LMFDB - Embedded newform 666.2.x.g.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(127,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("666.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.x (of order $9$, degree $6$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			379.2
Root			$2.14169 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	666.379
Dual form			666.2.x.g.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(0.773586 + 0.649116i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(0.773586 + 0.649116i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.173648 + 0.300767i) q^{10} +(-2.73237 - 4.73261i) q^{11} +(-5.97892 + 2.17615i) q^{13} +(0.504922 - 0.874551i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.490749 + 0.178618i) q^{17} +(0.869950 - 4.93373i) q^{19} +(0.326352 + 0.118782i) q^{20} +(-4.18624 + 3.51267i) q^{22} +(0.721492 - 1.24966i) q^{23} +(-0.847296 - 4.80526i) q^{25} +(3.18132 + 5.51020i) q^{26} +(-0.948944 - 0.345387i) q^{28} +(-3.16714 - 5.48565i) q^{29} +3.30777 q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.0906868 - 0.514310i) q^{34} +(-0.0609011 - 0.345387i) q^{35} +(-5.88521 + 1.53765i) q^{37} -5.00984 q^{38} +(0.0603074 - 0.342020i) q^{40} +(-1.03412 + 0.376390i) q^{41} -6.27037 q^{43} +(4.18624 + 3.51267i) q^{44} +(-1.35596 - 0.493529i) q^{46} +(-5.71910 + 9.90577i) q^{47} +(-1.03845 - 5.88936i) q^{49} +(-4.58512 + 1.66885i) q^{50} +(4.87406 - 4.08982i) q^{52} +(-0.0706817 + 0.0593090i) q^{53} +(-0.329565 + 1.86905i) q^{55} +(-0.175358 + 0.994503i) q^{56} +(-4.85235 + 4.07160i) q^{58} +(-2.29059 + 1.92203i) q^{59} +(-3.58571 + 1.30509i) q^{61} +(-0.574388 - 3.25751i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(2.07646 + 0.755769i) q^{65} +(-0.892251 - 0.748687i) q^{67} -0.522244 q^{68} +(-0.329565 + 0.119952i) q^{70} +(-0.0543332 + 0.308139i) q^{71} +13.2325 q^{73} +(2.53624 + 5.52879i) q^{74} +(0.869950 + 4.93373i) q^{76} +(0.958285 - 5.43471i) q^{77} +(7.12939 + 5.98227i) q^{79} -0.347296 q^{80} +(0.550245 + 0.953052i) q^{82} +(8.89395 + 3.23713i) q^{83} +(-0.0906868 - 0.157074i) q^{85} +(1.08884 + 6.17511i) q^{86} +(2.73237 - 4.73261i) q^{88} +(12.0788 - 10.1354i) q^{89} +(-6.03778 - 2.19757i) q^{91} +(-0.250571 + 1.42106i) q^{92} +(10.7484 + 3.91209i) q^{94} +(-1.33284 + 1.11839i) q^{95} +(0.464564 - 0.804648i) q^{97} +(-5.61956 + 2.04535i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) $ 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.266044	−	0.223238i	−0.118979	−	0.0998350i	0.581357	−	0.813649i	$-0.302522\pi$
$5$	−0.266044	−	0.223238i	−0.118979	−	0.0998350i	−0.700336	+	0.713814i	$0.746966\pi$
$6$		0			0
$7$	0.773586	+	0.649116i	0.292388	+	0.245343i	0.777168	−	0.629294i	$-0.216656\pi$
$7$	0.773586	+	0.649116i	0.292388	+	0.245343i	−0.484780	+	0.874636i	$0.661100\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	−0.173648	+	0.300767i	−0.0549124	+	0.0951110i
$11$	−2.73237	−	4.73261i	−0.823842	−	1.42694i	−0.902801	−	0.430058i	$-0.858493\pi$
$11$	−2.73237	−	4.73261i	−0.823842	−	1.42694i	0.0789595	−	0.996878i	$-0.474840\pi$
$12$		0			0
$13$	−5.97892	+	2.17615i	−1.65825	+	0.603555i	−0.990087	−	0.140456i	$-0.955143\pi$
$13$	−5.97892	+	2.17615i	−1.65825	+	0.603555i	−0.668167	+	0.744011i	$0.732921\pi$
$14$	0.504922	−	0.874551i	0.134946	−	0.233734i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.490749	+	0.178618i	0.119024	+	0.0433212i	0.400846	−	0.916146i	$-0.368716\pi$
$17$	0.490749	+	0.178618i	0.119024	+	0.0433212i	−0.281821	+	0.959467i	$0.590939\pi$
$18$		0			0
$19$	0.869950	−	4.93373i	0.199580	−	1.13188i	−0.706163	−	0.708049i	$-0.749575\pi$
$19$	0.869950	−	4.93373i	0.199580	−	1.13188i	0.905743	−	0.423827i	$-0.139313\pi$
$20$	0.326352	+	0.118782i	0.0729745	+	0.0265605i
$21$		0			0
$22$	−4.18624	+	3.51267i	−0.892509	+	0.748904i
$23$	0.721492	−	1.24966i	0.150441	−	0.260572i	−0.780948	−	0.624596i	$-0.785264\pi$
$23$	0.721492	−	1.24966i	0.150441	−	0.260572i	0.931390	+	0.364023i	$0.118597\pi$
$24$		0			0
$25$	−0.847296	−	4.80526i	−0.169459	−	0.961051i
$26$	3.18132	+	5.51020i	0.623908	+	1.08064i
$27$		0			0
$28$	−0.948944	−	0.345387i	−0.179333	−	0.0652720i
$29$	−3.16714	−	5.48565i	−0.588124	−	1.01866i	−0.994478	−	0.104945i	$-0.966533\pi$
$29$	−3.16714	−	5.48565i	−0.588124	−	1.01866i	0.406354	−	0.913716i	$-0.366800\pi$
$30$		0			0
$31$	3.30777			0.594092			0.297046	−	0.954863i	$-0.403998\pi$
$31$	3.30777			0.594092			0.297046	+	0.954863i	$0.403998\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$		0			0
$34$	0.0906868	−	0.514310i	0.0155527	−	0.0882035i
$35$	−0.0609011	−	0.345387i	−0.0102942	−	0.0583811i
$36$		0			0
$37$	−5.88521	+	1.53765i	−0.967522	+	0.252787i
$37$	−5.88521	+	1.53765i	−0.967522	+	0.252787i
$38$	−5.00984			−0.812704
$39$		0			0
$40$	0.0603074	−	0.342020i	0.00953543	−	0.0540781i
$41$	−1.03412	+	0.376390i	−0.161503	+	0.0587822i	−0.421506	−	0.906825i	$-0.638498\pi$
$41$	−1.03412	+	0.376390i	−0.161503	+	0.0587822i	0.260004	+	0.965608i	$0.416276\pi$
$42$		0			0
$43$	−6.27037			−0.956222			−0.478111	−	0.878299i	$-0.658678\pi$
$43$	−6.27037			−0.956222			−0.478111	+	0.878299i	$0.658678\pi$
$44$	4.18624	+	3.51267i	0.631099	+	0.529555i
$45$		0			0
$46$	−1.35596	−	0.493529i	−0.199926	−	0.0727670i
$47$	−5.71910	+	9.90577i	−0.834216	+	1.44491i	0.0604506	+	0.998171i	$0.480746\pi$
$47$	−5.71910	+	9.90577i	−0.834216	+	1.44491i	−0.894667	+	0.446734i	$0.852587\pi$
$48$		0			0
$49$	−1.03845	−	5.88936i	−0.148350	−	0.841337i
$50$	−4.58512	+	1.66885i	−0.648434	+	0.236011i
$51$		0			0
$52$	4.87406	−	4.08982i	0.675911	−	0.567156i
$53$	−0.0706817	+	0.0593090i	−0.00970887	+	0.00814671i	−0.647629	−	0.761956i	$-0.724239\pi$
$53$	−0.0706817	+	0.0593090i	−0.00970887	+	0.00814671i	0.637920	+	0.770102i	$0.279795\pi$
$54$		0			0
$55$	−0.329565	+	1.86905i	−0.0444385	+	0.252023i
$56$	−0.175358	+	0.994503i	−0.0234332	+	0.132896i
$57$		0			0
$58$	−4.85235	+	4.07160i	−0.637144	+	0.534628i
$59$	−2.29059	+	1.92203i	−0.298210	+	0.250228i	−0.779599	−	0.626279i	$-0.784577\pi$
$59$	−2.29059	+	1.92203i	−0.298210	+	0.250228i	0.481389	+	0.876507i	$0.340132\pi$
$60$		0			0
$61$	−3.58571	+	1.30509i	−0.459103	+	0.167100i	−0.561210	−	0.827674i	$-0.689664\pi$
$61$	−3.58571	+	1.30509i	−0.459103	+	0.167100i	0.102107	+	0.994773i	$0.467442\pi$
$62$	−0.574388	−	3.25751i	−0.0729473	−	0.413705i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.07646	+	0.755769i	0.257553	+	0.0937416i
$66$		0			0
$67$	−0.892251	−	0.748687i	−0.109006	−	0.0914667i	0.586656	−	0.809836i	$-0.300444\pi$
$67$	−0.892251	−	0.748687i	−0.109006	−	0.0914667i	−0.695662	+	0.718370i	$0.744889\pi$
$68$	−0.522244			−0.0633314
$69$		0			0
$70$	−0.329565	+	0.119952i	−0.0393905	+	0.0143370i
$71$	−0.0543332	+	0.308139i	−0.00644816	+	0.0365693i	−0.987862	−	0.155334i	$-0.950355\pi$
$71$	−0.0543332	+	0.308139i	−0.00644816	+	0.0365693i	0.981414	+	0.191903i	$0.0614659\pi$
$72$		0			0
$73$	13.2325			1.54875			0.774376	−	0.632726i	$-0.218064\pi$
$73$	13.2325			1.54875			0.774376	+	0.632726i	$0.218064\pi$
$74$	2.53624	+	5.52879i	0.294832	+	0.642708i
$75$		0			0
$76$	0.869950	+	4.93373i	0.0997902	+	0.565938i
$77$	0.958285	−	5.43471i	0.109207	−	0.619342i
$78$		0			0
$79$	7.12939	+	5.98227i	0.802119	+	0.673058i	0.948713	−	0.316139i	$-0.102387\pi$
$79$	7.12939	+	5.98227i	0.802119	+	0.673058i	−0.146594	+	0.989197i	$0.546831\pi$
$80$	−0.347296			−0.0388289
$81$		0			0
$82$	0.550245	+	0.953052i	0.0607644	+	0.105247i
$83$	8.89395	+	3.23713i	0.976238	+	0.355322i	0.780377	−	0.625310i	$-0.215027\pi$
$83$	8.89395	+	3.23713i	0.976238	+	0.355322i	0.195862	+	0.980632i	$0.437250\pi$
