LMFDB - Embedded newform 2880.2.u.a.719.13

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			719.13
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50698 + 1.65197i) q^{5} -4.30751i q^{7} +O(q^{10})$	$q+(-1.50698 + 1.65197i) q^{5} -4.30751i q^{7} +(4.26649 + 4.26649i) q^{11} +(-2.10930 - 2.10930i) q^{13} -3.59142 q^{17} +(-0.954870 - 0.954870i) q^{19} -6.53188 q^{23} +(-0.457999 - 4.97898i) q^{25} +(1.84857 + 1.84857i) q^{29} +7.64329i q^{31} +(7.11588 + 6.49135i) q^{35} +(-1.90965 + 1.90965i) q^{37} +7.67058 q^{41} +(5.43308 + 5.43308i) q^{43} +3.24864i q^{47} -11.5547 q^{49} +(-6.08323 - 6.08323i) q^{53} +(-13.4776 + 0.618574i) q^{55} +(2.97848 + 2.97848i) q^{59} +(-0.157020 + 0.157020i) q^{61} +(6.66318 - 0.305816i) q^{65} +(0.305394 - 0.305394i) q^{67} -1.61808i q^{71} -6.90696 q^{73} +(18.3780 - 18.3780i) q^{77} -5.39306i q^{79} +(5.82210 + 5.82210i) q^{83} +(5.41221 - 5.93291i) q^{85} -7.74878 q^{89} +(-9.08585 + 9.08585i) q^{91} +(3.01639 - 0.138441i) q^{95} +9.34141i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.50698	+	1.65197i	−0.673944	+	0.738783i
$5$	−1.50698	+	1.65197i	−0.673944	+	0.738783i
$6$		0			0
$7$		−	4.30751i		−	1.62809i	−0.580804	−	0.814044i	$-0.697262\pi$
$7$		−	4.30751i		−	1.62809i	0.580804	−	0.814044i	$-0.302738\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.26649	+	4.26649i	1.28640	+	1.28640i	0.936961	+	0.349435i	$0.113626\pi$
$11$	4.26649	+	4.26649i	1.28640	+	1.28640i	0.349435	+	0.936961i	$0.386374\pi$
$12$		0			0
$13$	−2.10930	−	2.10930i	−0.585015	−	0.585015i	0.351262	−	0.936277i	$-0.385753\pi$
$13$	−2.10930	−	2.10930i	−0.585015	−	0.585015i	−0.936277	+	0.351262i	$0.885753\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.59142			−0.871048			−0.435524	−	0.900177i	$-0.643437\pi$
$17$	−3.59142			−0.871048			−0.435524	+	0.900177i	$0.643437\pi$
$18$		0			0
$19$	−0.954870	−	0.954870i	−0.219062	−	0.219062i	0.589041	−	0.808103i	$-0.299506\pi$
$19$	−0.954870	−	0.954870i	−0.219062	−	0.219062i	−0.808103	+	0.589041i	$0.799506\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.53188			−1.36199			−0.680996	−	0.732287i	$-0.738453\pi$
$23$	−6.53188			−1.36199			−0.680996	+	0.732287i	$0.738453\pi$
$24$		0			0
$25$	−0.457999	−	4.97898i	−0.0915997	−	0.995796i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.84857	+	1.84857i	0.343270	+	0.343270i	0.857595	−	0.514325i	$-0.171958\pi$
$29$	1.84857	+	1.84857i	0.343270	+	0.343270i	−0.514325	+	0.857595i	$0.671958\pi$
$30$		0			0
$31$			7.64329i			1.37278i	0.727236	+	0.686388i	$0.240805\pi$
$31$			7.64329i			1.37278i	−0.727236	+	0.686388i	$0.759195\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.11588	+	6.49135i	1.20280	+	1.09724i
$36$		0			0
$37$	−1.90965	+	1.90965i	−0.313945	+	0.313945i	−0.846436	−	0.532491i	$-0.821256\pi$
$37$	−1.90965	+	1.90965i	−0.313945	+	0.313945i	0.532491	+	0.846436i	$0.321256\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.67058			1.19794			0.598972	−	0.800770i	$-0.295576\pi$
$41$	7.67058			1.19794			0.598972	+	0.800770i	$0.295576\pi$
$42$		0			0
$43$	5.43308	+	5.43308i	0.828537	+	0.828537i	0.987314	−	0.158777i	$-0.0507552\pi$
$43$	5.43308	+	5.43308i	0.828537	+	0.828537i	−0.158777	+	0.987314i	$0.550755\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.24864i			0.473863i	0.971526	+	0.236932i	$0.0761417\pi$
$47$			3.24864i			0.473863i	−0.971526	+	0.236932i	$0.923858\pi$
$48$		0			0
$49$	−11.5547			−1.65067
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.08323	−	6.08323i	−0.835596	−	0.835596i	0.152680	−	0.988276i	$-0.451210\pi$
$53$	−6.08323	−	6.08323i	−0.835596	−	0.835596i	−0.988276	+	0.152680i	$0.951210\pi$
$54$		0			0
$55$	−13.4776	+	0.618574i	−1.81732	+	0.0834085i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.97848	+	2.97848i	0.387765	+	0.387765i	0.873889	−	0.486125i	$-0.161590\pi$
$59$	2.97848	+	2.97848i	0.387765	+	0.387765i	−0.486125	+	0.873889i	$0.661590\pi$
$60$		0			0
$61$	−0.157020	+	0.157020i	−0.0201044	+	0.0201044i	−0.717088	−	0.696983i	$-0.754525\pi$
$61$	−0.157020	+	0.157020i	−0.0201044	+	0.0201044i	0.696983	+	0.717088i	$0.254525\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.66318	−	0.305816i	0.826466	−	0.0379318i
$66$		0			0
$67$	0.305394	−	0.305394i	0.0373098	−	0.0373098i	−0.688206	−	0.725516i	$-0.741601\pi$
$67$	0.305394	−	0.305394i	0.0373098	−	0.0373098i	0.725516	+	0.688206i	$0.241601\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.61808i		−	0.192030i	−0.995380	−	0.0960152i	$-0.969390\pi$
$71$		−	1.61808i		−	0.192030i	0.995380	−	0.0960152i	$-0.0306097\pi$
$72$		0			0
$73$	−6.90696			−0.808399			−0.404199	−	0.914671i	$-0.632450\pi$
$73$	−6.90696			−0.808399			−0.404199	+	0.914671i	$0.632450\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	18.3780	−	18.3780i	2.09436	−	2.09436i
$78$		0			0
$79$		−	5.39306i		−	0.606767i	−0.952869	−	0.303383i	$-0.901884\pi$
$79$		−	5.39306i		−	0.606767i	0.952869	−	0.303383i	$-0.0981163\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.82210	+	5.82210i	0.639059	+	0.639059i	0.950323	−	0.311265i	$-0.100753\pi$
$83$	5.82210	+	5.82210i	0.639059	+	0.639059i	−0.311265	+	0.950323i	$0.600753\pi$
$84$		0			0
$85$	5.41221	−	5.93291i	0.587037	−	0.643515i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.74878			−0.821369			−0.410684	−	0.911778i	$-0.634710\pi$
$89$	−7.74878			−0.821369			−0.410684	+	0.911778i	$0.634710\pi$
$90$		0			0
$91$	−9.08585	+	9.08585i	−0.952455	+	0.952455i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.01639	−	0.138441i	0.309475	−	0.0142038i
$96$		0			0
