LMFDB - Embedded newform 1440.2.cc.b.911.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(911,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("1440.911");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.cc (of order $6$, degree $2$, not 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			911.24
Character	$\chi$	$=$	1440.911
Dual form			1440.2.cc.b.1391.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 0.00397907i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(2.99997 - 0.0137839i) q^{9} +O(q^{10})$	\(q+(1.73205 - 0.00397907i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(2.99997 - 0.0137839i) q^{9} +(2.70422 + 1.56128i) q^{11} +(-3.30414 + 1.90765i) q^{13} +(0.869469 + 1.49801i) q^{15} -3.43533i q^{17} -1.31386 q^{19} +(4.17007 + 2.39484i) q^{21} +(2.13186 + 3.69249i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(5.19603 - 0.0358114i) q^{27} +(-0.266702 + 0.461941i) q^{29} +(-0.413107 + 0.238507i) q^{31} +(4.69004 + 2.69345i) q^{33} +2.77637i q^{35} -2.26255i q^{37} +(-5.71534 + 3.31728i) q^{39} +(-9.97758 + 5.76056i) q^{41} +(6.25878 - 10.8405i) q^{43} +(1.51192 + 2.59116i) q^{45} +(-1.52710 + 2.64501i) q^{47} +(0.354125 + 0.613362i) q^{49} +(-0.0136694 - 5.95014i) q^{51} -14.2847 q^{53} +3.12256i q^{55} +(-2.27567 + 0.00522795i) q^{57} +(8.89170 - 5.13363i) q^{59} +(10.7109 + 6.18395i) q^{61} +(7.23229 + 4.13137i) q^{63} +(-3.30414 - 1.90765i) q^{65} +(-3.47947 - 6.02663i) q^{67} +(3.70717 + 6.38708i) q^{69} -7.88557 q^{71} +7.92558 q^{73} +(-0.862577 + 1.50199i) q^{75} +(4.33470 + 7.50792i) q^{77} +(-0.187206 - 0.108084i) q^{79} +(8.99962 - 0.0827023i) q^{81} +(7.86428 + 4.54044i) q^{83} +(2.97508 - 1.71766i) q^{85} +(-0.460102 + 0.801164i) q^{87} -4.82215i q^{89} -10.5927 q^{91} +(-0.714571 + 0.414750i) q^{93} +(-0.656931 - 1.13784i) q^{95} +(-4.20125 + 7.27679i) q^{97} +(8.13409 + 4.64652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5}+O(q^{10}) $ 48 * q + 24 * q^5	$ 48 q + 24 q^{5} + 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} + 16 q^{39} + 12 q^{41} + 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} - 12 q^{61} + 56 q^{63} + 40 q^{69} - 8 q^{81} + 60 q^{83} + 36 q^{87} + 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 + 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 + 16 * q^39 + 12 * q^41 + 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 - 12 * q^61 + 56 * q^63 + 40 * q^69 - 8 * q^81 + 60 * q^83 + 36 * q^87 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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
$3$	1.73205	−	0.00397907i	0.999997	−	0.00229732i
$3$	1.73205	−	0.00397907i	0.999997	−	0.00229732i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.40441	+	1.38819i	0.908782	+	0.524685i	0.880039	−	0.474902i	$-0.157516\pi$
$7$	2.40441	+	1.38819i	0.908782	+	0.524685i	0.0287426	+	0.999587i	$0.490850\pi$
$8$		0			0
$9$	2.99997	−	0.0137839i	0.999989	−	0.00459462i
$10$		0			0
$11$	2.70422	+	1.56128i	0.815352	+	0.470744i	0.848811	−	0.528696i	$-0.177319\pi$
$11$	2.70422	+	1.56128i	0.815352	+	0.470744i	−0.0334589	+	0.999440i	$0.510652\pi$
$12$		0			0
$13$	−3.30414	+	1.90765i	−0.916405	+	0.529086i	−0.882486	−	0.470338i	$-0.844132\pi$
$13$	−3.30414	+	1.90765i	−0.916405	+	0.529086i	−0.0339183	+	0.999425i	$0.510799\pi$
$14$		0			0
$15$	0.869469	+	1.49801i	0.224496	+	0.386784i
$16$		0			0
$17$		−	3.43533i		−	0.833189i	−0.909092	−	0.416594i	$-0.863224\pi$
$17$		−	3.43533i		−	0.833189i	0.909092	−	0.416594i	$-0.136776\pi$
$18$		0			0
$19$	−1.31386			−0.301421			−0.150710	−	0.988578i	$-0.548156\pi$
$19$	−1.31386			−0.301421			−0.150710	+	0.988578i	$0.548156\pi$
$20$		0			0
$21$	4.17007	+	2.39484i	0.909984	+	0.522596i
$22$		0			0
$23$	2.13186	+	3.69249i	0.444524	+	0.769937i	0.998019	−	0.0629149i	$-0.0200397\pi$
$23$	2.13186	+	3.69249i	0.444524	+	0.769937i	−0.553495	+	0.832852i	$0.686706\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	5.19603	−	0.0358114i	0.999976	−	0.00689190i
$28$		0			0
$29$	−0.266702	+	0.461941i	−0.0495253	+	0.0857803i	−0.889725	−	0.456496i	$-0.849104\pi$
$29$	−0.266702	+	0.461941i	−0.0495253	+	0.0857803i	0.840200	+	0.542277i	$0.182437\pi$
$30$		0			0
$31$	−0.413107	+	0.238507i	−0.0741962	+	0.0428372i	−0.536639	−	0.843812i	$-0.680306\pi$
$31$	−0.413107	+	0.238507i	−0.0741962	+	0.0428372i	0.462443	+	0.886649i	$0.346973\pi$
$32$		0			0
$33$	4.69004	+	2.69345i	0.816431	+	0.468869i
$34$		0			0
$35$			2.77637i			0.469293i
$36$		0			0
$37$		−	2.26255i		−	0.371960i	−0.982554	−	0.185980i	$-0.940454\pi$
$37$		−	2.26255i		−	0.371960i	0.982554	−	0.185980i	$-0.0595460\pi$
$38$		0			0
$39$	−5.71534	+	3.31728i	−0.915187	+	0.531190i
$40$		0			0
$41$	−9.97758	+	5.76056i	−1.55824	+	0.899648i	−0.560809	+	0.827945i	$0.689510\pi$
$41$	−9.97758	+	5.76056i	−1.55824	+	0.899648i	−0.997426	+	0.0717028i	$0.977157\pi$
$42$		0			0
$43$	6.25878	−	10.8405i	0.954454	−	1.65316i	0.218842	−	0.975760i	$-0.429772\pi$
$43$	6.25878	−	10.8405i	0.954454	−	1.65316i	0.735612	−	0.677403i	$-0.236895\pi$
$44$		0			0
$45$	1.51192	+	2.59116i	0.225384	+	0.386267i
$46$		0			0
$47$	−1.52710	+	2.64501i	−0.222750	+	0.385814i	−0.955642	−	0.294531i	$-0.904837\pi$
$47$	−1.52710	+	2.64501i	−0.222750	+	0.385814i	0.732892	+	0.680345i	$0.238170\pi$
$48$		0			0
$49$	0.354125	+	0.613362i	0.0505892	+	0.0876231i
$50$		0			0
$51$	−0.0136694	−	5.95014i	−0.00191410	−	0.833187i
$52$		0			0
$53$	−14.2847			−1.96215			−0.981075	−	0.193629i	$-0.937974\pi$
$53$	−14.2847			−1.96215			−0.981075	+	0.193629i	$0.937974\pi$
$54$		0			0
$55$			3.12256i			0.421046i
$56$		0			0
$57$	−2.27567	+	0.00522795i	−0.301420	+	0.000692459i
$58$		0			0
$59$	8.89170	−	5.13363i	1.15760	−	0.668341i	0.206873	−	0.978368i	$-0.433671\pi$
$59$	8.89170	−	5.13363i	1.15760	−	0.668341i	0.950728	+	0.310026i	$0.100338\pi$
$60$		0			0
$61$	10.7109	+	6.18395i	1.37139	+	0.791774i	0.991103	−	0.133094i	$-0.0424913\pi$
$61$	10.7109	+	6.18395i	1.37139	+	0.791774i	0.380289	+	0.924868i	$0.375825\pi$
$62$		0			0
$63$	7.23229	+	4.13137i	0.911183	+	0.520504i
$64$		0			0
$65$	−3.30414	−	1.90765i	−0.409829	−	0.236615i
$66$		0			0
$67$	−3.47947	−	6.02663i	−0.425086	−	0.736270i	0.571343	−	0.820711i	$-0.306423\pi$
$67$	−3.47947	−	6.02663i	−0.425086	−	0.736270i	−0.996428	+	0.0844417i	$0.973089\pi$
$68$		0			0
$69$	3.70717	+	6.38708i	0.446291	+	0.768914i
$70$		0			0
$71$	−7.88557			−0.935845			−0.467922	−	0.883770i	$-0.654997\pi$
$71$	−7.88557			−0.935845			−0.467922	+	0.883770i	$0.654997\pi$
$72$		0			0
$73$	7.92558			0.927620			0.463810	−	0.885935i	$-0.346482\pi$
$73$	7.92558			0.927620			0.463810	+	0.885935i	$0.346482\pi$
$74$		0			0
$75$	−0.862577	+	1.50199i	−0.0996018	+	0.173434i
