LMFDB - Embedded newform 216.3.b.a.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(163,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 8x^{12} + 4x^{10} + 160x^{8} + 64x^{6} - 2048x^{4} + 4096x^{2} + 65536 $ x^16 + x^14 - 8x^12 + 4x^10 + 160x^8 + 64x^6 - 2048x^4 + 4096x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.2
Root			$-1.95589 + 0.417734i$ of defining polynomial
Character	$\chi$	$=$	216.163
Dual form			216.3.b.a.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95589 + 0.417734i) q^{2} +(3.65100 - 1.63408i) q^{4} -5.14075i q^{5} +12.6525i q^{7} +(-6.45833 + 4.72122i) q^{8} +O(q^{10})$	\(q+(-1.95589 + 0.417734i) q^{2} +(3.65100 - 1.63408i) q^{4} -5.14075i q^{5} +12.6525i q^{7} +(-6.45833 + 4.72122i) q^{8} +(2.14746 + 10.0547i) q^{10} +1.46281 q^{11} -5.68201i q^{13} +(-5.28537 - 24.7469i) q^{14} +(10.6596 - 11.9320i) q^{16} +14.2764 q^{17} +26.6211 q^{19} +(-8.40040 - 18.7688i) q^{20} +(-2.86110 + 0.611066i) q^{22} +36.7058i q^{23} -1.42727 q^{25} +(2.37357 + 11.1134i) q^{26} +(20.6752 + 46.1942i) q^{28} +19.4918i q^{29} -16.1884i q^{31} +(-15.8645 + 27.7906i) q^{32} +(-27.9231 + 5.96375i) q^{34} +65.0432 q^{35} +37.2185i q^{37} +(-52.0679 + 11.1205i) q^{38} +(24.2706 + 33.2006i) q^{40} +58.8886 q^{41} +61.2705 q^{43} +(5.34073 - 2.39036i) q^{44} +(-15.3333 - 71.7925i) q^{46} -61.6746i q^{47} -111.085 q^{49} +(2.79158 - 0.596220i) q^{50} +(-9.28487 - 20.7450i) q^{52} +42.0953i q^{53} -7.51995i q^{55} +(-59.7352 - 81.7140i) q^{56} +(-8.14240 - 38.1239i) q^{58} -2.74134 q^{59} -71.6574i q^{61} +(6.76244 + 31.6627i) q^{62} +(19.4201 - 60.9825i) q^{64} -29.2098 q^{65} -10.3192 q^{67} +(52.1232 - 23.3288i) q^{68} +(-127.217 + 27.1708i) q^{70} +70.6220i q^{71} -104.912 q^{73} +(-15.5474 - 72.7952i) q^{74} +(97.1936 - 43.5011i) q^{76} +18.5082i q^{77} +82.0064i q^{79} +(-61.3396 - 54.7981i) q^{80} +(-115.179 + 24.5997i) q^{82} -68.7766 q^{83} -73.3915i q^{85} +(-119.838 + 25.5948i) q^{86} +(-9.44733 + 6.90627i) q^{88} -65.6313 q^{89} +71.8916 q^{91} +(59.9803 + 134.013i) q^{92} +(25.7636 + 120.629i) q^{94} -136.852i q^{95} +5.31919 q^{97} +(217.271 - 46.4041i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4}+O(q^{10}) $ 16 * q - 2 * q^4	$ 16 q - 2 q^{4} - 18 q^{10} + 34 q^{16} + 32 q^{19} - 22 q^{22} - 80 q^{25} + 102 q^{28} + 68 q^{34} - 6 q^{40} + 128 q^{43} + 60 q^{46} - 80 q^{49} - 180 q^{52} - 156 q^{58} - 74 q^{64} + 128 q^{67} - 378 q^{70} - 160 q^{73} + 188 q^{76} - 508 q^{82} + 542 q^{88} - 96 q^{91} + 24 q^{94} - 208 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 - 18 * q^10 + 34 * q^16 + 32 * q^19 - 22 * q^22 - 80 * q^25 + 102 * q^28 + 68 * q^34 - 6 * q^40 + 128 * q^43 + 60 * q^46 - 80 * q^49 - 180 * q^52 - 156 * q^58 - 74 * q^64 + 128 * q^67 - 378 * q^70 - 160 * q^73 + 188 * q^76 - 508 * q^82 + 542 * q^88 - 96 * q^91 + 24 * q^94 - 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.95589	+	0.417734i	−0.977944	+	0.208867i
$2$	−1.95589	+	0.417734i	−0.977944	+	0.208867i
$3$		0			0
$3$		0			0
$4$	3.65100	−	1.63408i	0.912749	−	0.408520i
$5$		−	5.14075i		−	1.02815i	−0.857745	−	0.514075i	$-0.828135\pi$
$5$		−	5.14075i		−	1.02815i	0.857745	−	0.514075i	$-0.171865\pi$
$6$		0			0
$7$			12.6525i			1.80750i	0.428063	+	0.903749i	$0.359196\pi$
$7$			12.6525i			1.80750i	−0.428063	+	0.903749i	$0.640804\pi$
$8$	−6.45833	+	4.72122i	−0.807291	+	0.590153i
$9$		0			0
$10$	2.14746	+	10.0547i	0.214746	+	1.00547i
$11$	1.46281			0.132983			0.0664915	−	0.997787i	$-0.478819\pi$
$11$	1.46281			0.132983			0.0664915	+	0.997787i	$0.478819\pi$
$12$		0			0
$13$		−	5.68201i		−	0.437078i	−0.975828	−	0.218539i	$-0.929871\pi$
$13$		−	5.68201i		−	0.437078i	0.975828	−	0.218539i	$-0.0701291\pi$
$14$	−5.28537	−	24.7469i	−0.377526	−	1.76763i
$15$		0			0
$16$	10.6596	−	11.9320i	0.666222	−	0.745753i
$17$	14.2764			0.839790			0.419895	−	0.907573i	$-0.362067\pi$
$17$	14.2764			0.839790			0.419895	+	0.907573i	$0.362067\pi$
$18$		0			0
$19$	26.6211			1.40111			0.700556	−	0.713598i	$-0.252936\pi$
$19$	26.6211			1.40111			0.700556	+	0.713598i	$0.252936\pi$
$20$	−8.40040	−	18.7688i	−0.420020	−	0.938442i
$21$		0			0
$22$	−2.86110	+	0.611066i	−0.130050	+	0.0277757i
$23$			36.7058i			1.59590i	0.602721	+	0.797952i	$0.294083\pi$
$23$			36.7058i			1.59590i	−0.602721	+	0.797952i	$0.705917\pi$
$24$		0			0
$25$	−1.42727			−0.0570909
$26$	2.37357	+	11.1134i	0.0912911	+	0.427438i
$27$		0			0
$28$	20.6752	+	46.1942i	0.738400	+	1.64979i
$29$			19.4918i			0.672133i	0.941838	+	0.336066i	$0.109097\pi$
$29$			19.4918i			0.672133i	−0.941838	+	0.336066i	$0.890903\pi$
$30$		0			0
$31$		−	16.1884i		−	0.522206i	−0.965311	−	0.261103i	$-0.915914\pi$
$31$		−	16.1884i		−	0.522206i	0.965311	−	0.261103i	$-0.0840863\pi$
$32$	−15.8645	+	27.7906i	−0.495765	+	0.868457i
$33$		0			0
$34$	−27.9231	+	5.96375i	−0.821268	+	0.175404i
$35$	65.0432			1.85838
$36$		0			0
$37$			37.2185i			1.00590i	0.864314	+	0.502952i	$0.167753\pi$
$37$			37.2185i			1.00590i	−0.864314	+	0.502952i	$0.832247\pi$
$38$	−52.0679	+	11.1205i	−1.37021	+	0.292646i
$39$		0			0
$40$	24.2706	+	33.2006i	0.606765	+	0.830016i
$41$	58.8886			1.43631			0.718153	−	0.695885i	$-0.244988\pi$
$41$	58.8886			1.43631			0.718153	+	0.695885i	$0.244988\pi$
$42$		0			0
$43$	61.2705			1.42490			0.712448	−	0.701725i	$-0.247587\pi$
$43$	61.2705			1.42490			0.712448	+	0.701725i	$0.247587\pi$
$44$	5.34073	−	2.39036i	0.121380	−	0.0543263i
$45$		0			0
$46$	−15.3333	−	71.7925i	−0.333332	−	1.56071i
$47$		−	61.6746i		−	1.31223i	−0.754662	−	0.656113i	$-0.772199\pi$
$47$		−	61.6746i		−	1.31223i	0.754662	−	0.656113i	$-0.227801\pi$
$48$		0			0
$49$	−111.085			−2.26705
$50$	2.79158	−	0.596220i	0.0558317	−	0.0119244i
$51$		0			0
$52$	−9.28487	−	20.7450i	−0.178555	−	0.398943i
$53$			42.0953i			0.794251i	0.917764	+	0.397125i	$0.129992\pi$
$53$			42.0953i			0.794251i	−0.917764	+	0.397125i	$0.870008\pi$
$54$		0			0
$55$		−	7.51995i		−	0.136726i
$56$	−59.7352	−	81.7140i	−1.06670	−	1.45918i
$57$		0			0
$58$	−8.14240	−	38.1239i	−0.140386	−	0.657308i
$59$	−2.74134			−0.0464635			−0.0232317	−	0.999730i	$-0.507396\pi$
$59$	−2.74134			−0.0464635			−0.0232317	+	0.999730i	$0.507396\pi$
$60$		0			0
$61$		−	71.6574i		−	1.17471i	−0.809329	−	0.587355i	$-0.800169\pi$
$61$		−	71.6574i		−	1.17471i	0.809329	−	0.587355i	$-0.199831\pi$
$62$	6.76244	+	31.6627i	0.109072	+	0.510688i
$63$		0			0
$64$	19.4201	−	60.9825i	0.303439	−	0.952851i
$65$	−29.2098			−0.449381
$66$		0			0
$67$	−10.3192			−0.154018			−0.0770088	−	0.997030i	$-0.524537\pi$
$67$	−10.3192			−0.154018			−0.0770088	+	0.997030i	$0.524537\pi$
