LMFDB - Embedded newform 280.2.h.b.251.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(251,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

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

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

chi := DirichletCharacter("280.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.h (of order $2$, degree $1$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 $ x^16 - x^15 - 2x^12 + 6x^11 - 12x^9 + 8x^8 - 24x^7 + 48x^5 - 32x^4 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.16
Root			$1.41214 - 0.0765298i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.b.251.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41214 + 0.0765298i) q^{2} +2.21915i q^{3} +(1.98829 + 0.216142i) q^{4} +1.00000 q^{5} +(-0.169831 + 3.13376i) q^{6} +(1.20923 - 2.35325i) q^{7} +(2.79120 + 0.457386i) q^{8} -1.92464 q^{9} +O(q^{10})$	\(q+(1.41214 + 0.0765298i) q^{2} +2.21915i q^{3} +(1.98829 + 0.216142i) q^{4} +1.00000 q^{5} +(-0.169831 + 3.13376i) q^{6} +(1.20923 - 2.35325i) q^{7} +(2.79120 + 0.457386i) q^{8} -1.92464 q^{9} +(1.41214 + 0.0765298i) q^{10} -3.88394 q^{11} +(-0.479652 + 4.41231i) q^{12} -5.67503 q^{13} +(1.88769 - 3.23057i) q^{14} +2.21915i q^{15} +(3.90657 + 0.859503i) q^{16} -5.63892i q^{17} +(-2.71786 - 0.147292i) q^{18} +1.31134i q^{19} +(1.98829 + 0.216142i) q^{20} +(5.22221 + 2.68346i) q^{21} +(-5.48468 - 0.297237i) q^{22} +7.37559i q^{23} +(-1.01501 + 6.19410i) q^{24} +1.00000 q^{25} +(-8.01395 - 0.434309i) q^{26} +2.38639i q^{27} +(2.91293 - 4.41756i) q^{28} -9.07201i q^{29} +(-0.169831 + 3.13376i) q^{30} -2.23073 q^{31} +(5.45085 + 1.51271i) q^{32} -8.61906i q^{33} +(0.431546 - 7.96296i) q^{34} +(1.20923 - 2.35325i) q^{35} +(-3.82673 - 0.415995i) q^{36} +6.98438i q^{37} +(-0.100356 + 1.85179i) q^{38} -12.5938i q^{39} +(2.79120 + 0.457386i) q^{40} -7.47757i q^{41} +(7.16914 + 4.18908i) q^{42} -1.46735 q^{43} +(-7.72239 - 0.839482i) q^{44} -1.92464 q^{45} +(-0.564452 + 10.4154i) q^{46} +0.567314 q^{47} +(-1.90737 + 8.66927i) q^{48} +(-4.07554 - 5.69122i) q^{49} +(1.41214 + 0.0765298i) q^{50} +12.5136 q^{51} +(-11.2836 - 1.22661i) q^{52} +0.100950i q^{53} +(-0.182630 + 3.36992i) q^{54} -3.88394 q^{55} +(4.45154 - 6.01530i) q^{56} -2.91006 q^{57} +(0.694279 - 12.8110i) q^{58} -2.93497i q^{59} +(-0.479652 + 4.41231i) q^{60} +13.8324 q^{61} +(-3.15011 - 0.170717i) q^{62} +(-2.32733 + 4.52915i) q^{63} +(7.58160 + 2.55331i) q^{64} -5.67503 q^{65} +(0.659615 - 12.1713i) q^{66} +5.54736 q^{67} +(1.21881 - 11.2118i) q^{68} -16.3676 q^{69} +(1.88769 - 3.23057i) q^{70} +2.42368i q^{71} +(-5.37205 - 0.880303i) q^{72} +6.08011i q^{73} +(-0.534513 + 9.86293i) q^{74} +2.21915i q^{75} +(-0.283435 + 2.60731i) q^{76} +(-4.69657 + 9.13987i) q^{77} +(0.963798 - 17.7842i) q^{78} -2.83370i q^{79} +(3.90657 + 0.859503i) q^{80} -11.0697 q^{81} +(0.572257 - 10.5594i) q^{82} +2.52687i q^{83} +(9.80325 + 6.46423i) q^{84} -5.63892i q^{85} +(-2.07211 - 0.112296i) q^{86} +20.1322 q^{87} +(-10.8409 - 1.77646i) q^{88} +10.9114i q^{89} +(-2.71786 - 0.147292i) q^{90} +(-6.86240 + 13.3547i) q^{91} +(-1.59417 + 14.6648i) q^{92} -4.95033i q^{93} +(0.801127 + 0.0434164i) q^{94} +1.31134i q^{95} +(-3.35693 + 12.0963i) q^{96} +9.93165i q^{97} +(-5.31969 - 8.34871i) q^{98} +7.47519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.41214	+	0.0765298i	0.998535	+	0.0541147i
$2$	1.41214	+	0.0765298i	0.998535	+	0.0541147i
$3$			2.21915i			1.28123i	0.767863	+	0.640614i	$0.221320\pi$
$3$			2.21915i			1.28123i	−0.767863	+	0.640614i	$0.778680\pi$
$4$	1.98829	+	0.216142i	0.994143	+	0.108071i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.169831	+	3.13376i	−0.0693333	+	1.27935i
$7$	1.20923	−	2.35325i	0.457045	−	0.889444i
$7$	1.20923	−	2.35325i	0.457045	−	0.889444i
$8$	2.79120	+	0.457386i	0.986838	+	0.161710i
$9$	−1.92464			−0.641546
$10$	1.41214	+	0.0765298i	0.446558	+	0.0242008i
$11$	−3.88394			−1.17105			−0.585526	−	0.810653i	$-0.699112\pi$
$11$	−3.88394			−1.17105			−0.585526	+	0.810653i	$0.699112\pi$
$12$	−0.479652	+	4.41231i	−0.138463	+	1.27372i
$13$	−5.67503			−1.57397			−0.786985	−	0.616972i	$-0.788359\pi$
$13$	−5.67503			−1.57397			−0.786985	+	0.616972i	$0.788359\pi$
$14$	1.88769	−	3.23057i	0.504507	−	0.863407i
$15$			2.21915i			0.572983i
$16$	3.90657	+	0.859503i	0.976641	+	0.214876i
$17$		−	5.63892i		−	1.36764i	−0.729651	−	0.683820i	$-0.760317\pi$
$17$		−	5.63892i		−	1.36764i	0.729651	−	0.683820i	$-0.239683\pi$
$18$	−2.71786	−	0.147292i	−0.640606	−	0.0347171i
$19$			1.31134i			0.300841i	0.988622	+	0.150421i	$0.0480628\pi$
$19$			1.31134i			0.300841i	−0.988622	+	0.150421i	$0.951937\pi$
$20$	1.98829	+	0.216142i	0.444594	+	0.0483308i
$21$	5.22221	+	2.68346i	1.13958	+	0.585579i
$22$	−5.48468	−	0.297237i	−1.16934	−	0.0633712i
$23$			7.37559i			1.53792i	0.639299	+	0.768958i	$0.279225\pi$
$23$			7.37559i			1.53792i	−0.639299	+	0.768958i	$0.720775\pi$
$24$	−1.01501	+	6.19410i	−0.207188	+	1.26437i
$25$	1.00000			0.200000
$26$	−8.01395	−	0.434309i	−1.57166	−	0.0851750i
$27$			2.38639i			0.459261i
$28$	2.91293	−	4.41756i	0.550491	−	0.834841i
$29$		−	9.07201i		−	1.68463i	−0.538986	−	0.842315i	$-0.681192\pi$
$29$		−	9.07201i		−	1.68463i	0.538986	−	0.842315i	$-0.318808\pi$
$30$	−0.169831	+	3.13376i	−0.0310068	+	0.572143i
$31$	−2.23073			−0.400651			−0.200326	−	0.979729i	$-0.564200\pi$
$31$	−2.23073			−0.400651			−0.200326	+	0.979729i	$0.564200\pi$
$32$	5.45085	+	1.51271i	0.963582	+	0.267412i
$33$		−	8.61906i		−	1.50039i
$34$	0.431546	−	7.96296i	0.0740094	−	1.36564i
$35$	1.20923	−	2.35325i	0.204397	−	0.397771i
$36$	−3.82673	−	0.415995i	−0.637789	−	0.0693325i
$37$			6.98438i			1.14822i	0.818777	+	0.574112i	$0.194653\pi$
$37$			6.98438i			1.14822i	−0.818777	+	0.574112i	$0.805347\pi$
$38$	−0.100356	+	1.85179i	−0.0162799	+	0.300400i
$39$		−	12.5938i		−	2.01662i
$40$	2.79120	+	0.457386i	0.441327	+	0.0723191i
$41$		−	7.47757i		−	1.16780i	−0.811826	−	0.583900i	$-0.801526\pi$
$41$		−	7.47757i		−	1.16780i	0.811826	−	0.583900i	$-0.198474\pi$
$42$	7.16914	+	4.18908i	1.10622	+	0.646389i
$43$	−1.46735			−0.223769			−0.111884	−	0.993721i	$-0.535689\pi$
$43$	−1.46735			−0.223769			−0.111884	+	0.993721i	$0.535689\pi$
$44$	−7.72239	−	0.839482i	−1.16419	−	0.126557i
$45$	−1.92464			−0.286908
$46$	−0.564452	+	10.4154i	−0.0832239	+	1.53566i
$47$	0.567314			0.0827512			0.0413756	−	0.999144i	$-0.486826\pi$
$47$	0.567314			0.0827512			0.0413756	+	0.999144i	$0.486826\pi$
$48$	−1.90737	+	8.66927i	−0.275305	+	1.25130i
$49$	−4.07554	−	5.69122i	−0.582220	−	0.813032i
$50$	1.41214	+	0.0765298i	0.199707	+	0.0108229i
$51$	12.5136			1.75226
$52$	−11.2836	−	1.22661i	−1.56475	−	0.170100i
$53$			0.100950i			0.0138665i	0.999976	+	0.00693326i	$0.00220694\pi$
$53$			0.100950i			0.0138665i	−0.999976	+	0.00693326i	$0.997793\pi$
$54$	−0.182630	+	3.36992i	−0.0248528	+	0.458588i
$55$	−3.88394			−0.523711
$56$	4.45154	−	6.01530i	0.594862	−	0.803828i
$57$	−2.91006			−0.385446
$58$	0.694279	−	12.8110i	0.0911633	−	1.68216i
$59$		−	2.93497i		−	0.382101i	−0.981580	−	0.191050i	$-0.938811\pi$
$59$		−	2.93497i		−	0.382101i	0.981580	−	0.191050i	$-0.0611894\pi$
$60$	−0.479652	+	4.41231i	−0.0619228	+	0.569627i
$61$	13.8324			1.77106			0.885531	−	0.464580i	$-0.153795\pi$
$61$	13.8324			1.77106			0.885531	+	0.464580i	$0.153795\pi$
$62$	−3.15011	−	0.170717i	−0.400064	−	0.0216811i
$63$	−2.32733	+	4.52915i	−0.293216	+	0.570619i
$64$	7.58160	+	2.55331i	0.947700	+	0.319164i
$65$	−5.67503			−0.703901
$66$	0.659615	−	12.1713i	0.0811930	−	1.49819i
$67$	5.54736			0.677718			0.338859	−	0.940837i	$-0.389959\pi$
$67$	5.54736			0.677718			0.338859	+	0.940837i	$0.389959\pi$
$68$	1.21881	−	11.2118i	0.147802	−	1.35963i
$69$	−16.3676			−1.97042
$70$	1.88769	−	3.23057i	0.225623	−	0.386128i
$71$			2.42368i			0.287638i	0.989604	+	0.143819i	$0.0459384\pi$
$71$			2.42368i			0.287638i	−0.989604	+	0.143819i	$0.954062\pi$
