LMFDB - Embedded newform 3024.2.r.j.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:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2017.3
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	3024.2017
Dual form			3024.2.r.j.1009.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23025 + 2.13086i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})$	$q+(1.23025 + 2.13086i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.32383 + 4.02499i) q^{11} +(-3.55408 - 6.15585i) q^{13} +4.51459 q^{17} -4.32743 q^{19} +(-2.93346 - 5.08091i) q^{23} +(-0.527042 + 0.912864i) q^{25} +(-3.48755 + 6.04061i) q^{29} +(-3.69076 - 6.39258i) q^{31} -2.46050 q^{35} -0.726654 q^{37} +(0.136673 + 0.236725i) q^{41} +(-2.41741 + 4.18708i) q^{43} +(-1.83628 + 3.18054i) q^{47} +(-0.500000 - 0.866025i) q^{49} -5.05408 q^{53} -11.4356 q^{55} +(-4.56654 - 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(8.74484 - 15.1465i) q^{65} +(-0.663715 - 1.14959i) q^{67} +13.5218 q^{71} -4.32743 q^{73} +(-2.32383 - 4.02499i) q^{77} +(3.21780 - 5.57339i) q^{79} +(-0.742705 + 1.28640i) q^{83} +(5.55408 + 9.61996i) q^{85} -9.83482 q^{89} +7.10817 q^{91} +(-5.32383 - 9.22115i) q^{95} +(0.246304 - 0.426611i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q + q^5 - 3 * q^7	$ 6 q + q^{5} - 3 q^{7} - 2 q^{11} - 3 q^{13} - 4 q^{17} - 6 q^{19} - 14 q^{23} + 6 q^{25} + q^{29} - 3 q^{31} - 2 q^{35} - 6 q^{37} + 3 q^{43} - 21 q^{47} - 3 q^{49} - 12 q^{53} - 12 q^{55} - 31 q^{59} - 6 q^{61} + 15 q^{65} + 6 q^{67} + 34 q^{71} - 6 q^{73} - 2 q^{77} - 9 q^{79} - 20 q^{83} + 15 q^{85} - 24 q^{89} + 6 q^{91} - 20 q^{95} + 9 q^{97}+O(q^{100}) $ 6 * q + q^5 - 3 * q^7 - 2 * q^11 - 3 * q^13 - 4 * q^17 - 6 * q^19 - 14 * q^23 + 6 * q^25 + q^29 - 3 * q^31 - 2 * q^35 - 6 * q^37 + 3 * q^43 - 21 * q^47 - 3 * q^49 - 12 * q^53 - 12 * q^55 - 31 * q^59 - 6 * q^61 + 15 * q^65 + 6 * q^67 + 34 * q^71 - 6 * q^73 - 2 * q^77 - 9 * q^79 - 20 * q^83 + 15 * q^85 - 24 * q^89 + 6 * q^91 - 20 * q^95 + 9 * 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
$5$	1.23025	+	2.13086i	0.550186	+	0.952949i	0.998261	+	0.0589535i	$0.0187764\pi$
$5$	1.23025	+	2.13086i	0.550186	+	0.952949i	−0.448075	+	0.893996i	$0.647890\pi$
$6$		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
$11$	−2.32383	+	4.02499i	−0.700662	+	1.21358i	0.267573	+	0.963538i	$0.413778\pi$
$11$	−2.32383	+	4.02499i	−0.700662	+	1.21358i	−0.968234	+	0.250044i	$0.919555\pi$
$12$		0			0
$13$	−3.55408	−	6.15585i	−0.985726	−	1.70733i	−0.638667	−	0.769484i	$-0.720514\pi$
$13$	−3.55408	−	6.15585i	−0.985726	−	1.70733i	−0.347059	−	0.937843i	$-0.612820\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.51459			1.09495			0.547474	−	0.836822i	$-0.315589\pi$
$17$	4.51459			1.09495			0.547474	+	0.836822i	$0.315589\pi$
$18$		0			0
$19$	−4.32743			−0.992781			−0.496390	−	0.868099i	$-0.665342\pi$
$19$	−4.32743			−0.992781			−0.496390	+	0.868099i	$0.665342\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.93346	−	5.08091i	−0.611669	−	1.05944i	−0.990959	−	0.134164i	$-0.957165\pi$
$23$	−2.93346	−	5.08091i	−0.611669	−	1.05944i	0.379290	−	0.925278i	$-0.376168\pi$
$24$		0			0
$25$	−0.527042	+	0.912864i	−0.105408	+	0.182573i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.48755	+	6.04061i	−0.647621	+	1.12171i	0.336068	+	0.941838i	$0.390903\pi$
$29$	−3.48755	+	6.04061i	−0.647621	+	1.12171i	−0.983689	+	0.179875i	$0.942431\pi$
$30$		0			0
$31$	−3.69076	−	6.39258i	−0.662880	−	1.14814i	−0.979856	−	0.199708i	$-0.936001\pi$
$31$	−3.69076	−	6.39258i	−0.662880	−	1.14814i	0.316976	−	0.948434i	$-0.397333\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.46050			−0.415901
$36$		0			0
$37$	−0.726654			−0.119461			−0.0597306	−	0.998215i	$-0.519024\pi$
$37$	−0.726654			−0.119461			−0.0597306	+	0.998215i	$0.519024\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.136673	+	0.236725i	0.0213448	+	0.0369702i	0.876500	−	0.481401i	$-0.159872\pi$
$41$	0.136673	+	0.236725i	0.0213448	+	0.0369702i	−0.855156	+	0.518371i	$0.826539\pi$
$42$		0			0
$43$	−2.41741	+	4.18708i	−0.368652	+	0.638524i	−0.989355	−	0.145522i	$-0.953514\pi$
$43$	−2.41741	+	4.18708i	−0.368652	+	0.638524i	0.620703	+	0.784046i	$0.286847\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.83628	+	3.18054i	−0.267850	+	0.463929i	−0.968306	−	0.249766i	$-0.919646\pi$
$47$	−1.83628	+	3.18054i	−0.267850	+	0.463929i	0.700457	+	0.713695i	$0.252980\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.05408			−0.694232			−0.347116	−	0.937822i	$-0.612839\pi$
$53$	−5.05408			−0.694232			−0.347116	+	0.937822i	$0.612839\pi$
$54$		0			0
$55$	−11.4356			−1.54198
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.56654	−	7.90947i	−0.594513	−	1.02973i	−0.993615	−	0.112820i	$-0.964012\pi$
$59$	−4.56654	−	7.90947i	−0.594513	−	1.02973i	0.399103	−	0.916906i	$-0.369322\pi$
$60$		0			0
$61$	6.90856	−	11.9660i	0.884550	−	1.53209i	0.0383215	−	0.999265i	$-0.487799\pi$
$61$	6.90856	−	11.9660i	0.884550	−	1.53209i	0.846228	−	0.532820i	$-0.178868\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.74484	−	15.1465i	1.08466	−	1.87869i
$66$		0			0
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	0.822631	−	0.568576i	$-0.192505\pi$
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	−0.903717	+	0.428131i	$0.859172\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	13.5218			1.60474			0.802370	−	0.596826i	$-0.203572\pi$
$71$	13.5218			1.60474			0.802370	+	0.596826i	$0.203572\pi$
$72$		0			0
$73$	−4.32743			−0.506487			−0.253244	−	0.967403i	$-0.581497\pi$
$73$	−4.32743			−0.506487			−0.253244	+	0.967403i	$0.581497\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.32383	−	4.02499i	−0.264825	−	0.458691i
$78$		0			0
$79$	3.21780	−	5.57339i	0.362031	−	0.627056i	−0.626264	−	0.779611i	$-0.715417\pi$
$79$	3.21780	−	5.57339i	0.362031	−	0.627056i	0.988295	+	0.152555i	$0.0487502\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.742705	+	1.28640i	−0.0815225	+	0.141201i	−0.903904	−	0.427735i	$-0.859312\pi$
