LMFDB - Embedded newform 3024.2.r.c.1009.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1009.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.1009
Dual form			3024.2.r.c.2017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{13} +5.00000 q^{17} +7.00000 q^{19} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-2.00000 - 3.46410i) q^{29} +(-3.00000 + 5.19615i) q^{31} -2.00000 q^{35} +2.00000 q^{37} +(1.50000 - 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-0.500000 + 0.866025i) q^{49} -12.0000 q^{53} -2.00000 q^{55} +(3.50000 - 6.06218i) q^{59} +(6.00000 + 10.3923i) q^{61} +(-6.00000 - 10.3923i) q^{65} +(6.50000 - 11.2583i) q^{67} -8.00000 q^{71} +1.00000 q^{73} +(-0.500000 + 0.866025i) q^{77} +(-3.00000 - 5.19615i) q^{79} +(-8.00000 - 13.8564i) q^{83} +(5.00000 - 8.66025i) q^{85} +6.00000 q^{89} -6.00000 q^{91} +(7.00000 - 12.1244i) q^{95} +(2.50000 + 4.33013i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{5} - q^{7} - q^{11} + 6 q^{13} + 10 q^{17} + 14 q^{19} - 4 q^{23} + q^{25} - 4 q^{29} - 6 q^{31} - 4 q^{35} + 4 q^{37} + 3 q^{41} - q^{43} - q^{49} - 24 q^{53} - 4 q^{55} + 7 q^{59} + 12 q^{61}+ \cdots + 5 q^{97}+O(q^{100}) $ 2 * q + 2 * q^5 - q^7 - q^11 + 6 * q^13 + 10 * q^17 + 14 * q^19 - 4 * q^23 + q^25 - 4 * q^29 - 6 * q^31 - 4 * q^35 + 4 * q^37 + 3 * q^41 - q^43 - q^49 - 24 * q^53 - 4 * q^55 + 7 * q^59 + 12 * q^61 - 12 * q^65 + 13 * q^67 - 16 * q^71 + 2 * q^73 - q^77 - 6 * q^79 - 16 * q^83 + 10 * q^85 + 12 * q^89 - 12 * q^91 + 14 * q^95 + 5 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$12$		0			0
$13$	3.00000	−	5.19615i	0.832050	−	1.44115i	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	3.00000	−	5.19615i	0.832050	−	1.44115i	0.896410	−	0.443227i	$-0.146166\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.00000			1.21268			0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000			1.21268			0.606339	+	0.795206i	$0.292637\pi$
$18$		0			0
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.00000			−0.338062
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	−0.543065	−	0.839691i	$-0.682736\pi$
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	0.998726	+	0.0504625i	$0.0160695\pi$
$60$		0			0
$61$	6.00000	+	10.3923i	0.768221	+	1.33060i	0.938527	+	0.345207i	$0.112191\pi$
$61$	6.00000	+	10.3923i	0.768221	+	1.33060i	−0.170305	+	0.985391i	$0.554475\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.500000	+	0.866025i	−0.0569803	+	0.0986928i
$78$		0			0
$79$	−3.00000	−	5.19615i	−0.337526	−	0.584613i	0.646440	−	0.762964i	$-0.276257\pi$
$79$	−3.00000	−	5.19615i	−0.337526	−	0.584613i	−0.983967	+	0.178352i	$0.942924\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.00000	−	13.8564i	−0.878114	−	1.52094i	−0.853408	−	0.521243i	$-0.825468\pi$
$83$	−8.00000	−	13.8564i	−0.878114	−	1.52094i	−0.0247060	−	0.999695i	$-0.507865\pi$
$84$		0			0
$85$	5.00000	−	8.66025i	0.542326	−	0.939336i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.00000	−	12.1244i	0.718185	−	1.24393i
$96$		0			0
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	0.964579	−	0.263795i	$-0.0849741\pi$
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	0.749199	−	0.662344i	$-0.230438\pi$
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	−0.948207	+	0.317653i	$0.897105\pi$
$102$		0			0
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	−0.999425	−	0.0338931i	$-0.989209\pi$
$113$	−5.00000	+	8.66025i	−0.470360	+	0.814688i	0.529065	+	0.848581i	$0.322543\pi$
$114$		0			0
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.50000	−	4.33013i	−0.229175	−	0.396942i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$	−3.50000	−	6.06218i	−0.303488	−	0.525657i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.50000	−	16.4545i	−0.811640	−	1.40580i	−0.911716	−	0.410822i	$-0.865242\pi$
$137$	−9.50000	−	16.4545i	−0.811640	−	1.40580i	0.100076	−	0.994980i	$-0.468091\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.00000			−0.501745
$144$		0			0
