LMFDB - Embedded newform 3024.2.q.d.2881.1

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:	$2$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.d.2305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +(4.50000 - 7.79423i) q^{29} -4.00000 q^{31} +(-2.50000 + 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(3.50000 + 6.06218i) q^{41} +(1.50000 - 2.59808i) q^{43} +8.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(4.50000 - 7.79423i) q^{53} +3.00000 q^{55} -4.00000 q^{59} +2.00000 q^{61} -1.00000 q^{65} -12.0000 q^{67} +8.00000 q^{71} +(6.50000 - 11.2583i) q^{73} +(1.50000 - 7.79423i) q^{77} -8.00000 q^{79} +(6.50000 - 11.2583i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(-4.50000 - 7.79423i) q^{89} +(-0.500000 + 2.59808i) q^{91} +5.00000 q^{95} +(8.50000 - 14.7224i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{5} - 4 q^{7}+O(q^{10}) $ 2 * q + q^5 - 4 * q^7	$ 2 q + q^{5} - 4 q^{7} + 3 q^{11} - q^{13} + 3 q^{17} + 5 q^{19} - q^{23} + 4 q^{25} + 9 q^{29} - 8 q^{31} - 5 q^{35} - 5 q^{37} + 7 q^{41} + 3 q^{43} + 16 q^{47} + 2 q^{49} + 9 q^{53} + 6 q^{55} - 8 q^{59} + 4 q^{61} - 2 q^{65} - 24 q^{67} + 16 q^{71} + 13 q^{73} + 3 q^{77} - 16 q^{79} + 13 q^{83} - 3 q^{85} - 9 q^{89} - q^{91} + 10 q^{95} + 17 q^{97}+O(q^{100}) $ 2 * q + q^5 - 4 * q^7 + 3 * q^11 - q^13 + 3 * q^17 + 5 * q^19 - q^23 + 4 * q^25 + 9 * q^29 - 8 * q^31 - 5 * q^35 - 5 * q^37 + 7 * q^41 + 3 * q^43 + 16 * q^47 + 2 * q^49 + 9 * q^53 + 6 * q^55 - 8 * q^59 + 4 * q^61 - 2 * q^65 - 24 * q^67 + 16 * q^71 + 13 * q^73 + 3 * q^77 - 16 * q^79 + 13 * q^83 - 3 * q^85 - 9 * q^89 - q^91 + 10 * q^95 + 17 * 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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	−0.0578882	−	0.998323i	$-0.518437\pi$
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	0.893517	−	0.449029i	$-0.148230\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.50000	+	0.866025i	−0.422577	+	0.146385i
$36$		0			0
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	0.584002	−	0.811752i	$-0.301486\pi$
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	−0.994999	+	0.0998840i	$0.968153\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	0.998504	+	0.0546823i	$0.0174146\pi$
$41$	3.50000	+	6.06218i	0.546608	+	0.946753i	−0.451896	+	0.892071i	$0.649252\pi$
$42$		0			0
$43$	1.50000	−	2.59808i	0.228748	−	0.396203i	−0.728689	−	0.684844i	$-0.759870\pi$
$43$	1.50000	−	2.59808i	0.228748	−	0.396203i	0.957437	+	0.288641i	$0.0932035\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	−0.371706	−	0.928351i	$-0.621227\pi$
$53$	4.50000	−	7.79423i	0.618123	−	1.07062i	0.989828	−	0.142269i	$-0.0454398\pi$
$54$		0			0
$55$	3.00000			0.404520
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.00000			−0.124035
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	−0.181688	−	0.983356i	$-0.558156\pi$
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	0.942455	−	0.334332i	$-0.108511\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.50000	−	11.2583i	0.713468	−	1.23576i	−0.250080	−	0.968225i	$-0.580457\pi$
$83$	6.50000	−	11.2583i	0.713468	−	1.23576i	0.963548	−	0.267537i	$-0.0862098\pi$
$84$		0			0
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$	−0.500000	+	2.59808i	−0.0524142	+	0.272352i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.00000			0.512989
$96$		0			0
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	−0.00593185	−	0.999982i	$-0.501888\pi$
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	0.868976	−	0.494854i	$-0.164778\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	0.637678	−	0.770303i	$-0.279895\pi$
$101$	−3.50000	−	6.06218i	−0.348263	−	0.603209i	−0.985941	+	0.167094i	$0.946562\pi$
$102$		0			0
$103$	4.50000	−	7.79423i	0.443398	−	0.767988i	−0.554541	−	0.832156i	$-0.687106\pi$
$103$	4.50000	−	7.79423i	0.443398	−	0.767988i	0.997939	+	0.0641683i	$0.0204394\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	0.984124	−	0.177482i	$-0.0567953\pi$
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	−0.645766	+	0.763535i	$0.723462\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	0.841549	−	0.540181i	$-0.181644\pi$
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	−0.888585	+	0.458712i	$0.848311\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.50000	+	2.59808i	−0.687524	+	0.238165i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		0			0
