LMFDB - Embedded newform 2880.2.u.a.719.16

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			719.16
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +O(q^{10})$	$q+(-1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +(-0.176123 - 0.176123i) q^{11} +(1.72742 + 1.72742i) q^{13} -3.15721 q^{17} +(-3.47385 - 3.47385i) q^{19} +1.97613 q^{23} +(-1.55305 - 4.75269i) q^{25} +(2.62046 + 2.62046i) q^{29} -5.95492i q^{31} +(2.54675 + 1.84706i) q^{35} +(5.72522 - 5.72522i) q^{37} +0.159470 q^{41} +(6.63058 + 6.63058i) q^{43} -1.15223i q^{47} +5.02049 q^{49} +(-5.35087 - 5.35087i) q^{53} +(0.550020 - 0.0875872i) q^{55} +(4.48547 + 4.48547i) q^{59} +(6.80718 - 6.80718i) q^{61} +(-5.39461 + 0.859057i) q^{65} +(-9.97278 + 9.97278i) q^{67} +0.0951463i q^{71} -7.99125 q^{73} +(-0.247796 + 0.247796i) q^{77} -5.66620i q^{79} +(12.2672 + 12.2672i) q^{83} +(4.14481 - 5.71492i) q^{85} +10.9299 q^{89} +(2.43039 - 2.43039i) q^{91} +(10.8486 - 1.72757i) q^{95} -10.4415i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.31281	+	1.81012i	−0.587107	+	0.809509i
$5$	−1.31281	+	1.81012i	−0.587107	+	0.809509i
$6$		0			0
$7$		−	1.40695i		−	0.531777i	−0.964004	−	0.265889i	$-0.914335\pi$
$7$		−	1.40695i		−	0.531777i	0.964004	−	0.265889i	$-0.0856653\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.176123	−	0.176123i	−0.0531031	−	0.0531031i	0.680057	−	0.733160i	$-0.261955\pi$
$11$	−0.176123	−	0.176123i	−0.0531031	−	0.0531031i	−0.733160	+	0.680057i	$0.761955\pi$
$12$		0			0
$13$	1.72742	+	1.72742i	0.479100	+	0.479100i	0.904844	−	0.425744i	$-0.139988\pi$
$13$	1.72742	+	1.72742i	0.479100	+	0.479100i	−0.425744	+	0.904844i	$0.639988\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.15721			−0.765735			−0.382867	−	0.923803i	$-0.625063\pi$
$17$	−3.15721			−0.765735			−0.382867	+	0.923803i	$0.625063\pi$
$18$		0			0
$19$	−3.47385	−	3.47385i	−0.796956	−	0.796956i	0.185658	−	0.982614i	$-0.440558\pi$
$19$	−3.47385	−	3.47385i	−0.796956	−	0.796956i	−0.982614	+	0.185658i	$0.940558\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.97613			0.412052			0.206026	−	0.978546i	$-0.433947\pi$
$23$	1.97613			0.412052			0.206026	+	0.978546i	$0.433947\pi$
$24$		0			0
$25$	−1.55305	−	4.75269i	−0.310611	−	0.950537i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.62046	+	2.62046i	0.486607	+	0.486607i	0.907234	−	0.420627i	$-0.138190\pi$
$29$	2.62046	+	2.62046i	0.486607	+	0.486607i	−0.420627	+	0.907234i	$0.638190\pi$
$30$		0			0
$31$		−	5.95492i		−	1.06953i	−0.844999	−	0.534767i	$-0.820399\pi$
$31$		−	5.95492i		−	1.06953i	0.844999	−	0.534767i	$-0.179601\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.54675	+	1.84706i	0.430479	+	0.312210i
$36$		0			0
$37$	5.72522	−	5.72522i	0.941221	−	0.941221i	−0.0571453	−	0.998366i	$-0.518200\pi$
$37$	5.72522	−	5.72522i	0.941221	−	0.941221i	0.998366	+	0.0571453i	$0.0181998\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.159470			0.0249050			0.0124525	−	0.999922i	$-0.496036\pi$
$41$	0.159470			0.0249050			0.0124525	+	0.999922i	$0.496036\pi$
$42$		0			0
$43$	6.63058	+	6.63058i	1.01115	+	1.01115i	0.999937	+	0.0112162i	$0.00357031\pi$
$43$	6.63058	+	6.63058i	1.01115	+	1.01115i	0.0112162	+	0.999937i	$0.496430\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	1.15223i		−	0.168069i	−0.996463	−	0.0840347i	$-0.973219\pi$
$47$		−	1.15223i		−	0.168069i	0.996463	−	0.0840347i	$-0.0267807\pi$
$48$		0			0
$49$	5.02049			0.717213
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.35087	−	5.35087i	−0.734999	−	0.734999i	0.236606	−	0.971606i	$-0.423965\pi$
$53$	−5.35087	−	5.35087i	−0.734999	−	0.734999i	−0.971606	+	0.236606i	$0.923965\pi$
$54$		0			0
$55$	0.550020	−	0.0875872i	0.0741646	−	0.0118103i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.48547	+	4.48547i	0.583959	+	0.583959i	0.935989	−	0.352030i	$-0.114508\pi$
$59$	4.48547	+	4.48547i	0.583959	+	0.583959i	−0.352030	+	0.935989i	$0.614508\pi$
$60$		0			0
$61$	6.80718	−	6.80718i	0.871570	−	0.871570i	−0.121074	−	0.992643i	$-0.538634\pi$
$61$	6.80718	−	6.80718i	0.871570	−	0.871570i	0.992643	+	0.121074i	$0.0386338\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.39461	+	0.859057i	−0.669118	+	0.106553i
$66$		0			0
$67$	−9.97278	+	9.97278i	−1.21837	+	1.21837i	−0.250166	+	0.968203i	$0.580485\pi$
$67$	−9.97278	+	9.97278i	−1.21837	+	1.21837i	−0.968203	+	0.250166i	$0.919515\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.0951463i			0.0112918i	0.999984	+	0.00564589i	$0.00179715\pi$
$71$			0.0951463i			0.0112918i	−0.999984	+	0.00564589i	$0.998203\pi$
$72$		0			0
$73$	−7.99125			−0.935305			−0.467653	−	0.883912i	$-0.654900\pi$
$73$	−7.99125			−0.935305			−0.467653	+	0.883912i	$0.654900\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.247796	+	0.247796i	−0.0282390	+	0.0282390i
$78$		0			0
$79$		−	5.66620i		−	0.637497i	−0.947839	−	0.318748i	$-0.896737\pi$
$79$		−	5.66620i		−	0.637497i	0.947839	−	0.318748i	$-0.103263\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	12.2672	+	12.2672i	1.34650	+	1.34650i	0.889432	+	0.457068i	$0.151100\pi$
$83$	12.2672	+	12.2672i	1.34650	+	1.34650i	0.457068	+	0.889432i	$0.348900\pi$
$84$		0			0
$85$	4.14481	−	5.71492i	0.449568	−	0.619870i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	10.9299			1.15857			0.579284	−	0.815126i	$-0.303332\pi$
$89$	10.9299			1.15857			0.579284	+	0.815126i	$0.303332\pi$
$90$		0			0
$91$	2.43039	−	2.43039i	0.254774	−	0.254774i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	10.8486	−	1.72757i	1.11304	−	0.177245i
$96$		0			0
$97$		−	10.4415i		−	1.06017i	−0.847944	−	0.530086i	$-0.822160\pi$