$145$	−8.00000			−0.664364
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.332896	+	0.942964i	$0.608026\pi$
$149$	−12.0000	+	20.7846i	−0.983078	+	1.70274i	−0.650183	+	0.759778i	$0.725308\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.00000	+	10.3923i	0.481932	+	0.834730i
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.00000			0.315244
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.0000	+	17.3205i	−0.773823	+	1.34030i	0.161630	+	0.986851i	$0.448325\pi$
$167$	−10.0000	+	17.3205i	−0.773823	+	1.34030i	−0.935454	+	0.353450i	$0.885009\pi$
$168$		0			0
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	0.901533	−	0.432710i	$-0.142443\pi$
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	−0.825505	+	0.564396i	$0.809109\pi$
$174$		0			0
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	−2.50000	−	4.33013i	−0.182818	−	0.316650i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	0.379086	+	0.925361i	$0.376238\pi$
$193$	−8.50000	+	14.7224i	−0.611843	+	1.05974i	−0.990930	+	0.134382i	$0.957095\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$		0			0
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.00000	+	3.46410i	−0.140372	+	0.243132i
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.50000	−	6.06218i	−0.242100	−	0.419330i
$210$		0			0
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	0.447478	+	0.894295i	$0.352322\pi$
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.00000			−0.136399
$216$		0			0
$217$	6.00000			0.407307
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.0000	−	25.9808i	1.00901	−	1.74766i
$222$		0			0
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	13.0000	−	22.5167i	0.859064	−	1.48794i	−0.0137585	−	0.999905i	$-0.504380\pi$
$229$	13.0000	−	22.5167i	0.859064	−	1.48794i	0.872823	−	0.488037i	$-0.162287\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	29.0000			1.89985			0.949927	−	0.312473i	$-0.101157\pi$
$233$	29.0000			1.89985			0.949927	+	0.312473i	$0.101157\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$		0			0
$247$	21.0000	−	36.3731i	1.33620	−	2.31436i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$		0			0
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$		0			0
$265$	−12.0000	+	20.7846i	−0.737154	+	1.27679i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−20.0000			−1.21942			−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000			−1.21942			−0.609711	+	0.792624i	$0.708714\pi$
$270$		0			0
$271$	6.00000			0.364474			0.182237	−	0.983255i	$-0.441666\pi$
$271$	6.00000			0.364474			0.182237	+	0.983255i	$0.441666\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.0000	+	19.0526i	0.656205	+	1.13658i	0.981590	+	0.190999i	$0.0611727\pi$
$281$	11.0000	+	19.0526i	0.656205	+	1.13658i	−0.325385	+	0.945582i	$0.605494\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00000			−0.177084
$288$		0			0
$289$	8.00000			0.470588
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$	−7.00000	−	12.1244i	−0.407556	−	0.705907i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.0000	+	20.7846i	0.693978	+	1.20201i
$300$		0			0
$301$	−0.500000	+	0.866025i	−0.0288195	+	0.0499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	24.0000			1.37424
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.00000	+	1.73205i	−0.0567048	+	0.0982156i	−0.892984	−	0.450088i	$-0.851393\pi$
$311$	−1.00000	+	1.73205i	−0.0567048	+	0.0982156i	0.836280	+	0.548303i	$0.184726\pi$
$312$		0			0
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	0.999748	−	0.0224310i	$-0.00714060\pi$
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	−0.519300	+	0.854592i	$0.673807\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	−2.00000	+	3.46410i	−0.111979	+	0.193952i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	35.0000			1.94745
$324$		0			0
$325$	6.00000			0.332820
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.0000	−	22.5167i	−0.710266	−	1.23022i
$336$		0			0
