LMFDB - Embedded newform 3024.2.q.l.2881.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.2
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.l.2305.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89970 + 3.29038i) q^{5} +(0.841809 + 2.50826i) q^{7} +O(q^{10})$	$q+(-1.89970 + 3.29038i) q^{5} +(0.841809 + 2.50826i) q^{7} +(-2.25706 - 3.90934i) q^{11} +(0.588451 + 1.01923i) q^{13} +(2.95973 - 5.12641i) q^{17} +(-2.55676 - 4.42844i) q^{19} +(2.09082 - 3.62140i) q^{23} +(-4.71772 - 8.17134i) q^{25} +(-2.11164 + 3.65747i) q^{29} +6.24283 q^{31} +(-9.85230 - 1.99507i) q^{35} +(-3.87179 - 6.70614i) q^{37} +(-0.754693 - 1.30717i) q^{41} +(5.01709 - 8.68986i) q^{43} -2.23665 q^{47} +(-5.58272 + 4.22295i) q^{49} +(-6.49368 + 11.2474i) q^{53} +17.1510 q^{55} +12.3922 q^{59} +1.45834 q^{61} -4.47152 q^{65} -1.62638 q^{67} +8.48517 q^{71} +(3.72984 - 6.46027i) q^{73} +(7.90563 - 8.95221i) q^{77} +1.84185 q^{79} +(-0.307606 + 0.532789i) q^{83} +(11.2452 + 19.4773i) q^{85} +(1.25572 + 2.17496i) q^{89} +(-2.06112 + 2.33398i) q^{91} +19.4283 q^{95} +(2.36751 - 4.10064i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} - 5 q^{7}+O(q^{10}) $ 22 * q - q^5 - 5 * q^7	$ 22 q - q^{5} - 5 q^{7} + 3 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} - 22 q^{25} + 7 q^{29} + 12 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} - 34 q^{47} - 25 q^{49} - q^{53} - 2 q^{55} + 42 q^{59} - 62 q^{61} - 6 q^{65} - 52 q^{67} - 32 q^{71} + 17 q^{73} + q^{77} - 32 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} + 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 - 5 * q^7 + 3 * q^11 + 7 * q^13 + q^17 - 13 * q^19 - 22 * q^25 + 7 * q^29 + 12 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 - 34 * q^47 - 25 * q^49 - q^53 - 2 * q^55 + 42 * q^59 - 62 * q^61 - 6 * q^65 - 52 * q^67 - 32 * q^71 + 17 * q^73 + q^77 - 32 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 + 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.89970	+	3.29038i	−0.849572	+	1.47150i	0.0320189	+	0.999487i	$0.489806\pi$
$5$	−1.89970	+	3.29038i	−0.849572	+	1.47150i	−0.881591	+	0.472014i	$0.843527\pi$
$6$		0			0
$7$	0.841809	+	2.50826i	0.318174	+	0.948032i
$7$	0.841809	+	2.50826i	0.318174	+	0.948032i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.25706	−	3.90934i	−0.680529	−	1.17871i	−0.974820	−	0.222995i	$-0.928417\pi$
$11$	−2.25706	−	3.90934i	−0.680529	−	1.17871i	0.294290	−	0.955716i	$-0.404917\pi$
$12$		0			0
$13$	0.588451	+	1.01923i	0.163207	+	0.282683i	0.936017	−	0.351955i	$-0.114483\pi$
$13$	0.588451	+	1.01923i	0.163207	+	0.282683i	−0.772810	+	0.634637i	$0.781150\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.95973	−	5.12641i	0.717841	−	1.24334i	−0.244012	−	0.969772i	$-0.578464\pi$
$17$	2.95973	−	5.12641i	0.717841	−	1.24334i	0.961853	−	0.273565i	$-0.0882029\pi$
$18$		0			0
$19$	−2.55676	−	4.42844i	−0.586562	−	1.01595i	−0.994679	−	0.103025i	$-0.967148\pi$
$19$	−2.55676	−	4.42844i	−0.586562	−	1.01595i	0.408117	−	0.912930i	$-0.366185\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.09082	−	3.62140i	0.435966	−	0.755115i	−0.561408	−	0.827539i	$-0.689740\pi$
$23$	2.09082	−	3.62140i	0.435966	−	0.755115i	0.997374	+	0.0724243i	$0.0230736\pi$
$24$		0			0
$25$	−4.71772	−	8.17134i	−0.943545	−	1.63427i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.11164	+	3.65747i	−0.392122	+	0.679175i	−0.992729	−	0.120369i	$-0.961592\pi$
$29$	−2.11164	+	3.65747i	−0.392122	+	0.679175i	0.600607	+	0.799544i	$0.294925\pi$
$30$		0			0
$31$	6.24283			1.12124			0.560622	−	0.828072i	$-0.310562\pi$
$31$	6.24283			1.12124			0.560622	+	0.828072i	$0.310562\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−9.85230	−	1.99507i	−1.66534	−	0.337229i
$36$		0			0
$37$	−3.87179	−	6.70614i	−0.636519	−	1.10248i	−0.986191	−	0.165611i	$-0.947040\pi$
$37$	−3.87179	−	6.70614i	−0.636519	−	1.10248i	0.349672	−	0.936872i	$-0.386293\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.754693	−	1.30717i	−0.117863	−	0.204145i	0.801057	−	0.598587i	$-0.204271\pi$
$41$	−0.754693	−	1.30717i	−0.117863	−	0.204145i	−0.918921	+	0.394442i	$0.870938\pi$
$42$		0			0
$43$	5.01709	−	8.68986i	0.765099	−	1.32519i	−0.175095	−	0.984552i	$-0.556023\pi$
$43$	5.01709	−	8.68986i	0.765099	−	1.32519i	0.940194	−	0.340639i	$-0.110643\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.23665			−0.326248			−0.163124	−	0.986606i	$-0.552157\pi$
$47$	−2.23665			−0.326248			−0.163124	+	0.986606i	$0.552157\pi$
$48$		0			0
$49$	−5.58272	+	4.22295i	−0.797531	+	0.603278i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.49368	+	11.2474i	−0.891975	+	1.54495i	−0.0544716	+	0.998515i	$0.517347\pi$
$53$	−6.49368	+	11.2474i	−0.891975	+	1.54495i	−0.837504	+	0.546431i	$0.815986\pi$
$54$		0			0
$55$	17.1510			2.31263
$56$		0			0
$57$		0			0
$58$		0			0
$59$	12.3922			1.61332			0.806662	−	0.591013i	$-0.201272\pi$
$59$	12.3922			1.61332			0.806662	+	0.591013i	$0.201272\pi$
$60$		0			0
$61$	1.45834			0.186722			0.0933608	−	0.995632i	$-0.470239\pi$
$61$	1.45834			0.186722			0.0933608	+	0.995632i	$0.470239\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.47152			−0.554624
$66$		0			0
$67$	−1.62638			−0.198694			−0.0993472	−	0.995053i	$-0.531675\pi$
$67$	−1.62638			−0.198694			−0.0993472	+	0.995053i	$0.531675\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.48517			1.00700			0.503502	−	0.863994i	$-0.332045\pi$
$71$	8.48517			1.00700			0.503502	+	0.863994i	$0.332045\pi$
$72$		0			0
$73$	3.72984	−	6.46027i	0.436544	−	0.756117i	−0.560876	−	0.827900i	$-0.689535\pi$
$73$	3.72984	−	6.46027i	0.436544	−	0.756117i	0.997420	+	0.0717827i	$0.0228688\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.90563	−	8.95221i	0.900930	−	1.02020i
$78$		0			0
$79$	1.84185			0.207224			0.103612	−	0.994618i	$-0.466960\pi$
$79$	1.84185			0.207224			0.103612	+	0.994618i	$0.466960\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.307606	+	0.532789i	−0.0337641	+	0.0584812i	−0.882414	−	0.470474i	$-0.844083\pi$
