LMFDB - Embedded newform 3024.2.r.k.2017.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1009,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("3024.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.r (of order $3$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2017.3
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	3024.2017
Dual form			3024.2.r.k.1009.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26604 + 2.19285i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(1.26604 + 2.19285i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.233956 + 0.405223i) q^{11} +(-2.91147 - 5.04282i) q^{13} -3.87939 q^{17} +2.18479 q^{19} +(0.0530334 + 0.0918566i) q^{23} +(-0.705737 + 1.22237i) q^{25} +(4.39053 - 7.60462i) q^{29} +(-3.84002 - 6.65111i) q^{31} +2.53209 q^{35} -7.68004 q^{37} +(-1.11334 - 1.92836i) q^{41} +(0.613341 - 1.06234i) q^{43} +(2.66637 - 4.61830i) q^{47} +(-0.500000 - 0.866025i) q^{49} +0.716881 q^{53} -1.18479 q^{55} +(-0.368241 - 0.637812i) q^{59} +(-0.479055 + 0.829748i) q^{61} +(7.37211 - 12.7689i) q^{65} +(-4.81908 - 8.34689i) q^{67} +13.2344 q^{71} -10.2686 q^{73} +(0.233956 + 0.405223i) q^{77} +(-6.31908 + 10.9450i) q^{79} +(1.36571 - 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +8.11381 q^{89} -5.82295 q^{91} +(2.76604 + 4.79093i) q^{95} +(6.80200 - 11.7814i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 + 3 * q^7	$ 6 q + 3 q^{5} + 3 q^{7} - 6 q^{11} + 3 q^{13} - 12 q^{17} + 6 q^{19} - 12 q^{23} + 6 q^{25} + 9 q^{29} - 3 q^{31} + 6 q^{35} - 6 q^{37} - 3 q^{43} - 3 q^{47} - 3 q^{49} - 12 q^{53} + 3 q^{59} - 6 q^{61} + 15 q^{65} - 12 q^{67} + 18 q^{71} - 42 q^{73} + 6 q^{77} - 21 q^{79} + 18 q^{83} - 9 q^{85} - 24 q^{89} + 6 q^{91} + 12 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 - 6 * q^11 + 3 * q^13 - 12 * q^17 + 6 * q^19 - 12 * q^23 + 6 * q^25 + 9 * q^29 - 3 * q^31 + 6 * q^35 - 6 * q^37 - 3 * q^43 - 3 * q^47 - 3 * q^49 - 12 * q^53 + 3 * q^59 - 6 * q^61 + 15 * q^65 - 12 * q^67 + 18 * q^71 - 42 * q^73 + 6 * q^77 - 21 * q^79 + 18 * q^83 - 9 * q^85 - 24 * q^89 + 6 * q^91 + 12 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	0.996938	+	0.0782003i	$0.0249174\pi$
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	−0.430745	+	0.902473i	$0.641749\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.233956	+	0.405223i	−0.0705403	+	0.122179i	−0.899138	−	0.437665i	$-0.855806\pi$
$11$	−0.233956	+	0.405223i	−0.0705403	+	0.122179i	0.828598	+	0.559844i	$0.189139\pi$
$12$		0			0
$13$	−2.91147	−	5.04282i	−0.807498	−	1.39863i	−0.914592	−	0.404378i	$-0.867488\pi$
$13$	−2.91147	−	5.04282i	−0.807498	−	1.39863i	0.107094	−	0.994249i	$-0.465845\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.87939			−0.940889			−0.470445	−	0.882430i	$-0.655906\pi$
$17$	−3.87939			−0.940889			−0.470445	+	0.882430i	$0.655906\pi$
$18$		0			0
$19$	2.18479			0.501226			0.250613	−	0.968087i	$-0.419368\pi$
$19$	2.18479			0.501226			0.250613	+	0.968087i	$0.419368\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.0530334	+	0.0918566i	0.0110582	+	0.0191534i	0.871502	−	0.490393i	$-0.163147\pi$
$23$	0.0530334	+	0.0918566i	0.0110582	+	0.0191534i	−0.860443	+	0.509546i	$0.829813\pi$
$24$		0			0
$25$	−0.705737	+	1.22237i	−0.141147	+	0.244474i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.39053	−	7.60462i	0.815301	−	1.41214i	−0.0938108	−	0.995590i	$-0.529905\pi$
$29$	4.39053	−	7.60462i	0.815301	−	1.41214i	0.909112	−	0.416552i	$-0.136762\pi$
$30$		0			0
$31$	−3.84002	−	6.65111i	−0.689688	−	1.19458i	−0.971939	−	0.235235i	$-0.924414\pi$
$31$	−3.84002	−	6.65111i	−0.689688	−	1.19458i	0.282250	−	0.959341i	$-0.408919\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.53209			0.428001
$36$		0			0
$37$	−7.68004			−1.26259			−0.631296	−	0.775542i	$-0.717477\pi$
$37$	−7.68004			−1.26259			−0.631296	+	0.775542i	$0.717477\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.11334	−	1.92836i	−0.173875	−	0.301160i	0.765897	−	0.642964i	$-0.222295\pi$
$41$	−1.11334	−	1.92836i	−0.173875	−	0.301160i	−0.939771	+	0.341804i	$0.888962\pi$
$42$		0			0
$43$	0.613341	−	1.06234i	0.0935336	−	0.162005i	−0.815462	−	0.578811i	$-0.803517\pi$
$43$	0.613341	−	1.06234i	0.0935336	−	0.162005i	0.908996	+	0.416806i	$0.136850\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.66637	−	4.61830i	0.388931	−	0.673648i	−0.603375	−	0.797457i	$-0.706178\pi$
$47$	2.66637	−	4.61830i	0.388931	−	0.673648i	0.992306	+	0.123810i	$0.0395112\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.716881			0.0984712			0.0492356	−	0.998787i	$-0.484321\pi$
$53$	0.716881			0.0984712			0.0492356	+	0.998787i	$0.484321\pi$
$54$		0			0
$55$	−1.18479			−0.159757
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.368241	−	0.637812i	−0.0479409	−	0.0830360i	0.841059	−	0.540943i	$-0.181933\pi$
$59$	−0.368241	−	0.637812i	−0.0479409	−	0.0830360i	−0.889000	+	0.457907i	$0.848599\pi$
$60$		0			0
$61$	−0.479055	+	0.829748i	−0.0613368	+	0.106238i	−0.895063	−	0.445939i	$-0.852870\pi$
$61$	−0.479055	+	0.829748i	−0.0613368	+	0.106238i	0.833726	+	0.552178i	$0.186203\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.37211	−	12.7689i	0.914398	−	1.58378i
$66$		0			0
$67$	−4.81908	−	8.34689i	−0.588744	−	1.01973i	−0.994397	−	0.105708i	$-0.966289\pi$
$67$	−4.81908	−	8.34689i	−0.588744	−	1.01973i	0.405653	−	0.914027i	$-0.367044\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	13.2344			1.57064			0.785318	−	0.619092i	$-0.212499\pi$
$71$	13.2344			1.57064			0.785318	+	0.619092i	$0.212499\pi$
$72$		0			0
$73$	−10.2686			−1.20185			−0.600923	−	0.799307i	$-0.705200\pi$
$73$	−10.2686			−1.20185			−0.600923	+	0.799307i	$0.705200\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.233956	+	0.405223i	0.0266617	+	0.0461794i
$78$		0			0
$79$	−6.31908	+	10.9450i	−0.710952	+	1.23140i	0.253548	+	0.967323i	$0.418402\pi$
$79$	−6.31908	+	10.9450i	−0.710952	+	1.23140i	−0.964500	+	0.264082i	$0.914931\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.36571	−	2.36549i	0.149907	−	0.259646i	−0.781286	−	0.624173i	$-0.785436\pi$