$97$			9.34141i			0.948476i	0.880397	+	0.474238i	$0.157276\pi$
$97$			9.34141i			0.948476i	−0.880397	+	0.474238i	$0.842724\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.91178	+	7.91178i	−0.787251	+	0.787251i	−0.981043	−	0.193792i	$-0.937921\pi$
$101$	−7.91178	+	7.91178i	−0.787251	+	0.787251i	0.193792	+	0.981043i	$0.437921\pi$
$102$		0			0
$103$			16.1744i			1.59371i	0.604172	+	0.796854i	$0.293504\pi$
$103$			16.1744i			1.59371i	−0.604172	+	0.796854i	$0.706496\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.26603	+	5.26603i	−0.509086	+	0.509086i	−0.914246	−	0.405160i	$-0.867216\pi$
$107$	−5.26603	+	5.26603i	−0.509086	+	0.509086i	0.405160	+	0.914246i	$0.367216\pi$
$108$		0			0
$109$	−11.9434	+	11.9434i	−1.14397	+	1.14397i	−0.156248	+	0.987718i	$0.549940\pi$
$109$	−11.9434	+	11.9434i	−1.14397	+	1.14397i	−0.987718	+	0.156248i	$0.950060\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−18.0886			−1.70163			−0.850815	−	0.525466i	$-0.823891\pi$
$113$	−18.0886			−1.70163			−0.850815	+	0.525466i	$0.823891\pi$
$114$		0			0
$115$	9.84344	−	10.7905i	0.917906	−	1.00622i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			15.4701i			1.41814i
$120$		0			0
$121$			25.4059i			2.30963i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.91531	+	6.74664i	0.797410	+	0.603438i
$126$		0			0
$127$	7.28333			0.646291			0.323145	−	0.946349i	$-0.395260\pi$
$127$	7.28333			0.646291			0.323145	+	0.946349i	$0.395260\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.89718	+	9.89718i	−0.864721	+	0.864721i	−0.991882	−	0.127161i	$-0.959413\pi$
$131$	−9.89718	+	9.89718i	−0.864721	+	0.864721i	0.127161	+	0.991882i	$0.459413\pi$
$132$		0			0
$133$	−4.11312	+	4.11312i	−0.356652	+	0.356652i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			17.7974i			1.52054i	0.649608	+	0.760269i	$0.274933\pi$
$137$			17.7974i			1.52054i	−0.649608	+	0.760269i	$0.725067\pi$
$138$		0			0
$139$	−4.98268	+	4.98268i	−0.422625	+	0.422625i	−0.886107	−	0.463481i	$-0.846600\pi$
$139$	−4.98268	+	4.98268i	−0.422625	+	0.422625i	0.463481	+	0.886107i	$0.346600\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	17.9986i		−	1.50512i
$144$		0			0
$145$	−5.83953	+	0.268013i	−0.484947	+	0.0222573i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.78188	−	9.78188i	0.801363	−	0.801363i	−0.181946	−	0.983309i	$-0.558240\pi$
$149$	9.78188	−	9.78188i	0.801363	−	0.801363i	0.983309	+	0.181946i	$0.0582395\pi$
$150$		0			0
$151$	12.0108			0.977422			0.488711	−	0.872446i	$-0.337467\pi$
$151$	12.0108			0.977422			0.488711	+	0.872446i	$0.337467\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.6265	−	11.5183i	−1.01418	−	0.925173i
$156$		0			0
$157$	−8.81467	−	8.81467i	−0.703488	−	0.703488i	0.261670	−	0.965157i	$-0.415727\pi$
$157$	−8.81467	−	8.81467i	−0.703488	−	0.703488i	−0.965157	+	0.261670i	$0.915727\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			28.1362i			2.21744i
$162$		0			0
$163$	8.90000	−	8.90000i	0.697102	−	0.697102i	−0.266682	−	0.963784i	$-0.585927\pi$
$163$	8.90000	−	8.90000i	0.697102	−	0.697102i	0.963784	+	0.266682i	$0.0859275\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.24306			−0.328338			−0.164169	−	0.986432i	$-0.552494\pi$
$167$	−4.24306			−0.328338			−0.164169	+	0.986432i	$0.552494\pi$
$168$		0			0
$169$		−	4.10170i		−	0.315515i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.03165	+	4.03165i	−0.306521	+	0.306521i	−0.843558	−	0.537037i	$-0.819543\pi$
$173$	−4.03165	+	4.03165i	−0.306521	+	0.306521i	0.537037	+	0.843558i	$0.319543\pi$
$174$		0			0
$175$	−21.4470	+	1.97284i	−1.62124	+	0.149132i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.833880	+	0.833880i	−0.0623272	+	0.0623272i	−0.737583	−	0.675256i	$-0.764033\pi$
$179$	−0.833880	+	0.833880i	−0.0623272	+	0.0623272i	0.675256	+	0.737583i	$0.264033\pi$
$180$		0			0
$181$	−10.5947	−	10.5947i	−0.787501	−	0.787501i	0.193583	−	0.981084i	$-0.437989\pi$
$181$	−10.5947	−	10.5947i	−0.787501	−	0.787501i	−0.981084	+	0.193583i	$0.937989\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.276870	−	6.03250i	−0.0203559	−	0.443518i
$186$		0			0
$187$	−15.3228	−	15.3228i	−1.12051	−	1.12051i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.83158			−0.277244			−0.138622	−	0.990345i	$-0.544267\pi$
$191$	−3.83158			−0.277244			−0.138622	+	0.990345i	$0.544267\pi$
$192$		0			0
$193$			5.03272i			0.362263i	0.983459	+	0.181132i	$0.0579760\pi$
$193$			5.03272i			0.362263i	−0.983459	+	0.181132i	$0.942024\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.01759	+	7.01759i	0.499982	+	0.499982i	0.911432	−	0.411450i	$-0.134978\pi$
$197$	7.01759	+	7.01759i	0.499982	+	0.499982i	−0.411450	+	0.911432i	$0.634978\pi$
$198$		0			0
$199$	−13.7542			−0.975009			−0.487504	−	0.873121i	$-0.662093\pi$
$199$	−13.7542			−0.975009			−0.487504	+	0.873121i	$0.662093\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.96273	−	7.96273i	0.558874	−	0.558874i
$204$		0			0
$205$	−11.5594	+	12.6716i	−0.807346	+	0.885020i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	8.14789i		−	0.563601i
$210$		0			0
$211$	−12.8000	−	12.8000i	−0.881190	−	0.881190i	0.112466	−	0.993656i	$-0.464125\pi$
$211$	−12.8000	−	12.8000i	−0.881190	−	0.881190i	−0.993656	+	0.112466i	$0.964125\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−17.1628	+	0.787712i	−1.17050	+	0.0537215i
$216$		0			0
$217$	32.9236			2.23500
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.57539	+	7.57539i	0.509576	+	0.509576i
$222$		0			0
$223$	−12.7040			−0.850723			−0.425362	−	0.905023i	$-0.639853\pi$
