LMFDB - Embedded newform 740.2.d.a.149.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(149,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.149"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 26 x^{16} + 283 x^{14} + 1674 x^{12} + 5841 x^{10} + 12196 x^{8} + 14736 x^{6} + 9408 x^{4} + \cdots + 144 $ x^18 + 26x^16 + 283x^14 + 1674x^12 + 5841x^10 + 12196x^8 + 14736x^6 + 9408x^4 + 2592x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.17
Root			$0.807220i$ of defining polynomial
Character	$\chi$	$=$	740.149
Dual form			740.2.d.a.149.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+3.05716i q^{3} +(0.115303 + 2.23309i) q^{5} +0.448446i q^{7} -6.34624 q^{9} +1.79699 q^{11} +3.55175i q^{13} +(-6.82693 + 0.352499i) q^{15} -1.08306i q^{17} -0.502334 q^{19} -1.37097 q^{21} +1.38561i q^{23} +(-4.97341 + 0.514964i) q^{25} -10.2300i q^{27} +3.33072 q^{29} +2.17657 q^{31} +5.49370i q^{33} +(-1.00142 + 0.0517071i) q^{35} -1.00000i q^{37} -10.8583 q^{39} -0.833432 q^{41} -11.0621i q^{43} +(-0.731739 - 14.1717i) q^{45} -5.06914i q^{47} +6.79890 q^{49} +3.31109 q^{51} +2.12975i q^{53} +(0.207198 + 4.01285i) q^{55} -1.53572i q^{57} -8.02989 q^{59} +10.9546 q^{61} -2.84595i q^{63} +(-7.93139 + 0.409527i) q^{65} +7.15244i q^{67} -4.23603 q^{69} -8.82409 q^{71} +14.3995i q^{73} +(-1.57433 - 15.2045i) q^{75} +0.805855i q^{77} -8.21536 q^{79} +12.2360 q^{81} -13.0316i q^{83} +(2.41858 - 0.124880i) q^{85} +10.1826i q^{87} +4.73198 q^{89} -1.59277 q^{91} +6.65412i q^{93} +(-0.0579205 - 1.12176i) q^{95} +15.4101i q^{97} -11.4041 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{5} - 18 q^{9} + 6 q^{15} + 4 q^{19} - 16 q^{21} - 2 q^{25} - 4 q^{29} + 8 q^{31} - 2 q^{35} + 8 q^{39} - 4 q^{41} + 8 q^{45} + 6 q^{49} - 40 q^{51} - 6 q^{55} + 8 q^{59} - 12 q^{65} + 28 q^{69}+ \cdots + 16 q^{99}+O(q^{100}) $ 18 * q + 2 * q^5 - 18 * q^9 + 6 * q^15 + 4 * q^19 - 16 * q^21 - 2 * q^25 - 4 * q^29 + 8 * q^31 - 2 * q^35 + 8 * q^39 - 4 * q^41 + 8 * q^45 + 6 * q^49 - 40 * q^51 - 6 * q^55 + 8 * q^59 - 12 * q^65 + 28 * q^69 - 24 * q^71 - 16 * q^75 - 24 * q^79 + 34 * q^81 + 36 * q^91 + 24 * q^95 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$1$	$-1$	$1$

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
$3$			3.05716i			1.76505i	0.470262	+	0.882527i	$0.344159\pi$
$3$			3.05716i			1.76505i	−0.470262	+	0.882527i	$0.655841\pi$
$4$		0			0
$5$	0.115303	+	2.23309i	0.0515650	+	0.998670i
$5$	0.115303	+	2.23309i	0.0515650	+	0.998670i
$6$		0			0
$7$			0.448446i			0.169497i	0.996402	+	0.0847484i	$0.0270086\pi$
$7$			0.448446i			0.169497i	−0.996402	+	0.0847484i	$0.972991\pi$
$8$		0			0
$9$	−6.34624			−2.11541
$10$		0			0
$11$	1.79699			0.541814			0.270907	−	0.962606i	$-0.412676\pi$
$11$	1.79699			0.541814			0.270907	+	0.962606i	$0.412676\pi$
$12$		0			0
$13$			3.55175i			0.985078i	0.870290	+	0.492539i	$0.163931\pi$
$13$			3.55175i			0.985078i	−0.870290	+	0.492539i	$0.836069\pi$
$14$		0			0
$15$	−6.82693	+	0.352499i	−1.76271	+	0.0910149i
$16$		0			0
$17$		−	1.08306i		−	0.262681i	−0.991337	−	0.131340i	$-0.958072\pi$
$17$		−	1.08306i		−	0.262681i	0.991337	−	0.131340i	$-0.0419281\pi$
$18$		0			0
$19$	−0.502334			−0.115243			−0.0576217	−	0.998338i	$-0.518352\pi$
$19$	−0.502334			−0.115243			−0.0576217	+	0.998338i	$0.518352\pi$
$20$		0			0
$21$	−1.37097			−0.299171
$22$		0			0
$23$			1.38561i			0.288919i	0.989511	+	0.144460i	$0.0461444\pi$
$23$			1.38561i			0.288919i	−0.989511	+	0.144460i	$0.953856\pi$
$24$		0			0
$25$	−4.97341	+	0.514964i	−0.994682	+	0.102993i
$26$		0			0
$27$		−	10.2300i		−	1.96876i
$28$		0			0
$29$	3.33072			0.618499			0.309250	−	0.950981i	$-0.399922\pi$
$29$	3.33072			0.618499			0.309250	+	0.950981i	$0.399922\pi$
$30$		0			0
$31$	2.17657			0.390923			0.195462	−	0.980711i	$-0.437379\pi$
$31$	2.17657			0.390923			0.195462	+	0.980711i	$0.437379\pi$
$32$		0			0
$33$			5.49370i			0.956330i
$34$		0			0
$35$	−1.00142	+	0.0517071i	−0.169271	+	0.00874010i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		0			0
$39$	−10.8583			−1.73872
$40$		0			0
$41$	−0.833432			−0.130160			−0.0650801	−	0.997880i	$-0.520730\pi$
$41$	−0.833432			−0.130160			−0.0650801	+	0.997880i	$0.520730\pi$
$42$		0			0
$43$		−	11.0621i		−	1.68696i	−0.537160	−	0.843480i	$-0.680503\pi$
$43$		−	11.0621i		−	1.68696i	0.537160	−	0.843480i	$-0.319497\pi$
$44$		0			0
$45$	−0.731739	−	14.1717i	−0.109081	−	2.11260i
$46$		0			0
$47$		−	5.06914i		−	0.739409i	−0.929149	−	0.369705i	$-0.879459\pi$
$47$		−	5.06914i		−	0.739409i	0.929149	−	0.369705i	$-0.120541\pi$
$48$		0			0
$49$	6.79890			0.971271
$50$		0			0
$51$	3.31109			0.463646
$52$		0			0
$53$			2.12975i			0.292544i	0.989244	+	0.146272i	$0.0467274\pi$
$53$			2.12975i			0.292544i	−0.989244	+	0.146272i	$0.953273\pi$
$54$		0			0
$55$	0.207198	+	4.01285i	0.0279386	+	0.541093i
$56$		0			0
$57$		−	1.53572i		−	0.203411i
$58$		0			0
$59$	−8.02989			−1.04540			−0.522701	−	0.852516i	$-0.675076\pi$
$59$	−8.02989			−1.04540			−0.522701	+	0.852516i	$0.675076\pi$
$60$		0			0
$61$	10.9546			1.40259			0.701294	−	0.712872i	$-0.252606\pi$
$61$	10.9546			1.40259			0.701294	+	0.712872i	$0.252606\pi$
$62$		0			0
$63$		−	2.84595i		−	0.358556i
$64$		0			0
$65$	−7.93139	+	0.409527i	−0.983768	+	0.0507955i
$66$		0			0
$67$			7.15244i			0.873810i	0.899508	+	0.436905i	$0.143925\pi$
$67$			7.15244i			0.873810i	−0.899508	+	0.436905i	$0.856075\pi$
$68$		0			0
$69$	−4.23603			−0.509958
$70$		0			0
$71$	−8.82409			−1.04723			−0.523613	−	0.851956i	$-0.675416\pi$
