LMFDB - Embedded newform 1824.2.bb.a.1471.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1824,2,Mod(31,1824)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1824.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1824 = 2^{5} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1824.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.5647133287$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1471.14
Character	$\chi$	$=$	1824.1471
Dual form			1824.2.bb.a.31.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(0.680039 - 1.17786i) q^{5} -3.19193i q^{7} +(-0.500000 - 0.866025i) q^{9} +0.815036i q^{11} +(2.19194 - 1.26551i) q^{13} +(0.680039 + 1.17786i) q^{15} +(-1.26229 + 2.18635i) q^{17} +(-2.03784 - 3.85321i) q^{19} +(2.76429 + 1.59596i) q^{21} +(0.396301 - 0.228805i) q^{23} +(1.57509 + 2.72814i) q^{25} +1.00000 q^{27} +(5.37187 - 3.10145i) q^{29} -5.98492 q^{31} +(-0.705842 - 0.407518i) q^{33} +(-3.75965 - 2.17063i) q^{35} -7.06140i q^{37} +2.53103i q^{39} +(-4.33973 - 2.50554i) q^{41} +(-9.05081 - 5.22549i) q^{43} -1.36008 q^{45} +(-1.58170 + 0.913193i) q^{47} -3.18840 q^{49} +(-1.26229 - 2.18635i) q^{51} +(-1.88215 + 1.08666i) q^{53} +(0.960000 + 0.554257i) q^{55} +(4.35590 + 0.161782i) q^{57} +(-2.98569 + 5.17136i) q^{59} +(0.497154 + 0.861096i) q^{61} +(-2.76429 + 1.59596i) q^{63} -3.44240i q^{65} +(-2.82835 - 4.89884i) q^{67} +0.457609i q^{69} +(3.55868 - 6.16382i) q^{71} +(-0.533501 + 0.924052i) q^{73} -3.15019 q^{75} +2.60154 q^{77} +(-1.26133 + 2.18469i) q^{79} +(-0.500000 + 0.866025i) q^{81} -13.1722i q^{83} +(1.71681 + 2.97361i) q^{85} +6.20290i q^{87} +(6.83357 - 3.94536i) q^{89} +(-4.03943 - 6.99650i) q^{91} +(2.99246 - 5.18309i) q^{93} +(-5.92436 - 0.220036i) q^{95} +(1.14814 + 0.662881i) q^{97} +(0.705842 - 0.407518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) $ 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1824\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$799$	$1217$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	0.680039	−	1.17786i	0.304123	−	0.526756i	−0.672943	−	0.739694i	$-0.734970\pi$
$5$	0.680039	−	1.17786i	0.304123	−	0.526756i	0.977066	+	0.212938i	$0.0683034\pi$
$6$		0			0
$7$		−	3.19193i		−	1.20643i	−0.797577	−	0.603217i	$-0.793885\pi$
$7$		−	3.19193i		−	1.20643i	0.797577	−	0.603217i	$-0.206115\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$			0.815036i			0.245743i	0.992423	+	0.122871i	$0.0392103\pi$
$11$			0.815036i			0.245743i	−0.992423	+	0.122871i	$0.960790\pi$
$12$		0			0
$13$	2.19194	−	1.26551i	0.607933	−	0.350991i	−0.164223	−	0.986423i	$-0.552512\pi$
$13$	2.19194	−	1.26551i	0.607933	−	0.350991i	0.772156	+	0.635433i	$0.219178\pi$
$14$		0			0
$15$	0.680039	+	1.17786i	0.175585	+	0.304123i
$16$		0			0
$17$	−1.26229	+	2.18635i	−0.306150	+	0.530268i	−0.977517	−	0.210858i	$-0.932374\pi$
$17$	−1.26229	+	2.18635i	−0.306150	+	0.530268i	0.671367	+	0.741125i	$0.265708\pi$
$18$		0			0
$19$	−2.03784	−	3.85321i	−0.467513	−	0.883986i
$19$	−2.03784	−	3.85321i	−0.467513	−	0.883986i
$20$		0			0
$21$	2.76429	+	1.59596i	0.603217	+	0.348268i
$22$		0			0
$23$	0.396301	−	0.228805i	0.0826346	−	0.0477091i	−0.458113	−	0.888894i	$-0.651475\pi$
$23$	0.396301	−	0.228805i	0.0826346	−	0.0477091i	0.540748	+	0.841185i	$0.318141\pi$
$24$		0			0
$25$	1.57509	+	2.72814i	0.315019	+	0.545628i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	5.37187	−	3.10145i	0.997531	−	0.575925i	0.0900143	−	0.995940i	$-0.471309\pi$
$29$	5.37187	−	3.10145i	0.997531	−	0.575925i	0.907517	+	0.420016i	$0.137975\pi$
$30$		0			0
$31$	−5.98492			−1.07492			−0.537461	−	0.843288i	$-0.680617\pi$
$31$	−5.98492			−1.07492			−0.537461	+	0.843288i	$0.680617\pi$
$32$		0			0
$33$	−0.705842	−	0.407518i	−0.122871	−	0.0709398i
$34$		0			0
$35$	−3.75965	−	2.17063i	−0.635497	−	0.366904i
$36$		0			0
$37$		−	7.06140i		−	1.16089i	−0.814301	−	0.580443i	$-0.802879\pi$
$37$		−	7.06140i		−	1.16089i	0.814301	−	0.580443i	$-0.197121\pi$
$38$		0			0
$39$			2.53103i			0.405289i
$40$		0			0
$41$	−4.33973	−	2.50554i	−0.677752	−	0.391300i	0.121256	−	0.992621i	$-0.461308\pi$
$41$	−4.33973	−	2.50554i	−0.677752	−	0.391300i	−0.799007	+	0.601321i	$0.794641\pi$
$42$		0			0
$43$	−9.05081	−	5.22549i	−1.38024	−	0.796879i	−0.388048	−	0.921639i	$-0.626851\pi$
$43$	−9.05081	−	5.22549i	−1.38024	−	0.796879i	−0.992187	+	0.124760i	$0.960184\pi$
$44$		0			0
$45$	−1.36008			−0.202748
$46$		0			0
$47$	−1.58170	+	0.913193i	−0.230714	+	0.133203i	−0.610902	−	0.791707i	$-0.709193\pi$
$47$	−1.58170	+	0.913193i	−0.230714	+	0.133203i	0.380187	+	0.924910i	$0.375860\pi$
$48$		0			0
$49$	−3.18840			−0.455485
$50$		0			0
$51$	−1.26229	−	2.18635i	−0.176756	−	0.306150i
$52$		0			0
$53$	−1.88215	+	1.08666i	−0.258533	+	0.149264i	−0.623665	−	0.781691i	$-0.714357\pi$
$53$	−1.88215	+	1.08666i	−0.258533	+	0.149264i	0.365132	+	0.930956i	$0.381024\pi$
$54$		0			0
$55$	0.960000	+	0.554257i	0.129446	+	0.0747359i
$56$		0			0
$57$	4.35590	+	0.161782i	0.576952	+	0.0214286i
$58$		0			0
$59$	−2.98569	+	5.17136i	−0.388703	+	0.673254i	−0.992275	−	0.124054i	$-0.960410\pi$
$59$	−2.98569	+	5.17136i	−0.388703	+	0.673254i	0.603572	+	0.797308i	$0.293744\pi$
$60$		0			0
$61$	0.497154	+	0.861096i	0.0636541	+	0.110252i	0.896096	−	0.443860i	$-0.146391\pi$
$61$	0.497154	+	0.861096i	0.0636541	+	0.110252i	−0.832442	+	0.554112i	$0.813058\pi$
$62$		0			0
$63$	−2.76429	+	1.59596i	−0.348268	+	0.201072i
$64$		0			0
$65$		−	3.44240i		−	0.426977i
$66$		0			0
$67$	−2.82835	−	4.89884i	−0.345538	−	0.598489i	0.639914	−	0.768447i	$-0.278970\pi$
$67$	−2.82835	−	4.89884i	−0.345538	−	0.598489i	−0.985451	+	0.169958i	$0.945637\pi$
$68$		0			0
$69$			0.457609i			0.0550897i
$70$		0			0
$71$	3.55868	−	6.16382i	0.422338	−	0.731511i	−0.573830	−	0.818975i	$-0.694543\pi$
$71$	3.55868	−	6.16382i	0.422338	−	0.731511i	0.996168	+	0.0874637i	$0.0278762\pi$
$72$		0			0
$73$	−0.533501	+	0.924052i	−0.0624416	+	0.108152i	−0.895556	−	0.444948i	$-0.853222\pi$
$73$	−0.533501	+	0.924052i	−0.0624416	+	0.108152i	0.833115	+	0.553100i	$0.186555\pi$
$74$		0			0
$75$	−3.15019			−0.363752
$76$		0			0
$77$	2.60154			0.296473
$78$		0			0
$79$	−1.26133	+	2.18469i	−0.141911	+	0.245796i	−0.928216	−	0.372042i	$-0.878658\pi$
