LMFDB - Embedded newform 216.3.b.a.163.1

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

$q$-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	$0.171865\pi$
$5$			5.14075i			1.02815i	−0.857745	+	0.514075i	$0.828135\pi$
$6$		0			0
$7$		−	12.6525i		−	1.80750i	−0.428063	−	0.903749i	$-0.640804\pi$
$7$		−	12.6525i		−	1.80750i	0.428063	−	0.903749i	$-0.359196\pi$
$8$	−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	$0.0701291\pi$
$13$			5.68201i			0.437078i	−0.975828	+	0.218539i	$0.929871\pi$
$14$	−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	$-0.705917\pi$
$23$		−	36.7058i		−	1.59590i	0.602721	−	0.797952i	$-0.294083\pi$
$24$		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	$-0.890903\pi$
$29$		−	19.4918i		−	0.672133i	0.941838	−	0.336066i	$-0.109097\pi$
$30$		0			0
$31$			16.1884i			0.522206i	0.965311	+	0.261103i	$0.0840863\pi$
$31$			16.1884i			0.522206i	−0.965311	+	0.261103i	$0.915914\pi$
$32$	−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	$-0.832247\pi$
$37$		−	37.2185i		−	1.00590i	0.864314	−	0.502952i	$-0.167753\pi$
$38$	−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	$0.227801\pi$
$47$			61.6746i			1.31223i	−0.754662	+	0.656113i	$0.772199\pi$
$48$		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	$-0.870008\pi$
$53$		−	42.0953i		−	0.794251i	0.917764	−	0.397125i	$-0.129992\pi$
$54$		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	$0.199831\pi$
$61$			71.6574i			1.17471i	−0.809329	+	0.587355i	$0.800169\pi$
$62$	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	$-0.834311\pi$
$71$		−	70.6220i		−	0.994676i	0.867557	−	0.497338i	$-0.165689\pi$
$72$		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	$-0.826294\pi$
$79$		−	82.0064i		−	1.03806i	0.854757	−	0.519028i	$-0.173706\pi$
$80$	−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	$0.227670\pi$
$101$			132.472i			1.31161i	−0.754932	+	0.655803i	$0.772330\pi$
$102$		0			0
$103$			7.79346i			0.0756647i	0.999284	+	0.0378323i	$0.0120453\pi$
$103$			7.79346i			0.0756647i	−0.999284	+	0.0378323i	$0.987955\pi$
$104$	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	$0.206303\pi$
$109$			131.604i			1.20738i	−0.797221	+	0.603688i	$0.793697\pi$
$110$	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	$0.00296522\pi$
$127$			2.36611i			0.0186308i	−0.999957	+	0.00931539i	$0.997035\pi$
$128$	−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	$-0.835828\pi$
$149$		−	146.973i		−	0.986394i	0.869918	−	0.493197i	$-0.164172\pi$
$150$		0			0
$151$			62.7781i			0.415749i	0.978155	+	0.207875i	$0.0666546\pi$
$151$			62.7781i			0.415749i	−0.978155	+	0.207875i	$0.933345\pi$
$152$	−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	$-0.915325\pi$
$157$		−	82.5467i		−	0.525775i	0.964826	−	0.262888i	$-0.0846749\pi$
$158$	−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	$0.0897840\pi$
$167$			92.9654i			0.556679i	−0.960483	+	0.278339i	$0.910216\pi$
$168$		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	$-0.955345\pi$
$173$		−	48.3804i		−	0.279655i	0.990176	−	0.139828i	$-0.0446549\pi$
$174$		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	$-0.916036\pi$
$181$		−	94.3854i		−	0.521466i	0.965411	−	0.260733i	$-0.0839643\pi$
$182$	−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	$0.174014\pi$
$191$			198.584i			1.03971i	−0.854255	+	0.519854i	$0.825986\pi$
$192$		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	$0.166915\pi$
$197$			197.266i			1.00135i	−0.865635	+	0.500675i	$0.833085\pi$
$198$		0			0
$199$		−	275.188i		−	1.38285i	−0.722446	−	0.691427i	$-0.756982\pi$
$199$		−	275.188i		−	1.38285i	0.722446	−	0.691427i	$-0.243018\pi$
$200$	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	$0.125960\pi$
$223$			171.918i			0.770934i	−0.922722	+	0.385467i	$0.874040\pi$
$224$	−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	$0.363396\pi$
$229$			416.468i			1.81864i	−0.416102	+	0.909318i	$0.636604\pi$
$230$	−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	$-0.695752\pi$
$239$		−	390.425i		−	1.63358i	0.576937	−	0.816789i	$-0.304248\pi$
$240$		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	$-0.963633\pi$
$263$		−	59.9658i		−	0.228007i	0.993480	−	0.114003i	$-0.0363675\pi$
