LMFDB - Embedded newform 3024.2.r.k.1009.2

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			1009.2
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	3024.1009
Dual form			3024.2.r.k.2017.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.673648 - 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +O(q^{10})$	$q+(0.673648 - 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.826352 - 1.43128i) q^{11} +(1.68479 - 2.91815i) q^{13} -0.467911 q^{17} +3.22668 q^{19} +(-4.47178 + 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} +(3.13429 + 5.42874i) q^{29} +(4.61721 - 7.99724i) q^{31} +1.34730 q^{35} +9.23442 q^{37} +(1.70574 - 2.95442i) q^{41} +(-2.20574 - 3.82045i) q^{43} +(-4.67752 - 8.10170i) q^{47} +(-0.500000 + 0.866025i) q^{49} +0.573978 q^{53} -2.22668 q^{55} +(5.19846 - 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +(-2.26991 - 3.93161i) q^{65} +(0.298133 - 0.516382i) q^{67} -0.554378 q^{71} +2.04963 q^{73} +(0.826352 - 1.43128i) q^{77} +(-1.20187 - 2.08169i) q^{79} +(7.52481 + 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} -9.08647 q^{89} +3.36959 q^{91} +(2.17365 - 3.76487i) q^{95} +(0.949493 + 1.64457i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	−0.675158	−	0.737673i	$-0.735925\pi$
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	0.976423	+	0.215867i	$0.0692579\pi$
$6$		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
$11$	−0.826352	−	1.43128i	−0.249154	−	0.431548i	0.714137	−	0.700006i	$-0.246819\pi$
$11$	−0.826352	−	1.43128i	−0.249154	−	0.431548i	−0.963291	+	0.268458i	$0.913486\pi$
$12$		0			0
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	−0.532024	−	0.846729i	$-0.678568\pi$
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	0.999301	+	0.0373813i	$0.0119016\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.467911			−0.113485			−0.0567426	−	0.998389i	$-0.518071\pi$
$17$	−0.467911			−0.113485			−0.0567426	+	0.998389i	$0.518071\pi$
$18$		0			0
$19$	3.22668			0.740252			0.370126	−	0.928982i	$-0.379315\pi$
$19$	3.22668			0.740252			0.370126	+	0.928982i	$0.379315\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.47178	+	7.74535i	−0.932431	+	1.61502i	−0.153279	+	0.988183i	$0.548983\pi$
$23$	−4.47178	+	7.74535i	−0.932431	+	1.61502i	−0.779152	+	0.626835i	$0.784350\pi$
$24$		0			0
$25$	1.59240	+	2.75811i	0.318479	+	0.551622i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.13429	+	5.42874i	0.582022	+	1.00809i	0.995239	+	0.0974595i	$0.0310717\pi$
$29$	3.13429	+	5.42874i	0.582022	+	1.00809i	−0.413217	+	0.910632i	$0.635595\pi$
$30$		0			0
$31$	4.61721	−	7.99724i	0.829276	−	1.43635i	−0.0693317	−	0.997594i	$-0.522087\pi$
$31$	4.61721	−	7.99724i	0.829276	−	1.43635i	0.898607	−	0.438754i	$-0.144580\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.34730			0.227735
$36$		0			0
$37$	9.23442			1.51813			0.759065	−	0.651015i	$-0.225657\pi$
$37$	9.23442			1.51813			0.759065	+	0.651015i	$0.225657\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	−0.701536	−	0.712634i	$-0.747502\pi$
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	0.967927	+	0.251231i	$0.0808353\pi$
$42$		0			0
$43$	−2.20574	−	3.82045i	−0.336372	−	0.582613i	0.647376	−	0.762171i	$-0.275867\pi$
$43$	−2.20574	−	3.82045i	−0.336372	−	0.582613i	−0.983747	+	0.179558i	$0.942533\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.67752	−	8.10170i	−0.682286	−	1.18175i	−0.974281	−	0.225335i	$-0.927652\pi$
$47$	−4.67752	−	8.10170i	−0.682286	−	1.18175i	0.291995	−	0.956420i	$-0.405681\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.573978			0.0788419			0.0394210	−	0.999223i	$-0.487449\pi$
$53$	0.573978			0.0788419			0.0394210	+	0.999223i	$0.487449\pi$
$54$		0			0
$55$	−2.22668			−0.300246
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.19846	−	9.00400i	0.676782	−	1.17222i	−0.299162	−	0.954202i	$-0.596707\pi$
$59$	5.19846	−	9.00400i	0.676782	−	1.17222i	0.975945	−	0.218019i	$-0.0699595\pi$
$60$		0			0
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	0.510937	−	0.859618i	$-0.329299\pi$
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	−0.999920	+	0.0126752i	$0.995965\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.26991	−	3.93161i	−0.281548	−	0.487656i
$66$		0			0
$67$	0.298133	−	0.516382i	0.0364228	−	0.0630861i	−0.847239	−	0.531211i	$-0.821737\pi$
$67$	0.298133	−	0.516382i	0.0364228	−	0.0630861i	0.883662	+	0.468125i	$0.155070\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.554378			−0.0657925			−0.0328963	−	0.999459i	$-0.510473\pi$
$71$	−0.554378			−0.0657925			−0.0328963	+	0.999459i	$0.510473\pi$
$72$		0			0
$73$	2.04963			0.239891			0.119946	−	0.992780i	$-0.461728\pi$
$73$	2.04963			0.239891			0.119946	+	0.992780i	$0.461728\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.826352	−	1.43128i	0.0941715	−	0.163110i
$78$		0			0
$79$	−1.20187	−	2.08169i	−0.135221	−	0.234209i	0.790461	−	0.612512i	$-0.209841\pi$
$79$	−1.20187	−	2.08169i	−0.135221	−	0.234209i	−0.925682	+	0.378303i	$0.876508\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	0.901187	+	0.433431i	$0.142697\pi$
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	−0.0752309	+	0.997166i	$0.523969\pi$
$84$		0			0
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.08647			−0.963164			−0.481582	−	0.876401i	$-0.659938\pi$
$89$	−9.08647			−0.963164			−0.481582	+	0.876401i	$0.659938\pi$
$90$		0			0
$91$	3.36959			0.353228
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.17365	−	3.76487i	0.223012	−	0.386267i
$96$		0			0
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	0.910195	−	0.414181i	$-0.135932\pi$
