LMFDB - Embedded newform 1152.2.r.b.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(193,1152)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1152.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.r (of order $6$, degree $2$, 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:	$9.19876631285$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			961.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1152.961
Dual form			1152.2.r.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 1.50000i) q^{3} +(-2.00000 + 3.46410i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(3.46410 - 2.00000i) q^{13} -7.00000 q^{17} +5.00000i q^{19} +(-3.46410 - 6.00000i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(-2.50000 + 4.33013i) q^{25} +5.19615 q^{27} +(3.46410 + 2.00000i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(1.50000 - 0.866025i) q^{33} -8.00000i q^{37} +6.92820i q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.866025 + 0.500000i) q^{43} +(2.00000 - 3.46410i) q^{47} +(-4.50000 - 7.79423i) q^{49} +(6.06218 - 10.5000i) q^{51} -8.00000i q^{53} +(-7.50000 - 4.33013i) q^{57} +(-7.79423 + 4.50000i) q^{59} +12.0000 q^{63} +(2.59808 - 1.50000i) q^{67} +6.92820 q^{69} +8.00000 q^{71} -3.00000 q^{73} +(-4.33013 - 7.50000i) q^{75} +(3.46410 - 2.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-13.8564 - 8.00000i) q^{83} +(-6.00000 + 3.46410i) q^{87} +6.00000 q^{89} +16.0000i q^{91} +13.8564 q^{93} +(-0.500000 + 0.866025i) q^{97} +3.00000i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{7} - 6 q^{9} - 28 q^{17} - 8 q^{23} - 10 q^{25} - 16 q^{31} + 6 q^{33} - 6 q^{41} + 8 q^{47} - 18 q^{49} - 30 q^{57} + 48 q^{63} + 32 q^{71} - 12 q^{73} - 16 q^{79} - 18 q^{81} - 24 q^{87} + 24 q^{89}+ \cdots - 2 q^{97}+O(q^{100}) $ 4 * q - 8 * q^7 - 6 * q^9 - 28 * q^17 - 8 * q^23 - 10 * q^25 - 16 * q^31 + 6 * q^33 - 6 * q^41 + 8 * q^47 - 18 * q^49 - 30 * q^57 + 48 * q^63 + 32 * q^71 - 12 * q^73 - 16 * q^79 - 18 * q^81 - 24 * q^87 + 24 * q^89 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$		0			0
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$		0			0
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i	0.363727	−	0.931505i	$-0.381504\pi$
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i	−0.624844	+	0.780750i	$0.714837\pi$
$12$		0			0
$13$	3.46410	−	2.00000i	0.960769	−	0.554700i	0.0643593	−	0.997927i	$-0.479500\pi$
$13$	3.46410	−	2.00000i	0.960769	−	0.554700i	0.896410	+	0.443227i	$0.146166\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.00000			−1.69775			−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000			−1.69775			−0.848875	+	0.528594i	$0.822719\pi$
$18$		0			0
$19$			5.00000i			1.14708i	0.819178	+	0.573539i	$0.194430\pi$
$19$			5.00000i			1.14708i	−0.819178	+	0.573539i	$0.805570\pi$
$20$		0			0
$21$	−3.46410	−	6.00000i	−0.755929	−	1.30931i
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$		0			0
$27$	5.19615			1.00000
$28$		0			0
$29$	3.46410	+	2.00000i	0.643268	+	0.371391i	0.785872	−	0.618389i	$-0.212214\pi$
$29$	3.46410	+	2.00000i	0.643268	+	0.371391i	−0.142605	+	0.989780i	$0.545548\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$		0			0
$33$	1.50000	−	0.866025i	0.261116	−	0.150756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$		0			0
$39$			6.92820i			1.10940i
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	0.564578	−	0.825380i	$-0.309039\pi$
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	−0.432511	+	0.901629i	$0.642372\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	−0.682489	−	0.730896i	$-0.739102\pi$
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	0.974219	+	0.225605i	$0.0724358\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$		0			0
$51$	6.06218	−	10.5000i	0.848875	−	1.47029i
$52$		0			0
$53$		−	8.00000i		−	1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$53$		−	8.00000i		−	1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7.50000	−	4.33013i	−0.993399	−	0.573539i
$58$		0			0
$59$	−7.79423	+	4.50000i	−1.01472	+	0.585850i	−0.912571	−	0.408919i	$-0.865906\pi$
$59$	−7.79423	+	4.50000i	−1.01472	+	0.585850i	−0.102151	+	0.994769i	$0.532573\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	12.0000			1.51186
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	−0.332830	−	0.942987i	$-0.608004\pi$
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	0.650236	+	0.759733i	$0.274670\pi$
$68$		0			0
$69$	6.92820			0.834058
$70$		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
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$		0			0
$75$	−4.33013	−	7.50000i	−0.500000	−	0.866025i
$76$		0			0
$77$	3.46410	−	2.00000i	0.394771	−	0.227921i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−13.8564	−	8.00000i	−1.52094	−	0.878114i	−0.999695	−	0.0247060i	$-0.992135\pi$
$83$	−13.8564	−	8.00000i	−1.52094	−	0.878114i	−0.521243	−	0.853408i	$-0.674532\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.00000	+	3.46410i	−0.643268	+	0.371391i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$			16.0000i			1.67726i
$92$		0			0
$93$	13.8564			1.43684
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$			3.00000i			0.301511i