$79$	−1.26133	+	2.18469i	−0.141911	+	0.245796i	0.786305	+	0.617838i	$0.211991\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	13.1722i		−	1.44584i	−0.690931	−	0.722921i	$-0.742799\pi$
$83$		−	13.1722i		−	1.44584i	0.690931	−	0.722921i	$-0.257201\pi$
$84$		0			0
$85$	1.71681	+	2.97361i	0.186214	+	0.322533i
$86$		0			0
$87$			6.20290i			0.665021i
$88$		0			0
$89$	6.83357	−	3.94536i	0.724357	−	0.418208i	−0.0919973	−	0.995759i	$-0.529325\pi$
$89$	6.83357	−	3.94536i	0.724357	−	0.418208i	0.816354	+	0.577552i	$0.195992\pi$
$90$		0			0
$91$	−4.03943	−	6.99650i	−0.423447	−	0.733432i
$92$		0			0
$93$	2.99246	−	5.18309i	0.310303	−	0.537461i
$94$		0			0
$95$	−5.92436	−	0.220036i	−0.607826	−	0.0225753i
$96$		0			0
$97$	1.14814	+	0.662881i	0.116576	+	0.0673054i	0.557154	−	0.830409i	$-0.311893\pi$
$97$	1.14814	+	0.662881i	0.116576	+	0.0673054i	−0.440578	+	0.897714i	$0.645226\pi$
$98$		0			0
$99$	0.705842	−	0.407518i	0.0709398	−	0.0409571i
$100$		0			0
$101$	−4.95412	−	8.58078i	−0.492953	−	0.853820i	0.507014	−	0.861938i	$-0.330749\pi$
$101$	−4.95412	−	8.58078i	−0.492953	−	0.853820i	−0.999967	+	0.00811820i	$0.997416\pi$
$102$		0			0
$103$	−0.522149			−0.0514488			−0.0257244	−	0.999669i	$-0.508189\pi$
$103$	−0.522149			−0.0514488			−0.0257244	+	0.999669i	$0.508189\pi$
$104$		0			0
$105$	3.75965	−	2.17063i	0.366904	−	0.211832i
$106$		0			0
$107$	−4.51235			−0.436225			−0.218113	−	0.975924i	$-0.569990\pi$
$107$	−4.51235			−0.436225			−0.218113	+	0.975924i	$0.569990\pi$
$108$		0			0
$109$	−12.4683	−	7.19855i	−1.19424	−	0.689497i	−0.234977	−	0.972001i	$-0.575501\pi$
$109$	−12.4683	−	7.19855i	−1.19424	−	0.689497i	−0.959266	+	0.282504i	$0.908835\pi$
$110$		0			0
$111$	6.11535	+	3.53070i	0.580443	+	0.335119i
$112$		0			0
$113$		−	13.5013i		−	1.27010i	−0.772472	−	0.635049i	$-0.780980\pi$
$113$		−	13.5013i		−	1.27010i	0.772472	−	0.635049i	$-0.219020\pi$
$114$		0			0
$115$		−	0.622385i		−	0.0580377i
$116$		0			0
$117$	−2.19194	−	1.26551i	−0.202644	−	0.116997i
$118$		0			0
$119$	6.97867	+	4.02914i	0.639734	+	0.369350i
$120$		0			0
$121$	10.3357			0.939611
$122$		0			0
$123$	4.33973	−	2.50554i	0.391300	−	0.225917i
$124$		0			0
$125$	11.0849			0.991463
$126$		0			0
$127$	5.96269	+	10.3277i	0.529104	+	0.916434i	0.999424	+	0.0339384i	$0.0108050\pi$
$127$	5.96269	+	10.3277i	0.529104	+	0.916434i	−0.470320	+	0.882496i	$0.655862\pi$
$128$		0			0
$129$	9.05081	−	5.22549i	0.796879	−	0.460078i
$130$		0			0
$131$	8.95943	+	5.17273i	0.782789	+	0.451944i	0.837418	−	0.546563i	$-0.184064\pi$
$131$	8.95943	+	5.17273i	0.782789	+	0.451944i	−0.0546287	+	0.998507i	$0.517398\pi$
$132$		0			0
$133$	−12.2992	+	6.50464i	−1.06647	+	0.564024i
$134$		0			0
$135$	0.680039	−	1.17786i	0.0585284	−	0.101374i
$136$		0			0
$137$	2.61102	+	4.52243i	0.223075	+	0.386377i	0.955740	−	0.294212i	$-0.0950572\pi$
$137$	2.61102	+	4.52243i	0.223075	+	0.386377i	−0.732665	+	0.680589i	$0.761724\pi$
$138$		0			0
$139$	0.253607	−	0.146420i	0.0215107	−	0.0124192i	−0.489206	−	0.872168i	$-0.662713\pi$
$139$	0.253607	−	0.146420i	0.0215107	−	0.0124192i	0.510717	+	0.859749i	$0.329380\pi$
$140$		0			0
$141$		−	1.82639i		−	0.153810i
$142$		0			0
$143$	1.03144	+	1.78651i	0.0862534	+	0.149395i
$144$		0			0
$145$		−	8.43643i		−	0.700607i
$146$		0			0
$147$	1.59420	−	2.76123i	0.131487	−	0.227743i
$148$		0			0
$149$	6.53165	−	11.3131i	0.535093	−	0.926809i	−0.464066	−	0.885801i	$-0.653610\pi$
$149$	6.53165	−	11.3131i	0.535093	−	0.926809i	0.999159	−	0.0410079i	$-0.0130569\pi$
$150$		0			0
$151$	−6.88190			−0.560041			−0.280021	−	0.959994i	$-0.590341\pi$
$151$	−6.88190			−0.560041			−0.280021	+	0.959994i	$0.590341\pi$
$152$		0			0
$153$	2.52458			0.204100
$154$		0			0
$155$	−4.06998	+	7.04941i	−0.326908	+	0.566222i
$156$		0			0
$157$	3.63921	−	6.30330i	0.290441	−	0.503058i	−0.683473	−	0.729975i	$-0.739531\pi$
$157$	3.63921	−	6.30330i	0.290441	−	0.503058i	0.973914	+	0.226918i	$0.0728648\pi$
$158$		0			0
$159$		−	2.17332i		−	0.172356i
$160$		0			0
$161$	−0.730328	−	1.26497i	−0.0575579	−	0.0996932i
$162$		0			0
$163$		−	25.1818i		−	1.97239i	−0.165589	−	0.986195i	$-0.552953\pi$
$163$		−	25.1818i		−	1.97239i	0.165589	−	0.986195i	$-0.447047\pi$
$164$		0			0
$165$	−0.960000	+	0.554257i	−0.0747359	+	0.0431488i
$166$		0			0
$167$	9.24028	+	16.0046i	0.715034	+	1.23848i	0.962946	+	0.269693i	$0.0869222\pi$
$167$	9.24028	+	16.0046i	0.715034	+	1.23848i	−0.247912	+	0.968783i	$0.579744\pi$
$168$		0			0
$169$	−3.29695	+	5.71048i	−0.253611	+	0.439268i
$170$		0			0
$171$	−2.31806	+	3.69143i	−0.177266	+	0.282290i
$172$		0			0
$173$	20.3193	+	11.7313i	1.54484	+	0.891916i	0.998522	+	0.0543413i	$0.0173059\pi$
$173$	20.3193	+	11.7313i	1.54484	+	0.891916i	0.546322	+	0.837575i	$0.316027\pi$
$174$		0			0
$175$	8.70803	−	5.02758i	0.658265	−	0.380050i
$176$		0			0
$177$	−2.98569	−	5.17136i	−0.224418	−	0.388703i
$178$		0			0
$179$	−4.88650			−0.365234			−0.182617	−	0.983184i	$-0.558457\pi$
$179$	−4.88650			−0.365234			−0.182617	+	0.983184i	$0.558457\pi$
$180$		0			0
$181$	−11.5109	+	6.64584i	−0.855602	+	0.493982i	−0.862537	−	0.505994i	$-0.831126\pi$
$181$	−11.5109	+	6.64584i	−0.855602	+	0.493982i	0.00693538	+	0.999976i	$0.497792\pi$
$182$		0			0
$183$	−0.994308			−0.0735014
$184$		0			0
$185$	−8.31735	−	4.80202i	−0.611504	−	0.353052i
$186$		0			0
$187$	−1.78195	−	1.02881i	−0.130309	−	0.0752342i
$188$		0			0
$189$		−	3.19193i		−	0.232179i
$190$		0			0
$191$		−	1.87431i		−	0.135620i	−0.997698	−	0.0678102i	$-0.978399\pi$
$191$		−	1.87431i		−	0.135620i	0.997698	−	0.0678102i	$-0.0216012\pi$
$192$		0			0
$193$	−14.6260	−	8.44430i	−1.05280	−	0.607834i	−0.129367	−	0.991597i	$-0.541295\pi$
$193$	−14.6260	−	8.44430i	−1.05280	−	0.607834i	−0.923432	+	0.383763i	$0.874628\pi$
$194$		0			0
$195$	2.98120	+	1.72120i	0.213488	+	0.123258i
$196$		0			0
$197$	20.2011			1.43927			0.719633	−	0.694355i	$-0.244310\pi$
$197$	20.2011			1.43927			0.719633	+	0.694355i	$0.244310\pi$
$198$		0			0
$199$	−11.9245	+	6.88462i	−0.845306	+	0.488038i	−0.859064	−	0.511867i	$-0.828954\pi$
$199$	−11.9245	+	6.88462i	−0.845306	+	0.488038i	0.0137580	+	0.999905i	$0.495621\pi$
$200$		0			0
$201$	5.65670			0.398993
$202$		0			0
$203$	−9.89960	−	17.1466i	−0.694816	−	1.20346i
$204$		0			0
$205$	−5.90237	+	3.40773i	−0.412239	+	0.238006i
$206$		0			0
$207$	−0.396301	−	0.228805i	−0.0275449	−	0.0159030i