$83$	−0.307606	+	0.532789i	−0.0337641	+	0.0584812i	0.848650	+	0.528956i	$0.177416\pi$
$84$		0			0
$85$	11.2452	+	19.4773i	1.21972	+	2.11261i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.25572	+	2.17496i	0.133106	+	0.230546i	0.924872	−	0.380278i	$-0.124172\pi$
$89$	1.25572	+	2.17496i	0.133106	+	0.230546i	−0.791767	+	0.610824i	$0.790838\pi$
$90$		0			0
$91$	−2.06112	+	2.33398i	−0.216064	+	0.244668i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	19.4283			1.99330
$96$		0			0
$97$	2.36751	−	4.10064i	0.240384	−	0.416357i	−0.720440	−	0.693517i	$-0.756060\pi$
$97$	2.36751	−	4.10064i	0.240384	−	0.416357i	0.960824	+	0.277160i	$0.0893934\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.71081	−	9.89141i	−0.568247	−	0.984232i	−0.996739	−	0.0806872i	$-0.974289\pi$
$101$	−5.71081	−	9.89141i	−0.568247	−	0.984232i	0.428493	−	0.903545i	$-0.359045\pi$
$102$		0			0
$103$	−3.18752	+	5.52095i	−0.314076	+	0.543996i	−0.979241	−	0.202701i	$-0.935028\pi$
$103$	−3.18752	+	5.52095i	−0.314076	+	0.543996i	0.665165	+	0.746697i	$0.268361\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.11999	+	1.93988i	0.108274	+	0.187536i	0.915071	−	0.403293i	$-0.132134\pi$
$107$	1.11999	+	1.93988i	0.108274	+	0.187536i	−0.806797	+	0.590828i	$0.798801\pi$
$108$		0			0
$109$	−2.73089	+	4.73005i	−0.261572	+	0.453056i	−0.966660	−	0.256064i	$-0.917574\pi$
$109$	−2.73089	+	4.73005i	−0.261572	+	0.453056i	0.705088	+	0.709120i	$0.250908\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.45456	+	7.71553i	0.419050	+	0.725816i	0.995844	−	0.0910734i	$-0.0290298\pi$
$113$	4.45456	+	7.71553i	0.419050	+	0.725816i	−0.576794	+	0.816890i	$0.695696\pi$
$114$		0			0
$115$	7.94386	+	13.7592i	0.740768	+	1.28305i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.3499	+	3.10832i	1.40712	+	0.284939i
$120$		0			0
$121$	−4.68864	+	8.12096i	−0.426240	+	0.738269i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	16.8520			1.50729
$126$		0			0
$127$	−0.434918			−0.0385927			−0.0192964	−	0.999814i	$-0.506143\pi$
$127$	−0.434918			−0.0385927			−0.0192964	+	0.999814i	$0.506143\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.67633	−	4.63553i	0.233832	−	0.405009i	−0.725101	−	0.688643i	$-0.758207\pi$
$131$	2.67633	−	4.63553i	0.233832	−	0.405009i	0.958933	+	0.283634i	$0.0915402\pi$
$132$		0			0
$133$	8.95537	−	10.1409i	0.776529	−	0.879329i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.95121	+	5.11165i	0.252139	+	0.436718i	0.964115	−	0.265487i	$-0.0855326\pi$
$137$	2.95121	+	5.11165i	0.252139	+	0.436718i	−0.711976	+	0.702204i	$0.752199\pi$
$138$		0			0
$139$	−4.33649	−	7.51102i	−0.367816	−	0.637077i	0.621407	−	0.783488i	$-0.286561\pi$
$139$	−4.33649	−	7.51102i	−0.367816	−	0.637077i	−0.989224	+	0.146411i	$0.953228\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.65634	−	4.60091i	0.222134	−	0.384747i
$144$		0			0
$145$	−8.02297	−	13.8962i	−0.666271	−	1.15402i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.38860	+	9.33333i	−0.441451	+	0.764616i	−0.997797	−	0.0663346i	$-0.978870\pi$
$149$	−5.38860	+	9.33333i	−0.441451	+	0.764616i	0.556346	+	0.830951i	$0.312203\pi$
$150$		0			0
$151$	−8.41310	−	14.5719i	−0.684648	−	1.18585i	−0.973547	−	0.228486i	$-0.926622\pi$
$151$	−8.41310	−	14.5719i	−0.684648	−	1.18585i	0.288899	−	0.957360i	$-0.406711\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−11.8595	+	20.5413i	−0.952578	+	1.64991i
$156$		0			0
$157$	8.96136			0.715194			0.357597	−	0.933876i	$-0.383596\pi$
$157$	8.96136			0.715194			0.357597	+	0.933876i	$0.383596\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	10.8435	+	2.19578i	0.854586	+	0.173052i
$162$		0			0
$163$	3.71319	+	6.43144i	0.290840	+	0.503749i	0.974009	−	0.226511i	$-0.0727320\pi$
$163$	3.71319	+	6.43144i	0.290840	+	0.503749i	−0.683169	+	0.730261i	$0.739399\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.13764	−	8.89866i	−0.397563	−	0.688599i	0.595862	−	0.803087i	$-0.296811\pi$
$167$	−5.13764	−	8.89866i	−0.397563	−	0.688599i	−0.993425	+	0.114488i	$0.963477\pi$
$168$		0			0
$169$	5.80745	−	10.0588i	0.446727	−	0.773754i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.2099			0.776246			0.388123	−	0.921608i	$-0.373124\pi$
$173$	10.2099			0.776246			0.388123	+	0.921608i	$0.373124\pi$
$174$		0			0
$175$	16.5244	−	18.7120i	1.24913	−	1.41449i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.62985	−	16.6794i	0.719769	−	1.24668i	−0.241323	−	0.970445i	$-0.577581\pi$
$179$	9.62985	−	16.6794i	0.719769	−	1.24668i	0.961091	−	0.276231i	$-0.0890854\pi$
$180$		0			0
$181$	−1.39163			−0.103439			−0.0517195	−	0.998662i	$-0.516470\pi$
$181$	−1.39163			−0.103439			−0.0517195	+	0.998662i	$0.516470\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	29.4210			2.16307
$186$		0			0
$187$	−26.7212			−1.95405
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.71483			−0.196438			−0.0982190	−	0.995165i	$-0.531315\pi$
$191$	−2.71483			−0.196438			−0.0982190	+	0.995165i	$0.531315\pi$
$192$		0			0
$193$	1.84169			0.132568			0.0662839	−	0.997801i	$-0.478886\pi$
$193$	1.84169			0.132568			0.0662839	+	0.997801i	$0.478886\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−21.9198			−1.56172			−0.780860	−	0.624706i	$-0.785219\pi$
$197$	−21.9198			−1.56172			−0.780860	+	0.624706i	$0.785219\pi$
$198$		0			0
$199$	0.726101	−	1.25764i	0.0514719	−	0.0891520i	−0.839141	−	0.543913i	$-0.816942\pi$
$199$	0.726101	−	1.25764i	0.0514719	−	0.0891520i	0.890613	+	0.454761i	$0.150275\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.9515	−	2.21765i	−0.768643	−	0.155649i
$204$		0			0
$205$	5.73476			0.400533
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.5415	+	19.9905i	−0.798344	+	1.38277i
$210$		0			0
$211$	−0.771347	−	1.33601i	−0.0531017	−	0.0919749i	0.838253	−	0.545282i	$-0.183577\pi$
