LMFDB - Embedded newform 864.2.bk.a.37.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(37,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("864.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bk (of order $24$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.18
Character	$\chi$	$=$	864.37
Dual form			864.2.bk.a.397.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624817 - 1.26870i) q^{2} +(-1.21921 + 1.58541i) q^{4} +(1.33786 - 1.02658i) q^{5} +(-0.437818 + 1.63396i) q^{7} +(2.77320 + 0.556221i) q^{8} +O(q^{10})$	\(q+(-0.624817 - 1.26870i) q^{2} +(-1.21921 + 1.58541i) q^{4} +(1.33786 - 1.02658i) q^{5} +(-0.437818 + 1.63396i) q^{7} +(2.77320 + 0.556221i) q^{8} +(-2.13834 - 1.05592i) q^{10} +(-1.50780 + 0.198506i) q^{11} +(-0.427656 + 3.24837i) q^{13} +(2.34656 - 0.465464i) q^{14} +(-1.02706 - 3.86590i) q^{16} +4.41051i q^{17} +(2.86961 - 1.18863i) q^{19} +(-0.00358480 + 3.37267i) q^{20} +(1.19395 + 1.78892i) q^{22} +(-0.0685874 - 0.255972i) q^{23} +(-0.558085 + 2.08280i) q^{25} +(4.38842 - 1.48707i) q^{26} +(-2.05671 - 2.68626i) q^{28} +(-4.77447 + 6.22221i) q^{29} +(1.70850 - 2.95921i) q^{31} +(-4.26294 + 3.71851i) q^{32} +(5.59562 - 2.75576i) q^{34} +(1.09164 + 2.63546i) q^{35} +(4.55158 + 1.88532i) q^{37} +(-3.30100 - 2.89800i) q^{38} +(4.28115 - 2.10275i) q^{40} +(2.70179 + 10.0832i) q^{41} +(-11.3541 + 1.49479i) q^{43} +(1.52361 - 2.63251i) q^{44} +(-0.281897 + 0.246952i) q^{46} +(5.48788 - 3.16843i) q^{47} +(3.58404 + 2.06925i) q^{49} +(2.99115 - 0.593325i) q^{50} +(-4.62860 - 4.63845i) q^{52} +(-0.907259 + 2.19032i) q^{53} +(-1.81345 + 1.81345i) q^{55} +(-2.12300 + 4.28776i) q^{56} +(10.8773 + 2.16964i) q^{58} +(7.99535 - 6.13505i) q^{59} +(2.95479 - 3.85076i) q^{61} +(-4.82185 - 0.318614i) q^{62} +(7.38124 + 3.08502i) q^{64} +(2.76255 + 4.78489i) q^{65} +(10.1544 + 1.33685i) q^{67} +(-6.99247 - 5.37733i) q^{68} +(2.66154 - 3.03165i) q^{70} +(7.70797 + 7.70797i) q^{71} +(5.54934 - 5.54934i) q^{73} +(-0.451985 - 6.95258i) q^{74} +(-1.61418 + 5.99870i) q^{76} +(0.335793 - 2.55060i) q^{77} +(-7.63729 + 4.40939i) q^{79} +(-5.34270 - 4.11767i) q^{80} +(11.1045 - 9.72794i) q^{82} +(-3.96569 - 3.04298i) q^{83} +(4.52772 + 5.90064i) q^{85} +(8.99065 + 13.4709i) q^{86} +(-4.29185 - 0.288176i) q^{88} +(-3.40163 - 3.40163i) q^{89} +(-5.12047 - 2.12097i) q^{91} +(0.489443 + 0.203344i) q^{92} +(-7.44871 - 4.98279i) q^{94} +(2.61892 - 4.53609i) q^{95} +(-0.784666 - 1.35908i) q^{97} +(0.385890 - 5.83998i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.624817	−	1.26870i	−0.441812	−	0.897108i
$2$	−0.624817	−	1.26870i	−0.441812	−	0.897108i
$3$		0			0
$3$		0			0
$4$	−1.21921	+	1.58541i	−0.609604	+	0.792706i
$5$	1.33786	−	1.02658i	0.598309	−	0.459099i	−0.264670	−	0.964339i	$-0.585263\pi$
$5$	1.33786	−	1.02658i	0.598309	−	0.459099i	0.862979	+	0.505240i	$0.168596\pi$
$6$		0			0
$7$	−0.437818	+	1.63396i	−0.165480	+	0.617578i	0.832499	+	0.554027i	$0.186909\pi$
$7$	−0.437818	+	1.63396i	−0.165480	+	0.617578i	−0.997979	+	0.0635516i	$0.979757\pi$
$8$	2.77320	+	0.556221i	0.980473	+	0.196654i
$9$		0			0
$10$	−2.13834	−	1.05592i	−0.676201	−	0.333912i
$11$	−1.50780	+	0.198506i	−0.454620	+	0.0598519i	−0.354359	−	0.935109i	$-0.615301\pi$
$11$	−1.50780	+	0.198506i	−0.454620	+	0.0598519i	−0.100261	+	0.994961i	$0.531968\pi$
$12$		0			0
$13$	−0.427656	+	3.24837i	−0.118610	+	0.900936i	0.823894	+	0.566743i	$0.191797\pi$
$13$	−0.427656	+	3.24837i	−0.118610	+	0.900936i	−0.942505	+	0.334192i	$0.891536\pi$
$14$	2.34656	−	0.465464i	0.627145	−	0.124400i
$15$		0			0
$16$	−1.02706	−	3.86590i	−0.256765	−	0.966474i
$17$			4.41051i			1.06971i	0.844945	+	0.534853i	$0.179633\pi$
$17$			4.41051i			1.06971i	−0.844945	+	0.534853i	$0.820367\pi$
$18$		0			0
$19$	2.86961	−	1.18863i	0.658334	−	0.272691i	−0.0284035	−	0.999597i	$-0.509042\pi$
$19$	2.86961	−	1.18863i	0.658334	−	0.272691i	0.686737	+	0.726906i	$0.259042\pi$
$20$	−0.00358480	+	3.37267i	−0.000801585	+	0.754152i
$21$		0			0
$22$	1.19395	+	1.78892i	0.254550	+	0.381400i
$23$	−0.0685874	−	0.255972i	−0.0143015	−	0.0533738i	0.958406	−	0.285407i	$-0.0921288\pi$
$23$	−0.0685874	−	0.255972i	−0.0143015	−	0.0533738i	−0.972708	+	0.232033i	$0.925462\pi$
$24$		0			0
$25$	−0.558085	+	2.08280i	−0.111617	+	0.416560i
$26$	4.38842	−	1.48707i	0.860640	−	0.291638i
$27$		0			0
$28$	−2.05671	−	2.68626i	−0.388681	−	0.507655i
$29$	−4.77447	+	6.22221i	−0.886597	+	1.15544i	0.100440	+	0.994943i	$0.467975\pi$
$29$	−4.77447	+	6.22221i	−0.886597	+	1.15544i	−0.987037	+	0.160492i	$0.948692\pi$
$30$		0			0
$31$	1.70850	−	2.95921i	0.306856	−	0.531489i	−0.670817	−	0.741623i	$-0.734056\pi$
$31$	1.70850	−	2.95921i	0.306856	−	0.531489i	0.977673	+	0.210133i	$0.0673898\pi$
$32$	−4.26294	+	3.71851i	−0.753589	+	0.657346i
$33$		0			0
$34$	5.59562	−	2.75576i	0.959641	−	0.472609i
$35$	1.09164	+	2.63546i	0.184521	+	0.445474i
$36$		0			0
$37$	4.55158	+	1.88532i	0.748275	+	0.309945i	0.724037	−	0.689761i	$-0.242284\pi$
$37$	4.55158	+	1.88532i	0.748275	+	0.309945i	0.0242372	+	0.999706i	$0.492284\pi$
$38$	−3.30100	−	2.89800i	−0.535493	−	0.470118i
$39$		0			0
$40$	4.28115	−	2.10275i	0.676909	−	0.332474i
$41$	2.70179	+	10.0832i	0.421949	+	1.57474i	0.770496	+	0.637445i	$0.220009\pi$
$41$	2.70179	+	10.0832i	0.421949	+	1.57474i	−0.348547	+	0.937291i	$0.613325\pi$
$42$		0			0
$43$	−11.3541	+	1.49479i	−1.73148	+	0.227953i	−0.929350	−	0.369199i	$-0.879632\pi$
$43$	−11.3541	+	1.49479i	−1.73148	+	0.227953i	−0.802128	+	0.597153i	$0.796299\pi$
$44$	1.52361	−	2.63251i	0.229693	−	0.396866i
$45$		0			0
$46$	−0.281897	+	0.246952i	−0.0415635	+	0.0364111i
$47$	5.48788	−	3.16843i	0.800489	−	0.462163i	−0.0431530	−	0.999068i	$-0.513740\pi$
$47$	5.48788	−	3.16843i	0.800489	−	0.462163i	0.843642	+	0.536906i	$0.180407\pi$
$48$		0			0
$49$	3.58404	+	2.06925i	0.512006	+	0.295607i
$50$	2.99115	−	0.593325i	0.423013	−	0.0839088i
$51$		0			0
$52$	−4.62860	−	4.63845i	−0.641872	−	0.643238i
$53$	−0.907259	+	2.19032i	−0.124622	+	0.300863i	−0.973861	−	0.227145i	$-0.927061\pi$
$53$	−0.907259	+	2.19032i	−0.124622	+	0.300863i	0.849239	+	0.528008i	$0.177061\pi$
$54$		0			0
$55$	−1.81345	+	1.81345i	−0.244525	+	0.244525i
$56$	−2.12300	+	4.28776i	−0.283697	+	0.572977i
$57$		0			0
$58$	10.8773	+	2.16964i	1.42826	+	0.284888i
$59$	7.99535	−	6.13505i	1.04091	−	0.798715i	0.0609922	−	0.998138i	$-0.480574\pi$
$59$	7.99535	−	6.13505i	1.04091	−	0.798715i	0.979913	+	0.199423i	$0.0639069\pi$
$60$		0			0
$61$	2.95479	−	3.85076i	0.378322	−	0.493039i	−0.564920	−	0.825146i	$-0.691093\pi$
$61$	2.95479	−	3.85076i	0.378322	−	0.493039i	0.943242	+	0.332107i	$0.107760\pi$
$62$	−4.82185	−	0.318614i	−0.612376	−	0.0404641i
$63$		0			0
$64$	7.38124	+	3.08502i	0.922655	+	0.385627i
$65$	2.76255	+	4.78489i	0.342653	+	0.593492i
$66$		0			0
$67$	10.1544	+	1.33685i	1.24055	+	0.163322i	0.722103	−	0.691786i	$-0.243176\pi$
$67$	10.1544	+	1.33685i	1.24055	+	0.163322i	0.518451	+	0.855108i	$0.326509\pi$
$68$	−6.99247	−	5.37733i	−0.847962	−	0.652097i
$69$		0			0
$70$	2.66154	−	3.03165i	0.318114	−	0.362351i
$71$	7.70797	+	7.70797i	0.914768	+	0.914768i	0.996643	−	0.0818747i	$-0.0260907\pi$
$71$	7.70797	+	7.70797i	0.914768	+	0.914768i	−0.0818747	+	0.996643i	$0.526091\pi$
$72$		0			0
$73$	5.54934	−	5.54934i	0.649501	−	0.649501i	−0.303371	−	0.952873i	$-0.598112\pi$
$73$	5.54934	−	5.54934i	0.649501	−	0.649501i	0.952873	+	0.303371i	$0.0981122\pi$
$74$	−0.451985	−	6.95258i	−0.0525422	−	0.808221i
$75$		0			0
$76$	−1.61418	+	5.99870i	−0.185160	+	0.688098i
$77$	0.335793	−	2.55060i	0.0382671	−	0.290668i
$78$		0			0
$79$	−7.63729	+	4.40939i	−0.859262	+	0.496095i	−0.863765	−	0.503895i	$-0.831900\pi$
