LMFDB - Embedded newform 168.3.z.a.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,3,Mod(73,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.73"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	168.z (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.57766844125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.126303473664.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 2x^{5} + 92x^{4} + 14x^{3} - 441x^{2} - 686x + 2401 $ x^8 - 2x^7 - 9x^6 + 2x^5 + 92x^4 + 14x^3 - 441x^2 - 686*x + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.1
Root			$2.18070 - 1.49818i$ of defining polynomial
Character	$\chi$	$=$	168.73
Dual form			168.3.z.a.145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{3} +(-2.31749 + 1.33800i) q^{5} +(6.66796 - 2.13033i) q^{7} +(1.50000 + 2.59808i) q^{9} +(5.85047 - 10.1333i) q^{11} -20.4983i q^{13} +4.63498 q^{15} +(-14.2300 - 8.21568i) q^{17} +(26.9458 - 15.5572i) q^{19} +(-11.8469 - 2.57913i) q^{21} +(2.82843 + 4.89898i) q^{23} +(-8.91949 + 15.4490i) q^{25} -5.19615i q^{27} +21.6493 q^{29} +(-4.60166 - 2.65677i) q^{31} +(-17.5514 + 10.1333i) q^{33} +(-12.6026 + 13.8588i) q^{35} +(-9.64231 - 16.7010i) q^{37} +(-17.7520 + 30.7474i) q^{39} +28.0340i q^{41} +73.0145 q^{43} +(-6.95247 - 4.01401i) q^{45} +(-27.9972 + 16.1642i) q^{47} +(39.9234 - 28.4099i) q^{49} +(14.2300 + 24.6470i) q^{51} +(-47.3905 + 82.0828i) q^{53} +31.3118i q^{55} -53.8916 q^{57} +(-97.8171 - 56.4748i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(15.5367 + 14.1284i) q^{63} +(27.4267 + 47.5045i) q^{65} +(3.84366 - 6.65741i) q^{67} -9.79796i q^{69} +22.9843 q^{71} +(-5.83874 - 3.37100i) q^{73} +(26.7585 - 15.4490i) q^{75} +(17.4234 - 80.0320i) q^{77} +(23.5951 + 40.8679i) q^{79} +(-4.50000 + 7.79423i) q^{81} +39.2763i q^{83} +43.9704 q^{85} +(-32.4739 - 18.7488i) q^{87} +(87.5329 - 50.5371i) q^{89} +(-43.6680 - 136.682i) q^{91} +(4.60166 + 7.97031i) q^{93} +(-41.6311 + 72.1072i) q^{95} -30.0955i q^{97} +35.1028 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 6 q^{5} - 4 q^{7} + 12 q^{9} + 14 q^{11} - 12 q^{15} + 12 q^{17} + 78 q^{19} + 18 q^{21} - 6 q^{25} - 4 q^{29} - 24 q^{31} - 42 q^{33} - 156 q^{35} + 50 q^{37} - 6 q^{39} - 20 q^{43} + 18 q^{45}+ \cdots + 84 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 + 6 * q^5 - 4 * q^7 + 12 * q^9 + 14 * q^11 - 12 * q^15 + 12 * q^17 + 78 * q^19 + 18 * q^21 - 6 * q^25 - 4 * q^29 - 24 * q^31 - 42 * q^33 - 156 * q^35 + 50 * q^37 - 6 * q^39 - 20 * q^43 + 18 * q^45 + 12 * q^47 + 220 * q^49 - 12 * q^51 - 50 * q^53 - 156 * q^57 - 186 * q^59 - 240 * q^61 - 42 * q^63 - 148 * q^65 + 34 * q^67 + 424 * q^71 + 294 * q^73 + 18 * q^75 + 126 * q^77 - 40 * q^79 - 36 * q^81 - 232 * q^85 + 6 * q^87 - 132 * q^89 - 378 * q^91 + 24 * q^93 + 144 * q^95 + 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	−2.31749	+	1.33800i	−0.463498	+	0.267601i	−0.713514	−	0.700641i	$-0.752897\pi$
$5$	−2.31749	+	1.33800i	−0.463498	+	0.267601i	0.250016	+	0.968242i	$0.419564\pi$
$6$		0			0
$7$	6.66796	−	2.13033i	0.952566	−	0.304332i
$7$	6.66796	−	2.13033i	0.952566	−	0.304332i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	5.85047	−	10.1333i	0.531861	−	0.921210i	−0.467447	−	0.884021i	$-0.654826\pi$
$11$	5.85047	−	10.1333i	0.531861	−	0.921210i	0.999308	−	0.0371893i	$-0.0118404\pi$
$12$		0			0
$13$		−	20.4983i		−	1.57679i	−0.615170	−	0.788395i	$-0.710913\pi$
$13$		−	20.4983i		−	1.57679i	0.615170	−	0.788395i	$-0.289087\pi$
$14$		0			0
$15$	4.63498			0.308999
$16$		0			0
$17$	−14.2300	−	8.21568i	−0.837057	−	0.483275i	0.0192058	−	0.999816i	$-0.493886\pi$
$17$	−14.2300	−	8.21568i	−0.837057	−	0.483275i	−0.856263	+	0.516540i	$0.827220\pi$
$18$		0			0
$19$	26.9458	−	15.5572i	1.41820	−	0.818798i	0.422059	−	0.906568i	$-0.361307\pi$
$19$	26.9458	−	15.5572i	1.41820	−	0.818798i	0.996141	+	0.0877701i	$0.0279741\pi$
$20$		0			0
$21$	−11.8469	−	2.57913i	−0.564136	−	0.122816i
$22$		0			0
$23$	2.82843	+	4.89898i	0.122975	+	0.212999i	0.920940	−	0.389705i	$-0.127423\pi$
$23$	2.82843	+	4.89898i	0.122975	+	0.212999i	−0.797965	+	0.602704i	$0.794090\pi$
$24$		0			0
$25$	−8.91949	+	15.4490i	−0.356780	+	0.617961i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	21.6493			0.746527			0.373264	−	0.927725i	$-0.378239\pi$
$29$	21.6493			0.746527			0.373264	+	0.927725i	$0.378239\pi$
$30$		0			0
$31$	−4.60166	−	2.65677i	−0.148441	−	0.0857022i	0.423940	−	0.905690i	$-0.360647\pi$
$31$	−4.60166	−	2.65677i	−0.148441	−	0.0857022i	−0.572381	+	0.819988i	$0.693980\pi$
$32$		0			0
$33$	−17.5514	+	10.1333i	−0.531861	+	0.307070i
$34$		0			0
$35$	−12.6026	+	13.8588i	−0.360073	+	0.395965i
$36$		0			0
$37$	−9.64231	−	16.7010i	−0.260603	−	0.451377i	0.705799	−	0.708412i	$-0.250588\pi$
$37$	−9.64231	−	16.7010i	−0.260603	−	0.451377i	−0.966402	+	0.257034i	$0.917255\pi$
$38$		0			0
$39$	−17.7520	+	30.7474i	−0.455180	+	0.788395i
$40$		0			0
$41$			28.0340i			0.683756i	0.939744	+	0.341878i	$0.111063\pi$
$41$			28.0340i			0.683756i	−0.939744	+	0.341878i	$0.888937\pi$
$42$		0			0
$43$	73.0145			1.69801			0.849006	−	0.528383i	$-0.177202\pi$
$43$	73.0145			1.69801			0.849006	+	0.528383i	$0.177202\pi$
$44$		0			0
$45$	−6.95247	−	4.01401i	−0.154499	−	0.0892003i
$46$		0			0
$47$	−27.9972	+	16.1642i	−0.595685	+	0.343919i	−0.767342	−	0.641238i	$-0.778421\pi$
$47$	−27.9972	+	16.1642i	−0.595685	+	0.343919i	0.171657	+	0.985157i	$0.445088\pi$
$48$		0			0
$49$	39.9234	−	28.4099i	0.814764	−	0.579793i
$50$		0			0
$51$	14.2300	+	24.6470i	0.279019	+	0.483275i
$52$		0			0
$53$	−47.3905	+	82.0828i	−0.894161	+	1.54873i	−0.0593216	+	0.998239i	$0.518894\pi$
$53$	−47.3905	+	82.0828i	−0.894161	+	1.54873i	−0.834839	+	0.550493i	$0.814440\pi$
$54$		0			0
$55$			31.3118i			0.569306i
$56$		0			0
$57$	−53.8916			−0.945467
$58$		0			0
$59$	−97.8171	−	56.4748i	−1.65792	−	0.957199i	−0.973674	−	0.227946i	$-0.926799\pi$
$59$	−97.8171	−	56.4748i	−1.65792	−	0.957199i	−0.684244	−	0.729253i	$-0.739868\pi$
$60$		0			0
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	−0.725322	−	0.688409i	$-0.758309\pi$
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	0.233519	+	0.972352i	$0.424976\pi$
$62$		0			0
$63$	15.5367	+	14.1284i	0.246614	+	0.224260i
$64$		0			0
$65$	27.4267	+	47.5045i	0.421950	+	0.730839i
$66$		0			0
$67$	3.84366	−	6.65741i	0.0573680	−	0.0993643i	−0.835915	−	0.548859i	$-0.815062\pi$
$67$	3.84366	−	6.65741i	0.0573680	−	0.0993643i	0.893283	+	0.449494i	$0.148396\pi$
$68$		0			0
$69$		−	9.79796i		−	0.141999i
$70$		0			0
$71$	22.9843			0.323723			0.161861	−	0.986813i	$-0.448250\pi$
