LMFDB - Embedded newform 81.2.g.a.76.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] 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("81.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			76.4
Character	$\chi$	$=$	81.76
Dual form			81.2.g.a.16.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.643544 + 0.152523i) q^{2} +(-1.70947 + 0.278788i) q^{3} +(-1.39638 + 0.701288i) q^{4} +(-1.50096 - 2.01613i) q^{5} +(1.05760 - 0.440145i) q^{6} +(-3.43556 + 2.25960i) q^{7} +(1.80495 - 1.51453i) q^{8} +(2.84455 - 0.953158i) q^{9} +(1.27344 + 1.06854i) q^{10} +(-2.94058 - 0.343704i) q^{11} +(2.19155 - 1.58812i) q^{12} +(0.930150 + 3.10692i) q^{13} +(1.86629 - 1.97816i) q^{14} +(3.12791 + 3.02806i) q^{15} +(0.935660 - 1.25681i) q^{16} +(-0.572741 + 3.24818i) q^{17} +(-1.68522 + 1.04726i) q^{18} +(-0.571121 - 3.23899i) q^{19} +(3.50979 + 1.76268i) q^{20} +(5.24302 - 4.82051i) q^{21} +(1.94481 - 0.227316i) q^{22} +(-2.08548 - 1.37164i) q^{23} +(-2.66327 + 3.09224i) q^{24} +(-0.377908 + 1.26230i) q^{25} +(-1.07247 - 1.85757i) q^{26} +(-4.59694 + 2.42242i) q^{27} +(3.21271 - 5.56458i) q^{28} +(-3.82031 - 4.04929i) q^{29} +(-2.47480 - 1.47162i) q^{30} +(-0.373446 + 6.41181i) q^{31} +(-2.27693 + 5.27851i) q^{32} +(5.12264 - 0.232247i) q^{33} +(-0.126837 - 2.17770i) q^{34} +(9.71228 + 3.53498i) q^{35} +(-3.30364 + 3.32582i) q^{36} +(-2.56937 + 0.935175i) q^{37} +(0.861562 + 1.99733i) q^{38} +(-2.45623 - 5.05186i) q^{39} +(-5.76265 - 1.36577i) q^{40} +(-8.80462 - 2.08673i) q^{41} +(-2.63888 + 3.90189i) q^{42} +(-3.09638 - 7.17822i) q^{43} +(4.34719 - 1.58225i) q^{44} +(-6.19124 - 4.30435i) q^{45} +(1.55131 + 0.564629i) q^{46} +(0.588422 + 10.1028i) q^{47} +(-1.24910 + 2.40933i) q^{48} +(3.92470 - 9.09847i) q^{49} +(0.0506710 - 0.869987i) q^{50} +(0.0735294 - 5.71233i) q^{51} +(-3.47769 - 3.68613i) q^{52} +(0.00494432 - 0.00856381i) q^{53} +(2.58886 - 2.26007i) q^{54} +(3.72072 + 6.44448i) q^{55} +(-2.77877 + 9.28173i) q^{56} +(1.87930 + 5.37773i) q^{57} +(3.07615 + 2.02322i) q^{58} +(11.2961 - 1.32033i) q^{59} +(-6.49129 - 2.03476i) q^{60} +(8.05332 + 4.04453i) q^{61} +(-0.737619 - 4.18325i) q^{62} +(-7.61887 + 9.70219i) q^{63} +(0.116049 - 0.658144i) q^{64} +(4.86785 - 6.53865i) q^{65} +(-3.26122 + 0.930781i) q^{66} +(-4.01126 + 4.25169i) q^{67} +(-1.47814 - 4.93734i) q^{68} +(3.94746 + 1.76337i) q^{69} +(-6.78945 - 0.793572i) q^{70} +(-1.81817 - 1.52563i) q^{71} +(3.69069 - 6.02857i) q^{72} +(3.61987 - 3.03743i) q^{73} +(1.51087 - 0.993715i) q^{74} +(0.294107 - 2.26322i) q^{75} +(3.06897 + 4.12234i) q^{76} +(10.8792 - 5.46372i) q^{77} +(2.35122 + 2.87646i) q^{78} +(8.75936 - 2.07601i) q^{79} -3.93828 q^{80} +(7.18298 - 5.42262i) q^{81} +5.98444 q^{82} +(-3.60157 + 0.853588i) q^{83} +(-3.94068 + 10.4081i) q^{84} +(7.40842 - 3.72065i) q^{85} +(3.08750 + 4.14723i) q^{86} +(7.65959 + 5.85708i) q^{87} +(-5.82815 + 3.83323i) q^{88} +(-9.57258 + 8.03235i) q^{89} +(4.64085 + 1.82574i) q^{90} +(-10.2160 - 8.57223i) q^{91} +(3.87404 + 0.452810i) q^{92} +(-1.14914 - 11.0649i) q^{93} +(-1.91958 - 6.41186i) q^{94} +(-5.67301 + 6.01304i) q^{95} +(2.42075 - 9.65823i) q^{96} +(-4.27084 + 5.73673i) q^{97} +(-1.13799 + 6.45388i) q^{98} +(-8.69223 + 1.82515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{25}{27}\right)$

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 $

$2$	−0.643544	+	0.152523i	−0.455055	+	0.107850i	−0.451750	−	0.892145i	$-0.649200\pi$
$2$	−0.643544	+	0.152523i	−0.455055	+	0.107850i	−0.00330473	+	0.999995i	$0.501052\pi$
$3$	−1.70947	+	0.278788i	−0.986961	+	0.160958i
$3$	−1.70947	+	0.278788i	−0.986961	+	0.160958i
$4$	−1.39638	+	0.701288i	−0.698189	+	0.350644i
$5$	−1.50096	−	2.01613i	−0.671248	−	0.901642i	0.327823	−	0.944739i	$-0.393685\pi$
$5$	−1.50096	−	2.01613i	−0.671248	−	0.901642i	−0.999071	+	0.0430971i	$0.986278\pi$
$6$	1.05760	−	0.440145i	0.431762	−	0.179689i
$7$	−3.43556	+	2.25960i	−1.29852	+	0.854049i	−0.995106	−	0.0988101i	$-0.968496\pi$
$7$	−3.43556	+	2.25960i	−1.29852	+	0.854049i	−0.303412	+	0.952859i	$0.598126\pi$
$8$	1.80495	−	1.51453i	0.638146	−	0.535468i
$9$	2.84455	−	0.953158i	0.948185	−	0.317719i
$10$	1.27344	+	1.06854i	0.402696	+	0.337902i
$11$	−2.94058	−	0.343704i	−0.886617	−	0.103631i	−0.339421	−	0.940635i	$-0.610231\pi$
$11$	−2.94058	−	0.343704i	−0.886617	−	0.103631i	−0.547197	+	0.837004i	$0.684305\pi$
$12$	2.19155	−	1.58812i	0.632647	−	0.458451i
$13$	0.930150	+	3.10692i	0.257977	+	0.861704i	0.984623	+	0.174692i	$0.0558930\pi$
$13$	0.930150	+	3.10692i	0.257977	+	0.861704i	−0.726646	+	0.687012i	$0.758922\pi$
$14$	1.86629	−	1.97816i	0.498788	−	0.528684i
$15$	3.12791	+	3.02806i	0.807622	+	0.781843i
$16$	0.935660	−	1.25681i	0.233915	−	0.314202i
$17$	−0.572741	+	3.24818i	−0.138910	+	0.787799i	0.833146	+	0.553052i	$0.186537\pi$
$17$	−0.572741	+	3.24818i	−0.138910	+	0.787799i	−0.972057	+	0.234746i	$0.924574\pi$
$18$	−1.68522	+	1.04726i	−0.397210	+	0.246841i
$19$	−0.571121	−	3.23899i	−0.131024	−	0.743075i	−0.977546	−	0.210722i	$-0.932419\pi$
$19$	−0.571121	−	3.23899i	−0.131024	−	0.743075i	0.846522	−	0.532354i	$-0.178692\pi$
$20$	3.50979	+	1.76268i	0.784813	+	0.394148i
$21$	5.24302	−	4.82051i	1.14412	−	1.05192i
$22$	1.94481	−	0.227316i	0.414636	−	0.0484640i
$23$	−2.08548	−	1.37164i	−0.434853	−	0.286007i	0.313149	−	0.949704i	$-0.398616\pi$
$23$	−2.08548	−	1.37164i	−0.434853	−	0.286007i	−0.748002	+	0.663697i	$0.768986\pi$
$24$	−2.66327	+	3.09224i	−0.543637	+	0.631201i
$25$	−0.377908	+	1.26230i	−0.0755816	+	0.252460i
$26$	−1.07247	−	1.85757i	−0.210329	−	0.364300i
$27$	−4.59694	+	2.42242i	−0.884682	+	0.466195i
$28$	3.21271	−	5.56458i	0.607145	−	1.05161i
$29$	−3.82031	−	4.04929i	−0.709414	−	0.751935i	0.267965	−	0.963429i	$-0.413649\pi$
$29$	−3.82031	−	4.04929i	−0.709414	−	0.751935i	−0.977379	+	0.211494i	$0.932167\pi$
$30$	−2.47480	−	1.47162i	−0.451834	−	0.268679i
$31$	−0.373446	+	6.41181i	−0.0670728	+	1.15160i	0.781986	+	0.623297i	$0.214207\pi$
$31$	−0.373446	+	6.41181i	−0.0670728	+	1.15160i	−0.849058	+	0.528299i	$0.822830\pi$
$32$	−2.27693	+	5.27851i	−0.402508	+	0.933118i
$33$	5.12264	−	0.232247i	0.891737	−	0.0404290i
$34$	−0.126837	−	2.17770i	−0.0217523	−	0.373473i
$35$	9.71228	+	3.53498i	1.64167	+	0.597521i
$36$	−3.30364	+	3.32582i	−0.550606	+	0.554304i
$37$	−2.56937	+	0.935175i	−0.422402	+	0.153742i	−0.544471	−	0.838780i	$-0.683269\pi$
$37$	−2.56937	+	0.935175i	−0.422402	+	0.153742i	0.122069	+	0.992522i	$0.461047\pi$
$38$	0.861562	+	1.99733i	0.139764	+	0.324009i
$39$	−2.45623	−	5.05186i	−0.393312	−	0.808945i
$40$	−5.76265	−	1.36577i	−0.911155	−	0.215948i
$41$	−8.80462	−	2.08673i	−1.37505	−	0.325893i	−0.524332	−	0.851514i	$-0.675685\pi$
$41$	−8.80462	−	2.08673i	−1.37505	−	0.325893i	−0.850719	+	0.525621i	$0.823833\pi$
$42$	−2.63888	+	3.90189i	−0.407188	+	0.602075i
$43$	−3.09638	−	7.17822i	−0.472194	−	1.09467i	−0.973353	−	0.229313i	$-0.926352\pi$
$43$	−3.09638	−	7.17822i	−0.472194	−	1.09467i	0.501159	−	0.865355i	$-0.332907\pi$
$44$	4.34719	−	1.58225i	0.655364	−	0.238533i
$45$	−6.19124	−	4.30435i	−0.922936	−	0.641655i
$46$	1.55131	+	0.564629i	0.228728	+	0.0832500i
$47$	0.588422	+	10.1028i	0.0858301	+	1.47365i	0.716496	+	0.697591i	$0.245745\pi$
$47$	0.588422	+	10.1028i	0.0858301	+	1.47365i	−0.630666	+	0.776055i	$0.717218\pi$
$48$	−1.24910	+	2.40933i	−0.180292	+	0.347756i
$49$	3.92470	−	9.09847i	0.560671	−	1.29978i
$50$	0.0506710	−	0.869987i	0.00716596	−	0.123035i
$51$	0.0735294	−	5.71233i	0.0102962	−	0.799886i
$52$	−3.47769	−	3.68613i	−0.482268	−	0.511175i
$53$	0.00494432	−	0.00856381i	0.000679154	−	0.00117633i	−0.865686	−	0.500588i	$-0.833117\pi$
$53$	0.00494432	−	0.00856381i	0.000679154	−	0.00117633i	0.866365	+	0.499412i	$0.166450\pi$
$54$	2.58886	−	2.26007i	0.352300	−	0.307557i
$55$	3.72072	+	6.44448i	0.501702	+	0.868973i
$56$	−2.77877	+	9.28173i	−0.371329	+	1.24032i
$57$	1.87930	+	5.37773i	0.248920	+	0.712297i
$58$	3.07615	+	2.02322i	0.403918	+	0.265661i
$59$	11.2961	−	1.32033i	1.47063	−	0.171892i	0.657272	−	0.753654i	$-0.271710\pi$
$59$	11.2961	−	1.32033i	1.47063	−	0.171892i	0.813359	+	0.581762i	$0.197636\pi$
$60$	−6.49129	−	2.03476i	−0.838022	−	0.262687i
$61$	8.05332	+	4.04453i	1.03112	+	0.517849i	0.882138	−	0.470990i	$-0.156103\pi$
$61$	8.05332	+	4.04453i	1.03112	+	0.517849i	0.148984	+	0.988840i	$0.452400\pi$
$62$	−0.737619	−	4.18325i	−0.0936777	−	0.531273i
$63$	−7.61887	+	9.70219i	−0.959888	+	1.22236i
$64$	0.116049	−	0.658144i	0.0145061	−	0.0822680i
$65$	4.86785	−	6.53865i	0.603782	−	0.811020i
$66$	−3.26122	+	0.930781i	−0.401429	+	0.114571i
$67$	−4.01126	+	4.25169i	−0.490054	+	0.519427i	−0.924454	−	0.381293i	$-0.875479\pi$
$67$	−4.01126	+	4.25169i	−0.490054	+	0.519427i	0.434400	+	0.900720i	$0.356960\pi$
$68$	−1.47814	−	4.93734i	−0.179251	−	0.598741i
$69$	3.94746	+	1.76337i	0.475218	+	0.212285i
$70$	−6.78945	−	0.793572i	−0.811494	−	0.0948500i
$71$	−1.81817	−	1.52563i	−0.215777	−	0.181058i	0.528492	−	0.848938i	$-0.322758\pi$
$71$	−1.81817	−	1.52563i	−0.215777	−	0.181058i	−0.744269	+	0.667880i	$0.767202\pi$
$72$	3.69069	−	6.02857i	0.434952	−	0.710474i
$73$	3.61987	−	3.03743i	0.423674	−	0.355505i	−0.405885	−	0.913924i	$-0.633037\pi$
$73$	3.61987	−	3.03743i	0.423674	−	0.355505i	0.829559	+	0.558420i	$0.188592\pi$
$74$	1.51087	−	0.993715i	0.175635	−	0.115517i
$75$	0.294107	−	2.26322i	0.0339606	−	0.261334i
$76$	3.06897	+	4.12234i	0.352035	+	0.472865i
