LMFDB - Embedded newform 464.3.l.e.273.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,3,Mod(17,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("464.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	464.l (of order $4$, 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:	$12.6430842663$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 8 x^{12} + 26 x^{11} + 743 x^{10} - 2298 x^{9} + 3586 x^{8} + 2776 x^{7} + \cdots + 1623602 $ x^14 - 4x^13 + 8x^12 + 26x^11 + 743x^10 - 2298x^9 + 3586x^8 + 2776x^7 + 108967x^6 - 332156x^5 + 505068x^4 - 40690x^3 + 294849x^2 - 978486*x + 1623602
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 232)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			273.3
Root			$1.35465 + 1.35465i$ of defining polynomial
Character	$\chi$	$=$	464.273
Dual form			464.3.l.e.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35465 - 1.35465i) q^{3} -5.16278i q^{5} +10.3945 q^{7} -5.32984i q^{9} +O(q^{10})$	\(q+(-1.35465 - 1.35465i) q^{3} -5.16278i q^{5} +10.3945 q^{7} -5.32984i q^{9} +(14.7649 + 14.7649i) q^{11} +2.47995i q^{13} +(-6.99377 + 6.99377i) q^{15} +(4.05436 + 4.05436i) q^{17} +(-10.7898 - 10.7898i) q^{19} +(-14.0810 - 14.0810i) q^{21} +21.4294 q^{23} -1.65427 q^{25} +(-19.4119 + 19.4119i) q^{27} +(-3.57442 - 28.7789i) q^{29} +(-19.1239 - 19.1239i) q^{31} -40.0027i q^{33} -53.6647i q^{35} +(9.97016 - 9.97016i) q^{37} +(3.35946 - 3.35946i) q^{39} +(33.1757 - 33.1757i) q^{41} +(40.1601 + 40.1601i) q^{43} -27.5168 q^{45} +(25.8724 - 25.8724i) q^{47} +59.0463 q^{49} -10.9845i q^{51} -90.2013 q^{53} +(76.2281 - 76.2281i) q^{55} +29.2327i q^{57} -107.719 q^{59} +(27.9018 + 27.9018i) q^{61} -55.4012i q^{63} +12.8034 q^{65} -83.4168i q^{67} +(-29.0294 - 29.0294i) q^{69} +50.9557i q^{71} +(27.1116 - 27.1116i) q^{73} +(2.24096 + 2.24096i) q^{75} +(153.475 + 153.475i) q^{77} +(31.7458 + 31.7458i) q^{79} +4.62431 q^{81} -105.759 q^{83} +(20.9318 - 20.9318i) q^{85} +(-34.1433 + 43.8274i) q^{87} +(-83.1301 - 83.1301i) q^{89} +25.7779i q^{91} +51.8126i q^{93} +(-55.7051 + 55.7051i) q^{95} +(-53.1615 + 53.1615i) q^{97} +(78.6947 - 78.6947i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 14 * q - 4 * q^3 - 8 * q^7	$ 14 q - 4 q^{3} - 8 q^{7} + 6 q^{15} - 34 q^{17} - 50 q^{19} - 28 q^{21} + 12 q^{23} - 102 q^{25} + 38 q^{27} + 6 q^{29} - 60 q^{31} + 38 q^{37} - 82 q^{39} + 18 q^{41} + 48 q^{43} + 260 q^{45} + 136 q^{47} + 66 q^{49} - 60 q^{53} + 86 q^{55} - 60 q^{59} + 106 q^{61} - 272 q^{65} - 180 q^{69} + 182 q^{73} + 42 q^{75} + 260 q^{77} + 72 q^{79} - 6 q^{81} - 332 q^{83} - 144 q^{85} + 312 q^{87} + 30 q^{89} - 340 q^{95} + 58 q^{97} + 594 q^{99}+O(q^{100}) $ 14 * q - 4 * q^3 - 8 * q^7 + 6 * q^15 - 34 * q^17 - 50 * q^19 - 28 * q^21 + 12 * q^23 - 102 * q^25 + 38 * q^27 + 6 * q^29 - 60 * q^31 + 38 * q^37 - 82 * q^39 + 18 * q^41 + 48 * q^43 + 260 * q^45 + 136 * q^47 + 66 * q^49 - 60 * q^53 + 86 * q^55 - 60 * q^59 + 106 * q^61 - 272 * q^65 - 180 * q^69 + 182 * q^73 + 42 * q^75 + 260 * q^77 + 72 * q^79 - 6 * q^81 - 332 * q^83 - 144 * q^85 + 312 * q^87 + 30 * q^89 - 340 * q^95 + 58 * q^97 + 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.35465	−	1.35465i	−0.451551	−	0.451551i	0.444318	−	0.895869i	$-0.353446\pi$
$3$	−1.35465	−	1.35465i	−0.451551	−	0.451551i	−0.895869	+	0.444318i	$0.853446\pi$
$4$		0			0
$5$		−	5.16278i		−	1.03256i	−0.856421	−	0.516278i	$-0.827317\pi$
$5$		−	5.16278i		−	1.03256i	0.856421	−	0.516278i	$-0.172683\pi$
$6$		0			0
$7$	10.3945			1.48493			0.742467	−	0.669883i	$-0.233656\pi$
$7$	10.3945			1.48493			0.742467	+	0.669883i	$0.233656\pi$
$8$		0			0
$9$		−	5.32984i		−	0.592204i
$10$		0			0
$11$	14.7649	+	14.7649i	1.34227	+	1.34227i	0.893799	+	0.448468i	$0.148030\pi$
$11$	14.7649	+	14.7649i	1.34227	+	1.34227i	0.448468	+	0.893799i	$0.351970\pi$
$12$		0			0
$13$			2.47995i			0.190765i	0.995441	+	0.0953825i	$0.0304074\pi$
$13$			2.47995i			0.190765i	−0.995441	+	0.0953825i	$0.969593\pi$
$14$		0			0
$15$	−6.99377	+	6.99377i	−0.466251	+	0.466251i
$16$		0			0
$17$	4.05436	+	4.05436i	0.238492	+	0.238492i	0.816225	−	0.577734i	$-0.196063\pi$
$17$	4.05436	+	4.05436i	0.238492	+	0.238492i	−0.577734	+	0.816225i	$0.696063\pi$
$18$		0			0
$19$	−10.7898	−	10.7898i	−0.567882	−	0.567882i	0.363653	−	0.931535i	$-0.381529\pi$
$19$	−10.7898	−	10.7898i	−0.567882	−	0.567882i	−0.931535	+	0.363653i	$0.881529\pi$
$20$		0			0
$21$	−14.0810	−	14.0810i	−0.670523	−	0.670523i
$22$		0			0
$23$	21.4294			0.931713			0.465856	−	0.884860i	$-0.345746\pi$
$23$	21.4294			0.931713			0.465856	+	0.884860i	$0.345746\pi$
$24$		0			0
$25$	−1.65427			−0.0661707
$26$		0			0
$27$	−19.4119	+	19.4119i	−0.718961	+	0.718961i
$28$		0			0
$29$	−3.57442	−	28.7789i	−0.123256	−	0.992375i
$29$	−3.57442	−	28.7789i	−0.123256	−	0.992375i
$30$		0			0
$31$	−19.1239	−	19.1239i	−0.616901	−	0.616901i	0.327834	−	0.944735i	$-0.393681\pi$
$31$	−19.1239	−	19.1239i	−0.616901	−	0.616901i	−0.944735	+	0.327834i	$0.893681\pi$
$32$		0			0
$33$		−	40.0027i		−	1.21220i
$34$		0			0
$35$		−	53.6647i		−	1.53328i
$36$		0			0
$37$	9.97016	−	9.97016i	0.269464	−	0.269464i	−0.559420	−	0.828884i	$-0.688976\pi$
$37$	9.97016	−	9.97016i	0.269464	−	0.269464i	0.828884	+	0.559420i	$0.188976\pi$
$38$		0			0
$39$	3.35946	−	3.35946i	0.0861401	−	0.0861401i
$40$		0			0
$41$	33.1757	−	33.1757i	0.809164	−	0.809164i	−0.175344	−	0.984507i	$-0.556104\pi$
$41$	33.1757	−	33.1757i	0.809164	−	0.809164i	0.984507	+	0.175344i	$0.0561036\pi$
$42$		0			0
$43$	40.1601	+	40.1601i	0.933955	+	0.933955i	0.997950	−	0.0639952i	$-0.0203842\pi$
$43$	40.1601	+	40.1601i	0.933955	+	0.933955i	−0.0639952	+	0.997950i	$0.520384\pi$
$44$		0			0
$45$	−27.5168			−0.611484
$46$		0			0
$47$	25.8724	−	25.8724i	0.550476	−	0.550476i	−0.376102	−	0.926578i	$-0.622736\pi$
$47$	25.8724	−	25.8724i	0.550476	−	0.550476i	0.926578	+	0.376102i	$0.122736\pi$
$48$		0			0
$49$	59.0463			1.20503
$50$		0			0
$51$		−	10.9845i		−	0.215382i
$52$		0			0
$53$	−90.2013			−1.70191			−0.850955	−	0.525238i	$-0.823976\pi$
$53$	−90.2013			−1.70191			−0.850955	+	0.525238i	$0.823976\pi$
$54$		0			0
$55$	76.2281	−	76.2281i	1.38596	−	1.38596i
$56$		0			0
$57$			29.2327i			0.512855i
$58$		0			0
$59$	−107.719			−1.82575			−0.912876	−	0.408237i	$-0.866144\pi$
