LMFDB - Embedded newform 1080.2.m.c.539.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(539,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("1080.539");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.m (of order $2$, degree $1$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			539.32
Character	$\chi$	$=$	1080.539
Dual form			1080.2.m.c.539.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.482315 + 1.32943i) q^{2} +(-1.53474 + 1.28240i) q^{4} +(1.17345 + 1.90342i) q^{5} +0.450397 q^{7} +(-2.44509 - 1.42181i) q^{8} +(-1.96449 + 2.47806i) q^{10} +5.11202i q^{11} +1.15380 q^{13} +(0.217233 + 0.598769i) q^{14} +(0.710884 - 3.93632i) q^{16} -6.13070 q^{17} +2.16656 q^{19} +(-4.24190 - 1.41644i) q^{20} +(-6.79605 + 2.46560i) q^{22} +0.211029i q^{23} +(-2.24604 + 4.46713i) q^{25} +(0.556495 + 1.53389i) q^{26} +(-0.691244 + 0.577590i) q^{28} +6.08377 q^{29} -0.417311i q^{31} +(5.57592 - 0.953480i) q^{32} +(-2.95693 - 8.15031i) q^{34} +(0.528517 + 0.857296i) q^{35} -9.60013 q^{37} +(1.04496 + 2.88028i) q^{38} +(-0.162881 - 6.32246i) q^{40} +9.71138i q^{41} -3.06432i q^{43} +(-6.55567 - 7.84565i) q^{44} +(-0.280547 + 0.101782i) q^{46} -2.65854i q^{47} -6.79714 q^{49} +(-7.02202 - 0.831385i) q^{50} +(-1.77079 + 1.47964i) q^{52} +8.81551i q^{53} +(-9.73034 + 5.99869i) q^{55} +(-1.10126 - 0.640377i) q^{56} +(2.93429 + 8.08792i) q^{58} -4.73857i q^{59} -7.64787i q^{61} +(0.554784 - 0.201275i) q^{62} +(3.95693 + 6.95289i) q^{64} +(1.35392 + 2.19617i) q^{65} -6.49513i q^{67} +(9.40907 - 7.86203i) q^{68} +(-0.884800 + 1.11611i) q^{70} +11.4430 q^{71} +13.8904i q^{73} +(-4.63028 - 12.7627i) q^{74} +(-3.32511 + 2.77840i) q^{76} +2.30244i q^{77} -13.7469i q^{79} +(8.32668 - 3.26595i) q^{80} +(-12.9106 + 4.68394i) q^{82} -5.22116 q^{83} +(-7.19405 - 11.6693i) q^{85} +(4.07379 - 1.47797i) q^{86} +(7.26831 - 12.4994i) q^{88} -1.39700i q^{89} +0.519668 q^{91} +(-0.270624 - 0.323875i) q^{92} +(3.53433 - 1.28225i) q^{94} +(2.54234 + 4.12388i) q^{95} +4.41107i q^{97} +(-3.27836 - 9.03630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0.482315	+	1.32943i	0.341048	+	0.940046i
$2$	0.482315	+	1.32943i	0.341048	+	0.940046i
$3$		0			0
$3$		0			0
$4$	−1.53474	+	1.28240i	−0.767372	+	0.641202i
$5$	1.17345	+	1.90342i	0.524781	+	0.851237i
$5$	1.17345	+	1.90342i	0.524781	+	0.851237i
$6$		0			0
$7$	0.450397			0.170234			0.0851170	−	0.996371i	$-0.472874\pi$
$7$	0.450397			0.170234			0.0851170	+	0.996371i	$0.472874\pi$
$8$	−2.44509	−	1.42181i	−0.864470	−	0.502685i
$9$		0			0
$10$	−1.96449	+	2.47806i	−0.621226	+	0.783631i
$11$			5.11202i			1.54133i	0.637239	+	0.770666i	$0.280076\pi$
$11$			5.11202i			1.54133i	−0.637239	+	0.770666i	$0.719924\pi$
$12$		0			0
$13$	1.15380			0.320007			0.160003	−	0.987116i	$-0.448849\pi$
$13$	1.15380			0.320007			0.160003	+	0.987116i	$0.448849\pi$
$14$	0.217233	+	0.598769i	0.0580580	+	0.160028i
$15$		0			0
$16$	0.710884	−	3.93632i	0.177721	−	0.984081i
$17$	−6.13070			−1.48691			−0.743457	−	0.668784i	$-0.766815\pi$
$17$	−6.13070			−1.48691			−0.743457	+	0.668784i	$0.766815\pi$
$18$		0			0
$19$	2.16656			0.497043			0.248521	−	0.968626i	$-0.420055\pi$
$19$	2.16656			0.497043			0.248521	+	0.968626i	$0.420055\pi$
$20$	−4.24190	−	1.41644i	−0.948517	−	0.316725i
$21$		0			0
$22$	−6.79605	+	2.46560i	−1.44892	+	0.525668i
$23$			0.211029i			0.0440025i	0.999758	+	0.0220013i	$0.00700379\pi$
$23$			0.211029i			0.0440025i	−0.999758	+	0.0220013i	$0.992996\pi$
$24$		0			0
$25$	−2.24604	+	4.46713i	−0.449209	+	0.893427i
$26$	0.556495	+	1.53389i	0.109138	+	0.300821i
$27$		0			0
$28$	−0.691244	+	0.577590i	−0.130633	+	0.109154i
$29$	6.08377			1.12973			0.564864	−	0.825184i	$-0.308929\pi$
$29$	6.08377			1.12973			0.564864	+	0.825184i	$0.308929\pi$
$30$		0			0
$31$		−	0.417311i		−	0.0749512i	−0.999298	−	0.0374756i	$-0.988068\pi$
$31$		−	0.417311i		−	0.0749512i	0.999298	−	0.0374756i	$-0.0119317\pi$
$32$	5.57592	−	0.953480i	0.985693	−	0.168553i
$33$		0			0
$34$	−2.95693	−	8.15031i	−0.507109	−	1.39777i
$35$	0.528517	+	0.857296i	0.0893356	+	0.144909i
$36$		0			0
$37$	−9.60013			−1.57825			−0.789126	−	0.614232i	$-0.789466\pi$
$37$	−9.60013			−1.57825			−0.789126	+	0.614232i	$0.789466\pi$
$38$	1.04496	+	2.88028i	0.169515	+	0.467243i
$39$		0			0
$40$	−0.162881	−	6.32246i	−0.0257538	−	0.999668i
$41$			9.71138i			1.51666i	0.651869	+	0.758332i	$0.273985\pi$
$41$			9.71138i			1.51666i	−0.651869	+	0.758332i	$0.726015\pi$
$42$		0			0
$43$		−	3.06432i		−	0.467305i	−0.972320	−	0.233652i	$-0.924932\pi$
$43$		−	3.06432i		−	0.467305i	0.972320	−	0.233652i	$-0.0750678\pi$
$44$	−6.55567	−	7.84565i	−0.988305	−	1.18278i
$45$		0			0
$46$	−0.280547	+	0.101782i	−0.0413644	+	0.0150070i
$47$		−	2.65854i		−	0.387788i	−0.981023	−	0.193894i	$-0.937888\pi$
$47$		−	2.65854i		−	0.387788i	0.981023	−	0.193894i	$-0.0621117\pi$
$48$		0			0
$49$	−6.79714			−0.971020
$50$	−7.02202	−	0.831385i	−0.993064	−	0.117576i
$51$		0			0
$52$	−1.77079	+	1.47964i	−0.245564	+	0.205189i
$53$			8.81551i			1.21090i	0.795882	+	0.605452i	$0.207008\pi$
$53$			8.81551i			1.21090i	−0.795882	+	0.605452i	$0.792992\pi$
$54$		0			0
$55$	−9.73034	+	5.99869i	−1.31204	+	0.808863i
$56$	−1.10126	−	0.640377i	−0.147162	−	0.0855740i
$57$		0			0
$58$	2.93429	+	8.08792i	0.385291	+	1.06200i
$59$		−	4.73857i		−	0.616910i	−0.951239	−	0.308455i	$-0.900188\pi$
$59$		−	4.73857i		−	0.616910i	0.951239	−	0.308455i	$-0.0998119\pi$
$60$		0			0
$61$		−	7.64787i		−	0.979209i	−0.871945	−	0.489605i	$-0.837141\pi$
$61$		−	7.64787i		−	0.979209i	0.871945	−	0.489605i	$-0.162859\pi$
$62$	0.554784	−	0.201275i	0.0704576	−	0.0255620i
$63$		0			0
$64$	3.95693	+	6.95289i	0.494616	+	0.869112i
$65$	1.35392	+	2.19617i	0.167934	+	0.272402i
$66$		0			0
$67$		−	6.49513i		−	0.793506i	−0.917925	−	0.396753i	$-0.870137\pi$
$67$		−	6.49513i		−	0.793506i	0.917925	−	0.396753i	$-0.129863\pi$
$68$	9.40907	−	7.86203i	1.14102	−	0.953412i
$69$		0			0
$70$	−0.884800	+	1.11611i	−0.105754	+	0.133401i
$71$	11.4430			1.35803			0.679016	−	0.734124i	$-0.262407\pi$
$71$	11.4430			1.35803			0.679016	+	0.734124i	$0.262407\pi$
$72$		0			0
$73$			13.8904i			1.62574i	0.582443	+	0.812871i	$0.302097\pi$
$73$			13.8904i			1.62574i	−0.582443	+	0.812871i	$0.697903\pi$
$74$	−4.63028	−	12.7627i	−0.538260	−	1.48363i
$75$		0			0
$76$	−3.32511	+	2.77840i	−0.381417	+	0.318705i
$77$			2.30244i			0.262387i
$78$		0			0
$79$		−	13.7469i		−	1.54664i	−0.634015	−	0.773321i	$-0.718594\pi$
$79$		−	13.7469i		−	1.54664i	0.634015	−	0.773321i	$-0.281406\pi$
$80$	8.32668	−	3.26595i	0.930951	−	0.365145i
$81$		0			0
$82$	−12.9106	+	4.68394i	−1.42573	+	0.517255i
$83$	−5.22116			−0.573096			−0.286548	−	0.958066i	$-0.592508\pi$
