LMFDB - Embedded newform 207.2.i.d.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			100.2
Root			$-0.932269 + 2.04138i$ of defining polynomial
Character	$\chi$	$=$	207.100
Dual form			207.2.i.d.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.164520 - 1.14426i) q^{2} +(0.636711 + 0.186955i) q^{4} +(1.13298 + 1.30753i) q^{5} +(-0.589836 - 0.379064i) q^{7} +(1.27914 - 2.80093i) q^{8} +O(q^{10})$	\(q+(0.164520 - 1.14426i) q^{2} +(0.636711 + 0.186955i) q^{4} +(1.13298 + 1.30753i) q^{5} +(-0.589836 - 0.379064i) q^{7} +(1.27914 - 2.80093i) q^{8} +(1.68256 - 1.08131i) q^{10} +(0.485534 + 3.37697i) q^{11} +(3.32423 - 2.13635i) q^{13} +(-0.530790 + 0.612564i) q^{14} +(-1.87807 - 1.20696i) q^{16} +(-0.920848 + 0.270385i) q^{17} +(-5.70077 - 1.67390i) q^{19} +(0.476932 + 1.04433i) q^{20} +3.94402 q^{22} +(-2.27813 - 4.22021i) q^{23} +(0.285587 - 1.98630i) q^{25} +(-1.89765 - 4.15528i) q^{26} +(-0.304687 - 0.351627i) q^{28} +(-2.25187 + 0.661210i) q^{29} +(-3.58618 + 7.85263i) q^{31} +(2.34282 - 2.70376i) q^{32} +(0.157894 + 1.09818i) q^{34} +(-0.172634 - 1.20070i) q^{35} +(-6.17667 + 7.12826i) q^{37} +(-2.85328 + 6.24780i) q^{38} +(5.11155 - 1.50089i) q^{40} +(4.08680 + 4.71641i) q^{41} +(3.32229 + 7.27480i) q^{43} +(-0.322196 + 2.24093i) q^{44} +(-5.20383 + 1.91247i) q^{46} +2.99078 q^{47} +(-2.70369 - 5.92025i) q^{49} +(-2.22587 - 0.653574i) q^{50} +(2.51598 - 0.738758i) q^{52} +(-3.96305 - 2.54690i) q^{53} +(-3.86538 + 4.46088i) q^{55} +(-1.81622 + 1.16721i) q^{56} +(0.386120 + 2.68552i) q^{58} +(-7.51851 + 4.83185i) q^{59} +(3.64086 - 7.97236i) q^{61} +(8.39549 + 5.39545i) q^{62} +(-5.63228 - 6.50000i) q^{64} +(6.55963 + 1.92608i) q^{65} +(0.241257 - 1.67798i) q^{67} -0.636864 q^{68} -1.40232 q^{70} +(1.65698 - 11.5246i) q^{71} +(8.34684 + 2.45085i) q^{73} +(7.14042 + 8.24049i) q^{74} +(-3.31680 - 2.13158i) q^{76} +(0.993702 - 2.17590i) q^{77} +(-6.43376 + 4.13473i) q^{79} +(-0.549677 - 3.82309i) q^{80} +(6.06919 - 3.90043i) q^{82} +(-9.33402 + 10.7720i) q^{83} +(-1.39684 - 0.897694i) q^{85} +(8.87088 - 2.60472i) q^{86} +(10.0797 + 2.95968i) q^{88} +(-4.45010 - 9.74435i) q^{89} -2.77057 q^{91} +(-0.661520 - 3.11296i) q^{92} +(0.492045 - 3.42225i) q^{94} +(-4.27019 - 9.35041i) q^{95} +(-1.30891 - 1.51056i) q^{97} +(-7.21915 + 2.11973i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$	0.164520	−	1.14426i	0.116334	−	0.809117i	−0.845204	−	0.534444i	$-0.820521\pi$
$2$	0.164520	−	1.14426i	0.116334	−	0.809117i	0.961538	−	0.274674i	$-0.0885698\pi$
$3$		0			0
$3$		0			0
$4$	0.636711	+	0.186955i	0.318356	+	0.0934776i
$5$	1.13298	+	1.30753i	0.506684	+	0.584745i	0.950247	−	0.311499i	$-0.100831\pi$
$5$	1.13298	+	1.30753i	0.506684	+	0.584745i	−0.443562	+	0.896243i	$0.646286\pi$
$6$		0			0
$7$	−0.589836	−	0.379064i	−0.222937	−	0.143273i	0.424405	−	0.905472i	$-0.360483\pi$
$7$	−0.589836	−	0.379064i	−0.222937	−	0.143273i	−0.647342	+	0.762199i	$0.724120\pi$
$8$	1.27914	−	2.80093i	0.452246	−	0.990280i
$9$		0			0
$10$	1.68256	−	1.08131i	0.532071	−	0.341941i
$11$	0.485534	+	3.37697i	0.146394	+	1.01819i	0.922059	+	0.387049i	$0.126506\pi$
$11$	0.485534	+	3.37697i	0.146394	+	1.01819i	−0.775665	+	0.631145i	$0.782585\pi$
$12$		0			0
$13$	3.32423	−	2.13635i	0.921976	−	0.592518i	0.00874595	−	0.999962i	$-0.497216\pi$
$13$	3.32423	−	2.13635i	0.921976	−	0.592518i	0.913230	+	0.407444i	$0.133580\pi$
$14$	−0.530790	+	0.612564i	−0.141860	+	0.163715i
$15$		0			0
$16$	−1.87807	−	1.20696i	−0.469517	−	0.301740i
$17$	−0.920848	+	0.270385i	−0.223338	+	0.0655781i	−0.391487	−	0.920184i	$-0.628039\pi$
$17$	−0.920848	+	0.270385i	−0.223338	+	0.0655781i	0.168149	+	0.985762i	$0.446221\pi$
$18$		0			0
$19$	−5.70077	−	1.67390i	−1.30785	−	0.384018i	−0.447754	−	0.894157i	$-0.647776\pi$
$19$	−5.70077	−	1.67390i	−1.30785	−	0.384018i	−0.860092	+	0.510138i	$0.829594\pi$
$20$	0.476932	+	1.04433i	0.106645	+	0.233520i
$21$		0			0
$22$	3.94402			0.840869
$23$	−2.27813	−	4.22021i	−0.475022	−	0.879974i
$23$	−2.27813	−	4.22021i	−0.475022	−	0.879974i
$24$		0			0
$25$	0.285587	−	1.98630i	0.0571174	−	0.397260i
$26$	−1.89765	−	4.15528i	−0.372160	−	0.814917i
$27$		0			0
$28$	−0.304687	−	0.351627i	−0.0575804	−	0.0664513i
$29$	−2.25187	+	0.661210i	−0.418163	+	0.122784i	−0.484044	−	0.875044i	$-0.660832\pi$
$29$	−2.25187	+	0.661210i	−0.418163	+	0.122784i	0.0658810	+	0.997827i	$0.479014\pi$
$30$		0			0
$31$	−3.58618	+	7.85263i	−0.644096	+	1.41037i	0.252531	+	0.967589i	$0.418737\pi$
$31$	−3.58618	+	7.85263i	−0.644096	+	1.41037i	−0.896628	+	0.442785i	$0.853990\pi$
$32$	2.34282	−	2.70376i	0.414157	−	0.477962i
$33$		0			0
$34$	0.157894	+	1.09818i	0.0270786	+	0.188336i
$35$	−0.172634	−	1.20070i	−0.0291806	−	0.202955i
$36$		0			0
$37$	−6.17667	+	7.12826i	−1.01544	+	1.17188i	−0.0304007	+	0.999538i	$0.509678\pi$
$37$	−6.17667	+	7.12826i	−1.01544	+	1.17188i	−0.985037	+	0.172340i	$0.944867\pi$
$38$	−2.85328	+	6.24780i	−0.462862	+	1.01353i
$39$		0			0
$40$	5.11155	−	1.50089i	0.808206	−	0.237311i
$41$	4.08680	+	4.71641i	0.638250	+	0.736580i	0.979064	−	0.203551i	$-0.0652482\pi$
$41$	4.08680	+	4.71641i	0.638250	+	0.736580i	−0.340814	+	0.940131i	$0.610703\pi$
$42$		0			0
$43$	3.32229	+	7.27480i	0.506644	+	1.10940i	0.974252	+	0.225460i	$0.0723885\pi$
$43$	3.32229	+	7.27480i	0.506644	+	1.10940i	−0.467608	+	0.883936i	$0.654884\pi$
$44$	−0.322196	+	2.24093i	−0.0485729	+	0.337832i
$45$		0			0
$46$	−5.20383	+	1.91247i	−0.767263	+	0.281978i
$47$	2.99078			0.436251			0.218125	−	0.975921i	$-0.430006\pi$
$47$	2.99078			0.436251			0.218125	+	0.975921i	$0.430006\pi$
$48$		0			0
$49$	−2.70369	−	5.92025i	−0.386241	−	0.845750i
$50$	−2.22587	−	0.653574i	−0.314785	−	0.0924293i
$51$		0			0
$52$	2.51598	−	0.738758i	0.348904	−	0.102447i
$53$	−3.96305	−	2.54690i	−0.544367	−	0.349843i	0.239378	−	0.970927i	$-0.423057\pi$
$53$	−3.96305	−	2.54690i	−0.544367	−	0.349843i	−0.783745	+	0.621083i	$0.786693\pi$
$54$		0			0
$55$	−3.86538	+	4.46088i	−0.521208	+	0.601506i
$56$	−1.81622	+	1.16721i	−0.242702	+	0.155975i
$57$		0			0
$58$	0.386120	+	2.68552i	0.0507000	+	0.352626i
$59$	−7.51851	+	4.83185i	−0.978826	+	0.629053i	−0.929146	−	0.369712i	$-0.879456\pi$
$59$	−7.51851	+	4.83185i	−0.978826	+	0.629053i	−0.0496797	+	0.998765i	$0.515820\pi$
$60$		0			0
$61$	3.64086	−	7.97236i	0.466164	−	1.02076i	−0.519875	−	0.854242i	$-0.674022\pi$
$61$	3.64086	−	7.97236i	0.466164	−	1.02076i	0.986039	−	0.166514i	$-0.0532511\pi$
$62$	8.39549	+	5.39545i	1.06623	+	0.685223i
$63$		0			0
$64$	−5.63228	−	6.50000i	−0.704036	−	0.812500i
$65$	6.55963	+	1.92608i	0.813622	+	0.238901i
$66$		0			0
$67$	0.241257	−	1.67798i	0.0294742	−	0.204997i	−0.969763	−	0.244048i	$-0.921524\pi$
$67$	0.241257	−	1.67798i	0.0294742	−	0.204997i	0.999237	+	0.0390510i	$0.0124335\pi$
$68$	−0.636864			−0.0772311
$69$		0			0
$70$	−1.40232			−0.167609
$71$	1.65698	−	11.5246i	0.196648	−	1.36772i	−0.617277	−	0.786746i	$-0.711764\pi$
$71$	1.65698	−	11.5246i	0.196648	−	1.36772i	0.813925	−	0.580970i	$-0.197327\pi$
$72$		0			0
$73$	8.34684	+	2.45085i	0.976924	+	0.286851i	0.730954	−	0.682427i	$-0.239075\pi$
$73$	8.34684	+	2.45085i	0.976924	+	0.286851i	0.245970	+	0.969277i	$0.420894\pi$
$74$	7.14042	+	8.24049i	0.830057	+	0.957937i
$75$		0			0
$76$	−3.31680	−	2.13158i	−0.380463	−	0.244509i
$77$	0.993702	−	2.17590i	0.113243	−	0.247967i
$78$		0			0
$79$	−6.43376	+	4.13473i	−0.723854	+	0.465193i	−0.849976	−	0.526822i	$-0.823383\pi$
$79$	−6.43376	+	4.13473i	−0.723854	+	0.465193i	0.126121	+	0.992015i	$0.459747\pi$
$80$	−0.549677	−	3.82309i	−0.0614558	−	0.427435i