$211$	−0.771347	−	1.33601i	−0.0531017	−	0.0919749i	−0.891354	+	0.453307i	$0.850244\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	19.0619	+	33.0162i	1.30001	+	2.25169i
$216$		0			0
$217$	5.25527	+	15.6586i	0.356751	+	1.06298i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.96663			0.468626
$222$		0			0
$223$	0.346045	−	0.599368i	0.0231729	−	0.0401366i	−0.854206	−	0.519934i	$-0.825957\pi$
$223$	0.346045	−	0.599368i	0.0231729	−	0.0401366i	0.877379	+	0.479797i	$0.159290\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.20797	−	15.9487i	−0.611155	−	1.05855i	−0.991046	−	0.133520i	$-0.957372\pi$
$227$	−9.20797	−	15.9487i	−0.611155	−	1.05855i	0.379892	−	0.925031i	$-0.375961\pi$
$228$		0			0
$229$	2.69696	−	4.67127i	0.178220	−	0.308686i	−0.763051	−	0.646338i	$-0.776299\pi$
$229$	2.69696	−	4.67127i	0.178220	−	0.308686i	0.941271	+	0.337652i	$0.109633\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.27352	+	14.3302i	0.542016	+	0.938800i	0.998788	+	0.0492161i	$0.0156723\pi$
$233$	8.27352	+	14.3302i	0.542016	+	0.938800i	−0.456772	+	0.889584i	$0.650994\pi$
$234$		0			0
$235$	4.24896	−	7.35941i	0.277171	−	0.480075i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.56724	−	2.71454i	−0.101376	−	0.175589i	0.810876	−	0.585219i	$-0.198991\pi$
$239$	−1.56724	−	2.71454i	−0.101376	−	0.175589i	−0.912252	+	0.409630i	$0.865658\pi$
$240$		0			0
$241$	8.23730	+	14.2674i	0.530611	+	0.919046i	0.999362	+	0.0357151i	$0.0113709\pi$
$241$	8.23730	+	14.2674i	0.530611	+	0.919046i	−0.468751	+	0.883330i	$0.655296\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.28960	−	26.3916i	−0.210165	−	1.68610i
$246$		0			0
$247$	3.00906	−	5.21184i	0.191462	−	0.331621i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.8939			0.813858			0.406929	−	0.913460i	$-0.366600\pi$
$251$	12.8939			0.813858			0.406929	+	0.913460i	$0.366600\pi$
$252$		0			0
$253$	−18.8764			−1.18675
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.3045	−	17.8478i	0.642774	−	1.11332i	−0.342036	−	0.939687i	$-0.611117\pi$
$257$	10.3045	−	17.8478i	0.642774	−	1.11332i	0.984811	−	0.173631i	$-0.0555501\pi$
$258$		0			0
$259$	13.5614	−	15.3567i	0.842666	−	0.954222i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.56616	−	7.90883i	−0.281562	−	0.487679i	0.690208	−	0.723611i	$-0.257519\pi$
$263$	−4.56616	−	7.90883i	−0.281562	−	0.487679i	−0.971770	+	0.235932i	$0.924186\pi$
$264$		0			0
$265$	−24.6721	−	42.7333i	−1.51559	−	2.62509i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.4387	−	21.5445i	0.758401	−	1.31359i	−0.185265	−	0.982689i	$-0.559314\pi$
$269$	12.4387	−	21.5445i	0.758401	−	1.31359i	0.943666	−	0.330900i	$-0.107352\pi$
$270$		0			0
$271$	−5.70814	−	9.88679i	−0.346745	−	0.600580i	0.638924	−	0.769270i	$-0.279380\pi$
$271$	−5.70814	−	9.88679i	−0.346745	−	0.600580i	−0.985669	+	0.168690i	$0.946046\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−21.2964	+	36.8864i	−1.28422	+	2.22433i
$276$		0			0
$277$	−15.4938	−	26.8360i	−0.930932	−	1.61242i	−0.781732	−	0.623615i	$-0.785663\pi$
$277$	−15.4938	−	26.8360i	−0.930932	−	1.61242i	−0.149200	−	0.988807i	$-0.547670\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.40910	−	12.8329i	0.441990	−	0.765549i	−0.555847	−	0.831285i	$-0.687606\pi$
$281$	7.40910	−	12.8329i	0.441990	−	0.765549i	0.997837	+	0.0657354i	$0.0209393\pi$
$282$		0			0
$283$	−25.7431			−1.53027			−0.765134	−	0.643872i	$-0.777327\pi$
$283$	−25.7431			−1.53027			−0.765134	+	0.643872i	$0.777327\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.64340	−	2.99335i	0.156035	−	0.176692i
$288$		0			0
$289$	−9.02006	−	15.6232i	−0.530592	−	0.919012i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.41185	−	14.5697i	−0.491425	−	0.851174i	0.508526	−	0.861047i	$-0.330191\pi$
$293$	−8.41185	−	14.5697i	−0.491425	−	0.851174i	−0.999951	+	0.00987288i	$0.996857\pi$
$294$		0			0
$295$	−23.5414	+	40.7749i	−1.37063	+	2.37401i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.92137			0.284610
$300$		0			0
$301$	26.0198	+	5.26896i	1.49976	+	0.303698i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.77041	+	4.79849i	−0.158633	+	0.274761i
$306$		0			0
$307$	28.2972			1.61501			0.807504	−	0.589862i	$-0.200818\pi$
$307$	28.2972			1.61501			0.807504	+	0.589862i	$0.200818\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	19.8695			1.12670			0.563349	−	0.826219i	$-0.309513\pi$
$311$	19.8695			1.12670			0.563349	+	0.826219i	$0.309513\pi$
$312$		0			0
$313$	−18.2859			−1.03358			−0.516789	−	0.856113i	$-0.672873\pi$
$313$	−18.2859			−1.03358			−0.516789	+	0.856113i	$0.672873\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.9480			−0.783399			−0.391700	−	0.920093i	$-0.628113\pi$
$317$	−13.9480			−0.783399			−0.391700	+	0.920093i	$0.628113\pi$
$318$		0			0
$319$	19.0644			1.06740
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−30.2694			−1.68423
$324$		0			0
$325$	5.55230	−	9.61686i	0.307986	−	0.533447i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.88283	−	5.61009i	−0.103804	−	0.309294i
$330$		0			0
$331$	−20.8399			−1.14547			−0.572733	−	0.819742i	$-0.694117\pi$
$331$	−20.8399			−1.14547			−0.572733	+	0.819742i	$0.694117\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.08964	−	5.35142i	0.168805	−	0.292379i
$336$		0			0
$337$	15.4376	+	26.7387i	0.840939	+	1.45655i	0.889101	+	0.457710i	$0.151330\pi$
$337$	15.4376	+	26.7387i	0.840939	+	1.45655i	−0.0481619	+	0.998840i	$0.515336\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.0904	−	24.4054i	−0.763040	−	1.32162i
$342$		0			0
$343$	−15.2918	−	10.4480i	−0.825681	−	0.564138i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.2685			−0.551244			−0.275622	−	0.961266i	$-0.588884\pi$
$347$	−10.2685			−0.551244			−0.275622	+	0.961266i	$0.588884\pi$
$348$		0			0
$349$	4.61262	−	7.98930i	0.246908	−	0.427657i	−0.715758	−	0.698348i	$-0.753919\pi$
$349$	4.61262	−	7.98930i	0.246908	−	0.427657i	0.962666	+	0.270691i	$0.0872521\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.08660	+	7.07820i	0.217508	+	0.376735i	0.954045	−	0.299662i	$-0.0968739\pi$