$72$	−5.37205	−	0.880303i	−0.633102	−	0.103745i
$73$			6.08011i			0.711623i	0.934558	+	0.355811i	$0.115795\pi$
$73$			6.08011i			0.711623i	−0.934558	+	0.355811i	$0.884205\pi$
$74$	−0.534513	+	9.86293i	−0.0621359	+	1.14654i
$75$			2.21915i			0.256246i
$76$	−0.283435	+	2.60731i	−0.0325122	+	0.299079i
$77$	−4.69657	+	9.13987i	−0.535224	+	1.04159i
$78$	0.963798	−	17.7842i	0.109129	−	2.01366i
$79$		−	2.83370i		−	0.318816i	−0.987213	−	0.159408i	$-0.949041\pi$
$79$		−	2.83370i		−	0.318816i	0.987213	−	0.159408i	$-0.0509586\pi$
$80$	3.90657	+	0.859503i	0.436767	+	0.0960954i
$81$	−11.0697			−1.22996
$82$	0.572257	−	10.5594i	0.0631952	−	1.16609i
$83$			2.52687i			0.277360i	0.990337	+	0.138680i	$0.0442860\pi$
$83$			2.52687i			0.277360i	−0.990337	+	0.138680i	$0.955714\pi$
$84$	9.80325	+	6.46423i	1.06962	+	0.705305i
$85$		−	5.63892i		−	0.611627i
$86$	−2.07211	−	0.112296i	−0.223441	−	0.0121092i
$87$	20.1322			2.15840
$88$	−10.8409	−	1.77646i	−1.15564	−	0.189371i
$89$			10.9114i			1.15661i	0.815822	+	0.578303i	$0.196285\pi$
$89$			10.9114i			1.15661i	−0.815822	+	0.578303i	$0.803715\pi$
$90$	−2.71786	−	0.147292i	−0.286488	−	0.0155260i
$91$	−6.86240	+	13.3547i	−0.719375	+	1.39996i
$92$	−1.59417	+	14.6648i	−0.166204	+	1.52891i
$93$		−	4.95033i		−	0.513326i
$94$	0.801127	+	0.0434164i	0.0826299	+	0.00447806i
$95$			1.31134i			0.134540i
$96$	−3.35693	+	12.0963i	−0.342615	+	1.23457i
$97$			9.93165i			1.00841i	0.863585	+	0.504203i	$0.168214\pi$
$97$			9.93165i			1.00841i	−0.863585	+	0.504203i	$0.831786\pi$
$98$	−5.31969	−	8.34871i	−0.537370	−	0.843347i
$99$	7.47519			0.751285
$100$	1.98829	+	0.216142i	0.198829	+	0.0216142i
$101$	3.07042			0.305519			0.152759	−	0.988263i	$-0.451184\pi$
$101$	3.07042			0.305519			0.152759	+	0.988263i	$0.451184\pi$
$102$	17.6710	+	0.957665i	1.74969	+	0.0948230i
$103$	5.89112			0.580470			0.290235	−	0.956955i	$-0.406267\pi$
$103$	5.89112			0.580470			0.290235	+	0.956955i	$0.406267\pi$
$104$	−15.8401	−	2.59568i	−1.55325	−	0.254527i
$105$	5.22221	+	2.68346i	0.509636	+	0.261879i
$106$	−0.00772567	+	0.142555i	−0.000750383	+	0.0138462i
$107$	−11.0481			−1.06806			−0.534032	−	0.845464i	$-0.679324\pi$
$107$	−11.0481			−1.06806			−0.534032	+	0.845464i	$0.679324\pi$
$108$	−0.515799	+	4.74483i	−0.0496327	+	0.456571i
$109$			4.12606i			0.395205i	0.980282	+	0.197603i	$0.0633156\pi$
$109$			4.12606i			0.395205i	−0.980282	+	0.197603i	$0.936684\pi$
$110$	−5.48468	−	0.297237i	−0.522943	−	0.0283405i
$111$	−15.4994			−1.47114
$112$	6.74655	−	8.15378i	0.637489	−	0.770459i
$113$	−5.28550			−0.497218			−0.248609	−	0.968604i	$-0.579973\pi$
$113$	−5.28550			−0.497218			−0.248609	+	0.968604i	$0.579973\pi$
$114$	−4.10941	−	0.222706i	−0.384882	−	0.0208583i
$115$			7.37559i			0.687777i
$116$	1.96084	−	18.0378i	0.182059	−	1.67476i
$117$	10.9224			1.00977
$118$	0.224613	−	4.14460i	0.0206773	−	0.381541i
$119$	−13.2698	−	6.81874i	−1.21644	−	0.625073i
$120$	−1.01501	+	6.19410i	−0.0926572	+	0.565441i
$121$	4.08501			0.371364
$122$	19.5334	+	1.05859i	1.76847	+	0.0958406i
$123$	16.5939			1.49622
$124$	−4.43533	−	0.482154i	−0.398305	−	0.0432987i
$125$	1.00000			0.0894427
$126$	−3.63313	+	6.21769i	−0.323665	+	0.553916i
$127$			7.13436i			0.633072i	0.948580	+	0.316536i	$0.102520\pi$
$127$			7.13436i			0.633072i	−0.948580	+	0.316536i	$0.897480\pi$
$128$	10.5109	+	4.18585i	0.929039	+	0.369981i
$129$		−	3.25627i		−	0.286699i
$130$	−8.01395	−	0.434309i	−0.702870	−	0.0380914i
$131$		−	6.86654i		−	0.599932i	−0.953950	−	0.299966i	$-0.903025\pi$
$131$		−	6.86654i		−	0.599932i	0.953950	−	0.299966i	$-0.0969754\pi$
$132$	1.86294	−	17.1372i	0.162148	−	1.49160i
$133$	3.08590	+	1.58570i	0.267581	+	0.137498i
$134$	7.83366	+	0.424538i	0.676725	+	0.0366745i
$135$			2.38639i			0.205388i
$136$	2.57916	−	15.7394i	0.221161	−	1.34964i
$137$	5.74697			0.490996			0.245498	−	0.969397i	$-0.421048\pi$
$137$	5.74697			0.490996			0.245498	+	0.969397i	$0.421048\pi$
$138$	−23.1133	−	1.25261i	−1.96753	−	0.106629i
$139$			12.6356i			1.07174i	0.844301	+	0.535869i	$0.180016\pi$
$139$			12.6356i			1.07174i	−0.844301	+	0.535869i	$0.819984\pi$
$140$	2.91293	−	4.41756i	0.246187	−	0.373352i
$141$			1.25896i			0.106023i
$142$	−0.185484	+	3.42258i	−0.0155655	+	0.287217i
$143$	22.0415			1.84320
$144$	−7.51873	−	1.65423i	−0.626561	−	0.137853i
$145$		−	9.07201i		−	0.753389i
$146$	−0.465309	+	8.58597i	−0.0385093	+	0.710580i
$147$	12.6297	−	9.04424i	1.04168	−	0.745956i
$148$	−1.50962	+	13.8869i	−0.124090	+	1.14150i
$149$		−	11.9402i		−	0.978181i	−0.872233	−	0.489091i	$-0.837329\pi$
$149$		−	11.9402i		−	0.978181i	0.872233	−	0.489091i	$-0.162671\pi$
$150$	−0.169831	+	3.13376i	−0.0138667	+	0.255870i
$151$		−	7.62474i		−	0.620493i	−0.950656	−	0.310246i	$-0.899588\pi$
$151$		−	7.62474i		−	0.620493i	0.950656	−	0.310246i	$-0.100412\pi$
$152$	−0.599787	+	3.66020i	−0.0486491	+	0.296882i
$153$			10.8529i			0.877404i
$154$	−7.33169	+	12.5474i	−0.590805	+	1.01110i
$155$	−2.23073			−0.179177
$156$	2.72204	−	25.0400i	0.217937	−	2.00480i
$157$	−15.2157			−1.21435			−0.607174	−	0.794569i	$-0.707697\pi$
$157$	−15.2157			−1.21435			−0.607174	+	0.794569i	$0.707697\pi$
$158$	0.216862	−	4.00159i	0.0172527	−	0.318349i
$159$	−0.224023			−0.0177662
$160$	5.45085	+	1.51271i	0.430927	+	0.119590i
$161$	17.3566	+	8.91876i	1.36789	+	0.702897i
$162$	−15.6320	−	0.847160i	−1.22816	−	0.0665592i
$163$	−0.486426			−0.0380998			−0.0190499	−	0.999819i	$-0.506064\pi$
$163$	−0.486426			−0.0380998			−0.0190499	+	0.999819i	$0.506064\pi$
$164$	1.61621	−	14.8675i	0.126205	−	1.16096i
$165$		−	8.61906i		−	0.670993i
$166$	−0.193381	+	3.56830i	−0.0150093	+	0.276954i
$167$	−19.6159			−1.51793			−0.758963	−	0.651134i	$-0.774294\pi$
$167$	−19.6159			−1.51793			−0.758963	+	0.651134i	$0.774294\pi$
$168$	13.3489	+	9.87864i	1.02989	+	0.762154i
$169$	19.2060			1.47738
$170$	0.431546	−	7.96296i	0.0330980	−	0.610731i
$171$		−	2.52385i		−	0.193004i
$172$	−2.91751	−	0.317156i	−0.222458	−	0.0241829i
$173$	8.14454			0.619218			0.309609	−	0.950864i	$-0.399802\pi$
$173$	8.14454			0.619218			0.309609	+	0.950864i	$0.399802\pi$
$174$	28.4295	+	1.54071i	2.15523	+	0.116801i
$175$	1.20923	−	2.35325i	0.0914090	−	0.177889i
$176$	−15.1729	−	3.33826i	−1.14370	−	0.251631i
$177$	6.51315			0.489558
$178$	−0.835047	+	15.4084i	−0.0625894	+	1.15491i
$179$	−20.3812			−1.52336			−0.761680	−	0.647953i	$-0.775625\pi$
$179$	−20.3812			−1.52336			−0.761680	+	0.647953i	$0.775625\pi$
$180$	−3.82673	−	0.415995i	−0.285228	−	0.0310064i
$181$	−6.68992			−0.497258			−0.248629	−	0.968599i	$-0.579980\pi$
$181$	−6.68992			−0.497258			−0.248629	+	0.968599i	$0.579980\pi$
$182$	−10.7127	+	18.3336i	−0.794080	+	1.35898i
$183$			30.6963i			2.26914i
$184$	−3.37349	+	20.5867i	−0.248697	+	1.51767i
$185$			6.98438i			0.513502i
$186$	0.378848	−	6.99057i	0.0277785	−	0.512573i
$187$			21.9012i			1.60158i
$188$	1.12798	+	0.122620i	0.0822665	+	0.00894299i
$189$	5.61576	+	2.88569i	0.408487	+	0.209903i
$190$	−0.100356	+	1.85179i	−0.00728061	+	0.134343i
$191$		−	5.95641i		−	0.430991i	−0.976505	−	0.215495i	$-0.930863\pi$
$191$		−	5.95641i		−	0.430991i	0.976505	−	0.215495i	$-0.0691366\pi$
$192$	−5.66619	+	16.8247i	−0.408922	+	1.21422i
$193$	10.9141			0.785617			0.392808	−	0.919620i	$-0.371504\pi$
$193$	10.9141			0.785617			0.392808	+	0.919620i	$0.371504\pi$
$194$	−0.760067	+	14.0249i	−0.0545696	+	1.00693i
$195$		−	12.5938i		−	0.901858i
$196$	−6.87323	−	12.1967i	−0.490945	−	0.871191i
$197$			3.76694i			0.268384i	0.990955	+	0.134192i	$0.0428438\pi$
$197$			3.76694i			0.268384i	−0.990955	+	0.134192i	$0.957156\pi$
$198$	10.5560	+	0.572074i	0.750184	+	0.0406556i
$199$	7.52925			0.533734			0.266867	−	0.963733i	$-0.414012\pi$
$199$	7.52925			0.533734			0.266867	+	0.963733i	$0.414012\pi$
$200$	2.79120	+	0.457386i	0.197368	+	0.0323421i
$201$			12.3104i			0.868311i
$202$	4.33587	+	0.234979i	0.305071	+	0.0165331i
$203$	−21.3487	−	10.9701i	−1.49838	−	0.769952i
$204$	24.8807	+	2.70472i	1.74200	+	0.189368i
