LMFDB - Embedded newform 1080.2.m.c.539.18

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			539.18
Character	$\chi$	$=$	1080.539
Dual form			1080.2.m.c.539.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.482315 - 1.32943i) q^{2} +(-1.53474 + 1.28240i) q^{4} +(1.17345 - 1.90342i) q^{5} -0.450397 q^{7} +(2.44509 + 1.42181i) q^{8} +(-3.09643 - 0.641961i) q^{10} +5.11202i q^{11} -1.15380 q^{13} +(0.217233 + 0.598769i) q^{14} +(0.710884 - 3.93632i) q^{16} +6.13070 q^{17} +2.16656 q^{19} +(0.640015 + 4.42610i) q^{20} +(6.79605 - 2.46560i) q^{22} -0.211029i q^{23} +(-2.24604 - 4.46713i) q^{25} +(0.556495 + 1.53389i) q^{26} +(0.691244 - 0.577590i) q^{28} +6.08377 q^{29} -0.417311i q^{31} +(-5.57592 + 0.953480i) q^{32} +(-2.95693 - 8.15031i) q^{34} +(-0.528517 + 0.857296i) q^{35} +9.60013 q^{37} +(-1.04496 - 2.88028i) q^{38} +(5.57548 - 2.98563i) q^{40} +9.71138i q^{41} +3.06432i q^{43} +(-6.55567 - 7.84565i) q^{44} +(-0.280547 + 0.101782i) q^{46} +2.65854i q^{47} -6.79714 q^{49} +(-4.85542 + 5.14051i) q^{50} +(1.77079 - 1.47964i) q^{52} -8.81551i q^{53} +(9.73034 + 5.99869i) q^{55} +(-1.10126 - 0.640377i) q^{56} +(-2.93429 - 8.08792i) q^{58} -4.73857i q^{59} -7.64787i q^{61} +(-0.554784 + 0.201275i) q^{62} +(3.95693 + 6.95289i) q^{64} +(-1.35392 + 2.19617i) q^{65} +6.49513i q^{67} +(-9.40907 + 7.86203i) q^{68} +(1.39462 + 0.289137i) q^{70} +11.4430 q^{71} -13.8904i q^{73} +(-4.63028 - 12.7627i) q^{74} +(-3.32511 + 2.77840i) q^{76} -2.30244i q^{77} -13.7469i q^{79} +(-6.65831 - 5.97218i) q^{80} +(12.9106 - 4.68394i) q^{82} +5.22116 q^{83} +(7.19405 - 11.6693i) q^{85} +(4.07379 - 1.47797i) q^{86} +(-7.26831 + 12.4994i) q^{88} -1.39700i q^{89} +0.519668 q^{91} +(0.270624 + 0.323875i) q^{92} +(3.53433 - 1.28225i) q^{94} +(2.54234 - 4.12388i) q^{95} -4.41107i q^{97} +(3.27836 + 9.03630i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.527126\pi$
$7$	−0.450397			−0.170234			−0.0851170	+	0.996371i	$0.527126\pi$
$8$	2.44509	+	1.42181i	0.864470	+	0.502685i
$9$		0			0
$10$	−3.09643	−	0.641961i	−0.979178	−	0.203006i
$11$			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	$-0.551151\pi$
$13$	−1.15380			−0.320007			−0.160003	+	0.987116i	$0.551151\pi$
$14$	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	$-0.233185\pi$
$17$	6.13070			1.48691			0.743457	+	0.668784i	$0.233185\pi$
$18$		0			0
$19$	2.16656			0.497043			0.248521	−	0.968626i	$-0.420055\pi$
$19$	2.16656			0.497043			0.248521	+	0.968626i	$0.420055\pi$
$20$	0.640015	+	4.42610i	0.143112	+	0.989707i
$21$		0			0
$22$	6.79605	−	2.46560i	1.44892	−	0.525668i
$23$		−	0.211029i		−	0.0440025i	−0.999758	−	0.0220013i	$-0.992996\pi$
$23$		−	0.211029i		−	0.0440025i	0.999758	−	0.0220013i	$-0.00700379\pi$
$24$		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	$-0.210534\pi$
$37$	9.60013			1.57825			0.789126	+	0.614232i	$0.210534\pi$
$38$	−1.04496	−	2.88028i	−0.169515	−	0.467243i
$39$		0			0
$40$	5.57548	−	2.98563i	0.881562	−	0.472069i
$41$			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	$0.0750678\pi$
$43$			3.06432i			0.467305i	−0.972320	+	0.233652i	$0.924932\pi$
$44$	−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	$0.0621117\pi$