$79$	−7.63729	+	4.40939i	−0.859262	+	0.496095i	0.00450297	+	0.999990i	$0.498567\pi$
$80$	−5.34270	−	4.11767i	−0.597332	−	0.460370i
$81$		0			0
$82$	11.1045	−	9.72794i	1.22629	−	1.07427i
$83$	−3.96569	−	3.04298i	−0.435291	−	0.334011i	0.367760	−	0.929921i	$-0.380125\pi$
$83$	−3.96569	−	3.04298i	−0.435291	−	0.334011i	−0.803051	+	0.595910i	$0.796791\pi$
$84$		0			0
$85$	4.52772	+	5.90064i	0.491101	+	0.640015i
$86$	8.99065	+	13.4709i	0.969486	+	1.45261i
$87$		0			0
$88$	−4.29185	−	0.288176i	−0.457513	−	0.0307196i
$89$	−3.40163	−	3.40163i	−0.360572	−	0.360572i	0.503451	−	0.864024i	$-0.332063\pi$
$89$	−3.40163	−	3.40163i	−0.360572	−	0.360572i	−0.864024	+	0.503451i	$0.832063\pi$
$90$		0			0
$91$	−5.12047	−	2.12097i	−0.536771	−	0.222338i
$92$	0.489443	+	0.203344i	0.0510279	+	0.0212000i
$93$		0			0
$94$	−7.44871	−	4.98279i	−0.768275	−	0.513936i
$95$	2.61892	−	4.53609i	0.268695	−	0.465394i
$96$		0			0
$97$	−0.784666	−	1.35908i	−0.0796707	−	0.137994i	0.823437	−	0.567407i	$-0.192054\pi$
$97$	−0.784666	−	1.35908i	−0.0796707	−	0.137994i	−0.903108	+	0.429414i	$0.858720\pi$
$98$	0.385890	−	5.83998i	0.0389807	−	0.589927i
$99$		0			0
$100$	−2.62167	−	3.42416i	−0.262167	−	0.342416i
$101$	−0.842202	−	6.39716i	−0.0838022	−	0.636541i	−0.980872	−	0.194652i	$-0.937642\pi$
$101$	−0.842202	−	6.39716i	−0.0838022	−	0.636541i	0.897070	−	0.441888i	$-0.145691\pi$
$102$		0			0
$103$	−8.61309	+	2.30787i	−0.848673	+	0.227401i	−0.656843	−	0.754027i	$-0.728109\pi$
$103$	−8.61309	+	2.30787i	−0.848673	+	0.227401i	−0.191829	+	0.981428i	$0.561442\pi$
$104$	−2.99279	+	8.77050i	−0.293467	+	0.860018i
$105$		0			0
$106$	3.34573	−	0.217505i	0.324966	−	0.0211260i
$107$	1.32664	−	3.20278i	0.128251	−	0.309625i	−0.846691	−	0.532085i	$-0.821409\pi$
$107$	1.32664	−	3.20278i	0.128251	−	0.309625i	0.974942	+	0.222460i	$0.0714087\pi$
$108$		0			0
$109$	10.2155	−	4.23139i	0.978466	−	0.405294i	0.164609	−	0.986359i	$-0.447364\pi$
$109$	10.2155	−	4.23139i	0.978466	−	0.405294i	0.813857	+	0.581065i	$0.197364\pi$
$110$	3.43380	+	1.16765i	0.327400	+	0.111331i
$111$		0			0
$112$	6.76638	+	0.0143839i	0.639363	+	0.00135915i
$113$	7.14475	+	4.12502i	0.672122	+	0.388050i	0.796880	−	0.604137i	$-0.206482\pi$
$113$	7.14475	+	4.12502i	0.672122	+	0.388050i	−0.124758	+	0.992187i	$0.539816\pi$
$114$		0			0
$115$	−0.354535	−	0.272044i	−0.0330605	−	0.0253682i
$116$	−4.04369	−	15.1557i	−0.375447	−	1.40717i
$117$		0			0
$118$	−12.7792	−	6.31043i	−1.17642	−	0.580923i
$119$	−7.20659	−	1.93100i	−0.660627	−	0.177014i
$120$		0			0
$121$	−8.39111	+	2.24839i	−0.762829	+	0.204399i
$122$	−6.73166	−	1.34273i	−0.609456	−	0.121565i
$123$		0			0
$124$	2.60855	+	6.31657i	0.234254	+	0.567244i
$125$	4.61818	+	11.1493i	0.413062	+	0.997220i
$126$		0			0
$127$	−16.4359			−1.45845			−0.729225	−	0.684274i	$-0.760119\pi$
$127$	−16.4359			−1.45845			−0.729225	+	0.684274i	$0.760119\pi$
$128$	−0.697949	−	11.2922i	−0.0616905	−	0.998095i
$129$		0			0
$130$	4.34450	−	6.49453i	0.381038	−	0.569608i
$131$	−5.24655	−	0.690722i	−0.458394	−	0.0603487i	−0.102206	−	0.994763i	$-0.532590\pi$
$131$	−5.24655	−	0.690722i	−0.458394	−	0.0603487i	−0.356187	+	0.934415i	$0.615923\pi$
$132$		0			0
$133$	0.685808	+	5.20923i	0.0594671	+	0.451697i
$134$	−4.64855	−	13.7181i	−0.401574	−	1.18507i
$135$		0			0
$136$	−2.45322	+	12.2312i	−0.210362	+	1.04882i
$137$	18.5984	+	4.98343i	1.58897	+	0.425763i	0.941688	−	0.336488i	$-0.109239\pi$
$137$	18.5984	+	4.98343i	1.58897	+	0.425763i	0.647282	+	0.762251i	$0.275906\pi$
$138$		0			0
$139$	2.62307	+	3.41845i	0.222486	+	0.289949i	0.891238	−	0.453536i	$-0.149838\pi$
$139$	2.62307	+	3.41845i	0.222486	+	0.289949i	−0.668752	+	0.743486i	$0.733171\pi$
$140$	−5.50923	−	1.48247i	−0.465615	−	0.125292i
$141$		0			0
$142$	4.96305	−	14.5952i	0.416490	−	1.22480i
$143$		−	4.98280i		−	0.416683i
$144$		0			0
$145$			13.2258i			1.09834i
$146$	−10.5078	−	3.57314i	−0.869630	−	0.295715i
$147$		0			0
$148$	−8.53834	+	4.91752i	−0.701847	+	0.404218i
$149$	−13.0949	−	17.0656i	−1.07278	−	1.39807i	−0.911567	−	0.411151i	$-0.865127\pi$
$149$	−13.0949	−	17.0656i	−1.07278	−	1.39807i	−0.161210	−	0.986920i	$-0.551540\pi$
$150$		0			0
$151$	−5.70334	−	1.52821i	−0.464132	−	0.124364i	0.0191726	−	0.999816i	$-0.493897\pi$
$151$	−5.70334	−	1.52821i	−0.464132	−	0.124364i	−0.483304	+	0.875453i	$0.660563\pi$
$152$	8.61913	−	1.70017i	0.699104	−	0.137902i
$153$		0			0
$154$	−3.44576	+	1.16764i	−0.277667	+	0.0940908i
$155$	−0.752119	−	5.71291i	−0.0604116	−	0.458872i
$156$		0			0
$157$	−23.3999	−	3.08065i	−1.86751	−	0.245863i	−0.889882	−	0.456191i	$-0.849213\pi$
$157$	−23.3999	−	3.08065i	−1.86751	−	0.245863i	−0.977631	+	0.210329i	$0.932547\pi$
$158$	10.3661	+	6.93438i	0.824683	+	0.551670i
$159$		0			0
$160$	−1.88589	+	9.35108i	−0.149093	+	0.739268i
$161$	0.448276			0.0353291
$162$		0			0
$163$	8.99541	+	21.7168i	0.704575	+	1.70099i	0.713132	+	0.701030i	$0.247276\pi$
$163$	8.99541	+	21.7168i	0.704575	+	1.70099i	−0.00855734	+	0.999963i	$0.502724\pi$
$164$	−19.2801	−	8.01011i	−1.50552	−	0.625484i
$165$		0			0
$166$	−1.38281	+	6.93258i	−0.107327	+	0.538073i
$167$	−0.501235	+	0.134305i	−0.0387867	+	0.0103929i	−0.278160	−	0.960535i	$-0.589725\pi$
$167$	−0.501235	+	0.134305i	−0.0387867	+	0.0103929i	0.239374	+	0.970928i	$0.423058\pi$
$168$		0			0
$169$	2.18802	+	0.586277i	0.168309	+	0.0450982i
$170$	4.65716	−	9.43115i	0.357188	−	0.723336i
$171$		0			0
$172$	11.4731	−	19.8233i	0.874816	−	1.51151i
$173$	13.3025	+	10.2073i	1.01137	+	0.776050i	0.974754	−	0.223280i	$-0.0716763\pi$
$173$	13.3025	+	10.2073i	1.01137	+	0.776050i	0.0366133	+	0.999330i	$0.488343\pi$
$174$		0			0
$175$	−3.15887	−	1.82377i	−0.238788	−	0.137864i
$176$	2.31601	+	5.62514i	0.174576	+	0.424011i
$177$		0			0
$178$	−2.19026	+	6.44105i	−0.164167	+	0.482777i
$179$	1.92799	−	0.798600i	0.144105	−	0.0596901i	−0.309465	−	0.950911i	$-0.600150\pi$
$179$	1.92799	−	0.798600i	0.144105	−	0.0596901i	0.453570	+	0.891221i	$0.350150\pi$
$180$		0			0
$181$	2.34121	−	5.65218i	0.174021	−	0.420123i	−0.812672	−	0.582722i	$-0.801988\pi$
$181$	2.34121	−	5.65218i	0.174021	−	0.420123i	0.986692	+	0.162599i	$0.0519877\pi$
$182$	0.508478	+	7.82156i	0.0376909	+	0.579773i
$183$		0			0
$184$	−0.0478295	−	0.748009i	−0.00352604	−	0.0551440i
$185$	8.02480	−	2.15024i	0.589995	−	0.158089i
$186$		0			0
$187$	−0.875514	−	6.65019i	−0.0640239	−	0.486310i
$188$	−1.66761	+	12.5635i	−0.121623	+	0.916289i
$189$		0			0
$190$	−7.39129	−	0.488396i	−0.536221	−	0.0354320i
$191$	6.21403	+	10.7630i	0.449632	+	0.778785i	0.998362	−	0.0572147i	$-0.0182219\pi$
$191$	6.21403	+	10.7630i	0.449632	+	0.778785i	−0.548730	+	0.835999i	$0.684889\pi$
$192$		0			0
$193$	−2.09091	+	3.62157i	−0.150507	+	0.260686i	−0.931414	−	0.363961i	$-0.881424\pi$
$193$	−2.09091	+	3.62157i	−0.150507	+	0.260686i	0.780907	+	0.624648i	$0.214757\pi$
$194$	−1.23400	+	1.84468i	−0.0885958	+	0.132440i
$195$		0			0
$196$	−7.65030	+	3.15934i	−0.546450	+	0.225667i
$197$	−20.3832	−	8.44301i	−1.45224	−	0.601539i	−0.489512	−	0.871996i	$-0.662825\pi$
$197$	−20.3832	−	8.44301i	−1.45224	−	0.601539i	−0.962732	+	0.270457i	$0.912825\pi$
$198$		0			0
$199$	−15.4429	−	15.4429i	−1.09472	−	1.09472i	−0.995017	−	0.0997020i	$-0.968211\pi$
$199$	−15.4429	−	15.4429i	−1.09472	−	1.09472i	−0.0997020	−	0.995017i	$-0.531789\pi$
$200$	−2.70618	+	5.46560i	−0.191355	+	0.386476i
$201$		0			0
$202$	−7.58986	+	5.06555i	−0.534021	+	0.356411i
$203$	−8.07648	−	10.5255i	−0.566858	−	0.738744i
$204$		0			0
$205$	13.9658	+	10.7164i	0.975415	+	0.748463i
$206$	8.30960	+	9.48544i	0.578957	+	0.660882i
$207$		0			0
$208$	12.9971	−	1.68300i	0.901186	−	0.116695i
$209$	−4.09086	+	2.36186i	−0.282971	+	0.163373i
