LMFDB - Embedded newform 3024.2.cc.b.881.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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, 3]))

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (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} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.5
Root			$-0.0967785 - 1.72934i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.b.2897.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.183299 - 0.317483i) q^{5} +(-2.53871 - 0.744936i) q^{7} +O(q^{10})$	$q+(0.183299 - 0.317483i) q^{5} +(-2.53871 - 0.744936i) q^{7} +(0.579764 - 0.334727i) q^{11} +(-0.867380 - 0.500782i) q^{13} +4.98906 q^{17} +6.35722i q^{19} +(-6.66371 - 3.84729i) q^{23} +(2.43280 + 4.21374i) q^{25} +(-1.58394 + 0.914490i) q^{29} +(-5.47837 - 3.16294i) q^{31} +(-0.701849 + 0.669453i) q^{35} -5.16789 q^{37} +(2.15928 - 3.73998i) q^{41} +(-2.24922 - 3.89576i) q^{43} +(4.16450 + 7.21313i) q^{47} +(5.89014 + 3.78236i) q^{49} -0.245420i q^{55} +(4.36348 - 7.55776i) q^{59} +(-4.29351 + 2.47886i) q^{61} +(-0.317980 + 0.183586i) q^{65} +(-5.44537 + 9.43166i) q^{67} +5.49843i q^{71} +4.07314i q^{73} +(-1.72120 + 0.417889i) q^{77} +(4.17784 + 7.23623i) q^{79} +(8.50712 + 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} -10.7113 q^{89} +(1.82898 + 1.91749i) q^{91} +(2.01831 + 1.16527i) q^{95} +(-14.9093 + 8.60787i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.183299	−	0.317483i	0.0819738	−	0.141983i	−0.822124	−	0.569309i	$-0.807211\pi$
$5$	0.183299	−	0.317483i	0.0819738	−	0.141983i	0.904098	+	0.427326i	$0.140544\pi$
$6$		0			0
$7$	−2.53871	−	0.744936i	−0.959544	−	0.281559i
$7$	−2.53871	−	0.744936i	−0.959544	−	0.281559i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.579764	−	0.334727i	0.174805	−	0.100924i	−0.410044	−	0.912066i	$-0.634487\pi$
$11$	0.579764	−	0.334727i	0.174805	−	0.100924i	0.584850	+	0.811142i	$0.301153\pi$
$12$		0			0
$13$	−0.867380	−	0.500782i	−0.240568	−	0.138892i	0.374870	−	0.927077i	$-0.377687\pi$
$13$	−0.867380	−	0.500782i	−0.240568	−	0.138892i	−0.615438	+	0.788185i	$0.711021\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.98906			1.21003			0.605013	−	0.796216i	$-0.293168\pi$
$17$	4.98906			1.21003			0.605013	+	0.796216i	$0.293168\pi$
$18$		0			0
$19$			6.35722i			1.45845i	0.684275	+	0.729224i	$0.260119\pi$
$19$			6.35722i			1.45845i	−0.684275	+	0.729224i	$0.739881\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.66371	−	3.84729i	−1.38948	−	0.802216i	−0.396223	−	0.918154i	$-0.629679\pi$
$23$	−6.66371	−	3.84729i	−1.38948	−	0.802216i	−0.993256	+	0.115938i	$0.963012\pi$
$24$		0			0
$25$	2.43280	+	4.21374i	0.486561	+	0.842748i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.58394	+	0.914490i	−0.294131	+	0.169817i	−0.639803	−	0.768539i	$-0.720984\pi$
$29$	−1.58394	+	0.914490i	−0.294131	+	0.169817i	0.345672	+	0.938355i	$0.387651\pi$
$30$		0			0
$31$	−5.47837	−	3.16294i	−0.983944	−	0.568081i	−0.0804857	−	0.996756i	$-0.525647\pi$
$31$	−5.47837	−	3.16294i	−0.983944	−	0.568081i	−0.903459	+	0.428675i	$0.858980\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.701849	+	0.669453i	−0.118634	+	0.113158i
$36$		0			0
$37$	−5.16789			−0.849595			−0.424798	−	0.905288i	$-0.639655\pi$
$37$	−5.16789			−0.849595			−0.424798	+	0.905288i	$0.639655\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.15928	−	3.73998i	0.337223	−	0.584087i	−0.646686	−	0.762756i	$-0.723846\pi$
$41$	2.15928	−	3.73998i	0.337223	−	0.584087i	0.983909	+	0.178669i	$0.0571790\pi$
$42$		0			0
$43$	−2.24922	−	3.89576i	−0.343002	−	0.594098i	0.641986	−	0.766716i	$-0.278111\pi$
$43$	−2.24922	−	3.89576i	−0.343002	−	0.594098i	−0.984989	+	0.172618i	$0.944777\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.16450	+	7.21313i	0.607455	+	1.05214i	0.991658	+	0.128895i	$0.0411429\pi$
$47$	4.16450	+	7.21313i	0.607455	+	1.05214i	−0.384203	+	0.923249i	$0.625524\pi$
$48$		0			0
$49$	5.89014	+	3.78236i	0.841449	+	0.540337i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		−	0.245420i		−	0.0330925i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.36348	−	7.55776i	0.568076	−	0.983937i	−0.428680	−	0.903456i	$-0.641021\pi$
$59$	4.36348	−	7.55776i	0.568076	−	0.983937i	0.996756	−	0.0804804i	$-0.0256455\pi$
$60$		0			0
$61$	−4.29351	+	2.47886i	−0.549727	+	0.317385i	−0.749012	−	0.662556i	$-0.769471\pi$
$61$	−4.29351	+	2.47886i	−0.549727	+	0.317385i	0.199285	+	0.979942i	$0.436138\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.317980	+	0.183586i	−0.0394406	+	0.0227710i
$66$		0			0
$67$	−5.44537	+	9.43166i	−0.665258	+	1.15226i	0.313958	+	0.949437i	$0.398345\pi$
$67$	−5.44537	+	9.43166i	−0.665258	+	1.15226i	−0.979215	+	0.202823i	$0.934988\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5.49843i			0.652544i	0.945276	+	0.326272i	$0.105793\pi$
$71$			5.49843i			0.652544i	−0.945276	+	0.326272i	$0.894207\pi$
$72$		0			0
$73$			4.07314i			0.476725i	0.971176	+	0.238363i	$0.0766106\pi$
$73$			4.07314i			0.476725i	−0.971176	+	0.238363i	$0.923389\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.72120	+	0.417889i	−0.196149	+	0.0476229i
$78$		0			0
$79$	4.17784	+	7.23623i	0.470044	+	0.814140i	0.999413	−	0.0342518i	$-0.0109048\pi$
$79$	4.17784	+	7.23623i	0.470044	+	0.814140i	−0.529370	+	0.848391i	$0.677571\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.50712	+	14.7348i	0.933778	+	1.61735i	0.776798	+	0.629750i	$0.216842\pi$
$83$	8.50712	+	14.7348i	0.933778	+	1.61735i	0.156980	+	0.987602i	$0.449824\pi$
$84$		0			0
$85$	0.914490	−	1.58394i	0.0991904	−	0.171803i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−10.7113			−1.13540			−0.567699	−	0.823236i	$-0.692166\pi$
$89$	−10.7113			−1.13540			−0.567699	+	0.823236i	$0.692166\pi$
$90$		0			0
$91$	1.82898	+	1.91749i	0.191729	+	0.201007i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.01831	+	1.16527i	0.207074	+	0.119555i