$97$		−	10.4415i		−	1.06017i	0.847944	−	0.530086i	$-0.177840\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.54532	−	4.54532i	0.452276	−	0.452276i	−0.443833	−	0.896109i	$-0.646382\pi$
$101$	4.54532	−	4.54532i	0.452276	−	0.452276i	0.896109	+	0.443833i	$0.146382\pi$
$102$		0			0
$103$		−	7.65680i		−	0.754447i	−0.926122	−	0.377224i	$-0.876879\pi$
$103$		−	7.65680i		−	0.754447i	0.926122	−	0.377224i	$-0.123121\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.25185	−	4.25185i	0.411042	−	0.411042i	−0.471059	−	0.882102i	$-0.656128\pi$
$107$	4.25185	−	4.25185i	0.411042	−	0.411042i	0.882102	+	0.471059i	$0.156128\pi$
$108$		0			0
$109$	0.180834	−	0.180834i	0.0173208	−	0.0173208i	−0.698393	−	0.715714i	$-0.746101\pi$
$109$	0.180834	−	0.180834i	0.0173208	−	0.0173208i	0.715714	+	0.698393i	$0.246101\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.88868			−0.648032			−0.324016	−	0.946052i	$-0.605033\pi$
$113$	−6.88868			−0.648032			−0.324016	+	0.946052i	$0.605033\pi$
$114$		0			0
$115$	−2.59429	+	3.57703i	−0.241919	+	0.333560i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			4.44203i			0.407200i
$120$		0			0
$121$		−	10.9380i		−	0.994360i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.6418	+	3.42817i	0.951831	+	0.306625i
$126$		0			0
$127$	3.18115			0.282281			0.141141	−	0.989990i	$-0.454923\pi$
$127$	3.18115			0.282281			0.141141	+	0.989990i	$0.454923\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.49459	−	8.49459i	0.742175	−	0.742175i	−0.230821	−	0.972996i	$-0.574141\pi$
$131$	8.49459	−	8.49459i	0.742175	−	0.742175i	0.972996	+	0.230821i	$0.0741411\pi$
$132$		0			0
$133$	−4.88754	+	4.88754i	−0.423803	+	0.423803i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			15.1013i			1.29019i	0.764102	+	0.645096i	$0.223182\pi$
$137$			15.1013i			1.29019i	−0.764102	+	0.645096i	$0.776818\pi$
$138$		0			0
$139$	11.6635	−	11.6635i	0.989286	−	0.989286i	−0.0106573	−	0.999943i	$-0.503392\pi$
$139$	11.6635	−	11.6635i	0.989286	−	0.989286i	0.999943	+	0.0106573i	$0.00339237\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	0.608476i		−	0.0508833i
$144$		0			0
$145$	−8.18351	+	1.30317i	−0.679604	+	0.108223i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.1281	−	11.1281i	0.911646	−	0.911646i	−0.0847561	−	0.996402i	$-0.527011\pi$
$149$	11.1281	−	11.1281i	0.911646	−	0.911646i	0.996402	+	0.0847561i	$0.0270111\pi$
$150$		0			0
$151$	21.8766			1.78030			0.890148	−	0.455672i	$-0.150601\pi$
$151$	21.8766			1.78030			0.890148	+	0.455672i	$0.150601\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.7791	+	7.81768i	0.865798	+	0.627931i
$156$		0			0
$157$	15.3928	+	15.3928i	1.22848	+	1.22848i	0.964541	+	0.263935i	$0.0850204\pi$
$157$	15.3928	+	15.3928i	1.22848	+	1.22848i	0.263935	+	0.964541i	$0.414980\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	2.78032i		−	0.219120i
$162$		0			0
$163$	4.90113	−	4.90113i	0.383886	−	0.383886i	−0.488614	−	0.872500i	$-0.662497\pi$
$163$	4.90113	−	4.90113i	0.383886	−	0.383886i	0.872500	+	0.488614i	$0.162497\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.4380			−1.34939			−0.674695	−	0.738097i	$-0.735725\pi$
$167$	−17.4380			−1.34939			−0.674695	+	0.738097i	$0.735725\pi$
$168$		0			0
$169$		−	7.03205i		−	0.540927i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	17.4288	−	17.4288i	1.32509	−	1.32509i	0.415490	−	0.909598i	$-0.363610\pi$
$173$	17.4288	−	17.4288i	1.32509	−	1.32509i	0.909598	−	0.415490i	$-0.136390\pi$
$174$		0			0
$175$	−6.68679	+	2.18507i	−0.505474	+	0.165176i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.4635	+	12.4635i	−0.931565	+	0.931565i	−0.997804	−	0.0662383i	$-0.978900\pi$
$179$	−12.4635	+	12.4635i	−0.931565	+	0.931565i	0.0662383	+	0.997804i	$0.478900\pi$
$180$		0			0
$181$	−7.07994	−	7.07994i	−0.526248	−	0.526248i	0.393203	−	0.919451i	$-0.371367\pi$
$181$	−7.07994	−	7.07994i	−0.526248	−	0.526248i	−0.919451	+	0.393203i	$0.871367\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.84719	+	17.8795i	0.209330	+	1.31452i
$186$		0			0
$187$	0.556057	+	0.556057i	0.0406629	+	0.0406629i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.6011			0.911781			0.455891	−	0.890036i	$-0.349321\pi$
$191$	12.6011			0.911781			0.455891	+	0.890036i	$0.349321\pi$
$192$		0			0
$193$			5.15723i			0.371226i	0.982623	+	0.185613i	$0.0594270\pi$
$193$			5.15723i			0.371226i	−0.982623	+	0.185613i	$0.940573\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.59790	−	3.59790i	−0.256340	−	0.256340i	0.567224	−	0.823564i	$-0.308017\pi$
$197$	−3.59790	−	3.59790i	−0.256340	−	0.256340i	−0.823564	+	0.567224i	$0.808017\pi$
$198$		0			0
$199$	−7.58554			−0.537725			−0.268862	−	0.963179i	$-0.586648\pi$
$199$	−7.58554			−0.537725			−0.268862	+	0.963179i	$0.586648\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.68686	−	3.68686i	0.258767	−	0.258767i
$204$		0			0
$205$	−0.209353	+	0.288659i	−0.0146219	+	0.0201608i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			1.22365i			0.0846417i
$210$		0			0
$211$	−0.605008	−	0.605008i	−0.0416505	−	0.0416505i	0.685975	−	0.727625i	$-0.259376\pi$
$211$	−0.605008	−	0.605008i	−0.0416505	−	0.0416505i	−0.727625	+	0.685975i	$0.759376\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−20.7068	+	3.29743i	−1.41219	+	0.224883i
$216$		0			0
$217$	−8.37827			−0.568754
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.45382	−	5.45382i	−0.366863	−	0.366863i
$222$		0			0
$223$	25.2652			1.69188			0.845940	−	0.533278i	$-0.179040\pi$
$223$	25.2652			1.69188			0.845940	+	0.533278i	$0.179040\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.61823	+	6.61823i	0.439267	+	0.439267i	0.891765	−	0.452498i	$-0.149467\pi$