$77$	10.8792	−	5.46372i	1.23979	−	0.622648i
$78$	2.35122	+	2.87646i	0.266223	+	0.325696i
$79$	8.75936	−	2.07601i	0.985505	−	0.233569i	0.293893	−	0.955838i	$-0.405049\pi$
$79$	8.75936	−	2.07601i	0.985505	−	0.233569i	0.691612	+	0.722269i	$0.256901\pi$
$80$	−3.93828			−0.440313
$81$	7.18298	−	5.42262i	0.798109	−	0.602513i
$82$	5.98444			0.660871
$83$	−3.60157	+	0.853588i	−0.395324	+	0.0936935i	−0.423469	−	0.905910i	$-0.639188\pi$
$83$	−3.60157	+	0.853588i	−0.395324	+	0.0936935i	0.0281457	+	0.999604i	$0.491040\pi$
$84$	−3.94068	+	10.4081i	−0.429964	+	1.13562i
$85$	7.40842	−	3.72065i	0.803555	−	0.403561i
$86$	3.08750	+	4.14723i	0.332934	+	0.447208i
$87$	7.65959	+	5.85708i	0.821194	+	0.627945i
$88$	−5.82815	+	3.83323i	−0.621282	+	0.408624i
$89$	−9.57258	+	8.03235i	−1.01469	+	0.851427i	−0.988951	−	0.148242i	$-0.952639\pi$
$89$	−9.57258	+	8.03235i	−1.01469	+	0.851427i	−0.0257399	+	0.999669i	$0.508194\pi$
$90$	4.64085	+	1.82574i	0.489189	+	0.192449i
$91$	−10.2160	−	8.57223i	−1.07093	−	0.898614i
$92$	3.87404	+	0.452810i	0.403896	+	0.0472087i
$93$	−1.14914	−	11.0649i	−0.119161	−	1.14738i
$94$	−1.91958	−	6.41186i	−0.197990	−	0.661333i
$95$	−5.67301	+	6.01304i	−0.582038	+	0.616924i
$96$	2.42075	−	9.65823i	0.247067	−	0.985739i
$97$	−4.27084	+	5.73673i	−0.433638	+	0.582477i	−0.964202	−	0.265168i	$-0.914573\pi$
$97$	−4.27084	+	5.73673i	−0.433638	+	0.582477i	0.530565	+	0.847645i	$0.321980\pi$
$98$	−1.13799	+	6.45388i	−0.114955	+	0.651940i
$99$	−8.69223	+	1.82515i	−0.873602	+	0.183434i
$100$	−0.357534	−	2.02767i	−0.0357534	−	0.202767i
$101$	−1.88208	−	0.945217i	−0.187274	−	0.0940526i	0.352692	−	0.935740i	$-0.385267\pi$
$101$	−1.88208	−	0.945217i	−0.187274	−	0.0940526i	−0.539966	+	0.841687i	$0.681563\pi$
$102$	0.823941	+	3.68735i	0.0815823	+	0.365102i
$103$	2.05137	−	0.239771i	0.202128	−	0.0236254i	−0.0144264	−	0.999896i	$-0.504592\pi$
$103$	2.05137	−	0.239771i	0.202128	−	0.0236254i	0.216554	+	0.976271i	$0.430518\pi$
$104$	6.38441	+	4.19909i	0.626042	+	0.411755i
$105$	−17.5883	−	3.33526i	−1.71644	−	0.325488i
$106$	−0.00187571	+	0.00626531i	−0.000182185	+	0.000608541i
$107$	−7.13179	−	12.3526i	−0.689456	−	1.19417i	−0.972014	−	0.234923i	$-0.924516\pi$
$107$	−7.13179	−	12.3526i	−0.689456	−	1.19417i	0.282558	−	0.959250i	$-0.408817\pi$
$108$	4.72026	−	6.60640i	0.454207	−	0.635701i
$109$	−6.70237	+	11.6088i	−0.641970	+	1.11193i	0.343022	+	0.939327i	$0.388549\pi$
$109$	−6.70237	+	11.6088i	−0.641970	+	1.11193i	−0.984992	+	0.172598i	$0.944784\pi$
$110$	−3.37738	−	3.57981i	−0.322020	−	0.341322i
$111$	4.13154	−	2.31496i	0.392149	−	0.219726i
$112$	−0.374625	+	6.43206i	−0.0353987	+	0.607773i
$113$	−1.17253	+	2.71823i	−0.110302	+	0.255709i	−0.964422	−	0.264367i	$-0.914837\pi$
$113$	−1.17253	+	2.71823i	−0.110302	+	0.255709i	0.854120	+	0.520076i	$0.174096\pi$
$114$	−2.02964	−	3.17417i	−0.190093	−	0.297288i
$115$	0.364800	+	6.26337i	0.0340178	+	0.584063i
$116$	8.17432	+	2.97521i	0.758967	+	0.276241i
$117$	5.60725	+	7.95122i	0.518390	+	0.735090i
$118$	−7.06818	+	2.57261i	−0.650679	+	0.236828i
$119$	−5.37190	−	12.4535i	−0.492441	−	1.14161i
$120$	10.2318	+	0.728186i	0.934033	+	0.0664740i
$121$	−2.17464	−	0.515398i	−0.197694	−	0.0468544i
$122$	−5.79956	−	1.37452i	−0.525067	−	0.124443i
$123$	15.6330	+	1.11258i	1.40958	+	0.100318i
$124$	−3.97506	−	9.21521i	−0.356971	−	0.827551i
$125$	−8.69737	+	3.16558i	−0.777917	+	0.283139i
$126$	3.42328	−	7.40584i	0.304970	−	0.659765i
$127$	−11.3063	−	4.11514i	−1.00327	−	0.365160i	−0.212425	−	0.977177i	$-0.568136\pi$
$127$	−11.3063	−	4.11514i	−1.00327	−	0.365160i	−0.790844	+	0.612017i	$0.790358\pi$
$128$	−0.642810	−	11.0366i	−0.0568170	−	0.975509i
$129$	7.29436	+	11.4077i	0.642233	+	1.00439i
$130$	−2.13538	+	4.95037i	−0.187285	+	0.434176i
$131$	0.298647	−	5.12757i	0.0260929	−	0.447998i	−0.959807	−	0.280661i	$-0.909446\pi$
$131$	0.298647	−	5.12757i	0.0260929	−	0.447998i	0.985900	−	0.167337i	$-0.0535167\pi$
$132$	−6.99027	+	3.91675i	−0.608425	+	0.340909i
$133$	9.28095	+	9.83723i	0.804760	+	0.852996i
$134$	1.93295	−	3.34796i	0.166981	−	0.289220i
$135$	11.7837	+	5.63210i	1.01418	+	0.484734i
$136$	3.88570	+	6.73023i	0.333196	+	0.577113i
$137$	−0.545226	+	1.82118i	−0.0465818	+	0.155594i	−0.978116	−	0.208059i	$-0.933285\pi$
$137$	−0.545226	+	1.82118i	−0.0465818	+	0.155594i	0.931534	+	0.363653i	$0.118471\pi$
$138$	−2.80932	−	0.532729i	−0.239145	−	0.0453489i
$139$	−7.81835	−	5.14221i	−0.663144	−	0.436156i	0.172811	−	0.984955i	$-0.444715\pi$
$139$	−7.81835	−	5.14221i	−0.663144	−	0.436156i	−0.835955	+	0.548799i	$0.815085\pi$
$140$	−16.0411	+	1.87493i	−1.35572	+	0.158461i
$141$	−3.82243	−	17.1064i	−0.321907	−	1.44062i
$142$	1.40277	+	0.704496i	0.117718	+	0.0591200i
$143$	−1.66732	−	9.45583i	−0.139428	−	0.790736i
$144$	1.46360	−	4.46689i	0.121967	−	0.372241i
$145$	−2.42980	+	13.7801i	−0.201784	+	1.14437i
$146$	−1.86627	+	2.50684i	−0.154454	+	0.207467i
$147$	−4.17260	+	16.6477i	−0.344150	+	1.37308i
$148$	2.93199	−	3.10773i	0.241008	−	0.255454i
$149$	0.254865	+	0.851310i	0.0208794	+	0.0697420i	0.967794	−	0.251742i	$-0.0810035\pi$
$149$	0.254865	+	0.851310i	0.0208794	+	0.0697420i	−0.946915	+	0.321484i	$0.895818\pi$
$150$	0.155922	+	1.50134i	0.0127309	+	0.122584i
$151$	8.00406	+	0.935541i	0.651362	+	0.0761332i	0.435355	−	0.900259i	$-0.356623\pi$
$151$	8.00406	+	0.935541i	0.651362	+	0.0761332i	0.216006	+	0.976392i	$0.430697\pi$
$152$	−5.93640	−	4.98123i	−0.481506	−	0.404031i
$153$	1.46683	+	9.78553i	0.118586	+	0.791113i
$154$	−6.16788	+	5.17546i	−0.497022	+	0.417051i
$155$	13.4876	−	8.87093i	1.08335	−	0.712530i
$156$	6.97264	+	5.33178i	0.558258	+	0.426884i
$157$	−8.64121	−	11.6072i	−0.689643	−	0.926352i	0.310060	−	0.950717i	$-0.399651\pi$
$157$	−8.64121	−	11.6072i	−0.689643	−	0.926352i	−0.999703	+	0.0243652i	$0.992244\pi$
$158$	−5.32040	+	2.67201i	−0.423268	+	0.212573i
$159$	−0.00606466	+	0.0160180i	−0.000480959	+	0.00127031i
$160$	14.0598	−	3.33222i	1.11152	−	0.263435i
$161$	10.2641			0.808928
$162$	−3.79549	+	4.58526i	−0.298202	+	0.360252i
$163$	8.05495			0.630912			0.315456	−	0.948940i	$-0.397843\pi$
$163$	8.05495			0.630912			0.315456	+	0.948940i	$0.397843\pi$
$164$	13.7580	−	3.26070i	1.07432	−	0.254618i
$165$	−8.15709	−	9.97933i	−0.635029	−	0.776890i
$166$	2.18758	−	1.09864i	0.169789	−	0.0852713i
$167$	10.0814	+	13.5417i	0.780126	+	1.04789i	0.997420	+	0.0717845i	$0.0228694\pi$
$167$	10.0814	+	13.5417i	0.780126	+	1.04789i	−0.217295	+	0.976106i	$0.569723\pi$
$168$	2.16258	−	16.6415i	0.166846	−	1.28392i
$169$	2.07358	−	1.36381i	0.159506	−	0.104909i
$170$	−4.20016	+	3.52435i	−0.322138	+	0.270306i
$171$	−4.71186	−	8.66912i	−0.360325	−	0.662944i
$172$	9.35772	+	7.85206i	0.713520	+	0.598714i
$173$	−6.67771	−	0.780512i	−0.507697	−	0.0593412i	−0.141611	−	0.989922i	$-0.545228\pi$
$173$	−6.67771	−	0.780512i	−0.507697	−	0.0593412i	−0.366086	+	0.930581i	$0.619302\pi$
$174$	−5.82263	−	2.60103i	−0.441412	−	0.197183i
$175$	−1.55397	−	5.19063i	−0.117469	−	0.392375i
$176$	−3.18335	+	3.37415i	−0.239954	+	0.254336i
$177$	−18.9423	+	5.40628i	−1.42379	+	0.406361i
$178$	4.93526	−	6.62921i	0.369914	−	0.496880i
$179$	−2.64043	+	14.9746i	−0.197355	+	1.11926i	0.711669	+	0.702515i	$0.247940\pi$
$179$	−2.64043	+	14.9746i	−0.197355	+	1.11926i	−0.909024	+	0.416743i	$0.863172\pi$
$180$	11.6639	+	1.66866i	0.869376	+	0.124375i
$181$	−0.973297	−	5.51984i	−0.0723446	−	0.410287i	−0.999377	−	0.0353044i	$-0.988760\pi$
$181$	−0.973297	−	5.51984i	−0.0723446	−	0.410287i	0.927032	−	0.374982i	$-0.122351\pi$
$182$	7.88190	+	3.95844i	0.584245	+	0.293419i
$183$	−14.8945	−	4.66882i	−1.10103	−	0.345129i
$184$	−5.84158	+	0.682783i	−0.430647	+	0.0503354i
$185$	5.74195	+	3.77654i	0.422157	+	0.277657i
$186$	2.42717	+	6.94548i	0.177969	+	0.509267i
$187$	2.80060	−	9.35466i	0.204800	−	0.684081i
$188$	−7.90664	−	13.6947i	−0.576651	−	0.998788i
$189$	10.3194	−	18.7096i	0.750623	−	1.36092i
$190$	2.73371	−	4.73492i	0.198324	−	0.343507i
$191$	2.94787	+	3.12456i	0.213300	+	0.226085i	0.825186	−	0.564861i	$-0.191070\pi$
$191$	2.94787	+	3.12456i	0.213300	+	0.226085i	−0.611886	+	0.790946i	$0.709589\pi$
$192$	−0.0148985	+	1.15743i	−0.00107521	+	0.0835302i
$193$	−0.164764	+	2.82888i	−0.0118600	+	0.203628i	0.987173	+	0.159655i	$0.0510383\pi$
$193$	−0.164764	+	2.82888i	−0.0118600	+	0.203628i	−0.999033	+	0.0439721i	$0.985999\pi$
$194$	1.87349	−	4.34324i	0.134509	−	0.311826i
$195$	−6.49852	+	12.5347i	−0.465369	+	0.897629i
$196$	0.900283	+	15.4573i	0.0643059	+	1.10409i
$197$	19.9667	+	7.26729i	1.42257	+	0.517773i	0.934792	−	0.355195i	$-0.115586\pi$
$197$	19.9667	+	7.26729i	1.42257	+	0.517773i	0.487777	+	0.872968i	$0.337808\pi$
$198$	5.31546	−	2.50033i	0.377754	−	0.177691i
$199$	−9.14529	+	3.32862i	−0.648293	+	0.235959i	−0.645174	−	0.764036i	$-0.723215\pi$
$199$	−9.14529	+	3.32862i	−0.648293	+	0.235959i	−0.00311899	+	0.999995i	$0.500993\pi$
$200$	1.22969	+	2.85075i	0.0869523	+	0.201578i
$201$	5.67180	−	8.38642i	0.400058	−	0.591532i
$202$	1.35537	+	0.321229i	0.0953636	+	0.0226016i
$203$	22.2747	+	5.27920i	1.56338	+	0.370527i
$204$	3.90331	+	8.02814i	0.273286	+	0.562082i
$205$	9.00821	+	20.8834i	0.629161	+	1.45856i
$206$	−1.28358	+	0.467185i	−0.0894313	+	0.0325503i
$207$	−7.23965	−	1.91392i	−0.503190	−	0.133026i
$208$	4.77511	+	1.73800i	0.331094	+	0.120508i
$209$	0.566172	+	9.72080i	0.0391629	+	0.672402i
$210$	11.8276	−	0.536230i	0.816180	−	0.0370034i