$59$	−107.719			−1.82575			−0.912876	+	0.408237i	$0.866144\pi$
$60$		0			0
$61$	27.9018	+	27.9018i	0.457406	+	0.457406i	0.897803	−	0.440397i	$-0.145162\pi$
$61$	27.9018	+	27.9018i	0.457406	+	0.457406i	−0.440397	+	0.897803i	$0.645162\pi$
$62$		0			0
$63$		−	55.4012i		−	0.879384i
$64$		0			0
$65$	12.8034			0.196975
$66$		0			0
$67$		−	83.4168i		−	1.24503i	−0.782609	−	0.622513i	$-0.786112\pi$
$67$		−	83.4168i		−	1.24503i	0.782609	−	0.622513i	$-0.213888\pi$
$68$		0			0
$69$	−29.0294	−	29.0294i	−0.420715	−	0.420715i
$70$		0			0
$71$			50.9557i			0.717686i	0.933398	+	0.358843i	$0.116829\pi$
$71$			50.9557i			0.717686i	−0.933398	+	0.358843i	$0.883171\pi$
$72$		0			0
$73$	27.1116	−	27.1116i	0.371392	−	0.371392i	−0.496592	−	0.867984i	$-0.665415\pi$
$73$	27.1116	−	27.1116i	0.371392	−	0.371392i	0.867984	+	0.496592i	$0.165415\pi$
$74$		0			0
$75$	2.24096	+	2.24096i	0.0298794	+	0.0298794i
$76$		0			0
$77$	153.475	+	153.475i	1.99318	+	1.99318i
$78$		0			0
$79$	31.7458	+	31.7458i	0.401845	+	0.401845i	0.878883	−	0.477038i	$-0.158290\pi$
$79$	31.7458	+	31.7458i	0.401845	+	0.401845i	−0.477038	+	0.878883i	$0.658290\pi$
$80$		0			0
$81$	4.62431			0.0570902
$82$		0			0
$83$	−105.759			−1.27420			−0.637100	−	0.770781i	$-0.719866\pi$
$83$	−105.759			−1.27420			−0.637100	+	0.770781i	$0.719866\pi$
$84$		0			0
$85$	20.9318	−	20.9318i	0.246256	−	0.246256i
$86$		0			0
$87$	−34.1433	+	43.8274i	−0.392451	+	0.503764i
$88$		0			0
$89$	−83.1301	−	83.1301i	−0.934046	−	0.934046i	0.0639098	−	0.997956i	$-0.479643\pi$
$89$	−83.1301	−	83.1301i	−0.934046	−	0.934046i	−0.997956	+	0.0639098i	$0.979643\pi$
$90$		0			0
$91$			25.7779i			0.283273i
$92$		0			0
$93$			51.8126i			0.557124i
$94$		0			0
$95$	−55.7051	+	55.7051i	−0.586369	+	0.586369i
$96$		0			0
$97$	−53.1615	+	53.1615i	−0.548057	+	0.548057i	−0.925878	−	0.377822i	$-0.876673\pi$
$97$	−53.1615	+	53.1615i	−0.548057	+	0.548057i	0.377822	+	0.925878i	$0.376673\pi$
$98$		0			0
$99$	78.6947	−	78.6947i	0.794896	−	0.794896i
$100$		0			0
$101$	109.424	+	109.424i	1.08341	+	1.08341i	0.996189	+	0.0872209i	$0.0277986\pi$
$101$	109.424	+	109.424i	1.08341	+	1.08341i	0.0872209	+	0.996189i	$0.472201\pi$
$102$		0			0
$103$	49.5240			0.480815			0.240408	−	0.970672i	$-0.422719\pi$
$103$	49.5240			0.480815			0.240408	+	0.970672i	$0.422719\pi$
$104$		0			0
$105$	−72.6969	+	72.6969i	−0.692352	+	0.692352i
$106$		0			0
$107$	−54.9588			−0.513634			−0.256817	−	0.966460i	$-0.582674\pi$
$107$	−54.9588			−0.513634			−0.256817	+	0.966460i	$0.582674\pi$
$108$		0			0
$109$		−	90.0156i		−	0.825831i	−0.910769	−	0.412916i	$-0.864510\pi$
$109$		−	90.0156i		−	0.825831i	0.910769	−	0.412916i	$-0.135490\pi$
$110$		0			0
$111$	−27.0122			−0.243353
$112$		0			0
$113$	−3.20684	+	3.20684i	−0.0283791	+	0.0283791i	−0.721154	−	0.692775i	$-0.756388\pi$
$113$	−3.20684	+	3.20684i	−0.0283791	+	0.0283791i	0.692775	+	0.721154i	$0.256388\pi$
$114$		0			0
$115$		−	110.635i		−	0.962045i
$116$		0			0
$117$	13.2177			0.112972
$118$		0			0
$119$	42.1432	+	42.1432i	0.354145	+	0.354145i
$120$		0			0
$121$			315.007i			2.60336i
$122$		0			0
$123$	−89.8831			−0.730757
$124$		0			0
$125$		−	120.529i		−	0.964230i
$126$		0			0
$127$	119.450	+	119.450i	0.940553	+	0.940553i	0.998330	−	0.0577768i	$-0.0184012\pi$
$127$	119.450	+	119.450i	0.940553	+	0.940553i	−0.0577768	+	0.998330i	$0.518401\pi$
$128$		0			0
$129$		−	108.806i		−	0.843456i
$130$		0			0
$131$	−122.389	+	122.389i	−0.934270	+	0.934270i	−0.997969	−	0.0636992i	$-0.979710\pi$
$131$	−122.389	+	122.389i	−0.934270	+	0.934270i	0.0636992	+	0.997969i	$0.479710\pi$
$132$		0			0
$133$	−112.154	−	112.154i	−0.843266	−	0.843266i
$134$		0			0
$135$	100.220	+	100.220i	0.742367	+	0.742367i
$136$		0			0
$137$	−132.465	−	132.465i	−0.966894	−	0.966894i	0.0325749	−	0.999469i	$-0.489629\pi$
$137$	−132.465	−	132.465i	−0.966894	−	0.966894i	−0.999469	+	0.0325749i	$0.989629\pi$
$138$		0			0
$139$	210.992			1.51793			0.758963	−	0.651134i	$-0.225706\pi$
$139$	210.992			1.51793			0.758963	+	0.651134i	$0.225706\pi$
$140$		0			0
$141$	−70.0961			−0.497135
$142$		0			0
$143$	−36.6162	+	36.6162i	−0.256058	+	0.256058i
$144$		0			0
$145$	−148.579	+	18.4539i	−1.02468	+	0.127268i
$146$		0			0
$147$	−79.9872	−	79.9872i	−0.544131	−	0.544131i
$148$		0			0
$149$			21.0157i			0.141045i	0.997510	+	0.0705226i	$0.0224667\pi$
$149$			21.0157i			0.141045i	−0.997510	+	0.0705226i	$0.977533\pi$
$150$		0			0
$151$			148.175i			0.981290i	0.871359	+	0.490645i	$0.163239\pi$
$151$			148.175i			0.981290i	−0.871359	+	0.490645i	$0.836761\pi$
$152$		0			0
$153$	21.6091	−	21.6091i	0.141236	−	0.141236i
$154$		0			0
$155$	−98.7326	+	98.7326i	−0.636985	+	0.636985i
$156$		0			0
$157$	90.3739	−	90.3739i	0.575630	−	0.575630i	−0.358066	−	0.933696i	$-0.616564\pi$
$157$	90.3739	−	90.3739i	0.575630	−	0.575630i	0.933696	+	0.358066i	$0.116564\pi$
$158$		0			0
$159$	122.191	+	122.191i	0.768499	+	0.768499i
$160$		0			0
$161$	222.749			1.38353
$162$		0			0
$163$	−54.3316	+	54.3316i	−0.333323	+	0.333323i	−0.853847	−	0.520524i	$-0.825737\pi$
$163$	−54.3316	+	54.3316i	−0.333323	+	0.333323i	0.520524	+	0.853847i	$0.325737\pi$
$164$		0			0
$165$	−206.525			−1.25167
$166$		0			0
$167$			37.6881i			0.225677i	0.993613	+	0.112839i	$0.0359943\pi$
$167$			37.6881i			0.225677i	−0.993613	+	0.112839i	$0.964006\pi$
$168$		0			0
$169$	162.850			0.963609
$170$		0			0
$171$	−57.5076	+	57.5076i	−0.336302	+	0.336302i
$172$		0			0
$173$			232.913i			1.34632i	0.739497	+	0.673160i	$0.235064\pi$
$173$			232.913i			1.34632i	−0.739497	+	0.673160i	$0.764936\pi$
$174$		0			0
$175$	−17.1953			−0.0982591
$176$		0			0
$177$	145.922	+	145.922i	0.824419	+	0.824419i
$178$		0			0
$179$			39.6237i			0.221362i	0.993856	+	0.110681i	$0.0353031\pi$
$179$			39.6237i			0.221362i	−0.993856	+	0.110681i	$0.964697\pi$
$180$		0			0
$181$	−82.8157			−0.457545			−0.228773	−	0.973480i	$-0.573471\pi$
$181$	−82.8157			−0.457545			−0.228773	+	0.973480i	$0.573471\pi$
$182$		0			0
$183$		−	75.5944i		−	0.413084i
$184$		0			0
$185$	−51.4737	−	51.4737i	−0.278236	−	0.278236i
$186$		0			0
$187$			119.725i			0.640239i
$188$		0			0
$189$	−201.778	+	201.778i	−1.06761	+	1.06761i
$190$		0			0
$191$	214.534	+	214.534i	1.12321	+	1.12321i	0.991255	+	0.131957i	$0.0421261\pi$
$191$	214.534	+	214.534i	1.12321	+	1.12321i	0.131957	+	0.991255i	$0.457874\pi$