$71$	−8.82409			−1.04723			−0.523613	+	0.851956i	$0.675416\pi$
$72$		0			0
$73$			14.3995i			1.68534i	0.538431	+	0.842669i	$0.319017\pi$
$73$			14.3995i			1.68534i	−0.538431	+	0.842669i	$0.680983\pi$
$74$		0			0
$75$	−1.57433	−	15.2045i	−0.181788	−	1.75567i
$76$		0			0
$77$			0.805855i			0.0918357i
$78$		0			0
$79$	−8.21536			−0.924300			−0.462150	−	0.886802i	$-0.652922\pi$
$79$	−8.21536			−0.924300			−0.462150	+	0.886802i	$0.652922\pi$
$80$		0			0
$81$	12.2360			1.35956
$82$		0			0
$83$		−	13.0316i		−	1.43041i	−0.698915	−	0.715204i	$-0.746334\pi$
$83$		−	13.0316i		−	1.43041i	0.698915	−	0.715204i	$-0.253666\pi$
$84$		0			0
$85$	2.41858	−	0.124880i	0.262331	−	0.0135451i
$86$		0			0
$87$			10.1826i			1.09168i
$88$		0			0
$89$	4.73198			0.501589			0.250794	−	0.968040i	$-0.419308\pi$
$89$	4.73198			0.501589			0.250794	+	0.968040i	$0.419308\pi$
$90$		0			0
$91$	−1.59277			−0.166968
$92$		0			0
$93$			6.65412i			0.690000i
$94$		0			0
$95$	−0.0579205	−	1.12176i	−0.00594252	−	0.115090i
$96$		0			0
$97$			15.4101i			1.56466i	0.622862	+	0.782332i	$0.285970\pi$
$97$			15.4101i			1.56466i	−0.622862	+	0.782332i	$0.714030\pi$
$98$		0			0
$99$	−11.4041			−1.14616
$100$		0			0
$101$	11.6226			1.15649			0.578247	−	0.815862i	$-0.303737\pi$
$101$	11.6226			1.15649			0.578247	+	0.815862i	$0.303737\pi$
$102$		0			0
$103$			10.9452i			1.07846i	0.842158	+	0.539231i	$0.181285\pi$
$103$			10.9452i			1.07846i	−0.842158	+	0.539231i	$0.818715\pi$
$104$		0			0
$105$	−0.158077	−	3.06151i	−0.0154267	−	0.298773i
$106$		0			0
$107$			13.3841i			1.29389i	0.762537	+	0.646945i	$0.223954\pi$
$107$			13.3841i			1.29389i	−0.762537	+	0.646945i	$0.776046\pi$
$108$		0			0
$109$	10.2736			0.984029			0.492014	−	0.870587i	$-0.336261\pi$
$109$	10.2736			0.984029			0.492014	+	0.870587i	$0.336261\pi$
$110$		0			0
$111$	3.05716			0.290173
$112$		0			0
$113$			18.5406i			1.74416i	0.489366	+	0.872078i	$0.337228\pi$
$113$			18.5406i			1.74416i	−0.489366	+	0.872078i	$0.662772\pi$
$114$		0			0
$115$	−3.09419	+	0.159765i	−0.288535	+	0.0148981i
$116$		0			0
$117$		−	22.5403i		−	2.08385i
$118$		0			0
$119$	0.485695			0.0445236
$120$		0			0
$121$	−7.77082			−0.706438
$122$		0			0
$123$		−	2.54794i		−	0.229740i
$124$		0			0
$125$	−1.72341	−	11.0467i	−0.154147	−	0.988048i
$126$		0			0
$127$		−	9.07107i		−	0.804927i	−0.915436	−	0.402464i	$-0.868154\pi$
$127$		−	9.07107i		−	0.804927i	0.915436	−	0.402464i	$-0.131846\pi$
$128$		0			0
$129$	33.8188			2.97758
$130$		0			0
$131$	−4.71173			−0.411665			−0.205833	−	0.978587i	$-0.565990\pi$
$131$	−4.71173			−0.411665			−0.205833	+	0.978587i	$0.565990\pi$
$132$		0			0
$133$		−	0.225270i		−	0.0195334i
$134$		0			0
$135$	22.8445	−	1.17955i	1.96614	−	0.101519i
$136$		0			0
$137$			2.64911i			0.226329i	0.993576	+	0.113164i	$0.0360987\pi$
$137$			2.64911i			0.226329i	−0.993576	+	0.113164i	$0.963901\pi$
$138$		0			0
$139$	17.1883			1.45789			0.728946	−	0.684571i	$-0.240011\pi$
$139$	17.1883			1.45789			0.728946	+	0.684571i	$0.240011\pi$
$140$		0			0
$141$	15.4972			1.30510
$142$		0			0
$143$			6.38247i			0.533729i
$144$		0			0
$145$	0.384041	+	7.43781i	0.0318929	+	0.617676i
$146$		0			0
$147$			20.7853i			1.71434i
$148$		0			0
$149$	−15.6090			−1.27874			−0.639369	−	0.768900i	$-0.720804\pi$
$149$	−15.6090			−1.27874			−0.639369	+	0.768900i	$0.720804\pi$
$150$		0			0
$151$	20.0474			1.63143			0.815715	−	0.578454i	$-0.196344\pi$
$151$	20.0474			1.63143			0.815715	+	0.578454i	$0.196344\pi$
$152$		0			0
$153$			6.87337i			0.555679i
$154$		0			0
$155$	0.250964	+	4.86048i	0.0201579	+	0.390403i
$156$		0			0
$157$		−	10.3913i		−	0.829315i	−0.909978	−	0.414657i	$-0.863901\pi$
$157$		−	10.3913i		−	0.829315i	0.909978	−	0.414657i	$-0.136099\pi$
$158$		0			0
$159$	−6.51099			−0.516355
$160$		0			0
$161$	−0.621371			−0.0489709
$162$		0			0
$163$			18.1408i			1.42090i	0.703748	+	0.710450i	$0.251509\pi$
$163$			18.1408i			1.42090i	−0.703748	+	0.710450i	$0.748491\pi$
$164$		0			0
$165$	−12.2679	+	0.633439i	−0.955058	+	0.0493131i
$166$		0			0
$167$		−	20.5406i		−	1.58948i	−0.606949	−	0.794741i	$-0.707607\pi$
$167$		−	20.5406i		−	1.58948i	0.606949	−	0.794741i	$-0.292393\pi$
$168$		0			0
$169$	0.385066			0.0296205
$170$		0			0
$171$	3.18793			0.243787
$172$		0			0
$173$			10.1606i			0.772499i	0.922394	+	0.386249i	$0.126230\pi$
$173$			10.1606i			0.772499i	−0.922394	+	0.386249i	$0.873770\pi$
$174$		0			0
$175$	−0.230934	−	2.23031i	−0.0174569	−	0.168595i
$176$		0			0
$177$		−	24.5487i		−	1.84519i
$178$		0			0
$179$	−8.33088			−0.622679			−0.311340	−	0.950299i	$-0.600778\pi$
$179$	−8.33088			−0.622679			−0.311340	+	0.950299i	$0.600778\pi$
$180$		0			0
$181$	−18.7286			−1.39208			−0.696042	−	0.718001i	$-0.745057\pi$
$181$	−18.7286			−1.39208			−0.696042	+	0.718001i	$0.745057\pi$
$182$		0			0
$183$			33.4899i			2.47564i
$184$		0			0
$185$	2.23309	−	0.115303i	0.164180	−	0.00847723i
$186$		0			0
$187$		−	1.94625i		−	0.142324i
$188$		0			0
$189$	4.58760			0.333699
$190$		0			0
$191$	−11.9574			−0.865208			−0.432604	−	0.901584i	$-0.642405\pi$
$191$	−11.9574			−0.865208			−0.432604	+	0.901584i	$0.642405\pi$
$192$		0			0
$193$		−	12.9063i		−	0.929012i	−0.885570	−	0.464506i	$-0.846232\pi$
$193$		−	12.9063i		−	0.929012i	0.885570	−	0.464506i	$-0.153768\pi$
$194$		0			0
$195$	−1.25199	−	24.2475i	−0.0896569	−	1.73640i
$196$		0			0
$197$			6.94271i			0.494647i	0.968933	+	0.247324i	$0.0795511\pi$
$197$			6.94271i			0.494647i	−0.968933	+	0.247324i	$0.920449\pi$
$198$		0			0
$199$	24.6083			1.74444			0.872220	−	0.489114i	$-0.162680\pi$
