LMFDB - Embedded newform 3024.2.df.d.1601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(17,3024)]

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, 5, 1]))

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

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

chi := DirichletCharacter("3024.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.1
Root			$-0.213160 - 1.71888i$ of defining polynomial
Character	$\chi$	$=$	3024.1601
Dual form			3024.2.df.d.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.86804 q^{5} +(1.83240 + 1.90848i) q^{7} +O(q^{10})$	$q-2.86804 q^{5} +(1.83240 + 1.90848i) q^{7} -2.71286i q^{11} +(3.18987 - 1.84167i) q^{13} +(3.22192 + 5.58052i) q^{17} +(-2.73867 - 1.58117i) q^{19} -2.99146i q^{23} +3.22563 q^{25} +(2.48332 + 1.43375i) q^{29} +(-8.26739 - 4.77318i) q^{31} +(-5.25540 - 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(-0.794538 - 1.37618i) q^{41} +(4.67828 - 8.10302i) q^{43} +(5.65372 + 9.79254i) q^{47} +(-0.284592 + 6.99421i) q^{49} +(2.16419 - 1.24950i) q^{53} +7.78058i q^{55} +(-4.33680 + 7.51156i) q^{59} +(-0.566915 + 0.327308i) q^{61} +(-9.14867 + 5.28199i) q^{65} +(3.86146 - 6.68825i) q^{67} -7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(5.17744 - 4.97106i) q^{77} +(2.59566 + 4.49581i) q^{79} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(3.14826 - 5.45295i) q^{89} +(9.35993 + 2.71312i) q^{91} +(7.85460 + 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7}+O(q^{10}) $ 16 * q + q^7	$ 16 q + q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + 15 q^{35} + q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 13 q^{49} - 15 q^{59} + 3 q^{61} + 39 q^{65} + 7 q^{67} + 45 q^{77} + q^{79} + 6 q^{85} + 21 q^{89} - 9 q^{91} + 6 q^{95} + 3 q^{97}+O(q^{100}) $ 16 * q + q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + 15 * q^35 + q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 13 * q^49 - 15 * q^59 + 3 * q^61 + 39 * q^65 + 7 * q^67 + 45 * q^77 + q^79 + 6 * q^85 + 21 * q^89 - 9 * q^91 + 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	−2.86804			−1.28262			−0.641312	−	0.767280i	$-0.721610\pi$
$5$	−2.86804			−1.28262			−0.641312	+	0.767280i	$0.721610\pi$
$6$		0			0
$7$	1.83240	+	1.90848i	0.692584	+	0.721338i
$7$	1.83240	+	1.90848i	0.692584	+	0.721338i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	2.71286i		−	0.817958i	−0.912544	−	0.408979i	$-0.865885\pi$
$11$		−	2.71286i		−	0.817958i	0.912544	−	0.408979i	$-0.134115\pi$
$12$		0			0
$13$	3.18987	−	1.84167i	0.884712	−	0.510789i	0.0125026	−	0.999922i	$-0.496020\pi$
$13$	3.18987	−	1.84167i	0.884712	−	0.510789i	0.872209	+	0.489133i	$0.162687\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.22192	+	5.58052i	0.781429	+	1.35348i	0.931109	+	0.364741i	$0.118842\pi$
$17$	3.22192	+	5.58052i	0.781429	+	1.35348i	−0.149680	+	0.988735i	$0.547824\pi$
$18$		0			0
$19$	−2.73867	−	1.58117i	−0.628294	−	0.362746i	0.151797	−	0.988412i	$-0.451494\pi$
$19$	−2.73867	−	1.58117i	−0.628294	−	0.362746i	−0.780091	+	0.625666i	$0.784827\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	2.99146i		−	0.623763i	−0.950121	−	0.311882i	$-0.899041\pi$
$23$		−	2.99146i		−	0.623763i	0.950121	−	0.311882i	$-0.100959\pi$
$24$		0			0
$25$	3.22563			0.645126
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.48332	+	1.43375i	0.461142	+	0.266240i	0.712524	−	0.701648i	$-0.247552\pi$
$29$	2.48332	+	1.43375i	0.461142	+	0.266240i	−0.251383	+	0.967888i	$0.580885\pi$
$30$		0			0
$31$	−8.26739	−	4.77318i	−1.48487	−	0.857289i	−0.485016	−	0.874506i	$-0.661186\pi$
$31$	−8.26739	−	4.77318i	−1.48487	−	0.857289i	−0.999852	+	0.0172169i	$0.994519\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.25540	−	5.47359i	−0.888325	−	0.925205i
$36$		0			0
$37$	−1.70640	+	2.95556i	−0.280530	+	0.485892i	−0.971515	−	0.236977i	$-0.923843\pi$
$37$	−1.70640	+	2.95556i	−0.280530	+	0.485892i	0.690986	+	0.722868i	$0.257177\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.794538	−	1.37618i	−0.124086	−	0.214923i	0.797289	−	0.603597i	$-0.206267\pi$
$41$	−0.794538	−	1.37618i	−0.124086	−	0.214923i	−0.921375	+	0.388674i	$0.872933\pi$
$42$		0			0
$43$	4.67828	−	8.10302i	0.713431	−	1.23570i	−0.250131	−	0.968212i	$-0.580474\pi$
$43$	4.67828	−	8.10302i	0.713431	−	1.23570i	0.963562	−	0.267487i	$-0.0861931\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.65372	+	9.79254i	0.824680	+	1.42839i	0.902163	+	0.431394i	$0.141978\pi$
$47$	5.65372	+	9.79254i	0.824680	+	1.42839i	−0.0774831	+	0.996994i	$0.524688\pi$
$48$		0			0
$49$	−0.284592	+	6.99421i	−0.0406560	+	0.999173i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.16419	−	1.24950i	0.297275	−	0.171632i	−0.343943	−	0.938990i	$-0.611763\pi$
$53$	2.16419	−	1.24950i	0.297275	−	0.171632i	0.641218	+	0.767359i	$0.278429\pi$
$54$		0			0
$55$			7.78058i			1.04913i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.33680	+	7.51156i	−0.564604	+	0.977922i	0.432483	+	0.901642i	$0.357638\pi$
$59$	−4.33680	+	7.51156i	−0.564604	+	0.977922i	−0.997086	+	0.0762801i	$0.975696\pi$
$60$		0			0
$61$	−0.566915	+	0.327308i	−0.0725860	+	0.0419075i	−0.535854	−	0.844311i	$-0.680010\pi$
$61$	−0.566915	+	0.327308i	−0.0725860	+	0.0419075i	0.463268	+	0.886218i	$0.346677\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.14867	+	5.28199i	−1.13475	+	0.655150i
$66$		0			0
$67$	3.86146	−	6.68825i	0.471752	−	0.817099i	−0.527725	−	0.849415i	$-0.676955\pi$
$67$	3.86146	−	6.68825i	0.471752	−	0.817099i	0.999478	+	0.0323159i	$0.0102883\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.86582i		−	0.933501i	−0.884389	−	0.466750i	$-0.845425\pi$
$71$		−	7.86582i		−	0.933501i	0.884389	−	0.466750i	$-0.154575\pi$
$72$		0			0
$73$	11.0769	−	6.39527i	1.29646	−	0.748510i	0.316667	−	0.948537i	$-0.397436\pi$
$73$	11.0769	−	6.39527i	1.29646	−	0.748510i	0.979790	+	0.200027i	$0.0641028\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.17744	−	4.97106i	0.590024	−	0.566504i
$78$		0			0
$79$	2.59566	+	4.49581i	0.292034	+	0.505819i	0.974291	−	0.225295i	$-0.0723345\pi$
