LMFDB - Embedded newform 1470.2.d.g.1469.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.12
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.g.1469.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.321854 + 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 - 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} -1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.321854 + 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 - 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} -1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +(2.20838 + 0.350775i) q^{10} +3.78464i q^{11} +(-0.321854 + 1.70188i) q^{12} +6.40306 q^{13} +(1.30776 - 3.64551i) q^{15} +1.00000 q^{16} -5.57902i q^{17} +(2.79282 + 1.09552i) q^{18} -2.10349i q^{19} +(-2.20838 - 0.350775i) q^{20} -3.78464i q^{22} +4.70837 q^{23} +(0.321854 - 1.70188i) q^{24} +(4.75391 + 1.54929i) q^{25} -6.40306 q^{26} +(2.76332 - 4.40046i) q^{27} +7.55401i q^{29} +(-1.30776 + 3.64551i) q^{30} -3.43184i q^{31} -1.00000 q^{32} +(-6.44102 - 1.21810i) q^{33} +5.57902i q^{34} +(-2.79282 - 1.09552i) q^{36} -2.75706i q^{37} +2.10349i q^{38} +(-2.06085 + 10.8973i) q^{39} +(2.20838 + 0.350775i) q^{40} -8.77986 q^{41} +7.04507i q^{43} +3.78464i q^{44} +(5.78334 + 3.39897i) q^{45} -4.70837 q^{46} +2.55610i q^{47} +(-0.321854 + 1.70188i) q^{48} +(-4.75391 - 1.54929i) q^{50} +(9.49485 + 1.79563i) q^{51} +6.40306 q^{52} +3.08554 q^{53} +(-2.76332 + 4.40046i) q^{54} +(1.32756 - 8.35793i) q^{55} +(3.57990 + 0.677017i) q^{57} -7.55401i q^{58} +12.9727 q^{59} +(1.30776 - 3.64551i) q^{60} +10.3401i q^{61} +3.43184i q^{62} +1.00000 q^{64} +(-14.1404 - 2.24604i) q^{65} +(6.44102 + 1.21810i) q^{66} +1.48871i q^{67} -5.57902i q^{68} +(-1.51541 + 8.01310i) q^{69} +5.06254i q^{71} +(2.79282 + 1.09552i) q^{72} +3.33557 q^{73} +2.75706i q^{74} +(-4.16678 + 7.59197i) q^{75} -2.10349i q^{76} +(2.06085 - 10.8973i) q^{78} -7.07694 q^{79} +(-2.20838 - 0.350775i) q^{80} +(6.59969 + 6.11916i) q^{81} +8.77986 q^{82} +9.49058i q^{83} +(-1.95698 + 12.3206i) q^{85} -7.04507i q^{86} +(-12.8560 - 2.43129i) q^{87} -3.78464i q^{88} -10.6182 q^{89} +(-5.78334 - 3.39897i) q^{90} +4.70837 q^{92} +(5.84059 + 1.10455i) q^{93} -2.55610i q^{94} +(-0.737854 + 4.64532i) q^{95} +(0.321854 - 1.70188i) q^{96} -4.90516 q^{97} +(4.14613 - 10.5698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.321854	+	1.70188i	−0.185822	+	0.982583i
$3$	−0.321854	+	1.70188i	−0.185822	+	0.982583i
$4$	1.00000			0.500000
$5$	−2.20838	−	0.350775i	−0.987619	−	0.156871i
$5$	−2.20838	−	0.350775i	−0.987619	−	0.156871i
$6$	0.321854	−	1.70188i	0.131396	−	0.694791i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.79282	−	1.09552i	−0.930940	−	0.365172i
$10$	2.20838	+	0.350775i	0.698352	+	0.110925i
$11$			3.78464i			1.14111i	0.821259	+	0.570556i	$0.193272\pi$
$11$			3.78464i			1.14111i	−0.821259	+	0.570556i	$0.806728\pi$
$12$	−0.321854	+	1.70188i	−0.0929111	+	0.491292i
$13$	6.40306			1.77589			0.887945	−	0.459950i	$-0.152132\pi$
$13$	6.40306			1.77589			0.887945	+	0.459950i	$0.152132\pi$
$14$		0			0
$15$	1.30776	−	3.64551i	0.337661	−	0.941268i
$16$	1.00000			0.250000
$17$		−	5.57902i		−	1.35311i	−0.736391	−	0.676556i	$-0.763472\pi$
$17$		−	5.57902i		−	1.35311i	0.736391	−	0.676556i	$-0.236528\pi$
$18$	2.79282	+	1.09552i	0.658274	+	0.258215i
$19$		−	2.10349i		−	0.482575i	−0.970454	−	0.241287i	$-0.922430\pi$
$19$		−	2.10349i		−	0.482575i	0.970454	−	0.241287i	$-0.0775696\pi$
$20$	−2.20838	−	0.350775i	−0.493810	−	0.0784357i
$21$		0			0
$22$		−	3.78464i		−	0.806887i
$23$	4.70837			0.981763			0.490882	−	0.871226i	$-0.336675\pi$
$23$	4.70837			0.981763			0.490882	+	0.871226i	$0.336675\pi$
$24$	0.321854	−	1.70188i	0.0656981	−	0.347396i
$25$	4.75391	+	1.54929i	0.950783	+	0.309859i
$26$	−6.40306			−1.25574
$27$	2.76332	−	4.40046i	0.531801	−	0.846869i
$28$		0			0
$29$			7.55401i			1.40274i	0.712795	+	0.701372i	$0.247429\pi$
$29$			7.55401i			1.40274i	−0.712795	+	0.701372i	$0.752571\pi$
$30$	−1.30776	+	3.64551i	−0.238762	+	0.665577i
$31$		−	3.43184i		−	0.616377i	−0.951325	−	0.308188i	$-0.900277\pi$
$31$		−	3.43184i		−	0.616377i	0.951325	−	0.308188i	$-0.0997227\pi$
$32$	−1.00000			−0.176777
$33$	−6.44102	−	1.21810i	−1.12124	−	0.212044i
$34$			5.57902i			0.956794i
$35$		0			0
$36$	−2.79282	−	1.09552i	−0.465470	−	0.182586i
$37$		−	2.75706i		−	0.453259i	−0.973981	−	0.226629i	$-0.927229\pi$
$37$		−	2.75706i		−	0.453259i	0.973981	−	0.226629i	$-0.0727706\pi$
$38$			2.10349i			0.341232i
$39$	−2.06085	+	10.8973i	−0.330000	+	1.74496i
$40$	2.20838	+	0.350775i	0.349176	+	0.0554624i
$41$	−8.77986			−1.37118			−0.685592	−	0.727986i	$-0.740457\pi$
$41$	−8.77986			−1.37118			−0.685592	+	0.727986i	$0.740457\pi$
$42$		0			0
$43$			7.04507i			1.07436i	0.843467	+	0.537181i	$0.180511\pi$
$43$			7.04507i			1.07436i	−0.843467	+	0.537181i	$0.819489\pi$
$44$			3.78464i			0.570556i
$45$	5.78334	+	3.39897i	0.862129	+	0.506689i
$46$	−4.70837			−0.694211
$47$			2.55610i			0.372845i	0.982470	+	0.186422i	$0.0596893\pi$
$47$			2.55610i			0.372845i	−0.982470	+	0.186422i	$0.940311\pi$
$48$	−0.321854	+	1.70188i	−0.0464556	+	0.245646i
$49$		0			0
$50$	−4.75391	−	1.54929i	−0.672305	−	0.219103i
$51$	9.49485	+	1.79563i	1.32955	+	0.251438i
$52$	6.40306			0.887945
$53$	3.08554			0.423831			0.211916	−	0.977288i	$-0.432030\pi$
$53$	3.08554			0.423831			0.211916	+	0.977288i	$0.432030\pi$
$54$	−2.76332	+	4.40046i	−0.376040	+	0.598827i
$55$	1.32756	−	8.35793i	0.179008	−	1.12698i
$56$		0			0
$57$	3.57990	+	0.677017i	0.474170	+	0.0896731i
$58$		−	7.55401i		−	0.991890i
$59$	12.9727			1.68890			0.844452	−	0.535631i	$-0.179926\pi$
$59$	12.9727			1.68890			0.844452	+	0.535631i	$0.179926\pi$
$60$	1.30776	−	3.64551i	0.168830	−	0.470634i
$61$			10.3401i			1.32391i	0.749542	+	0.661957i	$0.230274\pi$
$61$			10.3401i			1.32391i	−0.749542	+	0.661957i	$0.769726\pi$
$62$			3.43184i			0.435844i
$63$		0			0
$64$	1.00000			0.125000
$65$	−14.1404	−	2.24604i	−1.75390	−	0.278587i
$66$	6.44102	+	1.21810i	0.792834	+	0.149938i
$67$			1.48871i			0.181875i	0.995857	+	0.0909373i	$0.0289863\pi$
$67$			1.48871i			0.181875i	−0.995857	+	0.0909373i	$0.971014\pi$
$68$		−	5.57902i		−	0.676556i
$69$	−1.51541	+	8.01310i	−0.182433	+	0.964664i
$70$		0			0
$71$			5.06254i			0.600812i	0.953811	+	0.300406i	$0.0971222\pi$
$71$			5.06254i			0.600812i	−0.953811	+	0.300406i	$0.902878\pi$
$72$	2.79282	+	1.09552i	0.329137	+	0.129108i
$73$	3.33557			0.390399			0.195199	−	0.980764i	$-0.437465\pi$
$73$	3.33557			0.390399			0.195199	+	0.980764i	$0.437465\pi$
$74$			2.75706i			0.320502i
$75$	−4.16678	+	7.59197i	−0.481138	+	0.876645i
$76$		−	2.10349i		−	0.241287i
$77$		0			0
$78$	2.06085	−	10.8973i	0.233345	−	1.23387i
$79$	−7.07694			−0.796218			−0.398109	−	0.917338i	$-0.630333\pi$
$79$	−7.07694			−0.796218			−0.398109	+	0.917338i	$0.630333\pi$
$80$	−2.20838	−	0.350775i	−0.246905	−	0.0392179i
$81$	6.59969	+	6.11916i	0.733299	+	0.679906i
$82$	8.77986			0.969573
$83$			9.49058i			1.04173i	0.853640	+	0.520863i	$0.174390\pi$
