LMFDB - Embedded newform 3024.2.q.f.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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})$	$q+(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(4.50000 - 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(1.50000 - 2.59808i) q^{29} -8.00000 q^{31} +(7.50000 - 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(1.00000 + 6.92820i) q^{49} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +2.00000 q^{61} +3.00000 q^{65} +4.00000 q^{67} +12.0000 q^{71} +(-5.50000 + 9.52628i) q^{73} +(-1.50000 + 7.79423i) q^{77} +16.0000 q^{79} +(4.50000 - 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(1.50000 + 2.59808i) q^{89} +(-0.500000 + 2.59808i) q^{91} -21.0000 q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{5} + 4 q^{7}+O(q^{10}) $ 2 * q + 3 * q^5 + 4 * q^7	$ 2 q + 3 q^{5} + 4 q^{7} + 3 q^{11} + q^{13} + 3 q^{17} - 7 q^{19} + 9 q^{23} - 4 q^{25} + 3 q^{29} - 16 q^{31} + 15 q^{35} + q^{37} + 3 q^{41} - q^{43} + 2 q^{49} + 3 q^{53} + 18 q^{55} + 4 q^{61} + 6 q^{65} + 8 q^{67} + 24 q^{71} - 11 q^{73} - 3 q^{77} + 32 q^{79} + 9 q^{83} - 9 q^{85} + 3 q^{89} - q^{91} - 42 q^{95} + q^{97}+O(q^{100}) $ 2 * q + 3 * q^5 + 4 * q^7 + 3 * q^11 + q^13 + 3 * q^17 - 7 * q^19 + 9 * q^23 - 4 * q^25 + 3 * q^29 - 16 * q^31 + 15 * q^35 + q^37 + 3 * q^41 - q^43 + 2 * q^49 + 3 * q^53 + 18 * q^55 + 4 * q^61 + 6 * q^65 + 8 * q^67 + 24 * q^71 - 11 * q^73 - 3 * q^77 + 32 * q^79 + 9 * q^83 - 9 * q^85 + 3 * q^89 - q^91 - 42 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		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	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		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
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.169701	−	0.985496i	$-0.445720\pi$
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.768613	−	0.639713i	$-0.220947\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.50000	−	2.59808i	1.26773	−	0.439155i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		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
$65$	3.00000			0.372104
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$		0			0
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	−4.50000	−	7.79423i	−0.488094	−	0.845403i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	0.934508	−	0.355942i	$-0.115840\pi$
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	−0.775509	+	0.631337i	$0.782506\pi$
$90$		0			0
$91$	−0.500000	+	2.59808i	−0.0524142	+	0.272352i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−21.0000			−2.15455
$96$		0			0
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	0.344865	+	0.938652i	$0.387925\pi$
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$		0			0
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	−0.366415	−	0.930451i	$-0.619415\pi$
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	0.989002	−	0.147901i	$-0.0472517\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.50000	−	7.79423i	−0.423324	−	0.733219i	0.572938	−	0.819599i	$-0.305804\pi$
$113$	−4.50000	−	7.79423i	−0.423324	−	0.733219i	−0.996262	+	0.0863794i	$0.972470\pi$
$114$		0			0
$115$	−13.5000	−	23.3827i	−1.25888	−	2.18045i
$116$		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
$125$	3.00000			0.268328
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$		0			0
$133$	3.50000	−	18.1865i	0.303488	−	1.57697i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		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
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	0.687741	−	0.725956i	$-0.258602\pi$
$151$	−3.50000	−	6.06218i	−0.284826	−	0.493333i	−0.972567	+	0.232623i	$0.925269\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.0000	+	20.7846i	−0.963863	+	1.66946i
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	22.5000	−	7.79423i	1.77325	−	0.614271i
$162$		0			0
$163$	−9.50000	−	16.4545i	−0.744097	−	1.28881i	−0.950615	−	0.310372i	$-0.899546\pi$
$163$	−9.50000	−	16.4545i	−0.744097	−	1.28881i	0.206518	−	0.978443i	$-0.433787\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.50000	+	12.9904i	0.580367	+	1.00523i	0.995436	+	0.0954356i	$0.0304244\pi$