$96$		0			0
$97$	−14.9093	+	8.60787i	−1.51381	+	0.873997i	−0.513937	+	0.857828i	$0.671814\pi$
$97$	−14.9093	+	8.60787i	−1.51381	+	0.873997i	−0.999869	+	0.0161687i	$0.994853\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.86586	+	13.6241i	0.782683	+	1.35565i	0.930374	+	0.366613i	$0.119483\pi$
$101$	7.86586	+	13.6241i	0.782683	+	1.35565i	−0.147691	+	0.989034i	$0.547184\pi$
$102$		0			0
$103$	9.91124	+	5.72226i	0.976584	+	0.563831i	0.901237	−	0.433327i	$-0.142660\pi$
$103$	9.91124	+	5.72226i	0.976584	+	0.563831i	0.0753467	+	0.997157i	$0.475994\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			11.0618i			1.06938i	0.845048	+	0.534690i	$0.179572\pi$
$107$			11.0618i			1.06938i	−0.845048	+	0.534690i	$0.820428\pi$
$108$		0			0
$109$	−10.5633			−1.01178			−0.505891	−	0.862597i	$-0.668836\pi$
$109$	−10.5633			−1.01178			−0.505891	+	0.862597i	$0.668836\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.60226	−	2.07976i	−0.338872	−	0.195648i	0.320901	−	0.947113i	$-0.396014\pi$
$113$	−3.60226	−	2.07976i	−0.338872	−	0.195648i	−0.659773	+	0.751465i	$0.729348\pi$
$114$		0			0
$115$	−2.44290	+	1.41041i	−0.227802	+	0.131521i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.6658	−	3.71653i	−1.16107	−	0.340694i
$120$		0			0
$121$	−5.27592	+	9.13815i	−0.479629	+	0.830741i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.61671			0.323489
$126$		0			0
$127$	1.66945			0.148140			0.0740700	−	0.997253i	$-0.476401\pi$
$127$	1.66945			0.148140			0.0740700	+	0.997253i	$0.476401\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.76607	−	11.7192i	0.591154	−	1.02391i	−0.402923	−	0.915234i	$-0.632006\pi$
$131$	6.76607	−	11.7192i	0.591154	−	1.02391i	0.994077	−	0.108675i	$-0.0346609\pi$
$132$		0			0
$133$	4.73572	−	16.1392i	0.410639	−	1.39944i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.78428	+	4.49425i	−0.665056	+	0.383970i	−0.794201	−	0.607656i	$-0.792110\pi$
$137$	−7.78428	+	4.49425i	−0.665056	+	0.383970i	0.129145	+	0.991626i	$0.458777\pi$
$138$		0			0
$139$	8.05336	+	4.64961i	0.683077	+	0.394375i	0.801014	−	0.598646i	$-0.204294\pi$
$139$	8.05336	+	4.64961i	0.683077	+	0.394375i	−0.117936	+	0.993021i	$0.537628\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.670501			−0.0560701
$144$		0			0
$145$			0.670501i			0.0556821i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.45268	+	1.41606i	0.200931	+	0.116008i	0.597090	−	0.802174i	$-0.296324\pi$
$149$	2.45268	+	1.41606i	0.200931	+	0.116008i	−0.396158	+	0.918182i	$0.629657\pi$
$150$		0			0
$151$	−8.27592	−	14.3343i	−0.673484	−	1.16651i	−0.976909	−	0.213654i	$-0.931463\pi$
$151$	−8.27592	−	14.3343i	−0.673484	−	1.16651i	0.303425	−	0.952855i	$-0.401870\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.00836	+	1.15953i	−0.161315	+	0.0931355i
$156$		0			0
$157$	2.45480	+	1.41728i	0.195914	+	0.113111i	0.594748	−	0.803912i	$-0.297252\pi$
$157$	2.45480	+	1.41728i	0.195914	+	0.113111i	−0.398834	+	0.917023i	$0.630585\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	14.0513	+	14.7312i	1.10739	+	1.16098i
$162$		0			0
$163$	−24.7281			−1.93685			−0.968426	−	0.249300i	$-0.919800\pi$
$163$	−24.7281			−1.93685			−0.968426	+	0.249300i	$0.919800\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.67422	+	16.7562i	−0.748614	+	1.29664i	0.199874	+	0.979822i	$0.435947\pi$
$167$	−9.67422	+	16.7562i	−0.748614	+	1.29664i	−0.948487	+	0.316815i	$0.897386\pi$
$168$		0			0
$169$	−5.99843	−	10.3896i	−0.461418	−	0.799199i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.41827	+	4.18856i	0.183858	+	0.318451i	0.943191	−	0.332251i	$-0.107808\pi$
$173$	2.41827	+	4.18856i	0.183858	+	0.318451i	−0.759333	+	0.650702i	$0.774475\pi$
$174$		0			0
$175$	−3.03723	−	12.5098i	−0.229593	−	0.945649i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			3.65796i			0.273409i	0.990612	+	0.136704i	$0.0436511\pi$
$179$			3.65796i			0.273409i	−0.990612	+	0.136704i	$0.956349\pi$
$180$		0			0
$181$			5.66796i			0.421296i	0.977562	+	0.210648i	$0.0675574\pi$
$181$			5.66796i			0.421296i	−0.977562	+	0.210648i	$0.932443\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.947269	+	1.64072i	−0.0696446	+	0.120628i
$186$		0			0
$187$	2.89248	−	1.66997i	0.211519	−	0.122120i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	23.7098	−	13.6888i	1.71558	−	0.990490i	0.788996	−	0.614398i	$-0.210601\pi$
$191$	23.7098	−	13.6888i	1.71558	−	0.990490i	0.926583	−	0.376091i	$-0.122732\pi$
$192$		0			0
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	−0.627188	−	0.778868i	$-0.715794\pi$
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	0.988113	+	0.153727i	$0.0491276\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.8258i			1.34129i	0.741780	+	0.670643i	$0.233982\pi$
$197$			18.8258i			1.34129i	−0.741780	+	0.670643i	$0.766018\pi$
$198$		0			0
$199$			5.36406i			0.380248i	0.981760	+	0.190124i	$0.0608890\pi$
$199$			5.36406i			0.380248i	−0.981760	+	0.190124i	$0.939111\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.70242	−	1.14169i	0.330045	−	0.0801312i
$204$		0			0
$205$	−0.791588	−	1.37107i	−0.0552869	−	0.0957597i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.12793	+	3.68569i	0.147192	+	0.254944i
$210$		0			0
$211$	0.828981	−	1.43584i	0.0570694	−	0.0988471i	−0.836079	−	0.548609i	$-0.815158\pi$
$211$	0.828981	−	1.43584i	0.0570694	−	0.0988471i	0.893149	+	0.449762i	$0.148491\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.64912			−0.112469
$216$		0			0
$217$	11.5518	+	12.1108i	0.784189	+	0.822137i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.32741	−	2.49843i	−0.291093	−	0.168063i
$222$		0			0
$223$	−14.7546	+	8.51860i	−0.988044	+	0.570448i	−0.904689	−	0.426072i	$-0.859897\pi$
$223$	−14.7546	+	8.51860i	−0.988044	+	0.570448i	−0.0833551	+	0.996520i	$0.526564\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.55512	+	4.42560i	0.169589	+	0.293737i	0.938276	−	0.345889i	$-0.112423\pi$