$353$	4.08660	+	7.07820i	0.217508	+	0.376735i	−0.736538	+	0.676397i	$0.763541\pi$
$354$		0			0
$355$	−16.1193	+	27.9194i	−0.855522	+	1.48181i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.35957	+	11.0151i	0.335645	+	0.581355i	0.983609	−	0.180317i	$-0.0577123\pi$
$359$	6.35957	+	11.0151i	0.335645	+	0.581355i	−0.647963	+	0.761672i	$0.724379\pi$
$360$		0			0
$361$	−3.57407	+	6.19047i	−0.188109	+	0.325814i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	14.1711	+	24.5452i	0.741752	+	1.28475i
$366$		0			0
$367$	−10.9431	−	18.9540i	−0.571224	−	0.989388i	−0.996441	−	0.0842970i	$-0.973136\pi$
$367$	−10.9431	−	18.9540i	−0.571224	−	0.989388i	0.425217	−	0.905091i	$-0.360198\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−33.6778	−	6.81968i	−1.74846	−	0.354060i
$372$		0			0
$373$	6.73126	−	11.6589i	0.348531	−	0.603674i	−0.637457	−	0.770486i	$-0.720014\pi$
$373$	6.73126	−	11.6589i	0.348531	−	0.603674i	0.985989	+	0.166811i	$0.0533471\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.97038			−0.255988
$378$		0			0
$379$	11.2180			0.576231			0.288115	−	0.957596i	$-0.406971\pi$
$379$	11.2180			0.576231			0.288115	+	0.957596i	$0.406971\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.00330	−	6.93392i	0.204559	−	0.354307i	−0.745433	−	0.666581i	$-0.767757\pi$
$383$	4.00330	−	6.93392i	0.204559	−	0.354307i	0.949992	+	0.312274i	$0.101091\pi$
$384$		0			0
$385$	14.4378	+	43.0190i	0.735819	+	2.19245i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.3931	+	24.9296i	0.729759	+	1.26398i	0.956985	+	0.290137i	$0.0937009\pi$
$389$	14.3931	+	24.9296i	0.729759	+	1.26398i	−0.227226	+	0.973842i	$0.572966\pi$
$390$		0			0
$391$	−12.3765	−	21.4368i	−0.625908	−	1.08410i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.49897	+	6.06039i	−0.176052	+	0.304931i
$396$		0			0
$397$	10.8138	+	18.7301i	0.542731	+	0.940037i	0.998746	+	0.0500651i	$0.0159429\pi$
$397$	10.8138	+	18.7301i	0.542731	+	0.940037i	−0.456015	+	0.889972i	$0.650724\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.4966	−	23.3768i	0.673987	−	1.16738i	−0.302777	−	0.953062i	$-0.597914\pi$
$401$	13.4966	−	23.3768i	0.673987	−	1.16738i	0.976764	−	0.214318i	$-0.0687530\pi$
$402$		0			0
$403$	3.67360	+	6.36285i	0.182995	+	0.316956i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.4777	+	30.2723i	−0.866339	+	1.50054i
$408$		0			0
$409$	−20.9473			−1.03578			−0.517889	−	0.855448i	$-0.673282\pi$
$409$	−20.9473			−1.03578			−0.517889	+	0.855448i	$0.673282\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.4318	+	31.0828i	0.513317	+	1.52948i
$414$		0			0
$415$	−1.16872	−	2.02428i	−0.0573701	−	0.0993680i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.91450	+	11.9763i	0.337795	+	0.585079i	0.984018	−	0.178070i	$-0.0569855\pi$
$419$	6.91450	+	11.9763i	0.337795	+	0.585079i	−0.646222	+	0.763149i	$0.723652\pi$
$420$		0			0
$421$	−6.86872	+	11.8970i	−0.334761	+	0.579823i	−0.983439	−	0.181240i	$-0.941989\pi$
$421$	−6.86872	+	11.8970i	−0.334761	+	0.579823i	0.648678	+	0.761063i	$0.275322\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−55.8529			−2.70926
$426$		0			0
$427$	1.22764	+	3.65790i	0.0594099	+	0.177018i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.20392	+	15.9417i	−0.443337	+	0.767882i	−0.997935	−	0.0642362i	$-0.979539\pi$
$431$	−9.20392	+	15.9417i	−0.443337	+	0.767882i	0.554598	+	0.832119i	$0.312872\pi$
$432$		0			0
$433$	24.3558			1.17047			0.585233	−	0.810865i	$-0.301003\pi$
$433$	24.3558			1.17047			0.585233	+	0.810865i	$0.301003\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−21.3829			−1.02288
$438$		0			0
$439$	5.83655			0.278564			0.139282	−	0.990253i	$-0.455521\pi$
$439$	5.83655			0.278564			0.139282	+	0.990253i	$0.455521\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.8400			0.705071			0.352536	−	0.935798i	$-0.385320\pi$
$443$	14.8400			0.705071			0.352536	+	0.935798i	$0.385320\pi$
$444$		0			0
$445$	−9.54194			−0.452331
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.26289			0.201178			0.100589	−	0.994928i	$-0.467927\pi$
$449$	4.26289			0.201178			0.100589	+	0.994928i	$0.467927\pi$
$450$		0			0
$451$	−3.40677	+	5.90070i	−0.160419	+	0.277853i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.76416	−	11.2157i	−0.176467	−	0.525801i
$456$		0			0
$457$	39.7459			1.85924			0.929618	−	0.368525i	$-0.120137\pi$
$457$	39.7459			1.85924			0.929618	+	0.368525i	$0.120137\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.68671	−	4.65353i	0.125133	−	0.216736i	−0.796652	−	0.604438i	$-0.793398\pi$
$461$	2.68671	−	4.65353i	0.125133	−	0.216736i	0.921785	+	0.387702i	$0.126731\pi$
$462$		0			0
$463$	−19.8205	−	34.3301i	−0.921136	−	1.59545i	−0.797661	−	0.603106i	$-0.793930\pi$
$463$	−19.8205	−	34.3301i	−0.921136	−	1.59545i	−0.123474	−	0.992348i	$-0.539404\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.43069	+	16.3344i	0.436400	+	0.755867i	0.997409	−	0.0719427i	$-0.0229199\pi$
$467$	9.43069	+	16.3344i	0.436400	+	0.755867i	−0.561009	+	0.827810i	$0.689587\pi$
$468$		0			0
$469$	−1.36910	−	4.07939i	−0.0632193	−	0.188369i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−45.2955			−2.08269
$474$		0			0
$475$	−24.1242	+	41.7843i	−1.10689	+	1.91720i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.50287	−	16.4595i	−0.434197	−	0.752052i	0.563032	−	0.826435i	$-0.309635\pi$
$479$	−9.50287	−	16.4595i	−0.434197	−	0.752052i	−0.997230	+	0.0743830i	$0.976301\pi$
$480$		0			0
$481$	4.55672	−	7.89247i	0.207768	−	0.359866i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.99511	+	15.5800i	0.408447	+	0.707451i
$486$		0			0
$487$	5.21626	−	9.03482i	0.236371	−	0.409407i	−0.723299	−	0.690535i	$-0.757375\pi$
$487$	5.21626	−	9.03482i	0.236371	−	0.409407i	0.959670	+	0.281128i	$0.0907085\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−14.3311	−	24.8221i	−0.646752	−	1.12021i	−0.983894	−	0.178753i	$-0.942794\pi$