$264$		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	$-0.868226\pi$
$269$		−	216.414i		−	0.804515i	0.915527	−	0.402257i	$-0.131774\pi$
$270$		0			0
$271$			153.616i			0.566849i	0.958995	+	0.283424i	$0.0914705\pi$
$271$			153.616i			0.566849i	−0.958995	+	0.283424i	$0.908530\pi$
$272$	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	$-0.839686\pi$
$277$		−	267.370i		−	0.965234i	0.875832	−	0.482617i	$-0.160314\pi$
$278$	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	$0.294924\pi$
$293$			468.531i			1.59908i	−0.600612	+	0.799540i	$0.705076\pi$
$294$		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	$0.141803\pi$
$311$			268.018i			0.861796i	−0.902401	+	0.430898i	$0.858197\pi$
$312$		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	$0.135631\pi$
$317$			262.045i			0.826639i	−0.910586	+	0.413320i	$0.864369\pi$
$318$		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	$0.144554\pi$
$349$			306.200i			0.877363i	−0.898643	+	0.438681i	$0.855446\pi$
$350$	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	$0.155108\pi$
$359$			336.189i			0.936459i	−0.883607	+	0.468230i	$0.844892\pi$
$360$		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	$-0.783278\pi$
$367$		−	462.021i		−	1.25891i	0.777036	−	0.629456i	$-0.216722\pi$
$368$	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	$0.0872249\pi$
$373$			201.874i			0.541217i	−0.962689	+	0.270608i	$0.912775\pi$
$374$	−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	$0.0239391\pi$
$383$			57.5543i			0.150272i	−0.997173	+	0.0751362i	$0.976061\pi$
$384$		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	$0.237488\pi$
$389$			528.085i			1.35755i	−0.734349	+	0.678773i	$0.762512\pi$
$390$		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	$-0.938969\pi$
$397$		−	151.307i		−	0.381125i	0.981675	−	0.190562i	$-0.0610312\pi$
$398$	−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	$0.217114\pi$
$421$			530.807i			1.26082i	−0.776261	+	0.630412i	$0.782886\pi$
$422$	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	$-0.966164\pi$
$431$		−	91.4566i		−	0.212196i	0.994356	−	0.106098i	$-0.0338358\pi$
$432$		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	$-0.978256\pi$
$439$		−	59.9309i		−	0.136517i	0.997668	−	0.0682585i	$-0.0217442\pi$
$440$	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	$0.0262113\pi$
$461$			75.8364i			0.164504i	−0.996612	+	0.0822521i	$0.973789\pi$
$462$		0			0
$463$		−	55.9734i		−	0.120893i	−0.998171	−	0.0604464i	$-0.980748\pi$
$463$		−	55.9734i		−	0.120893i	0.998171	−	0.0604464i	$-0.0192524\pi$
$464$	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	$0.130379\pi$
$479$			381.514i			0.796479i	−0.917281	+	0.398240i	$0.869621\pi$
$480$		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	$-0.791456\pi$
$487$		−	593.446i		−	1.21858i	0.792949	−	0.609288i	$-0.208544\pi$
$488$	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	$0.00685030\pi$
$503$			21.6483i			0.0430384i	−0.999768	+	0.0215192i	$0.993150\pi$
$504$		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	$0.205434\pi$
$509$			612.338i			1.20302i	−0.798865	+	0.601510i	$0.794566\pi$
$510$		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	$-0.999925\pi$
$541$		−	0.255704i		−	0.000472651i	1.00000		0.000236326i	$-7.52247e-5\pi$
$542$	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	$0.0754589\pi$
$557$			261.620i			0.469694i	−0.972032	+	0.234847i	$0.924541\pi$
$558$		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	$-0.655935\pi$
$599$		−	1057.10i		−	1.76477i	0.470525	−	0.882387i	$-0.344065\pi$
$600$		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	$-0.946047\pi$
$607$		−	204.786i		−	0.337374i	0.985670	−	0.168687i	$-0.0539527\pi$
$608$	−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	$0.165389\pi$
$613$			608.733i			0.993040i	−0.868025	+	0.496520i	$0.834611\pi$
$614$	−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	$-0.959296\pi$
$631$		−	160.940i		−	0.255055i	0.991835	−	0.127528i	$-0.0407041\pi$
$632$	−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	$-0.957920\pi$
$647$		−	170.568i		−	0.263630i	0.991274	−	0.131815i	$-0.0420804\pi$
$648$		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	$0.127500\pi$
$653$			509.245i			0.779855i	−0.920846	+	0.389927i	$0.872500\pi$