$192$		0			0
$193$	90.5075	+	90.5075i	0.468951	+	0.468951i	0.901575	−	0.432624i	$-0.142412\pi$
$193$	90.5075	+	90.5075i	0.468951	+	0.468951i	−0.432624	+	0.901575i	$0.642412\pi$
$194$		0			0
$195$	−17.3442	−	17.3442i	−0.0889444	−	0.0889444i
$196$		0			0
$197$	203.198			1.03146			0.515731	−	0.856751i	$-0.327520\pi$
$197$	203.198			1.03146			0.515731	+	0.856751i	$0.327520\pi$
$198$		0			0
$199$	−46.3103			−0.232715			−0.116357	−	0.993207i	$-0.537122\pi$
$199$	−46.3103			−0.232715			−0.116357	+	0.993207i	$0.537122\pi$
$200$		0			0
$201$	−113.001	+	113.001i	−0.562192	+	0.562192i
$202$		0			0
$203$	−37.1544	−	299.143i	−0.183027	−	1.47361i
$204$		0			0
$205$	−171.279	−	171.279i	−0.835506	−	0.835506i
$206$		0			0
$207$		−	114.215i		−	0.551764i
$208$		0			0
$209$		−	318.620i		−	1.52450i
$210$		0			0
$211$	−133.692	+	133.692i	−0.633613	+	0.633613i	−0.948972	−	0.315359i	$-0.897875\pi$
$211$	−133.692	+	133.692i	−0.633613	+	0.633613i	0.315359	+	0.948972i	$0.397875\pi$
$212$		0			0
$213$	69.0272	−	69.0272i	0.324071	−	0.324071i
$214$		0			0
$215$	207.337	−	207.337i	0.964360	−	0.964360i
$216$		0			0
$217$	−198.784	−	198.784i	−0.916057	−	0.916057i
$218$		0			0
$219$	−73.4536			−0.335405
$220$		0			0
$221$	−10.0546	+	10.0546i	−0.0454959	+	0.0454959i
$222$		0			0
$223$	62.8675			0.281917			0.140959	−	0.990015i	$-0.454982\pi$
$223$	62.8675			0.281917			0.140959	+	0.990015i	$0.454982\pi$
$224$		0			0
$225$			8.81698i			0.0391866i
$226$		0			0
$227$	−209.124			−0.921253			−0.460626	−	0.887594i	$-0.652375\pi$
$227$	−209.124			−0.921253			−0.460626	+	0.887594i	$0.652375\pi$
$228$		0			0
$229$	142.211	−	142.211i	0.621007	−	0.621007i	−0.324782	−	0.945789i	$-0.605291\pi$
$229$	142.211	−	142.211i	0.621007	−	0.621007i	0.945789	+	0.324782i	$0.105291\pi$
$230$		0			0
$231$		−	415.809i		−	1.80004i
$232$		0			0
$233$	−64.9836			−0.278900			−0.139450	−	0.990229i	$-0.544533\pi$
$233$	−64.9836			−0.278900			−0.139450	+	0.990229i	$0.544533\pi$
$234$		0			0
$235$	−133.573	−	133.573i	−0.568397	−	0.568397i
$236$		0			0
$237$		−	86.0089i		−	0.362907i
$238$		0			0
$239$	−282.522			−1.18210			−0.591050	−	0.806635i	$-0.701286\pi$
$239$	−282.522			−1.18210			−0.591050	+	0.806635i	$0.701286\pi$
$240$		0			0
$241$			158.123i			0.656113i	0.944658	+	0.328057i	$0.106394\pi$
$241$			158.123i			0.656113i	−0.944658	+	0.328057i	$0.893606\pi$
$242$		0			0
$243$	168.443	+	168.443i	0.693182	+	0.693182i
$244$		0			0
$245$		−	304.843i		−	1.24426i
$246$		0			0
$247$	26.7580	−	26.7580i	0.108332	−	0.108332i
$248$		0			0
$249$	143.266	+	143.266i	0.575366	+	0.575366i
$250$		0			0
$251$	−145.399	−	145.399i	−0.579278	−	0.579278i	0.355427	−	0.934704i	$-0.384336\pi$
$251$	−145.399	−	145.399i	−0.579278	−	0.579278i	−0.934704	+	0.355427i	$0.884336\pi$
$252$		0			0
$253$	316.404	+	316.404i	1.25061	+	1.25061i
$254$		0			0
$255$	−56.7105			−0.222394
$256$		0			0
$257$	−195.648			−0.761277			−0.380639	−	0.924724i	$-0.624296\pi$
$257$	−195.648			−0.761277			−0.380639	+	0.924724i	$0.624296\pi$
$258$		0			0
$259$	103.635	−	103.635i	0.400136	−	0.400136i
$260$		0			0
$261$	−153.387	+	19.0511i	−0.587688	+	0.0729926i
$262$		0			0
$263$	65.5180	+	65.5180i	0.249118	+	0.249118i	0.820609	−	0.571491i	$-0.193635\pi$
$263$	65.5180	+	65.5180i	0.249118	+	0.249118i	−0.571491	+	0.820609i	$0.693635\pi$
$264$		0			0
$265$			465.689i			1.75732i
$266$		0			0
$267$			225.225i			0.843538i
$268$		0			0
$269$	−177.191	+	177.191i	−0.658701	+	0.658701i	−0.955073	−	0.296371i	$-0.904223\pi$
$269$	−177.191	+	177.191i	−0.658701	+	0.658701i	0.296371	+	0.955073i	$0.404223\pi$
$270$		0			0
$271$	187.020	−	187.020i	0.690112	−	0.690112i	−0.272144	−	0.962256i	$-0.587733\pi$
$271$	187.020	−	187.020i	0.690112	−	0.690112i	0.962256	+	0.272144i	$0.0877328\pi$
$272$		0			0
$273$	34.9200	−	34.9200i	0.127912	−	0.127912i
$274$		0			0
$275$	−24.4252	−	24.4252i	−0.0888188	−	0.0888188i
$276$		0			0
$277$	251.268			0.907105			0.453553	−	0.891230i	$-0.350156\pi$
$277$	251.268			0.907105			0.453553	+	0.891230i	$0.350156\pi$
$278$		0			0
$279$	−101.927	+	101.927i	−0.365331	+	0.365331i
$280$		0			0
$281$	407.723			1.45097			0.725486	−	0.688237i	$-0.241615\pi$
$281$	407.723			1.45097			0.725486	+	0.688237i	$0.241615\pi$
$282$		0			0
$283$		−	52.0806i		−	0.184030i	−0.995758	−	0.0920152i	$-0.970669\pi$
$283$		−	52.0806i		−	0.184030i	0.995758	−	0.0920152i	$-0.0293308\pi$
$284$		0			0
$285$	150.922			0.529551
$286$		0			0
$287$	344.846	−	344.846i	1.20155	−	1.20155i
$288$		0			0
$289$		−	256.124i		−	0.886243i
$290$		0			0
$291$	144.031			0.494951
$292$		0			0
$293$	191.886	+	191.886i	0.654900	+	0.654900i	0.954169	−	0.299269i	$-0.0967426\pi$
$293$	191.886	+	191.886i	0.654900	+	0.654900i	−0.299269	+	0.954169i	$0.596743\pi$
$294$		0			0
$295$			556.131i			1.88519i
$296$		0			0
$297$	−573.232			−1.93007
$298$		0			0
$299$			53.1437i			0.177738i
$300$		0			0
$301$	417.445	+	417.445i	1.38686	+	1.38686i
$302$		0			0
$303$		−	296.464i		−	0.978429i
$304$		0			0
$305$	144.051	−	144.051i	0.472297	−	0.472297i
$306$		0			0
$307$	−130.592	−	130.592i	−0.425382	−	0.425382i	0.461670	−	0.887052i	$-0.347251\pi$
$307$	−130.592	−	130.592i	−0.425382	−	0.425382i	−0.887052	+	0.461670i	$0.847251\pi$
$308$		0			0
$309$	−67.0877	−	67.0877i	−0.217112	−	0.217112i
$310$		0			0
$311$	80.8820	+	80.8820i	0.260071	+	0.260071i	0.825083	−	0.565012i	$-0.191128\pi$
$311$	80.8820	+	80.8820i	0.260071	+	0.260071i	−0.565012	+	0.825083i	$0.691128\pi$
$312$		0			0
$313$	−339.306			−1.08404			−0.542022	−	0.840364i	$-0.682341\pi$
$313$	−339.306			−1.08404			−0.542022	+	0.840364i	$0.682341\pi$
$314$		0			0
$315$	−286.024			−0.908012
$316$		0			0
$317$	331.530	−	331.530i	1.04583	−	1.04583i	0.0469370	−	0.998898i	$-0.485054\pi$
$317$	331.530	−	331.530i	1.04583	−	1.04583i	0.998898	−	0.0469370i	$-0.0149460\pi$
$318$		0			0
$319$	372.142	−	477.694i	1.16659	−	1.49747i
$320$		0			0
$321$	74.4501	+	74.4501i	0.231932	+	0.231932i
$322$		0			0
$323$		−	87.4911i		−	0.270870i
$324$		0			0
$325$		−	4.10249i		−	0.0126231i
$326$		0			0
$327$	−121.940	+	121.940i	−0.372905	+	0.372905i
$328$		0			0
$329$	268.931	−	268.931i	0.817420	−	0.817420i
$330$		0			0
$331$	388.656	−	388.656i	1.17419	−	1.17419i	0.192986	−	0.981202i	$-0.438183\pi$