$68$	52.1232	−	23.3288i	0.766518	−	0.343071i
$69$		0			0
$70$	−127.217	+	27.1708i	−1.81739	+	0.388154i
$71$			70.6220i			0.994676i	0.867557	+	0.497338i	$0.165689\pi$
$71$			70.6220i			0.994676i	−0.867557	+	0.497338i	$0.834311\pi$
$72$		0			0
$73$	−104.912			−1.43715			−0.718573	−	0.695451i	$-0.755205\pi$
$73$	−104.912			−1.43715			−0.718573	+	0.695451i	$0.755205\pi$
$74$	−15.5474	−	72.7952i	−0.210100	−	0.983719i
$75$		0			0
$76$	97.1936	−	43.5011i	1.27886	−	0.572382i
$77$			18.5082i			0.240367i
$78$		0			0
$79$			82.0064i			1.03806i	0.854757	+	0.519028i	$0.173706\pi$
$79$			82.0064i			1.03806i	−0.854757	+	0.519028i	$0.826294\pi$
$80$	−61.3396	−	54.7981i	−0.766745	−	0.684976i
$81$		0			0
$82$	−115.179	+	24.5997i	−1.40463	+	0.299997i
$83$	−68.7766			−0.828633			−0.414317	−	0.910133i	$-0.635979\pi$
$83$	−68.7766			−0.828633			−0.414317	+	0.910133i	$0.635979\pi$
$84$		0			0
$85$		−	73.3915i		−	0.863430i
$86$	−119.838	+	25.5948i	−1.39347	+	0.297613i
$87$		0			0
$88$	−9.44733	+	6.90627i	−0.107356	+	0.0784803i
$89$	−65.6313			−0.737431			−0.368715	−	0.929542i	$-0.620202\pi$
$89$	−65.6313			−0.737431			−0.368715	+	0.929542i	$0.620202\pi$
$90$		0			0
$91$	71.8916			0.790018
$92$	59.9803	+	134.013i	0.651959	+	1.45666i
$93$		0			0
$94$	25.7636	+	120.629i	0.274081	+	1.28328i
$95$		−	136.852i		−	1.44055i
$96$		0			0
$97$	5.31919			0.0548370			0.0274185	−	0.999624i	$-0.491271\pi$
$97$	5.31919			0.0548370			0.0274185	+	0.999624i	$0.491271\pi$
$98$	217.271	−	46.4041i	2.21705	−	0.473512i
$99$		0			0
$100$	−5.21096	+	2.33228i	−0.0521096	+	0.0233228i
$101$		−	132.472i		−	1.31161i	−0.754932	−	0.655803i	$-0.772330\pi$
$101$		−	132.472i		−	1.31161i	0.754932	−	0.655803i	$-0.227670\pi$
$102$		0			0
$103$		−	7.79346i		−	0.0756647i	−0.999284	−	0.0378323i	$-0.987955\pi$
$103$		−	7.79346i		−	0.0756647i	0.999284	−	0.0378323i	$-0.0120453\pi$
$104$	26.8261	+	36.6963i	0.257943	+	0.352849i
$105$		0			0
$106$	−17.5846	−	82.3337i	−0.165893	−	0.776733i
$107$	70.3416			0.657398			0.328699	−	0.944435i	$-0.393390\pi$
$107$	70.3416			0.657398			0.328699	+	0.944435i	$0.393390\pi$
$108$		0			0
$109$		−	131.604i		−	1.20738i	−0.797221	−	0.603688i	$-0.793697\pi$
$109$		−	131.604i		−	1.20738i	0.797221	−	0.603688i	$-0.206303\pi$
$110$	3.14134	+	14.7082i	0.0285576	+	0.133711i
$111$		0			0
$112$	150.970	+	134.870i	1.34795	+	1.20420i
$113$	13.0165			0.115191			0.0575953	−	0.998340i	$-0.481657\pi$
$113$	13.0165			0.115191			0.0575953	+	0.998340i	$0.481657\pi$
$114$		0			0
$115$	188.695			1.64083
$116$	31.8513	+	71.1647i	0.274580	+	0.613489i
$117$		0			0
$118$	5.36176	−	1.14515i	0.0454387	−	0.00970468i
$119$			180.632i			1.51792i
$120$		0			0
$121$	−118.860			−0.982316
$122$	29.9337	+	140.154i	0.245358	+	1.14880i
$123$		0			0
$124$	−26.4531	−	59.1038i	−0.213332	−	0.476643i
$125$		−	121.181i		−	0.969451i
$126$		0			0
$127$		−	2.36611i		−	0.0186308i	−0.999957	−	0.00931539i	$-0.997035\pi$
$127$		−	2.36611i		−	0.0186308i	0.999957	−	0.00931539i	$-0.00296522\pi$
$128$	−12.5091	+	127.387i	−0.0977272	+	0.995213i
$129$		0			0
$130$	57.1311	−	12.2019i	0.439470	−	0.0938609i
$131$	−236.933			−1.80865			−0.904326	−	0.426842i	$-0.859626\pi$
$131$	−236.933			−1.80865			−0.904326	+	0.426842i	$0.859626\pi$
$132$		0			0
$133$			336.823i			2.53251i
$134$	20.1832	−	4.31067i	0.150621	−	0.0321692i
$135$		0			0
$136$	−92.2019	+	67.4022i	−0.677955	+	0.495605i
$137$	60.8593			0.444229			0.222114	−	0.975021i	$-0.428704\pi$
$137$	60.8593			0.444229			0.222114	+	0.975021i	$0.428704\pi$
$138$		0			0
$139$	−39.5897			−0.284818			−0.142409	−	0.989808i	$-0.545485\pi$
$139$	−39.5897			−0.284818			−0.142409	+	0.989808i	$0.545485\pi$
$140$	237.473	−	106.286i	1.69623	−	0.759185i
$141$		0			0
$142$	−29.5012	−	138.129i	−0.207755	−	0.972737i
$143$		−	8.31172i		−	0.0581239i
$144$		0			0
$145$	100.203			0.691053
$146$	205.196	−	43.8252i	1.40545	−	0.300172i
$147$		0			0
$148$	60.8180	+	135.885i	0.410932	+	0.918139i
$149$			146.973i			0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$149$			146.973i			0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$150$		0			0
$151$		−	62.7781i		−	0.415749i	−0.978155	−	0.207875i	$-0.933345\pi$
$151$		−	62.7781i		−	0.415749i	0.978155	−	0.207875i	$-0.0666546\pi$
$152$	−171.928	+	125.684i	−1.13111	+	0.826870i
$153$		0			0
$154$	−7.73151	−	36.2000i	−0.0502046	−	0.235065i
$155$	−83.2204			−0.536906
$156$		0			0
$157$			82.5467i			0.525775i	0.964826	+	0.262888i	$0.0846749\pi$
$157$			82.5467i			0.525775i	−0.964826	+	0.262888i	$0.915325\pi$
$158$	−34.2569	−	160.395i	−0.216816	−	1.01516i
$159$		0			0
$160$	142.864	+	81.5553i	0.892903	+	0.509721i
$161$	−464.420			−2.88459
$162$		0			0
$163$	29.4072			0.180412			0.0902060	−	0.995923i	$-0.471247\pi$
$163$	29.4072			0.180412			0.0902060	+	0.995923i	$0.471247\pi$
$164$	215.002	−	96.2287i	1.31099	−	0.586760i
$165$		0			0
$166$	134.519	−	28.7303i	0.810357	−	0.173074i
$167$		−	92.9654i		−	0.556679i	−0.960483	−	0.278339i	$-0.910216\pi$
$167$		−	92.9654i		−	0.556679i	0.960483	−	0.278339i	$-0.0897840\pi$
$168$		0			0
$169$	136.715			0.808963
$170$	30.6581	+	143.546i	0.180342	+	0.844386i
$171$		0			0
$172$	223.698	−	100.121i	1.30057	−	0.582099i
$173$			48.3804i			0.279655i	0.990176	+	0.139828i	$0.0446549\pi$
$173$			48.3804i			0.279655i	−0.990176	+	0.139828i	$0.955345\pi$
$174$		0			0
$175$		−	18.0585i		−	0.103192i
$176$	15.5929	−	17.4544i	0.0885963	−	0.0991725i
$177$		0			0
$178$	128.368	−	27.4164i	0.721166	−	0.154025i
$179$	148.467			0.829422			0.414711	−	0.909953i	$-0.363883\pi$
$179$	148.467			0.829422			0.414711	+	0.909953i	$0.363883\pi$
$180$		0			0
$181$			94.3854i			0.521466i	0.965411	+	0.260733i	$0.0839643\pi$
$181$			94.3854i			0.521466i	−0.965411	+	0.260733i	$0.916036\pi$
$182$	−140.612	+	30.0315i	−0.772593	+	0.165009i
$183$		0			0
$184$	−173.296	−	237.058i	−0.941828	−	1.28836i
$185$	191.331			1.03422
$186$		0			0
$187$	20.8838			0.111678
$188$	−100.781	−	225.174i	−0.536071	−	1.19773i
$189$		0			0
$190$	57.1679	+	267.668i	0.300883	+	1.40878i
$191$		−	198.584i		−	1.03971i	−0.854255	−	0.519854i	$-0.825986\pi$
$191$		−	198.584i		−	1.03971i	0.854255	−	0.519854i	$-0.174014\pi$
$192$		0			0
$193$	−2.71819			−0.0140839			−0.00704193	−	0.999975i	$-0.502242\pi$
$193$	−2.71819			−0.0140839			−0.00704193	+	0.999975i	$0.502242\pi$
$194$	−10.4037	+	2.22200i	−0.0536275	+	0.0114536i
$195$		0			0
$196$	−405.573	+	181.523i	−2.06925	+	0.926136i
$197$		−	197.266i		−	1.00135i	−0.865635	−	0.500675i	$-0.833085\pi$
$197$		−	197.266i		−	1.00135i	0.865635	−	0.500675i	$-0.166915\pi$
$198$		0			0
$199$			275.188i			1.38285i	0.722446	+	0.691427i	$0.243018\pi$
