LMFDB - Embedded newform 336.3.bh.h.145.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(145,336)] 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("336.145"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,12,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.15533688251$
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:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-2.38781 - 1.13946i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.3.bh.h.241.1

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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	0.250016	−	0.968242i	$-0.419564\pi$
$5$	−2.31749	−	1.33800i	−0.463498	−	0.267601i	−0.713514	+	0.700641i	$0.752897\pi$
$6$		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	−0.999308	−	0.0371893i	$-0.988160\pi$
$11$	−5.85047	−	10.1333i	−0.531861	−	0.921210i	0.467447	−	0.884021i	$-0.345174\pi$
$12$		0			0
$13$			20.4983i			1.57679i	0.615170	+	0.788395i	$0.289087\pi$
$13$			20.4983i			1.57679i	−0.615170	+	0.788395i	$0.710913\pi$
$14$		0			0
$15$	−4.63498			−0.308999
$16$		0			0
$17$	−14.2300	+	8.21568i	−0.837057	+	0.483275i	−0.856263	−	0.516540i	$-0.827220\pi$
$17$	−14.2300	+	8.21568i	−0.837057	+	0.483275i	0.0192058	+	0.999816i	$0.493886\pi$
$18$		0			0
$19$	−26.9458	−	15.5572i	−1.41820	−	0.818798i	−0.422059	−	0.906568i	$-0.638693\pi$
$19$	−26.9458	−	15.5572i	−1.41820	−	0.818798i	−0.996141	+	0.0877701i	$0.972026\pi$
$20$		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	$-0.872577\pi$
$23$	−2.82843	+	4.89898i	−0.122975	+	0.212999i	0.797965	+	0.602704i	$0.205910\pi$
$24$		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	$-0.639353\pi$
$31$	4.60166	−	2.65677i	0.148441	−	0.0857022i	0.572381	+	0.819988i	$0.306020\pi$
$32$		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	−0.966402	−	0.257034i	$-0.917255\pi$
$37$	−9.64231	+	16.7010i	−0.260603	+	0.451377i	0.705799	+	0.708412i	$0.250588\pi$
$38$		0			0
$39$	17.7520	+	30.7474i	0.455180	+	0.788395i
$40$		0			0
$41$		−	28.0340i		−	0.683756i	−0.939744	−	0.341878i	$-0.888937\pi$
$41$		−	28.0340i		−	0.683756i	0.939744	−	0.341878i	$-0.111063\pi$
$42$		0			0
$43$	−73.0145			−1.69801			−0.849006	−	0.528383i	$-0.822798\pi$
$43$	−73.0145			−1.69801			−0.849006	+	0.528383i	$0.822798\pi$
$44$		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	$-0.221579\pi$
$47$	27.9972	+	16.1642i	0.595685	+	0.343919i	−0.171657	+	0.985157i	$0.554912\pi$
$48$		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	−0.834839	−	0.550493i	$-0.814440\pi$
$53$	−47.3905	−	82.0828i	−0.894161	−	1.54873i	−0.0593216	−	0.998239i	$-0.518894\pi$
$54$		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	0.684244	−	0.729253i	$-0.260132\pi$
$59$	97.8171	−	56.4748i	1.65792	−	0.957199i	0.973674	−	0.227946i	$-0.0732010\pi$
$60$		0			0
$61$	−30.0000	−	17.3205i	−0.491803	−	0.283943i	0.233519	−	0.972352i	$-0.424976\pi$
$61$	−30.0000	−	17.3205i	−0.491803	−	0.283943i	−0.725322	+	0.688409i	$0.758309\pi$
$62$		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	$-0.184938\pi$
$67$	−3.84366	−	6.65741i	−0.0573680	−	0.0993643i	−0.893283	+	0.449494i	$0.851604\pi$
$68$		0			0
$69$			9.79796i			0.141999i
$70$		0			0
$71$	−22.9843			−0.323723			−0.161861	−	0.986813i	$-0.551750\pi$
$71$	−22.9843			−0.323723			−0.161861	+	0.986813i	$0.551750\pi$