$83$	−5.22116			−0.573096			−0.286548	+	0.958066i	$0.592508\pi$
$84$		0			0
$85$	−7.19405	−	11.6693i	−0.780305	−	1.26572i
$86$	4.07379	−	1.47797i	0.439288	−	0.159373i
$87$		0			0
$88$	7.26831	−	12.4994i	0.774804	−	1.33244i
$89$		−	1.39700i		−	0.148082i	−0.997255	−	0.0740408i	$-0.976411\pi$
$89$		−	1.39700i		−	0.148082i	0.997255	−	0.0740408i	$-0.0235895\pi$
$90$		0			0
$91$	0.519668			0.0544761
$92$	−0.270624	−	0.323875i	−0.0282145	−	0.0337663i
$93$		0			0
$94$	3.53433	−	1.28225i	0.364538	−	0.132254i
$95$	2.54234	+	4.12388i	0.260839	+	0.423101i
$96$		0			0
$97$			4.41107i			0.447876i	0.974603	+	0.223938i	$0.0718913\pi$
$97$			4.41107i			0.447876i	−0.974603	+	0.223938i	$0.928109\pi$
$98$	−3.27836	−	9.03630i	−0.331165	−	0.912804i
$99$		0			0
$100$	−2.28156	−	9.73625i	−0.228156	−	0.973625i
$101$	12.5630			1.25006			0.625031	−	0.780600i	$-0.285086\pi$
$101$	12.5630			1.25006			0.625031	+	0.780600i	$0.285086\pi$
$102$		0			0
$103$	5.95376			0.586641			0.293320	−	0.956014i	$-0.405240\pi$
$103$	5.95376			0.586641			0.293320	+	0.956014i	$0.405240\pi$
$104$	−2.82115	−	1.64048i	−0.276636	−	0.160863i
$105$		0			0
$106$	−11.7196	+	4.25185i	−1.13831	+	0.412976i
$107$	−8.98524			−0.868636			−0.434318	−	0.900760i	$-0.643011\pi$
$107$	−8.98524			−0.868636			−0.434318	+	0.900760i	$0.643011\pi$
$108$		0			0
$109$			11.7484i			1.12529i	0.826697	+	0.562647i	$0.190217\pi$
$109$			11.7484i			1.12529i	−0.826697	+	0.562647i	$0.809783\pi$
$110$	−12.6679	−	10.0425i	−1.20784	−	0.957516i
$111$		0			0
$112$	0.320180	−	1.77291i	0.0302542	−	0.167524i
$113$	0.926078			0.0871181			0.0435590	−	0.999051i	$-0.486130\pi$
$113$	0.926078			0.0871181			0.0435590	+	0.999051i	$0.486130\pi$
$114$		0			0
$115$	−0.401677	+	0.247631i	−0.0374566	+	0.0230917i
$116$	−9.33703	+	7.80184i	−0.866922	+	0.724383i
$117$		0			0
$118$	6.29958	−	2.28548i	0.579923	−	0.210396i
$119$	−2.76125			−0.253123
$120$		0			0
$121$	−15.1328			−1.37571
$122$	10.1673	−	3.68868i	0.920502	−	0.333957i
$123$		0			0
$124$	0.535161	+	0.640466i	0.0480589	+	0.0575155i
$125$	−11.1385	+	0.966769i	−0.996254	+	0.0864704i
$126$		0			0
$127$	16.6083			1.47375			0.736873	−	0.676031i	$-0.236302\pi$
$127$	16.6083			1.47375			0.736873	+	0.676031i	$0.236302\pi$
$128$	−7.33487	+	8.61393i	−0.648317	+	0.761371i
$129$		0			0
$130$	−2.26663	+	2.85919i	−0.198797	+	0.250767i
$131$			13.5426i			1.18323i	0.806222	+	0.591613i	$0.201509\pi$
$131$			13.5426i			1.18323i	−0.806222	+	0.591613i	$0.798491\pi$
$132$		0			0
$133$	0.975811			0.0846136
$134$	8.63479	−	3.13270i	0.745932	−	0.270624i
$135$		0			0
$136$	14.9901	+	8.71668i	1.28539	+	0.747449i
$137$	8.89160			0.759661			0.379830	−	0.925056i	$-0.375982\pi$
$137$	8.89160			0.759661			0.379830	+	0.925056i	$0.375982\pi$
$138$		0			0
$139$	14.2713			1.21047			0.605236	−	0.796046i	$-0.293079\pi$
$139$	14.2713			1.21047			0.605236	+	0.796046i	$0.293079\pi$
$140$	−1.91054	−	0.637959i	−0.161470	−	0.0539174i
$141$		0			0
$142$	5.51912	+	15.2126i	0.463154	+	1.27661i
$143$			5.89826i			0.493237i
$144$		0			0
$145$	7.13898	+	11.5800i	0.592860	+	0.961666i
$146$	−18.4662	+	6.69952i	−1.52827	+	0.554456i
$147$		0			0
$148$	14.7337	−	12.3112i	1.21111	−	1.01198i
$149$	8.96593			0.734518			0.367259	−	0.930119i	$-0.380296\pi$
$149$	8.96593			0.734518			0.367259	+	0.930119i	$0.380296\pi$
$150$		0			0
$151$			15.5560i			1.26593i	0.774180	+	0.632966i	$0.218163\pi$
$151$			15.5560i			1.26593i	−0.774180	+	0.632966i	$0.781837\pi$
$152$	−5.29743	−	3.08043i	−0.429678	−	0.249856i
$153$		0			0
$154$	−3.06092	+	1.11050i	−0.246656	+	0.0894867i
$155$	0.794319	−	0.489692i	0.0638013	−	0.0393330i
$156$		0			0
$157$	13.2345			1.05623			0.528115	−	0.849173i	$-0.322899\pi$
$157$	13.2345			1.05623			0.528115	+	0.849173i	$0.322899\pi$
$158$	18.2754	−	6.63031i	1.45391	−	0.527479i
$159$		0			0
$160$	8.35792	+	9.49448i	0.660752	+	0.750605i
$161$			0.0950467i			0.00749073i
$162$		0			0
$163$		−	15.3659i		−	1.20355i	−0.798666	−	0.601774i	$-0.794461\pi$
$163$		−	15.3659i		−	1.20355i	0.798666	−	0.601774i	$-0.205539\pi$
$164$	−12.4539	−	14.9045i	−0.972487	−	1.16385i
$165$		0			0
$166$	−2.51824	−	6.94114i	−0.195453	−	0.538737i
$167$			17.9401i			1.38824i	0.719857	+	0.694122i	$0.244207\pi$
$167$			17.9401i			1.38824i	−0.719857	+	0.694122i	$0.755793\pi$
$168$		0			0
$169$	−11.6687			−0.897596
$170$	12.0437	−	15.1922i	0.923710	−	1.16519i
$171$		0			0
$172$	3.92970	+	4.70295i	0.299637	+	0.358597i
$173$		−	17.2609i		−	1.31232i	−0.754622	−	0.656160i	$-0.772180\pi$
$173$		−	17.2609i		−	1.31232i	0.754622	−	0.656160i	$-0.227820\pi$
$174$		0			0
$175$	−1.01161	+	2.01198i	−0.0764706	+	0.152092i
$176$	20.1226	+	3.63405i	1.51680	+	0.273927i
$177$		0			0
$178$	1.85721	−	0.673793i	0.139203	−	0.0505029i
$179$		−	0.229984i		−	0.0171898i	−0.999963	−	0.00859490i	$-0.997264\pi$
$179$		−	0.229984i		−	0.0171898i	0.999963	−	0.00859490i	$-0.00273588\pi$
$180$		0			0
$181$			2.26929i			0.168675i	0.996437	+	0.0843377i	$0.0268774\pi$
$181$			2.26929i			0.168675i	−0.996437	+	0.0843377i	$0.973123\pi$
$182$	0.250644	+	0.690861i	0.0185790	+	0.0512100i
$183$		0			0
$184$	0.300042	−	0.515984i	0.0221194	−	0.0380389i
$185$	−11.2652	−	18.2731i	−0.828237	−	1.34347i
$186$		0			0
$187$		−	31.3403i		−	2.29183i
$188$	3.40932	+	4.08018i	0.248650	+	0.297578i
$189$		0			0
$190$	−4.25618	+	5.36886i	−0.308776	+	0.389498i
$191$	17.1688			1.24229			0.621145	−	0.783696i	$-0.286668\pi$
$191$	17.1688			1.24229			0.621145	+	0.783696i	$0.286668\pi$
$192$		0			0
$193$		−	0.900092i		−	0.0647901i	−0.999475	−	0.0323950i	$-0.989687\pi$
$193$		−	0.900092i		−	0.0647901i	0.999475	−	0.0323950i	$-0.0103135\pi$
$194$	−5.86419	+	2.12752i	−0.421024	+	0.152747i
$195$		0			0
$196$	10.4319	−	8.71668i	0.745134	−	0.622620i
$197$			1.61680i			0.115193i	0.998340	+	0.0575963i	$0.0183436\pi$
$197$			1.61680i			0.115193i	−0.998340	+	0.0575963i	$0.981656\pi$
$198$		0			0
$199$			13.9958i			0.992137i	0.868283	+	0.496069i	$0.165224\pi$
$199$			13.9958i			0.992137i	−0.868283	+	0.496069i	$0.834776\pi$
$200$	11.8432	−	7.72910i	0.837440	−	0.546530i
$201$		0			0
$202$	6.05931	+	16.7015i	0.426331	+	1.17512i
$203$	2.74011			0.192318
$204$		0			0
$205$	−18.4849	+	11.3958i	−1.29104	+	0.795917i
$206$	2.87158	+	7.91508i	0.200073	+	0.551469i
$207$		0			0
$208$	0.820219	−	4.54174i	0.0568719	−	0.314913i
$209$			11.0755i			0.766108i
$210$		0			0
$211$	24.9023			1.71435			0.857174	−	0.515028i	$-0.172218\pi$
$211$	24.9023			1.71435			0.857174	+	0.515028i	$0.172218\pi$
$212$	−11.3050	−	13.5296i	−0.776434	−	0.929214i
$213$		0			0
$214$	−4.33371	−	11.9452i	−0.296247	−	0.816557i
$215$	5.83270	−	3.59582i	0.397787	−	0.245233i
$216$		0			0
$217$		−	0.187956i		−	0.0127593i