$83$	1.36571	−	2.36549i	0.149907	−	0.259646i	0.931193	+	0.364527i	$0.118769\pi$
$84$		0			0
$85$	−4.91147	−	8.50692i	−0.532724	−	0.922705i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.11381			0.860062			0.430031	−	0.902814i	$-0.358503\pi$
$89$	8.11381			0.860062			0.430031	+	0.902814i	$0.358503\pi$
$90$		0			0
$91$	−5.82295			−0.610411
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.76604	+	4.79093i	0.283790	+	0.491539i
$96$		0			0
$97$	6.80200	−	11.7814i	0.690639	−	1.19622i	−0.280990	−	0.959711i	$-0.590663\pi$
$97$	6.80200	−	11.7814i	0.690639	−	1.19622i	0.971629	−	0.236511i	$-0.0760039\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.78699	+	8.29131i	−0.476323	+	0.825016i	−0.999632	−	0.0271271i	$-0.991364\pi$
$101$	−4.78699	+	8.29131i	−0.476323	+	0.825016i	0.523309	+	0.852143i	$0.324697\pi$
$102$		0			0
$103$	1.52094	+	2.63435i	0.149863	+	0.259571i	0.931177	−	0.364568i	$-0.118783\pi$
$103$	1.52094	+	2.63435i	0.149863	+	0.259571i	−0.781314	+	0.624139i	$0.785450\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.51754			−0.630074			−0.315037	−	0.949079i	$-0.602017\pi$
$107$	−6.51754			−0.630074			−0.315037	+	0.949079i	$0.602017\pi$
$108$		0			0
$109$	10.6382			1.01895			0.509475	−	0.860485i	$-0.329840\pi$
$109$	10.6382			1.01895			0.509475	+	0.860485i	$0.329840\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.58853	+	4.48346i	0.243508	+	0.421768i	0.961711	−	0.274065i	$-0.0883684\pi$
$113$	2.58853	+	4.48346i	0.243508	+	0.421768i	−0.718203	+	0.695834i	$0.755035\pi$
$114$		0			0
$115$	−0.134285	+	0.232589i	−0.0125222	+	0.0216890i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.93969	+	3.35965i	−0.177811	+	0.307978i
$120$		0			0
$121$	5.39053	+	9.33667i	0.490048	+	0.848788i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.08647			0.812718
$126$		0			0
$127$	8.88207			0.788157			0.394078	−	0.919077i	$-0.371064\pi$
$127$	8.88207			0.788157			0.394078	+	0.919077i	$0.371064\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.68139	−	9.84045i	−0.496385	−	0.859764i	0.503606	−	0.863933i	$-0.332006\pi$
$131$	−5.68139	−	9.84045i	−0.496385	−	0.859764i	−0.999991	+	0.00416893i	$0.998673\pi$
$132$		0			0
$133$	1.09240	−	1.89209i	0.0947228	−	0.164065i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.86231	+	4.95767i	−0.244544	+	0.423562i	−0.962003	−	0.273038i	$-0.911972\pi$
$137$	−2.86231	+	4.95767i	−0.244544	+	0.423562i	0.717459	+	0.696600i	$0.245305\pi$
$138$		0			0
$139$	−0.461981	−	0.800175i	−0.0391847	−	0.0678700i	0.845768	−	0.533551i	$-0.179143\pi$
$139$	−0.461981	−	0.800175i	−0.0391847	−	0.0678700i	−0.884953	+	0.465681i	$0.845809\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.72462			0.227844
$144$		0			0
$145$	22.2344			1.84647
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.36231	+	7.55574i	0.357374	+	0.618991i	0.987521	−	0.157485i	$-0.0503387\pi$
$149$	4.36231	+	7.55574i	0.357374	+	0.618991i	−0.630147	+	0.776476i	$0.717005\pi$
$150$		0			0
$151$	9.21348	−	15.9582i	0.749782	−	1.29866i	−0.198145	−	0.980173i	$-0.563492\pi$
$151$	9.21348	−	15.9582i	0.749782	−	1.29866i	0.947927	−	0.318488i	$-0.103175\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.72328	−	16.8412i	0.780992	−	1.35272i
$156$		0			0
$157$	−2.46198	−	4.26428i	−0.196488	−	0.340326i	0.750900	−	0.660416i	$-0.229620\pi$
$157$	−2.46198	−	4.26428i	−0.196488	−	0.340326i	−0.947387	+	0.320090i	$0.896287\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.106067			0.00835924
$162$		0			0
$163$	−7.63816			−0.598267			−0.299133	−	0.954211i	$-0.596698\pi$
$163$	−7.63816			−0.598267			−0.299133	+	0.954211i	$0.596698\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.82770	+	4.89771i	0.218814	+	0.378996i	0.954446	−	0.298385i	$-0.0964480\pi$
$167$	2.82770	+	4.89771i	0.218814	+	0.378996i	−0.735632	+	0.677382i	$0.763115\pi$
$168$		0			0
$169$	−10.4534	+	18.1058i	−0.804105	+	1.39275i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.5346	−	18.2465i	0.800932	−	1.38725i	−0.118071	−	0.993005i	$-0.537671\pi$
$173$	10.5346	−	18.2465i	0.800932	−	1.38725i	0.919003	−	0.394250i	$-0.128995\pi$
$174$		0			0
$175$	0.705737	+	1.22237i	0.0533487	+	0.0924027i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.12061			−0.382733			−0.191366	−	0.981519i	$-0.561292\pi$
$179$	−5.12061			−0.382733			−0.191366	+	0.981519i	$0.561292\pi$
$180$		0			0
$181$	−0.319955			−0.0237821			−0.0118910	−	0.999929i	$-0.503785\pi$
$181$	−0.319955			−0.0237821			−0.0118910	+	0.999929i	$0.503785\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.72328	−	16.8412i	−0.714870	−	1.23819i
$186$		0			0
$187$	0.907604	−	1.57202i	0.0663706	−	0.114957i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.78359	−	13.4816i	0.563200	−	0.975492i	−0.434014	−	0.900906i	$-0.642903\pi$
$191$	7.78359	−	13.4816i	0.563200	−	0.975492i	0.997215	−	0.0745858i	$-0.0237635\pi$
$192$		0			0
$193$	−3.02094	−	5.23243i	−0.217452	−	0.376639i	0.736576	−	0.676355i	$-0.236441\pi$
$193$	−3.02094	−	5.23243i	−0.217452	−	0.376639i	−0.954028	+	0.299716i	$0.903108\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−25.2344			−1.79788			−0.898939	−	0.438074i	$-0.855661\pi$
$197$	−25.2344			−1.79788			−0.898939	+	0.438074i	$0.855661\pi$
$198$		0			0
$199$	−3.04189			−0.215634			−0.107817	−	0.994171i	$-0.534386\pi$
$199$	−3.04189			−0.215634			−0.107817	+	0.994171i	$0.534386\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.39053	−	7.60462i	−0.308155	−	0.533740i
$204$		0			0
$205$	2.81908	−	4.88279i	0.196893	−	0.341029i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.511144	+	0.885328i	−0.0353566	+	0.0612394i
$210$		0			0
$211$	−2.72668	−	4.72275i	−0.187713	−	0.325128i	0.756775	−	0.653676i	$-0.226774\pi$
$211$	−2.72668	−	4.72275i	−0.187713	−	0.325128i	−0.944487	+	0.328548i	$0.893441\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.10607			0.211832
$216$		0			0
$217$	−7.68004			−0.521355
$218$		0			0
$219$		0			0
