LMFDB - Embedded newform 2880.2.u.a.719.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(719,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("2880.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.u (of order $4$, 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:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			719.19
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +O(q^{10})$	$q+(-0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(-3.48671 - 3.48671i) q^{11} +(3.41630 + 3.41630i) q^{13} +5.22898 q^{17} +(2.52907 + 2.52907i) q^{19} -2.90543 q^{23} +(-4.16343 - 2.76873i) q^{25} +(-0.201837 - 0.201837i) q^{29} +7.91354i q^{31} +(-1.27195 - 0.384318i) q^{35} +(-3.40301 + 3.40301i) q^{37} +4.36373 q^{41} +(-2.94210 - 2.94210i) q^{43} -10.7533i q^{47} +6.64689 q^{49} +(5.71919 + 5.71919i) q^{53} +(9.71830 - 5.20824i) q^{55} +(3.56275 + 3.56275i) q^{59} +(-9.03433 + 9.03433i) q^{61} +(-9.52206 + 5.10307i) q^{65} +(-7.72594 + 7.72594i) q^{67} +2.31103i q^{71} -2.62944 q^{73} +(2.07191 - 2.07191i) q^{77} +9.07044i q^{79} +(-3.75900 - 3.75900i) q^{83} +(-3.38184 + 11.1926i) q^{85} -17.3168 q^{89} +(-2.03007 + 2.03007i) q^{91} +(-7.04915 + 3.77779i) q^{95} -2.43368i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) $ 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.646750	+	2.14049i	−0.289236	+	0.957258i
$5$	−0.646750	+	2.14049i	−0.289236	+	0.957258i
$6$		0			0
$7$			0.594230i			0.224598i	0.993674	+	0.112299i	$0.0358214\pi$
$7$			0.594230i			0.224598i	−0.993674	+	0.112299i	$0.964179\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.48671	−	3.48671i	−1.05128	−	1.05128i	−0.998612	−	0.0526694i	$-0.983227\pi$
$11$	−3.48671	−	3.48671i	−1.05128	−	1.05128i	−0.0526694	−	0.998612i	$-0.516773\pi$
$12$		0			0
$13$	3.41630	+	3.41630i	0.947511	+	0.947511i	0.998690	−	0.0511786i	$-0.0162978\pi$
$13$	3.41630	+	3.41630i	0.947511	+	0.947511i	−0.0511786	+	0.998690i	$0.516298\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.22898			1.26821			0.634107	−	0.773246i	$-0.281368\pi$
$17$	5.22898			1.26821			0.634107	+	0.773246i	$0.281368\pi$
$18$		0			0
$19$	2.52907	+	2.52907i	0.580209	+	0.580209i	0.934961	−	0.354751i	$-0.115434\pi$
$19$	2.52907	+	2.52907i	0.580209	+	0.580209i	−0.354751	+	0.934961i	$0.615434\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.90543			−0.605824			−0.302912	−	0.953019i	$-0.597959\pi$
$23$	−2.90543			−0.605824			−0.302912	+	0.953019i	$0.597959\pi$
$24$		0			0
$25$	−4.16343	−	2.76873i	−0.832686	−	0.553746i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.201837	−	0.201837i	−0.0374802	−	0.0374802i	0.688118	−	0.725599i	$-0.258437\pi$
$29$	−0.201837	−	0.201837i	−0.0374802	−	0.0374802i	−0.725599	+	0.688118i	$0.758437\pi$
$30$		0			0
$31$			7.91354i			1.42131i	0.703538	+	0.710657i	$0.251602\pi$
$31$			7.91354i			1.42131i	−0.703538	+	0.710657i	$0.748398\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.27195	−	0.384318i	−0.214998	−	0.0649617i
$36$		0			0
$37$	−3.40301	+	3.40301i	−0.559452	+	0.559452i	−0.929151	−	0.369699i	$-0.879461\pi$
$37$	−3.40301	+	3.40301i	−0.559452	+	0.559452i	0.369699	+	0.929151i	$0.379461\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.36373			0.681500			0.340750	−	0.940154i	$-0.389319\pi$
$41$	4.36373			0.681500			0.340750	+	0.940154i	$0.389319\pi$
$42$		0			0
$43$	−2.94210	−	2.94210i	−0.448666	−	0.448666i	0.446245	−	0.894911i	$-0.352761\pi$
$43$	−2.94210	−	2.94210i	−0.448666	−	0.448666i	−0.894911	+	0.446245i	$0.852761\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	10.7533i		−	1.56853i	−0.620427	−	0.784264i	$-0.713041\pi$
$47$		−	10.7533i		−	1.56853i	0.620427	−	0.784264i	$-0.286959\pi$
$48$		0			0
$49$	6.64689			0.949556
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.71919	+	5.71919i	0.785591	+	0.785591i	0.980768	−	0.195177i	$-0.0625281\pi$
$53$	5.71919	+	5.71919i	0.785591	+	0.785591i	−0.195177	+	0.980768i	$0.562528\pi$
$54$		0			0
$55$	9.71830	−	5.20824i	1.31042	−	0.702280i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.56275	+	3.56275i	0.463831	+	0.463831i	0.899909	−	0.436078i	$-0.143633\pi$
$59$	3.56275	+	3.56275i	0.463831	+	0.463831i	−0.436078	+	0.899909i	$0.643633\pi$
$60$		0			0
$61$	−9.03433	+	9.03433i	−1.15673	+	1.15673i	−0.171553	+	0.985175i	$0.554878\pi$
$61$	−9.03433	+	9.03433i	−1.15673	+	1.15673i	−0.985175	+	0.171553i	$0.945122\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.52206	+	5.10307i	−1.18107	+	0.632958i
$66$		0			0
$67$	−7.72594	+	7.72594i	−0.943874	+	0.943874i	−0.998507	−	0.0546326i	$-0.982601\pi$
$67$	−7.72594	+	7.72594i	−0.943874	+	0.943874i	0.0546326	+	0.998507i	$0.482601\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			2.31103i			0.274269i	0.990552	+	0.137134i	$0.0437892\pi$
$71$			2.31103i			0.274269i	−0.990552	+	0.137134i	$0.956211\pi$
$72$		0			0
$73$	−2.62944			−0.307753			−0.153876	−	0.988090i	$-0.549176\pi$
$73$	−2.62944			−0.307753			−0.153876	+	0.988090i	$0.549176\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.07191	−	2.07191i	0.236116	−	0.236116i
$78$		0			0
$79$			9.07044i			1.02050i	0.860025	+	0.510252i	$0.170448\pi$
$79$			9.07044i			1.02050i	−0.860025	+	0.510252i	$0.829552\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.75900	−	3.75900i	−0.412604	−	0.412604i	0.470041	−	0.882645i	$-0.344239\pi$
$83$	−3.75900	−	3.75900i	−0.412604	−	0.412604i	−0.882645	+	0.470041i	$0.844239\pi$
$84$		0			0
$85$	−3.38184	+	11.1926i	−0.366812	+	1.21401i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−17.3168			−1.83558			−0.917788	−	0.397070i	$-0.870027\pi$
$89$	−17.3168			−1.83558			−0.917788	+	0.397070i	$0.870027\pi$