$223$	−12.7040			−0.850723			−0.425362	+	0.905023i	$0.639853\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.3440	+	13.3440i	0.885675	+	0.885675i	0.994104	−	0.108429i	$-0.0345821\pi$
$227$	13.3440	+	13.3440i	0.885675	+	0.885675i	−0.108429	+	0.994104i	$0.534582\pi$
$228$		0			0
$229$	−1.09552	−	1.09552i	−0.0723941	−	0.0723941i	0.669983	−	0.742377i	$-0.266302\pi$
$229$	−1.09552	−	1.09552i	−0.0723941	−	0.0723941i	−0.742377	+	0.669983i	$0.766302\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			17.1156i			1.12128i	0.828060	+	0.560640i	$0.189445\pi$
$233$			17.1156i			1.12128i	−0.828060	+	0.560640i	$0.810555\pi$
$234$		0			0
$235$	−5.36665	−	4.89565i	−0.350082	−	0.319357i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	17.8555			1.15498			0.577488	−	0.816399i	$-0.304033\pi$
$239$	17.8555			1.15498			0.577488	+	0.816399i	$0.304033\pi$
$240$		0			0
$241$	5.11525			0.329502			0.164751	−	0.986335i	$-0.447318\pi$
$241$	5.11525			0.329502			0.164751	+	0.986335i	$0.447318\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	17.4127	−	19.0880i	1.11246	−	1.21949i
$246$		0			0
$247$			4.02822i			0.256309i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.02622	+	4.02622i	0.254133	+	0.254133i	0.822663	−	0.568530i	$-0.192488\pi$
$251$	4.02622	+	4.02622i	0.254133	+	0.254133i	−0.568530	+	0.822663i	$0.692488\pi$
$252$		0			0
$253$	−27.8682	−	27.8682i	−1.75206	−	1.75206i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−29.1773			−1.82003			−0.910016	−	0.414573i	$-0.863931\pi$
$257$	−29.1773			−1.82003			−0.910016	+	0.414573i	$0.863931\pi$
$258$		0			0
$259$	8.22585	+	8.22585i	0.511130	+	0.511130i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.92706			−0.118828			−0.0594139	−	0.998233i	$-0.518923\pi$
$263$	−1.92706			−0.118828			−0.0594139	+	0.998233i	$0.518923\pi$
$264$		0			0
$265$	19.2166	−	0.881973i	1.18047	−	0.0541792i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.93701	−	9.93701i	−0.605870	−	0.605870i	0.335994	−	0.941864i	$-0.390928\pi$
$269$	−9.93701	−	9.93701i	−0.605870	−	0.605870i	−0.941864	+	0.335994i	$0.890928\pi$
$270$		0			0
$271$		−	15.0777i		−	0.915907i	−0.888976	−	0.457954i	$-0.848583\pi$
$271$		−	15.0777i		−	0.915907i	0.888976	−	0.457954i	$-0.151417\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	19.2887	−	23.1968i	1.16315	−	1.39882i
$276$		0			0
$277$	−4.33837	+	4.33837i	−0.260667	+	0.260667i	−0.825325	−	0.564658i	$-0.809008\pi$
$277$	−4.33837	+	4.33837i	−0.260667	+	0.260667i	0.564658	+	0.825325i	$0.309008\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.93138			−0.174871			−0.0874357	−	0.996170i	$-0.527867\pi$
$281$	−2.93138			−0.174871			−0.0874357	+	0.996170i	$0.527867\pi$
$282$		0			0
$283$	12.3064	+	12.3064i	0.731542	+	0.731542i	0.970925	−	0.239383i	$-0.0769452\pi$
$283$	12.3064	+	12.3064i	0.731542	+	0.731542i	−0.239383	+	0.970925i	$0.576945\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	33.0411i		−	1.95036i
$288$		0			0
$289$	−4.10170			−0.241276
$290$		0			0
$291$		0			0
$292$		0			0
$293$	15.2191	+	15.2191i	0.889109	+	0.889109i	0.994437	−	0.105328i	$-0.0335894\pi$
$293$	15.2191	+	15.2191i	0.889109	+	0.889109i	−0.105328	+	0.994437i	$0.533589\pi$
$294$		0			0
$295$	−9.40886	+	0.431832i	−0.547805	+	0.0251422i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	13.7777	+	13.7777i	0.796786	+	0.796786i
$300$		0			0
$301$	23.4031	−	23.4031i	1.34893	−	1.34893i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.0227655	−	0.496019i	−0.00130355	−	0.0284020i
$306$		0			0
$307$	−3.79402	+	3.79402i	−0.216536	+	0.216536i	−0.807037	−	0.590501i	$-0.798930\pi$
$307$	−3.79402	+	3.79402i	−0.216536	+	0.216536i	0.590501	+	0.807037i	$0.298930\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			18.1916i			1.03155i	0.856724	+	0.515775i	$0.172496\pi$
$311$			18.1916i			1.03155i	−0.856724	+	0.515775i	$0.827504\pi$
$312$		0			0
$313$	16.7785			0.948377			0.474188	−	0.880423i	$-0.342742\pi$
$313$	16.7785			0.948377			0.474188	+	0.880423i	$0.342742\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.103425	+	0.103425i	−0.00580894	+	0.00580894i	−0.710005	−	0.704196i	$-0.751307\pi$
$317$	−0.103425	+	0.103425i	−0.00580894	+	0.00580894i	0.704196	+	0.710005i	$0.251307\pi$
$318$		0			0
$319$			15.7738i			0.883163i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.42934	+	3.42934i	0.190814	+	0.190814i
$324$		0			0
$325$	−9.53611	+	11.4682i	−0.528968	+	0.636143i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.9936			0.771490
$330$		0			0
$331$	−2.18428	+	2.18428i	−0.120059	+	0.120059i	−0.764583	−	0.644525i	$-0.777055\pi$
$331$	−2.18428	+	2.18428i	−0.120059	+	0.120059i	0.644525	+	0.764583i	$0.277055\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.0442773	+	0.964725i	0.00241913	+	0.0527085i
$336$		0			0
$337$		−	20.9206i		−	1.13962i	−0.821778	−	0.569808i	$-0.807018\pi$
$337$		−	20.9206i		−	1.13962i	0.821778	−	0.569808i	$-0.192982\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−32.6100	+	32.6100i	−1.76593	+	1.76593i
$342$		0			0
$343$			19.6193i			1.05934i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.34853	+	4.34853i	−0.233441	+	0.233441i	−0.814127	−	0.580686i	$-0.802784\pi$
$347$	−4.34853	+	4.34853i	−0.233441	+	0.233441i	0.580686	+	0.814127i	$0.302784\pi$
$348$		0			0
$349$	3.70979	−	3.70979i	0.198580	−	0.198580i	−0.600811	−	0.799391i	$-0.705155\pi$
$349$	3.70979	−	3.70979i	0.198580	−	0.198580i	0.799391	+	0.600811i	$0.205155\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.3398			0.869681			0.434840	−	0.900508i	$-0.356805\pi$
$353$	16.3398			0.869681			0.434840	+	0.900508i	$0.356805\pi$
$354$		0			0