$100$		0			0
$101$	−13.8564	−	8.00000i	−1.37876	−	0.796030i	−0.386753	−	0.922183i	$-0.626403\pi$
$101$	−13.8564	−	8.00000i	−1.37876	−	0.796030i	−0.992011	+	0.126153i	$0.959737\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	17.0000i		−	1.64345i	−0.569883	−	0.821726i	$-0.693011\pi$
$107$		−	17.0000i		−	1.64345i	0.569883	−	0.821726i	$-0.306989\pi$
$108$		0			0
$109$			16.0000i			1.53252i	0.642529	+	0.766261i	$0.277885\pi$
$109$			16.0000i			1.53252i	−0.642529	+	0.766261i	$0.722115\pi$
$110$		0			0
$111$	12.0000	+	6.92820i	1.13899	+	0.657596i
$112$		0			0
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	0.815149	−	0.579252i	$-0.196655\pi$
$113$	−1.00000	−	1.73205i	−0.0940721	−	0.162938i	−0.909221	+	0.416314i	$0.863322\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−10.3923	−	6.00000i	−0.960769	−	0.554700i
$118$		0			0
$119$	14.0000	−	24.2487i	1.28338	−	2.22288i
$120$		0			0
$121$	−5.00000	−	8.66025i	−0.454545	−	0.787296i
$122$		0			0
$123$	5.19615			0.468521
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−20.0000			−1.77471			−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000			−1.77471			−0.887357	+	0.461084i	$0.847461\pi$
$128$		0			0
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$		0			0
$133$	−17.3205	−	10.0000i	−1.50188	−	0.867110i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	0.866025	−	0.500000i	0.0734553	−	0.0424094i	−0.462822	−	0.886451i	$-0.653163\pi$
$139$	0.866025	−	0.500000i	0.0734553	−	0.0424094i	0.536278	+	0.844042i	$0.319830\pi$
$140$		0			0
$141$	3.46410	+	6.00000i	0.291730	+	0.505291i
$142$		0			0
$143$	−4.00000			−0.334497
$144$		0			0
$145$		0			0
$146$		0			0
$147$	15.5885			1.28571
$148$		0			0
$149$	10.3923	−	6.00000i	0.851371	−	0.491539i	−0.00974235	−	0.999953i	$-0.503101\pi$
$149$	10.3923	−	6.00000i	0.851371	−	0.491539i	0.861113	+	0.508413i	$0.169768\pi$
$150$		0			0
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	−0.999909	−	0.0134886i	$-0.995706\pi$
$151$	−6.00000	+	10.3923i	−0.488273	+	0.845714i	0.511636	+	0.859202i	$0.329040\pi$
$152$		0			0
$153$	10.5000	+	18.1865i	0.848875	+	1.47029i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.92820	−	4.00000i	0.552931	−	0.319235i	−0.197372	−	0.980329i	$-0.563241\pi$
$157$	6.92820	−	4.00000i	0.552931	−	0.319235i	0.750303	+	0.661094i	$0.229907\pi$
$158$		0			0
$159$	12.0000	+	6.92820i	0.951662	+	0.549442i
$160$		0			0
$161$	16.0000			1.26098
$162$		0			0
$163$			16.0000i			1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$			16.0000i			1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.0000	−	20.7846i	−0.928588	−	1.60836i	−0.785687	−	0.618624i	$-0.787690\pi$
$167$	−12.0000	−	20.7846i	−0.928588	−	1.60836i	−0.142901	−	0.989737i	$-0.545643\pi$
$168$		0			0
$169$	1.50000	−	2.59808i	0.115385	−	0.199852i
$170$		0			0
$171$	12.9904	−	7.50000i	0.993399	−	0.573539i
$172$		0			0
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	0.840002	−	0.542583i	$-0.182554\pi$
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	−0.0498898	+	0.998755i	$0.515887\pi$
$174$		0			0
$175$	−10.0000	−	17.3205i	−0.755929	−	1.30931i
$176$		0			0
$177$		−	15.5885i		−	1.17170i
$178$		0			0
$179$			16.0000i			1.19590i	0.801535	+	0.597948i	$0.204017\pi$
$179$			16.0000i			1.19590i	−0.801535	+	0.597948i	$0.795983\pi$
$180$		0			0
$181$			20.0000i			1.48659i	0.668965	+	0.743294i	$0.266738\pi$
$181$			20.0000i			1.48659i	−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	6.06218	+	3.50000i	0.443310	+	0.255945i
$188$		0			0
$189$	−10.3923	+	18.0000i	−0.755929	+	1.30931i
$190$		0			0
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	0.235983	+	0.971757i	$0.424169\pi$
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	−0.959558	+	0.281511i	$0.909164\pi$
$192$		0			0
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	0.998911	+	0.0466572i	$0.0148568\pi$
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	−0.459049	+	0.888411i	$0.651810\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			24.0000i			1.70993i	0.518686	+	0.854965i	$0.326421\pi$
$197$			24.0000i			1.70993i	−0.518686	+	0.854965i	$0.673579\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$			5.19615i			0.366508i
$202$		0			0
$203$	−13.8564	+	8.00000i	−0.972529	+	0.561490i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$		0			0
$209$	2.50000	−	4.33013i	0.172929	−	0.299521i
$210$		0			0
$211$	−13.8564	+	8.00000i	−0.953914	+	0.550743i	−0.894295	−	0.447478i	$-0.852322\pi$
$211$	−13.8564	+	8.00000i	−0.953914	+	0.550743i	−0.0596196	+	0.998221i	$0.518989\pi$
$212$		0			0
$213$	−6.92820	+	12.0000i	−0.474713	+	0.822226i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	32.0000			2.17230
$218$		0			0
$219$	2.59808	−	4.50000i	0.175562	−	0.304082i
$220$		0			0
$221$	−24.2487	+	14.0000i	−1.63114	+	0.941742i
$222$		0			0
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$		0			0
$225$	15.0000			1.00000
$226$		0			0
$227$	−16.4545	−	9.50000i	−1.09212	−	0.630537i	−0.157982	−	0.987442i	$-0.550499\pi$
$227$	−16.4545	−	9.50000i	−1.09212	−	0.630537i	−0.934141	+	0.356905i	$0.883832\pi$
$228$		0			0