$133$	2.50000	−	12.9904i	0.216777	−	1.12641i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.50000	+	9.52628i	0.469897	+	0.813885i	0.999408	−	0.0344182i	$-0.0109578\pi$
$137$	5.50000	+	9.52628i	0.469897	+	0.813885i	−0.529511	+	0.848303i	$0.677624\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$		0			0
$151$	−8.50000	−	14.7224i	−0.691720	−	1.19809i	−0.971274	−	0.237964i	$-0.923520\pi$
$151$	−8.50000	−	14.7224i	−0.691720	−	1.19809i	0.279554	−	0.960130i	$-0.409814\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.00000	+	3.46410i	−0.160644	+	0.278243i
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.50000	−	0.866025i	0.197028	−	0.0682524i
$162$		0			0
$163$	8.50000	+	14.7224i	0.665771	+	1.15315i	0.979076	+	0.203497i	$0.0652307\pi$
$163$	8.50000	+	14.7224i	0.665771	+	1.15315i	−0.313304	+	0.949653i	$0.601436\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.500000	+	0.866025i	0.0386912	+	0.0670151i	0.884723	−	0.466118i	$-0.154348\pi$
$167$	0.500000	+	0.866025i	0.0386912	+	0.0670151i	−0.846031	+	0.533133i	$0.821014\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.00000			0.152057			0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000			0.152057			0.0760286	+	0.997106i	$0.475776\pi$
$174$		0			0
$175$	2.00000	−	10.3923i	0.151186	−	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	−0.144308	−	0.989533i	$-0.546095\pi$
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	0.929114	−	0.369792i	$-0.120571\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.00000			−0.367607
$186$		0			0
$187$	9.00000			0.658145
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$		0			0
$193$	−18.0000			−1.29567			−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000			−1.29567			−0.647834	+	0.761781i	$0.724325\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	−0.206184	−	0.978513i	$-0.566105\pi$
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	0.950509	−	0.310696i	$-0.100562\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−22.5000	+	7.79423i	−1.57919	+	0.547048i
$204$		0			0
$205$	7.00000			0.488901
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.50000	+	12.9904i	−0.518786	+	0.898563i
$210$		0			0
$211$	−13.5000	−	23.3827i	−0.929378	−	1.60973i	−0.784364	−	0.620301i	$-0.787010\pi$
$211$	−13.5000	−	23.3827i	−0.929378	−	1.60973i	−0.145014	−	0.989430i	$-0.546323\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.50000	−	2.59808i	−0.102299	−	0.177187i
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.00000			−0.201802
$222$		0			0
$223$	6.50000	−	11.2583i	0.435272	−	0.753914i	−0.562046	−	0.827106i	$-0.689985\pi$
$223$	6.50000	−	11.2583i	0.435272	−	0.753914i	0.997318	+	0.0731927i	$0.0233188\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$		0			0
$229$	−10.5000	+	18.1865i	−0.693860	+	1.20180i	0.276704	+	0.960955i	$0.410758\pi$
$229$	−10.5000	+	18.1865i	−0.693860	+	1.20180i	−0.970564	+	0.240845i	$0.922576\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	0.910968	−	0.412477i	$-0.135336\pi$
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	−0.812700	+	0.582683i	$0.802003\pi$
$234$		0			0
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.50000	+	7.79423i	0.291081	+	0.504167i	0.974066	−	0.226266i	$-0.0726518\pi$
$239$	4.50000	+	7.79423i	0.291081	+	0.504167i	−0.682985	+	0.730433i	$0.739318\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$	2.50000	−	4.33013i	0.159071	−	0.275519i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.50000	+	14.7224i	−0.530215	+	0.918360i	0.469163	+	0.883112i	$0.344556\pi$
$257$	−8.50000	+	14.7224i	−0.530215	+	0.918360i	−0.999379	+	0.0352486i	$0.988778\pi$
$258$		0			0
$259$	−2.50000	+	12.9904i	−0.155342	+	0.807183i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.50000	−	9.52628i	−0.339145	−	0.587416i	0.645128	−	0.764075i	$-0.276804\pi$
$263$	−5.50000	−	9.52628i	−0.339145	−	0.587416i	−0.984272	+	0.176659i	$0.943471\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.50000	+	6.06218i	−0.213399	+	0.369618i	−0.952776	−	0.303674i	$-0.901787\pi$
$269$	−3.50000	+	6.06218i	−0.213399	+	0.369618i	0.739377	+	0.673291i	$0.235120\pi$
$270$		0			0
$271$	15.5000	+	26.8468i	0.941558	+	1.63083i	0.762501	+	0.646988i	$0.223971\pi$