$355$	2.67301	+	2.43842i	0.141869	+	0.129418i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	24.6929i		−	1.30324i	−0.758545	−	0.651621i	$-0.774089\pi$
$359$		−	24.6929i		−	1.30324i	0.758545	−	0.651621i	$-0.225911\pi$
$360$		0			0
$361$		−	17.1764i		−	0.904024i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.4087	−	11.4101i	0.544815	−	0.597231i
$366$		0			0
$367$	−6.68177			−0.348786			−0.174393	−	0.984676i	$-0.555796\pi$
$367$	−6.68177			−0.348786			−0.174393	+	0.984676i	$0.555796\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−26.2036	+	26.2036i	−1.36042	+	1.36042i
$372$		0			0
$373$	18.9638	−	18.9638i	0.981911	−	0.981911i	−0.0179284	−	0.999839i	$-0.505707\pi$
$373$	18.9638	−	18.9638i	0.981911	−	0.981911i	0.999839	+	0.0179284i	$0.00570709\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	7.79837i		−	0.401636i
$378$		0			0
$379$	17.4207	−	17.4207i	0.894843	−	0.894843i	−0.100131	−	0.994974i	$-0.531926\pi$
$379$	17.4207	−	17.4207i	0.894843	−	0.894843i	0.994974	+	0.100131i	$0.0319263\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		−	10.4542i		−	0.534182i	−0.963671	−	0.267091i	$-0.913938\pi$
$383$		−	10.4542i		−	0.534182i	0.963671	−	0.267091i	$-0.0860625\pi$
$384$		0			0
$385$	2.66452	+	58.0551i	0.135796	+	2.95876i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.71454	+	6.71454i	−0.340441	+	0.340441i	−0.856533	−	0.516092i	$-0.827386\pi$
$389$	−6.71454	+	6.71454i	−0.340441	+	0.340441i	0.516092	+	0.856533i	$0.327386\pi$
$390$		0			0
$391$	23.4587			1.18636
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.90917	+	8.12726i	0.448269	+	0.408927i
$396$		0			0
$397$	25.8345	+	25.8345i	1.29660	+	1.29660i	0.930628	+	0.365968i	$0.119262\pi$
$397$	25.8345	+	25.8345i	1.29660	+	1.29660i	0.365968	+	0.930628i	$0.380738\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	18.5375i		−	0.925717i	−0.886432	−	0.462858i	$-0.846824\pi$
$401$		−	18.5375i		−	0.925717i	0.886432	−	0.462858i	$-0.153176\pi$
$402$		0			0
$403$	16.1220	−	16.1220i	0.803094	−	0.803094i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16.2950			−0.807715
$408$		0			0
$409$		−	6.45252i		−	0.319057i	−0.987193	−	0.159528i	$-0.949003\pi$
$409$		−	6.45252i		−	0.319057i	0.987193	−	0.159528i	$-0.0509973\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	12.8298	−	12.8298i	0.631315	−	0.631315i
$414$		0			0
$415$	−18.3917	+	0.844113i	−0.902815	+	0.0414359i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.0000	−	12.0000i	0.586236	−	0.586236i	−0.350374	−	0.936610i	$-0.613945\pi$
$419$	12.0000	−	12.0000i	0.586236	−	0.586236i	0.936610	+	0.350374i	$0.113945\pi$
$420$		0			0
$421$	23.9012	+	23.9012i	1.16487	+	1.16487i	0.983395	+	0.181478i	$0.0580882\pi$
$421$	23.9012	+	23.9012i	1.16487	+	1.16487i	0.181478	+	0.983395i	$0.441912\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.64487	+	17.8816i	0.0797877	+	0.867386i
$426$		0			0
$427$	0.676366	+	0.676366i	0.0327317	+	0.0327317i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.5590			−0.604944			−0.302472	−	0.953158i	$-0.597812\pi$
$431$	−12.5590			−0.604944			−0.302472	+	0.953158i	$0.597812\pi$
$432$		0			0
$433$		−	4.64837i		−	0.223386i	−0.993743	−	0.111693i	$-0.964373\pi$
$433$		−	4.64837i		−	0.223386i	0.993743	−	0.111693i	$-0.0356274\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.23710	+	6.23710i	0.298361	+	0.298361i
$438$		0			0
$439$	−7.09686			−0.338715			−0.169357	−	0.985555i	$-0.554169\pi$
$439$	−7.09686			−0.338715			−0.169357	+	0.985555i	$0.554169\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.7044	−	16.7044i	0.793649	−	0.793649i	−0.188436	−	0.982085i	$-0.560342\pi$
$443$	16.7044	−	16.7044i	0.793649	−	0.793649i	0.982085	+	0.188436i	$0.0603419\pi$
$444$		0			0
$445$	11.6773	−	12.8007i	0.553556	−	0.606813i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	22.3540i		−	1.05495i	−0.849571	−	0.527475i	$-0.823139\pi$
$449$		−	22.3540i		−	1.05495i	0.849571	−	0.527475i	$-0.176861\pi$
$450$		0			0
$451$	32.7265	+	32.7265i	1.54103	+	1.54103i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.31731	−	28.7018i	−0.0617562	−	1.34556i
$456$		0			0
$457$	−28.9883			−1.35602			−0.678008	−	0.735055i	$-0.737156\pi$
$457$	−28.9883			−1.35602			−0.678008	+	0.735055i	$0.737156\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.75610	−	3.75610i	−0.174939	−	0.174939i	0.614206	−	0.789146i	$-0.289476\pi$
$461$	−3.75610	−	3.75610i	−0.174939	−	0.174939i	−0.789146	+	0.614206i	$0.789476\pi$
$462$		0			0
$463$	18.4896			0.859286			0.429643	−	0.902999i	$-0.358639\pi$
$463$	18.4896			0.859286			0.429643	+	0.902999i	$0.358639\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.8623	+	17.8623i	0.826570	+	0.826570i	0.987041	−	0.160471i	$-0.0513012\pi$
$467$	17.8623	+	17.8623i	0.826570	+	0.826570i	−0.160471	+	0.987041i	$0.551301\pi$
$468$		0			0
$469$	−1.31549	−	1.31549i	−0.0607436	−	0.0607436i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			46.3604i			2.13165i
$474$		0			0
$475$	−4.31695	+	5.19161i	−0.198075	+	0.238207i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−21.2617			−0.971474			−0.485737	−	0.874105i	$-0.661449\pi$
$479$	−21.2617			−0.971474			−0.485737	+	0.874105i	$0.661449\pi$
$480$		0			0
$481$	8.05606			0.367325
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.4317	−	14.0773i	−0.700718	−	0.639219i
$486$		0			0
$487$			38.2041i			1.73119i	0.500744	+	0.865595i	$0.333060\pi$
$487$			38.2041i			1.73119i	−0.500744	+	0.865595i	$0.666940\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.2555	+	11.2555i	0.507953	+	0.507953i	0.913898	−	0.405945i	$-0.133057\pi$