$47$			2.65854i			0.387788i	−0.981023	+	0.193894i	$0.937888\pi$
$48$		0			0
$49$	−6.79714			−0.971020
$50$	−4.85542	+	5.14051i	−0.686660	+	0.726978i
$51$		0			0
$52$	1.77079	−	1.47964i	0.245564	−	0.205189i
$53$		−	8.81551i		−	1.21090i	−0.795882	−	0.605452i	$-0.792992\pi$
$53$		−	8.81551i		−	1.21090i	0.795882	−	0.605452i	$-0.207008\pi$
$54$		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	$0.129863\pi$
$67$			6.49513i			0.793506i	−0.917925	+	0.396753i	$0.870137\pi$
$68$	−9.40907	+	7.86203i	−1.14102	+	0.953412i
$69$		0			0
$70$	1.39462	+	0.289137i	0.166689	+	0.0345585i
$71$	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	$-0.697903\pi$
$73$		−	13.8904i		−	1.62574i	0.582443	−	0.812871i	$-0.302097\pi$
$74$	−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	$-0.281406\pi$
$80$	−6.65831	−	5.97218i	−0.744421	−	0.667710i
$81$		0			0
$82$	12.9106	−	4.68394i	1.42573	−	0.517255i
$83$	5.22116			0.573096			0.286548	−	0.958066i	$-0.407492\pi$
$83$	5.22116			0.573096			0.286548	+	0.958066i	$0.407492\pi$
$84$		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	$-0.928109\pi$
$97$		−	4.41107i		−	0.447876i	0.974603	−	0.223938i	$-0.0718913\pi$
$98$	3.27836	+	9.03630i	0.331165	+	0.912804i
$99$		0			0
$100$	9.17577	+	3.97558i	0.917577	+	0.397558i
$101$	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	$-0.594760\pi$
$103$	−5.95376			−0.586641			−0.293320	+	0.956014i	$0.594760\pi$
$104$	−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	$-0.356989\pi$
$107$	8.98524			0.868636			0.434318	+	0.900760i	$0.356989\pi$
$108$		0			0
$109$			11.7484i			1.12529i	0.826697	+	0.562647i	$0.190217\pi$
$109$			11.7484i			1.12529i	−0.826697	+	0.562647i	$0.809783\pi$
$110$	3.28172	−	15.8290i	0.312900	−	1.50924i
$111$		0			0
$112$	−0.320180	+	1.77291i	−0.0302542	+	0.167524i
$113$	−0.926078			−0.0871181			−0.0435590	−	0.999051i	$-0.513870\pi$
$113$	−0.926078			−0.0871181			−0.0435590	+	0.999051i	$0.513870\pi$
$114$		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	$-0.763698\pi$
$127$	−16.6083			−1.47375			−0.736873	+	0.676031i	$0.763698\pi$
$128$	7.33487	−	8.61393i	0.648317	−	0.761371i
$129$		0			0
$130$	3.57267	+	0.740695i	0.313344	+	0.0649633i
$131$			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	$-0.624018\pi$
$137$	−8.89160			−0.759661			−0.379830	+	0.925056i	$0.624018\pi$
$138$		0			0
$139$	14.2713			1.21047			0.605236	−	0.796046i	$-0.293079\pi$
$139$	14.2713			1.21047			0.605236	+	0.796046i	$0.293079\pi$
$140$	−0.288261	−	1.99350i	−0.0243625	−	0.168482i
$141$		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	$-0.677101\pi$
$157$	−13.2345			−1.05623			−0.528115	+	0.849173i	$0.677101\pi$
$158$	−18.2754	+	6.63031i	−1.45391	+	0.527479i
$159$		0			0
$160$	−4.72817	+	11.7322i	−0.373795	+	0.927512i
$161$			0.0950467i			0.00749073i
$162$		0			0
$163$			15.3659i			1.20355i	0.798666	+	0.601774i	$0.205539\pi$
$163$			15.3659i			1.20355i	−0.798666	+	0.601774i	$0.794461\pi$
$164$	−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	$-0.755793\pi$
$167$		−	17.9401i		−	1.38824i	0.719857	−	0.694122i	$-0.244207\pi$
$168$		0			0
$169$	−11.6687			−0.897596
$170$	−18.9833	−	3.93567i	−1.45595	−	0.301852i
$171$		0			0
$172$	−3.92970	−	4.70295i	−0.299637	−	0.358597i