$199$	24.6083			1.74444			0.872220	+	0.489114i	$0.162680\pi$
$200$		0			0
$201$	−21.8662			−1.54232
$202$		0			0
$203$			1.49365i			0.104834i
$204$		0			0
$205$	−0.0960971	−	1.86113i	−0.00671171	−	0.129987i
$206$		0			0
$207$		−	8.79341i		−	0.611184i
$208$		0			0
$209$	−0.902691			−0.0624404
$210$		0			0
$211$	13.2009			0.908788			0.454394	−	0.890801i	$-0.349856\pi$
$211$	13.2009			0.908788			0.454394	+	0.890801i	$0.349856\pi$
$212$		0			0
$213$		−	26.9767i		−	1.84841i
$214$		0			0
$215$	24.7028	−	1.27550i	1.68472	−	0.0869881i
$216$		0			0
$217$			0.976074i			0.0662602i
$218$		0			0
$219$	−44.0217			−2.97471
$220$		0			0
$221$	3.84676			0.258761
$222$		0			0
$223$		−	4.62772i		−	0.309895i	−0.987923	−	0.154947i	$-0.950479\pi$
$223$		−	4.62772i		−	0.309895i	0.987923	−	0.154947i	$-0.0495208\pi$
$224$		0			0
$225$	31.5625	−	3.26808i	2.10416	−	0.217872i
$226$		0			0
$227$		−	6.20796i		−	0.412037i	−0.978548	−	0.206018i	$-0.933949\pi$
$227$		−	6.20796i		−	0.412037i	0.978548	−	0.206018i	$-0.0660506\pi$
$228$		0			0
$229$	26.6510			1.76115			0.880573	−	0.473911i	$-0.157158\pi$
$229$	26.6510			1.76115			0.880573	+	0.473911i	$0.157158\pi$
$230$		0			0
$231$	−2.46363			−0.162095
$232$		0			0
$233$			20.2645i			1.32757i	0.747922	+	0.663787i	$0.231052\pi$
$233$			20.2645i			1.32757i	−0.747922	+	0.663787i	$0.768948\pi$
$234$		0			0
$235$	11.3199	−	0.584486i	0.738426	−	0.0381276i
$236$		0			0
$237$		−	25.1157i		−	1.63144i
$238$		0			0
$239$	8.60759			0.556779			0.278389	−	0.960468i	$-0.410199\pi$
$239$	8.60759			0.556779			0.278389	+	0.960468i	$0.410199\pi$
$240$		0			0
$241$	−0.683555			−0.0440316			−0.0220158	−	0.999758i	$-0.507008\pi$
$241$	−0.683555			−0.0440316			−0.0220158	+	0.999758i	$0.507008\pi$
$242$		0			0
$243$			6.71757i			0.430932i
$244$		0			0
$245$	0.783932	+	15.1826i	0.0500836	+	0.969979i
$246$		0			0
$247$		−	1.78417i		−	0.113524i
$248$		0			0
$249$	39.8398			2.52475
$250$		0			0
$251$	−18.5993			−1.17398			−0.586989	−	0.809595i	$-0.699687\pi$
$251$	−18.5993			−1.17398			−0.586989	+	0.809595i	$0.699687\pi$
$252$		0			0
$253$			2.48993i			0.156540i
$254$		0			0
$255$	0.381778	+	7.39398i	0.0239079	+	0.463029i
$256$		0			0
$257$		−	10.0027i		−	0.623948i	−0.950091	−	0.311974i	$-0.899010\pi$
$257$		−	10.0027i		−	0.623948i	0.950091	−	0.311974i	$-0.100990\pi$
$258$		0			0
$259$	0.448446			0.0278651
$260$		0			0
$261$	−21.1375			−1.30838
$262$		0			0
$263$		−	8.05851i		−	0.496909i	−0.968644	−	0.248455i	$-0.920077\pi$
$263$		−	8.05851i		−	0.496909i	0.968644	−	0.248455i	$-0.0799227\pi$
$264$		0			0
$265$	−4.75593	+	0.245566i	−0.292154	+	0.0150850i
$266$		0			0
$267$			14.4664i			0.885331i
$268$		0			0
$269$	19.6458			1.19782			0.598912	−	0.800815i	$-0.295600\pi$
$269$	19.6458			1.19782			0.598912	+	0.800815i	$0.295600\pi$
$270$		0			0
$271$	0.816358			0.0495902			0.0247951	−	0.999693i	$-0.492107\pi$
$271$	0.816358			0.0495902			0.0247951	+	0.999693i	$0.492107\pi$
$272$		0			0
$273$		−	4.86935i		−	0.294707i
$274$		0			0
$275$	−8.93718	+	0.925386i	−0.538932	+	0.0558029i
$276$		0			0
$277$		−	23.7950i		−	1.42970i	−0.699276	−	0.714852i	$-0.746494\pi$
$277$		−	23.7950i		−	1.42970i	0.699276	−	0.714852i	$-0.253506\pi$
$278$		0			0
$279$	−13.8130			−0.826964
$280$		0			0
$281$	−7.04816			−0.420458			−0.210229	−	0.977652i	$-0.567421\pi$
$281$	−7.04816			−0.420458			−0.210229	+	0.977652i	$0.567421\pi$
$282$		0			0
$283$		−	4.00339i		−	0.237977i	−0.992896	−	0.118988i	$-0.962035\pi$
$283$		−	4.00339i		−	0.237977i	0.992896	−	0.118988i	$-0.0379651\pi$
$284$		0			0
$285$	3.42940	−	0.177072i	0.203140	−	0.0104889i
$286$		0			0
$287$		−	0.373750i		−	0.0220617i
$288$		0			0
$289$	15.8270			0.930999
$290$		0			0
$291$	−47.1113			−2.76171
$292$		0			0
$293$		−	15.1899i		−	0.887404i	−0.896174	−	0.443702i	$-0.853665\pi$
$293$		−	15.1899i		−	0.887404i	0.896174	−	0.443702i	$-0.146335\pi$
$294$		0			0
$295$	−0.925869	−	17.9315i	−0.0539062	−	1.04401i
$296$		0			0
$297$		−	18.3832i		−	1.06670i
$298$		0			0
$299$	−4.92134			−0.284608
$300$		0			0
$301$	4.96078			0.285934
$302$		0			0
$303$			35.5322i			2.04127i
$304$		0			0
$305$	1.26309	+	24.4626i	0.0723244	+	1.40072i
$306$		0			0
$307$			13.4367i			0.766875i	0.923567	+	0.383438i	$0.125260\pi$
$307$			13.4367i			0.766875i	−0.923567	+	0.383438i	$0.874740\pi$
$308$		0			0
$309$	−33.4612			−1.90354
$310$		0			0
$311$	−27.1028			−1.53686			−0.768430	−	0.639934i	$-0.778962\pi$
$311$	−27.1028			−1.53686			−0.768430	+	0.639934i	$0.778962\pi$
$312$		0			0
$313$		−	13.1432i		−	0.742899i	−0.928453	−	0.371450i	$-0.878861\pi$
$313$		−	13.1432i		−	0.742899i	0.928453	−	0.371450i	$-0.121139\pi$
$314$		0			0
$315$	6.35527	−	0.328146i	0.358079	−	0.0184889i
$316$		0			0
$317$		−	8.69453i		−	0.488333i	−0.969733	−	0.244167i	$-0.921486\pi$
$317$		−	8.69453i		−	0.488333i	0.969733	−	0.244167i	$-0.0785144\pi$
$318$		0			0
$319$	5.98528			0.335111
$320$		0			0
$321$	−40.9174			−2.28379
$322$		0			0
$323$			0.544059i			0.0302722i
$324$		0			0
$325$	−1.82902	−	17.6643i	−0.101456	−	0.979840i
$326$		0			0
$327$			31.4080i			1.73686i
$328$		0			0
$329$	2.27324			0.125328
$330$		0			0
$331$	6.66210			0.366182			0.183091	−	0.983096i	$-0.441390\pi$
$331$	6.66210			0.366182			0.183091	+	0.983096i	$0.441390\pi$
$332$		0			0
$333$			6.34624i			0.347772i
$334$		0			0
$335$	−15.9721	+	0.824697i	−0.872648	+	0.0450580i
$336$		0			0
$337$			30.6358i			1.66884i	0.551131	+	0.834419i	$0.314196\pi$
$337$			30.6358i			1.66884i	−0.551131	+	0.834419i	$0.685804\pi$