$218$	−15.6186	+	5.66643i	−1.05783	+	0.383779i
$219$		0			0
$220$	7.24086	−	21.6847i	0.488179	−	1.46198i
$221$	−7.07361			−0.475823
$222$		0			0
$223$	19.2003			1.28574			0.642872	−	0.765974i	$-0.277743\pi$
$223$	19.2003			1.28574			0.642872	+	0.765974i	$0.277743\pi$
$224$	2.51138	−	0.429444i	0.167798	−	0.0286935i
$225$		0			0
$226$	0.446661	+	1.23115i	0.0297114	+	0.0818950i
$227$	28.6073			1.89874			0.949368	−	0.314167i	$-0.101725\pi$
$227$	28.6073			1.89874			0.949368	+	0.314167i	$0.101725\pi$
$228$		0			0
$229$		−	3.59647i		−	0.237662i	−0.992915	−	0.118831i	$-0.962085\pi$
$229$		−	3.59647i		−	0.237662i	0.992915	−	0.118831i	$-0.0379146\pi$
$230$	−0.522942	−	0.414564i	−0.0344818	−	0.0273355i
$231$		0			0
$232$	−14.8754	−	8.64995i	−0.976615	−	0.567897i
$233$	−9.78036			−0.640733			−0.320366	−	0.947294i	$-0.603806\pi$
$233$	−9.78036			−0.640733			−0.320366	+	0.947294i	$0.603806\pi$
$234$		0			0
$235$	5.06033	−	3.11965i	0.330099	−	0.203504i
$236$	6.07676	+	7.27250i	0.395564	+	0.473400i
$237$		0			0
$238$	−1.33179	−	3.67088i	−0.0863272	−	0.237948i
$239$	−17.5597			−1.13584			−0.567921	−	0.823083i	$-0.692252\pi$
$239$	−17.5597			−1.13584			−0.567921	+	0.823083i	$0.692252\pi$
$240$		0			0
$241$	11.7884			0.759356			0.379678	−	0.925119i	$-0.376035\pi$
$241$	11.7884			0.759356			0.379678	+	0.925119i	$0.376035\pi$
$242$	−7.29876	−	20.1179i	−0.469182	−	1.29323i
$243$		0			0
$244$	9.80765	+	11.7375i	0.627871	+	0.751418i
$245$	−7.97609	−	12.9378i	−0.509573	−	0.826569i
$246$		0			0
$247$	2.49978			0.159057
$248$	−0.593336	+	1.02036i	−0.0376768	+	0.0647931i
$249$		0			0
$250$	−6.65749	−	14.3415i	−0.421057	−	0.907034i
$251$			12.8261i			0.809578i	0.914410	+	0.404789i	$0.132655\pi$
$251$			12.8261i			0.809578i	−0.914410	+	0.404789i	$0.867345\pi$
$252$		0			0
$253$	−1.07878			−0.0678226
$254$	8.01042	+	22.0795i	0.502618	+	1.38539i
$255$		0			0
$256$	−14.9893	−	5.59654i	−0.936831	−	0.349784i
$257$	−7.70361			−0.480538			−0.240269	−	0.970706i	$-0.577236\pi$
$257$	−7.70361			−0.480538			−0.240269	+	0.970706i	$0.577236\pi$
$258$		0			0
$259$	−4.32387			−0.268672
$260$	−4.89431	−	1.63429i	−0.303532	−	0.101354i
$261$		0			0
$262$	−18.0039	+	6.53182i	−1.11229	+	0.403537i
$263$		−	0.422058i		−	0.0260252i	−0.999915	−	0.0130126i	$-0.995858\pi$
$263$		−	0.422058i		−	0.0260252i	0.999915	−	0.0130126i	$-0.00414215\pi$
$264$		0			0
$265$	−16.7797	+	10.3445i	−1.03077	+	0.635460i
$266$	0.470648	+	1.29727i	0.0288573	+	0.0795406i
$267$		0			0
$268$	8.32938	+	9.96837i	0.508798	+	0.608915i
$269$	1.49688			0.0912663			0.0456332	−	0.998958i	$-0.485469\pi$
$269$	1.49688			0.0912663			0.0456332	+	0.998958i	$0.485469\pi$
$270$		0			0
$271$		−	13.1516i		−	0.798904i	−0.916754	−	0.399452i	$-0.869200\pi$
$271$		−	13.1516i		−	0.798904i	0.916754	−	0.399452i	$-0.130800\pi$
$272$	−4.35822	+	24.1324i	−0.264256	+	1.46324i
$273$		0			0
$274$	4.28855	+	11.8207i	0.259081	+	0.714116i
$275$	−22.8361	−	11.4818i	−1.37707	−	0.692380i
$276$		0			0
$277$	28.3454			1.70311			0.851556	−	0.524263i	$-0.175659\pi$
$277$	28.3454			1.70311			0.851556	+	0.524263i	$0.175659\pi$
$278$	6.88324	+	18.9726i	0.412829	+	1.13790i
$279$		0			0
$280$	−0.0733613	−	2.84762i	−0.00438417	−	0.170178i
$281$			28.0322i			1.67226i	0.548529	+	0.836132i	$0.315188\pi$
$281$			28.0322i			1.67226i	−0.548529	+	0.836132i	$0.684812\pi$
$282$		0			0
$283$			4.04108i			0.240217i	0.992761	+	0.120109i	$0.0383243\pi$
$283$			4.04108i			0.240217i	−0.992761	+	0.120109i	$0.961676\pi$
$284$	−17.5621	+	14.6745i	−1.04212	+	0.870772i
$285$		0			0
$286$	−7.84129	+	2.84482i	−0.463665	+	0.168218i
$287$			4.37398i			0.258188i
$288$		0			0
$289$	20.5855			1.21091
$290$	−11.9515	+	15.0759i	−0.701816	+	0.885290i
$291$		0			0
$292$	−17.8130	−	21.3181i	−1.04243	−	1.24755i
$293$			9.69326i			0.566287i	0.959078	+	0.283143i	$0.0913772\pi$
$293$			9.69326i			0.566287i	−0.959078	+	0.283143i	$0.908623\pi$
$294$		0			0
$295$	9.01951	−	5.56046i	0.525136	−	0.323743i
$296$	23.4732	+	13.6495i	1.36435	+	0.793363i
$297$		0			0
$298$	4.32440	+	11.9195i	0.250506	+	0.690480i
$299$			0.243485i			0.0140811i
$300$		0			0
$301$		−	1.38016i		−	0.0795512i
$302$	−20.6806	+	7.50291i	−1.19003	+	0.431744i
$303$		0			0
$304$	1.54017	−	8.52828i	0.0883349	−	0.489130i
$305$	14.5571	−	8.97437i	0.833539	−	0.513871i
$306$		0			0
$307$		−	30.4121i		−	1.73571i	−0.496815	−	0.867856i	$-0.665497\pi$
$307$		−	30.4121i		−	1.73571i	0.496815	−	0.867856i	$-0.334503\pi$
$308$	−2.95265	−	3.53366i	−0.168243	−	0.201349i
$309$		0			0
$310$	1.03412	+	0.819803i	0.0587341	+	0.0465617i
$311$	−1.93254			−0.109584			−0.0547921	−	0.998498i	$-0.517450\pi$
$311$	−1.93254			−0.109584			−0.0547921	+	0.998498i	$0.517450\pi$
$312$		0			0
$313$			22.8246i			1.29012i	0.764130	+	0.645062i	$0.223168\pi$
$313$			22.8246i			1.29012i	−0.764130	+	0.645062i	$0.776832\pi$
$314$	6.38321	+	17.5943i	0.360225	+	0.992905i
$315$		0			0
$316$	17.6290	+	21.0979i	0.991709	+	1.18685i
$317$		−	3.60376i		−	0.202407i	−0.994866	−	0.101204i	$-0.967731\pi$
$317$		−	3.60376i		−	0.202407i	0.994866	−	0.101204i	$-0.0322694\pi$
$318$		0			0
$319$			31.1004i			1.74129i
$320$	−8.59106	+	15.6906i	−0.480255	+	0.877129i
$321$		0			0
$322$	−0.126358	+	0.0458424i	−0.00704163	+	0.00255470i
$323$	−13.2825			−0.739060
$324$		0			0
$325$	−2.59149	+	5.15418i	−0.143750	+	0.285903i
$326$	20.4278	−	7.41119i	1.13139	−	0.410468i
$327$		0			0
$328$	13.8077	−	23.7452i	0.762403	−	1.31111i
$329$		−	1.19740i		−	0.0660147i
$330$		0			0
$331$	−0.186551			−0.0102538			−0.00512689	−	0.999987i	$-0.501632\pi$
$331$	−0.186551			−0.0102538			−0.00512689	+	0.999987i	$0.501632\pi$
$332$	8.01314	−	6.69563i	0.439778	−	0.367470i
$333$		0			0
$334$	−23.8500	+	8.65276i	−1.30501	+	0.473458i
$335$	12.3630	−	7.62169i	0.675462	−	0.416417i
$336$		0			0
$337$		−	15.2379i		−	0.830063i	−0.909807	−	0.415032i	$-0.863770\pi$
$337$		−	15.2379i		−	0.830063i	0.909807	−	0.415032i	$-0.136230\pi$
$338$	−5.62801	−	15.5127i	−0.306123	−	0.843781i
$339$		0			0
$340$	26.0058	+	8.68376i	1.41036	+	0.470943i
$341$	2.13330			0.115525
$342$		0			0
$343$	−6.21419			−0.335535
$344$	−4.35687	+	7.49254i	−0.234907	+	0.403971i
$345$		0			0
$346$	22.9470	−	8.32517i	1.23364	−	0.447564i
$347$	−26.1263			−1.40253			−0.701266	−	0.712900i	$-0.747382\pi$
$347$	−26.1263			−1.40253			−0.701266	+	0.712900i	$0.747382\pi$
$348$		0			0
$349$		−	36.0891i		−	1.93180i	−0.258910	−	0.965901i	$-0.583363\pi$
$349$		−	36.0891i		−	1.93180i	0.258910	−	0.965901i	$-0.416637\pi$
$350$	−3.16270	−	0.374453i	−0.169053	−	0.0200154i
$351$		0			0
$352$	4.87421	+	28.5042i	0.259796	+	1.51928i
$353$	9.70998			0.516810			0.258405	−	0.966037i	$-0.416803\pi$
