LMFDB - Embedded newform 3024.2.t.i.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.i.1873.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +O(q^{10})$	$q+0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +1.66404 q^{11} +(0.0999454 + 0.173111i) q^{13} +(-3.13555 - 5.43093i) q^{17} +(-3.45879 + 5.99080i) q^{19} -6.18184 q^{23} -4.97861 q^{25} +(2.46757 - 4.27396i) q^{29} +(-1.25890 + 2.18047i) q^{31} +(-0.0117348 - 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(-1.15895 - 2.00736i) q^{41} +(0.940993 - 1.62985i) q^{43} +(0.905887 + 1.56904i) q^{47} +(-6.98712 + 0.424396i) q^{49} +(2.67307 + 4.62989i) q^{53} +0.243359 q^{55} +(2.28549 - 3.95859i) q^{59} +(0.339138 + 0.587404i) q^{61} +(0.0146166 + 0.0253167i) q^{65} +(-3.09342 + 5.35796i) q^{67} +1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(-0.133523 - 4.40061i) q^{77} +(6.39787 + 11.0814i) q^{79} +(3.75687 - 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-4.53394 + 7.85301i) q^{89} +(0.449777 - 0.278199i) q^{91} +(-0.505833 + 0.876128i) q^{95} +(-3.98514 + 6.90246i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{5} + q^{7}+O(q^{10}) $ 10 * q + 8 * q^5 + q^7	$ 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.146246			0.0654030			0.0327015	−	0.999465i	$-0.489589\pi$
$5$	0.146246			0.0654030			0.0327015	+	0.999465i	$0.489589\pi$
$6$		0			0
$7$	−0.0802402	−	2.64453i	−0.0303280	−	0.999540i
$7$	−0.0802402	−	2.64453i	−0.0303280	−	0.999540i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.66404			0.501727			0.250864	−	0.968022i	$-0.419285\pi$
$11$	1.66404			0.501727			0.250864	+	0.968022i	$0.419285\pi$
$12$		0			0
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	0.879553	−	0.475802i	$-0.157842\pi$
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	−0.851833	+	0.523814i	$0.824509\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.13555	−	5.43093i	−0.760483	−	1.31720i	−0.942602	−	0.333919i	$-0.891629\pi$
$17$	−3.13555	−	5.43093i	−0.760483	−	1.31720i	0.182119	−	0.983277i	$-0.441704\pi$
$18$		0			0
$19$	−3.45879	+	5.99080i	−0.793500	+	1.37438i	0.130287	+	0.991476i	$0.458410\pi$
$19$	−3.45879	+	5.99080i	−0.793500	+	1.37438i	−0.923787	+	0.382907i	$0.874923\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.18184			−1.28900			−0.644501	−	0.764604i	$-0.722935\pi$
$23$	−6.18184			−1.28900			−0.644501	+	0.764604i	$0.722935\pi$
$24$		0			0
$25$	−4.97861			−0.995722
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	−0.540650	−	0.841248i	$-0.681822\pi$
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	0.998867	+	0.0475930i	$0.0151551\pi$
$30$		0			0
$31$	−1.25890	+	2.18047i	−0.226105	+	0.391625i	−0.956650	−	0.291239i	$-0.905932\pi$
$31$	−1.25890	+	2.18047i	−0.226105	+	0.391625i	0.730546	+	0.682864i	$0.239266\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0117348	−	0.386752i	−0.00198354	−	0.0653730i
$36$		0			0
$37$	−3.50023	+	6.06257i	−0.575434	+	0.996681i	0.420560	+	0.907264i	$0.361833\pi$
$37$	−3.50023	+	6.06257i	−0.575434	+	0.996681i	−0.995994	+	0.0894162i	$0.971500\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	0.761223	−	0.648491i	$-0.224599\pi$
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	−0.942221	+	0.334993i	$0.891266\pi$
$42$		0			0
$43$	0.940993	−	1.62985i	0.143500	−	0.248550i	−0.785312	−	0.619100i	$-0.787498\pi$
$43$	0.940993	−	1.62985i	0.143500	−	0.248550i	0.928812	+	0.370550i	$0.120831\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.905887	+	1.56904i	0.132137	+	0.228868i	0.924500	−	0.381181i	$-0.124483\pi$
$47$	0.905887	+	1.56904i	0.132137	+	0.228868i	−0.792363	+	0.610050i	$0.791149\pi$
$48$		0			0
$49$	−6.98712	+	0.424396i	−0.998160	+	0.0606280i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.67307	+	4.62989i	0.367174	+	0.635964i	0.989123	−	0.147094i	$-0.0469920\pi$
$53$	2.67307	+	4.62989i	0.367174	+	0.635964i	−0.621948	+	0.783058i	$0.713659\pi$
$54$		0			0
$55$	0.243359			0.0328145
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.28549	−	3.95859i	0.297546	−	0.515364i	−0.678028	−	0.735036i	$-0.737165\pi$
$59$	2.28549	−	3.95859i	0.297546	−	0.515364i	0.975574	+	0.219672i	$0.0704986\pi$
$60$		0			0
$61$	0.339138	+	0.587404i	0.0434221	+	0.0752094i	0.886920	−	0.461924i	$-0.152841\pi$
$61$	0.339138	+	0.587404i	0.0434221	+	0.0752094i	−0.843498	+	0.537133i	$0.819507\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0146166	+	0.0253167i	0.00181296	+	0.00314015i
$66$		0			0
$67$	−3.09342	+	5.35796i	−0.377921	+	0.654579i	−0.990760	−	0.135630i	$-0.956694\pi$
$67$	−3.09342	+	5.35796i	−0.377921	+	0.654579i	0.612838	+	0.790208i	$0.290028\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.27749			0.151611			0.0758053	−	0.997123i	$-0.475847\pi$
$71$	1.27749			0.151611			0.0758053	+	0.997123i	$0.475847\pi$
$72$		0			0
$73$	−0.778603	−	1.34858i	−0.0911286	−	0.157839i	0.816858	−	0.576839i	$-0.195714\pi$
$73$	−0.778603	−	1.34858i	−0.0911286	−	0.157839i	−0.907986	+	0.419000i	$0.862381\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.133523	−	4.40061i	−0.0152164	−	0.501496i
$78$		0			0
$79$	6.39787	+	11.0814i	0.719817	+	1.24676i	0.961072	+	0.276298i	$0.0891075\pi$
$79$	6.39787	+	11.0814i	0.719817	+	1.24676i	−0.241255	+	0.970462i	$0.577559\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	−0.582778	−	0.812631i	$-0.698034\pi$
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	0.995148	+	0.0983854i	$0.0313678\pi$
$84$		0			0
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.53394	+	7.85301i	−0.480597	+	0.832418i	−0.999752	−	0.0222619i	$-0.992913\pi$
$89$	−4.53394	+	7.85301i	−0.480597	+	0.832418i	0.519155	+	0.854680i	$0.326247\pi$
$90$		0			0
$91$	0.449777	−	0.278199i	0.0471494	−	0.0291632i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.505833	+	0.876128i	−0.0518973	+	0.0898888i