$71$	22.9843			0.323723			0.161861	+	0.986813i	$0.448250\pi$
$72$		0			0
$73$	−5.83874	−	3.37100i	−0.0799828	−	0.0461781i	0.459475	−	0.888191i	$-0.348038\pi$
$73$	−5.83874	−	3.37100i	−0.0799828	−	0.0461781i	−0.539458	+	0.842013i	$0.681371\pi$
$74$		0			0
$75$	26.7585	−	15.4490i	0.356780	−	0.205987i
$76$		0			0
$77$	17.4234	−	80.0320i	0.226278	−	1.03938i
$78$		0			0
$79$	23.5951	+	40.8679i	0.298672	+	0.517316i	0.975832	−	0.218520i	$-0.0701229\pi$
$79$	23.5951	+	40.8679i	0.298672	+	0.517316i	−0.677160	+	0.735836i	$0.736790\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			39.2763i			0.473208i	0.971606	+	0.236604i	$0.0760345\pi$
$83$			39.2763i			0.473208i	−0.971606	+	0.236604i	$0.923966\pi$
$84$		0			0
$85$	43.9704			0.517299
$86$		0			0
$87$	−32.4739	−	18.7488i	−0.373264	−	0.215504i
$88$		0			0
$89$	87.5329	−	50.5371i	0.983516	−	0.567833i	0.0801860	−	0.996780i	$-0.474449\pi$
$89$	87.5329	−	50.5371i	0.983516	−	0.567833i	0.903330	+	0.428947i	$0.141115\pi$
$90$		0			0
$91$	−43.6680	−	136.682i	−0.479868	−	1.50200i
$92$		0			0
$93$	4.60166	+	7.97031i	0.0494802	+	0.0857022i
$94$		0			0
$95$	−41.6311	+	72.1072i	−0.438222	+	0.759023i
$96$		0			0
$97$		−	30.0955i		−	0.310263i	−0.987894	−	0.155132i	$-0.950420\pi$
$97$		−	30.0955i		−	0.310263i	0.987894	−	0.155132i	$-0.0495801\pi$
$98$		0			0
$99$	35.1028			0.354574
$100$		0			0
$101$	65.5570	+	37.8494i	0.649080	+	0.374746i	0.788104	−	0.615543i	$-0.211063\pi$
$101$	65.5570	+	37.8494i	0.649080	+	0.374746i	−0.139024	+	0.990289i	$0.544396\pi$
$102$		0			0
$103$	−56.7409	+	32.7594i	−0.550883	+	0.318052i	−0.749478	−	0.662029i	$-0.769695\pi$
$103$	−56.7409	+	32.7594i	−0.550883	+	0.318052i	0.198595	+	0.980082i	$0.436362\pi$
$104$		0			0
$105$	30.9059	−	9.87402i	0.294342	−	0.0940383i
$106$		0			0
$107$	−63.9724	−	110.803i	−0.597873	−	1.03555i	−0.993135	−	0.116977i	$-0.962679\pi$
$107$	−63.9724	−	110.803i	−0.597873	−	1.03555i	0.395262	−	0.918568i	$-0.370654\pi$
$108$		0			0
$109$	−39.5466	+	68.4967i	−0.362813	+	0.628410i	−0.988423	−	0.151726i	$-0.951517\pi$
$109$	−39.5466	+	68.4967i	−0.362813	+	0.628410i	0.625610	+	0.780136i	$0.284850\pi$
$110$		0			0
$111$			33.4019i			0.300918i
$112$		0			0
$113$	117.995			1.04420			0.522101	−	0.852884i	$-0.325148\pi$
$113$	117.995			1.04420			0.522101	+	0.852884i	$0.325148\pi$
$114$		0			0
$115$	−13.1097	−	7.56889i	−0.113997	−	0.0658165i
$116$		0			0
$117$	53.2560	−	30.7474i	0.455180	−	0.262798i
$118$		0			0
$119$	−112.387	−	24.4673i	−0.944428	−	0.205608i
$120$		0			0
$121$	−7.95601	−	13.7802i	−0.0657522	−	0.113886i
$122$		0			0
$123$	24.2781	−	42.0510i	0.197383	−	0.341878i
$124$		0			0
$125$		−	114.637i		−	0.917100i
$126$		0			0
$127$	37.9759			0.299022			0.149511	−	0.988760i	$-0.452230\pi$
$127$	37.9759			0.299022			0.149511	+	0.988760i	$0.452230\pi$
$128$		0			0
$129$	−109.522	−	63.2324i	−0.849006	−	0.490174i
$130$		0			0
$131$	223.325	−	128.937i	1.70477	−	0.984252i	0.764001	−	0.645215i	$-0.223232\pi$
$131$	223.325	−	128.937i	1.70477	−	0.984252i	0.940773	−	0.339037i	$-0.110101\pi$
$132$		0			0
$133$	146.532	−	161.138i	1.10174	−	1.21156i
$134$		0			0
$135$	6.95247	+	12.0420i	0.0514998	+	0.0892003i
$136$		0			0
$137$	52.4541	−	90.8531i	0.382876	−	0.663162i	−0.608596	−	0.793481i	$-0.708267\pi$
$137$	52.4541	−	90.8531i	0.382876	−	0.663162i	0.991472	+	0.130319i	$0.0416002\pi$
$138$		0			0
$139$			143.051i			1.02914i	0.857447	+	0.514572i	$0.172049\pi$
$139$			143.051i			1.02914i	−0.857447	+	0.514572i	$0.827951\pi$
$140$		0			0
$141$	55.9944			0.397124
$142$		0			0
$143$	−207.715	−	119.924i	−1.45255	−	0.838633i
$144$		0			0
$145$	−50.1720	+	28.9668i	−0.346014	+	0.199771i
$146$		0			0
$147$	−84.4888	+	8.04012i	−0.574754	+	0.0546947i
$148$		0			0
$149$	142.103	+	246.129i	0.953709	+	1.65187i	0.737295	+	0.675571i	$0.236103\pi$
$149$	142.103	+	246.129i	0.953709	+	1.65187i	0.216415	+	0.976302i	$0.430564\pi$
$150$		0			0
$151$	−94.6064	+	163.863i	−0.626532	+	1.08519i	0.361710	+	0.932291i	$0.382193\pi$
$151$	−94.6064	+	163.863i	−0.626532	+	1.08519i	−0.988242	+	0.152895i	$0.951140\pi$
$152$		0			0
$153$		−	49.2941i		−	0.322183i
$154$		0			0
$155$	14.2191			0.0917359
$156$		0			0
$157$	−131.112	−	75.6976i	−0.835108	−	0.482150i	0.0204901	−	0.999790i	$-0.493477\pi$
$157$	−131.112	−	75.6976i	−0.835108	−	0.482150i	−0.855599	+	0.517640i	$0.826811\pi$
$158$		0			0
$159$	142.172	−	82.0828i	0.894161	−	0.516244i
$160$		0			0
$161$	29.2963	+	26.6407i	0.181964	+	0.165470i
$162$		0			0
$163$	−84.2986	−	146.010i	−0.517170	−	0.895764i	−0.999801	−	0.0199405i	$-0.993652\pi$
$163$	−84.2986	−	146.010i	−0.517170	−	0.895764i	0.482632	−	0.875823i	$-0.339681\pi$
$164$		0			0
$165$	27.1168	−	46.9677i	0.164344	−	0.284653i
$166$		0			0
$167$			141.148i			0.845196i	0.906317	+	0.422598i	$0.138882\pi$
$167$			141.148i			0.845196i	−0.906317	+	0.422598i	$0.861118\pi$
$168$		0			0
$169$	−251.179			−1.48626
$170$		0			0
$171$	80.8374	+	46.6715i	0.472733	+	0.272933i
$172$		0			0
$173$	−54.3265	+	31.3654i	−0.314026	+	0.181303i	−0.648727	−	0.761021i	$-0.724698\pi$
$173$	−54.3265	+	31.3654i	−0.314026	+	0.181303i	0.334701	+	0.942325i	$0.391365\pi$
$174$		0			0
$175$	−26.5634	+	122.015i	−0.151791	+	0.697228i
$176$		0			0
$177$	97.8171	+	169.424i	0.552639	+	0.957199i
$178$		0			0
$179$	42.0038	−	72.7527i	0.234658	−	0.406440i	−0.724515	−	0.689259i	$-0.757936\pi$
$179$	42.0038	−	72.7527i	0.234658	−	0.406440i	0.959173	+	0.282819i	$0.0912696\pi$
$180$		0			0
$181$			289.875i			1.60152i	0.598987	+	0.800759i	$0.295570\pi$
$181$			289.875i			1.60152i	−0.598987	+	0.800759i	$0.704430\pi$
$182$		0			0
$183$	60.0000			0.327869
$184$		0			0
$185$	44.6919	+	25.8029i	0.241578	+	0.139475i
$186$		0			0
$187$	−166.504	+	96.1311i	−0.890396	+	0.514070i
$188$		0			0
$189$	−11.0695	−	34.6477i	−0.0585688	−	0.183321i
$190$		0			0
$191$	108.779	+	188.411i	0.569523	+	0.986443i	0.996613	+	0.0822338i	$0.0262054\pi$
$191$	108.779	+	188.411i	0.569523	+	0.986443i	−0.427090	+	0.904209i	$0.640461\pi$
$192$		0			0
$193$	−160.334	+	277.707i	−0.830747	+	1.43890i	0.0666991	+	0.997773i	$0.478753\pi$
$193$	−160.334	+	277.707i	−0.830747	+	1.43890i	−0.897446	+	0.441123i	$0.854580\pi$
$194$		0			0
$195$		−	95.0090i		−	0.487226i
$196$		0			0
$197$	−344.420			−1.74833			−0.874164	−	0.485632i	$-0.838590\pi$
$197$	−344.420			−1.74833			−0.874164	+	0.485632i	$0.838590\pi$
$198$		0			0
$199$	128.815	+	74.3716i	0.647313	+	0.373726i	0.787426	−	0.616409i	$-0.211413\pi$
$199$	128.815	+	74.3716i	0.647313	+	0.373726i	−0.140113	+	0.990136i	$0.544747\pi$
$200$		0			0
$201$	−11.5310	+	6.65741i	−0.0573680	+	0.0331214i
$202$		0			0
