LMFDB - Embedded newform 243.2.e.b.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.1
Root			$0.500000 - 1.27297i$ of defining polynomial
Character	$\chi$	$=$	243.28
Dual form			243.2.e.b.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.291887 - 1.65538i) q^{2} +(-0.775684 + 0.282326i) q^{4} +(0.865281 + 0.726057i) q^{5} +(3.67319 + 1.33693i) q^{7} +(-0.987144 - 1.70978i) q^{8} +O(q^{10})$	\(q+(-0.291887 - 1.65538i) q^{2} +(-0.775684 + 0.282326i) q^{4} +(0.865281 + 0.726057i) q^{5} +(3.67319 + 1.33693i) q^{7} +(-0.987144 - 1.70978i) q^{8} +(0.949332 - 1.64429i) q^{10} +(1.43285 - 1.20231i) q^{11} +(-0.127214 + 0.721468i) q^{13} +(1.14097 - 6.47073i) q^{14} +(-3.80689 + 3.19436i) q^{16} +(0.944822 - 1.63648i) q^{17} +(-1.37143 - 2.37538i) q^{19} +(-0.876169 - 0.318900i) q^{20} +(-2.40850 - 2.02097i) q^{22} +(-5.47625 + 1.99319i) q^{23} +(-0.646688 - 3.66755i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(0.923797 + 5.23911i) q^{29} +(-1.25975 + 0.458512i) q^{31} +(3.37426 + 2.83134i) q^{32} +(-2.98477 - 1.08637i) q^{34} +(2.20765 + 3.82376i) q^{35} +(-1.69806 + 2.94112i) q^{37} +(-3.53185 + 2.96357i) q^{38} +(0.387244 - 2.19617i) q^{40} +(-0.311930 + 1.76904i) q^{41} +(3.85332 - 3.23332i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(1.60563 + 0.584402i) q^{47} +(6.34260 + 5.32207i) q^{49} +(-5.88242 + 2.14102i) q^{50} +(-0.105011 - 0.595547i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(-1.34010 - 7.60010i) q^{56} +(8.40305 - 3.05846i) q^{58} +(8.62570 + 7.23782i) q^{59} +(-4.91543 - 1.78907i) q^{61} +(1.12672 + 1.95153i) q^{62} +(-1.26751 + 2.19540i) q^{64} +(-0.633903 + 0.531908i) q^{65} +(-0.328026 + 1.86033i) q^{67} +(-0.270863 + 1.53614i) q^{68} +(5.68538 - 4.77060i) q^{70} +(-6.09193 + 10.5515i) q^{71} +(-4.94384 - 8.56298i) q^{73} +(5.36430 + 1.95245i) q^{74} +(1.73443 + 1.45536i) q^{76} +(6.87053 - 2.50067i) q^{77} +(2.14505 + 12.1652i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(2.02876 + 11.5057i) q^{83} +(2.00571 - 0.730020i) q^{85} +(-6.47709 - 5.43493i) q^{86} +(-3.47012 - 1.26302i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(3.68511 - 3.09217i) q^{92} +(0.498741 - 2.82850i) q^{94} +(0.537993 - 3.05111i) q^{95} +(-0.263043 + 0.220719i) q^{97} +(6.95870 - 12.0528i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28} - 30 q^{29} - 15 q^{31} + 27 q^{32} - 9 q^{34} - 12 q^{35} - 3 q^{37} + 12 q^{38} - 6 q^{40} + 21 q^{41} + 12 q^{43} - 3 q^{44} - 3 q^{46} - 3 q^{47} + 21 q^{49} - 12 q^{50} + 36 q^{52} + 18 q^{53} - 12 q^{55} - 3 q^{56} + 30 q^{58} - 15 q^{59} + 21 q^{61} + 12 q^{62} + 12 q^{64} + 24 q^{65} + 21 q^{67} + 18 q^{68} + 30 q^{70} - 27 q^{71} + 6 q^{73} + 12 q^{74} + 42 q^{76} + 3 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 33 q^{83} - 9 q^{85} + 30 q^{86} - 12 q^{88} - 9 q^{89} + 6 q^{91} - 42 q^{92} - 33 q^{94} - 30 q^{95} - 42 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.291887	−	1.65538i	−0.206396	−	1.17053i	−0.895229	−	0.445607i	$-0.852988\pi$
$2$	−0.291887	−	1.65538i	−0.206396	−	1.17053i	0.688833	−	0.724920i	$-0.258123\pi$
$3$		0			0
$3$		0			0
$4$	−0.775684	+	0.282326i	−0.387842	+	0.141163i
$5$	0.865281	+	0.726057i	0.386965	+	0.324703i	0.815430	−	0.578856i	$-0.196501\pi$
$5$	0.865281	+	0.726057i	0.386965	+	0.324703i	−0.428464	+	0.903559i	$0.640945\pi$
$6$		0			0
$7$	3.67319	+	1.33693i	1.38833	+	0.505312i	0.924694	−	0.380712i	$-0.124321\pi$
$7$	3.67319	+	1.33693i	1.38833	+	0.505312i	0.463640	+	0.886024i	$0.346543\pi$
$8$	−0.987144	−	1.70978i	−0.349008	−	0.604500i
$9$		0			0
$10$	0.949332	−	1.64429i	0.300205	−	0.519971i
$11$	1.43285	−	1.20231i	0.432021	−	0.362509i	−0.400693	−	0.916213i	$-0.631230\pi$
$11$	1.43285	−	1.20231i	0.432021	−	0.362509i	0.832714	+	0.553704i	$0.186786\pi$
$12$		0			0
$13$	−0.127214	+	0.721468i	−0.0352829	+	0.200099i	−0.997354	−	0.0727001i	$-0.976838\pi$
$13$	−0.127214	+	0.721468i	−0.0352829	+	0.200099i	0.962071	+	0.272799i	$0.0879495\pi$
$14$	1.14097	−	6.47073i	0.304936	−	1.72938i
$15$		0			0
$16$	−3.80689	+	3.19436i	−0.951722	+	0.798589i
$17$	0.944822	−	1.63648i	0.229153	−	0.396905i	−0.728404	−	0.685147i	$-0.759738\pi$
$17$	0.944822	−	1.63648i	0.229153	−	0.396905i	0.957557	+	0.288243i	$0.0930711\pi$
$18$		0			0
$19$	−1.37143	−	2.37538i	−0.314627	−	0.544950i	0.664731	−	0.747083i	$-0.268546\pi$
$19$	−1.37143	−	2.37538i	−0.314627	−	0.544950i	−0.979358	+	0.202133i	$0.935213\pi$
$20$	−0.876169	−	0.318900i	−0.195917	−	0.0713081i
$21$		0			0
$22$	−2.40850	−	2.02097i	−0.513494	−	0.430872i
$23$	−5.47625	+	1.99319i	−1.14188	+	0.415609i	−0.842591	−	0.538555i	$-0.818971\pi$
$23$	−5.47625	+	1.99319i	−1.14188	+	0.415609i	−0.299286	+	0.954164i	$0.596748\pi$
$24$		0			0
$25$	−0.646688	−	3.66755i	−0.129338	−	0.733510i
$26$	1.23143			0.241504
$27$		0			0
$28$	−3.22668			−0.609786
$29$	0.923797	+	5.23911i	0.171545	+	0.972879i	0.942057	+	0.335453i	$0.108890\pi$
$29$	0.923797	+	5.23911i	0.171545	+	0.972879i	−0.770512	+	0.637426i	$0.779999\pi$
$30$		0			0
$31$	−1.25975	+	0.458512i	−0.226258	+	0.0823513i	−0.452662	−	0.891682i	$-0.649525\pi$
$31$	−1.25975	+	0.458512i	−0.226258	+	0.0823513i	0.226403	+	0.974034i	$0.427303\pi$
$32$	3.37426	+	2.83134i	0.596490	+	0.500514i
$33$		0			0
$34$	−2.98477	−	1.08637i	−0.511884	−	0.186310i
$35$	2.20765	+	3.82376i	0.373161	+	0.646334i
$36$		0			0
$37$	−1.69806	+	2.94112i	−0.279159	+	0.483517i	−0.971176	−	0.238364i	$-0.923389\pi$
$37$	−1.69806	+	2.94112i	−0.279159	+	0.483517i	0.692017	+	0.721881i	$0.256722\pi$
$38$	−3.53185	+	2.96357i	−0.572941	+	0.480755i
$39$		0			0
$40$	0.387244	−	2.19617i	0.0612286	−	0.347245i
$41$	−0.311930	+	1.76904i	−0.0487153	+	0.276278i	−0.999429	−	0.0337924i	$-0.989241\pi$
$41$	−0.311930	+	1.76904i	−0.0487153	+	0.276278i	0.950714	+	0.310070i	$0.100353\pi$
$42$		0			0
$43$	3.85332	−	3.23332i	0.587626	−	0.493077i	−0.299816	−	0.953997i	$-0.596925\pi$
$43$	3.85332	−	3.23332i	0.587626	−	0.493077i	0.887441	+	0.460921i	$0.152481\pi$
$44$	−0.771999	+	1.33714i	−0.116383	+	0.201582i
$45$		0			0
$46$	4.89793	+	8.48346i	0.722160	+	1.25082i
$47$	1.60563	+	0.584402i	0.234205	+	0.0852438i	0.456457	−	0.889746i	$-0.349118\pi$
$47$	1.60563	+	0.584402i	0.234205	+	0.0852438i	−0.222251	+	0.974989i	$0.571341\pi$
$48$		0			0
$49$	6.34260	+	5.32207i	0.906086	+	0.760296i
$50$	−5.88242	+	2.14102i	−0.831899	+	0.302787i
$51$		0			0
$52$	−0.105011	−	0.595547i	−0.0145624	−	0.0825875i
$53$	−2.84494			−0.390783			−0.195391	−	0.980725i	$-0.562598\pi$
$53$	−2.84494			−0.390783			−0.195391	+	0.980725i	$0.562598\pi$
$54$		0			0
$55$	2.11276			0.284885
$56$	−1.34010	−	7.60010i	−0.179079	−	1.01561i
$57$		0			0
$58$	8.40305	−	3.05846i	1.10338	−	0.401596i
$59$	8.62570	+	7.23782i	1.12297	+	0.942284i	0.998751	−	0.0499712i	$-0.0159130\pi$
$59$	8.62570	+	7.23782i	1.12297	+	0.942284i	0.124219	+	0.992255i	$0.460357\pi$
$60$		0			0
$61$	−4.91543	−	1.78907i	−0.629357	−	0.229067i	0.00759462	−	0.999971i	$-0.497583\pi$
$61$	−4.91543	−	1.78907i	−0.629357	−	0.229067i	−0.636951	+	0.770904i	$0.719805\pi$
$62$	1.12672	+	1.95153i	0.143093	+	0.247844i
$63$		0			0
$64$	−1.26751	+	2.19540i	−0.158439	+	0.274425i
$65$	−0.633903	+	0.531908i	−0.0786260	+	0.0659750i
$66$		0			0
$67$	−0.328026	+	1.86033i	−0.0400748	+	0.227275i	−0.998267	−	0.0588505i	$-0.981256\pi$
$67$	−0.328026	+	1.86033i	−0.0400748	+	0.227275i	0.958192	+	0.286126i	$0.0923676\pi$
$68$	−0.270863	+	1.53614i	−0.0328469	+	0.186284i
$69$		0			0
$70$	5.68538	−	4.77060i	0.679533	−	0.570195i
$71$	−6.09193	+	10.5515i	−0.722980	+	1.25224i	0.236821	+	0.971553i	$0.423895\pi$
$71$	−6.09193	+	10.5515i	−0.722980	+	1.25224i	−0.959800	+	0.280684i	$0.909439\pi$
$72$		0			0
$73$	−4.94384	−	8.56298i	−0.578633	−	1.00222i	−0.995637	−	0.0933164i	$-0.970253\pi$