$331$	388.656	−	388.656i	1.17419	−	1.17419i	0.981202	−	0.192986i	$-0.0618170\pi$
$332$		0			0
$333$	−53.1393	−	53.1393i	−0.159578	−	0.159578i
$334$		0			0
$335$	−430.662			−1.28556
$336$		0			0
$337$	−198.445	+	198.445i	−0.588857	+	0.588857i	−0.937322	−	0.348465i	$-0.886703\pi$
$337$	−198.445	+	198.445i	−0.588857	+	0.588857i	0.348465	+	0.937322i	$0.386703\pi$
$338$		0			0
$339$	8.68831			0.0256292
$340$		0			0
$341$		−	564.727i		−	1.65609i
$342$		0			0
$343$	104.427			0.304452
$344$		0			0
$345$	−149.872	+	149.872i	−0.434412	+	0.434412i
$346$		0			0
$347$			245.798i			0.708351i	0.935179	+	0.354175i	$0.115238\pi$
$347$			245.798i			0.708351i	−0.935179	+	0.354175i	$0.884762\pi$
$348$		0			0
$349$	−366.685			−1.05067			−0.525336	−	0.850895i	$-0.676061\pi$
$349$	−366.685			−1.05067			−0.525336	+	0.850895i	$0.676061\pi$
$350$		0			0
$351$	−48.1405	−	48.1405i	−0.137153	−	0.137153i
$352$		0			0
$353$		−	185.624i		−	0.525846i	−0.964817	−	0.262923i	$-0.915313\pi$
$353$		−	185.624i		−	0.525846i	0.964817	−	0.262923i	$-0.0846865\pi$
$354$		0			0
$355$	263.073			0.741050
$356$		0			0
$357$		−	114.179i		−	0.319828i
$358$		0			0
$359$	−55.9415	−	55.9415i	−0.155826	−	0.155826i	0.624888	−	0.780714i	$-0.285144\pi$
$359$	−55.9415	−	55.9415i	−0.155826	−	0.155826i	−0.780714	+	0.624888i	$0.785144\pi$
$360$		0			0
$361$		−	128.163i		−	0.355021i
$362$		0			0
$363$	426.724	−	426.724i	1.17555	−	1.17555i
$364$		0			0
$365$	−139.971	−	139.971i	−0.383483	−	0.383483i
$366$		0			0
$367$	−261.203	−	261.203i	−0.711725	−	0.711725i	0.255171	−	0.966896i	$-0.417868\pi$
$367$	−261.203	−	261.203i	−0.711725	−	0.711725i	−0.966896	+	0.255171i	$0.917868\pi$
$368$		0			0
$369$	−176.821	−	176.821i	−0.479190	−	0.479190i
$370$		0			0
$371$	−937.600			−2.52722
$372$		0			0
$373$	737.666			1.97766			0.988829	−	0.149057i	$-0.0476239\pi$
$373$	737.666			1.97766			0.988829	+	0.149057i	$0.0476239\pi$
$374$		0			0
$375$	−163.275	+	163.275i	−0.435399	+	0.435399i
$376$		0			0
$377$	71.3700	−	8.86436i	0.189310	−	0.0235129i
$378$		0			0
$379$	66.6930	+	66.6930i	0.175971	+	0.175971i	0.789597	−	0.613626i	$-0.210290\pi$
$379$	66.6930	+	66.6930i	0.175971	+	0.175971i	−0.613626	+	0.789597i	$0.710290\pi$
$380$		0			0
$381$		−	323.627i		−	0.849414i
$382$		0			0
$383$		−	40.4750i		−	0.105679i	−0.998603	−	0.0528394i	$-0.983173\pi$
$383$		−	40.4750i		−	0.105679i	0.998603	−	0.0528394i	$-0.0168271\pi$
$384$		0			0
$385$	792.355	−	792.355i	2.05807	−	2.05807i
$386$		0			0
$387$	214.047	−	214.047i	0.553092	−	0.553092i
$388$		0			0
$389$	−300.358	+	300.358i	−0.772128	+	0.772128i	−0.978478	−	0.206350i	$-0.933841\pi$
$389$	−300.358	+	300.358i	−0.772128	+	0.772128i	0.206350	+	0.978478i	$0.433841\pi$
$390$		0			0
$391$	86.8825	+	86.8825i	0.222206	+	0.222206i
$392$		0			0
$393$	331.590			0.843740
$394$		0			0
$395$	163.896	−	163.896i	0.414927	−	0.414927i
$396$		0			0
$397$	−281.675			−0.709508			−0.354754	−	0.934960i	$-0.615435\pi$
$397$	−281.675			−0.709508			−0.354754	+	0.934960i	$0.615435\pi$
$398$		0			0
$399$			303.860i			0.761555i
$400$		0			0
$401$	−423.264			−1.05552			−0.527761	−	0.849393i	$-0.676968\pi$
$401$	−423.264			−1.05552			−0.527761	+	0.849393i	$0.676968\pi$
$402$		0			0
$403$	47.4263	−	47.4263i	0.117683	−	0.117683i
$404$		0			0
$405$		−	23.8743i		−	0.0589488i
$406$		0			0
$407$	294.418			0.723385
$408$		0			0
$409$	291.305	+	291.305i	0.712238	+	0.712238i	0.967003	−	0.254765i	$-0.0819980\pi$
$409$	291.305	+	291.305i	0.712238	+	0.712238i	−0.254765	+	0.967003i	$0.581998\pi$
$410$		0			0
$411$			358.887i			0.873203i
$412$		0			0
$413$	−1119.69			−2.71112
$414$		0			0
$415$			546.008i			1.31568i
$416$		0			0
$417$	−285.820	−	285.820i	−0.685421	−	0.685421i
$418$		0			0
$419$			383.053i			0.914209i	0.889413	+	0.457104i	$0.151113\pi$
$419$			383.053i			0.914209i	−0.889413	+	0.457104i	$0.848887\pi$
$420$		0			0
$421$	−540.346	+	540.346i	−1.28348	+	1.28348i	−0.344808	+	0.938673i	$0.612056\pi$
$421$	−540.346	+	540.346i	−1.28348	+	1.28348i	−0.938673	+	0.344808i	$0.887944\pi$
$422$		0			0
$423$	−137.895	−	137.895i	−0.325994	−	0.325994i
$424$		0			0
$425$	−6.70700	−	6.70700i	−0.0157812	−	0.0157812i
$426$		0			0
$427$	290.026	+	290.026i	0.679217	+	0.679217i
$428$		0			0
$429$	99.2045			0.231246
$430$		0			0
$431$	−509.675			−1.18254			−0.591271	−	0.806473i	$-0.701374\pi$
$431$	−509.675			−1.18254			−0.591271	+	0.806473i	$0.701374\pi$
$432$		0			0
$433$	278.829	−	278.829i	0.643947	−	0.643947i	−0.307577	−	0.951523i	$-0.599518\pi$
$433$	278.829	−	278.829i	0.643947	−	0.643947i	0.951523	+	0.307577i	$0.0995181\pi$
$434$		0			0
$435$	226.271	+	176.274i	0.520164	+	0.405228i
$436$		0			0
$437$	−231.218	−	231.218i	−0.529102	−	0.529102i
$438$		0			0
$439$			702.099i			1.59931i	0.600456	+	0.799657i	$0.294986\pi$
$439$			702.099i			1.59931i	−0.600456	+	0.799657i	$0.705014\pi$
$440$		0			0
$441$		−	314.707i		−	0.713622i
$442$		0			0
$443$	397.097	−	397.097i	0.896382	−	0.896382i	−0.0987319	−	0.995114i	$-0.531479\pi$
$443$	397.097	−	397.097i	0.896382	−	0.896382i	0.995114	+	0.0987319i	$0.0314786\pi$
$444$		0			0
$445$	−429.182	+	429.182i	−0.964454	+	0.964454i
$446$		0			0
$447$	28.4690	−	28.4690i	0.0636891	−	0.0636891i
$448$		0			0
$449$	−182.787	−	182.787i	−0.407097	−	0.407097i	0.473628	−	0.880725i	$-0.342944\pi$
$449$	−182.787	−	182.787i	−0.407097	−	0.407097i	−0.880725	+	0.473628i	$0.842944\pi$
$450$		0			0
$451$	979.674			2.17223
$452$		0			0
$453$	200.725	−	200.725i	0.443102	−	0.443102i
$454$		0			0
$455$	133.085			0.292495
$456$		0			0
$457$			71.3056i			0.156030i	0.996952	+	0.0780149i	$0.0248582\pi$
$457$			71.3056i			0.156030i	−0.996952	+	0.0780149i	$0.975142\pi$
$458$		0			0
$459$	−157.406			−0.342933
$460$		0			0
$461$	−356.013	+	356.013i	−0.772262	+	0.772262i	−0.978502	−	0.206239i	$-0.933877\pi$
$461$	−356.013	+	356.013i	−0.772262	+	0.772262i	0.206239	+	0.978502i	$0.433877\pi$
$462$		0			0
$463$			348.265i			0.752192i	0.926581	+	0.376096i	$0.122734\pi$
$463$			348.265i			0.752192i	−0.926581	+	0.376096i	$0.877266\pi$
$464$		0			0
$465$	267.497			0.575262
$466$		0			0
$467$	−237.322	−	237.322i	−0.508184	−	0.508184i	0.405785	−	0.913969i	$-0.366998\pi$
$467$	−237.322	−	237.322i	−0.508184	−	0.508184i	−0.913969	+	0.405785i	$0.866998\pi$
$468$		0			0