$220$		0			0
$221$	11.2947	+	19.5630i	0.759766	+	1.31595i
$222$		0			0
$223$	7.09627	−	12.2911i	0.475201	−	0.823073i	−0.524395	−	0.851475i	$-0.675709\pi$
$223$	7.09627	−	12.2911i	0.475201	−	0.823073i	0.999597	+	0.0284023i	$0.00904195\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.44697	−	2.50622i	0.0960385	−	0.166344i	−0.814003	−	0.580861i	$-0.802716\pi$
$227$	1.44697	−	2.50622i	0.0960385	−	0.166344i	0.910042	+	0.414517i	$0.136049\pi$
$228$		0			0
$229$	−4.58378	−	7.93934i	−0.302905	−	0.524646i	0.673888	−	0.738834i	$-0.264623\pi$
$229$	−4.58378	−	7.93934i	−0.302905	−	0.524646i	−0.976793	+	0.214187i	$0.931290\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.2713			−0.869429			−0.434715	−	0.900568i	$-0.643151\pi$
$233$	−13.2713			−0.869429			−0.434715	+	0.900568i	$0.643151\pi$
$234$		0			0
$235$	13.5030			0.880838
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.76857	−	8.25941i	−0.308453	−	0.534257i	0.669571	−	0.742748i	$-0.266478\pi$
$239$	−4.76857	−	8.25941i	−0.308453	−	0.534257i	−0.978024	+	0.208491i	$0.933145\pi$
$240$		0			0
$241$	4.47906	−	7.75795i	0.288521	−	0.499734i	−0.684936	−	0.728604i	$-0.740170\pi$
$241$	4.47906	−	7.75795i	0.288521	−	0.499734i	0.973457	+	0.228870i	$0.0735031\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.26604	−	2.19285i	0.0808846	−	0.140096i
$246$		0			0
$247$	−6.36097	−	11.0175i	−0.404739	−	0.701028i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−24.9982			−1.57788			−0.788938	−	0.614473i	$-0.789369\pi$
$251$	−24.9982			−1.57788			−0.788938	+	0.614473i	$0.789369\pi$
$252$		0			0
$253$	−0.0496299			−0.00312020
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.42602	+	9.39815i	0.338466	+	0.586240i	0.984144	−	0.177369i	$-0.0567587\pi$
$257$	5.42602	+	9.39815i	0.338466	+	0.586240i	−0.645678	+	0.763609i	$0.723425\pi$
$258$		0			0
$259$	−3.84002	+	6.65111i	−0.238607	+	0.413280i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.0437	+	22.5924i	−0.804309	+	1.39310i	0.112448	+	0.993658i	$0.464131\pi$
$263$	−13.0437	+	22.5924i	−0.804309	+	1.39310i	−0.916757	+	0.399446i	$0.869202\pi$
$264$		0			0
$265$	0.907604	+	1.57202i	0.0557537	+	0.0965682i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.63310			0.465399			0.232699	−	0.972549i	$-0.425244\pi$
$269$	7.63310			0.465399			0.232699	+	0.972549i	$0.425244\pi$
$270$		0			0
$271$	−3.40373			−0.206762			−0.103381	−	0.994642i	$-0.532966\pi$
$271$	−3.40373			−0.206762			−0.103381	+	0.994642i	$0.532966\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.330222	−	0.571962i	−0.0199131	−	0.0344906i
$276$		0			0
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	−0.767185	−	0.641426i	$-0.778343\pi$
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	0.939084	+	0.343689i	$0.111676\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.1887	−	24.5755i	0.846425	−	1.46605i	−0.0379535	−	0.999280i	$-0.512084\pi$
$281$	14.1887	−	24.5755i	0.846425	−	1.46605i	0.884378	−	0.466771i	$-0.154583\pi$
$282$		0			0
$283$	2.28564	+	3.95885i	0.135867	+	0.235329i	0.925929	−	0.377699i	$-0.123285\pi$
$283$	2.28564	+	3.95885i	0.135867	+	0.235329i	−0.790061	+	0.613028i	$0.789951\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.22668			−0.131437
$288$		0			0
$289$	−1.95037			−0.114728
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.16385	+	3.74789i	0.126413	+	0.218954i	0.922285	−	0.386512i	$-0.126320\pi$
$293$	2.16385	+	3.74789i	0.126413	+	0.218954i	−0.795871	+	0.605466i	$0.792987\pi$
$294$		0			0
$295$	0.932419	−	1.61500i	0.0542875	−	0.0940287i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.308811	−	0.534876i	0.0178590	−	0.0309327i
$300$		0			0
$301$	−0.613341	−	1.06234i	−0.0353524	−	0.0612321i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.42602			−0.138914
$306$		0			0
$307$	−12.3773			−0.706411			−0.353206	−	0.935546i	$-0.614908\pi$
$307$	−12.3773			−0.706411			−0.353206	+	0.935546i	$0.614908\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.9927	+	19.0400i	0.623340	+	1.07966i	0.988859	+	0.148853i	$0.0475582\pi$
$311$	10.9927	+	19.0400i	0.623340	+	1.07966i	−0.365519	+	0.930804i	$0.619108\pi$
$312$		0			0
$313$	6.94491	−	12.0289i	0.392549	−	0.679915i	−0.600236	−	0.799823i	$-0.704927\pi$
$313$	6.94491	−	12.0289i	0.392549	−	0.679915i	0.992785	+	0.119908i	$0.0382599\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.09105	+	5.35386i	−0.173611	+	0.300703i	−0.939680	−	0.342056i	$-0.888877\pi$
$317$	−3.09105	+	5.35386i	−0.173611	+	0.300703i	0.766069	+	0.642759i	$0.222210\pi$
$318$		0			0
$319$	2.05438	+	3.55829i	0.115023	+	0.199226i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.47565			−0.471598
$324$		0			0
$325$	8.21894			0.455905
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.66637	−	4.61830i	−0.147002	−	0.254615i
$330$		0			0
$331$	5.36571	−	9.29369i	0.294926	−	0.510827i	−0.680041	−	0.733174i	$-0.738038\pi$
$331$	5.36571	−	9.29369i	0.294926	−	0.510827i	0.974968	+	0.222346i	$0.0713715\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	12.2023	−	21.1351i	0.666685	−	1.15473i
$336$		0			0
$337$	9.29726	+	16.1033i	0.506454	+	0.877204i	0.999972	+	0.00746831i	$0.00237726\pi$
$337$	9.29726	+	16.1033i	0.506454	+	0.877204i	−0.493518	+	0.869735i	$0.664289\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.59358			0.194603
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.2062	+	17.6777i	0.547898	+	0.948987i	0.998418	+	0.0562207i	$0.0179050\pi$
$347$	10.2062	+	17.6777i	0.547898	+	0.948987i	−0.450521	+	0.892766i	$0.648762\pi$
$348$		0			0
$349$	1.78106	−	3.08489i	0.0953379	−	0.165130i	−0.814412	−	0.580288i	$-0.802940\pi$
$349$	1.78106	−	3.08489i	0.0953379	−	0.165130i	0.909750	+	0.415157i	$0.136274\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.01114	−	8.67956i	0.266716	−	0.461966i	−0.701296	−	0.712871i	$-0.747395\pi$
$353$	5.01114	−	8.67956i	0.266716	−	0.461966i	0.968012	+	0.250904i	$0.0807280\pi$
$354$		0			0
$355$	16.7554	+	29.0211i	0.889283	+	1.54028i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.48070			0.500372			0.250186	−	0.968198i	$-0.419508\pi$