$76$		0			0
$77$	4.33470	+	7.50792i	0.493985	+	0.855606i
$78$		0			0
$79$	−0.187206	−	0.108084i	−0.0210624	−	0.0121604i	0.489432	−	0.872042i	$-0.337204\pi$
$79$	−0.187206	−	0.108084i	−0.0210624	−	0.0121604i	−0.510494	+	0.859881i	$0.670538\pi$
$80$		0			0
$81$	8.99962	−	0.0827023i	0.999958	−	0.00918915i
$82$		0			0
$83$	7.86428	+	4.54044i	0.863217	+	0.498378i	0.865088	−	0.501620i	$-0.167262\pi$
$83$	7.86428	+	4.54044i	0.863217	+	0.498378i	−0.00187155	+	0.999998i	$0.500596\pi$
$84$		0			0
$85$	2.97508	−	1.71766i	0.322693	−	0.186307i
$86$		0			0
$87$	−0.460102	+	0.801164i	−0.0493281	+	0.0858938i
$88$		0			0
$89$		−	4.82215i		−	0.511147i	−0.966790	−	0.255573i	$-0.917736\pi$
$89$		−	4.82215i		−	0.511147i	0.966790	−	0.255573i	$-0.0822642\pi$
$90$		0			0
$91$	−10.5927			−1.11042
$92$		0			0
$93$	−0.714571	+	0.414750i	−0.0740976	+	0.0430075i
$94$		0			0
$95$	−0.656931	−	1.13784i	−0.0673997	−	0.116740i
$96$		0			0
$97$	−4.20125	+	7.27679i	−0.426573	+	0.738846i	−0.996566	−	0.0828038i	$-0.973613\pi$
$97$	−4.20125	+	7.27679i	−0.426573	+	0.738846i	0.569993	+	0.821649i	$0.306946\pi$
$98$		0			0
$99$	8.13409	+	4.64652i	0.817506	+	0.466993i
$100$		0			0
$101$	1.11068	−	1.92376i	0.110517	−	0.191421i	−0.805462	−	0.592648i	$-0.798083\pi$
$101$	1.11068	−	1.92376i	0.110517	−	0.191421i	0.915979	+	0.401227i	$0.131416\pi$
$102$		0			0
$103$	12.7933	−	7.38623i	1.26056	−	0.727786i	0.287380	−	0.957817i	$-0.407216\pi$
$103$	12.7933	−	7.38623i	1.26056	−	0.727786i	0.973183	+	0.230030i	$0.0738825\pi$
$104$		0			0
$105$	0.0110474	+	4.80881i	0.00107811	+	0.469292i
$106$		0			0
$107$			14.0755i			1.36073i	0.732872	+	0.680367i	$0.238180\pi$
$107$			14.0755i			1.36073i	−0.732872	+	0.680367i	$0.761820\pi$
$108$		0			0
$109$		−	16.5073i		−	1.58111i	−0.612389	−	0.790557i	$-0.709791\pi$
$109$		−	16.5073i		−	1.58111i	0.612389	−	0.790557i	$-0.290209\pi$
$110$		0			0
$111$	−0.00900283	−	3.91883i	−0.000854511	−	0.371959i
$112$		0			0
$113$	0.459459	−	0.265268i	0.0432222	−	0.0249544i	−0.478233	−	0.878233i	$-0.658723\pi$
$113$	0.459459	−	0.265268i	0.0432222	−	0.0249544i	0.521455	+	0.853279i	$0.325389\pi$
$114$		0			0
$115$	−2.13186	+	3.69249i	−0.198797	+	0.344326i
$116$		0			0
$117$	−9.88603	+	5.76843i	−0.913964	+	0.533291i
$118$		0			0
$119$	4.76887	−	8.25993i	0.437162	−	0.757187i
$120$		0			0
$121$	−0.624807	−	1.08220i	−0.0568006	−	0.0983816i
$122$		0			0
$123$	−17.2587	+	10.0173i	−1.55616	+	0.903225i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$			0.554852i			0.0492352i	0.999697	+	0.0246176i	$0.00783681\pi$
$127$			0.554852i			0.0492352i	−0.999697	+	0.0246176i	$0.992163\pi$
$128$		0			0
$129$	10.7974	−	18.8012i	0.950654	−	1.65535i
$130$		0			0
$131$	−5.21744	+	3.01229i	−0.455850	+	0.263185i	−0.710298	−	0.703901i	$-0.751440\pi$
$131$	−5.21744	+	3.01229i	−0.455850	+	0.263185i	0.254448	+	0.967087i	$0.418106\pi$
$132$		0			0
$133$	−3.15906	−	1.82389i	−0.273926	−	0.158151i
$134$		0			0
$135$	2.62903	+	4.48199i	0.226271	+	0.385748i
$136$		0			0
$137$	7.48963	+	4.32414i	0.639883	+	0.369436i	0.784569	−	0.620041i	$-0.212884\pi$
$137$	7.48963	+	4.32414i	0.639883	+	0.369436i	−0.144687	+	0.989478i	$0.546217\pi$
$138$		0			0
$139$	−4.72886	−	8.19062i	−0.401096	−	0.694719i	0.592762	−	0.805378i	$-0.298037\pi$
$139$	−4.72886	−	8.19062i	−0.401096	−	0.694719i	−0.993859	+	0.110658i	$0.964704\pi$
$140$		0			0
$141$	−2.63448	+	4.58735i	−0.221863	+	0.386325i
$142$		0			0
$143$	−11.9135			−0.996257
$144$		0			0
$145$	−0.533403			−0.0442967
$146$		0			0
$147$	0.615801	+	1.06096i	0.0507904	+	0.0875067i
$148$		0			0
$149$	−5.42917	−	9.40360i	−0.444775	−	0.770373i	0.553261	−	0.833008i	$-0.313383\pi$
$149$	−5.42917	−	9.40360i	−0.444775	−	0.770373i	−0.998037	+	0.0626346i	$0.980050\pi$
$150$		0			0
$151$	9.37631	+	5.41342i	0.763033	+	0.440538i	0.830384	−	0.557192i	$-0.188121\pi$
$151$	9.37631	+	5.41342i	0.763033	+	0.440538i	−0.0673504	+	0.997729i	$0.521455\pi$
$152$		0			0
$153$	−0.0473521	−	10.3059i	−0.00382819	−	0.833180i
$154$		0			0
$155$	−0.413107	−	0.238507i	−0.0331815	−	0.0191574i
$156$		0			0
$157$	14.2718	−	8.23981i	1.13901	−	0.657608i	0.192826	−	0.981233i	$-0.438235\pi$
$157$	14.2718	−	8.23981i	1.13901	−	0.657608i	0.946186	+	0.323625i	$0.104902\pi$
$158$		0			0
$159$	−24.7417	+	0.0568397i	−1.96214	+	0.00450768i
$160$		0			0
$161$			11.8377i			0.932940i
$162$		0			0
$163$	−7.55915			−0.592078			−0.296039	−	0.955176i	$-0.595666\pi$
$163$	−7.55915			−0.592078			−0.296039	+	0.955176i	$0.595666\pi$
$164$		0			0
$165$	0.0124249	+	5.40842i	0.000967276	+	0.421045i
$166$		0			0
$167$	−10.6372	−	18.4242i	−0.823131	−	1.42570i	−0.903340	−	0.428926i	$-0.858892\pi$
$167$	−10.6372	−	18.4242i	−0.823131	−	1.42570i	0.0802091	−	0.996778i	$-0.474441\pi$
$168$		0			0
$169$	0.778243	−	1.34796i	0.0598649	−	0.103689i
$170$		0			0
$171$	−3.94155	+	0.0181101i	−0.301418	+	0.00138491i
$172$		0			0
$173$	10.3166	−	17.8689i	0.784356	−	1.35854i	−0.145027	−	0.989428i	$-0.546327\pi$
$173$	10.3166	−	17.8689i	0.784356	−	1.35854i	0.929383	−	0.369116i	$-0.120340\pi$
$174$		0			0
$175$	−2.40441	+	1.38819i	−0.181756	+	0.104937i
$176$		0			0
$177$	15.3804	−	8.92706i	1.15606	−	0.670999i
$178$		0			0
$179$			7.50778i			0.561158i	0.959831	+	0.280579i	$0.0905264\pi$
$179$			7.50778i			0.561158i	−0.959831	+	0.280579i	$0.909474\pi$
$180$		0			0
$181$			15.2146i			1.13089i	0.824785	+	0.565447i	$0.191296\pi$
$181$			15.2146i			1.13089i	−0.824785	+	0.565447i	$0.808704\pi$
$182$		0			0
$183$	18.5764	+	10.6683i	1.37321	+	0.788621i
$184$		0			0
$185$	1.95942	−	1.13127i	0.144060	−	0.0831728i
$186$		0			0
$187$	5.36351	−	9.28987i	0.392219	−	0.679342i
$188$		0			0
$189$	12.5431	+	7.12695i	0.912376	+	0.518410i
$190$		0			0
$191$	−6.80108	+	11.7798i	−0.492109	+	0.852358i	−0.999959	−	0.00908769i	$-0.997107\pi$
$191$	−6.80108	+	11.7798i	−0.492109	+	0.852358i	0.507850	+	0.861446i	$0.330441\pi$
$192$		0			0
$193$	−11.0958	−	19.2185i	−0.798696	−	1.38338i	−0.920466	−	0.390823i	$-0.872190\pi$
$193$	−11.0958	−	19.2185i	−0.798696	−	1.38338i	0.121770	−	0.992558i	$-0.461143\pi$
$194$		0			0
$195$	−5.73052	−	3.29099i	−0.410371	−	0.235673i
$196$		0			0
$197$	−5.87131			−0.418314			−0.209157	−	0.977882i	$-0.567072\pi$
$197$	−5.87131			−0.418314			−0.209157	+	0.977882i	$0.567072\pi$
$198$		0			0
$199$		−	17.4689i		−	1.23834i	−0.785259	−	0.619168i	$-0.787470\pi$
$199$		−	17.4689i		−	1.23834i	0.785259	−	0.619168i	$-0.212530\pi$
$200$		0			0
$201$	−6.05059	−	10.4246i	−0.426776	−	0.735291i
$202$		0			0
$203$	−1.28252	+	0.740464i	−0.0900153	+	0.0519704i
$204$		0			0
$205$	−9.97758	−	5.76056i	−0.696864	−	0.402335i
$206$		0			0
$207$	6.44641	+	11.0480i	0.448056	+	0.767887i
$208$		0			0