$73$	−4.94384	−	8.56298i	−0.578633	−	1.00222i	0.417004	−	0.908905i	$-0.363080\pi$
$74$	5.36430	+	1.95245i	0.623587	+	0.226967i
$75$		0			0
$76$	1.73443	+	1.45536i	0.198952	+	0.166941i
$77$	6.87053	−	2.50067i	0.782970	−	0.284978i
$78$		0			0
$79$	2.14505	+	12.1652i	0.241337	+	1.36869i	0.828847	+	0.559475i	$0.188997\pi$
$79$	2.14505	+	12.1652i	0.241337	+	1.36869i	−0.587509	+	0.809217i	$0.699892\pi$
$80$	−5.61331			−0.627587
$81$		0			0
$82$	3.01948			0.333445
$83$	2.02876	+	11.5057i	0.222685	+	1.26291i	0.867061	+	0.498202i	$0.166006\pi$
$83$	2.02876	+	11.5057i	0.222685	+	1.26291i	−0.644376	+	0.764709i	$0.722883\pi$
$84$		0			0
$85$	2.00571	−	0.730020i	0.217550	−	0.0791818i
$86$	−6.47709	−	5.43493i	−0.698443	−	0.586063i
$87$		0			0
$88$	−3.47012	−	1.26302i	−0.369916	−	0.134638i
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	0.673331	−	0.739341i	$-0.264863\pi$
$89$	−2.86437	−	4.96123i	−0.303622	−	0.525889i	−0.976954	+	0.213452i	$0.931529\pi$
$90$		0			0
$91$	−1.43183	+	2.48001i	−0.150097	+	0.259976i
$92$	3.68511	−	3.09217i	0.384199	−	0.322381i
$93$		0			0
$94$	0.498741	−	2.82850i	0.0514412	−	0.291738i
$95$	0.537993	−	3.05111i	0.0551969	−	0.313037i
$96$		0			0
$97$	−0.263043	+	0.220719i	−0.0267080	+	0.0224107i	−0.656044	−	0.754723i	$-0.727771\pi$
$97$	−0.263043	+	0.220719i	−0.0267080	+	0.0224107i	0.629336	+	0.777133i	$0.283327\pi$
$98$	6.95870	−	12.0528i	0.702935	−	1.21752i
$99$		0			0
$100$	1.53707	+	2.66228i	0.153707	+	0.266228i
$101$	−16.3528	−	5.95192i	−1.62716	−	0.592238i	−0.642434	−	0.766341i	$-0.722075\pi$
$101$	−16.3528	−	5.95192i	−1.62716	−	0.592238i	−0.984727	+	0.174103i	$0.944297\pi$
$102$		0			0
$103$	−12.1135	−	10.1644i	−1.19357	−	1.00153i	−0.999790	−	0.0204842i	$-0.993479\pi$
$103$	−12.1135	−	10.1644i	−1.19357	−	1.00153i	−0.193785	−	0.981044i	$-0.562076\pi$
$104$	1.35913	−	0.494684i	0.133274	−	0.0485078i
$105$		0			0
$106$	0.830403	+	4.70945i	0.0806558	+	0.457422i
$107$	16.5298			1.59800			0.798999	−	0.601332i	$-0.205363\pi$
$107$	16.5298			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$108$		0			0
$109$	−4.71844			−0.451945			−0.225972	−	0.974134i	$-0.572556\pi$
$109$	−4.71844			−0.451945			−0.225972	+	0.974134i	$0.572556\pi$
$110$	−0.616689	−	3.49741i	−0.0587990	−	0.333465i
$111$		0			0
$112$	−18.2540	+	6.64393i	−1.72484	+	0.627792i
$113$	−15.2786	−	12.8203i	−1.43729	−	1.20603i	−0.941241	−	0.337737i	$-0.890339\pi$
$113$	−15.2786	−	12.8203i	−1.43729	−	1.20603i	−0.496051	−	0.868294i	$-0.665217\pi$
$114$		0			0
$115$	−6.18566	−	2.25140i	−0.576816	−	0.209944i
$116$	−2.19571	−	3.80308i	−0.203867	−	0.353108i
$117$		0			0
$118$	9.46357	−	16.3914i	0.871193	−	1.50895i
$119$	5.65836	−	4.74793i	0.518701	−	0.435242i
$120$		0			0
$121$	−1.30260	+	7.38743i	−0.118419	+	0.671585i
$122$	−1.52683	+	8.65909i	−0.138233	+	0.783957i
$123$		0			0
$124$	0.847720	−	0.711322i	0.0761275	−	0.0638786i
$125$	4.92714	−	8.53407i	0.440697	−	0.763310i
$126$		0			0
$127$	−0.534728	−	0.926176i	−0.0474495	−	0.0821849i	0.841325	−	0.540529i	$-0.181776\pi$
$127$	−0.534728	−	0.926176i	−0.0474495	−	0.0821849i	−0.888775	+	0.458344i	$0.848443\pi$
$128$	12.2825	+	4.47045i	1.08563	+	0.395136i
$129$		0			0
$130$	1.06554	+	0.894090i	0.0934536	+	0.0784169i
$131$	7.17953	−	2.61314i	0.627279	−	0.228311i	−0.00876780	−	0.999962i	$-0.502791\pi$
$131$	7.17953	−	2.61314i	0.627279	−	0.228311i	0.636046	+	0.771651i	$0.280569\pi$
$132$		0			0
$133$	−1.86179	−	10.5587i	−0.161438	−	0.915558i
$134$	3.17529			0.274303
$135$		0			0
$136$	−3.73070			−0.319905
$137$	−2.71768	−	15.4127i	−0.232187	−	1.31680i	−0.848457	−	0.529264i	$-0.822468\pi$
$137$	−2.71768	−	15.4127i	−0.232187	−	1.31680i	0.616270	−	0.787535i	$-0.288643\pi$
$138$		0			0
$139$	−8.13486	+	2.96085i	−0.689990	+	0.251136i	−0.663131	−	0.748504i	$-0.730773\pi$
$139$	−8.13486	+	2.96085i	−0.689990	+	0.251136i	−0.0268588	+	0.999639i	$0.508550\pi$
$140$	−2.79199	−	2.34275i	−0.235966	−	0.197999i
$141$		0			0
$142$	19.2449	+	7.00458i	1.61500	+	0.587811i
$143$	0.685146	+	1.18671i	0.0572948	+	0.0992375i
$144$		0			0
$145$	−3.00455	+	5.20403i	−0.249514	+	0.432172i
$146$	−12.7319	+	10.6833i	−1.05370	+	0.884159i
$147$		0			0
$148$	0.486801	−	2.76079i	0.0400148	−	0.226935i
$149$	0.427838	−	2.42639i	0.0350499	−	0.198778i	−0.962255	−	0.272150i	$-0.912265\pi$
$149$	0.427838	−	2.42639i	0.0350499	−	0.198778i	0.997305	+	0.0733727i	$0.0233763\pi$
$150$		0			0
$151$	−8.05374	+	6.75789i	−0.655404	+	0.549949i	−0.908705	−	0.417438i	$-0.862928\pi$
$151$	−8.05374	+	6.75789i	−0.655404	+	0.549949i	0.253301	+	0.967387i	$0.418484\pi$
$152$	−2.70760	+	4.68969i	−0.219615	+	0.380384i
$153$		0			0
$154$	−6.14497	−	10.6434i	−0.495176	−	0.857669i
$155$	−1.42295	−	0.517910i	−0.114294	−	0.0415995i
$156$		0			0
$157$	0.275737	+	0.231371i	0.0220062	+	0.0184654i	0.653724	−	0.756733i	$-0.273206\pi$
$157$	0.275737	+	0.231371i	0.0220062	+	0.0184654i	−0.631718	+	0.775198i	$0.717650\pi$
$158$	19.5119	−	7.10174i	1.55228	−	0.564984i
$159$		0			0
$160$	0.863968	+	4.89980i	0.0683026	+	0.387364i
$161$	−22.7800			−1.79532
$162$		0			0
$163$	14.6186			1.14502			0.572508	−	0.819899i	$-0.305971\pi$
$163$	14.6186			1.14502			0.572508	+	0.819899i	$0.305971\pi$
$164$	−0.257487	−	1.46028i	−0.0201064	−	0.114029i
$165$		0			0
$166$	18.4540	−	6.71672i	1.43231	−	0.521319i
$167$	−1.66680	−	1.39861i	−0.128981	−	0.108228i	0.576015	−	0.817439i	$-0.304607\pi$
$167$	−1.66680	−	1.39861i	−0.128981	−	0.108228i	−0.704996	+	0.709211i	$0.749051\pi$
$168$		0			0
$169$	11.7117	+	4.26270i	0.900898	+	0.327900i
$170$	−1.79390	−	3.10712i	−0.137586	−	0.238306i
$171$		0			0
$172$	−2.07611	+	3.59593i	−0.158302	+	0.274187i
$173$	13.4571	−	11.2919i	1.02313	−	0.858505i	0.0331087	−	0.999452i	$-0.489459\pi$
$173$	13.4571	−	11.2919i	1.02313	−	0.858505i	0.990017	+	0.140947i	$0.0450148\pi$
$174$		0			0
$175$	2.52785	−	14.3362i	0.191088	−	1.08371i
$176$	−1.61411	+	9.15408i	−0.121668	+	0.690015i
$177$		0			0
$178$	−7.37662	+	6.18972i	−0.552901	+	0.463939i
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	−0.846646	−	0.532157i	$-0.821382\pi$
$179$	0.502236	−	0.869898i	0.0375388	−	0.0650192i	0.884184	+	0.467138i	$0.154715\pi$
$180$		0			0
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	0.927859	+	0.372932i	$0.121647\pi$
$181$	10.5866	+	18.3366i	0.786898	+	1.36295i	−0.140961	+	0.990015i	$0.545019\pi$
$182$	4.52328	+	1.64634i	0.335288	+	0.122035i
$183$		0			0
$184$	8.81377	+	7.39563i	0.649760	+	0.545213i
$185$	−3.60472	+	1.31201i	−0.265024	+	0.0964609i
$186$		0			0
$187$	−0.613759	−	3.48080i	−0.0448825	−	0.254541i
$188$	−1.41045			−0.102868
$189$		0			0
$190$	−5.20776			−0.377811
$191$	1.70668	+	9.67907i	0.123491	+	0.700353i	0.982193	+	0.187877i	$0.0601605\pi$
$191$	1.70668	+	9.67907i	0.123491	+	0.700353i	−0.858702	+	0.512476i	$0.828728\pi$
$192$		0			0
$193$	10.4833	−	3.81561i	0.754604	−	0.274653i	0.0640621	−	0.997946i	$-0.479594\pi$
$193$	10.4833	−	3.81561i	0.754604	−	0.274653i	0.690542	+	0.723293i	$0.257372\pi$
$194$	0.442152	+	0.371010i	0.0317447	+	0.0266370i
$195$		0			0
$196$	−6.42241	−	2.33757i	−0.458744	−	0.166969i
$197$	4.54497	+	7.87212i	0.323816	+	0.560865i	0.981272	−	0.192628i	$-0.0617009\pi$
$197$	4.54497	+	7.87212i	0.323816	+	0.560865i	−0.657456	+	0.753493i	$0.728368\pi$
$198$		0			0
$199$	7.34694	−	12.7253i	0.520811	−	0.902071i	−0.478896	−	0.877872i	$-0.658963\pi$
$199$	7.34694	−	12.7253i	0.520811	−	0.902071i	0.999707	−	0.0241994i	$-0.00770367\pi$
$200$	−5.63235	+	4.72610i	−0.398267	+	0.334186i
$201$		0			0
$202$	−5.07950	+	28.8073i	−0.357392	+	2.02687i
$203$	−3.61105	+	20.4793i	−0.253446	+	1.43736i
$204$		0			0
$205$	−1.55433	+	1.30424i	−0.108559	+	0.0910920i
$206$	−13.2901	+	23.0192i	−0.925968	+	1.60382i
$207$		0			0
$208$	−1.82034	−	3.15292i	−0.126218	−	0.218615i