$337$	4.50000	−	7.79423i	0.245131	−	0.424579i	−0.717038	−	0.697034i	$-0.754502\pi$
$337$	4.50000	−	7.79423i	0.245131	−	0.424579i	0.962168	+	0.272456i	$0.0878358\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000			0.324918
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	−0.822951	−	0.568112i	$-0.807674\pi$
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	0.903475	+	0.428640i	$0.141007\pi$
$348$		0			0
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	0.990282	−	0.139072i	$-0.0444119\pi$
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	−0.615581	+	0.788074i	$0.711079\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$		0			0
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.00000			0.105556			0.0527780	−	0.998606i	$-0.483192\pi$
$359$	2.00000			0.105556			0.0527780	+	0.998606i	$0.483192\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.00000	−	1.73205i	0.0523424	−	0.0906597i
$366$		0			0
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	−0.996129	−	0.0879086i	$-0.971982\pi$
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	0.421933	−	0.906627i	$-0.361352\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		0			0
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	17.0000			0.873231			0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000			0.873231			0.436616	+	0.899648i	$0.356177\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.00000	+	3.46410i	−0.102195	+	0.177007i	−0.912589	−	0.408879i	$-0.865920\pi$
$383$	−2.00000	+	3.46410i	−0.102195	+	0.177007i	0.810394	+	0.585886i	$0.199253\pi$
$384$		0			0
$385$	1.00000	+	1.73205i	0.0509647	+	0.0882735i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	0.949432	−	0.313972i	$-0.101660\pi$
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	−0.746624	+	0.665246i	$0.768327\pi$
$390$		0			0
$391$	−10.0000	+	17.3205i	−0.505722	+	0.875936i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−12.0000			−0.603786
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	−0.731516	−	0.681824i	$-0.761187\pi$
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	0.956235	+	0.292599i	$0.0945202\pi$
$402$		0			0
$403$	18.0000	+	31.1769i	0.896644	+	1.55303i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.00000	−	1.73205i	−0.0495682	−	0.0858546i
$408$		0			0
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	−0.969363	−	0.245633i	$-0.921004\pi$
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	0.697406	+	0.716677i	$0.254338\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.00000			−0.344447
$414$		0			0
$415$	−32.0000			−1.57082
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	6.00000	+	10.3923i	0.292422	+	0.506490i	0.974382	−	0.224900i	$-0.0722054\pi$
$421$	6.00000	+	10.3923i	0.292422	+	0.506490i	−0.681960	+	0.731390i	$0.738872\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.50000	+	4.33013i	0.121268	+	0.210042i
$426$		0			0
$427$	6.00000	−	10.3923i	0.290360	−	0.502919i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.0000	+	24.2487i	−0.669711	+	1.15997i
$438$		0			0
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.50000	−	6.06218i	−0.166290	−	0.288023i	0.770823	−	0.637050i	$-0.219845\pi$
$443$	−3.50000	−	6.06218i	−0.166290	−	0.288023i	−0.937113	+	0.349027i	$0.886512\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−17.0000			−0.802280			−0.401140	−	0.916017i	$-0.631386\pi$
$449$	−17.0000			−0.802280			−0.401140	+	0.916017i	$0.631386\pi$
$450$		0			0
$451$	−3.00000			−0.141264
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.00000	+	10.3923i	−0.281284	+	0.487199i
$456$		0			0
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	0.854094	−	0.520119i	$-0.174112\pi$
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	−0.877483	+	0.479608i	$0.840779\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	0.981719	−	0.190337i	$-0.0609581\pi$
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	−0.655696	+	0.755025i	$0.727625\pi$
$462$		0			0