$229$	17.3205	−	10.0000i	1.14457	−	0.660819i	0.197013	−	0.980401i	$-0.436876\pi$
$229$	17.3205	−	10.0000i	1.14457	−	0.660819i	0.947559	+	0.319582i	$0.103543\pi$
$230$		0			0
$231$			6.92820i			0.455842i
$232$		0			0
$233$	−19.0000			−1.24473			−0.622366	−	0.782727i	$-0.713828\pi$
$233$	−19.0000			−1.24473			−0.622366	+	0.782727i	$0.713828\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.92820	−	12.0000i	−0.450035	−	0.779484i
$238$		0			0
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$		0			0
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	0.110963	+	0.993825i	$0.464606\pi$
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	−0.916159	+	0.400815i	$0.868727\pi$
$242$		0			0
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.0000	+	17.3205i	0.636285	+	1.10208i
$248$		0			0
$249$	24.0000	−	13.8564i	1.52094	−	0.878114i
$250$		0			0
$251$			9.00000i			0.568075i	0.958813	+	0.284037i	$0.0916740\pi$
$251$			9.00000i			0.568075i	−0.958813	+	0.284037i	$0.908326\pi$
$252$		0			0
$253$			4.00000i			0.251478i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.50000	+	14.7224i	0.530215	+	0.918360i	0.999379	+	0.0352486i	$0.0112223\pi$
$257$	8.50000	+	14.7224i	0.530215	+	0.918360i	−0.469163	+	0.883112i	$0.655444\pi$
$258$		0			0
$259$	27.7128	+	16.0000i	1.72199	+	0.994192i
$260$		0			0
$261$		−	12.0000i		−	0.742781i
$262$		0			0
$263$	14.0000	−	24.2487i	0.863277	−	1.49524i	−0.00547092	−	0.999985i	$-0.501741\pi$
$263$	14.0000	−	24.2487i	0.863277	−	1.49524i	0.868748	−	0.495255i	$-0.164925\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.19615	+	9.00000i	−0.317999	+	0.550791i
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	−24.0000			−1.45790			−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000			−1.45790			−0.728948	+	0.684569i	$0.759990\pi$
$272$		0			0
$273$	−24.0000	−	13.8564i	−1.45255	−	0.838628i
$274$		0			0
$275$	4.33013	−	2.50000i	0.261116	−	0.150756i
$276$		0			0
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	0.392308	−	0.919834i	$-0.371677\pi$
$277$	−3.46410	−	2.00000i	−0.208138	−	0.120168i	−0.600446	+	0.799666i	$0.705010\pi$
$278$		0			0
$279$	−12.0000	+	20.7846i	−0.718421	+	1.24434i
$280$		0			0
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	−0.941526	−	0.336939i	$-0.890608\pi$
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	0.762561	+	0.646916i	$0.223942\pi$
$282$		0			0
$283$	−13.8564	+	8.00000i	−0.823678	+	0.475551i	−0.851683	−	0.524057i	$-0.824418\pi$
$283$	−13.8564	+	8.00000i	−0.823678	+	0.475551i	0.0280052	+	0.999608i	$0.491084\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.0000			0.708338
$288$		0			0
$289$	32.0000			1.88235
$290$		0			0
$291$	−0.866025	−	1.50000i	−0.0507673	−	0.0879316i
$292$		0			0
$293$	−10.3923	+	6.00000i	−0.607125	+	0.350524i	−0.771839	−	0.635818i	$-0.780663\pi$
$293$	−10.3923	+	6.00000i	−0.607125	+	0.350524i	0.164714	+	0.986341i	$0.447330\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$		0			0
$299$	−13.8564	−	8.00000i	−0.801337	−	0.462652i
$300$		0			0
$301$	−3.46410	+	2.00000i	−0.199667	+	0.115278i
$302$		0			0
$303$	24.0000	−	13.8564i	1.37876	−	0.796030i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	21.0000i		−	1.19853i	−0.800549	−	0.599267i	$-0.795459\pi$
$307$		−	21.0000i		−	1.19853i	0.800549	−	0.599267i	$-0.204541\pi$
$308$		0			0
$309$	−6.92820			−0.394132
$310$		0			0
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	0.917143	−	0.398559i	$-0.130489\pi$
$311$	2.00000	+	3.46410i	0.113410	+	0.196431i	−0.803733	+	0.594990i	$0.797156\pi$
$312$		0			0
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.3205	+	10.0000i	0.972817	+	0.561656i	0.900094	−	0.435696i	$-0.143498\pi$
$317$	17.3205	+	10.0000i	0.972817	+	0.561656i	0.0727229	+	0.997352i	$0.476831\pi$
$318$		0			0
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$		0			0
$321$	25.5000	+	14.7224i	1.42327	+	0.821726i
$322$		0			0
$323$		−	35.0000i		−	1.94745i
$324$		0			0
$325$			20.0000i			1.10940i
$326$		0			0
$327$	−24.0000	−	13.8564i	−1.32720	−	0.766261i
$328$		0			0
$329$	8.00000	+	13.8564i	0.441054	+	0.763928i
$330$		0			0
$331$	13.8564	+	8.00000i	0.761617	+	0.439720i	0.829876	−	0.557948i	$-0.188411\pi$
$331$	13.8564	+	8.00000i	0.761617	+	0.439720i	−0.0682590	+	0.997668i	$0.521744\pi$
$332$		0			0
$333$	−20.7846	+	12.0000i	−1.13899	+	0.657596i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	−0.988260	−	0.152784i	$-0.951176\pi$
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	0.361815	−	0.932250i	$-0.382157\pi$
$338$		0			0
$339$	3.46410			0.188144
$340$		0			0
$341$			8.00000i			0.433224i
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.79423	−	4.50000i	0.418416	−	0.241573i	−0.275983	−	0.961162i	$-0.589003\pi$
$347$	7.79423	−	4.50000i	0.418416	−	0.241573i	0.694399	+	0.719590i	$0.255670\pi$
$348$		0			0
$349$	−13.8564	−	8.00000i	−0.741716	−	0.428230i	0.0809766	−	0.996716i	$-0.474196\pi$
$349$	−13.8564	−	8.00000i	−0.741716	−	0.428230i	−0.822693	+	0.568486i	$0.807529\pi$
$350$		0			0
$351$	18.0000	−	10.3923i	0.960769	−	0.554700i
$352$		0			0
$353$	0.500000	−	0.866025i	0.0266123	−	0.0460939i	−0.852413	−	0.522870i	$-0.824861\pi$