$227$	2.55512	+	4.42560i	0.169589	+	0.293737i	−0.768686	+	0.639626i	$0.779089\pi$
$228$		0			0
$229$	−13.2215	−	7.63345i	−0.873703	−	0.504433i	−0.00512595	−	0.999987i	$-0.501632\pi$
$229$	−13.2215	−	7.63345i	−0.873703	−	0.504433i	−0.868577	+	0.495554i	$0.834965\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	10.1930i		−	0.667767i	−0.942614	−	0.333883i	$-0.891641\pi$
$233$		−	10.1930i		−	0.667767i	0.942614	−	0.333883i	$-0.108359\pi$
$234$		0			0
$235$	3.05340			0.199182
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−16.6117	−	9.59076i	−1.07452	−	0.620375i	−0.145108	−	0.989416i	$-0.546353\pi$
$239$	−16.6117	−	9.59076i	−1.07452	−	0.620375i	−0.929413	+	0.369041i	$0.879686\pi$
$240$		0			0
$241$	17.9140	−	10.3426i	1.15394	−	0.666227i	0.204095	−	0.978951i	$-0.434575\pi$
$241$	17.9140	−	10.3426i	1.15394	−	0.666227i	0.949844	+	0.312724i	$0.101241\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.28049	−	1.17672i	0.145695	−	0.0751778i
$246$		0			0
$247$	3.18359	−	5.51413i	0.202567	−	0.350856i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.81200			−0.114373			−0.0571864	−	0.998364i	$-0.518213\pi$
$251$	−1.81200			−0.114373			−0.0571864	+	0.998364i	$0.518213\pi$
$252$		0			0
$253$	−5.15117			−0.323851
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.22773	+	5.59059i	−0.201340	+	0.348731i	−0.948960	−	0.315395i	$-0.897863\pi$
$257$	−3.22773	+	5.59059i	−0.201340	+	0.348731i	0.747620	+	0.664126i	$0.231196\pi$
$258$		0			0
$259$	13.1198	+	3.84974i	0.815224	+	0.239211i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.63888	+	4.41031i	−0.471034	+	0.271951i	−0.716672	−	0.697410i	$-0.754336\pi$
$263$	−7.63888	+	4.41031i	−0.471034	+	0.271951i	0.245639	+	0.969361i	$0.421002\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.2653			−0.869773			−0.434886	−	0.900485i	$-0.643212\pi$
$269$	−14.2653			−0.869773			−0.434886	+	0.900485i	$0.643212\pi$
$270$		0			0
$271$		−	3.05281i		−	0.185445i	−0.995692	−	0.0927226i	$-0.970443\pi$
$271$		−	3.05281i		−	0.185445i	0.995692	−	0.0927226i	$-0.0295570\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.82090	+	1.62865i	0.170107	+	0.0982112i
$276$		0			0
$277$	−0.632828	−	1.09609i	−0.0380230	−	0.0658577i	0.846388	−	0.532567i	$-0.178773\pi$
$277$	−0.632828	−	1.09609i	−0.0380230	−	0.0658577i	−0.884411	+	0.466710i	$0.845439\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.11639	+	5.26335i	−0.543838	+	0.313985i	−0.746633	−	0.665236i	$-0.768331\pi$
$281$	−9.11639	+	5.26335i	−0.543838	+	0.313985i	0.202795	+	0.979221i	$0.434998\pi$
$282$		0			0
$283$	17.2094	+	9.93588i	1.02300	+	0.590627i	0.914970	−	0.403522i	$-0.132214\pi$
$283$	17.2094	+	9.93588i	1.02300	+	0.590627i	0.108025	+	0.994148i	$0.465547\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.26784	+	7.88623i	−0.488035	+	0.465509i
$288$		0			0
$289$	7.89074			0.464161
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.70606	+	11.6152i	−0.391772	+	0.678569i	−0.992683	−	0.120747i	$-0.961471\pi$
$293$	−6.70606	+	11.6152i	−0.391772	+	0.678569i	0.600911	+	0.799316i	$0.294804\pi$
$294$		0			0
$295$	−1.59964	−	2.77066i	−0.0931348	−	0.161314i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.85331	+	6.67413i	0.222843	+	0.385975i
$300$		0			0
$301$	2.80803	+	11.5657i	0.161852	+	0.666638i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.81749i			0.104069i
$306$		0			0
$307$		−	0.653728i		−	0.0373102i	−0.999826	−	0.0186551i	$-0.994062\pi$
$307$		−	0.653728i		−	0.0373102i	0.999826	−	0.0186551i	$-0.00593845\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.62246	−	8.00634i	0.262116	−	0.453998i	−0.704688	−	0.709517i	$-0.748913\pi$
$311$	4.62246	−	8.00634i	0.262116	−	0.453998i	0.966804	+	0.255519i	$0.0822464\pi$
$312$		0			0
$313$	−5.33830	+	3.08207i	−0.301739	+	0.174209i	−0.643224	−	0.765678i	$-0.722403\pi$
$313$	−5.33830	+	3.08207i	−0.301739	+	0.174209i	0.341485	+	0.939887i	$0.389070\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.8876	−	10.3274i	1.00467	−	0.580045i	0.0950420	−	0.995473i	$-0.469701\pi$
$317$	17.8876	−	10.3274i	1.00467	−	0.580045i	0.909626	+	0.415428i	$0.136368\pi$
$318$		0			0
$319$	−0.612209	+	1.06038i	−0.0342771	+	0.0593697i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			31.7166i			1.76476i
$324$		0			0
$325$		−	4.87322i		−	0.270318i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.19917	−	21.4144i	−0.286639	−	1.18061i
$330$		0			0
$331$	5.35568	+	9.27631i	0.294375	+	0.509872i	0.974839	−	0.222909i	$-0.0715553\pi$
$331$	5.35568	+	9.27631i	0.294375	+	0.509872i	−0.680464	+	0.732781i	$0.738222\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.99626	+	3.45763i	0.109067	+	0.188910i
$336$		0			0
$337$	3.77592	−	6.54008i	0.205687	−	0.356261i	−0.744664	−	0.667439i	$-0.767390\pi$
$337$	3.77592	−	6.54008i	0.205687	−	0.356261i	0.950351	+	0.311179i	$0.100724\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.23488			−0.229332
$342$		0			0
$343$	−12.1358	−	13.9901i	−0.655270	−	0.755394i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.46737	−	5.46599i	−0.508235	−	0.293430i	0.223873	−	0.974618i	$-0.428130\pi$
$347$	−9.46737	−	5.46599i	−0.508235	−	0.293430i	−0.732108	+	0.681189i	$0.761463\pi$
$348$		0			0
$349$	1.02562	−	0.592145i	0.0549004	−	0.0316968i	−0.472299	−	0.881439i	$-0.656576\pi$
$349$	1.02562	−	0.592145i	0.0549004	−	0.0316968i	0.527199	+	0.849742i	$0.323242\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16.7912	−	29.0832i	−0.893706	−	1.54794i	−0.835398	−	0.549646i	$-0.814763\pi$
$353$	−16.7912	−	29.0832i	−0.893706	−	1.54794i	−0.0583086	−	0.998299i	$-0.518571\pi$
$354$		0			0
$355$	1.74566	+	1.00786i	0.0926501	+	0.0534915i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	10.1281i		−	0.534542i	−0.963621	−	0.267271i	$-0.913878\pi$
$359$		−	10.1281i		−	0.534542i	0.963621	−	0.267271i	$-0.0861219\pi$
$360$		0			0