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	−0.943878	−	0.330294i	$-0.892852\pi$
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	0.757982	+	0.652275i	$0.226185\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.0000			−0.601568			−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000			−0.601568			−0.300784	+	0.953692i	$0.597248\pi$
$468$		0			0
$469$	−13.0000			−0.600284
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.500000	+	0.866025i	−0.0229900	+	0.0398199i
$474$		0			0
$475$	3.50000	+	6.06218i	0.160591	+	0.278152i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	0.998796	−	0.0490589i	$-0.0156222\pi$
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	−0.541884	+	0.840453i	$0.682289\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10.0000			0.454077
$486$		0			0
$487$	10.0000			0.453143			0.226572	−	0.973995i	$-0.427248\pi$
$487$	10.0000			0.453143			0.226572	+	0.973995i	$0.427248\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	0.205731	+	0.978609i	$0.434043\pi$
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	−0.950365	+	0.311136i	$0.899290\pi$
$492$		0			0
$493$	−10.0000	−	17.3205i	−0.450377	−	0.780076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.00000	+	6.92820i	0.179425	+	0.310772i
$498$		0			0
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	0.334227	+	0.942493i	$0.391525\pi$
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	−0.983336	+	0.181797i	$0.941809\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	−8.00000			−0.355995
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	−0.500000	−	0.866025i	−0.0221187	−	0.0383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−14.0000	−	24.2487i	−0.616914	−	1.06853i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$		0			0
$523$	28.0000			1.22435			0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000			1.22435			0.612177	+	0.790721i	$0.290294\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.00000	−	15.5885i	−0.389833	−	0.675211i
$534$		0			0
$535$	3.00000	−	5.19615i	0.129701	−	0.224649i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.00000			0.0430730
$540$		0			0
$541$	−24.0000			−1.03184			−0.515920	−	0.856637i	$-0.672550\pi$
$541$	−24.0000			−1.03184			−0.515920	+	0.856637i	$0.672550\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.00000	+	3.46410i	−0.0856706	+	0.148386i
$546$		0			0
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	0.549370	−	0.835579i	$-0.314868\pi$
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	−0.998318	+	0.0579790i	$0.981534\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−14.0000	−	24.2487i	−0.596420	−	1.03303i
$552$		0			0
$553$	−3.00000	+	5.19615i	−0.127573	+	0.220963i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	28.0000			1.18640			0.593199	−	0.805056i	$-0.297865\pi$
$557$	28.0000			1.18640			0.593199	+	0.805056i	$0.297865\pi$
$558$		0			0
$559$	−6.00000			−0.253773
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.5000	+	26.8468i	−0.653247	+	1.13146i	0.329083	+	0.944301i	$0.393260\pi$
$563$	−15.5000	+	26.8468i	−0.653247	+	1.13146i	−0.982330	+	0.187156i	$0.940073\pi$
$564$		0			0
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$		0			0
$571$	−16.5000	+	28.5788i	−0.690504	+	1.19599i	0.281170	+	0.959658i	$0.409278\pi$
$571$	−16.5000	+	28.5788i	−0.690504	+	1.19599i	−0.971673	+	0.236329i	$0.924056\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−35.0000			−1.45707			−0.728535	−	0.685009i	$-0.759798\pi$
$577$	−35.0000			−1.45707			−0.728535	+	0.685009i	$0.759798\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.00000	+	13.8564i	−0.331896	+	0.574861i
$582$		0			0
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.5000	+	40.7032i	0.969949	+	1.68000i	0.695686	+	0.718346i	$0.255100\pi$
$587$	23.5000	+	40.7032i	0.969949	+	1.68000i	0.274263	+	0.961655i	$0.411566\pi$
$588$		0			0
$589$	−21.0000	+	36.3731i	−0.865290	+	1.49873i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	−10.0000			−0.409960