$271$	15.5000	+	26.8468i	0.941558	+	1.63083i	0.179057	+	0.983839i	$0.442695\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	−0.110717	−	0.993852i	$-0.535315\pi$
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	0.916060	−	0.401042i	$-0.131352\pi$
$282$		0			0
$283$	24.0000			1.42665			0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000			1.42665			0.713326	+	0.700832i	$0.247188\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.50000	−	18.1865i	0.206598	−	1.07352i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.500000	+	0.866025i	0.0292103	+	0.0505937i	0.880261	−	0.474490i	$-0.157367\pi$
$293$	0.500000	+	0.866025i	0.0292103	+	0.0505937i	−0.851051	+	0.525084i	$0.824034\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.00000			0.0578315
$300$		0			0
$301$	−7.50000	+	2.59808i	−0.432293	+	0.149751i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.0000			−0.786318			−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000			−0.786318			−0.393159	+	0.919470i	$0.628618\pi$
$318$		0			0
$319$	27.0000			1.51171
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.0000			0.834622
$324$		0			0
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−16.0000	−	13.8564i	−0.882109	−	0.763928i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	−7.50000	−	12.9904i	−0.408551	−	0.707631i	0.586177	−	0.810183i	$-0.300632\pi$
$337$	−7.50000	−	12.9904i	−0.408551	−	0.707631i	−0.994728	+	0.102552i	$0.967299\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−28.0000			−1.50312			−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000			−1.50312			−0.751559	+	0.659665i	$0.770698\pi$
$348$		0			0
$349$	−8.50000	+	14.7224i	−0.454995	+	0.788074i	−0.998688	−	0.0512103i	$-0.983692\pi$
$349$	−8.50000	+	14.7224i	−0.454995	+	0.788074i	0.543693	+	0.839284i	$0.317025\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.5000	+	26.8468i	0.824982	+	1.42891i	0.901933	+	0.431875i	$0.142148\pi$
$353$	15.5000	+	26.8468i	0.824982	+	1.42891i	−0.0769515	+	0.997035i	$0.524519\pi$
$354$		0			0
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.5000	−	23.3827i	−0.712503	−	1.23409i	−0.963915	−	0.266211i	$-0.914228\pi$
$359$	−13.5000	−	23.3827i	−0.712503	−	1.23409i	0.251412	−	0.967880i	$-0.419105\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.50000	−	11.2583i	−0.340226	−	0.589288i
$366$		0			0
$367$	5.50000	+	9.52628i	0.287098	+	0.497268i	0.973116	−	0.230317i	$-0.0739762\pi$
$367$	5.50000	+	9.52628i	0.287098	+	0.497268i	−0.686018	+	0.727585i	$0.740643\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−22.5000	+	7.79423i	−1.16814	+	0.404656i
$372$		0			0
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	0.647225	+	0.762299i	$0.275929\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−32.0000			−1.64373			−0.821865	−	0.569683i	$-0.807066\pi$
$379$	−32.0000			−1.64373			−0.821865	+	0.569683i	$0.807066\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.5000	−	30.3109i	0.894208	−	1.54881i	0.0594268	−	0.998233i	$-0.481073\pi$
$383$	17.5000	−	30.3109i	0.894208	−	1.54881i	0.834781	−	0.550581i	$-0.185594\pi$
$384$		0			0
$385$	−6.00000	−	5.19615i	−0.305788	−	0.264820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	18.5000	+	32.0429i	0.937987	+	1.62464i	0.769218	+	0.638986i	$0.220646\pi$
$389$	18.5000	+	32.0429i	0.937987	+	1.62464i	0.168769	+	0.985656i	$0.446021\pi$
$390$		0			0
$391$	1.50000	+	2.59808i	0.0758583	+	0.131390i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$		0			0
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	−0.988080	−	0.153941i	$-0.950803\pi$
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	0.360723	−	0.932673i	$-0.382530\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	−0.981430	−	0.191820i	$-0.938561\pi$
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	0.656836	+	0.754034i	$0.271895\pi$
$402$		0			0
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.50000	−	12.9904i	0.371761	−	0.643909i
$408$		0			0
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.00000	+	6.92820i	0.393654	+	0.340915i
$414$		0			0
$415$	−6.50000	−	11.2583i	−0.319072	−	0.552650i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	−0.999887	−	0.0150285i	$-0.995216\pi$
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	0.486928	−	0.873442i	$-0.338117\pi$
$420$		0			0
$421$	1.50000	−	2.59808i	0.0731055	−	0.126622i	−0.827155	−	0.561973i	$-0.810042\pi$