$83$	−0.742705	+	1.28640i	−0.0815225	+	0.141201i	0.822382	+	0.568936i	$0.192645\pi$
$84$		0			0
$85$	5.55408	+	9.61996i	0.602425	+	1.04343i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.83482			−1.04249			−0.521245	−	0.853407i	$-0.674532\pi$
$89$	−9.83482			−1.04249			−0.521245	+	0.853407i	$0.674532\pi$
$90$		0			0
$91$	7.10817			0.745139
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.32383	−	9.22115i	−0.546214	−	0.946070i
$96$		0			0
$97$	0.246304	−	0.426611i	0.0250084	−	0.0433158i	−0.853250	−	0.521502i	$-0.825372\pi$
$97$	0.246304	−	0.426611i	0.0250084	−	0.0433158i	0.878259	+	0.478186i	$0.158705\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.70321	−	2.95005i	0.169476	−	0.293541i	−0.768760	−	0.639537i	$-0.779126\pi$
$101$	1.70321	−	2.95005i	0.169476	−	0.293541i	0.938236	+	0.345997i	$0.112459\pi$
$102$		0			0
$103$	2.58113	+	4.47064i	0.254326	+	0.440505i	0.964712	−	0.263307i	$-0.0848131\pi$
$103$	2.58113	+	4.47064i	0.254326	+	0.440505i	−0.710386	+	0.703812i	$0.751480\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.76303			−0.557133			−0.278567	−	0.960417i	$-0.589859\pi$
$107$	−5.76303			−0.557133			−0.278567	+	0.960417i	$0.589859\pi$
$108$		0			0
$109$	−8.98229			−0.860347			−0.430174	−	0.902746i	$-0.641548\pi$
$109$	−8.98229			−0.860347			−0.430174	+	0.902746i	$0.641548\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.679767	−	1.17739i	−0.0639471	−	0.110760i	0.832279	−	0.554356i	$-0.187036\pi$
$113$	−0.679767	−	1.17739i	−0.0639471	−	0.110760i	−0.896226	+	0.443597i	$0.853702\pi$
$114$		0			0
$115$	7.21780	−	12.5016i	0.673063	−	1.16578i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.25729	+	3.90975i	−0.206926	+	0.358406i
$120$		0			0
$121$	−5.30039	−	9.18054i	−0.481853	−	0.834595i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.70895			0.868394
$126$		0			0
$127$	0.820039			0.0727667			0.0363833	−	0.999338i	$-0.488416\pi$
$127$	0.820039			0.0727667			0.0363833	+	0.999338i	$0.488416\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.89397	−	6.74455i	−0.340218	−	0.589274i	0.644255	−	0.764810i	$-0.277167\pi$
$131$	−3.89397	−	6.74455i	−0.340218	−	0.589274i	−0.984473	+	0.175536i	$0.943834\pi$
$132$		0			0
$133$	2.16372	−	3.74766i	0.187618	−	0.324964i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.49640	+	2.59184i	−0.127846	+	0.221436i	−0.922842	−	0.385179i	$-0.874140\pi$
$137$	−1.49640	+	2.59184i	−0.127846	+	0.221436i	0.794996	+	0.606615i	$0.207473\pi$
$138$		0			0
$139$	3.16372	+	5.47972i	0.268343	+	0.464783i	0.968434	−	0.249270i	$-0.0801907\pi$
$139$	3.16372	+	5.47972i	0.268343	+	0.464783i	−0.700091	+	0.714053i	$0.746857\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	33.0364			2.76264
$144$		0			0
$145$	−17.1623			−1.42525
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.19076	−	3.79450i	−0.179474	−	0.310858i	0.762227	−	0.647310i	$-0.224106\pi$
$149$	−2.19076	−	3.79450i	−0.179474	−	0.310858i	−0.941700	+	0.336452i	$0.890773\pi$
$150$		0			0
$151$	3.30039	−	5.71644i	0.268582	−	0.465197i	−0.699914	−	0.714227i	$-0.746778\pi$
$151$	3.30039	−	5.71644i	0.268582	−	0.465197i	0.968496	+	0.249030i	$0.0801117\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.08113	−	15.7290i	0.729414	−	1.26338i
$156$		0			0
$157$	2.89037	+	5.00627i	0.230677	+	0.399544i	0.958007	−	0.286743i	$-0.0925727\pi$
$157$	2.89037	+	5.00627i	0.230677	+	0.399544i	−0.727331	+	0.686287i	$0.759239\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.86693			0.462379
$162$		0			0
$163$	−7.32743			−0.573929			−0.286964	−	0.957941i	$-0.592646\pi$
$163$	−7.32743			−0.573929			−0.286964	+	0.957941i	$0.592646\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.01459	+	10.4176i	0.465423	+	0.806136i	0.999221	−	0.0394762i	$-0.0125689\pi$
$167$	6.01459	+	10.4176i	0.465423	+	0.806136i	−0.533798	+	0.845612i	$0.679236\pi$
$168$		0			0
$169$	−18.7630	+	32.4985i	−1.44331	+	2.49989i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.44951	−	4.24268i	0.186233	−	0.322565i	−0.757758	−	0.652535i	$-0.773705\pi$
$173$	2.44951	−	4.24268i	0.186233	−	0.322565i	0.943991	+	0.329970i	$0.107039\pi$
$174$		0			0
$175$	−0.527042	−	0.912864i	−0.0398406	−	0.0690060i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.78074			−0.133099			−0.0665493	−	0.997783i	$-0.521199\pi$
$179$	−1.78074			−0.133099			−0.0665493	+	0.997783i	$0.521199\pi$
$180$		0			0
$181$	−16.9430			−1.25936			−0.629681	−	0.776854i	$-0.716815\pi$
$181$	−16.9430			−1.25936			−0.629681	+	0.776854i	$0.716815\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.893968	−	1.54840i	−0.0657258	−	0.113840i
$186$		0			0
$187$	−10.4911	+	18.1712i	−0.767189	+	1.32881i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.74484	−	4.75420i	0.198610	−	0.344002i	−0.749468	−	0.662040i	$-0.769691\pi$
$191$	2.74484	−	4.75420i	0.198610	−	0.344002i	0.948078	+	0.318038i	$0.103024\pi$
$192$		0			0
$193$	2.75370	+	4.76954i	0.198215	+	0.343319i	0.947950	−	0.318420i	$-0.103152\pi$
$193$	2.75370	+	4.76954i	0.198215	+	0.343319i	−0.749734	+	0.661739i	$0.769819\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.6300			−0.828600			−0.414300	−	0.910140i	$-0.635974\pi$
$197$	−11.6300			−0.828600			−0.414300	+	0.910140i	$0.635974\pi$
$198$		0			0
$199$	4.14747			0.294006			0.147003	−	0.989136i	$-0.453037\pi$
$199$	4.14747			0.294006			0.147003	+	0.989136i	$0.453037\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.48755	−	6.04061i	−0.244778	−	0.423968i
$204$		0			0
$205$	−0.336285	+	0.582462i	−0.0234871	+	0.0406809i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.0562	−	17.4179i	0.695603	−	1.20482i
$210$		0			0
$211$	−13.6082	−	23.5700i	−0.936825	−	1.62263i	−0.771347	−	0.636415i	$-0.780417\pi$
$211$	−13.6082	−	23.5700i	−0.936825	−	1.62263i	−0.165478	−	0.986213i	$-0.552917\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.8961			−0.811308
$216$		0			0
$217$	7.38151			0.501090