$84$		0			0
$85$	−0.0906868	−	0.157074i	−0.00983636	−	0.0170371i
$86$	1.08884	+	6.17511i	0.117412	+	0.665879i
$87$		0			0
$88$	2.73237	−	4.73261i	0.291272	−	0.504498i
$89$	12.0788	−	10.1354i	1.28035	−	1.07435i	0.287160	−	0.957883i	$-0.407289\pi$
$89$	12.0788	−	10.1354i	1.28035	−	1.07435i	0.993195	−	0.116463i	$-0.0371555\pi$
$90$		0			0
$91$	−6.03778	−	2.19757i	−0.632931	−	0.230368i
$92$	−0.250571	+	1.42106i	−0.0261239	+	0.148156i
$93$		0			0
$94$	10.7484	+	3.91209i	1.10861	+	0.403502i
$95$	−1.33284	+	1.11839i	−0.136747	+	0.114744i
$96$		0			0
$97$	0.464564	−	0.804648i	0.0471693	−	0.0816997i	−0.841477	−	0.540293i	$-0.818313\pi$
$97$	0.464564	−	0.804648i	0.0471693	−	0.0816997i	0.888646	+	0.458594i	$0.151647\pi$
$98$	−5.61956	+	2.04535i	−0.567662	+	0.206612i
$99$		0			0
$100$	2.43969	+	4.22567i	0.243969	+	0.422567i
$101$	4.28093	−	7.41479i	0.425969	−	0.737799i	−0.570542	−	0.821269i	$-0.693267\pi$
$101$	4.28093	−	7.41479i	0.425969	−	0.737799i	0.996510	+	0.0834694i	$0.0266001\pi$
$102$		0			0
$103$	−2.47956	−	4.29473i	−0.244319	−	0.423172i	0.717621	−	0.696434i	$-0.245231\pi$
$103$	−2.47956	−	4.29473i	−0.244319	−	0.423172i	−0.961940	+	0.273261i	$0.911898\pi$
$104$	−4.87406	−	4.08982i	−0.477941	−	0.401040i
$105$		0			0
$106$	0.0706817	+	0.0593090i	0.00686521	+	0.00576059i
$107$	−3.35307	+	1.22042i	−0.324153	+	0.117982i	−0.498971	−	0.866619i	$-0.666289\pi$
$107$	−3.35307	+	1.22042i	−0.324153	+	0.117982i	0.174818	+	0.984601i	$0.444066\pi$
$108$		0			0
$109$	−0.169947	−	0.963819i	−0.0162780	−	0.0923171i	0.975586	−	0.219616i	$-0.0704804\pi$
$109$	−0.169947	−	0.963819i	−0.0162780	−	0.0923171i	−0.991864	+	0.127299i	$0.959369\pi$
$110$	1.89789			0.180956
$111$		0			0
$112$	1.00984			0.0954213
$113$	−1.60399	−	9.09669i	−0.150891	−	0.855745i	−0.962447	−	0.271470i	$-0.912490\pi$
$113$	−1.60399	−	9.09669i	−0.150891	−	0.855745i	0.811556	−	0.584275i	$-0.198621\pi$
$114$		0			0
$115$	−0.470920	+	0.171401i	−0.0439136	+	0.0159832i
$116$	4.85235	+	4.07160i	0.450529	+	0.378039i
$117$		0			0
$118$	2.29059	+	1.92203i	0.210866	+	0.176938i
$119$	0.263693	+	0.456729i	0.0241727	+	0.0418683i
$120$		0			0
$121$	−9.43174	+	16.3362i	−0.857430	+	1.48511i
$122$	1.90792	+	3.30461i	0.172735	+	0.299185i
$123$		0			0
$124$	−3.10828	+	1.13132i	−0.279132	+	0.101596i
$125$	−1.71554	+	2.97140i	−0.153442	+	0.265770i
$126$		0			0
$127$	5.18728	−	4.35264i	0.460296	−	0.386235i	−0.382944	−	0.923772i	$-0.625090\pi$
$127$	5.18728	−	4.35264i	0.460296	−	0.386235i	0.843240	+	0.537537i	$0.180645\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$		0			0
$130$	0.383714	−	2.17615i	0.0336539	−	0.190861i
$131$	−14.2349	−	5.18108i	−1.24371	−	0.452673i	−0.365438	−	0.930836i	$-0.619081\pi$
$131$	−14.2349	−	5.18108i	−1.24371	−	0.452673i	−0.878271	+	0.478163i	$0.841303\pi$
$132$		0			0
$133$	3.87554	−	3.25197i	0.336052	−	0.281981i
$134$	−0.582375	+	1.00870i	−0.0503096	+	0.0871387i
$135$		0			0
$136$	0.0906868	+	0.514310i	0.00777633	+	0.0441017i
$137$	−4.24086	−	7.34539i	−0.362321	−	0.627559i	0.626021	−	0.779806i	$-0.284682\pi$
$137$	−4.24086	−	7.34539i	−0.362321	−	0.627559i	−0.988342	+	0.152247i	$0.951349\pi$
$138$		0			0
$139$	17.2324	+	6.27209i	1.46164	+	0.531992i	0.945815	−	0.324705i	$-0.105265\pi$
$139$	17.2324	+	6.27209i	1.46164	+	0.531992i	0.515820	+	0.856697i	$0.327487\pi$
$140$	0.175358	+	0.303728i	0.0148204	+	0.0256697i
$141$		0			0
$142$	0.312892			0.0262573
$143$	26.6355	+	22.3499i	2.22737	+	1.86899i
$144$		0			0
$145$	−0.382004	+	2.16645i	−0.0317237	+	0.179914i
$146$	−2.29781	−	13.0315i	−0.190168	−	1.07850i
$147$		0			0
$148$	5.00438	−	3.45777i	0.411357	−	0.284227i
$149$	−5.45291			−0.446720			−0.223360	−	0.974736i	$-0.571703\pi$
$149$	−5.45291			−0.446720			−0.223360	+	0.974736i	$0.571703\pi$
$150$		0			0
$151$	−2.70116	+	15.3190i	−0.219817	+	1.24665i	0.652531	+	0.757762i	$0.273707\pi$
$151$	−2.70116	+	15.3190i	−0.219817	+	1.24665i	−0.872349	+	0.488884i	$0.837404\pi$
$152$	4.70771	−	1.71347i	0.381846	−	0.138981i
$153$		0			0
$154$	−5.51855			−0.444697
$155$	−0.880013	−	0.738419i	−0.0706843	−	0.0593112i
$156$		0			0
$157$	3.76650	+	1.37089i	0.300599	+	0.109409i	0.487916	−	0.872890i	$-0.337757\pi$
$157$	3.76650	+	1.37089i	0.300599	+	0.109409i	−0.187317	+	0.982299i	$0.559979\pi$
$158$	4.65338	−	8.05989i	0.370203	−	0.641211i
$159$		0			0
$160$	0.0603074	+	0.342020i	0.00476772	+	0.0270391i
$161$	1.36931	−	0.498388i	0.107917	−	0.0392785i
$162$		0			0
$163$	3.59446	−	3.01611i	0.281540	−	0.236240i	−0.491072	−	0.871119i	$-0.663395\pi$
$163$	3.59446	−	3.01611i	0.281540	−	0.236240i	0.772611	+	0.634879i	$0.218950\pi$
$164$	0.843024	−	0.707381i	0.0658291	−	0.0552372i
$165$		0			0
$166$	1.64354	−	9.32096i	0.127563	−	0.723447i
$167$	0.134923	−	0.765189i	0.0104407	−	0.0592121i	−0.979142	−	0.203176i	$-0.934874\pi$
$167$	0.134923	−	0.765189i	0.0104407	−	0.0592121i	0.989583	+	0.143964i	$0.0459848\pi$
$168$		0			0
$169$	21.0533	−	17.6658i	1.61948	−	1.35891i
$170$	−0.138940	+	0.116585i	−0.0106562	+	0.00894164i
$171$		0			0
$172$	5.89222	−	2.14459i	0.449277	−	0.163524i
$173$	−1.86383	−	10.5703i	−0.141704	−	0.803644i	−0.969955	−	0.243286i	$-0.921775\pi$
$173$	−1.86383	−	10.5703i	−0.141704	−	0.803644i	0.828251	−	0.560358i	$-0.189336\pi$
$174$		0			0
$175$	2.46371	−	4.26727i	0.186239	−	0.322575i
$176$	−5.13518	−	1.86905i	−0.387079	−	0.140885i
$177$		0			0
$178$	−12.0788	−	10.1354i	−0.905348	−	0.759677i
$179$	11.8976			0.889267			0.444633	−	0.895713i	$-0.353334\pi$
$179$	11.8976			0.889267			0.444633	+	0.895713i	$0.353334\pi$
$180$		0			0
$181$	−4.12213	+	1.50033i	−0.306395	+	0.111519i	−0.490642	−	0.871361i	$-0.663238\pi$
$181$	−4.12213	+	1.50033i	−0.306395	+	0.111519i	0.184247	+	0.982880i	$0.441015\pi$
$182$	−1.11574	+	6.32766i	−0.0827039	+	0.469037i
$183$		0			0
$184$	1.44298			0.106378
$185$	1.90899	+	0.904718i	0.140352	+	0.0665162i
$186$		0			0
$187$	−0.495580	−	2.81058i	−0.0362404	−	0.205530i
$188$	1.98622	−	11.2644i	0.144860	−	0.821543i
$189$		0			0
$190$	1.33284	+	1.11839i	0.0966945	+	0.0811363i
$191$	10.4903			0.759053			0.379527	−	0.925181i	$-0.376087\pi$
$191$	10.4903			0.759053			0.379527	+	0.925181i	$0.376087\pi$
$192$		0			0
$193$	−4.91474	−	8.51259i	−0.353771	−	0.612749i	0.633136	−	0.774041i	$-0.281767\pi$
$193$	−4.91474	−	8.51259i	−0.353771	−	0.612749i	−0.986907	+	0.161291i	$0.948434\pi$
$194$	−0.873095	−	0.317780i	−0.0626845	−	0.0228153i
$195$		0			0
$196$	2.99011	+	5.17902i	0.213579	+	0.369930i
$197$	2.09473	+	11.8798i	0.149244	+	0.846402i	0.963861	+	0.266404i	$0.0858356\pi$
$197$	2.09473	+	11.8798i	0.149244	+	0.846402i	−0.814618	+	0.579998i	$0.803053\pi$
$198$		0			0
$199$	4.64995	−	8.05395i	0.329626	−	0.570929i	−0.652811	−	0.757520i	$-0.726411\pi$
$199$	4.64995	−	8.05395i	0.329626	−	0.570929i	0.982438	+	0.186591i	$0.0597439\pi$
$200$	3.73783	−	3.13641i	0.264304	−	0.221778i
$201$		0			0
$202$	−8.04552	−	2.92833i	−0.566081	−	0.206037i
$203$	1.11077	−	6.29947i	0.0779605	−	0.442136i
$204$		0			0
$205$	0.359147	+	0.130719i	0.0250839	+	0.00912980i
$206$	−3.79891	+	3.18767i	−0.264683	+	0.222095i
$207$		0			0
$208$	−3.18132	+	5.51020i	−0.220585	+	0.382064i
$209$	−25.7265	+	9.36367i	−1.77954	+	0.647699i
$210$		0			0
$211$	2.20002	+	3.81054i	0.151455	+	0.262329i	0.931763	−	0.363068i	$-0.118271\pi$
$211$	2.20002	+	3.81054i	0.151455	+	0.262329i	−0.780307	+	0.625396i	$0.784937\pi$
$212$	0.0461342	−	0.0799067i	0.00316851	−	0.00548802i
$213$		0			0
$214$	1.78413	+	3.09020i	0.121961	+	0.211242i
$215$	1.66820	+	1.39978i	0.113770	+	0.0954644i
$216$		0			0
$217$	2.55884	+	2.14712i	0.173705	+	0.145756i
