi$
$19$	1.78004	+	1.02771i	0.408369	+	0.235772i	−0.281720	+	0.959497i	$0.590905\pi$
$20$	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	0.997173	−	0.0751465i	$-0.0239424\pi$
$23$	0.165146	+	0.936587i	0.0344352	+	0.195292i	−0.962737	+	0.270438i	$0.912831\pi$
$24$	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	−0.0261974	−	0.999657i	$-0.508340\pi$
$29$	5.18495	−	6.17919i	0.962821	−	1.14745i	0.989019	−	0.147789i	$-0.0472157\pi$
$30$	−9.59629	+	0.571800i	−1.75203	+	0.104396i
$31$	0.331534	+	1.88022i	0.0595453	+	0.337698i	0.999998	−	0.00222778i	$-0.000709125\pi$
$31$	0.331534	+	1.88022i	0.0595453	+	0.337698i	−0.940452	+	0.339926i	$0.889598\pi$
$32$	−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	0.375816	−	0.926694i	$-0.377363\pi$
$37$	8.31066	−	4.79816i	1.36626	−	0.788813i	0.990449	+	0.137881i	$0.0440293\pi$
$38$	−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	−0.596278	−	0.802778i	$-0.703355\pi$
$41$	0.581151	−	0.487644i	0.0907605	−	0.0761571i	0.687039	+	0.726621i	$0.258910\pi$
$42$	−6.86016	+	1.63558i	−1.05855	+	0.252376i
$43$	−2.14125	−	5.88303i	−0.326537	−	0.897154i	−0.988981	−	0.148042i	$-0.952703\pi$
$43$	−2.14125	−	5.88303i	−0.326537	−	0.897154i	0.662444	−	0.749112i	$-0.269519\pi$
$44$	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	−0.838225	−	0.545325i	$-0.816406\pi$
$47$	0.932102	−	5.28621i	0.135961	−	0.771073i	0.974186	−	0.225748i	$-0.0724826\pi$
$48$	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	$-0.921780\pi$
$53$		−	3.54207i		−	0.486541i	0.969959	−	0.243270i	$-0.0782202\pi$
$54$	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	0.719926	+	0.694051i	$0.244176\pi$
$59$	−2.13303	+	5.86045i	−0.277697	+	0.762966i	−0.997623	+	0.0689146i	$0.978046\pi$
$60$	2.10020	−	13.4321i	0.271134	−	1.73407i
$61$	−3.22446	−	0.568559i	−0.412849	−	0.0727965i	−0.0366341	−	0.999329i	$-0.511664\pi$
$61$	−3.22446	−	0.568559i	−0.412849	−	0.0727965i	−0.376215	+	0.926532i	$0.622775\pi$
$62$	−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	0.964873	−	0.262718i	$-0.0846188\pi$
$67$	4.40861	+	5.25398i	0.538598	+	0.641876i	−0.426275	+	0.904594i	$0.640174\pi$
$68$	−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	0.998710	−	0.0507798i	$-0.0161707\pi$
$71$	3.83709	+	6.64603i	0.455378	+	0.788738i	−0.543332	+	0.839518i	$0.682837\pi$
$72$	−4.80896	−	6.99098i	−0.566742	−	0.823895i
$73$	3.46824	−	6.00718i	0.405927	−	0.703087i	−0.588502	−	0.808496i	$-0.700282\pi$
$73$	3.46824	−	6.00718i	0.405927	−	0.703087i	0.994429	+	0.105409i	$0.0336153\pi$
$74$	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	0.654262	−	0.756268i	$-0.272979\pi$
$79$	0.205269	+	0.172241i	0.0230945	+	0.0193786i	−0.631167	+	0.775647i	$0.717424\pi$
$80$	−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	0.130655	+	0.991428i	$0.458292\pi$
$83$	−7.91149	+	9.42855i	−0.868399	+	1.03492i	−0.999054	+	0.0434896i	$0.986152\pi$
$84$	−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	−0.997379	−	0.0723541i	$-0.976949\pi$
$89$	−4.11349	+	7.12477i	−0.436029	+	0.755224i	0.561350	+	0.827578i	$0.310282\pi$
$90$	−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	−0.0720406	−	0.997402i	$-0.522951\pi$
$97$	5.06123	−	1.84214i	0.513891	−	0.187041i	0.585931	+	0.810361i	$0.300729\pi$
$98$	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	−0.0280840	−	0.999606i	$-0.508941\pi$
$101$	−3.98336	−	0.702375i	−0.396360	−	0.0698889i	−0.368276	+	0.929717i	$0.620052\pi$
$102$	−7.26388	+	9.78438i	−0.719231	+	0.968798i
$103$	1.07241	+	0.390325i	0.105668	+	0.0384599i	0.394313	−	0.918976i	$-0.370983\pi$
$103$	1.07241	+	0.390325i	0.105668	+	0.0384599i	−0.288645	+	0.957436i	$0.593205\pi$