$211$	7.75452	−	17.9770i	0.533843	−	1.23759i	−0.411470	−	0.911423i	$-0.634984\pi$
$211$	7.75452	−	17.9770i	0.533843	−	1.23759i	0.945313	−	0.326164i	$-0.105756\pi$
$212$	−0.000898445		0.0154257i	−6.17055e−5		0.00105944i
$213$	3.53343	+	2.10112i	0.242107	+	0.143967i
$214$	6.47368	+	6.86170i	0.442532	+	0.469056i
$215$	−9.82471	+	17.0169i	−0.670040	+	1.16054i
$216$	−4.62842	+	11.3346i	−0.314924	+	0.771220i
$217$	−13.2052	−	22.8720i	−0.896424	−	1.55265i
$218$	2.54266	−	8.49307i	0.172211	−	0.575223i
$219$	−5.34125	+	6.20157i	−0.360928	+	0.419063i
$220$	−9.71497	−	6.38964i	−0.654983	−	0.430789i
$221$	−10.6246	+	1.24183i	−0.714685	+	0.0835347i
$222$	−2.30575	+	2.11993i	−0.154752	+	0.142281i
$223$	−14.4467	−	7.25542i	−0.967424	−	0.485859i	−0.106345	−	0.994329i	$-0.533915\pi$
$223$	−14.4467	−	7.25542i	−0.967424	−	0.485859i	−0.861079	+	0.508471i	$0.830211\pi$
$224$	−4.10482	−	23.2796i	−0.274265	−	1.55543i
$225$	0.128192	+	3.95089i	0.00854612	+	0.263393i
$226$	0.339982	−	1.92814i	0.0226153	−	0.128258i
$227$	12.6779	−	17.0294i	0.841463	−	1.13028i	−0.148494	−	0.988913i	$-0.547443\pi$
$227$	12.6779	−	17.0294i	0.841463	−	1.13028i	0.989957	−	0.141368i	$-0.0451500\pi$
$228$	−6.39556	−	6.19141i	−0.423556	−	0.410036i
$229$	5.92191	−	6.27686i	0.391331	−	0.414787i	−0.501515	−	0.865149i	$-0.667224\pi$
$229$	5.92191	−	6.27686i	0.391331	−	0.414787i	0.892846	+	0.450362i	$0.148705\pi$
$230$	−1.19007	−	3.97512i	−0.0784711	−	0.262112i
$231$	−17.0743	+	12.3730i	−1.12341	+	0.814085i
$232$	−13.0283	−	1.52279i	−0.855347	−	0.0999758i
$233$	−11.4634	−	9.61890i	−0.750989	−	0.630155i	0.184775	−	0.982781i	$-0.440844\pi$
$233$	−11.4634	−	9.61890i	−0.750989	−	0.630155i	−0.935764	+	0.352626i	$0.885289\pi$
$234$	−4.82126	−	4.26173i	−0.315175	−	0.278598i
$235$	19.4854	−	16.3502i	1.27109	−	1.06657i
$236$	−14.8477	+	9.76552i	−0.966506	+	0.635681i
$237$	−14.3951	+	5.99087i	−0.935060	+	0.389149i
$238$	5.35650	+	7.19502i	0.347210	+	0.466384i
$239$	−3.22647	+	1.62040i	−0.208703	+	0.104815i	−0.550080	−	0.835112i	$-0.685403\pi$
$239$	−3.22647	+	1.62040i	−0.208703	+	0.104815i	0.341377	+	0.939926i	$0.389107\pi$
$240$	6.73236	−	1.09794i	0.434572	−	0.0708720i
$241$	−22.2744	+	5.27912i	−1.43482	+	0.340058i	−0.873210	−	0.487345i	$-0.837966\pi$
$241$	−22.2744	+	5.27912i	−1.43482	+	0.340058i	−0.561609	+	0.827403i	$0.689817\pi$
$242$	1.47808			0.0950149
$243$	−10.7673	+	11.2723i	−0.690723	+	0.723119i
$244$	−14.0819			−0.901500
$245$	−24.2345	+	5.74369i	−1.54829	+	0.366951i
$246$	−10.2302	+	1.66839i	−0.652254	+	0.106373i
$247$	9.53205	−	4.78718i	0.606510	−	0.304601i
$248$	9.03685	+	12.1386i	0.573841	+	0.770802i
$249$	5.91880	−	2.46326i	0.375089	−	0.156102i
$250$	5.11432	−	3.36374i	0.323458	−	0.212742i
$251$	−16.2193	+	13.6096i	−1.02375	+	0.859031i	−0.990095	−	0.140402i	$-0.955160\pi$
$251$	−16.2193	+	13.6096i	−1.02375	+	0.859031i	−0.0336587	+	0.999433i	$0.510716\pi$
$252$	3.83481	−	18.8910i	0.241570	−	1.19002i
$253$	5.66107	+	4.75020i	0.355909	+	0.298643i
$254$	7.90374	+	0.923815i	0.495925	+	0.0579653i
$255$	−11.6272	+	8.42570i	−0.728122	+	0.527638i
$256$	2.48035	+	8.28496i	0.155022	+	0.517810i
$257$	5.34379	−	5.66408i	0.333336	−	0.353316i	−0.538927	−	0.842353i	$-0.681170\pi$
$257$	5.34379	−	5.66408i	0.333336	−	0.353316i	0.872263	+	0.489037i	$0.162652\pi$
$258$	−6.43418	−	6.22880i	−0.400575	−	0.387788i
$259$	6.71410	−	9.01861i	0.417194	−	0.560389i
$260$	−2.21188	+	12.5442i	−0.137175	+	0.777958i
$261$	−14.7267	−	7.87708i	−0.911560	−	0.487579i
$262$	0.589879	+	3.34537i	0.0364428	+	0.206678i
$263$	1.36411	+	0.685083i	0.0841148	+	0.0422440i	0.490359	−	0.871520i	$-0.336866\pi$
$263$	1.36411	+	0.685083i	0.0841148	+	0.0422440i	−0.406244	+	0.913764i	$0.633162\pi$
$264$	8.89436	−	8.17760i	0.547410	−	0.503296i
$265$	−0.0246870	+	0.00288549i	−0.00151651	+	0.000177254i
$266$	−7.47311	−	4.91514i	−0.458206	−	0.301367i
$267$	14.1247	−	16.3997i	0.864416	−	1.00365i
$268$	2.61959	−	8.75002i	0.160017	−	0.534493i
$269$	14.7193	+	25.4946i	0.897454	+	1.55444i	0.830738	+	0.556663i	$0.187919\pi$
$269$	14.7193	+	25.4946i	0.897454	+	1.55444i	0.0667154	+	0.997772i	$0.478748\pi$
$270$	−8.44237	−	1.82722i	−0.513787	−	0.111201i
$271$	−7.28643	+	12.6205i	−0.442619	+	0.766639i	−0.997883	−	0.0650354i	$-0.979284\pi$
$271$	−7.28643	+	12.6205i	−0.442619	+	0.766639i	0.555264	+	0.831674i	$0.312617\pi$
$272$	3.54645	+	3.75902i	0.215035	+	0.227924i
$273$	19.8537	+	11.8058i	1.20160	+	0.714522i
$274$	0.0731054	−	1.25517i	0.00441646	−	0.0758277i
$275$	1.54513	−	3.58201i	0.0931746	−	0.216003i
$276$	−6.74877	+	0.305971i	−0.406228	+	0.0184173i
$277$	−0.594623	−	10.2093i	−0.0357274	−	0.613416i	−0.967890	−	0.251375i	$-0.919117\pi$
$277$	−0.594623	−	10.2093i	−0.0357274	−	0.613416i	0.932162	−	0.362041i	$-0.117920\pi$
$278$	5.81576	+	2.11676i	0.348806	+	0.126955i
$279$	5.04918	+	18.5947i	0.302287	+	1.11324i
$280$	22.8840	−	8.32910i	1.36758	−	0.497759i
$281$	2.78193	+	6.44925i	0.165956	+	0.384730i	0.980818	−	0.194925i	$-0.0624465\pi$
$281$	2.78193	+	6.44925i	0.165956	+	0.384730i	−0.814862	+	0.579655i	$0.803187\pi$
$282$	5.06902	+	10.4257i	0.301856	+	0.620842i
$283$	−21.0395	−	4.98645i	−1.25067	−	0.296414i	−0.448647	−	0.893709i	$-0.648094\pi$
$283$	−21.0395	−	4.98645i	−1.25067	−	0.296414i	−0.802021	+	0.597295i	$0.796242\pi$
$284$	3.60876	+	0.855291i	0.214140	+	0.0507522i
$285$	8.02146	−	11.8607i	0.475150	−	0.702564i
$286$	2.51522	+	5.83094i	0.148728	+	0.344791i
$287$	34.9640	−	12.7258i	2.06386	−	0.751183i
$288$	−1.44559	+	17.1853i	−0.0851823	+	1.01265i
$289$	5.75215	+	2.09361i	0.338362	+	0.123154i
$290$	−0.538092	−	9.23868i	−0.0315979	−	0.542514i
$291$	5.70152	−	10.9974i	0.334229	−	0.644679i
$292$	−2.92460	+	6.77998i	−0.171149	+	0.396768i
$293$	0.635343	−	10.9084i	0.0371171	−	0.637276i	−0.927533	−	0.373742i	$-0.878075\pi$
$293$	0.635343	−	10.9084i	0.0371171	−	0.637276i	0.964650	−	0.263535i	$-0.0848883\pi$
$294$	0.146097	−	11.3500i	0.00852057	−	0.661943i
$295$	−19.6169	−	20.7927i	−1.14214	−	1.21060i
$296$	−3.22124	+	5.57934i	−0.187230	+	0.324293i
$297$	14.3503	−	5.54332i	0.832686	−	0.321656i
$298$	−0.293862	−	0.508983i	−0.0170229	−	0.0294846i
$299$	2.32177	−	7.75525i	0.134271	−	0.448498i
$300$	1.17648	+	3.36656i	0.0679243	+	0.194369i
$301$	26.8577	+	17.6646i	1.54805	+	1.01817i
$302$	−5.29366	+	0.618740i	−0.304616	+	0.0356045i
$303$	3.48087	+	1.09112i	0.199971	+	0.0626830i
$304$	−4.60517	−	2.31280i	−0.264125	−	0.132648i
$305$	−3.93337	−	22.3072i	−0.225224	−	1.27731i
$306$	−2.43649	−	6.07370i	−0.139285	−	0.347210i
$307$	0.798574	−	4.52894i	0.0455770	−	0.258480i	−0.953502	−	0.301386i	$-0.902551\pi$
$307$	0.798574	−	4.52894i	0.0455770	−	0.258480i	0.999079	+	0.0429063i	$0.0136617\pi$
$308$	−11.3598	+	15.2588i	−0.647284	+	0.869453i
$309$	−3.43991	+	0.981780i	−0.195690	+	0.0558515i
$310$	−7.32685	+	7.76600i	−0.416137	+	0.441079i
$311$	5.00159	+	16.7065i	0.283614	+	0.947336i	0.974503	+	0.224375i	$0.0720342\pi$
$311$	5.00159	+	16.7065i	0.283614	+	0.947336i	−0.690889	+	0.722961i	$0.742781\pi$
$312$	−12.0846	−	5.39831i	−0.684155	−	0.305619i
$313$	15.7201	+	1.83741i	0.888550	+	0.103857i	0.548107	−	0.836408i	$-0.315349\pi$
$313$	15.7201	+	1.83741i	0.888550	+	0.103857i	0.340443	+	0.940265i	$0.389423\pi$
$314$	7.33136	+	6.15174i	0.413732	+	0.347163i
$315$	30.9965	+	0.798110i	1.74645	+	0.0449684i
$316$	−10.7755	+	9.04173i	−0.606170	+	0.508637i
$317$	−16.3777	+	10.7718i	−0.919864	+	0.605004i	−0.918683	−	0.394995i	$-0.870746\pi$
$317$	−16.3777	+	10.7718i	−0.919864	+	0.605004i	−0.00118078	+	0.999999i	$0.500376\pi$
$318$	0.00145977	−	0.0112333i	8.18600e−5	−	0.000629931i
$319$	9.84216	+	13.2203i	0.551055	+	0.740196i
$320$	−1.50109	+	0.753875i	−0.0839134	+	0.0421429i
$321$	15.6353	+	19.1281i	0.872679	+	1.06763i
$322$	−6.60544	+	1.56552i	−0.368107	+	0.0872429i
$323$	10.8479			0.603594
$324$	−6.22735	+	12.6094i	−0.345964	+	0.700520i
$325$	−4.27338			−0.237044
$326$	−5.18372	+	1.22856i	−0.287099	+	0.0680438i
$327$	8.22107	−	21.7135i	0.454626	−	1.20076i
$328$	−19.0523	+	9.56844i	−1.05199	+	0.528329i
$329$	−24.8499	−	33.3792i	−1.37002	−	1.84025i
$330$	6.77153	+	5.17800i	0.372760	+	0.285039i
$331$	18.2792	−	12.0224i	1.00472	−	0.660813i	0.0632779	−	0.997996i	$-0.479845\pi$
$331$	18.2792	−	12.0224i	1.00472	−	0.660813i	0.941439	+	0.337183i	$0.109474\pi$
$332$	4.43055	−	3.71767i	0.243158	−	0.204034i
$333$	−6.41735	+	5.10917i	−0.351669	+	0.279981i
$334$	−8.55328	−	7.17706i	−0.468015	−	0.392711i
$335$	14.5927	+	1.70564i	0.797284	+	0.0931892i
$336$	−1.15277	−	11.0998i	−0.0628889	−	0.605546i
$337$	2.57060	+	8.58639i	0.140029	+	0.467730i	0.999020	−	0.0442608i	$-0.0140932\pi$
$337$	2.57060	+	8.58639i	0.140029	+	0.467730i	−0.858991	+	0.511991i	$0.828908\pi$
$338$	−1.12643	+	1.19394i	−0.0612696	+	0.0649419i
$339$	1.24659	−	4.97360i	0.0677054	−	0.270129i
$340$	−7.73571	+	10.3909i	−0.419528	+	0.563524i
$341$	3.30191	−	18.7261i	0.178809	−	1.01407i
$342$	4.35453	+	4.86030i	0.235466	+	0.262815i
$343$	2.07706	+	11.7796i	0.112151	+	0.636040i
$344$	−16.4605	−	8.26676i	−0.887489	−	0.445714i
$345$	−2.36977	−	10.6053i	−0.127584	−	0.570972i
$346$	4.41645	−	0.516209i	0.237430	−	0.0277516i
$347$	−16.0680	−	10.5681i	−0.862574	−	0.567324i	0.0393465	−	0.999226i	$-0.487472\pi$
$347$	−16.0680	−	10.5681i	−0.862574	−	0.567324i	−0.901921	+	0.431902i	$0.857843\pi$
$348$	−14.8032	−	2.80712i	−0.793534	−	0.150477i
$349$	−6.12442	+	20.4570i	−0.327833	+	1.09504i	0.622192	+	0.782864i	$0.286242\pi$