$218$	−0.919666	+	0.334731i	−0.0622876	+	0.0226708i
$219$		0			0
$220$	−0.329565	−	1.86905i	−0.0222192	−	0.126012i
$221$	−3.32285			−0.223519
$222$		0			0
$223$	11.2311			0.752092			0.376046	−	0.926601i	$-0.377283\pi$
$223$	11.2311			0.752092			0.376046	+	0.926601i	$0.377283\pi$
$224$	−0.175358	−	0.994503i	−0.0117166	−	0.0664480i
$225$		0			0
$226$	−8.67996	+	3.15925i	−0.577382	+	0.210150i
$227$	11.6086	+	9.74076i	0.770489	+	0.646517i	0.940834	−	0.338868i	$-0.110044\pi$
$227$	11.6086	+	9.74076i	0.770489	+	0.646517i	−0.170345	+	0.985384i	$0.554488\pi$
$228$		0			0
$229$	−11.9210	−	10.0029i	−0.787759	−	0.661008i	0.157431	−	0.987530i	$-0.449679\pi$
$229$	−11.9210	−	10.0029i	−0.787759	−	0.661008i	−0.945190	+	0.326522i	$0.894123\pi$
$230$	0.250571	+	0.434003i	0.0165222	+	0.0286173i
$231$		0			0
$232$	3.16714	−	5.48565i	0.207933	−	0.360151i
$233$	6.79356	+	11.7668i	0.445061	+	0.770868i	0.998056	−	0.0623159i	$-0.0198486\pi$
$233$	6.79356	+	11.7668i	0.445061	+	0.770868i	−0.552995	+	0.833184i	$0.686515\pi$
$234$		0			0
$235$	3.73288	−	1.35866i	0.243506	−	0.0886289i
$236$	1.49508	−	2.58955i	0.0973213	−	0.168565i
$237$		0			0
$238$	0.404001	−	0.338997i	0.0261875	−	0.0219739i
$239$	−18.3188	−	6.66750i	−1.18494	−	0.431285i	−0.326999	−	0.945025i	$-0.606037\pi$
$239$	−18.3188	−	6.66750i	−1.18494	−	0.431285i	−0.857946	+	0.513740i	$0.828260\pi$
$240$		0			0
$241$	0.250684	−	1.42170i	0.0161480	−	0.0915797i	−0.975669	−	0.219250i	$-0.929639\pi$
$241$	0.250684	−	1.42170i	0.0161480	−	0.0915797i	0.991817	+	0.127671i	$0.0407500\pi$
$242$	17.7259	+	6.45169i	1.13946	+	0.414730i
$243$		0			0
$244$	2.92310	−	2.45277i	0.187132	−	0.157022i
$245$	−1.03845	+	1.79865i	−0.0663443	+	0.114912i
$246$		0			0
$247$	5.53518	+	31.3915i	0.352195	+	1.99740i
$248$	1.65388	+	2.86461i	0.105022	+	0.181903i
$249$		0			0
$250$	3.22416	+	1.17350i	0.203913	+	0.0742184i
$251$	5.03646	+	8.72340i	0.317898	+	0.550616i	0.980049	−	0.198754i	$-0.0636895\pi$
$251$	5.03646	+	8.72340i	0.317898	+	0.550616i	−0.662151	+	0.749371i	$0.730356\pi$
$252$		0			0
$253$	−7.88554			−0.495760
$254$	−5.18728	−	4.35264i	−0.325479	−	0.273109i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.21293	+	6.87888i	0.0756607	+	0.429093i	0.998984	+	0.0450692i	$0.0143508\pi$
$257$	1.21293	+	6.87888i	0.0756607	+	0.429093i	−0.923323	+	0.384024i	$0.874538\pi$
$258$		0			0
$259$	−5.55082	−	2.63068i	−0.344911	−	0.163462i
$260$	−2.20972			−0.137041
$261$		0			0
$262$	−2.63050	+	14.9183i	−0.162513	+	0.921657i
$263$	2.50225	−	0.910746i	0.154296	−	0.0561590i	−0.263718	−	0.964600i	$-0.584949\pi$
$263$	2.50225	−	0.910746i	0.154296	−	0.0561590i	0.418013	+	0.908441i	$0.362727\pi$
$264$		0			0
$265$	0.0320445			0.00196848
$266$	−3.87554	−	3.25197i	−0.237625	−	0.199391i
$267$		0			0
$268$	1.09451	+	0.398368i	0.0668577	+	0.0243342i
$269$	1.20752	−	2.09148i	0.0736236	−	0.127520i	−0.826863	−	0.562403i	$-0.809877\pi$
$269$	1.20752	−	2.09148i	0.0736236	−	0.127520i	0.900487	+	0.434883i	$0.143210\pi$
$270$		0			0
$271$	−4.38472	−	24.8670i	−0.266353	−	1.51056i	−0.765156	−	0.643845i	$-0.777338\pi$
$271$	−4.38472	−	24.8670i	−0.266353	−	1.51056i	0.498803	−	0.866715i	$-0.333773\pi$
$272$	0.490749	−	0.178618i	0.0297560	−	0.0108303i
$273$		0			0
$274$	−6.49738	+	5.45195i	−0.392521	+	0.329364i
$275$	−20.4263	+	17.1397i	−1.23175	+	1.03356i
$276$		0			0
$277$	−3.07913	+	17.4626i	−0.185007	+	1.04923i	0.740940	+	0.671571i	$0.234380\pi$
$277$	−3.07913	+	17.4626i	−0.185007	+	1.04923i	−0.925947	+	0.377654i	$0.876731\pi$
$278$	3.18442	−	18.0598i	0.190989	−	1.08315i
$279$		0			0
$280$	0.268664	−	0.225435i	0.0160557	−	0.0134723i
$281$	−15.1288	+	12.6946i	−0.902511	+	0.757297i	−0.970680	−	0.240377i	$-0.922729\pi$
$281$	−15.1288	+	12.6946i	−0.902511	+	0.757297i	0.0681682	+	0.997674i	$0.478285\pi$
$282$		0			0
$283$	−22.8810	+	8.32799i	−1.36013	+	0.495047i	−0.916095	−	0.400961i	$-0.868676\pi$
$283$	−22.8810	+	8.32799i	−1.36013	+	0.495047i	−0.444037	+	0.896009i	$0.646454\pi$
$284$	−0.0543332	−	0.308139i	−0.00322408	−	0.0182847i
$285$		0			0
$286$	17.3851	−	30.1119i	1.02800	−	1.78055i
$287$	−1.04430	−	0.380095i	−0.0616432	−	0.0224363i
$288$		0			0
$289$	−12.8138	−	10.7521i	−0.753754	−	0.632475i
$290$	2.19988			0.129181
$291$		0			0
$292$	−12.4345	+	4.52580i	−0.727675	+	0.264852i
$293$	4.03707	−	22.8954i	0.235848	−	1.33756i	−0.604972	−	0.796247i	$-0.706816\pi$
$293$	4.03707	−	22.8954i	0.235848	−	1.33756i	0.840820	−	0.541315i	$-0.182073\pi$
$294$		0			0
$295$	1.03847			0.0604621
$296$	−4.27424	−	4.32791i	−0.248435	−	0.251555i
$297$		0			0
$298$	0.946888	+	5.37007i	0.0548518	+	0.311080i
$299$	−1.59429	+	9.04170i	−0.0922005	+	0.522895i
$300$		0			0
$301$	−4.85067	−	4.07019i	−0.279588	−	0.234602i
$302$	15.5554			0.895111
$303$		0			0
$304$	−2.50492	−	4.33865i	−0.143667	−	0.248839i
$305$	1.24530	+	0.453253i	0.0713059	+	0.0259532i
$306$		0			0
$307$	5.33508	+	9.24063i	0.304489	+	0.527391i	0.977147	−	0.212563i	$-0.0681809\pi$
$307$	5.33508	+	9.24063i	0.304489	+	0.527391i	−0.672658	+	0.739953i	$0.734848\pi$
$308$	0.958285	+	5.43471i	0.0546034	+	0.309671i
$309$		0			0
$310$	−0.574388	+	0.994869i	−0.0326230	+	0.0565047i
$311$	−13.0382	+	10.9403i	−0.739326	+	0.620368i	−0.932657	−	0.360765i	$-0.882516\pi$
$311$	−13.0382	+	10.9403i	−0.739326	+	0.620368i	0.193330	+	0.981134i	$0.438071\pi$
$312$		0			0
$313$	−10.2525	−	3.73159i	−0.579503	−	0.210922i	0.0356035	−	0.999366i	$-0.488665\pi$
$313$	−10.2525	−	3.73159i	−0.579503	−	0.210922i	−0.615106	+	0.788444i	$0.710887\pi$
$314$	0.696020	−	3.94733i	0.0392787	−	0.222761i
$315$		0			0
$316$	−8.74550	−	3.18310i	−0.491973	−	0.179063i
$317$	22.0930	−	18.5382i	1.24086	−	1.04121i	0.243409	−	0.969924i	$-0.421734\pi$
$317$	22.0930	−	18.5382i	1.24086	−	1.04121i	0.997456	−	0.0712854i	$-0.0227101\pi$
$318$		0			0
$319$	−17.3076	+	29.9777i	−0.969042	+	1.67843i
$320$	0.326352	−	0.118782i	0.0182436	−	0.00664014i
$321$		0			0
$322$	−0.728595	−	1.26196i	−0.0406030	−	0.0703264i
$323$	1.30818	−	2.26584i	0.0727892	−	0.126075i
$324$		0			0
$325$	15.5229	+	26.8864i	0.861054	+	1.49139i
$326$	−3.59446	−	3.01611i	−0.199079	−	0.167047i
$327$		0			0
$328$	−0.843024	−	0.707381i	−0.0465482	−	0.0390586i
$329$	−10.8542	+	3.95061i	−0.598412	+	0.217804i
$330$		0			0
$331$	0.687569	+	3.89939i	0.0377922	+	0.214330i	0.997856	−	0.0654519i	$-0.0208489\pi$
$331$	0.687569	+	3.89939i	0.0377922	+	0.214330i	−0.960064	+	0.279782i	$0.909738\pi$
$332$	−9.46475			−0.519446
$333$		0			0
$334$	−0.776993			−0.0425152
$335$	0.0702431	+	0.398368i	0.00383779	+	0.0217652i
$336$		0			0
$337$	4.01886	−	1.46274i	0.218921	−	0.0796807i	−0.230231	−	0.973136i	$-0.573948\pi$
$337$	4.01886	−	1.46274i	0.218921	−	0.0796807i	0.449152	+	0.893455i	$0.351726\pi$
$338$	−21.0533	−	17.6658i	−1.14515	−	0.960893i
$339$		0			0
$340$	0.138940	+	0.116585i	0.00753509	+	0.00632269i
$341$	−9.03806	−	15.6544i	−0.489438	−	0.847732i
$342$		0			0
$343$	6.55400	−	11.3519i	0.353883	−	0.612943i
$344$	−3.13518	−	5.43030i	−0.169038	−	0.292782i
$345$		0			0
$346$	−10.0860	+	3.67102i	−0.542229	+	0.197355i
$347$	−5.06401	+	8.77113i	−0.271850	+	0.470859i	−0.969336	−	0.245740i	$-0.920969\pi$
$347$	−5.06401	+	8.77113i	−0.271850	+	0.470859i	0.697485	+	0.716599i	$0.254302\pi$
$348$		0			0
$349$	−5.50852	+	4.62220i	−0.294864	+	0.247421i	−0.778203	−	0.628013i	$-0.783869\pi$
$349$	−5.50852	+	4.62220i	−0.294864	+	0.247421i	0.483338	+	0.875434i	$0.339424\pi$
$350$	−4.63026	−	1.68528i	−0.247498	−	0.0900819i
$351$		0			0
$352$	−0.948944	+	5.38173i	−0.0505789	+	0.286847i
$353$	−32.0012	−	11.6475i	−1.70325	−	0.619933i	−0.707064	−	0.707150i	$-0.749981\pi$