$104$	−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	$0.0757276\pi$
$107$			4.87553i			0.471335i	−0.971834	+	0.235667i	$0.924272\pi$
$108$	−1.35170	+	10.3040i	−0.130068	+	0.991505i
$109$			2.52010i			0.241382i	0.992690	+	0.120691i	$0.0385111\pi$
$109$			2.52010i			0.241382i	−0.992690	+	0.120691i	$0.961489\pi$
$110$	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	0.00195583	−	0.999998i	$-0.499377\pi$
$113$	−6.79620	−	2.47361i	−0.639332	−	0.232698i	−0.641288	+	0.767300i	$0.721600\pi$
$114$	−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	−0.952228	−	0.305387i	$-0.901214\pi$
$127$	−2.38507	+	4.13106i	−0.211641	+	0.366573i	0.740587	+	0.671960i	$0.234547\pi$
$128$	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	−0.322338	−	0.946625i	$-0.604469\pi$
$131$	−3.45051	+	0.608417i	−0.301472	+	0.0531577i	0.0208660	+	0.999782i	$0.493358\pi$
$132$	−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	−0.0853611	−	0.996350i	$-0.527204\pi$
$137$	−12.6574	−	10.6208i	−1.08140	−	0.907400i	−0.996036	+	0.0889501i	$0.971649\pi$
$138$	−1.94460	+	1.28271i	−0.165535	+	0.109192i
$139$	19.5648	−	3.44981i	1.65947	−	0.292609i	0.736199	−	0.676765i	$-0.236619\pi$
$139$	19.5648	−	3.44981i	1.65947	−	0.292609i	0.923268	+	0.384157i	$0.125508\pi$
$140$	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	0.978630	−	0.205627i	$-0.0659233\pi$
$149$	7.39950	+	8.81838i	0.606190	+	0.722429i	−0.372440	+	0.928056i	$0.621479\pi$
$150$	7.27541	−	24.4204i	0.594034	−	1.99392i
$151$	−3.42462	+	1.24646i	−0.278692	+	0.101436i	−0.477585	−	0.878586i	$-0.658488\pi$
$151$	−3.42462	+	1.24646i	−0.278692	+	0.101436i	0.198893	+	0.980021i	$0.436265\pi$
$152$	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	−0.562960	−	0.826484i	$-0.690338\pi$
$157$	5.00630	−	13.7547i	0.399546	−	1.09774i	0.962506	−	0.271259i	$-0.0874402\pi$
$158$	−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	$-0.925281\pi$
$163$		−	5.93891i		−	0.465171i	0.972576	−	0.232586i	$-0.0747186\pi$
$164$	−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	−0.505818	−	0.862640i	$-0.668809\pi$
$167$	−18.7096	−	6.80974i	−1.44779	−	0.526953i	−0.941974	+	0.335687i	$0.891032\pi$
$168$	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	0.996545	+	0.0830547i	$0.0264676\pi$
$173$	3.76876	+	10.3546i	0.286534	+	0.787245i	−0.710011	+	0.704190i	$0.751310\pi$
$174$	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	−0.356796	−	0.934182i	$-0.616131\pi$
$179$	3.66363	−	2.11520i	0.273832	−	0.158097i	0.630628	+	0.776085i	$0.282797\pi$
$180$	−10.6244	−	21.0146i	−0.791899	−	1.56634i
$181$	−16.4676	−	9.50759i	−1.22403	−	0.706694i	−0.258255	−	0.966077i	$-0.583147\pi$
$181$	−16.4676	−	9.50759i	−1.22403	−	0.706694i	−0.965775	+	0.259383i	$0.916481\pi$
$182$	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	0.839673	−	0.543092i	$-0.182747\pi$
$191$	6.22796	+	5.22588i	0.450639	+	0.378131i	−0.389034	+	0.921224i	$0.627191\pi$
$192$	−10.9081	−	8.54476i	−0.787225	−	0.616665i
$193$	−2.29037	−	12.9893i	−0.164864	−	0.934993i	−0.949204	−	0.314661i	$-0.898109\pi$
$193$	−2.29037	−	12.9893i	−0.164864	−	0.934993i	0.784340	−	0.620332i	$-0.213002\pi$
$194$	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	0.297071	−	0.954855i	$-0.403990\pi$
$197$	−5.35211	−	3.09004i	−0.381322	−	0.220156i	−0.678393	+	0.734699i	$0.737323\pi$
$198$	−2.33282	+	12.1330i	−0.165787	+	0.862257i
$199$	4.43708	+	7.68525i	0.314537	+	0.544793i	0.979339	−	0.202226i	$-0.0648176\pi$
$199$	4.43708	+	7.68525i	0.314537	+	0.544793i	−0.664802	+	0.747019i	$0.731484\pi$
$200$	−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	0.537767	+	0.843093i	$0.319268\pi$