$81$		0			0
$82$	6.06919	−	3.90043i	0.670230	−	0.430730i
$83$	−9.33402	+	10.7720i	−1.02454	+	1.18238i	−0.0414747	+	0.999140i	$0.513206\pi$
$83$	−9.33402	+	10.7720i	−1.02454	+	1.18238i	−0.983067	+	0.183245i	$0.941340\pi$
$84$		0			0
$85$	−1.39684	−	0.897694i	−0.151508	−	0.0973686i
$86$	8.87088	−	2.60472i	0.956571	−	0.280875i
$87$		0			0
$88$	10.0797	+	2.95968i	1.07450	+	0.315502i
$89$	−4.45010	−	9.74435i	−0.471709	−	1.03290i	−0.984660	−	0.174481i	$-0.944175\pi$
$89$	−4.45010	−	9.74435i	−0.471709	−	1.03290i	0.512951	−	0.858418i	$-0.328552\pi$
$90$		0			0
$91$	−2.77057			−0.290434
$92$	−0.661520	−	3.11296i	−0.0689682	−	0.324549i
$93$		0			0
$94$	0.492045	−	3.42225i	0.0507506	−	0.352978i
$95$	−4.27019	−	9.35041i	−0.438112	−	0.959332i
$96$		0			0
$97$	−1.30891	−	1.51056i	−0.132899	−	0.153374i	0.685399	−	0.728168i	$-0.259628\pi$
$97$	−1.30891	−	1.51056i	−0.132899	−	0.153374i	−0.818298	+	0.574794i	$0.805082\pi$
$98$	−7.21915	+	2.11973i	−0.729244	+	0.214125i
$99$		0			0
$100$	0.553186	−	1.21131i	0.0553186	−	0.121131i
$101$	−6.28290	+	7.25085i	−0.625172	+	0.721487i	−0.976681	−	0.214698i	$-0.931123\pi$
$101$	−6.28290	+	7.25085i	−0.625172	+	0.721487i	0.351509	+	0.936185i	$0.385669\pi$
$102$		0			0
$103$	−0.244984	−	1.70390i	−0.0241389	−	0.167890i	0.974186	−	0.225747i	$-0.0724823\pi$
$103$	−0.244984	−	1.70390i	−0.0241389	−	0.167890i	−0.998325	+	0.0578571i	$0.981573\pi$
$104$	−1.73162	−	12.0437i	−0.169799	−	1.18098i
$105$		0			0
$106$	−3.56633	+	4.11576i	−0.346393	+	0.399758i
$107$	5.63063	−	12.3294i	0.544333	−	1.19192i	−0.415045	−	0.909801i	$-0.636234\pi$
$107$	5.63063	−	12.3294i	0.544333	−	1.19192i	0.959378	−	0.282123i	$-0.0910385\pi$
$108$		0			0
$109$	18.9174	−	5.55464i	1.81195	−	0.532038i	0.813202	−	0.581981i	$-0.197722\pi$
$109$	18.9174	−	5.55464i	1.81195	−	0.532038i	0.998752	+	0.0499435i	$0.0159041\pi$
$110$	4.46850	+	5.15692i	0.426055	+	0.491693i
$111$		0			0
$112$	0.650236	+	1.42382i	0.0614415	+	0.134538i
$113$	−0.642387	+	4.46790i	−0.0604307	+	0.420305i	0.937040	+	0.349223i	$0.113554\pi$
$113$	−0.642387	+	4.46790i	−0.0604307	+	0.420305i	−0.997470	+	0.0710821i	$0.977355\pi$
$114$		0			0
$115$	2.93697	−	7.76012i	0.273873	−	0.723635i
$116$	−1.55741			−0.144602
$117$		0			0
$118$	4.29197	+	9.39810i	0.395108	+	0.865165i
$119$	0.645642	+	0.189578i	0.0591859	+	0.0173786i
$120$		0			0
$121$	−0.613732	+	0.180208i	−0.0557938	+	0.0163825i
$122$	−8.52350	−	5.47772i	−0.771681	−	0.495929i
$123$		0			0
$124$	−3.75145	+	4.32940i	−0.336890	+	0.388792i
$125$	10.1980	−	6.55386i	0.912137	−	0.586195i
$126$		0			0
$127$	−1.54704	−	10.7599i	−0.137278	−	0.954788i	−0.935727	−	0.352726i	$-0.885255\pi$
$127$	−1.54704	−	10.7599i	−0.137278	−	0.954788i	0.798449	−	0.602063i	$-0.205654\pi$
$128$	−2.34503	+	1.50706i	−0.207273	+	0.133206i
$129$		0			0
$130$	3.28314	−	7.18908i	0.287951	−	0.630524i
$131$	12.5648	+	8.07490i	1.09779	+	0.705507i	0.958599	−	0.284758i	$-0.0919133\pi$
$131$	12.5648	+	8.07490i	1.09779	+	0.705507i	0.139192	+	0.990265i	$0.455550\pi$
$132$		0			0
$133$	2.72800	+	3.14828i	0.236548	+	0.272991i
$134$	−1.88036	−	0.552123i	−0.162438	−	0.0476962i
$135$		0			0
$136$	−0.420565	+	2.92510i	−0.0360632	+	0.250825i
$137$	13.0209			1.11245			0.556226	−	0.831031i	$-0.312249\pi$
$137$	13.0209			1.11245			0.556226	+	0.831031i	$0.312249\pi$
$138$		0			0
$139$	−7.77065			−0.659098			−0.329549	−	0.944139i	$-0.606897\pi$
$139$	−7.77065			−0.659098			−0.329549	+	0.944139i	$0.606897\pi$
$140$	0.114559	−	0.796774i	0.00968198	−	0.0673397i
$141$		0			0
$142$	−12.9146	−	3.79206i	−1.08377	−	0.318223i
$143$	8.82843	+	10.1885i	0.738270	+	0.852009i
$144$		0			0
$145$	−3.41588	−	2.19525i	−0.283673	−	0.182306i
$146$	4.17765	−	9.14778i	0.345745	−	0.757076i
$147$		0			0
$148$	−5.26542	+	3.38388i	−0.432815	+	0.278153i
$149$	1.10872	+	7.71135i	0.0908302	+	0.631738i	0.983484	+	0.180995i	$0.0579318\pi$
$149$	1.10872	+	7.71135i	0.0908302	+	0.631738i	−0.892654	+	0.450743i	$0.851159\pi$
$150$		0			0
$151$	2.56615	−	1.64917i	0.208830	−	0.134207i	−0.432045	−	0.901852i	$-0.642208\pi$
$151$	2.56615	−	1.64917i	0.208830	−	0.134207i	0.640875	+	0.767645i	$0.278571\pi$
$152$	−11.9806	+	13.8263i	−0.971754	+	1.12146i
$153$		0			0
$154$	−2.32633	−	1.49504i	−0.187461	−	0.120474i
$155$	−14.3306	+	4.20785i	−1.15106	+	0.337982i
$156$		0			0
$157$	9.12488	+	2.67931i	0.728245	+	0.213832i	0.624780	−	0.780801i	$-0.285189\pi$
$157$	9.12488	+	2.67931i	0.728245	+	0.213832i	0.103465	+	0.994633i	$0.467007\pi$
$158$	3.67274	+	8.04217i	0.292187	+	0.639801i
$159$		0			0
$160$	6.18962			0.489333
$161$	−0.256008	+	3.35278i	−0.0201763	+	0.264236i
$162$		0			0
$163$	2.09196	−	14.5499i	0.163855	−	1.13964i	−0.727426	−	0.686186i	$-0.759284\pi$
$163$	2.09196	−	14.5499i	0.163855	−	1.13964i	0.891281	−	0.453451i	$-0.149807\pi$
$164$	1.72035	+	3.76704i	0.134337	+	0.294156i
$165$		0			0
$166$	10.7904	+	12.4528i	0.837499	+	0.966526i
$167$	6.52044	−	1.91457i	0.504567	−	0.148154i	−0.0195361	−	0.999809i	$-0.506219\pi$
$167$	6.52044	−	1.91457i	0.504567	−	0.148154i	0.524103	+	0.851655i	$0.324401\pi$
$168$		0			0
$169$	1.08612	−	2.37827i	0.0835475	−	0.182944i
$170$	−1.25701	+	1.45066i	−0.0964081	+	0.111261i
$171$		0			0
$172$	0.755276	+	5.25306i	0.0575893	+	0.400542i
$173$	1.95943	+	13.6281i	0.148972	+	1.03613i	0.917906	+	0.396798i	$0.129879\pi$
$173$	1.95943	+	13.6281i	0.148972	+	1.03613i	−0.768934	+	0.639329i	$0.779212\pi$
$174$		0			0
$175$	−0.921385	+	1.06333i	−0.0696501	+	0.0803806i
$176$	3.16400	−	6.92819i	0.238495	−	0.522232i
$177$		0			0
$178$	−11.8822	+	3.48894i	−0.890612	+	0.261507i
$179$	−13.7642	−	15.8848i	−1.02879	−	1.18728i	−0.982097	−	0.188376i	$-0.939678\pi$
$179$	−13.7642	−	15.8848i	−1.02879	−	1.18728i	−0.0466911	−	0.998909i	$-0.514868\pi$
$180$		0			0
$181$	7.68650	+	16.8311i	0.571333	+	1.25105i	0.946085	+	0.323920i	$0.105001\pi$
$181$	7.68650	+	16.8311i	0.571333	+	1.25105i	−0.374751	+	0.927125i	$0.622272\pi$
$182$	−0.455815	+	3.17026i	−0.0337872	+	0.234995i
$183$		0			0
$184$	−14.7346	+	0.982636i	−1.08625	+	0.0724409i
$185$	−16.3184			−1.19976
$186$		0			0
$187$	−1.36019	−	2.97839i	−0.0994666	−	0.217802i
$188$	1.90427	+	0.559143i	0.138883	+	0.0407797i
$189$		0			0
$190$	−11.4019	+	3.34789i	−0.827179	+	0.242882i
$191$	−0.347803	−	0.223520i	−0.0251662	−	0.0161733i	0.527997	−	0.849246i	$-0.322943\pi$
$191$	−0.347803	−	0.223520i	−0.0251662	−	0.0161733i	−0.553163	+	0.833073i	$0.686579\pi$
$192$		0			0
$193$	−5.88092	+	6.78694i	−0.423318	+	0.488535i	−0.926845	−	0.375445i	$-0.877490\pi$
$193$	−5.88092	+	6.78694i	−0.423318	+	0.488535i	0.503527	+	0.863979i	$0.332035\pi$
$194$	−1.94382	+	1.24922i	−0.139558	+	0.0896887i
$195$		0			0
$196$	−0.614646	−	4.27496i	−0.0439033	−	0.305354i
$197$	14.0999	−	9.06148i	1.00458	−	0.645604i	0.0685945	−	0.997645i	$-0.478149\pi$
$197$	14.0999	−	9.06148i	1.00458	−	0.645604i	0.935985	+	0.352041i	$0.114512\pi$
$198$		0			0
$199$	−2.39487	+	5.24404i	−0.169768	+	0.371740i	−0.975324	−	0.220780i	$-0.929140\pi$
$199$	−2.39487	+	5.24404i	−0.169768	+	0.371740i	0.805555	+	0.592520i	$0.201867\pi$
$200$	−5.19819	−	3.34067i	−0.367568	−	0.236221i
$201$		0			0
$202$	7.26323	+	8.38222i	0.511039	+	0.589771i
$203$	1.57888	+	0.463600i	0.110815	+	0.0325384i
$204$		0			0
$205$	−1.53659	+	10.6872i	−0.107320	+	0.746427i
$206$	−1.99002			−0.138651
$207$		0			0
$208$	−8.82163			−0.611670
$209$	2.88477	−	20.0640i	0.199544	−	1.38786i
$210$		0			0
$211$	−4.78535	−	1.40511i	−0.329437	−	0.0967315i	0.112831	−	0.993614i	$-0.464008\pi$