$203$	144.357	−	46.1201i	0.711116	−	0.227192i
$204$		0			0
$205$	−37.5096	−	64.9685i	−0.182974	−	0.316920i
$206$		0			0
$207$	−8.48528	+	14.6969i	−0.0409917	+	0.0709997i
$208$		0			0
$209$		−	364.067i		−	1.74195i
$210$		0			0
$211$	299.342			1.41868			0.709342	−	0.704864i	$-0.248992\pi$
$211$	299.342			1.41868			0.709342	+	0.704864i	$0.248992\pi$
$212$		0			0
$213$	−34.4765	−	19.9050i	−0.161861	−	0.0934508i
$214$		0			0
$215$	−169.210	+	97.6937i	−0.787025	+	0.454389i
$216$		0			0
$217$	−36.3435	−	7.91220i	−0.167481	−	0.0364617i
$218$		0			0
$219$	5.83874	+	10.1130i	0.0266609	+	0.0461781i
$220$		0			0
$221$	−168.407	+	291.690i	−0.762023	+	1.31986i
$222$		0			0
$223$			55.5613i			0.249154i	0.992210	+	0.124577i	$0.0397574\pi$
$223$			55.5613i			0.249154i	−0.992210	+	0.124577i	$0.960243\pi$
$224$		0			0
$225$	−53.5169			−0.237853
$226$		0			0
$227$	10.2970	+	5.94497i	0.0453612	+	0.0261893i	0.522509	−	0.852634i	$-0.324996\pi$
$227$	10.2970	+	5.94497i	0.0453612	+	0.0261893i	−0.477148	+	0.878823i	$0.658329\pi$
$228$		0			0
$229$	−127.851	+	73.8146i	−0.558300	+	0.322335i	−0.752463	−	0.658635i	$-0.771134\pi$
$229$	−127.851	+	73.8146i	−0.558300	+	0.322335i	0.194163	+	0.980969i	$0.437801\pi$
$230$		0			0
$231$	−95.4449	+	104.959i	−0.413181	+	0.454367i
$232$		0			0
$233$	−22.9405	−	39.7340i	−0.0984569	−	0.170532i	0.812589	−	0.582837i	$-0.198057\pi$
$233$	−22.9405	−	39.7340i	−0.0984569	−	0.170532i	−0.911046	+	0.412304i	$0.864724\pi$
$234$		0			0
$235$	43.2555	−	74.9208i	0.184066	−	0.318812i
$236$		0			0
$237$		−	81.7359i		−	0.344877i
$238$		0			0
$239$	423.448			1.77175			0.885875	−	0.463923i	$-0.153559\pi$
$239$	423.448			1.77175			0.885875	+	0.463923i	$0.153559\pi$
$240$		0			0
$241$	300.996	+	173.780i	1.24895	+	0.721080i	0.970900	−	0.239487i	$-0.0769793\pi$
$241$	300.996	+	173.780i	1.24895	+	0.721080i	0.278048	+	0.960567i	$0.410313\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−54.5096	+	119.257i	−0.222488	+	0.486764i
$246$		0			0
$247$	−318.895	−	552.342i	−1.29107	−	2.23620i
$248$		0			0
$249$	34.0143	−	58.9145i	0.136604	−	0.236604i
$250$		0			0
$251$			166.117i			0.661822i	0.943662	+	0.330911i	$0.107356\pi$
$251$			166.117i			0.661822i	−0.943662	+	0.330911i	$0.892644\pi$
$252$		0			0
$253$	66.1905			0.261623
$254$		0			0
$255$	−65.9556	−	38.0795i	−0.258650	−	0.149331i
$256$		0			0
$257$	181.559	−	104.823i	0.706457	−	0.407873i	−0.103291	−	0.994651i	$-0.532937\pi$
$257$	181.559	−	104.823i	0.706457	−	0.407873i	0.809748	+	0.586778i	$0.199604\pi$
$258$		0			0
$259$	−99.8730	−	90.8201i	−0.385610	−	0.350657i
$260$		0			0
$261$	32.4739	+	56.2465i	0.124421	+	0.215504i
$262$		0			0
$263$	232.621	−	402.911i	0.884490	−	1.53198i	0.0381935	−	0.999270i	$-0.487840\pi$
$263$	232.621	−	402.911i	0.884490	−	1.53198i	0.846297	−	0.532712i	$-0.178827\pi$
$264$		0			0
$265$		−	253.635i		−	0.957113i
$266$		0			0
$267$	−175.066			−0.655677
$268$		0			0
$269$	−323.787	−	186.938i	−1.20367	−	0.694939i	−0.242300	−	0.970201i	$-0.577902\pi$
$269$	−323.787	−	186.938i	−1.20367	−	0.694939i	−0.961369	+	0.275263i	$0.911235\pi$
$270$		0			0
$271$	−152.527	+	88.0615i	−0.562830	+	0.324950i	−0.754281	−	0.656552i	$-0.772014\pi$
$271$	−152.527	+	88.0615i	−0.562830	+	0.324950i	0.191450	+	0.981502i	$0.438681\pi$
$272$		0			0
$273$	−52.8677	+	242.840i	−0.193655	+	0.889524i
$274$		0			0
$275$	104.366	+	180.768i	0.379514	+	0.657338i
$276$		0			0
$277$	218.419	−	378.314i	0.788518	−	1.36575i	−0.138357	−	0.990382i	$-0.544182\pi$
$277$	218.419	−	378.314i	0.788518	−	1.36575i	0.926875	−	0.375371i	$-0.122485\pi$
$278$		0			0
$279$		−	15.9406i		−	0.0571348i
$280$		0			0
$281$	−275.670			−0.981034			−0.490517	−	0.871432i	$-0.663192\pi$
$281$	−275.670			−0.981034			−0.490517	+	0.871432i	$0.663192\pi$
$282$		0			0
$283$	257.688	+	148.776i	0.910558	+	0.525711i	0.880611	−	0.473841i	$-0.157133\pi$
$283$	257.688	+	148.776i	0.910558	+	0.525711i	0.0299473	+	0.999551i	$0.490466\pi$
$284$		0			0
$285$	124.893	−	72.1072i	0.438222	−	0.253008i
$286$		0			0
$287$	59.7216	+	186.930i	0.208089	+	0.651323i
$288$		0			0
$289$	−9.50532	−	16.4637i	−0.0328904	−	0.0569678i
$290$		0			0
$291$	−26.0635	+	45.1433i	−0.0895652	+	0.155132i
$292$		0			0
$293$		−	196.735i		−	0.671449i	−0.941960	−	0.335724i	$-0.891019\pi$
$293$		−	196.735i		−	0.671449i	0.941960	−	0.335724i	$-0.108981\pi$
$294$		0			0
$295$	302.254			1.02459
$296$		0			0
$297$	−52.6542	−	30.3999i	−0.177287	−	0.102357i
$298$		0			0
$299$	100.421	−	57.9778i	0.335855	−	0.193906i
$300$		0			0
$301$	486.858	−	155.545i	1.61747	−	0.516760i
$302$		0			0
$303$	−65.5570	−	113.548i	−0.216360	−	0.374746i
$304$		0			0
$305$	46.3498	−	80.2802i	0.151967	−	0.263214i
$306$		0			0
$307$			84.9923i			0.276848i	0.990373	+	0.138424i	$0.0442036\pi$
$307$			84.9923i			0.276848i	−0.990373	+	0.138424i	$0.955796\pi$
$308$		0			0
$309$	113.482			0.367255
$310$		0			0
$311$	126.508	+	73.0396i	0.406779	+	0.234854i	0.689405	−	0.724376i	$-0.257872\pi$
$311$	126.508	+	73.0396i	0.406779	+	0.234854i	−0.282626	+	0.959230i	$0.591205\pi$
$312$		0			0
$313$	−367.131	+	211.963i	−1.17294	+	0.677198i	−0.954371	−	0.298623i	$-0.903473\pi$
$313$	−367.131	+	211.963i	−1.17294	+	0.677198i	−0.218570	+	0.975821i	$0.570139\pi$
$314$		0			0
$315$	−54.9100	−	11.9542i	−0.174317	−	0.0379500i
$316$		0			0
$317$	−146.082	−	253.021i	−0.460826	−	0.798174i	0.538176	−	0.842832i	$-0.319113\pi$
$317$	−146.082	−	253.021i	−0.460826	−	0.798174i	−0.999002	+	0.0446581i	$0.985780\pi$
$318$		0			0
$319$	126.659	−	219.379i	0.397049	−	0.687709i
$320$		0			0
$321$			221.607i			0.690364i
$322$		0			0
$323$	−511.251			−1.58282
$324$		0			0
$325$	316.678	+	182.834i	0.974393	+	0.562566i
$326$		0			0
$327$	118.640	−	68.4967i	0.362813	−	0.209470i
$328$		0			0
$329$	−152.249	+	167.425i	−0.462764	+	0.508892i
$330$		0			0
$331$	−89.2476	−	154.581i	−0.269630	−	0.467013i	0.699136	−	0.714988i	$-0.253568\pi$
$331$	−89.2476	−	154.581i	−0.269630	−	0.467013i	−0.968766	+	0.247975i	$0.920235\pi$
$332$		0			0
$333$	28.9269	−	50.1029i	0.0868676	−	0.150459i
$334$		0			0
$335$			20.5713i			0.0614069i
$336$		0			0
$337$	−27.2722			−0.0809263			−0.0404631	−	0.999181i	$-0.512883\pi$
$337$	−27.2722			−0.0809263			−0.0404631	+	0.999181i	$0.512883\pi$
$338$		0			0
$339$	−176.992	−	102.187i	−0.522101	−	0.301435i
$340$		0			0
$341$	−53.8438	+	31.0867i	−0.157900	+	0.0911634i
$342$		0			0
$343$	205.685	−	274.486i	0.599666	−	0.800250i
$344$		0			0
$345$	13.1097	+	22.7067i	0.0379991	+	0.0658165i
$346$		0			0
$347$	62.7376	−	108.665i	0.180800	−	0.313155i	−0.761353	−	0.648337i	$-0.775465\pi$
