LMFDB - Embedded newform 1690.2.c.e.1689.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(1689,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.1689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,0,8,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.50027374224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1689.8
Root			$3.07108i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.e.1689.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +3.07108i q^{3} +1.00000 q^{4} +(-1.36822 - 1.76861i) q^{5} -3.07108i q^{6} +3.69510 q^{7} -1.00000 q^{8} -6.43154 q^{9} +(1.36822 + 1.76861i) q^{10} -1.06735i q^{11} +3.07108i q^{12} -3.69510 q^{14} +(5.43154 - 4.20191i) q^{15} +1.00000 q^{16} -2.79940i q^{17} +6.43154 q^{18} -2.19819i q^{19} +(-1.36822 - 1.76861i) q^{20} +11.3479i q^{21} +1.06735i q^{22} +1.13083i q^{23} -3.07108i q^{24} +(-1.25595 + 4.83969i) q^{25} -10.5385i q^{27} +3.69510 q^{28} +2.73644 q^{29} +(-5.43154 + 4.20191i) q^{30} -4.20191i q^{31} -1.00000 q^{32} +3.27793 q^{33} +2.79940i q^{34} +(-5.05571 - 6.53518i) q^{35} -6.43154 q^{36} +10.3193 q^{37} +2.19819i q^{38} +(1.36822 + 1.76861i) q^{40} +4.93821i q^{41} -11.3479i q^{42} +4.39637i q^{43} -1.06735i q^{44} +(8.79976 + 11.3749i) q^{45} -1.13083i q^{46} +10.5582 q^{47} +3.07108i q^{48} +6.65376 q^{49} +(1.25595 - 4.83969i) q^{50} +8.59720 q^{51} -3.81853i q^{53} +10.5385i q^{54} +(-1.88773 + 1.46037i) q^{55} -3.69510 q^{56} +6.75081 q^{57} -2.73644 q^{58} +3.61033i q^{59} +(5.43154 - 4.20191i) q^{60} +15.2214 q^{61} +4.20191i q^{62} -23.7652 q^{63} +1.00000 q^{64} -3.27793 q^{66} -4.00000 q^{67} -2.79940i q^{68} -3.47288 q^{69} +(5.05571 + 6.53518i) q^{70} -12.2843i q^{71} +6.43154 q^{72} -1.23397 q^{73} -10.3193 q^{74} +(-14.8631 - 3.85712i) q^{75} -2.19819i q^{76} -3.94398i q^{77} +14.2237 q^{79} +(-1.36822 - 1.76861i) q^{80} +13.0701 q^{81} -4.93821i q^{82} -8.18235 q^{83} +11.3479i q^{84} +(-4.95105 + 3.83020i) q^{85} -4.39637i q^{86} +8.40383i q^{87} +1.06735i q^{88} -8.80497i q^{89} +(-8.79976 - 11.3749i) q^{90} +1.13083i q^{92} +12.9044 q^{93} -10.5582 q^{94} +(-3.88773 + 3.00760i) q^{95} -3.07108i q^{96} +8.75081 q^{97} -6.65376 q^{98} +6.86472i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 3 q^{5} + 10 q^{7} - 8 q^{8} - 16 q^{9} + 3 q^{10} - 10 q^{14} + 8 q^{15} + 8 q^{16} + 16 q^{18} - 3 q^{20} + 5 q^{25} + 10 q^{28} + 6 q^{29} - 8 q^{30} - 8 q^{32} - 20 q^{33}+ \cdots - 30 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 3 * q^5 + 10 * q^7 - 8 * q^8 - 16 * q^9 + 3 * q^10 - 10 * q^14 + 8 * q^15 + 8 * q^16 + 16 * q^18 - 3 * q^20 + 5 * q^25 + 10 * q^28 + 6 * q^29 - 8 * q^30 - 8 * q^32 - 20 * q^33 + 18 * q^35 - 16 * q^36 + 40 * q^37 + 3 * q^40 + 27 * q^45 - 6 * q^47 + 30 * q^49 - 5 * q^50 - 20 * q^51 - 8 * q^55 - 10 * q^56 - 24 * q^57 - 6 * q^58 + 8 * q^60 + 10 * q^61 - 50 * q^63 + 8 * q^64 + 20 * q^66 - 32 * q^67 + 4 * q^69 - 18 * q^70 + 16 * q^72 - 26 * q^73 - 40 * q^74 - 48 * q^75 + 4 * q^79 - 3 * q^80 - 16 * q^81 + 48 * q^83 - 5 * q^85 - 27 * q^90 + 36 * q^93 + 6 * q^94 - 24 * q^95 - 8 * q^97 - 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			3.07108i			1.77309i	0.462643	+	0.886545i	$0.346901\pi$
$3$			3.07108i			1.77309i	−0.462643	+	0.886545i	$0.653099\pi$
$4$	1.00000			0.500000
$5$	−1.36822	−	1.76861i	−0.611886	−	0.790946i
$5$	−1.36822	−	1.76861i	−0.611886	−	0.790946i
$6$		−	3.07108i		−	1.25376i
$7$	3.69510			1.39662			0.698308	−	0.715797i	$-0.253937\pi$
$7$	3.69510			1.39662			0.698308	+	0.715797i	$0.253937\pi$
$8$	−1.00000			−0.353553
$9$	−6.43154			−2.14385
$10$	1.36822	+	1.76861i	0.432669	+	0.559283i
$11$		−	1.06735i		−	0.321819i	−0.986969	−	0.160910i	$-0.948557\pi$
$11$		−	1.06735i		−	0.321819i	0.986969	−	0.160910i	$-0.0514427\pi$
$12$			3.07108i			0.886545i
$13$		0			0
$13$		0			0
$14$	−3.69510			−0.987557
$15$	5.43154	−	4.20191i	1.40242	−	1.08493i
$16$	1.00000			0.250000
$17$		−	2.79940i		−	0.678955i	−0.940614	−	0.339478i	$-0.889750\pi$
$17$		−	2.79940i		−	0.678955i	0.940614	−	0.339478i	$-0.110250\pi$
$18$	6.43154			1.51593
$19$		−	2.19819i		−	0.504298i	−0.967688	−	0.252149i	$-0.918863\pi$
$19$		−	2.19819i		−	0.504298i	0.967688	−	0.252149i	$-0.0811374\pi$
$20$	−1.36822	−	1.76861i	−0.305943	−	0.395473i
$21$			11.3479i			2.47633i
$22$			1.06735i			0.227560i
$23$			1.13083i			0.235795i	0.993026	+	0.117897i	$0.0376154\pi$
$23$			1.13083i			0.235795i	−0.993026	+	0.117897i	$0.962385\pi$
$24$		−	3.07108i		−	0.626882i
$25$	−1.25595	+	4.83969i	−0.251190	+	0.967938i
$26$		0			0
$27$		−	10.5385i		−	2.02814i
$28$	3.69510			0.698308
$29$	2.73644			0.508144			0.254072	−	0.967185i	$-0.418230\pi$
$29$	2.73644			0.508144			0.254072	+	0.967185i	$0.418230\pi$
$30$	−5.43154	+	4.20191i	−0.991659	+	0.767161i
$31$		−	4.20191i		−	0.754686i	−0.926074	−	0.377343i	$-0.876838\pi$
$31$		−	4.20191i		−	0.754686i	0.926074	−	0.377343i	$-0.123162\pi$
$32$	−1.00000			−0.176777
$33$	3.27793			0.570614
$34$			2.79940i			0.480094i
$35$	−5.05571	−	6.53518i	−0.854571	−	1.10465i
$36$	−6.43154			−1.07192
$37$	10.3193			1.69648			0.848239	−	0.529614i	$-0.177663\pi$
$37$	10.3193			1.69648			0.848239	+	0.529614i	$0.177663\pi$
$38$			2.19819i			0.356593i
$39$		0			0
$40$	1.36822	+	1.76861i	0.216335	+	0.279641i
$41$			4.93821i			0.771220i	0.922662	+	0.385610i	$0.126009\pi$
$41$			4.93821i			0.771220i	−0.922662	+	0.385610i	$0.873991\pi$
$42$		−	11.3479i		−	1.75103i
$43$			4.39637i			0.670440i	0.942140	+	0.335220i	$0.108811\pi$
$43$			4.39637i			0.670440i	−0.942140	+	0.335220i	$0.891189\pi$
$44$		−	1.06735i		−	0.160910i
$45$	8.79976	+	11.3749i	1.31179	+	1.69567i
$46$		−	1.13083i		−	0.166732i
$47$	10.5582			1.54007			0.770034	−	0.638003i	$-0.220239\pi$
$47$	10.5582			1.54007			0.770034	+	0.638003i	$0.220239\pi$
$48$			3.07108i			0.443272i
$49$	6.65376			0.950537
$50$	1.25595	−	4.83969i	0.177618	−	0.684435i
$51$	8.59720			1.20385
$52$		0			0
$53$		−	3.81853i		−	0.524515i	−0.964998	−	0.262258i	$-0.915533\pi$
$53$		−	3.81853i		−	0.524515i	0.964998	−	0.262258i	$-0.0844670\pi$
$54$			10.5385i			1.43411i
$55$	−1.88773	+	1.46037i	−0.254541	+	0.196917i
$56$	−3.69510			−0.493778
$57$	6.75081			0.894166
$58$	−2.73644			−0.359312
$59$			3.61033i			0.470025i	0.971992	+	0.235013i	$0.0755131\pi$
$59$			3.61033i			0.470025i	−0.971992	+	0.235013i	$0.924487\pi$
$60$	5.43154	−	4.20191i	0.701209	−	0.542465i
$61$	15.2214			1.94890			0.974448	−	0.224613i	$-0.0721117\pi$
$61$	15.2214			1.94890			0.974448	+	0.224613i	$0.0721117\pi$
$62$			4.20191i			0.533644i
$63$	−23.7652			−2.99413
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.27793			−0.403485
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		−	2.79940i		−	0.339478i
$69$	−3.47288			−0.418086
$70$	5.05571	+	6.53518i	0.604273	+	0.781104i
$71$		−	12.2843i		−	1.45788i	−0.684577	−	0.728941i	$-0.740013\pi$
$71$		−	12.2843i		−	1.45788i	0.684577	−	0.728941i	$-0.259987\pi$
$72$	6.43154			0.757964