$338$		0			0
$339$	−56.6817			−3.07853
$340$		0			0
$341$	3.91128			0.211808
$342$		0			0
$343$			6.18806i			0.334124i
$344$		0			0
$345$	−0.488426	−	9.45945i	−0.0262960	−	0.509280i
$346$		0			0
$347$			9.70306i			0.520888i	0.965489	+	0.260444i	$0.0838689\pi$
$347$			9.70306i			0.520888i	−0.965489	+	0.260444i	$0.916131\pi$
$348$		0			0
$349$	13.2195			0.707623			0.353812	−	0.935317i	$-0.384885\pi$
$349$	13.2195			0.707623			0.353812	+	0.935317i	$0.384885\pi$
$350$		0			0
$351$	36.3344			1.93939
$352$		0			0
$353$			12.1558i			0.646986i	0.946231	+	0.323493i	$0.104857\pi$
$353$			12.1558i			0.646986i	−0.946231	+	0.323493i	$0.895143\pi$
$354$		0			0
$355$	−1.01744	−	19.7050i	−0.0540002	−	1.04583i
$356$		0			0
$357$			1.48485i			0.0785865i
$358$		0			0
$359$	12.3936			0.654109			0.327055	−	0.945005i	$-0.393944\pi$
$359$	12.3936			0.654109			0.327055	+	0.945005i	$0.393944\pi$
$360$		0			0
$361$	−18.7477			−0.986719
$362$		0			0
$363$		−	23.7567i		−	1.24690i
$364$		0			0
$365$	−32.1555	+	1.66031i	−1.68310	+	0.0869044i
$366$		0			0
$367$		−	10.5473i		−	0.550567i	−0.961363	−	0.275283i	$-0.911228\pi$
$367$		−	10.5473i		−	0.550567i	0.961363	−	0.275283i	$-0.0887717\pi$
$368$		0			0
$369$	5.28916			0.275343
$370$		0			0
$371$	−0.955078			−0.0495852
$372$		0			0
$373$			3.16321i			0.163785i	0.996641	+	0.0818923i	$0.0260964\pi$
$373$			3.16321i			0.163785i	−0.996641	+	0.0818923i	$0.973904\pi$
$374$		0			0
$375$	33.7716	−	5.26874i	1.74396	−	0.272077i
$376$		0			0
$377$			11.8299i			0.609270i
$378$		0			0
$379$	−26.2277			−1.34723			−0.673614	−	0.739084i	$-0.735259\pi$
$379$	−26.2277			−1.34723			−0.673614	+	0.739084i	$0.735259\pi$
$380$		0			0
$381$	27.7317			1.42074
$382$		0			0
$383$		−	6.10204i		−	0.311799i	−0.987773	−	0.155900i	$-0.950172\pi$
$383$		−	6.10204i		−	0.311799i	0.987773	−	0.155900i	$-0.0498277\pi$
$384$		0			0
$385$	−1.79955	+	0.0929173i	−0.0917135	+	0.00473550i
$386$		0			0
$387$			70.2030i			3.56862i
$388$		0			0
$389$	11.0799			0.561771			0.280886	−	0.959741i	$-0.409372\pi$
$389$	11.0799			0.561771			0.280886	+	0.959741i	$0.409372\pi$
$390$		0			0
$391$	1.50070			0.0758936
$392$		0			0
$393$		−	14.4045i		−	0.726611i
$394$		0			0
$395$	−0.947254	−	18.3457i	−0.0476615	−	0.923070i
$396$		0			0
$397$			11.3837i			0.571329i	0.958330	+	0.285665i	$0.0922144\pi$
$397$			11.3837i			0.571329i	−0.958330	+	0.285665i	$0.907786\pi$
$398$		0			0
$399$	0.688687			0.0344775
$400$		0			0
$401$	−7.96999			−0.398002			−0.199001	−	0.979999i	$-0.563770\pi$
$401$	−7.96999			−0.398002			−0.199001	+	0.979999i	$0.563770\pi$
$402$		0			0
$403$			7.73063i			0.385090i
$404$		0			0
$405$	1.41085	+	27.3242i	0.0701057	+	1.35775i
$406$		0			0
$407$		−	1.79699i		−	0.0890736i
$408$		0			0
$409$	−35.7633			−1.76838			−0.884191	−	0.467126i	$-0.845289\pi$
$409$	−35.7633			−1.76838			−0.884191	+	0.467126i	$0.845289\pi$
$410$		0			0
$411$	−8.09876			−0.399482
$412$		0			0
$413$		−	3.60098i		−	0.177192i
$414$		0			0
$415$	29.1009	−	1.50258i	1.42851	−	0.0737590i
$416$		0			0
$417$			52.5474i			2.57326i
$418$		0			0
$419$	30.4526			1.48771			0.743853	−	0.668343i	$-0.232996\pi$
$419$	30.4526			1.48771			0.743853	+	0.668343i	$0.232996\pi$
$420$		0			0
$421$	6.37088			0.310498			0.155249	−	0.987875i	$-0.450382\pi$
$421$	6.37088			0.310498			0.155249	+	0.987875i	$0.450382\pi$
$422$		0			0
$423$			32.1700i			1.56416i
$424$		0			0
$425$	0.557737	+	5.38651i	0.0270542	+	0.261284i
$426$		0			0
$427$			4.91253i			0.237734i
$428$		0			0
$429$	−19.5122			−0.942060
$430$		0			0
$431$	25.5381			1.23013			0.615064	−	0.788477i	$-0.289130\pi$
$431$	25.5381			1.23013			0.615064	+	0.788477i	$0.289130\pi$
$432$		0			0
$433$		−	19.2955i		−	0.927285i	−0.886022	−	0.463642i	$-0.846542\pi$
$433$		−	19.2955i		−	0.927285i	0.886022	−	0.463642i	$-0.153458\pi$
$434$		0			0
$435$	−22.7386	+	1.17408i	−1.09023	+	0.0562927i
$436$		0			0
$437$		−	0.696039i		−	0.0332961i
$438$		0			0
$439$	12.9250			0.616876			0.308438	−	0.951244i	$-0.400194\pi$
$439$	12.9250			0.616876			0.308438	+	0.951244i	$0.400194\pi$
$440$		0			0
$441$	−43.1474			−2.05464
$442$		0			0
$443$		−	19.8707i		−	0.944085i	−0.881576	−	0.472042i	$-0.843517\pi$
$443$		−	19.8707i		−	0.944085i	0.881576	−	0.472042i	$-0.156483\pi$
$444$		0			0
$445$	0.545611	+	10.5670i	0.0258644	+	0.500922i
$446$		0			0
$447$		−	47.7192i		−	2.25704i
$448$		0			0
$449$	−23.1727			−1.09359			−0.546793	−	0.837268i	$-0.684152\pi$
$449$	−23.1727			−1.09359			−0.546793	+	0.837268i	$0.684152\pi$
$450$		0			0
$451$	−1.49767			−0.0705226
$452$		0			0
$453$			61.2880i			2.87956i
$454$		0			0
$455$	−0.183651	−	3.55680i	−0.00860968	−	0.166745i
$456$		0			0
$457$		−	12.5062i		−	0.585013i	−0.956264	−	0.292507i	$-0.905511\pi$
$457$		−	12.5062i		−	0.585013i	0.956264	−	0.292507i	$-0.0944893\pi$
$458$		0			0
$459$	−11.0797			−0.517157
$460$		0			0
$461$	−41.4167			−1.92897			−0.964484	−	0.264143i	$-0.914911\pi$
$461$	−41.4167			−1.92897			−0.964484	+	0.264143i	$0.914911\pi$
$462$		0			0
$463$		−	14.2735i		−	0.663344i	−0.943395	−	0.331672i	$-0.892387\pi$
$463$		−	14.2735i		−	0.663344i	0.943395	−	0.331672i	$-0.107613\pi$
$464$		0			0
$465$	−14.8593	+	0.767239i	−0.689082	+	0.0355799i
$466$		0			0
$467$		−	38.3655i		−	1.77534i	−0.460475	−	0.887672i	$-0.652321\pi$
$467$		−	38.3655i		−	1.77534i	0.460475	−	0.887672i	$-0.347679\pi$
$468$		0			0
$469$	−3.20749			−0.148108
$470$		0			0
$471$	31.7678			1.46378
$472$		0			0
$473$		−	19.8786i		−	0.914018i
$474$		0			0
