LMFDB - Embedded newform 243.2.g.a.118.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(10,243)] 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("243.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			118.5
Character	$\chi$	$=$	243.118
Dual form			243.2.g.a.208.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.643544 - 0.152523i) q^{2} +(-1.39638 + 0.701288i) q^{4} +(1.50096 + 2.01613i) q^{5} +(-3.43556 + 2.25960i) q^{7} +(-1.80495 + 1.51453i) q^{8} +(1.27344 + 1.06854i) q^{10} +(2.94058 + 0.343704i) q^{11} +(0.930150 + 3.10692i) q^{13} +(-1.86629 + 1.97816i) q^{14} +(0.935660 - 1.25681i) q^{16} +(0.572741 - 3.24818i) q^{17} +(-0.571121 - 3.23899i) q^{19} +(-3.50979 - 1.76268i) q^{20} +(1.94481 - 0.227316i) q^{22} +(2.08548 + 1.37164i) q^{23} +(-0.377908 + 1.26230i) q^{25} +(1.07247 + 1.85757i) q^{26} +(3.21271 - 5.56458i) q^{28} +(3.82031 + 4.04929i) q^{29} +(-0.373446 + 6.41181i) q^{31} +(2.27693 - 5.27851i) q^{32} +(-0.126837 - 2.17770i) q^{34} +(-9.71228 - 3.53498i) q^{35} +(-2.56937 + 0.935175i) q^{37} +(-0.861562 - 1.99733i) q^{38} +(-5.76265 - 1.36577i) q^{40} +(8.80462 + 2.08673i) q^{41} +(-3.09638 - 7.17822i) q^{43} +(-4.34719 + 1.58225i) q^{44} +(1.55131 + 0.564629i) q^{46} +(-0.588422 - 10.1028i) q^{47} +(3.92470 - 9.09847i) q^{49} +(-0.0506710 + 0.869987i) q^{50} +(-3.47769 - 3.68613i) q^{52} +(-0.00494432 + 0.00856381i) q^{53} +(3.72072 + 6.44448i) q^{55} +(2.77877 - 9.28173i) q^{56} +(3.07615 + 2.02322i) q^{58} +(-11.2961 + 1.32033i) q^{59} +(8.05332 + 4.04453i) q^{61} +(0.737619 + 4.18325i) q^{62} +(0.116049 - 0.658144i) q^{64} +(-4.86785 + 6.53865i) q^{65} +(-4.01126 + 4.25169i) q^{67} +(1.47814 + 4.93734i) q^{68} +(-6.78945 - 0.793572i) q^{70} +(1.81817 + 1.52563i) q^{71} +(3.61987 - 3.03743i) q^{73} +(-1.51087 + 0.993715i) q^{74} +(3.06897 + 4.12234i) q^{76} +(-10.8792 + 5.46372i) q^{77} +(8.75936 - 2.07601i) q^{79} +3.93828 q^{80} +5.98444 q^{82} +(3.60157 - 0.853588i) q^{83} +(7.40842 - 3.72065i) q^{85} +(-3.08750 - 4.14723i) q^{86} +(-5.82815 + 3.83323i) q^{88} +(9.57258 - 8.03235i) q^{89} +(-10.2160 - 8.57223i) q^{91} +(-3.87404 - 0.452810i) q^{92} +(-1.91958 - 6.41186i) q^{94} +(5.67301 - 6.01304i) q^{95} +(-4.27084 + 5.73673i) q^{97} +(1.13799 - 6.45388i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

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

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

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	0.00330473	−	0.999995i	$-0.498948\pi$
$2$	0.643544	−	0.152523i	0.455055	−	0.107850i	0.451750	+	0.892145i	$0.350800\pi$
$3$		0			0
$3$		0			0
$4$	−1.39638	+	0.701288i	−0.698189	+	0.350644i
$5$	1.50096	+	2.01613i	0.671248	+	0.901642i	0.999071	−	0.0430971i	$-0.0137225\pi$
$5$	1.50096	+	2.01613i	0.671248	+	0.901642i	−0.327823	+	0.944739i	$0.606315\pi$
$6$		0			0
$7$	−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
$9$		0			0
$10$	1.27344	+	1.06854i	0.402696	+	0.337902i
$11$	2.94058	+	0.343704i	0.886617	+	0.103631i	0.547197	−	0.837004i	$-0.315695\pi$
$11$	2.94058	+	0.343704i	0.886617	+	0.103631i	0.339421	+	0.940635i	$0.389769\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	0.935660	−	1.25681i	0.233915	−	0.314202i
$17$	0.572741	−	3.24818i	0.138910	−	0.787799i	−0.833146	−	0.553052i	$-0.813463\pi$
$17$	0.572741	−	3.24818i	0.138910	−	0.787799i	0.972057	−	0.234746i	$-0.0754260\pi$
$18$		0			0
$19$	−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
$21$		0			0
$22$	1.94481	−	0.227316i	0.414636	−	0.0484640i
$23$	2.08548	+	1.37164i	0.434853	+	0.286007i	0.748002	−	0.663697i	$-0.231014\pi$
$23$	2.08548	+	1.37164i	0.434853	+	0.286007i	−0.313149	+	0.949704i	$0.601384\pi$
$24$		0			0
$25$	−0.377908	+	1.26230i	−0.0755816	+	0.252460i
$26$	1.07247	+	1.85757i	0.210329	+	0.364300i
$27$		0			0
$28$	3.21271	−	5.56458i	0.607145	−	1.05161i
$29$	3.82031	+	4.04929i	0.709414	+	0.751935i	0.977379	−	0.211494i	$-0.0678327\pi$
$29$	3.82031	+	4.04929i	0.709414	+	0.751935i	−0.267965	+	0.963429i	$0.586351\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	−0.126837	−	2.17770i	−0.0217523	−	0.373473i
$35$	−9.71228	−	3.53498i	−1.64167	−	0.597521i
$36$		0			0
$37$	−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
$39$		0			0
$40$	−5.76265	−	1.36577i	−0.911155	−	0.215948i
$41$	8.80462	+	2.08673i	1.37505	+	0.325893i	0.850719	−	0.525621i	$-0.176167\pi$
$41$	8.80462	+	2.08673i	1.37505	+	0.325893i	0.524332	+	0.851514i	$0.324315\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	1.55131	+	0.564629i	0.228728	+	0.0832500i
$47$	−0.588422	−	10.1028i	−0.0858301	−	1.47365i	−0.716496	−	0.697591i	$-0.754255\pi$
$47$	−0.588422	−	10.1028i	−0.0858301	−	1.47365i	0.630666	−	0.776055i	$-0.282782\pi$
$48$		0			0
$49$	3.92470	−	9.09847i	0.560671	−	1.29978i
$50$	−0.0506710	+	0.869987i	−0.00716596	+	0.123035i
$51$		0			0
$52$	−3.47769	−	3.68613i	−0.482268	−	0.511175i
$53$	−0.00494432	+	0.00856381i	−0.000679154	+	0.00117633i	−0.866365	−	0.499412i	$-0.833550\pi$
$53$	−0.00494432	+	0.00856381i	−0.000679154	+	0.00117633i	0.865686	+	0.500588i	$0.166883\pi$
$54$		0			0
$55$	3.72072	+	6.44448i	0.501702	+	0.868973i
$56$	2.77877	−	9.28173i	0.371329	−	1.24032i
$57$		0			0
$58$	3.07615	+	2.02322i	0.403918	+	0.265661i
$59$	−11.2961	+	1.32033i	−1.47063	+	0.171892i	−0.813359	−	0.581762i	$-0.802364\pi$
$59$	−11.2961	+	1.32033i	−1.47063	+	0.171892i	−0.657272	+	0.753654i	$0.728290\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$	0.116049	−	0.658144i	0.0145061	−	0.0822680i
$65$	−4.86785	+	6.53865i	−0.603782	+	0.811020i
$66$		0			0
$67$	−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
$69$		0			0
$70$	−6.78945	−	0.793572i	−0.811494	−	0.0948500i
$71$	1.81817	+	1.52563i	0.215777	+	0.181058i	0.744269	−	0.667880i	$-0.232798\pi$
$71$	1.81817	+	1.52563i	0.215777	+	0.181058i	−0.528492	+	0.848938i	$0.677242\pi$
$72$		0			0