$353$	−32.0012	−	11.6475i	−1.70325	−	0.619933i	−0.996189	+	0.0872167i	$0.972203\pi$
$354$		0			0
$355$	0.0832432	−	0.0698494i	0.00441809	−	0.00370722i
$356$	−7.88391	+	13.6553i	−0.417846	+	0.723731i
$357$		0			0
$358$	−2.06599	−	11.7168i	−0.109191	−	0.619254i
$359$	4.93976	+	8.55592i	0.260711	+	0.451564i	0.966431	−	0.256926i	$-0.0827098\pi$
$359$	4.93976	+	8.55592i	0.260711	+	0.451564i	−0.705720	+	0.708491i	$0.749376\pi$
$360$		0			0
$361$	−5.73076	−	2.08582i	−0.301619	−	0.109780i
$362$	2.19334	+	3.79897i	0.115279	+	0.199670i
$363$		0			0
$364$	6.42527			0.336776
$365$	−3.52044	−	2.95400i	−0.184268	−	0.154620i
$366$		0			0
$367$	−5.88735	+	33.3888i	−0.307317	+	1.74288i	0.305074	+	0.952329i	$0.401319\pi$
$367$	−5.88735	+	33.3888i	−0.307317	+	1.74288i	−0.612391	+	0.790555i	$0.709792\pi$
$368$	−0.250571	−	1.42106i	−0.0130619	−	0.0740780i
$369$		0			0
$370$	0.559481	−	2.03709i	0.0290860	−	0.105903i
$371$	−0.0931767			−0.00483749
$372$		0			0
$373$	5.44457	−	30.8777i	0.281909	−	1.59879i	−0.434212	−	0.900811i	$-0.642973\pi$
$373$	5.44457	−	30.8777i	0.281909	−	1.59879i	0.716121	−	0.697976i	$-0.245916\pi$
$374$	−2.68182	+	0.976103i	−0.138674	+	0.0504731i
$375$		0			0
$376$	−11.4382			−0.589880
$377$	30.8737	+	25.9061i	1.59008	+	1.33423i
$378$		0			0
$379$	−10.0119	−	3.64403i	−0.514276	−	0.187181i	0.0718279	−	0.997417i	$-0.477117\pi$
$379$	−10.0119	−	3.64403i	−0.514276	−	0.187181i	−0.586104	+	0.810236i	$0.699339\pi$
$380$	0.869950	−	1.50680i	0.0446275	−	0.0772971i
$381$		0			0
$382$	−1.82163	−	10.3310i	−0.0932025	−	0.528577i
$383$	18.2315	−	6.63571i	0.931585	−	0.339069i	0.168747	−	0.985659i	$-0.446028\pi$
$383$	18.2315	−	6.63571i	0.931585	−	0.339069i	0.762838	+	0.646590i	$0.223806\pi$
$384$		0			0
$385$	−1.46818	+	1.23195i	−0.0748253	+	0.0627859i
$386$	−7.52982	+	6.31827i	−0.383258	+	0.321592i
$387$		0			0
$388$	−0.161341	+	0.915012i	−0.00819087	+	0.0464527i
$389$	−3.24705	+	18.4149i	−0.164632	+	0.933674i	0.784811	+	0.619735i	$0.212760\pi$
$389$	−3.24705	+	18.4149i	−0.164632	+	0.933674i	−0.949443	+	0.313939i	$0.898351\pi$
$390$		0			0
$391$	0.577283	−	0.484398i	0.0291945	−	0.0244971i
$392$	4.58111	−	3.84401i	0.231381	−	0.194152i
$393$		0			0
$394$	11.3356	−	4.12582i	0.571079	−	0.207856i
$395$	−0.561266	−	3.18310i	−0.0282404	−	0.160159i
$396$		0			0
$397$	11.9316	−	20.6661i	0.598829	−	1.03720i	−0.394165	−	0.919040i	$-0.628966\pi$
$397$	11.9316	−	20.6661i	0.598829	−	1.03720i	0.992994	−	0.118163i	$-0.0377005\pi$
$398$	−8.73905	−	3.18075i	−0.438049	−	0.159437i
$399$		0			0
$400$	−3.73783	−	3.13641i	−0.186891	−	0.156820i
$401$	−17.8350			−0.890638			−0.445319	−	0.895372i	$-0.646910\pi$
$401$	−17.8350			−0.890638			−0.445319	+	0.895372i	$0.646910\pi$
$402$		0			0
$403$	−19.7769	+	7.19819i	−0.985156	+	0.358568i
$404$	−1.48675	+	8.43179i	−0.0739687	+	0.419497i
$405$		0			0
$406$	−6.39665			−0.317460
$407$	23.3577	+	23.6510i	1.15780	+	1.17233i
$408$		0			0
$409$	−1.73417	−	9.83496i	−0.0857492	−	0.486308i	−0.997192	−	0.0748818i	$-0.976142\pi$
$409$	−1.73417	−	9.83496i	−0.0857492	−	0.486308i	0.911443	−	0.411426i	$-0.134969\pi$
$410$	0.0663677	−	0.376390i	0.00327767	−	0.0185886i
$411$		0			0
$412$	3.79891	+	3.18767i	0.187159	+	0.157045i
$413$	−3.01959			−0.148584
$414$		0			0
$415$	−1.64354	−	2.84669i	−0.0806780	−	0.139738i
$416$	5.97892	+	2.17615i	0.293141	+	0.106694i
$417$		0			0
$418$	13.6888	+	23.7096i	0.669540	+	1.15968i
$419$	−6.25638	−	35.4817i	−0.305644	−	1.73340i	−0.620456	−	0.784241i	$-0.713052\pi$
$419$	−6.25638	−	35.4817i	−0.305644	−	1.73340i	0.314812	−	0.949154i	$-0.398059\pi$
$420$		0			0
$421$	−11.1668	+	19.3414i	−0.544235	+	0.942643i	0.454419	+	0.890788i	$0.349847\pi$
$421$	−11.1668	+	19.3414i	−0.544235	+	0.942643i	−0.998655	+	0.0518555i	$0.983486\pi$
$422$	3.37062	−	2.82829i	0.164079	−	0.137679i
$423$		0			0
$424$	−0.0867039	−	0.0315576i	−0.00421071	−	0.00153257i
$425$	0.442496	−	2.50952i	0.0214642	−	0.121729i
$426$		0			0
$427$	−3.62101	−	1.31794i	−0.175233	−	0.0637796i
$428$	2.73344	−	2.29363i	0.132126	−	0.110867i
$429$		0			0
$430$	1.08884	−	1.88592i	0.0525084	−	0.0909472i
$431$	29.3710	−	10.6902i	1.41475	−	0.514928i	0.482231	−	0.876044i	$-0.339827\pi$
$431$	29.3710	−	10.6902i	1.41475	−	0.514928i	0.932521	+	0.361116i	$0.117604\pi$
$432$		0			0
$433$	−2.71093	−	4.69547i	−0.130279	−	0.225650i	0.793505	−	0.608564i	$-0.208254\pi$
$433$	−2.71093	−	4.69547i	−0.130279	−	0.225650i	−0.923784	+	0.382914i	$0.874921\pi$
$434$	1.67017	−	2.89281i	0.0801705	−	0.138859i
$435$		0			0
$436$	0.489344	+	0.847568i	0.0234353	+	0.0405912i
$437$	−5.53783	−	4.64679i	−0.264910	−	0.222286i
$438$		0			0
$439$	−11.8195	−	9.91772i	−0.564113	−	0.473347i	0.315573	−	0.948901i	$-0.397803\pi$
$439$	−11.8195	−	9.91772i	−0.564113	−	0.473347i	−0.879687	+	0.475554i	$0.842248\pi$
$440$	−1.78343	+	0.649116i	−0.0850217	+	0.0309454i
$441$		0			0
$442$	0.577007	+	3.27237i	0.0274454	+	0.155651i
$443$	8.45523			0.401720			0.200860	−	0.979620i	$-0.435626\pi$
$443$	8.45523			0.401720			0.200860	+	0.979620i	$0.435626\pi$
$444$		0			0
$445$	−5.47610			−0.259592
$446$	−1.95027	−	11.0605i	−0.0923478	−	0.523730i
$447$		0			0
$448$	−0.948944	+	0.345387i	−0.0448334	+	0.0163180i
$449$	−27.8798	−	23.3939i	−1.31573	−	1.10403i	−0.987192	−	0.159538i	$-0.949000\pi$
$449$	−27.8798	−	23.3939i	−1.31573	−	1.10403i	−0.328538	−	0.944491i	$-0.606556\pi$
$450$		0			0
$451$	4.60691	+	3.86566i	0.216931	+	0.182027i
$452$	4.61851	+	7.99950i	0.217236	+	0.376265i
$453$		0			0
$454$	7.57697	−	13.1237i	0.355605	−	0.615925i
$455$	1.11574	+	1.93251i	0.0523066	+	0.0905976i
$456$		0			0
$457$	−12.2550	+	4.46044i	−0.573263	+	0.208651i	−0.612352	−	0.790585i	$-0.709777\pi$
$457$	−12.2550	+	4.46044i	−0.573263	+	0.208651i	0.0390893	+	0.999236i	$0.487554\pi$
$458$	−7.78085	+	13.4768i	−0.363575	+	0.629731i
$459$		0			0
$460$	0.383898	−	0.322128i	0.0178993	−	0.0150193i
$461$	16.5840	+	6.03608i	0.772393	+	0.281128i	0.697997	−	0.716101i	$-0.254075\pi$
$461$	16.5840	+	6.03608i	0.772393	+	0.281128i	0.0743962	+	0.997229i	$0.476297\pi$
$462$		0			0
$463$	4.60063	−	26.0915i	0.213809	−	1.21257i	−0.669151	−	0.743126i	$-0.733342\pi$
$463$	4.60063	−	26.0915i	0.213809	−	1.21257i	0.882961	−	0.469447i	$-0.155547\pi$
$464$	−5.95228	−	2.16645i	−0.276328	−	0.100575i
$465$		0			0
$466$	10.4083	−	8.73363i	0.482157	−	0.404578i
$467$	−9.54875	+	16.5389i	−0.441864	+	0.765330i	−0.997828	−	0.0658760i	$-0.979016\pi$
$467$	−9.54875	+	16.5389i	−0.441864	+	0.765330i	0.555964	+	0.831206i	$0.312349\pi$
$468$		0			0
$469$	−0.204248	−	1.15835i	−0.00943129	−	0.0534875i
$470$	−1.98622	−	3.44024i	−0.0916176	−	0.158686i
$471$		0			0
$472$	−2.80983	−	1.02269i	−0.129333	−	0.0470733i
$473$	17.1330	+	29.6752i	0.787776	+	1.36447i
$474$		0			0
$475$	−24.4450			−1.12161
$476$	−0.404001	−	0.338997i	−0.0185173	−	0.0155379i
$477$		0			0
$478$	−3.38518	+	19.1983i	−0.154834	+	0.878110i
$479$	−3.33101	−	18.8911i	−0.152198	−	0.863156i	−0.961303	−	0.275492i	$-0.911159\pi$
$479$	−3.33101	−	18.8911i	−0.152198	−	0.863156i	0.809106	−	0.587663i	$-0.199952\pi$
$480$		0			0
$481$	31.8410	−	22.0006i	1.45183	−	1.00314i
$482$	−1.44363			−0.0657556
$483$		0			0
$484$	3.27561	−	18.5769i	0.148891	−	0.844404i
$485$	−0.303223	+	0.110364i	−0.0137686	+	0.00501137i
$486$		0			0
$487$	−35.7577			−1.62034			−0.810168	−	0.586197i	$-0.800624\pi$
$487$	−35.7577			−1.62034			−0.810168	+	0.586197i	$0.800624\pi$
$488$	−2.92310	−	2.45277i	−0.132322	−	0.111032i
$489$		0			0
$490$	1.95165	+	0.710344i	0.0881667	+	0.0320901i
$491$	14.8866	−	25.7843i	0.671822	−	1.16363i	−0.305565	−	0.952171i	$-0.598845\pi$