$209$	−4.82099	−	1.75470i	−0.333475	−	0.121375i
$210$		0			0
$211$	6.01981	+	5.05122i	0.414421	+	0.347740i	0.826036	−	0.563618i	$-0.190591\pi$
$211$	6.01981	+	5.05122i	0.414421	+	0.347740i	−0.411615	+	0.911358i	$0.635035\pi$
$212$	2.20678	−	0.803201i	0.151562	−	0.0551641i
$213$		0			0
$214$	−4.82485	−	27.3631i	−0.329820	−	1.87050i
$215$	5.68178			0.387494
$216$		0			0
$217$	−5.24030			−0.355735
$218$	1.37725	+	7.81079i	0.0932793	+	0.529013i
$219$		0			0
$220$	−1.63884	+	0.596488i	−0.110490	+	0.0402152i
$221$	1.06047	+	0.889842i	0.0713351	+	0.0598573i
$222$		0			0
$223$	8.21375	+	2.98956i	0.550033	+	0.200196i	0.602061	−	0.798450i	$-0.294346\pi$
$223$	8.21375	+	2.98956i	0.550033	+	0.200196i	−0.0520281	+	0.998646i	$0.516569\pi$
$224$	8.60897	+	14.9112i	0.575211	+	0.996295i
$225$		0			0
$226$	−16.7627	+	29.0339i	−1.11504	+	1.93131i
$227$	−3.11659	+	2.61513i	−0.206855	+	0.173572i	−0.740330	−	0.672244i	$-0.765331\pi$
$227$	−3.11659	+	2.61513i	−0.206855	+	0.173572i	0.533474	+	0.845816i	$0.320886\pi$
$228$		0			0
$229$	2.80544	−	15.9104i	0.185389	−	1.05139i	−0.740067	−	0.672534i	$-0.765206\pi$
$229$	2.80544	−	15.9104i	0.185389	−	1.05139i	0.925455	−	0.378857i	$-0.123683\pi$
$230$	−1.92139	+	10.8967i	−0.126693	+	0.718510i
$231$		0			0
$232$	8.04583	−	6.75126i	0.528235	−	0.443242i
$233$	8.60658	−	14.9070i	0.563836	−	0.976592i	−0.433321	−	0.901240i	$-0.642658\pi$
$233$	8.60658	−	14.9070i	0.563836	−	0.976592i	0.997157	−	0.0753527i	$-0.0240083\pi$
$234$		0			0
$235$	0.965013	+	1.67145i	0.0629505	+	0.109034i
$236$	−8.73424	−	3.17900i	−0.568550	−	0.206935i
$237$		0			0
$238$	−9.51121	−	7.98086i	−0.616520	−	0.517322i
$239$	−1.44284	+	0.525151i	−0.0933296	+	0.0339692i	−0.388263	−	0.921549i	$-0.626925\pi$
$239$	−1.44284	+	0.525151i	−0.0933296	+	0.0339692i	0.294933	+	0.955518i	$0.404703\pi$
$240$		0			0
$241$	−0.958828	−	5.43779i	−0.0617636	−	0.350279i	−0.999991	−	0.00425921i	$-0.998644\pi$
$241$	−0.958828	−	5.43779i	−0.0617636	−	0.350279i	0.938227	−	0.346019i	$-0.112467\pi$
$242$	12.6092			0.810549
$243$		0			0
$244$	4.31792			0.276427
$245$	1.62400	+	9.21018i	0.103754	+	0.588417i
$246$		0			0
$247$	1.88823	−	0.687259i	0.120145	−	0.0437292i
$248$	2.02752	+	1.70129i	0.128747	+	0.108032i
$249$		0			0
$250$	−15.5653	−	5.66529i	−0.984433	−	0.358304i
$251$	−10.7204	−	18.5683i	−0.676668	−	1.17202i	−0.975978	−	0.217868i	$-0.930090\pi$
$251$	−10.7204	−	18.5683i	−0.676668	−	1.17202i	0.299310	−	0.954156i	$-0.403244\pi$
$252$		0			0
$253$	−5.45023	+	9.44007i	−0.342653	+	0.593492i
$254$	−1.37709	+	1.15552i	−0.0864063	+	0.0725035i
$255$		0			0
$256$	2.93477	−	16.6439i	0.183423	−	1.04024i
$257$	2.56764	−	14.5618i	0.160165	−	0.908342i	−0.793745	−	0.608250i	$-0.791872\pi$
$257$	2.56764	−	14.5618i	0.160165	−	0.908342i	0.953910	−	0.300092i	$-0.0970173\pi$
$258$		0			0
$259$	−10.1693	+	8.53310i	−0.631893	+	0.530221i
$260$	0.341537	−	0.591560i	0.0211812	−	0.0366870i
$261$		0			0
$262$	−6.42133	−	11.1221i	−0.396711	−	0.687124i
$263$	2.63373	+	0.958600i	0.162403	+	0.0591098i	0.421942	−	0.906623i	$-0.361349\pi$
$263$	2.63373	+	0.958600i	0.162403	+	0.0591098i	−0.259539	+	0.965733i	$0.583571\pi$
$264$		0			0
$265$	−2.46167	−	2.06559i	−0.151219	−	0.126888i
$266$	−16.9352	+	6.16392i	−1.03837	+	0.377934i
$267$		0			0
$268$	−0.270774	−	1.53564i	−0.0165402	−	0.0938040i
$269$	0.356528			0.0217379			0.0108689	−	0.999941i	$-0.496540\pi$
$269$	0.356528			0.0217379			0.0108689	+	0.999941i	$0.496540\pi$
$270$		0			0
$271$	−12.1467			−0.737857			−0.368928	−	0.929458i	$-0.620275\pi$
$271$	−12.1467			−0.737857			−0.368928	+	0.929458i	$0.620275\pi$
$272$	1.63067	+	9.24799i	0.0988739	+	0.560742i
$273$		0			0
$274$	−24.7206	+	8.99756i	−1.49343	+	0.543563i
$275$	−5.33613	−	4.47754i	−0.321781	−	0.270006i
$276$		0			0
$277$	−23.4829	−	8.54707i	−1.41095	−	0.513544i	−0.479541	−	0.877519i	$-0.659197\pi$
$277$	−23.4829	−	8.54707i	−1.41095	−	0.513544i	−0.931408	+	0.363976i	$0.881419\pi$
$278$	7.27577	+	12.6020i	0.436372	+	0.755818i
$279$		0			0
$280$	4.35854	−	7.54921i	0.260473	−	0.451152i
$281$	−5.60964	+	4.70705i	−0.334643	+	0.280799i	−0.794589	−	0.607148i	$-0.792313\pi$
$281$	−5.60964	+	4.70705i	−0.334643	+	0.280799i	0.459945	+	0.887947i	$0.347869\pi$
$282$		0			0
$283$	−2.49847	+	14.1695i	−0.148518	+	0.842289i	0.815956	+	0.578114i	$0.196211\pi$
$283$	−2.49847	+	14.1695i	−0.148518	+	0.842289i	−0.964475	+	0.264176i	$0.914900\pi$
$284$	1.74644	−	9.90457i	0.103632	−	0.587728i
$285$		0			0
$286$	1.76446	−	1.48056i	0.104335	−	0.0875473i
$287$	−3.51086	+	6.08099i	−0.207240	+	0.358950i
$288$		0			0
$289$	6.71462	+	11.6301i	0.394978	+	0.684122i
$290$	9.49162	+	3.45467i	0.557367	+	0.202865i
$291$		0			0
$292$	6.25241	+	5.24639i	0.365895	+	0.307022i
$293$	−13.5461	+	4.93039i	−0.791374	+	0.288037i	−0.705907	−	0.708304i	$-0.749460\pi$
$293$	−13.5461	+	4.93039i	−0.791374	+	0.288037i	−0.0854672	+	0.996341i	$0.527238\pi$
$294$		0			0
$295$	2.20858	+	12.5255i	0.128589	+	0.729262i
$296$	6.70491			0.389715
$297$		0			0
$298$	−4.14147			−0.239909
$299$	−0.741367	−	4.20450i	−0.0428743	−	0.243152i
$300$		0			0
$301$	18.4767	−	6.72496i	1.06498	−	0.387620i
$302$	13.5376	+	11.3594i	0.779003	+	0.653661i
$303$		0			0
$304$	12.8087	+	4.66198i	0.734629	+	0.267383i
$305$	−2.95426	−	5.11693i	−0.169161	−	0.292995i
$306$		0			0
$307$	15.2163	−	26.3554i	0.868440	−	1.50418i	0.00484869	−	0.999988i	$-0.498457\pi$
$307$	15.2163	−	26.3554i	0.868440	−	1.50418i	0.863591	−	0.504193i	$-0.168210\pi$
$308$	−4.62336	+	3.87946i	−0.263440	+	0.221053i
$309$		0			0
$310$	−0.441996	+	2.50668i	−0.0251037	+	0.142370i
$311$	2.43031	−	13.7830i	0.137810	−	0.781561i	−0.835051	−	0.550172i	$-0.814562\pi$
$311$	2.43031	−	13.7830i	0.137810	−	0.781561i	0.972861	−	0.231389i	$-0.0743269\pi$
$312$		0			0
$313$	16.9201	−	14.1976i	0.956378	−	0.802497i	−0.0239820	−	0.999712i	$-0.507634\pi$
$313$	16.9201	−	14.1976i	0.956378	−	0.802497i	0.980360	+	0.197216i	$0.0631900\pi$
$314$	0.302521	−	0.523982i	0.0170722	−	0.0295700i
$315$		0			0
$316$	−5.09844	−	8.83075i	−0.286810	−	0.496769i
$317$	16.3401	+	5.94729i	0.917749	+	0.334033i	0.757343	−	0.653018i	$-0.226497\pi$
$317$	16.3401	+	5.94729i	0.917749	+	0.334033i	0.160406	+	0.987051i	$0.448720\pi$
$318$		0			0
$319$	7.62268	+	6.39619i	0.426788	+	0.358118i
$320$	−2.69074	+	0.979350i	−0.150417	+	0.0547473i
$321$		0			0
$322$	6.64920	+	37.7095i	0.370545	+	2.10147i
$323$	−5.18302			−0.288391
$324$		0			0
$325$	2.72829			0.151338
$326$	−4.26698	−	24.1992i	−0.236326	−	1.34027i
$327$		0			0
$328$	3.33260	−	1.21297i	0.184012	−	0.0669749i
$329$	5.11648	+	4.29323i	0.282081	+	0.236694i
$330$		0			0
$331$	−0.812033	−	0.295556i	−0.0446334	−	0.0162452i	0.319607	−	0.947550i	$-0.396449\pi$
$331$	−0.812033	−	0.295556i	−0.0446334	−	0.0162452i	−0.364240	+	0.931305i	$0.618671\pi$
$332$	−4.82203	−	8.35199i	−0.264643	−	0.458375i
$333$		0			0
$334$	−1.82870	+	3.16741i	−0.100062	+	0.173313i
$335$	−1.63454	+	1.37154i	−0.0893045	+	0.0749353i
$336$		0			0
$337$	0.0726768	−	0.412171i	0.00395896	−	0.0224524i	−0.982764	−	0.184863i	$-0.940816\pi$
$337$	0.0726768	−	0.412171i	0.00395896	−	0.0224524i	0.986723	+	0.162411i	$0.0519269\pi$
$338$	3.63788	−	20.6314i	0.197875	−	1.12220i
$339$		0			0
$340$	−1.34970	+	1.13253i	−0.0731976	+	0.0614200i
$341$	−1.25377	+	2.17159i	−0.0678953	+	0.117598i
$342$		0			0
$343$	2.50108	+	4.33199i	0.135046	+	0.233906i
$344$	−9.33206	−	3.39659i	−0.503151	−	0.183132i
$345$		0			0
$346$	−22.6202	−	18.9806i	−1.21607	−	1.02041i
$347$	21.9980	−	8.00660i	1.18091	−	0.429817i	0.324388	−	0.945924i	$-0.394841\pi$
$347$	21.9980	−	8.00660i	1.18091	−	0.429817i	0.856524	+	0.516107i	$0.172619\pi$
$348$		0			0
$349$	3.67724	+	20.8547i	0.196838	+	1.11633i	0.909776	+	0.415099i	$0.136253\pi$
$349$	3.67724	+	20.8547i	0.196838	+	1.11633i	−0.712938	+	0.701227i	$0.752636\pi$