$209$	−3.55297	−	2.05131i	−0.245764	−	0.141892i
$210$		0			0
$211$	8.80440	+	15.2497i	0.606120	+	1.04983i	0.991873	+	0.127228i	$0.0406081\pi$
$211$	8.80440	+	15.2497i	0.606120	+	1.04983i	−0.385754	+	0.922602i	$0.626059\pi$
$212$		0			0
$213$	−13.6582	+	0.0313772i	−0.935842	+	0.00214993i
$214$		0			0
$215$	12.5176			0.853690
$216$		0			0
$217$	−1.32437			−0.0899042
$218$		0			0
$219$	13.7275	−	0.0315365i	0.927617	−	0.00213104i
$220$		0			0
$221$	6.55339	+	11.3508i	0.440829	+	0.763538i
$222$		0			0
$223$	−7.41753	−	4.28251i	−0.496714	−	0.286778i	0.230641	−	0.973039i	$-0.425918\pi$
$223$	−7.41753	−	4.28251i	−0.496714	−	0.286778i	−0.727356	+	0.686261i	$0.759251\pi$
$224$		0			0
$225$	−1.48805	+	2.60494i	−0.0992031	+	0.173663i
$226$		0			0
$227$	−20.0247	−	11.5612i	−1.32908	−	0.767347i	−0.343925	−	0.938997i	$-0.611757\pi$
$227$	−20.0247	−	11.5612i	−1.32908	−	0.767347i	−0.985158	+	0.171651i	$0.945090\pi$
$228$		0			0
$229$	−6.36677	+	3.67586i	−0.420728	+	0.242907i	−0.695389	−	0.718634i	$-0.744768\pi$
$229$	−6.36677	+	3.67586i	−0.420728	+	0.242907i	0.274661	+	0.961541i	$0.411434\pi$
$230$		0			0
$231$	7.53777	+	12.9868i	0.495949	+	0.854469i
$232$		0			0
$233$			20.6717i			1.35425i	0.735868	+	0.677125i	$0.236774\pi$
$233$			20.6717i			1.35425i	−0.735868	+	0.677125i	$0.763226\pi$
$234$		0			0
$235$	−3.05419			−0.199233
$236$		0			0
$237$	−0.324680	−	0.186461i	−0.0210902	−	0.0121119i
$238$		0			0
$239$	2.31092	+	4.00263i	0.149481	+	0.258908i	0.931036	−	0.364928i	$-0.118906\pi$
$239$	2.31092	+	4.00263i	0.149481	+	0.258908i	−0.781555	+	0.623837i	$0.785573\pi$
$240$		0			0
$241$	−10.0859	+	17.4693i	−0.649690	+	1.12530i	0.333507	+	0.942748i	$0.391768\pi$
$241$	−10.0859	+	17.4693i	−0.649690	+	1.12530i	−0.983197	+	0.182548i	$0.941565\pi$
$242$		0			0
$243$	15.5874	−	0.179054i	0.999934	−	0.0114863i
$244$		0			0
$245$	−0.354125	+	0.613362i	−0.0226242	+	0.0391863i
$246$		0			0
$247$	4.34119	−	2.50639i	0.276223	−	0.159478i
$248$		0			0
$249$	13.6394	+	7.83296i	0.864359	+	0.496394i
$250$		0			0
$251$			15.2472i			0.962397i	0.876612	+	0.481199i	$0.159798\pi$
$251$			15.2472i			0.962397i	−0.876612	+	0.481199i	$0.840202\pi$
$252$		0			0
$253$			13.3137i			0.837027i
$254$		0			0
$255$	5.14614	−	2.98691i	0.322264	−	0.187048i
$256$		0			0
$257$	1.24545	−	0.719060i	0.0776889	−	0.0448537i	−0.460652	−	0.887581i	$-0.652384\pi$
$257$	1.24545	−	0.719060i	0.0776889	−	0.0448537i	0.538341	+	0.842727i	$0.319051\pi$
$258$		0			0
$259$	3.14084	−	5.44009i	0.195162	−	0.338031i
$260$		0			0
$261$	−0.793729	+	1.38948i	−0.0491306	+	0.0860069i
$262$		0			0
$263$	2.20868	−	3.82555i	0.136193	−	0.235893i	−0.789860	−	0.613288i	$-0.789847\pi$
$263$	2.20868	−	3.82555i	0.136193	−	0.235893i	0.926053	+	0.377395i	$0.123180\pi$
$264$		0			0
$265$	−7.14233	−	12.3709i	−0.438750	−	0.759937i
$266$		0			0
$267$	−0.0191877	−	8.35219i	−0.00117427	−	0.511145i
$268$		0			0
$269$	−24.9314			−1.52010			−0.760048	−	0.649867i	$-0.774825\pi$
$269$	−24.9314			−1.52010			−0.760048	+	0.649867i	$0.774825\pi$
$270$		0			0
$271$		−	21.5066i		−	1.30643i	−0.757172	−	0.653215i	$-0.773420\pi$
$271$		−	21.5066i		−	1.30643i	0.757172	−	0.653215i	$-0.226580\pi$
$272$		0			0
$273$	−18.3470	+	0.0421491i	−1.11041	+	0.00255098i
$274$		0			0
$275$	−2.70422	+	1.56128i	−0.163070	+	0.0941488i
$276$		0			0
$277$	−0.693110	−	0.400167i	−0.0416449	−	0.0240437i	0.479033	−	0.877797i	$-0.340987\pi$
$277$	−0.693110	−	0.400167i	−0.0416449	−	0.0240437i	−0.520678	+	0.853753i	$0.674321\pi$
$278$		0			0
$279$	−1.23602	+	0.721209i	−0.0739986	+	0.0431776i
$280$		0			0
$281$	−17.8052	−	10.2798i	−1.06217	−	0.613244i	−0.136139	−	0.990690i	$-0.543469\pi$
$281$	−17.8052	−	10.2798i	−1.06217	−	0.613244i	−0.926032	+	0.377445i	$0.876803\pi$
$282$		0			0
$283$	−7.32132	−	12.6809i	−0.435207	−	0.753801i	0.562105	−	0.827066i	$-0.309992\pi$
$283$	−7.32132	−	12.6809i	−0.435207	−	0.753801i	−0.997313	+	0.0732645i	$0.976658\pi$
$284$		0			0
$285$	−1.14236	−	1.96817i	−0.0676677	−	0.116585i
$286$		0			0
$287$	−31.9869			−1.88813
$288$		0			0
$289$	5.19853			0.305796
$290$		0			0
$291$	−7.24781	+	12.6204i	−0.424874	+	0.739824i
$292$		0			0
$293$	−13.4417	−	23.2817i	−0.785273	−	1.36013i	−0.928836	−	0.370491i	$-0.879189\pi$
$293$	−13.4417	−	23.2817i	−0.785273	−	1.36013i	0.143563	−	0.989641i	$-0.454144\pi$
$294$		0			0
$295$	8.89170	+	5.13363i	0.517695	+	0.298891i
$296$		0			0
$297$	14.1071	+	8.01562i	0.818577	+	0.465113i
$298$		0			0
$299$	−14.0879	−	8.13368i	−0.814727	−	0.470383i
$300$		0			0
$301$	30.0973	−	17.3767i	1.73478	−	1.00158i
$302$		0			0
$303$	1.91610	−	3.33646i	0.110077	−	0.191675i
$304$		0			0
$305$			12.3679i			0.708184i
$306$		0			0
$307$	21.3839			1.22044			0.610221	−	0.792231i	$-0.291080\pi$
$307$	21.3839			1.22044			0.610221	+	0.792231i	$0.291080\pi$
$308$		0			0
$309$	22.1292	−	12.8442i	1.25889	−	0.730680i
$310$		0			0
$311$	10.7043	+	18.5404i	0.606985	+	1.05133i	0.991734	+	0.128308i	$0.0409547\pi$
$311$	10.7043	+	18.5404i	0.606985	+	1.05133i	−0.384749	+	0.923021i	$0.625712\pi$
$312$		0			0
$313$	2.91819	−	5.05445i	0.164946	−	0.285694i	−0.771690	−	0.635998i	$-0.780588\pi$
$313$	2.91819	−	5.05445i	0.164946	−	0.285694i	0.936636	+	0.350304i	$0.113922\pi$
$314$		0			0
$315$	0.0382692	+	8.32903i	0.00215622	+	0.469288i
$316$		0			0
$317$	4.19064	−	7.25841i	0.235370	−	0.407673i	−0.724010	−	0.689789i	$-0.757703\pi$
$317$	4.19064	−	7.25841i	0.235370	−	0.407673i	0.959380	+	0.282117i	$0.0910365\pi$
$318$		0			0
$319$	−1.44244	+	0.832792i	−0.0807611	+	0.0466274i
$320$		0			0
$321$	0.0560076	+	24.3795i	0.00312604	+	1.36073i
$322$		0			0
$323$			4.51355i			0.251140i
$324$		0			0
$325$		−	3.81530i		−	0.211635i
$326$		0			0
$327$	−0.0656837	−	28.5914i	−0.00363232	−	1.58111i
$328$		0			0
$329$	−7.34353	+	4.23979i	−0.404862	+	0.233747i
$330$		0			0
$331$	0.901119	−	1.56078i	0.0495300	−	0.0857884i	−0.840197	−	0.542281i	$-0.817561\pi$
$331$	0.901119	−	1.56078i	0.0495300	−	0.0857884i	0.889727	+	0.456492i	$0.150894\pi$
$332$		0			0
$333$	−0.0311866	−	6.78757i	−0.00170902	−	0.371956i
$334$		0			0
$335$	3.47947	−	6.02663i	0.190104	−	0.329270i
$336$		0			0
$337$	−11.9797	−	20.7495i	−0.652577	−	1.13030i	−0.982495	−	0.186287i	$-0.940355\pi$
$337$	−11.9797	−	20.7495i	−0.652577	−	1.13030i	0.329918	−	0.944009i	$-0.392979\pi$
$338$		0			0
$339$	0.794748	−	0.461286i	0.0431648	−	0.0250536i
$340$		0			0
$341$	−1.48951			−0.0806614
$342$		0			0
$343$		−	17.4682i		−	0.943197i
$344$		0			0
$345$	−3.67779	+	6.40405i	−0.198005	+	0.344782i
$346$		0			0
$347$	15.0256	−	8.67502i	0.806615	−	0.465699i	−0.0391641	−	0.999233i	$-0.512470\pi$
$347$	15.0256	−	8.67502i	0.806615	−	0.465699i	0.845779	+	0.533533i	$0.179136\pi$
$348$		0			0
