LMFDB - Embedded newform 288.2.s.a.95.2

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			95.2
Character	$\chi$	$=$	288.95
Dual form			288.2.s.a.191.2

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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	0.847916	−	0.530131i	$-0.177857\pi$
$5$	1.81740	+	1.04928i	0.812767	+	0.469251i	−0.0351491	+	0.999382i	$0.511191\pi$
$6$		0			0
$7$	−0.143714	+	0.0829731i	−0.0543187	+	0.0313609i	−0.526913	−	0.849919i	$-0.676651\pi$
$7$	−0.143714	+	0.0829731i	−0.0543187	+	0.0313609i	0.472595	+	0.881280i	$0.343317\pi$
$8$		0			0
$9$	1.82863	−	2.37826i	0.609544	−	0.792752i
$10$		0			0
$11$	0.784910	+	1.35950i	0.236659	+	0.409906i	0.959754	−	0.280843i	$-0.0906141\pi$
$11$	0.784910	+	1.35950i	0.236659	+	0.409906i	−0.723094	+	0.690749i	$0.757281\pi$
$12$		0			0
$13$	−1.93212	+	3.34652i	−0.535872	+	0.928158i	0.463248	+	0.886229i	$0.346684\pi$
$13$	−1.93212	+	3.34652i	−0.535872	+	0.928158i	−0.999121	+	0.0419297i	$0.986649\pi$
$14$		0			0
$15$	−3.62690	−	0.239518i	−0.936462	−	0.0618433i
$16$		0			0
$17$			5.27221i			1.27870i	0.768917	+	0.639349i	$0.220796\pi$
$17$			5.27221i			1.27870i	−0.768917	+	0.639349i	$0.779204\pi$
$18$		0			0
$19$			8.05210i			1.84728i	0.383264	+	0.923639i	$0.374800\pi$
$19$			8.05210i			1.84728i	−0.383264	+	0.923639i	$0.625200\pi$
$20$		0			0
$21$	0.159804	−	0.238908i	0.0348721	−	0.0521340i
$22$		0			0
$23$	2.67564	−	4.63435i	0.557910	−	0.966328i	−0.439761	−	0.898115i	$-0.644937\pi$
$23$	2.67564	−	4.63435i	0.557910	−	0.966328i	0.997671	−	0.0682135i	$-0.0217299\pi$
$24$		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	0.282150	−	0.959370i	$-0.408952\pi$
$29$	6.75334	−	3.89904i	1.25406	−	0.724034i	0.971914	+	0.235336i	$0.0756191\pi$
$30$		0			0
$31$	2.10800	+	1.21705i	0.378608	+	0.218589i	0.677212	−	0.735788i	$-0.263188\pi$
$31$	2.10800	+	1.21705i	0.378608	+	0.218589i	−0.298604	+	0.954377i	$0.596521\pi$
$32$		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	0.680923	−	0.732355i	$-0.261579\pi$
$41$	2.47895	+	1.43122i	0.387146	+	0.223519i	−0.293777	+	0.955874i	$0.594912\pi$
$42$		0			0
$43$	3.42127	−	1.97527i	0.521739	−	0.301226i	−0.215907	−	0.976414i	$-0.569271\pi$
$43$	3.42127	−	1.97527i	0.521739	−	0.301226i	0.737646	+	0.675188i	$0.235937\pi$
$44$		0			0
$45$	5.81881	−	2.40350i	0.867417	−	0.358293i
$46$		0			0
$47$	−3.68689	−	6.38588i	−0.537788	−	0.931477i	−0.999023	−	0.0441985i	$-0.985927\pi$
$47$	−3.68689	−	6.38588i	−0.537788	−	0.931477i	0.461234	−	0.887278i	$-0.347407\pi$
$48$		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	$-0.947253\pi$
$53$		−	2.40174i		−	0.329904i	0.986302	−	0.164952i	$-0.0527469\pi$
$54$		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	−0.246781	−	0.969071i	$-0.579373\pi$
$59$	5.49855	−	9.52376i	0.715850	−	1.23989i	0.962631	−	0.270817i	$-0.0872939\pi$
$60$		0			0
$61$	−7.11998	−	12.3322i	−0.911620	−	1.57897i	−0.811776	−	0.583969i	$-0.801499\pi$
$61$	−7.11998	−	12.3322i	−0.911620	−	1.57897i	−0.0998446	−	0.995003i	$-0.531835\pi$
$62$		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	0.408353	−	0.912824i	$-0.366103\pi$
$67$	−1.45698	−	0.841190i	−0.177999	−	0.102768i	−0.586352	+	0.810056i	$0.699436\pi$
$68$		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	−0.100602	−	0.994927i	$-0.532077\pi$
$79$	6.31710	−	3.64718i	0.710729	−	0.410339i	0.811331	+	0.584587i	$0.198744\pi$