$475$	2.49831	−	0.258684i	0.114631	−	0.0118692i
$476$		0			0
$477$		−	13.5159i		−	0.618851i
$478$		0			0
$479$	6.76138			0.308935			0.154468	−	0.987998i	$-0.450634\pi$
$479$	6.76138			0.308935			0.154468	+	0.987998i	$0.450634\pi$
$480$		0			0
$481$	3.55175			0.161946
$482$		0			0
$483$		−	1.89963i		−	0.0864363i
$484$		0			0
$485$	−34.4123	+	1.77683i	−1.56258	+	0.0806818i
$486$		0			0
$487$			5.55868i			0.251888i	0.992037	+	0.125944i	$0.0401960\pi$
$487$			5.55868i			0.251888i	−0.992037	+	0.125944i	$0.959804\pi$
$488$		0			0
$489$	−55.4595			−2.50796
$490$		0			0
$491$	−15.4135			−0.695600			−0.347800	−	0.937569i	$-0.613071\pi$
$491$	−15.4135			−0.695600			−0.347800	+	0.937569i	$0.613071\pi$
$492$		0			0
$493$		−	3.60737i		−	0.162468i
$494$		0			0
$495$	−1.31493	−	25.4665i	−0.0591017	−	1.14463i
$496$		0			0
$497$		−	3.95713i		−	0.177502i
$498$		0			0
$499$	31.7897			1.42310			0.711550	−	0.702635i	$-0.247993\pi$
$499$	31.7897			1.42310			0.711550	+	0.702635i	$0.247993\pi$
$500$		0			0
$501$	62.7960			2.80552
$502$		0			0
$503$		−	30.1261i		−	1.34326i	−0.740889	−	0.671628i	$-0.765596\pi$
$503$		−	30.1261i		−	1.34326i	0.740889	−	0.671628i	$-0.234404\pi$
$504$		0			0
$505$	1.34012	+	25.9544i	0.0596346	+	1.15496i
$506$		0			0
$507$			1.17721i			0.0522818i
$508$		0			0
$509$	37.0537			1.64238			0.821189	−	0.570657i	$-0.193311\pi$
$509$	37.0537			1.64238			0.821189	+	0.570657i	$0.193311\pi$
$510$		0			0
$511$	−6.45742			−0.285659
$512$		0			0
$513$			5.13888i			0.226887i
$514$		0			0
$515$	−24.4416	+	1.26201i	−1.07703	+	0.0556109i
$516$		0			0
$517$		−	9.10920i		−	0.400622i
$518$		0			0
$519$	−31.0627			−1.36350
$520$		0			0
$521$	5.20283			0.227940			0.113970	−	0.993484i	$-0.463643\pi$
$521$	5.20283			0.227940			0.113970	+	0.993484i	$0.463643\pi$
$522$		0			0
$523$		−	31.0528i		−	1.35784i	−0.734210	−	0.678922i	$-0.762447\pi$
$523$		−	31.0528i		−	1.35784i	0.734210	−	0.678922i	$-0.237553\pi$
$524$		0			0
$525$	6.81841	−	0.706001i	0.297580	−	0.0308124i
$526$		0			0
$527$		−	2.35736i		−	0.102688i
$528$		0			0
$529$	21.0801			0.916526
$530$		0			0
$531$	50.9596			2.21146
$532$		0			0
$533$		−	2.96014i		−	0.128218i
$534$		0			0
$535$	−29.8880	+	1.54322i	−1.29217	+	0.0667194i
$536$		0			0
$537$		−	25.4689i		−	1.09906i
$538$		0			0
$539$	12.2176			0.526248
$540$		0			0
$541$	21.7498			0.935097			0.467548	−	0.883967i	$-0.345137\pi$
$541$	21.7498			0.935097			0.467548	+	0.883967i	$0.345137\pi$
$542$		0			0
$543$		−	57.2563i		−	2.45710i
$544$		0			0
$545$	1.18457	+	22.9418i	0.0507414	+	0.982720i
$546$		0			0
$547$		−	6.97017i		−	0.298023i	−0.988835	−	0.149012i	$-0.952391\pi$
$547$		−	6.97017i		−	0.298023i	0.988835	−	0.149012i	$-0.0476092\pi$
$548$		0			0
$549$	−69.5203			−2.96705
$550$		0			0
$551$	−1.67313			−0.0712779
$552$		0			0
$553$		−	3.68415i		−	0.156666i
$554$		0			0
$555$	0.352499	+	6.82693i	0.0149628	+	0.289787i
$556$		0			0
$557$		−	26.7192i		−	1.13213i	−0.824361	−	0.566065i	$-0.808465\pi$
$557$		−	26.7192i		−	1.13213i	0.824361	−	0.566065i	$-0.191535\pi$
$558$		0			0
$559$	39.2900			1.66179
$560$		0			0
$561$	5.95001			0.251210
$562$		0			0
$563$			38.2345i			1.61139i	0.592331	+	0.805695i	$0.298208\pi$
$563$			38.2345i			1.61139i	−0.592331	+	0.805695i	$0.701792\pi$
$564$		0			0
$565$	−41.4030	+	2.13779i	−1.74184	+	0.0899374i
$566$		0			0
$567$			5.48721i			0.230441i
$568$		0			0
$569$	2.63777			0.110581			0.0552904	−	0.998470i	$-0.482392\pi$
$569$	2.63777			0.110581			0.0552904	+	0.998470i	$0.482392\pi$
$570$		0			0
$571$	11.0844			0.463867			0.231934	−	0.972732i	$-0.425495\pi$
$571$	11.0844			0.463867			0.231934	+	0.972732i	$0.425495\pi$
$572$		0			0
$573$		−	36.5557i		−	1.52714i
$574$		0			0
$575$	−0.713538	−	6.89120i	−0.0297566	−	0.287383i
$576$		0			0
$577$			5.87140i			0.244430i	0.992504	+	0.122215i	$0.0389997\pi$
$577$			5.87140i			0.244430i	−0.992504	+	0.122215i	$0.961000\pi$
$578$		0			0
$579$	39.4565			1.63976
$580$		0			0
$581$	5.84399			0.242450
$582$		0			0
$583$			3.82714i			0.158504i
$584$		0			0
$585$	50.3345	−	2.59896i	2.08108	−	0.107454i
$586$		0			0
$587$		−	35.9503i		−	1.48383i	−0.670494	−	0.741915i	$-0.733918\pi$
$587$		−	35.9503i		−	1.48383i	0.670494	−	0.741915i	$-0.266082\pi$
$588$		0			0
$589$	−1.09336			−0.0450513
$590$		0			0
$591$	−21.2250			−0.873079
$592$		0			0
$593$			11.3178i			0.464768i	0.972624	+	0.232384i	$0.0746526\pi$
$593$			11.3178i			0.464768i	−0.972624	+	0.232384i	$0.925347\pi$
$594$		0			0
$595$	0.0560020	+	1.08460i	0.00229586	+	0.0444643i
$596$		0			0
$597$			75.2317i			3.07903i
$598$		0			0
$599$	−28.4210			−1.16125			−0.580626	−	0.814171i	$-0.697192\pi$
$599$	−28.4210			−1.16125			−0.580626	+	0.814171i	$0.697192\pi$
$600$		0			0
$601$	23.0837			0.941602			0.470801	−	0.882239i	$-0.343965\pi$
$601$	23.0837			0.941602			0.470801	+	0.882239i	$0.343965\pi$
$602$		0			0
$603$		−	45.3911i		−	1.84847i
$604$		0			0
$605$	−0.895997	−	17.3530i	−0.0364275	−	0.705498i
$606$		0			0
$607$			8.55759i			0.347342i	0.984804	+	0.173671i	$0.0555629\pi$
$607$			8.55759i			0.347342i	−0.984804	+	0.173671i	$0.944437\pi$
$608$		0			0
$609$	−4.56633			−0.185037
$610$		0			0
$611$	18.0043			0.728376
$612$		0			0
$613$		−	6.23495i		−	0.251827i	−0.992041	−	0.125914i	$-0.959814\pi$
$613$		−	6.23495i		−	0.251827i	0.992041	−	0.125914i	$-0.0401862\pi$
$614$		0			0
$615$	5.68978	−	0.293784i	0.229434	−	0.0118465i
$616$		0			0
$617$		−	40.1159i		−	1.61500i	−0.589865	−	0.807502i	$-0.700819\pi$
$617$		−	40.1159i		−	1.61500i	0.589865	−	0.807502i	$-0.299181\pi$