$469$		−	867.078i		−	1.84878i
$470$		0			0
$471$	−244.850			−0.519852
$472$		0			0
$473$			1185.92i			2.50723i
$474$		0			0
$475$	17.8491	+	17.8491i	0.0375771	+	0.0375771i
$476$		0			0
$477$			480.758i			1.00788i
$478$		0			0
$479$	−23.1924	+	23.1924i	−0.0484183	+	0.0484183i	−0.730901	−	0.682483i	$-0.760900\pi$
$479$	−23.1924	+	23.1924i	−0.0484183	+	0.0484183i	0.682483	+	0.730901i	$0.260900\pi$
$480$		0			0
$481$	24.7255	+	24.7255i	0.0514043	+	0.0514043i
$482$		0			0
$483$	−301.747	−	301.747i	−0.624734	−	0.624734i
$484$		0			0
$485$	274.461	+	274.461i	0.565899	+	0.565899i
$486$		0			0
$487$	−669.935			−1.37564			−0.687818	−	0.725883i	$-0.741431\pi$
$487$	−669.935			−1.37564			−0.687818	+	0.725883i	$0.741431\pi$
$488$		0			0
$489$	147.201			0.301024
$490$		0			0
$491$	−396.640	+	396.640i	−0.807822	+	0.807822i	−0.984304	−	0.176482i	$-0.943528\pi$
$491$	−396.640	+	396.640i	−0.807822	+	0.807822i	0.176482	+	0.984304i	$0.443528\pi$
$492$		0			0
$493$	102.188	−	131.172i	0.207278	−	0.266069i
$494$		0			0
$495$	−406.283	−	406.283i	−0.820774	−	0.820774i
$496$		0			0
$497$			529.661i			1.06572i
$498$		0			0
$499$			701.148i			1.40511i	0.711631	+	0.702553i	$0.247957\pi$
$499$			701.148i			1.40511i	−0.711631	+	0.702553i	$0.752043\pi$
$500$		0			0
$501$	51.0542	−	51.0542i	0.101905	−	0.101905i
$502$		0			0
$503$	42.0606	−	42.0606i	0.0836195	−	0.0836195i	−0.664060	−	0.747679i	$-0.731168\pi$
$503$	42.0606	−	42.0606i	0.0836195	−	0.0836195i	0.747679	+	0.664060i	$0.231168\pi$
$504$		0			0
$505$	564.934	−	564.934i	1.11868	−	1.11868i
$506$		0			0
$507$	−220.605	−	220.605i	−0.435118	−	0.435118i
$508$		0			0
$509$	−367.656			−0.722311			−0.361156	−	0.932506i	$-0.617618\pi$
$509$	−367.656			−0.722311			−0.361156	+	0.932506i	$0.617618\pi$
$510$		0			0
$511$	281.813	−	281.813i	0.551492	−	0.551492i
$512$		0			0
$513$	418.900			0.816569
$514$		0			0
$515$		−	255.681i		−	0.496468i
$516$		0			0
$517$	764.007			1.47777
$518$		0			0
$519$	315.517	−	315.517i	0.607932	−	0.607932i
$520$		0			0
$521$			896.590i			1.72090i	0.509533	+	0.860451i	$0.329818\pi$
$521$			896.590i			1.72090i	−0.509533	+	0.860451i	$0.670182\pi$
$522$		0			0
$523$	−118.341			−0.226273			−0.113136	−	0.993579i	$-0.536090\pi$
$523$	−118.341			−0.226273			−0.113136	+	0.993579i	$0.536090\pi$
$524$		0			0
$525$	23.2937	+	23.2937i	0.0443690	+	0.0443690i
$526$		0			0
$527$		−	155.071i		−	0.294252i
$528$		0			0
$529$	−69.7812			−0.131911
$530$		0			0
$531$			574.127i			1.08122i
$532$		0			0
$533$	82.2739	+	82.2739i	0.154360	+	0.154360i
$534$		0			0
$535$			283.740i			0.530356i
$536$		0			0
$537$	53.6763	−	53.6763i	0.0999559	−	0.0999559i
$538$		0			0
$539$	871.815	+	871.815i	1.61747	+	1.61747i
$540$		0			0
$541$	459.879	+	459.879i	0.850054	+	0.850054i	0.990139	−	0.140086i	$-0.0447378\pi$
$541$	459.879	+	459.879i	0.850054	+	0.850054i	−0.140086	+	0.990139i	$0.544738\pi$
$542$		0			0
$543$	112.186	+	112.186i	0.206605	+	0.206605i
$544$		0			0
$545$	−464.730			−0.852716
$546$		0			0
$547$	−27.5099			−0.0502923			−0.0251462	−	0.999684i	$-0.508005\pi$
$547$	−27.5099			−0.0502923			−0.0251462	+	0.999684i	$0.508005\pi$
$548$		0			0
$549$	148.712	−	148.712i	0.270878	−	0.270878i
$550$		0			0
$551$	−271.950	+	349.084i	−0.493557	+	0.633546i
$552$		0			0
$553$	329.982	+	329.982i	0.596713	+	0.596713i
$554$		0			0
$555$			139.458i			0.251276i
$556$		0			0
$557$			633.905i			1.13807i	0.822314	+	0.569035i	$0.192683\pi$
$557$			633.905i			1.13807i	−0.822314	+	0.569035i	$0.807317\pi$
$558$		0			0
$559$	−99.5948	+	99.5948i	−0.178166	+	0.178166i
$560$		0			0
$561$	162.185	−	162.185i	0.289101	−	0.289101i
$562$		0			0
$563$	199.908	−	199.908i	0.355077	−	0.355077i	−0.506918	−	0.861995i	$-0.669215\pi$
$563$	199.908	−	199.908i	0.355077	−	0.355077i	0.861995	+	0.506918i	$0.169215\pi$
$564$		0			0
$565$	16.5562	+	16.5562i	0.0293030	+	0.0293030i
$566$		0			0
$567$	48.0675			0.0847752
$568$		0			0
$569$	−519.969	+	519.969i	−0.913829	+	0.913829i	−0.996571	−	0.0827418i	$-0.973632\pi$
$569$	−519.969	+	519.969i	−0.913829	+	0.913829i	0.0827418	+	0.996571i	$0.473632\pi$
$570$		0			0
$571$	732.511			1.28286			0.641428	−	0.767183i	$-0.278342\pi$
$571$	732.511			1.28286			0.641428	+	0.767183i	$0.278342\pi$
$572$		0			0
$573$		−	581.237i		−	1.01437i
$574$		0			0
$575$	−35.4500			−0.0616521
$576$		0			0
$577$	−588.633	+	588.633i	−1.02016	+	1.02016i	−0.0203695	+	0.999793i	$0.506484\pi$
$577$	−588.633	+	588.633i	−1.02016	+	1.02016i	−0.999793	+	0.0203695i	$0.993516\pi$
$578$		0			0
$579$		−	245.212i		−	0.423510i
$580$		0			0
$581$	−1099.31			−1.89210
$582$		0			0
$583$	−1331.82	−	1331.82i	−2.28442	−	2.28442i
$584$		0			0
$585$		−	68.2401i		−	0.116650i
$586$		0			0
$587$	48.1685			0.0820588			0.0410294	−	0.999158i	$-0.486936\pi$
$587$	48.1685			0.0820588			0.0410294	+	0.999158i	$0.486936\pi$
$588$		0			0
$589$			412.685i			0.700654i
$590$		0			0
$591$	−275.263	−	275.263i	−0.465757	−	0.465757i
$592$		0			0
$593$		−	1098.45i		−	1.85237i	−0.377075	−	0.926183i	$-0.623070\pi$
$593$		−	1098.45i		−	1.85237i	0.377075	−	0.926183i	$-0.376930\pi$
$594$		0			0
$595$	217.576	−	217.576i	0.365674	−	0.365674i
$596$		0			0
$597$	62.7343	+	62.7343i	0.105083	+	0.105083i
$598$		0			0
$599$	306.821	+	306.821i	0.512222	+	0.512222i	0.915207	−	0.402985i	$-0.132027\pi$
$599$	306.821	+	306.821i	0.512222	+	0.512222i	−0.402985	+	0.915207i	$0.632027\pi$
$600$		0			0
$601$	723.532	+	723.532i	1.20388	+	1.20388i	0.972977	+	0.230904i	$0.0741683\pi$
$601$	723.532	+	723.532i	1.20388	+	1.20388i	0.230904	+	0.972977i	$0.425832\pi$
$602$		0			0
$603$	−444.598			−0.737310
$604$		0			0
$605$	1626.31			2.68811
$606$		0			0
$607$	−376.327	+	376.327i	−0.619978	+	0.619978i	−0.945526	−	0.325547i	$-0.894451\pi$
$607$	−376.327	+	376.327i	−0.619978	+	0.619978i	0.325547	+	0.945526i	$0.394451\pi$
$608$		0			0
$609$	−354.903	+	455.566i	−0.582764	+	0.748056i
$610$		0			0
$611$	64.1620	+	64.1620i	0.105011	+	0.105011i
$612$		0			0
$613$			250.396i			0.408476i	0.978921	+	0.204238i	$0.0654717\pi$
$613$			250.396i			0.408476i	−0.978921	+	0.204238i	$0.934528\pi$
$614$		0			0
$615$			464.046i			0.754547i
$616$		0			0
$617$	−751.002	+	751.002i	−1.21718	+	1.21718i	−0.248570	+	0.968614i	$0.579960\pi$
