LMFDB - Embedded newform 288.2.s.a.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(95,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("288.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.s (of order $6$, degree $2$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.2
Character	$\chi$	$=$	288.191
Dual form			288.2.s.a.95.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55381 - 0.765299i) q^{3} +(1.81740 - 1.04928i) q^{5} +(-0.143714 - 0.0829731i) q^{7} +(1.82863 + 2.37826i) q^{9} +O(q^{10})$	\(q+(-1.55381 - 0.765299i) q^{3} +(1.81740 - 1.04928i) q^{5} +(-0.143714 - 0.0829731i) q^{7} +(1.82863 + 2.37826i) q^{9} +(0.784910 - 1.35950i) q^{11} +(-1.93212 - 3.34652i) q^{13} +(-3.62690 + 0.239518i) q^{15} -5.27221i q^{17} -8.05210i q^{19} +(0.159804 + 0.238908i) q^{21} +(2.67564 + 4.63435i) q^{23} +(-0.298034 + 0.516211i) q^{25} +(-1.02127 - 5.09480i) q^{27} +(6.75334 + 3.89904i) q^{29} +(2.10800 - 1.21705i) q^{31} +(-2.26003 + 1.51172i) q^{33} -0.348247 q^{35} -8.53566 q^{37} +(0.441043 + 6.67850i) q^{39} +(2.47895 - 1.43122i) q^{41} +(3.42127 + 1.97527i) q^{43} +(5.81881 + 2.40350i) q^{45} +(-3.68689 + 6.38588i) q^{47} +(-3.48623 - 6.03833i) q^{49} +(-4.03482 + 8.19199i) q^{51} +2.40174i q^{53} -3.29435i q^{55} +(-6.16227 + 12.5114i) q^{57} +(5.49855 + 9.52376i) q^{59} +(-7.11998 + 12.3322i) q^{61} +(-0.0654683 - 0.493515i) q^{63} +(-7.02286 - 4.05465i) q^{65} +(-1.45698 + 0.841190i) q^{67} +(-0.610768 - 9.24855i) q^{69} +12.5669 q^{71} +10.4679 q^{73} +(0.858144 - 0.574006i) q^{75} +(-0.225605 + 0.130253i) q^{77} +(6.31710 + 3.64718i) q^{79} +(-2.31220 + 8.69792i) q^{81} +(1.35365 - 2.34460i) q^{83} +(-5.53201 - 9.58172i) q^{85} +(-7.50945 - 11.2267i) q^{87} -2.40174i q^{89} +0.641255i q^{91} +(-4.20684 + 0.277816i) q^{93} +(-8.44888 - 14.6339i) q^{95} +(0.903600 - 1.56508i) q^{97} +(4.66856 - 0.619318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.55381	−	0.765299i	−0.897091	−	0.441846i
$3$	−1.55381	−	0.765299i	−0.897091	−	0.441846i
$4$		0			0
$5$	1.81740	−	1.04928i	0.812767	−	0.469251i	−0.0351491	−	0.999382i	$-0.511191\pi$
$5$	1.81740	−	1.04928i	0.812767	−	0.469251i	0.847916	+	0.530131i	$0.177857\pi$
$6$		0			0
$7$	−0.143714	−	0.0829731i	−0.0543187	−	0.0313609i	0.472595	−	0.881280i	$-0.343317\pi$
$7$	−0.143714	−	0.0829731i	−0.0543187	−	0.0313609i	−0.526913	+	0.849919i	$0.676651\pi$
$8$		0			0
$9$	1.82863	+	2.37826i	0.609544	+	0.792752i
$10$		0			0
$11$	0.784910	−	1.35950i	0.236659	−	0.409906i	−0.723094	−	0.690749i	$-0.757281\pi$
$11$	0.784910	−	1.35950i	0.236659	−	0.409906i	0.959754	+	0.280843i	$0.0906141\pi$
$12$		0			0
$13$	−1.93212	−	3.34652i	−0.535872	−	0.928158i	−0.999121	−	0.0419297i	$-0.986649\pi$
$13$	−1.93212	−	3.34652i	−0.535872	−	0.928158i	0.463248	−	0.886229i	$-0.346684\pi$
$14$		0			0
$15$	−3.62690	+	0.239518i	−0.936462	+	0.0618433i
$16$		0			0
$17$		−	5.27221i		−	1.27870i	−0.768917	−	0.639349i	$-0.779204\pi$
$17$		−	5.27221i		−	1.27870i	0.768917	−	0.639349i	$-0.220796\pi$
$18$		0			0
$19$		−	8.05210i		−	1.84728i	−0.383264	−	0.923639i	$-0.625200\pi$
$19$		−	8.05210i		−	1.84728i	0.383264	−	0.923639i	$-0.374800\pi$
$20$		0			0
$21$	0.159804	+	0.238908i	0.0348721	+	0.0521340i
$22$		0			0
$23$	2.67564	+	4.63435i	0.557910	+	0.966328i	0.997671	+	0.0682135i	$0.0217299\pi$
$23$	2.67564	+	4.63435i	0.557910	+	0.966328i	−0.439761	+	0.898115i	$0.644937\pi$
$24$		0			0
$25$	−0.298034	+	0.516211i	−0.0596069	+	0.103242i
$26$		0			0
$27$	−1.02127	−	5.09480i	−0.196543	−	0.980495i
$28$		0			0
$29$	6.75334	+	3.89904i	1.25406	+	0.724034i	0.971914	−	0.235336i	$-0.0756191\pi$
$29$	6.75334	+	3.89904i	1.25406	+	0.724034i	0.282150	+	0.959370i	$0.408952\pi$
$30$		0			0
$31$	2.10800	−	1.21705i	0.378608	−	0.218589i	−0.298604	−	0.954377i	$-0.596521\pi$
$31$	2.10800	−	1.21705i	0.378608	−	0.218589i	0.677212	+	0.735788i	$0.263188\pi$
$32$		0			0
$33$	−2.26003	+	1.51172i	−0.393420	+	0.263156i
$34$		0			0
$35$	−0.348247			−0.0588645
$36$		0			0
$37$	−8.53566			−1.40325			−0.701627	−	0.712544i	$-0.747543\pi$
$37$	−8.53566			−1.40325			−0.701627	+	0.712544i	$0.747543\pi$
$38$		0			0
$39$	0.441043	+	6.67850i	0.0706234	+	1.06942i
$40$		0			0
$41$	2.47895	−	1.43122i	0.387146	−	0.223519i	−0.293777	−	0.955874i	$-0.594912\pi$
$41$	2.47895	−	1.43122i	0.387146	−	0.223519i	0.680923	+	0.732355i	$0.261579\pi$
$42$		0			0
$43$	3.42127	+	1.97527i	0.521739	+	0.301226i	0.737646	−	0.675188i	$-0.235937\pi$
$43$	3.42127	+	1.97527i	0.521739	+	0.301226i	−0.215907	+	0.976414i	$0.569271\pi$
$44$		0			0
$45$	5.81881	+	2.40350i	0.867417	+	0.358293i
$46$		0			0
$47$	−3.68689	+	6.38588i	−0.537788	+	0.931477i	0.461234	+	0.887278i	$0.347407\pi$
$47$	−3.68689	+	6.38588i	−0.537788	+	0.931477i	−0.999023	+	0.0441985i	$0.985927\pi$
$48$		0			0
$49$	−3.48623	−	6.03833i	−0.498033	−	0.862618i
$50$		0			0
$51$	−4.03482	+	8.19199i	−0.564988	+	1.14711i
$52$		0			0
$53$			2.40174i			0.329904i	0.986302	+	0.164952i	$0.0527469\pi$
$53$			2.40174i			0.329904i	−0.986302	+	0.164952i	$0.947253\pi$
$54$		0			0
$55$		−	3.29435i		−	0.444211i
$56$		0			0
$57$	−6.16227	+	12.5114i	−0.816212	+	1.65718i
$58$		0			0
$59$	5.49855	+	9.52376i	0.715850	+	1.23989i	0.962631	+	0.270817i	$0.0872939\pi$
$59$	5.49855	+	9.52376i	0.715850	+	1.23989i	−0.246781	+	0.969071i	$0.579373\pi$
$60$		0			0
$61$	−7.11998	+	12.3322i	−0.911620	+	1.57897i	−0.0998446	+	0.995003i	$0.531835\pi$
$61$	−7.11998	+	12.3322i	−0.911620	+	1.57897i	−0.811776	+	0.583969i	$0.801499\pi$
$62$		0			0
$63$	−0.0654683	−	0.493515i	−0.00824823	−	0.0621771i
$64$		0			0
$65$	−7.02286	−	4.05465i	−0.871079	−	0.502917i
$66$		0			0
$67$	−1.45698	+	0.841190i	−0.177999	+	0.102768i	−0.586352	−	0.810056i	$-0.699436\pi$
$67$	−1.45698	+	0.841190i	−0.177999	+	0.102768i	0.408353	+	0.912824i	$0.366103\pi$
$68$		0			0
$69$	−0.610768	−	9.24855i	−0.0735278	−	1.11339i
$70$		0			0
$71$	12.5669			1.49142			0.745709	−	0.666272i	$-0.232111\pi$
$71$	12.5669			1.49142			0.745709	+	0.666272i	$0.232111\pi$
$72$		0			0
$73$	10.4679			1.22518			0.612590	−	0.790401i	$-0.290128\pi$
$73$	10.4679			1.22518			0.612590	+	0.790401i	$0.290128\pi$
$74$		0			0
$75$	0.858144	−	0.574006i	0.0990899	−	0.0662805i
$76$		0			0
$77$	−0.225605	+	0.130253i	−0.0257100	+	0.0148437i
$78$		0			0
$79$	6.31710	+	3.64718i	0.710729	+	0.410339i	0.811331	−	0.584587i	$-0.198744\pi$
$79$	6.31710	+	3.64718i	0.710729	+	0.410339i	−0.100602	+	0.994927i	$0.532077\pi$
$80$		0			0
$81$	−2.31220	+	8.69792i	−0.256911	+	0.966435i
$82$		0			0
$83$	1.35365	−	2.34460i	0.148583	−	0.257353i	−0.782121	−	0.623126i	$-0.785862\pi$
$83$	1.35365	−	2.34460i	0.148583	−	0.257353i	0.930704	+	0.365774i	$0.119196\pi$
$84$		0			0