$210$		0			0
$211$	1.95250	−	14.8307i	0.134416	−	1.02099i	−0.782709	−	0.622388i	$-0.786163\pi$
$211$	1.95250	−	14.8307i	0.134416	−	1.02099i	0.917125	−	0.398601i	$-0.130504\pi$
$212$	−2.36642	−	4.10883i	−0.162526	−	0.282196i
$213$		0			0
$214$	−4.89228	+	0.318046i	−0.334429	+	0.0217412i
$215$	−13.6556	+	13.6556i	−0.931306	+	0.931306i
$216$		0			0
$217$	4.08721	+	4.08721i	0.277458	+	0.277458i
$218$	−11.7512	−	10.3166i	−0.795890	−	0.698726i
$219$		0			0
$220$	−0.664091	−	5.08604i	−0.0447730	−	0.342901i
$221$	−14.3270	−	1.88618i	−0.963736	−	0.126878i
$222$		0			0
$223$	2.52017	+	4.36506i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$223$	2.52017	+	4.36506i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$224$	−4.20950	−	8.59350i	−0.281259	−	0.574178i
$225$		0			0
$226$	0.769267	−	11.6419i	0.0511709	−	0.774411i
$227$	7.81587	−	10.1858i	0.518758	−	0.676058i	−0.458358	−	0.888768i	$-0.651562\pi$
$227$	7.81587	−	10.1858i	0.518758	−	0.676058i	0.977115	+	0.212710i	$0.0682288\pi$
$228$		0			0
$229$	−3.10314	+	2.38112i	−0.205061	+	0.157349i	−0.706187	−	0.708026i	$-0.749586\pi$
$229$	−3.10314	+	2.38112i	−0.205061	+	0.157349i	0.501126	+	0.865375i	$0.332919\pi$
$230$	−0.123624	+	0.619776i	−0.00815150	+	0.0408668i
$231$		0			0
$232$	−16.7015	+	14.5997i	−1.09650	+	0.958520i
$233$	−13.8895	+	13.8895i	−0.909930	+	0.909930i	−0.996266	−	0.0863363i	$-0.972484\pi$
$233$	−13.8895	+	13.8895i	−0.909930	+	0.909930i	0.0863363	+	0.996266i	$0.472484\pi$
$234$		0			0
$235$	4.08938	−	9.87263i	0.266762	−	0.644020i
$236$	−0.0214235	+	20.1558i	−0.00139455	+	1.31203i
$237$		0			0
$238$	2.05293	+	10.3495i	0.133072	+	0.670861i
$239$	−20.8616	−	12.0444i	−1.34942	−	0.779089i	−0.361255	−	0.932467i	$-0.617651\pi$
$239$	−20.8616	−	12.0444i	−1.34942	−	0.779089i	−0.988168	+	0.153378i	$0.950985\pi$
$240$		0			0
$241$	−18.9896	+	10.9636i	−1.22323	+	0.706230i	−0.965604	−	0.260015i	$-0.916272\pi$
$241$	−18.9896	+	10.9636i	−1.22323	+	0.706230i	−0.257622	+	0.966246i	$0.582939\pi$
$242$	8.09545	+	9.24099i	0.520395	+	0.594033i
$243$		0			0
$244$	2.50253	+	9.37943i	0.160208	+	0.600457i
$245$	6.91919	−	0.910928i	0.442051	−	0.0581971i
$246$		0			0
$247$	2.63391	+	9.82988i	0.167592	+	0.625460i
$248$	6.38398	−	7.25616i	0.405383	−	0.460767i
$249$		0			0
$250$	11.2596	−	12.8253i	0.712118	−	0.811145i
$251$	2.87787	+	1.19205i	0.181649	+	0.0752416i	0.471654	−	0.881783i	$-0.343657\pi$
$251$	2.87787	+	1.19205i	0.181649	+	0.0752416i	−0.290005	+	0.957025i	$0.593657\pi$
$252$		0			0
$253$	0.154228	+	0.372340i	0.00969625	+	0.0234088i
$254$	10.2694	+	20.8523i	0.644361	+	1.30839i
$255$		0			0
$256$	−13.8903	+	7.94102i	−0.868143	+	0.496314i
$257$	−9.68935	+	16.7825i	−0.604405	+	1.04686i	0.387740	+	0.921769i	$0.373256\pi$
$257$	−9.68935	+	16.7825i	−0.604405	+	1.04686i	−0.992145	+	0.125092i	$0.960077\pi$
$258$		0			0
$259$	−5.07330	+	6.61166i	−0.315240	+	0.410828i
$260$	−10.9541	−	1.45399i	−0.679347	−	0.0901724i
$261$		0			0
$262$	2.40181	+	7.08789i	0.148385	+	0.437891i
$263$	−5.21581	+	19.4657i	−0.321621	+	1.20031i	0.596044	+	0.802951i	$0.296738\pi$
$263$	−5.21581	+	19.4657i	−0.321621	+	1.20031i	−0.917665	+	0.397354i	$0.869928\pi$
$264$		0			0
$265$	1.03474	+	3.86171i	0.0635637	+	0.237223i
$266$	6.18045	−	4.12490i	0.378948	−	0.252914i
$267$		0			0
$268$	−14.4997	+	14.4690i	−0.885713	+	0.883832i
$269$	7.02856	−	2.91132i	0.428539	−	0.177507i	−0.157980	−	0.987442i	$-0.550498\pi$
$269$	7.02856	−	2.91132i	0.428539	−	0.177507i	0.586519	+	0.809936i	$0.300498\pi$
$270$		0			0
$271$		−	22.8081i		−	1.38550i	−0.721180	−	0.692748i	$-0.756400\pi$
$271$		−	22.8081i		−	1.38550i	0.721180	−	0.692748i	$-0.243600\pi$
$272$	17.0506	−	4.52986i	1.03384	−	0.274663i
$273$		0			0
$274$	−5.29811	−	26.7096i	−0.320070	−	1.61358i
$275$	0.428034	−	3.25124i	0.0258114	−	0.196057i
$276$		0			0
$277$	2.67963	−	0.352780i	0.161003	−	0.0211965i	−0.0495936	−	0.998769i	$-0.515793\pi$
$277$	2.67963	−	0.352780i	0.161003	−	0.0211965i	0.210597	+	0.977573i	$0.432459\pi$
$278$	2.69806	−	5.46380i	0.161819	−	0.327697i
$279$		0			0
$280$	1.56144	+	7.91584i	0.0933141	+	0.473062i
$281$	2.38877	−	8.91501i	0.142502	−	0.531825i	−0.857352	−	0.514731i	$-0.827892\pi$
$281$	2.38877	−	8.91501i	0.142502	−	0.531825i	0.999854	−	0.0170942i	$-0.00544152\pi$
$282$		0			0
$283$	3.71546	−	2.85097i	0.220861	−	0.169473i	−0.492405	−	0.870366i	$-0.663882\pi$
$283$	3.71546	−	2.85097i	0.220861	−	0.169473i	0.713266	+	0.700894i	$0.247215\pi$
$284$	−21.6179	+	2.82268i	−1.28279	+	0.167495i
$285$		0			0
$286$	−6.32169	+	3.11334i	−0.373809	+	0.184095i
$287$	−17.6585			−1.04235
$288$		0			0
$289$	−2.45260			−0.144271
$290$	16.7796	−	8.26370i	0.985332	−	0.485261i
$291$		0			0
$292$	2.03219	+	15.5638i	0.118925	+	0.910803i
$293$	−4.44030	+	3.40716i	−0.259405	+	0.199048i	−0.730273	−	0.683155i	$-0.760607\pi$
$293$	−4.44030	+	3.40716i	−0.259405	+	0.199048i	0.470868	+	0.882203i	$0.343941\pi$
$294$		0			0
$295$	4.39856	−	16.4157i	0.256094	−	0.955757i
$296$	11.5738	+	7.76006i	0.672711	+	0.451044i
$297$		0			0
$298$	−13.4693	+	27.2764i	−0.780254	+	1.58008i
$299$	0.860822	−	0.113329i	0.0497826	−	0.00655401i
$300$		0			0
$301$	2.52858	−	19.2065i	0.145745	−	1.10704i
$302$	1.62471	+	8.19069i	0.0934913	+	0.471321i
$303$		0			0
$304$	−7.54239	−	9.87282i	−0.432586	−	0.566245i
$305$		−	8.18509i		−	0.468677i
$306$		0			0
$307$	24.4588	−	10.1311i	1.39593	−	0.578215i	0.447242	−	0.894413i	$-0.352406\pi$
$307$	24.4588	−	10.1311i	1.39593	−	0.578215i	0.948693	+	0.316198i	$0.102406\pi$
$308$	3.63435	+	3.64208i	0.207086	+	0.207527i
$309$		0			0
$310$	−6.77804	+	4.52373i	−0.384967	+	0.256931i
$311$	−2.86927	−	10.7082i	−0.162701	−	0.607209i	−0.998322	−	0.0579027i	$-0.981559\pi$
$311$	−2.86927	−	10.7082i	−0.162701	−	0.607209i	0.835621	−	0.549306i	$-0.185108\pi$
$312$		0			0
$313$	5.11934	−	19.1057i	0.289362	−	1.07992i	−0.656230	−	0.754561i	$-0.727850\pi$
$313$	5.11934	−	19.1057i	0.289362	−	1.07992i	0.945592	−	0.325354i	$-0.105484\pi$
$314$	10.7122	+	31.6123i	0.604524	+	1.78398i
$315$		0			0
$316$	2.32075	−	17.4842i	0.130552	−	0.983564i
$317$	17.3714	−	22.6389i	0.975677	−	1.27153i	0.0132711	−	0.999912i	$-0.495776\pi$
$317$	17.3714	−	22.6389i	0.975677	−	1.27153i	0.962406	−	0.271615i	$-0.0875578\pi$
$318$		0			0
$319$	5.96382	−	10.3296i	0.333910	−	0.578349i
$320$	13.0421	−	3.45008i	0.729074	−	0.192865i
$321$		0			0
$322$	−0.280090	−	0.568728i	−0.0156088	−	0.0316940i
$323$	5.24247	+	12.6564i	0.291699	+	0.704223i
$324$		0			0
$325$	−6.52704	−	2.70359i	−0.362055	−	0.149968i
$326$	21.9317	−	24.9815i	1.21468	−	1.38360i
$327$		0			0
$328$	1.88410	+	29.4656i	0.104032	+	1.62696i
$329$	2.77439	+	10.3542i	0.152957	+	0.570843i
$330$		0			0
$331$	11.4893	−	1.51260i	0.631510	−	0.0831398i	0.192025	−	0.981390i	$-0.438494\pi$
$331$	11.4893	−	1.51260i	0.631510	−	0.0831398i	0.439484	+	0.898250i	$0.355161\pi$
$332$	9.65938	−	2.57722i	0.530127	−	0.141443i
$333$		0			0
$334$	0.483573	+	0.552001i	0.0264600	+	0.0302042i
$335$	14.9575	−	8.63571i	0.817215	−	0.471819i
$336$		0			0
$337$	25.3042	+	14.6094i	1.37841	+	0.795824i	0.991968	−	0.126490i	$-0.0403712\pi$
$337$	25.3042	+	14.6094i	1.37841	+	0.795824i	0.386440	+	0.922314i	$0.373705\pi$
$338$	−0.623298	−	3.14226i	−0.0339029	−	0.170916i
$339$		0			0
$340$	−14.8752	−	0.0158108i	−0.806720	−	0.000857460i
$341$	−1.98866	+	4.80106i	−0.107692	+	0.259992i
$342$		0			0
$343$	−13.3232	+	13.3232i	−0.719386	+	0.719386i
$344$	−32.3185	−	2.17002i	−1.74250	−	0.117000i
$345$		0			0
$346$	4.63847	−	23.2546i	0.249366	−	1.25017i
$347$	21.0213	−	16.1302i	1.12848	−	0.865914i	0.136294	−	0.990668i	$-0.456481\pi$
$347$	21.0213	−	16.1302i	1.12848	−	0.865914i	0.992188	+	0.124754i	$0.0398142\pi$