$421$	1.50000	−	2.59808i	0.0731055	−	0.126622i	0.900261	+	0.435351i	$0.143376\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000			0.582086
$426$		0			0
$427$	−4.00000	−	3.46410i	−0.193574	−	0.167640i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	−0.626907	−	0.779094i	$-0.715679\pi$
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	0.988169	+	0.153370i	$0.0490126\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.00000			−0.239182
$438$		0			0
$439$	−24.0000			−1.14546			−0.572729	−	0.819745i	$-0.694115\pi$
$439$	−24.0000			−1.14546			−0.572729	+	0.819745i	$0.694115\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.0000			0.760183			0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000			0.760183			0.380091	+	0.924949i	$0.375893\pi$
$444$		0			0
$445$	−9.00000			−0.426641
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$		0			0
$451$	−10.5000	+	18.1865i	−0.494426	+	0.856370i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.00000	+	1.73205i	0.0937614	+	0.0811998i
$456$		0			0
$457$	−26.0000			−1.21623			−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000			−1.21623			−0.608114	+	0.793849i	$0.708074\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	0.359044	+	0.933321i	$0.383103\pi$
$461$	−13.5000	+	23.3827i	−0.628758	+	1.08904i	−0.987801	+	0.155719i	$0.950230\pi$
$462$		0			0
$463$	−0.500000	−	0.866025i	−0.0232370	−	0.0402476i	0.854173	−	0.519989i	$-0.174064\pi$
$463$	−0.500000	−	0.866025i	−0.0232370	−	0.0402476i	−0.877410	+	0.479741i	$0.840731\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	0.675530	−	0.737333i	$-0.263915\pi$
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	−0.976314	+	0.216359i	$0.930582\pi$
$468$		0			0
$469$	24.0000	+	20.7846i	1.10822	+	0.959744i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	9.00000			0.413820
$474$		0			0
$475$	−10.0000	+	17.3205i	−0.458831	+	0.794719i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	0.999730	−	0.0232187i	$-0.00739140\pi$
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	−0.519973	+	0.854183i	$0.674058\pi$
$480$		0			0
$481$	−2.50000	+	4.33013i	−0.113990	+	0.197437i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.50000	−	14.7224i	−0.385965	−	0.668511i
$486$		0			0
$487$	18.5000	−	32.0429i	0.838315	−	1.45200i	−0.0529875	−	0.998595i	$-0.516874\pi$
$487$	18.5000	−	32.0429i	0.838315	−	1.45200i	0.891303	−	0.453409i	$-0.149792\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	0.746438	−	0.665455i	$-0.231763\pi$
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	−0.949520	+	0.313707i	$0.898429\pi$
$492$		0			0
$493$	−13.5000	−	23.3827i	−0.608009	−	1.05310i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.0000	−	13.8564i	−0.717698	−	0.621545i
$498$		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
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−7.00000			−0.311496
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	−0.224957	−	0.974369i	$-0.572224\pi$
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	0.956306	−	0.292366i	$-0.0944425\pi$
$510$		0			0
$511$	−32.5000	+	11.2583i	−1.43772	+	0.498039i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.50000	−	7.79423i	−0.198294	−	0.343455i
$516$		0			0
$517$	12.0000	+	20.7846i	0.527759	+	0.914106i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	−0.831295	−	0.555831i	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$		0			0
$523$	16.5000	+	28.5788i	0.721495	+	1.24967i	0.960401	+	0.278623i	$0.0898779\pi$
$523$	16.5000	+	28.5788i	0.721495	+	1.24967i	−0.238906	+	0.971043i	$0.576789\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.50000	−	6.06218i	0.151602	−	0.262582i
$534$		0			0
$535$	7.00000			0.302636
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−16.5000	+	12.9904i	−0.710705	+	0.559535i
$540$		0			0
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	0.959697	−	0.281037i	$-0.0906783\pi$
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	−0.723234	+	0.690604i	$0.757345\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.50000	+	4.33013i	0.107088	+	0.185482i
$546$		0			0
$547$	−2.50000	+	4.33013i	−0.106892	+	0.185143i	−0.914510	−	0.404564i	$-0.867423\pi$
$547$	−2.50000	+	4.33013i	−0.106892	+	0.185143i	0.807617	+	0.589707i	$0.200757\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	45.0000			1.91706