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−16.0452	−	27.7912i	−1.07932	−	1.86944i
$222$		0			0
$223$	−1.60817	+	2.78543i	−0.107691	+	0.186526i	−0.914834	−	0.403829i	$-0.867679\pi$
$223$	−1.60817	+	2.78543i	−0.107691	+	0.186526i	0.807144	+	0.590355i	$0.201012\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.97296	+	13.8096i	−0.529184	+	0.916573i	0.470237	+	0.882540i	$0.344168\pi$
$227$	−7.97296	+	13.8096i	−0.529184	+	0.916573i	−0.999421	+	0.0340330i	$0.989165\pi$
$228$		0			0
$229$	0.608168	+	1.05338i	0.0401889	+	0.0696092i	0.885420	−	0.464791i	$-0.153871\pi$
$229$	0.608168	+	1.05338i	0.0401889	+	0.0696092i	−0.845231	+	0.534401i	$0.820537\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−19.9722			−1.30842			−0.654210	−	0.756313i	$-0.726999\pi$
$233$	−19.9722			−1.30842			−0.654210	+	0.756313i	$0.726999\pi$
$234$		0			0
$235$	−9.03638			−0.589468
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.00739	−	5.20896i	−0.194532	−	0.336939i	0.752215	−	0.658918i	$-0.228985\pi$
$239$	−3.00739	−	5.20896i	−0.194532	−	0.336939i	−0.946747	+	0.321978i	$0.895652\pi$
$240$		0			0
$241$	9.30778	−	16.1215i	0.599567	−	1.03848i	−0.393318	−	0.919402i	$-0.628673\pi$
$241$	9.30778	−	16.1215i	0.599567	−	1.03848i	0.992885	−	0.119078i	$-0.0379938\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.23025	−	2.13086i	0.0785979	−	0.136136i
$246$		0			0
$247$	15.3801	+	26.6390i	0.978609	+	1.69500i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.99707			0.441651			0.220826	−	0.975313i	$-0.429125\pi$
$251$	6.99707			0.441651			0.220826	+	0.975313i	$0.429125\pi$
$252$		0			0
$253$	27.2675			1.71429
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.88891	−	15.3960i	−0.554475	−	0.960378i	−0.997944	−	0.0640889i	$-0.979586\pi$
$257$	−8.88891	−	15.3960i	−0.554475	−	0.960378i	0.443469	−	0.896289i	$-0.353747\pi$
$258$		0			0
$259$	0.363327	−	0.629301i	0.0225760	−	0.0391028i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.5993	−	23.5547i	0.838570	−	1.45245i	−0.0525210	−	0.998620i	$-0.516726\pi$
$263$	13.5993	−	23.5547i	0.838570	−	1.45245i	0.891091	−	0.453825i	$-0.149941\pi$
$264$		0			0
$265$	−6.21780	−	10.7695i	−0.381956	−	0.661568i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−23.8961			−1.45697			−0.728486	−	0.685061i	$-0.759775\pi$
$269$	−23.8961			−1.45697			−0.728486	+	0.685061i	$0.759775\pi$
$270$		0			0
$271$	−12.2733			−0.745553			−0.372776	−	0.927921i	$-0.621594\pi$
$271$	−12.2733			−0.745553			−0.372776	+	0.927921i	$0.621594\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.44951	−	4.24268i	−0.147711	−	0.255843i
$276$		0			0
$277$	−6.39037	+	11.0684i	−0.383960	+	0.665038i	−0.991624	−	0.129156i	$-0.958773\pi$
$277$	−6.39037	+	11.0684i	−0.383960	+	0.665038i	0.607664	+	0.794194i	$0.292107\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.2573	+	24.6944i	−0.850519	+	1.47314i	0.0302219	+	0.999543i	$0.490379\pi$
$281$	−14.2573	+	24.6944i	−0.850519	+	1.47314i	−0.880741	+	0.473599i	$0.842955\pi$
$282$		0			0
$283$	0.363327	+	0.629301i	0.0215975	+	0.0374080i	0.876622	−	0.481179i	$-0.159791\pi$
$283$	0.363327	+	0.629301i	0.0215975	+	0.0374080i	−0.855025	+	0.518587i	$0.826458\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.273346			−0.0161351
$288$		0			0
$289$	3.38151			0.198913
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.7901	+	22.1531i	0.747204	+	1.29420i	0.949158	+	0.314800i	$0.101938\pi$
$293$	12.7901	+	22.1531i	0.747204	+	1.29420i	−0.201954	+	0.979395i	$0.564729\pi$
$294$		0			0
$295$	11.2360	−	19.4613i	0.654184	−	1.13308i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−20.8515	+	36.1159i	−1.20588	+	2.08864i
$300$		0			0
$301$	−2.41741	−	4.18708i	−0.139337	−	0.241339i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	33.9971			1.94667
$306$		0			0
$307$	6.23405			0.355796			0.177898	−	0.984049i	$-0.443070\pi$
$307$	6.23405			0.355796			0.177898	+	0.984049i	$0.443070\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.6192	−	25.3211i	−0.828976	−	1.43583i	−0.898842	−	0.438273i	$-0.855590\pi$
$311$	−14.6192	−	25.3211i	−0.828976	−	1.43583i	0.0698655	−	0.997556i	$-0.477743\pi$
$312$		0			0
$313$	−14.2434	+	24.6703i	−0.805083	+	1.39445i	0.111151	+	0.993803i	$0.464546\pi$
$313$	−14.2434	+	24.6703i	−0.805083	+	1.39445i	−0.916235	+	0.400642i	$0.868787\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.809243	−	1.40165i	0.0454516	−	0.0787245i	−0.842405	−	0.538846i	$-0.818861\pi$
$317$	0.809243	−	1.40165i	0.0454516	−	0.0787245i	0.887856	+	0.460121i	$0.152194\pi$
$318$		0			0
$319$	−16.2089	−	28.0747i	−0.907527	−	1.57188i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−19.5366			−1.08704
$324$		0			0
$325$	7.49261			0.415615
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.83628	−	3.18054i	−0.101238	−	0.175349i
$330$		0			0
$331$	−6.99115	+	12.1090i	−0.384268	+	0.665572i	−0.991667	−	0.128825i	$-0.958880\pi$
$331$	−6.99115	+	12.1090i	−0.384268	+	0.665572i	0.607399	+	0.794397i	$0.292213\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.63307	−	2.82857i	0.0892244	−	0.154541i
$336$		0			0
$337$	−13.8619	−	24.0095i	−0.755104	−	1.30788i	−0.945323	−	0.326137i	$-0.894253\pi$
$337$	−13.8619	−	24.0095i	−0.755104	−	1.30788i	0.190219	−	0.981742i	$-0.439080\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	34.3068			1.85782
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.76449	−	6.52029i	−0.202089	−	0.350028i	0.747113	−	0.664697i	$-0.231440\pi$
$347$	−3.76449	−	6.52029i	−0.202089	−	0.350028i	−0.949201	+	0.314670i	$0.898106\pi$
$348$		0			0
$349$	15.0541	−	26.0744i	0.805827	−	1.39573i	−0.109905	−	0.993942i	$-0.535055\pi$
$349$	15.0541	−	26.0744i	0.805827	−	1.39573i	0.915732	−	0.401791i	$-0.131612\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.1819	+	17.6356i	−0.541928	+	0.938647i	0.456865	+	0.889536i	$0.348972\pi$
$353$	−10.1819	+	17.6356i	−0.541928	+	0.938647i	−0.998793	+	0.0491110i	$0.984361\pi$
$354$		0			0
