LMFDB - Embedded newform 1470.2.d.h.1469.13

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			1469.13
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.h.1469.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.321854 - 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 + 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} +1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.321854 - 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 + 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} +1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +(-2.20838 + 0.350775i) q^{10} +3.78464i q^{11} +(0.321854 - 1.70188i) q^{12} -6.40306 q^{13} +(-0.113797 + 3.87131i) q^{15} +1.00000 q^{16} +5.57902i q^{17} +(-2.79282 - 1.09552i) q^{18} -2.10349i q^{19} +(-2.20838 + 0.350775i) q^{20} +3.78464i q^{22} -4.70837 q^{23} +(0.321854 - 1.70188i) q^{24} +(4.75391 - 1.54929i) q^{25} -6.40306 q^{26} +(-2.76332 + 4.40046i) q^{27} +7.55401i q^{29} +(-0.113797 + 3.87131i) q^{30} -3.43184i q^{31} +1.00000 q^{32} +(6.44102 + 1.21810i) q^{33} +5.57902i q^{34} +(-2.79282 - 1.09552i) q^{36} +2.75706i q^{37} -2.10349i q^{38} +(-2.06085 + 10.8973i) q^{39} +(-2.20838 + 0.350775i) q^{40} -8.77986 q^{41} -7.04507i q^{43} +3.78464i q^{44} +(6.55190 + 1.43967i) q^{45} -4.70837 q^{46} -2.55610i q^{47} +(0.321854 - 1.70188i) q^{48} +(4.75391 - 1.54929i) q^{50} +(9.49485 + 1.79563i) q^{51} -6.40306 q^{52} -3.08554 q^{53} +(-2.76332 + 4.40046i) q^{54} +(-1.32756 - 8.35793i) q^{55} +(-3.57990 - 0.677017i) q^{57} +7.55401i q^{58} +12.9727 q^{59} +(-0.113797 + 3.87131i) q^{60} +10.3401i q^{61} -3.43184i q^{62} +1.00000 q^{64} +(14.1404 - 2.24604i) q^{65} +(6.44102 + 1.21810i) q^{66} -1.48871i q^{67} +5.57902i q^{68} +(-1.51541 + 8.01310i) q^{69} +5.06254i q^{71} +(-2.79282 - 1.09552i) q^{72} -3.33557 q^{73} +2.75706i q^{74} +(-1.10665 - 8.58926i) q^{75} -2.10349i q^{76} +(-2.06085 + 10.8973i) q^{78} -7.07694 q^{79} +(-2.20838 + 0.350775i) q^{80} +(6.59969 + 6.11916i) q^{81} -8.77986 q^{82} -9.49058i q^{83} +(-1.95698 - 12.3206i) q^{85} -7.04507i q^{86} +(12.8560 + 2.43129i) q^{87} +3.78464i q^{88} -10.6182 q^{89} +(6.55190 + 1.43967i) q^{90} -4.70837 q^{92} +(-5.84059 - 1.10455i) q^{93} -2.55610i q^{94} +(0.737854 + 4.64532i) q^{95} +(0.321854 - 1.70188i) q^{96} +4.90516 q^{97} +(4.14613 - 10.5698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 16 q^{15} + 24 q^{16} + 8 q^{18} + 16 q^{23} + 8 q^{25} - 16 q^{30} + 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} + 8 q^{50} + 16 q^{51} - 16 q^{53} - 16 q^{57} - 16 q^{60} + 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 - 16 * q^15 + 24 * q^16 + 8 * q^18 + 16 * q^23 + 8 * q^25 - 16 * q^30 + 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 + 8 * q^50 + 16 * q^51 - 16 * q^53 - 16 * q^57 - 16 * q^60 + 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	$-0.847868\pi$
$13$	−6.40306			−1.77589			−0.887945	+	0.459950i	$0.847868\pi$
$14$		0			0
$15$	−0.113797	+	3.87131i	−0.0293823	+	0.999568i
$16$	1.00000			0.250000
$17$			5.57902i			1.35311i	0.736391	+	0.676556i	$0.236528\pi$
$17$			5.57902i			1.35311i	−0.736391	+	0.676556i	$0.763472\pi$
$18$	−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	$-0.663325\pi$
$23$	−4.70837			−0.981763			−0.490882	+	0.871226i	$0.663325\pi$
$24$	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	$0.752571\pi$
$30$	−0.113797	+	3.87131i	−0.0207764	+	0.706801i
$31$		−	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	$0.0727706\pi$
$37$			2.75706i			0.453259i	−0.973981	+	0.226629i	$0.927229\pi$