$353$	9.70998			0.516810			0.258405	+	0.966037i	$0.416803\pi$
$354$		0			0
$355$	13.4277	+	21.7808i	0.712670	+	1.15601i
$356$	1.79152	+	2.14404i	0.0949501	+	0.113634i
$357$		0			0
$358$	0.305746	−	0.110925i	0.0161592	−	0.00586255i
$359$	−33.8455			−1.78630			−0.893149	−	0.449761i	$-0.851509\pi$
$359$	−33.8455			−1.78630			−0.893149	+	0.449761i	$0.851509\pi$
$360$		0			0
$361$	−14.3060			−0.752949
$362$	−3.01686	+	1.09451i	−0.158563	+	0.0575264i
$363$		0			0
$364$	−0.797559	+	0.666425i	−0.0418034	+	0.0349301i
$365$	−26.4392	+	16.2996i	−1.38389	+	0.853160i
$366$		0			0
$367$	−2.14159			−0.111790			−0.0558949	−	0.998437i	$-0.517801\pi$
$367$	−2.14159			−0.111790			−0.0558949	+	0.998437i	$0.517801\pi$
$368$	0.830678	+	0.150017i	0.0433021	+	0.00782018i
$369$		0			0
$370$	18.8594	−	23.7897i	0.980451	−	1.23677i
$371$			3.97048i			0.206137i
$372$		0			0
$373$	−14.6799			−0.760097			−0.380049	−	0.924967i	$-0.624093\pi$
$373$	−14.6799			−0.760097			−0.380049	+	0.924967i	$0.624093\pi$
$374$	41.6646	−	15.1159i	2.15442	−	0.781624i
$375$		0			0
$376$	−3.77993	+	6.50037i	−0.194935	+	0.335231i
$377$	7.01946			0.361521
$378$		0			0
$379$	−4.44355			−0.228250			−0.114125	−	0.993466i	$-0.536406\pi$
$379$	−4.44355			−0.228250			−0.114125	+	0.993466i	$0.536406\pi$
$380$	−9.19032	−	3.06880i	−0.471454	−	0.157426i
$381$		0			0
$382$	8.28076	+	22.8246i	0.423680	+	1.16781i
$383$		−	15.1342i		−	0.773324i	−0.922222	−	0.386662i	$-0.873628\pi$
$383$		−	15.1342i		−	0.773324i	0.922222	−	0.386662i	$-0.126372\pi$
$384$		0			0
$385$	−4.38252	+	2.70179i	−0.223354	+	0.137696i
$386$	1.19661	−	0.434128i	0.0609056	−	0.0220965i
$387$		0			0
$388$	−5.65677	−	6.76986i	−0.287179	−	0.343688i
$389$	27.0036			1.36914			0.684570	−	0.728948i	$-0.259990\pi$
$389$	27.0036			1.36914			0.684570	+	0.728948i	$0.259990\pi$
$390$		0			0
$391$		−	1.29375i		−	0.0654280i
$392$	16.6196	+	9.66423i	0.839418	+	0.488117i
$393$		0			0
$394$	−2.14942	+	0.779808i	−0.108286	+	0.0392862i
$395$	26.1661	−	16.1312i	1.31656	−	0.811649i
$396$		0			0
$397$	−3.18855			−0.160029			−0.0800143	−	0.996794i	$-0.525497\pi$
$397$	−3.18855			−0.160029			−0.0800143	+	0.996794i	$0.525497\pi$
$398$	−18.6064	+	6.75039i	−0.932654	+	0.338366i
$399$		0			0
$400$	15.9874	+	12.0168i	0.799370	+	0.600839i
$401$		−	25.1792i		−	1.25739i	−0.777652	−	0.628695i	$-0.783589\pi$
$401$		−	25.1792i		−	1.25739i	0.777652	−	0.628695i	$-0.216411\pi$
$402$		0			0
$403$		−	0.481494i		−	0.0239849i
$404$	−19.2810	+	16.1108i	−0.959264	+	0.801542i
$405$		0			0
$406$	1.32160	+	3.64277i	0.0655897	+	0.180788i
$407$		−	49.0761i		−	2.43261i
$408$		0			0
$409$	−27.5416			−1.36185			−0.680923	−	0.732355i	$-0.738421\pi$
$409$	−27.5416			−1.36185			−0.680923	+	0.732355i	$0.738421\pi$
$410$	−24.0654	−	19.0779i	−1.18850	−	0.942191i
$411$		0			0
$412$	−9.13750	+	7.63512i	−0.450172	+	0.376155i
$413$		−	2.13424i		−	0.105019i
$414$		0			0
$415$	−6.12675	−	9.93808i	−0.300750	−	0.487841i
$416$	6.43350	−	1.10013i	0.315428	−	0.0539381i
$417$		0			0
$418$	−14.7240	+	5.34188i	−0.720177	+	0.261280i
$419$		−	27.5259i		−	1.34473i	−0.740221	−	0.672364i	$-0.765279\pi$
$419$		−	27.5259i		−	1.34473i	0.740221	−	0.672364i	$-0.234721\pi$
$420$		0			0
$421$			29.6555i			1.44532i	0.691203	+	0.722660i	$0.257081\pi$
$421$			29.6555i			1.44532i	−0.691203	+	0.722660i	$0.742919\pi$
$422$	12.0108	+	33.1058i	0.584675	+	1.61157i
$423$		0			0
$424$	12.5340	−	21.5547i	0.608703	−	1.04679i
$425$	13.7698	−	27.3867i	0.667935	−	1.32845i
$426$		0			0
$427$		−	3.44458i		−	0.166695i
$428$	13.7900	−	11.5227i	0.666567	−	0.556971i
$429$		0			0
$430$	7.59357	+	6.01983i	0.366195	+	0.290302i
$431$	−15.1134			−0.727986			−0.363993	−	0.931402i	$-0.618587\pi$
$431$	−15.1134			−0.727986			−0.363993	+	0.931402i	$0.618587\pi$
$432$		0			0
$433$			10.1697i			0.488726i	0.969684	+	0.244363i	$0.0785788\pi$
$433$			10.1697i			0.488726i	−0.969684	+	0.244363i	$0.921421\pi$
$434$	0.249873	−	0.0906537i	0.0119943	−	0.00435152i
$435$		0			0
$436$	−15.0662	−	18.0308i	−0.721540	−	0.863519i
$437$			0.457206i			0.0218711i
$438$		0			0
$439$		−	17.3055i		−	0.825947i	−0.910743	−	0.412974i	$-0.864490\pi$
$439$		−	17.3055i		−	0.825947i	0.910743	−	0.412974i	$-0.135510\pi$
$440$	32.3205	−	0.832653i	1.54082	−	0.0396952i
$441$		0			0
$442$	−3.41171	−	9.40384i	−0.162278	−	0.447295i
$443$	28.5925			1.35847			0.679235	−	0.733921i	$-0.262312\pi$
$443$	28.5925			1.35847			0.679235	+	0.733921i	$0.262312\pi$
$444$		0			0
$445$	2.65908	−	1.63930i	0.126053	−	0.0777104i
$446$	9.26057	+	25.5253i	0.438501	+	1.20866i
$447$		0			0
$448$	1.78219	+	3.13156i	0.0842005	+	0.147952i
$449$			3.59276i			0.169553i	0.996400	+	0.0847763i	$0.0270176\pi$
$449$			3.59276i			0.169553i	−0.996400	+	0.0847763i	$0.972982\pi$
$450$		0			0
$451$	−49.6448			−2.33768
$452$	−1.42129	+	1.18761i	−0.0668520	+	0.0558602i
$453$		0			0
$454$	13.7977	+	38.0313i	0.647560	+	1.78490i
$455$	0.609803	+	0.989149i	0.0285880	+	0.0463720i
$456$		0			0
$457$		−	11.2098i		−	0.524372i	−0.965017	−	0.262186i	$-0.915557\pi$
$457$		−	11.2098i		−	0.524372i	0.965017	−	0.262186i	$-0.0844434\pi$
$458$	4.78124	−	1.73463i	0.223413	−	0.0810540i
$459$		0			0
$460$	0.298909	−	0.895163i	0.0139367	−	0.0417372i
$461$	−29.8529			−1.39039			−0.695194	−	0.718823i	$-0.744681\pi$
$461$	−29.8529			−1.39039			−0.695194	+	0.718823i	$0.744681\pi$
$462$		0			0
$463$	−34.4700			−1.60196			−0.800978	−	0.598694i	$-0.795687\pi$
$463$	−34.4700			−1.60196			−0.800978	+	0.598694i	$0.795687\pi$
$464$	4.32485	−	23.9477i	0.200776	−	1.11174i
$465$		0			0
$466$	−4.71721	−	13.0023i	−0.218521	−	0.602318i
$467$	15.7950			0.730907			0.365453	−	0.930830i	$-0.380914\pi$
$467$	15.7950			0.730907			0.365453	+	0.930830i	$0.380914\pi$
$468$		0			0
$469$		−	2.92539i		−	0.135082i
$470$	6.58802	+	5.22267i	0.303883	+	0.240904i
$471$		0			0
$472$	−6.73734	+	11.5862i	−0.310111	+	0.533300i
$473$	15.6649			0.720272
$474$		0			0
$475$	−4.86619	+	9.67831i	−0.223276	+	0.444071i
$476$	4.23781	−	3.54104i	0.194240	−	0.162303i
$477$		0			0
$478$	−8.46929	−	23.3443i	−0.387376	−	1.06774i
$479$	−32.1810			−1.47039			−0.735194	−	0.677857i	$-0.762909\pi$
$479$	−32.1810			−1.47039			−0.735194	+	0.677857i	$0.762909\pi$
$480$		0			0
$481$	−11.0766			−0.505051
$482$	5.68571	+	15.6718i	0.258977	+	0.713830i
$483$		0			0
$484$	23.2249	−	19.4063i	1.05568	−	0.882105i
$485$	−8.39613	+	5.17615i	−0.381249	+	0.235037i
$486$		0			0
$487$	35.6312			1.61460			0.807302	−	0.590139i	$-0.200927\pi$
$487$	35.6312			1.61460			0.807302	+	0.590139i	$0.200927\pi$
$488$	−10.8738	+	18.6997i	−0.492234	+	0.846497i
$489$		0			0
$490$	13.3529	−	16.8437i	0.603223	−	0.760922i
$491$		−	20.1909i		−	0.911201i	−0.890184	−	0.455600i	$-0.849425\pi$