$347$	62.7376	−	108.665i	0.180800	−	0.313155i	0.942153	+	0.335183i	$0.108798\pi$
$348$		0			0
$349$		−	413.962i		−	1.18614i	−0.805152	−	0.593068i	$-0.797916\pi$
$349$		−	413.962i		−	1.18614i	0.805152	−	0.593068i	$-0.202084\pi$
$350$		0			0
$351$	−106.512			−0.303453
$352$		0			0
$353$	599.009	+	345.838i	1.69691	+	0.979712i	0.948661	+	0.316294i	$0.102439\pi$
$353$	599.009	+	345.838i	1.69691	+	0.979712i	0.748250	+	0.663417i	$0.230895\pi$
$354$		0			0
$355$	−53.2660	+	30.7531i	−0.150045	+	0.0866285i
$356$		0			0
$357$	147.391	+	134.031i	0.412860	+	0.375437i
$358$		0			0
$359$	−189.194	−	327.693i	−0.527002	−	0.912794i	−0.999505	−	0.0314649i	$-0.989983\pi$
$359$	−189.194	−	327.693i	−0.527002	−	0.912794i	0.472503	−	0.881329i	$-0.343351\pi$
$360$		0			0
$361$	303.551	−	525.765i	0.840861	−	1.45641i
$362$		0			0
$363$			27.5604i			0.0759241i
$364$		0			0
$365$	18.0416			0.0494292
$366$		0			0
$367$	150.969	+	87.1620i	0.411360	+	0.237499i	0.691374	−	0.722497i	$-0.257006\pi$
$367$	150.969	+	87.1620i	0.411360	+	0.237499i	−0.280014	+	0.959996i	$0.590339\pi$
$368$		0			0
$369$	−72.8344	+	42.0510i	−0.197383	+	0.113959i
$370$		0			0
$371$	−141.135	+	648.282i	−0.380418	+	1.74739i
$372$		0			0
$373$	83.2147	+	144.132i	0.223096	+	0.386413i	0.955746	−	0.294192i	$-0.0950504\pi$
$373$	83.2147	+	144.132i	0.223096	+	0.386413i	−0.732651	+	0.680605i	$0.761717\pi$
$374$		0			0
$375$	−99.2789	+	171.956i	−0.264744	+	0.458550i
$376$		0			0
$377$		−	443.773i		−	1.17712i
$378$		0			0
$379$	−484.521			−1.27842			−0.639210	−	0.769033i	$-0.720738\pi$
$379$	−484.521			−1.27842			−0.639210	+	0.769033i	$0.720738\pi$
$380$		0			0
$381$	−56.9638	−	32.8881i	−0.149511	−	0.0863204i
$382$		0			0
$383$	−61.2723	+	35.3756i	−0.159980	+	0.0923645i	−0.577853	−	0.816141i	$-0.696109\pi$
$383$	−61.2723	+	35.3756i	−0.159980	+	0.0923645i	0.417873	+	0.908506i	$0.362776\pi$
$384$		0			0
$385$	66.7044	+	208.786i	0.173258	+	0.542301i
$386$		0			0
$387$	109.522	+	189.697i	0.283002	+	0.490174i
$388$		0			0
$389$	−358.124	+	620.288i	−0.920626	+	1.59457i	−0.122178	+	0.992508i	$0.538988\pi$
$389$	−358.124	+	620.288i	−0.920626	+	1.59457i	−0.798448	+	0.602063i	$0.794345\pi$
$390$		0			0
$391$		−	92.9498i		−	0.237723i
$392$		0			0
$393$	−446.651			−1.13652
$394$		0			0
$395$	−109.363	−	63.1407i	−0.276868	−	0.159850i
$396$		0			0
$397$	107.582	−	62.1124i	0.270987	−	0.156454i	−0.358349	−	0.933588i	$-0.616660\pi$
$397$	107.582	−	62.1124i	0.270987	−	0.156454i	0.629336	+	0.777133i	$0.283327\pi$
$398$		0			0
$399$	−359.347	+	114.807i	−0.900619	+	0.287736i
$400$		0			0
$401$	163.279	+	282.807i	0.407179	+	0.705255i	0.994572	−	0.104047i	$-0.0331792\pi$
$401$	163.279	+	282.807i	0.407179	+	0.705255i	−0.587393	+	0.809301i	$0.699846\pi$
$402$		0			0
$403$	−54.4592	+	94.3260i	−0.135134	+	0.234060i
$404$		0			0
$405$		−	24.0841i		−	0.0594668i
$406$		0			0
$407$	−225.648			−0.554418
$408$		0			0
$409$	439.282	+	253.620i	1.07404	+	0.620097i	0.929282	−	0.369370i	$-0.120426\pi$
$409$	439.282	+	253.620i	1.07404	+	0.620097i	0.144757	+	0.989467i	$0.453760\pi$
$410$		0			0
$411$	−157.362	+	90.8531i	−0.382876	+	0.221054i
$412$		0			0
$413$	−772.551	−	168.189i	−1.87058	−	0.407237i
$414$		0			0
$415$	−52.5518	−	91.0225i	−0.126631	−	0.219331i
$416$		0			0
$417$	123.886	−	214.577i	0.297088	−	0.514572i
$418$		0			0
$419$			367.851i			0.877926i	0.898505	+	0.438963i	$0.144654\pi$
$419$			367.851i			0.877926i	−0.898505	+	0.438963i	$0.855346\pi$
$420$		0			0
$421$	311.187			0.739162			0.369581	−	0.929199i	$-0.379501\pi$
$421$	311.187			0.739162			0.369581	+	0.929199i	$0.379501\pi$
$422$		0			0
$423$	−83.9916	−	48.4926i	−0.198562	−	0.114640i
$424$		0			0
$425$	253.848	−	146.559i	0.597290	−	0.344845i
$426$		0			0
$427$	−163.140	+	179.402i	−0.382062	+	0.420146i
$428$		0			0
$429$	207.715	+	359.773i	0.484185	+	0.838633i
$430$		0			0
$431$	290.773	−	503.634i	0.674648	−	1.16852i	−0.301924	−	0.953332i	$-0.597629\pi$
$431$	290.773	−	503.634i	0.674648	−	1.16852i	0.976572	−	0.215192i	$-0.0690378\pi$
$432$		0			0
$433$			786.154i			1.81560i	0.419406	+	0.907799i	$0.362238\pi$
$433$			786.154i			1.81560i	−0.419406	+	0.907799i	$0.637762\pi$
$434$		0			0
$435$	100.344			0.230676
$436$		0			0
$437$	152.428	+	88.0046i	0.348807	+	0.201384i
$438$		0			0
$439$	−3.68643	+	2.12836i	−0.00839733	+	0.00484820i	−0.504193	−	0.863591i	$-0.668210\pi$
$439$	−3.68643	+	2.12836i	−0.00839733	+	0.00484820i	0.495795	+	0.868439i	$0.334877\pi$
$440$		0			0
$441$	133.696	+	61.1093i	0.303166	+	0.138570i
$442$		0			0
$443$	240.189	+	416.020i	0.542188	+	0.939097i	0.998778	+	0.0494200i	$0.0157373\pi$
$443$	240.189	+	416.020i	0.542188	+	0.939097i	−0.456590	+	0.889677i	$0.650929\pi$
$444$		0			0
$445$	−135.238	+	234.239i	−0.303905	+	0.526379i
$446$		0			0
$447$		−	492.258i		−	1.10125i
$448$		0			0
$449$	−343.206			−0.764379			−0.382189	−	0.924084i	$-0.624830\pi$
$449$	−343.206			−0.764379			−0.382189	+	0.924084i	$0.624830\pi$
$450$		0			0
$451$	284.077	+	164.012i	0.629883	+	0.363663i
$452$		0			0
$453$	283.819	−	163.863i	0.626532	−	0.361729i
$454$		0			0
$455$	284.081	+	258.330i	0.624353	+	0.567759i
$456$		0			0
$457$	−379.304	−	656.973i	−0.829986	−	1.43758i	−0.898048	−	0.439897i	$-0.855015\pi$
$457$	−379.304	−	656.973i	−0.829986	−	1.43758i	0.0680618	−	0.997681i	$-0.478319\pi$
$458$		0			0
$459$	−42.6899	+	73.9411i	−0.0930063	+	0.161092i
$460$		0			0
$461$			395.110i			0.857073i	0.903525	+	0.428536i	$0.140971\pi$
$461$			395.110i			0.857073i	−0.903525	+	0.428536i	$0.859029\pi$
$462$		0			0
$463$	−466.432			−1.00741			−0.503706	−	0.863875i	$-0.668031\pi$
$463$	−466.432			−1.00741			−0.503706	+	0.863875i	$0.668031\pi$
$464$		0			0
$465$	−21.3286	−	12.3141i	−0.0458680	−	0.0264819i
$466$		0			0
$467$	−309.725	+	178.820i	−0.663223	+	0.382912i	−0.793504	−	0.608565i	$-0.791746\pi$
$467$	−309.725	+	178.820i	−0.663223	+	0.382912i	0.130281	+	0.991477i	$0.458412\pi$
$468$		0			0
$469$	11.4469	−	52.5796i	0.0244070	−	0.112110i
$470$		0			0
$471$	131.112	+	227.093i	0.278369	+	0.482150i
$472$		0			0
$473$	427.169	−	739.879i	0.903106	−	1.56423i
$474$		0			0
$475$			555.048i			1.16852i
$476$		0			0
$477$	−284.343			−0.596107
$478$		0			0
$479$	−103.564	−	59.7927i	−0.216209	−	0.124828i	0.387985	−	0.921666i	$-0.373171\pi$
$479$	−103.564	−	59.7927i	−0.216209	−	0.124828i	−0.604194	+	0.796838i	$0.706505\pi$
$480$		0			0
$481$	−342.341	+	197.650i	−0.711727	+	0.410916i
$482$		0			0
$483$	−20.8729	−	65.3324i	−0.0432150	−	0.135264i
$484$		0			0
$485$	40.2679	+	69.7461i	0.0830266	+	0.143806i
$486$		0			0
$487$	−146.513	+	253.769i	−0.300849	+	0.521085i	−0.976328	−	0.216293i	$-0.930603\pi$