$199$			275.188i			1.38285i	−0.722446	+	0.691427i	$0.756982\pi$
$200$	9.21779	−	6.73847i	0.0460890	−	0.0336923i
$201$		0			0
$202$	55.3381	+	259.101i	0.273951	+	1.28268i
$203$	−246.620			−1.21488
$204$		0			0
$205$		−	302.731i		−	1.47674i
$206$	3.25559	+	15.2431i	0.0158038	+	0.0739958i
$207$		0			0
$208$	−67.7981	−	60.5678i	−0.325952	−	0.291191i
$209$	38.9417			0.186324
$210$		0			0
$211$	−301.299			−1.42796			−0.713979	−	0.700167i	$-0.753109\pi$
$211$	−301.299			−1.42796			−0.713979	+	0.700167i	$0.753109\pi$
$212$	68.7871	+	153.690i	0.324467	+	0.724952i
$213$		0			0
$214$	−137.580	+	29.3841i	−0.642899	+	0.137309i
$215$		−	314.976i		−	1.46500i
$216$		0			0
$217$	204.823			0.943887
$218$	54.9754	+	257.403i	0.252181	+	1.18075i
$219$		0			0
$220$	−12.2882	−	27.4553i	−0.0558555	−	0.124797i
$221$		−	81.1189i		−	0.367054i
$222$		0			0
$223$		−	171.918i		−	0.770934i	−0.922722	−	0.385467i	$-0.874040\pi$
$223$		−	171.918i		−	0.770934i	0.922722	−	0.385467i	$-0.125960\pi$
$224$	−351.620	−	200.725i	−1.56973	−	0.896095i
$225$		0			0
$226$	−25.4589	+	5.43745i	−0.112650	+	0.0240595i
$227$	240.769			1.06066			0.530329	−	0.847792i	$-0.322069\pi$
$227$	240.769			1.06066			0.530329	+	0.847792i	$0.322069\pi$
$228$		0			0
$229$		−	416.468i		−	1.81864i	−0.416102	−	0.909318i	$-0.636604\pi$
$229$		−	416.468i		−	1.81864i	0.416102	−	0.909318i	$-0.363396\pi$
$230$	−369.067	+	78.8244i	−1.60464	+	0.342715i
$231$		0			0
$232$	−92.0254	−	125.885i	−0.396661	−	0.542607i
$233$	−39.4647			−0.169376			−0.0846881	−	0.996408i	$-0.526989\pi$
$233$	−39.4647			−0.169376			−0.0846881	+	0.996408i	$0.526989\pi$
$234$		0			0
$235$	−317.054			−1.34916
$236$	−10.0086	+	4.47958i	−0.0424095	+	0.0189813i
$237$		0			0
$238$	−75.4562	−	353.297i	−0.317043	−	1.48444i
$239$			390.425i			1.63358i	0.576937	+	0.816789i	$0.304248\pi$
$239$			390.425i			1.63358i	−0.576937	+	0.816789i	$0.695752\pi$
$240$		0			0
$241$	107.903			0.447729			0.223864	−	0.974620i	$-0.428133\pi$
$241$	107.903			0.447729			0.223864	+	0.974620i	$0.428133\pi$
$242$	232.477	−	49.6519i	0.960650	−	0.205173i
$243$		0			0
$244$	−117.094	−	261.621i	−0.479893	−	1.07222i
$245$			571.062i			2.33087i
$246$		0			0
$247$		−	151.262i		−	0.612395i
$248$	76.4290	+	104.550i	0.308182	+	0.421573i
$249$		0			0
$250$	50.6216	+	237.017i	0.202486	+	0.948069i
$251$	239.656			0.954805			0.477403	−	0.878685i	$-0.341578\pi$
$251$	239.656			0.954805			0.477403	+	0.878685i	$0.341578\pi$
$252$		0			0
$253$			53.6937i			0.212228i
$254$	0.988403	+	4.62784i	0.00389135	+	0.0182199i
$255$		0			0
$256$	−28.7476	−	254.381i	−0.112295	−	0.993675i
$257$	219.964			0.855893			0.427946	−	0.903804i	$-0.359237\pi$
$257$	219.964			0.855893			0.427946	+	0.903804i	$0.359237\pi$
$258$		0			0
$259$	−470.906			−1.81817
$260$	−106.645	+	47.7312i	−0.410173	+	0.183581i
$261$		0			0
$262$	463.415	−	98.9751i	1.76876	−	0.377768i
$263$			59.9658i			0.228007i	0.993480	+	0.114003i	$0.0363675\pi$
$263$			59.9658i			0.228007i	−0.993480	+	0.114003i	$0.963633\pi$
$264$		0			0
$265$	216.401			0.816608
$266$	−140.702	−	658.789i	−0.528957	−	2.47665i
$267$		0			0
$268$	−37.6753	+	16.8624i	−0.140580	+	0.0629193i
$269$			216.414i			0.804515i	0.915527	+	0.402257i	$0.131774\pi$
$269$			216.414i			0.804515i	−0.915527	+	0.402257i	$0.868226\pi$
$270$		0			0
$271$		−	153.616i		−	0.566849i	−0.958995	−	0.283424i	$-0.908530\pi$
$271$		−	153.616i		−	0.566849i	0.958995	−	0.283424i	$-0.0914705\pi$
$272$	152.180	−	170.347i	0.559487	−	0.626276i
$273$		0			0
$274$	−119.034	+	25.4230i	−0.434431	+	0.0927847i
$275$	−2.08783			−0.00759212
$276$		0			0
$277$			267.370i			0.965234i	0.875832	+	0.482617i	$0.160314\pi$
$277$			267.370i			0.965234i	−0.875832	+	0.482617i	$0.839686\pi$
$278$	77.4330	−	16.5379i	0.278536	−	0.0594890i
$279$		0			0
$280$	−420.071	+	307.084i	−1.50025	+	1.09673i
$281$	485.895			1.72916			0.864582	−	0.502492i	$-0.167584\pi$
$281$	485.895			1.72916			0.864582	+	0.502492i	$0.167584\pi$
$282$		0			0
$283$	−74.3478			−0.262713			−0.131357	−	0.991335i	$-0.541933\pi$
$283$	−74.3478			−0.262713			−0.131357	+	0.991335i	$0.541933\pi$
$284$	115.402	+	257.841i	0.406345	+	0.907889i
$285$		0			0
$286$	3.47209	+	16.2568i	0.0121402	+	0.0568420i
$287$			745.087i			2.59612i
$288$		0			0
$289$	−85.1835			−0.294752
$290$	−195.985	+	41.8580i	−0.675811	+	0.144338i
$291$		0			0
$292$	−383.032	+	171.434i	−1.31175	+	0.587104i
$293$		−	468.531i		−	1.59908i	−0.600612	−	0.799540i	$-0.705076\pi$
$293$		−	468.531i		−	1.59908i	0.600612	−	0.799540i	$-0.294924\pi$
$294$		0			0
$295$			14.0926i			0.0477714i
$296$	−175.717	−	240.369i	−0.593638	−	0.812058i
$297$		0			0
$298$	−61.3954	−	287.462i	−0.206025	−	0.964638i
$299$	208.563			0.697535
$300$		0			0
$301$			775.224i			2.57550i
$302$	26.2245	+	122.787i	0.0868362	+	0.406579i
$303$		0			0
$304$	283.769	−	317.644i	0.933452	−	1.04488i
$305$	−368.372			−1.20778
$306$		0			0
$307$	58.3993			0.190226			0.0951129	−	0.995466i	$-0.469679\pi$
$307$	58.3993			0.190226			0.0951129	+	0.995466i	$0.469679\pi$
$308$	30.2439	+	67.5735i	0.0981946	+	0.219394i
$309$		0			0
$310$	162.770	−	34.7640i	0.525064	−	0.112142i
$311$		−	268.018i		−	0.861796i	−0.902401	−	0.430898i	$-0.858197\pi$
$311$		−	268.018i		−	0.861796i	0.902401	−	0.430898i	$-0.141803\pi$
$312$		0			0
$313$	−78.0050			−0.249217			−0.124609	−	0.992206i	$-0.539768\pi$
$313$	−78.0050			−0.249217			−0.124609	+	0.992206i	$0.539768\pi$
$314$	−34.4826	−	161.452i	−0.109817	−	0.514179i
$315$		0			0
$316$	134.005	+	299.405i	0.424067	+	0.947485i
$317$		−	262.045i		−	0.826639i	−0.910586	−	0.413320i	$-0.864369\pi$
$317$		−	262.045i		−	0.826639i	0.910586	−	0.413320i	$-0.135631\pi$
$318$		0			0
$319$			28.5129i			0.0893822i
$320$	−313.495	−	99.8337i	−0.979673	−	0.311980i
$321$		0			0
$322$	908.353	−	194.004i	2.82097	−	0.602496i
$323$	380.055			1.17664
$324$		0			0
$325$			8.10978i			0.0249532i
$326$	−57.5171	+	12.2844i	−0.176433	+	0.0376821i
$327$		0			0
$328$	−380.322	+	278.026i	−1.15952	+	0.847641i
$329$	780.338			2.37185
$330$		0			0
$331$	−279.482			−0.844355			−0.422178	−	0.906513i	$-0.638734\pi$
$331$	−279.482			−0.844355			−0.422178	+	0.906513i	$0.638734\pi$
$332$	−251.103	+	112.386i	−0.756334	+	0.338513i
$333$		0			0
$334$	38.8348	+	181.830i	0.116272	+	0.544401i
$335$			53.0483i			0.158353i
$336$		0			0
$337$	552.770			1.64027			0.820133	−	0.572173i	$-0.193899\pi$
$337$	552.770			1.64027			0.820133	+	0.572173i	$0.193899\pi$
$338$	−267.399	+	57.1104i	−0.791120	+	0.168966i
$339$		0			0
$340$	−119.928	−	267.952i	−0.352728	−	0.788095i
$341$		−	23.6806i		−	0.0694446i
$342$		0			0