$349$	−6.12442	+	20.4570i	−0.327833	+	1.09504i	−0.950025	+	0.312173i	$0.898943\pi$
$350$	1.79174	+	3.10339i	0.0957726	+	0.165883i
$351$	−11.8021	−	12.0291i	−0.629950	−	0.642067i
$352$	8.50973	−	14.7393i	0.453570	−	0.785607i
$353$	10.0961	+	10.7013i	0.537364	+	0.569572i	0.937987	−	0.346671i	$-0.112688\pi$
$353$	10.0961	+	10.7013i	0.537364	+	0.569572i	−0.400623	+	0.916243i	$0.631206\pi$
$354$	11.3656	−	6.36831i	0.604075	−	0.338472i
$355$	−0.346872	+	5.95557i	−0.0184101	+	0.316089i
$356$	7.73396	−	17.9293i	0.409899	−	0.950253i
$357$	12.6550	+	19.7912i	0.669772	+	1.04746i
$358$	−0.584739	−	10.0396i	−0.0309044	−	0.530608i
$359$	−10.0637	−	3.66289i	−0.531142	−	0.193320i	0.0625063	−	0.998045i	$-0.480091\pi$
$359$	−10.0637	−	3.66289i	−0.531142	−	0.193320i	−0.593648	+	0.804725i	$0.702313\pi$
$360$	−17.6940	+	1.60770i	−0.932554	+	0.0847331i
$361$	7.68928	−	2.79867i	0.404699	−	0.147298i
$362$	1.46826	+	3.40381i	0.0771701	+	0.178901i
$363$	3.86115	+	0.274794i	0.202658	+	0.0144229i
$364$	20.2770	+	4.80573i	1.06280	+	0.251889i
$365$	−11.5571	−	2.73909i	−0.604928	−	0.143371i
$366$	10.2973	+	0.732850i	0.538251	+	0.0383067i
$367$	−1.57072	−	3.64134i	−0.0819909	−	0.190076i	0.872289	−	0.488991i	$-0.162635\pi$
$367$	−1.57072	−	3.64134i	−0.0819909	−	0.190076i	−0.954280	+	0.298914i	$0.903376\pi$
$368$	−3.67519	+	1.33766i	−0.191583	+	0.0697304i
$369$	−27.0342	+	2.45637i	−1.40735	+	0.127873i
$370$	−4.27121	−	1.55459i	−0.222050	−	0.0808194i
$371$	0.00236431	+	0.0405936i	0.000122749	+	0.00210752i
$372$	9.36432	+	14.6449i	0.485517	+	0.759303i
$373$	−9.39616	+	21.7827i	−0.486515	+	1.12787i	0.481380	+	0.876512i	$0.340136\pi$
$373$	−9.39616	+	21.7827i	−0.486515	+	1.12787i	−0.967895	+	0.251356i	$0.919124\pi$
$374$	−0.375512	+	6.44730i	−0.0194173	+	0.333382i
$375$	13.9853	−	7.83619i	0.722200	−	0.404659i
$376$	16.3631	+	17.3439i	0.843863	+	0.894442i
$377$	9.02736	−	15.6359i	0.464933	−	0.805287i
$378$	−3.78732	+	13.6144i	−0.194799	+	0.700250i
$379$	13.0094	+	22.5330i	0.668249	+	1.15744i	0.978393	+	0.206752i	$0.0662892\pi$
$379$	13.0094	+	22.5330i	0.668249	+	1.15744i	−0.310145	+	0.950689i	$0.600377\pi$
$380$	3.70480	−	12.3749i	0.190052	−	0.634818i
$381$	20.4749	+	3.88265i	1.04896	+	0.198914i
$382$	−2.37365	−	1.56118i	−0.121447	−	0.0798767i
$383$	29.2263	−	3.41606i	1.49339	−	0.174553i	0.670144	−	0.742231i	$-0.266232\pi$
$383$	29.2263	−	3.41606i	1.49339	−	0.174553i	0.823250	+	0.567678i	$0.192158\pi$
$384$	4.17574	+	18.6875i	0.213092	+	0.953645i
$385$	−27.3447	−	13.7330i	−1.39362	−	0.699900i
$386$	−0.325437	−	1.84564i	−0.0165643	−	0.0939407i
$387$	−15.6498	−	17.4675i	−0.795524	−	0.887923i
$388$	1.94061	−	11.0057i	0.0985194	−	0.558731i
$389$	−15.8270	+	21.2594i	−0.802462	+	1.07789i	0.192855	+	0.981227i	$0.438225\pi$
$389$	−15.8270	+	21.2594i	−0.802462	+	1.07789i	−0.995317	+	0.0966658i	$0.969182\pi$
$390$	2.27026	−	9.05781i	0.114959	−	0.458660i
$391$	5.64977	−	5.98841i	0.285721	−	0.302847i
$392$	−6.69605	−	22.3664i	−0.338202	−	1.12967i
$393$	0.918978	+	8.84867i	0.0463563	+	0.446356i
$394$	−13.9579	−	1.63144i	−0.703189	−	0.0821910i
$395$	−17.3329	−	14.5440i	−0.872114	−	0.731790i
$396$	10.8577	−	8.64436i	0.545620	−	0.434395i
$397$	−21.8020	+	18.2941i	−1.09421	+	0.918154i	−0.997022	−	0.0771123i	$-0.975430\pi$
$397$	−21.8020	+	18.2941i	−1.09421	+	0.918154i	−0.0971903	+	0.995266i	$0.530986\pi$
$398$	5.37771	−	3.53698i	0.269560	−	0.177293i
$399$	−18.6080	−	14.2290i	−0.931564	−	0.712341i
$400$	1.23288	+	1.65604i	0.0616439	+	0.0828022i
$401$	−12.7098	+	6.38308i	−0.634695	+	0.318756i	−0.736894	−	0.676008i	$-0.763708\pi$
$401$	−12.7098	+	6.38308i	−0.634695	+	0.318756i	0.102199	+	0.994764i	$0.467412\pi$
$402$	−2.37094	+	6.26211i	−0.118252	+	0.312326i
$403$	−20.2683	+	4.80369i	−1.00964	+	0.239289i
$404$	3.29097			0.163732
$405$	−21.7140	−	6.34273i	−1.07898	−	0.315173i
$406$	−15.1400			−0.751383
$407$	7.87686	−	1.86685i	0.390441	−	0.0925363i
$408$	−8.51879	−	10.4218i	−0.421743	−	0.515957i
$409$	2.78276	−	1.39755i	0.137598	−	0.0691045i	−0.378668	−	0.925533i	$-0.623618\pi$
$409$	2.78276	−	1.39755i	0.137598	−	0.0691045i	0.516266	+	0.856428i	$0.327321\pi$
$410$	−8.98238	−	12.0654i	−0.443608	−	0.595869i
$411$	0.424322	−	3.26525i	0.0209303	−	0.161063i
$412$	−2.69635	+	1.77342i	−0.132840	+	0.0873699i
$413$	−35.8251	+	30.0608i	−1.76284	+	1.47920i
$414$	4.95095	+	0.127479i	0.243326	+	0.00626526i
$415$	7.12674	+	5.98005i	0.349838	+	0.293549i
$416$	−18.5178	−	2.16442i	−0.907910	−	0.106119i
$417$	14.7988	+	6.61077i	0.724700	+	0.323731i
$418$	−1.84700	−	6.16941i	−0.0903397	−	0.301756i
$419$	4.70149	−	4.98329i	0.229683	−	0.243450i	−0.602275	−	0.798289i	$-0.705739\pi$
$419$	4.70149	−	4.98329i	0.229683	−	0.243450i	0.831958	+	0.554839i	$0.187220\pi$
$420$	26.8989	−	7.67719i	1.31253	−	0.374608i
$421$	−8.91706	+	11.9777i	−0.434591	+	0.583757i	−0.964429	−	0.264342i	$-0.914845\pi$
$421$	−8.91706	+	11.9777i	−0.434591	+	0.583757i	0.529838	+	0.848099i	$0.322253\pi$
$422$	−2.24848	+	12.7517i	−0.109454	+	0.620745i
$423$	11.3034	+	28.1771i	0.549589	+	1.37002i
$424$	−0.00404592	−	0.0229456i	−0.000196487	−	0.00111434i
$425$	−3.88374	−	1.95049i	−0.188389	−	0.0946124i
$426$	−2.59439	−	0.813238i	−0.125698	−	0.0394015i
$427$	−36.8067	+	4.30209i	−1.78120	+	0.208193i
$428$	18.6214	+	12.2475i	0.900101	+	0.592006i
$429$	5.48640	+	15.6996i	0.264886	+	0.757984i
$430$	3.72717	−	12.4496i	0.179740	−	0.600374i
$431$	−15.4334	−	26.7314i	−0.743399	−	1.28760i	−0.950939	−	0.309378i	$-0.899879\pi$
$431$	−15.4334	−	26.7314i	−0.743399	−	1.28760i	0.207540	−	0.978227i	$-0.433454\pi$
$432$	−1.25666	+	8.04404i	−0.0604609	+	0.387019i
$433$	14.3849	−	24.9154i	0.691295	−	1.19736i	−0.280119	−	0.959965i	$-0.590374\pi$
$433$	14.3849	−	24.9154i	0.691295	−	1.19736i	0.971414	−	0.237393i	$-0.0762928\pi$
$434$	11.9866	+	12.7051i	0.575375	+	0.609862i
$435$	0.311941	−	24.2340i	0.0149564	−	1.16193i
$436$	1.21791	−	20.9106i	0.0583271	−	1.00144i
$437$	−3.25167	+	7.53822i	−0.155549	+	0.360602i
$438$	2.49145	−	4.80565i	0.119046	−	0.229623i
$439$	0.257222	+	4.41633i	0.0122765	+	0.210780i	0.998868	+	0.0475701i	$0.0151478\pi$
$439$	0.257222	+	4.41633i	0.0122765	+	0.210780i	−0.986591	+	0.163210i	$0.947815\pi$
$440$	16.4761	+	5.99681i	0.785467	+	0.285886i
$441$	2.49174	−	29.6220i	0.118654	−	1.41057i
$442$	6.64797	−	2.41966i	0.316212	−	0.115092i
$443$	−1.05658	−	2.44942i	−0.0501994	−	0.116375i	0.891271	−	0.453471i	$-0.149815\pi$
$443$	−1.05658	−	2.44942i	−0.0501994	−	0.116375i	−0.941470	+	0.337096i	$0.890555\pi$
$444$	−4.14574	+	6.12996i	−0.196748	+	0.290915i
$445$	30.5623	+	7.24339i	1.44879	+	0.343370i
$446$	10.4037	+	2.46573i	0.492631	+	0.116756i
$447$	−0.673019	−	1.38423i	−0.0318327	−	0.0654720i
$448$	1.08845	+	2.52331i	0.0514245	+	0.119215i
$449$	39.1256	−	14.2405i	1.84645	−	0.672053i	0.859474	−	0.511179i	$-0.170791\pi$
$449$	39.1256	−	14.2405i	1.84645	−	0.672053i	0.986975	−	0.160874i	$-0.0514312\pi$
$450$	−0.685098	−	2.52302i	−0.0322958	−	0.118936i
$451$	25.1735	+	9.16239i	1.18537	+	0.431440i
$452$	−0.268965	−	4.61795i	−0.0126511	−	0.217210i
$453$	−13.9435	+	0.632161i	−0.655123	+	0.0297015i
$454$	−5.56143	+	12.8928i	−0.261011	+	0.605091i
$455$	−1.94902	+	33.4633i	−0.0913713	+	1.56878i
$456$	11.5368	+	6.86026i	0.540260	+	0.321261i
$457$	−5.25995	−	5.57522i	−0.246050	−	0.260798i	0.592565	−	0.805523i	$-0.298116\pi$
$457$	−5.25995	−	5.57522i	−0.246050	−	0.260798i	−0.838615	+	0.544725i	$0.816634\pi$
$458$	−2.85365	+	4.94267i	−0.133342	+	0.230956i
$459$	−5.23559	−	16.3191i	−0.244376	−	0.761711i
$460$	−4.90183	−	8.49022i	−0.228549	−	0.395858i
$461$	−6.32202	+	21.1170i	−0.294446	+	0.983517i	0.674919	+	0.737892i	$0.264179\pi$
$461$	−6.32202	+	21.1170i	−0.294446	+	0.983517i	−0.969365	+	0.245625i	$0.921007\pi$
$462$	9.10093	−	10.5668i	0.423413	−	0.491613i
$463$	−31.0464	−	20.4195i	−1.44285	−	0.948975i	−0.998591	−	0.0530751i	$-0.983098\pi$
$463$	−31.0464	−	20.4195i	−1.44285	−	0.948975i	−0.444256	−	0.895900i	$-0.646532\pi$
$464$	−8.66370	+	1.01264i	−0.402202	+	0.0470107i
$465$	−20.5835	+	18.9247i	−0.954536	+	0.877614i
$466$	8.84428	+	4.44177i	0.409703	+	0.205761i
$467$	1.44385	+	8.18848i	0.0668134	+	0.378918i	0.999818	+	0.0190543i	$0.00606555\pi$
$467$	1.44385	+	8.18848i	0.0668134	+	0.378918i	−0.933005	+	0.359863i	$0.882823\pi$
$468$	−13.4059	−	7.17062i	−0.619690	−	0.331462i
$469$	4.17380	−	23.6708i	0.192728	−	1.09302i
$470$	−10.0459	+	13.4941i	−0.463385	+	0.622434i
$471$	18.0078	+	17.4330i	0.829755	+	0.803270i
$472$	18.3893	−	19.4915i	0.846435	−	0.897168i
$473$	6.63796	+	22.1723i	0.305214	+	1.01949i
$474$	8.35013	−	6.05097i	0.383534	−	0.277930i
$475$	4.30441	+	0.503114i	0.197500	+	0.0230844i
$476$	16.2347	+	13.6225i	0.744115	+	0.624387i
$477$	0.00590172	−	0.0290729i	0.000270221	−	0.00133116i
$478$	1.82923	−	1.53491i	0.0836671	−	0.0702050i
$479$	−2.13297	+	1.40288i	−0.0974580	+	0.0640991i	−0.597303	−	0.802016i	$-0.703761\pi$
$479$	−2.13297	+	1.40288i	−0.0974580	+	0.0640991i	0.499845	+	0.866115i	$0.333390\pi$
$480$	−23.1057	+	9.61602i	−1.05463	+	0.438909i
$481$	−5.29542	−	7.11298i	−0.241450	−	0.324324i
$482$	13.5294	−	6.79470i	0.616246	−	0.309490i
$483$	−17.5462	+	2.86152i	−0.798381	+	0.130204i
$484$	3.39806	−	0.805354i	0.154457	−	0.0366070i
$485$	17.9763			0.816263
$486$	5.20996	−	8.89650i	0.236328	−	0.403553i
$487$	16.3628			0.741468			0.370734	−	0.928739i	$-0.379106\pi$
$487$	16.3628			0.741468			0.370734	+	0.928739i	$0.379106\pi$