$552$		0			0
$553$	16.0000	+	13.8564i	0.680389	+	0.589234i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	0.0747252	+	0.997204i	$0.476192\pi$
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	−0.900967	+	0.433888i	$0.857141\pi$
$558$		0			0
$559$	−3.00000			−0.126886
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	−1.00000			−0.0420703
$566$		0			0
$567$		0			0
$568$		0			0
$569$	42.0000			1.76073			0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000			1.76073			0.880366	+	0.474295i	$0.157297\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−1.50000	+	2.59808i	−0.0624458	+	0.108159i	−0.895558	−	0.444945i	$-0.853223\pi$
$577$	−1.50000	+	2.59808i	−0.0624458	+	0.108159i	0.833112	+	0.553104i	$0.186557\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−32.5000	+	11.2583i	−1.34833	+	0.467074i
$582$		0			0
$583$	27.0000			1.11823
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.50000	+	12.9904i	−0.309558	+	0.536170i	−0.978266	−	0.207355i	$-0.933514\pi$
$587$	−7.50000	+	12.9904i	−0.309558	+	0.536170i	0.668708	+	0.743525i	$0.266848\pi$
$588$		0			0
$589$	−10.0000	−	17.3205i	−0.412043	−	0.713679i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	0.565792	−	0.824548i	$-0.308570\pi$
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	−0.996976	+	0.0777165i	$0.975237\pi$
$594$		0			0
$595$	−1.50000	+	7.79423i	−0.0614940	+	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	−0.999279	−	0.0379540i	$-0.987916\pi$
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	0.532509	+	0.846424i	$0.321249\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$		0			0
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	−0.912086	−	0.409998i	$-0.865529\pi$
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	0.811112	+	0.584891i	$0.198863\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	0.996138	−	0.0878015i	$-0.0279841\pi$
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	−0.574107	+	0.818780i	$0.694651\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.50000	+	23.3827i	−0.180289	+	0.936808i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−15.0000			−0.598089
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$		0			0
$637$	5.50000	−	4.33013i	0.217918	−	0.171566i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	0.812421	−	0.583071i	$-0.198149\pi$
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	−0.911165	+	0.412042i	$0.864816\pi$
$642$		0			0
$643$	18.5000	+	32.0429i	0.729569	+	1.26365i	0.957066	+	0.289871i	$0.0936125\pi$
$643$	18.5000	+	32.0429i	0.729569	+	1.26365i	−0.227497	+	0.973779i	$0.573054\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.5000	+	35.5070i	−0.805938	+	1.39593i	0.109718	+	0.993963i	$0.465005\pi$
$647$	−20.5000	+	35.5070i	−0.805938	+	1.39593i	−0.915656	+	0.401963i	$0.868328\pi$
$648$		0			0
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$		0			0
$655$	1.50000	+	2.59808i	0.0586098	+	0.101515i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$		0			0
$661$	38.0000			1.47803			0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000			1.47803			0.739014	+	0.673690i	$0.235292\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−10.0000	−	8.66025i	−0.387783	−	0.335830i
$666$		0			0
$667$	4.50000	+	7.79423i	0.174241	+	0.301794i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.00000	+	5.19615i	0.115814	+	0.200595i
$672$		0			0
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	0.302017	+	0.953302i	$0.402340\pi$
$673$	−17.5000	+	30.3109i	−0.674575	+	1.16840i	−0.976593	+	0.215096i	$0.930993\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.0000			−1.46046			−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000			−1.46046			−0.730229	+	0.683202i	$0.760587\pi$
$678$		0			0
$679$	−42.5000	+	14.7224i	−1.63100	+	0.564995i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.5000	+	26.8468i	−0.593091	+	1.02726i	0.400722	+	0.916200i	$0.368759\pi$
$683$	−15.5000	+	26.8468i	−0.593091	+	1.02726i	−0.993813	+	0.111064i	$0.964574\pi$
$684$		0			0
$685$	11.0000			0.420288
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.00000			−0.342873
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.00000			0.189661
$696$		0			0
$697$	21.0000			0.795432
$698$		0			0
$699$		0			0
$700$		0			0