$491$	11.2555	+	11.2555i	0.507953	+	0.507953i	−0.405945	+	0.913898i	$0.633057\pi$
$492$		0			0
$493$	−6.63898	−	6.63898i	−0.299005	−	0.299005i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.96989			−0.312642
$498$		0			0
$499$	−19.2924	−	19.2924i	−0.863646	−	0.863646i	0.128114	−	0.991759i	$-0.459108\pi$
$499$	−19.2924	−	19.2924i	−0.863646	−	0.863646i	−0.991759	+	0.128114i	$0.959108\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.8587			1.24216			0.621078	−	0.783748i	$-0.286695\pi$
$503$	27.8587			1.24216			0.621078	+	0.783748i	$0.286695\pi$
$504$		0			0
$505$	−1.14708	−	24.9929i	−0.0510445	−	1.11217i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.475925	+	0.475925i	0.0210950	+	0.0210950i	0.717576	−	0.696481i	$-0.245252\pi$
$509$	0.475925	+	0.475925i	0.0210950	+	0.0210950i	−0.696481	+	0.717576i	$0.745252\pi$
$510$		0			0
$511$			29.7518i			1.31614i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−26.7196	−	24.3745i	−1.17740	−	1.07407i
$516$		0			0
$517$	−13.8603	+	13.8603i	−0.609575	+	0.609575i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−28.2023			−1.23557			−0.617783	−	0.786348i	$-0.711969\pi$
$521$	−28.2023			−1.23557			−0.617783	+	0.786348i	$0.711969\pi$
$522$		0			0
$523$	−10.5066	−	10.5066i	−0.459420	−	0.459420i	0.439045	−	0.898465i	$-0.355317\pi$
$523$	−10.5066	−	10.5066i	−0.459420	−	0.459420i	−0.898465	+	0.439045i	$0.855317\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	27.4503i		−	1.19575i
$528$		0			0
$529$	19.6655			0.855022
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−16.1796	−	16.1796i	−0.700815	−	0.700815i
$534$		0			0
$535$	−0.763491	−	16.6351i	−0.0330086	−	0.719199i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−49.2979	−	49.2979i	−2.12341	−	2.12341i
$540$		0			0
$541$	−12.4368	+	12.4368i	−0.534698	+	0.534698i	−0.921967	−	0.387269i	$-0.873419\pi$
$541$	−12.4368	+	12.4368i	−0.534698	+	0.534698i	0.387269	+	0.921967i	$0.373419\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.73160	−	37.7285i	−0.0741736	−	1.61611i
$546$		0			0
$547$	−5.78283	+	5.78283i	−0.247256	+	0.247256i	−0.819844	−	0.572588i	$-0.805940\pi$
$547$	−5.78283	+	5.78283i	−0.247256	+	0.247256i	0.572588	+	0.819844i	$0.305940\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	3.53028i		−	0.150395i
$552$		0			0
$553$	−23.2307			−0.987870
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.9551	−	12.9551i	0.548924	−	0.548924i	−0.377205	−	0.926130i	$-0.623115\pi$
$557$	12.9551	−	12.9551i	0.548924	−	0.548924i	0.926130	+	0.377205i	$0.123115\pi$
$558$		0			0
$559$		−	22.9200i		−	0.969413i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.1388	+	14.1388i	0.595881	+	0.595881i	0.939214	−	0.343333i	$-0.111556\pi$
$563$	14.1388	+	14.1388i	0.595881	+	0.595881i	−0.343333	+	0.939214i	$0.611556\pi$
$564$		0			0
$565$	27.2592	−	29.8817i	1.14680	−	1.25713i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.34936			0.0565679			0.0282840	−	0.999600i	$-0.490996\pi$
$569$	1.34936			0.0565679			0.0282840	+	0.999600i	$0.490996\pi$
$570$		0			0
$571$	32.6417	−	32.6417i	1.36601	−	1.36601i	0.499967	−	0.866045i	$-0.333346\pi$
$571$	32.6417	−	32.6417i	1.36601	−	1.36601i	0.866045	−	0.499967i	$-0.166654\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.99159	+	32.5221i	0.124758	+	1.35627i
$576$		0			0
$577$		−	40.3389i		−	1.67933i	−0.543104	−	0.839665i	$-0.682751\pi$
$577$		−	40.3389i		−	1.67933i	0.543104	−	0.839665i	$-0.317249\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	25.0788	−	25.0788i	1.04044	−	1.04044i
$582$		0			0
$583$		−	51.9081i		−	2.14981i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.96452	+	9.96452i	−0.411280	+	0.411280i	−0.882184	−	0.470905i	$-0.843928\pi$
$587$	−9.96452	+	9.96452i	−0.411280	+	0.411280i	0.470905	+	0.882184i	$0.343928\pi$
$588$		0			0
$589$	7.29835	−	7.29835i	0.300723	−	0.300723i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19.4892			−0.800324			−0.400162	−	0.916444i	$-0.631046\pi$
$593$	−19.4892			−0.800324			−0.400162	+	0.916444i	$0.631046\pi$
$594$		0			0
$595$	−25.5561	−	23.3132i	−1.04770	−	0.955748i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	16.4963i		−	0.674020i	−0.941501	−	0.337010i	$-0.890584\pi$
$599$		−	16.4963i		−	0.674020i	0.941501	−	0.337010i	$-0.109416\pi$
$600$		0			0
$601$			8.09948i			0.330385i	0.986261	+	0.165192i	$0.0528245\pi$
$601$			8.09948i			0.330385i	−0.986261	+	0.165192i	$0.947176\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−41.9697	−	38.2863i	−1.70631	−	1.55656i
$606$		0			0
$607$	−0.975144			−0.0395799			−0.0197899	−	0.999804i	$-0.506300\pi$
$607$	−0.975144			−0.0395799			−0.0197899	+	0.999804i	$0.506300\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.85236	−	6.85236i	0.277217	−	0.277217i
$612$		0			0
$613$	7.41162	−	7.41162i	0.299353	−	0.299353i	−0.541408	−	0.840760i	$-0.682108\pi$
$613$	7.41162	−	7.41162i	0.299353	−	0.299353i	0.840760	+	0.541408i	$0.182108\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	15.5875i		−	0.627531i	−0.949501	−	0.313765i	$-0.898409\pi$
$617$		−	15.5875i		−	0.627531i	0.949501	−	0.313765i	$-0.101591\pi$
$618$		0			0
$619$	3.34655	−	3.34655i	0.134509	−	0.134509i	−0.636647	−	0.771156i	$-0.719679\pi$
$619$	3.34655	−	3.34655i	0.134509	−	0.134509i	0.771156	+	0.636647i	$0.219679\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			33.3780i			1.33726i
$624$		0			0
$625$	−24.5805	+	4.56073i	−0.983219	+	0.182429i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6.85837	−	6.85837i	0.273461	−	0.273461i
$630$		0			0
$631$	17.5464			0.698510			0.349255	−	0.937028i	$-0.386435\pi$