$361$	−21.4143			−1.12707
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.29315	+	0.746603i	0.0676868	+	0.0390790i
$366$		0			0
$367$	15.5903	−	9.00104i	0.813805	−	0.469850i	−0.0344706	−	0.999406i	$-0.510975\pi$
$367$	15.5903	−	9.00104i	0.813805	−	0.469850i	0.848275	+	0.529555i	$0.177641\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.20451	+	14.2106i	−0.424814	+	0.735799i	−0.996403	−	0.0847411i	$-0.972994\pi$
$373$	−8.20451	+	14.2106i	−0.424814	+	0.735799i	0.571589	+	0.820540i	$0.306327\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.83184			0.0943447
$378$		0			0
$379$	2.91372			0.149668			0.0748339	−	0.997196i	$-0.476157\pi$
$379$	2.91372			0.149668			0.0748339	+	0.997196i	$0.476157\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.28721	+	7.42567i	−0.219066	+	0.379434i	−0.954523	−	0.298138i	$-0.903634\pi$
$383$	−4.28721	+	7.42567i	−0.219066	+	0.379434i	0.735456	+	0.677572i	$0.236968\pi$
$384$		0			0
$385$	−0.182822	+	0.623052i	−0.00931749	+	0.0317537i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	30.7906	−	17.7770i	1.56115	−	0.901328i	0.564004	−	0.825772i	$-0.309260\pi$
$389$	30.7906	−	17.7770i	1.56115	−	0.901328i	0.997142	−	0.0755559i	$-0.0240731\pi$
$390$		0			0
$391$	−33.2456	−	19.1944i	−1.68130	−	0.970702i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.06318			0.154125
$396$		0			0
$397$		−	3.58034i		−	0.179692i	−0.995956	−	0.0898460i	$-0.971363\pi$
$397$		−	3.58034i		−	0.179692i	0.995956	−	0.0898460i	$-0.0286375\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.165300	−	0.0954357i	−0.00825467	−	0.00476583i	0.495867	−	0.868398i	$-0.334850\pi$
$401$	−0.165300	−	0.0954357i	−0.00825467	−	0.00476583i	−0.504122	+	0.863633i	$0.668184\pi$
$402$		0			0
$403$	3.16789	+	5.48694i	0.157804	+	0.273324i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.99615	+	1.72983i	−0.148514	+	0.0857445i
$408$		0			0
$409$	−3.00832	−	1.73685i	−0.148752	−	0.0858819i	0.423777	−	0.905767i	$-0.360704\pi$
$409$	−3.00832	−	1.73685i	−0.148752	−	0.0858819i	−0.572529	+	0.819885i	$0.694037\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.7077	+	15.9365i	−0.822130	+	0.784183i
$414$		0			0
$415$	6.23739			0.306182
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.703955	−	1.21929i	0.0343905	−	0.0595660i	−0.848318	−	0.529487i	$-0.822384\pi$
$419$	0.703955	−	1.21929i	0.0343905	−	0.0595660i	0.882708	+	0.469921i	$0.155718\pi$
$420$		0			0
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	0.952285	+	0.305211i	$0.0987268\pi$
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	−0.211822	+	0.977308i	$0.567940\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.1374	+	21.0226i	0.588751	+	1.01975i
$426$		0			0
$427$	12.7466	−	3.09472i	0.616850	−	0.149764i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	27.2747i		−	1.31378i	−0.753988	−	0.656888i	$-0.771873\pi$
$431$		−	27.2747i		−	1.31378i	0.753988	−	0.656888i	$-0.228127\pi$
$432$		0			0
$433$			8.15047i			0.391686i	0.980635	+	0.195843i	$0.0627444\pi$
$433$			8.15047i			0.391686i	−0.980635	+	0.195843i	$0.937256\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	24.4581	−	42.3627i	1.16999	−	2.02648i
$438$		0			0
$439$	−10.6005	+	6.12020i	−0.505934	+	0.292101i	−0.731161	−	0.682205i	$-0.761021\pi$
$439$	−10.6005	+	6.12020i	−0.505934	+	0.292101i	0.225226	+	0.974306i	$0.427688\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.93544	−	4.00418i	0.329513	−	0.190244i	−0.326112	−	0.945331i	$-0.605739\pi$
$443$	6.93544	−	4.00418i	0.329513	−	0.190244i	0.655625	+	0.755087i	$0.272405\pi$
$444$		0			0
$445$	−1.96337	+	3.40067i	−0.0930729	+	0.161207i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	14.5183i		−	0.685163i	−0.939488	−	0.342581i	$-0.888699\pi$
$449$		−	14.5183i		−	0.685163i	0.939488	−	0.342581i	$-0.111301\pi$
$450$		0			0
$451$		−	2.89108i		−	0.136135i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.944020	−	0.229197i	0.0442563	−	0.0107449i
$456$		0			0
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	0.725804	−	0.687901i	$-0.241468\pi$
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	−0.958642	+	0.284614i	$0.908135\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.1635	+	27.9960i	0.752810	+	1.30391i	0.946456	+	0.322834i	$0.104636\pi$
$461$	16.1635	+	27.9960i	0.752810	+	1.30391i	−0.193645	+	0.981072i	$0.562031\pi$
$462$		0			0
$463$	4.72516	−	8.18421i	0.219597	−	0.380353i	−0.735088	−	0.677972i	$-0.762859\pi$
$463$	4.72516	−	8.18421i	0.219597	−	0.380353i	0.954685	+	0.297619i	$0.0961925\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.6623			0.956138			0.478069	−	0.878322i	$-0.341337\pi$
$467$	20.6623			0.956138			0.478069	+	0.878322i	$0.341337\pi$
$468$		0			0
$469$	20.8502	−	19.8878i	0.962773	−	0.918335i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.60803	−	1.50575i	−0.119917	−	0.0692343i
$474$		0			0
$475$	−26.7877	+	15.4659i	−1.22910	+	0.709623i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.08042	−	8.79955i	−0.232131	−	0.402062i	0.726304	−	0.687373i	$-0.241236\pi$
$479$	−5.08042	−	8.79955i	−0.232131	−	0.402062i	−0.958435	+	0.285311i	$0.907903\pi$
$480$		0			0
$481$	4.48252	+	2.58799i	0.204386	+	0.118002i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			6.31126i			0.286579i
$486$		0			0
$487$	31.2296			1.41515			0.707575	−	0.706638i	$-0.249789\pi$
$487$	31.2296			1.41515			0.707575	+	0.706638i	$0.249789\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.8314	+	10.2950i	0.804720	+	0.464605i	0.845119	−	0.534578i	$-0.179529\pi$
$491$	17.8314	+	10.2950i	0.804720	+	0.464605i	−0.0403987	+	0.999184i	$0.512863\pi$
$492$		0			0
$493$	−7.90239	+	4.56245i	−0.355906	+	0.205482i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.09598	−	13.9590i	0.183730	−	0.626145i
$498$		0			0
$499$	−12.5766	+	21.7834i	−0.563007	+	0.975157i	0.434225	+	0.900805i	$0.357022\pi$