$85$	−5.53201	−	9.58172i	−0.600031	−	1.03928i
$86$		0			0
$87$	−7.50945	−	11.2267i	−0.805098	−	1.20363i
$88$		0			0
$89$		−	2.40174i		−	0.254584i	−0.991865	−	0.127292i	$-0.959372\pi$
$89$		−	2.40174i		−	0.254584i	0.991865	−	0.127292i	$-0.0406285\pi$
$90$		0			0
$91$			0.641255i			0.0672217i
$92$		0			0
$93$	−4.20684	+	0.277816i	−0.436229	+	0.0288082i
$94$		0			0
$95$	−8.44888	−	14.6339i	−0.866837	−	1.50141i
$96$		0			0
$97$	0.903600	−	1.56508i	0.0917467	−	0.158910i	−0.816499	−	0.577346i	$-0.804088\pi$
$97$	0.903600	−	1.56508i	0.0917467	−	0.158910i	0.908246	+	0.418436i	$0.137422\pi$
$98$		0			0
$99$	4.66856	−	0.619318i	0.469208	−	0.0622438i
$100$		0			0
$101$	−3.08158	−	1.77915i	−0.306628	−	0.177032i	0.338788	−	0.940863i	$-0.389983\pi$
$101$	−3.08158	−	1.77915i	−0.306628	−	0.177032i	−0.645417	+	0.763831i	$0.723316\pi$
$102$		0			0
$103$	−8.28138	+	4.78126i	−0.815989	+	0.471111i	−0.849031	−	0.528343i	$-0.822814\pi$
$103$	−8.28138	+	4.78126i	−0.815989	+	0.471111i	0.0330425	+	0.999454i	$0.489480\pi$
$104$		0			0
$105$	0.541109	+	0.266513i	0.0528068	+	0.0260090i
$106$		0			0
$107$	−5.60313			−0.541675			−0.270838	−	0.962625i	$-0.587301\pi$
$107$	−5.60313			−0.541675			−0.270838	+	0.962625i	$0.587301\pi$
$108$		0			0
$109$	7.56853			0.724934			0.362467	−	0.931997i	$-0.381935\pi$
$109$	7.56853			0.724934			0.362467	+	0.931997i	$0.381935\pi$
$110$		0			0
$111$	13.2628	+	6.53234i	1.25885	+	0.620022i
$112$		0			0
$113$	0.495124	−	0.285860i	0.0465773	−	0.0268914i	−0.476531	−	0.879158i	$-0.658106\pi$
$113$	0.495124	−	0.285860i	0.0465773	−	0.0268914i	0.523108	+	0.852266i	$0.324772\pi$
$114$		0			0
$115$	9.72543	+	5.61498i	0.906901	+	0.523600i
$116$		0			0
$117$	4.42575	−	10.7146i	0.409161	−	0.990568i
$118$		0			0
$119$	−0.437452	+	0.757688i	−0.0401011	+	0.0694572i
$120$		0			0
$121$	4.26783	+	7.39210i	0.387985	+	0.672009i
$122$		0			0
$123$	−4.94712	+	0.326704i	−0.446066	+	0.0294579i
$124$		0			0
$125$			11.7437i			1.05038i
$126$		0			0
$127$		−	14.0438i		−	1.24619i	−0.782146	−	0.623095i	$-0.785875\pi$
$127$		−	14.0438i		−	1.24619i	0.782146	−	0.623095i	$-0.214125\pi$
$128$		0			0
$129$	−3.80432	−	5.68749i	−0.334952	−	0.500755i
$130$		0			0
$131$	−0.699837	−	1.21215i	−0.0611450	−	0.105906i	0.833832	−	0.552018i	$-0.186142\pi$
$131$	−0.699837	−	1.21215i	−0.0611450	−	0.105906i	−0.894977	+	0.446111i	$0.852809\pi$
$132$		0			0
$133$	−0.668108	+	1.15720i	−0.0579323	+	0.100342i
$134$		0			0
$135$	−7.20191	−	8.18771i	−0.619842	−	0.704686i
$136$		0			0
$137$	−1.21477	−	0.701347i	−0.103785	−	0.0599201i	0.447209	−	0.894429i	$-0.352418\pi$
$137$	−1.21477	−	0.701347i	−0.103785	−	0.0599201i	−0.550994	+	0.834509i	$0.685751\pi$
$138$		0			0
$139$	−18.6630	+	10.7751i	−1.58298	+	0.913933i	−0.588557	+	0.808456i	$0.700304\pi$
$139$	−18.6630	+	10.7751i	−1.58298	+	0.913933i	−0.994422	+	0.105477i	$0.966363\pi$
$140$		0			0
$141$	10.6158	−	7.10086i	0.894014	−	0.598000i
$142$		0			0
$143$	−6.06615			−0.507277
$144$		0			0
$145$	16.3647			1.35902
$146$		0			0
$147$	0.795800	+	12.0504i	0.0656365	+	0.993901i
$148$		0			0
$149$	5.10263	−	2.94601i	0.418024	−	0.241346i	−0.276208	−	0.961098i	$-0.589078\pi$
$149$	5.10263	−	2.94601i	0.418024	−	0.241346i	0.694232	+	0.719752i	$0.255744\pi$
$150$		0			0
$151$	−6.86723	−	3.96480i	−0.558847	−	0.322651i	0.193835	−	0.981034i	$-0.437907\pi$
$151$	−6.86723	−	3.96480i	−0.558847	−	0.322651i	−0.752683	+	0.658383i	$0.771241\pi$
$152$		0			0
$153$	12.5387	−	9.64094i	1.01369	−	0.779423i
$154$		0			0
$155$	2.55405	−	4.42375i	0.205147	−	0.355324i
$156$		0			0
$157$	1.00382	+	1.73867i	0.0801138	+	0.138761i	0.903299	−	0.429012i	$-0.141138\pi$
$157$	1.00382	+	1.73867i	0.0801138	+	0.138761i	−0.823185	+	0.567773i	$0.807805\pi$
$158$		0			0
$159$	1.83805	−	3.73184i	0.145767	−	0.295954i
$160$		0			0
$161$		−	0.888025i		−	0.0699862i
$162$		0			0
$163$			2.06036i			0.161379i	0.996739	+	0.0806897i	$0.0257123\pi$
$163$			2.06036i			0.161379i	−0.996739	+	0.0806897i	$0.974288\pi$
$164$		0			0
$165$	−2.52117	+	5.11879i	−0.196273	+	0.398497i
$166$		0			0
$167$	−9.45382	−	16.3745i	−0.731559	−	1.26710i	−0.956217	−	0.292659i	$-0.905460\pi$
$167$	−9.45382	−	16.3745i	−0.731559	−	1.26710i	0.224658	−	0.974438i	$-0.427873\pi$
$168$		0			0
$169$	−0.966142	+	1.67341i	−0.0743186	+	0.128724i
$170$		0			0
$171$	19.1499	−	14.7243i	1.46443	−	1.12600i
$172$		0			0
$173$	9.29843	+	5.36845i	0.706946	+	0.408156i	0.809929	−	0.586528i	$-0.199505\pi$
$173$	9.29843	+	5.36845i	0.706946	+	0.408156i	−0.102983	+	0.994683i	$0.532839\pi$
$174$		0			0
$175$	0.0856632	−	0.0494577i	0.00647553	−	0.00373865i
$176$		0			0
$177$	−1.25515	−	19.0061i	−0.0943429	−	1.42859i
$178$		0			0
$179$	−22.7748			−1.70227			−0.851133	−	0.524950i	$-0.824084\pi$
$179$	−22.7748			−1.70227			−0.851133	+	0.524950i	$0.824084\pi$
$180$		0			0
$181$	9.72780			0.723062			0.361531	−	0.932360i	$-0.382254\pi$
$181$	9.72780			0.723062			0.361531	+	0.932360i	$0.382254\pi$
$182$		0			0
$183$	20.5009	−	13.7129i	1.51547	−	1.01369i
$184$		0			0
$185$	−15.5127	+	8.95628i	−1.14052	+	0.658479i
$186$		0			0
$187$	−7.16759	−	4.13821i	−0.524146	−	0.302616i
$188$		0			0
$189$	−0.275962	+	0.816930i	−0.0200733	+	0.0594229i
$190$		0			0
$191$	1.27410	−	2.20681i	0.0921908	−	0.159679i	−0.816242	−	0.577710i	$-0.803946\pi$
$191$	1.27410	−	2.20681i	0.0921908	−	0.159679i	0.908433	+	0.418031i	$0.137280\pi$
$192$		0			0
$193$	−2.49967	−	4.32955i	−0.179930	−	0.311648i	0.761926	−	0.647664i	$-0.224254\pi$
$193$	−2.49967	−	4.32955i	−0.179930	−	0.311648i	−0.941856	+	0.336016i	$0.890921\pi$
$194$		0			0
$195$	7.80915	+	11.6747i	0.559225	+	0.836045i
$196$		0			0
$197$			5.65685i			0.403034i	0.979485	+	0.201517i	$0.0645872\pi$
$197$			5.65685i			0.403034i	−0.979485	+	0.201517i	$0.935413\pi$
$198$		0			0
$199$			14.4713i			1.02584i	0.858436	+	0.512921i	$0.171436\pi$
$199$			14.4713i			1.02584i	−0.858436	+	0.512921i	$0.828564\pi$
$200$		0			0
$201$	2.90763	−	0.192018i	0.205089	−	0.0135439i
$202$		0			0
$203$	−0.647031	−	1.12069i	−0.0454127	−	0.0786571i
$204$		0			0
$205$	3.00349	−	5.20220i	0.209773	−	0.363338i
$206$		0			0
$207$	−6.12890	+	14.8379i	−0.425988	+	1.03130i
$208$		0			0
$209$	−10.9469	−	6.32017i	−0.757210	−	0.437176i
$210$		0			0
$211$	12.7320	−	7.35080i	0.876505	−	0.506050i	0.00700041	−	0.999975i	$-0.497772\pi$
$211$	12.7320	−	7.35080i	0.876505	−	0.506050i	0.869504	+	0.493925i	$0.164438\pi$
$212$		0			0
$213$	−19.5266	−	9.61745i	−1.33794	−	0.658977i
$214$		0			0
$215$	8.29043			0.565403
$216$		0			0
$217$	−0.403931			−0.0274206
$218$		0			0
$219$	−16.2652	−	8.01111i	−1.09910	−	0.541341i
$220$		0			0
$221$	−17.6436	+	10.1865i	−1.18683	+	0.685219i