$73$	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			0
$76$	3.06897	+	4.12234i	0.352035	+	0.472865i
$77$	−10.8792	+	5.46372i	−1.23979	+	0.622648i
$78$		0			0
$79$	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
$81$		0			0
$82$	5.98444			0.660871
$83$	3.60157	−	0.853588i	0.395324	−	0.0936935i	−0.0281457	−	0.999604i	$-0.508960\pi$
$83$	3.60157	−	0.853588i	0.395324	−	0.0936935i	0.423469	+	0.905910i	$0.360812\pi$
$84$		0			0
$85$	7.40842	−	3.72065i	0.803555	−	0.403561i
$86$	−3.08750	−	4.14723i	−0.332934	−	0.447208i
$87$		0			0
$88$	−5.82815	+	3.83323i	−0.621282	+	0.408624i
$89$	9.57258	−	8.03235i	1.01469	−	0.851427i	0.0257399	−	0.999669i	$-0.491806\pi$
$89$	9.57258	−	8.03235i	1.01469	−	0.851427i	0.988951	+	0.148242i	$0.0473614\pi$
$90$		0			0
$91$	−10.2160	−	8.57223i	−1.07093	−	0.898614i
$92$	−3.87404	−	0.452810i	−0.403896	−	0.0472087i
$93$		0			0
$94$	−1.91958	−	6.41186i	−0.197990	−	0.661333i
$95$	5.67301	−	6.01304i	0.582038	−	0.616924i
$96$		0			0
$97$	−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
$99$		0			0
$100$	−0.357534	−	2.02767i	−0.0357534	−	0.202767i
$101$	1.88208	+	0.945217i	0.187274	+	0.0940526i	0.539966	−	0.841687i	$-0.318437\pi$
$101$	1.88208	+	0.945217i	0.187274	+	0.0940526i	−0.352692	+	0.935740i	$0.614733\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	−0.00187571	+	0.00626531i	−0.000182185	+	0.000608541i
$107$	7.13179	+	12.3526i	0.689456	+	1.19417i	0.972014	+	0.234923i	$0.0754838\pi$
$107$	7.13179	+	12.3526i	0.689456	+	1.19417i	−0.282558	+	0.959250i	$0.591183\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	−0.374625	+	6.43206i	−0.0353987	+	0.607773i
$113$	1.17253	−	2.71823i	0.110302	−	0.255709i	−0.854120	−	0.520076i	$-0.825904\pi$
$113$	1.17253	−	2.71823i	0.110302	−	0.255709i	0.964422	+	0.264367i	$0.0851629\pi$
$114$		0			0
$115$	0.364800	+	6.26337i	0.0340178	+	0.584063i
$116$	−8.17432	−	2.97521i	−0.758967	−	0.276241i
$117$		0			0
$118$	−7.06818	+	2.57261i	−0.650679	+	0.236828i
$119$	5.37190	+	12.4535i	0.492441	+	1.14161i
$120$		0			0
$121$	−2.17464	−	0.515398i	−0.197694	−	0.0468544i
$122$	5.79956	+	1.37452i	0.525067	+	0.124443i
$123$		0			0
$124$	−3.97506	−	9.21521i	−0.356971	−	0.827551i
$125$	8.69737	−	3.16558i	0.777917	−	0.283139i
$126$		0			0
$127$	−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
$129$		0			0
$130$	−2.13538	+	4.95037i	−0.187285	+	0.434176i
$131$	−0.298647	+	5.12757i	−0.0260929	+	0.447998i	0.959807	+	0.280661i	$0.0905537\pi$
$131$	−0.298647	+	5.12757i	−0.0260929	+	0.447998i	−0.985900	+	0.167337i	$0.946483\pi$
$132$		0			0
$133$	9.28095	+	9.83723i	0.804760	+	0.852996i
$134$	−1.93295	+	3.34796i	−0.166981	+	0.289220i
$135$		0			0
$136$	3.88570	+	6.73023i	0.333196	+	0.577113i
$137$	0.545226	−	1.82118i	0.0465818	−	0.155594i	−0.931534	−	0.363653i	$-0.881529\pi$
$137$	0.545226	−	1.82118i	0.0465818	−	0.155594i	0.978116	+	0.208059i	$0.0667146\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	1.40277	+	0.704496i	0.117718	+	0.0591200i
$143$	1.66732	+	9.45583i	0.139428	+	0.790736i
$144$		0			0
$145$	−2.42980	+	13.7801i	−0.201784	+	1.14437i
$146$	1.86627	−	2.50684i	0.154454	−	0.207467i
$147$		0			0
$148$	2.93199	−	3.10773i	0.241008	−	0.255454i
$149$	−0.254865	−	0.851310i	−0.0208794	−	0.0697420i	0.946915	−	0.321484i	$-0.104182\pi$
$149$	−0.254865	−	0.851310i	−0.0208794	−	0.0697420i	−0.967794	+	0.251742i	$0.918997\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−6.16788	+	5.17546i	−0.497022	+	0.417051i
$155$	−13.4876	+	8.87093i	−1.08335	+	0.712530i
$156$		0			0
$157$	−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			0
$160$	14.0598	−	3.33222i	1.11152	−	0.263435i
$161$	−10.2641			−0.808928
$162$		0			0
$163$	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
$165$		0			0
$166$	2.18758	−	1.09864i	0.169789	−	0.0852713i
$167$	−10.0814	−	13.5417i	−0.780126	−	1.04789i	−0.997420	−	0.0717845i	$-0.977131\pi$
$167$	−10.0814	−	13.5417i	−0.780126	−	1.04789i	0.217295	−	0.976106i	$-0.430277\pi$
$168$		0			0
$169$	2.07358	−	1.36381i	0.159506	−	0.104909i
$170$	4.20016	−	3.52435i	0.322138	−	0.270306i
$171$		0			0
$172$	9.35772	+	7.85206i	0.713520	+	0.598714i
$173$	6.67771	+	0.780512i	0.507697	+	0.0593412i	0.366086	−	0.930581i	$-0.380698\pi$
$173$	6.67771	+	0.780512i	0.507697	+	0.0593412i	0.141611	+	0.989922i	$0.454772\pi$
$174$		0			0
$175$	−1.55397	−	5.19063i	−0.117469	−	0.392375i
$176$	3.18335	−	3.37415i	0.239954	−	0.254336i
$177$		0			0
$178$	4.93526	−	6.62921i	0.369914	−	0.496880i
$179$	2.64043	−	14.9746i	0.197355	−	1.11926i	−0.711669	−	0.702515i	$-0.752060\pi$
$179$	2.64043	−	14.9746i	0.197355	−	1.11926i	0.909024	−	0.416743i	$-0.136828\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−5.84158	+	0.682783i	−0.430647	+	0.0503354i
$185$	−5.74195	−	3.77654i	−0.422157	−	0.277657i
$186$		0			0
$187$	2.80060	−	9.35466i	0.204800	−	0.684081i
$188$	7.90664	+	13.6947i	0.576651	+	0.998788i
$189$		0			0
$190$	2.73371	−	4.73492i	0.198324	−	0.343507i
$191$	−2.94787	−	3.12456i	−0.213300	−	0.226085i	0.611886	−	0.790946i	$-0.290411\pi$
$191$	−2.94787	−	3.12456i	−0.213300	−	0.226085i	−0.825186	+	0.564861i	$0.808930\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	0.900283	+	15.4573i	0.0643059	+	1.10409i
$197$	−19.9667	−	7.26729i	−1.42257	−	0.517773i	−0.487777	−	0.872968i	$-0.662192\pi$
$197$	−19.9667	−	7.26729i	−1.42257	−	0.517773i	−0.934792	+	0.355195i	$0.884414\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	1.35537	+	0.321229i	0.0953636	+	0.0226016i
$203$	−22.2747	−	5.27920i	−1.56338	−	0.370527i
$204$		0			0
$205$	9.00821	+	20.8834i	0.629161	+	1.45856i
$206$	1.28358	−	0.467185i	0.0894313	−	0.0325503i
$207$		0			0
$208$	4.77511	+	1.73800i	0.331094	+	0.120508i
$209$	−0.566172	−	9.72080i	−0.0391629	−	0.672402i
$210$		0			0
$211$	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
$213$		0			0
$214$	6.47368	+	6.86170i	0.442532	+	0.469056i
