LMFDB - Embedded newform 2880.2.u.a.2159.28

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			2159.28
Character	$\chi$	$=$	2880.2159
Dual form			2880.2.u.a.719.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.419806 - 2.19631i) q^{5} +0.263783i q^{7} +(-0.913594 + 0.913594i) q^{11} +(-1.49018 + 1.49018i) q^{13} +2.90538 q^{17} +(0.296217 - 0.296217i) q^{19} +3.14640 q^{23} +(-4.64753 - 1.84404i) q^{25} +(2.43765 - 2.43765i) q^{29} -2.53546i q^{31} +(0.579348 + 0.110738i) q^{35} +(-1.53556 - 1.53556i) q^{37} +10.7792 q^{41} +(4.51269 - 4.51269i) q^{43} -6.67809i q^{47} +6.93042 q^{49} +(2.95356 - 2.95356i) q^{53} +(1.62300 + 2.39006i) q^{55} +(-9.76773 + 9.76773i) q^{59} +(-1.02388 - 1.02388i) q^{61} +(2.64730 + 3.89847i) q^{65} +(-3.67191 - 3.67191i) q^{67} -7.85546i q^{71} -12.4323 q^{73} +(-0.240990 - 0.240990i) q^{77} -10.7196i q^{79} +(3.50410 - 3.50410i) q^{83} +(1.21970 - 6.38111i) q^{85} +13.2383 q^{89} +(-0.393083 - 0.393083i) q^{91} +(-0.526229 - 0.774936i) q^{95} -11.1057i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$5$	0.419806	−	2.19631i	0.187743	−	0.982218i
$5$	0.419806	−	2.19631i	0.187743	−	0.982218i
$6$		0			0
$7$			0.263783i			0.0997006i	0.998757	+	0.0498503i	$0.0158744\pi$
$7$			0.263783i			0.0997006i	−0.998757	+	0.0498503i	$0.984126\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.913594	+	0.913594i	−0.275459	+	0.275459i	−0.831293	−	0.555834i	$-0.812399\pi$
$11$	−0.913594	+	0.913594i	−0.275459	+	0.275459i	0.555834	+	0.831293i	$0.312399\pi$
$12$		0			0
$13$	−1.49018	+	1.49018i	−0.413300	+	0.413300i	−0.882887	−	0.469586i	$-0.844403\pi$
$13$	−1.49018	+	1.49018i	−0.413300	+	0.413300i	0.469586	+	0.882887i	$0.344403\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.90538			0.704659			0.352329	−	0.935876i	$-0.385390\pi$
$17$	2.90538			0.704659			0.352329	+	0.935876i	$0.385390\pi$
$18$		0			0
$19$	0.296217	−	0.296217i	0.0679568	−	0.0679568i	−0.672312	−	0.740268i	$-0.734698\pi$
$19$	0.296217	−	0.296217i	0.0679568	−	0.0679568i	0.740268	+	0.672312i	$0.234698\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.14640			0.656070			0.328035	−	0.944666i	$-0.393614\pi$
$23$	3.14640			0.656070			0.328035	+	0.944666i	$0.393614\pi$
$24$		0			0
$25$	−4.64753	−	1.84404i	−0.929505	−	0.368809i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.43765	−	2.43765i	0.452660	−	0.452660i	−0.443577	−	0.896236i	$-0.646291\pi$
$29$	2.43765	−	2.43765i	0.452660	−	0.452660i	0.896236	+	0.443577i	$0.146291\pi$
$30$		0			0
$31$		−	2.53546i		−	0.455382i	−0.973733	−	0.227691i	$-0.926882\pi$
$31$		−	2.53546i		−	0.455382i	0.973733	−	0.227691i	$-0.0731177\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.579348	+	0.110738i	0.0979277	+	0.0187181i
$36$		0			0
$37$	−1.53556	−	1.53556i	−0.252444	−	0.252444i	0.569528	−	0.821972i	$-0.307126\pi$
$37$	−1.53556	−	1.53556i	−0.252444	−	0.252444i	−0.821972	+	0.569528i	$0.807126\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	10.7792			1.68343			0.841713	−	0.539925i	$-0.181547\pi$
$41$	10.7792			1.68343			0.841713	+	0.539925i	$0.181547\pi$
$42$		0			0
$43$	4.51269	−	4.51269i	0.688178	−	0.688178i	−0.273651	−	0.961829i	$-0.588231\pi$
$43$	4.51269	−	4.51269i	0.688178	−	0.688178i	0.961829	+	0.273651i	$0.0882313\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	6.67809i		−	0.974100i	−0.873374	−	0.487050i	$-0.838073\pi$
$47$		−	6.67809i		−	0.974100i	0.873374	−	0.487050i	$-0.161927\pi$
$48$		0			0
$49$	6.93042			0.990060
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.95356	−	2.95356i	0.405703	−	0.405703i	−0.474534	−	0.880237i	$-0.657383\pi$
$53$	2.95356	−	2.95356i	0.405703	−	0.405703i	0.880237	+	0.474534i	$0.157383\pi$
$54$		0			0
$55$	1.62300	+	2.39006i	0.218845	+	0.322276i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.76773	+	9.76773i	−1.27165	+	1.27165i	−0.326428	+	0.945222i	$0.605845\pi$
$59$	−9.76773	+	9.76773i	−1.27165	+	1.27165i	−0.945222	+	0.326428i	$0.894155\pi$
$60$		0			0
$61$	−1.02388	−	1.02388i	−0.131095	−	0.131095i	0.638515	−	0.769610i	$-0.279549\pi$
$61$	−1.02388	−	1.02388i	−0.131095	−	0.131095i	−0.769610	+	0.638515i	$0.779549\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.64730	+	3.89847i	0.328357	+	0.483545i
$66$		0			0
$67$	−3.67191	−	3.67191i	−0.448595	−	0.448595i	0.446292	−	0.894887i	$-0.352744\pi$
$67$	−3.67191	−	3.67191i	−0.448595	−	0.448595i	−0.894887	+	0.446292i	$0.852744\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.85546i		−	0.932272i	−0.884713	−	0.466136i	$-0.845646\pi$
$71$		−	7.85546i		−	0.932272i	0.884713	−	0.466136i	$-0.154354\pi$
$72$		0			0
$73$	−12.4323			−1.45509			−0.727543	−	0.686062i	$-0.759338\pi$
$73$	−12.4323			−1.45509			−0.727543	+	0.686062i	$0.759338\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.240990	−	0.240990i	−0.0274634	−	0.0274634i
$78$		0			0
$79$		−	10.7196i		−	1.20605i	−0.797724	−	0.603023i	$-0.793963\pi$
$79$		−	10.7196i		−	1.20605i	0.797724	−	0.603023i	$-0.206037\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.50410	−	3.50410i	0.384625	−	0.384625i	−0.488140	−	0.872765i	$-0.662325\pi$
$83$	3.50410	−	3.50410i	0.384625	−	0.384625i	0.872765	+	0.488140i	$0.162325\pi$
$84$		0			0
$85$	1.21970	−	6.38111i	0.132295	−	0.692129i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	13.2383			1.40326			0.701629	−	0.712542i	$-0.252456\pi$
$89$	13.2383			1.40326			0.701629	+	0.712542i	$0.252456\pi$
$90$		0			0
$91$	−0.393083	−	0.393083i	−0.0412063	−	0.0412063i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.526229	−	0.774936i	−0.0539900	−	0.0795068i
$96$		0			0