$211$	−6.04444	+	16.6070i	−0.416116	+	1.14327i	−0.953884	+	0.300177i	$0.902954\pi$
$212$	−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	0.479330	+	0.877635i	$0.340880\pi$
$223$	−4.05080	+	22.9732i	−0.271262	+	1.53840i	−0.750592	+	0.660767i	$0.770231\pi$
$224$	−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	−0.814726	−	0.579846i	$-0.803113\pi$
$227$	−8.48739	−	23.3189i	−0.563328	−	1.54773i	0.251398	−	0.967884i	$-0.419110\pi$
$228$	−6.73682	−	2.30477i	−0.446157	−	0.152637i
$229$	3.58229	+	4.26921i	0.236724	+	0.282117i	0.871307	−	0.490738i	$-0.163273\pi$
$229$	3.58229	+	4.26921i	0.236724	+	0.282117i	−0.634583	+	0.772855i	$0.718828\pi$
$230$	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	0.736283	−	0.676673i	$-0.236579\pi$
$233$	−3.32571	−	5.76031i	−0.217875	−	0.377370i	−0.954158	+	0.299303i	$0.903246\pi$
$234$	−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	−0.671717	−	0.740808i	$-0.734443\pi$
$239$	−4.54329	−	25.7663i	−0.293881	−	1.66668i	0.377836	−	0.925872i	$-0.376668\pi$
$240$	−14.9995	+	22.6791i	−0.968212	+	1.46393i
$241$	−19.2391	−	16.1435i	−1.23930	−	1.03989i	−0.997579	−	0.0695464i	$-0.977845\pi$
$241$	−19.2391	−	16.1435i	−1.23930	−	1.03989i	−0.241718	−	0.970347i	$-0.577711\pi$
$242$	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	0.992719	+	0.120450i	$0.0384337\pi$
$251$	25.2441	+	14.5747i	1.59339	+	0.919945i	0.600672	+	0.799495i	$0.294900\pi$
$252$	−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	−0.796145	−	0.605106i	$-0.793131\pi$
$257$	−5.42626	+	4.55318i	−0.338481	+	0.284019i	0.457664	+	0.889125i	$0.348686\pi$
$258$	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	−0.859718	−	0.510770i	$-0.829361\pi$
$263$	1.99223	−	11.2985i	0.122846	−	0.696695i	0.982564	−	0.185926i	$-0.0595283\pi$
$264$	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	$-0.846834\pi$
$269$		−	15.1820i		−	0.925661i	0.886447	−	0.462831i	$-0.153166\pi$
$270$	−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	0.249259	−	0.968437i	$-0.419813\pi$
$277$	2.53413	+	0.446836i	0.152261	+	0.0268478i	−0.0969979	+	0.995285i	$0.530924\pi$
$278$	−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	0.556518	−	0.830835i	$-0.312137\pi$
$281$	25.4277	−	9.25491i	1.51689	−	0.552102i	0.960368	+	0.278734i	$0.0899147\pi$
$282$	12.7898	−	3.04931i	0.761621	−	0.181584i
$283$	−17.1845	−	20.4797i	−1.02151	−	1.21739i	−0.975851	−	0.218436i	$-0.929905\pi$
$283$	−17.1845	−	20.4797i	−1.02151	−	1.21739i	−0.0456626	−	0.998957i	$-0.514540\pi$
$284$	−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	−0.655245	−	0.755416i	$-0.727435\pi$
$293$	−17.3330	+	3.05628i	−1.01261	+	0.178550i	−0.357361	+	0.933966i	$0.616323\pi$
$294$	−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	−0.761898	−	0.647696i	$-0.775732\pi$
$307$	−10.1962	+	5.88676i	−0.581926	+	0.335975i	0.179972	+	0.983672i	$0.442399\pi$
$308$	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	0.567965	−	0.823053i	$-0.307731\pi$
$311$	26.0496	−	21.8582i	1.47714	−	1.23947i	0.909175	−	0.416414i	$-0.136713\pi$
$312$	−15.1882	+	12.2190i	−0.859864	+	0.691763i
$313$	6.64081	−	2.41706i	0.375361	−	0.136620i	−0.147449	−	0.989070i	$-0.547106\pi$
$313$	6.64081	−	2.41706i	0.375361	−	0.136620i	0.522809	+	0.852450i	$0.324884\pi$
$314$	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	0.321616	−	0.946870i	$-0.395774\pi$
$317$	5.34112	+	0.941783i	0.299987	+	0.0528958i	−0.0216287	+	0.999766i	$0.506885\pi$
$318$	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	0.318535	−	0.947911i	$-0.396809\pi$
$331$	5.34260	+	0.942044i	0.293656	+	0.0517794i	−0.0248795	+	0.999690i	$0.507920\pi$