$348$		0			0
$349$	18.9050	−	24.6375i	1.01196	−	1.31882i	0.0648588	−	0.997894i	$-0.479340\pi$
$349$	18.9050	−	24.6375i	1.01196	−	1.31882i	0.947105	−	0.320923i	$-0.103993\pi$
$350$	−0.340112	+	5.14719i	−0.0181797	+	0.275129i
$351$		0			0
$352$	5.68954	−	6.45301i	0.303253	−	0.343946i
$353$	1.57460	+	2.72729i	0.0838077	+	0.145159i	0.904883	−	0.425661i	$-0.139959\pi$
$353$	1.57460	+	2.72729i	0.0838077	+	0.145159i	−0.821075	+	0.570821i	$0.806625\pi$
$354$		0			0
$355$	18.2250	+	2.39937i	0.967283	+	0.127345i
$356$	9.54029	−	1.24569i	0.505634	−	0.0660213i
$357$		0			0
$358$	−2.21782	−	1.94707i	−0.117216	−	0.102906i
$359$	−21.3264	−	21.3264i	−1.12556	−	1.12556i	−0.990890	−	0.134673i	$-0.957002\pi$
$359$	−21.3264	−	21.3264i	−1.12556	−	1.12556i	−0.134673	−	0.990890i	$-0.542998\pi$
$360$		0			0
$361$	−6.61321	+	6.61321i	−0.348064	+	0.348064i
$362$	−8.63375	+	0.561278i	−0.453780	+	0.0295001i
$363$		0			0
$364$	9.60552	−	5.53215i	0.503466	−	0.289963i
$365$	1.72742	−	13.1211i	0.0904173	−	0.686788i
$366$		0			0
$367$	3.18199	−	1.83712i	0.166098	−	0.0958970i	−0.414646	−	0.909983i	$-0.636095\pi$
$367$	3.18199	−	1.83712i	0.166098	−	0.0958970i	0.580745	+	0.814086i	$0.302761\pi$
$368$	−0.919116	+	0.528050i	−0.0479122	+	0.0275265i
$369$		0			0
$370$	−7.74204	−	8.83757i	−0.402489	−	0.459444i
$371$	−3.18167	−	2.44138i	−0.165184	−	0.126750i
$372$		0			0
$373$	−8.19145	−	10.6753i	−0.424137	−	0.552746i	0.531590	−	0.847002i	$-0.321595\pi$
$373$	−8.19145	−	10.6753i	−0.424137	−	0.552746i	−0.955727	+	0.294256i	$0.904928\pi$
$374$	−7.89007	+	5.26591i	−0.407986	+	0.272294i
$375$		0			0
$376$	16.9813	−	5.73420i	0.875744	−	0.295719i
$377$	−18.1702	−	18.1702i	−0.935813	−	0.935813i
$378$		0			0
$379$	−21.1913	−	8.77772i	−1.08852	−	0.450881i	−0.235032	−	0.971988i	$-0.575520\pi$
$379$	−21.1913	−	8.77772i	−1.08852	−	0.450881i	−0.853492	+	0.521106i	$0.825520\pi$
$380$	3.99857	+	9.68251i	0.205122	+	0.496702i
$381$		0			0
$382$	9.77243	−	14.6087i	0.500001	−	0.747444i
$383$	0.0799120	−	0.138412i	0.00408331	−	0.00707251i	−0.863977	−	0.503532i	$-0.832034\pi$
$383$	0.0799120	−	0.138412i	0.00408331	−	0.00707251i	0.868060	+	0.496460i	$0.165367\pi$
$384$		0			0
$385$	−2.16914	−	3.75706i	−0.110550	−	0.191478i
$386$	5.90113	+	0.389930i	0.300360	+	0.0198469i
$387$		0			0
$388$	3.11137	+	0.412985i	0.157956	+	0.0209661i
$389$	0.0159740	+	0.121335i	0.000809915	+	0.00615191i	0.991845	−	0.127450i	$-0.0406791\pi$
$389$	0.0159740	+	0.121335i	0.000809915	+	0.00615191i	−0.991035	+	0.133602i	$0.957346\pi$
$390$		0			0
$391$	1.12897	−	0.302505i	0.0570942	−	0.0152984i
$392$	8.78829	+	7.73195i	0.443876	+	0.390522i
$393$		0			0
$394$	2.02411	+	31.1356i	0.101973	+	1.56859i
$395$	−5.69105	+	13.7394i	−0.286348	+	0.691304i
$396$		0			0
$397$	32.2458	−	13.3567i	1.61837	−	0.670352i	0.624514	−	0.781013i	$-0.285297\pi$
$397$	32.2458	−	13.3567i	1.61837	−	0.670352i	0.993858	+	0.110662i	$0.0352970\pi$
$398$	−9.94347	+	29.2414i	−0.498421	+	1.46574i
$399$		0			0
$400$	8.62507	+	0.0183351i	0.431254	+	0.000916757i
$401$	2.07252	+	1.19657i	0.103497	+	0.0597538i	0.550855	−	0.834601i	$-0.314302\pi$
$401$	2.07252	+	1.19657i	0.103497	+	0.0597538i	−0.447358	+	0.894355i	$0.647635\pi$
$402$		0			0
$403$	8.88195	+	6.81536i	0.442442	+	0.339497i
$404$	11.1689	+	6.46423i	0.555676	+	0.321608i
$405$		0			0
$406$	−8.30737	+	16.8231i	−0.412288	+	0.834919i
$407$	−7.23714	−	1.93919i	−0.358732	−	0.0961218i
$408$		0			0
$409$	−5.34325	+	1.43172i	−0.264206	+	0.0707939i	−0.388490	−	0.921453i	$-0.627003\pi$
$409$	−5.34325	+	1.43172i	−0.264206	+	0.0707939i	0.124284	+	0.992247i	$0.460337\pi$
$410$	4.86978	−	24.4142i	0.240501	−	1.20573i
$411$		0			0
$412$	6.84223	−	16.4691i	0.337092	−	0.811372i
$413$	6.52390	+	15.7501i	0.321020	+	0.775012i
$414$		0			0
$415$	−8.42939			−0.413782
$416$	−10.2560	−	15.4379i	−0.502843	−	0.756904i
$417$		0			0
$418$	5.55253	+	3.71435i	0.271583	+	0.181675i
$419$	−3.69254	−	0.486132i	−0.180392	−	0.0237491i	0.0397888	−	0.999208i	$-0.487331\pi$
$419$	−3.69254	−	0.486132i	−0.180392	−	0.0237491i	−0.220181	+	0.975459i	$0.570665\pi$
$420$		0			0
$421$	−3.12026	−	23.7007i	−0.152072	−	1.15510i	−0.881888	−	0.471458i	$-0.843728\pi$
$421$	−3.12026	−	23.7007i	−0.152072	−	1.15510i	0.729816	−	0.683643i	$-0.239606\pi$
$422$	−20.0357	+	6.78934i	−0.975324	+	0.330500i
$423$		0			0
$424$	−3.73431	+	5.56954i	−0.181354	+	0.270481i
$425$	−9.18621	−	2.46144i	−0.445597	−	0.119397i
$426$		0			0
$427$	4.99832	+	6.51393i	0.241886	+	0.315231i
$428$	3.46028	+	6.00812i	0.167259	+	0.290414i
$429$		0			0
$430$	25.8572	+	8.79266i	1.24694	+	0.424019i
$431$		−	19.4688i		−	0.937780i	−0.883257	−	0.468890i	$-0.844654\pi$
$431$		−	19.4688i		−	0.937780i	0.883257	−	0.468890i	$-0.155346\pi$
$432$		0			0
$433$			33.5242i			1.61107i	0.592549	+	0.805534i	$0.298122\pi$
$433$			33.5242i			1.61107i	−0.592549	+	0.805534i	$0.701878\pi$
$434$	2.63170	−	7.73921i	0.126325	−	0.371494i
$435$		0			0
$436$	−5.74631	+	21.3547i	−0.275198	+	1.02270i
$437$	−0.501075	−	0.653014i	−0.0239697	−	0.0312379i
$438$		0			0
$439$	0.387909	+	0.103940i	0.0185139	+	0.00496079i	0.268064	−	0.963401i	$-0.413616\pi$
$439$	0.387909	+	0.103940i	0.0185139	+	0.00496079i	−0.249550	+	0.968362i	$0.580283\pi$
$440$	−6.03773	+	4.02037i	−0.287837	+	0.191664i
$441$		0			0
$442$	6.55873	+	19.3552i	0.311967	+	0.920632i
$443$	−4.04455	−	30.7214i	−0.192163	−	1.45962i	−0.767156	−	0.641461i	$-0.778329\pi$
$443$	−4.04455	−	30.7214i	−0.192163	−	1.45962i	0.574993	−	0.818158i	$-0.305005\pi$
$444$		0			0
$445$	−8.04294	−	1.05887i	−0.381272	−	0.0501954i
$446$	3.96332	−	5.92471i	0.187669	−	0.280543i
$447$		0			0
$448$	−8.27243	+	10.7100i	−0.390836	+	0.505998i
$449$	29.1609			1.37619			0.688094	−	0.725622i	$-0.258448\pi$
$449$	29.1609			1.37619			0.688094	+	0.725622i	$0.258448\pi$
$450$		0			0
$451$	−6.07536	−	14.6672i	−0.286078	−	0.690652i
$452$	−15.2508	+	6.29811i	−0.717338	+	0.296238i
$453$		0			0
$454$	−17.8063	−	3.55173i	−0.835690	−	0.166691i
$455$	−9.02780	+	2.41899i	−0.423230	+	0.113404i
$456$		0			0
$457$	27.3933	+	7.34002i	1.28141	+	0.343352i	0.834390	−	0.551174i	$-0.185820\pi$
$457$	27.3933	+	7.34002i	1.28141	+	0.343352i	0.447016	+	0.894526i	$0.352487\pi$
$458$	4.95983	+	2.44919i	0.231757	+	0.114443i
$459$		0			0
$460$	0.863553	−	0.230405i	0.0402634	−	0.0107427i
$461$	9.20643	+	7.06434i	0.428786	+	0.329019i	0.800505	−	0.599326i	$-0.204565\pi$
$461$	9.20643	+	7.06434i	0.428786	+	0.329019i	−0.371719	+	0.928345i	$0.621231\pi$
$462$		0			0
$463$	29.3483	+	16.9443i	1.36393	+	0.787467i	0.990145	−	0.140048i	$-0.0447256\pi$
$463$	29.3483	+	16.9443i	1.36393	+	0.787467i	0.373788	+	0.927514i	$0.378059\pi$
$464$	28.9581	+	12.0670i	1.34435	+	0.560197i
$465$		0			0
$466$	26.3000	+	8.94323i	1.21832	+	0.414287i
$467$	30.8911	−	12.7955i	1.42947	−	0.592105i	0.472249	−	0.881465i	$-0.343442\pi$
$467$	30.8911	−	12.7955i	1.42947	−	0.592105i	0.957220	+	0.289360i	$0.0934425\pi$
$468$		0			0
$469$	−6.63012	+	16.0065i	−0.306150	+	0.739112i
$470$	−15.0805	+	0.980382i	−0.695613	+	0.0452217i
$471$		0			0
$472$	25.5851	−	12.5665i	1.17765	−	0.578420i
$473$	16.8230	−	4.50770i	0.773521	−	0.207264i
$474$		0			0
$475$	0.874197	+	6.64018i	0.0401109	+	0.304672i
$476$	11.8478	−	9.07112i	0.543042	−	0.415774i
$477$		0			0
$478$	−2.24614	+	33.9927i	−0.102736	+	1.55479i
$479$	20.0665	+	34.7563i	0.916864	+	1.58805i	0.804149	+	0.594427i	$0.202621\pi$
$479$	20.0665	+	34.7563i	0.916864	+	1.58805i	0.112715	+	0.993627i	$0.464045\pi$
$480$		0			0
$481$	−8.07074	+	13.9789i	−0.367994	+	0.637385i
$482$	25.7746	+	17.2419i	1.17400	+	0.785345i
$483$		0			0
$484$	6.66589	−	16.0446i	0.302995	−	0.729301i