$97$		−	11.1057i		−	1.12761i	−0.825908	−	0.563804i	$-0.809337\pi$
$97$		−	11.1057i		−	1.12761i	0.825908	−	0.563804i	$-0.190663\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.625096	+	0.625096i	0.0621994	+	0.0621994i	0.737522	−	0.675323i	$-0.235996\pi$
$101$	0.625096	+	0.625096i	0.0621994	+	0.0621994i	−0.675323	+	0.737522i	$0.735996\pi$
$102$		0			0
$103$		−	7.47669i		−	0.736701i	−0.929687	−	0.368350i	$-0.879923\pi$
$103$		−	7.47669i		−	0.736701i	0.929687	−	0.368350i	$-0.120077\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.7929	−	10.7929i	−1.04339	−	1.04339i	−0.999015	−	0.0443705i	$-0.985872\pi$
$107$	−10.7929	−	10.7929i	−1.04339	−	1.04339i	−0.0443705	−	0.999015i	$-0.514128\pi$
$108$		0			0
$109$	−0.260948	−	0.260948i	−0.0249942	−	0.0249942i	0.694499	−	0.719493i	$-0.255626\pi$
$109$	−0.260948	−	0.260948i	−0.0249942	−	0.0249942i	−0.719493	+	0.694499i	$0.755626\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.88893			−0.365839			−0.182920	−	0.983128i	$-0.558555\pi$
$113$	−3.88893			−0.365839			−0.182920	+	0.983128i	$0.558555\pi$
$114$		0			0
$115$	1.32088	−	6.91046i	0.123173	−	0.644404i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			0.766390i			0.0702549i
$120$		0			0
$121$			9.33069i			0.848245i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.00115	+	9.43325i	−0.536759	+	0.843736i
$126$		0			0
$127$	−18.1176			−1.60768			−0.803840	−	0.594846i	$-0.797213\pi$
$127$	−18.1176			−1.60768			−0.803840	+	0.594846i	$0.797213\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	14.0610	+	14.0610i	1.22851	+	1.22851i	0.964526	+	0.263988i	$0.0850378\pi$
$131$	14.0610	+	14.0610i	1.22851	+	1.22851i	0.263988	+	0.964526i	$0.414962\pi$
$132$		0			0
$133$	0.0781369	+	0.0781369i	0.00677533	+	0.00677533i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			10.3404i			0.883440i	0.897153	+	0.441720i	$0.145632\pi$
$137$			10.3404i			0.883440i	−0.897153	+	0.441720i	$0.854368\pi$
$138$		0			0
$139$	−11.8106	−	11.8106i	−1.00176	−	1.00176i	−0.999998	−	0.00176137i	$-0.999439\pi$
$139$	−11.8106	−	11.8106i	−1.00176	−	1.00176i	−0.00176137	−	0.999998i	$-0.500561\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	2.72283i		−	0.227695i
$144$		0			0
$145$	−4.33048	−	6.37716i	−0.359627	−	0.529594i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.72046	−	5.72046i	−0.468639	−	0.468639i	0.432835	−	0.901473i	$-0.357513\pi$
$149$	−5.72046	−	5.72046i	−0.468639	−	0.468639i	−0.901473	+	0.432835i	$0.857513\pi$
$150$		0			0
$151$	14.9974			1.22047			0.610234	−	0.792221i	$-0.291075\pi$
$151$	14.9974			1.22047			0.610234	+	0.792221i	$0.291075\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.56865	−	1.06440i	−0.447285	−	0.0854948i
$156$		0			0
$157$	0.0261720	−	0.0261720i	0.00208875	−	0.00208875i	−0.706062	−	0.708150i	$-0.749530\pi$
$157$	0.0261720	−	0.0261720i	0.00208875	−	0.00208875i	0.708150	+	0.706062i	$0.249530\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			0.829967i			0.0654106i
$162$		0			0
$163$	−17.1126	−	17.1126i	−1.34036	−	1.34036i	−0.895700	−	0.444659i	$-0.853325\pi$
$163$	−17.1126	−	17.1126i	−1.34036	−	1.34036i	−0.444659	−	0.895700i	$-0.646675\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	19.4611			1.50594			0.752971	−	0.658053i	$-0.228620\pi$
$167$	19.4611			1.50594			0.752971	+	0.658053i	$0.228620\pi$
$168$		0			0
$169$			8.55875i			0.658365i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−11.3427	−	11.3427i	−0.862367	−	0.862367i	0.129245	−	0.991613i	$-0.458744\pi$
$173$	−11.3427	−	11.3427i	−0.862367	−	0.862367i	−0.991613	+	0.129245i	$0.958744\pi$
$174$		0			0
$175$	0.486428	−	1.22594i	0.0367705	−	0.0926722i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.50621	+	4.50621i	0.336810	+	0.336810i	0.855165	−	0.518356i	$-0.173456\pi$
$179$	4.50621	+	4.50621i	0.336810	+	0.336810i	−0.518356	+	0.855165i	$0.673456\pi$
$180$		0			0
$181$	10.0971	−	10.0971i	0.750512	−	0.750512i	−0.224062	−	0.974575i	$-0.571932\pi$
$181$	10.0971	−	10.0971i	0.750512	−	0.750512i	0.974575	+	0.224062i	$0.0719320\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.01719	+	2.72792i	−0.295350	+	0.200561i
$186$		0			0
$187$	−2.65434	+	2.65434i	−0.194104	+	0.194104i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	23.8545			1.72605			0.863025	−	0.505161i	$-0.168567\pi$
$191$	23.8545			1.72605			0.863025	+	0.505161i	$0.168567\pi$
$192$		0			0
$193$			13.8585i			0.997560i	0.866729	+	0.498780i	$0.166218\pi$
$193$			13.8585i			0.997560i	−0.866729	+	0.498780i	$0.833782\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.9818	−	11.9818i	0.853664	−	0.853664i	−0.136918	−	0.990582i	$-0.543720\pi$
$197$	11.9818	−	11.9818i	0.853664	−	0.853664i	0.990582	+	0.136918i	$0.0437197\pi$
$198$		0			0
$199$	11.4336			0.810507			0.405253	−	0.914204i	$-0.367183\pi$
$199$	11.4336			0.810507			0.405253	+	0.914204i	$0.367183\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.643010	+	0.643010i	0.0451304	+	0.0451304i
$204$		0			0
$205$	4.52517	−	23.6744i	0.316051	−	1.65349i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			0.541243i			0.0374386i
$210$		0			0
$211$	−6.45820	+	6.45820i	−0.444601	+	0.444601i	−0.893555	−	0.448954i	$-0.851797\pi$
$211$	−6.45820	+	6.45820i	−0.444601	+	0.444601i	0.448954	+	0.893555i	$0.351797\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.01679	−	11.8057i	−0.546741	−	0.805142i
$216$		0			0
$217$	0.668811			0.0454019
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.32953	+	4.32953i	−0.291236	+	0.291236i
$222$		0			0
$223$	0.620487			0.0415509			0.0207754	−	0.999784i	$-0.493386\pi$