$215$	9.82471	−	17.0169i	0.670040	−	1.16054i
$216$		0			0
$217$	−13.2052	−	22.8720i	−0.896424	−	1.55265i
$218$	−2.54266	+	8.49307i	−0.172211	+	0.575223i
$219$		0			0
$220$	−9.71497	−	6.38964i	−0.654983	−	0.430789i
$221$	10.6246	−	1.24183i	0.714685	−	0.0835347i
$222$		0			0
$223$	−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			0
$226$	0.339982	−	1.92814i	0.0226153	−	0.128258i
$227$	−12.6779	+	17.0294i	−0.841463	+	1.13028i	0.148494	+	0.988913i	$0.452557\pi$
$227$	−12.6779	+	17.0294i	−0.841463	+	1.13028i	−0.989957	+	0.141368i	$0.954850\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−13.0283	−	1.52279i	−0.855347	−	0.0999758i
$233$	11.4634	+	9.61890i	0.750989	+	0.630155i	0.935764	−	0.352626i	$-0.114711\pi$
$233$	11.4634	+	9.61890i	0.750989	+	0.630155i	−0.184775	+	0.982781i	$0.559156\pi$
$234$		0			0
$235$	19.4854	−	16.3502i	1.27109	−	1.06657i
$236$	14.8477	−	9.76552i	0.966506	−	0.635681i
$237$		0			0
$238$	5.35650	+	7.19502i	0.347210	+	0.466384i
$239$	3.22647	−	1.62040i	0.208703	−	0.104815i	−0.341377	−	0.939926i	$-0.610893\pi$
$239$	3.22647	−	1.62040i	0.208703	−	0.104815i	0.550080	+	0.835112i	$0.314597\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−14.0819			−0.901500
$245$	24.2345	−	5.74369i	1.54829	−	0.366951i
$246$		0			0
$247$	9.53205	−	4.78718i	0.606510	−	0.304601i
$248$	−9.03685	−	12.1386i	−0.573841	−	0.770802i
$249$		0			0
$250$	5.11432	−	3.36374i	0.323458	−	0.212742i
$251$	16.2193	−	13.6096i	1.02375	−	0.859031i	0.0336587	−	0.999433i	$-0.489284\pi$
$251$	16.2193	−	13.6096i	1.02375	−	0.859031i	0.990095	+	0.140402i	$0.0448396\pi$
$252$		0			0
$253$	5.66107	+	4.75020i	0.355909	+	0.298643i
$254$	−7.90374	−	0.923815i	−0.495925	−	0.0579653i
$255$		0			0
$256$	2.48035	+	8.28496i	0.155022	+	0.517810i
$257$	−5.34379	+	5.66408i	−0.333336	+	0.353316i	−0.872263	−	0.489037i	$-0.837348\pi$
$257$	−5.34379	+	5.66408i	−0.333336	+	0.353316i	0.538927	+	0.842353i	$0.318830\pi$
$258$		0			0
$259$	6.71410	−	9.01861i	0.417194	−	0.560389i
$260$	2.21188	−	12.5442i	0.137175	−	0.777958i
$261$		0			0
$262$	0.589879	+	3.34537i	0.0364428	+	0.206678i
$263$	−1.36411	−	0.685083i	−0.0841148	−	0.0422440i	0.406244	−	0.913764i	$-0.366838\pi$
$263$	−1.36411	−	0.685083i	−0.0841148	−	0.0422440i	−0.490359	+	0.871520i	$0.663134\pi$
$264$		0			0
$265$	−0.0246870	+	0.00288549i	−0.00151651	+	0.000177254i
$266$	7.47311	+	4.91514i	0.458206	+	0.301367i
$267$		0			0
$268$	2.61959	−	8.75002i	0.160017	−	0.534493i
$269$	−14.7193	−	25.4946i	−0.897454	−	1.55444i	−0.830738	−	0.556663i	$-0.812081\pi$
$269$	−14.7193	−	25.4946i	−0.897454	−	1.55444i	−0.0667154	−	0.997772i	$-0.521252\pi$
$270$		0			0
$271$	−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
$273$		0			0
$274$	0.0731054	−	1.25517i	0.00441646	−	0.0758277i
$275$	−1.54513	+	3.58201i	−0.0931746	+	0.216003i
$276$		0			0
$277$	−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
$279$		0			0
$280$	22.8840	−	8.32910i	1.36758	−	0.497759i
$281$	−2.78193	−	6.44925i	−0.165956	−	0.384730i	0.814862	−	0.579655i	$-0.196813\pi$
$281$	−2.78193	−	6.44925i	−0.165956	−	0.384730i	−0.980818	+	0.194925i	$0.937554\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	2.51522	+	5.83094i	0.148728	+	0.344791i
$287$	−34.9640	+	12.7258i	−2.06386	+	0.751183i
$288$		0			0
$289$	5.75215	+	2.09361i	0.338362	+	0.123154i
$290$	0.538092	+	9.23868i	0.0315979	+	0.542514i
$291$		0			0
$292$	−2.92460	+	6.77998i	−0.171149	+	0.396768i
$293$	−0.635343	+	10.9084i	−0.0371171	+	0.637276i	0.927533	+	0.373742i	$0.121925\pi$
$293$	−0.635343	+	10.9084i	−0.0371171	+	0.637276i	−0.964650	+	0.263535i	$0.915112\pi$
$294$		0			0
$295$	−19.6169	−	20.7927i	−1.14214	−	1.21060i
$296$	3.22124	−	5.57934i	0.187230	−	0.324293i
$297$		0			0
$298$	−0.293862	−	0.508983i	−0.0170229	−	0.0294846i
$299$	−2.32177	+	7.75525i	−0.134271	+	0.448498i
$300$		0			0
$301$	26.8577	+	17.6646i	1.54805	+	1.01817i
$302$	5.29366	−	0.618740i	0.304616	−	0.0356045i
$303$		0			0
$304$	−4.60517	−	2.31280i	−0.264125	−	0.132648i
$305$	3.93337	+	22.3072i	0.225224	+	1.27731i
$306$		0			0
$307$	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
$309$		0			0
$310$	−7.32685	+	7.76600i	−0.416137	+	0.441079i
$311$	−5.00159	−	16.7065i	−0.283614	−	0.947336i	−0.974503	−	0.224375i	$-0.927966\pi$
$311$	−5.00159	−	16.7065i	−0.283614	−	0.947336i	0.690889	−	0.722961i	$-0.257219\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	−10.7755	+	9.04173i	−0.606170	+	0.508637i
$317$	16.3777	−	10.7718i	0.919864	−	0.605004i	0.00118078	−	0.999999i	$-0.499624\pi$
$317$	16.3777	−	10.7718i	0.919864	−	0.605004i	0.918683	+	0.394995i	$0.129254\pi$
$318$		0			0
$319$	9.84216	+	13.2203i	0.551055	+	0.740196i
$320$	1.50109	−	0.753875i	0.0839134	−	0.0421429i
$321$		0			0
$322$	−6.60544	+	1.56552i	−0.368107	+	0.0872429i
$323$	−10.8479			−0.603594
$324$		0			0
$325$	−4.27338			−0.237044
$326$	5.18372	−	1.22856i	0.287099	−	0.0680438i
$327$		0			0
$328$	−19.0523	+	9.56844i	−1.05199	+	0.528329i
$329$	24.8499	+	33.3792i	1.37002	+	1.84025i
$330$		0			0
$331$	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
$333$		0			0
$334$	−8.55328	−	7.17706i	−0.468015	−	0.392711i
$335$	−14.5927	−	1.70564i	−0.797284	−	0.0931892i
$336$		0			0
$337$	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
$339$		0			0
$340$	−7.73571	+	10.3909i	−0.419528	+	0.563524i
$341$	−3.30191	+	18.7261i	−0.178809	+	1.01407i
$342$		0			0
$343$	2.07706	+	11.7796i	0.112151	+	0.636040i
$344$	16.4605	+	8.26676i	0.887489	+	0.445714i
$345$		0			0
$346$	4.41645	−	0.516209i	0.237430	−	0.0277516i
$347$	16.0680	+	10.5681i	0.862574	+	0.567324i	0.901921	−	0.431902i	$-0.142157\pi$
$347$	16.0680	+	10.5681i	0.862574	+	0.567324i	−0.0393465	+	0.999226i	$0.512528\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	8.50973	−	14.7393i	0.453570	−	0.785607i
$353$	−10.0961	−	10.7013i	−0.537364	−	0.569572i	0.400623	−	0.916243i	$-0.368794\pi$