$332$	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	−0.217528	+	0.976054i	$0.569799\pi$
$337$	−22.3325	+	18.7392i	−1.21653	+	1.02079i	−0.998999	+	0.0447328i	$0.985756\pi$
$338$	−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	−0.613203	−	0.789925i	$-0.710119\pi$
$347$	−17.1238	+	3.01939i	−0.919255	+	0.162089i	−0.306052	+	0.952015i	$0.599008\pi$
$348$	−13.4985	+	24.4660i	−0.723595	+	1.31151i
$349$	3.38478	−	4.03383i	0.181183	−	0.215926i	−0.667807	−	0.744335i	$-0.732767\pi$
$349$	3.38478	−	4.03383i	0.181183	−	0.215926i	0.848990	+	0.528409i	$0.177211\pi$
$350$	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	0.430090	−	0.902786i	$-0.358482\pi$
$353$	−7.22029	−	6.05854i	−0.384297	−	0.322463i	−0.814387	+	0.580323i	$0.802926\pi$
$354$	−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	−0.996763	−	0.0803962i	$-0.974381\pi$
$359$	−8.12377	+	14.0708i	−0.428756	+	0.742628i	0.568007	+	0.823024i	$0.307715\pi$
$360$	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	−0.00833711	−	0.999965i	$-0.502654\pi$
$367$	12.0315	−	4.37912i	0.628042	−	0.228588i	0.636379	+	0.771377i	$0.280432\pi$
$368$	−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	−0.983030	−	0.183445i	$-0.941275\pi$
$373$	−2.16442	+	5.94669i	−0.112069	+	0.307908i	0.870961	+	0.491353i	$0.163497\pi$
$374$	−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	$-0.738521\pi$
$379$		−	28.5066i		−	1.46428i	0.681152	−	0.732142i	$-0.261479\pi$
$380$	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	−0.550983	−	0.834517i	$-0.685747\pi$
$383$	−29.5410	−	10.7521i	−1.50948	−	0.549405i	−0.958494	+	0.285112i	$0.907969\pi$
$384$	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	0.969093	−	0.246696i	$-0.0793448\pi$
$389$	1.34416	+	3.69306i	0.0681518	+	0.187246i	−0.900941	+	0.433941i	$0.857123\pi$
$390$	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	0.878237	−	0.478226i	$-0.158720\pi$
$397$	17.9961	+	10.3901i	0.903200	+	0.521463i	0.0249629	+	0.999688i	$0.492053\pi$
$398$	−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	−0.903709	−	0.428147i	$-0.859166\pi$
$401$	−4.02373	−	22.8197i	−0.200935	−	1.13956i	0.702774	−	0.711413i	$-0.251945\pi$
$402$	−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	0.806768	+	0.590868i	$0.201215\pi$
$409$	5.07096	+	28.7589i	0.250743	+	1.42203i	−0.556025	+	0.831165i	$0.687674\pi$
$410$	−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	0.930258	−	0.366905i	$-0.119583\pi$
$419$	8.33906	+	9.93810i	0.407390	+	0.485508i	−0.522869	+	0.852413i	$0.675138\pi$
$420$	37.0354	+	12.6704i	1.80714	+	0.618252i
$421$	−1.49536	−	4.10848i	−0.0728795	−	0.200235i	0.897904	−	0.440191i	$-0.145089\pi$
$421$	−1.49536	−	4.10848i	−0.0728795	−	0.200235i	−0.970784	+	0.239956i	$0.922867\pi$
$422$	−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	0.639715	+	0.768612i	$0.279052\pi$
$439$	−4.69964	+	26.6530i	−0.224301	+	1.27208i	−0.864016	+	0.503464i	$0.832059\pi$
$440$	−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	−0.898584	−	0.438802i	$-0.855403\pi$
$443$	−10.3614	−	28.4677i	−0.492285	−	1.35254i	0.406299	−	0.913740i	$-0.366819\pi$
$444$	−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	0.823003	−	0.568037i	$-0.192297\pi$
$449$	−1.70434	−	2.95201i	−0.0804330	−	0.139314i	−0.903436	+	0.428723i	$0.858964\pi$
$450$	−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	0.796933	−	0.604068i	$-0.206454\pi$
$457$	7.27754	+	6.10658i	0.340429	+	0.285654i	−0.456504	+	0.889721i	$0.650899\pi$
$458$	−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	0.0680433	+	0.997682i	$0.478324\pi$
$461$	−19.8885	+	23.7021i	−0.926298	+	1.10392i	−0.994341	+	0.106236i	$0.966120\pi$