$487$	−146.513	+	253.769i	−0.300849	+	0.521085i	0.675480	+	0.737379i	$0.263937\pi$
$488$		0			0
$489$			292.019i			0.597176i
$490$		0			0
$491$	95.4062			0.194310			0.0971549	−	0.995269i	$-0.469026\pi$
$491$	95.4062			0.194310			0.0971549	+	0.995269i	$0.469026\pi$
$492$		0			0
$493$	−308.069	−	177.864i	−0.624886	−	0.360778i
$494$		0			0
$495$	−81.3505	+	46.9677i	−0.164344	+	0.0948843i
$496$		0			0
$497$	153.259	−	48.9641i	0.308367	−	0.0985194i
$498$		0			0
$499$	−346.465	−	600.095i	−0.694319	−	1.20260i	−0.970410	−	0.241464i	$-0.922372\pi$
$499$	−346.465	−	600.095i	−0.694319	−	1.20260i	0.276090	−	0.961132i	$-0.410961\pi$
$500$		0			0
$501$	122.237	−	211.721i	0.243987	−	0.422598i
$502$		0			0
$503$			11.1075i			0.0220824i	0.999939	+	0.0110412i	$0.00351460\pi$
$503$			11.1075i			0.0220824i	−0.999939	+	0.0110412i	$0.996485\pi$
$504$		0			0
$505$	−202.570			−0.401130
$506$		0			0
$507$	376.768	+	217.527i	0.743132	+	0.429047i
$508$		0			0
$509$	143.706	−	82.9689i	0.282331	−	0.163004i	−0.352147	−	0.935945i	$-0.614548\pi$
$509$	143.706	−	82.9689i	0.282331	−	0.163004i	0.634478	+	0.772941i	$0.281215\pi$
$510$		0			0
$511$	−46.1139	−	10.0393i	−0.0902424	−	0.0196463i
$512$		0			0
$513$	−80.8374	−	140.014i	−0.157578	−	0.272933i
$514$		0			0
$515$	87.6643	−	151.839i	0.170222	−	0.294833i
$516$		0			0
$517$			378.273i			0.731669i
$518$		0			0
$519$	108.653			0.209351
$520$		0			0
$521$	−60.3444	−	34.8399i	−0.115824	−	0.0668712i	0.440969	−	0.897522i	$-0.354635\pi$
$521$	−60.3444	−	34.8399i	−0.115824	−	0.0668712i	−0.556793	+	0.830651i	$0.687968\pi$
$522$		0			0
$523$	64.3593	−	37.1578i	0.123058	−	0.0710475i	−0.437208	−	0.899361i	$-0.644032\pi$
$523$	64.3593	−	37.1578i	0.123058	−	0.0710475i	0.560265	+	0.828313i	$0.310699\pi$
$524$		0			0
$525$	145.513	−	160.018i	0.277168	−	0.304796i
$526$		0			0
$527$	43.6543	+	75.6115i	0.0828355	+	0.143475i
$528$		0			0
$529$	248.500	−	430.415i	0.469754	−	0.813638i
$530$		0			0
$531$		−	338.849i		−	0.638133i
$532$		0			0
$533$	574.648			1.07814
$534$		0			0
$535$	296.511	+	171.191i	0.554226	+	0.319982i
$536$		0			0
$537$	−126.011	+	72.7527i	−0.234658	+	0.135480i
$538$		0			0
$539$	−54.3154	−	570.768i	−0.100771	−	1.05894i
$540$		0			0
$541$	−96.2717	−	166.748i	−0.177951	−	0.308221i	0.763227	−	0.646130i	$-0.223614\pi$
$541$	−96.2717	−	166.748i	−0.177951	−	0.308221i	−0.941179	+	0.337909i	$0.890280\pi$
$542$		0			0
$543$	251.039	−	434.812i	0.462318	−	0.800759i
$544$		0			0
$545$		−	211.654i		−	0.388356i
$546$		0			0
$547$	−43.1121			−0.0788156			−0.0394078	−	0.999223i	$-0.512547\pi$
$547$	−43.1121			−0.0788156			−0.0394078	+	0.999223i	$0.512547\pi$
$548$		0			0
$549$	−90.0000	−	51.9615i	−0.163934	−	0.0946476i
$550$		0			0
$551$	583.357	−	336.802i	1.05872	−	0.611255i
$552$		0			0
$553$	244.393	+	222.241i	0.441941	+	0.401882i
$554$		0			0
$555$	−44.6919	−	77.4087i	−0.0805260	−	0.139475i
$556$		0			0
$557$	−107.492	+	186.182i	−0.192985	+	0.334259i	−0.946238	−	0.323471i	$-0.895150\pi$
$557$	−107.492	+	186.182i	−0.192985	+	0.334259i	0.753253	+	0.657730i	$0.228483\pi$
$558$		0			0
$559$		−	1496.67i		−	2.67741i
$560$		0			0
$561$	333.008			0.593597
$562$		0			0
$563$	−432.752	−	249.850i	−0.768654	−	0.443783i	0.0637401	−	0.997967i	$-0.479697\pi$
$563$	−432.752	−	249.850i	−0.768654	−	0.443783i	−0.832394	+	0.554184i	$0.813030\pi$
$564$		0			0
$565$	−273.452	+	157.878i	−0.483986	+	0.279429i
$566$		0			0
$567$	−13.4016	+	61.5581i	−0.0236359	+	0.108568i
$568$		0			0
$569$	−518.601	−	898.244i	−0.911426	−	1.57864i	−0.812052	−	0.583586i	$-0.801649\pi$
$569$	−518.601	−	898.244i	−0.911426	−	1.57864i	−0.0993742	−	0.995050i	$-0.531684\pi$
$570$		0			0
$571$	−212.807	+	368.593i	−0.372692	+	0.645521i	−0.989979	−	0.141217i	$-0.954899\pi$
$571$	−212.807	+	368.593i	−0.372692	+	0.645521i	0.617287	+	0.786738i	$0.288232\pi$
$572$		0			0
$573$		−	376.821i		−	0.657629i
$574$		0			0
$575$	−100.913			−0.175500
$576$		0			0
$577$	−182.211	−	105.199i	−0.315790	−	0.182321i	0.333725	−	0.942671i	$-0.391694\pi$
$577$	−182.211	−	105.199i	−0.315790	−	0.182321i	−0.649514	+	0.760349i	$0.725028\pi$
$578$		0			0
$579$	481.003	−	277.707i	0.830747	−	0.479632i
$580$		0			0
$581$	83.6714	+	261.893i	0.144013	+	0.450762i
$582$		0			0
$583$	554.514	+	960.446i	0.951139	+	1.64742i
$584$		0			0
$585$	−82.2802	+	142.514i	−0.140650	+	0.243613i
$586$		0			0
$587$		−	440.365i		−	0.750196i	−0.926985	−	0.375098i	$-0.877609\pi$
$587$		−	440.365i		−	0.750196i	0.926985	−	0.375098i	$-0.122391\pi$
$588$		0			0
$589$	−165.327			−0.280691
$590$		0			0
$591$	516.631	+	298.277i	0.874164	+	0.504699i
$592$		0			0
$593$	−39.7888	+	22.9721i	−0.0670975	+	0.0387388i	−0.533173	−	0.846006i	$-0.679001\pi$
$593$	−39.7888	+	22.9721i	−0.0670975	+	0.0387388i	0.466076	+	0.884745i	$0.345667\pi$
$594$		0			0
$595$	293.193	−	93.6714i	0.492761	−	0.157431i
$596$		0			0
$597$	−128.815	−	223.115i	−0.215771	−	0.373726i
$598$		0			0
$599$	150.377	−	260.461i	0.251047	−	0.434827i	−0.712767	−	0.701401i	$-0.752558\pi$
$599$	150.377	−	260.461i	0.251047	−	0.434827i	0.963814	+	0.266574i	$0.0858917\pi$
$600$		0			0
$601$			55.0039i			0.0915206i	0.998952	+	0.0457603i	$0.0145710\pi$
$601$			55.0039i			0.0915206i	−0.998952	+	0.0457603i	$0.985429\pi$
$602$		0			0
$603$	23.0619			0.0382453
$604$		0			0
$605$	36.8760	+	21.2904i	0.0609520	+	0.0351907i
$606$		0			0
$607$	393.383	−	227.120i	0.648078	−	0.374168i	−0.139642	−	0.990202i	$-0.544595\pi$
$607$	393.383	−	227.120i	0.648078	−	0.374168i	0.787719	+	0.616034i	$0.211262\pi$
$608$		0			0
$609$	−256.476	−	55.8364i	−0.421143	−	0.0916854i
$610$		0			0
$611$	331.338	+	573.894i	0.542288	+	0.939270i
$612$		0			0
$613$	−404.692	+	700.946i	−0.660182	+	1.14347i	0.320386	+	0.947287i	$0.396188\pi$
$613$	−404.692	+	700.946i	−0.660182	+	1.14347i	−0.980568	+	0.196182i	$0.937146\pi$
$614$		0			0
$615$			129.937i			0.211280i
$616$		0			0
$617$	398.646			0.646104			0.323052	−	0.946381i	$-0.395291\pi$
$617$	398.646			0.646104			0.323052	+	0.946381i	$0.395291\pi$
$618$		0			0
$619$	628.037	+	362.597i	1.01460	+	0.585779i	0.912535	−	0.408998i	$-0.134122\pi$
$619$	628.037	+	362.597i	1.01460	+	0.585779i	0.102065	+	0.994778i	$0.467455\pi$
$620$		0			0
$621$	25.4558	−	14.6969i	0.0409917	−	0.0236666i
$622$		0			0
$623$	476.005	−	523.453i	0.764054	−	0.840214i
$624$		0			0
$625$	−69.6020	−	120.554i	−0.111363	−	0.192887i
$626$		0			0
$627$	−315.291	+	546.100i	−0.502857	+	0.870974i
$628$		0			0
$629$			316.872i			0.503771i
$630$		0			0
$631$	−124.396			−0.197140			−0.0985702	−	0.995130i	$-0.531427\pi$