$173$			17.2609i			1.31232i	0.754622	+	0.656160i	$0.227820\pi$
$173$			17.2609i			1.31232i	−0.754622	+	0.656160i	$0.772180\pi$
$174$		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
$190$	−6.70860	−	1.39085i	−0.486693	−	0.100903i
$191$	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	$0.0103135\pi$
$193$			0.900092i			0.0647901i	−0.999475	+	0.0323950i	$0.989687\pi$
$194$	−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	$-0.981656\pi$
$197$		−	1.61680i		−	0.115193i	0.998340	−	0.0575963i	$-0.0183436\pi$
$198$		0			0
$199$			13.9958i			0.992137i	0.868283	+	0.496069i	$0.165224\pi$
$199$			13.9958i			0.992137i	−0.868283	+	0.496069i	$0.834776\pi$
$200$	0.859622	−	14.1160i	0.0607844	−	0.998151i
$201$		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
$220$	−22.6263	+	3.27177i	−1.52547	+	0.220583i
$221$	−7.07361			−0.475823
$222$		0			0
$223$	−19.2003			−1.28574			−0.642872	−	0.765974i	$-0.722257\pi$
$223$	−19.2003			−1.28574			−0.642872	+	0.765974i	$0.722257\pi$
$224$	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	$-0.898275\pi$
$227$	−28.6073			−1.89874			−0.949368	+	0.314167i	$0.898275\pi$
$228$		0			0
$229$		−	3.59647i		−	0.237662i	−0.992915	−	0.118831i	$-0.962085\pi$
$229$		−	3.59647i		−	0.237662i	0.992915	−	0.118831i	$-0.0379146\pi$
$230$	−0.135472	+	0.653436i	−0.00893277	+	0.0430863i
$231$		0			0
$232$	14.8754	+	8.64995i	0.976615	+	0.567897i
$233$	9.78036			0.640733			0.320366	−	0.947294i	$-0.396194\pi$
$233$	9.78036			0.640733			0.320366	+	0.947294i	$0.396194\pi$
$234$		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
$250$	4.08700	+	15.2740i	0.258484	+	0.966015i
$251$			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	$-0.422764\pi$
$257$	7.70361			0.480538			0.240269	+	0.970706i	$0.422764\pi$
$258$		0			0
$259$	−4.32387			−0.268672
$260$	−0.738450	−	5.10684i	−0.0457967	−	0.316713i
$261$		0			0
$262$	18.0039	−	6.53182i	1.11229	−	0.403537i
$263$			0.422058i			0.0260252i	0.999915	+	0.0130126i	$0.00414215\pi$
$263$			0.422058i			0.0260252i	−0.999915	+	0.0130126i	$0.995858\pi$
$264$		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	$-0.824341\pi$
$277$	−28.3454			−1.70311			−0.851556	+	0.524263i	$0.824341\pi$
$278$	−6.88324	−	18.9726i	−0.412829	−	1.13790i
$279$		0			0
$280$	−2.51118	+	1.34472i	−0.150072	+	0.0803622i
$281$			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	$-0.961676\pi$
$283$		−	4.04108i		−	0.240217i	0.992761	−	0.120109i	$-0.0383243\pi$
$284$	−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
$290$	−18.8380	−	3.90554i	−1.10620	−	0.229341i
$291$		0			0
$292$	17.8130	+	21.3181i	1.04243	+	1.24755i
$293$		−	9.69326i		−	0.566287i	−0.959078	−	0.283143i	$-0.908623\pi$
$293$		−	9.69326i		−	0.566287i	0.959078	−	0.283143i	$-0.0913772\pi$
$294$		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	$0.334503\pi$
$307$			30.4121i			1.73571i	−0.496815	+	0.867856i	$0.665497\pi$
$308$	2.95265	+	3.53366i	0.168243	+	0.201349i
$309$		0			0
$310$	−0.267897	+	1.29217i	−0.0152155	+	0.0733906i
$311$	−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	$-0.776832\pi$
$313$		−	22.8246i		−	1.29012i	0.764130	−	0.645062i	$-0.223168\pi$
$314$	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	$0.0322694\pi$