$227$	6.61823	+	6.61823i	0.439267	+	0.439267i	−0.452498	+	0.891765i	$0.649467\pi$
$228$		0			0
$229$	−0.0446899	−	0.0446899i	−0.00295319	−	0.00295319i	0.705629	−	0.708582i	$-0.250665\pi$
$229$	−0.0446899	−	0.0446899i	−0.00295319	−	0.00295319i	−0.708582	+	0.705629i	$0.750665\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			13.5011i			0.884488i	0.896895	+	0.442244i	$0.145817\pi$
$233$			13.5011i			0.884488i	−0.896895	+	0.442244i	$0.854183\pi$
$234$		0			0
$235$	2.08566	+	1.51265i	0.136054	+	0.0986747i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.58106			−0.361009			−0.180504	−	0.983574i	$-0.557773\pi$
$239$	−5.58106			−0.361009			−0.180504	+	0.983574i	$0.557773\pi$
$240$		0			0
$241$	15.7677			1.01569			0.507845	−	0.861449i	$-0.330442\pi$
$241$	15.7677			1.01569			0.507845	+	0.861449i	$0.330442\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.59096	+	9.08768i	−0.421081	+	0.580591i
$246$		0			0
$247$		−	12.0016i		−	0.763643i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−10.5401	−	10.5401i	−0.665287	−	0.665287i	0.291334	−	0.956621i	$-0.405901\pi$
$251$	−10.5401	−	10.5401i	−0.665287	−	0.665287i	−0.956621	+	0.291334i	$0.905901\pi$
$252$		0			0
$253$	−0.348043	−	0.348043i	−0.0218812	−	0.0218812i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.0698			1.25192			0.625959	−	0.779856i	$-0.284708\pi$
$257$	20.0698			1.25192			0.625959	+	0.779856i	$0.284708\pi$
$258$		0			0
$259$	−8.05510	−	8.05510i	−0.500520	−	0.500520i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−28.6944			−1.76937			−0.884687	−	0.466185i	$-0.845628\pi$
$263$	−28.6944			−1.76937			−0.884687	+	0.466185i	$0.845628\pi$
$264$		0			0
$265$	16.7104	−	2.66103i	1.02651	−	0.163466i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.7007	+	13.7007i	0.835349	+	0.835349i	0.988243	−	0.152894i	$-0.0488592\pi$
$269$	13.7007	+	13.7007i	0.835349	+	0.835349i	−0.152894	+	0.988243i	$0.548859\pi$
$270$		0			0
$271$		−	6.47842i		−	0.393536i	−0.980450	−	0.196768i	$-0.936955\pi$
$271$		−	6.47842i		−	0.393536i	0.980450	−	0.196768i	$-0.0630445\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.563529	+	1.11059i	−0.0339821	+	0.0669708i
$276$		0			0
$277$	−10.7023	+	10.7023i	−0.643041	+	0.643041i	−0.951302	−	0.308261i	$-0.900253\pi$
$277$	−10.7023	+	10.7023i	−0.643041	+	0.643041i	0.308261	+	0.951302i	$0.400253\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−23.3237			−1.39138			−0.695688	−	0.718344i	$-0.744900\pi$
$281$	−23.3237			−1.39138			−0.695688	+	0.718344i	$0.744900\pi$
$282$		0			0
$283$	−7.39967	−	7.39967i	−0.439865	−	0.439865i	0.452102	−	0.891966i	$-0.350674\pi$
$283$	−7.39967	−	7.39967i	−0.439865	−	0.439865i	−0.891966	+	0.452102i	$0.850674\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	0.224366i		−	0.0132439i
$288$		0			0
$289$	−7.03205			−0.413650
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.94867	−	5.94867i	−0.347525	−	0.347525i	0.511662	−	0.859187i	$-0.329030\pi$
$293$	−5.94867	−	5.94867i	−0.347525	−	0.347525i	−0.859187	+	0.511662i	$0.829030\pi$
$294$		0			0
$295$	−14.0078	+	2.23066i	−0.815567	+	0.129874i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.41361	+	3.41361i	0.197414	+	0.197414i
$300$		0			0
$301$	9.32889	−	9.32889i	0.537708	−	0.537708i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.38526	+	21.2583i	0.193839	+	1.21725i
$306$		0			0
$307$	−12.0570	+	12.0570i	−0.688130	+	0.688130i	−0.961818	−	0.273689i	$-0.911756\pi$
$307$	−12.0570	+	12.0570i	−0.688130	+	0.688130i	0.273689	+	0.961818i	$0.411756\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	31.3243i		−	1.77624i	−0.459615	−	0.888118i	$-0.652012\pi$
$311$		−	31.3243i		−	1.77624i	0.459615	−	0.888118i	$-0.347988\pi$
$312$		0			0
$313$	−24.0690			−1.36046			−0.680230	−	0.732999i	$-0.738120\pi$
$313$	−24.0690			−1.36046			−0.680230	+	0.732999i	$0.738120\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.2657	−	10.2657i	0.576579	−	0.576579i	−0.357380	−	0.933959i	$-0.616330\pi$
$317$	10.2657	−	10.2657i	0.576579	−	0.576579i	0.933959	+	0.357380i	$0.116330\pi$
$318$		0			0
$319$		−	0.923046i		−	0.0516807i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	10.9677	+	10.9677i	0.610257	+	0.610257i
$324$		0			0
$325$	5.52710	−	10.8927i	0.306589	−	0.604216i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.62112			−0.0893755
$330$		0			0
$331$	12.7608	−	12.7608i	0.701395	−	0.701395i	−0.263315	−	0.964710i	$-0.584816\pi$
$331$	12.7608	−	12.7608i	0.701395	−	0.701395i	0.964710	+	0.263315i	$0.0848157\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.95953	−	31.1443i	−0.270968	−	1.70159i
$336$		0			0
$337$		−	17.3967i		−	0.947660i	−0.880616	−	0.473830i	$-0.842871\pi$
$337$		−	17.3967i		−	0.947660i	0.880616	−	0.473830i	$-0.157129\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.04880	+	1.04880i	−0.0567956	+	0.0567956i
$342$		0			0
$343$		−	16.9122i		−	0.913175i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.64234	−	9.64234i	0.517628	−	0.517628i	−0.399225	−	0.916853i	$-0.630721\pi$
$347$	9.64234	−	9.64234i	0.517628	−	0.517628i	0.916853	+	0.399225i	$0.130721\pi$
$348$		0			0
$349$	−3.66120	+	3.66120i	−0.195980	+	0.195980i	−0.798274	−	0.602294i	$-0.794253\pi$
$349$	−3.66120	+	3.66120i	−0.195980	+	0.195980i	0.602294	+	0.798274i	$0.294253\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.9960			−1.01106			−0.505528	−	0.862810i	$-0.668702\pi$
$353$	−18.9960			−1.01106			−0.505528	+	0.862810i	$0.668702\pi$
$354$		0			0
$355$	−0.172226	−	0.124909i	−0.00914081	−	0.00662949i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			8.71770i			0.460103i	0.973178	+	0.230051i	$0.0738894\pi$