$462$	−11.3087	−	17.1440i	−0.526128	−	0.797612i
$463$	−4.27095	−	24.2217i	−0.198488	−	1.12568i	−0.907364	−	0.420347i	$-0.861908\pi$
$463$	−4.27095	−	24.2217i	−0.198488	−	1.12568i	0.708876	−	0.705333i	$-0.249203\pi$
$464$	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	0.480219	−	0.877149i	$-0.340557\pi$
$467$	−0.849394	−	0.490398i	−0.0393052	−	0.0226929i	−0.519524	+	0.854456i	$0.673891\pi$
$468$	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	−0.999969	−	0.00787960i	$-0.997492\pi$
$479$	−1.26087	+	7.15074i	−0.0576105	+	0.326726i	0.942358	+	0.334605i	$0.108603\pi$
$480$	−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	−0.669543	−	0.742774i	$-0.733510\pi$
$491$	7.10851	−	19.5305i	0.320802	−	0.881398i	0.990345	−	0.138624i	$-0.0442679\pi$
$492$	−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	0.964871	−	0.262726i	$-0.0846214\pi$
$499$	12.0312	+	14.3382i	0.538588	+	0.641865i	−0.426282	+	0.904590i	$0.640177\pi$
$500$	−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	0.974919	+	0.222558i	$0.0714406\pi$
$503$	15.2553	+	26.4230i	0.680200	+	1.17814i	−0.294719	+	0.955584i	$0.595226\pi$
$504$	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	0.413590	−	0.910463i	$-0.364275\pi$
$509$	25.1247	−	4.43017i	1.11363	−	0.196364i	0.700044	+	0.714099i	$0.253164\pi$
$510$	−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	−0.990470	−	0.137729i	$-0.956020\pi$
$521$	−8.58140	+	14.8634i	−0.375958	+	0.651178i	0.614512	+	0.788908i	$0.289353\pi$
$522$	32.3354	−	11.2076i	1.41528	−	0.490543i
$523$	−35.9656	+	20.7647i	−1.57266	+	0.907978i	−0.576824	+	0.816869i	$0.695708\pi$
$523$	−35.9656	+	20.7647i	−1.57266	+	0.907978i	−0.995841	+	0.0911099i	$0.970959\pi$
$524$	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	$0.0776152\pi$
$541$			11.2309i			0.482852i	−0.970419	+	0.241426i	$0.922385\pi$
$542$	−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	−0.268137	−	0.963381i	$-0.586408\pi$
$547$	−19.8704	−	3.50369i	−0.849599	−	0.149807i	−0.581462	+	0.813574i	$0.697519\pi$
$548$	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	−0.945094	−	0.326798i	$-0.894030\pi$
$557$	−26.7781	+	15.4604i	−1.13463	+	0.655076i	−0.189532	+	0.981875i	$0.560697\pi$
$558$	−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	0.271479	−	0.962444i	$-0.412487\pi$
$563$	20.3052	−	3.58035i	0.855761	−	0.150894i	0.584282	+	0.811551i	$0.301376\pi$
$564$	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	0.559038	−	0.829142i	$-0.311171\pi$
$569$	−3.82688	−	3.21114i	−0.160431	−	0.134618i	−0.719469	+	0.694524i	$0.755615\pi$
$570$	−17.6694	−	8.84434i	−0.740091	−	0.370449i
$571$	−7.54047	+	1.32959i	−0.315559	+	0.0556415i	−0.329184	−	0.944266i	$-0.606774\pi$
$571$	−7.54047	+	1.32959i	−0.315559	+	0.0556415i	0.0136257	+	0.999907i	$0.495663\pi$
$572$	−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	0.969410	−	0.245449i	$-0.0789352\pi$
$577$	6.53703	+	11.3225i	0.272140	+	0.471361i	−0.697269	+	0.716809i	$0.745602\pi$
$578$	−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	−0.261126	−	0.965305i	$-0.584094\pi$
$587$	−20.2706	−	3.57425i	−0.836657	−	0.147525i	−0.575532	+	0.817780i	$0.695205\pi$
$588$	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	0.441193	−	0.897412i	$-0.354555\pi$
$599$	4.95171	+	1.80227i	0.202321	+	0.0736389i	−0.238872	+	0.971051i	$0.576778\pi$
$600$	−33.5570	+	38.3545i	−1.36996	+	1.56582i
$601$	−6.16086	+	34.9400i	−0.251307	+	1.42523i	0.554071	+	0.832469i	$0.313074\pi$
$601$	−6.16086	+	34.9400i	−0.251307	+	1.42523i	−0.805378	+	0.592762i	$0.798038\pi$
$602$	−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	−0.768322	−	0.640063i	$-0.778908\pi$