$167$	7.50000	+	12.9904i	0.580367	+	1.00523i	−0.415068	+	0.909790i	$0.636242\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		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
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.00000			0.220564
$186$		0			0
$187$	9.00000			0.658145
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−12.5000	+	21.6506i	−0.886102	+	1.53477i	−0.0416556	+	0.999132i	$0.513263\pi$
$199$	−12.5000	+	21.6506i	−0.886102	+	1.53477i	−0.844446	+	0.535641i	$0.820070\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$		0			0
$205$	9.00000			0.628587
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.5000	−	18.1865i	0.726300	−	1.25799i
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.50000	+	2.59808i	0.102299	+	0.177187i
$216$		0			0
$217$	−16.0000	−	13.8564i	−1.08615	−	0.940634i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.00000			0.201802
$222$		0			0
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	−0.882281	−	0.470723i	$-0.843993\pi$
$223$	−0.500000	+	0.866025i	−0.0334825	+	0.0579934i	0.848799	+	0.528716i	$0.177326\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$		0			0
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		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
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	0.910453	−	0.413613i	$-0.135733\pi$
$239$	1.50000	+	2.59808i	0.0970269	+	0.168056i	−0.813426	+	0.581669i	$0.802400\pi$
$240$		0			0
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	19.5000	+	7.79423i	1.24581	+	0.497955i
$246$		0			0
$247$	3.50000	−	6.06218i	0.222700	−	0.385727i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	27.0000			1.69748
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	0.326929	+	0.945049i	$0.393986\pi$
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	−0.981901	+	0.189396i	$0.939347\pi$
$258$		0			0
$259$	−0.500000	+	2.59808i	−0.0310685	+	0.161437i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	2.50000	+	4.33013i	0.151864	+	0.263036i	0.931913	−	0.362682i	$-0.118139\pi$
$271$	2.50000	+	4.33013i	0.151864	+	0.263036i	−0.780049	+	0.625719i	$0.784806\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	0.361895	+	0.932219i	$0.382130\pi$
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	−0.988273	+	0.152699i	$0.951204\pi$
$282$		0			0
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.50000	+	7.79423i	−0.0885422	+	0.460079i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	9.00000			0.520483
$300$		0			0
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$	9.00000			0.503903
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−21.0000			−1.16847
$324$		0			0
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.0000	−	20.7846i	−0.649836	−	1.12555i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$		0			0
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	0.374701	+	0.927146i	$0.377745\pi$
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$	18.0000	−	31.1769i	0.955341	−	1.65470i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.50000	−	7.79423i	−0.237501	−	0.411364i	0.722496	−	0.691375i	$-0.242995\pi$
$359$	−4.50000	−	7.79423i	−0.237501	−	0.411364i	−0.959997	+	0.280012i	$0.909662\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	16.5000	+	28.5788i	0.863649	+	1.49588i
$366$		0			0
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	0.997960	−	0.0638362i	$-0.0203335\pi$
$367$	8.50000	+	14.7224i	0.443696	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.50000	−	2.59808i	0.389381	−	0.134885i
$372$		0			0
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$	18.0000	+	15.5885i	0.917365	+	0.794461i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	0.973601	+	0.228257i	$0.0733028\pi$
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	−0.289124	+	0.957292i	$0.593364\pi$
$390$		0			0
$391$	−13.5000	−	23.3827i	−0.682724	−	1.18251i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	24.0000	−	41.5692i	1.20757	−	2.09157i
$396$		0			0