$491$		−	20.1909i		−	0.911201i	0.890184	−	0.455600i	$-0.150575\pi$
$492$		0			0
$493$	−37.2978			−1.67981
$494$	1.20568	+	3.32327i	0.0542461	+	0.149521i
$495$		0			0
$496$	−1.64267	−	0.296660i	−0.0737581	−	0.0133204i
$497$	5.15388			0.231183
$498$		0			0
$499$	15.9850			0.715588			0.357794	−	0.933801i	$-0.383529\pi$
$499$	15.9850			0.715588			0.357794	+	0.933801i	$0.383529\pi$
$500$	15.8549	−	15.7677i	0.709053	−	0.705155i
$501$		0			0
$502$	−17.0514	+	6.18623i	−0.761041	+	0.276105i
$503$		−	2.13750i		−	0.0953062i	−0.998864	−	0.0476531i	$-0.984826\pi$
$503$		−	2.13750i		−	0.0953062i	0.998864	−	0.0476531i	$-0.0151742\pi$
$504$		0			0
$505$	14.7420	+	23.9127i	0.656010	+	1.06410i
$506$	−0.520313	−	1.43416i	−0.0231308	−	0.0637563i
$507$		0			0
$508$	−25.4895	+	21.2985i	−1.13091	+	0.944968i
$509$	−9.67611			−0.428886			−0.214443	−	0.976736i	$-0.568794\pi$
$509$	−9.67611			−0.428886			−0.214443	+	0.976736i	$0.568794\pi$
$510$		0			0
$511$			6.25617i			0.276757i
$512$	0.210627	−	22.6264i	0.00930847	−	0.999957i
$513$		0			0
$514$	−3.71557	−	10.2414i	−0.163887	−	0.451728i
$515$	6.98642	+	11.3325i	0.307858	+	0.499371i
$516$		0			0
$517$	13.5905			0.597710
$518$	−2.08547	−	5.74826i	−0.0916301	−	0.252564i
$519$		0			0
$520$	−0.187933	−	7.29486i	−0.00824140	−	0.319901i
$521$		−	3.11652i		−	0.136537i	−0.997667	−	0.0682687i	$-0.978252\pi$
$521$		−	3.11652i		−	0.136537i	0.997667	−	0.0682687i	$-0.0217475\pi$
$522$		0			0
$523$			23.5599i			1.03020i	0.857129	+	0.515102i	$0.172246\pi$
$523$			23.5599i			1.03020i	−0.857129	+	0.515102i	$0.827754\pi$
$524$	−17.3671	−	20.7845i	−0.758687	−	0.907976i
$525$		0			0
$526$	0.561094	−	0.203565i	0.0244649	−	0.00887584i
$527$			2.55841i			0.111446i
$528$		0			0
$529$	22.9555			0.998064
$530$	−21.8454	−	17.3180i	−0.948902	−	0.752245i
$531$		0			0
$532$	−1.49762	+	1.25138i	−0.0649301	+	0.0542544i
$533$			11.2050i			0.485343i
$534$		0			0
$535$	−10.5437	−	17.1027i	−0.455844	−	0.739415i
$536$	−9.23482	+	15.8812i	−0.398884	+	0.685962i
$537$		0			0
$538$	0.721967	+	1.98999i	0.0311262	+	0.0857945i
$539$		−	34.7471i		−	1.49667i
$540$		0			0
$541$		−	21.4076i		−	0.920384i	−0.887819	−	0.460192i	$-0.847781\pi$
$541$		−	21.4076i		−	0.920384i	0.887819	−	0.460192i	$-0.152219\pi$
$542$	17.4841	−	6.34322i	0.751006	−	0.272465i
$543$		0			0
$544$	−34.1843	+	5.84550i	−1.46564	+	0.250624i
$545$	−22.3622	+	13.7861i	−0.957892	+	0.590533i
$546$		0			0
$547$			7.81382i			0.334095i	0.985949	+	0.167047i	$0.0534233\pi$
$547$			7.81382i			0.334095i	−0.985949	+	0.167047i	$0.946577\pi$
$548$	−13.6463	+	11.4026i	−0.582943	+	0.487096i
$549$		0			0
$550$	4.25006	−	35.8967i	0.181223	−	1.53064i
$551$	13.1808			0.561523
$552$		0			0
$553$		−	6.19154i		−	0.263291i
$554$	13.6714	+	37.6832i	0.580843	+	1.60100i
$555$		0			0
$556$	−21.9027	+	18.3015i	−0.928883	+	0.776157i
$557$		−	26.4914i		−	1.12248i	−0.827655	−	0.561238i	$-0.810325\pi$
$557$		−	26.4914i		−	1.12248i	0.827655	−	0.561238i	$-0.189675\pi$
$558$		0			0
$559$		−	3.53562i		−	0.149541i
$560$	3.75031	−	1.47098i	0.158479	−	0.0621600i
$561$		0			0
$562$	−37.2668	+	13.5204i	−1.57200	+	0.570322i
$563$	40.0138			1.68638			0.843191	−	0.537614i	$-0.180674\pi$
$563$	40.0138			1.68638			0.843191	+	0.537614i	$0.180674\pi$
$564$		0			0
$565$	1.08670	+	1.76272i	0.0457179	+	0.0741581i
$566$	−5.37231	+	1.94907i	−0.225815	+	0.0819256i
$567$		0			0
$568$	−27.9791	−	16.2697i	−1.17398	−	0.682662i
$569$		−	17.5658i		−	0.736397i	−0.929747	−	0.368198i	$-0.879975\pi$
$569$		−	17.5658i		−	0.736397i	0.929747	−	0.368198i	$-0.120025\pi$
$570$		0			0
$571$	31.8630			1.33342			0.666712	−	0.745315i	$-0.267701\pi$
$571$	31.8630			1.33342			0.666712	+	0.745315i	$0.267701\pi$
$572$	−7.56394	−	9.05232i	−0.316264	−	0.378497i
$573$		0			0
$574$	−5.81488	+	2.10963i	−0.242708	+	0.0880544i
$575$	−0.942694	−	0.473980i	−0.0393130	−	0.0197663i
$576$		0			0
$577$		−	13.2498i		−	0.551596i	−0.961216	−	0.275798i	$-0.911058\pi$
$577$		−	13.2498i		−	0.551596i	0.961216	−	0.275798i	$-0.0889421\pi$
$578$	9.92870	+	27.3669i	0.412980	+	1.13831i
$579$		0			0
$580$	−25.8067	−	8.61728i	−1.07157	−	0.357813i
$581$	−2.35159			−0.0975605
$582$		0			0
$583$	−45.0651			−1.86641
$584$	19.7494	−	33.9632i	0.817236	−	1.40541i
$585$		0			0
$586$	−12.8865	+	4.67520i	−0.532335	+	0.193131i
$587$	−21.1959			−0.874848			−0.437424	−	0.899255i	$-0.644109\pi$
$587$	−21.1959			−0.874848			−0.437424	+	0.899255i	$0.644109\pi$
$588$		0			0
$589$		−	0.904128i		−	0.0372540i
$590$	11.7425	+	9.30888i	0.483430	+	0.383240i
$591$		0			0
$592$	−6.82458	+	37.7892i	−0.280488	+	1.55313i
$593$	−24.0661			−0.988275			−0.494137	−	0.869384i	$-0.664516\pi$
$593$	−24.0661			−0.988275			−0.494137	+	0.869384i	$0.664516\pi$
$594$		0			0
$595$	−3.24018	−	5.25583i	−0.132834	−	0.215468i
$596$	−13.7604	+	11.4979i	−0.563649	+	0.470974i
$597$		0			0
$598$	−0.323696	+	0.117437i	−0.0132369	+	0.00480234i
$599$	−37.1635			−1.51846			−0.759231	−	0.650822i	$-0.774425\pi$
$599$	−37.1635			−1.51846			−0.759231	+	0.650822i	$0.774425\pi$
$600$		0			0
$601$	23.4082			0.954841			0.477421	−	0.878675i	$-0.341572\pi$
$601$	23.4082			0.954841			0.477421	+	0.878675i	$0.341572\pi$
$602$	1.83482	−	0.665672i	0.0747817	−	0.0271308i
$603$		0			0
$604$	−19.9491	−	23.8745i	−0.811718	−	0.971442i
$605$	−17.7575	−	28.8041i	−0.721945	−	1.17105i
$606$		0			0
$607$	11.7302			0.476114			0.238057	−	0.971251i	$-0.423490\pi$
$607$	11.7302			0.476114			0.238057	+	0.971251i	$0.423490\pi$
$608$	12.0806	−	2.06577i	0.489931	−	0.0837780i
$609$		0			0
$610$	18.9519	+	15.0242i	0.767339	+	0.608311i
$611$		−	3.06743i		−	0.124095i
$612$		0			0
$613$	−10.9631			−0.442797			−0.221399	−	0.975183i	$-0.571062\pi$
$613$	−10.9631			−0.442797			−0.221399	+	0.975183i	$0.571062\pi$
$614$	40.4307	−	14.6682i	1.63165	−	0.591961i
$615$		0			0
$616$	3.27362	−	5.62967i	0.131898	−	0.226826i
$617$	−13.0317			−0.524635			−0.262318	−	0.964982i	$-0.584487\pi$
$617$	−13.0317			−0.524635			−0.262318	+	0.964982i	$0.584487\pi$
$618$		0			0
$619$	−36.3769			−1.46211			−0.731056	−	0.682317i	$-0.760972\pi$
$619$	−36.3769			−1.46211			−0.731056	+	0.682317i	$0.760972\pi$
$620$	−0.591095	+	1.77019i	−0.0237389	+	0.0710926i
$621$		0			0
$622$	−0.932092	−	2.56917i	−0.0373735	−	0.103014i
$623$		−	0.629204i		−	0.0252085i
$624$		0			0
$625$	−14.9106	−	20.0668i	−0.596423	−	0.802671i
$626$	−30.3436	+	11.0087i	−1.21278	+	0.439994i
$627$		0			0
$628$	−20.3116	+	16.9720i	−0.810522	+	0.677256i
$629$	58.8555			2.34672
$630$		0			0
$631$		−	42.0264i		−	1.67304i	−0.547933	−	0.836522i	$-0.684585\pi$
$631$		−	42.0264i		−	1.67304i	0.547933	−	0.836522i	$-0.315415\pi$
$632$	−19.5454	+	33.6123i	−0.777473	+	1.33703i
$633$		0			0