$359$			8.71770i			0.460103i	−0.973178	+	0.230051i	$0.926111\pi$
$360$		0			0
$361$			5.13530i			0.270279i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.4910	−	14.4651i	0.549124	−	0.757138i
$366$		0			0
$367$	28.0501			1.46420			0.732101	−	0.681196i	$-0.238540\pi$
$367$	28.0501			1.46420			0.732101	+	0.681196i	$0.238540\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.52841	+	7.52841i	−0.390856	+	0.390856i
$372$		0			0
$373$	−4.90740	+	4.90740i	−0.254096	+	0.254096i	−0.822647	−	0.568552i	$-0.807504\pi$
$373$	−4.90740	+	4.90740i	−0.254096	+	0.254096i	0.568552	+	0.822647i	$0.307504\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			9.05326i			0.466267i
$378$		0			0
$379$	−26.0620	+	26.0620i	−1.33872	+	1.33872i	−0.441412	+	0.897305i	$0.645522\pi$
$379$	−26.0620	+	26.0620i	−1.33872	+	1.33872i	−0.897305	+	0.441412i	$0.854478\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$			6.91314i			0.353245i	0.984279	+	0.176623i	$0.0565172\pi$
$383$			6.91314i			0.353245i	−0.984279	+	0.176623i	$0.943483\pi$
$384$		0			0
$385$	−0.123231	−	0.773850i	−0.00628042	−	0.0394391i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.5222	+	14.5222i	−0.736302	+	0.736302i	−0.971860	−	0.235558i	$-0.924308\pi$
$389$	−14.5222	+	14.5222i	−0.736302	+	0.736302i	0.235558	+	0.971860i	$0.424308\pi$
$390$		0			0
$391$	−6.23906			−0.315523
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.2565	+	7.43864i	0.516060	+	0.374279i
$396$		0			0
$397$	18.3367	+	18.3367i	0.920291	+	0.920291i	0.997050	−	0.0767588i	$-0.0244571\pi$
$397$	18.3367	+	18.3367i	0.920291	+	0.920291i	−0.0767588	+	0.997050i	$0.524457\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	33.5380i		−	1.67481i	−0.546585	−	0.837404i	$-0.684073\pi$
$401$		−	33.5380i		−	1.67481i	0.546585	−	0.837404i	$-0.315927\pi$
$402$		0			0
$403$	10.2866	−	10.2866i	0.512414	−	0.512414i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.01669			−0.0999634
$408$		0			0
$409$			18.0044i			0.890260i	0.895466	+	0.445130i	$0.146842\pi$
$409$			18.0044i			0.890260i	−0.895466	+	0.445130i	$0.853158\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.31084	−	6.31084i	0.310536	−	0.310536i
$414$		0			0
$415$	−38.3096	+	6.10056i	−1.88054	+	0.299465i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.7671	−	16.7671i	0.819126	−	0.819126i	−0.166856	−	0.985981i	$-0.553361\pi$
$419$	16.7671	−	16.7671i	0.819126	−	0.819126i	0.985981	+	0.166856i	$0.0533614\pi$
$420$		0			0
$421$	9.17528	+	9.17528i	0.447176	+	0.447176i	0.894415	−	0.447239i	$-0.147593\pi$
$421$	9.17528	+	9.17528i	0.447176	+	0.447176i	−0.447239	+	0.894415i	$0.647593\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.90331	+	15.0052i	0.237846	+	0.727859i
$426$		0			0
$427$	−9.57736	−	9.57736i	−0.463481	−	0.463481i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−36.6726			−1.76646			−0.883228	−	0.468943i	$-0.844635\pi$
$431$	−36.6726			−1.76646			−0.883228	+	0.468943i	$0.844635\pi$
$432$		0			0
$433$			28.1455i			1.35259i	0.736633	+	0.676293i	$0.236414\pi$
$433$			28.1455i			1.35259i	−0.736633	+	0.676293i	$0.763586\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.86480	−	6.86480i	−0.328388	−	0.328388i
$438$		0			0
$439$	3.32665			0.158772			0.0793862	−	0.996844i	$-0.474704\pi$
$439$	3.32665			0.158772			0.0793862	+	0.996844i	$0.474704\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.03644	+	6.03644i	−0.286800	+	0.286800i	−0.835814	−	0.549013i	$-0.815004\pi$
$443$	−6.03644	+	6.03644i	−0.286800	+	0.286800i	0.549013	+	0.835814i	$0.315004\pi$
$444$		0			0
$445$	−14.3489	+	19.7844i	−0.680203	+	0.937871i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			14.2691i			0.673402i	0.941612	+	0.336701i	$0.109311\pi$
$449$			14.2691i			0.673402i	−0.941612	+	0.336701i	$0.890689\pi$
$450$		0			0
$451$	−0.0280862	−	0.0280862i	−0.00132253	−	0.00132253i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.20865	+	7.58994i	0.0566624	+	0.355822i
$456$		0			0
$457$	−25.0611			−1.17231			−0.586154	−	0.810200i	$-0.699359\pi$
$457$	−25.0611			−1.17231			−0.586154	+	0.810200i	$0.699359\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.6030	−	11.6030i	−0.540407	−	0.540407i	0.383241	−	0.923648i	$-0.374808\pi$
$461$	−11.6030	−	11.6030i	−0.540407	−	0.540407i	−0.923648	+	0.383241i	$0.874808\pi$
$462$		0			0
$463$	−8.74913			−0.406607			−0.203303	−	0.979116i	$-0.565168\pi$
$463$	−8.74913			−0.406607			−0.203303	+	0.979116i	$0.565168\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.3047	−	19.3047i	−0.893316	−	0.893316i	0.101518	−	0.994834i	$-0.467630\pi$
$467$	−19.3047	−	19.3047i	−0.893316	−	0.893316i	−0.994834	+	0.101518i	$0.967630\pi$
$468$		0			0
$469$	14.0312	+	14.0312i	0.647901	+	0.647901i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	2.33559i		−	0.107391i
$474$		0			0
$475$	−11.1150	+	21.9052i	−0.509993	+	1.00508i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	19.9695			0.912431			0.456215	−	0.889869i	$-0.349205\pi$
$479$	19.9695			0.912431			0.456215	+	0.889869i	$0.349205\pi$
$480$		0			0
$481$	19.7797			0.901877
$482$		0			0
$483$		0			0
$484$		0			0
$485$	18.9003	+	13.7077i	0.858219	+	0.622434i
$486$		0			0
$487$		−	34.8592i		−	1.57962i	−0.613351	−	0.789811i	$-0.710179\pi$
$487$		−	34.8592i		−	1.57962i	0.613351	−	0.789811i	$-0.289821\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−21.4659	−	21.4659i	−0.968743	−	0.968743i	0.0307829	−	0.999526i	$-0.490200\pi$
$491$	−21.4659	−	21.4659i	−0.968743	−	0.968743i	−0.999526	+	0.0307829i	$0.990200\pi$
$492$		0			0
