LMFDB - Embedded newform 1080.2.k.d.541.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(541,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1080.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.k (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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + 5x^{16} + 28x^{12} - 28x^{10} + 112x^{8} + 320x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + 5x^16 + 28x^12 - 28x^10 + 112x^8 + 320x^4 - 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			541.9
Root			$-0.444539 + 1.34253i$ of defining polynomial
Character	$\chi$	$=$	1080.541
Dual form			1080.2.k.d.541.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.444539 - 1.34253i) q^{2} +(-1.60477 + 1.19361i) q^{4} -1.00000i q^{5} -1.61609 q^{7} +(2.31584 + 1.62384i) q^{8} +O(q^{10})$	\(q+(-0.444539 - 1.34253i) q^{2} +(-1.60477 + 1.19361i) q^{4} -1.00000i q^{5} -1.61609 q^{7} +(2.31584 + 1.62384i) q^{8} +(-1.34253 + 0.444539i) q^{10} +2.72320i q^{11} -6.12984i q^{13} +(0.718415 + 2.16965i) q^{14} +(1.15057 - 3.83095i) q^{16} +4.31621 q^{17} -2.87938i q^{19} +(1.19361 + 1.60477i) q^{20} +(3.65598 - 1.21057i) q^{22} -7.44975 q^{23} -1.00000 q^{25} +(-8.22949 + 2.72495i) q^{26} +(2.59345 - 1.92899i) q^{28} +1.43287i q^{29} -9.17311 q^{31} +(-5.65464 + 0.158328i) q^{32} +(-1.91873 - 5.79464i) q^{34} +1.61609i q^{35} +9.26338i q^{37} +(-3.86566 + 1.28000i) q^{38} +(1.62384 - 2.31584i) q^{40} -6.77282 q^{41} -7.56667i q^{43} +(-3.25045 - 4.37012i) q^{44} +(3.31171 + 10.0015i) q^{46} +0.642985 q^{47} -4.38826 q^{49} +(0.444539 + 1.34253i) q^{50} +(7.31666 + 9.83698i) q^{52} -10.0660i q^{53} +2.72320 q^{55} +(-3.74261 - 2.62427i) q^{56} +(1.92368 - 0.636968i) q^{58} +14.5124i q^{59} -9.00922i q^{61} +(4.07781 + 12.3152i) q^{62} +(2.72627 + 7.52113i) q^{64} -6.12984 q^{65} -6.55261i q^{67} +(-6.92653 + 5.15189i) q^{68} +(2.16965 - 0.718415i) q^{70} -3.13354 q^{71} -11.0660 q^{73} +(12.4364 - 4.11793i) q^{74} +(3.43687 + 4.62075i) q^{76} -4.40094i q^{77} -1.53999 q^{79} +(-3.83095 - 1.15057i) q^{80} +(3.01078 + 9.09271i) q^{82} +8.44990i q^{83} -4.31621i q^{85} +(-10.1585 + 3.36368i) q^{86} +(-4.42206 + 6.30652i) q^{88} -7.56667 q^{89} +9.90636i q^{91} +(11.9551 - 8.89212i) q^{92} +(-0.285832 - 0.863227i) q^{94} -2.87938 q^{95} -1.11061 q^{97} +(1.95075 + 5.89136i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4}+O(q^{10}) $ 20 * q + 2 * q^4	$ 20 q + 2 q^{4} - 2 q^{10} - 18 q^{16} + 16 q^{22} - 20 q^{25} + 16 q^{28} + 20 q^{31} - 6 q^{34} - 4 q^{40} + 54 q^{46} + 36 q^{49} + 56 q^{52} - 72 q^{58} - 28 q^{64} - 40 q^{73} + 58 q^{76} - 4 q^{79} - 92 q^{82} - 116 q^{88} + 72 q^{94} + 40 q^{97}+O(q^{100}) $ 20 * q + 2 * q^4 - 2 * q^10 - 18 * q^16 + 16 * q^22 - 20 * q^25 + 16 * q^28 + 20 * q^31 - 6 * q^34 - 4 * q^40 + 54 * q^46 + 36 * q^49 + 56 * q^52 - 72 * q^58 - 28 * q^64 - 40 * q^73 + 58 * q^76 - 4 * q^79 - 92 * q^82 - 116 * q^88 + 72 * q^94 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.444539	−	1.34253i	−0.314337	−	0.949312i
$2$	−0.444539	−	1.34253i	−0.314337	−	0.949312i
$3$		0			0
$3$		0			0
$4$	−1.60477	+	1.19361i	−0.802385	+	0.596807i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−1.61609			−0.610824			−0.305412	−	0.952220i	$-0.598794\pi$
