LMFDB - Embedded newform 243.2.i.a.61.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] 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("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			61.9
Character	$\chi$	$=$	243.61
Dual form			243.2.i.a.4.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04754 + 0.0406495i) q^{2} +(0.956457 - 1.44402i) q^{3} +(-0.898290 + 0.0698206i) q^{4} +(-2.13661 + 2.64898i) q^{5} +(-0.943232 + 1.55155i) q^{6} +(1.55684 + 0.707671i) q^{7} +(3.02065 - 0.353063i) q^{8} +(-1.17038 - 2.76228i) q^{9} +(2.13051 - 2.86177i) q^{10} +(-0.111562 + 5.75211i) q^{11} +(-0.758353 + 1.36393i) q^{12} +(-3.31592 + 1.06321i) q^{13} +(-1.65963 - 0.678032i) q^{14} +(1.78160 + 5.61893i) q^{15} +(-1.36955 + 0.214194i) q^{16} +(-0.724593 + 2.42031i) q^{17} +(1.33831 + 2.84604i) q^{18} +(6.60241 + 1.56480i) q^{19} +(1.73434 - 2.52873i) q^{20} +(2.51094 - 1.57125i) q^{21} +(-0.116954 - 6.03012i) q^{22} +(3.72324 + 2.66121i) q^{23} +(2.37929 - 4.69956i) q^{24} +(-1.39347 - 6.43296i) q^{25} +(3.43036 - 1.24855i) q^{26} +(-5.10821 - 0.951951i) q^{27} +(-1.44790 - 0.526994i) q^{28} +(-0.199738 + 1.46234i) q^{29} +(-2.09471 - 5.81365i) q^{30} +(-2.04042 + 2.00123i) q^{31} +(-4.54245 + 0.892108i) q^{32} +(8.19945 + 5.66274i) q^{33} +(0.660658 - 2.56483i) q^{34} +(-5.20096 + 2.61202i) q^{35} +(1.24421 + 2.39961i) q^{36} +(1.07019 - 0.703872i) q^{37} +(-6.97992 - 1.37081i) q^{38} +(-1.63624 + 5.80517i) q^{39} +(-5.51868 + 8.75598i) q^{40} +(0.0580046 + 0.110119i) q^{41} +(-2.56645 + 1.74802i) q^{42} +(-0.546726 - 1.59787i) q^{43} +(-0.301400 - 5.17485i) q^{44} +(9.81786 + 2.80160i) q^{45} +(-4.00843 - 2.63639i) q^{46} +(-9.47337 - 9.29142i) q^{47} +(-1.00062 + 2.18253i) q^{48} +(-2.67969 - 3.07059i) q^{49} +(1.72121 + 6.68216i) q^{50} +(2.80193 + 3.36124i) q^{51} +(2.90442 - 1.18659i) q^{52} +(-5.69747 + 4.78075i) q^{53} +(5.38977 + 0.789564i) q^{54} +(-14.9988 - 12.5855i) q^{55} +(4.95252 + 1.58796i) q^{56} +(8.57451 - 8.03734i) q^{57} +(0.149791 - 1.53999i) q^{58} +(2.94484 + 1.62490i) q^{59} +(-1.99271 - 4.92303i) q^{60} +(3.73135 + 0.290023i) q^{61} +(2.05608 - 2.17931i) q^{62} +(0.132690 - 5.12868i) q^{63} +(7.41983 - 1.75853i) q^{64} +(4.26841 - 11.0554i) q^{65} +(-8.81947 - 5.59866i) q^{66} +(-0.110239 - 0.807089i) q^{67} +(0.481907 - 2.22473i) q^{68} +(7.40395 - 2.83109i) q^{69} +(5.34205 - 2.94762i) q^{70} +(1.82852 + 4.23899i) q^{71} +(-4.51057 - 7.93067i) q^{72} +(2.83346 + 3.80600i) q^{73} +(-1.09245 + 0.780839i) q^{74} +(-10.6221 - 4.14065i) q^{75} +(-6.04013 - 0.944659i) q^{76} +(-4.24428 + 8.87616i) q^{77} +(1.47806 - 6.14768i) q^{78} +(4.70874 + 7.47093i) q^{79} +(2.35880 - 4.08556i) q^{80} +(-6.26041 + 6.46585i) q^{81} +(-0.0652386 - 0.112997i) q^{82} +(5.78205 - 10.9769i) q^{83} +(-2.14585 + 1.58675i) q^{84} +(-4.86317 - 7.09067i) q^{85} +(0.637673 + 1.65161i) q^{86} +(1.92061 + 1.68709i) q^{87} +(1.69387 + 17.4145i) q^{88} +(7.00705 - 16.2442i) q^{89} +(-10.3985 - 2.53571i) q^{90} +(-5.91476 - 0.691337i) q^{91} +(-3.53035 - 2.13058i) q^{92} +(0.938239 + 4.86048i) q^{93} +(10.3015 + 9.34808i) q^{94} +(-18.2518 + 14.1463i) q^{95} +(-3.05643 + 7.41264i) q^{96} +(9.65191 + 11.9665i) q^{97} +(2.93192 + 3.10765i) q^{98} +(16.0195 - 6.42399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{80}{81}\right)$

Coefficient data

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

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

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

$2$	−1.04754	+	0.0406495i	−0.740726	+	0.0287435i	−0.406376	−	0.913706i	$-0.633208\pi$
$2$	−1.04754	+	0.0406495i	−0.740726	+	0.0287435i	−0.334349	+	0.942449i	$0.608516\pi$
$3$	0.956457	−	1.44402i	0.552210	−	0.833705i
$3$	0.956457	−	1.44402i	0.552210	−	0.833705i
$4$	−0.898290	+	0.0698206i	−0.449145	+	0.0349103i
$5$	−2.13661	+	2.64898i	−0.955519	+	1.18466i	0.0272143	+	0.999630i	$0.491336\pi$
$5$	−2.13661	+	2.64898i	−0.955519	+	1.18466i	−0.982733	+	0.185028i	$0.940762\pi$
$6$	−0.943232	+	1.55155i	−0.385073	+	0.633419i
$7$	1.55684	+	0.707671i	0.588430	+	0.267474i	0.685819	−	0.727772i	$-0.259444\pi$
$7$	1.55684	+	0.707671i	0.588430	+	0.267474i	−0.0973887	+	0.995246i	$0.531049\pi$
$8$	3.02065	−	0.353063i	1.06796	−	0.124827i
$9$	−1.17038	−	2.76228i	−0.390127	−	0.920761i
$10$	2.13051	−	2.86177i	0.673726	−	0.904971i
$11$	−0.111562	+	5.75211i	−0.0336372	+	1.73433i	0.480829	+	0.876814i	$0.340336\pi$
$11$	−0.111562	+	5.75211i	−0.0336372	+	1.73433i	−0.514466	+	0.857511i	$0.672010\pi$
$12$	−0.758353	+	1.36393i	−0.218918	+	0.393732i
$13$	−3.31592	+	1.06321i	−0.919671	+	0.294881i	−0.727203	−	0.686423i	$-0.759180\pi$
$13$	−3.31592	+	1.06321i	−0.919671	+	0.294881i	−0.192468	+	0.981303i	$0.561649\pi$
$14$	−1.65963	−	0.678032i	−0.443554	−	0.181212i
$15$	1.78160	+	5.61893i	0.460007	+	1.45080i
$16$	−1.36955	+	0.214194i	−0.342389	+	0.0535486i
$17$	−0.724593	+	2.42031i	−0.175740	+	0.587011i	0.824050	+	0.566516i	$0.191709\pi$
$17$	−0.724593	+	2.42031i	−0.175740	+	0.587011i	−0.999790	+	0.0204945i	$0.993476\pi$
$18$	1.33831	+	2.84604i	0.315443	+	0.670818i
$19$	6.60241	+	1.56480i	1.51470	+	0.358989i	0.902142	−	0.431439i	$-0.141994\pi$
$19$	6.60241	+	1.56480i	1.51470	+	0.358989i	0.612554	+	0.790429i	$0.290142\pi$
$20$	1.73434	−	2.52873i	0.387810	−	0.565440i
$21$	2.51094	−	1.57125i	0.547932	−	0.342875i
$22$	−0.116954	−	6.03012i	−0.0249347	−	1.28563i
$23$	3.72324	+	2.66121i	0.776349	+	0.554901i	0.899207	−	0.437523i	$-0.144144\pi$
$23$	3.72324	+	2.66121i	0.776349	+	0.554901i	−0.122858	+	0.992424i	$0.539206\pi$
$24$	2.37929	−	4.69956i	0.485670	−	0.959294i
$25$	−1.39347	−	6.43296i	−0.278693	−	1.28659i
$26$	3.43036	−	1.24855i	0.672748	−	0.244860i
$27$	−5.10821	−	0.951951i	−0.983075	−	0.183203i
$28$	−1.44790	−	0.526994i	−0.273628	−	0.0995925i
$29$	−0.199738	+	1.46234i	−0.0370905	+	0.271550i	0.962908	+	0.269830i	$0.0869674\pi$
$29$	−0.199738	+	1.46234i	−0.0370905	+	0.271550i	−0.999999	+	0.00172053i	$0.999452\pi$
$30$	−2.09471	−	5.81365i	−0.382440	−	1.06142i
$31$	−2.04042	+	2.00123i	−0.366469	+	0.359431i	−0.859997	−	0.510300i	$-0.829534\pi$
$31$	−2.04042	+	2.00123i	−0.366469	+	0.359431i	0.493527	+	0.869730i	$0.335707\pi$
$32$	−4.54245	+	0.892108i	−0.802999	+	0.157704i
$33$	8.19945	+	5.66274i	1.42734	+	0.985756i
$34$	0.660658	−	2.56483i	0.113302	−	0.439865i
$35$	−5.20096	+	2.61202i	−0.879122	+	0.441512i
$36$	1.24421	+	2.39961i	0.207368	+	0.399936i
$37$	1.07019	−	0.703872i	0.175937	−	0.115716i	−0.458486	−	0.888702i	$-0.651608\pi$
$37$	1.07019	−	0.703872i	0.175937	−	0.115716i	0.634423	+	0.772986i	$0.281238\pi$
$38$	−6.97992	−	1.37081i	−1.13229	−	0.222375i
$39$	−1.63624	+	5.80517i	−0.262009	+	0.929570i
$40$	−5.51868	+	8.75598i	−0.872579	+	1.38444i
$41$	0.0580046	+	0.110119i	0.00905879	+	0.0171977i	0.889249	−	0.457423i	$-0.151227\pi$
$41$	0.0580046	+	0.110119i	0.00905879	+	0.0171977i	−0.880191	+	0.474620i	$0.842585\pi$
$42$	−2.56645	+	1.74802i	−0.396012	+	0.269726i
$43$	−0.546726	−	1.59787i	−0.0833750	−	0.243673i	0.896583	−	0.442875i	$-0.146041\pi$
$43$	−0.546726	−	1.59787i	−0.0833750	−	0.243673i	−0.979958	+	0.199202i	$0.936165\pi$
$44$	−0.301400	−	5.17485i	−0.0454378	−	0.780137i
$45$	9.81786	+	2.80160i	1.46356	+	0.417637i
$46$	−4.00843	−	2.63639i	−0.591011	−	0.388714i
$47$	−9.47337	−	9.29142i	−1.38183	−	1.35529i	−0.867268	−	0.497841i	$-0.834126\pi$
$47$	−9.47337	−	9.29142i	−1.38183	−	1.35529i	−0.514565	−	0.857451i	$-0.672047\pi$
$48$	−1.00062	+	2.18253i	−0.144427	+	0.315021i
$49$	−2.67969	−	3.07059i	−0.382814	−	0.438656i
$50$	1.72121	+	6.68216i	0.243416	+	0.945001i
$51$	2.80193	+	3.36124i	0.392349	+	0.470668i
$52$	2.90442	−	1.18659i	0.402771	−	0.164550i
$53$	−5.69747	+	4.78075i	−0.782608	+	0.656686i	−0.943904	−	0.330220i	$-0.892877\pi$
$53$	−5.69747	+	4.78075i	−0.782608	+	0.656686i	0.161296	+	0.986906i	$0.448433\pi$
$54$	5.38977	+	0.789564i	0.733455	+	0.107446i
$55$	−14.9988	−	12.5855i	−2.02244	−	1.69703i
$56$	4.95252	+	1.58796i	0.661808	+	0.212200i
$57$	8.57451	−	8.03734i	1.13572	−	1.06457i
$58$	0.149791	−	1.53999i	0.0196685	−	0.202210i
$59$	2.94484	+	1.62490i	0.383386	+	0.211543i	0.663085	−	0.748544i	$-0.269247\pi$
$59$	2.94484	+	1.62490i	0.383386	+	0.211543i	−0.279699	+	0.960088i	$0.590235\pi$
$60$	−1.99271	−	4.92303i	−0.257258	−	0.635561i
$61$	3.73135	+	0.290023i	0.477750	+	0.0371336i	0.314110	−	0.949387i	$-0.398294\pi$
$61$	3.73135	+	0.290023i	0.477750	+	0.0371336i	0.163640	+	0.986520i	$0.447677\pi$
$62$	2.05608	−	2.17931i	0.261122	−	0.276773i
$63$	0.132690	−	5.12868i	0.0167173	−	0.646153i
$64$	7.41983	−	1.75853i	0.927478	−	0.219816i
$65$	4.26841	−	11.0554i	0.529431	−	1.37126i
$66$	−8.81947	−	5.59866i	−1.08560	−	0.689148i
$67$	−0.110239	−	0.807089i	−0.0134678	−	0.0986016i	0.982839	−	0.184464i	$-0.0590551\pi$
$67$	−0.110239	−	0.807089i	−0.0134678	−	0.0986016i	−0.996307	+	0.0858629i	$0.972635\pi$
$68$	0.481907	−	2.22473i	0.0584398	−	0.269788i
$69$	7.40395	−	2.83109i	0.891331	−	0.340824i
$70$	5.34205	−	2.94762i	0.638498	−	0.352308i
$71$	1.82852	+	4.23899i	0.217006	+	0.503076i	0.991594	−	0.129390i	$-0.0413021\pi$
$71$	1.82852	+	4.23899i	0.217006	+	0.503076i	−0.774588	+	0.632466i	$0.782043\pi$
$72$	−4.51057	−	7.93067i	−0.531576	−	0.934638i
$73$	2.83346	+	3.80600i	0.331631	+	0.445458i	0.936396	−	0.350946i	$-0.114140\pi$
$73$	2.83346	+	3.80600i	0.331631	+	0.445458i	−0.604764	+	0.796405i	$0.706733\pi$
