LMFDB - Embedded newform 900.2.bj.e.523.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(127,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [224,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			523.24
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.e.487.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28840 - 0.583112i) q^{2} +(1.31996 - 1.50257i) q^{4} +(-1.38078 + 1.75882i) q^{5} +(-3.44825 - 3.44825i) q^{7} +(0.824475 - 2.70559i) q^{8} +(-0.753412 + 3.07122i) q^{10} +(-0.665578 - 0.916089i) q^{11} +(-0.0598699 - 0.378004i) q^{13} +(-6.45345 - 2.43201i) q^{14} +(-0.515411 - 3.96665i) q^{16} +(0.869332 + 0.442947i) q^{17} +(-0.904594 - 2.78406i) q^{19} +(0.820167 + 4.39629i) q^{20} +(-1.39171 - 0.792185i) q^{22} +(0.211827 - 1.33742i) q^{23} +(-1.18689 - 4.85709i) q^{25} +(-0.297555 - 0.452110i) q^{26} +(-9.73277 + 0.629671i) q^{28} +(-6.57862 - 2.13752i) q^{29} +(-5.91690 + 1.92252i) q^{31} +(-2.97706 - 4.81010i) q^{32} +(1.37834 + 0.0637754i) q^{34} +(10.8261 - 1.30357i) q^{35} +(-8.95424 + 1.41821i) q^{37} +(-2.78890 - 3.05950i) q^{38} +(3.62023 + 5.18593i) q^{40} +(5.06982 + 3.68344i) q^{41} +(4.02869 - 4.02869i) q^{43} +(-2.25502 - 0.209126i) q^{44} +(-0.506950 - 1.84666i) q^{46} +(9.68440 - 4.93445i) q^{47} +16.7808i q^{49} +(-4.36142 - 5.56579i) q^{50} +(-0.647001 - 0.408991i) q^{52} +(8.69751 - 4.43160i) q^{53} +(2.53025 + 0.0942872i) q^{55} +(-12.1726 + 6.48657i) q^{56} +(-9.72232 + 1.08208i) q^{58} +(-3.65195 - 2.65330i) q^{59} +(6.58194 - 4.78206i) q^{61} +(-6.50231 + 5.92720i) q^{62} +(-6.64048 - 4.46139i) q^{64} +(0.747507 + 0.416640i) q^{65} +(5.19430 - 10.1944i) q^{67} +(1.81304 - 0.721557i) q^{68} +(13.1883 - 7.99237i) q^{70} +(2.75549 + 0.895311i) q^{71} +(3.17780 + 0.503314i) q^{73} +(-10.7097 + 7.04856i) q^{74} +(-5.37726 - 2.31563i) q^{76} +(-0.863825 + 5.45398i) q^{77} +(-3.19543 + 9.83453i) q^{79} +(7.68830 + 4.57057i) q^{80} +(8.67982 + 1.78948i) q^{82} +(9.67363 + 4.92896i) q^{83} +(-1.97942 + 0.917386i) q^{85} +(2.84139 - 7.53974i) q^{86} +(-3.02732 + 1.04549i) q^{88} +(8.22988 + 11.3275i) q^{89} +(-1.09700 + 1.50990i) q^{91} +(-1.72997 - 2.08363i) q^{92} +(9.60007 - 12.0046i) q^{94} +(6.14570 + 2.25315i) q^{95} +(-4.93021 - 9.67608i) q^{97} +(9.78511 + 21.6205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 4 q^{10} + 16 q^{13} - 16 q^{16} + 28 q^{22} - 32 q^{25} + 28 q^{28} - 100 q^{34} - 104 q^{37} + 60 q^{40} + 156 q^{52} + 144 q^{58} - 48 q^{61} + 60 q^{64} + 28 q^{70} + 40 q^{73} + 64 q^{82} + 136 q^{85}+ \cdots - 160 q^{97}+O(q^{100}) $ 224 * q - 4 * q^10 + 16 * q^13 - 16 * q^16 + 28 * q^22 - 32 * q^25 + 28 * q^28 - 100 * q^34 - 104 * q^37 + 60 * q^40 + 156 * q^52 + 144 * q^58 - 48 * q^61 + 60 * q^64 + 28 * q^70 + 40 * q^73 + 64 * q^82 + 136 * q^85 + 148 * q^88 + 40 * q^94 - 160 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	1.28840	−	0.583112i	0.911038	−	0.412323i
$2$	1.28840	−	0.583112i	0.911038	−	0.412323i
$3$		0			0
$3$		0			0
$4$	1.31996	−	1.50257i	0.659980	−	0.751283i
$5$	−1.38078	+	1.75882i	−0.617504	+	0.786568i
$5$	−1.38078	+	1.75882i	−0.617504	+	0.786568i
$6$		0			0
$7$	−3.44825	−	3.44825i	−1.30332	−	1.30332i	−0.926143	−	0.377172i	$-0.876897\pi$
$7$	−3.44825	−	3.44825i	−1.30332	−	1.30332i	−0.377172	−	0.926143i	$-0.623103\pi$
$8$	0.824475	−	2.70559i	0.291496	−	0.956572i
$9$		0			0
$10$	−0.753412	+	3.07122i	−0.238250	+	0.971204i
$11$	−0.665578	−	0.916089i	−0.200679	−	0.276211i	0.696802	−	0.717263i	$-0.254605\pi$
$11$	−0.665578	−	0.916089i	−0.200679	−	0.276211i	−0.897482	+	0.441052i	$0.854605\pi$
$12$		0			0
$13$	−0.0598699	−	0.378004i	−0.0166049	−	0.104839i	0.977994	−	0.208634i	$-0.0669016\pi$
$13$	−0.0598699	−	0.378004i	−0.0166049	−	0.104839i	−0.994599	+	0.103794i	$0.966902\pi$
$14$	−6.45345	−	2.43201i	−1.72476	−	0.649983i
$15$		0			0
$16$	−0.515411	−	3.96665i	−0.128853	−	0.991664i
$17$	0.869332	+	0.442947i	0.210844	+	0.107430i	0.556224	−	0.831033i	$-0.312250\pi$
$17$	0.869332	+	0.442947i	0.210844	+	0.107430i	−0.345380	+	0.938463i	$0.612250\pi$
$18$		0			0
$19$	−0.904594	−	2.78406i	−0.207528	−	0.638706i	−0.999600	−	0.0282783i	$-0.990998\pi$
$19$	−0.904594	−	2.78406i	−0.207528	−	0.638706i	0.792072	−	0.610428i	$-0.209002\pi$
$20$	0.820167	+	4.39629i	0.183395	+	0.983039i
$21$		0			0
$22$	−1.39171	−	0.792185i	−0.296714	−	0.168894i
$23$	0.211827	−	1.33742i	0.0441690	−	0.278872i	−0.955712	−	0.294304i	$-0.904912\pi$
$23$	0.211827	−	1.33742i	0.0441690	−	0.278872i	0.999881	+	0.0154316i	$0.00491221\pi$
$24$		0			0
$25$	−1.18689	−	4.85709i	−0.237378	−	0.971417i
$26$	−0.297555	−	0.452110i	−0.0583554	−	0.0886660i
$27$		0			0
$28$	−9.73277	+	0.629671i	−1.83932	+	0.118997i
$29$	−6.57862	−	2.13752i	−1.22162	−	0.396928i	−0.373948	−	0.927450i	$-0.621996\pi$
$29$	−6.57862	−	2.13752i	−1.22162	−	0.396928i	−0.847671	+	0.530522i	$0.821996\pi$
$30$		0			0
$31$	−5.91690	+	1.92252i	−1.06271	+	0.345294i	−0.787643	−	0.616132i	$-0.788699\pi$
$31$	−5.91690	+	1.92252i	−1.06271	+	0.345294i	−0.275064	+	0.961426i	$0.588699\pi$
$32$	−2.97706	−	4.81010i	−0.526275	−	0.850314i
$33$		0			0
$34$	1.37834	+	0.0637754i	0.236383	+	0.0109374i
$35$	10.8261	−	1.30357i	1.82995	−	0.220344i
$36$		0			0
$37$	−8.95424	+	1.41821i	−1.47207	+	0.233153i	−0.840350	−	0.542045i	$-0.817650\pi$
$37$	−8.95424	+	1.41821i	−1.47207	+	0.233153i	−0.631719	+	0.775198i	$0.717650\pi$
$38$	−2.78890	−	3.05950i	−0.452419	−	0.496317i
$39$		0			0
$40$	3.62023	+	5.18593i	0.572409	+	0.819968i
$41$	5.06982	+	3.68344i	0.791772	+	0.575256i	0.908489	−	0.417909i	$-0.137237\pi$
$41$	5.06982	+	3.68344i	0.791772	+	0.575256i	−0.116717	+	0.993165i	$0.537237\pi$
$42$		0			0
$43$	4.02869	−	4.02869i	0.614369	−	0.614369i	−0.329713	−	0.944081i	$-0.606952\pi$
$43$	4.02869	−	4.02869i	0.614369	−	0.614369i	0.944081	+	0.329713i	$0.106952\pi$
$44$	−2.25502	−	0.209126i	−0.339957	−	0.0315270i
$45$		0			0
$46$	−0.506950	−	1.84666i	−0.0747457	−	0.272275i
$47$	9.68440	−	4.93445i	1.41262	−	0.719763i	0.429554	−	0.903041i	$-0.358671\pi$
$47$	9.68440	−	4.93445i	1.41262	−	0.719763i	0.983061	+	0.183278i	$0.0586707\pi$
$48$		0			0
$49$			16.7808i			2.39726i
$50$	−4.36142	−	5.56579i	−0.616798	−	0.787122i
$51$		0			0
$52$	−0.647001	−	0.408991i	−0.0897230	−	0.0567169i
$53$	8.69751	−	4.43160i	1.19469	−	0.608727i	0.260494	−	0.965475i	$-0.416114\pi$
$53$	8.69751	−	4.43160i	1.19469	−	0.608727i	0.934201	+	0.356748i	$0.116114\pi$
$54$		0			0
$55$	2.53025	+	0.0942872i	0.341179	+	0.0127137i
$56$	−12.1726	+	6.48657i	−1.62663	+	0.866804i
$57$		0			0
$58$	−9.72232	+	1.08208i	−1.27660	+	0.142085i
$59$	−3.65195	−	2.65330i	−0.475443	−	0.345430i	0.324116	−	0.946018i	$-0.394933\pi$
$59$	−3.65195	−	2.65330i	−0.475443	−	0.345430i	−0.799559	+	0.600588i	$0.794933\pi$
$60$		0			0
$61$	6.58194	−	4.78206i	0.842732	−	0.612280i	−0.0804007	−	0.996763i	$-0.525620\pi$
$61$	6.58194	−	4.78206i	0.842732	−	0.612280i	0.923132	+	0.384482i	$0.125620\pi$
$62$	−6.50231	+	5.92720i	−0.825794	+	0.752755i
$63$		0			0
$64$	−6.64048	−	4.46139i	−0.830060	−	0.557673i
$65$	0.747507	+	0.416640i	0.0927169	+	0.0516778i
$66$		0			0
$67$	5.19430	−	10.1944i	0.634585	−	1.24544i	−0.319976	−	0.947426i	$-0.603675\pi$
$67$	5.19430	−	10.1944i	0.634585	−	1.24544i	0.954561	−	0.298017i	$-0.0963251\pi$
$68$	1.81304	−	0.721557i	0.219863	−	0.0875016i
$69$		0			0
$70$	13.1883	−	7.99237i	1.57630	−	0.955270i
$71$	2.75549	+	0.895311i	0.327016	+	0.106254i	0.467924	−	0.883769i	$-0.345002\pi$
$71$	2.75549	+	0.895311i	0.327016	+	0.106254i	−0.140908	+	0.990023i	$0.545002\pi$
$72$		0			0
$73$	3.17780	+	0.503314i	0.371933	+	0.0589084i	0.339603	−	0.940569i	$-0.389707\pi$
$73$	3.17780	+	0.503314i	0.371933	+	0.0589084i	0.0323299	+	0.999477i	$0.489707\pi$
$74$	−10.7097	+	7.04856i	−1.24498	+	0.819378i