$79$	2.59566	+	4.49581i	0.292034	+	0.505819i	−0.682256	+	0.731113i	$0.739001\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.92948	−	13.7343i	0.870373	−	1.50753i	0.00876173	−	0.999962i	$-0.497211\pi$
$83$	7.92948	−	13.7343i	0.870373	−	1.50753i	0.861611	−	0.507569i	$-0.169456\pi$
$84$		0			0
$85$	−9.24057	−	16.0051i	−1.00228	−	1.73600i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.14826	−	5.45295i	0.333715	−	0.578012i	−0.649522	−	0.760343i	$-0.725031\pi$
$89$	3.14826	−	5.45295i	0.333715	−	0.578012i	0.983237	+	0.182331i	$0.0583643\pi$
$90$		0			0
$91$	9.35993	+	2.71312i	0.981188	+	0.284412i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.85460	+	4.53486i	0.805865	+	0.465267i
$96$		0			0
$97$	13.2065	+	7.62477i	1.34092	+	0.774178i	0.986942	−	0.161077i	$-0.0514967\pi$
$97$	13.2065	+	7.62477i	1.34092	+	0.774178i	0.353974	+	0.935255i	$0.384830\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.48902			0.347170			0.173585	−	0.984819i	$-0.444465\pi$
$101$	3.48902			0.347170			0.173585	+	0.984819i	$0.444465\pi$
$102$		0			0
$103$			3.33894i			0.328996i	0.986377	+	0.164498i	$0.0526004\pi$
$103$			3.33894i			0.328996i	−0.986377	+	0.164498i	$0.947400\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.10776	+	1.79427i	0.300439	+	0.173458i	0.642640	−	0.766168i	$-0.277839\pi$
$107$	3.10776	+	1.79427i	0.300439	+	0.173458i	−0.342201	+	0.939627i	$0.611172\pi$
$108$		0			0
$109$	6.89673	+	11.9455i	0.660587	+	1.14417i	0.980462	+	0.196710i	$0.0630258\pi$
$109$	6.89673	+	11.9455i	0.660587	+	1.14417i	−0.319875	+	0.947460i	$0.603641\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.28607	−	3.05191i	0.497271	−	0.287100i	−0.230315	−	0.973116i	$-0.573976\pi$
$113$	5.28607	−	3.05191i	0.497271	−	0.287100i	0.727586	+	0.686016i	$0.240642\pi$
$114$		0			0
$115$			8.57963i			0.800054i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.74646	+	16.3747i	−0.435108	+	1.50107i
$120$		0			0
$121$	3.64039			0.330945
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.08895			0.455170
$126$		0			0
$127$	13.3819			1.18745			0.593727	−	0.804666i	$-0.297656\pi$
$127$	13.3819			1.18745			0.593727	+	0.804666i	$0.297656\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.777928			−0.0679679			−0.0339839	−	0.999422i	$-0.510820\pi$
$131$	−0.777928			−0.0679679			−0.0339839	+	0.999422i	$0.510820\pi$
$132$		0			0
$133$	−2.00071	−	8.12404i	−0.173484	−	0.704444i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			16.5217i			1.41154i	0.708440	+	0.705771i	$0.249399\pi$
$137$			16.5217i			1.41154i	−0.708440	+	0.705771i	$0.750601\pi$
$138$		0			0
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	−0.0164348	−	0.999865i	$-0.505232\pi$
$139$	9.91826	−	5.72631i	0.841256	−	0.485699i	0.857691	+	0.514165i	$0.171898\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.99620	−	8.65368i	−0.417804	−	0.723657i
$144$		0			0
$145$	−7.12226	−	4.11204i	−0.591472	−	0.341486i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	4.90494i		−	0.401829i	−0.979609	−	0.200914i	$-0.935609\pi$
$149$		−	4.90494i		−	0.401829i	0.979609	−	0.200914i	$-0.0643913\pi$
$150$		0			0
$151$	−9.85629			−0.802093			−0.401047	−	0.916058i	$-0.631353\pi$
$151$	−9.85629			−0.802093			−0.401047	+	0.916058i	$0.631353\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	23.7112	+	13.6897i	1.90453	+	1.09958i
$156$		0			0
$157$	−13.3514	−	7.70843i	−1.06556	−	0.615200i	−0.138593	−	0.990349i	$-0.544258\pi$
$157$	−13.3514	−	7.70843i	−1.06556	−	0.615200i	−0.926964	+	0.375149i	$0.877591\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.70915	−	5.48157i	0.449944	−	0.432008i
$162$		0			0
$163$	5.72053	−	9.90825i	0.448066	−	0.776074i	−0.550194	−	0.835037i	$-0.685446\pi$
$163$	5.72053	−	9.90825i	0.448066	−	0.776074i	0.998260	+	0.0589632i	$0.0187795\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.49103	+	11.2428i	0.502291	+	0.869993i	0.999996	+	0.00264735i	$0.000842678\pi$
$167$	6.49103	+	11.2428i	0.502291	+	0.869993i	−0.497706	+	0.867346i	$0.665824\pi$
$168$		0			0
$169$	0.283528	−	0.491084i	0.0218098	−	0.0377757i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.79984	+	16.9738i	0.745068	+	1.29050i	0.950163	+	0.311754i	$0.100916\pi$
$173$	9.79984	+	16.9738i	0.745068	+	1.29050i	−0.205095	+	0.978742i	$0.565750\pi$
$174$		0			0
$175$	5.91066	+	6.15605i	0.446804	+	0.465354i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	16.2630	−	9.38942i	1.21555	−	0.701799i	0.251588	−	0.967835i	$-0.419047\pi$
$179$	16.2630	−	9.38942i	1.21555	−	0.701799i	0.963963	+	0.266036i	$0.0857140\pi$
$180$		0			0
$181$			4.47775i			0.332829i	0.986056	+	0.166414i	$0.0532190\pi$
$181$			4.47775i			0.332829i	−0.986056	+	0.166414i	$0.946781\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.89400	−	8.47666i	0.359814	−	0.623217i
$186$		0			0
$187$	15.1392	−	8.74061i	1.10709	−	0.639177i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.90050	+	3.40665i	−0.426945	+	0.246497i	−0.698044	−	0.716055i	$-0.745946\pi$
$191$	−5.90050	+	3.40665i	−0.426945	+	0.246497i	0.271099	+	0.962551i	$0.412613\pi$
$192$		0			0
$193$	7.97694	−	13.8165i	0.574193	−	0.994531i	−0.421936	−	0.906626i	$-0.638649\pi$
$193$	7.97694	−	13.8165i	0.574193	−	0.994531i	0.996129	−	0.0879053i	$-0.0280173\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	25.9511i		−	1.84894i	−0.381254	−	0.924470i	$-0.624508\pi$
$197$		−	25.9511i		−	1.84894i	0.381254	−	0.924470i	$-0.375492\pi$
$198$		0			0
$199$	−2.75706	+	1.59179i	−0.195443	+	0.112839i	−0.594528	−	0.804075i	$-0.702661\pi$
$199$	−2.75706	+	1.59179i	−0.195443	+	0.112839i	0.399085	+	0.916914i	$0.369328\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.81417	+	7.36658i	0.127330	+	0.517032i
$204$		0			0
$205$	2.27876	+	3.94693i	0.159156	+	0.275666i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.28950	+	7.42963i	−0.296711	+	0.513918i
$210$		0			0
$211$	0.0552411	+	0.0956804i	0.00380295	+	0.00658691i	0.867921	−	0.496703i	$-0.165456\pi$
$211$	0.0552411	+	0.0956804i	0.00380295	+	0.00658691i	−0.864118	+	0.503290i	$0.832123\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.4175	+	23.2397i	−0.915064	+	1.58494i