$38$		−	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	$-0.819489\pi$
$43$		−	7.04507i		−	1.07436i	0.843467	−	0.537181i	$-0.180511\pi$
$44$			3.78464i			0.570556i
$45$	6.55190	+	1.43967i	0.976699	+	0.214613i
$46$	−4.70837			−0.694211
$47$		−	2.55610i		−	0.372845i	−0.982470	−	0.186422i	$-0.940311\pi$
$47$		−	2.55610i		−	0.372845i	0.982470	−	0.186422i	$-0.0596893\pi$
$48$	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	$-0.567970\pi$
$53$	−3.08554			−0.423831			−0.211916	+	0.977288i	$0.567970\pi$
$54$	−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	$0.179926\pi$
$60$	−0.113797	+	3.87131i	−0.0146912	+	0.499784i
$61$			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	$-0.971014\pi$
$67$		−	1.48871i		−	0.181875i	0.995857	−	0.0909373i	$-0.0289863\pi$
$68$			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	$-0.562535\pi$
$73$	−3.33557			−0.390399			−0.195199	+	0.980764i	$0.562535\pi$
$74$			2.75706i			0.320502i
$75$	−1.10665	−	8.58926i	−0.127785	−	0.991802i
$76$		−	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	$-0.825610\pi$
$83$		−	9.49058i		−	1.04173i	0.853640	−	0.520863i	$-0.174390\pi$
$84$		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	$0.690261\pi$
$90$	6.55190	+	1.43967i	0.690631	+	0.151754i
$91$		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	$-0.419891\pi$
$97$	4.90516			0.498044			0.249022	+	0.968498i	$0.419891\pi$
$98$		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	$-0.608192\pi$
$103$	−6.76706			−0.666779			−0.333389	+	0.942789i	$0.608192\pi$
$104$	−6.40306			−0.627872
$105$		0			0
$106$	−3.08554			−0.299694
$107$	−9.09162			−0.878920			−0.439460	−	0.898262i	$-0.644830\pi$
$107$	−9.09162			−0.878920			−0.439460	+	0.898262i	$0.644830\pi$
$108$	−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	$-0.542506\pi$
$113$	−2.83057			−0.266277			−0.133139	+	0.991097i	$0.542506\pi$
$114$	−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
$120$	−0.113797	+	3.87131i	−0.0103882	+	0.353401i
$121$	−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	$-0.735908\pi$
$127$		−	16.6271i		−	1.47542i	0.675119	−	0.737709i	$-0.264092\pi$
$128$	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
$135$	4.55890	−	10.6872i	0.392367	−	0.919809i
$136$			5.57902i			0.478397i
$137$	3.87172			0.330784			0.165392	−	0.986228i	$-0.447111\pi$
$137$	3.87172			0.330784			0.165392	+	0.986228i	$0.447111\pi$
$138$	−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	$0.884605\pi$
$150$	−1.10665	−	8.58926i	−0.0903578	−	0.701310i
$151$	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	$-0.419931\pi$
$157$	6.23745			0.497802			0.248901	+	0.968529i	$0.419931\pi$
$158$	−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	$0.0403500\pi$
$163$			3.22815i			0.252848i	−0.991976	+	0.126424i	$0.959650\pi$
$164$	−8.77986			−0.685592
$165$	−14.6515	−	0.430681i	−1.14062	−	0.0335285i
$166$		−	9.49058i		−	0.736612i
$167$			10.9301i			0.845797i	0.906177	+	0.422899i	$0.138987\pi$
$167$			10.9301i			0.845797i	−0.906177	+	0.422899i	$0.861013\pi$
$168$		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	$-0.941187\pi$
$173$		−	4.83283i		−	0.367434i	0.982979	−	0.183717i	$-0.0588129\pi$
$174$	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	$-0.103595\pi$
$180$	6.55190	+	1.43967i	0.488350	+	0.107306i
$181$		−	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	$-0.585900\pi$
$193$		−	26.7793i		−	1.92762i	0.266598	−	0.963808i	$-0.414100\pi$
$194$	4.90516			0.352170
$195$	0.728651	−	24.7882i	0.0521798	−	1.77512i