$353$	−10.0961	−	10.7013i	−0.537364	−	0.569572i	−0.937987	+	0.346671i	$0.887312\pi$
$354$		0			0
$355$	−0.346872	+	5.95557i	−0.0184101	+	0.316089i
$356$	−7.73396	+	17.9293i	−0.409899	+	0.950253i
$357$		0			0
$358$	−0.584739	−	10.0396i	−0.0309044	−	0.530608i
$359$	10.0637	+	3.66289i	0.531142	+	0.193320i	0.593648	−	0.804725i	$-0.297687\pi$
$359$	10.0637	+	3.66289i	0.531142	+	0.193320i	−0.0625063	+	0.998045i	$0.519909\pi$
$360$		0			0
$361$	7.68928	−	2.79867i	0.404699	−	0.147298i
$362$	−1.46826	−	3.40381i	−0.0771701	−	0.178901i
$363$		0			0
$364$	20.2770	+	4.80573i	1.06280	+	0.251889i
$365$	11.5571	+	2.73909i	0.604928	+	0.143371i
$366$		0			0
$367$	−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
$369$		0			0
$370$	−4.27121	−	1.55459i	−0.222050	−	0.0808194i
$371$	−0.00236431	−	0.0405936i	−0.000122749	−	0.00210752i
$372$		0			0
$373$	−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
$375$		0			0
$376$	16.3631	+	17.3439i	0.843863	+	0.894442i
$377$	−9.02736	+	15.6359i	−0.464933	+	0.805287i
$378$		0			0
$379$	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
$381$		0			0
$382$	−2.37365	−	1.56118i	−0.121447	−	0.0798767i
$383$	−29.2263	+	3.41606i	−1.49339	+	0.174553i	−0.823250	−	0.567678i	$-0.807842\pi$
$383$	−29.2263	+	3.41606i	−1.49339	+	0.174553i	−0.670144	+	0.742231i	$0.733768\pi$
$384$		0			0
$385$	−27.3447	−	13.7330i	−1.39362	−	0.699900i
$386$	0.325437	+	1.84564i	0.0165643	+	0.0939407i
$387$		0			0
$388$	1.94061	−	11.0057i	0.0985194	−	0.558731i
$389$	15.8270	−	21.2594i	0.802462	−	1.07789i	−0.192855	−	0.981227i	$-0.561775\pi$
$389$	15.8270	−	21.2594i	0.802462	−	1.07789i	0.995317	−	0.0966658i	$-0.0308178\pi$
$390$		0			0
$391$	5.64977	−	5.98841i	0.285721	−	0.302847i
$392$	6.69605	+	22.3664i	0.338202	+	1.12967i
$393$		0			0
$394$	−13.9579	−	1.63144i	−0.703189	−	0.0821910i
$395$	17.3329	+	14.5440i	0.872114	+	0.731790i
$396$		0			0
$397$	−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
$399$		0			0
$400$	1.23288	+	1.65604i	0.0616439	+	0.0828022i
$401$	12.7098	−	6.38308i	0.634695	−	0.318756i	−0.102199	−	0.994764i	$-0.532588\pi$
$401$	12.7098	−	6.38308i	0.634695	−	0.318756i	0.736894	+	0.676008i	$0.236292\pi$
$402$		0			0
$403$	−20.2683	+	4.80369i	−1.00964	+	0.239289i
$404$	−3.29097			−0.163732
$405$		0			0
$406$	−15.1400			−0.751383
$407$	−7.87686	+	1.86685i	−0.390441	+	0.0925363i
$408$		0			0
$409$	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			0
$412$	−2.69635	+	1.77342i	−0.132840	+	0.0873699i
$413$	35.8251	−	30.0608i	1.76284	−	1.47920i
$414$		0			0
$415$	7.12674	+	5.98005i	0.349838	+	0.293549i
$416$	18.5178	+	2.16442i	0.907910	+	0.106119i
$417$		0			0
$418$	−1.84700	−	6.16941i	−0.0903397	−	0.301756i
$419$	−4.70149	+	4.98329i	−0.229683	+	0.243450i	−0.831958	−	0.554839i	$-0.812780\pi$
$419$	−4.70149	+	4.98329i	−0.229683	+	0.243450i	0.602275	+	0.798289i	$0.294261\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−0.00404592	−	0.0229456i	−0.000196487	−	0.00111434i
$425$	3.88374	+	1.95049i	0.188389	+	0.0946124i
$426$		0			0
$427$	−36.8067	+	4.30209i	−1.78120	+	0.208193i
$428$	−18.6214	−	12.2475i	−0.900101	−	0.592006i
$429$		0			0
$430$	3.72717	−	12.4496i	0.179740	−	0.600374i
$431$	15.4334	+	26.7314i	0.743399	+	1.28760i	0.950939	+	0.309378i	$0.100121\pi$
$431$	15.4334	+	26.7314i	0.743399	+	1.28760i	−0.207540	+	0.978227i	$0.566546\pi$
$432$		0			0
$433$	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			0
$436$	1.21791	−	20.9106i	0.0583271	−	1.00144i
$437$	3.25167	−	7.53822i	0.155549	−	0.360602i
$438$		0			0
$439$	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
$441$		0			0
$442$	6.64797	−	2.41966i	0.316212	−	0.115092i
$443$	1.05658	+	2.44942i	0.0501994	+	0.116375i	0.941470	−	0.337096i	$-0.109445\pi$
$443$	1.05658	+	2.44942i	0.0501994	+	0.116375i	−0.891271	+	0.453471i	$0.850185\pi$
$444$		0			0
$445$	30.5623	+	7.24339i	1.44879	+	0.343370i
$446$	−10.4037	−	2.46573i	−0.492631	−	0.116756i
$447$		0			0
$448$	1.08845	+	2.52331i	0.0514245	+	0.119215i
$449$	−39.1256	+	14.2405i	−1.84645	+	0.672053i	−0.859474	+	0.511179i	$0.829209\pi$
$449$	−39.1256	+	14.2405i	−1.84645	+	0.672053i	−0.986975	+	0.160874i	$0.948569\pi$
$450$		0			0
$451$	25.1735	+	9.16239i	1.18537	+	0.431440i
$452$	0.268965	+	4.61795i	0.0126511	+	0.217210i
$453$		0			0
$454$	−5.56143	+	12.8928i	−0.261011	+	0.605091i
$455$	1.94902	−	33.4633i	0.0913713	−	1.56878i
$456$		0			0
$457$	−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
$459$		0			0
$460$	−4.90183	−	8.49022i	−0.228549	−	0.395858i
$461$	6.32202	−	21.1170i	0.294446	−	0.983517i	−0.674919	−	0.737892i	$-0.735821\pi$
$461$	6.32202	−	21.1170i	0.294446	−	0.983517i	0.969365	−	0.245625i	$-0.0789933\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	8.84428	+	4.44177i	0.409703	+	0.205761i
$467$	−1.44385	−	8.18848i	−0.0668134	−	0.378918i	−0.999818	−	0.0190543i	$-0.993934\pi$
$467$	−1.44385	−	8.18848i	−0.0668134	−	0.378918i	0.933005	−	0.359863i	$-0.117177\pi$
$468$		0			0
$469$	4.17380	−	23.6708i	0.192728	−	1.09302i
$470$	10.0459	−	13.4941i	0.463385	−	0.622434i
$471$		0			0
$472$	18.3893	−	19.4915i	0.846435	−	0.897168i
$473$	−6.63796	−	22.1723i	−0.305214	−	1.01949i
$474$		0			0
$475$	4.30441	+	0.503114i	0.197500	+	0.0230844i
$476$	−16.2347	−	13.6225i	−0.744115	−	0.624387i
$477$		0			0
$478$	1.82923	−	1.53491i	0.0836671	−	0.0702050i
$479$	2.13297	−	1.40288i	0.0974580	−	0.0640991i	−0.499845	−	0.866115i	$-0.666610\pi$
$479$	2.13297	−	1.40288i	0.0974580	−	0.0640991i	0.597303	+	0.802016i	$0.296239\pi$
$480$		0			0
$481$	−5.29542	−	7.11298i	−0.241450	−	0.324324i
$482$	−13.5294	+	6.79470i	−0.616246	+	0.309490i
$483$		0			0
$484$	3.39806	−	0.805354i	0.154457	−	0.0366070i
$485$	−17.9763			−0.816263
$486$		0			0
$487$	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
$489$		0			0
$490$	14.7200	−	7.39264i	0.664980	−	0.333965i