$96$		0			0
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	−0.994278	−	0.106821i	$-0.965933\pi$
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	0.589649	+	0.807660i	$0.299266\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−14.8430			−1.47693			−0.738467	−	0.674290i	$-0.764450\pi$
$101$	−14.8430			−1.47693			−0.738467	+	0.674290i	$0.764450\pi$
$102$		0			0
$103$	0.203948			0.0200956			0.0100478	−	0.999950i	$-0.496802\pi$
$103$	0.203948			0.0200956			0.0100478	+	0.999950i	$0.496802\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.48444	−	6.03524i	0.336854	−	0.583448i	−0.646985	−	0.762503i	$-0.723970\pi$
$107$	3.48444	−	6.03524i	0.336854	−	0.583448i	0.983839	+	0.179054i	$0.0573038\pi$
$108$		0			0
$109$	3.33058	+	5.76874i	0.319012	+	0.552545i	0.980282	−	0.197603i	$-0.0633157\pi$
$109$	3.33058	+	5.76874i	0.319012	+	0.552545i	−0.661270	+	0.750148i	$0.729982\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	0.866933	−	0.498425i	$-0.166088\pi$
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	−0.865115	+	0.501573i	$0.832755\pi$
$114$		0			0
$115$	−0.904067			−0.0843047
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−14.1107	+	8.72785i	−1.29353	+	0.800081i
$120$		0			0
$121$	−8.23097			−0.748270
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.45933			−0.130526
$126$		0			0
$127$	−13.4788			−1.19605			−0.598027	−	0.801476i	$-0.704048\pi$
$127$	−13.4788			−1.19605			−0.598027	+	0.801476i	$0.704048\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−19.8333			−1.73284			−0.866422	−	0.499312i	$-0.833586\pi$
$131$	−19.8333			−1.73284			−0.866422	+	0.499312i	$0.833586\pi$
$132$		0			0
$133$	16.1204	+	8.66618i	1.39782	+	0.751453i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.44509			0.550642			0.275321	−	0.961352i	$-0.411216\pi$
$137$	6.44509			0.550642			0.275321	+	0.961352i	$0.411216\pi$
$138$		0			0
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	−0.999328	−	0.0366611i	$-0.988328\pi$
$139$	−6.26527	−	10.8518i	−0.531413	−	0.920435i	0.467914	−	0.883774i	$-0.345006\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.166313	+	0.288063i	0.0139078	+	0.0240890i
$144$		0			0
$145$	0.360872	−	0.625048i	0.0299688	−	0.0519074i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.7673			−1.45555			−0.727776	−	0.685815i	$-0.759446\pi$
$149$	−17.7673			−1.45555			−0.727776	+	0.685815i	$0.759446\pi$
$150$		0			0
$151$	−8.46599			−0.688953			−0.344476	−	0.938795i	$-0.611944\pi$
$151$	−8.46599			−0.688953			−0.344476	+	0.938795i	$0.611944\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.184108	+	0.318885i	−0.0147879	+	0.0256135i
$156$		0			0
$157$	−2.84968	+	4.93579i	−0.227429	+	0.393919i	−0.957045	−	0.289938i	$-0.906365\pi$
$157$	−2.84968	+	4.93579i	−0.227429	+	0.393919i	0.729616	+	0.683857i	$0.239699\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.496032	+	16.3481i	0.0390928	+	1.28841i
$162$		0			0
$163$	1.06267	−	1.84060i	0.0832349	−	0.144167i	−0.821403	−	0.570349i	$-0.806808\pi$
$163$	1.06267	−	1.84060i	0.0832349	−	0.144167i	0.904638	+	0.426181i	$0.140141\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	0.550415	−	0.834891i	$-0.314470\pi$
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	−0.998244	+	0.0592278i	$0.981136\pi$
$168$		0			0
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.95546	−	13.7793i	−0.604842	−	1.04762i	−0.992076	−	0.125636i	$-0.959903\pi$
$173$	−7.95546	−	13.7793i	−0.604842	−	1.04762i	0.387234	−	0.921981i	$-0.373430\pi$
$174$		0			0
$175$	0.399485	+	13.1661i	0.0301982	+	0.995264i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.87665	+	6.71456i	0.289755	+	0.501870i	0.973751	−	0.227615i	$-0.0730929\pi$
$179$	3.87665	+	6.71456i	0.289755	+	0.501870i	−0.683996	+	0.729485i	$0.739760\pi$
$180$		0			0
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.511893	+	0.886625i	−0.0376351	+	0.0651860i
$186$		0			0
$187$	−5.21769	−	9.03730i	−0.381555	−	0.660873i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.48383	+	4.30211i	0.179723	+	0.311290i	0.941786	−	0.336214i	$-0.109146\pi$
$191$	2.48383	+	4.30211i	0.179723	+	0.311290i	−0.762062	+	0.647504i	$0.775813\pi$
$192$		0			0
$193$	7.45221	−	12.9076i	0.536422	−	0.929110i	−0.462671	−	0.886530i	$-0.653109\pi$
$193$	7.45221	−	12.9076i	0.536422	−	0.929110i	0.999093	−	0.0425800i	$-0.0135577\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.2608			1.51477			0.757386	−	0.652968i	$-0.226476\pi$
$197$	21.2608			1.51477			0.757386	+	0.652968i	$0.226476\pi$
$198$		0			0
$199$	9.97208	+	17.2722i	0.706902	+	1.22439i	0.966001	+	0.258540i	$0.0832413\pi$
$199$	9.97208	+	17.2722i	0.706902	+	1.22439i	−0.259098	+	0.965851i	$0.583425\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−11.5006	−	6.18264i	−0.807186	−	0.433936i
$204$		0			0
$205$	−0.169492	−	0.293568i	−0.0118378	−	0.0205037i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.75556	+	9.96893i	−0.398121	+	0.689565i
$210$		0			0
$211$	−11.7569	−	20.3636i	−0.809381	−	1.40189i	−0.913293	−	0.407303i	$-0.866469\pi$
$211$	−11.7569	−	20.3636i	−0.809381	−	1.40189i	0.103912	−	0.994587i	$-0.466864\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.137616	−	0.238358i	0.00938535	−	0.0162559i
$216$		0			0
$217$	5.86735	+	3.15424i	0.398302	+	0.214123i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.626768	−	1.08559i	0.0421610	−	0.0730250i
$222$		0			0
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	−0.925969	−	0.377600i	$-0.876750\pi$
$223$	−2.03052	+	3.51696i	−0.135974	+	0.235513i	0.789995	+	0.613113i	$0.210083\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.85285			−0.255723			−0.127861	−	0.991792i	$-0.540811\pi$