$499$	−12.5766	+	21.7834i	−0.563007	+	0.975157i	−0.997232	+	0.0743527i	$0.976311\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−31.1553			−1.38915			−0.694574	−	0.719421i	$-0.744407\pi$
$503$	−31.1553			−1.38915			−0.694574	+	0.719421i	$0.744407\pi$
$504$		0			0
$505$	5.76722			0.256638
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.41674	−	4.18591i	0.107120	−	0.185537i	−0.807482	−	0.589892i	$-0.799170\pi$
$509$	2.41674	−	4.18591i	0.107120	−	0.185537i	0.914602	+	0.404354i	$0.132504\pi$
$510$		0			0
$511$	3.03423	−	10.3405i	0.134226	−	0.457439i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.63344	−	2.09777i	0.160109	−	0.0924387i
$516$		0			0
$517$	4.82886	+	2.78794i	0.212373	+	0.122613i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.5322			−0.768101			−0.384050	−	0.923312i	$-0.625471\pi$
$521$	−17.5322			−0.768101			−0.384050	+	0.923312i	$0.625471\pi$
$522$		0			0
$523$			19.1019i			0.835267i	0.908616	+	0.417633i	$0.137140\pi$
$523$			19.1019i			0.835267i	−0.908616	+	0.417633i	$0.862860\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−27.3319	−	15.7801i	−1.19060	−	0.687392i
$528$		0			0
$529$	18.1033	+	31.3559i	0.787101	+	1.36330i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.74584	+	2.16266i	−0.162250	+	0.0936752i
$534$		0			0
$535$	3.51192	+	2.02761i	0.151834	+	0.0876612i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.68095	+	0.221286i	0.201623	+	0.00953144i
$540$		0			0
$541$	13.6642			0.587471			0.293735	−	0.955887i	$-0.405102\pi$
$541$	13.6642			0.587471			0.293735	+	0.955887i	$0.405102\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.93625	+	3.35368i	−0.0829397	+	0.143656i
$546$		0			0
$547$	−4.94380	−	8.56292i	−0.211382	−	0.366124i	0.740765	−	0.671764i	$-0.234463\pi$
$547$	−4.94380	−	8.56292i	−0.211382	−	0.366124i	−0.952147	+	0.305640i	$0.901130\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.81362	−	10.0695i	−0.247669	−	0.428975i
$552$		0			0
$553$	−5.21582	−	21.4829i	−0.221799	−	0.913548i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			12.5800i			0.533034i	0.963830	+	0.266517i	$0.0858728\pi$
$557$			12.5800i			0.533034i	−0.963830	+	0.266517i	$0.914127\pi$
$558$		0			0
$559$			4.50547i			0.190561i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.1666	−	21.0732i	0.512763	−	0.888132i	−0.487127	−	0.873331i	$-0.661955\pi$
$563$	12.1666	−	21.0732i	0.512763	−	0.888132i	0.999890	−	0.0148007i	$-0.00471137\pi$
$564$		0			0
$565$	−1.32058	+	0.762437i	−0.0555572	+	0.0320760i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.18746	−	4.72703i	0.343236	−	0.198167i	−0.318466	−	0.947934i	$-0.603168\pi$
$569$	8.18746	−	4.72703i	0.343236	−	0.198167i	0.661702	+	0.749767i	$0.269834\pi$
$570$		0			0
$571$	−15.7843	+	27.3392i	−0.660551	+	1.14411i	0.319920	+	0.947445i	$0.396344\pi$
$571$	−15.7843	+	27.3392i	−0.660551	+	1.14411i	−0.980471	+	0.196664i	$0.936989\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	37.4388i		−	1.56131i
$576$		0			0
$577$		−	33.5794i		−	1.39793i	−0.715157	−	0.698964i	$-0.753645\pi$
$577$		−	33.5794i		−	1.39793i	0.715157	−	0.698964i	$-0.246355\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−10.6207	−	43.7446i	−0.440621	−	1.81483i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.65855	−	16.7291i	−0.398651	−	0.690484i	0.594909	−	0.803793i	$-0.297188\pi$
$587$	−9.65855	−	16.7291i	−0.398651	−	0.690484i	−0.993560	+	0.113310i	$0.963855\pi$
$588$		0			0
$589$	20.1075	−	34.8272i	0.828516	−	1.43503i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.733196			−0.0301088			−0.0150544	−	0.999887i	$-0.504792\pi$
$593$	−0.733196			−0.0301088			−0.0150544	+	0.999887i	$0.504792\pi$
$594$		0			0
$595$	−3.50157	+	3.33994i	−0.143550	+	0.136924i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	26.6548	+	15.3892i	1.08909	+	0.628785i	0.933333	−	0.359011i	$-0.116886\pi$
$599$	26.6548	+	15.3892i	1.08909	+	0.628785i	0.155754	+	0.987796i	$0.450219\pi$
$600$		0			0
$601$	−0.786931	+	0.454335i	−0.0320996	+	0.0185327i	−0.515964	−	0.856610i	$-0.672566\pi$
$601$	−0.786931	+	0.454335i	−0.0320996	+	0.0185327i	0.483864	+	0.875143i	$0.339233\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.93414	+	3.35003i	0.0786340	+	0.136198i
$606$		0			0
$607$	−38.7783	−	22.3887i	−1.57396	−	0.908728i	−0.995676	−	0.0928949i	$-0.970388\pi$
$607$	−38.7783	−	22.3887i	−1.57396	−	0.908728i	−0.578287	−	0.815833i	$-0.696279\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	8.34204i		−	0.337483i
$612$		0			0
$613$	18.1480			0.732992			0.366496	−	0.930420i	$-0.380557\pi$
$613$	18.1480			0.732992			0.366496	+	0.930420i	$0.380557\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.7393	+	11.3965i	0.794674	+	0.458805i	0.841605	−	0.540093i	$-0.181611\pi$
$617$	19.7393	+	11.3965i	0.794674	+	0.458805i	−0.0469315	+	0.998898i	$0.514944\pi$
$618$		0			0
$619$	38.4228	−	22.1834i	1.54434	−	0.891626i	0.545785	−	0.837925i	$-0.316232\pi$
$619$	38.4228	−	22.1834i	1.54434	−	0.891626i	0.998557	−	0.0537011i	$-0.0171018\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	27.1930	+	7.97924i	1.08946	+	0.319682i
$624$		0			0
$625$	−11.5011	+	19.9204i	−0.460043	+	0.796818i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−25.7829			−1.02803
$630$		0			0
$631$	32.5707			1.29662			0.648310	−	0.761377i	$-0.275476\pi$
$631$	32.5707			1.29662			0.648310	+	0.761377i	$0.275476\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.306009	−	0.530024i	0.0121436	−	0.0210333i
$636$		0			0
$637$	−3.21486	−	6.23042i	−0.127377	−	0.246858i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.2270	−	5.90456i	0.403942	−	0.233216i	−0.284241	−	0.958753i	$-0.591742\pi$
$641$	10.2270	−	5.90456i	0.403942	−	0.233216i	0.688184	+	0.725537i	$0.258408\pi$
$642$		0			0
$643$	−25.3714	−	14.6482i	−1.00055	−	0.577668i	−0.0921392	−	0.995746i	$-0.529370\pi$