$72$		0			0
$73$	−5.83874	+	3.37100i	−0.0799828	+	0.0461781i	−0.539458	−	0.842013i	$-0.681371\pi$
$73$	−5.83874	+	3.37100i	−0.0799828	+	0.0461781i	0.459475	+	0.888191i	$0.348038\pi$
$74$		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	$-0.929877\pi$
$79$	−23.5951	+	40.8679i	−0.298672	+	0.517316i	0.677160	+	0.735836i	$0.263210\pi$
$80$		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	0.903330	−	0.428947i	$-0.141115\pi$
$89$	87.5329	+	50.5371i	0.983516	+	0.567833i	0.0801860	+	0.996780i	$0.474449\pi$
$90$		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	$0.0495801\pi$
$97$			30.0955i			0.310263i	−0.987894	+	0.155132i	$0.950420\pi$
$98$		0			0
$99$	−35.1028			−0.354574
$100$		0			0
$101$	65.5570	−	37.8494i	0.649080	−	0.374746i	−0.139024	−	0.990289i	$-0.544396\pi$
$101$	65.5570	−	37.8494i	0.649080	−	0.374746i	0.788104	+	0.615543i	$0.211063\pi$
$102$		0			0
$103$	56.7409	+	32.7594i	0.550883	+	0.318052i	0.749478	−	0.662029i	$-0.230305\pi$
$103$	56.7409	+	32.7594i	0.550883	+	0.318052i	−0.198595	+	0.980082i	$0.563638\pi$
$104$		0			0
$105$	30.9059	+	9.87402i	0.294342	+	0.0940383i
$106$		0			0
$107$	63.9724	−	110.803i	0.597873	−	1.03555i	−0.395262	−	0.918568i	$-0.629346\pi$
$107$	63.9724	−	110.803i	0.597873	−	1.03555i	0.993135	−	0.116977i	$-0.0373205\pi$
$108$		0			0
$109$	−39.5466	−	68.4967i	−0.362813	−	0.628410i	0.625610	−	0.780136i	$-0.284850\pi$
$109$	−39.5466	−	68.4967i	−0.362813	−	0.628410i	−0.988423	+	0.151726i	$0.951517\pi$
$110$		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	$-0.547770\pi$
$127$	−37.9759			−0.299022			−0.149511	+	0.988760i	$0.547770\pi$
$128$		0			0
$129$	−109.522	+	63.2324i	−0.849006	+	0.490174i
$130$		0			0
$131$	−223.325	−	128.937i	−1.70477	−	0.984252i	−0.940773	−	0.339037i	$-0.889899\pi$
$131$	−223.325	−	128.937i	−1.70477	−	0.984252i	−0.764001	−	0.645215i	$-0.776768\pi$
$132$		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	0.991472	−	0.130319i	$-0.0416002\pi$
$137$	52.4541	+	90.8531i	0.382876	+	0.663162i	−0.608596	+	0.793481i	$0.708267\pi$
$138$		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	0.216415	−	0.976302i	$-0.430564\pi$
$149$	142.103	−	246.129i	0.953709	−	1.65187i	0.737295	−	0.675571i	$-0.236103\pi$
$150$		0			0
$151$	94.6064	+	163.863i	0.626532	+	1.08519i	0.988242	+	0.152895i	$0.0488597\pi$
$151$	94.6064	+	163.863i	0.626532	+	1.08519i	−0.361710	+	0.932291i	$0.617807\pi$
$152$		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	−0.855599	−	0.517640i	$-0.826811\pi$
$157$	−131.112	+	75.6976i	−0.835108	+	0.482150i	0.0204901	+	0.999790i	$0.493477\pi$
$158$		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	−0.482632	−	0.875823i	$-0.660319\pi$
$163$	84.2986	−	146.010i	0.517170	−	0.895764i	0.999801	−	0.0199405i	$-0.00634768\pi$
$164$		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	0.334701	−	0.942325i	$-0.391365\pi$
$173$	−54.3265	−	31.3654i	−0.314026	−	0.181303i	−0.648727	+	0.761021i	$0.724698\pi$
$174$		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	$-0.242064\pi$
$179$	−42.0038	−	72.7527i	−0.234658	−	0.406440i	−0.959173	+	0.282819i	$0.908730\pi$
$180$		0			0
$181$		−	289.875i		−	1.60152i	−0.598987	−	0.800759i	$-0.704430\pi$
$181$		−	289.875i		−	1.60152i	0.598987	−	0.800759i	$-0.295570\pi$