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	0.981760	−	0.190126i	$-0.0608897\pi$
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	−0.655534	+	0.755166i	$0.727556\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	−4.00000	−	6.92820i	−0.199254	−	0.345118i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.50000	+	2.59808i	−0.0743522	+	0.128782i
$408$		0			0
$409$	−34.0000			−1.68119			−0.840596	−	0.541663i	$-0.817795\pi$
$409$	−34.0000			−1.68119			−0.840596	+	0.541663i	$0.817795\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−13.5000	−	23.3827i	−0.662689	−	1.14781i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$		0			0
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	0.0256838	+	0.999670i	$0.491824\pi$
$421$	−17.5000	+	30.3109i	−0.852898	+	1.47726i	−0.878582	+	0.477592i	$0.841510\pi$
$422$		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
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	0.332785	+	0.943003i	$0.392012\pi$
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	−0.983057	+	0.183301i	$0.941322\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−63.0000			−3.01370
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$		0			0
$445$	9.00000			0.426641
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.00000	+	5.19615i	0.281284	+	0.243599i
$456$		0			0
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		0			0
$463$	20.5000	+	35.5070i	0.952716	+	1.65015i	0.739511	+	0.673145i	$0.235057\pi$
$463$	20.5000	+	35.5070i	0.952716	+	1.65015i	0.213205	+	0.977007i	$0.431610\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$		0			0
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.00000			−0.137940
$474$		0			0
$475$	−14.0000	+	24.2487i	−0.642364	+	1.11261i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	0.898257	−	0.439470i	$-0.144834\pi$
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	−0.829721	+	0.558179i	$0.811500\pi$
$480$		0			0
$481$	−0.500000	+	0.866025i	−0.0227980	+	0.0394874i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.50000	−	2.59808i	−0.0681115	−	0.117973i
$486$		0			0
$487$	−12.5000	+	21.6506i	−0.566429	+	0.981084i	0.430486	+	0.902597i	$0.358342\pi$
$487$	−12.5000	+	21.6506i	−0.566429	+	0.981084i	−0.996915	+	0.0784867i	$0.974991\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	0.525694	−	0.850674i	$-0.323806\pi$
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	−0.999552	+	0.0299272i	$0.990472\pi$
$492$		0			0
$493$	−4.50000	−	7.79423i	−0.202670	−	0.351034i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.0000	+	20.7846i	1.07655	+	0.932317i
$498$		0			0
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	0.437955	+	0.898997i	$0.355703\pi$
$499$	−12.5000	+	21.6506i	−0.559577	+	0.969216i	−0.997532	+	0.0702185i	$0.977630\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	−0.948353	−	0.317217i	$-0.897252\pi$
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	0.748894	+	0.662690i	$0.230585\pi$
$510$		0			0
$511$	−27.5000	+	9.52628i	−1.21653	+	0.421418i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	19.5000	+	33.7750i	0.859273	+	1.48830i
$516$		0			0
$517$		0			0
$518$		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
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	0.779301	−	0.626650i	$-0.215574\pi$
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	−0.932345	+	0.361569i	$0.882241\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.50000	+	2.59808i	−0.0649722	+	0.112535i
$534$		0			0
$535$	−27.0000			−1.16731
$536$		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	0.723234	−	0.690604i	$-0.242655\pi$
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	−0.959697	+	0.281037i	$0.909322\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−19.5000	−	33.7750i	−0.835288	−	1.44676i
$546$		0			0
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	−0.724157	−	0.689635i	$-0.757771\pi$
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	0.959320	+	0.282321i	$0.0911043\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.0000			−0.894630
$552$		0			0
$553$	32.0000	+	27.7128i	1.36078	+	1.17847i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$		0			0