$317$			3.60376i			0.202407i	−0.994866	+	0.101204i	$0.967731\pi$
$318$		0			0
$319$			31.1004i			1.74129i
$320$	17.8775	+	0.627138i	0.999385	+	0.0350581i
$321$		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	$0.136230\pi$
$337$			15.2379i			0.830063i	−0.909807	+	0.415032i	$0.863770\pi$
$338$	5.62801	+	15.5127i	0.306123	+	0.843781i
$339$		0			0
$340$	3.92374	+	27.1351i	0.212795	+	1.47161i
$341$	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	$-0.252618\pi$
$347$	26.1263			1.40253			0.701266	+	0.712900i	$0.252618\pi$
$348$		0			0
$349$		−	36.0891i		−	1.93180i	−0.258910	−	0.965901i	$-0.583363\pi$
$349$		−	36.0891i		−	1.93180i	0.258910	−	0.965901i	$-0.416637\pi$
$350$	2.18687	−	2.31527i	0.116893	−	0.123756i
$351$		0			0
$352$	−4.87421	−	28.5042i	−0.259796	−	1.51928i
$353$	−9.70998			−0.516810			−0.258405	−	0.966037i	$-0.583197\pi$
$353$	−9.70998			−0.516810			−0.258405	+	0.966037i	$0.583197\pi$
$354$		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	$-0.482199\pi$
$367$	2.14159			0.111790			0.0558949	+	0.998437i	$0.482199\pi$
$368$	−0.830678	−	0.150017i	−0.0433021	−	0.00782018i
$369$		0			0
$370$	−29.7261	−	6.16291i	−1.54539	−	0.320394i
$371$			3.97048i			0.206137i
$372$		0			0
$373$	14.6799			0.760097			0.380049	−	0.924967i	$-0.375907\pi$
$373$	14.6799			0.760097			0.380049	+	0.924967i	$0.375907\pi$
$374$	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	$0.536406\pi$
$380$	1.38663	+	9.58941i	0.0711326	+	0.491926i
$381$		0			0
$382$	−8.28076	−	22.8246i	−0.423680	−	1.16781i
$383$			15.1342i			0.773324i	0.922222	+	0.386662i	$0.126372\pi$
$383$			15.1342i			0.773324i	−0.922222	+	0.386662i	$0.873628\pi$
$384$		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	$-0.474503\pi$
$397$	3.18855			0.160029			0.0800143	+	0.996794i	$0.474503\pi$
$398$	18.6064	−	6.75039i	0.932654	−	0.338366i
$399$		0			0
$400$	−19.1808	+	5.66555i	−0.959038	+	0.283277i
$401$		−	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	$0.738421\pi$
$410$	6.23433	−	30.0706i	0.307892	−	1.48508i
$411$		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
$430$	1.96717	−	9.48846i	0.0948656	−	0.457574i
$431$	−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	$-0.921421\pi$
$433$		−	10.1697i		−	0.488726i	0.969684	−	0.244363i	$-0.0785788\pi$
$434$	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	$-0.135510\pi$
$440$	15.2626	+	28.5020i	0.727615	+	1.35878i
$441$		0			0
$442$	3.41171	+	9.40384i	0.162278	+	0.447295i
$443$	−28.5925			−1.35847			−0.679235	−	0.733921i	$-0.737688\pi$
$443$	−28.5925			−1.35847			−0.679235	+	0.733921i	$0.737688\pi$
$444$		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	$0.0844434\pi$
$457$			11.2098i			0.524372i	−0.965017	+	0.262186i	$0.915557\pi$
$458$	−4.78124	+	1.73463i	−0.223413	+	0.0810540i
$459$		0			0
$460$	0.934035	−	0.135062i	0.0435496	−	0.00629728i
$461$	−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	$-0.204313\pi$
$463$	34.4700			1.60196			0.800978	+	0.598694i	$0.204313\pi$
$464$	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	$-0.619086\pi$
$467$	−15.7950			−0.730907			−0.365453	+	0.930830i	$0.619086\pi$
$468$		0			0
$469$		−	2.92539i		−	0.135082i