$223$	0.620487			0.0415509			0.0207754	+	0.999784i	$0.493386\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.0579	+	10.0579i	−0.667564	+	0.667564i	−0.957152	−	0.289588i	$-0.906482\pi$
$227$	−10.0579	+	10.0579i	−0.667564	+	0.667564i	0.289588	+	0.957152i	$0.406482\pi$
$228$		0			0
$229$	14.9831	−	14.9831i	0.990113	−	0.990113i	−0.00983872	−	0.999952i	$-0.503132\pi$
$229$	14.9831	−	14.9831i	0.990113	−	0.990113i	0.999952	+	0.00983872i	$0.00313181\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	2.07914i		−	0.136209i	−0.997678	−	0.0681046i	$-0.978305\pi$
$233$		−	2.07914i		−	0.136209i	0.997678	−	0.0681046i	$-0.0216952\pi$
$234$		0			0
$235$	−14.6671	−	2.80350i	−0.956779	−	0.182880i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.2816			−0.859113			−0.429557	−	0.903040i	$-0.641330\pi$
$239$	−13.2816			−0.859113			−0.429557	+	0.903040i	$0.641330\pi$
$240$		0			0
$241$	−3.84064			−0.247397			−0.123699	−	0.992320i	$-0.539476\pi$
$241$	−3.84064			−0.247397			−0.123699	+	0.992320i	$0.539476\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.90943	−	15.2213i	0.185877	−	0.972455i
$246$		0			0
$247$			0.882830i			0.0561731i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.6627	−	10.6627i	0.673022	−	0.673022i	−0.285389	−	0.958412i	$-0.592123\pi$
$251$	10.6627	−	10.6627i	0.673022	−	0.673022i	0.958412	+	0.285389i	$0.0921229\pi$
$252$		0			0
$253$	−2.87453	+	2.87453i	−0.180720	+	0.180720i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.6239			0.725081			0.362540	−	0.931968i	$-0.381910\pi$
$257$	11.6239			0.725081			0.362540	+	0.931968i	$0.381910\pi$
$258$		0			0
$259$	0.405054	−	0.405054i	0.0251688	−	0.0251688i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	29.3422			1.80932			0.904658	−	0.426138i	$-0.140126\pi$
$263$	29.3422			1.80932			0.904658	+	0.426138i	$0.140126\pi$
$264$		0			0
$265$	−5.24701	−	7.72685i	−0.322321	−	0.474657i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.91793	+	8.91793i	−0.543736	+	0.543736i	−0.924622	−	0.380886i	$-0.875619\pi$
$269$	−8.91793	+	8.91793i	−0.543736	+	0.543736i	0.380886	+	0.924622i	$0.375619\pi$
$270$		0			0
$271$			31.2790i			1.90007i	0.312150	+	0.950033i	$0.398951\pi$
$271$			31.2790i			1.90007i	−0.312150	+	0.950033i	$0.601049\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.93066	−	2.56124i	0.357632	−	0.154449i
$276$		0			0
$277$	−4.04579	−	4.04579i	−0.243088	−	0.243088i	0.575038	−	0.818126i	$-0.304987\pi$
$277$	−4.04579	−	4.04579i	−0.243088	−	0.243088i	−0.818126	+	0.575038i	$0.804987\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	19.2114			1.14606			0.573029	−	0.819535i	$-0.305768\pi$
$281$	19.2114			1.14606			0.573029	+	0.819535i	$0.305768\pi$
$282$		0			0
$283$	10.0809	−	10.0809i	0.599247	−	0.599247i	−0.340865	−	0.940112i	$-0.610720\pi$
$283$	10.0809	−	10.0809i	0.599247	−	0.599247i	0.940112	+	0.340865i	$0.110720\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			2.84337i			0.167839i
$288$		0			0
$289$	−8.55875			−0.503456
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.81368	−	4.81368i	0.281218	−	0.281218i	−0.552376	−	0.833595i	$-0.686279\pi$
$293$	4.81368	−	4.81368i	0.281218	−	0.281218i	0.833595	+	0.552376i	$0.186279\pi$
$294$		0			0
$295$	17.3524	+	25.5535i	1.01029	+	1.48778i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.68869	+	4.68869i	−0.271154	+	0.271154i
$300$		0			0
$301$	1.19037	+	1.19037i	0.0686118	+	0.0686118i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.67859	+	1.81893i	−0.153376	+	0.104152i
$306$		0			0
$307$	17.1791	+	17.1791i	0.980465	+	0.980465i	0.999813	−	0.0193480i	$-0.00615904\pi$
$307$	17.1791	+	17.1791i	0.980465	+	0.980465i	−0.0193480	+	0.999813i	$0.506159\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	16.6032i		−	0.941479i	−0.882272	−	0.470740i	$-0.843987\pi$
$311$		−	16.6032i		−	0.941479i	0.882272	−	0.470740i	$-0.156013\pi$
$312$		0			0
$313$	−10.8345			−0.612404			−0.306202	−	0.951967i	$-0.599058\pi$
$313$	−10.8345			−0.612404			−0.306202	+	0.951967i	$0.599058\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.3464	−	15.3464i	−0.861942	−	0.861942i	0.129621	−	0.991564i	$-0.458624\pi$
$317$	−15.3464	−	15.3464i	−0.861942	−	0.861942i	−0.991564	+	0.129621i	$0.958624\pi$
$318$		0			0
$319$			4.45404i			0.249378i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.860623	−	0.860623i	0.0478863	−	0.0478863i
$324$		0			0
$325$	9.67358	−	4.17768i	0.536594	−	0.231736i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.76157			0.0971183
$330$		0			0
$331$	6.23806	+	6.23806i	0.342875	+	0.342875i	0.857447	−	0.514572i	$-0.172049\pi$
$331$	6.23806	+	6.23806i	0.342875	+	0.342875i	−0.514572	+	0.857447i	$0.672049\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.60613	+	6.52315i	−0.524839	+	0.356398i
$336$		0			0
$337$		−	8.87003i		−	0.483181i	−0.970378	−	0.241591i	$-0.922331\pi$
$337$		−	8.87003i		−	0.483181i	0.970378	−	0.241591i	$-0.0776691\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.31638	+	2.31638i	0.125439	+	0.125439i
$342$		0			0
$343$			3.67461i			0.198410i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.3990	+	11.3990i	0.611932	+	0.611932i	0.943449	−	0.331517i	$-0.107560\pi$
$347$	11.3990	+	11.3990i	0.611932	+	0.611932i	−0.331517	+	0.943449i	$0.607560\pi$
$348$		0			0
$349$	−11.5358	−	11.5358i	−0.617496	−	0.617496i	0.327393	−	0.944888i	$-0.393830\pi$
$349$	−11.5358	−	11.5358i	−0.617496	−	0.617496i	−0.944888	+	0.327393i	$0.893830\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−20.5642			−1.09452			−0.547260	−	0.836963i	$-0.684329\pi$
$353$	−20.5642			−1.09452			−0.547260	+	0.836963i	$0.684329\pi$
$354$		0			0