$353$	0.500000	−	0.866025i	0.0266123	−	0.0460939i	0.879025	+	0.476776i	$0.158195\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	24.2487	+	42.0000i	1.28338	+	2.22288i
$358$		0			0
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−6.00000			−0.315789
$362$		0			0
$363$	17.3205			0.909091
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$		0			0
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$		0			0
$371$	27.7128	+	16.0000i	1.43878	+	0.830679i
$372$		0			0
$373$	3.46410	−	2.00000i	0.179364	−	0.103556i	−0.407630	−	0.913147i	$-0.633645\pi$
$373$	3.46410	−	2.00000i	0.179364	−	0.103556i	0.586994	+	0.809591i	$0.300311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.0000			0.824042
$378$		0			0
$379$		−	25.0000i		−	1.28416i	−0.766636	−	0.642082i	$-0.778071\pi$
$379$		−	25.0000i		−	1.28416i	0.766636	−	0.642082i	$-0.221929\pi$
$380$		0			0
$381$	17.3205	−	30.0000i	0.887357	−	1.53695i
$382$		0			0
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	3.00000i		−	0.152499i
$388$		0			0
$389$	3.46410	+	2.00000i	0.175637	+	0.101404i	0.585241	−	0.810859i	$-0.301000\pi$
$389$	3.46410	+	2.00000i	0.175637	+	0.101404i	−0.409604	+	0.912263i	$0.634333\pi$
$390$		0			0
$391$	14.0000	+	24.2487i	0.708010	+	1.22631i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	8.00000i		−	0.401508i	−0.979642	−	0.200754i	$-0.935661\pi$
$397$		−	8.00000i		−	0.401508i	0.979642	−	0.200754i	$-0.0643393\pi$
$398$		0			0
$399$	30.0000	−	17.3205i	1.50188	−	0.867110i
$400$		0			0
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	−0.988691	−	0.149966i	$-0.952083\pi$
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	0.364471	−	0.931215i	$-0.381250\pi$
$402$		0			0
$403$	−27.7128	−	16.0000i	−1.38047	−	0.797017i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$		0			0
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$		0			0
$411$	−2.59808	−	4.50000i	−0.128154	−	0.221969i
$412$		0			0
$413$		−	36.0000i		−	1.77144i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			1.73205i			0.0848189i
$418$		0			0
$419$	−13.8564	+	8.00000i	−0.676930	+	0.390826i	−0.798697	−	0.601733i	$-0.794477\pi$
$419$	−13.8564	+	8.00000i	−0.676930	+	0.390826i	0.121768	+	0.992559i	$0.461144\pi$
$420$		0			0
$421$	6.92820	+	4.00000i	0.337660	+	0.194948i	0.659237	−	0.751935i	$-0.270879\pi$
$421$	6.92820	+	4.00000i	0.337660	+	0.194948i	−0.321577	+	0.946883i	$0.604213\pi$
$422$		0			0
$423$	−12.0000			−0.583460
$424$		0			0
$425$	17.5000	−	30.3109i	0.848875	−	1.47029i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.46410	−	6.00000i	0.167248	−	0.289683i
$430$		0			0
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$		0			0
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.3205	−	10.0000i	0.828552	−	0.478365i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−13.5000	+	23.3827i	−0.642857	+	1.11346i
$442$		0			0
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	0.673596	−	0.739100i	$-0.264749\pi$
$443$	7.79423	+	4.50000i	0.370315	+	0.213801i	−0.303281	+	0.952901i	$0.598082\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			20.7846i			0.983078i
$448$		0			0
$449$	1.00000			0.0471929			0.0235965	−	0.999722i	$-0.492488\pi$
$449$	1.00000			0.0471929			0.0235965	+	0.999722i	$0.492488\pi$
$450$		0			0
$451$			3.00000i			0.141264i
$452$		0			0
$453$	−10.3923	−	18.0000i	−0.488273	−	0.845714i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.50000	+	16.4545i	−0.444391	+	0.769708i	−0.998010	−	0.0630623i	$-0.979913\pi$
$457$	−9.50000	+	16.4545i	−0.444391	+	0.769708i	0.553618	+	0.832771i	$0.313247\pi$
$458$		0			0
$459$	−36.3731			−1.69775
$460$		0			0
$461$	−31.1769	−	18.0000i	−1.45205	−	0.838344i	−0.453456	−	0.891279i	$-0.649809\pi$
$461$	−31.1769	−	18.0000i	−1.45205	−	0.838344i	−0.998598	+	0.0529352i	$0.983142\pi$
$462$		0			0
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	0.757982	−	0.652275i	$-0.226185\pi$
$463$	−4.00000	−	6.92820i	−0.185896	−	0.321981i	−0.943878	+	0.330294i	$0.892852\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			27.0000i			1.24941i	0.780860	+	0.624705i	$0.214781\pi$
$467$			27.0000i			1.24941i	−0.780860	+	0.624705i	$0.785219\pi$
$468$		0			0
$469$			12.0000i			0.554109i
$470$		0			0
$471$			13.8564i			0.638470i
$472$		0			0
$473$	−0.500000	−	0.866025i	−0.0229900	−	0.0398199i
$474$		0			0
$475$	−21.6506	−	12.5000i	−0.993399	−	0.573539i
$476$		0			0
$477$	−20.7846	+	12.0000i	−0.951662	+	0.549442i
$478$		0			0
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$		0			0
$481$	−16.0000	−	27.7128i	−0.729537	−	1.26360i
$482$		0			0
$483$	−13.8564	+	24.0000i	−0.630488	+	1.09204i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$		0			0
$489$	−24.0000	−	13.8564i	−1.08532	−	0.626608i
$490$		0			0
$491$	28.5788	−	16.5000i	1.28974	−	0.744635i	0.311136	−	0.950365i	$-0.399290\pi$
$491$	28.5788	−	16.5000i	1.28974	−	0.744635i	0.978609	+	0.205731i	$0.0659571\pi$
$492$		0			0
$493$	−24.2487	−	14.0000i	−1.09211	−	0.630528i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.0000	+	27.7128i	−0.717698	+	1.24309i
$498$		0			0
$499$	4.33013	−	2.50000i	0.193843	−	0.111915i	−0.399937	−	0.916542i	$-0.630968\pi$