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$		0			0
$565$	−27.0000			−1.13590
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−36.0000			−1.50130
$576$		0			0
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	−0.479337	−	0.877631i	$-0.659123\pi$
$577$	12.5000	−	21.6506i	0.520382	−	0.901328i	0.999719	−	0.0236970i	$-0.00754370\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	22.5000	−	7.79423i	0.933457	−	0.323359i
$582$		0			0
$583$	9.00000			0.372742
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	−0.895320	−	0.445424i	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$		0			0
$589$	28.0000	+	48.4974i	1.15372	+	1.99830i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	19.5000	+	33.7750i	0.800769	+	1.38697i	0.919111	+	0.394000i	$0.128909\pi$
$593$	19.5000	+	33.7750i	0.800769	+	1.38697i	−0.118342	+	0.992973i	$0.537758\pi$
$594$		0			0
$595$	4.50000	−	23.3827i	0.184482	−	0.958597i
$596$		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
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	−0.490049	−	0.871695i	$-0.663021\pi$
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	0.999934	−	0.0114528i	$-0.00364562\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$		0			0
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	−0.967256	−	0.253804i	$-0.918318\pi$
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	0.703429	+	0.710766i	$0.251651\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	−0.999178	−	0.0405396i	$-0.987092\pi$
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	0.534697	+	0.845044i	$0.320426\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.5000	−	38.9711i	−0.905816	−	1.56892i	−0.819818	−	0.572624i	$-0.805926\pi$
$617$	−22.5000	−	38.9711i	−0.905816	−	1.56892i	−0.0859976	−	0.996295i	$-0.527408\pi$
$618$		0			0
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.50000	+	7.79423i	−0.0600962	+	0.312269i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.00000			0.119618
$630$		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
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$		0			0
$637$	−5.50000	+	4.33013i	−0.217918	+	0.171566i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	0.996379	+	0.0850262i	$0.0270974\pi$
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	−0.424555	+	0.905402i	$0.639569\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	−0.582397	−	0.812905i	$-0.697885\pi$
$647$	10.5000	−	18.1865i	0.412798	−	0.714986i	0.995194	+	0.0979182i	$0.0312184\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	−0.681137	−	0.732156i	$-0.738514\pi$
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	0.974634	+	0.223803i	$0.0718474\pi$
$654$		0			0
$655$	22.5000	+	38.9711i	0.879148	+	1.52273i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	−0.893762	−	0.448542i	$-0.851943\pi$
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	0.835330	+	0.549749i	$0.185277\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−42.0000	−	36.3731i	−1.62869	−	1.41049i
$666$		0			0
$667$	−13.5000	−	23.3827i	−0.522722	−	0.905381i
$668$		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
$677$	30.0000			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$678$		0			0
$679$	2.50000	−	0.866025i	0.0959412	−	0.0332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$		0			0
$685$	−27.0000			−1.03162
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.00000			0.114291
$690$		0			0
$691$	−44.0000			−1.67384			−0.836919	−	0.547326i	$-0.815646\pi$
$691$	−44.0000			−1.67384			−0.836919	+	0.547326i	$0.815646\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−21.0000			−0.796575
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	3.50000	−	6.06218i	0.132005	−	0.228639i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.50000	+	7.79423i	−0.0564133	+	0.293132i
$708$		0			0
$709$	26.0000			0.976450			0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000			0.976450			0.488225	+	0.872718i	$0.337644\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−36.0000	+	62.3538i	−1.34821	+	2.33517i
