LMFDB - Embedded newform 693.2.by.d.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(37,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 6]))

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

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

chi := DirichletCharacter("693.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.by (of order $15$, degree $8$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	693.163
Dual form			693.2.by.d.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.872627 - 0.969151i) q^{2} +(0.0312821 - 0.297629i) q^{4} +(-0.151225 - 0.0321438i) q^{5} +(2.55326 + 0.693447i) q^{7} +(-2.42586 + 1.76249i) q^{8} +O(q^{10})$	\(q+(-0.872627 - 0.969151i) q^{2} +(0.0312821 - 0.297629i) q^{4} +(-0.151225 - 0.0321438i) q^{5} +(2.55326 + 0.693447i) q^{7} +(-2.42586 + 1.76249i) q^{8} +(0.100810 + 0.174609i) q^{10} +(-0.991882 + 3.16483i) q^{11} +(-1.38817 + 4.27234i) q^{13} +(-1.55599 - 3.07961i) q^{14} +(3.23953 + 0.688583i) q^{16} +(-2.36496 + 2.62656i) q^{17} +(0.389198 + 3.70297i) q^{19} +(-0.0142975 + 0.0440033i) q^{20} +(3.93274 - 1.80044i) q^{22} +(0.285690 - 0.494829i) q^{23} +(-4.54589 - 2.02396i) q^{25} +(5.35190 - 2.38282i) q^{26} +(0.286261 - 0.738232i) q^{28} +(1.95460 + 1.42010i) q^{29} +(-7.01784 + 1.49169i) q^{31} +(0.838964 + 1.45313i) q^{32} +4.60926 q^{34} +(-0.363825 - 0.186938i) q^{35} +(-4.37659 + 1.94858i) q^{37} +(3.24912 - 3.60851i) q^{38} +(0.423502 - 0.188555i) q^{40} +(4.14207 - 3.00939i) q^{41} +6.28052 q^{43} +(0.910919 + 0.394215i) q^{44} +(-0.728864 + 0.154925i) q^{46} +(0.797854 + 7.59108i) q^{47} +(6.03826 + 3.54110i) q^{49} +(2.00535 + 6.17182i) q^{50} +(1.22815 + 0.546807i) q^{52} +(6.02258 - 1.28014i) q^{53} +(0.251726 - 0.446718i) q^{55} +(-7.41603 + 2.81789i) q^{56} +(-0.329347 - 3.13352i) q^{58} +(0.984287 - 9.36486i) q^{59} +(-6.89786 - 1.46619i) q^{61} +(7.56963 + 5.49966i) q^{62} +(2.72307 - 8.38073i) q^{64} +(0.347254 - 0.601462i) q^{65} +(6.87041 + 11.8999i) q^{67} +(0.707759 + 0.786046i) q^{68} +(0.136313 + 0.515728i) q^{70} +(-1.82585 - 5.61938i) q^{71} +(0.770924 - 7.33485i) q^{73} +(5.70760 + 2.54119i) q^{74} +1.11429 q^{76} +(-4.72717 + 7.39282i) q^{77} +(2.85339 + 3.16901i) q^{79} +(-0.467763 - 0.208261i) q^{80} +(-6.53104 - 1.38822i) q^{82} +(1.10089 + 3.38819i) q^{83} +(0.442068 - 0.321181i) q^{85} +(-5.48055 - 6.08677i) q^{86} +(-3.17182 - 9.42561i) q^{88} +(-5.82649 + 10.0918i) q^{89} +(-6.50700 + 9.94578i) q^{91} +(-0.138338 - 0.100509i) q^{92} +(6.66067 - 7.39742i) q^{94} +(0.0601712 - 0.572491i) q^{95} +(-2.74944 + 8.46191i) q^{97} +(-1.83730 - 8.94205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 10 q^{4} - q^{7} - 8 q^{8}+O(q^{10}) $ 64 * q + 10 * q^4 - q^7 - 8 * q^8	$ 64 q + 10 q^{4} - q^{7} - 8 q^{8} - 22 q^{10} + 13 q^{11} - 8 q^{13} + 26 q^{14} - 4 q^{17} + 10 q^{19} - 24 q^{20} - 38 q^{22} + 8 q^{23} - 2 q^{25} - 4 q^{26} - 67 q^{28} - 2 q^{29} + 25 q^{31} - 72 q^{32} - 56 q^{34} - 19 q^{35} - 12 q^{37} + 37 q^{38} - 9 q^{40} - 20 q^{41} - 100 q^{43} + 5 q^{44} - 33 q^{46} + 18 q^{47} + 29 q^{49} + 46 q^{50} + 26 q^{52} + 49 q^{53} - 24 q^{55} + 48 q^{56} - 40 q^{58} - q^{59} + 3 q^{61} - 4 q^{62} - 24 q^{64} - 82 q^{65} + 76 q^{67} + 39 q^{68} + 59 q^{70} - 70 q^{71} - 3 q^{73} - 32 q^{74} + 104 q^{76} - 38 q^{77} - 15 q^{79} + 83 q^{80} + 42 q^{82} - 68 q^{83} + 62 q^{85} + 47 q^{86} - 64 q^{88} - 82 q^{89} - 10 q^{91} - 190 q^{92} - 6 q^{94} + 53 q^{95} - 32 q^{97} + 152 q^{98}+O(q^{100}) $ 64 * q + 10 * q^4 - q^7 - 8 * q^8 - 22 * q^10 + 13 * q^11 - 8 * q^13 + 26 * q^14 - 4 * q^17 + 10 * q^19 - 24 * q^20 - 38 * q^22 + 8 * q^23 - 2 * q^25 - 4 * q^26 - 67 * q^28 - 2 * q^29 + 25 * q^31 - 72 * q^32 - 56 * q^34 - 19 * q^35 - 12 * q^37 + 37 * q^38 - 9 * q^40 - 20 * q^41 - 100 * q^43 + 5 * q^44 - 33 * q^46 + 18 * q^47 + 29 * q^49 + 46 * q^50 + 26 * q^52 + 49 * q^53 - 24 * q^55 + 48 * q^56 - 40 * q^58 - q^59 + 3 * q^61 - 4 * q^62 - 24 * q^64 - 82 * q^65 + 76 * q^67 + 39 * q^68 + 59 * q^70 - 70 * q^71 - 3 * q^73 - 32 * q^74 + 104 * q^76 - 38 * q^77 - 15 * q^79 + 83 * q^80 + 42 * q^82 - 68 * q^83 + 62 * q^85 + 47 * q^86 - 64 * q^88 - 82 * q^89 - 10 * q^91 - 190 * q^92 - 6 * q^94 + 53 * q^95 - 32 * q^97 + 152 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.872627	−	0.969151i	−0.617041	−	0.685293i	0.350917	−	0.936407i	$-0.385870\pi$
$2$	−0.872627	−	0.969151i	−0.617041	−	0.685293i	−0.967958	+	0.251114i	$0.919203\pi$
$3$		0			0
$3$		0			0
$4$	0.0312821	−	0.297629i	0.0156410	−	0.148815i
$5$	−0.151225	−	0.0321438i	−0.0676297	−	0.0143751i	0.173973	−	0.984750i	$-0.444340\pi$
$5$	−0.151225	−	0.0321438i	−0.0676297	−	0.0143751i	−0.241602	+	0.970375i	$0.577673\pi$
$6$		0			0
$7$	2.55326	+	0.693447i	0.965041	+	0.262098i
$7$	2.55326	+	0.693447i	0.965041	+	0.262098i
$8$	−2.42586	+	1.76249i	−0.857670	+	0.623134i
$9$		0			0
$10$	0.100810	+	0.174609i	0.0318791	+	0.0552162i
$11$	−0.991882	+	3.16483i	−0.299064	+	0.954233i
$11$	−0.991882	+	3.16483i	−0.299064	+	0.954233i
$12$		0			0
$13$	−1.38817	+	4.27234i	−0.385009	+	1.18494i	0.551465	+	0.834198i	$0.314069\pi$
$13$	−1.38817	+	4.27234i	−0.385009	+	1.18494i	−0.936474	+	0.350737i	$0.885931\pi$
$14$	−1.55599	−	3.07961i	−0.415856	−	0.823061i
$15$		0			0
$16$	3.23953	+	0.688583i	0.809882	+	0.172146i
$17$	−2.36496	+	2.62656i	−0.573588	+	0.637034i	−0.958219	−	0.286037i	$-0.907662\pi$
$17$	−2.36496	+	2.62656i	−0.573588	+	0.637034i	0.384631	+	0.923070i	$0.374329\pi$
$18$		0			0
$19$	0.389198	+	3.70297i	0.0892882	+	0.849521i	0.943895	+	0.330245i	$0.107131\pi$
$19$	0.389198	+	3.70297i	0.0892882	+	0.849521i	−0.854607	+	0.519275i	$0.826202\pi$
$20$	−0.0142975	+	0.0440033i	−0.00319703	+	0.00983944i
$21$		0			0
$22$	3.93274	−	1.80044i	0.838464	−	0.383855i
$23$	0.285690	−	0.494829i	0.0595704	−	0.103179i	−0.834702	−	0.550702i	$-0.814360\pi$
$23$	0.285690	−	0.494829i	0.0595704	−	0.103179i	0.894273	+	0.447523i	$0.147694\pi$
$24$		0			0
$25$	−4.54589	−	2.02396i	−0.909178	−	0.404792i
$26$	5.35190	−	2.38282i	1.04959	−	0.467309i
$27$		0			0
$28$	0.286261	−	0.738232i	0.0540983	−	0.139513i
$29$	1.95460	+	1.42010i	0.362961	+	0.263706i	0.754286	−	0.656546i	$-0.227983\pi$
$29$	1.95460	+	1.42010i	0.362961	+	0.263706i	−0.391325	+	0.920252i	$0.627983\pi$
$30$		0			0
$31$	−7.01784	+	1.49169i	−1.26044	+	0.267915i	−0.789226	−	0.614103i	$-0.789518\pi$
$31$	−7.01784	+	1.49169i	−1.26044	+	0.267915i	−0.471216	+	0.882018i	$0.656185\pi$
$32$	0.838964	+	1.45313i	0.148309	+	0.256879i
$33$		0			0
$34$	4.60926			0.790482
$35$	−0.363825	−	0.186938i	−0.0614977	−	0.0315982i
$36$		0			0
$37$	−4.37659	+	1.94858i	−0.719506	+	0.320345i	−0.733624	−	0.679555i	$-0.762173\pi$
$37$	−4.37659	+	1.94858i	−0.719506	+	0.320345i	0.0141178	+	0.999900i	$0.495506\pi$
$38$	3.24912	−	3.60851i	0.527076	−	0.585377i
$39$		0			0
$40$	0.423502	−	0.188555i	0.0669616	−	0.0298132i
$41$	4.14207	−	3.00939i	0.646883	−	0.469988i	−0.215325	−	0.976542i	$-0.569081\pi$
$41$	4.14207	−	3.00939i	0.646883	−	0.469988i	0.862208	+	0.506554i	$0.169081\pi$
$42$		0			0
$43$	6.28052			0.957770			0.478885	−	0.877878i	$-0.341041\pi$
$43$	6.28052			0.957770			0.478885	+	0.877878i	$0.341041\pi$
$44$	0.910919	+	0.394215i	0.137326	+	0.0594302i
$45$		0			0
$46$	−0.728864	+	0.154925i	−0.107465	+	0.0228424i
$47$	0.797854	+	7.59108i	0.116379	+	1.10727i	0.884362	+	0.466802i	$0.154594\pi$
$47$	0.797854	+	7.59108i	0.116379	+	1.10727i	−0.767983	+	0.640470i	$0.778739\pi$
$48$		0			0
$49$	6.03826	+	3.54110i	0.862609	+	0.505871i
$50$	2.00535	+	6.17182i	0.283599	+	0.872827i
$51$		0			0
$52$	1.22815	+	0.546807i	0.170314	+	0.0758285i
$53$	6.02258	−	1.28014i	0.827265	−	0.175841i	0.225225	−	0.974307i	$-0.427688\pi$
$53$	6.02258	−	1.28014i	0.827265	−	0.175841i	0.602040	+	0.798466i	$0.294355\pi$
$54$		0			0
$55$	0.251726	−	0.446718i	0.0339428	−	0.0602354i
$56$	−7.41603	+	2.81789i	−0.991009	+	0.376556i
$57$		0			0
$58$	−0.329347	−	3.13352i	−0.0432453	−	0.411452i
$59$	0.984287	−	9.36486i	0.128143	−	1.21920i	−0.721715	−	0.692190i	$-0.756646\pi$
$59$	0.984287	−	9.36486i	0.128143	−	1.21920i	0.849858	−	0.527011i	$-0.176687\pi$