$205$		−	7.47757i		−	0.522256i
$206$	8.31910	+	0.450847i	0.579619	+	0.0314120i
$207$		−	14.1953i		−	0.986644i
$208$	−22.1699	−	4.87771i	−1.53720	−	0.338208i
$209$		−	5.09315i		−	0.352301i
$210$	7.16914	+	4.18908i	0.494718	+	0.289074i
$211$	−3.93687			−0.271026			−0.135513	−	0.990776i	$-0.543268\pi$
$211$	−3.93687			−0.271026			−0.135513	+	0.990776i	$0.543268\pi$
$212$	−0.0218195	+	0.200717i	−0.00149857	+	0.0137853i
$213$	−5.37852			−0.368530
$214$	−15.6015	−	0.845512i	−1.06650	−	0.0577980i
$215$	−1.46735			−0.100072
$216$	−1.09150	+	6.66089i	−0.0742672	+	0.453216i
$217$	−2.69746	+	5.24946i	−0.183116	+	0.356357i
$218$	−0.315767	+	5.82658i	−0.0213864	+	0.394626i
$219$	−13.4927			−0.911752
$220$	−7.72239	−	0.839482i	−0.520643	−	0.0565979i
$221$			32.0011i			2.15262i
$222$	−21.8873	−	1.18617i	−1.46898	−	0.0796102i
$223$	17.3868			1.16431			0.582154	−	0.813078i	$-0.302210\pi$
$223$	17.3868			1.16431			0.582154	+	0.813078i	$0.302210\pi$
$224$	10.1511	−	10.9980i	0.678248	−	0.734833i
$225$	−1.92464			−0.128309
$226$	−7.46388	−	0.404499i	−0.496490	−	0.0269068i
$227$		−	22.9676i		−	1.52441i	−0.647334	−	0.762206i	$-0.724116\pi$
$227$		−	22.9676i		−	1.52441i	0.647334	−	0.762206i	$-0.275884\pi$
$228$	−5.78602	−	0.628985i	−0.383189	−	0.0416555i
$229$	14.1945			0.938000			0.469000	−	0.883198i	$-0.344614\pi$
$229$	14.1945			0.938000			0.469000	+	0.883198i	$0.344614\pi$
$230$	−0.564452	+	10.4154i	−0.0372189	+	0.686769i
$231$	−20.2828	−	10.4224i	−1.33451	−	0.685744i
$232$	4.14941	−	25.3218i	0.272422	−	1.66246i
$233$	14.0393			0.919743			0.459872	−	0.887985i	$-0.347895\pi$
$233$	14.0393			0.919743			0.459872	+	0.887985i	$0.347895\pi$
$234$	15.4240	+	0.835888i	1.00830	+	0.0546437i
$235$	0.567314			0.0370075
$236$	0.634370	−	5.83557i	0.0412940	−	0.379863i
$237$	6.28841			0.408476
$238$	−18.2170	−	10.6446i	−1.18083	−	0.689984i
$239$		−	12.7467i		−	0.824517i	−0.911067	−	0.412259i	$-0.864740\pi$
$239$		−	12.7467i		−	0.824517i	0.911067	−	0.412259i	$-0.135260\pi$
$240$	−1.90737	+	8.66927i	−0.123120	+	0.559599i
$241$			5.80924i			0.374206i	0.982340	+	0.187103i	$0.0599098\pi$
$241$			5.80924i			0.374206i	−0.982340	+	0.187103i	$0.940090\pi$
$242$	5.76861	+	0.312625i	0.370820	+	0.0200963i
$243$		−	17.4061i		−	1.11660i
$244$	27.5029	+	2.98977i	1.76069	+	0.191400i
$245$	−4.07554	−	5.69122i	−0.260377	−	0.363599i
$246$	23.4329	+	1.26992i	1.49403	+	0.0809675i
$247$		−	7.44187i		−	0.473515i
$248$	−6.22642	−	1.02030i	−0.395378	−	0.0647894i
$249$	−5.60752			−0.355362
$250$	1.41214	+	0.0765298i	0.0893117	+	0.00484017i
$251$		−	26.0680i		−	1.64540i	−0.568478	−	0.822698i	$-0.692468\pi$
$251$		−	26.0680i		−	1.64540i	0.568478	−	0.822698i	$-0.307532\pi$
$252$	−5.60633	+	8.50221i	−0.353166	+	0.535589i
$253$		−	28.6464i		−	1.80098i
$254$	−0.545991	+	10.0747i	−0.0342585	+	0.632145i
$255$	12.5136			0.783634
$256$	14.5225	+	6.71541i	0.907657	+	0.419713i
$257$		−	18.1281i		−	1.13080i	−0.824816	−	0.565401i	$-0.808722\pi$
$257$		−	18.1281i		−	1.13080i	0.824816	−	0.565401i	$-0.191278\pi$
$258$	0.249202	−	4.59832i	0.0155146	−	0.286279i
$259$	16.4360	+	8.44570i	1.02128	+	0.524790i
$260$	−11.2836	−	1.22661i	−0.699778	−	0.0760712i
$261$			17.4603i			1.08077i
$262$	0.525495	−	9.69652i	0.0324652	−	0.599053i
$263$			22.7053i			1.40007i	0.714110	+	0.700034i	$0.246832\pi$
$263$			22.7053i			1.40007i	−0.714110	+	0.700034i	$0.753168\pi$
$264$	3.94224	−	24.0575i	0.242628	−	1.48064i
$265$			0.100950i			0.00620130i
$266$	4.23637	+	2.47540i	0.259749	+	0.151777i
$267$	−24.2140			−1.48188
$268$	11.0297	+	1.19902i	0.673749	+	0.0732416i
$269$	−9.24420			−0.563629			−0.281814	−	0.959469i	$-0.590936\pi$
$269$	−9.24420			−0.563629			−0.281814	+	0.959469i	$0.590936\pi$
$270$	−0.182630	+	3.36992i	−0.0111145	+	0.205087i
$271$	−14.5888			−0.886206			−0.443103	−	0.896471i	$-0.646122\pi$
$271$	−14.5888			−0.886206			−0.443103	+	0.896471i	$0.646122\pi$
$272$	4.84667	−	22.0288i	0.293873	−	1.33569i
$273$	−29.6362	−	15.2287i	−1.79367	−	0.921684i
$274$	8.11553	+	0.439814i	0.490277	+	0.0265701i
$275$	−3.88394			−0.234211
$276$	−32.5434	−	3.53771i	−1.95888	−	0.212945i
$277$			17.6637i			1.06131i	0.847588	+	0.530654i	$0.178054\pi$
$277$			17.6637i			1.06131i	−0.847588	+	0.530654i	$0.821946\pi$
$278$	−0.967000	+	17.8433i	−0.0579968	+	1.07017i
$279$	4.29335			0.257036
$280$	4.45154	−	6.01530i	0.266030	−	0.359483i
$281$	−20.0874			−1.19832			−0.599158	−	0.800631i	$-0.704498\pi$
$281$	−20.0874			−1.19832			−0.599158	+	0.800631i	$0.704498\pi$
$282$	−0.0963476	+	1.77782i	−0.00573742	+	0.105868i
$283$			1.40295i			0.0833969i	0.999130	+	0.0416985i	$0.0132769\pi$
$283$			1.40295i			0.0833969i	−0.999130	+	0.0416985i	$0.986723\pi$
$284$	−0.523859	+	4.81898i	−0.0310853	+	0.285954i
$285$	−2.91006			−0.172377
$286$	31.1257	+	1.68683i	1.84050	+	0.0997444i
$287$	−17.5966	−	9.04208i	−1.03869	−	0.533737i
$288$	−10.4909	−	2.91142i	−0.618183	−	0.171557i
$289$	−14.7974			−0.870438
$290$	0.694279	−	12.8110i	0.0407695	−	0.752286i
$291$	−22.0399			−1.29200
$292$	−1.31417	+	12.0890i	−0.0769057	+	0.707455i
$293$	−14.9167			−0.871446			−0.435723	−	0.900081i	$-0.643507\pi$
$293$	−14.9167			−0.871446			−0.435723	+	0.900081i	$0.643507\pi$
$294$	18.5271	−	11.8052i	1.08052	−	0.688493i
$295$		−	2.93497i		−	0.170881i
$296$	−3.19455	+	19.4948i	−0.185680	+	1.13311i
$297$		−	9.26860i		−	0.537819i
$298$	0.913783	−	16.8613i	0.0529340	−	0.976748i
$299$		−	41.8567i		−	2.42063i
$300$	−0.479652	+	4.41231i	−0.0276927	+	0.254745i
$301$	−1.77436	+	3.45304i	−0.102272	+	0.199030i
$302$	0.583520	−	10.7672i	0.0335778	−	0.619584i
$303$			6.81374i			0.391439i
$304$	−1.12710	+	5.12282i	−0.0646435	+	0.293814i
$305$	13.8324			0.792043
$306$	−0.830569	+	15.3258i	−0.0474805	+	0.876119i
$307$		−	3.67891i		−	0.209966i	−0.994474	−	0.104983i	$-0.966521\pi$
$307$		−	3.67891i		−	0.209966i	0.994474	−	0.104983i	$-0.0334789\pi$
$308$	−11.3136	+	17.1576i	−0.644654	+	0.977643i
$309$			13.0733i			0.743714i
$310$	−3.15011	−	0.170717i	−0.178914	−	0.00969609i
$311$	31.1614			1.76700			0.883501	−	0.468429i	$-0.155180\pi$
$311$	31.1614			1.76700			0.883501	+	0.468429i	$0.155180\pi$
$312$	5.76021	−	35.1517i	0.326108	−	1.99007i
$313$			24.0566i			1.35976i	0.733323	+	0.679880i	$0.237968\pi$
$313$			24.0566i			1.35976i	−0.733323	+	0.679880i	$0.762032\pi$
$314$	−21.4868	−	1.16446i	−1.21257	−	0.0657141i
$315$	−2.32733	+	4.52915i	−0.131130	+	0.255189i
$316$	0.612481	−	5.63421i	0.0344547	−	0.316949i
$317$		−	19.3274i		−	1.08554i	−0.839883	−	0.542768i	$-0.817376\pi$
$317$		−	19.3274i		−	1.08554i	0.839883	−	0.542768i	$-0.182624\pi$
$318$	−0.316352	−	0.0171444i	−0.0177401	−	0.000961412i
$319$			35.2352i			1.97279i
$320$	7.58160	+	2.55331i	0.423824	+	0.142734i
$321$		−	24.5175i		−	1.36843i
$322$	23.8274	+	13.9228i	1.32785	+	0.775890i
$323$	7.39452			0.411442
$324$	−22.0097	−	2.39262i	−1.22276	−	0.132923i
$325$	−5.67503			−0.314794
$326$	−0.686903	−	0.0372261i	−0.0380440	−	0.00206176i
$327$	−9.15636			−0.506348
$328$	3.42013	−	20.8714i	0.188845	−	1.15243i
$329$	0.686011	−	1.33503i	0.0378210	−	0.0736025i
$330$	0.659615	−	12.1713i	0.0363106	−	0.670010i
$331$	19.5607			1.07515			0.537576	−	0.843216i	$-0.319340\pi$
$331$	19.5607			1.07515			0.537576	+	0.843216i	$0.319340\pi$
$332$	−0.546163	+	5.02415i	−0.0299746	+	0.275736i
$333$		−	13.4424i		−	0.736639i
$334$	−27.7005	−	1.50120i	−1.51570	−	0.0821422i
$335$	5.54736			0.303085
$336$	18.0945	+	14.9716i	0.987135	+	0.816769i
$337$	−10.2860			−0.560314			−0.280157	−	0.959954i	$-0.590387\pi$
$337$	−10.2860			−0.560314			−0.280157	+	0.959954i	$0.590387\pi$
$338$	27.1216	+	1.46983i	1.47522	+	0.0799482i
$339$		−	11.7293i		−	0.637050i
$340$	1.21881	−	11.2118i	0.0660991	−	0.608045i
$341$	8.66403			0.469183
$342$	0.193150	−	3.56403i	0.0104443	−	0.192721i
$343$	−18.3211	+	2.70876i	−0.989246	+	0.146260i
$344$	−4.09567	−	0.671145i	−0.220824	−	0.0361857i
$345$	−16.3676			−0.881199
$346$	11.5012	+	0.623300i	0.618311	+	0.0335088i