$714$		0			0
$715$	4.50000	+	7.79423i	0.168290	+	0.291488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	0.971311	−	0.237814i	$-0.0764307\pi$
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	−0.691608	+	0.722273i	$0.743097\pi$
$720$		0			0
$721$	−32.5000	+	11.2583i	−1.21036	+	0.419282i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−12.0000			−0.445669
$726$		0			0
$727$	−6.50000	+	11.2583i	−0.241072	+	0.417548i	−0.961020	−	0.276479i	$-0.910832\pi$
$727$	−6.50000	+	11.2583i	−0.241072	+	0.417548i	0.719948	+	0.694028i	$0.244166\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	−0.856644	−	0.515908i	$-0.827454\pi$
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	0.875112	+	0.483921i	$0.160788\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$		0			0
$739$	11.5000	−	19.9186i	0.423034	−	0.732717i	−0.573200	−	0.819415i	$-0.694298\pi$
$739$	11.5000	−	19.9186i	0.423034	−	0.732717i	0.996235	+	0.0866983i	$0.0276316\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	0.606590	−	0.795015i	$-0.292537\pi$
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	−0.991798	+	0.127815i	$0.959204\pi$
$744$		0			0
$745$	13.5000	+	23.3827i	0.494602	+	0.856675i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.50000	−	23.3827i	0.164426	−	0.854385i
$750$		0			0
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	−0.959906	−	0.280321i	$-0.909559\pi$
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	0.722718	+	0.691143i	$0.242893\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−21.0000			−0.764268
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		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
$763$	32.5000	−	11.2583i	1.17658	−	0.407579i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	−0.514301	−	0.857610i	$-0.671949\pi$
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	0.999862	+	0.0165929i	$0.00528194\pi$
$774$		0			0
$775$	16.0000	+	27.7128i	0.574737	+	0.995474i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.5000	−	18.1865i	0.376202	−	0.651600i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−33.0000	+	57.1577i	−1.17782	+	2.04004i
$786$		0			0
$787$	28.0000			0.998092			0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000			0.998092			0.499046	+	0.866575i	$0.333684\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.50000	−	23.3827i	0.160002	−	0.831393i
$792$		0			0
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−10.5000	−	18.1865i	−0.371929	−	0.644200i	0.617933	−	0.786231i	$-0.287970\pi$
$797$	−10.5000	−	18.1865i	−0.371929	−	0.644200i	−0.989862	+	0.142031i	$0.954637\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−33.0000			−1.16454
$804$		0			0
$805$	13.5000	−	70.1481i	0.475812	−	2.47239i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	0.415357	+	0.909659i	$0.363657\pi$
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	−0.995466	+	0.0951198i	$0.969677\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−57.0000			−1.99662
$816$		0			0
$817$	7.00000			0.244899
$818$		0			0
$819$		0			0
$820$		0			0
$821$	42.0000			1.46581			0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000			1.46581			0.732905	+	0.680331i	$0.238164\pi$
$822$		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
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	19.5000	+	7.79423i	0.675635	+	0.270054i
$834$		0			0
$835$	45.0000			1.55729
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.50000	+	12.9904i	−0.258929	+	0.448478i	−0.965955	−	0.258709i	$-0.916703\pi$
$839$	−7.50000	+	12.9904i	−0.258929	+	0.448478i	0.707026	+	0.707187i	$0.250036\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.0000	−	31.1769i	−0.619219	−	1.07252i
$846$		0			0
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.00000			0.308516
$852$		0			0
$853$	0.500000	−	0.866025i	0.0171197	−	0.0296521i	−0.857339	−	0.514753i	$-0.827884\pi$
$853$	0.500000	−	0.866025i	0.0171197	−	0.0296521i	0.874458	+	0.485101i	$0.161217\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	0.890507	−	0.454969i	$-0.150350\pi$
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	−0.839268	+	0.543718i	$0.817016\pi$