$493$	−8.27333	−	8.27333i	−0.372612	−	0.372612i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.133866			0.00600471
$498$		0			0
$499$	18.0781	+	18.0781i	0.809287	+	0.809287i	0.984526	−	0.175239i	$-0.0560697\pi$
$499$	18.0781	+	18.0781i	0.809287	+	0.809287i	−0.175239	+	0.984526i	$0.556070\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.90394			−0.174068			−0.0870341	−	0.996205i	$-0.527739\pi$
$503$	−3.90394			−0.174068			−0.0870341	+	0.996205i	$0.527739\pi$
$504$		0			0
$505$	2.26042	+	14.1947i	0.100587	+	0.631656i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.0778	−	11.0778i	−0.491014	−	0.491014i	0.417612	−	0.908626i	$-0.362867\pi$
$509$	−11.0778	−	11.0778i	−0.491014	−	0.491014i	−0.908626	+	0.417612i	$0.862867\pi$
$510$		0			0
$511$			11.2433i			0.497374i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	13.8597	+	10.0519i	0.610732	+	0.442941i
$516$		0			0
$517$	−0.202933	+	0.202933i	−0.00892500	+	0.00892500i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.61052			−0.114369			−0.0571844	−	0.998364i	$-0.518212\pi$
$521$	−2.61052			−0.114369			−0.0571844	+	0.998364i	$0.518212\pi$
$522$		0			0
$523$	21.2735	+	21.2735i	0.930226	+	0.930226i	0.997720	−	0.0674935i	$-0.0215002\pi$
$523$	21.2735	+	21.2735i	0.930226	+	0.930226i	−0.0674935	+	0.997720i	$0.521500\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			18.8009i			0.818980i
$528$		0			0
$529$	−19.0949			−0.830213
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.275471	+	0.275471i	0.0119320	+	0.0119320i
$534$		0			0
$535$	2.11448	+	13.2782i	0.0914168	+	0.574068i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.884224	−	0.884224i	−0.0380862	−	0.0380862i
$540$		0			0
$541$	−8.92150	+	8.92150i	−0.383565	+	0.383565i	−0.872385	−	0.488820i	$-0.837428\pi$
$541$	−8.92150	+	8.92150i	−0.383565	+	0.383565i	0.488820	+	0.872385i	$0.337428\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.0899300	+	0.564732i	0.00385218	+	0.0241905i
$546$		0			0
$547$	−24.0470	+	24.0470i	−1.02818	+	1.02818i	−0.0285840	+	0.999591i	$0.509100\pi$
$547$	−24.0470	+	24.0470i	−1.02818	+	1.02818i	−0.999591	+	0.0285840i	$0.990900\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	18.2062i		−	0.775609i
$552$		0			0
$553$	−7.97205			−0.339006
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.5090	+	17.5090i	−0.741879	+	0.741879i	−0.972939	−	0.231060i	$-0.925780\pi$
$557$	−17.5090	+	17.5090i	−0.741879	+	0.741879i	0.231060	+	0.972939i	$0.425780\pi$
$558$		0			0
$559$			22.9076i			0.968886i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.2032	+	11.2032i	0.472157	+	0.472157i	0.902612	−	0.430455i	$-0.141647\pi$
$563$	11.2032	+	11.2032i	0.472157	+	0.472157i	−0.430455	+	0.902612i	$0.641647\pi$
$564$		0			0
$565$	9.04353	−	12.4693i	0.380464	−	0.524588i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.83805			−0.202821			−0.101411	−	0.994845i	$-0.532336\pi$
$569$	−4.83805			−0.202821			−0.101411	+	0.994845i	$0.532336\pi$
$570$		0			0
$571$	−9.64695	+	9.64695i	−0.403712	+	0.403712i	−0.879539	−	0.475827i	$-0.842149\pi$
$571$	−9.64695	+	9.64695i	−0.403712	+	0.403712i	0.475827	+	0.879539i	$0.342149\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.06904	−	9.39194i	−0.127988	−	0.391671i
$576$		0			0
$577$		−	18.0261i		−	0.750438i	−0.926936	−	0.375219i	$-0.877568\pi$
$577$		−	18.0261i		−	0.750438i	0.926936	−	0.375219i	$-0.122432\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	17.2593	−	17.2593i	0.716038	−	0.716038i
$582$		0			0
$583$			1.88482i			0.0780614i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.25140	+	5.25140i	−0.216749	+	0.216749i	−0.807127	−	0.590378i	$-0.798979\pi$
$587$	−5.25140	+	5.25140i	−0.216749	+	0.216749i	0.590378	+	0.807127i	$0.298979\pi$
$588$		0			0
$589$	−20.6865	+	20.6865i	−0.852373	+	0.852373i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0811054			0.00333060			0.00166530	−	0.999999i	$-0.499470\pi$
$593$	0.0811054			0.00333060			0.00166530	+	0.999999i	$0.499470\pi$
$594$		0			0
$595$	−8.04060	−	5.83155i	−0.329632	−	0.239070i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	8.29253i		−	0.338824i	−0.985545	−	0.169412i	$-0.945813\pi$
$599$		−	8.29253i		−	0.338824i	0.985545	−	0.169412i	$-0.0541868\pi$
$600$		0			0
$601$			5.82196i			0.237483i	0.992925	+	0.118741i	$0.0378859\pi$
$601$			5.82196i			0.237483i	−0.992925	+	0.118741i	$0.962114\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	19.7990	+	14.3595i	0.804944	+	0.583796i
$606$		0			0
$607$	22.0548			0.895178			0.447589	−	0.894239i	$-0.352283\pi$
$607$	22.0548			0.895178			0.447589	+	0.894239i	$0.352283\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.99038	−	1.99038i	0.0805220	−	0.0805220i
$612$		0			0
$613$	14.9250	−	14.9250i	0.602816	−	0.602816i	−0.338243	−	0.941059i	$-0.609832\pi$
$613$	14.9250	−	14.9250i	0.602816	−	0.602816i	0.941059	+	0.338243i	$0.109832\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	31.5403i		−	1.26976i	−0.772609	−	0.634882i	$-0.781049\pi$
$617$		−	31.5403i		−	1.26976i	0.772609	−	0.634882i	$-0.218951\pi$
$618$		0			0
$619$	−6.89013	+	6.89013i	−0.276938	+	0.276938i	−0.831885	−	0.554947i	$-0.812738\pi$
$619$	−6.89013	+	6.89013i	−0.276938	+	0.276938i	0.554947	+	0.831885i	$0.312738\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	15.3778i		−	0.616100i
$624$		0			0
$625$	−20.1760	+	14.7624i	−0.807042	+	0.590494i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−18.0757	+	18.0757i	−0.720725	+	0.720725i
$630$		0			0
$631$	32.9043			1.30990			0.654950	−	0.755672i	$-0.272690\pi$