$73$	−1.23397			−0.144425			−0.0722127	−	0.997389i	$-0.523006\pi$
$73$	−1.23397			−0.144425			−0.0722127	+	0.997389i	$0.523006\pi$
$74$	−10.3193			−1.19959
$75$	−14.8631	−	3.85712i	−1.71624	−	0.445382i
$76$		−	2.19819i		−	0.252149i
$77$		−	3.94398i		−	0.449458i
$78$		0			0
$79$	14.2237			1.60029			0.800145	−	0.599807i	$-0.204756\pi$
$79$	14.2237			1.60029			0.800145	+	0.599807i	$0.204756\pi$
$80$	−1.36822	−	1.76861i	−0.152972	−	0.197736i
$81$	13.0701			1.45223
$82$		−	4.93821i		−	0.545335i
$83$	−8.18235			−0.898129			−0.449065	−	0.893499i	$-0.648243\pi$
$83$	−8.18235			−0.898129			−0.449065	+	0.893499i	$0.648243\pi$
$84$			11.3479i			1.23816i
$85$	−4.95105	+	3.83020i	−0.537017	+	0.415444i
$86$		−	4.39637i		−	0.474073i
$87$			8.40383i			0.900985i
$88$			1.06735i			0.113780i
$89$		−	8.80497i		−	0.933325i	−0.884435	−	0.466663i	$-0.845456\pi$
$89$		−	8.80497i		−	0.933325i	0.884435	−	0.466663i	$-0.154544\pi$
$90$	−8.79976	−	11.3749i	−0.927576	−	1.19902i
$91$		0			0
$92$			1.13083i			0.117897i
$93$	12.9044			1.33813
$94$	−10.5582			−1.08899
$95$	−3.88773	+	3.00760i	−0.398873	+	0.308573i
$96$		−	3.07108i		−	0.313441i
$97$	8.75081			0.888510			0.444255	−	0.895900i	$-0.353468\pi$
$97$	8.75081			0.888510			0.444255	+	0.895900i	$0.353468\pi$
$98$	−6.65376			−0.672131
$99$			6.86472i			0.689931i
$100$	−1.25595	+	4.83969i	−0.125595	+	0.483969i
$101$	2.58283			0.257001			0.128501	−	0.991709i	$-0.458984\pi$
$101$	2.58283			0.257001			0.128501	+	0.991709i	$0.458984\pi$
$102$	−8.59720			−0.851249
$103$			3.00760i			0.296348i	0.988961	+	0.148174i	$0.0473395\pi$
$103$			3.00760i			0.296348i	−0.988961	+	0.148174i	$0.952660\pi$
$104$		0			0
$105$	20.0701	−	15.5265i	1.95864	−	1.51523i
$106$			3.81853i			0.370888i
$107$			5.47595i			0.529380i	0.964334	+	0.264690i	$0.0852697\pi$
$107$			5.47595i			0.529380i	−0.964334	+	0.264690i	$0.914730\pi$
$108$		−	10.5385i		−	1.01407i
$109$			11.8872i			1.13859i	0.822134	+	0.569294i	$0.192783\pi$
$109$			11.8872i			1.13859i	−0.822134	+	0.569294i	$0.807217\pi$
$110$	1.88773	−	1.46037i	0.179988	−	0.139241i
$111$			31.6913i			3.00801i
$112$	3.69510			0.349154
$113$			9.26298i			0.871388i	0.900095	+	0.435694i	$0.143497\pi$
$113$			9.26298i			0.871388i	−0.900095	+	0.435694i	$0.856503\pi$
$114$	−6.75081			−0.632271
$115$	2.00000	−	1.54723i	0.186501	−	0.144280i
$116$	2.73644			0.254072
$117$		0			0
$118$		−	3.61033i		−	0.332358i
$119$		−	10.3441i		−	0.948240i
$120$	−5.43154	+	4.20191i	−0.495829	+	0.383580i
$121$	9.86076			0.896432
$122$	−15.2214			−1.37808
$123$	−15.1657			−1.36744
$124$		−	4.20191i		−	0.377343i
$125$	10.2779	−	4.40048i	0.919286	−	0.393591i
$126$	23.7652			2.11717
$127$			7.40397i			0.656996i	0.944505	+	0.328498i	$0.106542\pi$
$127$			7.40397i			0.656996i	−0.944505	+	0.328498i	$0.893458\pi$
$128$	−1.00000			−0.0883883
$129$	−13.5016			−1.18875
$130$		0			0
$131$	−7.35829			−0.642897			−0.321448	−	0.946927i	$-0.604170\pi$
$131$	−7.35829			−0.642897			−0.321448	+	0.946927i	$0.604170\pi$
$132$	3.27793			0.285307
$133$		−	8.12252i		−	0.704311i
$134$	4.00000			0.345547
$135$	−18.6385	+	14.4190i	−1.60415	+	1.24099i
$136$			2.79940i			0.240047i
$137$	−13.4046			−1.14523			−0.572615	−	0.819825i	$-0.694071\pi$
$137$	−13.4046			−1.14523			−0.572615	+	0.819825i	$0.694071\pi$
$138$	3.47288			0.295631
$139$	−11.3583			−0.963397			−0.481699	−	0.876337i	$-0.659980\pi$
$139$	−11.3583			−0.963397			−0.481699	+	0.876337i	$0.659980\pi$
$140$	−5.05571	−	6.53518i	−0.427285	−	0.552324i
$141$			32.4250i			2.73068i
$142$			12.2843i			1.03088i
$143$		0			0
$144$	−6.43154			−0.535962
$145$	−3.74405	−	4.83969i	−0.310926	−	0.401914i
$146$	1.23397			0.102124
$147$			20.4342i			1.68539i
$148$	10.3193			0.848239
$149$		−	7.00132i		−	0.573570i	−0.957995	−	0.286785i	$-0.907413\pi$
$149$		−	7.00132i		−	0.573570i	0.957995	−	0.286785i	$-0.0925866\pi$
$150$	14.8631	+	3.85712i	1.21357	+	0.314933i
$151$		−	0.194458i		−	0.0158248i	−0.999969	−	0.00791239i	$-0.997481\pi$
$151$		−	0.194458i		−	0.0158248i	0.999969	−	0.00791239i	$-0.00251862\pi$
$152$			2.19819i			0.178296i
$153$			18.0045i			1.45558i
$154$			3.94398i			0.317815i
$155$	−7.43154	+	5.74914i	−0.596916	+	0.461782i
$156$		0			0
$157$			16.8889i			1.34788i	0.738786	+	0.673940i	$0.235399\pi$
$157$			16.8889i			1.34788i	−0.738786	+	0.673940i	$0.764601\pi$
$158$	−14.2237			−1.13158
$159$	11.7270			0.930012
$160$	1.36822	+	1.76861i	0.108167	+	0.139821i
$161$			4.17854i			0.329315i
$162$	−13.0701			−1.02688
$163$	−2.23165			−0.174796			−0.0873982	−	0.996173i	$-0.527855\pi$
$163$	−2.23165			−0.174796			−0.0873982	+	0.996173i	$0.527855\pi$
$164$			4.93821i			0.385610i
$165$	−4.48493	−	5.79737i	−0.349151	−	0.451325i
$166$	8.18235			0.635073
$167$	2.03902			0.157784			0.0788920	−	0.996883i	$-0.474862\pi$
$167$	2.03902			0.157784			0.0788920	+	0.996883i	$0.474862\pi$
$168$		−	11.3479i		−	0.875513i
$169$		0			0
$170$	4.95105	−	3.83020i	0.379728	−	0.293763i
$171$			14.1377i			1.08114i
$172$			4.39637i			0.335220i
$173$			10.8722i			0.826596i	0.910596	+	0.413298i	$0.135623\pi$
$173$			10.8722i			0.826596i	−0.910596	+	0.413298i	$0.864377\pi$
$174$		−	8.40383i		−	0.637093i
$175$	−4.64086	+	17.8831i	−0.350816	+	1.35184i
$176$		−	1.06735i		−	0.0804548i
$177$	−11.0876			−0.833396
$178$			8.80497i			0.659961i
$179$	−3.91732			−0.292794			−0.146397	−	0.989226i	$-0.546768\pi$
$179$	−3.91732			−0.292794			−0.146397	+	0.989226i	$0.546768\pi$
$180$	8.79976	+	11.3749i	0.655895	+	0.847833i
$181$	−14.1976			−1.05530			−0.527648	−	0.849463i	$-0.676926\pi$
$181$	−14.1976			−1.05530			−0.527648	+	0.849463i	$0.676926\pi$
$182$		0			0
$183$			46.7460i			3.45557i
$184$		−	1.13083i		−	0.0833661i
$185$	−14.1190	−	18.2507i	−1.03805	−	1.34182i
$186$	−12.9044			−0.946198
$187$	−2.98795			−0.218501
$188$	10.5582			0.770034
$189$		−	38.9409i		−	2.83254i
$190$	3.88773	−	3.00760i	0.282046	−	0.218194i
$191$	−0.336811			−0.0243708			−0.0121854	−	0.999926i	$-0.503879\pi$
$191$	−0.336811			−0.0243708			−0.0121854	+	0.999926i	$0.503879\pi$
$192$			3.07108i			0.221636i
$193$	6.76518			0.486968			0.243484	−	0.969905i	$-0.421710\pi$
$193$	6.76518			0.486968			0.243484	+	0.969905i	$0.421710\pi$
$194$	−8.75081			−0.628271
$195$		0			0
$196$	6.65376			0.475269
$197$	14.9363			1.06417			0.532085	−	0.846691i	$-0.321409\pi$
$197$	14.9363			1.06417			0.532085	+	0.846691i	$0.321409\pi$
$198$		−	6.86472i		−	0.487855i
$199$	−0.302580			−0.0214493			−0.0107247	−	0.999942i	$-0.503414\pi$
$199$	−0.302580			−0.0214493			−0.0107247	+	0.999942i	$0.503414\pi$
$200$	1.25595	−	4.83969i	0.0888090	−	0.342218i
$201$		−	12.2843i		−	0.866469i
$202$	−2.58283			−0.181727
$203$	10.1114			0.709682
$204$	8.59720			0.601924
$205$	8.73377	−	6.75656i	0.609993	−	0.471899i
$206$		−	3.00760i		−	0.209550i
$207$		−	7.27299i		−	0.505508i
$208$		0			0
$209$	−2.34624			−0.162293
$210$	−20.0701	+	15.5265i	−1.38497	+	1.07143i
$211$	0.404566			0.0278515			0.0139258	−	0.999903i	$-0.495567\pi$