$182$		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	0.427090	+	0.904209i	$0.359539\pi$
$191$	−108.779	+	188.411i	−0.569523	+	0.986443i	−0.996613	+	0.0822338i	$0.973795\pi$
$192$		0			0
$193$	−160.334	−	277.707i	−0.830747	−	1.43890i	−0.897446	−	0.441123i	$-0.854580\pi$
$193$	−160.334	−	277.707i	−0.830747	−	1.43890i	0.0666991	−	0.997773i	$-0.478753\pi$
$194$		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	$-0.788587\pi$
$199$	−128.815	+	74.3716i	−0.647313	+	0.373726i	0.140113	+	0.990136i	$0.455253\pi$
$200$		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	$-0.751008\pi$
$211$	−299.342			−1.41868			−0.709342	+	0.704864i	$0.751008\pi$
$212$		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	$-0.675004\pi$
$227$	−10.2970	+	5.94497i	−0.0453612	+	0.0261893i	0.477148	+	0.878823i	$0.341671\pi$
$228$		0			0
$229$	−127.851	−	73.8146i	−0.558300	−	0.322335i	0.194163	−	0.980969i	$-0.437801\pi$
$229$	−127.851	−	73.8146i	−0.558300	−	0.322335i	−0.752463	+	0.658635i	$0.771134\pi$
$230$		0			0
$231$	95.4449	+	104.959i	0.413181	+	0.454367i
$232$		0			0
$233$	−22.9405	+	39.7340i	−0.0984569	+	0.170532i	−0.911046	−	0.412304i	$-0.864724\pi$
$233$	−22.9405	+	39.7340i	−0.0984569	+	0.170532i	0.812589	+	0.582837i	$0.198057\pi$
$234$		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	$-0.846441\pi$
$239$	−423.448			−1.77175			−0.885875	+	0.463923i	$0.846441\pi$
$240$		0			0
$241$	300.996	−	173.780i	1.24895	−	0.721080i	0.278048	−	0.960567i	$-0.410313\pi$
$241$	300.996	−	173.780i	1.24895	−	0.721080i	0.970900	+	0.239487i	$0.0769793\pi$
$242$		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	0.809748	−	0.586778i	$-0.199604\pi$
$257$	181.559	+	104.823i	0.706457	+	0.407873i	−0.103291	+	0.994651i	$0.532937\pi$
$258$		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	−0.846297	−	0.532712i	$-0.821173\pi$
$263$	−232.621	−	402.911i	−0.884490	−	1.53198i	−0.0381935	−	0.999270i	$-0.512160\pi$
$264$		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	−0.961369	−	0.275263i	$-0.911235\pi$
$269$	−323.787	+	186.938i	−1.20367	+	0.694939i	−0.242300	+	0.970201i	$0.577902\pi$
$270$		0			0
$271$	152.527	+	88.0615i	0.562830	+	0.324950i	0.754281	−	0.656552i	$-0.227986\pi$
$271$	152.527	+	88.0615i	0.562830	+	0.324950i	−0.191450	+	0.981502i	$0.561319\pi$
$272$		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	0.926875	+	0.375371i	$0.122485\pi$
$277$	218.419	+	378.314i	0.788518	+	1.36575i	−0.138357	+	0.990382i	$0.544182\pi$
$278$		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	$-0.842867\pi$
$283$	−257.688	+	148.776i	−0.910558	+	0.525711i	−0.0299473	+	0.999551i	$0.509534\pi$
$284$		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	$0.108981\pi$
$293$			196.735i			0.671449i	−0.941960	+	0.335724i	$0.891019\pi$
$294$		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	$-0.742128\pi$
$311$	−126.508	+	73.0396i	−0.406779	+	0.234854i	0.282626	+	0.959230i	$0.408795\pi$
$312$		0			0
$313$	−367.131	−	211.963i	−1.17294	−	0.677198i	−0.218570	−	0.975821i	$-0.570139\pi$
$313$	−367.131	−	211.963i	−1.17294	−	0.677198i	−0.954371	+	0.298623i	$0.903473\pi$
$314$		0			0
$315$	54.9100	−	11.9542i	0.174317	−	0.0379500i
$316$		0			0
$317$	−146.082	+	253.021i	−0.460826	+	0.798174i	−0.999002	−	0.0446581i	$-0.985780\pi$