$349$	−7.29528	−	4.21193i	−0.390507	−	0.225460i	0.291873	−	0.956457i	$-0.405722\pi$
$349$	−7.29528	−	4.21193i	−0.390507	−	0.225460i	−0.682380	+	0.730998i	$0.739055\pi$
$350$		0			0
$351$	−17.1001	+	10.0305i	−0.912736	+	0.535390i
$352$		0			0
$353$	14.9442	+	8.62801i	0.795397	+	0.459223i	0.841859	−	0.539697i	$-0.181461\pi$
$353$	14.9442	+	8.62801i	0.795397	+	0.459223i	−0.0464619	+	0.998920i	$0.514795\pi$
$354$		0			0
$355$	−3.94278	−	6.82910i	−0.209261	−	0.362451i
$356$		0			0
$357$	8.22704	−	14.3256i	0.435421	−	0.758189i
$358$		0			0
$359$	7.13071			0.376344			0.188172	−	0.982136i	$-0.439744\pi$
$359$	7.13071			0.376344			0.188172	+	0.982136i	$0.439744\pi$
$360$		0			0
$361$	−17.2738			−0.909146
$362$		0			0
$363$	−1.08650	−	1.87193i	−0.0570265	−	0.0982508i
$364$		0			0
$365$	3.96279	+	6.86376i	0.207422	+	0.359266i
$366$		0			0
$367$	−29.3780	−	16.9614i	−1.53352	−	0.885379i	−0.999196	−	0.0401004i	$-0.987232\pi$
$367$	−29.3780	−	16.9614i	−1.53352	−	0.885379i	−0.534326	−	0.845279i	$-0.679434\pi$
$368$		0			0
$369$	−29.8530	+	17.4190i	−1.55409	+	0.906798i
$370$		0			0
$371$	−34.3462	−	19.8298i	−1.78317	−	1.02951i
$372$		0			0
$373$	−8.48032	+	4.89612i	−0.439095	+	0.253511i	−0.703213	−	0.710979i	$-0.748252\pi$
$373$	−8.48032	+	4.89612i	−0.439095	+	0.253511i	0.264119	+	0.964490i	$0.414919\pi$
$374$		0			0
$375$	−1.73205	+	0.00397907i	−0.0894425	+	0.000205478i
$376$		0			0
$377$		−	2.03509i		−	0.104813i
$378$		0			0
$379$	−15.9453			−0.819054			−0.409527	−	0.912298i	$-0.634306\pi$
$379$	−15.9453			−0.819054			−0.409527	+	0.912298i	$0.634306\pi$
$380$		0			0
$381$	0.00220780	+	0.961030i	0.000113109	+	0.0492350i
$382$		0			0
$383$	−3.70162	−	6.41139i	−0.189144	−	0.327607i	0.755821	−	0.654778i	$-0.227238\pi$
$383$	−3.70162	−	6.41139i	−0.189144	−	0.327607i	−0.944965	+	0.327171i	$0.893905\pi$
$384$		0			0
$385$	−4.33470	+	7.50792i	−0.220917	+	0.382639i
$386$		0			0
$387$	18.6267	−	32.6075i	0.946849	−	1.65753i
$388$		0			0
$389$	−13.0021	+	22.5203i	−0.659233	+	1.14182i	0.321582	+	0.946882i	$0.395786\pi$
$389$	−13.0021	+	22.5203i	−0.659233	+	1.14182i	−0.980815	+	0.194943i	$0.937548\pi$
$390$		0			0
$391$	12.6849	−	7.32363i	0.641503	−	0.370372i
$392$		0			0
$393$	−9.02487	+	5.23819i	−0.455244	+	0.264232i
$394$		0			0
$395$		−	0.216167i		−	0.0108766i
$396$		0			0
$397$		−	26.9039i		−	1.35027i	−0.737694	−	0.675135i	$-0.764085\pi$
$397$		−	26.9039i		−	1.35027i	0.737694	−	0.675135i	$-0.235915\pi$
$398$		0			0
$399$	−5.47890	−	3.14649i	−0.274288	−	0.157521i
$400$		0			0
$401$	−9.03940	+	5.21890i	−0.451406	+	0.260619i	−0.708424	−	0.705787i	$-0.750593\pi$
$401$	−9.03940	+	5.21890i	−0.451406	+	0.260619i	0.257018	+	0.966407i	$0.417260\pi$
$402$		0			0
$403$	0.909976	−	1.57613i	0.0453291	−	0.0785124i
$404$		0			0
$405$	4.57143	+	7.75255i	0.227156	+	0.385227i
$406$		0			0
$407$	3.53247	−	6.11842i	0.175098	−	0.303279i
$408$		0			0
$409$	2.09390	+	3.62675i	0.103537	+	0.179331i	0.913140	−	0.407647i	$-0.133651\pi$
$409$	2.09390	+	3.62675i	0.103537	+	0.179331i	−0.809603	+	0.586978i	$0.800317\pi$
$410$		0			0
$411$	12.9896	+	7.45981i	0.640730	+	0.367965i
$412$		0			0
$413$	28.5057			1.40268
$414$		0			0
$415$			9.08089i			0.445763i
$416$		0			0
$417$	−8.22319	−	14.1677i	−0.402691	−	0.693796i
$418$		0			0
$419$	−2.80884	+	1.62169i	−0.137221	+	0.0792245i	−0.567039	−	0.823691i	$-0.691911\pi$
$419$	−2.80884	+	1.62169i	−0.137221	+	0.0792245i	0.429818	+	0.902916i	$0.358578\pi$
$420$		0			0
$421$	5.45534	+	3.14964i	0.265877	+	0.153504i	0.627013	−	0.779009i	$-0.284277\pi$
$421$	5.45534	+	3.14964i	0.265877	+	0.153504i	−0.361135	+	0.932513i	$0.617611\pi$
$422$		0			0
$423$	−4.54478	+	7.95599i	−0.220975	+	0.386833i
$424$		0			0
$425$	2.97508	+	1.71766i	0.144313	+	0.0833189i
$426$		0			0
$427$	17.1690	+	29.7375i	0.830864	+	1.43910i
$428$		0			0
$429$	−20.6347	+	0.0474046i	−0.996254	+	0.00228872i
$430$		0			0
$431$	−16.9856			−0.818167			−0.409084	−	0.912497i	$-0.634152\pi$
$431$	−16.9856			−0.818167			−0.409084	+	0.912497i	$0.634152\pi$
$432$		0			0
$433$	−17.6526			−0.848331			−0.424166	−	0.905585i	$-0.639433\pi$
$433$	−17.6526			−0.848331			−0.424166	+	0.905585i	$0.639433\pi$
$434$		0			0
$435$	−0.923879	+	0.00212245i	−0.0442966	+	0.000101764i
$436$		0			0
$437$	−2.80097	−	4.85142i	−0.133989	−	0.232075i
$438$		0			0
$439$	33.1600	+	19.1449i	1.58264	+	0.913738i	0.994472	+	0.105000i	$0.0334841\pi$
$439$	33.1600	+	19.1449i	1.58264	+	0.913738i	0.588168	+	0.808738i	$0.299849\pi$
$440$		0			0
$441$	1.07082	+	1.83519i	0.0509913	+	0.0873898i
$442$		0			0
$443$	11.3515	+	6.55380i	0.539327	+	0.311381i	0.744806	−	0.667281i	$-0.232542\pi$
$443$	11.3515	+	6.55380i	0.539327	+	0.311381i	−0.205479	+	0.978661i	$0.565875\pi$
$444$		0			0
$445$	4.17610	−	2.41107i	0.197966	−	0.114296i
$446$		0			0
$447$	−9.44099	−	16.2659i	−0.446544	−	0.769349i
$448$		0			0
$449$			24.9459i			1.17727i	0.808400	+	0.588634i	$0.200334\pi$
$449$			24.9459i			1.17727i	−0.808400	+	0.588634i	$0.799666\pi$
$450$		0			0
$451$	−35.9754			−1.69401
$452$		0			0
$453$	16.2617	+	9.33898i	0.764043	+	0.438783i
$454$		0			0
$455$	−5.29634	−	9.17354i	−0.248296	−	0.430062i
$456$		0			0
$457$	13.2777	−	22.9976i	0.621103	−	1.07578i	−0.368178	−	0.929755i	$-0.620018\pi$
$457$	13.2777	−	22.9976i	0.621103	−	1.07578i	0.989281	−	0.146026i	$-0.0466483\pi$
$458$		0			0
$459$	−0.123024	−	17.8501i	−0.00574226	−	0.833169i
$460$		0			0
$461$	−5.99710	+	10.3873i	−0.279313	+	0.483784i	−0.971214	−	0.238208i	$-0.923440\pi$
$461$	−5.99710	+	10.3873i	−0.279313	+	0.483784i	0.691901	+	0.721992i	$0.256773\pi$
$462$		0			0
$463$	−21.9062	+	12.6476i	−1.01807	+	0.587782i	−0.913544	−	0.406740i	$-0.866666\pi$
$463$	−21.9062	+	12.6476i	−1.01807	+	0.587782i	−0.104525	+	0.994522i	$0.533332\pi$
$464$		0			0
$465$	−0.716469	−	0.411462i	−0.0332255	−	0.0190811i
$466$		0			0
$467$		−	7.44030i		−	0.344296i	−0.985071	−	0.172148i	$-0.944929\pi$
$467$		−	7.44030i		−	0.344296i	0.985071	−	0.172148i	$-0.0550707\pi$
$468$		0			0
$469$		−	19.3206i		−	0.892144i
$470$		0			0
$471$	24.6866	−	14.3285i	1.13750	−	0.660223i
$472$		0			0
$473$	33.8502	−	19.5434i	1.55643	−	0.898607i
$474$		0			0
$475$	0.656931	−	1.13784i	0.0301421	−	0.0522076i
$476$		0			0
$477$	−42.8535	+	0.196898i	−1.96213	+	0.00901534i
$478$		0			0
$479$	19.5734	−	33.9022i	0.894333	−	1.54903i	0.0597054	−	0.998216i	$-0.480984\pi$
$479$	19.5734	−	33.9022i	0.894333	−	1.54903i	0.834628	−	0.550814i	$-0.185683\pi$
$480$		0			0
$481$	4.31614	+	7.47578i	0.196799	+	0.340866i
$482$		0			0
$483$	0.0471030	+	20.5034i	0.00214326	+	0.932937i
$484$		0			0
$485$	−8.40251			−0.381538
$486$		0			0
$487$			20.0755i			0.909707i	0.890566	+	0.454854i	$0.150308\pi$