$470$	1.70668	−	8.23198i	0.0787232	−	0.379713i
$471$		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	$-0.799073\pi$
$487$	−35.6312			−1.61460			−0.807302	+	0.590139i	$0.799073\pi$
$488$	10.8738	−	18.6997i	0.492234	−	0.846497i
$489$		0			0
$490$	21.0469	+	4.36350i	0.950801	+	0.197123i
$491$		−	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	$0.383529\pi$
$500$	18.3345	−	12.8003i	0.819943	−	0.572445i
$501$		0			0
$502$	17.0514	−	6.18623i	0.761041	−	0.276105i
$503$			2.13750i			0.0953062i	0.998864	+	0.0476531i	$0.0151742\pi$
$503$			2.13750i			0.0953062i	−0.998864	+	0.0476531i	$0.984826\pi$
$504$		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
$520$	−6.43300	+	3.44482i	−0.282106	+	0.151065i
$521$		−	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	$-0.827754\pi$
$523$		−	23.5599i		−	1.03020i	0.857129	−	0.515102i	$-0.172246\pi$
$524$	−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
$530$	−5.65921	+	27.2966i	−0.245821	+	1.18569i
$531$		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	$-0.946577\pi$
$547$		−	7.81382i		−	0.334095i	0.985949	−	0.167047i	$-0.0534233\pi$
$548$	13.6463	−	11.4026i	0.582943	−	0.487096i
$549$		0			0
$550$	−26.2784	−	24.8210i	−1.12052	−	1.05837i
$551$	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	$0.189675\pi$
$557$			26.4914i			1.12248i	−0.827655	+	0.561238i	$0.810325\pi$
$558$		0			0
$559$		−	3.53562i		−	0.149541i
$560$	2.99888	+	2.68985i	0.126726	+	0.113667i
$561$		0			0
$562$	37.2668	−	13.5204i	1.57200	−	0.570322i
$563$	−40.0138			−1.68638			−0.843191	−	0.537614i	$-0.819326\pi$
$563$	−40.0138			−1.68638			−0.843191	+	0.537614i	$0.819326\pi$
$564$		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	$0.0889421\pi$
$577$			13.2498i			0.551596i	−0.961216	+	0.275798i	$0.911058\pi$
$578$	−9.92870	−	27.3669i	−0.412980	−	1.13831i
$579$		0			0
$580$	3.89370	+	26.9274i	0.161677	+	1.11810i
$581$	−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	$-0.355891\pi$
$587$	21.1959			0.874848			0.437424	+	0.899255i	$0.355891\pi$
$588$		0			0
$589$		−	0.904128i		−	0.0372540i
$590$	−3.04198	+	14.6727i	−0.125236	+	0.604064i
$591$		0			0
$592$	6.82458	−	37.7892i	0.280488	−	1.55313i
$593$	24.0661			0.988275			0.494137	−	0.869384i	$-0.335484\pi$
$593$	24.0661			0.988275			0.494137	+	0.869384i	$0.335484\pi$
$594$		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	$-0.576510\pi$
$607$	−11.7302			−0.476114			−0.238057	+	0.971251i	$0.576510\pi$
$608$	−12.0806	+	2.06577i	−0.489931	+	0.0837780i
$609$		0			0
$610$	−4.90963	+	23.6811i	−0.198785	+	0.958820i
$611$		−	3.06743i		−	0.124095i
$612$		0			0
$613$	10.9631			0.442797			0.221399	−	0.975183i	$-0.428938\pi$
$613$	10.9631			0.442797			0.221399	+	0.975183i	$0.428938\pi$
$614$	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	$-0.415513\pi$
$617$	13.0317			0.524635			0.262318	+	0.964982i	$0.415513\pi$
$618$		0			0
$619$	−36.3769			−1.46211			−0.731056	−	0.682317i	$-0.760972\pi$
$619$	−36.3769			−1.46211			−0.731056	+	0.682317i	$0.760972\pi$
$620$	1.84706	−	0.267085i	0.0741797	−	0.0107264i
$621$		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
$640$	−7.78887	−	24.0693i	−0.307882	−	0.951424i
$641$		−	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	$-0.709857\pi$