$607$	−6.68660	+	5.61072i	−0.271401	+	0.227732i	0.496922	+	0.867795i	$0.334464\pi$
$608$	−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	−0.201321	−	0.979525i	$-0.564523\pi$
$613$	−28.4795	−	16.4426i	−1.15028	−	0.664112i	−0.948954	+	0.315414i	$0.897857\pi$
$614$	−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	0.848119	+	0.529805i	$0.177735\pi$
$617$	5.77150	+	32.7318i	0.232352	+	1.31773i	−0.615767	+	0.787928i	$0.711154\pi$
$618$	0.166273	+	2.79049i	0.00668848	+	0.112250i
$619$	−22.6481	+	26.9910i	−0.910305	+	1.08486i	0.0857667	+	0.996315i	$0.472666\pi$
$619$	−22.6481	+	26.9910i	−0.910305	+	1.08486i	−0.996072	+	0.0885446i	$0.971778\pi$
$620$	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	−0.912466	−	0.409152i	$-0.865825\pi$
$631$	−20.3613	−	35.2667i	−0.810569	−	1.40395i	0.101898	−	0.994795i	$-0.467509\pi$
$632$	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	−0.0995006	+	0.995038i	$0.531725\pi$
$641$	−8.76821	+	49.7270i	−0.346323	+	1.96410i	−0.246823	+	0.969061i	$0.579387\pi$
$642$	−10.9595	+	4.74487i	−0.432537	+	0.187265i
$643$	15.1261	−	41.5587i	0.596517	−	1.63892i	−0.161645	−	0.986849i	$-0.551680\pi$
$643$	15.1261	−	41.5587i	0.596517	−	1.63892i	0.758162	−	0.652067i	$-0.226098\pi$
$644$	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	−0.954860	−	0.297055i	$-0.903995\pi$
$653$	−0.829258	+	2.27837i	−0.0324514	+	0.0891594i	0.922409	+	0.386215i	$0.126218\pi$
$654$	−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	0.795738	+	0.605641i	$0.207083\pi$
$659$	14.7728	+	40.5879i	0.575466	+	1.58108i	−0.220272	+	0.975438i	$0.570695\pi$
$660$	38.8492	−	7.63133i	1.51220	−	0.297049i
$661$	11.3612	+	13.5398i	0.441901	+	0.526637i	0.940317	−	0.340301i	$-0.110529\pi$
$661$	11.3612	+	13.5398i	0.441901	+	0.526637i	−0.498415	+	0.866938i	$0.666085\pi$
$662$	−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	0.666105	−	0.745858i	$-0.267960\pi$
$673$	1.22568	+	1.02847i	0.0472465	+	0.0396445i	−0.618859	+	0.785502i	$0.712405\pi$
$674$	−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	$-0.735680\pi$
$677$	4.41092	−	5.25673i	0.169526	−	0.202033i	0.844118	+	0.536158i	$0.180125\pi$
$678$	−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	0.419107	−	0.907937i	$-0.362343\pi$
$683$	−4.11971	−	2.37852i	−0.157636	−	0.0910113i	−0.576743	+	0.816926i	$0.695677\pi$
$684$	−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	0.829034	−	0.559198i	$-0.188891\pi$
$691$	−4.35017	−	11.9520i	−0.165488	−	0.454675i	−0.994523	+	0.104523i	$0.966669\pi$
$692$	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	$-0.925573\pi$
$701$		−	12.2688i		−	0.463386i	0.972789	−	0.231693i	$-0.0744265\pi$
$702$	−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	0.638680	−	0.769473i	$-0.279481\pi$
$709$	25.9792	+	4.58083i	0.975668	+	0.172037i	0.336988	+	0.941509i	$0.390592\pi$
$710$	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	−0.993617	−	0.112807i	$-0.964016\pi$
$719$	−15.9411	−	27.6108i	−0.594502	−	1.02971i	0.399115	−	0.916901i	$-0.369317\pi$
$720$	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	0.999586	−	0.0287706i	$-0.00915924\pi$
$727$	30.8679	+	25.9013i	1.14483	+	0.960625i	0.145243	+	0.989396i	$0.453604\pi$
$728$	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	−0.171738	−	0.985143i	$-0.554938\pi$
$733$	0.103428	−	0.0182371i	0.00382018	−	0.000673601i	0.175558	+	0.984469i	$0.443827\pi$
$734$	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	−0.899074	−	0.437798i	$-0.855759\pi$
$739$	−26.3545	+	15.2158i	−0.969466	+	0.559722i	−0.0703928	+	0.997519i	$0.522425\pi$