$355$	−17.2530	−	3.29777i	−0.915695	−	0.175027i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	18.8141i		−	0.992972i	−0.868045	−	0.496486i	$-0.834623\pi$
$359$		−	18.8141i		−	0.992972i	0.868045	−	0.496486i	$-0.165377\pi$
$360$		0			0
$361$			18.8245i			0.990764i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.21914	+	27.3051i	−0.273182	+	1.42921i
$366$		0			0
$367$	12.1654			0.635031			0.317515	−	0.948253i	$-0.397151\pi$
$367$	12.1654			0.635031			0.317515	+	0.948253i	$0.397151\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.779099	+	0.779099i	0.0404488	+	0.0404488i
$372$		0			0
$373$	14.7424	+	14.7424i	0.763330	+	0.763330i	0.976923	−	0.213592i	$-0.0685164\pi$
$373$	14.7424	+	14.7424i	0.763330	+	0.763330i	−0.213592	+	0.976923i	$0.568516\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			7.26505i			0.374169i
$378$		0			0
$379$	−1.59803	−	1.59803i	−0.0820853	−	0.0820853i	0.664872	−	0.746957i	$-0.268486\pi$
$379$	−1.59803	−	1.59803i	−0.0820853	−	0.0820853i	−0.746957	+	0.664872i	$0.768486\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$			24.9035i			1.27251i	0.771479	+	0.636255i	$0.219517\pi$
$383$			24.9035i			1.27251i	−0.771479	+	0.636255i	$0.780483\pi$
$384$		0			0
$385$	−0.630458	+	0.428120i	−0.0321311	+	0.0218190i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.9793	−	11.9793i	−0.607375	−	0.607375i	0.334884	−	0.942259i	$-0.391303\pi$
$389$	−11.9793	−	11.9793i	−0.607375	−	0.607375i	−0.942259	+	0.334884i	$0.891303\pi$
$390$		0			0
$391$	9.14150			0.462306
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−23.5435	−	4.50014i	−1.18460	−	0.226427i
$396$		0			0
$397$	−16.0845	+	16.0845i	−0.807258	+	0.807258i	−0.984218	−	0.176960i	$-0.943374\pi$
$397$	−16.0845	+	16.0845i	−0.807258	+	0.807258i	0.176960	+	0.984218i	$0.443374\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			3.56411i			0.177983i	0.996032	+	0.0889915i	$0.0283644\pi$
$401$			3.56411i			0.177983i	−0.996032	+	0.0889915i	$0.971636\pi$
$402$		0			0
$403$	3.77828	+	3.77828i	0.188210	+	0.188210i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.80575			0.139076
$408$		0			0
$409$		−	0.455458i		−	0.0225209i	−0.999937	−	0.0112605i	$-0.996416\pi$
$409$		−	0.455458i		−	0.0225209i	0.999937	−	0.0112605i	$-0.00358439\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.57656	−	2.57656i	−0.126784	−	0.126784i
$414$		0			0
$415$	−6.22503	−	9.16712i	−0.305575	−	0.449996i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.20612	+	7.20612i	0.352042	+	0.352042i	0.860869	−	0.508827i	$-0.169921\pi$
$419$	7.20612	+	7.20612i	0.352042	+	0.352042i	−0.508827	+	0.860869i	$0.669921\pi$
$420$		0			0
$421$	−13.9138	+	13.9138i	−0.678119	+	0.678119i	−0.959574	−	0.281455i	$-0.909183\pi$
$421$	−13.9138	+	13.9138i	−0.678119	+	0.678119i	0.281455	+	0.959574i	$0.409183\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−13.5028	−	5.35766i	−0.654984	−	0.259885i
$426$		0			0
$427$	0.270083	−	0.270083i	0.0130702	−	0.0130702i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.2896			0.977314			0.488657	−	0.872476i	$-0.337487\pi$
$431$	20.2896			0.977314			0.488657	+	0.872476i	$0.337487\pi$
$432$		0			0
$433$			13.2049i			0.634587i	0.948327	+	0.317294i	$0.102774\pi$
$433$			13.2049i			0.634587i	−0.948327	+	0.317294i	$0.897226\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.932017	−	0.932017i	0.0445844	−	0.0445844i
$438$		0			0
$439$	−4.81740			−0.229922			−0.114961	−	0.993370i	$-0.536674\pi$
$439$	−4.81740			−0.229922			−0.114961	+	0.993370i	$0.536674\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.16428	+	9.16428i	0.435408	+	0.435408i	0.890463	−	0.455055i	$-0.150380\pi$
$443$	9.16428	+	9.16428i	0.435408	+	0.435408i	−0.455055	+	0.890463i	$0.650380\pi$
$444$		0			0
$445$	5.55752	−	29.0754i	0.263452	−	1.37831i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	3.67981i		−	0.173661i	−0.996223	−	0.0868305i	$-0.972326\pi$
$449$		−	3.67981i		−	0.173661i	0.996223	−	0.0868305i	$-0.0276739\pi$
$450$		0			0
$451$	−9.84780	+	9.84780i	−0.463715	+	0.463715i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.02835	+	0.698312i	−0.0482098	+	0.0327374i
$456$		0			0
$457$	18.1968			0.851212			0.425606	−	0.904908i	$-0.360061\pi$
$457$	18.1968			0.851212			0.425606	+	0.904908i	$0.360061\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.4826	−	20.4826i	0.953971	−	0.953971i	−0.0450155	−	0.998986i	$-0.514334\pi$
$461$	20.4826	−	20.4826i	0.953971	−	0.953971i	0.998986	+	0.0450155i	$0.0143337\pi$
$462$		0			0
$463$	22.5416			1.04760			0.523799	−	0.851842i	$-0.324514\pi$
$463$	22.5416			1.04760			0.523799	+	0.851842i	$0.324514\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−26.2704	+	26.2704i	−1.21565	+	1.21565i	−0.246507	+	0.969141i	$0.579283\pi$
$467$	−26.2704	+	26.2704i	−1.21565	+	1.21565i	−0.969141	+	0.246507i	$0.920717\pi$
$468$		0			0
$469$	0.968587	−	0.968587i	0.0447252	−	0.0447252i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			8.24552i			0.379130i
$474$		0			0
$475$	−1.92291	+	0.830438i	−0.0882292	+	0.0381031i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.723719			0.0330676			0.0165338	−	0.999863i	$-0.494737\pi$
$479$	0.723719			0.0330676			0.0165338	+	0.999863i	$0.494737\pi$
$480$		0			0
$481$	4.57651			0.208671
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.3914	−	4.66222i	−1.10756	−	0.211701i
$486$		0			0
$487$		−	15.0222i		−	0.680719i	−0.940295	−	0.340360i	$-0.889451\pi$
$487$		−	15.0222i		−	0.680719i	0.940295	−	0.340360i	$-0.110549\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.04102	+	3.04102i	−0.137239	+	0.137239i	−0.772389	−	0.635150i	$-0.780938\pi$