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10.0000	−	17.3205i	−0.406558	−	0.704179i
$606$		0			0
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	−0.999889	−	0.0148722i	$-0.995266\pi$
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	0.512824	+	0.858494i	$0.328599\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	42.0000			1.69636			0.848182	−	0.529705i	$-0.177697\pi$
$613$	42.0000			1.69636			0.848182	+	0.529705i	$0.177697\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.50000	+	14.7224i	−0.342197	+	0.592703i	−0.984840	−	0.173463i	$-0.944504\pi$
$617$	−8.50000	+	14.7224i	−0.342197	+	0.592703i	0.642643	+	0.766165i	$0.277838\pi$
$618$		0			0
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	0.950856	+	0.309633i	$0.100206\pi$
$619$	18.5000	+	32.0429i	0.743578	+	1.28791i	−0.207279	+	0.978282i	$0.566461\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.00000	−	5.19615i	−0.120192	−	0.208179i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	10.0000			0.398726
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	12.0000	−	20.7846i	0.476205	−	0.824812i
$636$		0			0
$637$	3.00000	+	5.19615i	0.118864	+	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.500000	+	0.866025i	0.0197488	+	0.0342059i	0.875731	−	0.482800i	$-0.160380\pi$
$641$	0.500000	+	0.866025i	0.0197488	+	0.0342059i	−0.855982	+	0.517005i	$0.827047\pi$
$642$		0			0
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	0.788723	+	0.614749i	$0.210743\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		0			0
$649$	−7.00000			−0.274774
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$		0			0
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.00000	−	13.8564i	−0.311636	−	0.539769i	0.667081	−	0.744985i	$-0.267544\pi$
$659$	−8.00000	−	13.8564i	−0.311636	−	0.539769i	−0.978717	+	0.205216i	$0.934210\pi$
$660$		0			0
$661$	−14.0000	+	24.2487i	−0.544537	+	0.943166i	0.454099	+	0.890951i	$0.349961\pi$
$661$	−14.0000	+	24.2487i	−0.544537	+	0.943166i	−0.998636	+	0.0522143i	$0.983372\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−14.0000			−0.542897
$666$		0			0
$667$	16.0000			0.619522
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.00000	−	10.3923i	0.231627	−	0.401190i
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	0.995877	+	0.0907112i	$0.0289140\pi$
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	−0.419380	+	0.907811i	$0.637753\pi$
$678$		0			0
$679$	2.50000	−	4.33013i	0.0959412	−	0.166175i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	39.0000			1.49229			0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000			1.49229			0.746147	+	0.665782i	$0.231902\pi$
$684$		0			0
$685$	−38.0000			−1.45191
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−36.0000	+	62.3538i	−1.37149	+	2.37549i
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.00000	+	8.66025i	0.189661	+	0.328502i
$696$		0			0
$697$	7.50000	−	12.9904i	0.284083	−	0.492046i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.00000			−0.302156			−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000			−0.302156			−0.151078	+	0.988522i	$0.548274\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.00000	+	3.46410i	−0.0752177	+	0.130281i
$708$		0			0
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	0.901135	−	0.433539i	$-0.142735\pi$
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	−0.826023	+	0.563636i	$0.809402\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$		0			0
$715$	−6.00000	+	10.3923i	−0.224387	+	0.388650i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$	−14.0000			−0.521387
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$		0			0
$727$	−7.00000	−	12.1244i	−0.259616	−	0.449667i	0.706523	−	0.707690i	$-0.250263\pi$
$727$	−7.00000	−	12.1244i	−0.259616	−	0.449667i	−0.966139	+	0.258022i	$0.916929\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.50000	−	4.33013i	−0.0924658	−	0.160156i
$732$		0			0