$196$		0			0
$197$	−14.7242			−1.04905			−0.524527	−	0.851394i	$-0.675758\pi$
$197$	−14.7242			−1.04905			−0.524527	+	0.851394i	$0.675758\pi$
$198$	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	$-0.763345\pi$
$223$	−21.9853			−1.47224			−0.736122	+	0.676849i	$0.763345\pi$
$224$		0			0
$225$	−14.9741	−	0.881089i	−0.998273	−	0.0587393i
$226$	−2.83057			−0.188286
$227$			27.5101i			1.82591i	0.408063	+	0.912954i	$0.366204\pi$
$227$			27.5101i			1.82591i	−0.408063	+	0.912954i	$0.633796\pi$
$228$	−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	$-0.698565\pi$
$233$	−17.8328			−1.16827			−0.584133	+	0.811658i	$0.698565\pi$
$234$	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	$-0.203538\pi$
$240$	−0.113797	+	3.87131i	−0.00734558	+	0.249892i
$241$		−	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
$255$	−21.5981	−	0.634877i	−1.35253	−	0.0397576i
$256$	1.00000			0.0625000
$257$		−	13.2419i		−	0.826004i	−0.910730	−	0.413002i	$-0.864480\pi$
$257$		−	13.2419i		−	0.826004i	0.910730	−	0.413002i	$-0.135520\pi$
$258$	−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	$-0.340644\pi$
$263$	15.5680			0.959961			0.479981	+	0.877279i	$0.340644\pi$
$264$	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	$0.582208\pi$
$270$	4.55890	−	10.6872i	0.277446	−	0.650403i
$271$		−	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	$-0.782778\pi$
$277$		−	20.9930i		−	1.26135i	0.776047	−	0.630675i	$-0.217222\pi$
$278$			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	$-0.343955\pi$
$283$	15.8411			0.941658			0.470829	+	0.882224i	$0.343955\pi$
$284$			5.06254i			0.300406i
$285$	8.14328	+	0.239372i	0.482366	+	0.0141792i
$286$		−	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	$0.238040\pi$
$293$			23.2810i			1.36009i	−0.733170	+	0.680045i	$0.761960\pi$
$294$		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
$300$	−1.10665	−	8.58926i	−0.0638926	−	0.495901i
$301$		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	$-0.696402\pi$
$307$	−20.2759			−1.15721			−0.578604	+	0.815608i	$0.696402\pi$
$308$		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	$-0.536100\pi$
$313$	−4.00427			−0.226335			−0.113167	+	0.993576i	$0.536100\pi$
$314$	6.23745			0.351999
$315$		0			0
$316$	−7.07694			−0.398109
$317$	−0.211278			−0.0118665			−0.00593327	−	0.999982i	$-0.501889\pi$
$317$	−0.211278			−0.0118665			−0.00593327	+	0.999982i	$0.501889\pi$
$318$	−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
$330$	−14.6515	−	0.430681i	−0.806539	−	0.0237082i
$331$	−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	$0.0172792\pi$
$337$			1.99207i			0.108515i	−0.998527	+	0.0542576i	$0.982721\pi$
$338$	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
$345$	0.535799	−	18.2276i	0.0288465	−	0.981339i
$346$		−	4.83283i		−	0.259815i
$347$	−21.4429			−1.15111			−0.575557	−	0.817761i	$-0.695215\pi$
$347$	−21.4429			−1.15111			−0.575557	+	0.817761i	$0.695215\pi$
$348$	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	$0.0259112\pi$
$353$			3.05545i			0.162625i	−0.996689	+	0.0813125i	$0.974089\pi$
$354$	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	$-0.132859\pi$
$360$	6.55190	+	1.43967i	0.345315	+	0.0758770i
$361$	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	$-0.534331\pi$
$367$	−4.12440			−0.215292			−0.107646	+	0.994189i	$0.534331\pi$
$368$	−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	$0.211645\pi$
$373$			23.8319i			1.23397i	−0.786976	+	0.616983i	$0.788355\pi$
$374$	−21.1146			−1.09181
$375$	5.45681	+	18.5802i	0.281789	+	0.959477i