$643$	−25.3714	−	14.6482i	−1.00055	−	0.577668i	−0.908411	+	0.418078i	$0.862704\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−28.1683			−1.10741			−0.553705	−	0.832713i	$-0.686786\pi$
$647$	−28.1683			−1.10741			−0.553705	+	0.832713i	$0.686786\pi$
$648$		0			0
$649$		−	5.84229i		−	0.229330i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−39.0555	−	22.5487i	−1.52836	−	0.882399i	−0.999431	−	0.0337326i	$-0.989261\pi$
$653$	−39.0555	−	22.5487i	−1.52836	−	0.882399i	−0.528929	−	0.848666i	$-0.677406\pi$
$654$		0			0
$655$	−2.48043	−	4.29623i	−0.0969184	−	0.167868i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	27.5435	−	15.9022i	1.07294	−	0.619463i	0.143958	−	0.989584i	$-0.454017\pi$
$659$	27.5435	−	15.9022i	1.07294	−	0.619463i	0.928984	+	0.370121i	$0.120684\pi$
$660$		0			0
$661$	17.1234	+	9.88619i	0.666022	+	0.384528i	0.794568	−	0.607175i	$-0.207698\pi$
$661$	17.1234	+	9.88619i	0.666022	+	0.384528i	−0.128546	+	0.991704i	$0.541031\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.25587	−	4.46181i	−0.165035	−	0.173022i
$666$		0			0
$667$	14.0733			0.544918
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.65948	+	2.87430i	−0.0640635	+	0.110961i
$672$		0			0
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	0.847230	−	0.531227i	$-0.178269\pi$
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	−0.883671	+	0.468109i	$0.844936\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.5661	−	18.3010i	−0.406088	−	0.703364i	0.588360	−	0.808599i	$-0.299774\pi$
$677$	−10.5661	−	18.3010i	−0.406088	−	0.703364i	−0.994447	+	0.105235i	$0.966441\pi$
$678$		0			0
$679$	44.2627	−	10.7465i	1.69865	−	0.412412i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	8.71972i		−	0.333651i	−0.985986	−	0.166825i	$-0.946648\pi$
$683$		−	8.71972i		−	0.333651i	0.985986	−	0.166825i	$-0.0533516\pi$
$684$		0			0
$685$			3.29517i			0.125902i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	15.7071	−	9.06850i	0.597526	−	0.344982i	−0.170542	−	0.985350i	$-0.554552\pi$
$691$	15.7071	−	9.06850i	0.597526	−	0.344982i	0.768068	+	0.640369i	$0.221218\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.95235	−	1.70454i	0.111989	−	0.0646568i
$696$		0			0
$697$	10.7728	−	18.6590i	0.408048	−	0.706760i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	35.6167i		−	1.34523i	−0.739995	−	0.672613i	$-0.765172\pi$
$701$		−	35.6167i		−	1.34523i	0.739995	−	0.672613i	$-0.234828\pi$
$702$		0			0
$703$		−	32.8534i		−	1.23909i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.82012	−	40.4472i	−0.369324	−	1.52117i
$708$		0			0
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	24.3375	+	42.1538i	0.911447	+	1.57867i
$714$		0			0
$715$	−0.122902	+	0.212873i	−0.00459628	+	0.00796099i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−25.7829			−0.961540			−0.480770	−	0.876847i	$-0.659643\pi$
$719$	−25.7829			−0.961540			−0.480770	+	0.876847i	$0.659643\pi$
$720$		0			0
$721$	−20.8991	−	21.9104i	−0.778323	−	0.815987i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.70685	−	4.44955i	−0.286225	−	0.165252i
$726$		0			0
$727$	−1.32423	+	0.764544i	−0.0491129	+	0.0283554i	−0.524355	−	0.851499i	$-0.675694\pi$
$727$	−1.32423	+	0.764544i	−0.0491129	+	0.0283554i	0.475242	+	0.879855i	$0.342360\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−11.2215	−	19.4362i	−0.415042	−	0.718873i
$732$		0			0
$733$	−17.9908	−	10.3870i	−0.664504	−	0.383651i	0.129487	−	0.991581i	$-0.458667\pi$
$733$	−17.9908	−	10.3870i	−0.664504	−	0.383651i	−0.793991	+	0.607930i	$0.792000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			7.29084i			0.268562i
$738$		0			0
$739$	11.8709			0.436678			0.218339	−	0.975873i	$-0.429936\pi$
$739$	11.8709			0.436678			0.218339	+	0.975873i	$0.429936\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−37.5906	−	21.7029i	−1.37907	−	0.796204i	−0.387019	−	0.922072i	$-0.626495\pi$
$743$	−37.5906	−	21.7029i	−1.37907	−	0.796204i	−0.992047	+	0.125868i	$0.959828\pi$
$744$		0			0
$745$	0.899148	−	0.519124i	0.0329422	−	0.0190192i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.24030	−	28.0826i	0.301094	−	1.02612i
$750$		0			0
$751$	1.15691	−	2.00383i	0.0422164	−	0.0731209i	−0.844145	−	0.536115i	$-0.819891\pi$
$751$	1.15691	−	2.00383i	0.0422164	−	0.0731209i	0.886362	+	0.462994i	$0.153225\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.06787			−0.220832
$756$		0			0
$757$	−15.0946			−0.548624			−0.274312	−	0.961641i	$-0.588450\pi$
$757$	−15.0946			−0.548624			−0.274312	+	0.961641i	$0.588450\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.6690	+	20.2112i	−0.422999	+	0.732656i	−0.996231	−	0.0867370i	$-0.972356\pi$
$761$	−11.6690	+	20.2112i	−0.422999	+	0.732656i	0.573232	+	0.819393i	$0.305689\pi$
$762$		0			0
$763$	26.8173	+	7.86900i	0.970850	+	0.284877i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.56959	+	4.37030i	−0.273322	+	0.157803i
$768$		0			0
$769$	−15.8266	−	9.13748i	−0.570721	−	0.329506i	0.186716	−	0.982414i	$-0.440216\pi$
$769$	−15.8266	−	9.13748i	−0.570721	−	0.329506i	−0.757437	+	0.652908i	$0.773549\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.438507			0.0157720			0.00788600	−	0.999969i	$-0.497490\pi$
$773$	0.438507			0.0157720			0.00788600	+	0.999969i	$0.497490\pi$
$774$		0			0
$775$		−	30.7792i		−	1.10562i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	23.7759	+	13.7270i	0.851861	+	0.491822i
$780$		0			0
$781$	1.84047	+	3.18779i	0.0658573	+	0.114068i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.899924	−	0.519571i	0.0321197	−	0.0185443i
$786$		0			0
$787$	33.1317	+	19.1286i	1.18102	+	0.681861i	0.956250	−	0.292551i	$-0.0945040\pi$
$787$	33.1317	+	19.1286i	1.18102	+	0.681861i	0.224769	+	0.974412i	$0.427837\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.59581	+	7.96337i	0.270076	+	0.283145i
$792$		0			0
$793$	4.96547			0.176329
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.6613	+	30.5902i	−0.625594	+	1.08356i	0.362832	+	0.931855i	$0.381810\pi$