$643$		−	40.0866i		−	1.58086i	0.612552	−	0.790431i	$-0.290143\pi$
$644$	−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	$-0.935606\pi$
$647$		−	10.2214i		−	0.401844i	0.979607	−	0.200922i	$-0.0643938\pi$
$648$		0			0
$649$	24.2237			0.950863
$650$	5.60219	−	5.93113i	0.219736	−	0.232638i
$651$		0			0
$652$	−19.7052	−	23.5827i	−0.771717	−	0.923570i
$653$			33.7435i			1.32049i	0.751052	+	0.660243i	$0.229547\pi$
$653$			33.7435i			1.32049i	−0.751052	+	0.660243i	$0.770453\pi$
$654$		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
$670$	4.16962	−	20.1117i	0.161086	−	0.776984i
$671$	39.0961			1.50929
$672$		0			0
$673$			3.17561i			0.122411i	0.998125	+	0.0612055i	$0.0194945\pi$
$673$			3.17561i			0.122411i	−0.998125	+	0.0612055i	$0.980506\pi$
$674$	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	$-0.787996\pi$
$677$		−	32.1530i		−	1.23574i	0.786280	−	0.617870i	$-0.212004\pi$
$678$		0			0
$679$			1.98673i			0.0762437i
$680$	34.1816	−	18.3040i	1.31081	−	0.701926i
$681$		0			0
$682$	−1.02892	−	2.83607i	−0.0393995	−	0.108599i
$683$	25.5185			0.976437			0.488219	−	0.872721i	$-0.337647\pi$
$683$	25.5185			0.976437			0.488219	+	0.872721i	$0.337647\pi$
$684$		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
$700$	−4.13274	−	1.79059i	−0.156203	−	0.0676778i
$701$	−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	$0.892292\pi$
$710$	−35.4324	−	7.34594i	−1.32975	−	0.275688i
$711$		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	$-0.719283\pi$
$727$	−34.2800			−1.27138			−0.635688	+	0.771946i	$0.719283\pi$
$728$	1.27064	+	0.738868i	0.0470929	+	0.0273843i
$729$		0			0
$730$	−8.91706	+	43.0105i	−0.330035	+	1.59189i
$731$			18.7864i			0.694842i
$732$		0			0
$733$	−16.8179			−0.621182			−0.310591	−	0.950544i	$-0.600527\pi$
$733$	−16.8179			−0.621182			−0.310591	+	0.950544i	$0.600527\pi$
$734$	−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	$0.655379\pi$
$740$	6.14423	+	42.4911i	0.225866	+	1.56201i
$741$		0			0
$742$	5.27846	−	1.91502i	0.193778	−	0.0703026i
$743$			2.19747i			0.0806172i	0.999187	+	0.0403086i	$0.0128341\pi$
$743$			2.19747i			0.0806172i	−0.999187	+	0.0403086i	$0.987166\pi$
$744$		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	$-0.627789\pi$
$757$	−21.5026			−0.781527			−0.390763	+	0.920491i	$0.627789\pi$
$758$	2.14319	+	5.90737i	0.0778441	+	0.214565i
$759$		0			0
$760$	12.0796	−	6.46854i	0.438174	−	0.234638i
$761$			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	$0.587884\pi$
$770$	−1.47808	+	7.12934i	−0.0532661	+	0.256924i
$771$		0			0
$772$	−1.15428	−	1.38141i	−0.0415435	−	0.0497181i
$773$		−	13.0796i		−	0.470439i	−0.971942	−	0.235220i	$-0.924419\pi$
$773$		−	13.0796i		−	0.470439i	0.971942	−	0.235220i	$-0.0755810\pi$
$774$		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	$-0.852743\pi$
$787$		−	25.0403i		−	0.892591i	0.894886	−	0.446296i	$-0.147257\pi$
$788$	2.07339	+	2.48138i	0.0738616	+	0.0883956i
$789$		0			0
$790$	−8.82494	+	42.5662i	−0.313977	+	1.51444i
$791$	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	$0.172173\pi$
$797$			29.0728i			1.02981i	−0.857247	+	0.514905i	$0.827827\pi$
$798$		0			0
$799$			16.2987i			0.576607i
$800$	16.7831	+	22.7668i	0.593372	+	0.804929i