$631$	−124.396			−0.197140			−0.0985702	+	0.995130i	$0.531427\pi$
$632$		0			0
$633$	−449.014	−	259.238i	−0.709342	−	0.409539i
$634$		0			0
$635$	−88.0087	+	50.8118i	−0.138596	+	0.0800186i
$636$		0			0
$637$	−582.353	−	818.360i	−0.914212	−	1.28471i
$638$		0			0
$639$	34.4765	+	59.7150i	0.0539538	+	0.0934508i
$640$		0			0
$641$	−316.428	+	548.069i	−0.493647	+	0.855021i	−0.999973	−	0.00732074i	$-0.997670\pi$
$641$	−316.428	+	548.069i	−0.493647	+	0.855021i	0.506327	+	0.862342i	$0.331003\pi$
$642$		0			0
$643$			172.306i			0.267973i	0.990983	+	0.133986i	$0.0427778\pi$
$643$			172.306i			0.267973i	−0.990983	+	0.133986i	$0.957222\pi$
$644$		0			0
$645$	338.421			0.524684
$646$		0			0
$647$	−719.891	−	415.629i	−1.11266	−	0.642395i	−0.173143	−	0.984897i	$-0.555392\pi$
$647$	−719.891	−	415.629i	−1.11266	−	0.642395i	−0.939517	+	0.342502i	$0.888726\pi$
$648$		0			0
$649$	−1144.55	+	660.808i	−1.76356	+	1.01819i
$650$		0			0
$651$	47.6631	+	43.3427i	0.0732151	+	0.0665786i
$652$		0			0
$653$	−88.7540	−	153.726i	−0.135917	−	0.235416i	0.790030	−	0.613068i	$-0.210065\pi$
$653$	−88.7540	−	153.726i	−0.135917	−	0.235416i	−0.925948	+	0.377652i	$0.876731\pi$
$654$		0			0
$655$	−345.036	+	597.620i	−0.526773	+	0.912398i
$656$		0			0
$657$		−	20.2260i		−	0.0307854i
$658$		0			0
$659$	363.665			0.551843			0.275922	−	0.961180i	$-0.411017\pi$
$659$	363.665			0.551843			0.275922	+	0.961180i	$0.411017\pi$
$660$		0			0
$661$	−1056.92	−	610.213i	−1.59897	−	0.923167i	−0.991686	−	0.128684i	$-0.958925\pi$
$661$	−1056.92	−	610.213i	−1.59897	−	0.923167i	−0.607287	−	0.794483i	$-0.707742\pi$
$662$		0			0
$663$	505.221	−	291.690i	0.762023	−	0.439954i
$664$		0			0
$665$	−123.983	+	569.496i	−0.186440	+	0.856384i
$666$		0			0
$667$	61.2334	+	106.059i	0.0918043	+	0.159010i
$668$		0			0
$669$	48.1175	−	83.3420i	0.0719245	−	0.124577i
$670$		0			0
$671$			405.332i			0.604072i
$672$		0			0
$673$	−56.4549			−0.0838855			−0.0419427	−	0.999120i	$-0.513355\pi$
$673$	−56.4549			−0.0838855			−0.0419427	+	0.999120i	$0.513355\pi$
$674$		0			0
$675$	80.2754	+	46.3470i	0.118927	+	0.0686623i
$676$		0			0
$677$	508.499	−	293.582i	0.751106	−	0.433651i	−0.0749875	−	0.997184i	$-0.523892\pi$
$677$	508.499	−	293.582i	0.751106	−	0.433651i	0.826093	+	0.563533i	$0.190558\pi$
$678$		0			0
$679$	−64.1133	−	200.676i	−0.0944231	−	0.295546i
$680$		0			0
$681$	−10.2970	−	17.8349i	−0.0151204	−	0.0261893i
$682$		0			0
$683$	298.555	−	517.112i	0.437122	−	0.757118i	−0.560344	−	0.828260i	$-0.689331\pi$
$683$	298.555	−	517.112i	0.437122	−	0.757118i	0.997466	+	0.0711418i	$0.0226643\pi$
$684$		0			0
$685$			280.735i			0.409832i
$686$		0			0
$687$	255.701			0.372200
$688$		0			0
$689$	1682.55	+	971.423i	2.44202	+	1.40990i
$690$		0			0
$691$	−595.855	+	344.017i	−0.862309	+	0.497854i	−0.864785	−	0.502143i	$-0.832545\pi$
$691$	−595.855	+	344.017i	−0.862309	+	0.497854i	0.00247593	+	0.999997i	$0.499212\pi$
$692$		0			0
$693$	234.064	−	74.7805i	0.337755	−	0.107908i
$694$		0			0
$695$	−191.403	−	331.520i	−0.275400	−	0.477007i
$696$		0			0
$697$	230.318	−	398.923i	0.330442	−	0.572343i
$698$		0			0
$699$			79.4681i			0.113688i
$700$		0			0
$701$	868.040			1.23829			0.619144	−	0.785278i	$-0.287480\pi$
$701$	868.040			1.23829			0.619144	+	0.785278i	$0.287480\pi$
$702$		0			0
$703$	−519.639	−	300.014i	−0.739174	−	0.426762i
$704$		0			0
$705$	−129.767	+	74.9208i	−0.184066	+	0.106271i
$706$		0			0
$707$	517.763	+	112.720i	0.732339	+	0.159435i
$708$		0			0
$709$	392.954	+	680.617i	0.554237	+	0.959967i	0.997962	+	0.0638042i	$0.0203233\pi$
$709$	392.954	+	680.617i	0.554237	+	0.959967i	−0.443725	+	0.896163i	$0.646343\pi$
$710$		0			0
$711$	−70.7854	+	122.604i	−0.0995575	+	0.172439i
$712$		0			0
$713$		−	30.0579i		−	0.0421570i
$714$		0			0
$715$	641.838			0.897675
$716$		0			0
$717$	−635.173	−	366.717i	−0.885875	−	0.511460i
$718$		0			0
$719$	−1131.39	+	653.208i	−1.57356	+	0.908496i	−0.577833	+	0.816155i	$0.696102\pi$
$719$	−1131.39	+	653.208i	−1.57356	+	0.908496i	−0.995727	+	0.0923406i	$0.970565\pi$
$720$		0			0
$721$	−308.558	+	339.315i	−0.427958	+	0.470617i
$722$		0			0
$723$	−300.996	−	521.341i	−0.416316	−	0.721080i
$724$		0			0
$725$	−193.101	+	334.460i	−0.266346	+	0.461324i
$726$		0			0
$727$			577.725i			0.794670i	0.917674	+	0.397335i	$0.130065\pi$
$727$			577.725i			0.794670i	−0.917674	+	0.397335i	$0.869935\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−1038.99	−	599.864i	−1.42133	−	0.820607i
$732$		0			0
$733$	494.627	−	285.573i	0.674799	−	0.389595i	−0.123094	−	0.992395i	$-0.539282\pi$
$733$	494.627	−	285.573i	0.674799	−	0.389595i	0.797892	+	0.602800i	$0.205948\pi$
$734$		0			0
$735$	185.044	−	131.679i	0.251761	−	0.179155i
$736$		0			0
$737$	−44.9744	−	77.8980i	−0.0610236	−	0.105696i
$738$		0			0
$739$	−101.263	+	175.393i	−0.137027	+	0.237338i	−0.926370	−	0.376614i	$-0.877088\pi$
$739$	−101.263	+	175.393i	−0.137027	+	0.237338i	0.789343	+	0.613953i	$0.210422\pi$
$740$		0			0
$741$			1104.68i			1.49080i
$742$		0			0
$743$	−968.312			−1.30325			−0.651623	−	0.758543i	$-0.725911\pi$
$743$	−968.312			−1.30325			−0.651623	+	0.758543i	$0.725911\pi$
$744$		0			0
$745$	−658.643	−	380.268i	−0.884085	−	0.510427i
$746$		0			0
$747$	−102.043	+	58.9145i	−0.136604	+	0.0788681i
$748$		0			0
$749$	−662.613	−	602.551i	−0.884663	−	0.804474i
$750$		0			0
$751$	363.545	+	629.678i	0.484081	+	0.838453i	0.999833	−	0.0182854i	$-0.00582074\pi$
$751$	363.545	+	629.678i	0.484081	+	0.838453i	−0.515752	+	0.856738i	$0.672487\pi$
$752$		0			0
$753$	143.862	−	249.176i	0.191052	−	0.330911i
$754$		0			0
$755$		−	506.335i		−	0.670642i
$756$		0			0
$757$	1414.08			1.86800			0.934001	−	0.357269i	$-0.116292\pi$
$757$	1414.08			1.86800			0.934001	+	0.357269i	$0.116292\pi$
$758$		0			0
$759$	−99.2858	−	57.3227i	−0.130811	−	0.0755239i
$760$		0			0
$761$	143.869	−	83.0627i	0.189052	−	0.109149i	−0.402487	−	0.915426i	$-0.631854\pi$
$761$	143.869	−	83.0627i	0.189052	−	0.109149i	0.591539	+	0.806277i	$0.298521\pi$
$762$		0			0
$763$	−117.775	+	540.980i	−0.154357	+	0.709017i
$764$		0			0
$765$	65.9556	+	114.239i	0.0862165	+	0.149331i
$766$		0			0
$767$	−1157.63	+	2005.08i	−1.50930	+	2.61419i
$768$		0			0
$769$			361.961i			0.470690i	0.971912	+	0.235345i	$0.0756221\pi$
$769$			361.961i			0.470690i	−0.971912	+	0.235345i	$0.924378\pi$
$770$		0			0
$771$	−363.119			−0.470971
$772$		0			0
$773$	−1126.07	−	650.139i	−1.45676	−	0.841059i	−0.457907	−	0.889000i	$-0.651401\pi$
$773$	−1126.07	−	650.139i	−1.45676	−	0.841059i	−0.998850	+	0.0479409i	$0.984734\pi$
$774$		0			0
$775$	82.0889	−	47.3941i	0.105921	−	0.0611536i
$776$		0			0