$83$			9.49058i			1.04173i	−0.853640	+	0.520863i	$0.825610\pi$
$84$		0			0
$85$	−1.95698	+	12.3206i	−0.212265	+	1.33636i
$86$		−	7.04507i		−	0.759689i
$87$	−12.8560	−	2.43129i	−1.37831	−	0.260661i
$88$		−	3.78464i		−	0.403444i
$89$	−10.6182			−1.12552			−0.562761	−	0.826620i	$-0.690261\pi$
$89$	−10.6182			−1.12552			−0.562761	+	0.826620i	$0.690261\pi$
$90$	−5.78334	−	3.39897i	−0.609617	−	0.358283i
$91$		0			0
$92$	4.70837			0.490882
$93$	5.84059	+	1.10455i	0.605641	+	0.114537i
$94$		−	2.55610i		−	0.263641i
$95$	−0.737854	+	4.64532i	−0.0757022	+	0.476600i
$96$	0.321854	−	1.70188i	0.0328491	−	0.173698i
$97$	−4.90516			−0.498044			−0.249022	−	0.968498i	$-0.580109\pi$
$97$	−4.90516			−0.498044			−0.249022	+	0.968498i	$0.580109\pi$
$98$		0			0
$99$	4.14613	−	10.5698i	0.416702	−	1.06231i
$100$	4.75391	+	1.54929i	0.475391	+	0.154929i
$101$	5.63646			0.560849			0.280424	−	0.959876i	$-0.409525\pi$
$101$	5.63646			0.560849			0.280424	+	0.959876i	$0.409525\pi$
$102$	−9.49485	−	1.79563i	−0.940130	−	0.177794i
$103$	6.76706			0.666779			0.333389	−	0.942789i	$-0.391808\pi$
$103$	6.76706			0.666779			0.333389	+	0.942789i	$0.391808\pi$
$104$	−6.40306			−0.627872
$105$		0			0
$106$	−3.08554			−0.299694
$107$	9.09162			0.878920			0.439460	−	0.898262i	$-0.355170\pi$
$107$	9.09162			0.878920			0.439460	+	0.898262i	$0.355170\pi$
$108$	2.76332	−	4.40046i	0.265901	−	0.423435i
$109$	−15.3307			−1.46842			−0.734208	−	0.678925i	$-0.762446\pi$
$109$	−15.3307			−1.46842			−0.734208	+	0.678925i	$0.762446\pi$
$110$	−1.32756	+	8.35793i	−0.126578	+	0.796897i
$111$	4.69220	+	0.887371i	0.445364	+	0.0842255i
$112$		0			0
$113$	2.83057			0.266277			0.133139	−	0.991097i	$-0.457494\pi$
$113$	2.83057			0.266277			0.133139	+	0.991097i	$0.457494\pi$
$114$	−3.57990	−	0.677017i	−0.335289	−	0.0634085i
$115$	−10.3979	−	1.65158i	−0.969608	−	0.154011i
$116$			7.55401i			0.701372i
$117$	−17.8826	−	7.01465i	−1.65325	−	0.648505i
$118$	−12.9727			−1.19424
$119$		0			0
$120$	−1.30776	+	3.64551i	−0.119381	+	0.332788i
$121$	−3.32348			−0.302135
$122$		−	10.3401i		−	0.936148i
$123$	2.82583	−	14.9423i	0.254797	−	1.34730i
$124$		−	3.43184i		−	0.308188i
$125$	−9.95501	−	5.08899i	−0.890403	−	0.455173i
$126$		0			0
$127$			16.6271i			1.47542i	0.675119	+	0.737709i	$0.264092\pi$
$127$			16.6271i			1.47542i	−0.675119	+	0.737709i	$0.735908\pi$
$128$	−1.00000			−0.0883883
$129$	−11.9899	−	2.26748i	−1.05565	−	0.199640i
$130$	14.1404	+	2.24604i	1.24020	+	0.196990i
$131$	0.210484			0.0183901			0.00919504	−	0.999958i	$-0.497073\pi$
$131$	0.210484			0.0183901			0.00919504	+	0.999958i	$0.497073\pi$
$132$	−6.44102	−	1.21810i	−0.560618	−	0.106022i
$133$		0			0
$134$		−	1.48871i		−	0.128605i
$135$	−7.64604	+	8.74860i	−0.658067	+	0.752960i
$136$			5.57902i			0.478397i
$137$	−3.87172			−0.330784			−0.165392	−	0.986228i	$-0.552889\pi$
$137$	−3.87172			−0.330784			−0.165392	+	0.986228i	$0.552889\pi$
$138$	1.51541	−	8.01310i	0.129000	−	0.682121i
$139$			17.4338i			1.47871i	0.673314	+	0.739357i	$0.264870\pi$
$139$			17.4338i			1.47871i	−0.673314	+	0.739357i	$0.735130\pi$
$140$		0			0
$141$	−4.35018	−	0.822689i	−0.366351	−	0.0692829i
$142$		−	5.06254i		−	0.424839i
$143$			24.2333i			2.02649i
$144$	−2.79282	−	1.09552i	−0.232735	−	0.0912929i
$145$	2.64976	−	16.6821i	0.220051	−	1.38538i
$146$	−3.33557			−0.276053
$147$		0			0
$148$		−	2.75706i		−	0.226629i
$149$			8.65775i			0.709270i	0.935005	+	0.354635i	$0.115395\pi$
$149$			8.65775i			0.709270i	−0.935005	+	0.354635i	$0.884605\pi$
$150$	4.16678	−	7.59197i	0.340216	−	0.619881i
$151$	16.8301			1.36961			0.684806	−	0.728726i	$-0.259887\pi$
$151$	16.8301			1.36961			0.684806	+	0.728726i	$0.259887\pi$
$152$			2.10349i			0.170616i
$153$	−6.11191	+	15.5812i	−0.494118	+	1.25967i
$154$		0			0
$155$	−1.20380	+	7.57882i	−0.0966919	+	0.608745i
$156$	−2.06085	+	10.8973i	−0.165000	+	0.872480i
$157$	−6.23745			−0.497802			−0.248901	−	0.968529i	$-0.580069\pi$
$157$	−6.23745			−0.497802			−0.248901	+	0.968529i	$0.580069\pi$
$158$	7.07694			0.563011
$159$	−0.993092	+	5.25123i	−0.0787573	+	0.416450i
$160$	2.20838	+	0.350775i	0.174588	+	0.0277312i
$161$		0			0
$162$	−6.59969	−	6.11916i	−0.518521	−	0.480766i
$163$		−	3.22815i		−	0.252848i	−0.991976	−	0.126424i	$-0.959650\pi$
$163$		−	3.22815i		−	0.252848i	0.991976	−	0.126424i	$-0.0403500\pi$
$164$	−8.77986			−0.685592
$165$	13.7970	+	4.94938i	1.07409	+	0.385309i
$166$		−	9.49058i		−	0.736612i
$167$		−	10.9301i		−	0.845797i	−0.906177	−	0.422899i	$-0.861013\pi$
$167$		−	10.9301i		−	0.845797i	0.906177	−	0.422899i	$-0.138987\pi$
$168$		0			0
$169$	27.9992			2.15379
$170$	1.95698	−	12.3206i	0.150094	−	0.944948i
$171$	−2.30441	+	5.87468i	−0.176223	+	0.449248i
$172$			7.04507i			0.537181i
$173$			4.83283i			0.367434i	0.982979	+	0.183717i	$0.0588129\pi$
$173$			4.83283i			0.367434i	−0.982979	+	0.183717i	$0.941187\pi$
$174$	12.8560	+	2.43129i	0.974614	+	0.184315i
$175$		0			0
$176$			3.78464i			0.285278i
$177$	−4.17532	+	22.0781i	−0.313836	+	1.65949i
$178$	10.6182			0.795864
$179$		−	8.55562i		−	0.639477i	−0.947506	−	0.319739i	$-0.896405\pi$
$179$		−	8.55562i		−	0.639477i	0.947506	−	0.319739i	$-0.103595\pi$
$180$	5.78334	+	3.39897i	0.431065	+	0.253344i
$181$		−	11.2205i		−	0.834013i	−0.908904	−	0.417006i	$-0.863079\pi$
$181$		−	11.2205i		−	0.834013i	0.908904	−	0.417006i	$-0.136921\pi$
$182$		0			0
$183$	−17.5976	−	3.32800i	−1.30086	−	0.246013i
$184$	−4.70837			−0.347106
$185$	−0.967110	+	6.08865i	−0.0711033	+	0.447647i
$186$	−5.84059	−	1.10455i	−0.428253	−	0.0809895i
$187$	21.1146			1.54405
$188$			2.55610i			0.186422i
$189$		0			0
$190$	0.737854	−	4.64532i	0.0535295	−	0.337007i
$191$			2.85343i			0.206467i	0.994657	+	0.103234i	$0.0329189\pi$
$191$			2.85343i			0.206467i	−0.994657	+	0.103234i	$0.967081\pi$
$192$	−0.321854	+	1.70188i	−0.0232278	+	0.122823i
$193$			26.7793i			1.92762i	0.266598	+	0.963808i	$0.414100\pi$
$193$			26.7793i			1.92762i	−0.266598	+	0.963808i	$0.585900\pi$
$194$	4.90516			0.352170
$195$	8.37364	−	23.3425i	0.599649	−	1.67159i
$196$		0			0
$197$	14.7242			1.04905			0.524527	−	0.851394i	$-0.324242\pi$
$197$	14.7242			1.04905			0.524527	+	0.851394i	$0.324242\pi$
$198$	−4.14613	+	10.5698i	−0.294653	+	0.751164i
$199$			16.4657i			1.16722i	0.812032	+	0.583612i	$0.198361\pi$
$199$			16.4657i			1.16722i	−0.812032	+	0.583612i	$0.801639\pi$
$200$	−4.75391	−	1.54929i	−0.336152	−	0.109552i
$201$	−2.53361	−	0.479146i	−0.178707	−	0.0337964i
$202$	−5.63646			−0.396580
$203$		0			0
$204$	9.49485	+	1.79563i	0.664773	+	0.125719i
$205$	19.3893	+	3.07976i	1.35421	+	0.215100i
$206$	−6.76706			−0.471484
$207$	−13.1496	−	5.15809i	−0.913963	−	0.358512i
$208$	6.40306			0.443973
$209$	7.96096			0.550671
$210$		0			0
$211$	−15.8206			−1.08913			−0.544567	−	0.838717i	$-0.683306\pi$
$211$	−15.8206			−1.08913			−0.544567	+	0.838717i	$0.683306\pi$
$212$	3.08554			0.211916
$213$	−8.61585	−	1.62940i	−0.590348	−	0.111644i
$214$	−9.09162			−0.621490
$215$	2.47124	−	15.5582i	0.168537	−	1.06106i