$80$		0			0
$81$	−2.31220	−	8.69792i	−0.256911	−	0.966435i
$82$		0			0
$83$	1.35365	+	2.34460i	0.148583	+	0.257353i	0.930704	−	0.365774i	$-0.119196\pi$
$83$	1.35365	+	2.34460i	0.148583	+	0.257353i	−0.782121	+	0.623126i	$0.785862\pi$
$84$		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	$0.0406285\pi$
$89$			2.40174i			0.254584i	−0.991865	+	0.127292i	$0.959372\pi$
$90$		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	0.908246	−	0.418436i	$-0.137422\pi$
$97$	0.903600	+	1.56508i	0.0917467	+	0.158910i	−0.816499	+	0.577346i	$0.804088\pi$
$98$		0			0
$99$	4.66856	+	0.619318i	0.469208	+	0.0622438i
$100$		0			0
$101$	−3.08158	+	1.77915i	−0.306628	+	0.177032i	−0.645417	−	0.763831i	$-0.723316\pi$
$101$	−3.08158	+	1.77915i	−0.306628	+	0.177032i	0.338788	+	0.940863i	$0.389983\pi$
$102$		0			0
$103$	−8.28138	−	4.78126i	−0.815989	−	0.471111i	0.0330425	−	0.999454i	$-0.489480\pi$
$103$	−8.28138	−	4.78126i	−0.815989	−	0.471111i	−0.849031	+	0.528343i	$0.822814\pi$
$104$		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	0.523108	−	0.852266i	$-0.324772\pi$
$113$	0.495124	+	0.285860i	0.0465773	+	0.0268914i	−0.476531	+	0.879158i	$0.658106\pi$
$114$		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	$0.214125\pi$
$127$			14.0438i			1.24619i	−0.782146	+	0.623095i	$0.785875\pi$
$128$		0			0
$129$	−3.80432	+	5.68749i	−0.334952	+	0.500755i
$130$		0			0
$131$	−0.699837	+	1.21215i	−0.0611450	+	0.105906i	−0.894977	−	0.446111i	$-0.852809\pi$
$131$	−0.699837	+	1.21215i	−0.0611450	+	0.105906i	0.833832	+	0.552018i	$0.186142\pi$
$132$		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	−0.550994	−	0.834509i	$-0.685751\pi$
$137$	−1.21477	+	0.701347i	−0.103785	+	0.0599201i	0.447209	+	0.894429i	$0.352418\pi$
$138$		0			0
$139$	−18.6630	−	10.7751i	−1.58298	−	0.913933i	−0.994422	−	0.105477i	$-0.966363\pi$
$139$	−18.6630	−	10.7751i	−1.58298	−	0.913933i	−0.588557	−	0.808456i	$-0.700304\pi$
$140$		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	0.694232	−	0.719752i	$-0.255744\pi$
$149$	5.10263	+	2.94601i	0.418024	+	0.241346i	−0.276208	+	0.961098i	$0.589078\pi$
$150$		0			0
$151$	−6.86723	+	3.96480i	−0.558847	+	0.322651i	−0.752683	−	0.658383i	$-0.771241\pi$
$151$	−6.86723	+	3.96480i	−0.558847	+	0.322651i	0.193835	+	0.981034i	$0.437907\pi$
$152$		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	−0.823185	−	0.567773i	$-0.807805\pi$
$157$	1.00382	−	1.73867i	0.0801138	−	0.138761i	0.903299	+	0.429012i	$0.141138\pi$
$158$		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	$-0.974288\pi$
$163$		−	2.06036i		−	0.161379i	0.996739	−	0.0806897i	$-0.0257123\pi$
$164$		0			0
$165$	−2.52117	−	5.11879i	−0.196273	−	0.398497i
$166$		0			0
$167$	−9.45382	+	16.3745i	−0.731559	+	1.26710i	0.224658	+	0.974438i	$0.427873\pi$
$167$	−9.45382	+	16.3745i	−0.731559	+	1.26710i	−0.956217	+	0.292659i	$0.905460\pi$
$168$		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	−0.102983	−	0.994683i	$-0.532839\pi$
$173$	9.29843	−	5.36845i	0.706946	−	0.408156i	0.809929	+	0.586528i	$0.199505\pi$
$174$		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	0.908433	−	0.418031i	$-0.137280\pi$
$191$	1.27410	+	2.20681i	0.0921908	+	0.159679i	−0.816242	+	0.577710i	$0.803946\pi$
$192$		0			0
$193$	−2.49967	+	4.32955i	−0.179930	+	0.311648i	−0.941856	−	0.336016i	$-0.890921\pi$
$193$	−2.49967	+	4.32955i	−0.179930	+	0.311648i	0.761926	+	0.647664i	$0.224254\pi$