$491$	14.8866	−	25.7843i	0.671822	−	1.16363i	0.977387	−	0.211459i	$-0.0678214\pi$
$492$		0			0
$493$	−0.574436	−	3.25779i	−0.0258713	−	0.146723i
$494$	29.9535	−	10.9022i	1.34767	−	0.490512i
$495$		0			0
$496$	2.53390	−	2.12619i	0.113775	−	0.0954688i
$497$	−0.242049	+	0.203103i	−0.0108574	+	0.00911043i
$498$		0			0
$499$	4.30958	−	24.4409i	0.192923	−	1.09412i	−0.722422	−	0.691453i	$-0.756971\pi$
$499$	4.30958	−	24.4409i	0.192923	−	1.09412i	0.915345	−	0.402670i	$-0.131918\pi$
$500$	0.595800	−	3.37895i	0.0266450	−	0.151111i
$501$		0			0
$502$	7.71630	−	6.47475i	0.344395	−	0.288982i
$503$	−10.4375	+	8.75811i	−0.465386	+	0.390505i	−0.845108	−	0.534596i	$-0.820464\pi$
$503$	−10.4375	+	8.75811i	−0.465386	+	0.390505i	0.379722	+	0.925100i	$0.376019\pi$
$504$		0			0
$505$	−2.79418	+	1.01700i	−0.124339	+	0.0452558i
$506$	1.36931	+	7.76574i	0.0608733	+	0.345229i
$507$		0			0
$508$	−3.38575	+	5.86430i	−0.150219	+	0.260186i
$509$	19.8285	+	7.21697i	0.878881	+	0.319886i	0.741758	−	0.670668i	$-0.233992\pi$
$509$	19.8285	+	7.21697i	0.878881	+	0.319886i	0.137123	+	0.990554i	$0.456215\pi$
$510$		0			0
$511$	10.2365	+	8.58945i	0.452836	+	0.379975i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.56375	−	2.38901i	0.289515	−	0.105375i
$515$	−0.299072	+	1.69612i	−0.0131787	+	0.0747400i
$516$		0			0
$517$	62.5069			2.74905
$518$	−1.62682	+	5.92330i	−0.0714784	+	0.260255i
$519$		0			0
$520$	0.383714	+	2.17615i	0.0168270	+	0.0954305i
$521$	−0.510798	+	2.89688i	−0.0223784	+	0.126914i	−0.993950	−	0.109830i	$-0.964969\pi$
$521$	−0.510798	+	2.89688i	−0.0223784	+	0.126914i	0.971572	+	0.236745i	$0.0760804\pi$
$522$		0			0
$523$	8.30708	+	6.97047i	0.363243	+	0.304797i	0.806082	−	0.591804i	$-0.201584\pi$
$523$	8.30708	+	6.97047i	0.363243	+	0.304797i	−0.442839	+	0.896601i	$0.646029\pi$
$524$	15.1485			0.661764
$525$		0			0
$526$	−1.33142	−	2.30609i	−0.0580527	−	0.100550i
$527$	1.62328	+	0.590827i	0.0707113	+	0.0257368i
$528$		0			0
$529$	10.4589	+	18.1153i	0.454735	+	0.787624i
$530$	−0.00556446	−	0.0315576i	−0.000241705	−	0.00137078i
$531$		0			0
$532$	−2.52958	+	4.38137i	−0.109671	+	0.189956i
$533$	5.36386	−	4.50081i	0.232334	−	0.194952i
$534$		0			0
$535$	1.16451	+	0.423846i	0.0503461	+	0.0183245i
$536$	0.202257	−	1.14706i	0.00873616	−	0.0495452i
$537$		0			0
$538$	−2.26939	−	0.825991i	−0.0978404	−	0.0356110i
$539$	−25.0346	+	21.0065i	−1.07832	+	0.904815i
$540$		0			0
$541$	−4.43868	+	7.68801i	−0.190834	+	0.330534i	−0.945527	−	0.325544i	$-0.894452\pi$
$541$	−4.43868	+	7.68801i	−0.190834	+	0.330534i	0.754693	+	0.656078i	$0.227786\pi$
$542$	−23.7278	+	8.63621i	−1.01920	+	0.370957i
$543$		0			0
$544$	−0.261122	−	0.452277i	−0.0111955	−	0.0193912i
$545$	−0.169947	+	0.294357i	−0.00727974	+	0.0126089i
$546$		0			0
$547$	18.2649	+	31.6358i	0.780952	+	1.35265i	0.931388	+	0.364028i	$0.118599\pi$
$547$	18.2649	+	31.6358i	0.780952	+	1.35265i	−0.150436	+	0.988620i	$0.548068\pi$
$548$	6.49738	+	5.45195i	0.277554	+	0.232896i
$549$		0			0
$550$	20.4263	+	17.1397i	0.870979	+	0.730838i
$551$	−29.8200	+	10.8536i	−1.27038	+	0.462379i
$552$		0			0
$553$	1.63201	+	9.25560i	0.0694002	+	0.393588i
$554$	17.7320			0.753360
$555$		0			0
$556$	−18.3384			−0.777720
$557$	−6.37699	−	36.1657i	−0.270202	−	1.53239i	−0.753803	−	0.657101i	$-0.771783\pi$
$557$	−6.37699	−	36.1657i	−0.270202	−	1.53239i	0.483601	−	0.875288i	$-0.339329\pi$
$558$		0			0
$559$	37.4900	−	13.6453i	1.58566	−	0.577133i
$560$	−0.268664	−	0.225435i	−0.0113531	−	0.00952639i
$561$		0			0
$562$	15.1288	+	12.6946i	0.638172	+	0.535490i
$563$	0.238456	+	0.413018i	0.0100497	+	0.0174066i	0.871007	−	0.491271i	$-0.163468\pi$
$563$	0.238456	+	0.413018i	0.0100497	+	0.0174066i	−0.860957	+	0.508678i	$0.830134\pi$
$564$		0			0
$565$	−1.60399	+	2.77820i	−0.0674805	+	0.116880i
$566$	12.1747	+	21.0872i	0.511741	+	0.886361i
$567$		0			0
$568$	−0.294023	+	0.107015i	−0.0123369	+	0.00449027i
$569$	4.54906	−	7.87920i	0.190706	−	0.330313i	−0.754778	−	0.655980i	$-0.772255\pi$
$569$	4.54906	−	7.87920i	0.190706	−	0.330313i	0.945485	+	0.325667i	$0.105589\pi$
$570$		0			0
$571$	19.6081	−	16.4532i	0.820574	−	0.688543i	−0.132532	−	0.991179i	$-0.542311\pi$
$571$	19.6081	−	16.4532i	0.820574	−	0.688543i	0.953106	+	0.302635i	$0.0978664\pi$
$572$	−32.6733	−	11.8921i	−1.36614	−	0.497234i
$573$		0			0
$574$	−0.192979	+	1.09444i	−0.00805480	+	0.0456811i
$575$	−6.61626	−	2.40812i	−0.275917	−	0.100426i
$576$		0			0
$577$	11.8194	−	9.91764i	0.492048	−	0.412877i	−0.362712	−	0.931901i	$-0.618149\pi$
$577$	11.8194	−	9.91764i	0.492048	−	0.412877i	0.854759	+	0.519024i	$0.173705\pi$
$578$	−8.36363	+	14.4862i	−0.347881	+	0.602548i
$579$		0			0
$580$	−0.382004	−	2.16645i	−0.0158619	−	0.0899571i
$581$	4.77896	+	8.27741i	0.198265	+	0.343405i
$582$		0			0
$583$	0.473815	+	0.172455i	0.0196234	+	0.00714234i
$584$	6.61627	+	11.4597i	0.273783	+	0.474207i
$585$		0			0
$586$	−23.2486			−0.960390
$587$	−12.4394	−	10.4379i	−0.513430	−	0.430819i	0.348904	−	0.937158i	$-0.386554\pi$
$587$	−12.4394	−	10.4379i	−0.513430	−	0.430819i	−0.862334	+	0.506340i	$0.830998\pi$
$588$		0			0
$589$	2.87759	−	16.3196i	0.118569	−	0.672439i
$590$	−0.180328	−	1.02269i	−0.00742400	−	0.0421036i
$591$		0			0
$592$	−3.51995	+	4.96084i	−0.144669	+	0.203889i
$593$	27.0626			1.11133			0.555663	−	0.831407i	$-0.312464\pi$
$593$	27.0626			1.11133			0.555663	+	0.831407i	$0.312464\pi$
$594$		0			0
$595$	0.0318052	−	0.180376i	0.00130389	−	0.00739472i
$596$	5.12406	−	1.86501i	0.209890	−	0.0763936i
$597$		0			0
$598$	9.18118			0.375446
$599$	30.5258	+	25.6142i	1.24725	+	1.04657i	0.996922	+	0.0784059i	$0.0249830\pi$
$599$	30.5258	+	25.6142i	1.24725	+	1.04657i	0.250328	+	0.968161i	$0.419461\pi$
$600$		0			0
$601$	−33.5222	−	12.2011i	−1.36740	−	0.497692i	−0.449065	−	0.893499i	$-0.648243\pi$
$601$	−33.5222	−	12.2011i	−1.36740	−	0.497692i	−0.918334	+	0.395807i	$0.870465\pi$
$602$	−3.16605	+	5.48376i	−0.129038	+	0.223501i
$603$		0			0
$604$	−2.70116	−	15.3190i	−0.109909	−	0.623323i
$605$	6.15613	−	2.24065i	0.250282	−	0.0910953i
$606$		0			0
$607$	−9.76538	+	8.19413i	−0.396365	+	0.332589i	−0.819086	−	0.573670i	$-0.805519\pi$
$607$	−9.76538	+	8.19413i	−0.396365	+	0.332589i	0.422722	+	0.906259i	$0.361075\pi$
$608$	−3.83776	+	3.22027i	−0.155642	+	0.130599i
$609$		0			0
$610$	0.230123	−	1.30509i	0.00931740	−	0.0528416i
$611$	12.6376	−	71.6714i	0.511263	−	2.89952i
$612$		0			0
$613$	−3.13519	+	2.63074i	−0.126629	+	0.106255i	−0.703903	−	0.710296i	$-0.748561\pi$
$613$	−3.13519	+	2.63074i	−0.126629	+	0.106255i	0.577274	+	0.816551i	$0.304117\pi$
$614$	8.17382	−	6.85865i	0.329868	−	0.276792i
$615$		0			0
$616$	5.18574	−	1.88745i	0.208939	−	0.0760477i
$617$	−8.20856	−	46.5531i	−0.330464	−	1.87416i	−0.468104	−	0.883673i	$-0.655063\pi$
$617$	−8.20856	−	46.5531i	−0.330464	−	1.87416i	0.137640	−	0.990482i	$-0.456048\pi$
$618$		0			0
$619$	10.5169	−	18.2157i	0.422708	−	0.732152i	−0.573495	−	0.819209i	$-0.694413\pi$
$619$	10.5169	−	18.2157i	0.422708	−	0.732152i	0.996203	+	0.0870571i	$0.0277463\pi$
$620$	1.07950	+	0.392904i	0.0433536	+	0.0157794i
$621$		0			0
$622$	13.0382	+	10.9403i	0.522783	+	0.438667i
$623$	15.9230			0.637943
$624$		0			0
$625$	−21.8059	+	7.93669i	−0.872235	+	0.317468i
$626$	−1.89458	+	10.7447i	−0.0757225	+	0.429444i
$627$		0			0
$628$	−4.00822			−0.159945
$629$	−3.16281	−	0.296606i	−0.126110	−	0.0118264i
$630$		0			0
$631$	−5.68830	−	32.2599i	−0.226448	−	1.28425i	−0.859898	−	0.510465i	$-0.829473\pi$
$631$	−5.68830	−	32.2599i	−0.226448	−	1.28425i	0.633451	−	0.773783i	$-0.281638\pi$
$632$	−1.61610	+	9.16537i	−0.0642851	+	0.364579i
