LMFDB - Embedded newform 864.2.bk.a.37.17

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			37.17
Character	$\chi$	$=$	864.37
Dual form			864.2.bk.a.397.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.683019 + 1.23834i) q^{2} +(-1.06697 - 1.69162i) q^{4} +(0.526137 - 0.403719i) q^{5} +(0.911495 - 3.40174i) q^{7} +(2.82356 - 0.165864i) q^{8} +O(q^{10})$	\(q+(-0.683019 + 1.23834i) q^{2} +(-1.06697 - 1.69162i) q^{4} +(0.526137 - 0.403719i) q^{5} +(0.911495 - 3.40174i) q^{7} +(2.82356 - 0.165864i) q^{8} +(0.140580 + 0.927284i) q^{10} +(-5.10279 + 0.671795i) q^{11} +(0.389161 - 2.95597i) q^{13} +(3.58995 + 3.45220i) q^{14} +(-1.72315 + 3.60981i) q^{16} -0.364422i q^{17} +(-4.46287 + 1.84858i) q^{19} +(-1.24431 - 0.459267i) q^{20} +(2.65339 - 6.77783i) q^{22} +(-1.33499 - 4.98224i) q^{23} +(-1.18026 + 4.40481i) q^{25} +(3.39469 + 2.50090i) q^{26} +(-6.72699 + 2.08766i) q^{28} +(-3.55450 + 4.63232i) q^{29} +(-3.01601 + 5.22388i) q^{31} +(-3.29323 - 4.59941i) q^{32} +(0.451278 + 0.248907i) q^{34} +(-0.893778 - 2.15777i) q^{35} +(-7.56014 - 3.13151i) q^{37} +(0.759053 - 6.78917i) q^{38} +(1.41862 - 1.22719i) q^{40} +(0.884042 + 3.29929i) q^{41} +(-9.64364 + 1.26961i) q^{43} +(6.58094 + 7.91518i) q^{44} +(7.08153 + 1.74980i) q^{46} +(4.45774 - 2.57368i) q^{47} +(-4.67887 - 2.70134i) q^{49} +(-4.64850 - 4.47013i) q^{50} +(-5.41559 + 2.49562i) q^{52} +(3.65397 - 8.82145i) q^{53} +(-2.41355 + 2.41355i) q^{55} +(2.00943 - 9.75621i) q^{56} +(-3.30859 - 7.56564i) q^{58} +(-2.32430 + 1.78350i) q^{59} +(6.44833 - 8.40362i) q^{61} +(-4.40895 - 7.30285i) q^{62} +(7.94498 - 0.936655i) q^{64} +(-0.988629 - 1.71236i) q^{65} +(7.30385 + 0.961570i) q^{67} +(-0.616463 + 0.388827i) q^{68} +(3.28252 + 0.366998i) q^{70} +(-5.87298 - 5.87298i) q^{71} +(5.72879 - 5.72879i) q^{73} +(9.04159 - 7.22313i) q^{74} +(7.88885 + 5.57709i) q^{76} +(-2.36589 + 17.9707i) q^{77} +(4.12486 - 2.38149i) q^{79} +(0.550739 + 2.59492i) q^{80} +(-4.68946 - 1.15873i) q^{82} +(-6.59994 - 5.06432i) q^{83} +(-0.147124 - 0.191736i) q^{85} +(5.01458 - 12.8093i) q^{86} +(-14.2966 + 2.74322i) q^{88} +(-1.17717 - 1.17717i) q^{89} +(-9.70073 - 4.01817i) q^{91} +(-7.00366 + 7.57419i) q^{92} +(0.142366 + 7.27806i) q^{94} +(-1.60177 + 2.77435i) q^{95} +(0.00601054 + 0.0104106i) q^{97} +(6.54094 - 3.94896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.683019	+	1.23834i	−0.482967	+	0.875638i
$2$	−0.683019	+	1.23834i	−0.482967	+	0.875638i
$3$		0			0
$3$		0			0
$4$	−1.06697	−	1.69162i	−0.533485	−	0.845809i
$5$	0.526137	−	0.403719i	0.235296	−	0.180549i	−0.484383	−	0.874856i	$-0.660956\pi$
$5$	0.526137	−	0.403719i	0.235296	−	0.180549i	0.719679	+	0.694307i	$0.244289\pi$
$6$		0			0
$7$	0.911495	−	3.40174i	0.344513	−	1.28574i	−0.548668	−	0.836040i	$-0.684865\pi$
$7$	0.911495	−	3.40174i	0.344513	−	1.28574i	0.893181	−	0.449698i	$-0.148468\pi$
$8$	2.82356	−	0.165864i	0.998279	−	0.0586419i
$9$		0			0
$10$	0.140580	+	0.927284i	0.0444553	+	0.293233i
$11$	−5.10279	+	0.671795i	−1.53855	+	0.202554i	−0.851615	−	0.524167i	$-0.824377\pi$
$11$	−5.10279	+	0.671795i	−1.53855	+	0.202554i	−0.686933	+	0.726721i	$0.741043\pi$
$12$		0			0
$13$	0.389161	−	2.95597i	0.107934	−	0.819838i	−0.848767	−	0.528766i	$-0.822655\pi$
$13$	0.389161	−	2.95597i	0.107934	−	0.819838i	0.956701	−	0.291072i	$-0.0940119\pi$
$14$	3.58995	+	3.45220i	0.959454	+	0.922638i
$15$		0			0
$16$	−1.72315	+	3.60981i	−0.430787	+	0.902454i
$17$		−	0.364422i		−	0.0883853i	−0.999023	−	0.0441926i	$-0.985928\pi$
$17$		−	0.364422i		−	0.0883853i	0.999023	−	0.0441926i	$-0.0140715\pi$
$18$		0			0
$19$	−4.46287	+	1.84858i	−1.02385	+	0.424094i	−0.830490	−	0.557034i	$-0.811939\pi$
$19$	−4.46287	+	1.84858i	−1.02385	+	0.424094i	−0.193363	+	0.981127i	$0.561939\pi$
$20$	−1.24431	−	0.459267i	−0.278236	−	0.102695i
$21$		0			0
$22$	2.65339	−	6.77783i	0.565705	−	1.44504i
$23$	−1.33499	−	4.98224i	−0.278364	−	1.03887i	−0.953553	−	0.301224i	$-0.902605\pi$
$23$	−1.33499	−	4.98224i	−0.278364	−	1.03887i	0.675189	−	0.737645i	$-0.264062\pi$
$24$		0			0
$25$	−1.18026	+	4.40481i	−0.236053	+	0.880961i
$26$	3.39469	+	2.50090i	0.665753	+	0.490466i
$27$		0			0
$28$	−6.72699	+	2.08766i	−1.27128	+	0.394531i
$29$	−3.55450	+	4.63232i	−0.660054	+	0.860199i	−0.996678	−	0.0814397i	$-0.974048\pi$
$29$	−3.55450	+	4.63232i	−0.660054	+	0.860199i	0.336624	+	0.941639i	$0.390715\pi$
$30$		0			0
$31$	−3.01601	+	5.22388i	−0.541691	+	0.938236i	0.457116	+	0.889407i	$0.348882\pi$
$31$	−3.01601	+	5.22388i	−0.541691	+	0.938236i	−0.998807	+	0.0488293i	$0.984451\pi$
$32$	−3.29323	−	4.59941i	−0.582167	−	0.813069i
$33$		0			0
$34$	0.451278	+	0.248907i	0.0773935	+	0.0426872i
$35$	−0.893778	−	2.15777i	−0.151076	−	0.364730i
$36$		0			0
$37$	−7.56014	−	3.13151i	−1.24288	−	0.514817i	−0.338265	−	0.941051i	$-0.609840\pi$
$37$	−7.56014	−	3.13151i	−1.24288	−	0.514817i	−0.904613	+	0.426234i	$0.859840\pi$
$38$	0.759053	−	6.78917i	0.123135	−	1.10135i
$39$		0			0
$40$	1.41862	−	1.22719i	0.224303	−	0.194036i
$41$	0.884042	+	3.29929i	0.138064	+	0.515263i	0.999966	+	0.00818826i	$0.00260643\pi$
$41$	0.884042	+	3.29929i	0.138064	+	0.515263i	−0.861902	+	0.507074i	$0.830727\pi$
$42$		0			0
$43$	−9.64364	+	1.26961i	−1.47064	+	0.193614i	−0.822874	−	0.568224i	$-0.807631\pi$
$43$	−9.64364	+	1.26961i	−1.47064	+	0.193614i	−0.647768	+	0.761838i	$0.724297\pi$
$44$	6.58094	+	7.91518i	0.992114	+	1.19326i
$45$		0			0
$46$	7.08153	+	1.74980i	1.04411	+	0.257993i
$47$	4.45774	−	2.57368i	0.650228	−	0.375409i	−0.138316	−	0.990388i	$-0.544169\pi$
$47$	4.45774	−	2.57368i	0.650228	−	0.375409i	0.788543	+	0.614979i	$0.210836\pi$
$48$		0			0
$49$	−4.67887	−	2.70134i	−0.668409	−	0.385906i
$50$	−4.64850	−	4.47013i	−0.657398	−	0.632172i
$51$		0			0
$52$	−5.41559	+	2.49562i	−0.751008	+	0.346080i
$53$	3.65397	−	8.82145i	0.501911	−	1.21172i	−0.446531	−	0.894768i	$-0.647341\pi$
$53$	3.65397	−	8.82145i	0.501911	−	1.21172i	0.948442	−	0.316952i	$-0.102659\pi$
$54$		0			0
$55$	−2.41355	+	2.41355i	−0.325443	+	0.325443i
$56$	2.00943	−	9.75621i	0.268522	−	1.30373i
$57$		0			0
$58$	−3.30859	−	7.56564i	−0.434439	−	0.993417i
$59$	−2.32430	+	1.78350i	−0.302598	+	0.232192i	−0.748888	−	0.662697i	$-0.769412\pi$
$59$	−2.32430	+	1.78350i	−0.302598	+	0.232192i	0.446290	+	0.894889i	$0.352745\pi$
$60$		0			0
$61$	6.44833	−	8.40362i	0.825624	−	1.07597i	−0.170266	−	0.985398i	$-0.554463\pi$
$61$	6.44833	−	8.40362i	0.825624	−	1.07597i	0.995890	−	0.0905756i	$-0.0288707\pi$
$62$	−4.40895	−	7.30285i	−0.559937	−	0.927463i
$63$		0			0
$64$	7.94498	−	0.936655i	0.993122	−	0.117082i
$65$	−0.988629	−	1.71236i	−0.122624	−	0.212392i
$66$		0			0
$67$	7.30385	+	0.961570i	0.892307	+	0.117474i	0.562717	−	0.826650i	$-0.309756\pi$
$67$	7.30385	+	0.961570i	0.892307	+	0.117474i	0.329590	+	0.944124i	$0.393089\pi$
$68$	−0.616463	+	0.388827i	−0.0747571	+	0.0471522i
$69$		0			0
$70$	3.28252	+	0.366998i	0.392336	+	0.0438646i
$71$	−5.87298	−	5.87298i	−0.696995	−	0.696995i	0.266766	−	0.963761i	$-0.414045\pi$
$71$	−5.87298	−	5.87298i	−0.696995	−	0.696995i	−0.963761	+	0.266766i	$0.914045\pi$
$72$		0			0
$73$	5.72879	−	5.72879i	0.670504	−	0.670504i	−0.287328	−	0.957832i	$-0.592767\pi$
$73$	5.72879	−	5.72879i	0.670504	−	0.670504i	0.957832	+	0.287328i	$0.0927669\pi$
$74$	9.04159	−	7.22313i	1.05106	−	0.839672i
$75$		0			0
$76$	7.88885	+	5.57709i	0.904913	+	0.639737i
$77$	−2.36589	+	17.9707i	−0.269618	+	2.04795i
$78$		0			0
$79$	4.12486	−	2.38149i	0.464083	−	0.267939i	−0.249676	−	0.968329i	$-0.580324\pi$
$79$	4.12486	−	2.38149i	0.464083	−	0.267939i	0.713760	+	0.700391i	$0.246991\pi$
$80$	0.550739	+	2.59492i	0.0615745	+	0.290121i
$81$		0			0