$211$	−4.78535	−	1.40511i	−0.329437	−	0.0967315i	−0.442269	+	0.896883i	$0.645826\pi$
$212$	−2.04716	−	2.36255i	−0.140600	−	0.162261i
$213$		0			0
$214$	−13.1817	−	8.47136i	−0.901082	−	0.579090i
$215$	−5.74792	+	12.5862i	−0.392005	+	0.858371i
$216$		0			0
$217$	5.09191	−	3.27237i	0.345661	−	0.222143i
$218$	−3.24368	−	22.5603i	−0.219690	−	1.52798i
$219$		0			0
$220$	−3.29512	+	2.11764i	−0.222157	+	0.142771i
$221$	−2.48347	+	2.86608i	−0.167057	+	0.192794i
$222$		0			0
$223$	13.5387	+	8.70081i	0.906620	+	0.582649i	0.908746	−	0.417349i	$-0.137041\pi$
$223$	13.5387	+	8.70081i	0.906620	+	0.582649i	−0.00212667	+	0.999998i	$0.500677\pi$
$224$	−2.40678	+	0.706695i	−0.160810	+	0.0472180i
$225$		0			0
$226$	5.00678	+	1.47012i	0.333046	+	0.0977911i
$227$	5.51919	+	12.0853i	0.366322	+	0.802133i	0.999602	+	0.0282101i	$0.00898073\pi$
$227$	5.51919	+	12.0853i	0.366322	+	0.802133i	−0.633280	+	0.773922i	$0.718292\pi$
$228$		0			0
$229$	−2.11353			−0.139666			−0.0698330	−	0.997559i	$-0.522247\pi$
$229$	−2.11353			−0.139666			−0.0698330	+	0.997559i	$0.522247\pi$
$230$	−8.39645	−	4.63737i	−0.553645	−	0.305779i
$231$		0			0
$232$	−1.02847	+	7.15314i	−0.0675221	+	0.469626i
$233$	−6.18779	−	13.5494i	−0.405376	−	0.887649i	−0.996697	−	0.0812126i	$-0.974121\pi$
$233$	−6.18779	−	13.5494i	−0.405376	−	0.887649i	0.591321	−	0.806436i	$-0.298607\pi$
$234$		0			0
$235$	3.38850	+	3.91054i	0.221041	+	0.255095i
$236$	−5.69046	+	1.67087i	−0.370417	+	0.108764i
$237$		0			0
$238$	0.323148	−	0.707596i	0.0209466	−	0.0458667i
$239$	−12.1799	+	14.0564i	−0.787854	+	0.909232i	−0.997650	−	0.0685134i	$-0.978174\pi$
$239$	−12.1799	+	14.0564i	−0.787854	+	0.909232i	0.209796	+	0.977745i	$0.432720\pi$
$240$		0			0
$241$	−0.952069	−	6.62178i	−0.0613281	−	0.426547i	−0.997236	−	0.0743012i	$-0.976327\pi$
$241$	−0.952069	−	6.62178i	−0.0613281	−	0.426547i	0.935908	−	0.352245i	$-0.114582\pi$
$242$	0.105234	+	0.731919i	0.00676471	+	0.0470496i
$243$		0			0
$244$	3.80865	−	4.39541i	0.243824	−	0.281388i
$245$	4.67767	−	10.2427i	0.298846	−	0.654381i
$246$		0			0
$247$	−22.5267	+	6.61445i	−1.43334	+	0.420867i
$248$	17.4075	+	20.0893i	1.10538	+	1.27567i
$249$		0			0
$250$	−5.82157	−	12.7475i	−0.368188	−	0.806220i
$251$	−2.56489	+	17.8392i	−0.161895	+	1.12600i	0.733163	+	0.680053i	$0.238043\pi$
$251$	−2.56489	+	17.8392i	−0.161895	+	1.12600i	−0.895058	+	0.445950i	$0.852866\pi$
$252$		0			0
$253$	13.1454	−	9.74221i	0.826443	−	0.612488i
$254$	−12.5667			−0.788506
$255$		0			0
$256$	−5.80708	−	12.7157i	−0.362943	−	0.794734i
$257$	−13.0326	−	3.82671i	−0.812949	−	0.238703i	−0.151272	−	0.988492i	$-0.548337\pi$
$257$	−13.0326	−	3.82671i	−0.812949	−	0.238703i	−0.661677	+	0.749789i	$0.730155\pi$
$258$		0			0
$259$	6.34529	−	1.86314i	0.394277	−	0.115770i
$260$	3.81650	+	2.45272i	0.236689	+	0.152111i
$261$		0			0
$262$	11.3070	−	13.0490i	0.698548	−	0.806168i
$263$	15.6675	−	10.0689i	0.966100	−	0.620875i	0.0404201	−	0.999183i	$-0.487130\pi$
$263$	15.6675	−	10.0689i	0.966100	−	0.620875i	0.925680	+	0.378308i	$0.123494\pi$
$264$		0			0
$265$	−1.15992	−	8.06739i	−0.0712530	−	0.495576i
$266$	4.05128	−	2.60360i	0.248400	−	0.159637i
$267$		0			0
$268$	0.467317	−	1.02328i	0.0285460	−	0.0625069i
$269$	15.2705	+	9.81376i	0.931059	+	0.598356i	0.915846	−	0.401529i	$-0.131521\pi$
$269$	15.2705	+	9.81376i	0.931059	+	0.598356i	0.0152130	+	0.999884i	$0.495157\pi$
$270$		0			0
$271$	8.86191	+	10.2272i	0.538323	+	0.621257i	0.958122	−	0.286359i	$-0.0924451\pi$
$271$	8.86191	+	10.2272i	0.538323	+	0.621257i	−0.419800	+	0.907617i	$0.637900\pi$
$272$	2.05576	+	0.603626i	0.124649	+	0.0366002i
$273$		0			0
$274$	2.14221	−	14.8994i	0.129415	−	0.900104i
$275$	6.84633			0.412849
$276$		0			0
$277$	16.1449			0.970051			0.485026	−	0.874500i	$-0.338810\pi$
$277$	16.1449			0.970051			0.485026	+	0.874500i	$0.338810\pi$
$278$	−1.27843	+	8.89168i	−0.0766752	+	0.533287i
$279$		0			0
$280$	−3.58390	−	1.05233i	−0.214179	−	0.0628887i
$281$	3.62572	+	4.18430i	0.216292	+	0.249615i	0.853519	−	0.521062i	$-0.174464\pi$
$281$	3.62572	+	4.18430i	0.216292	+	0.249615i	−0.637227	+	0.770676i	$0.719918\pi$
$282$		0			0
$283$	2.89150	+	1.85826i	0.171882	+	0.110462i	0.623753	−	0.781621i	$-0.285607\pi$
$283$	2.89150	+	1.85826i	0.171882	+	0.110462i	−0.451871	+	0.892083i	$0.649243\pi$
$284$	3.20960	−	7.02805i	0.190455	−	0.417038i
$285$		0			0
$286$	13.1109	−	8.42583i	0.775261	−	0.498230i
$287$	−0.622713	−	4.33107i	−0.0367576	−	0.255655i
$288$		0			0
$289$	−13.5265	+	8.69293i	−0.795674	+	0.511349i
$290$	−3.07393	+	3.54751i	−0.180508	+	0.208317i
$291$		0			0
$292$	4.85633	+	3.12097i	0.284195	+	0.182641i
$293$	27.4240	−	8.05241i	1.60213	−	0.470427i	0.645990	−	0.763346i	$-0.276445\pi$
$293$	27.4240	−	8.05241i	1.60213	−	0.470427i	0.956137	+	0.292919i	$0.0946267\pi$
$294$		0			0
$295$	−14.8361	−	4.35627i	−0.863791	−	0.253632i
$296$	12.0649	+	26.4185i	0.701260	+	1.53554i
$297$		0			0
$298$	9.00623			0.521717
$299$	−16.5889	−	9.16206i	−0.959360	−	0.529855i
$300$		0			0
$301$	0.798012	−	5.55029i	0.0459966	−	0.319914i
$302$	−1.46490	−	3.20768i	−0.0842954	−	0.184581i
$303$		0			0
$304$	8.68611	+	10.0243i	0.498182	+	0.574933i
$305$	14.5491	−	4.27200i	0.833079	−	0.244614i
$306$		0			0
$307$	7.04603	−	15.4286i	0.402138	−	0.880559i	−0.594911	−	0.803792i	$-0.702813\pi$
$307$	7.04603	−	15.4286i	0.402138	−	0.880559i	0.997049	−	0.0767678i	$-0.0244600\pi$
$308$	1.03950	−	1.19964i	0.0592309	−	0.0683561i
$309$		0			0
$310$	2.45721	+	17.0903i	0.139560	+	0.970663i
$311$	−0.0675021	−	0.469487i	−0.00382769	−	0.0266222i	0.987818	−	0.155613i	$-0.0497353\pi$
$311$	−0.0675021	−	0.469487i	−0.00382769	−	0.0266222i	−0.991646	+	0.128991i	$0.958826\pi$
$312$		0			0
$313$	−11.3589	+	13.1089i	−0.642043	+	0.740957i	−0.979735	−	0.200300i	$-0.935808\pi$
$313$	−11.3589	+	13.1089i	−0.642043	+	0.740957i	0.337692	+	0.941257i	$0.390354\pi$
$314$	4.56707	−	10.0005i	0.257734	−	0.564360i
$315$		0			0
$316$	−4.86945	+	1.42980i	−0.273928	+	0.0804326i
$317$	−11.1679	−	12.8884i	−0.627251	−	0.723886i	0.349816	−	0.936818i	$-0.386244\pi$
$317$	−11.1679	−	12.8884i	−0.627251	−	0.723886i	−0.977067	+	0.212932i	$0.931699\pi$
$318$		0			0
$319$	−3.32625	−	7.28346i	−0.186234	−	0.407796i
$320$	2.11767	−	14.7287i	0.118382	−	0.823362i
$321$		0			0
$322$	3.79435	+	0.844543i	0.211451	+	0.0470645i
$323$	5.70214			0.317276
$324$		0			0
$325$	−3.29408	−	7.21304i	−0.182723	−	0.400107i
$326$	−16.3048	−	4.78751i	−0.903038	−	0.265156i
$327$		0			0
$328$	18.4380	−	5.41387i	1.01807	−	0.298931i
$329$	−1.76407	−	1.13370i	−0.0972564	−	0.0625029i
$330$		0			0
$331$	2.87641	−	3.31955i	0.158102	−	0.182459i	−0.671172	−	0.741301i	$-0.734209\pi$
$331$	2.87641	−	3.31955i	0.158102	−	0.182459i	0.829274	+	0.558842i	$0.188754\pi$
$332$	−7.95697	+	5.11363i	−0.436695	+	0.280647i
$333$		0			0
$334$	−1.11803	−	7.77609i	−0.0611761	−	0.425489i
$335$	2.46734	−	1.58566i	0.134805	−	0.0866341i
$336$		0			0
$337$	−4.79510	+	10.4998i	−0.261206	+	0.571961i	−0.994111	−	0.108370i	$-0.965437\pi$
$337$	−4.79510	+	10.4998i	−0.261206	+	0.571961i	0.732905	+	0.680331i	$0.238164\pi$
$338$	−2.54268	−	1.63408i	−0.138303	−	0.0888822i
$339$		0			0
$340$	−0.721554	−	0.832718i	−0.0391318	−	0.0451605i
$341$	−28.2593	−	8.29767i	−1.53033	−	0.449344i
$342$		0			0
$343$	−1.34790	+	9.37486i	−0.0727799	+	0.506195i
$344$	24.6259			1.32774
$345$		0			0
$346$	15.9165			0.855678
$347$	−2.64630	+	18.4054i	−0.142061	+	0.988055i	0.786689	+	0.617349i	$0.211793\pi$
$347$	−2.64630	+	18.4054i	−0.142061	+	0.988055i	−0.928750	+	0.370706i	$0.879116\pi$
$348$		0			0