$208$		0			0
$209$	3.14050	−	1.66091i	0.217233	−	0.114888i
$210$		0			0
$211$	11.1743	−	19.3544i	0.769267	−	1.33241i	−0.168693	−	0.985669i	$-0.553955\pi$
$211$	11.1743	−	19.3544i	0.769267	−	1.33241i	0.937961	−	0.346742i	$-0.112712\pi$
$212$		0			0
$213$	3.55868	+	6.16382i	0.243837	+	0.422338i
$214$		0			0
$215$	−12.3098	+	7.10707i	−0.839522	+	0.484698i
$216$		0			0
$217$			19.1034i			1.29682i
$218$		0			0
$219$	−0.533501	−	0.924052i	−0.0360507	−	0.0624416i
$220$		0			0
$221$			6.38978i			0.429823i
$222$		0			0
$223$	8.05761	−	13.9562i	0.539577	−	0.934575i	−0.459349	−	0.888256i	$-0.651917\pi$
$223$	8.05761	−	13.9562i	0.539577	−	0.934575i	0.998927	−	0.0463196i	$-0.0147493\pi$
$224$		0			0
$225$	1.57509	−	2.72814i	0.105006	−	0.181876i
$226$		0			0
$227$	−8.98401			−0.596290			−0.298145	−	0.954521i	$-0.596368\pi$
$227$	−8.98401			−0.596290			−0.298145	+	0.954521i	$0.596368\pi$
$228$		0			0
$229$	−20.0571			−1.32541			−0.662706	−	0.748880i	$-0.730592\pi$
$229$	−20.0571			−1.32541			−0.662706	+	0.748880i	$0.730592\pi$
$230$		0			0
$231$	−1.30077	+	2.25300i	−0.0855843	+	0.148236i
$232$		0			0
$233$	−2.16481	+	3.74957i	−0.141822	+	0.245642i	−0.928183	−	0.372125i	$-0.878629\pi$
$233$	−2.16481	+	3.74957i	−0.141822	+	0.245642i	0.786361	+	0.617767i	$0.211963\pi$
$234$		0			0
$235$			2.48403i			0.162040i
$236$		0			0
$237$	−1.26133	−	2.18469i	−0.0819321	−	0.141911i
$238$		0			0
$239$			9.34522i			0.604492i	0.953230	+	0.302246i	$0.0977364\pi$
$239$			9.34522i			0.604492i	−0.953230	+	0.302246i	$0.902264\pi$
$240$		0			0
$241$	−9.78580	+	5.64984i	−0.630359	+	0.363938i	−0.780891	−	0.624667i	$-0.785235\pi$
$241$	−9.78580	+	5.64984i	−0.630359	+	0.363938i	0.150532	+	0.988605i	$0.451901\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−2.16823	+	3.75549i	−0.138523	+	0.239930i
$246$		0			0
$247$	−9.34310	−	5.86706i	−0.594487	−	0.373312i
$248$		0			0
$249$	11.4075	+	6.58612i	0.722921	+	0.417379i
$250$		0			0
$251$	18.3054	−	10.5686i	1.15543	−	0.667085i	0.205222	−	0.978715i	$-0.434208\pi$
$251$	18.3054	−	10.5686i	1.15543	−	0.667085i	0.950203	+	0.311630i	$0.100875\pi$
$252$		0			0
$253$	0.186484	+	0.323000i	0.0117242	+	0.0203068i
$254$		0			0
$255$	−3.43363			−0.215022
$256$		0			0
$257$	−14.2020	+	8.19950i	−0.885894	+	0.511471i	−0.872597	−	0.488441i	$-0.837566\pi$
$257$	−14.2020	+	8.19950i	−0.885894	+	0.511471i	−0.0132965	+	0.999912i	$0.504233\pi$
$258$		0			0
$259$	−22.5395			−1.40053
$260$		0			0
$261$	−5.37187	−	3.10145i	−0.332510	−	0.191975i
$262$		0			0
$263$	18.6815	+	10.7858i	1.15195	+	0.665080i	0.949362	−	0.314184i	$-0.101731\pi$
$263$	18.6815	+	10.7858i	1.15195	+	0.665080i	0.202590	+	0.979264i	$0.435064\pi$
$264$		0			0
$265$			2.95589i			0.181579i
$266$		0			0
$267$			7.89073i			0.482905i
$268$		0			0
$269$	17.8072	+	10.2810i	1.08572	+	0.626842i	0.932434	−	0.361340i	$-0.117681\pi$
$269$	17.8072	+	10.2810i	1.08572	+	0.626842i	0.153288	+	0.988182i	$0.451014\pi$
$270$		0			0
$271$	1.29676	+	0.748682i	0.0787723	+	0.0454792i	0.538869	−	0.842390i	$-0.318852\pi$
$271$	1.29676	+	0.748682i	0.0787723	+	0.0454792i	−0.460097	+	0.887869i	$0.652185\pi$
$272$		0			0
$273$	8.07886			0.488955
$274$		0			0
$275$	−2.22354	+	1.28376i	−0.134084	+	0.0774136i
$276$		0			0
$277$	−9.23660			−0.554973			−0.277487	−	0.960729i	$-0.589501\pi$
$277$	−9.23660			−0.554973			−0.277487	+	0.960729i	$0.589501\pi$
$278$		0			0
$279$	2.99246	+	5.18309i	0.179154	+	0.310303i
$280$		0			0
$281$	−9.31629	+	5.37876i	−0.555763	+	0.320870i	−0.751443	−	0.659798i	$-0.770642\pi$
$281$	−9.31629	+	5.37876i	−0.555763	+	0.320870i	0.195680	+	0.980668i	$0.437309\pi$
$282$		0			0
$283$	16.6346	+	9.60401i	0.988826	+	0.570899i	0.904923	−	0.425575i	$-0.139928\pi$
$283$	16.6346	+	9.60401i	0.988826	+	0.570899i	0.0839028	+	0.996474i	$0.473261\pi$
$284$		0			0
$285$	3.15274	−	5.02063i	0.186752	−	0.297396i
$286$		0			0
$287$	−7.99751	+	13.8521i	−0.472078	+	0.817663i
$288$		0			0
$289$	5.31325	+	9.20282i	0.312544	+	0.541342i
$290$		0			0
$291$	−1.14814	+	0.662881i	−0.0673054	+	0.0388588i
$292$		0			0
$293$		−	3.18687i		−	0.186179i	−0.995658	−	0.0930896i	$-0.970326\pi$
$293$		−	3.18687i		−	0.186179i	0.995658	−	0.0930896i	$-0.0296743\pi$
$294$		0			0
$295$	4.06077	+	7.03346i	0.236427	+	0.409504i
$296$		0			0
$297$			0.815036i			0.0472932i
$298$		0			0
$299$	0.579111	−	1.00305i	0.0334909	−	0.0580079i
$300$		0			0
$301$	−16.6794	+	28.8895i	−0.961383	+	1.66516i
$302$		0			0
$303$	9.90823			0.569213
$304$		0			0
$305$	1.35234			0.0774346
$306$		0			0
$307$	−8.62186	+	14.9335i	−0.492075	+	0.852300i	−0.999958	−	0.00912646i	$-0.997095\pi$
$307$	−8.62186	+	14.9335i	−0.492075	+	0.852300i	0.507883	+	0.861426i	$0.330428\pi$
$308$		0			0
$309$	0.261074	−	0.452194i	0.0148520	−	0.0257244i
$310$		0			0
$311$			6.63930i			0.376480i	0.982123	+	0.188240i	$0.0602783\pi$
$311$			6.63930i			0.376480i	−0.982123	+	0.188240i	$0.939722\pi$
$312$		0			0
$313$	2.13197	+	3.69268i	0.120506	+	0.208723i	0.919967	−	0.391995i	$-0.128215\pi$
$313$	2.13197	+	3.69268i	0.120506	+	0.208723i	−0.799461	+	0.600718i	$0.794882\pi$
$314$		0			0
$315$			4.34127i			0.244603i
$316$		0			0
$317$	−22.7804	+	13.1523i	−1.27947	+	0.738705i	−0.976752	−	0.214374i	$-0.931229\pi$
$317$	−22.7804	+	13.1523i	−1.27947	+	0.738705i	−0.302723	+	0.953079i	$0.597896\pi$
$318$		0			0
$319$	2.52779	+	4.37827i	0.141529	+	0.245136i
$320$		0			0
$321$	2.25617	−	3.90781i	0.125927	−	0.218113i
$322$		0			0
$323$	10.9968	+	0.408432i	0.611879	+	0.0227258i
$324$		0			0
$325$	6.90501	+	3.98661i	0.383021	+	0.221137i
$326$		0			0
$327$	12.4683	−	7.19855i	0.689497	−	0.398081i
$328$		0			0
$329$	2.91485	+	5.04866i	0.160701	+	0.278342i
$330$		0			0
$331$	−23.0448			−1.26666			−0.633328	−	0.773884i	$-0.718312\pi$
$331$	−23.0448			−1.26666			−0.633328	+	0.773884i	$0.718312\pi$
$332$		0			0
$333$	−6.11535	+	3.53070i	−0.335119	+	0.193481i
$334$		0			0
$335$	−7.69355			−0.420344
$336$		0			0
$337$	−17.3138	−	9.99611i	−0.943141	−	0.544523i	−0.0521976	−	0.998637i	$-0.516623\pi$
$337$	−17.3138	−	9.99611i	−0.943141	−	0.544523i	−0.890944	+	0.454114i	$0.849956\pi$
$338$		0			0
$339$	11.6925	+	6.75066i	0.635049	+	0.366646i
$340$		0			0
$341$		−	4.87792i		−	0.264154i
$342$		0			0
$343$		−	12.1664i		−	0.656922i
$344$		0			0