$75$		0			0
$76$	−5.37726	−	2.31563i	−0.616814	−	0.265621i
$77$	−0.863825	+	5.45398i	−0.0984420	+	0.621539i
$78$		0			0
$79$	−3.19543	+	9.83453i	−0.359514	+	1.10647i	0.593831	+	0.804590i	$0.297615\pi$
$79$	−3.19543	+	9.83453i	−0.359514	+	1.10647i	−0.953345	+	0.301881i	$0.902385\pi$
$80$	7.68830	+	4.57057i	0.859578	+	0.511005i
$81$		0			0
$82$	8.67982	+	1.78948i	0.958525	+	0.197615i
$83$	9.67363	+	4.92896i	1.06182	+	0.541023i	0.895506	−	0.445050i	$-0.146814\pi$
$83$	9.67363	+	4.92896i	1.06182	+	0.541023i	0.166312	+	0.986073i	$0.446814\pi$
$84$		0			0
$85$	−1.97942	+	0.917386i	−0.214698	+	0.0995044i
$86$	2.84139	−	7.53974i	0.306395	−	0.813032i
$87$		0			0
$88$	−3.02732	+	1.04549i	−0.322713	+	0.111450i
$89$	8.22988	+	11.3275i	0.872366	+	1.20071i	0.978477	+	0.206354i	$0.0661599\pi$
$89$	8.22988	+	11.3275i	0.872366	+	1.20071i	−0.106112	+	0.994354i	$0.533840\pi$
$90$		0			0
$91$	−1.09700	+	1.50990i	−0.114997	+	0.158280i
$92$	−1.72997	−	2.08363i	−0.180361	−	0.217234i
$93$		0			0
$94$	9.60007	−	12.0046i	0.990171	−	1.23819i
$95$	6.14570	+	2.25315i	0.630535	+	0.231168i
$96$		0			0
$97$	−4.93021	−	9.67608i	−0.500587	−	0.982457i	−0.993655	−	0.112467i	$-0.964125\pi$
$97$	−4.93021	−	9.67608i	−0.500587	−	0.982457i	0.493069	−	0.869990i	$-0.335875\pi$
$98$	9.78511	+	21.6205i	0.988445	+	2.18400i
$99$		0			0
$100$	−8.86474	−	4.62778i	−0.886474	−	0.462778i
$101$	0.642043			0.0638857			0.0319429	−	0.999490i	$-0.489831\pi$
$101$	0.642043			0.0638857			0.0319429	+	0.999490i	$0.489831\pi$
$102$		0			0
$103$	0.889862	+	1.74645i	0.0876807	+	0.172083i	0.930683	−	0.365827i	$-0.119214\pi$
$103$	0.889862	+	1.74645i	0.0876807	+	0.172083i	−0.843002	+	0.537910i	$0.819214\pi$
$104$	−1.07209	−	0.149671i	−0.105127	−	0.0146764i
$105$		0			0
$106$	8.62177	−	10.7813i	0.837420	−	1.04717i
$107$	−2.25202	−	2.25202i	−0.217711	−	0.217711i	0.589822	−	0.807533i	$-0.299198\pi$
$107$	−2.25202	−	2.25202i	−0.217711	−	0.217711i	−0.807533	+	0.589822i	$0.799198\pi$
$108$		0			0
$109$	−5.68371	+	7.82296i	−0.544401	+	0.749303i	−0.989239	−	0.146307i	$-0.953261\pi$
$109$	−5.68371	+	7.82296i	−0.544401	+	0.749303i	0.444838	+	0.895611i	$0.353261\pi$
$110$	3.31496	−	1.35394i	0.316069	−	0.129093i
$111$		0			0
$112$	−11.9007	+	15.4553i	−1.12451	+	1.46039i
$113$	3.29273	+	20.7895i	0.309754	+	1.95571i	0.293912	+	0.955832i	$0.405043\pi$
$113$	3.29273	+	20.7895i	0.309754	+	1.95571i	0.0158414	+	0.999875i	$0.494957\pi$
$114$		0			0
$115$	2.05980	+	2.21926i	0.192077	+	0.206947i
$116$	−11.8953	+	7.06337i	−1.10445	+	0.655817i
$117$		0			0
$118$	−6.25235	−	1.28902i	−0.575575	−	0.118664i
$119$	−1.47028	−	4.52506i	−0.134781	−	0.414812i
$120$		0			0
$121$	3.00296	−	9.24217i	0.272996	−	0.840197i
$122$	5.69171	−	9.99923i	0.515303	−	0.905288i
$123$		0			0
$124$	−4.92136	+	11.4282i	−0.441952	+	1.02628i
$125$	10.1816	+	4.61905i	0.910668	+	0.413140i
$126$		0			0
$127$	−6.98557	−	1.10641i	−0.619869	−	0.0981777i	−0.161402	−	0.986889i	$-0.551601\pi$
$127$	−6.98557	−	1.10641i	−0.619869	−	0.0981777i	−0.458468	+	0.888711i	$0.651601\pi$
$128$	−11.1571	−	1.87591i	−0.986158	−	0.165809i
$129$		0			0
$130$	1.20604	+	0.100919i	0.105777	+	0.00885117i
$131$	−17.4296	+	5.66323i	−1.52283	+	0.494798i	−0.946579	−	0.322473i	$-0.895486\pi$
$131$	−17.4296	+	5.66323i	−1.52283	+	0.494798i	−0.576254	+	0.817271i	$0.695486\pi$
$132$		0			0
$133$	−6.48085	+	12.7194i	−0.561961	+	1.10291i
$134$	0.747874	−	16.1633i	0.0646065	−	1.39630i
$135$		0			0
$136$	1.91518	−	1.98686i	0.164225	−	0.170372i
$137$	−12.3832	+	1.96131i	−1.05797	+	0.167566i	−0.661092	−	0.750305i	$-0.729907\pi$
$137$	−12.3832	+	1.96131i	−1.05797	+	0.167566i	−0.396879	+	0.917871i	$0.629907\pi$
$138$		0			0
$139$	2.48077	−	1.80238i	0.210416	−	0.152876i	−0.477586	−	0.878585i	$-0.658488\pi$
$139$	2.48077	−	1.80238i	0.210416	−	0.152876i	0.688002	+	0.725709i	$0.258488\pi$
$140$	12.3313	−	17.9876i	1.04219	−	1.52023i
$141$		0			0
$142$	4.07224	−	0.453236i	0.341735	−	0.0380347i
$143$	−0.306437	+	0.306437i	−0.0256255	+	0.0256255i
$144$		0			0
$145$	12.8431	−	8.61915i	1.06657	−	0.715782i
$146$	4.38777	−	1.20454i	0.363134	−	0.0996886i
$147$		0			0
$148$	−9.68828	+	15.3263i	−0.796372	+	1.25982i
$149$			4.15928i			0.340741i	0.985380	+	0.170371i	$0.0544965\pi$
$149$			4.15928i			0.340741i	−0.985380	+	0.170371i	$0.945504\pi$
$150$		0			0
$151$			6.04909i			0.492268i	0.969236	+	0.246134i	$0.0791603\pi$
$151$			6.04909i			0.492268i	−0.969236	+	0.246134i	$0.920840\pi$
$152$	−8.27834	+	0.152083i	−0.671462	+	0.0123356i
$153$		0			0
$154$	2.06733	+	7.53062i	0.166590	+	0.606835i
$155$	4.78858	−	13.0613i	0.384628	−	1.04911i
$156$		0			0
$157$	7.27059	−	7.27059i	0.580256	−	0.580256i	−0.354717	−	0.934974i	$-0.615423\pi$
$157$	7.27059	−	7.27059i	0.580256	−	0.580256i	0.934974	+	0.354717i	$0.115423\pi$
$158$	1.61763	+	14.5341i	0.128692	+	1.15627i
$159$		0			0
$160$	12.5708	+	1.40559i	0.993807	+	0.111121i
$161$	−5.34221	+	3.88134i	−0.421025	+	0.305892i
$162$		0			0
$163$	15.3694	−	2.43428i	1.20383	−	0.190667i	0.477883	−	0.878423i	$-0.341404\pi$
$163$	15.3694	−	2.43428i	1.20383	−	0.190667i	0.725942	+	0.687756i	$0.241404\pi$
$164$	12.2266	−	2.75574i	0.954734	−	0.215187i
$165$		0			0
$166$	15.3377	+	0.709671i	1.19043	+	0.0550811i
$167$	6.72665	−	13.2018i	0.520524	−	1.02159i	−0.469795	−	0.882775i	$-0.655672\pi$
$167$	6.72665	−	13.2018i	0.520524	−	1.02159i	0.990319	−	0.138810i	$-0.0443277\pi$
$168$		0			0
$169$	12.2244	−	3.97196i	0.940341	−	0.305535i
$170$	−2.01535	+	2.33619i	−0.154570	+	0.179177i
$171$		0			0
$172$	−0.735663	−	11.3711i	−0.0560938	−	0.867036i
$173$	−13.1116	−	2.07667i	−0.996857	−	0.157887i	−0.363374	−	0.931643i	$-0.618375\pi$
$173$	−13.1116	−	2.07667i	−0.996857	−	0.157887i	−0.633483	+	0.773757i	$0.718375\pi$
$174$		0			0
$175$	−12.6557	+	20.8411i	−0.956685	+	1.57544i
$176$	−3.29076	+	3.11228i	−0.248051	+	0.234597i
$177$		0			0
$178$	17.2086	+	9.79538i	1.28984	+	0.734195i
$179$	7.26523	−	22.3601i	0.543029	−	1.67127i	−0.182602	−	0.983187i	$-0.558452\pi$
$179$	7.26523	−	22.3601i	0.543029	−	1.67127i	0.725631	−	0.688084i	$-0.241548\pi$
$180$		0			0
$181$	−5.35786	−	16.4898i	−0.398247	−	1.22568i	−0.926404	−	0.376531i	$-0.877117\pi$
$181$	−5.35786	−	16.4898i	−0.398247	−	1.22568i	0.528157	−	0.849147i	$-0.322883\pi$
$182$	−0.532943	+	2.58503i	−0.0395044	+	0.191615i
$183$		0			0
$184$	−3.44388	−	1.67579i	−0.253886	−	0.123541i
$185$	9.86946	−	17.7071i	0.725617	−	1.30185i
$186$		0			0
$187$	−0.172829	−	1.09120i	−0.0126385	−	0.0797965i
$188$	5.36869	−	21.0647i	0.391552	−	1.53630i
$189$		0			0
$190$	9.23197	−	0.680666i	0.669757	−	0.0493807i
$191$	−1.56971	+	2.16053i	−0.113581	+	0.156330i	−0.862022	−	0.506870i	$-0.830802\pi$
$191$	−1.56971	+	2.16053i	−0.113581	+	0.156330i	0.748442	+	0.663200i	$0.230802\pi$
$192$		0			0
$193$	5.46235	+	5.46235i	0.393188	+	0.393188i	0.875822	−	0.482634i	$-0.160320\pi$
$193$	5.46235	+	5.46235i	0.393188	+	0.393188i	−0.482634	+	0.875822i	$0.660320\pi$
$194$	−11.9943	−	9.59182i	−0.861143	−	0.688652i
$195$		0			0
$196$	25.2143	+	22.1500i	1.80102	+	1.58214i
$197$	−7.08233	−	13.8998i	−0.504595	−	0.990323i	−0.993045	−	0.117732i	$-0.962438\pi$
$197$	−7.08233	−	13.8998i	−0.504595	−	0.990323i	0.488451	−	0.872592i	$-0.337562\pi$
$198$		0			0
$199$	16.7739			1.18907			0.594534	−	0.804070i	$-0.297337\pi$
$199$	16.7739			1.18907			0.594534	+	0.804070i	$0.297337\pi$
$200$	−14.1199	−	0.793301i	−0.998425	−	0.0560949i
$201$		0			0
$202$	0.827210	−	0.374383i	0.0582023	−	0.0263415i
$203$	15.3140	+	30.0554i	1.07483	+	2.10948i
$204$		0			0
$205$	−13.4788	+	3.83087i	−0.941400	+	0.267560i
$206$	2.16488	+	1.73124i	0.150834	+	0.120621i
$207$		0			0
$208$	−1.46855	+	0.432310i	−0.101826	+	0.0299753i
$209$	−1.94836	+	2.68169i	−0.134771	+	0.185497i