$654$		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	$0.0624059\pi$
$661$			257.526i			0.389600i	−0.980843	+	0.194800i	$0.937594\pi$
$662$	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	$-0.944432\pi$
$677$		−	235.171i		−	0.347372i	0.984801	−	0.173686i	$-0.0555678\pi$
$678$		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	$-0.993498\pi$
$701$		−	28.6350i		−	0.0408488i	0.999791	−	0.0204244i	$-0.00650174\pi$
$702$		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	$-0.941155\pi$
$709$		−	260.652i		−	0.367634i	0.982961	−	0.183817i	$-0.0588453\pi$
$710$	−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	$0.218651\pi$
$719$			911.912i			1.26831i	−0.773208	+	0.634153i	$0.781349\pi$
$720$		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	$0.0277449\pi$
$727$			126.575i			0.174105i	−0.996204	+	0.0870527i	$0.972255\pi$
$728$	−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	$0.190317\pi$
$733$			825.221i			1.12581i	−0.826521	+	0.562906i	$0.809683\pi$
$734$	−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	$-0.802891\pi$
$743$		−	862.493i		−	1.16082i	0.814323	−	0.580412i	$-0.197109\pi$
$744$		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	$-0.934297\pi$
$751$		−	307.835i		−	0.409900i	0.978772	−	0.204950i	$-0.0657032\pi$
$752$	−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	$-0.918468\pi$
$757$		−	383.571i		−	0.506698i	0.967375	−	0.253349i	$-0.0815321\pi$
$758$	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	$-0.713645\pi$
$773$		−	1210.65i		−	1.56617i	0.621914	−	0.783085i	$-0.286355\pi$
$774$		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	$-0.862314\pi$
$797$		−	668.187i		−	0.838378i	0.907899	−	0.419189i	$-0.137686\pi$
$798$		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	$-0.908699\pi$
$821$		−	464.546i		−	0.565830i	0.959145	−	0.282915i	$-0.0913014\pi$
$822$		0			0
$823$			609.423i			0.740490i	0.928934	+	0.370245i	$0.120726\pi$
$823$			609.423i			0.740490i	−0.928934	+	0.370245i	$0.879274\pi$
$824$	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	$-0.872641\pi$
$829$		−	645.824i		−	0.779040i	0.921018	−	0.389520i	$-0.127359\pi$
$830$	−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	$-0.784563\pi$
$839$		−	1050.96i		−	1.25263i	0.779571	−	0.626314i	$-0.215437\pi$
$840$		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	$0.180711\pi$
$853$			917.334i			1.07542i	−0.843130	+	0.537710i	$0.819289\pi$
$854$	−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	$0.122315\pi$
$863$			647.037i			0.749753i	−0.927075	+	0.374877i	$0.877685\pi$
$864$		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	$0.376079\pi$
$877$			1622.75i			1.85034i	−0.379549	+	0.925172i	$0.623921\pi$
$878$	−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	$0.308666\pi$
$887$			1463.05i			1.64943i	−0.565545	+	0.824717i	$0.691334\pi$
$888$		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	$-0.809773\pi$
$911$		−	1025.19i		−	1.12535i	0.826680	−	0.562673i	$-0.190227\pi$
$912$		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	$0.224622\pi$
$919$			1192.03i			1.29709i	−0.761176	+	0.648545i	$0.775378\pi$
$920$	−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	$-0.866140\pi$
$941$		−	768.324i		−	0.816497i	0.912871	−	0.408249i	$-0.133860\pi$
$942$		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	$-0.876280\pi$
$967$		−	732.916i		−	0.757928i	0.925411	−	0.378964i	$-0.123720\pi$
$968$	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	$0.119506\pi$
$983$			720.894i			0.733361i	−0.930347	+	0.366681i	$0.880494\pi$
$984$		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	$-0.856783\pi$
$991$		−	861.974i		−	0.869802i	0.900478	−	0.434901i	$-0.143217\pi$
$992$	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	$0.0748875\pi$
$997$			464.804i			0.466203i	−0.972452	+	0.233102i	$0.925113\pi$
$998$	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.163.1	✓	16
3.2	odd	2	inner	216.3.b.a.163.16	yes	16
4.3	odd	2		864.3.b.a.271.14		16
8.3	odd	2	inner	216.3.b.a.163.2	yes	16
8.5	even	2		864.3.b.a.271.3		16
12.11	even	2		864.3.b.a.271.4		16
24.5	odd	2		864.3.b.a.271.13		16
24.11	even	2	inner	216.3.b.a.163.15	yes	16

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