$216$		0			0
$217$	−6.03968	−	24.5245i	−0.410000	−	1.66483i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	20.5550	+	11.8674i	1.38268	+	0.798290i
$222$		0			0
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	0.828265	−	0.560336i	$-0.189328\pi$
$223$	11.3064	+	6.52775i	0.757132	+	0.437130i	−0.0711331	+	0.997467i	$0.522661\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.26784			0.615128			0.307564	−	0.951527i	$-0.400486\pi$
$227$	9.26784			0.615128			0.307564	+	0.951527i	$0.400486\pi$
$228$		0			0
$229$			13.4180i			0.886689i	0.896351	+	0.443344i	$0.146208\pi$
$229$			13.4180i			0.886689i	−0.896351	+	0.443344i	$0.853792\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.3415	−	10.5895i	−1.20159	−	0.693738i	−0.240681	−	0.970604i	$-0.577371\pi$
$233$	−18.3415	−	10.5895i	−1.20159	−	0.693738i	−0.960909	+	0.276866i	$0.910704\pi$
$234$		0			0
$235$	−16.2151	−	28.0853i	−1.05776	−	1.83209i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.73342	+	4.46489i	−0.500233	+	0.288810i	−0.728810	−	0.684716i	$-0.759926\pi$
$239$	−7.73342	+	4.46489i	−0.500233	+	0.288810i	0.228577	+	0.973526i	$0.426593\pi$
$240$		0			0
$241$		−	18.4094i		−	1.18585i	−0.805257	−	0.592926i	$-0.797973\pi$
$241$		−	18.4094i		−	1.18585i	0.805257	−	0.592926i	$-0.202027\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.816219	−	20.0597i	0.0521463	−	1.28156i
$246$		0			0
$247$	−11.6480			−0.741145
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.33194			0.399669			0.199834	−	0.979830i	$-0.435960\pi$
$251$	6.33194			0.399669			0.199834	+	0.979830i	$0.435960\pi$
$252$		0			0
$253$	−8.11542			−0.510212
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.3857			−1.02211			−0.511054	−	0.859548i	$-0.670745\pi$
$257$	−16.3857			−1.02211			−0.511054	+	0.859548i	$0.670745\pi$
$258$		0			0
$259$	−8.76744	+	2.15916i	−0.544782	+	0.134164i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	12.0854i		−	0.745217i	−0.927989	−	0.372609i	$-0.878463\pi$
$263$		−	12.0854i		−	0.745217i	0.927989	−	0.372609i	$-0.121537\pi$
$264$		0			0
$265$	−6.20698	+	3.58360i	−0.381292	+	0.220139i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.6652	+	21.9368i	0.772212	+	1.33751i	0.936348	+	0.351072i	$0.114183\pi$
$269$	12.6652	+	21.9368i	0.772212	+	1.33751i	−0.164136	+	0.986438i	$0.552484\pi$
$270$		0			0
$271$	0.195591	+	0.112924i	0.0118813	+	0.00685967i	0.505929	−	0.862575i	$-0.331150\pi$
$271$	0.195591	+	0.112924i	0.0118813	+	0.00685967i	−0.494048	+	0.869435i	$0.664483\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	8.75069i		−	0.527686i
$276$		0			0
$277$	−20.4339			−1.22776			−0.613878	−	0.789401i	$-0.710391\pi$
$277$	−20.4339			−1.22776			−0.613878	+	0.789401i	$0.710391\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.96635	−	5.17672i	−0.534887	−	0.308817i	0.208117	−	0.978104i	$-0.433267\pi$
$281$	−8.96635	−	5.17672i	−0.534887	−	0.308817i	−0.743004	+	0.669287i	$0.766600\pi$
$282$		0			0
$283$	−11.8781	−	6.85783i	−0.706080	−	0.407656i	0.103528	−	0.994627i	$-0.466987\pi$
$283$	−11.8781	−	6.85783i	−0.706080	−	0.407656i	−0.809608	+	0.586971i	$0.800320\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.17050	−	4.03808i	0.0690923	−	0.238360i
$288$		0			0
$289$	−12.2615	+	21.2375i	−0.721264	+	1.24927i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.21527	+	7.30105i	0.246258	+	0.426532i	0.962485	−	0.271336i	$-0.0874655\pi$
$293$	4.21527	+	7.30105i	0.246258	+	0.426532i	−0.716226	+	0.697868i	$0.754132\pi$
$294$		0			0
$295$	12.4381	−	21.5434i	0.724175	−	1.25431i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.50930	−	9.54239i	−0.318611	−	0.551851i
$300$		0			0
$301$	24.0369	−	5.91960i	1.38547	−	0.341200i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.62593	−	0.938732i	0.0931006	−	0.0537516i
$306$		0			0
$307$			5.34345i			0.304967i	0.988306	+	0.152484i	$0.0487271\pi$
$307$			5.34345i			0.304967i	−0.988306	+	0.152484i	$0.951273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.70867	+	8.15565i	−0.267004	+	0.462465i	−0.968087	−	0.250615i	$-0.919367\pi$
$311$	−4.70867	+	8.15565i	−0.267004	+	0.462465i	0.701083	+	0.713080i	$0.252700\pi$
$312$		0			0
$313$	14.3347	−	8.27614i	0.810245	−	0.467795i	−0.0367961	−	0.999323i	$-0.511715\pi$
$313$	14.3347	−	8.27614i	0.810245	−	0.467795i	0.847041	+	0.531528i	$0.178382\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.9725	−	13.2632i	1.29026	−	0.744934i	0.311563	−	0.950225i	$-0.399147\pi$
$317$	22.9725	−	13.2632i	1.29026	−	0.744934i	0.978701	+	0.205291i	$0.0658141\pi$
$318$		0			0
$319$	3.88956	−	6.73691i	0.217773	−	0.377194i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	20.3776i		−	1.13384i
$324$		0			0
$325$	10.2894	−	5.94056i	0.570751	−	0.329523i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−8.32895	+	28.7339i	−0.459190	+	1.58415i
$330$		0			0
$331$	−8.82000	−	15.2767i	−0.484791	−	0.839682i	0.515056	−	0.857156i	$-0.327771\pi$
$331$	−8.82000	−	15.2767i	−0.484791	−	0.839682i	−0.999847	+	0.0174739i	$0.994438\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.0748	+	19.1821i	−0.605081	+	1.04803i
$336$		0			0
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	0.993515	−	0.113697i	$-0.0362694\pi$
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	−0.595222	+	0.803561i	$0.702936\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.9490	+	22.4283i	−0.701226	+	1.21456i
$342$		0			0
$343$	−13.8698	+	12.2731i	−0.748899	+	0.662684i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.05563	+	0.609467i	0.0566691	+	0.0327179i	0.528067	−	0.849203i	$-0.322917\pi$
$347$	1.05563	+	0.609467i	0.0566691	+	0.0327179i	−0.471398	+	0.881921i	$0.656250\pi$
$348$		0			0
$349$	10.6857	+	6.16942i	0.571995	+	0.330241i	0.757946	−	0.652318i	$-0.226203\pi$
$349$	10.6857	+	6.16942i	0.571995	+	0.330241i	−0.185951	+	0.982559i	$0.559537\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	22.2969			1.18674			0.593372	−	0.804928i	$-0.297796\pi$
$353$	22.2969			1.18674			0.593372	+	0.804928i	$0.297796\pi$
$354$		0			0