$222$		0			0
$223$	15.6729	+	9.04876i	1.04954	+	0.605950i	0.922519	−	0.385951i	$-0.126127\pi$
$223$	15.6729	+	9.04876i	1.04954	+	0.605950i	0.127016	+	0.991901i	$0.459460\pi$
$224$		0			0
$225$	−1.77268	+	0.235158i	−0.118178	+	0.0156772i
$226$		0			0
$227$	6.29529	−	10.9038i	0.417833	−	0.723708i	−0.577888	−	0.816116i	$-0.696123\pi$
$227$	6.29529	−	10.9038i	0.417833	−	0.723708i	0.995721	+	0.0924078i	$0.0294564\pi$
$228$		0			0
$229$	6.19995	+	10.7386i	0.409704	+	0.709628i	0.994856	−	0.101295i	$-0.0322986\pi$
$229$	6.19995	+	10.7386i	0.409704	+	0.709628i	−0.585152	+	0.810923i	$0.698965\pi$
$230$		0			0
$231$	0.450229	−	0.0297328i	0.0296229	−	0.00195627i
$232$		0			0
$233$			7.13560i			0.467469i	0.972300	+	0.233734i	$0.0750947\pi$
$233$			7.13560i			0.467469i	−0.972300	+	0.233734i	$0.924905\pi$
$234$		0			0
$235$			15.4743i			1.00943i
$236$		0			0
$237$	−7.02437	−	10.5015i	−0.456282	−	0.682144i
$238$		0			0
$239$	0.273904	+	0.474416i	0.0177174	+	0.0306874i	0.874748	−	0.484578i	$-0.161027\pi$
$239$	0.273904	+	0.474416i	0.0177174	+	0.0306874i	−0.857031	+	0.515265i	$0.827693\pi$
$240$		0			0
$241$	−9.28792	+	16.0872i	−0.598288	+	1.03626i	0.394786	+	0.918773i	$0.370819\pi$
$241$	−9.28792	+	16.0872i	−0.598288	+	1.03626i	−0.993074	+	0.117491i	$0.962515\pi$
$242$		0			0
$243$	10.2492	−	11.7454i	0.657488	−	0.753465i
$244$		0			0
$245$	−12.6718	−	7.31605i	−0.809569	−	0.467405i
$246$		0			0
$247$	−26.9465	+	15.5576i	−1.71457	+	0.989905i
$248$		0			0
$249$	−3.89764	+	2.60710i	−0.247003	+	0.165218i
$250$		0			0
$251$	19.2012			1.21197			0.605985	−	0.795476i	$-0.292779\pi$
$251$	19.2012			1.21197			0.605985	+	0.795476i	$0.292779\pi$
$252$		0			0
$253$	8.40056			0.528138
$254$		0			0
$255$	1.26279	+	19.1218i	0.0790789	+	1.19745i
$256$		0			0
$257$	3.90205	−	2.25285i	0.243403	−	0.140529i	−0.373337	−	0.927696i	$-0.621786\pi$
$257$	3.90205	−	2.25285i	0.243403	−	0.140529i	0.616740	+	0.787167i	$0.288453\pi$
$258$		0			0
$259$	1.22669	+	0.708231i	0.0762229	+	0.0440073i
$260$		0			0
$261$	3.07646	+	23.1911i	0.190428	+	1.43549i
$262$		0			0
$263$	−9.92767	+	17.1952i	−0.612166	+	1.06030i	0.378708	+	0.925516i	$0.376368\pi$
$263$	−9.92767	+	17.1952i	−0.612166	+	1.06030i	−0.990875	+	0.134787i	$0.956965\pi$
$264$		0			0
$265$	2.52009	+	4.36492i	0.154808	+	0.268135i
$266$		0			0
$267$	−1.83805	+	3.73184i	−0.112487	+	0.228385i
$268$		0			0
$269$		−	31.3938i		−	1.91411i	−0.289901	−	0.957057i	$-0.593622\pi$
$269$		−	31.3938i		−	1.91411i	0.289901	−	0.957057i	$-0.406378\pi$
$270$		0			0
$271$		−	0.868217i		−	0.0527405i	−0.999652	−	0.0263702i	$-0.991605\pi$
$271$		−	0.868217i		−	0.0527405i	0.999652	−	0.0263702i	$-0.00839488\pi$
$272$		0			0
$273$	0.490752	−	0.996386i	0.0297017	−	0.0603040i
$274$		0			0
$275$	0.467861	+	0.810358i	0.0282131	+	0.0488664i
$276$		0			0
$277$	2.25608	−	3.90765i	0.135555	−	0.234788i	−0.790254	−	0.612779i	$-0.790052\pi$
$277$	2.25608	−	3.90765i	0.135555	−	0.234788i	0.925809	+	0.377991i	$0.123385\pi$
$278$		0			0
$279$	6.74923	+	2.78782i	0.404066	+	0.166902i
$280$		0			0
$281$	24.6156	+	14.2118i	1.46844	+	0.847805i	0.999375	−	0.0353583i	$-0.0112572\pi$
$281$	24.6156	+	14.2118i	1.46844	+	0.847805i	0.469066	+	0.883163i	$0.344591\pi$
$282$		0			0
$283$	−3.92629	+	2.26684i	−0.233394	+	0.134750i	−0.612137	−	0.790752i	$-0.709690\pi$
$283$	−3.92629	+	2.26684i	−0.233394	+	0.134750i	0.378743	+	0.925502i	$0.376356\pi$
$284$		0			0
$285$	1.92862	+	29.2042i	0.114242	+	1.72991i
$286$		0			0
$287$	−0.475011			−0.0280390
$288$		0			0
$289$	−10.7962			−0.635069
$290$		0			0
$291$	−2.60178	+	1.74031i	−0.152519	+	0.102019i
$292$		0			0
$293$	−13.2072	+	7.62516i	−0.771570	+	0.445466i	−0.833435	−	0.552618i	$-0.813629\pi$
$293$	−13.2072	+	7.62516i	−0.771570	+	0.445466i	0.0618642	+	0.998085i	$0.480295\pi$
$294$		0			0
$295$	19.9861	+	11.5390i	1.16364	+	0.671827i
$296$		0			0
$297$	−7.72801	−	2.61055i	−0.448425	−	0.151479i
$298$		0			0
$299$	10.3393	−	17.9082i	0.597937	−	1.03566i
$300$		0			0
$301$	−0.327789	−	0.567747i	−0.0188934	−	0.0327244i
$302$		0			0
$303$	3.42660	+	5.12279i	0.196853	+	0.294296i
$304$		0			0
$305$			29.8833i			1.71111i
$306$		0			0
$307$		−	6.85996i		−	0.391519i	−0.980652	−	0.195759i	$-0.937283\pi$
$307$		−	6.85996i		−	0.391519i	0.980652	−	0.195759i	$-0.0627171\pi$
$308$		0			0
$309$	16.5268	−	1.09142i	0.940175	−	0.0620885i
$310$		0			0
$311$	12.1876	+	21.1096i	0.691097	+	1.19702i	0.971479	+	0.237127i	$0.0762058\pi$
$311$	12.1876	+	21.1096i	0.691097	+	1.19702i	−0.280381	+	0.959889i	$0.590461\pi$
$312$		0			0
$313$	3.96030	−	6.85944i	0.223849	−	0.387719i	−0.732124	−	0.681171i	$-0.761471\pi$
$313$	3.96030	−	6.85944i	0.223849	−	0.387719i	0.955974	+	0.293453i	$0.0948043\pi$
$314$		0			0
$315$	−0.636816	−	0.828221i	−0.0358805	−	0.0466650i
$316$		0			0
$317$	−17.4030	−	10.0476i	−0.977447	−	0.564329i	−0.0759487	−	0.997112i	$-0.524199\pi$
$317$	−17.4030	−	10.0476i	−0.977447	−	0.564329i	−0.901498	+	0.432782i	$0.857532\pi$
$318$		0			0
$319$	10.6015	−	6.12080i	0.593572	−	0.342699i
$320$		0			0
$321$	8.70619	+	4.28807i	0.485932	+	0.239337i
$322$		0			0
$323$	−42.4523			−2.36211
$324$		0			0
$325$	2.30335			0.127767
$326$		0			0
$327$	−11.7600	−	5.79219i	−0.650332	−	0.320309i
$328$		0			0
$329$	1.05971	−	0.611826i	0.0584239	−	0.0337310i
$330$		0			0
$331$	−11.2223	−	6.47921i	−0.616835	−	0.356130i	0.158801	−	0.987311i	$-0.449237\pi$
$331$	−11.2223	−	6.47921i	−0.616835	−	0.356130i	−0.775636	+	0.631181i	$0.782571\pi$
$332$		0			0
$333$	−15.6086	−	20.3000i	−0.855346	−	1.11243i
$334$		0			0
$335$	−1.76528	+	3.05756i	−0.0964477	+	0.167052i
$336$		0			0
$337$	−6.96429	−	12.0625i	−0.379369	−	0.657086i	0.611602	−	0.791166i	$-0.290526\pi$
$337$	−6.96429	−	12.0625i	−0.379369	−	0.657086i	−0.990971	+	0.134080i	$0.957192\pi$
$338$		0			0
$339$	−0.988095	+	0.0652531i	−0.0536660	+	0.00354406i
$340$		0			0
$341$		−	3.82111i		−	0.206925i
$342$		0			0
$343$			2.31868i			0.125197i
$344$		0			0
$345$	−10.8143	−	16.1675i	−0.582223	−	0.870427i
$346$		0			0
$347$	17.0232	+	29.4851i	0.913854	+	1.58284i	0.808570	+	0.588399i	$0.200242\pi$
$347$	17.0232	+	29.4851i	0.913854	+	1.58284i	0.105284	+	0.994442i	$0.466425\pi$
$348$		0			0
$349$	−0.599892	+	1.03904i	−0.0321115	+	0.0556188i	−0.881635	−	0.471933i	$-0.843557\pi$
$349$	−0.599892	+	1.03904i	−0.0321115	+	0.0556188i	0.849523	+	0.527552i	$0.176890\pi$
$350$		0			0
$351$	−15.0767	+	13.2614i	−0.804733	+	0.707843i
$352$		0			0
$353$	19.6933	+	11.3699i	1.04817	+	0.605159i	0.922135	−	0.386867i	$-0.126443\pi$
$353$	19.6933	+	11.3699i	1.04817	+	0.605159i	0.126031	+	0.992026i	$0.459776\pi$
$354$		0			0
$355$	22.8391	−	13.1862i	1.21218	−	0.699850i
$356$		0			0