$317$	−146.082	+	253.021i	−0.460826	+	0.798174i	0.538176	+	0.842832i	$0.319113\pi$
$318$		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	$-0.746432\pi$
$331$	89.2476	−	154.581i	0.269630	−	0.467013i	0.968766	+	0.247975i	$0.0797652\pi$
$332$		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	$-0.224535\pi$
$347$	−62.7376	−	108.665i	−0.180800	−	0.313155i	−0.942153	+	0.335183i	$0.891202\pi$
$348$		0			0
$349$			413.962i			1.18614i	0.805152	+	0.593068i	$0.202084\pi$
$349$			413.962i			1.18614i	−0.805152	+	0.593068i	$0.797916\pi$
$350$		0			0
$351$	106.512			0.303453
$352$		0			0
$353$	599.009	−	345.838i	1.69691	−	0.979712i	0.748250	−	0.663417i	$-0.230895\pi$
$353$	599.009	−	345.838i	1.69691	−	0.979712i	0.948661	−	0.316294i	$-0.102439\pi$
$354$		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	−0.472503	−	0.881329i	$-0.656649\pi$
$359$	189.194	−	327.693i	0.527002	−	0.912794i	0.999505	−	0.0314649i	$-0.0100173\pi$
$360$		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	$-0.742994\pi$
$367$	−150.969	+	87.1620i	−0.411360	+	0.237499i	0.280014	+	0.959996i	$0.409661\pi$
$368$		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	−0.732651	−	0.680605i	$-0.761717\pi$
$373$	83.2147	−	144.132i	0.223096	−	0.386413i	0.955746	+	0.294192i	$0.0950504\pi$
$374$		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	$-0.279262\pi$
$379$	484.521			1.27842			0.639210	+	0.769033i	$0.279262\pi$
$380$		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	$-0.303891\pi$
$383$	61.2723	+	35.3756i	0.159980	+	0.0923645i	−0.417873	+	0.908506i	$0.637224\pi$
$384$		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	−0.798448	−	0.602063i	$-0.794345\pi$
$389$	−358.124	−	620.288i	−0.920626	−	1.59457i	−0.122178	−	0.992508i	$-0.538988\pi$
$390$		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	0.629336	−	0.777133i	$-0.283327\pi$
$397$	107.582	+	62.1124i	0.270987	+	0.156454i	−0.358349	+	0.933588i	$0.616660\pi$
$398$		0			0
$399$	359.347	+	114.807i	0.900619	+	0.287736i
$400$		0			0
$401$	163.279	−	282.807i	0.407179	−	0.705255i	−0.587393	−	0.809301i	$-0.699846\pi$
$401$	163.279	−	282.807i	0.407179	−	0.705255i	0.994572	+	0.104047i	$0.0331792\pi$
$402$		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	0.144757	−	0.989467i	$-0.453760\pi$
$409$	439.282	−	253.620i	1.07404	−	0.620097i	0.929282	+	0.369370i	$0.120426\pi$
$410$		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	−0.976572	−	0.215192i	$-0.930962\pi$
$431$	−290.773	−	503.634i	−0.674648	−	1.16852i	0.301924	−	0.953332i	$-0.402371\pi$
$432$		0			0
$433$		−	786.154i		−	1.81560i	−0.419406	−	0.907799i	$-0.637762\pi$
$433$		−	786.154i		−	1.81560i	0.419406	−	0.907799i	$-0.362238\pi$
$434$		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	$-0.331790\pi$
$439$	3.68643	+	2.12836i	0.00839733	+	0.00484820i	−0.495795	+	0.868439i	$0.665123\pi$
$440$		0			0
$441$	133.696	−	61.1093i	0.303166	−	0.138570i
$442$		0			0
$443$	−240.189	+	416.020i	−0.542188	+	0.939097i	0.456590	+	0.889677i	$0.349071\pi$
$443$	−240.189	+	416.020i	−0.542188	+	0.939097i	−0.998778	+	0.0494200i	$0.984263\pi$
$444$		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	0.0680618	+	0.997681i	$0.478319\pi$
$457$	−379.304	+	656.973i	−0.829986	+	1.43758i	−0.898048	+	0.439897i	$0.855015\pi$
$458$		0			0