$777$	71.1570	+	222.723i	0.0915792	+	0.286644i
$778$		0			0
$779$	436.129	+	755.398i	0.559858	+	0.969703i
$780$		0			0
$781$	134.469	−	232.907i	0.172176	−	0.298217i
$782$		0			0
$783$		−	112.493i		−	0.143669i
$784$		0			0
$785$	405.135			0.516095
$786$		0			0
$787$	−759.144	−	438.292i	−0.964605	−	0.556915i	−0.0670180	−	0.997752i	$-0.521348\pi$
$787$	−759.144	−	438.292i	−0.964605	−	0.556915i	−0.897587	+	0.440837i	$0.854682\pi$
$788$		0			0
$789$	−697.863	+	402.911i	−0.884490	+	0.510661i
$790$		0			0
$791$	786.785	−	251.368i	0.994671	−	0.317785i
$792$		0			0
$793$	355.040	+	614.948i	0.447718	+	0.775470i
$794$		0			0
$795$	−219.654	+	380.452i	−0.276295	+	0.478556i
$796$		0			0
$797$		−	101.354i		−	0.127170i	−0.997976	−	0.0635850i	$-0.979747\pi$
$797$		−	101.354i		−	0.127170i	0.997976	−	0.0635850i	$-0.0202534\pi$
$798$		0			0
$799$	531.199			0.664830
$800$		0			0
$801$	262.599	+	151.611i	0.327839	+	0.189278i
$802$		0			0
$803$	−68.3188	+	39.4439i	−0.0850795	+	0.0491206i
$804$		0			0
$805$	−103.539	−	22.5411i	−0.128620	−	0.0280014i
$806$		0			0
$807$	323.787	+	560.815i	0.401223	+	0.694939i
$808$		0			0
$809$	−257.364	+	445.768i	−0.318127	+	0.551012i	−0.980097	−	0.198518i	$-0.936387\pi$
$809$	−257.364	+	445.768i	−0.318127	+	0.551012i	0.661970	+	0.749530i	$0.269720\pi$
$810$		0			0
$811$		−	1599.34i		−	1.97206i	−0.166576	−	0.986029i	$-0.553271\pi$
$811$		−	1599.34i		−	1.97206i	0.166576	−	0.986029i	$-0.446729\pi$
$812$		0			0
$813$	305.054			0.375220
$814$		0			0
$815$	390.723	+	225.584i	0.479414	+	0.276790i
$816$		0			0
$817$	1967.43	−	1135.90i	2.40812	−	1.39033i
$818$		0			0
$819$	289.607	−	318.475i	0.353611	−	0.388859i
$820$		0			0
$821$	601.727	+	1042.22i	0.732920	+	1.26945i	0.955630	+	0.294569i	$0.0951762\pi$
$821$	601.727	+	1042.22i	0.732920	+	1.26945i	−0.222711	+	0.974885i	$0.571490\pi$
$822$		0			0
$823$	−98.2519	+	170.177i	−0.119383	+	0.206777i	−0.919523	−	0.393036i	$-0.871425\pi$
$823$	−98.2519	+	170.177i	−0.119383	+	0.206777i	0.800141	+	0.599812i	$0.204758\pi$
$824$		0			0
$825$		−	361.536i		−	0.438225i
$826$		0			0
$827$	−921.653			−1.11445			−0.557227	−	0.830360i	$-0.688135\pi$
$827$	−921.653			−1.11445			−0.557227	+	0.830360i	$0.688135\pi$
$828$		0			0
$829$	−213.872	−	123.479i	−0.257988	−	0.148950i	0.365428	−	0.930840i	$-0.380923\pi$
$829$	−213.872	−	123.479i	−0.257988	−	0.148950i	−0.623417	+	0.781890i	$0.714256\pi$
$830$		0			0
$831$	−655.258	+	378.314i	−0.788518	+	0.455251i
$832$		0			0
$833$	−801.515	+	76.2738i	−0.962203	+	0.0915651i
$834$		0			0
$835$	−188.856	−	327.108i	−0.226175	−	0.391747i
$836$		0			0
$837$	−13.8050	+	23.9109i	−0.0164934	+	0.0285674i
$838$		0			0
$839$		−	132.800i		−	0.158284i	−0.996863	−	0.0791418i	$-0.974782\pi$
$839$		−	132.800i		−	0.158284i	0.996863	−	0.0791418i	$-0.0252180\pi$
$840$		0			0
$841$	−372.308			−0.442697
$842$		0			0
$843$	413.506	+	238.738i	0.490517	+	0.283200i
$844$		0			0
$845$	582.104	−	336.078i	0.688881	−	0.397725i
$846$		0			0
$847$	−82.4068	−	74.9371i	−0.0972925	−	0.0884735i
$848$		0			0
$849$	−257.688	−	446.329i	−0.303519	−	0.525711i
$850$		0			0
$851$	54.5451	−	94.4749i	0.0640953	−	0.111016i
$852$		0			0
$853$			387.617i			0.454416i	0.973846	+	0.227208i	$0.0729598\pi$
$853$			387.617i			0.454416i	−0.973846	+	0.227208i	$0.927040\pi$
$854$		0			0
$855$	−249.787			−0.292148
$856$		0			0
$857$	468.967	+	270.758i	0.547219	+	0.315937i	0.748000	−	0.663699i	$-0.231014\pi$
$857$	468.967	+	270.758i	0.547219	+	0.315937i	−0.200780	+	0.979636i	$0.564348\pi$
$858$		0			0
$859$	1032.64	−	596.196i	1.20214	−	0.694059i	0.241113	−	0.970497i	$-0.422488\pi$
$859$	1032.64	−	596.196i	1.20214	−	0.694059i	0.961032	+	0.276439i	$0.0891542\pi$
$860$		0			0
$861$	72.3034	−	332.115i	0.0839761	−	0.385731i
$862$		0			0
$863$	−249.748	−	432.576i	−0.289395	−	0.501247i	0.684271	−	0.729228i	$-0.260121\pi$
$863$	−249.748	−	432.576i	−0.289395	−	0.501247i	−0.973665	+	0.227982i	$0.926787\pi$
$864$		0			0
$865$	83.9341	−	145.378i	0.0970337	−	0.168067i
$866$		0			0
$867$			32.9274i			0.0379786i
$868$		0			0
$869$	552.170			0.635409
$870$		0			0
$871$	−136.465	−	78.7883i	−0.156677	−	0.0904573i
$872$		0			0
$873$	78.1904	−	45.1433i	0.0895652	−	0.0517105i
$874$		0			0
$875$	−244.215	−	764.398i	−0.279103	−	0.873598i
$876$		0			0
$877$	−337.810	−	585.105i	−0.385189	−	0.667166i	0.606607	−	0.795002i	$-0.292530\pi$
$877$	−337.810	−	585.105i	−0.385189	−	0.667166i	−0.991795	+	0.127836i	$0.959197\pi$
$878$		0			0
$879$	−170.377	+	295.102i	−0.193831	+	0.335724i
$880$		0			0
$881$			98.9362i			0.112300i	0.998422	+	0.0561500i	$0.0178825\pi$
$881$			98.9362i			0.112300i	−0.998422	+	0.0561500i	$0.982118\pi$
$882$		0			0
$883$	550.179			0.623079			0.311540	−	0.950233i	$-0.399155\pi$
$883$	550.179			0.623079			0.311540	+	0.950233i	$0.399155\pi$
$884$		0			0
$885$	−453.381	−	261.759i	−0.512294	−	0.295773i
$886$		0			0
$887$	−249.102	+	143.819i	−0.280836	+	0.162141i	−0.633802	−	0.773495i	$-0.718507\pi$
$887$	−249.102	+	143.819i	−0.280836	+	0.162141i	0.352966	+	0.935636i	$0.385173\pi$
$888$		0			0
$889$	253.222	−	80.9010i	0.284839	−	0.0910022i
$890$		0			0
$891$	52.6542	+	91.1998i	0.0590957	+	0.102357i
$892$		0			0
$893$	−502.938	+	871.114i	−0.563201	+	0.975492i
$894$		0			0
$895$			224.805i			0.251179i
$896$		0			0
$897$	−200.841			−0.223903
$898$		0			0
$899$	−99.6227	−	57.5172i	−0.110815	−	0.0639791i
$900$		0			0
$901$	1348.73	−	778.691i	1.49693	−	0.864252i
$902$		0			0
$903$	−864.993	−	188.314i	−0.957910	−	0.208543i
$904$		0			0
$905$	−387.853	−	671.782i	−0.428567	−	0.742300i
$906$		0			0
$907$	109.150	−	189.054i	0.120342	−	0.208439i	−0.799560	−	0.600586i	$-0.794934\pi$
$907$	109.150	−	189.054i	0.120342	−	0.208439i	0.919903	+	0.392147i	$0.128267\pi$
$908$		0			0
$909$			227.096i			0.249831i
$910$		0			0
$911$	−8.50926			−0.00934057			−0.00467029	−	0.999989i	$-0.501487\pi$
$911$	−8.50926			−0.00934057			−0.00467029	+	0.999989i	$0.501487\pi$
$912$		0			0
$913$	397.999	+	229.785i	0.435924	+	0.251681i
$914$		0			0
$915$	−139.049	+	80.2802i	−0.151967	+	0.0877380i
$916$		0			0
$917$	1214.45	−	1335.50i	1.32437	−	1.45638i
$918$		0			0
$919$	215.082	+	372.533i	0.234039	+	0.405367i	0.958993	−	0.283430i	$-0.0914723\pi$
$919$	215.082	+	372.533i	0.234039	+	0.405367i	−0.724954	+	0.688797i	$0.758139\pi$
$920$		0			0
$921$	73.6055	−	127.488i	0.0799191	−	0.138424i
$922$		0			0
$923$		−	471.139i		−	0.510443i
$924$		0			0
$925$	344.018			0.371911
$926$		0			0
$927$	−170.223	−	98.2781i	−0.183628	−	0.106017i
$928$		0			0
$929$	−471.602	+	272.280i	−0.507645	+	0.293089i	−0.731865	−	0.681450i	$-0.761350\pi$