$60$		0			0
$61$	−6.89786	−	1.46619i	−0.883181	−	0.187726i	−0.256072	−	0.966658i	$-0.582428\pi$
$61$	−6.89786	−	1.46619i	−0.883181	−	0.187726i	−0.627109	+	0.778932i	$0.715762\pi$
$62$	7.56963	+	5.49966i	0.961344	+	0.698458i
$63$		0			0
$64$	2.72307	−	8.38073i	0.340383	−	1.04759i
$65$	0.347254	−	0.601462i	0.0430716	−	0.0746022i
$66$		0			0
$67$	6.87041	+	11.8999i	0.839354	+	1.45380i	0.890436	+	0.455109i	$0.150400\pi$
$67$	6.87041	+	11.8999i	0.839354	+	1.45380i	−0.0510822	+	0.998694i	$0.516267\pi$
$68$	0.707759	+	0.786046i	0.0858284	+	0.0953221i
$69$		0			0
$70$	0.136313	+	0.515728i	0.0162926	+	0.0616413i
$71$	−1.82585	−	5.61938i	−0.216688	−	0.666898i	−0.999029	−	0.0440477i	$-0.985975\pi$
$71$	−1.82585	−	5.61938i	−0.216688	−	0.666898i	0.782341	−	0.622850i	$-0.214025\pi$
$72$		0			0
$73$	0.770924	−	7.33485i	0.0902299	−	0.858480i	−0.852007	−	0.523531i	$-0.824614\pi$
$73$	0.770924	−	7.33485i	0.0902299	−	0.858480i	0.942236	−	0.334949i	$-0.108719\pi$
$74$	5.70760	+	2.54119i	0.663495	+	0.295407i
$75$		0			0
$76$	1.11429			0.127818
$77$	−4.72717	+	7.39282i	−0.538711	+	0.842490i
$78$		0			0
$79$	2.85339	+	3.16901i	0.321031	+	0.356541i	0.881961	−	0.471322i	$-0.156223\pi$
$79$	2.85339	+	3.16901i	0.321031	+	0.356541i	−0.560930	+	0.827863i	$0.689556\pi$
$80$	−0.467763	−	0.208261i	−0.0522974	−	0.0232843i
$81$		0			0
$82$	−6.53104	−	1.38822i	−0.721233	−	0.153303i
$83$	1.10089	+	3.38819i	0.120838	+	0.371902i	0.993120	−	0.117102i	$-0.0373604\pi$
$83$	1.10089	+	3.38819i	0.120838	+	0.371902i	−0.872282	+	0.489004i	$0.837360\pi$
$84$		0			0
$85$	0.442068	−	0.321181i	0.0479490	−	0.0348370i
$86$	−5.48055	−	6.08677i	−0.590983	−	0.656353i
$87$		0			0
$88$	−3.17182	−	9.42561i	−0.338117	−	1.00477i
$89$	−5.82649	+	10.0918i	−0.617607	+	1.06973i	0.372314	+	0.928107i	$0.378564\pi$
$89$	−5.82649	+	10.0918i	−0.617607	+	1.06973i	−0.989921	+	0.141620i	$0.954769\pi$
$90$		0			0
$91$	−6.50700	+	9.94578i	−0.682119	+	1.04260i
$92$	−0.138338	−	0.100509i	−0.0144228	−	0.0104788i
$93$		0			0
$94$	6.66067	−	7.39742i	0.686995	−	0.762986i
$95$	0.0601712	−	0.572491i	0.00617344	−	0.0587363i
$96$		0			0
$97$	−2.74944	+	8.46191i	−0.279164	+	0.859177i	0.708924	+	0.705285i	$0.249181\pi$
$97$	−2.74944	+	8.46191i	−0.279164	+	0.859177i	−0.988088	+	0.153892i	$0.950819\pi$
$98$	−1.83730	−	8.94205i	−0.185595	−	0.903283i
$99$		0			0
$100$	−0.744595	+	1.28968i	−0.0744595	+	0.128968i
$101$	18.2202	−	3.87282i	1.81298	−	0.385360i	0.828376	−	0.560173i	$-0.189265\pi$
$101$	18.2202	−	3.87282i	1.81298	−	0.385360i	0.984602	+	0.174812i	$0.0559319\pi$
$102$		0			0
$103$	5.61532	−	2.50010i	0.553294	−	0.246342i	−0.110992	−	0.993821i	$-0.535403\pi$
$103$	5.61532	−	2.50010i	0.553294	−	0.246342i	0.664285	+	0.747479i	$0.268736\pi$
$104$	−4.16246	−	12.8107i	−0.408163	−	1.25620i
$105$		0			0
$106$	−6.49611	−	4.71970i	−0.630958	−	0.458418i
$107$	−1.96244	−	18.6714i	−0.189716	−	1.80503i	−0.512639	−	0.858604i	$-0.671332\pi$
$107$	−1.96244	−	18.6714i	−0.189716	−	1.80503i	0.322923	−	0.946425i	$-0.395335\pi$
$108$		0			0
$109$	−0.414639	−	0.718176i	−0.0397152	−	0.0687888i	0.845485	−	0.534000i	$-0.179312\pi$
$109$	−0.414639	−	0.718176i	−0.0397152	−	0.0687888i	−0.885200	+	0.465211i	$0.845978\pi$
$110$	−0.652600	+	0.145857i	−0.0622230	+	0.0139069i
$111$		0			0
$112$	7.79386	+	4.00457i	0.736450	+	0.378396i
$113$	0.819785	−	0.595608i	0.0771188	−	0.0560301i	−0.548558	−	0.836113i	$-0.684823\pi$
$113$	0.819785	−	0.595608i	0.0771188	−	0.0560301i	0.625677	+	0.780083i	$0.284823\pi$
$114$		0			0
$115$	−0.0591089	+	0.0656471i	−0.00551194	+	0.00612162i
$116$	0.483808	−	0.537323i	0.0449204	−	0.0498892i
$117$		0			0
$118$	−9.93488	+	7.21811i	−0.914580	+	0.664481i
$119$	−7.85974	+	5.06631i	−0.720501	+	0.464428i
$120$		0			0
$121$	−9.03234	−	6.27828i	−0.821122	−	0.570753i
$122$	4.59831	+	7.96450i	0.416311	+	0.721072i
$123$		0			0
$124$	0.224437	+	2.13538i	0.0201551	+	0.191763i
$125$	1.24777	+	0.906561i	0.111604	+	0.0810853i
$126$		0			0
$127$	−6.50604	−	20.0235i	−0.577318	−	1.77680i	−0.628147	−	0.778095i	$-0.716186\pi$
$127$	−6.50604	−	20.0235i	−0.577318	−	1.77680i	0.0508289	−	0.998707i	$-0.483814\pi$
$128$	−7.43269	+	3.30925i	−0.656963	+	0.292499i
$129$		0			0
$130$	−0.885931	+	0.188311i	−0.0777013	+	0.0165159i
$131$	−7.59250	+	13.1506i	−0.663359	+	1.14897i	0.316368	+	0.948637i	$0.397537\pi$
$131$	−7.59250	+	13.1506i	−0.663359	+	1.14897i	−0.979727	+	0.200336i	$0.935797\pi$
$132$		0			0
$133$	−1.57409	+	9.72454i	−0.136491	+	0.843225i
$134$	5.53749	−	17.0426i	0.478366	−	1.47226i
$135$		0			0
$136$	1.10779	−	10.5399i	0.0949918	−	0.903787i
$137$	−6.65517	+	7.39132i	−0.568590	+	0.631483i	−0.957029	−	0.289991i	$-0.906348\pi$
$137$	−6.65517	+	7.39132i	−0.568590	+	0.631483i	0.388440	+	0.921474i	$0.373014\pi$
$138$		0			0
$139$	12.5939	+	9.14999i	1.06820	+	0.776092i	0.975588	−	0.219610i	$-0.0704785\pi$
$139$	12.5939	+	9.14999i	1.06820	+	0.776092i	0.0926115	+	0.995702i	$0.470479\pi$
$140$	−0.0670193	+	0.102437i	−0.00566416	+	0.00865753i
$141$		0			0
$142$	−3.85274	+	6.67315i	−0.323315	+	0.559998i
$143$	−12.1444	−	8.63098i	−1.01556	−	0.721759i
$144$		0			0
$145$	−0.249936	−	0.277583i	−0.0207561	−	0.0230520i
$146$	−7.78131	+	5.65345i	−0.643986	+	0.467883i
$147$		0			0
$148$	0.443046	+	1.36356i	0.0364182	+	0.112084i
$149$	−8.37510	−	1.78018i	−0.686115	−	0.145838i	−0.148352	−	0.988935i	$-0.547397\pi$
$149$	−8.37510	−	1.78018i	−0.686115	−	0.145838i	−0.537763	+	0.843096i	$0.680730\pi$
$150$		0			0
$151$	3.32888	+	1.48211i	0.270900	+	0.120613i	0.537691	−	0.843142i	$-0.319297\pi$
$151$	3.32888	+	1.48211i	0.270900	+	0.120613i	−0.266791	+	0.963754i	$0.585963\pi$
$152$	−7.47059	−	8.29693i	−0.605945	−	0.672970i
$153$		0			0
$154$	11.2898	−	1.86983i	0.909760	−	0.150676i
$155$	1.10922			0.0890946
$156$		0			0
$157$	3.37105	+	1.50089i	0.269039	+	0.119784i	0.536823	−	0.843695i	$-0.319624\pi$
$157$	3.37105	+	1.50089i	0.269039	+	0.119784i	−0.267783	+	0.963479i	$0.586291\pi$
$158$	0.581303	−	5.53073i	0.0462460	−	0.440001i
$159$		0			0
$160$	−0.0801630	−	0.246716i	−0.00633744	−	0.0195046i
$161$	1.07258	−	1.06532i	0.0845309	−	0.0839586i
$162$		0			0
$163$	−16.4059	−	18.2205i	−1.28501	−	1.42714i	−0.850059	−	0.526687i	$-0.823434\pi$
$163$	−16.4059	−	18.2205i	−1.28501	−	1.42714i	−0.434946	−	0.900456i	$-0.643233\pi$
$164$	−0.766110	−	1.32694i	−0.0598231	−	0.103617i
$165$		0			0
$166$	2.32300	−	4.02355i	0.180300	−	0.312288i
$167$	−4.34417	+	13.3700i	−0.336162	+	1.03460i	0.629985	+	0.776608i	$0.283061\pi$
$167$	−4.34417	+	13.3700i	−0.336162	+	1.03460i	−0.966147	+	0.257993i	$0.916939\pi$
$168$		0			0
$169$	−5.80870	−	4.22027i	−0.446823	−	0.324636i
$170$	−0.697034	−	0.148159i	−0.0534600	−	0.0113633i
$171$		0			0
$172$	0.196468	−	1.86927i	0.0149805	−	0.142530i
$173$	1.52268	+	14.4873i	0.115767	+	1.10145i	0.886000	+	0.463686i	$0.153473\pi$
$173$	1.52268	+	14.4873i	0.115767	+	1.10145i	−0.770233	+	0.637763i	$0.779860\pi$
$174$		0			0
$175$	−10.2033	−	8.32003i	−0.771299	−	0.628935i
$176$	−5.39248	+	9.56957i	−0.406473	+	0.721334i
$177$		0			0
$178$	14.8648	−	3.15961i	1.11416	−	0.236823i
$179$	−23.1941	−	10.3267i	−1.73361	−	0.771852i	−0.995240	−	0.0974547i	$-0.968930\pi$
$179$	−23.1941	−	10.3267i	−1.73361	−	0.771852i	−0.738368	−	0.674398i	$-0.764403\pi$
$180$		0			0
$181$	−0.175056	−	0.538765i	−0.0130118	−	0.0400461i	0.944340	−	0.328972i	$-0.106702\pi$
$181$	−0.175056	−	0.538765i	−0.0130118	−	0.0400461i	−0.957352	+	0.288925i	$0.906702\pi$
$182$	15.3171	−	2.37270i	1.13538	−	0.175876i
$183$		0			0
$184$	0.179088	+	1.70391i	0.0132025	+	0.125614i
$185$	0.724482	−	0.153993i	0.0532650	−	0.0113218i
$186$		0			0
$187$	−5.96685	−	10.0899i	−0.436340	−	0.737850i
$188$	2.28428			0.166599
$189$		0			0
$190$	−0.607337	+	0.441256i	−0.0440609	+	0.0320121i
$191$	−3.80908	+	1.69591i	−0.275616	+	0.122712i	−0.539890	−	0.841736i	$-0.681534\pi$
$191$	−3.80908	+	1.69591i	−0.275616	+	0.122712i	0.264274	+	0.964448i	$0.414868\pi$
$192$		0			0
$193$	−9.36587	+	10.4019i	−0.674170	+	0.748742i	−0.979044	−	0.203651i	$-0.934719\pi$
$193$	−9.36587	+	10.4019i	−0.674170	+	0.748742i	0.304873	+	0.952393i	$0.401386\pi$