$376$		−	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	$-0.834007\pi$
$383$		−	19.4986i		−	0.996333i	0.867081	−	0.498166i	$-0.165993\pi$
$384$	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	$0.947189\pi$
$390$	0.728651	−	24.7882i	0.0368967	−	1.25520i
$391$		−	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	$-0.188739\pi$
$397$	33.0474			1.65860			0.829300	+	0.558803i	$0.188739\pi$
$398$			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
$405$	−16.7211	−	11.1984i	−0.830878	−	0.556455i
$406$		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	$-0.0950171\pi$
$433$	39.7769			1.91155			0.955777	+	0.294092i	$0.0950171\pi$
$434$		0			0
$435$	−29.2439	−	0.859625i	−1.40214	−	0.0412159i
$436$	−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	$-0.328886\pi$
$443$	21.5549			1.02410			0.512052	+	0.858955i	$0.328886\pi$
$444$	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	$-0.00955781\pi$
$450$	−14.9741	−	0.881089i	−0.705886	−	0.0415349i
$451$		−	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	$-0.944749\pi$
$457$		−	7.38402i		−	0.345410i	0.984974	−	0.172705i	$-0.0552507\pi$
$458$			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	$0.224103\pi$
$463$			27.8566i			1.29460i	−0.762233	+	0.647302i	$0.775897\pi$
$464$			7.55401i			0.350686i
$465$	13.2857	+	0.390534i	0.616110	+	0.0181106i
$466$	−17.8328			−0.826089
$467$			17.7307i			0.820478i	0.911978	+	0.410239i	$0.134555\pi$
$467$			17.7307i			0.820478i	−0.911978	+	0.410239i	$0.865445\pi$
$468$	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	$0.466247\pi$
$480$	−0.113797	+	3.87131i	−0.00519411	+	0.176700i
$481$		−	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	$0.451791\pi$
$487$			43.6309i			1.97711i	−0.150876	+	0.988553i	$0.548209\pi$
$488$			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
$495$	−5.44861	+	24.7966i	−0.244897	+	1.11452i
$496$		−	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	$0.0687763\pi$
$503$			9.61653i			0.428780i	−0.976748	+	0.214390i	$0.931224\pi$
$504$		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	$0.572361\pi$
$510$	−21.5981	−	0.634877i	−0.956381	−	0.0281128i
$511$		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	$-0.854573\pi$
$523$	−41.0473			−1.79487			−0.897436	+	0.441144i	$0.854573\pi$
$524$	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
$540$	4.55890	−	10.6872i	0.196184	−	0.459904i
$541$	−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	$0.0279218\pi$
$547$			4.09789i			0.175213i	−0.996155	+	0.0876066i	$0.972078\pi$
$548$	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
$555$	−10.6735	−	0.313746i	−0.453063	−	0.0133178i
$556$			17.4338i			0.739357i
$557$	−37.9488			−1.60794			−0.803971	−	0.594669i	$-0.797283\pi$
$557$	−37.9488			−1.60794			−0.803971	+	0.594669i	$0.797283\pi$
$558$	−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	$0.0184599\pi$
$563$			2.75056i			0.115922i	−0.998319	+	0.0579611i	$0.981540\pi$
$564$	−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	$0.771899\pi$
$570$	8.14328	+	0.239372i	0.341084	+	0.0100262i
$571$	−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	$-0.616853\pi$
$577$	−17.2429			−0.717829			−0.358915	+	0.933370i	$0.616853\pi$
$578$	−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
$585$	−41.9522	−	9.21827i	−1.73451	−	0.381128i
$586$			23.2810i			0.961729i
$587$			14.3325i			0.591567i	0.955255	+	0.295784i	$0.0955807\pi$
$587$			14.3325i			0.591567i	−0.955255	+	0.295784i	$0.904419\pi$