$631$	32.9043			1.30990			0.654950	+	0.755672i	$0.272690\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.17625	+	5.75825i	−0.165729	+	0.228509i
$636$		0			0
$637$	8.67249	+	8.67249i	0.343617	+	0.343617i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	28.3921i		−	1.12142i	−0.828013	−	0.560710i	$-0.810528\pi$
$641$		−	28.3921i		−	1.12142i	0.828013	−	0.560710i	$-0.189472\pi$
$642$		0			0
$643$	2.71547	−	2.71547i	0.107088	−	0.107088i	−0.651533	−	0.758621i	$-0.725874\pi$
$643$	2.71547	−	2.71547i	0.107088	−	0.107088i	0.758621	+	0.651533i	$0.225874\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	33.2882			1.30869			0.654346	−	0.756195i	$-0.272944\pi$
$647$	33.2882			1.30869			0.654346	+	0.756195i	$0.272944\pi$
$648$		0			0
$649$		−	1.57999i		−	0.0620200i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.82719	+	4.82719i	−0.188902	+	0.188902i	−0.795221	−	0.606319i	$-0.792645\pi$
$653$	−4.82719	+	4.82719i	−0.188902	+	0.188902i	0.606319	+	0.795221i	$0.292645\pi$
$654$		0			0
$655$	4.22442	+	26.5280i	0.165062	+	1.03653i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−22.5484	+	22.5484i	−0.878359	+	0.878359i	−0.993365	−	0.115005i	$-0.963311\pi$
$659$	−22.5484	+	22.5484i	−0.878359	+	0.878359i	0.115005	+	0.993365i	$0.463311\pi$
$660$		0			0
$661$	17.3551	+	17.3551i	0.675035	+	0.675035i	0.958872	−	0.283838i	$-0.0916077\pi$
$661$	17.3551	+	17.3551i	0.675035	+	0.675035i	−0.283838	+	0.958872i	$0.591608\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.43061	−	15.2634i	−0.0942548	−	0.591890i
$666$		0			0
$667$	5.17838	+	5.17838i	0.200508	+	0.200508i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.39780			−0.0925661
$672$		0			0
$673$		−	20.2889i		−	0.782080i	−0.920374	−	0.391040i	$-0.872115\pi$
$673$		−	20.2889i		−	0.782080i	0.920374	−	0.391040i	$-0.127885\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.349388	+	0.349388i	0.0134281	+	0.0134281i	0.713789	−	0.700361i	$-0.246978\pi$
$677$	0.349388	+	0.349388i	0.0134281	+	0.0134281i	−0.700361	+	0.713789i	$0.746978\pi$
$678$		0			0
$679$	−14.6906			−0.563775
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.40464	+	4.40464i	−0.168539	+	0.168539i	−0.786337	−	0.617798i	$-0.788025\pi$
$683$	−4.40464	+	4.40464i	−0.168539	+	0.168539i	0.617798	+	0.786337i	$0.288025\pi$
$684$		0			0
$685$	−27.3351	−	19.8252i	−1.04442	−	0.757480i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		−	18.4864i		−	0.704276i
$690$		0			0
$691$	22.7615	+	22.7615i	0.865890	+	0.865890i	0.992014	−	0.126125i	$-0.0402539\pi$
$691$	22.7615	+	22.7615i	0.865890	+	0.865890i	−0.126125	+	0.992014i	$0.540254\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.80034	+	36.4243i	0.220020	+	1.38165i
$696$		0			0
$697$	−0.503478			−0.0190706
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.9589	−	34.9589i	−1.32038	−	1.32038i	−0.913467	−	0.406913i	$-0.866605\pi$
$701$	−34.9589	−	34.9589i	−1.32038	−	1.32038i	−0.406913	−	0.913467i	$-0.633395\pi$
$702$		0			0
$703$	−39.7771			−1.50022
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.39503	−	6.39503i	−0.240510	−	0.240510i
$708$		0			0
$709$	−20.7652	−	20.7652i	−0.779854	−	0.779854i	0.199952	−	0.979806i	$-0.435922\pi$
$709$	−20.7652	−	20.7652i	−0.779854	−	0.779854i	−0.979806	+	0.199952i	$0.935922\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	11.7677i		−	0.440704i
$714$		0			0
$715$	1.10141	+	0.798814i	0.0411905	+	0.0298740i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.48453			−0.353713			−0.176857	−	0.984237i	$-0.556593\pi$
$719$	−9.48453			−0.353713			−0.176857	+	0.984237i	$0.556593\pi$
$720$		0			0
$721$	−10.7727			−0.401198
$722$		0			0
$723$		0			0
$724$		0			0
$725$	8.38451	−	16.5239i	0.311393	−	0.613684i
$726$		0			0
$727$			29.4631i			1.09272i	0.837549	+	0.546362i	$0.183988\pi$
$727$			29.4631i			1.09272i	−0.837549	+	0.546362i	$0.816012\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−20.9341	−	20.9341i	−0.774275	−	0.774275i
$732$		0			0
$733$	−13.5703	−	13.5703i	−0.501231	−	0.501231i	0.410590	−	0.911820i	$-0.365323\pi$
$733$	−13.5703	−	13.5703i	−0.501231	−	0.501231i	−0.911820	+	0.410590i	$0.865323\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.51287			0.129398
$738$		0			0
$739$	1.19592	+	1.19592i	0.0439927	+	0.0439927i	0.728761	−	0.684768i	$-0.240097\pi$
$739$	1.19592	+	1.19592i	0.0439927	+	0.0439927i	−0.684768	+	0.728761i	$0.740097\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	48.8695			1.79285			0.896424	−	0.443197i	$-0.146156\pi$
$743$	48.8695			1.79285			0.896424	+	0.443197i	$0.146156\pi$
$744$		0			0
$745$	5.53406	+	34.7521i	0.202752	+	1.27322i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.98214	−	5.98214i	−0.218583	−	0.218583i
$750$		0			0
$751$			17.8326i			0.650721i	0.945590	+	0.325360i	$0.105486\pi$
$751$			17.8326i			0.650721i	−0.945590	+	0.325360i	$0.894514\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−28.7199	+	39.5993i	−1.04522	+	1.44117i
$756$		0			0
$757$	19.7676	−	19.7676i	0.718467	−	0.718467i	−0.249824	−	0.968291i	$-0.580373\pi$
$757$	19.7676	−	19.7676i	0.718467	−	0.718467i	0.968291	+	0.249824i	$0.0803728\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.72357			−0.134979			−0.0674896	−	0.997720i	$-0.521499\pi$
$761$	−3.72357			−0.134979			−0.0674896	+	0.997720i	$0.521499\pi$
$762$		0			0
$763$	−0.254425	−	0.254425i	−0.00921079	−	0.00921079i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			15.4966i			0.559549i
$768$		0			0
$769$	−17.9937			−0.648868			−0.324434	−	0.945908i	$-0.605174\pi$
$769$	−17.9937			−0.648868			−0.324434	+	0.945908i	$0.605174\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−14.5506	−	14.5506i	−0.523350	−	0.523350i	0.395232	−	0.918582i	$-0.370664\pi$