$349$	14.3921	+	4.22589i	0.770390	+	0.226207i	0.643228	−	0.765675i	$-0.277595\pi$
$349$	14.3921	+	4.22589i	0.770390	+	0.226207i	0.127162	+	0.991882i	$0.459413\pi$
$350$	1.06515	+	1.22925i	0.0569347	+	0.0657061i
$351$		0			0
$352$	10.2680	+	6.59887i	0.547288	+	0.351721i
$353$	5.64873	−	12.3690i	0.300651	−	0.658335i	−0.697660	−	0.716429i	$-0.745775\pi$
$353$	5.64873	−	12.3690i	0.300651	−	0.658335i	0.998311	+	0.0580947i	$0.0185025\pi$
$354$		0			0
$355$	16.9461	−	10.8906i	0.899403	−	0.578011i
$356$	−1.01167	−	7.03631i	−0.0536183	−	0.372924i
$357$		0			0
$358$	−20.4409	+	13.1366i	−1.08034	+	0.694289i
$359$	−2.82547	+	3.26077i	−0.149123	+	0.172097i	−0.825396	−	0.564554i	$-0.809048\pi$
$359$	−2.82547	+	3.26077i	−0.149123	+	0.172097i	0.676274	+	0.736651i	$0.263594\pi$
$360$		0			0
$361$	13.7130	+	8.81284i	0.721739	+	0.463834i
$362$	20.5238	−	6.02633i	1.07871	−	0.316737i
$363$		0			0
$364$	−1.76405	−	0.517972i	−0.0924614	−	0.0271491i
$365$	6.25224	+	13.6905i	0.327257	+	0.716593i
$366$		0			0
$367$	−10.8916			−0.568535			−0.284267	−	0.958745i	$-0.591750\pi$
$367$	−10.8916			−0.568535			−0.284267	+	0.958745i	$0.591750\pi$
$368$	−0.815145	+	10.6754i	−0.0424924	+	0.556496i
$369$		0			0
$370$	−2.68472	+	18.6726i	−0.139572	+	0.970743i
$371$	1.37211	+	3.00450i	0.0712364	+	0.155986i
$372$		0			0
$373$	−7.48393	−	8.63692i	−0.387503	−	0.447203i	0.528162	−	0.849143i	$-0.322881\pi$
$373$	−7.48393	−	8.63692i	−0.387503	−	0.447203i	−0.915666	+	0.401941i	$0.868336\pi$
$374$	−3.63185	+	1.06641i	−0.187798	+	0.0551425i
$375$		0			0
$376$	3.82564	−	8.37699i	0.197293	−	0.432010i
$377$	−6.07318	+	7.00882i	−0.312785	+	0.360973i
$378$		0			0
$379$	−4.90875	−	34.1411i	−0.252146	−	1.75371i	−0.585279	−	0.810832i	$-0.699015\pi$
$379$	−4.90875	−	34.1411i	−0.252146	−	1.75371i	0.333133	−	0.942880i	$-0.391894\pi$
$380$	−0.970769	−	6.75185i	−0.0497994	−	0.346362i
$381$		0			0
$382$	−0.312986	+	0.361206i	−0.0160138	+	0.0184809i
$383$	2.05523	−	4.50033i	0.105017	−	0.229956i	−0.849827	−	0.527061i	$-0.823294\pi$
$383$	2.05523	−	4.50033i	0.105017	−	0.229956i	0.954845	+	0.297105i	$0.0960211\pi$
$384$		0			0
$385$	3.97090	−	1.16596i	0.202376	−	0.0594229i
$386$	6.79853	+	7.84592i	0.346036	+	0.399347i
$387$		0			0
$388$	−0.550989	−	1.20650i	−0.0279722	−	0.0612506i
$389$	1.66969	−	11.6130i	0.0846568	−	0.588801i	−0.902698	−	0.430275i	$-0.858417\pi$
$389$	1.66969	−	11.6130i	0.0846568	−	0.588801i	0.987355	−	0.158526i	$-0.0506742\pi$
$390$		0			0
$391$	3.23889	+	3.27020i	0.163798	+	0.165381i
$392$	−20.0406			−1.01221
$393$		0			0
$394$	−8.04901	−	17.6249i	−0.405503	−	0.887928i
$395$	−12.6956	−	3.72776i	−0.638784	−	0.187564i
$396$		0			0
$397$	−27.1680	+	7.97725i	−1.36352	+	0.400367i	−0.880004	−	0.474966i	$-0.842460\pi$
$397$	−27.1680	+	7.97725i	−1.36352	+	0.400367i	−0.483520	+	0.875333i	$0.660642\pi$
$398$	5.60657	+	3.60312i	0.281032	+	0.180608i
$399$		0			0
$400$	−2.93374	+	3.38571i	−0.146687	+	0.169286i
$401$	−23.7395	+	15.2565i	−1.18550	+	0.761872i	−0.976389	−	0.216021i	$-0.930692\pi$
$401$	−23.7395	+	15.2565i	−1.18550	+	0.761872i	−0.209107	+	0.977893i	$0.567056\pi$
$402$		0			0
$403$	4.85472	+	33.7653i	0.241831	+	1.68197i
$404$	−5.35598	+	3.44208i	−0.266470	+	0.171250i
$405$		0			0
$406$	0.790239	−	1.73038i	0.0392189	−	0.0858774i
$407$	−27.0709	−	17.3974i	−1.34185	−	0.862357i
$408$		0			0
$409$	−15.6532	−	18.0648i	−0.774002	−	0.893246i	0.222659	−	0.974896i	$-0.428526\pi$
$409$	−15.6532	−	18.0648i	−0.774002	−	0.893246i	−0.996661	+	0.0816507i	$0.973981\pi$
$410$	11.9762	+	3.51653i	0.591462	+	0.173669i
$411$		0			0
$412$	0.162569	−	1.13069i	0.00800920	−	0.0557052i
$413$	6.26627			0.308343
$414$		0			0
$415$	−24.6600			−1.21051
$416$	2.01190	−	13.9930i	0.0986413	−	0.686065i
$417$		0			0
$418$	−22.4840	−	6.60189i	−1.09973	−	0.322909i
$419$	−4.13517	−	4.77224i	−0.202016	−	0.233139i	0.645697	−	0.763594i	$-0.276567\pi$
$419$	−4.13517	−	4.77224i	−0.202016	−	0.233139i	−0.847714	+	0.530454i	$0.822021\pi$
$420$		0			0
$421$	13.2789	+	8.53385i	0.647176	+	0.415915i	0.822633	−	0.568572i	$-0.192504\pi$
$421$	13.2789	+	8.53385i	0.647176	+	0.415915i	−0.175457	+	0.984487i	$0.556140\pi$
$422$	−2.39510	+	5.24454i	−0.116592	+	0.255300i
$423$		0			0
$424$	−12.2030	+	7.84240i	−0.592631	+	0.380861i
$425$	0.274084	+	1.90630i	0.0132950	+	0.0924691i
$426$		0			0
$427$	−5.16954	+	3.32226i	−0.250172	+	0.160776i
$428$	5.89012	−	6.79756i	0.284710	−	0.328572i
$429$		0			0
$430$	13.4563	+	8.64782i	0.648919	+	0.417035i
$431$	−4.11677	+	1.20879i	−0.198298	+	0.0582255i	−0.379373	−	0.925244i	$-0.623860\pi$
$431$	−4.11677	+	1.20879i	−0.198298	+	0.0582255i	0.181075	+	0.983469i	$0.442042\pi$
$432$		0			0
$433$	−25.5847	−	7.51236i	−1.22952	−	0.361021i	−0.398454	−	0.917188i	$-0.630453\pi$
$433$	−25.5847	−	7.51236i	−1.22952	−	0.361021i	−0.831070	+	0.556168i	$0.812271\pi$
$434$	−2.90673	−	6.36486i	−0.139528	−	0.305523i
$435$		0			0
$436$	13.0834			0.626579
$437$	5.92289	+	27.8718i	0.283330	+	1.33329i
$438$		0			0
$439$	1.79597	−	12.4913i	0.0857171	−	0.596176i	−0.901011	−	0.433796i	$-0.857174\pi$
$439$	1.79597	−	12.4913i	0.0857171	−	0.596176i	0.986728	−	0.162380i	$-0.0519170\pi$
$440$	7.55027	+	16.5328i	0.359945	+	0.788170i
$441$		0			0
$442$	2.87097	+	3.31328i	0.136558	+	0.157597i
$443$	5.37110	−	1.57710i	0.255189	−	0.0749302i	−0.151636	−	0.988436i	$-0.548454\pi$
$443$	5.37110	−	1.57710i	0.255189	−	0.0749302i	0.406825	+	0.913506i	$0.366636\pi$
$444$		0			0
$445$	7.69915	−	16.8588i	0.364975	−	0.799183i
$446$	12.1834	−	14.0604i	0.576902	−	0.665780i
$447$		0			0
$448$	0.858203	+	5.96893i	0.0405463	+	0.282006i
$449$	2.35429	+	16.3745i	0.111106	+	0.772759i	0.966847	+	0.255355i	$0.0821924\pi$
$449$	2.35429	+	16.3745i	0.111106	+	0.772759i	−0.855741	+	0.517404i	$0.826898\pi$
$450$		0			0
$451$	−13.9429	+	16.0909i	−0.656545	+	0.757693i
$452$	−1.24431	+	2.72466i	−0.0585275	+	0.128157i
$453$		0			0
$454$	14.7369	−	4.32713i	0.691635	−	0.203082i
$455$	−3.13900	−	3.62260i	−0.147158	−	0.169830i
$456$		0			0
$457$	−16.2613	−	35.6074i	−0.760674	−	1.66564i	−0.746177	−	0.665748i	$-0.768113\pi$
$457$	−16.2613	−	35.6074i	−0.760674	−	1.66564i	−0.0144970	−	0.999895i	$-0.504615\pi$
$458$	−0.347719	+	2.41844i	−0.0162478	+	0.113006i
$459$		0			0
$460$	3.32080	−	4.39188i	0.154833	−	0.204772i
$461$	−15.1721			−0.706635			−0.353318	−	0.935503i	$-0.614947\pi$
$461$	−15.1721			−0.706635			−0.353318	+	0.935503i	$0.614947\pi$
$462$		0			0
$463$	8.12864	+	17.7992i	0.377770	+	0.827201i	0.999049	+	0.0436112i	$0.0138863\pi$
$463$	8.12864	+	17.7992i	0.377770	+	0.827201i	−0.621279	+	0.783590i	$0.713386\pi$
$464$	5.02723	+	1.47613i	0.233383	+	0.0685275i
$465$		0			0
$466$	−16.5221	+	4.85132i	−0.765371	+	0.224733i
$467$	22.1453	+	14.2319i	1.02476	+	0.658575i	0.941173	−	0.337925i	$-0.109725\pi$
$467$	22.1453	+	14.2319i	1.02476	+	0.658575i	0.0835896	+	0.996500i	$0.473362\pi$
$468$		0			0
$469$	−0.778363	+	0.898279i	−0.0359415	+	0.0414787i
$470$	5.03217	−	3.23398i	0.232117	−	0.149172i
$471$		0			0
$472$	3.91645	+	27.2395i	0.180269	+	1.25380i
$473$	−22.9537	+	14.7514i	−1.05541	+	0.678271i
$474$		0			0
$475$	−4.95293	+	10.8454i	−0.227256	+	0.497621i
$476$	0.375645	+	0.241413i	0.0172177	+	0.0110651i
$477$		0			0
$478$	14.0804	+	16.2496i	0.644021	+	0.743240i
$479$	12.4125	+	3.64463i	0.567141	+	0.166528i	0.552718	−	0.833368i	$-0.313591\pi$
$479$	12.4125	+	3.64463i	0.567141	+	0.166528i	0.0144229	+	0.999896i	$0.495409\pi$
$480$		0			0
$481$	−5.30420	+	36.8915i	−0.241851	+	1.68211i
$482$	−7.73371			−0.352261