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$	12.5000	−	21.6506i	0.471446	−	0.816569i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.50000	+	18.1865i	−0.131631	+	0.683975i
$708$		0			0
$709$	−18.0000			−0.676004			−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000			−0.676004			−0.338002	+	0.941145i	$0.609751\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.00000	−	3.46410i	0.0749006	−	0.129732i
$714$		0			0
$715$	−1.50000	−	2.59808i	−0.0560968	−	0.0971625i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.50000	−	16.4545i	−0.354290	−	0.613649i	0.632706	−	0.774392i	$-0.281944\pi$
$719$	−9.50000	−	16.4545i	−0.354290	−	0.613649i	−0.986996	+	0.160743i	$0.948611\pi$
$720$		0			0
$721$	−22.5000	+	7.79423i	−0.837944	+	0.290272i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	36.0000			1.33701
$726$		0			0
$727$	8.50000	−	14.7224i	0.315248	−	0.546025i	−0.664243	−	0.747517i	$-0.731246\pi$
$727$	8.50000	−	14.7224i	0.315248	−	0.546025i	0.979490	+	0.201492i	$0.0645791\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.50000	−	7.79423i	−0.166439	−	0.288280i
$732$		0			0
$733$	21.5000	−	37.2391i	0.794121	−	1.37546i	−0.129275	−	0.991609i	$-0.541265\pi$
$733$	21.5000	−	37.2391i	0.794121	−	1.37546i	0.923396	−	0.383849i	$-0.125402\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.0000	−	31.1769i	−0.663039	−	1.14842i
$738$		0			0
$739$	−8.50000	+	14.7224i	−0.312678	+	0.541573i	−0.978941	−	0.204143i	$-0.934559\pi$
$739$	−8.50000	+	14.7224i	−0.312678	+	0.541573i	0.666264	+	0.745716i	$0.267893\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.500000	+	0.866025i	0.0183432	+	0.0317714i	0.875051	−	0.484030i	$-0.160828\pi$
$743$	0.500000	+	0.866025i	0.0183432	+	0.0317714i	−0.856708	+	0.515802i	$0.827494\pi$
$744$		0			0
$745$	7.50000	+	12.9904i	0.274779	+	0.475931i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.50000	−	18.1865i	0.127887	−	0.664521i
$750$		0			0
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	−0.969801	−	0.243898i	$-0.921574\pi$
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	0.696122	+	0.717923i	$0.254907\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.0000			−0.618693
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	0.0932544	+	0.995642i	$0.470273\pi$
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	−0.908879	+	0.417061i	$0.863060\pi$
$762$		0			0
$763$	12.5000	−	4.33013i	0.452530	−	0.156761i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.00000	+	3.46410i	0.0722158	+	0.125081i
$768$		0			0
$769$	20.5000	+	35.5070i	0.739249	+	1.28042i	0.952834	+	0.303492i	$0.0981526\pi$
$769$	20.5000	+	35.5070i	0.739249	+	1.28042i	−0.213585	+	0.976924i	$0.568514\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.50000	+	6.06218i	−0.125886	+	0.218041i	−0.922079	−	0.387002i	$-0.873511\pi$
$773$	−3.50000	+	6.06218i	−0.125886	+	0.218041i	0.796193	+	0.605043i	$0.206844\pi$
$774$		0			0
$775$	−8.00000	−	13.8564i	−0.287368	−	0.497737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−17.5000	+	30.3109i	−0.627003	+	1.08600i
$780$		0			0
$781$	12.0000	+	20.7846i	0.429394	+	0.743732i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.00000	−	12.1244i	0.249841	−	0.432737i
$786$		0			0
$787$	−20.0000			−0.712923			−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000			−0.712923			−0.356462	+	0.934310i	$0.616017\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.500000	+	2.59808i	−0.0177780	+	0.0923770i
$792$		0			0
$793$	−1.00000	−	1.73205i	−0.0355110	−	0.0615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.5000	−	33.7750i	−0.690725	−	1.19637i	−0.971601	−	0.236627i	$-0.923958\pi$
$797$	−19.5000	−	33.7750i	−0.690725	−	1.19637i	0.280875	−	0.959744i	$-0.409375\pi$
$798$		0			0
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	39.0000			1.37628
$804$		0			0
$805$	0.500000	−	2.59808i	0.0176227	−	0.0915702i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	27.5000	−	47.6314i	0.966849	−	1.67463i	0.262284	−	0.964991i	$-0.415524\pi$
$809$	27.5000	−	47.6314i	0.966849	−	1.67463i	0.704564	−	0.709640i	$-0.251142\pi$
$810$		0			0
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	17.0000			0.595484
$816$		0			0
$817$	15.0000			0.524784
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−42.0000			−1.46581			−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000			−1.46581			−0.732905	+	0.680331i	$0.761836\pi$