$74$	−1.09245	+	0.780839i	−0.126995	+	0.0907707i
$75$	−10.6221	−	4.14065i	−1.22654	−	0.478122i
$76$	−6.04013	−	0.944659i	−0.692850	−	0.108360i
$77$	−4.24428	+	8.87616i	−0.483681	+	1.01153i
$78$	1.47806	−	6.14768i	0.167357	−	0.696088i
$79$	4.70874	+	7.47093i	0.529775	+	0.840545i	0.999097	−	0.0424816i	$-0.0135264\pi$
$79$	4.70874	+	7.47093i	0.529775	+	0.840545i	−0.469322	+	0.883027i	$0.655502\pi$
$80$	2.35880	−	4.08556i	0.263722	−	0.456780i
$81$	−6.26041	+	6.46585i	−0.695602	+	0.718428i
$82$	−0.0652386	−	0.112997i	−0.00720440	−	0.0124784i
$83$	5.78205	−	10.9769i	0.634662	−	1.20488i	−0.330644	−	0.943755i	$-0.607266\pi$
$83$	5.78205	−	10.9769i	0.634662	−	1.20488i	0.965306	−	0.261121i	$-0.0840920\pi$
$84$	−2.14585	+	1.58675i	−0.234131	+	0.173129i
$85$	−4.86317	−	7.09067i	−0.527484	−	0.769091i
$86$	0.637673	+	1.65161i	0.0687620	+	0.178098i
$87$	1.92061	+	1.68709i	0.205911	+	0.180875i
$88$	1.69387	+	17.4145i	0.180567	+	1.85639i
$89$	7.00705	−	16.2442i	0.742746	−	1.72188i	0.0521479	−	0.998639i	$-0.483393\pi$
$89$	7.00705	−	16.2442i	0.742746	−	1.72188i	0.690598	−	0.723239i	$-0.257347\pi$
$90$	−10.3985	−	2.53571i	−1.09610	−	0.267287i
$91$	−5.91476	−	0.691337i	−0.620036	−	0.0724718i
$92$	−3.53035	−	2.13058i	−0.368065	−	0.222128i
$93$	0.938239	+	4.86048i	0.0972908	+	0.504009i
$94$	10.3015	+	9.34808i	1.06251	+	0.964181i
$95$	−18.2518	+	14.1463i	−1.87260	+	1.45137i
$96$	−3.05643	+	7.41264i	−0.311946	+	0.756550i
$97$	9.65191	+	11.9665i	0.980003	+	1.21501i	0.976610	+	0.215019i	$0.0689814\pi$
$97$	9.65191	+	11.9665i	0.980003	+	1.21501i	0.00339356	+	0.999994i	$0.498920\pi$
$98$	2.93192	+	3.10765i	0.296168	+	0.313920i
$99$	16.0195	−	6.42399i	1.61002	−	0.645635i
$100$	1.70089	+	5.68137i	0.170089	+	0.568137i
$101$	−0.0881146	−	0.184276i	−0.00876773	−	0.0183361i	0.897737	−	0.440532i	$-0.145210\pi$
$101$	−0.0881146	−	0.184276i	−0.00876773	−	0.0183361i	−0.906505	+	0.422196i	$0.861259\pi$
$102$	−3.07178	−	3.40716i	−0.304151	−	0.337359i
$103$	12.2857	−	7.41444i	1.21054	−	0.730567i	0.239832	−	0.970814i	$-0.422908\pi$
$103$	12.2857	−	7.41444i	1.21054	−	0.730567i	0.970712	+	0.240248i	$0.0772287\pi$
$104$	−9.64085	+	4.38230i	−0.945363	+	0.429720i
$105$	−1.20269	+	10.0086i	−0.117370	+	0.976736i
$106$	5.77402	−	5.23964i	0.560822	−	0.508919i
$107$	−0.942140	+	5.34314i	−0.0910801	+	0.516541i	0.904798	+	0.425841i	$0.140022\pi$
$107$	−0.942140	+	5.34314i	−0.0910801	+	0.516541i	−0.995878	+	0.0907002i	$0.971089\pi$
$108$	4.65512	+	0.498469i	0.447939	+	0.0479652i
$109$	1.85432	+	10.5164i	0.177612	+	1.00729i	0.935086	+	0.354422i	$0.115322\pi$
$109$	1.85432	+	10.5164i	0.177612	+	1.00729i	−0.757474	+	0.652866i	$0.773567\pi$
$110$	16.2235	+	12.5742i	1.54685	+	1.19890i
$111$	0.00718139	−	2.21859i	0.000681628	−	0.210579i
$112$	−2.28376	−	0.635727i	−0.215795	−	0.0600706i
$113$	6.09830	−	17.8230i	0.573680	−	1.67664i	−0.151809	−	0.988410i	$-0.548510\pi$
$113$	6.09830	−	17.8230i	0.573680	−	1.67664i	0.725489	−	0.688234i	$-0.241614\pi$
$114$	−8.65547	+	8.76801i	−0.810659	+	0.821200i
$115$	−15.0046	+	4.17681i	−1.39918	+	0.389489i
$116$	0.0773212	−	1.32755i	0.00717909	−	0.123260i
$117$	6.81777	+	7.91516i	0.630303	+	0.731756i
$118$	−3.15091	−	1.58244i	−0.290064	−	0.145676i
$119$	−2.84086	+	3.25526i	−0.260421	+	0.298409i
$120$	7.36542	+	16.3438i	0.672368	+	1.49198i
$121$	−22.0825	−	0.856903i	−2.00750	−	0.0779003i
$122$	−3.92054	−	0.152135i	−0.354949	−	0.0137736i
$123$	0.214493	+	0.0215643i	0.0193402	+	0.00194439i
$124$	1.69316	−	1.94014i	0.152050	−	0.174230i
$125$	4.81173	+	2.41654i	0.430375	+	0.216142i
$126$	0.0694797	+	5.37791i	0.00618974	+	0.479102i
$127$	−0.288924	+	4.96063i	−0.0256378	+	0.440185i	0.960926	+	0.276807i	$0.0892761\pi$
$127$	−0.288924	+	4.96063i	−0.0256378	+	0.440185i	−0.986564	+	0.163378i	$0.947761\pi$
$128$	1.21820	−	0.339110i	0.107675	−	0.0299734i
$129$	−2.83027	−	0.738808i	−0.249192	−	0.0650484i
$130$	−4.02194	+	11.7546i	−0.352748	+	1.03094i
$131$	7.34375	+	2.04427i	0.641626	+	0.178609i	0.573679	−	0.819080i	$-0.305516\pi$
$131$	7.34375	+	2.04427i	0.641626	+	0.178609i	0.0679471	+	0.997689i	$0.478355\pi$
$132$	−7.76085	−	4.51429i	−0.675496	−	0.392918i
$133$	9.17153	+	7.10847i	0.795273	+	0.616383i
$134$	0.148287	+	0.840980i	0.0128101	+	0.0726496i
$135$	13.4359	−	11.4976i	1.15638	−	0.989553i
$136$	−1.33422	+	7.56672i	−0.114408	+	0.648841i
$137$	9.03760	−	8.20118i	0.772134	−	0.700674i	−0.187395	−	0.982285i	$-0.560004\pi$
$137$	9.03760	−	8.20118i	0.772134	−	0.700674i	0.959529	+	0.281610i	$0.0908685\pi$
$138$	−7.64089	+	3.26666i	−0.650435	+	0.278077i
$139$	−4.58778	+	2.08540i	−0.389130	+	0.176881i	−0.598814	−	0.800888i	$-0.704361\pi$
$139$	−4.58778	+	2.08540i	−0.389130	+	0.176881i	0.209684	+	0.977769i	$0.432756\pi$
$140$	4.48959	−	2.70948i	0.379440	−	0.228993i
$141$	−22.4779	+	4.79289i	−1.89298	+	0.403634i
$142$	−2.08777	−	4.36620i	−0.175202	−	0.366403i
$143$	−5.74575	−	19.1921i	−0.480484	−	1.60493i
$144$	2.19457	+	3.53241i	0.182881	+	0.294367i
$145$	−3.44695	−	3.65355i	−0.286253	−	0.303411i
$146$	−3.12289	−	3.87177i	−0.258452	−	0.320430i
$147$	−6.99700	+	0.932644i	−0.577103	+	0.0769232i
$148$	−0.912192	+	0.707002i	−0.0749817	+	0.0581152i
$149$	9.41931	+	8.54757i	0.771660	+	0.700244i	0.959423	−	0.281970i	$-0.0909879\pi$
$149$	9.41931	+	8.54757i	0.771660	+	0.700244i	−0.187763	+	0.982214i	$0.560124\pi$
$150$	11.2954	+	3.90573i	0.922269	+	0.318902i
$151$	−0.569361	−	0.343611i	−0.0463339	−	0.0279627i	0.493343	−	0.869835i	$-0.335775\pi$
$151$	−0.569361	−	0.343611i	−0.0463339	−	0.0279627i	−0.539677	+	0.841872i	$0.681454\pi$
$152$	20.4960	+	2.39564i	1.66245	+	0.194312i
$153$	7.53363	−	0.831154i	0.609057	−	0.0671948i
$154$	4.08526	−	9.47070i	0.329200	−	0.763171i
$155$	−0.941633	−	9.68084i	−0.0756338	−	0.777584i
$156$	1.06450	−	5.32896i	0.0852282	−	0.426659i
$157$	5.87021	+	15.2042i	0.468493	+	1.21343i	0.942886	+	0.333115i	$0.108100\pi$
$157$	5.87021	+	15.2042i	0.468493	+	1.21343i	−0.474393	+	0.880313i	$0.657332\pi$
$158$	−5.23631	−	7.63472i	−0.416578	−	0.607386i
$159$	1.45410	+	12.7998i	0.115318	+	1.01509i
$160$	7.34225	−	13.9389i	0.580456	−	1.10197i
$161$	3.91323	+	6.77791i	0.308406	+	0.534174i
$162$	6.29523	−	7.02774i	0.494600	−	0.552152i
$163$	9.79874	−	16.9719i	0.767496	−	1.32934i	−0.171420	−	0.985198i	$-0.554836\pi$
$163$	9.79874	−	16.9719i	0.767496	−	1.32934i	0.938917	−	0.344145i	$-0.111831\pi$
$164$	−0.0597935	−	0.0948688i	−0.00466909	−	0.00740801i
$165$	−32.5194	+	9.62109i	−2.53163	+	0.749001i
$166$	−5.61074	+	11.7339i	−0.435478	+	0.910725i
$167$	21.3805	+	3.34385i	1.65447	+	0.258755i	0.911721	−	0.410810i	$-0.134754\pi$
$167$	21.3805	+	3.34385i	1.65447	+	0.258755i	0.742753	+	0.669565i	$0.233520\pi$
$168$	7.02992	−	5.63272i	0.542370	−	0.434573i
$169$	−0.711252	+	0.508372i	−0.0547117	+	0.0391055i
$170$	5.38261	+	7.23010i	0.412828	+	0.554524i
$171$	−3.40492	−	20.0691i	−0.260380	−	1.53472i
$172$	0.602683	+	1.39718i	0.0459541	+	0.106534i
$173$	−5.45445	+	3.00964i	−0.414695	+	0.228819i	−0.676717	−	0.736243i	$-0.736598\pi$
$173$	−5.45445	+	3.00964i	−0.414695	+	0.228819i	0.262023	+	0.965062i	$0.415610\pi$
$174$	−2.08050	−	1.68923i	−0.157723	−	0.128060i
$175$	2.38301	−	11.0012i	0.180139	−	0.831613i
$176$	−1.07928	−	7.90172i	−0.0813537	−	0.595614i
$177$	5.16300	−	2.69827i	0.388075	−	0.202814i
$178$	−6.67988	+	17.3013i	−0.500678	+	1.29679i
$179$	−17.1781	+	4.07129i	−1.28395	+	0.304302i	−0.815279	−	0.579069i	$-0.803416\pi$
$179$	−17.1781	+	4.07129i	−1.28395	+	0.304302i	−0.468674	+	0.883371i	$0.655268\pi$
$180$	−9.01489	−	1.83116i	−0.671930	−	0.136486i
$181$	−6.46085	+	6.84810i	−0.480231	+	0.509015i	−0.921510	−	0.388355i	$-0.873043\pi$
$181$	−6.46085	+	6.84810i	−0.480231	+	0.509015i	0.441279	+	0.897370i	$0.354525\pi$
$182$	6.22408	+	0.483773i	0.461359	+	0.0358597i
$183$	3.98767	−	5.11074i	0.294777	−	0.377797i
$184$	12.1862	+	6.72404i	0.898376	+	0.495703i
$185$	−0.422024	+	4.33879i	−0.0310279	+	0.318994i
$186$	−1.18042	−	5.05343i	−0.0865528	−	0.370536i
$187$	−13.8410	−	4.43795i	−1.01216	−	0.324535i
$188$	9.15856	+	7.68495i	0.667957	+	0.560482i
$189$	−7.27900	−	5.09697i	−0.529469	−	0.370750i
$190$	18.5446	−	15.5607i	1.34537	−	1.12890i
$191$	−19.7511	+	8.06921i	−1.42914	+	0.583868i	−0.955006	−	0.296585i	$-0.904152\pi$
$191$	−19.7511	+	8.06921i	−1.42914	+	0.583868i	−0.474133	+	0.880453i	$0.657238\pi$
$192$	4.55739	−	12.3963i	0.328901	−	0.894628i
$193$	−1.49836	−	5.81699i	−0.107854	−	0.418716i	0.891561	−	0.452900i	$-0.149611\pi$
$193$	−1.49836	−	5.81699i	−0.107854	−	0.418716i	−0.999416	+	0.0341841i	$0.989117\pi$
$194$	−10.5972	−	12.1431i	−0.760837	−	0.871823i
$195$	−11.8817	−	16.7377i	−0.850868	−	1.19861i
$196$	2.62153	+	2.57118i	0.187252	+	0.183656i
$197$	−0.100426	−	0.0660514i	−0.00715507	−	0.00470597i	0.545926	−	0.837833i	$-0.316178\pi$
$197$	−0.100426	−	0.0660514i	−0.00715507	−	0.00470597i	−0.553081	+	0.833127i	$0.686548\pi$
$198$	−16.5200	+	7.38060i	−1.17403	+	0.524516i
$199$	−1.22095	−	20.9628i	−0.0865505	−	1.48602i	−0.710028	−	0.704174i	$-0.751318\pi$
$199$	−1.22095	−	20.9628i	−0.0865505	−	1.48602i	0.623477	−	0.781841i	$-0.285719\pi$
$200$	−6.48041	−	18.9397i	−0.458234	−	1.33924i
$201$	−1.27089	−	0.612759i	−0.0896417	−	0.0432207i
$202$	0.0997946	+	0.189455i	0.00702153	+	0.0133300i
$203$	−1.34582	+	2.13529i	−0.0944579	+	0.149868i
$204$	−2.75163	−	2.82374i	−0.192652	−	0.197701i
$205$	−0.415635	−	0.0816281i	−0.0290292	−	0.00570116i