$82$	−4.68946	−	1.15873i	−0.517864	−	0.127961i
$83$	−6.59994	−	5.06432i	−0.724438	−	0.555881i	0.179389	−	0.983778i	$-0.442588\pi$
$83$	−6.59994	−	5.06432i	−0.724438	−	0.555881i	−0.903827	+	0.427897i	$0.859254\pi$
$84$		0			0
$85$	−0.147124	−	0.191736i	−0.0159578	−	0.0207967i
$86$	5.01458	−	12.8093i	0.540736	−	1.38126i
$87$		0			0
$88$	−14.2966	+	2.74322i	−1.52402	+	0.292428i
$89$	−1.17717	−	1.17717i	−0.124780	−	0.124780i	0.641959	−	0.766739i	$-0.278122\pi$
$89$	−1.17717	−	1.17717i	−0.124780	−	0.124780i	−0.766739	+	0.641959i	$0.778122\pi$
$90$		0			0
$91$	−9.70073	−	4.01817i	−1.01691	−	0.421219i
$92$	−7.00366	+	7.57419i	−0.730182	+	0.789664i
$93$		0			0
$94$	0.142366	+	7.27806i	0.0146839	+	0.750675i
$95$	−1.60177	+	2.77435i	−0.164338	+	0.284643i
$96$		0			0
$97$	0.00601054	+	0.0104106i	0.000610278	+	0.00105703i	0.866330	−	0.499471i	$-0.166472\pi$
$97$	0.00601054	+	0.0104106i	0.000610278	+	0.00105703i	−0.865720	+	0.500528i	$0.833139\pi$
$98$	6.54094	−	3.94896i	0.660734	−	0.398905i
$99$		0			0
$100$	8.71056	−	2.70324i	0.871056	−	0.270324i
$101$	1.96464	+	14.9229i	0.195489	+	1.48489i	0.754815	+	0.655938i	$0.227727\pi$
$101$	1.96464	+	14.9229i	0.195489	+	1.48489i	−0.559326	+	0.828948i	$0.688940\pi$
$102$		0			0
$103$	5.91718	−	1.58550i	0.583037	−	0.156224i	0.0447682	−	0.998997i	$-0.485745\pi$
$103$	5.91718	−	1.58550i	0.583037	−	0.156224i	0.538269	+	0.842773i	$0.319078\pi$
$104$	0.608529	−	8.41090i	0.0596712	−	0.824757i
$105$		0			0
$106$	8.42823	+	10.5501i	0.818622	+	1.02471i
$107$	6.78660	−	16.3843i	0.656086	−	1.58393i	−0.147714	−	0.989030i	$-0.547191\pi$
$107$	6.78660	−	16.3843i	0.656086	−	1.58393i	0.803799	−	0.594901i	$-0.202809\pi$
$108$		0			0
$109$	−1.32634	+	0.549387i	−0.127040	+	0.0526217i	−0.445298	−	0.895382i	$-0.646902\pi$
$109$	−1.32634	+	0.549387i	−0.127040	+	0.0526217i	0.318258	+	0.948004i	$0.396902\pi$
$110$	−1.34029	−	4.63729i	−0.127792	−	0.442148i
$111$		0			0
$112$	10.7090	+	9.15204i	1.01191	+	0.864786i
$113$	2.03598	+	1.17547i	0.191529	+	0.110579i	0.592698	−	0.805425i	$-0.298063\pi$
$113$	2.03598	+	1.17547i	0.191529	+	0.110579i	−0.401169	+	0.916004i	$0.631396\pi$
$114$		0			0
$115$	−2.71381	−	2.08238i	−0.253064	−	0.194183i
$116$	11.6287	+	1.07032i	1.07969	+	0.0993764i
$117$		0			0
$118$	−0.621035	−	4.09643i	−0.0571709	−	0.377107i
$119$	−1.23967	−	0.332169i	−0.113640	−	0.0304498i
$120$		0			0
$121$	14.9619	−	4.00904i	1.36018	−	0.364458i
$122$	6.00221	+	13.7251i	0.543415	+	1.24261i
$123$		0			0
$124$	12.0548	−	0.471788i	1.08255	−	0.0423679i
$125$	2.42627	+	5.85752i	0.217012	+	0.523913i
$126$		0			0
$127$	−6.25944			−0.555435			−0.277718	−	0.960663i	$-0.589578\pi$
$127$	−6.25944			−0.555435			−0.277718	+	0.960663i	$0.589578\pi$
$128$	−4.26667	+	10.4783i	−0.377124	+	0.926163i
$129$		0			0
$130$	2.79573	−	0.0546873i	0.245202	−	0.00479639i
$131$	4.07654	+	0.536686i	0.356169	+	0.0468905i	0.306488	−	0.951875i	$-0.400846\pi$
$131$	4.07654	+	0.536686i	0.356169	+	0.0468905i	0.0496810	+	0.998765i	$0.484180\pi$
$132$		0			0
$133$	2.22052	+	16.8665i	0.192543	+	1.46251i
$134$	−6.17942	+	8.38788i	−0.533820	+	0.724602i
$135$		0			0
$136$	−0.0604445	−	1.02897i	−0.00518308	−	0.0882332i
$137$	−9.01232	−	2.41484i	−0.769974	−	0.206314i	−0.147614	−	0.989045i	$-0.547159\pi$
$137$	−9.01232	−	2.41484i	−0.769974	−	0.206314i	−0.622360	+	0.782731i	$0.713826\pi$
$138$		0			0
$139$	−12.9755	−	16.9100i	−1.10057	−	1.43429i	−0.889568	−	0.456802i	$-0.848995\pi$
$139$	−12.9755	−	16.9100i	−1.10057	−	1.43429i	−0.211000	−	0.977486i	$-0.567672\pi$
$140$	−2.69649	+	3.81421i	−0.227895	+	0.322359i
$141$		0			0
$142$	11.2841	−	3.26139i	0.946941	−	0.273690i
$143$			15.3451i			1.28322i
$144$		0			0
$145$			3.87225i			0.321573i
$146$	3.18132	+	11.0071i	0.263288	+	0.910951i
$147$		0			0
$148$	2.76912	+	16.1301i	0.227620	+	1.32589i
$149$	0.653845	+	0.852107i	0.0535651	+	0.0698074i	0.819368	−	0.573268i	$-0.194325\pi$
$149$	0.653845	+	0.852107i	0.0535651	+	0.0698074i	−0.765803	+	0.643076i	$0.777658\pi$
$150$		0			0
$151$	−6.65612	−	1.78350i	−0.541667	−	0.145139i	−0.0223966	−	0.999749i	$-0.507130\pi$
$151$	−6.65612	−	1.78350i	−0.541667	−	0.145139i	−0.519271	+	0.854610i	$0.673796\pi$
$152$	−12.2946	+	5.95981i	−0.997221	+	0.483405i
$153$		0			0
$154$	−20.6379	−	15.2041i	−1.66305	−	1.22518i
$155$	0.522146	+	3.96609i	0.0419398	+	0.318564i
$156$		0			0
$157$	−6.86728	−	0.904094i	−0.548068	−	0.0721546i	−0.148593	−	0.988898i	$-0.547474\pi$
$157$	−6.86728	−	0.904094i	−0.548068	−	0.0721546i	−0.399475	+	0.916744i	$0.630808\pi$
$158$	0.131735	+	6.73459i	0.0104803	+	0.535775i
$159$		0			0
$160$	−3.58956	−	1.09038i	−0.283780	−	0.0862021i
$161$	−18.1651			−1.43161
$162$		0			0
$163$	−8.00966	−	19.3370i	−0.627365	−	1.51459i	−0.842885	−	0.538094i	$-0.819145\pi$
$163$	−8.00966	−	19.3370i	−0.627365	−	1.51459i	0.215520	−	0.976499i	$-0.430855\pi$
$164$	4.63790	−	5.01571i	0.362159	−	0.391661i
$165$		0			0
$166$	10.7792	−	4.71395i	0.836631	−	0.365874i
$167$	−2.77221	+	0.742811i	−0.214520	+	0.0574804i	−0.364478	−	0.931212i	$-0.618753\pi$
$167$	−2.77221	+	0.742811i	−0.214520	+	0.0574804i	0.149958	+	0.988692i	$0.452086\pi$
$168$		0			0
$169$	3.97073	+	1.06395i	0.305441	+	0.0818427i
$170$	0.337922	−	0.0512304i	0.0259175	−	0.00392919i
$171$		0			0
$172$	12.4372	+	14.9587i	0.948326	+	1.14059i
$173$	15.2398	+	11.6939i	1.15866	+	0.889072i	0.995237	−	0.0974841i	$-0.0310795\pi$
$173$	15.2398	+	11.6939i	1.15866	+	0.889072i	0.163424	+	0.986556i	$0.447746\pi$
$174$		0			0
$175$	13.9082	+	8.02992i	1.05136	+	0.607005i
$176$	6.36780	−	19.5777i	0.479991	−	1.47573i
$177$		0			0
$178$	2.26177	−	0.653708i	0.169527	−	0.0489975i
$179$	−9.45002	+	3.91433i	−0.706328	+	0.292571i	−0.706784	−	0.707429i	$-0.749855\pi$
$179$	−9.45002	+	3.91433i	−0.706328	+	0.292571i	0.000456333		1.00000i	$0.499855\pi$
$180$		0			0
$181$	3.88557	−	9.38059i	0.288812	−	0.697254i	−0.711171	−	0.703019i	$-0.751835\pi$
$181$	3.88557	−	9.38059i	0.288812	−	0.697254i	0.999983	+	0.00576488i	$0.00183503\pi$
$182$	11.6016	−	9.26831i	0.859971	−	0.687013i
$183$		0			0
$184$	−4.59579	−	13.8462i	−0.338806	−	1.02076i
$185$	−5.24192	+	1.40457i	−0.385393	+	0.103266i
$186$		0			0
$187$	0.244817	+	1.85957i	0.0179028	+	0.135985i
$188$	−9.10995	−	4.79476i	−0.664412	−	0.349694i
$189$		0			0
$190$	−2.34155	−	3.87847i	−0.169874	−	0.281374i
$191$	−8.97326	−	15.5421i	−0.649283	−	1.12459i	−0.983295	−	0.182022i	$-0.941736\pi$
$191$	−8.97326	−	15.5421i	−0.649283	−	1.12459i	0.334012	−	0.942569i	$-0.391597\pi$
$192$		0			0
$193$	2.28960	−	3.96571i	0.164809	−	0.285458i	−0.771778	−	0.635892i	$-0.780632\pi$
$193$	2.28960	−	3.96571i	0.164809	−	0.285458i	0.936588	+	0.350434i	$0.113966\pi$
$194$	−0.0169971		0.000332481i	−0.00122032		2.38707e-5i
$195$		0			0
$196$	0.422566	+	10.7971i	0.0301833	+	0.771222i
$197$	6.24771	+	2.58789i	0.445131	+	0.184379i	0.593978	−	0.804481i	$-0.297556\pi$
$197$	6.24771	+	2.58789i	0.445131	+	0.184379i	−0.148848	+	0.988860i	$0.547556\pi$
$198$		0			0
$199$	−10.8310	−	10.8310i	−0.767787	−	0.767787i	0.209930	−	0.977716i	$-0.432676\pi$
$199$	−10.8310	−	10.8310i	−0.767787	−	0.767787i	−0.977716	+	0.209930i	$0.932676\pi$
$200$	−2.60195	+	12.6330i	−0.183985	+	0.893288i
$201$		0			0
$202$	−19.8215	−	7.75975i	−1.39464	−	0.545974i
$203$	12.5180	+	16.3138i	0.878595	+	1.14501i
$204$		0			0
$205$	1.79711	+	1.37897i	0.125516	+	0.0963117i
$206$	−2.07815	+	8.41041i	−0.144792	+	0.585981i
$207$		0			0
$208$	9.99992	+	6.49837i	0.693369	+	0.450581i
$209$	21.5312	−	12.4311i	1.48934	−	0.859874i
$210$		0			0
$211$	−3.39507	+	25.7881i	−0.233726	+	1.77533i	0.324742	+	0.945803i	$0.394723\pi$
$211$	−3.39507	+	25.7881i	−0.233726	+	1.77533i	−0.558468	+	0.829526i	$0.688611\pi$