$740$	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	−0.374298	−	0.927308i	$-0.622116\pi$
$743$	12.9183	−	10.8397i	0.473926	−	0.397671i	0.848224	+	0.529637i	$0.177672\pi$
$744$	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	0.595751	−	0.803169i	$-0.296855\pi$
$751$	14.6848	+	5.34482i	0.535855	+	0.195035i	−0.0598958	+	0.998205i	$0.519077\pi$
$752$	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	$-0.834624\pi$
$757$		−	27.3201i		−	0.992967i	0.868046	−	0.496484i	$-0.165376\pi$
$758$	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	0.0719327	−	0.997409i	$-0.477083\pi$
$761$	−14.1817	−	5.16172i	−0.514086	−	0.187112i	−0.586019	+	0.810297i	$0.699306\pi$
$762$	−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	−0.825038	−	0.565077i	$-0.808846\pi$
$769$	−11.4199	+	9.58242i	−0.411811	+	0.345551i	0.413226	+	0.910628i	$0.364402\pi$
$770$	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	−0.909931	−	0.414759i	$-0.863866\pi$
$773$	−27.9615	+	16.1436i	−1.00571	+	0.580644i	−0.0957742	+	0.995403i	$0.530533\pi$
$774$	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	0.586204	−	0.810163i	$-0.300622\pi$
$787$	39.6718	−	6.99522i	1.41415	−	0.249353i	0.827944	+	0.560811i	$0.189510\pi$
$788$	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	0.806131	−	0.591737i	$-0.201558\pi$
$797$	2.35451	+	2.80599i	0.0834009	+	0.0993934i	−0.722730	+	0.691130i	$0.757113\pi$
$798$	−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	$0.148748\pi$
$811$			25.6578i			0.900966i	−0.892785	+	0.450483i	$0.851252\pi$
$812$	−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	−0.994403	−	0.105653i	$-0.966307\pi$
$821$	−8.61194	−	23.6611i	−0.300559	−	0.825778i	0.693844	−	0.720125i	$-0.255916\pi$
$822$	11.5560	−	38.7884i	0.403061	−	1.35290i
$823$	10.3916	−	8.71956i	0.362227	−	0.303945i	−0.443450	−	0.896299i	$-0.646246\pi$
$823$	10.3916	−	8.71956i	0.362227	−	0.303945i	0.805678	+	0.592354i	$0.201801\pi$
$824$	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	−0.323197	−	0.946332i	$-0.604758\pi$
$827$	9.62668	−	5.55796i	0.334752	−	0.193269i	0.657949	+	0.753062i	$0.271424\pi$
$828$	−4.77584	−	3.12285i	−0.165972	−	0.108527i
$829$	−26.4493	−	15.2705i	−0.918621	−	0.530366i	−0.0354262	−	0.999372i	$-0.511279\pi$
$829$	−26.4493	−	15.2705i	−0.918621	−	0.530366i	−0.883195	+	0.469006i	$0.844612\pi$
$830$	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	0.577194	−	0.816607i	$-0.304148\pi$
$839$	−3.67221	−	3.08135i	−0.126779	−	0.106380i	−0.703972	+	0.710227i	$0.748592\pi$
$840$	−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	0.999314	+	0.0370424i	$0.0117937\pi$
$853$	7.52367	+	20.6711i	0.257605	+	0.707765i	−0.741708	+	0.670723i	$0.765984\pi$
$854$	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	−0.999760	−	0.0219232i	$-0.993021\pi$
$857$	−1.54554	+	8.76520i	−0.0527947	+	0.299414i	0.946965	+	0.321337i	$0.104132\pi$
$858$	28.1962	+	3.25744i	0.962602	+	0.111207i
$859$	−7.12897	+	19.5867i	−0.243237	+	0.668289i	0.756658	+	0.653811i	$0.226831\pi$
$859$	−7.12897	+	19.5867i	−0.243237	+	0.668289i	−0.999895	+	0.0144780i	$0.995391\pi$
$860$	−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	0.769017	−	0.639228i	$-0.220746\pi$
$877$	0.176559	+	0.210415i	0.00596198	+	0.00710521i	−0.763055	+	0.646333i	$0.776302\pi$
$878$	−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	0.592176	−	0.805809i	$-0.298269\pi$
$881$	−11.9250	−	20.6547i	−0.401763	−	0.695873i	−0.993939	+	0.109935i	$0.964936\pi$
$882$	−3.45155	−	4.24463i	−0.116220	−	0.142924i
$883$	4.93626	+	2.84995i	0.166118	+	0.0959085i	0.580754	−	0.814079i	$-0.302758\pi$
$883$	4.93626	+	2.84995i	0.166118	+	0.0959085i	−0.414636	+	0.909987i	$0.636091\pi$