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	−0.813788	+	0.581161i	$0.802598\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.854570	−	1.48016i	−0.0850329	−	0.147281i	0.820372	−	0.571830i	$-0.193766\pi$
$101$	−0.854570	−	1.48016i	−0.0850329	−	0.147281i	−0.905405	+	0.424548i	$0.860433\pi$
$102$		0			0
$103$	−1.81908	+	3.15074i	−0.179239	+	0.310451i	−0.941620	−	0.336677i	$-0.890697\pi$
$103$	−1.81908	+	3.15074i	−0.179239	+	0.310451i	0.762381	+	0.647128i	$0.224030\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.12836			0.689124			0.344562	−	0.938764i	$-0.388027\pi$
$107$	7.12836			0.689124			0.344562	+	0.938764i	$0.388027\pi$
$108$		0			0
$109$	0.403733			0.0386706			0.0193353	−	0.999813i	$-0.493845\pi$
$109$	0.403733			0.0386706			0.0193353	+	0.999813i	$0.493845\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.18479	−	12.4444i	0.675888	−	1.17067i	−0.300320	−	0.953839i	$-0.597093\pi$
$113$	7.18479	−	12.4444i	0.675888	−	1.17067i	0.976208	−	0.216835i	$-0.0695732\pi$
$114$		0			0
$115$	6.02481	+	10.4353i	0.561817	+	0.973095i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.233956	−	0.405223i	−0.0214467	−	0.0371467i
$120$		0			0
$121$	4.13429	−	7.16079i	0.375844	−	0.650981i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.0273			0.986315
$126$		0			0
$127$	20.7716			1.84318			0.921589	−	0.388167i	$-0.126892\pi$
$127$	20.7716			1.84318			0.921589	+	0.388167i	$0.126892\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.58260	−	6.20524i	0.313013	−	0.542154i	−0.666000	−	0.745952i	$-0.731995\pi$
$131$	3.58260	−	6.20524i	0.313013	−	0.542154i	0.979013	+	0.203797i	$0.0653284\pi$
$132$		0			0
$133$	1.61334	+	2.79439i	0.139894	+	0.242304i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.28446	+	2.22475i	0.109739	+	0.190074i	0.915665	−	0.401943i	$-0.131665\pi$
$137$	1.28446	+	2.22475i	0.109739	+	0.190074i	−0.805925	+	0.592017i	$0.798332\pi$
$138$		0			0
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	−0.966272	−	0.257523i	$-0.917094\pi$
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	0.706158	+	0.708055i	$0.250427\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.56893			−0.465697
$144$		0			0
$145$	8.44562			0.701371
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.215537	−	0.373321i	0.0176575	−	0.0305837i	−0.857062	−	0.515214i	$-0.827712\pi$
$149$	0.215537	−	0.373321i	0.0176575	−	0.0305837i	0.874719	+	0.484630i	$0.161046\pi$
$150$		0			0
$151$	−1.23530	−	2.13960i	−0.100527	−	0.174118i	0.811375	−	0.584526i	$-0.198720\pi$
$151$	−1.23530	−	2.13960i	−0.100527	−	0.174118i	−0.911902	+	0.410408i	$0.865386\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.22075	−	10.7747i	−0.499663	−	0.865441i
$156$		0			0
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	−0.994248	−	0.107106i	$-0.965841\pi$
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	0.589881	+	0.807491i	$0.299175\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.94356			−0.704852
$162$		0			0
$163$	2.59627			0.203355			0.101678	−	0.994817i	$-0.467579\pi$
$163$	2.59627			0.203355			0.101678	+	0.994817i	$0.467579\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.0656422	−	0.997843i	$-0.479090\pi$
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.831337	−	0.555769i	$-0.187576\pi$
$168$		0			0
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.37598	−	4.11532i	−0.180643	−	0.312882i	0.761457	−	0.648215i	$-0.224484\pi$
$173$	−2.37598	−	4.11532i	−0.180643	−	0.312882i	−0.942100	+	0.335333i	$0.891151\pi$
$174$		0			0
$175$	−1.59240	+	2.75811i	−0.120374	+	0.208494i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.53209			−0.637718			−0.318859	−	0.947802i	$-0.603300\pi$
$179$	−8.53209			−0.637718			−0.318859	+	0.947802i	$0.603300\pi$
$180$		0			0
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.22075	−	10.7747i	0.457359	−	0.792169i
$186$		0			0
$187$	0.386659	+	0.669713i	0.0282753	+	0.0489743i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.45471	−	11.1799i	−0.467046	−	0.808948i	0.532245	−	0.846590i	$-0.321349\pi$
$191$	−6.45471	−	11.1799i	−0.467046	−	0.808948i	−0.999291	+	0.0376425i	$0.988015\pi$
$192$		0			0
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	−0.854313	−	0.519759i	$-0.826022\pi$
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	0.877281	+	0.479977i	$0.159355\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.4456			−0.815467			−0.407733	−	0.913101i	$-0.633681\pi$
$197$	−11.4456			−0.815467			−0.407733	+	0.913101i	$0.633681\pi$
$198$		0			0
$199$	3.63816			0.257902			0.128951	−	0.991651i	$-0.458839\pi$
$199$	3.63816			0.257902			0.128951	+	0.991651i	$0.458839\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.13429	+	5.42874i	−0.219984	+	0.381023i
$204$		0			0
$205$	−2.29813	−	3.98048i	−0.160509	−	0.278009i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.66637	−	4.61830i	−0.184437	−	0.319454i
$210$		0			0
$211$	2.91147	−	5.04282i	0.200434	−	0.347162i	−0.748234	−	0.663435i	$-0.769098\pi$
$211$	2.91147	−	5.04282i	0.200434	−	0.347162i	0.948668	+	0.316273i	$0.102431\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.94356			−0.405348
$216$		0			0
$217$	9.23442			0.626873
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.788333	+	1.36543i	−0.0530290	+	0.0918490i
$222$		0			0
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	0.959905	−	0.280327i	$-0.0904428\pi$
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	−0.722722	+	0.691139i	$0.757109\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.97178	+	10.3434i	0.396361	+	0.686517i	0.993274	−	0.115789i	$-0.0369395\pi$
$227$	5.97178	+	10.3434i	0.396361	+	0.686517i	−0.596913	+	0.802306i	$0.703606\pi$
$228$		0			0