$90$		0			0
$91$	−2.03007	+	2.03007i	−0.212809	+	0.212809i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.04915	+	3.77779i	−0.723227	+	0.387593i
$96$		0			0
$97$		−	2.43368i		−	0.247103i	−0.992338	−	0.123551i	$-0.960572\pi$
$97$		−	2.43368i		−	0.247103i	0.992338	−	0.123551i	$-0.0394284\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.22586	+	9.22586i	−0.918007	+	0.918007i	−0.996884	−	0.0788774i	$-0.974866\pi$
$101$	−9.22586	+	9.22586i	−0.918007	+	0.918007i	0.0788774	+	0.996884i	$0.474866\pi$
$102$		0			0
$103$			0.353806i			0.0348615i	0.999848	+	0.0174308i	$0.00554866\pi$
$103$			0.353806i			0.0348615i	−0.999848	+	0.0174308i	$0.994451\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.83739	+	7.83739i	−0.757670	+	0.757670i	−0.975898	−	0.218228i	$-0.929972\pi$
$107$	−7.83739	+	7.83739i	−0.757670	+	0.757670i	0.218228	+	0.975898i	$0.429972\pi$
$108$		0			0
$109$	5.04082	−	5.04082i	0.482823	−	0.482823i	−0.423209	−	0.906032i	$-0.639096\pi$
$109$	5.04082	−	5.04082i	0.482823	−	0.482823i	0.906032	+	0.423209i	$0.139096\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.6858			−1.28745			−0.643724	−	0.765257i	$-0.722612\pi$
$113$	−13.6858			−1.28745			−0.643724	+	0.765257i	$0.722612\pi$
$114$		0			0
$115$	1.87909	−	6.21906i	0.175226	−	0.579930i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			3.10721i			0.284838i
$120$		0			0
$121$			13.3142i			1.21039i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.61915	−	7.12111i	0.770920	−	0.636932i
$126$		0			0
$127$	21.2399			1.88474			0.942369	−	0.334575i	$-0.108593\pi$
$127$	21.2399			1.88474			0.942369	+	0.334575i	$0.108593\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.47505	+	2.47505i	−0.216246	+	0.216246i	−0.806914	−	0.590668i	$-0.798864\pi$
$131$	−2.47505	+	2.47505i	−0.216246	+	0.216246i	0.590668	+	0.806914i	$0.298864\pi$
$132$		0			0
$133$	−1.50285	+	1.50285i	−0.130314	+	0.130314i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			1.05127i			0.0898162i	0.998991	+	0.0449081i	$0.0142995\pi$
$137$			1.05127i			0.0898162i	−0.998991	+	0.0449081i	$0.985700\pi$
$138$		0			0
$139$	2.76139	−	2.76139i	0.234218	−	0.234218i	−0.580233	−	0.814451i	$-0.697038\pi$
$139$	2.76139	−	2.76139i	0.234218	−	0.234218i	0.814451	+	0.580233i	$0.197038\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	23.8233i		−	1.99220i
$144$		0			0
$145$	0.562570	−	0.301493i	0.0467189	−	0.0250376i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.00428	+	6.00428i	−0.491890	+	0.491890i	−0.908901	−	0.417011i	$-0.863078\pi$
$149$	−6.00428	+	6.00428i	−0.491890	+	0.491890i	0.417011	+	0.908901i	$0.363078\pi$
$150$		0			0
$151$	5.86656			0.477414			0.238707	−	0.971092i	$-0.423276\pi$
$151$	5.86656			0.477414			0.238707	+	0.971092i	$0.423276\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−16.9389	−	5.11809i	−1.36056	−	0.411095i
$156$		0			0
$157$	−3.07654	−	3.07654i	−0.245535	−	0.245535i	0.573600	−	0.819135i	$-0.305546\pi$
$157$	−3.07654	−	3.07654i	−0.245535	−	0.245535i	−0.819135	+	0.573600i	$0.805546\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	1.72649i		−	0.136067i
$162$		0			0
$163$	−11.6108	+	11.6108i	−0.909426	+	0.909426i	−0.996226	−	0.0867995i	$-0.972336\pi$
$163$	−11.6108	+	11.6108i	−0.909426	+	0.909426i	0.0867995	+	0.996226i	$0.472336\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−15.2444			−1.17965			−0.589823	−	0.807533i	$-0.700802\pi$
$167$	−15.2444			−1.17965			−0.589823	+	0.807533i	$0.700802\pi$
$168$		0			0
$169$			10.3422i			0.795554i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.88472	−	8.88472i	0.675493	−	0.675493i	−0.283484	−	0.958977i	$-0.591490\pi$
$173$	8.88472	−	8.88472i	0.675493	−	0.675493i	0.958977	+	0.283484i	$0.0914903\pi$
$174$		0			0
$175$	1.64526	−	2.47403i	0.124370	−	0.187019i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.3484	+	16.3484i	−1.22193	+	1.22193i	−0.254990	+	0.966944i	$0.582072\pi$
$179$	−16.3484	+	16.3484i	−1.22193	+	1.22193i	−0.966944	+	0.254990i	$0.917928\pi$
$180$		0			0
$181$	7.64457	+	7.64457i	0.568216	+	0.568216i	0.931628	−	0.363412i	$-0.118388\pi$
$181$	7.64457	+	7.64457i	0.568216	+	0.568216i	−0.363412	+	0.931628i	$0.618388\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.08323	−	9.48503i	−0.373726	−	0.697353i
$186$		0			0
$187$	−18.2319	−	18.2319i	−1.33325	−	1.33325i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	23.6358			1.71023			0.855113	−	0.518442i	$-0.173488\pi$
$191$	23.6358			1.71023			0.855113	+	0.518442i	$0.173488\pi$
$192$		0			0
$193$		−	11.6874i		−	0.841281i	−0.907227	−	0.420640i	$-0.861805\pi$
$193$		−	11.6874i		−	0.841281i	0.907227	−	0.420640i	$-0.138195\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.52719	−	7.52719i	−0.536290	−	0.536290i	0.386147	−	0.922437i	$-0.373806\pi$
$197$	−7.52719	−	7.52719i	−0.536290	−	0.536290i	−0.922437	+	0.386147i	$0.873806\pi$
$198$		0			0
$199$	−9.24585			−0.655421			−0.327710	−	0.944778i	$-0.606277\pi$
$199$	−9.24585			−0.655421			−0.327710	+	0.944778i	$0.606277\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.119938	−	0.119938i	0.00841798	−	0.00841798i
$204$		0			0
$205$	−2.82224	+	9.34054i	−0.197114	+	0.652371i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	17.6363i		−	1.21993i
$210$		0			0
$211$	13.2934	+	13.2934i	0.915154	+	0.915154i	0.996672	−	0.0815182i	$-0.0259769\pi$
$211$	13.2934	+	13.2934i	0.915154	+	0.915154i	−0.0815182	+	0.996672i	$0.525977\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.20035	−	4.39474i	0.559259	−	0.299719i
$216$		0			0
$217$	−4.70246			−0.319224
$218$		0			0
$219$		0			0
$220$		0			0