$355$			22.5595i			1.19733i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.4819	−	6.05173i	−0.553214	−	0.319398i	0.197204	−	0.980363i	$-0.436814\pi$
$359$	−10.4819	−	6.05173i	−0.553214	−	0.319398i	−0.750417	+	0.660965i	$0.770147\pi$
$360$		0			0
$361$	−4.49979	−	7.79387i	−0.236831	−	0.410204i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−31.7691	+	18.3419i	−1.66287	+	0.960058i
$366$		0			0
$367$			14.7275i			0.768769i	0.923173	+	0.384385i	$0.125586\pi$
$367$			14.7275i			0.768769i	−0.923173	+	0.384385i	$0.874414\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.35032	+	1.84073i	0.329692	+	0.0955662i
$372$		0			0
$373$	−9.08558			−0.470433			−0.235217	−	0.971943i	$-0.575580\pi$
$373$	−9.08558			−0.470433			−0.235217	+	0.971943i	$0.575580\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.5620			0.543970
$378$		0			0
$379$	−21.2298			−1.09050			−0.545250	−	0.838273i	$-0.683565\pi$
$379$	−21.2298			−1.09050			−0.545250	+	0.838273i	$0.683565\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.70454			0.342586			0.171293	−	0.985220i	$-0.445206\pi$
$383$	6.70454			0.342586			0.171293	+	0.985220i	$0.445206\pi$
$384$		0			0
$385$	−14.8491	+	14.2572i	−0.756779	+	0.726613i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			7.69794i			0.390301i	0.980773	+	0.195151i	$0.0625195\pi$
$389$			7.69794i			0.390301i	−0.980773	+	0.195151i	$0.937480\pi$
$390$		0			0
$391$	16.6939	−	9.63825i	0.844249	−	0.487427i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.44444	−	12.8942i	−0.374571	−	0.648775i
$396$		0			0
$397$	−0.0428112	−	0.0247170i	−0.00214863	−	0.00124051i	0.498925	−	0.866645i	$-0.333728\pi$
$397$	−0.0428112	−	0.0247170i	−0.00214863	−	0.00124051i	−0.501074	+	0.865404i	$0.667062\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			20.3272i			1.01509i	0.861625	+	0.507546i	$0.169447\pi$
$401$			20.3272i			1.01509i	−0.861625	+	0.507546i	$0.830553\pi$
$402$		0			0
$403$	−35.1626			−1.75157
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.01803	+	4.62921i	0.397439	+	0.229461i
$408$		0			0
$409$	12.1144	+	6.99428i	0.599021	+	0.345845i	0.768656	−	0.639662i	$-0.220926\pi$
$409$	12.1144	+	6.99428i	0.599021	+	0.345845i	−0.169636	+	0.985507i	$0.554259\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−22.2824	+	5.48752i	−1.09645	+	0.270023i
$414$		0			0
$415$	−22.7420	+	39.3903i	−1.11636	+	1.93360i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.6718	−	18.4842i	−0.521353	−	0.903010i	−0.999692	−	0.0248344i	$-0.992094\pi$
$419$	−10.6718	−	18.4842i	−0.521353	−	0.903010i	0.478339	−	0.878176i	$-0.341239\pi$
$420$		0			0
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	−0.752823	−	0.658223i	$-0.771309\pi$
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	0.946449	+	0.322853i	$0.104642\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.3927	+	18.0007i	0.504121	+	0.873163i
$426$		0			0
$427$	−1.66348	−	0.482184i	−0.0805013	−	0.0233345i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	27.6515	−	15.9646i	1.33193	−	0.768989i	0.346333	−	0.938112i	$-0.387427\pi$
$431$	27.6515	−	15.9646i	1.33193	−	0.768989i	0.985595	+	0.169123i	$0.0540934\pi$
$432$		0			0
$433$			18.5300i			0.890493i	0.895408	+	0.445247i	$0.146884\pi$
$433$			18.5300i			0.890493i	−0.895408	+	0.445247i	$0.853116\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.73002	+	8.19263i	−0.226267	+	0.391907i
$438$		0			0
$439$	−1.80316	+	1.04106i	−0.0860603	+	0.0496869i	−0.542413	−	0.840112i	$-0.682489\pi$
$439$	−1.80316	+	1.04106i	−0.0860603	+	0.0496869i	0.456352	+	0.889799i	$0.349156\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.13895	−	1.23493i	0.101625	−	0.0586731i	−0.448326	−	0.893870i	$-0.647980\pi$
$443$	2.13895	−	1.23493i	0.101625	−	0.0586731i	0.549951	+	0.835197i	$0.314646\pi$
$444$		0			0
$445$	−9.02933	+	15.6393i	−0.428031	+	0.741372i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	37.5094i		−	1.77018i	−0.465424	−	0.885088i	$-0.654098\pi$
$449$		−	37.5094i		−	1.77018i	0.465424	−	0.885088i	$-0.345902\pi$
$450$		0			0
$451$	−3.73338	+	2.15547i	−0.175798	+	0.101497i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−26.8446	−	7.78132i	−1.25850	−	0.364794i
$456$		0			0
$457$	−2.92345	−	5.06356i	−0.136753	−	0.236864i	0.789513	−	0.613734i	$-0.210333\pi$
$457$	−2.92345	−	5.06356i	−0.136753	−	0.236864i	−0.926266	+	0.376871i	$0.877000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.82830	−	6.63081i	0.178302	−	0.308827i	−0.762997	−	0.646402i	$-0.776273\pi$
$461$	3.82830	−	6.63081i	0.178302	−	0.308827i	0.941299	+	0.337574i	$0.109606\pi$
$462$		0			0
$463$	−4.89449	−	8.47751i	−0.227466	−	0.393983i	0.729590	−	0.683885i	$-0.239711\pi$
$463$	−4.89449	−	8.47751i	−0.227466	−	0.393983i	−0.957057	+	0.289901i	$0.906378\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.0806	+	24.3883i	−0.651572	+	1.12856i	0.331169	+	0.943571i	$0.392557\pi$
$467$	−14.0806	+	24.3883i	−0.651572	+	1.12856i	−0.982741	+	0.184985i	$0.940776\pi$
$468$		0			0
$469$	19.8401	−	4.88605i	0.916132	−	0.225617i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−21.9824	−	12.6915i	−1.01075	−	0.583557i
$474$		0			0
$475$	−8.83394	−	5.10028i	−0.405329	−	0.234017i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−29.6105			−1.35294			−0.676470	−	0.736470i	$-0.736491\pi$
$479$	−29.6105			−1.35294			−0.676470	+	0.736470i	$0.736491\pi$
$480$		0			0
$481$			12.5705i			0.573165i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−37.8767	−	21.8681i	−1.71989	−	0.992980i
$486$		0			0
$487$	14.6701	+	25.4094i	0.664767	+	1.15141i	0.979348	+	0.202180i	$0.0648025\pi$
$487$	14.6701	+	25.4094i	0.664767	+	1.15141i	−0.314582	+	0.949230i	$0.601864\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	−0.682075	−	0.731283i	$-0.738922\pi$
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	0.292272	+	0.956335i	$0.405589\pi$
$492$		0			0
$493$			18.4777i			0.832192i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	15.0118	−	14.4134i	0.673369	−	0.646527i
$498$		0			0
$499$	19.5957			0.877223			0.438611	−	0.898677i	$-0.355470\pi$
$499$	19.5957			0.877223			0.438611	+	0.898677i	$0.355470\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−21.2907			−0.949304			−0.474652	−	0.880174i	$-0.657426\pi$