$487$			20.0755i			0.909707i	−0.890566	+	0.454854i	$0.849692\pi$
$488$		0			0
$489$	−13.0928	+	0.0300784i	−0.592077	+	0.00136019i
$490$		0			0
$491$	−18.3558	+	10.5977i	−0.828385	+	0.478268i	−0.853299	−	0.521421i	$-0.825402\pi$
$491$	−18.3558	+	10.5977i	−0.828385	+	0.478268i	0.0249145	+	0.999690i	$0.492069\pi$
$492$		0			0
$493$	1.58692	+	0.916207i	0.0714712	+	0.0412639i
$494$		0			0
$495$	0.0430410	+	9.36758i	0.00193455	+	0.421042i
$496$		0			0
$497$	−18.9601	−	10.9466i	−0.850479	−	0.491024i
$498$		0			0
$499$	4.07075	+	7.05075i	0.182232	+	0.315635i	0.942640	−	0.333810i	$-0.108335\pi$
$499$	4.07075	+	7.05075i	0.182232	+	0.315635i	−0.760408	+	0.649445i	$0.775001\pi$
$500$		0			0
$501$	−18.4974	−	31.8692i	−0.826404	−	1.42381i
$502$		0			0
$503$	−9.59614			−0.427871			−0.213935	−	0.976848i	$-0.568628\pi$
$503$	−9.59614			−0.427871			−0.213935	+	0.976848i	$0.568628\pi$
$504$		0			0
$505$	2.22137			0.0988495
$506$		0			0
$507$	1.34259	−	2.33782i	0.0596265	−	0.103826i
$508$		0			0
$509$	−0.164517	−	0.284953i	−0.00729211	−	0.0126303i	0.862356	−	0.506302i	$-0.168988\pi$
$509$	−0.164517	−	0.284953i	−0.00729211	−	0.0126303i	−0.869648	+	0.493672i	$0.835655\pi$
$510$		0			0
$511$	19.0564	+	11.0022i	0.843004	+	0.486708i
$512$		0			0
$513$	−6.82687	+	0.0470512i	−0.301414	+	0.00207736i
$514$		0			0
$515$	12.7933	+	7.38623i	0.563741	+	0.325476i
$516$		0			0
$517$	−8.25920	+	4.76845i	−0.363239	+	0.209716i
$518$		0			0
$519$	17.7977	−	30.9907i	0.781233	−	1.36034i
$520$		0			0
$521$		−	14.4490i		−	0.633021i	−0.948589	−	0.316510i	$-0.897489\pi$
$521$		−	14.4490i		−	0.633021i	0.948589	−	0.316510i	$-0.102511\pi$
$522$		0			0
$523$	−18.1246			−0.792534			−0.396267	−	0.918135i	$-0.629695\pi$
$523$	−18.1246			−0.792534			−0.396267	+	0.918135i	$0.629695\pi$
$524$		0			0
$525$	−4.15903	+	2.41397i	−0.181515	+	0.105354i
$526$		0			0
$527$	0.819351	+	1.41916i	0.0356915	+	0.0618194i
$528$		0			0
$529$	2.41035	−	4.17484i	0.104798	−	0.181515i
$530$		0			0
$531$	26.6041	−	15.5233i	1.15452	−	0.673653i
$532$		0			0
$533$	21.9782	−	38.0674i	0.951983	−	1.64888i
$534$		0			0
$535$	−12.1898	+	7.03777i	−0.527010	+	0.304269i
$536$		0			0
$537$	0.0298740	+	13.0038i	0.00128916	+	0.561156i
$538$		0			0
$539$			2.21155i			0.0952583i
$540$		0			0
$541$			3.63353i			0.156218i	0.996945	+	0.0781089i	$0.0248882\pi$
$541$			3.63353i			0.156218i	−0.996945	+	0.0781089i	$0.975112\pi$
$542$		0			0
$543$	0.0605401	+	26.3524i	0.00259802	+	1.13089i
$544$		0			0
$545$	14.2957	−	8.25365i	0.612363	−	0.353548i
$546$		0			0
$547$	−11.7873	+	20.4162i	−0.503987	+	0.872932i	0.496002	+	0.868321i	$0.334801\pi$
$547$	−11.7873	+	20.4162i	−0.503987	+	0.872932i	−0.999989	+	0.00461043i	$0.998532\pi$
$548$		0			0
$549$	32.2176	+	18.4040i	1.37502	+	0.785464i
$550$		0			0
$551$	0.350409	−	0.606927i	0.0149279	−	0.0258560i
$552$		0			0
$553$	−0.300081	−	0.519755i	−0.0127607	−	0.0221022i
$554$		0			0
$555$	3.38931	−	1.96721i	0.143868	−	0.0835036i
$556$		0			0
$557$	−32.3117			−1.36909			−0.684544	−	0.728971i	$-0.739999\pi$
$557$	−32.3117			−1.36909			−0.684544	+	0.728971i	$0.739999\pi$
$558$		0			0
$559$			47.7582i			2.01996i
$560$		0			0
$561$	9.25288	−	16.1118i	0.390657	−	0.680242i
$562$		0			0
$563$	13.2429	−	7.64582i	0.558124	−	0.322233i	−0.194268	−	0.980948i	$-0.562233\pi$
$563$	13.2429	−	7.64582i	0.558124	−	0.322233i	0.752392	+	0.658716i	$0.228900\pi$
$564$		0			0
$565$	0.459459	+	0.265268i	0.0193296	+	0.0111599i
$566$		0			0
$567$	21.7536	+	12.2943i	0.913565	+	0.516312i
$568$		0			0
$569$	−18.3848	−	10.6145i	−0.770730	−	0.444981i	0.0624050	−	0.998051i	$-0.480123\pi$
$569$	−18.3848	−	10.6145i	−0.770730	−	0.444981i	−0.833135	+	0.553070i	$0.813456\pi$
$570$		0			0
$571$	20.3971	+	35.3288i	0.853591	+	1.47846i	0.877946	+	0.478760i	$0.158914\pi$
$571$	20.3971	+	35.3288i	0.853591	+	1.47846i	−0.0243545	+	0.999703i	$0.507753\pi$
$572$		0			0
$573$	−11.7329	+	20.4303i	−0.490150	+	0.853486i
$574$		0			0
$575$	−4.26372			−0.177809
$576$		0			0
$577$	29.2113			1.21608			0.608040	−	0.793906i	$-0.291956\pi$
$577$	29.2113			1.21608			0.608040	+	0.793906i	$0.291956\pi$
$578$		0			0
$579$	−19.2950	−	33.2433i	−0.801872	−	1.38154i
$580$		0			0
$581$	12.6060	+	21.8342i	0.522984	+	0.905834i
$582$		0			0
$583$	−38.6288	−	22.3024i	−1.59984	−	0.923670i
$584$		0			0
$585$	−9.93862	−	5.67734i	−0.410911	−	0.234729i
$586$		0			0
$587$	2.09726	+	1.21086i	0.0865634	+	0.0499774i	0.542657	−	0.839954i	$-0.317418\pi$
$587$	2.09726	+	1.21086i	0.0865634	+	0.0499774i	−0.456093	+	0.889932i	$0.650752\pi$
$588$		0			0
$589$	0.542766	−	0.313366i	0.0223643	−	0.0129120i
$590$		0			0
$591$	−10.1694	+	0.0233624i	−0.418313	+	0.000961000i
$592$		0			0
$593$			7.77622i			0.319331i	0.987171	+	0.159666i	$0.0510416\pi$
$593$			7.77622i			0.319331i	−0.987171	+	0.159666i	$0.948958\pi$
$594$		0			0
$595$	9.53775			0.391010
$596$		0			0
$597$	−0.0695099	−	30.2569i	−0.00284485	−	1.23833i
$598$		0			0
$599$	9.47635	+	16.4135i	0.387193	+	0.670638i	0.992071	−	0.125680i	$-0.0401113\pi$
$599$	9.47635	+	16.4135i	0.387193	+	0.670638i	−0.604878	+	0.796318i	$0.706778\pi$
$600$		0			0
$601$	−11.5216	+	19.9560i	−0.469976	+	0.814023i	−0.999411	−	0.0343283i	$-0.989071\pi$
$601$	−11.5216	+	19.9560i	−0.469976	+	0.814023i	0.529434	+	0.848351i	$0.322404\pi$
$602$		0			0
$603$	−10.5214	−	18.0317i	−0.428464	−	0.734309i
$604$		0			0
$605$	0.624807	−	1.08220i	0.0254020	−	0.0439976i
$606$		0			0
$607$	26.8628	−	15.5092i	1.09033	−	0.629500i	0.156662	−	0.987652i	$-0.449927\pi$
$607$	26.8628	−	15.5092i	1.09033	−	0.629500i	0.933663	+	0.358153i	$0.116593\pi$
$608$		0			0
$609$	−2.21844	+	1.28762i	−0.0898957	+	0.0521770i
$610$		0			0
$611$		−	11.6526i		−	0.471416i
$612$		0			0
$613$			43.8644i			1.77167i	0.464002	+	0.885834i	$0.346413\pi$
$613$			43.8644i			1.77167i	−0.464002	+	0.885834i	$0.653587\pi$
$614$		0			0
$615$	−17.3045	−	9.93785i	−0.697787	−	0.400733i
$616$		0			0
$617$	20.2819	−	11.7098i	0.816520	−	0.471418i	−0.0326947	−	0.999465i	$-0.510409\pi$
$617$	20.2819	−	11.7098i	0.816520	−	0.471418i	0.849215	+	0.528047i	$0.177076\pi$
$618$		0			0
$619$	−13.1137	+	22.7136i	−0.527084	+	0.912935i	0.472418	+	0.881374i	$0.343381\pi$
$619$	−13.1137	+	22.7136i	−0.527084	+	0.912935i	−0.999502	+	0.0315610i	$0.989952\pi$
$620$		0			0
$621$	11.2094	+	19.1099i	0.449819	+	0.766855i
$622$		0			0
$623$	6.69404	−	11.5944i	0.268191	−	0.464521i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−6.16207	−	3.53882i	−0.246089	−	0.141327i
$628$		0			0
$629$	−7.77258			−0.309913
$630$		0			0
$631$		−	7.35292i		−	0.292715i	−0.989232	−	0.146358i	$-0.953245\pi$
$631$		−	7.35292i		−	0.292715i	0.989232	−	0.146358i	$-0.0467550\pi$
$632$		0			0
$633$	15.3103	+	26.3781i	0.608530	+	1.04843i