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	−0.415529	−	0.909580i	$-0.636403\pi$
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	0.995484	−	0.0949315i	$-0.0302632\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.2540			−1.06484			−0.532418	−	0.846481i	$-0.678717\pi$
$233$	−16.2540			−1.06484			−0.532418	+	0.846481i	$0.678717\pi$
$234$		0			0
$235$	−12.6040			−0.822195
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	−0.511565	−	0.859244i	$-0.670934\pi$
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	0.999910	+	0.0134062i	$0.00426745\pi$
$240$		0			0
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	0.999991	+	0.00424420i	$0.00135097\pi$
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	−0.496320	+	0.868140i	$0.665316\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.673648	+	1.16679i	0.0430378	+	0.0745437i
$246$		0			0
$247$	5.43629	−	9.41593i	0.345903	−	0.599121i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	19.0651			1.20338			0.601690	−	0.798730i	$-0.294494\pi$
$251$	19.0651			1.20338			0.601690	+	0.798730i	$0.294494\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.2909	−	23.0204i	0.829061	−	1.43598i	−0.0697146	−	0.997567i	$-0.522209\pi$
$257$	13.2909	−	23.0204i	0.829061	−	1.43598i	0.898776	−	0.438409i	$-0.144458\pi$
$258$		0			0
$259$	4.61721	+	7.99724i	0.286900	+	0.496925i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.367059	+	0.635765i	0.0226338	+	0.0392029i	0.877120	−	0.480270i	$-0.159461\pi$
$263$	0.367059	+	0.635765i	0.0226338	+	0.0392029i	−0.854487	+	0.519473i	$0.826128\pi$
$264$		0			0
$265$	0.386659	−	0.669713i	0.0237523	−	0.0411402i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	20.8503			1.27126			0.635632	−	0.771992i	$-0.280739\pi$
$269$	20.8503			1.27126			0.635632	+	0.771992i	$0.280739\pi$
$270$		0			0
$271$	−6.95811			−0.422675			−0.211338	−	0.977413i	$-0.567782\pi$
$271$	−6.95811			−0.422675			−0.211338	+	0.977413i	$0.567782\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.63176	−	4.55834i	0.158701	−	0.274878i
$276$		0			0
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	−0.999067	−	0.0431811i	$-0.986251\pi$
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	0.462138	−	0.886808i	$-0.347083\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.1552	+	19.3214i	0.665465	+	1.15262i	0.979159	+	0.203095i	$0.0651001\pi$
$281$	11.1552	+	19.3214i	0.665465	+	1.15262i	−0.313694	+	0.949524i	$0.601567\pi$
$282$		0			0
$283$	−9.29726	+	16.1033i	−0.552665	+	0.957243i	0.445417	+	0.895323i	$0.353056\pi$
$283$	−9.29726	+	16.1033i	−0.552665	+	0.957243i	−0.998081	+	0.0619196i	$0.980278\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.41147			0.201373
$288$		0			0
$289$	−16.7811			−0.987121
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	−0.608998	−	0.793171i	$-0.708428\pi$
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	0.991406	+	0.130822i	$0.0417618\pi$
$294$		0			0
$295$	−7.00387	−	12.1311i	−0.407781	−	0.706298i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	15.0680	+	26.0986i	0.871408	+	1.50932i
$300$		0			0
$301$	2.20574	−	3.82045i	0.127137	−	0.220207i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.2909			−0.589253
$306$		0			0
$307$	−6.31046			−0.360157			−0.180078	−	0.983652i	$-0.557635\pi$
$307$	−6.31046			−0.360157			−0.180078	+	0.983652i	$0.557635\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.76217	−	8.24833i	0.270038	−	0.467720i	−0.698833	−	0.715285i	$-0.746297\pi$
$311$	4.76217	−	8.24833i	0.270038	−	0.467720i	0.968871	+	0.247565i	$0.0796304\pi$
$312$		0			0
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	0.999998	−	0.00205946i	$-0.000655547\pi$
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	−0.501782	+	0.864994i	$0.667322\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.03849	+	6.99486i	0.226824	+	0.392871i	0.956865	−	0.290533i	$-0.0938325\pi$
$317$	4.03849	+	6.99486i	0.226824	+	0.392871i	−0.730041	+	0.683403i	$0.760499\pi$
$318$		0			0
$319$	5.18004	−	8.97210i	0.290027	−	0.502341i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.50980			−0.0840075
$324$		0			0
$325$	10.7314			0.595273
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.67752	−	8.10170i	0.257880	−	0.446661i
$330$		0			0
$331$	11.5248	+	19.9616i	0.633461	+	1.09719i	0.986839	+	0.161706i	$0.0516997\pi$
$331$	11.5248	+	19.9616i	0.633461	+	1.09719i	−0.353378	+	0.935481i	$0.614967\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.401674	−	0.695720i	−0.0219458	−	0.0380112i
$336$		0			0
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.2618			−0.826471
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.47313	+	11.2118i	−0.347496	+	0.601880i	−0.985804	−	0.167901i	$-0.946301\pi$
$347$	−6.47313	+	11.2118i	−0.347496	+	0.601880i	0.638308	+	0.769781i	$0.279635\pi$
$348$		0			0
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	0.845785	−	0.533524i	$-0.179132\pi$
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	−0.884938	+	0.465710i	$0.845799\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	0.991267	−	0.131873i	$-0.0420992\pi$
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	−0.609839	+	0.792525i	$0.708766\pi$
$354$		0			0
$355$	−0.373455	+	0.646844i	−0.0198210	+	0.0343309i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.9368			−1.10500			−0.552500	−	0.833513i	$-0.686326\pi$
$359$	−20.9368			−1.10500			−0.552500	+	0.833513i	$0.686326\pi$
$360$		0			0
$361$	−8.58853			−0.452028
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.38073	−	2.39149i	0.0722707	−	0.125176i
$366$		0			0
$367$	−6.02869	−	10.4420i	−0.314695	−	0.545067i	0.664678	−	0.747130i	$-0.268569\pi$