$212$	−18.8212	+	3.23111i	−1.29265	+	0.221914i
$213$		0			0
$214$	15.6540	+	19.5949i	1.07008	+	1.33948i
$215$	−4.56131	+	4.56131i	−0.311079	+	0.311079i
$216$		0			0
$217$	15.0212	+	15.0212i	1.01971	+	1.01971i
$218$	0.225586	−	2.01770i	0.0152786	−	0.136656i
$219$		0			0
$220$	6.65799	+	1.50762i	0.448881	+	0.101644i
$221$	−1.07722	−	0.141819i	−0.0724616	−	0.00953975i
$222$		0			0
$223$	7.49609	+	12.9836i	0.501976	+	0.869447i	0.999997	+	0.00228276i	$0.000726627\pi$
$223$	7.49609	+	12.9836i	0.501976	+	0.869447i	−0.498022	+	0.867165i	$0.665940\pi$
$224$	−18.6478	+	7.01040i	−1.24596	+	0.468402i
$225$		0			0
$226$	−2.84624	+	1.71836i	−0.189329	+	0.114304i
$227$	−15.9796	+	20.8251i	−1.06061	+	1.38221i	−0.140709	+	0.990051i	$0.544938\pi$
$227$	−15.9796	+	20.8251i	−1.06061	+	1.38221i	−0.919898	+	0.392158i	$0.871729\pi$
$228$		0			0
$229$	−11.0776	+	8.50016i	−0.732030	+	0.561707i	−0.906119	−	0.423023i	$-0.860969\pi$
$229$	−11.0776	+	8.50016i	−0.732030	+	0.561707i	0.174088	+	0.984730i	$0.444302\pi$
$230$	4.43228	−	1.93831i	0.292256	−	0.127809i
$231$		0			0
$232$	−9.26801	+	13.6692i	−0.608475	+	0.897426i
$233$	10.0276	−	10.0276i	0.656932	−	0.656932i	−0.297721	−	0.954653i	$-0.596227\pi$
$233$	10.0276	−	10.0276i	0.656932	−	0.656932i	0.954653	+	0.297721i	$0.0962265\pi$
$234$		0			0
$235$	1.30634	−	3.15378i	0.0852161	−	0.205730i
$236$	5.49696	+	2.02889i	0.357821	+	0.132069i
$237$		0			0
$238$	1.25806	−	1.30825i	0.0815476	−	0.0848016i
$239$	14.6640	+	8.46629i	0.948538	+	0.547639i	0.892627	−	0.450797i	$-0.148860\pi$
$239$	14.6640	+	8.46629i	0.948538	+	0.547639i	0.0559118	+	0.998436i	$0.482193\pi$
$240$		0			0
$241$	9.10955	−	5.25940i	0.586798	−	0.338788i	−0.177032	−	0.984205i	$-0.556650\pi$
$241$	9.10955	−	5.25940i	0.586798	−	0.338788i	0.763830	+	0.645417i	$0.223316\pi$
$242$	−5.25473	+	21.2662i	−0.337787	+	1.36704i
$243$		0			0
$244$	−21.0959	−	1.94169i	−1.35053	−	0.124304i
$245$	−3.55231	+	0.467670i	−0.226949	+	0.0298784i
$246$		0			0
$247$	3.72758	+	13.9115i	0.237180	+	0.885168i
$248$	−7.64942	+	15.2502i	−0.485739	+	0.968387i
$249$		0			0
$250$	−8.91079	−	0.996258i	−0.563568	−	0.0630089i
$251$	−1.80970	−	0.749602i	−0.114227	−	0.0473144i	0.324838	−	0.945770i	$-0.394690\pi$
$251$	−1.80970	−	0.749602i	−0.114227	−	0.0473144i	−0.439065	+	0.898455i	$0.644690\pi$
$252$		0			0
$253$	10.1592	+	24.5265i	0.638703	+	1.54197i
$254$	4.27531	−	7.75131i	0.268257	−	0.486361i
$255$		0			0
$256$	−10.0615	−	12.4405i	−0.628845	−	0.777531i
$257$	7.85438	−	13.6042i	0.489943	−	0.848606i	−0.509990	−	0.860180i	$-0.670351\pi$
$257$	7.85438	−	13.6042i	0.489943	−	0.848606i	0.999933	+	0.0115743i	$0.00368429\pi$
$258$		0			0
$259$	−17.5436	+	22.8633i	−1.09011	+	1.42066i
$260$	−1.84181	+	3.49942i	−0.114224	+	0.217025i
$261$		0			0
$262$	−3.44895	+	4.68157i	−0.213077	+	0.289228i
$263$	3.27241	−	12.2128i	0.201786	−	0.753075i	−0.788620	−	0.614881i	$-0.789204\pi$
$263$	3.27241	−	12.2128i	0.201786	−	0.753075i	0.990405	−	0.138193i	$-0.0441295\pi$
$264$		0			0
$265$	−1.63890	−	6.11647i	−0.100677	−	0.375732i
$266$	−22.4031	−	8.77039i	−1.37362	−	0.537747i
$267$		0			0
$268$	−6.16638	−	13.3813i	−0.376672	−	0.817393i
$269$	−1.03549	+	0.428914i	−0.0631350	+	0.0261514i	−0.414027	−	0.910264i	$-0.635878\pi$
$269$	−1.03549	+	0.428914i	−0.0631350	+	0.0261514i	0.350892	+	0.936416i	$0.385878\pi$
$270$		0			0
$271$			11.2278i			0.682043i	0.940055	+	0.341022i	$0.110773\pi$
$271$			11.2278i			0.682043i	−0.940055	+	0.341022i	$0.889227\pi$
$272$	1.31549	+	0.627953i	0.0797636	+	0.0380752i
$273$		0			0
$274$	9.14598	−	9.51093i	0.552529	−	0.574576i
$275$	3.06351	−	23.2697i	0.184737	−	1.40321i
$276$		0			0
$277$	−8.84144	+	1.16400i	−0.531231	+	0.0699378i	−0.391370	−	0.920233i	$-0.627999\pi$
$277$	−8.84144	+	1.16400i	−0.531231	+	0.0699378i	−0.139861	+	0.990171i	$0.544665\pi$
$278$	29.8029	−	4.51823i	1.78746	−	0.270985i
$279$		0			0
$280$	−2.88153	−	5.94435i	−0.172204	−	0.355243i
$281$	−4.77995	+	17.8390i	−0.285148	+	1.06419i	0.663583	+	0.748103i	$0.269035\pi$
$281$	−4.77995	+	17.8390i	−0.285148	+	1.06419i	−0.948731	+	0.316085i	$0.897632\pi$
$282$		0			0
$283$	20.3214	−	15.5932i	1.20798	−	0.926919i	0.209282	−	0.977855i	$-0.432887\pi$
$283$	20.3214	−	15.5932i	1.20798	−	0.926919i	0.998702	+	0.0509363i	$0.0162206\pi$
$284$	−3.66855	+	16.2011i	−0.217688	+	0.961361i
$285$		0			0
$286$	−19.0025	−	10.4810i	−1.12364	−	0.619755i
$287$	12.0291			0.710058
$288$		0			0
$289$	16.8672			0.992188
$290$	−4.79516	−	2.64482i	−0.281582	−	0.155309i
$291$		0			0
$292$	−15.8034	−	3.57848i	−0.924823	−	0.209415i
$293$	−0.908240	+	0.696917i	−0.0530599	+	0.0407143i	−0.634951	−	0.772552i	$-0.718980\pi$
$293$	−0.908240	+	0.696917i	−0.0530599	+	0.0407143i	0.581891	+	0.813267i	$0.302313\pi$
$294$		0			0
$295$	−0.502867	+	1.87673i	−0.0292781	+	0.109267i
$296$	−21.8659	−	7.58805i	−1.27093	−	0.441046i
$297$		0			0
$298$	−1.50179	+	0.227677i	−0.0869962	+	0.0131890i
$299$	−15.2469	+	2.00729i	−0.881749	+	0.116084i
$300$		0			0
$301$	−4.47124	+	33.9624i	−0.257718	+	1.95756i
$302$	6.75484	−	7.02437i	0.388697	−	0.404207i
$303$		0			0
$304$	1.01715	−	19.2955i	0.0583377	−	1.10667i
$305$		−	7.02477i		−	0.402237i
$306$		0			0
$307$	0.619785	−	0.256723i	0.0353730	−	0.0146520i	−0.364927	−	0.931036i	$-0.618906\pi$
$307$	0.619785	−	0.256723i	0.0353730	−	0.0146520i	0.400300	+	0.916384i	$0.368906\pi$
$308$	32.9239	−	15.1720i	1.87602	−	0.864507i
$309$		0			0
$310$	−5.26801	−	2.06232i	−0.299203	−	0.117132i
$311$	3.39980	+	12.6882i	0.192785	+	0.719484i	0.992829	+	0.119543i	$0.0381428\pi$
$311$	3.39980	+	12.6882i	0.192785	+	0.719484i	−0.800044	+	0.599941i	$0.795191\pi$
$312$		0			0
$313$	6.83546	−	25.5103i	0.386363	−	1.44193i	−0.449644	−	0.893208i	$-0.648449\pi$
$313$	6.83546	−	25.5103i	0.386363	−	1.44193i	0.836007	−	0.548718i	$-0.184884\pi$
$314$	5.81006	−	7.88651i	0.327880	−	0.445061i
$315$		0			0
$316$	−8.42968	−	4.43672i	−0.474207	−	0.249585i
$317$	−10.5799	+	13.7879i	−0.594224	+	0.774407i	−0.989559	−	0.144129i	$-0.953962\pi$
$317$	−10.5799	+	13.7879i	−0.594224	+	0.774407i	0.395335	+	0.918537i	$0.370628\pi$
$318$		0			0
$319$	15.0259	−	26.0256i	0.841288	−	1.45715i
$320$	3.80200	−	3.70035i	0.212538	−	0.206856i
$321$		0			0
$322$	12.4071	−	22.4946i	0.691423	−	1.25358i
$323$	0.673663	+	1.62637i	0.0374836	+	0.0904935i
$324$		0			0
$325$	12.5612	+	5.20300i	0.696768	+	0.288611i
$326$	29.4166	+	3.28888i	1.62923	+	0.182154i
$327$		0			0
$328$	3.04338	+	9.16911i	0.168043	+	0.506280i
$329$	−4.69178	−	17.5100i	−0.258666	−	0.965356i
$330$		0			0
$331$	14.5022	−	1.90924i	0.797110	−	0.104942i	0.279040	−	0.960280i	$-0.409984\pi$
$331$	14.5022	−	1.90924i	0.797110	−	0.104942i	0.518070	+	0.855338i	$0.326650\pi$
$332$	−1.52495	+	16.5681i	−0.0836923	+	0.909291i
$333$		0			0
$334$	0.973618	−	3.94029i	0.0532740	−	0.215603i
$335$	4.23103	−	2.44279i	0.231166	−	0.133464i
$336$		0			0
$337$	−28.8231	−	16.6410i	−1.57010	−	0.906495i	−0.996156	−	0.0875974i	$-0.972081\pi$
$337$	−28.8231	−	16.6410i	−1.57010	−	0.906495i	−0.573940	−	0.818898i	$-0.694586\pi$
$338$	−4.02962	+	4.19042i	−0.219183	+	0.227929i
$339$		0			0
$340$	−0.167367	+	0.453454i	−0.00907674	+	0.0245920i
$341$	11.8807	−	28.6825i	0.643374	−	1.55324i
$342$		0			0
$343$	3.97770	−	3.97770i	0.214776	−	0.214776i
$344$	−27.0188	+	5.18435i	−1.45676	+	0.279522i
$345$		0			0
$346$	−24.8901	+	10.8849i	−1.33810	+	0.585175i
$347$	18.7227	−	14.3664i	1.00509	−	0.771230i	0.0314898	−	0.999504i	$-0.489975\pi$
$347$	18.7227	−	14.3664i	1.00509	−	0.771230i	0.973597	+	0.228274i	$0.0733082\pi$
$348$		0			0
$349$	8.63989	−	11.2597i	0.462483	−	0.602719i	−0.502647	−	0.864492i	$-0.667640\pi$