$588$		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	$-0.814907\pi$
$593$		−	26.7511i		−	1.09854i	0.835646	−	0.549268i	$-0.185093\pi$
$594$	−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	$0.890555\pi$
$600$	−1.10665	−	8.58926i	−0.0451789	−	0.350655i
$601$			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	$-0.597365\pi$
$607$	−14.8382			−0.602266			−0.301133	+	0.953582i	$0.597365\pi$
$608$		−	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	$0.0538143\pi$
$613$			8.33176i			0.336517i	−0.985743	+	0.168258i	$0.946186\pi$
$614$	−20.2759			−0.818270
$615$	0.999124	−	33.9896i	0.0402886	−	1.37059i
$616$		0			0
$617$	−14.6210			−0.588620			−0.294310	−	0.955710i	$-0.595090\pi$
$617$	−14.6210			−0.588620			−0.294310	+	0.955710i	$0.595090\pi$
$618$	−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	$-0.315467\pi$
$643$	27.7814			1.09559			0.547796	+	0.836612i	$0.315467\pi$
$644$		0			0
$645$	27.2736	+	0.801709i	1.07390	+	0.0315673i
$646$	11.7354			0.461725
$647$			4.09747i			0.161088i	0.996751	+	0.0805441i	$0.0256658\pi$
$647$			4.09747i			0.161088i	−0.996751	+	0.0805441i	$0.974334\pi$
$648$	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	$-0.707328\pi$
$653$	−30.9842			−1.21251			−0.606253	+	0.795272i	$0.707328\pi$
$654$	−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	$0.758971\pi$
$660$	−14.6515	−	0.430681i	−0.570309	−	0.0167642i
$661$			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	$0.0198769\pi$
$673$			3.23782i			0.124809i	−0.998051	+	0.0624045i	$0.980123\pi$
$674$			1.99207i			0.0767318i
$675$	−6.31898	+	25.2006i	−0.243218	+	0.969972i
$676$	27.9992			1.07689
$677$		−	10.5188i		−	0.404271i	−0.979358	−	0.202136i	$-0.935212\pi$
$677$		−	10.5188i		−	0.404271i	0.979358	−	0.202136i	$-0.0647881\pi$
$678$	−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	$-0.144620\pi$
$683$	46.9660			1.79710			0.898552	+	0.438867i	$0.144620\pi$
$684$	−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
$690$	0.535799	−	18.2276i	0.0203975	−	0.693912i
$691$			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
$705$	9.89544	+	0.290877i	0.372684	+	0.0109550i
$706$			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	$0.677153\pi$
$720$	6.55190	+	1.43967i	0.244175	+	0.0536532i
$721$		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	$-0.470193\pi$
$727$	5.04231			0.187009			0.0935045	+	0.995619i	$0.470193\pi$
$728$		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	$-0.218268\pi$
$733$	41.9089			1.54794			0.773969	+	0.633223i	$0.218268\pi$
$734$	−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	$-0.599640\pi$
$743$	−16.7877			−0.615880			−0.307940	+	0.951406i	$0.599640\pi$
$744$	−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
$750$	5.45681	+	18.5802i	0.199255	+	0.678452i
$751$	−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	$0.276095\pi$
$757$			41.9657i			1.52527i	−0.646829	+	0.762635i	$0.723905\pi$
$758$	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
$765$	−8.03193	+	36.5532i	−0.290395	+	1.32158i
$766$		−	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	$-0.979478\pi$
$773$		−	3.58252i		−	0.128854i	0.997922	−	0.0644271i	$-0.0205220\pi$
$774$	−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
$780$	0.728651	−	24.7882i	0.0260899	−	0.887562i
$781$	−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	$-0.410417\pi$
$787$	15.5828			0.555466			0.277733	+	0.960658i	$0.410417\pi$
$788$	−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
$795$	0.351126	−	11.9451i	0.0124531	−	0.423648i
$796$			16.4657i			0.583612i