$929$	−471.602	+	272.280i	−0.507645	+	0.293089i	0.224220	+	0.974539i	$0.428017\pi$
$930$		0			0
$931$	633.791	−	1386.62i	0.680764	−	1.48939i
$932$		0			0
$933$	−126.508	−	219.119i	−0.135593	−	0.234854i
$934$		0			0
$935$	257.248	−	445.566i	0.275131	−	0.476541i
$936$		0			0
$937$			152.767i			0.163038i	0.996672	+	0.0815190i	$0.0259771\pi$
$937$			152.767i			0.163038i	−0.996672	+	0.0815190i	$0.974023\pi$
$938$		0			0
$939$	734.261			0.781961
$940$		0			0
$941$	−486.649	−	280.967i	−0.517161	−	0.298583i	0.218611	−	0.975812i	$-0.429847\pi$
$941$	−486.649	−	280.967i	−0.517161	−	0.298583i	−0.735773	+	0.677229i	$0.763181\pi$
$942$		0			0
$943$	−137.338	+	79.2921i	−0.145639	+	0.0840849i
$944$		0			0
$945$	72.0123	+	65.4848i	0.0762035	+	0.0692961i
$946$		0			0
$947$	41.2983	+	71.5308i	0.0436096	+	0.0755341i	0.887006	−	0.461757i	$-0.152781\pi$
$947$	41.2983	+	71.5308i	0.0436096	+	0.0755341i	−0.843397	+	0.537291i	$0.819448\pi$
$948$		0			0
$949$	−69.0996	+	119.684i	−0.0728131	+	0.126116i
$950$		0			0
$951$			506.042i			0.532116i
$952$		0			0
$953$	1171.84			1.22963			0.614817	−	0.788670i	$-0.289230\pi$
$953$	1171.84			1.22963			0.614817	+	0.788670i	$0.289230\pi$
$954$		0			0
$955$	−504.188	−	291.093i	−0.527946	−	0.304810i
$956$		0			0
$957$	−379.976	+	219.379i	−0.397049	+	0.229236i
$958$		0			0
$959$	156.215	−	717.549i	0.162894	−	0.748227i
$960$		0			0
$961$	−466.383	−	807.799i	−0.485310	−	0.840582i
$962$		0			0
$963$	191.917	−	332.410i	0.199291	−	0.345182i
$964$		0			0
$965$		−	858.111i		−	0.889234i
$966$		0			0
$967$	−1587.63			−1.64181			−0.820906	−	0.571063i	$-0.806531\pi$
$967$	−1587.63			−1.64181			−0.820906	+	0.571063i	$0.806531\pi$
$968$		0			0
$969$	766.876	+	442.756i	0.791409	+	0.456920i
$970$		0			0
$971$	202.765	−	117.067i	0.208821	−	0.120563i	−0.391942	−	0.919990i	$-0.628197\pi$
$971$	202.765	−	117.067i	0.208821	−	0.120563i	0.600763	+	0.799427i	$0.294863\pi$
$972$		0			0
$973$	304.746	+	953.859i	0.313202	+	0.980328i
$974$		0			0
$975$	−316.678	−	548.502i	−0.324798	−	0.562566i
$976$		0			0
$977$	−36.7223	+	63.6049i	−0.0375868	+	0.0651023i	−0.884207	−	0.467096i	$-0.845300\pi$
$977$	−36.7223	+	63.6049i	−0.0375868	+	0.0651023i	0.846620	+	0.532198i	$0.178634\pi$
$978$		0			0
$979$		−	1182.66i		−	1.20803i
$980$		0			0
$981$	−237.279			−0.241875
$982$		0			0
$983$	598.399	+	345.486i	0.608748	+	0.351461i	0.772475	−	0.635045i	$-0.219018\pi$
$983$	598.399	+	345.486i	0.608748	+	0.351461i	−0.163727	+	0.986506i	$0.552352\pi$
$984$		0			0
$985$	798.191	−	460.836i	0.810346	−	0.467854i
$986$		0			0
$987$	373.369	−	119.286i	0.378286	−	0.120858i
$988$		0			0
$989$	206.516	+	357.697i	0.208813	+	0.361675i
$990$		0			0
$991$	486.214	−	842.148i	0.490630	−	0.849796i	−0.509312	−	0.860582i	$-0.670100\pi$
$991$	486.214	−	842.148i	0.490630	−	0.849796i	0.999942	+	0.0107862i	$0.00343342\pi$
$992$		0			0
$993$			309.163i			0.311342i
$994$		0			0
$995$	−398.038			−0.400038
$996$		0			0
$997$	−1351.99	−	780.573i	−1.35606	−	0.782922i	−0.366971	−	0.930233i	$-0.619605\pi$
$997$	−1351.99	−	780.573i	−1.35606	−	0.782922i	−0.989090	+	0.147310i	$0.952938\pi$
$998$		0			0
$999$	−86.7808	+	50.1029i	−0.0868676	+	0.0501530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.3.z.a.73.1	✓	8
3.2	odd	2		504.3.by.a.73.4		8
4.3	odd	2		336.3.bh.h.241.1		8
7.2	even	3		1176.3.z.d.313.4		8
7.3	odd	6		1176.3.f.a.97.4		8
7.4	even	3		1176.3.f.a.97.5		8
7.5	odd	6	inner	168.3.z.a.145.1	yes	8
7.6	odd	2		1176.3.z.d.913.4		8
12.11	even	2		1008.3.cg.n.577.4		8
21.5	even	6		504.3.by.a.145.4		8
21.11	odd	6		3528.3.f.f.2449.7		8
21.17	even	6		3528.3.f.f.2449.2		8
28.3	even	6		2352.3.f.k.97.8		8
28.11	odd	6		2352.3.f.k.97.1		8
28.19	even	6		336.3.bh.h.145.1		8
84.47	odd	6		1008.3.cg.n.145.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.a.73.1	✓	8	1.1	even	1	trivial
168.3.z.a.145.1	yes	8	7.5	odd	6	inner
336.3.bh.h.145.1		8	28.19	even	6
336.3.bh.h.241.1		8	4.3	odd	2
504.3.by.a.73.4		8	3.2	odd	2
504.3.by.a.145.4		8	21.5	even	6
1008.3.cg.n.145.4		8	84.47	odd	6
1008.3.cg.n.577.4		8	12.11	even	2
1176.3.f.a.97.4		8	7.3	odd	6
1176.3.f.a.97.5		8	7.4	even	3
1176.3.z.d.313.4		8	7.2	even	3
1176.3.z.d.913.4		8	7.6	odd	2
2352.3.f.k.97.1		8	28.11	odd	6
2352.3.f.k.97.8		8	28.3	even	6
3528.3.f.f.2449.2		8	21.17	even	6
3528.3.f.f.2449.7		8	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	168.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-2.31749 + 1.33800i) q^{5} +(6.66796 - 2.13033i) q^{7} +(1.50000 + 2.59808i) q^{9} +(5.85047 - 10.1333i) q^{11} -20.4983i q^{13} +4.63498 q^{15} +(-14.2300 - 8.21568i) q^{17} +(26.9458 - 15.5572i) q^{19} +(-11.8469 - 2.57913i) q^{21} +(2.82843 + 4.89898i) q^{23} +(-8.91949 + 15.4490i) q^{25} -5.19615i q^{27} +21.6493 q^{29} +(-4.60166 - 2.65677i) q^{31} +(-17.5514 + 10.1333i) q^{33} +(-12.6026 + 13.8588i) q^{35} +(-9.64231 - 16.7010i) q^{37} +(-17.7520 + 30.7474i) q^{39} +28.0340i q^{41} +73.0145 q^{43} +(-6.95247 - 4.01401i) q^{45} +(-27.9972 + 16.1642i) q^{47} +(39.9234 - 28.4099i) q^{49} +(14.2300 + 24.6470i) q^{51} +(-47.3905 + 82.0828i) q^{53} +31.3118i q^{55} -53.8916 q^{57} +(-97.8171 - 56.4748i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(15.5367 + 14.1284i) q^{63} +(27.4267 + 47.5045i) q^{65} +(3.84366 - 6.65741i) q^{67} -9.79796i q^{69} +22.9843 q^{71} +(-5.83874 - 3.37100i) q^{73} +(26.7585 - 15.4490i) q^{75} +(17.4234 - 80.0320i) q^{77} +(23.5951 + 40.8679i) q^{79} +(-4.50000 + 7.79423i) q^{81} +39.2763i q^{83} +43.9704 q^{85} +(-32.4739 - 18.7488i) q^{87} +(87.5329 - 50.5371i) q^{89} +(-43.6680 - 136.682i) q^{91} +(4.60166 + 7.97031i) q^{93} +(-41.6311 + 72.1072i) q^{95} -30.0955i q^{97} +35.1028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 6 q^{5} - 4 q^{7} + 12 q^{9} + 14 q^{11} - 12 q^{15} + 12 q^{17} + 78 q^{19} + 18 q^{21} - 6 q^{25} - 4 q^{29} - 24 q^{31} - 42 q^{33} - 156 q^{35} + 50 q^{37} - 6 q^{39} - 20 q^{43} + 18 q^{45}+ \cdots + 84 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 + 6 * q^5 - 4 * q^7 + 12 * q^9 + 14 * q^11 - 12 * q^15 + 12 * q^17 + 78 * q^19 + 18 * q^21 - 6 * q^25 - 4 * q^29 - 24 * q^31 - 42 * q^33 - 156 * q^35 + 50 * q^37 - 6 * q^39 - 20 * q^43 + 18 * q^45 + 12 * q^47 + 220 * q^49 - 12 * q^51 - 50 * q^53 - 156 * q^57 - 186 * q^59 - 240 * q^61 - 42 * q^63 - 148 * q^65 + 34 * q^67 + 424 * q^71 + 294 * q^73 + 18 * q^75 + 126 * q^77 - 40 * q^79 - 36 * q^81 - 232 * q^85 + 6 * q^87 - 132 * q^89 - 378 * q^91 + 24 * q^93 + 144 * q^95 + 84 * q^99

Introduction

L-functions

Modular forms

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