$216$	−2.76332	+	4.40046i	−0.188020	+	0.299413i
$217$		0			0
$218$	15.3307			1.03833
$219$	−1.07356	+	5.67675i	−0.0725447	+	0.383599i
$220$	1.32756	−	8.35793i	0.0895039	−	0.563492i
$221$		−	35.7228i		−	2.40298i
$222$	−4.69220	−	0.887371i	−0.314920	−	0.0595565i
$223$	21.9853			1.47224			0.736122	−	0.676849i	$-0.236655\pi$
$223$	21.9853			1.47224			0.736122	+	0.676849i	$0.236655\pi$
$224$		0			0
$225$	−11.5796	−	9.53488i	−0.771970	−	0.635659i
$226$	−2.83057			−0.188286
$227$		−	27.5101i		−	1.82591i	−0.408063	−	0.912954i	$-0.633796\pi$
$227$		−	27.5101i		−	1.82591i	0.408063	−	0.912954i	$-0.366204\pi$
$228$	3.57990	+	0.677017i	0.237085	+	0.0448366i
$229$			16.1836i			1.06944i	0.845029	+	0.534720i	$0.179583\pi$
$229$			16.1836i			1.06944i	−0.845029	+	0.534720i	$0.820417\pi$
$230$	10.3979	+	1.65158i	0.685616	+	0.108902i
$231$		0			0
$232$		−	7.55401i		−	0.495945i
$233$	17.8328			1.16827			0.584133	−	0.811658i	$-0.301435\pi$
$233$	17.8328			1.16827			0.584133	+	0.811658i	$0.301435\pi$
$234$	17.8826	+	7.01465i	1.16902	+	0.458562i
$235$	0.896615	−	5.64484i	0.0584887	−	0.368229i
$236$	12.9727			0.844452
$237$	2.27774	−	12.0441i	0.147955	−	0.782351i
$238$		0			0
$239$		−	18.4508i		−	1.19348i	−0.802433	−	0.596742i	$-0.796462\pi$
$239$		−	18.4508i		−	1.19348i	0.802433	−	0.596742i	$-0.203538\pi$
$240$	1.30776	−	3.64551i	0.0844152	−	0.235317i
$241$		−	13.4629i		−	0.867223i	−0.901100	−	0.433612i	$-0.857239\pi$
$241$		−	13.4629i		−	0.867223i	0.901100	−	0.433612i	$-0.142761\pi$
$242$	3.32348			0.213641
$243$	−12.5382	+	9.26244i	−0.804328	+	0.594186i
$244$			10.3401i			0.661957i
$245$		0			0
$246$	−2.82583	+	14.9423i	−0.180168	+	0.952687i
$247$		−	13.4688i		−	0.857000i
$248$			3.43184i			0.217922i
$249$	−16.1519	−	3.05458i	−1.02358	−	0.193576i
$250$	9.95501	+	5.08899i	0.629610	+	0.321856i
$251$	21.5154			1.35804			0.679020	−	0.734120i	$-0.262405\pi$
$251$	21.5154			1.35804			0.679020	+	0.734120i	$0.262405\pi$
$252$		0			0
$253$			17.8195i			1.12030i
$254$		−	16.6271i		−	1.04328i
$255$	−20.3384	−	7.29600i	−1.27364	−	0.456893i
$256$	1.00000			0.0625000
$257$			13.2419i			0.826004i	0.910730	+	0.413002i	$0.135520\pi$
$257$			13.2419i			0.826004i	−0.910730	+	0.413002i	$0.864480\pi$
$258$	11.9899	+	2.26748i	0.746458	+	0.141167i
$259$		0			0
$260$	−14.1404	−	2.24604i	−0.876951	−	0.139293i
$261$	8.27553	−	21.0970i	0.512243	−	1.30587i
$262$	−0.210484			−0.0130038
$263$	−15.5680			−0.959961			−0.479981	−	0.877279i	$-0.659356\pi$
$263$	−15.5680			−0.959961			−0.479981	+	0.877279i	$0.659356\pi$
$264$	6.44102	+	1.21810i	0.396417	+	0.0749688i
$265$	−6.81405	−	1.08233i	−0.418584	−	0.0664871i
$266$		0			0
$267$	3.41749	−	18.0709i	0.209147	−	1.10592i
$268$			1.48871i			0.0909373i
$269$	−8.37779			−0.510803			−0.255401	−	0.966835i	$-0.582208\pi$
$269$	−8.37779			−0.510803			−0.255401	+	0.966835i	$0.582208\pi$
$270$	7.64604	−	8.74860i	0.465323	−	0.532423i
$271$		−	0.305606i		−	0.0185642i	−0.999957	−	0.00928212i	$-0.997045\pi$
$271$		−	0.305606i		−	0.0185642i	0.999957	−	0.00928212i	$-0.00295463\pi$
$272$		−	5.57902i		−	0.338278i
$273$		0			0
$274$	3.87172			0.233899
$275$	−5.86351	+	17.9918i	−0.353583	+	1.08495i
$276$	−1.51541	+	8.01310i	−0.0912167	+	0.482332i
$277$			20.9930i			1.26135i	0.776047	+	0.630675i	$0.217222\pi$
$277$			20.9930i			1.26135i	−0.776047	+	0.630675i	$0.782778\pi$
$278$		−	17.4338i		−	1.04561i
$279$	−3.75963	+	9.58451i	−0.225083	+	0.573810i
$280$		0			0
$281$		−	5.67638i		−	0.338624i	−0.985562	−	0.169312i	$-0.945845\pi$
$281$		−	5.67638i		−	0.338624i	0.985562	−	0.169312i	$-0.0541546\pi$
$282$	4.35018	+	0.822689i	0.259049	+	0.0489904i
$283$	−15.8411			−0.941658			−0.470829	−	0.882224i	$-0.656045\pi$
$283$	−15.8411			−0.941658			−0.470829	+	0.882224i	$0.656045\pi$
$284$			5.06254i			0.300406i
$285$	−7.66832	−	2.75086i	−0.454232	−	0.162947i
$286$		−	24.2333i		−	1.43294i
$287$		0			0
$288$	2.79282	+	1.09552i	0.164569	+	0.0645539i
$289$	−14.1255			−0.830911
$290$	−2.64976	+	16.6821i	−0.155599	+	0.979609i
$291$	1.57875	−	8.34802i	0.0925477	−	0.489370i
$292$	3.33557			0.195199
$293$		−	23.2810i		−	1.36009i	−0.733170	−	0.680045i	$-0.761960\pi$
$293$		−	23.2810i		−	1.36009i	0.733170	−	0.680045i	$-0.238040\pi$
$294$		0			0
$295$	−28.6487	−	4.55051i	−1.66799	−	0.264941i
$296$			2.75706i			0.160251i
$297$	16.6542	+	10.4582i	0.966372	+	0.606844i
$298$		−	8.65775i		−	0.501530i
$299$	30.1480			1.74350
$300$	−4.16678	+	7.59197i	−0.240569	+	0.438322i
$301$		0			0
$302$	−16.8301			−0.968462
$303$	−1.81412	+	9.59260i	−0.104218	+	0.551081i
$304$		−	2.10349i		−	0.120644i
$305$	3.62705	−	22.8349i	0.207684	−	1.30752i
$306$	6.11191	−	15.5812i	0.349394	−	0.890718i
$307$	20.2759			1.15721			0.578604	−	0.815608i	$-0.303598\pi$
$307$	20.2759			1.15721			0.578604	+	0.815608i	$0.303598\pi$
$308$		0			0
$309$	−2.17800	+	11.5168i	−0.123902	+	0.655165i
$310$	1.20380	−	7.57882i	0.0683715	−	0.430448i
$311$	−11.8199			−0.670244			−0.335122	−	0.942175i	$-0.608778\pi$
$311$	−11.8199			−0.670244			−0.335122	+	0.942175i	$0.608778\pi$
$312$	2.06085	−	10.8973i	0.116673	−	0.616937i
$313$	4.00427			0.226335			0.113167	−	0.993576i	$-0.463900\pi$
$313$	4.00427			0.226335			0.113167	+	0.993576i	$0.463900\pi$
$314$	6.23745			0.351999
$315$		0			0
$316$	−7.07694			−0.398109
$317$	0.211278			0.0118665			0.00593327	−	0.999982i	$-0.498111\pi$
$317$	0.211278			0.0118665			0.00593327	+	0.999982i	$0.498111\pi$
$318$	0.993092	−	5.25123i	0.0556898	−	0.294474i
$319$	−28.5892			−1.60069
$320$	−2.20838	−	0.350775i	−0.123452	−	0.0196089i
$321$	−2.92617	+	15.4729i	−0.163323	+	0.863612i
$322$		0			0
$323$	−11.7354			−0.652977
$324$	6.59969	+	6.11916i	0.366650	+	0.339953i
$325$	30.4396	+	9.92022i	1.68849	+	0.550275i
$326$			3.22815i			0.178790i
$327$	4.93424	−	26.0911i	0.272864	−	1.44284i
$328$	8.77986			0.484787
$329$		0			0
$330$	−13.7970	−	4.94938i	−0.759497	−	0.272454i
$331$	−4.13421			−0.227237			−0.113618	−	0.993524i	$-0.536244\pi$
$331$	−4.13421			−0.227237			−0.113618	+	0.993524i	$0.536244\pi$
$332$			9.49058i			0.520863i
$333$	−3.02041	+	7.69999i	−0.165517	+	0.421957i
$334$			10.9301i			0.598069i
$335$	0.522202	−	3.28764i	0.0285310	−	0.179623i
$336$		0			0
$337$		−	1.99207i		−	0.108515i	−0.998527	−	0.0542576i	$-0.982721\pi$
$337$		−	1.99207i		−	0.108515i	0.998527	−	0.0542576i	$-0.0172792\pi$
$338$	−27.9992			−1.52296
$339$	−0.911028	+	4.81730i	−0.0494803	+	0.261640i
$340$	−1.95698	+	12.3206i	−0.106132	+	0.668179i
$341$	12.9883			0.703354
$342$	2.30441	−	5.87468i	0.124608	−	0.317666i
$343$		0			0
$344$		−	7.04507i		−	0.379844i
$345$	6.15740	−	17.1644i	0.331503	−	0.924102i
$346$		−	4.83283i		−	0.259815i
$347$	21.4429			1.15111			0.575557	−	0.817761i	$-0.304785\pi$
$347$	21.4429			1.15111			0.575557	+	0.817761i	$0.304785\pi$
$348$	−12.8560	−	2.43129i	−0.689157	−	0.130331i
$349$			17.1982i			0.920598i	0.887764	+	0.460299i	$0.152258\pi$
$349$			17.1982i			0.920598i	−0.887764	+	0.460299i	$0.847742\pi$
$350$		0			0
$351$	17.6937	−	28.1764i	0.944420	−	1.50395i
$352$		−	3.78464i		−	0.201722i