$485$	−2.44497	−	1.01274i	−0.111020	−	0.0459862i
$486$		0			0
$487$	19.0013	+	19.0013i	0.861032	+	0.861032i	0.991458	−	0.130426i	$-0.0416345\pi$
$487$	19.0013	+	19.0013i	0.861032	+	0.861032i	−0.130426	+	0.991458i	$0.541634\pi$
$488$	10.3361	−	9.03539i	0.467892	−	0.409013i
$489$		0			0
$490$	−5.47892	−	8.20922i	−0.247512	−	0.370855i
$491$	11.9422	+	15.5634i	0.538943	+	0.702365i	0.980865	−	0.194689i	$-0.0623697\pi$
$491$	11.9422	+	15.5634i	0.538943	+	0.702365i	−0.441922	+	0.897054i	$0.645703\pi$
$492$		0			0
$493$	−27.4431	−	21.0578i	−1.23598	−	0.948398i
$494$	10.8255	−	9.48352i	0.487061	−	0.426684i
$495$		0			0
$496$	−13.1947	−	3.56560i	−0.592460	−	0.160100i
$497$	−15.9692	+	9.21982i	−0.716316	+	0.413565i
$498$		0			0
$499$	2.99180	−	22.7250i	0.133931	−	1.01731i	−0.784053	−	0.620693i	$-0.786851\pi$
$499$	2.99180	−	22.7250i	0.133931	−	1.01731i	0.917985	−	0.396616i	$-0.129816\pi$
$500$	−23.3067	−	6.27157i	−1.04231	−	0.280473i
$501$		0			0
$502$	−0.285781	−	4.39597i	−0.0127550	−	0.196202i
$503$	−9.49321	+	9.49321i	−0.423281	+	0.423281i	−0.886332	−	0.463051i	$-0.846755\pi$
$503$	−9.49321	+	9.49321i	−0.423281	+	0.423281i	0.463051	+	0.886332i	$0.346755\pi$
$504$		0			0
$505$	−7.69391	−	7.69391i	−0.342375	−	0.342375i
$506$	0.376024	−	0.428314i	0.0167163	−	0.0190409i
$507$		0			0
$508$	20.0388	−	26.0577i	0.889078	−	1.15612i
$509$	−27.8696	−	3.66911i	−1.23530	−	0.162630i	−0.515547	−	0.856861i	$-0.672411\pi$
$509$	−27.8696	−	3.66911i	−1.23530	−	0.162630i	−0.719752	+	0.694231i	$0.755745\pi$
$510$		0			0
$511$	6.63779	+	11.4970i	0.293639	+	0.508597i
$512$	18.7537	+	12.6610i	0.828803	+	0.559541i
$513$		0			0
$514$	27.3460	+	1.80695i	1.20618	+	0.0797010i
$515$	−9.15390	+	11.9296i	−0.403369	+	0.525681i
$516$		0			0
$517$	−7.64569	+	5.86675i	−0.336257	+	0.258019i
$518$	11.5581	+	2.30544i	0.507834	+	0.101295i
$519$		0			0
$520$	4.99965	+	14.8060i	0.219249	+	0.649287i
$521$	15.5551	−	15.5551i	0.681481	−	0.681481i	−0.278853	−	0.960334i	$-0.589954\pi$
$521$	15.5551	−	15.5551i	0.681481	−	0.681481i	0.960334	+	0.278853i	$0.0899541\pi$
$522$		0			0
$523$	−4.62972	+	11.1771i	−0.202443	+	0.488742i	−0.992197	−	0.124683i	$-0.960209\pi$
$523$	−4.62972	+	11.1771i	−0.202443	+	0.488742i	0.789753	+	0.613425i	$0.210209\pi$
$524$	7.49172	−	7.47581i	0.327277	−	0.326582i
$525$		0			0
$526$	27.9551	−	5.54517i	1.21890	−	0.241781i
$527$	13.0516	+	7.53536i	0.568537	+	0.328245i
$528$		0			0
$529$	19.8578	−	11.4649i	0.863381	−	0.498473i
$530$	4.25283	−	3.72564i	0.184731	−	0.161831i
$531$		0			0
$532$	−9.09491	−	5.26385i	−0.394315	−	0.228217i
$533$	−33.9095	+	4.46427i	−1.46878	+	0.193369i
$534$		0			0
$535$	−1.51305	−	5.64676i	−0.0654147	−	0.244131i
$536$	27.4165	+	9.35541i	1.18421	+	0.404092i
$537$		0			0
$538$	−8.08516	−	7.09810i	−0.348576	−	0.306021i
$539$	−5.81479	−	2.40857i	−0.250461	−	0.103744i
$540$		0			0
$541$	1.69081	+	4.08197i	0.0726936	+	0.175498i	0.956050	−	0.293205i	$-0.0947217\pi$
$541$	1.69081	+	4.08197i	0.0726936	+	0.175498i	−0.883356	+	0.468702i	$0.844722\pi$
$542$	−28.9367	+	14.2509i	−1.24294	+	0.612129i
$543$		0			0
$544$	−16.4005	−	18.8018i	−0.703167	−	0.806119i
$545$	9.32304	−	16.1480i	0.399355	−	0.691704i
$546$		0			0
$547$	−18.7296	+	24.4089i	−0.800819	+	1.04365i	0.197177	+	0.980368i	$0.436823\pi$
$547$	−18.7296	+	24.4089i	−0.800819	+	1.04365i	−0.997996	+	0.0632800i	$0.979844\pi$
$548$	−30.5761	+	23.4103i	−1.30615	+	1.00004i
$549$		0			0
$550$	−4.39230	+	1.48838i	−0.187288	+	0.0634648i
$551$	−6.30495	+	23.5304i	−0.268600	+	1.00243i
$552$		0			0
$553$	−3.86102	−	14.4095i	−0.164187	−	0.612755i
$554$	−2.12185	−	3.17923i	−0.0901487	−	0.135072i
$555$		0			0
$556$	−8.61773	−	0.00915975i	−0.365473	−	0.000388460i
$557$	5.80716	−	2.40541i	0.246057	−	0.101920i	−0.256247	−	0.966611i	$-0.582486\pi$
$557$	5.80716	−	2.40541i	0.246057	−	0.101920i	0.502304	+	0.864691i	$0.332486\pi$
$558$		0			0
$559$		−	37.5214i		−	1.58699i
$560$	9.06723	−	6.92696i	0.383160	−	0.292717i
$561$		0			0
$562$	−12.8030	+	2.53961i	−0.540064	+	0.107127i
$563$	−3.40626	+	25.8731i	−0.143557	+	1.09042i	0.756297	+	0.654229i	$0.227007\pi$
$563$	−3.40626	+	25.8731i	−0.143557	+	1.09042i	−0.899853	+	0.436193i	$0.856327\pi$
$564$		0			0
$565$	13.7933	−	1.81593i	0.580290	−	0.0763966i
$566$	−5.93852	−	2.93248i	−0.249615	−	0.123261i
$567$		0			0
$568$	17.0884	+	25.6631i	0.717013	+	1.07680i
$569$	0.769260	−	2.87092i	0.0322491	−	0.120355i	−0.947925	−	0.318494i	$-0.896823\pi$
$569$	0.769260	−	2.87092i	0.0322491	−	0.120355i	0.980174	+	0.198139i	$0.0634897\pi$
$570$		0			0
$571$	−15.0397	+	11.5404i	−0.629393	+	0.482950i	−0.873517	−	0.486794i	$-0.838166\pi$
$571$	−15.0397	+	11.5404i	−0.629393	+	0.482950i	0.244124	+	0.969744i	$0.421500\pi$
$572$	7.89979	+	6.07507i	0.330307	+	0.254012i
$573$		0			0
$574$	11.0333	+	22.4033i	0.460521	+	0.935097i
$575$	0.571415			0.0238297
$576$		0			0
$577$	−10.3704			−0.431725			−0.215862	−	0.976424i	$-0.569256\pi$
$577$	−10.3704			−0.431725			−0.215862	+	0.976424i	$0.569256\pi$
$578$	1.53243	+	3.11162i	0.0637405	+	0.129426i
$579$		0			0
$580$	−20.9683	−	16.1250i	−0.870663	−	0.669554i
$581$	6.70836	−	5.14750i	0.278309	−	0.213554i
$582$		0			0
$583$	0.933178	−	3.48267i	0.0386483	−	0.144237i
$584$	18.4761	−	12.3028i	0.764546	−	0.509092i
$585$		0			0
$586$	7.09704	+	3.50456i	0.293176	+	0.144772i
$587$	23.7322	−	3.12440i	0.979532	−	0.128958i	0.376278	−	0.926507i	$-0.377204\pi$
$587$	23.7322	−	3.12440i	0.979532	−	0.128958i	0.603254	+	0.797549i	$0.293871\pi$
$588$		0			0
$589$	1.38532	−	10.5226i	0.0570811	−	0.433574i
$590$	−23.5749	+	4.67631i	−0.970562	+	0.192521i
$591$		0			0
$592$	2.61372	−	19.5323i	0.107423	−	0.802771i
$593$			8.10188i			0.332704i	0.986066	+	0.166352i	$0.0531988\pi$
$593$			8.10188i			0.332704i	−0.986066	+	0.166352i	$0.946801\pi$
$594$		0			0
$595$	−11.6237	+	4.81470i	−0.476526	+	0.197384i
$596$	43.0215	+	0.0457274i	1.76223	+	0.00187307i
$597$		0			0
$598$	−0.681637	−	1.02132i	−0.0278742	−	0.0417648i
$599$	3.11924	+	11.6412i	0.127449	+	0.475645i	0.999915	−	0.0130288i	$-0.00414733\pi$
$599$	3.11924	+	11.6412i	0.127449	+	0.475645i	−0.872466	+	0.488674i	$0.837481\pi$
$600$		0			0
$601$	5.51080	−	20.5666i	0.224790	−	0.838929i	−0.757698	−	0.652605i	$-0.773676\pi$
$601$	5.51080	−	20.5666i	0.224790	−	0.838929i	0.982488	−	0.186324i	$-0.0596573\pi$
$602$	−25.9472	+	8.79252i	−1.05753	+	0.358356i
$603$		0			0
$604$	9.37640	−	7.17895i	0.381520	−	0.292107i
$605$	−8.91799	+	11.6221i	−0.362568	+	0.472508i
$606$		0			0
$607$	5.27315	−	9.13337i	0.214031	−	0.370712i	−0.738942	−	0.673770i	$-0.764674\pi$
$607$	5.27315	−	9.13337i	0.214031	−	0.370712i	0.952972	+	0.303057i	$0.0980074\pi$
$608$	−7.81305	+	15.7377i	−0.316861	+	0.638250i
$609$		0			0
$610$	−10.3844	+	5.11418i	−0.420454	+	0.207067i
$611$	7.94530	+	19.1817i	0.321432	+	0.776007i
$612$		0			0
$613$	−34.2121	−	14.1711i	−1.38181	−	0.572366i	−0.436848	−	0.899535i	$-0.643905\pi$
$613$	−34.2121	−	14.1711i	−1.38181	−	0.572366i	−0.944966	+	0.327169i	$0.893905\pi$
$614$	−28.1356	−	24.7008i	−1.13546	−	0.996842i
$615$		0			0
$616$	2.34992	−	6.88654i	0.0946808	−	0.277467i
$617$	−3.39826	−	12.6825i	−0.136809	−	0.510577i	−0.999984	−	0.00567237i	$-0.998194\pi$
$617$	−3.39826	−	12.6825i	−0.136809	−	0.510577i	0.863175	−	0.504904i	$-0.168472\pi$
$618$		0			0
$619$	−9.56153	+	1.25880i	−0.384310	+	0.0505954i	−0.320206	−	0.947348i	$-0.603752\pi$
$619$	−9.56153	+	1.25880i	−0.384310	+	0.0505954i	−0.0641040	+	0.997943i	$0.520419\pi$
$620$	9.97430	+	5.77281i	0.400578	+	0.231842i
$621$		0			0
$622$	−11.7928	+	10.3309i	−0.472849	+	0.414233i
$623$	7.04742	−	4.06883i	0.282349	−	0.163014i
$624$		0			0