$367$	−6.02869	−	10.4420i	−0.314695	−	0.545067i	−0.979373	+	0.202063i	$0.935236\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.286989	+	0.497079i	0.0148997	+	0.0258071i
$372$		0			0
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	−0.855738	−	0.517410i	$-0.826896\pi$
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	0.875959	+	0.482386i	$0.160230\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	21.1225			1.08786
$378$		0			0
$379$	6.92396			0.355660			0.177830	−	0.984061i	$-0.443092\pi$
$379$	6.92396			0.355660			0.177830	+	0.984061i	$0.443092\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.86618	+	6.69642i	−0.197553	+	0.342171i	−0.947734	−	0.319061i	$-0.896633\pi$
$383$	−3.86618	+	6.69642i	−0.197553	+	0.342171i	0.750182	+	0.661232i	$0.229966\pi$
$384$		0			0
$385$	−1.11334	−	1.92836i	−0.0567411	−	0.0982785i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.69981	+	4.67620i	0.136886	+	0.237093i	0.926316	−	0.376747i	$-0.122957\pi$
$389$	2.69981	+	4.67620i	0.136886	+	0.237093i	−0.789431	+	0.613840i	$0.789624\pi$
$390$		0			0
$391$	2.09240	−	3.62414i	0.105817	−	0.183280i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.23854			−0.162949
$396$		0			0
$397$	−29.2344			−1.46723			−0.733617	−	0.679563i	$-0.762169\pi$
$397$	−29.2344			−1.46723			−0.733617	+	0.679563i	$0.762169\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.6989	+	23.7272i	−0.684092	+	1.18488i	0.289629	+	0.957139i	$0.406468\pi$
$401$	−13.6989	+	23.7272i	−0.684092	+	1.18488i	−0.973721	+	0.227743i	$0.926865\pi$
$402$		0			0
$403$	−15.5581	−	26.9474i	−0.775003	−	1.34235i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.63088	−	13.2171i	−0.378249	−	0.655146i
$408$		0			0
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	−0.732628	−	0.680629i	$-0.761706\pi$
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	0.955756	+	0.294160i	$0.0950398\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.3969			0.511599
$414$		0			0
$415$	20.2763			0.995325
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	−0.868158	−	0.496287i	$-0.834696\pi$
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	0.863877	+	0.503704i	$0.168030\pi$
$420$		0			0
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.745100	−	1.29055i	−0.0361427	−	0.0626009i
$426$		0			0
$427$	3.81908	−	6.61484i	0.184818	−	0.320114i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−29.3191			−1.41225			−0.706126	−	0.708086i	$-0.749559\pi$
$431$	−29.3191			−1.41225			−0.706126	+	0.708086i	$0.749559\pi$
$432$		0			0
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.4290	+	24.9918i	−0.690233	+	1.19552i
$438$		0			0
$439$	−10.9650	−	18.9919i	−0.523330	−	0.906434i	−0.999631	−	0.0271516i	$-0.991356\pi$
$439$	−10.9650	−	18.9919i	−0.523330	−	0.906434i	0.476302	−	0.879282i	$-0.341977\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.35504	+	16.2034i	0.444471	+	0.769847i	0.998015	−	0.0629732i	$-0.0200583\pi$
$443$	9.35504	+	16.2034i	0.444471	+	0.769847i	−0.553544	+	0.832820i	$0.686725\pi$
$444$		0			0
$445$	−6.12108	+	10.6020i	−0.290167	+	0.502584i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.68004			−0.315251			−0.157625	−	0.987499i	$-0.550384\pi$
$449$	−6.68004			−0.315251			−0.157625	+	0.987499i	$0.550384\pi$
$450$		0			0
$451$	−5.63816			−0.265490
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.26991	−	3.93161i	0.106415	−	0.184317i
$456$		0			0
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	0.998655	−	0.0518563i	$-0.0165138\pi$
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	−0.544236	+	0.838932i	$0.683180\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	0.854560	−	0.519352i	$-0.173827\pi$
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	−0.877052	+	0.480395i	$0.840493\pi$
$462$		0			0
$463$	−0.222811	+	0.385920i	−0.0103549	+	0.0179352i	−0.871156	−	0.491006i	$-0.836629\pi$
$463$	−0.222811	+	0.385920i	−0.0103549	+	0.0179352i	0.860802	+	0.508941i	$0.169963\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−34.2148			−1.58327			−0.791637	−	0.610992i	$-0.790771\pi$
$467$	−34.2148			−1.58327			−0.791637	+	0.610992i	$0.790771\pi$
$468$		0			0
$469$	0.596267			0.0275330
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.64543	+	6.31407i	−0.167617	+	0.290321i
$474$		0			0
$475$	5.13816	+	8.89955i	0.235755	+	0.408339i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.8965	+	18.8732i	0.497872	+	0.862339i	0.999997	−	0.00245553i	$-0.000781622\pi$
$479$	10.8965	+	18.8732i	0.497872	+	0.862339i	−0.502125	+	0.864795i	$0.667448\pi$
$480$		0			0
$481$	15.5581	−	26.9474i	0.709388	−	1.22870i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.55850			0.116175
$486$		0			0
$487$	−19.3928			−0.878772			−0.439386	−	0.898298i	$-0.644804\pi$
$487$	−19.3928			−0.878772			−0.439386	+	0.898298i	$0.644804\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	0.403987	+	0.914765i	$0.367624\pi$
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	−0.994203	+	0.107519i	$0.965709\pi$
$492$		0			0
$493$	−1.46657	−	2.54017i	−0.0660509	−	0.114403i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.277189	−	0.480105i	−0.0124336	−	0.0215357i
$498$		0			0
$499$	−7.15064	+	12.3853i	−0.320107	+	0.554441i	−0.980510	−	0.196470i	$-0.937052\pi$
$499$	−7.15064	+	12.3853i	−0.320107	+	0.554441i	0.660403	+	0.750911i	$0.270385\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.7033			0.833937			0.416969	−	0.908921i	$-0.363092\pi$
$503$	18.7033			0.833937			0.416969	+	0.908921i	$0.363092\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.8045	+	22.1781i	−0.567551	+	0.983027i	0.429257	+	0.903183i	$0.358776\pi$