$210$		0			0
$211$	−8.21221	−	11.3031i	−0.565352	−	0.778140i	0.426643	−	0.904420i	$-0.359696\pi$
$211$	−8.21221	−	11.3031i	−0.565352	−	0.778140i	−0.991995	+	0.126280i	$0.959696\pi$
$212$	4.82159	−	18.9181i	0.331148	−	1.29930i
$213$		0			0
$214$	−4.21469	−	1.58833i	−0.288111	−	0.108576i
$215$	1.52300	+	12.6485i	0.103868	+	0.862618i
$216$		0			0
$217$	27.0323	+	13.7736i	1.83507	+	0.935015i
$218$	−2.76124	+	13.3934i	−0.187015	+	0.907113i
$219$		0			0
$220$	3.48150	−	3.67742i	0.234723	−	0.247931i
$221$	0.115389	−	0.355130i	0.00776188	−	0.0238886i
$222$		0			0
$223$	1.10929	−	7.00378i	0.0742836	−	0.469008i	−0.922304	−	0.386465i	$-0.873696\pi$
$223$	1.10929	−	7.00378i	0.0742836	−	0.469008i	0.996588	−	0.0825427i	$-0.0263041\pi$
$224$	−6.32079	+	26.8521i	−0.422325	+	1.79413i
$225$		0			0
$226$	16.3649	+	24.8651i	1.08858	+	1.65400i
$227$	2.15510	+	0.341335i	0.143039	+	0.0226552i	0.227543	−	0.973768i	$-0.426931\pi$
$227$	2.15510	+	0.341335i	0.143039	+	0.0226552i	−0.0845042	+	0.996423i	$0.526931\pi$
$228$		0			0
$229$	−7.26018	−	2.35897i	−0.479766	−	0.155885i	0.0591428	−	0.998250i	$-0.481163\pi$
$229$	−7.26018	−	2.35897i	−0.479766	−	0.155885i	−0.538909	+	0.842364i	$0.681163\pi$
$230$	3.94793	+	1.65820i	0.260319	+	0.109338i
$231$		0			0
$232$	−11.2072	+	16.0367i	−0.735787	+	1.05286i
$233$	12.0468	−	23.6432i	0.789214	−	1.54892i	−0.0459655	−	0.998943i	$-0.514636\pi$
$233$	12.0468	−	23.6432i	0.789214	−	1.54892i	0.835180	−	0.549977i	$-0.185364\pi$
$234$		0			0
$235$	−4.69323	+	23.8465i	−0.306153	+	1.55557i
$236$	−8.80718	+	1.98505i	−0.573299	+	0.129216i
$237$		0			0
$238$	−4.53293	−	4.97276i	−0.293826	−	0.322336i
$239$	−18.9812	+	13.7906i	−1.22779	+	0.892042i	−0.996723	−	0.0808951i	$-0.974222\pi$
$239$	−18.9812	+	13.7906i	−1.22779	+	0.892042i	−0.231068	+	0.972938i	$0.574222\pi$
$240$		0			0
$241$	−4.98282	−	3.62023i	−0.320972	−	0.233199i	0.415618	−	0.909539i	$-0.363565\pi$
$241$	−4.98282	−	3.62023i	−0.320972	−	0.233199i	−0.736590	+	0.676340i	$0.763565\pi$
$242$	−1.52020	−	13.6587i	−0.0977220	−	0.878014i
$243$		0			0
$244$	1.50254	−	16.2019i	0.0961902	−	1.03722i
$245$	−29.5144	−	23.1706i	−1.88561	−	1.48032i
$246$		0			0
$247$	−0.998225	+	0.508621i	−0.0635155	+	0.0323628i
$248$	0.323219	+	17.5938i	0.0205244	+	1.11721i
$249$		0			0
$250$	15.8114	+	0.0141887i	1.00000	+	0.000897373i
$251$			2.57211i			0.162350i	0.996700	+	0.0811750i	$0.0258673\pi$
$251$			2.57211i			0.162350i	−0.996700	+	0.0811750i	$0.974133\pi$
$252$		0			0
$253$	−1.36619	+	0.696107i	−0.0858915	+	0.0437639i
$254$	−9.64539	+	2.64788i	−0.605205	+	0.166143i
$255$		0			0
$256$	−15.4687	+	4.08891i	−0.966794	+	0.255557i
$257$	11.1652	−	11.1652i	0.696464	−	0.696464i	−0.267182	−	0.963646i	$-0.586093\pi$
$257$	11.1652	−	11.1652i	0.696464	−	0.696464i	0.963646	+	0.267182i	$0.0860926\pi$
$258$		0			0
$259$	35.7668	+	25.9861i	2.22244	+	1.61470i
$260$	1.61271	−	0.573231i	0.100016	−	0.0355503i
$261$		0			0
$262$	−19.1541	+	17.4599i	−1.18334	+	1.07868i
$263$	−25.4425	+	4.02970i	−1.56885	+	0.248482i	−0.879484	−	0.475929i	$-0.842112\pi$
$263$	−25.4425	+	4.02970i	−1.56885	+	0.248482i	−0.689368	+	0.724411i	$0.742112\pi$
$264$		0			0
$265$	−4.21496	+	21.4164i	−0.258923	+	1.31560i
$266$	−0.933111	+	20.1667i	−0.0572127	+	1.23650i
$267$		0			0
$268$	−8.46147	−	21.2610i	−0.516867	−	1.29872i
$269$	16.5916	−	5.39093i	1.01161	−	0.328691i	0.244112	−	0.969747i	$-0.421504\pi$
$269$	16.5916	−	5.39093i	1.01161	−	0.328691i	0.767494	+	0.641057i	$0.221504\pi$
$270$		0			0
$271$	−11.1341	−	3.61770i	−0.676351	−	0.219760i	−0.0493541	−	0.998781i	$-0.515716\pi$
$271$	−11.1341	−	3.61770i	−0.676351	−	0.219760i	−0.626997	+	0.779021i	$0.715716\pi$
$272$	1.30895	−	3.67664i	0.0793670	−	0.222929i
$273$		0			0
$274$	−14.8109	+	9.74777i	−0.894760	+	0.588884i
$275$	−3.65956	+	4.32007i	−0.220680	+	0.260510i
$276$		0			0
$277$	3.29508	−	20.8043i	0.197982	−	1.25001i	−0.665795	−	0.746135i	$-0.731907\pi$
$277$	3.29508	−	20.8043i	0.197982	−	1.25001i	0.863777	−	0.503875i	$-0.168093\pi$
$278$	2.14523	−	3.76876i	0.128662	−	0.226035i
$279$		0			0
$280$	5.39892	−	30.3658i	0.322647	−	1.81471i
$281$	4.13211	+	12.7173i	0.246501	+	0.758653i	0.995386	+	0.0959525i	$0.0305897\pi$
$281$	4.13211	+	12.7173i	0.246501	+	0.758653i	−0.748885	+	0.662700i	$0.769410\pi$
$282$		0			0
$283$	−18.3418	−	9.34561i	−1.09031	−	0.555539i	−0.186055	−	0.982539i	$-0.559570\pi$
$283$	−18.3418	−	9.34561i	−1.09031	−	0.555539i	−0.904251	+	0.427000i	$0.859570\pi$
$284$	4.98239	−	2.95852i	0.295651	−	0.175556i
$285$		0			0
$286$	−0.216127	+	0.573501i	−0.0127798	+	0.0339118i
$287$	−4.78058	−	30.1834i	−0.282189	−	1.78167i
$288$		0			0
$289$	−9.43281	−	12.9832i	−0.554871	−	0.763715i
$290$	11.5212	−	18.5939i	0.676548	−	1.09187i
$291$		0			0
$292$	4.95083	−	4.11050i	0.289725	−	0.240549i
$293$	−11.5164	−	11.5164i	−0.672794	−	0.672794i	0.285565	−	0.958359i	$-0.407819\pi$
$293$	−11.5164	−	11.5164i	−0.672794	−	0.672794i	−0.958359	+	0.285565i	$0.907819\pi$
$294$		0			0
$295$	9.70921	−	2.75950i	0.565292	−	0.160664i
$296$	−3.54544	+	25.3958i	−0.206074	+	1.47610i
$297$		0			0
$298$	2.42533	+	5.35882i	0.140495	+	0.310428i
$299$	−0.518234			−0.0299702
$300$		0			0
$301$	−27.7838			−1.60143
$302$	3.52730	+	7.79366i	0.202973	+	0.448475i
$303$		0			0
$304$	−10.5771	+	5.02315i	−0.606641	+	0.288097i
$305$	−0.677437	+	18.1794i	−0.0387900	+	1.04095i
$306$		0			0
$307$	−2.86400	−	2.86400i	−0.163457	−	0.163457i	0.620639	−	0.784096i	$-0.286873\pi$
$307$	−2.86400	−	2.86400i	−0.163457	−	0.163457i	−0.784096	+	0.620639i	$0.786873\pi$
$308$	7.05475	+	8.49699i	0.401982	+	0.484161i
$309$		0			0
$310$	−1.44661	−	19.6205i	−0.0821618	−	1.11437i
$311$	17.2238	+	23.7066i	0.976674	+	1.34428i	0.938602	+	0.345002i	$0.112122\pi$
$311$	17.2238	+	23.7066i	0.976674	+	1.34428i	0.0380720	+	0.999275i	$0.487878\pi$
$312$		0			0
$313$	3.25048	+	20.5227i	0.183728	+	1.16001i	0.891314	+	0.453387i	$0.149784\pi$
$313$	3.25048	+	20.5227i	0.183728	+	1.16001i	−0.707586	+	0.706627i	$0.750216\pi$
$314$	5.12787	−	13.6070i	0.289383	−	0.767888i
$315$		0			0
$316$	10.5592	+	17.7825i	0.594001	+	1.00035i
$317$	12.4309	+	6.33384i	0.698187	+	0.355744i	0.766788	−	0.641900i	$-0.221854\pi$
$317$	12.4309	+	6.33384i	0.698187	+	0.355744i	−0.0686013	+	0.997644i	$0.521854\pi$
$318$		0			0
$319$	2.42042	+	7.44929i	0.135518	+	0.417080i
$320$	17.0158	−	5.51921i	0.951214	−	0.308533i
$321$		0			0
$322$	−4.61965	+	8.11583i	−0.257443	+	0.452278i
$323$	0.446796	−	2.82096i	0.0248604	−	0.156962i
$324$		0			0
$325$	−1.76494	+	0.739442i	−0.0979011	+	0.0410169i
$326$	18.3825	−	12.0984i	1.01811	−	0.670069i
$327$		0			0
$328$	14.1458	−	10.6800i	0.781072	−	0.589702i
$329$	−50.4094	−	16.3790i	−2.77916	−	0.903004i
$330$		0			0
$331$	−26.4957	+	8.60896i	−1.45633	+	0.473191i	−0.926948	−	0.375190i	$-0.877577\pi$
$331$	−26.4957	+	8.60896i	−1.45633	+	0.473191i	−0.529386	+	0.848381i	$0.677577\pi$
$332$	20.1749	−	8.02923i	1.10724	−	0.440661i
$333$		0			0
$334$	0.968502	−	20.9316i	0.0529940	−	1.14533i
$335$	10.7579	+	23.2120i	0.587766	+	1.26821i
$336$		0			0
$337$	23.7132	−	3.75580i	1.29174	−	0.204591i	0.527517	−	0.849545i	$-0.323123\pi$
$337$	23.7132	−	3.75580i	1.29174	−	0.204591i	0.764222	+	0.644953i	$0.223123\pi$
$338$	13.4339	−	12.2457i	0.730707	−	0.666078i
$339$		0			0
$340$	−1.23432	+	4.18512i	−0.0669406	+	0.226970i
$341$	5.69936	+	4.14082i	0.308637	+	0.224238i
$342$		0			0
$343$	33.7267	−	33.7267i	1.82107	−	1.82107i
$344$	−7.57844	−	14.2215i	−0.408602	−	0.766774i
$345$		0			0
$346$	−18.1040	+	4.96995i	−0.973275	+	0.267186i
$347$	−17.5573	+	8.94587i	−0.942523	+	0.480239i	−0.856553	−	0.516058i	$-0.827399\pi$
$347$	−17.5573	+	8.94587i	−0.942523	+	0.480239i	−0.0859695	+	0.996298i	$0.527399\pi$