$345$	0.539001	+	0.311192i	0.0290188	+	0.0167540i
$346$		0			0
$347$	13.6726	+	7.89388i	0.733984	+	0.423766i	0.819878	−	0.572539i	$-0.194041\pi$
$347$	13.6726	+	7.89388i	0.733984	+	0.423766i	−0.0858941	+	0.996304i	$0.527375\pi$
$348$		0			0
$349$	14.5286			0.777699			0.388849	−	0.921301i	$-0.372873\pi$
$349$	14.5286			0.777699			0.388849	+	0.921301i	$0.372873\pi$
$350$		0			0
$351$	2.19194	−	1.26551i	0.116997	−	0.0675482i
$352$		0			0
$353$	−26.1997			−1.39447			−0.697235	−	0.716843i	$-0.745586\pi$
$353$	−26.1997			−1.39447			−0.697235	+	0.716843i	$0.745586\pi$
$354$		0			0
$355$	−4.84009	−	8.38328i	−0.256885	−	0.444938i
$356$		0			0
$357$	−6.97867	+	4.02914i	−0.369350	+	0.213245i
$358$		0			0
$359$	20.5978	+	11.8922i	1.08711	+	0.627644i	0.932806	−	0.360379i	$-0.117352\pi$
$359$	20.5978	+	11.8922i	1.08711	+	0.627644i	0.154306	+	0.988023i	$0.450686\pi$
$360$		0			0
$361$	−10.6944	+	15.7044i	−0.562864	+	0.826550i
$362$		0			0
$363$	−5.16786	+	8.95099i	−0.271242	+	0.469805i
$364$		0			0
$365$	0.725604	+	1.25678i	0.0379798	+	0.0657830i
$366$		0			0
$367$	29.8775	−	17.2498i	1.55959	−	0.900430i	0.562295	−	0.826937i	$-0.309919\pi$
$367$	29.8775	−	17.2498i	1.55959	−	0.900430i	0.997296	−	0.0734935i	$-0.0234148\pi$
$368$		0			0
$369$			5.01109i			0.260867i
$370$		0			0
$371$	3.46854	+	6.00769i	0.180078	+	0.311904i
$372$		0			0
$373$			0.832538i			0.0431072i	0.999768	+	0.0215536i	$0.00686125\pi$
$373$			0.832538i			0.0431072i	−0.999768	+	0.0215536i	$0.993139\pi$
$374$		0			0
$375$	−5.54245	+	9.59980i	−0.286211	+	0.495731i
$376$		0			0
$377$	7.84986	−	13.5964i	0.404288	−	0.700248i
$378$		0			0
$379$	19.6123			1.00742			0.503709	−	0.863873i	$-0.331968\pi$
$379$	19.6123			1.00742			0.503709	+	0.863873i	$0.331968\pi$
$380$		0			0
$381$	−11.9254			−0.610956
$382$		0			0
$383$	−3.09036	+	5.35266i	−0.157910	+	0.273508i	−0.934115	−	0.356973i	$-0.883809\pi$
$383$	−3.09036	+	5.35266i	−0.157910	+	0.273508i	0.776205	+	0.630481i	$0.217142\pi$
$384$		0			0
$385$	1.76915	−	3.06425i	0.0901640	−	0.156169i
$386$		0			0
$387$			10.4510i			0.531253i
$388$		0			0
$389$	−1.99527	−	3.45591i	−0.101164	−	0.175222i	0.811000	−	0.585046i	$-0.198923\pi$
$389$	−1.99527	−	3.45591i	−0.101164	−	0.175222i	−0.912165	+	0.409824i	$0.865590\pi$
$390$		0			0
$391$			1.15527i			0.0584246i
$392$		0			0
$393$	−8.95943	+	5.17273i	−0.451944	+	0.260930i
$394$		0			0
$395$	1.71551	+	2.97134i	0.0863165	+	0.149505i
$396$		0			0
$397$	−5.06348	+	8.77021i	−0.254129	+	0.440164i	−0.964659	−	0.263503i	$-0.915122\pi$
$397$	−5.06348	+	8.77021i	−0.254129	+	0.440164i	0.710530	+	0.703667i	$0.248455\pi$
$398$		0			0
$399$	0.516397	−	13.9037i	0.0258522	−	0.696056i
$400$		0			0
$401$	1.17546	+	0.678651i	0.0586996	+	0.0338902i	0.529063	−	0.848583i	$-0.322544\pi$
$401$	1.17546	+	0.678651i	0.0586996	+	0.0338902i	−0.470363	+	0.882473i	$0.655877\pi$
$402$		0			0
$403$	−13.1185	+	7.57400i	−0.653481	+	0.377288i
$404$		0			0
$405$	0.680039	+	1.17786i	0.0337914	+	0.0585284i
$406$		0			0
$407$	5.75529			0.285279
$408$		0			0
$409$	26.2823	−	15.1741i	1.29958	−	0.750310i	0.319245	−	0.947672i	$-0.396571\pi$
$409$	26.2823	−	15.1741i	1.29958	−	0.750310i	0.980331	+	0.197362i	$0.0632375\pi$
$410$		0			0
$411$	−5.22205			−0.257585
$412$		0			0
$413$	16.5066	+	9.53010i	0.812237	+	0.468945i
$414$		0			0
$415$	−15.5151	−	8.95764i	−0.761606	−	0.439713i
$416$		0			0
$417$			0.292840i			0.0143405i
$418$		0			0
$419$			24.5003i			1.19692i	0.801154	+	0.598458i	$0.204220\pi$
$419$			24.5003i			1.19692i	−0.801154	+	0.598458i	$0.795780\pi$
$420$		0			0
$421$	−3.71552	−	2.14516i	−0.181083	−	0.104549i	0.406718	−	0.913554i	$-0.366673\pi$
$421$	−3.71552	−	2.14516i	−0.181083	−	0.104549i	−0.587802	+	0.809005i	$0.700006\pi$
$422$		0			0
$423$	1.58170	+	0.913193i	0.0769048	+	0.0444010i
$424$		0			0
$425$	−7.95290			−0.385772
$426$		0			0
$427$	2.74856	−	1.58688i	0.133012	−	0.0767945i
$428$		0			0
$429$	−2.06288			−0.0995968
$430$		0			0
$431$	7.64144	+	13.2354i	0.368075	+	0.637525i	0.989265	−	0.146136i	$-0.0466836\pi$
$431$	7.64144	+	13.2354i	0.368075	+	0.637525i	−0.621189	+	0.783660i	$0.713350\pi$
$432$		0			0
$433$	8.61795	−	4.97558i	0.414152	−	0.239111i	−0.278420	−	0.960459i	$-0.589811\pi$
$433$	8.61795	−	4.97558i	0.414152	−	0.239111i	0.692572	+	0.721348i	$0.256477\pi$
$434$		0			0
$435$	7.30616	+	4.21821i	0.350304	+	0.202248i
$436$		0			0
$437$	−1.68923	−	1.06076i	−0.0808069	−	0.0507432i
$438$		0			0
$439$	−1.05795	+	1.83243i	−0.0504933	+	0.0874569i	−0.890167	−	0.455634i	$-0.849413\pi$
$439$	−1.05795	+	1.83243i	−0.0504933	+	0.0874569i	0.839674	+	0.543091i	$0.182746\pi$
$440$		0			0
$441$	1.59420	+	2.76123i	0.0759142	+	0.131487i
$442$		0			0
$443$	12.6417	−	7.29871i	0.600627	−	0.346772i	−0.168661	−	0.985674i	$-0.553944\pi$
$443$	12.6417	−	7.29871i	0.600627	−	0.346772i	0.769288	+	0.638902i	$0.220611\pi$
$444$		0			0
$445$		−	10.7320i		−	0.508746i
$446$		0			0
$447$	6.53165	+	11.3131i	0.308936	+	0.535093i
$448$		0			0
$449$			38.9286i			1.83716i	0.395240	+	0.918578i	$0.370662\pi$
$449$			38.9286i			1.83716i	−0.395240	+	0.918578i	$0.629338\pi$
$450$		0			0
$451$	2.04211	−	3.53704i	0.0961591	−	0.166552i
$452$		0			0
$453$	3.44095	−	5.95990i	0.161670	−	0.280021i
$454$		0			0
$455$	−10.9879			−0.515120
$456$		0			0
$457$	21.3893			1.00055			0.500274	−	0.865867i	$-0.333232\pi$
$457$	21.3893			1.00055			0.500274	+	0.865867i	$0.333232\pi$
$458$		0			0
$459$	−1.26229	+	2.18635i	−0.0589186	+	0.102050i
$460$		0			0
$461$	8.75205	−	15.1590i	0.407624	−	0.706025i	−0.586999	−	0.809587i	$-0.699691\pi$
$461$	8.75205	−	15.1590i	0.407624	−	0.706025i	0.994623	+	0.103563i	$0.0330242\pi$
$462$		0			0
$463$		−	14.3545i		−	0.667109i	−0.942731	−	0.333554i	$-0.891752\pi$
$463$		−	14.3545i		−	0.667109i	0.942731	−	0.333554i	$-0.108248\pi$
$464$		0			0
$465$	−4.06998	−	7.04941i	−0.188741	−	0.326908i
$466$		0			0
$467$			7.15526i			0.331106i	0.986201	+	0.165553i	$0.0529409\pi$
$467$			7.15526i			0.331106i	−0.986201	+	0.165553i	$0.947059\pi$
$468$		0			0
$469$	−15.6368	+	9.02788i	−0.722038	+	0.416869i
$470$		0			0
$471$	3.63921	+	6.30330i	0.167686	+	0.290441i
$472$		0			0
$473$	4.25896	−	7.37674i	0.195827	−	0.339183i
$474$		0			0
$475$	7.30231	−	11.6287i	0.335053	−	0.533560i
$476$		0			0
$477$	1.88215	+	1.08666i	0.0861778	+	0.0497548i