$350$	−24.4696			−1.30796
$351$		0			0
$352$	8.23894			0.439137
$353$	−4.08845	−	23.1868i	−0.217606	−	1.23411i	−0.876326	−	0.481719i	$-0.840013\pi$
$353$	−4.08845	−	23.1868i	−0.217606	−	1.23411i	0.658720	−	0.752389i	$-0.271098\pi$
$354$		0			0
$355$	−12.9323	+	4.70696i	−0.686373	+	0.249819i
$356$	3.62253	+	3.03966i	0.191994	+	0.161102i
$357$		0			0
$358$	−1.58660	−	0.577476i	−0.0838546	−	0.0305206i
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	0.694347	−	0.719640i	$-0.255693\pi$
$359$	−5.23047	−	9.05943i	−0.276053	−	0.478139i	−0.970400	+	0.241502i	$0.922360\pi$
$360$		0			0
$361$	5.73837	−	9.93915i	0.302019	−	0.523113i
$362$	27.2638	−	22.8771i	1.43295	−	1.20239i
$363$		0			0
$364$	0.410480	−	2.32795i	0.0215150	−	0.122018i
$365$	1.93940	−	10.9989i	0.101513	−	0.575708i
$366$		0			0
$367$	16.2848	−	13.6646i	0.850059	−	0.713284i	−0.109744	−	0.993960i	$-0.535003\pi$
$367$	16.2848	−	13.6646i	0.850059	−	0.713284i	0.959803	+	0.280676i	$0.0905586\pi$
$368$	14.4805	−	25.0809i	0.754848	−	1.30743i
$369$		0			0
$370$	3.22404	+	5.58420i	0.167610	+	0.290309i
$371$	−10.4500	−	3.80349i	−0.542537	−	0.197467i
$372$		0			0
$373$	1.76963	+	1.48489i	0.0916279	+	0.0768849i	0.687451	−	0.726231i	$-0.258730\pi$
$373$	1.76963	+	1.48489i	0.0916279	+	0.0768849i	−0.595823	+	0.803116i	$0.703174\pi$
$374$	−5.58288	+	2.03200i	−0.288684	+	0.105072i
$375$		0			0
$376$	−0.585789	−	3.32217i	−0.0302097	−	0.171328i
$377$	−3.89737			−0.200725
$378$		0			0
$379$	12.5539			0.644850			0.322425	−	0.946595i	$-0.395502\pi$
$379$	12.5539			0.644850			0.322425	+	0.946595i	$0.395502\pi$
$380$	0.444095	+	2.51859i	0.0227816	+	0.129201i
$381$		0			0
$382$	15.5243	−	5.65039i	0.794294	−	0.289099i
$383$	15.0562	+	12.6337i	0.769338	+	0.645551i	0.940539	−	0.339685i	$-0.110320\pi$
$383$	15.0562	+	12.6337i	0.769338	+	0.645551i	−0.171201	+	0.985236i	$0.554765\pi$
$384$		0			0
$385$	7.76057	+	2.82462i	0.395515	+	0.143956i
$386$	−9.37620	−	16.2401i	−0.477236	−	0.826597i
$387$		0			0
$388$	0.141724	−	0.245472i	0.00719492	−	0.0124620i
$389$	14.4343	−	12.1118i	0.731846	−	0.614092i	−0.198788	−	0.980042i	$-0.563701\pi$
$389$	14.4343	−	12.1118i	0.731846	−	0.614092i	0.930634	+	0.365951i	$0.119256\pi$
$390$		0			0
$391$	−1.91226	+	10.8450i	−0.0967072	+	0.548454i
$392$	2.83854	−	16.0981i	0.143368	−	0.813079i
$393$		0			0
$394$	11.7047	−	9.82140i	0.589674	−	0.494795i
$395$	−6.97656	+	12.0838i	−0.351029	+	0.608000i
$396$		0			0
$397$	−10.0589	−	17.4225i	−0.504841	−	0.874410i	−0.999984	−	0.00559897i	$-0.998218\pi$
$397$	−10.0589	−	17.4225i	−0.504841	−	0.874410i	0.495143	−	0.868811i	$-0.335116\pi$
$398$	−23.2096	−	8.44760i	−1.16339	−	0.423440i
$399$		0			0
$400$	14.1773	+	11.8962i	0.708867	+	0.594810i
$401$	−28.9479	+	10.5362i	−1.44559	+	0.526151i	−0.941355	−	0.337417i	$-0.890447\pi$
$401$	−28.9479	+	10.5362i	−1.44559	+	0.526151i	−0.504233	+	0.863568i	$0.668225\pi$
$402$		0			0
$403$	−0.170544	−	0.967201i	−0.00849538	−	0.0481797i
$404$	14.3650			0.714684
$405$		0			0
$406$	34.9549			1.73478
$407$	1.10306	+	6.25577i	0.0546767	+	0.310087i
$408$		0			0
$409$	−37.2983	+	13.5755i	−1.84428	+	0.671265i	−0.856349	+	0.516398i	$0.827273\pi$
$409$	−37.2983	+	13.5755i	−1.84428	+	0.671265i	−0.987935	+	0.154867i	$0.950505\pi$
$410$	2.61270	+	2.19231i	0.129032	+	0.108271i
$411$		0			0
$412$	12.2659	+	4.46442i	0.604297	+	0.219946i
$413$	22.0073	+	38.1178i	1.08291	+	1.87565i
$414$		0			0
$415$	−6.59832	+	11.4286i	−0.323899	+	0.561010i
$416$	−2.47197	+	2.07423i	−0.121198	+	0.101698i
$417$		0			0
$418$	−1.49750	+	8.49272i	−0.0732449	+	0.415393i
$419$	−2.68132	+	15.2065i	−0.130991	+	0.742888i	0.846576	+	0.532267i	$0.178660\pi$
$419$	−2.68132	+	15.2065i	−0.130991	+	0.742888i	−0.977568	+	0.210621i	$0.932451\pi$
$420$		0			0
$421$	−13.8605	+	11.6304i	−0.675521	+	0.566830i	−0.914694	−	0.404148i	$-0.867568\pi$
$421$	−13.8605	+	11.6304i	−0.675521	+	0.566830i	0.239173	+	0.970977i	$0.423124\pi$
$422$	6.60456	−	11.4394i	0.321505	−	0.556863i
$423$		0			0
$424$	2.80837	+	4.86424i	0.136386	+	0.236228i
$425$	−6.61288	−	2.40689i	−0.320772	−	0.116751i
$426$		0			0
$427$	−15.6634	−	13.1432i	−0.758007	−	0.636043i
$428$	−12.8219	+	4.66680i	−0.619771	+	0.225578i
$429$		0			0
$430$	−1.65844	−	9.40548i	−0.0799771	−	0.453572i
$431$	28.9683			1.39535			0.697677	−	0.716412i	$-0.254217\pi$
$431$	28.9683			1.39535			0.697677	+	0.716412i	$0.254217\pi$
$432$		0			0
$433$	−37.5902			−1.80647			−0.903235	−	0.429146i	$-0.858815\pi$
$433$	−37.5902			−1.80647			−0.903235	+	0.429146i	$0.858815\pi$
$434$	1.52958	+	8.67467i	0.0734221	+	0.416398i
$435$		0			0
$436$	3.66002	−	1.33214i	0.175283	−	0.0637978i
$437$	12.2449	+	10.2747i	0.585752	+	0.491504i
$438$		0			0
$439$	−9.64457	−	3.51034i	−0.460310	−	0.167539i	0.101448	−	0.994841i	$-0.467653\pi$
$439$	−9.64457	−	3.51034i	−0.460310	−	0.167539i	−0.561758	+	0.827302i	$0.689875\pi$
$440$	−2.08560	−	3.61237i	−0.0994272	−	0.172213i
$441$		0			0
$442$	1.16348	−	2.01521i	0.0553413	−	0.0958540i
$443$	−16.7829	+	14.0825i	−0.797379	+	0.669080i	−0.947560	−	0.319578i	$-0.896459\pi$
$443$	−16.7829	+	14.0825i	−0.797379	+	0.669080i	0.150181	+	0.988659i	$0.452014\pi$
$444$		0			0
$445$	1.12365	−	6.37255i	0.0532662	−	0.302088i
$446$	2.55135	−	14.4694i	0.120810	−	0.685148i
$447$		0			0
$448$	−7.59091	+	6.36953i	−0.358637	+	0.300932i
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	−0.724069	−	0.689728i	$-0.757730\pi$
$449$	4.98565	−	8.63540i	0.235287	−	0.407530i	0.959356	+	0.282198i	$0.0910635\pi$
$450$		0			0
$451$	1.67998	+	2.90981i	0.0791072	+	0.137018i
$452$	15.4709	+	5.63094i	0.727689	+	0.264857i
$453$		0			0
$454$	5.23871	+	4.39580i	0.245865	+	0.206305i
$455$	−3.03957	+	1.10631i	−0.142497	+	0.0518647i
$456$		0			0
$457$	−1.32287	−	7.50236i	−0.0618812	−	0.350946i	−0.999989	−	0.00460343i	$-0.998535\pi$
$457$	−1.32287	−	7.50236i	−0.0618812	−	0.350946i	0.938108	−	0.346342i	$-0.112576\pi$
$458$	−27.1566			−1.26894
$459$		0			0
$460$	5.43375			0.253350
$461$	3.95927	+	22.4541i	0.184402	+	1.04579i	0.926722	+	0.375748i	$0.122614\pi$
$461$	3.95927	+	22.4541i	0.184402	+	1.04579i	−0.742320	+	0.670045i	$0.766275\pi$
$462$		0			0
$463$	8.26529	−	3.00832i	0.384120	−	0.139808i	−0.142740	−	0.989760i	$-0.545591\pi$
$463$	8.26529	−	3.00832i	0.384120	−	0.139808i	0.526860	+	0.849952i	$0.323369\pi$
$464$	−20.2524	−	16.9938i	−0.940194	−	0.788916i
$465$		0			0
$466$	−27.1889	−	9.89595i	−1.25950	−	0.458421i
$467$	−5.49878	−	9.52416i	−0.254453	−	0.440726i	0.710294	−	0.703905i	$-0.248562\pi$
$467$	−5.49878	−	9.52416i	−0.254453	−	0.440726i	−0.964747	+	0.263180i	$0.915229\pi$
$468$		0			0
$469$	−3.69203	+	6.39479i	−0.170482	+	0.295284i
$470$	2.48521	−	2.08533i	0.114634	−	0.0961893i
$471$		0			0
$472$	3.86030	−	21.8929i	0.177685	−	1.00770i
$473$	1.63380	−	9.26574i	0.0751222	−	0.426039i
$474$		0			0
$475$	−7.82496	+	6.56592i	−0.359034	+	0.301265i
$476$	−3.04864	+	5.28040i	−0.139734	+	0.242027i
$477$		0			0
$478$	1.29047	+	2.23516i	0.0590247	+	0.102234i
$479$	24.1431	+	8.78736i	1.10312	+	0.401505i	0.828467	−	0.560037i	$-0.189213\pi$
$479$	24.1431	+	8.78736i	1.10312	+	0.401505i	0.274658	+	0.961542i	$0.411435\pi$
$480$		0			0
$481$	−1.90591	−	1.59925i	−0.0869019	−	0.0729193i
$482$	−8.72171	+	3.17444i	−0.397263	+	0.144592i
$483$		0			0
$484$	−1.07525	−	6.09807i	−0.0488752	−	0.277185i
$485$	−0.387861			−0.0176119
$486$		0			0
$487$	−30.3800			−1.37665			−0.688325	−	0.725402i	$-0.741654\pi$
$487$	−30.3800			−1.37665			−0.688325	+	0.725402i	$0.741654\pi$
$488$	1.79332	+	10.1704i	0.0811796	+	0.460392i
$489$		0			0
$490$	14.7723	−	5.37667i	0.667343	−	0.242893i
$491$	−6.67092	−	5.59757i	−0.301055	−	0.252615i	0.479728	−	0.877417i	$-0.340735\pi$
$491$	−6.67092	−	5.59757i	−0.301055	−	0.252615i	−0.780783	+	0.624802i	$0.785180\pi$