$491$	21.7872	+	29.2653i	0.983242	+	1.32072i	0.946950	+	0.321382i	$0.104147\pi$
$491$	21.7872	+	29.2653i	0.983242	+	1.32072i	0.0362928	+	0.999341i	$0.488445\pi$
$492$		0			0
$493$	15.3409	−	10.0899i	0.690918	−	0.454424i
$494$	5.40415	−	4.53462i	0.243144	−	0.204022i
$495$		0			0
$496$	7.70901	+	6.46863i	0.346145	+	0.290450i
$497$	−9.69374	−	1.13304i	−0.434823	−	0.0508236i
$498$		0			0
$499$	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
$501$		0			0
$502$	8.36207	−	11.2322i	0.373217	−	0.501318i
$503$	−1.04817	+	5.94449i	−0.0467358	+	0.265052i	−0.999218	−	0.0395428i	$-0.987410\pi$
$503$	−1.04817	+	5.94449i	−0.0467358	+	0.265052i	0.952482	+	0.304595i	$0.0985210\pi$
$504$		0			0
$505$	0.919238	+	5.21326i	0.0409055	+	0.231987i
$506$	4.36767	+	2.19352i	0.194166	+	0.0975141i
$507$		0			0
$508$	18.6737	−	2.18265i	0.828513	−	0.0968393i
$509$	21.9762	+	14.4540i	0.974079	+	0.640662i	0.933524	−	0.358516i	$-0.116717\pi$
$509$	21.9762	+	14.4540i	0.974079	+	0.640662i	0.0405551	+	0.999177i	$0.487087\pi$
$510$		0			0
$511$	−5.57289	+	18.6147i	−0.246530	+	0.823468i
$512$	−8.19547	−	14.1950i	−0.362192	−	0.627335i
$513$		0			0
$514$	−2.57506	+	4.46014i	−0.113581	+	0.196728i
$515$	3.56243	+	3.77596i	0.156980	+	0.166389i
$516$		0			0
$517$	1.74208	−	29.9103i	0.0766165	−	1.31545i
$518$	2.94528	−	6.82793i	0.129408	−	0.300002i
$519$		0			0
$520$	−1.11678	−	19.1745i	−0.0489742	−	0.840855i
$521$	−23.7819	−	8.65589i	−1.04190	−	0.379221i	−0.236301	−	0.971680i	$-0.575935\pi$
$521$	−23.7819	−	8.65589i	−1.04190	−	0.379221i	−0.805601	+	0.592459i	$0.798157\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	−0.982358	−	0.232823i	−0.0428328	−	0.0101516i
$527$	20.6128	+	4.88533i	0.897909	+	0.212808i
$528$		0			0
$529$	−6.64201	−	15.3979i	−0.288783	−	0.669474i
$530$	−0.0154471	+	0.00562227i	−0.000670977	+	0.000244216i
$531$		0			0
$532$	−19.8585	−	7.22789i	−0.860973	−	0.313369i
$533$	1.70631	+	29.2962i	0.0739085	+	1.26896i
$534$		0			0
$535$	−14.2000	+	32.9194i	−0.613921	+	1.42323i
$536$	0.800805	−	13.7493i	0.0345895	−	0.593879i
$537$		0			0
$538$	−13.3611	−	14.1619i	−0.576036	−	0.610563i
$539$	14.6681	−	25.4058i	0.631798	−	1.09431i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−15.8415	−	10.4191i	−0.679197	−	0.446715i
$545$	−33.4649	+	3.91149i	−1.43348	+	0.167550i
$546$		0			0
$547$	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
$549$		0			0
$550$	−0.448020	+	2.54085i	−0.0191036	+	0.108342i
$551$	10.9338	−	14.6866i	0.465794	−	0.625670i
$552$		0			0
$553$	−25.4023	+	26.9249i	−1.08022	+	1.14496i
$554$	−1.93981	−	6.47943i	−0.0824148	−	0.275285i
$555$		0			0
$556$	14.5235	+	1.69756i	0.615935	+	0.0719925i
$557$	23.1644	+	19.4372i	0.981505	+	0.823581i	0.984316	−	0.176415i	$-0.0564501\pi$
$557$	23.1644	+	19.4372i	0.981505	+	0.823581i	−0.00281036	+	0.999996i	$0.500895\pi$
$558$		0			0
$559$	19.4220	−	16.2970i	0.821465	−	0.689291i
$560$	−13.5302	+	8.89894i	−0.571755	+	0.376049i
$561$		0			0
$562$	−2.77396	−	3.72607i	−0.117012	−	0.157175i
$563$	16.5135	−	8.29337i	0.695959	−	0.349524i	−0.0653954	−	0.997859i	$-0.520831\pi$
$563$	16.5135	−	8.29337i	0.695959	−	0.349524i	0.761355	+	0.648336i	$0.224535\pi$
$564$		0			0
$565$	7.24021	−	1.71596i	0.304598	−	0.0721911i
$566$	−14.3004			−0.601091
$567$		0			0
$568$	−5.59232			−0.234648
$569$	−8.75519	+	2.07502i	−0.367037	+	0.0869893i	−0.409995	−	0.912088i	$-0.634470\pi$
$569$	−8.75519	+	2.07502i	−0.367037	+	0.0869893i	0.0429589	+	0.999077i	$0.486322\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−20.5599	+	13.5225i	−0.858153	+	0.564416i
$575$	−2.51954	+	2.11415i	−0.105072	+	0.0881661i
$576$		0			0
$577$	−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			0
$580$	−6.27087	−	20.9462i	−0.260384	−	0.869743i
$581$	−10.4446	+	11.0707i	−0.433317	+	0.459289i
$582$		0			0
$583$	−0.0174826	+	0.0234832i	−0.000724054	+	0.000972573i
$584$	−1.93340	+	10.9648i	−0.0800045	+	0.453728i
$585$		0			0
$586$	1.25491	+	7.11695i	0.0518399	+	0.293999i
$587$	1.23033	+	0.617896i	0.0507812	+	0.0255033i	0.474009	−	0.880520i	$-0.342807\pi$
$587$	1.23033	+	0.617896i	0.0507812	+	0.0255033i	−0.423227	+	0.906024i	$0.639103\pi$
$588$		0			0
$589$	20.9811	−	2.45234i	0.864511	−	0.101047i
$590$	−15.7957	−	10.3890i	−0.650300	−	0.427709i
$591$		0			0
$592$	−1.22872	+	4.10422i	−0.0505002	+	0.168682i
$593$	−15.4929	−	26.8346i	−0.636219	−	1.10196i	−0.986256	−	0.165227i	$-0.947164\pi$
$593$	−15.4929	−	26.8346i	−0.636219	−	1.10196i	0.350037	−	0.936736i	$-0.386169\pi$
$594$		0			0
$595$	−17.0449	+	29.5226i	−0.698771	+	1.21031i
$596$	0.952902	+	1.01002i	0.0390324	+	0.0413719i
$597$		0			0
$598$	−0.311309	+	5.34497i	−0.0127304	+	0.218572i
$599$	9.60548	−	22.2680i	0.392469	−	0.909846i	−0.601365	−	0.798974i	$-0.705376\pi$
$599$	9.60548	−	22.2680i	0.392469	−	0.909846i	0.993835	−	0.110872i	$-0.0353644\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−11.8328	+	4.30678i	−0.481469	+	0.175241i
$605$	−2.22492	−	5.15794i	−0.0904558	−	0.209700i
$606$		0			0
$607$	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
$609$		0			0
$610$	5.93366	+	13.7558i	0.240247	+	0.556955i
$611$	30.8413	−	11.2253i	1.24770	−	0.454127i
$612$		0			0
$613$	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
$615$		0			0
$616$	11.3614	−	26.3386i	0.457762	−	1.06121i
$617$	−0.923932	+	15.8633i	−0.0371961	+	0.638632i	0.927265	+	0.374406i	$0.122153\pi$
$617$	−0.923932	+	15.8633i	−0.0371961	+	0.638632i	−0.964461	+	0.264226i	$0.914884\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	−5.76686	−	9.98849i	−0.231230	−	0.400502i
$623$	−14.7372	+	49.2258i	−0.590435	+	1.97219i
$624$		0			0
$625$	24.9410	+	16.4040i	0.997641	+	0.656159i
$626$	10.3968	−	1.21521i	0.415540	−	0.0485696i
$627$		0			0
$628$	20.2064	+	10.1480i	0.806321	+	0.404950i
$629$	1.56603	+	8.88139i	0.0624417	+	0.354124i
$630$		0			0
$631$	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
$633$		0			0