$491$	−3.04102	+	3.04102i	−0.137239	+	0.137239i	0.635150	+	0.772389i	$0.280938\pi$
$492$		0			0
$493$	7.08230	−	7.08230i	0.318971	−	0.318971i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.07214			0.0929481
$498$		0			0
$499$	−11.3545	+	11.3545i	−0.508298	+	0.508298i	−0.914004	−	0.405706i	$-0.867026\pi$
$499$	−11.3545	+	11.3545i	−0.508298	+	0.508298i	0.405706	+	0.914004i	$0.367026\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.8256			−1.10692			−0.553459	−	0.832876i	$-0.686692\pi$
$503$	−24.8256			−1.10692			−0.553459	+	0.832876i	$0.686692\pi$
$504$		0			0
$505$	1.63532	−	1.11048i	0.0727708	−	0.0494159i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−22.3544	+	22.3544i	−0.990841	+	0.990841i	−0.999958	−	0.00911778i	$-0.997098\pi$
$509$	−22.3544	+	22.3544i	−0.990841	+	0.990841i	0.00911778	+	0.999958i	$0.497098\pi$
$510$		0			0
$511$		−	3.27942i		−	0.145073i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−16.4211	−	3.13876i	−0.723601	−	0.138310i
$516$		0			0
$517$	6.10106	+	6.10106i	0.268324	+	0.268324i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	30.7334			1.34646			0.673228	−	0.739435i	$-0.264907\pi$
$521$	30.7334			1.34646			0.673228	+	0.739435i	$0.264907\pi$
$522$		0			0
$523$	12.6215	−	12.6215i	0.551898	−	0.551898i	−0.375090	−	0.926988i	$-0.622388\pi$
$523$	12.6215	−	12.6215i	0.551898	−	0.551898i	0.926988	+	0.375090i	$0.122388\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	7.36649i		−	0.320889i
$528$		0			0
$529$	−13.1002			−0.569572
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−16.0629	+	16.0629i	−0.695761	+	0.695761i
$534$		0			0
$535$	−28.2353	+	19.1735i	−1.22072	+	0.828944i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.33159	+	6.33159i	−0.272721	+	0.272721i
$540$		0			0
$541$	18.0279	+	18.0279i	0.775081	+	0.775081i	0.978990	−	0.203909i	$-0.0653645\pi$
$541$	18.0279	+	18.0279i	0.775081	+	0.775081i	−0.203909	+	0.978990i	$0.565365\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.682668	+	0.463574i	−0.0292423	+	0.0198573i
$546$		0			0
$547$	26.0749	+	26.0749i	1.11488	+	1.11488i	0.992480	+	0.122403i	$0.0390600\pi$
$547$	26.0749	+	26.0749i	1.11488	+	1.11488i	0.122403	+	0.992480i	$0.460940\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	1.44414i		−	0.0615226i
$552$		0			0
$553$	2.82764			0.120244
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−23.2849	−	23.2849i	−0.986612	−	0.986612i	0.0132999	−	0.999912i	$-0.495766\pi$
$557$	−23.2849	−	23.2849i	−0.986612	−	0.986612i	−0.999912	+	0.0132999i	$0.995766\pi$
$558$		0			0
$559$			13.4494i			0.568849i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.08207	+	2.08207i	−0.0877489	+	0.0877489i	−0.749619	−	0.661870i	$-0.769763\pi$
$563$	−2.08207	+	2.08207i	−0.0877489	+	0.0877489i	0.661870	+	0.749619i	$0.269763\pi$
$564$		0			0
$565$	−1.63259	+	8.54127i	−0.0686837	+	0.359334i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.4930			−0.942957			−0.471478	−	0.881878i	$-0.656279\pi$
$569$	−22.4930			−0.942957			−0.471478	+	0.881878i	$0.656279\pi$
$570$		0			0
$571$	17.5867	+	17.5867i	0.735979	+	0.735979i	0.971797	−	0.235818i	$-0.0757770\pi$
$571$	17.5867	+	17.5867i	0.735979	+	0.735979i	−0.235818	+	0.971797i	$0.575777\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−14.6230	−	5.80211i	−0.609821	−	0.241965i
$576$		0			0
$577$		−	24.8497i		−	1.03450i	−0.855833	−	0.517252i	$-0.826955\pi$
$577$		−	24.8497i		−	1.03450i	0.855833	−	0.517252i	$-0.173045\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.924321	+	0.924321i	0.0383473	+	0.0383473i
$582$		0			0
$583$			5.39671i			0.223509i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.8896	−	22.8896i	−0.944753	−	0.944753i	0.0537988	−	0.998552i	$-0.482867\pi$
$587$	−22.8896	−	22.8896i	−0.944753	−	0.944753i	−0.998552	+	0.0537988i	$0.982867\pi$
$588$		0			0
$589$	−0.751046	−	0.751046i	−0.0309463	−	0.0309463i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.3090			−0.546536			−0.273268	−	0.961938i	$-0.588105\pi$
$593$	−13.3090			−0.546536			−0.273268	+	0.961938i	$0.588105\pi$
$594$		0			0
$595$	1.68323	+	0.321735i	0.0690056	+	0.0131899i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	7.33982i		−	0.299897i	−0.988694	−	0.149948i	$-0.952089\pi$
$599$		−	7.33982i		−	0.299897i	0.988694	−	0.149948i	$-0.0479108\pi$
$600$		0			0
$601$			27.4748i			1.12072i	0.828250	+	0.560359i	$0.189337\pi$
$601$			27.4748i			1.12072i	−0.828250	+	0.560359i	$0.810663\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	20.4931	+	3.91708i	0.833162	+	0.159252i
$606$		0			0
$607$	−27.4473			−1.11405			−0.557026	−	0.830495i	$-0.688058\pi$
$607$	−27.4473			−1.11405			−0.557026	+	0.830495i	$0.688058\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.95153	+	9.95153i	0.402596	+	0.402596i
$612$		0			0
$613$	17.6219	+	17.6219i	0.711742	+	0.711742i	0.966899	−	0.255158i	$-0.0821274\pi$
$613$	17.6219	+	17.6219i	0.711742	+	0.711742i	−0.255158	+	0.966899i	$0.582127\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			41.8102i			1.68322i	0.540088	+	0.841608i	$0.318391\pi$
$617$			41.8102i			1.68322i	−0.540088	+	0.841608i	$0.681609\pi$
$618$		0			0
$619$	−1.39925	−	1.39925i	−0.0562406	−	0.0562406i	0.678427	−	0.734668i	$-0.262662\pi$
$619$	−1.39925	−	1.39925i	−0.0562406	−	0.0562406i	−0.734668	+	0.678427i	$0.762662\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			3.49204i			0.139906i
$624$		0			0
$625$	18.1990	+	17.1405i	0.727960	+	0.685620i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.46139	−	4.46139i	−0.177887	−	0.177887i
$630$		0			0