$355$	16.6352	+	28.8130i	0.882905	+	1.52924i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−16.0263			−0.845833			−0.422917	−	0.906169i	$-0.638994\pi$
$359$	−16.0263			−0.845833			−0.422917	+	0.906169i	$0.638994\pi$
$360$		0			0
$361$	−0.273346			−0.0143866
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.32383	−	9.22115i	−0.278662	−	0.482657i
$366$		0			0
$367$	−6.79893	+	11.7761i	−0.354901	+	0.614707i	−0.987101	−	0.160099i	$-0.948819\pi$
$367$	−6.79893	+	11.7761i	−0.354901	+	0.614707i	0.632200	+	0.774805i	$0.282152\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.52704	−	4.37697i	0.131197	−	0.227241i
$372$		0			0
$373$	10.9641	+	18.9904i	0.567700	+	0.983285i	0.996793	+	0.0800246i	$0.0254999\pi$
$373$	10.9641	+	18.9904i	0.567700	+	0.983285i	−0.429093	+	0.903260i	$0.641167\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	49.5801			2.55351
$378$		0			0
$379$	29.7965			1.53054			0.765271	−	0.643708i	$-0.222605\pi$
$379$	29.7965			1.53054			0.765271	+	0.643708i	$0.222605\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.0109905	+	0.0190361i	0.000561587	+	0.000972697i	0.866306	−	0.499514i	$-0.166488\pi$
$383$	0.0109905	+	0.0190361i	0.000561587	+	0.000972697i	−0.865744	+	0.500486i	$0.833155\pi$
$384$		0			0
$385$	5.71780	−	9.90352i	0.291406	−	0.504730i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.6783	+	30.6197i	−0.896326	+	1.55248i	−0.0641702	+	0.997939i	$0.520440\pi$
$389$	−17.6783	+	30.6197i	−0.896326	+	1.55248i	−0.832155	+	0.554543i	$0.812893\pi$
$390$		0			0
$391$	−13.2434	−	22.9382i	−0.669746	−	1.16003i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	15.8348			0.796736
$396$		0			0
$397$	−16.9430			−0.850344			−0.425172	−	0.905112i	$-0.639786\pi$
$397$	−16.9430			−0.850344			−0.425172	+	0.905112i	$0.639786\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.48181	−	2.56657i	−0.0739982	−	0.128169i	0.826652	−	0.562713i	$-0.190243\pi$
$401$	−1.48181	−	2.56657i	−0.0739982	−	0.128169i	−0.900650	+	0.434545i	$0.856909\pi$
$402$		0			0
$403$	−26.2345	+	45.4395i	−1.30683	+	2.26350i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.68862	−	2.92478i	0.0837018	−	0.144976i
$408$		0			0
$409$	7.32743	+	12.6915i	0.362318	+	0.627553i	0.988342	−	0.152251i	$-0.0486521\pi$
$409$	7.32743	+	12.6915i	0.362318	+	0.627553i	−0.626024	+	0.779804i	$0.715319\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.13307			0.449409
$414$		0			0
$415$	−3.65486			−0.179410
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.6352	+	21.8848i	0.617270	+	1.06914i	0.989982	+	0.141196i	$0.0450949\pi$
$419$	12.6352	+	21.8848i	0.617270	+	1.06914i	−0.372711	+	0.927947i	$0.621572\pi$
$420$		0			0
$421$	7.99854	−	13.8539i	0.389825	−	0.675196i	−0.602601	−	0.798043i	$-0.705869\pi$
$421$	7.99854	−	13.8539i	0.389825	−	0.675196i	0.992426	+	0.122846i	$0.0392022\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.37938	+	4.12120i	−0.115417	+	0.199908i
$426$		0			0
$427$	6.90856	+	11.9660i	0.334328	+	0.579074i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.0335			0.627799			0.313900	−	0.949456i	$-0.398364\pi$
$431$	13.0335			0.627799			0.313900	+	0.949456i	$0.398364\pi$
$432$		0			0
$433$	23.5467			1.13158			0.565791	−	0.824549i	$-0.308571\pi$
$433$	23.5467			1.13158			0.565791	+	0.824549i	$0.308571\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.6944	+	21.9873i	0.607253	+	1.05179i
$438$		0			0
$439$	3.35447	−	5.81012i	0.160100	−	0.277302i	−0.774804	−	0.632201i	$-0.782152\pi$
$439$	3.35447	−	5.81012i	0.160100	−	0.277302i	0.934904	+	0.354900i	$0.115485\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−17.6228	+	30.5235i	−0.837282	+	1.45022i	0.0548760	+	0.998493i	$0.482524\pi$
$443$	−17.6228	+	30.5235i	−0.837282	+	1.45022i	−0.892158	+	0.451723i	$0.850810\pi$
$444$		0			0
$445$	−12.0993	−	20.9566i	−0.573562	−	0.993439i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.9387			0.610616			0.305308	−	0.952254i	$-0.401241\pi$
$449$	12.9387			0.610616			0.305308	+	0.952254i	$0.401241\pi$
$450$		0			0
$451$	−1.27042			−0.0598218
$452$		0			0
$453$		0			0
$454$		0			0
$455$	8.74484	+	15.1465i	0.409964	+	0.710079i
$456$		0			0
$457$	14.5993	−	25.2868i	0.682927	−	1.18286i	−0.291156	−	0.956675i	$-0.594040\pi$
$457$	14.5993	−	25.2868i	0.682927	−	1.18286i	0.974083	−	0.226189i	$-0.0726267\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.34348	+	16.1834i	−0.435169	+	0.753735i	−0.997309	−	0.0733066i	$-0.976645\pi$
$461$	−9.34348	+	16.1834i	−0.435169	+	0.753735i	0.562140	+	0.827042i	$0.309978\pi$
$462$		0			0
$463$	−19.1249	−	33.1253i	−0.888809	−	1.53946i	−0.841285	−	0.540593i	$-0.818200\pi$
$463$	−19.1249	−	33.1253i	−0.888809	−	1.53946i	−0.0475247	−	0.998870i	$-0.515133\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.2877			−0.707432			−0.353716	−	0.935353i	$-0.615082\pi$
$467$	−15.2877			−0.707432			−0.353716	+	0.935353i	$0.615082\pi$
$468$		0			0
$469$	1.32743			0.0612950
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.2353	−	19.4601i	−0.516600	−	0.894778i
$474$		0			0
$475$	2.28074	−	3.95035i	0.104647	−	0.181255i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.51605	+	9.55408i	−0.252035	+	0.436537i	−0.964086	−	0.265591i	$-0.914433\pi$
$479$	−5.51605	+	9.55408i	−0.252035	+	0.436537i	0.712051	+	0.702128i	$0.247766\pi$
$480$		0			0
$481$	2.58259	+	4.47318i	0.117756	+	0.203959i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.21206			0.0550370
$486$		0			0
$487$	−16.6008			−0.752253			−0.376126	−	0.926568i	$-0.622744\pi$
$487$	−16.6008			−0.752253			−0.376126	+	0.926568i	$0.622744\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.3633	+	23.1460i	0.603079	+	1.04456i	0.992352	+	0.123440i	$0.0393928\pi$
$491$	13.3633	+	23.1460i	0.603079	+	1.04456i	−0.389273	+	0.921122i	$0.627274\pi$
$492$		0			0
$493$	−15.7448	+	27.2709i	−0.709112	+	1.22822i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.76089	+	11.7102i	−0.303268	+	0.525275i
$498$		0			0