$194$	10.6001	−	4.71947i	0.761043	−	0.338838i
$195$		0			0
$196$	1.24282	−	1.68639i	0.0887731	−	0.120456i
$197$	13.6176			0.970217			0.485108	−	0.874454i	$-0.338780\pi$
$197$	13.6176			0.970217			0.485108	+	0.874454i	$0.338780\pi$
$198$		0			0
$199$	−0.860980	−	1.49126i	−0.0610333	−	0.105713i	0.833894	−	0.551924i	$-0.186106\pi$
$199$	−0.860980	−	1.49126i	−0.0610333	−	0.105713i	−0.894928	+	0.446211i	$0.852773\pi$
$200$	14.5949	−	3.10224i	1.03201	−	0.219361i
$201$		0			0
$202$	−19.6528	−	14.2786i	−1.38277	−	1.00464i
$203$	4.00584	+	4.98130i	0.281155	+	0.349619i
$204$		0			0
$205$	−0.723116	+	0.321952i	−0.0505046	+	0.0224861i
$206$	−7.32305	−	3.26043i	−0.510221	−	0.227165i
$207$		0			0
$208$	−7.43888	+	12.8845i	−0.515793	+	0.893380i
$209$	−12.1053	−	2.44116i	−0.837344	−	0.168859i
$210$		0			0
$211$	−2.02805	+	6.24168i	−0.139616	+	0.429695i	−0.996279	−	0.0861812i	$-0.972534\pi$
$211$	−2.02805	+	6.24168i	−0.139616	+	0.429695i	0.856663	+	0.515876i	$0.172534\pi$
$212$	−0.192608	−	1.83254i	−0.0132284	−	0.125859i
$213$		0			0
$214$	−16.3829	+	18.1950i	−1.11991	+	1.24379i
$215$	−0.949769	−	0.201880i	−0.0647737	−	0.0137681i
$216$		0			0
$217$	−18.9528	−	1.05783i	−1.28660	−	0.0718104i
$218$	−0.334195	+	1.02855i	−0.0226346	+	0.0696620i
$219$		0			0
$220$	−0.125082	−	0.0888954i	−0.00843300	−	0.00599333i
$221$	−7.93859	−	13.7500i	−0.534008	−	0.924928i
$222$		0			0
$223$	12.1530	−	8.82965i	0.813823	−	0.591277i	−0.101113	−	0.994875i	$-0.532240\pi$
$223$	12.1530	−	8.82965i	0.813823	−	0.591277i	0.914937	+	0.403598i	$0.132240\pi$
$224$	1.13443	+	4.29199i	0.0757970	+	0.286771i
$225$		0			0
$226$	−1.29260	−	0.274751i	−0.0859825	−	0.0182761i
$227$	−1.48051	+	14.0861i	−0.0982646	+	0.934925i	0.828679	+	0.559724i	$0.189093\pi$
$227$	−1.48051	+	14.0861i	−0.0982646	+	0.934925i	−0.926944	+	0.375201i	$0.877574\pi$
$228$		0			0
$229$	8.14644	+	9.04754i	0.538332	+	0.597878i	0.949533	−	0.313666i	$-0.101557\pi$
$229$	8.14644	+	9.04754i	0.538332	+	0.597878i	−0.411201	+	0.911545i	$0.634891\pi$
$230$	0.115202			0.00759620
$231$		0			0
$232$	−7.24450			−0.475625
$233$	10.0863	+	11.2020i	0.660775	+	0.733865i	0.976626	−	0.214944i	$-0.0689569\pi$
$233$	10.0863	+	11.2020i	0.660775	+	0.733865i	−0.315852	+	0.948809i	$0.602290\pi$
$234$		0			0
$235$	0.123351	−	1.17360i	0.00804651	−	0.0765574i
$236$	−2.75647	−	0.585905i	−0.179431	−	0.0381391i
$237$		0			0
$238$	11.7686	+	3.19628i	0.762848	+	0.207184i
$239$	11.7175	−	8.51324i	0.757940	−	0.550676i	−0.140338	−	0.990104i	$-0.544819\pi$
$239$	11.7175	−	8.51324i	0.757940	−	0.550676i	0.898278	+	0.439428i	$0.144819\pi$
$240$		0			0
$241$	−6.87041	−	11.8999i	−0.442562	−	0.766540i	0.555317	−	0.831639i	$-0.312597\pi$
$241$	−6.87041	−	11.8999i	−0.442562	−	0.766540i	−0.997879	+	0.0650991i	$0.979264\pi$
$242$	1.79727	+	14.2323i	0.115533	+	0.914887i
$243$		0			0
$244$	−0.652159	+	2.00714i	−0.0417502	+	0.128494i
$245$	−0.799309	−	0.729593i	−0.0510660	−	0.0466120i
$246$		0			0
$247$	−16.3607	−	3.47756i	−1.04100	−	0.221272i
$248$	14.3952	−	15.9875i	0.914096	−	1.01521i
$249$		0			0
$250$	−0.210248	−	2.00037i	−0.0132972	−	0.126515i
$251$	4.35998	−	13.4186i	0.275200	−	0.846977i	−0.713967	−	0.700179i	$-0.753103\pi$
$251$	4.35998	−	13.4186i	0.275200	−	0.846977i	0.989167	−	0.146798i	$-0.0468967\pi$
$252$		0			0
$253$	1.28268	+	1.39497i	0.0806414	+	0.0877011i
$254$	−13.7285	+	23.7784i	−0.861401	+	1.49199i
$255$		0			0
$256$	−6.40725	−	2.85269i	−0.400453	−	0.178293i
$257$	−0.214055	+	0.0953033i	−0.0133524	+	0.00594486i	−0.413402	−	0.910549i	$-0.635660\pi$
$257$	−0.214055	+	0.0953033i	−0.0133524	+	0.00594486i	0.400050	+	0.916493i	$0.368993\pi$
$258$		0			0
$259$	−12.5258	+	1.94030i	−0.778315	+	0.120565i
$260$	−0.168150	−	0.122168i	−0.0104282	−	0.00757654i
$261$		0			0
$262$	19.3703	−	4.11729i	1.19670	−	0.254367i
$263$	6.62526	+	11.4753i	0.408531	+	0.707597i	0.994725	−	0.102574i	$-0.0327078\pi$
$263$	6.62526	+	11.4753i	0.408531	+	0.707597i	−0.586194	+	0.810171i	$0.699374\pi$
$264$		0			0
$265$	−0.951910			−0.0584754
$266$	10.7981	−	6.96037i	0.662076	−	0.426768i
$267$		0			0
$268$	3.75668	−	1.67258i	0.229475	−	0.102169i
$269$	−0.482964	+	0.536385i	−0.0294468	+	0.0327040i	−0.757688	−	0.652617i	$-0.773671\pi$
$269$	−0.482964	+	0.536385i	−0.0294468	+	0.0327040i	0.728241	+	0.685321i	$0.240338\pi$
$270$		0			0
$271$	−9.41657	+	4.19253i	−0.572016	+	0.254678i	−0.672297	−	0.740281i	$-0.734692\pi$
$271$	−9.41657	+	4.19253i	−0.572016	+	0.254678i	0.100282	+	0.994959i	$0.468026\pi$
$272$	−9.46997	+	6.88033i	−0.574201	+	0.417182i
$273$		0			0
$274$	12.9708			0.783594
$275$	10.9145	−	12.3795i	0.658168	−	0.746510i
$276$		0			0
$277$	30.1388	−	6.40621i	1.81087	−	0.384912i	0.826770	−	0.562541i	$-0.190176\pi$
$277$	30.1388	−	6.40621i	1.81087	−	0.384912i	0.984098	+	0.177629i	$0.0568427\pi$
$278$	−2.12204	−	20.1899i	−0.127272	−	1.21091i
$279$		0			0
$280$	1.21206	−	0.187754i	0.0724347	−	0.0112205i
$281$	−3.21099	−	9.88241i	−0.191551	−	0.589535i	−1.00000		0.000967316i	$-0.999692\pi$
$281$	−3.21099	−	9.88241i	−0.191551	−	0.589535i	0.808448	−	0.588568i	$-0.200308\pi$
$282$		0			0
$283$	1.50845	+	0.671606i	0.0896681	+	0.0399228i	0.451081	−	0.892483i	$-0.351039\pi$
$283$	1.50845	+	0.671606i	0.0896681	+	0.0399228i	−0.361412	+	0.932406i	$0.617705\pi$
$284$	−1.72961	+	0.367639i	−0.102633	+	0.0218154i
$285$		0			0
$286$	2.23278	+	19.3013i	0.132027	+	1.14131i
$287$	12.6626	−	4.81145i	0.747452	−	0.284011i
$288$		0			0
$289$	0.471229	+	4.48345i	0.0277194	+	0.263732i
$290$	−0.0509180	+	0.484452i	−0.00299001	+	0.0284480i
$291$		0			0
$292$	−2.15895	−	0.458899i	−0.126343	−	0.0268550i
$293$	21.5073	+	15.6260i	1.25647	+	0.912881i	0.998579	−	0.0532928i	$-0.0169717\pi$
$293$	21.5073	+	15.6260i	1.25647	+	0.912881i	0.257893	+	0.966173i	$0.416972\pi$
$294$		0			0
$295$	−0.449870	+	1.38456i	−0.0261925	+	0.0806121i
$296$	7.18262	−	12.4407i	0.417481	−	0.723099i
$297$		0			0
$298$	5.58308	+	9.67017i	0.323419	+	0.560178i
$299$	1.71749	+	1.90747i	0.0993252	+	0.110312i
$300$		0			0
$301$	16.0358	+	4.35520i	0.924288	+	0.251030i
$302$	−1.46848	−	4.51952i	−0.0845015	−	0.260069i
$303$		0			0
$304$	−1.28899	+	12.2639i	−0.0739284	+	0.703382i
$305$	0.995997	+	0.443446i	0.0570306	+	0.0253917i
$306$		0			0
$307$	25.7622			1.47033			0.735163	−	0.677891i	$-0.237106\pi$
$307$	25.7622			1.47033			0.735163	+	0.677891i	$0.237106\pi$
$308$	2.05244	+	1.63821i	0.116949	+	0.0933455i
$309$		0			0
$310$	−0.967934	−	1.07500i	−0.0549750	−	0.0610559i
$311$	−19.2710	−	8.58001i	−1.09276	−	0.486527i	−0.220408	−	0.975408i	$-0.570739\pi$
$311$	−19.2710	−	8.58001i	−1.09276	−	0.486527i	−0.872351	+	0.488880i	$0.837405\pi$
$312$		0			0
$313$	25.7070	+	5.46419i	1.45305	+	0.308854i	0.865733	−	0.500506i	$-0.166853\pi$
$313$	25.7070	+	5.46419i	1.45305	+	0.308854i	0.587312	+	0.809360i	$0.300186\pi$
$314$	−1.48708	−	4.57678i	−0.0839210	−	0.258282i
$315$		0			0
$316$	1.03245	−	0.750118i	0.0580798	−	0.0421975i
$317$	12.4548	+	13.8324i	0.699530	+	0.776907i	0.983301	−	0.181985i	$-0.0582522\pi$
$317$	12.4548	+	13.8324i	0.699530	+	0.776907i	−0.283771	+	0.958892i	$0.591586\pi$
$318$		0			0
$319$	−6.43312	+	4.77742i	−0.360186	+	0.267484i
$320$	−0.681183	+	1.17984i	−0.0380793	+	0.0659552i
$321$		0			0
$322$	−1.96841	−	0.109865i	−0.109695	−	0.00612254i
$323$	−10.6465	−	7.73515i	−0.592388	−	0.430395i
$324$		0			0
$325$	14.9575	−	16.6120i	0.829694	−	0.921469i
$326$	−3.34226	+	31.7995i	−0.185111	+	1.76121i
$327$		0			0
$328$	−4.74406	+	14.6007i	−0.261947	+	0.806189i
$329$	−3.22688	+	19.9353i	−0.177904	+	1.09907i
$330$		0			0
$331$	9.23885	−	16.0022i	0.507813	−	0.879558i	−0.492146	−	0.870513i	$-0.663787\pi$
$331$	9.23885	−	16.0022i	0.507813	−	0.879558i	0.999959	−	0.00904536i	$-0.00287927\pi$
$332$	1.04286	−	0.221667i	0.0572345	−	0.0121656i
$333$		0			0
$334$	16.7484	−	7.45686i	0.916430	−	0.408021i
$335$	−0.656467	−	2.02040i	−0.0358666	−	0.110386i
$336$		0			0
$337$	17.8136	+	12.9423i	0.970369	+	0.705014i	0.955536	−	0.294876i	$-0.0952783\pi$
$337$	17.8136	+	12.9423i	0.970369	+	0.705014i	0.0148333	+	0.999890i	$0.495278\pi$