$733$	9.00000	−	15.5885i	0.332423	−	0.575773i	−0.650564	−	0.759452i	$-0.725467\pi$
$733$	9.00000	−	15.5885i	0.332423	−	0.575773i	0.982986	+	0.183679i	$0.0588007\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.0000			−0.478861
$738$		0			0
$739$	33.0000			1.21392			0.606962	−	0.794731i	$-0.292388\pi$
$739$	33.0000			1.21392			0.606962	+	0.794731i	$0.292388\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$		0			0
$745$	24.0000	+	41.5692i	0.879292	+	1.52298i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.50000	−	2.59808i	−0.0548088	−	0.0949316i
$750$		0			0
$751$	−9.00000	+	15.5885i	−0.328415	+	0.568831i	−0.982197	−	0.187851i	$-0.939848\pi$
$751$	−9.00000	+	15.5885i	−0.328415	+	0.568831i	0.653783	+	0.756682i	$0.273181\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.0000			0.727875
$756$		0			0
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	−0.761057	−	0.648686i	$-0.775319\pi$
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	0.942306	+	0.334752i	$0.108652\pi$
$762$		0			0
$763$	1.00000	+	1.73205i	0.0362024	+	0.0627044i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−21.0000	−	36.3731i	−0.758266	−	1.31336i
$768$		0			0
$769$	−11.0000	+	19.0526i	−0.396670	+	0.687053i	−0.993313	−	0.115454i	$-0.963168\pi$
$769$	−11.0000	+	19.0526i	−0.396670	+	0.687053i	0.596643	+	0.802507i	$0.296501\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	52.0000			1.87031			0.935155	−	0.354239i	$-0.115260\pi$
$773$	52.0000			1.87031			0.935155	+	0.354239i	$0.115260\pi$
$774$		0			0
$775$	−6.00000			−0.215526
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.5000	−	18.1865i	0.376202	−	0.651600i
$780$		0			0
$781$	4.00000	+	6.92820i	0.143131	+	0.247911i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.00000	+	3.46410i	0.0713831	+	0.123639i
$786$		0			0
$787$	−6.00000	+	10.3923i	−0.213877	+	0.370446i	−0.952925	−	0.303207i	$-0.901942\pi$
$787$	−6.00000	+	10.3923i	−0.213877	+	0.370446i	0.739048	+	0.673653i	$0.235276\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	10.0000			0.355559
$792$		0			0
$793$	72.0000			2.55679
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.500000	−	0.866025i	−0.0176446	−	0.0305614i
$804$		0			0
$805$	4.00000	−	6.92820i	0.140981	−	0.244187i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	43.0000			1.51180			0.755900	−	0.654687i	$-0.227200\pi$
$809$	43.0000			1.51180			0.755900	+	0.654687i	$0.227200\pi$
$810$		0			0
$811$	−31.0000			−1.08856			−0.544279	−	0.838905i	$-0.683197\pi$
$811$	−31.0000			−1.08856			−0.544279	+	0.838905i	$0.683197\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$	−3.50000	−	6.06218i	−0.122449	−	0.212089i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	23.0000	+	39.8372i	0.802706	+	1.39033i	0.917829	+	0.396976i	$0.129940\pi$
$821$	23.0000	+	39.8372i	0.802706	+	1.39033i	−0.115124	+	0.993351i	$0.536726\pi$
$822$		0			0
$823$	17.0000	−	29.4449i	0.592583	−	1.02638i	−0.401300	−	0.915947i	$-0.631442\pi$
$823$	17.0000	−	29.4449i	0.592583	−	1.02638i	0.993883	−	0.110437i	$-0.0352250\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	4.00000			0.138926			0.0694629	−	0.997585i	$-0.477871\pi$
$829$	4.00000			0.138926			0.0694629	+	0.997585i	$0.477871\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.50000	+	4.33013i	−0.0866199	+	0.150030i
$834$		0			0
$835$	20.0000	+	34.6410i	0.692129	+	1.19880i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	10.0000	+	17.3205i	0.345238	+	0.597970i	0.985397	−	0.170272i	$-0.0544647\pi$
$839$	10.0000	+	17.3205i	0.345238	+	0.597970i	−0.640159	+	0.768243i	$0.721131\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−46.0000			−1.58245
$846$		0			0
$847$	−10.0000			−0.343604
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$		0			0
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	−0.946232	−	0.323489i	$-0.895144\pi$
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	0.192966	−	0.981205i	$-0.438189\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.0000	+	25.9808i	0.512390	+	0.887486i	0.999897	+	0.0143666i	$0.00457319\pi$