$211$	0.404566			0.0278515			0.0139258	+	0.999903i	$0.495567\pi$
$212$		−	3.81853i		−	0.262258i
$213$	37.7262			2.58495
$214$		−	5.47595i		−	0.374328i
$215$	7.77546	−	6.01520i	0.530282	−	0.410233i
$216$			10.5385i			0.717056i
$217$		−	15.5265i		−	1.05401i
$218$		−	11.8872i		−	0.805103i
$219$		−	3.78962i		−	0.256079i
$220$	−1.88773	+	1.46037i	−0.127271	+	0.0984584i
$221$		0			0
$222$		−	31.6913i		−	2.12698i
$223$	0.832022			0.0557163			0.0278581	−	0.999612i	$-0.491131\pi$
$223$	0.832022			0.0557163			0.0278581	+	0.999612i	$0.491131\pi$
$224$	−3.69510			−0.246889
$225$	8.07769	−	31.1266i	0.538512	−	2.07511i
$226$		−	9.26298i		−	0.616164i
$227$	7.77546			0.516075			0.258038	−	0.966135i	$-0.416924\pi$
$227$	7.77546			0.516075			0.258038	+	0.966135i	$0.416924\pi$
$228$	6.75081			0.447083
$229$		−	7.73762i		−	0.511316i	−0.966767	−	0.255658i	$-0.917708\pi$
$229$		−	7.73762i		−	0.511316i	0.966767	−	0.255658i	$-0.0822921\pi$
$230$	−2.00000	+	1.54723i	−0.131876	+	0.102021i
$231$	12.1123			0.796929
$232$	−2.73644			−0.179656
$233$			6.86070i			0.449460i	0.974421	+	0.224730i	$0.0721500\pi$
$233$			6.86070i			0.449460i	−0.974421	+	0.224730i	$0.927850\pi$
$234$		0			0
$235$	−14.4459	−	18.6733i	−0.942347	−	1.21811i
$236$			3.61033i			0.235013i
$237$			43.6821i			2.83746i
$238$			10.3441i			0.670507i
$239$		−	22.3277i		−	1.44426i	−0.691757	−	0.722130i	$-0.743163\pi$
$239$		−	22.3277i		−	1.44426i	0.691757	−	0.722130i	$-0.256837\pi$
$240$	5.43154	−	4.20191i	0.350604	−	0.271232i
$241$		−	5.68717i		−	0.366343i	−0.983081	−	0.183172i	$-0.941364\pi$
$241$		−	5.68717i		−	0.366343i	0.983081	−	0.183172i	$-0.0586364\pi$
$242$	−9.86076			−0.633873
$243$			8.52366i			0.546793i
$244$	15.2214			0.974448
$245$	−9.10380	−	11.7679i	−0.581621	−	0.751823i
$246$	15.1657			0.966927
$247$		0			0
$248$			4.20191i			0.266822i
$249$		−	25.1286i		−	1.59246i
$250$	−10.2779	+	4.40048i	−0.650033	+	0.278311i
$251$	17.6162			1.11193			0.555963	−	0.831207i	$-0.312350\pi$
$251$	17.6162			1.11193			0.555963	+	0.831207i	$0.312350\pi$
$252$	−23.7652			−1.49707
$253$	1.20700			0.0758833
$254$		−	7.40397i		−	0.464567i
$255$	−11.7629	−	15.2051i	−0.736619	−	0.952179i
$256$	1.00000			0.0625000
$257$		−	25.8167i		−	1.61040i	−0.593001	−	0.805201i	$-0.702057\pi$
$257$		−	25.8167i		−	1.61040i	0.593001	−	0.805201i	$-0.297943\pi$
$258$	13.5016			0.840574
$259$	38.1307			2.36933
$260$		0			0
$261$	−17.5995			−1.08938
$262$	7.35829			0.454597
$263$		−	21.2163i		−	1.30825i	−0.756386	−	0.654125i	$-0.773037\pi$
$263$		−	21.2163i		−	1.30825i	0.756386	−	0.654125i	$-0.226963\pi$
$264$	−3.27793			−0.201743
$265$	−6.75348	+	5.22459i	−0.414863	+	0.320944i
$266$			8.12252i			0.498023i
$267$	27.0408			1.65487
$268$	−4.00000			−0.244339
$269$	−14.4896			−0.883445			−0.441722	−	0.897152i	$-0.645632\pi$
$269$	−14.4896			−0.883445			−0.441722	+	0.897152i	$0.645632\pi$
$270$	18.6385	−	14.4190i	1.13431	−	0.877514i
$271$		−	29.0838i		−	1.76671i	−0.468701	−	0.883357i	$-0.655278\pi$
$271$		−	29.0838i		−	1.76671i	0.468701	−	0.883357i	$-0.344722\pi$
$272$		−	2.79940i		−	0.169739i
$273$		0			0
$274$	13.4046			0.809799
$275$	5.16566	+	1.34054i	0.311501	+	0.0808377i
$276$	−3.47288			−0.209043
$277$		−	2.54147i		−	0.152702i	−0.997081	−	0.0763510i	$-0.975673\pi$
$277$		−	2.54147i		−	0.152702i	0.997081	−	0.0763510i	$-0.0243269\pi$
$278$	11.3583			0.681225
$279$			27.0248i			1.61793i
$280$	5.05571	+	6.53518i	0.302136	+	0.390552i
$281$			15.2066i			0.907149i	0.891218	+	0.453574i	$0.149851\pi$
$281$			15.2066i			0.907149i	−0.891218	+	0.453574i	$0.850149\pi$
$282$		−	32.4250i		−	1.93088i
$283$			24.7921i			1.47374i	0.676037	+	0.736868i	$0.263696\pi$
$283$			24.7921i			1.47374i	−0.676037	+	0.736868i	$0.736304\pi$
$284$		−	12.2843i		−	0.728941i
$285$	−9.23659	−	11.9395i	−0.547128	−	0.707237i
$286$		0			0
$287$			18.2472i			1.07710i
$288$	6.43154			0.378982
$289$	9.16334			0.539020
$290$	3.74405	+	4.83969i	0.219858	+	0.284196i
$291$			26.8744i			1.57541i
$292$	−1.23397			−0.0722127
$293$	−21.0630			−1.23051			−0.615256	−	0.788328i	$-0.710947\pi$
$293$	−21.0630			−1.23051			−0.615256	+	0.788328i	$0.710947\pi$
$294$		−	20.4342i		−	1.19175i
$295$	6.38526	−	4.93973i	0.371764	−	0.287602i
$296$	−10.3193			−0.599795
$297$	−11.2483			−0.652695
$298$			7.00132i			0.405575i
$299$		0			0
$300$	−14.8631	−	3.85712i	−0.858120	−	0.222691i
$301$			16.2450i			0.936348i
$302$			0.194458i			0.0111898i
$303$			7.93208i			0.455686i
$304$		−	2.19819i		−	0.126075i
$305$	−20.8262	−	26.9206i	−1.19250	−	1.54147i
$306$		−	18.0045i		−	1.02925i
$307$	−8.89181			−0.507483			−0.253741	−	0.967272i	$-0.581661\pi$
$307$	−8.89181			−0.507483			−0.253741	+	0.967272i	$0.581661\pi$
$308$		−	3.94398i		−	0.224729i
$309$	−9.23659			−0.525451
$310$	7.43154	−	5.74914i	0.422083	−	0.326529i
$311$	28.7015			1.62751			0.813756	−	0.581206i	$-0.197419\pi$
$311$	28.7015			1.62751			0.813756	+	0.581206i	$0.197419\pi$
$312$		0			0
$313$			7.84120i			0.443211i	0.975136	+	0.221606i	$0.0711297\pi$
$313$			7.84120i			0.443211i	−0.975136	+	0.221606i	$0.928870\pi$
$314$		−	16.8889i		−	0.953095i
$315$	32.5160	+	42.0313i	1.83207	+	2.36819i
$316$	14.2237			0.800145
$317$	6.17741			0.346958			0.173479	−	0.984838i	$-0.444499\pi$
$317$	6.17741			0.346958			0.173479	+	0.984838i	$0.444499\pi$
$318$	−11.7270			−0.657618
$319$		−	2.92075i		−	0.163530i
$320$	−1.36822	−	1.76861i	−0.0764858	−	0.0988682i
$321$	−16.8171			−0.938639
$322$		−	4.17854i		−	0.232861i
$323$	−6.15361			−0.342396
$324$	13.0701			0.726115
$325$		0			0
$326$	2.23165			0.123600
$327$	−36.5066			−2.01882
$328$		−	4.93821i		−	0.272667i
$329$	39.0135			2.15088
$330$	4.48493	+	5.79737i	0.246887	+	0.319135i
$331$		−	26.6566i		−	1.46518i	−0.680670	−	0.732590i	$-0.738311\pi$
$331$		−	26.6566i		−	1.46518i	0.680670	−	0.732590i	$-0.261689\pi$
$332$	−8.18235			−0.449065
$333$	−66.3688			−3.63699
$334$	−2.03902			−0.111570
$335$	5.47288	+	7.07443i	0.299015	+	0.386518i
$336$			11.3479i			0.619081i
$337$		−	22.4283i		−	1.22175i	−0.791728	−	0.610874i	$-0.790818\pi$
$337$		−	22.4283i		−	1.22175i	0.791728	−	0.610874i	$-0.209182\pi$
$338$		0			0
$339$	−28.4474			−1.54505
$340$	−4.95105	+	3.83020i	−0.268508	+	0.207722i
$341$	−4.48493			−0.242872
$342$		−	14.1377i		−	0.764480i
$343$	−1.27939			−0.0690808
$344$		−	4.39637i		−	0.237036i
$345$	4.75166	+	6.14216i	0.255821	+	0.330683i
$346$		−	10.8722i		−	0.584492i
$347$			0.412291i			0.0221329i	0.999939	+	0.0110665i	$0.00352264\pi$
$347$			0.412291i			0.0221329i	−0.999939	+	0.0110665i	$0.996477\pi$
$348$			8.40383i			0.450492i
$349$			3.34125i			0.178853i	0.995993	+	0.0894264i	$0.0285034\pi$
$349$			3.34125i			0.178853i	−0.995993	+	0.0894264i	$0.971497\pi$
$350$	4.64086	−	17.8831i	0.248064	−	0.955894i
$351$		0			0
$352$			1.06735i			0.0568901i
$353$	21.1208			1.12415			0.562075	−	0.827087i	$-0.310003\pi$
$353$	21.1208			1.12415			0.562075	+	0.827087i	$0.310003\pi$
$354$	11.0876			0.589300