$499$	0.618485	+	1.07125i	0.0276872	+	0.0479557i	0.879537	−	0.475830i	$-0.157852\pi$
$499$	0.618485	+	1.07125i	0.0276872	+	0.0479557i	−0.851850	+	0.523786i	$0.824519\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.07179			−0.0477889			−0.0238944	−	0.999714i	$-0.507607\pi$
$503$	−1.07179			−0.0477889			−0.0238944	+	0.999714i	$0.507607\pi$
$504$		0			0
$505$	8.38151			0.372973
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.0344	+	17.3801i	0.444768	+	0.770362i	0.998036	−	0.0626420i	$-0.0199526\pi$
$509$	10.0344	+	17.3801i	0.444768	+	0.770362i	−0.553268	+	0.833004i	$0.686619\pi$
$510$		0			0
$511$	2.16372	−	3.74766i	0.0957171	−	0.165787i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.35087	+	11.0000i	−0.279853	+	0.484720i
$516$		0			0
$517$	−8.53443	−	14.7821i	−0.375344	−	0.650115i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	30.8860			1.35314			0.676570	−	0.736379i	$-0.263466\pi$
$521$	30.8860			1.35314			0.676570	+	0.736379i	$0.263466\pi$
$522$		0			0
$523$	7.39922			0.323545			0.161773	−	0.986828i	$-0.448279\pi$
$523$	7.39922			0.323545			0.161773	+	0.986828i	$0.448279\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−16.6623	−	28.8599i	−0.725819	−	1.25716i
$528$		0			0
$529$	−5.71041	+	9.89072i	−0.248279	+	0.430031i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.971495	−	1.68268i	0.0420801	−	0.0728849i
$534$		0			0
$535$	−7.08998	−	12.2802i	−0.306527	−	0.530920i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.64766			0.200189
$540$		0			0
$541$	22.6696			0.974644			0.487322	−	0.873222i	$-0.337974\pi$
$541$	22.6696			0.974644			0.487322	+	0.873222i	$0.337974\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.0505	−	19.1400i	−0.473351	−	0.819868i
$546$		0			0
$547$	−3.07373	+	5.32386i	−0.131423	+	0.227632i	−0.924225	−	0.381847i	$-0.875288\pi$
$547$	−3.07373	+	5.32386i	−0.131423	+	0.227632i	0.792802	+	0.609479i	$0.208621\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.0921	−	26.1403i	0.642946	−	1.11361i
$552$		0			0
$553$	3.21780	+	5.57339i	0.136835	+	0.237005i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−29.6739			−1.25732			−0.628662	−	0.777679i	$-0.716397\pi$
$557$	−29.6739			−1.25732			−0.628662	+	0.777679i	$0.716397\pi$
$558$		0			0
$559$	34.3667			1.45356
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.6555	+	25.3841i	0.617657	+	1.06981i	0.989912	+	0.141683i	$0.0452514\pi$
$563$	14.6555	+	25.3841i	0.617657	+	1.06981i	−0.372255	+	0.928131i	$0.621415\pi$
$564$		0			0
$565$	1.67257	−	2.89698i	0.0703655	−	0.121877i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.4430	+	31.9442i	−0.773170	+	1.33917i	0.162647	+	0.986684i	$0.447997\pi$
$569$	−18.4430	+	31.9442i	−0.773170	+	1.33917i	−0.935817	+	0.352486i	$0.885336\pi$
$570$		0			0
$571$	16.1893	+	28.0407i	0.677501	+	1.17347i	0.975731	+	0.218972i	$0.0702703\pi$
$571$	16.1893	+	28.0407i	0.677501	+	1.17347i	−0.298230	+	0.954494i	$0.596396\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	6.18423			0.257900
$576$		0			0
$577$	23.0187			0.958280			0.479140	−	0.877739i	$-0.340949\pi$
$577$	23.0187			0.958280			0.479140	+	0.877739i	$0.340949\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.742705	−	1.28640i	−0.0308126	−	0.0533690i
$582$		0			0
$583$	11.7448	−	20.3427i	0.486422	−	0.842507i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.87052	+	4.97189i	−0.118479	+	0.205212i	−0.919165	−	0.393872i	$-0.871135\pi$
$587$	−2.87052	+	4.97189i	−0.118479	+	0.205212i	0.800686	+	0.599084i	$0.204469\pi$
$588$		0			0
$589$	15.9715	+	27.6634i	0.658094	+	1.13985i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−27.7453			−1.13936			−0.569682	−	0.821865i	$-0.692934\pi$
$593$	−27.7453			−1.13936			−0.569682	+	0.821865i	$0.692934\pi$
$594$		0			0
$595$	−11.1082			−0.455391
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.05408	−	3.55778i	−0.0839276	−	0.145367i	0.821006	−	0.570919i	$-0.193413\pi$
$599$	−2.05408	−	3.55778i	−0.0839276	−	0.145367i	−0.904934	+	0.425552i	$0.860080\pi$
$600$		0			0
$601$	−7.80924	+	13.5260i	−0.318546	+	0.551737i	−0.980185	−	0.198085i	$-0.936528\pi$
$601$	−7.80924	+	13.5260i	−0.318546	+	0.551737i	0.661639	+	0.749822i	$0.269861\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	13.0416	−	22.5888i	0.530218	−	0.918364i
$606$		0			0
$607$	−0.280738	−	0.486253i	−0.0113948	−	0.0197364i	0.860272	−	0.509836i	$-0.170294\pi$
$607$	−0.280738	−	0.486253i	−0.0113948	−	0.0197364i	−0.871667	+	0.490099i	$0.836960\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	26.1052			1.05611
$612$		0			0
$613$	−20.2016			−0.815933			−0.407967	−	0.912997i	$-0.633762\pi$
$613$	−20.2016			−0.815933			−0.407967	+	0.912997i	$0.633762\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.4569	−	19.8439i	−0.461238	−	0.798887i	0.537785	−	0.843082i	$-0.319261\pi$
$617$	−11.4569	−	19.8439i	−0.461238	−	0.798887i	−0.999023	+	0.0441948i	$0.985928\pi$
$618$		0			0
$619$	19.8515	−	34.3839i	0.797901	−	1.38201i	−0.123080	−	0.992397i	$-0.539277\pi$
$619$	19.8515	−	34.3839i	0.797901	−	1.38201i	0.920981	−	0.389608i	$-0.127390\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.91741	−	8.51721i	0.197012	−	0.341235i
$624$		0			0
$625$	14.5797	+	25.2527i	0.583187	+	1.01011i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.28054			−0.130804
$630$		0			0
$631$	31.0364			1.23554			0.617769	−	0.786359i	$-0.288037\pi$
$631$	31.0364			1.23554			0.617769	+	0.786359i	$0.288037\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.00885	+	1.74739i	0.0400352	+	0.0693429i
$636$		0			0
$637$	−3.55408	+	6.15585i	−0.140818	+	0.243904i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.7932	+	25.6226i	−0.584296	+	1.01203i	0.410667	+	0.911785i	$0.365296\pi$
$641$	−14.7932	+	25.6226i	−0.584296	+	1.01203i	−0.994963	+	0.100245i	$0.968037\pi$
$642$		0			0
$643$	12.8442	+	22.2467i	0.506524	+	0.877325i	0.999972	+	0.00754978i	$0.00240319\pi$