$509$	−12.8045	+	22.1781i	−0.567551	+	0.983027i	−0.996807	+	0.0798442i	$0.974558\pi$
$510$		0			0
$511$	1.02481	+	1.77503i	0.0453351	+	0.0785228i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.45084	+	4.24497i	0.107997	+	0.187056i
$516$		0			0
$517$	−7.73055	+	13.3897i	−0.339989	+	0.588879i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	21.2121			0.929320			0.464660	−	0.885489i	$-0.346176\pi$
$521$	21.2121			0.929320			0.464660	+	0.885489i	$0.346176\pi$
$522$		0			0
$523$	−20.8057			−0.909770			−0.454885	−	0.890550i	$-0.650320\pi$
$523$	−20.8057			−0.909770			−0.454885	+	0.890550i	$0.650320\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.16044	+	3.74200i	−0.0941104	+	0.163004i
$528$		0			0
$529$	−28.4937	−	49.3525i	−1.23885	−	2.14576i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.74763	−	9.95518i	−0.248957	−	0.431207i
$534$		0			0
$535$	4.80200	−	8.31731i	0.207609	−	0.359589i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.65270			0.0711870
$540$		0			0
$541$	26.7297			1.14920			0.574599	−	0.818435i	$-0.305158\pi$
$541$	26.7297			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.271974	−	0.471073i	0.0116501	−	0.0201786i
$546$		0			0
$547$	18.3812	+	31.8372i	0.785923	+	1.36126i	0.928446	+	0.371467i	$0.121145\pi$
$547$	18.3812	+	31.8372i	0.785923	+	1.36126i	−0.142523	+	0.989792i	$0.545521\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.1133	+	17.5168i	0.430843	+	0.746242i
$552$		0			0
$553$	1.20187	−	2.08169i	0.0511086	−	0.0885226i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−32.3387			−1.37024			−0.685118	−	0.728432i	$-0.740249\pi$
$557$	−32.3387			−1.37024			−0.685118	+	0.728432i	$0.740249\pi$
$558$		0			0
$559$	−14.8648			−0.628716
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.87093	−	15.3649i	0.373865	−	0.647553i	−0.616291	−	0.787518i	$-0.711366\pi$
$563$	8.87093	−	15.3649i	0.373865	−	0.647553i	0.990156	+	0.139965i	$0.0446990\pi$
$564$		0			0
$565$	−9.68004	−	16.7663i	−0.407243	−	0.705365i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.3007	−	23.0374i	−0.557593	−	0.965779i	−0.997697	−	0.0678320i	$-0.978392\pi$
$569$	−13.3007	−	23.0374i	−0.557593	−	0.965779i	0.440104	−	0.897947i	$-0.354942\pi$
$570$		0			0
$571$	−5.00862	+	8.67518i	−0.209604	+	0.363045i	−0.951590	−	0.307371i	$-0.900551\pi$
$571$	−5.00862	+	8.67518i	−0.209604	+	0.363045i	0.741986	+	0.670416i	$0.233884\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−28.4834			−1.18784
$576$		0			0
$577$	−32.9145			−1.37025			−0.685124	−	0.728427i	$-0.740252\pi$
$577$	−32.9145			−1.37025			−0.685124	+	0.728427i	$0.740252\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.52481	+	13.0334i	−0.312182	+	0.540715i
$582$		0			0
$583$	−0.474308	−	0.821525i	−0.0196438	−	0.0340241i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	0.978592	−	0.205808i	$-0.0659821\pi$
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	−0.667531	+	0.744582i	$0.732649\pi$
$588$		0			0
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−41.0009			−1.68371			−0.841853	−	0.539706i	$-0.818535\pi$
$593$	−41.0009			−1.68371			−0.841853	+	0.539706i	$0.818535\pi$
$594$		0			0
$595$	−0.630415			−0.0258445
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.03684	+	5.25996i	−0.124082	+	0.214916i	−0.921374	−	0.388678i	$-0.872932\pi$
$599$	−3.03684	+	5.25996i	−0.124082	+	0.214916i	0.797292	+	0.603594i	$0.206265\pi$
$600$		0			0
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	0.973402	−	0.229102i	$-0.0735791\pi$
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	−0.685110	+	0.728440i	$0.740246\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.57011	−	9.64771i	−0.226457	−	0.392235i
$606$		0			0
$607$	23.0449	−	39.9149i	0.935363	−	1.62010i	0.161377	−	0.986893i	$-0.448406\pi$
$607$	23.0449	−	39.9149i	0.935363	−	1.62010i	0.773986	−	0.633203i	$-0.218260\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−31.5226			−1.27527
$612$		0			0
$613$	−26.4938			−1.07008			−0.535038	−	0.844828i	$-0.679703\pi$
$613$	−26.4938			−1.07008			−0.535038	+	0.844828i	$0.679703\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.12495	+	1.94847i	−0.0452889	+	0.0784426i	−0.887781	−	0.460266i	$-0.847754\pi$
$617$	−1.12495	+	1.94847i	−0.0452889	+	0.0784426i	0.842492	+	0.538708i	$0.181087\pi$
$618$		0			0
$619$	3.09539	+	5.36137i	0.124414	+	0.215492i	0.921504	−	0.388369i	$-0.126962\pi$
$619$	3.09539	+	5.36137i	0.124414	+	0.215492i	−0.797090	+	0.603861i	$0.793628\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.54323	−	7.86911i	−0.182021	−	0.315269i
$624$		0			0
$625$	−0.533433	+	0.923933i	−0.0213373	+	0.0369573i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.32089			−0.172285
$630$		0			0
$631$	−26.1661			−1.04166			−0.520829	−	0.853661i	$-0.674377\pi$
$631$	−26.1661			−1.04166			−0.520829	+	0.853661i	$0.674377\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	13.9927	−	24.2361i	0.555284	−	0.961781i
$636$		0			0
$637$	1.68479	+	2.91815i	0.0667539	+	0.115621i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.44444	+	4.23389i	0.0965496	+	0.167229i	0.910254	−	0.414050i	$-0.135886\pi$
$641$	2.44444	+	4.23389i	0.0965496	+	0.167229i	−0.813705	+	0.581278i	$0.802553\pi$
$642$		0			0
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	0.126242	+	0.992000i	$0.459709\pi$
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	−0.922218	+	0.386671i	$0.873625\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.28075			−0.0896657			−0.0448329	−	0.998995i	$-0.514276\pi$
$647$	−2.28075			−0.0896657			−0.0448329	+	0.998995i	$0.514276\pi$
$648$		0			0
$649$	−17.1830			−0.674493