$634$		0			0
$635$	−0.480516	+	0.277426i	−0.0190687	+	0.0110093i
$636$		0			0
$637$	−2.34016	−	1.35109i	−0.0927204	−	0.0535322i
$638$		0			0
$639$	−23.6565	+	0.108694i	−0.935835	+	0.00429985i
$640$		0			0
$641$	4.75502	+	2.74531i	0.187812	+	0.108433i	0.590958	−	0.806702i	$-0.298750\pi$
$641$	4.75502	+	2.74531i	0.187812	+	0.108433i	−0.403146	+	0.915136i	$0.632083\pi$
$642$		0			0
$643$	10.2614	+	17.7733i	0.404670	+	0.700909i	0.994283	−	0.106777i	$-0.0340530\pi$
$643$	10.2614	+	17.7733i	0.404670	+	0.700909i	−0.589613	+	0.807686i	$0.700720\pi$
$644$		0			0
$645$	21.6810	−	0.0498082i	0.853688	−	0.00196120i
$646$		0			0
$647$	39.5969			1.55672			0.778358	−	0.627820i	$-0.216053\pi$
$647$	39.5969			1.55672			0.778358	+	0.627820i	$0.216053\pi$
$648$		0			0
$649$	32.0601			1.25847
$650$		0			0
$651$	−2.29387	+	0.00526977i	−0.0899039	+	0.000206538i
$652$		0			0
$653$	22.5179	+	39.0021i	0.881193	+	1.52627i	0.850016	+	0.526757i	$0.176592\pi$
$653$	22.5179	+	39.0021i	0.881193	+	1.52627i	0.0311765	+	0.999514i	$0.490075\pi$
$654$		0			0
$655$	−5.21744	−	3.01229i	−0.203862	−	0.117700i
$656$		0			0
$657$	23.7765	−	0.109245i	0.927610	−	0.00426206i
$658$		0			0
$659$	22.1927	+	12.8129i	0.864504	+	0.499121i	0.865518	−	0.500878i	$-0.166990\pi$
$659$	22.1927	+	12.8129i	0.864504	+	0.499121i	−0.00101427	+	0.999999i	$0.500323\pi$
$660$		0			0
$661$	−9.96758	+	5.75478i	−0.387694	+	0.223835i	−0.681160	−	0.732134i	$-0.738524\pi$
$661$	−9.96758	+	5.75478i	−0.387694	+	0.223835i	0.293467	+	0.955969i	$0.405191\pi$
$662$		0			0
$663$	11.3959	+	19.6341i	0.442582	+	0.762523i
$664$		0			0
$665$		−	3.64777i		−	0.141455i
$666$		0			0
$667$	−2.27428			−0.0880606
$668$		0			0
$669$	−12.8645	−	7.38799i	−0.497372	−	0.285636i
$670$		0			0
$671$	19.3098	+	33.4455i	0.745445	+	1.29115i
$672$		0			0
$673$	23.4948	−	40.6943i	0.905660	−	1.56865i	0.0856300	−	0.996327i	$-0.472710\pi$
$673$	23.4948	−	40.6943i	0.905660	−	1.56865i	0.820029	−	0.572321i	$-0.193957\pi$
$674$		0			0
$675$	−2.56700	+	4.51780i	−0.0988039	+	0.173890i
$676$		0			0
$677$	8.46874	−	14.6683i	0.325480	−	0.563748i	−0.656129	−	0.754649i	$-0.727807\pi$
$677$	8.46874	−	14.6683i	0.325480	−	0.563748i	0.981609	+	0.190900i	$0.0611407\pi$
$678$		0			0
$679$	−20.2031	+	11.6642i	−0.775323	+	0.447633i
$680$		0			0
$681$	−34.7296	−	19.9449i	−1.33084	−	0.764291i
$682$		0			0
$683$		−	2.98462i		−	0.114203i	−0.998368	−	0.0571017i	$-0.981814\pi$
$683$		−	2.98462i		−	0.114203i	0.998368	−	0.0571017i	$-0.0181859\pi$
$684$		0			0
$685$			8.64828i			0.330434i
$686$		0			0
$687$	−11.0129	+	6.39209i	−0.420169	+	0.243873i
$688$		0			0
$689$	47.1986	−	27.2501i	1.79812	−	1.03815i
$690$		0			0
$691$	−4.17425	+	7.23001i	−0.158796	+	0.275043i	−0.934435	−	0.356134i	$-0.884095\pi$
$691$	−4.17425	+	7.23001i	−0.158796	+	0.275043i	0.775639	+	0.631177i	$0.217428\pi$
$692$		0			0
$693$	13.1074	+	22.4638i	0.497911	+	0.853328i
$694$		0			0
$695$	4.72886	−	8.19062i	0.179376	−	0.310688i
$696$		0			0
$697$	19.7894	+	34.2762i	0.749577	+	1.29830i
$698$		0			0
$699$	0.0822543	+	35.8044i	0.00311114	+	1.35425i
$700$		0			0
$701$	9.37518			0.354096			0.177048	−	0.984202i	$-0.443345\pi$
$701$	9.37518			0.354096			0.177048	+	0.984202i	$0.443345\pi$
$702$		0			0
$703$			2.97267i			0.112117i
$704$		0			0
$705$	−5.29000	+	0.0121528i	−0.199233	+	0.000457703i
$706$		0			0
$707$	5.34107	−	3.08367i	0.200872	−	0.115973i
$708$		0			0
$709$	33.2487	+	19.1962i	1.24868	+	0.720927i	0.970847	−	0.239702i	$-0.0770496\pi$
$709$	33.2487	+	19.1962i	1.24868	+	0.720927i	0.277836	+	0.960629i	$0.410383\pi$
$710$		0			0
$711$	−0.563103	−	0.321667i	−0.0211180	−	0.0120635i
$712$		0			0
$713$	−1.76137	−	1.01693i	−0.0659639	−	0.0380843i
$714$		0			0
$715$	−5.95675	−	10.3174i	−0.222770	−	0.385848i
$716$		0			0
$717$	4.01854	+	6.92354i	0.150075	+	0.258564i
$718$		0			0
$719$	−12.8804			−0.480356			−0.240178	−	0.970729i	$-0.577206\pi$
$719$	−12.8804			−0.480356			−0.240178	+	0.970729i	$0.577206\pi$
$720$		0			0
$721$	41.0138			1.52744
$722$		0			0
$723$	−17.3997	+	30.2977i	−0.647103	+	1.12679i
$724$		0			0
$725$	−0.266702	−	0.461941i	−0.00990505	−	0.0171561i
$726$		0			0
$727$	3.75846	+	2.16995i	0.139393	+	0.0804788i	0.568075	−	0.822977i	$-0.307688\pi$
$727$	3.75846	+	2.16995i	0.139393	+	0.0804788i	−0.428681	+	0.903456i	$0.641022\pi$
$728$		0			0
$729$	26.9974	−	0.372154i	0.999905	−	0.0137835i
$730$		0			0
$731$	−37.2407	−	21.5009i	−1.37740	−	0.795241i
$732$		0			0
$733$	−18.8815	+	10.9012i	−0.697404	+	0.402646i	−0.806380	−	0.591398i	$-0.798576\pi$
$733$	−18.8815	+	10.9012i	−0.697404	+	0.402646i	0.108976	+	0.994044i	$0.465243\pi$
$734$		0			0
$735$	−0.610920	+	1.06378i	−0.0225341	+	0.0392381i
$736$		0			0
$737$		−	21.7297i		−	0.800425i
$738$		0			0
$739$	31.8843			1.17288			0.586441	−	0.809992i	$-0.300529\pi$
$739$	31.8843			1.17288			0.586441	+	0.809992i	$0.300529\pi$
$740$		0			0
$741$	7.50917	−	4.35845i	0.275856	−	0.160112i
$742$		0			0
$743$	12.2533	+	21.2234i	0.449532	+	0.778612i	0.998355	−	0.0573263i	$-0.0182575\pi$
$743$	12.2533	+	21.2234i	0.449532	+	0.778612i	−0.548824	+	0.835938i	$0.684924\pi$
$744$		0			0
$745$	5.42917	−	9.40360i	0.198909	−	0.344521i
$746$		0			0
$747$	23.6552	+	13.5128i	0.865497	+	0.494407i
$748$		0			0
$749$	−19.5395	+	33.8434i	−0.713957	+	1.23661i
$750$		0			0
$751$	−5.51362	+	3.18329i	−0.201195	+	0.116160i	−0.597213	−	0.802083i	$-0.703725\pi$
$751$	−5.51362	+	3.18329i	−0.201195	+	0.116160i	0.396018	+	0.918243i	$0.370392\pi$
$752$		0			0
$753$	0.0606699	+	26.4089i	0.00221093	+	0.962395i
$754$		0			0
$755$			10.8268i			0.394029i
$756$		0			0
$757$			25.0713i			0.911232i	0.890176	+	0.455616i	$0.150581\pi$
$757$			25.0713i			0.911232i	−0.890176	+	0.455616i	$0.849419\pi$
$758$		0			0
$759$	0.0529763	+	23.0600i	0.00192292	+	0.837024i
$760$		0			0
$761$	11.3876	−	6.57465i	0.412801	−	0.238331i	−0.279191	−	0.960235i	$-0.590066\pi$
$761$	11.3876	−	6.57465i	0.412801	−	0.238331i	0.691993	+	0.721905i	$0.256733\pi$
$762$		0			0
$763$	22.9152	−	39.6903i	0.829587	−	1.43689i
$764$		0			0
$765$	8.90147	−	5.19394i	0.321833	−	0.187787i
$766$		0			0
$767$	−19.5863	+	33.9245i	−0.707221	+	1.22494i
$768$		0			0
$769$	−11.6041	−	20.0990i	−0.418456	−	0.724787i	0.577329	−	0.816512i	$-0.304095\pi$
$769$	−11.6041	−	20.0990i	−0.418456	−	0.724787i	−0.995784	+	0.0917252i	$0.970762\pi$
$770$		0			0
$771$	2.15431	−	1.25040i	0.0775856	−	0.0450321i
$772$		0			0
$773$	32.0701			1.15348			0.576740	−	0.816928i	$-0.304325\pi$
$773$	32.0701			1.15348			0.576740	+	0.816928i	$0.304325\pi$
$774$		0			0
$775$		−	0.477015i		−	0.0171349i
$776$		0			0
$777$	5.41843	−	9.43498i	0.194385	−	0.338478i
$778$		0			0
$779$	13.1092	−	7.56858i	0.469685	−	0.271172i