$822$		0			0
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−40.0000			−1.39094			−0.695468	−	0.718557i	$-0.744803\pi$
$827$	−40.0000			−1.39094			−0.695468	+	0.718557i	$0.744803\pi$
$828$		0			0
$829$	−2.50000	+	4.33013i	−0.0868286	+	0.150392i	−0.906169	−	0.422916i	$-0.861007\pi$
$829$	−2.50000	+	4.33013i	−0.0868286	+	0.150392i	0.819340	+	0.573307i	$0.194340\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	19.5000	+	7.79423i	0.675635	+	0.270054i
$834$		0			0
$835$	1.00000			0.0346064
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−22.5000	+	38.9711i	−0.776786	+	1.34543i	0.156999	+	0.987599i	$0.449818\pi$
$839$	−22.5000	+	38.9711i	−0.776786	+	1.34543i	−0.933785	+	0.357834i	$0.883515\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	−5.00000	+	1.73205i	−0.171802	+	0.0595140i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.00000			0.171398
$852$		0			0
$853$	−14.5000	+	25.1147i	−0.496471	+	0.859912i	−0.999992	−	0.00407068i	$-0.998704\pi$
$853$	−14.5000	+	25.1147i	−0.496471	+	0.859912i	0.503521	+	0.863983i	$0.332038\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.50000	+	6.06218i	0.119558	+	0.207080i	0.919592	−	0.392874i	$-0.128519\pi$
$857$	3.50000	+	6.06218i	0.119558	+	0.207080i	−0.800035	+	0.599954i	$0.795186\pi$
$858$		0			0
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	−0.657201	−	0.753715i	$-0.728260\pi$
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	0.981337	+	0.192295i	$0.0615932\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	0.757101	−	0.653298i	$-0.226615\pi$
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	−0.944323	+	0.329020i	$0.893282\pi$
$864$		0			0
$865$	1.00000	−	1.73205i	0.0340010	−	0.0588915i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	6.00000	+	10.3923i	0.203302	+	0.352130i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.0000	−	15.5885i	−0.608511	−	0.526986i
$876$		0			0
$877$	11.5000	−	19.9186i	0.388327	−	0.672603i	−0.603897	−	0.797062i	$-0.706386\pi$
$877$	11.5000	−	19.9186i	0.388327	−	0.672603i	0.992225	+	0.124459i	$0.0397196\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	−0.545302	−	0.838240i	$-0.683585\pi$
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	0.998588	+	0.0531258i	$0.0169184\pi$
$888$		0			0
$889$	16.0000	+	13.8564i	0.536623	+	0.464729i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	20.0000	+	34.6410i	0.669274	+	1.15922i
$894$		0			0
$895$	−10.5000	−	18.1865i	−0.350976	−	0.607909i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$	−13.5000	−	23.3827i	−0.449750	−	0.778990i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.00000	+	15.5885i	−0.299170	+	0.518178i
$906$		0			0
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	0.802049	−	0.597258i	$-0.203743\pi$
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	−0.918265	+	0.395966i	$0.870410\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.5000	−	23.3827i	0.447275	−	0.774703i	−0.550933	−	0.834550i	$-0.685728\pi$
$911$	13.5000	−	23.3827i	0.447275	−	0.774703i	0.998208	+	0.0598468i	$0.0190612\pi$
$912$		0			0
$913$	39.0000			1.29071
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.50000	−	2.59808i	0.247672	−	0.0857960i
$918$		0			0
$919$	−6.50000	−	11.2583i	−0.214415	−	0.371378i	0.738676	−	0.674060i	$-0.235451\pi$
$919$	−6.50000	−	11.2583i	−0.214415	−	0.371378i	−0.953092	+	0.302682i	$0.902118\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.00000	−	6.92820i	−0.131662	−	0.228045i
$924$		0			0
$925$	10.0000	−	17.3205i	0.328798	−	0.569495i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$		0			0
$931$	−27.5000	+	21.6506i	−0.901276	+	0.709571i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.50000	−	7.79423i	0.147166	−	0.254899i
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	50.0000			1.62995			0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000			1.62995			0.814977	+	0.579494i	$0.196750\pi$
$942$		0			0
$943$	−7.00000			−0.227951
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−36.0000			−1.16984			−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000			−1.16984			−0.584921	+	0.811090i	$0.698875\pi$
$948$		0			0
$949$	−13.0000			−0.421998