$349$	8.63989	−	11.2597i	0.462483	−	0.602719i	0.965130	+	0.261773i	$0.0843071\pi$
$350$	−19.4433	+	11.7385i	−1.03929	+	0.627450i
$351$		0			0
$352$	19.8945	+	21.2575i	1.06038	+	1.13303i
$353$	−5.11951	−	8.86725i	−0.272484	−	0.471956i	0.697013	−	0.717058i	$-0.254512\pi$
$353$	−5.11951	−	8.86725i	−0.272484	−	0.471956i	−0.969497	+	0.245102i	$0.921179\pi$
$354$		0			0
$355$	−5.46103	−	0.718958i	−0.289841	−	0.0381583i
$356$	−0.735319	+	3.24733i	−0.0389718	+	0.172108i
$357$		0			0
$358$	1.60728	−	14.3759i	0.0849472	−	0.759790i
$359$	−7.16055	−	7.16055i	−0.377919	−	0.377919i	0.492432	−	0.870351i	$-0.336108\pi$
$359$	−7.16055	−	7.16055i	−0.377919	−	0.377919i	−0.870351	+	0.492432i	$0.836108\pi$
$360$		0			0
$361$	3.06494	−	3.06494i	0.161312	−	0.161312i
$362$	8.96244	+	11.2188i	0.471055	+	0.589646i
$363$		0			0
$364$	3.55317	+	20.6972i	0.186237	+	1.08483i
$365$	0.701306	−	5.32695i	0.0367081	−	0.278825i
$366$		0			0
$367$	−11.9247	+	6.88475i	−0.622466	+	0.359381i	−0.777829	−	0.628476i	$-0.783679\pi$
$367$	−11.9247	+	6.88475i	−0.622466	+	0.359381i	0.155362	+	0.987858i	$0.450345\pi$
$368$	20.2853	+	3.76608i	1.05745	+	0.196321i
$369$		0			0
$370$	1.84100	−	7.45062i	0.0957088	−	0.387339i
$371$	−26.6778	−	20.4706i	−1.38504	−	1.06278i
$372$		0			0
$373$	−2.62505	−	3.42103i	−0.135920	−	0.177134i	0.720434	−	0.693523i	$-0.243943\pi$
$373$	−2.62505	−	3.42103i	−0.135920	−	0.177134i	−0.856354	+	0.516389i	$0.827276\pi$
$374$	−2.46999	−	0.966953i	−0.127720	−	0.0499999i
$375$		0			0
$376$	12.1598	−	8.00631i	0.627094	−	0.412894i
$377$	12.3097	+	12.3097i	0.633982	+	0.633982i
$378$		0			0
$379$	19.5152	+	8.08347i	1.00243	+	0.415220i	0.822688	−	0.568494i	$-0.192474\pi$
$379$	19.5152	+	8.08347i	1.00243	+	0.415220i	0.179742	+	0.983714i	$0.442474\pi$
$380$	6.40219	−	0.250562i	0.328425	−	0.0128536i
$381$		0			0
$382$	25.3754	−	0.496368i	1.29832	−	0.0253964i
$383$	18.6303	−	32.2686i	0.951962	−	1.64885i	0.210791	−	0.977531i	$-0.432396\pi$
$383$	18.6303	−	32.2686i	0.951962	−	1.64885i	0.741171	−	0.671316i	$-0.234271\pi$
$384$		0			0
$385$	6.01034	+	10.4102i	0.306315	+	0.530553i
$386$	3.34705	+	5.54396i	0.170361	+	0.282180i
$387$		0			0
$388$	0.0111976	−	0.0212753i	0.000568473	−	0.00108009i
$389$	−2.28752	−	17.3755i	−0.115982	−	0.880972i	−0.946211	−	0.323549i	$-0.895124\pi$
$389$	−2.28752	−	17.3755i	−0.115982	−	0.880972i	0.830229	−	0.557422i	$-0.188210\pi$
$390$		0			0
$391$	−1.81564	+	0.486498i	−0.0918207	+	0.0246033i
$392$	−13.6591	−	6.85135i	−0.689889	−	0.346046i
$393$		0			0
$394$	−7.47198	+	5.96921i	−0.376433	+	0.300724i
$395$	1.20879	−	2.91828i	0.0608208	−	0.146834i
$396$		0			0
$397$	−15.8643	+	6.57122i	−0.796208	+	0.329800i	−0.743437	−	0.668806i	$-0.766806\pi$
$397$	−15.8643	+	6.57122i	−0.796208	+	0.329800i	−0.0527716	+	0.998607i	$0.516806\pi$
$398$	20.8102	−	6.01466i	1.04312	−	0.301488i
$399$		0			0
$400$	−13.8668	−	11.8507i	−0.693338	−	0.592533i
$401$	10.2206	+	5.90086i	0.510392	+	0.294675i	0.732995	−	0.680234i	$-0.238122\pi$
$401$	10.2206	+	5.90086i	0.510392	+	0.294675i	−0.222603	+	0.974909i	$0.571455\pi$
$402$		0			0
$403$	14.2679	+	10.9482i	0.710735	+	0.545366i
$404$	23.1477	−	19.2457i	1.15164	−	0.957511i
$405$		0			0
$406$	−28.7521	+	4.35894i	−1.42694	+	0.216330i
$407$	40.6815	+	10.9006i	2.01651	+	0.540321i
$408$		0			0
$409$	28.8411	−	7.72795i	1.42610	−	0.382123i	0.538457	−	0.842653i	$-0.319007\pi$
$409$	28.8411	−	7.72795i	1.42610	−	0.382123i	0.887644	+	0.460531i	$0.152341\pi$
$410$	−2.93510	+	1.28357i	−0.144954	+	0.0633911i
$411$		0			0
$412$	−8.99553	−	8.31793i	−0.443178	−	0.409795i
$413$	3.94842	+	9.53232i	0.194289	+	0.469055i
$414$		0			0
$415$	−5.51703			−0.270821
$416$	−14.8773	+	7.94478i	−0.729421	+	0.389525i
$417$		0			0
$418$	0.687639	+	35.1536i	0.0336335	+	1.71942i
$419$	−21.2173	−	2.79331i	−1.03653	−	0.136462i	−0.406994	−	0.913431i	$-0.633423\pi$
$419$	−21.2173	−	2.79331i	−1.03653	−	0.136462i	−0.629539	+	0.776968i	$0.716756\pi$
$420$		0			0
$421$	−1.82883	−	13.8913i	−0.0891317	−	0.677022i	−0.976431	−	0.215829i	$-0.930755\pi$
$421$	−1.82883	−	13.8913i	−0.0891317	−	0.677022i	0.887300	−	0.461194i	$-0.152579\pi$
$422$	−29.6156	−	21.8180i	−1.44166	−	1.06209i
$423$		0			0
$424$	8.85403	−	25.5140i	0.429990	−	1.23907i
$425$	1.60521	+	0.430114i	0.0778640	+	0.0208636i
$426$		0			0
$427$	−22.7094	−	29.5954i	−1.09898	−	1.43222i
$428$	−34.9571	+	6.00123i	−1.68972	+	0.290080i
$429$		0			0
$430$	−2.53299	−	8.76391i	−0.122152	−	0.422633i
$431$		−	18.2965i		−	0.881310i	−0.897677	−	0.440655i	$-0.854746\pi$
$431$		−	18.2965i		−	0.881310i	0.897677	−	0.440655i	$-0.145254\pi$
$432$		0			0
$433$			25.3301i			1.21729i	0.793443	+	0.608644i	$0.208286\pi$
$433$			25.3301i			1.21729i	−0.793443	+	0.608644i	$0.791714\pi$
$434$	−28.8612	+	8.34160i	−1.38538	+	0.400410i
$435$		0			0
$436$	2.34452	+	1.65748i	0.112282	+	0.0793788i
$437$	15.1680	+	19.7673i	0.725582	+	0.945596i
$438$		0			0
$439$	5.33132	+	1.42852i	0.254450	+	0.0681796i	0.383789	−	0.923421i	$-0.374619\pi$
$439$	5.33132	+	1.42852i	0.254450	+	0.0681796i	−0.129339	+	0.991600i	$0.541286\pi$
$440$	−6.41447	+	7.21512i	−0.305798	+	0.343967i
$441$		0			0
$442$	0.911381	−	1.23710i	0.0433500	−	0.0588428i
$443$	3.55957	+	27.0376i	0.169120	+	1.28460i	0.839819	+	0.542866i	$0.182661\pi$
$443$	3.55957	+	27.0376i	0.169120	+	1.28460i	−0.670699	+	0.741730i	$0.734006\pi$
$444$		0			0
$445$	−1.09460	−	0.144107i	−0.0518890	−	0.00683132i
$446$	−21.1981	+	0.414656i	−1.00376	+	0.0196345i
$447$		0			0
$448$	4.05554	−	27.8805i	0.191606	−	1.31723i
$449$	−19.5429			−0.922287			−0.461144	−	0.887325i	$-0.652561\pi$
$449$	−19.5429			−0.922287			−0.461144	+	0.887325i	$0.652561\pi$
$450$		0			0
$451$	−6.72753	−	16.2417i	−0.316787	−	0.764791i
$452$	−0.183877	−	4.69829i	−0.00864884	−	0.220989i
$453$		0			0
$454$	−14.8741	−	34.0122i	−0.698077	−	1.59627i
$455$	−6.72612	+	1.80226i	−0.315326	+	0.0844912i
$456$		0			0
$457$	−19.3015	−	5.17182i	−0.902886	−	0.241928i	−0.222631	−	0.974903i	$-0.571464\pi$
$457$	−19.3015	−	5.17182i	−0.902886	−	0.241928i	−0.680255	+	0.732975i	$0.738131\pi$
$458$	−2.95986	−	19.5236i	−0.138305	−	0.912280i
$459$		0			0
$460$	−0.627038	+	6.81257i	−0.0292358	+	0.317638i
$461$	−22.6154	−	17.3534i	−1.05331	−	0.808230i	−0.0713710	−	0.997450i	$-0.522737\pi$
$461$	−22.6154	−	17.3534i	−1.05331	−	0.808230i	−0.981935	+	0.189220i	$0.939404\pi$
$462$		0			0
$463$	27.8633	+	16.0869i	1.29492	+	0.747620i	0.979521	−	0.201341i	$-0.0645300\pi$
$463$	27.8633	+	16.0869i	1.29492	+	0.747620i	0.315394	+	0.948961i	$0.397863\pi$
$464$	−10.5969	−	20.8133i	−0.491947	−	0.966231i
$465$		0			0
$466$	5.56855	+	19.2667i	0.257958	+	0.892511i
$467$	−24.3959	+	10.1051i	−1.12891	+	0.467609i	−0.867409	−	0.497595i	$-0.834217\pi$
$467$	−24.3959	+	10.1051i	−1.12891	+	0.467609i	−0.261498	+	0.965204i	$0.584217\pi$
$468$		0			0
$469$	9.92844	−	23.9694i	0.458453	−	1.10680i
$470$	3.01320	+	3.77178i	0.138988	+	0.173979i
$471$		0			0
$472$	−6.26698	+	5.42133i	−0.288461	+	0.249537i
$473$	48.3565	−	12.9571i	2.22344	−	0.595768i
$474$		0			0
$475$	−2.87528	−	21.8399i	−0.131927	−	1.00208i
$476$	0.760788	+	2.45146i	0.0348707	+	0.112363i
$477$		0			0
$478$	−20.5000	+	12.3764i	−0.937647	+	0.566085i
$479$	15.7051	+	27.2021i	0.717586	+	1.24289i	0.961954	+	0.273212i	$0.0880862\pi$
$479$	15.7051	+	27.2021i	0.717586	+	1.24289i	−0.244368	+	0.969683i	$0.578581\pi$
$480$		0			0
$481$	−12.1988	+	21.1289i	−0.556215	+	0.963393i
$482$	0.290931	+	14.8730i	0.0132515	+	0.677446i
$483$		0			0
$484$	−22.7457	−	21.0324i	−1.03390	−	0.956017i
$485$	0.00736530	+	0.00305081i	0.000334441	+	0.000138530i
$486$		0			0