$634$	8.89684	−	9.43010i	0.353339	−	0.374517i
$635$	−8.67352	−	28.9716i	−0.344198	−	1.14970i
$636$		0			0
$637$	31.9188	+	3.73077i	1.26467	+	0.147818i
$638$	8.35027	+	7.00671i	0.330590	+	0.277398i
$639$		0			0
$640$	−21.2865	+	17.8615i	−0.841422	+	0.706037i
$641$	−7.82391	+	5.14587i	−0.309026	+	0.203249i	−0.694543	−	0.719451i	$-0.744393\pi$
$641$	−7.82391	+	5.14587i	−0.309026	+	0.203249i	0.385517	+	0.922701i	$0.374023\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	−6.98112	+	1.65456i	−0.274668	+	0.0650976i
$647$	14.2593			0.560591			0.280295	−	0.959914i	$-0.409568\pi$
$647$	14.2593			0.560591			0.280295	+	0.959914i	$0.409568\pi$
$648$		0			0
$649$	−33.6709			−1.32170
$650$	−2.75011	+	0.651788i	−0.107868	+	0.0255652i
$651$		0			0
$652$	−11.2478	+	5.64884i	−0.440496	+	0.221225i
$653$	−24.3576	−	32.7179i	−0.953185	−	1.28035i	−0.959891	−	0.280372i	$-0.909542\pi$
$653$	−24.3576	−	32.7179i	−0.953185	−	1.28035i	0.00670674	−	0.999978i	$-0.497865\pi$
$654$		0			0
$655$	−10.7861	+	7.09414i	−0.421448	+	0.277191i
$656$	10.8608	−	9.11326i	0.424042	−	0.355813i
$657$		0			0
$658$	21.0831	+	17.6908i	0.821905	+	0.689660i
$659$	2.57161	+	0.300578i	0.100176	+	0.0117089i	0.166033	−	0.986120i	$-0.446904\pi$
$659$	2.57161	+	0.300578i	0.100176	+	0.0117089i	−0.0658573	+	0.997829i	$0.520978\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$	−5.20787	+	6.99538i	−0.202105	+	0.271473i
$665$	−5.90288	+	33.4769i	−0.228904	+	1.29818i
$666$		0			0
$667$	2.41300	+	13.6848i	0.0934318	+	0.529878i
$668$	23.5742	+	11.8394i	0.912112	+	0.458080i
$669$		0			0
$670$	−9.65120	+	1.12806i	−0.372858	+	0.0435809i
$671$	22.2913	+	14.6612i	0.860546	+	0.565990i
$672$		0			0
$673$	−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
$675$		0			0
$676$	−1.93907	+	3.35858i	−0.0745798	+	0.129176i
$677$	13.7507	+	14.5749i	0.528482	+	0.560158i	0.935529	−	0.353249i	$-0.114923\pi$
$677$	13.7507	+	14.5749i	0.528482	+	0.560158i	−0.407048	+	0.913407i	$0.633442\pi$
$678$		0			0
$679$	1.70998	−	29.3593i	0.0656231	−	1.12670i
$680$	−7.73678	+	17.9359i	−0.296692	+	0.687809i
$681$		0			0
$682$	0.731227	+	12.5547i	0.0280001	+	0.480743i
$683$	29.9877	+	10.9146i	1.14745	+	0.417636i	0.844597	−	0.535402i	$-0.179840\pi$
$683$	29.9877	+	10.9146i	1.14745	+	0.417636i	0.302849	+	0.953039i	$0.402062\pi$
$684$		0			0
$685$	4.49011	−	1.63426i	0.171558	−	0.0624421i
$686$	3.13334	+	7.26391i	0.119632	+	0.277337i
$687$		0			0
$688$	−11.9188	−	2.82481i	−0.454401	−	0.107695i
$689$	−0.0312060	−	0.00739596i	−0.00118885	−	0.000281764i
$690$		0			0
$691$	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
$693$		0			0
$694$	11.9523	+	4.35029i	0.453704	+	0.165135i
$695$	−1.36762	−	23.4810i	−0.0518766	−	0.890687i
$696$		0			0
$697$	11.8209	−	27.4038i	0.447747	−	1.03799i
$698$	−0.821179	+	14.0991i	−0.0310821	+	0.533659i
$699$		0			0
$700$	5.81006	+	6.15831i	0.219600	+	0.232762i
$701$	−11.5923	+	20.0785i	−0.437836	+	0.758355i	−0.997522	−	0.0703498i	$-0.977588\pi$
$701$	−11.5923	+	20.0785i	−0.437836	+	0.758355i	0.559686	+	0.828705i	$0.310922\pi$
$702$		0			0
$703$	4.49645	+	7.78807i	0.169587	+	0.293733i
$704$	0.567456	−	1.89544i	0.0213868	−	0.0714369i
$705$		0			0
$706$	−8.12951	−	5.34686i	−0.305958	−	0.201232i
$707$	−8.60182	+	1.00541i	−0.323505	+	0.0378123i
$708$		0			0
$709$	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
$711$		0			0
$712$	−5.11277	+	28.9960i	−0.191609	+	1.08667i
$713$	−9.57352	+	12.8595i	−0.358531	+	0.481591i
$714$		0			0
$715$	−16.5616	+	17.5543i	−0.619370	+	0.656494i
$716$	6.81449	+	22.7620i	0.254669	+	0.850655i
$717$		0			0
$718$	7.03511	+	0.822287i	0.262548	+	0.0306875i
$719$	−13.4111	−	11.2533i	−0.500151	−	0.419677i	0.357497	−	0.933914i	$-0.383630\pi$
$719$	−13.4111	−	11.2533i	−0.500151	−	0.419677i	−0.857648	+	0.514238i	$0.828075\pi$
$720$		0			0
$721$	−6.50583	+	5.45904i	−0.242290	+	0.203305i
$722$	4.52153	−	2.97386i	0.168274	−	0.110676i
$723$		0			0
$724$	5.23009	+	7.02523i	0.194375	+	0.261091i
$725$	−6.55516	+	3.29212i	−0.243452	+	0.122266i
$726$		0			0
$727$	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
$729$		0			0
$730$	7.85530			0.290738
$731$	−25.0896	+	5.94633i	−0.927971	+	0.219933i
$732$		0			0
$733$	−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
$735$		0			0
$736$	11.9887	−	7.88510i	0.441910	−	0.290649i
$737$	−13.2568	+	11.1237i	−0.488319	+	0.409748i
$738$		0			0
$739$	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
$741$		0			0
$742$	−0.00771300	−	0.0257632i	−0.000283153	−	0.000945797i
$743$	13.4927	−	14.3015i	0.495000	−	0.524670i	−0.430919	−	0.902391i	$-0.641811\pi$
$743$	13.4927	−	14.3015i	0.495000	−	0.524670i	0.925920	+	0.377721i	$0.123292\pi$
$744$		0			0
$745$	1.33381	−	1.79162i	0.0488671	−	0.0656399i
$746$	−2.72448	+	15.4513i	−0.0997503	+	0.565712i
$747$		0			0
$748$	2.64961	+	15.0267i	0.0968793	+	0.549430i
$749$	−52.4137	−	26.3231i	−1.91515	−	0.961827i
$750$		0			0
$751$	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
$753$		0			0
$754$	−3.42468	+	11.4392i	−0.124720	+	0.416593i
$755$	10.1276	+	17.5415i	0.368580	+	0.638399i
$756$		0			0
$757$	−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
$759$		0			0
$760$	−1.13255	+	19.4452i	−0.0410820	+	0.705351i
$761$	−6.89394	+	15.9819i	−0.249905	+	0.579345i	−0.996279	−	0.0861814i	$-0.972534\pi$
$761$	−6.89394	+	15.9819i	−0.249905	+	0.579345i	0.746375	+	0.665526i	$0.231793\pi$
$762$		0			0
$763$	−3.20499	−	55.0275i	−0.116028	−	1.99213i
$764$	6.30756	+	2.29576i	0.228200	+	0.0830578i
$765$		0			0
$766$	−18.2874	+	6.65607i	−0.660751	+	0.240494i
$767$	−14.6093	−	33.8681i	−0.527510	−	1.22290i
$768$		0			0
$769$	−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
$771$		0			0
$772$	−1.75379	−	4.06574i	−0.0631203	−	0.146329i
$773$	27.2264	−	9.90961i	0.979267	−	0.356424i	0.197712	−	0.980260i	$-0.436649\pi$
$773$	27.2264	−	9.90961i	0.979267	−	0.356424i	0.781555	+	0.623836i	$0.214427\pi$