$347$	3.49360			0.187546			0.0937732	−	0.995594i	$-0.470107\pi$
$347$	3.49360			0.187546			0.0937732	+	0.995594i	$0.470107\pi$
$348$	40.0285	+	4.35140i	2.14575	+	0.233260i
$349$	10.8420			0.580361			0.290180	−	0.956972i	$-0.406285\pi$
$349$	10.8420			0.580361			0.290180	+	0.956972i	$0.406285\pi$
$350$	1.88769	−	3.23057i	0.100901	−	0.172681i
$351$		−	13.5428i		−	0.722863i
$352$	−21.1708	−	5.87527i	−1.12841	−	0.313153i
$353$			0.494060i			0.0262961i	0.999914	+	0.0131481i	$0.00418528\pi$
$353$			0.494060i			0.0262961i	−0.999914	+	0.0131481i	$0.995815\pi$
$354$	9.19749	+	0.498450i	0.488841	+	0.0264923i
$355$			2.42368i			0.128636i
$356$	−2.35841	+	21.6950i	−0.124995	+	1.14983i
$357$	15.1318	−	29.4477i	0.800861	−	1.55854i
$358$	−28.7811	−	1.55977i	−1.52113	−	0.0824362i
$359$			4.33537i			0.228812i	0.993434	+	0.114406i	$0.0364965\pi$
$359$			4.33537i			0.228812i	−0.993434	+	0.114406i	$0.963503\pi$
$360$	−5.37205	−	0.880303i	−0.283132	−	0.0463960i
$361$	17.2804			0.909495
$362$	−9.44711	−	0.511978i	−0.496529	−	0.0269090i
$363$			9.06525i			0.475802i
$364$	−16.5309	+	25.0698i	−0.866457	+	1.31401i
$365$			6.08011i			0.318247i
$366$	−2.34918	+	43.3475i	−0.122794	+	2.26581i
$367$	−32.9836			−1.72173			−0.860866	−	0.508832i	$-0.830077\pi$
$367$	−32.9836			−1.72173			−0.860866	+	0.508832i	$0.830077\pi$
$368$	−6.33934	+	28.8132i	−0.330461	+	1.50199i
$369$			14.3916i			0.749198i
$370$	−0.534513	+	9.86293i	−0.0277880	+	0.512749i
$371$	0.237560	+	0.122071i	0.0123335	+	0.00633762i
$372$	1.06997	−	9.84268i	0.0554755	−	0.510319i
$373$		−	14.2525i		−	0.737967i	−0.929436	−	0.368984i	$-0.879706\pi$
$373$		−	14.2525i		−	0.737967i	0.929436	−	0.368984i	$-0.120294\pi$
$374$	−1.67610	+	30.9277i	−0.0866690	+	1.59923i
$375$			2.21915i			0.114597i
$376$	1.58349	+	0.259481i	0.0816621	+	0.0133817i
$377$			51.4839i			2.65156i
$378$	7.70941	+	4.50477i	0.396529	+	0.231701i
$379$	20.1528			1.03518			0.517590	−	0.855629i	$-0.326829\pi$
$379$	20.1528			1.03518			0.517590	+	0.855629i	$0.326829\pi$
$380$	−0.283435	+	2.60731i	−0.0145399	+	0.133752i
$381$	−15.8322			−0.811110
$382$	0.455843	−	8.41130i	0.0233230	−	0.430359i
$383$	6.39302			0.326668			0.163334	−	0.986571i	$-0.447775\pi$
$383$	6.39302			0.326668			0.163334	+	0.986571i	$0.447775\pi$
$384$	−9.28905	+	23.3253i	−0.474030	+	1.19031i
$385$	−4.69657	+	9.13987i	−0.239359	+	0.465811i
$386$	15.4123	+	0.835257i	0.784466	+	0.0425134i
$387$	2.82412			0.143558
$388$	−2.14664	+	19.7470i	−0.108979	+	1.00250i
$389$		−	15.2150i		−	0.771432i	−0.922618	−	0.385716i	$-0.873955\pi$
$389$		−	15.2150i		−	0.771432i	0.922618	−	0.385716i	$-0.126045\pi$
$390$	0.963798	−	17.7842i	0.0488038	−	0.900536i
$391$	41.5904			2.10332
$392$	−8.77256	−	17.7494i	−0.443081	−	0.896482i
$393$	15.2379			0.768650
$394$	−0.288283	+	5.31946i	−0.0145235	+	0.267990i
$395$		−	2.83370i		−	0.142579i
$396$	14.8628	+	1.61570i	0.746884	+	0.0811920i
$397$	27.8429			1.39739			0.698696	−	0.715418i	$-0.253764\pi$
$397$	27.8429			1.39739			0.698696	+	0.715418i	$0.253764\pi$
$398$	10.6324	+	0.576212i	0.532952	+	0.0288829i
$399$	−3.51892	+	6.84808i	−0.176166	+	0.342833i
$400$	3.90657	+	0.859503i	0.195328	+	0.0429752i
$401$	4.49415			0.224427			0.112214	−	0.993684i	$-0.464206\pi$
$401$	4.49415			0.224427			0.112214	+	0.993684i	$0.464206\pi$
$402$	−0.942115	+	17.3841i	−0.0469884	+	0.867039i
$403$	12.6595			0.630613
$404$	6.10488	+	0.663647i	0.303729	+	0.0330177i
$405$	−11.0697			−0.550057
$406$	−29.3078	−	17.1252i	−1.45452	−	0.849908i
$407$		−	27.1269i		−	1.34463i
$408$	34.9280	+	5.72356i	1.72920	+	0.283358i
$409$			9.16042i			0.452954i	0.974017	+	0.226477i	$0.0727207\pi$
$409$			9.16042i			0.452954i	−0.974017	+	0.226477i	$0.927279\pi$
$410$	0.572257	−	10.5594i	0.0282617	−	0.521491i
$411$			12.7534i			0.629079i
$412$	11.7132	+	1.27332i	0.577070	+	0.0627319i
$413$	−6.90671	−	3.54905i	−0.339857	−	0.174637i
$414$	1.08637	−	20.0458i	0.0533920	−	0.985199i
$415$			2.52687i			0.124039i
$416$	−30.9337	−	8.58467i	−1.51665	−	0.420898i
$417$	−28.0403			−1.37314
$418$	0.389778	−	7.19225i	0.0190647	−	0.351785i
$419$			18.8059i			0.918726i	0.888249	+	0.459363i	$0.151922\pi$
$419$			18.8059i			0.918726i	−0.888249	+	0.459363i	$0.848078\pi$
$420$	9.80325	+	6.46423i	0.478350	+	0.315422i
$421$			34.3816i			1.67566i	0.545934	+	0.837828i	$0.316175\pi$
$421$			34.3816i			1.67566i	−0.545934	+	0.837828i	$0.683825\pi$
$422$	−5.55942	−	0.301288i	−0.270628	−	0.0146665i
$423$	−1.09187			−0.0530887
$424$	−0.0461730	+	0.281771i	−0.00224236	+	0.0136840i
$425$		−	5.63892i		−	0.273528i
$426$	−7.59524	−	0.411617i	−0.367990	−	0.0199429i
$427$	16.7266	−	32.5511i	0.809455	−	1.57526i
$428$	−21.9669	−	2.38796i	−1.06181	−	0.115427i
$429$			48.9134i			2.36156i
$430$	−2.07211	−	0.112296i	−0.0999258	−	0.00541539i
$431$		−	3.54360i		−	0.170689i	−0.996351	−	0.0853447i	$-0.972801\pi$
$431$		−	3.54360i		−	0.170689i	0.996351	−	0.0853447i	$-0.0271991\pi$
$432$	−2.05111	+	9.32259i	−0.0986841	+	0.448533i
$433$		−	35.6627i		−	1.71384i	−0.515451	−	0.856919i	$-0.672376\pi$
$433$		−	35.6627i		−	1.71384i	0.515451	−	0.856919i	$-0.327624\pi$
$434$	−4.21094	+	7.20654i	−0.202131	+	0.345925i
$435$	20.1322			0.965264
$436$	−0.891815	+	8.20380i	−0.0427102	+	0.392891i
$437$	−9.67188			−0.462669
$438$	−19.0536	−	1.03259i	−0.910416	−	0.0493392i
$439$	−12.9572			−0.618415			−0.309207	−	0.950995i	$-0.600064\pi$
$439$	−12.9572			−0.618415			−0.309207	+	0.950995i	$0.600064\pi$
$440$	−10.8409	−	1.77646i	−0.516818	−	0.0846894i
$441$	7.84394	+	10.9535i	0.373521	+	0.521597i
$442$	−2.44903	+	45.1900i	−0.116489	+	2.14947i
$443$	0.593530			0.0281994			0.0140997	−	0.999901i	$-0.495512\pi$
$443$	0.593530			0.0281994			0.0140997	+	0.999901i	$0.495512\pi$
$444$	−30.8172	−	3.35007i	−1.46252	−	0.158987i
$445$			10.9114i			0.517250i
$446$	24.5527	+	1.33061i	1.16260	+	0.0630063i
$447$	26.4972			1.25327
$448$	15.1764	−	14.7538i	0.717020	−	0.697053i
$449$	26.9305			1.27093			0.635464	−	0.772130i	$-0.280809\pi$
$449$	26.9305			1.27093			0.635464	+	0.772130i	$0.280809\pi$
$450$	−2.71786	−	0.147292i	−0.128121	−	0.00694342i
$451$			29.0424i			1.36756i
$452$	−10.5091	−	1.14242i	−0.494306	−	0.0537348i
$453$	16.9205			0.794993
$454$	1.75770	−	32.4335i	0.0824932	−	1.52218i
$455$	−6.86240	+	13.3547i	−0.321714	+	0.626080i
$456$	−8.12255	−	1.33102i	−0.380373	−	0.0623306i
$457$	30.8127			1.44136			0.720678	−	0.693270i	$-0.243831\pi$
$457$	30.8127			1.44136			0.720678	+	0.693270i	$0.243831\pi$
$458$	20.0447	+	1.08630i	0.936626	+	0.0507596i
$459$	13.4567			0.628104
$460$	−1.59417	+	14.6648i	−0.0743287	+	0.683749i
$461$	0.701982			0.0326946			0.0163473	−	0.999866i	$-0.494796\pi$
$461$	0.701982			0.0326946			0.0163473	+	0.999866i	$0.494796\pi$
$462$	−27.8445	−	16.2701i	−1.29544	−	0.756956i
$463$		−	26.4984i		−	1.23148i	−0.787948	−	0.615742i	$-0.788857\pi$
$463$		−	26.4984i		−	1.23148i	0.787948	−	0.615742i	$-0.211143\pi$
$464$	7.79742	−	35.4404i	0.361986	−	1.64528i
$465$		−	4.95033i		−	0.229566i
$466$	19.8254	+	1.07442i	0.918396	+	0.0497717i
$467$			41.6876i			1.92907i	0.263947	+	0.964537i	$0.414976\pi$
$467$			41.6876i			1.92907i	−0.263947	+	0.964537i	$0.585024\pi$
$468$	21.7168	+	2.36078i	1.00386	+	0.109127i
$469$	6.70802	−	13.0543i	0.309748	−	0.602792i
$470$	0.801127	+	0.0434164i	0.0369532	+	0.00200265i
$471$		−	33.7660i		−	1.55586i
$472$	1.34241	−	8.19209i	0.0617896	−	0.377072i
$473$	5.69910			0.262045
$474$	8.88013	+	0.481251i	0.407878	+	0.0221046i
$475$			1.31134i			0.0601682i
$476$	−24.9103	−	16.4258i	−1.14176	−	0.752873i
$477$		−	0.194292i		−	0.00889602i
$478$	0.975504	−	18.0002i	0.0446185	−	0.823309i
$479$	−1.36128			−0.0621983			−0.0310991	−	0.999516i	$-0.509901\pi$
$479$	−1.36128			−0.0621983			−0.0310991	+	0.999516i	$0.509901\pi$
$480$	−3.35693	+	12.0963i	−0.153222	+	0.552116i
$481$		−	39.6366i		−	1.80727i
$482$	−0.444580	+	8.20346i	−0.0202500	+	0.373657i
$483$	−19.7921	+	38.5169i	−0.900572	+	1.75258i