$206$	−12.5684	+	8.26636i	−0.875681	+	0.575945i
$207$	2.99341	−	13.3993i	0.208056	−	0.931314i
$208$	4.31360	−	2.16637i	0.299094	−	0.150211i
$209$	−9.73747	+	37.8032i	−0.673555	+	2.61490i
$210$	0.853023	−	10.5333i	0.0588642	−	0.726867i
$211$	21.4512	−	4.21288i	1.47676	−	0.290027i	0.611460	−	0.791276i	$-0.290583\pi$
$211$	21.4512	−	4.21288i	1.47676	−	0.290027i	0.865303	+	0.501249i	$0.167126\pi$
$212$	4.78419	−	4.69230i	0.328579	−	0.322268i
$213$	7.87008	+	1.41399i	0.539249	+	0.0968850i
$214$	0.769737	−	5.63547i	0.0526181	−	0.385233i
$215$	5.40085	+	1.96575i	0.368335	+	0.134063i
$216$	−15.7662	−	1.07199i	−1.07275	−	0.0729396i
$217$	−4.59281	+	1.67165i	−0.311780	+	0.113479i
$218$	−2.36997	−	10.9410i	−0.160515	−	0.741018i
$219$	8.20601	−	0.451298i	0.554511	−	0.0304959i
$220$	14.3520	+	10.2582i	0.967612	+	0.691608i
$221$	−0.170597	−	8.79594i	−0.0114756	−	0.591679i
$222$	0.0826617	+	2.32436i	0.00554789	+	0.156001i
$223$	7.24857	−	10.5687i	0.485400	−	0.707731i	−0.502195	−	0.864755i	$-0.667474\pi$
$223$	7.24857	−	10.5687i	0.485400	−	0.707731i	0.987595	+	0.157024i	$0.0501900\pi$
$224$	−7.70319	−	1.82569i	−0.514691	−	0.121984i
$225$	−16.1388	+	11.3782i	−1.07592	+	0.758544i
$226$	−5.66375	+	18.9182i	−0.376747	+	1.25842i
$227$	−14.6237	+	2.28710i	−0.970607	+	0.151800i	−0.619896	−	0.784684i	$-0.712825\pi$
$227$	−14.6237	+	2.28710i	−0.970607	+	0.151800i	−0.350710	+	0.936484i	$0.614060\pi$
$228$	−7.14123	+	7.81853i	−0.472939	+	0.517795i
$229$	15.0903	+	6.16506i	0.997194	+	0.407399i	0.817253	−	0.576279i	$-0.195496\pi$
$229$	15.0903	+	6.16506i	0.997194	+	0.407399i	0.179941	+	0.983677i	$0.442409\pi$
$230$	15.5482	−	4.98532i	1.02522	−	0.328722i
$231$	8.75788	+	14.6185i	0.576226	+	0.961826i
$232$	−0.0870397	+	4.48774i	−0.00571444	+	0.294635i
$233$	9.78201	−	13.1395i	0.640841	−	0.860799i	−0.356453	−	0.934313i	$-0.616014\pi$
$233$	9.78201	−	13.1395i	0.640841	−	0.860799i	0.997294	+	0.0735146i	$0.0234215\pi$
$234$	−7.46366	−	8.01434i	−0.487915	−	0.523913i
$235$	44.8536	−	5.24263i	2.92593	−	0.341992i
$236$	−2.75877	−	1.25402i	−0.179581	−	0.0816295i
$237$	15.2919	+	0.346106i	0.993314	+	0.0224820i
$238$	2.84360	−	3.52551i	0.184323	−	0.228525i
$239$	−9.56624	+	0.743547i	−0.618789	+	0.0480961i	−0.383061	−	0.923723i	$-0.625130\pi$
$239$	−9.56624	+	0.743547i	−0.618789	+	0.0480961i	−0.235728	+	0.971819i	$0.575747\pi$
$240$	−3.64354	−	7.31382i	−0.235190	−	0.472105i
$241$	−17.0759	+	0.662624i	−1.09996	+	0.0426834i	−0.582353	−	0.812936i	$-0.697868\pi$
$241$	−17.0759	+	0.662624i	−1.09996	+	0.0426834i	−0.517605	+	0.855620i	$0.673176\pi$
$242$	23.1673			1.48925
$243$	3.34899	+	15.2245i	0.214838	+	0.976650i
$244$	−3.37208			−0.215875
$245$	13.8594	−	0.537807i	0.885442	−	0.0343592i
$246$	−0.225567	−	0.0138706i	−0.0143816	−	0.000884354i
$247$	−23.5568	+	1.83098i	−1.49888	+	0.116502i
$248$	−5.45682	+	6.76539i	−0.346508	+	0.429603i
$249$	−10.3206	−	18.8484i	−0.654044	−	1.19447i
$250$	−5.13873	−	2.33584i	−0.325002	−	0.147732i
$251$	6.18184	−	0.722554i	0.390194	−	0.0456072i	0.0812659	−	0.996692i	$-0.474104\pi$
$251$	6.18184	−	0.722554i	0.390194	−	0.0456072i	0.308928	+	0.951085i	$0.400030\pi$
$252$	0.238894	+	4.61630i	0.0150489	+	0.290800i
$253$	−15.7229	+	21.1196i	−0.988493	+	1.32778i
$254$	0.101013	−	5.20822i	0.00633814	−	0.326793i
$255$	−14.8905	+	0.240586i	−0.932477	+	0.0150661i
$256$	−15.7848	+	5.06120i	−0.986551	+	0.316325i
$257$	−10.4929	−	4.28681i	−0.654528	−	0.267404i	0.0265142	−	0.999648i	$-0.491559\pi$
$257$	−10.4929	−	4.28681i	−0.654528	−	0.267404i	−0.681042	+	0.732244i	$0.738473\pi$
$258$	2.99487	+	0.658885i	0.186452	+	0.0410204i
$259$	2.16422	−	0.338477i	0.134478	−	0.0210320i
$260$	−3.06237	+	10.2290i	−0.189920	+	0.634377i
$261$	4.27317	−	1.15977i	0.264503	−	0.0717877i
$262$	−7.77600	−	1.84295i	−0.480403	−	0.113858i
$263$	−10.8110	+	15.7629i	−0.666636	+	0.971979i	0.332942	+	0.942947i	$0.391959\pi$
$263$	−10.8110	+	15.7629i	−0.666636	+	0.971979i	−0.999578	+	0.0290320i	$0.990758\pi$
$264$	26.7669	+	14.2102i	1.64739	+	0.874578i
$265$	−0.490829	−	25.3070i	−0.0301514	−	1.55460i
$266$	−9.89654	−	7.07362i	−0.606796	−	0.433712i
$267$	−16.7549	−	25.6552i	−1.02539	−	1.57007i
$268$	0.155378	+	0.717303i	0.00949120	+	0.0438162i
$269$	7.51411	−	2.73491i	0.458143	−	0.166751i	−0.102631	−	0.994720i	$-0.532726\pi$
$269$	7.51411	−	2.73491i	0.458143	−	0.166751i	0.560774	+	0.827969i	$0.310504\pi$
$270$	−13.6073	+	12.5904i	−0.828117	+	0.766226i
$271$	−29.4816	−	10.7304i	−1.79088	−	0.651828i	−0.999161	−	0.0409435i	$-0.986964\pi$
$271$	−29.4816	−	10.7304i	−1.79088	−	0.651828i	−0.791720	−	0.610884i	$-0.790814\pi$
$272$	0.473953	−	3.46995i	0.0287376	−	0.210396i
$273$	−6.65552	+	7.87980i	−0.402810	+	0.476907i
$274$	−9.13391	+	8.95848i	−0.551800	+	0.541201i
$275$	37.1585	−	7.29769i	2.24074	−	0.440068i
$276$	−6.45323	+	3.06009i	−0.388439	+	0.184196i
$277$	−0.0362001	+	0.140538i	−0.00217505	+	0.00844408i	−0.969468	−	0.245217i	$-0.921141\pi$
$277$	−0.0362001	+	0.140538i	−0.00217505	+	0.00844408i	0.967293	+	0.253661i	$0.0816347\pi$
$278$	4.72113	−	2.37104i	0.283154	−	0.142205i
$279$	7.91602	+	3.29401i	0.473919	+	0.197207i
$280$	−14.7881	+	9.72625i	−0.883755	+	0.581255i
$281$	2.49168	+	0.489350i	0.148641	+	0.0291922i	0.266479	−	0.963841i	$-0.414140\pi$
$281$	2.49168	+	0.489350i	0.148641	+	0.0291922i	−0.117838	+	0.993033i	$0.537596\pi$
$282$	23.3517	−	5.93448i	1.39057	−	0.353393i
$283$	15.1018	−	23.9607i	0.897711	−	1.42432i	−0.00778923	−	0.999970i	$-0.502479\pi$
$283$	15.1018	−	23.9607i	0.897711	−	1.42432i	0.905500	−	0.424346i	$-0.139496\pi$
$284$	−1.93851	−	3.68017i	−0.115029	−	0.218378i
$285$	2.97035	+	39.8863i	0.175948	+	2.36266i
$286$	6.79908	+	19.8711i	0.402038	+	1.17500i
$287$	0.0123759	+	0.212486i	0.000730526	+	0.0125426i
$288$	7.78065	+	11.5034i	0.458479	+	0.677846i
$289$	8.87044	+	5.83418i	0.521790	+	0.343187i
$290$	3.75934	+	3.68714i	0.220756	+	0.216516i
$291$	26.5115	−	2.49211i	1.55413	−	0.146090i
$292$	−2.81100	−	3.22105i	−0.164502	−	0.188498i
$293$	−2.02528	−	7.86261i	−0.118318	−	0.459338i	0.881602	−	0.471994i	$-0.156465\pi$
$293$	−2.02528	−	7.86261i	−0.118318	−	0.459338i	−0.999920	+	0.0126551i	$0.995972\pi$
$294$	7.29176	−	1.26141i	0.425264	−	0.0735670i
$295$	−10.5963	+	4.32906i	−0.616939	+	0.252047i
$296$	2.98414	−	2.50399i	0.173450	−	0.145542i
$297$	6.04560	−	29.2768i	0.350802	−	1.69881i
$298$	−10.2146	−	8.57107i	−0.591716	−	0.496509i
$299$	−15.1754	−	4.86579i	−0.877615	−	0.281396i
$300$	9.83083	+	2.97786i	0.567583	+	0.171927i
$301$	0.279599	−	2.87453i	0.0161158	−	0.165685i
$302$	0.610398	+	0.336803i	0.0351245	+	0.0193809i
$303$	−0.350376	−	0.0490129i	−0.0201286	−	0.00281572i
$304$	−9.37752	−	0.728879i	−0.537838	−	0.0418041i
$305$	−8.74068	+	9.26457i	−0.500490	+	0.530488i
$306$	−7.85802	+	1.17691i	−0.449213	+	0.0672794i
$307$	13.8858	−	3.29100i	0.792506	−	0.187827i	0.185625	−	0.982621i	$-0.440569\pi$
$307$	13.8858	−	3.29100i	0.792506	−	0.187827i	0.606880	+	0.794793i	$0.292421\pi$
$308$	3.19286	−	8.26970i	0.181930	−	0.471210i
$309$	1.04412	−	24.8323i	0.0593979	−	1.41266i
$310$	1.37992	+	10.1028i	0.0783744	+	0.573802i
$311$	0.0869130	−	0.401235i	0.00492838	−	0.0227519i	−0.974803	−	0.223066i	$-0.928394\pi$
$311$	0.0869130	−	0.401235i	0.00492838	−	0.0227519i	0.979732	+	0.200314i	$0.0641961\pi$
$312$	−2.89293	+	18.1131i	−0.163780	+	1.02545i
$313$	6.67492	−	3.68306i	0.377289	−	0.208179i	−0.283122	−	0.959084i	$-0.591370\pi$
$313$	6.67492	−	3.68306i	0.377289	−	0.208179i	0.660410	+	0.750905i	$0.270382\pi$
$314$	−6.76734	−	15.6885i	−0.381903	−	0.885351i
$315$	13.3022	+	11.3095i	0.749496	+	0.637216i
$316$	−4.75144	−	6.38229i	−0.267289	−	0.359032i
$317$	9.35726	−	6.68817i	0.525556	−	0.375645i	−0.287545	−	0.957767i	$-0.592839\pi$
$317$	9.35726	−	6.68817i	0.525556	−	0.375645i	0.813101	+	0.582122i	$0.197777\pi$
$318$	−2.04354	−	13.3493i	−0.114596	−	0.748591i
$319$	−8.38927	−	1.31206i	−0.469709	−	0.0734611i
$320$	−11.1949	+	23.4122i	−0.625816	+	1.30878i
$321$	6.81448	+	6.47095i	0.380347	+	0.361173i
$322$	−4.37480	−	6.94109i	−0.243798	−	0.386812i
$323$	−8.57135	+	14.8460i	−0.476923	+	0.826054i
$324$	5.17222	−	6.24531i	0.287345	−	0.346962i
$325$	11.4602	+	19.8496i	0.635697	+	1.10106i
$326$	−9.57471	+	18.1771i	−0.530294	+	1.00674i
$327$	16.9594	+	7.38079i	0.937860	+	0.408159i
$328$	0.214090	+	0.312151i	0.0118212	+	0.0172357i
$329$	−8.17326	−	21.1693i	−0.450607	−	1.16710i
$330$	33.6744	−	11.4004i	1.85372	−	0.627572i
$331$	2.08723	+	21.4586i	0.114724	+	1.17947i	0.859136	+	0.511748i	$0.171002\pi$
$331$	2.08723	+	21.4586i	0.114724	+	1.17947i	−0.744411	+	0.667721i	$0.767270\pi$
$332$	−4.42754	+	10.2642i	−0.242993	+	0.563320i
$333$	−3.19682	−	2.13236i	−0.175185	−	0.116852i
$334$	−22.5330	−	2.63373i	−1.23295	−	0.144111i
$335$	2.37349	+	1.43241i	0.129678	+	0.0782610i
$336$	−3.10232	+	2.68974i	−0.169245	+	0.146737i
$337$	5.32453	+	4.83175i	0.290046	+	0.263202i	0.804019	−	0.594604i	$-0.202691\pi$
$337$	5.32453	+	4.83175i	0.290046	+	0.263202i	−0.513973	+	0.857806i	$0.671827\pi$
$338$	0.724402	−	0.561454i	0.0394023	−	0.0305391i
$339$	−19.9039	−	25.8530i	−1.08103	−	1.40414i
$340$	4.86361	+	6.02993i	0.263766	+	0.327019i
$341$	−11.2836	−	11.9599i	−0.611043	−	0.647667i
$342$	4.38260	+	20.8849i	0.236984	+	1.12933i
$343$	−5.43219	−	18.1448i	−0.293311	−	0.979726i
$344$	−2.21562	−	4.63357i	−0.119458	−	0.249825i
$345$	−8.31983	+	25.6618i	−0.447925	+	1.38159i
$346$	5.59144	−	3.37445i	0.300598	−	0.181412i