$618$		0			0
$619$	41.2861			1.65943			0.829714	−	0.558188i	$-0.188503\pi$
$619$	41.2861			1.65943			0.829714	+	0.558188i	$0.188503\pi$
$620$		0			0
$621$	14.1748			0.568814
$622$		0			0
$623$			2.12204i			0.0850177i
$624$		0			0
$625$	24.4696	−	5.12225i	0.978785	−	0.204890i
$626$		0			0
$627$		−	2.75967i		−	0.110211i
$628$		0			0
$629$	−1.08306			−0.0431845
$630$		0			0
$631$	−12.6926			−0.505284			−0.252642	−	0.967560i	$-0.581299\pi$
$631$	−12.6926			−0.505284			−0.252642	+	0.967560i	$0.581299\pi$
$632$		0			0
$633$			40.3573i			1.60406i
$634$		0			0
$635$	20.2565	−	1.04592i	0.803857	−	0.0415061i
$636$		0			0
$637$			24.1480i			0.956778i
$638$		0			0
$639$	55.9998			2.21532
$640$		0			0
$641$	25.3440			1.00103			0.500514	−	0.865729i	$-0.333145\pi$
$641$	25.3440			1.00103			0.500514	+	0.865729i	$0.333145\pi$
$642$		0			0
$643$		−	23.5901i		−	0.930304i	−0.885231	−	0.465152i	$-0.846000\pi$
$643$		−	23.5901i		−	0.930304i	0.885231	−	0.465152i	$-0.154000\pi$
$644$		0			0
$645$	3.89940	+	75.5205i	0.153539	+	2.97361i
$646$		0			0
$647$		−	23.3132i		−	0.916535i	−0.888814	−	0.458267i	$-0.848470\pi$
$647$		−	23.3132i		−	0.916535i	0.888814	−	0.458267i	$-0.151530\pi$
$648$		0			0
$649$	−14.4297			−0.566414
$650$		0			0
$651$	−2.98402			−0.116953
$652$		0			0
$653$			40.8357i			1.59802i	0.601315	+	0.799012i	$0.294644\pi$
$653$			40.8357i			1.59802i	−0.601315	+	0.799012i	$0.705356\pi$
$654$		0			0
$655$	−0.543275	−	10.5217i	−0.0212275	−	0.411118i
$656$		0			0
$657$		−	91.3829i		−	3.56519i
$658$		0			0
$659$	−22.6517			−0.882384			−0.441192	−	0.897413i	$-0.645444\pi$
$659$	−22.6517			−0.882384			−0.441192	+	0.897413i	$0.645444\pi$
$660$		0			0
$661$	0.230985			0.00898429			0.00449214	−	0.999990i	$-0.498570\pi$
$661$	0.230985			0.00898429			0.00449214	+	0.999990i	$0.498570\pi$
$662$		0			0
$663$			11.7602i			0.456728i
$664$		0			0
$665$	0.503049	−	0.0259743i	0.0195074	−	0.00100724i
$666$		0			0
$667$			4.61508i			0.178696i
$668$		0			0
$669$	14.1477			0.546981
$670$		0			0
$671$	19.6853			0.759941
$672$		0			0
$673$		−	23.5437i		−	0.907543i	−0.891118	−	0.453771i	$-0.850078\pi$
$673$		−	23.5437i		−	0.907543i	0.891118	−	0.453771i	$-0.149922\pi$
$674$		0			0
$675$	5.26808	+	50.8780i	0.202768	+	1.95829i
$676$		0			0
$677$		−	5.61986i		−	0.215989i	−0.994151	−	0.107994i	$-0.965557\pi$
$677$		−	5.61986i		−	0.215989i	0.994151	−	0.107994i	$-0.0344429\pi$
$678$		0			0
$679$	−6.91062			−0.265205
$680$		0			0
$681$	18.9787			0.727267
$682$		0			0
$683$			9.37947i			0.358896i	0.983767	+	0.179448i	$0.0574311\pi$
$683$			9.37947i			0.358896i	−0.983767	+	0.179448i	$0.942569\pi$
$684$		0			0
$685$	−5.91571	+	0.305450i	−0.226028	+	0.0116706i
$686$		0			0
$687$			81.4763i			3.10852i
$688$		0			0
$689$	−7.56434			−0.288178
$690$		0			0
$691$	−2.58554			−0.0983584			−0.0491792	−	0.998790i	$-0.515661\pi$
$691$	−2.58554			−0.0983584			−0.0491792	+	0.998790i	$0.515661\pi$
$692$		0			0
$693$		−	5.11415i		−	0.194270i
$694$		0			0
$695$	1.98186	+	38.3830i	0.0751761	+	1.45595i
$696$		0			0
$697$			0.902658i			0.0341906i
$698$		0			0
$699$	−61.9520			−2.34324
$700$		0			0
$701$	25.1954			0.951618			0.475809	−	0.879549i	$-0.342155\pi$
$701$	25.1954			0.951618			0.475809	+	0.879549i	$0.342155\pi$
$702$		0			0
$703$			0.502334i			0.0189459i
$704$		0			0
$705$	1.78687	+	34.6066i	0.0672973	+	1.30336i
$706$		0			0
$707$			5.21212i			0.196022i
$708$		0			0
$709$	−42.7884			−1.60695			−0.803476	−	0.595337i	$-0.797019\pi$
$709$	−42.7884			−1.60695			−0.803476	+	0.595337i	$0.797019\pi$
$710$		0			0
$711$	52.1366			1.95528
$712$		0			0
$713$			3.01587i			0.112945i
$714$		0			0
$715$	−14.2526	+	0.735917i	−0.533019	+	0.0275217i
$716$		0			0
$717$			26.3148i			0.982744i
$718$		0			0
$719$	21.4988			0.801771			0.400886	−	0.916128i	$-0.368702\pi$
$719$	21.4988			0.801771			0.400886	+	0.916128i	$0.368702\pi$
$720$		0			0
$721$	−4.90833			−0.182796
$722$		0			0
$723$		−	2.08974i		−	0.0777182i
$724$		0			0
$725$	−16.5650	+	1.71520i	−0.615210	+	0.0637009i
$726$		0			0
$727$		−	3.85916i		−	0.143128i	−0.997436	−	0.0715641i	$-0.977201\pi$
$727$		−	3.85916i		−	0.143128i	0.997436	−	0.0715641i	$-0.0227991\pi$
$728$		0			0
$729$	16.1714			0.598942
$730$		0			0
$731$	−11.9810			−0.443133
$732$		0			0
$733$			18.9340i			0.699345i	0.936872	+	0.349672i	$0.113707\pi$
$733$			18.9340i			0.699345i	−0.936872	+	0.349672i	$0.886293\pi$
$734$		0			0
$735$	−46.4156	+	2.39661i	−1.71206	+	0.0884002i
$736$		0			0
$737$			12.8529i			0.473442i
$738$		0			0
$739$	28.4508			1.04658			0.523290	−	0.852155i	$-0.324704\pi$
$739$	28.4508			1.04658			0.523290	+	0.852155i	$0.324704\pi$
$740$		0			0
$741$	5.45448			0.200375
$742$		0			0
$743$		−	45.2282i		−	1.65926i	−0.558313	−	0.829630i	$-0.688551\pi$
$743$		−	45.2282i		−	1.65926i	0.558313	−	0.829630i	$-0.311449\pi$
$744$		0			0
$745$	−1.79976	−	34.8563i	−0.0659381	−	1.27704i
$746$		0			0
$747$			82.7019i			3.02591i
$748$		0			0
$749$	−6.00205			−0.219310
$750$		0			0
$751$	28.6127			1.04409			0.522046	−	0.852917i	$-0.325169\pi$
$751$	28.6127			1.04409			0.522046	+	0.852917i	$0.325169\pi$
$752$		0			0
$753$		−	56.8611i		−	2.07213i
$754$		0			0
$755$	2.31152	+	44.7676i	0.0841247	+	1.62926i
$756$		0			0
$757$			37.0006i			1.34481i	0.740183	+	0.672406i	$0.234739\pi$
$757$			37.0006i			1.34481i	−0.740183	+	0.672406i	$0.765261\pi$
$758$		0			0
$759$	−7.61212			−0.276302
$760$		0			0
$761$	−23.8512			−0.864605			−0.432303	−	0.901729i	$-0.642299\pi$
$761$	−23.8512			−0.864605			−0.432303	+	0.901729i	$0.642299\pi$