$221$	17.8637	+	17.8637i	1.20165	+	1.20165i
$222$		0			0
$223$	−22.4740			−1.50497			−0.752487	−	0.658607i	$-0.771146\pi$
$223$	−22.4740			−1.50497			−0.752487	+	0.658607i	$0.771146\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	20.4123	+	20.4123i	1.35481	+	1.35481i	0.880190	+	0.474622i	$0.157415\pi$
$227$	20.4123	+	20.4123i	1.35481	+	1.35481i	0.474622	+	0.880190i	$0.342585\pi$
$228$		0			0
$229$	−1.13042	−	1.13042i	−0.0747005	−	0.0747005i	0.668769	−	0.743470i	$-0.266821\pi$
$229$	−1.13042	−	1.13042i	−0.0747005	−	0.0747005i	−0.743470	+	0.668769i	$0.766821\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			6.91098i			0.452753i	0.974040	+	0.226377i	$0.0726880\pi$
$233$			6.91098i			0.452753i	−0.974040	+	0.226377i	$0.927312\pi$
$234$		0			0
$235$	23.0174	+	6.95469i	1.50149	+	0.453674i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.97843			0.257343			0.128672	−	0.991687i	$-0.458929\pi$
$239$	3.97843			0.257343			0.128672	+	0.991687i	$0.458929\pi$
$240$		0			0
$241$	12.1568			0.783086			0.391543	−	0.920160i	$-0.371941\pi$
$241$	12.1568			0.783086			0.391543	+	0.920160i	$0.371941\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.29888	+	14.2276i	−0.274645	+	0.908970i
$246$		0			0
$247$			17.2801i			1.09951i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.68497	+	9.68497i	0.611310	+	0.611310i	0.943287	−	0.331977i	$-0.107716\pi$
$251$	9.68497	+	9.68497i	0.611310	+	0.611310i	−0.331977	+	0.943287i	$0.607716\pi$
$252$		0			0
$253$	10.1304	+	10.1304i	0.636892	+	0.636892i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−22.8387			−1.42464			−0.712320	−	0.701855i	$-0.752356\pi$
$257$	−22.8387			−1.42464			−0.712320	+	0.701855i	$0.752356\pi$
$258$		0			0
$259$	−2.02217	−	2.02217i	−0.125652	−	0.125652i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.69609			0.474562			0.237281	−	0.971441i	$-0.423744\pi$
$263$	7.69609			0.474562			0.237281	+	0.971441i	$0.423744\pi$
$264$		0			0
$265$	−15.9408	+	8.54300i	−0.979234	+	0.524792i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.3047	−	10.3047i	−0.628286	−	0.628286i	0.319351	−	0.947637i	$-0.396535\pi$
$269$	−10.3047	−	10.3047i	−0.628286	−	0.628286i	−0.947637	+	0.319351i	$0.896535\pi$
$270$		0			0
$271$			11.2542i			0.683642i	0.939765	+	0.341821i	$0.111044\pi$
$271$			11.2542i			0.683642i	−0.939765	+	0.341821i	$0.888956\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.86290	+	24.1704i	0.293244	+	1.45753i
$276$		0			0
$277$	−17.5560	+	17.5560i	−1.05484	+	1.05484i	−0.0564290	+	0.998407i	$0.517971\pi$
$277$	−17.5560	+	17.5560i	−1.05484	+	1.05484i	−0.998407	+	0.0564290i	$0.982029\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.7416			0.819753			0.409876	−	0.912141i	$-0.365572\pi$
$281$	13.7416			0.819753			0.409876	+	0.912141i	$0.365572\pi$
$282$		0			0
$283$	−4.27900	−	4.27900i	−0.254360	−	0.254360i	0.568395	−	0.822756i	$-0.307564\pi$
$283$	−4.27900	−	4.27900i	−0.254360	−	0.254360i	−0.822756	+	0.568395i	$0.807564\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			2.59306i			0.153063i
$288$		0			0
$289$	10.3422			0.608365
$290$		0			0
$291$		0			0
$292$		0			0
$293$	11.6595	+	11.6595i	0.681153	+	0.681153i	0.960260	−	0.279107i	$-0.0900385\pi$
$293$	11.6595	+	11.6595i	0.681153	+	0.681153i	−0.279107	+	0.960260i	$0.590038\pi$
$294$		0			0
$295$	−9.93026	+	5.32184i	−0.578162	+	0.309849i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.92582	−	9.92582i	−0.574025	−	0.574025i
$300$		0			0
$301$	1.74828	−	1.74828i	0.100769	−	0.100769i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−13.4950	−	25.1809i	−0.772720	−	1.44185i
$306$		0			0
$307$	4.64313	−	4.64313i	0.264997	−	0.264997i	−0.562083	−	0.827081i	$-0.690000\pi$
$307$	4.64313	−	4.64313i	0.264997	−	0.264997i	0.827081	+	0.562083i	$0.190000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			0.760850i			0.0431438i	0.999767	+	0.0215719i	$0.00686709\pi$
$311$			0.760850i			0.0431438i	−0.999767	+	0.0215719i	$0.993133\pi$
$312$		0			0
$313$	31.2608			1.76697			0.883483	−	0.468464i	$-0.155192\pi$
$313$	31.2608			1.76697			0.883483	+	0.468464i	$0.155192\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.38359	−	3.38359i	0.190041	−	0.190041i	−0.605673	−	0.795714i	$-0.707096\pi$
$317$	3.38359	−	3.38359i	0.190041	−	0.190041i	0.795714	+	0.605673i	$0.207096\pi$
$318$		0			0
$319$			1.40749i			0.0788046i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	13.2245	+	13.2245i	0.735829	+	0.735829i
$324$		0			0
$325$	−4.76470	−	23.6823i	−0.264298	−	1.31366i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.38993			0.352288
$330$		0			0
$331$	0.0840779	−	0.0840779i	0.00462134	−	0.00462134i	−0.704792	−	0.709414i	$-0.748960\pi$
$331$	0.0840779	−	0.0840779i	0.00462134	−	0.00462134i	0.709414	+	0.704792i	$0.248960\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.5406	−	21.5341i	−0.630529	−	1.17653i
$336$		0			0
$337$		−	27.7179i		−	1.50989i	−0.655787	−	0.754946i	$-0.727663\pi$
$337$		−	27.7179i		−	1.50989i	0.655787	−	0.754946i	$-0.272337\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	27.5922	−	27.5922i	1.49420	−	1.49420i
$342$		0			0
$343$			8.10939i			0.437866i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.7819	−	11.7819i	0.632487	−	0.632487i	−0.316204	−	0.948691i	$-0.602408\pi$
$347$	11.7819	−	11.7819i	0.632487	−	0.632487i	0.948691	+	0.316204i	$0.102408\pi$
$348$		0			0
$349$	1.41586	−	1.41586i	0.0757895	−	0.0757895i	−0.668196	−	0.743985i	$-0.732933\pi$
$349$	1.41586	−	1.41586i	0.0757895	−	0.0757895i	0.743985	+	0.668196i	$0.232933\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.4948			−0.665031			−0.332515	−	0.943098i	$-0.607897\pi$