$478$		0			0
$479$	15.9376	−	9.20159i	0.728208	−	0.420431i	−0.0895581	−	0.995982i	$-0.528545\pi$
$479$	15.9376	−	9.20159i	0.728208	−	0.420431i	0.817766	+	0.575550i	$0.195212\pi$
$480$		0			0
$481$	−8.93630	−	15.4781i	−0.407460	−	0.705742i
$482$		0			0
$483$	1.46066			0.0664621
$484$		0			0
$485$	1.56157	−	0.901570i	0.0709070	−	0.0409382i
$486$		0			0
$487$	−2.84071			−0.128725			−0.0643625	−	0.997927i	$-0.520501\pi$
$487$	−2.84071			−0.128725			−0.0643625	+	0.997927i	$0.520501\pi$
$488$		0			0
$489$	21.8081	+	12.5909i	0.986195	+	0.569380i
$490$		0			0
$491$	−17.5739	−	10.1463i	−0.793100	−	0.457896i	0.0479529	−	0.998850i	$-0.484730\pi$
$491$	−17.5739	−	10.1463i	−0.793100	−	0.457896i	−0.841053	+	0.540953i	$0.818064\pi$
$492$		0			0
$493$			15.6597i			0.705278i
$494$		0			0
$495$		−	1.10851i		−	0.0498240i
$496$		0			0
$497$	−19.6745	−	11.3591i	−0.882520	−	0.509523i
$498$		0			0
$499$	33.2101	+	19.1739i	1.48669	+	0.858340i	0.999885	−	0.0151717i	$-0.00482948\pi$
$499$	33.2101	+	19.1739i	1.48669	+	0.858340i	0.486803	+	0.873512i	$0.338163\pi$
$500$		0			0
$501$	−18.4806			−0.825650
$502$		0			0
$503$	22.0135	−	12.7095i	0.981532	−	0.566688i	0.0787998	−	0.996890i	$-0.474891\pi$
$503$	22.0135	−	12.7095i	0.981532	−	0.566688i	0.902732	+	0.430203i	$0.141558\pi$
$504$		0			0
$505$	−13.4760			−0.599673
$506$		0			0
$507$	−3.29695	−	5.71048i	−0.146423	−	0.253611i
$508$		0			0
$509$	8.99961	−	5.19593i	0.398901	−	0.230305i	−0.287109	−	0.957898i	$-0.592694\pi$
$509$	8.99961	−	5.19593i	0.398901	−	0.230305i	0.686010	+	0.727593i	$0.259361\pi$
$510$		0			0
$511$	2.94951	+	1.70290i	0.130478	+	0.0753318i
$512$		0			0
$513$	−2.03784	−	3.85321i	−0.0899728	−	0.170123i
$514$		0			0
$515$	−0.355081	+	0.615019i	−0.0156468	+	0.0271010i
$516$		0			0
$517$	−0.744286	−	1.28914i	−0.0327336	−	0.0566963i
$518$		0			0
$519$	−20.3193	+	11.7313i	−0.891916	+	0.514948i
$520$		0			0
$521$			33.4183i			1.46408i	0.681260	+	0.732042i	$0.261432\pi$
$521$			33.4183i			1.46408i	−0.681260	+	0.732042i	$0.738568\pi$
$522$		0			0
$523$	9.27666	+	16.0676i	0.405640	+	0.702589i	0.994396	−	0.105722i	$-0.0337154\pi$
$523$	9.27666	+	16.0676i	0.405640	+	0.702589i	−0.588756	+	0.808311i	$0.700382\pi$
$524$		0			0
$525$			10.0552i			0.438844i
$526$		0			0
$527$	7.55470	−	13.0851i	0.329088	−	0.569997i
$528$		0			0
$529$	−11.3953	+	19.7372i	−0.495448	+	0.858141i
$530$		0			0
$531$	5.97137			0.259136
$532$		0			0
$533$	−12.6832			−0.549370
$534$		0			0
$535$	−3.06857	+	5.31493i	−0.132666	+	0.229784i
$536$		0			0
$537$	2.44325	−	4.23183i	0.105434	−	0.182617i
$538$		0			0
$539$		−	2.59866i		−	0.111932i
$540$		0			0
$541$	−0.416972	−	0.722217i	−0.0179270	−	0.0310505i	0.856923	−	0.515445i	$-0.172373\pi$
$541$	−0.416972	−	0.722217i	−0.0179270	−	0.0310505i	−0.874850	+	0.484394i	$0.839040\pi$
$542$		0			0
$543$		−	13.2917i		−	0.570401i
$544$		0			0
$545$	−16.9578	+	9.79060i	−0.726393	+	0.419383i
$546$		0			0
$547$	0.360313	+	0.624081i	0.0154059	+	0.0266838i	0.873626	−	0.486599i	$-0.161763\pi$
$547$	0.360313	+	0.624081i	0.0154059	+	0.0266838i	−0.858220	+	0.513283i	$0.828429\pi$
$548$		0			0
$549$	0.497154	−	0.861096i	0.0212180	−	0.0367507i
$550$		0			0
$551$	−22.8975	−	14.3787i	−0.975468	−	0.612552i
$552$		0			0
$553$	6.97336	+	4.02607i	0.296537	+	0.171206i
$554$		0			0
$555$	8.31735	−	4.80202i	0.353052	−	0.203835i
$556$		0			0
$557$	12.2451	+	21.2091i	0.518841	+	0.898659i	0.999760	+	0.0218943i	$0.00696972\pi$
$557$	12.2451	+	21.2091i	0.518841	+	0.898659i	−0.480919	+	0.876765i	$0.659697\pi$
$558$		0			0
$559$	−26.4517			−1.11879
$560$		0			0
$561$	1.78195	−	1.02881i	0.0752342	−	0.0434365i
$562$		0			0
$563$	−8.83717			−0.372442			−0.186221	−	0.982508i	$-0.559624\pi$
$563$	−8.83717			−0.372442			−0.186221	+	0.982508i	$0.559624\pi$
$564$		0			0
$565$	−15.9027	−	9.18143i	−0.669032	−	0.386266i
$566$		0			0
$567$	2.76429	+	1.59596i	0.116089	+	0.0670242i
$568$		0			0
$569$		−	44.5270i		−	1.86667i	−0.359008	−	0.933335i	$-0.616885\pi$
$569$		−	44.5270i		−	1.86667i	0.359008	−	0.933335i	$-0.383115\pi$
$570$		0			0
$571$			6.83228i			0.285922i	0.989728	+	0.142961i	$0.0456624\pi$
$571$			6.83228i			0.285922i	−0.989728	+	0.142961i	$0.954338\pi$
$572$		0			0
$573$	1.62320	+	0.937156i	0.0678102	+	0.0391502i
$574$		0			0
$575$	1.24842	+	0.720778i	0.0520629	+	0.0300585i
$576$		0			0
$577$	9.38182			0.390570			0.195285	−	0.980747i	$-0.437437\pi$
$577$	9.38182			0.390570			0.195285	+	0.980747i	$0.437437\pi$
$578$		0			0
$579$	14.6260	−	8.44430i	0.607834	−	0.350933i
$580$		0			0
$581$	−42.0448			−1.74431
$582$		0			0
$583$	−0.885668	−	1.53402i	−0.0366806	−	0.0635327i
$584$		0			0
$585$	−2.98120	+	1.72120i	−0.123258	+	0.0711628i
$586$		0			0
$587$	24.6717	+	14.2442i	1.01831	+	0.587923i	0.913615	−	0.406581i	$-0.133279\pi$
$587$	24.6717	+	14.2442i	1.01831	+	0.587923i	0.104697	+	0.994504i	$0.466613\pi$
$588$		0			0
$589$	12.1963	+	23.0611i	0.502540	+	0.950217i
$590$		0			0
$591$	−10.1005	+	17.4946i	−0.415480	+	0.719633i
$592$		0			0
$593$	1.68664	+	2.92135i	0.0692622	+	0.119966i	0.898577	−	0.438816i	$-0.144602\pi$
$593$	1.68664	+	2.92135i	0.0692622	+	0.119966i	−0.829315	+	0.558782i	$0.811269\pi$
$594$		0			0
$595$	9.49154	−	5.47994i	0.389115	−	0.224656i
$596$		0			0
$597$		−	13.7692i		−	0.563538i
$598$		0			0
$599$	−0.463791	−	0.803310i	−0.0189500	−	0.0328224i	0.856395	−	0.516321i	$-0.172699\pi$
$599$	−0.463791	−	0.803310i	−0.0189500	−	0.0328224i	−0.875345	+	0.483499i	$0.839366\pi$
$600$		0			0
$601$			25.7094i			1.04871i	0.851501	+	0.524353i	$0.175693\pi$
$601$			25.7094i			1.04871i	−0.851501	+	0.524353i	$0.824307\pi$
$602$		0			0
$603$	−2.82835	+	4.89884i	−0.115179	+	0.199496i
$604$		0			0
$605$	7.02869	−	12.1740i	0.285757	−	0.494945i
$606$		0			0
$607$	7.05732			0.286448			0.143224	−	0.989690i	$-0.454253\pi$
$607$	7.05732			0.286448			0.143224	+	0.989690i	$0.454253\pi$
$608$		0			0
$609$	19.7992			0.802304
$610$		0			0
$611$	−2.31132	+	4.00332i	−0.0935059	+	0.161957i
$612$		0			0
$613$	3.53993	−	6.13133i	0.142976	−	0.247642i	−0.785640	−	0.618684i	$-0.787666\pi$
$613$	3.53993	−	6.13133i	0.142976	−	0.247642i	0.928616	+	0.371042i	$0.120999\pi$
$614$		0			0
$615$		−	6.81547i		−	0.274826i
$616$		0			0
$617$	−7.35470	−	12.7387i	−0.296089	−	0.512842i	0.679148	−	0.734001i	$-0.262349\pi$