$348$		0			0
$349$		−	5.15255i		−	0.275810i	−0.990445	−	0.137905i	$-0.955963\pi$
$349$		−	5.15255i		−	0.275810i	0.990445	−	0.137905i	$-0.0440368\pi$
$350$	−4.15297	+	34.2315i	−0.221986	+	1.82975i
$351$		0			0
$352$	−2.42502	+	5.92875i	−0.129254	+	0.316003i
$353$	12.0507	−	6.14012i	0.641392	−	0.326806i	−0.102869	−	0.994695i	$-0.532802\pi$
$353$	12.0507	−	6.14012i	0.641392	−	0.326806i	0.744261	+	0.667889i	$0.232802\pi$
$354$		0			0
$355$	−5.37941	+	3.61017i	−0.285509	+	0.191608i
$356$	27.8834	+	2.58585i	1.47782	+	0.137050i
$357$		0			0
$358$	−3.67790	−	33.0452i	−0.194383	−	1.74649i
$359$	−26.0169	−	18.9024i	−1.37312	−	0.997632i	−0.997486	−	0.0708643i	$-0.977424\pi$
$359$	−26.0169	−	18.9024i	−1.37312	−	0.997632i	−0.375636	−	0.926767i	$-0.622576\pi$
$360$		0			0
$361$	8.43865	−	6.13104i	0.444139	−	0.322686i
$362$	−16.5185	−	18.1213i	−0.868192	−	0.952432i
$363$		0			0
$364$	0.820718	+	3.64132i	0.0430173	+	0.190857i
$365$	−5.27308	+	4.89420i	−0.276005	+	0.256174i
$366$		0			0
$367$	9.01595	−	17.6948i	0.470629	−	0.923661i	−0.526660	−	0.850076i	$-0.676556\pi$
$367$	9.01595	−	17.6948i	0.470629	−	0.923661i	0.997289	−	0.0735850i	$-0.0234440\pi$
$368$	−5.41428	−	0.150923i	−0.282239	−	0.00786739i
$369$		0			0
$370$	2.39059	−	28.5689i	0.124281	−	1.48523i
$371$	−45.2724	−	14.7099i	−2.35043	−	0.763700i
$372$		0			0
$373$	12.5823	+	1.99284i	0.651487	+	0.103185i	0.473425	−	0.880834i	$-0.343017\pi$
$373$	12.5823	+	1.99284i	0.651487	+	0.103185i	0.178061	+	0.984019i	$0.443017\pi$
$374$	−0.858966	−	1.30513i	−0.0444161	−	0.0674865i
$375$		0			0
$376$	−5.36608	−	30.2704i	−0.276734	−	1.56108i
$377$	−0.414130	+	2.61472i	−0.0213288	+	0.134665i
$378$		0			0
$379$	1.14962	−	3.53817i	0.0590521	−	0.181744i	−0.917179	−	0.398475i	$-0.869540\pi$
$379$	1.14962	−	3.53817i	0.0590521	−	0.181744i	0.976231	+	0.216731i	$0.0695396\pi$
$380$	11.4976	−	6.26025i	0.589814	−	0.321144i
$381$		0			0
$382$	−0.762594	+	3.69895i	−0.0390177	+	0.189255i
$383$	−9.64571	−	4.91473i	−0.492873	−	0.251131i	0.189844	−	0.981814i	$-0.439202\pi$
$383$	−9.64571	−	4.91473i	−0.492873	−	0.251131i	−0.682717	+	0.730683i	$0.739202\pi$
$384$		0			0
$385$	−8.39981	−	9.05006i	−0.428094	−	0.461234i
$386$	10.2229	+	3.85254i	0.520330	+	0.196089i
$387$		0			0
$388$	−21.0466	−	5.36407i	−1.06848	−	0.272320i
$389$	10.4403	+	14.3698i	0.529342	+	0.728577i	0.987030	−	0.160536i	$-0.0513223\pi$
$389$	10.4403	+	14.3698i	0.529342	+	0.728577i	−0.457688	+	0.889113i	$0.651322\pi$
$390$		0			0
$391$	0.776556	−	1.06884i	0.0392721	−	0.0540535i
$392$	45.4021	+	13.8354i	2.29315	+	0.698791i
$393$		0			0
$394$	−17.2301	−	13.7788i	−0.868038	−	0.694166i
$395$	−12.8850	−	19.1995i	−0.648313	−	0.966033i
$396$		0			0
$397$	13.9286	+	27.3364i	0.699057	+	1.37198i	0.918134	+	0.396269i	$0.129695\pi$
$397$	13.9286	+	27.3364i	0.699057	+	1.37198i	−0.219077	+	0.975708i	$0.570305\pi$
$398$	21.6115	−	9.78105i	1.08329	−	0.490280i
$399$		0			0
$400$	−18.6547	+	7.21138i	−0.932733	+	0.360569i
$401$	−5.94140			−0.296699			−0.148350	−	0.988935i	$-0.547396\pi$
$401$	−5.94140			−0.296699			−0.148350	+	0.988935i	$0.547396\pi$
$402$		0			0
$403$	1.08096	+	2.12151i	0.0538466	+	0.105680i
$404$	0.847472	−	0.964713i	0.0421633	−	0.0479963i
$405$		0			0
$406$	37.2563	+	29.7937i	1.84900	+	1.47864i
$407$	7.25895	+	7.25895i	0.359813	+	0.359813i
$408$		0			0
$409$	1.52169	−	2.09443i	0.0752427	−	0.103563i	−0.769737	−	0.638361i	$-0.779613\pi$
$409$	1.52169	−	2.09443i	0.0752427	−	0.103563i	0.844979	+	0.534799i	$0.179613\pi$
$410$	−15.1323	+	12.7954i	−0.747330	+	0.631918i
$411$		0			0
$412$	3.79874	+	0.968171i	0.187151	+	0.0476984i
$413$	3.44360	+	21.7421i	0.169449	+	1.06986i
$414$		0			0
$415$	−22.0263	+	10.2083i	−1.08123	+	0.501108i
$416$	−1.64000	+	1.41332i	−0.0804077	+	0.0692937i
$417$		0			0
$418$	−0.946549	+	4.59122i	−0.0462972	+	0.224564i
$419$	4.92657	+	15.1624i	0.240679	+	0.740733i	0.996317	+	0.0857438i	$0.0273267\pi$
$419$	4.92657	+	15.1624i	0.240679	+	0.740733i	−0.755639	+	0.654989i	$0.772673\pi$
$420$		0			0
$421$	−3.87186	+	11.9164i	−0.188703	+	0.580768i	−0.999992	−	0.00387660i	$-0.998766\pi$
$421$	−3.87186	+	11.9164i	−0.188703	+	0.580768i	0.811290	+	0.584645i	$0.198766\pi$
$422$	−17.1716	−	9.77435i	−0.835902	−	0.475808i
$423$		0			0
$424$	−4.81924	−	27.1857i	−0.234043	−	1.32025i
$425$	1.11963	−	4.74815i	0.0543100	−	0.230319i
$426$		0			0
$427$	−39.1859	−	6.20644i	−1.89634	−	0.300351i
$428$	−6.35639	+	0.411233i	−0.307248	+	0.0198777i
$429$		0			0
$430$	9.33771	+	15.4082i	0.450304	+	0.743051i
$431$	0.172476	−	0.0560408i	0.00830786	−	0.00269939i	−0.304860	−	0.952397i	$-0.598610\pi$
$431$	0.172476	−	0.0560408i	0.00830786	−	0.00269939i	0.313168	+	0.949698i	$0.398610\pi$
$432$		0			0
$433$	−0.946710	+	1.85802i	−0.0454960	+	0.0892909i	−0.912635	−	0.408775i	$-0.865956\pi$
$433$	−0.946710	+	1.85802i	−0.0454960	+	0.0892909i	0.867139	+	0.498066i	$0.165956\pi$
$434$	42.8600	+	1.98312i	2.05735	+	0.0951930i
$435$		0			0
$436$	4.25224	+	18.8661i	0.203645	+	0.903524i
$437$	−3.91508	+	0.620088i	−0.187284	+	0.0296628i
$438$		0			0
$439$	25.8490	−	18.7804i	1.23371	−	0.896340i	0.236544	−	0.971621i	$-0.423985\pi$
$439$	25.8490	−	18.7804i	1.23371	−	0.896340i	0.997162	+	0.0752806i	$0.0239853\pi$
$440$	2.34123	−	6.76810i	0.111614	−	0.322656i
$441$		0			0
$442$	−0.0584136	−	0.524835i	−0.00277845	−	0.0249638i
$443$	−15.5829	+	15.5829i	−0.740368	+	0.740368i	−0.972649	−	0.232281i	$-0.925381\pi$
$443$	−15.5829	+	15.5829i	−0.740368	+	0.740368i	0.232281	+	0.972649i	$0.425381\pi$
$444$		0			0
$445$	−31.2866	−	1.16586i	−1.48313	−	0.0552672i
$446$	−2.65478	−	9.67053i	−0.125707	−	0.457913i
$447$		0			0
$448$	7.51406	+	38.2820i	0.355006	+	1.80865i
$449$			4.93653i			0.232969i	0.993192	+	0.116485i	$0.0371626\pi$
$449$			4.93653i			0.232969i	−0.993192	+	0.116485i	$0.962837\pi$
$450$		0			0
$451$		−	7.09601i		−	0.334138i
$452$	35.5838	+	22.4937i	1.67372	+	1.05801i
$453$		0			0
$454$	2.97568	−	0.816891i	0.139655	−	0.0383386i
$455$	−1.14091	−	4.01427i	−0.0534868	−	0.188192i
$456$		0			0
$457$	6.22919	−	6.22919i	0.291389	−	0.291389i	−0.546240	−	0.837629i	$-0.683941\pi$
$457$	6.22919	−	6.22919i	0.291389	−	0.291389i	0.837629	+	0.546240i	$0.183941\pi$
$458$	−10.7296	+	1.19419i	−0.501360	+	0.0558009i
$459$		0			0
$460$	6.05344	−	0.165659i	0.282243	−	0.00772388i
$461$	0.269250	−	0.195622i	0.0125402	−	0.00911102i	−0.581497	−	0.813548i	$-0.697533\pi$
$461$	0.269250	−	0.195622i	0.0125402	−	0.00911102i	0.594038	+	0.804437i	$0.297533\pi$
$462$		0			0
$463$	10.3280	−	1.63579i	0.479982	−	0.0760217i	0.0882447	−	0.996099i	$-0.471874\pi$
$463$	10.3280	−	1.63579i	0.479982	−	0.0760217i	0.391737	+	0.920077i	$0.371874\pi$
$464$	−5.08813	+	27.1968i	−0.236210	+	1.26258i
$465$		0			0
$466$	1.73450	−	37.4867i	0.0803492	−	1.73654i
$467$	−9.29525	+	18.2429i	−0.430133	+	0.844183i	0.569619	+	0.821909i	$0.307091\pi$
$467$	−9.29525	+	18.2429i	−0.430133	+	0.844183i	−0.999752	+	0.0222742i	$0.992909\pi$
$468$		0			0
$469$	−53.0640	+	17.2415i	−2.45027	+	0.796140i
$470$	7.85842	+	33.4606i	0.362482	+	1.54342i
$471$		0			0
$472$	−10.1897	+	7.69312i	−0.469018	+	0.354105i
$473$	−6.37204	−	1.00923i	−0.292987	−	0.0464045i
$474$		0			0
$475$	−12.4487	+	7.69806i	−0.571188	+	0.353211i
$476$	−8.73992	−	3.76371i	−0.400594	−	0.172509i
$477$		0			0
$478$	−16.4139	+	28.8361i	−0.750755	+	1.31893i
$479$	−6.48175	+	19.9488i	−0.296159	+	0.911482i	0.686671	+	0.726968i	$0.259071\pi$
$479$	−6.48175	+	19.9488i	−0.296159	+	0.911482i	−0.982830	+	0.184514i	$0.940929\pi$
$480$		0			0
$481$	1.07218	+	3.29983i	0.0488872	+	0.150459i
$482$	−8.53087	−	1.75877i	−0.388571	−	0.0801097i
$483$		0			0
$484$	−9.92318	−	16.7114i	−0.451053	−	0.759611i
$485$	23.8260	+	4.68920i	1.08188	+	0.212925i
$486$		0			0