$227$	−3.85285			−0.255723			−0.127861	+	0.991792i	$0.540811\pi$
$228$		0			0
$229$	13.1162			0.866746			0.433373	−	0.901215i	$-0.357323\pi$
$229$	13.1162			0.866746			0.433373	+	0.901215i	$0.357323\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.75115	−	15.1574i	0.573307	−	0.992997i	−0.422916	−	0.906169i	$-0.638993\pi$
$233$	8.75115	−	15.1574i	0.573307	−	0.992997i	0.996223	−	0.0868284i	$-0.0276732\pi$
$234$		0			0
$235$	0.132482	+	0.229466i	0.00864218	+	0.0149687i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	0.959752	−	0.280849i	$-0.0906161\pi$
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	−0.723099	+	0.690745i	$0.757283\pi$
$240$		0			0
$241$	6.23107			0.401378			0.200689	−	0.979655i	$-0.435682\pi$
$241$	6.23107			0.401378			0.200689	+	0.979655i	$0.435682\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.02184	+	0.0620661i	−0.0652827	+	0.00396526i
$246$		0			0
$247$	−1.38276			−0.0879829
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.65283			0.356803			0.178402	−	0.983958i	$-0.442907\pi$
$251$	5.65283			0.356803			0.178402	+	0.983958i	$0.442907\pi$
$252$		0			0
$253$	−10.2868			−0.646727
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.8016			−0.736166			−0.368083	−	0.929793i	$-0.619986\pi$
$257$	−11.8016			−0.736166			−0.368083	+	0.929793i	$0.619986\pi$
$258$		0			0
$259$	16.3135	+	8.77001i	1.01367	+	0.544942i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−22.2401			−1.37138			−0.685691	−	0.727893i	$-0.740500\pi$
$263$	−22.2401			−1.37138			−0.685691	+	0.727893i	$0.740500\pi$
$264$		0			0
$265$	0.390925	+	0.677101i	0.0240143	+	0.0415940i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.19442	+	2.06880i	0.0728251	+	0.126137i	0.900138	−	0.435604i	$-0.143465\pi$
$269$	1.19442	+	2.06880i	0.0728251	+	0.126137i	−0.827313	+	0.561741i	$0.810132\pi$
$270$		0			0
$271$	11.6129	−	20.1142i	0.705435	−	1.22185i	−0.261100	−	0.965312i	$-0.584085\pi$
$271$	11.6129	−	20.1142i	0.705435	−	1.22185i	0.966534	−	0.256537i	$-0.0825815\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.28461			−0.499581
$276$		0			0
$277$	−4.61800			−0.277469			−0.138734	−	0.990330i	$-0.544303\pi$
$277$	−4.61800			−0.277469			−0.138734	+	0.990330i	$0.544303\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	−0.986681	−	0.162668i	$-0.947990\pi$
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	0.634215	+	0.773157i	$0.281324\pi$
$282$		0			0
$283$	7.92483	−	13.7262i	0.471082	−	0.815939i	−0.528370	−	0.849014i	$-0.677197\pi$
$283$	7.92483	−	13.7262i	0.471082	−	0.815939i	0.999453	+	0.0330753i	$0.0105301\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.21555	+	3.22596i	−0.307864	+	0.190422i
$288$		0			0
$289$	−11.1634	+	19.3355i	−0.656669	+	1.13738i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	0.583330	−	0.812235i	$-0.301749\pi$
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	−0.995081	+	0.0990615i	$0.968416\pi$
$294$		0			0
$295$	0.334243	−	0.578927i	0.0194604	−	0.0337064i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.617846	−	1.07014i	−0.0357310	−	0.0618878i
$300$		0			0
$301$	−4.38569	−	2.35771i	−0.252787	−	0.135896i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.0495974	+	0.0859053i	0.00283994	+	0.00491892i
$306$		0			0
$307$	−27.3916			−1.56332			−0.781660	−	0.623704i	$-0.785627\pi$
$307$	−27.3916			−1.56332			−0.781660	+	0.623704i	$0.785627\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.02785	−	12.1726i	0.398513	−	0.690244i	−0.595030	−	0.803704i	$-0.702860\pi$
$311$	7.02785	−	12.1726i	0.398513	−	0.690244i	0.993543	+	0.113459i	$0.0361931\pi$
$312$		0			0
$313$	−10.8723	−	18.8314i	−0.614540	−	1.06441i	−0.990465	−	0.137764i	$-0.956008\pi$
$313$	−10.8723	−	18.8314i	−0.614540	−	1.06441i	0.375925	−	0.926650i	$-0.377325\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.28148	+	7.41575i	0.240472	+	0.416510i	0.960849	−	0.277073i	$-0.0893644\pi$
$317$	4.28148	+	7.41575i	0.240472	+	0.416510i	−0.720377	+	0.693583i	$0.756031\pi$
$318$		0			0
$319$	4.10614	−	7.11204i	0.229900	−	0.398198i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	43.3808			2.41377
$324$		0			0
$325$	−0.497589	−	0.861850i	−0.0276013	−	0.0478068i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.07670	−	2.52155i	0.224756	−	0.139018i
$330$		0			0
$331$	5.42360	+	9.39396i	0.298108	+	0.516339i	0.975703	−	0.219097i	$-0.0703110\pi$
$331$	5.42360	+	9.39396i	0.298108	+	0.516339i	−0.677595	+	0.735435i	$0.736978\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.452399	+	0.783578i	−0.0247172	+	0.0428114i
$336$		0			0
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.09486	+	3.62840i	−0.113443	+	0.196489i
$342$		0			0
$343$	1.68298	+	18.4436i	0.0908723	+	0.995863i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.76652	−	9.98790i	0.309563	−	0.536178i	−0.668704	−	0.743529i	$-0.733151\pi$
$347$	5.76652	−	9.98790i	0.309563	−	0.536178i	0.978267	+	0.207350i	$0.0664840\pi$
$348$		0			0
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	−0.960186	−	0.279362i	$-0.909877\pi$
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	0.722027	+	0.691865i	$0.243211\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.64699			0.140885			0.0704424	−	0.997516i	$-0.477559\pi$
$353$	2.64699			0.140885			0.0704424	+	0.997516i	$0.477559\pi$
$354$		0			0
$355$	0.186828			0.00991579
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.9835	+	22.4882i	−0.685245	+	1.18688i	0.288114	+	0.957596i	$0.406972\pi$
$359$	−12.9835	+	22.4882i	−0.685245	+	1.18688i	−0.973360	+	0.229284i	$0.926362\pi$
$360$		0			0
$361$	−14.4264	−	24.9873i	−0.759286	−	1.31512i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.113867	−	0.197224i	−0.00596009	−	0.0103232i
$366$		0			0