$194$		0			0
$195$	7.80915	−	11.6747i	0.559225	−	0.836045i
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$		0			0
$199$		−	14.4713i		−	1.02584i	−0.858436	−	0.512921i	$-0.828564\pi$
$199$		−	14.4713i		−	1.02584i	0.858436	−	0.512921i	$-0.171436\pi$
$200$		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	0.869504	−	0.493925i	$-0.164438\pi$
$211$	12.7320	+	7.35080i	0.876505	+	0.506050i	0.00700041	+	0.999975i	$0.497772\pi$
$212$		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	0.127016	−	0.991901i	$-0.459460\pi$
$223$	15.6729	−	9.04876i	1.04954	−	0.605950i	0.922519	+	0.385951i	$0.126127\pi$
$224$		0			0
$225$	−1.77268	−	0.235158i	−0.118178	−	0.0156772i
$226$		0			0
$227$	6.29529	+	10.9038i	0.417833	+	0.723708i	0.995721	−	0.0924078i	$-0.0294564\pi$
$227$	6.29529	+	10.9038i	0.417833	+	0.723708i	−0.577888	+	0.816116i	$0.696123\pi$
$228$		0			0
$229$	6.19995	−	10.7386i	0.409704	−	0.709628i	−0.585152	−	0.810923i	$-0.698965\pi$
$229$	6.19995	−	10.7386i	0.409704	−	0.709628i	0.994856	+	0.101295i	$0.0322986\pi$
$230$		0			0
$231$	0.450229	+	0.0297328i	0.0296229	+	0.00195627i
$232$		0			0
$233$		−	7.13560i		−	0.467469i	−0.972300	−	0.233734i	$-0.924905\pi$
$233$		−	7.13560i		−	0.467469i	0.972300	−	0.233734i	$-0.0750947\pi$
$234$		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	−0.857031	−	0.515265i	$-0.827693\pi$
$239$	0.273904	−	0.474416i	0.0177174	−	0.0306874i	0.874748	+	0.484578i	$0.161027\pi$
$240$		0			0
$241$	−9.28792	−	16.0872i	−0.598288	−	1.03626i	−0.993074	−	0.117491i	$-0.962515\pi$
$241$	−9.28792	−	16.0872i	−0.598288	−	1.03626i	0.394786	−	0.918773i	$-0.370819\pi$
$242$		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	0.616740	−	0.787167i	$-0.288453\pi$
$257$	3.90205	+	2.25285i	0.243403	+	0.140529i	−0.373337	+	0.927696i	$0.621786\pi$
$258$		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	−0.990875	−	0.134787i	$-0.956965\pi$
$263$	−9.92767	−	17.1952i	−0.612166	−	1.06030i	0.378708	−	0.925516i	$-0.376368\pi$
$264$		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	$0.406378\pi$
$269$			31.3938i			1.91411i	−0.289901	+	0.957057i	$0.593622\pi$
$270$		0			0
$271$			0.868217i			0.0527405i	0.999652	+	0.0263702i	$0.00839488\pi$
$271$			0.868217i			0.0527405i	−0.999652	+	0.0263702i	$0.991605\pi$
$272$		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	0.925809	−	0.377991i	$-0.123385\pi$
$277$	2.25608	+	3.90765i	0.135555	+	0.234788i	−0.790254	+	0.612779i	$0.790052\pi$
$278$		0			0
$279$	6.74923	−	2.78782i	0.404066	−	0.166902i
$280$		0			0
$281$	24.6156	−	14.2118i	1.46844	−	0.847805i	0.469066	−	0.883163i	$-0.344591\pi$
$281$	24.6156	−	14.2118i	1.46844	−	0.847805i	0.999375	+	0.0353583i	$0.0112572\pi$
$282$		0			0
$283$	−3.92629	−	2.26684i	−0.233394	−	0.134750i	0.378743	−	0.925502i	$-0.376356\pi$
$283$	−3.92629	−	2.26684i	−0.233394	−	0.134750i	−0.612137	+	0.790752i	$0.709690\pi$
$284$		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	0.0618642	−	0.998085i	$-0.480295\pi$
$293$	−13.2072	−	7.62516i	−0.771570	−	0.445466i	−0.833435	+	0.552618i	$0.813629\pi$
$294$		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	$0.0627171\pi$
$307$			6.85996i			0.391519i	−0.980652	+	0.195759i	$0.937283\pi$
$308$		0			0
$309$	16.5268	+	1.09142i	0.940175	+	0.0620885i
$310$		0			0
$311$	12.1876	−	21.1096i	0.691097	−	1.19702i	−0.280381	−	0.959889i	$-0.590461\pi$