$625$	8.28710	+	4.78456i	0.331484	+	0.191382i
$626$	−27.4380	+	5.44261i	−1.09664	+	0.217530i
$627$		0			0
$628$	33.4134	−	33.3425i	1.33334	−	1.33051i
$629$	−8.31524	+	20.0748i	−0.331551	+	0.800434i
$630$		0			0
$631$	−24.0104	+	24.0104i	−0.955838	+	0.955838i	−0.999065	−	0.0432274i	$-0.986236\pi$
$631$	−24.0104	+	24.0104i	−0.955838	+	0.955838i	0.0432274	+	0.999065i	$0.486236\pi$
$632$	−23.6323	+	7.98009i	−0.940042	+	0.317431i
$633$		0			0
$634$	−39.5760	−	7.89402i	−1.57176	−	0.313511i
$635$	−21.9889	+	16.8727i	−0.872604	+	0.669573i
$636$		0			0
$637$	−8.25442	+	10.7574i	−0.327052	+	0.426222i
$638$	−16.8315	−	1.11218i	−0.666366	−	0.0440316i
$639$		0			0
$640$	−12.5260	−	14.3908i	−0.495134	−	0.568847i
$641$	−2.50026	−	4.33058i	−0.0987544	−	0.171048i	0.812415	−	0.583080i	$-0.198152\pi$
$641$	−2.50026	−	4.33058i	−0.0987544	−	0.171048i	−0.911169	+	0.412032i	$0.864819\pi$
$642$		0			0
$643$	−7.64282	−	1.00620i	−0.301404	−	0.0396805i	−0.0216923	−	0.999765i	$-0.506905\pi$
$643$	−7.64282	−	1.00620i	−0.301404	−	0.0396805i	−0.279711	+	0.960084i	$0.590239\pi$
$644$	−0.546542	+	0.710702i	−0.0215368	+	0.0280056i
$645$		0			0
$646$	12.7817	−	14.5591i	0.502888	−	0.572820i
$647$	−6.14577	−	6.14577i	−0.241615	−	0.241615i	0.575903	−	0.817518i	$-0.304651\pi$
$647$	−6.14577	−	6.14577i	−0.241615	−	0.241615i	−0.817518	+	0.575903i	$0.804651\pi$
$648$		0			0
$649$	−10.8376	+	10.8376i	−0.425412	+	0.425412i
$650$	0.648154	+	9.97011i	0.0254227	+	0.391060i
$651$		0			0
$652$	−45.3974	−	12.2159i	−1.77790	−	0.478413i
$653$	0.204395	−	1.55253i	0.00799858	−	0.0607552i	−0.986980	−	0.160843i	$-0.948579\pi$
$653$	0.204395	−	1.55253i	0.00799858	−	0.0607552i	0.994979	+	0.100087i	$0.0319122\pi$
$654$		0			0
$655$	−7.72823	+	4.46190i	−0.301967	+	0.174341i
$656$	36.2058	−	20.8009i	1.41360	−	0.812140i
$657$		0			0
$658$	11.4029	−	9.98932i	0.444530	−	0.389424i
$659$	3.36974	+	2.58569i	0.131266	+	0.100724i	0.672308	−	0.740272i	$-0.265303\pi$
$659$	3.36974	+	2.58569i	0.131266	+	0.100724i	−0.541042	+	0.840996i	$0.681970\pi$
$660$		0			0
$661$	−15.2293	−	19.8472i	−0.592352	−	0.771968i	0.396952	−	0.917839i	$-0.370068\pi$
$661$	−15.2293	−	19.8472i	−0.592352	−	0.771968i	−0.989304	+	0.145872i	$0.953401\pi$
$662$	−9.09774	−	13.6314i	−0.353594	−	0.529800i
$663$		0			0
$664$	−9.30507	−	10.6446i	−0.361107	−	0.413090i
$665$	6.26518	+	6.26518i	0.242953	+	0.242953i
$666$		0			0
$667$	1.92018	+	0.795364i	0.0743496	+	0.0307966i
$668$	0.398180	−	0.958410i	0.0154061	−	0.0370820i
$669$		0			0
$670$	−20.3018	−	13.5809i	−0.784328	−	0.524675i
$671$	−3.69085	+	6.39273i	−0.142484	+	0.246789i
$672$		0			0
$673$	−3.02334	−	5.23658i	−0.116541	−	0.201856i	0.801854	−	0.597521i	$-0.203847\pi$
$673$	−3.02334	−	5.23658i	−0.116541	−	0.201856i	−0.918395	+	0.395665i	$0.870514\pi$
$674$	2.72447	−	41.2317i	0.104943	−	1.58819i
$675$		0			0
$676$	−3.59714	+	2.75411i	−0.138352	+	0.105927i
$677$	−5.56436	−	42.2655i	−0.213856	−	1.62439i	−0.675521	−	0.737341i	$-0.736081\pi$
$677$	−5.56436	−	42.2655i	−0.213856	−	1.62439i	0.461665	−	0.887054i	$-0.347252\pi$
$678$		0			0
$679$	2.56422	−	0.687081i	0.0984058	−	0.0263678i
$680$	9.27420	+	18.8821i	0.355650	+	0.724094i
$681$		0			0
$682$	7.33366	−	0.476759i	0.280820	−	0.0182561i
$683$	14.7415	−	35.5892i	0.564069	−	1.36178i	−0.342418	−	0.939548i	$-0.611246\pi$
$683$	14.7415	−	35.5892i	0.564069	−	1.36178i	0.906486	−	0.422235i	$-0.138754\pi$
$684$		0			0
$685$	29.9979	−	12.4256i	1.14616	−	0.474756i
$686$	25.2277	+	8.57862i	0.963199	+	0.327533i
$687$		0			0
$688$	17.4400	+	42.3584i	0.664894	+	1.61490i
$689$	−6.72697	−	3.88382i	−0.256277	−	0.147962i
$690$		0			0
$691$	36.0252	+	27.6431i	1.37046	+	1.05159i	0.992035	+	0.125961i	$0.0402013\pi$
$691$	36.0252	+	27.6431i	1.37046	+	1.05159i	0.378426	+	0.925631i	$0.376465\pi$
$692$	−32.4013	+	8.64501i	−1.23171	+	0.328634i
$693$		0			0
$694$	−33.5989	−	16.5913i	−1.27540	−	0.629798i
$695$	7.01860	+	1.88063i	0.266231	+	0.0713363i
$696$		0			0
$697$	−44.4722	+	11.9163i	−1.68450	+	0.451362i
$698$	−43.0699	−	8.59093i	−1.63022	−	0.325171i
$699$		0			0
$700$	6.74275	−	2.78455i	0.254852	−	0.105246i
$701$	−2.76225	−	6.66866i	−0.104329	−	0.251872i	0.863092	−	0.505047i	$-0.168525\pi$
$701$	−2.76225	−	6.66866i	−0.104329	−	0.251872i	−0.967420	+	0.253176i	$0.918525\pi$
$702$		0			0
$703$	15.3022			0.577134
$704$	−11.7419	−	3.18639i	−0.442538	−	0.120091i
$705$		0			0
$706$	2.47628	−	3.70176i	0.0931961	−	0.139318i
$707$	10.8214	+	1.42467i	0.406981	+	0.0535801i
$708$		0			0
$709$	3.77625	+	28.6835i	0.141820	+	1.07723i	0.903290	+	0.429030i	$0.141145\pi$
$709$	3.77625	+	28.6835i	0.141820	+	1.07723i	−0.761470	+	0.648200i	$0.775522\pi$
$710$	−8.34320	−	24.6213i	−0.313115	−	0.924019i
$711$		0			0
$712$	−7.54133	−	11.3255i	−0.282623	−	0.424439i
$713$	−0.874655	−	0.234363i	−0.0327561	−	0.00877697i
$714$		0			0
$715$	−5.11522	−	6.66629i	−0.191298	−	0.249305i
$716$	−1.08451	+	4.03032i	−0.0405302	+	0.150620i
$717$		0			0
$718$	−13.7317	+	40.3819i	−0.512464	+	1.50704i
$719$			8.15498i			0.304129i	0.988371	+	0.152065i	$0.0485922\pi$
$719$			8.15498i			0.304129i	−0.988371	+	0.152065i	$0.951408\pi$
$720$		0			0
$721$		−	15.0839i		−	0.561752i
$722$	12.5222	+	4.25815i	0.466029	+	0.158472i
$723$		0			0
$724$	6.10661	+	10.6030i	0.226950	+	0.394056i
$725$	−10.2951	−	13.4168i	−0.382349	−	0.498287i
$726$		0			0
$727$	16.0216	+	4.29297i	0.594207	+	0.159217i	0.543375	−	0.839490i	$-0.317146\pi$
$727$	16.0216	+	4.29297i	0.594207	+	0.159217i	0.0508318	+	0.998707i	$0.483813\pi$
$728$	−13.0203	−	8.72997i	−0.482566	−	0.323554i
$729$		0			0
$730$	−17.7260	+	6.00668i	−0.656070	+	0.222317i
$731$	−6.59279	−	50.0772i	−0.243843	−	1.85217i
$732$		0			0
$733$	29.2323	+	3.84851i	1.07972	+	0.142148i	0.649339	−	0.760499i	$-0.275046\pi$
$733$	29.2323	+	3.84851i	1.07972	+	0.142148i	0.430382	+	0.902647i	$0.358379\pi$
$734$	−4.31892	−	2.88913i	−0.159414	−	0.106640i
$735$		0			0
$736$	1.24422	+	0.836150i	0.0458624	+	0.0308209i
$737$	−15.5762			−0.573756
$738$		0			0
$739$	11.5254	+	27.8248i	0.423969	+	1.02355i	0.981165	+	0.193171i	$0.0618771\pi$
$739$	11.5254	+	27.8248i	0.423969	+	1.02355i	−0.557196	+	0.830381i	$0.688123\pi$
$740$	−6.37489	+	15.3442i	−0.234346	+	0.564064i
$741$		0			0
$742$	−1.10943	+	5.56201i	−0.0407283	+	0.204188i
$743$	0.691052	−	0.185167i	0.0253522	−	0.00679311i	−0.246121	−	0.969239i	$-0.579156\pi$
$743$	0.691052	−	0.185167i	0.0253522	−	0.00679311i	0.271473	+	0.962446i	$0.412489\pi$
$744$		0			0
$745$	−35.0383	−	9.38849i	−1.28371	−	0.343968i
$746$	−8.42562	+	17.0626i	−0.308484	+	0.624707i
$747$		0			0
$748$	11.6107	+	6.71992i	0.424530	+	0.245704i
$749$	4.65239	+	3.56990i	0.169995	+	0.130441i
$750$		0			0
$751$	−40.1090	−	23.1569i	−1.46360	−	0.845008i	−0.464422	−	0.885614i	$-0.653738\pi$
$751$	−40.1090	−	23.1569i	−1.46360	−	0.845008i	−0.999175	+	0.0406055i	$0.987071\pi$
$752$	−17.8852	−	17.9614i	−0.652206	−	0.654985i
$753$		0			0
$754$	−11.6995	+	34.4056i	−0.426072	+	1.25298i
$755$	−9.19909	+	3.81039i	−0.334789	+	0.138674i
$756$		0			0
$757$	−8.60103	+	20.7647i	−0.312610	+	0.754707i	0.686997	+	0.726660i	$0.258929\pi$
$757$	−8.60103	+	20.7647i	−0.312610	+	0.754707i	−0.999607	+	0.0280464i	$0.991071\pi$
$758$	2.10436	+	32.3699i	0.0764338	+	1.17573i
$759$		0			0
$760$	9.78584	−	11.1228i	0.354970	−	0.403466i
$761$	16.3399	−	4.37826i	0.592321	−	0.158712i	0.0498071	−	0.998759i	$-0.484139\pi$
$761$	16.3399	−	4.37826i	0.592321	−	0.158712i	0.542514	+	0.840047i	$0.317473\pi$
$762$		0			0
$763$	2.44140	+	18.5443i	0.0883845	+	0.671347i
$764$	−24.6400	−	3.27057i	−0.891445	−	0.118325i
$765$		0			0
$766$	−0.225533	−	0.0149026i	−0.00814886	−	0.000538454i
$767$	16.5096	+	28.5955i	0.596129	+	1.03253i