$483$		0			0
$484$	−0.424461			−0.0192937
$485$	0.492134	−	3.42287i	0.0223467	−	0.155424i
$486$		0			0
$487$	7.65688	+	2.24826i	0.346966	+	0.101878i	0.450572	−	0.892740i	$-0.351220\pi$
$487$	7.65688	+	2.24826i	0.346966	+	0.101878i	−0.103606	+	0.994618i	$0.533038\pi$
$488$	−17.6729	−	20.3956i	−0.800014	−	0.923265i
$489$		0			0
$490$	−10.9508	−	7.03763i	−0.494705	−	0.317928i
$491$	−0.273712	+	0.599345i	−0.0123524	+	0.0270481i	−0.915708	−	0.401845i	$-0.868369\pi$
$491$	−0.273712	+	0.599345i	−0.0123524	+	0.0270481i	0.903355	+	0.428893i	$0.141096\pi$
$492$		0			0
$493$	1.89485	−	1.21775i	0.0853399	−	0.0548446i
$494$	3.86257	+	26.8648i	0.173785	+	1.20870i
$495$		0			0
$496$	16.2129	−	10.4194i	0.727981	−	0.467845i
$497$	−5.34591	+	6.16951i	−0.239797	+	0.276740i
$498$		0			0
$499$	17.0771	+	10.9748i	0.764476	+	0.491299i	0.863849	−	0.503751i	$-0.168047\pi$
$499$	17.0771	+	10.9748i	0.764476	+	0.491299i	−0.0993725	+	0.995050i	$0.531684\pi$
$500$	7.71846	−	2.26635i	0.345180	−	0.101354i
$501$		0			0
$502$	19.9908	+	5.86984i	0.892234	+	0.261984i
$503$	−5.09665	−	11.1601i	−0.227249	−	0.497605i	0.761320	−	0.648376i	$-0.224552\pi$
$503$	−5.09665	−	11.1601i	−0.227249	−	0.497605i	−0.988569	+	0.150771i	$0.951824\pi$
$504$		0			0
$505$	−16.5991			−0.738650
$506$	−8.98499	−	16.6446i	−0.399431	−	0.739942i
$507$		0			0
$508$	1.02660	−	7.14019i	0.0455482	−	0.316795i
$509$	−3.50514	−	7.67519i	−0.155363	−	0.340197i	0.815905	−	0.578186i	$-0.196239\pi$
$509$	−3.50514	−	7.67519i	−0.155363	−	0.340197i	−0.971268	+	0.237989i	$0.923512\pi$
$510$		0			0
$511$	−3.99423	−	4.60959i	−0.176694	−	0.203916i
$512$	−20.8548	+	6.12352i	−0.921661	+	0.270624i
$513$		0			0
$514$	−6.52289	+	14.2831i	−0.287712	+	0.630002i
$515$	1.95033	−	2.25081i	0.0859420	−	0.0991823i
$516$		0			0
$517$	1.45213	+	10.0998i	0.0638646	+	0.444188i
$518$	−1.08800	−	7.56721i	−0.0478040	−	0.332484i
$519$		0			0
$520$	13.7855	−	15.9094i	0.604536	−	0.697672i
$521$	−0.313228	+	0.685873i	−0.0137228	+	0.0300487i	−0.916369	−	0.400334i	$-0.868894\pi$
$521$	−0.313228	+	0.685873i	−0.0137228	+	0.0300487i	0.902647	+	0.430383i	$0.141621\pi$
$522$		0			0
$523$	−21.1241	+	6.20259i	−0.923692	+	0.271220i	−0.708794	−	0.705416i	$-0.750760\pi$
$523$	−21.1241	+	6.20259i	−0.923692	+	0.271220i	−0.214898	+	0.976636i	$0.568942\pi$
$524$	6.49050	+	7.49043i	0.283539	+	0.327221i
$525$		0			0
$526$	−8.94386	−	19.5843i	−0.389971	−	0.853917i
$527$	1.17909	−	8.20073i	0.0513618	−	0.357229i
$528$		0			0
$529$	−12.6203	+	19.2283i	−0.548707	+	0.836015i
$530$	−9.42206			−0.409268
$531$		0			0
$532$	1.14836	+	2.51456i	0.0497878	+	0.109020i
$533$	23.6614	+	6.94761i	1.02489	+	0.300934i
$534$		0			0
$535$	22.5004	−	6.60670i	0.972776	−	0.285633i
$536$	−4.39130	−	2.82212i	−0.189675	−	0.121897i
$537$		0			0
$538$	13.7419	−	15.8589i	0.592453	−	0.683728i
$539$	18.6798	−	12.0048i	0.804594	−	0.517081i
$540$		0			0
$541$	2.17878	+	15.1537i	0.0936730	+	0.651510i	0.981518	+	0.191368i	$0.0612924\pi$
$541$	2.17878	+	15.1537i	0.0936730	+	0.651510i	−0.887845	+	0.460142i	$0.847798\pi$
$542$	13.1606	−	8.45779i	0.565295	−	0.363293i
$543$		0			0
$544$	−1.42633	+	3.12322i	−0.0611533	+	0.133907i
$545$	28.6958	+	18.4417i	1.22919	+	0.789955i
$546$		0			0
$547$	−2.84283	−	3.28081i	−0.121551	−	0.140277i	0.691712	−	0.722173i	$-0.256857\pi$
$547$	−2.84283	−	3.28081i	−0.121551	−	0.140277i	−0.813263	+	0.581896i	$0.802311\pi$
$548$	8.29056	+	2.43433i	0.354155	+	0.103989i
$549$		0			0
$550$	1.12636	−	7.83401i	0.0480282	−	0.334043i
$551$	13.9442			0.594044
$552$		0			0
$553$	5.36219			0.228023
$554$	2.65616	−	18.4740i	0.112849	−	0.784885i
$555$		0			0
$556$	−4.94766	−	1.45276i	−0.209827	−	0.0616109i
$557$	−1.51952	−	1.75362i	−0.0643841	−	0.0743032i	0.722644	−	0.691221i	$-0.242927\pi$
$557$	−1.51952	−	1.75362i	−0.0643841	−	0.0743032i	−0.787028	+	0.616917i	$0.788381\pi$
$558$		0			0
$559$	26.5856	+	17.0855i	1.12445	+	0.722641i
$560$	−1.12498	+	2.46336i	−0.0475390	+	0.104096i
$561$		0			0
$562$	5.38445	−	3.46038i	0.227129	−	0.145967i
$563$	−5.34799	−	37.1961i	−0.225391	−	1.56763i	−0.717163	−	0.696905i	$-0.754560\pi$
$563$	−5.34799	−	37.1961i	−0.225391	−	1.56763i	0.491772	−	0.870724i	$-0.336349\pi$
$564$		0			0
$565$	−6.56972	+	4.22210i	−0.276390	+	0.177625i
$566$	2.60205	−	3.00292i	0.109372	−	0.126222i
$567$		0			0
$568$	−30.1601	−	19.3827i	−1.26549	−	0.813280i
$569$	−38.5871	+	11.3302i	−1.61765	+	0.474986i	−0.960387	−	0.278671i	$-0.910106\pi$
$569$	−38.5871	+	11.3302i	−1.61765	+	0.474986i	−0.657268	+	0.753657i	$0.728288\pi$
$570$		0			0
$571$	3.62322	+	1.06387i	0.151627	+	0.0445217i	0.356665	−	0.934232i	$-0.383914\pi$
$571$	3.62322	+	1.06387i	0.151627	+	0.0445217i	−0.205038	+	0.978754i	$0.565732\pi$
$572$	3.71636	+	8.13768i	0.155389	+	0.340254i
$573$		0			0
$574$	−5.05834			−0.211131
$575$	−9.03320	+	3.31981i	−0.376710	+	0.138446i
$576$		0			0
$577$	−0.523644	+	3.64203i	−0.0217996	+	0.151620i	−0.997814	−	0.0660871i	$-0.978948\pi$
$577$	−0.523644	+	3.64203i	−0.0217996	+	0.151620i	0.976014	+	0.217707i	$0.0698576\pi$
$578$	7.72163	+	16.9080i	0.321177	+	0.703281i
$579$		0			0
$580$	−1.76451	−	2.03636i	−0.0732675	−	0.0845552i
$581$	9.58883	−	2.81554i	0.397812	−	0.116808i
$582$		0			0
$583$	6.67659	−	14.6197i	0.276516	−	0.605486i
$584$	17.5415	−	20.2440i	0.725872	−	0.837701i
$585$		0			0
$586$	−4.70228	−	32.7051i	−0.194250	−	1.35104i
$587$	1.46701	+	10.2033i	0.0605499	+	0.421134i	0.997440	+	0.0715096i	$0.0227817\pi$
$587$	1.46701	+	10.2033i	0.0605499	+	0.421134i	−0.936890	+	0.349624i	$0.886309\pi$
$588$		0			0
$589$	33.5885	−	38.7632i	1.38399	−	1.59721i
$590$	−7.42557	+	16.2597i	−0.305706	+	0.669402i
$591$		0			0
$592$	20.2037	−	5.93235i	0.830368	−	0.243818i
$593$	−1.00032	−	1.15443i	−0.0410781	−	0.0474067i	0.734839	−	0.678242i	$-0.237258\pi$
$593$	−1.00032	−	1.15443i	−0.0410781	−	0.0474067i	−0.775917	+	0.630835i	$0.782712\pi$
$594$		0			0
$595$	0.483622	+	1.05898i	0.0198266	+	0.0434141i
$596$	−0.735740	+	5.11718i	−0.0301371	+	0.209608i
$597$		0			0
$598$	−13.2130	+	17.4747i	−0.540321	+	0.714595i
$599$	41.8601			1.71036			0.855178	−	0.518335i	$-0.173448\pi$
$599$	41.8601			1.71036			0.855178	+	0.518335i	$0.173448\pi$
$600$		0			0
$601$	2.34216	+	5.12861i	0.0955386	+	0.209200i	0.951367	−	0.308059i	$-0.0996795\pi$
$601$	2.34216	+	5.12861i	0.0955386	+	0.209200i	−0.855829	+	0.517259i	$0.826952\pi$
$602$	−6.21972	−	1.82627i	−0.253497	−	0.0744334i
$603$		0			0
$604$	1.94222	−	0.570287i	0.0790277	−	0.0232046i
$605$	−0.930973	−	0.598300i	−0.0378494	−	0.0243243i
$606$		0			0
$607$	0.682821	−	0.788018i	0.0277149	−	0.0319846i	−0.741723	−	0.670706i	$-0.765991\pi$
$607$	0.682821	−	0.788018i	0.0277149	−	0.0319846i	0.769438	+	0.638722i	$0.220537\pi$
$608$	−17.8817	+	11.4919i	−0.725200	+	0.466058i
$609$		0			0
$610$	−2.49468	−	17.3509i	−0.101007	−	0.702516i
$611$	9.94207	−	6.38938i	0.402213	−	0.258487i
$612$		0			0
$613$	11.9534	−	26.1743i	0.482794	−	1.05717i	−0.498891	−	0.866664i	$-0.666259\pi$
$613$	11.9534	−	26.1743i	0.482794	−	1.05717i	0.981686	−	0.190508i	$-0.0610134\pi$
$614$	−16.4952	−	10.6008i	−0.665694	−	0.427815i
$615$		0			0
$616$	−4.82348	−	5.56659i	−0.194343	−	0.224284i
$617$	−38.4153	−	11.2797i	−1.54654	−	0.454106i	−0.606477	−	0.795101i	$-0.707418\pi$
$617$	−38.4153	−	11.2797i	−1.54654	−	0.454106i	−0.940065	+	0.340996i	$0.889236\pi$
$618$		0			0
$619$	4.65013	−	32.3424i	0.186905	−	1.29995i	−0.653059	−	0.757307i	$-0.726515\pi$
$619$	4.65013	−	32.3424i	0.186905	−	1.29995i	0.839964	−	0.542643i	$-0.182576\pi$
$620$	−9.91114			−0.398041