$367$	−17.5874			−0.918056			−0.459028	−	0.888422i	$-0.651802\pi$
$367$	−17.5874			−0.918056			−0.459028	+	0.888422i	$0.651802\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.0294	−	7.44052i	0.624536	−	0.386293i
$372$		0			0
$373$	0.815075			0.0422030			0.0211015	−	0.999777i	$-0.493283\pi$
$373$	0.815075			0.0422030			0.0211015	+	0.999777i	$0.493283\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.986490			0.0508068
$378$		0			0
$379$	20.4312			1.04948			0.524741	−	0.851262i	$-0.324162\pi$
$379$	20.4312			1.04948			0.524741	+	0.851262i	$0.324162\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.8928			0.914278			0.457139	−	0.889395i	$-0.348874\pi$
$383$	17.8928			0.914278			0.457139	+	0.889395i	$0.348874\pi$
$384$		0			0
$385$	−0.0195272	−	0.643571i	−0.000995196	−	0.0327994i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.6278			−0.792363			−0.396181	−	0.918172i	$-0.629665\pi$
$389$	−15.6278			−0.792363			−0.396181	+	0.918172i	$0.629665\pi$
$390$		0			0
$391$	19.3835	+	33.5731i	0.980264	+	1.69787i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.935661	+	1.62061i	0.0470782	+	0.0815419i
$396$		0			0
$397$	9.63064	−	16.6808i	0.483348	−	0.837183i	−0.516469	−	0.856306i	$-0.672754\pi$
$397$	9.63064	−	16.6808i	0.483348	−	0.837183i	0.999817	+	0.0191225i	$0.00608724\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.3013			−0.714172			−0.357086	−	0.934072i	$-0.616230\pi$
$401$	−14.3013			−0.714172			−0.357086	+	0.934072i	$0.616230\pi$
$402$		0			0
$403$	−0.503284			−0.0250704
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.82452	+	10.0884i	−0.288711	+	0.500062i
$408$		0			0
$409$	−15.9305	+	27.5924i	−0.787712	+	1.36436i	0.139654	+	0.990200i	$0.455401\pi$
$409$	−15.9305	+	27.5924i	−0.787712	+	1.36436i	−0.927366	+	0.374156i	$0.877932\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.6520	−	5.72643i	−0.524151	−	0.281779i
$414$		0			0
$415$	0.549426	−	0.951633i	0.0269702	−	0.0467138i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	0.995036	+	0.0995110i	$0.0317278\pi$
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	−0.411339	+	0.911482i	$0.634939\pi$
$420$		0			0
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	15.6107	+	27.0385i	0.757230	+	1.31156i
$426$		0			0
$427$	1.52620	−	0.943995i	0.0738579	−	0.0456831i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.46382	+	4.26746i	0.118678	+	0.205556i	0.919244	−	0.393688i	$-0.128801\pi$
$431$	2.46382	+	4.26746i	0.118678	+	0.205556i	−0.800566	+	0.599244i	$0.795468\pi$
$432$		0			0
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	21.3817	−	37.0341i	1.02282	−	1.77158i
$438$		0			0
$439$	1.22411	+	2.12022i	0.0584235	+	0.101192i	0.893758	−	0.448550i	$-0.148059\pi$
$439$	1.22411	+	2.12022i	0.0584235	+	0.101192i	−0.835334	+	0.549742i	$0.814726\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.1475	+	22.7722i	0.624657	+	1.08194i	0.988607	+	0.150520i	$0.0480946\pi$
$443$	13.1475	+	22.7722i	0.624657	+	1.08194i	−0.363950	+	0.931419i	$0.618572\pi$
$444$		0			0
$445$	−0.663069	+	1.14847i	−0.0314325	+	0.0544427i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	38.7077			1.82673			0.913365	−	0.407141i	$-0.133474\pi$
$449$	38.7077			1.82673			0.913365	+	0.407141i	$0.133474\pi$
$450$		0			0
$451$	−1.92854	−	3.34034i	−0.0908116	−	0.157290i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0657779	−	0.0406855i	0.00308372	−	0.00190736i
$456$		0			0
$457$	4.57756	+	7.92856i	0.214129	+	0.370882i	0.953003	−	0.302961i	$-0.0979754\pi$
$457$	4.57756	+	7.92856i	0.214129	+	0.370882i	−0.738874	+	0.673844i	$0.764642\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	0.294070	+	0.955784i	$0.404990\pi$
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	−0.974768	+	0.223220i	$0.928343\pi$
$462$		0			0
$463$	8.21031	+	14.2207i	0.381565	+	0.660891i	0.991286	−	0.131726i	$-0.0420518\pi$
$463$	8.21031	+	14.2207i	0.381565	+	0.660891i	−0.609721	+	0.792616i	$0.708718\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.68632	−	13.3131i	0.355680	−	0.616057i	−0.631554	−	0.775332i	$-0.717582\pi$
$467$	7.68632	−	13.3131i	0.355680	−	0.616057i	0.987234	+	0.159276i	$0.0509158\pi$
$468$		0			0
$469$	14.4175	+	7.75073i	0.665739	+	0.357895i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.56585	−	2.71213i	0.0719979	−	0.124704i
$474$		0			0
$475$	17.2200	−	29.8259i	0.790106	−	1.36850i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−37.9291			−1.73303			−0.866513	−	0.499155i	$-0.833644\pi$
$479$	−37.9291			−1.73303			−0.866513	+	0.499155i	$0.833644\pi$
$480$		0			0
$481$	−1.39933			−0.0638038
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.582809	+	1.00946i	−0.0264640	+	0.0458370i
$486$		0			0
$487$	−2.30247	−	3.98800i	−0.104335	−	0.180714i	0.809131	−	0.587628i	$-0.199938\pi$
$487$	−2.30247	−	3.98800i	−0.104335	−	0.180714i	−0.913466	+	0.406914i	$0.866605\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	−0.973309	−	0.229497i	$-0.926292\pi$
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	0.287904	−	0.957659i	$-0.407042\pi$
$492$		0			0
$493$	−30.9488			−1.39386
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.102506	−	3.37837i	−0.00459804	−	0.151541i
$498$		0			0
$499$	−9.26871			−0.414925			−0.207462	−	0.978243i	$-0.566520\pi$
$499$	−9.26871			−0.414925			−0.207462	+	0.978243i	$0.566520\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−22.4230			−0.999791			−0.499896	−	0.866086i	$-0.666628\pi$
$503$	−22.4230			−0.999791			−0.499896	+	0.866086i	$0.666628\pi$
$504$		0			0
$505$	−2.17072			−0.0965960
$506$		0			0
$507$		0			0
$508$		0			0
$509$	37.6414			1.66843			0.834213	−	0.551443i	$-0.185923\pi$
$509$	37.6414			1.66843			0.834213	+	0.551443i	$0.185923\pi$
$510$		0			0