$633$		0			0
$634$	−22.0930	−	18.5382i	−0.877424	−	0.736246i
$635$	−2.35172			−0.0933252
$636$		0			0
$637$	19.0250	+	32.9522i	0.753796	+	1.30561i
$638$	32.5277	+	11.8391i	1.28779	+	0.468716i
$639$		0			0
$640$	−0.173648	−	0.300767i	−0.00686405	−	0.0118889i
$641$	−3.47857	−	19.7280i	−0.137395	−	0.779208i	−0.973162	−	0.230123i	$-0.926087\pi$
$641$	−3.47857	−	19.7280i	−0.137395	−	0.779208i	0.835766	−	0.549085i	$-0.185024\pi$
$642$		0			0
$643$	6.69618	−	11.5981i	0.264071	−	0.457385i	−0.703249	−	0.710944i	$-0.748268\pi$
$643$	6.69618	−	11.5981i	0.264071	−	0.457385i	0.967320	+	0.253559i	$0.0816012\pi$
$644$	−1.11627	+	0.936663i	−0.0439873	+	0.0369097i
$645$		0			0
$646$	−2.45858	−	0.894849i	−0.0967314	−	0.0352074i
$647$	−2.56647	+	14.5551i	−0.100898	+	0.572222i	0.891881	+	0.452269i	$0.149385\pi$
$647$	−2.56647	+	14.5551i	−0.100898	+	0.572222i	−0.992780	+	0.119953i	$0.961726\pi$
$648$		0			0
$649$	15.3550	+	5.58876i	0.602736	+	0.219378i
$650$	23.7824	−	19.9558i	0.932823	−	0.782732i
$651$		0			0
$652$	−2.34612	+	4.06359i	−0.0918810	+	0.159143i
$653$	−25.4991	+	9.28092i	−0.997857	+	0.363190i	−0.788758	−	0.614704i	$-0.789275\pi$
$653$	−25.4991	+	9.28092i	−0.997857	+	0.363190i	−0.209099	+	0.977894i	$0.567053\pi$
$654$		0			0
$655$	2.63050	+	4.55617i	0.102782	+	0.178024i
$656$	−0.550245	+	0.953052i	−0.0214835	+	0.0372104i
$657$		0			0
$658$	5.77540	+	10.0033i	0.225149	+	0.389969i
$659$	−24.2414	−	20.3409i	−0.944311	−	0.792371i	0.0340197	−	0.999421i	$-0.489169\pi$
$659$	−24.2414	−	20.3409i	−0.944311	−	0.792371i	−0.978330	+	0.207050i	$0.933614\pi$
$660$		0			0
$661$	26.0376	+	21.8481i	1.01274	+	0.849793i	0.988698	−	0.149918i	$-0.0479009\pi$
$661$	26.0376	+	21.8481i	1.01274	+	0.849793i	0.0240454	+	0.999711i	$0.492345\pi$
$662$	3.72076	−	1.35425i	0.144611	−	0.0526343i
$663$		0			0
$664$	1.64354	+	9.32096i	0.0637816	+	0.361723i
$665$	−1.75703			−0.0681347
$666$		0			0
$667$	−9.14028			−0.353913
$668$	0.134923	+	0.765189i	0.00522035	+	0.0296060i
$669$		0			0
$670$	0.380118	−	0.138352i	0.0146853	−	0.00534500i
$671$	15.9740	+	13.4038i	0.616669	+	0.517447i
$672$		0			0
$673$	30.3717	+	25.4849i	1.17074	+	0.982372i	0.999996	−	0.00294292i	$-0.000936763\pi$
$673$	30.3717	+	25.4849i	1.17074	+	0.982372i	0.170749	+	0.985315i	$0.445381\pi$
$674$	−2.13839	−	3.70380i	−0.0823676	−	0.142665i
$675$		0			0
$676$	−13.7416	+	23.8011i	−0.528522	+	0.915426i
$677$	9.65303	+	16.7195i	0.370996	+	0.642584i	0.989719	−	0.143025i	$-0.0456830\pi$
$677$	9.65303	+	16.7195i	0.370996	+	0.642584i	−0.618723	+	0.785609i	$0.712350\pi$
$678$		0			0
$679$	0.881690	−	0.320909i	0.0338362	−	0.0123154i
$680$	0.0906868	−	0.157074i	0.00347768	−	0.00602352i
$681$		0			0
$682$	−13.8471	+	11.6191i	−0.530233	+	0.444918i
$683$	1.90109	+	0.691940i	0.0727432	+	0.0264764i	0.378135	−	0.925750i	$-0.376565\pi$
$683$	1.90109	+	0.691940i	0.0727432	+	0.0264764i	−0.305392	+	0.952227i	$0.598788\pi$
$684$		0			0
$685$	−0.511511	+	2.90092i	−0.0195438	+	0.110838i
$686$	−12.3175	−	4.48320i	−0.470284	−	0.171169i
$687$		0			0
$688$	−4.80338	+	4.03051i	−0.183127	+	0.153662i
$689$	0.293535	−	0.508417i	0.0111828	−	0.0193692i
$690$		0			0
$691$	−0.242292	−	1.37410i	−0.00921721	−	0.0522734i	0.979852	−	0.199724i	$-0.0640045\pi$
$691$	−0.242292	−	1.37410i	−0.00921721	−	0.0522734i	−0.989069	+	0.147450i	$0.952893\pi$
$692$	5.36667	+	9.29535i	0.204010	+	0.353356i
$693$		0			0
$694$	9.51723	+	3.46399i	0.361269	+	0.131491i
$695$	−3.18442	−	5.51559i	−0.120792	−	0.209218i
$696$		0			0
$697$	−0.574725			−0.0217692
$698$	5.50852	+	4.62220i	0.208501	+	0.174953i
$699$		0			0
$700$	−0.855638	+	4.85256i	−0.0323401	+	0.183410i
$701$	7.84895	+	44.5136i	0.296451	+	1.68126i	0.661247	+	0.750168i	$0.270027\pi$
$701$	7.84895	+	44.5136i	0.296451	+	1.68126i	−0.364797	+	0.931087i	$0.618862\pi$
$702$		0			0
$703$	2.46650	+	30.3737i	0.0930258	+	1.14557i
$704$	5.46475			0.205960
$705$		0			0
$706$	−5.91359	+	33.5376i	−0.222561	+	1.26220i
$707$	8.12472	−	2.95716i	0.305562	−	0.111215i
$708$		0			0
$709$	−28.5445			−1.07201			−0.536005	−	0.844215i	$-0.680067\pi$
$709$	−28.5445			−1.07201			−0.536005	+	0.844215i	$0.680067\pi$
$710$	−0.0832432	−	0.0698494i	−0.00312406	−	0.00262140i
$711$		0			0
$712$	14.8169	+	5.39291i	0.555287	+	0.202108i
$713$	2.38653	−	4.13359i	0.0893761	−	0.154804i
$714$		0			0
$715$	−2.09690	−	11.8921i	−0.0784196	−	0.444740i
$716$	−11.1801	+	4.06921i	−0.417819	+	0.152074i
$717$		0			0
$718$	7.56816	−	6.35044i	0.282441	−	0.236996i
$719$	13.6923	−	11.4892i	0.510637	−	0.428475i	−0.350717	−	0.936482i	$-0.614062\pi$
$719$	13.6923	−	11.4892i	0.510637	−	0.428475i	0.861353	+	0.508007i	$0.169617\pi$
$720$		0			0
$721$	0.869621	−	4.93187i	0.0323864	−	0.183672i
$722$	−1.05900	+	6.00589i	−0.0394119	+	0.223516i
$723$		0			0
$724$	3.36039	−	2.81970i	0.124888	−	0.104793i
$725$	−23.6765	+	19.8669i	−0.879322	+	0.737839i
$726$		0			0
$727$	16.3955	−	5.96747i	0.608075	−	0.221321i	−0.0195860	−	0.999808i	$-0.506235\pi$
$727$	16.3955	−	5.96747i	0.608075	−	0.221321i	0.627661	+	0.778487i	$0.284013\pi$
$728$	−1.11574	−	6.32766i	−0.0413520	−	0.234519i
$729$		0			0
$730$	−2.29781	+	3.97992i	−0.0850457	+	0.147303i
$731$	−3.07718	−	1.12000i	−0.113813	−	0.0414247i
$732$		0			0
$733$	−33.6087	−	28.2011i	−1.24137	−	1.04163i	−0.997416	−	0.0718424i	$-0.977112\pi$
$733$	−33.6087	−	28.2011i	−1.24137	−	1.04163i	−0.243950	−	0.969788i	$-0.578443\pi$
$734$	33.9039			1.25142
$735$		0			0
$736$	−1.35596	+	0.493529i	−0.0499814	+	0.0181917i
$737$	−1.10528	+	6.26837i	−0.0407136	+	0.230898i
$738$		0			0
$739$	39.5017			1.45309			0.726546	−	0.687118i	$-0.241124\pi$
$739$	39.5017			1.45309			0.726546	+	0.687118i	$0.241124\pi$
$740$	−2.10329	−	0.197245i	−0.0773186	−	0.00725087i
$741$		0			0
$742$	0.0161800	+	0.0917611i	0.000593985	+	0.00336866i
$743$	−3.45404	+	19.5888i	−0.126716	+	0.718644i	0.853557	+	0.520999i	$0.174440\pi$
$743$	−3.45404	+	19.5888i	−0.126716	+	0.718644i	−0.980274	+	0.197645i	$0.936671\pi$
$744$		0			0
$745$	1.45072	+	1.21730i	0.0531502	+	0.0445983i
$746$	−31.3540			−1.14795
$747$		0			0
$748$	1.42697	+	2.47158i	0.0521751	+	0.0903699i
$749$	−3.38608	−	1.23243i	−0.123725	−	0.0450320i
$750$		0			0
$751$	16.6184	+	28.7839i	0.606413	+	1.05034i	0.991826	+	0.127594i	$0.0407255\pi$
$751$	16.6184	+	28.7839i	0.606413	+	1.05034i	−0.385413	+	0.922744i	$0.625941\pi$
$752$	1.98622	+	11.2644i	0.0724301	+	0.410771i
$753$		0			0
$754$	20.1514	−	34.9032i	0.733870	−	1.27110i
$755$	4.13842	−	3.47255i	0.150612	−	0.126379i
$756$		0			0
$757$	−40.7915	−	14.8469i	−1.48259	−	0.539620i	−0.531105	−	0.847306i	$-0.678223\pi$
$757$	−40.7915	−	14.8469i	−1.48259	−	0.539620i	−0.951488	+	0.307686i	$0.900445\pi$
$758$	−1.85012	+	10.4926i	−0.0671994	+	0.381107i
$759$		0			0
$760$	−1.63497	−	0.595081i	−0.0593067	−	0.0215859i
$761$	−19.3702	+	16.2536i	−0.702171	+	0.589191i	−0.922390	−	0.386259i	$-0.873767\pi$
$761$	−19.3702	+	16.2536i	−0.702171	+	0.589191i	0.220220	+	0.975450i	$0.429323\pi$
$762$		0			0
$763$	0.494161	−	0.855912i	0.0178898	−	0.0309861i
$764$	−9.85768	+	3.58790i	−0.356638	+	0.129806i
$765$		0			0
$766$	−9.70076	−	16.8022i	−0.350503	−	0.607089i
$767$	9.51263	−	16.4764i	0.343481	−	0.594927i
$768$		0			0
$769$	−13.8992	−	24.0740i	−0.501216	−	0.868132i	−0.999999	−	0.00140492i	$-0.999553\pi$
$769$	−13.8992	−	24.0740i	−0.501216	−	0.868132i	0.498783	−	0.866727i	$-0.333781\pi$
$770$	1.46818	+	1.23195i	0.0529095	+	0.0443963i
$771$		0			0
$772$	7.52982	+	6.31827i	0.271004	+	0.227400i
$773$	−0.927201	+	0.337474i	−0.0333491	+	0.0121381i	−0.358641	−	0.933476i	$-0.616760\pi$