$359$	9.48070			0.500372			0.250186	+	0.968198i	$0.419508\pi$
$360$		0			0
$361$	−14.2267			−0.748773
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.0005	−	22.5175i	−0.680476	−	1.17862i
$366$		0			0
$367$	8.06670	−	13.9719i	0.421079	−	0.729329i	−0.574967	−	0.818177i	$-0.694985\pi$
$367$	8.06670	−	13.9719i	0.421079	−	0.729329i	0.996045	+	0.0888474i	$0.0283183\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.358441	−	0.620838i	0.0186093	−	0.0322323i
$372$		0			0
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	0.624841	−	0.780752i	$-0.285164\pi$
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	−0.988572	+	0.150752i	$0.951831\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−51.1317			−2.63341
$378$		0			0
$379$	−16.0574			−0.824812			−0.412406	−	0.911000i	$-0.635311\pi$
$379$	−16.0574			−0.824812			−0.412406	+	0.911000i	$0.635311\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.0103	+	27.7306i	0.818086	+	1.41697i	0.907090	+	0.420936i	$0.138298\pi$
$383$	16.0103	+	27.7306i	0.818086	+	1.41697i	−0.0890039	+	0.996031i	$0.528368\pi$
$384$		0			0
$385$	−0.592396	+	1.02606i	−0.0301913	+	0.0522929i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.0214	+	26.0178i	−0.761616	+	1.31916i	0.180402	+	0.983593i	$0.442260\pi$
$389$	−15.0214	+	26.0178i	−0.761616	+	1.31916i	−0.942017	+	0.335564i	$0.891073\pi$
$390$		0			0
$391$	−0.205737	−	0.356347i	−0.0104046	−	0.0180212i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−32.0009			−1.61014
$396$		0			0
$397$	−12.3200			−0.618321			−0.309160	−	0.951010i	$-0.600048\pi$
$397$	−12.3200			−0.618321			−0.309160	+	0.951010i	$0.600048\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.4880	+	18.1657i	0.523745	+	0.907152i	0.999618	+	0.0276385i	$0.00879873\pi$
$401$	10.4880	+	18.1657i	0.523745	+	0.907152i	−0.475873	+	0.879514i	$0.657868\pi$
$402$		0			0
$403$	−22.3603	+	38.7291i	−1.11384	+	1.92923i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.79679	−	3.11213i	0.0890635	−	0.154263i
$408$		0			0
$409$	−12.8307	−	22.2234i	−0.634437	−	1.09888i	−0.986634	−	0.162951i	$-0.947899\pi$
$409$	−12.8307	−	22.2234i	−0.634437	−	1.09888i	0.352197	−	0.935926i	$-0.385435\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.736482			−0.0362399
$414$		0			0
$415$	6.91622			0.339504
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.739885	+	1.28152i	0.0361458	+	0.0626063i	0.883532	−	0.468370i	$-0.155159\pi$
$419$	0.739885	+	1.28152i	0.0361458	+	0.0626063i	−0.847387	+	0.530976i	$0.821825\pi$
$420$		0			0
$421$	−6.55350	+	11.3510i	−0.319398	+	0.553214i	−0.980363	−	0.197203i	$-0.936814\pi$
$421$	−6.55350	+	11.3510i	−0.319398	+	0.553214i	0.660965	+	0.750417i	$0.270147\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.73783	−	4.74205i	0.132804	−	0.230023i
$426$		0			0
$427$	0.479055	+	0.829748i	0.0231831	+	0.0401543i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.7270			0.853879			0.426939	−	0.904280i	$-0.359592\pi$
$431$	17.7270			0.853879			0.426939	+	0.904280i	$0.359592\pi$
$432$		0			0
$433$	−5.83843			−0.280577			−0.140289	−	0.990111i	$-0.544803\pi$
$433$	−5.83843			−0.280577			−0.140289	+	0.990111i	$0.544803\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.115867	+	0.200688i	0.00554267	+	0.00960019i
$438$		0			0
$439$	14.9277	−	25.8555i	0.712459	−	1.23401i	−0.251473	−	0.967864i	$-0.580915\pi$
$439$	14.9277	−	25.8555i	0.712459	−	1.23401i	0.963931	−	0.266151i	$-0.0857518\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.33275	+	9.23659i	−0.253367	+	0.438844i	−0.964451	−	0.264263i	$-0.914871\pi$
$443$	−5.33275	+	9.23659i	−0.253367	+	0.438844i	0.711084	+	0.703107i	$0.248205\pi$
$444$		0			0
$445$	10.2724	+	17.7924i	0.486960	+	0.843440i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.55438			−0.167741			−0.0838707	−	0.996477i	$-0.526728\pi$
$449$	−3.55438			−0.167741			−0.0838707	+	0.996477i	$0.526728\pi$
$450$		0			0
$451$	1.04189			0.0490606
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.37211	−	12.7689i	−0.345610	−	0.598614i
$456$		0			0
$457$	−2.51161	+	4.35024i	−0.117488	+	0.203496i	−0.918772	−	0.394789i	$-0.870818\pi$
$457$	−2.51161	+	4.35024i	−0.117488	+	0.203496i	0.801283	+	0.598285i	$0.204151\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.23055	−	15.9878i	0.429910	−	0.744625i	−0.566955	−	0.823749i	$-0.691879\pi$
$461$	9.23055	−	15.9878i	0.429910	−	0.744625i	0.996865	+	0.0791233i	$0.0252121\pi$
$462$		0			0
$463$	−7.11721	−	12.3274i	−0.330765	−	0.572902i	0.651897	−	0.758307i	$-0.273973\pi$
$463$	−7.11721	−	12.3274i	−0.330765	−	0.572902i	−0.982662	+	0.185406i	$0.940640\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.36865			−0.155883			−0.0779413	−	0.996958i	$-0.524835\pi$
$467$	−3.36865			−0.155883			−0.0779413	+	0.996958i	$0.524835\pi$
$468$		0			0
$469$	−9.63816			−0.445049
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.286989	+	0.497079i	0.0131958	+	0.0228557i
$474$		0			0
$475$	−1.54189	+	2.67063i	−0.0707467	+	0.122537i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	18.3833	−	31.8407i	0.839952	−	1.45484i	−0.0499812	−	0.998750i	$-0.515916\pi$
$479$	18.3833	−	31.8407i	0.839952	−	1.45484i	0.889934	−	0.456090i	$-0.150751\pi$
$480$		0			0
$481$	22.3603	+	38.7291i	1.01954	+	1.76589i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	34.4466			1.56414
$486$		0			0
$487$	37.4175			1.69555			0.847773	−	0.530358i	$-0.177943\pi$
$487$	37.4175			1.69555			0.847773	+	0.530358i	$0.177943\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.3353	+	23.0974i	0.601813	+	1.04237i	0.992547	+	0.121866i	$0.0388879\pi$
$491$	13.3353	+	23.0974i	0.601813	+	1.04237i	−0.390734	+	0.920504i	$0.627779\pi$
$492$		0			0
$493$	−17.0326	+	29.5013i	−0.767108	+	1.32867i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.61721	−	11.4613i	0.296822	−	0.514112i
$498$		0			0
$499$	16.8726	+	29.2242i	0.755320	+	1.30825i	0.945215	+	0.326449i	$0.105852\pi$