$780$		0			0
$781$	−21.3243	−	12.3116i	−0.763043	−	0.440543i
$782$		0			0
$783$	−1.36925	+	2.40981i	−0.0489329	+	0.0861196i
$784$		0			0
$785$	14.2718	+	8.23981i	0.509381	+	0.294091i
$786$		0			0
$787$	−20.0375	−	34.7059i	−0.714258	−	1.23713i	−0.963245	−	0.268624i	$-0.913431\pi$
$787$	−20.0375	−	34.7059i	−0.714258	−	1.23713i	0.248987	−	0.968507i	$-0.419902\pi$
$788$		0			0
$789$	3.81031	−	6.63481i	0.135651	−	0.236205i
$790$		0			0
$791$	1.47297			0.0523727
$792$		0			0
$793$	−47.1872			−1.67567
$794$		0			0
$795$	−12.4201	−	21.3985i	−0.440495	−	0.758927i
$796$		0			0
$797$	28.1638	+	48.7811i	0.997612	+	1.72791i	0.558622	+	0.829423i	$0.311330\pi$
$797$	28.1638	+	48.7811i	0.997612	+	1.72791i	0.438990	+	0.898492i	$0.355336\pi$
$798$		0			0
$799$	9.08646	+	5.24607i	0.321456	+	0.185593i
$800$		0			0
$801$	−0.0664679	−	14.4663i	−0.00234853	−	0.511141i
$802$		0			0
$803$	21.4325	+	12.3741i	0.756337	+	0.436671i
$804$		0			0
$805$	−10.2517	+	5.91884i	−0.361326	+	0.208612i
$806$		0			0
$807$	−43.1824	+	0.0992039i	−1.52009	+	0.00349214i
$808$		0			0
$809$			17.2021i			0.604793i	0.953182	+	0.302397i	$0.0977867\pi$
$809$			17.2021i			0.604793i	−0.953182	+	0.302397i	$0.902213\pi$
$810$		0			0
$811$	56.3100			1.97731			0.988656	−	0.150196i	$-0.0479904\pi$
$811$	56.3100			1.97731			0.988656	+	0.150196i	$0.0479904\pi$
$812$		0			0
$813$	−0.0855761	−	37.2503i	−0.00300128	−	1.30643i
$814$		0			0
$815$	−3.77957	−	6.54641i	−0.132393	−	0.229311i
$816$		0			0
$817$	−8.22317	+	14.2430i	−0.287692	+	0.498298i
$818$		0			0
$819$	−31.7777	+	0.146008i	−1.11040	+	0.00510194i
$820$		0			0
$821$	1.37477	−	2.38117i	0.0479797	−	0.0831033i	−0.841038	−	0.540976i	$-0.818055\pi$
$821$	1.37477	−	2.38117i	0.0479797	−	0.0831033i	0.889018	+	0.457873i	$0.151388\pi$
$822$		0			0
$823$	−23.4482	+	13.5378i	−0.817353	+	0.471899i	−0.849503	−	0.527584i	$-0.823098\pi$
$823$	−23.4482	+	13.5378i	−0.817353	+	0.471899i	0.0321498	+	0.999483i	$0.489765\pi$
$824$		0			0
$825$	−4.67762	+	2.71497i	−0.162854	+	0.0945231i
$826$		0			0
$827$		−	29.3670i		−	1.02119i	−0.859821	−	0.510596i	$-0.829425\pi$
$827$		−	29.3670i		−	1.02119i	0.859821	−	0.510596i	$-0.170575\pi$
$828$		0			0
$829$		−	30.1503i		−	1.04716i	−0.851975	−	0.523582i	$-0.824595\pi$
$829$		−	30.1503i		−	1.04716i	0.851975	−	0.523582i	$-0.175405\pi$
$830$		0			0
$831$	−1.20209	−	0.690350i	−0.0417001	−	0.0239480i
$832$		0			0
$833$	2.10710	−	1.21653i	0.0730066	−	0.0421504i
$834$		0			0
$835$	10.6372	−	18.4242i	0.368115	−	0.637594i
$836$		0			0
$837$	−2.13797	+	1.25409i	−0.0738992	+	0.0433475i
$838$		0			0
$839$	−3.81222	+	6.60296i	−0.131612	+	0.227959i	−0.924298	−	0.381671i	$-0.875349\pi$
$839$	−3.81222	+	6.60296i	−0.131612	+	0.227959i	0.792686	+	0.609630i	$0.208682\pi$
$840$		0			0
$841$	14.3577	+	24.8683i	0.495094	+	0.857529i
$842$		0			0
$843$	−30.8804	−	17.7343i	−1.06358	−	0.610803i
$844$		0			0
$845$	1.55649			0.0535448
$846$		0			0
$847$		−	3.46939i		−	0.119210i
$848$		0			0
$849$	−12.7313	−	21.9348i	−0.436938	−	0.752799i
$850$		0			0
$851$	8.35443	−	4.82343i	0.286386	−	0.165345i
$852$		0			0
$853$	−19.9923	−	11.5426i	−0.684525	−	0.395211i	0.117033	−	0.993128i	$-0.462662\pi$
$853$	−19.9923	−	11.5426i	−0.684525	−	0.395211i	−0.801558	+	0.597917i	$0.795995\pi$
$854$		0			0
$855$	−1.98646	−	3.40442i	−0.0679354	−	0.116429i
$856$		0			0
$857$	0.537623	+	0.310397i	0.0183649	+	0.0106030i	0.509154	−	0.860675i	$-0.329958\pi$
$857$	0.537623	+	0.310397i	0.0183649	+	0.0106030i	−0.490789	+	0.871278i	$0.663292\pi$
$858$		0			0
$859$	12.4175	+	21.5077i	0.423678	+	0.733833i	0.996296	−	0.0859901i	$-0.0274053\pi$
$859$	12.4175	+	21.5077i	0.423678	+	0.733833i	−0.572618	+	0.819823i	$0.694072\pi$
$860$		0			0
$861$	−55.4028	+	0.127278i	−1.88812	+	0.00433763i
$862$		0			0
$863$	2.55660			0.0870275			0.0435138	−	0.999053i	$-0.486145\pi$
$863$	2.55660			0.0870275			0.0435138	+	0.999053i	$0.486145\pi$
$864$		0			0
$865$	20.6332			0.701549
$866$		0			0
$867$	9.00410	−	0.0206853i	0.305795	−	0.000702511i
$868$		0			0
$869$	−0.337498	−	0.584563i	−0.0114488	−	0.0198299i
$870$		0			0
$871$	22.9934	+	13.2752i	0.779101	+	0.449814i
$872$		0			0
$873$	−12.5033	+	21.8880i	−0.423173	+	0.740798i
$874$		0			0
$875$	−2.40441	−	1.38819i	−0.0812839	−	0.0469293i
$876$		0			0
$877$	−14.8560	+	8.57713i	−0.501653	+	0.289629i	−0.729396	−	0.684092i	$-0.760199\pi$
$877$	−14.8560	+	8.57713i	−0.501653	+	0.289629i	0.227743	+	0.973721i	$0.426865\pi$
$878$		0			0
$879$	−23.3743	−	40.2715i	−0.788396	−	1.35832i
$880$		0			0
$881$			0.662030i			0.0223043i	0.999938	+	0.0111522i	$0.00354992\pi$
$881$			0.662030i			0.0223043i	−0.999938	+	0.0111522i	$0.996450\pi$
$882$		0			0
$883$	11.4683			0.385939			0.192969	−	0.981205i	$-0.438188\pi$
$883$	11.4683			0.385939			0.192969	+	0.981205i	$0.438188\pi$
$884$		0			0
$885$	15.4213	+	8.85630i	0.518380	+	0.297701i
$886$		0			0
$887$	23.5408	+	40.7738i	0.790422	+	1.36905i	0.925706	+	0.378245i	$0.123472\pi$
$887$	23.5408	+	40.7738i	0.790422	+	1.36905i	−0.135283	+	0.990807i	$0.543194\pi$
$888$		0			0
$889$	−0.770239	+	1.33409i	−0.0258330	+	0.0447440i
$890$		0			0
$891$	24.4660	+	13.8273i	0.819643	+	0.463231i
$892$		0			0
$893$	2.00639	−	3.47518i	0.0671414	−	0.116292i
$894$		0			0
$895$	−6.50193	+	3.75389i	−0.217335	+	0.125479i
$896$		0			0
$897$	−24.4333	−	14.0318i	−0.815805	−	0.468510i
$898$		0			0
$899$		−	0.254441i		−	0.00848609i
$900$		0			0
$901$			49.0725i			1.63484i
$902$		0			0
$903$	52.0608	−	30.2170i	1.73248	−	1.00556i
$904$		0			0
$905$	−13.1762	+	7.60731i	−0.437993	+	0.252876i
$906$		0			0
$907$	−5.68246	+	9.84232i	−0.188683	+	0.326809i	−0.944811	−	0.327615i	$-0.893755\pi$
$907$	−5.68246	+	9.84232i	−0.188683	+	0.326809i	0.756128	+	0.654423i	$0.227089\pi$
$908$		0			0
$909$	3.30550	−	5.78653i	0.109636	−	0.191927i
$910$		0			0
$911$	0.698984	−	1.21068i	0.0231584	−	0.0401115i	−0.854214	−	0.519922i	$-0.825961\pi$
$911$	0.698984	−	1.21068i	0.0231584	−	0.0401115i	0.877372	+	0.479810i	$0.159294\pi$
$912$		0			0
$913$	14.1778	+	24.5567i	0.469217	+	0.812708i
$914$		0			0
$915$	0.0492127	+	21.4218i	0.00162692	+	0.708182i
$916$		0			0
$917$	−16.7265			−0.552358
$918$		0			0
$919$		−	7.89210i		−	0.260336i	−0.991492	−	0.130168i	$-0.958448\pi$
$919$		−	7.89210i		−	0.260336i	0.991492	−	0.130168i	$-0.0415517\pi$
$920$		0			0
$921$	37.0379	−	0.0850880i	1.22044	−	0.00280374i
$922$		0			0
$923$	26.0551	−	15.0429i	0.857612	−	0.495143i
$924$		0			0
$925$	1.95942	+	1.13127i	0.0644254	+	0.0371960i
$926$		0			0
$927$	38.2777	−	22.3348i	1.25721	−	0.733571i
$928$		0			0
$929$	−15.9015	−	9.18072i	−0.521710	−	0.301210i	0.215924	−	0.976410i	$-0.430724\pi$