$617$	−7.35470	−	12.7387i	−0.296089	−	0.512842i	−0.975238	+	0.221159i	$0.929016\pi$
$618$		0			0
$619$		−	7.12552i		−	0.286399i	−0.989694	−	0.143199i	$-0.954261\pi$
$619$		−	7.12552i		−	0.286399i	0.989694	−	0.143199i	$-0.0457390\pi$
$620$		0			0
$621$	0.396301	−	0.228805i	0.0159030	−	0.00918162i
$622$		0			0
$623$	−12.5933	−	21.8123i	−0.504540	−	0.873889i
$624$		0			0
$625$	−0.337309	+	0.584237i	−0.0134924	+	0.0233695i
$626$		0			0
$627$	−0.131858	+	3.55021i	−0.00526592	+	0.141782i
$628$		0			0
$629$	15.4387	+	8.91353i	0.615581	+	0.355406i
$630$		0			0
$631$	−4.93065	+	2.84671i	−0.196286	+	0.113326i	−0.594922	−	0.803783i	$-0.702817\pi$
$631$	−4.93065	+	2.84671i	−0.196286	+	0.113326i	0.398636	+	0.917109i	$0.369484\pi$
$632$		0			0
$633$	11.1743	+	19.3544i	0.444137	+	0.769267i
$634$		0			0
$635$	16.2195			0.643650
$636$		0			0
$637$	−6.98876	+	4.03496i	−0.276905	+	0.159871i
$638$		0			0
$639$	−7.11737			−0.281559
$640$		0			0
$641$	−19.3178	−	11.1532i	−0.763009	−	0.440523i	0.0673661	−	0.997728i	$-0.478540\pi$
$641$	−19.3178	−	11.1532i	−0.763009	−	0.440523i	−0.830375	+	0.557205i	$0.811874\pi$
$642$		0			0
$643$	−20.0419	−	11.5712i	−0.790376	−	0.456324i	0.0497186	−	0.998763i	$-0.484168\pi$
$643$	−20.0419	−	11.5712i	−0.790376	−	0.456324i	−0.840095	+	0.542439i	$0.817501\pi$
$644$		0			0
$645$		−	14.2141i		−	0.559681i
$646$		0			0
$647$		−	41.9410i		−	1.64887i	−0.565957	−	0.824435i	$-0.691493\pi$
$647$		−	41.9410i		−	1.64887i	0.565957	−	0.824435i	$-0.308507\pi$
$648$		0			0
$649$	−4.21485	−	2.43344i	−0.165447	−	0.0955210i
$650$		0			0
$651$	−16.5440	−	9.55171i	−0.648412	−	0.374361i
$652$		0			0
$653$	43.9617			1.72036			0.860178	−	0.509994i	$-0.170352\pi$
$653$	43.9617			1.72036			0.860178	+	0.509994i	$0.170352\pi$
$654$		0			0
$655$	12.1855	−	7.03532i	0.476128	−	0.274893i
$656$		0			0
$657$	1.06700			0.0416278
$658$		0			0
$659$	−1.56095	−	2.70365i	−0.0608061	−	0.105319i	0.834020	−	0.551734i	$-0.186034\pi$
$659$	−1.56095	−	2.70365i	−0.0608061	−	0.105319i	−0.894826	+	0.446415i	$0.852700\pi$
$660$		0			0
$661$	4.30829	−	2.48739i	0.167573	−	0.0967483i	−0.413868	−	0.910337i	$-0.635822\pi$
$661$	4.30829	−	2.48739i	0.167573	−	0.0967483i	0.581441	+	0.813589i	$0.302489\pi$
$662$		0			0
$663$	−5.53371	−	3.19489i	−0.214912	−	0.124079i
$664$		0			0
$665$	−0.702340	+	18.9101i	−0.0272356	+	0.733303i
$666$		0			0
$667$	1.41925	−	2.45822i	0.0549537	−	0.0951826i
$668$		0			0
$669$	8.05761	+	13.9562i	0.311525	+	0.539577i
$670$		0			0
$671$	−0.701825	+	0.405199i	−0.0270936	+	0.0156425i
$672$		0			0
$673$		−	21.4458i		−	0.826673i	−0.910578	−	0.413337i	$-0.864363\pi$
$673$		−	21.4458i		−	0.826673i	0.910578	−	0.413337i	$-0.135637\pi$
$674$		0			0
$675$	1.57509	+	2.72814i	0.0606254	+	0.105006i
$676$		0			0
$677$		−	35.6558i		−	1.37036i	−0.728373	−	0.685181i	$-0.759723\pi$
$677$		−	35.6558i		−	1.37036i	0.728373	−	0.685181i	$-0.240277\pi$
$678$		0			0
$679$	2.11587	−	3.66479i	0.0811996	−	0.140642i
$680$		0			0
$681$	4.49200	−	7.78038i	0.172134	−	0.298145i
$682$		0			0
$683$	18.2026			0.696504			0.348252	−	0.937401i	$-0.386775\pi$
$683$	18.2026			0.696504			0.348252	+	0.937401i	$0.386775\pi$
$684$		0			0
$685$	7.10240			0.271369
$686$		0			0
$687$	10.0286	−	17.3700i	0.382614	−	0.662706i
$688$		0			0
$689$	−2.75037	+	4.76378i	−0.104781	+	0.181486i
$690$		0			0
$691$			24.1474i			0.918609i	0.888279	+	0.459304i	$0.151901\pi$
$691$			24.1474i			0.918609i	−0.888279	+	0.459304i	$0.848099\pi$
$692$		0			0
$693$	−1.30077	−	2.25300i	−0.0494121	−	0.0855843i
$694$		0			0
$695$		−	0.398286i		−	0.0151078i
$696$		0			0
$697$	10.9560	−	6.32544i	0.414988	−	0.239593i
$698$		0			0
$699$	−2.16481	−	3.74957i	−0.0818808	−	0.141822i
$700$		0			0
$701$	21.6821	−	37.5544i	0.818920	−	1.41841i	−0.0875585	−	0.996159i	$-0.527906\pi$
$701$	21.6821	−	37.5544i	0.818920	−	1.41841i	0.906479	−	0.422252i	$-0.138760\pi$
$702$		0			0
$703$	−27.2090	+	14.3900i	−1.02621	+	0.542729i
$704$		0			0
$705$	−2.15123	−	1.24201i	−0.0810201	−	0.0467770i
$706$		0			0
$707$	−27.3892	+	15.8132i	−1.03008	+	0.594716i
$708$		0			0
$709$	−21.4501	−	37.1527i	−0.805575	−	1.39530i	−0.915902	−	0.401402i	$-0.868523\pi$
$709$	−21.4501	−	37.1527i	−0.805575	−	1.39530i	0.110327	−	0.993895i	$-0.464810\pi$
$710$		0			0
$711$	2.52266			0.0946071
$712$		0			0
$713$	−2.37183	+	1.36938i	−0.0888257	+	0.0512836i
$714$		0			0
$715$	2.80568			0.104926
$716$		0			0
$717$	−8.09320	−	4.67261i	−0.302246	−	0.174502i
$718$		0			0
$719$	−6.00523	−	3.46712i	−0.223957	−	0.129302i	0.383824	−	0.923406i	$-0.374607\pi$
$719$	−6.00523	−	3.46712i	−0.223957	−	0.129302i	−0.607781	+	0.794104i	$0.707940\pi$
$720$		0			0
$721$			1.66666i			0.0620697i
$722$		0			0
$723$		−	11.2997i		−	0.420239i
$724$		0			0
$725$	16.9224	+	9.77015i	0.628482	+	0.362854i
$726$		0			0
$727$	14.5089	+	8.37670i	0.538104	+	0.310674i	0.744310	−	0.667834i	$-0.232778\pi$
$727$	14.5089	+	8.37670i	0.538104	+	0.310674i	−0.206206	+	0.978509i	$0.566112\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	22.8495	−	13.1922i	0.845119	−	0.487930i
$732$		0			0
$733$	0.0389329			0.00143802			0.000719010	−	1.00000i	$-0.499771\pi$
$733$	0.0389329			0.00143802			0.000719010		1.00000i	$0.499771\pi$
$734$		0			0
$735$	−2.16823	−	3.75549i	−0.0799765	−	0.138523i
$736$		0			0
$737$	3.99274	−	2.30521i	0.147074	−	0.0849134i
$738$		0			0
$739$	32.0677	+	18.5143i	1.17963	+	0.681059i	0.955928	−	0.293600i	$-0.0948532\pi$
$739$	32.0677	+	18.5143i	1.17963	+	0.681059i	0.223700	+	0.974658i	$0.428187\pi$
$740$		0			0
$741$	9.75258	−	5.15783i	0.358270	−	0.189478i
$742$		0			0
$743$	−3.35804	+	5.81630i	−0.123195	+	0.213379i	−0.921026	−	0.389502i	$-0.872647\pi$
$743$	−3.35804	+	5.81630i	−0.123195	+	0.213379i	0.797831	+	0.602881i	$0.205981\pi$
$744$		0			0
$745$	−8.88355	−	15.3868i	−0.325468	−	0.563727i
$746$		0			0
$747$	−11.4075	+	6.58612i	−0.417379	+	0.240974i
$748$		0			0
$749$			14.4031i			0.526277i
$750$		0			0
$751$	24.1661	+	41.8568i	0.881832	+	1.52738i	0.849302	+	0.527907i	$0.177023\pi$
$751$	24.1661	+	41.8568i	0.881832	+	1.52738i	0.0325296	+	0.999471i	$0.489644\pi$
$752$		0			0
$753$			21.1372i			0.770284i
$754$		0			0
$755$	−4.67996	+	8.10593i	−0.170321	+	0.295005i
$756$		0			0
$757$	13.3014	−	23.0386i	0.483446	−	0.837354i	−0.516373	−	0.856364i	$-0.672718\pi$