$773$	−0.927201	+	0.337474i	−0.0333491	+	0.0121381i	0.325292	+	0.945614i	$0.394537\pi$
$774$		0			0
$775$	−2.80266	−	15.8947i	−0.100674	−	0.570953i
$776$	0.929128			0.0333538
$777$		0			0
$778$	18.6990			0.670392
$779$	0.957372	+	5.42952i	0.0343014	+	0.194533i
$780$		0			0
$781$	1.60676	−	0.584812i	0.0574944	−	0.0209262i
$782$	−0.577283	−	0.484398i	−0.0206436	−	0.0173220i
$783$		0			0
$784$	−4.58111	−	3.84401i	−0.163611	−	0.137286i
$785$	−0.696020	−	1.20554i	−0.0248420	−	0.0430277i
$786$		0			0
$787$	−12.8990	+	22.3417i	−0.459799	+	0.796394i	−0.998950	−	0.0458144i	$-0.985412\pi$
$787$	−12.8990	+	22.3417i	−0.459799	+	0.796394i	0.539151	+	0.842209i	$0.318745\pi$
$788$	−6.03154	−	10.4469i	−0.214865	−	0.372157i
$789$		0			0
$790$	−3.03728	+	1.10548i	−0.108062	+	0.0393312i
$791$	4.66398	−	8.07825i	0.165832	−	0.287229i
$792$		0			0
$793$	18.5986	−	15.6061i	0.660455	−	0.554188i
$794$	−22.4240	−	8.16169i	−0.795800	−	0.289647i
$795$		0			0
$796$	−1.61491	+	9.15861i	−0.0572390	+	0.324618i
$797$	14.1958	+	5.16684i	0.502841	+	0.183019i	0.580971	−	0.813924i	$-0.302673\pi$
$797$	14.1958	+	5.16684i	0.502841	+	0.183019i	−0.0781306	+	0.996943i	$0.524895\pi$
$798$		0			0
$799$	−4.57599	+	3.83971i	−0.161887	+	0.135839i
$800$	−2.43969	+	4.22567i	−0.0862562	+	0.149400i
$801$		0			0
$802$	3.09702	+	17.5641i	0.109359	+	0.620208i
$803$	−36.1563	−	62.6245i	−1.27593	−	2.20997i
$804$		0			0
$805$	−0.475556	−	0.173088i	−0.0167612	−	0.00610056i
$806$	10.5231	+	18.2265i	0.370659	+	0.642000i
$807$		0			0
$808$	8.56186			0.301205
$809$	32.7023	+	27.4405i	1.14975	+	0.964757i	0.999714	−	0.0239226i	$-0.00761551\pi$
$809$	32.7023	+	27.4405i	1.14975	+	0.964757i	0.150039	+	0.988680i	$0.452060\pi$
$810$		0			0
$811$	3.54555	−	20.1078i	0.124501	−	0.706081i	−0.857102	−	0.515147i	$-0.827737\pi$
$811$	3.54555	−	20.1078i	0.124501	−	0.706081i	0.981603	−	0.190934i	$-0.0611517\pi$
$812$	1.11077	+	6.29947i	0.0389802	+	0.221068i
$813$		0			0
$814$	19.2356	−	27.1098i	0.674209	−	0.950196i
$815$	−1.62960			−0.0570822
$816$		0			0
$817$	−5.45491	+	30.9363i	−0.190843	+	1.08232i
$818$	−9.38441	+	3.41565i	−0.328118	+	0.119425i
$819$		0			0
$820$	−0.382196			−0.0133469
$821$	−10.3004	−	8.64304i	−0.359485	−	0.301644i	0.445100	−	0.895481i	$-0.353168\pi$
$821$	−10.3004	−	8.64304i	−0.359485	−	0.301644i	−0.804586	+	0.593837i	$0.797613\pi$
$822$		0			0
$823$	38.3237	+	13.9487i	1.33588	+	0.486221i	0.908513	−	0.417857i	$-0.137219\pi$
$823$	38.3237	+	13.9487i	1.33588	+	0.486221i	0.427368	+	0.904078i	$0.359441\pi$
$824$	2.47956	−	4.29473i	0.0863797	−	0.149614i
$825$		0			0
$826$	0.524347	+	2.97372i	0.0182444	+	0.103469i
$827$	−38.0037	+	13.8322i	−1.32152	+	0.480993i	−0.903945	−	0.427650i	$-0.859342\pi$
$827$	−38.0037	+	13.8322i	−1.32152	+	0.480993i	−0.417574	+	0.908643i	$0.637120\pi$
$828$		0			0
$829$	2.03399	−	1.70672i	0.0706435	−	0.0592770i	−0.606782	−	0.794868i	$-0.707540\pi$
$829$	2.03399	−	1.70672i	0.0706435	−	0.0592770i	0.677426	+	0.735591i	$0.263096\pi$
$830$	−2.51804	+	2.11289i	−0.0874026	+	0.0733395i
$831$		0			0
$832$	1.10486	−	6.26597i	0.0383041	−	0.217234i
$833$	0.542326	−	3.07569i	0.0187905	−	0.106566i
$834$		0			0
$835$	−0.206715	+	0.173454i	−0.00715366	+	0.00600263i
$836$	20.9724	−	17.5979i	0.725346	−	0.608638i
$837$		0			0
$838$	−33.8563	+	12.3227i	−1.16955	+	0.425680i
$839$	7.48912	+	42.4729i	0.258553	+	1.46633i	0.786785	+	0.617228i	$0.211744\pi$
$839$	7.48912	+	42.4729i	0.258553	+	1.46633i	−0.528231	+	0.849101i	$0.677145\pi$
$840$		0			0
$841$	−5.56161	+	9.63298i	−0.191780	+	0.332172i
$842$	20.9867	+	7.63853i	0.723249	+	0.263241i
$843$		0			0
$844$	−3.37062	−	2.82829i	−0.116022	−	0.0973537i
$845$	−9.54479			−0.328351
$846$		0			0
$847$	−17.9004	+	6.51520i	−0.615064	+	0.223865i
$848$	−0.0160222	+	0.0908666i	−0.000550206	+	0.00312037i
$849$		0			0
$850$	−2.54823			−0.0874036
$851$	−2.32459	+	8.46391i	−0.0796860	+	0.290139i
$852$		0			0
$853$	−7.79993	−	44.2356i	−0.267064	−	1.51460i	−0.763092	−	0.646290i	$-0.776319\pi$
$853$	−7.79993	−	44.2356i	−0.267064	−	1.51460i	0.496027	−	0.868307i	$-0.334792\pi$
$854$	−0.669135	+	3.79485i	−0.0228973	+	0.129857i
$855$		0			0
$856$	−2.73344	−	2.29363i	−0.0934272	−	0.0783947i
$857$	1.14287			0.0390395			0.0195198	−	0.999809i	$-0.493786\pi$
$857$	1.14287			0.0390395			0.0195198	+	0.999809i	$0.493786\pi$
$858$		0			0
$859$	−10.3483	−	17.9238i	−0.353080	−	0.611552i	0.633708	−	0.773573i	$-0.281532\pi$
$859$	−10.3483	−	17.9238i	−0.353080	−	0.611552i	−0.986787	+	0.162020i	$0.948199\pi$
$860$	−2.04635	−	0.744809i	−0.0697798	−	0.0253978i
$861$		0			0
$862$	−15.6280	−	27.0685i	−0.532291	−	0.921956i
$863$	1.91838	+	10.8797i	0.0653023	+	0.370348i	0.999893	+	0.0146230i	$0.00465482\pi$
$863$	1.91838	+	10.8797i	0.0653023	+	0.370348i	−0.934591	+	0.355725i	$0.884234\pi$
$864$		0			0
$865$	−1.86383	+	3.22824i	−0.0633720	+	0.109764i
$866$	−4.15339	+	3.48511i	−0.141138	+	0.118429i
$867$		0			0
$868$	−3.13888	−	1.14246i	−0.106541	−	0.0387776i
$869$	8.83159	−	50.0864i	0.299591	−	1.69907i
$870$		0			0
$871$	6.96395	+	2.53467i	0.235965	+	0.0858841i
$872$	0.749718	−	0.629088i	0.0253887	−	0.0213036i
$873$		0			0
$874$	−3.61456	+	6.26061i	−0.122264	+	0.211768i
$875$	−3.25590	+	1.18505i	−0.110069	+	0.0400620i
$876$		0			0
$877$	6.18401	+	10.7110i	0.208819	+	0.361686i	0.951343	−	0.308134i	$-0.0997046\pi$
$877$	6.18401	+	10.7110i	0.208819	+	0.361686i	−0.742524	+	0.669820i	$0.766371\pi$
$878$	−7.71462	+	13.3621i	−0.260356	+	0.450950i
$879$		0			0
$880$	0.948944	+	1.64362i	0.0319889	+	0.0554064i
$881$	−13.7758	−	11.5593i	−0.464120	−	0.389443i	0.380524	−	0.924771i	$-0.375744\pi$
$881$	−13.7758	−	11.5593i	−0.464120	−	0.389443i	−0.844644	+	0.535328i	$0.820188\pi$
$882$		0			0
$883$	−8.21722	−	6.89507i	−0.276532	−	0.232038i	0.493965	−	0.869482i	$-0.335547\pi$
$883$	−8.21722	−	6.89507i	−0.276532	−	0.232038i	−0.770496	+	0.637444i	$0.779992\pi$
$884$	3.12246	−	1.13648i	0.105020	−	0.0382240i
$885$		0			0
$886$	−1.46824	−	8.32678i	−0.0493263	−	0.279744i
$887$	16.7444			0.562222			0.281111	−	0.959675i	$-0.409297\pi$
$887$	16.7444			0.562222			0.281111	+	0.959675i	$0.409297\pi$
$888$		0			0
$889$	6.83817			0.229345
$890$	0.950915	+	5.39291i	0.0318748	+	0.180771i
$891$		0			0
$892$	−10.5538	+	3.84127i	−0.353368	+	0.128615i
$893$	43.8971	+	36.8340i	1.46896	+	1.23260i
$894$		0			0
$895$	−3.16528	−	2.65599i	−0.105804	−	0.0887799i
$896$	0.504922	+	0.874551i	0.0168683	+	0.0292167i
$897$		0			0
$898$	−18.1973	+	31.5186i	−0.607250	+	1.05179i
$899$	−10.4762	−	18.1453i	−0.349400	−	0.605179i
$900$		0			0
$901$	−0.0452806	+	0.0164808i	−0.00150852	+	0.000549055i
$902$	3.00695	−	5.20819i	0.100120	−	0.173414i
$903$		0			0
$904$	7.07597	−	5.93744i	0.235343	−	0.197476i
$905$	1.43160	+	0.521060i	0.0475880	+	0.0173206i
$906$		0			0
$907$	7.53327	−	42.7233i	0.250138	−	1.41860i	−0.558113	−	0.829765i	$-0.688474\pi$
$907$	7.53327	−	42.7233i	0.250138	−	1.41860i	0.808251	−	0.588838i	$-0.200415\pi$
$908$	−14.2400	−	5.18295i	−0.472572	−	0.172002i
$909$		0			0
$910$	1.70941	−	1.43436i	0.0566663	−	0.0475487i
$911$	5.05307	−	8.75217i	0.167416	−	0.289972i	−0.770095	−	0.637929i	$-0.779791\pi$
$911$	5.05307	−	8.75217i	0.167416	−	0.289972i	0.937510	+	0.347957i	$0.113124\pi$
$912$		0			0
$913$	−8.98151	−	50.9367i	−0.297245	−	1.68576i
$914$	6.52073	+	11.2942i	0.215687	+	0.373580i
$915$		0			0
$916$	14.6232	+	5.32242i	0.483165	+	0.175858i
$917$	−7.64880	−	13.2481i	−0.252586	−	0.437491i
$918$		0			0
$919$	2.82736			0.0932661			0.0466330	−	0.998912i	$-0.485151\pi$
$919$	2.82736			0.0932661			0.0466330	+	0.998912i	$0.485151\pi$