$347$	5.56487	−	2.52955i	0.298738	−	0.135793i	−0.258834	−	0.965922i	$-0.583338\pi$
$347$	5.56487	−	2.52955i	0.298738	−	0.135793i	0.557572	+	0.830129i	$0.311733\pi$
$348$	−1.84306	−	1.38140i	−0.0987983	−	0.0740508i
$349$	23.5316	−	21.3538i	1.25962	−	1.14304i	0.276312	−	0.961068i	$-0.410888\pi$
$349$	23.5316	−	21.3538i	1.25962	−	1.14304i	0.983304	−	0.181972i	$-0.0582480\pi$
$350$	−2.04912	+	11.6211i	−0.109530	+	0.621175i
$351$	17.9505	−	2.27449i	0.958129	−	0.121403i
$352$	−4.62473	−	26.2282i	−0.246499	−	1.39797i
$353$	8.09549	+	6.27448i	0.430879	+	0.333957i	0.804844	−	0.593486i	$-0.202249\pi$
$353$	8.09549	+	6.27448i	0.430879	+	0.333957i	−0.373965	+	0.927443i	$0.622002\pi$
$354$	−5.29878	+	3.03643i	−0.281627	+	0.161384i
$355$	−15.1358	−	4.21334i	−0.803325	−	0.223621i
$356$	−5.16018	+	15.0812i	−0.273489	+	0.799302i
$357$	1.98350	+	7.21577i	0.104978	+	0.381899i
$358$	17.8293	−	4.96314i	0.942310	−	0.262310i
$359$	0.100243	−	1.72111i	0.00529062	−	0.0908365i	−0.994629	−	0.103503i	$-0.966995\pi$
$359$	0.100243	−	1.72111i	0.00529062	−	0.0908365i	0.999920	+	0.0126664i	$0.00403194\pi$
$360$	30.6454	+	4.99631i	1.61516	+	0.263329i
$361$	24.1641	+	12.1357i	1.27180	+	0.638721i
$362$	6.48965	−	7.43631i	0.341088	−	0.390844i
$363$	−22.3584	+	31.0680i	−1.17351	+	1.63065i
$364$	5.36144	+	0.208048i	0.281016	+	0.0109047i
$365$	−16.1360	−	0.626149i	−0.844595	−	0.0327741i
$366$	−3.96951	+	5.51582i	−0.207490	+	0.288317i
$367$	−20.8018	+	23.8363i	−1.08585	+	1.24424i	−0.117917	+	0.993023i	$0.537622\pi$
$367$	−20.8018	+	23.8363i	−1.08585	+	1.24424i	−0.967930	+	0.251219i	$0.919168\pi$
$368$	−5.66919	−	2.84718i	−0.295527	−	0.148419i
$369$	0.236292	−	0.289106i	0.0123009	−	0.0150503i
$370$	0.265720	−	4.56223i	0.0138141	−	0.237179i
$371$	−12.2533	+	3.41093i	−0.636157	+	0.177086i
$372$	−1.18217	−	4.30061i	−0.0612928	−	0.222976i
$373$	6.43429	−	18.8049i	0.333155	−	0.973682i	−0.644707	−	0.764430i	$-0.723021\pi$
$373$	6.43429	−	18.8049i	0.333155	−	0.973682i	0.977862	−	0.209252i	$-0.0671029\pi$
$374$	14.6795	+	4.08632i	0.759058	+	0.211298i
$375$	8.09175	−	4.63692i	0.417856	−	0.239449i
$376$	−31.8962	−	24.7214i	−1.64492	−	1.27491i
$377$	−0.892457	−	5.06138i	−0.0459639	−	0.260674i
$378$	7.83226	+	5.04341i	0.402848	+	0.259405i
$379$	−3.00330	+	17.0325i	−0.154269	+	0.874903i	0.805182	+	0.593028i	$0.202068\pi$
$379$	−3.00330	+	17.0325i	−0.154269	+	0.874903i	−0.959451	+	0.281875i	$0.909044\pi$
$380$	15.4077	−	13.9818i	0.790401	−	0.717250i
$381$	6.88690	+	5.16184i	0.352827	+	0.264449i
$382$	20.3621	−	9.25573i	1.04182	−	0.473564i
$383$	−21.5800	+	13.0236i	−1.10269	+	0.665475i	−0.946646	−	0.322276i	$-0.895552\pi$
$383$	−21.5800	+	13.0236i	−1.10269	+	0.665475i	−0.156040	+	0.987751i	$0.549873\pi$
$384$	0.675477	−	2.08345i	0.0344703	−	0.106321i
$385$	−14.4444	−	30.2079i	−0.736154	−	1.53953i
$386$	1.80606	+	6.03264i	0.0919258	+	0.307053i
$387$	−3.77389	+	3.38033i	−0.191837	+	0.171832i
$388$	−9.50572	−	10.0755i	−0.482580	−	0.511505i
$389$	19.0093	+	23.5678i	0.963808	+	1.19493i	0.980788	+	0.195079i	$0.0624964\pi$
$389$	19.0093	+	23.5678i	0.963808	+	1.19493i	−0.0169791	+	0.999856i	$0.505405\pi$
$390$	13.1270	+	17.0505i	0.664712	+	0.863386i
$391$	−9.13878	+	7.08309i	−0.462168	+	0.358207i
$392$	−9.17853	−	8.32907i	−0.463586	−	0.420682i
$393$	9.97595	−	8.64926i	0.503220	−	0.436297i
$394$	0.107886	+	0.0651094i	0.00543521	+	0.00328017i
$395$	−29.8510	−	3.48909i	−1.50197	−	0.175555i
$396$	−13.9416	+	6.88910i	−0.700594	+	0.346190i
$397$	−4.68291	+	10.8562i	−0.235029	+	0.544857i	−0.994386	−	0.105817i	$-0.966254\pi$
$397$	−4.68291	+	10.8562i	−0.235029	+	0.544857i	0.759357	+	0.650674i	$0.225514\pi$
$398$	2.13112	+	21.9098i	0.106823	+	1.09824i
$399$	19.0369	−	6.44492i	0.953039	−	0.322649i
$400$	3.28633	+	8.51181i	0.164317	+	0.425591i
$401$	4.42932	+	6.45811i	0.221190	+	0.322503i	0.919351	−	0.393438i	$-0.128714\pi$
$401$	4.42932	+	6.45811i	0.221190	+	0.322503i	−0.698161	+	0.715940i	$0.745998\pi$
$402$	1.35622	+	0.590231i	0.0676422	+	0.0294381i
$403$	4.63814	−	8.80529i	0.231042	−	0.438623i
$404$	0.0920187	+	0.159381i	0.00457810	+	0.00792950i
$405$	−3.75184	−	30.3987i	−0.186430	−	1.51052i
$406$	1.32301	−	2.29151i	0.0656597	−	0.113726i
$407$	3.92935	+	6.23434i	0.194771	+	0.309025i
$408$	9.65037	+	9.16388i	0.477765	+	0.453680i
$409$	−1.06622	+	2.22981i	−0.0527213	+	0.110257i	−0.926842	−	0.375451i	$-0.877488\pi$
$409$	−1.06622	+	2.22981i	−0.0527213	+	0.110257i	0.874121	+	0.485709i	$0.161438\pi$
$410$	0.438714	+	0.0686137i	0.0216666	+	0.00338859i
$411$	−3.19859	−	20.8945i	−0.157775	−	1.03065i
$412$	−10.5184	+	7.51811i	−0.518205	+	0.370391i
$413$	3.43476	+	4.61368i	0.169014	+	0.227025i
$414$	−2.59105	+	14.1580i	−0.127343	+	0.695828i
$415$	16.7237	+	38.7699i	0.820934	+	1.90314i
$416$	14.1139	−	7.78772i	0.691991	−	0.381825i
$417$	−1.37665	+	8.61943i	−0.0674149	+	0.422095i
$418$	8.66375	−	39.9963i	0.423758	−	1.95628i
$419$	1.33390	+	9.76590i	0.0651655	+	0.477096i	0.994238	+	0.107197i	$0.0341877\pi$
$419$	1.33390	+	9.76590i	0.0651655	+	0.477096i	−0.929072	+	0.369898i	$0.879393\pi$
$420$	0.381556	−	9.07456i	0.0186180	−	0.442793i
$421$	−1.95020	+	5.05116i	−0.0950472	+	0.246178i	−0.972251	−	0.233940i	$-0.924838\pi$
$421$	−1.95020	+	5.05116i	−0.0950472	+	0.246178i	0.877204	+	0.480118i	$0.159406\pi$
$422$	−22.2998	+	5.28516i	−1.08554	+	0.257278i
$423$	−14.5781	+	37.0426i	−0.708810	+	1.80107i
$424$	−15.5222	+	16.4525i	−0.753822	+	0.799005i
$425$	16.5794	+	1.28866i	0.804221	+	0.0625090i
$426$	−8.30174	−	1.16130i	−0.402220	−	0.0562653i
$427$	5.60387	+	3.09208i	0.271190	+	0.149636i
$428$	0.473253	−	4.86547i	0.0228756	−	0.235181i
$429$	−33.2094	−	10.0595i	−1.60336	−	0.485676i
$430$	−5.73754	−	1.83967i	−0.276689	−	0.0887166i
$431$	16.8406	+	14.1310i	0.811185	+	0.680665i	0.950890	−	0.309528i	$-0.100171\pi$
$431$	16.8406	+	14.1310i	0.811185	+	0.680665i	−0.139705	+	0.990193i	$0.544616\pi$
$432$	7.19987	+	0.209599i	0.346404	+	0.0100843i
$433$	−10.2765	+	8.62301i	−0.493857	+	0.414395i	−0.855406	−	0.517958i	$-0.826692\pi$
$433$	−10.2765	+	8.62301i	−0.493857	+	0.414395i	0.361549	+	0.932353i	$0.382248\pi$
$434$	4.74322	−	1.93782i	0.227682	−	0.0930183i
$435$	−8.57265	+	1.48299i	−0.411027	+	0.0711042i
$436$	−2.39998	−	9.31730i	−0.114938	−	0.446218i
$437$	20.4181	+	23.3965i	0.976729	+	1.11921i
$438$	−8.57781	+	0.806325i	−0.409864	+	0.0385277i
$439$	−7.18825	−	7.05019i	−0.343076	−	0.336487i	0.508166	−	0.861259i	$-0.330323\pi$
$439$	−7.18825	−	7.05019i	−0.343076	−	0.336487i	−0.851243	+	0.524772i	$0.824151\pi$
$440$	−49.7496	−	32.7208i	−2.37172	−	1.55991i
$441$	−5.34557	+	10.9958i	−0.254551	+	0.523611i
$442$	0.536259	+	9.20720i	0.0255072	+	0.437942i
$443$	0.941972	+	2.75302i	0.0447544	+	0.130800i	0.966262	−	0.257560i	$-0.0829184\pi$
$443$	0.941972	+	2.75302i	0.0447544	+	0.130800i	−0.921508	+	0.388360i	$0.873042\pi$
$444$	0.148452	+	1.99344i	0.00704524	+	0.0946044i
$445$	28.0591	+	53.2689i	1.33013	+	2.52519i
$446$	−7.16358	+	11.3658i	−0.339206	+	0.538186i
$447$	21.3520	−	5.42629i	1.00992	−	0.256654i
$448$	12.7959	+	2.51304i	0.604552	+	0.118730i
$449$	−16.5736	+	10.9006i	−0.782154	+	0.514431i	−0.876670	−	0.481092i	$-0.840240\pi$
$449$	−16.5736	+	10.9006i	−0.782154	+	0.514431i	0.0945156	+	0.995523i	$0.469870\pi$
$450$	16.4436	−	12.5752i	0.775156	−	0.592799i
$451$	−0.639887	+	0.321363i	−0.0301311	+	0.0151324i
$452$	−4.23363	+	16.4360i	−0.199133	+	0.773083i
$453$	−1.04075	+	0.493519i	−0.0488987	+	0.0231875i
$454$	15.2260	−	2.99028i	0.714590	−	0.140341i
$455$	14.4688	−	14.1909i	0.678310	−	0.665282i
$456$	23.0629	−	27.3053i	1.08002	−	1.27869i
$457$	1.89910	−	13.9038i	0.0888359	−	0.650394i	−0.891495	−	0.453031i	$-0.850343\pi$
$457$	1.89910	−	13.9038i	0.0888359	−	0.650394i	0.980331	−	0.197363i	$-0.0632377\pi$
$458$	−16.0583	−	5.84476i	−0.750357	−	0.273108i
$459$	6.00538	−	11.6737i	0.280307	−	0.544880i
$460$	13.1868	−	4.79961i	0.614839	−	0.223783i
$461$	−3.35192	−	15.4742i	−0.156115	−	0.720705i	−0.986533	−	0.163564i	$-0.947701\pi$
$461$	−3.35192	−	15.4742i	−0.156115	−	0.720705i	0.830418	−	0.557141i	$-0.188102\pi$
$462$	−9.76849	−	14.9575i	−0.454471	−	0.695886i
$463$	−13.5770	−	9.70423i	−0.630975	−	0.450994i	0.220501	−	0.975387i	$-0.429231\pi$
$463$	−13.5770	−	9.70423i	−0.630975	−	0.450994i	−0.851477	+	0.524393i	$0.824292\pi$
$464$	−0.0396732	−	2.04554i	−0.00184178	−	0.0949618i
$465$	−14.8799	−	7.89957i	−0.690041	−	0.366334i
$466$	−9.71297	+	14.1619i	−0.449945	+	0.656035i
$467$	−4.01447	−	0.951447i	−0.185768	−	0.0440277i	0.136679	−	0.990615i	$-0.456357\pi$
$467$	−4.01447	−	0.951447i	−0.185768	−	0.0440277i	−0.322447	+	0.946588i	$0.604505\pi$
$468$	−6.67698	−	6.63408i	−0.308643	−	0.306661i
$469$	0.399530	−	1.33452i	0.0184486	−	0.0616225i
$470$	−46.7730	+	7.31516i	−2.15748	+	0.337423i
$471$	27.5698	+	6.06548i	1.27035	+	0.279483i
$472$	9.46903	+	3.86852i	0.435847	+	0.178063i
$473$	9.25210	−	2.96657i	0.425412	−	0.136403i
$474$	−16.0330	+	0.259046i	−0.736419	+	0.0118984i
$475$	0.866054	−	44.6535i	0.0397373	−	2.04884i
$476$	2.32463	−	3.12252i	0.106549	−	0.143120i
$477$	19.8740	+	10.1427i	0.909968	+	0.464404i
$478$	9.99084	−	1.16776i	0.456970	−	0.0534122i
$479$	22.5762	+	10.2621i	1.03153	+	0.468888i	0.856757	−	0.515720i	$-0.172476\pi$
$479$	22.5762	+	10.2621i	1.03153	+	0.468888i	0.174774	+	0.984609i	$0.444080\pi$
$480$	−13.1055	−	23.9343i	−0.598182	−	1.09245i