$487$	−3.28173	−	20.7200i	−0.148709	−	0.938914i	−0.943342	−	0.331823i	$-0.892336\pi$
$487$	−3.28173	−	20.7200i	−0.148709	−	0.938914i	0.794632	−	0.607091i	$-0.207664\pi$
$488$	−7.51168	−	21.7508i	−0.340038	−	0.984611i
$489$		0			0
$490$	−51.5375	−	12.6429i	−2.32823	−	0.571146i
$491$	7.62203	−	10.4908i	0.343977	−	0.473444i	−0.601620	−	0.798782i	$-0.705478\pi$
$491$	7.62203	−	10.4908i	0.343977	−	0.473444i	0.945598	+	0.325338i	$0.105478\pi$
$492$		0			0
$493$	−4.77220	−	4.77220i	−0.214929	−	0.214929i
$494$	−0.989532	+	1.23739i	−0.0445212	+	0.0556726i
$495$		0			0
$496$	10.6756	+	22.4794i	0.479349	+	1.00936i
$497$	−6.41434	−	12.5889i	−0.287722	−	0.564687i
$498$		0			0
$499$	−30.5022			−1.36547			−0.682733	−	0.730668i	$-0.739209\pi$
$499$	−30.5022			−1.36547			−0.682733	+	0.730668i	$0.739209\pi$
$500$	20.3797	−	9.20153i	0.911408	−	0.411505i
$501$		0			0
$502$	1.49983	+	3.31391i	0.0669406	+	0.147907i
$503$	4.26886	+	8.37810i	0.190339	+	0.373561i	0.966379	−	0.257123i	$-0.0827745\pi$
$503$	4.26886	+	8.37810i	0.190339	+	0.373561i	−0.776040	+	0.630684i	$0.782774\pi$
$504$		0			0
$505$	−0.886521	+	1.12924i	−0.0394497	+	0.0502504i
$506$	−1.35429	+	1.69351i	−0.0602055	+	0.0752856i
$507$		0			0
$508$	−10.8831	+	9.03587i	−0.482861	+	0.400902i
$509$	12.1536	−	16.7281i	0.538701	−	0.741458i	−0.449724	−	0.893167i	$-0.648478\pi$
$509$	12.1536	−	16.7281i	0.538701	−	0.741458i	0.988425	+	0.151709i	$0.0484778\pi$
$510$		0			0
$511$	−9.22228	−	12.6934i	−0.407970	−	0.561522i
$512$	−17.5456	+	14.2882i	−0.775414	+	0.631453i
$513$		0			0
$514$	7.87468	−	20.8958i	0.347337	−	0.921673i
$515$	−4.30040	−	0.846361i	−0.189498	−	0.0372951i
$516$		0			0
$517$	−10.9661	−	5.58752i	−0.482289	−	0.245739i
$518$	61.2348	+	12.6245i	2.69050	+	0.554688i
$519$		0			0
$520$	1.74356	−	1.67894i	0.0764601	−	0.0736265i
$521$	7.34822	−	22.6155i	0.321931	−	0.990803i	−0.650875	−	0.759185i	$-0.725598\pi$
$521$	7.34822	−	22.6155i	0.321931	−	0.990803i	0.972807	−	0.231618i	$-0.0744020\pi$
$522$		0			0
$523$	−3.90499	+	24.6551i	−0.170753	+	1.07809i	0.742245	+	0.670129i	$0.233761\pi$
$523$	−3.90499	+	24.6551i	−0.170753	+	1.07809i	−0.912998	+	0.407964i	$0.866239\pi$
$524$	−14.4970	+	33.6644i	−0.633305	+	1.47064i
$525$		0			0
$526$	−30.4304	+	20.0277i	−1.32683	+	0.873249i
$527$	−5.99533	−	0.949566i	−0.261161	−	0.0413638i
$528$		0			0
$529$	20.1305	+	6.54078i	0.875238	+	0.284382i
$530$	7.05761	+	30.0508i	0.306563	+	1.30532i
$531$		0			0
$532$	10.5572	+	26.5270i	0.457715	+	1.15009i
$533$	1.08882	−	2.13694i	0.0471622	−	0.0925610i
$534$		0			0
$535$	7.07045	−	0.851352i	0.305682	−	0.0368071i
$536$	−23.2993	−	22.4587i	−1.00638	−	0.970067i
$537$		0			0
$538$	18.2331	−	16.6204i	0.786084	−	0.716557i
$539$	15.3727	−	11.1689i	0.662150	−	0.481080i
$540$		0			0
$541$	1.77850	+	1.29215i	0.0764635	+	0.0555540i	0.625360	−	0.780336i	$-0.284952\pi$
$541$	1.77850	+	1.29215i	0.0764635	+	0.0555540i	−0.548897	+	0.835890i	$0.684952\pi$
$542$	−16.4548	+	1.83140i	−0.706794	+	0.0786654i
$543$		0			0
$544$	−0.457435	−	5.50026i	−0.0196123	−	0.235822i
$545$	−5.91121	−	20.7984i	−0.253208	−	0.890906i
$546$		0			0
$547$	21.9911	−	11.2050i	0.940272	−	0.479092i	0.0844870	−	0.996425i	$-0.473075\pi$
$547$	21.9911	−	11.2050i	0.940272	−	0.479092i	0.855785	+	0.517332i	$0.173075\pi$
$548$	−13.3984	+	21.1955i	−0.572350	+	0.905425i
$549$		0			0
$550$	−2.19590	+	7.69991i	−0.0936334	+	0.328325i
$551$			20.2488i			0.862629i
$552$		0			0
$553$	44.9305	−	22.8933i	1.91064	−	0.973520i
$554$	−7.88586	−	28.7257i	−0.335038	−	1.22044i
$555$		0			0
$556$	0.566314	−	6.10659i	0.0240170	−	0.258977i
$557$	−9.15739	+	9.15739i	−0.388011	+	0.388011i	−0.873978	−	0.485966i	$-0.838468\pi$
$557$	−9.15739	+	9.15739i	−0.388011	+	0.388011i	0.485966	+	0.873978i	$0.338468\pi$
$558$		0			0
$559$	−1.76406	−	1.28166i	−0.0746116	−	0.0542085i
$560$	−10.7507	−	42.2716i	−0.454301	−	1.78630i
$561$		0			0
$562$	12.7395	+	13.9756i	0.537382	+	0.589523i
$563$	28.6678	−	4.54054i	1.20820	−	0.191361i	0.480340	−	0.877082i	$-0.340513\pi$
$563$	28.6678	−	4.54054i	1.20820	−	0.191361i	0.727864	+	0.685721i	$0.240513\pi$
$564$		0			0
$565$	−41.1114	−	22.9144i	−1.72957	−	0.964014i
$566$	−29.0811	−	1.34558i	−1.22237	−	0.0565589i
$567$		0			0
$568$	4.69418	−	6.71706i	0.196963	−	0.281842i
$569$	14.1150	−	4.58626i	0.591734	−	0.192266i	0.00218334	−	0.999998i	$-0.499305\pi$
$569$	14.1150	−	4.58626i	0.591734	−	0.192266i	0.589550	+	0.807732i	$0.299305\pi$
$570$		0			0
$571$	−15.9952	−	5.19714i	−0.669376	−	0.217494i	−0.0454380	−	0.998967i	$-0.514468\pi$
$571$	−15.9952	−	5.19714i	−0.669376	−	0.217494i	−0.623938	+	0.781474i	$0.714468\pi$
$572$	0.0559573	+	0.864926i	0.00233969	+	0.0361644i
$573$		0			0
$574$	−23.7596	−	36.1007i	−0.991707	−	1.50681i
$575$	−6.74740	+	0.558513i	−0.281386	+	0.0232916i
$576$		0			0
$577$	−0.474490	+	2.99581i	−0.0197533	+	0.124717i	−0.995594	−	0.0937637i	$-0.970110\pi$
$577$	−0.474490	+	2.99581i	−0.0197533	+	0.124717i	0.975841	+	0.218481i	$0.0701102\pi$
$578$	−19.7239	−	11.2271i	−0.820406	−	0.466987i
$579$		0			0
$580$	4.00159	−	30.6746i	0.166157	−	1.27369i
$581$	−16.3608	−	50.3533i	−0.678760	−	2.08901i
$582$		0			0
$583$	−9.84861	−	5.01812i	−0.407888	−	0.207829i
$584$	3.98177	−	8.18286i	0.164767	−	0.338609i
$585$		0			0
$586$	−21.5531	−	8.12239i	−0.890349	−	0.335533i
$587$	5.91133	+	37.3227i	0.243987	+	1.54047i	0.740269	+	0.672311i	$0.234698\pi$
$587$	5.91133	+	37.3227i	0.243987	+	1.54047i	−0.496282	+	0.868161i	$0.665302\pi$
$588$		0			0
$589$	10.7048	+	14.7339i	0.441083	+	0.607099i
$590$	10.9003	−	9.21690i	0.448757	−	0.379454i
$591$		0			0
$592$	10.2407	+	34.7874i	0.420889	+	1.42975i
$593$	3.22677	+	3.22677i	0.132507	+	0.132507i	0.770250	−	0.637742i	$-0.220132\pi$
$593$	3.22677	+	3.22677i	0.132507	+	0.132507i	−0.637742	+	0.770250i	$0.720132\pi$
$594$		0			0
$595$	9.98890	+	3.66216i	0.409505	+	0.150134i
$596$	6.24959	+	5.49008i	0.255993	+	0.224882i
$597$		0			0
$598$	−0.667693	+	0.302188i	−0.0273040	+	0.0123574i
$599$	−17.2089			−0.703136			−0.351568	−	0.936162i	$-0.614351\pi$
$599$	−17.2089			−0.703136			−0.351568	+	0.936162i	$0.614351\pi$
$600$		0			0
$601$	38.1195			1.55493			0.777463	−	0.628929i	$-0.216506\pi$
$601$	38.1195			1.55493			0.777463	+	0.628929i	$0.216506\pi$
$602$	−35.7967	+	16.2011i	−1.45897	+	0.660307i
$603$		0			0
$604$	9.08916	+	7.98456i	0.369833	+	0.324887i
$605$	12.1089	+	18.0431i	0.492295	+	0.733555i
$606$		0			0
$607$	−20.3631	−	20.3631i	−0.826511	−	0.826511i	0.160521	−	0.987032i	$-0.448683\pi$
$607$	−20.3631	−	20.3631i	−0.826511	−	0.826511i	−0.987032	+	0.160521i	$0.948683\pi$
$608$	−10.6986	+	12.6395i	−0.433884	+	0.512599i
$609$		0			0
$610$	9.72784	+	23.8174i	0.393869	+	0.964340i
$611$	−2.44504	−	3.36531i	−0.0989159	−	0.136146i
$612$		0			0
$613$	−3.33954	−	21.0850i	−0.134883	−	0.851616i	−0.958629	−	0.284658i	$-0.908120\pi$
$613$	−3.33954	−	21.0850i	−0.134883	−	0.851616i	0.823746	−	0.566958i	$-0.191880\pi$
$614$	−5.36002	−	2.01995i	−0.216313	−	0.0815185i
$615$		0			0
$616$	14.0441	+	6.83383i	0.565851	+	0.275343i
$617$	−20.9180	−	10.6583i	−0.842127	−	0.429085i	−0.0209650	−	0.999780i	$-0.506674\pi$
$617$	−20.9180	−	10.6583i	−0.842127	−	0.429085i	−0.821162	+	0.570695i	$0.806674\pi$
$618$		0			0
$619$	0.134035	+	0.412516i	0.00538731	+	0.0165804i	0.953714	−	0.300715i	$-0.0972253\pi$
$619$	0.134035	+	0.412516i	0.00538731	+	0.0165804i	−0.948327	+	0.317295i	$0.897225\pi$
$620$	−13.3048	−	24.4356i	−0.534333	−	0.981358i
$621$		0			0
$622$	36.0148	+	20.5002i	1.44406	+	0.821982i
$623$	10.6812	−	67.4386i	0.427934	−	2.70187i
$624$		0			0
$625$	−22.1826	+	11.5297i	−0.887303	+	0.461186i
$626$	16.1550	+	24.5461i	0.645683	+	0.981061i
$627$		0			0
$628$	−1.32765	−	20.5214i	−0.0529792	−	0.818894i