$774$		0			0
$775$	−7.95251	−	2.89448i	−0.285663	−	0.103973i
$776$	−0.979818	−	16.8228i	−0.0351734	−	0.603904i
$777$		0			0
$778$	6.94285	−	16.0953i	0.248913	−	0.577046i
$779$	1.73040	−	29.7099i	0.0619981	−	1.06447i
$780$		0			0
$781$	4.82210	+	5.11113i	0.172548	+	0.182891i
$782$	2.72251	−	4.71553i	0.0973568	−	0.168627i
$783$		0			0
$784$	−7.76286	−	13.4457i	−0.277245	−	0.480203i
$785$	10.4315	−	34.8436i	0.372316	−	1.24362i
$786$		0			0
$787$	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
$789$		0			0
$790$	13.3728	+	6.71607i	0.475783	+	0.238947i
$791$	2.11382	+	11.9881i	0.0751588	+	0.426247i
$792$		0			0
$793$	−5.07523	+	28.7830i	−0.180227	+	1.02212i
$794$	−11.2403	+	15.0984i	−0.398904	+	0.535821i
$795$		0			0
$796$	10.4360	−	11.0615i	0.369894	−	0.392064i
$797$	5.04957	+	16.8667i	0.178865	+	0.597450i	0.999656	+	0.0262221i	$0.00834772\pi$
$797$	5.04957	+	16.8667i	0.178865	+	0.597450i	−0.820791	+	0.571228i	$0.806467\pi$
$798$		0			0
$799$	−33.1527	−	3.87500i	−1.17286	−	0.137088i
$800$	5.80261	+	4.86896i	0.205153	+	0.172144i
$801$		0			0
$802$	7.20573	−	6.04632i	0.254443	−	0.213503i
$803$	11.6885	−	7.68764i	0.412478	−	0.271291i
$804$		0			0
$805$	−15.4060	−	20.6939i	−0.542991	−	0.729364i
$806$	−12.3109	+	6.18277i	−0.433633	+	0.217779i
$807$		0			0
$808$	−4.82863	+	1.14441i	−0.169871	+	0.0402601i
$809$	13.3577			0.469632			0.234816	−	0.972040i	$-0.424551\pi$
$809$	13.3577			0.469632			0.234816	+	0.972040i	$0.424551\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	−4.78437	+	2.40280i	−0.167692	+	0.0842182i
$815$	12.0901	+	16.2398i	0.423498	+	0.568857i
$816$		0			0
$817$	−21.4818	+	14.1288i	−0.751552	+	0.494304i
$818$	1.57767	−	1.32382i	0.0551619	−	0.0462863i
$819$		0			0
$820$	−27.2241	−	22.8438i	−0.950708	−	0.797739i
$821$	9.97247	+	1.16561i	0.348041	+	0.0406802i	0.288318	−	0.957535i	$-0.406904\pi$
$821$	9.97247	+	1.16561i	0.348041	+	0.0406802i	0.0597236	+	0.998215i	$0.480978\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	18.4701	−	24.8096i	0.642656	−	0.863237i
$827$	8.16805	−	46.3233i	0.284031	−	1.61082i	−0.424695	−	0.905336i	$-0.639619\pi$
$827$	8.16805	−	46.3233i	0.284031	−	1.61082i	0.708726	−	0.705483i	$-0.249270\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	2.15274	−	0.251619i	0.0746329	−	0.00872333i
$833$	−27.3056	−	17.9592i	−0.946084	−	0.622249i
$834$		0			0
$835$	12.1701	−	40.6511i	0.421165	−	1.40679i
$836$	7.60767	+	13.1769i	0.263117	+	0.455731i
$837$		0			0
$838$	−2.26555	+	3.92405i	−0.0782622	+	0.135554i
$839$	25.2637	+	26.7780i	0.872201	+	0.924479i	0.997712	−	0.0676133i	$-0.0215384\pi$
$839$	25.2637	+	26.7780i	0.872201	+	0.924479i	−0.125511	+	0.992092i	$0.540057\pi$
$840$		0			0
$841$	−0.115799	+	1.98820i	−0.00399308	+	0.0685585i
$842$	−3.91165	+	9.06823i	−0.134804	+	0.312512i
$843$		0			0
$844$	1.77880	+	30.5409i	0.0612289	+	1.05126i
$845$	5.86198	+	2.13359i	0.201658	+	0.0733976i
$846$		0			0
$847$	8.63568	−	3.14313i	0.296725	−	0.107999i
$848$	0.00613688	+	0.0142269i	0.000210741	+	0.000488553i
$849$		0			0
$850$	2.79685	+	0.662866i	0.0959312	+	0.0227361i
$851$	−6.64110	−	1.57397i	−0.227654	−	0.0539550i
$852$		0			0
$853$	−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
$855$		0			0
$856$	−31.5810	−	11.4945i	−1.07942	−	0.392875i
$857$	1.75026	+	30.0508i	0.0597877	+	1.02652i	0.886156	+	0.463386i	$0.153366\pi$
$857$	1.75026	+	30.0508i	0.0597877	+	1.02652i	−0.826369	+	0.563129i	$0.809597\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	14.0092	+	14.8489i	0.477155	+	0.505755i
$863$	−14.3566	+	24.8664i	−0.488706	+	0.846463i	−0.999916	−	0.0129930i	$-0.995864\pi$
$863$	−14.3566	+	24.8664i	−0.488706	+	0.846463i	0.511210	+	0.859456i	$0.329197\pi$
$864$		0			0
$865$	8.44932	+	14.6347i	0.287286	+	0.497593i
$866$	5.45716	−	18.2282i	0.185442	−	0.619419i
$867$		0			0
$868$	34.4792	+	22.6774i	1.17030	+	0.769720i
$869$	26.4711	−	3.09403i	0.897971	−	0.104958i
$870$		0			0
$871$	−16.9407	−	8.50796i	−0.574015	−	0.288281i
$872$	−5.48453	−	31.1043i	−0.185730	−	1.05333i
$873$		0			0
$874$	0.942844	−	5.34714i	0.0318922	−	0.180870i
$875$	−22.7274	+	30.5282i	−0.768325	+	1.03204i
$876$		0			0
$877$	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
$879$		0			0
$880$	11.5808	+	1.35360i	0.390389	+	0.0456299i
$881$	−35.7695	−	30.0142i	−1.20510	−	1.01120i	−0.999469	−	0.0325741i	$-0.989630\pi$
$881$	−35.7695	−	30.0142i	−1.20510	−	1.01120i	−0.205635	−	0.978629i	$-0.565926\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	1.05355	+	1.41516i	0.0353945	+	0.0475431i
$887$	9.26435	−	4.65273i	0.311066	−	0.156223i	−0.286416	−	0.958105i	$-0.592464\pi$
$887$	9.26435	−	4.65273i	0.311066	−	0.156223i	0.597483	+	0.801882i	$0.296168\pi$
$888$		0			0
$889$	48.1419	−	11.4098i	1.61463	−	0.382674i
$890$	20.7730			0.696312
$891$		0			0
$892$	25.2612			0.845809
$893$	−32.3868	+	7.67582i	−1.08378	+	0.256862i
$894$		0			0
$895$	34.1540	−	17.1528i	1.14164	−	0.573355i
$896$	−27.1468	−	36.4645i	−0.906911	−	1.21819i
$897$		0			0
$898$	−23.0070	+	15.1320i	−0.767755	+	0.504960i
$899$	−27.3900	+	22.9829i	−0.913508	+	0.766524i
$900$		0			0
$901$	0.0249850	+	0.0209649i	0.000832370	+	0.000698441i
$902$	17.5977	+	2.05688i	0.585940	+	0.0684865i
$903$		0			0
$904$	2.00049	+	6.68209i	0.0665352	+	0.222243i
$905$	9.66786	−	10.2473i	0.321371	−	0.340633i
$906$		0			0
$907$	−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
$909$		0			0
$910$	−3.84964	−	21.8324i	−0.127614	−	0.723737i
$911$	5.68443	+	2.85483i	0.188334	+	0.0945846i	0.540467	−	0.841365i	$-0.318247\pi$
$911$	5.68443	+	2.85483i	0.188334	+	0.0945846i	−0.352134	+	0.935950i	$0.614544\pi$
$912$		0			0
$913$	10.8841	−	1.27217i	0.360210	−	0.0421026i
$914$	−4.23536	−	2.78564i	−0.140093	−	0.0921408i
$915$		0			0
$916$	−3.86735	+	12.9178i	−0.127781	+	0.426818i
$917$	−10.5602	−	18.2909i	−0.348730	−	0.604018i
$918$		0			0