$311$	12.1876	−	21.1096i	0.691097	−	1.19702i	0.971479	−	0.237127i	$-0.0762058\pi$
$312$		0			0
$313$	3.96030	+	6.85944i	0.223849	+	0.387719i	0.955974	−	0.293453i	$-0.0948043\pi$
$313$	3.96030	+	6.85944i	0.223849	+	0.387719i	−0.732124	+	0.681171i	$0.761471\pi$
$314$		0			0
$315$	−0.636816	+	0.828221i	−0.0358805	+	0.0466650i
$316$		0			0
$317$	−17.4030	+	10.0476i	−0.977447	+	0.564329i	−0.901498	−	0.432782i	$-0.857532\pi$
$317$	−17.4030	+	10.0476i	−0.977447	+	0.564329i	−0.0759487	+	0.997112i	$0.524199\pi$
$318$		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	−0.775636	−	0.631181i	$-0.782571\pi$
$331$	−11.2223	+	6.47921i	−0.616835	+	0.356130i	0.158801	+	0.987311i	$0.449237\pi$
$332$		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	−0.990971	−	0.134080i	$-0.957192\pi$
$337$	−6.96429	+	12.0625i	−0.379369	+	0.657086i	0.611602	+	0.791166i	$0.290526\pi$
$338$		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	0.105284	−	0.994442i	$-0.466425\pi$
$347$	17.0232	−	29.4851i	0.913854	−	1.58284i	0.808570	−	0.588399i	$-0.200242\pi$
$348$		0			0
$349$	−0.599892	−	1.03904i	−0.0321115	−	0.0556188i	0.849523	−	0.527552i	$-0.176890\pi$
$349$	−0.599892	−	1.03904i	−0.0321115	−	0.0556188i	−0.881635	+	0.471933i	$0.843557\pi$
$350$		0			0
$351$	−15.0767	−	13.2614i	−0.804733	−	0.707843i
$352$		0			0
$353$	19.6933	−	11.3699i	1.04817	−	0.605159i	0.126031	−	0.992026i	$-0.459776\pi$
$353$	19.6933	−	11.3699i	1.04817	−	0.605159i	0.922135	+	0.386867i	$0.126443\pi$
$354$		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	−0.999179	−	0.0405253i	$-0.987097\pi$
$367$	−28.0399	+	16.1889i	−1.46367	+	0.845051i	−0.464493	+	0.885577i	$0.653764\pi$
$368$		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	−0.699564	−	0.714570i	$-0.746622\pi$
$373$	5.19629	−	9.00024i	0.269054	−	0.466015i	0.968618	+	0.248555i	$0.0799557\pi$
$374$		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	$0.173394\pi$
$379$			20.1762i			1.03638i	−0.855265	+	0.518190i	$0.826606\pi$
$380$		0			0
$381$	−10.7477	−	21.8214i	−0.550624	−	1.11795i
$382$		0			0
$383$	−11.8556	+	20.5344i	−0.605791	+	1.04926i	0.386135	+	0.922442i	$0.373810\pi$
$383$	−11.8556	+	20.5344i	−0.605791	+	1.04926i	−0.991926	+	0.126818i	$0.959524\pi$
$384$		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	−0.454621	−	0.890685i	$-0.650225\pi$
$389$	1.76371	−	1.01828i	0.0894236	−	0.0516288i	0.544045	+	0.839056i	$0.316892\pi$
$390$		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	0.913942	−	0.405846i	$-0.133023\pi$
$401$	20.4143	+	11.7862i	1.01944	+	0.588574i	0.105498	+	0.994419i	$0.466356\pi$
$402$		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	0.459995	+	0.887922i	$0.347851\pi$
$409$	−10.8999	+	18.8792i	−0.538965	+	0.933515i	−0.998960	+	0.0455934i	$0.985482\pi$
$410$		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	0.486552	+	0.873652i	$0.338255\pi$
$419$	−10.5076	+	18.1997i	−0.513329	+	0.889112i	−0.999880	+	0.0154599i	$0.995079\pi$
$420$		0			0
$421$	6.86839	+	11.8964i	0.334745	+	0.579795i	0.983436	−	0.181257i	$-0.0580166\pi$
$421$	6.86839	+	11.8964i	0.334745	+	0.579795i	−0.648691	+	0.761052i	$0.724683\pi$
$422$		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	−0.996549	−	0.0830082i	$-0.973547\pi$
$439$	−29.8138	+	17.2130i	−1.42294	+	0.821533i	−0.426387	+	0.904541i	$0.640214\pi$
$440$		0			0