$773$	−14.5506	−	14.5506i	−0.523350	−	0.523350i	−0.918582	+	0.395232i	$0.870664\pi$
$774$		0			0
$775$	−28.3019	+	9.24831i	−1.01663	+	0.332209i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.553973	−	0.553973i	−0.0198482	−	0.0198482i
$780$		0			0
$781$	0.0167574	−	0.0167574i	0.000599629	−	0.000599629i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−48.0705	+	7.65492i	−1.71571	+	0.273216i
$786$		0			0
$787$	−27.4478	+	27.4478i	−0.978410	+	0.978410i	−0.999772	−	0.0213618i	$-0.993200\pi$
$787$	−27.4478	+	27.4478i	−0.978410	+	0.978410i	0.0213618	+	0.999772i	$0.493200\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			9.69203i			0.344609i
$792$		0			0
$793$	23.5177			0.835137
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−33.5148	+	33.5148i	−1.18715	+	1.18715i	−0.209303	+	0.977851i	$0.567120\pi$
$797$	−33.5148	+	33.5148i	−1.18715	+	1.18715i	−0.977851	+	0.209303i	$0.932880\pi$
$798$		0			0
$799$			3.63781i			0.128697i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.40744	+	1.40744i	0.0496676	+	0.0496676i
$804$		0			0
$805$	5.03271	+	3.65004i	0.177380	+	0.128647i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−44.1238			−1.55131			−0.775654	−	0.631158i	$-0.782580\pi$
$809$	−44.1238			−1.55131			−0.775654	+	0.631158i	$0.782580\pi$
$810$		0			0
$811$	27.5547	−	27.5547i	0.967578	−	0.967578i	−0.0319126	−	0.999491i	$-0.510160\pi$
$811$	27.5547	−	27.5547i	0.967578	−	0.967578i	0.999491	+	0.0319126i	$0.0101598\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.43737	+	15.3059i	0.0853772	+	0.536142i
$816$		0			0
$817$		−	46.0673i		−	1.61169i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.29165	+	8.29165i	−0.289381	+	0.289381i	−0.836835	−	0.547455i	$-0.815597\pi$
$821$	−8.29165	+	8.29165i	−0.289381	+	0.289381i	0.547455	+	0.836835i	$0.315597\pi$
$822$		0			0
$823$			16.2616i			0.566845i	0.958995	+	0.283422i	$0.0914698\pi$
$823$			16.2616i			0.566845i	−0.958995	+	0.283422i	$0.908530\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.8727	−	18.8727i	0.656266	−	0.656266i	−0.298228	−	0.954495i	$-0.596396\pi$
$827$	18.8727	−	18.8727i	0.656266	−	0.656266i	0.954495	+	0.298228i	$0.0963956\pi$
$828$		0			0
$829$	7.56155	−	7.56155i	0.262624	−	0.262624i	−0.563495	−	0.826119i	$-0.690544\pi$
$829$	7.56155	−	7.56155i	0.262624	−	0.262624i	0.826119	+	0.563495i	$0.190544\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.8507			−0.549195
$834$		0			0
$835$	22.8927	−	31.5648i	0.792236	−	1.09234i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	1.30357i		−	0.0450042i	−0.999747	−	0.0225021i	$-0.992837\pi$
$839$		−	1.30357i		−	0.0450042i	0.999747	−	0.0225021i	$-0.00716324\pi$
$840$		0			0
$841$		−	15.2664i		−	0.526427i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.7288	+	9.23175i	0.437885	+	0.317582i
$846$		0			0
$847$	−15.3892			−0.528778
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.3138	−	11.3138i	0.387832	−	0.387832i
$852$		0			0
$853$	−20.3937	+	20.3937i	−0.698268	+	0.698268i	−0.964037	−	0.265769i	$-0.914374\pi$
$853$	−20.3937	+	20.3937i	−0.698268	+	0.698268i	0.265769	+	0.964037i	$0.414374\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	17.9066i		−	0.611678i	−0.952083	−	0.305839i	$-0.901063\pi$
$857$		−	17.9066i		−	0.611678i	0.952083	−	0.305839i	$-0.0989369\pi$
$858$		0			0
$859$	−17.0524	+	17.0524i	−0.581821	+	0.581821i	−0.935403	−	0.353582i	$-0.884963\pi$
$859$	−17.0524	+	17.0524i	−0.581821	+	0.581821i	0.353582	+	0.935403i	$0.384963\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1.33105i			0.0453095i	0.999743	+	0.0226548i	$0.00721185\pi$
$863$			1.33105i			0.0453095i	−0.999743	+	0.0226548i	$0.992788\pi$
$864$		0			0
$865$	8.66746	+	54.4289i	0.294703	+	1.85064i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.997947	+	0.997947i	−0.0338530	+	0.0338530i
$870$		0			0
$871$	−34.4543			−1.16744
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.82326	−	14.9725i	0.163056	−	0.506162i
$876$		0			0
$877$	19.7763	+	19.7763i	0.667799	+	0.667799i	0.957206	−	0.289407i	$-0.0934581\pi$
$877$	19.7763	+	19.7763i	0.667799	+	0.667799i	−0.289407	+	0.957206i	$0.593458\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			16.6926i			0.562389i	0.959651	+	0.281194i	$0.0907305\pi$
$881$			16.6926i			0.562389i	−0.959651	+	0.281194i	$0.909269\pi$
$882$		0			0
$883$	17.2285	−	17.2285i	0.579785	−	0.579785i	−0.355059	−	0.934844i	$-0.615539\pi$
$883$	17.2285	−	17.2285i	0.579785	−	0.579785i	0.934844	+	0.355059i	$0.115539\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.0017			0.604436			0.302218	−	0.953239i	$-0.402273\pi$
$887$	18.0017			0.604436			0.302218	+	0.953239i	$0.402273\pi$
$888$		0			0
$889$		−	4.47572i		−	0.150111i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.00266	+	4.00266i	−0.133944	+	0.133944i
$894$		0			0
$895$	−6.19818	−	38.9226i	−0.207182	−	1.30104i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	15.6046	−	15.6046i	0.520443	−	0.520443i
$900$		0			0
$901$	16.8938	+	16.8938i	0.562814	+	0.562814i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	22.1102	−	3.52090i	0.734967	−	0.117039i
$906$		0			0
$907$	−25.3515	−	25.3515i	−0.841784	−	0.841784i	0.147307	−	0.989091i	$-0.452940\pi$
$907$	−25.3515	−	25.3515i	−0.841784	−	0.841784i	−0.989091	+	0.147307i	$0.952940\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−54.8371			−1.81683			−0.908417	−	0.418066i	$-0.862708\pi$
$911$	−54.8371			−1.81683			−0.908417	+	0.418066i	$0.862708\pi$
$912$		0			0
$913$		−	4.32107i		−	0.143007i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.9515	−	11.9515i	−0.394672	−	0.394672i