$338$	0.978754	+	9.31222i	0.0532372	+	0.506518i
$339$		0			0
$340$	−0.0817641	−	0.141620i	−0.00443428	−	0.00768040i
$341$	2.23992	−	23.6899i	0.121299	−	1.28288i
$342$		0			0
$343$	12.9617	+	13.2286i	0.699865	+	0.714275i
$344$	−15.2356	+	11.0693i	−0.821451	+	0.596819i
$345$		0			0
$346$	12.7116	−	14.1177i	0.683382	−	0.758973i
$347$	5.86225	−	6.51069i	0.314702	−	0.349512i	−0.564954	−	0.825123i	$-0.691106\pi$
$347$	5.86225	−	6.51069i	0.314702	−	0.349512i	0.879656	+	0.475610i	$0.157773\pi$
$348$		0			0
$349$	−2.99184	+	2.17370i	−0.160150	+	0.116356i	−0.664974	−	0.746867i	$-0.731557\pi$
$349$	−2.99184	+	2.17370i	−0.160150	+	0.116356i	0.504824	+	0.863222i	$0.331557\pi$
$350$	0.840339	+	17.1489i	0.0449180	+	0.916645i
$351$		0			0
$352$	−5.43106	+	1.21385i	−0.289477	+	0.0646985i
$353$	4.30583	+	7.45792i	0.229176	+	0.396945i	0.957564	−	0.288220i	$-0.0930634\pi$
$353$	4.30583	+	7.45792i	0.229176	+	0.396945i	−0.728388	+	0.685165i	$0.759730\pi$
$354$		0			0
$355$	0.0954849	+	0.908478i	0.00506781	+	0.0482170i
$356$	2.82134	+	2.04983i	0.149531	+	0.108641i
$357$		0			0
$358$	10.2317	+	31.4899i	0.540762	+	1.66429i
$359$	−11.9346	+	5.31364i	−0.629885	+	0.280443i	−0.696744	−	0.717319i	$-0.745369\pi$
$359$	−11.9346	+	5.31364i	−0.629885	+	0.280443i	0.0668592	+	0.997762i	$0.478702\pi$
$360$		0			0
$361$	5.02426	−	1.06794i	0.264435	−	0.0562074i
$362$	−0.369387	+	0.639797i	−0.0194145	+	0.0336270i
$363$		0			0
$364$	2.75660	+	2.24780i	0.144485	+	0.117817i
$365$	−0.352353	+	1.08443i	−0.0184430	+	0.0567616i
$366$		0			0
$367$	−1.73219	+	16.4807i	−0.0904197	+	0.860286i	0.851479	+	0.524389i	$0.175706\pi$
$367$	−1.73219	+	16.4807i	−0.0904197	+	0.860286i	−0.941899	+	0.335897i	$0.890961\pi$
$368$	1.26623	−	1.40629i	0.0660068	−	0.0733080i
$369$		0			0
$370$	−0.781445	−	0.567753i	−0.0406254	−	0.0295161i
$371$	16.2649	+	0.907812i	0.844432	+	0.0471312i
$372$		0			0
$373$	−0.319637	+	0.553628i	−0.0165502	+	0.0286658i	−0.874182	−	0.485599i	$-0.838602\pi$
$373$	−0.319637	+	0.553628i	−0.0165502	+	0.0286658i	0.857632	+	0.514264i	$0.171935\pi$
$374$	−4.57184	+	14.5875i	−0.236404	+	0.754304i
$375$		0			0
$376$	−15.3147	−	17.0087i	−0.789793	−	0.877154i
$377$	−8.78048	+	6.37940i	−0.452218	+	0.328556i
$378$		0			0
$379$	−2.10990	−	6.49361i	−0.108378	−	0.333554i	0.882130	−	0.471006i	$-0.156109\pi$
$379$	−2.10990	−	6.49361i	−0.108378	−	0.333554i	−0.990509	+	0.137451i	$0.956109\pi$
$380$	−0.168508	−	0.0358174i	−0.00864426	−	0.00183739i
$381$		0			0
$382$	4.96750	+	2.21168i	0.254160	+	0.113159i
$383$	−9.76407	−	10.8441i	−0.498921	−	0.554108i	0.440109	−	0.897945i	$-0.354940\pi$
$383$	−9.76407	−	10.8441i	−0.498921	−	0.554108i	−0.939029	+	0.343837i	$0.888273\pi$
$384$		0			0
$385$	0.952498	−	0.966027i	0.0485438	−	0.0492333i
$386$	18.2539			0.929098
$387$		0			0
$388$	2.43250	+	1.08302i	0.123492	+	0.0549820i
$389$	3.33747	−	31.7539i	0.169217	−	1.60999i	−0.499393	−	0.866375i	$-0.666444\pi$
$389$	3.33747	−	31.7539i	0.169217	−	1.60999i	0.668610	−	0.743613i	$-0.266890\pi$
$390$		0			0
$391$	0.624051	+	1.92063i	0.0315596	+	0.0971305i
$392$	−20.8891	+	2.05217i	−1.05506	+	0.103650i
$393$		0			0
$394$	−11.8831	−	13.1975i	−0.598663	−	0.664883i
$395$	−0.329639	−	0.570951i	−0.0165859	−	0.0287276i
$396$		0			0
$397$	−5.48354	+	9.49778i	−0.275211	+	0.476680i	−0.970188	−	0.242352i	$-0.922081\pi$
$397$	−5.48354	+	9.49778i	−0.275211	+	0.476680i	0.694977	+	0.719032i	$0.255414\pi$
$398$	−0.693943	+	2.13574i	−0.0347842	+	0.107055i
$399$		0			0
$400$	−13.3329	−	9.68690i	−0.666644	−	0.484345i
$401$	−5.60032	−	1.19038i	−0.279666	−	0.0594449i	0.0659430	−	0.997823i	$-0.478994\pi$
$401$	−5.60032	−	1.19038i	−0.279666	−	0.0594449i	−0.345609	+	0.938378i	$0.612328\pi$
$402$		0			0
$403$	3.36894	−	32.0534i	0.167819	−	1.59669i
$404$	−0.582699	−	5.54401i	−0.0289904	−	0.275825i
$405$		0			0
$406$	1.33202	−	8.22908i	0.0661073	−	0.408403i
$407$	−1.82588	−	15.7839i	−0.0905056	−	0.782380i
$408$		0			0
$409$	8.39779	−	1.78500i	0.415244	−	0.0882628i	0.00444786	−	0.999990i	$-0.498584\pi$
$409$	8.39779	−	1.78500i	0.415244	−	0.0882628i	0.410796	+	0.911727i	$0.365251\pi$
$410$	0.943031	+	0.419864i	0.0465730	+	0.0207356i
$411$		0			0
$412$	−0.568444	−	1.74949i	−0.0280052	−	0.0861912i
$413$	9.00717	−	23.2284i	0.443214	−	1.14299i
$414$		0			0
$415$	−0.0575723	−	0.547764i	−0.00282611	−	0.0268887i
$416$	−7.37289	+	1.56716i	−0.361486	+	0.0768362i
$417$		0			0
$418$	8.19759	+	13.8621i	0.400957	+	0.678018i
$419$	39.3947			1.92455			0.962277	−	0.272070i	$-0.0877082\pi$
$419$	39.3947			1.92455			0.962277	+	0.272070i	$0.0877082\pi$
$420$		0			0
$421$	−28.0607	+	20.3873i	−1.36760	+	0.993616i	−0.369674	+	0.929161i	$0.620531\pi$
$421$	−28.0607	+	20.3873i	−1.36760	+	0.993616i	−0.997921	+	0.0644546i	$0.979469\pi$
$422$	7.81886	−	3.48118i	0.380616	−	0.169461i
$423$		0			0
$424$	−12.3537	+	13.7202i	−0.599948	+	0.666310i
$425$	16.0669	−	7.15345i	0.779360	−	0.346993i
$426$		0			0
$427$	−16.5953	−	8.52685i	−0.803103	−	0.412643i
$428$	−5.61853			−0.271582
$429$		0			0
$430$	0.633142	+	1.09663i	0.0305328	+	0.0528844i
$431$	−16.6042	+	3.52933i	−0.799795	+	0.170002i	−0.589640	−	0.807666i	$-0.700730\pi$
$431$	−16.6042	+	3.52933i	−0.799795	+	0.170002i	−0.210155	+	0.977668i	$0.567397\pi$
$432$		0			0
$433$	19.2167	+	13.9617i	0.923494	+	0.670958i	0.944391	−	0.328824i	$-0.106652\pi$
$433$	19.2167	+	13.9617i	0.923494	+	0.670958i	−0.0208974	+	0.999782i	$0.506652\pi$
$434$	15.5135	+	19.2912i	0.744672	+	0.926007i
$435$		0			0
$436$	−0.226721	+	0.100943i	−0.0108580	+	0.00483428i
$437$	1.94353	+	0.865314i	0.0929716	+	0.0413936i
$438$		0			0
$439$	−3.08551	+	5.34426i	−0.147263	+	0.255067i	−0.930215	−	0.367015i	$-0.880380\pi$
$439$	−3.08551	+	5.34426i	−0.147263	+	0.255067i	0.782952	+	0.622082i	$0.213713\pi$
$440$	0.176682	+	1.52734i	0.00842299	+	0.0728130i
$441$		0			0
$442$	−6.39843	+	19.6924i	−0.304342	+	0.936670i
$443$	0.295771	+	2.81407i	0.0140525	+	0.133701i	0.999299	−	0.0374417i	$-0.0119208\pi$
$443$	0.295771	+	2.81407i	0.0140525	+	0.133701i	−0.985246	+	0.171142i	$0.945254\pi$
$444$		0			0
$445$	1.20550	−	1.33884i	0.0571460	−	0.0634671i
$446$	−19.1623	−	4.07307i	−0.907360	−	0.192865i
$447$		0			0
$448$	12.7643	−	19.5099i	0.603056	−	0.921755i
$449$	−1.13543	+	3.49449i	−0.0535842	+	0.164915i	−0.974267	−	0.225396i	$-0.927632\pi$
$449$	−1.13543	+	3.49449i	−0.0535842	+	0.164915i	0.920683	+	0.390311i	$0.127632\pi$
$450$		0			0
$451$	5.41578	+	16.0939i	0.255019	+	0.757833i
$452$	−0.151626	−	0.262624i	−0.00713188	−	0.0123528i
$453$		0			0
$454$	14.9435	−	10.8571i	0.701331	−	0.509547i
$455$	1.30371	−	1.29489i	0.0611190	−	0.0607052i
$456$		0			0
$457$	24.6830	+	5.24654i	1.15462	+	0.245423i	0.745148	−	0.666899i	$-0.232379\pi$
$457$	24.6830	+	5.24654i	1.15462	+	0.245423i	0.409475	+	0.912321i	$0.365712\pi$
$458$	1.65962	−	15.7903i	0.0775491	−	0.737830i
$459$		0			0
$460$	0.0176894	+	0.0196461i	0.000824775	+	0.000916005i
$461$	1.65417			0.0770423			0.0385212	−	0.999258i	$-0.487735\pi$
$461$	1.65417			0.0770423			0.0385212	+	0.999258i	$0.487735\pi$
$462$		0			0
$463$	−23.8870			−1.11012			−0.555061	−	0.831810i	$-0.687305\pi$
$463$	−23.8870			−1.11012			−0.555061	+	0.831810i	$0.687305\pi$
$464$	5.35413	+	5.94637i	0.248559	+	0.276053i
$465$		0			0
$466$	2.05482	−	19.5503i	0.0951875	−	0.905649i
$467$	16.9367	+	3.60000i	0.783735	+	0.166588i	0.582365	−	0.812927i	$-0.302127\pi$
$467$	16.9367	+	3.60000i	0.783735	+	0.166588i	0.201370	+	0.979515i	$0.435461\pi$
$468$		0			0
$469$	9.28999	+	35.1478i	0.428972	+	1.62297i
$470$	−1.24504	+	0.904573i	−0.0574293	+	0.0417248i
$471$		0			0
$472$	14.1177	+	24.4526i	0.649821	+	1.12552i
$473$	−6.22953	+	19.8768i	−0.286434	+	0.913936i
$474$		0			0
$475$	5.72542	−	17.6210i	0.262700	−	0.808509i
$476$	1.26201	+	2.49777i	0.0578442	+	0.114485i
$477$		0			0
$478$	−18.4756	−	3.92711i	−0.845054	−	0.179622i
$479$	−5.79649	+	6.43765i	−0.264848	+	0.294144i	−0.860870	−	0.508824i	$-0.830080\pi$
$479$	−5.79649	+	6.43765i	−0.264848	+	0.294144i	0.596022	+	0.802968i	$0.296747\pi$
$480$		0			0
$481$	−2.24957	−	21.4032i	−0.102572	−	0.975904i
$482$	−5.53749	+	17.0426i	−0.252226	+	0.776271i