$353$		−	3.05545i		−	0.162625i	−0.996689	−	0.0813125i	$-0.974089\pi$
$353$		−	3.05545i		−	0.162625i	0.996689	−	0.0813125i	$-0.0259112\pi$
$354$	4.17532	−	22.0781i	0.221916	−	1.17344i
$355$	1.77581	−	11.1800i	0.0942503	−	0.593374i
$356$	−10.6182			−0.562761
$357$		0			0
$358$			8.55562i			0.452179i
$359$		−	15.3615i		−	0.810751i	−0.914150	−	0.405375i	$-0.867141\pi$
$359$		−	15.3615i		−	0.810751i	0.914150	−	0.405375i	$-0.132859\pi$
$360$	−5.78334	−	3.39897i	−0.304809	−	0.179141i
$361$	14.5753			0.767122
$362$			11.2205i			0.589736i
$363$	1.06967	−	5.65618i	0.0561433	−	0.296872i
$364$		0			0
$365$	−7.36621	−	1.17003i	−0.385565	−	0.0612424i
$366$	17.5976	+	3.32800i	0.919844	+	0.173957i
$367$	4.12440			0.215292			0.107646	−	0.994189i	$-0.465669\pi$
$367$	4.12440			0.215292			0.107646	+	0.994189i	$0.465669\pi$
$368$	4.70837			0.245441
$369$	24.5206	+	9.61847i	1.27649	+	0.500718i
$370$	0.967110	−	6.08865i	0.0502777	−	0.316534i
$371$		0			0
$372$	5.84059	+	1.10455i	0.302821	+	0.0572683i
$373$		−	23.8319i		−	1.23397i	−0.786976	−	0.616983i	$-0.788355\pi$
$373$		−	23.8319i		−	1.23397i	0.786976	−	0.616983i	$-0.211645\pi$
$374$	−21.1146			−1.09181
$375$	11.8649	−	15.3044i	0.612702	−	0.790314i
$376$		−	2.55610i		−	0.131821i
$377$			48.3688i			2.49112i
$378$		0			0
$379$	29.0694			1.49319			0.746596	−	0.665277i	$-0.231687\pi$
$379$	29.0694			1.49319			0.746596	+	0.665277i	$0.231687\pi$
$380$	−0.737854	+	4.64532i	−0.0378511	+	0.238300i
$381$	−28.2974	−	5.35150i	−1.44972	−	0.274165i
$382$		−	2.85343i		−	0.145994i
$383$			19.4986i			0.996333i	0.867081	+	0.498166i	$0.165993\pi$
$383$			19.4986i			0.996333i	−0.867081	+	0.498166i	$0.834007\pi$
$384$	0.321854	−	1.70188i	0.0164245	−	0.0868489i
$385$		0			0
$386$		−	26.7793i		−	1.36303i
$387$	7.71798	−	19.6756i	0.392327	−	1.00017i
$388$	−4.90516			−0.249022
$389$			6.51453i			0.330300i	0.986268	+	0.165150i	$0.0528108\pi$
$389$			6.51453i			0.330300i	−0.986268	+	0.165150i	$0.947189\pi$
$390$	−8.37364	+	23.3425i	−0.424016	+	1.18199i
$391$		−	26.2681i		−	1.32844i
$392$		0			0
$393$	−0.0677451	+	0.358220i	−0.00341729	+	0.0180698i
$394$	−14.7242			−0.741793
$395$	15.6286	+	2.48242i	0.786360	+	0.124904i
$396$	4.14613	−	10.5698i	0.208351	−	0.531153i
$397$	−33.0474			−1.65860			−0.829300	−	0.558803i	$-0.811261\pi$
$397$	−33.0474			−1.65860			−0.829300	+	0.558803i	$0.811261\pi$
$398$		−	16.4657i		−	0.825352i
$399$		0			0
$400$	4.75391	+	1.54929i	0.237696	+	0.0774646i
$401$			13.3058i			0.664461i	0.943198	+	0.332230i	$0.107801\pi$
$401$			13.3058i			0.664461i	−0.943198	+	0.332230i	$0.892199\pi$
$402$	2.53361	+	0.479146i	0.126365	+	0.0238976i
$403$		−	21.9743i		−	1.09462i
$404$	5.63646			0.280424
$405$	−12.4282	−	15.8284i	−0.617562	−	0.786522i
$406$		0			0
$407$	10.4345			0.517218
$408$	−9.49485	−	1.79563i	−0.470065	−	0.0888969i
$409$			24.4460i			1.20877i	0.796691	+	0.604387i	$0.206582\pi$
$409$			24.4460i			1.20877i	−0.796691	+	0.604387i	$0.793418\pi$
$410$	−19.3893	−	3.07976i	−0.957569	−	0.152098i
$411$	1.24613	−	6.58923i	0.0614670	−	0.325023i
$412$	6.76706			0.333389
$413$		0			0
$414$	13.1496	+	5.15809i	0.646269	+	0.253506i
$415$	3.32906	−	20.9588i	0.163417	−	1.02883i
$416$	−6.40306			−0.313936
$417$	−29.6703	−	5.61112i	−1.45296	−	0.274778i
$418$	−7.96096			−0.389383
$419$	27.0524			1.32160			0.660799	−	0.750563i	$-0.270217\pi$
$419$	27.0524			1.32160			0.660799	+	0.750563i	$0.270217\pi$
$420$		0			0
$421$	5.39064			0.262724			0.131362	−	0.991334i	$-0.458065\pi$
$421$	5.39064			0.262724			0.131362	+	0.991334i	$0.458065\pi$
$422$	15.8206			0.770134
$423$	2.80024	−	7.13872i	0.136152	−	0.347096i
$424$	−3.08554			−0.149847
$425$	8.64354	−	26.5222i	0.419273	−	1.28652i
$426$	8.61585	+	1.62940i	0.417439	+	0.0789445i
$427$		0			0
$428$	9.09162			0.439460
$429$	−41.2422	−	7.79957i	−1.99119	−	0.376567i
$430$	−2.47124	+	15.5582i	−0.119174	+	0.750283i
$431$			3.21022i			0.154631i	0.997007	+	0.0773155i	$0.0246349\pi$
$431$			3.21022i			0.154631i	−0.997007	+	0.0773155i	$0.975365\pi$
$432$	2.76332	−	4.40046i	0.132950	−	0.211717i
$433$	−39.7769			−1.91155			−0.955777	−	0.294092i	$-0.904983\pi$
$433$	−39.7769			−1.91155			−0.955777	+	0.294092i	$0.904983\pi$
$434$		0			0
$435$	27.5382	+	9.87879i	1.32036	+	0.473652i
$436$	−15.3307			−0.734208
$437$		−	9.90403i		−	0.473774i
$438$	1.07356	−	5.67675i	0.0512969	−	0.271246i
$439$		−	26.5159i		−	1.26553i	−0.774342	−	0.632767i	$-0.781919\pi$
$439$		−	26.5159i		−	1.26553i	0.774342	−	0.632767i	$-0.218081\pi$
$440$	−1.32756	+	8.35793i	−0.0632888	+	0.398449i
$441$		0			0
$442$			35.7228i			1.69916i
$443$	−21.5549			−1.02410			−0.512052	−	0.858955i	$-0.671114\pi$
$443$	−21.5549			−1.02410			−0.512052	+	0.858955i	$0.671114\pi$
$444$	4.69220	+	0.887371i	0.222682	+	0.0421128i
$445$	23.4489	+	3.72459i	1.11159	+	0.176562i
$446$	−21.9853			−1.04103
$447$	−14.7345	−	2.78653i	−0.696917	−	0.131798i
$448$		0			0
$449$		−	1.27232i		−	0.0600445i	−0.999549	−	0.0300222i	$-0.990442\pi$
$449$		−	1.27232i		−	0.0600445i	0.999549	−	0.0300222i	$-0.00955781\pi$
$450$	11.5796	+	9.53488i	0.545865	+	0.449479i
$451$		−	33.2286i		−	1.56467i
$452$	2.83057			0.133139
$453$	−5.41682	+	28.6428i	−0.254504	+	1.34576i
$454$			27.5101i			1.29111i
$455$		0			0
$456$	−3.57990	−	0.677017i	−0.167644	−	0.0317042i
$457$			7.38402i			0.345410i	0.984974	+	0.172705i	$0.0552507\pi$
$457$			7.38402i			0.345410i	−0.984974	+	0.172705i	$0.944749\pi$
$458$		−	16.1836i		−	0.756209i
$459$	−24.5503	−	15.4166i	−1.14591	−	0.719586i
$460$	−10.3979	−	1.65158i	−0.484804	−	0.0770053i
$461$	14.6635			0.682950			0.341475	−	0.939891i	$-0.389074\pi$
$461$	14.6635			0.682950			0.341475	+	0.939891i	$0.389074\pi$
$462$		0			0
$463$		−	27.8566i		−	1.29460i	−0.762233	−	0.647302i	$-0.775897\pi$
$463$		−	27.8566i		−	1.29460i	0.762233	−	0.647302i	$-0.224103\pi$
$464$			7.55401i			0.350686i
$465$	−12.5108	−	4.48801i	−0.580175	−	0.208126i
$466$	−17.8328			−0.826089
$467$		−	17.7307i		−	0.820478i	−0.911978	−	0.410239i	$-0.865445\pi$
$467$		−	17.7307i		−	0.820478i	0.911978	−	0.410239i	$-0.134555\pi$
$468$	−17.8826	−	7.01465i	−0.826624	−	0.324252i
$469$		0			0
$470$	−0.896615	+	5.64484i	−0.0413578	+	0.260377i
$471$	2.00754	−	10.6154i	0.0925028	−	0.489132i
$472$	−12.9727			−0.597118
$473$	−26.6630			−1.22597
$474$	−2.27774	+	12.0441i	−0.104620	+	0.553205i
$475$	3.25893	−	9.99983i	0.149530	−	0.458824i
$476$		0			0
$477$	−8.61736	−	3.38026i	−0.394562	−	0.154771i
$478$			18.4508i			0.843920i
$479$	4.63276			0.211676			0.105838	−	0.994383i	$-0.466247\pi$
$479$	4.63276			0.211676			0.105838	+	0.994383i	$0.466247\pi$
$480$	−1.30776	+	3.64551i	−0.0596906	+	0.166394i
$481$		−	17.6537i		−	0.804937i
$482$			13.4629i			0.613220i
$483$		0			0
$484$	−3.32348			−0.151067
$485$	10.8325	+	1.72061i	0.491878	+	0.0781289i
$486$	12.5382	−	9.26244i	0.568746	−	0.420153i
$487$		−	43.6309i		−	1.97711i	−0.150876	−	0.988553i	$-0.548209\pi$
$487$		−	43.6309i		−	1.97711i	0.150876	−	0.988553i	$-0.451791\pi$
$488$		−	10.3401i		−	0.468074i