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.7396	−	20.3336i	0.459407	−	0.795717i	−0.539522	−	0.841971i	$-0.681395\pi$
$653$	11.7396	−	20.3336i	0.459407	−	0.795717i	0.998930	+	0.0462542i	$0.0147284\pi$
$654$		0			0
$655$	−4.82682	−	8.36030i	−0.188599	−	0.326664i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.776101	+	0.630609i	$0.217195\pi$
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.158073	+	0.987427i	$0.449472\pi$
$660$		0			0
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	0.426571	+	0.904454i	$0.359721\pi$
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	−0.996566	+	0.0828055i	$0.973612\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.34730			0.168581
$666$		0			0
$667$	−56.0634			−2.17078
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.31180	+	10.9324i	−0.243664	+	0.422039i
$672$		0			0
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.9454	+	31.0823i	0.689697	+	1.19459i	0.971936	+	0.235246i	$0.0755895\pi$
$677$	17.9454	+	31.0823i	0.689697	+	1.19459i	−0.282239	+	0.959344i	$0.591077\pi$
$678$		0			0
$679$	−0.949493	+	1.64457i	−0.0364382	+	0.0631128i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	35.0642			1.34169			0.670847	−	0.741596i	$-0.265931\pi$
$683$	35.0642			1.34169			0.670847	+	0.741596i	$0.265931\pi$
$684$		0			0
$685$	3.46110			0.132242
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.967034	−	1.67495i	0.0368411	−	0.0638106i
$690$		0			0
$691$	1.03343	+	1.78996i	0.0393136	+	0.0680932i	0.885013	−	0.465567i	$-0.154150\pi$
$691$	1.03343	+	1.78996i	0.0393136	+	0.0680932i	−0.845699	+	0.533660i	$0.820816\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.13176	+	7.15642i	0.156727	+	0.271458i
$696$		0			0
$697$	−0.798133	+	1.38241i	−0.0302315	+	0.0523624i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	7.36009			0.277987			0.138993	−	0.990293i	$-0.455613\pi$
$701$	7.36009			0.277987			0.138993	+	0.990293i	$0.455613\pi$
$702$		0			0
$703$	29.7965			1.12380
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.854570	−	1.48016i	0.0321394	−	0.0556671i
$708$		0			0
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	0.767742	−	0.640760i	$-0.221380\pi$
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	−0.938785	+	0.344504i	$0.888047\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	41.2943	+	71.5239i	1.54648	+	2.67859i
$714$		0			0
$715$	−3.75150	+	6.49778i	−0.140298	+	0.243003i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−25.9537			−0.967908			−0.483954	−	0.875093i	$-0.660800\pi$
$719$	−25.9537			−0.967908			−0.483954	+	0.875093i	$0.660800\pi$
$720$		0			0
$721$	−3.63816			−0.135492
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.98205	+	17.2894i	−0.370724	+	0.642113i
$726$		0			0
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	0.756311	−	0.654213i	$-0.227000\pi$
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	−0.944720	+	0.327878i	$0.893667\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.03209	+	1.78763i	0.0381732	+	0.0661179i
$732$		0			0
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	0.196441	+	0.980516i	$0.437062\pi$
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	−0.947372	+	0.320135i	$0.896272\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.985452			−0.0362996
$738$		0			0
$739$	25.3618			0.932951			0.466475	−	0.884534i	$-0.345524\pi$
$739$	25.3618			0.932951			0.466475	+	0.884534i	$0.345524\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	−0.583377	−	0.812202i	$-0.698269\pi$
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	0.995076	+	0.0991184i	$0.0316023\pi$
$744$		0			0
$745$	−0.290393	−	0.502975i	−0.0106392	−	0.0184276i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.56418	+	6.17334i	0.130232	+	0.225569i
$750$		0			0
$751$	12.1086	−	20.9727i	0.441849	−	0.765305i	−0.555978	−	0.831197i	$-0.687656\pi$
$751$	12.1086	−	20.9727i	0.441849	−	0.765305i	0.997827	+	0.0658924i	$0.0209894\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.32863			−0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.13610	+	15.8242i	−0.331183	+	0.573626i	−0.982744	−	0.184970i	$-0.940781\pi$
$761$	−9.13610	+	15.8242i	−0.331183	+	0.573626i	0.651561	+	0.758596i	$0.274114\pi$
$762$		0			0
$763$	0.201867	+	0.349643i	0.00730806	+	0.0126579i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.5167	−	30.3398i	−0.632490	−	1.09550i
$768$		0			0
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	−0.983310	−	0.181936i	$-0.941764\pi$
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	0.649217	+	0.760604i	$0.275097\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.96080			0.106493			0.0532463	−	0.998581i	$-0.483043\pi$
$773$	2.96080			0.106493			0.0532463	+	0.998581i	$0.483043\pi$
$774$		0			0
$775$	29.4097			1.05643
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.50387	−	9.53298i	0.197197	−	0.341555i
$780$		0			0
$781$	0.458111	+	0.793471i	0.0163925	+	0.0283926i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.82635	+	11.8236i	0.243643	+	0.422002i
$786$		0			0
$787$	−16.7010	+	28.9270i	−0.595326	+	1.03113i	0.398175	+	0.917310i	$0.369644\pi$
$787$	−16.7010	+	28.9270i	−0.595326	+	1.03113i	−0.993501	+	0.113825i	$0.963690\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	14.3696			0.510924
$792$		0			0
$793$	−25.7374			−0.913962
$794$		0			0
$795$		0			0
$796$		0			0
$797$	24.6755	−	42.7391i	0.874050	−	1.51390i	0.0162779	−	0.999868i	$-0.494818\pi$
$797$	24.6755	−	42.7391i	0.874050	−	1.51390i	0.857772	−	0.514031i	$-0.171848\pi$
$798$		0			0
$799$	2.18866	+	3.79088i	0.0774293	+	0.134112i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.69372	−	2.93360i	−0.0597699	−	0.103525i
$804$		0			0