$631$	17.5464			0.698510			0.349255	+	0.937028i	$0.386435\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.9759	+	12.0318i	−0.435564	+	0.477468i
$636$		0			0
$637$	24.3723	+	24.3723i	0.965666	+	0.965666i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			30.7369i			1.21403i	0.794689	+	0.607016i	$0.207634\pi$
$641$			30.7369i			1.21403i	−0.794689	+	0.607016i	$0.792366\pi$
$642$		0			0
$643$	−2.00487	+	2.00487i	−0.0790643	+	0.0790643i	−0.745533	−	0.666469i	$-0.767805\pi$
$643$	−2.00487	+	2.00487i	−0.0790643	+	0.0790643i	0.666469	+	0.745533i	$0.267805\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−41.0262			−1.61291			−0.806453	−	0.591298i	$-0.798616\pi$
$647$	−41.0262			−1.61291			−0.806453	+	0.591298i	$0.798616\pi$
$648$		0			0
$649$			25.4153i			0.997637i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−10.2034	+	10.2034i	−0.399291	+	0.399291i	−0.877983	−	0.478692i	$-0.841111\pi$
$653$	−10.2034	+	10.2034i	−0.399291	+	0.399291i	0.478692	+	0.877983i	$0.341111\pi$
$654$		0			0
$655$	−1.43494	−	31.2647i	−0.0560676	−	1.22161i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.6544	−	14.6544i	0.570853	−	0.570853i	−0.361514	−	0.932367i	$-0.617740\pi$
$659$	14.6544	−	14.6544i	0.570853	−	0.570853i	0.932367	+	0.361514i	$0.117740\pi$
$660$		0			0
$661$	31.9191	+	31.9191i	1.24151	+	1.24151i	0.959376	+	0.282131i	$0.0910414\pi$
$661$	31.9191	+	31.9191i	1.24151	+	1.24151i	0.282131	+	0.959376i	$0.408959\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.596337	−	12.9931i	−0.0231250	−	0.503852i
$666$		0			0
$667$	−12.0746	−	12.0746i	−0.467531	−	0.467531i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.33985			−0.0517243
$672$		0			0
$673$			3.74068i			0.144193i	0.997398	+	0.0720963i	$0.0229689\pi$
$673$			3.74068i			0.144193i	−0.997398	+	0.0720963i	$0.977031\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.8520	−	14.8520i	−0.570808	−	0.570808i	0.361546	−	0.932354i	$-0.382249\pi$
$677$	−14.8520	−	14.8520i	−0.570808	−	0.570808i	−0.932354	+	0.361546i	$0.882249\pi$
$678$		0			0
$679$	40.2382			1.54420
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.704118	+	0.704118i	−0.0269423	+	0.0269423i	−0.720450	−	0.693507i	$-0.756065\pi$
$683$	−0.704118	+	0.704118i	−0.0269423	+	0.0269423i	0.693507	+	0.720450i	$0.256065\pi$
$684$		0			0
$685$	−29.4008	−	26.8205i	−1.12335	−	1.02476i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			25.6627i			0.977672i
$690$		0			0
$691$	27.9600	+	27.9600i	1.06365	+	1.06365i	0.997832	+	0.0658160i	$0.0209650\pi$
$691$	27.9600	+	27.9600i	1.06365	+	1.06365i	0.0658160	+	0.997832i	$0.479035\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.722410	−	15.7400i	−0.0274026	−	0.597054i
$696$		0			0
$697$	−27.5483			−1.04347
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.89364	+	3.89364i	0.147061	+	0.147061i	0.776804	−	0.629743i	$-0.216840\pi$
$701$	3.89364	+	3.89364i	0.147061	+	0.147061i	−0.629743	+	0.776804i	$0.716840\pi$
$702$		0			0
$703$	3.64694			0.137547
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.0801	+	34.0801i	1.28171	+	1.28171i
$708$		0			0
$709$	−24.4875	−	24.4875i	−0.919648	−	0.919648i	0.0773555	−	0.997004i	$-0.475352\pi$
$709$	−24.4875	−	24.4875i	−0.919648	−	0.919648i	−0.997004	+	0.0773555i	$0.975352\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	49.9251i		−	1.86971i
$714$		0			0
$715$	29.7332	+	27.1236i	1.11196	+	1.01437i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−16.1711			−0.603079			−0.301540	−	0.953454i	$-0.597501\pi$
$719$	−16.1711			−0.603079			−0.301540	+	0.953454i	$0.597501\pi$
$720$		0			0
$721$	69.6714			2.59470
$722$		0			0
$723$		0			0
$724$		0			0
$725$	8.35734	−	10.0506i	0.310384	−	0.373271i
$726$		0			0
$727$		−	37.5868i		−	1.39402i	−0.717063	−	0.697008i	$-0.754514\pi$
$727$		−	37.5868i		−	1.39402i	0.717063	−	0.697008i	$-0.245486\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−19.5125	−	19.5125i	−0.721695	−	0.721695i
$732$		0			0
$733$	−10.5565	−	10.5565i	−0.389913	−	0.389913i	0.484744	−	0.874656i	$-0.338913\pi$
$733$	−10.5565	−	10.5565i	−0.389913	−	0.389913i	−0.874656	+	0.484744i	$0.838913\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.60592			0.0959903
$738$		0			0
$739$	5.50334	+	5.50334i	0.202444	+	0.202444i	0.801046	−	0.598603i	$-0.204277\pi$
$739$	5.50334	+	5.50334i	0.202444	+	0.202444i	−0.598603	+	0.801046i	$0.704277\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.53668			−0.203121			−0.101561	−	0.994829i	$-0.532384\pi$
$743$	−5.53668			−0.203121			−0.101561	+	0.994829i	$0.532384\pi$
$744$		0			0
$745$	1.41822	+	30.9005i	0.0519595	+	1.13211i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	22.6835	+	22.6835i	0.828837	+	0.828837i
$750$		0			0
$751$		−	30.2295i		−	1.10309i	−0.834145	−	0.551546i	$-0.814038\pi$
$751$		−	30.2295i		−	1.10309i	0.834145	−	0.551546i	$-0.185962\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−18.1000	+	19.8414i	−0.658728	+	0.722103i
$756$		0			0
$757$	−25.8317	+	25.8317i	−0.938870	+	0.938870i	−0.998236	−	0.0593667i	$-0.981092\pi$
$757$	−25.8317	+	25.8317i	−0.938870	+	0.938870i	0.0593667	+	0.998236i	$0.481092\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.93351			0.251340			0.125670	−	0.992072i	$-0.459892\pi$
$761$	6.93351			0.251340			0.125670	+	0.992072i	$0.459892\pi$
$762$		0			0
$763$	51.4462	+	51.4462i	1.86248	+	1.86248i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	12.5650i		−	0.453696i
$768$		0			0
$769$	18.4481			0.665257			0.332629	−	0.943058i	$-0.392064\pi$