$488$	20.6614	−	4.89685i	0.935299	−	0.221670i
$489$	−13.7697	+	2.24562i	−0.622686	+	0.101551i
$490$	14.7200	−	7.39264i	0.664980	−	0.333965i
$491$	−21.7872	−	29.2653i	−0.983242	−	1.32072i	−0.946950	−	0.321382i	$-0.895853\pi$
$491$	−21.7872	−	29.2653i	−0.983242	−	1.32072i	−0.0362928	−	0.999341i	$-0.511555\pi$
$492$	−22.6098	+	9.40963i	−1.01933	+	0.424219i
$493$	15.3409	−	10.0899i	0.690918	−	0.454424i
$494$	−5.40415	+	4.53462i	−0.243144	+	0.204022i
$495$	16.7264	+	14.7852i	0.751796	+	0.664547i
$496$	7.70901	+	6.46863i	0.346145	+	0.290450i
$497$	9.69374	+	1.13304i	0.434823	+	0.0508236i
$498$	−3.43331	+	2.48797i	−0.153850	+	0.111488i
$499$	9.10246	+	30.4043i	0.407482	+	1.36108i	0.877986	+	0.478687i	$0.158887\pi$
$499$	9.10246	+	30.4043i	0.407482	+	1.36108i	−0.470504	+	0.882398i	$0.655928\pi$
$500$	9.92484	−	10.5197i	0.443852	−	0.470456i
$501$	−21.0092	−	20.3386i	−0.938620	−	0.908660i
$502$	8.36207	−	11.2322i	0.373217	−	0.501318i
$503$	1.04817	−	5.94449i	0.0467358	−	0.265052i	−0.952482	−	0.304595i	$-0.901479\pi$
$503$	1.04817	−	5.94449i	0.0467358	−	0.265052i	0.999218	+	0.0395428i	$0.0125902\pi$
$504$	0.942598	+	29.0510i	0.0419867	+	1.29403i
$505$	0.919238	+	5.21326i	0.0409055	+	0.231987i
$506$	−4.36767	−	2.19352i	−0.194166	−	0.0975141i
$507$	−3.16450	+	2.90948i	−0.140540	+	0.129215i
$508$	18.6737	−	2.18265i	0.828513	−	0.0968393i
$509$	−21.9762	−	14.4540i	−0.974079	−	0.640662i	−0.0405551	−	0.999177i	$-0.512913\pi$
$509$	−21.9762	−	14.4540i	−0.974079	−	0.640662i	−0.933524	+	0.358516i	$0.883283\pi$
$510$	6.19749	−	7.19572i	0.274429	−	0.318632i
$511$	−5.57289	+	18.6147i	−0.246530	+	0.823468i
$512$	8.19547	+	14.1950i	0.362192	+	0.627335i
$513$	10.4716	+	13.5060i	0.462333	+	0.596303i
$514$	−2.57506	+	4.46014i	−0.113581	+	0.196728i
$515$	−3.56243	−	3.77596i	−0.156980	−	0.166389i
$516$	−18.1858	−	10.8140i	−0.800584	−	0.476061i
$517$	1.74208	−	29.9103i	0.0766165	−	1.31545i
$518$	−2.94528	+	6.82793i	−0.129408	+	0.300002i
$519$	11.6329	−	0.527405i	0.510628	−	0.0231505i
$520$	−1.11678	−	19.1745i	−0.0489742	−	0.840855i
$521$	23.7819	+	8.65589i	1.04190	+	0.379221i	0.805601	−	0.592459i	$-0.201843\pi$
$521$	23.7819	+	8.65589i	1.04190	+	0.379221i	0.236301	+	0.971680i	$0.424065\pi$
$522$	10.6787	+	2.82309i	0.467395	+	0.123563i
$523$	2.76727	−	1.00720i	0.121004	−	0.0440420i	−0.280808	−	0.959764i	$-0.590603\pi$
$523$	2.76727	−	1.00720i	0.121004	−	0.0440420i	0.401813	+	0.915722i	$0.368380\pi$
$524$	3.17888	+	7.36947i	0.138870	+	0.321937i
$525$	4.10355	+	8.43998i	0.179094	+	0.368351i
$526$	−0.982358	−	0.232823i	−0.0428328	−	0.0101516i
$527$	−20.6128	−	4.88533i	−0.897909	−	0.212808i
$528$	4.50116	−	6.65549i	0.195888	−	0.289643i
$529$	−6.64201	−	15.3979i	−0.288783	−	0.669474i
$530$	0.0154471	−	0.00562227i	0.000670977	−	0.000244216i
$531$	30.8740	−	14.5227i	1.33982	−	0.630233i
$532$	−19.8585	−	7.22789i	−0.860973	−	0.313369i
$533$	−1.70631	−	29.2962i	−0.0739085	−	1.26896i
$534$	−6.58852	+	12.7083i	−0.285113	+	0.549942i
$535$	−14.2000	+	32.9194i	−0.613921	+	1.42323i
$536$	−0.800805	+	13.7493i	−0.0345895	+	0.593879i
$537$	0.338983	−	26.3348i	0.0146282	−	1.13643i
$538$	−13.3611	−	14.1619i	−0.576036	−	0.610563i
$539$	−14.6681	+	25.4058i	−0.631798	+	1.09431i
$540$	−20.4043	+	0.399232i	−0.878060	+	0.0171802i
$541$	−8.84669	−	15.3229i	−0.380349	−	0.658784i	0.610763	−	0.791813i	$-0.290863\pi$
$541$	−8.84669	−	15.3229i	−0.380349	−	0.658784i	−0.991112	+	0.133030i	$0.957529\pi$
$542$	2.76423	−	9.23318i	0.118734	−	0.396599i
$543$	3.20269	+	9.16465i	0.137440	+	0.393293i
$544$	−15.8415	−	10.4191i	−0.679197	−	0.446715i
$545$	33.4649	−	3.91149i	1.43348	−	0.167550i
$546$	−14.5774	−	4.56944i	−0.623856	−	0.195554i
$547$	36.4161	+	18.2889i	1.55704	+	0.781975i	0.998860	−	0.0477434i	$-0.0152030\pi$
$547$	36.4161	+	18.2889i	1.55704	+	0.781975i	0.558182	+	0.829719i	$0.311499\pi$
$548$	−0.515831	−	2.92542i	−0.0220352	−	0.124968i
$549$	26.7632	+	3.82880i	1.14223	+	0.163409i
$550$	−0.448020	+	2.54085i	−0.0191036	+	0.108342i
$551$	−10.9338	+	14.6866i	−0.465794	+	0.625670i
$552$	9.79564	−	2.79576i	0.416930	−	0.118995i
$553$	−25.4023	+	26.9249i	−1.08022	+	1.14496i
$554$	1.93981	+	6.47943i	0.0824148	+	0.275285i
$555$	−10.8685	−	4.85508i	−0.461343	−	0.206087i
$556$	14.5235	+	1.69756i	0.615935	+	0.0719925i
$557$	−23.1644	−	19.4372i	−0.981505	−	0.823581i	0.00281036	−	0.999996i	$-0.499105\pi$
$557$	−23.1644	−	19.4372i	−0.981505	−	0.823581i	−0.984316	+	0.176415i	$0.943550\pi$
$558$	−6.08549	−	11.1964i	−0.257619	−	0.473982i
$559$	19.4220	−	16.2970i	0.821465	−	0.689291i
$560$	13.5302	−	8.89894i	0.571755	−	0.376049i
$561$	−2.17957	+	16.7723i	−0.0920215	+	0.708125i
$562$	−2.77396	−	3.72607i	−0.117012	−	0.157175i
$563$	−16.5135	+	8.29337i	−0.695959	+	0.349524i	−0.761355	−	0.648336i	$-0.775465\pi$
$563$	−16.5135	+	8.29337i	−0.695959	+	0.349524i	0.0653954	+	0.997859i	$0.479169\pi$
$564$	17.3341	+	21.2064i	0.729895	+	0.892949i
$565$	7.24021	−	1.71596i	0.304598	−	0.0721911i
$566$	14.3004			0.601091
$567$	−12.4246	+	34.8604i	−0.521784	+	1.46400i
$568$	−5.59232			−0.234648
$569$	8.75519	−	2.07502i	0.367037	−	0.0869893i	−0.0429589	−	0.999077i	$-0.513678\pi$
$569$	8.75519	−	2.07502i	0.367037	−	0.0869893i	0.409995	+	0.912088i	$0.365530\pi$
$570$	−3.35314	+	8.85631i	−0.140448	+	0.370950i
$571$	−15.0828	+	7.57485i	−0.631194	+	0.316998i	−0.735477	−	0.677550i	$-0.763042\pi$
$571$	−15.0828	+	7.57485i	−0.631194	+	0.316998i	0.104282	+	0.994548i	$0.466745\pi$
$572$	8.95947	+	12.0347i	0.374614	+	0.503194i
$573$	−5.91038	−	4.51950i	−0.246910	−	0.188805i
$574$	−20.5599	+	13.5225i	−0.858153	+	0.564416i
$575$	2.51954	−	2.11415i	0.105072	−	0.0881661i
$576$	−0.297209	−	1.98274i	−0.0123837	−	0.0826141i
$577$	−24.0567	−	20.1860i	−1.00149	−	0.840352i	−0.0143022	−	0.999898i	$-0.504553\pi$
$577$	−24.0567	−	20.1860i	−1.00149	−	0.840352i	−0.987191	+	0.159545i	$0.948997\pi$
$578$	−4.02109	−	0.469998i	−0.167255	−	0.0195493i
$579$	−0.507001	−	4.88182i	−0.0210702	−	0.202881i
$580$	−6.27087	−	20.9462i	−0.260384	−	0.869743i
$581$	10.4446	−	11.0707i	0.433317	−	0.459289i
$582$	−1.99183	+	7.94693i	−0.0825639	+	0.329411i
$583$	−0.0174826	+	0.0234832i	−0.000724054	+	0.000972573i
$584$	1.93340	−	10.9648i	0.0800045	−	0.453728i
$585$	7.61449	−	23.2394i	0.314820	−	0.960830i
$586$	1.25491	+	7.11695i	0.0518399	+	0.293999i
$587$	−1.23033	−	0.617896i	−0.0507812	−	0.0255033i	0.423227	−	0.906024i	$-0.360897\pi$
$587$	−1.23033	−	0.617896i	−0.0507812	−	0.0255033i	−0.474009	+	0.880520i	$0.657193\pi$
$588$	−5.84830	−	26.1727i	−0.241180	−	1.07934i
$589$	20.9811	−	2.45234i	0.864511	−	0.101047i
$590$	15.7957	+	10.3890i	0.650300	+	0.427709i
$591$	−36.1585	−	6.85671i	−1.48736	−	0.282047i
$592$	−1.22872	+	4.10422i	−0.0505002	+	0.168682i
$593$	15.4929	+	26.8346i	0.636219	+	1.10196i	0.986256	+	0.165227i	$0.0528358\pi$
$593$	15.4929	+	26.8346i	0.636219	+	1.10196i	−0.350037	+	0.936736i	$0.613831\pi$
$594$	−8.38955	+	5.75612i	−0.344227	+	0.236176i
$595$	−17.0449	+	29.5226i	−0.698771	+	1.21031i
$596$	−0.952902	−	1.01002i	−0.0390324	−	0.0413719i
$597$	14.7056	−	8.23976i	0.601860	−	0.337231i
$598$	−0.311309	+	5.34497i	−0.0127304	+	0.218572i
$599$	−9.60548	+	22.2680i	−0.392469	+	0.909846i	0.601365	+	0.798974i	$0.294624\pi$
$599$	−9.60548	+	22.2680i	−0.392469	+	0.909846i	−0.993835	+	0.110872i	$0.964636\pi$
$600$	−2.89687	−	4.53043i	−0.118264	−	0.184954i
$601$	−0.441108	−	7.57353i	−0.0179932	−	0.308931i	−0.995282	−	0.0970208i	$-0.969069\pi$
$601$	−0.441108	−	7.57353i	−0.0179932	−	0.308931i	0.977289	−	0.211910i	$-0.0679684\pi$
$602$	−19.9784	−	7.27154i	−0.814258	−	0.296366i
$603$	−7.35773	+	15.9175i	−0.299630	+	0.648212i
$604$	−11.8328	+	4.30678i	−0.481469	+	0.175241i
$605$	2.22492	+	5.15794i	0.0904558	+	0.209700i
$606$	−2.40652	−	0.171269i	−0.0977581	−	0.00695732i
$607$	29.1570	+	6.91033i	1.18345	+	0.280482i	0.774797	−	0.632210i	$-0.217852\pi$
$607$	29.1570	+	6.91033i	1.18345	+	0.280482i	0.408649	+	0.912692i	$0.366000\pi$
$608$	18.3975	+	4.36028i	0.746116	+	0.176833i
$609$	−39.5496	−	2.81470i	−1.60263	−	0.114057i
$610$	5.93366	+	13.7558i	0.240247	+	0.556955i
$611$	−30.8413	+	11.2253i	−1.24770	+	0.454127i
$612$	−8.91073	−	12.6356i	−0.360195	−	0.510765i
$613$	11.4606	+	4.17132i	0.462890	+	0.168478i	0.562929	−	0.826505i	$-0.309675\pi$
$613$	11.4606	+	4.17132i	0.462890	+	0.168478i	−0.100039	+	0.994984i	$0.531897\pi$
$614$	0.176849	+	3.03637i	0.00713703	+	0.122538i
$615$	−21.2213	−	33.1881i	−0.855724	−	1.33827i
$616$	11.3614	−	26.3386i	0.457762	−	1.06121i
$617$	0.923932	−	15.8633i	0.0371961	−	0.638632i	−0.927265	−	0.374406i	$-0.877847\pi$
$617$	0.923932	−	15.8633i	0.0371961	−	0.638632i	0.964461	−	0.264226i	$-0.0851164\pi$
$618$	2.06399	−	1.15648i	0.0830260	−	0.0465206i
$619$	−15.9608	−	16.9174i	−0.641518	−	0.679970i	0.322267	−	0.946649i	$-0.395555\pi$
$619$	−15.9608	−	16.9174i	−0.641518	−	0.679970i	−0.963785	+	0.266679i	$0.914074\pi$
$620$	−12.6127	+	21.8459i	−0.506539	+	0.877351i
$621$	12.9095	+	1.25345i	0.518041	+	0.0502993i
$622$	−5.76686	−	9.98849i	−0.231230	−	0.400502i
$623$	14.7372	−	49.2258i	0.590435	−	1.97219i
$624$	−8.64742	−	1.63981i	−0.346174	−	0.0656448i
$625$	24.9410	+	16.4040i	0.997641	+	0.656159i
$626$	−10.3968	+	1.21521i	−0.415540	+	0.0485696i
$627$	−3.67789	−	16.4595i	−0.146881	−	0.657331i
$628$	20.2064	+	10.1480i	0.806321	+	0.404950i
$629$	−1.56603	−	8.88139i	−0.0624417	−	0.354124i