$768$		0			0
$769$	8.24598	−	14.2825i	0.297358	−	0.515038i	−0.678173	−	0.734902i	$-0.737228\pi$
$769$	8.24598	−	14.2825i	0.297358	−	0.515038i	0.975531	+	0.219864i	$0.0705613\pi$
$770$	−3.41128	+	5.09947i	−0.122934	+	0.183772i
$771$		0			0
$772$	−3.19242	−	7.73041i	−0.114898	−	0.278223i
$773$	29.2079	+	12.0983i	1.05053	+	0.435145i	0.840082	−	0.542459i	$-0.182507\pi$
$773$	29.2079	+	12.0983i	1.05053	+	0.435145i	0.210452	+	0.977604i	$0.432507\pi$
$774$		0			0
$775$	5.20995	+	5.20995i	0.187147	+	0.187147i
$776$	−1.42008	−	4.20544i	−0.0509780	−	0.150967i
$777$		0			0
$778$	0.143957	−	0.0960782i	0.00516110	−	0.00344457i
$779$	19.7383	+	25.7235i	0.707200	+	0.921640i
$780$		0			0
$781$	−13.1522	−	10.0920i	−0.470623	−	0.361121i
$782$	−1.08919	−	1.24331i	−0.0389492	−	0.0444607i
$783$		0			0
$784$	4.31847	−	15.9808i	0.154231	−	0.570742i
$785$	−34.4683	+	19.9003i	−1.23022	+	0.710271i
$786$		0			0
$787$	1.72837	−	13.1283i	0.0616099	−	0.467974i	−0.932633	−	0.360826i	$-0.882495\pi$
$787$	1.72837	−	13.1283i	0.0616099	−	0.467974i	0.994243	−	0.107148i	$-0.0341718\pi$
$788$	38.2370	−	22.0220i	1.36214	−	0.784502i
$789$		0			0
$790$	20.9871	−	1.36436i	0.746686	−	0.0485419i
$791$	−9.86822	+	9.86822i	−0.350873	+	0.350873i
$792$		0			0
$793$	11.2450	+	11.2450i	0.399323	+	0.399323i
$794$	−37.0934	−	32.5649i	−1.31639	−	1.15568i
$795$		0			0
$796$	43.3115	−	5.65524i	1.53514	−	0.200445i
$797$	5.17355	+	0.681111i	0.183257	+	0.0241262i	0.221596	−	0.975139i	$-0.428873\pi$
$797$	5.17355	+	0.681111i	0.183257	+	0.0241262i	−0.0383392	+	0.999265i	$0.512207\pi$
$798$		0			0
$799$	13.9744	+	24.2043i	0.494378	+	0.856288i
$800$	−5.36583	−	10.9541i	−0.189711	−	0.387286i
$801$		0			0
$802$	0.223146	−	3.37704i	0.00787955	−	0.119248i
$803$	−7.26575	+	9.46890i	−0.256403	+	0.334150i
$804$		0			0
$805$	0.599730	−	0.460189i	0.0211377	−	0.0162195i
$806$	3.09707	−	15.5269i	0.109090	−	0.546912i
$807$		0			0
$808$	1.22264	−	18.2090i	0.0430124	−	0.640591i
$809$	24.1097	−	24.1097i	0.847652	−	0.847652i	−0.142188	−	0.989840i	$-0.545414\pi$
$809$	24.1097	−	24.1097i	0.847652	−	0.847652i	0.989840	+	0.142188i	$0.0454137\pi$
$810$		0			0
$811$	11.0614	−	26.7045i	0.388417	−	0.937722i	−0.601859	−	0.798603i	$-0.705573\pi$
$811$	11.0614	−	26.7045i	0.388417	−	0.937722i	0.990276	−	0.139119i	$-0.0444270\pi$
$812$	26.5341	+	0.0282030i	0.931166	+	0.000989732i
$813$		0			0
$814$	2.06164	+	10.3934i	0.0722603	+	0.364289i
$815$	34.3286	+	19.8196i	1.20248	+	0.694250i
$816$		0			0
$817$	−30.8050	+	17.7853i	−1.07773	+	0.622227i
$818$	5.15497	+	5.88442i	0.180239	+	0.205744i
$819$		0			0
$820$	−34.0171	+	9.07611i	−1.18793	+	0.316951i
$821$	−30.0421	+	3.95511i	−1.04848	+	0.138034i	−0.635025	−	0.772492i	$-0.719010\pi$
$821$	−30.0421	+	3.95511i	−1.04848	+	0.138034i	−0.413451	+	0.910526i	$0.635677\pi$
$822$		0			0
$823$	7.16191	+	26.7286i	0.249649	+	0.931701i	0.970990	+	0.239121i	$0.0768594\pi$
$823$	7.16191	+	26.7286i	0.249649	+	0.931701i	−0.721341	+	0.692580i	$0.756474\pi$
$824$	−25.1695	+	1.60940i	−0.876820	+	0.0560660i
$825$		0			0
$826$	15.9059	−	18.1178i	0.553438	−	0.630399i
$827$	−12.9280	−	5.35495i	−0.449551	−	0.186210i	0.146409	−	0.989224i	$-0.453228\pi$
$827$	−12.9280	−	5.35495i	−0.449551	−	0.186210i	−0.595960	+	0.803014i	$0.703228\pi$
$828$		0			0
$829$	12.7277	+	30.7274i	0.442051	+	1.06721i	0.975228	+	0.221202i	$0.0709979\pi$
$829$	12.7277	+	30.7274i	0.442051	+	1.06721i	−0.533177	+	0.846004i	$0.679002\pi$
$830$	5.26682	+	10.6944i	0.182814	+	0.371207i
$831$		0			0
$832$	−13.1779	+	22.6577i	−0.456862	+	0.785513i
$833$	−9.12644	+	15.8075i	−0.316212	+	0.547696i
$834$		0			0
$835$	−0.532707	+	0.694238i	−0.0184351	+	0.0240251i
$836$	1.24309	−	9.36530i	0.0429933	−	0.323906i
$837$		0			0
$838$	1.69040	+	4.98847i	0.0583940	+	0.172324i
$839$	2.75566	−	10.2843i	0.0951359	−	0.355052i	−0.901904	−	0.431936i	$-0.857831\pi$
$839$	2.75566	−	10.2843i	0.0951359	−	0.355052i	0.997040	+	0.0768842i	$0.0244972\pi$
$840$		0			0
$841$	−8.41458	−	31.4036i	−0.290158	−	1.08288i
$842$	−28.1195	+	18.7673i	−0.969063	+	0.646763i
$843$		0			0
$844$	21.1323	+	21.1773i	0.727404	+	0.728951i
$845$	3.52912	−	1.46181i	0.121405	−	0.0502877i
$846$		0			0
$847$		−	14.6951i		−	0.504930i
$848$	9.39935	+	1.25778i	0.322775	+	0.0431924i
$849$		0			0
$850$	2.61687	+	13.1925i	0.0897578	+	0.452499i
$851$	0.170409	−	1.29438i	0.00584154	−	0.0443709i
$852$		0			0
$853$	−15.7760	+	2.07695i	−0.540159	+	0.0711133i	−0.395669	−	0.918393i	$-0.629487\pi$
$853$	−15.7760	+	2.07695i	−0.540159	+	0.0711133i	−0.144490	+	0.989506i	$0.546154\pi$
$854$	5.14121	−	10.4114i	0.175929	−	0.356270i
$855$		0			0
$856$	5.46048	−	8.14404i	0.186635	−	0.278358i
$857$	3.78432	−	14.1233i	0.129270	−	0.482442i	−0.870686	−	0.491840i	$-0.836325\pi$
$857$	3.78432	−	14.1233i	0.129270	−	0.482442i	0.999956	+	0.00939732i	$0.00299130\pi$
$858$		0			0
$859$	−15.3196	+	11.7552i	−0.522699	+	0.401081i	−0.836131	−	0.548530i	$-0.815188\pi$
$859$	−15.3196	+	11.7552i	−0.522699	+	0.401081i	0.313432	+	0.949611i	$0.398521\pi$
$860$	−5.00073	−	38.2988i	−0.170523	−	1.30598i
$861$		0			0
$862$	−24.7001	+	12.1644i	−0.841289	+	0.414322i
$863$	18.9698			0.645741			0.322870	−	0.946443i	$-0.395352\pi$
$863$	18.9698			0.645741			0.322870	+	0.946443i	$0.395352\pi$
$864$		0			0
$865$	28.2754			0.961394
$866$	42.5322	−	20.9464i	1.44530	−	0.711789i
$867$		0			0
$868$	−11.4631	+	1.49675i	−0.389082	+	0.0508030i
$869$	10.6402	−	8.16455i	0.360946	−	0.276963i
$870$		0			0
$871$	−8.68515	+	32.4134i	−0.294285	+	1.09829i
$872$	30.6831	−	6.05242i	1.03906	−	0.204961i
$873$		0			0
$874$	−0.515400	+	1.04373i	−0.0174337	+	0.0353046i
$875$	−20.2394	+	2.66456i	−0.684215	+	0.0900786i
$876$		0			0
$877$	−3.24722	+	24.6651i	−0.109651	+	0.832880i	0.844919	+	0.534894i	$0.179648\pi$
$877$	−3.24722	+	24.6651i	−0.109651	+	0.832880i	−0.954570	+	0.297986i	$0.903685\pi$
$878$	−0.110503	−	0.557085i	−0.00372931	−	0.0188007i
$879$		0			0
$880$	8.87313	+	5.14808i	0.299113	+	0.173542i
$881$			6.47311i			0.218085i	0.994037	+	0.109042i	$0.0347784\pi$
$881$			6.47311i			0.218085i	−0.994037	+	0.109042i	$0.965222\pi$
$882$		0			0
$883$	−40.6004	+	16.8172i	−1.36631	+	0.565944i	−0.940786	−	0.339002i	$-0.889911\pi$
$883$	−40.6004	+	16.8172i	−1.36631	+	0.565944i	−0.425525	+	0.904947i	$0.639911\pi$
$884$	20.4579	−	20.4145i	0.688075	−	0.686614i
$885$		0			0
$886$	−36.4492	+	24.3266i	−1.22454	+	0.817268i
$887$	−8.16806	−	30.4836i	−0.274257	−	1.02354i	−0.956338	−	0.292263i	$-0.905592\pi$
$887$	−8.16806	−	30.4836i	−0.274257	−	1.02354i	0.682081	−	0.731276i	$-0.261075\pi$
$888$		0			0
$889$	7.19593	−	26.8556i	0.241344	−	0.900707i
$890$	3.68197	+	10.8657i	0.123420	+	0.364219i
$891$		0			0
$892$	−9.99304	−	1.32642i	−0.334592	−	0.0444117i
$893$	11.9820	−	15.6152i	0.400962	−	0.522543i
$894$		0			0
$895$	1.75956	−	3.04764i	0.0588155	−	0.101871i
$896$	18.7565	+	3.80349i	0.626610	+	0.127066i
$897$		0			0
$898$	−18.2202	−	36.9965i	−0.608016	−	1.23459i
$899$	10.2556	+	24.7593i	0.342045	+	0.825769i
$900$		0			0
$901$	−9.66042	−	4.00148i	−0.321835	−	0.133308i
$902$	−14.8123	+	16.8721i	−0.493197	+	0.561781i
$903$		0			0
$904$	17.5194	+	15.4136i	0.582686	+	0.512648i
$905$	−2.67018	−	9.96525i	−0.0887598	−	0.331256i
$906$		0			0
$907$	3.60365	−	0.474430i	0.119657	−	0.0157532i	−0.0704596	−	0.997515i	$-0.522447\pi$
$907$	3.60365	−	0.474430i	0.119657	−	0.0157532i	0.190117	+	0.981761i	$0.439113\pi$
$908$	6.61958	+	24.8100i	0.219678	+	0.823350i
$909$		0			0
$910$	8.70970	+	9.94216i	0.288724	+	0.329579i
$911$	−0.465525	+	0.268771i	−0.0154235	+	0.00890478i	−0.507692	−	0.861539i	$-0.669501\pi$