$343$		−	785.535i		−	2.29019i
$344$	−395.705	+	289.272i	−1.15031	+	0.840906i
$345$		0			0
$346$	−20.2101	−	94.6266i	−0.0584107	−	0.273487i
$347$	−210.871			−0.607697			−0.303848	−	0.952720i	$-0.598272\pi$
$347$	−210.871			−0.607697			−0.303848	+	0.952720i	$0.598272\pi$
$348$		0			0
$349$		−	306.200i		−	0.877363i	−0.898643	−	0.438681i	$-0.855446\pi$
$349$		−	306.200i		−	0.877363i	0.898643	−	0.438681i	$-0.144554\pi$
$350$	7.54366	+	35.3205i	0.0215533	+	0.100916i
$351$		0			0
$352$	−23.2068	+	40.6525i	−0.0659283	+	0.115490i
$353$	−359.324			−1.01791			−0.508957	−	0.860792i	$-0.669969\pi$
$353$	−359.324			−1.01791			−0.508957	+	0.860792i	$0.669969\pi$
$354$		0			0
$355$	363.050			1.02267
$356$	−239.620	+	107.247i	−0.673089	+	0.301255i
$357$		0			0
$358$	−290.384	+	62.0195i	−0.811129	+	0.173239i
$359$		−	336.189i		−	0.936459i	−0.883607	−	0.468230i	$-0.844892\pi$
$359$		−	336.189i		−	0.936459i	0.883607	−	0.468230i	$-0.155108\pi$
$360$		0			0
$361$	347.684			0.963113
$362$	−39.4280	−	184.607i	−0.108917	−	0.509965i
$363$		0			0
$364$	262.476	−	117.477i	0.721088	−	0.322738i
$365$			539.325i			1.47760i
$366$		0			0
$367$			462.021i			1.25891i	0.777036	+	0.629456i	$0.216722\pi$
$367$			462.021i			1.25891i	−0.777036	+	0.629456i	$0.783278\pi$
$368$	437.976	+	391.268i	1.19015	+	1.06323i
$369$		0			0
$370$	−374.222	+	79.9253i	−1.01141	+	0.216014i
$371$	−532.610			−1.43561
$372$		0			0
$373$		−	201.874i		−	0.541217i	−0.962689	−	0.270608i	$-0.912775\pi$
$373$		−	201.874i		−	0.541217i	0.962689	−	0.270608i	$-0.0872249\pi$
$374$	−40.8463	+	8.72385i	−0.109215	+	0.0233258i
$375$		0			0
$376$	291.180	+	398.315i	0.774414	+	1.05935i
$377$	110.753			0.293774
$378$		0			0
$379$	−328.194			−0.865946			−0.432973	−	0.901407i	$-0.642535\pi$
$379$	−328.194			−0.865946			−0.432973	+	0.901407i	$0.642535\pi$
$380$	−223.628	−	499.648i	−0.588494	−	1.31486i
$381$		0			0
$382$	82.9553	+	388.409i	0.217161	+	1.01678i
$383$		−	57.5543i		−	0.150272i	−0.997173	−	0.0751362i	$-0.976061\pi$
$383$		−	57.5543i		−	0.150272i	0.997173	−	0.0751362i	$-0.0239391\pi$
$384$		0			0
$385$	95.1461			0.247133
$386$	5.31647	−	1.13548i	0.0137732	−	0.00294165i
$387$		0			0
$388$	19.4203	−	8.69198i	0.0500524	−	0.0224020i
$389$		−	528.085i		−	1.35755i	−0.734349	−	0.678773i	$-0.762512\pi$
$389$		−	528.085i		−	1.35755i	0.734349	−	0.678773i	$-0.237488\pi$
$390$		0			0
$391$			524.028i			1.34023i
$392$	717.427	−	524.459i	1.83017	−	1.33791i
$393$		0			0
$394$	82.4047	+	385.830i	0.209149	+	0.979265i
$395$	421.574			1.06728
$396$		0			0
$397$			151.307i			0.381125i	0.981675	+	0.190562i	$0.0610312\pi$
$397$			151.307i			0.381125i	−0.981675	+	0.190562i	$0.938969\pi$
$398$	−114.955	−	538.237i	−0.288832	−	1.35235i
$399$		0			0
$400$	−15.2141	+	17.0303i	−0.0380352	+	0.0425757i
$401$	−730.954			−1.82283			−0.911413	−	0.411492i	$-0.865008\pi$
$401$	−730.954			−1.82283			−0.911413	+	0.411492i	$0.865008\pi$
$402$		0			0
$403$	−91.9827			−0.228245
$404$	−216.470	−	483.655i	−0.535817	−	1.19717i
$405$		0			0
$406$	482.362	−	103.022i	1.18808	−	0.253748i
$407$			54.4437i			0.133768i
$408$		0			0
$409$	314.720			0.769487			0.384744	−	0.923023i	$-0.374290\pi$
$409$	314.720			0.769487			0.384744	+	0.923023i	$0.374290\pi$
$410$	126.461	+	592.108i	0.308442	+	1.44417i
$411$		0			0
$412$	−12.7352	−	28.4539i	−0.0309106	−	0.0690629i
$413$		−	34.6848i		−	0.0839826i
$414$		0			0
$415$			353.563i			0.851959i
$416$	157.907	+	90.1422i	0.379583	+	0.216688i
$417$		0			0
$418$	−76.1656	+	16.2673i	−0.182214	+	0.0389169i
$419$	114.634			0.273589			0.136794	−	0.990599i	$-0.456320\pi$
$419$	114.634			0.273589			0.136794	+	0.990599i	$0.456320\pi$
$420$		0			0
$421$		−	530.807i		−	1.26082i	−0.776261	−	0.630412i	$-0.782886\pi$
$421$		−	530.807i		−	1.26082i	0.776261	−	0.630412i	$-0.217114\pi$
$422$	589.307	−	125.863i	1.39646	−	0.298253i
$423$		0			0
$424$	−198.741	−	271.865i	−0.468729	−	0.641192i
$425$	−20.3763			−0.0479443
$426$		0			0
$427$	906.644			2.12329
$428$	256.817	−	114.944i	0.600040	−	0.268561i
$429$		0			0
$430$	131.576	+	616.058i	0.305991	+	1.43269i
$431$			91.4566i			0.212196i	0.994356	+	0.106098i	$0.0338358\pi$
$431$			91.4566i			0.212196i	−0.994356	+	0.106098i	$0.966164\pi$
$432$		0			0
$433$	−449.530			−1.03817			−0.519087	−	0.854721i	$-0.673728\pi$
$433$	−449.530			−1.03817			−0.519087	+	0.854721i	$0.673728\pi$
$434$	−400.612	+	85.5617i	−0.923069	+	0.197147i
$435$		0			0
$436$	−215.051	−	480.485i	−0.493237	−	1.10203i
$437$			977.149i			2.23604i
$438$		0			0
$439$			59.9309i			0.136517i	0.997668	+	0.0682585i	$0.0217442\pi$
$439$			59.9309i			0.136517i	−0.997668	+	0.0682585i	$0.978256\pi$
$440$	35.5034	+	48.5663i	0.0806895	+	0.110378i
$441$		0			0
$442$	33.8861	+	158.659i	0.0766654	+	0.358958i
$443$	−332.627			−0.750851			−0.375425	−	0.926853i	$-0.622503\pi$
$443$	−332.627			−0.750851			−0.375425	+	0.926853i	$0.622503\pi$
$444$		0			0
$445$			337.394i			0.758189i
$446$	71.8161	+	336.253i	0.161023	+	0.753930i
$447$		0			0
$448$	771.580	+	245.712i	1.72228	+	0.548465i
$449$	204.039			0.454431			0.227215	−	0.973845i	$-0.427038\pi$
$449$	204.039			0.454431			0.227215	+	0.973845i	$0.427038\pi$
$450$		0			0
$451$	86.1430			0.191004
$452$	47.5234	−	21.2701i	0.105140	−	0.0470577i
$453$		0			0
$454$	−470.918	+	100.577i	−1.03726	+	0.221536i
$455$		−	369.577i		−	0.812256i
$456$		0			0
$457$	−483.610			−1.05823			−0.529114	−	0.848551i	$-0.677476\pi$
$457$	−483.610			−1.05823			−0.529114	+	0.848551i	$0.677476\pi$
$458$	173.973	+	814.564i	0.379853	+	1.77852i
$459$		0			0
$460$	688.926	−	308.343i	1.49766	−	0.670312i
$461$		−	75.8364i		−	0.164504i	−0.996612	−	0.0822521i	$-0.973789\pi$
$461$		−	75.8364i		−	0.164504i	0.996612	−	0.0822521i	$-0.0262113\pi$
$462$		0			0
$463$			55.9734i			0.120893i	0.998171	+	0.0604464i	$0.0192524\pi$
$463$			55.9734i			0.120893i	−0.998171	+	0.0604464i	$0.980748\pi$
$464$	232.578	+	207.774i	0.501245	+	0.447790i
$465$		0			0
$466$	77.1885	−	16.4857i	0.165641	−	0.0353771i
$467$	−519.757			−1.11297			−0.556485	−	0.830857i	$-0.687850\pi$
$467$	−519.757			−1.11297			−0.556485	+	0.830857i	$0.687850\pi$
$468$		0			0
$469$		−	130.563i		−	0.278387i
$470$	620.122	−	132.444i	1.31941	−	0.281796i
$471$		0			0
$472$	17.7045	−	12.9425i	0.0375096	−	0.0274206i
$473$	89.6273			0.189487
$474$		0			0
$475$	−37.9956			−0.0799907
$476$	295.168	+	659.488i	0.620101	+	1.38548i
$477$		0			0
$478$	−163.094	−	763.628i	−0.341200	−	1.59755i
$479$		−	381.514i		−	0.796479i	−0.917281	−	0.398240i	$-0.869621\pi$
$479$		−	381.514i		−	0.796479i	0.917281	−	0.398240i	$-0.130379\pi$
$480$		0			0
$481$	211.476			0.439659