$489$	5.49393	+	1.03899i	0.248444	+	0.0469848i
$490$		0			0
$491$			29.4021i			1.32690i	0.748221	+	0.663449i	$0.230908\pi$
$491$			29.4021i			1.32690i	−0.748221	+	0.663449i	$0.769092\pi$
$492$	2.82583	−	14.9423i	0.127398	−	0.673651i
$493$	42.1440			1.89807
$494$			13.4688i			0.605990i
$495$	−12.8639	+	21.8878i	−0.578188	+	0.983785i
$496$		−	3.43184i		−	0.154094i
$497$		0			0
$498$	16.1519	+	3.05458i	0.723782	+	0.136879i
$499$	21.1826			0.948264			0.474132	−	0.880454i	$-0.342762\pi$
$499$	21.1826			0.948264			0.474132	+	0.880454i	$0.342762\pi$
$500$	−9.95501	−	5.08899i	−0.445202	−	0.227586i
$501$	18.6018	+	3.51790i	0.831067	+	0.157168i
$502$	−21.5154			−0.960279
$503$		−	9.61653i		−	0.428780i	−0.976748	−	0.214390i	$-0.931224\pi$
$503$		−	9.61653i		−	0.428780i	0.976748	−	0.214390i	$-0.0687763\pi$
$504$		0			0
$505$	−12.4475	−	1.97713i	−0.553905	−	0.0879812i
$506$		−	17.8195i		−	0.792172i
$507$	−9.01165	+	47.6514i	−0.400221	+	2.11627i
$508$			16.6271i			0.737709i
$509$	−10.1694			−0.450750			−0.225375	−	0.974272i	$-0.572361\pi$
$509$	−10.1694			−0.450750			−0.225375	+	0.974272i	$0.572361\pi$
$510$	20.3384	+	7.29600i	0.900600	+	0.323072i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−9.25635	−	5.81263i	−0.408678	−	0.256634i
$514$		−	13.2419i		−	0.584073i
$515$	−14.9443	−	2.37372i	−0.658523	−	0.104599i
$516$	−11.9899	−	2.26748i	−0.527825	−	0.0998202i
$517$	−9.67389			−0.425457
$518$		0			0
$519$	−8.22492	−	1.55547i	−0.361034	−	0.0682773i
$520$	14.1404	+	2.24604i	0.620098	+	0.0984952i
$521$	20.3300			0.890674			0.445337	−	0.895363i	$-0.353084\pi$
$521$	20.3300			0.890674			0.445337	+	0.895363i	$0.353084\pi$
$522$	−8.27553	+	21.0970i	−0.362210	+	0.923390i
$523$	41.0473			1.79487			0.897436	−	0.441144i	$-0.145427\pi$
$523$	41.0473			1.79487			0.897436	+	0.441144i	$0.145427\pi$
$524$	0.210484			0.00919504
$525$		0			0
$526$	15.5680			0.678795
$527$	−19.1463			−0.834026
$528$	−6.44102	−	1.21810i	−0.280309	−	0.0530110i
$529$	−0.831243			−0.0361410
$530$	6.81405	+	1.08233i	0.295984	+	0.0470135i
$531$	−36.2305	−	14.2118i	−1.57227	−	0.616740i
$532$		0			0
$533$	−56.2180			−2.43507
$534$	−3.41749	+	18.0709i	−0.147889	+	0.782003i
$535$	−20.0778	−	3.18912i	−0.868038	−	0.137877i
$536$		−	1.48871i		−	0.0643024i
$537$	14.5607	+	2.75366i	0.628340	+	0.118829i
$538$	8.37779			0.361192
$539$		0			0
$540$	−7.64604	+	8.74860i	−0.329033	+	0.376480i
$541$	−2.37649			−0.102173			−0.0510866	−	0.998694i	$-0.516268\pi$
$541$	−2.37649			−0.102173			−0.0510866	+	0.998694i	$0.516268\pi$
$542$			0.305606i			0.0131269i
$543$	19.0960	+	3.61136i	0.819487	+	0.154978i
$544$			5.57902i			0.239199i
$545$	33.8561	+	5.37763i	1.45024	+	0.230353i
$546$		0			0
$547$		−	4.09789i		−	0.175213i	−0.996155	−	0.0876066i	$-0.972078\pi$
$547$		−	4.09789i		−	0.175213i	0.996155	−	0.0876066i	$-0.0279218\pi$
$548$	−3.87172			−0.165392
$549$	11.3277	−	28.8780i	0.483456	−	1.23248i
$550$	5.86351	−	17.9918i	0.250021	−	0.767175i
$551$	15.8898			0.676929
$552$	1.51541	−	8.01310i	0.0645000	−	0.341060i
$553$		0			0
$554$		−	20.9930i		−	0.891909i
$555$	−10.0509	−	3.60557i	−0.426638	−	0.153048i
$556$			17.4338i			0.739357i
$557$	37.9488			1.60794			0.803971	−	0.594669i	$-0.202717\pi$
$557$	37.9488			1.60794			0.803971	+	0.594669i	$0.202717\pi$
$558$	3.75963	−	9.58451i	0.159158	−	0.405745i
$559$			45.1100i			1.90795i
$560$		0			0
$561$	−6.79580	+	35.9346i	−0.286919	+	1.51716i
$562$			5.67638i			0.239443i
$563$		−	2.75056i		−	0.115922i	−0.998319	−	0.0579611i	$-0.981540\pi$
$563$		−	2.75056i		−	0.115922i	0.998319	−	0.0579611i	$-0.0184599\pi$
$564$	−4.35018	−	0.822689i	−0.183176	−	0.0346414i
$565$	−6.25098	−	0.992893i	−0.262981	−	0.0417713i
$566$	15.8411			0.665853
$567$		0			0
$568$		−	5.06254i		−	0.212419i
$569$			31.3355i			1.31365i	0.754043	+	0.656825i	$0.228101\pi$
$569$			31.3355i			1.31365i	−0.754043	+	0.656825i	$0.771899\pi$
$570$	7.66832	+	2.75086i	0.321191	+	0.115221i
$571$	−17.2218			−0.720709			−0.360354	−	0.932816i	$-0.617344\pi$
$571$	−17.2218			−0.720709			−0.360354	+	0.932816i	$0.617344\pi$
$572$			24.2333i			1.01324i
$573$	−4.85622	−	0.918388i	−0.202871	−	0.0383662i
$574$		0			0
$575$	22.3832	+	7.29464i	0.933443	+	0.304208i
$576$	−2.79282	−	1.09552i	−0.116368	−	0.0456465i
$577$	17.2429			0.717829			0.358915	−	0.933370i	$-0.383147\pi$
$577$	17.2429			0.717829			0.358915	+	0.933370i	$0.383147\pi$
$578$	14.1255			0.587543
$579$	−45.5753	−	8.61901i	−1.89404	−	0.358194i
$580$	2.64976	−	16.6821i	0.110025	−	0.692688i
$581$		0			0
$582$	−1.57875	+	8.34802i	−0.0654411	+	0.346037i
$583$			11.6776i			0.483639i
$584$	−3.33557			−0.138027
$585$	37.0311	+	21.7638i	1.53105	+	0.899823i
$586$			23.2810i			0.961729i
$587$		−	14.3325i		−	0.591567i	−0.955255	−	0.295784i	$-0.904419\pi$
$587$		−	14.3325i		−	0.591567i	0.955255	−	0.295784i	$-0.0955807\pi$
$588$		0			0
$589$	−7.21885			−0.297448
$590$	28.6487	+	4.55051i	1.17945	+	0.187341i
$591$	−4.73903	+	25.0588i	−0.194938	+	1.03078i
$592$		−	2.75706i		−	0.113315i
$593$			26.7511i			1.09854i	0.835646	+	0.549268i	$0.185093\pi$
$593$			26.7511i			1.09854i	−0.835646	+	0.549268i	$0.814907\pi$
$594$	−16.6542	−	10.4582i	−0.683328	−	0.429104i
$595$		0			0
$596$			8.65775i			0.354635i
$597$	−28.0228	−	5.29956i	−1.14690	−	0.216896i
$598$	−30.1480			−1.23284
$599$			16.5006i			0.674195i	0.941470	+	0.337097i	$0.109445\pi$
$599$			16.5006i			0.674195i	−0.941470	+	0.337097i	$0.890555\pi$
$600$	4.16678	−	7.59197i	0.170108	−	0.309941i
$601$			2.77557i			0.113218i	0.998396	+	0.0566089i	$0.0180288\pi$
$601$			2.77557i			0.113218i	−0.998396	+	0.0566089i	$0.981971\pi$
$602$		0			0
$603$	1.63090	−	4.15770i	0.0664155	−	0.169314i
$604$	16.8301			0.684806
$605$	7.33952	+	1.16579i	0.298394	+	0.0473963i
$606$	1.81412	−	9.59260i	0.0736934	−	0.389673i
$607$	14.8382			0.602266			0.301133	−	0.953582i	$-0.402635\pi$
$607$	14.8382			0.602266			0.301133	+	0.953582i	$0.402635\pi$
$608$			2.10349i			0.0853080i
$609$		0			0
$610$	−3.62705	+	22.8349i	−0.146855	+	0.924558i
$611$			16.3668i			0.662132i
$612$	−6.11191	+	15.5812i	−0.247059	+	0.629833i
$613$		−	8.33176i		−	0.336517i	−0.985743	−	0.168258i	$-0.946186\pi$
$613$		−	8.33176i		−	0.336517i	0.985743	−	0.168258i	$-0.0538143\pi$
$614$	−20.2759			−0.818270
$615$	−11.4819	+	32.0071i	−0.462995	+	1.29065i
$616$		0			0
$617$	14.6210			0.588620			0.294310	−	0.955710i	$-0.404910\pi$
$617$	14.6210			0.588620			0.294310	+	0.955710i	$0.404910\pi$
$618$	2.17800	−	11.5168i	0.0876122	−	0.463272i
$619$		−	2.57516i		−	0.103504i	−0.998660	−	0.0517522i	$-0.983519\pi$
$619$		−	2.57516i		−	0.103504i	0.998660	−	0.0517522i	$-0.0164806\pi$
$620$	−1.20380	+	7.57882i	−0.0483460	+	0.304373i
$621$	13.0107	−	20.7190i	0.522103	−	0.831425i
$622$	11.8199			0.473934
$623$		0			0
$624$	−2.06085	+	10.8973i	−0.0825000	+	0.436240i
$625$	20.1994	+	14.7304i	0.807975	+	0.589216i
$626$	−4.00427			−0.160043
$627$	−2.56226	+	13.5486i	−0.102327	+	0.541080i
$628$	−6.23745			−0.248901
$629$	−15.3817			−0.613309
$630$		0			0
$631$	−3.65345			−0.145442			−0.0727208	−	0.997352i	$-0.523168\pi$