$499$	4.33013	−	2.50000i	0.193843	−	0.111915i	0.593780	+	0.804627i	$0.297635\pi$
$500$		0			0
$501$	41.5692			1.85718
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.59808	+	4.50000i	0.115385	+	0.199852i
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$	6.00000	−	10.3923i	0.265424	−	0.459728i
$512$		0			0
$513$			25.9808i			1.14708i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.46410	+	2.00000i	−0.152351	+	0.0879599i
$518$		0			0
$519$	−18.0000	+	10.3923i	−0.790112	+	0.456172i
$520$		0			0
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$			16.0000i			0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$			16.0000i			0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$		0			0
$525$	34.6410			1.51186
$526$		0			0
$527$	28.0000	+	48.4974i	1.21970	+	2.11258i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	23.3827	+	13.5000i	1.01472	+	0.585850i
$532$		0			0
$533$	−10.3923	−	6.00000i	−0.450141	−	0.259889i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−24.0000	−	13.8564i	−1.03568	−	0.597948i
$538$		0			0
$539$			9.00000i			0.387657i
$540$		0			0
$541$			8.00000i			0.343947i	0.985102	+	0.171973i	$0.0550143\pi$
$541$			8.00000i			0.343947i	−0.985102	+	0.171973i	$0.944986\pi$
$542$		0			0
$543$	−30.0000	−	17.3205i	−1.28742	−	0.743294i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	2.59808	+	1.50000i	0.111086	+	0.0641354i	0.554513	−	0.832175i	$-0.312904\pi$
$547$	2.59808	+	1.50000i	0.111086	+	0.0641354i	−0.443428	+	0.896310i	$0.646238\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.0000	+	17.3205i	−0.426014	+	0.737878i
$552$		0			0
$553$	−16.0000	−	27.7128i	−0.680389	−	1.17847i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$	−10.5000	+	6.06218i	−0.443310	+	0.255945i
$562$		0			0
$563$	−18.1865	+	10.5000i	−0.766471	+	0.442522i	−0.831614	−	0.555354i	$-0.812583\pi$
$563$	−18.1865	+	10.5000i	−0.766471	+	0.442522i	0.0651433	+	0.997876i	$0.479250\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−18.0000	−	31.1769i	−0.755929	−	1.30931i
$568$		0			0
$569$	−5.50000	+	9.52628i	−0.230572	+	0.399362i	−0.957977	−	0.286846i	$-0.907393\pi$
$569$	−5.50000	+	9.52628i	−0.230572	+	0.399362i	0.727405	+	0.686209i	$0.240726\pi$
$570$		0			0
$571$	19.9186	−	11.5000i	0.833567	−	0.481260i	−0.0215055	−	0.999769i	$-0.506846\pi$
$571$	19.9186	−	11.5000i	0.833567	−	0.481260i	0.855072	+	0.518509i	$0.173513\pi$
$572$		0			0
$573$	−17.3205	−	30.0000i	−0.723575	−	1.25327i
$574$		0			0
$575$	20.0000			0.834058
$576$		0			0
$577$	15.0000			0.624458			0.312229	−	0.950007i	$-0.398924\pi$
$577$	15.0000			0.624458			0.312229	+	0.950007i	$0.398924\pi$
$578$		0			0
$579$	−25.9808			−1.07972
$580$		0			0
$581$	55.4256	−	32.0000i	2.29944	−	1.32758i
$582$		0			0
$583$	−4.00000	+	6.92820i	−0.165663	+	0.286937i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.7224	+	8.50000i	0.607660	+	0.350833i	0.772049	−	0.635563i	$-0.219232\pi$
$587$	14.7224	+	8.50000i	0.607660	+	0.350833i	−0.164389	+	0.986396i	$0.552565\pi$
$588$		0			0
$589$	34.6410	−	20.0000i	1.42736	−	0.824086i
$590$		0			0
$591$	−36.0000	−	20.7846i	−1.48084	−	0.854965i
$592$		0			0
$593$	−30.0000			−1.23195			−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.46410	−	6.00000i	0.141776	−	0.245564i
$598$		0			0
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$		0			0
$603$	−7.79423	−	4.50000i	−0.317406	−	0.183254i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$		0			0
$609$		−	27.7128i		−	1.12298i
$610$		0			0
$611$		−	16.0000i		−	0.647291i
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.50000	−	11.2583i	−0.261680	−	0.453243i	0.705008	−	0.709199i	$-0.250943\pi$
$617$	−6.50000	−	11.2583i	−0.261680	−	0.453243i	−0.966689	+	0.255956i	$0.917610\pi$
$618$		0			0
$619$	14.7224	+	8.50000i	0.591744	+	0.341644i	0.765787	−	0.643094i	$-0.222350\pi$
$619$	14.7224	+	8.50000i	0.591744	+	0.341644i	−0.174042	+	0.984738i	$0.555683\pi$
$620$		0			0
$621$	−10.3923	−	18.0000i	−0.417029	−	0.722315i
$622$		0			0
$623$	−12.0000	+	20.7846i	−0.480770	+	0.832718i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$	4.33013	+	7.50000i	0.172929	+	0.299521i
$628$		0			0
$629$			56.0000i			2.23287i
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$		0			0
$633$		−	27.7128i		−	1.10149i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−31.1769	−	18.0000i	−1.23527	−	0.713186i
$638$		0			0
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$		0			0
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	−0.679039	−	0.734103i	$-0.737603\pi$
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	0.975271	+	0.221013i	$0.0709364\pi$
$642$		0			0
$643$	38.9711	−	22.5000i	1.53687	−	0.887313i	0.537852	−	0.843039i	$-0.319236\pi$
$643$	38.9711	−	22.5000i	1.53687	−	0.887313i	0.999019	−	0.0442744i	$-0.0140976\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$		0			0
$649$	9.00000			0.353281
$650$		0			0
$651$	−27.7128	+	48.0000i	−1.08615	+	1.88127i
$652$		0			0
$653$	−24.2487	+	14.0000i	−0.948925	+	0.547862i	−0.892747	−	0.450558i	$-0.851225\pi$
$653$	−24.2487	+	14.0000i	−0.948925	+	0.547862i	−0.0561784	+	0.998421i	$0.517892\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	4.50000	+	7.79423i	0.175562	+	0.304082i