$631$	−33.0559			−1.31593			−0.657967	−	0.753047i	$-0.728583\pi$
$631$	−33.0559			−1.31593			−0.657967	+	0.753047i	$0.728583\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−7.60589	+	39.7919i	−0.301830	+	1.57909i
$636$		0			0
$637$	−10.3275	+	10.3275i	−0.409192	+	0.409192i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	8.31451i		−	0.328404i	−0.986427	−	0.164202i	$-0.947495\pi$
$641$		−	8.31451i		−	0.328404i	0.986427	−	0.164202i	$-0.0525048\pi$
$642$		0			0
$643$	−17.1504	−	17.1504i	−0.676344	−	0.676344i	0.282827	−	0.959171i	$-0.408728\pi$
$643$	−17.1504	−	17.1504i	−0.676344	−	0.676344i	−0.959171	+	0.282827i	$0.908728\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.95293			−0.234034			−0.117017	−	0.993130i	$-0.537333\pi$
$647$	−5.95293			−0.234034			−0.117017	+	0.993130i	$0.537333\pi$
$648$		0			0
$649$		−	17.8475i		−	0.700575i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	24.1739	+	24.1739i	0.945997	+	0.945997i	0.998615	−	0.0526174i	$-0.0167564\pi$
$653$	24.1739	+	24.1739i	0.945997	+	0.945997i	−0.0526174	+	0.998615i	$0.516756\pi$
$654$		0			0
$655$	36.7851	−	24.9793i	1.43731	−	0.976024i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−25.0108	−	25.0108i	−0.974284	−	0.974284i	0.0253938	−	0.999678i	$-0.491916\pi$
$659$	−25.0108	−	25.0108i	−0.974284	−	0.974284i	−0.999678	+	0.0253938i	$0.991916\pi$
$660$		0			0
$661$	−28.8800	+	28.8800i	−1.12330	+	1.12330i	−0.132061	+	0.991242i	$0.542159\pi$
$661$	−28.8800	+	28.8800i	−1.12330	+	1.12330i	−0.991242	+	0.132061i	$0.957841\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.204415	−	0.138810i	0.00792687	−	0.00538283i
$666$		0			0
$667$	7.66982	−	7.66982i	0.296977	−	0.296977i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.87083			0.0722224
$672$		0			0
$673$			26.0623i			1.00463i	0.864685	+	0.502315i	$0.167518\pi$
$673$			26.0623i			1.00463i	−0.864685	+	0.502315i	$0.832482\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.70043	+	9.70043i	−0.372818	+	0.372818i	−0.868503	−	0.495685i	$-0.834917\pi$
$677$	−9.70043	+	9.70043i	−0.372818	+	0.372818i	0.495685	+	0.868503i	$0.334917\pi$
$678$		0			0
$679$	2.92948			0.112423
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.36855	−	8.36855i	−0.320214	−	0.320214i	0.528635	−	0.848849i	$-0.322704\pi$
$683$	−8.36855	−	8.36855i	−0.320214	−	0.320214i	−0.848849	+	0.528635i	$0.822704\pi$
$684$		0			0
$685$	22.7107	+	4.34096i	0.867731	+	0.165860i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			8.80266i			0.335355i
$690$		0			0
$691$	−16.7998	+	16.7998i	−0.639095	+	0.639095i	−0.950332	−	0.311237i	$-0.899257\pi$
$691$	−16.7998	+	16.7998i	−0.639095	+	0.639095i	0.311237	+	0.950332i	$0.399257\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−30.8978	+	20.9815i	−1.17202	+	0.795873i
$696$		0			0
$697$	31.3177			1.18624
$698$		0			0
$699$		0			0
$700$		0			0
$701$	26.5344	−	26.5344i	1.00219	−	1.00219i	0.00219271	−	0.999998i	$-0.499302\pi$
$701$	26.5344	−	26.5344i	1.00219	−	1.00219i	0.999998	−	0.00219271i	$-0.000697963\pi$
$702$		0			0
$703$	−0.909716			−0.0343106
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.164890	+	0.164890i	−0.00620131	+	0.00620131i
$708$		0			0
$709$	−32.4351	+	32.4351i	−1.21813	+	1.21813i	−0.249840	+	0.968287i	$0.580378\pi$
$709$	−32.4351	+	32.4351i	−1.21813	+	1.21813i	−0.968287	+	0.249840i	$0.919622\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	7.97758i		−	0.298763i
$714$		0			0
$715$	−5.98017	−	1.14306i	−0.223646	−	0.0427480i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.81868			−0.328881			−0.164441	−	0.986387i	$-0.552582\pi$
$719$	−8.81868			−0.328881			−0.164441	+	0.986387i	$0.552582\pi$
$720$		0			0
$721$	1.97222			0.0734495
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.8242	+	6.83390i	−0.587695	+	0.253805i
$726$		0			0
$727$		−	10.5815i		−	0.392448i	−0.980559	−	0.196224i	$-0.937132\pi$
$727$		−	10.5815i		−	0.392448i	0.980559	−	0.196224i	$-0.0628679\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	13.1111	−	13.1111i	0.484931	−	0.484931i
$732$		0			0
$733$	−0.891694	+	0.891694i	−0.0329355	+	0.0329355i	−0.723383	−	0.690447i	$-0.757414\pi$
$733$	−0.891694	+	0.891694i	−0.0329355	+	0.0329355i	0.690447	+	0.723383i	$0.257414\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.70927			0.247139
$738$		0			0
$739$	22.1859	−	22.1859i	0.816120	−	0.816120i	−0.169423	−	0.985543i	$-0.554190\pi$
$739$	22.1859	−	22.1859i	0.816120	−	0.816120i	0.985543	+	0.169423i	$0.0541905\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.89487			0.289635			0.144817	−	0.989458i	$-0.453741\pi$
$743$	7.89487			0.289635			0.144817	+	0.989458i	$0.453741\pi$
$744$		0			0
$745$	−14.9654	+	10.1624i	−0.548289	+	0.372322i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.84697	−	2.84697i	0.104026	−	0.104026i
$750$		0			0
$751$			4.43117i			0.161696i	0.996726	+	0.0808478i	$0.0257628\pi$
$751$			4.43117i			0.161696i	−0.996726	+	0.0808478i	$0.974237\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.29598	−	32.9388i	0.229134	−	1.19877i
$756$		0			0
$757$	22.8329	+	22.8329i	0.829876	+	0.829876i	0.987499	−	0.157623i	$-0.0503832\pi$
$757$	22.8329	+	22.8329i	0.829876	+	0.829876i	−0.157623	+	0.987499i	$0.550383\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.3941			0.666784			0.333392	−	0.942788i	$-0.391807\pi$
$761$	18.3941			0.666784			0.333392	+	0.942788i	$0.391807\pi$
$762$		0			0
$763$	0.0688335	−	0.0688335i	0.00249194	−	0.00249194i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	29.1113i		−	1.05115i
$768$		0			0
$769$	12.2959			0.443402			0.221701	−	0.975115i	$-0.428839\pi$