$629$	−8.41240	−	2.73336i	−0.335424	−	0.108986i
$630$		0			0
$631$	−16.2307	+	5.27366i	−0.646132	+	0.209941i	−0.613708	−	0.789533i	$-0.710323\pi$
$631$	−16.2307	+	5.27366i	−0.646132	+	0.209941i	−0.0324242	+	0.999474i	$0.510323\pi$
$632$	23.9737	+	16.7539i	0.953623	+	0.666433i
$633$		0			0
$634$	19.7093	+	0.911945i	0.782756	+	0.0362180i
$635$	11.5915	−	10.7587i	0.459995	−	0.426944i
$636$		0			0
$637$	6.34321	−	1.00467i	0.251327	−	0.0398063i
$638$	7.46225	+	8.18630i	0.295433	+	0.324099i
$639$		0			0
$640$	18.7049	−	17.0331i	0.739376	−	0.673292i
$641$	12.5185	+	9.09522i	0.494451	+	0.359240i	0.806893	−	0.590697i	$-0.201147\pi$
$641$	12.5185	+	9.09522i	0.494451	+	0.359240i	−0.312442	+	0.949937i	$0.601147\pi$
$642$		0			0
$643$	28.3880	−	28.3880i	1.11951	−	1.11951i	0.127702	−	0.991813i	$-0.459240\pi$
$643$	28.3880	−	28.3880i	1.11951	−	1.11951i	0.991813	−	0.127702i	$-0.0407600\pi$
$644$	−1.21953	+	13.1502i	−0.0480561	+	0.518192i
$645$		0			0
$646$	−1.06928	−	3.89506i	−0.0420703	−	0.153249i
$647$	18.4230	−	9.38699i	0.724283	−	0.369041i	−0.0526593	−	0.998613i	$-0.516770\pi$
$647$	18.4230	−	9.38699i	0.724283	−	0.369041i	0.776942	+	0.629572i	$0.216770\pi$
$648$		0			0
$649$			5.11149i			0.200643i
$650$	−1.84277	+	1.98186i	−0.0722795	+	0.0777348i
$651$		0			0
$652$	16.6293	−	26.3067i	0.651256	−	1.03025i
$653$	−8.91662	+	4.54324i	−0.348934	+	0.177791i	−0.619669	−	0.784863i	$-0.712733\pi$
$653$	−8.91662	+	4.54324i	−0.348934	+	0.177791i	0.270735	+	0.962654i	$0.412733\pi$
$654$		0			0
$655$	14.1059	−	38.4752i	0.551163	−	1.50335i
$656$	11.9979	−	22.0087i	0.468439	−	0.859295i
$657$		0			0
$658$	−74.4984	+	8.29160i	−2.90425	+	0.323240i
$659$	33.4079	+	24.2722i	1.30139	+	0.945512i	0.999968	−	0.00798023i	$-0.00254021\pi$
$659$	33.4079	+	24.2722i	1.30139	+	0.945512i	0.301418	+	0.953492i	$0.402540\pi$
$660$		0			0
$661$	−14.7870	+	10.7434i	−0.575150	+	0.417871i	−0.836972	−	0.547245i	$-0.815676\pi$
$661$	−14.7870	+	10.7434i	−0.575150	+	0.417871i	0.261823	+	0.965116i	$0.415676\pi$
$662$	−29.1171	+	26.5418i	−1.13167	+	1.03157i
$663$		0			0
$664$	21.3114	−	22.1091i	0.827044	−	0.858000i
$665$	−13.4225	−	28.9613i	−0.520501	−	1.12307i
$666$		0			0
$667$	−4.25231	+	8.34562i	−0.164650	+	0.323144i
$668$	−10.9577	−	27.5331i	−0.423964	−	1.06529i
$669$		0			0
$670$	27.3957	+	23.6334i	1.05839	+	0.913037i
$671$	−8.76159	−	2.84681i	−0.338237	−	0.109900i
$672$		0			0
$673$	48.1900	+	7.63255i	1.85759	+	0.294213i	0.982005	−	0.188853i	$-0.0604769\pi$
$673$	48.1900	+	7.63255i	1.85759	+	0.294213i	0.875584	+	0.483066i	$0.160477\pi$
$674$	28.3621	−	18.6664i	1.09247	−	0.719004i
$675$		0			0
$676$	10.1676	−	23.6108i	0.391063	−	0.908109i
$677$	−3.79889	+	23.9853i	−0.146003	+	0.921829i	0.800546	+	0.599271i	$0.204543\pi$
$677$	−3.79889	+	23.9853i	−0.146003	+	0.921829i	−0.946550	+	0.322558i	$0.895457\pi$
$678$		0			0
$679$	−16.3649	+	50.3661i	−0.628029	+	1.93287i
$680$	0.850092	+	6.11187i	0.0325995	+	0.234380i
$681$		0			0
$682$	9.75763	+	2.01168i	0.373639	+	0.0770313i
$683$	−22.8040	−	11.6192i	−0.872573	−	0.444598i	−0.0404447	−	0.999182i	$-0.512877\pi$
$683$	−22.8040	−	11.6192i	−0.872573	−	0.444598i	−0.832128	+	0.554584i	$0.812877\pi$
$684$		0			0
$685$	13.6489	−	24.4880i	0.521499	−	0.935638i
$686$	23.7871	−	63.1200i	0.908196	−	2.40993i
$687$		0			0
$688$	−18.0568	−	13.9040i	−0.688410	−	0.530084i
$689$	−2.19588	−	3.02237i	−0.0836564	−	0.115143i
$690$		0			0
$691$	−25.8483	+	35.5771i	−0.983315	+	1.35342i	−0.0482902	+	0.998833i	$0.515377\pi$
$691$	−25.8483	+	35.5771i	−0.983315	+	1.35342i	−0.935024	+	0.354583i	$0.884623\pi$
$692$	−20.4271	+	16.9599i	−0.776523	+	0.644720i
$693$		0			0
$694$	−17.4044	+	21.7637i	−0.660660	+	0.826140i
$695$	−0.255329	+	6.85191i	−0.00968519	+	0.259908i
$696$		0			0
$697$	2.77579	+	5.44779i	0.105140	+	0.206350i
$698$	−3.00452	−	6.63856i	−0.113723	−	0.251273i
$699$		0			0
$700$	14.6101	+	46.5256i	0.552210	+	1.75850i
$701$	3.03450			0.114612			0.0573058	−	0.998357i	$-0.481749\pi$
$701$	3.03450			0.114612			0.0573058	+	0.998357i	$0.481749\pi$
$702$		0			0
$703$	12.0483	+	23.6462i	0.454412	+	0.891833i
$704$	0.332729	+	9.05267i	0.0125402	+	0.341185i
$705$		0			0
$706$	11.9457	−	14.9378i	0.449583	−	0.562193i
$707$	−2.21392	−	2.21392i	−0.0832632	−	0.0832632i
$708$		0			0
$709$	2.95107	−	4.06180i	0.110830	−	0.152544i	−0.749999	−	0.661439i	$-0.769946\pi$
$709$	2.95107	−	4.06180i	0.110830	−	0.152544i	0.860829	+	0.508895i	$0.169946\pi$
$710$	−4.82571	+	7.78815i	−0.181106	+	0.292284i
$711$		0			0
$712$	37.4328	−	12.9275i	1.40286	−	0.484479i
$713$	1.31786	+	8.32065i	0.0493543	+	0.311611i
$714$		0			0
$715$	−0.115845	−	0.962089i	−0.00433236	−	0.0359801i
$716$	−24.0077	−	40.4309i	−0.897209	−	1.51097i
$717$		0			0
$718$	−44.5425	−	9.18312i	−1.66231	−	0.342711i
$719$	2.16330	+	6.65796i	0.0806776	+	0.248300i	0.983257	−	0.182223i	$-0.0583292\pi$
$719$	2.16330	+	6.65796i	0.0806776	+	0.248300i	−0.902580	+	0.430523i	$0.858329\pi$
$720$		0			0
$721$	2.95374	−	9.09067i	0.110003	−	0.338554i
$722$	7.29729	−	12.8199i	0.271577	−	0.477108i
$723$		0			0
$724$	−31.8492	−	13.7153i	−1.18367	−	0.509727i
$725$	−2.57404	+	34.4899i	−0.0955973	+	1.28092i
$726$		0			0
$727$	32.4515	+	5.13982i	1.20356	+	0.190625i	0.725826	−	0.687878i	$-0.241458\pi$
$727$	32.4515	+	5.13982i	1.20356	+	0.190625i	0.477735	+	0.878504i	$0.341458\pi$
$728$	3.18072	+	4.21292i	0.117885	+	0.156141i
$729$		0			0
$730$	−3.93997	+	9.38050i	−0.145825	+	0.347188i
$731$	5.28676	−	1.71777i	0.195538	−	0.0635341i
$732$		0			0
$733$	−1.41894	+	2.78484i	−0.0524099	+	0.102860i	−0.915726	−	0.401803i	$-0.868384\pi$
$733$	−1.41894	+	2.78484i	−0.0524099	+	0.102860i	0.863316	+	0.504664i	$0.168384\pi$
$734$	1.29811	−	28.0553i	0.0479143	−	1.03554i
$735$		0			0
$736$	−7.06378	+	2.96268i	−0.260374	+	0.109206i
$737$	−12.7962	+	2.02671i	−0.471353	+	0.0746550i
$738$		0			0
$739$	20.2292	−	14.6973i	0.744142	−	0.540651i	−0.149864	−	0.988707i	$-0.547884\pi$
$739$	20.2292	−	14.6973i	0.744142	−	0.540651i	0.894005	+	0.448056i	$0.147884\pi$
$740$	−13.5788	−	38.2022i	−0.499168	−	1.40434i
$741$		0			0
$742$	−66.9066	+	7.44664i	−2.45622	+	0.273375i
$743$	−14.2547	+	14.2547i	−0.522956	+	0.522956i	−0.918463	−	0.395507i	$-0.870569\pi$
$743$	−14.2547	+	14.2547i	−0.522956	+	0.522956i	0.395507	+	0.918463i	$0.370569\pi$
$744$		0			0
$745$	−7.31542	−	5.74305i	−0.268016	−	0.210409i
$746$	17.3731	−	4.76931i	0.636075	−	0.174617i
$747$		0			0
$748$	−1.86773	−	1.18065i	−0.0682910	−	0.0431690i
$749$			15.5311i			0.567493i
$750$		0			0
$751$			19.9242i			0.727043i	0.931586	+	0.363522i	$0.118426\pi$
$751$			19.9242i			0.727043i	−0.931586	+	0.363522i	$0.881574\pi$
$752$	−24.5647	−	35.8714i	−0.895783	−	1.30810i
$753$		0			0
$754$	0.991106	+	3.61029i	0.0360940	+	0.131479i
$755$	−10.6393	−	8.35247i	−0.387202	−	0.303977i
$756$		0			0
$757$	−22.1849	+	22.1849i	−0.806324	+	0.806324i	−0.984075	−	0.177752i	$-0.943118\pi$
$757$	−22.1849	+	22.1849i	−0.806324	+	0.806324i	0.177752	+	0.984075i	$0.443118\pi$
$758$	−0.581977	−	5.22895i	−0.0211383	−	0.189924i
$759$		0			0
$760$	11.1631	−	14.7701i	0.404928	−	0.535768i
$761$	−41.1545	+	29.9005i	−1.49185	+	1.08389i	−0.518361	+	0.855162i	$0.673458\pi$
$761$	−41.1545	+	29.9005i	−1.49185	+	1.08389i	−0.973490	+	0.228732i	$0.926542\pi$
$762$		0			0
$763$	46.5743	−	7.37665i	1.68610	−	0.267053i
$764$	1.17437	+	5.21041i	0.0424874	+	0.188506i
$765$		0			0
$766$	−15.2934	−	0.707623i	−0.552573	−	0.0255674i
$767$	−0.784314	+	1.53930i	−0.0283199	+	0.0555810i
$768$		0			0
$769$	−32.6790	+	10.6180i	−1.17843	+	0.382896i	−0.831785	−	0.555099i	$-0.812681\pi$
$769$	−32.6790	+	10.6180i	−1.17843	+	0.382896i	−0.346649	+	0.937995i	$0.612681\pi$
$770$	−16.0995	−	6.76208i	−0.580187	−	0.243689i
$771$		0			0