$919$	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			0
$922$	0.847673	−	14.5540i	0.0279166	−	0.479310i
$923$	−3.04882	+	7.06797i	−0.100353	+	0.232645i
$924$		0			0
$925$	−0.209486	−	3.59673i	−0.00688785	−	0.118260i
$926$	−23.0942	−	8.40558i	−0.758921	−	0.276225i
$927$		0			0
$928$	30.0728	−	10.9456i	0.987189	−	0.359307i
$929$	17.7858	+	41.2322i	0.583535	+	1.35279i	0.912745	+	0.408529i	$0.133958\pi$
$929$	17.7858	+	41.2322i	0.583535	+	1.35279i	−0.329210	+	0.944257i	$0.606783\pi$
$930$		0			0
$931$	−31.7113	−	7.51573i	−1.03930	−	0.246318i
$932$	−22.7528	−	5.39251i	−0.745293	−	0.176638i
$933$		0			0
$934$	−2.17811	−	5.04943i	−0.0712700	−	0.165222i
$935$	23.0638	−	8.39454i	0.754267	−	0.274531i
$936$		0			0
$937$	−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
$939$		0			0
$940$	−15.7428	+	36.4960i	−0.513474	+	1.19037i
$941$	0.606271	−	10.4093i	0.0197639	−	0.339333i	−0.973903	−	0.226965i	$-0.927120\pi$
$941$	0.606271	−	10.4093i	0.0197639	−	0.339333i	0.993667	−	0.112367i	$-0.0358434\pi$
$942$		0			0
$943$	15.4996	+	16.4286i	0.504737	+	0.534990i
$944$	−8.90994	+	15.4325i	−0.289994	+	0.502284i
$945$		0			0
$946$	−7.65361	−	13.2564i	−0.248840	−	0.431004i
$947$	12.9484	−	43.2508i	0.420767	−	1.40546i	−0.440703	−	0.897653i	$-0.645271\pi$
$947$	12.9484	−	43.2508i	0.420767	−	1.40546i	0.861470	−	0.507808i	$-0.169544\pi$
$948$		0			0
$949$	12.8041	+	8.42138i	0.415638	+	0.273370i
$950$	2.84682	−	0.332745i	0.0923630	−	0.0107957i
$951$		0			0
$952$	−28.5572	−	14.3420i	−0.925544	−	0.464826i
$953$	−5.08752	−	28.8527i	−0.164801	−	0.934632i	−0.949270	−	0.314463i	$-0.898175\pi$
$953$	−5.08752	−	28.8527i	−0.164801	−	0.934632i	0.784469	−	0.620168i	$-0.212936\pi$
$954$		0			0
$955$	1.87491	−	10.6331i	0.0606705	−	0.344080i
$956$	−3.36901	+	4.52537i	−0.108962	+	0.146361i
$957$		0			0
$958$	1.15869	−	1.22814i	0.0374356	−	0.0396794i
$959$	2.24199	+	7.48877i	0.0723977	+	0.241825i
$960$		0			0
$961$	−10.1815	−	1.19005i	−0.328435	−	0.0383886i
$962$	−4.49273	−	3.76985i	−0.144851	−	0.121545i
$963$		0			0
$964$	27.4013	−	22.9924i	0.882536	−	0.740536i
$965$	−5.95071	+	3.91384i	−0.191560	+	0.125991i
$966$		0			0
$967$	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
$969$		0			0
$970$	−11.5686	+	2.74180i	−0.371444	+	0.0880340i
$971$	−45.6691			−1.46559			−0.732795	−	0.680449i	$-0.761785\pi$
$971$	−45.6691			−1.46559			−0.732795	+	0.680449i	$0.761785\pi$
$972$		0			0
$973$	38.4797			1.23360
$974$	10.5302	−	2.49570i	0.337409	−	0.0799673i
$975$		0			0
$976$	12.6184	−	6.33719i	0.403905	−	0.202848i
$977$	0.740310	+	0.994408i	0.0236846	+	0.0318139i	0.813808	−	0.581134i	$-0.197391\pi$
$977$	0.740310	+	0.994408i	0.0236846	+	0.0318139i	−0.790123	+	0.612948i	$0.789983\pi$
$978$		0			0
$979$	30.9096	−	20.3296i	0.987877	−	0.649737i
$980$	−29.8126	+	25.0157i	−0.952329	+	0.799099i
$981$		0			0
$982$	18.4847	+	15.5105i	0.589869	+	0.494959i
$983$	−36.3380	−	4.24731i	−1.15900	−	0.135468i	−0.485217	−	0.874394i	$-0.661259\pi$
$983$	−36.3380	−	4.24731i	−1.15900	−	0.135468i	−0.673787	+	0.738926i	$0.735333\pi$
$984$		0			0
$985$	−15.3173	−	51.1634i	−0.488050	−	1.63020i
$986$	8.33360	−	8.83310i	0.265396	−	0.281303i
$987$		0			0
$988$	−9.95317	+	13.3694i	−0.316652	+	0.425338i
$989$	3.38850	−	19.2172i	0.107748	−	0.611070i
$990$		0			0
$991$	−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
$993$		0			0
$994$	−6.41116	+	0.749358i	−0.203350	+	0.0237682i
$995$	−20.4376	−	13.4420i	−0.647916	−	0.426141i
$996$		0			0
$997$	−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
$999$		0			0

Twists

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

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

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.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.643544 - 0.152523i) q^{2} +(-1.39638 + 0.701288i) q^{4} +(1.50096 + 2.01613i) q^{5} +(-3.43556 + 2.25960i) q^{7} +(-1.80495 + 1.51453i) q^{8} +(1.27344 + 1.06854i) q^{10} +(2.94058 + 0.343704i) q^{11} +(0.930150 + 3.10692i) q^{13} +(-1.86629 + 1.97816i) q^{14} +(0.935660 - 1.25681i) q^{16} +(0.572741 - 3.24818i) q^{17} +(-0.571121 - 3.23899i) q^{19} +(-3.50979 - 1.76268i) q^{20} +(1.94481 - 0.227316i) q^{22} +(2.08548 + 1.37164i) q^{23} +(-0.377908 + 1.26230i) q^{25} +(1.07247 + 1.85757i) q^{26} +(3.21271 - 5.56458i) q^{28} +(3.82031 + 4.04929i) q^{29} +(-0.373446 + 6.41181i) q^{31} +(2.27693 - 5.27851i) q^{32} +(-0.126837 - 2.17770i) q^{34} +(-9.71228 - 3.53498i) q^{35} +(-2.56937 + 0.935175i) q^{37} +(-0.861562 - 1.99733i) q^{38} +(-5.76265 - 1.36577i) q^{40} +(8.80462 + 2.08673i) q^{41} +(-3.09638 - 7.17822i) q^{43} +(-4.34719 + 1.58225i) q^{44} +(1.55131 + 0.564629i) q^{46} +(-0.588422 - 10.1028i) q^{47} +(3.92470 - 9.09847i) q^{49} +(-0.0506710 + 0.869987i) q^{50} +(-3.47769 - 3.68613i) q^{52} +(-0.00494432 + 0.00856381i) q^{53} +(3.72072 + 6.44448i) q^{55} +(2.77877 - 9.28173i) q^{56} +(3.07615 + 2.02322i) q^{58} +(-11.2961 + 1.32033i) q^{59} +(8.05332 + 4.04453i) q^{61} +(0.737619 + 4.18325i) q^{62} +(0.116049 - 0.658144i) q^{64} +(-4.86785 + 6.53865i) q^{65} +(-4.01126 + 4.25169i) q^{67} +(1.47814 + 4.93734i) q^{68} +(-6.78945 - 0.793572i) q^{70} +(1.81817 + 1.52563i) q^{71} +(3.61987 - 3.03743i) q^{73} +(-1.51087 + 0.993715i) q^{74} +(3.06897 + 4.12234i) q^{76} +(-10.8792 + 5.46372i) q^{77} +(8.75936 - 2.07601i) q^{79} +3.93828 q^{80} +5.98444 q^{82} +(3.60157 - 0.853588i) q^{83} +(7.40842 - 3.72065i) q^{85} +(-3.08750 - 4.14723i) q^{86} +(-5.82815 + 3.83323i) q^{88} +(9.57258 - 8.03235i) q^{89} +(-10.2160 - 8.57223i) q^{91} +(-3.87404 - 0.452810i) q^{92} +(-1.91958 - 6.41186i) q^{94} +(5.67301 - 6.01304i) q^{95} +(-4.27084 + 5.73673i) q^{97} +(1.13799 - 6.45388i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

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Database

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