$483$		0			0
$484$	−2.15115	+	2.49189i	−0.0977795	+	0.113268i
$485$	0.687781	−	1.19127i	0.0312305	−	0.0540928i
$486$		0			0
$487$	−38.1733	−	16.9959i	−1.72980	−	0.770156i	−0.995856	−	0.0909438i	$-0.971012\pi$
$487$	−38.1733	−	16.9959i	−1.72980	−	0.770156i	−0.733942	−	0.679212i	$-0.762322\pi$
$488$	19.3174	−	8.60064i	0.874456	−	0.389333i
$489$		0			0
$490$	−0.00958689	+	1.41131i	−0.000433092	+	0.0637567i
$491$	−26.8166	−	19.4834i	−1.21022	−	0.879274i	−0.214966	−	0.976621i	$-0.568964\pi$
$491$	−26.8166	−	19.4834i	−1.21022	−	0.879274i	−0.995250	+	0.0973476i	$0.968964\pi$
$492$		0			0
$493$	−8.35254	+	1.77539i	−0.376180	+	0.0799595i
$494$	10.9065	+	18.8906i	0.490705	+	0.849926i
$495$		0			0
$496$	−23.7617			−1.06693
$497$	−0.765121	−	15.6139i	−0.0343204	−	0.700377i
$498$		0			0
$499$	−8.47645	+	3.77396i	−0.379458	+	0.168945i	−0.587597	−	0.809154i	$-0.699926\pi$
$499$	−8.47645	+	3.77396i	−0.379458	+	0.168945i	0.208139	+	0.978099i	$0.433259\pi$
$500$	0.308852	−	0.343015i	0.0138123	−	0.0153401i
$501$		0			0
$502$	−16.8093	+	7.48399i	−0.750237	+	0.334027i
$503$	−25.4389	+	18.4825i	−1.13427	+	0.824093i	−0.986310	−	0.164901i	$-0.947270\pi$
$503$	−25.4389	+	18.4825i	−1.13427	+	0.824093i	−0.147956	+	0.988994i	$0.547270\pi$
$504$		0			0
$505$	−2.87983			−0.128151
$506$	0.232636	−	2.46040i	0.0103419	−	0.109378i
$507$		0			0
$508$	−6.16311	+	1.31001i	−0.273444	+	0.0581223i
$509$	−1.83438	−	17.4530i	−0.0813076	−	0.773591i	−0.956876	−	0.290496i	$-0.906180\pi$
$509$	−1.83438	−	17.4530i	−0.0813076	−	0.773591i	0.875568	−	0.483094i	$-0.160487\pi$
$510$		0			0
$511$	7.05470	−	18.1932i	0.312082	−	0.804819i
$512$	7.85483	+	24.1747i	0.347138	+	1.06838i
$513$		0			0
$514$	0.279153	+	0.124287i	0.0123129	+	0.00548207i
$515$	−0.929536	+	0.197579i	−0.0409603	+	0.00870637i
$516$		0			0
$517$	−24.8159	−	5.00437i	−1.09140	−	0.220092i
$518$	12.8108	+	10.4462i	0.562874	+	0.458981i
$519$		0			0
$520$	0.217681	+	2.07109i	0.00954593	+	0.0908235i
$521$	0.150177	−	1.42884i	0.00657937	−	0.0625986i	−0.990740	−	0.135776i	$-0.956647\pi$
$521$	0.150177	−	1.42884i	0.00657937	−	0.0625986i	0.997319	+	0.0731774i	$0.0233139\pi$
$522$		0			0
$523$	0.281825	+	0.0599037i	0.0123233	+	0.00261940i	0.214069	−	0.976818i	$-0.431328\pi$
$523$	0.281825	+	0.0599037i	0.0123233	+	0.00261940i	−0.201746	+	0.979438i	$0.564662\pi$
$524$	3.67649	+	2.67113i	0.160608	+	0.116689i
$525$		0			0
$526$	5.33990	−	16.4345i	0.232831	−	0.716579i
$527$	12.6789	−	21.9606i	0.552303	−	0.956617i
$528$		0			0
$529$	11.3368	+	19.6358i	0.492903	+	0.853733i
$530$	0.830663	+	0.922545i	0.0360817	+	0.0400728i
$531$		0			0
$532$	2.84507	+	0.772699i	0.123349	+	0.0335008i
$533$	7.10726	+	21.8739i	0.307850	+	0.947464i
$534$		0			0
$535$	−0.303399	+	2.88665i	−0.0131171	+	0.124801i
$536$	−37.6400	−	16.7584i	−1.62580	−	0.723854i
$537$		0			0
$538$	0.941285			0.0405817
$539$	−17.1962	+	15.5977i	−0.740694	+	0.671843i
$540$		0			0
$541$	−11.3389	−	12.5931i	−0.487495	−	0.541418i	0.448337	−	0.893865i	$-0.352017\pi$
$541$	−11.3389	−	12.5931i	−0.487495	−	0.541418i	−0.935832	+	0.352446i	$0.885350\pi$
$542$	12.2803	+	5.46756i	0.527486	+	0.234852i
$543$		0			0
$544$	−5.80085	−	1.23301i	−0.248709	−	0.0528648i
$545$	0.0396187	+	0.121934i	0.00169708	+	0.00522307i
$546$		0			0
$547$	31.4138	−	22.8235i	1.34316	−	0.975862i	0.343837	−	0.939029i	$-0.388273\pi$
$547$	31.4138	−	22.8235i	1.34316	−	0.975862i	0.999321	−	0.0368329i	$-0.0117269\pi$
$548$	1.99168	+	2.21199i	0.0850805	+	0.0944915i
$549$		0			0
$550$	−21.5218	+	0.224871i	−0.917694	+	0.00958855i
$551$	−4.49787	+	7.79054i	−0.191616	+	0.331888i
$552$		0			0
$553$	5.08790	+	10.0700i	0.216360	+	0.428219i
$554$	−32.5086	−	23.6188i	−1.38116	−	1.00347i
$555$		0			0
$556$	3.11727	−	3.46208i	0.132202	−	0.146825i
$557$	0.527010	−	5.01417i	0.0223301	−	0.212457i	−0.977667	−	0.210159i	$-0.932602\pi$
$557$	0.527010	−	5.01417i	0.0223301	−	0.212457i	0.999997	−	0.00229811i	$-0.000731511\pi$
$558$		0			0
$559$	−8.71842	+	26.8325i	−0.368750	+	1.13490i
$560$	−1.04990	−	0.856113i	−0.0443664	−	0.0361774i
$561$		0			0
$562$	−6.77554	+	11.7356i	−0.285809	+	0.495036i
$563$	19.2210	−	4.08555i	0.810068	−	0.172185i	0.215785	−	0.976441i	$-0.430769\pi$
$563$	19.2210	−	4.08555i	0.810068	−	0.172185i	0.594283	+	0.804256i	$0.297436\pi$
$564$		0			0
$565$	−0.143117	+	0.0637196i	−0.00602096	+	0.00268070i
$566$	−0.665428	−	2.04798i	−0.0279700	−	0.0860829i
$567$		0			0
$568$	14.3333	+	10.4138i	0.601413	+	0.436952i
$569$	3.50361	+	33.3346i	0.146879	+	1.39746i	0.781148	+	0.624346i	$0.214635\pi$
$569$	3.50361	+	33.3346i	0.146879	+	1.39746i	−0.634269	+	0.773112i	$0.718699\pi$
$570$		0			0
$571$	−9.83114	−	17.0280i	−0.411420	−	0.712601i	0.583625	−	0.812023i	$-0.301634\pi$
$571$	−9.83114	−	17.0280i	−0.411420	−	0.712601i	−0.995045	+	0.0994224i	$0.968301\pi$
$572$	−2.94873	+	3.34452i	−0.123293	+	0.139841i
$573$		0			0
$574$	−15.7128	−	8.07340i	−0.655839	−	0.336977i
$575$	−2.30023	+	1.67121i	−0.0959261	+	0.0696944i
$576$		0			0
$577$	13.8099	−	15.3375i	0.574915	−	0.638508i	−0.383617	−	0.923492i	$-0.625322\pi$
$577$	13.8099	−	15.3375i	0.574915	−	0.638508i	0.958532	+	0.284984i	$0.0919883\pi$
$578$	3.93393	−	4.36907i	0.163630	−	0.181729i
$579$		0			0
$580$	−0.0904352	+	0.0657050i	−0.00375512	+	0.00272825i
$581$	0.461327	+	9.41433i	0.0191391	+	0.390572i
$582$		0			0
$583$	−1.92226	+	20.3302i	−0.0796118	+	0.841991i
$584$	11.0574	+	19.1521i	0.457560	+	0.792518i
$585$		0			0
$586$	−3.62394	−	34.4795i	−0.149704	−	1.42434i
$587$	−26.1653	−	19.0102i	−1.07996	−	0.784635i	−0.102282	−	0.994755i	$-0.532614\pi$
$587$	−26.1653	−	19.0102i	−1.07996	−	0.784635i	−0.977675	+	0.210121i	$0.932614\pi$
$588$		0			0
$589$	−8.25502	−	25.4063i	−0.340142	−	1.04685i
$590$	1.73441	−	0.772211i	0.0714047	−	0.0317914i
$591$		0			0
$592$	−15.5198	+	3.29884i	−0.637861	+	0.135582i
$593$	−12.0475	+	20.8669i	−0.494732	+	0.856901i	−0.999982	−	0.00607259i	$-0.998067\pi$
$593$	−12.0475	+	20.8669i	−0.494732	+	0.856901i	0.505250	+	0.862973i	$0.331400\pi$
$594$		0			0
$595$	1.35144	−	0.513508i	0.0554035	−	0.0210518i
$596$	−0.791825	+	2.43699i	−0.0324344	+	0.0998228i
$597$		0			0
$598$	0.349894	−	3.32902i	0.0143082	−	0.136134i
$599$	23.8894	−	26.5319i	0.976096	−	1.08406i	−0.0203473	−	0.999793i	$-0.506477\pi$
$599$	23.8894	−	26.5319i	0.976096	−	1.08406i	0.996443	−	0.0842710i	$-0.0268561\pi$
$600$		0			0
$601$	−32.6349	−	23.7106i	−1.33120	−	0.967176i	−0.999719	−	0.0237157i	$-0.992450\pi$
$601$	−32.6349	−	23.7106i	−1.33120	−	0.967176i	−0.331485	−	0.943460i	$-0.607550\pi$
$602$	−9.77242	−	19.3416i	−0.398294	−	0.788304i
$603$		0			0
$604$	0.545254	−	0.944407i	0.0221861	−	0.0384274i
$605$	1.16410	+	1.23976i	0.0473276	+	0.0504036i
$606$		0			0
$607$	−10.6934	−	11.8762i	−0.434031	−	0.482040i	0.485959	−	0.873982i	$-0.338470\pi$
$607$	−10.6934	−	11.8762i	−0.434031	−	0.482040i	−0.919990	+	0.391941i	$0.871804\pi$
$608$	−5.05438	+	3.67222i	−0.204982	+	0.148928i
$609$		0			0
$610$	−0.439368	−	1.35223i	−0.0177895	−	0.0547504i
$611$	−33.5393	−	7.12899i	−1.35685	−	0.288408i
$612$		0			0
$613$	42.0977	+	18.7431i	1.70031	+	0.757027i	0.999025	+	0.0441459i	$0.0140566\pi$
$613$	42.0977	+	18.7431i	1.70031	+	0.757027i	0.701285	+	0.712881i	$0.252610\pi$
$614$	−22.4808	−	24.9674i	−0.907250	−	1.00760i
$615$		0			0
$616$	−1.56232	−	26.2655i	−0.0629475	−	1.05827i
$617$	18.3023			0.736824			0.368412	−	0.929663i	$-0.379902\pi$
$617$	18.3023			0.736824			0.368412	+	0.929663i	$0.379902\pi$
$618$		0			0
$619$	−19.2213	−	8.55787i	−0.772569	−	0.343970i	−0.0176982	−	0.999843i	$-0.505634\pi$
$619$	−19.2213	−	8.55787i	−0.772569	−	0.343970i	−0.754871	+	0.655873i	$0.772300\pi$
$620$	0.0346987	−	0.330136i	0.00139353	−	0.0132586i
$621$		0			0
$622$	8.50109	+	26.1637i	0.340863	+	1.04907i
$623$	−21.8747	+	21.7266i	−0.876390	+	0.870457i
$624$		0			0
$625$	16.4887	+	18.3126i	0.659550	+	0.732504i
$626$	−17.1370	−	29.6822i	−0.684932	−	1.18634i
$627$		0			0
$628$	0.552162	−	0.956373i	0.0220337	−	0.0381634i
$629$	5.23240	−	16.1037i	0.208630	−	0.642096i
$630$		0			0
$631$	−0.0702369	−	0.0510301i	−0.00279608	−	0.00203147i	0.586386	−	0.810032i	$-0.300550\pi$