$499$	16.8726	+	29.2242i	0.755320	+	1.30825i	−0.189895	+	0.981804i	$0.560815\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−32.0401			−1.42860			−0.714299	−	0.699840i	$-0.753255\pi$
$503$	−32.0401			−1.42860			−0.714299	+	0.699840i	$0.753255\pi$
$504$		0			0
$505$	−24.2422			−1.07876
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.96926	−	6.87495i	−0.175934	−	0.304727i	0.764550	−	0.644564i	$-0.222961\pi$
$509$	−3.96926	−	6.87495i	−0.175934	−	0.304727i	−0.940484	+	0.339838i	$0.889628\pi$
$510$		0			0
$511$	−5.13429	+	8.89284i	−0.227127	+	0.393396i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.85117	+	6.67042i	−0.169703	+	0.293934i
$516$		0			0
$517$	1.24763	+	2.16095i	0.0548705	+	0.0950386i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.6750			0.642923			0.321462	−	0.946923i	$-0.395826\pi$
$521$	14.6750			0.642923			0.321462	+	0.946923i	$0.395826\pi$
$522$		0			0
$523$	−28.3432			−1.23936			−0.619680	−	0.784854i	$-0.712738\pi$
$523$	−28.3432			−1.23936			−0.619680	+	0.784854i	$0.712738\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.8969	+	25.8022i	0.648920	+	1.12396i
$528$		0			0
$529$	11.4944	−	19.9088i	0.499755	−	0.865602i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.48293	+	11.2288i	−0.280807	+	0.486371i
$534$		0			0
$535$	−8.25150	−	14.2920i	−0.356743	−	0.617898i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.467911			0.0201544
$540$		0			0
$541$	11.2858			0.485215			0.242607	−	0.970125i	$-0.421997\pi$
$541$	11.2858			0.485215			0.242607	+	0.970125i	$0.421997\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.4684	+	23.3279i	0.576922	+	0.999258i
$546$		0			0
$547$	−14.6202	+	25.3229i	−0.625115	+	1.08273i	0.363404	+	0.931632i	$0.381615\pi$
$547$	−14.6202	+	25.3229i	−0.625115	+	1.08273i	−0.988519	+	0.151099i	$0.951719\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.59240	−	16.6145i	0.408650	−	0.707802i
$552$		0			0
$553$	6.31908	+	10.9450i	0.268715	+	0.465427i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.775682			0.0328667			0.0164334	−	0.999865i	$-0.494769\pi$
$557$	0.775682			0.0328667			0.0164334	+	0.999865i	$0.494769\pi$
$558$		0			0
$559$	−7.14290			−0.302113
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.4761	−	21.6093i	−0.525806	−	0.910722i	−0.999548	−	0.0300588i	$-0.990431\pi$
$563$	−12.4761	−	21.6093i	−0.525806	−	0.910722i	0.473742	−	0.880663i	$-0.342903\pi$
$564$		0			0
$565$	−6.55438	+	11.3525i	−0.275745	+	0.477604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.4017	+	21.4803i	−0.519905	+	0.900502i	0.479827	+	0.877363i	$0.340699\pi$
$569$	−12.4017	+	21.4803i	−0.519905	+	0.900502i	−0.999732	+	0.0231391i	$0.992634\pi$
$570$		0			0
$571$	4.39827	+	7.61803i	0.184062	+	0.318805i	0.943260	−	0.332055i	$-0.107742\pi$
$571$	4.39827	+	7.61803i	0.184062	+	0.318805i	−0.759198	+	0.650860i	$0.774409\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.149711			−0.00624336
$576$		0			0
$577$	−12.8743			−0.535965			−0.267983	−	0.963424i	$-0.586357\pi$
$577$	−12.8743			−0.535965			−0.267983	+	0.963424i	$0.586357\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.36571	−	2.36549i	−0.0566594	−	0.0981369i
$582$		0			0
$583$	−0.167718	+	0.290497i	−0.00694619	+	0.0120311i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.4315	+	38.8526i	−0.925849	+	1.60362i	−0.135658	+	0.990756i	$0.543315\pi$
$587$	−22.4315	+	38.8526i	−0.925849	+	1.60362i	−0.790190	+	0.612861i	$0.790018\pi$
$588$		0			0
$589$	−8.38965	−	14.5313i	−0.345690	−	0.598752i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.76053			−0.154426			−0.0772131	−	0.997015i	$-0.524602\pi$
$593$	−3.76053			−0.154426			−0.0772131	+	0.997015i	$0.524602\pi$
$594$		0			0
$595$	−9.82295			−0.402702
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.84524	+	3.19604i	0.0753943	+	0.130587i	0.901258	−	0.433283i	$-0.142645\pi$
$599$	1.84524	+	3.19604i	0.0753943	+	0.130587i	−0.825863	+	0.563870i	$0.809312\pi$
$600$		0			0
$601$	10.9285	−	18.9288i	0.445785	−	0.772122i	−0.552322	−	0.833631i	$-0.686258\pi$
$601$	10.9285	−	18.9288i	0.445785	−	0.772122i	0.998107	+	0.0615091i	$0.0195913\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.6493	+	23.6413i	−0.554923	+	0.961155i
$606$		0			0
$607$	12.1973	+	21.1263i	0.495072	+	0.857490i	0.999984	−	0.00568063i	$-0.00180821\pi$
$607$	12.1973	+	21.1263i	0.495072	+	0.857490i	−0.504911	+	0.863171i	$0.668475\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−31.0523			−1.25624
$612$		0			0
$613$	42.0215			1.69723			0.848616	−	0.529010i	$-0.177437\pi$
$613$	42.0215			1.69723			0.848616	+	0.529010i	$0.177437\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	23.2049	+	40.1920i	0.934192	+	1.61807i	0.776068	+	0.630650i	$0.217212\pi$
$617$	23.2049	+	40.1920i	0.934192	+	1.61807i	0.158125	+	0.987419i	$0.449455\pi$
$618$		0			0
$619$	−13.6047	+	23.5641i	−0.546820	+	0.947120i	0.451670	+	0.892185i	$0.350828\pi$
$619$	−13.6047	+	23.5641i	−0.546820	+	0.947120i	−0.998490	+	0.0549349i	$0.982505\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.05690	−	7.02676i	0.162536	−	0.281521i
$624$		0			0
$625$	15.0326	+	26.0372i	0.601302	+	1.04149i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	29.7939			1.18796
$630$		0			0
$631$	29.6023			1.17845			0.589224	−	0.807970i	$-0.299434\pi$
$631$	29.6023			1.17845			0.589224	+	0.807970i	$0.299434\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	11.2451	+	19.4771i	0.446248	+	0.772925i
$636$		0			0
$637$	−2.91147	+	5.04282i	−0.115357	+	0.199804i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.139500	+	0.241621i	−0.00550991	+	0.00954345i	−0.868767	−	0.495221i	$-0.835087\pi$
$641$	−0.139500	+	0.241621i	−0.00550991	+	0.00954345i	0.863257	+	0.504764i	$0.168421\pi$
$642$		0			0
$643$	−9.12196	−	15.7997i	−0.359735	−	0.623079i	0.628181	−	0.778067i	$-0.283800\pi$
$643$	−9.12196	−	15.7997i	−0.359735	−	0.623079i	−0.987916	+	0.154988i	$0.950466\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.4570			0.882875			0.441438	−	0.897292i	$-0.354469\pi$