$355$	−21.7262	+	16.8077i	−1.15310	+	0.892058i
$356$		−	8.80497i		−	0.466663i
$357$	31.7675			1.68131
$358$	3.91732			0.207037
$359$			5.57954i			0.294477i	0.989101	+	0.147238i	$0.0470384\pi$
$359$			5.57954i			0.294477i	−0.989101	+	0.147238i	$0.952962\pi$
$360$	−8.79976	−	11.3749i	−0.463788	−	0.599508i
$361$	14.1680			0.745683
$362$	14.1976			0.746208
$363$			30.2832i			1.58945i
$364$		0			0
$365$	1.68834	+	2.18241i	0.0883719	+	0.114233i
$366$		−	46.7460i		−	2.44346i
$367$		−	1.30192i		−	0.0679595i	−0.999423	−	0.0339797i	$-0.989182\pi$
$367$		−	1.30192i		−	0.0679595i	0.999423	−	0.0339797i	$-0.0108182\pi$
$368$			1.13083i			0.0589487i
$369$		−	31.7603i		−	1.65338i
$370$	14.1190	+	18.2507i	0.734013	+	0.948811i
$371$		−	14.1098i		−	0.732546i
$372$	12.9044			0.669063
$373$		−	33.9971i		−	1.76030i	−0.474691	−	0.880152i	$-0.657440\pi$
$373$		−	33.9971i		−	1.76030i	0.474691	−	0.880152i	$-0.342560\pi$
$374$	2.98795			0.154503
$375$	13.5142	+	31.5644i	0.697871	+	1.62998i
$376$	−10.5582			−0.544496
$377$		0			0
$378$			38.9409i			2.00291i
$379$			4.67768i			0.240276i	0.992757	+	0.120138i	$0.0383338\pi$
$379$			4.67768i			0.240276i	−0.992757	+	0.120138i	$0.961666\pi$
$380$	−3.88773	+	3.00760i	−0.199436	+	0.154287i
$381$	−22.7382			−1.16491
$382$	0.336811			0.0172328
$383$	−13.7388			−0.702018			−0.351009	−	0.936372i	$-0.614161\pi$
$383$	−13.7388			−0.702018			−0.351009	+	0.936372i	$0.614161\pi$
$384$		−	3.07108i		−	0.156720i
$385$	−6.97535	+	5.39623i	−0.355497	+	0.275017i
$386$	−6.76518			−0.344338
$387$		−	28.2754i		−	1.43732i
$388$	8.75081			0.444255
$389$	17.9138			0.908268			0.454134	−	0.890933i	$-0.349949\pi$
$389$	17.9138			0.908268			0.454134	+	0.890933i	$0.349949\pi$
$390$		0			0
$391$	3.16566			0.160094
$392$	−6.65376			−0.336066
$393$		−	22.5979i		−	1.13991i
$394$	−14.9363			−0.752481
$395$	−19.4611	−	25.1561i	−0.979196	−	1.26574i
$396$			6.86472i			0.344965i
$397$	0.458511			0.0230120			0.0115060	−	0.999934i	$-0.496337\pi$
$397$	0.458511			0.0230120			0.0115060	+	0.999934i	$0.496337\pi$
$398$	0.302580			0.0151670
$399$	24.9449			1.24881
$400$	−1.25595	+	4.83969i	−0.0627975	+	0.241984i
$401$			26.0554i			1.30114i	0.759445	+	0.650572i	$0.225471\pi$
$401$			26.0554i			1.30114i	−0.759445	+	0.650572i	$0.774529\pi$
$402$			12.2843i			0.612686i
$403$		0			0
$404$	2.58283			0.128501
$405$	−17.8827	−	23.1158i	−0.888600	−	1.14864i
$406$	−10.1114			−0.501821
$407$		−	11.0143i		−	0.545959i
$408$	−8.59720			−0.425625
$409$		−	0.358531i		−	0.0177282i	−0.999961	−	0.00886411i	$-0.997178\pi$
$409$		−	0.358531i		−	0.0177282i	0.999961	−	0.00886411i	$-0.00282157\pi$
$410$	−8.73377	+	6.75656i	−0.431330	+	0.333683i
$411$		−	41.1665i		−	2.03059i
$412$			3.00760i			0.148174i
$413$			13.3405i			0.656445i
$414$			7.27299i			0.357448i
$415$	11.1952	+	14.4714i	0.549553	+	0.710371i
$416$		0			0
$417$		−	34.8822i		−	1.70819i
$418$	2.34624			0.114758
$419$	19.3184			0.943766			0.471883	−	0.881661i	$-0.343574\pi$
$419$	19.3184			0.943766			0.471883	+	0.881661i	$0.343574\pi$
$420$	20.0701	−	15.5265i	0.979319	−	0.757615i
$421$			0.220426i			0.0107429i	0.999986	+	0.00537144i	$0.00170979\pi$
$421$			0.220426i			0.0107429i	−0.999986	+	0.00537144i	$0.998290\pi$
$422$	−0.404566			−0.0196940
$423$	−67.9053			−3.30167
$424$			3.81853i			0.185444i
$425$	13.5482	+	3.51591i	0.657186	+	0.170547i
$426$	−37.7262			−1.82784
$427$	56.2445			2.72186
$428$			5.47595i			0.264690i
$429$		0			0
$430$	−7.77546	+	6.01520i	−0.374966	+	0.290079i
$431$		−	19.9696i		−	0.961902i	−0.876747	−	0.480951i	$-0.840291\pi$
$431$		−	19.9696i		−	0.961902i	0.876747	−	0.480951i	$-0.159709\pi$
$432$		−	10.5385i		−	0.507035i
$433$		−	31.4155i		−	1.50973i	−0.655878	−	0.754867i	$-0.727701\pi$
$433$		−	31.4155i		−	1.50973i	0.655878	−	0.754867i	$-0.272299\pi$
$434$			15.5265i			0.745295i
$435$	14.8631	−	11.4983i	0.712630	−	0.551300i
$436$			11.8872i			0.569294i
$437$	2.48578			0.118911
$438$			3.78962i			0.181075i
$439$	−25.6139			−1.22248			−0.611242	−	0.791444i	$-0.709330\pi$
$439$	−25.6139			−1.22248			−0.611242	+	0.791444i	$0.709330\pi$
$440$	1.88773	−	1.46037i	0.0899940	−	0.0696206i
$441$	−42.7939			−2.03781
$442$		0			0
$443$			28.4024i			1.34944i	0.738074	+	0.674719i	$0.235735\pi$
$443$			28.4024i			1.34944i	−0.738074	+	0.674719i	$0.764265\pi$
$444$			31.6913i			1.50400i
$445$	−15.5725	+	12.0471i	−0.738209	+	0.571089i
$446$	−0.832022			−0.0393974
$447$	21.5016			1.01699
$448$	3.69510			0.174577
$449$			22.4217i			1.05815i	0.848576	+	0.529073i	$0.177460\pi$
$449$			22.4217i			1.05815i	−0.848576	+	0.529073i	$0.822540\pi$
$450$	−8.07769	+	31.1266i	−0.380786	+	1.46732i
$451$	5.27082			0.248193
$452$			9.26298i			0.435694i
$453$	0.597197			0.0280587
$454$	−7.77546			−0.364920
$455$		0			0
$456$	−6.75081			−0.316136
$457$	−23.5987			−1.10390			−0.551949	−	0.833878i	$-0.686116\pi$
$457$	−23.5987			−1.10390			−0.551949	+	0.833878i	$0.686116\pi$
$458$			7.73762i			0.361555i
$459$	−29.5016			−1.37702
$460$	2.00000	−	1.54723i	0.0932505	−	0.0721399i
$461$			32.5063i			1.51397i	0.653432	+	0.756986i	$0.273329\pi$
$461$			32.5063i			1.51397i	−0.653432	+	0.756986i	$0.726671\pi$
$462$	−12.1123			−0.563514
$463$	7.70367			0.358020			0.179010	−	0.983847i	$-0.442711\pi$
$463$	7.70367			0.358020			0.179010	+	0.983847i	$0.442711\pi$
$464$	2.73644			0.127036
$465$	−17.6561	−	22.8229i	−0.818781	−	1.05838i
$466$		−	6.86070i		−	0.317816i
$467$		−	20.9339i		−	0.968704i	−0.874873	−	0.484352i	$-0.839055\pi$
$467$		−	20.9339i		−	0.968704i	0.874873	−	0.484352i	$-0.160945\pi$
$468$		0			0
$469$	−14.7804			−0.682495
$470$	14.4459	+	18.6733i	0.666340	+	0.861334i
$471$	−51.8672			−2.38991
$472$		−	3.61033i		−	0.166179i
$473$	4.69248			0.215761
$474$		−	43.6821i		−	2.00639i
$475$	10.6385	+	2.76081i	0.488130	+	0.126675i
$476$		−	10.3441i		−	0.474120i
$477$			24.5590i			1.12448i
$478$			22.3277i			1.02125i
$479$		−	0.980499i		−	0.0448002i	−0.999749	−	0.0224001i	$-0.992869\pi$
$479$		−	0.980499i		−	0.0448002i	0.999749	−	0.0224001i	$-0.00713076\pi$
$480$	−5.43154	+	4.20191i	−0.247915	+	0.191790i
$481$		0			0
$482$			5.68717i			0.259044i
$483$	−12.8326			−0.583905
$484$	9.86076			0.448216
$485$	−11.9730	−	15.4767i	−0.543667	−	0.702763i
$486$		−	8.52366i		−	0.386641i
$487$	−38.6283			−1.75041			−0.875207	−	0.483749i	$-0.839275\pi$
$487$	−38.6283			−1.75041			−0.875207	+	0.483749i	$0.839275\pi$
$488$	−15.2214			−0.689039
$489$		−	6.85358i		−	0.309929i
$490$	9.10380	+	11.7679i	0.411268	+	0.531619i
$491$	17.7068			0.799099			0.399549	−	0.916712i	$-0.369167\pi$
$491$	17.7068			0.799099			0.399549	+	0.916712i	$0.369167\pi$
$492$	−15.1657			−0.683721
$493$		−	7.66040i		−	0.345007i
$494$		0			0
$495$	12.1410	−	9.39245i	0.545698	−	0.422159i
$496$		−	4.20191i		−	0.188672i
$497$		−	45.3918i		−	2.03610i
$498$			25.1286i			1.12604i
$499$			35.5402i			1.59100i	0.605954	+	0.795499i	$0.292791\pi$
$499$			35.5402i			1.59100i	−0.605954	+	0.795499i	$0.707209\pi$