$459$	42.6899	+	73.9411i	0.0930063	+	0.161092i
$460$		0			0
$461$		−	395.110i		−	0.857073i	−0.903525	−	0.428536i	$-0.859029\pi$
$461$		−	395.110i		−	0.857073i	0.903525	−	0.428536i	$-0.140971\pi$
$462$		0			0
$463$	466.432			1.00741			0.503706	−	0.863875i	$-0.331969\pi$
$463$	466.432			1.00741			0.503706	+	0.863875i	$0.331969\pi$
$464$		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	$-0.208254\pi$
$467$	309.725	+	178.820i	0.663223	+	0.382912i	−0.130281	+	0.991477i	$0.541588\pi$
$468$		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	$-0.626829\pi$
$479$	103.564	−	59.7927i	0.216209	−	0.124828i	0.604194	+	0.796838i	$0.293495\pi$
$480$		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	$-0.0693967\pi$
$487$	146.513	+	253.769i	0.300849	+	0.521085i	−0.675480	+	0.737379i	$0.736063\pi$
$488$		0			0
$489$		−	292.019i		−	0.597176i
$490$		0			0
$491$	−95.4062			−0.194310			−0.0971549	−	0.995269i	$-0.530974\pi$
$491$	−95.4062			−0.194310			−0.0971549	+	0.995269i	$0.530974\pi$
$492$		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	−0.276090	−	0.961132i	$-0.589039\pi$
$499$	346.465	−	600.095i	0.694319	−	1.20260i	0.970410	−	0.241464i	$-0.0776277\pi$
$500$		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	0.634478	−	0.772941i	$-0.281215\pi$
$509$	143.706	+	82.9689i	0.282331	+	0.163004i	−0.352147	+	0.935945i	$0.614548\pi$
$510$		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	−0.556793	−	0.830651i	$-0.687968\pi$
$521$	−60.3444	+	34.8399i	−0.115824	+	0.0668712i	0.440969	+	0.897522i	$0.354635\pi$
$522$		0			0
$523$	−64.3593	−	37.1578i	−0.123058	−	0.0710475i	0.437208	−	0.899361i	$-0.355968\pi$
$523$	−64.3593	−	37.1578i	−0.123058	−	0.0710475i	−0.560265	+	0.828313i	$0.689301\pi$
$524$		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	−0.941179	−	0.337909i	$-0.890280\pi$
$541$	−96.2717	+	166.748i	−0.177951	+	0.308221i	0.763227	+	0.646130i	$0.223614\pi$
$542$		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	$-0.487453\pi$
$547$	43.1121			0.0788156			0.0394078	+	0.999223i	$0.487453\pi$
$548$		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	0.753253	−	0.657730i	$-0.228483\pi$
$557$	−107.492	−	186.182i	−0.192985	−	0.334259i	−0.946238	+	0.323471i	$0.895150\pi$
$558$		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	$-0.520303\pi$
$563$	432.752	−	249.850i	0.768654	−	0.443783i	0.832394	+	0.554184i	$0.186970\pi$
$564$		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	−0.0993742	+	0.995050i	$0.531684\pi$
$569$	−518.601	+	898.244i	−0.911426	+	1.57864i	−0.812052	+	0.583586i	$0.801649\pi$
$570$		0			0
$571$	212.807	+	368.593i	0.372692	+	0.645521i	0.989979	−	0.141217i	$-0.0451015\pi$
$571$	212.807	+	368.593i	0.372692	+	0.645521i	−0.617287	+	0.786738i	$0.711768\pi$
$572$		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	−0.649514	−	0.760349i	$-0.725028\pi$
$577$	−182.211	+	105.199i	−0.315790	+	0.182321i	0.333725	+	0.942671i	$0.391694\pi$
$578$		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	0.466076	−	0.884745i	$-0.345667\pi$
$593$	−39.7888	−	22.9721i	−0.0670975	−	0.0387388i	−0.533173	+	0.846006i	$0.679001\pi$
$594$		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	$-0.247442\pi$
$599$	−150.377	−	260.461i	−0.251047	−	0.434827i	−0.963814	+	0.266574i	$0.914108\pi$