$647$	22.4570			0.882875			0.441438	+	0.897292i	$0.354469\pi$
$648$		0			0
$649$	0.344608			0.0135270
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−25.2656	−	43.7614i	−0.988721	−	1.71251i	−0.624066	−	0.781372i	$-0.714520\pi$
$653$	−25.2656	−	43.7614i	−0.988721	−	1.71251i	−0.364655	−	0.931143i	$-0.618813\pi$
$654$		0			0
$655$	14.3858	−	24.9169i	0.562099	−	0.973584i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.33631	−	2.31456i	0.0520554	−	0.0901626i	−0.838824	−	0.544403i	$-0.816756\pi$
$659$	1.33631	−	2.31456i	0.0520554	−	0.0901626i	0.890879	+	0.454241i	$0.150089\pi$
$660$		0			0
$661$	17.3050	+	29.9731i	0.673086	+	1.16582i	0.977024	+	0.213128i	$0.0683651\pi$
$661$	17.3050	+	29.9731i	0.673086	+	1.16582i	−0.303938	+	0.952692i	$0.598302\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.53209			0.214525
$666$		0			0
$667$	0.931379			0.0360631
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.224155	−	0.388249i	−0.00865342	−	0.0149882i
$672$		0			0
$673$	−8.25624	+	14.3002i	−0.318255	+	0.551234i	−0.980124	−	0.198386i	$-0.936430\pi$
$673$	−8.25624	+	14.3002i	−0.318255	+	0.551234i	0.661869	+	0.749619i	$0.269763\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.8790	+	37.8955i	−0.840877	+	1.45644i	0.0482766	+	0.998834i	$0.484627\pi$
$677$	−21.8790	+	37.8955i	−0.840877	+	1.45644i	−0.889154	+	0.457608i	$0.848706\pi$
$678$		0			0
$679$	−6.80200	−	11.7814i	−0.261037	−	0.452129i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	28.2412			1.08062			0.540310	−	0.841466i	$-0.318307\pi$
$683$	28.2412			1.08062			0.540310	+	0.841466i	$0.318307\pi$
$684$		0			0
$685$	−14.4953			−0.553835
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.08718	−	3.61510i	−0.0795153	−	0.137725i
$690$		0			0
$691$	−14.5326	+	25.1711i	−0.552844	+	0.957555i	0.445223	+	0.895420i	$0.353124\pi$
$691$	−14.5326	+	25.1711i	−0.552844	+	0.957555i	−0.998068	+	0.0621351i	$0.980209\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.16978	−	2.02611i	0.0443722	−	0.0768549i
$696$		0			0
$697$	4.31908	+	7.48086i	0.163597	+	0.283358i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.10876			0.0418771			0.0209386	−	0.999781i	$-0.493335\pi$
$701$	1.10876			0.0418771			0.0209386	+	0.999781i	$0.493335\pi$
$702$		0			0
$703$	−16.7793			−0.632843
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.78699	+	8.29131i	0.180033	+	0.311827i
$708$		0			0
$709$	9.23442	−	15.9945i	0.346806	−	0.600686i	−0.638874	−	0.769311i	$-0.720600\pi$
$709$	9.23442	−	15.9945i	0.346806	−	0.600686i	0.985680	+	0.168626i	$0.0539329\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.407299	−	0.705463i	0.0152535	−	0.0264198i
$714$		0			0
$715$	3.44949	+	5.97470i	0.129004	+	0.223441i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−33.7769			−1.25967			−0.629834	−	0.776730i	$-0.716877\pi$
$719$	−33.7769			−1.25967			−0.629834	+	0.776730i	$0.716877\pi$
$720$		0			0
$721$	3.04189			0.113286
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.19712	+	10.7337i	0.230155	+	0.398641i
$726$		0			0
$727$	8.40214	−	14.5529i	0.311618	−	0.539738i	−0.667095	−	0.744973i	$-0.732462\pi$
$727$	8.40214	−	14.5529i	0.311618	−	0.539738i	0.978713	+	0.205234i	$0.0657957\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.37939	+	4.12122i	−0.0880047	+	0.152429i
$732$		0			0
$733$	6.81820	+	11.8095i	0.251836	+	0.436193i	0.964031	−	0.265789i	$-0.0856323\pi$
$733$	6.81820	+	11.8095i	0.251836	+	0.436193i	−0.712195	+	0.701981i	$0.752299\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.50980			0.166121
$738$		0			0
$739$	32.0419			1.17868			0.589340	−	0.807885i	$-0.299388\pi$
$739$	32.0419			1.17868			0.589340	+	0.807885i	$0.299388\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.8764	−	29.2309i	−0.619137	−	1.07238i	−0.989644	−	0.143547i	$-0.954149\pi$
$743$	−16.8764	−	29.2309i	−0.619137	−	1.07238i	0.370507	−	0.928830i	$-0.379184\pi$
$744$		0			0
$745$	−11.0458	+	19.1318i	−0.404685	+	0.700936i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.25877	+	5.64436i	−0.119073	+	0.206240i
$750$		0			0
$751$	13.0582	+	22.6175i	0.476502	+	0.825326i	0.999637	−	0.0269236i	$-0.00857108\pi$
$751$	13.0582	+	22.6175i	0.476502	+	0.825326i	−0.523135	+	0.852250i	$0.675238\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	46.6587			1.69808
$756$		0			0
$757$	35.6536			1.29585			0.647927	−	0.761703i	$-0.275636\pi$
$757$	35.6536			1.29585			0.647927	+	0.761703i	$0.275636\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	20.3824	+	35.3033i	0.738861	+	1.27974i	0.953009	+	0.302943i	$0.0979692\pi$
$761$	20.3824	+	35.3033i	0.738861	+	1.27974i	−0.214148	+	0.976801i	$0.568698\pi$
$762$		0			0
$763$	5.31908	−	9.21291i	0.192564	−	0.333530i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.14425	+	3.71395i	−0.0774243	+	0.134103i
$768$		0			0
$769$	−19.7135	−	34.1447i	−0.710886	−	1.23129i	−0.964525	−	0.263992i	$-0.914961\pi$
$769$	−19.7135	−	34.1447i	−0.710886	−	1.23129i	0.253639	−	0.967299i	$-0.418373\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−24.9026			−0.895685			−0.447842	−	0.894113i	$-0.647807\pi$
$773$	−24.9026			−0.895685			−0.447842	+	0.894113i	$0.647807\pi$
$774$		0			0
$775$	10.8402			0.389391
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.43242	−	4.21307i	−0.0871504	−	0.150949i
$780$		0			0
$781$	−3.09627	+	5.36289i	−0.110793	+	0.191899i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.23396	−	10.7975i	0.222499	−	0.385380i
$786$		0			0
$787$	−15.3525	−	26.5913i	−0.547258	−	0.947879i	−0.998461	−	0.0554572i	$-0.982338\pi$
$787$	−15.3525	−	26.5913i	−0.547258	−	0.947879i	0.451203	−	0.892421i	$-0.350995\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	5.17705			0.184075
$792$		0			0
$793$	5.57903			0.198117
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.50686	−	9.53817i	−0.195063	−	0.337859i	0.751858	−	0.659325i	$-0.229158\pi$
$797$	−5.50686	−	9.53817i	−0.195063	−	0.337859i	−0.946921	+	0.321466i	$0.895825\pi$
$798$		0			0