$441$	7.98565	+	19.3330i	0.380269	+	0.920621i
$442$		0			0
$443$	−4.84473	−	8.39132i	−0.230180	−	0.398684i	0.727681	−	0.685916i	$-0.240598\pi$
$443$	−4.84473	−	8.39132i	−0.230180	−	0.398684i	−0.957861	+	0.287232i	$0.907265\pi$
$444$		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	$-0.860542\pi$
$449$		−	17.9789i		−	0.848477i	0.905550	−	0.424239i	$-0.139458\pi$
$450$		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	0.981557	−	0.191172i	$-0.0612289\pi$
$457$	6.95237	+	12.0419i	0.325218	+	0.563295i	−0.656338	+	0.754467i	$0.727896\pi$
$458$		0			0
$459$	−26.8609	−	5.38433i	−1.25376	−	0.251319i
$460$		0			0
$461$	−1.80521	+	1.04224i	−0.0840772	+	0.0485420i	−0.541449	−	0.840733i	$-0.682124\pi$
$461$	−1.80521	+	1.04224i	−0.0840772	+	0.0485420i	0.457372	+	0.889275i	$0.348791\pi$
$462$		0			0
$463$	31.0337	+	17.9173i	1.44226	+	0.832688i	0.998000	−	0.0632104i	$-0.0201339\pi$
$463$	31.0337	+	17.9173i	1.44226	+	0.832688i	0.444258	+	0.895899i	$0.353467\pi$
$464$		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	−0.999630	−	0.0271987i	$-0.991341\pi$
$479$	−11.4545	−	19.8398i	−0.523370	−	0.906503i	0.476260	−	0.879304i	$-0.341992\pi$
$480$		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	$-0.884355\pi$
$487$		−	15.6846i		−	0.710738i	0.934726	−	0.355369i	$-0.115645\pi$
$488$		0			0
$489$	1.57679	+	3.20139i	0.0713049	+	0.144772i
$490$		0			0
$491$	12.2976	−	21.3001i	0.554982	−	0.961258i	−0.442922	−	0.896560i	$-0.646058\pi$
$491$	12.2976	−	21.3001i	0.554982	−	0.961258i	0.997905	−	0.0646979i	$-0.0206084\pi$
$492$		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	0.360548	−	0.932741i	$-0.382590\pi$
$499$	−5.96333	−	3.44293i	−0.266955	−	0.154127i	−0.627503	+	0.778614i	$0.715923\pi$
$500$		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	0.153240	−	0.988189i	$-0.451029\pi$
$509$	−14.1218	−	8.15320i	−0.625936	−	0.361384i	−0.779177	+	0.626805i	$0.784362\pi$
$510$		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	$0.0663290\pi$
$521$			9.44397i			0.413748i	−0.978368	+	0.206874i	$0.933671\pi$
$522$		0			0
$523$		−	22.5688i		−	0.986865i	−0.869784	−	0.493433i	$-0.835742\pi$
$523$		−	22.5688i		−	0.986865i	0.869784	−	0.493433i	$-0.164258\pi$
$524$		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	−0.153384	−	0.988167i	$-0.549017\pi$
$547$	14.6339	−	8.44889i	0.625701	−	0.361249i	0.779085	+	0.626918i	$0.215684\pi$
$548$		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	$0.242708\pi$
$557$			32.6034i			1.38145i	−0.723118	+	0.690725i	$0.757292\pi$
$558$		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	−0.660774	−	0.750585i	$-0.729772\pi$
$563$	7.58426	−	13.1363i	0.319639	−	0.553630i	0.980413	+	0.196955i	$0.0631052\pi$
$564$		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	−0.585062	−	0.810988i	$-0.698930\pi$
$569$	−4.18052	+	2.41363i	−0.175257	+	0.101184i	0.409806	+	0.912173i	$0.365597\pi$
$570$		0			0
$571$	4.07311	+	2.35161i	0.170454	+	0.0984118i	0.582800	−	0.812616i	$-0.301957\pi$
$571$	4.07311	+	2.35161i	0.170454	+	0.0984118i	−0.412346	+	0.911027i	$0.635290\pi$
$572$		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	0.624108	−	0.781338i	$-0.285463\pi$
$587$	−8.83368	−	15.3004i	−0.364605	−	0.631515i	−0.988713	+	0.149824i	$0.952129\pi$
$588$		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	$-0.906127\pi$
$593$		−	14.1557i		−	0.581307i	0.956828	−	0.290653i	$-0.0938727\pi$