$484$	8.12216	+	0.882940i	0.369189	+	0.0401337i
$485$			9.93165i			0.450973i
$486$	1.33209	−	24.5799i	0.0604248	−	1.11497i
$487$			10.7466i			0.486976i	0.969904	+	0.243488i	$0.0782916\pi$
$487$			10.7466i			0.486976i	−0.969904	+	0.243488i	$0.921708\pi$
$488$	38.6091	+	6.32676i	1.74775	+	0.286399i
$489$		−	1.07945i		−	0.0488146i
$490$	−5.31969	−	8.34871i	−0.240319	−	0.377156i
$491$	23.1188			1.04334			0.521670	−	0.853148i	$-0.325309\pi$
$491$	23.1188			1.04334			0.521670	+	0.853148i	$0.325309\pi$
$492$	32.9934	+	3.58663i	1.48746	+	0.161698i
$493$	−51.1564			−2.30397
$494$	0.569525	−	10.5090i	0.0256241	−	0.472821i
$495$	7.47519			0.335985
$496$	−8.71450	−	1.91732i	−0.391292	−	0.0860902i
$497$	5.70353	+	2.93079i	0.255838	+	0.131464i
$498$	−7.91861	−	0.429142i	−0.354841	−	0.0192303i
$499$	−23.5311			−1.05340			−0.526698	−	0.850053i	$-0.676570\pi$
$499$	−23.5311			−1.05340			−0.526698	+	0.850053i	$0.676570\pi$
$500$	1.98829	+	0.216142i	0.0889189	+	0.00966615i
$501$		−	43.5307i		−	1.94481i
$502$	1.99498	−	36.8117i	0.0890402	−	1.64299i
$503$	−20.3215			−0.906093			−0.453046	−	0.891487i	$-0.649663\pi$
$503$	−20.3215			−0.906093			−0.453046	+	0.891487i	$0.649663\pi$
$504$	−8.56760	+	11.5773i	−0.381631	+	0.515693i
$505$	3.07042			0.136632
$506$	2.19230	−	40.4527i	0.0974596	−	1.79834i
$507$			42.6210i			1.89286i
$508$	−1.54203	+	14.1852i	−0.0684167	+	0.629365i
$509$	32.6233			1.44600			0.723001	−	0.690847i	$-0.242762\pi$
$509$	32.6233			1.44600			0.723001	+	0.690847i	$0.242762\pi$
$510$	17.6710	+	0.957665i	0.782486	+	0.0424061i
$511$	14.3080	+	7.35224i	0.632948	+	0.325244i
$512$	19.9939	+	10.5945i	0.883614	+	0.468216i
$513$	−3.12936			−0.138165
$514$	1.38734	−	25.5995i	0.0611930	−	1.12914i
$515$	5.89112			0.259594
$516$	0.703817	−	6.47441i	0.0309838	−	0.285020i
$517$	−2.20341			−0.0969060
$518$	22.5636	+	13.1844i	0.991385	+	0.579288i
$519$			18.0740i			0.793360i
$520$	−15.8401	−	2.59568i	−0.694636	−	0.113828i
$521$			30.2799i			1.32659i	0.748360	+	0.663293i	$0.230842\pi$
$521$			30.2799i			1.32659i	−0.748360	+	0.663293i	$0.769158\pi$
$522$	−1.33624	+	24.6565i	−0.0584855	+	1.07918i
$523$			4.23380i			0.185131i	0.995707	+	0.0925655i	$0.0295067\pi$
$523$			4.23380i			0.185131i	−0.995707	+	0.0925655i	$0.970493\pi$
$524$	1.48415	−	13.6526i	0.0648352	−	0.596418i
$525$	5.22221	+	2.68346i	0.227916	+	0.117116i
$526$	−1.73763	+	32.0631i	−0.0757643	+	1.39802i
$527$			12.5789i			0.547946i
$528$	7.40811	−	33.6709i	0.322397	−	1.46534i
$529$	−31.3993			−1.36519
$530$	−0.00772567	+	0.142555i	−0.000335581	+	0.00619221i
$531$			5.64876i			0.245135i
$532$	5.79291	+	3.81983i	0.251155	+	0.165610i
$533$			42.4354i			1.83808i
$534$	−34.1937	−	1.85310i	−1.47970	−	0.0801913i
$535$	−11.0481			−0.477653
$536$	15.4838	+	2.53728i	0.668798	+	0.109594i
$537$		−	45.2289i		−	1.95177i
$538$	−13.0541	−	0.707457i	−0.562803	−	0.0305006i
$539$	15.8292	+	22.1044i	0.681810	+	0.952103i
$540$	−0.515799	+	4.74483i	−0.0221964	+	0.204185i
$541$		−	20.3843i		−	0.876390i	−0.898880	−	0.438195i	$-0.855618\pi$
$541$		−	20.3843i		−	0.876390i	0.898880	−	0.438195i	$-0.144382\pi$
$542$	−20.6014	−	1.11648i	−0.884908	−	0.0479568i
$543$		−	14.8459i		−	0.637101i
$544$	8.53005	−	30.7369i	0.365723	−	1.31783i
$545$			4.12606i			0.176741i
$546$	−40.6851	−	23.7732i	−1.74116	−	1.01740i
$547$	−38.6889			−1.65422			−0.827110	−	0.562041i	$-0.810016\pi$
$547$	−38.6889			−1.65422			−0.827110	+	0.562041i	$0.810016\pi$
$548$	11.4266	+	1.24216i	0.488121	+	0.0530624i
$549$	−26.6225			−1.13622
$550$	−5.48468	−	0.297237i	−0.233867	−	0.0126742i
$551$	11.8965			0.506806
$552$	−45.6851	−	7.48629i	−1.94449	−	0.318638i
$553$	−6.66839	−	3.42659i	−0.283569	−	0.145713i
$554$	−1.35180	+	24.9436i	−0.0574324	+	1.05975i
$555$	−15.4994			−0.657913
$556$	−2.73108	+	25.1232i	−0.115824	+	1.06546i
$557$		−	27.3750i		−	1.15991i	−0.814647	−	0.579957i	$-0.803069\pi$
$557$		−	27.3750i		−	1.15991i	0.814647	−	0.579957i	$-0.196931\pi$
$558$	6.06282	+	0.328569i	0.256660	+	0.0139094i
$559$	8.32726			0.352206
$560$	6.74655	−	8.15378i	0.285094	−	0.344560i
$561$	−48.6022			−2.05199
$562$	−28.3663	−	1.53729i	−1.19656	−	0.0648466i
$563$		−	13.1643i		−	0.554811i	−0.960753	−	0.277405i	$-0.910526\pi$
$563$		−	13.1643i		−	0.554811i	0.960753	−	0.277405i	$-0.0894745\pi$
$564$	−0.272113	+	2.50316i	−0.0114580	+	0.105402i
$565$	−5.28550			−0.222363
$566$	−0.107368	+	1.98117i	−0.00451300	+	0.0832747i
$567$	−13.3858	+	26.0497i	−0.562149	+	1.09398i
$568$	−1.10856	+	6.76499i	−0.0465141	+	0.283853i
$569$	−16.3200			−0.684168			−0.342084	−	0.939669i	$-0.611133\pi$
$569$	−16.3200			−0.684168			−0.342084	+	0.939669i	$0.611133\pi$
$570$	−4.10941	−	0.222706i	−0.172124	−	0.00932813i
$571$	−23.5552			−0.985754			−0.492877	−	0.870099i	$-0.664055\pi$
$571$	−23.5552			−0.985754			−0.492877	+	0.870099i	$0.664055\pi$
$572$	43.8248	+	4.76409i	1.83241	+	0.199196i
$573$	13.2182			0.552198
$574$	−24.1568	−	14.1154i	−1.00829	−	0.589164i
$575$			7.37559i			0.307583i
$576$	−14.5918	−	4.91420i	−0.607993	−	0.204758i
$577$		−	29.3020i		−	1.21986i	−0.792457	−	0.609928i	$-0.791198\pi$
$577$		−	29.3020i		−	1.21986i	0.792457	−	0.609928i	$-0.208802\pi$
$578$	−20.8961	−	1.13245i	−0.869163	−	0.0471035i
$579$			24.2201i			1.00655i
$580$	1.96084	−	18.0378i	0.0814195	−	0.748977i
$581$	5.94635	+	3.05556i	0.246696	+	0.126766i
$582$	−31.1234	−	1.68671i	−1.29011	−	0.0699162i
$583$		−	0.392083i		−	0.0162384i
$584$	−2.78096	+	16.9708i	−0.115077	+	0.702257i
$585$	10.9224			0.451585
$586$	−21.0646	−	1.14158i	−0.870169	−	0.0471580i
$587$		−	18.3219i		−	0.756225i	−0.925760	−	0.378113i	$-0.876573\pi$
$587$		−	18.3219i		−	0.756225i	0.925760	−	0.378113i	$-0.123427\pi$
$588$	27.0663	−	15.2527i	1.11619	−	0.629012i
$589$		−	2.92524i		−	0.120532i
$590$	0.224613	−	4.14460i	0.00924716	−	0.170630i
$591$	−8.35942			−0.343861
$592$	−6.00310	+	27.2849i	−0.246726	+	1.12140i
$593$			35.9919i			1.47801i	0.673699	+	0.739006i	$0.264704\pi$
$593$			35.9919i			1.47801i	−0.673699	+	0.739006i	$0.735296\pi$
$594$	0.709324	−	13.0886i	0.0291039	−	0.537031i
$595$	−13.2698	−	6.81874i	−0.544008	−	0.279541i
$596$	2.58078	−	23.7406i	0.105713	−	0.972452i
$597$			16.7085i			0.683835i
$598$	3.20328	−	59.1076i	0.130992	−	2.41709i
$599$		−	8.44016i		−	0.344856i	−0.985022	−	0.172428i	$-0.944839\pi$
$599$		−	8.44016i		−	0.344856i	0.985022	−	0.172428i	$-0.0551611\pi$
$600$	−1.01501	+	6.19410i	−0.0414376	+	0.252873i
$601$			1.25783i			0.0513079i	0.999671	+	0.0256539i	$0.00816680\pi$
$601$			1.25783i			0.0513079i	−0.999671	+	0.0256539i	$0.991833\pi$
$602$	−2.76991	+	4.74039i	−0.112893	+	0.193204i
$603$	−10.6767			−0.434787
$604$	1.64803	−	15.1602i	0.0670572	−	0.616859i
$605$	4.08501			0.166079
$606$	−0.521454	+	9.62196i	−0.0211826	+	0.390865i
$607$	−9.60051			−0.389673			−0.194836	−	0.980836i	$-0.562418\pi$
$607$	−9.60051			−0.389673			−0.194836	+	0.980836i	$0.562418\pi$
$608$	−1.98367	+	7.14789i	−0.0804485	+	0.289885i
$609$	24.3444	−	47.3760i	0.986484	−	1.91977i
$610$	19.5334	+	1.05859i	0.790883	+	0.0428612i
$611$	−3.21952			−0.130248
$612$	−2.34576	+	21.5787i	−0.0948218	+	0.872265i
$613$		−	31.9083i		−	1.28877i	−0.764703	−	0.644383i	$-0.777114\pi$
$613$		−	31.9083i		−	1.28877i	0.764703	−	0.644383i	$-0.222886\pi$
$614$	0.281546	−	5.19513i	0.0113623	−	0.209659i
$615$	16.5939			0.669129
$616$	−17.2895	+	23.3631i	−0.696614	+	0.941325i
$617$	28.7928			1.15916			0.579578	−	0.814917i	$-0.303217\pi$
$617$	28.7928			1.15916			0.579578	+	0.814917i	$0.303217\pi$
$618$	−1.00050	+	18.4614i	−0.0402459	+	0.742625i
$619$		−	15.2907i		−	0.614586i	−0.951615	−	0.307293i	$-0.900577\pi$
$619$		−	15.2907i		−	0.614586i	0.951615	−	0.307293i	$-0.0994232\pi$
$620$	−4.43533	−	0.482154i	−0.178127	−	0.0193638i
$621$	−17.6010			−0.706305
$622$	44.0043	+	2.38478i	1.76441	+	0.0956208i
$623$	25.6772	+	13.1944i	1.02874	+	0.528621i
$624$	10.8244	−	49.1984i	0.433322	−	1.96951i
$625$	1.00000			0.0400000
$626$	−1.84105	+	33.9713i	−0.0735831	+	1.35777i