$631$	−0.0702369	−	0.0510301i	−0.00279608	−	0.00203147i	−0.589182	+	0.808000i	$0.700550\pi$
$632$	−12.5073	−	2.65850i	−0.497512	−	0.105749i
$633$		0			0
$634$	2.53733	−	24.1411i	0.100770	−	0.958767i
$635$	0.340241	+	3.23718i	0.0135021	+	0.128464i
$636$		0			0
$637$	−23.5109	+	20.8819i	−0.931537	+	0.827371i
$638$	10.2438	+	2.06576i	0.405554	+	0.0817841i
$639$		0			0
$640$	1.23038	−	0.261525i	0.0486349	−	0.0103377i
$641$	−18.4535	−	8.21603i	−0.728869	−	0.324514i	0.00853648	−	0.999964i	$-0.497283\pi$
$641$	−18.4535	−	8.21603i	−0.728869	−	0.324514i	−0.737406	+	0.675450i	$0.763949\pi$
$642$		0			0
$643$	−11.8403	−	36.4406i	−0.466935	−	1.43708i	−0.856533	−	0.516093i	$-0.827386\pi$
$643$	−11.8403	−	36.4406i	−0.466935	−	1.43708i	0.389598	−	0.920985i	$-0.372614\pi$
$644$	−0.283517	−	0.352555i	−0.0111721	−	0.0138926i
$645$		0			0
$646$	1.79392	+	17.0680i	0.0705807	+	0.671531i
$647$	38.7962	−	8.24640i	1.52524	−	0.324199i	0.632423	−	0.774623i	$-0.282060\pi$
$647$	38.7962	−	8.24640i	1.52524	−	0.324199i	0.892815	+	0.450424i	$0.148727\pi$
$648$		0			0
$649$	28.6619	+	12.4039i	1.12508	+	0.486897i
$650$	−29.1519			−1.14343
$651$		0			0
$652$	−5.93617	+	4.31288i	−0.232479	+	0.168906i
$653$	5.51500	−	2.45544i	0.215819	−	0.0960886i	−0.295980	−	0.955194i	$-0.595646\pi$
$653$	5.51500	−	2.45544i	0.215819	−	0.0960886i	0.511798	+	0.859106i	$0.328979\pi$
$654$		0			0
$655$	1.57088	−	1.74464i	0.0613794	−	0.0681687i
$656$	15.4906	−	6.89685i	0.604805	−	0.269277i
$657$		0			0
$658$	22.1361	−	14.2687i	0.862956	−	0.556252i
$659$	16.5792			0.645833			0.322916	−	0.946427i	$-0.395337\pi$
$659$	16.5792			0.645833			0.322916	+	0.946427i	$0.395337\pi$
$660$		0			0
$661$	−9.56491	−	16.5669i	−0.372032	−	0.644378i	0.617846	−	0.786299i	$-0.288005\pi$
$661$	−9.56491	−	16.5669i	−0.372032	−	0.644378i	−0.989878	+	0.141921i	$0.954672\pi$
$662$	−23.5706	+	5.01008i	−0.916096	+	0.194722i
$663$		0			0
$664$	−8.64224	−	6.27895i	−0.335384	−	0.243671i
$665$	0.550625	−	1.41999i	0.0213523	−	0.0550649i
$666$		0			0
$667$	1.26112	−	0.561485i	0.0488306	−	0.0217408i
$668$	3.84340	+	1.71119i	0.148706	+	0.0662080i
$669$		0			0
$670$	−1.38522	+	2.39927i	−0.0535156	+	0.0926918i
$671$	11.4821	−	20.3763i	0.443261	−	0.786618i
$672$		0			0
$673$	4.37491	−	13.4646i	0.168640	−	0.519022i	−0.830646	−	0.556801i	$-0.812028\pi$
$673$	4.37491	−	13.4646i	0.168640	−	0.519022i	0.999286	+	0.0377795i	$0.0120285\pi$
$674$	−3.00156	−	28.5579i	−0.115616	−	1.10001i
$675$		0			0
$676$	−1.43778	+	1.59682i	−0.0552993	+	0.0614161i
$677$	−24.1047	−	5.12362i	−0.926421	−	0.196917i	−0.280090	−	0.959974i	$-0.590364\pi$
$677$	−24.1047	−	5.12362i	−0.926421	−	0.196917i	−0.646331	+	0.763057i	$0.723697\pi$
$678$		0			0
$679$	−12.8879	+	19.6989i	−0.494593	+	0.755973i
$680$	−0.506316	+	1.55828i	−0.0194163	+	0.0597573i
$681$		0			0
$682$	−24.9137	+	18.5016i	−0.953994	+	0.708463i
$683$	−5.33531	−	9.24103i	−0.204150	−	0.353598i	0.745712	−	0.666269i	$-0.232110\pi$
$683$	−5.33531	−	9.24103i	−0.204150	−	0.353598i	−0.949862	+	0.312671i	$0.898776\pi$
$684$		0			0
$685$	1.24401	−	0.903826i	0.0475312	−	0.0345334i
$686$	1.50974	−	24.1054i	0.0576422	−	0.920349i
$687$		0			0
$688$	20.3459	+	4.32466i	0.775681	+	0.164876i
$689$	−2.89116	+	27.5076i	−0.110145	+	1.04796i
$690$		0			0
$691$	18.7363	+	20.8087i	0.712761	+	0.791601i	0.985353	−	0.170529i	$-0.0545476\pi$
$691$	18.7363	+	20.8087i	0.712761	+	0.791601i	−0.272592	+	0.962130i	$0.587881\pi$
$692$	4.35947			0.165722
$693$		0			0
$694$	−11.4254			−0.433702
$695$	−1.61039	−	1.78852i	−0.0610855	−	0.0678424i
$696$		0			0
$697$	−1.89151	+	17.9965i	−0.0716460	+	0.681666i
$698$	4.71741	+	1.00272i	0.178556	+	0.0379533i
$699$		0			0
$700$	−2.79547	+	2.77654i	−0.105659	+	0.104943i
$701$	−22.2889	+	16.1938i	−0.841841	+	0.611633i	−0.922884	−	0.385078i	$-0.874175\pi$
$701$	−22.2889	+	16.1938i	−0.841841	+	0.611633i	0.0810436	+	0.996711i	$0.474175\pi$
$702$		0			0
$703$	−8.91891	−	15.4480i	−0.336383	−	0.582632i
$704$	23.8227	+	16.9307i	0.897851	+	0.638101i
$705$		0			0
$706$	3.47046	−	10.6810i	0.130613	−	0.401984i
$707$	49.2065	+	2.74642i	1.85060	+	0.103290i
$708$		0			0
$709$	24.0722	+	5.11670i	0.904050	+	0.192162i	0.636404	−	0.771356i	$-0.280421\pi$
$709$	24.0722	+	5.11670i	0.904050	+	0.192162i	0.267646	+	0.963517i	$0.413754\pi$
$710$	0.797129	−	0.885302i	0.0299157	−	0.0332248i
$711$		0			0
$712$	−3.65241	−	34.7503i	−0.136880	−	1.30232i
$713$	−1.26679	+	3.89879i	−0.0474418	+	0.146011i
$714$		0			0
$715$	1.55909	+	1.69558i	0.0583068	+	0.0634112i
$716$	−3.79908	+	6.58020i	−0.141978	+	0.245914i
$717$		0			0
$718$	15.5642	+	6.92962i	0.580850	+	0.258611i
$719$	3.31484	−	1.47586i	0.123623	−	0.0550403i	−0.343993	−	0.938972i	$-0.611780\pi$
$719$	3.31484	−	1.47586i	0.123623	−	0.0550403i	0.467616	+	0.883932i	$0.345113\pi$
$720$		0			0
$721$	16.0710	−	2.48948i	0.598517	−	0.0927131i
$722$	−5.41930	−	3.93735i	−0.201686	−	0.146533i
$723$		0			0
$724$	−0.165828	+	0.0352479i	−0.00616296	+	0.00130998i
$725$	−6.01118	−	10.4117i	−0.223250	−	0.386680i
$726$		0			0
$727$	26.0955			0.967830			0.483915	−	0.875115i	$-0.339214\pi$
$727$	26.0955			0.967830			0.483915	+	0.875115i	$0.339214\pi$
$728$	−1.74428	−	35.5956i	−0.0646472	−	1.31926i
$729$		0			0
$730$	1.35845	−	0.604820i	0.0502784	−	0.0223854i
$731$	−14.8532	+	16.4961i	−0.549365	+	0.610132i
$732$		0			0
$733$	−48.6589	+	21.6644i	−1.79726	+	0.800191i	−0.825430	+	0.564505i	$0.809067\pi$
$733$	−48.6589	+	21.6644i	−1.79726	+	0.800191i	−0.971829	+	0.235686i	$0.924266\pi$
$734$	17.4838	−	12.7028i	0.645341	−	0.468867i
$735$		0			0
$736$	0.958733			0.0353394
$737$	−44.4758	+	9.94041i	−1.63829	+	0.366160i
$738$		0			0
$739$	17.6989	−	3.76201i	0.651064	−	0.138388i	0.129472	−	0.991583i	$-0.458672\pi$
$739$	17.6989	−	3.76201i	0.651064	−	0.138388i	0.521592	+	0.853195i	$0.325338\pi$
$740$	−0.0231696	−	0.220444i	−0.000851732	−	0.00810369i
$741$		0			0
$742$	−13.3134	−	16.5553i	−0.488750	−	0.607765i
$743$	6.14504	+	18.9125i	0.225440	+	0.693832i	0.998247	+	0.0591909i	$0.0188521\pi$
$743$	6.14504	+	18.9125i	0.225440	+	0.693832i	−0.772807	+	0.634641i	$0.781148\pi$
$744$		0			0
$745$	1.20930	+	0.538415i	0.0443053	+	0.0197260i
$746$	0.815473	−	0.173334i	0.0298566	−	0.00634621i
$747$		0			0
$748$	−3.18972	+	1.46028i	−0.116628	+	0.0533930i
$749$	7.93698	−	49.0337i	0.290011	−	1.79165i
$750$		0			0
$751$	−3.76377	−	35.8099i	−0.137342	−	1.30672i	−0.818467	−	0.574554i	$-0.805176\pi$
$751$	−3.76377	−	35.8099i	−0.137342	−	1.30672i	0.681125	−	0.732167i	$-0.261491\pi$
$752$	−2.64241	+	25.1409i	−0.0963589	+	0.916794i
$753$		0			0
$754$	13.8447	+	2.94278i	0.504194	+	0.107170i
$755$	−0.455767	−	0.331134i	−0.0165871	−	0.0120512i
$756$		0			0
$757$	3.76954	−	11.6014i	0.137006	−	0.421662i	−0.858891	−	0.512159i	$-0.828846\pi$
$757$	3.76954	−	11.6014i	0.137006	−	0.421662i	0.995897	+	0.0904977i	$0.0288458\pi$
$758$	−4.45213	+	7.71131i	−0.161709	+	0.280087i
$759$		0			0
$760$	0.863042	+	1.49483i	0.0313058	+	0.0542233i
$761$	26.3156	+	29.2264i	0.953939	+	1.05946i	0.998172	+	0.0604348i	$0.0192487\pi$
$761$	26.3156	+	29.2264i	0.953939	+	1.05946i	−0.0442336	+	0.999021i	$0.514085\pi$
$762$		0			0
$763$	−0.560664	−	2.12122i	−0.0202974	−	0.0767933i
$764$	0.385597	+	1.18675i	0.0139504	+	0.0429350i
$765$		0			0
$766$	−1.98917	+	18.9257i	−0.0718717	+	0.683814i
$767$	38.6436	+	17.2052i	1.39534	+	0.621245i
$768$		0			0
$769$	3.32739			0.119989			0.0599943	−	0.998199i	$-0.480892\pi$
$769$	3.32739			0.119989			0.0599943	+	0.998199i	$0.480892\pi$
$770$	−1.76740	−	0.0801325i	−0.0636927	−	0.00288777i
$771$		0			0
$772$	2.80291	+	3.11295i	0.100879	+	0.112037i
$773$	21.4478	+	9.54917i	0.771423	+	0.343460i	0.754417	−	0.656396i	$-0.227920\pi$
$773$	21.4478	+	9.54917i	0.771423	+	0.343460i	0.0170063	+	0.999855i	$0.494586\pi$
$774$		0			0
$775$	34.9215	+	7.42279i	1.25442	+	0.266634i
$776$	−8.24427	−	25.3732i	−0.295952	−	0.910847i
$777$		0			0
$778$	−33.6867	+	24.4748i	−1.20773	+	0.877466i
$779$	12.7558	+	14.1667i	0.457023	+	0.507576i
$780$		0			0
$781$	19.5954	−	0.204743i	0.701180	−	0.00732629i