$634$	4.79093	−	1.73815i	0.190272	−	0.0690306i
$635$	19.4889	+	31.6126i	0.773394	+	1.25451i
$636$		0			0
$637$	−7.84255			−0.310733
$638$	−41.3456	+	15.0002i	−1.63689	+	0.593862i
$639$		0			0
$640$	−25.0030	−	3.85338i	−0.988332	−	0.152318i
$641$		−	39.2028i		−	1.54842i	−0.632931	−	0.774208i	$-0.718148\pi$
$641$		−	39.2028i		−	1.54842i	0.632931	−	0.774208i	$-0.281852\pi$
$642$		0			0
$643$			40.0866i			1.58086i	0.612552	+	0.790431i	$0.290143\pi$
$643$			40.0866i			1.58086i	−0.612552	+	0.790431i	$0.709857\pi$
$644$	−0.121888	−	0.145872i	−0.00480307	−	0.00574818i
$645$		0			0
$646$	−6.40636	−	17.6581i	−0.252055	−	0.694750i
$647$			10.2214i			0.401844i	0.979607	+	0.200922i	$0.0643938\pi$
$647$			10.2214i			0.401844i	−0.979607	+	0.200922i	$0.935606\pi$
$648$		0			0
$649$	24.2237			0.950863
$650$	−8.10202	−	0.959253i	−0.317787	−	0.0376250i
$651$		0			0
$652$	19.7052	+	23.5827i	0.771717	+	0.923570i
$653$		−	33.7435i		−	1.32049i	−0.751052	−	0.660243i	$-0.770453\pi$
$653$		−	33.7435i		−	1.32049i	0.751052	−	0.660243i	$-0.229547\pi$
$654$		0			0
$655$	−25.7774	+	15.8916i	−1.00721	+	0.620935i
$656$	38.2271	+	6.90367i	1.49252	+	0.269543i
$657$		0			0
$658$	1.59185	−	0.577522i	0.0620568	−	0.0225142i
$659$		−	7.62965i		−	0.297209i	−0.988897	−	0.148604i	$-0.952522\pi$
$659$		−	7.62965i		−	0.297209i	0.988897	−	0.148604i	$-0.0474781\pi$
$660$		0			0
$661$		−	27.2772i		−	1.06096i	−0.847698	−	0.530480i	$-0.822012\pi$
$661$		−	27.2772i		−	1.06096i	0.847698	−	0.530480i	$-0.177988\pi$
$662$	−0.0899764	−	0.248006i	−0.00349703	−	0.00963902i
$663$		0			0
$664$	12.7662	+	7.42348i	0.495425	+	0.288087i
$665$	1.14506	+	1.85738i	0.0444036	+	0.0720262i
$666$		0			0
$667$			1.28385i			0.0497109i
$668$	−23.0064	−	27.5334i	−0.890144	−	1.06530i
$669$		0			0
$670$	16.0953	+	12.7596i	0.621816	+	0.492947i
$671$	39.0961			1.50929
$672$		0			0
$673$		−	3.17561i		−	0.122411i	−0.998125	−	0.0612055i	$-0.980506\pi$
$673$		−	3.17561i		−	0.122411i	0.998125	−	0.0612055i	$-0.0194945\pi$
$674$	20.2577	−	7.34948i	0.780298	−	0.283092i
$675$		0			0
$676$	17.9085	−	14.9640i	0.688790	−	0.575540i
$677$			32.1530i			1.23574i	0.786280	+	0.617870i	$0.212004\pi$
$677$			32.1530i			1.23574i	−0.786280	+	0.617870i	$0.787996\pi$
$678$		0			0
$679$			1.98673i			0.0762437i
$680$	0.998577	+	38.7611i	0.0382937	+	1.48642i
$681$		0			0
$682$	1.02892	+	2.83607i	0.0393995	+	0.108599i
$683$	−25.5185			−0.976437			−0.488219	−	0.872721i	$-0.662353\pi$
$683$	−25.5185			−0.976437			−0.488219	+	0.872721i	$0.662353\pi$
$684$		0			0
$685$	10.4338	+	16.9245i	0.398656	+	0.646651i
$686$	−2.99720	−	8.26130i	−0.114433	−	0.315418i
$687$		0			0
$688$	−12.0622	−	2.17838i	−0.459866	−	0.0830498i
$689$			10.1714i			0.387498i
$690$		0			0
$691$	32.6320			1.24138			0.620691	−	0.784056i	$-0.286852\pi$
$691$	32.6320			1.24138			0.620691	+	0.784056i	$0.286852\pi$
$692$	22.1354	+	26.4910i	0.841462	+	1.00704i
$693$		0			0
$694$	−12.6011	−	34.7330i	−0.478331	−	1.31844i
$695$	16.7466	+	27.1643i	0.635234	+	1.03040i
$696$		0			0
$697$		−	59.5376i		−	2.25515i
$698$	47.9777	−	17.4063i	1.81598	−	0.658838i
$699$		0			0
$700$	−1.02761	−	4.38517i	−0.0388399	−	0.165744i
$701$	−35.0817			−1.32502			−0.662509	−	0.749054i	$-0.730508\pi$
$701$	−35.0817			−1.32502			−0.662509	+	0.749054i	$0.730508\pi$
$702$		0			0
$703$	−20.7992			−0.784458
$704$	−35.5433	+	20.2279i	−1.33959	+	0.762368i
$705$		0			0
$706$	4.68326	+	12.9087i	0.176257	+	0.485825i
$707$	5.65832			0.212803
$708$		0			0
$709$			17.6779i			0.663907i	0.943296	+	0.331954i	$0.107708\pi$
$709$			17.6779i			0.663907i	−0.943296	+	0.331954i	$0.892292\pi$
$710$	−22.4796	+	28.3564i	−0.843645	+	1.06420i
$711$		0			0
$712$	−1.98626	+	3.41579i	−0.0744383	+	0.128012i
$713$	0.0880646			0.00329805
$714$		0			0
$715$	−11.2269	+	6.92129i	−0.419862	+	0.258842i
$716$	0.294932	+	0.352967i	0.0110221	+	0.0131910i
$717$		0			0
$718$	−16.3242	−	44.9951i	−0.609213	−	1.67920i
$719$	−21.9011			−0.816773			−0.408386	−	0.912809i	$-0.633908\pi$
$719$	−21.9011			−0.816773			−0.408386	+	0.912809i	$0.633908\pi$
$720$		0			0
$721$	2.68155			0.0998662
$722$	−6.90001	−	19.0188i	−0.256792	−	0.707806i
$723$		0			0
$724$	−2.91015	−	3.48279i	−0.108155	−	0.129437i
$725$	−13.6644	+	27.1770i	−0.507484	+	1.00933i
$726$		0			0
$727$	34.2800			1.27138			0.635688	−	0.771946i	$-0.280717\pi$
$727$	34.2800			1.27138			0.635688	+	0.771946i	$0.280717\pi$
$728$	−1.27064	−	0.738868i	−0.0470929	−	0.0273843i
$729$		0			0
$730$	−34.4211	−	27.2875i	−1.27398	−	1.00995i
$731$			18.7864i			0.694842i
$732$		0			0
$733$	16.8179			0.621182			0.310591	−	0.950544i	$-0.399473\pi$
$733$	16.8179			0.621182			0.310591	+	0.950544i	$0.399473\pi$
$734$	−1.03292	−	2.84708i	−0.0381257	−	0.105088i
$735$		0			0
$736$	0.201212	+	1.17668i	0.00741676	+	0.0433730i
$737$	33.2032			1.22306
$738$		0			0
$739$	−25.4981			−0.937964			−0.468982	−	0.883208i	$-0.655379\pi$
$739$	−25.4981			−0.937964			−0.468982	+	0.883208i	$0.655379\pi$
$740$	40.7228	+	13.5980i	1.49700	+	0.499872i
$741$		0			0
$742$	−5.27846	+	1.91502i	−0.193778	+	0.0703026i
$743$		−	2.19747i		−	0.0806172i	−0.999187	−	0.0403086i	$-0.987166\pi$
$743$		−	2.19747i		−	0.0806172i	0.999187	−	0.0403086i	$-0.0128341\pi$
$744$		0			0
$745$	10.5210	+	17.0660i	0.385461	+	0.625249i
$746$	−7.08034	−	19.5159i	−0.259230	−	0.714526i
$747$		0			0
$748$	40.1909	+	48.0993i	1.46952	+	1.75869i
$749$	−4.04692			−0.147871
$750$		0			0
$751$			34.8488i			1.27165i	0.771832	+	0.635826i	$0.219340\pi$
$751$			34.8488i			1.27165i	−0.771832	+	0.635826i	$0.780660\pi$
$752$	−10.4649	−	1.88991i	−0.381614	−	0.0689180i
$753$		0			0
$754$	3.38559	+	9.33185i	0.123296	+	0.339846i
$755$	−29.6097	+	18.2542i	−1.07761	+	0.664338i
$756$		0			0
$757$	21.5026			0.781527			0.390763	−	0.920491i	$-0.372211\pi$
$757$	21.5026			0.781527			0.390763	+	0.920491i	$0.372211\pi$
$758$	−2.14319	−	5.90737i	−0.0778441	−	0.214565i
$759$		0			0
$760$	−0.352892	−	13.6980i	−0.0128007	−	0.496878i
$761$			6.95386i			0.252077i	0.992025	+	0.126039i	$0.0402263\pi$
$761$			6.95386i			0.252077i	−0.992025	+	0.126039i	$0.959774\pi$
$762$		0			0
$763$			5.29145i			0.191563i
$764$	−26.3497	+	22.0173i	−0.953299	+	0.796558i
$765$		0			0
$766$	20.1198	−	7.29947i	0.726960	−	0.263741i
$767$		−	5.46737i		−	0.197415i
$768$		0			0
$769$	−15.1190			−0.545205			−0.272602	−	0.962127i	$-0.587884\pi$
$769$	−15.1190			−0.545205			−0.272602	+	0.962127i	$0.587884\pi$
$770$	−5.70558	−	4.52312i	−0.205615	−	0.163002i
$771$		0			0
$772$	1.15428	+	1.38141i	0.0415435	+	0.0497181i
$773$			13.0796i			0.470439i	0.971942	+	0.235220i	$0.0755810\pi$
$773$			13.0796i			0.470439i	−0.971942	+	0.235220i	$0.924419\pi$
$774$		0			0