$481$	−2.80029	+	3.47181i	−0.127682	+	0.158301i
$482$	17.8609	−	1.38826i	0.813540	−	0.0632333i
$483$	13.5303	+	0.832001i	0.615648	+	0.0378574i
$484$	19.8964	−	0.772069i	0.904380	−	0.0350940i
$485$	−52.3213			−2.37579
$486$	−4.12709	−	15.8122i	−0.187208	−	0.717254i
$487$	1.36812			0.0619954			0.0309977	−	0.999519i	$-0.490132\pi$
$487$	1.36812			0.0619954			0.0309977	+	0.999519i	$0.490132\pi$
$488$	11.3735	−	0.441343i	0.514853	−	0.0199786i
$489$	−15.1357	−	30.3825i	−0.684460	−	1.37394i
$490$	−14.4964	+	1.12675i	−0.654882	+	0.0509015i
$491$	23.3724	−	28.9772i	1.05478	−	1.30772i	0.105114	−	0.994460i	$-0.466479\pi$
$491$	23.3724	−	28.9772i	1.05478	−	1.30772i	0.949666	−	0.313263i	$-0.101422\pi$
$492$	−0.194182	−	0.00439499i	−0.00875441	−	0.000198141i
$493$	−3.39459	−	1.54303i	−0.152885	−	0.0694946i
$494$	24.6023	−	2.87560i	1.10691	−	0.129379i
$495$	−17.2104	+	56.1608i	−0.773549	+	2.52424i
$496$	2.36581	−	3.17783i	0.106228	−	0.142689i
$497$	−0.153093	+	7.89342i	−0.00686715	+	0.354068i
$498$	11.5775	+	19.3250i	0.518800	+	0.865972i
$499$	−39.7468	+	12.7443i	−1.77931	+	0.570513i	−0.998526	−	0.0542847i	$-0.982712\pi$
$499$	−39.7468	+	12.7443i	−1.77931	+	0.570513i	−0.780786	+	0.624798i	$0.785181\pi$
$500$	−4.49105	−	1.83480i	−0.200846	−	0.0820547i
$501$	25.2781	−	27.6756i	1.12934	−	1.23646i
$502$	−6.44638	+	1.00820i	−0.287716	+	0.0449980i
$503$	4.76442	−	15.9143i	0.212435	−	0.709583i	−0.783652	−	0.621201i	$-0.786645\pi$
$503$	4.76442	−	15.9143i	0.212435	−	0.709583i	0.996087	−	0.0883821i	$-0.0281696\pi$
$504$	−1.40994	−	15.5388i	−0.0628036	−	0.692152i
$505$	0.676409	+	0.160312i	0.0300998	+	0.00713378i
$506$	15.6120	−	22.7628i	0.694037	−	1.01193i
$507$	0.0538176	+	1.51330i	0.00239012	+	0.0672079i
$508$	−0.0868169	−	4.47626i	−0.00385188	−	0.198602i
$509$	0.871241	+	0.622726i	0.0386171	+	0.0276018i	0.600637	−	0.799522i	$-0.294914\pi$
$509$	0.871241	+	0.622726i	0.0386171	+	0.0276018i	−0.562020	+	0.827124i	$0.689976\pi$
$510$	15.5886	−	0.857314i	0.690277	−	0.0379625i
$511$	1.71785	+	7.93049i	0.0759933	+	0.350824i
$512$	13.9530	−	5.07849i	0.616643	−	0.224440i
$513$	−32.2369	−	14.2785i	−1.42329	−	0.630410i
$514$	11.1660	+	4.06409i	0.492511	+	0.179260i
$515$	−6.60896	+	48.3862i	−0.291226	+	2.13215i
$516$	2.59399	+	0.466053i	0.114194	+	0.0205168i
$517$	54.5021	−	53.4553i	2.39700	−	2.35096i
$518$	−2.25335	+	0.442544i	−0.0990067	+	0.0194443i
$519$	−0.870971	+	10.7549i	−0.0382314	+	0.472089i
$520$	8.99008	−	34.9016i	0.394241	−	1.53054i
$521$	3.01191	−	1.51264i	0.131954	−	0.0662699i	−0.381597	−	0.924329i	$-0.624626\pi$
$521$	3.01191	−	1.51264i	0.131954	−	0.0662699i	0.513551	+	0.858059i	$0.328330\pi$
$522$	−4.42920	+	1.38861i	−0.193861	+	0.0607777i
$523$	2.56164	−	1.68482i	0.112013	−	0.0736720i	−0.492267	−	0.870445i	$-0.663831\pi$
$523$	2.56164	−	1.68482i	0.112013	−	0.0736720i	0.604279	+	0.796773i	$0.293461\pi$
$524$	−6.73955	−	1.32360i	−0.294419	−	0.0578219i
$525$	−13.6067	−	13.9633i	−0.593845	−	0.609408i
$526$	10.6843	−	16.9517i	0.465856	−	0.739131i
$527$	−3.36511	−	6.38851i	−0.146587	−	0.278288i
$528$	−12.4425	−	5.99915i	−0.541491	−	0.261080i
$529$	−0.665420	−	1.94476i	−0.0289313	−	0.0845549i
$530$	1.54288	+	26.4903i	0.0670186	+	1.15066i
$531$	1.04183	−	10.0362i	0.0452117	−	0.435536i
$532$	−8.73501	−	5.74511i	−0.378711	−	0.249082i
$533$	−0.309418	−	0.303475i	−0.0134024	−	0.0131450i
$534$	18.5944	+	26.1938i	0.804659	+	1.13352i
$535$	−12.1409	−	13.9119i	−0.524895	−	0.601463i
$536$	−0.617945	−	2.39901i	−0.0266912	−	0.103621i
$537$	−10.5511	+	28.6995i	−0.455314	+	1.23848i
$538$	−7.76019	+	3.17039i	−0.334565	+	0.136685i
$539$	17.9613	−	15.0713i	0.773648	−	0.649168i
$540$	−11.2666	+	11.2663i	−0.484836	+	0.484822i
$541$	−4.50041	−	3.77629i	−0.193488	−	0.162355i	0.540897	−	0.841089i	$-0.318085\pi$
$541$	−4.50041	−	3.77629i	−0.193488	−	0.162355i	−0.734385	+	0.678733i	$0.762529\pi$
$542$	31.3195	+	10.0422i	1.34529	+	0.431349i
$543$	3.70926	+	15.8795i	0.159180	+	0.681454i
$544$	1.13225	−	11.6405i	0.0485448	−	0.499084i
$545$	−31.8196	−	17.5573i	−1.36300	−	0.752073i
$546$	6.65164	−	8.52498i	0.284664	−	0.364835i
$547$	−24.6155	−	1.91326i	−1.05248	−	0.0818053i	−0.460422	−	0.887700i	$-0.652302\pi$
$547$	−24.6155	−	1.91326i	−1.05248	−	0.0818053i	−0.592059	+	0.805895i	$0.701685\pi$
$548$	−7.54577	+	7.99805i	−0.322339	+	0.341660i
$549$	−3.56597	−	10.6465i	−0.152192	−	0.454380i
$550$	−38.6285	+	9.15513i	−1.64713	+	0.390376i
$551$	−3.60703	+	9.34243i	−0.153664	+	0.398001i
$552$	21.3652	−	11.1658i	0.909363	−	0.475248i
$553$	2.04380	+	14.9633i	0.0869114	+	0.636304i
$554$	0.0322085	−	0.148691i	0.00136841	−	0.00631727i
$555$	5.86165	+	4.75928i	0.248813	+	0.202020i
$556$	3.97555	−	2.19361i	0.168601	−	0.0930300i
$557$	−6.50286	−	15.0753i	−0.275535	−	0.638762i	0.723114	−	0.690729i	$-0.242710\pi$
$557$	−6.50286	−	15.0753i	−0.275535	−	0.638762i	−0.998649	+	0.0519669i	$0.983451\pi$
$558$	−8.42627	−	3.12884i	−0.356713	−	0.132454i
$559$	3.51177	+	4.71712i	0.148532	+	0.199513i
$560$	6.56351	−	4.69132i	0.277359	−	0.198244i
$561$	−19.6468	+	15.7420i	−0.829490	+	0.664628i
$562$	−2.63004	−	0.411331i	−0.110941	−	0.0173509i
$563$	−1.10134	+	2.30326i	−0.0464159	+	0.0970706i	−0.924069	−	0.382226i	$-0.875158\pi$
$563$	−1.10134	+	2.30326i	−0.0464159	+	0.0970706i	0.877653	+	0.479297i	$0.159108\pi$
$564$	19.8570	−	5.87482i	0.836130	−	0.247375i
$565$	34.1829	+	54.2349i	1.43809	+	2.28168i
$566$	−14.8458	+	25.7138i	−0.624018	+	1.08083i
$567$	−14.3222	+	5.63598i	−0.601474	+	0.236689i
$568$	7.01995	+	12.1589i	0.294551	+	0.510177i
$569$	−1.45290	+	2.75827i	−0.0609089	+	0.115633i	−0.913325	−	0.407231i	$-0.866494\pi$
$569$	−1.45290	+	2.75827i	−0.0609089	+	0.115633i	0.852416	+	0.522864i	$0.175136\pi$
$570$	−4.73293	−	41.6619i	−0.198241	−	1.74503i
$571$	−8.10448	−	11.8166i	−0.339162	−	0.494510i	0.617155	−	0.786841i	$-0.288285\pi$
$571$	−8.10448	−	11.8166i	−0.339162	−	0.494510i	−0.956317	+	0.292331i	$0.905569\pi$
$572$	6.50136	+	16.8389i	0.271835	+	0.704071i
$573$	−7.23897	+	36.2388i	−0.302413	+	1.51390i
$574$	−0.0216017	−	0.222085i	−0.000901639	−	0.00926966i
$575$	11.9313	−	27.6597i	0.497568	−	1.15349i
$576$	−13.5416	−	18.4375i	−0.564233	−	0.768229i
$577$	16.0978	+	1.88156i	0.670160	+	0.0783304i	0.444367	−	0.895845i	$-0.353429\pi$
$577$	16.0978	+	1.88156i	0.670160	+	0.0783304i	0.225793	+	0.974175i	$0.427503\pi$
$578$	−9.52933	−	5.75098i	−0.396368	−	0.239209i
$579$	−9.83296	−	3.40004i	−0.408644	−	0.141301i
$580$	3.35145	+	3.04128i	0.139161	+	0.126282i
$581$	16.7698	−	12.9976i	0.695728	−	0.539230i
$582$	−27.6706	+	3.68828i	−1.14699	+	0.152884i
$583$	−26.8637	−	33.3058i	−1.11258	−	1.37939i
$584$	9.90264	+	10.4962i	0.409774	+	0.434335i
$585$	−35.5339	+	1.14855i	−1.46915	+	0.0474866i
$586$	2.44118	+	8.15410i	0.100844	+	0.336843i
$587$	−9.06497	−	18.9578i	−0.374151	−	0.782471i	−0.999997	−	0.00252415i	$-0.999197\pi$
$587$	−9.06497	−	18.9578i	−0.374151	−	0.782471i	0.625845	−	0.779947i	$-0.284754\pi$
$588$	6.22022	−	1.32632i	0.256517	−	0.0546965i
$589$	−16.6032	+	10.0201i	−0.684122	+	0.412869i
$590$	10.9241	−	4.96561i	0.449738	−	0.204431i
$591$	−0.191433	+	0.0818421i	−0.00787449	+	0.00336653i
$592$	−1.31491	+	1.19322i	−0.0540425	+	0.0490410i
$593$	5.92568	−	33.6062i	0.243339	−	1.38004i	−0.580981	−	0.813917i	$-0.697331\pi$
$593$	5.92568	−	33.6062i	0.243339	−	1.38004i	0.824320	−	0.566124i	$-0.191558\pi$
$594$	−5.14295	+	30.9144i	−0.211018	+	1.26843i
$595$	−2.55331	−	14.4806i	−0.104676	−	0.593645i
$596$	−9.05807	−	7.02053i	−0.371033	−	0.287572i
$597$	−31.4385	−	18.2870i	−1.28669	−	0.748436i
$598$	16.0947	+	4.48026i	0.658160	+	0.183211i
$599$	4.05159	−	11.8412i	0.165543	−	0.483819i	−0.831928	−	0.554883i	$-0.812763\pi$
$599$	4.05159	−	11.8412i	0.165543	−	0.483819i	0.997472	+	0.0710641i	$0.0226395\pi$
$600$	−33.5476	−	8.75718i	−1.36957	−	0.357511i
$601$	−9.68667	+	2.69647i	−0.395128	+	0.109991i	−0.460037	−	0.887900i	$-0.652164\pi$
$601$	−9.68667	+	2.69647i	−0.395128	+	0.109991i	0.0649091	+	0.997891i	$0.479324\pi$
$602$	−0.176044	+	3.02256i	−0.00717502	+	0.123190i
$603$	−2.10039	+	1.24911i	−0.0855344	+	0.0508678i
$604$	0.535442	+	0.268909i	0.0217868	+	0.0109418i
$605$	49.4516	−	56.6652i	2.01049	−	2.30377i
$606$	0.369026	+	0.0371006i	0.0149907	+	0.00150711i
$607$	−24.9186	−	0.966954i	−1.01141	−	0.0392474i	−0.472264	−	0.881457i	$-0.656563\pi$
$607$	−24.9186	−	0.966954i	−1.01141	−	0.0392474i	−0.539150	+	0.842210i	$0.681254\pi$
$608$	−31.3871	−	1.21796i	−1.27291	−	0.0493948i
$609$	1.79618	+	3.98570i	0.0727847	+	0.161509i
$610$	8.77964	−	10.0604i	0.355477	−	0.407332i
$611$	41.2917	+	20.7374i	1.67048	+	0.838947i
$612$	−6.70935	+	1.27262i	−0.271209	+	0.0514426i
$613$	−1.37251	+	23.5651i	−0.0554351	+	0.951784i	0.849862	+	0.527005i	$0.176685\pi$
$613$	−1.37251	+	23.5651i	−0.0554351	+	0.951784i	−0.905297	+	0.424779i	$0.860352\pi$
$614$	−14.4122	+	4.01192i	−0.581630	+	0.161908i
$615$	−0.515410	+	0.522112i	−0.0207833	+	0.0210536i
$616$	−9.68664	+	28.3103i	−0.390286	+	1.14065i
$617$	29.3849	+	8.17986i	1.18299	+	0.329309i	0.803170	−	0.595750i	$-0.203145\pi$
$617$	29.3849	+	8.17986i	1.18299	+	0.329309i	0.379823	+	0.925059i	$0.375985\pi$
$618$	−0.0843392	+	26.0554i	−0.00339262	+	1.04810i
$619$	20.2775	+	15.7163i	0.815023	+	0.631690i	0.932413	−	0.361396i	$-0.117700\pi$
$619$	20.2775	+	15.7163i	0.815023	+	0.631690i	−0.117390	+	0.993086i	$0.537453\pi$
$620$	1.52178	+	8.63045i	0.0611162	+	0.346607i