$757$	13.3014	−	23.0386i	0.483446	−	0.837354i	0.999819	+	0.0190101i	$0.00605145\pi$
$758$		0			0
$759$	−0.372968			−0.0135379
$760$		0			0
$761$	7.29404			0.264409			0.132204	−	0.991222i	$-0.457794\pi$
$761$	7.29404			0.264409			0.132204	+	0.991222i	$0.457794\pi$
$762$		0			0
$763$	−22.9773	+	39.7978i	−0.831833	+	1.44078i
$764$		0			0
$765$	1.71681	−	2.97361i	0.0620715	−	0.107511i
$766$		0			0
$767$			15.1137i			0.545725i
$768$		0			0
$769$	−12.2903	−	21.2874i	−0.443199	−	0.767643i	0.554726	−	0.832033i	$-0.312823\pi$
$769$	−12.2903	−	21.2874i	−0.443199	−	0.767643i	−0.997925	+	0.0643900i	$0.979490\pi$
$770$		0			0
$771$		−	16.3990i		−	0.590596i
$772$		0			0
$773$	17.8715	−	10.3181i	0.642792	−	0.371116i	−0.142897	−	0.989738i	$-0.545642\pi$
$773$	17.8715	−	10.3181i	0.642792	−	0.371116i	0.785689	+	0.618621i	$0.212308\pi$
$774$		0			0
$775$	−9.42680	−	16.3277i	−0.338621	−	0.586508i
$776$		0			0
$777$	11.2697	−	19.5197i	0.404299	−	0.700267i
$778$		0			0
$779$	−0.810704	+	21.8278i	−0.0290465	+	0.782061i
$780$		0			0
$781$	5.02374	+	2.90046i	0.179763	+	0.103786i
$782$		0			0
$783$	5.37187	−	3.10145i	0.191975	−	0.110837i
$784$		0			0
$785$	−4.94961	−	8.57297i	−0.176659	−	0.305983i
$786$		0			0
$787$	−7.12095			−0.253835			−0.126917	−	0.991913i	$-0.540508\pi$
$787$	−7.12095			−0.253835			−0.126917	+	0.991913i	$0.540508\pi$
$788$		0			0
$789$	−18.6815	+	10.7858i	−0.665080	+	0.383984i
$790$		0			0
$791$	−43.0952			−1.53229
$792$		0			0
$793$	2.17946	+	1.25831i	0.0773949	+	0.0446840i
$794$		0			0
$795$	−2.55987	−	1.47794i	−0.0907894	−	0.0524173i
$796$		0			0
$797$			22.2823i			0.789279i	0.918836	+	0.394640i	$0.129131\pi$
$797$			22.2823i			0.789279i	−0.918836	+	0.394640i	$0.870869\pi$
$798$		0			0
$799$		−	4.61086i		−	0.163120i
$800$		0			0
$801$	−6.83357	−	3.94536i	−0.241452	−	0.139403i
$802$		0			0
$803$	−0.753136	−	0.434823i	−0.0265776	−	0.0153446i
$804$		0			0
$805$	−1.98661			−0.0700187
$806$		0			0
$807$	−17.8072	+	10.2810i	−0.626842	+	0.361907i
$808$		0			0
$809$	−48.8066			−1.71595			−0.857974	−	0.513694i	$-0.828277\pi$
$809$	−48.8066			−1.71595			−0.857974	+	0.513694i	$0.828277\pi$
$810$		0			0
$811$	2.84729	+	4.93165i	0.0999819	+	0.173174i	0.911677	−	0.410908i	$-0.134788\pi$
$811$	2.84729	+	4.93165i	0.0999819	+	0.173174i	−0.811695	+	0.584082i	$0.801455\pi$
$812$		0			0
$813$	−1.29676	+	0.748682i	−0.0454792	+	0.0262574i
$814$		0			0
$815$	−29.6607	−	17.1246i	−1.03897	−	0.599848i
$816$		0			0
$817$	−1.69078	+	45.5233i	−0.0591529	+	1.59266i
$818$		0			0
$819$	−4.03943	+	6.99650i	−0.141149	+	0.244477i
$820$		0			0
$821$	−7.75928	−	13.4395i	−0.270801	−	0.469041i	0.698266	−	0.715838i	$-0.253955\pi$
$821$	−7.75928	−	13.4395i	−0.270801	−	0.469041i	−0.969067	+	0.246797i	$0.920622\pi$
$822$		0			0
$823$	−9.98402	+	5.76427i	−0.348021	+	0.200930i	−0.663813	−	0.747898i	$-0.731063\pi$
$823$	−9.98402	+	5.76427i	−0.348021	+	0.200930i	0.315792	+	0.948828i	$0.397730\pi$
$824$		0			0
$825$		−	2.56752i		−	0.0893895i
$826$		0			0
$827$	10.2704	+	17.7889i	0.357138	+	0.618581i	0.987481	−	0.157736i	$-0.0504194\pi$
$827$	10.2704	+	17.7889i	0.357138	+	0.618581i	−0.630344	+	0.776316i	$0.717086\pi$
$828$		0			0
$829$		−	9.67745i		−	0.336112i	−0.985777	−	0.168056i	$-0.946251\pi$
$829$		−	9.67745i		−	0.336112i	0.985777	−	0.168056i	$-0.0537489\pi$
$830$		0			0
$831$	4.61830	−	7.99913i	0.160207	−	0.277487i
$832$		0			0
$833$	4.02468	−	6.97095i	0.139447	−	0.241529i
$834$		0			0
$835$	25.1350			0.869833
$836$		0			0
$837$	−5.98492			−0.206869
$838$		0			0
$839$	27.5193	−	47.6649i	0.950073	−	1.64557i	0.204813	−	0.978801i	$-0.434341\pi$
$839$	27.5193	−	47.6649i	0.950073	−	1.64557i	0.745260	−	0.666774i	$-0.232325\pi$
$840$		0			0
$841$	4.73799	−	8.20644i	0.163379	−	0.282981i
$842$		0			0
$843$		−	10.7575i		−	0.370509i
$844$		0			0
$845$	4.48411	+	7.76670i	0.154258	+	0.267183i
$846$		0			0
$847$		−	32.9908i		−	1.13358i
$848$		0			0
$849$	−16.6346	+	9.60401i	−0.570899	+	0.329609i
$850$		0			0
$851$	−1.61568	−	2.79844i	−0.0553848	−	0.0959293i
$852$		0			0
$853$	11.0083	−	19.0670i	0.376918	−	0.652840i	−0.613694	−	0.789544i	$-0.710317\pi$
$853$	11.0083	−	19.0670i	0.376918	−	0.652840i	0.990612	+	0.136703i	$0.0436507\pi$
$854$		0			0
$855$	2.77162	+	5.24066i	0.0947875	+	0.179227i
$856$		0			0
$857$	4.23150	+	2.44306i	0.144545	+	0.0834532i	0.570528	−	0.821278i	$-0.306738\pi$
$857$	4.23150	+	2.44306i	0.144545	+	0.0834532i	−0.425983	+	0.904731i	$0.640072\pi$
$858$		0			0
$859$	−31.8248	+	18.3740i	−1.08585	+	0.626914i	−0.932468	−	0.361253i	$-0.882349\pi$
$859$	−31.8248	+	18.3740i	−1.08585	+	0.626914i	−0.153380	+	0.988167i	$0.549016\pi$
$860$		0			0
$861$	−7.99751	−	13.8521i	−0.272554	−	0.472078i
$862$		0			0
$863$	−54.2500			−1.84669			−0.923345	−	0.383971i	$-0.874556\pi$
$863$	−54.2500			−1.84669			−0.923345	+	0.383971i	$0.874556\pi$
$864$		0			0
$865$	27.6358	−	15.9555i	0.939645	−	0.542504i
$866$		0			0
$867$	−10.6265			−0.360895
$868$		0			0
$869$	−1.78060	−	1.02803i	−0.0604027	−	0.0348735i
$870$		0			0
$871$	−12.3991	−	7.15863i	−0.420128	−	0.242561i
$872$		0			0
$873$		−	1.32576i		−	0.0448703i
$874$		0			0
$875$		−	35.3822i		−	1.19614i
$876$		0			0
$877$	37.9181	+	21.8920i	1.28040	+	0.739240i	0.976922	−	0.213598i	$-0.0685181\pi$
$877$	37.9181	+	21.8920i	1.28040	+	0.739240i	0.303480	+	0.952838i	$0.401851\pi$
$878$		0			0
$879$	2.75991	+	1.59344i	0.0930896	+	0.0537453i
$880$		0			0
$881$	−49.0180			−1.65146			−0.825729	−	0.564067i	$-0.809236\pi$
$881$	−49.0180			−1.65146			−0.825729	+	0.564067i	$0.809236\pi$
$882$		0			0
$883$	11.8069	−	6.81671i	0.397333	−	0.229400i	−0.287999	−	0.957631i	$-0.592990\pi$
$883$	11.8069	−	6.81671i	0.397333	−	0.229400i	0.685333	+	0.728230i	$0.259657\pi$
$884$		0			0
$885$	−8.12154			−0.273002
$886$		0			0
$887$	−9.13155	−	15.8163i	−0.306607	−	0.531059i	0.671011	−	0.741448i	$-0.265861\pi$
$887$	−9.13155	−	15.8163i	−0.306607	−	0.531059i	−0.977618	+	0.210388i	$0.932527\pi$
$888$		0			0
$889$	32.9652	−	19.0325i	1.10562	−	0.638329i
$890$		0			0
$891$	−0.705842	−	0.407518i	−0.0236466	−	0.0136524i
$892$		0			0
$893$	6.74197	+	4.23367i	0.225611	+	0.141674i
$894$		0			0
$895$	−3.32301	+	5.75562i	−0.111076	+	0.192389i
$896$		0			0
$897$	0.579111	+	1.00305i	0.0193360	+	0.0334909i