$491$	−14.3311	−	24.8221i	−0.646752	−	1.12021i	0.337142	−	0.941454i	$-0.390540\pi$
$492$		0			0
$493$	12.4998	+	21.6503i	0.562962	+	0.975079i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.14289	+	21.2830i	0.320402	+	0.954673i
$498$		0			0
$499$	−16.5396	+	28.6475i	−0.740416	+	1.28244i	0.211890	+	0.977294i	$0.432038\pi$
$499$	−16.5396	+	28.6475i	−0.740416	+	1.28244i	−0.952306	+	0.305145i	$0.901295\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−28.9523			−1.29092			−0.645460	−	0.763794i	$-0.723334\pi$
$503$	−28.9523			−1.29092			−0.645460	+	0.763794i	$0.723334\pi$
$504$		0			0
$505$	43.3953			1.93107
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.8820	−	27.5085i	0.703959	−	1.21929i	−0.263107	−	0.964767i	$-0.584747\pi$
$509$	15.8820	−	27.5085i	0.703959	−	1.21929i	0.967066	−	0.254526i	$-0.0819194\pi$
$510$		0			0
$511$	19.3438	+	3.91709i	0.855721	+	0.173282i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.1107	−	20.9763i	−0.533660	−	0.924327i
$516$		0			0
$517$	5.04825	+	8.74382i	0.222022	+	0.384553i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.87897	−	4.98652i	0.126130	−	0.218463i	−0.796044	−	0.605239i	$-0.793078\pi$
$521$	2.87897	−	4.98652i	0.126130	−	0.218463i	0.922174	+	0.386775i	$0.126411\pi$
$522$		0			0
$523$	22.3123	+	38.6461i	0.975650	+	1.68987i	0.677774	+	0.735270i	$0.262945\pi$
$523$	22.3123	+	38.6461i	0.975650	+	1.68987i	0.297875	+	0.954605i	$0.403722\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	18.4771	−	32.0033i	0.804876	−	1.39409i
$528$		0			0
$529$	2.75696	+	4.77520i	0.119868	+	0.207617i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.888199	−	1.53841i	0.0384722	−	0.0666357i
$534$		0			0
$535$	−8.51060			−0.367945
$536$		0			0
$537$		0			0
$538$		0			0
$539$	29.1095	+	12.2933i	1.25383	+	0.529510i
$540$		0			0
$541$	15.6719	+	27.1445i	0.673786	+	1.16703i	0.976822	+	0.214053i	$0.0686665\pi$
$541$	15.6719	+	27.1445i	0.673786	+	1.16703i	−0.303036	+	0.952979i	$0.598000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−10.3758	−	17.9713i	−0.444449	−	0.769808i
$546$		0			0
$547$	−1.37567	+	2.38273i	−0.0588195	+	0.101878i	−0.893936	−	0.448195i	$-0.852067\pi$
$547$	−1.37567	+	2.38273i	−0.0588195	+	0.101878i	0.835116	+	0.550073i	$0.185400\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	21.5959			0.920014
$552$		0			0
$553$	1.55049	+	4.61984i	0.0659334	+	0.196455i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.42197	+	5.92703i	−0.144994	+	0.251136i	−0.929371	−	0.369148i	$-0.879650\pi$
$557$	−3.42197	+	5.92703i	−0.144994	+	0.251136i	0.784377	+	0.620284i	$0.212983\pi$
$558$		0			0
$559$	11.8092			0.499478
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.1001			0.636395			0.318197	−	0.948025i	$-0.396923\pi$
$563$	15.1001			0.636395			0.318197	+	0.948025i	$0.396923\pi$
$564$		0			0
$565$	−33.8494			−1.42405
$566$		0			0
$567$		0			0
$568$		0			0
$569$	27.5276			1.15402			0.577008	−	0.816738i	$-0.304220\pi$
$569$	27.5276			1.15402			0.577008	+	0.816738i	$0.304220\pi$
$570$		0			0
$571$	38.8755			1.62689			0.813444	−	0.581643i	$-0.197590\pi$
$571$	38.8755			1.62689			0.813444	+	0.581643i	$0.197590\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−39.4556			−1.64541
$576$		0			0
$577$	−9.84330	+	17.0491i	−0.409782	+	0.709763i	−0.994865	−	0.101210i	$-0.967729\pi$
$577$	−9.84330	+	17.0491i	−0.409782	+	0.709763i	0.585083	+	0.810973i	$0.301062\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.59532	−	0.323049i	−0.0661849	−	0.0134023i
$582$		0			0
$583$	58.6265			2.42806
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.14068	−	5.43982i	0.129630	−	0.224525i	−0.793903	−	0.608044i	$-0.791954\pi$
$587$	3.14068	−	5.43982i	0.129630	−	0.224525i	0.923533	+	0.383519i	$0.125288\pi$
$588$		0			0
$589$	−15.9614	−	27.6460i	−0.657679	−	1.13913i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.79280	−	13.4975i	−0.320012	−	0.554277i	0.660478	−	0.750845i	$-0.270354\pi$
$593$	−7.79280	−	13.4975i	−0.320012	−	0.554277i	−0.980490	+	0.196568i	$0.937020\pi$
$594$		0			0
$595$	−39.3877	+	44.6021i	−1.61474	+	1.82851i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.05557			0.0431292			0.0215646	−	0.999767i	$-0.493135\pi$
$599$	1.05557			0.0431292			0.0215646	+	0.999767i	$0.493135\pi$
$600$		0			0
$601$	−12.1622	+	21.0656i	−0.496107	+	0.859283i	−0.999990	−	0.00448941i	$-0.998571\pi$
$601$	−12.1622	+	21.0656i	−0.496107	+	0.859283i	0.503883	+	0.863772i	$0.331904\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−17.8140	−	30.8548i	−0.724243	−	1.25443i
$606$		0			0
$607$	2.16502	−	3.74993i	0.0878756	−	0.152205i	−0.818737	−	0.574168i	$-0.805326\pi$
$607$	2.16502	−	3.74993i	0.0878756	−	0.152205i	0.906613	+	0.421963i	$0.138659\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.31616	−	2.27965i	−0.0532460	−	0.0922247i
$612$		0			0
$613$	−24.3556	+	42.1852i	−0.983714	+	1.70384i	−0.336196	+	0.941792i	$0.609140\pi$
$613$	−24.3556	+	42.1852i	−0.983714	+	1.70384i	−0.647518	+	0.762050i	$0.724193\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.6366	−	25.3514i	−0.589249	−	1.02061i	−0.994331	−	0.106329i	$-0.966090\pi$
$617$	−14.6366	−	25.3514i	−0.589249	−	1.02061i	0.405082	−	0.914280i	$-0.367243\pi$
$618$		0			0
$619$	−18.2381	−	31.5893i	−0.733050	−	1.26968i	−0.955573	−	0.294753i	$-0.904763\pi$
$619$	−18.2381	−	31.5893i	−0.733050	−	1.26968i	0.222523	−	0.974927i	$-0.428571\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.39830	+	4.98056i	−0.176214	+	0.199542i
$624$		0			0
$625$	−8.42523	+	14.5929i	−0.337009	+	0.583717i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−45.8379			−1.82768
$630$		0			0
$631$	−0.501625			−0.0199694			−0.00998468	−	0.999950i	$-0.503178\pi$
$631$	−0.501625			−0.0199694			−0.00998468	+	0.999950i	$0.503178\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.826214	−	1.43104i	0.0327873	−	0.0567893i