$353$	−12.4948			−0.665031			−0.332515	+	0.943098i	$0.607897\pi$
$354$		0			0
$355$	−4.94674	−	1.49466i	−0.262546	−	0.0793283i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			1.11928i			0.0590733i	0.999564	+	0.0295366i	$0.00940317\pi$
$359$			1.11928i			0.0590733i	−0.999564	+	0.0295366i	$0.990597\pi$
$360$		0			0
$361$		−	6.20757i		−	0.326714i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.70059	−	5.62830i	0.0890130	−	0.294599i
$366$		0			0
$367$	12.5630			0.655784			0.327892	−	0.944715i	$-0.393662\pi$
$367$	12.5630			0.655784			0.327892	+	0.944715i	$0.393662\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.39851	+	3.39851i	−0.176442	+	0.176442i
$372$		0			0
$373$	20.4047	−	20.4047i	1.05652	−	1.05652i	0.0582111	−	0.998304i	$-0.481460\pi$
$373$	20.4047	−	20.4047i	1.05652	−	1.05652i	0.998304	−	0.0582111i	$-0.0185397\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	1.37907i		−	0.0710259i
$378$		0			0
$379$	−9.82205	+	9.82205i	−0.504525	+	0.504525i	−0.912841	−	0.408316i	$-0.866116\pi$
$379$	−9.82205	+	9.82205i	−0.504525	+	0.504525i	0.408316	+	0.912841i	$0.366116\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		−	16.0018i		−	0.817655i	−0.912612	−	0.408827i	$-0.865938\pi$
$383$		−	16.0018i		−	0.817655i	0.912612	−	0.408827i	$-0.134062\pi$
$384$		0			0
$385$	3.09489	+	5.77491i	0.157730	+	0.294316i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.41189	+	1.41189i	−0.0715855	+	0.0715855i	−0.741993	−	0.670408i	$-0.766119\pi$
$389$	−1.41189	+	1.41189i	−0.0715855	+	0.0715855i	0.670408	+	0.741993i	$0.266119\pi$
$390$		0			0
$391$	−15.1924			−0.768314
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−19.4152	−	5.86631i	−0.976886	−	0.295166i
$396$		0			0
$397$	11.3004	+	11.3004i	0.567153	+	0.567153i	0.931330	−	0.364177i	$-0.118650\pi$
$397$	11.3004	+	11.3004i	0.567153	+	0.567153i	−0.364177	+	0.931330i	$0.618650\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			17.8120i			0.889491i	0.895657	+	0.444745i	$0.146706\pi$
$401$			17.8120i			0.889491i	−0.895657	+	0.444745i	$0.853294\pi$
$402$		0			0
$403$	−27.0350	+	27.0350i	−1.34671	+	1.34671i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	23.7306			1.17628
$408$		0			0
$409$		−	33.7224i		−	1.66747i	−0.552168	−	0.833733i	$-0.686199\pi$
$409$		−	33.7224i		−	1.66747i	0.552168	−	0.833733i	$-0.313801\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.11709	+	2.11709i	−0.104175	+	0.104175i
$414$		0			0
$415$	10.4772	−	5.61498i	0.514308	−	0.275629i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	10.1570	−	10.1570i	0.496200	−	0.496200i	−0.414053	−	0.910253i	$-0.635887\pi$
$419$	10.1570	−	10.1570i	0.496200	−	0.496200i	0.910253	+	0.414053i	$0.135887\pi$
$420$		0			0
$421$	3.90653	+	3.90653i	0.190393	+	0.190393i	0.795866	−	0.605473i	$-0.207016\pi$
$421$	3.90653	+	3.90653i	0.190393	+	0.190393i	−0.605473	+	0.795866i	$0.707016\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−21.7705	−	14.4776i	−1.05602	−	0.702268i
$426$		0			0
$427$	−5.36847	−	5.36847i	−0.259798	−	0.259798i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.155915			0.00751015			0.00375507	−	0.999993i	$-0.498805\pi$
$431$	0.155915			0.00751015			0.00375507	+	0.999993i	$0.498805\pi$
$432$		0			0
$433$		−	4.49972i		−	0.216243i	−0.994138	−	0.108121i	$-0.965517\pi$
$433$		−	4.49972i		−	0.216243i	0.994138	−	0.108121i	$-0.0344835\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.34805	−	7.34805i	−0.351505	−	0.351505i
$438$		0			0
$439$	22.8807			1.09204			0.546018	−	0.837773i	$-0.316143\pi$
$439$	22.8807			1.09204			0.546018	+	0.837773i	$0.316143\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−23.6054	+	23.6054i	−1.12153	+	1.12153i	−0.130015	+	0.991512i	$0.541502\pi$
$443$	−23.6054	+	23.6054i	−1.12153	+	1.12153i	−0.991512	+	0.130015i	$0.958498\pi$
$444$		0			0
$445$	11.1996	−	37.0665i	0.530914	−	1.75712i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	13.5006i		−	0.637132i	−0.947901	−	0.318566i	$-0.896799\pi$
$449$		−	13.5006i		−	0.637132i	0.947901	−	0.318566i	$-0.103201\pi$
$450$		0			0
$451$	−15.2150	−	15.2150i	−0.716448	−	0.716448i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.03240	−	5.65829i	−0.142161	−	0.265265i
$456$		0			0
$457$	21.9008			1.02448			0.512238	−	0.858844i	$-0.328817\pi$
$457$	21.9008			1.02448			0.512238	+	0.858844i	$0.328817\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.7061	+	20.7061i	0.964381	+	0.964381i	0.999387	−	0.0350065i	$-0.0111452\pi$
$461$	20.7061	+	20.7061i	0.964381	+	0.964381i	−0.0350065	+	0.999387i	$0.511145\pi$
$462$		0			0
$463$	15.1973			0.706277			0.353139	−	0.935571i	$-0.385114\pi$
$463$	15.1973			0.706277			0.353139	+	0.935571i	$0.385114\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.4255	−	10.4255i	−0.482432	−	0.482432i	0.423475	−	0.905908i	$-0.360810\pi$
$467$	−10.4255	−	10.4255i	−0.482432	−	0.482432i	−0.905908	+	0.423475i	$0.860810\pi$
$468$		0			0
$469$	−4.59099	−	4.59099i	−0.211992	−	0.211992i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			20.5165i			0.943349i
$474$		0			0
$475$	−3.52729	−	17.5319i	−0.161843	−	0.804421i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.69764			0.397406			0.198703	−	0.980060i	$-0.436327\pi$
$479$	8.69764			0.397406			0.198703	+	0.980060i	$0.436327\pi$
$480$		0			0
$481$	−23.2514			−1.06017
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.20928	+	1.57398i	0.236541	+	0.0714709i
$486$		0			0
$487$		−	18.9603i		−	0.859172i	−0.903026	−	0.429586i	$-0.858659\pi$
$487$		−	18.9603i		−	0.859172i	0.903026	−	0.429586i	$-0.141341\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	30.6747	+	30.6747i	1.38433	+	1.38433i	0.836758	+	0.547573i	$0.184448\pi$