$911$	−0.465525	+	0.268771i	−0.0154235	+	0.00890478i	0.492268	+	0.870443i	$0.336168\pi$
$912$		0			0
$913$	6.58354	+	3.80101i	0.217883	+	0.125795i
$914$	−7.80351	−	39.3402i	−0.258117	−	1.30126i
$915$		0			0
$916$	0.00831486	−	7.82284i	0.000274731	−	0.258474i
$917$	3.42565	−	8.27024i	0.113125	−	0.273107i
$918$		0			0
$919$	22.5820	−	22.5820i	0.744911	−	0.744911i	−0.228608	−	0.973519i	$-0.573417\pi$
$919$	22.5820	−	22.5820i	0.744911	−	0.744911i	0.973519	+	0.228608i	$0.0734173\pi$
$920$	−0.831878	−	0.951631i	−0.0274262	−	0.0313743i
$921$		0			0
$922$	3.21021	−	16.0941i	0.105723	−	0.530032i
$923$	−28.3347	+	21.7420i	−0.932648	+	0.715646i
$924$		0			0
$925$	−6.46692	+	8.42785i	−0.212631	+	0.277106i
$926$	3.15990	−	47.8213i	0.103841	−	1.57151i
$927$		0			0
$928$	−2.78404	−	44.2788i	−0.0913907	−	1.45352i
$929$	−13.8436	−	23.9777i	−0.454192	−	0.786684i	0.544449	−	0.838794i	$-0.316739\pi$
$929$	−13.8436	−	23.9777i	−0.454192	−	0.786684i	−0.998641	+	0.0521098i	$0.983405\pi$
$930$		0			0
$931$	12.7444	+	1.67783i	0.417680	+	0.0549886i
$932$	−5.08637	−	38.9547i	−0.166610	−	1.27600i
$933$		0			0
$934$	−35.5349	−	31.1967i	−1.16274	−	1.02079i
$935$	−7.99824	−	7.99824i	−0.261570	−	0.261570i
$936$		0			0
$937$	−11.9521	+	11.9521i	−0.390457	+	0.390457i	−0.874850	−	0.484393i	$-0.839040\pi$
$937$	−11.9521	+	11.9521i	−0.390457	+	0.390457i	0.484393	+	0.874850i	$0.339040\pi$
$938$	24.4501	−	1.58950i	0.798324	−	0.0518989i
$939$		0			0
$940$	10.6664	+	18.5201i	0.347899	+	0.604061i
$941$	−3.69048	+	28.0320i	−0.120306	+	0.913816i	0.819732	+	0.572747i	$0.194122\pi$
$941$	−3.69048	+	28.0320i	−0.120306	+	0.913816i	−0.940038	+	0.341069i	$0.889211\pi$
$942$		0			0
$943$	2.39571	−	1.38317i	0.0780151	−	0.0450421i
$944$	−31.9292	−	24.6081i	−1.03921	−	0.800926i
$945$		0			0
$946$	−16.2302	−	18.5269i	−0.527689	−	0.602360i
$947$	7.55254	+	5.79527i	0.245425	+	0.188321i	0.724147	−	0.689645i	$-0.242233\pi$
$947$	7.55254	+	5.79527i	0.245425	+	0.188321i	−0.478723	+	0.877966i	$0.658900\pi$
$948$		0			0
$949$	15.6531	+	20.3995i	0.508121	+	0.662197i
$950$	7.87820	−	5.25799i	0.255603	−	0.170592i
$951$		0			0
$952$	−18.9112	−	9.36350i	−0.612916	−	0.303473i
$953$	−33.5836	−	33.5836i	−1.08788	−	1.08788i	−0.995747	−	0.0921329i	$-0.970632\pi$
$953$	−33.5836	−	33.5836i	−1.08788	−	1.08788i	−0.0921329	−	0.995747i	$-0.529368\pi$
$954$		0			0
$955$	19.3626	+	8.02023i	0.626558	+	0.259529i
$956$	44.5300	−	18.3895i	1.44020	−	0.594759i
$957$		0			0
$958$	31.5574	−	47.1748i	1.01957	−	1.52415i
$959$	−16.2854	+	28.2072i	−0.525884	+	0.910858i
$960$		0			0
$961$	9.66206	+	16.7352i	0.311679	+	0.539844i
$962$	22.7778	+	1.50510i	0.734387	+	0.0485262i
$963$		0			0
$964$	5.77038	−	43.4733i	0.185851	−	1.40018i
$965$	0.920466	+	6.99163i	0.0296308	+	0.225069i
$966$		0			0
$967$	3.60024	−	0.964680i	0.115776	−	0.0310220i	−0.200466	−	0.979701i	$-0.564246\pi$
$967$	3.60024	−	0.964680i	0.115776	−	0.0310220i	0.316242	+	0.948679i	$0.397579\pi$
$968$	−24.5208	+	1.56792i	−0.788129	+	0.0503949i
$969$		0			0
$970$	0.242793	+	3.73472i	0.00779561	+	0.119915i
$971$	−3.07941	+	7.43435i	−0.0988229	+	0.238580i	−0.965557	−	0.260190i	$-0.916215\pi$
$971$	−3.07941	+	7.43435i	−0.0988229	+	0.238580i	0.866734	+	0.498770i	$0.166215\pi$
$972$		0			0
$973$	−6.73404	+	2.78933i	−0.215883	+	0.0894218i
$974$	12.2347	−	35.9794i	0.392024	−	1.15285i
$975$		0			0
$976$	−17.9214	−	7.46795i	−0.573649	−	0.239043i
$977$	36.4497	+	21.0443i	1.16613	+	0.673265i	0.952765	−	0.303707i	$-0.0982245\pi$
$977$	36.4497	+	21.0443i	1.16613	+	0.673265i	0.213364	+	0.976973i	$0.431558\pi$
$978$		0			0
$979$	5.80424	+	4.45375i	0.185504	+	0.142342i
$980$	−6.99173	+	12.0804i	−0.223343	+	0.385893i
$981$		0			0
$982$	12.2836	−	24.8753i	0.391985	−	0.793803i
$983$	−45.9691	−	12.3174i	−1.46619	−	0.392864i	−0.564565	−	0.825389i	$-0.690956\pi$
$983$	−45.9691	−	12.3174i	−1.46619	−	0.392864i	−0.901622	+	0.432525i	$0.857623\pi$
$984$		0			0
$985$	−35.9373	+	9.62936i	−1.14506	+	0.306817i
$986$	−9.56921	+	47.9744i	−0.304746	+	1.52782i
$987$		0			0
$988$	−18.7957	−	7.80885i	−0.597971	−	0.248433i
$989$	1.16137	+	2.80379i	0.0369294	+	0.0891554i
$990$		0			0
$991$	28.3715			0.901251			0.450625	−	0.892713i	$-0.351201\pi$
$991$	28.3715			0.901251			0.450625	+	0.892713i	$0.351201\pi$
$992$	3.72060	+	18.9680i	0.118129	+	0.602235i
$993$		0			0
$994$	21.6750	+	14.4995i	0.687490	+	0.459895i
$995$	−36.5138	−	4.80713i	−1.15756	−	0.152396i
$996$		0			0
$997$	−1.23864	−	9.40843i	−0.0392282	−	0.297968i	−0.999801	−	0.0199398i	$-0.993653\pi$
$997$	−1.23864	−	9.40843i	−0.0392282	−	0.297968i	0.960573	−	0.278028i	$-0.0896808\pi$
$998$	−30.7005	+	10.4032i	−0.971808	+	0.329309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.37.18		368
3.2	odd	2		288.2.bc.a.229.29	yes	368
9.2	odd	6		288.2.bc.a.133.34	yes	368
9.7	even	3	inner	864.2.bk.a.613.13		368
32.13	even	8	inner	864.2.bk.a.685.13		368
96.77	odd	8		288.2.bc.a.13.34	✓	368
288.173	odd	24		288.2.bc.a.205.29	yes	368
288.205	even	24	inner	864.2.bk.a.397.18		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.34	✓	368	96.77	odd	8
288.2.bc.a.133.34	yes	368	9.2	odd	6
288.2.bc.a.205.29	yes	368	288.173	odd	24
288.2.bc.a.229.29	yes	368	3.2	odd	2
864.2.bk.a.37.18		368	1.1	even	1	trivial
864.2.bk.a.397.18		368	288.205	even	24	inner
864.2.bk.a.613.13		368	9.7	even	3	inner
864.2.bk.a.685.13		368	32.13	even	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bk (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.624817 - 1.26870i) q^{2} +(-1.21921 + 1.58541i) q^{4} +(1.33786 - 1.02658i) q^{5} +(-0.437818 + 1.63396i) q^{7} +(2.77320 + 0.556221i) q^{8} +O(q^{10})\)	\(q+(-0.624817 - 1.26870i) q^{2} +(-1.21921 + 1.58541i) q^{4} +(1.33786 - 1.02658i) q^{5} +(-0.437818 + 1.63396i) q^{7} +(2.77320 + 0.556221i) q^{8} +(-2.13834 - 1.05592i) q^{10} +(-1.50780 + 0.198506i) q^{11} +(-0.427656 + 3.24837i) q^{13} +(2.34656 - 0.465464i) q^{14} +(-1.02706 - 3.86590i) q^{16} +4.41051i q^{17} +(2.86961 - 1.18863i) q^{19} +(-0.00358480 + 3.37267i) q^{20} +(1.19395 + 1.78892i) q^{22} +(-0.0685874 - 0.255972i) q^{23} +(-0.558085 + 2.08280i) q^{25} +(4.38842 - 1.48707i) q^{26} +(-2.05671 - 2.68626i) q^{28} +(-4.77447 + 6.22221i) q^{29} +(1.70850 - 2.95921i) q^{31} +(-4.26294 + 3.71851i) q^{32} +(5.59562 - 2.75576i) q^{34} +(1.09164 + 2.63546i) q^{35} +(4.55158 + 1.88532i) q^{37} +(-3.30100 - 2.89800i) q^{38} +(4.28115 - 2.10275i) q^{40} +(2.70179 + 10.0832i) q^{41} +(-11.3541 + 1.49479i) q^{43} +(1.52361 - 2.63251i) q^{44} +(-0.281897 + 0.246952i) q^{46} +(5.48788 - 3.16843i) q^{47} +(3.58404 + 2.06925i) q^{49} +(2.99115 - 0.593325i) q^{50} +(-4.62860 - 4.63845i) q^{52} +(-0.907259 + 2.19032i) q^{53} +(-1.81345 + 1.81345i) q^{55} +(-2.12300 + 4.28776i) q^{56} +(10.8773 + 2.16964i) q^{58} +(7.99535 - 6.13505i) q^{59} +(2.95479 - 3.85076i) q^{61} +(-4.82185 - 0.318614i) q^{62} +(7.38124 + 3.08502i) q^{64} +(2.76255 + 4.78489i) q^{65} +(10.1544 + 1.33685i) q^{67} +(-6.99247 - 5.37733i) q^{68} +(2.66154 - 3.03165i) q^{70} +(7.70797 + 7.70797i) q^{71} +(5.54934 - 5.54934i) q^{73} +(-0.451985 - 6.95258i) q^{74} +(-1.61418 + 5.99870i) q^{76} +(0.335793 - 2.55060i) q^{77} +(-7.63729 + 4.40939i) q^{79} +(-5.34270 - 4.11767i) q^{80} +(11.1045 - 9.72794i) q^{82} +(-3.96569 - 3.04298i) q^{83} +(4.52772 + 5.90064i) q^{85} +(8.99065 + 13.4709i) q^{86} +(-4.29185 - 0.288176i) q^{88} +(-3.40163 - 3.40163i) q^{89} +(-5.12047 - 2.12097i) q^{91} +(0.489443 + 0.203344i) q^{92} +(-7.44871 - 4.98279i) q^{94} +(2.61892 - 4.53609i) q^{95} +(-0.784666 - 1.35908i) q^{97} +(0.385890 - 5.83998i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

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