$511$	−3.50389	+	2.16725i	−0.155003	+	0.0958736i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.0298266			0.00131432
$516$		0			0
$517$	1.50743	+	2.61095i	0.0662969	+	0.114830i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.4641	−	30.2488i	−0.765117	−	1.32522i	−0.940185	−	0.340666i	$-0.889348\pi$
$521$	−17.4641	−	30.2488i	−0.765117	−	1.32522i	0.175067	−	0.984556i	$-0.443986\pi$
$522$		0			0
$523$	11.8735	−	20.5656i	0.519194	−	0.899270i	−0.480557	−	0.876963i	$-0.659566\pi$
$523$	11.8735	−	20.5656i	0.519194	−	0.899270i	0.999751	−	0.0223069i	$-0.00710109\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	15.7894			0.687795
$528$		0			0
$529$	15.2151			0.661526
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.231664	−	0.401254i	0.0100345	−	0.0173802i
$534$		0			0
$535$	0.509585	−	0.882627i	0.0220313	−	0.0381593i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11.6269	+	0.706212i	−0.500804	+	0.0304187i
$540$		0			0
$541$	8.58542	−	14.8704i	0.369116	−	0.639328i	−0.620311	−	0.784356i	$-0.712994\pi$
$541$	8.58542	−	14.8704i	0.369116	−	0.639328i	0.989428	+	0.145028i	$0.0463271\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.487083	+	0.843653i	0.0208643	+	0.0361381i
$546$		0			0
$547$	10.0046	−	17.3284i	0.427765	−	0.740910i	−0.568910	−	0.822400i	$-0.692635\pi$
$547$	10.0046	−	17.3284i	0.427765	−	0.740910i	0.996674	+	0.0814901i	$0.0259679\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	17.0696	+	29.5654i	0.727190	+	1.25953i
$552$		0			0
$553$	28.7919	−	17.8086i	1.22436	−	0.757297i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.122740	+	0.212593i	0.00520068	+	0.00900784i	0.868614	−	0.495489i	$-0.165011\pi$
$557$	0.122740	+	0.212593i	0.00520068	+	0.00900784i	−0.863413	+	0.504497i	$0.831678\pi$
$558$		0			0
$559$	0.376192			0.0159112
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.1255	−	38.3224i	0.932477	−	1.61510i	0.153404	−	0.988164i	$-0.450976\pi$
$563$	22.1255	−	38.3224i	0.932477	−	1.61510i	0.779073	−	0.626934i	$-0.215690\pi$
$564$		0			0
$565$	0.00282596	+	0.00489471i	0.000118889	+	0.000205922i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.76767	−	4.79374i	−0.116027	−	0.200964i	0.802163	−	0.597105i	$-0.203682\pi$
$569$	−2.76767	−	4.79374i	−0.116027	−	0.200964i	−0.918190	+	0.396141i	$0.870349\pi$
$570$		0			0
$571$	−2.05191	+	3.55400i	−0.0858696	+	0.148730i	−0.905761	−	0.423788i	$-0.860700\pi$
$571$	−2.05191	+	3.55400i	−0.0858696	+	0.148730i	0.819892	+	0.572518i	$0.194034\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	30.7770			1.28349
$576$		0			0
$577$	−2.82275	−	4.88915i	−0.117513	−	0.203538i	0.801269	−	0.598305i	$-0.204159\pi$
$577$	−2.82275	−	4.88915i	−0.117513	−	0.203538i	−0.918781	+	0.394767i	$0.870825\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−17.5097	−	9.41304i	−0.726423	−	0.390519i
$582$		0			0
$583$	4.44809	+	7.70433i	0.184221	+	0.319081i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	−0.605394	−	0.795926i	$-0.706985\pi$
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	0.991989	+	0.126324i	$0.0403180\pi$
$588$		0			0
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.43516	−	16.3422i	0.387456	−	0.671093i	−0.604651	−	0.796491i	$-0.706687\pi$
$593$	9.43516	−	16.3422i	0.387456	−	0.671093i	0.992107	+	0.125398i	$0.0400207\pi$
$594$		0			0
$595$	−2.06363	+	1.27641i	−0.0846005	+	0.0523277i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.33726	+	2.31620i	−0.0546388	+	0.0946372i	−0.892051	−	0.451934i	$-0.850734\pi$
$599$	−1.33726	+	2.31620i	−0.0546388	+	0.0946372i	0.837412	+	0.546572i	$0.184067\pi$
$600$		0			0
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	−0.968736	−	0.248095i	$-0.920196\pi$
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	0.699224	+	0.714902i	$0.253529\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.20374			−0.0489391
$606$		0			0
$607$	−25.8052			−1.04740			−0.523701	−	0.851902i	$-0.675449\pi$
$607$	−25.8052			−1.04740			−0.523701	+	0.851902i	$0.675449\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.181079	+	0.313637i	−0.00732565	+	0.0126884i
$612$		0			0
$613$	13.4766	+	23.3422i	0.544316	+	0.942784i	0.998650	+	0.0519519i	$0.0165443\pi$
$613$	13.4766	+	23.3422i	0.544316	+	0.942784i	−0.454333	+	0.890832i	$0.650122\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	0.945869	−	0.324549i	$-0.105212\pi$
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	−0.754002	+	0.656872i	$0.771879\pi$
$618$		0			0
$619$	−34.7071			−1.39500			−0.697499	−	0.716586i	$-0.745704\pi$
$619$	−34.7071			−1.39500			−0.697499	+	0.716586i	$0.745704\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	21.1314	+	11.3600i	0.846610	+	0.455130i
$624$		0			0
$625$	24.6796			0.987186
$626$		0			0
$627$		0			0
$628$		0			0
$629$	43.9006			1.75043
$630$		0			0
$631$	36.7963			1.46484			0.732419	−	0.680854i	$-0.238391\pi$
$631$	36.7963			1.46484			0.732419	+	0.680854i	$0.238391\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.97122			−0.0782256
$636$		0			0
$637$	−0.771798	−	1.16713i	−0.0305798	−	0.0462433i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	44.1844			1.74518			0.872590	−	0.488454i	$-0.162439\pi$
$641$	44.1844			1.74518			0.872590	+	0.488454i	$0.162439\pi$
$642$		0			0
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	0.687197	−	0.726471i	$-0.258841\pi$
$643$	−7.24065	−	12.5412i	−0.285543	−	0.494575i	−0.972741	+	0.231895i	$0.925507\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.6536	−	28.8448i	−0.654719	−	1.13401i	−0.981964	−	0.189068i	$-0.939453\pi$
$647$	−16.6536	−	28.8448i	−0.654719	−	1.13401i	0.327245	−	0.944940i	$-0.393880\pi$
$648$		0			0
$649$	3.80315	−	6.58725i	0.149287	−	0.258572i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.06643			0.354797			0.177398	−	0.984139i	$-0.443232\pi$