$630$	−20.0693	+	4.21405i	−0.799582	+	0.167892i
$631$	2.13182	−	12.0902i	0.0848665	−	0.481302i	−0.912519	−	0.409035i	$-0.865866\pi$
$631$	2.13182	−	12.0902i	0.0848665	−	0.481302i	0.997385	−	0.0722670i	$-0.0230234\pi$
$632$	12.6660	−	17.0134i	0.503828	−	0.676758i
$633$	−8.24432	+	32.8930i	−0.327682	+	1.30738i
$634$	8.89684	−	9.43010i	0.353339	−	0.374517i
$635$	8.67352	+	28.9716i	0.344198	+	1.14970i
$636$	−0.00276464	−	0.0266202i	−0.000109625	−	0.00105556i
$637$	31.9188	+	3.73077i	1.26467	+	0.147818i
$638$	−8.35027	−	7.00671i	−0.330590	−	0.277398i
$639$	−6.62605	−	2.60672i	−0.262122	−	0.103120i
$640$	−21.2865	+	17.8615i	−0.841422	+	0.706037i
$641$	7.82391	−	5.14587i	0.309026	−	0.203249i	−0.385517	−	0.922701i	$-0.625977\pi$
$641$	7.82391	−	5.14587i	0.309026	−	0.203249i	0.694543	+	0.719451i	$0.255607\pi$
$642$	−12.9795	−	9.92507i	−0.512260	−	0.391711i
$643$	−11.7429	−	15.7734i	−0.463094	−	0.622043i	0.507823	−	0.861462i	$-0.330451\pi$
$643$	−11.7429	−	15.7734i	−0.463094	−	0.622043i	−0.970916	+	0.239419i	$0.923043\pi$
$644$	−14.3326	+	7.19812i	−0.564785	+	0.283646i
$645$	12.0509	−	31.8288i	0.474504	−	1.25326i
$646$	−6.98112	+	1.65456i	−0.274668	+	0.0650976i
$647$	−14.2593			−0.560591			−0.280295	−	0.959914i	$-0.590432\pi$
$647$	−14.2593			−0.560591			−0.280295	+	0.959914i	$0.590432\pi$
$648$	4.75219	−	20.6664i	0.186684	−	0.811853i
$649$	−33.6709			−1.32170
$650$	2.75011	−	0.651788i	0.107868	−	0.0255652i
$651$	28.9502	+	35.4175i	1.13465	+	1.38812i
$652$	−11.2478	+	5.64884i	−0.440496	+	0.221225i
$653$	24.3576	+	32.7179i	0.953185	+	1.28035i	0.959891	+	0.280372i	$0.0904578\pi$
$653$	24.3576	+	32.7179i	0.953185	+	1.28035i	−0.00670674	+	0.999978i	$0.502135\pi$
$654$	−1.97882	+	15.2275i	−0.0773781	+	0.595442i
$655$	−10.7861	+	7.09414i	−0.421448	+	0.277191i
$656$	−10.8608	+	9.11326i	−0.424042	+	0.355813i
$657$	7.40177	−	12.0905i	0.288771	−	0.471694i
$658$	21.0831	+	17.6908i	0.821905	+	0.689660i
$659$	−2.57161	−	0.300578i	−0.100176	−	0.0117089i	0.0658573	−	0.997829i	$-0.479022\pi$
$659$	−2.57161	−	0.300578i	−0.100176	−	0.0117089i	−0.166033	+	0.986120i	$0.553096\pi$
$660$	18.3888	+	8.21445i	0.715782	+	0.319747i
$661$	−8.61351	−	28.7711i	−0.335027	−	1.11907i	−0.945116	−	0.326735i	$-0.894052\pi$
$661$	−8.61351	−	28.7711i	−0.335027	−	1.11907i	0.610089	−	0.792333i	$-0.291134\pi$
$662$	−9.92980	+	10.5250i	−0.385933	+	0.409065i
$663$	17.8161	−	5.08487i	0.691921	−	0.197480i
$664$	−5.20787	+	6.99538i	−0.202105	+	0.271473i
$665$	5.90288	−	33.4769i	0.228904	−	1.29818i
$666$	3.35058	−	4.26677i	0.129833	−	0.165334i
$667$	2.41300	+	13.6848i	0.0934318	+	0.529878i
$668$	−23.5742	−	11.8394i	−0.912112	−	0.458080i
$669$	26.7189	+	8.37532i	1.03301	+	0.323809i
$670$	−9.65120	+	1.12806i	−0.372858	+	0.0435809i
$671$	−22.2913	−	14.6612i	−0.860546	−	0.565990i
$672$	13.5071	+	38.6513i	0.521049	+	1.49101i
$673$	−3.97739	+	13.2854i	−0.153317	+	0.512115i	−0.999794	−	0.0203111i	$-0.993534\pi$
$673$	−3.97739	+	13.2854i	−0.153317	+	0.512115i	0.846477	+	0.532426i	$0.178720\pi$
$674$	−2.96391	−	5.13365i	−0.114166	−	0.197741i
$675$	−1.32060	−	6.71818i	−0.0508300	−	0.258583i
$676$	−1.93907	+	3.35858i	−0.0745798	+	0.129176i
$677$	−13.7507	−	14.5749i	−0.528482	−	0.560158i	0.407048	−	0.913407i	$-0.366558\pi$
$677$	−13.7507	−	14.5749i	−0.528482	−	0.560158i	−0.935529	+	0.353249i	$0.885077\pi$
$678$	−0.0436475	+	3.39087i	−0.00167627	+	0.130226i
$679$	1.70998	−	29.3593i	0.0656231	−	1.12670i
$680$	7.73678	−	17.9359i	0.296692	−	0.687809i
$681$	−16.9249	+	32.6457i	−0.648563	+	1.25098i
$682$	0.731227	+	12.5547i	0.0280001	+	0.480743i
$683$	−29.9877	−	10.9146i	−1.14745	−	0.417636i	−0.302849	−	0.953039i	$-0.597938\pi$
$683$	−29.9877	−	10.9146i	−1.14745	−	0.417636i	−0.844597	+	0.535402i	$0.820160\pi$
$684$	12.6591	+	8.80101i	0.484032	+	0.336515i
$685$	4.49011	−	1.63426i	0.171558	−	0.0624421i
$686$	−3.13334	−	7.26391i	−0.119632	−	0.277337i
$687$	−8.37340	+	12.3810i	−0.319465	+	0.472366i
$688$	−11.9188	−	2.82481i	−0.454401	−	0.107695i
$689$	0.0312060	+	0.00739596i	0.00118885	+	0.000281764i
$690$	3.14261	+	6.46356i	0.119637	+	0.246063i
$691$	14.8306	+	34.3813i	0.564184	+	1.30793i	0.926649	+	0.375929i	$0.122676\pi$
$691$	14.8306	+	34.3813i	0.564184	+	1.30793i	−0.362464	+	0.931998i	$0.618064\pi$
$692$	9.87198	−	3.59311i	0.375276	−	0.136589i
$693$	25.7386	−	25.9114i	0.977727	−	0.984292i
$694$	11.9523	+	4.35029i	0.453704	+	0.165135i
$695$	1.36762	+	23.4810i	0.0518766	+	0.890687i
$696$	22.6959	−	1.02897i	0.860286	−	0.0390031i
$697$	11.8209	−	27.4038i	0.447747	−	1.03799i
$698$	0.821179	−	14.0991i	0.0310821	−	0.533659i
$699$	22.2779	+	13.2473i	0.842626	+	0.501061i
$700$	5.81006	+	6.15831i	0.219600	+	0.232762i
$701$	11.5923	−	20.0785i	0.437836	−	0.758355i	−0.559686	−	0.828705i	$-0.689078\pi$
$701$	11.5923	−	20.0785i	0.437836	−	0.758355i	0.997522	+	0.0703498i	$0.0224116\pi$
$702$	9.42990	+	5.94118i	0.355908	+	0.224235i
$703$	4.49645	+	7.78807i	0.169587	+	0.293733i
$704$	−0.567456	+	1.89544i	−0.0213868	+	0.0714369i
$705$	−28.7514	+	33.3824i	−1.08284	+	1.25725i
$706$	−8.12951	−	5.34686i	−0.305958	−	0.201232i
$707$	8.60182	−	1.00541i	0.323505	−	0.0378123i
$708$	22.6592	−	20.8332i	0.851586	−	0.782960i
$709$	4.45037	+	2.23506i	0.167137	+	0.0839393i	0.530401	−	0.847747i	$-0.322041\pi$
$709$	4.45037	+	2.23506i	0.167137	+	0.0839393i	−0.363264	+	0.931686i	$0.618338\pi$
$710$	−0.685132	−	3.88558i	−0.0257126	−	0.145823i
$711$	22.9377	−	14.2544i	0.860232	−	0.534581i
$712$	−5.11277	+	28.9960i	−0.191609	+	1.08667i
$713$	9.57352	−	12.8595i	0.358531	−	0.481591i
$714$	−11.1626	−	10.8063i	−0.417751	−	0.404417i
$715$	−16.5616	+	17.5543i	−0.619370	+	0.656494i
$716$	−6.81449	−	22.7620i	−0.254669	−	0.850655i
$717$	5.06380	−	3.66951i	0.189111	−	0.137040i
$718$	7.03511	+	0.822287i	0.262548	+	0.0306875i
$719$	13.4111	+	11.2533i	0.500151	+	0.419677i	0.857648	−	0.514238i	$-0.171925\pi$
$719$	13.4111	+	11.2533i	0.500151	+	0.419677i	−0.357497	+	0.933914i	$0.616370\pi$
$720$	−11.2026	+	3.75380i	−0.417498	+	0.139896i
$721$	−6.50583	+	5.45904i	−0.242290	+	0.203305i
$722$	−4.52153	+	2.97386i	−0.168274	+	0.110676i
$723$	36.6056	−	15.2343i	1.36138	−	0.566570i
$724$	5.23009	+	7.02523i	0.194375	+	0.261091i
$725$	6.55516	−	3.29212i	0.243452	−	0.122266i
$726$	−2.52674	+	0.412072i	−0.0937760	+	0.0152934i
$727$	7.81381	−	1.85191i	0.289798	−	0.0686834i	−0.0831456	−	0.996537i	$-0.526497\pi$
$727$	7.81381	−	1.85191i	0.289798	−	0.0686834i	0.372944	+	0.927854i	$0.378348\pi$
$728$	−31.4223			−1.16459
$729$	15.2638	−	22.2714i	0.565325	−	0.824868i
$730$	7.85530			0.290738
$731$	25.0896	−	5.94633i	0.927971	−	0.219933i
$732$	24.0725	−	3.92586i	0.889745	−	0.145104i
$733$	−26.8789	+	13.4991i	−0.992794	+	0.498600i	−0.869586	−	0.493781i	$-0.835614\pi$
$733$	−26.8789	+	13.4991i	−0.992794	+	0.498600i	−0.123207	+	0.992381i	$0.539318\pi$
$734$	1.56622	+	2.10379i	0.0578101	+	0.0776524i
$735$	39.8268	−	16.5749i	1.46904	−	0.611376i
$736$	11.9887	−	7.88510i	0.441910	−	0.290649i
$737$	13.2568	−	11.1237i	0.488319	−	0.409748i
$738$	17.0231	−	5.70412i	0.626628	−	0.209971i
$739$	1.84741	+	1.55016i	0.0679580	+	0.0570236i	0.676134	−	0.736779i	$-0.263654\pi$
$739$	1.84741	+	1.55016i	0.0679580	+	0.0570236i	−0.608176	+	0.793802i	$0.708098\pi$
$740$	−10.6664	−	1.24672i	−0.392104	−	0.0458304i
$741$	−14.9601	+	10.8409i	−0.549574	+	0.398252i
$742$	−0.00771300	−	0.0257632i	−0.000283153	−	0.000945797i
$743$	−13.4927	+	14.3015i	−0.495000	+	0.524670i	−0.925920	−	0.377721i	$-0.876708\pi$
$743$	−13.4927	+	14.3015i	−0.495000	+	0.524670i	0.430919	+	0.902391i	$0.358189\pi$
$744$	−18.8323	−	18.2312i	−0.690425	−	0.668387i
$745$	1.33381	−	1.79162i	0.0488671	−	0.0656399i
$746$	2.72448	−	15.4513i	0.0997503	−	0.565712i
$747$	−9.43126	+	5.86094i	−0.345072	+	0.214441i
$748$	2.64961	+	15.0267i	0.0968793	+	0.549430i
$749$	52.4137	+	26.3231i	1.91515	+	0.961827i
$750$	−7.80499	+	7.17602i	−0.284998	+	0.262031i
$751$	6.82312	−	0.797508i	0.248979	−	0.0291015i	0.00931213	−	0.999957i	$-0.497036\pi$
$751$	6.82312	−	0.797508i	0.248979	−	0.0291015i	0.239667	+	0.970855i	$0.422962\pi$
$752$	13.2479	+	8.71326i	0.483100	+	0.317740i
$753$	23.9322	−	27.7869i	0.872137	−	1.01261i
$754$	−3.42468	+	11.4392i	−0.124720	+	0.416593i
$755$	−10.1276	−	17.5415i	−0.368580	−	0.638399i
$756$	−1.28890	+	33.3626i	−0.0468770	+	1.21338i
$757$	−6.50209	+	11.2620i	−0.236323	+	0.409323i	−0.959656	−	0.281176i	$-0.909276\pi$
$757$	−6.50209	+	11.2620i	−0.236323	+	0.409323i	0.723334	+	0.690499i	$0.242609\pi$
$758$	−11.8089	−	12.5167i	−0.428920	−	0.454628i
$759$	−11.0017	−	6.54208i	−0.399337	−	0.237462i
$760$	−1.13255	+	19.4452i	−0.0410820	+	0.705351i
$761$	6.89394	−	15.9819i	0.249905	−	0.579345i	−0.746375	−	0.665526i	$-0.768207\pi$
$761$	6.89394	−	15.9819i	0.249905	−	0.579345i	0.996279	+	0.0861814i	$0.0274665\pi$
$762$	−13.7687	+	0.624237i	−0.498788	+	0.0226137i
$763$	−3.20499	−	55.0275i	−0.116028	−	1.99213i
$764$	−6.30756	−	2.29576i	−0.228200	−	0.0830578i
$765$	17.5273	−	17.6450i	0.633700	−	0.637955i
$766$	−18.2874	+	6.65607i	−0.660751	+	0.240494i
$767$	14.6093	+	33.8681i	0.527510	+	1.22290i
$768$	−6.54983	−	13.4714i	−0.236347	−	0.486106i
$769$	−18.1275	−	4.29629i	−0.653693	−	0.154928i	−0.109630	−	0.993972i	$-0.534967\pi$
$769$	−18.1275	−	4.29629i	−0.653693	−	0.154928i	−0.544063	+	0.839044i	$0.683115\pi$
$770$	19.6921	+	4.66712i	0.709655	+	0.168191i
$771$	−7.55595	+	11.1723i	−0.272121	+	0.402362i