$643$	12.8442	+	22.2467i	0.506524	+	0.877325i	−0.493447	+	0.869776i	$0.664263\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.0177			0.669035			0.334518	−	0.942390i	$-0.391427\pi$
$647$	17.0177			0.669035			0.334518	+	0.942390i	$0.391427\pi$
$648$		0			0
$649$	42.4475			1.66621
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.735508	+	1.27394i	0.0287827	+	0.0498530i	0.880058	−	0.474866i	$-0.157504\pi$
$653$	0.735508	+	1.27394i	0.0287827	+	0.0498530i	−0.851275	+	0.524719i	$0.824170\pi$
$654$		0			0
$655$	9.58113	−	16.5950i	0.374366	−	0.648420i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	20.7003	−	35.8539i	0.806369	−	1.39667i	−0.108995	−	0.994042i	$-0.534763\pi$
$659$	20.7003	−	35.8539i	0.806369	−	1.39667i	0.915363	−	0.402629i	$-0.131904\pi$
$660$		0			0
$661$	−19.1352	−	33.1432i	−0.744273	−	1.28912i	−0.950533	−	0.310622i	$-0.899463\pi$
$661$	−19.1352	−	33.1432i	−0.744273	−	1.28912i	0.206260	−	0.978497i	$-0.433871\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.6477			0.412899
$666$		0			0
$667$	40.9224			1.58452
$668$		0			0
$669$		0			0
$670$		0			0
$671$	32.1086	+	55.6138i	1.23954	+	2.14695i
$672$		0			0
$673$	15.2448	−	26.4048i	0.587645	−	1.01783i	−0.406894	−	0.913475i	$-0.633388\pi$
$673$	15.2448	−	26.4048i	0.587645	−	1.01783i	0.994540	−	0.104357i	$-0.0332783\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.4626	−	38.9064i	0.863309	−	1.49530i	−0.00540665	−	0.999985i	$-0.501721\pi$
$677$	22.4626	−	38.9064i	0.863309	−	1.49530i	0.868716	−	0.495310i	$-0.164946\pi$
$678$		0			0
$679$	0.246304	+	0.426611i	0.00945228	+	0.0163718i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−48.3973			−1.85187			−0.925935	−	0.377683i	$-0.876721\pi$
$683$	−48.3973			−1.85187			−0.925935	+	0.377683i	$0.876721\pi$
$684$		0			0
$685$	−7.36381			−0.281357
$686$		0			0
$687$		0			0
$688$		0			0
$689$	17.9626	+	31.1122i	0.684322	+	1.18528i
$690$		0			0
$691$	9.19076	−	15.9189i	0.349633	−	0.605582i	−0.636551	−	0.771234i	$-0.719640\pi$
$691$	9.19076	−	15.9189i	0.349633	−	0.605582i	0.986184	+	0.165652i	$0.0529730\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.78434	+	13.4829i	−0.295277	+	0.511434i
$696$		0			0
$697$	0.617023	+	1.06871i	0.0233714	+	0.0404805i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	27.0292			1.02088			0.510439	−	0.859914i	$-0.329483\pi$
$701$	27.0292			1.02088			0.510439	+	0.859914i	$0.329483\pi$
$702$		0			0
$703$	3.14454			0.118599
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.70321	+	2.95005i	0.0640558	+	0.110948i
$708$		0			0
$709$	−2.49261	+	4.31732i	−0.0936119	+	0.162141i	−0.909028	−	0.416734i	$-0.863175\pi$
$709$	−2.49261	+	4.31732i	−0.0936119	+	0.162141i	0.815417	+	0.578875i	$0.196508\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−21.6534	+	37.5048i	−0.810926	+	1.40457i
$714$		0			0
$715$	40.6431	+	70.3959i	1.51997	+	2.63266i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.6942			0.585293			0.292647	−	0.956221i	$-0.405464\pi$
$719$	15.6942			0.585293			0.292647	+	0.956221i	$0.405464\pi$
$720$		0			0
$721$	−5.16225			−0.192252
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.67617	−	6.36731i	−0.136529	−	0.236476i
$726$		0			0
$727$	10.9071	−	18.8916i	0.404522	−	0.700652i	−0.589744	−	0.807590i	$-0.700771\pi$
$727$	10.9071	−	18.8916i	0.404522	−	0.700652i	0.994266	+	0.106938i	$0.0341047\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.9136	+	18.9029i	−0.403655	+	0.699151i
$732$		0			0
$733$	12.0074	+	20.7974i	0.443503	+	0.768170i	0.997947	−	0.0640514i	$-0.0204022\pi$
$733$	12.0074	+	20.7974i	0.443503	+	0.768170i	−0.554443	+	0.832221i	$0.687069\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.16945			0.227255
$738$		0			0
$739$	−18.7089			−0.688220			−0.344110	−	0.938929i	$-0.611819\pi$
$739$	−18.7089			−0.688220			−0.344110	+	0.938929i	$0.611819\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.1534	+	34.9067i	0.739356	+	1.28060i	0.952785	+	0.303644i	$0.0982035\pi$
$743$	20.1534	+	34.9067i	0.739356	+	1.28060i	−0.213429	+	0.976959i	$0.568463\pi$
$744$		0			0
$745$	5.39037	−	9.33639i	0.197488	−	0.342059i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.88151	−	4.99093i	0.105288	−	0.182365i
$750$		0			0
$751$	−10.5629	−	18.2955i	−0.385447	−	0.667614i	0.606384	−	0.795172i	$-0.292619\pi$
$751$	−10.5629	−	18.2955i	−0.385447	−	0.667614i	−0.991831	+	0.127558i	$0.959286\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.2412			0.591079
$756$		0			0
$757$	8.85934			0.321998			0.160999	−	0.986955i	$-0.448528\pi$
$757$	8.85934			0.321998			0.160999	+	0.986955i	$0.448528\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.694551	+	1.20300i	0.0251774	+	0.0436086i	0.878340	−	0.478037i	$-0.158652\pi$
$761$	0.694551	+	1.20300i	0.0251774	+	0.0436086i	−0.853162	+	0.521646i	$0.825318\pi$
$762$		0			0
$763$	4.49115	−	7.77889i	0.162590	−	0.281615i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−32.4597	+	56.2219i	−1.17205	+	2.03005i
$768$		0			0
$769$	18.9626	+	32.8443i	0.683810	+	1.18439i	0.973809	+	0.227367i	$0.0730118\pi$
$769$	18.9626	+	32.8443i	0.683810	+	1.18439i	−0.289999	+	0.957027i	$0.593655\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.31596			−0.0473318			−0.0236659	−	0.999720i	$-0.507534\pi$
$773$	−1.31596			−0.0473318			−0.0236659	+	0.999720i	$0.507534\pi$
$774$		0			0
$775$	7.78074			0.279492
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.591443	−	1.02441i	−0.0211907	−	0.0367033i
$780$		0			0
$781$	−31.4224	+	54.4251i	−1.12438	+	1.94748i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.11177	+	12.3179i	−0.253830	+	0.439646i
$786$		0			0
$787$	6.12928	+	10.6162i	0.218485	+	0.378428i	0.954345	−	0.298706i	$-0.0965551\pi$
$787$	6.12928	+	10.6162i	0.218485	+	0.378428i	−0.735860	+	0.677134i	$0.763222\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.35953			0.0483395
$792$		0			0
$793$	−98.2144			−3.48769
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.7178	+	18.5638i	0.379644	+	0.657563i	0.991010	−	0.133785i	$-0.0427132\pi$