$594$		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	−0.454373	−	0.890812i	$-0.650137\pi$
$599$	13.3209	−	23.0726i	0.544279	−	0.942719i	0.998652	−	0.0519076i	$-0.0165301\pi$
$600$		0			0
$601$	−12.2321	−	21.1866i	−0.498959	−	0.864221i	0.501041	−	0.865424i	$-0.332951\pi$
$601$	−12.2321	−	21.1866i	−0.498959	−	0.864221i	−0.999999	+	0.00120220i	$0.999617\pi$
$602$		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	0.907729	−	0.419556i	$-0.137814\pi$
$607$	24.5942	+	14.1995i	0.998247	+	0.576338i	0.0905181	+	0.995895i	$0.471148\pi$
$608$		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	−0.332678	−	0.943040i	$-0.607952\pi$
$617$	−32.6817	−	18.8688i	−1.31571	−	0.759628i	−0.983036	+	0.183412i	$0.941286\pi$
$618$		0			0
$619$	−7.89600	+	4.55876i	−0.317367	+	0.183232i	−0.650218	−	0.759747i	$-0.725323\pi$
$619$	−7.89600	+	4.55876i	−0.317367	+	0.183232i	0.332851	+	0.942979i	$0.391989\pi$
$620$		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	$0.0576628\pi$
$631$			9.05133i			0.360328i	−0.983637	+	0.180164i	$0.942337\pi$
$632$		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	−0.929217	−	0.369533i	$-0.879518\pi$
$641$	−27.1865	+	15.6961i	−1.07380	+	0.619959i	−0.144583	+	0.989493i	$0.546184\pi$
$642$		0			0
$643$	6.03917	+	3.48672i	0.238162	+	0.137503i	0.614332	−	0.789048i	$-0.289426\pi$
$643$	6.03917	+	3.48672i	0.238162	+	0.137503i	−0.376170	+	0.926551i	$0.622759\pi$
$644$		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	−0.160159	−	0.987091i	$-0.551201\pi$
$653$	−27.9837	−	16.1564i	−1.09509	−	0.632248i	−0.934926	+	0.354843i	$0.884534\pi$
$654$		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	0.812562	−	0.582875i	$-0.198072\pi$
$659$	−2.52870	−	4.37984i	−0.0985042	−	0.170614i	−0.911066	+	0.412261i	$0.864739\pi$
$660$		0			0
$661$	6.31245	−	10.9335i	0.245526	−	0.425263i	−0.716753	−	0.697327i	$-0.754373\pi$
$661$	6.31245	−	10.9335i	0.245526	−	0.425263i	0.962279	+	0.272063i	$0.0877060\pi$
$662$		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	0.816884	+	0.576802i	$0.195700\pi$
$673$	23.5547	+	40.7980i	0.907967	+	1.57265i	0.0910837	+	0.995843i	$0.470967\pi$
$674$		0			0
$675$	2.93436	−	0.991238i	0.112944	−	0.0381528i
$676$		0			0
$677$	16.1335	−	9.31465i	0.620059	−	0.357991i	−0.156833	−	0.987625i	$-0.550128\pi$
$677$	16.1335	−	9.31465i	0.620059	−	0.357991i	0.776892	+	0.629634i	$0.216795\pi$
$678$		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	−0.667179	−	0.744897i	$-0.732498\pi$
$691$	−9.34942	+	5.39789i	−0.355669	+	0.205345i	0.311510	+	0.950243i	$0.399165\pi$
$692$		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	$0.0458127\pi$
$701$			7.59493i			0.286857i	−0.989661	+	0.143428i	$0.954187\pi$
$702$		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	0.562517	−	0.826786i	$-0.309833\pi$
$709$	−11.5763	−	20.0508i	−0.434759	−	0.753024i	−0.997276	+	0.0737615i	$0.976500\pi$
$710$		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	−0.922501	−	0.385995i	$-0.873858\pi$
$727$	−28.2968	+	16.3372i	−1.04947	+	0.605911i	−0.126969	+	0.991907i	$0.540525\pi$
$728$		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	0.0606693	−	0.998158i	$-0.480676\pi$
$733$	24.2248	−	41.9586i	0.894765	−	1.54978i	0.834095	−	0.551620i	$-0.185990\pi$
$734$		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	$0.0268684\pi$