$762$		0			0
$763$			4.60714i			0.166790i
$764$		0			0
$765$	−15.3489	+	0.792518i	−0.554940	+	0.0286536i
$766$		0			0
$767$		−	28.5202i		−	1.02980i
$768$		0			0
$769$	−18.8200			−0.678665			−0.339333	−	0.940666i	$-0.610201\pi$
$769$	−18.8200			−0.678665			−0.339333	+	0.940666i	$0.610201\pi$
$770$		0			0
$771$	30.5797			1.10130
$772$		0			0
$773$			8.85107i			0.318351i	0.987250	+	0.159175i	$0.0508835\pi$
$773$			8.85107i			0.318351i	−0.987250	+	0.159175i	$0.949116\pi$
$774$		0			0
$775$	−10.8250	+	1.12085i	−0.388844	+	0.0402623i
$776$		0			0
$777$			1.37097i			0.0491834i
$778$		0			0
$779$	0.418662			0.0150001
$780$		0			0
$781$	−15.8568			−0.567402
$782$		0			0
$783$		−	34.0733i		−	1.21768i
$784$		0			0
$785$	23.2047	−	1.19814i	0.828211	−	0.0427636i
$786$		0			0
$787$			50.4985i			1.80008i	0.435810	+	0.900039i	$0.356462\pi$
$787$			50.4985i			1.80008i	−0.435810	+	0.900039i	$0.643538\pi$
$788$		0			0
$789$	24.6362			0.877071
$790$		0			0
$791$	−8.31448			−0.295629
$792$		0			0
$793$			38.9079i			1.38166i
$794$		0			0
$795$	−0.750735	−	14.5396i	−0.0266258	−	0.515668i
$796$		0			0
$797$		−	28.6495i		−	1.01482i	−0.861706	−	0.507408i	$-0.830604\pi$
$797$		−	28.6495i		−	1.01482i	0.861706	−	0.507408i	$-0.169396\pi$
$798$		0			0
$799$	−5.49018			−0.194229
$800$		0			0
$801$	−30.0303			−1.06107
$802$		0			0
$803$			25.8759i			0.913139i
$804$		0			0
$805$	−0.0716458	−	1.38758i	−0.00252518	−	0.0489058i
$806$		0			0
$807$			60.0603i			2.11422i
$808$		0			0
$809$	42.7386			1.50261			0.751305	−	0.659955i	$-0.229425\pi$
$809$	42.7386			1.50261			0.751305	+	0.659955i	$0.229425\pi$
$810$		0			0
$811$	−2.86550			−0.100621			−0.0503107	−	0.998734i	$-0.516021\pi$
$811$	−2.86550			−0.100621			−0.0503107	+	0.998734i	$0.516021\pi$
$812$		0			0
$813$			2.49574i			0.0875294i
$814$		0			0
$815$	−40.5102	+	2.09169i	−1.41901	+	0.0732687i
$816$		0			0
$817$			5.55689i			0.194411i
$818$		0			0
$819$	10.1081			0.353206
$820$		0			0
$821$	36.5616			1.27601			0.638004	−	0.770033i	$-0.279760\pi$
$821$	36.5616			1.27601			0.638004	+	0.770033i	$0.279760\pi$
$822$		0			0
$823$			31.5554i			1.09995i	0.835180	+	0.549976i	$0.185363\pi$
$823$			31.5554i			1.09995i	−0.835180	+	0.549976i	$0.814637\pi$
$824$		0			0
$825$	−2.82906	−	27.3224i	−0.0984951	−	0.951244i
$826$		0			0
$827$		−	6.47860i		−	0.225283i	−0.993636	−	0.112642i	$-0.964069\pi$
$827$		−	6.47860i		−	0.225283i	0.993636	−	0.112642i	$-0.0359312\pi$
$828$		0			0
$829$	0.642832			0.0223265			0.0111632	−	0.999938i	$-0.496447\pi$
$829$	0.642832			0.0223265			0.0111632	+	0.999938i	$0.496447\pi$
$830$		0			0
$831$	72.7452			2.52350
$832$		0			0
$833$		−	7.36362i		−	0.255134i
$834$		0			0
$835$	45.8691	−	2.36839i	1.58737	−	0.0819616i
$836$		0			0
$837$		−	22.2663i		−	0.769636i
$838$		0			0
$839$	29.4919			1.01817			0.509087	−	0.860715i	$-0.329983\pi$
$839$	29.4919			1.01817			0.509087	+	0.860715i	$0.329983\pi$
$840$		0			0
$841$	−17.9063			−0.617459
$842$		0			0
$843$		−	21.5474i		−	0.742130i
$844$		0			0
$845$	0.0443992	+	0.859889i	0.00152738	+	0.0295811i
$846$		0			0
$847$		−	3.48479i		−	0.119739i
$848$		0			0
$849$	12.2390			0.420042
$850$		0			0
$851$	1.38561			0.0474981
$852$		0			0
$853$		−	4.06198i		−	0.139080i	−0.997579	−	0.0695398i	$-0.977847\pi$
$853$		−	4.06198i		−	0.139080i	0.997579	−	0.0695398i	$-0.0221531\pi$
$854$		0			0
$855$	0.367578	+	7.11895i	0.0125709	+	0.243463i
$856$		0			0
$857$		−	15.9330i		−	0.544260i	−0.962260	−	0.272130i	$-0.912272\pi$
$857$		−	15.9330i		−	0.544260i	0.962260	−	0.272130i	$-0.0877281\pi$
$858$		0			0
$859$	3.60380			0.122960			0.0614801	−	0.998108i	$-0.480418\pi$
$859$	3.60380			0.122960			0.0614801	+	0.998108i	$0.480418\pi$
$860$		0			0
$861$	1.14261			0.0389401
$862$		0			0
$863$		−	24.7833i		−	0.843634i	−0.906681	−	0.421817i	$-0.861393\pi$
$863$		−	24.7833i		−	0.843634i	0.906681	−	0.421817i	$-0.138607\pi$
$864$		0			0
$865$	−22.6896	+	1.17155i	−0.771471	+	0.0398339i
$866$		0			0
$867$			48.3856i			1.64326i
$868$		0			0
$869$	−14.7629			−0.500798
$870$		0			0
$871$	−25.4037			−0.860771
$872$		0			0
$873$		−	97.7965i		−	3.30991i
$874$		0			0
$875$	4.95386	−	0.772857i	0.167471	−	0.0261273i
$876$		0			0
$877$		−	21.3618i		−	0.721337i	−0.932694	−	0.360669i	$-0.882549\pi$
$877$		−	21.3618i		−	0.721337i	0.932694	−	0.360669i	$-0.117451\pi$
$878$		0			0
$879$	46.4380			1.56632
$880$		0			0
$881$	47.1125			1.58726			0.793630	−	0.608401i	$-0.208189\pi$
$881$	47.1125			1.58726			0.793630	+	0.608401i	$0.208189\pi$
$882$		0			0
$883$		−	43.0287i		−	1.44803i	−0.689784	−	0.724015i	$-0.742295\pi$
$883$		−	43.0287i		−	1.44803i	0.689784	−	0.724015i	$-0.257705\pi$
$884$		0			0
$885$	54.8195	−	2.83053i	1.84274	−	0.0951473i
$886$		0			0
$887$			39.2127i			1.31663i	0.752741	+	0.658317i	$0.228731\pi$
$887$			39.2127i			1.31663i	−0.752741	+	0.658317i	$0.771269\pi$
$888$		0			0
$889$	4.06789			0.136433
$890$		0			0
$891$	21.9881			0.736628
$892$		0			0
$893$			2.54640i			0.0852120i
$894$		0			0
$895$	−0.960574	−	18.6036i	−0.0321084	−	0.621851i
$896$		0			0
$897$		−	15.0453i		−	0.502349i
$898$		0			0
$899$	7.24954			0.241786
$900$		0			0
$901$	2.30665			0.0768456
$902$		0			0
$903$			15.1659i			0.504690i
$904$		0			0
$905$	−2.15946	−	41.8227i	−0.0717828	−	1.39023i
$906$		0			0
$907$		−	37.0368i		−	1.22979i	−0.788610	−	0.614893i	$-0.789199\pi$
$907$		−	37.0368i		−	1.22979i	0.788610	−	0.614893i	$-0.210801\pi$
$908$		0			0
$909$	−73.7599			−2.44646
$910$		0			0