$858$		0			0
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	−0.996559	−	0.0828900i	$-0.973585\pi$
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	0.570064	+	0.821600i	$0.306918\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.864007	+	0.503480i	$0.167947\pi$
$863$	25.5000	+	44.1673i	0.868030	+	1.50347i	0.00402340	+	0.999992i	$0.498719\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	24.0000	+	41.5692i	0.814144	+	1.41014i
$870$		0			0
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.00000	+	5.19615i	0.202837	+	0.175662i
$876$		0			0
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	0.130224	+	0.991485i	$0.458430\pi$
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	−0.923763	+	0.382965i	$0.874903\pi$
$878$		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
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	−0.443964	−	0.896045i	$-0.646428\pi$
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	0.997979	−	0.0635387i	$-0.0202386\pi$
$888$		0			0
$889$	8.00000	+	6.92820i	0.268311	+	0.232364i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−31.5000	−	54.5596i	−1.05293	−	1.82373i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$	−4.50000	−	7.79423i	−0.149917	−	0.259663i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$		0			0
$907$	−21.5000	−	37.2391i	−0.713896	−	1.23650i	−0.963384	−	0.268126i	$-0.913596\pi$
$907$	−21.5000	−	37.2391i	−0.713896	−	1.23650i	0.249488	−	0.968378i	$-0.419738\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	0.337991	+	0.941149i	$0.390253\pi$
$911$	−19.5000	+	33.7750i	−0.646064	+	1.11902i	−0.984055	+	0.177866i	$0.943081\pi$
$912$		0			0
$913$	27.0000			0.893570
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−37.5000	+	12.9904i	−1.23836	+	0.428980i
$918$		0			0
$919$	26.5000	+	45.8993i	0.874154	+	1.51408i	0.857661	+	0.514216i	$0.171917\pi$
$919$	26.5000	+	45.8993i	0.874154	+	1.51408i	0.0164935	+	0.999864i	$0.494750\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.00000	+	10.3923i	0.197492	+	0.342067i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−18.0000			−0.590561			−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$		0			0
$931$	38.5000	−	30.3109i	1.26179	−	0.993399i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13.5000	−	23.3827i	0.441497	−	0.764696i
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.00000			0.195594			0.0977972	−	0.995206i	$-0.468820\pi$
$941$	6.00000			0.195594			0.0977972	+	0.995206i	$0.468820\pi$
$942$		0			0
$943$	27.0000			0.879241
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	−11.0000			−0.357075
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.50000	−	23.3827i	0.145313	−	0.755066i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$		0			0
$964$		0			0
$965$	21.0000	−	36.3731i	0.676014	−	1.17089i
$966$		0			0
$967$	20.5000	+	35.5070i	0.659236	+	1.14183i	0.980814	+	0.194946i	$0.0624533\pi$
$967$	20.5000	+	35.5070i	0.659236	+	1.14183i	−0.321578	+	0.946883i	$0.604213\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$		0			0
$973$	3.50000	−	18.1865i	0.112205	−	0.583033i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.0000			0.959785			0.479893	−	0.877327i	$-0.340676\pi$
$977$	30.0000			0.959785			0.479893	+	0.877327i	$0.340676\pi$
$978$		0			0
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	0.960489	−	0.278319i	$-0.0897773\pi$
$983$	7.50000	+	12.9904i	0.239213	+	0.414329i	−0.721276	+	0.692648i	$0.756444\pi$
$984$		0			0
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.50000	+	7.79423i	0.143092	+	0.247842i
$990$		0			0
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	−0.993364	−	0.115015i	$-0.963308\pi$
$991$	−12.5000	+	21.6506i	−0.397076	+	0.687755i	0.596288	+	0.802771i	$0.296642\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	37.5000	+	64.9519i	1.18883	+	2.05911i
$996$		0			0
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	0.950405	−	0.311014i	$-0.100668\pi$
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	−0.744548	+	0.667568i	$0.767335\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.f.2881.1		2