$653$	9.06643			0.354797			0.177398	+	0.984139i	$0.443232\pi$
$654$		0			0
$655$	−2.90054			−0.113333
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	−0.357184	−	0.934034i	$-0.616263\pi$
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	0.987489	−	0.157686i	$-0.0504035\pi$
$660$		0			0
$661$	4.32958	−	7.49905i	0.168401	−	0.291679i	−0.769457	−	0.638699i	$-0.779473\pi$
$661$	4.32958	−	7.49905i	0.168401	−	0.291679i	0.937858	+	0.347020i	$0.112806\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.35754	+	1.26739i	0.0914214	+	0.0491473i
$666$		0			0
$667$	−15.2541	+	26.4209i	−0.590642	+	1.02302i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.564339	+	0.977464i	0.0217861	+	0.0377346i
$672$		0			0
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.1657	+	33.1960i	0.736600	+	1.27583i	0.954018	+	0.299749i	$0.0969030\pi$
$677$	19.1657	+	33.1960i	0.736600	+	1.27583i	−0.217418	+	0.976078i	$0.569764\pi$
$678$		0			0
$679$	18.5736	+	9.98498i	0.712788	+	0.383188i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.31659	−	5.74450i	−0.126906	−	0.219807i	0.795570	−	0.605861i	$-0.207171\pi$
$683$	−3.31659	−	5.74450i	−0.126906	−	0.219807i	−0.922476	+	0.386054i	$0.873838\pi$
$684$		0			0
$685$	0.942567			0.0360136
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.534322	+	0.925472i	−0.0203560	+	0.0352577i
$690$		0			0
$691$	−11.6938	−	20.2542i	−0.444852	−	0.770506i	0.553190	−	0.833055i	$-0.313410\pi$
$691$	−11.6938	−	20.2542i	−0.444852	−	0.770506i	−0.998042	+	0.0625490i	$0.980077\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.916269	−	1.58702i	−0.0347561	−	0.0601992i
$696$		0			0
$697$	−7.26791	+	12.5884i	−0.275292	+	0.476819i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−9.26736			−0.350023			−0.175012	−	0.984566i	$-0.555996\pi$
$701$	−9.26736			−0.350023			−0.175012	+	0.984566i	$0.555996\pi$
$702$		0			0
$703$	−24.2131	−	41.9383i	−0.913214	−	1.58173i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.19101	+	39.2528i	0.0447924	+	1.47625i
$708$		0			0
$709$	−7.11775	−	12.3283i	−0.267313	−	0.462999i	0.700854	−	0.713305i	$-0.252802\pi$
$709$	−7.11775	−	12.3283i	−0.267313	−	0.462999i	−0.968167	+	0.250305i	$0.919469\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.78230	−	13.4793i	0.291449	−	0.504805i
$714$		0			0
$715$	0.0243226	+	0.0421280i	0.000909613	+	0.00157550i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.92848	−	12.0005i	0.258389	−	0.447542i	−0.707422	−	0.706792i	$-0.750142\pi$
$719$	6.92848	−	12.0005i	0.258389	−	0.447542i	0.965810	+	0.259249i	$0.0834752\pi$
$720$		0			0
$721$	−0.0163649	−	0.539348i	−0.000609459	−	0.0200864i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−12.2851	+	21.2784i	−0.456257	+	0.790260i
$726$		0			0
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	0.412928	+	0.910764i	$0.364506\pi$
$727$	−15.7000	+	27.1932i	−0.582280	+	1.00854i	−0.995208	+	0.0977755i	$0.968827\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−11.8021			−0.436518
$732$		0			0
$733$	−26.6006			−0.982515			−0.491257	−	0.871014i	$-0.663463\pi$
$733$	−26.6006			−0.982515			−0.491257	+	0.871014i	$0.663463\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.14757	+	8.91586i	−0.189613	+	0.328420i
$738$		0			0
$739$	−16.5019	−	28.5822i	−0.607034	−	1.05141i	−0.991727	−	0.128368i	$-0.959026\pi$
$739$	−16.5019	−	28.5822i	−0.607034	−	1.05141i	0.384693	−	0.923045i	$-0.374307\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	0.965570	+	0.260144i	$0.0837701\pi$
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	−0.257493	+	0.966280i	$0.582897\pi$
$744$		0			0
$745$	−2.59839			−0.0951975
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.2400	−	8.73047i	−0.593396	−	0.319004i
$750$		0			0
$751$	37.8996			1.38297			0.691487	−	0.722389i	$-0.256956\pi$
$751$	37.8996			1.38297			0.691487	+	0.722389i	$0.256956\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.23811			−0.0450596
$756$		0			0
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−27.7470			−1.00583			−0.502913	−	0.864337i	$-0.667739\pi$
$761$	−27.7470			−1.00583			−0.502913	+	0.864337i	$0.667739\pi$
$762$		0			0
$763$	14.9884	−	9.27072i	0.542616	−	0.335623i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.913698			0.0329917
$768$		0			0
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	0.735412	−	0.677621i	$-0.236989\pi$
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	−0.954542	+	0.298075i	$0.903655\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.7795	+	35.9912i	0.747388	+	1.29451i	0.949071	+	0.315063i	$0.102026\pi$
$773$	20.7795	+	35.9912i	0.747388	+	1.29451i	−0.201682	+	0.979451i	$0.564641\pi$
$774$		0			0
$775$	6.26756	−	10.8557i	0.225137	−	0.389950i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.0343			0.574488
$780$		0			0
$781$	2.12580			0.0760671
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.416753	+	0.721837i	−0.0148746	+	0.0257635i
$786$		0			0
$787$	−10.4484	+	18.0972i	−0.372446	+	0.645096i	−0.989941	−	0.141479i	$-0.954814\pi$
$787$	−10.4484	+	18.0972i	−0.372446	+	0.645096i	0.617495	+	0.786575i	$0.288148\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.0869596	−	0.0537869i	0.00309193	−	0.00191244i
$792$		0			0
$793$	−0.0677905	+	0.117417i	−0.00240731	+	0.00416959i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	0.871627	−	0.490171i	$-0.163066\pi$
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	−0.860313	+	0.509765i	$0.829732\pi$
$798$		0			0
$799$	5.68091	−	9.83963i	0.200976	−	0.348101i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.29563	−	2.24409i	−0.0457217	−	0.0791923i
$804$		0			0