$500$	10.2779	−	4.40048i	0.459643	−	0.196795i
$501$			6.26199i			0.279765i
$502$	−17.6162			−0.786250
$503$			44.3839i			1.97898i	0.144600	+	0.989490i	$0.453811\pi$
$503$			44.3839i			1.97898i	−0.144600	+	0.989490i	$0.546189\pi$
$504$	23.7652			1.05859
$505$	−3.53388	−	4.56801i	−0.157255	−	0.203274i
$506$	−1.20700			−0.0536576
$507$		0			0
$508$			7.40397i			0.328498i
$509$			0.715949i			0.0317339i	0.999874	+	0.0158669i	$0.00505082\pi$
$509$			0.715949i			0.0317339i	−0.999874	+	0.0158669i	$0.994949\pi$
$510$	11.7629	+	15.2051i	0.520868	+	0.673292i
$511$	−4.55964			−0.201707
$512$	−1.00000			−0.0441942
$513$	−23.1657			−1.02279
$514$			25.8167i			1.13873i
$515$	5.31927	−	4.11506i	0.234395	−	0.181331i
$516$	−13.5016			−0.594375
$517$		−	11.2693i		−	0.495623i
$518$	−38.1307			−1.67537
$519$	−33.3893			−1.46563
$520$		0			0
$521$	7.33132			0.321191			0.160595	−	0.987020i	$-0.448659\pi$
$521$	7.33132			0.321191			0.160595	+	0.987020i	$0.448659\pi$
$522$	17.5995			0.770310
$523$			11.8872i			0.519791i	0.965637	+	0.259895i	$0.0836881\pi$
$523$			11.8872i			0.519791i	−0.965637	+	0.259895i	$0.916312\pi$
$524$	−7.35829			−0.321448
$525$	−54.9205	−	14.2524i	−2.39693	−	0.622028i
$526$			21.2163i			0.925073i
$527$	−11.7629			−0.512398
$528$	3.27793			0.142654
$529$	21.7212			0.944401
$530$	6.75348	−	5.22459i	0.293352	−	0.226942i
$531$		−	23.2200i		−	1.00766i
$532$		−	8.12252i		−	0.352156i
$533$		0			0
$534$	−27.0408			−1.17017
$535$	9.68482	−	7.49231i	0.418711	−	0.323921i
$536$	4.00000			0.172774
$537$		−	12.0304i		−	0.519150i
$538$	14.4896			0.624690
$539$		−	7.10191i		−	0.305901i
$540$	−18.6385	+	14.4190i	−0.802075	+	0.620496i
$541$		−	20.5115i		−	0.881856i	−0.897542	−	0.440928i	$-0.854649\pi$
$541$		−	20.5115i		−	0.881856i	0.897542	−	0.440928i	$-0.145351\pi$
$542$			29.0838i			1.24925i
$543$		−	43.6019i		−	1.87114i
$544$			2.79940i			0.120023i
$545$	21.0238	−	16.2643i	0.900561	−	0.696686i
$546$		0			0
$547$		−	16.4268i		−	0.702358i	−0.936308	−	0.351179i	$-0.885781\pi$
$547$		−	16.4268i		−	0.702358i	0.936308	−	0.351179i	$-0.114219\pi$
$548$	−13.4046			−0.572615
$549$	−97.8968			−4.17813
$550$	−5.16566	−	1.34054i	−0.220264	−	0.0571609i
$551$		−	6.01520i		−	0.256256i
$552$	3.47288			0.147816
$553$	52.5579			2.23499
$554$			2.54147i			0.107977i
$555$	56.0495	−	43.3607i	2.37917	−	1.84056i
$556$	−11.3583			−0.481699
$557$	−36.1459			−1.53155			−0.765776	−	0.643107i	$-0.777645\pi$
$557$	−36.1459			−1.53155			−0.765776	+	0.643107i	$0.777645\pi$
$558$		−	27.0248i		−	1.14405i
$559$		0			0
$560$	−5.05571	−	6.53518i	−0.213643	−	0.276162i
$561$		−	9.17625i		−	0.387421i
$562$		−	15.2066i		−	0.641451i
$563$		−	26.5601i		−	1.11938i	−0.828703	−	0.559688i	$-0.810921\pi$
$563$		−	26.5601i		−	1.11938i	0.828703	−	0.559688i	$-0.189079\pi$
$564$			32.4250i			1.36534i
$565$	16.3826	−	12.6738i	0.689221	−	0.533191i
$566$		−	24.7921i		−	1.04209i
$567$	48.2952			2.02821
$568$			12.2843i			0.515439i
$569$	43.1841			1.81037			0.905186	−	0.425016i	$-0.139731\pi$
$569$	43.1841			1.81037			0.905186	+	0.425016i	$0.139731\pi$
$570$	9.23659	+	11.9395i	0.386878	+	0.500092i
$571$	−31.5110			−1.31870			−0.659348	−	0.751838i	$-0.729168\pi$
$571$	−31.5110			−1.31870			−0.659348	+	0.751838i	$0.729168\pi$
$572$		0			0
$573$		−	1.03437i		−	0.0432116i
$574$		−	18.2472i		−	0.761623i
$575$	−5.47288	−	1.42027i	−0.228235	−	0.0592293i
$576$	−6.43154			−0.267981
$577$	−26.9555			−1.12217			−0.561086	−	0.827758i	$-0.689616\pi$
$577$	−26.9555			−1.12217			−0.561086	+	0.827758i	$0.689616\pi$
$578$	−9.16334			−0.381145
$579$			20.7764i			0.863438i
$580$	−3.74405	−	4.83969i	−0.155463	−	0.200957i
$581$	−30.2346			−1.25434
$582$		−	26.8744i		−	1.11398i
$583$	−4.07572			−0.168799
$584$	1.23397			0.0510621
$585$		0			0
$586$	21.0630			0.870103
$587$	−29.7262			−1.22693			−0.613465	−	0.789722i	$-0.710225\pi$
$587$	−29.7262			−1.22693			−0.613465	+	0.789722i	$0.710225\pi$
$588$			20.4342i			0.842694i
$589$	−9.23659			−0.380587
$590$	−6.38526	+	4.93973i	−0.262877	+	0.203365i
$591$			45.8707i			1.88687i
$592$	10.3193			0.424119
$593$	15.3561			0.630600			0.315300	−	0.948992i	$-0.397895\pi$
$593$	15.3561			0.630600			0.315300	+	0.948992i	$0.397895\pi$
$594$	11.2483			0.461525
$595$	−18.2946	+	14.1530i	−0.750006	+	0.580215i
$596$		−	7.00132i		−	0.286785i
$597$		−	0.929248i		−	0.0380316i
$598$		0			0
$599$	23.6928			0.968061			0.484030	−	0.875051i	$-0.339172\pi$
$599$	23.6928			0.968061			0.484030	+	0.875051i	$0.339172\pi$
$600$	14.8631	+	3.85712i	0.606783	+	0.157466i
$601$	−3.49668			−0.142632			−0.0713162	−	0.997454i	$-0.522720\pi$
$601$	−3.49668			−0.142632			−0.0713162	+	0.997454i	$0.522720\pi$
$602$		−	16.2450i		−	0.662098i
$603$	25.7262			1.04765
$604$		−	0.194458i		−	0.00791239i
$605$	−13.4917	−	17.4398i	−0.548515	−	0.709029i
$606$		−	7.93208i		−	0.322219i
$607$		−	37.2982i		−	1.51389i	−0.653479	−	0.756944i	$-0.726691\pi$
$607$		−	37.2982i		−	1.51389i	0.653479	−	0.756944i	$-0.273309\pi$
$608$			2.19819i			0.0891482i
$609$			31.0530i			1.25833i
$610$	20.8262	+	26.9206i	0.843227	+	1.08998i
$611$		0			0
$612$			18.0045i			0.727788i
$613$	15.3242			0.618939			0.309469	−	0.950909i	$-0.399849\pi$
$613$	15.3242			0.618939			0.309469	+	0.950909i	$0.399849\pi$
$614$	8.89181			0.358844
$615$	20.7500	+	26.8221i	0.836719	+	1.08157i
$616$			3.94398i			0.158907i
$617$	−5.07240			−0.204207			−0.102103	−	0.994774i	$-0.532557\pi$
$617$	−5.07240			−0.204207			−0.102103	+	0.994774i	$0.532557\pi$
$618$	9.23659			0.371550
$619$			20.6770i			0.831079i	0.909575	+	0.415540i	$0.136407\pi$
$619$			20.6770i			0.831079i	−0.909575	+	0.415540i	$0.863593\pi$
$620$	−7.43154	+	5.74914i	−0.298458	+	0.230891i
$621$	11.9173			0.478226
$622$	−28.7015			−1.15083
$623$		−	32.5352i		−	1.30350i
$624$		0			0
$625$	−21.8452	−	12.1568i	−0.873807	−	0.486272i
$626$		−	7.84120i		−	0.313398i
$627$		−	7.20550i		−	0.287760i
$628$			16.8889i			0.673940i
$629$		−	28.8878i		−	1.15183i
$630$	−32.5160	−	42.0313i	−1.29547	−	1.67457i
$631$			21.4904i			0.855521i	0.903892	+	0.427760i	$0.140697\pi$
$631$			21.4904i			0.855521i	−0.903892	+	0.427760i	$0.859303\pi$
$632$	−14.2237			−0.565788
$633$			1.24246i			0.0493832i
$634$	−6.17741			−0.245336
$635$	13.0947	−	10.1303i	0.519648	−	0.402007i
$636$	11.7270			0.465006
$637$		0			0
$638$			2.92075i			0.115634i
$639$			79.0071i			3.12547i
$640$	1.36822	+	1.76861i	0.0540836	+	0.0699104i
$641$	−35.7724			−1.41293			−0.706463	−	0.707750i	$-0.749710\pi$
$641$	−35.7724			−1.41293			−0.706463	+	0.707750i	$0.749710\pi$
$642$	16.8171			0.663718
$643$	28.0216			1.10507			0.552533	−	0.833491i	$-0.313662\pi$
$643$	28.0216			1.10507			0.552533	+	0.833491i	$0.313662\pi$
$644$			4.17854i			0.164658i
$645$	18.4732	+	23.8791i	0.727381	+	0.940237i
$646$	6.15361			0.242111
$647$		−	19.4623i		−	0.765140i	−0.923926	−	0.382570i	$-0.875039\pi$
$647$		−	19.4623i		−	0.765140i	0.923926	−	0.382570i	$-0.124961\pi$