$627$	11.3025			0.451378
$628$	−30.2532	−	3.28876i	−1.20724	−	0.131236i
$629$	39.3844			1.57036
$630$	−3.63313	+	6.21769i	−0.144747	+	0.247719i
$631$		−	38.9523i		−	1.55067i	−0.631551	−	0.775334i	$-0.717581\pi$
$631$		−	38.9523i		−	1.55067i	0.631551	−	0.775334i	$-0.282419\pi$
$632$	1.29609	−	7.90942i	0.0515559	−	0.314620i
$633$		−	8.73652i		−	0.347246i
$634$	1.47912	−	27.2930i	0.0587435	−	1.08394i
$635$			7.13436i			0.283119i
$636$	−0.445422	−	0.0484207i	−0.0176621	−	0.00192001i
$637$	23.1288	+	32.2979i	0.916397	+	1.27969i
$638$	−2.69654	+	49.7570i	−0.106757	+	1.96990i
$639$		−	4.66472i		−	0.184533i
$640$	10.5109	+	4.18585i	0.415479	+	0.165460i
$641$	−8.27890			−0.326997			−0.163498	−	0.986544i	$-0.552278\pi$
$641$	−8.27890			−0.326997			−0.163498	+	0.986544i	$0.552278\pi$
$642$	1.87632	−	34.6222i	0.0740525	−	1.36643i
$643$			18.0050i			0.710048i	0.934857	+	0.355024i	$0.115527\pi$
$643$			18.0050i			0.710048i	−0.934857	+	0.355024i	$0.884473\pi$
$644$	32.5821	+	21.4845i	1.28392	+	0.846609i
$645$		−	3.25627i		−	0.128216i
$646$	10.4421	+	0.565901i	0.410839	+	0.0222651i
$647$	36.7978			1.44667			0.723336	−	0.690496i	$-0.242608\pi$
$647$	36.7978			1.44667			0.723336	+	0.690496i	$0.242608\pi$
$648$	−30.8977	−	5.06312i	−1.21378	−	0.198898i
$649$			11.3993i			0.447460i
$650$	−8.01395	−	0.434309i	−0.314333	−	0.0170350i
$651$	−11.6494	−	5.98608i	−0.456574	−	0.234613i
$652$	−0.967155	−	0.105137i	−0.0378767	−	0.00411748i
$653$		−	13.5053i		−	0.528504i	−0.964454	−	0.264252i	$-0.914875\pi$
$653$		−	13.5053i		−	0.528504i	0.964454	−	0.264252i	$-0.0851250\pi$
$654$	−12.9301	−	0.700735i	−0.505606	−	0.0274009i
$655$		−	6.86654i		−	0.268298i
$656$	6.42699	−	29.2116i	0.250932	−	1.14052i
$657$		−	11.7020i		−	0.456539i
$658$	1.07091	−	1.83275i	0.0417486	−	0.0714480i
$659$	−21.7852			−0.848629			−0.424315	−	0.905515i	$-0.639485\pi$
$659$	−21.7852			−0.848629			−0.424315	+	0.905515i	$0.639485\pi$
$660$	1.86294	−	17.1372i	0.0725148	−	0.667063i
$661$	−27.4541			−1.06784			−0.533921	−	0.845534i	$-0.679282\pi$
$661$	−27.4541			−1.06784			−0.533921	+	0.845534i	$0.679282\pi$
$662$	27.6224	+	1.49697i	1.07358	+	0.0581815i
$663$	−71.0152			−2.75800
$664$	−1.15576	+	7.05301i	−0.0448520	+	0.273710i
$665$	3.08590	+	1.58570i	0.119666	+	0.0614910i
$666$	1.02874	−	18.9826i	0.0398630	−	0.735560i
$667$	66.9114			2.59082
$668$	−39.0021	−	4.23982i	−1.50904	−	0.164044i
$669$			38.5841i			1.49175i
$670$	7.83366	+	0.424538i	0.302641	+	0.0164013i
$671$	−53.7244			−2.07401
$672$	24.4062	+	22.5268i	0.941489	+	0.868991i
$673$	−15.2602			−0.588238			−0.294119	−	0.955769i	$-0.595026\pi$
$673$	−15.2602			−0.588238			−0.294119	+	0.955769i	$0.595026\pi$
$674$	−14.5253	−	0.787186i	−0.559493	−	0.0303213i
$675$			2.38639i			0.0918522i
$676$	38.1870	+	4.15121i	1.46873	+	0.159662i
$677$	−29.8069			−1.14557			−0.572787	−	0.819704i	$-0.694138\pi$
$677$	−29.8069			−1.14557			−0.572787	+	0.819704i	$0.694138\pi$
$678$	0.897644	−	16.5635i	0.0344738	−	0.636117i
$679$	23.3716	+	12.0096i	0.896921	+	0.460887i
$680$	2.57916	−	15.7394i	0.0989064	−	0.603577i
$681$	50.9686			1.95312
$682$	12.2348	+	0.663056i	0.468496	+	0.0253897i
$683$	45.4219			1.73802			0.869010	−	0.494795i	$-0.164757\pi$
$683$	45.4219			1.73802			0.869010	+	0.494795i	$0.164757\pi$
$684$	0.545509	−	5.01814i	0.0208581	−	0.191873i
$685$	5.74697			0.219580
$686$	−26.0793	+	2.42305i	−0.995712	+	0.0925124i
$687$			31.4998i			1.20179i
$688$	−5.73230	−	1.26119i	−0.218542	−	0.0480825i
$689$		−	0.572893i		−	0.0218255i
$690$	−23.1133	−	1.25261i	−0.879908	−	0.0476859i
$691$		−	25.4854i		−	0.969510i	−0.874650	−	0.484755i	$-0.838909\pi$
$691$		−	25.4854i		−	0.969510i	0.874650	−	0.484755i	$-0.161091\pi$
$692$	16.1937	+	1.76038i	0.615592	+	0.0669195i
$693$	9.03920	−	17.5910i	0.343371	−	0.668225i
$694$	4.93346	+	0.267365i	0.187272	+	0.0101490i
$695$			12.6356i			0.479296i
$696$	56.1929	+	9.20817i	2.12999	+	0.349035i
$697$	−42.1654			−1.59713
$698$	15.3105	+	0.829739i	0.579510	+	0.0314061i
$699$			31.1553i			1.17840i
$700$	2.91293	−	4.41756i	0.110098	−	0.166968i
$701$		−	24.4503i		−	0.923473i	−0.887017	−	0.461737i	$-0.847227\pi$
$701$		−	24.4503i		−	0.923473i	0.887017	−	0.461737i	$-0.152773\pi$
$702$	1.03643	−	19.1244i	0.0391176	−	0.721804i
$703$	−9.15887			−0.345433
$704$	−29.4465	−	9.91691i	−1.10981	−	0.373758i
$705$			1.25896i			0.0474150i
$706$	−0.0378103	+	0.697682i	−0.00142301	+	0.0262576i
$707$	3.71284	−	7.22546i	0.139636	−	0.271742i
$708$	12.9500	+	1.40776i	0.486691	+	0.0529070i
$709$		−	32.1784i		−	1.20848i	−0.796801	−	0.604242i	$-0.793476\pi$
$709$		−	32.1784i		−	1.20848i	0.796801	−	0.604242i	$-0.206524\pi$
$710$	−0.185484	+	3.42258i	−0.00696109	+	0.128447i
$711$			5.45385i			0.204535i
$712$	−4.99072	+	30.4559i	−0.187035	+	1.14138i
$713$		−	16.4529i		−	0.616168i
$714$	23.6219	−	40.4262i	0.884027	−	1.51291i
$715$	22.0415			0.824305
$716$	−40.5236	−	4.40522i	−1.51444	−	0.164631i
$717$	28.2869			1.05639
$718$	−0.331785	+	6.12216i	−0.0123821	+	0.228477i
$719$	−14.5688			−0.543324			−0.271662	−	0.962393i	$-0.587573\pi$
$719$	−14.5688			−0.543324			−0.271662	+	0.962393i	$0.587573\pi$
$720$	−7.51873	−	1.65423i	−0.280206	−	0.0616497i
$721$	7.12371	−	13.8633i	0.265301	−	0.516295i
$722$	24.4024	+	1.32247i	0.908162	+	0.0492171i
$723$	−12.8916			−0.479443
$724$	−13.3015	−	1.44597i	−0.494345	−	0.0537391i
$725$		−	9.07201i		−	0.336926i
$726$	−0.693762	+	12.8014i	−0.0257479	+	0.475105i
$727$	36.7720			1.36380			0.681899	−	0.731447i	$-0.261154\pi$
$727$	36.7720			1.36380			0.681899	+	0.731447i	$0.261154\pi$
$728$	−25.2626	+	34.1370i	−0.936295	+	1.26520i
$729$	5.41785			0.200661
$730$	−0.465309	+	8.58597i	−0.0172219	+	0.317781i
$731$			8.27428i			0.306035i
$732$	−6.63475	+	61.0330i	−0.245228	+	2.25585i
$733$	−44.4405			−1.64145			−0.820725	−	0.571324i	$-0.806430\pi$
$733$	−44.4405			−1.64145			−0.820725	+	0.571324i	$0.806430\pi$
$734$	−46.5775	−	2.52423i	−1.71921	−	0.0931710i
$735$	12.6297	−	9.04424i	0.465853	−	0.333602i
$736$	−11.1571	+	40.2032i	−0.411257	+	1.48191i
$737$	−21.5456			−0.793643
$738$	−1.10139	+	20.3230i	−0.0405426	+	0.748100i
$739$	4.41504			0.162410			0.0812049	−	0.996697i	$-0.474123\pi$
$739$	4.41504			0.162410			0.0812049	+	0.996697i	$0.474123\pi$
$740$	−1.50962	+	13.8869i	−0.0554946	+	0.510494i
$741$	16.5147			0.606681
$742$	0.326126	+	0.190562i	0.0119725	+	0.00699576i
$743$		−	47.0540i		−	1.72625i	−0.504994	−	0.863123i	$-0.668505\pi$
$743$		−	47.0540i		−	1.72625i	0.504994	−	0.863123i	$-0.331495\pi$
$744$	2.26421	−	13.8174i	0.0830100	−	0.506569i
$745$		−	11.9402i		−	0.437456i
$746$	1.09074	−	20.1266i	0.0399349	−	0.736886i
$747$		−	4.86332i		−	0.177939i
$748$	−4.73377	+	43.5460i	−0.173084	+	1.59220i
$749$	−13.3597	+	25.9990i	−0.488153	+	0.949983i
$750$	−0.169831	+	3.13376i	−0.00620136	+	0.114429i
$751$			32.7742i			1.19595i	0.801516	+	0.597974i	$0.204027\pi$
$751$			32.7742i			1.19595i	−0.801516	+	0.597974i	$0.795973\pi$
$752$	2.21625	+	0.487608i	0.0808182	+	0.0177812i
$753$	57.8488			2.10813
$754$	−3.94006	+	72.7026i	−0.143488	+	2.64767i
$755$		−	7.62474i		−	0.277493i
$756$	10.5420	+	6.95138i	0.383410	+	0.252819i
$757$			40.7277i			1.48027i	0.672457	+	0.740136i	$0.265239\pi$
$757$			40.7277i			1.48027i	−0.672457	+	0.740136i	$0.734761\pi$
$758$	28.4586	+	1.54229i	1.03366	+	0.0560184i
$759$	63.5706			2.30747
$760$	−0.599787	+	3.66020i	−0.0217566	+	0.132769i
$761$			17.5757i			0.637118i	0.947903	+	0.318559i	$0.103199\pi$
$761$			17.5757i			0.637118i	−0.947903	+	0.318559i	$0.896801\pi$
$762$	−22.3574	−	1.21164i	−0.809922	−	0.0438930i
$763$	9.70964	+	4.98935i	0.351513	+	0.180627i
$764$	1.28743	−	11.8431i	0.0465776	−	0.428467i
$765$			10.8529i			0.392387i
$766$	9.02784	+	0.489256i	0.326189	+	0.0176775i
$767$			16.6561i			0.601415i
$768$	−14.9025	+	32.2277i	−0.537749	+	1.16292i
$769$		−	31.9583i		−	1.15245i	−0.817292	−	0.576223i	$-0.804526\pi$
$769$		−	31.9583i		−	1.15245i	0.817292	−	0.576223i	$-0.195474\pi$