$805$	0.0725425	+	2.39084i	0.00255679	+	0.0842659i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−25.2796	−	43.7856i	−0.888783	−	1.53942i	−0.841315	−	0.540545i	$-0.818218\pi$
$809$	−25.2796	−	43.7856i	−0.888783	−	1.53942i	−0.0474686	−	0.998873i	$-0.515115\pi$
$810$		0			0
$811$	0.784071			0.0275325			0.0137662	−	0.999905i	$-0.495618\pi$
$811$	0.784071			0.0275325			0.0137662	+	0.999905i	$0.495618\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.155411	−	0.269180i	0.00544382	−	0.00942897i
$816$		0			0
$817$	6.50939	+	11.2746i	0.227735	+	0.394448i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.7207	+	37.6213i	0.758056	+	1.31299i	0.943841	+	0.330401i	$0.107184\pi$
$821$	21.7207	+	37.6213i	0.758056	+	1.31299i	−0.185784	+	0.982591i	$0.559483\pi$
$822$		0			0
$823$	1.98273	−	3.43419i	0.0691136	−	0.119708i	−0.829398	−	0.558659i	$-0.811316\pi$
$823$	1.98273	−	3.43419i	0.0691136	−	0.119708i	0.898511	+	0.438950i	$0.144650\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	29.3159			1.01941			0.509707	−	0.860348i	$-0.329754\pi$
$827$	29.3159			1.01941			0.509707	+	0.860348i	$0.329754\pi$
$828$		0			0
$829$	−17.5213	−	30.3478i	−0.608541	−	1.05402i	−0.991481	−	0.130251i	$-0.958422\pi$
$829$	−17.5213	−	30.3478i	−0.608541	−	1.05402i	0.382940	−	0.923773i	$-0.374912\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	24.2134	+	36.6159i	0.838943	+	1.26867i
$834$		0			0
$835$	−0.846358	−	1.46593i	−0.0292894	−	0.0507308i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	0.334639	+	0.942347i	$0.391386\pi$
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	−0.983415	+	0.181368i	$0.941948\pi$
$840$		0			0
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.947675	−	1.64142i	0.0326010	−	0.0564666i
$846$		0			0
$847$	0.660455	+	21.7671i	0.0226935	+	0.747926i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	21.6378	−	37.4778i	0.741735	−	1.28472i
$852$		0			0
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	−0.436400	−	0.899753i	$-0.643747\pi$
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	0.997409	−	0.0719434i	$-0.0229201\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.5347			−0.940566			−0.470283	−	0.882516i	$-0.655848\pi$
$857$	−27.5347			−0.940566			−0.470283	+	0.882516i	$0.655848\pi$
$858$		0			0
$859$	46.5101			1.58690			0.793451	−	0.608634i	$-0.208282\pi$
$859$	46.5101			1.58690			0.793451	+	0.608634i	$0.208282\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.44007	−	4.22633i	0.0830610	−	0.143866i	−0.821502	−	0.570205i	$-0.806864\pi$
$863$	2.44007	−	4.22633i	0.0830610	−	0.143866i	0.904563	+	0.426339i	$0.140197\pi$
$864$		0			0
$865$	−1.16345	−	2.01516i	−0.0395585	−	0.0685174i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.6463	+	18.4400i	0.361152	+	0.625533i
$870$		0			0
$871$	−1.23669			−0.0419037
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.117097	+	3.85924i	0.00395860	+	0.130466i
$876$		0			0
$877$	39.2892			1.32670			0.663352	−	0.748308i	$-0.269133\pi$
$877$	39.2892			1.32670			0.663352	+	0.748308i	$0.269133\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−47.3713			−1.59598			−0.797990	−	0.602670i	$-0.794103\pi$
$881$	−47.3713			−1.59598			−0.797990	+	0.602670i	$0.794103\pi$
$882$		0			0
$883$	2.67206			0.0899221			0.0449610	−	0.998989i	$-0.485684\pi$
$883$	2.67206			0.0899221			0.0449610	+	0.998989i	$0.485684\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.9600			−0.770922			−0.385461	−	0.922724i	$-0.625958\pi$
$887$	−22.9600			−0.770922			−0.385461	+	0.922724i	$0.625958\pi$
$888$		0			0
$889$	1.08155	+	35.6453i	0.0362739	+	1.19550i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.5331			−0.419404
$894$		0			0
$895$	0.566944	+	0.981976i	0.0189508	+	0.0328238i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.21284	+	10.7610i	0.207210	+	0.358898i
$900$		0			0
$901$	16.7631	−	29.0345i	0.558459	−	0.967280i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.77862			−0.0591232
$906$		0			0
$907$	27.8982			0.926345			0.463173	−	0.886268i	$-0.346711\pi$
$907$	27.8982			0.926345			0.463173	+	0.886268i	$0.346711\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	0.368513	+	0.929623i	$0.379867\pi$
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	−0.989333	+	0.145670i	$0.953466\pi$
$912$		0			0
$913$	6.25158	−	10.8281i	0.206897	−	0.358356i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.59143	+	52.4499i	0.0525536	+	1.73205i
$918$		0			0
$919$	15.1073	−	26.1667i	0.498345	−	0.863160i	−0.501653	−	0.865069i	$-0.667274\pi$
$919$	15.1073	−	26.1667i	0.498345	−	0.863160i	0.999998	+	0.00190951i	$0.000607816\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.127680	+	0.221147i	0.00420262	+	0.00727916i
$924$		0			0
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−22.9675	−	39.7809i	−0.753540	−	1.30517i	−0.946097	−	0.323884i	$-0.895011\pi$
$929$	−22.9675	−	39.7809i	−0.753540	−	1.30517i	0.192556	−	0.981286i	$-0.438322\pi$
$930$		0			0
$931$	21.6245	−	43.3263i	0.708715	−	1.41996i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.763064	−	1.32167i	−0.0249549	−	0.0432231i
$936$		0			0
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	24.7002	−	42.7819i	0.805202	−	1.39465i	−0.110952	−	0.993826i	$-0.535390\pi$
$941$	24.7002	−	42.7819i	0.805202	−	1.39465i	0.916154	−	0.400825i	$-0.131277\pi$
$942$		0			0
$943$	7.16445	+	12.4092i	0.233307	+	0.404099i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.8253	−	27.4102i	−0.514252	−	0.890711i	−0.999863	−	0.0165357i	$-0.994736\pi$
$947$	−15.8253	−	27.4102i	−0.514252	−	0.890711i	0.485611	−	0.874175i	$-0.338597\pi$
$948$		0			0
$949$	0.155636	−	0.269569i	0.00505214	−	0.00875057i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	19.1237			0.619477			0.309739	−	0.950822i	$-0.399758\pi$
$953$	19.1237			0.619477			0.309739	+	0.950822i	$0.399758\pi$