$487$	5.85560	+	5.85560i	0.265343	+	0.265343i	0.827220	−	0.561878i	$-0.189921\pi$
$487$	5.85560	+	5.85560i	0.265343	+	0.265343i	−0.561878	+	0.827220i	$0.689921\pi$
$488$	16.8134	−	24.7977i	0.761106	−	1.12254i
$489$		0			0
$490$	1.84716	−	4.71839i	0.0834461	−	0.213155i
$491$	−13.9023	−	18.1179i	−0.627404	−	0.817649i	0.366204	−	0.930535i	$-0.380657\pi$
$491$	−13.9023	−	18.1179i	−0.627404	−	0.817649i	−0.993608	+	0.112886i	$0.963991\pi$
$492$		0			0
$493$	1.68812	+	1.29534i	0.0760289	+	0.0583391i
$494$	−19.7732	−	4.88581i	−0.889637	−	0.219823i
$495$		0			0
$496$	−13.6602	−	19.8887i	−0.613361	−	0.893031i
$497$	−25.3316	+	14.6252i	−1.13628	+	0.656030i
$498$		0			0
$499$	1.26745	−	9.62721i	0.0567387	−	0.430973i	−0.939375	−	0.342892i	$-0.888593\pi$
$499$	1.26745	−	9.62721i	0.0567387	−	0.430973i	0.996113	−	0.0880806i	$-0.0280733\pi$
$500$	7.31994	−	10.3541i	0.327358	−	0.463050i
$501$		0			0
$502$	2.16432	−	1.72903i	0.0965983	−	0.0771704i
$503$	19.8682	−	19.8682i	0.885879	−	0.885879i	−0.108245	−	0.994124i	$-0.534523\pi$
$503$	19.8682	−	19.8682i	0.885879	−	0.885879i	0.994124	+	0.108245i	$0.0345231\pi$
$504$		0			0
$505$	7.05834	+	7.05834i	0.314092	+	0.314092i
$506$	−37.3110	−	4.17151i	−1.65868	−	0.185446i
$507$		0			0
$508$	6.67864	+	10.5886i	0.296317	+	0.469792i
$509$	−4.39242	−	0.578273i	−0.194690	−	0.0256315i	0.0325503	−	0.999470i	$-0.489637\pi$
$509$	−4.39242	−	0.578273i	−0.194690	−	0.0256315i	−0.227241	+	0.973839i	$0.572970\pi$
$510$		0			0
$511$	−14.2661	−	24.7097i	−0.631096	−	1.09309i
$512$	22.2778	−	3.96249i	0.984547	−	0.175119i
$513$		0			0
$514$	11.4819	+	19.0183i	0.506446	+	0.838862i
$515$	2.47315	−	3.22307i	0.108980	−	0.142025i
$516$		0			0
$517$	−21.0179	+	16.1276i	−0.924366	+	0.709291i
$518$	−16.3299	−	37.3410i	−0.717495	−	1.64067i
$519$		0			0
$520$	−3.07547	−	4.67096i	−0.134868	−	0.204835i
$521$	−2.21180	+	2.21180i	−0.0969006	+	0.0969006i	−0.753895	−	0.656995i	$-0.771827\pi$
$521$	−2.21180	+	2.21180i	−0.0969006	+	0.0969006i	0.656995	+	0.753895i	$0.271827\pi$
$522$		0			0
$523$	5.64862	−	13.6370i	0.246997	−	0.596303i	−0.750949	−	0.660360i	$-0.770404\pi$
$523$	5.64862	−	13.6370i	0.246997	−	0.596303i	0.997946	+	0.0640565i	$0.0204038\pi$
$524$	−3.44168	−	7.46858i	−0.150350	−	0.326266i
$525$		0			0
$526$	12.8885	+	12.3939i	0.561965	+	0.540402i
$527$	1.90369	+	1.09910i	0.0829263	+	0.0478775i
$528$		0			0
$529$	−3.12194	+	1.80245i	−0.135736	+	0.0783674i
$530$	8.69367	+	2.14814i	0.377629	+	0.0933094i
$531$		0			0
$532$	26.1625	−	21.7524i	1.13429	−	0.943084i
$533$	10.0966	−	1.32925i	0.437334	−	0.0575761i
$534$		0			0
$535$	−3.04397	−	11.3603i	−0.131602	−	0.491147i
$536$	20.7823	+	1.50360i	0.897661	+	0.0649458i
$537$		0			0
$538$	0.176118	−	1.57525i	0.00759299	−	0.0679137i
$539$	25.6900	+	10.6411i	1.10655	+	0.458347i
$540$		0			0
$541$	6.82229	+	16.4705i	0.293313	+	0.708120i	1.00000		0.000593663i	$0.000188969\pi$
$541$	6.82229	+	16.4705i	0.293313	+	0.708120i	−0.706687	+	0.707526i	$0.749811\pi$
$542$	−13.9039	−	7.66883i	−0.597223	−	0.329405i
$543$		0			0
$544$	−1.67613	+	1.20013i	−0.0718633	+	0.0514550i
$545$	−0.476037	+	0.824520i	−0.0203912	+	0.0353186i
$546$		0			0
$547$	−3.77777	+	4.92329i	−0.161526	+	0.210505i	−0.867104	−	0.498128i	$-0.834021\pi$
$547$	−3.77777	+	4.92329i	−0.161526	+	0.210505i	0.705578	+	0.708633i	$0.250688\pi$
$548$	5.53088	+	17.8220i	0.236268	+	0.761317i
$549$		0			0
$550$	26.7233	+	19.6873i	1.13949	+	0.839469i
$551$	7.30006	−	27.2442i	0.310993	−	1.16064i
$552$		0			0
$553$	−4.34143	−	16.2025i	−0.184617	−	0.688998i
$554$	4.59745	−	11.7437i	0.195327	−	0.498944i
$555$		0			0
$556$	−14.7608	+	39.9921i	−0.625998	+	1.69604i
$557$	4.90627	−	2.03224i	0.207885	−	0.0861089i	−0.276311	−	0.961068i	$-0.589112\pi$
$557$	4.90627	−	2.03224i	0.207885	−	0.0861089i	0.484196	+	0.874959i	$0.339112\pi$
$558$		0			0
$559$			29.0004i			1.22659i
$560$	9.32926	+	0.491787i	0.394233	+	0.0207818i
$561$		0			0
$562$	−18.8260	−	18.1036i	−0.794126	−	0.763654i
$563$	−4.16537	+	31.6391i	−0.175549	+	1.33343i	0.646020	+	0.763321i	$0.276432\pi$
$563$	−4.16537	+	31.6391i	−0.175549	+	1.33343i	−0.821569	+	0.570109i	$0.806901\pi$
$564$		0			0
$565$	1.54576	−	0.203503i	0.0650307	−	0.00856146i
$566$	5.42974	+	35.8153i	0.228229	+	1.50543i
$567$		0			0
$568$	−17.5568	−	15.6086i	−0.736669	−	0.654922i
$569$	2.31938	−	8.65606i	0.0972336	−	0.362881i	−0.900115	−	0.435652i	$-0.856518\pi$
$569$	2.31938	−	8.65606i	0.0972336	−	0.362881i	0.997349	+	0.0727715i	$0.0231844\pi$
$570$		0			0
$571$	−18.5366	+	14.2236i	−0.775732	+	0.595240i	−0.918915	−	0.394456i	$-0.870933\pi$
$571$	−18.5366	+	14.2236i	−0.775732	+	0.595240i	0.143183	+	0.989696i	$0.454266\pi$
$572$	25.9581	−	16.3728i	1.08536	−	0.684580i
$573$		0			0
$574$	−8.21613	+	14.8962i	−0.342935	+	0.621754i
$575$	23.5214			0.980912
$576$		0			0
$577$	−37.3273			−1.55396			−0.776978	−	0.629528i	$-0.783248\pi$
$577$	−37.3273			−1.55396			−0.776978	+	0.629528i	$0.783248\pi$
$578$	−11.5206	+	20.8873i	−0.479194	+	0.868798i
$579$		0			0
$580$	6.55037	−	4.13158i	0.271989	−	0.171554i
$581$	−23.2433	+	17.8352i	−0.964296	+	0.739930i
$582$		0			0
$583$	−12.7192	+	47.4687i	−0.526776	+	1.96595i
$584$	15.2254	−	17.1258i	0.630031	−	0.708670i
$585$		0			0
$586$	−0.242675	−	1.60072i	−0.0100248	−	0.0661250i
$587$	3.95447	−	0.520616i	0.163218	−	0.0214881i	−0.0484740	−	0.998824i	$-0.515436\pi$
$587$	3.95447	−	0.520616i	0.163218	−	0.0214881i	0.211692	+	0.977336i	$0.432102\pi$
$588$		0			0
$589$	3.80329	−	28.8888i	0.156712	−	1.19034i
$590$	−1.98056	−	1.90456i	−0.0815383	−	0.0784095i
$591$		0			0
$592$	24.3314	−	21.8946i	1.00001	−	0.899864i
$593$			15.9184i			0.653691i	0.945078	+	0.326845i	$0.105986\pi$
$593$			15.9184i			0.653691i	−0.945078	+	0.326845i	$0.894014\pi$
$594$		0			0
$595$	−0.786339	+	0.325712i	−0.0322367	+	0.0133529i
$596$	0.743808	−	2.01523i	0.0304675	−	0.0825470i
$597$		0			0
$598$	7.92819	−	20.2518i	0.324208	−	0.828158i
$599$	−0.282184	−	1.05313i	−0.0115297	−	0.0430296i	0.959921	−	0.280270i	$-0.0904239\pi$
$599$	−0.282184	−	1.05313i	−0.0115297	−	0.0430296i	−0.971451	+	0.237240i	$0.923757\pi$
$600$		0			0
$601$	3.38870	−	12.6468i	0.138228	−	0.515874i	−0.861736	−	0.507358i	$-0.830622\pi$
$601$	3.38870	−	12.6468i	0.138228	−	0.515874i	0.999964	−	0.00851666i	$-0.00271097\pi$
$602$	−39.0031	−	28.7339i	−1.58965	−	1.17111i
$603$		0			0
$604$	4.08488	+	13.1626i	0.166211	+	0.535577i
$605$	6.25350	−	8.14972i	0.254241	−	0.331333i
$606$		0			0
$607$	−12.8234	+	22.2108i	−0.520486	+	0.901508i	0.479231	+	0.877689i	$0.340916\pi$
$607$	−12.8234	+	22.2108i	−0.520486	+	0.901508i	−0.999716	+	0.0238187i	$0.992418\pi$
$608$	23.1997	+	14.4388i	0.940871	+	0.585570i
$609$		0			0
$610$	8.69905	+	4.79805i	0.352214	+	0.194267i
$611$	−5.87293	−	14.1785i	−0.237593	−	0.573601i
$612$		0			0
$613$	3.23462	+	1.33982i	0.130645	+	0.0541149i	0.447048	−	0.894510i	$-0.352475\pi$
$613$	3.23462	+	1.33982i	0.130645	+	0.0541149i	−0.316403	+	0.948625i	$0.602475\pi$
$614$	−0.105414	+	0.942851i	−0.00425417	+	0.0380504i
$615$		0			0
$616$	−3.69953	+	51.1338i	−0.149058	+	2.06024i
$617$	−5.45373	−	20.3536i	−0.219559	−	0.819405i	−0.984512	−	0.175319i	$-0.943904\pi$
$617$	−5.45373	−	20.3536i	−0.219559	−	0.819405i	0.764953	−	0.644086i	$-0.222762\pi$
$618$		0			0
$619$	−9.37900	+	1.23477i	−0.376974	+	0.0496296i	−0.316633	−	0.948548i	$-0.602552\pi$
$619$	−9.37900	+	1.23477i	−0.376974	+	0.0496296i	−0.0603413	+	0.998178i	$0.519219\pi$
$620$	6.15200	−	5.11498i	0.247070	−	0.205422i
$621$		0			0
$622$	−18.0345	−	4.45619i	−0.723117	−	0.178677i
$623$	−5.07743	+	2.93145i	−0.203423	+	0.117446i
$624$		0			0
$625$	−16.1049	−	9.29815i	−0.644195	−	0.371926i