3.2	odd	2		1008.2.q.a.529.1		2
4.3	odd	2		378.2.e.b.235.1		2
7.2	even	3		3024.2.t.a.289.1		2
9.4	even	3		3024.2.t.a.1873.1		2
9.5	odd	6		1008.2.t.f.193.1		2
12.11	even	2		126.2.e.a.25.1	✓	2
21.2	odd	6		1008.2.t.f.961.1		2
28.3	even	6		2646.2.f.a.883.1		2
28.11	odd	6		2646.2.f.d.883.1		2
28.19	even	6		2646.2.h.d.667.1		2
28.23	odd	6		378.2.h.a.289.1		2
28.27	even	2		2646.2.e.g.2125.1		2
36.7	odd	6		1134.2.g.c.487.1		2
36.11	even	6		1134.2.g.e.487.1		2
36.23	even	6		126.2.h.b.67.1	yes	2
36.31	odd	6		378.2.h.a.361.1		2
63.23	odd	6		1008.2.q.a.625.1		2
63.58	even	3	inner	3024.2.q.f.2305.1		2
84.11	even	6		882.2.f.i.295.1		2
84.23	even	6		126.2.h.b.79.1	yes	2
84.47	odd	6		882.2.h.i.79.1		2
84.59	odd	6		882.2.f.g.295.1		2
84.83	odd	2		882.2.e.c.655.1		2
252.11	even	6		7938.2.a.m.1.1		1
252.23	even	6		126.2.e.a.121.1	yes	2
252.31	even	6		2646.2.f.a.1765.1		2
252.59	odd	6		882.2.f.g.589.1		2
252.67	odd	6		2646.2.f.d.1765.1		2
252.79	odd	6		1134.2.g.c.163.1		2
252.95	even	6		882.2.f.i.589.1		2
252.103	even	6		2646.2.e.g.1549.1		2
252.115	even	6		7938.2.a.be.1.1		1
252.131	odd	6		882.2.e.c.373.1		2
252.139	even	6		2646.2.h.d.361.1		2
252.151	odd	6		7938.2.a.t.1.1		1
252.167	odd	6		882.2.h.i.67.1		2
252.191	even	6		1134.2.g.e.163.1		2
252.227	odd	6		7938.2.a.b.1.1		1
252.247	odd	6		378.2.e.b.37.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	12.11	even	2
126.2.e.a.121.1	yes	2	252.23	even	6
126.2.h.b.67.1	yes	2	36.23	even	6
126.2.h.b.79.1	yes	2	84.23	even	6
378.2.e.b.37.1		2	252.247	odd	6
378.2.e.b.235.1		2	4.3	odd	2
378.2.h.a.289.1		2	28.23	odd	6
378.2.h.a.361.1		2	36.31	odd	6
882.2.e.c.373.1		2	252.131	odd	6
882.2.e.c.655.1		2	84.83	odd	2
882.2.f.g.295.1		2	84.59	odd	6
882.2.f.g.589.1		2	252.59	odd	6
882.2.f.i.295.1		2	84.11	even	6
882.2.f.i.589.1		2	252.95	even	6
882.2.h.i.67.1		2	252.167	odd	6
882.2.h.i.79.1		2	84.47	odd	6
1008.2.q.a.529.1		2	3.2	odd	2
1008.2.q.a.625.1		2	63.23	odd	6
1008.2.t.f.193.1		2	9.5	odd	6
1008.2.t.f.961.1		2	21.2	odd	6
1134.2.g.c.163.1		2	252.79	odd	6
1134.2.g.c.487.1		2	36.7	odd	6
1134.2.g.e.163.1		2	252.191	even	6
1134.2.g.e.487.1		2	36.11	even	6
2646.2.e.g.1549.1		2	252.103	even	6
2646.2.e.g.2125.1		2	28.27	even	2
2646.2.f.a.883.1		2	28.3	even	6
2646.2.f.a.1765.1		2	252.31	even	6
2646.2.f.d.883.1		2	28.11	odd	6
2646.2.f.d.1765.1		2	252.67	odd	6
2646.2.h.d.361.1		2	252.139	even	6
2646.2.h.d.667.1		2	28.19	even	6
3024.2.q.f.2305.1		2	63.58	even	3	inner
3024.2.q.f.2881.1		2	1.1	even	1	trivial
3024.2.t.a.289.1		2	7.2	even	3
3024.2.t.a.1873.1		2	9.4	even	3
7938.2.a.b.1.1		1	252.227	odd	6
7938.2.a.m.1.1		1	252.11	even	6
7938.2.a.t.1.1		1	252.151	odd	6
7938.2.a.be.1.1		1	252.115	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(4.50000 - 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(1.50000 - 2.59808i) q^{29} -8.00000 q^{31} +(7.50000 - 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(1.00000 + 6.92820i) q^{49} +(1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +2.00000 q^{61} +3.00000 q^{65} +4.00000 q^{67} +12.0000 q^{71} +(-5.50000 + 9.52628i) q^{73} +(-1.50000 + 7.79423i) q^{77} +16.0000 q^{79} +(4.50000 - 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(1.50000 + 2.59808i) q^{89} +(-0.500000 + 2.59808i) q^{91} -21.0000 q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{5} + 4 q^{7}+O(q^{10}) \) 2 * q + 3 * q^5 + 4 * q^7	\( 2 q + 3 q^{5} + 4 q^{7} + 3 q^{11} + q^{13} + 3 q^{17} - 7 q^{19} + 9 q^{23} - 4 q^{25} + 3 q^{29} - 16 q^{31} + 15 q^{35} + q^{37} + 3 q^{41} - q^{43} + 2 q^{49} + 3 q^{53} + 18 q^{55} + 4 q^{61} + 6 q^{65} + 8 q^{67} + 24 q^{71} - 11 q^{73} - 3 q^{77} + 32 q^{79} + 9 q^{83} - 9 q^{85} + 3 q^{89} - q^{91} - 42 q^{95} + q^{97}+O(q^{100}) \) 2 * q + 3 * q^5 + 4 * q^7 + 3 * q^11 + q^13 + 3 * q^17 - 7 * q^19 + 9 * q^23 - 4 * q^25 + 3 * q^29 - 16 * q^31 + 15 * q^35 + q^37 + 3 * q^41 - q^43 + 2 * q^49 + 3 * q^53 + 18 * q^55 + 4 * q^61 + 6 * q^65 + 8 * q^67 + 24 * q^71 - 11 * q^73 - 3 * q^77 + 32 * q^79 + 9 * q^83 - 9 * q^85 + 3 * q^89 - q^91 - 42 * q^95 + q^97

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