$797$	−17.6613	+	30.5902i	−0.625594	+	1.08356i	−0.988426	+	0.151706i	$0.951523\pi$
$798$		0			0
$799$	20.7770	+	35.9868i	0.735036	+	1.27312i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.36339	+	2.36146i	0.0481130	+	0.0833341i
$804$		0			0
$805$	7.25250	−	1.76082i	0.255617	−	0.0620609i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	21.7669i		−	0.765282i	−0.923897	−	0.382641i	$-0.875015\pi$
$809$		−	21.7669i		−	0.765282i	0.923897	−	0.382641i	$-0.124985\pi$
$810$		0			0
$811$			17.0184i			0.597598i	0.954316	+	0.298799i	$0.0965860\pi$
$811$			17.0184i			0.597598i	−0.954316	+	0.298799i	$0.903414\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.53263	+	7.85075i	−0.158771	+	0.275000i
$816$		0			0
$817$	24.7662	−	14.2988i	0.866460	−	0.500251i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.4786	−	12.4007i	0.749608	−	0.432786i	−0.0759445	−	0.997112i	$-0.524197\pi$
$821$	21.4786	−	12.4007i	0.749608	−	0.432786i	0.825552	+	0.564326i	$0.190864\pi$
$822$		0			0
$823$	10.6572	−	18.4588i	0.371486	−	0.643433i	−0.618308	−	0.785936i	$-0.712182\pi$
$823$	10.6572	−	18.4588i	0.371486	−	0.643433i	0.989794	+	0.142503i	$0.0455149\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			49.7585i			1.73027i	0.501537	+	0.865136i	$0.332768\pi$
$827$			49.7585i			1.73027i	−0.501537	+	0.865136i	$0.667232\pi$
$828$		0			0
$829$			43.1190i			1.49759i	0.662804	+	0.748793i	$0.269366\pi$
$829$			43.1190i			1.49759i	−0.662804	+	0.748793i	$0.730634\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	29.3863	+	18.8704i	1.01817	+	0.653821i
$834$		0			0
$835$	3.54655	+	6.14281i	0.122733	+	0.212581i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.9985	+	25.9782i	0.517807	+	0.896868i	0.999786	+	0.0206851i	$0.00658476\pi$
$839$	14.9985	+	25.9782i	0.517807	+	0.896868i	−0.481979	+	0.876183i	$0.660082\pi$
$840$		0			0
$841$	−12.8274	+	22.2177i	−0.442325	+	0.766129i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.39803			−0.151297
$846$		0			0
$847$	20.2014	−	19.2689i	0.694128	−	0.662089i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	34.4373	+	19.8824i	1.18050	+	0.681559i
$852$		0			0
$853$	−25.7693	+	14.8779i	−0.882325	+	0.509411i	−0.871424	−	0.490530i	$-0.836803\pi$
$853$	−25.7693	+	14.8779i	−0.882325	+	0.509411i	−0.0109007	+	0.999941i	$0.503470\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.9296	−	39.7152i	−0.783260	−	1.35665i	−0.930033	−	0.367476i	$-0.880222\pi$
$857$	−22.9296	−	39.7152i	−0.783260	−	1.35665i	0.146773	−	0.989170i	$-0.453111\pi$
$858$		0			0
$859$	3.24073	+	1.87104i	0.110572	+	0.0638390i	0.554266	−	0.832339i	$-0.312999\pi$
$859$	3.24073	+	1.87104i	0.110572	+	0.0638390i	−0.443694	+	0.896178i	$0.646332\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			31.3944i			1.06868i	0.845270	+	0.534339i	$0.179439\pi$
$863$			31.3944i			1.06868i	−0.845270	+	0.534339i	$0.820561\pi$
$864$		0			0
$865$	1.77307			0.0602860
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.84432	+	2.79687i	0.164332	+	0.0948773i
$870$		0			0
$871$	9.44641	−	5.45389i	0.320080	−	0.184798i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−9.18180	−	2.69422i	−0.310402	−	0.0910812i
$876$		0			0
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21.2010			−0.714280			−0.357140	−	0.934051i	$-0.616248\pi$
$881$	−21.2010			−0.714280			−0.357140	+	0.934051i	$0.616248\pi$
$882$		0			0
$883$	−38.6157			−1.29952			−0.649761	−	0.760139i	$-0.725131\pi$
$883$	−38.6157			−1.29952			−0.649761	+	0.760139i	$0.725131\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.09606	+	5.36253i	−0.103955	+	0.180056i	−0.913311	−	0.407263i	$-0.866483\pi$
$887$	−3.09606	+	5.36253i	−0.103955	+	0.180056i	0.809356	+	0.587319i	$0.199817\pi$
$888$		0			0
$889$	−4.23827	−	1.24364i	−0.142147	−	0.0417102i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−45.8555	+	26.4747i	−1.53450	+	0.885941i
$894$		0			0
$895$	1.16134	+	0.670501i	0.0388194	+	0.0224124i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.5699			0.385878
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.79948	+	1.03893i	0.0598168	+	0.0345353i
$906$		0			0
$907$	−0.0645566	−	0.111815i	−0.00214357	−	0.00371277i	0.864952	−	0.501855i	$-0.167349\pi$
$907$	−0.0645566	−	0.111815i	−0.00214357	−	0.00371277i	−0.867095	+	0.498142i	$0.834016\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	29.6682	−	17.1290i	0.982952	−	0.567508i	0.0797919	−	0.996812i	$-0.474574\pi$
$911$	29.6682	−	17.1290i	0.982952	−	0.567508i	0.903160	+	0.429304i	$0.141241\pi$
$912$		0			0
$913$	9.86424	+	5.69512i	0.326459	+	0.188481i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−25.9072	+	24.7114i	−0.855530	+	0.816041i
$918$		0			0
$919$	−14.3054			−0.471892			−0.235946	−	0.971766i	$-0.575819\pi$
$919$	−14.3054			−0.471892			−0.235946	+	0.971766i	$0.575819\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.75352	−	4.76923i	0.0906332	−	0.156981i
$924$		0			0
$925$	−12.5725	−	21.7761i	−0.413380	−	0.715995i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−5.87364	−	10.1734i	−0.192708	−	0.333780i	0.753439	−	0.657518i	$-0.228394\pi$
$929$	−5.87364	−	10.1734i	−0.192708	−	0.333780i	−0.946147	+	0.323738i	$0.895060\pi$
$930$		0			0
$931$	−24.0453	+	37.4450i	−0.788053	+	1.22721i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	1.22442i		−	0.0400427i
$936$		0			0
$937$			2.63611i			0.0861179i	0.999073	+	0.0430589i	$0.0137103\pi$
$937$			2.63611i			0.0861179i	−0.999073	+	0.0430589i	$0.986290\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.96557	−	10.3327i	0.194472	−	0.336836i	−0.752255	−	0.658872i	$-0.771034\pi$
$941$	5.96557	−	10.3327i	0.194472	−	0.336836i	0.946727	+	0.322036i	$0.104367\pi$
$942$		0			0
$943$	−28.7776	+	16.6148i	−0.937128	+	0.541051i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.70267	−	3.86979i	0.217807	−	0.125751i	−0.387127	−	0.922026i	$-0.626533\pi$