$772$	15.4176	−	0.997458i	0.554892	−	0.0358993i
$773$	11.0837	+	1.75548i	0.398652	+	0.0631403i	0.352542	−	0.935796i	$-0.385317\pi$
$773$	11.0837	+	1.75548i	0.398652	+	0.0631403i	0.0461104	+	0.998936i	$0.485317\pi$
$774$		0			0
$775$	16.3606	+	26.4571i	0.587688	+	0.950367i
$776$	−30.2444	+	5.36147i	−1.08571	+	0.192465i
$777$		0			0
$778$	21.8304	+	12.4262i	0.782659	+	0.445501i
$779$	5.66876	−	17.4467i	0.203105	−	0.625092i
$780$		0			0
$781$	−1.01380	−	3.12017i	−0.0362768	−	0.111648i
$782$	0.377264	−	1.82991i	0.0134909	−	0.0654376i
$783$		0			0
$784$	66.5637	−	8.64902i	2.37728	−	0.308893i
$785$	2.74856	+	22.8267i	0.0981004	+	0.814721i
$786$		0			0
$787$	−4.95187	−	31.2648i	−0.176515	−	1.11447i	−0.903743	−	0.428076i	$-0.859192\pi$
$787$	−4.95187	−	31.2648i	−0.176515	−	1.11447i	0.727228	−	0.686396i	$-0.240808\pi$
$788$	−30.2338	−	7.70558i	−1.07704	−	0.274500i
$789$		0			0
$790$	−27.7965	−	17.2233i	−0.988955	−	0.612778i
$791$	60.3330	−	83.0413i	2.14520	−	2.95261i
$792$		0			0
$793$	−2.20170	−	2.20170i	−0.0781846	−	0.0781846i
$794$	33.8859	+	27.0984i	1.20256	+	0.961686i
$795$		0			0
$796$	22.1408	−	25.2039i	0.784761	−	0.893327i
$797$	8.73067	+	17.1349i	0.309256	+	0.606949i	0.992361	−	0.123371i	$-0.0393707\pi$
$797$	8.73067	+	17.1349i	0.309256	+	0.606949i	−0.683104	+	0.730321i	$0.739371\pi$
$798$		0			0
$799$	10.6047			0.375166
$800$	−19.8297	+	20.1689i	−0.701084	+	0.713079i
$801$		0			0
$802$	−7.65491	+	3.46450i	−0.270304	+	0.122336i
$803$	−1.65399	−	3.24614i	−0.0583681	−	0.114554i
$804$		0			0
$805$	0.549839	−	14.7553i	0.0193793	−	0.520054i
$806$	2.62979	+	2.10303i	0.0926305	+	0.0740762i
$807$		0			0
$808$	0.529349	−	1.73711i	0.0186224	−	0.0611113i
$809$	7.61410	−	10.4799i	0.267698	−	0.368454i	−0.653913	−	0.756570i	$-0.726874\pi$
$809$	7.61410	−	10.4799i	0.267698	−	0.368454i	0.921611	+	0.388116i	$0.126874\pi$
$810$		0			0
$811$	12.7466	+	17.5442i	0.447595	+	0.616061i	0.971879	−	0.235482i	$-0.0756669\pi$
$811$	12.7466	+	17.5442i	0.447595	+	0.616061i	−0.524284	+	0.851544i	$0.675667\pi$
$812$	65.3741	+	16.6617i	2.29418	+	0.584709i
$813$		0			0
$814$	13.5852	+	5.11966i	0.476162	+	0.179444i
$815$	−16.9403	+	30.3932i	−0.593394	+	1.06463i
$816$		0			0
$817$	−14.8604	−	7.57176i	−0.519900	−	0.264902i
$818$	0.739262	−	3.58578i	0.0258477	−	0.125374i
$819$		0			0
$820$	−12.0353	+	25.3094i	−0.420292	+	0.883842i
$821$	4.44219	−	13.6717i	0.155033	−	0.477144i	−0.843131	−	0.537709i	$-0.819290\pi$
$821$	4.44219	−	13.6717i	0.155033	−	0.477144i	0.998164	+	0.0605645i	$0.0192901\pi$
$822$		0			0
$823$	−4.81502	+	30.4008i	−0.167841	+	1.05971i	0.749616	+	0.661873i	$0.230238\pi$
$823$	−4.81502	+	30.4008i	−0.167841	+	1.05971i	−0.917457	+	0.397834i	$0.869762\pi$
$824$	5.45886	−	0.967700i	0.190168	−	0.0337114i
$825$		0			0
$826$	17.1148	+	26.0045i	0.595500	+	0.904812i
$827$	−9.24250	−	1.46387i	−0.321393	−	0.0509037i	−0.00634652	−	0.999980i	$-0.502020\pi$
$827$	−9.24250	−	1.46387i	−0.321393	−	0.0509037i	−0.315047	+	0.949076i	$0.602020\pi$
$828$		0			0
$829$	3.27588	+	1.06440i	0.113776	+	0.0369681i	0.365352	−	0.930870i	$-0.380949\pi$
$829$	3.27588	+	1.06440i	0.113776	+	0.0369681i	−0.251576	+	0.967838i	$0.580949\pi$
$830$	−22.4261	+	25.9963i	−0.778422	+	0.902344i
$831$		0			0
$832$	−1.28886	+	2.77723i	−0.0446830	+	0.0962831i
$833$	−7.43301	+	14.5881i	−0.257539	+	0.505448i
$834$		0			0
$835$	13.9315	+	30.0597i	0.482121	+	1.04026i
$836$	1.45766	+	6.46728i	0.0504142	+	0.223675i
$837$		0			0
$838$	15.1888	+	16.6625i	0.524688	+	0.575598i
$839$	−1.69383	+	1.23064i	−0.0584776	+	0.0424864i	−0.616640	−	0.787245i	$-0.711507\pi$
$839$	−1.69383	+	1.23064i	−0.0584776	+	0.0424864i	0.558162	+	0.829732i	$0.311507\pi$
$840$		0			0
$841$	15.2477	+	11.0781i	0.525784	+	0.382004i
$842$	1.96006	+	17.6108i	0.0675483	+	0.606908i
$843$		0			0
$844$	−27.8235	−	2.58030i	−0.957725	−	0.0888177i
$845$	−9.89330	+	26.9850i	−0.340340	+	0.928311i
$846$		0			0
$847$	−42.2242	+	21.5143i	−1.45084	+	0.739241i
$848$	−22.0614	−	32.2159i	−0.757593	−	1.10630i
$849$		0			0
$850$	−1.32617	−	6.77040i	−0.0454873	−	0.232223i
$851$			12.2760i			0.420817i
$852$		0			0
$853$	−33.8979	+	17.2718i	−1.16064	+	0.591376i	−0.924814	−	0.380419i	$-0.875780\pi$
$853$	−33.8979	+	17.2718i	−1.16064	+	0.591376i	−0.235827	+	0.971795i	$0.575780\pi$
$854$	−54.1063	+	14.8534i	−1.85148	+	0.508273i
$855$		0			0
$856$	−7.94980	+	4.23633i	−0.271718	+	0.144795i
$857$	32.6730	−	32.6730i	1.11609	−	1.11609i	0.123779	−	0.992310i	$-0.460499\pi$
$857$	32.6730	−	32.6730i	1.11609	−	1.11609i	0.992310	−	0.123779i	$-0.0395013\pi$
$858$		0			0
$859$	30.2637	+	21.9879i	1.03258	+	0.750217i	0.968824	−	0.247748i	$-0.0796906\pi$
$859$	30.2637	+	21.9879i	1.03258	+	0.750217i	0.0637605	+	0.997965i	$0.479691\pi$
$860$	21.0155	+	14.4071i	0.716621	+	0.491277i
$861$		0			0
$862$	0.189540	−	0.172776i	0.00645576	−	0.00588477i
$863$	52.4831	−	8.31251i	1.78655	−	0.282961i	0.826527	−	0.562897i	$-0.190313\pi$
$863$	52.4831	−	8.31251i	1.78655	−	0.282961i	0.960019	+	0.279936i	$0.0903134\pi$
$864$		0			0
$865$	21.7567	−	20.1935i	0.739752	−	0.686600i
$866$	−0.136307	+	2.94592i	−0.00463191	+	0.100106i
$867$		0			0
$868$	56.3773	−	22.4371i	1.91357	−	0.761566i
$869$	11.1361	−	3.61834i	0.377767	−	0.122744i
$870$		0			0
$871$	−4.16450	−	1.35313i	−0.141109	−	0.0458490i
$872$	16.4797	+	21.8276i	0.558072	+	0.739177i
$873$		0			0
$874$	−4.68262	+	3.08186i	−0.158392	+	0.104245i
$875$	−19.1810	−	51.0362i	−0.648435	−	1.72534i
$876$		0			0
$877$	0.559164	−	3.53042i	0.0188816	−	0.119214i	−0.976447	−	0.215756i	$-0.930778\pi$
$877$	0.559164	−	3.53042i	0.0188816	−	0.119214i	0.995329	+	0.0965424i	$0.0307783\pi$
$878$	22.3528	−	39.2696i	0.754372	−	1.32528i
$879$		0			0
$880$	−0.930114	−	10.0852i	−0.0313541	−	0.339973i
$881$	7.33129	+	22.5634i	0.246997	+	0.760180i	0.995302	+	0.0968241i	$0.0308684\pi$
$881$	7.33129	+	22.5634i	0.246997	+	0.760180i	−0.748304	+	0.663356i	$0.769132\pi$
$882$		0			0
$883$	−34.4658	−	17.5612i	−1.15987	−	0.590982i	−0.235271	−	0.971930i	$-0.575598\pi$
$883$	−34.4658	−	17.5612i	−1.15987	−	0.590982i	−0.924596	+	0.380948i	$0.875598\pi$
$884$	−0.381298	−	0.642136i	−0.0128244	−	0.0215974i
$885$		0			0
$886$	−10.9905	+	29.1637i	−0.369233	+	0.979774i
$887$	5.52267	+	34.8688i	0.185433	+	1.17078i	0.888233	+	0.459392i	$0.151933\pi$
$887$	5.52267	+	34.8688i	0.185433	+	1.17078i	−0.702800	+	0.711387i	$0.748067\pi$
$888$		0			0
$889$	20.2728	+	27.9031i	0.679929	+	0.935842i
$890$	−40.9896	+	16.7415i	−1.37397	+	0.561177i
$891$		0			0
$892$	−9.05943	−	10.9115i	−0.303332	−	0.365344i
$893$	−22.4982	−	22.4982i	−0.752875	−	0.752875i
$894$		0			0
$895$	29.2957	+	43.6526i	0.979246	+	1.45915i
$896$	32.0038	+	44.9411i	1.06917	+	1.50138i
$897$		0			0
$898$	2.87855	+	6.36024i	0.0960585	+	0.212244i
$899$	43.0345			1.43528
$900$		0			0
$901$	9.52399			0.317290
$902$	−4.13777	−	9.14252i	−0.137773	−	0.304413i
$903$		0			0
$904$	58.9626	+	8.23159i	1.96107	+	0.273779i
$905$	36.4006	+	13.3453i	1.21000	+	0.443612i
$906$		0			0
$907$	12.7734	+	12.7734i	0.424135	+	0.424135i	0.886625	−	0.462489i	$-0.153044\pi$
$907$	12.7734	+	12.7734i	0.424135	+	0.424135i	−0.462489	+	0.886625i	$0.653044\pi$
$908$	3.35753	−	2.78764i	0.111423	−	0.0925110i
$909$		0			0
$910$	−3.81072	−	4.50671i	−0.126324	−	0.149396i
$911$	21.0752	+	29.0075i	0.698253	+	0.961062i	0.999971	+	0.00766504i	$0.00243988\pi$
$911$	21.0752	+	29.0075i	0.698253	+	0.961062i	−0.301718	+	0.953397i	$0.597560\pi$
$912$		0			0
$913$	−1.92318	−	12.1425i	−0.0636481	−	0.401858i
$914$	4.39339	−	11.6580i	0.145320	−	0.385613i
$915$		0			0
$916$	−13.1277	+	7.79515i	−0.433750	+	0.257559i
$917$	79.6298	+	40.5734i	2.62961	+	1.33985i
$918$		0			0
$919$	−4.91425	−	15.1245i	−0.162106	−	0.498912i	0.836705	−	0.547654i	$-0.184479\pi$