$491$	30.6747	+	30.6747i	1.38433	+	1.38433i	0.547573	+	0.836758i	$0.315552\pi$
$492$		0			0
$493$	−1.05540	−	1.05540i	−0.0475329	−	0.0475329i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.37328			−0.0616002
$498$		0			0
$499$	−25.7124	−	25.7124i	−1.15105	−	1.15105i	−0.986343	−	0.164704i	$-0.947333\pi$
$499$	−25.7124	−	25.7124i	−1.15105	−	1.15105i	−0.164704	−	0.986343i	$-0.552667\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8.27958			−0.369168			−0.184584	−	0.982817i	$-0.559094\pi$
$503$	−8.27958			−0.369168			−0.184584	+	0.982817i	$0.559094\pi$
$504$		0			0
$505$	−13.7811	−	25.7147i	−0.613249	−	1.14429i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.07951	+	9.07951i	0.402442	+	0.402442i	0.879093	−	0.476651i	$-0.158149\pi$
$509$	9.07951	+	9.07951i	0.402442	+	0.402442i	−0.476651	+	0.879093i	$0.658149\pi$
$510$		0			0
$511$		−	1.56249i		−	0.0691206i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.757319	−	0.228824i	−0.0333715	−	0.0100832i
$516$		0			0
$517$	−37.4936	+	37.4936i	−1.64896	+	1.64896i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.5377			1.16264			0.581320	−	0.813675i	$-0.302537\pi$
$521$	26.5377			1.16264			0.581320	+	0.813675i	$0.302537\pi$
$522$		0			0
$523$	3.66089	+	3.66089i	0.160080	+	0.160080i	0.782602	−	0.622522i	$-0.213892\pi$
$523$	3.66089	+	3.66089i	0.160080	+	0.160080i	−0.622522	+	0.782602i	$0.713892\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			41.3797i			1.80253i
$528$		0			0
$529$	−14.5585			−0.632977
$530$		0			0
$531$		0			0
$532$		0			0
$533$	14.9078	+	14.9078i	0.645729	+	0.645729i
$534$		0			0
$535$	−11.7071	−	21.8447i	−0.506140	−	0.944430i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−23.1758	−	23.1758i	−0.998250	−	0.998250i
$540$		0			0
$541$	−25.5381	+	25.5381i	−1.09797	+	1.09797i	−0.103321	+	0.994648i	$0.532947\pi$
$541$	−25.5381	+	25.5381i	−1.09797	+	1.09797i	−0.994648	+	0.103321i	$0.967053\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.52970	+	14.0500i	0.322537	+	0.601836i
$546$		0			0
$547$	10.4273	−	10.4273i	0.445837	−	0.445837i	−0.448131	−	0.893968i	$-0.647910\pi$
$547$	10.4273	−	10.4273i	0.445837	−	0.445837i	0.893968	+	0.448131i	$0.147910\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	1.02092i		−	0.0434928i
$552$		0			0
$553$	−5.38993			−0.229203
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.6374	−	22.6374i	0.959178	−	0.959178i	−0.0400207	−	0.999199i	$-0.512742\pi$
$557$	22.6374	−	22.6374i	0.959178	−	0.959178i	0.999199	+	0.0400207i	$0.0127424\pi$
$558$		0			0
$559$		−	20.1022i		−	0.850232i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.9776	−	14.9776i	−0.631231	−	0.631231i	0.317146	−	0.948377i	$-0.397276\pi$
$563$	−14.9776	−	14.9776i	−0.631231	−	0.631231i	−0.948377	+	0.317146i	$0.897276\pi$
$564$		0			0
$565$	8.85127	−	29.2943i	0.372376	−	1.23242i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.3967			0.771229			0.385615	−	0.922660i	$-0.373989\pi$
$569$	18.3967			0.771229			0.385615	+	0.922660i	$0.373989\pi$
$570$		0			0
$571$	−20.5645	+	20.5645i	−0.860599	+	0.860599i	−0.991408	−	0.130808i	$-0.958243\pi$
$571$	−20.5645	+	20.5645i	−0.860599	+	0.860599i	0.130808	+	0.991408i	$0.458243\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.0966	+	8.04435i	0.504461	+	0.335473i
$576$		0			0
$577$		−	32.3657i		−	1.34740i	−0.739004	−	0.673701i	$-0.764703\pi$
$577$		−	32.3657i		−	1.34740i	0.739004	−	0.673701i	$-0.235297\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.23371	−	2.23371i	0.0926699	−	0.0926699i
$582$		0			0
$583$		−	39.8823i		−	1.65175i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.4315	−	19.4315i	0.802026	−	0.802026i	−0.181386	−	0.983412i	$-0.558058\pi$
$587$	19.4315	−	19.4315i	0.802026	−	0.802026i	0.983412	+	0.181386i	$0.0580584\pi$
$588$		0			0
$589$	−20.0139	+	20.0139i	−0.824660	+	0.824660i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.88255			0.282633			0.141316	−	0.989965i	$-0.454867\pi$
$593$	6.88255			0.282633			0.141316	+	0.989965i	$0.454867\pi$
$594$		0			0
$595$	−6.65097	−	2.00959i	−0.272663	−	0.0823852i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			9.77996i			0.399598i	0.979837	+	0.199799i	$0.0640290\pi$
$599$			9.77996i			0.399598i	−0.979837	+	0.199799i	$0.935971\pi$
$600$		0			0
$601$			39.7298i			1.62061i	0.586008	+	0.810305i	$0.300699\pi$
$601$			39.7298i			1.62061i	−0.586008	+	0.810305i	$0.699301\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−28.4990	−	8.61099i	−1.15865	−	0.350086i
$606$		0			0
$607$	39.5940			1.60707			0.803535	−	0.595257i	$-0.202950\pi$
$607$	39.5940			1.60707			0.803535	+	0.595257i	$0.202950\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	36.7365	−	36.7365i	1.48620	−	1.48620i
$612$		0			0
$613$	22.7872	−	22.7872i	0.920367	−	0.920367i	−0.0766879	−	0.997055i	$-0.524435\pi$
$613$	22.7872	−	22.7872i	0.920367	−	0.920367i	0.997055	+	0.0766879i	$0.0244345\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			24.4206i			0.983136i	0.870839	+	0.491568i	$0.163576\pi$
$617$			24.4206i			0.983136i	−0.870839	+	0.491568i	$0.836424\pi$
$618$		0			0
$619$	33.1727	−	33.1727i	1.33332	−	1.33332i	0.430945	−	0.902378i	$-0.358180\pi$
$619$	33.1727	−	33.1727i	1.33332	−	1.33332i	0.902378	−	0.430945i	$-0.141820\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	10.2902i		−	0.412267i
$624$		0			0
$625$	9.66826	+	23.0548i	0.386731	+	0.922193i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−17.7943	+	17.7943i	−0.709504	+	0.709504i
$630$		0			0
$631$	1.09691			0.0436675			0.0218337	−	0.999762i	$-0.493050\pi$