$648$	−13.0701			−0.513441
$649$	3.85350			0.151263
$650$		0			0
$651$	47.6831			1.86885
$652$	−2.23165			−0.0873982
$653$			12.9628i			0.507272i	0.967300	+	0.253636i	$0.0816265\pi$
$653$			12.9628i			0.507272i	−0.967300	+	0.253636i	$0.918373\pi$
$654$	36.5066			1.42752
$655$	10.0678	+	13.0139i	0.393380	+	0.508496i
$656$			4.93821i			0.192805i
$657$	7.93633			0.309626
$658$	−39.0135			−1.52091
$659$	−2.20670			−0.0859609			−0.0429804	−	0.999076i	$-0.513685\pi$
$659$	−2.20670			−0.0859609			−0.0429804	+	0.999076i	$0.513685\pi$
$660$	−4.48493	−	5.79737i	−0.174576	−	0.225662i
$661$		−	43.5415i		−	1.69357i	−0.531937	−	0.846784i	$-0.678536\pi$
$661$		−	43.5415i		−	1.69357i	0.531937	−	0.846784i	$-0.321464\pi$
$662$			26.6566i			1.03604i
$663$		0			0
$664$	8.18235			0.317537
$665$	−14.3655	+	11.1134i	−0.557072	+	0.430959i
$666$	66.3688			2.57174
$667$			3.09446i			0.119818i
$668$	2.03902			0.0788920
$669$			2.55521i			0.0987900i
$670$	−5.47288	−	7.07443i	−0.211436	−	0.273309i
$671$		−	16.2466i		−	0.627192i
$672$		−	11.3479i		−	0.437757i
$673$		−	0.588990i		−	0.0227039i	−0.999936	−	0.0113519i	$-0.996386\pi$
$673$		−	0.588990i		−	0.0227039i	0.999936	−	0.0113519i	$-0.00361351\pi$
$674$			22.4283i			0.863907i
$675$	51.0032	+	13.2359i	1.96312	+	0.509449i
$676$		0			0
$677$			7.61779i			0.292775i	0.989227	+	0.146388i	$0.0467647\pi$
$677$			7.61779i			0.292775i	−0.989227	+	0.146388i	$0.953235\pi$
$678$	28.4474			1.09251
$679$	32.3351			1.24091
$680$	4.95105	−	3.83020i	0.189864	−	0.146881i
$681$			23.8791i			0.915048i
$682$	4.48493			0.171737
$683$	−28.3647			−1.08534			−0.542672	−	0.839944i	$-0.682587\pi$
$683$	−28.3647			−1.08534			−0.542672	+	0.839944i	$0.682587\pi$
$684$			14.1377i			0.540569i
$685$	18.3404	+	23.7074i	0.700750	+	0.905814i
$686$	1.27939			0.0488475
$687$	23.7629			0.906609
$688$			4.39637i			0.167610i
$689$		0			0
$690$	−4.75166	−	6.14216i	−0.180893	−	0.233828i
$691$			41.3046i			1.57130i	0.618670	+	0.785651i	$0.287672\pi$
$691$			41.3046i			1.57130i	−0.618670	+	0.785651i	$0.712328\pi$
$692$			10.8722i			0.413298i
$693$			25.3658i			0.963568i
$694$		−	0.412291i		−	0.0156503i
$695$	15.5406	+	20.0884i	0.589490	+	0.761995i
$696$		−	8.40383i		−	0.318546i
$697$	13.8241			0.523624
$698$		−	3.34125i		−	0.126468i
$699$	−21.0698			−0.796932
$700$	−4.64086	+	17.8831i	−0.175408	+	0.675919i
$701$	−32.7428			−1.23668			−0.618340	−	0.785911i	$-0.712195\pi$
$701$	−32.7428			−1.23668			−0.618340	+	0.785911i	$0.712195\pi$
$702$		0			0
$703$		−	22.6837i		−	0.855531i
$704$		−	1.06735i		−	0.0402274i
$705$	57.3471	−	44.3646i	2.15982	−	1.67087i
$706$	−21.1208			−0.794894
$707$	9.54381			0.358932
$708$	−11.0876			−0.416698
$709$			21.5484i			0.809267i	0.914479	+	0.404633i	$0.132601\pi$
$709$			21.5484i			0.809267i	−0.914479	+	0.404633i	$0.867399\pi$
$710$	21.7262	−	16.8077i	0.815368	−	0.630780i
$711$	−91.4802			−3.43078
$712$			8.80497i			0.329980i
$713$	4.75166			0.177951
$714$	−31.7675			−1.18887
$715$		0			0
$716$	−3.91732			−0.146397
$717$	68.5703			2.56080
$718$		−	5.57954i		−	0.208227i
$719$	42.0862			1.56955			0.784775	−	0.619780i	$-0.212778\pi$
$719$	42.0862			1.56955			0.784775	+	0.619780i	$0.212778\pi$
$720$	8.79976	+	11.3749i	0.327948	+	0.423916i
$721$			11.1134i			0.413884i
$722$	−14.1680			−0.527278
$723$	17.4658			0.649559
$724$	−14.1976			−0.527648
$725$	−3.43683	+	13.2435i	−0.127641	+	0.491852i
$726$		−	30.2832i		−	1.12391i
$727$			21.7707i			0.807429i	0.914885	+	0.403715i	$0.132281\pi$
$727$			21.7707i			0.807429i	−0.914885	+	0.403715i	$0.867719\pi$
$728$		0			0
$729$	13.0334			0.482718
$730$	−1.68834	−	2.18241i	−0.0624884	−	0.0807746i
$731$	12.3072			0.455199
$732$			46.7460i			1.72778i
$733$	16.2319			0.599541			0.299770	−	0.954011i	$-0.403090\pi$
$733$	16.2319			0.599541			0.299770	+	0.954011i	$0.403090\pi$
$734$			1.30192i			0.0480546i
$735$	36.1402	−	27.9585i	1.33305	−	1.03127i
$736$		−	1.13083i		−	0.0416830i
$737$			4.26941i			0.157266i
$738$			31.7603i			1.16911i
$739$			18.4432i			0.678445i	0.940706	+	0.339222i	$0.110164\pi$
$739$			18.4432i			0.678445i	−0.940706	+	0.339222i	$0.889836\pi$
$740$	−14.1190	−	18.2507i	−0.519026	−	0.670911i
$741$		0			0
$742$			14.1098i			0.517989i
$743$	8.21194			0.301267			0.150633	−	0.988590i	$-0.451869\pi$
$743$	8.21194			0.301267			0.150633	+	0.988590i	$0.451869\pi$
$744$	−12.9044			−0.473099
$745$	−12.3826	+	9.57934i	−0.453663	+	0.350960i
$746$			33.9971i			1.24472i
$747$	52.6251			1.92545
$748$	−2.98795			−0.109250
$749$			20.2342i			0.739341i
$750$	−13.5142	−	31.5644i	−0.493470	−	1.15257i
$751$	−38.0908			−1.38995			−0.694977	−	0.719032i	$-0.744586\pi$
$751$	−38.0908			−1.38995			−0.694977	+	0.719032i	$0.744586\pi$
$752$	10.5582			0.385017
$753$			54.1008i			1.97154i
$754$		0			0
$755$	−0.343920	+	0.266061i	−0.0125165	+	0.00968297i
$756$		−	38.9409i		−	1.41627i
$757$			25.2668i			0.918336i	0.888350	+	0.459168i	$0.151852\pi$
$757$			25.2668i			0.918336i	−0.888350	+	0.459168i	$0.848148\pi$
$758$		−	4.67768i		−	0.169901i
$759$			3.70679i			0.134548i
$760$	3.88773	−	3.00760i	0.141023	−	0.109097i
$761$		−	36.5040i		−	1.32327i	−0.749827	−	0.661634i	$-0.769863\pi$
$761$		−	36.5040i		−	1.32327i	0.749827	−	0.661634i	$-0.230137\pi$
$762$	22.7382			0.823718
$763$			43.9244i			1.59017i
$764$	−0.336811			−0.0121854
$765$	31.8429	−	24.6341i	1.15128	−	0.890647i
$766$	13.7388			0.496402
$767$		0			0
$768$			3.07108i			0.110818i
$769$		−	27.7956i		−	1.00234i	−0.865350	−	0.501168i	$-0.832904\pi$
$769$		−	27.7956i		−	1.00234i	0.865350	−	0.501168i	$-0.167096\pi$
$770$	6.97535	−	5.39623i	0.251374	−	0.194466i
$771$	79.2852			2.85539
$772$	6.76518			0.243484
$773$	3.09705			0.111393			0.0556965	−	0.998448i	$-0.482262\pi$
$773$	3.09705			0.111393			0.0556965	+	0.998448i	$0.482262\pi$
$774$			28.2754i			1.01634i
$775$	20.3360	+	5.27739i	0.730489	+	0.189569i
$776$	−8.75081			−0.314136
$777$			117.103i			4.20103i
$778$	−17.9138			−0.642243
$779$	10.8551			0.388925
$780$		0			0
$781$	−13.1117			−0.469174
$782$	−3.16566			−0.113204
$783$		−	28.8381i		−	1.03059i
$784$	6.65376			0.237634
$785$	29.8698	−	23.1077i	1.06610	−	0.824750i
$786$			22.5979i			0.806040i
$787$	30.4310			1.08475			0.542374	−	0.840137i	$-0.317526\pi$
$787$	30.4310			1.08475			0.542374	+	0.840137i	$0.317526\pi$
$788$	14.9363			0.532085
$789$	65.1568			2.31964
$790$	19.4611	+	25.1561i	0.692396	+	0.895015i
$791$			34.2276i			1.21699i
$792$		−	6.86472i		−	0.243927i
$793$		0			0
$794$	−0.458511			−0.0162720
$795$	−16.0451	−	20.7405i	−0.569062	−	0.735589i
$796$	−0.302580			−0.0107247
$797$			47.5544i			1.68446i	0.539116	+	0.842231i	$0.318758\pi$
$797$			47.5544i			1.68446i	−0.539116	+	0.842231i	$0.681242\pi$
$798$	−24.9449			−0.883040
$799$		−	29.5566i		−	1.04564i
$800$	1.25595	−	4.83969i	0.0444045	−	0.171109i
$801$			56.6295i			2.00091i
$802$		−	26.0554i		−	0.920048i
$803$			1.31708i			0.0464788i
$804$		−	12.2843i		−	0.433235i