$621$		0			0
$622$	−0.548323			−0.0219858
$623$	−1.06891	+	7.43444i	−0.0428250	+	0.297855i
$624$		0			0
$625$	10.4963	+	3.08199i	0.419852	+	0.123280i
$626$	13.1312	+	15.1543i	0.524830	+	0.605686i
$627$		0			0
$628$	5.30900	+	3.41189i	0.211852	+	0.136149i
$629$	3.76040	−	8.23412i	0.149937	−	0.328316i
$630$		0			0
$631$	−4.94602	+	3.17862i	−0.196898	+	0.126539i	−0.635375	−	0.772204i	$-0.719154\pi$
$631$	−4.94602	+	3.17862i	−0.196898	+	0.126539i	0.438477	+	0.898742i	$0.355518\pi$
$632$	3.35139	+	23.3094i	0.133311	+	0.927200i
$633$		0			0
$634$	−16.5851	+	10.6586i	−0.658679	+	0.423307i
$635$	12.3161	−	14.2136i	0.488751	−	0.564049i
$636$		0			0
$637$	−21.6355	−	13.9043i	−0.857228	−	0.550907i
$638$	−8.88145	+	2.60783i	−0.351620	+	0.103245i
$639$		0			0
$640$	−4.62739	−	1.35872i	−0.182914	−	0.0537083i
$641$	−18.7747	−	41.1108i	−0.741555	−	1.62378i	−0.780980	−	0.624556i	$-0.785280\pi$
$641$	−18.7747	−	41.1108i	−0.741555	−	1.62378i	0.0394258	−	0.999222i	$-0.487447\pi$
$642$		0			0
$643$	33.5453			1.32290			0.661449	−	0.749990i	$-0.269942\pi$
$643$	33.5453			1.32290			0.661449	+	0.749990i	$0.269942\pi$
$644$	−0.789824	+	2.08689i	−0.0311234	+	0.0822351i
$645$		0			0
$646$	0.938119	−	6.52476i	0.0369098	−	0.256713i
$647$	−2.40384	−	5.26368i	−0.0945048	−	0.206937i	0.856476	−	0.516187i	$-0.172649\pi$
$647$	−2.40384	−	5.26368i	−0.0945048	−	0.206937i	−0.950981	+	0.309251i	$0.899922\pi$
$648$		0			0
$649$	−19.9675	−	23.0437i	−0.783792	−	0.904545i
$650$	−8.79557	+	2.58261i	−0.344991	+	0.101298i
$651$		0			0
$652$	4.05216	−	8.87299i	0.158695	−	0.347493i
$653$	−25.6574	+	29.6103i	−1.00405	+	1.15874i	−0.0167555	+	0.999860i	$0.505334\pi$
$653$	−25.6574	+	29.6103i	−1.00405	+	1.15874i	−0.987298	+	0.158880i	$0.949212\pi$
$654$		0			0
$655$	3.67749	+	25.5775i	0.143692	+	0.999397i
$656$	−1.98275	−	13.7903i	−0.0774135	−	0.538423i
$657$		0			0
$658$	−1.58748	+	1.83205i	−0.0618864	+	0.0714207i
$659$	−2.40123	+	5.25796i	−0.0935387	+	0.204821i	−0.950618	−	0.310363i	$-0.899549\pi$
$659$	−2.40123	+	5.25796i	−0.0935387	+	0.204821i	0.857079	+	0.515184i	$0.172277\pi$
$660$		0			0
$661$	−9.17712	+	2.69465i	−0.356949	+	0.104810i	−0.455290	−	0.890343i	$-0.650464\pi$
$661$	−9.17712	+	2.69465i	−0.356949	+	0.104810i	0.0983415	+	0.995153i	$0.468646\pi$
$662$	−3.32522	−	3.83750i	−0.129238	−	0.149149i
$663$		0			0
$664$	18.2322	+	39.9230i	0.707547	+	1.54931i
$665$	−1.02570	+	7.13388i	−0.0397748	+	0.276640i
$666$		0			0
$667$	7.92050	+	7.99705i	0.306683	+	0.309647i
$668$	4.50958			0.174481
$669$		0			0
$670$	−1.40849	−	3.08417i	−0.0544148	−	0.119152i
$671$	28.6902	+	8.42419i	1.10757	+	0.325212i
$672$		0			0
$673$	−10.2614	+	3.01303i	−0.395549	+	0.116144i	−0.473457	−	0.880817i	$-0.656994\pi$
$673$	−10.2614	+	3.01303i	−0.395549	+	0.116144i	0.0779079	+	0.996961i	$0.475176\pi$
$674$	11.2257	+	7.21430i	0.432397	+	0.277884i
$675$		0			0
$676$	1.13617	−	1.31121i	0.0436990	−	0.0504313i
$677$	26.7147	−	17.1685i	1.02673	−	0.659838i	0.0850577	−	0.996376i	$-0.472893\pi$
$677$	26.7147	−	17.1685i	1.02673	−	0.659838i	0.941670	+	0.336538i	$0.109256\pi$
$678$		0			0
$679$	0.199441	+	1.38714i	0.00765384	+	0.0532336i
$680$	−4.30114	+	2.76417i	−0.164941	+	0.106001i
$681$		0			0
$682$	−14.1440	+	30.9710i	−0.541600	+	1.18594i
$683$	7.74023	+	4.97434i	0.296172	+	0.190338i	0.680284	−	0.732948i	$-0.261856\pi$
$683$	7.74023	+	4.97434i	0.296172	+	0.190338i	−0.384113	+	0.923286i	$0.625493\pi$
$684$		0			0
$685$	14.7524	+	17.0252i	0.563661	+	0.650500i
$686$	10.5056	+	3.08471i	0.401105	+	0.117775i
$687$		0			0
$688$	2.54091	−	17.6724i	0.0968714	−	0.673755i
$689$	−18.6152			−0.709182
$690$		0			0
$691$	−28.7634			−1.09421			−0.547105	−	0.837064i	$-0.684270\pi$
$691$	−28.7634			−1.09421			−0.547105	+	0.837064i	$0.684270\pi$
$692$	−1.30026	+	9.04350i	−0.0494284	+	0.343782i
$693$		0			0
$694$	20.6253	+	6.05614i	0.782926	+	0.229888i
$695$	−8.80399	−	10.1603i	−0.333954	−	0.385404i
$696$		0			0
$697$	−5.03857	−	3.23809i	−0.190849	−	0.122651i
$698$	7.20333	−	15.7731i	0.272650	−	0.597020i
$699$		0			0
$700$	−0.785452	+	0.504779i	−0.0296873	+	0.0190789i
$701$	−0.839552	−	5.83921i	−0.0317094	−	0.220544i	0.967805	−	0.251701i	$-0.0809899\pi$
$701$	−0.839552	−	5.83921i	−0.0317094	−	0.220544i	−0.999515	+	0.0311569i	$0.990081\pi$
$702$		0			0
$703$	47.1438	−	30.2974i	1.77806	−	1.14269i
$704$	19.2156	−	22.1760i	0.724216	−	0.835790i
$705$		0			0
$706$	−13.2241	−	8.49859i	−0.497694	−	0.319849i
$707$	6.45442	−	1.89519i	0.242743	−	0.0712759i
$708$		0			0
$709$	−10.1644	−	2.98454i	−0.381733	−	0.112087i	0.0852358	−	0.996361i	$-0.472836\pi$
$709$	−10.1644	−	2.98454i	−0.381733	−	0.112087i	−0.466968	+	0.884274i	$0.654654\pi$
$710$	−9.67372	−	21.1825i	−0.363048	−	0.794965i
$711$		0			0
$712$	−32.9856			−1.23619
$713$	41.3095	−	2.75490i	1.54705	−	0.103172i
$714$		0			0
$715$	−3.31939	+	23.0868i	−0.124138	+	0.863399i
$716$	−5.79411	−	12.6873i	−0.216536	−	0.474147i
$717$		0			0
$718$	3.26634	+	3.76955i	0.121899	+	0.140678i
$719$	−11.9533	+	3.50982i	−0.445784	+	0.130894i	−0.496918	−	0.867798i	$-0.665535\pi$
$719$	−11.9533	+	3.50982i	−0.445784	+	0.130894i	0.0511331	+	0.998692i	$0.483717\pi$
$720$		0			0
$721$	−0.501387	+	1.09788i	−0.0186726	+	0.0408873i
$722$	12.3403	−	14.2415i	0.459258	−	0.530012i
$723$		0			0
$724$	1.74742	+	12.1536i	0.0649424	+	0.451684i
$725$	0.670256	+	4.66173i	0.0248927	+	0.173132i
$726$		0			0
$727$	13.6473	−	15.7498i	0.506151	−	0.584130i	−0.443958	−	0.896048i	$-0.646426\pi$
$727$	13.6473	−	15.7498i	0.506151	−	0.584130i	0.950109	+	0.311918i	$0.100971\pi$
$728$	−3.54395	+	7.76018i	−0.131348	+	0.287611i
$729$		0			0
$730$	16.6942	−	4.90185i	0.617879	−	0.181426i
$731$	−5.02632	−	5.80068i	−0.185905	−	0.214546i
$732$		0			0
$733$	11.1825	+	24.4863i	0.413035	+	0.904420i	0.995781	+	0.0917658i	$0.0292511\pi$
$733$	11.1825	+	24.4863i	0.413035	+	0.904420i	−0.582746	+	0.812655i	$0.698022\pi$
$734$	−1.79188	+	12.4628i	−0.0661397	+	0.460011i
$735$		0			0
$736$	−16.7477	−	3.72768i	−0.617328	−	0.137404i
$737$	5.78361			0.213042
$738$		0			0
$739$	13.9697	+	30.5895i	0.513886	+	1.12525i	0.971703	+	0.236206i	$0.0759040\pi$
$739$	13.9697	+	30.5895i	0.513886	+	1.12525i	−0.457817	+	0.889046i	$0.651369\pi$
$740$	−10.3901	−	3.05082i	−0.381949	−	0.112150i
$741$		0			0
$742$	3.66369	−	1.07576i	0.134498	−	0.0394922i
$743$	−14.7677	−	9.49063i	−0.541775	−	0.348177i	0.240958	−	0.970536i	$-0.422538\pi$
$743$	−14.7677	−	9.49063i	−0.541775	−	0.348177i	−0.782733	+	0.622358i	$0.786175\pi$
$744$		0			0
$745$	−8.82665	+	10.1865i	−0.323383	+	0.373204i
$746$	−11.1142	+	7.14265i	−0.406919	+	0.261511i
$747$		0			0
$748$	−0.309219	−	2.15067i	−0.0113062	−	0.0786362i
$749$	−7.99476	+	5.13792i	−0.292122	+	0.187736i
$750$		0			0
$751$	10.8737	−	23.8101i	0.396788	−	0.868844i	−0.600798	−	0.799401i	$-0.705150\pi$
$751$	10.8737	−	23.8101i	0.396788	−	0.868844i	0.997586	−	0.0694434i	$-0.0221223\pi$
$752$	−5.61690	−	3.60976i	−0.204827	−	0.131634i
$753$		0			0
$754$	7.02078	+	8.10242i	0.255682	+	0.295073i
$755$	5.06373	+	1.48685i	0.184288	+	0.0541118i
$756$		0			0
$757$	−2.30452	+	16.0283i	−0.0837592	+	0.582558i	0.904114	+	0.427292i	$0.140532\pi$
$757$	−2.30452	+	16.0283i	−0.0837592	+	0.582558i	−0.987873	+	0.155266i	$0.950377\pi$
$758$	−39.8741			−1.44829
$759$		0			0
$760$	−31.6521			−1.14814
$761$	−7.12949	+	49.5867i	−0.258444	+	1.79752i	0.285484	+	0.958383i	$0.407846\pi$
$761$	−7.12949	+	49.5867i	−0.258444	+	1.79752i	−0.543928	+	0.839132i	$0.683064\pi$
$762$		0			0
$763$	−13.2637	−	3.89457i	−0.480178	−	0.140993i