$801$		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
$820$	−42.9836	+	6.21543i	−1.50105	+	0.217052i
$821$	−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	$-0.585335\pi$
$823$	−15.1981			−0.529773			−0.264887	+	0.964280i	$0.585335\pi$
$824$	−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	$-0.481020\pi$
$827$	3.42753			0.119187			0.0595934	+	0.998223i	$0.481020\pi$
$828$		0			0
$829$			16.1960i			0.562511i	0.959633	+	0.281256i	$0.0907509\pi$
$829$			16.1960i			0.562511i	−0.959633	+	0.281256i	$0.909249\pi$
$830$	−16.1670	−	3.35178i	−0.561163	−	0.116342i
$831$		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
$850$	−29.7671	+	31.5150i	−1.02100	+	1.08095i
$851$		−	2.02590i		−	0.0694471i
$852$		0			0
$853$	−15.9478			−0.546044			−0.273022	−	0.962008i	$-0.588023\pi$
$853$	−15.9478			−0.546044			−0.273022	+	0.962008i	$0.588023\pi$
$854$	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	$-0.287081\pi$
$857$	36.3078			1.24025			0.620126	+	0.784502i	$0.287081\pi$
$858$		0			0
$859$	16.7215			0.570530			0.285265	−	0.958449i	$-0.407918\pi$
$859$	16.7215			0.570530			0.285265	+	0.958449i	$0.407918\pi$
$860$	−13.5630	+	1.96121i	−0.462495	+	0.0668768i
$861$		0			0
$862$	7.28941	+	20.0921i	0.248278	+	0.684340i
$863$		−	32.0732i		−	1.09178i	−0.837856	−	0.545892i	$-0.816191\pi$
$863$		−	32.0732i		−	1.09178i	0.837856	−	0.545892i	$-0.183809\pi$
$864$		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	$-0.633780\pi$
$877$	−24.1662			−0.816035			−0.408018	+	0.912974i	$0.633780\pi$
$878$	−23.0064	+	8.34671i	−0.776428	+	0.281688i
$879$		0			0
$880$	30.5299	−	34.0374i	1.02916	−	1.14740i
$881$			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	$0.0942534\pi$
$883$			17.3417i			0.583595i	−0.956480	+	0.291798i	$0.905747\pi$
$884$	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	$-0.703346\pi$
$887$		−	47.8185i		−	1.60559i	0.596256	−	0.802794i	$-0.296654\pi$
$888$		0			0
$889$	7.48031			0.250882
$890$	−0.896819	+	4.32571i	−0.0300614	+	0.144998i
$891$		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	$-0.956387\pi$
$907$		−	8.22699i		−	0.273173i	0.990628	−	0.136586i	$-0.0436131\pi$
$908$	43.9050	−	36.6861i	1.45704	−	1.21747i
$909$		0			0
$910$	−1.60912	−	0.333607i	−0.0533417	−	0.0110590i
$911$	−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	$-0.193623\pi$
$920$	−0.630053	−	1.17659i	−0.0207722	−	0.0387910i
$921$		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	$0.150857\pi$
$937$			27.9404i			0.912773i	−0.889782	+	0.456386i	$0.849143\pi$
$938$	−3.88908	+	1.41096i	−0.126983	+	0.0460694i
$939$		0			0
$940$	−11.7670	+	1.70151i	−0.383796	+	0.0554970i
$941$	−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	$-0.694436\pi$
$947$	−35.3004			−1.14711			−0.573554	+	0.819167i	$0.694436\pi$
$948$		0			0
$949$			16.0267i			0.520249i
$950$	−10.5196	+	11.1372i	−0.341299	+	0.361339i
$951$		0			0
$952$	−6.75150	−	3.92596i	−0.218817	−	0.127241i
$953$	12.1033			0.392064			0.196032	−	0.980598i	$-0.437194\pi$
$953$	12.1033			0.392064			0.196032	+	0.980598i	$0.437194\pi$
$954$		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	$-0.335774\pi$
$967$	30.6826			0.986687			0.493344	+	0.869834i	$0.335774\pi$