$769$	18.4481			0.665257			0.332629	+	0.943058i	$0.392064\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.74138	+	8.74138i	0.314405	+	0.314405i	0.846614	−	0.532208i	$-0.178638\pi$
$773$	8.74138	+	8.74138i	0.314405	+	0.314405i	−0.532208	+	0.846614i	$0.678638\pi$
$774$		0			0
$775$	38.0558	−	3.50062i	1.36700	−	0.125746i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.32440	−	7.32440i	−0.262424	−	0.262424i
$780$		0			0
$781$	6.90351	−	6.90351i	0.247027	−	0.247027i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	27.8451	−	1.27799i	0.993836	−	0.0456134i
$786$		0			0
$787$	−16.3355	+	16.3355i	−0.582299	+	0.582299i	−0.935534	−	0.353235i	$-0.885081\pi$
$787$	−16.3355	+	16.3355i	−0.582299	+	0.582299i	0.353235	+	0.935534i	$0.385081\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			77.9168i			2.77040i
$792$		0			0
$793$	0.662406			0.0235227
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.3444	+	11.3444i	−0.401841	+	0.401841i	−0.878881	−	0.477040i	$-0.841710\pi$
$797$	−11.3444	+	11.3444i	−0.401841	+	0.401841i	0.477040	+	0.878881i	$0.341710\pi$
$798$		0			0
$799$		−	11.6672i		−	0.412757i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−29.4685	−	29.4685i	−1.03992	−	1.03992i
$804$		0			0
$805$	−46.4801	−	42.4008i	−1.63821	−	1.49443i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.8157			−0.520893			−0.260446	−	0.965488i	$-0.583870\pi$
$809$	−14.8157			−0.520893			−0.260446	+	0.965488i	$0.583870\pi$
$810$		0			0
$811$	9.73571	−	9.73571i	0.341867	−	0.341867i	−0.515202	−	0.857069i	$-0.672283\pi$
$811$	9.73571	−	9.73571i	0.341867	−	0.341867i	0.857069	+	0.515202i	$0.172283\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.29036	+	28.1147i	0.0451994	+	0.984815i
$816$		0			0
$817$		−	10.3758i		−	0.363002i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.499371	+	0.499371i	−0.0174282	+	0.0174282i	−0.715767	−	0.698339i	$-0.753923\pi$
$821$	−0.499371	+	0.499371i	−0.0174282	+	0.0174282i	0.698339	+	0.715767i	$0.253923\pi$
$822$		0			0
$823$			33.6494i			1.17295i	0.809969	+	0.586473i	$0.199484\pi$
$823$			33.6494i			1.17295i	−0.809969	+	0.586473i	$0.800516\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−11.7750	+	11.7750i	−0.409456	+	0.409456i	−0.881549	−	0.472093i	$-0.843499\pi$
$827$	−11.7750	+	11.7750i	−0.409456	+	0.409456i	0.472093	+	0.881549i	$0.343499\pi$
$828$		0			0
$829$	35.3882	−	35.3882i	1.22908	−	1.22908i	0.264772	−	0.964311i	$-0.414703\pi$
$829$	35.3882	−	35.3882i	1.22908	−	1.22908i	0.964311	−	0.264772i	$-0.0852968\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	41.4977			1.43781
$834$		0			0
$835$	6.39422	−	7.00940i	0.221281	−	0.242570i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	20.9084i		−	0.721838i	−0.932597	−	0.360919i	$-0.882463\pi$
$839$		−	20.9084i		−	0.721838i	0.932597	−	0.360919i	$-0.117537\pi$
$840$		0			0
$841$		−	22.1656i		−	0.764331i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.77587	+	6.18119i	0.233097	+	0.212639i
$846$		0			0
$847$	109.436			3.76027
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.4736	−	12.4736i	0.427590	−	0.427590i
$852$		0			0
$853$	−33.7697	+	33.7697i	−1.15625	+	1.15625i	−0.170976	+	0.985275i	$0.554692\pi$
$853$	−33.7697	+	33.7697i	−1.15625	+	1.15625i	−0.985275	+	0.170976i	$0.945308\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	44.3305i		−	1.51430i	−0.653241	−	0.757150i	$-0.726591\pi$
$857$		−	44.3305i		−	1.51430i	0.653241	−	0.757150i	$-0.273409\pi$
$858$		0			0
$859$	−31.2008	+	31.2008i	−1.06456	+	1.06456i	−0.0667892	+	0.997767i	$0.521276\pi$
$859$	−31.2008	+	31.2008i	−1.06456	+	1.06456i	−0.997767	+	0.0667892i	$0.978724\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			47.7067i			1.62396i	0.583689	+	0.811978i	$0.301609\pi$
$863$			47.7067i			1.62396i	−0.583689	+	0.811978i	$0.698391\pi$
$864$		0			0
$865$	−0.584527	−	12.7358i	−0.0198745	−	0.433030i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	23.0095	−	23.0095i	0.780542	−	0.780542i
$870$		0			0
$871$	−1.28834			−0.0436536
$872$		0			0
$873$		0			0
$874$		0			0
$875$	29.0613	−	38.4028i	0.982450	−	1.29825i
$876$		0			0
$877$	11.6792	+	11.6792i	0.394379	+	0.394379i	0.876245	−	0.481866i	$-0.160041\pi$
$877$	11.6792	+	11.6792i	0.394379	+	0.394379i	−0.481866	+	0.876245i	$0.660041\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			26.5637i			0.894953i	0.894296	+	0.447477i	$0.147677\pi$
$881$			26.5637i			0.894953i	−0.894296	+	0.447477i	$0.852323\pi$
$882$		0			0
$883$	−23.1556	+	23.1556i	−0.779249	+	0.779249i	−0.979703	−	0.200454i	$-0.935758\pi$
$883$	−23.1556	+	23.1556i	−0.779249	+	0.779249i	0.200454	+	0.979703i	$0.435758\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	44.2415			1.48549			0.742743	−	0.669577i	$-0.233525\pi$
$887$	44.2415			1.48549			0.742743	+	0.669577i	$0.233525\pi$
$888$		0			0
$889$		−	31.3730i		−	1.05222i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.10203	−	3.10203i	0.103805	−	0.103805i
$894$		0			0
$895$	−0.120900	−	2.63419i	−0.00404123	−	0.0880512i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−14.1291	+	14.1291i	−0.471233	+	0.471233i
$900$		0			0
$901$	21.8474	+	21.8474i	0.727844	+	0.727844i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	33.4683	−	1.53607i	1.11252	−	0.0510607i
$906$		0			0
$907$	−36.0867	−	36.0867i	−1.19824	−	1.19824i	−0.974694	−	0.223545i	$-0.928237\pi$
$907$	−36.0867	−	36.0867i	−1.19824	−	1.19824i	−0.223545	−	0.974694i	$-0.571763\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.93520			0.163510			0.0817552	−	0.996652i	$-0.473947\pi$
$911$	4.93520			0.163510			0.0817552	+	0.996652i	$0.473947\pi$
$912$		0			0