$739$			4.58382i			0.168619i	−0.996440	+	0.0843094i	$0.973132\pi$
$740$		0			0
$741$	53.7759	+	3.55132i	1.97551	+	0.130461i
$742$		0			0
$743$	−18.5816	+	32.1842i	−0.681691	+	1.18072i	0.292773	+	0.956182i	$0.405422\pi$
$743$	−18.5816	+	32.1842i	−0.681691	+	1.18072i	−0.974464	+	0.224542i	$0.927911\pi$
$744$		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	−0.190503	−	0.981687i	$-0.561012\pi$
$751$	−31.1292	−	17.9724i	−1.13592	−	0.655824i	−0.945417	+	0.325863i	$0.894345\pi$
$752$		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	0.305838	−	0.952084i	$-0.401063\pi$
$761$	−10.0903	−	5.82561i	−0.365771	−	0.211178i	−0.671609	+	0.740905i	$0.734397\pi$
$762$		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	−0.631582	−	0.775309i	$-0.717594\pi$
$769$	9.86238	−	17.0821i	0.355646	−	0.615998i	0.987228	+	0.159312i	$0.0509274\pi$
$770$		0			0
$771$	−7.78714	−	0.514257i	−0.280447	−	0.0185205i
$772$		0			0
$773$		−	39.5946i		−	1.42412i	−0.702120	−	0.712059i	$-0.747763\pi$
$773$		−	39.5946i		−	1.42412i	0.702120	−	0.712059i	$-0.252237\pi$
$774$		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	0.807329	−	0.590102i	$-0.200913\pi$
$787$	19.6360	+	11.3369i	0.699949	+	0.404116i	−0.107379	+	0.994218i	$0.534246\pi$
$788$		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	0.475278	−	0.879836i	$-0.342347\pi$
$797$	−1.38454	−	0.799367i	−0.0490431	−	0.0283150i	−0.524321	+	0.851521i	$0.675681\pi$
$798$		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	$0.345003\pi$
$809$			50.2740i			1.76754i	−0.467922	+	0.883770i	$0.654997\pi$
$810$		0			0
$811$			36.5884i			1.28479i	0.766372	+	0.642397i	$0.222060\pi$
$811$			36.5884i			1.28479i	−0.766372	+	0.642397i	$0.777940\pi$
$812$		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	−0.950410	−	0.311000i	$-0.899336\pi$
$821$	−33.1310	+	19.1282i	−1.15628	+	0.667579i	−0.205871	+	0.978579i	$0.566003\pi$
$822$		0			0
$823$	0.874309	+	0.504783i	0.0304765	+	0.0175956i	0.515161	−	0.857094i	$-0.327732\pi$
$823$	0.874309	+	0.504783i	0.0304765	+	0.0175956i	−0.484684	+	0.874689i	$0.661066\pi$
$824$		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	0.797252	+	0.603646i	$0.206286\pi$
$839$	26.6888	+	46.2263i	0.921399	+	1.59591i	0.124147	+	0.992264i	$0.460381\pi$
$840$		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	0.963704	−	0.266975i	$-0.0860240\pi$
$853$	7.32038	+	12.6793i	0.250645	+	0.434130i	−0.713059	+	0.701104i	$0.752691\pi$
$854$		0			0
$855$	19.3532	+	46.8536i	0.661867	+	1.60236i
$856$		0			0
$857$	−21.8376	+	12.6080i	−0.745959	+	0.430680i	−0.824232	−	0.566252i	$-0.808393\pi$
$857$	−21.8376	+	12.6080i	−0.745959	+	0.430680i	0.0782730	+	0.996932i	$0.475059\pi$
$858$		0			0
$859$	−3.77869	−	2.18163i	−0.128927	−	0.0744361i	0.434149	−	0.900841i	$-0.357049\pi$
$859$	−3.77869	−	2.18163i	−0.128927	−	0.0744361i	−0.563076	+	0.826405i	$0.690382\pi$
$860$		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	−0.829744	−	0.558144i	$-0.811514\pi$
$877$	2.02843	−	3.51334i	0.0684951	−	0.118637i	0.898239	+	0.439507i	$0.144847\pi$
$878$		0			0
$879$	26.3569	+	1.74059i	0.888996	+	0.0587087i
$880$		0			0
$881$			29.5979i			0.997179i	0.866838	+	0.498589i	$0.166148\pi$
$881$			29.5979i			0.997179i	−0.866838	+	0.498589i	$0.833852\pi$
$882$		0			0
$883$		−	42.1894i		−	1.41979i	−0.704309	−	0.709894i	$-0.748743\pi$
$883$		−	42.1894i		−	1.41979i	0.704309	−	0.709894i	$-0.251257\pi$