$357$	1.25957	−	0.842520i	0.0666637	−	0.0445909i
$358$		0			0
$359$	21.5652			1.13817			0.569083	−	0.822280i	$-0.307298\pi$
$359$	21.5652			1.13817			0.569083	+	0.822280i	$0.307298\pi$
$360$		0			0
$361$	−45.8363			−2.41244
$362$		0			0
$363$	−0.974216	−	14.7521i	−0.0511331	−	0.774283i
$364$		0			0
$365$	19.0245	−	10.9838i	0.995786	−	0.574917i
$366$		0			0
$367$	−28.0399	−	16.1889i	−1.46367	−	0.845051i	−0.464493	−	0.885577i	$-0.653764\pi$
$367$	−28.0399	−	16.1889i	−1.46367	−	0.845051i	−0.999179	+	0.0405253i	$0.987097\pi$
$368$		0			0
$369$	7.93689	+	3.27839i	0.413178	+	0.170666i
$370$		0			0
$371$	0.199280	−	0.345163i	0.0103461	−	0.0179199i
$372$		0			0
$373$	5.19629	+	9.00024i	0.269054	+	0.466015i	0.968618	−	0.248555i	$-0.0799557\pi$
$373$	5.19629	+	9.00024i	0.269054	+	0.466015i	−0.699564	+	0.714570i	$0.746622\pi$
$374$		0			0
$375$	8.98741	−	18.2474i	0.464108	−	0.942290i
$376$		0			0
$377$		−	30.1336i		−	1.55196i
$378$		0			0
$379$		−	20.1762i		−	1.03638i	−0.855265	−	0.518190i	$-0.826606\pi$
$379$		−	20.1762i		−	1.03638i	0.855265	−	0.518190i	$-0.173394\pi$
$380$		0			0
$381$	−10.7477	+	21.8214i	−0.550624	+	1.11795i
$382$		0			0
$383$	−11.8556	−	20.5344i	−0.605791	−	1.04926i	−0.991926	−	0.126818i	$-0.959524\pi$
$383$	−11.8556	−	20.5344i	−0.605791	−	1.04926i	0.386135	−	0.922442i	$-0.373810\pi$
$384$		0			0
$385$	−0.273343	+	0.473444i	−0.0139308	+	0.0241289i
$386$		0			0
$387$	1.55855	+	11.7487i	0.0792255	+	0.597220i
$388$		0			0
$389$	1.76371	+	1.01828i	0.0894236	+	0.0516288i	0.544045	−	0.839056i	$-0.316892\pi$
$389$	1.76371	+	1.01828i	0.0894236	+	0.0516288i	−0.454621	+	0.890685i	$0.650225\pi$
$390$		0			0
$391$	24.4332	−	14.1065i	1.23564	−	0.713399i
$392$		0			0
$393$	0.159751	+	2.41904i	0.00805840	+	0.122024i
$394$		0			0
$395$	15.3076			0.770209
$396$		0			0
$397$	1.74252			0.0874547			0.0437274	−	0.999044i	$-0.486077\pi$
$397$	1.74252			0.0874547			0.0437274	+	0.999044i	$0.486077\pi$
$398$		0			0
$399$	1.92371	−	1.28676i	0.0963061	−	0.0644184i
$400$		0			0
$401$	20.4143	−	11.7862i	1.01944	−	0.588574i	0.105498	−	0.994419i	$-0.466356\pi$
$401$	20.4143	−	11.7862i	1.01944	−	0.588574i	0.913942	+	0.405846i	$0.133023\pi$
$402$		0			0
$403$	−8.14580	−	4.70298i	−0.405771	−	0.234272i
$404$		0			0
$405$	4.92433	+	18.2337i	0.244692	+	0.906042i
$406$		0			0
$407$	−6.69973	+	11.6043i	−0.332093	+	0.575202i
$408$		0			0
$409$	−10.8999	−	18.8792i	−0.538965	−	0.933515i	−0.998960	−	0.0455934i	$-0.985482\pi$
$409$	−10.8999	−	18.8792i	−0.538965	−	0.933515i	0.459995	−	0.887922i	$-0.347851\pi$
$410$		0			0
$411$	1.35078	+	2.01942i	0.0666289	+	0.0996107i
$412$		0			0
$413$		−	1.82493i		−	0.0897988i
$414$		0			0
$415$		−	5.68143i		−	0.278891i
$416$		0			0
$417$	37.2450	−	2.45963i	1.82389	−	0.120449i
$418$		0			0
$419$	−10.5076	−	18.1997i	−0.513329	−	0.889112i	−0.999880	−	0.0154599i	$-0.995079\pi$
$419$	−10.5076	−	18.1997i	−0.513329	−	0.889112i	0.486552	−	0.873652i	$-0.338255\pi$
$420$		0			0
$421$	6.86839	−	11.8964i	0.334745	−	0.579795i	−0.648691	−	0.761052i	$-0.724683\pi$
$421$	6.86839	−	11.8964i	0.334745	−	0.579795i	0.983436	+	0.181257i	$0.0580166\pi$
$422$		0			0
$423$	−21.9292	+	2.90907i	−1.06624	+	0.141444i
$424$		0			0
$425$	2.72157	+	1.57130i	0.132016	+	0.0762192i
$426$		0			0
$427$	2.04648	−	1.18153i	0.0990360	−	0.0571784i
$428$		0			0
$429$	9.42563	+	4.64242i	0.455074	+	0.224138i
$430$		0			0
$431$	−0.476344			−0.0229447			−0.0114723	−	0.999934i	$-0.503652\pi$
$431$	−0.476344			−0.0229447			−0.0114723	+	0.999934i	$0.503652\pi$
$432$		0			0
$433$	−11.6601			−0.560348			−0.280174	−	0.959949i	$-0.590392\pi$
$433$	−11.6601			−0.560348			−0.280174	+	0.959949i	$0.590392\pi$
$434$		0			0
$435$	−25.4276	−	12.5239i	−1.21916	−	0.600475i
$436$		0			0
$437$	37.3162	−	21.5445i	1.78508	−	1.03061i
$438$		0			0
$439$	−29.8138	−	17.2130i	−1.42294	−	0.821533i	−0.426387	−	0.904541i	$-0.640214\pi$
$439$	−29.8138	−	17.2130i	−1.42294	−	0.821533i	−0.996549	+	0.0830082i	$0.973547\pi$
$440$		0			0
$441$	7.98565	−	19.3330i	0.380269	−	0.920621i
$442$		0			0
$443$	−4.84473	+	8.39132i	−0.230180	+	0.398684i	−0.957861	−	0.287232i	$-0.907265\pi$
$443$	−4.84473	+	8.39132i	−0.230180	+	0.398684i	0.727681	+	0.685916i	$0.240598\pi$
$444$		0			0
$445$	−2.52009	−	4.36492i	−0.119464	−	0.206917i
$446$		0			0
$447$	−10.1831	+	0.672484i	−0.481643	+	0.0318074i
$448$		0			0
$449$			17.9789i			0.848477i	0.905550	+	0.424239i	$0.139458\pi$
$449$			17.9789i			0.848477i	−0.905550	+	0.424239i	$0.860542\pi$
$450$		0			0
$451$		−	4.49352i		−	0.211591i
$452$		0			0
$453$	7.63609	+	11.4160i	0.358775	+	0.536371i
$454$		0			0
$455$	0.672854	+	1.16542i	0.0315439	+	0.0546356i
$456$		0			0
$457$	6.95237	−	12.0419i	0.325218	−	0.563295i	−0.656338	−	0.754467i	$-0.727896\pi$
$457$	6.95237	−	12.0419i	0.325218	−	0.563295i	0.981557	+	0.191172i	$0.0612289\pi$
$458$		0			0
$459$	−26.8609	+	5.38433i	−1.25376	+	0.251319i
$460$		0			0
$461$	−1.80521	−	1.04224i	−0.0840772	−	0.0485420i	0.457372	−	0.889275i	$-0.348791\pi$
$461$	−1.80521	−	1.04224i	−0.0840772	−	0.0485420i	−0.541449	+	0.840733i	$0.682124\pi$
$462$		0			0
$463$	31.0337	−	17.9173i	1.44226	−	0.832688i	0.444258	−	0.895899i	$-0.353467\pi$
$463$	31.0337	−	17.9173i	1.44226	−	0.832688i	0.998000	+	0.0632104i	$0.0201339\pi$
$464$		0			0
$465$	−7.35400	+	4.91904i	−0.341034	+	0.228115i
$466$		0			0
$467$	25.4185			1.17623			0.588114	−	0.808778i	$-0.299871\pi$
$467$	25.4185			1.17623			0.588114	+	0.808778i	$0.299871\pi$
$468$		0			0
$469$	0.279185			0.0128915
$470$		0			0
$471$	−0.229142	−	3.46979i	−0.0105583	−	0.159879i
$472$		0			0
$473$	5.37078	−	3.10082i	0.246949	−	0.142576i
$474$		0			0
$475$	4.15658	+	2.39980i	0.190717	+	0.110110i
$476$		0			0
$477$	−5.71195	+	4.39190i	−0.261532	+	0.201091i
$478$		0			0
$479$	−11.4545	+	19.8398i	−0.523370	+	0.906503i	0.476260	+	0.879304i	$0.341992\pi$
$479$	−11.4545	+	19.8398i	−0.523370	+	0.906503i	−0.999630	+	0.0271987i	$0.991341\pi$
$480$		0			0
$481$	16.4919	+	28.5648i	0.751965	+	1.30244i
$482$		0			0
$483$	−0.679605	+	1.37982i	−0.0309231	+	0.0627840i
$484$		0			0
$485$		−	3.79251i		−	0.172209i
$486$		0			0
$487$			15.6846i			0.710738i	0.934726	+	0.355369i	$0.115645\pi$
$487$			15.6846i			0.710738i	−0.934726	+	0.355369i	$0.884355\pi$
$488$		0			0
$489$	1.57679	−	3.20139i	0.0713049	−	0.144772i
$490$		0			0
$491$	12.2976	+	21.3001i	0.554982	+	0.961258i	0.997905	+	0.0646979i	$0.0206084\pi$
$491$	12.2976	+	21.3001i	0.554982	+	0.961258i	−0.442922	+	0.896560i	$0.646058\pi$
$492$		0			0
$493$	20.5566	−	35.6050i	0.925821	−	1.60357i
$494$		0			0
$495$	7.83482	−	6.02417i	0.352149	−	0.270766i
$496$		0			0
$497$	−1.80604	−	1.04272i	−0.0810118	−	0.0467722i