$782$	1.31682	−	2.28080i	0.0470893	−	0.0815611i
$783$		0			0
$784$	17.1228	+	15.6293i	0.611528	+	0.558190i
$785$	−0.461542	−	0.335330i	−0.0164731	−	0.0119684i
$786$		0			0
$787$	7.50608	−	8.33635i	0.267563	−	0.297159i	−0.594359	−	0.804200i	$-0.702594\pi$
$787$	7.50608	−	8.33635i	0.267563	−	0.297159i	0.861922	+	0.507041i	$0.169261\pi$
$788$	0.425988	−	4.05301i	0.0151752	−	0.144382i
$789$		0			0
$790$	−0.265686	+	0.817697i	−0.00945267	+	0.0290923i
$791$	2.50614	−	0.952265i	0.0891083	−	0.0338587i
$792$		0			0
$793$	15.8394	−	27.4347i	0.562475	−	0.974236i
$794$	13.9899	−	2.97364i	0.496482	−	0.105530i
$795$		0			0
$796$	−0.470776	+	0.209603i	−0.0166862	+	0.00742918i
$797$	−0.271756	−	0.836380i	−0.00962610	−	0.0296261i	0.946128	−	0.323793i	$-0.104958\pi$
$797$	−0.271756	−	0.836380i	−0.00962610	−	0.0296261i	−0.955754	+	0.294166i	$0.904958\pi$
$798$		0			0
$799$	−21.8253	−	15.8570i	−0.772123	−	0.560981i
$800$	−0.872764	−	8.30380i	−0.0308569	−	0.293584i
$801$		0			0
$802$	3.73333	+	6.46631i	0.131828	+	0.228333i
$803$	22.4489	+	9.71515i	0.792205	+	0.342840i
$804$		0			0
$805$	−0.196443	+	0.126625i	−0.00692371	+	0.00446295i
$806$	−34.0044	+	24.7056i	−1.19775	+	0.870219i
$807$		0			0
$808$	−37.3738	+	41.5078i	−1.31481	+	1.46024i
$809$	30.6574	−	34.0485i	1.07786	−	1.19708i	0.0984589	−	0.995141i	$-0.468609\pi$
$809$	30.6574	−	34.0485i	1.07786	−	1.19708i	0.979398	−	0.201940i	$-0.0647246\pi$
$810$		0			0
$811$	12.5481	−	9.11676i	0.440625	−	0.320133i	−0.345258	−	0.938508i	$-0.612209\pi$
$811$	12.5481	−	9.11676i	0.440625	−	0.320133i	0.785883	+	0.618375i	$0.212209\pi$
$812$	1.60789	−	1.03643i	0.0564259	−	0.0363716i
$813$		0			0
$814$	−13.7037	+	15.5430i	−0.480314	+	0.544783i
$815$	1.89529	+	3.28274i	0.0663891	+	0.114989i
$816$		0			0
$817$	2.44437	+	23.2566i	0.0855176	+	0.813645i
$818$	−9.05808	−	6.58108i	−0.316708	−	0.230102i
$819$		0			0
$820$	0.0732017	+	0.225292i	0.00255632	+	0.00786753i
$821$	11.2838	−	5.02388i	0.393808	−	0.175334i	−0.200273	−	0.979740i	$-0.564183\pi$
$821$	11.2838	−	5.02388i	0.393808	−	0.175334i	0.594080	+	0.804406i	$0.297516\pi$
$822$		0			0
$823$	13.6679	−	2.90521i	0.476434	−	0.101269i	0.0365654	−	0.999331i	$-0.488358\pi$
$823$	13.6679	−	2.90521i	0.476434	−	0.101269i	0.439869	+	0.898062i	$0.355025\pi$
$824$	−9.21556	+	15.9618i	−0.321039	+	0.556056i
$825$		0			0
$826$	−30.3717	+	11.5404i	−1.05677	+	0.401542i
$827$	−4.65409	+	14.3238i	−0.161839	+	0.498088i	−0.998789	−	0.0491902i	$-0.984336\pi$
$827$	−4.65409	+	14.3238i	−0.161839	+	0.498088i	0.836951	+	0.547278i	$0.184336\pi$
$828$		0			0
$829$	−1.49151	+	14.1908i	−0.0518024	+	0.492867i	0.937605	+	0.347702i	$0.113038\pi$
$829$	−1.49151	+	14.1908i	−0.0518024	+	0.492867i	−0.989407	+	0.145165i	$0.953629\pi$
$830$	−0.480626	+	0.533790i	−0.0166828	+	0.0185281i
$831$		0			0
$832$	32.0253	+	23.2677i	1.11028	+	0.806664i
$833$	−23.5812	+	7.48528i	−0.817039	+	0.259350i
$834$		0			0
$835$	1.08671	−	1.88223i	0.0376070	−	0.0651373i
$836$	−1.10524	+	3.52654i	−0.0382256	+	0.121968i
$837$		0			0
$838$	−34.3769	−	38.1794i	−1.18753	−	1.31888i
$839$	−8.87876	+	6.45080i	−0.306529	+	0.222706i	−0.730406	−	0.683014i	$-0.760669\pi$
$839$	−8.87876	+	6.45080i	−0.306529	+	0.222706i	0.423877	+	0.905720i	$0.360669\pi$
$840$		0			0
$841$	−7.15771	−	22.0292i	−0.246818	−	0.759626i
$842$	44.2449	+	9.40454i	1.52478	+	0.324102i
$843$		0			0
$844$	1.79426	+	0.798858i	0.0617611	+	0.0274978i
$845$	0.742762	+	0.824921i	0.0255518	+	0.0283781i
$846$		0			0
$847$	−18.7083	−	22.2935i	−0.642823	−	0.766014i
$848$	20.3918			0.700257
$849$		0			0
$850$	−20.9532	−	9.32897i	−0.718689	−	0.319981i
$851$	−0.286131	+	2.72235i	−0.00980843	+	0.0933210i
$852$		0			0
$853$	−13.0482	−	40.1581i	−0.446761	−	1.37499i	−0.880541	−	0.473969i	$-0.842821\pi$
$853$	−13.0482	−	40.1581i	−0.446761	−	1.37499i	0.433781	−	0.901018i	$-0.357179\pi$
$854$	6.21771	+	23.5241i	0.212766	+	0.804978i
$855$		0			0
$856$	37.6687	+	41.8353i	1.28749	+	1.42990i
$857$	−15.5761	−	26.9785i	−0.532068	−	0.921569i	−0.999299	−	0.0374336i	$-0.988082\pi$
$857$	−15.5761	−	26.9785i	−0.532068	−	0.921569i	0.467231	−	0.884135i	$-0.345252\pi$
$858$		0			0
$859$	26.8597	−	46.5224i	0.916441	−	1.58732i	0.111663	−	0.993746i	$-0.464382\pi$
$859$	26.8597	−	46.5224i	0.916441	−	1.58732i	0.804778	−	0.593576i	$-0.202284\pi$
$860$	−0.0897960	+	0.276364i	−0.00306202	+	0.00942392i
$861$		0			0
$862$	17.9097	+	13.0122i	0.610007	+	0.443196i
$863$	16.6228	+	3.53329i	0.565847	+	0.120275i	0.481948	−	0.876200i	$-0.339929\pi$
$863$	16.6228	+	3.53329i	0.565847	+	0.120275i	0.0838991	+	0.996474i	$0.473263\pi$
$864$		0			0
$865$	0.235410	−	2.23978i	0.00800419	−	0.0761548i
$866$	−3.23797	−	30.8072i	−0.110031	−	1.04687i
$867$		0			0
$868$	−0.907724	+	5.60781i	−0.0308102	+	0.190341i
$869$	−12.8596	+	5.88722i	−0.436232	+	0.199710i
$870$		0			0
$871$	−60.3777	+	12.8337i	−2.04582	+	0.434853i
$872$	2.27163	+	1.01140i	0.0769272	+	0.0342502i
$873$		0			0
$874$	−0.857355	−	2.63867i	−0.0290005	−	0.0892543i
$875$	2.55724	+	3.17995i	0.0864505	+	0.107502i
$876$		0			0
$877$	1.62687	+	15.4786i	0.0549355	+	0.522676i	0.987039	+	0.160483i	$0.0513052\pi$
$877$	1.62687	+	15.4786i	0.0549355	+	0.522676i	−0.932103	+	0.362193i	$0.882028\pi$
$878$	7.87189	−	1.67322i	0.265663	−	0.0564685i
$879$		0			0
$880$	1.12308	−	1.27382i	0.0378589	−	0.0429405i
$881$	−2.11673			−0.0713145			−0.0356572	−	0.999364i	$-0.511352\pi$
$881$	−2.11673			−0.0713145			−0.0356572	+	0.999364i	$0.511352\pi$
$882$		0			0
$883$	0.998367	−	0.725356i	0.0335977	−	0.0244102i	−0.570860	−	0.821048i	$-0.693390\pi$
$883$	0.998367	−	0.725356i	0.0335977	−	0.0244102i	0.604457	+	0.796637i	$0.293390\pi$
$884$	−4.34075	+	1.93263i	−0.145995	+	0.0650013i
$885$		0			0
$886$	2.46916	−	2.74229i	0.0829532	−	0.0921289i
$887$	−23.1270	+	10.2968i	−0.776530	+	0.345733i	−0.756439	−	0.654065i	$-0.773062\pi$
$887$	−23.1270	+	10.2968i	−0.776530	+	0.345733i	−0.0200913	+	0.999798i	$0.506396\pi$
$888$		0			0
$889$	−2.72636	−	55.6369i	−0.0914390	−	1.86600i
$890$	−2.34949			−0.0787550
$891$		0			0
$892$	−2.24779	−	3.89329i	−0.0752616	−	0.130357i
$893$	−27.7990	+	5.90887i	−0.930259	+	0.197733i
$894$		0			0
$895$	3.17558	+	2.30719i	0.106148	+	0.0771210i
$896$	−21.2724	+	3.29519i	−0.710660	+	0.110085i
$897$		0			0
$898$	4.37749	−	1.94898i	0.146079	−	0.0650385i
$899$	−15.8354	−	7.05040i	−0.528142	−	0.235144i
$900$		0			0
$901$	−10.8808	+	18.8461i	−0.362493	+	0.627856i
$902$	10.8715	−	19.2927i	0.361981	−	0.642377i
$903$		0			0
$904$	−0.938927	+	2.88972i	−0.0312283	+	0.0961107i
$905$	0.00915474	+	0.0871015i	0.000304314	+	0.00289535i
$906$		0			0
$907$	−20.8157	+	23.1182i	−0.691173	+	0.767626i	−0.981945	−	0.189167i	$-0.939421\pi$
$907$	−20.8157	+	23.1182i	−0.691173	+	0.767626i	0.290772	+	0.956792i	$0.406088\pi$
$908$	4.14611	+	0.881283i	0.137594	+	0.0292464i
$909$		0			0
$910$	−2.39260	−	0.133541i	−0.0793138	−	0.00442683i
$911$	−10.0692	+	30.9897i	−0.333606	+	1.02673i	0.633798	+	0.773498i	$0.281495\pi$
$911$	−10.0692	+	30.9897i	−0.333606	+	1.02673i	−0.967405	+	0.253236i	$0.918505\pi$
$912$		0			0
$913$	−11.8150	+	0.123449i	−0.391019	+	0.00408558i
$914$	−16.4544	−	28.4998i	−0.544263	−	0.942691i
$915$		0			0
$916$	2.94765	−	2.14159i	0.0973930	−	0.0707602i
$917$	−28.5048	+	28.3119i	−0.941313	+	0.934940i
$918$		0			0
$919$	1.09938	+	0.233681i	0.0362653	+	0.00770843i	0.226009	−	0.974125i	$-0.427432\pi$
$919$	1.09938	+	0.233681i	0.0362653	+	0.00770843i	−0.189743	+	0.981834i	$0.560766\pi$
$920$	0.0276875	−	0.263429i	0.000912831	−	0.00868501i
$921$		0			0
$922$	−1.44347	−	1.60314i	−0.0475383	−	0.0527966i
$923$	26.5425			0.873658
$924$		0			0
$925$	23.8393			0.783833
$926$	20.8444	+	23.1501i	0.684990	+	0.760759i
$927$		0			0
$928$	−0.423749	+	4.03171i	−0.0139103	+	0.132347i
$929$	36.1696	+	7.68809i	1.18669	+	0.252238i	0.758635	−	0.651516i	$-0.225867\pi$
$929$	36.1696	+	7.68809i	1.18669	+	0.252238i	0.428052	+	0.903754i	$0.359200\pi$
$930$		0			0
$931$	−10.7625	+	23.7377i	−0.352727	+	0.777972i
$932$	3.64955	−	2.65155i	0.119545	−	0.0868545i
$933$		0			0
$934$	−11.2904	−	19.5556i	−0.369435	−	0.639880i