$929$	−15.9015	−	9.18072i	−0.521710	−	0.301210i	−0.737634	+	0.675201i	$0.764057\pi$
$930$		0			0
$931$	−0.465271	−	0.805873i	−0.0152486	−	0.0264114i
$932$		0			0
$933$	18.6141	+	32.0702i	0.609399	+	1.04993i
$934$		0			0
$935$	10.7270			0.350811
$936$		0			0
$937$	−11.5833			−0.378411			−0.189205	−	0.981938i	$-0.560591\pi$
$937$	−11.5833			−0.378411			−0.189205	+	0.981938i	$0.560591\pi$
$938$		0			0
$939$	5.03432	−	8.76614i	0.164289	−	0.286072i
$940$		0			0
$941$	−2.75857	−	4.77799i	−0.0899270	−	0.155758i	0.817553	−	0.575853i	$-0.195330\pi$
$941$	−2.75857	−	4.77799i	−0.0899270	−	0.155758i	−0.907480	+	0.420095i	$0.861997\pi$
$942$		0			0
$943$	−42.5416	−	24.5614i	−1.38534	−	0.799829i
$944$		0			0
$945$	0.0994258	+	14.4261i	0.00323432	+	0.469282i
$946$		0			0
$947$	14.0517	+	8.11276i	0.456620	+	0.263629i	0.710622	−	0.703574i	$-0.248414\pi$
$947$	14.0517	+	8.11276i	0.456620	+	0.263629i	−0.254002	+	0.967204i	$0.581747\pi$
$948$		0			0
$949$	−26.1873	+	15.1192i	−0.850075	+	0.490791i
$950$		0			0
$951$	7.22951	−	12.5886i	0.234433	−	0.408212i
$952$		0			0
$953$		−	0.197221i		−	0.00638861i	−0.999995	−	0.00319431i	$-0.998983\pi$
$953$		−	0.197221i		−	0.00638861i	0.999995	−	0.00319431i	$-0.00101678\pi$
$954$		0			0
$955$	−13.6022			−0.440156
$956$		0			0
$957$	−2.49506	+	1.44817i	−0.0806537	+	0.0468128i
$958$		0			0
$959$	12.0054	+	20.7940i	0.387676	+	0.671474i
$960$		0			0
$961$	−15.3862	+	26.6497i	−0.496330	+	0.859669i
$962$		0			0
$963$	0.194015	+	42.2262i	0.00625206	+	1.36072i
$964$		0			0
$965$	11.0958	−	19.2185i	0.357188	−	0.618667i
$966$		0			0
$967$	21.8675	−	12.6252i	0.703213	−	0.406000i	−0.105330	−	0.994437i	$-0.533590\pi$
$967$	21.8675	−	12.6252i	0.703213	−	0.406000i	0.808543	+	0.588437i	$0.200257\pi$
$968$		0			0
$969$	0.0179597	+	7.81767i	0.000576949	+	0.251140i
$970$		0			0
$971$			10.6137i			0.340610i	0.985391	+	0.170305i	$0.0544753\pi$
$971$			10.6137i			0.340610i	−0.985391	+	0.170305i	$0.945525\pi$
$972$		0			0
$973$		−	26.2581i		−	0.841798i
$974$		0			0
$975$	−0.0151813	−	6.60827i	−0.000486192	−	0.211634i
$976$		0			0
$977$	−24.4452	+	14.1134i	−0.782071	+	0.451529i	−0.837164	−	0.546952i	$-0.815788\pi$
$977$	−24.4452	+	14.1134i	−0.782071	+	0.451529i	0.0550925	+	0.998481i	$0.482455\pi$
$978$		0			0
$979$	7.52873	−	13.0401i	0.240619	−	0.416765i
$980$		0			0
$981$	−0.227535	−	49.5214i	−0.00726462	−	1.58110i
$982$		0			0
$983$	22.5114	−	38.9908i	0.718001	−	1.24361i	−0.243790	−	0.969828i	$-0.578391\pi$
$983$	22.5114	−	38.9908i	0.718001	−	1.24361i	0.961791	−	0.273786i	$-0.0882760\pi$
$984$		0			0
$985$	−2.93566	−	5.08471i	−0.0935378	−	0.162012i
$986$		0			0
$987$	−12.7025	+	7.37273i	−0.404324	+	0.234677i
$988$		0			0
$989$	53.3713			1.69711
$990$		0			0
$991$			45.4039i			1.44230i	0.692778	+	0.721151i	$0.256387\pi$
$991$			45.4039i			1.44230i	−0.692778	+	0.721151i	$0.743613\pi$
$992$		0			0
$993$	1.55457	−	2.70694i	0.0493328	−	0.0859020i
$994$		0			0
$995$	15.1285	−	8.73444i	0.479605	−	0.276900i
$996$		0			0
$997$	15.3295	+	8.85052i	0.485492	+	0.280299i	0.722702	−	0.691160i	$-0.242900\pi$
$997$	15.3295	+	8.85052i	0.485492	+	0.280299i	−0.237211	+	0.971458i	$0.576233\pi$
$998$		0			0
$999$	−0.0810249	−	11.7563i	−0.00256351	−	0.371951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.cc.b.911.24		48
3.2	odd	2		4320.2.cc.a.1871.19		48
4.3	odd	2		360.2.bm.b.11.15	yes	48
8.3	odd	2		1440.2.cc.a.911.24		48
8.5	even	2		360.2.bm.a.11.24	✓	48
9.4	even	3		4320.2.cc.b.3311.6		48
9.5	odd	6		1440.2.cc.a.1391.24		48
12.11	even	2		1080.2.bm.a.251.10		48
24.5	odd	2		1080.2.bm.b.251.1		48
24.11	even	2		4320.2.cc.b.1871.6		48
36.23	even	6		360.2.bm.a.131.24	yes	48
36.31	odd	6		1080.2.bm.b.611.1		48
72.5	odd	6		360.2.bm.b.131.15	yes	48
72.13	even	6		1080.2.bm.a.611.10		48
72.59	even	6	inner	1440.2.cc.b.1391.24		48
72.67	odd	6		4320.2.cc.a.3311.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.24	✓	48	8.5	even	2
360.2.bm.a.131.24	yes	48	36.23	even	6
360.2.bm.b.11.15	yes	48	4.3	odd	2
360.2.bm.b.131.15	yes	48	72.5	odd	6
1080.2.bm.a.251.10		48	12.11	even	2
1080.2.bm.a.611.10		48	72.13	even	6
1080.2.bm.b.251.1		48	24.5	odd	2
1080.2.bm.b.611.1		48	36.31	odd	6
1440.2.cc.a.911.24		48	8.3	odd	2
1440.2.cc.a.1391.24		48	9.5	odd	6
1440.2.cc.b.911.24		48	1.1	even	1	trivial
1440.2.cc.b.1391.24		48	72.59	even	6	inner
4320.2.cc.a.1871.19		48	3.2	odd	2
4320.2.cc.a.3311.19		48	72.67	odd	6
4320.2.cc.b.1871.6		48	24.11	even	2
4320.2.cc.b.3311.6		48	9.4	even	3

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 0.00397907i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(2.99997 - 0.0137839i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 0.00397907i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.40441 + 1.38819i) q^{7} +(2.99997 - 0.0137839i) q^{9} +(2.70422 + 1.56128i) q^{11} +(-3.30414 + 1.90765i) q^{13} +(0.869469 + 1.49801i) q^{15} -3.43533i q^{17} -1.31386 q^{19} +(4.17007 + 2.39484i) q^{21} +(2.13186 + 3.69249i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(5.19603 - 0.0358114i) q^{27} +(-0.266702 + 0.461941i) q^{29} +(-0.413107 + 0.238507i) q^{31} +(4.69004 + 2.69345i) q^{33} +2.77637i q^{35} -2.26255i q^{37} +(-5.71534 + 3.31728i) q^{39} +(-9.97758 + 5.76056i) q^{41} +(6.25878 - 10.8405i) q^{43} +(1.51192 + 2.59116i) q^{45} +(-1.52710 + 2.64501i) q^{47} +(0.354125 + 0.613362i) q^{49} +(-0.0136694 - 5.95014i) q^{51} -14.2847 q^{53} +3.12256i q^{55} +(-2.27567 + 0.00522795i) q^{57} +(8.89170 - 5.13363i) q^{59} +(10.7109 + 6.18395i) q^{61} +(7.23229 + 4.13137i) q^{63} +(-3.30414 - 1.90765i) q^{65} +(-3.47947 - 6.02663i) q^{67} +(3.70717 + 6.38708i) q^{69} -7.88557 q^{71} +7.92558 q^{73} +(-0.862577 + 1.50199i) q^{75} +(4.33470 + 7.50792i) q^{77} +(-0.187206 - 0.108084i) q^{79} +(8.99962 - 0.0827023i) q^{81} +(7.86428 + 4.54044i) q^{83} +(2.97508 - 1.71766i) q^{85} +(-0.460102 + 0.801164i) q^{87} -4.82215i q^{89} -10.5927 q^{91} +(-0.714571 + 0.414750i) q^{93} +(-0.656931 - 1.13784i) q^{95} +(-4.20125 + 7.27679i) q^{97} +(8.13409 + 4.64652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5}+O(q^{10}) \) 48 * q + 24 * q^5	\( 48 q + 24 q^{5} + 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} + 16 q^{39} + 12 q^{41} + 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} - 12 q^{61} + 56 q^{63} + 40 q^{69} - 8 q^{81} + 60 q^{83} + 36 q^{87} + 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 + 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 + 16 * q^39 + 12 * q^41 + 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 - 12 * q^61 + 56 * q^63 + 40 * q^69 - 8 * q^81 + 60 * q^83 + 36 * q^87 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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