$805$	−6.02481	+	10.4353i	−0.212347	+	0.367795i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−19.8280			−0.697115			−0.348558	−	0.937287i	$-0.613328\pi$
$809$	−19.8280			−0.697115			−0.348558	+	0.937287i	$0.613328\pi$
$810$		0			0
$811$	23.8557			0.837686			0.418843	−	0.908059i	$-0.362436\pi$
$811$	23.8557			0.837686			0.418843	+	0.908059i	$0.362436\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.74897	−	3.02931i	0.0612638	−	0.106112i
$816$		0			0
$817$	−7.11721	−	12.3274i	−0.249000	−	0.431280i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.4714	−	44.1177i	−0.888957	−	1.53972i	−0.841110	−	0.540864i	$-0.818097\pi$
$821$	−25.4714	−	44.1177i	−0.888957	−	1.53972i	−0.0478469	−	0.998855i	$-0.515236\pi$
$822$		0			0
$823$	6.80747	−	11.7909i	0.237293	−	0.411004i	−0.722643	−	0.691221i	$-0.757073\pi$
$823$	6.80747	−	11.7909i	0.237293	−	0.411004i	0.959937	+	0.280217i	$0.0904064\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.2158			1.25935			0.629673	−	0.776861i	$-0.283189\pi$
$827$	36.2158			1.25935			0.629673	+	0.776861i	$0.283189\pi$
$828$		0			0
$829$	25.3259			0.879606			0.439803	−	0.898094i	$-0.355048\pi$
$829$	25.3259			0.879606			0.439803	+	0.898094i	$0.355048\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.233956	−	0.405223i	0.00810608	−	0.0140401i
$834$		0			0
$835$	−15.6172	−	27.0498i	−0.540456	−	0.936097i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.35710	−	7.54671i	−0.150424	−	0.260541i	0.780960	−	0.624582i	$-0.214730\pi$
$839$	−4.35710	−	7.54671i	−0.150424	−	0.260541i	−0.931383	+	0.364040i	$0.881397\pi$
$840$		0			0
$841$	−5.14749	+	8.91571i	−0.177500	+	0.307438i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.21751			0.0762847
$846$		0			0
$847$	8.26857			0.284111
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−41.2943	+	71.5239i	−1.41555	+	2.45181i
$852$		0			0
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	0.950170	−	0.311733i	$-0.100909\pi$
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	−0.745053	+	0.667005i	$0.767576\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.25015	+	5.62943i	0.111023	+	0.192298i	0.916183	−	0.400760i	$-0.131254\pi$
$857$	3.25015	+	5.62943i	0.111023	+	0.192298i	−0.805160	+	0.593058i	$0.797921\pi$
$858$		0			0
$859$	−26.7763	+	46.3779i	−0.913596	+	1.58239i	−0.104652	+	0.994509i	$0.533373\pi$
$859$	−26.7763	+	46.3779i	−0.913596	+	1.58239i	−0.808944	+	0.587886i	$0.799960\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.69965			0.125937			0.0629687	−	0.998016i	$-0.479943\pi$
$863$	3.69965			0.125937			0.0629687	+	0.998016i	$0.479943\pi$
$864$		0			0
$865$	−6.40230			−0.217685
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.98633	+	3.44042i	−0.0673816	+	0.116708i
$870$		0			0
$871$	−1.00459	−	1.73999i	−0.0340391	−	0.0589574i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.51367	+	9.54996i	0.186396	+	0.322847i
$876$		0			0
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	−0.749178	−	0.662369i	$-0.769551\pi$
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	0.948217	+	0.317622i	$0.102884\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−49.4858			−1.66722			−0.833609	−	0.552355i	$-0.813729\pi$
$881$	−49.4858			−1.66722			−0.833609	+	0.552355i	$0.813729\pi$
$882$		0			0
$883$	21.5357			0.724734			0.362367	−	0.932035i	$-0.381969\pi$
$883$	21.5357			0.724734			0.362367	+	0.932035i	$0.381969\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.94238	+	10.2925i	−0.199526	+	0.345589i	−0.948375	−	0.317152i	$-0.897273\pi$
$887$	−5.94238	+	10.2925i	−0.199526	+	0.345589i	0.748849	+	0.662741i	$0.230607\pi$
$888$		0			0
$889$	10.3858	+	17.9887i	0.348328	+	0.603322i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−15.0929	−	26.1416i	−0.505063	−	0.874795i
$894$		0			0
$895$	−5.74763	+	9.95518i	−0.192122	+	0.332765i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	57.8866			1.93063
$900$		0			0
$901$	−0.268571			−0.00894739
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−11.6099	+	20.1090i	−0.385927	+	0.668446i
$906$		0			0
$907$	−13.0107	−	22.5353i	−0.432014	−	0.748271i	0.565032	−	0.825069i	$-0.308864\pi$
$907$	−13.0107	−	22.5353i	−0.432014	−	0.748271i	−0.997047	+	0.0767980i	$0.975530\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	2.01636	+	3.49244i	0.0668050	+	0.115710i	0.897493	−	0.441028i	$-0.145386\pi$
$911$	2.01636	+	3.49244i	0.0668050	+	0.115710i	−0.830688	+	0.556738i	$0.812053\pi$
$912$		0			0
$913$	12.4363	−	21.5403i	0.411581	−	0.712879i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.16519			0.236615
$918$		0			0
$919$	−27.4270			−0.904732			−0.452366	−	0.891832i	$-0.649420\pi$
$919$	−27.4270			−0.904732			−0.452366	+	0.891832i	$0.649420\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.934011	+	1.61775i	−0.0307434	+	0.0532491i
$924$		0			0
$925$	14.7049	+	25.4696i	0.483493	+	0.837434i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.83837	+	6.64826i	0.125933	+	0.218122i	0.922097	−	0.386958i	$-0.126474\pi$
$929$	3.83837	+	6.64826i	0.125933	+	0.218122i	−0.796164	+	0.605081i	$0.793141\pi$
$930$		0			0
$931$	−1.61334	+	2.79439i	−0.0528751	+	0.0915824i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.04189			0.0340734
$936$		0			0
$937$	−2.02465			−0.0661425			−0.0330713	−	0.999453i	$-0.510529\pi$
$937$	−2.02465			−0.0661425			−0.0330713	+	0.999453i	$0.510529\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.06964	+	5.31677i	−0.100067	+	0.173322i	−0.911712	−	0.410829i	$-0.865239\pi$
$941$	−3.06964	+	5.31677i	−0.100067	+	0.173322i	0.811645	+	0.584151i	$0.198573\pi$
$942$		0			0