$631$	−3.65345			−0.145442			−0.0727208	+	0.997352i	$0.523168\pi$
$632$	7.07694			0.281506
$633$	5.09191	−	26.9248i	0.202385	−	1.07017i
$634$	−0.211278			−0.00839092
$635$	5.83238	−	36.7190i	0.231451	−	1.45715i
$636$	−0.993092	+	5.25123i	−0.0393787	+	0.208225i
$637$		0			0
$638$	28.5892			1.13186
$639$	5.54608	−	14.1388i	0.219400	−	0.559320i
$640$	2.20838	+	0.350775i	0.0872940	+	0.0138656i
$641$			45.2701i			1.78806i	0.448005	+	0.894031i	$0.352135\pi$
$641$			45.2701i			1.78806i	−0.448005	+	0.894031i	$0.647865\pi$
$642$	2.92617	−	15.4729i	0.115487	−	0.610666i
$643$	−27.7814			−1.09559			−0.547796	−	0.836612i	$-0.684533\pi$
$643$	−27.7814			−1.09559			−0.547796	+	0.836612i	$0.684533\pi$
$644$		0			0
$645$	25.6829	+	9.21322i	1.01126	+	0.362770i
$646$	11.7354			0.461725
$647$		−	4.09747i		−	0.161088i	−0.996751	−	0.0805441i	$-0.974334\pi$
$647$		−	4.09747i		−	0.161088i	0.996751	−	0.0805441i	$-0.0256658\pi$
$648$	−6.59969	−	6.11916i	−0.259260	−	0.240383i
$649$			49.0970i			1.92723i
$650$	−30.4396	−	9.92022i	−1.19394	−	0.389103i
$651$		0			0
$652$		−	3.22815i		−	0.126424i
$653$	30.9842			1.21251			0.606253	−	0.795272i	$-0.292672\pi$
$653$	30.9842			1.21251			0.606253	+	0.795272i	$0.292672\pi$
$654$	−4.93424	+	26.0911i	−0.192944	+	1.02024i
$655$	−0.464830	−	0.0738326i	−0.0181624	−	0.00288488i
$656$	−8.77986			−0.342796
$657$	−9.31564	−	3.65416i	−0.363438	−	0.142563i
$658$		0			0
$659$			35.2668i			1.37380i	0.726752	+	0.686900i	$0.241029\pi$
$659$			35.2668i			1.37380i	−0.726752	+	0.686900i	$0.758971\pi$
$660$	13.7970	+	4.94938i	0.537046	+	0.192654i
$661$			21.8678i			0.850560i	0.905062	+	0.425280i	$0.139824\pi$
$661$			21.8678i			0.850560i	−0.905062	+	0.425280i	$0.860176\pi$
$662$	4.13421			0.160681
$663$	60.7961	+	11.4975i	2.36113	+	0.446527i
$664$		−	9.49058i		−	0.368306i
$665$		0			0
$666$	3.02041	−	7.69999i	0.117038	−	0.298368i
$667$			35.5671i			1.37716i
$668$		−	10.9301i		−	0.422899i
$669$	−7.07605	+	37.4164i	−0.273576	+	1.44660i
$670$	−0.522202	+	3.28764i	−0.0201744	+	0.127013i
$671$	−39.1335			−1.51073
$672$		0			0
$673$		−	3.23782i		−	0.124809i	−0.998051	−	0.0624045i	$-0.980123\pi$
$673$		−	3.23782i		−	0.124809i	0.998051	−	0.0624045i	$-0.0198769\pi$
$674$			1.99207i			0.0767318i
$675$	19.9542	−	16.6382i	0.768037	−	0.640405i
$676$	27.9992			1.07689
$677$			10.5188i			0.404271i	0.979358	+	0.202136i	$0.0647881\pi$
$677$			10.5188i			0.404271i	−0.979358	+	0.202136i	$0.935212\pi$
$678$	0.911028	−	4.81730i	0.0349878	−	0.185007i
$679$		0			0
$680$	1.95698	−	12.3206i	0.0750469	−	0.472474i
$681$	46.8190	+	8.85422i	1.79411	+	0.339294i
$682$	−12.9883			−0.497346
$683$	−46.9660			−1.79710			−0.898552	−	0.438867i	$-0.855380\pi$
$683$	−46.9660			−1.79710			−0.898552	+	0.438867i	$0.855380\pi$
$684$	−2.30441	+	5.87468i	−0.0881113	+	0.224624i
$685$	8.55025	+	1.35811i	0.326688	+	0.0518905i
$686$		0			0
$687$	−27.5426	−	5.20874i	−1.05081	−	0.198726i
$688$			7.04507i			0.268591i
$689$	19.7569			0.752678
$690$	−6.15740	+	17.1644i	−0.234408	+	0.653439i
$691$			35.7893i			1.36149i	0.732520	+	0.680745i	$0.238344\pi$
$691$			35.7893i			1.36149i	−0.732520	+	0.680745i	$0.761656\pi$
$692$			4.83283i			0.183717i
$693$		0			0
$694$	−21.4429			−0.813961
$695$	6.11534	−	38.5005i	0.231968	−	1.46041i
$696$	12.8560	+	2.43129i	0.487307	+	0.0921576i
$697$			48.9830i			1.85537i
$698$		−	17.1982i		−	0.650961i
$699$	−5.73955	+	30.3494i	−0.217090	+	1.14792i
$700$		0			0
$701$		−	36.5930i		−	1.38210i	−0.722808	−	0.691049i	$-0.757149\pi$
$701$		−	36.5930i		−	1.38210i	0.722808	−	0.691049i	$-0.242851\pi$
$702$	−17.6937	+	28.1764i	−0.667806	+	1.06345i
$703$	−5.79947			−0.218731
$704$			3.78464i			0.142639i
$705$	9.31828	+	3.34275i	0.350947	+	0.125895i
$706$			3.05545i			0.114993i
$707$		0			0
$708$	−4.17532	+	22.0781i	−0.156918	+	0.829744i
$709$	−23.6152			−0.886888			−0.443444	−	0.896302i	$-0.646243\pi$
$709$	−23.6152			−0.886888			−0.443444	+	0.896302i	$0.646243\pi$
$710$	−1.77581	+	11.1800i	−0.0666450	+	0.419579i
$711$	19.7646	+	7.75290i	0.741231	+	0.290756i
$712$	10.6182			0.397932
$713$		−	16.1584i		−	0.605136i
$714$		0			0
$715$	8.50043	−	53.5164i	0.317898	−	2.00140i
$716$		−	8.55562i		−	0.319739i
$717$	31.4011	+	5.93846i	1.17270	+	0.221776i
$718$			15.3615i			0.573287i
$719$	−28.3294			−1.05651			−0.528255	−	0.849086i	$-0.677153\pi$
$719$	−28.3294			−1.05651			−0.528255	+	0.849086i	$0.677153\pi$
$720$	5.78334	+	3.39897i	0.215532	+	0.126672i
$721$		0			0
$722$	−14.5753			−0.542437
$723$	22.9123	+	4.33309i	0.852119	+	0.161149i
$724$		−	11.2205i		−	0.417006i
$725$	−11.7034	+	35.9111i	−0.434652	+	1.33370i
$726$	−1.06967	+	5.65618i	−0.0396993	+	0.209920i
$727$	−5.04231			−0.187009			−0.0935045	−	0.995619i	$-0.529807\pi$
$727$	−5.04231			−0.187009			−0.0935045	+	0.995619i	$0.529807\pi$
$728$		0			0
$729$	−11.7281	−	24.3198i	−0.434375	−	0.900732i
$730$	7.36621	+	1.17003i	0.272636	+	0.0433049i
$731$	39.3046			1.45373
$732$	−17.5976	−	3.32800i	−0.650428	−	0.123006i
$733$	−41.9089			−1.54794			−0.773969	−	0.633223i	$-0.781732\pi$
$733$	−41.9089			−1.54794			−0.773969	+	0.633223i	$0.781732\pi$
$734$	−4.12440			−0.152234
$735$		0			0
$736$	−4.70837			−0.173553
$737$	−5.63422			−0.207539
$738$	−24.5206	−	9.61847i	−0.902615	−	0.354061i
$739$	24.0720			0.885502			0.442751	−	0.896645i	$-0.354003\pi$
$739$	24.0720			0.885502			0.442751	+	0.896645i	$0.354003\pi$
$740$	−0.967110	+	6.08865i	−0.0355517	+	0.223823i
$741$	22.9223	+	4.33498i	0.842074	+	0.159250i
$742$		0			0
$743$	16.7877			0.615880			0.307940	−	0.951406i	$-0.400360\pi$
$743$	16.7877			0.615880			0.307940	+	0.951406i	$0.400360\pi$
$744$	−5.84059	−	1.10455i	−0.214127	−	0.0404948i
$745$	3.03692	−	19.1196i	0.111264	−	0.700489i
$746$			23.8319i			0.872546i
$747$	10.3971	−	26.5055i	0.380409	−	0.969785i
$748$	21.1146			0.772025
$749$		0			0
$750$	−11.8649	+	15.3044i	−0.433246	+	0.558836i
$751$	−44.2677			−1.61535			−0.807675	−	0.589627i	$-0.799275\pi$
$751$	−44.2677			−1.61535			−0.807675	+	0.589627i	$0.799275\pi$
$752$			2.55610i			0.0932112i
$753$	−6.92481	+	36.6167i	−0.252354	+	1.33439i
$754$		−	48.3688i		−	1.76149i
$755$	−37.1672	−	5.90357i	−1.35265	−	0.214853i
$756$		0			0
$757$		−	41.9657i		−	1.52527i	−0.646829	−	0.762635i	$-0.723905\pi$
$757$		−	41.9657i		−	1.52527i	0.646829	−	0.762635i	$-0.276095\pi$
$758$	−29.0694			−1.05585
$759$	−30.3267	−	5.73526i	−1.10079	−	0.208177i
$760$	0.737854	−	4.64532i	0.0267648	−	0.168504i
$761$	−51.0849			−1.85183			−0.925913	−	0.377736i	$-0.876703\pi$
$761$	−51.0849			−1.85183			−0.925913	+	0.377736i	$0.876703\pi$
$762$	28.2974	+	5.35150i	1.02511	+	0.193864i
$763$		0			0
$764$			2.85343i			0.103234i
$765$	18.9629	−	32.2654i	0.685606	−	1.16656i
$766$		−	19.4986i		−	0.704514i
$767$	83.0651			2.99931
$768$	−0.321854	+	1.70188i	−0.0116139	+	0.0614115i
$769$		−	34.0876i		−	1.22923i	−0.788827	−	0.614616i	$-0.789311\pi$
$769$		−	34.0876i		−	1.22923i	0.788827	−	0.614616i	$-0.210689\pi$
$770$		0			0
$771$	−22.5361	−	4.26194i	−0.811618	−	0.153490i