$503$	−21.2907			−0.949304			−0.474652	+	0.880174i	$0.657426\pi$
$504$		0			0
$505$	−10.0066			−0.445289
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−43.6614			−1.93526			−0.967630	−	0.252375i	$-0.918788\pi$
$509$	−43.6614			−1.93526			−0.967630	+	0.252375i	$0.918788\pi$
$510$		0			0
$511$	32.5027	+	9.42139i	1.43783	+	0.416778i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	9.57621i		−	0.421978i
$516$		0			0
$517$	26.5658	−	15.3378i	1.16836	−	0.674554i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.60043	+	4.50408i	0.113927	+	0.197327i	0.917350	−	0.398081i	$-0.130324\pi$
$521$	2.60043	+	4.50408i	0.113927	+	0.197327i	−0.803423	+	0.595408i	$0.796990\pi$
$522$		0			0
$523$	34.7043	+	20.0365i	1.51751	+	0.876137i	0.999788	+	0.0205902i	$0.00655454\pi$
$523$	34.7043	+	20.0365i	1.51751	+	0.876137i	0.517726	+	0.855547i	$0.326779\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	61.5152i		−	2.67964i
$528$		0			0
$529$	14.0511			0.610919
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.06895	−	2.92656i	−0.219561	−	0.126763i
$534$		0			0
$535$	−8.91317	−	5.14602i	−0.385350	−	0.222482i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	18.9743	+	0.772057i	0.817282	+	0.0332549i
$540$		0			0
$541$	−4.12096	+	7.13771i	−0.177174	+	0.306874i	−0.940911	−	0.338653i	$-0.890029\pi$
$541$	−4.12096	+	7.13771i	−0.177174	+	0.306874i	0.763738	+	0.645527i	$0.223362\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−19.7801	−	34.2601i	−0.847285	−	1.46754i
$546$		0			0
$547$	2.53756	−	4.39518i	0.108498	−	0.187925i	−0.806664	−	0.591011i	$-0.798729\pi$
$547$	2.53756	−	4.39518i	0.108498	−	0.187925i	0.915162	+	0.403086i	$0.132062\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.53400	−	7.85312i	−0.193155	−	0.334554i
$552$		0			0
$553$	−3.82387	+	13.1919i	−0.162608	+	0.560977i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	37.6102	−	21.7142i	1.59359	−	0.920062i	0.600910	−	0.799316i	$-0.294805\pi$
$557$	37.6102	−	21.7142i	1.59359	−	0.920062i	0.992684	−	0.120745i	$-0.0385285\pi$
$558$		0			0
$559$		−	34.4635i		−	1.45765i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.99118	+	8.64498i	−0.210353	+	0.364343i	−0.951825	−	0.306641i	$-0.900795\pi$
$563$	−4.99118	+	8.64498i	−0.210353	+	0.364343i	0.741472	+	0.670984i	$0.234128\pi$
$564$		0			0
$565$	−15.1606	+	8.75300i	−0.637813	+	0.368241i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.0597	−	8.11739i	0.589415	−	0.340299i	−0.175451	−	0.984488i	$-0.556138\pi$
$569$	14.0597	−	8.11739i	0.589415	−	0.340299i	0.764866	+	0.644189i	$0.222805\pi$
$570$		0			0
$571$	−6.31028	+	10.9297i	−0.264077	+	0.457395i	−0.967321	−	0.253553i	$-0.918401\pi$
$571$	−6.31028	+	10.9297i	−0.264077	+	0.457395i	0.703244	+	0.710948i	$0.251734\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	9.64936i		−	0.402406i
$576$		0			0
$577$	−4.18012	+	2.41339i	−0.174020	+	0.100471i	−0.584480	−	0.811408i	$-0.698702\pi$
$577$	−4.18012	+	2.41339i	−0.174020	+	0.100471i	0.410460	+	0.911879i	$0.365368\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	40.7416	−	10.0335i	1.69024	−	0.416258i
$582$		0			0
$583$	−3.38971	−	5.87115i	−0.140387	−	0.243158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.26032	+	9.11114i	−0.217117	+	0.376057i	−0.953925	−	0.300044i	$-0.902999\pi$
$587$	−5.26032	+	9.11114i	−0.217117	+	0.376057i	0.736809	+	0.676101i	$0.236332\pi$
$588$		0			0
$589$	15.0944	+	26.1443i	0.621955	+	1.07726i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.7342	−	25.5205i	0.605063	−	1.04800i	−0.386979	−	0.922089i	$-0.626481\pi$
$593$	14.7342	−	25.5205i	0.605063	−	1.04800i	0.992042	−	0.125911i	$-0.0401853\pi$
$594$		0			0
$595$	13.6130	−	46.9633i	0.558080	−	1.92531i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.11658	−	4.10876i	−0.290776	−	0.167879i	0.347516	−	0.937674i	$-0.387025\pi$
$599$	−7.11658	−	4.10876i	−0.290776	−	0.167879i	−0.638292	+	0.769795i	$0.720359\pi$
$600$		0			0
$601$	−32.7131	−	18.8869i	−1.33439	−	0.770413i	−0.348425	−	0.937337i	$-0.613283\pi$
$601$	−32.7131	−	18.8869i	−1.33439	−	0.770413i	−0.985970	+	0.166924i	$0.946617\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10.4408			−0.424478
$606$		0			0
$607$			35.6221i			1.44586i	0.690923	+	0.722929i	$0.257204\pi$
$607$			35.6221i			1.44586i	−0.690923	+	0.722929i	$0.742796\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	36.0693	+	20.8246i	1.45921	+	0.842474i
$612$		0			0
$613$	11.9660	+	20.7256i	0.483301	+	0.837101i	0.999816	−	0.0191767i	$-0.00610451\pi$
$613$	11.9660	+	20.7256i	0.483301	+	0.837101i	−0.516516	+	0.856278i	$0.672771\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.98622	−	1.14675i	0.0799623	−	0.0461663i	−0.459486	−	0.888185i	$-0.651966\pi$
$617$	1.98622	−	1.14675i	0.0799623	−	0.0461663i	0.539448	+	0.842019i	$0.318633\pi$
$618$		0			0
$619$		−	10.5171i		−	0.422717i	−0.977409	−	0.211359i	$-0.932211\pi$
$619$		−	10.5171i		−	0.422717i	0.977409	−	0.211359i	$-0.0677888\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	16.1757	−	3.98361i	0.648067	−	0.159600i
$624$		0			0
$625$	−30.7235			−1.22894
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−21.9914			−0.876856
$630$		0			0
$631$	2.02836			0.0807477			0.0403739	−	0.999185i	$-0.487145\pi$
$631$	2.02836			0.0807477			0.0403739	+	0.999185i	$0.487145\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−38.3799			−1.52306
$636$		0			0
$637$	11.9732	+	22.8348i	0.474397	+	0.904747i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	12.4451i		−	0.491553i	−0.969326	−	0.245777i	$-0.920957\pi$
$641$		−	12.4451i		−	0.491553i	0.969326	−	0.245777i	$-0.0790430\pi$
$642$		0			0
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	−0.723112	−	0.690731i	$-0.757289\pi$
$643$	−12.3358	+	7.12209i	−0.486477	+	0.280868i	0.236635	+	0.971599i	$0.423956\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.1910	+	17.6513i	0.400649	+	0.693945i	0.993804	−	0.111143i	$-0.0354512\pi$
$647$	10.1910	+	17.6513i	0.400649	+	0.693945i	−0.593155	+	0.805088i	$0.702118\pi$