$631$	1.09691			0.0436675			0.0218337	+	0.999762i	$0.493050\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−13.7369	+	45.4639i	−0.545133	+	1.80418i
$636$		0			0
$637$	22.7078	+	22.7078i	0.899714	+	0.899714i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	37.4511i		−	1.47923i	−0.673030	−	0.739615i	$-0.735007\pi$
$641$		−	37.4511i		−	1.47923i	0.673030	−	0.739615i	$-0.264993\pi$
$642$		0			0
$643$	33.6486	−	33.6486i	1.32697	−	1.32697i	0.418973	−	0.907998i	$-0.362390\pi$
$643$	33.6486	−	33.6486i	1.32697	−	1.32697i	0.907998	−	0.418973i	$-0.137610\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−35.0053			−1.37620			−0.688099	−	0.725617i	$-0.741555\pi$
$647$	−35.0053			−1.37620			−0.688099	+	0.725617i	$0.741555\pi$
$648$		0			0
$649$		−	24.8445i		−	0.975234i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−29.4066	+	29.4066i	−1.15077	+	1.15077i	−0.164370	+	0.986399i	$0.552559\pi$
$653$	−29.4066	+	29.4066i	−1.15077	+	1.15077i	−0.986399	+	0.164370i	$0.947441\pi$
$654$		0			0
$655$	−3.69709	−	6.89857i	−0.144457	−	0.269549i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	15.5185	−	15.5185i	0.604517	−	0.604517i	−0.336991	−	0.941508i	$-0.609409\pi$
$659$	15.5185	−	15.5185i	0.604517	−	0.604517i	0.941508	+	0.336991i	$0.109409\pi$
$660$		0			0
$661$	−28.6602	−	28.6602i	−1.11475	−	1.11475i	−0.992499	−	0.122253i	$-0.960988\pi$
$661$	−28.6602	−	28.6602i	−1.11475	−	1.11475i	−0.122253	−	0.992499i	$-0.539012\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.24487	−	4.18881i	−0.0870525	−	0.162435i
$666$		0			0
$667$	0.586424	+	0.586424i	0.0227064	+	0.0227064i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	63.0001			2.43209
$672$		0			0
$673$			18.9415i			0.730143i	0.930979	+	0.365071i	$0.118955\pi$
$673$			18.9415i			0.730143i	−0.930979	+	0.365071i	$0.881045\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.06741	+	2.06741i	0.0794572	+	0.0794572i	0.745718	−	0.666261i	$-0.232106\pi$
$677$	2.06741	+	2.06741i	0.0794572	+	0.0794572i	−0.666261	+	0.745718i	$0.732106\pi$
$678$		0			0
$679$	1.44617			0.0554987
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.5476	−	16.5476i	0.633174	−	0.633174i	−0.315688	−	0.948863i	$-0.602235\pi$
$683$	16.5476	−	16.5476i	0.633174	−	0.633174i	0.948863	+	0.315688i	$0.102235\pi$
$684$		0			0
$685$	−2.25024	−	0.679911i	−0.0859773	−	0.0259780i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			39.0769i			1.48871i
$690$		0			0
$691$	−2.10025	−	2.10025i	−0.0798972	−	0.0798972i	0.666029	−	0.745926i	$-0.267993\pi$
$691$	−2.10025	−	2.10025i	−0.0798972	−	0.0798972i	−0.745926	+	0.666029i	$0.767993\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.12481	+	7.69666i	0.156463	+	0.291951i
$696$		0			0
$697$	22.8178			0.864287
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−22.6892	−	22.6892i	−0.856960	−	0.856960i	0.134018	−	0.990979i	$-0.457212\pi$
$701$	−22.6892	−	22.6892i	−0.856960	−	0.856960i	−0.990979	+	0.134018i	$0.957212\pi$
$702$		0			0
$703$	−17.2129			−0.649199
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.48228	−	5.48228i	−0.206182	−	0.206182i
$708$		0			0
$709$	−6.85782	−	6.85782i	−0.257551	−	0.257551i	0.566506	−	0.824057i	$-0.308295\pi$
$709$	−6.85782	−	6.85782i	−0.257551	−	0.257551i	−0.824057	+	0.566506i	$0.808295\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	22.9923i		−	0.861067i
$714$		0			0
$715$	50.9935	+	15.4077i	1.90705	+	0.576215i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−44.1136			−1.64516			−0.822580	−	0.568649i	$-0.807466\pi$
$719$	−44.1136			−1.64516			−0.822580	+	0.568649i	$0.807466\pi$
$720$		0			0
$721$	−0.210242			−0.00782982
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.281502	+	1.39917i	0.0104547	+	0.0519638i
$726$		0			0
$727$			49.5060i			1.83608i	0.396491	+	0.918039i	$0.370228\pi$
$727$			49.5060i			1.83608i	−0.396491	+	0.918039i	$0.629772\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−15.3842	−	15.3842i	−0.569004	−	0.569004i
$732$		0			0
$733$	−1.73352	−	1.73352i	−0.0640290	−	0.0640290i	0.674367	−	0.738396i	$-0.264417\pi$
$733$	−1.73352	−	1.73352i	−0.0640290	−	0.0640290i	−0.738396	+	0.674367i	$0.764417\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	53.8762			1.98455
$738$		0			0
$739$	−12.4907	−	12.4907i	−0.459479	−	0.459479i	0.439005	−	0.898484i	$-0.355331\pi$
$739$	−12.4907	−	12.4907i	−0.459479	−	0.459479i	−0.898484	+	0.439005i	$0.855331\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.6402			0.610469			0.305235	−	0.952277i	$-0.401265\pi$
$743$	16.6402			0.610469			0.305235	+	0.952277i	$0.401265\pi$
$744$		0			0
$745$	−8.96886	−	16.7354i	−0.328593	−	0.613138i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−4.65721	−	4.65721i	−0.170171	−	0.170171i
$750$		0			0
$751$			40.3813i			1.47353i	0.676146	+	0.736767i	$0.263649\pi$
$751$			40.3813i			1.47353i	−0.676146	+	0.736767i	$0.736351\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.79420	+	12.5573i	−0.138085	+	0.457008i
$756$		0			0
$757$	−0.105334	+	0.105334i	−0.00382842	+	0.00382842i	−0.709018	−	0.705190i	$-0.750862\pi$
$757$	−0.105334	+	0.105334i	−0.00382842	+	0.00382842i	0.705190	+	0.709018i	$0.250862\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.6399			0.711944			0.355972	−	0.934497i	$-0.384150\pi$
$761$	19.6399			0.711944			0.355972	+	0.934497i	$0.384150\pi$
$762$		0			0
$763$	2.99541	+	2.99541i	0.108441	+	0.108441i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			24.3429i			0.878970i
$768$		0			0
$769$	0.0910921			0.00328487			0.00164243	−	0.999999i	$-0.499477\pi$