$772$			26.7793i			0.963808i
$773$			3.58252i			0.128854i	0.997922	+	0.0644271i	$0.0205220\pi$
$773$			3.58252i			0.128854i	−0.997922	+	0.0644271i	$0.979478\pi$
$774$	−7.71798	+	19.6756i	−0.277417	+	0.707225i
$775$	5.31692	−	16.3147i	0.190990	−	0.586040i
$776$	4.90516			0.176085
$777$		0			0
$778$		−	6.51453i		−	0.233557i
$779$			18.4684i			0.661699i
$780$	8.37364	−	23.3425i	0.299824	−	0.835794i
$781$	−19.1599			−0.685594
$782$			26.2681i			0.939346i
$783$	33.2411	+	20.8741i	1.18794	+	0.745981i
$784$		0			0
$785$	13.7747	+	2.18794i	0.491639	+	0.0780910i
$786$	0.0677451	−	0.358220i	0.00241639	−	0.0127773i
$787$	−15.5828			−0.555466			−0.277733	−	0.960658i	$-0.589583\pi$
$787$	−15.5828			−0.555466			−0.277733	+	0.960658i	$0.589583\pi$
$788$	14.7242			0.524527
$789$	5.01060	−	26.4949i	0.178382	−	0.943242i
$790$	−15.6286	−	2.48242i	−0.556041	−	0.0883204i
$791$		0			0
$792$	−4.14613	+	10.5698i	−0.147326	+	0.375582i
$793$			66.2083i			2.35113i
$794$	33.0474			1.17281
$795$	4.03513	−	11.2484i	0.143111	−	0.398939i
$796$			16.4657i			0.583612i
$797$			33.4891i			1.18625i	0.805112	+	0.593123i	$0.202105\pi$
$797$			33.4891i			1.18625i	−0.805112	+	0.593123i	$0.797895\pi$
$798$		0			0
$799$	14.2605			0.504501
$800$	−4.75391	−	1.54929i	−0.168076	−	0.0547758i
$801$	29.6546	+	11.6323i	1.04779	+	0.411009i
$802$		−	13.3058i		−	0.469845i
$803$			12.6239i			0.445488i
$804$	−2.53361	−	0.479146i	−0.0893535	−	0.0168982i
$805$		0			0
$806$			21.9743i			0.774011i
$807$	2.69642	−	14.2580i	0.0949185	−	0.501906i
$808$	−5.63646			−0.198290
$809$		−	18.8243i		−	0.661827i	−0.943661	−	0.330914i	$-0.892643\pi$
$809$		−	18.8243i		−	0.661827i	0.943661	−	0.330914i	$-0.107357\pi$
$810$	12.4282	+	15.8284i	0.436682	+	0.556155i
$811$			9.05687i			0.318030i	0.987276	+	0.159015i	$0.0508318\pi$
$811$			9.05687i			0.318030i	−0.987276	+	0.159015i	$0.949168\pi$
$812$		0			0
$813$	0.520106	+	0.0983604i	0.0182409	+	0.00344965i
$814$	−10.4345			−0.365729
$815$	−1.13235	+	7.12898i	−0.0396646	+	0.249717i
$816$	9.49485	+	1.79563i	0.332386	+	0.0628596i
$817$	14.8193			0.518460
$818$		−	24.4460i		−	0.854733i
$819$		0			0
$820$	19.3893	+	3.07976i	0.677104	+	0.107550i
$821$		−	0.724927i		−	0.0253001i	−0.999920	−	0.0126501i	$-0.995973\pi$
$821$		−	0.724927i		−	0.0253001i	0.999920	−	0.0126501i	$-0.00402675\pi$
$822$	−1.24613	+	6.58923i	−0.0434637	+	0.229826i
$823$		−	7.32363i		−	0.255286i	−0.991820	−	0.127643i	$-0.959259\pi$
$823$		−	7.32363i		−	0.255286i	0.991820	−	0.127643i	$-0.0407411\pi$
$824$	−6.76706			−0.235742
$825$	−28.7328	−	15.7698i	−1.00035	−	0.549032i
$826$		0			0
$827$	−24.6605			−0.857529			−0.428764	−	0.903416i	$-0.641051\pi$
$827$	−24.6605			−0.857529			−0.428764	+	0.903416i	$0.641051\pi$
$828$	−13.1496	−	5.15809i	−0.456981	−	0.179256i
$829$		−	43.1620i		−	1.49908i	−0.661961	−	0.749538i	$-0.730276\pi$
$829$		−	43.1620i		−	1.49908i	0.661961	−	0.749538i	$-0.269724\pi$
$830$	−3.32906	+	20.9588i	−0.115553	+	0.727492i
$831$	−35.7277	−	6.75669i	−1.23938	−	0.234387i
$832$	6.40306			0.221986
$833$		0			0
$834$	29.6703	+	5.61112i	1.02740	+	0.194297i
$835$	−3.83401	+	24.1379i	−0.132682	+	0.835326i
$836$	7.96096			0.275336
$837$	−15.1017	−	9.48327i	−0.521990	−	0.327790i
$838$	−27.0524			−0.934511
$839$	−14.2292			−0.491247			−0.245623	−	0.969365i	$-0.578993\pi$
$839$	−14.2292			−0.491247			−0.245623	+	0.969365i	$0.578993\pi$
$840$		0			0
$841$	−28.0630			−0.967691
$842$	−5.39064			−0.185774
$843$	9.66053	+	1.82696i	0.332726	+	0.0629239i
$844$	−15.8206			−0.544567
$845$	−61.8330	−	9.82143i	−2.12712	−	0.337868i
$846$	−2.80024	+	7.13872i	−0.0962743	+	0.245434i
$847$		0			0
$848$	3.08554			0.105958
$849$	5.09853	−	26.9598i	0.174981	−	0.925258i
$850$	−8.64354	+	26.5222i	−0.296471	+	0.909704i
$851$		−	12.9813i		−	0.444993i
$852$	−8.61585	−	1.62940i	−0.295174	−	0.0558222i
$853$	10.7205			0.367064			0.183532	−	0.983014i	$-0.441247\pi$
$853$	10.7205			0.367064			0.183532	+	0.983014i	$0.441247\pi$
$854$		0			0
$855$	7.14971	−	12.1652i	0.244515	−	0.416042i
$856$	−9.09162			−0.310745
$857$			17.2656i			0.589781i	0.955531	+	0.294890i	$0.0952831\pi$
$857$			17.2656i			0.589781i	−0.955531	+	0.294890i	$0.904717\pi$
$858$	41.2422	+	7.79957i	1.40799	+	0.266273i
$859$			6.33253i			0.216063i	0.994147	+	0.108032i	$0.0344548\pi$
$859$			6.33253i			0.216063i	−0.994147	+	0.108032i	$0.965545\pi$
$860$	2.47124	−	15.5582i	0.0842684	−	0.530530i
$861$		0			0
$862$		−	3.21022i		−	0.109341i
$863$	4.44663			0.151365			0.0756826	−	0.997132i	$-0.475886\pi$
$863$	4.44663			0.151365			0.0756826	+	0.997132i	$0.475886\pi$
$864$	−2.76332	+	4.40046i	−0.0940101	+	0.149707i
$865$	1.69524	−	10.6727i	0.0576398	−	0.362884i
$866$	39.7769			1.35167
$867$	4.54634	−	24.0400i	0.154402	−	0.816440i
$868$		0			0
$869$		−	26.7837i		−	0.908573i
$870$	−27.5382	−	9.87879i	−0.933634	−	0.334922i
$871$			9.53229i			0.322989i
$872$	15.3307			0.519163
$873$	13.6992	+	5.37368i	0.463649	+	0.181872i
$874$			9.90403i			0.335009i
$875$		0			0
$876$	−1.07356	+	5.67675i	−0.0362724	+	0.191800i
$877$		−	40.7210i		−	1.37505i	−0.726161	−	0.687525i	$-0.758697\pi$
$877$		−	40.7210i		−	1.37505i	0.726161	−	0.687525i	$-0.241303\pi$
$878$			26.5159i			0.894868i
$879$	39.6215	+	7.49307i	1.33640	+	0.252735i
$880$	1.32756	−	8.35793i	0.0447520	−	0.281746i
$881$	−16.0602			−0.541081			−0.270540	−	0.962709i	$-0.587202\pi$
$881$	−16.0602			−0.541081			−0.270540	+	0.962709i	$0.587202\pi$
$882$		0			0
$883$			18.9924i			0.639145i	0.947562	+	0.319572i	$0.103539\pi$
$883$			18.9924i			0.639145i	−0.947562	+	0.319572i	$0.896461\pi$
$884$		−	35.7228i		−	1.20149i
$885$	16.9651	−	47.2922i	0.570277	−	1.58971i
$886$	21.5549			0.724151
$887$			32.7978i			1.10124i	0.834755	+	0.550621i	$0.185609\pi$
$887$			32.7978i			1.10124i	−0.834755	+	0.550621i	$0.814391\pi$
$888$	−4.69220	−	0.887371i	−0.157460	−	0.0297782i
$889$		0			0
$890$	−23.4489	−	3.72459i	−0.786010	−	0.124848i
$891$	−23.1588	+	24.9774i	−0.775848	+	0.836776i
$892$	21.9853			0.736122
$893$	5.37673			0.179925
$894$	14.7345	+	2.78653i	0.492795	+	0.0931954i
$895$	−3.00110	+	18.8941i	−0.100316	+	0.631560i
$896$		0			0
$897$	−9.70324	+	51.3084i	−0.323982	+	1.71314i
$898$			1.27232i			0.0424578i
$899$	25.9241			0.864619
$900$	−11.5796	−	9.53488i	−0.385985	−	0.317829i
$901$		−	17.2143i		−	0.573491i
$902$			33.2286i			1.10639i
$903$		0			0
$904$	−2.83057			−0.0941432
$905$	−3.93587	+	24.7791i	−0.130833	+	0.823687i
$906$	5.41682	−	28.6428i	0.179962	−	0.951594i
$907$		−	57.7453i		−	1.91740i	−0.284420	−	0.958700i	$-0.591801\pi$
$907$		−	57.7453i		−	1.91740i	0.284420	−	0.958700i	$-0.408199\pi$
$908$		−	27.5101i		−	0.912954i
$909$	−15.7416	−	6.17483i	−0.522117	−	0.204806i
$910$		0			0
$911$			29.3826i			0.973490i	0.873544	+	0.486745i	$0.161816\pi$
$911$			29.3826i			0.973490i	−0.873544	+	0.486745i	$0.838184\pi$
$912$	3.57990	+	0.677017i	0.118542	+	0.0224183i
$913$	−35.9184			−1.18873
$914$		−	7.38402i		−	0.244242i
$915$	37.6950	+	13.5223i	1.24616	+	0.447034i
$916$			16.1836i			0.534720i