$775$	1.86418	+	0.937299i	0.0669634	+	0.0336688i
$776$	6.27169	−	10.7855i	0.225140	−	0.387175i
$777$		0			0
$778$	13.0243	+	35.8993i	0.466942	+	1.28705i
$779$			21.0403i			0.753846i
$780$		0			0
$781$			58.4968i			2.09318i
$782$	1.71995	−	0.623997i	0.0615053	−	0.0223141i
$783$		0			0
$784$	−4.83198	+	26.7558i	−0.172571	+	0.955563i
$785$	15.5300	+	25.1909i	0.554290	+	0.899102i
$786$		0			0
$787$			25.0403i			0.892591i	0.894886	+	0.446296i	$0.147257\pi$
$787$			25.0403i			0.892591i	−0.894886	+	0.446296i	$0.852743\pi$
$788$	−2.07339	−	2.48138i	−0.0738616	−	0.0883956i
$789$		0			0
$790$	34.0655	+	27.0055i	1.21200	+	0.960814i
$791$	0.417102			0.0148305
$792$		0			0
$793$		−	8.82412i		−	0.313354i
$794$	−1.53788	−	4.23894i	−0.0545775	−	0.150434i
$795$		0			0
$796$	−17.9483	−	21.4800i	−0.636160	−	0.761339i
$797$		−	29.0728i		−	1.02981i	−0.857247	−	0.514905i	$-0.827827\pi$
$797$		−	29.0728i		−	1.02981i	0.857247	−	0.514905i	$-0.172173\pi$
$798$		0			0
$799$			16.2987i			0.576607i
$800$	−8.26444	+	27.0499i	−0.292192	+	0.956360i
$801$		0			0
$802$	33.4739	−	12.1443i	1.18200	−	0.428831i
$803$	−71.0078			−2.50581
$804$		0			0
$805$	−0.180914	+	0.111532i	−0.00637639	+	0.00393100i
$806$	0.640110	−	0.232232i	0.0225469	−	0.00818001i
$807$		0			0
$808$	−30.7176	−	17.8621i	−1.08064	−	0.628387i
$809$			17.8537i			0.627702i	0.949472	+	0.313851i	$0.101619\pi$
$809$			17.8537i			0.627702i	−0.949472	+	0.313851i	$0.898381\pi$
$810$		0			0
$811$	−47.8173			−1.67909			−0.839546	−	0.543289i	$-0.817179\pi$
$811$	−47.8173			−1.67909			−0.839546	+	0.543289i	$0.817179\pi$
$812$	−4.20537	+	3.51393i	−0.147580	+	0.123315i
$813$		0			0
$814$	65.2430	−	23.6701i	2.28677	−	0.829637i
$815$	29.2478	−	18.0310i	1.02450	−	0.631600i
$816$		0			0
$817$		−	6.63903i		−	0.232270i
$818$	−13.2837	−	36.6146i	−0.464455	−	1.28020i
$819$		0			0
$820$	13.7556	−	41.1947i	0.480365	−	1.43858i
$821$	−0.00469899			−0.000163996			−8.19979e−5	−	1.00000i	$-0.500026\pi$
$821$	−0.00469899			−0.000163996			−8.19979e−5		1.00000i	$0.500026\pi$
$822$		0			0
$823$	15.1981			0.529773			0.264887	−	0.964280i	$-0.414665\pi$
$823$	15.1981			0.529773			0.264887	+	0.964280i	$0.414665\pi$
$824$	−14.5575	−	8.46509i	−0.507133	−	0.294895i
$825$		0			0
$826$	2.83731	−	1.02937i	0.0987227	−	0.0358165i
$827$	−3.42753			−0.119187			−0.0595934	−	0.998223i	$-0.518980\pi$
$827$	−3.42753			−0.119187			−0.0595934	+	0.998223i	$0.518980\pi$
$828$		0			0
$829$			16.1960i			0.562511i	0.959633	+	0.281256i	$0.0907509\pi$
$829$			16.1960i			0.562511i	−0.959633	+	0.281256i	$0.909249\pi$
$830$	10.2569	−	12.9383i	0.356023	−	0.449096i
$831$		0			0
$832$	4.56551	+	8.02226i	0.158281	+	0.278122i
$833$	41.6713			1.44382
$834$		0			0
$835$	−34.1475	+	21.0517i	−1.18172	+	0.728525i
$836$	−14.2033	−	16.9981i	−0.491230	−	0.587890i
$837$		0			0
$838$	36.5936	−	13.2761i	1.26411	−	0.458617i
$839$	12.9846			0.448279			0.224139	−	0.974557i	$-0.428043\pi$
$839$	12.9846			0.448279			0.224139	+	0.974557i	$0.428043\pi$
$840$		0			0
$841$	8.01224			0.276284
$842$	−39.4248	+	14.3033i	−1.35867	+	0.492924i
$843$		0			0
$844$	−38.2187	+	31.9348i	−1.31554	+	1.09924i
$845$	−13.6926	−	22.2106i	−0.471041	−	0.764067i
$846$		0			0
$847$	−6.81575			−0.234192
$848$	34.7007	+	6.26681i	1.19163	+	0.215203i
$849$		0			0
$850$	43.0499	+	5.09697i	1.47660	+	0.174825i
$851$		−	2.02590i		−	0.0694471i
$852$		0			0
$853$	15.9478			0.546044			0.273022	−	0.962008i	$-0.411977\pi$
$853$	15.9478			0.546044			0.273022	+	0.962008i	$0.411977\pi$
$854$	4.57931	−	1.66137i	0.156701	−	0.0568509i
$855$		0			0
$856$	21.9697	+	12.7753i	0.750909	+	0.436650i
$857$	−36.3078			−1.24025			−0.620126	−	0.784502i	$-0.712919\pi$
$857$	−36.3078			−1.24025			−0.620126	+	0.784502i	$0.712919\pi$
$858$		0			0
$859$	16.7215			0.570530			0.285265	−	0.958449i	$-0.407918\pi$
$859$	16.7215			0.570530			0.285265	+	0.958449i	$0.407918\pi$
$860$	−4.34042	+	12.9985i	−0.148007	+	0.443247i
$861$		0			0
$862$	−7.28941	−	20.0921i	−0.248278	−	0.684340i
$863$			32.0732i			1.09178i	0.837856	+	0.545892i	$0.183809\pi$
$863$			32.0732i			1.09178i	−0.837856	+	0.545892i	$0.816191\pi$
$864$		0			0
$865$	32.8548	−	20.2547i	1.11710	−	0.688681i
$866$	−13.5199	+	4.90501i	−0.459424	+	0.166679i
$867$		0			0
$868$	0.241035	+	0.288464i	0.00818125	+	0.00979110i
$869$	70.2742			2.38389
$870$		0			0
$871$		−	7.49409i		−	0.253928i
$872$	16.7040	−	28.7259i	0.565668	−	0.972782i
$873$		0			0
$874$	−0.607822	+	0.220517i	−0.0205599	+	0.00745911i
$875$	−5.01673	+	0.435430i	−0.169596	+	0.0147202i
$876$		0			0
$877$	24.1662			0.816035			0.408018	−	0.912974i	$-0.366220\pi$
$877$	24.1662			0.816035			0.408018	+	0.912974i	$0.366220\pi$
$878$	23.0064	−	8.34671i	0.776428	−	0.281688i
$879$		0			0
$880$	16.6956	+	42.5662i	0.562809	+	1.43490i
$881$			16.3886i			0.552146i	0.961137	+	0.276073i	$0.0890332\pi$
$881$			16.3886i			0.552146i	−0.961137	+	0.276073i	$0.910967\pi$
$882$		0			0
$883$		−	17.3417i		−	0.583595i	−0.956480	−	0.291798i	$-0.905747\pi$
$883$		−	17.3417i		−	0.583595i	0.956480	−	0.291798i	$-0.0942534\pi$
$884$	10.8562	−	9.07122i	0.365133	−	0.305098i
$885$		0			0
$886$	13.7906	+	38.0116i	0.463304	+	1.27702i
$887$			47.8185i			1.60559i	0.596256	+	0.802794i	$0.296654\pi$
$887$			47.8185i			1.60559i	−0.596256	+	0.802794i	$0.703346\pi$
$888$		0			0
$889$	7.48031			0.250882
$890$	3.46185	+	2.74439i	0.116041	+	0.0919921i
$891$		0			0
$892$	−29.4675	+	24.6225i	−0.986645	+	0.824421i
$893$		−	5.75988i		−	0.192747i
$894$		0			0
$895$	0.437757	−	0.269874i	0.0146326	−	0.00902089i
$896$	−3.30360	+	3.87968i	−0.110366	+	0.129611i
$897$		0			0
$898$	−4.77630	+	1.73284i	−0.159387	+	0.0578256i
$899$		−	2.53882i		−	0.0846745i
$900$		0			0
$901$		−	54.0453i		−	1.80051i
$902$	−23.9444	−	65.9991i	−0.797262	−	2.19753i
$903$		0			0
$904$	−2.26434	−	1.31670i	−0.0753109	−	0.0437929i
$905$	−4.31943	+	2.66290i	−0.143583	+	0.0885177i
$906$		0			0
$907$			8.22699i			0.273173i	0.990628	+	0.136586i	$0.0436131\pi$
$907$			8.22699i			0.273173i	−0.990628	+	0.136586i	$0.956387\pi$
$908$	−43.9050	+	36.6861i	−1.45704	+	1.21747i
$909$		0			0
$910$	−1.02088	+	1.28777i	−0.0338420	+	0.0426891i
$911$	−22.9871			−0.761597			−0.380798	−	0.924658i	$-0.624351\pi$
$911$	−22.9871			−0.761597			−0.380798	+	0.924658i	$0.624351\pi$
$912$		0			0
$913$		−	26.6907i		−	0.883332i
$914$	14.9026	−	5.40665i	0.492934	−	0.178836i
$915$		0			0
$916$	4.61213	+	5.51967i	0.152389	+	0.182375i
$917$			6.09957i			0.201425i
$918$		0			0
$919$		−	34.6477i		−	1.14292i	−0.820629	−	0.571461i	$-0.806377\pi$
$919$		−	34.6477i		−	1.14292i	0.820629	−	0.571461i	$-0.193623\pi$
$920$	1.33422	−	0.0343727i	0.0439879	−	0.00113323i
$921$		0			0
$922$	−14.3985	−	39.6872i	−0.474189	−	1.30703i