$770$	−7.33169	+	12.5474i	−0.264216	+	0.452176i
$771$	40.2291			1.44882
$772$	21.7004	+	2.35900i	0.781016	+	0.0849023i
$773$	15.3325			0.551470			0.275735	−	0.961234i	$-0.411079\pi$
$773$	15.3325			0.551470			0.275735	+	0.961234i	$0.411079\pi$
$774$	3.98806	+	0.216129i	0.143348	+	0.00776861i
$775$	−2.23073			−0.0801302
$776$	−4.54260	+	27.7212i	−0.163070	+	0.995134i
$777$	−18.7423	+	36.4739i	−0.672376	+	1.30849i
$778$	1.16440	−	21.4857i	0.0417458	−	0.770301i
$779$	9.80561			0.351322
$780$	2.72204	−	25.0400i	0.0974646	−	0.896576i
$781$		−	9.41345i		−	0.336840i
$782$	58.7315	+	3.18290i	2.10023	+	0.113820i
$783$	21.6494			0.773685
$784$	−11.0297	−	25.7361i	−0.393919	−	0.919145i
$785$	−15.2157			−0.543073
$786$	21.5181	+	1.16615i	0.767524	+	0.0415953i
$787$			7.87957i			0.280876i	0.990089	+	0.140438i	$0.0448511\pi$
$787$			7.87957i			0.280876i	−0.990089	+	0.140438i	$0.955149\pi$
$788$	−0.814194	+	7.48976i	−0.0290045	+	0.266812i
$789$	−50.3865			−1.79381
$790$	0.216862	−	4.00159i	0.00771562	−	0.142370i
$791$	−6.39138	+	12.4381i	−0.227251	+	0.442248i
$792$	20.8647	+	3.41904i	0.741396	+	0.121490i
$793$	−78.4995			−2.78760
$794$	39.3180	+	2.13081i	1.39535	+	0.0756195i
$795$	−0.224023			−0.00794528
$796$	14.9703	+	1.62738i	0.530608	+	0.0576811i
$797$	−25.0570			−0.887563			−0.443781	−	0.896135i	$-0.646363\pi$
$797$	−25.0570			−0.887563			−0.443781	+	0.896135i	$0.646363\pi$
$798$	−5.49329	+	9.40115i	−0.194460	+	0.332797i
$799$		−	3.19904i		−	0.113174i
$800$	5.45085	+	1.51271i	0.192716	+	0.0534823i
$801$		−	21.0005i		−	0.742016i
$802$	6.34637	+	0.343936i	0.224098	+	0.0121448i
$803$		−	23.6148i		−	0.833348i
$804$	−2.66080	+	24.4767i	−0.0938392	+	0.863226i
$805$	17.3566	+	8.91876i	0.611739	+	0.314345i
$806$	17.8770	+	0.968826i	0.629689	+	0.0341254i
$807$		−	20.5143i		−	0.722137i
$808$	8.57017	+	1.40437i	0.301497	+	0.0494055i
$809$	−4.94114			−0.173721			−0.0868606	−	0.996220i	$-0.527683\pi$
$809$	−4.94114			−0.173721			−0.0868606	+	0.996220i	$0.527683\pi$
$810$	−15.6320	−	0.847160i	−0.549251	−	0.0297662i
$811$		−	0.565648i		−	0.0198626i	−0.999951	−	0.00993130i	$-0.996839\pi$
$811$		−	0.565648i		−	0.0198626i	0.999951	−	0.00993130i	$-0.00316128\pi$
$812$	−40.0762	−	26.4261i	−1.40640	−	0.927374i
$813$		−	32.3748i		−	1.13543i
$814$	2.07602	−	38.3070i	0.0727644	−	1.34266i
$815$	−0.486426			−0.0170388
$816$	48.8853	+	10.7555i	1.71133	+	0.376518i
$817$		−	1.92419i		−	0.0673189i
$818$	−0.701045	+	12.9358i	−0.0245115	+	0.452290i
$819$	13.2076	−	25.7031i	0.461513	−	0.898138i
$820$	1.61621	−	14.8675i	0.0564407	−	0.519197i
$821$			23.2920i			0.812897i	0.913674	+	0.406448i	$0.133233\pi$
$821$			23.2920i			0.812897i	−0.913674	+	0.406448i	$0.866767\pi$
$822$	−0.976015	+	18.0096i	−0.0340424	+	0.628157i
$823$		−	30.2227i		−	1.05350i	−0.850021	−	0.526748i	$-0.823411\pi$
$823$		−	30.2227i		−	1.05350i	0.850021	−	0.526748i	$-0.176589\pi$
$824$	16.4433	+	2.69452i	0.572830	+	0.0938679i
$825$		−	8.61906i		−	0.300077i
$826$	−9.48165	−	5.54033i	−0.329909	−	0.192773i
$827$	−18.8086			−0.654040			−0.327020	−	0.945017i	$-0.606044\pi$
$827$	−18.8086			−0.654040			−0.327020	+	0.945017i	$0.606044\pi$
$828$	3.06821	−	28.2244i	0.106628	−	0.980866i
$829$	12.6773			0.440301			0.220150	−	0.975466i	$-0.429345\pi$
$829$	12.6773			0.440301			0.220150	+	0.975466i	$0.429345\pi$
$830$	−0.193381	+	3.56830i	−0.00671235	+	0.123858i
$831$	−39.1984			−1.35978
$832$	−43.0258	−	14.4901i	−1.49165	−	0.502354i
$833$	−32.0924	+	22.9816i	−1.11193	+	0.796267i
$834$	−39.5969	−	2.14592i	−1.37113	−	0.0743072i
$835$	−19.6159			−0.678837
$836$	1.10084	−	10.1267i	0.0380735	−	0.350238i
$837$		−	5.32339i		−	0.184003i
$838$	−1.43921	+	26.5565i	−0.0497166	+	0.917380i
$839$	−28.4650			−0.982722			−0.491361	−	0.870956i	$-0.663500\pi$
$839$	−28.4650			−0.982722			−0.491361	+	0.870956i	$0.663500\pi$
$840$	13.3489	+	9.87864i	0.460580	+	0.340846i
$841$	−53.3014			−1.83798
$842$	−2.63122	+	48.5517i	−0.0906777	+	1.67320i
$843$		−	44.5771i		−	1.53532i
$844$	−7.82763	−	0.850923i	−0.269438	−	0.0292900i
$845$	19.2060			0.660706
$846$	−1.54188	−	0.0835609i	−0.0530109	−	0.00287288i
$847$	4.93970	−	9.61303i	0.169730	−	0.330308i
$848$	−0.0867667	+	0.394367i	−0.00297958	+	0.0135426i
$849$	−3.11337			−0.106851
$850$	0.431546	−	7.96296i	0.0148019	−	0.273127i
$851$	−51.5139			−1.76587
$852$	−10.6940	−	1.16252i	−0.366372	−	0.0398274i
$853$	30.6148			1.04823			0.524115	−	0.851647i	$-0.324396\pi$
$853$	30.6148			1.04823			0.524115	+	0.851647i	$0.324396\pi$
$854$	26.1114	−	44.6867i	0.893514	−	1.52915i
$855$		−	2.52385i		−	0.0863138i
$856$	−30.8376	−	5.05326i	−1.05401	−	0.172717i
$857$			29.2591i			0.999473i	0.866177	+	0.499737i	$0.166570\pi$
$857$			29.2591i			0.999473i	−0.866177	+	0.499737i	$0.833430\pi$
$858$	−3.74333	+	69.0727i	−0.127795	+	2.35810i
$859$		−	37.5302i		−	1.28052i	−0.768160	−	0.640258i	$-0.778828\pi$
$859$		−	37.5302i		−	1.28052i	0.768160	−	0.640258i	$-0.221172\pi$
$860$	−2.91751	−	0.317156i	−0.0994864	−	0.0108149i
$861$	20.0658	−	39.0495i	0.683839	−	1.33080i
$862$	0.271191	−	5.00407i	0.00923681	−	0.170439i
$863$		−	42.5541i		−	1.44856i	−0.689507	−	0.724279i	$-0.742173\pi$
$863$		−	42.5541i		−	1.44856i	0.689507	−	0.724279i	$-0.257827\pi$
$864$	−3.60991	+	13.0078i	−0.122812	+	0.442536i
$865$	8.14454			0.276923
$866$	2.72926	−	50.3607i	0.0927439	−	1.71133i
$867$		−	32.8378i		−	1.11523i
$868$	−6.49795	+	9.85439i	−0.220555	+	0.334480i
$869$			11.0059i			0.373351i
$870$	28.4295	+	1.54071i	0.963850	+	0.0522350i
$871$	−31.4814			−1.06671
$872$	−1.88720	+	11.5167i	−0.0639088	+	0.390004i
$873$		−	19.1148i		−	0.646939i
$874$	−13.6581	−	0.740187i	−0.461991	−	0.0250372i
$875$	1.20923	−	2.35325i	0.0408794	−	0.0795543i
$876$	−26.8273	−	2.91633i	−0.906412	−	0.0985338i
$877$			29.0477i			0.980870i	0.871478	+	0.490435i	$0.163162\pi$
$877$			29.0477i			0.980870i	−0.871478	+	0.490435i	$0.836838\pi$
$878$	−18.2974	−	0.991614i	−0.617508	−	0.0334653i
$879$		−	33.1025i		−	1.11652i
$880$	−15.1729	−	3.33826i	−0.511477	−	0.112533i
$881$			45.7311i			1.54072i	0.637610	+	0.770360i	$0.279923\pi$
$881$			45.7311i			1.54072i	−0.637610	+	0.770360i	$0.720077\pi$
$882$	10.2385	+	16.0682i	0.344747	+	0.541046i
$883$	−27.4055			−0.922269			−0.461135	−	0.887330i	$-0.652558\pi$
$883$	−27.4055			−0.922269			−0.461135	+	0.887330i	$0.652558\pi$
$884$	−6.91676	+	63.6273i	−0.232636	+	2.14002i
$885$	6.51315			0.218937
$886$	0.838148	+	0.0454227i	0.0281581	+	0.00152601i
$887$	−7.53368			−0.252956			−0.126478	−	0.991969i	$-0.540367\pi$
$887$	−7.53368			−0.252956			−0.126478	+	0.991969i	$0.540367\pi$
$888$	−43.2619	−	7.08921i	−1.45178	−	0.237898i
$889$	16.7889	+	8.62707i	0.563082	+	0.289343i
$890$	−0.835047	+	15.4084i	−0.0279908	+	0.516492i
$891$	42.9940			1.44035
$892$	34.5700	+	3.75802i	1.15749	+	0.125828i
$893$			0.743939i			0.0248950i
$894$	37.4178	+	2.02782i	1.25144	+	0.0678205i
$895$	−20.3812			−0.681268
$896$	22.5604	−	19.6730i	0.753690	−	0.657230i
$897$	92.8864			3.10139
$898$	38.0296	+	2.06098i	1.26907	+	0.0687759i
$899$			20.2372i			0.674949i
$900$	−3.82673	−	0.415995i	−0.127558	−	0.0138665i
$901$	0.569248			0.0189644
$902$	−2.22261	+	41.0120i	−0.0740049	+	1.36555i
$903$	−7.66282	−	3.93758i	−0.255003	−	0.131034i
$904$	−14.7529	−	2.41751i	−0.490674	−	0.0804053i
$905$	−6.68992			−0.222380
$906$	23.8941	+	1.29492i	0.793828	+	0.0430208i
$907$	−40.1412			−1.33287			−0.666433	−	0.745565i	$-0.732180\pi$
$907$	−40.1412			−1.33287			−0.666433	+	0.745565i	$0.732180\pi$
$908$	4.96425	−	45.6661i	0.164745	−	1.51548i
$909$	−5.90946			−0.196004
$910$	−10.7127	+	18.3336i	−0.355123	+	0.607753i
$911$			47.5516i			1.57545i	0.616024	+	0.787727i	$0.288742\pi$
$911$			47.5516i			1.57545i	−0.616024	+	0.787727i	$0.711258\pi$
$912$	−11.3683	−	2.50120i	−0.376443	−	0.0828231i
$913$		−	9.81423i		−	0.324804i
$914$	43.5119	+	2.35809i	1.43924	+	0.0779986i
$915$			30.6963i			1.01479i
$916$	28.2228	+	3.06803i	0.932506	+	0.101370i