$917$		0			0
$918$	24.5503	+	15.4166i	0.810280	+	0.508824i
$919$	42.6061			1.40545			0.702723	−	0.711464i	$-0.251967\pi$
$919$	42.6061			1.40545			0.702723	+	0.711464i	$0.251967\pi$
$920$	10.3979	+	1.65158i	0.342808	+	0.0544510i
$921$	−6.52588	+	34.5073i	−0.215035	+	1.13705i
$922$	−14.6635			−0.482918
$923$			32.4157i			1.06698i
$924$		0			0
$925$	4.27150	−	13.1068i	0.140446	−	0.430950i
$926$			27.8566i			0.915424i
$927$	−18.8992	−	7.41342i	−0.620731	−	0.243489i
$928$		−	7.55401i		−	0.247972i
$929$	26.5385			0.870700			0.435350	−	0.900261i	$-0.356625\pi$
$929$	26.5385			0.870700			0.435350	+	0.900261i	$0.356625\pi$
$930$	12.5108	+	4.48801i	0.410246	+	0.147168i
$931$		0			0
$932$	17.8328			0.584133
$933$	3.80427	−	20.1161i	0.124546	−	0.658571i
$934$			17.7307i			0.580165i
$935$	−46.6291	−	7.40647i	−1.52493	−	0.242218i
$936$	17.8826	+	7.01465i	0.584511	+	0.229281i
$937$	−33.5524			−1.09611			−0.548054	−	0.836443i	$-0.684631\pi$
$937$	−33.5524			−1.09611			−0.548054	+	0.836443i	$0.684631\pi$
$938$		0			0
$939$	−1.28879	+	6.81481i	−0.0420581	+	0.222393i
$940$	0.896615	−	5.64484i	0.0292444	−	0.184114i
$941$	−14.9463			−0.487237			−0.243618	−	0.969871i	$-0.578334\pi$
$941$	−14.9463			−0.487237			−0.243618	+	0.969871i	$0.578334\pi$
$942$	−2.00754	+	10.6154i	−0.0654093	+	0.345869i
$943$	−41.3388			−1.34618
$944$	12.9727			0.422226
$945$		0			0
$946$	26.6630			0.866890
$947$	21.5510			0.700312			0.350156	−	0.936691i	$-0.386129\pi$
$947$	21.5510			0.700312			0.350156	+	0.936691i	$0.386129\pi$
$948$	2.27774	−	12.0441i	0.0739775	−	0.391175i
$949$	21.3578			0.693305
$950$	−3.25893	+	9.99983i	−0.105734	+	0.324437i
$951$	−0.0680006	+	0.359571i	−0.00220507	+	0.0116599i
$952$		0			0
$953$	−0.489212			−0.0158471			−0.00792356	−	0.999969i	$-0.502522\pi$
$953$	−0.489212			−0.0158471			−0.00792356	+	0.999969i	$0.502522\pi$
$954$	8.61736	+	3.38026i	0.278997	+	0.109440i
$955$	1.00091	−	6.30148i	0.0323888	−	0.203911i
$956$		−	18.4508i		−	0.596742i
$957$	9.20153	−	48.6555i	0.297443	−	1.57281i
$958$	−4.63276			−0.149678
$959$		0			0
$960$	1.30776	−	3.64551i	0.0422076	−	0.117658i
$961$	19.2225			0.620080
$962$			17.6537i			0.569177i
$963$	−25.3913	−	9.96001i	−0.818222	−	0.320957i
$964$		−	13.4629i		−	0.433612i
$965$	9.39351	−	59.1389i	0.302388	−	1.90375i
$966$		0			0
$967$		−	44.7126i		−	1.43786i	−0.695083	−	0.718930i	$-0.744632\pi$
$967$		−	44.7126i		−	1.43786i	0.695083	−	0.718930i	$-0.255368\pi$
$968$	3.32348			0.106821
$969$	3.77709	−	19.9724i	0.121338	−	0.641605i
$970$	−10.8325	−	1.72061i	−0.347810	−	0.0552455i
$971$	−8.30533			−0.266531			−0.133265	−	0.991080i	$-0.542546\pi$
$971$	−8.30533			−0.266531			−0.133265	+	0.991080i	$0.542546\pi$
$972$	−12.5382	+	9.26244i	−0.402164	+	0.297093i
$973$		0			0
$974$			43.6309i			1.39802i
$975$	−26.6802	+	48.6118i	−0.854449	+	1.55682i
$976$			10.3401i			0.330978i
$977$	11.6472			0.372625			0.186313	−	0.982490i	$-0.440346\pi$
$977$	11.6472			0.372625			0.186313	+	0.982490i	$0.440346\pi$
$978$	−5.49393	−	1.03899i	−0.175677	−	0.0332233i
$979$		−	40.1859i		−	1.28435i
$980$		0			0
$981$	42.8159	+	16.7950i	1.36701	+	0.536224i
$982$		−	29.4021i		−	0.938259i
$983$		−	18.4536i		−	0.588577i	−0.955717	−	0.294289i	$-0.904917\pi$
$983$		−	18.4536i		−	0.588577i	0.955717	−	0.294289i	$-0.0950827\pi$
$984$	−2.82583	+	14.9423i	−0.0900842	+	0.476343i
$985$	−32.5166	−	5.16488i	−1.03607	−	0.164567i
$986$	−42.1440			−1.34214
$987$		0			0
$988$		−	13.4688i		−	0.428500i
$989$			33.1708i			1.05477i
$990$	12.8639	−	21.8878i	0.408841	−	0.695641i
$991$	−51.2911			−1.62932			−0.814658	−	0.579942i	$-0.803075\pi$
$991$	−51.2911			−1.62932			−0.814658	+	0.579942i	$0.803075\pi$
$992$			3.43184i			0.108961i
$993$	1.33061	−	7.03594i	0.0422256	−	0.223279i
$994$		0			0
$995$	5.77577	−	36.3626i	0.183104	−	1.15277i
$996$	−16.1519	−	3.05458i	−0.511791	−	0.0967880i
$997$	17.6179			0.557964			0.278982	−	0.960296i	$-0.410003\pi$
$997$	17.6179			0.557964			0.278982	+	0.960296i	$0.410003\pi$
$998$	−21.1826			−0.670524
$999$	−12.1324	−	7.61865i	−0.383851	−	0.241043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.g.1469.12	yes	24
3.2	odd	2		1470.2.d.h.1469.11	yes	24
5.4	even	2		1470.2.d.h.1469.13	yes	24
7.6	odd	2	inner	1470.2.d.g.1469.13	yes	24
15.14	odd	2	inner	1470.2.d.g.1469.14	yes	24
21.20	even	2		1470.2.d.h.1469.14	yes	24
35.34	odd	2		1470.2.d.h.1469.12	yes	24
105.104	even	2	inner	1470.2.d.g.1469.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.d.g.1469.11	✓	24	105.104	even	2	inner
1470.2.d.g.1469.12	yes	24	1.1	even	1	trivial
1470.2.d.g.1469.13	yes	24	7.6	odd	2	inner
1470.2.d.g.1469.14	yes	24	15.14	odd	2	inner
1470.2.d.h.1469.11	yes	24	3.2	odd	2
1470.2.d.h.1469.12	yes	24	35.34	odd	2
1470.2.d.h.1469.13	yes	24	5.4	even	2
1470.2.d.h.1469.14	yes	24	21.20	even	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.321854 + 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 - 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} -1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.321854 + 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 - 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} -1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +(2.20838 + 0.350775i) q^{10} +3.78464i q^{11} +(-0.321854 + 1.70188i) q^{12} +6.40306 q^{13} +(1.30776 - 3.64551i) q^{15} +1.00000 q^{16} -5.57902i q^{17} +(2.79282 + 1.09552i) q^{18} -2.10349i q^{19} +(-2.20838 - 0.350775i) q^{20} -3.78464i q^{22} +4.70837 q^{23} +(0.321854 - 1.70188i) q^{24} +(4.75391 + 1.54929i) q^{25} -6.40306 q^{26} +(2.76332 - 4.40046i) q^{27} +7.55401i q^{29} +(-1.30776 + 3.64551i) q^{30} -3.43184i q^{31} -1.00000 q^{32} +(-6.44102 - 1.21810i) q^{33} +5.57902i q^{34} +(-2.79282 - 1.09552i) q^{36} -2.75706i q^{37} +2.10349i q^{38} +(-2.06085 + 10.8973i) q^{39} +(2.20838 + 0.350775i) q^{40} -8.77986 q^{41} +7.04507i q^{43} +3.78464i q^{44} +(5.78334 + 3.39897i) q^{45} -4.70837 q^{46} +2.55610i q^{47} +(-0.321854 + 1.70188i) q^{48} +(-4.75391 - 1.54929i) q^{50} +(9.49485 + 1.79563i) q^{51} +6.40306 q^{52} +3.08554 q^{53} +(-2.76332 + 4.40046i) q^{54} +(1.32756 - 8.35793i) q^{55} +(3.57990 + 0.677017i) q^{57} -7.55401i q^{58} +12.9727 q^{59} +(1.30776 - 3.64551i) q^{60} +10.3401i q^{61} +3.43184i q^{62} +1.00000 q^{64} +(-14.1404 - 2.24604i) q^{65} +(6.44102 + 1.21810i) q^{66} +1.48871i q^{67} -5.57902i q^{68} +(-1.51541 + 8.01310i) q^{69} +5.06254i q^{71} +(2.79282 + 1.09552i) q^{72} +3.33557 q^{73} +2.75706i q^{74} +(-4.16678 + 7.59197i) q^{75} -2.10349i q^{76} +(2.06085 - 10.8973i) q^{78} -7.07694 q^{79} +(-2.20838 - 0.350775i) q^{80} +(6.59969 + 6.11916i) q^{81} +8.77986 q^{82} +9.49058i q^{83} +(-1.95698 + 12.3206i) q^{85} -7.04507i q^{86} +(-12.8560 - 2.43129i) q^{87} -3.78464i q^{88} -10.6182 q^{89} +(-5.78334 - 3.39897i) q^{90} +4.70837 q^{92} +(5.84059 + 1.10455i) q^{93} -2.55610i q^{94} +(-0.737854 + 4.64532i) q^{95} +(0.321854 - 1.70188i) q^{96} -4.90516 q^{97} +(4.14613 - 10.5698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more