$648$		0			0
$649$	20.3778	+	11.7651i	0.799899	+	0.461822i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			8.72186i			0.341313i	0.985331	+	0.170656i	$0.0545888\pi$
$653$			8.72186i			0.341313i	−0.985331	+	0.170656i	$0.945411\pi$
$654$		0			0
$655$	2.23113			0.0871773
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16.7524	−	9.67200i	−0.652581	−	0.376768i	0.136864	−	0.990590i	$-0.456298\pi$
$659$	−16.7524	−	9.67200i	−0.652581	−	0.376768i	−0.789444	+	0.613822i	$0.789631\pi$
$660$		0			0
$661$	−31.8948	−	18.4145i	−1.24056	−	0.716240i	−0.271355	−	0.962479i	$-0.587472\pi$
$661$	−31.8948	−	18.4145i	−1.24056	−	0.716240i	−0.969209	+	0.246239i	$0.920805\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.73812	+	23.3000i	0.222515	+	0.903537i
$666$		0			0
$667$	4.28900	−	7.42877i	0.166071	−	0.287643i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.887942	+	1.53796i	0.0342786	+	0.0593723i
$672$		0			0
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	−0.645319	−	0.763913i	$-0.723276\pi$
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	0.984228	+	0.176907i	$0.0566091\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−20.4146	−	35.3590i	−0.784595	−	1.35896i	−0.929241	−	0.369475i	$-0.879538\pi$
$677$	−20.4146	−	35.3590i	−0.784595	−	1.35896i	0.144646	−	0.989484i	$-0.453796\pi$
$678$		0			0
$679$	9.64790	+	39.1760i	0.370253	+	1.50344i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.56287	−	4.94377i	0.327649	−	0.189168i	−0.327148	−	0.944973i	$-0.606088\pi$
$683$	8.56287	−	4.94377i	0.327649	−	0.189168i	0.654797	+	0.755805i	$0.272754\pi$
$684$		0			0
$685$		−	47.3847i		−	1.81048i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.60233	−	7.97148i	0.175335	−	0.303689i
$690$		0			0
$691$	−37.9217	+	21.8941i	−1.44261	+	0.832891i	−0.998023	−	0.0628444i	$-0.979983\pi$
$691$	−37.9217	+	21.8941i	−1.44261	+	0.832891i	−0.444587	+	0.895736i	$0.646649\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.4459	+	16.4233i	−1.07902	+	0.622970i
$696$		0			0
$697$	5.11987	−	8.86787i	0.193929	−	0.335894i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			29.6742i			1.12078i	0.828229	+	0.560389i	$0.189349\pi$
$701$			29.6742i			1.12078i	−0.828229	+	0.560389i	$0.810651\pi$
$702$		0			0
$703$	9.34651	−	5.39621i	0.352510	−	0.203522i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.39329	+	6.65872i	0.240445	+	0.250427i
$708$		0			0
$709$	−23.5269	−	40.7498i	−0.883572	−	1.53039i	−0.847342	−	0.531048i	$-0.821799\pi$
$709$	−23.5269	−	40.7498i	−0.883572	−	1.53039i	−0.0362296	−	0.999343i	$-0.511535\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−14.2788	+	24.7316i	−0.534745	+	0.926206i
$714$		0			0
$715$	14.3293	+	24.8191i	0.535885	+	0.928180i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.909148	+	1.57469i	−0.0339055	+	0.0587261i	−0.882480	−	0.470349i	$-0.844128\pi$
$719$	−0.909148	+	1.57469i	−0.0339055	+	0.0587261i	0.848575	+	0.529076i	$0.177461\pi$
$720$		0			0
$721$	−6.37230	+	6.11829i	−0.237317	+	0.227857i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	8.01029	+	4.62474i	0.297495	+	0.171759i
$726$		0			0
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	0.846252	−	0.532782i	$-0.178853\pi$
$727$	21.7854	+	12.5778i	0.807976	+	0.466485i	−0.0382766	+	0.999267i	$0.512187\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	60.2921			2.22998
$732$		0			0
$733$		−	4.44032i		−	0.164007i	−0.996632	−	0.0820034i	$-0.973868\pi$
$733$		−	4.44032i		−	0.164007i	0.996632	−	0.0820034i	$-0.0261319\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.1443	−	10.4756i	−0.668353	−	0.385874i
$738$		0			0
$739$	8.97608	+	15.5470i	0.330191	+	0.571907i	0.982549	−	0.186004i	$-0.0595536\pi$
$739$	8.97608	+	15.5470i	0.330191	+	0.571907i	−0.652358	+	0.757911i	$0.726220\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.949106	−	0.314956i	$-0.898010\pi$
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.201793	+	0.979428i	$0.564677\pi$
$744$		0			0
$745$			14.0676i			0.515395i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.27035	+	9.21892i	0.0829568	+	0.336852i
$750$		0			0
$751$	−11.9642			−0.436580			−0.218290	−	0.975884i	$-0.570048\pi$
$751$	−11.9642			−0.436580			−0.218290	+	0.975884i	$0.570048\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	28.2682			1.02878
$756$		0			0
$757$	−49.4440			−1.79707			−0.898537	−	0.438898i	$-0.855369\pi$
$757$	−49.4440			−1.79707			−0.898537	+	0.438898i	$0.855369\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−29.2384			−1.05989			−0.529945	−	0.848032i	$-0.677788\pi$
$761$	−29.2384			−1.05989			−0.529945	+	0.848032i	$0.677788\pi$
$762$		0			0
$763$	−10.1601	+	35.0512i	−0.367821	+	1.26894i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			31.9479i			1.15357i
$768$		0			0
$769$	4.54689	−	2.62515i	0.163965	−	0.0946653i	−0.415772	−	0.909469i	$-0.636489\pi$
$769$	4.54689	−	2.62515i	0.163965	−	0.0946653i	0.579737	+	0.814804i	$0.303155\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15.6829	−	27.1635i	−0.564073	−	0.977003i	−0.997135	−	0.0756393i	$-0.975900\pi$
$773$	−15.6829	−	27.1635i	−0.564073	−	0.977003i	0.433062	−	0.901364i	$-0.357433\pi$
$774$		0			0
$775$	−26.6676	−	15.3965i	−0.957927	−	0.553059i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			5.02520i			0.180047i
$780$		0			0
$781$	−21.3389			−0.763565
$782$		0			0
$783$		0			0
$784$		0			0
$785$	38.2923	+	22.1081i	1.36671	+	0.789071i
$786$		0			0
$787$	1.59324	+	0.919855i	0.0567927	+	0.0327893i	0.528128	−	0.849165i	$-0.322894\pi$
$787$	1.59324	+	0.919855i	0.0567927	+	0.0327893i	−0.471335	+	0.881954i	$0.656228\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.5107	+	4.49602i	0.551498	+	0.159860i
$792$		0			0
$793$	−1.20559	+	2.08814i	−0.0428118	+	0.0741522i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.39659	−	11.0792i	−0.226579	−	0.392446i	0.730213	−	0.683219i	$-0.239421\pi$
$797$	−6.39659	−	11.0792i	−0.226579	−	0.392446i	−0.956792	+	0.290773i	$0.906087\pi$
$798$		0			0
$799$	−36.4316	+	63.1015i	−1.28886	+	2.23237i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.3495	−	30.0502i	−0.612250	−	1.06045i