$797$	10.7178	+	18.5638i	0.379644	+	0.657563i	−0.611366	+	0.791348i	$0.709380\pi$
$798$		0			0
$799$	−8.29007	+	14.3588i	−0.293282	+	0.507979i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.0562	−	17.4179i	0.354876	−	0.614664i
$804$		0			0
$805$	7.21780	+	12.5016i	0.254394	+	0.440623i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−26.6955			−0.938564			−0.469282	−	0.883048i	$-0.655487\pi$
$809$	−26.6955			−0.938564			−0.469282	+	0.883048i	$0.655487\pi$
$810$		0			0
$811$	−38.2852			−1.34438			−0.672188	−	0.740381i	$-0.734645\pi$
$811$	−38.2852			−1.34438			−0.672188	+	0.740381i	$0.734645\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.01459	−	15.6137i	−0.315767	−	0.546925i
$816$		0			0
$817$	10.4612	−	18.1193i	0.365990	−	0.633914i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.24990	+	9.09310i	−0.183223	+	0.317351i	−0.942976	−	0.332860i	$-0.891986\pi$
$821$	−5.24990	+	9.09310i	−0.183223	+	0.317351i	0.759753	+	0.650211i	$0.225320\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−48.7817			−1.69631			−0.848153	−	0.529752i	$-0.822285\pi$
$827$	−48.7817			−1.69631			−0.848153	+	0.529752i	$0.822285\pi$
$828$		0			0
$829$	−6.21926			−0.216004			−0.108002	−	0.994151i	$-0.534445\pi$
$829$	−6.21926			−0.216004			−0.108002	+	0.994151i	$0.534445\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.25729	−	3.90975i	−0.0782106	−	0.135465i
$834$		0			0
$835$	−14.7989	+	25.6325i	−0.512138	+	0.887049i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.0366	−	36.4364i	0.726263	−	1.25792i	−0.232189	−	0.972671i	$-0.574589\pi$
$839$	21.0366	−	36.4364i	0.726263	−	1.25792i	0.958452	−	0.285254i	$-0.0920779\pi$
$840$		0			0
$841$	−9.82597	−	17.0191i	−0.338826	−	0.586865i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−92.3330			−3.17635
$846$		0			0
$847$	10.6008			0.364247
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.13161	+	3.69206i	0.0730707	+	0.126562i
$852$		0			0
$853$	6.72519	−	11.6484i	0.230266	−	0.398833i	−0.727620	−	0.685980i	$-0.759374\pi$
$853$	6.72519	−	11.6484i	0.230266	−	0.398833i	0.957886	+	0.287147i	$0.0927070\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.6893	−	35.8349i	0.706733	−	1.22410i	−0.259330	−	0.965789i	$-0.583502\pi$
$857$	20.6893	−	35.8349i	0.706733	−	1.22410i	0.966063	−	0.258308i	$-0.0831650\pi$
$858$		0			0
$859$	−19.8815	−	34.4358i	−0.678349	−	1.17493i	−0.975478	−	0.220097i	$-0.929363\pi$
$859$	−19.8815	−	34.4358i	−0.678349	−	1.17493i	0.297129	−	0.954837i	$-0.403971\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	53.3858			1.81727			0.908637	−	0.417588i	$-0.137124\pi$
$863$	53.3858			1.81727			0.908637	+	0.417588i	$0.137124\pi$
$864$		0			0
$865$	12.0541			0.409851
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.9552	+	25.9033i	0.507322	+	0.878708i
$870$		0			0
$871$	−4.71780	+	8.17147i	−0.159857	+	0.276880i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.85447	+	8.40819i	−0.164111	+	0.284249i
$876$		0			0
$877$	3.42674	+	5.93530i	0.115713	+	0.200421i	0.918065	−	0.396431i	$-0.129751\pi$
$877$	3.42674	+	5.93530i	0.115713	+	0.200421i	−0.802352	+	0.596852i	$0.796418\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.5103			0.421483			0.210742	−	0.977542i	$-0.432412\pi$
$881$	12.5103			0.421483			0.210742	+	0.977542i	$0.432412\pi$
$882$		0			0
$883$	−6.69124			−0.225178			−0.112589	−	0.993642i	$-0.535914\pi$
$883$	−6.69124			−0.225178			−0.112589	+	0.993642i	$0.535914\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.0708	−	27.8355i	−0.539605	−	0.934623i	−0.998925	−	0.0463524i	$-0.985240\pi$
$887$	−16.0708	−	27.8355i	−0.539605	−	0.934623i	0.459320	−	0.888271i	$-0.348093\pi$
$888$		0			0
$889$	−0.410019	+	0.710174i	−0.0137516	+	0.0238185i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.94639	−	13.7636i	0.265916	−	0.460580i
$894$		0			0
$895$	−2.19076	−	3.79450i	−0.0732289	−	0.126836i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	51.4868			1.71718
$900$		0			0
$901$	−22.8171			−0.760148
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−20.8442	−	36.1031i	−0.692883	−	1.20011i
$906$		0			0
$907$	−15.7016	+	27.1959i	−0.521362	+	0.903025i	0.478330	+	0.878180i	$0.341242\pi$
$907$	−15.7016	+	27.1959i	−0.521362	+	0.903025i	−0.999691	+	0.0248444i	$0.992091\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−22.8982	+	39.6609i	−0.758653	+	1.31402i	0.184885	+	0.982760i	$0.440809\pi$
$911$	−22.8982	+	39.6609i	−0.758653	+	1.31402i	−0.943538	+	0.331265i	$0.892525\pi$
$912$		0			0
$913$	−3.45185	−	5.97877i	−0.114239	−	0.197868i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.78794			0.257180
$918$		0			0
$919$	−27.1800			−0.896584			−0.448292	−	0.893887i	$-0.647968\pi$
$919$	−27.1800			−0.896584			−0.448292	+	0.893887i	$0.647968\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−48.0576	−	83.2381i	−1.58183	−	2.73982i
$924$		0			0
$925$	0.382977	−	0.663336i	0.0125922	−	0.0218104i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−20.3338	+	35.2192i	−0.667132	+	1.15551i	0.311571	+	0.950223i	$0.399145\pi$
$929$	−20.3338	+	35.2192i	−0.667132	+	1.15551i	−0.978703	+	0.205283i	$0.934189\pi$
$930$		0			0
$931$	2.16372	+	3.74766i	0.0709129	+	0.122825i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−51.6270			−1.68838
$936$		0			0
$937$	16.4150			0.536254			0.268127	−	0.963384i	$-0.413595\pi$
$937$	16.4150			0.536254			0.268127	+	0.963384i	$0.413595\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.66878	+	6.35451i	0.119599	+	0.207151i	0.919609	−	0.392836i	$-0.128506\pi$
$941$	3.66878	+	6.35451i	0.119599	+	0.207151i	−0.800010	+	0.599987i	$0.795173\pi$
$942$		0			0
$943$	0.801851	−	1.38885i	0.0261119	−	0.0452271i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.5562	+	51.1929i	−0.960448	+	1.66354i	−0.239071	+	0.971002i	$0.576843\pi$
$947$	−29.5562	+	51.1929i	−0.960448	+	1.66354i	−0.721377	+	0.692543i	$0.756490\pi$
$948$		0			0