$658$		0			0
$659$	41.5692	+	24.0000i	1.61931	+	0.934907i	0.987099	+	0.160108i	$0.0511843\pi$
$659$	41.5692	+	24.0000i	1.61931	+	0.934907i	0.632207	+	0.774799i	$0.282149\pi$
$660$		0			0
$661$	34.6410	−	20.0000i	1.34738	−	0.777910i	0.359502	−	0.933144i	$-0.382947\pi$
$661$	34.6410	−	20.0000i	1.34738	−	0.777910i	0.987878	+	0.155235i	$0.0496133\pi$
$662$		0			0
$663$		−	48.4974i		−	1.88348i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	16.0000i		−	0.619522i
$668$		0			0
$669$	3.46410	+	6.00000i	0.133930	+	0.231973i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$		0			0
$675$	−12.9904	+	22.5000i	−0.500000	+	0.866025i
$676$		0			0
$677$	−6.92820	−	4.00000i	−0.266272	−	0.153732i	0.360920	−	0.932597i	$-0.382463\pi$
$677$	−6.92820	−	4.00000i	−0.266272	−	0.153732i	−0.627192	+	0.778864i	$0.715796\pi$
$678$		0			0
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$		0			0
$681$	28.5000	−	16.4545i	1.09212	−	0.630537i
$682$		0			0
$683$			31.0000i			1.18618i	0.805135	+	0.593091i	$0.202093\pi$
$683$			31.0000i			1.18618i	−0.805135	+	0.593091i	$0.797907\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			34.6410i			1.32164i
$688$		0			0
$689$	−16.0000	−	27.7128i	−0.609551	−	1.05577i
$690$		0			0
$691$	−27.7128	−	16.0000i	−1.05425	−	0.608669i	−0.130410	−	0.991460i	$-0.541629\pi$
$691$	−27.7128	−	16.0000i	−1.05425	−	0.608669i	−0.923835	+	0.382791i	$0.874963\pi$
$692$		0			0
$693$	−10.3923	−	6.00000i	−0.394771	−	0.227921i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.5000	+	18.1865i	0.397716	+	0.688864i
$698$		0			0
$699$	16.4545	−	28.5000i	0.622366	−	1.07797i
$700$		0			0
$701$		−	20.0000i		−	0.755390i	−0.925930	−	0.377695i	$-0.876717\pi$
$701$		−	20.0000i		−	0.755390i	0.925930	−	0.377695i	$-0.123283\pi$
$702$		0			0
$703$	40.0000			1.50863
$704$		0			0
$705$		0			0
$706$		0			0
$707$	55.4256	−	32.0000i	2.08450	−	1.20348i
$708$		0			0
$709$	6.92820	+	4.00000i	0.260194	+	0.150223i	0.624423	−	0.781086i	$-0.285334\pi$
$709$	6.92820	+	4.00000i	0.260194	+	0.150223i	−0.364229	+	0.931309i	$0.618667\pi$
$710$		0			0
$711$	24.0000			0.900070
$712$		0			0
$713$	−16.0000	+	27.7128i	−0.599205	+	1.03785i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20.7846			−0.776215
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	−16.0000			−0.595871
$722$		0			0
$723$	−21.6506	−	37.5000i	−0.805196	−	1.39464i
$724$		0			0
$725$	−17.3205	+	10.0000i	−0.643268	+	0.371391i
$726$		0			0
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	−0.480519	−	0.876984i	$-0.659552\pi$
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	0.999750	−	0.0223506i	$-0.00711500\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−6.06218	−	3.50000i	−0.224218	−	0.129452i
$732$		0			0
$733$	38.1051	−	22.0000i	1.40744	−	0.812589i	0.412303	−	0.911047i	$-0.364724\pi$
$733$	38.1051	−	22.0000i	1.40744	−	0.812589i	0.995141	+	0.0984580i	$0.0313910\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.00000			−0.110506
$738$		0			0
$739$		−	35.0000i		−	1.28750i	−0.765238	−	0.643748i	$-0.777379\pi$
$739$		−	35.0000i		−	1.28750i	0.765238	−	0.643748i	$-0.222621\pi$
$740$		0			0
$741$	−34.6410			−1.27257
$742$		0			0
$743$	10.0000	+	17.3205i	0.366864	+	0.635428i	0.989073	−	0.147423i	$-0.0470980\pi$
$743$	10.0000	+	17.3205i	0.366864	+	0.635428i	−0.622209	+	0.782851i	$0.713765\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			48.0000i			1.75623i
$748$		0			0
$749$	58.8897	+	34.0000i	2.15178	+	1.24233i
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$		0			0
$753$	−13.5000	−	7.79423i	−0.491967	−	0.284037i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	36.0000i		−	1.30844i	−0.756303	−	0.654221i	$-0.772997\pi$
$757$		−	36.0000i		−	1.30844i	0.756303	−	0.654221i	$-0.227003\pi$
$758$		0			0
$759$	−6.00000	−	3.46410i	−0.217786	−	0.125739i
$760$		0			0
$761$	−13.0000	−	22.5167i	−0.471250	−	0.816228i	0.528209	−	0.849114i	$-0.322864\pi$
$761$	−13.0000	−	22.5167i	−0.471250	−	0.816228i	−0.999459	+	0.0328858i	$0.989530\pi$
$762$		0			0
$763$	−55.4256	−	32.0000i	−2.00654	−	1.15848i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.0000	+	31.1769i	−0.649942	+	1.12573i
$768$		0			0
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$	−29.4449			−1.06043
$772$		0			0
$773$		−	4.00000i		−	0.143870i	−0.997409	−	0.0719350i	$-0.977083\pi$
$773$		−	4.00000i		−	0.143870i	0.997409	−	0.0719350i	$-0.0229174\pi$
$774$		0			0
$775$	40.0000			1.43684
$776$		0			0
$777$	−48.0000	+	27.7128i	−1.72199	+	0.994192i
$778$		0			0
$779$	12.9904	−	7.50000i	0.465429	−	0.268715i
$780$		0			0
$781$	−6.92820	−	4.00000i	−0.247911	−	0.143131i
$782$		0			0
$783$	18.0000	+	10.3923i	0.643268	+	0.371391i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−41.5692	+	24.0000i	−1.48178	+	0.855508i	−0.999786	−	0.0206657i	$-0.993421\pi$
$787$	−41.5692	+	24.0000i	−1.48178	+	0.855508i	−0.481996	+	0.876173i	$0.660088\pi$
$788$		0			0
$789$	24.2487	+	42.0000i	0.863277	+	1.49524i
$790$		0			0
$791$	8.00000			0.284447
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.92820	+	4.00000i	−0.245410	+	0.141687i	−0.617661	−	0.786445i	$-0.711919\pi$