$636$		0			0
$637$	−7.58929	−	3.20506i	−0.300699	−	0.126989i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.5112	−	30.3303i	−0.691651	−	1.19797i	−0.971297	−	0.237871i	$-0.923551\pi$
$641$	−17.5112	−	30.3303i	−0.691651	−	1.19797i	0.279646	−	0.960103i	$-0.409783\pi$
$642$		0			0
$643$	−7.29049	−	12.6275i	−0.287509	−	0.497980i	0.685706	−	0.727879i	$-0.259494\pi$
$643$	−7.29049	−	12.6275i	−0.287509	−	0.497980i	−0.973215	+	0.229899i	$0.926160\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.6503	+	20.1790i	−0.458022	+	0.793318i	−0.998856	−	0.0478116i	$-0.984775\pi$
$647$	−11.6503	+	20.1790i	−0.458022	+	0.793318i	0.540834	+	0.841129i	$0.318109\pi$
$648$		0			0
$649$	−27.9699	−	48.4453i	−1.09791	−	1.90164i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.26780	+	7.39204i	−0.167012	+	0.289273i	−0.937368	−	0.348341i	$-0.886745\pi$
$653$	−4.26780	+	7.39204i	−0.167012	+	0.289273i	0.770356	+	0.637614i	$0.220078\pi$
$654$		0			0
$655$	10.1684	+	17.6123i	0.397314	+	0.688168i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.81616	+	3.14568i	−0.0707476	+	0.122538i	−0.899229	−	0.437478i	$-0.855872\pi$
$659$	−1.81616	+	3.14568i	−0.0707476	+	0.122538i	0.828482	+	0.560016i	$0.189205\pi$
$660$		0			0
$661$	−31.0231			−1.20666			−0.603330	−	0.797492i	$-0.706160\pi$
$661$	−31.0231			−1.20666			−0.603330	+	0.797492i	$0.706160\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	16.3549	+	48.7313i	0.634217	+	1.88972i
$666$		0			0
$667$	8.83011	+	15.2942i	0.341903	+	0.592194i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.29156	−	5.70116i	−0.127069	−	0.220091i
$672$		0			0
$673$	0.291838	−	0.505478i	0.0112495	−	0.0194848i	−0.860346	−	0.509711i	$-0.829752\pi$
$673$	0.291838	−	0.505478i	0.0112495	−	0.0194848i	0.871595	+	0.490226i	$0.163086\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	33.7332			1.29647			0.648237	−	0.761439i	$-0.275507\pi$
$677$	33.7332			1.29647			0.648237	+	0.761439i	$0.275507\pi$
$678$		0			0
$679$	12.2785	+	2.48636i	0.471204	+	0.0954178i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.60312	+	2.77668i	−0.0613417	+	0.106247i	−0.895065	−	0.445935i	$-0.852871\pi$
$683$	−1.60312	+	2.77668i	−0.0613417	+	0.106247i	0.833724	+	0.552182i	$0.186205\pi$
$684$		0			0
$685$	−22.4257			−0.856841
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−15.2848			−0.582306
$690$		0			0
$691$	32.3674			1.23131			0.615657	−	0.788014i	$-0.288891\pi$
$691$	32.3674			1.23131			0.615657	+	0.788014i	$0.288891\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	32.9521			1.24995
$696$		0			0
$697$	−8.93476			−0.338428
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−21.2591			−0.802943			−0.401472	−	0.915871i	$-0.631501\pi$
$701$	−21.2591			−0.802943			−0.401472	+	0.915871i	$0.631501\pi$
$702$		0			0
$703$	−19.7985	+	34.2920i	−0.746715	+	1.29335i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.0028	−	22.6509i	0.752283	−	0.851873i
$708$		0			0
$709$	31.6544			1.18880			0.594402	−	0.804168i	$-0.297389\pi$
$709$	31.6544			1.18880			0.594402	+	0.804168i	$0.297389\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	13.0526	−	22.6078i	0.488824	−	0.846669i
$714$		0			0
$715$	10.0925	+	17.4807i	0.377438	+	0.653741i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−14.9776	−	25.9420i	−0.558571	−	0.967473i	−0.997616	−	0.0690079i	$-0.978017\pi$
$719$	−14.9776	−	25.9420i	−0.558571	−	0.967473i	0.439045	−	0.898465i	$-0.355317\pi$
$720$		0			0
$721$	−16.5313	−	3.34755i	−0.615656	−	0.124669i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	39.8486			1.47994
$726$		0			0
$727$	13.6310	−	23.6095i	0.505544	−	0.875629i	−0.494435	−	0.869215i	$-0.664625\pi$
$727$	13.6310	−	23.6095i	0.505544	−	0.875629i	0.999979	−	0.00641398i	$-0.00204165\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−29.6985	−	51.4393i	−1.09844	−	1.90255i
$732$		0			0
$733$	11.2717	−	19.5232i	0.416330	−	0.721105i	−0.579237	−	0.815159i	$-0.696649\pi$
$733$	11.2717	−	19.5232i	0.416330	−	0.721105i	0.995567	+	0.0940545i	$0.0299828\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.67085	+	6.35809i	0.135217	+	0.234203i
$738$		0			0
$739$	8.82742	−	15.2895i	0.324722	−	0.562435i	−0.656734	−	0.754122i	$-0.728063\pi$
$739$	8.82742	−	15.2895i	0.324722	−	0.562435i	0.981456	+	0.191687i	$0.0613960\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.31474	−	5.74130i	−0.121606	−	0.210628i	0.798795	−	0.601603i	$-0.205471\pi$
$743$	−3.31474	−	5.74130i	−0.121606	−	0.210628i	−0.920401	+	0.390975i	$0.872138\pi$
$744$		0			0
$745$	−20.4735	−	35.4611i	−0.750089	−	1.29919i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.92291	+	4.44224i	−0.143340	+	0.162316i
$750$		0			0
$751$	3.93721	−	6.81944i	0.143671	−	0.248845i	−0.785206	−	0.619235i	$-0.787443\pi$
$751$	3.93721	−	6.81944i	0.143671	−	0.248845i	0.928876	+	0.370390i	$0.120776\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	63.9295			2.32663
$756$		0			0
$757$	−37.1503			−1.35025			−0.675125	−	0.737703i	$-0.735910\pi$
$757$	−37.1503			−1.35025			−0.675125	+	0.737703i	$0.735910\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−16.2273	+	28.1065i	−0.588238	+	1.01886i	0.406225	+	0.913773i	$0.366845\pi$
$761$	−16.2273	+	28.1065i	−0.588238	+	1.01886i	−0.994463	+	0.105085i	$0.966488\pi$
$762$		0			0
$763$	−14.1631	−	2.86799i	−0.512737	−	0.103828i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.29218	+	12.6304i	0.263305	+	0.456058i
$768$		0			0
$769$	11.4992	+	19.9172i	0.414671	+	0.718232i	0.995394	−	0.0958699i	$-0.0305633\pi$
$769$	11.4992	+	19.9172i	0.414671	+	0.718232i	−0.580723	+	0.814101i	$0.697230\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13.2117	+	22.8834i	−0.475194	+	0.823059i	−0.999596	−	0.0284109i	$-0.990955\pi$
$773$	−13.2117	+	22.8834i	−0.475194	+	0.823059i	0.524403	+	0.851470i	$0.324289\pi$
$774$		0			0