$498$		0			0
$499$	−5.96333	+	3.44293i	−0.266955	+	0.154127i	−0.627503	−	0.778614i	$-0.715923\pi$
$499$	−5.96333	+	3.44293i	−0.266955	+	0.154127i	0.360548	+	0.932741i	$0.382590\pi$
$500$		0			0
$501$	2.15802	+	32.6778i	0.0964132	+	1.45994i
$502$		0			0
$503$	17.6347			0.786294			0.393147	−	0.919476i	$-0.371386\pi$
$503$	17.6347			0.786294			0.393147	+	0.919476i	$0.371386\pi$
$504$		0			0
$505$	−7.46729			−0.332290
$506$		0			0
$507$	2.78186	−	1.86076i	0.123547	−	0.0826394i
$508$		0			0
$509$	−14.1218	+	8.15320i	−0.625936	+	0.361384i	−0.779177	−	0.626805i	$-0.784362\pi$
$509$	−14.1218	+	8.15320i	−0.625936	+	0.361384i	0.153240	+	0.988189i	$0.451029\pi$
$510$		0			0
$511$	−1.50439	−	0.868558i	−0.0665502	−	0.0384228i
$512$		0			0
$513$	−41.0238	+	8.22333i	−1.81125	+	0.363069i
$514$		0			0
$515$	−10.0337	+	17.3789i	−0.442139	+	0.765807i
$516$		0			0
$517$	5.78776	+	10.0247i	0.254545	+	0.440885i
$518$		0			0
$519$	−10.3395	−	15.4576i	−0.453853	−	0.678514i
$520$		0			0
$521$		−	9.44397i		−	0.413748i	−0.978368	−	0.206874i	$-0.933671\pi$
$521$		−	9.44397i		−	0.413748i	0.978368	−	0.206874i	$-0.0663290\pi$
$522$		0			0
$523$			22.5688i			0.986865i	0.869784	+	0.493433i	$0.164258\pi$
$523$			22.5688i			0.986865i	−0.869784	+	0.493433i	$0.835742\pi$
$524$		0			0
$525$	−0.170954	+	0.0112897i	−0.00746105	+	0.000492722i
$526$		0			0
$527$	−6.41656	−	11.1138i	−0.279510	−	0.484125i
$528$		0			0
$529$	−2.81812	+	4.88113i	−0.122527	+	0.212223i
$530$		0			0
$531$	−12.5951	+	30.4924i	−0.546582	+	1.32326i
$532$		0			0
$533$	−9.57922	−	5.53056i	−0.414922	−	0.239555i
$534$		0			0
$535$	−10.1831	+	5.87924i	−0.440256	+	0.254182i
$536$		0			0
$537$	35.3876	+	17.4295i	1.52709	+	0.752139i
$538$		0			0
$539$	−10.9455			−0.471457
$540$		0			0
$541$	−32.0491			−1.37790			−0.688950	−	0.724809i	$-0.741928\pi$
$541$	−32.0491			−1.37790			−0.688950	+	0.724809i	$0.741928\pi$
$542$		0			0
$543$	−15.1151	−	7.44468i	−0.648652	−	0.319482i
$544$		0			0
$545$	13.7551	−	7.94149i	0.589202	−	0.340176i
$546$		0			0
$547$	14.6339	+	8.44889i	0.625701	+	0.361249i	0.779085	−	0.626918i	$-0.215684\pi$
$547$	14.6339	+	8.44889i	0.625701	+	0.361249i	−0.153384	+	0.988167i	$0.549017\pi$
$548$		0			0
$549$	−42.3489	+	5.61788i	−1.80741	+	0.239765i
$550$		0			0
$551$	31.3955	−	54.3786i	1.33749	−	2.31660i
$552$		0			0
$553$	−0.605235	−	1.04830i	−0.0257372	−	0.0445782i
$554$		0			0
$555$	30.9580	−	2.04445i	1.31409	−	0.0867819i
$556$		0			0
$557$		−	32.6034i		−	1.38145i	−0.723118	−	0.690725i	$-0.757292\pi$
$557$		−	32.6034i		−	1.38145i	0.723118	−	0.690725i	$-0.242708\pi$
$558$		0			0
$559$		−	15.2658i		−	0.645675i
$560$		0			0
$561$	7.97008	+	11.9153i	0.336497	+	0.503066i
$562$		0			0
$563$	7.58426	+	13.1363i	0.319639	+	0.553630i	0.980413	−	0.196955i	$-0.0631052\pi$
$563$	7.58426	+	13.1363i	0.319639	+	0.553630i	−0.660774	+	0.750585i	$0.729772\pi$
$564$		0			0
$565$	0.599892	−	1.03904i	0.0252377	−	0.0437129i
$566$		0			0
$567$	1.05399	−	1.05816i	0.0442633	−	0.0444385i
$568$		0			0
$569$	−4.18052	−	2.41363i	−0.175257	−	0.101184i	0.409806	−	0.912173i	$-0.365597\pi$
$569$	−4.18052	−	2.41363i	−0.175257	−	0.101184i	−0.585062	+	0.810988i	$0.698930\pi$
$570$		0			0
$571$	4.07311	−	2.35161i	0.170454	−	0.0984118i	−0.412346	−	0.911027i	$-0.635290\pi$
$571$	4.07311	−	2.35161i	0.170454	−	0.0984118i	0.582800	+	0.812616i	$0.301957\pi$
$572$		0			0
$573$	−3.66858	+	2.45389i	−0.153257	+	0.102513i
$574$		0			0
$575$	−3.18973			−0.133021
$576$		0			0
$577$	−19.5812			−0.815175			−0.407587	−	0.913166i	$-0.633630\pi$
$577$	−19.5812			−0.815175			−0.407587	+	0.913166i	$0.633630\pi$
$578$		0			0
$579$	0.570598	+	8.64029i	0.0237133	+	0.359078i
$580$		0			0
$581$	−0.389077	+	0.224634i	−0.0161416	+	0.00931938i
$582$		0			0
$583$	3.26517	+	1.88515i	0.135230	+	0.0780749i
$584$		0			0
$585$	−3.19924	−	24.1166i	−0.132272	−	0.997100i
$586$		0			0
$587$	−8.83368	+	15.3004i	−0.364605	+	0.631515i	−0.988713	−	0.149824i	$-0.952129\pi$
$587$	−8.83368	+	15.3004i	−0.364605	+	0.631515i	0.624108	+	0.781338i	$0.285463\pi$
$588$		0			0
$589$	−9.79984	−	16.9738i	−0.403795	−	0.699394i
$590$		0			0
$591$	4.32919	−	8.78966i	0.178079	−	0.361558i
$592$		0			0
$593$			14.1557i			0.581307i	0.956828	+	0.290653i	$0.0938727\pi$
$593$			14.1557i			0.581307i	−0.956828	+	0.290653i	$0.906127\pi$
$594$		0			0
$595$			1.83603i			0.0752700i
$596$		0			0
$597$	11.0749	−	22.4856i	0.453264	−	0.920273i
$598$		0			0
$599$	13.3209	+	23.0726i	0.544279	+	0.942719i	0.998652	+	0.0519076i	$0.0165301\pi$
$599$	13.3209	+	23.0726i	0.544279	+	0.942719i	−0.454373	+	0.890812i	$0.650137\pi$
$600$		0			0
$601$	−12.2321	+	21.1866i	−0.498959	+	0.864221i	−0.999999	−	0.00120220i	$-0.999617\pi$
$601$	−12.2321	+	21.1866i	−0.498959	+	0.864221i	0.501041	+	0.865424i	$0.332951\pi$
$602$		0			0
$603$	−4.66485	−	1.92685i	−0.189968	−	0.0784675i
$604$		0			0
$605$	15.5127	+	8.95628i	0.630682	+	0.364124i
$606$		0			0
$607$	24.5942	−	14.1995i	0.998247	−	0.576338i	0.0905181	−	0.995895i	$-0.471148\pi$
$607$	24.5942	−	14.1995i	0.998247	−	0.576338i	0.907729	+	0.419556i	$0.137814\pi$
$608$		0			0
$609$	0.147698	+	2.23651i	0.00598501	+	0.0906280i
$610$		0			0
$611$	28.4940			1.15274
$612$		0			0
$613$	−6.79923			−0.274618			−0.137309	−	0.990528i	$-0.543845\pi$
$613$	−6.79923			−0.274618			−0.137309	+	0.990528i	$0.543845\pi$
$614$		0			0
$615$	−8.64809	+	5.78465i	−0.348725	+	0.233260i
$616$		0			0
$617$	−32.6817	+	18.8688i	−1.31571	+	0.759628i	−0.983036	−	0.183412i	$-0.941286\pi$
$617$	−32.6817	+	18.8688i	−1.31571	+	0.759628i	−0.332678	+	0.943040i	$0.607952\pi$
$618$		0			0
$619$	−7.89600	−	4.55876i	−0.317367	−	0.183232i	0.332851	−	0.942979i	$-0.391989\pi$
$619$	−7.89600	−	4.55876i	−0.317367	−	0.183232i	−0.650218	+	0.759747i	$0.725323\pi$
$620$		0			0
$621$	20.8785	−	18.3648i	0.837827	−	0.736953i
$622$		0			0
$623$	−0.199280	+	0.345163i	−0.00798397	+	0.0138286i
$624$		0			0
$625$	10.8322	+	18.7619i	0.433287	+	0.750475i
$626$		0			0
$627$	12.1725	+	18.1980i	0.486122	+	0.726756i
$628$		0			0
$629$			45.0018i			1.79434i
$630$		0			0
$631$		−	9.05133i		−	0.360328i	−0.983637	−	0.180164i	$-0.942337\pi$
$631$		−	9.05133i		−	0.360328i	0.983637	−	0.180164i	$-0.0576628\pi$
$632$		0			0
$633$	−25.4086	+	1.67797i	−1.00990	+	0.0666931i
$634$		0			0
$635$	−14.7359	−	25.5233i	−0.584776	−	1.01286i
$636$		0			0
$637$	−13.4716	+	23.3335i	−0.533764	+	0.924507i
$638$		0			0
$639$	22.9803	+	29.8873i	0.909086	+	1.18232i
$640$		0			0
$641$	−27.1865	−	15.6961i	−1.07380	−	0.619959i	−0.144583	−	0.989493i	$-0.546184\pi$
$641$	−27.1865	−	15.6961i	−1.07380	−	0.619959i	−0.929217	+	0.369533i	$0.879518\pi$
$642$		0			0