$764$	−0.179662	−	0.207341i	−0.00649995	−	0.00750134i
$765$		0			0
$766$	−4.81144	−	3.09213i	−0.173845	−	0.111723i
$767$	−14.6707	+	32.1244i	−0.529729	+	1.15994i
$768$		0			0
$769$	−15.4147	+	9.90642i	−0.555868	+	0.357235i	−0.788217	−	0.615398i	$-0.788995\pi$
$769$	−15.4147	+	9.90642i	−0.555868	+	0.357235i	0.232349	+	0.972633i	$0.425359\pi$
$770$	−0.680874	−	4.73559i	−0.0245370	−	0.170659i
$771$		0			0
$772$	−5.01330	+	3.22185i	−0.180433	+	0.115957i
$773$	22.4455	−	25.9035i	0.807308	−	0.931683i	−0.191451	−	0.981502i	$-0.561319\pi$
$773$	22.4455	−	25.9035i	0.807308	−	0.931683i	0.998758	+	0.0498196i	$0.0158646\pi$
$774$		0			0
$775$	14.5735	+	9.36583i	0.523496	+	0.336431i
$776$	−5.90526	+	1.73394i	−0.211987	+	0.0622449i
$777$		0			0
$778$	−13.0136	−	3.82114i	−0.466560	−	0.136995i
$779$	−15.4031	−	33.7281i	−0.551873	−	1.20843i
$780$		0			0
$781$	39.7226			1.42139
$782$	4.27483	−	3.16813i	0.152868	−	0.113292i
$783$		0			0
$784$	−2.06780	+	14.3819i	−0.0738501	+	0.513639i
$785$	6.83504	+	14.9666i	0.243953	+	0.534182i
$786$		0			0
$787$	−6.11416	−	7.05611i	−0.217946	−	0.251523i	0.636239	−	0.771492i	$-0.280489\pi$
$787$	−6.11416	−	7.05611i	−0.217946	−	0.251523i	−0.854185	+	0.519969i	$0.825944\pi$
$788$	10.6717	−	3.13349i	0.380163	−	0.111626i
$789$		0			0
$790$	−6.35423	+	13.9138i	−0.226073	+	0.495032i
$791$	2.07252	−	2.39182i	0.0736905	−	0.0850434i
$792$		0			0
$793$	−4.92874	−	34.2801i	−0.175025	−	1.21732i
$794$	4.65839	+	32.3998i	0.165320	+	1.14983i
$795$		0			0
$796$	−2.50525	+	2.89121i	−0.0887961	+	0.102476i
$797$	−17.7241	+	38.8104i	−0.627821	+	1.37474i	0.281871	+	0.959452i	$0.409045\pi$
$797$	−17.7241	+	38.8104i	−0.627821	+	1.37474i	−0.909692	+	0.415283i	$0.863682\pi$
$798$		0			0
$799$	−2.75406	+	0.808664i	−0.0974316	+	0.0286085i
$800$	−4.70141	−	5.42571i	−0.166220	−	0.191828i
$801$		0			0
$802$	13.5518	+	29.6743i	0.478531	+	1.04784i
$803$	−4.22377	+	29.3770i	−0.149054	+	1.03669i
$804$		0			0
$805$	−4.67391	+	3.46390i	−0.164734	+	0.122086i
$806$	39.4352			1.38904
$807$		0			0
$808$	12.2724	+	26.8729i	0.431743	+	0.945385i
$809$	23.3411	+	6.85357i	0.820631	+	0.240959i	0.664987	−	0.746855i	$-0.268437\pi$
$809$	23.3411	+	6.85357i	0.820631	+	0.240959i	0.155643	+	0.987813i	$0.450255\pi$
$810$		0			0
$811$	2.69179	−	0.790382i	0.0945216	−	0.0277541i	−0.234130	−	0.972205i	$-0.575224\pi$
$811$	2.69179	−	0.790382i	0.0945216	−	0.0277541i	0.328651	+	0.944451i	$0.393406\pi$
$812$	0.918616	+	0.590359i	0.0322371	+	0.0207175i
$813$		0			0
$814$	−24.3609	+	28.1140i	−0.853850	+	0.985395i
$815$	21.3946	−	13.7495i	0.749419	−	0.481622i
$816$		0			0
$817$	−6.76234	−	47.0331i	−0.236584	−	1.64548i
$818$	−23.2462	+	14.9394i	−0.812783	+	0.522344i
$819$		0			0
$820$	−2.97639	+	6.51739i	−0.103940	+	0.227597i
$821$	17.1180	+	11.0011i	0.597423	+	0.383941i	0.804122	−	0.594464i	$-0.202636\pi$
$821$	17.1180	+	11.0011i	0.597423	+	0.383941i	−0.206699	+	0.978405i	$0.566272\pi$
$822$		0			0
$823$	−31.8028	−	36.7024i	−1.10858	−	1.27937i	−0.956735	−	0.290960i	$-0.906025\pi$
$823$	−31.8028	−	36.7024i	−1.10858	−	1.27937i	−0.151841	−	0.988405i	$-0.548520\pi$
$824$	−5.08588	−	1.49335i	−0.177175	−	0.0520232i
$825$		0			0
$826$	1.03093	−	7.17027i	0.0358706	−	0.249485i
$827$	−34.2876			−1.19230			−0.596148	−	0.802875i	$-0.703303\pi$
$827$	−34.2876			−1.19230			−0.596148	+	0.802875i	$0.703303\pi$
$828$		0			0
$829$	11.8024			0.409916			0.204958	−	0.978771i	$-0.434294\pi$
$829$	11.8024			0.409916			0.204958	+	0.978771i	$0.434294\pi$
$830$	−4.05707	+	28.2176i	−0.140823	+	0.979446i
$831$		0			0
$832$	−32.6093	−	9.57497i	−1.13053	−	0.331952i
$833$	4.09044	+	4.72061i	0.141725	+	0.163560i
$834$		0			0
$835$	9.89088	+	6.35649i	0.342288	+	0.219975i
$836$	5.58785	−	12.2357i	0.193260	−	0.423180i
$837$		0			0
$838$	−6.14103	+	3.94660i	−0.212138	+	0.136333i
$839$	6.15046	+	42.7774i	0.212338	+	1.47684i	0.765322	+	0.643648i	$0.222580\pi$
$839$	6.15046	+	42.7774i	0.212338	+	1.47684i	−0.552984	+	0.833192i	$0.686511\pi$
$840$		0			0
$841$	−19.7626	+	12.7007i	−0.681469	+	0.437954i
$842$	11.9496	−	13.7906i	0.411812	−	0.475256i
$843$		0			0
$844$	−2.78420	−	1.78929i	−0.0958360	−	0.0615900i
$845$	4.34020	−	1.27440i	0.149307	−	0.0438406i
$846$		0			0
$847$	0.430311	+	0.126351i	0.0147857	+	0.00434146i
$848$	4.36887	+	9.56650i	0.150028	+	0.328515i
$849$		0			0
$850$	2.22640			0.0763650
$851$	44.1539	+	9.82774i	1.51358	+	0.336890i
$852$		0			0
$853$	−4.54279	+	31.5958i	−0.155542	+	1.08182i	0.751182	+	0.660095i	$0.229484\pi$
$853$	−4.54279	+	31.5958i	−0.155542	+	1.08182i	−0.906724	+	0.421725i	$0.861425\pi$
$854$	2.95105	+	6.46191i	0.100983	+	0.221122i
$855$		0			0
$856$	−27.3313	−	31.5420i	−0.934165	−	1.07808i
$857$	8.00629	−	2.35086i	0.273490	−	0.0803038i	−0.142112	−	0.989851i	$-0.545389\pi$
$857$	8.00629	−	2.35086i	0.273490	−	0.0803038i	0.415602	+	0.909547i	$0.363571\pi$
$858$		0			0
$859$	−22.7113	+	49.7307i	−0.774899	+	1.69679i	−0.0593407	+	0.998238i	$0.518900\pi$
$859$	−22.7113	+	49.7307i	−0.774899	+	1.69679i	−0.715558	+	0.698553i	$0.753827\pi$
$860$	−6.01282	+	6.93916i	−0.205035	+	0.236623i
$861$		0			0
$862$	0.705886	+	4.90955i	0.0240426	+	0.167220i
$863$	−2.93394	−	20.4060i	−0.0998724	−	0.694628i	−0.976823	−	0.214048i	$-0.931335\pi$
$863$	−2.93394	−	20.4060i	−0.0998724	−	0.694628i	0.876951	−	0.480580i	$-0.159574\pi$
$864$		0			0
$865$	−15.5992	+	18.0024i	−0.530387	+	0.612099i
$866$	−12.8053	+	28.0398i	−0.435143	+	0.952830i
$867$		0			0
$868$	3.85386	−	1.13160i	0.130809	−	0.0384089i
$869$	−17.0866	−	19.7190i	−0.579624	−	0.668922i
$870$		0			0
$871$	−2.78276	−	6.09340i	−0.0942902	−	0.206467i
$872$	8.63985	−	60.0915i	0.292582	−	2.03495i
$873$		0			0
$874$	32.8671	−	2.19188i	1.11175	−	0.0741415i
$875$	−8.49948			−0.287335
$876$		0			0
$877$	−14.8242	−	32.4605i	−0.500578	−	1.09611i	−0.976281	−	0.216507i	$-0.930533\pi$
$877$	−14.8242	−	32.4605i	−0.500578	−	1.09611i	0.475703	−	0.879606i	$-0.342194\pi$
$878$	−13.9978	−	4.11014i	−0.472404	−	0.138710i
$879$		0			0
$880$	12.6436	−	3.71248i	0.426214	−	0.125148i
$881$	−38.0771	−	24.4707i	−1.28285	−	0.824438i	−0.291614	−	0.956536i	$-0.594192\pi$
$881$	−38.0771	−	24.4707i	−1.28285	−	0.824438i	−0.991237	+	0.132098i	$0.957829\pi$
$882$		0			0
$883$	31.3719	−	36.2052i	1.05575	−	1.21840i	0.0806253	−	0.996744i	$-0.474308\pi$
$883$	31.3719	−	36.2052i	1.05575	−	1.21840i	0.975125	−	0.221656i	$-0.0711463\pi$
$884$	−2.11708	+	1.36057i	−0.0712053	+	0.0457609i
$885$		0			0
$886$	−0.920962	−	6.40543i	−0.0309403	−	0.215195i
$887$	14.1225	−	9.07599i	0.474188	−	0.304742i	−0.281631	−	0.959523i	$-0.590875\pi$
$887$	14.1225	−	9.07599i	0.474188	−	0.304742i	0.755819	+	0.654781i	$0.227239\pi$
$888$		0			0
$889$	−3.16620	+	6.93301i	−0.106191	+	0.232526i
$890$	−18.0242	−	11.5835i	−0.604174	−	0.388279i
$891$		0			0
$892$	6.99359	+	8.07104i	0.234163	+	0.270238i
$893$	−17.0498	−	5.00627i	−0.570549	−	0.167528i
$894$		0			0
$895$	5.17520	−	35.9943i	0.172988	−	1.20316i
$896$	1.95445			0.0652936
$897$		0			0
$898$	19.1241			0.638178
$899$	2.88338	−	20.0544i	0.0961661	−	0.668850i
$900$		0			0
$901$	4.33801	+	1.27376i	0.144520	+	0.0424349i
$902$	16.1184	+	18.6016i	0.536685	+	0.619367i
$903$		0			0
$904$	11.6926	+	7.51437i	0.388890	+	0.249924i
$905$	−13.2985	+	29.1196i	−0.442056	+	0.967969i
$906$		0			0
$907$	−8.42322	+	5.41328i	−0.279689	+	0.179745i	−0.672963	−	0.739676i	$-0.734979\pi$
$907$	−8.42322	+	5.41328i	−0.279689	+	0.179745i	0.393274	+	0.919421i	$0.371342\pi$
$908$	1.25471	+	8.72672i	0.0416391	+	0.289606i
$909$		0			0