$775$	−29.4519	−	51.0123i	−1.05794	−	1.83241i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.85914	+	6.68423i	−0.138268	+	0.239487i
$780$		0			0
$781$	−19.1515	−	33.1714i	−0.685296	−	1.18697i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−17.0239	+	29.4862i	−0.607609	+	1.05241i
$786$		0			0
$787$	9.11300			0.324843			0.162422	−	0.986721i	$-0.448069\pi$
$787$	9.11300			0.324843			0.162422	+	0.986721i	$0.448069\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−15.6027	+	17.6682i	−0.554767	+	0.628209i
$792$		0			0
$793$	0.858162	+	1.48638i	0.0304742	+	0.0527829i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	27.5330	+	47.6886i	0.975270	+	1.68922i	0.679042	+	0.734099i	$0.262395\pi$
$797$	27.5330	+	47.6886i	0.975270	+	1.68922i	0.296228	+	0.955117i	$0.404271\pi$
$798$		0			0
$799$	−6.61988	+	11.4660i	−0.234195	+	0.405637i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−33.6739			−1.18833
$804$		0			0
$805$	−27.8243	+	31.5078i	−0.980679	+	1.11050i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.0961	+	19.2191i	−0.390119	+	0.675707i	−0.992465	−	0.122529i	$-0.960900\pi$
$809$	−11.0961	+	19.2191i	−0.390119	+	0.675707i	0.602346	+	0.798235i	$0.294233\pi$
$810$		0			0
$811$	−52.0941			−1.82927			−0.914636	−	0.404279i	$-0.867522\pi$
$811$	−52.0941			−1.82927			−0.914636	+	0.404279i	$0.867522\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−28.2158			−0.988357
$816$		0			0
$817$	−51.3100			−1.79511
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−39.6107			−1.38242			−0.691212	−	0.722652i	$-0.742923\pi$
$821$	−39.6107			−1.38242			−0.691212	+	0.722652i	$0.742923\pi$
$822$		0			0
$823$	32.3470			1.12755			0.563773	−	0.825930i	$-0.309349\pi$
$823$	32.3470			1.12755			0.563773	+	0.825930i	$0.309349\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.1724			−1.32738			−0.663692	−	0.748006i	$-0.731012\pi$
$827$	−38.1724			−1.32738			−0.663692	+	0.748006i	$0.731012\pi$
$828$		0			0
$829$	27.7372	−	48.0422i	0.963353	−	1.66858i	0.249375	−	0.968407i	$-0.419775\pi$
$829$	27.7372	−	48.0422i	0.963353	−	1.66858i	0.713977	−	0.700169i	$-0.246892\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.12520	+	41.1181i	0.177578	+	1.42466i
$834$		0			0
$835$	39.0399			1.35103
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.35256	−	4.07475i	0.0812193	−	0.140676i	−0.822555	−	0.568686i	$-0.807452\pi$
$839$	2.35256	−	4.07475i	0.0812193	−	0.140676i	0.903774	+	0.428010i	$0.140785\pi$
$840$		0			0
$841$	5.58195	+	9.66822i	0.192481	+	0.333387i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	22.0648	+	38.2174i	0.759054	+	1.31472i
$846$		0			0
$847$	−24.3164	−	4.92402i	−0.835522	−	0.169191i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−32.3809			−1.11000
$852$		0			0
$853$	1.87889	−	3.25434i	0.0643321	−	0.111426i	−0.832065	−	0.554678i	$-0.812842\pi$
$853$	1.87889	−	3.25434i	0.0643321	−	0.111426i	0.896398	+	0.443251i	$0.146175\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.5780	−	46.0345i	−0.907888	−	1.57251i	−0.816993	−	0.576648i	$-0.804360\pi$
$857$	−26.5780	−	46.0345i	−0.907888	−	1.57251i	−0.0908957	−	0.995860i	$-0.528973\pi$
$858$		0			0
$859$	−26.4888	+	45.8799i	−0.903786	+	1.56540i	−0.0812476	+	0.996694i	$0.525890\pi$
$859$	−26.4888	+	45.8799i	−0.903786	+	1.56540i	−0.822538	+	0.568709i	$0.807443\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.57834	+	16.5902i	0.326051	+	0.564736i	0.981724	−	0.190308i	$-0.0609487\pi$
$863$	9.57834	+	16.5902i	0.326051	+	0.564736i	−0.655674	+	0.755044i	$0.727615\pi$
$864$		0			0
$865$	−19.3958	+	33.5945i	−0.659477	+	1.14225i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.15717	−	7.20043i	−0.141022	−	0.244258i
$870$		0			0
$871$	−0.957046	−	1.65765i	−0.0324283	−	0.0561674i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	14.1862	+	42.2693i	0.479581	+	1.42896i
$876$		0			0
$877$	−1.83865	+	3.18463i	−0.0620868	+	0.107537i	−0.895398	−	0.445267i	$-0.853109\pi$
$877$	−1.83865	+	3.18463i	−0.0620868	+	0.107537i	0.833311	+	0.552804i	$0.186442\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	14.8862			0.501529			0.250765	−	0.968048i	$-0.419318\pi$
$881$	14.8862			0.501529			0.250765	+	0.968048i	$0.419318\pi$
$882$		0			0
$883$	−39.9262			−1.34362			−0.671811	−	0.740722i	$-0.734483\pi$
$883$	−39.9262			−1.34362			−0.671811	+	0.740722i	$0.734483\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.25124	−	7.36336i	0.142743	−	0.247237i	−0.785786	−	0.618499i	$-0.787741\pi$
$887$	4.25124	−	7.36336i	0.142743	−	0.247237i	0.928528	+	0.371261i	$0.121075\pi$
$888$		0			0
$889$	−0.366118	−	1.09089i	−0.0122792	−	0.0365872i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.71857	+	9.90486i	0.191365	+	0.331453i
$894$		0			0
$895$	36.5877	+	63.3717i	1.22299	+	2.11828i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.1826	+	22.8329i	−0.439665	+	0.761521i
$900$		0			0
$901$	38.4391	+	66.5785i	1.28059	+	2.21805i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.64368	−	4.57899i	0.0878789	−	0.152211i
$906$		0			0
$907$	−1.59544	−	2.76339i	−0.0529758	−	0.0917568i	0.838321	−	0.545176i	$-0.183537\pi$
$907$	−1.59544	−	2.76339i	−0.0529758	−	0.0917568i	−0.891297	+	0.453419i	$0.850204\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.63889	−	13.2309i	0.253088	−	0.438361i	−0.711287	−	0.702902i	$-0.751887\pi$
$911$	7.63889	−	13.2309i	0.253088	−	0.438361i	0.964374	+	0.264541i	$0.0852206\pi$
$912$		0			0
$913$	2.77714			0.0919099
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.8801	+	2.81069i	0.458360	+	0.0928170i
$918$		0			0
$919$	−25.2681	−	43.7656i	−0.833516	−	1.44369i	−0.895233	−	0.445599i	$-0.852991\pi$
$919$	−25.2681	−	43.7656i	−0.833516	−	1.44369i	0.0617164	−	0.998094i	$-0.480343\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.99310	+	8.64831i	0.164350	+	0.284662i
$924$		0			0
$925$	−36.5321	+	63.2755i	−1.20117	+	2.08048i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−47.9781			−1.57411			−0.787055	−	0.616883i	$-0.788395\pi$