$804$		0			0
$805$	−16.3740	+	15.7213i	−0.577109	+	0.554105i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.9217	−	7.46032i	0.454301	−	0.262291i	−0.255344	−	0.966850i	$-0.582189\pi$
$809$	12.9217	−	7.46032i	0.454301	−	0.262291i	0.709645	+	0.704559i	$0.248855\pi$
$810$		0			0
$811$		−	37.5478i		−	1.31848i	−0.751933	−	0.659240i	$-0.770878\pi$
$811$		−	37.5478i		−	1.31848i	0.751933	−	0.659240i	$-0.229122\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16.4067	+	28.4172i	−0.574701	+	0.995411i
$816$		0			0
$817$	−25.6245	+	14.7943i	−0.896489	+	0.517588i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.88164	−	1.66371i	0.100570	−	0.0580640i	−0.448872	−	0.893596i	$-0.648174\pi$
$821$	2.88164	−	1.66371i	0.100570	−	0.0580640i	0.549441	+	0.835532i	$0.314841\pi$
$822$		0			0
$823$	25.4654	−	44.1073i	0.887667	−	1.53748i	0.0450407	−	0.998985i	$-0.485658\pi$
$823$	25.4654	−	44.1073i	0.887667	−	1.53748i	0.842626	−	0.538499i	$-0.181008\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			16.9198i			0.588360i	0.955750	+	0.294180i	$0.0950465\pi$
$827$			16.9198i			0.588360i	−0.955750	+	0.294180i	$0.904954\pi$
$828$		0			0
$829$	−4.65467	+	2.68737i	−0.161663	+	0.0933364i	−0.578649	−	0.815577i	$-0.696420\pi$
$829$	−4.65467	+	2.68737i	−0.161663	+	0.0933364i	0.416986	+	0.908913i	$0.363087\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−39.9483	+	20.9466i	−1.38413	+	0.725757i
$834$		0			0
$835$	−18.6165	−	32.2447i	−0.644251	−	1.11588i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.8714	−	20.5618i	0.409846	−	0.709874i	−0.585026	−	0.811014i	$-0.698916\pi$
$839$	11.8714	−	20.5618i	0.409846	−	0.709874i	0.994872	+	0.101140i	$0.0322492\pi$
$840$		0			0
$841$	−10.3887	−	17.9938i	−0.358232	−	0.620477i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.813168	+	1.40845i	−0.0279738	+	0.0484521i
$846$		0			0
$847$	6.67066	+	6.94761i	0.229207	+	0.238723i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.84146	+	5.10462i	0.303081	+	0.174984i
$852$		0			0
$853$	10.3810	+	5.99345i	0.355437	+	0.205212i	0.667077	−	0.744988i	$-0.267545\pi$
$853$	10.3810	+	5.99345i	0.355437	+	0.205212i	−0.311640	+	0.950200i	$0.600878\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−55.0635			−1.88093			−0.940467	−	0.339885i	$-0.889612\pi$
$857$	−55.0635			−1.88093			−0.940467	+	0.339885i	$0.889612\pi$
$858$		0			0
$859$		−	39.1210i		−	1.33479i	−0.744704	−	0.667395i	$-0.767409\pi$
$859$		−	39.1210i		−	1.33479i	0.744704	−	0.667395i	$-0.232591\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−39.2319	−	22.6506i	−1.33547	−	0.771034i	−0.349338	−	0.936997i	$-0.613593\pi$
$863$	−39.2319	−	22.6506i	−1.33547	−	0.771034i	−0.986132	+	0.165963i	$0.946927\pi$
$864$		0			0
$865$	−28.1063	−	48.6815i	−0.955643	−	1.65522i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.1965	−	7.04166i	0.413738	−	0.238872i
$870$		0			0
$871$		−	28.4462i		−	0.963863i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.32502	+	9.71217i	0.315243	+	0.328331i
$876$		0			0
$877$	−4.05651			−0.136979			−0.0684893	−	0.997652i	$-0.521818\pi$
$877$	−4.05651			−0.136979			−0.0684893	+	0.997652i	$0.521818\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	54.3727			1.83186			0.915931	−	0.401336i	$-0.131454\pi$
$881$	54.3727			1.83186			0.915931	+	0.401336i	$0.131454\pi$
$882$		0			0
$883$	−23.1175			−0.777965			−0.388982	−	0.921245i	$-0.627173\pi$
$883$	−23.1175			−0.777965			−0.388982	+	0.921245i	$0.627173\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	25.5636			0.858342			0.429171	−	0.903223i	$-0.358806\pi$
$887$	25.5636			0.858342			0.429171	+	0.903223i	$0.358806\pi$
$888$		0			0
$889$	24.5211	+	25.5392i	0.822412	+	0.856556i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	35.7580i		−	1.19660i
$894$		0			0
$895$	−46.6428	+	26.9292i	−1.55910	+	0.900144i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.6871	−	23.7067i	−0.456489	−	0.790663i
$900$		0			0
$901$	13.9457	+	8.05155i	0.464598	+	0.268236i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	12.8424i		−	0.426895i
$906$		0			0
$907$	37.0130			1.22900			0.614498	−	0.788918i	$-0.289359\pi$
$907$	37.0130			1.22900			0.614498	+	0.788918i	$0.289359\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	0.551476	−	0.834191i	$-0.314065\pi$
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	−0.446692	+	0.894688i	$0.647398\pi$
$912$		0			0
$913$	−37.2591	−	21.5116i	−1.23310	−	0.711929i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.42548	−	1.48466i	−0.0470734	−	0.0490278i
$918$		0			0
$919$	−17.3994	+	30.1367i	−0.573954	+	0.994117i	0.422201	+	0.906502i	$0.361258\pi$
$919$	−17.3994	+	30.1367i	−0.573954	+	0.994117i	−0.996154	+	0.0876145i	$0.972076\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.4863	−	25.0910i	−0.476822	−	0.825879i
$924$		0			0
$925$	−5.50420	+	9.53356i	−0.180977	+	0.313461i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.1736	+	43.6019i	0.825917	+	1.43053i	0.901216	+	0.433370i	$0.142676\pi$
$929$	25.1736	+	43.6019i	0.825917	+	1.43053i	−0.0752987	+	0.997161i	$0.523991\pi$
$930$		0			0
$931$	11.8385	−	18.7048i	0.387990	−	0.613027i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−43.4197	+	25.0684i	−1.41998	+	0.819824i
$936$		0			0
$937$			6.48087i			0.211721i	0.994381	+	0.105860i	$0.0337596\pi$
$937$			6.48087i			0.211721i	−0.994381	+	0.105860i	$0.966240\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.334024	+	0.578547i	−0.0108889	+	0.0188601i	−0.871418	−	0.490540i	$-0.836799\pi$
$941$	−0.334024	+	0.578547i	−0.0108889	+	0.0188601i	0.860530	+	0.509400i	$0.170133\pi$
$942$		0			0
$943$	−4.11679	+	2.37683i	−0.134061	+	0.0774003i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−50.7461	+	29.2983i	−1.64903	+	0.952067i	−0.671569	+	0.740942i	$0.734379\pi$
$947$	−50.7461	+	29.2983i	−1.64903	+	0.952067i	−0.977459	+	0.211125i	$0.932287\pi$
$948$		0			0
$949$	23.5560	−	40.8002i	0.764661	−	1.32443i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			48.3707i			1.56688i	0.621467	+	0.783441i	$0.286537\pi$