$600$		0			0
$601$		−	55.0039i		−	0.0915206i	−0.998952	−	0.0457603i	$-0.985429\pi$
$601$		−	55.0039i		−	0.0915206i	0.998952	−	0.0457603i	$-0.0145710\pi$
$602$		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	$-0.455405\pi$
$607$	−393.383	−	227.120i	−0.648078	−	0.374168i	−0.787719	+	0.616034i	$0.788738\pi$
$608$		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	−0.980568	−	0.196182i	$-0.937146\pi$
$613$	−404.692	−	700.946i	−0.660182	−	1.14347i	0.320386	−	0.947287i	$-0.396188\pi$
$614$		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	$-0.865878\pi$
$619$	−628.037	+	362.597i	−1.01460	+	0.585779i	−0.102065	+	0.994778i	$0.532545\pi$
$620$		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	$-0.468573\pi$
$631$	124.396			0.197140			0.0985702	+	0.995130i	$0.468573\pi$
$632$		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	0.506327	−	0.862342i	$-0.331003\pi$
$641$	−316.428	−	548.069i	−0.493647	−	0.855021i	−0.999973	+	0.00732074i	$0.997670\pi$
$642$		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	$-0.444608\pi$
$647$	719.891	−	415.629i	1.11266	−	0.642395i	0.939517	+	0.342502i	$0.111274\pi$
$648$		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	−0.925948	−	0.377652i	$-0.876731\pi$
$653$	−88.7540	+	153.726i	−0.135917	+	0.235416i	0.790030	+	0.613068i	$0.210065\pi$
$654$		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	$-0.588983\pi$
$659$	−363.665			−0.551843			−0.275922	+	0.961180i	$0.588983\pi$
$660$		0			0
$661$	−1056.92	+	610.213i	−1.59897	+	0.923167i	−0.607287	+	0.794483i	$0.707742\pi$
$661$	−1056.92	+	610.213i	−1.59897	+	0.923167i	−0.991686	+	0.128684i	$0.958925\pi$
$662$		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	0.826093	−	0.563533i	$-0.190558\pi$
$677$	508.499	+	293.582i	0.751106	+	0.433651i	−0.0749875	+	0.997184i	$0.523892\pi$
$678$		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	$-0.310669\pi$
$683$	−298.555	−	517.112i	−0.437122	−	0.757118i	−0.997466	+	0.0711418i	$0.977336\pi$
$684$		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	$-0.167455\pi$
$691$	595.855	+	344.017i	0.862309	+	0.497854i	−0.00247593	+	0.999997i	$0.500788\pi$
$692$		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	−0.443725	−	0.896163i	$-0.646343\pi$
$709$	392.954	−	680.617i	0.554237	−	0.959967i	0.997962	−	0.0638042i	$-0.0203233\pi$
$710$		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	0.995727	+	0.0923406i	$0.0294349\pi$
$719$	1131.39	+	653.208i	1.57356	+	0.908496i	0.577833	+	0.816155i	$0.303898\pi$
$720$		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	0.797892	−	0.602800i	$-0.205948\pi$
$733$	494.627	+	285.573i	0.674799	+	0.389595i	−0.123094	+	0.992395i	$0.539282\pi$
$734$		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	$-0.122912\pi$
$739$	101.263	+	175.393i	0.137027	+	0.237338i	−0.789343	+	0.613953i	$0.789578\pi$
$740$		0			0
$741$		−	1104.68i		−	1.49080i
$742$		0			0
$743$	968.312			1.30325			0.651623	−	0.758543i	$-0.274089\pi$
$743$	968.312			1.30325			0.651623	+	0.758543i	$0.274089\pi$
$744$		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	$-0.994179\pi$
$751$	−363.545	+	629.678i	−0.484081	+	0.838453i	0.515752	+	0.856738i	$0.327513\pi$
$752$		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	0.591539	−	0.806277i	$-0.298521\pi$