$643$	6.03917	−	3.48672i	0.238162	−	0.137503i	−0.376170	−	0.926551i	$-0.622759\pi$
$643$	6.03917	−	3.48672i	0.238162	−	0.137503i	0.614332	+	0.789048i	$0.289426\pi$
$644$		0			0
$645$	−12.8817	−	6.34466i	−0.507218	−	0.249821i
$646$		0			0
$647$	−36.4189			−1.43178			−0.715888	−	0.698215i	$-0.753978\pi$
$647$	−36.4189			−1.43178			−0.715888	+	0.698215i	$0.753978\pi$
$648$		0			0
$649$	17.2635			0.677650
$650$		0			0
$651$	0.627631	+	0.309128i	0.0245988	+	0.0121157i
$652$		0			0
$653$	−27.9837	+	16.1564i	−1.09509	+	0.632248i	−0.934926	−	0.354843i	$-0.884534\pi$
$653$	−27.9837	+	16.1564i	−1.09509	+	0.632248i	−0.160159	+	0.987091i	$0.551201\pi$
$654$		0			0
$655$	−2.54377	−	1.46865i	−0.0993933	−	0.0573847i
$656$		0			0
$657$	19.1420	+	24.8955i	0.746802	+	0.971264i
$658$		0			0
$659$	−2.52870	+	4.37984i	−0.0985042	+	0.170614i	−0.911066	−	0.412261i	$-0.864739\pi$
$659$	−2.52870	+	4.37984i	−0.0985042	+	0.170614i	0.812562	+	0.582875i	$0.198072\pi$
$660$		0			0
$661$	6.31245	+	10.9335i	0.245526	+	0.425263i	0.962279	−	0.272063i	$-0.0877060\pi$
$661$	6.31245	+	10.9335i	0.245526	+	0.425263i	−0.716753	+	0.697327i	$0.754373\pi$
$662$		0			0
$663$	35.2104	−	2.32527i	1.36746	−	0.0903061i
$664$		0			0
$665$			2.80412i			0.108739i
$666$		0			0
$667$			41.7298i			1.61578i
$668$		0			0
$669$	−17.4277	−	26.0545i	−0.673793	−	1.00733i
$670$		0			0
$671$	11.1771	+	19.3593i	0.431487	+	0.747357i
$672$		0			0
$673$	23.5547	−	40.7980i	0.907967	−	1.57265i	0.0910837	−	0.995843i	$-0.470967\pi$
$673$	23.5547	−	40.7980i	0.907967	−	1.57265i	0.816884	−	0.576802i	$-0.195700\pi$
$674$		0			0
$675$	2.93436	+	0.991238i	0.112944	+	0.0381528i
$676$		0			0
$677$	16.1335	+	9.31465i	0.620059	+	0.357991i	0.776892	−	0.629634i	$-0.216795\pi$
$677$	16.1335	+	9.31465i	0.620059	+	0.357991i	−0.156833	+	0.987625i	$0.550128\pi$
$678$		0			0
$679$	−0.259719	+	0.149949i	−0.00996712	+	0.00575452i
$680$		0			0
$681$	−18.1263	+	12.1246i	−0.694602	+	0.464614i
$682$		0			0
$683$	−15.4857			−0.592544			−0.296272	−	0.955104i	$-0.595743\pi$
$683$	−15.4857			−0.592544			−0.296272	+	0.955104i	$0.595743\pi$
$684$		0			0
$685$	−2.94363			−0.112470
$686$		0			0
$687$	−1.41526	−	21.4306i	−0.0539955	−	0.817627i
$688$		0			0
$689$	8.03747	−	4.64044i	0.306203	−	0.176787i
$690$		0			0
$691$	−9.34942	−	5.39789i	−0.355669	−	0.205345i	0.311510	−	0.950243i	$-0.399165\pi$
$691$	−9.34942	−	5.39789i	−0.355669	−	0.205345i	−0.667179	+	0.744897i	$0.732498\pi$
$692$		0			0
$693$	−0.722323	−	0.298361i	−0.0274388	−	0.0113338i
$694$		0			0
$695$	−22.6122	+	39.1654i	−0.857728	+	1.48563i
$696$		0			0
$697$	−7.54569	−	13.0695i	−0.285813	−	0.495043i
$698$		0			0
$699$	5.46087	−	11.0874i	0.206549	−	0.419362i
$700$		0			0
$701$		−	7.59493i		−	0.286857i	−0.989661	−	0.143428i	$-0.954187\pi$
$701$		−	7.59493i		−	0.286857i	0.989661	−	0.143428i	$-0.0458127\pi$
$702$		0			0
$703$			68.7300i			2.59220i
$704$		0			0
$705$	11.8425	−	24.0441i	0.446013	−	0.905552i
$706$		0			0
$707$	0.295243	+	0.511376i	0.0111038	+	0.0192323i
$708$		0			0
$709$	−11.5763	+	20.0508i	−0.434759	+	0.753024i	−0.997276	−	0.0737615i	$-0.976500\pi$
$709$	−11.5763	+	20.0508i	−0.434759	+	0.753024i	0.562517	+	0.826786i	$0.309833\pi$
$710$		0			0
$711$	2.87773	+	21.6930i	0.107923	+	0.813552i
$712$		0			0
$713$	11.2805	+	6.51280i	0.422458	+	0.243906i
$714$		0			0
$715$	−11.0246	+	6.36507i	−0.412298	+	0.238040i
$716$		0			0
$717$	−0.0625240	−	0.946771i	−0.00233500	−	0.0353578i
$718$		0			0
$719$	−7.49075			−0.279358			−0.139679	−	0.990197i	$-0.544607\pi$
$719$	−7.49075			−0.279358			−0.139679	+	0.990197i	$0.544607\pi$
$720$		0			0
$721$	1.58686			0.0590979
$722$		0			0
$723$	26.7431	−	17.8883i	0.994588	−	0.665273i
$724$		0			0
$725$	−4.02546	+	2.32410i	−0.149502	+	0.0863148i
$726$		0			0
$727$	−28.2968	−	16.3372i	−1.04947	−	0.605911i	−0.126969	−	0.991907i	$-0.540525\pi$
$727$	−28.2968	−	16.3372i	−1.04947	−	0.605911i	−0.922501	+	0.385995i	$0.873858\pi$
$728$		0			0
$729$	−24.9140	+	10.4063i	−0.922742	+	0.385418i
$730$		0			0
$731$	10.4140	−	18.0376i	0.385177	−	0.667146i
$732$		0			0
$733$	24.2248	+	41.9586i	0.894765	+	1.54978i	0.834095	+	0.551620i	$0.185990\pi$
$733$	24.2248	+	41.9586i	0.894765	+	1.54978i	0.0606693	+	0.998158i	$0.480676\pi$
$734$		0			0
$735$	14.0905	+	21.0654i	0.519736	+	0.777010i
$736$		0			0
$737$			2.64103i			0.0972838i
$738$		0			0
$739$		−	4.58382i		−	0.168619i	−0.996440	−	0.0843094i	$-0.973132\pi$
$739$		−	4.58382i		−	0.168619i	0.996440	−	0.0843094i	$-0.0268684\pi$
$740$		0			0
$741$	53.7759	−	3.55132i	1.97551	−	0.130461i
$742$		0			0
$743$	−18.5816	−	32.1842i	−0.681691	−	1.18072i	−0.974464	−	0.224542i	$-0.927911\pi$
$743$	−18.5816	−	32.1842i	−0.681691	−	1.18072i	0.292773	−	0.956182i	$-0.405422\pi$
$744$		0			0
$745$	6.18235	−	10.7082i	0.226504	−	0.392316i
$746$		0			0
$747$	8.05139	−	1.06807i	0.294585	−	0.0390788i
$748$		0			0
$749$	0.805247	+	0.464909i	0.0294231	+	0.0169874i
$750$		0			0
$751$	−31.1292	+	17.9724i	−1.13592	+	0.655824i	−0.945417	−	0.325863i	$-0.894345\pi$
$751$	−31.1292	+	17.9724i	−1.13592	+	0.655824i	−0.190503	+	0.981687i	$0.561012\pi$
$752$		0			0
$753$	−29.8350	−	14.6947i	−1.08725	−	0.535504i
$754$		0			0
$755$	−16.6407			−0.605617
$756$		0			0
$757$	−4.99097			−0.181400			−0.0907000	−	0.995878i	$-0.528910\pi$
$757$	−4.99097			−0.181400			−0.0907000	+	0.995878i	$0.528910\pi$
$758$		0			0
$759$	−13.0528	−	6.42894i	−0.473788	−	0.233356i
$760$		0			0
$761$	−10.0903	+	5.82561i	−0.365771	+	0.211178i	−0.671609	−	0.740905i	$-0.734397\pi$
$761$	−10.0903	+	5.82561i	−0.365771	+	0.211178i	0.305838	+	0.952084i	$0.401063\pi$
$762$		0			0
$763$	−1.08770	−	0.627985i	−0.0393774	−	0.0227346i
$764$		0			0
$765$	12.6718	−	30.6780i	0.458149	−	1.10916i
$766$		0			0
$767$	21.2477	−	36.8020i	0.767208	−	1.32884i
$768$		0			0
$769$	9.86238	+	17.0821i	0.355646	+	0.615998i	0.987228	−	0.159312i	$-0.0509274\pi$
$769$	9.86238	+	17.0821i	0.355646	+	0.615998i	−0.631582	+	0.775309i	$0.717594\pi$
$770$		0			0
$771$	−7.78714	+	0.514257i	−0.280447	+	0.0185205i
$772$		0			0
$773$			39.5946i			1.42412i	0.702120	+	0.712059i	$0.252237\pi$
$773$			39.5946i			1.42412i	−0.702120	+	0.712059i	$0.747763\pi$
$774$		0			0
$775$			1.45090i			0.0521177i
$776$		0			0
$777$	−1.36403	−	2.03924i	−0.0489344	−	0.0731573i
$778$		0			0
$779$	−11.5243	−	19.9607i	−0.412902	−	0.715167i
$780$		0			0
$781$	9.86390	−	17.0848i	0.352958	−	0.611341i
$782$		0			0
$783$	12.9679	−	38.3889i	0.463435	−	1.37191i
$784$		0			0
$785$	3.64870	+	2.10658i	0.130228	+	0.0751870i
$786$		0			0
$787$	19.6360	−	11.3369i	0.699949	−	0.404116i	−0.107379	−	0.994218i	$-0.534246\pi$
$787$	19.6360	−	11.3369i	0.699949	−	0.404116i	0.807329	+	0.590102i	$0.200913\pi$