$919$	−4.91425	−	15.1245i	−0.162106	−	0.498912i	−0.998811	+	0.0487419i	$0.984479\pi$
$920$	7.70266	−	3.74327i	0.253949	−	0.123412i
$921$		0			0
$922$	0.232833	−	0.409043i	0.00766796	−	0.0134711i
$923$	0.173460	−	1.09519i	0.00570952	−	0.0360485i
$924$		0			0
$925$	17.5161	+	41.8083i	0.575925	+	1.37465i
$926$	12.3527	−	8.12993i	0.405936	−	0.267166i
$927$		0			0
$928$	9.30324	+	38.0074i	0.305394	+	1.24765i
$929$	13.9497	+	4.53255i	0.457676	+	0.148708i	0.528776	−	0.848761i	$-0.322651\pi$
$929$	13.9497	+	4.53255i	0.457676	+	0.148708i	−0.0711001	+	0.997469i	$0.522651\pi$
$930$		0			0
$931$	46.7187	−	15.1798i	1.53115	−	0.497499i
$932$	−19.6242	−	49.3093i	−0.642812	−	1.61518i
$933$		0			0
$934$	−1.33833	+	28.9244i	−0.0437914	+	0.946436i
$935$	2.15786	+	1.20273i	0.0705697	+	0.0393336i
$936$		0			0
$937$	17.6258	−	2.79165i	0.575809	−	0.0911992i	0.138264	−	0.990395i	$-0.455848\pi$
$937$	17.6258	−	2.79165i	0.575809	−	0.0911992i	0.437545	+	0.899196i	$0.355848\pi$
$938$	−58.3140	+	53.1563i	−1.90402	+	1.73561i
$939$		0			0
$940$	29.6361	+	38.5283i	0.966622	+	1.25666i
$941$	32.8555	+	23.8709i	1.07106	+	0.778169i	0.976102	−	0.217312i	$-0.0697290\pi$
$941$	32.8555	+	23.8709i	1.07106	+	0.778169i	0.0949560	+	0.995481i	$0.469729\pi$
$942$		0			0
$943$	6.00024	−	6.00024i	0.195395	−	0.195395i
$944$	−8.64246	+	15.8536i	−0.281288	+	0.515989i
$945$		0			0
$946$	−8.79824	+	2.41532i	−0.286056	+	0.0785287i
$947$	6.28337	−	3.20154i	0.204182	−	0.104036i	−0.348909	−	0.937156i	$-0.613448\pi$
$947$	6.28337	−	3.20154i	0.204182	−	0.104036i	0.553092	+	0.833120i	$0.313448\pi$
$948$		0			0
$949$		−	1.23135i		−	0.0399714i
$950$	−11.5502	+	17.1772i	−0.374737	+	0.557302i
$951$		0			0
$952$	−13.4552	+	0.247188i	−0.436085	+	0.00801140i
$953$	−32.3125	+	16.4640i	−1.04671	+	0.533323i	−0.890775	−	0.454445i	$-0.849838\pi$
$953$	−32.3125	+	16.4640i	−1.04671	+	0.533323i	−0.155930	+	0.987768i	$0.549838\pi$
$954$		0			0
$955$	−1.63254	−	5.74406i	−0.0528279	−	0.185873i
$956$	−4.33306	+	46.7236i	−0.140141	+	1.51115i
$957$		0			0
$958$	3.28127	+	29.4816i	0.106013	+	0.952508i
$959$	49.4635	+	35.9373i	1.59726	+	1.16048i
$960$		0			0
$961$	6.23413	−	4.52936i	0.201101	−	0.146108i
$962$	3.30557	+	3.62630i	0.106576	+	0.116917i
$963$		0			0
$964$	−12.0168	+	2.70846i	−0.387034	+	0.0872335i
$965$	−17.1496	+	2.06498i	−0.552065	+	0.0664740i
$966$		0			0
$967$	1.56312	−	3.06780i	0.0502667	−	0.0986539i	−0.864507	−	0.502621i	$-0.832369\pi$
$967$	1.56312	−	3.06780i	0.0502667	−	0.0986539i	0.914773	+	0.403967i	$0.132369\pi$
$968$	−22.5297	−	15.7447i	−0.724132	−	0.506055i
$969$		0			0
$970$	33.4318	−	7.85167i	1.07343	−	0.252102i
$971$	27.4780	+	8.92814i	0.881810	+	0.286517i	0.714709	−	0.699422i	$-0.246559\pi$
$971$	27.4780	+	8.92814i	0.881810	+	0.286517i	0.167101	+	0.985940i	$0.446559\pi$
$972$		0			0
$973$	−14.7693	−	2.33924i	−0.473484	−	0.0749924i
$974$	−16.3103	−	24.7821i	−0.522615	−	0.794070i
$975$		0			0
$976$	−22.3612	−	23.6436i	−0.715764	−	0.756812i
$977$	−0.124456	+	0.785785i	−0.00398170	+	0.0251395i	−0.989599	−	0.143852i	$-0.954051\pi$
$977$	−0.124456	+	0.785785i	−0.00398170	+	0.0251395i	0.985618	+	0.168992i	$0.0540511\pi$
$978$		0			0
$979$	4.89934	−	15.0786i	0.156583	−	0.481914i
$980$	−73.7733	+	13.7631i	−2.35660	+	0.439645i
$981$		0			0
$982$	3.70291	−	17.9609i	0.118165	−	0.573155i
$983$	−42.2667	−	21.5360i	−1.34810	−	0.686891i	−0.377145	−	0.926154i	$-0.623094\pi$
$983$	−42.2667	−	21.5360i	−1.34810	−	0.686891i	−0.970955	+	0.239263i	$0.923094\pi$
$984$		0			0
$985$	34.2265	+	6.73611i	1.09055	+	0.214630i
$986$	−8.93123	−	3.36578i	−0.284428	−	0.107188i
$987$		0			0
$988$	−0.553380	+	2.17126i	−0.0176054	+	0.0690770i
$989$	−4.53468	−	6.24145i	−0.144194	−	0.198467i
$990$		0			0
$991$	9.79781	−	13.4855i	0.311238	−	0.428382i	−0.624529	−	0.781002i	$-0.714709\pi$
$991$	9.79781	−	13.4855i	0.311238	−	0.428382i	0.935767	+	0.352620i	$0.114709\pi$
$992$	26.8625	+	22.7375i	0.852885	+	0.721915i
$993$		0			0
$994$	−15.6050	−	12.4792i	−0.494959	−	0.395817i
$995$	−23.1610	+	29.5022i	−0.734254	+	0.935283i
$996$		0			0
$997$	−16.4461	−	32.2773i	−0.520853	−	1.02223i	−0.990257	−	0.139249i	$-0.955531\pi$
$997$	−16.4461	−	32.2773i	−0.520853	−	1.02223i	0.469404	−	0.882983i	$-0.344469\pi$
$998$	−39.2991	+	17.7862i	−1.24399	+	0.563012i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.e.523.24	yes	224
3.2	odd	2	inner	900.2.bj.e.523.5	yes	224
4.3	odd	2	inner	900.2.bj.e.523.8	yes	224
12.11	even	2	inner	900.2.bj.e.523.21	yes	224
25.12	odd	20	inner	900.2.bj.e.487.8	yes	224
75.62	even	20	inner	900.2.bj.e.487.21	yes	224
100.87	even	20	inner	900.2.bj.e.487.24	yes	224
300.287	odd	20	inner	900.2.bj.e.487.5	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.bj.e.487.5	✓	224	300.287	odd	20	inner
900.2.bj.e.487.8	yes	224	25.12	odd	20	inner
900.2.bj.e.487.21	yes	224	75.62	even	20	inner
900.2.bj.e.487.24	yes	224	100.87	even	20	inner
900.2.bj.e.523.5	yes	224	3.2	odd	2	inner
900.2.bj.e.523.8	yes	224	4.3	odd	2	inner
900.2.bj.e.523.21	yes	224	12.11	even	2	inner
900.2.bj.e.523.24	yes	224	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28840 - 0.583112i) q^{2} +(1.31996 - 1.50257i) q^{4} +(-1.38078 + 1.75882i) q^{5} +(-3.44825 - 3.44825i) q^{7} +(0.824475 - 2.70559i) q^{8} +(-0.753412 + 3.07122i) q^{10} +(-0.665578 - 0.916089i) q^{11} +(-0.0598699 - 0.378004i) q^{13} +(-6.45345 - 2.43201i) q^{14} +(-0.515411 - 3.96665i) q^{16} +(0.869332 + 0.442947i) q^{17} +(-0.904594 - 2.78406i) q^{19} +(0.820167 + 4.39629i) q^{20} +(-1.39171 - 0.792185i) q^{22} +(0.211827 - 1.33742i) q^{23} +(-1.18689 - 4.85709i) q^{25} +(-0.297555 - 0.452110i) q^{26} +(-9.73277 + 0.629671i) q^{28} +(-6.57862 - 2.13752i) q^{29} +(-5.91690 + 1.92252i) q^{31} +(-2.97706 - 4.81010i) q^{32} +(1.37834 + 0.0637754i) q^{34} +(10.8261 - 1.30357i) q^{35} +(-8.95424 + 1.41821i) q^{37} +(-2.78890 - 3.05950i) q^{38} +(3.62023 + 5.18593i) q^{40} +(5.06982 + 3.68344i) q^{41} +(4.02869 - 4.02869i) q^{43} +(-2.25502 - 0.209126i) q^{44} +(-0.506950 - 1.84666i) q^{46} +(9.68440 - 4.93445i) q^{47} +16.7808i q^{49} +(-4.36142 - 5.56579i) q^{50} +(-0.647001 - 0.408991i) q^{52} +(8.69751 - 4.43160i) q^{53} +(2.53025 + 0.0942872i) q^{55} +(-12.1726 + 6.48657i) q^{56} +(-9.72232 + 1.08208i) q^{58} +(-3.65195 - 2.65330i) q^{59} +(6.58194 - 4.78206i) q^{61} +(-6.50231 + 5.92720i) q^{62} +(-6.64048 - 4.46139i) q^{64} +(0.747507 + 0.416640i) q^{65} +(5.19430 - 10.1944i) q^{67} +(1.81304 - 0.721557i) q^{68} +(13.1883 - 7.99237i) q^{70} +(2.75549 + 0.895311i) q^{71} +(3.17780 + 0.503314i) q^{73} +(-10.7097 + 7.04856i) q^{74} +(-5.37726 - 2.31563i) q^{76} +(-0.863825 + 5.45398i) q^{77} +(-3.19543 + 9.83453i) q^{79} +(7.68830 + 4.57057i) q^{80} +(8.67982 + 1.78948i) q^{82} +(9.67363 + 4.92896i) q^{83} +(-1.97942 + 0.917386i) q^{85} +(2.84139 - 7.53974i) q^{86} +(-3.02732 + 1.04549i) q^{88} +(8.22988 + 11.3275i) q^{89} +(-1.09700 + 1.50990i) q^{91} +(-1.72997 - 2.08363i) q^{92} +(9.60007 - 12.0046i) q^{94} +(6.14570 + 2.25315i) q^{95} +(-4.93021 - 9.67608i) q^{97} +(9.78511 + 21.6205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 4 q^{10} + 16 q^{13} - 16 q^{16} + 28 q^{22} - 32 q^{25} + 28 q^{28} - 100 q^{34} - 104 q^{37} + 60 q^{40} + 156 q^{52} + 144 q^{58} - 48 q^{61} + 60 q^{64} + 28 q^{70} + 40 q^{73} + 64 q^{82} + 136 q^{85}+ \cdots - 160 q^{97}+O(q^{100}) \) 224 * q - 4 * q^10 + 16 * q^13 - 16 * q^16 + 28 * q^22 - 32 * q^25 + 28 * q^28 - 100 * q^34 - 104 * q^37 + 60 * q^40 + 156 * q^52 + 144 * q^58 - 48 * q^61 + 60 * q^64 + 28 * q^70 + 40 * q^73 + 64 * q^82 + 136 * q^85 + 148 * q^88 + 40 * q^94 - 160 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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