$761$	143.869	+	83.0627i	0.189052	+	0.109149i	−0.402487	+	0.915426i	$0.631854\pi$
$762$		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	$-0.924378\pi$
$769$		−	361.961i		−	0.470690i	0.971912	−	0.235345i	$-0.0756221\pi$
$770$		0			0
$771$	363.119			0.470971
$772$		0			0
$773$	−1126.07	+	650.139i	−1.45676	+	0.841059i	−0.998850	−	0.0479409i	$-0.984734\pi$
$773$	−1126.07	+	650.139i	−1.45676	+	0.841059i	−0.457907	+	0.889000i	$0.651401\pi$
$774$		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	$-0.478652\pi$
$787$	759.144	−	438.292i	0.964605	−	0.556915i	0.897587	+	0.440837i	$0.145318\pi$
$788$		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	$0.0202534\pi$
$797$			101.354i			0.127170i	−0.997976	+	0.0635850i	$0.979747\pi$
$798$		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	0.661970	−	0.749530i	$-0.269720\pi$
$809$	−257.364	−	445.768i	−0.318127	−	0.551012i	−0.980097	+	0.198518i	$0.936387\pi$
$810$		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	−0.222711	−	0.974885i	$-0.571490\pi$
$821$	601.727	−	1042.22i	0.732920	−	1.26945i	0.955630	−	0.294569i	$-0.0951762\pi$
$822$		0			0
$823$	98.2519	+	170.177i	0.119383	+	0.206777i	0.919523	−	0.393036i	$-0.128575\pi$
$823$	98.2519	+	170.177i	0.119383	+	0.206777i	−0.800141	+	0.599812i	$0.795242\pi$
$824$		0			0
$825$			361.536i			0.438225i
$826$		0			0
$827$	921.653			1.11445			0.557227	−	0.830360i	$-0.311865\pi$
$827$	921.653			1.11445			0.557227	+	0.830360i	$0.311865\pi$
$828$		0			0
$829$	−213.872	+	123.479i	−0.257988	+	0.148950i	−0.623417	−	0.781890i	$-0.714256\pi$
$829$	−213.872	+	123.479i	−0.257988	+	0.148950i	0.365428	+	0.930840i	$0.380923\pi$
$830$		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	$-0.927040\pi$
$853$		−	387.617i		−	0.454416i	0.973846	−	0.227208i	$-0.0729598\pi$
$854$		0			0
$855$	249.787			0.292148
$856$		0			0
$857$	468.967	−	270.758i	0.547219	−	0.315937i	−0.200780	−	0.979636i	$-0.564348\pi$
$857$	468.967	−	270.758i	0.547219	−	0.315937i	0.748000	+	0.663699i	$0.231014\pi$
$858$		0			0
$859$	−1032.64	−	596.196i	−1.20214	−	0.694059i	−0.241113	−	0.970497i	$-0.577512\pi$
$859$	−1032.64	−	596.196i	−1.20214	−	0.694059i	−0.961032	+	0.276439i	$0.910846\pi$
$860$		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	$-0.739879\pi$
$863$	249.748	−	432.576i	0.289395	−	0.501247i	0.973665	+	0.227982i	$0.0732126\pi$
$864$		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	−0.991795	−	0.127836i	$-0.959197\pi$
$877$	−337.810	+	585.105i	−0.385189	+	0.667166i	0.606607	+	0.795002i	$0.292530\pi$
$878$		0			0
$879$	170.377	+	295.102i	0.193831	+	0.335724i
$880$		0			0
$881$		−	98.9362i		−	0.112300i	−0.998422	−	0.0561500i	$-0.982118\pi$
$881$		−	98.9362i		−	0.112300i	0.998422	−	0.0561500i	$-0.0178825\pi$
$882$		0			0
$883$	−550.179			−0.623079			−0.311540	−	0.950233i	$-0.600845\pi$
$883$	−550.179			−0.623079			−0.311540	+	0.950233i	$0.600845\pi$
$884$		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	$-0.281493\pi$
$887$	249.102	+	143.819i	0.280836	+	0.162141i	−0.352966	+	0.935636i	$0.614827\pi$
$888$		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	$-0.205066\pi$
$907$	−109.150	−	189.054i	−0.120342	−	0.208439i	−0.919903	+	0.392147i	$0.871733\pi$
$908$		0			0
$909$		−	227.096i		−	0.249831i
$910$		0			0