$772$	−1.75379	−	4.06574i	−0.0631203	−	0.146329i
$773$	−27.2264	+	9.90961i	−0.979267	+	0.356424i	−0.781555	−	0.623836i	$-0.785573\pi$
$773$	−27.2264	+	9.90961i	−0.979267	+	0.356424i	−0.197712	+	0.980260i	$0.563351\pi$
$774$	12.7355	+	8.85416i	0.457769	+	0.318256i
$775$	−7.95251	−	2.89448i	−0.285663	−	0.103973i
$776$	0.979818	+	16.8228i	0.0351734	+	0.603904i
$777$	−8.96326	+	17.2888i	−0.321555	+	0.620233i
$778$	6.94285	−	16.0953i	0.248913	−	0.577046i
$779$	−1.73040	+	29.7099i	−0.0619981	+	1.06447i
$780$	0.283965	−	22.0605i	0.0101676	−	0.789894i
$781$	4.82210	+	5.11113i	0.172548	+	0.182891i
$782$	−2.72251	+	4.71553i	−0.0973568	+	0.168627i
$783$	27.3708	+	9.35998i	0.978154	+	0.334498i
$784$	−7.76286	−	13.4457i	−0.277245	−	0.480203i
$785$	−10.4315	+	34.8436i	−0.372316	+	1.24362i
$786$	−1.94103	−	5.55435i	−0.0692342	−	0.198117i
$787$	12.3774	+	8.14073i	0.441206	+	0.290186i	0.750611	−	0.660745i	$-0.229759\pi$
$787$	12.3774	+	8.14073i	0.441206	+	0.290186i	−0.309405	+	0.950930i	$0.600130\pi$
$788$	−32.9776	+	3.85452i	−1.17478	+	0.137312i
$789$	−2.52290	−	0.790829i	−0.0898175	−	0.0281542i
$790$	13.3728	+	6.71607i	0.475783	+	0.238947i
$791$	−2.11382	−	11.9881i	−0.0751588	−	0.426247i
$792$	−12.9248	+	16.4590i	−0.459263	+	0.584844i
$793$	−5.07523	+	28.7830i	−0.180227	+	1.02212i
$794$	11.2403	−	15.0984i	0.398904	−	0.535821i
$795$	0.0413971	−	0.0118151i	0.00146820	−	0.000419038i
$796$	10.4360	−	11.0615i	0.369894	−	0.392064i
$797$	−5.04957	−	16.8667i	−0.178865	−	0.597450i	−0.999656	−	0.0262221i	$-0.991652\pi$
$797$	−5.04957	−	16.8667i	−0.178865	−	0.597450i	0.820791	−	0.571228i	$-0.193533\pi$
$798$	14.1453	+	6.31886i	0.500739	+	0.223685i
$799$	−33.1527	−	3.87500i	−1.17286	−	0.137088i
$800$	−5.80261	−	4.86896i	−0.205153	−	0.172144i
$801$	−19.5736	+	31.9726i	−0.691600	+	1.12970i
$802$	7.20573	−	6.04632i	0.254443	−	0.213503i
$803$	−11.6885	+	7.68764i	−0.412478	+	0.271291i
$804$	−2.03869	+	15.6882i	−0.0718991	+	0.553280i
$805$	−15.4060	−	20.6939i	−0.542991	−	0.729364i
$806$	12.3109	−	6.18277i	0.433633	−	0.217779i
$807$	−32.2698	−	39.4787i	−1.13595	−	1.38971i
$808$	−4.82863	+	1.14441i	−0.169871	+	0.0402601i
$809$	−13.3577			−0.469632			−0.234816	−	0.972040i	$-0.575449\pi$
$809$	−13.3577			−0.469632			−0.234816	+	0.972040i	$0.575449\pi$
$810$	14.9414	+	0.769943i	0.524986	+	0.0270530i
$811$	13.6700			0.480017			0.240009	−	0.970771i	$-0.422850\pi$
$811$	13.6700			0.480017			0.240009	+	0.970771i	$0.422850\pi$
$812$	−34.8062	+	8.24921i	−1.22146	+	0.289491i
$813$	8.93748	−	23.6056i	0.313451	−	0.827886i
$814$	−4.78437	+	2.40280i	−0.167692	+	0.0842182i
$815$	−12.0901	−	16.2398i	−0.423498	−	0.568857i
$816$	−7.11051	−	5.43721i	−0.248918	−	0.190340i
$817$	−21.4818	+	14.1288i	−0.751552	+	0.494304i
$818$	−1.57767	+	1.32382i	−0.0551619	+	0.0462863i
$819$	−37.2306	−	14.6467i	−1.30094	−	0.511798i
$820$	−27.2241	−	22.8438i	−0.950708	−	0.797739i
$821$	−9.97247	−	1.16561i	−0.348041	−	0.0406802i	−0.0597236	−	0.998215i	$-0.519022\pi$
$821$	−9.97247	−	1.16561i	−0.348041	−	0.0406802i	−0.288318	+	0.957535i	$0.593096\pi$
$822$	0.224955	+	2.16606i	0.00784622	+	0.0755499i
$823$	8.67546	+	28.9781i	0.302408	+	1.01011i	0.965245	+	0.261348i	$0.0841670\pi$
$823$	8.67546	+	28.9781i	0.302408	+	1.01011i	−0.662837	+	0.748764i	$0.730648\pi$
$824$	3.33949	−	3.53965i	0.116337	−	0.123310i
$825$	−1.64272	+	6.55408i	−0.0571922	+	0.228184i
$826$	18.4701	−	24.8096i	0.642656	−	0.863237i
$827$	−8.16805	+	46.3233i	−0.284031	+	1.61082i	0.424695	+	0.905336i	$0.360381\pi$
$827$	−8.16805	+	46.3233i	−0.284031	+	1.61082i	−0.708726	+	0.705483i	$0.750730\pi$
$828$	11.4515	−	2.40452i	0.397967	−	0.0835630i
$829$	−0.608907	−	3.45328i	−0.0211482	−	0.119938i	0.972406	−	0.233295i	$-0.0749507\pi$
$829$	−0.608907	−	3.45328i	−0.0211482	−	0.119938i	−0.993554	+	0.113357i	$0.963840\pi$
$830$	−5.49847	−	2.76144i	−0.190855	−	0.0958508i
$831$	3.86271	+	17.2866i	0.133996	+	0.599667i
$832$	2.15274	−	0.251619i	0.0746329	−	0.00872333i
$833$	27.3056	+	17.9592i	0.946084	+	0.622249i
$834$	−10.5320	−	1.99717i	−0.364692	−	0.0691564i
$835$	12.1701	−	40.6511i	0.421165	−	1.40679i
$836$	−7.60767	−	13.1769i	−0.263117	−	0.455731i
$837$	−13.8154	−	30.3794i	−0.477530	−	1.05007i
$838$	−2.26555	+	3.92405i	−0.0782622	+	0.135554i
$839$	−25.2637	−	26.7780i	−0.872201	−	0.924479i	0.125511	−	0.992092i	$-0.459943\pi$
$839$	−25.2637	−	26.7780i	−0.872201	−	0.924479i	−0.997712	+	0.0676133i	$0.978462\pi$
$840$	−36.7974	+	20.6181i	−1.26963	+	0.711392i
$841$	−0.115799	+	1.98820i	−0.00399308	+	0.0685585i
$842$	3.91165	−	9.06823i	0.134804	−	0.312512i
$843$	−6.55360	−	10.2492i	−0.225718	−	0.353001i
$844$	1.77880	+	30.5409i	0.0612289	+	1.05126i
$845$	−5.86198	−	2.13359i	−0.201658	−	0.0733976i
$846$	−11.5719	−	16.4092i	−0.397849	−	0.564160i
$847$	8.63568	−	3.14313i	0.296725	−	0.107999i
$848$	−0.00613688	−	0.0142269i	−0.000210741	−	0.000488553i
$849$	37.3565	+	2.65862i	1.28207	+	0.0912435i
$850$	2.79685	+	0.662866i	0.0959312	+	0.0227361i
$851$	6.64110	+	1.57397i	0.227654	+	0.0539550i
$852$	−6.40750	−	0.456014i	−0.219517	−	0.0156228i
$853$	−14.6197	−	33.8923i	−0.500569	−	1.16045i	−0.961945	−	0.273244i	$-0.911903\pi$
$853$	−14.6197	−	33.8923i	−0.500569	−	1.16045i	0.461376	−	0.887205i	$-0.347356\pi$
$854$	23.0306	−	8.38245i	0.788090	−	0.286841i
$855$	−10.4058	+	22.5117i	−0.355871	+	0.769883i
$856$	−31.5810	−	11.4945i	−1.07942	−	0.392875i
$857$	−1.75026	−	30.0508i	−0.0597877	−	1.02652i	−0.886156	−	0.463386i	$-0.846634\pi$
$857$	−1.75026	−	30.0508i	−0.0597877	−	1.02652i	0.826369	−	0.563129i	$-0.190403\pi$
$858$	−5.92529	−	9.26659i	−0.202286	−	0.316356i
$859$	−7.70264	+	17.8567i	−0.262811	+	0.609264i	−0.997616	−	0.0690147i	$-0.978014\pi$
$859$	−7.70264	+	17.8567i	−0.262811	+	0.609264i	0.734805	+	0.678279i	$0.237274\pi$
$860$	1.78528	−	30.6520i	0.0608774	−	1.04522i
$861$	−56.2220	+	31.5020i	−1.91604	+	1.07358i
$862$	14.0092	+	14.8489i	0.477155	+	0.505755i
$863$	14.3566	−	24.8664i	0.488706	−	0.846463i	−0.511210	−	0.859456i	$-0.670803\pi$
$863$	14.3566	−	24.8664i	0.488706	−	0.846463i	0.999916	+	0.0129930i	$0.00413590\pi$
$864$	−2.31986	−	29.7807i	−0.0789234	−	1.01316i
$865$	8.44932	+	14.6347i	0.287286	+	0.497593i
$866$	−5.45716	+	18.2282i	−0.185442	+	0.619419i
$867$	−10.4168	−	1.97533i	−0.353773	−	0.0670857i
$868$	34.4792	+	22.6774i	1.17030	+	0.769720i
$869$	−26.4711	+	3.09403i	−0.897971	+	0.104958i
$870$	3.49548	+	15.6432i	0.118508	+	0.530355i
$871$	−16.9407	−	8.50796i	−0.574015	−	0.288281i
$872$	5.48453	+	31.1043i	0.185730	+	1.05333i
$873$	−6.68062	+	20.3892i	−0.226105	+	0.690070i
$874$	0.942844	−	5.34714i	0.0318922	−	0.180870i
$875$	22.7274	−	30.5282i	0.768325	−	1.03204i
$876$	3.10933	−	12.4055i	0.105054	−	0.419143i
$877$	13.1238	−	13.9104i	0.443158	−	0.469720i	−0.466835	−	0.884345i	$-0.654606\pi$
$877$	13.1238	−	13.9104i	0.443158	−	0.469720i	0.909992	+	0.414625i	$0.136087\pi$
$878$	−0.839125	−	2.80287i	−0.0283191	−	0.0945924i
$879$	1.95504	+	18.8247i	0.0659418	+	0.634941i
$880$	11.5808	+	1.35360i	0.390389	+	0.0456299i
$881$	35.7695	+	30.0142i	1.20510	+	1.01120i	0.999469	+	0.0325741i	$0.0103705\pi$
$881$	35.7695	+	30.0142i	1.20510	+	1.01120i	0.205635	+	0.978629i	$0.434074\pi$
$882$	2.91448	+	19.4431i	0.0981357	+	0.654683i
$883$	−10.7311	+	9.00449i	−0.361131	+	0.303025i	−0.805241	−	0.592947i	$-0.797964\pi$
$883$	−10.7311	+	9.00449i	−0.361131	+	0.303025i	0.444110	+	0.895972i	$0.353520\pi$
$884$	13.9650	−	9.18494i	0.469695	−	0.308923i
$885$	39.3313	+	30.0755i	1.32211	+	1.01098i
$886$	1.05355	+	1.41516i	0.0353945	+	0.0475431i
$887$	−9.26435	+	4.65273i	−0.311066	+	0.156223i	−0.597483	−	0.801882i	$-0.703832\pi$
$887$	−9.26435	+	4.65273i	−0.311066	+	0.156223i	0.286416	+	0.958105i	$0.407536\pi$
$888$	3.95114	−	10.4357i	0.132592	−	0.350201i
$889$	48.1419	−	11.4098i	1.61463	−	0.382674i
$890$	−20.7730			−0.696312
$891$	−22.9859	+	13.4768i	−0.770056	+	0.451490i
$892$	25.2612			0.845809
$893$	32.3868	−	7.67582i	1.08378	−	0.256862i
$894$	0.644245	+	0.788165i	0.0215468	+	0.0263602i
$895$	34.1540	−	17.1528i	1.14164	−	0.573355i
$896$	27.1468	+	36.4645i	0.906911	+	1.21819i
$897$	−1.80692	+	13.9046i	−0.0603312	+	0.464262i
$898$	−23.0070	+	15.1320i	−0.767755	+	0.504960i
$899$	27.3900	−	22.9829i	0.913508	−	0.766524i
$900$	−2.94972	−	5.42704i	−0.0983239	−	0.180901i
$901$	0.0249850	+	0.0209649i	0.000832370	+	0.000698441i
$902$	−17.5977	−	2.05688i	−0.585940	−	0.0684865i
$903$	−50.8371	−	22.7094i	−1.69175	−	0.755723i
$904$	2.00049	+	6.68209i	0.0665352	+	0.222243i
$905$	−9.66786	+	10.2473i	−0.321371	+	0.340633i
$906$	8.87684	−	2.53353i	0.294913	−	0.0841708i
$907$	−21.4775	+	28.8493i	−0.713149	+	0.957926i	−1.00000		4.96814e-5i	$-0.999984\pi$
$907$	−21.4775	+	28.8493i	−0.713149	+	0.957926i	0.286851	+	0.957975i	$0.407392\pi$
$908$	−5.76067	+	32.6704i	−0.191174	+	1.08420i
$909$	−6.25463	−	0.894801i	−0.207453	−	0.0296787i
$910$	−3.84964	−	21.8324i	−0.127614	−	0.723737i
$911$	−5.68443	−	2.85483i	−0.188334	−	0.0945846i	0.352134	−	0.935950i	$-0.385456\pi$
$911$	−5.68443	−	2.85483i	−0.188334	−	0.0945846i	−0.540467	+	0.841365i	$0.681753\pi$
$912$	8.51717	+	2.66979i	0.282032	+	0.0884057i
$913$	10.8841	−	1.27217i	0.360210	−	0.0421026i
$914$	4.23536	+	2.78564i	0.140093	+	0.0921408i
$915$	12.9429	+	37.0369i	0.427881	+	1.22440i
$916$	−3.86735	+	12.9178i	−0.127781	+	0.426818i
$917$	10.5602	+	18.2909i	0.348730	+	0.604018i
$918$	5.85837	+	9.70352i	0.193355	+	0.320264i