$788$		0			0
$789$	28.5852	−	19.1204i	1.01766	−	0.680705i
$790$		0			0
$791$	−0.0948747			−0.00337336
$792$		0			0
$793$	55.0265			1.95405
$794$		0			0
$795$	−0.575260	−	8.71087i	−0.0204024	−	0.308943i
$796$		0			0
$797$	−1.38454	+	0.799367i	−0.0490431	+	0.0283150i	−0.524321	−	0.851521i	$-0.675681\pi$
$797$	−1.38454	+	0.799367i	−0.0490431	+	0.0283150i	0.475278	+	0.879836i	$0.342347\pi$
$798$		0			0
$799$	33.6677	+	19.4381i	1.19108	+	0.687669i
$800$		0			0
$801$	5.71195	−	4.39190i	0.201822	−	0.155180i
$802$		0			0
$803$	8.21640	−	14.2312i	0.289950	−	0.502209i
$804$		0			0
$805$	−0.931785	−	1.61390i	−0.0328411	−	0.0568825i
$806$		0			0
$807$	−24.0257	+	48.7799i	−0.845743	+	1.71713i
$808$		0			0
$809$		−	50.2740i		−	1.76754i	−0.467922	−	0.883770i	$-0.654997\pi$
$809$		−	50.2740i		−	1.76754i	0.467922	−	0.883770i	$-0.345003\pi$
$810$		0			0
$811$		−	36.5884i		−	1.28479i	−0.766372	−	0.642397i	$-0.777940\pi$
$811$		−	36.5884i		−	1.28479i	0.766372	−	0.642397i	$-0.222060\pi$
$812$		0			0
$813$	−0.664446	+	1.34904i	−0.0233032	+	0.0473130i
$814$		0			0
$815$	2.16188	+	3.74449i	0.0757275	+	0.131164i
$816$		0			0
$817$	15.9051	−	27.5484i	0.556448	−	0.963796i
$818$		0			0
$819$	−1.52507	+	1.17262i	−0.0532902	+	0.0409746i
$820$		0			0
$821$	−33.1310	−	19.1282i	−1.15628	−	0.667579i	−0.205871	−	0.978579i	$-0.566003\pi$
$821$	−33.1310	−	19.1282i	−1.15628	−	0.667579i	−0.950410	+	0.311000i	$0.899336\pi$
$822$		0			0
$823$	0.874309	−	0.504783i	0.0304765	−	0.0175956i	−0.484684	−	0.874689i	$-0.661066\pi$
$823$	0.874309	−	0.504783i	0.0304765	−	0.0175956i	0.515161	+	0.857094i	$0.327732\pi$
$824$		0			0
$825$	−0.106798	−	1.61719i	−0.00371824	−	0.0563035i
$826$		0			0
$827$	−6.17121			−0.214594			−0.107297	−	0.994227i	$-0.534220\pi$
$827$	−6.17121			−0.214594			−0.107297	+	0.994227i	$0.534220\pi$
$828$		0			0
$829$	−10.6949			−0.371450			−0.185725	−	0.982602i	$-0.559463\pi$
$829$	−10.6949			−0.371450			−0.185725	+	0.982602i	$0.559463\pi$
$830$		0			0
$831$	−6.49603	+	4.34515i	−0.225345	+	0.150732i
$832$		0			0
$833$	−31.8353	+	18.3801i	−1.10303	+	0.636834i
$834$		0			0
$835$	−34.3628	−	19.8394i	−1.18917	−	0.686569i
$836$		0			0
$837$	−8.35348	−	9.49691i	−0.288739	−	0.328261i
$838$		0			0
$839$	26.6888	−	46.2263i	0.921399	−	1.59591i	0.124147	−	0.992264i	$-0.460381\pi$
$839$	26.6888	−	46.2263i	0.921399	−	1.59591i	0.797252	−	0.603646i	$-0.206286\pi$
$840$		0			0
$841$	15.9051	+	27.5484i	0.548451	+	0.949945i
$842$		0			0
$843$	−27.3715	−	40.9207i	−0.942726	−	1.40938i
$844$		0			0
$845$			4.05500i			0.139496i
$846$		0			0
$847$		−	1.41646i		−	0.0486702i
$848$		0			0
$849$	7.83551	−	0.517451i	0.268914	−	0.0177589i
$850$		0			0
$851$	−22.8384	−	39.5572i	−0.782890	−	1.35600i
$852$		0			0
$853$	7.32038	−	12.6793i	0.250645	−	0.434130i	−0.713059	−	0.701104i	$-0.752691\pi$
$853$	7.32038	−	12.6793i	0.250645	−	0.434130i	0.963704	+	0.266975i	$0.0860240\pi$
$854$		0			0
$855$	19.3532	−	46.8536i	0.661867	−	1.60236i
$856$		0			0
$857$	−21.8376	−	12.6080i	−0.745959	−	0.430680i	0.0782730	−	0.996932i	$-0.475059\pi$
$857$	−21.8376	−	12.6080i	−0.745959	−	0.430680i	−0.824232	+	0.566252i	$0.808393\pi$
$858$		0			0
$859$	−3.77869	+	2.18163i	−0.128927	+	0.0744361i	−0.563076	−	0.826405i	$-0.690382\pi$
$859$	−3.77869	+	2.18163i	−0.128927	+	0.0744361i	0.434149	+	0.900841i	$0.357049\pi$
$860$		0			0
$861$	0.738076	+	0.363526i	0.0251535	+	0.0123889i
$862$		0			0
$863$	−36.7626			−1.25141			−0.625706	−	0.780059i	$-0.715189\pi$
$863$	−36.7626			−1.25141			−0.625706	+	0.780059i	$0.715189\pi$
$864$		0			0
$865$	22.5320			0.766110
$866$		0			0
$867$	16.7752	+	8.26231i	0.569715	+	0.280603i
$868$		0			0
$869$	9.91671	−	5.72541i	0.336401	−	0.194221i
$870$		0			0
$871$	5.63012	+	3.25055i	0.190769	+	0.110141i
$872$		0			0
$873$	5.37452	−	0.712968i	0.181900	−	0.0241303i
$874$		0			0
$875$	0.974408	−	1.68772i	0.0329410	−	0.0570555i
$876$		0			0
$877$	2.02843	+	3.51334i	0.0684951	+	0.118637i	0.898239	−	0.439507i	$-0.144847\pi$
$877$	2.02843	+	3.51334i	0.0684951	+	0.118637i	−0.829744	+	0.558144i	$0.811514\pi$
$878$		0			0
$879$	26.3569	−	1.74059i	0.888996	−	0.0587087i
$880$		0			0
$881$		−	29.5979i		−	0.997179i	−0.866838	−	0.498589i	$-0.833852\pi$
$881$		−	29.5979i		−	0.997179i	0.866838	−	0.498589i	$-0.166148\pi$
$882$		0			0
$883$			42.1894i			1.41979i	0.704309	+	0.709894i	$0.251257\pi$
$883$			42.1894i			1.41979i	−0.704309	+	0.709894i	$0.748743\pi$
$884$		0			0
$885$	−22.2238	−	33.2248i	−0.747045	−	1.11684i
$886$		0			0
$887$	15.1442	+	26.2305i	0.508491	+	0.880733i	0.999952	+	0.00983292i	$0.00312997\pi$
$887$	15.1442	+	26.2305i	0.508491	+	0.880733i	−0.491460	+	0.870900i	$0.663537\pi$
$888$		0			0
$889$	−1.16526	+	2.01829i	−0.0390816	+	0.0676913i
$890$		0			0
$891$	10.0100	+	9.97053i	0.335347	+	0.334025i
$892$		0			0
$893$	51.4198	+	29.6872i	1.72070	+	0.993445i
$894$		0			0
$895$	−41.3909	+	23.8970i	−1.38355	+	0.798790i
$896$		0			0
$897$	−29.7704	+	19.9132i	−0.994005	+	0.664883i
$898$		0			0
$899$	18.9814			0.633065
$900$		0			0
$901$	12.6625			0.421848
$902$		0			0
$903$	0.0748242	+	1.13303i	0.00248999	+	0.0377047i
$904$		0			0
$905$	17.6793	−	10.2072i	0.587681	−	0.339298i
$906$		0			0
$907$	20.8861	+	12.0586i	0.693510	+	0.400398i	0.804926	−	0.593376i	$-0.202205\pi$
$907$	20.8861	+	12.0586i	0.693510	+	0.400398i	−0.111416	+	0.993774i	$0.535538\pi$
$908$		0			0
$909$	−1.40380	−	10.5822i	−0.0465612	−	0.350989i
$910$		0			0
$911$	−10.0067	+	17.3322i	−0.331538	+	0.574241i	−0.982814	−	0.184600i	$-0.940901\pi$
$911$	−10.0067	+	17.3322i	−0.331538	+	0.574241i	0.651276	+	0.758841i	$0.274234\pi$
$912$		0			0
$913$	−2.12499	−	3.68060i	−0.0703270	−	0.121810i
$914$		0			0
$915$	22.8697	−	46.4329i	0.756049	−	1.53503i
$916$		0			0
$917$			0.232271i			0.00767025i
$918$		0			0
$919$			7.25070i			0.239178i	0.992823	+	0.119589i	$0.0381578\pi$
$919$			7.25070i			0.239178i	−0.992823	+	0.119589i	$0.961842\pi$
$920$		0			0
$921$	−5.24992	+	10.6591i	−0.172991	+	0.351228i
$922$		0			0
$923$	−24.2807	−	42.0555i	−0.799210	−	1.38427i
$924$		0			0
$925$	2.54392	−	4.40620i	0.0836436	−	0.144875i
$926$		0			0
$927$	−26.5147	−	10.9521i	−0.870856	−	0.359713i
$928$		0			0
$929$	−15.6167	−	9.01628i	−0.512366	−	0.295815i	0.221440	−	0.975174i	$-0.428924\pi$
$929$	−15.6167	−	9.01628i	−0.512366	−	0.295815i	−0.733806	+	0.679360i	$0.762258\pi$
$930$		0			0
$931$	−48.6212	+	28.0715i	−1.59350	+	0.920005i
$932$		0			0
$933$	−2.78207	−	42.1275i	−0.0910808	−	1.37919i
$934$		0			0
$935$	−17.3685			−0.568011
$936$		0			0
$937$	26.2806			0.858551			0.429276	−	0.903174i	$-0.358769\pi$
$937$	26.2806			0.858551			0.429276	+	0.903174i	$0.358769\pi$