$911$	8.50926			0.00934057			0.00467029	−	0.999989i	$-0.498513\pi$
$911$	8.50926			0.00934057			0.00467029	+	0.999989i	$0.498513\pi$
$912$		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	$-0.908528\pi$
$919$	−215.082	+	372.533i	−0.234039	+	0.405367i	0.724954	+	0.688797i	$0.241861\pi$
$920$		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	0.224220	−	0.974539i	$-0.428017\pi$
$929$	−471.602	−	272.280i	−0.507645	−	0.293089i	−0.731865	+	0.681450i	$0.761350\pi$
$930$		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	$-0.974023\pi$
$937$		−	152.767i		−	0.163038i	0.996672	−	0.0815190i	$-0.0259771\pi$
$938$		0			0
$939$	−734.261			−0.781961
$940$		0			0
$941$	−486.649	+	280.967i	−0.517161	+	0.298583i	−0.735773	−	0.677229i	$-0.763181\pi$
$941$	−486.649	+	280.967i	−0.517161	+	0.298583i	0.218611	+	0.975812i	$0.429847\pi$
$942$		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	$-0.847219\pi$
$947$	−41.2983	+	71.5308i	−0.0436096	+	0.0755341i	0.843397	+	0.537291i	$0.180552\pi$
$948$		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	$-0.193469\pi$
$967$	1587.63			1.64181			0.820906	+	0.571063i	$0.193469\pi$
$968$		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	$-0.371803\pi$
$971$	−202.765	−	117.067i	−0.208821	−	0.120563i	−0.600763	+	0.799427i	$0.705137\pi$
$972$		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	0.846620	−	0.532198i	$-0.178634\pi$
$977$	−36.7223	−	63.6049i	−0.0375868	−	0.0651023i	−0.884207	+	0.467096i	$0.845300\pi$
$978$		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	$-0.780982\pi$
$983$	−598.399	+	345.486i	−0.608748	+	0.351461i	0.163727	+	0.986506i	$0.447648\pi$
$984$		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	$-0.329900\pi$
$991$	−486.214	−	842.148i	−0.490630	−	0.849796i	−0.999942	+	0.0107862i	$0.996567\pi$
$992$		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	−0.989090	−	0.147310i	$-0.952938\pi$
$997$	−1351.99	+	780.573i	−1.35606	+	0.782922i	−0.366971	+	0.930233i	$0.619605\pi$
$998$		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	336.3.bh.h.145.1		8
3.2	odd	2		1008.3.cg.n.145.4		8
4.3	odd	2		168.3.z.a.145.1	yes	8
7.2	even	3		2352.3.f.k.97.8		8
7.3	odd	6	inner	336.3.bh.h.241.1		8
7.5	odd	6		2352.3.f.k.97.1		8
12.11	even	2		504.3.by.a.145.4		8
21.17	even	6		1008.3.cg.n.577.4		8
28.3	even	6		168.3.z.a.73.1	✓	8
28.11	odd	6		1176.3.z.d.913.4		8
28.19	even	6		1176.3.f.a.97.5		8
28.23	odd	6		1176.3.f.a.97.4		8
28.27	even	2		1176.3.z.d.313.4		8
84.23	even	6		3528.3.f.f.2449.2		8
84.47	odd	6		3528.3.f.f.2449.7		8
84.59	odd	6		504.3.by.a.73.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.a.73.1	✓	8	28.3	even	6
168.3.z.a.145.1	yes	8	4.3	odd	2
336.3.bh.h.145.1		8	1.1	even	1	trivial
336.3.bh.h.241.1		8	7.3	odd	6	inner
504.3.by.a.73.4		8	84.59	odd	6
504.3.by.a.145.4		8	12.11	even	2
1008.3.cg.n.145.4		8	3.2	odd	2
1008.3.cg.n.577.4		8	21.17	even	6
1176.3.f.a.97.4		8	28.23	odd	6
1176.3.f.a.97.5		8	28.19	even	6
1176.3.z.d.313.4		8	28.27	even	2
1176.3.z.d.913.4		8	28.11	odd	6
2352.3.f.k.97.1		8	7.5	odd	6
2352.3.f.k.97.8		8	7.2	even	3
3528.3.f.f.2449.2		8	84.23	even	6
3528.3.f.f.2449.7		8	84.47	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not 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

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