$943$	15.2554	+	26.4231i	0.496783	+	0.860454i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.78224	−	4.81898i	−0.0904107	−	0.156596i	0.817273	−	0.576250i	$-0.195485\pi$
$947$	−2.78224	−	4.81898i	−0.0904107	−	0.156596i	−0.907684	+	0.419654i	$0.862151\pi$
$948$		0			0
$949$	3.45320	−	5.98112i	0.112096	−	0.194155i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	8.72018			0.282474			0.141237	−	0.989976i	$-0.454892\pi$
$953$	8.72018			0.282474			0.141237	+	0.989976i	$0.454892\pi$
$954$		0			0
$955$	−17.3928			−0.562818
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.28446	+	2.22475i	−0.0414775	+	0.0718411i
$960$		0			0
$961$	−27.1373	−	47.0031i	−0.875396	−	1.51623i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.429892	−	0.744596i	−0.0138387	−	0.0239694i
$966$		0			0
$967$	−28.8849	+	50.0301i	−0.928876	+	1.60886i	−0.143670	+	0.989626i	$0.545890\pi$
$967$	−28.8849	+	50.0301i	−0.928876	+	1.60886i	−0.785206	+	0.619235i	$0.787443\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−30.7192			−0.985828			−0.492914	−	0.870078i	$-0.664068\pi$
$971$	−30.7192			−0.985828			−0.492914	+	0.870078i	$0.664068\pi$
$972$		0			0
$973$	−6.13341			−0.196628
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.15002	−	8.92009i	0.164764	−	0.285379i	−0.771808	−	0.635856i	$-0.780647\pi$
$977$	5.15002	−	8.92009i	0.164764	−	0.285379i	0.936571	+	0.350477i	$0.113981\pi$
$978$		0			0
$979$	7.50862	+	13.0053i	0.239976	+	0.415651i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.84817	−	11.8614i	−0.218423	−	0.378319i	0.735903	−	0.677087i	$-0.236758\pi$
$983$	−6.84817	−	11.8614i	−0.218423	−	0.378319i	−0.954326	+	0.298767i	$0.903425\pi$
$984$		0			0
$985$	−7.71032	+	13.3547i	−0.245671	+	0.425515i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	39.4543			1.25457
$990$		0			0
$991$	−57.9813			−1.84184			−0.920919	−	0.389754i	$-0.872560\pi$
$991$	−57.9813			−1.84184			−0.920919	+	0.389754i	$0.872560\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.45084	−	4.24497i	0.0776968	−	0.134575i
$996$		0			0
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	0.708578	−	0.705633i	$-0.249337\pi$
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	−0.965385	+	0.260830i	$0.916004\pi$
$998$		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.1009.2		6
3.2	odd	2		1008.2.r.h.337.2		6
4.3	odd	2		189.2.f.b.64.1		6
9.2	odd	6		1008.2.r.h.673.2		6
9.4	even	3		9072.2.a.bs.1.2		3
9.5	odd	6		9072.2.a.ca.1.2		3
9.7	even	3	inner	3024.2.r.k.2017.2		6
12.11	even	2		63.2.f.a.22.3	✓	6
28.3	even	6		1323.2.h.b.226.3		6
28.11	odd	6		1323.2.h.c.226.3		6
28.19	even	6		1323.2.g.e.361.1		6
28.23	odd	6		1323.2.g.d.361.1		6
28.27	even	2		1323.2.f.d.442.1		6
36.7	odd	6		189.2.f.b.127.1		6
36.11	even	6		63.2.f.a.43.3	yes	6
36.23	even	6		567.2.a.h.1.1		3
36.31	odd	6		567.2.a.c.1.3		3
84.11	even	6		441.2.h.d.373.1		6
84.23	even	6		441.2.g.c.67.3		6
84.47	odd	6		441.2.g.b.67.3		6
84.59	odd	6		441.2.h.e.373.1		6
84.83	odd	2		441.2.f.c.148.3		6
252.11	even	6		441.2.g.c.79.3		6
252.47	odd	6		441.2.h.e.214.1		6
252.79	odd	6		1323.2.h.c.802.3		6
252.83	odd	6		441.2.f.c.295.3		6
252.115	even	6		1323.2.g.e.667.1		6
252.139	even	6		3969.2.a.l.1.3		3
252.151	odd	6		1323.2.g.d.667.1		6
252.167	odd	6		3969.2.a.q.1.1		3
252.187	even	6		1323.2.h.b.802.3		6
252.191	even	6		441.2.h.d.214.1		6
252.223	even	6		1323.2.f.d.883.1		6
252.227	odd	6		441.2.g.b.79.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	12.11	even	2
63.2.f.a.43.3	yes	6	36.11	even	6
189.2.f.b.64.1		6	4.3	odd	2
189.2.f.b.127.1		6	36.7	odd	6
441.2.f.c.148.3		6	84.83	odd	2
441.2.f.c.295.3		6	252.83	odd	6
441.2.g.b.67.3		6	84.47	odd	6
441.2.g.b.79.3		6	252.227	odd	6
441.2.g.c.67.3		6	84.23	even	6
441.2.g.c.79.3		6	252.11	even	6
441.2.h.d.214.1		6	252.191	even	6
441.2.h.d.373.1		6	84.11	even	6
441.2.h.e.214.1		6	252.47	odd	6
441.2.h.e.373.1		6	84.59	odd	6
567.2.a.c.1.3		3	36.31	odd	6
567.2.a.h.1.1		3	36.23	even	6
1008.2.r.h.337.2		6	3.2	odd	2
1008.2.r.h.673.2		6	9.2	odd	6
1323.2.f.d.442.1		6	28.27	even	2
1323.2.f.d.883.1		6	252.223	even	6
1323.2.g.d.361.1		6	28.23	odd	6
1323.2.g.d.667.1		6	252.151	odd	6
1323.2.g.e.361.1		6	28.19	even	6
1323.2.g.e.667.1		6	252.115	even	6
1323.2.h.b.226.3		6	28.3	even	6
1323.2.h.b.802.3		6	252.187	even	6
1323.2.h.c.226.3		6	28.11	odd	6
1323.2.h.c.802.3		6	252.79	odd	6
3024.2.r.k.1009.2		6	1.1	even	1	trivial
3024.2.r.k.2017.2		6	9.7	even	3	inner
3969.2.a.l.1.3		3	252.139	even	6
3969.2.a.q.1.1		3	252.167	odd	6
9072.2.a.bs.1.2		3	9.4	even	3
9072.2.a.ca.1.2		3	9.5	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)

\(f(q)\)	\(=\)	\(q+(0.673648 - 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(0.673648 - 1.16679i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.826352 - 1.43128i) q^{11} +(1.68479 - 2.91815i) q^{13} -0.467911 q^{17} +3.22668 q^{19} +(-4.47178 + 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} +(3.13429 + 5.42874i) q^{29} +(4.61721 - 7.99724i) q^{31} +1.34730 q^{35} +9.23442 q^{37} +(1.70574 - 2.95442i) q^{41} +(-2.20574 - 3.82045i) q^{43} +(-4.67752 - 8.10170i) q^{47} +(-0.500000 + 0.866025i) q^{49} +0.573978 q^{53} -2.22668 q^{55} +(5.19846 - 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +(-2.26991 - 3.93161i) q^{65} +(0.298133 - 0.516382i) q^{67} -0.554378 q^{71} +2.04963 q^{73} +(0.826352 - 1.43128i) q^{77} +(-1.20187 - 2.08169i) q^{79} +(7.52481 + 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} -9.08647 q^{89} +3.36959 q^{91} +(2.17365 - 3.76487i) q^{95} +(0.949493 + 1.64457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7}+O(q^{10}) \) 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

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