$621$	−16.4857	−	17.1384i	−0.661550	−	0.687739i
$622$	−0.0747352	+	0.423844i	−0.00299661	+	0.0169946i
$623$	22.4044	−	20.3309i	0.897613	−	0.814540i
$624$	0.997490	−	8.30096i	0.0399316	−	0.332304i
$625$	13.2786	−	6.03586i	0.531144	−	0.241434i
$626$	−6.84256	+	4.12950i	−0.273484	+	0.165048i
$627$	45.2750	+	50.2182i	1.80811	+	2.00552i
$628$	−6.33471	−	13.2479i	−0.252783	−	0.528650i
$629$	0.928138	+	3.10020i	0.0370073	+	0.123613i
$630$	−14.3944	−	11.3064i	−0.573487	−	0.450459i
$631$	−1.21124	−	1.28384i	−0.0482187	−	0.0511089i	0.702815	−	0.711372i	$-0.251926\pi$
$631$	−1.21124	−	1.28384i	−0.0482187	−	0.0511089i	−0.751034	+	0.660264i	$0.770445\pi$
$632$	16.8612	+	20.9046i	0.670701	+	0.831539i
$633$	14.4337	−	35.0054i	0.573687	−	1.39134i
$634$	−9.53027	+	7.38652i	−0.378495	+	0.293356i
$635$	−12.5233	−	11.3643i	−0.496971	−	0.450977i
$636$	−2.19990	−	11.3964i	−0.0872317	−	0.451898i
$637$	12.1503	+	7.33276i	0.481414	+	0.290535i
$638$	8.84146	+	1.03342i	0.350037	+	0.0409134i
$639$	9.56922	−	10.0121i	0.378553	−	0.396074i
$640$	−1.70453	+	3.95153i	−0.0673773	+	0.156198i
$641$	2.10936	+	21.6862i	0.0833149	+	0.856552i	0.940105	+	0.340886i	$0.110727\pi$
$641$	2.10936	+	21.6862i	0.0833149	+	0.856552i	−0.856790	+	0.515666i	$0.827545\pi$
$642$	−7.40151	−	6.50160i	−0.292114	−	0.256598i
$643$	10.8335	+	28.0595i	0.427232	+	1.10656i	0.964718	+	0.263287i	$0.0848065\pi$
$643$	10.8335	+	28.0595i	0.427232	+	1.10656i	−0.537485	+	0.843273i	$0.680626\pi$
$644$	−3.98845	−	5.81530i	−0.157167	−	0.229155i
$645$	8.00426	−	5.91878i	0.315167	−	0.233052i
$646$	8.37538	−	15.9003i	0.329525	−	0.625588i
$647$	−2.50107	−	4.33198i	−0.0983272	−	0.170308i	0.812665	−	0.582731i	$-0.198016\pi$
$647$	−2.50107	−	4.33198i	−0.0983272	−	0.170308i	−0.910992	+	0.412423i	$0.864683\pi$
$648$	−16.6277	+	21.7414i	−0.653196	+	0.854082i
$649$	−9.67511	+	16.7578i	−0.379781	+	0.657800i
$650$	−12.8119	−	20.3275i	−0.502526	−	0.797311i
$651$	−1.97894	+	8.23096i	−0.0775606	+	0.322597i
$652$	−7.61711	+	15.9298i	−0.298309	+	0.623861i
$653$	9.76114	+	1.52661i	0.381983	+	0.0597410i	0.342596	−	0.939483i	$-0.388694\pi$
$653$	9.76114	+	1.52661i	0.381983	+	0.0597410i	0.0393873	+	0.999224i	$0.487459\pi$
$654$	−18.0658	−	7.04231i	−0.706428	−	0.275376i
$655$	−21.1059	+	15.0856i	−0.824677	+	0.589443i
$656$	−0.103027	−	0.138390i	−0.00402254	−	0.00540321i
$657$	7.19701	−	12.2813i	0.280782	−	0.479139i
$658$	9.42237	+	21.8435i	0.367322	+	0.851549i
$659$	−17.7710	+	9.80560i	−0.692258	+	0.381972i	−0.789888	−	0.613251i	$-0.789861\pi$
$659$	−17.7710	+	9.80560i	−0.692258	+	0.381972i	0.0976301	+	0.995223i	$0.468874\pi$
$660$	28.5401	−	10.9131i	1.11092	−	0.424790i
$661$	2.78865	−	12.8738i	0.108466	−	0.500734i	−0.890488	−	0.455006i	$-0.849637\pi$
$661$	2.78865	−	12.8738i	0.108466	−	0.500734i	0.998954	−	0.0457273i	$-0.0145605\pi$
$662$	−3.05874	−	22.3939i	−0.118881	−	0.870365i
$663$	−12.8647	−	8.16659i	−0.499623	−	0.317164i
$664$	13.5900	−	35.1989i	0.527393	−	1.36598i
$665$	−38.4261	+	9.10716i	−1.49010	+	0.353160i
$666$	3.43549	+	2.10379i	0.133122	+	0.0815201i
$667$	−4.63528	+	4.91311i	−0.179479	+	0.190236i
$668$	−19.4394	−	1.51095i	−0.752132	−	0.0584603i
$669$	−8.32842	−	20.5755i	−0.321995	−	0.795497i
$670$	−2.54457	−	1.40403i	−0.0983052	−	0.0542425i
$671$	−2.08452	+	21.4307i	−0.0804720	+	0.827324i
$672$	−10.0041	+	9.37736i	−0.385916	+	0.361739i
$673$	−13.8671	−	4.44630i	−0.534537	−	0.171392i	0.0257846	−	0.999668i	$-0.491792\pi$
$673$	−13.8671	−	4.44630i	−0.534537	−	0.171392i	−0.560322	+	0.828275i	$0.689322\pi$
$674$	−5.77409	−	4.84503i	−0.222409	−	0.186624i
$675$	0.994258	+	34.1874i	0.0382690	+	1.31587i
$676$	0.603415	−	0.506325i	0.0232083	−	0.0194741i
$677$	23.5997	−	9.64154i	0.907011	−	0.370555i	0.123797	−	0.992308i	$-0.460493\pi$
$677$	23.5997	−	9.64154i	0.907011	−	0.370555i	0.783213	+	0.621753i	$0.213579\pi$
$678$	21.9012	+	26.2730i	0.841109	+	1.00901i
$679$	6.55815	+	25.4603i	0.251679	+	0.977077i
$680$	−17.1934	−	19.7014i	−0.659336	−	0.755515i
$681$	−10.6843	+	23.3044i	−0.409423	+	0.893025i
$682$	12.3063	+	12.0699i	0.471231	+	0.462180i
$683$	12.4162	+	8.16627i	0.475093	+	0.312474i	0.764377	−	0.644770i	$-0.223047\pi$
$683$	12.4162	+	8.16627i	0.475093	+	0.312474i	−0.289284	+	0.957243i	$0.593417\pi$
$684$	4.45984	+	17.7902i	0.170526	+	0.680224i
$685$	2.41495	+	41.4631i	0.0922705	+	1.58422i
$686$	6.42803	+	18.7866i	0.245424	+	0.717277i
$687$	23.3357	−	15.8940i	0.890311	−	0.606396i
$688$	1.09103	+	2.07126i	0.0415950	+	0.0789661i
$689$	13.8094	−	21.9102i	0.526098	−	0.834711i
$690$	7.67225	−	27.2201i	0.292078	−	1.03625i
$691$	13.5809	+	2.66720i	0.516642	+	0.101465i	0.444236	−	0.895910i	$-0.353475\pi$
$691$	13.5809	+	2.66720i	0.516642	+	0.101465i	0.0724065	+	0.997375i	$0.476932\pi$
$692$	4.68955	−	3.08436i	0.178270	−	0.117250i
$693$	29.4859	+	1.33541i	1.12008	+	0.0507281i
$694$	−5.72663	+	2.87602i	−0.217380	+	0.109172i
$695$	4.27809	−	16.6086i	0.162277	−	0.629999i
$696$	6.39714	+	4.41802i	0.242483	+	0.167465i
$697$	−0.308552	+	0.0605975i	−0.0116872	+	0.00229530i
$698$	−23.7823	+	23.3255i	−0.900174	+	0.882885i
$699$	−9.61765	−	26.6928i	−0.363773	−	1.00961i
$700$	−1.37252	+	10.0487i	−0.0518765	+	0.379803i
$701$	19.2821	+	7.01811i	0.728275	+	0.265070i	0.679435	−	0.733736i	$-0.262225\pi$
$701$	19.2821	+	7.01811i	0.728275	+	0.265070i	0.0488405	+	0.998807i	$0.484447\pi$
$702$	−18.7115	+	3.11231i	−0.706221	+	0.117467i
$703$	8.16722	−	2.97262i	0.308032	−	0.112115i
$704$	9.28749	+	42.8758i	0.350035	+	1.61594i
$705$	35.3300	−	69.7838i	1.33061	−	2.62821i
$706$	−8.73544	−	6.24371i	−0.328763	−	0.234985i
$707$	−0.00677359	−	0.349244i	−0.000254747	−	0.0131347i
$708$	−4.44947	+	2.78431i	−0.167221	+	0.104641i
$709$	−12.2169	+	17.8127i	−0.458815	+	0.668969i	−0.983204	−	0.182510i	$-0.941578\pi$
$709$	−12.2169	+	17.8127i	−0.458815	+	0.668969i	0.524389	+	0.851479i	$0.324294\pi$
$710$	16.0267	+	3.79840i	0.601471	+	0.142551i
$711$	15.1258	−	21.7507i	0.567262	−	0.815716i
$712$	15.4306	−	51.5418i	0.578287	−	1.93161i
$713$	−12.9226	+	2.02106i	−0.483957	+	0.0756894i
$714$	−2.37112	−	7.47821i	−0.0887370	−	0.279865i
$715$	63.1159	+	25.7857i	2.36040	+	0.964330i
$716$	15.1467	−	4.85658i	0.566057	−	0.181499i
$717$	−8.07600	+	14.5250i	−0.301604	+	0.542446i
$718$	−0.0350469	+	1.80701i	−0.00130794	+	0.0674370i
$719$	−21.3258	+	28.6456i	−0.795319	+	1.06830i	0.200743	+	0.979644i	$0.435664\pi$
$719$	−21.3258	+	28.6456i	−0.795319	+	1.06830i	−0.996062	+	0.0886552i	$0.971743\pi$
$720$	−14.0462	−	1.73401i	−0.523470	−	0.0646227i
$721$	24.3738	−	2.84889i	0.907728	−	0.106098i
$722$	−25.8063	−	11.7304i	−0.960412	−	0.436561i
$723$	−15.3756	+	25.2918i	−0.571823	+	0.940610i
$724$	5.32557	−	6.60267i	0.197923	−	0.245386i
$725$	9.68552	−	0.752818i	0.359711	−	0.0279590i
$726$	22.1585	−	33.4540i	0.822379	−	1.24159i
$727$	38.6107	−	1.49827i	1.43199	−	0.0555678i	0.688948	−	0.724811i	$-0.258073\pi$
$727$	38.6107	−	1.49827i	1.43199	−	0.0555678i	0.743044	+	0.669243i	$0.233381\pi$
$728$	−18.1105			−0.671220
$729$	25.1876	+	9.72553i	0.932873	+	0.360205i
$730$	16.9286			0.626555
$731$	4.26349	−	0.165443i	0.157691	−	0.00611912i
$732$	−3.22525	+	4.86934i	−0.119209	+	0.179976i
$733$	7.21168	−	0.560536i	0.266369	−	0.0207039i	0.0563869	−	0.998409i	$-0.482042\pi$
$733$	7.21168	−	0.560536i	0.266369	−	0.0207039i	0.209983	+	0.977705i	$0.432659\pi$
$734$	20.8219	−	25.8151i	0.768551	−	0.952853i
$735$	12.4793	−	20.5276i	0.460305	−	0.757171i
$736$	−19.2867	−	8.76688i	−0.710917	−	0.323152i
$737$	4.65476	−	0.544063i	0.171460	−	0.0200408i
$738$	−0.235775	+	0.312457i	−0.00867898	+	0.0115017i
$739$	−1.35201	+	1.81606i	−0.0497344	+	0.0668049i	−0.826295	−	0.563238i	$-0.809555\pi$
$739$	−1.35201	+	1.81606i	−0.0497344	+	0.0668049i	0.776560	+	0.630043i	$0.216963\pi$
$740$	0.0761632	−	3.92696i	0.00279982	−	0.144358i
$741$	−19.8871	+	35.7677i	−0.730569	+	1.31396i
$742$	12.6972	−	4.07118i	0.466128	−	0.149458i
$743$	−12.2359	−	4.99890i	−0.448890	−	0.183392i	0.142471	−	0.989799i	$-0.454495\pi$
$743$	−12.2359	−	4.99890i	−0.448890	−	0.183392i	−0.591361	+	0.806407i	$0.701409\pi$
$744$	4.55015	+	14.3506i	0.166816	+	0.526117i
$745$	−42.7677	+	6.68874i	−1.56689	+	0.245056i
$746$	−5.97579	+	19.9605i	−0.218789	+	0.730807i
$747$	−37.0886	−	3.12444i	−1.35700	−	0.114317i
$748$	12.7431	+	3.02017i	0.465934	+	0.110428i
$749$	−5.24795	+	7.65169i	−0.191756	+	0.279587i
$750$	−8.28797	+	5.18630i	−0.302634	+	0.189377i
$751$	−0.229818	−	11.8494i	−0.00838618	−	0.432389i	−0.980351	−	0.197262i	$-0.936795\pi$
$751$	−0.229818	−	11.8494i	−0.00838618	−	0.432389i	0.971965	−	0.235127i	$-0.0755506\pi$
$752$	14.9645	+	10.6960i	0.545698	+	0.390041i
$753$	4.86928	−	9.61779i	0.177446	−	0.350492i
$754$	1.14063	+	5.26574i	0.0415393	+	0.191767i
$755$	2.12672	−	0.774061i	0.0773991	−	0.0281710i
$756$	6.89452	+	4.07033i	0.250751	+	0.148036i
$757$	9.72392	+	3.53922i	0.353422	+	0.128635i	0.512629	−	0.858610i	$-0.328672\pi$
$757$	9.72392	+	3.53922i	0.353422	+	0.128635i	−0.159207	+	0.987245i	$0.550894\pi$
$758$	2.45372	−	17.9644i	0.0891232	−	0.652497i
$759$	15.4588	+	42.9042i	0.561117	+	1.55732i
$760$	−50.1379	+	49.1749i	−1.81869	+	1.78376i
$761$	−36.3513	+	7.13916i	−1.31773	+	0.258794i	−0.801675	−	0.597760i	$-0.796058\pi$
$761$	−36.3513	+	7.13916i	−1.31773	+	0.258794i	−0.516057	+	0.856554i	$0.672601\pi$
$762$	−7.42416	−	5.12731i	−0.268949	−	0.185743i
$763$	−4.55526	+	17.6846i	−0.164911	+	0.640225i