$492$		0			0
$493$	9.44652	+	3.43825i	0.425450	+	0.154851i
$494$	−1.68882	−	2.92512i	−0.0759837	−	0.131608i
$495$		0			0
$496$	3.33108	−	5.76961i	0.149570	−	0.259063i
$497$	−36.4835	+	30.6133i	−1.63651	+	1.37319i
$498$		0			0
$499$	2.02048	−	11.4587i	0.0904491	−	0.512962i	−0.905598	−	0.424137i	$-0.860578\pi$
$499$	2.02048	−	11.4587i	0.0904491	−	0.512962i	0.996047	−	0.0888254i	$-0.0283113\pi$
$500$	−1.41252	+	8.01080i	−0.0631698	+	0.358254i
$501$		0			0
$502$	−27.6084	+	23.1662i	−1.23222	+	1.03396i
$503$	−18.8996	+	32.7350i	−0.842689	+	1.45958i	0.0449234	+	0.998990i	$0.485696\pi$
$503$	−18.8996	+	32.7350i	−0.842689	+	1.45958i	−0.887613	+	0.460590i	$0.847638\pi$
$504$		0			0
$505$	−9.82831	−	17.0231i	−0.437354	−	0.757519i
$506$	17.2177	+	6.26673i	0.765421	+	0.278590i
$507$		0			0
$508$	0.676264	+	0.567453i	0.0300044	+	0.0251766i
$509$	22.1520	−	8.06266i	0.981869	−	0.357371i	0.199303	−	0.979938i	$-0.436132\pi$
$509$	22.1520	−	8.06266i	0.981869	−	0.357371i	0.782567	+	0.622567i	$0.213910\pi$
$510$		0			0
$511$	−6.71153	−	38.0630i	−0.296901	−	1.68381i
$512$	−2.26711			−0.100193
$513$		0			0
$514$	−24.8548			−1.09630
$515$	−3.10161	−	17.5901i	−0.136673	−	0.775114i
$516$		0			0
$517$	3.00326	−	1.09310i	0.132083	−	0.0480744i
$518$	17.0938	+	14.3434i	0.751058	+	0.630212i
$519$		0			0
$520$	1.53520	+	0.558768i	0.0673230	+	0.0245036i
$521$	3.93474	+	6.81517i	0.172384	+	0.298578i	0.939253	−	0.343226i	$-0.111520\pi$
$521$	3.93474	+	6.81517i	0.172384	+	0.298578i	−0.766869	+	0.641804i	$0.778186\pi$
$522$		0			0
$523$	−16.6467	+	28.8330i	−0.727911	+	1.26078i	0.229854	+	0.973225i	$0.426175\pi$
$523$	−16.6467	+	28.8330i	−0.727911	+	1.26078i	−0.957765	+	0.287554i	$0.907158\pi$
$524$	−4.83129	+	4.05394i	−0.211056	+	0.177097i
$525$		0			0
$526$	0.818090	−	4.63962i	0.0356704	−	0.202297i
$527$	−0.439896	+	2.49477i	−0.0191622	+	0.108674i
$528$		0			0
$529$	8.39744	−	7.04629i	0.365106	−	0.306360i
$530$	−2.70080	+	4.67792i	−0.117315	+	0.203196i
$531$		0			0
$532$	4.42516	+	7.66461i	0.191855	+	0.332303i
$533$	−1.23663	−	0.450095i	−0.0535642	−	0.0194958i
$534$		0			0
$535$	14.3029	+	12.0016i	0.618370	+	0.518874i
$536$	3.50457	−	1.27556i	0.151374	−	0.0550958i
$537$		0			0
$538$	−0.104066	−	0.590187i	−0.00448660	−	0.0254448i
$539$	15.4868			0.667062
$540$		0			0
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$	3.54546	+	20.1073i	0.152290	+	0.863682i
$543$		0			0
$544$	7.82149	−	2.84679i	0.335344	−	0.122055i
$545$	−4.08278	−	3.42586i	−0.174887	−	0.146748i
$546$		0			0
$547$	19.6313	+	7.14519i	0.839372	+	0.305506i	0.725699	−	0.688012i	$-0.241516\pi$
$547$	19.6313	+	7.14519i	0.839372	+	0.305506i	0.113673	+	0.993518i	$0.463739\pi$
$548$	6.45948	+	11.1881i	0.275935	+	0.477934i
$549$		0			0
$550$	−5.85447	+	10.1402i	−0.249635	+	0.432381i
$551$	11.1780	−	9.37944i	0.476198	−	0.399578i
$552$		0			0
$553$	−8.38485	+	47.5529i	−0.356560	+	2.02215i
$554$	−7.29425	+	41.3678i	−0.309903	+	1.75755i
$555$		0			0
$556$	5.47416	−	4.59336i	0.232156	−	0.194802i
$557$	4.28920	−	7.42911i	0.181739	−	0.314782i	−0.760734	−	0.649064i	$-0.775161\pi$
$557$	4.28920	−	7.42911i	0.181739	−	0.314782i	0.942473	+	0.334283i	$0.108494\pi$
$558$		0			0
$559$	1.84254	+	3.19137i	0.0779311	+	0.134981i
$560$	−20.6187	−	7.50461i	−0.871301	−	0.317128i
$561$		0			0
$562$	9.42932	+	7.91214i	0.397752	+	0.333753i
$563$	−14.7672	+	5.37480i	−0.622361	+	0.226521i	−0.633903	−	0.773412i	$-0.718548\pi$
$563$	−14.7672	+	5.37480i	−0.622361	+	0.226521i	0.0115419	+	0.999933i	$0.496326\pi$
$564$		0			0
$565$	−3.91204	−	22.1863i	−0.164581	−	0.933384i
$566$	24.1851			1.01658
$567$		0			0
$568$	24.0545			1.00930
$569$	−2.20061	−	12.4803i	−0.0922542	−	0.523200i	−0.995554	−	0.0941902i	$-0.969974\pi$
$569$	−2.20061	−	12.4803i	−0.0922542	−	0.523200i	0.903300	−	0.429009i	$-0.141137\pi$
$570$		0			0
$571$	24.7352	−	9.00289i	1.03514	−	0.376759i	0.232103	−	0.972691i	$-0.425439\pi$
$571$	24.7352	−	9.00289i	1.03514	−	0.376759i	0.803035	+	0.595932i	$0.203217\pi$
$572$	−0.866495	−	0.727076i	−0.0362300	−	0.0304006i
$573$		0			0
$574$	11.0911	+	4.03683i	0.462934	+	0.168494i
$575$	10.8516	+	18.7954i	0.452541	+	0.783824i
$576$		0			0
$577$	11.0577	−	19.1525i	0.460338	−	0.797329i	−0.538640	−	0.842536i	$-0.681062\pi$
$577$	11.0577	−	19.1525i	0.460338	−	0.797329i	0.998978	+	0.0452074i	$0.0143949\pi$
$578$	17.2922	−	14.5099i	0.719261	−	0.603532i
$579$		0			0
$580$	0.861348	−	4.88495i	0.0357655	−	0.202836i
$581$	−7.93027	+	44.9748i	−0.329003	+	1.86587i
$582$		0			0
$583$	−4.07638	+	3.42049i	−0.168827	+	0.141662i
$584$	−9.76057	+	16.9058i	−0.403895	+	0.699567i
$585$		0			0
$586$	12.1156	+	20.9848i	0.500491	+	0.866876i
$587$	13.4405	+	4.89196i	0.554751	+	0.201913i	0.604156	−	0.796866i	$-0.293510\pi$
$587$	13.4405	+	4.89196i	0.554751	+	0.201913i	−0.0494052	+	0.998779i	$0.515733\pi$
$588$		0			0
$589$	2.81680	+	2.36358i	0.116064	+	0.0973895i
$590$	20.0897	−	7.31206i	0.827081	−	0.301033i
$591$		0			0
$592$	−2.93068	−	16.6207i	−0.120450	−	0.683107i
$593$	−47.7300			−1.96004			−0.980018	−	0.198908i	$-0.936260\pi$
$593$	−47.7300			−1.96004			−0.980018	+	0.198908i	$0.936260\pi$
$594$		0			0
$595$	8.34334			0.342044
$596$	0.353166	+	2.00290i	0.0144662	+	0.0820421i
$597$		0			0
$598$	−6.74363	+	2.45448i	−0.275768	+	0.100371i
$599$	0.382692	+	0.321117i	0.0156364	+	0.0131205i	0.650572	−	0.759444i	$-0.274529\pi$
$599$	0.382692	+	0.321117i	0.0156364	+	0.0131205i	−0.634936	+	0.772565i	$0.718974\pi$
$600$		0			0
$601$	15.9063	+	5.78940i	0.648830	+	0.236155i	0.645406	−	0.763839i	$-0.276688\pi$
$601$	15.9063	+	5.78940i	0.648830	+	0.236155i	0.00342336	+	0.999994i	$0.498910\pi$
$602$	−16.5254	−	28.6229i	−0.673527	−	1.16658i
$603$		0			0
$604$	4.33923	−	7.51577i	0.176561	−	0.305812i
$605$	−6.49081	+	5.44644i	−0.263889	+	0.221429i
$606$		0			0
$607$	0.120622	−	0.684080i	0.00489588	−	0.0277659i	−0.982262	−	0.187514i	$-0.939957\pi$
$607$	0.120622	−	0.684080i	0.00489588	−	0.0277659i	0.987158	+	0.159748i	$0.0510682\pi$
$608$	2.09796	−	11.8981i	0.0850835	−	0.482533i
$609$		0			0
$610$	−7.60813	+	6.38398i	−0.308044	+	0.258480i
$611$	−0.625887	+	1.08407i	−0.0253207	+	0.0438567i
$612$		0			0
$613$	16.3317	+	28.2873i	0.659630	+	1.14251i	0.980711	+	0.195461i	$0.0626204\pi$
$613$	16.3317	+	28.2873i	0.659630	+	1.14251i	−0.321081	+	0.947052i	$0.604046\pi$
$614$	−48.0695	−	17.4959i	−1.93993	−	0.706076i
$615$		0			0
$616$	−11.0578	−	9.27861i	−0.445532	−	0.373846i
$617$	21.5043	−	7.82694i	0.865732	−	0.315101i	0.129294	−	0.991606i	$-0.458729\pi$
$617$	21.5043	−	7.82694i	0.865732	−	0.315101i	0.736437	+	0.676506i	$0.236507\pi$
$618$		0			0
$619$	1.47353	+	8.35682i	0.0592263	+	0.335889i	0.999995	−	0.00316005i	$-0.00100588\pi$
$619$	1.47353	+	8.35682i	0.0592263	+	0.335889i	−0.940769	+	0.339049i	$0.889895\pi$
$620$	1.24998			0.0502002
$621$		0			0
$622$	−23.5254			−0.943282
$623$	−3.88853	−	22.0530i	−0.155791	−	0.883534i
$624$		0			0
$625$	−7.03811	+	2.56166i	−0.281524	+	0.102466i
$626$	−28.4411	−	23.8649i	−1.13674	−	0.953835i
$627$		0			0
$628$	−0.279206	−	0.101623i	−0.0111415	−	0.00405519i
$629$	3.20872	+	5.55767i	0.127940	+	0.221599i
$630$		0			0
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	−0.881432	−	0.472311i	$-0.843420\pi$
$631$	−0.795865	+	1.37848i	−0.0316829	+	0.0548763i	0.849749	+	0.527187i	$0.176753\pi$
$632$	18.6824	−	15.6764i	0.743146	−	0.623574i
$633$		0			0
$634$	5.07555	−	28.7849i	0.201576	−	1.14319i
$635$	0.209767	−	1.18965i	0.00832434	−	0.0472097i
$636$		0			0
$637$	−4.64658	+	3.89894i	−0.184104	+	0.154482i
$638$	8.36313	−	14.4854i	0.331099	−	0.573481i
$639$		0			0
$640$	7.38198	+	12.7860i	0.291798	+	0.505409i
$641$	20.3675	+	7.41317i	0.804469	+	0.292803i	0.711337	−	0.702851i	$-0.248090\pi$