$626$	26.9216	+	25.8886i	1.07601	+	1.03472i
$627$		0			0
$628$	5.79780	+	12.5815i	0.231357	+	0.502055i
$629$	−1.14119	+	2.75508i	−0.0455022	+	0.109852i
$630$		0			0
$631$	2.19037	−	2.19037i	0.0871974	−	0.0871974i	−0.662163	−	0.749360i	$-0.730361\pi$
$631$	2.19037	−	2.19037i	0.0871974	−	0.0871974i	0.749360	+	0.662163i	$0.230361\pi$
$632$	11.2518	−	7.40845i	0.447572	−	0.294692i
$633$		0			0
$634$	−9.84791	−	22.5189i	−0.391110	−	0.894339i
$635$	−3.29332	+	2.52705i	−0.130691	+	0.100283i
$636$		0			0
$637$	−9.80592	+	12.7793i	−0.388525	+	0.506335i
$638$	21.9656	+	36.3831i	0.869626	+	1.44042i
$639$		0			0
$640$	1.98545	+	7.23557i	0.0784818	+	0.286011i
$641$	−0.687774	−	1.19126i	−0.0271654	−	0.0470519i	0.852123	−	0.523341i	$-0.175315\pi$
$641$	−0.687774	−	1.19126i	−0.0271654	−	0.0470519i	−0.879289	+	0.476290i	$0.841981\pi$
$642$		0			0
$643$	36.1711	+	4.76202i	1.42645	+	0.187796i	0.803891	−	0.594777i	$-0.202760\pi$
$643$	36.1711	+	4.76202i	1.42645	+	0.187796i	0.622559	+	0.782573i	$0.286093\pi$
$644$	19.3817	+	30.7285i	0.763745	+	1.21087i
$645$		0			0
$646$	−2.47412	−	0.276615i	−0.0973430	−	0.0108833i
$647$	1.20432	+	1.20432i	0.0473466	+	0.0473466i	0.730384	−	0.683037i	$-0.239341\pi$
$647$	1.20432	+	1.20432i	0.0473466	+	0.0473466i	−0.683037	+	0.730384i	$0.739341\pi$
$648$		0			0
$649$	10.6623	−	10.6623i	0.418530	−	0.418530i
$650$	−15.0226	+	12.0012i	−0.589234	+	0.470727i
$651$		0			0
$652$	−24.1648	+	34.1813i	−0.946367	+	1.33864i
$653$	−4.54597	+	34.5301i	−0.177898	+	1.35127i	0.636642	+	0.771159i	$0.280323\pi$
$653$	−4.54597	+	34.5301i	−0.177898	+	1.35127i	−0.814540	+	0.580108i	$0.803010\pi$
$654$		0			0
$655$	2.36149	−	1.36340i	0.0922709	−	0.0532726i
$656$	−13.4332	−	2.49394i	−0.524477	−	0.0973720i
$657$		0			0
$658$	24.8879	+	6.14962i	0.970230	+	0.239737i
$659$	18.5413	+	14.2272i	0.722265	+	0.554214i	0.903168	−	0.429287i	$-0.141235\pi$
$659$	18.5413	+	14.2272i	0.722265	+	0.554214i	−0.180903	+	0.983501i	$0.557902\pi$
$660$		0			0
$661$	−7.01686	−	9.14455i	−0.272924	−	0.355682i	0.636702	−	0.771110i	$-0.280298\pi$
$661$	−7.01686	−	9.14455i	−0.272924	−	0.355682i	−0.909626	+	0.415429i	$0.863632\pi$
$662$	−7.54095	+	19.2626i	−0.293087	+	0.748664i
$663$		0			0
$664$	−19.4753	−	13.2047i	−0.755789	−	0.512442i
$665$	7.97763	+	7.97763i	0.309359	+	0.309359i
$666$		0			0
$667$	27.8245	+	11.5253i	1.07737	+	0.446261i
$668$	4.21442	+	3.89696i	0.163061	+	0.150778i
$669$		0			0
$670$	0.135126	+	6.90792i	0.00522036	+	0.266876i
$671$	−27.2589	+	47.2138i	−1.05232	+	1.82267i
$672$		0			0
$673$	−21.3364	−	36.9557i	−0.822458	−	1.42454i	−0.903847	−	0.427857i	$-0.859269\pi$
$673$	−21.3364	−	36.9557i	−0.822458	−	1.42454i	0.0813884	−	0.996682i	$-0.474065\pi$
$674$	40.2940	−	24.3267i	1.55207	−	0.937028i
$675$		0			0
$676$	−2.43685	−	7.85218i	−0.0937250	−	0.302007i
$677$	−4.87762	−	37.0492i	−0.187462	−	1.42392i	−0.783715	−	0.621120i	$-0.786678\pi$
$677$	−4.87762	−	37.0492i	−0.187462	−	1.42392i	0.596253	−	0.802797i	$-0.296656\pi$
$678$		0			0
$679$	0.0408926	−	0.0109571i	0.00156931	−	0.000420497i
$680$	−0.447215	−	0.516975i	−0.0171499	−	0.0198251i
$681$		0			0
$682$	27.4039	+	34.3030i	1.04935	+	1.31353i
$683$	−1.78395	+	4.30684i	−0.0682611	+	0.164797i	−0.954328	−	0.298760i	$-0.903427\pi$
$683$	−1.78395	+	4.30684i	−0.0682611	+	0.164797i	0.886067	+	0.463557i	$0.153427\pi$
$684$		0			0
$685$	−5.71663	+	2.36791i	−0.218421	+	0.0904730i
$686$	2.20890	+	7.64259i	0.0843362	+	0.291796i
$687$		0			0
$688$	12.0344	−	36.9995i	0.458806	−	1.41059i
$689$	−24.6540	−	14.2340i	−0.939241	−	0.542271i
$690$		0			0
$691$	−7.76824	−	5.96078i	−0.295518	−	0.226759i	0.450351	−	0.892851i	$-0.351299\pi$
$691$	−7.76824	−	5.96078i	−0.295518	−	0.226759i	−0.745869	+	0.666093i	$0.767965\pi$
$692$	3.52122	−	38.2570i	0.133857	−	1.45431i
$693$		0			0
$694$	5.00256	+	32.9976i	0.189895	+	1.25257i
$695$	−13.6538	−	3.65852i	−0.517918	−	0.138776i
$696$		0			0
$697$	1.20233	−	0.322164i	0.0455416	−	0.0122028i
$698$	8.04215	+	18.3897i	0.304400	+	0.696061i
$699$		0			0
$700$	−1.25610	−	32.0951i	−0.0474763	−	1.21308i
$701$	−1.53880	−	3.71500i	−0.0581197	−	0.140313i	0.892152	−	0.451735i	$-0.149195\pi$
$701$	−1.53880	−	3.71500i	−0.0581197	−	0.140313i	−0.950272	+	0.311422i	$0.899195\pi$
$702$		0			0
$703$	39.5288			1.49086
$704$	−39.9123	+	10.1169i	−1.50425	+	0.381297i
$705$		0			0
$706$	14.4774	−	0.283192i	0.544864	−	0.0106581i
$707$	52.5547	+	6.91896i	1.97652	+	0.260214i
$708$		0			0
$709$	−4.54255	−	34.5041i	−0.170599	−	1.29583i	−0.835746	−	0.549116i	$-0.814965\pi$
$709$	−4.54255	−	34.5041i	−0.170599	−	1.29583i	0.665147	−	0.746712i	$-0.268369\pi$
$710$	4.62030	−	6.27155i	0.173397	−	0.235367i
$711$		0			0
$712$	−3.51907	−	3.12856i	−0.131883	−	0.117248i
$713$	30.0529	+	8.05266i	1.12549	+	0.301575i
$714$		0			0
$715$	6.19511	+	8.07363i	0.231684	+	0.301937i
$716$	16.7044	+	11.8094i	0.624274	+	0.441337i
$717$		0			0
$718$	13.7580	−	3.97640i	0.513443	−	0.148398i
$719$			48.6842i			1.81562i	0.419386	+	0.907808i	$0.362245\pi$
$719$			48.6842i			1.81562i	−0.419386	+	0.907808i	$0.637755\pi$
$720$		0			0
$721$		−	21.5739i		−	0.803455i
$722$	1.70202	+	5.88884i	0.0633427	+	0.219160i
$723$		0			0
$724$	−20.0142	+	3.43591i	−0.743821	+	0.127695i
$725$	−16.2092	−	21.1242i	−0.601995	−	0.784535i
$726$		0			0
$727$	19.8906	+	5.32966i	0.737701	+	0.197666i	0.608056	−	0.793894i	$-0.291950\pi$
$727$	19.8906	+	5.32966i	0.737701	+	0.197666i	0.129645	+	0.991560i	$0.458616\pi$
$728$	−28.0571	−	9.73655i	−1.03986	−	0.360861i
$729$		0			0
$730$	6.11757	+	4.50686i	0.226421	+	0.166806i
$731$	0.462673	+	3.51435i	0.0171126	+	0.129983i
$732$		0			0
$733$	−15.6428	−	2.05941i	−0.577780	−	0.0760662i	−0.164028	−	0.986456i	$-0.552449\pi$
$733$	−15.6428	−	2.05941i	−0.577780	−	0.0760662i	−0.413752	+	0.910389i	$0.635782\pi$
$734$	−0.380839	−	19.4693i	−0.0140570	−	0.718625i
$735$		0			0
$736$	−18.5190	+	22.5478i	−0.682618	+	0.831124i
$737$	−37.9160			−1.39665
$738$		0			0
$739$	0.521486	+	1.25898i	0.0191832	+	0.0463123i	0.933181	−	0.359407i	$-0.117021\pi$
$739$	0.521486	+	1.25898i	0.0191832	+	0.0463123i	−0.913998	+	0.405719i	$0.867021\pi$
$740$	7.96896	+	7.36869i	0.292945	+	0.270878i
$741$		0			0
$742$	43.5709	−	19.0544i	1.59954	−	0.699507i
$743$	−46.2290	+	12.3870i	−1.69598	+	0.454436i	−0.971922	−	0.235304i	$-0.924391\pi$
$743$	−46.2290	+	12.3870i	−1.69598	+	0.454436i	−0.724057	+	0.689740i	$0.757725\pi$
$744$		0			0
$745$	0.688024	+	0.184355i	0.0252072	+	0.00675426i
$746$	6.02936	−	0.914074i	0.220750	−	0.0334666i
$747$		0			0
$748$	2.88447	−	2.39824i	0.105467	−	0.0876883i
$749$	−49.5493	−	38.0205i	−1.81049	−	1.38924i
$750$		0			0
$751$	23.6971	+	13.6815i	0.864721	+	0.499247i	0.865590	−	0.500753i	$-0.166943\pi$
$751$	23.6971	+	13.6815i	0.864721	+	0.499247i	−0.000869577		1.00000i	$0.500277\pi$
$752$	1.60915	+	20.5264i	0.0586796	+	0.748522i
$753$		0			0
$754$	−23.6514	+	6.83584i	−0.861332	+	0.248946i
$755$	−4.22206	+	1.74884i	−0.153657	+	0.0636466i
$756$		0			0
$757$	−10.1539	+	24.5137i	−0.369050	+	0.890966i	0.624856	+	0.780740i	$0.285157\pi$
$757$	−10.1539	+	24.5137i	−0.369050	+	0.890966i	−0.993907	+	0.110226i	$0.964843\pi$
$758$	−23.3394	+	18.6453i	−0.847724	+	0.677228i
$759$		0			0
$760$	−4.06254	+	8.09923i	−0.147364	+	0.293790i
$761$	−5.59207	+	1.49839i	−0.202712	+	0.0543166i	−0.358746	−	0.933435i	$-0.616796\pi$
$761$	−5.59207	+	1.49839i	−0.202712	+	0.0543166i	0.156034	+	0.987752i	$0.450129\pi$
$762$		0			0
$763$	0.659925	+	5.01262i	0.0238909	+	0.181469i
$764$	−16.7172	+	31.7624i	−0.604806	+	1.14912i
$765$		0			0
$766$	27.2346	+	45.1106i	0.984027	+	1.62991i
$767$	4.36744	+	7.56462i	0.157699	+	0.273143i
$768$		0			0