$764$	17.1788	−	8.62752i	0.621508	−	0.312133i
$765$	−13.8947	+	21.7322i	−0.502363	+	0.785730i
$766$	22.0766	−	14.5200i	0.797660	−	0.524629i
$767$	−11.4925	−	2.25705i	−0.414969	−	0.0814973i
$768$	−7.78903	+	27.6344i	−0.281062	+	0.997170i
$769$	−19.5957	+	31.0906i	−0.706638	+	1.12116i	0.280278	+	0.959919i	$0.409573\pi$
$769$	−19.5957	+	31.0906i	−0.706638	+	1.12116i	−0.986916	+	0.161238i	$0.948451\pi$
$770$	16.3591	+	31.0569i	0.589539	+	1.11921i
$771$	−16.2262	+	11.0518i	−0.584373	+	0.398020i
$772$	1.75211	+	5.12072i	0.0630597	+	0.184299i
$773$	−1.73879	−	29.8539i	−0.0625400	−	1.07377i	−0.872919	−	0.487864i	$-0.837776\pi$
$773$	−1.73879	−	29.8539i	−0.0625400	−	1.07377i	0.810379	−	0.585905i	$-0.199261\pi$
$774$	3.81590	−	3.69445i	0.137160	−	0.132794i
$775$	15.7171	+	10.3373i	0.564573	+	0.371326i
$776$	33.3800	+	32.7388i	1.19827	+	1.17526i
$777$	1.58121	−	3.44891i	0.0567257	−	0.123729i
$778$	−20.8711	−	23.9156i	−0.748264	−	0.857416i
$779$	0.210656	+	0.817816i	0.00754752	+	0.0293013i
$780$	11.8419	+	14.2057i	0.424007	+	0.508647i
$781$	−24.5871	+	10.0449i	−0.879796	+	0.359436i
$782$	9.28535	−	7.79134i	0.332043	−	0.278618i
$783$	2.41238	−	7.27981i	0.0862115	−	0.260159i
$784$	4.32769	+	3.63136i	0.154560	+	0.129692i
$785$	−52.8179	−	16.9354i	−1.88515	−	0.604450i
$786$	−10.0987	+	9.46600i	−0.360207	+	0.337641i
$787$	−1.80904	+	18.5986i	−0.0644854	+	0.662968i	0.906238	+	0.422768i	$0.138941\pi$
$787$	−1.80904	+	18.5986i	−0.0644854	+	0.662968i	−0.970723	+	0.240200i	$0.922787\pi$
$788$	0.0948236	+	0.0523214i	0.00337795	+	0.00186387i
$789$	12.4216	+	30.6878i	0.442220	+	1.09251i
$790$	31.4121	+	2.44154i	1.11759	+	0.0868662i
$791$	22.1069	−	23.4319i	0.786030	−	0.833143i
$792$	46.1212	−	25.0605i	1.63885	−	0.890487i
$793$	−12.6812	+	3.00550i	−0.450323	+	0.106728i
$794$	4.46426	−	11.5627i	0.158431	−	0.410345i
$795$	−37.0133	−	23.4963i	−1.31273	−	0.833328i
$796$	2.56040	+	18.7454i	0.0907509	+	0.664414i
$797$	0.314640	−	1.45254i	0.0111451	−	0.0514516i	−0.971423	−	0.237356i	$-0.923719\pi$
$797$	0.314640	−	1.45254i	0.0111451	−	0.0514516i	0.982568	+	0.185905i	$0.0595216\pi$
$798$	−19.6801	+	7.52518i	−0.696666	+	0.266388i
$799$	29.3524	−	16.1960i	1.03841	−	0.572973i
$800$	12.0686	+	27.9783i	0.426691	+	0.989181i
$801$	−53.0719	−	0.343582i	−1.87520	−	0.0121399i
$802$	−4.90243	−	6.58511i	−0.173111	−	0.232528i
$803$	−22.2086	+	15.8738i	−0.783724	+	0.560173i
$804$	1.18441	+	0.461701i	0.0417709	+	0.0162829i
$805$	−26.3155	−	4.11567i	−0.927501	−	0.145058i
$806$	−4.50073	+	9.41247i	−0.158531	+	0.331540i
$807$	3.23765	−	13.4663i	0.113971	−	0.474038i
$808$	−0.331224	−	0.525523i	−0.0116524	−	0.0184878i
$809$	−2.22120	+	3.84724i	−0.0780933	+	0.135262i	−0.902427	−	0.430842i	$-0.858217\pi$
$809$	−2.22120	+	3.84724i	−0.0780933	+	0.135262i	0.824334	+	0.566104i	$0.191550\pi$
$810$	5.16591	+	31.6914i	0.181511	+	1.11352i
$811$	18.2564	+	31.6210i	0.641069	+	1.11036i	0.985194	+	0.171441i	$0.0548422\pi$
$811$	18.2564	+	31.6210i	0.641069	+	1.11036i	−0.344125	+	0.938924i	$0.611824\pi$
$812$	1.05985	−	2.01207i	0.0371934	−	0.0706099i
$813$	−43.6929	+	32.3088i	−1.53238	+	1.13312i
$814$	−4.36959	−	6.37102i	−0.153154	−	0.223304i
$815$	24.0221	+	62.2189i	0.841459	+	2.17943i
$816$	−4.55735	−	4.00325i	−0.159539	−	0.140142i
$817$	−1.10937	−	11.4053i	−0.0388118	−	0.399021i
$818$	1.02627	−	2.37917i	0.0358828	−	0.0831857i
$819$	5.01286	+	17.1474i	0.175164	+	0.599178i
$820$	0.379060	+	0.0443058i	0.0132374	+	0.00154723i
$821$	45.5605	+	27.4959i	1.59007	+	0.959615i	0.986774	+	0.162100i	$0.0518267\pi$
$821$	45.5605	+	27.4959i	1.59007	+	0.959615i	0.603300	+	0.797515i	$0.293852\pi$
$822$	4.20002	+	21.7579i	0.146493	+	0.758895i
$823$	−7.36122	−	6.67995i	−0.256596	−	0.232848i	0.533548	−	0.845770i	$-0.320858\pi$
$823$	−7.36122	−	6.67995i	−0.256596	−	0.232848i	−0.790144	+	0.612921i	$0.789994\pi$
$824$	34.4929	−	26.7340i	1.20162	−	0.931324i
$825$	25.0025	−	60.6375i	0.870475	−	2.11113i
$826$	−3.78561	−	4.69342i	−0.131718	−	0.163305i
$827$	−33.3760	−	35.3765i	−1.16060	−	1.23016i	−0.968562	−	0.248772i	$-0.919973\pi$
$827$	−33.3760	−	35.3765i	−1.16060	−	1.23016i	−0.192034	−	0.981388i	$-0.561508\pi$
$828$	−1.75340	+	12.2454i	−0.0609350	+	0.425558i
$829$	−15.0451	−	50.2540i	−0.522536	−	1.74539i	−0.656420	−	0.754396i	$-0.727930\pi$
$829$	−15.0451	−	50.2540i	−0.522536	−	1.74539i	0.133883	−	0.990997i	$-0.457255\pi$
$830$	−19.0948	−	39.9334i	−0.662790	−	1.38611i
$831$	0.168315	+	0.186692i	0.00583878	+	0.00647626i
$832$	−22.7339	+	13.7200i	−0.788155	+	0.475654i
$833$	9.37346	−	4.26076i	0.324771	−	0.147627i
$834$	1.09173	−	9.08519i	0.0378034	−	0.314594i
$835$	−54.5395	+	49.4920i	−1.88742	+	1.71274i
$836$	6.10763	−	34.6381i	0.211237	−	1.19798i
$837$	12.3279	−	8.28030i	0.426116	−	0.286209i
$838$	−1.79430	−	10.1760i	−0.0619831	−	0.351524i
$839$	3.00526	+	2.32925i	0.103753	+	0.0804147i	0.663156	−	0.748481i	$-0.269217\pi$
$839$	3.00526	+	2.32925i	0.103753	+	0.0804147i	−0.559403	+	0.828896i	$0.688970\pi$
$840$	−0.0992340	+	30.6570i	−0.00342390	+	1.05777i
$841$	25.8392	+	7.19283i	0.891007	+	0.248029i
$842$	1.83760	−	5.37058i	0.0633278	−	0.185083i
$843$	3.08982	−	3.12999i	0.106419	−	0.107803i
$844$	−18.9753	+	5.28213i	−0.653155	+	0.181818i
$845$	0.172999	−	2.97028i	0.00595135	−	0.102181i
$846$	13.7654	−	39.3964i	0.473264	−	1.35448i
$847$	−33.7726	−	16.9612i	−1.16044	−	0.582795i
$848$	6.77899	−	7.76786i	0.232791	−	0.266749i
$849$	−20.1554	−	44.7247i	−0.691733	−	1.53495i
$850$	−17.4201	−	0.675978i	−0.597504	−	0.0231859i
$851$	5.85771	+	0.227306i	0.200800	+	0.00779194i
$852$	−7.16834	−	0.720679i	−0.245583	−	0.0246900i
$853$	21.8168	−	24.9992i	0.746991	−	0.855957i	−0.246585	−	0.969121i	$-0.579308\pi$
$853$	21.8168	−	24.9992i	0.746991	−	0.855957i	0.993576	+	0.113164i	$0.0360986\pi$
$854$	−5.99599	−	3.01130i	−0.205179	−	0.103045i
$855$	60.4376	+	33.8603i	2.06692	+	1.15800i
$856$	−0.959407	+	16.4724i	−0.0327919	+	0.563014i
$857$	15.4468	−	4.29991i	0.527653	−	0.146882i	0.00590605	−	0.999983i	$-0.498120\pi$
$857$	15.4468	−	4.29991i	0.527653	−	0.146882i	0.521747	+	0.853100i	$0.325281\pi$
$858$	35.1972	+	9.18781i	1.20161	+	0.313666i
$859$	10.1053	−	29.5339i	0.344789	−	1.00768i	−0.628442	−	0.777856i	$-0.716307\pi$
$859$	10.1053	−	29.5339i	0.344789	−	1.00768i	0.973231	−	0.229828i	$-0.0738163\pi$
$860$	−4.98878	−	1.38872i	−0.170116	−	0.0473550i
$861$	0.318671	+	0.185362i	0.0108603	+	0.00631714i
$862$	−18.2157	−	14.1183i	−0.620430	−	0.480870i
$863$	−3.62569	−	20.5623i	−0.123420	−	0.699950i	−0.982234	−	0.187662i	$-0.939909\pi$
$863$	−3.62569	−	20.5623i	−0.123420	−	0.699950i	0.858814	−	0.512288i	$-0.171202\pi$
$864$	24.0530	−	0.232884i	0.818300	−	0.00792289i
$865$	3.68155	−	20.8791i	0.125177	−	0.709912i
$866$	10.4146	−	9.45072i	0.353901	−	0.321148i
$867$	16.9089	−	7.22894i	0.574255	−	0.245508i
$868$	4.00896	−	1.82230i	0.136073	−	0.0618527i
$869$	−43.4989	+	26.2517i	−1.47560	+	0.890529i
$870$	8.91995	−	1.90198i	0.302415	−	0.0644830i
$871$	1.22365	+	2.55904i	0.0414616	+	0.0867097i
$872$	9.31421	+	31.1116i	0.315419	+	1.05357i
$873$	21.7584	−	40.6667i	0.736411	−	1.37636i
$874$	−22.3399	−	23.6789i	−0.755658	−	0.800951i
$875$	5.78098	+	7.16730i	0.195433	+	0.242299i
$876$	−7.33987	+	0.978345i	−0.247991	+	0.0330552i
$877$	−8.78403	+	6.80813i	−0.296615	+	0.229894i	−0.750027	−	0.661407i	$-0.769960\pi$
$877$	−8.78403	+	6.80813i	−0.296615	+	0.229894i	0.453412	+	0.891301i	$0.350207\pi$
$878$	7.81659	+	7.09318i	0.263797	+	0.239383i
$879$	−13.2908	−	4.59571i	−0.448289	−	0.155009i
$880$	23.2374	+	14.0239i	0.783334	+	0.472744i
$881$	41.9803	+	4.90679i	1.41435	+	0.165314i	0.788695	−	0.614785i	$-0.210757\pi$
$881$	41.9803	+	4.90679i	1.41435	+	0.165314i	0.625656	+	0.780099i	$0.284831\pi$
$882$	5.15275	−	11.7359i	0.173502	−	0.395169i
$883$	−4.20300	+	9.74364i	−0.141442	+	0.327900i	−0.974182	−	0.225765i	$-0.927512\pi$
$883$	−4.20300	+	9.74364i	−0.141442	+	0.327900i	0.832740	+	0.553665i	$0.186771\pi$
$884$	0.767384	+	7.88939i	0.0258099	+	0.265349i
$885$	−3.88364	+	19.4418i	−0.130547	+	0.653528i
$886$	−1.09867	−	2.84562i	−0.0369104	−	0.0956004i
$887$	−23.3410	−	34.0319i	−0.783713	−	1.14268i	−0.986549	−	0.163468i	$-0.947732\pi$
$887$	−23.3410	−	34.0319i	−0.783713	−	1.14268i	0.202836	−	0.979213i	$-0.434984\pi$
$888$	−0.761610	−	6.70412i	−0.0255580	−	0.224975i
$889$	−3.96030	+	7.51845i	−0.132824	+	0.252161i
$890$	−31.5585	−	54.6609i	−1.05784	−	1.83224i
$891$	−36.4938	−	36.7319i	−1.22259	−	1.23057i
$892$	−5.77340	+	9.99983i	−0.193308	+	0.334819i
$893$	−48.0078	−	76.1696i	−1.60652	−	2.54892i
$894$	−22.1466	+	6.55222i	−0.740693	+	0.219139i
$895$	25.9181	−	54.2031i	0.866347	−	1.81181i
$896$	2.13653	+	0.334147i	0.0713764	+	0.0111631i
$897$	−21.5409	+	17.2596i	−0.719229	+	0.576282i
$898$	16.9184	−	12.0926i	0.564575	−	0.403534i
$899$	−2.51893	−	3.38351i	−0.0840110	−	0.112846i
$900$	13.7029	−	11.3477i	0.456762	−	0.378257i
$901$	−7.44253	−	17.2537i	−0.247947	−	0.574805i
$902$	0.657247	−	0.362653i	0.0218839	−	0.0120750i
$903$	−3.88345	−	3.15311i	−0.129233	−	0.104929i
$904$	12.1282	−	55.9900i	0.403378	−	1.86220i
$905$	−4.33616	−	31.7463i	−0.144139	−	1.05528i
$906$	1.07017	−	0.559288i	0.0355540	−	0.0185811i
$907$	−19.0219	+	49.2680i	−0.631612	+	1.63592i	0.132766	+	0.991147i	$0.457614\pi$
$907$	−19.0219	+	49.2680i	−0.631612	+	1.63592i	−0.764378	+	0.644769i	$0.776954\pi$
$908$	12.9766	−	3.07551i	0.430644	−	0.102064i
$909$	−0.405895	+	0.459071i	−0.0134627	+	0.0152264i