$857$	15.0000	+	25.9808i	0.512390	+	0.887486i	−0.487507	+	0.873119i	$0.662093\pi$
$858$		0			0
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	−0.505248	−	0.862974i	$-0.668599\pi$
$859$	14.5000	−	25.1147i	0.494734	−	0.856904i	0.999982	+	0.00607046i	$0.00193230\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	38.0000			1.29354			0.646768	−	0.762687i	$-0.276120\pi$
$863$	38.0000			1.29354			0.646768	+	0.762687i	$0.276120\pi$
$864$		0			0
$865$	4.00000			0.136004
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.00000	+	5.19615i	−0.101768	+	0.176267i
$870$		0			0
$871$	−39.0000	−	67.5500i	−1.32146	−	2.28884i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.00000	−	10.3923i	−0.202837	−	0.351324i
$876$		0			0
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	−0.968898	−	0.247462i	$-0.920404\pi$
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	0.698757	+	0.715359i	$0.253737\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	−53.0000			−1.78359			−0.891796	−	0.452438i	$-0.850554\pi$
$883$	−53.0000			−1.78359			−0.891796	+	0.452438i	$0.850554\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	−0.811256	−	0.584692i	$-0.801215\pi$
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	0.911986	+	0.410222i	$0.134549\pi$
$888$		0			0
$889$	−6.00000	−	10.3923i	−0.201234	−	0.348547i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	24.0000	−	41.5692i	0.802232	−	1.38951i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	24.0000			0.800445
$900$		0			0
$901$	−60.0000			−1.99889
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−13.5000	−	23.3827i	−0.448260	−	0.776409i	0.550013	−	0.835156i	$-0.314623\pi$
$907$	−13.5000	−	23.3827i	−0.448260	−	0.776409i	−0.998273	+	0.0587469i	$0.981290\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.00000			−0.132092
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−24.0000	+	41.5692i	−0.789970	+	1.36827i
$924$		0			0
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$	−3.50000	+	6.06218i	−0.114708	+	0.198680i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−10.0000			−0.327035
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.0000	−	17.3205i	0.325991	−	0.564632i	−0.655722	−	0.755003i	$-0.727636\pi$
$941$	10.0000	−	17.3205i	0.325991	−	0.564632i	0.981712	+	0.190370i	$0.0609689\pi$
$942$		0			0
$943$	6.00000	+	10.3923i	0.195387	+	0.338420i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.5000	+	32.0429i	0.601169	+	1.04126i	0.992644	+	0.121067i	$0.0386316\pi$
$947$	18.5000	+	32.0429i	0.601169	+	1.04126i	−0.391475	+	0.920189i	$0.628035\pi$
$948$		0			0
$949$	3.00000	−	5.19615i	0.0973841	−	0.168674i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	35.0000			1.13376			0.566881	−	0.823800i	$-0.308150\pi$
$953$	35.0000			1.13376			0.566881	+	0.823800i	$0.308150\pi$
$954$		0			0
$955$	−24.0000			−0.776622
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.50000	+	16.4545i	−0.306771	+	0.531343i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	17.0000	+	29.4449i	0.547249	+	0.947864i
$966$		0			0
$967$	7.00000	−	12.1244i	0.225105	−	0.389893i	−0.731246	−	0.682114i	$-0.761061\pi$
$967$	7.00000	−	12.1244i	0.225105	−	0.389893i	0.956351	+	0.292221i	$0.0943942\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		0			0
$973$	5.00000			0.160293
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.50000	+	12.9904i	−0.239946	+	0.415599i	−0.960699	−	0.277594i	$-0.910463\pi$
$977$	−7.50000	+	12.9904i	−0.239946	+	0.415599i	0.720752	+	0.693193i	$0.243796\pi$
$978$		0			0
$979$	−3.00000	−	5.19615i	−0.0958804	−	0.166070i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	30.0000	+	51.9615i	0.956851	+	1.65732i	0.730073	+	0.683369i	$0.239486\pi$
$983$	30.0000	+	51.9615i	0.956851	+	1.65732i	0.226778	+	0.973946i	$0.427181\pi$
$984$		0			0
$985$	−10.0000	+	17.3205i	−0.318626	+	0.551877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.00000			0.127193