$919$	23.2884	−	40.3367i	0.768213	−	1.33058i	−0.170318	−	0.985389i	$-0.554480\pi$
$919$	23.2884	−	40.3367i	0.768213	−	1.33058i	0.938531	−	0.345194i	$-0.112187\pi$
$920$	10.1445	+	10.7526i	0.334455	+	0.354502i
$921$	−0.102522	+	7.96470i	−0.00337822	+	0.262446i
$922$	0.847673	−	14.5540i	0.0279166	−	0.479310i
$923$	3.04882	−	7.06797i	0.100353	−	0.232645i
$924$	15.1652	−	29.2515i	0.498898	−	0.962302i
$925$	−0.209486	−	3.59673i	−0.00688785	−	0.118260i
$926$	23.0942	+	8.40558i	0.758921	+	0.276225i
$927$	5.60671	−	2.63733i	0.184148	−	0.0866212i
$928$	30.0728	−	10.9456i	0.987189	−	0.359307i
$929$	−17.7858	−	41.2322i	−0.583535	−	1.35279i	−0.912745	−	0.408529i	$-0.866042\pi$
$929$	−17.7858	−	41.2322i	−0.583535	−	1.35279i	0.329210	−	0.944257i	$-0.393217\pi$
$930$	10.3599	−	15.3184i	0.339716	−	0.502309i
$931$	−31.7113	−	7.51573i	−1.03930	−	0.246318i
$932$	22.7528	+	5.39251i	0.745293	+	0.176638i
$933$	−13.2076	−	27.1648i	−0.432398	−	0.889334i
$934$	−2.17811	−	5.04943i	−0.0712700	−	0.165222i
$935$	−23.0638	+	8.39454i	−0.754267	+	0.274531i
$936$	22.1632	+	5.85919i	0.724426	+	0.191514i
$937$	−48.3251	−	17.5889i	−1.57871	−	0.574605i	−0.603790	−	0.797144i	$-0.706343\pi$
$937$	−48.3251	−	17.5889i	−1.57871	−	0.574605i	−0.974924	+	0.222539i	$0.928565\pi$
$938$	0.924311	+	15.8698i	0.0301798	+	0.518168i
$939$	−27.3852	+	1.24157i	−0.893681	+	0.0405171i
$940$	−15.7428	+	36.4960i	−0.513474	+	1.19037i
$941$	−0.606271	+	10.4093i	−0.0197639	+	0.339333i	0.973903	+	0.226965i	$0.0728804\pi$
$941$	−0.606271	+	10.4093i	−0.0197639	+	0.339333i	−0.993667	+	0.112367i	$0.964157\pi$
$942$	−14.2477	−	8.47230i	−0.464217	−	0.276042i
$943$	15.4996	+	16.4286i	0.504737	+	0.534990i
$944$	8.90994	−	15.4325i	0.289994	−	0.502284i
$945$	−53.2100	+	7.27711i	−1.73092	+	0.236724i
$946$	−7.65361	−	13.2564i	−0.248840	−	0.431004i
$947$	−12.9484	+	43.2508i	−0.420767	+	1.40546i	0.440703	+	0.897653i	$0.354729\pi$
$947$	−12.9484	+	43.2508i	−0.420767	+	1.40546i	−0.861470	+	0.507808i	$0.830456\pi$
$948$	15.8997	−	18.4606i	0.516397	−	0.599573i
$949$	12.8041	+	8.42138i	0.415638	+	0.273370i
$950$	−2.84682	+	0.332745i	−0.0923630	+	0.0107957i
$951$	24.9941	−	22.9799i	0.810490	−	0.745175i
$952$	−28.5572	−	14.3420i	−0.925544	−	0.464826i
$953$	5.08752	+	28.8527i	0.164801	+	0.934632i	0.949270	+	0.314463i	$0.101825\pi$
$953$	5.08752	+	28.8527i	0.164801	+	0.934632i	−0.784469	+	0.620168i	$0.787064\pi$
$954$	0.000636268		0.0196099i	2.05999e−5		0.000634893i
$955$	1.87491	−	10.6331i	0.0606705	−	0.344080i
$956$	3.36901	−	4.52537i	0.108962	−	0.146361i
$957$	−20.5105	−	19.8558i	−0.663011	−	0.641847i
$958$	1.15869	−	1.22814i	0.0374356	−	0.0396794i
$959$	−2.24199	−	7.48877i	−0.0723977	−	0.241825i
$960$	2.35589	−	1.70721i	0.0760360	−	0.0551000i
$961$	−10.1815	−	1.19005i	−0.328435	−	0.0383886i
$962$	4.49273	+	3.76985i	0.144851	+	0.121545i
$963$	−32.0608	−	28.3400i	−1.03314	−	0.913243i
$964$	27.4013	−	22.9924i	0.882536	−	0.740536i
$965$	5.95071	−	3.91384i	0.191560	−	0.125991i
$966$	10.8553	−	4.51772i	0.349264	−	0.145355i
$967$	27.9986	+	37.6086i	0.900374	+	1.20941i	0.977190	+	0.212367i	$0.0681172\pi$
$967$	27.9986	+	37.6086i	0.900374	+	1.20941i	−0.0768159	+	0.997045i	$0.524475\pi$
$968$	−4.70569	+	2.36329i	−0.151247	+	0.0759590i
$969$	−18.5442	+	3.02427i	−0.595724	+	0.0971536i
$970$	−11.5686	+	2.74180i	−0.371444	+	0.0880340i
$971$	45.6691			1.46559			0.732795	−	0.680449i	$-0.238215\pi$
$971$	45.6691			1.46559			0.732795	+	0.680449i	$0.238215\pi$
$972$	7.13010	−	23.2914i	0.228698	−	0.747072i
$973$	38.4797			1.23360
$974$	−10.5302	+	2.49570i	−0.337409	+	0.0799673i
$975$	7.30520	−	1.19137i	0.233954	−	0.0381543i
$976$	12.6184	−	6.33719i	0.403905	−	0.202848i
$977$	−0.740310	−	0.994408i	−0.0236846	−	0.0318139i	0.790123	−	0.612948i	$-0.210017\pi$
$977$	−0.740310	−	0.994408i	−0.0236846	−	0.0318139i	−0.813808	+	0.581134i	$0.802609\pi$
$978$	8.51888	−	3.54535i	0.272404	−	0.113368i
$979$	30.9096	−	20.3296i	0.987877	−	0.649737i
$980$	29.8126	−	25.0157i	0.952329	−	0.799099i
$981$	−8.00019	+	39.4104i	−0.255426	+	1.25828i
$982$	18.4847	+	15.5105i	0.589869	+	0.494959i
$983$	36.3380	+	4.24731i	1.15900	+	0.135468i	0.673787	−	0.738926i	$-0.264667\pi$
$983$	36.3380	+	4.24731i	1.15900	+	0.135468i	0.485217	+	0.874394i	$0.338741\pi$
$984$	29.9018	−	21.6685i	0.953234	−	0.690766i
$985$	−15.3173	−	51.1634i	−0.488050	−	1.63020i
$986$	−8.33360	+	8.83310i	−0.265396	+	0.281303i
$987$	51.7858	+	50.1328i	1.64836	+	1.59574i
$988$	−9.95317	+	13.3694i	−0.316652	+	0.425338i
$989$	−3.38850	+	19.2172i	−0.107748	+	0.611070i
$990$	−13.0193	−	6.96380i	−0.413779	−	0.221324i
$991$	−7.21791	−	40.9348i	−0.229285	−	1.30034i	−0.854323	−	0.519743i	$-0.826028\pi$
$991$	−7.21791	−	40.9348i	−0.229285	−	1.30034i	0.625038	−	0.780594i	$-0.285083\pi$
$992$	−32.9945	−	16.5705i	−1.04758	−	0.526113i
$993$	−27.8960	+	25.6480i	−0.885253	+	0.813914i
$994$	−6.41116	+	0.749358i	−0.203350	+	0.0237682i
$995$	20.4376	+	13.4420i	0.647916	+	0.426141i
$996$	−6.53743	+	7.59042i	−0.207146	+	0.240512i
$997$	−6.06973	+	20.2743i	−0.192230	+	0.642094i	0.806477	+	0.591265i	$0.201371\pi$
$997$	−6.06973	+	20.2743i	−0.192230	+	0.642094i	−0.998707	+	0.0508285i	$0.983814\pi$
$998$	−10.4952	−	18.1782i	−0.332220	−	0.575421i
$999$	9.54587	−	10.5230i	0.302018	−	0.332934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.76.4	yes	144
3.2	odd	2		243.2.g.a.118.5		144
9.2	odd	6		729.2.g.a.109.4		144
9.4	even	3		729.2.g.c.352.5		144
9.5	odd	6		729.2.g.b.352.4		144
9.7	even	3		729.2.g.d.109.5		144
81.4	even	27		6561.2.a.c.1.31		72
81.11	odd	54		729.2.g.b.379.4		144
81.16	even	27	inner	81.2.g.a.16.4	✓	144
81.38	odd	54		729.2.g.a.622.4		144
81.43	even	27		729.2.g.d.622.5		144
81.65	odd	54		243.2.g.a.208.5		144
81.70	even	27		729.2.g.c.379.5		144
81.77	odd	54		6561.2.a.d.1.42		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.4	✓	144	81.16	even	27	inner
81.2.g.a.76.4	yes	144	1.1	even	1	trivial
243.2.g.a.118.5		144	3.2	odd	2
243.2.g.a.208.5		144	81.65	odd	54
729.2.g.a.109.4		144	9.2	odd	6
729.2.g.a.622.4		144	81.38	odd	54
729.2.g.b.352.4		144	9.5	odd	6
729.2.g.b.379.4		144	81.11	odd	54
729.2.g.c.352.5		144	9.4	even	3
729.2.g.c.379.5		144	81.70	even	27
729.2.g.d.109.5		144	9.7	even	3
729.2.g.d.622.5		144	81.43	even	27
6561.2.a.c.1.31		72	81.4	even	27
6561.2.a.d.1.42		72	81.77	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.643544 + 0.152523i) q^{2} +(-1.70947 + 0.278788i) q^{3} +(-1.39638 + 0.701288i) q^{4} +(-1.50096 - 2.01613i) q^{5} +(1.05760 - 0.440145i) q^{6} +(-3.43556 + 2.25960i) q^{7} +(1.80495 - 1.51453i) q^{8} +(2.84455 - 0.953158i) q^{9} +(1.27344 + 1.06854i) q^{10} +(-2.94058 - 0.343704i) q^{11} +(2.19155 - 1.58812i) q^{12} +(0.930150 + 3.10692i) q^{13} +(1.86629 - 1.97816i) q^{14} +(3.12791 + 3.02806i) q^{15} +(0.935660 - 1.25681i) q^{16} +(-0.572741 + 3.24818i) q^{17} +(-1.68522 + 1.04726i) q^{18} +(-0.571121 - 3.23899i) q^{19} +(3.50979 + 1.76268i) q^{20} +(5.24302 - 4.82051i) q^{21} +(1.94481 - 0.227316i) q^{22} +(-2.08548 - 1.37164i) q^{23} +(-2.66327 + 3.09224i) q^{24} +(-0.377908 + 1.26230i) q^{25} +(-1.07247 - 1.85757i) q^{26} +(-4.59694 + 2.42242i) q^{27} +(3.21271 - 5.56458i) q^{28} +(-3.82031 - 4.04929i) q^{29} +(-2.47480 - 1.47162i) q^{30} +(-0.373446 + 6.41181i) q^{31} +(-2.27693 + 5.27851i) q^{32} +(5.12264 - 0.232247i) q^{33} +(-0.126837 - 2.17770i) q^{34} +(9.71228 + 3.53498i) q^{35} +(-3.30364 + 3.32582i) q^{36} +(-2.56937 + 0.935175i) q^{37} +(0.861562 + 1.99733i) q^{38} +(-2.45623 - 5.05186i) q^{39} +(-5.76265 - 1.36577i) q^{40} +(-8.80462 - 2.08673i) q^{41} +(-2.63888 + 3.90189i) q^{42} +(-3.09638 - 7.17822i) q^{43} +(4.34719 - 1.58225i) q^{44} +(-6.19124 - 4.30435i) q^{45} +(1.55131 + 0.564629i) q^{46} +(0.588422 + 10.1028i) q^{47} +(-1.24910 + 2.40933i) q^{48} +(3.92470 - 9.09847i) q^{49} +(0.0506710 - 0.869987i) q^{50} +(0.0735294 - 5.71233i) q^{51} +(-3.47769 - 3.68613i) q^{52} +(0.00494432 - 0.00856381i) q^{53} +(2.58886 - 2.26007i) q^{54} +(3.72072 + 6.44448i) q^{55} +(-2.77877 + 9.28173i) q^{56} +(1.87930 + 5.37773i) q^{57} +(3.07615 + 2.02322i) q^{58} +(11.2961 - 1.32033i) q^{59} +(-6.49129 - 2.03476i) q^{60} +(8.05332 + 4.04453i) q^{61} +(-0.737619 - 4.18325i) q^{62} +(-7.61887 + 9.70219i) q^{63} +(0.116049 - 0.658144i) q^{64} +(4.86785 - 6.53865i) q^{65} +(-3.26122 + 0.930781i) q^{66} +(-4.01126 + 4.25169i) q^{67} +(-1.47814 - 4.93734i) q^{68} +(3.94746 + 1.76337i) q^{69} +(-6.78945 - 0.793572i) q^{70} +(-1.81817 - 1.52563i) q^{71} +(3.69069 - 6.02857i) q^{72} +(3.61987 - 3.03743i) q^{73} +(1.51087 - 0.993715i) q^{74} +(0.294107 - 2.26322i) q^{75} +(3.06897 + 4.12234i) q^{76} +(10.8792 - 5.46372i) q^{77} +(2.35122 + 2.87646i) q^{78} +(8.75936 - 2.07601i) q^{79} -3.93828 q^{80} +(7.18298 - 5.42262i) q^{81} +5.98444 q^{82} +(-3.60157 + 0.853588i) q^{83} +(-3.94068 + 10.4081i) q^{84} +(7.40842 - 3.72065i) q^{85} +(3.08750 + 4.14723i) q^{86} +(7.65959 + 5.85708i) q^{87} +(-5.82815 + 3.83323i) q^{88} +(-9.57258 + 8.03235i) q^{89} +(4.64085 + 1.82574i) q^{90} +(-10.2160 - 8.57223i) q^{91} +(3.87404 + 0.452810i) q^{92} +(-1.14914 - 11.0649i) q^{93} +(-1.91958 - 6.41186i) q^{94} +(-5.67301 + 6.01304i) q^{95} +(2.42075 - 9.65823i) q^{96} +(-4.27084 + 5.73673i) q^{97} +(-1.13799 + 6.45388i) q^{98} +(-8.69223 + 1.82515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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