$799$	−10.3439	+	17.9161i	−0.365941	+	0.633828i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.40239	−	4.16106i	0.0847785	−	0.146841i
$804$		0			0
$805$	0.134285	+	0.232589i	0.00473294	+	0.00819769i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.9881			−0.597271			−0.298636	−	0.954367i	$-0.596532\pi$
$809$	−16.9881			−0.597271			−0.298636	+	0.954367i	$0.596532\pi$
$810$		0			0
$811$	−37.9796			−1.33364			−0.666822	−	0.745217i	$-0.732346\pi$
$811$	−37.9796			−1.33364			−0.666822	+	0.745217i	$0.732346\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.67024	−	16.7494i	−0.338734	−	0.586704i
$816$		0			0
$817$	1.34002	−	2.32099i	0.0468814	−	0.0812011i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4.13934	−	7.16954i	0.144464	−	0.250219i	−0.784709	−	0.619864i	$-0.787188\pi$
$821$	4.13934	−	7.16954i	0.144464	−	0.250219i	0.929173	+	0.369646i	$0.120521\pi$
$822$		0			0
$823$	27.2763	+	47.2440i	0.950792	+	1.64682i	0.743716	+	0.668496i	$0.233062\pi$
$823$	27.2763	+	47.2440i	0.950792	+	1.64682i	0.207077	+	0.978325i	$0.433605\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−31.8708			−1.10826			−0.554129	−	0.832431i	$-0.686948\pi$
$827$	−31.8708			−1.10826			−0.554129	+	0.832431i	$0.686948\pi$
$828$		0			0
$829$	−0.352349			−0.0122376			−0.00611879	−	0.999981i	$-0.501948\pi$
$829$	−0.352349			−0.0122376			−0.00611879	+	0.999981i	$0.501948\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.93969	+	3.35965i	0.0672064	+	0.116405i
$834$		0			0
$835$	−7.15998	+	12.4014i	−0.247781	+	0.429170i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.5077	+	21.6640i	−0.431815	+	0.747926i	−0.997030	−	0.0770182i	$-0.975460\pi$
$839$	−12.5077	+	21.6640i	−0.431815	+	0.747926i	0.565215	+	0.824944i	$0.308793\pi$
$840$		0			0
$841$	−24.0535	−	41.6619i	−0.829431	−	1.43662i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−52.9377			−1.82111
$846$		0			0
$847$	10.7811			0.370442
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.407299	−	0.705463i	−0.0139620	−	0.0241829i
$852$		0			0
$853$	−19.5954	+	33.9402i	−0.670933	+	1.16209i	0.306706	+	0.951804i	$0.400773\pi$
$853$	−19.5954	+	33.9402i	−0.670933	+	1.16209i	−0.977640	+	0.210286i	$0.932560\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.20368	−	14.2092i	0.280232	−	0.485377i	−0.691210	−	0.722654i	$-0.742922\pi$
$857$	8.20368	−	14.2092i	0.280232	−	0.485377i	0.971442	+	0.237278i	$0.0762552\pi$
$858$		0			0
$859$	−13.4162	−	23.2376i	−0.457756	−	0.792856i	0.541086	−	0.840967i	$-0.318013\pi$
$859$	−13.4162	−	23.2376i	−0.457756	−	0.792856i	−0.998842	+	0.0481111i	$0.984680\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.5057			0.493779			0.246890	−	0.969044i	$-0.420592\pi$
$863$	14.5057			0.493779			0.246890	+	0.969044i	$0.420592\pi$
$864$		0			0
$865$	53.3492			1.81393
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.95677	−	5.12127i	−0.100301	−	0.173727i
$870$		0			0
$871$	−28.0612	+	48.6035i	−0.950819	+	1.64687i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.54323	−	7.86911i	0.153589	−	0.266024i
$876$		0			0
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270131\pi$
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	−0.980352	+	0.197255i	$0.936797\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−53.8976			−1.81585			−0.907927	−	0.419128i	$-0.862336\pi$
$881$	−53.8976			−1.81585			−0.907927	+	0.419128i	$0.862336\pi$
$882$		0			0
$883$	−43.4252			−1.46137			−0.730687	−	0.682712i	$-0.760800\pi$
$883$	−43.4252			−1.46137			−0.730687	+	0.682712i	$0.760800\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.4800	+	33.7403i	0.654074	+	1.13289i	0.982125	+	0.188229i	$0.0602749\pi$
$887$	19.4800	+	33.7403i	0.654074	+	1.13289i	−0.328051	+	0.944660i	$0.606392\pi$
$888$		0			0
$889$	4.44104	−	7.69210i	0.148948	−	0.257985i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.82547	−	10.0900i	0.194942	−	0.337650i
$894$		0			0
$895$	−6.48293	−	11.2288i	−0.216700	−	0.375336i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−67.4389			−2.24921
$900$		0			0
$901$	−2.78106			−0.0926505
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.405078	−	0.701615i	−0.0134652	−	0.0233225i
$906$		0			0
$907$	17.2638	−	29.9018i	0.573236	−	0.992874i	−0.422995	−	0.906132i	$-0.639021\pi$
$907$	17.2638	−	29.9018i	0.573236	−	0.992874i	0.996231	−	0.0867416i	$-0.0276454\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.2631	+	40.2929i	−0.770741	+	1.33496i	0.166416	+	0.986056i	$0.446780\pi$
$911$	−23.2631	+	40.2929i	−0.770741	+	1.33496i	−0.937157	+	0.348907i	$0.886553\pi$
$912$		0			0
$913$	0.639033	+	1.10684i	0.0211489	+	0.0366310i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.3628			−0.375232
$918$		0			0
$919$	9.95636			0.328430			0.164215	−	0.986425i	$-0.447491\pi$
$919$	9.95636			0.328430			0.164215	+	0.986425i	$0.447491\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−38.5317	−	66.7388i	−1.26829	−	2.19674i
$924$		0			0
$925$	5.42009	−	9.38788i	0.178212	−	0.308671i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	4.52300	−	7.83407i	0.148395	−	0.257028i	−0.782239	−	0.622978i	$-0.785923\pi$
$929$	4.52300	−	7.83407i	0.148395	−	0.257028i	0.930634	+	0.365950i	$0.119256\pi$
$930$		0			0
$931$	−1.09240	−	1.89209i	−0.0358018	−	0.0620106i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.59627			0.150314
$936$		0			0
$937$	−24.3928			−0.796878			−0.398439	−	0.917195i	$-0.630448\pi$
$937$	−24.3928			−0.796878			−0.398439	+	0.917195i	$0.630448\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−29.7690	−	51.5615i	−0.970443	−	1.68086i	−0.694220	−	0.719763i	$-0.744251\pi$
$941$	−29.7690	−	51.5615i	−0.970443	−	1.68086i	−0.276223	−	0.961094i	$-0.589083\pi$
$942$		0			0
$943$	0.118089	−	0.204535i	0.00384549	−	0.00666059i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.32429	+	7.48989i	−0.140521	+	0.243389i	−0.927693	−	0.373344i	$-0.878211\pi$
$947$	−4.32429	+	7.48989i	−0.140521	+	0.243389i	0.787172	+	0.616733i	$0.211544\pi$
$948$		0			0