$990$		0			0
$991$	28.0000			0.889449			0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000			0.889449			0.444725	+	0.895667i	$0.353302\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−14.0000	+	24.2487i	−0.443830	+	0.768736i
$996$		0			0
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.c.1009.1		2
3.2	odd	2		1008.2.r.a.337.1		2
4.3	odd	2		378.2.f.b.253.1		2
9.2	odd	6		1008.2.r.a.673.1		2
9.4	even	3		9072.2.a.f.1.1		1
9.5	odd	6		9072.2.a.t.1.1		1
9.7	even	3	inner	3024.2.r.c.2017.1		2
12.11	even	2		126.2.f.b.85.1	yes	2
28.3	even	6		2646.2.e.h.1549.1		2
28.11	odd	6		2646.2.e.i.1549.1		2
28.19	even	6		2646.2.h.c.361.1		2
28.23	odd	6		2646.2.h.b.361.1		2
28.27	even	2		2646.2.f.b.1765.1		2
36.7	odd	6		378.2.f.b.127.1		2
36.11	even	6		126.2.f.b.43.1	✓	2
36.23	even	6		1134.2.a.c.1.1		1
36.31	odd	6		1134.2.a.f.1.1		1
84.11	even	6		882.2.e.a.373.1		2
84.23	even	6		882.2.h.h.67.1		2
84.47	odd	6		882.2.h.g.67.1		2
84.59	odd	6		882.2.e.e.373.1		2
84.83	odd	2		882.2.f.f.589.1		2
252.11	even	6		882.2.h.h.79.1		2
252.47	odd	6		882.2.e.e.655.1		2
252.79	odd	6		2646.2.e.i.2125.1		2
252.83	odd	6		882.2.f.f.295.1		2
252.115	even	6		2646.2.h.c.667.1		2
252.139	even	6		7938.2.a.bb.1.1		1
252.151	odd	6		2646.2.h.b.667.1		2
252.167	odd	6		7938.2.a.e.1.1		1
252.187	even	6		2646.2.e.h.2125.1		2
252.191	even	6		882.2.e.a.655.1		2
252.223	even	6		2646.2.f.b.883.1		2
252.227	odd	6		882.2.h.g.79.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.b.43.1	✓	2	36.11	even	6
126.2.f.b.85.1	yes	2	12.11	even	2
378.2.f.b.127.1		2	36.7	odd	6
378.2.f.b.253.1		2	4.3	odd	2
882.2.e.a.373.1		2	84.11	even	6
882.2.e.a.655.1		2	252.191	even	6
882.2.e.e.373.1		2	84.59	odd	6
882.2.e.e.655.1		2	252.47	odd	6
882.2.f.f.295.1		2	252.83	odd	6
882.2.f.f.589.1		2	84.83	odd	2
882.2.h.g.67.1		2	84.47	odd	6
882.2.h.g.79.1		2	252.227	odd	6
882.2.h.h.67.1		2	84.23	even	6
882.2.h.h.79.1		2	252.11	even	6
1008.2.r.a.337.1		2	3.2	odd	2
1008.2.r.a.673.1		2	9.2	odd	6
1134.2.a.c.1.1		1	36.23	even	6
1134.2.a.f.1.1		1	36.31	odd	6
2646.2.e.h.1549.1		2	28.3	even	6
2646.2.e.h.2125.1		2	252.187	even	6
2646.2.e.i.1549.1		2	28.11	odd	6
2646.2.e.i.2125.1		2	252.79	odd	6
2646.2.f.b.883.1		2	252.223	even	6
2646.2.f.b.1765.1		2	28.27	even	2
2646.2.h.b.361.1		2	28.23	odd	6
2646.2.h.b.667.1		2	252.151	odd	6
2646.2.h.c.361.1		2	28.19	even	6
2646.2.h.c.667.1		2	252.115	even	6
3024.2.r.c.1009.1		2	1.1	even	1	trivial
3024.2.r.c.2017.1		2	9.7	even	3	inner
7938.2.a.e.1.1		1	252.167	odd	6
7938.2.a.bb.1.1		1	252.139	even	6
9072.2.a.f.1.1		1	9.4	even	3
9072.2.a.t.1.1		1	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{13} +5.00000 q^{17} +7.00000 q^{19} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-2.00000 - 3.46410i) q^{29} +(-3.00000 + 5.19615i) q^{31} -2.00000 q^{35} +2.00000 q^{37} +(1.50000 - 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-0.500000 + 0.866025i) q^{49} -12.0000 q^{53} -2.00000 q^{55} +(3.50000 - 6.06218i) q^{59} +(6.00000 + 10.3923i) q^{61} +(-6.00000 - 10.3923i) q^{65} +(6.50000 - 11.2583i) q^{67} -8.00000 q^{71} +1.00000 q^{73} +(-0.500000 + 0.866025i) q^{77} +(-3.00000 - 5.19615i) q^{79} +(-8.00000 - 13.8564i) q^{83} +(5.00000 - 8.66025i) q^{85} +6.00000 q^{89} -6.00000 q^{91} +(7.00000 - 12.1244i) q^{95} +(2.50000 + 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} - q^{7} - q^{11} + 6 q^{13} + 10 q^{17} + 14 q^{19} - 4 q^{23} + q^{25} - 4 q^{29} - 6 q^{31} - 4 q^{35} + 4 q^{37} + 3 q^{41} - q^{43} - q^{49} - 24 q^{53} - 4 q^{55} + 7 q^{59} + 12 q^{61}+ \cdots + 5 q^{97}+O(q^{100}) \) 2 * q + 2 * q^5 - q^7 - q^11 + 6 * q^13 + 10 * q^17 + 14 * q^19 - 4 * q^23 + q^25 - 4 * q^29 - 6 * q^31 - 4 * q^35 + 4 * q^37 + 3 * q^41 - q^43 - q^49 - 24 * q^53 - 4 * q^55 + 7 * q^59 + 12 * q^61 - 12 * q^65 + 13 * q^67 - 16 * q^71 + 2 * q^73 - q^77 - 6 * q^79 - 16 * q^83 + 10 * q^85 + 12 * q^89 - 12 * q^91 + 14 * q^95 + 5 * q^97

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