$947$	6.70267	−	3.86979i	0.217807	−	0.125751i	0.604935	+	0.796275i	$0.293199\pi$
$948$		0			0
$949$	2.03976	−	3.53296i	0.0662133	−	0.114685i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	3.76685i		−	0.122020i	−0.998137	−	0.0610102i	$-0.980568\pi$
$953$		−	3.76685i		−	0.122020i	0.998137	−	0.0610102i	$-0.0194322\pi$
$954$		0			0
$955$		−	10.0366i		−	0.324777i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	23.1100	−	5.61084i	0.746260	−	0.181184i
$960$		0			0
$961$	4.50836	+	7.80871i	0.145431	+	0.251894i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.83817	−	3.18381i	−0.0591728	−	0.102490i
$966$		0			0
$967$	2.28741	−	3.96191i	0.0735581	−	0.127406i	−0.826900	−	0.562349i	$-0.809898\pi$
$967$	2.28741	−	3.96191i	0.0735581	−	0.127406i	0.900458	+	0.434942i	$0.143231\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−25.8445			−0.829388			−0.414694	−	0.909961i	$-0.636111\pi$
$971$	−25.8445			−0.829388			−0.414694	+	0.909961i	$0.636111\pi$
$972$		0			0
$973$	−16.9815	−	17.8033i	−0.544403	−	0.570747i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	26.0950	+	15.0659i	0.834852	+	0.482002i	0.855511	−	0.517785i	$-0.173243\pi$
$977$	26.0950	+	15.0659i	0.834852	+	0.482002i	−0.0206590	+	0.999787i	$0.506576\pi$
$978$		0			0
$979$	−6.21003	+	3.58536i	−0.198474	+	0.114589i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.30293	−	10.9170i	−0.201032	−	0.348198i	0.747829	−	0.663891i	$-0.231096\pi$
$983$	−6.30293	−	10.9170i	−0.201032	−	0.348198i	−0.948861	+	0.315693i	$0.897763\pi$
$984$		0			0
$985$	5.97689	+	3.45076i	0.190440	+	0.109950i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			34.6136i			1.10065i
$990$		0			0
$991$	−51.6852			−1.64184			−0.820918	−	0.571046i	$-0.806538\pi$
$991$	−51.6852			−1.64184			−0.820918	+	0.571046i	$0.806538\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.70300	+	0.983227i	0.0539887	+	0.0311704i
$996$		0			0
$997$	35.1469	−	20.2921i	1.11311	−	0.642656i	0.173479	−	0.984837i	$-0.444499\pi$
$997$	35.1469	−	20.2921i	1.11311	−	0.642656i	0.939634	+	0.342181i	$0.111166\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.b.881.5		16
3.2	odd	2		1008.2.cc.b.545.5		16
4.3	odd	2		378.2.m.a.125.3		16
7.6	odd	2	inner	3024.2.cc.b.881.4		16
9.2	odd	6	inner	3024.2.cc.b.2897.4		16
9.7	even	3		1008.2.cc.b.209.4		16
12.11	even	2		126.2.m.a.41.6	✓	16
21.20	even	2		1008.2.cc.b.545.4		16
28.3	even	6		2646.2.l.b.1097.2		16
28.11	odd	6		2646.2.l.b.1097.3		16
28.19	even	6		2646.2.t.a.2285.7		16
28.23	odd	6		2646.2.t.a.2285.6		16
28.27	even	2		378.2.m.a.125.2		16
36.7	odd	6		126.2.m.a.83.7	yes	16
36.11	even	6		378.2.m.a.251.2		16
36.23	even	6		1134.2.d.a.1133.13		16
36.31	odd	6		1134.2.d.a.1133.4		16
63.20	even	6	inner	3024.2.cc.b.2897.5		16
63.34	odd	6		1008.2.cc.b.209.5		16
84.11	even	6		882.2.l.a.509.8		16
84.23	even	6		882.2.t.b.815.1		16
84.47	odd	6		882.2.t.b.815.4		16
84.59	odd	6		882.2.l.a.509.5		16
84.83	odd	2		126.2.m.a.41.7	yes	16
252.11	even	6		2646.2.t.a.1979.7		16
252.47	odd	6		2646.2.l.b.521.7		16
252.79	odd	6		882.2.l.a.227.1		16
252.83	odd	6		378.2.m.a.251.3		16
252.115	even	6		882.2.t.b.803.1		16
252.139	even	6		1134.2.d.a.1133.5		16
252.151	odd	6		882.2.t.b.803.4		16
252.167	odd	6		1134.2.d.a.1133.12		16
252.187	even	6		882.2.l.a.227.4		16
252.191	even	6		2646.2.l.b.521.6		16
252.223	even	6		126.2.m.a.83.6	yes	16
252.227	odd	6		2646.2.t.a.1979.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.6	✓	16	12.11	even	2
126.2.m.a.41.7	yes	16	84.83	odd	2
126.2.m.a.83.6	yes	16	252.223	even	6
126.2.m.a.83.7	yes	16	36.7	odd	6
378.2.m.a.125.2		16	28.27	even	2
378.2.m.a.125.3		16	4.3	odd	2
378.2.m.a.251.2		16	36.11	even	6
378.2.m.a.251.3		16	252.83	odd	6
882.2.l.a.227.1		16	252.79	odd	6
882.2.l.a.227.4		16	252.187	even	6
882.2.l.a.509.5		16	84.59	odd	6
882.2.l.a.509.8		16	84.11	even	6
882.2.t.b.803.1		16	252.115	even	6
882.2.t.b.803.4		16	252.151	odd	6
882.2.t.b.815.1		16	84.23	even	6
882.2.t.b.815.4		16	84.47	odd	6
1008.2.cc.b.209.4		16	9.7	even	3
1008.2.cc.b.209.5		16	63.34	odd	6
1008.2.cc.b.545.4		16	21.20	even	2
1008.2.cc.b.545.5		16	3.2	odd	2
1134.2.d.a.1133.4		16	36.31	odd	6
1134.2.d.a.1133.5		16	252.139	even	6
1134.2.d.a.1133.12		16	252.167	odd	6
1134.2.d.a.1133.13		16	36.23	even	6
2646.2.l.b.521.6		16	252.191	even	6
2646.2.l.b.521.7		16	252.47	odd	6
2646.2.l.b.1097.2		16	28.3	even	6
2646.2.l.b.1097.3		16	28.11	odd	6
2646.2.t.a.1979.6		16	252.227	odd	6
2646.2.t.a.1979.7		16	252.11	even	6
2646.2.t.a.2285.6		16	28.23	odd	6
2646.2.t.a.2285.7		16	28.19	even	6
3024.2.cc.b.881.4		16	7.6	odd	2	inner
3024.2.cc.b.881.5		16	1.1	even	1	trivial
3024.2.cc.b.2897.4		16	9.2	odd	6	inner
3024.2.cc.b.2897.5		16	63.20	even	6	inner

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.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.183299 - 0.317483i) q^{5} +(-2.53871 - 0.744936i) q^{7} +O(q^{10})\)	\(q+(0.183299 - 0.317483i) q^{5} +(-2.53871 - 0.744936i) q^{7} +(0.579764 - 0.334727i) q^{11} +(-0.867380 - 0.500782i) q^{13} +4.98906 q^{17} +6.35722i q^{19} +(-6.66371 - 3.84729i) q^{23} +(2.43280 + 4.21374i) q^{25} +(-1.58394 + 0.914490i) q^{29} +(-5.47837 - 3.16294i) q^{31} +(-0.701849 + 0.669453i) q^{35} -5.16789 q^{37} +(2.15928 - 3.73998i) q^{41} +(-2.24922 - 3.89576i) q^{43} +(4.16450 + 7.21313i) q^{47} +(5.89014 + 3.78236i) q^{49} -0.245420i q^{55} +(4.36348 - 7.55776i) q^{59} +(-4.29351 + 2.47886i) q^{61} +(-0.317980 + 0.183586i) q^{65} +(-5.44537 + 9.43166i) q^{67} +5.49843i q^{71} +4.07314i q^{73} +(-1.72120 + 0.417889i) q^{77} +(4.17784 + 7.23623i) q^{79} +(8.50712 + 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} -10.7113 q^{89} +(1.82898 + 1.91749i) q^{91} +(2.01831 + 1.16527i) q^{95} +(-14.9093 + 8.60787i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

Introduction

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