$641$	20.3675	+	7.41317i	0.804469	+	0.292803i	0.0931317	+	0.995654i	$0.470312\pi$
$642$		0			0
$643$	−5.28729	−	4.43656i	−0.208510	−	0.174961i	0.532552	−	0.846397i	$-0.321233\pi$
$643$	−5.28729	−	4.43656i	−0.208510	−	0.174961i	−0.741062	+	0.671437i	$0.765678\pi$
$644$	17.6701	−	6.43139i	0.696300	−	0.253432i
$645$		0			0
$646$	1.51286	+	8.57984i	0.0595226	+	0.337569i
$647$	6.18972			0.243343			0.121671	−	0.992570i	$-0.461175\pi$
$647$	6.18972			0.243343			0.121671	+	0.992570i	$0.461175\pi$
$648$		0			0
$649$	21.0614			0.826733
$650$	−0.796353	−	4.51634i	−0.0312355	−	0.177146i
$651$		0			0
$652$	−11.3394	+	4.12720i	−0.444085	+	0.161634i
$653$	20.8475	+	17.4931i	0.815826	+	0.684559i	0.951991	−	0.306127i	$-0.0990333\pi$
$653$	20.8475	+	17.4931i	0.815826	+	0.684559i	−0.136165	+	0.990686i	$0.543478\pi$
$654$		0			0
$655$	8.10960	+	2.95165i	0.316868	+	0.115331i
$656$	−4.46347	−	7.73096i	−0.174269	−	0.301843i
$657$		0			0
$658$	5.61348	−	9.72283i	0.218836	−	0.379035i
$659$	−4.04624	+	3.39520i	−0.157619	+	0.132258i	−0.718187	−	0.695851i	$-0.755028\pi$
$659$	−4.04624	+	3.39520i	−0.157619	+	0.132258i	0.560567	+	0.828109i	$0.310583\pi$
$660$		0			0
$661$	2.02561	−	11.4878i	0.0787872	−	0.446824i	−0.919738	−	0.392533i	$-0.871599\pi$
$661$	2.02561	−	11.4878i	0.0787872	−	0.446824i	0.998525	−	0.0542915i	$-0.0172900\pi$
$662$	−0.252234	+	1.43049i	−0.00980334	+	0.0555975i
$663$		0			0
$664$	17.6695	−	14.8265i	0.685711	−	0.575380i
$665$	6.05527	−	10.4880i	0.234813	−	0.406708i
$666$		0			0
$667$	−15.5015	−	26.8494i	−0.600220	−	1.03961i
$668$	1.68777	+	0.614298i	0.0653018	+	0.0237679i
$669$		0			0
$670$	2.74752	+	2.30544i	0.106146	+	0.0890670i
$671$	−9.19410	+	3.34638i	−0.354934	+	0.129186i
$672$		0			0
$673$	8.52655	+	48.3564i	0.328674	+	1.86400i	0.482486	+	0.875904i	$0.339734\pi$
$673$	8.52655	+	48.3564i	0.328674	+	1.86400i	−0.153811	+	0.988100i	$0.549155\pi$
$674$	−0.703510			−0.0270982
$675$		0			0
$676$	−10.2880			−0.395693
$677$	3.92776	+	22.2754i	0.150956	+	0.856114i	0.962390	+	0.271670i	$0.0875760\pi$
$677$	3.92776	+	22.2754i	0.150956	+	0.856114i	−0.811434	+	0.584443i	$0.801313\pi$
$678$		0			0
$679$	−1.26129	+	0.459073i	−0.0484040	+	0.0176176i
$680$	−3.22811	−	2.70870i	−0.123792	−	0.103874i
$681$		0			0
$682$	3.96075	+	1.44160i	0.151665	+	0.0552016i
$683$	−8.56931	−	14.8425i	−0.327896	−	0.567932i	0.654198	−	0.756323i	$-0.273006\pi$
$683$	−8.56931	−	14.8425i	−0.327896	−	0.567932i	−0.982094	+	0.188391i	$0.939673\pi$
$684$		0			0
$685$	8.83897	−	15.3095i	0.337720	−	0.584947i
$686$	6.44104	−	5.40468i	0.245920	−	0.206352i
$687$		0			0
$688$	−4.34078	+	24.6178i	−0.165491	+	0.938544i
$689$	0.361917	−	2.05254i	0.0137880	−	0.0781954i
$690$		0			0
$691$	13.9848	−	11.7347i	0.532008	−	0.446408i	−0.336786	−	0.941581i	$-0.609340\pi$
$691$	13.9848	−	11.7347i	0.532008	−	0.446408i	0.868794	+	0.495173i	$0.164895\pi$
$692$	−7.25049	+	12.5582i	−0.275622	+	0.477392i
$693$		0			0
$694$	−19.6749	−	34.0779i	−0.746848	−	1.29358i
$695$	−9.18868	−	3.34441i	−0.348546	−	0.126861i
$696$		0			0
$697$	2.60028	+	2.18190i	0.0984927	+	0.0826452i
$698$	33.4490	−	12.1744i	1.26606	−	0.460809i
$699$		0			0
$700$	2.08666	+	11.8340i	0.0788682	+	0.447284i
$701$	2.92075			0.110315			0.0551575	−	0.998478i	$-0.482434\pi$
$701$	2.92075			0.110315			0.0551575	+	0.998478i	$0.482434\pi$
$702$		0			0
$703$	9.31505			0.351324
$704$	0.823381	+	4.66962i	0.0310323	+	0.175993i
$705$		0			0
$706$	−37.1894	+	13.5358i	−1.39964	+	0.509428i
$707$	−52.1095	−	43.7250i	−1.95978	−	1.64445i
$708$		0			0
$709$	−28.2165	−	10.2700i	−1.05969	−	0.385696i	−0.247379	−	0.968919i	$-0.579569\pi$
$709$	−28.2165	−	10.2700i	−1.05969	−	0.385696i	−0.812312	+	0.583223i	$0.801791\pi$
$710$	11.5665	+	20.0338i	0.434084	+	0.751856i
$711$		0			0
$712$	−5.65509	+	9.79490i	−0.211933	+	0.367079i
$713$	5.98481	−	5.02185i	0.224133	−	0.188070i
$714$		0			0
$715$	−0.268774	+	1.52429i	−0.0100516	+	0.0570052i
$716$	−0.143982	+	0.816560i	−0.00538084	+	0.0305163i
$717$		0			0
$718$	−13.4701	+	11.3027i	−0.502698	+	0.421814i
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	−0.202349	−	0.979314i	$-0.564857\pi$
$719$	20.0285	−	34.6903i	0.746936	−	1.29373i	0.949285	−	0.314418i	$-0.101809\pi$
$720$		0			0
$721$	−30.9059	−	53.5306i	−1.15100	−	1.99358i
$722$	−18.1280	−	6.59804i	−0.674654	−	0.245554i
$723$		0			0
$724$	−13.3888	−	11.2345i	−0.497590	−	0.417527i
$725$	18.6173	−	6.77615i	0.691430	−	0.251660i
$726$		0			0
$727$	−0.267206	−	1.51540i	−0.00991014	−	0.0562032i	0.979452	−	0.201679i	$-0.0646398\pi$
$727$	−0.267206	−	1.51540i	−0.00991014	−	0.0562032i	−0.989362	+	0.145476i	$0.953529\pi$
$728$	5.65371			0.209540
$729$		0			0
$730$	−18.7734			−0.694834
$731$	−1.65056	−	9.36079i	−0.0610482	−	0.346221i
$732$		0			0
$733$	1.42072	−	0.517098i	0.0524753	−	0.0190995i	−0.315649	−	0.948876i	$-0.602222\pi$
$733$	1.42072	−	0.517098i	0.0524753	−	0.0190995i	0.368124	+	0.929777i	$0.380000\pi$
$734$	−27.3733	−	22.9689i	−1.01037	−	0.847798i
$735$		0			0
$736$	−24.1217	−	8.77956i	−0.889136	−	0.323619i
$737$	1.76667	+	3.05997i	0.0650762	+	0.112715i
$738$		0			0
$739$	−10.6779	+	18.4946i	−0.392792	+	0.680336i	−0.992817	−	0.119646i	$-0.961824\pi$
$739$	−10.6779	+	18.4946i	−0.392792	+	0.680336i	0.600024	+	0.799982i	$0.295157\pi$
$740$	2.42571	−	2.03541i	0.0891708	−	0.0748232i
$741$		0			0
$742$	−3.24598	+	18.4089i	−0.119164	+	0.675811i
$743$	3.53005	−	20.0199i	0.129505	−	0.734459i	−0.849025	−	0.528353i	$-0.822810\pi$
$743$	3.53005	−	20.0199i	0.129505	−	0.734459i	0.978530	−	0.206106i	$-0.0660791\pi$
$744$		0			0
$745$	2.13190	−	1.78888i	0.0781067	−	0.0655393i
$746$	1.94153	−	3.36282i	0.0710843	−	0.123122i
$747$		0			0
$748$	1.45880	+	2.52672i	0.0533391	+	0.0923860i
$749$	60.7171	+	22.0992i	2.21855	+	0.807488i
$750$		0			0
$751$	3.26577	+	2.74030i	0.119170	+	0.0999951i	0.700425	−	0.713726i	$-0.252994\pi$
$751$	3.26577	+	2.74030i	0.119170	+	0.0999951i	−0.581255	+	0.813721i	$0.697438\pi$
$752$	−7.97925	+	2.90421i	−0.290973	+	0.105906i
$753$		0			0
$754$	1.13759	+	6.45162i	0.0414287	+	0.234954i
$755$	−11.8754			−0.432189
$756$		0			0
$757$	54.3419			1.97509			0.987546	−	0.157332i	$-0.0502892\pi$
$757$	54.3419			1.97509			0.987546	+	0.157332i	$0.0502892\pi$
$758$	−3.66432	−	20.7814i	−0.133094	−	0.754814i
$759$		0			0
$760$	−5.74781	+	2.09203i	−0.208495	+	0.0758860i
$761$	−13.9122	−	11.6737i	−0.504318	−	0.423173i	0.354807	−	0.934940i	$-0.384547\pi$
$761$	−13.9122	−	11.6737i	−0.504318	−	0.423173i	−0.859124	+	0.511767i	$0.828991\pi$
$762$		0			0
$763$	−17.3317	−	6.30823i	−0.627450	−	0.228373i
$764$	−4.05650	−	7.02606i	−0.146759	−	0.254194i
$765$		0			0
$766$	16.5188	−	28.6113i	0.596847	−	1.03377i
$767$	−6.31917	+	5.30241i	−0.228172	+	0.191459i
$768$		0			0
$769$	4.31598	−	24.4771i	0.155638	−	0.882668i	−0.802562	−	0.596569i	$-0.796530\pi$
$769$	4.31598	−	24.4771i	0.155638	−	0.882668i	0.958200	−	0.286099i	$-0.0923586\pi$
$770$	2.41059	−	13.6711i	0.0868716	−	0.492673i
$771$		0			0
$772$	−7.05448	+	5.91941i	−0.253896	+	0.213044i
$773$	19.2416	−	33.3274i	0.692071	−	1.19870i	−0.279087	−	0.960266i	$-0.590032\pi$
$773$	19.2416	−	33.3274i	0.692071	−	1.19870i	0.971158	−	0.238437i	$-0.0766350\pi$
$774$		0			0
$775$	2.49629	+	4.32369i	0.0896692	+	0.155312i
$776$	0.637044	+	0.231865i	0.0228685	+	0.00832347i
$777$		0			0
$778$	−24.2627	−	20.3588i	−0.869861	−	0.729900i
$779$	4.62994	−	1.68516i	0.165885	−	0.0603772i
$780$		0			0
$781$	3.95734	+	22.4432i	0.141605	+	0.803080i
$782$	18.5107			0.661940
$783$		0			0
$784$	−41.1462			−1.46951
$785$	0.0706015	+	0.400401i	0.00251988	+	0.0142909i
$786$		0			0
$787$	1.00780	−	0.366809i	0.0359242	−	0.0130753i	−0.323996	−	0.946059i	$-0.605026\pi$
$787$	1.00780	−	0.366809i	0.0359242	−	0.0130753i	0.359920	+	0.932983i	$0.382804\pi$