$482$	−211.045	+	45.0746i	−0.437854	+	0.0935157i
$483$		0			0
$484$	−433.958	+	194.227i	−0.896608	+	0.401296i
$485$		−	27.3446i		−	0.0563806i
$486$		0			0
$487$			593.446i			1.21858i	0.792949	+	0.609288i	$0.208544\pi$
$487$			593.446i			1.21858i	−0.792949	+	0.609288i	$0.791456\pi$
$488$	338.310	+	462.787i	0.693259	+	0.948334i
$489$		0			0
$490$	−238.552	−	1116.93i	−0.486841	−	2.27946i
$491$	125.688			0.255984			0.127992	−	0.991775i	$-0.459147\pi$
$491$	125.688			0.255984			0.127992	+	0.991775i	$0.459147\pi$
$492$		0			0
$493$			278.274i			0.564450i
$494$	63.1870	+	295.851i	0.127909	+	0.598888i
$495$		0			0
$496$	−193.161	−	172.561i	−0.389437	−	0.347905i
$497$	−893.544			−1.79787
$498$		0			0
$499$	−470.104			−0.942093			−0.471046	−	0.882108i	$-0.656124\pi$
$499$	−470.104			−0.942093			−0.471046	+	0.882108i	$0.656124\pi$
$500$	−198.020	−	442.433i	−0.396040	−	0.884866i
$501$		0			0
$502$	−468.741	+	100.112i	−0.933746	+	0.199427i
$503$		−	21.6483i		−	0.0430384i	−0.999768	−	0.0215192i	$-0.993150\pi$
$503$		−	21.6483i		−	0.0430384i	0.999768	−	0.0215192i	$-0.00685030\pi$
$504$		0			0
$505$	−681.006			−1.34853
$506$	−22.4297	−	105.019i	−0.0443274	−	0.207547i
$507$		0			0
$508$	−3.86641	−	8.63866i	−0.00761105	−	0.0170052i
$509$		−	612.338i		−	1.20302i	−0.798865	−	0.601510i	$-0.794566\pi$
$509$		−	612.338i		−	1.20302i	0.798865	−	0.601510i	$-0.205434\pi$
$510$		0			0
$511$		−	1327.39i		−	2.59764i
$512$	162.491	+	485.531i	0.317364	+	0.948304i
$513$		0			0
$514$	−430.226	+	91.8865i	−0.837015	+	0.178768i
$515$	−40.0642			−0.0777946
$516$		0			0
$517$		−	90.2185i		−	0.174504i
$518$	921.040	−	196.713i	1.77807	−	0.379756i
$519$		0			0
$520$	188.646	−	137.906i	0.362782	−	0.265204i
$521$	449.648			0.863047			0.431524	−	0.902102i	$-0.357976\pi$
$521$	449.648			0.863047			0.431524	+	0.902102i	$0.357976\pi$
$522$		0			0
$523$	314.249			0.600859			0.300429	−	0.953804i	$-0.402870\pi$
$523$	314.249			0.600859			0.300429	+	0.953804i	$0.402870\pi$
$524$	−865.044	+	387.169i	−1.65085	+	0.738871i
$525$		0			0
$526$	−25.0497	−	117.286i	−0.0476230	−	0.222978i
$527$		−	231.113i		−	0.438544i
$528$		0			0
$529$	−818.316			−1.54691
$530$	−423.256	+	90.3981i	−0.798597	+	0.170562i
$531$		0			0
$532$	550.397	+	1229.74i	1.03458	+	2.31154i
$533$		−	334.606i		−	0.627778i
$534$		0			0
$535$		−	361.609i		−	0.675904i
$536$	66.6447	−	48.7192i	0.124337	−	0.0908940i
$537$		0			0
$538$	−90.4036	−	423.282i	−0.168036	−	0.786770i
$539$	−162.497			−0.301479
$540$		0			0
$541$			0.255704i			0.000472651i	1.00000		0.000236326i	$7.52247e-5\pi$
$541$			0.255704i			0.000472651i	−1.00000		0.000236326i	$0.999925\pi$
$542$	64.1706	+	300.456i	0.118396	+	0.554346i
$543$		0			0
$544$	−226.488	+	396.751i	−0.416339	+	0.729321i
$545$	−676.542			−1.24136
$546$		0			0
$547$	341.864			0.624980			0.312490	−	0.949921i	$-0.398837\pi$
$547$	341.864			0.624980			0.312490	+	0.949921i	$0.398837\pi$
$548$	222.197	−	99.4491i	0.405470	−	0.181476i
$549$		0			0
$550$	4.08357	−	0.872158i	0.00742466	−	0.00158574i
$551$			518.895i			0.941733i
$552$		0			0
$553$	−1037.59			−1.87628
$554$	−111.689	−	522.945i	−0.201605	−	0.943945i
$555$		0			0
$556$	−144.542	+	64.6927i	−0.259967	+	0.116354i
$557$		−	261.620i		−	0.469694i	−0.972032	−	0.234847i	$-0.924541\pi$
$557$		−	261.620i		−	0.469694i	0.972032	−	0.234847i	$-0.0754589\pi$
$558$		0			0
$559$		−	348.140i		−	0.622790i
$560$	693.332	−	776.099i	1.23809	−	1.38589i
$561$		0			0
$562$	−950.356	+	202.975i	−1.69102	+	0.361165i
$563$	−354.965			−0.630489			−0.315244	−	0.949011i	$-0.602087\pi$
$563$	−354.965			−0.630489			−0.315244	+	0.949011i	$0.602087\pi$
$564$		0			0
$565$		−	66.9147i		−	0.118433i
$566$	145.416	−	31.0576i	0.256919	−	0.0548720i
$567$		0			0
$568$	−333.422	−	456.100i	−0.587011	−	0.802993i
$569$	528.724			0.929216			0.464608	−	0.885517i	$-0.346195\pi$
$569$	528.724			0.929216			0.464608	+	0.885517i	$0.346195\pi$
$570$		0			0
$571$	500.724			0.876924			0.438462	−	0.898750i	$-0.355523\pi$
$571$	500.724			0.876924			0.438462	+	0.898750i	$0.355523\pi$
$572$	−13.5820	−	30.3461i	−0.0237448	−	0.0530526i
$573$		0			0
$574$	−311.248	−	1457.31i	−0.542244	−	2.53886i
$575$		−	52.3892i		−	0.0911116i
$576$		0			0
$577$	308.270			0.534263			0.267131	−	0.963660i	$-0.413924\pi$
$577$	308.270			0.534263			0.267131	+	0.963660i	$0.413924\pi$
$578$	166.609	−	35.5840i	0.288251	−	0.0615640i
$579$		0			0
$580$	365.840	−	163.739i	0.630758	−	0.282309i
$581$		−	870.195i		−	1.49775i
$582$		0			0
$583$			61.5775i			0.105622i
$584$	677.555	−	495.312i	1.16020	−	0.848137i
$585$		0			0
$586$	195.721	+	916.394i	0.333995	+	1.56381i
$587$	−434.777			−0.740676			−0.370338	−	0.928897i	$-0.620758\pi$
$587$	−434.777			−0.740676			−0.370338	+	0.928897i	$0.620758\pi$
$588$		0			0
$589$		−	430.953i		−	0.731669i
$590$	−5.88694	−	27.5635i	−0.00997786	−	0.0467177i
$591$		0			0
$592$	444.093	+	396.733i	0.750157	+	0.670156i
$593$	−1007.42			−1.69885			−0.849427	−	0.527707i	$-0.823052\pi$
$593$	−1007.42			−1.69885			−0.849427	+	0.527707i	$0.823052\pi$
$594$		0			0
$595$	928.585			1.56065
$596$	240.165	+	536.597i	0.402962	+	0.900330i
$597$		0			0
$598$	−407.926	+	87.1238i	−0.682150	+	0.145692i
$599$			1057.10i			1.76477i	0.470525	+	0.882387i	$0.344065\pi$
$599$			1057.10i			1.76477i	−0.470525	+	0.882387i	$0.655935\pi$
$600$		0			0
$601$	−122.611			−0.204011			−0.102006	−	0.994784i	$-0.532526\pi$
$601$	−122.611			−0.204011			−0.102006	+	0.994784i	$0.532526\pi$
$602$	−323.837	−	1516.25i	−0.537936	−	2.51869i
$603$		0			0
$604$	−102.585	−	229.203i	−0.169842	−	0.379475i
$605$			611.030i			1.00997i
$606$		0			0
$607$			204.786i			0.337374i	0.985670	+	0.168687i	$0.0539527\pi$
$607$			204.786i			0.337374i	−0.985670	+	0.168687i	$0.946047\pi$
$608$	−422.330	+	739.817i	−0.694622	+	1.21680i
$609$		0			0
$610$	720.495	−	153.882i	1.18114	−	0.252265i
$611$	−350.436			−0.573545
$612$		0			0
$613$		−	608.733i		−	0.993040i	−0.868025	−	0.496520i	$-0.834611\pi$
$613$		−	608.733i		−	0.993040i	0.868025	−	0.496520i	$-0.165389\pi$
$614$	−114.223	+	24.3954i	−0.186030	+	0.0397319i
$615$		0			0
$616$	−87.3815	−	119.532i	−0.141853	−	0.194046i
$617$	−17.0108			−0.0275701			−0.0137851	−	0.999905i	$-0.504388\pi$
$617$	−17.0108			−0.0275701			−0.0137851	+	0.999905i	$0.504388\pi$
$618$		0			0
$619$	175.916			0.284193			0.142097	−	0.989853i	$-0.454616\pi$
$619$	175.916			0.284193			0.142097	+	0.989853i	$0.454616\pi$
$620$	−303.838	+	135.989i	−0.490060	+	0.219337i
$621$		0			0
$622$	111.960	+	524.214i	0.180001	+	0.842788i
$623$		−	830.400i		−	1.33290i
$624$		0			0
$625$	−658.645			−1.05383
$626$	152.569	−	32.5853i	0.243721	−	0.0520532i