$923$	13.2029			0.434579
$924$		0			0
$925$	21.5623	−	42.8851i	0.708965	−	1.41005i
$926$	−16.6254	−	45.8253i	−0.546344	−	1.50591i
$927$		0			0
$928$	33.9226	−	5.80075i	1.11356	−	0.190419i
$929$			37.7103i			1.23723i	0.785692	+	0.618617i	$0.212307\pi$
$929$			37.7103i			1.23723i	−0.785692	+	0.618617i	$0.787693\pi$
$930$		0			0
$931$	−14.7264			−0.482639
$932$	15.0104	−	12.5424i	0.491681	−	0.410839i
$933$		0			0
$934$	7.61818	+	20.9983i	0.249274	+	0.687086i
$935$	59.6539	−	36.7762i	1.95089	−	1.20271i
$936$		0			0
$937$		−	27.9404i		−	0.912773i	−0.889782	−	0.456386i	$-0.849143\pi$
$937$		−	27.9404i		−	0.912773i	0.889782	−	0.456386i	$-0.150857\pi$
$938$	3.88908	−	1.41096i	0.126983	−	0.0460694i
$939$		0			0
$940$	−3.76565	+	11.2773i	−0.122822	+	0.367823i
$941$	−30.4349			−0.992148			−0.496074	−	0.868280i	$-0.665226\pi$
$941$	−30.4349			−0.992148			−0.496074	+	0.868280i	$0.665226\pi$
$942$		0			0
$943$	−2.04938			−0.0667370
$944$	−18.6526	−	3.36858i	−0.607089	−	0.109638i
$945$		0			0
$946$	7.55540	+	20.8253i	0.245647	+	0.677089i
$947$	35.3004			1.14711			0.573554	−	0.819167i	$-0.305564\pi$
$947$	35.3004			1.14711			0.573554	+	0.819167i	$0.305564\pi$
$948$		0			0
$949$			16.0267i			0.520249i
$950$	−15.2136	−	1.80124i	−0.493595	−	0.0584401i
$951$		0			0
$952$	6.75150	+	3.92596i	0.218817	+	0.127241i
$953$	−12.1033			−0.392064			−0.196032	−	0.980598i	$-0.562806\pi$
$953$	−12.1033			−0.392064			−0.196032	+	0.980598i	$0.562806\pi$
$954$		0			0
$955$	20.1467	+	32.6795i	0.651930	+	1.05748i
$956$	26.9496	−	22.5186i	0.871613	−	0.728303i
$957$		0			0
$958$	−15.5214	−	42.7823i	−0.501473	−	1.38223i
$959$	4.00475			0.129320
$960$		0			0
$961$	30.8259			0.994382
$962$	−5.34243	−	14.7256i	−0.172247	−	0.474771i
$963$		0			0
$964$	−18.0922	+	15.1175i	−0.582709	+	0.486900i
$965$	1.71326	−	1.05621i	0.0551517	−	0.0340006i
$966$		0			0
$967$	−30.6826			−0.986687			−0.493344	−	0.869834i	$-0.664226\pi$
$967$	−30.6826			−0.986687			−0.493344	+	0.869834i	$0.664226\pi$
$968$	37.0010	+	21.5159i	1.18926	+	0.691547i
$969$		0			0
$970$	−10.9309	−	8.66550i	−0.350970	−	0.278232i
$971$			4.77033i			0.153087i	0.997066	+	0.0765436i	$0.0243884\pi$
$971$			4.77033i			0.153087i	−0.997066	+	0.0765436i	$0.975612\pi$
$972$		0			0
$973$	6.42773			0.206064
$974$	17.1855	+	47.3690i	0.550658	+	1.51780i
$975$		0			0
$976$	−30.1045	−	5.43675i	−0.963621	−	0.174026i
$977$	28.1550			0.900760			0.450380	−	0.892837i	$-0.351289\pi$
$977$	28.1550			0.900760			0.450380	+	0.892837i	$0.351289\pi$
$978$		0			0
$979$	7.14149			0.228243
$980$	28.8328	+	9.62773i	0.921030	+	0.307547i
$981$		0			0
$982$	26.8422	−	9.73835i	0.856570	−	0.310763i
$983$			24.2134i			0.772288i	0.922439	+	0.386144i	$0.126193\pi$
$983$			24.2134i			0.772288i	−0.922439	+	0.386144i	$0.873807\pi$
$984$		0			0
$985$	−3.07746	+	1.89723i	−0.0980561	+	0.0604509i
$986$	−17.9893	−	49.5846i	−0.572895	−	1.57910i
$987$		0			0
$988$	−3.83652	+	3.20572i	−0.122056	+	0.101988i
$989$	0.646660			0.0205626
$990$		0			0
$991$		−	18.6181i		−	0.591424i	−0.955277	−	0.295712i	$-0.904443\pi$
$991$		−	18.6181i		−	0.591424i	0.955277	−	0.295712i	$-0.0955569\pi$
$992$	−0.397897	−	2.32689i	−0.0126333	−	0.0738789i
$993$		0			0
$994$	2.48579	+	6.85170i	0.0788446	+	0.217323i
$995$	−26.6400	+	16.4233i	−0.844544	+	0.520655i
$996$		0			0
$997$	−13.7405			−0.435167			−0.217584	−	0.976042i	$-0.569817\pi$
$997$	−13.7405			−0.435167			−0.217584	+	0.976042i	$0.569817\pi$
$998$	7.70981	+	21.2509i	0.244050	+	0.672685i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.m.c.539.32	yes	48
3.2	odd	2	inner	1080.2.m.c.539.17	✓	48
4.3	odd	2		4320.2.m.c.2159.35		48
5.4	even	2	inner	1080.2.m.c.539.18	yes	48
8.3	odd	2	inner	1080.2.m.c.539.29	yes	48
8.5	even	2		4320.2.m.c.2159.14		48
12.11	even	2		4320.2.m.c.2159.13		48
15.14	odd	2	inner	1080.2.m.c.539.31	yes	48
20.19	odd	2		4320.2.m.c.2159.34		48
24.5	odd	2		4320.2.m.c.2159.36		48
24.11	even	2	inner	1080.2.m.c.539.20	yes	48
40.19	odd	2	inner	1080.2.m.c.539.19	yes	48
40.29	even	2		4320.2.m.c.2159.15		48
60.59	even	2		4320.2.m.c.2159.16		48
120.29	odd	2		4320.2.m.c.2159.33		48
120.59	even	2	inner	1080.2.m.c.539.30	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.m.c.539.17	✓	48	3.2	odd	2	inner
1080.2.m.c.539.18	yes	48	5.4	even	2	inner
1080.2.m.c.539.19	yes	48	40.19	odd	2	inner
1080.2.m.c.539.20	yes	48	24.11	even	2	inner
1080.2.m.c.539.29	yes	48	8.3	odd	2	inner
1080.2.m.c.539.30	yes	48	120.59	even	2	inner
1080.2.m.c.539.31	yes	48	15.14	odd	2	inner
1080.2.m.c.539.32	yes	48	1.1	even	1	trivial
4320.2.m.c.2159.13		48	12.11	even	2
4320.2.m.c.2159.14		48	8.5	even	2
4320.2.m.c.2159.15		48	40.29	even	2
4320.2.m.c.2159.16		48	60.59	even	2
4320.2.m.c.2159.33		48	120.29	odd	2
4320.2.m.c.2159.34		48	20.19	odd	2
4320.2.m.c.2159.35		48	4.3	odd	2
4320.2.m.c.2159.36		48	24.5	odd	2

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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.482315 + 1.32943i) q^{2} +(-1.53474 + 1.28240i) q^{4} +(1.17345 + 1.90342i) q^{5} +0.450397 q^{7} +(-2.44509 - 1.42181i) q^{8} +(-1.96449 + 2.47806i) q^{10} +5.11202i q^{11} +1.15380 q^{13} +(0.217233 + 0.598769i) q^{14} +(0.710884 - 3.93632i) q^{16} -6.13070 q^{17} +2.16656 q^{19} +(-4.24190 - 1.41644i) q^{20} +(-6.79605 + 2.46560i) q^{22} +0.211029i q^{23} +(-2.24604 + 4.46713i) q^{25} +(0.556495 + 1.53389i) q^{26} +(-0.691244 + 0.577590i) q^{28} +6.08377 q^{29} -0.417311i q^{31} +(5.57592 - 0.953480i) q^{32} +(-2.95693 - 8.15031i) q^{34} +(0.528517 + 0.857296i) q^{35} -9.60013 q^{37} +(1.04496 + 2.88028i) q^{38} +(-0.162881 - 6.32246i) q^{40} +9.71138i q^{41} -3.06432i q^{43} +(-6.55567 - 7.84565i) q^{44} +(-0.280547 + 0.101782i) q^{46} -2.65854i q^{47} -6.79714 q^{49} +(-7.02202 - 0.831385i) q^{50} +(-1.77079 + 1.47964i) q^{52} +8.81551i q^{53} +(-9.73034 + 5.99869i) q^{55} +(-1.10126 - 0.640377i) q^{56} +(2.93429 + 8.08792i) q^{58} -4.73857i q^{59} -7.64787i q^{61} +(0.554784 - 0.201275i) q^{62} +(3.95693 + 6.95289i) q^{64} +(1.35392 + 2.19617i) q^{65} -6.49513i q^{67} +(9.40907 - 7.86203i) q^{68} +(-0.884800 + 1.11611i) q^{70} +11.4430 q^{71} +13.8904i q^{73} +(-4.63028 - 12.7627i) q^{74} +(-3.32511 + 2.77840i) q^{76} +2.30244i q^{77} -13.7469i q^{79} +(8.32668 - 3.26595i) q^{80} +(-12.9106 + 4.68394i) q^{82} -5.22116 q^{83} +(-7.19405 - 11.6693i) q^{85} +(4.07379 - 1.47797i) q^{86} +(7.26831 - 12.4994i) q^{88} -1.39700i q^{89} +0.519668 q^{91} +(-0.270624 - 0.323875i) q^{92} +(3.53433 - 1.28225i) q^{94} +(2.54234 + 4.12388i) q^{95} +4.41107i q^{97} +(-3.27836 - 9.03630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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