$917$	−16.1587	−	8.30321i	−0.533606	−	0.274196i
$918$	19.0027	+	1.02984i	0.627183	+	0.0339897i
$919$			51.6665i			1.70432i	0.523281	+	0.852160i	$0.324708\pi$
$919$			51.6665i			1.70432i	−0.523281	+	0.852160i	$0.675292\pi$
$920$	−3.37349	+	20.5867i	−0.111221	+	0.678725i
$921$	8.16405			0.269015
$922$	0.991298	+	0.0537225i	0.0326467	+	0.00176926i
$923$		−	13.7545i		−	0.452734i
$924$	−38.0752	−	25.1067i	−1.25258	−	0.825949i
$925$			6.98438i			0.229645i
$926$	2.02791	−	37.4194i	0.0666414	−	1.22968i
$927$	−11.3383			−0.372398
$928$	13.7233	−	49.4501i	0.450490	−	1.62328i
$929$			41.5413i			1.36293i	0.731852	+	0.681464i	$0.238656\pi$
$929$			41.5413i			1.36293i	−0.731852	+	0.681464i	$0.761344\pi$
$930$	0.378848	−	6.99057i	0.0124229	−	0.229230i
$931$	7.46310	−	5.34440i	0.244593	−	0.175156i
$932$	27.9141	+	3.03447i	0.914357	+	0.0993975i
$933$			69.1520i			2.26393i
$934$	−3.19035	+	58.8689i	−0.104391	+	1.92625i
$935$			21.9012i			0.716247i
$936$	30.4866	+	4.99574i	0.996485	+	0.163291i
$937$			15.1513i			0.494970i	0.968892	+	0.247485i	$0.0796041\pi$
$937$			15.1513i			0.494970i	−0.968892	+	0.247485i	$0.920396\pi$
$938$	10.4717	−	17.9212i	0.341914	−	0.585147i
$939$	−53.3853			−1.74216
$940$	1.12798	+	0.122620i	0.0367907	+	0.00399943i
$941$	12.3761			0.403451			0.201725	−	0.979442i	$-0.435345\pi$
$941$	12.3761			0.403451			0.201725	+	0.979442i	$0.435345\pi$
$942$	2.58411	−	47.6824i	0.0841948	−	1.55358i
$943$	55.1514			1.79598
$944$	2.52262	−	11.4657i	0.0821042	−	0.373175i
$945$	5.61576	+	2.88569i	0.182681	+	0.0938715i
$946$	8.04794	+	0.436151i	0.261661	+	0.0141805i
$947$	−37.6021			−1.22190			−0.610952	−	0.791668i	$-0.709213\pi$
$947$	−37.6021			−1.22190			−0.610952	+	0.791668i	$0.709213\pi$
$948$	12.5032	+	1.35919i	0.406084	+	0.0441444i
$949$		−	34.5048i		−	1.12007i
$950$	−0.100356	+	1.85179i	−0.00325599	+	0.0600801i
$951$	42.8905			1.39082
$952$	−33.9198	−	25.1019i	−1.09935	−	0.813556i
$953$	11.4843			0.372014			0.186007	−	0.982548i	$-0.440445\pi$
$953$	11.4843			0.372014			0.186007	+	0.982548i	$0.440445\pi$
$954$	0.0148691	−	0.274368i	0.000481405	−	0.00888298i
$955$		−	5.95641i		−	0.192745i
$956$	2.75510	−	25.3441i	0.0891063	−	0.819688i
$957$	−78.1922			−2.52760
$958$	−1.92231	−	0.104178i	−0.0621071	−	0.00336584i
$959$	6.94939	−	13.5240i	0.224407	−	0.436714i
$960$	−5.66619	+	16.8247i	−0.182875	+	0.543016i
$961$	−26.0238			−0.839479
$962$	3.03338	−	55.9724i	0.0978000	−	1.80462i
$963$	21.2637			0.685213
$964$	−1.25562	+	11.5504i	−0.0404407	+	0.372014i
$965$	10.9141			0.351339
$966$	−30.8969	+	52.8766i	−0.994092	+	1.70128i
$967$		−	23.0158i		−	0.740139i	−0.929004	−	0.370069i	$-0.879334\pi$
$967$		−	23.0158i		−	0.740139i	0.929004	−	0.370069i	$-0.120666\pi$
$968$	11.4021	+	1.86842i	0.366476	+	0.0600534i
$969$			16.4096i			0.527152i
$970$	−0.760067	+	14.0249i	−0.0244043	+	0.450312i
$971$		−	0.820067i		−	0.0263172i	−0.999913	−	0.0131586i	$-0.995811\pi$
$971$		−	0.820067i		−	0.0263172i	0.999913	−	0.0131586i	$-0.00418863\pi$
$972$	3.76219	−	34.6084i	0.120672	−	1.11006i
$973$	29.7347	+	15.2793i	0.953250	+	0.489832i
$974$	−0.822437	+	15.1757i	−0.0263526	+	0.486262i
$975$		−	12.5938i		−	0.403323i
$976$	54.0373	+	11.8890i	1.72969	+	0.380559i
$977$	−37.3536			−1.19505			−0.597524	−	0.801851i	$-0.703849\pi$
$977$	−37.3536			−1.19505			−0.597524	+	0.801851i	$0.703849\pi$
$978$	0.0826104	−	1.52434i	0.00264159	−	0.0487431i
$979$		−	42.3792i		−	1.35445i
$980$	−6.87323	−	12.1967i	−0.219557	−	0.389608i
$981$		−	7.94118i		−	0.253542i
$982$	32.6471	+	1.76928i	1.04181	+	0.0564600i
$983$	24.6621			0.786598			0.393299	−	0.919411i	$-0.371334\pi$
$983$	24.6621			0.786598			0.393299	+	0.919411i	$0.371334\pi$
$984$	46.3168	+	7.58980i	1.47653	+	0.241954i
$985$			3.76694i			0.120025i
$986$	−72.2400	−	3.91499i	−2.30059	−	0.124679i
$987$	2.96263	+	1.52236i	0.0943016	+	0.0484574i
$988$	1.60850	−	14.7966i	0.0511732	−	0.470742i
$989$		−	10.8226i		−	0.344138i
$990$	10.5560	+	0.572074i	0.335492	+	0.0181817i
$991$			39.5414i			1.25608i	0.778183	+	0.628038i	$0.216142\pi$
$991$			39.5414i			1.25608i	−0.778183	+	0.628038i	$0.783858\pi$
$992$	−12.1594	−	3.37445i	−0.386060	−	0.107139i
$993$			43.4081i			1.37751i
$994$	7.82989	+	4.57517i	0.248349	+	0.145116i
$995$	7.52925			0.238693
$996$	−11.1493	−	1.21202i	−0.353281	−	0.0384043i
$997$	11.9761			0.379286			0.189643	−	0.981853i	$-0.439267\pi$
$997$	11.9761			0.379286			0.189643	+	0.981853i	$0.439267\pi$
$998$	−33.2292	−	1.80083i	−1.05185	−	0.0570042i
$999$	−16.6674			−0.527335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.b.251.16	yes	16
4.3	odd	2		1120.2.h.b.111.3		16
7.6	odd	2		280.2.h.a.251.16	yes	16
8.3	odd	2		280.2.h.a.251.15	✓	16
8.5	even	2		1120.2.h.a.111.3		16
28.27	even	2		1120.2.h.a.111.14		16
56.13	odd	2		1120.2.h.b.111.14		16
56.27	even	2	inner	280.2.h.b.251.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.15	✓	16	8.3	odd	2
280.2.h.a.251.16	yes	16	7.6	odd	2
280.2.h.b.251.15	yes	16	56.27	even	2	inner
280.2.h.b.251.16	yes	16	1.1	even	1	trivial
1120.2.h.a.111.3		16	8.5	even	2
1120.2.h.a.111.14		16	28.27	even	2
1120.2.h.b.111.3		16	4.3	odd	2
1120.2.h.b.111.14		16	56.13	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41214 + 0.0765298i) q^{2} +2.21915i q^{3} +(1.98829 + 0.216142i) q^{4} +1.00000 q^{5} +(-0.169831 + 3.13376i) q^{6} +(1.20923 - 2.35325i) q^{7} +(2.79120 + 0.457386i) q^{8} -1.92464 q^{9} +O(q^{10})\)	\(q+(1.41214 + 0.0765298i) q^{2} +2.21915i q^{3} +(1.98829 + 0.216142i) q^{4} +1.00000 q^{5} +(-0.169831 + 3.13376i) q^{6} +(1.20923 - 2.35325i) q^{7} +(2.79120 + 0.457386i) q^{8} -1.92464 q^{9} +(1.41214 + 0.0765298i) q^{10} -3.88394 q^{11} +(-0.479652 + 4.41231i) q^{12} -5.67503 q^{13} +(1.88769 - 3.23057i) q^{14} +2.21915i q^{15} +(3.90657 + 0.859503i) q^{16} -5.63892i q^{17} +(-2.71786 - 0.147292i) q^{18} +1.31134i q^{19} +(1.98829 + 0.216142i) q^{20} +(5.22221 + 2.68346i) q^{21} +(-5.48468 - 0.297237i) q^{22} +7.37559i q^{23} +(-1.01501 + 6.19410i) q^{24} +1.00000 q^{25} +(-8.01395 - 0.434309i) q^{26} +2.38639i q^{27} +(2.91293 - 4.41756i) q^{28} -9.07201i q^{29} +(-0.169831 + 3.13376i) q^{30} -2.23073 q^{31} +(5.45085 + 1.51271i) q^{32} -8.61906i q^{33} +(0.431546 - 7.96296i) q^{34} +(1.20923 - 2.35325i) q^{35} +(-3.82673 - 0.415995i) q^{36} +6.98438i q^{37} +(-0.100356 + 1.85179i) q^{38} -12.5938i q^{39} +(2.79120 + 0.457386i) q^{40} -7.47757i q^{41} +(7.16914 + 4.18908i) q^{42} -1.46735 q^{43} +(-7.72239 - 0.839482i) q^{44} -1.92464 q^{45} +(-0.564452 + 10.4154i) q^{46} +0.567314 q^{47} +(-1.90737 + 8.66927i) q^{48} +(-4.07554 - 5.69122i) q^{49} +(1.41214 + 0.0765298i) q^{50} +12.5136 q^{51} +(-11.2836 - 1.22661i) q^{52} +0.100950i q^{53} +(-0.182630 + 3.36992i) q^{54} -3.88394 q^{55} +(4.45154 - 6.01530i) q^{56} -2.91006 q^{57} +(0.694279 - 12.8110i) q^{58} -2.93497i q^{59} +(-0.479652 + 4.41231i) q^{60} +13.8324 q^{61} +(-3.15011 - 0.170717i) q^{62} +(-2.32733 + 4.52915i) q^{63} +(7.58160 + 2.55331i) q^{64} -5.67503 q^{65} +(0.659615 - 12.1713i) q^{66} +5.54736 q^{67} +(1.21881 - 11.2118i) q^{68} -16.3676 q^{69} +(1.88769 - 3.23057i) q^{70} +2.42368i q^{71} +(-5.37205 - 0.880303i) q^{72} +6.08011i q^{73} +(-0.534513 + 9.86293i) q^{74} +2.21915i q^{75} +(-0.283435 + 2.60731i) q^{76} +(-4.69657 + 9.13987i) q^{77} +(0.963798 - 17.7842i) q^{78} -2.83370i q^{79} +(3.90657 + 0.859503i) q^{80} -11.0697 q^{81} +(0.572257 - 10.5594i) q^{82} +2.52687i q^{83} +(9.80325 + 6.46423i) q^{84} -5.63892i q^{85} +(-2.07211 - 0.112296i) q^{86} +20.1322 q^{87} +(-10.8409 - 1.77646i) q^{88} +10.9114i q^{89} +(-2.71786 - 0.147292i) q^{90} +(-6.86240 + 13.3547i) q^{91} +(-1.59417 + 14.6648i) q^{92} -4.95033i q^{93} +(0.801127 + 0.0434164i) q^{94} +1.31134i q^{95} +(-3.35693 + 12.0963i) q^{96} +9.93165i q^{97} +(-5.31969 - 8.34871i) q^{98} +7.47519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

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