$769$	−23.5101	+	40.7207i	−0.847795	+	1.46842i	0.0353762	+	0.999374i	$0.488737\pi$
$769$	−23.5101	+	40.7207i	−0.847795	+	1.46842i	−0.883171	+	0.469050i	$0.844596\pi$
$770$	−16.9965	+	0.332469i	−0.612513	+	0.0119814i
$771$		0			0
$772$	−9.15141	+	0.358159i	−0.329366	+	0.0128904i
$773$	42.6292	+	17.6576i	1.53326	+	0.635099i	0.980195	−	0.198036i	$-0.0634562\pi$
$773$	42.6292	+	17.6576i	1.53326	+	0.635099i	0.553070	+	0.833135i	$0.313456\pi$
$774$		0			0
$775$	−19.4505	−	19.4505i	−0.698682	−	0.698682i
$776$	0.0186978	+	0.0283979i	0.000671214	+	0.00101942i
$777$		0			0
$778$	23.0792	+	9.03504i	0.827428	+	0.323922i
$779$	−10.0444	−	13.0901i	−0.359877	−	0.469001i
$780$		0			0
$781$	33.9140	+	26.0231i	1.21354	+	0.931181i
$782$	0.637664	−	2.58066i	0.0228028	−	0.0922843i
$783$		0			0
$784$	17.8137	−	12.2350i	0.636205	−	0.436965i
$785$	−3.97813	+	2.29677i	−0.141985	+	0.0819753i
$786$		0			0
$787$	−5.21244	+	39.5924i	−0.185803	+	1.41132i	0.603524	+	0.797345i	$0.293763\pi$
$787$	−5.21244	+	39.5924i	−0.185803	+	1.41132i	−0.789327	+	0.613972i	$0.789571\pi$
$788$	−2.28840	−	13.3299i	−0.0815210	−	0.474859i
$789$		0			0
$790$	2.78819	+	3.49013i	0.0991994	+	0.124173i
$791$	5.85444	−	5.85444i	0.208160	−	0.208160i
$792$		0			0
$793$	−22.3314	−	22.3314i	−0.793012	−	0.793012i
$794$	2.69823	−	24.1337i	0.0957568	−	0.856473i
$795$		0			0
$796$	−6.76554	+	29.8782i	−0.239798	+	1.05900i
$797$	24.7257	+	3.25520i	0.875830	+	0.115305i	0.555019	−	0.831838i	$-0.312711\pi$
$797$	24.7257	+	3.25520i	0.875830	+	0.115305i	0.320811	+	0.947143i	$0.396044\pi$
$798$		0			0
$799$	−0.937903	−	1.62450i	−0.0331806	−	0.0574706i
$800$	24.1464	−	9.07753i	0.853705	−	0.320939i
$801$		0			0
$802$	−14.2881	+	8.62616i	−0.504531	+	0.304600i
$803$	−25.3842	+	33.0814i	−0.895790	+	1.16742i
$804$		0			0
$805$	−9.55735	+	7.33361i	−0.336852	+	0.258476i
$806$	−23.3028	+	10.1907i	−0.820805	+	0.358953i
$807$		0			0
$808$	8.02246	+	41.8099i	0.282229	+	1.47087i
$809$	−38.0030	+	38.0030i	−1.33611	+	1.33611i	−0.436325	+	0.899789i	$0.643720\pi$
$809$	−38.0030	+	38.0030i	−1.33611	+	1.33611i	−0.899789	+	0.436325i	$0.856280\pi$
$810$		0			0
$811$	2.57804	−	6.22395i	0.0905273	−	0.218552i	−0.872131	−	0.489273i	$-0.837262\pi$
$811$	2.57804	−	6.22395i	0.0905273	−	0.218552i	0.962658	+	0.270721i	$0.0872621\pi$
$812$	14.2404	−	38.5821i	0.499740	−	1.35397i
$813$		0			0
$814$	−41.2848	+	42.9322i	−1.44703	+	1.50477i
$815$	−12.0209	−	6.94027i	−0.421074	−	0.243107i
$816$		0			0
$817$	40.6913	−	23.4932i	1.42361	−	0.821922i
$818$	−10.1292	+	40.9934i	−0.354159	+	1.43330i
$819$		0			0
$820$	0.415231	−	4.51136i	0.0145005	−	0.157543i
$821$	38.5054	−	5.06934i	1.34385	−	0.176921i	0.575946	−	0.817488i	$-0.304634\pi$
$821$	38.5054	−	5.06934i	1.34385	−	0.176921i	0.767903	+	0.640567i	$0.221300\pi$
$822$		0			0
$823$	−4.52971	−	16.9051i	−0.157896	−	0.589275i	−0.998840	−	0.0481532i	$-0.984666\pi$
$823$	−4.52971	−	16.9051i	−0.157896	−	0.589275i	0.840944	−	0.541122i	$-0.182000\pi$
$824$	16.4445	−	5.45821i	0.572873	−	0.190146i
$825$		0			0
$826$	−14.5011	−	1.62127i	−0.504558	−	0.0564113i
$827$	−6.40373	−	2.65251i	−0.222679	−	0.0922368i	0.268555	−	0.963264i	$-0.413454\pi$
$827$	−6.40373	−	2.65251i	−0.222679	−	0.0922368i	−0.491234	+	0.871028i	$0.663454\pi$
$828$		0			0
$829$	−7.76228	−	18.7398i	−0.269595	−	0.650860i	0.729869	−	0.683587i	$-0.239581\pi$
$829$	−7.76228	−	18.7398i	−0.269595	−	0.650860i	−0.999464	+	0.0327264i	$0.989581\pi$
$830$	3.76824	−	6.83196i	0.130797	−	0.237141i
$831$		0			0
$832$	0.323150	−	23.8496i	0.0112032	−	0.826837i
$833$	−0.984429	+	1.70508i	−0.0341084	+	0.0590775i
$834$		0			0
$835$	−1.15867	+	1.51001i	−0.0400976	+	0.0522562i
$836$	−44.0018	−	23.1590i	−1.52183	−	0.800972i
$837$		0			0
$838$	17.9509	−	24.3664i	0.620103	−	0.841722i
$839$	11.7000	−	43.6649i	0.403928	−	1.50748i	−0.402096	−	0.915598i	$-0.631718\pi$
$839$	11.7000	−	43.6649i	0.403928	−	1.50748i	0.806024	−	0.591883i	$-0.201615\pi$
$840$		0			0
$841$	−1.31812	−	4.91929i	−0.0454524	−	0.169631i
$842$	18.4513	+	7.22333i	0.635875	+	0.248933i
$843$		0			0
$844$	47.2461	−	21.7720i	1.62628	−	0.749424i
$845$	2.51869	−	1.04327i	0.0866455	−	0.0358897i
$846$		0			0
$847$		−	54.5509i		−	1.87439i
$848$	25.5475	+	28.3908i	0.877304	+	0.974945i
$849$		0			0
$850$	−1.62901	+	1.69402i	−0.0558747	+	0.0581043i
$851$	−5.50925	+	41.8469i	−0.188855	+	1.43449i
$852$		0			0
$853$	−15.4839	+	2.03850i	−0.530160	+	0.0697969i	−0.390854	−	0.920453i	$-0.627820\pi$
$853$	−15.4839	+	2.03850i	−0.530160	+	0.0697969i	−0.139306	+	0.990249i	$0.544487\pi$
$854$	52.1601	−	7.90768i	1.78488	−	0.270595i
$855$		0			0
$856$	16.4448	−	47.3877i	0.562072	−	1.61968i
$857$	−6.36520	+	23.7553i	−0.217431	+	0.811464i	0.767865	+	0.640611i	$0.221319\pi$
$857$	−6.36520	+	23.7553i	−0.217431	+	0.811464i	−0.985297	+	0.170853i	$0.945348\pi$
$858$		0			0
$859$	−7.35907	+	5.64681i	−0.251088	+	0.192667i	−0.726635	−	0.687024i	$-0.758917\pi$
$859$	−7.35907	+	5.64681i	−0.251088	+	0.192667i	0.475547	+	0.879690i	$0.342250\pi$
$860$	12.5828	+	2.84921i	0.429069	+	0.0971574i
$861$		0			0
$862$	22.6572	+	12.4968i	0.771709	+	0.425644i
$863$	−20.8415			−0.709454			−0.354727	−	0.934970i	$-0.615426\pi$
$863$	−20.8415			−0.709454			−0.354727	+	0.934970i	$0.615426\pi$
$864$		0			0
$865$	12.7393			0.433148
$866$	−31.3673	−	17.3009i	−1.06590	−	0.587910i
$867$		0			0
$868$	9.38298	−	41.4374i	0.318479	−	1.40648i
$869$	−19.4484	+	14.9233i	−0.659743	+	0.506238i
$870$		0			0
$871$	5.68474	−	21.2157i	0.192620	−	0.718868i
$872$	−3.65387	+	1.77122i	−0.123736	+	0.0599810i
$873$		0			0
$874$	−34.8386	+	5.28167i	−1.17843	+	0.178655i
$875$	22.1373	−	2.91443i	0.748378	−	0.0985258i
$876$		0			0
$877$	−3.95256	+	30.0227i	−0.133469	+	1.01379i	0.785333	+	0.619074i	$0.212492\pi$
$877$	−3.95256	+	30.0227i	−0.133469	+	1.01379i	−0.918801	+	0.394720i	$0.870841\pi$
$878$	−5.41039	+	5.62627i	−0.182592	+	0.189878i
$879$		0			0
$880$	−4.55356	−	12.8714i	−0.153500	−	0.433893i
$881$		−	33.1137i		−	1.11563i	−0.829966	−	0.557814i	$-0.811640\pi$
$881$		−	33.1137i		−	1.11563i	0.829966	−	0.557814i	$-0.188360\pi$
$882$		0			0
$883$	7.72620	−	3.20030i	0.260007	−	0.107699i	−0.248872	−	0.968536i	$-0.580060\pi$
$883$	7.72620	−	3.20030i	0.260007	−	0.107699i	0.508879	+	0.860838i	$0.330060\pi$
$884$	0.909458	+	1.97356i	0.0305884	+	0.0663780i
$885$		0			0
$886$	−35.9130	−	14.0592i	−1.20652	−	0.472330i
$887$	−7.20893	−	26.9041i	−0.242052	−	0.903351i	−0.974842	−	0.222896i	$-0.928449\pi$
$887$	−7.20893	−	26.9041i	−0.242052	−	0.903351i	0.732790	−	0.680455i	$-0.238218\pi$
$888$		0			0
$889$	−5.70545	+	21.2930i	−0.191354	+	0.714145i
$890$	0.926086	−	1.25706i	0.0310425	−	0.0421367i
$891$		0			0
$892$	13.9652	−	26.5337i	0.467590	−	0.888413i
$893$	−15.1367	+	19.7265i	−0.506529	+	0.660121i
$894$		0			0
$895$	−3.39172	+	5.87462i	−0.113373	+	0.196367i
$896$	31.7556	+	24.0651i	1.06088	+	0.803958i
$897$		0			0
$898$	13.3482	−	24.2008i	0.445435	−	0.807590i
$899$	−13.4783	−	32.5394i	−0.449525	−	1.08525i
$900$		0			0
$901$	−3.21473	−	1.33158i	−0.107098	−	0.0443615i
$902$	24.7077	+	2.76241i	0.822678	+	0.0919783i
$903$		0			0
$904$	5.94367	+	2.98132i	0.197684	+	0.0991572i
$905$	−1.74278	−	6.50415i	−0.0579320	−	0.216205i
$906$		0			0
$907$	29.6142	−	3.89879i	0.983325	−	0.129457i	0.378316	−	0.925676i	$-0.376503\pi$
$907$	29.6142	−	3.89879i	0.983325	−	0.129457i	0.605008	+	0.796219i	$0.293170\pi$
$908$	52.2779	+	4.81173i	1.73490	+	0.159683i
$909$		0			0
$910$	2.36226	−	9.56020i	0.0783082	−	0.316918i
$911$	−3.23823	+	1.86959i	−0.107287	+	0.0619423i	−0.552683	−	0.833391i	$-0.686396\pi$
$911$	−3.23823	+	1.86959i	−0.107287	+	0.0619423i	0.445396	+	0.895334i	$0.353063\pi$