$797$		−	33.4891i		−	1.18625i	−0.805112	−	0.593123i	$-0.797895\pi$
$797$		−	33.4891i		−	1.18625i	0.805112	−	0.593123i	$-0.202105\pi$
$798$		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	$-0.107357\pi$
$810$	−16.7211	−	11.1984i	−0.587520	−	0.393473i
$811$			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	$0.0407411\pi$
$823$			7.32363i			0.255286i	−0.991820	+	0.127643i	$0.959259\pi$
$824$	−6.76706			−0.235742
$825$	32.5072	−	4.18828i	1.13176	−	0.145817i
$826$		0			0
$827$	24.6605			0.857529			0.428764	−	0.903416i	$-0.358949\pi$
$827$	24.6605			0.857529			0.428764	+	0.903416i	$0.358949\pi$
$828$	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	$-0.558753\pi$
$853$	−10.7205			−0.367064			−0.183532	+	0.983014i	$0.558753\pi$
$854$		0			0
$855$	3.02833	−	13.7819i	0.103567	−	0.471330i
$856$	−9.09162			−0.310745
$857$		−	17.2656i		−	0.589781i	−0.955531	−	0.294890i	$-0.904717\pi$
$857$		−	17.2656i		−	0.589781i	0.955531	−	0.294890i	$-0.0952831\pi$
$858$	−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	$-0.524114\pi$
$863$	−4.44663			−0.151365			−0.0756826	+	0.997132i	$0.524114\pi$
$864$	−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
$870$	−29.2439	−	0.859625i	−0.991462	−	0.0291440i
$871$			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	$0.241303\pi$
$877$			40.7210i			1.37505i	−0.726161	+	0.687525i	$0.758697\pi$
$878$		−	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	$-0.896461\pi$
$883$		−	18.9924i		−	0.639145i	0.947562	−	0.319572i	$-0.103539\pi$
$884$		−	35.7228i		−	1.20149i
$885$	−1.47626	+	50.2214i	−0.0496239	+	1.68817i
$886$	21.5549			0.724151
$887$		−	32.7978i		−	1.10124i	−0.834755	−	0.550621i	$-0.814391\pi$
$887$		−	32.7978i		−	1.10124i	0.834755	−	0.550621i	$-0.185609\pi$
$888$	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
$900$	−14.9741	−	0.881089i	−0.499137	−	0.0293696i
$901$		−	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	$0.408199\pi$
$907$			57.7453i			1.91740i	−0.284420	+	0.958700i	$0.591801\pi$
$908$			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
$915$	−40.0297	−	1.17667i	−1.32334	−	0.0388996i
$916$			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	$0.356625\pi$
$930$	13.2857	+	0.390534i	0.435656	+	0.0128061i
$931$		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	$-0.315369\pi$
$937$	33.5524			1.09611			0.548054	+	0.836443i	$0.315369\pi$
$938$		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	$-0.613871\pi$
$947$	−21.5510			−0.700312			−0.350156	+	0.936691i	$0.613871\pi$
$948$	−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	$-0.497478\pi$
$953$	0.489212			0.0158471			0.00792356	+	0.999969i	$0.497478\pi$
$954$	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
$960$	−0.113797	+	3.87131i	−0.00367279	+	0.124946i
$961$	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	$0.255368\pi$
$967$			44.7126i			1.43786i	−0.695083	+	0.718930i	$0.744632\pi$
$968$	−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
$975$	7.08597	+	54.9975i	0.226933	+	1.76133i
$976$			10.3401i			0.330978i
$977$	−11.6472			−0.372625			−0.186313	−	0.982490i	$-0.559654\pi$
$977$	−11.6472			−0.372625			−0.186313	+	0.982490i	$0.559654\pi$
$978$	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	$0.0950827\pi$
$983$			18.4536i			0.588577i	−0.955717	+	0.294289i	$0.904917\pi$
$984$	−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
$990$	−5.44861	+	24.7966i	−0.173168	+	0.788086i
$991$	−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	$-0.589997\pi$
$997$	−17.6179			−0.557964			−0.278982	+	0.960296i	$0.589997\pi$