$913$			49.6799i			1.64416i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	42.6323	+	42.6323i	1.40784	+	1.40784i
$918$		0			0
$919$	−28.2846			−0.933023			−0.466511	−	0.884515i	$-0.654489\pi$
$919$	−28.2846			−0.933023			−0.466511	+	0.884515i	$0.654489\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.41301	+	3.41301i	−0.112341	+	0.112341i
$924$		0			0
$925$	10.3827	+	8.63350i	0.341382	+	0.283868i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		−	27.7896i		−	0.911746i	−0.890045	−	0.455873i	$-0.849327\pi$
$929$		−	27.7896i		−	0.911746i	0.890045	−	0.455873i	$-0.150673\pi$
$930$		0			0
$931$	11.0332	+	11.0332i	0.361599	+	0.361599i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	48.4039	−	2.22156i	1.58298	−	0.0726528i
$936$		0			0
$937$	39.5362			1.29159			0.645796	−	0.763510i	$-0.276526\pi$
$937$	39.5362			1.29159			0.645796	+	0.763510i	$0.276526\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	12.9497	+	12.9497i	0.422149	+	0.422149i	0.885943	−	0.463794i	$-0.153512\pi$
$941$	12.9497	+	12.9497i	0.422149	+	0.422149i	−0.463794	+	0.885943i	$0.653512\pi$
$942$		0			0
$943$	−50.1033			−1.63159
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.0330	−	21.0330i	−0.683481	−	0.683481i	0.277302	−	0.960783i	$-0.410560\pi$
$947$	−21.0330	−	21.0330i	−0.683481	−	0.683481i	−0.960783	+	0.277302i	$0.910560\pi$
$948$		0			0
$949$	14.5689	+	14.5689i	0.472925	+	0.472925i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	25.8627i		−	0.837774i	−0.908038	−	0.418887i	$-0.862420\pi$
$953$		−	25.8627i		−	0.837774i	0.908038	−	0.418887i	$-0.137580\pi$
$954$		0			0
$955$	5.77413	−	6.32965i	0.186847	−	0.204823i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	76.6628			2.47557
$960$		0			0
$961$	−27.4199			−0.884512
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.31389	−	7.58423i	−0.267634	−	0.244145i
$966$		0			0
$967$		−	29.5467i		−	0.950157i	−0.879943	−	0.475079i	$-0.842420\pi$
$967$		−	29.5467i		−	0.950157i	0.879943	−	0.475079i	$-0.157580\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.28841	+	4.28841i	0.137621	+	0.137621i	0.772561	−	0.634940i	$-0.218975\pi$
$971$	4.28841	+	4.28841i	0.137621	+	0.137621i	−0.634940	+	0.772561i	$0.718975\pi$
$972$		0			0
$973$	21.4630	+	21.4630i	0.688071	+	0.688071i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.9714			0.478976			0.239488	−	0.970899i	$-0.423020\pi$
$977$	14.9714			0.478976			0.239488	+	0.970899i	$0.423020\pi$
$978$		0			0
$979$	−33.0601	−	33.0601i	−1.05660	−	1.05660i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−9.58755			−0.305795			−0.152898	−	0.988242i	$-0.548861\pi$
$983$	−9.58755			−0.305795			−0.152898	+	0.988242i	$0.548861\pi$
$984$		0			0
$985$	−22.1682	+	1.01744i	−0.706338	+	0.0324183i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−35.4883	−	35.4883i	−1.12846	−	1.12846i
$990$		0			0
$991$			43.4685i			1.38082i	0.723417	+	0.690412i	$0.242571\pi$
$991$			43.4685i			1.38082i	−0.723417	+	0.690412i	$0.757429\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	20.7273	−	22.7215i	0.657101	−	0.720320i
$996$		0			0
$997$	−1.90040	+	1.90040i	−0.0601862	+	0.0601862i	−0.736559	−	0.676373i	$-0.763551\pi$
$997$	−1.90040	+	1.90040i	−0.0601862	+	0.0601862i	0.676373	+	0.736559i	$0.263551\pi$
$998$		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.719.13		96
3.2	odd	2	inner	2880.2.u.a.719.36		96
4.3	odd	2		720.2.u.a.539.5	yes	96
5.4	even	2	inner	2880.2.u.a.719.12		96
12.11	even	2		720.2.u.a.539.44	yes	96
15.14	odd	2	inner	2880.2.u.a.719.37		96
16.3	odd	4	inner	2880.2.u.a.2159.37		96
16.13	even	4		720.2.u.a.179.6	yes	96
20.19	odd	2		720.2.u.a.539.43	yes	96
48.29	odd	4		720.2.u.a.179.43	yes	96
48.35	even	4	inner	2880.2.u.a.2159.12		96
60.59	even	2		720.2.u.a.539.6	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.36		96
80.29	even	4		720.2.u.a.179.44	yes	96
240.29	odd	4		720.2.u.a.179.5	✓	96
240.179	even	4	inner	2880.2.u.a.2159.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.5	✓	96	240.29	odd	4
720.2.u.a.179.6	yes	96	16.13	even	4
720.2.u.a.179.43	yes	96	48.29	odd	4
720.2.u.a.179.44	yes	96	80.29	even	4
720.2.u.a.539.5	yes	96	4.3	odd	2
720.2.u.a.539.6	yes	96	60.59	even	2
720.2.u.a.539.43	yes	96	20.19	odd	2
720.2.u.a.539.44	yes	96	12.11	even	2
2880.2.u.a.719.12		96	5.4	even	2	inner
2880.2.u.a.719.13		96	1.1	even	1	trivial
2880.2.u.a.719.36		96	3.2	odd	2	inner
2880.2.u.a.719.37		96	15.14	odd	2	inner
2880.2.u.a.2159.12		96	48.35	even	4	inner
2880.2.u.a.2159.13		96	240.179	even	4	inner
2880.2.u.a.2159.36		96	80.19	odd	4	inner
2880.2.u.a.2159.37		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)

\(f(q)\)	\(=\)	\(q+(-1.50698 + 1.65197i) q^{5} -4.30751i q^{7} +O(q^{10})\)	\(q+(-1.50698 + 1.65197i) q^{5} -4.30751i q^{7} +(4.26649 + 4.26649i) q^{11} +(-2.10930 - 2.10930i) q^{13} -3.59142 q^{17} +(-0.954870 - 0.954870i) q^{19} -6.53188 q^{23} +(-0.457999 - 4.97898i) q^{25} +(1.84857 + 1.84857i) q^{29} +7.64329i q^{31} +(7.11588 + 6.49135i) q^{35} +(-1.90965 + 1.90965i) q^{37} +7.67058 q^{41} +(5.43308 + 5.43308i) q^{43} +3.24864i q^{47} -11.5547 q^{49} +(-6.08323 - 6.08323i) q^{53} +(-13.4776 + 0.618574i) q^{55} +(2.97848 + 2.97848i) q^{59} +(-0.157020 + 0.157020i) q^{61} +(6.66318 - 0.305816i) q^{65} +(0.305394 - 0.305394i) q^{67} -1.61808i q^{71} -6.90696 q^{73} +(18.3780 - 18.3780i) q^{77} -5.39306i q^{79} +(5.82210 + 5.82210i) q^{83} +(5.41221 - 5.93291i) q^{85} -7.74878 q^{89} +(-9.08585 + 9.08585i) q^{91} +(3.01639 - 0.138441i) q^{95} +9.34141i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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