$938$		0			0
$939$	−11.4031	+	7.62743i	−0.372125	+	0.248912i
$940$		0			0
$941$	−30.6987	+	17.7239i	−1.00075	+	0.577782i	−0.908469	−	0.417951i	$-0.862748\pi$
$941$	−30.6987	+	17.7239i	−1.00075	+	0.577782i	−0.0922782	+	0.995733i	$0.529415\pi$
$942$		0			0
$943$	13.2655	+	7.65886i	0.431986	+	0.249407i
$944$		0			0
$945$	0.355653	+	1.77425i	0.0115694	+	0.0577164i
$946$		0			0
$947$	10.1432	−	17.5686i	0.329610	−	0.570901i	−0.652824	−	0.757509i	$-0.726416\pi$
$947$	10.1432	−	17.5686i	0.329610	−	0.570901i	0.982434	+	0.186608i	$0.0597494\pi$
$948$		0			0
$949$	−20.2253	−	35.0312i	−0.656541	−	1.13716i
$950$		0			0
$951$	19.3514	+	28.9305i	0.627512	+	0.938136i
$952$		0			0
$953$			27.1172i			0.878411i	0.898387	+	0.439205i	$0.144740\pi$
$953$			27.1172i			0.878411i	−0.898387	+	0.439205i	$0.855260\pi$
$954$		0			0
$955$		−	5.34755i		−	0.173043i
$956$		0			0
$957$	−21.1570	+	1.39719i	−0.683908	+	0.0451648i
$958$		0			0
$959$	0.116386	+	0.201586i	0.00375830	+	0.00650956i
$960$		0			0
$961$	−12.5376	+	21.7157i	−0.404437	+	0.700506i
$962$		0			0
$963$	−10.2461	−	13.3257i	−0.330175	−	0.429414i
$964$		0			0
$965$	−9.08581	−	5.24569i	−0.292482	−	0.168865i
$966$		0			0
$967$	18.4921	−	10.6764i	0.594665	−	0.343330i	−0.172275	−	0.985049i	$-0.555112\pi$
$967$	18.4921	−	10.6764i	0.594665	−	0.343330i	0.766940	+	0.641719i	$0.221778\pi$
$968$		0			0
$969$	65.9627	+	32.4887i	2.11903	+	1.04369i
$970$		0			0
$971$	11.9224			0.382608			0.191304	−	0.981531i	$-0.438728\pi$
$971$	11.9224			0.382608			0.191304	+	0.981531i	$0.438728\pi$
$972$		0			0
$973$	3.57618			0.114647
$974$		0			0
$975$	−3.57896	−	1.76275i	−0.114618	−	0.0564532i
$976$		0			0
$977$	−16.3300	+	9.42812i	−0.522442	+	0.301632i	−0.737933	−	0.674874i	$-0.764198\pi$
$977$	−16.3300	+	9.42812i	−0.522442	+	0.301632i	0.215491	+	0.976506i	$0.430865\pi$
$978$		0			0
$979$	−3.26517	−	1.88515i	−0.104355	−	0.0602496i
$980$		0			0
$981$	13.8401	+	17.9999i	0.441879	+	0.574693i
$982$		0			0
$983$	−24.3810	+	42.2290i	−0.777632	+	1.34690i	0.155672	+	0.987809i	$0.450246\pi$
$983$	−24.3810	+	42.2290i	−0.777632	+	1.34690i	−0.933303	+	0.359089i	$0.883088\pi$
$984$		0			0
$985$	5.93561	+	10.2808i	0.189124	+	0.327573i
$986$		0			0
$987$	−2.11482	+	0.139661i	−0.0673155	+	0.00444547i
$988$		0			0
$989$			21.1405i			0.672228i
$990$		0			0
$991$		−	27.4703i		−	0.872622i	−0.899796	−	0.436311i	$-0.856285\pi$
$991$		−	27.4703i		−	0.872622i	0.899796	−	0.436311i	$-0.143715\pi$
$992$		0			0
$993$	12.4788	+	18.6559i	0.396002	+	0.592027i
$994$		0			0
$995$	15.1844	+	26.3001i	0.481377	+	0.833770i
$996$		0			0
$997$	−22.0675	+	38.2220i	−0.698885	+	1.21050i	0.269969	+	0.962869i	$0.412987\pi$
$997$	−22.0675	+	38.2220i	−0.698885	+	1.21050i	−0.968853	+	0.247635i	$0.920347\pi$
$998$		0			0
$999$	8.71718	+	43.4875i	0.275799	+	1.37588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.s.a.191.2	yes	24
3.2	odd	2		864.2.s.a.575.3		24
4.3	odd	2	inner	288.2.s.a.191.11	yes	24
8.3	odd	2		576.2.s.g.191.2		24
8.5	even	2		576.2.s.g.191.11		24
9.2	odd	6		2592.2.c.c.2591.6		24
9.4	even	3		864.2.s.a.287.4		24
9.5	odd	6	inner	288.2.s.a.95.11	yes	24
9.7	even	3		2592.2.c.c.2591.20		24
12.11	even	2		864.2.s.a.575.4		24
24.5	odd	2		1728.2.s.g.575.9		24
24.11	even	2		1728.2.s.g.575.10		24
36.7	odd	6		2592.2.c.c.2591.19		24
36.11	even	6		2592.2.c.c.2591.5		24
36.23	even	6	inner	288.2.s.a.95.2	✓	24
36.31	odd	6		864.2.s.a.287.3		24
72.5	odd	6		576.2.s.g.383.2		24
72.11	even	6		5184.2.c.m.5183.19		24
72.13	even	6		1728.2.s.g.1151.10		24
72.29	odd	6		5184.2.c.m.5183.20		24
72.43	odd	6		5184.2.c.m.5183.5		24
72.59	even	6		576.2.s.g.383.11		24
72.61	even	6		5184.2.c.m.5183.6		24
72.67	odd	6		1728.2.s.g.1151.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.2	✓	24	36.23	even	6	inner
288.2.s.a.95.11	yes	24	9.5	odd	6	inner
288.2.s.a.191.2	yes	24	1.1	even	1	trivial
288.2.s.a.191.11	yes	24	4.3	odd	2	inner
576.2.s.g.191.2		24	8.3	odd	2
576.2.s.g.191.11		24	8.5	even	2
576.2.s.g.383.2		24	72.5	odd	6
576.2.s.g.383.11		24	72.59	even	6
864.2.s.a.287.3		24	36.31	odd	6
864.2.s.a.287.4		24	9.4	even	3
864.2.s.a.575.3		24	3.2	odd	2
864.2.s.a.575.4		24	12.11	even	2
1728.2.s.g.575.9		24	24.5	odd	2
1728.2.s.g.575.10		24	24.11	even	2
1728.2.s.g.1151.9		24	72.67	odd	6
1728.2.s.g.1151.10		24	72.13	even	6
2592.2.c.c.2591.5		24	36.11	even	6
2592.2.c.c.2591.6		24	9.2	odd	6
2592.2.c.c.2591.19		24	36.7	odd	6
2592.2.c.c.2591.20		24	9.7	even	3
5184.2.c.m.5183.5		24	72.43	odd	6
5184.2.c.m.5183.6		24	72.61	even	6
5184.2.c.m.5183.19		24	72.11	even	6
5184.2.c.m.5183.20		24	72.29	odd	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55381 - 0.765299i) q^{3} +(1.81740 - 1.04928i) q^{5} +(-0.143714 - 0.0829731i) q^{7} +(1.82863 + 2.37826i) q^{9} +O(q^{10})\)	\(q+(-1.55381 - 0.765299i) q^{3} +(1.81740 - 1.04928i) q^{5} +(-0.143714 - 0.0829731i) q^{7} +(1.82863 + 2.37826i) q^{9} +(0.784910 - 1.35950i) q^{11} +(-1.93212 - 3.34652i) q^{13} +(-3.62690 + 0.239518i) q^{15} -5.27221i q^{17} -8.05210i q^{19} +(0.159804 + 0.238908i) q^{21} +(2.67564 + 4.63435i) q^{23} +(-0.298034 + 0.516211i) q^{25} +(-1.02127 - 5.09480i) q^{27} +(6.75334 + 3.89904i) q^{29} +(2.10800 - 1.21705i) q^{31} +(-2.26003 + 1.51172i) q^{33} -0.348247 q^{35} -8.53566 q^{37} +(0.441043 + 6.67850i) q^{39} +(2.47895 - 1.43122i) q^{41} +(3.42127 + 1.97527i) q^{43} +(5.81881 + 2.40350i) q^{45} +(-3.68689 + 6.38588i) q^{47} +(-3.48623 - 6.03833i) q^{49} +(-4.03482 + 8.19199i) q^{51} +2.40174i q^{53} -3.29435i q^{55} +(-6.16227 + 12.5114i) q^{57} +(5.49855 + 9.52376i) q^{59} +(-7.11998 + 12.3322i) q^{61} +(-0.0654683 - 0.493515i) q^{63} +(-7.02286 - 4.05465i) q^{65} +(-1.45698 + 0.841190i) q^{67} +(-0.610768 - 9.24855i) q^{69} +12.5669 q^{71} +10.4679 q^{73} +(0.858144 - 0.574006i) q^{75} +(-0.225605 + 0.130253i) q^{77} +(6.31710 + 3.64718i) q^{79} +(-2.31220 + 8.69792i) q^{81} +(1.35365 - 2.34460i) q^{83} +(-5.53201 - 9.58172i) q^{85} +(-7.50945 - 11.2267i) q^{87} -2.40174i q^{89} +0.641255i q^{91} +(-4.20684 + 0.277816i) q^{93} +(-8.44888 - 14.6339i) q^{95} +(0.903600 - 1.56508i) q^{97} +(4.66856 - 0.619318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} + 8 q^{21} + 12 q^{25} + 24 q^{29} - 20 q^{33} - 36 q^{41} - 8 q^{45} + 12 q^{49} - 36 q^{57} - 48 q^{65} - 16 q^{69} + 24 q^{73} - 48 q^{77} - 20 q^{81} - 64 q^{93} + 12 q^{97}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^21 + 12 * q^25 + 24 * q^29 - 20 * q^33 - 36 * q^41 - 8 * q^45 + 12 * q^49 - 36 * q^57 - 48 * q^65 - 16 * q^69 + 24 * q^73 - 48 * q^77 - 20 * q^81 - 64 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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