$918$		0			0
$919$	26.4141			0.871321			0.435661	−	0.900111i	$-0.356515\pi$
$919$	26.4141			0.871321			0.435661	+	0.900111i	$0.356515\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.164357	+	0.164357i	−0.00540989	+	0.00540989i
$924$		0			0
$925$	−36.1018	−	18.3186i	−1.18702	−	0.602312i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			43.1302i			1.41506i	0.706685	+	0.707528i	$0.250190\pi$
$929$			43.1302i			1.41506i	−0.706685	+	0.707528i	$0.749810\pi$
$930$		0			0
$931$	−17.4404	−	17.4404i	−0.571588	−	0.571588i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.73653	+	0.276531i	−0.0567904	+	0.00904352i
$936$		0			0
$937$	17.0711			0.557689			0.278845	−	0.960336i	$-0.410049\pi$
$937$	17.0711			0.557689			0.278845	+	0.960336i	$0.410049\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−27.6649	−	27.6649i	−0.901850	−	0.901850i	0.0937464	−	0.995596i	$-0.470116\pi$
$941$	−27.6649	−	27.6649i	−0.901850	−	0.901850i	−0.995596	+	0.0937464i	$0.970116\pi$
$942$		0			0
$943$	0.315133			0.0102621
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−38.6985	−	38.6985i	−1.25753	−	1.25753i	−0.952267	−	0.305265i	$-0.901255\pi$
$947$	−38.6985	−	38.6985i	−1.25753	−	1.25753i	−0.305265	−	0.952267i	$-0.598745\pi$
$948$		0			0
$949$	−13.8042	−	13.8042i	−0.448104	−	0.448104i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	21.7149i		−	0.703413i	−0.936110	−	0.351707i	$-0.885601\pi$
$953$		−	21.7149i		−	0.703413i	0.936110	−	0.351707i	$-0.114399\pi$
$954$		0			0
$955$	−16.5428	+	22.8094i	−0.535313	+	0.738095i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	21.2468			0.686094
$960$		0			0
$961$	−4.46104			−0.143905
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.33520	−	6.77047i	−0.300511	−	0.217949i
$966$		0			0
$967$			7.39782i			0.237898i	0.992900	+	0.118949i	$0.0379525\pi$
$967$			7.39782i			0.237898i	−0.992900	+	0.118949i	$0.962048\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.0731	+	14.0731i	0.451626	+	0.451626i	0.895894	−	0.444268i	$-0.146536\pi$
$971$	14.0731	+	14.0731i	0.451626	+	0.451626i	−0.444268	+	0.895894i	$0.646536\pi$
$972$		0			0
$973$	−16.4100	−	16.4100i	−0.526080	−	0.526080i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	60.5514			1.93721			0.968605	−	0.248603i	$-0.0799714\pi$
$977$	60.5514			1.93721			0.968605	+	0.248603i	$0.0799714\pi$
$978$		0			0
$979$	−1.92501	−	1.92501i	−0.0615235	−	0.0615235i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.63756			0.211705			0.105853	−	0.994382i	$-0.466243\pi$
$983$	6.63756			0.211705			0.105853	+	0.994382i	$0.466243\pi$
$984$		0			0
$985$	11.2360	−	1.78926i	0.358008	−	0.0570106i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13.1029	+	13.1029i	0.416648	+	0.416648i
$990$		0			0
$991$		−	48.7239i		−	1.54777i	−0.633328	−	0.773883i	$-0.718312\pi$
$991$		−	48.7239i		−	1.54777i	0.633328	−	0.773883i	$-0.281688\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.95839	−	13.7307i	0.315702	−	0.435293i
$996$		0			0
$997$	−40.6755	+	40.6755i	−1.28821	+	1.28821i	−0.352330	+	0.935876i	$0.614611\pi$
$997$	−40.6755	+	40.6755i	−1.28821	+	1.28821i	−0.935876	+	0.352330i	$0.885389\pi$
$998$		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.719.16		96
3.2	odd	2	inner	2880.2.u.a.719.33		96
4.3	odd	2		720.2.u.a.539.47	yes	96
5.4	even	2	inner	2880.2.u.a.719.9		96
12.11	even	2		720.2.u.a.539.2	yes	96
15.14	odd	2	inner	2880.2.u.a.719.40		96
16.3	odd	4	inner	2880.2.u.a.2159.40		96
16.13	even	4		720.2.u.a.179.48	yes	96
20.19	odd	2		720.2.u.a.539.1	yes	96
48.29	odd	4		720.2.u.a.179.1	✓	96
48.35	even	4	inner	2880.2.u.a.2159.9		96
60.59	even	2		720.2.u.a.539.48	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.33		96
80.29	even	4		720.2.u.a.179.2	yes	96
240.29	odd	4		720.2.u.a.179.47	yes	96
240.179	even	4	inner	2880.2.u.a.2159.16		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.1	✓	96	48.29	odd	4
720.2.u.a.179.2	yes	96	80.29	even	4
720.2.u.a.179.47	yes	96	240.29	odd	4
720.2.u.a.179.48	yes	96	16.13	even	4
720.2.u.a.539.1	yes	96	20.19	odd	2
720.2.u.a.539.2	yes	96	12.11	even	2
720.2.u.a.539.47	yes	96	4.3	odd	2
720.2.u.a.539.48	yes	96	60.59	even	2
2880.2.u.a.719.9		96	5.4	even	2	inner
2880.2.u.a.719.16		96	1.1	even	1	trivial
2880.2.u.a.719.33		96	3.2	odd	2	inner
2880.2.u.a.719.40		96	15.14	odd	2	inner
2880.2.u.a.2159.9		96	48.35	even	4	inner
2880.2.u.a.2159.16		96	240.179	even	4	inner
2880.2.u.a.2159.33		96	80.19	odd	4	inner
2880.2.u.a.2159.40		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)

\(f(q)\)	\(=\)	\(q+(-1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +O(q^{10})\)	\(q+(-1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +(-0.176123 - 0.176123i) q^{11} +(1.72742 + 1.72742i) q^{13} -3.15721 q^{17} +(-3.47385 - 3.47385i) q^{19} +1.97613 q^{23} +(-1.55305 - 4.75269i) q^{25} +(2.62046 + 2.62046i) q^{29} -5.95492i q^{31} +(2.54675 + 1.84706i) q^{35} +(5.72522 - 5.72522i) q^{37} +0.159470 q^{41} +(6.63058 + 6.63058i) q^{43} -1.15223i q^{47} +5.02049 q^{49} +(-5.35087 - 5.35087i) q^{53} +(0.550020 - 0.0875872i) q^{55} +(4.48547 + 4.48547i) q^{59} +(6.80718 - 6.80718i) q^{61} +(-5.39461 + 0.859057i) q^{65} +(-9.97278 + 9.97278i) q^{67} +0.0951463i q^{71} -7.99125 q^{73} +(-0.247796 + 0.247796i) q^{77} -5.66620i q^{79} +(12.2672 + 12.2672i) q^{83} +(4.14481 - 5.71492i) q^{85} +10.9299 q^{89} +(2.43039 - 2.43039i) q^{91} +(10.8486 - 1.72757i) q^{95} -10.4415i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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

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