$769$	12.2959			0.443402			0.221701	+	0.975115i	$0.428839\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−16.8697	+	16.8697i	−0.606762	+	0.606762i	−0.942098	−	0.335337i	$-0.891150\pi$
$773$	−16.8697	+	16.8697i	−0.606762	+	0.606762i	0.335337	+	0.942098i	$0.391150\pi$
$774$		0			0
$775$	−4.67551	+	11.7836i	−0.167949	+	0.423280i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.19298	−	3.19298i	0.114400	−	0.114400i
$780$		0			0
$781$	7.17670	+	7.17670i	0.256803	+	0.256803i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.0464945	−	0.0684688i	−0.00165946	−	0.00244376i
$786$		0			0
$787$	32.0462	+	32.0462i	1.14232	+	1.14232i	0.988024	+	0.154299i	$0.0493118\pi$
$787$	32.0462	+	32.0462i	1.14232	+	1.14232i	0.154299	+	0.988024i	$0.450688\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	1.02583i		−	0.0364744i
$792$		0			0
$793$	3.05153			0.108363
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.6812	+	16.6812i	0.590879	+	0.590879i	0.937869	−	0.346990i	$-0.112796\pi$
$797$	16.6812	+	16.6812i	0.590879	+	0.590879i	−0.346990	+	0.937869i	$0.612796\pi$
$798$		0			0
$799$		−	19.4024i		−	0.686408i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	11.3580	−	11.3580i	0.400816	−	0.400816i
$804$		0			0
$805$	1.82286	+	0.348425i	0.0642475	+	0.0122804i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−26.5382			−0.933032			−0.466516	−	0.884513i	$-0.654491\pi$
$809$	−26.5382			−0.933032			−0.466516	+	0.884513i	$0.654491\pi$
$810$		0			0
$811$	−19.0246	−	19.0246i	−0.668044	−	0.668044i	0.289219	−	0.957263i	$-0.406604\pi$
$811$	−19.0246	−	19.0246i	−0.668044	−	0.668044i	−0.957263	+	0.289219i	$0.906604\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−44.7684	+	30.4005i	−1.56817	+	1.06488i
$816$		0			0
$817$		−	2.67347i		−	0.0935328i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.92298	+	8.92298i	0.311414	+	0.311414i	0.845457	−	0.534043i	$-0.179328\pi$
$821$	8.92298	+	8.92298i	0.311414	+	0.311414i	−0.534043	+	0.845457i	$0.679328\pi$
$822$		0			0
$823$			28.4770i			0.992646i	0.868138	+	0.496323i	$0.165317\pi$
$823$			28.4770i			0.992646i	−0.868138	+	0.496323i	$0.834683\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.8892	+	14.8892i	0.517748	+	0.517748i	0.916889	−	0.399141i	$-0.130692\pi$
$827$	14.8892	+	14.8892i	0.517748	+	0.517748i	−0.399141	+	0.916889i	$0.630692\pi$
$828$		0			0
$829$	11.4041	+	11.4041i	0.396082	+	0.396082i	0.876849	−	0.480767i	$-0.159642\pi$
$829$	11.4041	+	11.4041i	0.396082	+	0.396082i	−0.480767	+	0.876849i	$0.659642\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	20.1355			0.697654
$834$		0			0
$835$	8.16987	−	42.7425i	0.282730	−	1.47916i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			16.2531i			0.561118i	0.959837	+	0.280559i	$0.0905199\pi$
$839$			16.2531i			0.561118i	−0.959837	+	0.280559i	$0.909480\pi$
$840$		0			0
$841$			17.1157i			0.590198i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	18.7976	+	3.59301i	0.646659	+	0.123603i
$846$		0			0
$847$	−2.46128			−0.0845705
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.83149	−	4.83149i	−0.165621	−	0.165621i
$852$		0			0
$853$	−23.0418	−	23.0418i	−0.788935	−	0.788935i	0.192385	−	0.981320i	$-0.438378\pi$
$853$	−23.0418	−	23.0418i	−0.788935	−	0.788935i	−0.981320	+	0.192385i	$0.938378\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			30.7846i			1.05158i	0.850614	+	0.525791i	$0.176231\pi$
$857$			30.7846i			1.05158i	−0.850614	+	0.525791i	$0.823769\pi$
$858$		0			0
$859$	18.4753	+	18.4753i	0.630370	+	0.630370i	0.948161	−	0.317791i	$-0.102941\pi$
$859$	18.4753	+	18.4753i	0.630370	+	0.630370i	−0.317791	+	0.948161i	$0.602941\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	25.8775i		−	0.880879i	−0.897782	−	0.440440i	$-0.854823\pi$
$863$		−	25.8775i		−	0.880879i	0.897782	−	0.440440i	$-0.145177\pi$
$864$		0			0
$865$	−29.6737	+	20.1503i	−1.00894	+	0.685129i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.79333	+	9.79333i	0.332216	+	0.332216i
$870$		0			0
$871$	10.9436			0.370809
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.48833	−	1.58300i	−0.0841209	−	0.0535152i
$876$		0			0
$877$	−21.3569	+	21.3569i	−0.721171	+	0.721171i	−0.968844	−	0.247673i	$-0.920334\pi$
$877$	−21.3569	+	21.3569i	−0.721171	+	0.721171i	0.247673	+	0.968844i	$0.420334\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	38.6737i		−	1.30295i	−0.758670	−	0.651475i	$-0.774151\pi$
$881$		−	38.6737i		−	1.30295i	0.758670	−	0.651475i	$-0.225849\pi$
$882$		0			0
$883$	31.7478	+	31.7478i	1.06840	+	1.06840i	0.997482	+	0.0709157i	$0.0225921\pi$
$883$	31.7478	+	31.7478i	1.06840	+	1.06840i	0.0709157	+	0.997482i	$0.477408\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.1784			0.543217			0.271609	−	0.962408i	$-0.412444\pi$
$887$	16.1784			0.543217			0.271609	+	0.962408i	$0.412444\pi$
$888$		0			0
$889$		−	4.77912i		−	0.160287i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.97816	−	1.97816i	−0.0661967	−	0.0661967i
$894$		0			0
$895$	11.7887	−	8.00528i	0.394054	−	0.267587i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.18056	−	6.18056i	−0.206133	−	0.206133i
$900$		0			0
$901$	8.58123	−	8.58123i	0.285882	−	0.285882i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.9375	−	26.4152i	−0.596264	−	0.878070i
$906$		0			0
$907$	−28.4899	+	28.4899i	−0.945992	+	0.945992i	−0.998614	−	0.0526227i	$-0.983242\pi$
$907$	−28.4899	+	28.4899i	−0.945992	+	0.945992i	0.0526227	+	0.998614i	$0.483242\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	2.49312			0.0826008			0.0413004	−	0.999147i	$-0.486850\pi$
$911$	2.49312			0.0826008			0.0413004	+	0.999147i	$0.486850\pi$