$910$	−14.5799	+	15.4538i	−0.483319	+	0.512288i
$911$	−11.7712	−	0.914930i	−0.389997	−	0.0303130i	−0.119003	−	0.992894i	$-0.537970\pi$
$911$	−11.7712	−	0.914930i	−0.389997	−	0.0303130i	−0.270994	+	0.962581i	$0.587352\pi$
$912$	−10.0217	+	12.8442i	−0.331852	+	0.425313i
$913$	62.4955	+	34.4835i	2.06830	+	1.14124i
$914$	−1.42420	+	14.6421i	−0.0471084	+	0.484317i
$915$	5.01814	+	21.4829i	0.165895	+	0.710202i
$916$	−13.9859	−	4.48440i	−0.462107	−	0.148169i
$917$	9.98638	+	8.37957i	0.329779	+	0.276718i
$918$	−5.81638	+	12.4728i	−0.191969	+	0.411663i
$919$	−34.1267	+	28.6357i	−1.12574	+	0.944604i	−0.998880	−	0.0473173i	$-0.984933\pi$
$919$	−34.1267	+	28.6357i	−1.12574	+	0.944604i	−0.126855	+	0.991921i	$0.540488\pi$
$920$	−43.8489	+	17.9142i	−1.44565	+	0.590615i
$921$	8.52892	−	23.1991i	0.281037	−	0.764436i
$922$	4.14030	+	16.0736i	0.136354	+	0.529357i
$923$	−10.5702	−	12.1121i	−0.347921	−	0.398673i
$924$	−8.88778	−	12.5202i	−0.292387	−	0.411883i
$925$	−6.01925	−	5.90364i	−0.197912	−	0.194110i
$926$	14.6169	+	9.61372i	0.480343	+	0.315926i
$927$	−34.8597	−	25.2588i	−1.14494	−	0.829607i
$928$	−0.397267	−	6.82081i	−0.0130409	−	0.223904i
$929$	−7.70939	−	22.5315i	−0.252937	−	0.739236i	−0.997433	−	0.0716088i	$-0.977187\pi$
$929$	−7.70939	−	22.5315i	−0.252937	−	0.739236i	0.744496	−	0.667627i	$-0.232690\pi$
$930$	15.9085	+	7.67028i	0.521661	+	0.251518i
$931$	−12.8876	−	24.4665i	−0.422373	−	0.801856i
$932$	−7.86967	+	12.4861i	−0.257780	+	0.408995i
$933$	−0.496262	−	0.509268i	−0.0162469	−	0.0166727i
$934$	4.24401	+	0.833497i	0.138868	+	0.0272728i
$935$	41.3288	−	27.1824i	1.35160	−	0.888960i
$936$	23.3886	+	21.5018i	0.764482	+	0.702808i
$937$	0.993725	−	0.499067i	0.0324636	−	0.0163038i	−0.432493	−	0.901637i	$-0.642366\pi$
$937$	0.993725	−	0.499067i	0.0324636	−	0.0163038i	0.464957	+	0.885333i	$0.346070\pi$
$938$	−0.364277	+	1.41421i	−0.0118941	+	0.0461756i
$939$	1.06586	−	13.1614i	0.0347829	−	0.429506i
$940$	−39.9255	+	7.84111i	−1.30223	+	0.255749i
$941$	23.9647	−	23.5045i	0.781228	−	0.766223i	−0.195500	−	0.980704i	$-0.562633\pi$
$941$	23.9647	−	23.5045i	0.781228	−	0.766223i	0.976728	+	0.214480i	$0.0688058\pi$
$942$	−29.1271	−	5.23316i	−0.949013	−	0.170506i
$943$	−0.0770849	+	0.564362i	−0.00251023	+	0.0183781i
$944$	−4.38117	−	1.59461i	−0.142595	−	0.0519003i
$945$	29.0541	−	8.39168i	0.945129	−	0.272981i
$946$	−9.57139	+	3.48370i	−0.311193	+	0.113265i
$947$	4.65691	+	21.4987i	0.151329	+	0.698614i	0.988444	+	0.151586i	$0.0484381\pi$
$947$	4.65691	+	21.4987i	0.151329	+	0.698614i	−0.837115	+	0.547027i	$0.815759\pi$
$948$	−13.7607	+	0.756785i	−0.446927	+	0.0245792i
$949$	−13.4421	−	9.60783i	−0.436349	−	0.311883i
$950$	0.907912	+	46.8117i	0.0294566	+	1.51877i
$951$	−0.708027	−	19.9090i	−0.0229594	−	0.645594i
$952$	−7.43192	+	10.8360i	−0.240870	+	0.351197i
$953$	3.47097	+	0.822635i	0.112436	+	0.0266478i	0.286449	−	0.958096i	$-0.407525\pi$
$953$	3.47097	+	0.822635i	0.112436	+	0.0266478i	−0.174013	+	0.984743i	$0.555673\pi$
$954$	−21.2312	−	9.81709i	−0.687385	−	0.317840i
$955$	20.8252	−	69.5609i	0.673886	−	2.25094i
$956$	8.54134	−	1.33584i	0.276247	−	0.0432042i
$957$	−9.91861	+	10.8593i	−0.320623	+	0.351032i
$958$	−24.0667	−	9.83232i	−0.777559	−	0.317668i
$959$	19.8738	−	6.37229i	0.641760	−	0.205772i
$960$	23.1002	+	38.5585i	0.745556	+	1.24447i
$961$	−0.442739	+	22.8275i	−0.0142819	+	0.736371i
$962$	2.79230	−	3.75071i	0.0900273	−	0.120928i
$963$	15.8619	−	3.65106i	0.511144	−	0.117654i
$964$	15.2929	−	1.78748i	0.492550	−	0.0575709i
$965$	18.6105	+	8.45949i	0.599092	+	0.272321i
$966$	−14.2074	−	0.321560i	−0.457114	−	0.0103460i
$967$	4.34500	−	5.38696i	0.139726	−	0.173233i	−0.703668	−	0.710529i	$-0.748456\pi$
$967$	4.34500	−	5.38696i	0.139726	−	0.173233i	0.843393	+	0.537296i	$0.180554\pi$
$968$	−67.0061	+	5.20813i	−2.15366	+	0.167396i
$969$	13.2398	+	26.5768i	0.425324	+	0.853769i
$970$	54.8088	−	2.12683i	1.75981	−	0.0682885i
$971$	−44.4719			−1.42717			−0.713586	−	0.700567i	$-0.752930\pi$
$971$	−44.4719			−1.42717			−0.713586	+	0.700567i	$0.752930\pi$
$972$	−4.07135	−	13.4421i	−0.130589	−	0.431157i
$973$	−8.61821			−0.276287
$974$	−1.43317	+	0.0556134i	−0.0459216	+	0.00178197i
$975$	39.6244	+	2.43658i	1.26900	+	0.0780331i
$976$	−5.17240	+	0.402031i	−0.165565	+	0.0128687i
$977$	−12.7940	+	15.8621i	−0.409318	+	0.507474i	−0.940505	−	0.339780i	$-0.889647\pi$
$977$	−12.7940	+	15.8621i	−0.409318	+	0.507474i	0.531187	+	0.847255i	$0.321746\pi$
$978$	17.0903	+	31.2117i	0.546489	+	0.998040i
$979$	92.6564	+	42.1175i	2.96131	+	1.34608i
$980$	−12.4122	+	1.45078i	−0.396492	+	0.0463433i
$981$	26.8790	−	17.4304i	0.858180	−	0.556508i
$982$	−23.3057	+	31.3050i	−0.743714	+	0.998982i
$983$	0.0929012	−	4.78996i	0.00296309	−	0.152776i	−0.995408	−	0.0957227i	$-0.969484\pi$
$983$	0.0929012	−	4.78996i	0.00296309	−	0.152776i	0.998371	−	0.0570534i	$-0.0181705\pi$
$984$	0.655521	−	0.0105913i	0.0208972	−	0.000337638i
$985$	0.389540	−	0.124901i	0.0124118	−	0.00397967i
$986$	3.61871	+	1.47840i	0.115243	+	0.0470820i
$987$	−38.3862	−	8.44515i	−1.22185	−	0.268812i
$988$	21.0330	−	3.28949i	0.669148	−	0.104653i
$989$	2.21667	−	7.40420i	0.0704861	−	0.235440i
$990$	15.7457	−	59.5305i	0.500432	−	1.89200i
$991$	−16.2658	−	3.85506i	−0.516700	−	0.122460i	−0.0360109	−	0.999351i	$-0.511465\pi$
$991$	−16.2658	−	3.85506i	−0.516700	−	0.122460i	−0.480689	+	0.876891i	$0.659613\pi$
$992$	7.48317	−	10.9107i	0.237591	−	0.346416i
$993$	32.9829	+	17.5102i	1.04668	+	0.555669i
$994$	−0.160492	−	8.27493i	−0.00509050	−	0.262465i
$995$	58.1387	+	41.5550i	1.84312	+	1.31738i
$996$	10.5869	+	16.2107i	0.335460	+	0.513655i
$997$	−5.40227	−	24.9397i	−0.171092	−	0.789847i	−0.979535	−	0.201273i	$-0.935492\pi$
$997$	−5.40227	−	24.9397i	−0.171092	−	0.789847i	0.808444	−	0.588574i	$-0.200310\pi$
$998$	41.1185	−	14.9659i	1.30158	−	0.473738i
$999$	−6.13678	+	2.57676i	−0.194159	+	0.0815251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.61.9	yes	1404
3.2	odd	2		729.2.i.a.262.18		1404
243.4	even	81	inner	243.2.i.a.4.9	✓	1404
243.239	odd	162		729.2.i.a.64.18		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.9	✓	1404	243.4	even	81	inner
243.2.i.a.61.9	yes	1404	1.1	even	1	trivial
729.2.i.a.64.18		1404	243.239	odd	162
729.2.i.a.262.18		1404	3.2	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04754 + 0.0406495i) q^{2} +(0.956457 - 1.44402i) q^{3} +(-0.898290 + 0.0698206i) q^{4} +(-2.13661 + 2.64898i) q^{5} +(-0.943232 + 1.55155i) q^{6} +(1.55684 + 0.707671i) q^{7} +(3.02065 - 0.353063i) q^{8} +(-1.17038 - 2.76228i) q^{9} +(2.13051 - 2.86177i) q^{10} +(-0.111562 + 5.75211i) q^{11} +(-0.758353 + 1.36393i) q^{12} +(-3.31592 + 1.06321i) q^{13} +(-1.65963 - 0.678032i) q^{14} +(1.78160 + 5.61893i) q^{15} +(-1.36955 + 0.214194i) q^{16} +(-0.724593 + 2.42031i) q^{17} +(1.33831 + 2.84604i) q^{18} +(6.60241 + 1.56480i) q^{19} +(1.73434 - 2.52873i) q^{20} +(2.51094 - 1.57125i) q^{21} +(-0.116954 - 6.03012i) q^{22} +(3.72324 + 2.66121i) q^{23} +(2.37929 - 4.69956i) q^{24} +(-1.39347 - 6.43296i) q^{25} +(3.43036 - 1.24855i) q^{26} +(-5.10821 - 0.951951i) q^{27} +(-1.44790 - 0.526994i) q^{28} +(-0.199738 + 1.46234i) q^{29} +(-2.09471 - 5.81365i) q^{30} +(-2.04042 + 2.00123i) q^{31} +(-4.54245 + 0.892108i) q^{32} +(8.19945 + 5.66274i) q^{33} +(0.660658 - 2.56483i) q^{34} +(-5.20096 + 2.61202i) q^{35} +(1.24421 + 2.39961i) q^{36} +(1.07019 - 0.703872i) q^{37} +(-6.97992 - 1.37081i) q^{38} +(-1.63624 + 5.80517i) q^{39} +(-5.51868 + 8.75598i) q^{40} +(0.0580046 + 0.110119i) q^{41} +(-2.56645 + 1.74802i) q^{42} +(-0.546726 - 1.59787i) q^{43} +(-0.301400 - 5.17485i) q^{44} +(9.81786 + 2.80160i) q^{45} +(-4.00843 - 2.63639i) q^{46} +(-9.47337 - 9.29142i) q^{47} +(-1.00062 + 2.18253i) q^{48} +(-2.67969 - 3.07059i) q^{49} +(1.72121 + 6.68216i) q^{50} +(2.80193 + 3.36124i) q^{51} +(2.90442 - 1.18659i) q^{52} +(-5.69747 + 4.78075i) q^{53} +(5.38977 + 0.789564i) q^{54} +(-14.9988 - 12.5855i) q^{55} +(4.95252 + 1.58796i) q^{56} +(8.57451 - 8.03734i) q^{57} +(0.149791 - 1.53999i) q^{58} +(2.94484 + 1.62490i) q^{59} +(-1.99271 - 4.92303i) q^{60} +(3.73135 + 0.290023i) q^{61} +(2.05608 - 2.17931i) q^{62} +(0.132690 - 5.12868i) q^{63} +(7.41983 - 1.75853i) q^{64} +(4.26841 - 11.0554i) q^{65} +(-8.81947 - 5.59866i) q^{66} +(-0.110239 - 0.807089i) q^{67} +(0.481907 - 2.22473i) q^{68} +(7.40395 - 2.83109i) q^{69} +(5.34205 - 2.94762i) q^{70} +(1.82852 + 4.23899i) q^{71} +(-4.51057 - 7.93067i) q^{72} +(2.83346 + 3.80600i) q^{73} +(-1.09245 + 0.780839i) q^{74} +(-10.6221 - 4.14065i) q^{75} +(-6.04013 - 0.944659i) q^{76} +(-4.24428 + 8.87616i) q^{77} +(1.47806 - 6.14768i) q^{78} +(4.70874 + 7.47093i) q^{79} +(2.35880 - 4.08556i) q^{80} +(-6.26041 + 6.46585i) q^{81} +(-0.0652386 - 0.112997i) q^{82} +(5.78205 - 10.9769i) q^{83} +(-2.14585 + 1.58675i) q^{84} +(-4.86317 - 7.09067i) q^{85} +(0.637673 + 1.65161i) q^{86} +(1.92061 + 1.68709i) q^{87} +(1.69387 + 17.4145i) q^{88} +(7.00705 - 16.2442i) q^{89} +(-10.3985 - 2.53571i) q^{90} +(-5.91476 - 0.691337i) q^{91} +(-3.53035 - 2.13058i) q^{92} +(0.938239 + 4.86048i) q^{93} +(10.3015 + 9.34808i) q^{94} +(-18.2518 + 14.1463i) q^{95} +(-3.05643 + 7.41264i) q^{96} +(9.65191 + 11.9665i) q^{97} +(2.93192 + 3.10765i) q^{98} +(16.0195 - 6.42399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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