$920$	−0.383898	−	0.322128i	−0.0126567	−	0.0106203i
$921$		0			0
$922$	3.06460	−	17.3802i	0.100927	−	0.572386i
$923$	−0.345702	−	1.96057i	−0.0113789	−	0.0645331i
$924$		0			0
$925$	12.3753	+	26.9771i	0.406897	+	0.887001i
$926$	−26.4940			−0.870646
$927$		0			0
$928$	−1.09994	+	6.23806i	−0.0361072	+	0.204774i
$929$	31.4473	−	11.4459i	1.03175	−	0.375528i	0.230005	−	0.973189i	$-0.426126\pi$
$929$	31.4473	−	11.4459i	1.03175	−	0.375528i	0.801748	+	0.597662i	$0.203903\pi$
$930$		0			0
$931$	−29.9599			−0.981897
$932$	−10.4083	−	8.73363i	−0.340937	−	0.286080i
$933$		0			0
$934$	17.9458	+	6.53173i	0.587204	+	0.213725i
$935$	−0.495580	+	0.858370i	−0.0162072	+	0.0280717i
$936$		0			0
$937$	7.99787	+	45.3582i	0.261279	+	1.48179i	0.779425	+	0.626495i	$0.215511\pi$
$937$	7.99787	+	45.3582i	0.261279	+	1.48179i	−0.518146	+	0.855292i	$0.673378\pi$
$938$	−1.10528	+	0.402290i	−0.0360888	+	0.0131352i
$939$		0			0
$940$	−3.04307	+	2.55344i	−0.0992540	+	0.0832840i
$941$	13.4316	−	11.2705i	0.437858	−	0.367406i	−0.397049	−	0.917797i	$-0.629966\pi$
$941$	13.4316	−	11.2705i	0.437858	−	0.367406i	0.834907	+	0.550391i	$0.185521\pi$
$942$		0			0
$943$	−0.275751	+	1.56386i	−0.00897970	+	0.0509264i
$944$	−0.519235	+	2.94473i	−0.0168997	+	0.0958427i
$945$		0			0
$946$	26.2493	−	22.0257i	0.853437	−	0.716119i
$947$	−20.0641	+	16.8357i	−0.651994	+	0.547088i	−0.907675	−	0.419673i	$-0.862145\pi$
$947$	−20.0641	+	16.8357i	−0.651994	+	0.547088i	0.255681	+	0.966761i	$0.417700\pi$
$948$		0			0
$949$	−79.1163	+	28.7960i	−2.56822	+	0.934757i
$950$	4.24482	+	24.0736i	0.137720	+	0.781050i
$951$		0			0
$952$	−0.263693	+	0.456729i	−0.00854633	+	0.0148027i
$953$	−24.4034	−	8.88209i	−0.790502	−	0.287719i	−0.0849574	−	0.996385i	$-0.527075\pi$
$953$	−24.4034	−	8.88209i	−0.790502	−	0.287719i	−0.705545	+	0.708665i	$0.749298\pi$
$954$		0			0
$955$	−2.79089	−	2.34184i	−0.0903112	−	0.0757801i
$956$	19.4945			0.630496
$957$		0			0
$958$	−18.0257	+	6.56080i	−0.582383	+	0.211970i
$959$	1.48734	−	8.43510i	0.0480286	−	0.272384i
$960$		0			0
$961$	−20.0587			−0.647054
$962$	−27.1955	−	27.5369i	−0.876817	−	0.887827i
$963$		0			0
$964$	0.250684	+	1.42170i	0.00807398	+	0.0457898i
$965$	−0.592791	+	3.36188i	−0.0190826	+	0.108223i
$966$		0			0
$967$	25.8686	+	21.7064i	0.831879	+	0.698029i	0.955722	−	0.294273i	$-0.0950773\pi$
$967$	25.8686	+	21.7064i	0.831879	+	0.698029i	−0.123843	+	0.992302i	$0.539522\pi$
$968$	−18.8635			−0.606295
$969$		0			0
$970$	0.161341	+	0.279451i	0.00518036	+	0.00897265i
$971$	−12.9625	−	4.71796i	−0.415986	−	0.151407i	0.125544	−	0.992088i	$-0.459932\pi$
$971$	−12.9625	−	4.71796i	−0.415986	−	0.151407i	−0.541530	+	0.840682i	$0.682155\pi$
$972$		0			0
$973$	9.25945	+	16.0378i	0.296844	+	0.514150i
$974$	6.20926	+	35.2145i	0.198958	+	1.12834i
$975$		0			0
$976$	−1.90792	+	3.30461i	−0.0610709	+	0.105778i
$977$	29.8644	−	25.0592i	0.955448	−	0.801716i	−0.0247589	−	0.999693i	$-0.507882\pi$
$977$	29.8644	−	25.0592i	0.955448	−	0.801716i	0.980207	+	0.197978i	$0.0634374\pi$
$978$		0			0
$979$	−80.9706	−	29.4709i	−2.58783	−	0.941894i
$980$	0.360651	−	2.04535i	0.0115206	−	0.0653364i
$981$		0			0
$982$	−27.9776	−	10.1830i	−0.892802	−	0.324953i
$983$	−9.34290	+	7.83963i	−0.297992	+	0.250045i	−0.779508	−	0.626392i	$-0.784531\pi$
$983$	−9.34290	+	7.83963i	−0.297992	+	0.250045i	0.481516	+	0.876437i	$0.340086\pi$
$984$		0			0
$985$	2.09473	−	3.62818i	0.0667438	−	0.115604i
$986$	−3.10855	+	1.13142i	−0.0989963	+	0.0360317i
$987$		0			0
$988$	−15.9379	−	27.6053i	−0.507052	−	0.878240i
$989$	−4.52402	+	7.83583i	−0.143855	+	0.249165i
$990$		0			0
$991$	−13.2303	−	22.9156i	−0.420275	−	0.727937i	0.575691	−	0.817667i	$-0.304733\pi$
$991$	−13.2303	−	22.9156i	−0.420275	−	0.727937i	−0.995966	+	0.0897299i	$0.971400\pi$
$992$	−2.53390	−	2.12619i	−0.0804513	−	0.0675067i
$993$		0			0
$994$	0.242049	+	0.203103i	0.00767733	+	0.00644204i
$995$	−3.03504	+	1.10466i	−0.0962172	+	0.0350202i
$996$		0			0
$997$	−2.31702	−	13.1405i	−0.0733809	−	0.416164i	−0.999264	−	0.0383540i	$-0.987789\pi$
$997$	−2.31702	−	13.1405i	−0.0733809	−	0.416164i	0.925883	−	0.377809i	$-0.123323\pi$
$998$	−24.8179			−0.785597
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.x.g.379.2		12
3.2	odd	2		74.2.f.b.9.2	✓	12
12.11	even	2		592.2.bc.d.305.1		12
37.33	even	9	inner	666.2.x.g.181.2		12
111.62	odd	18		2738.2.a.q.1.6		6
111.86	odd	18		2738.2.a.t.1.6		6
111.107	odd	18		74.2.f.b.33.2	yes	12
444.107	even	18		592.2.bc.d.33.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.9.2	✓	12	3.2	odd	2
74.2.f.b.33.2	yes	12	111.107	odd	18
592.2.bc.d.33.1		12	444.107	even	18
592.2.bc.d.305.1		12	12.11	even	2
666.2.x.g.181.2		12	37.33	even	9	inner
666.2.x.g.379.2		12	1.1	even	1	trivial
2738.2.a.q.1.6		6	111.62	odd	18
2738.2.a.t.1.6		6	111.86	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.x (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(0.773586 + 0.649116i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(0.773586 + 0.649116i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.173648 + 0.300767i) q^{10} +(-2.73237 - 4.73261i) q^{11} +(-5.97892 + 2.17615i) q^{13} +(0.504922 - 0.874551i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.490749 + 0.178618i) q^{17} +(0.869950 - 4.93373i) q^{19} +(0.326352 + 0.118782i) q^{20} +(-4.18624 + 3.51267i) q^{22} +(0.721492 - 1.24966i) q^{23} +(-0.847296 - 4.80526i) q^{25} +(3.18132 + 5.51020i) q^{26} +(-0.948944 - 0.345387i) q^{28} +(-3.16714 - 5.48565i) q^{29} +3.30777 q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.0906868 - 0.514310i) q^{34} +(-0.0609011 - 0.345387i) q^{35} +(-5.88521 + 1.53765i) q^{37} -5.00984 q^{38} +(0.0603074 - 0.342020i) q^{40} +(-1.03412 + 0.376390i) q^{41} -6.27037 q^{43} +(4.18624 + 3.51267i) q^{44} +(-1.35596 - 0.493529i) q^{46} +(-5.71910 + 9.90577i) q^{47} +(-1.03845 - 5.88936i) q^{49} +(-4.58512 + 1.66885i) q^{50} +(4.87406 - 4.08982i) q^{52} +(-0.0706817 + 0.0593090i) q^{53} +(-0.329565 + 1.86905i) q^{55} +(-0.175358 + 0.994503i) q^{56} +(-4.85235 + 4.07160i) q^{58} +(-2.29059 + 1.92203i) q^{59} +(-3.58571 + 1.30509i) q^{61} +(-0.574388 - 3.25751i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(2.07646 + 0.755769i) q^{65} +(-0.892251 - 0.748687i) q^{67} -0.522244 q^{68} +(-0.329565 + 0.119952i) q^{70} +(-0.0543332 + 0.308139i) q^{71} +13.2325 q^{73} +(2.53624 + 5.52879i) q^{74} +(0.869950 + 4.93373i) q^{76} +(0.958285 - 5.43471i) q^{77} +(7.12939 + 5.98227i) q^{79} -0.347296 q^{80} +(0.550245 + 0.953052i) q^{82} +(8.89395 + 3.23713i) q^{83} +(-0.0906868 - 0.157074i) q^{85} +(1.08884 + 6.17511i) q^{86} +(2.73237 - 4.73261i) q^{88} +(12.0788 - 10.1354i) q^{89} +(-6.03778 - 2.19757i) q^{91} +(-0.250571 + 1.42106i) q^{92} +(10.7484 + 3.91209i) q^{94} +(-1.33284 + 1.11839i) q^{95} +(0.464564 - 0.804648i) q^{97} +(-5.61956 + 2.04535i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) \) 12 * q + 6 * q^5 + 6 * q^7 + 6 * q^8 - 3 * q^11 - 6 * q^13 - 3 * q^14 + 3 * q^17 - 3 * q^19 + 6 * q^20 - 3 * q^22 + 21 * q^23 - 6 * q^25 - 3 * q^28 - 6 * q^29 + 42 * q^31 - 3 * q^34 + 9 * q^35 - 3 * q^37 - 42 * q^38 + 12 * q^40 + 21 * q^41 + 36 * q^43 + 3 * q^44 + 3 * q^46 - 9 * q^47 - 12 * q^49 - 12 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^56 - 3 * q^58 + 6 * q^59 - 18 * q^61 + 33 * q^62 - 6 * q^64 - 3 * q^65 - 27 * q^67 - 6 * q^68 + 18 * q^71 + 54 * q^73 - 3 * q^74 - 3 * q^76 - 51 * q^77 - 12 * q^79 - 18 * q^82 + 6 * q^83 + 3 * q^85 + 3 * q^88 + 15 * q^89 - 51 * q^91 + 6 * q^92 - 12 * q^94 + 15 * q^95 - 42 * q^97 - 51 * q^98

Introduction

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