$911$	−36.5966			−1.21250			−0.606250	−	0.795274i	$-0.707327\pi$
$911$	−36.5966			−1.21250			−0.606250	+	0.795274i	$0.707327\pi$
$912$		0			0
$913$		−	23.4178i		−	0.775015i
$914$		0			0
$915$	−74.7860	+	3.86148i	−2.47235	+	0.127656i
$916$		0			0
$917$		−	2.11296i		−	0.0697760i
$918$		0			0
$919$	−15.2311			−0.502426			−0.251213	−	0.967932i	$-0.580829\pi$
$919$	−15.2311			−0.502426			−0.251213	+	0.967932i	$0.580829\pi$
$920$		0			0
$921$	−41.0783			−1.35358
$922$		0			0
$923$		−	31.3410i		−	1.03160i
$924$		0			0
$925$	0.514964	+	4.97341i	0.0169319	+	0.163525i
$926$		0			0
$927$		−	69.4609i		−	2.28139i
$928$		0			0
$929$	12.2944			0.403365			0.201683	−	0.979451i	$-0.435359\pi$
$929$	12.2944			0.403365			0.201683	+	0.979451i	$0.435359\pi$
$930$		0			0
$931$	−3.41532			−0.111933
$932$		0			0
$933$		−	82.8577i		−	2.71264i
$934$		0			0
$935$	4.34616	−	0.224408i	0.142135	−	0.00733894i
$936$		0			0
$937$			32.9738i			1.07721i	0.842560	+	0.538603i	$0.181048\pi$
$937$			32.9738i			1.07721i	−0.842560	+	0.538603i	$0.818952\pi$
$938$		0			0
$939$	40.1810			1.31126
$940$		0			0
$941$	−35.0646			−1.14307			−0.571537	−	0.820576i	$-0.693653\pi$
$941$	−35.0646			−1.14307			−0.571537	+	0.820576i	$0.693653\pi$
$942$		0			0
$943$		−	1.15481i		−	0.0376058i
$944$		0			0
$945$	0.528964	+	10.2445i	0.0172072	+	0.333255i
$946$		0			0
$947$			31.6836i			1.02958i	0.857317	+	0.514789i	$0.172130\pi$
$947$			31.6836i			1.02958i	−0.857317	+	0.514789i	$0.827870\pi$
$948$		0			0
$949$	−51.1436			−1.66019
$950$		0			0
$951$	26.5806			0.861934
$952$		0			0
$953$			16.1636i			0.523589i	0.965124	+	0.261795i	$0.0843143\pi$
$953$			16.1636i			0.523589i	−0.965124	+	0.261795i	$0.915686\pi$
$954$		0			0
$955$	−1.37872	−	26.7020i	−0.0446144	−	0.864057i
$956$		0			0
$957$			18.2980i			0.591489i
$958$		0			0
$959$	−1.18798			−0.0383620
$960$		0			0
$961$	−26.2626			−0.847179
$962$		0			0
$963$		−	84.9387i		−	2.73711i
$964$		0			0
$965$	28.8209	−	1.48813i	0.927776	−	0.0479045i
$966$		0			0
$967$			28.4425i			0.914649i	0.889300	+	0.457325i	$0.151192\pi$
$967$			28.4425i			0.914649i	−0.889300	+	0.457325i	$0.848808\pi$
$968$		0			0
$969$	−1.66328			−0.0534321
$970$		0			0
$971$	−48.2297			−1.54776			−0.773882	−	0.633329i	$-0.781688\pi$
$971$	−48.2297			−1.54776			−0.773882	+	0.633329i	$0.781688\pi$
$972$		0			0
$973$			7.70802i			0.247108i
$974$		0			0
$975$	54.0027	−	5.59162i	1.72947	−	0.179075i
$976$		0			0
$977$		−	6.29722i		−	0.201466i	−0.994913	−	0.100733i	$-0.967881\pi$
$977$		−	6.29722i		−	0.201466i	0.994913	−	0.100733i	$-0.0321188\pi$
$978$		0			0
$979$	8.50333			0.271768
$980$		0			0
$981$	−65.1985			−2.08163
$982$		0			0
$983$			44.7044i			1.42585i	0.701241	+	0.712924i	$0.252630\pi$
$983$			44.7044i			1.42585i	−0.701241	+	0.712924i	$0.747370\pi$
$984$		0			0
$985$	−15.5037	+	0.800514i	−0.493989	+	0.0255065i
$986$		0			0
$987$			6.94965i			0.221210i
$988$		0			0
$989$	15.3278			0.487396
$990$		0			0
$991$	−48.1874			−1.53072			−0.765362	−	0.643600i	$-0.777440\pi$
$991$	−48.1874			−1.53072			−0.765362	+	0.643600i	$0.777440\pi$
$992$		0			0
$993$			20.3671i			0.646331i
$994$		0			0
$995$	2.83741	+	54.9527i	0.0899520	+	1.74212i
$996$		0			0
$997$		−	12.1005i		−	0.383225i	−0.981471	−	0.191613i	$-0.938628\pi$
$997$		−	12.1005i		−	0.383225i	0.981471	−	0.191613i	$-0.0613717\pi$
$998$		0			0
$999$	−10.2300			−0.323663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.d.a.149.17	yes	18
3.2	odd	2		6660.2.f.c.5329.9		18
5.2	odd	4		3700.2.a.p.1.9		9
5.3	odd	4		3700.2.a.o.1.1		9
5.4	even	2	inner	740.2.d.a.149.2	✓	18
15.14	odd	2		6660.2.f.c.5329.10		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.d.a.149.2	✓	18	5.4	even	2	inner
740.2.d.a.149.17	yes	18	1.1	even	1	trivial
3700.2.a.o.1.1		9	5.3	odd	4
3700.2.a.p.1.9		9	5.2	odd	4
6660.2.f.c.5329.9		18	3.2	odd	2
6660.2.f.c.5329.10		18	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.05716i q^{3} +(0.115303 + 2.23309i) q^{5} +0.448446i q^{7} -6.34624 q^{9} +1.79699 q^{11} +3.55175i q^{13} +(-6.82693 + 0.352499i) q^{15} -1.08306i q^{17} -0.502334 q^{19} -1.37097 q^{21} +1.38561i q^{23} +(-4.97341 + 0.514964i) q^{25} -10.2300i q^{27} +3.33072 q^{29} +2.17657 q^{31} +5.49370i q^{33} +(-1.00142 + 0.0517071i) q^{35} -1.00000i q^{37} -10.8583 q^{39} -0.833432 q^{41} -11.0621i q^{43} +(-0.731739 - 14.1717i) q^{45} -5.06914i q^{47} +6.79890 q^{49} +3.31109 q^{51} +2.12975i q^{53} +(0.207198 + 4.01285i) q^{55} -1.53572i q^{57} -8.02989 q^{59} +10.9546 q^{61} -2.84595i q^{63} +(-7.93139 + 0.409527i) q^{65} +7.15244i q^{67} -4.23603 q^{69} -8.82409 q^{71} +14.3995i q^{73} +(-1.57433 - 15.2045i) q^{75} +0.805855i q^{77} -8.21536 q^{79} +12.2360 q^{81} -13.0316i q^{83} +(2.41858 - 0.124880i) q^{85} +10.1826i q^{87} +4.73198 q^{89} -1.59277 q^{91} +6.65412i q^{93} +(-0.0579205 - 1.12176i) q^{95} +15.4101i q^{97} -11.4041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{5} - 18 q^{9} + 6 q^{15} + 4 q^{19} - 16 q^{21} - 2 q^{25} - 4 q^{29} + 8 q^{31} - 2 q^{35} + 8 q^{39} - 4 q^{41} + 8 q^{45} + 6 q^{49} - 40 q^{51} - 6 q^{55} + 8 q^{59} - 12 q^{65} + 28 q^{69}+ \cdots + 16 q^{99}+O(q^{100}) \) 18 * q + 2 * q^5 - 18 * q^9 + 6 * q^15 + 4 * q^19 - 16 * q^21 - 2 * q^25 - 4 * q^29 + 8 * q^31 - 2 * q^35 + 8 * q^39 - 4 * q^41 + 8 * q^45 + 6 * q^49 - 40 * q^51 - 6 * q^55 + 8 * q^59 - 12 * q^65 + 28 * q^69 - 24 * q^71 - 16 * q^75 - 24 * q^79 + 34 * q^81 + 36 * q^91 + 24 * q^95 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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