$788$	−5.74796	−	4.82311i	−0.204763	−	0.171816i
$789$		0			0
$790$	22.0395	+	8.02173i	0.784131	+	0.285400i
$791$	−38.9814	−	67.5177i	−1.38602	−	2.40065i
$792$		0			0
$793$	1.91607	−	3.31873i	0.0680417	−	0.117852i
$794$	−25.9047	+	21.7366i	−0.919324	+	0.771404i
$795$		0			0
$796$	−2.10623	+	11.9450i	−0.0746534	+	0.423380i
$797$	−4.38413	+	24.8636i	−0.155294	+	0.880716i	0.803223	+	0.595679i	$0.203117\pi$
$797$	−4.38413	+	24.8636i	−0.155294	+	0.880716i	−0.958517	+	0.285037i	$0.907994\pi$
$798$		0			0
$799$	2.47340	−	2.07543i	0.0875025	−	0.0734233i
$800$	8.20198	−	14.2063i	0.289984	−	0.502267i
$801$		0			0
$802$	25.8908	+	44.8442i	0.914237	+	1.58350i
$803$	−17.3791	−	6.32548i	−0.613296	−	0.223221i
$804$		0			0
$805$	−19.7111	−	16.5396i	−0.694726	−	0.582944i
$806$	−1.55130	+	0.564627i	−0.0546422	+	0.0198881i
$807$		0			0
$808$	5.96604	+	33.8351i	0.209885	+	1.19032i
$809$	11.7337			0.412536			0.206268	−	0.978495i	$-0.433868\pi$
$809$	11.7337			0.412536			0.206268	+	0.978495i	$0.433868\pi$
$810$		0			0
$811$	−38.4085			−1.34871			−0.674353	−	0.738409i	$-0.735577\pi$
$811$	−38.4085			−1.34871			−0.674353	+	0.738409i	$0.735577\pi$
$812$	−2.98080	−	16.9050i	−0.104606	−	0.593247i
$813$		0			0
$814$	10.0337	−	3.65196i	0.351680	−	0.128001i
$815$	12.6492	+	10.6139i	0.443081	+	0.371789i
$816$		0			0
$817$	−12.9649	−	4.71885i	−0.453585	−	0.165092i
$818$	33.3594	+	57.7802i	1.16639	+	2.02024i
$819$		0			0
$820$	0.837450	−	1.45051i	0.0292450	−	0.0506539i
$821$	−20.4779	+	17.1830i	−0.714685	+	0.599692i	−0.925909	−	0.377746i	$-0.876699\pi$
$821$	−20.4779	+	17.1830i	−0.714685	+	0.599692i	0.211224	+	0.977438i	$0.432255\pi$
$822$		0			0
$823$	0.757847	−	4.29796i	0.0264169	−	0.149818i	−0.968746	−	0.248054i	$-0.920209\pi$
$823$	0.757847	−	4.29796i	0.0264169	−	0.149818i	0.995163	+	0.0982363i	$0.0313201\pi$
$824$	−5.42120	+	30.7451i	−0.188856	+	1.07106i
$825$		0			0
$826$	56.6756	−	47.5565i	1.97200	−	1.65470i
$827$	−19.5727	+	33.9009i	−0.680610	+	1.17885i	0.294185	+	0.955748i	$0.404952\pi$
$827$	−19.5727	+	33.9009i	−0.680610	+	1.17885i	−0.974795	+	0.223102i	$0.928382\pi$
$828$		0			0
$829$	16.4433	+	28.4807i	0.571101	+	0.989176i	0.996453	+	0.0841481i	$0.0268169\pi$
$829$	16.4433	+	28.4807i	0.571101	+	0.989176i	−0.425352	+	0.905028i	$0.639850\pi$
$830$	20.8446	+	7.58683i	0.723528	+	0.263343i
$831$		0			0
$832$	−1.42267	−	1.19376i	−0.0493220	−	0.0413861i
$833$	14.7021	−	5.35112i	0.509397	−	0.185405i
$834$		0			0
$835$	−0.426778	−	2.42038i	−0.0147693	−	0.0837606i
$836$	4.23496			0.146469
$837$		0			0
$838$	25.9552			0.896607
$839$	−5.49429	−	31.1596i	−0.189684	−	1.07575i	−0.919788	−	0.392415i	$-0.871640\pi$
$839$	−5.49429	−	31.1596i	−0.189684	−	1.07575i	0.730105	−	0.683335i	$-0.239471\pi$
$840$		0			0
$841$	0.656177	−	0.238829i	0.0226268	−	0.00823548i
$842$	23.2983	+	19.5496i	0.802914	+	0.673725i
$843$		0			0
$844$	−6.09556	−	2.21860i	−0.209818	−	0.0763674i
$845$	7.03892	+	12.1918i	0.242146	+	0.419410i
$846$		0			0
$847$	−14.6612	+	25.3939i	−0.503764	+	0.872545i
$848$	10.8304	−	9.08776i	0.371917	−	0.312075i
$849$		0			0
$850$	−2.05409	+	11.6493i	−0.0704548	+	0.399569i
$851$	3.43676	−	19.4908i	0.117811	−	0.668138i
$852$		0			0
$853$	−4.33401	+	3.63667i	−0.148394	+	0.124517i	−0.713962	−	0.700184i	$-0.753101\pi$
$853$	−4.33401	+	3.63667i	−0.148394	+	0.124517i	0.565569	+	0.824701i	$0.308657\pi$
$854$	−17.1849	+	29.7652i	−0.588057	+	1.01854i
$855$		0			0
$856$	−16.3173	−	28.2624i	−0.557715	−	0.965990i
$857$	−38.7251	−	14.0948i	−1.32282	−	0.481468i	−0.418461	−	0.908235i	$-0.637430\pi$
$857$	−38.7251	−	14.0948i	−1.32282	−	0.481468i	−0.904362	+	0.426766i	$0.859653\pi$
$858$		0			0
$859$	27.4661	+	23.0468i	0.937130	+	0.786346i	0.977084	−	0.212856i	$-0.0682765\pi$
$859$	27.4661	+	23.0468i	0.937130	+	0.786346i	−0.0399533	+	0.999202i	$0.512721\pi$
$860$	−4.40727	+	1.60411i	−0.150287	+	0.0546998i
$861$		0			0
$862$	−8.45549	−	47.9534i	−0.287995	−	1.63330i
$863$	−20.9694			−0.713806			−0.356903	−	0.934142i	$-0.616167\pi$
$863$	−20.9694			−0.713806			−0.356903	+	0.934142i	$0.616167\pi$
$864$		0			0
$865$	19.8427			0.674673
$866$	10.9721	+	62.2259i	0.372847	+	2.11452i
$867$		0			0
$868$	4.06482	−	1.47947i	0.137969	−	0.0502166i
$869$	17.6998	+	14.8519i	0.600426	+	0.503817i
$870$		0			0
$871$	−1.30044	−	0.473321i	−0.0440637	−	0.0160379i
$872$	4.65778	+	8.06751i	0.157732	+	0.273201i
$873$		0			0
$874$	13.4343	−	23.2689i	0.454422	−	0.787082i
$875$	29.5078	−	24.7600i	0.997545	−	0.837039i
$876$		0			0
$877$	3.56160	−	20.1988i	0.120267	−	0.682066i	−0.863741	−	0.503937i	$-0.831884\pi$
$877$	3.56160	−	20.1988i	0.120267	−	0.682066i	0.984007	−	0.178129i	$-0.0570044\pi$
$878$	−2.99580	+	16.9900i	−0.101103	+	0.573385i
$879$		0			0
$880$	−8.04305	+	6.74892i	−0.271131	+	0.227506i
$881$	−19.1438	+	33.1581i	−0.644972	+	1.11712i	0.339336	+	0.940665i	$0.389798\pi$
$881$	−19.1438	+	33.1581i	−0.644972	+	1.11712i	−0.984308	+	0.176459i	$0.943536\pi$
$882$		0			0
$883$	8.72326	+	15.1091i	0.293561	+	0.508463i	0.974649	−	0.223739i	$-0.0718263\pi$
$883$	8.72326	+	15.1091i	0.293561	+	0.508463i	−0.681088	+	0.732201i	$0.738493\pi$
$884$	−1.07382	−	0.390838i	−0.0361164	−	0.0131453i
$885$		0			0
$886$	28.2106	+	23.6715i	0.947752	+	0.795259i
$887$	−50.9472	+	18.5433i	−1.71064	+	0.622622i	−0.996965	−	0.0778547i	$-0.975193\pi$
$887$	−50.9472	+	18.5433i	−1.71064	+	0.622622i	−0.713675	+	0.700477i	$0.752971\pi$
$888$		0			0
$889$	−0.725923	−	4.11691i	−0.0243467	−	0.138077i
$890$	−10.8769			−0.364596
$891$		0			0
$892$	−7.21530			−0.241586
$893$	−0.813829	−	4.61546i	−0.0272338	−	0.154450i
$894$		0			0
$895$	1.06617	−	0.388054i	0.0356381	−	0.0129712i
$896$	39.1391	+	32.8416i	1.30754	+	1.09716i
$897$		0			0
$898$	−15.7501	−	5.73256i	−0.525587	−	0.191298i
$899$	−3.56595	−	6.17641i	−0.118931	−	0.205995i
$900$		0			0
$901$	−2.68796	+	4.65569i	−0.0895491	+	0.155104i
$902$	4.32646	−	3.63033i	0.144056	−	0.120877i
$903$		0			0
$904$	−6.83771	+	38.7786i	−0.227419	+	1.28976i
$905$	−4.15299	+	23.5528i	−0.138050	+	0.782921i
$906$		0			0
$907$	21.9726	−	18.4372i	0.729587	−	0.612196i	−0.200432	−	0.979708i	$-0.564235\pi$
$907$	21.9726	−	18.4372i	0.729587	−	0.612196i	0.930019	+	0.367511i	$0.119790\pi$
$908$	1.67917	−	2.90841i	0.0557252	−	0.0965188i
$909$		0			0
$910$	2.71857	+	4.70871i	0.0901198	+	0.156092i
$911$	−26.6700	−	9.70708i	−0.883616	−	0.321610i	−0.139948	−	0.990159i	$-0.544693\pi$
$911$	−26.6700	−	9.70708i	−0.883616	−	0.321610i	−0.743668	+	0.668549i	$0.766916\pi$
$912$		0			0
$913$	16.7402	+	14.0467i	0.554021	+	0.464879i
$914$	−12.0331	+	4.37969i	−0.398020	+	0.144867i
$915$		0			0
$916$	2.31579	+	13.1335i	0.0765159	+	0.433943i
$917$	29.8653			0.986240
$918$		0			0
$919$	37.7786			1.24620			0.623101	−	0.782141i	$-0.285873\pi$
$919$	37.7786			1.24620			0.623101	+	0.782141i	$0.285873\pi$
$920$	2.25674	+	12.7986i	0.0744025	+	0.421957i
$921$		0			0
$922$	36.0144	−	13.1082i	1.18607	−	0.431694i
$923$	−6.83762	−	5.73744i	−0.225063	−	0.188850i
$924$		0			0
$925$	11.8848	+	4.32572i	0.390771	+	0.142229i
$926$	−7.39243	−	12.8041i	−0.242930	−	0.420768i
$927$		0			0
$928$	−11.7166	+	20.2937i	−0.384615	+	0.666173i
$929$	26.4874	−	22.2256i	0.869024	−	0.729198i	−0.0948685	−	0.995490i	$-0.530243\pi$
$929$	26.4874	−	22.2256i	0.869024	−	0.729198i	0.963892	+	0.266292i	$0.0857986\pi$
$930$		0			0
$931$	3.94354	−	22.3649i	0.129244	−	0.732982i
$932$	−2.46735	+	13.9930i	−0.0808206	+	0.458356i
$933$		0			0
$934$	−14.1610	+	11.8825i	−0.463363	+	0.388808i
$935$	1.99618	−	3.45749i	0.0652822	−	0.113072i
$936$		0			0
$937$	9.71839	+	16.8328i	0.317486	+	0.549902i	0.979963	−	0.199180i	$-0.0638280\pi$
$937$	9.71839	+	16.8328i	0.317486	+	0.549902i	−0.662477	+	0.749082i	$0.730495\pi$
$938$	11.6634	+	4.24514i	0.380825	+	0.138609i
$939$		0			0