$797$	−6.92820	+	4.00000i	−0.245410	+	0.141687i	0.372251	+	0.928132i	$0.378586\pi$
$798$		0			0
$799$	−14.0000	+	24.2487i	−0.495284	+	0.857858i
$800$		0			0
$801$	−9.00000	−	15.5885i	−0.317999	−	0.550791i
$802$		0			0
$803$	2.59808	+	1.50000i	0.0916841	+	0.0529339i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−29.0000			−1.01959			−0.509793	−	0.860297i	$-0.670278\pi$
$809$	−29.0000			−1.01959			−0.509793	+	0.860297i	$0.670278\pi$
$810$		0			0
$811$		−	31.0000i		−	1.08856i	−0.838905	−	0.544279i	$-0.816803\pi$
$811$		−	31.0000i		−	1.08856i	0.838905	−	0.544279i	$-0.183197\pi$
$812$		0			0
$813$	20.7846	−	36.0000i	0.728948	−	1.26258i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.50000	+	4.33013i	−0.0874639	+	0.151492i
$818$		0			0
$819$	41.5692	−	24.0000i	1.45255	−	0.838628i
$820$		0			0
$821$	−31.1769	−	18.0000i	−1.08808	−	0.628204i	−0.155017	−	0.987912i	$-0.549543\pi$
$821$	−31.1769	−	18.0000i	−1.08808	−	0.628204i	−0.933065	+	0.359708i	$0.882876\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$			8.66025i			0.301511i
$826$		0			0
$827$			16.0000i			0.556375i	0.960527	+	0.278187i	$0.0897336\pi$
$827$			16.0000i			0.556375i	−0.960527	+	0.278187i	$0.910266\pi$
$828$		0			0
$829$			28.0000i			0.972480i	0.873825	+	0.486240i	$0.161632\pi$
$829$			28.0000i			0.972480i	−0.873825	+	0.486240i	$0.838368\pi$
$830$		0			0
$831$	6.00000	−	3.46410i	0.208138	−	0.120168i
$832$		0			0
$833$	31.5000	+	54.5596i	1.09141	+	1.89038i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−20.7846	−	36.0000i	−0.718421	−	1.24434i
$838$		0			0
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	−0.995353	−	0.0962912i	$-0.969302\pi$
$839$	−12.0000	+	20.7846i	−0.414286	+	0.717564i	0.581067	+	0.813856i	$0.302635\pi$
$840$		0			0
$841$	−6.50000	−	11.2583i	−0.224138	−	0.388218i
$842$		0			0
$843$	−5.19615	−	9.00000i	−0.178965	−	0.309976i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	40.0000			1.37442
$848$		0			0
$849$		−	27.7128i		−	0.951101i
$850$		0			0
$851$	−27.7128	+	16.0000i	−0.949983	+	0.548473i
$852$		0			0
$853$	−24.2487	−	14.0000i	−0.830260	−	0.479351i	0.0236816	−	0.999720i	$-0.492461\pi$
$853$	−24.2487	−	14.0000i	−0.830260	−	0.479351i	−0.853942	+	0.520369i	$0.825795\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	−0.938699	−	0.344739i	$-0.887967\pi$
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	0.767902	+	0.640567i	$0.221301\pi$
$858$		0			0
$859$	6.06218	−	3.50000i	0.206839	−	0.119418i	−0.393003	−	0.919537i	$-0.628564\pi$
$859$	6.06218	−	3.50000i	0.206839	−	0.119418i	0.599841	+	0.800119i	$0.295230\pi$
$860$		0			0
$861$	−10.3923	+	18.0000i	−0.354169	+	0.613438i
$862$		0			0
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−27.7128	+	48.0000i	−0.941176	+	1.63017i
$868$		0			0
$869$	6.92820	−	4.00000i	0.235023	−	0.135691i
$870$		0			0
$871$	6.00000	−	10.3923i	0.203302	−	0.352130i
$872$		0			0
$873$	3.00000			0.101535
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.888640	−	0.458606i	$-0.848349\pi$
$877$	−27.7128	+	16.0000i	−0.935795	+	0.540282i	−0.0471555	+	0.998888i	$0.515016\pi$
$878$		0			0
$879$		−	20.7846i		−	0.701047i
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$		−	5.00000i		−	0.168263i	−0.996455	−	0.0841317i	$-0.973188\pi$
$883$		−	5.00000i		−	0.168263i	0.996455	−	0.0841317i	$-0.0268116\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$		0			0
$889$	40.0000	−	69.2820i	1.34156	−	2.32364i
$890$		0			0
$891$	7.79423	−	4.50000i	0.261116	−	0.150756i
$892$		0			0
$893$	17.3205	+	10.0000i	0.579609	+	0.334637i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	24.0000	−	13.8564i	0.801337	−	0.462652i
$898$		0			0
$899$		−	32.0000i		−	1.06726i
$900$		0			0
$901$			56.0000i			1.86563i
$902$		0			0
$903$		−	6.92820i		−	0.230556i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−14.7224	−	8.50000i	−0.488850	−	0.282238i	0.235247	−	0.971936i	$-0.424410\pi$
$907$	−14.7224	−	8.50000i	−0.488850	−	0.282238i	−0.724097	+	0.689698i	$0.757743\pi$
$908$		0			0
$909$			48.0000i			1.59206i
$910$		0			0
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	−0.127585	−	0.991828i	$-0.540723\pi$
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	0.922740	−	0.385422i	$-0.125944\pi$
$912$		0			0
$913$	8.00000	+	13.8564i	0.264761	+	0.458580i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	12.0000			0.395843			0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000			0.395843			0.197922	+	0.980218i	$0.436581\pi$
$920$		0			0
$921$	31.5000	+	18.1865i	1.03796	+	0.599267i
$922$		0			0
$923$	27.7128	−	16.0000i	0.912178	−	0.526646i
$924$		0			0
$925$	34.6410	+	20.0000i	1.13899	+	0.657596i
$926$		0			0
$927$	6.00000	−	10.3923i	0.197066	−	0.341328i
$928$		0			0
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	−0.0852924	−	0.996356i	$-0.527182\pi$
$929$	25.0000	−	43.3013i	0.820223	−	1.42067i	0.905516	−	0.424313i	$-0.139484\pi$
$930$		0			0
$931$	38.9711	−	22.5000i	1.27723	−	0.737408i
$932$		0			0
$933$	−6.92820			−0.226819
$934$		0			0
$935$		0			0
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	−9.52628	−	16.5000i	−0.310878	−	0.538457i
$940$		0			0
$941$	−34.6410	+	20.0000i	−1.12926	+	0.651981i	−0.943750	−	0.330660i	$-0.892729\pi$