$769$	0.0910921			0.00328487			0.00164243	+	0.999999i	$0.499477\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.00151	+	7.00151i	0.251827	+	0.251827i	0.821719	−	0.569892i	$-0.193015\pi$
$773$	7.00151	+	7.00151i	0.251827	+	0.251827i	−0.569892	+	0.821719i	$0.693015\pi$
$774$		0			0
$775$	21.9105	−	32.9475i	0.787047	−	1.18351i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	11.0362	+	11.0362i	0.395413	+	0.395413i
$780$		0			0
$781$	8.05788	−	8.05788i	0.288334	−	0.288334i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.57507	−	4.59556i	0.306057	−	0.164023i
$786$		0			0
$787$	15.1938	−	15.1938i	0.541601	−	0.541601i	−0.382397	−	0.923998i	$-0.624901\pi$
$787$	15.1938	−	15.1938i	0.541601	−	0.541601i	0.923998	+	0.382397i	$0.124901\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	8.13249i		−	0.289158i
$792$		0			0
$793$	−61.7280			−2.19202
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.48483	+	7.48483i	−0.265126	+	0.265126i	−0.827133	−	0.562007i	$-0.810030\pi$
$797$	−7.48483	+	7.48483i	−0.265126	+	0.265126i	0.562007	+	0.827133i	$0.310030\pi$
$798$		0			0
$799$		−	56.2287i		−	1.98923i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.16809	+	9.16809i	0.323535	+	0.323535i
$804$		0			0
$805$	3.69555	+	1.11661i	0.130251	+	0.0393554i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.4272			−0.542391			−0.271195	−	0.962524i	$-0.587419\pi$
$809$	−15.4272			−0.542391			−0.271195	+	0.962524i	$0.587419\pi$
$810$		0			0
$811$	−7.22410	+	7.22410i	−0.253672	+	0.253672i	−0.822474	−	0.568802i	$-0.807407\pi$
$811$	−7.22410	+	7.22410i	−0.253672	+	0.253672i	0.568802	+	0.822474i	$0.307407\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−17.3435	−	32.3621i	−0.607517	−	1.13359i
$816$		0			0
$817$		−	14.8816i		−	0.520640i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.62118	−	2.62118i	0.0914799	−	0.0914799i	−0.659886	−	0.751366i	$-0.729395\pi$
$821$	2.62118	−	2.62118i	0.0914799	−	0.0914799i	0.751366	+	0.659886i	$0.229395\pi$
$822$		0			0
$823$			31.3537i			1.09292i	0.837485	+	0.546461i	$0.184025\pi$
$823$			31.3537i			1.09292i	−0.837485	+	0.546461i	$0.815975\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.0938	−	28.0938i	0.976915	−	0.976915i	−0.0228240	−	0.999739i	$-0.507266\pi$
$827$	28.0938	−	28.0938i	0.976915	−	0.976915i	0.999739	+	0.0228240i	$0.00726574\pi$
$828$		0			0
$829$	9.99625	−	9.99625i	0.347184	−	0.347184i	−0.511876	−	0.859060i	$-0.671049\pi$
$829$	9.99625	−	9.99625i	0.347184	−	0.347184i	0.859060	+	0.511876i	$0.171049\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	34.7564			1.20424
$834$		0			0
$835$	9.85930	−	32.6305i	0.341195	−	1.12922i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	53.0820i		−	1.83260i	−0.400498	−	0.916298i	$-0.631163\pi$
$839$		−	53.0820i		−	1.83260i	0.400498	−	0.916298i	$-0.368837\pi$
$840$		0			0
$841$		−	28.9185i		−	0.997190i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−22.1374	−	6.68882i	−0.761550	−	0.230102i
$846$		0			0
$847$	−7.91172			−0.271850
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.88722	−	9.88722i	0.338930	−	0.338930i
$852$		0			0
$853$	−16.8340	+	16.8340i	−0.576384	+	0.576384i	−0.933905	−	0.357521i	$-0.883622\pi$
$853$	−16.8340	+	16.8340i	−0.576384	+	0.576384i	0.357521	+	0.933905i	$0.383622\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			26.8832i			0.918312i	0.888356	+	0.459156i	$0.151848\pi$
$857$			26.8832i			0.918312i	−0.888356	+	0.459156i	$0.848152\pi$
$858$		0			0
$859$	−6.63355	+	6.63355i	−0.226334	+	0.226334i	−0.811159	−	0.584825i	$-0.801163\pi$
$859$	−6.63355	+	6.63355i	−0.226334	+	0.226334i	0.584825	+	0.811159i	$0.301163\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			11.6526i			0.396659i	0.980135	+	0.198329i	$0.0635516\pi$
$863$			11.6526i			0.396659i	−0.980135	+	0.198329i	$0.936448\pi$
$864$		0			0
$865$	13.2715	+	24.7639i	0.451244	+	0.841998i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	31.6260	−	31.6260i	1.07284	−	1.07284i
$870$		0			0
$871$	−52.7882			−1.78866
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.23158	+	5.12176i	0.143053	+	0.173147i
$876$		0			0
$877$	−27.4457	−	27.4457i	−0.926776	−	0.926776i	0.0707206	−	0.997496i	$-0.477470\pi$
$877$	−27.4457	−	27.4457i	−0.926776	−	0.926776i	−0.997496	+	0.0707206i	$0.977470\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			22.3792i			0.753973i	0.926219	+	0.376986i	$0.123040\pi$
$881$			22.3792i			0.753973i	−0.926219	+	0.376986i	$0.876960\pi$
$882$		0			0
$883$	1.02098	−	1.02098i	0.0343587	−	0.0343587i	−0.689719	−	0.724077i	$-0.742266\pi$
$883$	1.02098	−	1.02098i	0.0343587	−	0.0343587i	0.724077	+	0.689719i	$0.242266\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.7448			−0.730118			−0.365059	−	0.930984i	$-0.618951\pi$
$887$	−21.7448			−0.730118			−0.365059	+	0.930984i	$0.618951\pi$
$888$		0			0
$889$			12.6214i			0.423308i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	27.1959	−	27.1959i	0.910075	−	0.910075i
$894$		0			0
$895$	−24.4203	−	45.5669i	−0.816279	−	1.52313i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.59725	−	1.59725i	0.0532712	−	0.0532712i
$900$		0			0
$901$	29.9055	+	29.9055i	0.996297	+	0.996297i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.3073	+	11.4190i	−0.708278	+	0.379581i
$906$		0			0
$907$	−40.1300	−	40.1300i	−1.33249	−	1.33249i	−0.903132	−	0.429363i	$-0.858738\pi$
$907$	−40.1300	−	40.1300i	−1.33249	−	1.33249i	−0.429363	−	0.903132i	$-0.641262\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	18.2944			0.606119			0.303060	−	0.952972i	$-0.401992\pi$
$911$	18.2944			0.606119			0.303060	+	0.952972i	$0.401992\pi$
$912$		0			0