$898$		0			0
$899$	−32.1502	+	18.5619i	−1.07227	+	0.619075i
$900$		0			0
$901$		−	5.48672i		−	0.182789i
$902$		0			0
$903$	−16.6794	−	28.8895i	−0.555055	−	0.961383i
$904$		0			0
$905$			18.0777i			0.600924i
$906$		0			0
$907$	9.17887	−	15.8983i	0.304779	−	0.527893i	−0.672433	−	0.740158i	$-0.734751\pi$
$907$	9.17887	−	15.8983i	0.304779	−	0.527893i	0.977212	+	0.212265i	$0.0680840\pi$
$908$		0			0
$909$	−4.95412	+	8.58078i	−0.164318	+	0.284607i
$910$		0			0
$911$	−21.4173			−0.709586			−0.354793	−	0.934945i	$-0.615449\pi$
$911$	−21.4173			−0.709586			−0.354793	+	0.934945i	$0.615449\pi$
$912$		0			0
$913$	10.7359			0.355305
$914$		0			0
$915$	−0.676169	+	1.17116i	−0.0223534	+	0.0387173i
$916$		0			0
$917$	16.5110	−	28.5979i	0.545240	−	0.944384i
$918$		0			0
$919$			3.75300i			0.123800i	0.998082	+	0.0619001i	$0.0197160\pi$
$919$			3.75300i			0.123800i	−0.998082	+	0.0619001i	$0.980284\pi$
$920$		0			0
$921$	−8.62186	−	14.9335i	−0.284100	−	0.492075i
$922$		0			0
$923$		−	18.0143i		−	0.592947i
$924$		0			0
$925$	19.2645	−	11.1224i	0.633413	−	0.365701i
$926$		0			0
$927$	0.261074	+	0.452194i	0.00857481	+	0.0148520i
$928$		0			0
$929$	10.9369	−	18.9433i	0.358829	−	0.621511i	−0.628936	−	0.777457i	$-0.716509\pi$
$929$	10.9369	−	18.9433i	0.358829	−	0.621511i	0.987766	+	0.155946i	$0.0498426\pi$
$930$		0			0
$931$	6.49744	+	12.2856i	0.212945	+	0.402643i
$932$		0			0
$933$	−5.74980	−	3.31965i	−0.188240	−	0.108680i
$934$		0			0
$935$	−2.42360	+	1.39926i	−0.0792601	+	0.0457608i
$936$		0			0
$937$	18.6543	+	32.3102i	0.609409	+	1.05553i	0.991338	+	0.131336i	$0.0419266\pi$
$937$	18.6543	+	32.3102i	0.609409	+	1.05553i	−0.381929	+	0.924192i	$0.624740\pi$
$938$		0			0
$939$	−4.26394			−0.139148
$940$		0			0
$941$	−30.1328	+	17.3972i	−0.982302	+	0.567132i	−0.902964	−	0.429716i	$-0.858614\pi$
$941$	−30.1328	+	17.3972i	−0.982302	+	0.567132i	−0.0793375	+	0.996848i	$0.525280\pi$
$942$		0			0
$943$	−2.29312			−0.0746743
$944$		0			0
$945$	−3.75965	−	2.17063i	−0.122301	−	0.0706108i
$946$		0			0
$947$	−0.368948	−	0.213012i	−0.0119892	−	0.00692196i	0.493993	−	0.869466i	$-0.335537\pi$
$947$	−0.368948	−	0.213012i	−0.0119892	−	0.00692196i	−0.505983	+	0.862544i	$0.668870\pi$
$948$		0			0
$949$			2.70062i			0.0876657i
$950$		0			0
$951$		−	26.3045i		−	0.852983i
$952$		0			0
$953$	43.0070	+	24.8301i	1.39313	+	0.804325i	0.993661	−	0.112420i	$-0.0358603\pi$
$953$	43.0070	+	24.8301i	1.39313	+	0.804325i	0.399471	+	0.916746i	$0.369194\pi$
$954$		0			0
$955$	−2.20768	−	1.27460i	−0.0714389	−	0.0412452i
$956$		0			0
$957$	−5.05559			−0.163424
$958$		0			0
$959$	14.4353	−	8.33420i	0.466139	−	0.269125i
$960$		0			0
$961$	4.81921			0.155458
$962$		0			0
$963$	2.25617	+	3.90781i	0.0727042	+	0.125927i
$964$		0			0
$965$	−19.8924	+	11.4849i	−0.640360	+	0.369712i
$966$		0			0
$967$	−25.4959	−	14.7200i	−0.819892	−	0.473365i	0.0304874	−	0.999535i	$-0.490294\pi$
$967$	−25.4959	−	14.7200i	−0.819892	−	0.473365i	−0.850379	+	0.526170i	$0.823627\pi$
$968$		0			0
$969$	−5.85211	+	9.31930i	−0.187997	+	0.299379i
$970$		0			0
$971$	−30.2269	+	52.3545i	−0.970027	+	1.68014i	−0.274571	+	0.961567i	$0.588536\pi$
$971$	−30.2269	+	52.3545i	−0.970027	+	1.68014i	−0.695456	+	0.718569i	$0.744798\pi$
$972$		0			0
$973$	−0.467362	−	0.809495i	−0.0149829	−	0.0259512i
$974$		0			0
$975$	−6.90501	+	3.98661i	−0.221137	+	0.127674i
$976$		0			0
$977$		−	47.3648i		−	1.51533i	−0.652642	−	0.757667i	$-0.726339\pi$
$977$		−	47.3648i		−	1.51533i	0.652642	−	0.757667i	$-0.273661\pi$
$978$		0			0
$979$	3.21561	+	5.56961i	0.102771	+	0.178005i
$980$		0			0
$981$			14.3971i			0.459664i
$982$		0			0
$983$	28.4043	−	49.1977i	0.905956	−	1.56916i	0.0863269	−	0.996267i	$-0.472487\pi$
$983$	28.4043	−	49.1977i	0.905956	−	1.56916i	0.819629	−	0.572895i	$-0.194180\pi$
$984$		0			0
$985$	13.7375	−	23.7941i	0.437713	−	0.758142i
$986$		0			0
$987$	−5.82969			−0.185561
$988$		0			0
$989$	−4.78246			−0.152073
$990$		0			0
$991$	−6.05888	+	10.4943i	−0.192467	+	0.333362i	−0.946067	−	0.323971i	$-0.894982\pi$
$991$	−6.05888	+	10.4943i	−0.192467	+	0.333362i	0.753600	+	0.657333i	$0.228315\pi$
$992$		0			0
$993$	11.5224	−	19.9574i	0.365652	−	0.633328i
$994$		0			0
$995$			18.7272i			0.593694i
$996$		0			0
$997$	13.2196	+	22.8970i	0.418669	+	0.725157i	0.995806	−	0.0914910i	$-0.0291633\pi$
$997$	13.2196	+	22.8970i	0.418669	+	0.725157i	−0.577137	+	0.816648i	$0.695830\pi$
$998$		0			0
$999$		−	7.06140i		−	0.223413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1824.2.bb.a.1471.14	yes	40
4.3	odd	2		1824.2.bb.b.1471.14	yes	40
19.12	odd	6		1824.2.bb.b.31.14	yes	40
76.31	even	6	inner	1824.2.bb.a.31.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1824.2.bb.a.31.14	✓	40	76.31	even	6	inner
1824.2.bb.a.1471.14	yes	40	1.1	even	1	trivial
1824.2.bb.b.31.14	yes	40	19.12	odd	6
1824.2.bb.b.1471.14	yes	40	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.680039 - 1.17786i) q^{5} -3.19193i q^{7} +(-0.500000 - 0.866025i) q^{9} +0.815036i q^{11} +(2.19194 - 1.26551i) q^{13} +(0.680039 + 1.17786i) q^{15} +(-1.26229 + 2.18635i) q^{17} +(-2.03784 - 3.85321i) q^{19} +(2.76429 + 1.59596i) q^{21} +(0.396301 - 0.228805i) q^{23} +(1.57509 + 2.72814i) q^{25} +1.00000 q^{27} +(5.37187 - 3.10145i) q^{29} -5.98492 q^{31} +(-0.705842 - 0.407518i) q^{33} +(-3.75965 - 2.17063i) q^{35} -7.06140i q^{37} +2.53103i q^{39} +(-4.33973 - 2.50554i) q^{41} +(-9.05081 - 5.22549i) q^{43} -1.36008 q^{45} +(-1.58170 + 0.913193i) q^{47} -3.18840 q^{49} +(-1.26229 - 2.18635i) q^{51} +(-1.88215 + 1.08666i) q^{53} +(0.960000 + 0.554257i) q^{55} +(4.35590 + 0.161782i) q^{57} +(-2.98569 + 5.17136i) q^{59} +(0.497154 + 0.861096i) q^{61} +(-2.76429 + 1.59596i) q^{63} -3.44240i q^{65} +(-2.82835 - 4.89884i) q^{67} +0.457609i q^{69} +(3.55868 - 6.16382i) q^{71} +(-0.533501 + 0.924052i) q^{73} -3.15019 q^{75} +2.60154 q^{77} +(-1.26133 + 2.18469i) q^{79} +(-0.500000 + 0.866025i) q^{81} -13.1722i q^{83} +(1.71681 + 2.97361i) q^{85} +6.20290i q^{87} +(6.83357 - 3.94536i) q^{89} +(-4.03943 - 6.99650i) q^{91} +(2.99246 - 5.18309i) q^{93} +(-5.92436 - 0.220036i) q^{95} +(1.14814 + 0.662881i) q^{97} +(0.705842 - 0.407518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) \) 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more