$805$	7.39020	−	5.71716i	0.260470	−	0.201503i
$806$		0			0
$807$		−	44.4986i		−	1.56643i
$808$	−2.58283			−0.0908636
$809$	36.0836			1.26863			0.634316	−	0.773074i	$-0.281282\pi$
$809$	36.0836			1.26863			0.634316	+	0.773074i	$0.281282\pi$
$810$	17.8827	+	23.1158i	0.628335	+	0.812208i
$811$		−	36.3456i		−	1.27627i	−0.769926	−	0.638134i	$-0.779707\pi$
$811$		−	36.3456i		−	1.27627i	0.769926	−	0.638134i	$-0.220293\pi$
$812$	10.1114			0.354841
$813$	89.3186			3.13254
$814$			11.0143i			0.386051i
$815$	3.05339	+	3.94691i	0.106955	+	0.138254i
$816$	8.59720			0.300962
$817$	9.66404			0.338102
$818$			0.358531i			0.0125357i
$819$		0			0
$820$	8.73377	−	6.75656i	0.304996	−	0.235949i
$821$			21.3321i			0.744494i	0.928134	+	0.372247i	$0.121413\pi$
$821$			21.3321i			0.744494i	−0.928134	+	0.372247i	$0.878587\pi$
$822$			41.1665i			1.43585i
$823$		−	19.9585i		−	0.695708i	−0.937549	−	0.347854i	$-0.886910\pi$
$823$		−	19.9585i		−	0.695708i	0.937549	−	0.347854i	$-0.113090\pi$
$824$		−	3.00760i		−	0.104775i
$825$	−4.11691	+	15.8642i	−0.143332	+	0.552319i
$826$		−	13.3405i		−	0.464176i
$827$	−28.9529			−1.00679			−0.503395	−	0.864056i	$-0.667916\pi$
$827$	−28.9529			−1.00679			−0.503395	+	0.864056i	$0.667916\pi$
$828$		−	7.27299i		−	0.252754i
$829$	27.1011			0.941261			0.470631	−	0.882330i	$-0.344026\pi$
$829$	27.1011			0.941261			0.470631	+	0.882330i	$0.344026\pi$
$830$	−11.1952	−	14.4714i	−0.388593	−	0.502308i
$831$	7.80505			0.270754
$832$		0			0
$833$		−	18.6266i		−	0.645372i
$834$			34.8822i			1.20787i
$835$	−2.78983	−	3.60623i	−0.0965459	−	0.124799i
$836$	−2.34624			−0.0811464
$837$	−44.2820			−1.53061
$838$	−19.3184			−0.667344
$839$		−	33.7213i		−	1.16419i	−0.813121	−	0.582095i	$-0.802233\pi$
$839$		−	33.7213i		−	1.16419i	0.813121	−	0.582095i	$-0.197767\pi$
$840$	−20.0701	+	15.5265i	−0.692483	+	0.535715i
$841$	−21.5119			−0.741790
$842$		−	0.220426i		−	0.00759637i
$843$	−46.7006			−1.60846
$844$	0.404566			0.0139258
$845$		0			0
$846$	67.9053			2.33463
$847$	36.4365			1.25197
$848$		−	3.81853i		−	0.131129i
$849$	−76.1384			−2.61306
$850$	−13.5482	−	3.51591i	−0.464701	−	0.120595i
$851$			11.6694i			0.400021i
$852$	37.7262			1.29248
$853$	−30.0853			−1.03010			−0.515050	−	0.857160i	$-0.672227\pi$
$853$	−30.0853			−1.03010			−0.515050	+	0.857160i	$0.672227\pi$
$854$	−56.2445			−1.92465
$855$	25.0041	−	19.3435i	0.855122	−	0.661534i
$856$		−	5.47595i		−	0.187164i
$857$		−	21.6341i		−	0.739006i	−0.929230	−	0.369503i	$-0.879528\pi$
$857$		−	21.6341i		−	0.739006i	0.929230	−	0.369503i	$-0.120472\pi$
$858$		0			0
$859$	−6.57516			−0.224342			−0.112171	−	0.993689i	$-0.535780\pi$
$859$	−6.57516			−0.224342			−0.112171	+	0.993689i	$0.535780\pi$
$860$	7.77546	−	6.01520i	0.265141	−	0.205117i
$861$	−56.0386			−1.90979
$862$			19.9696i			0.680168i
$863$	−45.3471			−1.54363			−0.771817	−	0.635844i	$-0.780652\pi$
$863$	−45.3471			−1.54363			−0.771817	+	0.635844i	$0.780652\pi$
$864$			10.5385i			0.358528i
$865$	19.2286	−	14.8755i	0.653793	−	0.505783i
$866$			31.4155i			1.06754i
$867$			28.1414i			0.955730i
$868$		−	15.5265i		−	0.527003i
$869$		−	15.1817i		−	0.515004i
$870$	−14.8631	+	11.4983i	−0.503906	+	0.389828i
$871$		0			0
$872$		−	11.8872i		−	0.402551i
$873$	−56.2812			−1.90483
$874$	−2.48578			−0.0840828
$875$	37.9780	−	16.2602i	1.28389	−	0.549695i
$876$		−	3.78962i		−	0.128040i
$877$	−47.7890			−1.61372			−0.806859	−	0.590743i	$-0.798835\pi$
$877$	−47.7890			−1.61372			−0.806859	+	0.590743i	$0.798835\pi$
$878$	25.6139			0.864427
$879$		−	64.6861i		−	2.18181i
$880$	−1.88773	+	1.46037i	−0.0636354	+	0.0492292i
$881$	−12.4378			−0.419040			−0.209520	−	0.977804i	$-0.567190\pi$
$881$	−12.4378			−0.419040			−0.209520	+	0.977804i	$0.567190\pi$
$882$	42.7939			1.44095
$883$		−	16.6655i		−	0.560840i	−0.959877	−	0.280420i	$-0.909526\pi$
$883$		−	16.6655i		−	0.560840i	0.959877	−	0.280420i	$-0.0904737\pi$
$884$		0			0
$885$	15.1703	+	19.6097i	0.509944	+	0.659171i
$886$		−	28.4024i		−	0.954197i
$887$			39.8662i			1.33857i	0.743004	+	0.669287i	$0.233400\pi$
$887$			39.8662i			1.33857i	−0.743004	+	0.669287i	$0.766600\pi$
$888$		−	31.6913i		−	1.06349i
$889$			27.3584i			0.917572i
$890$	15.5725	−	12.0471i	0.521993	−	0.403821i
$891$		−	13.9504i		−	0.467356i
$892$	0.832022			0.0278581
$893$		−	23.2088i		−	0.776654i
$894$	−21.5016			−0.719122
$895$	5.35975	+	6.92820i	0.179157	+	0.231584i
$896$	−3.69510			−0.123445
$897$		0			0
$898$		−	22.4217i		−	0.748222i
$899$		−	11.4983i		−	0.383489i
$900$	8.07769	−	31.1266i	0.269256	−	1.03755i
$901$	−10.6896			−0.356122
$902$	−5.27082			−0.175499
$903$	−49.8898			−1.66023
$904$		−	9.26298i		−	0.308082i
$905$	19.4254	+	25.1099i	0.645722	+	0.834682i
$906$	−0.597197			−0.0198405
$907$		−	12.2772i		−	0.407658i	−0.979007	−	0.203829i	$-0.934661\pi$
$907$		−	12.2772i		−	0.407658i	0.979007	−	0.203829i	$-0.0653386\pi$
$908$	7.77546			0.258038
$909$	−16.6116			−0.550971
$910$		0			0
$911$	−47.4729			−1.57285			−0.786423	−	0.617688i	$-0.788070\pi$
$911$	−47.4729			−1.57285			−0.786423	+	0.617688i	$0.788070\pi$
$912$	6.75081			0.223542
$913$			8.73345i			0.289035i
$914$	23.5987			0.780574
$915$	82.6754	−	63.9589i	2.73317	−	2.11441i
$916$		−	7.73762i		−	0.255658i
$917$	−27.1896			−0.897880
$918$	29.5016			0.973698
$919$	−12.0621			−0.397892			−0.198946	−	0.980010i	$-0.563752\pi$
$919$	−12.0621			−0.397892			−0.198946	+	0.980010i	$0.563752\pi$
$920$	−2.00000	+	1.54723i	−0.0659380	+	0.0510106i
$921$		−	27.3075i		−	0.899812i
$922$		−	32.5063i		−	1.07054i
$923$		0			0
$924$	12.1123			0.398464
$925$	−12.9605	+	49.9421i	−0.426138	+	1.64208i
$926$	−7.70367			−0.253158
$927$		−	19.3435i		−	0.635324i
$928$	−2.73644			−0.0898280
$929$		−	19.2582i		−	0.631840i	−0.948786	−	0.315920i	$-0.897687\pi$
$929$		−	19.2582i		−	0.631840i	0.948786	−	0.315920i	$-0.102313\pi$
$930$	17.6561	+	22.8229i	0.578966	+	0.748391i
$931$		−	14.6262i		−	0.479354i
$932$			6.86070i			0.224730i
$933$			88.1446i			2.88573i
$934$			20.9339i			0.684977i
$935$	4.08818	+	5.28452i	0.133698	+	0.172822i
$936$		0			0
$937$			17.1012i			0.558671i	0.960194	+	0.279335i	$0.0901141\pi$
$937$			17.1012i			0.558671i	−0.960194	+	0.279335i	$0.909886\pi$
$938$	14.7804			0.482597
$939$	−24.0810			−0.785853
$940$	−14.4459	−	18.6733i	−0.471174	−	0.609055i
$941$			12.5077i			0.407741i	0.978998	+	0.203870i	$0.0653521\pi$
$941$			12.5077i			0.407741i	−0.978998	+	0.203870i	$0.934648\pi$
$942$	51.8672			1.68992
$943$	−5.58430			−0.181850
$944$			3.61033i			0.117506i
$945$	−68.8712	+	53.2798i	−2.24038	+	1.73319i
$946$	−4.69248			−0.152566
$947$	−60.2398			−1.95753			−0.978766	−	0.204983i	$-0.934286\pi$
$947$	−60.2398			−1.95753			−0.978766	+	0.204983i	$0.934286\pi$
$948$			43.6821i			1.41873i
$949$		0			0
$950$	−10.6385	−	2.76081i	−0.345160	−	0.0895725i
$951$			18.9713i			0.615187i
$952$			10.3441i			0.335253i
$953$			11.6460i			0.377251i	0.982049	+	0.188625i	$0.0604032\pi$
$953$			11.6460i			0.377251i	−0.982049	+	0.188625i	$0.939597\pi$