$627$		0			0
$628$	134.888	+	301.378i	0.214790	+	0.479901i
$629$			531.347i			0.844749i
$630$		0			0
$631$			160.940i			0.255055i	0.991835	+	0.127528i	$0.0407041\pi$
$631$			160.940i			0.255055i	−0.991835	+	0.127528i	$0.959296\pi$
$632$	−387.171	−	529.625i	−0.612612	−	0.838014i
$633$		0			0
$634$	109.465	+	512.530i	0.172658	+	0.808407i
$635$	−12.1636			−0.0191552
$636$		0			0
$637$			631.189i			0.990878i
$638$	−11.9108	−	55.7681i	−0.0186690	−	0.0874108i
$639$		0			0
$640$	654.866	+	64.3060i	1.02323	+	0.100478i
$641$	−301.976			−0.471101			−0.235551	−	0.971862i	$-0.575689\pi$
$641$	−301.976			−0.471101			−0.235551	+	0.971862i	$0.575689\pi$
$642$		0			0
$643$	356.979			0.555177			0.277589	−	0.960700i	$-0.410465\pi$
$643$	356.979			0.555177			0.277589	+	0.960700i	$0.410465\pi$
$644$	−1695.60	+	758.900i	−2.63291	+	1.17842i
$645$		0			0
$646$	−743.344	+	158.762i	−1.15069	+	0.245761i
$647$			170.568i			0.263630i	0.991274	+	0.131815i	$0.0420804\pi$
$647$			170.568i			0.263630i	−0.991274	+	0.131815i	$0.957920\pi$
$648$		0			0
$649$	−4.01008			−0.00617885
$650$	−3.38773	−	15.8618i	−0.00521189	−	0.0244028i
$651$		0			0
$652$	107.365	−	48.0537i	0.164671	−	0.0737020i
$653$		−	509.245i		−	0.779855i	−0.920846	−	0.389927i	$-0.872500\pi$
$653$		−	509.245i		−	0.779855i	0.920846	−	0.389927i	$-0.127500\pi$
$654$		0			0
$655$			1218.01i			1.85956i
$656$	627.726	−	702.661i	0.956900	−	1.07113i
$657$		0			0
$658$	−1526.25	+	325.973i	−2.31953	+	0.495400i
$659$	1224.45			1.85804			0.929019	−	0.370033i	$-0.120653\pi$
$659$	1224.45			1.85804			0.929019	+	0.370033i	$0.120653\pi$
$660$		0			0
$661$		−	257.526i		−	0.389600i	−0.980843	−	0.194800i	$-0.937594\pi$
$661$		−	257.526i		−	0.389600i	0.980843	−	0.194800i	$-0.0624059\pi$
$662$	546.635	−	116.749i	0.825732	−	0.176358i
$663$		0			0
$664$	444.182	−	324.710i	0.668949	−	0.489020i
$665$	1731.52			2.60379
$666$		0			0
$667$	−715.464			−1.07266
$668$	−151.913	−	339.416i	−0.227415	−	0.508108i
$669$		0			0
$670$	−22.1601	−	103.757i	−0.0330747	−	0.154861i
$671$		−	104.821i		−	0.156217i
$672$		0			0
$673$	−432.596			−0.642787			−0.321394	−	0.946946i	$-0.604151\pi$
$673$	−432.596			−0.642787			−0.321394	+	0.946946i	$0.604151\pi$
$674$	−1081.16	+	230.911i	−1.60409	+	0.342597i
$675$		0			0
$676$	499.145	−	223.403i	0.738380	−	0.330478i
$677$			235.171i			0.347372i	0.984801	+	0.173686i	$0.0555678\pi$
$677$			235.171i			0.347372i	−0.984801	+	0.173686i	$0.944432\pi$
$678$		0			0
$679$			67.3009i			0.0991177i
$680$	346.498	+	473.987i	0.509556	+	0.697039i
$681$		0			0
$682$	9.89218	+	46.3166i	0.0145047	+	0.0679129i
$683$	−1040.38			−1.52326			−0.761628	−	0.648015i	$-0.775599\pi$
$683$	−1040.38			−1.52326			−0.761628	+	0.648015i	$0.775599\pi$
$684$		0			0
$685$		−	312.862i		−	0.456734i
$686$	328.145	+	1536.42i	0.478345	+	2.23968i
$687$		0			0
$688$	653.116	−	731.083i	0.949297	−	1.06262i
$689$	239.186			0.347149
$690$		0			0
$691$	121.607			0.175987			0.0879937	−	0.996121i	$-0.471954\pi$
$691$	121.607			0.175987			0.0879937	+	0.996121i	$0.471954\pi$
$692$	79.0575	+	176.637i	0.114245	+	0.255255i
$693$		0			0
$694$	412.440	−	88.0878i	0.594293	−	0.126928i
$695$			203.521i			0.292835i
$696$		0			0
$697$	840.719			1.20620
$698$	127.910	+	598.892i	0.183252	+	0.858011i
$699$		0			0
$700$	−29.5091	−	65.9317i	−0.0421559	−	0.0941881i
$701$			28.6350i			0.0408488i	0.999791	+	0.0204244i	$0.00650174\pi$
$701$			28.6350i			0.0408488i	−0.999791	+	0.0204244i	$0.993498\pi$
$702$		0			0
$703$			990.797i			1.40938i
$704$	28.4080	−	89.2059i	0.0403522	−	0.126713i
$705$		0			0
$706$	702.797	−	150.102i	0.995463	−	0.212609i
$707$	1676.10			2.37072
$708$		0			0
$709$			260.652i			0.367634i	0.982961	+	0.183817i	$0.0588453\pi$
$709$			260.652i			0.367634i	−0.982961	+	0.183817i	$0.941155\pi$
$710$	−710.084	+	151.658i	−1.00012	+	0.213603i
$711$		0			0
$712$	423.869	−	309.860i	0.595322	−	0.435197i
$713$	594.208			0.833391
$714$		0			0
$715$	−42.7285			−0.0597601
$716$	542.051	−	242.606i	0.757054	−	0.338836i
$717$		0			0
$718$	140.437	+	657.548i	0.195595	+	0.915805i
$719$		−	911.912i		−	1.26831i	−0.773208	−	0.634153i	$-0.781349\pi$
$719$		−	911.912i		−	1.26831i	0.773208	−	0.634153i	$-0.218651\pi$
$720$		0			0
$721$	98.6067			0.136764
$722$	−680.030	+	145.239i	−0.941870	+	0.201162i
$723$		0			0
$724$	154.233	+	344.601i	0.213030	+	0.475968i
$725$		−	27.8202i		−	0.0383726i
$726$		0			0
$727$		−	126.575i		−	0.174105i	−0.996204	−	0.0870527i	$-0.972255\pi$
$727$		−	126.575i		−	0.174105i	0.996204	−	0.0870527i	$-0.0277449\pi$
$728$	−464.300	+	339.416i	−0.637774	+	0.466231i
$729$		0			0
$730$	−225.294	−	1054.86i	−0.308622	−	1.44501i
$731$	874.724			1.19661
$732$		0			0
$733$		−	825.221i		−	1.12581i	−0.826521	−	0.562906i	$-0.809683\pi$
$733$		−	825.221i		−	1.12581i	0.826521	−	0.562906i	$-0.190317\pi$
$734$	−193.002	−	903.661i	−0.262945	−	1.23115i
$735$		0			0
$736$	−1020.08	−	582.319i	−1.38597	−	0.791194i
$737$	−15.0950			−0.0204817
$738$		0			0
$739$	1098.07			1.48588			0.742942	−	0.669356i	$-0.233430\pi$
$739$	1098.07			1.48588			0.742942	+	0.669356i	$0.233430\pi$
$740$	698.548	−	312.650i	0.943984	−	0.422500i
$741$		0			0
$742$	1041.73	−	222.489i	1.40394	−	0.299851i
$743$			862.493i			1.16082i	0.814323	+	0.580412i	$0.197109\pi$
$743$			862.493i			1.16082i	−0.814323	+	0.580412i	$0.802891\pi$
$744$		0			0
$745$	755.549			1.01416
$746$	84.3295	+	394.843i	0.113042	+	0.529280i
$747$		0			0
$748$	76.2465	−	34.1257i	0.101934	−	0.0456227i
$749$			889.997i			1.18825i
$750$		0			0
$751$			307.835i			0.409900i	0.978772	+	0.204950i	$0.0657032\pi$
$751$			307.835i			0.409900i	−0.978772	+	0.204950i	$0.934297\pi$
$752$	−735.905	−	657.425i	−0.978597	−	0.874235i
$753$		0			0
$754$	−216.620	+	46.2652i	−0.287295	+	0.0613597i
$755$	−322.726			−0.427452
$756$		0			0
$757$			383.571i			0.506698i	0.967375	+	0.253349i	$0.0815321\pi$
$757$			383.571i			0.506698i	−0.967375	+	0.253349i	$0.918468\pi$
$758$	641.910	−	137.098i	0.846847	−	0.180867i
$759$		0			0
$760$	646.111	+	883.838i	0.850146	+	1.16294i
$761$	−424.861			−0.558294			−0.279147	−	0.960248i	$-0.590052\pi$
$761$	−424.861			−0.558294			−0.279147	+	0.960248i	$0.590052\pi$
$762$		0			0
$763$	1665.12			2.18233
$764$	−324.503	−	725.031i	−0.424742	−	0.948993i
$765$		0			0
$766$	24.0424	+	112.570i	0.0313869	+	0.146958i
$767$			15.5764i			0.0203082i
$768$		0			0
$769$	−1172.64			−1.52489			−0.762443	−	0.647055i	$-0.776000\pi$
$769$	−1172.64			−1.52489			−0.762443	+	0.647055i	$0.776000\pi$
$770$	−186.095	+	39.7457i	−0.241682	+	0.0516178i
$771$		0			0
$772$	−9.92409	+	4.44173i	−0.0128550	+	0.00575354i