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	2.00000	−	3.46410i	0.0647185	−	0.112096i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.50000	−	28.5788i	0.177604	−	0.922859i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.00000	+	15.5885i	−0.289720	+	0.501810i
$966$		0			0
$967$	13.5000	+	23.3827i	0.434131	+	0.751936i	0.997224	−	0.0744567i	$-0.0237223\pi$
$967$	13.5000	+	23.3827i	0.434131	+	0.751936i	−0.563094	+	0.826393i	$0.690389\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.5000	+	37.2391i	0.689968	+	1.19506i	0.971848	+	0.235610i	$0.0757087\pi$
$971$	21.5000	+	37.2391i	0.689968	+	1.19506i	−0.281880	+	0.959450i	$0.590958\pi$
$972$		0			0
$973$	2.50000	−	12.9904i	0.0801463	−	0.416452i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.0000			−0.703842			−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000			−0.703842			−0.351921	+	0.936030i	$0.614471\pi$
$978$		0			0
$979$	13.5000	−	23.3827i	0.431462	−	0.747314i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.5000	+	35.5070i	0.653848	+	1.13250i	0.982181	+	0.187937i	$0.0601800\pi$
$983$	20.5000	+	35.5070i	0.653848	+	1.13250i	−0.328333	+	0.944562i	$0.606487\pi$
$984$		0			0
$985$	11.0000	−	19.0526i	0.350489	−	0.607065i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.50000	+	2.59808i	0.0476972	+	0.0826140i
$990$		0			0
$991$	−7.50000	+	12.9904i	−0.238245	+	0.412653i	−0.960211	−	0.279276i	$-0.909906\pi$
$991$	−7.50000	+	12.9904i	−0.238245	+	0.412653i	0.721966	+	0.691929i	$0.243239\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.5000	−	18.1865i	−0.332872	−	0.576552i
$996$		0			0
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	0.744548	−	0.667568i	$-0.232665\pi$
$997$	−6.50000	−	11.2583i	−0.205857	−	0.356555i	−0.950405	+	0.311014i	$0.899332\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.d.2881.1		2
3.2	odd	2		1008.2.q.b.529.1		2
4.3	odd	2		1512.2.q.b.1369.1		2
7.2	even	3		3024.2.t.c.289.1		2
9.4	even	3		3024.2.t.c.1873.1		2
9.5	odd	6		1008.2.t.e.193.1		2
12.11	even	2		504.2.q.a.25.1	✓	2
21.2	odd	6		1008.2.t.e.961.1		2
28.23	odd	6		1512.2.t.a.289.1		2
36.23	even	6		504.2.t.a.193.1	yes	2
36.31	odd	6		1512.2.t.a.361.1		2
63.23	odd	6		1008.2.q.b.625.1		2
63.58	even	3	inner	3024.2.q.d.2305.1		2
84.23	even	6		504.2.t.a.457.1	yes	2
252.23	even	6		504.2.q.a.121.1	yes	2
252.247	odd	6		1512.2.q.b.793.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.a.25.1	✓	2	12.11	even	2
504.2.q.a.121.1	yes	2	252.23	even	6
504.2.t.a.193.1	yes	2	36.23	even	6
504.2.t.a.457.1	yes	2	84.23	even	6
1008.2.q.b.529.1		2	3.2	odd	2
1008.2.q.b.625.1		2	63.23	odd	6
1008.2.t.e.193.1		2	9.5	odd	6
1008.2.t.e.961.1		2	21.2	odd	6
1512.2.q.b.793.1		2	252.247	odd	6
1512.2.q.b.1369.1		2	4.3	odd	2
1512.2.t.a.289.1		2	28.23	odd	6
1512.2.t.a.361.1		2	36.31	odd	6
3024.2.q.d.2305.1		2	63.58	even	3	inner
3024.2.q.d.2881.1		2	1.1	even	1	trivial
3024.2.t.c.289.1		2	7.2	even	3
3024.2.t.c.1873.1		2	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +(4.50000 - 7.79423i) q^{29} -4.00000 q^{31} +(-2.50000 + 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(3.50000 + 6.06218i) q^{41} +(1.50000 - 2.59808i) q^{43} +8.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(4.50000 - 7.79423i) q^{53} +3.00000 q^{55} -4.00000 q^{59} +2.00000 q^{61} -1.00000 q^{65} -12.0000 q^{67} +8.00000 q^{71} +(6.50000 - 11.2583i) q^{73} +(1.50000 - 7.79423i) q^{77} -8.00000 q^{79} +(6.50000 - 11.2583i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(-4.50000 - 7.79423i) q^{89} +(-0.500000 + 2.59808i) q^{91} +5.00000 q^{95} +(8.50000 - 14.7224i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{5} - 4 q^{7}+O(q^{10}) \) 2 * q + q^5 - 4 * q^7	\( 2 q + q^{5} - 4 q^{7} + 3 q^{11} - q^{13} + 3 q^{17} + 5 q^{19} - q^{23} + 4 q^{25} + 9 q^{29} - 8 q^{31} - 5 q^{35} - 5 q^{37} + 7 q^{41} + 3 q^{43} + 16 q^{47} + 2 q^{49} + 9 q^{53} + 6 q^{55} - 8 q^{59} + 4 q^{61} - 2 q^{65} - 24 q^{67} + 16 q^{71} + 13 q^{73} + 3 q^{77} - 16 q^{79} + 13 q^{83} - 3 q^{85} - 9 q^{89} - q^{91} + 10 q^{95} + 17 q^{97}+O(q^{100}) \) 2 * q + q^5 - 4 * q^7 + 3 * q^11 - q^13 + 3 * q^17 + 5 * q^19 - q^23 + 4 * q^25 + 9 * q^29 - 8 * q^31 - 5 * q^35 - 5 * q^37 + 7 * q^41 + 3 * q^43 + 16 * q^47 + 2 * q^49 + 9 * q^53 + 6 * q^55 - 8 * q^59 + 4 * q^61 - 2 * q^65 - 24 * q^67 + 16 * q^71 + 13 * q^73 + 3 * q^77 - 16 * q^79 + 13 * q^83 - 3 * q^85 - 9 * q^89 - q^91 + 10 * q^95 + 17 * q^97

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