$912$		0			0
$913$	37.0803	+	21.4083i	1.22718	+	0.708512i
$914$	19.5878	−	20.3694i	0.647906	−	0.673759i
$915$		0			0
$916$	26.1985	+	9.66970i	0.865624	+	0.319496i
$917$	5.54141	−	13.3782i	0.182994	−	0.441785i
$918$		0			0
$919$	−19.7686	+	19.7686i	−0.652106	+	0.652106i	−0.953500	−	0.301394i	$-0.902548\pi$
$919$	−19.7686	+	19.7686i	−0.652106	+	0.652106i	0.301394	+	0.953500i	$0.402548\pi$
$920$	−8.00800	−	5.42960i	−0.264016	−	0.179009i
$921$		0			0
$922$	36.9362	−	16.1529i	1.21643	−	0.531966i
$923$	−19.6459	+	15.0748i	−0.646652	+	0.496194i
$924$		0			0
$925$	22.7167	−	29.6049i	0.746919	−	0.973404i
$926$	−38.9521	+	23.5165i	−1.28005	+	0.772802i
$927$		0			0
$928$	33.0117	+	1.09332i	1.08366	+	0.0358901i
$929$	−0.818762	−	1.41814i	−0.0268627	−	0.0465276i	0.852282	−	0.523083i	$-0.175218\pi$
$929$	−0.818762	−	1.41814i	−0.0268627	−	0.0465276i	−0.879144	+	0.476556i	$0.841885\pi$
$930$		0			0
$931$	25.8748	+	3.40649i	0.848013	+	0.111643i
$932$	−27.6621	−	6.26374i	−0.906102	−	0.205176i
$933$		0			0
$934$	4.14930	−	37.1124i	0.135769	−	1.21435i
$935$	0.879549	+	0.879549i	0.0287643	+	0.0287643i
$936$		0			0
$937$	−34.2841	+	34.2841i	−1.12001	+	1.12001i	−0.128273	+	0.991739i	$0.540943\pi$
$937$	−34.2841	+	34.2841i	−1.12001	+	1.12001i	−0.991739	+	0.128273i	$0.959057\pi$
$938$	22.9009	+	28.6663i	0.747741	+	0.935988i
$939$		0			0
$940$	−6.72881	+	1.15516i	−0.219470	+	0.0376773i
$941$	1.17410	−	8.91816i	0.0382745	−	0.290724i	−0.961594	−	0.274478i	$-0.911495\pi$
$941$	1.17410	−	8.91816i	0.0382745	−	0.290724i	0.999868	−	0.0162462i	$-0.00517157\pi$
$942$		0			0
$943$	15.2577	−	8.80902i	0.496858	−	0.286861i
$944$	−2.43298	−	11.4635i	−0.0791868	−	0.373106i
$945$		0			0
$946$	−16.9831	+	68.7317i	−0.552169	+	2.23466i
$947$	10.3095	+	7.91078i	0.335015	+	0.257066i	0.762545	−	0.646935i	$-0.223950\pi$
$947$	10.3095	+	7.91078i	0.335015	+	0.257066i	−0.427530	+	0.904001i	$0.640616\pi$
$948$		0			0
$949$	−14.7047	−	19.1635i	−0.477335	−	0.622075i
$950$	29.0091	+	11.3565i	0.941179	+	0.368453i
$951$		0			0
$952$	−3.55538	−	0.732281i	−0.115230	−	0.0237334i
$953$	−28.2602	−	28.2602i	−0.915437	−	0.915437i	0.0812562	−	0.996693i	$-0.474107\pi$
$953$	−28.2602	−	28.2602i	−0.915437	−	0.915437i	−0.996693	+	0.0812562i	$0.974107\pi$
$954$		0			0
$955$	−10.9958	−	4.55462i	−0.355817	−	0.147384i
$956$	−1.32437	−	33.8393i	−0.0428331	−	1.09444i
$957$		0			0
$958$	−44.4123	+	0.868749i	−1.43490	+	0.0280680i
$959$	−16.4294	+	28.4565i	−0.530532	+	0.918908i
$960$		0			0
$961$	−2.69260	−	4.66373i	−0.0868582	−	0.150443i
$962$	−17.8327	−	29.5376i	−0.574950	−	0.952331i
$963$		0			0
$964$	−18.6165	−	9.79826i	−0.599598	−	0.315581i
$965$	−0.396388	−	3.01086i	−0.0127602	−	0.0969231i
$966$		0			0
$967$	−32.1519	+	8.61509i	−1.03394	+	0.277043i	−0.735599	−	0.677418i	$-0.763099\pi$
$967$	−32.1519	+	8.61509i	−1.03394	+	0.277043i	−0.298338	+	0.954460i	$0.596432\pi$
$968$	41.5810	−	13.8014i	1.33646	−	0.443594i
$969$		0			0
$970$	−0.00880858	+	0.00703699i	−0.000282826	+	0.000225944i
$971$	15.4074	−	37.1968i	0.494448	−	1.19370i	−0.457987	−	0.888959i	$-0.651429\pi$
$971$	15.4074	−	37.1968i	0.494448	−	1.19370i	0.952435	−	0.304743i	$-0.0985706\pi$
$972$		0			0
$973$	−69.3506	+	28.7260i	−2.22328	+	0.920913i
$974$	−11.2507	+	3.25174i	−0.360496	+	0.104192i
$975$		0			0
$976$	19.2241	+	37.7580i	0.615348	+	1.20860i
$977$	−31.2571	−	18.0463i	−1.00000	−	0.577352i	−0.0917535	−	0.995782i	$-0.529247\pi$
$977$	−31.2571	−	18.0463i	−1.00000	−	0.577352i	−0.908249	+	0.418430i	$0.862581\pi$
$978$		0			0
$979$	6.79768	+	5.21604i	0.217255	+	0.166705i
$980$	4.58133	+	5.51016i	0.146345	+	0.176016i
$981$		0			0
$982$	31.9317	−	4.84097i	1.01898	−	0.154481i
$983$	−0.923447	−	0.247437i	−0.0294534	−	0.00789201i	0.244062	−	0.969760i	$-0.421520\pi$
$983$	−0.923447	−	0.247437i	−0.0294534	−	0.00789201i	−0.273516	+	0.961868i	$0.588187\pi$
$984$		0			0
$985$	4.33193	−	1.16074i	0.138027	−	0.0369841i
$986$	−2.75708	+	1.20572i	−0.0878034	+	0.0383980i
$987$		0			0
$988$	19.5557	−	21.1488i	0.622151	−	0.672833i
$989$	19.1996	+	46.3520i	0.610513	+	1.47391i
$990$		0			0
$991$	42.0988			1.33731			0.668657	−	0.743571i	$-0.266869\pi$
$991$	42.0988			1.33731			0.668657	+	0.743571i	$0.266869\pi$
$992$	33.9592	−	3.33158i	1.07821	−	0.105778i
$993$		0			0
$994$	−0.809012	−	41.3584i	−0.0256603	−	1.31181i
$995$	−10.0712	−	1.32590i	−0.319280	−	0.0420339i
$996$		0			0
$997$	−0.935630	−	7.10681i	−0.0296317	−	0.225075i	0.970221	−	0.242220i	$-0.0778756\pi$
$997$	−0.935630	−	7.10681i	−0.0296317	−	0.225075i	−0.999853	+	0.0171451i	$0.994542\pi$
$998$	11.0561	+	8.14509i	0.349974	+	0.257828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.37.17		368
3.2	odd	2		288.2.bc.a.229.30	yes	368
9.2	odd	6		288.2.bc.a.133.1	yes	368
9.7	even	3	inner	864.2.bk.a.613.46		368
32.13	even	8	inner	864.2.bk.a.685.46		368
96.77	odd	8		288.2.bc.a.13.1	✓	368
288.173	odd	24		288.2.bc.a.205.30	yes	368
288.205	even	24	inner	864.2.bk.a.397.17		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.1	✓	368	96.77	odd	8
288.2.bc.a.133.1	yes	368	9.2	odd	6
288.2.bc.a.205.30	yes	368	288.173	odd	24
288.2.bc.a.229.30	yes	368	3.2	odd	2
864.2.bk.a.37.17		368	1.1	even	1	trivial
864.2.bk.a.397.17		368	288.205	even	24	inner
864.2.bk.a.613.46		368	9.7	even	3	inner
864.2.bk.a.685.46		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)

\(f(q)\)	\(=\)	\(q+(-0.683019 + 1.23834i) q^{2} +(-1.06697 - 1.69162i) q^{4} +(0.526137 - 0.403719i) q^{5} +(0.911495 - 3.40174i) q^{7} +(2.82356 - 0.165864i) q^{8} +O(q^{10})\)	\(q+(-0.683019 + 1.23834i) q^{2} +(-1.06697 - 1.69162i) q^{4} +(0.526137 - 0.403719i) q^{5} +(0.911495 - 3.40174i) q^{7} +(2.82356 - 0.165864i) q^{8} +(0.140580 + 0.927284i) q^{10} +(-5.10279 + 0.671795i) q^{11} +(0.389161 - 2.95597i) q^{13} +(3.58995 + 3.45220i) q^{14} +(-1.72315 + 3.60981i) q^{16} -0.364422i q^{17} +(-4.46287 + 1.84858i) q^{19} +(-1.24431 - 0.459267i) q^{20} +(2.65339 - 6.77783i) q^{22} +(-1.33499 - 4.98224i) q^{23} +(-1.18026 + 4.40481i) q^{25} +(3.39469 + 2.50090i) q^{26} +(-6.72699 + 2.08766i) q^{28} +(-3.55450 + 4.63232i) q^{29} +(-3.01601 + 5.22388i) q^{31} +(-3.29323 - 4.59941i) q^{32} +(0.451278 + 0.248907i) q^{34} +(-0.893778 - 2.15777i) q^{35} +(-7.56014 - 3.13151i) q^{37} +(0.759053 - 6.78917i) q^{38} +(1.41862 - 1.22719i) q^{40} +(0.884042 + 3.29929i) q^{41} +(-9.64364 + 1.26961i) q^{43} +(6.58094 + 7.91518i) q^{44} +(7.08153 + 1.74980i) q^{46} +(4.45774 - 2.57368i) q^{47} +(-4.67887 - 2.70134i) q^{49} +(-4.64850 - 4.47013i) q^{50} +(-5.41559 + 2.49562i) q^{52} +(3.65397 - 8.82145i) q^{53} +(-2.41355 + 2.41355i) q^{55} +(2.00943 - 9.75621i) q^{56} +(-3.30859 - 7.56564i) q^{58} +(-2.32430 + 1.78350i) q^{59} +(6.44833 - 8.40362i) q^{61} +(-4.40895 - 7.30285i) q^{62} +(7.94498 - 0.936655i) q^{64} +(-0.988629 - 1.71236i) q^{65} +(7.30385 + 0.961570i) q^{67} +(-0.616463 + 0.388827i) q^{68} +(3.28252 + 0.366998i) q^{70} +(-5.87298 - 5.87298i) q^{71} +(5.72879 - 5.72879i) q^{73} +(9.04159 - 7.22313i) q^{74} +(7.88885 + 5.57709i) q^{76} +(-2.36589 + 17.9707i) q^{77} +(4.12486 - 2.38149i) q^{79} +(0.550739 + 2.59492i) q^{80} +(-4.68946 - 1.15873i) q^{82} +(-6.59994 - 5.06432i) q^{83} +(-0.147124 - 0.191736i) q^{85} +(5.01458 - 12.8093i) q^{86} +(-14.2966 + 2.74322i) q^{88} +(-1.17717 - 1.17717i) q^{89} +(-9.70073 - 4.01817i) q^{91} +(-7.00366 + 7.57419i) q^{92} +(0.142366 + 7.27806i) q^{94} +(-1.60177 + 2.77435i) q^{95} +(0.00601054 + 0.0104106i) q^{97} +(6.54094 - 3.94896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 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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