$949$	15.3801	+	26.6390i	0.499258	+	0.864740i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.9354			0.548592			0.274296	−	0.961645i	$-0.411555\pi$
$953$	16.9354			0.548592			0.274296	+	0.961645i	$0.411555\pi$
$954$		0			0
$955$	13.5074			0.437089
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.49640	−	2.59184i	−0.0483213	−	0.0836950i
$960$		0			0
$961$	−11.7434	+	20.3401i	−0.378819	+	0.656133i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.77548	+	11.7355i	−0.218110	+	0.377778i
$966$		0			0
$967$	−3.55555	−	6.15839i	−0.114339	−	0.198040i	0.803177	−	0.595741i	$-0.203142\pi$
$967$	−3.55555	−	6.15839i	−0.114339	−	0.198040i	−0.917515	+	0.397701i	$0.869808\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.47102			−0.0472072			−0.0236036	−	0.999721i	$-0.507514\pi$
$971$	−1.47102			−0.0472072			−0.0236036	+	0.999721i	$0.507514\pi$
$972$		0			0
$973$	−6.32743			−0.202848
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.71634	−	16.8292i	−0.310853	−	0.538413i	0.667694	−	0.744436i	$-0.267281\pi$
$977$	−9.71634	−	16.8292i	−0.310853	−	0.538413i	−0.978547	+	0.206022i	$0.933948\pi$
$978$		0			0
$979$	22.8545	−	39.5851i	0.730432	−	1.26515i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−3.87218	+	6.70681i	−0.123503	+	0.213914i	−0.921147	−	0.389215i	$-0.872746\pi$
$983$	−3.87218	+	6.70681i	−0.123503	+	0.213914i	0.797644	+	0.603129i	$0.206080\pi$
$984$		0			0
$985$	−14.3078	−	24.7818i	−0.455884	−	0.789614i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	28.3655			0.901972
$990$		0			0
$991$	14.4710			0.459687			0.229843	−	0.973228i	$-0.426179\pi$
$991$	14.4710			0.459687			0.229843	+	0.973228i	$0.426179\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5.10243	+	8.83767i	0.161758	+	0.280173i
$996$		0			0
$997$	27.6549	−	47.8996i	0.875838	−	1.51700i	0.0199711	−	0.999801i	$-0.493643\pi$
$997$	27.6549	−	47.8996i	0.875838	−	1.51700i	0.855867	−	0.517196i	$-0.173024\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.j.2017.3		6
3.2	odd	2		1008.2.r.j.673.2		6
4.3	odd	2		756.2.j.b.505.3		6
9.2	odd	6		9072.2.a.by.1.3		3
9.4	even	3	inner	3024.2.r.j.1009.3		6
9.5	odd	6		1008.2.r.j.337.2		6
9.7	even	3		9072.2.a.bv.1.1		3
12.11	even	2		252.2.j.a.169.2	yes	6
28.3	even	6		5292.2.l.f.3313.3		6
28.11	odd	6		5292.2.l.e.3313.1		6
28.19	even	6		5292.2.i.e.2125.1		6
28.23	odd	6		5292.2.i.f.2125.3		6
28.27	even	2		5292.2.j.d.3529.1		6
36.7	odd	6		2268.2.a.h.1.1		3
36.11	even	6		2268.2.a.i.1.3		3
36.23	even	6		252.2.j.a.85.2	✓	6
36.31	odd	6		756.2.j.b.253.3		6
84.11	even	6		1764.2.l.e.961.2		6
84.23	even	6		1764.2.i.g.1537.3		6
84.47	odd	6		1764.2.i.d.1537.1		6
84.59	odd	6		1764.2.l.f.961.2		6
84.83	odd	2		1764.2.j.e.1177.2		6
252.23	even	6		1764.2.l.e.949.2		6
252.31	even	6		5292.2.i.e.1549.1		6
252.59	odd	6		1764.2.i.d.373.1		6
252.67	odd	6		5292.2.i.f.1549.3		6
252.95	even	6		1764.2.i.g.373.3		6
252.103	even	6		5292.2.l.f.361.3		6
252.131	odd	6		1764.2.l.f.949.2		6
252.139	even	6		5292.2.j.d.1765.1		6
252.167	odd	6		1764.2.j.e.589.2		6
252.247	odd	6		5292.2.l.e.361.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.2	✓	6	36.23	even	6
252.2.j.a.169.2	yes	6	12.11	even	2
756.2.j.b.253.3		6	36.31	odd	6
756.2.j.b.505.3		6	4.3	odd	2
1008.2.r.j.337.2		6	9.5	odd	6
1008.2.r.j.673.2		6	3.2	odd	2
1764.2.i.d.373.1		6	252.59	odd	6
1764.2.i.d.1537.1		6	84.47	odd	6
1764.2.i.g.373.3		6	252.95	even	6
1764.2.i.g.1537.3		6	84.23	even	6
1764.2.j.e.589.2		6	252.167	odd	6
1764.2.j.e.1177.2		6	84.83	odd	2
1764.2.l.e.949.2		6	252.23	even	6
1764.2.l.e.961.2		6	84.11	even	6
1764.2.l.f.949.2		6	252.131	odd	6
1764.2.l.f.961.2		6	84.59	odd	6
2268.2.a.h.1.1		3	36.7	odd	6
2268.2.a.i.1.3		3	36.11	even	6
3024.2.r.j.1009.3		6	9.4	even	3	inner
3024.2.r.j.2017.3		6	1.1	even	1	trivial
5292.2.i.e.1549.1		6	252.31	even	6
5292.2.i.e.2125.1		6	28.19	even	6
5292.2.i.f.1549.3		6	252.67	odd	6
5292.2.i.f.2125.3		6	28.23	odd	6
5292.2.j.d.1765.1		6	252.139	even	6
5292.2.j.d.3529.1		6	28.27	even	2
5292.2.l.e.361.1		6	252.247	odd	6
5292.2.l.e.3313.1		6	28.11	odd	6
5292.2.l.f.361.3		6	252.103	even	6
5292.2.l.f.3313.3		6	28.3	even	6
9072.2.a.bv.1.1		3	9.7	even	3
9072.2.a.by.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)

\(f(q)\)	\(=\)	\(q+(1.23025 + 2.13086i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(1.23025 + 2.13086i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.32383 + 4.02499i) q^{11} +(-3.55408 - 6.15585i) q^{13} +4.51459 q^{17} -4.32743 q^{19} +(-2.93346 - 5.08091i) q^{23} +(-0.527042 + 0.912864i) q^{25} +(-3.48755 + 6.04061i) q^{29} +(-3.69076 - 6.39258i) q^{31} -2.46050 q^{35} -0.726654 q^{37} +(0.136673 + 0.236725i) q^{41} +(-2.41741 + 4.18708i) q^{43} +(-1.83628 + 3.18054i) q^{47} +(-0.500000 - 0.866025i) q^{49} -5.05408 q^{53} -11.4356 q^{55} +(-4.56654 - 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(8.74484 - 15.1465i) q^{65} +(-0.663715 - 1.14959i) q^{67} +13.5218 q^{71} -4.32743 q^{73} +(-2.32383 - 4.02499i) q^{77} +(3.21780 - 5.57339i) q^{79} +(-0.742705 + 1.28640i) q^{83} +(5.55408 + 9.61996i) q^{85} -9.83482 q^{89} +7.10817 q^{91} +(-5.32383 - 9.22115i) q^{95} +(0.246304 - 0.426611i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q + q^5 - 3 * q^7	\( 6 q + q^{5} - 3 q^{7} - 2 q^{11} - 3 q^{13} - 4 q^{17} - 6 q^{19} - 14 q^{23} + 6 q^{25} + q^{29} - 3 q^{31} - 2 q^{35} - 6 q^{37} + 3 q^{43} - 21 q^{47} - 3 q^{49} - 12 q^{53} - 12 q^{55} - 31 q^{59} - 6 q^{61} + 15 q^{65} + 6 q^{67} + 34 q^{71} - 6 q^{73} - 2 q^{77} - 9 q^{79} - 20 q^{83} + 15 q^{85} - 24 q^{89} + 6 q^{91} - 20 q^{95} + 9 q^{97}+O(q^{100}) \) 6 * q + q^5 - 3 * q^7 - 2 * q^11 - 3 * q^13 - 4 * q^17 - 6 * q^19 - 14 * q^23 + 6 * q^25 + q^29 - 3 * q^31 - 2 * q^35 - 6 * q^37 + 3 * q^43 - 21 * q^47 - 3 * q^49 - 12 * q^53 - 12 * q^55 - 31 * q^59 - 6 * q^61 + 15 * q^65 + 6 * q^67 + 34 * q^71 - 6 * q^73 - 2 * q^77 - 9 * q^79 - 20 * q^83 + 15 * q^85 - 24 * q^89 + 6 * q^91 - 20 * q^95 + 9 * q^97

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