$912$		0			0
$913$			6.40264i			0.211897i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.70905	+	3.70905i	−0.122484	+	0.122484i
$918$		0			0
$919$	−22.3205			−0.736287			−0.368143	−	0.929769i	$-0.620006\pi$
$919$	−22.3205			−0.736287			−0.368143	+	0.929769i	$0.620006\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	11.7060	+	11.7060i	0.385308	+	0.385308i
$924$		0			0
$925$	4.30491	+	9.96819i	0.141545	+	0.327752i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			6.44533i			0.211464i	0.994395	+	0.105732i	$0.0337186\pi$
$929$			6.44533i			0.211464i	−0.994395	+	0.105732i	$0.966281\pi$
$930$		0			0
$931$	2.05291	−	2.05291i	0.0672813	−	0.0672813i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.71544	+	6.94405i	0.154211	+	0.227095i
$936$		0			0
$937$	56.5439			1.84721			0.923605	−	0.383346i	$-0.125228\pi$
$937$	56.5439			1.84721			0.923605	+	0.383346i	$0.125228\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.57877	−	1.57877i	0.0514663	−	0.0514663i	−0.680905	−	0.732372i	$-0.738413\pi$
$941$	1.57877	−	1.57877i	0.0514663	−	0.0514663i	0.732372	+	0.680905i	$0.238413\pi$
$942$		0			0
$943$	33.9157			1.10445
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.1004	+	12.1004i	−0.393210	+	0.393210i	−0.875830	−	0.482620i	$-0.839685\pi$
$947$	−12.1004	+	12.1004i	−0.393210	+	0.393210i	0.482620	+	0.875830i	$0.339685\pi$
$948$		0			0
$949$	18.5263	−	18.5263i	0.601388	−	0.601388i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	25.9757i		−	0.841435i	−0.907192	−	0.420718i	$-0.861778\pi$
$953$		−	25.9757i		−	0.841435i	0.907192	−	0.420718i	$-0.138222\pi$
$954$		0			0
$955$	10.0143	−	52.3918i	0.324054	−	1.69536i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.72762			−0.0880795
$960$		0			0
$961$	24.5714			0.792627
$962$		0			0
$963$		0			0
$964$		0			0
$965$	30.4376	+	5.81790i	0.979822	+	0.187285i
$966$		0			0
$967$		−	61.3307i		−	1.97226i	−0.165969	−	0.986131i	$-0.553075\pi$
$967$		−	61.3307i		−	1.97226i	0.165969	−	0.986131i	$-0.446925\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	30.0810	−	30.0810i	0.965346	−	0.965346i	−0.0340737	−	0.999419i	$-0.510848\pi$
$971$	30.0810	−	30.0810i	0.965346	−	0.965346i	0.999419	+	0.0340737i	$0.0108481\pi$
$972$		0			0
$973$	3.11543	−	3.11543i	0.0998760	−	0.0998760i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	33.3131			1.06578			0.532891	−	0.846184i	$-0.321106\pi$
$977$	33.3131			1.06578			0.532891	+	0.846184i	$0.321106\pi$
$978$		0			0
$979$	−12.0944	+	12.0944i	−0.386540	+	0.386540i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−54.1424			−1.72687			−0.863437	−	0.504456i	$-0.831693\pi$
$983$	−54.1424			−1.72687			−0.863437	+	0.504456i	$0.831693\pi$
$984$		0			0
$985$	−21.2856	−	31.3456i	−0.678215	−	0.998754i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.1987	−	14.1987i	0.451493	−	0.451493i
$990$		0			0
$991$			39.3653i			1.25048i	0.780433	+	0.625240i	$0.214999\pi$
$991$			39.3653i			1.25048i	−0.780433	+	0.625240i	$0.785001\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.79989	−	25.1117i	0.152167	−	0.796094i
$996$		0			0
$997$	−28.9457	−	28.9457i	−0.916720	−	0.916720i	0.0800697	−	0.996789i	$-0.474486\pi$
$997$	−28.9457	−	28.9457i	−0.916720	−	0.916720i	−0.996789	+	0.0800697i	$0.974486\pi$
$998$		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.2159.28		96
3.2	odd	2	inner	2880.2.u.a.2159.21		96
4.3	odd	2		720.2.u.a.179.41	yes	96
5.4	even	2	inner	2880.2.u.a.2159.4		96
12.11	even	2		720.2.u.a.179.8	yes	96
15.14	odd	2	inner	2880.2.u.a.2159.45		96
16.5	even	4		720.2.u.a.539.42	yes	96
16.11	odd	4	inner	2880.2.u.a.719.45		96
20.19	odd	2		720.2.u.a.179.7	✓	96
48.5	odd	4		720.2.u.a.539.7	yes	96
48.11	even	4	inner	2880.2.u.a.719.4		96
60.59	even	2		720.2.u.a.179.42	yes	96
80.59	odd	4	inner	2880.2.u.a.719.21		96
80.69	even	4		720.2.u.a.539.8	yes	96
240.59	even	4	inner	2880.2.u.a.719.28		96
240.149	odd	4		720.2.u.a.539.41	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.7	✓	96	20.19	odd	2
720.2.u.a.179.8	yes	96	12.11	even	2
720.2.u.a.179.41	yes	96	4.3	odd	2
720.2.u.a.179.42	yes	96	60.59	even	2
720.2.u.a.539.7	yes	96	48.5	odd	4
720.2.u.a.539.8	yes	96	80.69	even	4
720.2.u.a.539.41	yes	96	240.149	odd	4
720.2.u.a.539.42	yes	96	16.5	even	4
2880.2.u.a.719.4		96	48.11	even	4	inner
2880.2.u.a.719.21		96	80.59	odd	4	inner
2880.2.u.a.719.28		96	240.59	even	4	inner
2880.2.u.a.719.45		96	16.11	odd	4	inner
2880.2.u.a.2159.4		96	5.4	even	2	inner
2880.2.u.a.2159.21		96	3.2	odd	2	inner
2880.2.u.a.2159.28		96	1.1	even	1	trivial
2880.2.u.a.2159.45		96	15.14	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.419806 - 2.19631i) q^{5} +0.263783i q^{7} +(-0.913594 + 0.913594i) q^{11} +(-1.49018 + 1.49018i) q^{13} +2.90538 q^{17} +(0.296217 - 0.296217i) q^{19} +3.14640 q^{23} +(-4.64753 - 1.84404i) q^{25} +(2.43765 - 2.43765i) q^{29} -2.53546i q^{31} +(0.579348 + 0.110738i) q^{35} +(-1.53556 - 1.53556i) q^{37} +10.7792 q^{41} +(4.51269 - 4.51269i) q^{43} -6.67809i q^{47} +6.93042 q^{49} +(2.95356 - 2.95356i) q^{53} +(1.62300 + 2.39006i) q^{55} +(-9.76773 + 9.76773i) q^{59} +(-1.02388 - 1.02388i) q^{61} +(2.64730 + 3.89847i) q^{65} +(-3.67191 - 3.67191i) q^{67} -7.85546i q^{71} -12.4323 q^{73} +(-0.240990 - 0.240990i) q^{77} -10.7196i q^{79} +(3.50410 - 3.50410i) q^{83} +(1.21970 - 6.38111i) q^{85} +13.2383 q^{89} +(-0.393083 - 0.393083i) q^{91} +(-0.526229 - 0.774936i) q^{95} -11.1057i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) \) 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

Related objects

Downloads

Learn more