$949$	29.8967	+	51.7826i	0.970487	+	1.68093i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−3.78249			−0.122527			−0.0612634	−	0.998122i	$-0.519513\pi$
$953$	−3.78249			−0.122527			−0.0612634	+	0.998122i	$0.519513\pi$
$954$		0			0
$955$	39.4175			1.27552
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.86231	+	4.95767i	0.0924288	+	0.160091i
$960$		0			0
$961$	−13.9915	+	24.2341i	−0.451340	+	0.781744i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.64930	−	13.2490i	0.246240	−	0.426500i
$966$		0			0
$967$	−16.4745	−	28.5346i	−0.529783	−	0.917611i	−0.999396	−	0.0347392i	$-0.988940\pi$
$967$	−16.4745	−	28.5346i	−0.529783	−	0.917611i	0.469613	−	0.882872i	$-0.344393\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−55.4570			−1.77970			−0.889850	−	0.456254i	$-0.849191\pi$
$971$	−55.4570			−1.77970			−0.889850	+	0.456254i	$0.849191\pi$
$972$		0			0
$973$	−0.923963			−0.0296209
$974$		0			0
$975$		0			0
$976$		0			0
$977$	28.2743	+	48.9724i	0.904573	+	1.56677i	0.821489	+	0.570225i	$0.193144\pi$
$977$	28.2743	+	48.9724i	0.904573	+	1.56677i	0.0830847	+	0.996542i	$0.473523\pi$
$978$		0			0
$979$	−1.89827	+	3.28790i	−0.0606690	+	0.105082i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−14.4987	+	25.1124i	−0.462435	+	0.800961i	−0.999082	−	0.0428458i	$-0.986358\pi$
$983$	−14.4987	+	25.1124i	−0.462435	+	0.800961i	0.536646	+	0.843807i	$0.319691\pi$
$984$		0			0
$985$	−31.9479	−	55.3354i	−1.01794	−	1.76313i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.130110			0.00413726
$990$		0			0
$991$	−6.80922			−0.216302			−0.108151	−	0.994134i	$-0.534493\pi$
$991$	−6.80922			−0.216302			−0.108151	+	0.994134i	$0.534493\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.85117	−	6.67042i	−0.122090	−	0.211466i
$996$		0			0
$997$	19.4688	−	33.7210i	0.616585	−	1.06796i	−0.373520	−	0.927622i	$-0.621849\pi$
$997$	19.4688	−	33.7210i	0.616585	−	1.06796i	0.990104	−	0.140333i	$-0.0448175\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.k.2017.3		6
3.2	odd	2		1008.2.r.h.673.1		6
4.3	odd	2		189.2.f.b.127.2		6
9.2	odd	6		9072.2.a.ca.1.3		3
9.4	even	3	inner	3024.2.r.k.1009.3		6
9.5	odd	6		1008.2.r.h.337.1		6
9.7	even	3		9072.2.a.bs.1.1		3
12.11	even	2		63.2.f.a.43.2	yes	6
28.3	even	6		1323.2.g.e.667.2		6
28.11	odd	6		1323.2.g.d.667.2		6
28.19	even	6		1323.2.h.b.802.2		6
28.23	odd	6		1323.2.h.c.802.2		6
28.27	even	2		1323.2.f.d.883.2		6
36.7	odd	6		567.2.a.c.1.2		3
36.11	even	6		567.2.a.h.1.2		3
36.23	even	6		63.2.f.a.22.2	✓	6
36.31	odd	6		189.2.f.b.64.2		6
84.11	even	6		441.2.g.c.79.2		6
84.23	even	6		441.2.h.d.214.2		6
84.47	odd	6		441.2.h.e.214.2		6
84.59	odd	6		441.2.g.b.79.2		6
84.83	odd	2		441.2.f.c.295.2		6
252.23	even	6		441.2.g.c.67.2		6
252.31	even	6		1323.2.h.b.226.2		6
252.59	odd	6		441.2.h.e.373.2		6
252.67	odd	6		1323.2.h.c.226.2		6
252.83	odd	6		3969.2.a.q.1.2		3
252.95	even	6		441.2.h.d.373.2		6
252.103	even	6		1323.2.g.e.361.2		6
252.131	odd	6		441.2.g.b.67.2		6
252.139	even	6		1323.2.f.d.442.2		6
252.167	odd	6		441.2.f.c.148.2		6
252.223	even	6		3969.2.a.l.1.2		3
252.247	odd	6		1323.2.g.d.361.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	36.23	even	6
63.2.f.a.43.2	yes	6	12.11	even	2
189.2.f.b.64.2		6	36.31	odd	6
189.2.f.b.127.2		6	4.3	odd	2
441.2.f.c.148.2		6	252.167	odd	6
441.2.f.c.295.2		6	84.83	odd	2
441.2.g.b.67.2		6	252.131	odd	6
441.2.g.b.79.2		6	84.59	odd	6
441.2.g.c.67.2		6	252.23	even	6
441.2.g.c.79.2		6	84.11	even	6
441.2.h.d.214.2		6	84.23	even	6
441.2.h.d.373.2		6	252.95	even	6
441.2.h.e.214.2		6	84.47	odd	6
441.2.h.e.373.2		6	252.59	odd	6
567.2.a.c.1.2		3	36.7	odd	6
567.2.a.h.1.2		3	36.11	even	6
1008.2.r.h.337.1		6	9.5	odd	6
1008.2.r.h.673.1		6	3.2	odd	2
1323.2.f.d.442.2		6	252.139	even	6
1323.2.f.d.883.2		6	28.27	even	2
1323.2.g.d.361.2		6	252.247	odd	6
1323.2.g.d.667.2		6	28.11	odd	6
1323.2.g.e.361.2		6	252.103	even	6
1323.2.g.e.667.2		6	28.3	even	6
1323.2.h.b.226.2		6	252.31	even	6
1323.2.h.b.802.2		6	28.19	even	6
1323.2.h.c.226.2		6	252.67	odd	6
1323.2.h.c.802.2		6	28.23	odd	6
3024.2.r.k.1009.3		6	9.4	even	3	inner
3024.2.r.k.2017.3		6	1.1	even	1	trivial
3969.2.a.l.1.2		3	252.223	even	6
3969.2.a.q.1.2		3	252.83	odd	6
9072.2.a.bs.1.1		3	9.7	even	3
9072.2.a.ca.1.3		3	9.2	odd	6

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 + 2.19285i) q^{5} +(0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(1.26604 + 2.19285i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.233956 + 0.405223i) q^{11} +(-2.91147 - 5.04282i) q^{13} -3.87939 q^{17} +2.18479 q^{19} +(0.0530334 + 0.0918566i) q^{23} +(-0.705737 + 1.22237i) q^{25} +(4.39053 - 7.60462i) q^{29} +(-3.84002 - 6.65111i) q^{31} +2.53209 q^{35} -7.68004 q^{37} +(-1.11334 - 1.92836i) q^{41} +(0.613341 - 1.06234i) q^{43} +(2.66637 - 4.61830i) q^{47} +(-0.500000 - 0.866025i) q^{49} +0.716881 q^{53} -1.18479 q^{55} +(-0.368241 - 0.637812i) q^{59} +(-0.479055 + 0.829748i) q^{61} +(7.37211 - 12.7689i) q^{65} +(-4.81908 - 8.34689i) q^{67} +13.2344 q^{71} -10.2686 q^{73} +(0.233956 + 0.405223i) q^{77} +(-6.31908 + 10.9450i) q^{79} +(1.36571 - 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +8.11381 q^{89} -5.82295 q^{91} +(2.76604 + 4.79093i) q^{95} +(6.80200 - 11.7814i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 + 3 * q^7	\( 6 q + 3 q^{5} + 3 q^{7} - 6 q^{11} + 3 q^{13} - 12 q^{17} + 6 q^{19} - 12 q^{23} + 6 q^{25} + 9 q^{29} - 3 q^{31} + 6 q^{35} - 6 q^{37} - 3 q^{43} - 3 q^{47} - 3 q^{49} - 12 q^{53} + 3 q^{59} - 6 q^{61} + 15 q^{65} - 12 q^{67} + 18 q^{71} - 42 q^{73} + 6 q^{77} - 21 q^{79} + 18 q^{83} - 9 q^{85} - 24 q^{89} + 6 q^{91} + 12 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 - 6 * q^11 + 3 * q^13 - 12 * q^17 + 6 * q^19 - 12 * q^23 + 6 * q^25 + 9 * q^29 - 3 * q^31 + 6 * q^35 - 6 * q^37 - 3 * q^43 - 3 * q^47 - 3 * q^49 - 12 * q^53 + 3 * q^59 - 6 * q^61 + 15 * q^65 - 12 * q^67 + 18 * q^71 - 42 * q^73 + 6 * q^77 - 21 * q^79 + 18 * q^83 - 9 * q^85 - 24 * q^89 + 6 * q^91 + 12 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more