$968$	−37.0010	−	21.5159i	−1.18926	−	0.691547i
$969$		0			0
$970$	−2.83173	+	13.6586i	−0.0909215	+	0.438550i
$971$			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	$-0.648711\pi$
$977$	−28.1550			−0.900760			−0.450380	+	0.892837i	$0.648711\pi$
$978$		0			0
$979$	7.14149			0.228243
$980$	−4.35027	−	30.0848i	−0.138964	−	0.961025i
$981$		0			0
$982$	−26.8422	+	9.73835i	−0.856570	+	0.310763i
$983$		−	24.2134i		−	0.772288i	−0.922439	−	0.386144i	$-0.873807\pi$
$983$		−	24.2134i		−	0.772288i	0.922439	−	0.386144i	$-0.126193\pi$
$984$		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	$-0.430183\pi$
$997$	13.7405			0.435167			0.217584	+	0.976042i	$0.430183\pi$
$998$	−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.539.18	yes	48
3.2	odd	2	inner	1080.2.m.c.539.31	yes	48
4.3	odd	2		4320.2.m.c.2159.34		48
5.4	even	2	inner	1080.2.m.c.539.32	yes	48
8.3	odd	2	inner	1080.2.m.c.539.19	yes	48
8.5	even	2		4320.2.m.c.2159.15		48
12.11	even	2		4320.2.m.c.2159.16		48
15.14	odd	2	inner	1080.2.m.c.539.17	✓	48
20.19	odd	2		4320.2.m.c.2159.35		48
24.5	odd	2		4320.2.m.c.2159.33		48
24.11	even	2	inner	1080.2.m.c.539.30	yes	48
40.19	odd	2	inner	1080.2.m.c.539.29	yes	48
40.29	even	2		4320.2.m.c.2159.14		48
60.59	even	2		4320.2.m.c.2159.13		48
120.29	odd	2		4320.2.m.c.2159.36		48
120.59	even	2	inner	1080.2.m.c.539.20	yes	48

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

\(f(q)\)	\(=\)	\(q+(-0.482315 - 1.32943i) q^{2} +(-1.53474 + 1.28240i) q^{4} +(1.17345 - 1.90342i) q^{5} -0.450397 q^{7} +(2.44509 + 1.42181i) q^{8} +(-3.09643 - 0.641961i) q^{10} +5.11202i q^{11} -1.15380 q^{13} +(0.217233 + 0.598769i) q^{14} +(0.710884 - 3.93632i) q^{16} +6.13070 q^{17} +2.16656 q^{19} +(0.640015 + 4.42610i) q^{20} +(6.79605 - 2.46560i) q^{22} -0.211029i q^{23} +(-2.24604 - 4.46713i) q^{25} +(0.556495 + 1.53389i) q^{26} +(0.691244 - 0.577590i) q^{28} +6.08377 q^{29} -0.417311i q^{31} +(-5.57592 + 0.953480i) q^{32} +(-2.95693 - 8.15031i) q^{34} +(-0.528517 + 0.857296i) q^{35} +9.60013 q^{37} +(-1.04496 - 2.88028i) q^{38} +(5.57548 - 2.98563i) q^{40} +9.71138i q^{41} +3.06432i q^{43} +(-6.55567 - 7.84565i) q^{44} +(-0.280547 + 0.101782i) q^{46} +2.65854i q^{47} -6.79714 q^{49} +(-4.85542 + 5.14051i) q^{50} +(1.77079 - 1.47964i) q^{52} -8.81551i q^{53} +(9.73034 + 5.99869i) q^{55} +(-1.10126 - 0.640377i) q^{56} +(-2.93429 - 8.08792i) q^{58} -4.73857i q^{59} -7.64787i q^{61} +(-0.554784 + 0.201275i) q^{62} +(3.95693 + 6.95289i) q^{64} +(-1.35392 + 2.19617i) q^{65} +6.49513i q^{67} +(-9.40907 + 7.86203i) q^{68} +(1.39462 + 0.289137i) q^{70} +11.4430 q^{71} -13.8904i q^{73} +(-4.63028 - 12.7627i) q^{74} +(-3.32511 + 2.77840i) q^{76} -2.30244i q^{77} -13.7469i q^{79} +(-6.65831 - 5.97218i) q^{80} +(12.9106 - 4.68394i) q^{82} +5.22116 q^{83} +(7.19405 - 11.6693i) q^{85} +(4.07379 - 1.47797i) q^{86} +(-7.26831 + 12.4994i) q^{88} -1.39700i q^{89} +0.519668 q^{91} +(0.270624 + 0.323875i) q^{92} +(3.53433 - 1.28225i) q^{94} +(2.54234 - 4.12388i) q^{95} -4.41107i q^{97} +(3.27836 + 9.03630i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) \) 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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