$884$	−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	−0.993076	−	0.117477i	$-0.962519\pi$
$887$	−2.98032	−	16.9022i	−0.100069	−	0.567521i	0.893006	−	0.450044i	$-0.148592\pi$
$888$	−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	−0.894342	−	0.447383i	$-0.852356\pi$
$907$	−14.9621	−	41.1081i	−0.496809	−	1.36497i	0.397533	−	0.917588i	$-0.369866\pi$
$908$	−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	−0.976481	−	0.215602i	$-0.930828\pi$
$911$	0.448255	−	2.54218i	0.0148514	−	0.0842262i	0.991333	+	0.131376i	$0.0419396\pi$
$912$	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	−0.785567	−	0.618777i	$-0.787629\pi$
$929$	−30.1626	+	10.9783i	−0.989604	+	0.360186i	−0.204037	+	0.978963i	$0.565406\pi$
$930$	−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	−0.695358	−	0.718663i	$-0.744754\pi$
$937$	8.40875	−	14.5644i	0.274702	−	0.475797i	0.970060	+	0.242866i	$0.0780875\pi$
$938$	−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	−0.496613	−	0.867972i	$-0.665423\pi$
$941$	−20.4427	+	3.60459i	−0.666412	+	0.117506i	−0.169799	+	0.985479i	$0.554312\pi$
$942$	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	−0.922785	−	0.385316i	$-0.874092\pi$
$947$	−11.7887	+	14.0493i	−0.383082	+	0.456540i	0.539702	+	0.841856i	$0.318537\pi$
$948$	−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	−0.836549	−	0.547892i	$-0.815431\pi$
$953$	1.73534	−	3.00570i	0.0562133	−	0.0973643i	0.892763	+	0.450527i	$0.148764\pi$
$954$	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	−0.170388	−	0.985377i	$-0.554502\pi$
$967$	−29.0536	−	10.5747i	−0.934301	−	0.340058i	−0.763913	+	0.645319i	$0.776724\pi$
$968$	−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	$0.00142484\pi$
$971$			0.278968i			0.00895249i	−0.999990	+	0.00447625i	$0.998575\pi$
$972$	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	0.643238	−	0.765666i	$-0.277591\pi$
$977$	20.1241	+	7.32457i	0.643827	+	0.234334i	0.000588326		1.00000i	$0.499813\pi$
$978$	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	−0.428698	−	0.903448i	$-0.641027\pi$
$983$	−5.52983	+	2.01269i	−0.176374	+	0.0641950i	0.252324	+	0.967643i	$0.418805\pi$
$984$	−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	−0.440063	−	0.897967i	$-0.645044\pi$
$991$	17.5543	−	30.4049i	0.557631	−	0.965845i	0.997694	−	0.0678778i	$-0.0216228\pi$
$992$	−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	−0.446302	−	0.894883i	$-0.647259\pi$
$997$	16.1819	−	19.2848i	0.512485	−	0.610756i	0.958787	+	0.284127i	$0.0917036\pi$
$998$	−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.205.17	yes	204
3.2	odd	2		648.2.t.a.613.18		204
4.3	odd	2		864.2.bf.a.529.7		204
8.3	odd	2		864.2.bf.a.529.28		204
8.5	even	2	inner	216.2.t.a.205.31	yes	204
24.5	odd	2		648.2.t.a.613.4		204
27.5	odd	18		648.2.t.a.37.4		204
27.22	even	9	inner	216.2.t.a.157.31	yes	204
108.103	odd	18		864.2.bf.a.49.28		204
216.5	odd	18		648.2.t.a.37.18		204
216.157	even	18	inner	216.2.t.a.157.17	✓	204
216.211	odd	18		864.2.bf.a.49.7		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.17	✓	204	216.157	even	18	inner
216.2.t.a.157.31	yes	204	27.22	even	9	inner
216.2.t.a.205.17	yes	204	1.1	even	1	trivial
216.2.t.a.205.31	yes	204	8.5	even	2	inner
648.2.t.a.37.4		204	27.5	odd	18
648.2.t.a.37.18		204	216.5	odd	18
648.2.t.a.613.4		204	24.5	odd	2
648.2.t.a.613.18		204	3.2	odd	2
864.2.bf.a.49.7		204	216.211	odd	18
864.2.bf.a.49.28		204	108.103	odd	18
864.2.bf.a.529.7		204	4.3	odd	2
864.2.bf.a.529.28		204	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
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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