$910$	−4.66164	+	2.99585i	−0.154532	+	0.0993115i
$911$	−22.6336	+	26.1205i	−0.749884	+	0.865412i	−0.994557	−	0.104194i	$-0.966774\pi$
$911$	−22.6336	+	26.1205i	−0.749884	+	0.865412i	0.244673	+	0.969606i	$0.421319\pi$
$912$		0			0
$913$	−40.9088	−	26.2905i	−1.35388	−	0.870088i
$914$	−43.4196	+	12.7491i	−1.43619	+	0.421704i
$915$		0			0
$916$	−1.34571	−	0.395136i	−0.0444635	−	0.0130557i
$917$	−4.35025	−	9.52573i	−0.143658	−	0.314567i
$918$		0			0
$919$	−5.18631			−0.171080			−0.0855402	−	0.996335i	$-0.527262\pi$
$919$	−5.18631			−0.171080			−0.0855402	+	0.996335i	$0.527262\pi$
$920$	−17.9788	−	18.1526i	−0.592743	−	0.598472i
$921$		0			0
$922$	−2.49612	+	17.3609i	−0.0822054	+	0.571751i
$923$	−19.1124	−	41.8503i	−0.629092	−	1.37752i
$924$		0			0
$925$	12.3949	+	14.3045i	0.407541	+	0.470328i
$926$	21.7044	−	6.37298i	0.713250	−	0.209429i
$927$		0			0
$928$	−3.48799	+	7.63764i	−0.114499	+	0.250718i
$929$	36.6945	−	42.3477i	1.20391	−	1.38938i	0.304363	−	0.952556i	$-0.401557\pi$
$929$	36.6945	−	42.3477i	1.20391	−	1.38938i	0.899545	−	0.436827i	$-0.143898\pi$
$930$		0			0
$931$	5.50322	+	38.2757i	0.180361	+	1.25444i
$932$	−1.40671	−	9.78387i	−0.0460783	−	0.320481i
$933$		0			0
$934$	19.9284	−	22.9986i	0.652079	−	0.752539i
$935$	2.35327	−	5.15294i	0.0769601	−	0.168519i
$936$		0			0
$937$	−6.67339	+	1.95949i	−0.218010	+	0.0640136i	−0.388914	−	0.921274i	$-0.627150\pi$
$937$	−6.67339	+	1.95949i	−0.218010	+	0.0640136i	0.170903	+	0.985288i	$0.445331\pi$
$938$	0.899812	+	1.03844i	0.0293799	+	0.0339062i
$939$		0			0
$940$	1.42640	+	3.12338i	0.0465240	+	0.101873i
$941$	7.16070	−	49.8038i	0.233432	−	1.62356i	−0.449643	−	0.893208i	$-0.648449\pi$
$941$	7.16070	−	49.8038i	0.233432	−	1.62356i	0.683075	−	0.730348i	$-0.260642\pi$
$942$		0			0
$943$	10.5940	−	27.9917i	0.344988	−	0.911535i
$944$	19.9521			0.649386
$945$		0			0
$946$	13.1032	+	28.6920i	0.426021	+	0.932856i
$947$	29.9542	+	8.79533i	0.973379	+	0.285810i	0.729489	−	0.683993i	$-0.239758\pi$
$947$	29.9542	+	8.79533i	0.973379	+	0.285810i	0.243890	+	0.969803i	$0.421576\pi$
$948$		0			0
$949$	32.9827	−	9.68460i	1.07066	−	0.314376i
$950$	11.5952	+	7.45175i	0.376196	+	0.241767i
$951$		0			0
$952$	1.35686	−	1.56590i	0.0439762	−	0.0507513i
$953$	−38.4314	+	24.6984i	−1.24492	+	0.800059i	−0.986146	−	0.165880i	$-0.946954\pi$
$953$	−38.4314	+	24.6984i	−1.24492	+	0.800059i	−0.258770	+	0.965939i	$0.583317\pi$
$954$		0			0
$955$	−0.101796	−	0.708006i	−0.00329404	−	0.0229105i
$956$	−10.3830	+	6.67275i	−0.335810	+	0.215812i
$957$		0			0
$958$	6.21253	−	13.6035i	0.200718	−	0.439511i
$959$	−7.68020	−	4.93576i	−0.248006	−	0.159384i
$960$		0			0
$961$	−28.5025	−	32.8936i	−0.919434	−	1.06108i
$962$	41.3410	+	12.1388i	1.33289	+	0.391371i
$963$		0			0
$964$	0.631784	−	4.39416i	0.0203484	−	0.141526i
$965$	−15.5371			−0.500156
$966$		0			0
$967$	46.4073			1.49236			0.746180	−	0.665745i	$-0.231886\pi$
$967$	46.4073			1.49236			0.746180	+	0.665745i	$0.231886\pi$
$968$	−0.280301	+	1.94953i	−0.00900921	+	0.0626604i
$969$		0			0
$970$	−3.83570	−	1.12626i	−0.123157	−	0.0361621i
$971$	−15.1815	−	17.5204i	−0.487199	−	0.562257i	0.457916	−	0.888995i	$-0.348596\pi$
$971$	−15.1815	−	17.5204i	−0.487199	−	0.562257i	−0.945115	+	0.326738i	$0.894051\pi$
$972$		0			0
$973$	4.58341	+	2.94558i	0.146937	+	0.0944308i
$974$	3.83232	−	8.39161i	0.122795	−	0.268885i
$975$		0			0
$976$	−16.4601	+	10.5783i	−0.526875	+	0.338602i
$977$	−6.28322	−	43.7007i	−0.201018	−	1.39811i	−0.801272	−	0.598301i	$-0.795843\pi$
$977$	−6.28322	−	43.7007i	−0.201018	−	1.39811i	0.600254	−	0.799810i	$-0.295066\pi$
$978$		0			0
$979$	30.7457	−	19.7590i	0.982636	−	0.631502i
$980$	4.89325	−	5.64711i	0.156309	−	0.180390i
$981$		0			0
$982$	0.640778	+	0.411803i	0.0204481	+	0.0131412i
$983$	−51.4331	+	15.1021i	−1.64046	+	0.481683i	−0.966411	−	0.257002i	$-0.917265\pi$
$983$	−51.4331	+	15.1021i	−1.64046	+	0.481683i	−0.674051	+	0.738685i	$0.735447\pi$
$984$		0			0
$985$	27.8231	+	8.16960i	0.886518	+	0.260305i
$986$	−1.08168	−	2.36856i	−0.0344478	−	0.0754302i
$987$		0			0
$988$	−15.5796			−0.495654
$989$	23.1325	−	30.5936i	0.735572	−	0.972821i
$990$		0			0
$991$	4.59139	−	31.9338i	0.145850	−	1.01441i	−0.777069	−	0.629416i	$-0.783294\pi$
$991$	4.59139	−	31.9338i	0.145850	−	1.01441i	0.922919	−	0.384995i	$-0.125797\pi$
$992$	12.8299	+	28.0935i	0.407349	+	0.891970i
$993$		0			0
$994$	6.18004	+	7.13214i	0.196019	+	0.226218i
$995$	−9.57008	+	2.81003i	−0.303392	+	0.0890839i
$996$		0			0
$997$	−20.8174	+	45.5838i	−0.659294	+	1.44365i	0.223884	+	0.974616i	$0.428126\pi$
$997$	−20.8174	+	45.5838i	−0.659294	+	1.44365i	−0.883178	+	0.469037i	$0.844601\pi$
$998$	15.3676	−	17.7352i	0.486453	−	0.561396i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.100.2		20
3.2	odd	2		69.2.e.c.31.1	✓	20
23.3	even	11	inner	207.2.i.d.118.2		20
23.7	odd	22		4761.2.a.bu.1.4		10
23.16	even	11		4761.2.a.bt.1.4		10
69.26	odd	22		69.2.e.c.49.1	yes	20
69.53	even	22		1587.2.a.t.1.7		10
69.62	odd	22		1587.2.a.u.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.31.1	✓	20	3.2	odd	2
69.2.e.c.49.1	yes	20	69.26	odd	22
207.2.i.d.100.2		20	1.1	even	1	trivial
207.2.i.d.118.2		20	23.3	even	11	inner
1587.2.a.t.1.7		10	69.53	even	22
1587.2.a.u.1.7		10	69.62	odd	22
4761.2.a.bt.1.4		10	23.16	even	11
4761.2.a.bu.1.4		10	23.7	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.164520 - 1.14426i) q^{2} +(0.636711 + 0.186955i) q^{4} +(1.13298 + 1.30753i) q^{5} +(-0.589836 - 0.379064i) q^{7} +(1.27914 - 2.80093i) q^{8} +O(q^{10})\)	\(q+(0.164520 - 1.14426i) q^{2} +(0.636711 + 0.186955i) q^{4} +(1.13298 + 1.30753i) q^{5} +(-0.589836 - 0.379064i) q^{7} +(1.27914 - 2.80093i) q^{8} +(1.68256 - 1.08131i) q^{10} +(0.485534 + 3.37697i) q^{11} +(3.32423 - 2.13635i) q^{13} +(-0.530790 + 0.612564i) q^{14} +(-1.87807 - 1.20696i) q^{16} +(-0.920848 + 0.270385i) q^{17} +(-5.70077 - 1.67390i) q^{19} +(0.476932 + 1.04433i) q^{20} +3.94402 q^{22} +(-2.27813 - 4.22021i) q^{23} +(0.285587 - 1.98630i) q^{25} +(-1.89765 - 4.15528i) q^{26} +(-0.304687 - 0.351627i) q^{28} +(-2.25187 + 0.661210i) q^{29} +(-3.58618 + 7.85263i) q^{31} +(2.34282 - 2.70376i) q^{32} +(0.157894 + 1.09818i) q^{34} +(-0.172634 - 1.20070i) q^{35} +(-6.17667 + 7.12826i) q^{37} +(-2.85328 + 6.24780i) q^{38} +(5.11155 - 1.50089i) q^{40} +(4.08680 + 4.71641i) q^{41} +(3.32229 + 7.27480i) q^{43} +(-0.322196 + 2.24093i) q^{44} +(-5.20383 + 1.91247i) q^{46} +2.99078 q^{47} +(-2.70369 - 5.92025i) q^{49} +(-2.22587 - 0.653574i) q^{50} +(2.51598 - 0.738758i) q^{52} +(-3.96305 - 2.54690i) q^{53} +(-3.86538 + 4.46088i) q^{55} +(-1.81622 + 1.16721i) q^{56} +(0.386120 + 2.68552i) q^{58} +(-7.51851 + 4.83185i) q^{59} +(3.64086 - 7.97236i) q^{61} +(8.39549 + 5.39545i) q^{62} +(-5.63228 - 6.50000i) q^{64} +(6.55963 + 1.92608i) q^{65} +(0.241257 - 1.67798i) q^{67} -0.636864 q^{68} -1.40232 q^{70} +(1.65698 - 11.5246i) q^{71} +(8.34684 + 2.45085i) q^{73} +(7.14042 + 8.24049i) q^{74} +(-3.31680 - 2.13158i) q^{76} +(0.993702 - 2.17590i) q^{77} +(-6.43376 + 4.13473i) q^{79} +(-0.549677 - 3.82309i) q^{80} +(6.06919 - 3.90043i) q^{82} +(-9.33402 + 10.7720i) q^{83} +(-1.39684 - 0.897694i) q^{85} +(8.87088 - 2.60472i) q^{86} +(10.0797 + 2.95968i) q^{88} +(-4.45010 - 9.74435i) q^{89} -2.77057 q^{91} +(-0.661520 - 3.11296i) q^{92} +(0.492045 - 3.42225i) q^{94} +(-4.27019 - 9.35041i) q^{95} +(-1.30891 - 1.51056i) q^{97} +(-7.21915 + 2.11973i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

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