$773$			1210.65i			1.56617i	0.621914	+	0.783085i	$0.286355\pi$
$773$			1210.65i			1.56617i	−0.621914	+	0.783085i	$0.713645\pi$
$774$		0			0
$775$			23.1052i			0.0298132i
$776$	−34.3531	+	25.1131i	−0.0442694	+	0.0323622i
$777$		0			0
$778$	220.599	+	1032.88i	0.283546	+	1.32760i
$779$	1567.68			2.01243
$780$		0			0
$781$			103.307i			0.132275i
$782$	−218.904	−	1024.94i	−0.279929	−	1.31067i
$783$		0			0
$784$	−1184.12	+	1325.48i	−1.51036	+	1.69066i
$785$	424.352			0.540576
$786$		0			0
$787$	−949.469			−1.20644			−0.603220	−	0.797574i	$-0.706116\pi$
$787$	−949.469			−1.20644			−0.603220	+	0.797574i	$0.706116\pi$
$788$	−322.349	−	720.218i	−0.409072	−	0.913982i
$789$		0			0
$790$	−824.552	+	176.106i	−1.04374	+	0.222919i
$791$			164.692i			0.208207i
$792$		0			0
$793$	−407.158			−0.513440
$794$	−63.2059	−	295.939i	−0.0796044	−	0.372719i
$795$		0			0
$796$	449.679	+	1004.71i	0.564924	+	1.26220i
$797$			668.187i			0.838378i	0.907899	+	0.419189i	$0.137686\pi$
$797$			668.187i			0.838378i	−0.907899	+	0.419189i	$0.862314\pi$
$798$		0			0
$799$		−	880.494i		−	1.10199i
$800$	22.6429	−	39.6648i	0.0283037	−	0.0495809i
$801$		0			0
$802$	1429.66	−	305.344i	1.78262	−	0.380728i
$803$	−153.466			−0.191116
$804$		0			0
$805$			2387.46i			2.96579i
$806$	179.908	−	38.4243i	0.223211	−	0.0476728i
$807$		0			0
$808$	625.431	+	855.549i	0.774048	+	1.05885i
$809$	896.533			1.10820			0.554099	−	0.832451i	$-0.313063\pi$
$809$	896.533			1.10820			0.554099	+	0.832451i	$0.313063\pi$
$810$		0			0
$811$	−1083.73			−1.33628			−0.668141	−	0.744034i	$-0.732910\pi$
$811$	−1083.73			−1.33628			−0.668141	+	0.744034i	$0.732910\pi$
$812$	−900.410	+	402.998i	−1.10888	+	0.496302i
$813$		0			0
$814$	−22.7430	−	106.486i	−0.0279398	−	0.130818i
$815$		−	151.175i		−	0.185490i
$816$		0			0
$817$	1631.09			1.99644
$818$	−615.558	+	131.469i	−0.752516	+	0.160720i
$819$		0			0
$820$	−494.687	−	1105.27i	−0.603277	−	1.34789i
$821$			464.546i			0.565830i	0.959145	+	0.282915i	$0.0913014\pi$
$821$			464.546i			0.565830i	−0.959145	+	0.282915i	$0.908699\pi$
$822$		0			0
$823$		−	609.423i		−	0.740490i	−0.928934	−	0.370245i	$-0.879274\pi$
$823$		−	609.423i		−	0.740490i	0.928934	−	0.370245i	$-0.120726\pi$
$824$	36.7947	+	50.3328i	0.0446538	+	0.0610835i
$825$		0			0
$826$	14.4890	+	67.8396i	0.0175412	+	0.0821303i
$827$	−1179.52			−1.42627			−0.713133	−	0.701029i	$-0.752725\pi$
$827$	−1179.52			−1.42627			−0.713133	+	0.701029i	$0.752725\pi$
$828$		0			0
$829$			645.824i			0.779040i	0.921018	+	0.389520i	$0.127359\pi$
$829$			645.824i			0.779040i	−0.921018	+	0.389520i	$0.872641\pi$
$830$	−147.695	−	691.529i	−0.177946	−	0.833168i
$831$		0			0
$832$	−346.503	−	110.345i	−0.416470	−	0.132626i
$833$	−1585.90			−1.90385
$834$		0			0
$835$	−477.911			−0.572349
$836$	142.176	−	63.6339i	0.170067	−	0.0761171i
$837$		0			0
$838$	−224.211	+	47.8863i	−0.267554	+	0.0571436i
$839$			1050.96i			1.25263i	0.779571	+	0.626314i	$0.215437\pi$
$839$			1050.96i			1.25263i	−0.779571	+	0.626314i	$0.784563\pi$
$840$		0			0
$841$	461.068			0.548238
$842$	221.736	+	1038.20i	0.263344	+	1.23301i
$843$		0			0
$844$	−1100.04	+	492.347i	−1.30337	+	0.583350i
$845$		−	702.816i		−	0.831735i
$846$		0			0
$847$		−	1503.88i		−	1.77553i
$848$	502.283	+	448.717i	0.592315	+	0.529148i
$849$		0			0
$850$	39.8539	−	8.51189i	0.0468869	−	0.0100140i
$851$	−1366.13			−1.60533
$852$		0			0
$853$		−	917.334i		−	1.07542i	−0.843130	−	0.537710i	$-0.819289\pi$
$853$		−	917.334i		−	1.07542i	0.843130	−	0.537710i	$-0.180711\pi$
$854$	−1773.29	+	378.736i	−2.07646	+	0.443485i
$855$		0			0
$856$	−454.290	+	332.099i	−0.530712	+	0.387966i
$857$	714.451			0.833665			0.416832	−	0.908983i	$-0.363140\pi$
$857$	714.451			0.833665			0.416832	+	0.908983i	$0.363140\pi$
$858$		0			0
$859$	151.374			0.176221			0.0881104	−	0.996111i	$-0.471917\pi$
$859$	151.374			0.176221			0.0881104	+	0.996111i	$0.471917\pi$
$860$	−514.696	−	1149.98i	−0.598484	−	1.33718i
$861$		0			0
$862$	−38.2045	−	178.879i	−0.0443208	−	0.207516i
$863$		−	647.037i		−	0.749753i	−0.927075	−	0.374877i	$-0.877685\pi$
$863$		−	647.037i		−	0.749753i	0.927075	−	0.374877i	$-0.122315\pi$
$864$		0			0
$865$	248.711			0.287527
$866$	879.230	−	187.784i	1.01528	−	0.216840i
$867$		0			0
$868$	747.810	−	334.698i	0.861532	−	0.385597i
$869$			119.960i			0.138044i
$870$		0			0
$871$			58.6338i			0.0673177i
$872$	621.332	+	849.942i	0.712536	+	0.974704i
$873$		0			0
$874$	−408.188	−	1911.20i	−0.467035	−	2.18672i
$875$	1533.25			1.75228
$876$		0			0
$877$		−	1622.75i		−	1.85034i	−0.379549	−	0.925172i	$-0.623921\pi$
$877$		−	1622.75i		−	1.85034i	0.379549	−	0.925172i	$-0.376079\pi$
$878$	−25.0352	−	117.218i	−0.0285139	−	0.133506i
$879$		0			0
$880$	−89.7284	−	80.1594i	−0.101964	−	0.0910902i
$881$	1008.69			1.14494			0.572471	−	0.819925i	$-0.305985\pi$
$881$	1008.69			1.14494			0.572471	+	0.819925i	$0.305985\pi$
$882$		0			0
$883$	76.0921			0.0861745			0.0430873	−	0.999071i	$-0.486281\pi$
$883$	76.0921			0.0861745			0.0430873	+	0.999071i	$0.486281\pi$
$884$	−132.555	−	296.165i	−0.149949	−	0.335028i
$885$		0			0
$886$	650.581	−	138.949i	0.734290	−	0.156828i
$887$		−	1463.05i		−	1.64943i	−0.565545	−	0.824717i	$-0.691334\pi$
$887$		−	1463.05i		−	1.64943i	0.565545	−	0.824717i	$-0.308666\pi$
$888$		0			0
$889$	29.9372			0.0336751
$890$	−140.941	−	659.905i	−0.158361	−	0.741466i
$891$		0			0
$892$	−280.928	−	627.673i	−0.314942	−	0.703669i
$893$		−	1641.85i		−	1.83858i
$894$		0			0
$895$		−	763.229i		−	0.852770i
$896$	−1611.77	−	158.271i	−1.79885	−	0.176642i
$897$		0			0
$898$	−399.078	+	85.2342i	−0.444408	+	0.0949156i
$899$	315.542			0.350992
$900$		0			0
$901$			600.970i			0.667004i
$902$	−168.486	+	35.9848i	−0.186792	+	0.0398945i
$903$		0			0
$904$	−84.0651	+	61.4540i	−0.0929924	+	0.0679801i
$905$	485.212			0.536145
$906$		0			0
$907$	−535.897			−0.590846			−0.295423	−	0.955367i	$-0.595461\pi$
$907$	−535.897			−0.590846			−0.295423	+	0.955367i	$0.595461\pi$
$908$	879.047	−	393.436i	0.968114	−	0.433300i
$909$		0			0
$910$	154.385	+	722.850i	0.169653	+	0.794341i
$911$			1025.19i			1.12535i	0.826680	+	0.562673i	$0.190227\pi$
$911$			1025.19i			1.12535i	−0.826680	+	0.562673i	$0.809773\pi$
$912$		0			0
$913$	−100.607			−0.110194
$914$	945.887	−	202.020i	1.03489	−	0.221029i
$915$		0			0
$916$	−680.542	−	1520.52i	−0.742950	−	1.65996i
$917$		−	2997.80i		−	3.26914i
$918$		0			0
$919$		−	1192.03i		−	1.29709i	−0.761176	−	0.648545i	$-0.775378\pi$
$919$		−	1192.03i		−	1.29709i	0.761176	−	0.648545i	$-0.224622\pi$
$920$	−1218.66	+	890.873i	−1.32463	+	0.968340i
$921$		0			0