$617$	−751.002	+	751.002i	−1.21718	+	1.21718i	−0.968614	+	0.248570i	$0.920040\pi$
$618$		0			0
$619$	−634.535	+	634.535i	−1.02510	+	1.02510i	−0.0254206	+	0.999677i	$0.508092\pi$
$619$	−634.535	+	634.535i	−1.02510	+	1.02510i	−0.999677	+	0.0254206i	$0.991908\pi$
$620$		0			0
$621$	−415.986	+	415.986i	−0.669865	+	0.669865i
$622$		0			0
$623$	−864.098	−	864.098i	−1.38700	−	1.38700i
$624$		0			0
$625$	−663.620			−1.06179
$626$		0			0
$627$	−431.619	+	431.619i	−0.688388	+	0.688388i
$628$		0			0
$629$	80.8453			0.128530
$630$		0			0
$631$		−	465.674i		−	0.737993i	−0.929431	−	0.368997i	$-0.879701\pi$
$631$		−	465.674i		−	0.737993i	0.929431	−	0.368997i	$-0.120299\pi$
$632$		0			0
$633$	362.213			0.572217
$634$		0			0
$635$	616.695	−	616.695i	0.971173	−	0.971173i
$636$		0			0
$637$			146.432i			0.229877i
$638$		0			0
$639$	271.586			0.425016
$640$		0			0
$641$	93.3103	+	93.3103i	0.145570	+	0.145570i	0.776136	−	0.630566i	$-0.217177\pi$
$641$	93.3103	+	93.3103i	0.145570	+	0.145570i	−0.630566	+	0.776136i	$0.717177\pi$
$642$		0			0
$643$		−	1109.25i		−	1.72511i	−0.505964	−	0.862555i	$-0.668863\pi$
$643$		−	1109.25i		−	1.72511i	0.505964	−	0.862555i	$-0.331137\pi$
$644$		0			0
$645$	−561.740			−0.870915
$646$		0			0
$647$		−	999.636i		−	1.54503i	−0.634995	−	0.772516i	$-0.718998\pi$
$647$		−	999.636i		−	1.54503i	0.634995	−	0.772516i	$-0.281002\pi$
$648$		0			0
$649$	−1590.47	−	1590.47i	−2.45065	−	2.45065i
$650$		0			0
$651$			538.567i			0.827292i
$652$		0			0
$653$	329.921	−	329.921i	0.505239	−	0.505239i	−0.407822	−	0.913061i	$-0.633712\pi$
$653$	329.921	−	329.921i	0.505239	−	0.505239i	0.913061	+	0.407822i	$0.133712\pi$
$654$		0			0
$655$	631.869	+	631.869i	0.964685	+	0.964685i
$656$		0			0
$657$	−144.500	−	144.500i	−0.219940	−	0.219940i
$658$		0			0
$659$	718.993	+	718.993i	1.09104	+	1.09104i	0.995418	+	0.0956177i	$0.0304826\pi$
$659$	718.993	+	718.993i	1.09104	+	1.09104i	0.0956177	+	0.995418i	$0.469517\pi$
$660$		0			0
$661$	706.777			1.06925			0.534627	−	0.845088i	$-0.320452\pi$
$661$	706.777			1.06925			0.534627	+	0.845088i	$0.320452\pi$
$662$		0			0
$663$	27.2410			0.0410874
$664$		0			0
$665$	−579.028	+	579.028i	−0.870719	+	0.870719i
$666$		0			0
$667$	−76.5976	−	616.714i	−0.114839	−	0.924608i
$668$		0			0
$669$	−85.1636	−	85.1636i	−0.127300	−	0.127300i
$670$		0			0
$671$			823.936i			1.22792i
$672$		0			0
$673$		−	519.815i		−	0.772385i	−0.922418	−	0.386192i	$-0.873790\pi$
$673$		−	519.815i		−	0.772385i	0.922418	−	0.386192i	$-0.126210\pi$
$674$		0			0
$675$	32.1125	−	32.1125i	0.0475741	−	0.0475741i
$676$		0			0
$677$	668.470	−	668.470i	0.987400	−	0.987400i	−0.0125213	−	0.999922i	$-0.503986\pi$
$677$	668.470	−	668.470i	0.987400	−	0.987400i	0.999922	+	0.0125213i	$0.00398575\pi$
$678$		0			0
$679$	−552.589	+	552.589i	−0.813828	+	0.813828i
$680$		0			0
$681$	283.291	+	283.291i	0.415992	+	0.415992i
$682$		0			0
$683$	−611.830			−0.895797			−0.447899	−	0.894084i	$-0.647827\pi$
$683$	−611.830			−0.895797			−0.447899	+	0.894084i	$0.647827\pi$
$684$		0			0
$685$	−683.885	+	683.885i	−0.998372	+	0.998372i
$686$		0			0
$687$	−385.292			−0.560832
$688$		0			0
$689$		−	223.694i		−	0.324665i
$690$		0			0
$691$	−723.038			−1.04636			−0.523182	−	0.852221i	$-0.675255\pi$
$691$	−723.038			−1.04636			−0.523182	+	0.852221i	$0.675255\pi$
$692$		0			0
$693$	817.995	−	817.995i	1.18037	−	1.18037i
$694$		0			0
$695$		−	1089.30i		−	1.56734i
$696$		0			0
$697$	269.013			0.385958
$698$		0			0
$699$	88.0302	+	88.0302i	0.125937	+	0.125937i
$700$		0			0
$701$		−	25.1307i		−	0.0358498i	−0.999839	−	0.0179249i	$-0.994294\pi$
$701$		−	25.1307i		−	0.0358498i	0.999839	−	0.0179249i	$-0.00570598\pi$
$702$		0			0
$703$	−215.151			−0.306047
$704$		0			0
$705$			361.890i			0.513320i
$706$		0			0
$707$	1137.42	+	1137.42i	1.60879	+	1.60879i
$708$		0			0
$709$			66.4111i			0.0936687i	0.998903	+	0.0468344i	$0.0149133\pi$
$709$			66.4111i			0.0936687i	−0.998903	+	0.0468344i	$0.985087\pi$
$710$		0			0
$711$	169.200	−	169.200i	0.237974	−	0.237974i
$712$		0			0
$713$	−409.814	−	409.814i	−0.574775	−	0.574775i
$714$		0			0
$715$	189.041	+	189.041i	0.264394	+	0.264394i
$716$		0			0
$717$	382.719	+	382.719i	0.533778	+	0.533778i
$718$		0			0
$719$	255.911			0.355927			0.177963	−	0.984037i	$-0.443049\pi$
$719$	255.911			0.355927			0.177963	+	0.984037i	$0.443049\pi$
$720$		0			0
$721$	514.778			0.713978
$722$		0			0
$723$	214.202	−	214.202i	0.296268	−	0.296268i
$724$		0			0
$725$	5.91304	+	47.6080i	0.00815592	+	0.0656662i
$726$		0			0
$727$	−40.7970	−	40.7970i	−0.0561169	−	0.0561169i	0.678491	−	0.734608i	$-0.262634\pi$
$727$	−40.7970	−	40.7970i	−0.0561169	−	0.0561169i	−0.734608	+	0.678491i	$0.762634\pi$
$728$		0			0
$729$		−	497.982i		−	0.683103i
$730$		0			0
$731$			325.647i			0.445481i
$732$		0			0
$733$	482.560	−	482.560i	0.658335	−	0.658335i	−0.296651	−	0.954986i	$-0.595870\pi$
$733$	482.560	−	482.560i	0.658335	−	0.658335i	0.954986	+	0.296651i	$0.0958697\pi$
$734$		0			0
$735$	−412.956	+	412.956i	−0.561845	+	0.561845i
$736$		0			0
$737$	1231.64	−	1231.64i	1.67116	−	1.67116i
$738$		0			0
$739$	134.347	+	134.347i	0.181796	+	0.181796i	0.792138	−	0.610342i	$-0.208968\pi$
$739$	134.347	+	134.347i	0.181796	+	0.181796i	−0.610342	+	0.792138i	$0.708968\pi$
$740$		0			0
$741$	−72.4955			−0.0978347
$742$		0			0
$743$	725.144	−	725.144i	0.975968	−	0.975968i	−0.0237499	−	0.999718i	$-0.507561\pi$
$743$	725.144	−	725.144i	0.975968	−	0.975968i	0.999718	+	0.0237499i	$0.00756054\pi$
$744$		0			0
$745$	108.500			0.145637
$746$		0			0
$747$			563.676i			0.754587i
$748$		0			0
$749$	−571.272			−0.762712
$750$		0			0
$751$	101.031	−	101.031i	0.134528	−	0.134528i	−0.636636	−	0.771164i	$-0.719675\pi$
$751$	101.031	−	101.031i	0.134528	−	0.134528i	0.771164	+	0.636636i	$0.219675\pi$
$752$		0			0
$753$			393.929i			0.523146i
$754$		0			0
$755$	764.994			1.01324
$756$		0			0
$757$	−643.740	−	643.740i	−0.850383	−	0.850383i	0.139797	−	0.990180i	$-0.455355\pi$
$757$	−643.740	−	643.740i	−0.850383	−	0.850383i	−0.990180	+	0.139797i	$0.955355\pi$
$758$		0			0
$759$		−	857.233i		−	1.12942i
$760$		0			0
$761$	769.857			1.01164			0.505819	−	0.862639i	$-0.331190\pi$
$761$	769.857			1.01164			0.505819	+	0.862639i	$0.331190\pi$
$762$		0			0
$763$		−	935.670i		−	1.22630i
$764$		0			0
$765$	−111.563	−	111.563i	−0.145834	−	0.145834i