$953$			48.3707i			1.56688i	−0.621467	+	0.783441i	$0.713463\pi$
$954$		0			0
$955$	16.9228	−	9.77041i	0.547610	−	0.316163i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−31.5313	+	30.2744i	−1.01820	+	0.977610i
$960$		0			0
$961$	30.0665	+	52.0767i	0.969887	+	1.67989i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−22.8781	+	39.6261i	−0.736474	+	1.27561i
$966$		0			0
$967$	−8.51390	−	14.7465i	−0.273788	−	0.474216i	0.696040	−	0.718003i	$-0.254943\pi$
$967$	−8.51390	−	14.7465i	−0.273788	−	0.474216i	−0.969829	+	0.243787i	$0.921610\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.5651	+	23.4955i	−0.435325	+	0.754006i	−0.997322	−	0.0731339i	$-0.976700\pi$
$971$	−13.5651	+	23.4955i	−0.435325	+	0.754006i	0.561997	+	0.827139i	$0.310033\pi$
$972$		0			0
$973$	29.1028	+	8.43589i	0.932994	+	0.270442i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.49838	−	3.17449i	−0.175909	−	0.101561i	0.409460	−	0.912328i	$-0.365717\pi$
$977$	−5.49838	−	3.17449i	−0.175909	−	0.101561i	−0.585369	+	0.810767i	$0.699050\pi$
$978$		0			0
$979$	−14.7931	−	8.54080i	−0.472789	−	0.272965i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.9660			0.636817			0.318408	−	0.947954i	$-0.396852\pi$
$983$	19.9660			0.636817			0.318408	+	0.947954i	$0.396852\pi$
$984$		0			0
$985$			74.4288i			2.37150i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.2399	−	13.9949i	−0.770784	−	0.445012i
$990$		0			0
$991$	−6.38803	−	11.0644i	−0.202922	−	0.351472i	0.746546	−	0.665333i	$-0.231711\pi$
$991$	−6.38803	−	11.0644i	−0.202922	−	0.351472i	−0.949469	+	0.313861i	$0.898377\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.90734	−	4.56530i	0.250679	−	0.144730i
$996$		0			0
$997$			20.7669i			0.657694i	0.944383	+	0.328847i	$0.106660\pi$
$997$			20.7669i			0.657694i	−0.944383	+	0.328847i	$0.893340\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.d.1601.1		16
3.2	odd	2		1008.2.df.d.929.7		16
4.3	odd	2		756.2.bm.a.89.1		16
7.3	odd	6		3024.2.ca.d.2033.1		16
9.4	even	3		1008.2.ca.d.257.4		16
9.5	odd	6		3024.2.ca.d.2609.1		16
12.11	even	2		252.2.bm.a.173.2	yes	16
21.17	even	6		1008.2.ca.d.353.4		16
28.3	even	6		756.2.w.a.521.1		16
28.11	odd	6		5292.2.w.b.521.8		16
28.19	even	6		5292.2.x.a.4409.1		16
28.23	odd	6		5292.2.x.b.4409.8		16
28.27	even	2		5292.2.bm.a.4625.8		16
36.7	odd	6		2268.2.t.b.2105.8		16
36.11	even	6		2268.2.t.a.2105.1		16
36.23	even	6		756.2.w.a.341.1		16
36.31	odd	6		252.2.w.a.5.5	✓	16
63.31	odd	6		1008.2.df.d.689.7		16
63.59	even	6	inner	3024.2.df.d.17.1		16
84.11	even	6		1764.2.w.b.1109.4		16
84.23	even	6		1764.2.x.b.1469.8		16
84.47	odd	6		1764.2.x.a.1469.1		16
84.59	odd	6		252.2.w.a.101.5	yes	16
84.83	odd	2		1764.2.bm.a.1685.7		16
252.23	even	6		5292.2.x.a.881.1		16
252.31	even	6		252.2.bm.a.185.2	yes	16
252.59	odd	6		756.2.bm.a.17.1		16
252.67	odd	6		1764.2.bm.a.1697.7		16
252.95	even	6		5292.2.bm.a.2285.8		16
252.103	even	6		1764.2.x.b.293.8		16
252.115	even	6		2268.2.t.a.1781.1		16
252.131	odd	6		5292.2.x.b.881.8		16
252.139	even	6		1764.2.w.b.509.4		16
252.167	odd	6		5292.2.w.b.1097.8		16
252.227	odd	6		2268.2.t.b.1781.8		16
252.247	odd	6		1764.2.x.a.293.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	36.31	odd	6
252.2.w.a.101.5	yes	16	84.59	odd	6
252.2.bm.a.173.2	yes	16	12.11	even	2
252.2.bm.a.185.2	yes	16	252.31	even	6
756.2.w.a.341.1		16	36.23	even	6
756.2.w.a.521.1		16	28.3	even	6
756.2.bm.a.17.1		16	252.59	odd	6
756.2.bm.a.89.1		16	4.3	odd	2
1008.2.ca.d.257.4		16	9.4	even	3
1008.2.ca.d.353.4		16	21.17	even	6
1008.2.df.d.689.7		16	63.31	odd	6
1008.2.df.d.929.7		16	3.2	odd	2
1764.2.w.b.509.4		16	252.139	even	6
1764.2.w.b.1109.4		16	84.11	even	6
1764.2.x.a.293.1		16	252.247	odd	6
1764.2.x.a.1469.1		16	84.47	odd	6
1764.2.x.b.293.8		16	252.103	even	6
1764.2.x.b.1469.8		16	84.23	even	6
1764.2.bm.a.1685.7		16	84.83	odd	2
1764.2.bm.a.1697.7		16	252.67	odd	6
2268.2.t.a.1781.1		16	252.115	even	6
2268.2.t.a.2105.1		16	36.11	even	6
2268.2.t.b.1781.8		16	252.227	odd	6
2268.2.t.b.2105.8		16	36.7	odd	6
3024.2.ca.d.2033.1		16	7.3	odd	6
3024.2.ca.d.2609.1		16	9.5	odd	6
3024.2.df.d.17.1		16	63.59	even	6	inner
3024.2.df.d.1601.1		16	1.1	even	1	trivial
5292.2.w.b.521.8		16	28.11	odd	6
5292.2.w.b.1097.8		16	252.167	odd	6
5292.2.x.a.881.1		16	252.23	even	6
5292.2.x.a.4409.1		16	28.19	even	6
5292.2.x.b.881.8		16	252.131	odd	6
5292.2.x.b.4409.8		16	28.23	odd	6
5292.2.bm.a.2285.8		16	252.95	even	6
5292.2.bm.a.4625.8		16	28.27	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.86804 q^{5} +(1.83240 + 1.90848i) q^{7} +O(q^{10})\)	\(q-2.86804 q^{5} +(1.83240 + 1.90848i) q^{7} -2.71286i q^{11} +(3.18987 - 1.84167i) q^{13} +(3.22192 + 5.58052i) q^{17} +(-2.73867 - 1.58117i) q^{19} -2.99146i q^{23} +3.22563 q^{25} +(2.48332 + 1.43375i) q^{29} +(-8.26739 - 4.77318i) q^{31} +(-5.25540 - 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(-0.794538 - 1.37618i) q^{41} +(4.67828 - 8.10302i) q^{43} +(5.65372 + 9.79254i) q^{47} +(-0.284592 + 6.99421i) q^{49} +(2.16419 - 1.24950i) q^{53} +7.78058i q^{55} +(-4.33680 + 7.51156i) q^{59} +(-0.566915 + 0.327308i) q^{61} +(-9.14867 + 5.28199i) q^{65} +(3.86146 - 6.68825i) q^{67} -7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(5.17744 - 4.97106i) q^{77} +(2.59566 + 4.49581i) q^{79} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(3.14826 - 5.45295i) q^{89} +(9.35993 + 2.71312i) q^{91} +(7.85460 + 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7}+O(q^{10}) \) 16 * q + q^7	\( 16 q + q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + 15 q^{35} + q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 13 q^{49} - 15 q^{59} + 3 q^{61} + 39 q^{65} + 7 q^{67} + 45 q^{77} + q^{79} + 6 q^{85} + 21 q^{89} - 9 q^{91} + 6 q^{95} + 3 q^{97}+O(q^{100}) \) 16 * q + q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + 15 * q^35 + q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 13 * q^49 - 15 * q^59 + 3 * q^61 + 39 * q^65 + 7 * q^67 + 45 * q^77 + q^79 + 6 * q^85 + 21 * q^89 - 9 * q^91 + 6 * q^95 + 3 * q^97

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