$929$	−47.9781			−1.57411			−0.787055	+	0.616883i	$0.788395\pi$
$930$		0			0
$931$	32.9748	+	13.9257i	1.08070	+	0.456395i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	50.7623	−	87.9228i	1.66010	−	2.87538i
$936$		0			0
$937$	20.5226			0.670443			0.335222	−	0.942139i	$-0.391189\pi$
$937$	20.5226			0.670443			0.335222	+	0.942139i	$0.391189\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.95586			0.324552			0.162276	−	0.986745i	$-0.448117\pi$
$941$	9.95586			0.324552			0.162276	+	0.986745i	$0.448117\pi$
$942$		0			0
$943$	−6.31170			−0.205537
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.2213			−0.689601			−0.344800	−	0.938676i	$-0.612053\pi$
$947$	−21.2213			−0.689601			−0.344800	+	0.938676i	$0.612053\pi$
$948$		0			0
$949$	8.77930			0.284988
$950$		0			0
$951$		0			0
$952$		0			0
$953$	35.9191			1.16353			0.581767	−	0.813355i	$-0.302361\pi$
$953$	35.9191			1.16353			0.581767	+	0.813355i	$0.302361\pi$
$954$		0			0
$955$	5.15736	−	8.93281i	0.166888	−	0.289059i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−10.3370	+	11.7054i	−0.333798	+	0.377988i
$960$		0			0
$961$	7.97290			0.257190
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.49866	+	6.05986i	−0.112626	+	0.195074i
$966$		0			0
$967$	−15.9559	−	27.6365i	−0.513108	−	0.888729i	−0.999884	−	0.0152023i	$-0.995161\pi$
$967$	−15.9559	−	27.6365i	−0.513108	−	0.888729i	0.486777	−	0.873526i	$-0.338173\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.6645	−	49.6483i	−0.919886	−	1.59329i	−0.799585	−	0.600553i	$-0.794947\pi$
$971$	−28.6645	−	49.6483i	−0.919886	−	1.59329i	−0.120301	−	0.992737i	$-0.538386\pi$
$972$		0			0
$973$	15.1891	−	17.1999i	0.486940	−	0.551403i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−8.58455			−0.274644			−0.137322	−	0.990526i	$-0.543850\pi$
$977$	−8.58455			−0.274644			−0.137322	+	0.990526i	$0.543850\pi$
$978$		0			0
$979$	5.66845	−	9.81805i	0.181164	−	0.313786i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.2504	+	19.4863i	0.358834	+	0.621518i	0.987766	−	0.155942i	$-0.0498412\pi$
$983$	11.2504	+	19.4863i	0.358834	+	0.621518i	−0.628933	+	0.777460i	$0.716508\pi$
$984$		0			0
$985$	41.6411	−	72.1244i	1.32679	−	2.29807i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−20.9796	−	36.3378i	−0.667114	−	1.15548i
$990$		0			0
$991$	−19.3652	+	33.5415i	−0.615156	+	1.06548i	0.375201	+	0.926944i	$0.377574\pi$
$991$	−19.3652	+	33.5415i	−0.615156	+	1.06548i	−0.990357	+	0.138538i	$0.955760\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.75875	+	4.77829i	0.0874582	+	0.151482i
$996$		0			0
$997$	−18.3955	−	31.8619i	−0.582590	−	1.00908i	−0.995171	−	0.0981549i	$-0.968706\pi$
$997$	−18.3955	−	31.8619i	−0.582590	−	1.00908i	0.412581	−	0.910921i	$-0.364627\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.l.2881.2		22
3.2	odd	2		1008.2.q.l.529.9		22
4.3	odd	2		1512.2.q.d.1369.2		22
7.2	even	3		3024.2.t.k.289.10		22
9.4	even	3		3024.2.t.k.1873.10		22
9.5	odd	6		1008.2.t.l.193.2		22
12.11	even	2		504.2.q.c.25.3	✓	22
21.2	odd	6		1008.2.t.l.961.2		22
28.23	odd	6		1512.2.t.c.289.10		22
36.23	even	6		504.2.t.c.193.10	yes	22
36.31	odd	6		1512.2.t.c.361.10		22
63.23	odd	6		1008.2.q.l.625.9		22
63.58	even	3	inner	3024.2.q.l.2305.2		22
84.23	even	6		504.2.t.c.457.10	yes	22
252.23	even	6		504.2.q.c.121.3	yes	22
252.247	odd	6		1512.2.q.d.793.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.3	✓	22	12.11	even	2
504.2.q.c.121.3	yes	22	252.23	even	6
504.2.t.c.193.10	yes	22	36.23	even	6
504.2.t.c.457.10	yes	22	84.23	even	6
1008.2.q.l.529.9		22	3.2	odd	2
1008.2.q.l.625.9		22	63.23	odd	6
1008.2.t.l.193.2		22	9.5	odd	6
1008.2.t.l.961.2		22	21.2	odd	6
1512.2.q.d.793.2		22	252.247	odd	6
1512.2.q.d.1369.2		22	4.3	odd	2
1512.2.t.c.289.10		22	28.23	odd	6
1512.2.t.c.361.10		22	36.31	odd	6
3024.2.q.l.2305.2		22	63.58	even	3	inner
3024.2.q.l.2881.2		22	1.1	even	1	trivial
3024.2.t.k.289.10		22	7.2	even	3
3024.2.t.k.1873.10		22	9.4	even	3

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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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.89970 + 3.29038i) q^{5} +(0.841809 + 2.50826i) q^{7} +O(q^{10})\)	\(q+(-1.89970 + 3.29038i) q^{5} +(0.841809 + 2.50826i) q^{7} +(-2.25706 - 3.90934i) q^{11} +(0.588451 + 1.01923i) q^{13} +(2.95973 - 5.12641i) q^{17} +(-2.55676 - 4.42844i) q^{19} +(2.09082 - 3.62140i) q^{23} +(-4.71772 - 8.17134i) q^{25} +(-2.11164 + 3.65747i) q^{29} +6.24283 q^{31} +(-9.85230 - 1.99507i) q^{35} +(-3.87179 - 6.70614i) q^{37} +(-0.754693 - 1.30717i) q^{41} +(5.01709 - 8.68986i) q^{43} -2.23665 q^{47} +(-5.58272 + 4.22295i) q^{49} +(-6.49368 + 11.2474i) q^{53} +17.1510 q^{55} +12.3922 q^{59} +1.45834 q^{61} -4.47152 q^{65} -1.62638 q^{67} +8.48517 q^{71} +(3.72984 - 6.46027i) q^{73} +(7.90563 - 8.95221i) q^{77} +1.84185 q^{79} +(-0.307606 + 0.532789i) q^{83} +(11.2452 + 19.4773i) q^{85} +(1.25572 + 2.17496i) q^{89} +(-2.06112 + 2.33398i) q^{91} +19.4283 q^{95} +(2.36751 - 4.10064i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} - 5 q^{7}+O(q^{10}) \) 22 * q - q^5 - 5 * q^7	\( 22 q - q^{5} - 5 q^{7} + 3 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} - 22 q^{25} + 7 q^{29} + 12 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} - 34 q^{47} - 25 q^{49} - q^{53} - 2 q^{55} + 42 q^{59} - 62 q^{61} - 6 q^{65} - 52 q^{67} - 32 q^{71} + 17 q^{73} + q^{77} - 32 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} + 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 - 5 * q^7 + 3 * q^11 + 7 * q^13 + q^17 - 13 * q^19 - 22 * q^25 + 7 * q^29 + 12 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 - 34 * q^47 - 25 * q^49 - q^53 - 2 * q^55 + 42 * q^59 - 62 * q^61 - 6 * q^65 - 52 * q^67 - 32 * q^71 + 17 * q^73 + q^77 - 32 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 + 48 * q^95 + 19 * q^97

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