$766$		0			0
$767$		−	267.138i		−	0.348290i
$768$		0			0
$769$	548.981	−	548.981i	0.713889	−	0.713889i	−0.253458	−	0.967346i	$-0.581568\pi$
$769$	548.981	−	548.981i	0.713889	−	0.713889i	0.967346	+	0.253458i	$0.0815678\pi$
$770$		0			0
$771$	265.035	+	265.035i	0.343755	+	0.343755i
$772$		0			0
$773$	63.9566	+	63.9566i	0.0827382	+	0.0827382i	0.747265	−	0.664526i	$-0.231367\pi$
$773$	63.9566	+	63.9566i	0.0827382	+	0.0827382i	−0.664526	+	0.747265i	$0.731367\pi$
$774$		0			0
$775$	31.6361	+	31.6361i	0.0408208	+	0.0408208i
$776$		0			0
$777$	−280.779			−0.361363
$778$		0			0
$779$	−715.915			−0.919018
$780$		0			0
$781$	−752.358	+	752.358i	−0.963326	+	0.963326i
$782$		0			0
$783$	628.040	+	489.267i	0.802095	+	0.624863i
$784$		0			0
$785$	−466.581	−	466.581i	−0.594370	−	0.594370i
$786$		0			0
$787$		−	1145.63i		−	1.45569i	−0.685743	−	0.727843i	$-0.740523\pi$
$787$		−	1145.63i		−	1.45569i	0.685743	−	0.727843i	$-0.259477\pi$
$788$		0			0
$789$		−	177.508i		−	0.224979i
$790$		0			0
$791$	−33.3336	+	33.3336i	−0.0421411	+	0.0421411i
$792$		0			0
$793$	−69.1948	+	69.1948i	−0.0872571	+	0.0872571i
$794$		0			0
$795$	630.846	−	630.846i	0.793518	−	0.793518i
$796$		0			0
$797$	199.267	+	199.267i	0.250021	+	0.250021i	0.820979	−	0.570958i	$-0.193428\pi$
$797$	199.267	+	199.267i	0.250021	+	0.250021i	−0.570958	+	0.820979i	$0.693428\pi$
$798$		0			0
$799$	209.792			0.262568
$800$		0			0
$801$	−443.070	+	443.070i	−0.553146	+	0.553146i
$802$		0			0
$803$	800.602			0.997014
$804$		0			0
$805$		−	1150.00i		−	1.42857i
$806$		0			0
$807$	480.063			0.594874
$808$		0			0
$809$	92.8326	−	92.8326i	0.114750	−	0.114750i	−0.647400	−	0.762150i	$-0.724144\pi$
$809$	92.8326	−	92.8326i	0.114750	−	0.114750i	0.762150	+	0.647400i	$0.224144\pi$
$810$		0			0
$811$			1070.02i			1.31938i	0.751536	+	0.659692i	$0.229313\pi$
$811$			1070.02i			1.31938i	−0.751536	+	0.659692i	$0.770687\pi$
$812$		0			0
$813$	−506.695			−0.623241
$814$		0			0
$815$	280.502	+	280.502i	0.344174	+	0.344174i
$816$		0			0
$817$		−	866.634i		−	1.06075i
$818$		0			0
$819$	137.392			0.167756
$820$		0			0
$821$		−	1128.45i		−	1.37448i	−0.726432	−	0.687239i	$-0.758823\pi$
$821$		−	1128.45i		−	1.37448i	0.726432	−	0.687239i	$-0.241177\pi$
$822$		0			0
$823$	−998.351	−	998.351i	−1.21306	−	1.21306i	−0.970014	−	0.243049i	$-0.921852\pi$
$823$	−998.351	−	998.351i	−1.21306	−	1.21306i	−0.243049	−	0.970014i	$-0.578148\pi$
$824$		0			0
$825$			66.1752i			0.0802123i
$826$		0			0
$827$	418.942	−	418.942i	0.506580	−	0.506580i	−0.406895	−	0.913475i	$-0.633388\pi$
$827$	418.942	−	418.942i	0.506580	−	0.506580i	0.913475	+	0.406895i	$0.133388\pi$
$828$		0			0
$829$	96.8486	+	96.8486i	0.116826	+	0.116826i	0.763103	−	0.646277i	$-0.223675\pi$
$829$	96.8486	+	96.8486i	0.116826	+	0.116826i	−0.646277	+	0.763103i	$0.723675\pi$
$830$		0			0
$831$	−340.381	−	340.381i	−0.409604	−	0.409604i
$832$		0			0
$833$	239.395	+	239.395i	0.287389	+	0.287389i
$834$		0			0
$835$	194.575			0.233024
$836$		0			0
$837$	742.465			0.887055
$838$		0			0
$839$	−1113.92	+	1113.92i	−1.32768	+	1.32768i	−0.420282	+	0.907394i	$0.638069\pi$
$839$	−1113.92	+	1113.92i	−1.32768	+	1.32768i	−0.907394	+	0.420282i	$0.861931\pi$
$840$		0			0
$841$	−815.447	+	205.735i	−0.969616	+	0.244632i
$842$		0			0
$843$	−552.323	−	552.323i	−0.655187	−	0.655187i
$844$		0			0
$845$		−	840.758i		−	0.994979i
$846$		0			0
$847$			3274.35i			3.86582i
$848$		0			0
$849$	−70.5511	+	70.5511i	−0.0830990	+	0.0830990i
$850$		0			0
$851$	213.654	−	213.654i	0.251063	−	0.251063i
$852$		0			0
$853$	−71.2347	+	71.2347i	−0.0835108	+	0.0835108i	−0.747628	−	0.664117i	$-0.768807\pi$
$853$	−71.2347	+	71.2347i	−0.0835108	+	0.0835108i	0.664117	+	0.747628i	$0.268807\pi$
$854$		0			0
$855$	296.899	+	296.899i	0.347250	+	0.347250i
$856$		0			0
$857$	−1278.96			−1.49237			−0.746186	−	0.665738i	$-0.768117\pi$
$857$	−1278.96			−1.49237			−0.746186	+	0.665738i	$0.768117\pi$
$858$		0			0
$859$	165.456	−	165.456i	0.192615	−	0.192615i	−0.604210	−	0.796825i	$-0.706511\pi$
$859$	165.456	−	165.456i	0.192615	−	0.192615i	0.796825	+	0.604210i	$0.206511\pi$
$860$		0			0
$861$	−934.293			−1.08513
$862$		0			0
$863$			325.579i			0.377265i	0.982048	+	0.188632i	$0.0604055\pi$
$863$			325.579i			0.377265i	−0.982048	+	0.188632i	$0.939595\pi$
$864$		0			0
$865$	1202.48			1.39015
$866$		0			0
$867$	−346.959	+	346.959i	−0.400184	+	0.400184i
$868$		0			0
$869$			937.448i			1.07877i
$870$		0			0
$871$	206.869			0.237507
$872$		0			0
$873$	283.342	+	283.342i	0.324561	+	0.324561i
$874$		0			0
$875$		−	1252.84i		−	1.43182i
$876$		0			0
$877$	688.398			0.784947			0.392473	−	0.919763i	$-0.371620\pi$
$877$	688.398			0.784947			0.392473	+	0.919763i	$0.371620\pi$
$878$		0			0
$879$		−	519.877i		−	0.591441i
$880$		0			0
$881$	−135.178	−	135.178i	−0.153437	−	0.153437i	0.626214	−	0.779651i	$-0.284604\pi$
$881$	−135.178	−	135.178i	−0.153437	−	0.153437i	−0.779651	+	0.626214i	$0.784604\pi$
$882$		0			0
$883$			1449.80i			1.64190i	0.570999	+	0.820950i	$0.306556\pi$
$883$			1449.80i			1.64190i	−0.570999	+	0.820950i	$0.693444\pi$
$884$		0			0
$885$	753.364	−	753.364i	0.851259	−	0.851259i
$886$		0			0
$887$	145.126	+	145.126i	0.163614	+	0.163614i	0.784166	−	0.620551i	$-0.213091\pi$
$887$	145.126	+	145.126i	0.163614	+	0.163614i	−0.620551	+	0.784166i	$0.713091\pi$
$888$		0			0
$889$	1241.63	+	1241.63i	1.39666	+	1.39666i
$890$		0			0
$891$	68.2776	+	68.2776i	0.0766303	+	0.0766303i
$892$		0			0
$893$	−558.313			−0.625210
$894$		0			0
$895$	204.568			0.228568
$896$		0			0
$897$	71.9912	−	71.9912i	0.0802578	−	0.0802578i
$898$		0			0
$899$	−482.008	+	618.722i	−0.536161	+	0.688234i
$900$		0			0
$901$	−365.709	−	365.709i	−0.405892	−	0.405892i
$902$		0			0
$903$		−	1130.99i		−	1.25248i
$904$		0			0
$905$			427.559i			0.472441i
$906$		0			0
$907$	−454.771	+	454.771i	−0.501401	+	0.501401i	−0.911873	−	0.410472i	$-0.865364\pi$
$907$	−454.771	+	454.771i	−0.501401	+	0.501401i	0.410472	+	0.911873i	$0.365364\pi$
$908$		0			0
$909$	583.214	−	583.214i	0.641600	−	0.641600i
$910$		0			0
$911$	698.987	−	698.987i	0.767274	−	0.767274i	−0.210351	−	0.977626i	$-0.567461\pi$
$911$	698.987	−	698.987i	0.767274	−	0.767274i	0.977626	+	0.210351i	$0.0674608\pi$
$912$		0			0
$913$	−1561.52	−	1561.52i	−1.71032	−	1.71032i