$940$	−1.22044	−	1.02407i	−0.0398063	−	0.0334015i
$941$	9.33910	−	3.39915i	0.304446	−	0.110809i	−0.185280	−	0.982686i	$-0.559319\pi$
$941$	9.33910	−	3.39915i	0.304446	−	0.110809i	0.489726	+	0.871877i	$0.337097\pi$
$942$		0			0
$943$	−1.81783	−	10.3094i	−0.0591968	−	0.335722i
$944$	−55.9572			−1.82125
$945$		0			0
$946$	−15.8152			−0.514195
$947$	−2.93651	−	16.6538i	−0.0954239	−	0.541176i	−0.994617	−	0.103623i	$-0.966956\pi$
$947$	−2.93651	−	16.6538i	−0.0954239	−	0.541176i	0.899193	−	0.437553i	$-0.144155\pi$
$948$		0			0
$949$	6.80685	−	2.47749i	0.220960	−	0.0804227i
$950$	13.1531	+	11.0367i	0.426742	+	0.358079i
$951$		0			0
$952$	−13.7036	−	4.98769i	−0.444135	−	0.161652i
$953$	8.67866	+	15.0319i	0.281129	+	0.486930i	0.971663	−	0.236370i	$-0.0759577\pi$
$953$	8.67866	+	15.0319i	0.281129	+	0.486930i	−0.690534	+	0.723300i	$0.742624\pi$
$954$		0			0
$955$	−5.55079	+	9.61426i	−0.179620	+	0.311110i
$956$	0.970925	−	0.814703i	0.0314020	−	0.0263494i
$957$		0			0
$958$	7.49932	−	42.5308i	0.242292	−	1.37411i
$959$	10.6232	−	60.2472i	0.343041	−	1.94548i
$960$		0			0
$961$	−22.3706	+	18.7712i	−0.721633	+	0.605522i
$962$	−2.09104	+	3.62179i	−0.0674179	+	0.116771i
$963$		0			0
$964$	2.27898	+	3.94730i	0.0734009	+	0.127134i
$965$	11.8413	+	4.30990i	0.381186	+	0.138740i
$966$		0			0
$967$	−12.8568	−	10.7881i	−0.413447	−	0.346923i	0.412217	−	0.911086i	$-0.364755\pi$
$967$	−12.8568	−	10.7881i	−0.413447	−	0.346923i	−0.825664	+	0.564163i	$0.809199\pi$
$968$	13.9168	−	5.06529i	0.447302	−	0.162805i
$969$		0			0
$970$	0.113212	+	0.642056i	0.00363501	+	0.0206152i
$971$	33.4811			1.07446			0.537230	−	0.843436i	$-0.319471\pi$
$971$	33.4811			1.07446			0.537230	+	0.843436i	$0.319471\pi$
$972$		0			0
$973$	−33.8393			−1.08484
$974$	8.86755	+	50.2904i	0.284135	+	1.61141i
$975$		0			0
$976$	24.4274	−	8.89086i	0.781903	−	0.284589i
$977$	−17.4159	−	14.6137i	−0.557184	−	0.467533i	0.320181	−	0.947356i	$-0.396256\pi$
$977$	−17.4159	−	14.6137i	−0.557184	−	0.467533i	−0.877365	+	0.479824i	$0.840701\pi$
$978$		0			0
$979$	−10.0691	−	3.66486i	−0.321811	−	0.117130i
$980$	−3.85998	−	6.68569i	−0.123303	−	0.213567i
$981$		0			0
$982$	−7.31892	+	12.6767i	−0.233556	+	0.404531i
$983$	−36.1263	+	30.3136i	−1.15225	+	0.966853i	−0.999770	−	0.0214531i	$-0.993171\pi$
$983$	−36.1263	+	30.3136i	−1.15225	+	0.966853i	−0.152481	+	0.988306i	$0.548726\pi$
$984$		0			0
$985$	−1.78293	+	10.1115i	−0.0568089	+	0.322179i
$986$	2.93428	−	16.6411i	0.0934465	−	0.529961i
$987$		0			0
$988$	−1.27064	+	1.06619i	−0.0404244	+	0.0339201i
$989$	−14.6571	+	25.3869i	−0.466069	+	0.807255i
$990$		0			0
$991$	2.18837	+	3.79036i	0.0695158	+	0.120405i	0.898688	−	0.438588i	$-0.144521\pi$
$991$	2.18837	+	3.79036i	0.0695158	+	0.120405i	−0.829172	+	0.558993i	$0.811188\pi$
$992$	−5.54893	−	2.01965i	−0.176179	−	0.0641238i
$993$		0			0
$994$	61.3255	+	51.4582i	1.94513	+	1.63216i
$995$	15.5964	−	5.67664i	0.494441	−	0.179962i
$996$		0			0
$997$	−0.372389	−	2.11192i	−0.0117937	−	0.0668852i	0.978343	−	0.206991i	$-0.0663670\pi$
$997$	−0.372389	−	2.11192i	−0.0117937	−	0.0668852i	−0.990137	+	0.140105i	$0.955256\pi$
$998$	−19.5582			−0.619104
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.e.b.28.1		12
3.2	odd	2		243.2.e.c.28.2		12
9.2	odd	6		243.2.e.d.109.2		12
9.4	even	3		81.2.e.a.64.2		12
9.5	odd	6		27.2.e.a.4.1	✓	12
9.7	even	3		243.2.e.a.109.1		12
27.2	odd	18		243.2.e.c.217.2		12
27.4	even	9		729.2.c.b.487.6		12
27.5	odd	18		729.2.a.a.1.6		6
27.7	even	9		243.2.e.a.136.1		12
27.11	odd	18		27.2.e.a.7.1	yes	12
27.13	even	9		729.2.c.b.244.6		12
27.14	odd	18		729.2.c.e.244.1		12
27.16	even	9		81.2.e.a.19.2		12
27.20	odd	18		243.2.e.d.136.2		12
27.22	even	9		729.2.a.d.1.1		6
27.23	odd	18		729.2.c.e.487.1		12
27.25	even	9	inner	243.2.e.b.217.1		12
36.23	even	6		432.2.u.c.193.1		12
45.14	odd	6		675.2.l.c.301.2		12
45.23	even	12		675.2.u.b.274.1		24
45.32	even	12		675.2.u.b.274.4		24
108.11	even	18		432.2.u.c.385.1		12
135.38	even	36		675.2.u.b.574.4		24
135.92	even	36		675.2.u.b.574.1		24
135.119	odd	18		675.2.l.c.601.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.1	✓	12	9.5	odd	6
27.2.e.a.7.1	yes	12	27.11	odd	18
81.2.e.a.19.2		12	27.16	even	9
81.2.e.a.64.2		12	9.4	even	3
243.2.e.a.109.1		12	9.7	even	3
243.2.e.a.136.1		12	27.7	even	9
243.2.e.b.28.1		12	1.1	even	1	trivial
243.2.e.b.217.1		12	27.25	even	9	inner
243.2.e.c.28.2		12	3.2	odd	2
243.2.e.c.217.2		12	27.2	odd	18
243.2.e.d.109.2		12	9.2	odd	6
243.2.e.d.136.2		12	27.20	odd	18
432.2.u.c.193.1		12	36.23	even	6
432.2.u.c.385.1		12	108.11	even	18
675.2.l.c.301.2		12	45.14	odd	6
675.2.l.c.601.2		12	135.119	odd	18
675.2.u.b.274.1		24	45.23	even	12
675.2.u.b.274.4		24	45.32	even	12
675.2.u.b.574.1		24	135.92	even	36
675.2.u.b.574.4		24	135.38	even	36
729.2.a.a.1.6		6	27.5	odd	18
729.2.a.d.1.1		6	27.22	even	9
729.2.c.b.244.6		12	27.13	even	9
729.2.c.b.487.6		12	27.4	even	9
729.2.c.e.244.1		12	27.14	odd	18
729.2.c.e.487.1		12	27.23	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.291887 - 1.65538i) q^{2} +(-0.775684 + 0.282326i) q^{4} +(0.865281 + 0.726057i) q^{5} +(3.67319 + 1.33693i) q^{7} +(-0.987144 - 1.70978i) q^{8} +O(q^{10})\)	\(q+(-0.291887 - 1.65538i) q^{2} +(-0.775684 + 0.282326i) q^{4} +(0.865281 + 0.726057i) q^{5} +(3.67319 + 1.33693i) q^{7} +(-0.987144 - 1.70978i) q^{8} +(0.949332 - 1.64429i) q^{10} +(1.43285 - 1.20231i) q^{11} +(-0.127214 + 0.721468i) q^{13} +(1.14097 - 6.47073i) q^{14} +(-3.80689 + 3.19436i) q^{16} +(0.944822 - 1.63648i) q^{17} +(-1.37143 - 2.37538i) q^{19} +(-0.876169 - 0.318900i) q^{20} +(-2.40850 - 2.02097i) q^{22} +(-5.47625 + 1.99319i) q^{23} +(-0.646688 - 3.66755i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(0.923797 + 5.23911i) q^{29} +(-1.25975 + 0.458512i) q^{31} +(3.37426 + 2.83134i) q^{32} +(-2.98477 - 1.08637i) q^{34} +(2.20765 + 3.82376i) q^{35} +(-1.69806 + 2.94112i) q^{37} +(-3.53185 + 2.96357i) q^{38} +(0.387244 - 2.19617i) q^{40} +(-0.311930 + 1.76904i) q^{41} +(3.85332 - 3.23332i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(1.60563 + 0.584402i) q^{47} +(6.34260 + 5.32207i) q^{49} +(-5.88242 + 2.14102i) q^{50} +(-0.105011 - 0.595547i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(-1.34010 - 7.60010i) q^{56} +(8.40305 - 3.05846i) q^{58} +(8.62570 + 7.23782i) q^{59} +(-4.91543 - 1.78907i) q^{61} +(1.12672 + 1.95153i) q^{62} +(-1.26751 + 2.19540i) q^{64} +(-0.633903 + 0.531908i) q^{65} +(-0.328026 + 1.86033i) q^{67} +(-0.270863 + 1.53614i) q^{68} +(5.68538 - 4.77060i) q^{70} +(-6.09193 + 10.5515i) q^{71} +(-4.94384 - 8.56298i) q^{73} +(5.36430 + 1.95245i) q^{74} +(1.73443 + 1.45536i) q^{76} +(6.87053 - 2.50067i) q^{77} +(2.14505 + 12.1652i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(2.02876 + 11.5057i) q^{83} +(2.00571 - 0.730020i) q^{85} +(-6.47709 - 5.43493i) q^{86} +(-3.47012 - 1.26302i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(3.68511 - 3.09217i) q^{92} +(0.498741 - 2.82850i) q^{94} +(0.537993 - 3.05111i) q^{95} +(-0.263043 + 0.220719i) q^{97} +(6.95870 - 12.0528i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28} - 30 q^{29} - 15 q^{31} + 27 q^{32} - 9 q^{34} - 12 q^{35} - 3 q^{37} + 12 q^{38} - 6 q^{40} + 21 q^{41} + 12 q^{43} - 3 q^{44} - 3 q^{46} - 3 q^{47} + 21 q^{49} - 12 q^{50} + 36 q^{52} + 18 q^{53} - 12 q^{55} - 3 q^{56} + 30 q^{58} - 15 q^{59} + 21 q^{61} + 12 q^{62} + 12 q^{64} + 24 q^{65} + 21 q^{67} + 18 q^{68} + 30 q^{70} - 27 q^{71} + 6 q^{73} + 12 q^{74} + 42 q^{76} + 3 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 33 q^{83} - 9 q^{85} + 30 q^{86} - 12 q^{88} - 9 q^{89} + 6 q^{91} - 42 q^{92} - 33 q^{94} - 30 q^{95} - 42 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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