$913$			26.2131i			0.867525i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.47075	−	1.47075i	−0.0485684	−	0.0485684i
$918$		0			0
$919$	10.7894			0.355908			0.177954	−	0.984039i	$-0.443052\pi$
$919$	10.7894			0.355908			0.177954	+	0.984039i	$0.443052\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−7.89517	+	7.89517i	−0.259873	+	0.259873i
$924$		0			0
$925$	23.5902	−	4.74618i	0.775642	−	0.156053i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			13.5504i			0.444573i	0.974981	+	0.222286i	$0.0713520\pi$
$929$			13.5504i			0.444573i	−0.974981	+	0.222286i	$0.928648\pi$
$930$		0			0
$931$	16.8105	+	16.8105i	0.550941	+	0.550941i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	50.8168	−	27.2338i	1.66189	−	0.890640i
$936$		0			0
$937$	9.32301			0.304570			0.152285	−	0.988337i	$-0.451337\pi$
$937$	9.32301			0.304570			0.152285	+	0.988337i	$0.451337\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	35.3372	+	35.3372i	1.15196	+	1.15196i	0.986159	+	0.165802i	$0.0530214\pi$
$941$	35.3372	+	35.3372i	1.15196	+	1.15196i	0.165802	+	0.986159i	$0.446979\pi$
$942$		0			0
$943$	−12.6785			−0.412869
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−38.0391	−	38.0391i	−1.23611	−	1.23611i	−0.961580	−	0.274525i	$-0.911479\pi$
$947$	−38.0391	−	38.0391i	−1.23611	−	1.23611i	−0.274525	−	0.961580i	$-0.588521\pi$
$948$		0			0
$949$	−8.98296	−	8.98296i	−0.291599	−	0.291599i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	14.7622i		−	0.478194i	−0.970996	−	0.239097i	$-0.923149\pi$
$953$		−	14.7622i		−	0.478194i	0.970996	−	0.239097i	$-0.0768514\pi$
$954$		0			0
$955$	−15.2865	+	50.5923i	−0.494658	+	1.63713i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.624697			−0.0201725
$960$		0			0
$961$	−31.6242			−1.02013
$962$		0			0
$963$		0			0
$964$		0			0
$965$	25.0169	+	7.55886i	0.805323	+	0.243328i
$966$		0			0
$967$			19.8012i			0.636765i	0.947962	+	0.318383i	$0.103140\pi$
$967$			19.8012i			0.636765i	−0.947962	+	0.318383i	$0.896860\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	26.7823	+	26.7823i	0.859484	+	0.859484i	0.991277	−	0.131793i	$-0.0420734\pi$
$971$	26.7823	+	26.7823i	0.859484	+	0.859484i	−0.131793	+	0.991277i	$0.542073\pi$
$972$		0			0
$973$	1.64090	+	1.64090i	0.0526048	+	0.0526048i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.7382			0.695467			0.347734	−	0.937593i	$-0.386951\pi$
$977$	21.7382			0.695467			0.347734	+	0.937593i	$0.386951\pi$
$978$		0			0
$979$	60.3786	+	60.3786i	1.92971	+	1.92971i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.7762			−0.662658			−0.331329	−	0.943515i	$-0.607497\pi$
$983$	−20.7762			−0.662658			−0.331329	+	0.943515i	$0.607497\pi$
$984$		0			0
$985$	20.9801	−	11.2437i	0.668482	−	0.358254i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.54807	+	8.54807i	0.271813	+	0.271813i
$990$		0			0
$991$			0.442922i			0.0140699i	0.999975	+	0.00703494i	$0.00223931\pi$
$991$			0.442922i			0.0140699i	−0.999975	+	0.00703494i	$0.997761\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5.97976	−	19.7907i	0.189571	−	0.627407i
$996$		0			0
$997$	6.59897	−	6.59897i	0.208991	−	0.208991i	−0.594847	−	0.803839i	$-0.702787\pi$
$997$	6.59897	−	6.59897i	0.208991	−	0.208991i	0.803839	+	0.594847i	$0.202787\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.u.a.719.19		96
3.2	odd	2	inner	2880.2.u.a.719.30		96
4.3	odd	2		720.2.u.a.539.33	yes	96
5.4	even	2	inner	2880.2.u.a.719.6		96
12.11	even	2		720.2.u.a.539.16	yes	96
15.14	odd	2	inner	2880.2.u.a.719.43		96
16.3	odd	4	inner	2880.2.u.a.2159.43		96
16.13	even	4		720.2.u.a.179.34	yes	96
20.19	odd	2		720.2.u.a.539.15	yes	96
48.29	odd	4		720.2.u.a.179.15	✓	96
48.35	even	4	inner	2880.2.u.a.2159.6		96
60.59	even	2		720.2.u.a.539.34	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.30		96
80.29	even	4		720.2.u.a.179.16	yes	96
240.29	odd	4		720.2.u.a.179.33	yes	96
240.179	even	4	inner	2880.2.u.a.2159.19		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.15	✓	96	48.29	odd	4
720.2.u.a.179.16	yes	96	80.29	even	4
720.2.u.a.179.33	yes	96	240.29	odd	4
720.2.u.a.179.34	yes	96	16.13	even	4
720.2.u.a.539.15	yes	96	20.19	odd	2
720.2.u.a.539.16	yes	96	12.11	even	2
720.2.u.a.539.33	yes	96	4.3	odd	2
720.2.u.a.539.34	yes	96	60.59	even	2
2880.2.u.a.719.6		96	5.4	even	2	inner
2880.2.u.a.719.19		96	1.1	even	1	trivial
2880.2.u.a.719.30		96	3.2	odd	2	inner
2880.2.u.a.719.43		96	15.14	odd	2	inner
2880.2.u.a.2159.6		96	48.35	even	4	inner
2880.2.u.a.2159.19		96	240.179	even	4	inner
2880.2.u.a.2159.30		96	80.19	odd	4	inner
2880.2.u.a.2159.43		96	16.3	odd	4	inner

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:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +O(q^{10})\)	\(q+(-0.646750 + 2.14049i) q^{5} +0.594230i q^{7} +(-3.48671 - 3.48671i) q^{11} +(3.41630 + 3.41630i) q^{13} +5.22898 q^{17} +(2.52907 + 2.52907i) q^{19} -2.90543 q^{23} +(-4.16343 - 2.76873i) q^{25} +(-0.201837 - 0.201837i) q^{29} +7.91354i q^{31} +(-1.27195 - 0.384318i) q^{35} +(-3.40301 + 3.40301i) q^{37} +4.36373 q^{41} +(-2.94210 - 2.94210i) q^{43} -10.7533i q^{47} +6.64689 q^{49} +(5.71919 + 5.71919i) q^{53} +(9.71830 - 5.20824i) q^{55} +(3.56275 + 3.56275i) q^{59} +(-9.03433 + 9.03433i) q^{61} +(-9.52206 + 5.10307i) q^{65} +(-7.72594 + 7.72594i) q^{67} +2.31103i q^{71} -2.62944 q^{73} +(2.07191 - 2.07191i) q^{77} +9.07044i q^{79} +(-3.75900 - 3.75900i) q^{83} +(-3.38184 + 11.1926i) q^{85} -17.3168 q^{89} +(-2.03007 + 2.03007i) q^{91} +(-7.04915 + 3.77779i) q^{95} -2.43368i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) \) 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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