$884$		0			0
$885$	−22.2238	+	33.2248i	−0.747045	+	1.11684i
$886$		0			0
$887$	15.1442	−	26.2305i	0.508491	−	0.880733i	−0.491460	−	0.870900i	$-0.663537\pi$
$887$	15.1442	−	26.2305i	0.508491	−	0.880733i	0.999952	−	0.00983292i	$-0.00312997\pi$
$888$		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	−0.111416	−	0.993774i	$-0.535538\pi$
$907$	20.8861	−	12.0586i	0.693510	−	0.400398i	0.804926	+	0.593376i	$0.202205\pi$
$908$		0			0
$909$	−1.40380	+	10.5822i	−0.0465612	+	0.350989i
$910$		0			0
$911$	−10.0067	−	17.3322i	−0.331538	−	0.574241i	0.651276	−	0.758841i	$-0.274234\pi$
$911$	−10.0067	−	17.3322i	−0.331538	−	0.574241i	−0.982814	+	0.184600i	$0.940901\pi$
$912$		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	$-0.961842\pi$
$919$		−	7.25070i		−	0.239178i	0.992823	−	0.119589i	$-0.0381578\pi$
$920$		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	−0.733806	−	0.679360i	$-0.762258\pi$
$929$	−15.6167	+	9.01628i	−0.512366	+	0.295815i	0.221440	+	0.975174i	$0.428924\pi$
$930$		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	−0.0922782	−	0.995733i	$-0.529415\pi$
$941$	−30.6987	−	17.7239i	−1.00075	−	0.577782i	−0.908469	+	0.417951i	$0.862748\pi$
$942$		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	0.982434	−	0.186608i	$-0.0597494\pi$
$947$	10.1432	+	17.5686i	0.329610	+	0.570901i	−0.652824	+	0.757509i	$0.726416\pi$
$948$		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	$-0.855260\pi$
$953$		−	27.1172i		−	0.878411i	0.898387	−	0.439205i	$-0.144740\pi$
$954$		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	0.766940	−	0.641719i	$-0.221778\pi$
$967$	18.4921	+	10.6764i	0.594665	+	0.343330i	−0.172275	+	0.985049i	$0.555112\pi$
$968$		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	0.215491	−	0.976506i	$-0.430865\pi$
$977$	−16.3300	−	9.42812i	−0.522442	−	0.301632i	−0.737933	+	0.674874i	$0.764198\pi$
$978$		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	−0.933303	−	0.359089i	$-0.883088\pi$
$983$	−24.3810	−	42.2290i	−0.777632	−	1.34690i	0.155672	−	0.987809i	$-0.450246\pi$
$984$		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	$0.143715\pi$
$991$			27.4703i			0.872622i	−0.899796	+	0.436311i	$0.856285\pi$
$992$		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	−0.968853	−	0.247635i	$-0.920347\pi$
$997$	−22.0675	−	38.2220i	−0.698885	−	1.21050i	0.269969	−	0.962869i	$-0.412987\pi$
$998$		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.95.2	✓	24
3.2	odd	2		864.2.s.a.287.3		24
4.3	odd	2	inner	288.2.s.a.95.11	yes	24
8.3	odd	2		576.2.s.g.383.2		24
8.5	even	2		576.2.s.g.383.11		24
9.2	odd	6	inner	288.2.s.a.191.11	yes	24
9.4	even	3		2592.2.c.c.2591.5		24
9.5	odd	6		2592.2.c.c.2591.19		24
9.7	even	3		864.2.s.a.575.4		24
12.11	even	2		864.2.s.a.287.4		24
24.5	odd	2		1728.2.s.g.1151.9		24
24.11	even	2		1728.2.s.g.1151.10		24
36.7	odd	6		864.2.s.a.575.3		24
36.11	even	6	inner	288.2.s.a.191.2	yes	24
36.23	even	6		2592.2.c.c.2591.20		24
36.31	odd	6		2592.2.c.c.2591.6		24
72.5	odd	6		5184.2.c.m.5183.5		24
72.11	even	6		576.2.s.g.191.11		24
72.13	even	6		5184.2.c.m.5183.19		24
72.29	odd	6		576.2.s.g.191.2		24
72.43	odd	6		1728.2.s.g.575.9		24
72.59	even	6		5184.2.c.m.5183.6		24
72.61	even	6		1728.2.s.g.575.10		24
72.67	odd	6		5184.2.c.m.5183.20		24

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

Related objects

Downloads

Learn more