$954$		0			0
$955$	0.363249	+	0.629165i	0.0117545	+	0.0203593i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.517156	−	17.0443i	−0.0166998	−	0.550388i
$960$		0			0
$961$	12.3304	+	21.3568i	0.397753	+	0.688929i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.08985	−	1.88768i	0.0350836	−	0.0607666i
$966$		0			0
$967$	−4.98525	−	8.63470i	−0.160315	−	0.277673i	0.774667	−	0.632370i	$-0.217918\pi$
$967$	−4.98525	−	8.63470i	−0.160315	−	0.277673i	−0.934982	+	0.354696i	$0.884584\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.522554	−	0.905090i	0.0167695	−	0.0290457i	−0.857519	−	0.514453i	$-0.827995\pi$
$971$	0.522554	−	0.905090i	0.0167695	−	0.0290457i	0.874288	+	0.485407i	$0.161329\pi$
$972$		0			0
$973$	−28.1951	+	17.4395i	−0.903895	+	0.559084i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.44308	+	16.3559i	−0.302111	+	0.523272i	−0.976614	−	0.215001i	$-0.931025\pi$
$977$	−9.44308	+	16.3559i	−0.302111	+	0.523272i	0.674503	+	0.738272i	$0.264358\pi$
$978$		0			0
$979$	−7.54466	+	13.0677i	−0.241128	+	0.417647i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.28891			0.0730050			0.0365025	−	0.999334i	$-0.488378\pi$
$983$	2.28891			0.0730050			0.0365025	+	0.999334i	$0.488378\pi$
$984$		0			0
$985$	3.10930			0.0990707
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.81707	+	10.0755i	−0.184972	+	0.320381i
$990$		0			0
$991$	9.53491	+	16.5150i	0.302886	+	0.524615i	0.976789	−	0.214206i	$-0.0687164\pi$
$991$	9.53491	+	16.5150i	0.302886	+	0.524615i	−0.673902	+	0.738821i	$0.735383\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.45837	+	2.52598i	0.0462336	+	0.0800789i
$996$		0			0
$997$	37.0151			1.17228			0.586139	−	0.810210i	$-0.300647\pi$
$997$	37.0151			1.17228			0.586139	+	0.810210i	$0.300647\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.i.289.3		10
3.2	odd	2		1008.2.t.i.961.2		10
4.3	odd	2		189.2.g.b.100.5		10
7.4	even	3		3024.2.q.i.2881.3		10
9.4	even	3		3024.2.q.i.2305.3		10
9.5	odd	6		1008.2.q.i.625.5		10
12.11	even	2		63.2.g.b.16.1	yes	10
21.11	odd	6		1008.2.q.i.529.5		10
28.3	even	6		1323.2.h.f.802.1		10
28.11	odd	6		189.2.h.b.46.1		10
28.19	even	6		1323.2.f.f.883.5		10
28.23	odd	6		1323.2.f.e.883.5		10
28.27	even	2		1323.2.g.f.667.5		10
36.7	odd	6		567.2.e.e.163.5		10
36.11	even	6		567.2.e.f.163.1		10
36.23	even	6		63.2.h.b.58.5	yes	10
36.31	odd	6		189.2.h.b.37.1		10
63.4	even	3	inner	3024.2.t.i.1873.3		10
63.32	odd	6		1008.2.t.i.193.2		10
84.11	even	6		63.2.h.b.25.5	yes	10
84.23	even	6		441.2.f.e.295.1		10
84.47	odd	6		441.2.f.f.295.1		10
84.59	odd	6		441.2.h.f.214.5		10
84.83	odd	2		441.2.g.f.79.1		10
252.11	even	6		567.2.e.f.487.1		10
252.23	even	6		441.2.f.e.148.1		10
252.31	even	6		1323.2.g.f.361.5		10
252.47	odd	6		3969.2.a.ba.1.5		5
252.59	odd	6		441.2.g.f.67.1		10
252.67	odd	6		189.2.g.b.172.5		10
252.79	odd	6		3969.2.a.bc.1.1		5
252.95	even	6		63.2.g.b.4.1	✓	10
252.103	even	6		1323.2.f.f.442.5		10
252.131	odd	6		441.2.f.f.148.1		10
252.139	even	6		1323.2.h.f.226.1		10
252.151	odd	6		567.2.e.e.487.5		10
252.167	odd	6		441.2.h.f.373.5		10
252.187	even	6		3969.2.a.bb.1.1		5
252.191	even	6		3969.2.a.z.1.5		5
252.247	odd	6		1323.2.f.e.442.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	252.95	even	6
63.2.g.b.16.1	yes	10	12.11	even	2
63.2.h.b.25.5	yes	10	84.11	even	6
63.2.h.b.58.5	yes	10	36.23	even	6
189.2.g.b.100.5		10	4.3	odd	2
189.2.g.b.172.5		10	252.67	odd	6
189.2.h.b.37.1		10	36.31	odd	6
189.2.h.b.46.1		10	28.11	odd	6
441.2.f.e.148.1		10	252.23	even	6
441.2.f.e.295.1		10	84.23	even	6
441.2.f.f.148.1		10	252.131	odd	6
441.2.f.f.295.1		10	84.47	odd	6
441.2.g.f.67.1		10	252.59	odd	6
441.2.g.f.79.1		10	84.83	odd	2
441.2.h.f.214.5		10	84.59	odd	6
441.2.h.f.373.5		10	252.167	odd	6
567.2.e.e.163.5		10	36.7	odd	6
567.2.e.e.487.5		10	252.151	odd	6
567.2.e.f.163.1		10	36.11	even	6
567.2.e.f.487.1		10	252.11	even	6
1008.2.q.i.529.5		10	21.11	odd	6
1008.2.q.i.625.5		10	9.5	odd	6
1008.2.t.i.193.2		10	63.32	odd	6
1008.2.t.i.961.2		10	3.2	odd	2
1323.2.f.e.442.5		10	252.247	odd	6
1323.2.f.e.883.5		10	28.23	odd	6
1323.2.f.f.442.5		10	252.103	even	6
1323.2.f.f.883.5		10	28.19	even	6
1323.2.g.f.361.5		10	252.31	even	6
1323.2.g.f.667.5		10	28.27	even	2
1323.2.h.f.226.1		10	252.139	even	6
1323.2.h.f.802.1		10	28.3	even	6
3024.2.q.i.2305.3		10	9.4	even	3
3024.2.q.i.2881.3		10	7.4	even	3
3024.2.t.i.289.3		10	1.1	even	1	trivial
3024.2.t.i.1873.3		10	63.4	even	3	inner
3969.2.a.z.1.5		5	252.191	even	6
3969.2.a.ba.1.5		5	252.47	odd	6
3969.2.a.bb.1.1		5	252.187	even	6
3969.2.a.bc.1.1		5	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +O(q^{10})\)	\(q+0.146246 q^{5} +(-0.0802402 - 2.64453i) q^{7} +1.66404 q^{11} +(0.0999454 + 0.173111i) q^{13} +(-3.13555 - 5.43093i) q^{17} +(-3.45879 + 5.99080i) q^{19} -6.18184 q^{23} -4.97861 q^{25} +(2.46757 - 4.27396i) q^{29} +(-1.25890 + 2.18047i) q^{31} +(-0.0117348 - 0.386752i) q^{35} +(-3.50023 + 6.06257i) q^{37} +(-1.15895 - 2.00736i) q^{41} +(0.940993 - 1.62985i) q^{43} +(0.905887 + 1.56904i) q^{47} +(-6.98712 + 0.424396i) q^{49} +(2.67307 + 4.62989i) q^{53} +0.243359 q^{55} +(2.28549 - 3.95859i) q^{59} +(0.339138 + 0.587404i) q^{61} +(0.0146166 + 0.0253167i) q^{65} +(-3.09342 + 5.35796i) q^{67} +1.27749 q^{71} +(-0.778603 - 1.34858i) q^{73} +(-0.133523 - 4.40061i) q^{77} +(6.39787 + 11.0814i) q^{79} +(3.75687 - 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-4.53394 + 7.85301i) q^{89} +(0.449777 - 0.278199i) q^{91} +(-0.505833 + 0.876128i) q^{95} +(-3.98514 + 6.90246i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{5} + q^{7}+O(q^{10}) \) 10 * q + 8 * q^5 + q^7	\( 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

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