$922$	31.6794	+	148.328i	0.0343595	+	0.160876i
$923$	401.275			0.434751
$924$		0			0
$925$		−	53.1209i		−	0.0574280i
$926$	−23.3820	−	109.478i	−0.0252505	−	0.118226i
$927$		0			0
$928$	−541.690	−	309.228i	−0.583718	−	0.333220i
$929$	−1133.29			−1.21991			−0.609954	−	0.792437i	$-0.708812\pi$
$929$	−1133.29			−1.21991			−0.609954	+	0.792437i	$0.708812\pi$
$930$		0			0
$931$	−2957.22			−3.17639
$932$	−144.085	+	64.4885i	−0.154598	+	0.0691936i
$933$		0			0
$934$	1016.59	−	217.120i	1.08842	−	0.232463i
$935$		−	107.358i		−	0.114821i
$936$		0			0
$937$	−389.378			−0.415558			−0.207779	−	0.978176i	$-0.566624\pi$
$937$	−389.378			−0.415558			−0.207779	+	0.978176i	$0.566624\pi$
$938$	54.5407	+	255.367i	0.0581458	+	0.272247i
$939$		0			0
$940$	−1157.56	+	518.091i	−1.23145	+	0.551161i
$941$			768.324i			0.816497i	0.912871	+	0.408249i	$0.133860\pi$
$941$			768.324i			0.816497i	−0.912871	+	0.408249i	$0.866140\pi$
$942$		0			0
$943$			2161.55i			2.29221i
$944$	−29.2215	+	32.7099i	−0.0309550	+	0.0346503i
$945$		0			0
$946$	−175.301	+	37.4403i	−0.185308	+	0.0395775i
$947$	−1592.82			−1.68196			−0.840980	−	0.541066i	$-0.818021\pi$
$947$	−1592.82			−1.68196			−0.840980	+	0.541066i	$0.818021\pi$
$948$		0			0
$949$			596.110i			0.628145i
$950$	74.3151	−	15.8720i	0.0782264	−	0.0167074i
$951$		0			0
$952$	−852.806	−	1166.58i	−0.895805	−	1.22540i
$953$	204.697			0.214792			0.107396	−	0.994216i	$-0.465749\pi$
$953$	204.697			0.214792			0.107396	+	0.994216i	$0.465749\pi$
$954$		0			0
$955$	−1020.87			−1.06898
$956$	637.986	+	1425.44i	0.667349	+	1.49105i
$957$		0			0
$958$	159.371	+	746.198i	0.166358	+	0.778912i
$959$			770.022i			0.802943i
$960$		0			0
$961$	698.936			0.727301
$962$	−413.623	+	88.3406i	−0.429962	+	0.0918302i
$963$		0			0
$964$	393.952	−	176.322i	0.408664	−	0.182906i
$965$			13.9735i			0.0144803i
$966$		0			0
$967$			732.916i			0.757928i	0.925411	+	0.378964i	$0.123720\pi$
$967$			732.916i			0.757928i	−0.925411	+	0.378964i	$0.876280\pi$
$968$	767.638	−	561.166i	0.793015	−	0.579716i
$969$		0			0
$970$	11.4228	+	53.4829i	0.0117760	+	0.0551371i
$971$	−101.413			−0.104442			−0.0522210	−	0.998636i	$-0.516630\pi$
$971$	−101.413			−0.104442			−0.0522210	+	0.998636i	$0.516630\pi$
$972$		0			0
$973$		−	500.908i		−	0.514808i
$974$	−247.902	−	1160.71i	−0.254520	−	1.19170i
$975$		0			0
$976$	−855.019	−	763.836i	−0.876044	−	0.782619i
$977$	−1439.84			−1.47374			−0.736868	−	0.676037i	$-0.763696\pi$
$977$	−1439.84			−1.47374			−0.736868	+	0.676037i	$0.763696\pi$
$978$		0			0
$979$	−96.0064			−0.0980658
$980$	933.162	+	2084.95i	0.952206	+	2.12750i
$981$		0			0
$982$	−245.832	+	52.5042i	−0.250338	+	0.0534666i
$983$		−	720.894i		−	0.733361i	−0.930347	−	0.366681i	$-0.880494\pi$
$983$		−	720.894i		−	0.733361i	0.930347	−	0.366681i	$-0.119506\pi$
$984$		0			0
$985$	−1014.09			−1.02954
$986$	−116.244	−	544.273i	−0.117895	−	0.552001i
$987$		0			0
$988$	−247.174	−	552.255i	−0.250176	−	0.558963i
$989$			2248.98i			2.27400i
$990$		0			0
$991$			861.974i			0.869802i	0.900478	+	0.434901i	$0.143217\pi$
$991$			861.974i			0.869802i	−0.900478	+	0.434901i	$0.856783\pi$
$992$	449.885	+	256.821i	0.453513	+	0.258892i
$993$		0			0
$994$	1747.67	−	373.263i	1.75822	−	0.375516i
$995$	1414.67			1.42178
$996$		0			0
$997$		−	464.804i		−	0.466203i	−0.972452	−	0.233102i	$-0.925113\pi$
$997$		−	464.804i		−	0.466203i	0.972452	−	0.233102i	$-0.0748875\pi$
$998$	919.471	−	196.378i	0.921314	−	0.196772i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.b.a.163.2	yes	16
3.2	odd	2	inner	216.3.b.a.163.15	yes	16
4.3	odd	2		864.3.b.a.271.3		16
8.3	odd	2	inner	216.3.b.a.163.1	✓	16
8.5	even	2		864.3.b.a.271.14		16
12.11	even	2		864.3.b.a.271.13		16
24.5	odd	2		864.3.b.a.271.4		16
24.11	even	2	inner	216.3.b.a.163.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.b.a.163.1	✓	16	8.3	odd	2	inner
216.3.b.a.163.2	yes	16	1.1	even	1	trivial
216.3.b.a.163.15	yes	16	3.2	odd	2	inner
216.3.b.a.163.16	yes	16	24.11	even	2	inner
864.3.b.a.271.3		16	4.3	odd	2
864.3.b.a.271.4		16	24.5	odd	2
864.3.b.a.271.13		16	12.11	even	2
864.3.b.a.271.14		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95589 + 0.417734i) q^{2} +(3.65100 - 1.63408i) q^{4} -5.14075i q^{5} +12.6525i q^{7} +(-6.45833 + 4.72122i) q^{8} +O(q^{10})\)	\(q+(-1.95589 + 0.417734i) q^{2} +(3.65100 - 1.63408i) q^{4} -5.14075i q^{5} +12.6525i q^{7} +(-6.45833 + 4.72122i) q^{8} +(2.14746 + 10.0547i) q^{10} +1.46281 q^{11} -5.68201i q^{13} +(-5.28537 - 24.7469i) q^{14} +(10.6596 - 11.9320i) q^{16} +14.2764 q^{17} +26.6211 q^{19} +(-8.40040 - 18.7688i) q^{20} +(-2.86110 + 0.611066i) q^{22} +36.7058i q^{23} -1.42727 q^{25} +(2.37357 + 11.1134i) q^{26} +(20.6752 + 46.1942i) q^{28} +19.4918i q^{29} -16.1884i q^{31} +(-15.8645 + 27.7906i) q^{32} +(-27.9231 + 5.96375i) q^{34} +65.0432 q^{35} +37.2185i q^{37} +(-52.0679 + 11.1205i) q^{38} +(24.2706 + 33.2006i) q^{40} +58.8886 q^{41} +61.2705 q^{43} +(5.34073 - 2.39036i) q^{44} +(-15.3333 - 71.7925i) q^{46} -61.6746i q^{47} -111.085 q^{49} +(2.79158 - 0.596220i) q^{50} +(-9.28487 - 20.7450i) q^{52} +42.0953i q^{53} -7.51995i q^{55} +(-59.7352 - 81.7140i) q^{56} +(-8.14240 - 38.1239i) q^{58} -2.74134 q^{59} -71.6574i q^{61} +(6.76244 + 31.6627i) q^{62} +(19.4201 - 60.9825i) q^{64} -29.2098 q^{65} -10.3192 q^{67} +(52.1232 - 23.3288i) q^{68} +(-127.217 + 27.1708i) q^{70} +70.6220i q^{71} -104.912 q^{73} +(-15.5474 - 72.7952i) q^{74} +(97.1936 - 43.5011i) q^{76} +18.5082i q^{77} +82.0064i q^{79} +(-61.3396 - 54.7981i) q^{80} +(-115.179 + 24.5997i) q^{82} -68.7766 q^{83} -73.3915i q^{85} +(-119.838 + 25.5948i) q^{86} +(-9.44733 + 6.90627i) q^{88} -65.6313 q^{89} +71.8916 q^{91} +(59.9803 + 134.013i) q^{92} +(25.7636 + 120.629i) q^{94} -136.852i q^{95} +5.31919 q^{97} +(217.271 - 46.4041i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4}+O(q^{10}) \) 16 * q - 2 * q^4	\( 16 q - 2 q^{4} - 18 q^{10} + 34 q^{16} + 32 q^{19} - 22 q^{22} - 80 q^{25} + 102 q^{28} + 68 q^{34} - 6 q^{40} + 128 q^{43} + 60 q^{46} - 80 q^{49} - 180 q^{52} - 156 q^{58} - 74 q^{64} + 128 q^{67} - 378 q^{70} - 160 q^{73} + 188 q^{76} - 508 q^{82} + 542 q^{88} - 96 q^{91} + 24 q^{94} - 208 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 - 18 * q^10 + 34 * q^16 + 32 * q^19 - 22 * q^22 - 80 * q^25 + 102 * q^28 + 68 * q^34 - 6 * q^40 + 128 * q^43 + 60 * q^46 - 80 * q^49 - 180 * q^52 - 156 * q^58 - 74 * q^64 + 128 * q^67 - 378 * q^70 - 160 * q^73 + 188 * q^76 - 508 * q^82 + 542 * q^88 - 96 * q^91 + 24 * q^94 - 208 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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