$941$	−34.6410	+	20.0000i	−1.12926	+	0.651981i	−0.185515	+	0.982641i	$0.559395\pi$
$942$		0			0
$943$	−6.00000	+	10.3923i	−0.195387	+	0.338420i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.3827	+	13.5000i	0.759835	+	0.438691i	0.829237	−	0.558898i	$-0.188776\pi$
$947$	23.3827	+	13.5000i	0.759835	+	0.438691i	−0.0694014	+	0.997589i	$0.522109\pi$
$948$		0			0
$949$	−10.3923	+	6.00000i	−0.337348	+	0.194768i
$950$		0			0
$951$	−30.0000	+	17.3205i	−0.972817	+	0.561656i
$952$		0			0
$953$	27.0000			0.874616			0.437308	−	0.899312i	$-0.355932\pi$
$953$	27.0000			0.874616			0.437308	+	0.899312i	$0.355932\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.92820			0.223957
$958$		0			0
$959$	−6.00000	−	10.3923i	−0.193750	−	0.335585i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		0			0
$963$	−44.1673	+	25.5000i	−1.42327	+	0.821726i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−18.0000	−	31.1769i	−0.578841	−	1.00258i	−0.995613	−	0.0935708i	$-0.970172\pi$
$967$	−18.0000	−	31.1769i	−0.578841	−	1.00258i	0.416772	−	0.909011i	$-0.363161\pi$
$968$		0			0
$969$	52.5000	+	30.3109i	1.68654	+	0.973726i
$970$		0			0
$971$		−	16.0000i		−	0.513464i	−0.966483	−	0.256732i	$-0.917354\pi$
$971$		−	16.0000i		−	0.513464i	0.966483	−	0.256732i	$-0.0826458\pi$
$972$		0			0
$973$			4.00000i			0.128234i
$974$		0			0
$975$	−30.0000	−	17.3205i	−0.960769	−	0.554700i
$976$		0			0
$977$	19.5000	+	33.7750i	0.623860	+	1.08056i	0.988760	+	0.149511i	$0.0477699\pi$
$977$	19.5000	+	33.7750i	0.623860	+	1.08056i	−0.364900	+	0.931047i	$0.618897\pi$
$978$		0			0
$979$	−5.19615	−	3.00000i	−0.166070	−	0.0958804i
$980$		0			0
$981$	41.5692	−	24.0000i	1.32720	−	0.766261i
$982$		0			0
$983$	−8.00000	+	13.8564i	−0.255160	+	0.441951i	−0.964939	−	0.262474i	$-0.915462\pi$
$983$	−8.00000	+	13.8564i	−0.255160	+	0.441951i	0.709779	+	0.704425i	$0.248795\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−27.7128			−0.882109
$988$		0			0
$989$		−	4.00000i		−	0.127193i
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$	−24.0000	+	13.8564i	−0.761617	+	0.439720i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.92820	+	4.00000i	0.219418	+	0.126681i	0.605681	−	0.795708i	$-0.292901\pi$
$997$	6.92820	+	4.00000i	0.219418	+	0.126681i	−0.386263	+	0.922389i	$0.626234\pi$
$998$		0			0
$999$		−	41.5692i		−	1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.r.b.961.1	yes	4
3.2	odd	2		3456.2.r.a.2881.2		4
4.3	odd	2		1152.2.r.c.961.2	yes	4
8.3	odd	2		1152.2.r.c.961.1	yes	4
8.5	even	2	inner	1152.2.r.b.961.2	yes	4
9.4	even	3	inner	1152.2.r.b.193.2	yes	4
9.5	odd	6		3456.2.r.a.577.1		4
12.11	even	2		3456.2.r.d.2881.1		4
24.5	odd	2		3456.2.r.a.2881.1		4
24.11	even	2		3456.2.r.d.2881.2		4
36.23	even	6		3456.2.r.d.577.2		4
36.31	odd	6		1152.2.r.c.193.1	yes	4
72.5	odd	6		3456.2.r.a.577.2		4
72.13	even	6	inner	1152.2.r.b.193.1	✓	4
72.59	even	6		3456.2.r.d.577.1		4
72.67	odd	6		1152.2.r.c.193.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.r.b.193.1	✓	4	72.13	even	6	inner
1152.2.r.b.193.2	yes	4	9.4	even	3	inner
1152.2.r.b.961.1	yes	4	1.1	even	1	trivial
1152.2.r.b.961.2	yes	4	8.5	even	2	inner
1152.2.r.c.193.1	yes	4	36.31	odd	6
1152.2.r.c.193.2	yes	4	72.67	odd	6
1152.2.r.c.961.1	yes	4	8.3	odd	2
1152.2.r.c.961.2	yes	4	4.3	odd	2
3456.2.r.a.577.1		4	9.5	odd	6
3456.2.r.a.577.2		4	72.5	odd	6
3456.2.r.a.2881.1		4	24.5	odd	2
3456.2.r.a.2881.2		4	3.2	odd	2
3456.2.r.d.577.1		4	72.59	even	6
3456.2.r.d.577.2		4	36.23	even	6
3456.2.r.d.2881.1		4	12.11	even	2
3456.2.r.d.2881.2		4	24.11	even	2

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.50000i) q^{3} +(-2.00000 + 3.46410i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(3.46410 - 2.00000i) q^{13} -7.00000 q^{17} +5.00000i q^{19} +(-3.46410 - 6.00000i) q^{21} +(-2.00000 - 3.46410i) q^{23} +(-2.50000 + 4.33013i) q^{25} +5.19615 q^{27} +(3.46410 + 2.00000i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(1.50000 - 0.866025i) q^{33} -8.00000i q^{37} +6.92820i q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.866025 + 0.500000i) q^{43} +(2.00000 - 3.46410i) q^{47} +(-4.50000 - 7.79423i) q^{49} +(6.06218 - 10.5000i) q^{51} -8.00000i q^{53} +(-7.50000 - 4.33013i) q^{57} +(-7.79423 + 4.50000i) q^{59} +12.0000 q^{63} +(2.59808 - 1.50000i) q^{67} +6.92820 q^{69} +8.00000 q^{71} -3.00000 q^{73} +(-4.33013 - 7.50000i) q^{75} +(3.46410 - 2.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-13.8564 - 8.00000i) q^{83} +(-6.00000 + 3.46410i) q^{87} +6.00000 q^{89} +16.0000i q^{91} +13.8564 q^{93} +(-0.500000 + 0.866025i) q^{97} +3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{7} - 6 q^{9} - 28 q^{17} - 8 q^{23} - 10 q^{25} - 16 q^{31} + 6 q^{33} - 6 q^{41} + 8 q^{47} - 18 q^{49} - 30 q^{57} + 48 q^{63} + 32 q^{71} - 12 q^{73} - 16 q^{79} - 18 q^{81} - 24 q^{87} + 24 q^{89}+ \cdots - 2 q^{97}+O(q^{100}) \) 4 * q - 8 * q^7 - 6 * q^9 - 28 * q^17 - 8 * q^23 - 10 * q^25 - 16 * q^31 + 6 * q^33 - 6 * q^41 + 8 * q^47 - 18 * q^49 - 30 * q^57 + 48 * q^63 + 32 * q^71 - 12 * q^73 - 16 * q^79 - 18 * q^81 - 24 * q^87 + 24 * q^89 - 2 * q^97

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