$954$		−	24.5590i		−	0.795127i
$955$	0.460832	+	0.595687i	0.0149122	+	0.0192760i
$956$		−	22.3277i		−	0.722130i
$957$	8.96985			0.289954
$958$			0.980499i			0.0316785i
$959$	−49.5312			−1.59945
$960$	5.43154	−	4.20191i	0.175302	−	0.135616i
$961$	13.3439			0.430449
$962$		0			0
$963$		−	35.2188i		−	1.13491i
$964$		−	5.68717i		−	0.183172i
$965$	−9.25625	−	11.9649i	−0.297969	−	0.385165i
$966$	12.8326			0.412883
$967$	−2.95604			−0.0950599			−0.0475300	−	0.998870i	$-0.515135\pi$
$967$	−2.95604			−0.0950599			−0.0475300	+	0.998870i	$0.515135\pi$
$968$	−9.86076			−0.316937
$969$		−	18.8982i		−	0.607099i
$970$	11.9730	+	15.4767i	0.384431	+	0.496928i
$971$	32.2421			1.03470			0.517350	−	0.855774i	$-0.326919\pi$
$971$	32.2421			1.03470			0.517350	+	0.855774i	$0.326919\pi$
$972$			8.52366i			0.273397i
$973$	−41.9700			−1.34550
$974$	38.6283			1.23773
$975$		0			0
$976$	15.2214			0.487224
$977$	−37.2619			−1.19211			−0.596056	−	0.802943i	$-0.703266\pi$
$977$	−37.2619			−1.19211			−0.596056	+	0.802943i	$0.703266\pi$
$978$			6.85358i			0.219153i
$979$	−9.39802			−0.300362
$980$	−9.10380	−	11.7679i	−0.290810	−	0.375912i
$981$		−	76.4530i		−	2.44096i
$982$	−17.7068			−0.565048
$983$	31.3081			0.998574			0.499287	−	0.866437i	$-0.333595\pi$
$983$	31.3081			0.998574			0.499287	+	0.866437i	$0.333595\pi$
$984$	15.1657			0.483464
$985$	−20.4362	−	26.4165i	−0.651151	−	0.841700i
$986$			7.66040i			0.243957i
$987$			119.814i			3.81371i
$988$		0			0
$989$	−4.97156			−0.158086
$990$	−12.1410	+	9.39245i	−0.385867	+	0.298512i
$991$	−8.16536			−0.259381			−0.129691	−	0.991555i	$-0.541398\pi$
$991$	−8.16536			−0.259381			−0.129691	+	0.991555i	$0.541398\pi$
$992$			4.20191i			0.133411i
$993$	81.8646			2.59789
$994$			45.3918i			1.43974i
$995$	0.413996	+	0.535145i	0.0131246	+	0.0169653i
$996$		−	25.1286i		−	0.796232i
$997$		−	47.5225i		−	1.50505i	−0.658563	−	0.752526i	$-0.728835\pi$
$997$		−	47.5225i		−	1.50505i	0.658563	−	0.752526i	$-0.271165\pi$
$998$		−	35.5402i		−	1.12501i
$999$		−	108.750i		−	3.44070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.e.1689.8		8
5.4	even	2		1690.2.c.f.1689.1		8
13.5	odd	4		1690.2.b.e.339.16		16
13.8	odd	4		1690.2.b.e.339.8		16
13.9	even	3		130.2.m.b.49.4	yes	8
13.10	even	6		130.2.m.a.69.1	yes	8
13.12	even	2		1690.2.c.f.1689.8		8
39.23	odd	6		1170.2.bj.b.199.2		8
39.35	odd	6		1170.2.bj.a.829.3		8
52.23	odd	6		1040.2.df.c.849.4		8
52.35	odd	6		1040.2.df.a.49.1		8
65.8	even	4		8450.2.a.cr.1.1		8
65.9	even	6		130.2.m.a.49.1	✓	8
65.18	even	4		8450.2.a.cs.1.1		8
65.22	odd	12		650.2.m.e.101.1		16
65.23	odd	12		650.2.m.e.251.8		16
65.34	odd	4		1690.2.b.e.339.9		16
65.44	odd	4		1690.2.b.e.339.1		16
65.47	even	4		8450.2.a.cs.1.8		8
65.48	odd	12		650.2.m.e.101.8		16
65.49	even	6		130.2.m.b.69.4	yes	8
65.57	even	4		8450.2.a.cr.1.8		8
65.62	odd	12		650.2.m.e.251.1		16
65.64	even	2	inner	1690.2.c.e.1689.1		8
195.74	odd	6		1170.2.bj.b.829.2		8
195.179	odd	6		1170.2.bj.a.199.3		8
260.139	odd	6		1040.2.df.c.49.4		8
260.179	odd	6		1040.2.df.a.849.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.1	✓	8	65.9	even	6
130.2.m.a.69.1	yes	8	13.10	even	6
130.2.m.b.49.4	yes	8	13.9	even	3
130.2.m.b.69.4	yes	8	65.49	even	6
650.2.m.e.101.1		16	65.22	odd	12
650.2.m.e.101.8		16	65.48	odd	12
650.2.m.e.251.1		16	65.62	odd	12
650.2.m.e.251.8		16	65.23	odd	12
1040.2.df.a.49.1		8	52.35	odd	6
1040.2.df.a.849.1		8	260.179	odd	6
1040.2.df.c.49.4		8	260.139	odd	6
1040.2.df.c.849.4		8	52.23	odd	6
1170.2.bj.a.199.3		8	195.179	odd	6
1170.2.bj.a.829.3		8	39.35	odd	6
1170.2.bj.b.199.2		8	39.23	odd	6
1170.2.bj.b.829.2		8	195.74	odd	6
1690.2.b.e.339.1		16	65.44	odd	4
1690.2.b.e.339.8		16	13.8	odd	4
1690.2.b.e.339.9		16	65.34	odd	4
1690.2.b.e.339.16		16	13.5	odd	4
1690.2.c.e.1689.1		8	65.64	even	2	inner
1690.2.c.e.1689.8		8	1.1	even	1	trivial
1690.2.c.f.1689.1		8	5.4	even	2
1690.2.c.f.1689.8		8	13.12	even	2
8450.2.a.cr.1.1		8	65.8	even	4
8450.2.a.cr.1.8		8	65.57	even	4
8450.2.a.cs.1.1		8	65.18	even	4
8450.2.a.cs.1.8		8	65.47	even	4

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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.07108i q^{3} +1.00000 q^{4} +(-1.36822 - 1.76861i) q^{5} -3.07108i q^{6} +3.69510 q^{7} -1.00000 q^{8} -6.43154 q^{9} +(1.36822 + 1.76861i) q^{10} -1.06735i q^{11} +3.07108i q^{12} -3.69510 q^{14} +(5.43154 - 4.20191i) q^{15} +1.00000 q^{16} -2.79940i q^{17} +6.43154 q^{18} -2.19819i q^{19} +(-1.36822 - 1.76861i) q^{20} +11.3479i q^{21} +1.06735i q^{22} +1.13083i q^{23} -3.07108i q^{24} +(-1.25595 + 4.83969i) q^{25} -10.5385i q^{27} +3.69510 q^{28} +2.73644 q^{29} +(-5.43154 + 4.20191i) q^{30} -4.20191i q^{31} -1.00000 q^{32} +3.27793 q^{33} +2.79940i q^{34} +(-5.05571 - 6.53518i) q^{35} -6.43154 q^{36} +10.3193 q^{37} +2.19819i q^{38} +(1.36822 + 1.76861i) q^{40} +4.93821i q^{41} -11.3479i q^{42} +4.39637i q^{43} -1.06735i q^{44} +(8.79976 + 11.3749i) q^{45} -1.13083i q^{46} +10.5582 q^{47} +3.07108i q^{48} +6.65376 q^{49} +(1.25595 - 4.83969i) q^{50} +8.59720 q^{51} -3.81853i q^{53} +10.5385i q^{54} +(-1.88773 + 1.46037i) q^{55} -3.69510 q^{56} +6.75081 q^{57} -2.73644 q^{58} +3.61033i q^{59} +(5.43154 - 4.20191i) q^{60} +15.2214 q^{61} +4.20191i q^{62} -23.7652 q^{63} +1.00000 q^{64} -3.27793 q^{66} -4.00000 q^{67} -2.79940i q^{68} -3.47288 q^{69} +(5.05571 + 6.53518i) q^{70} -12.2843i q^{71} +6.43154 q^{72} -1.23397 q^{73} -10.3193 q^{74} +(-14.8631 - 3.85712i) q^{75} -2.19819i q^{76} -3.94398i q^{77} +14.2237 q^{79} +(-1.36822 - 1.76861i) q^{80} +13.0701 q^{81} -4.93821i q^{82} -8.18235 q^{83} +11.3479i q^{84} +(-4.95105 + 3.83020i) q^{85} -4.39637i q^{86} +8.40383i q^{87} +1.06735i q^{88} -8.80497i q^{89} +(-8.79976 - 11.3749i) q^{90} +1.13083i q^{92} +12.9044 q^{93} -10.5582 q^{94} +(-3.88773 + 3.00760i) q^{95} -3.07108i q^{96} +8.75081 q^{97} -6.65376 q^{98} +6.86472i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 3 q^{5} + 10 q^{7} - 8 q^{8} - 16 q^{9} + 3 q^{10} - 10 q^{14} + 8 q^{15} + 8 q^{16} + 16 q^{18} - 3 q^{20} + 5 q^{25} + 10 q^{28} + 6 q^{29} - 8 q^{30} - 8 q^{32} - 20 q^{33}+ \cdots - 30 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 3 * q^5 + 10 * q^7 - 8 * q^8 - 16 * q^9 + 3 * q^10 - 10 * q^14 + 8 * q^15 + 8 * q^16 + 16 * q^18 - 3 * q^20 + 5 * q^25 + 10 * q^28 + 6 * q^29 - 8 * q^30 - 8 * q^32 - 20 * q^33 + 18 * q^35 - 16 * q^36 + 40 * q^37 + 3 * q^40 + 27 * q^45 - 6 * q^47 + 30 * q^49 - 5 * q^50 - 20 * q^51 - 8 * q^55 - 10 * q^56 - 24 * q^57 - 6 * q^58 + 8 * q^60 + 10 * q^61 - 50 * q^63 + 8 * q^64 + 20 * q^66 - 32 * q^67 + 4 * q^69 - 18 * q^70 + 16 * q^72 - 26 * q^73 - 40 * q^74 - 48 * q^75 + 4 * q^79 - 3 * q^80 - 16 * q^81 + 48 * q^83 - 5 * q^85 - 27 * q^90 + 36 * q^93 + 6 * q^94 - 24 * q^95 - 8 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

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Representations

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