$935$	0.578006	+	1.71765i	0.0189028	+	0.0561730i
$936$		0			0
$937$	−4.27983	+	13.1719i	−0.139816	+	0.430309i	−0.996308	−	0.0858512i	$-0.972639\pi$
$937$	−4.27983	+	13.1719i	−0.139816	+	0.430309i	0.856492	+	0.516160i	$0.172639\pi$
$938$	25.9568	−	39.6743i	0.847519	−	1.29541i
$939$		0			0
$940$	−0.345440	−	0.0734255i	−0.0112670	−	0.00239488i
$941$	−1.25685	+	1.39588i	−0.0409722	+	0.0455043i	−0.763283	−	0.646065i	$-0.776414\pi$
$941$	−1.25685	+	1.39588i	−0.0409722	+	0.0455043i	0.722310	+	0.691569i	$0.243080\pi$
$942$		0			0
$943$	−0.305787	−	2.90937i	−0.00995779	−	0.0947421i
$944$	9.63711	−	29.6600i	0.313661	−	0.965350i
$945$		0			0
$946$	24.6997	−	11.3077i	0.803056	−	0.367644i
$947$	24.9177	−	43.1587i	0.809717	−	1.40247i	−0.103343	−	0.994646i	$-0.532954\pi$
$947$	24.9177	−	43.1587i	0.809717	−	1.40247i	0.913060	−	0.407825i	$-0.133713\pi$
$948$		0			0
$949$	30.2669	+	13.4757i	0.982504	+	0.437439i
$950$	−22.0736	+	9.82780i	−0.716162	+	0.318856i
$951$		0			0
$952$	10.1373	−	26.1428i	0.328552	−	0.847294i
$953$	−43.7611	−	31.7943i	−1.41756	−	1.02992i	−0.992168	−	0.124909i	$-0.960136\pi$
$953$	−43.7611	−	31.7943i	−1.41756	−	1.02992i	−0.425393	−	0.905009i	$-0.639864\pi$
$954$		0			0
$955$	0.630540	−	0.134025i	0.0204038	−	0.00433696i
$956$	−2.16724	−	3.75377i	−0.0700936	−	0.121406i
$957$		0			0
$958$	11.2972			0.364997
$959$	−22.1179	+	14.2569i	−0.714223	+	0.460381i
$960$		0			0
$961$	18.7051	−	8.32804i	0.603390	−	0.268646i
$962$	−18.7799	+	20.8572i	−0.605489	+	0.672464i
$963$		0			0
$964$	−3.75668	+	1.67258i	−0.120994	+	0.0538702i
$965$	1.75070	−	1.27196i	0.0563572	−	0.0409459i
$966$		0			0
$967$	36.6625			1.17899			0.589493	−	0.807774i	$-0.299328\pi$
$967$	36.6625			1.17899			0.589493	+	0.807774i	$0.299328\pi$
$968$	32.9766	−	0.689188i	1.05991	−	0.0221513i
$969$		0			0
$970$	−1.75470	+	0.372973i	−0.0563399	+	0.0119754i
$971$	3.12029	+	29.6876i	0.100135	+	0.952721i	0.923082	+	0.384603i	$0.125662\pi$
$971$	3.12029	+	29.6876i	0.100135	+	0.952721i	−0.822947	+	0.568118i	$0.807672\pi$
$972$		0			0
$973$	25.8104	+	32.0955i	0.827444	+	1.02893i
$974$	16.8395	+	51.8267i	0.539573	+	1.66064i
$975$		0			0
$976$	−21.3362	−	9.49950i	−0.682956	−	0.304072i
$977$	41.4504	−	8.81056i	1.32612	−	0.281875i	0.510206	−	0.860052i	$-0.329569\pi$
$977$	41.4504	−	8.81056i	1.32612	−	0.281875i	0.815911	+	0.578177i	$0.196236\pi$
$978$		0			0
$979$	−26.1596	−	28.4497i	−0.836065	−	0.909257i
$980$	−0.242152	+	0.215075i	−0.00773527	+	0.00687030i
$981$		0			0
$982$	4.51855	+	42.9911i	0.144193	+	1.37190i
$983$	0.330223	−	3.14186i	0.0105325	−	0.100210i	−0.987993	−	0.154501i	$-0.950623\pi$
$983$	0.330223	−	3.14186i	0.0105325	−	0.100210i	0.998525	+	0.0542908i	$0.0172898\pi$
$984$		0			0
$985$	−2.05932	−	0.437722i	−0.0656154	−	0.0139470i
$986$	9.00928	+	6.54562i	0.286914	+	0.208455i
$987$		0			0
$988$	−1.54682	+	4.76062i	−0.0492109	+	0.151456i
$989$	1.79428	−	3.10778i	0.0570547	−	0.0988217i
$990$		0			0
$991$	−17.3315	−	30.0190i	−0.550552	−	0.953584i	−0.998235	−	0.0593913i	$-0.981084\pi$
$991$	−17.3315	−	30.0190i	−0.550552	−	0.953584i	0.447683	−	0.894192i	$-0.352249\pi$
$992$	−8.05534	−	8.94636i	−0.255757	−	0.284047i
$993$		0			0
$994$	−14.4645	+	14.3666i	−0.458787	+	0.455681i
$995$	0.0822666	+	0.253191i	0.00260803	+	0.00802668i
$996$		0			0
$997$	−4.41001	+	41.9584i	−0.139666	+	1.32884i	0.670182	+	0.742197i	$0.266216\pi$
$997$	−4.41001	+	41.9584i	−0.139666	+	1.32884i	−0.809848	+	0.586639i	$0.800451\pi$
$998$	11.0543	+	4.92170i	0.349918	+	0.155794i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.by.d.163.2		64
3.2	odd	2		231.2.y.a.163.7	yes	64
7.4	even	3	inner	693.2.by.d.361.7		64
11.5	even	5	inner	693.2.by.d.478.7		64
21.11	odd	6		231.2.y.a.130.2	yes	64
33.5	odd	10		231.2.y.a.16.2	✓	64
77.60	even	15	inner	693.2.by.d.676.2		64
231.137	odd	30		231.2.y.a.214.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.16.2	✓	64	33.5	odd	10
231.2.y.a.130.2	yes	64	21.11	odd	6
231.2.y.a.163.7	yes	64	3.2	odd	2
231.2.y.a.214.7	yes	64	231.137	odd	30
693.2.by.d.163.2		64	1.1	even	1	trivial
693.2.by.d.361.7		64	7.4	even	3	inner
693.2.by.d.478.7		64	11.5	even	5	inner
693.2.by.d.676.2		64	77.60	even	15	inner

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.by (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.872627 - 0.969151i) q^{2} +(0.0312821 - 0.297629i) q^{4} +(-0.151225 - 0.0321438i) q^{5} +(2.55326 + 0.693447i) q^{7} +(-2.42586 + 1.76249i) q^{8} +O(q^{10})\)	\(q+(-0.872627 - 0.969151i) q^{2} +(0.0312821 - 0.297629i) q^{4} +(-0.151225 - 0.0321438i) q^{5} +(2.55326 + 0.693447i) q^{7} +(-2.42586 + 1.76249i) q^{8} +(0.100810 + 0.174609i) q^{10} +(-0.991882 + 3.16483i) q^{11} +(-1.38817 + 4.27234i) q^{13} +(-1.55599 - 3.07961i) q^{14} +(3.23953 + 0.688583i) q^{16} +(-2.36496 + 2.62656i) q^{17} +(0.389198 + 3.70297i) q^{19} +(-0.0142975 + 0.0440033i) q^{20} +(3.93274 - 1.80044i) q^{22} +(0.285690 - 0.494829i) q^{23} +(-4.54589 - 2.02396i) q^{25} +(5.35190 - 2.38282i) q^{26} +(0.286261 - 0.738232i) q^{28} +(1.95460 + 1.42010i) q^{29} +(-7.01784 + 1.49169i) q^{31} +(0.838964 + 1.45313i) q^{32} +4.60926 q^{34} +(-0.363825 - 0.186938i) q^{35} +(-4.37659 + 1.94858i) q^{37} +(3.24912 - 3.60851i) q^{38} +(0.423502 - 0.188555i) q^{40} +(4.14207 - 3.00939i) q^{41} +6.28052 q^{43} +(0.910919 + 0.394215i) q^{44} +(-0.728864 + 0.154925i) q^{46} +(0.797854 + 7.59108i) q^{47} +(6.03826 + 3.54110i) q^{49} +(2.00535 + 6.17182i) q^{50} +(1.22815 + 0.546807i) q^{52} +(6.02258 - 1.28014i) q^{53} +(0.251726 - 0.446718i) q^{55} +(-7.41603 + 2.81789i) q^{56} +(-0.329347 - 3.13352i) q^{58} +(0.984287 - 9.36486i) q^{59} +(-6.89786 - 1.46619i) q^{61} +(7.56963 + 5.49966i) q^{62} +(2.72307 - 8.38073i) q^{64} +(0.347254 - 0.601462i) q^{65} +(6.87041 + 11.8999i) q^{67} +(0.707759 + 0.786046i) q^{68} +(0.136313 + 0.515728i) q^{70} +(-1.82585 - 5.61938i) q^{71} +(0.770924 - 7.33485i) q^{73} +(5.70760 + 2.54119i) q^{74} +1.11429 q^{76} +(-4.72717 + 7.39282i) q^{77} +(2.85339 + 3.16901i) q^{79} +(-0.467763 - 0.208261i) q^{80} +(-6.53104 - 1.38822i) q^{82} +(1.10089 + 3.38819i) q^{83} +(0.442068 - 0.321181i) q^{85} +(-5.48055 - 6.08677i) q^{86} +(-3.17182 - 9.42561i) q^{88} +(-5.82649 + 10.0918i) q^{89} +(-6.50700 + 9.94578i) q^{91} +(-0.138338 - 0.100509i) q^{92} +(6.66067 - 7.39742i) q^{94} +(0.0601712 - 0.572491i) q^{95} +(-2.74944 + 8.46191i) q^{97} +(-1.83730 - 8.94205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 10 q^{4} - q^{7} - 8 q^{8}+O(q^{10}) \) 64 * q + 10 * q^4 - q^7 - 8 * q^8	\( 64 q + 10 q^{4} - q^{7} - 8 q^{8} - 22 q^{10} + 13 q^{11} - 8 q^{13} + 26 q^{14} - 4 q^{17} + 10 q^{19} - 24 q^{20} - 38 q^{22} + 8 q^{23} - 2 q^{25} - 4 q^{26} - 67 q^{28} - 2 q^{29} + 25 q^{31} - 72 q^{32} - 56 q^{34} - 19 q^{35} - 12 q^{37} + 37 q^{38} - 9 q^{40} - 20 q^{41} - 100 q^{43} + 5 q^{44} - 33 q^{46} + 18 q^{47} + 29 q^{49} + 46 q^{50} + 26 q^{52} + 49 q^{53} - 24 q^{55} + 48 q^{56} - 40 q^{58} - q^{59} + 3 q^{61} - 4 q^{62} - 24 q^{64} - 82 q^{65} + 76 q^{67} + 39 q^{68} + 59 q^{70} - 70 q^{71} - 3 q^{73} - 32 q^{74} + 104 q^{76} - 38 q^{77} - 15 q^{79} + 83 q^{80} + 42 q^{82} - 68 q^{83} + 62 q^{85} + 47 q^{86} - 64 q^{88} - 82 q^{89} - 10 q^{91} - 190 q^{92} - 6 q^{94} + 53 q^{95} - 32 q^{97} + 152 q^{98}+O(q^{100}) \) 64 * q + 10 * q^4 - q^7 - 8 * q^8 - 22 * q^10 + 13 * q^11 - 8 * q^13 + 26 * q^14 - 4 * q^17 + 10 * q^19 - 24 * q^20 - 38 * q^22 + 8 * q^23 - 2 * q^25 - 4 * q^26 - 67 * q^28 - 2 * q^29 + 25 * q^31 - 72 * q^32 - 56 * q^34 - 19 * q^35 - 12 * q^37 + 37 * q^38 - 9 * q^40 - 20 * q^41 - 100 * q^43 + 5 * q^44 - 33 * q^46 + 18 * q^47 + 29 * q^49 + 46 * q^50 + 26 * q^52 + 49 * q^53 - 24 * q^55 + 48 * q^56 - 40 * q^58 - q^59 + 3 * q^61 - 4 * q^62 - 24 * q^64 - 82 * q^65 + 76 * q^67 + 39 * q^68 + 59 * q^70 - 70 * q^71 - 3 * q^73 - 32 * q^74 + 104 * q^76 - 38 * q^77 - 15 * q^79 + 83 * q^80 + 42 * q^82 - 68 * q^83 + 62 * q^85 + 47 * q^86 - 64 * q^88 - 82 * q^89 - 10 * q^91 - 190 * q^92 - 6 * q^94 + 53 * q^95 - 32 * q^97 + 152 * q^98

Introduction

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