$914$		0			0
$915$	−390.277			−0.426532
$916$		0			0
$917$	−1272.18	+	1272.18i	−1.38733	+	1.38733i
$918$		0			0
$919$	−366.627			−0.398941			−0.199471	−	0.979904i	$-0.563922\pi$
$919$	−366.627			−0.398941			−0.199471	+	0.979904i	$0.563922\pi$
$920$		0			0
$921$			353.814i			0.384163i
$922$		0			0
$923$	−126.367			−0.136909
$924$		0			0
$925$	−16.4933	+	16.4933i	−0.0178306	+	0.0178306i
$926$		0			0
$927$		−	263.955i		−	0.284741i
$928$		0			0
$929$	93.4614			0.100604			0.0503022	−	0.998734i	$-0.483982\pi$
$929$	93.4614			0.100604			0.0503022	+	0.998734i	$0.483982\pi$
$930$		0			0
$931$	−637.095	−	637.095i	−0.684313	−	0.684313i
$932$		0			0
$933$		−	219.134i		−	0.234870i
$934$		0			0
$935$	618.112			0.661083
$936$		0			0
$937$			799.169i			0.852902i	0.904511	+	0.426451i	$0.140236\pi$
$937$			799.169i			0.852902i	−0.904511	+	0.426451i	$0.859764\pi$
$938$		0			0
$939$	459.641	+	459.641i	0.489501	+	0.489501i
$940$		0			0
$941$		−	920.680i		−	0.978406i	−0.872170	−	0.489203i	$-0.837288\pi$
$941$		−	920.680i		−	0.978406i	0.872170	−	0.489203i	$-0.162712\pi$
$942$		0			0
$943$	710.935	−	710.935i	0.753908	−	0.753908i
$944$		0			0
$945$	1041.74	+	1041.74i	1.10237	+	1.10237i
$946$		0			0
$947$	−133.574	−	133.574i	−0.141050	−	0.141050i	0.633056	−	0.774106i	$-0.281800\pi$
$947$	−133.574	−	133.574i	−0.141050	−	0.141050i	−0.774106	+	0.633056i	$0.781800\pi$
$948$		0			0
$949$	67.2353	+	67.2353i	0.0708486	+	0.0708486i
$950$		0			0
$951$	−898.214			−0.944495
$952$		0			0
$953$	−117.308			−0.123093			−0.0615466	−	0.998104i	$-0.519603\pi$
$953$	−117.308			−0.123093			−0.0615466	+	0.998104i	$0.519603\pi$
$954$		0			0
$955$	1107.59	−	1107.59i	1.15978	−	1.15978i
$956$		0			0
$957$	−1151.23	+	142.986i	−1.20296	+	0.149411i
$958$		0			0
$959$	−1376.91	−	1376.91i	−1.43577	−	1.43577i
$960$		0			0
$961$		−	229.550i		−	0.238866i
$962$		0			0
$963$			292.922i			0.304176i
$964$		0			0
$965$	467.270	−	467.270i	0.484218	−	0.484218i
$966$		0			0
$967$	728.794	−	728.794i	0.753665	−	0.753665i	−0.221496	−	0.975161i	$-0.571094\pi$
$967$	728.794	−	728.794i	0.753665	−	0.753665i	0.975161	+	0.221496i	$0.0710941\pi$
$968$		0			0
$969$	−118.520	+	118.520i	−0.122312	+	0.122312i
$970$		0			0
$971$	−738.215	−	738.215i	−0.760263	−	0.760263i	0.216107	−	0.976370i	$-0.430664\pi$
$971$	−738.215	−	738.215i	−0.760263	−	0.760263i	−0.976370	+	0.216107i	$0.930664\pi$
$972$		0			0
$973$	2193.16			2.25402
$974$		0			0
$975$	−5.55745	+	5.55745i	−0.00569995	+	0.00569995i
$976$		0			0
$977$	1847.70			1.89120			0.945599	−	0.325336i	$-0.105477\pi$
$977$	1847.70			1.89120			0.945599	+	0.325336i	$0.105477\pi$
$978$		0			0
$979$		−	2454.82i		−	2.50748i
$980$		0			0
$981$	−479.768			−0.489061
$982$		0			0
$983$	1156.36	−	1156.36i	1.17635	−	1.17635i	0.195687	−	0.980666i	$-0.437306\pi$
$983$	1156.36	−	1156.36i	1.17635	−	1.17635i	0.980666	−	0.195687i	$-0.0626938\pi$
$984$		0			0
$985$		−	1049.07i		−	1.06504i
$986$		0			0
$987$	−728.616			−0.738213
$988$		0			0
$989$	860.606	+	860.606i	0.870178	+	0.870178i
$990$		0			0
$991$			366.164i			0.369490i	0.982787	+	0.184745i	$0.0591459\pi$
$991$			366.164i			0.369490i	−0.982787	+	0.184745i	$0.940854\pi$
$992$		0			0
$993$	−1052.99			−1.06041
$994$		0			0
$995$			239.090i			0.240291i
$996$		0			0
$997$	233.267	+	233.267i	0.233969	+	0.233969i	0.814347	−	0.580378i	$-0.197095\pi$
$997$	233.267	+	233.267i	0.233969	+	0.233969i	−0.580378	+	0.814347i	$0.697095\pi$
$998$		0			0
$999$			387.080i			0.387468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.3.l.e.273.3		14
4.3	odd	2		232.3.j.a.41.5	yes	14
29.17	odd	4	inner	464.3.l.e.17.3		14
116.75	even	4		232.3.j.a.17.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.3.j.a.17.5	✓	14	116.75	even	4
232.3.j.a.41.5	yes	14	4.3	odd	2
464.3.l.e.17.3		14	29.17	odd	4	inner
464.3.l.e.273.3		14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	464.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35465 - 1.35465i) q^{3} -5.16278i q^{5} +10.3945 q^{7} -5.32984i q^{9} +O(q^{10})\)	\(q+(-1.35465 - 1.35465i) q^{3} -5.16278i q^{5} +10.3945 q^{7} -5.32984i q^{9} +(14.7649 + 14.7649i) q^{11} +2.47995i q^{13} +(-6.99377 + 6.99377i) q^{15} +(4.05436 + 4.05436i) q^{17} +(-10.7898 - 10.7898i) q^{19} +(-14.0810 - 14.0810i) q^{21} +21.4294 q^{23} -1.65427 q^{25} +(-19.4119 + 19.4119i) q^{27} +(-3.57442 - 28.7789i) q^{29} +(-19.1239 - 19.1239i) q^{31} -40.0027i q^{33} -53.6647i q^{35} +(9.97016 - 9.97016i) q^{37} +(3.35946 - 3.35946i) q^{39} +(33.1757 - 33.1757i) q^{41} +(40.1601 + 40.1601i) q^{43} -27.5168 q^{45} +(25.8724 - 25.8724i) q^{47} +59.0463 q^{49} -10.9845i q^{51} -90.2013 q^{53} +(76.2281 - 76.2281i) q^{55} +29.2327i q^{57} -107.719 q^{59} +(27.9018 + 27.9018i) q^{61} -55.4012i q^{63} +12.8034 q^{65} -83.4168i q^{67} +(-29.0294 - 29.0294i) q^{69} +50.9557i q^{71} +(27.1116 - 27.1116i) q^{73} +(2.24096 + 2.24096i) q^{75} +(153.475 + 153.475i) q^{77} +(31.7458 + 31.7458i) q^{79} +4.62431 q^{81} -105.759 q^{83} +(20.9318 - 20.9318i) q^{85} +(-34.1433 + 43.8274i) q^{87} +(-83.1301 - 83.1301i) q^{89} +25.7779i q^{91} +51.8126i q^{93} +(-55.7051 + 55.7051i) q^{95} +(-53.1615 + 53.1615i) q^{97} +(78.6947 - 78.6947i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 14 * q - 4 * q^3 - 8 * q^7	\( 14 q - 4 q^{3} - 8 q^{7} + 6 q^{15} - 34 q^{17} - 50 q^{19} - 28 q^{21} + 12 q^{23} - 102 q^{25} + 38 q^{27} + 6 q^{29} - 60 q^{31} + 38 q^{37} - 82 q^{39} + 18 q^{41} + 48 q^{43} + 260 q^{45} + 136 q^{47} + 66 q^{49} - 60 q^{53} + 86 q^{55} - 60 q^{59} + 106 q^{61} - 272 q^{65} - 180 q^{69} + 182 q^{73} + 42 q^{75} + 260 q^{77} + 72 q^{79} - 6 q^{81} - 332 q^{83} - 144 q^{85} + 312 q^{87} + 30 q^{89} - 340 q^{95} + 58 q^{97} + 594 q^{99}+O(q^{100}) \) 14 * q - 4 * q^3 - 8 * q^7 + 6 * q^15 - 34 * q^17 - 50 * q^19 - 28 * q^21 + 12 * q^23 - 102 * q^25 + 38 * q^27 + 6 * q^29 - 60 * q^31 + 38 * q^37 - 82 * q^39 + 18 * q^41 + 48 * q^43 + 260 * q^45 + 136 * q^47 + 66 * q^49 - 60 * q^53 + 86 * q^55 - 60 * q^59 + 106 * q^61 - 272 * q^65 - 180 * q^69 + 182 * q^73 + 42 * q^75 + 260 * q^77 + 72 * q^79 - 6 * q^81 - 332 * q^83 - 144 * q^85 + 312 * q^87 + 30 * q^89 - 340 * q^95 + 58 * q^97 + 594 * q^99

Introduction

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