$998$	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.h.1469.13	yes	24
3.2	odd	2		1470.2.d.g.1469.14	yes	24
5.4	even	2		1470.2.d.g.1469.12	yes	24
7.6	odd	2	inner	1470.2.d.h.1469.12	yes	24
15.14	odd	2	inner	1470.2.d.h.1469.11	yes	24
21.20	even	2		1470.2.d.g.1469.11	✓	24
35.34	odd	2		1470.2.d.g.1469.13	yes	24
105.104	even	2	inner	1470.2.d.h.1469.14	yes	24

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

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.321854 - 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 + 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} +1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.321854 - 1.70188i) q^{3} +1.00000 q^{4} +(-2.20838 + 0.350775i) q^{5} +(0.321854 - 1.70188i) q^{6} +1.00000 q^{8} +(-2.79282 - 1.09552i) q^{9} +(-2.20838 + 0.350775i) q^{10} +3.78464i q^{11} +(0.321854 - 1.70188i) q^{12} -6.40306 q^{13} +(-0.113797 + 3.87131i) q^{15} +1.00000 q^{16} +5.57902i q^{17} +(-2.79282 - 1.09552i) q^{18} -2.10349i q^{19} +(-2.20838 + 0.350775i) q^{20} +3.78464i q^{22} -4.70837 q^{23} +(0.321854 - 1.70188i) q^{24} +(4.75391 - 1.54929i) q^{25} -6.40306 q^{26} +(-2.76332 + 4.40046i) q^{27} +7.55401i q^{29} +(-0.113797 + 3.87131i) q^{30} -3.43184i q^{31} +1.00000 q^{32} +(6.44102 + 1.21810i) q^{33} +5.57902i q^{34} +(-2.79282 - 1.09552i) q^{36} +2.75706i q^{37} -2.10349i q^{38} +(-2.06085 + 10.8973i) q^{39} +(-2.20838 + 0.350775i) q^{40} -8.77986 q^{41} -7.04507i q^{43} +3.78464i q^{44} +(6.55190 + 1.43967i) q^{45} -4.70837 q^{46} -2.55610i q^{47} +(0.321854 - 1.70188i) q^{48} +(4.75391 - 1.54929i) q^{50} +(9.49485 + 1.79563i) q^{51} -6.40306 q^{52} -3.08554 q^{53} +(-2.76332 + 4.40046i) q^{54} +(-1.32756 - 8.35793i) q^{55} +(-3.57990 - 0.677017i) q^{57} +7.55401i q^{58} +12.9727 q^{59} +(-0.113797 + 3.87131i) q^{60} +10.3401i q^{61} -3.43184i q^{62} +1.00000 q^{64} +(14.1404 - 2.24604i) q^{65} +(6.44102 + 1.21810i) q^{66} -1.48871i q^{67} +5.57902i q^{68} +(-1.51541 + 8.01310i) q^{69} +5.06254i q^{71} +(-2.79282 - 1.09552i) q^{72} -3.33557 q^{73} +2.75706i q^{74} +(-1.10665 - 8.58926i) q^{75} -2.10349i q^{76} +(-2.06085 + 10.8973i) q^{78} -7.07694 q^{79} +(-2.20838 + 0.350775i) q^{80} +(6.59969 + 6.11916i) q^{81} -8.77986 q^{82} -9.49058i q^{83} +(-1.95698 - 12.3206i) q^{85} -7.04507i q^{86} +(12.8560 + 2.43129i) q^{87} +3.78464i q^{88} -10.6182 q^{89} +(6.55190 + 1.43967i) q^{90} -4.70837 q^{92} +(-5.84059 - 1.10455i) q^{93} -2.55610i q^{94} +(0.737854 + 4.64532i) q^{95} +(0.321854 - 1.70188i) q^{96} +4.90516 q^{97} +(4.14613 - 10.5698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 24 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 24 * q^4 + 24 * q^8 + 8 * q^9	\( 24 q + 24 q^{2} + 24 q^{4} + 24 q^{8} + 8 q^{9} - 16 q^{15} + 24 q^{16} + 8 q^{18} + 16 q^{23} + 8 q^{25} - 16 q^{30} + 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} + 8 q^{50} + 16 q^{51} - 16 q^{53} - 16 q^{57} - 16 q^{60} + 24 q^{64} + 48 q^{65} + 8 q^{72} + 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} + 16 q^{92} - 64 q^{93} + 112 q^{95} - 64 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 24 * q^4 + 24 * q^8 + 8 * q^9 - 16 * q^15 + 24 * q^16 + 8 * q^18 + 16 * q^23 + 8 * q^25 - 16 * q^30 + 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 + 8 * q^50 + 16 * q^51 - 16 * q^53 - 16 * q^57 - 16 * q^60 + 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

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Database

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