$7$	−1.61609			−0.610824			−0.305412	+	0.952220i	$0.598794\pi$
$8$	2.31584	+	1.62384i	0.818775	+	0.574115i
$9$		0			0
$10$	−1.34253	+	0.444539i	−0.424545	+	0.140576i
$11$			2.72320i			0.821077i	0.911843	+	0.410539i	$0.134659\pi$
$11$			2.72320i			0.821077i	−0.911843	+	0.410539i	$0.865341\pi$
$12$		0			0
$13$		−	6.12984i		−	1.70011i	−0.526693	−	0.850055i	$-0.676568\pi$
$13$		−	6.12984i		−	1.70011i	0.526693	−	0.850055i	$-0.323432\pi$
$14$	0.718415	+	2.16965i	0.192004	+	0.579863i
$15$		0			0
$16$	1.15057	−	3.83095i	0.287643	−	0.957738i
$17$	4.31621			1.04684			0.523418	−	0.852076i	$-0.324657\pi$
$17$	4.31621			1.04684			0.523418	+	0.852076i	$0.324657\pi$
$18$		0			0
$19$		−	2.87938i		−	0.660576i	−0.943880	−	0.330288i	$-0.892854\pi$
$19$		−	2.87938i		−	0.660576i	0.943880	−	0.330288i	$-0.107146\pi$
$20$	1.19361	+	1.60477i	0.266900	+	0.358837i
$21$		0			0
$22$	3.65598	−	1.21057i	0.779458	−	0.258095i
$23$	−7.44975			−1.55338			−0.776690	−	0.629883i	$-0.783103\pi$
$23$	−7.44975			−1.55338			−0.776690	+	0.629883i	$0.783103\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−8.22949	+	2.72495i	−1.61393	+	0.534407i
$27$		0			0
$28$	2.59345	−	1.92899i	0.490116	−	0.364544i
$29$			1.43287i			0.266078i	0.991111	+	0.133039i	$0.0424736\pi$
$29$			1.43287i			0.266078i	−0.991111	+	0.133039i	$0.957526\pi$
$30$		0			0
$31$	−9.17311			−1.64754			−0.823769	−	0.566925i	$-0.808133\pi$
$31$	−9.17311			−1.64754			−0.823769	+	0.566925i	$0.808133\pi$
$32$	−5.65464	+	0.158328i	−0.999608	+	0.0279887i
$33$		0			0
$34$	−1.91873	−	5.79464i	−0.329059	−	0.993773i
$35$			1.61609i			0.273169i
$36$		0			0
$37$			9.26338i			1.52289i	0.648230	+	0.761445i	$0.275510\pi$
$37$			9.26338i			1.52289i	−0.648230	+	0.761445i	$0.724490\pi$
$38$	−3.86566	+	1.28000i	−0.627092	+	0.207643i
$39$		0			0
$40$	1.62384	−	2.31584i	0.256752	−	0.366167i
$41$	−6.77282			−1.05774			−0.528869	−	0.848704i	$-0.677384\pi$
$41$	−6.77282			−1.05774			−0.528869	+	0.848704i	$0.677384\pi$
$42$		0			0
$43$		−	7.56667i		−	1.15391i	−0.816777	−	0.576953i	$-0.804242\pi$
$43$		−	7.56667i		−	1.15391i	0.816777	−	0.576953i	$-0.195758\pi$
$44$	−3.25045	−	4.37012i	−0.490024	−	0.658820i
$45$		0			0
$46$	3.31171	+	10.0015i	0.488284	+	1.47464i
$47$	0.642985			0.0937891			0.0468945	−	0.998900i	$-0.485068\pi$
$47$	0.642985			0.0937891			0.0468945	+	0.998900i	$0.485068\pi$
$48$		0			0
$49$	−4.38826			−0.626894
$50$	0.444539	+	1.34253i	0.0628673	+	0.189862i
$51$		0			0
$52$	7.31666	+	9.83698i	1.01464	+	1.36414i
$53$		−	10.0660i		−	1.38267i	−0.722534	−	0.691335i	$-0.757023\pi$
$53$		−	10.0660i		−	1.38267i	0.722534	−	0.691335i	$-0.242977\pi$
$54$		0			0
$55$	2.72320			0.367197
$56$	−3.74261	−	2.62427i	−0.500127	−	0.350683i
$57$		0			0
$58$	1.92368	−	0.636968i	0.252591	−	0.0836380i
$59$			14.5124i			1.88935i	0.328002	+	0.944677i	$0.393625\pi$
$59$			14.5124i			1.88935i	−0.328002	+	0.944677i	$0.606375\pi$
$60$		0			0
$61$		−	9.00922i		−	1.15351i	−0.816916	−	0.576756i	$-0.804318\pi$
$61$		−	9.00922i		−	1.15351i	0.816916	−	0.576756i	$-0.195682\pi$
$62$	4.07781	+	12.3152i	0.517882	+	1.56403i
$63$		0			0
$64$	2.72627	+	7.52113i	0.340783	+	0.940142i
$65$	−6.12984			−0.760313
$66$		0			0
$67$		−	6.55261i		−	0.800529i	−0.916400	−	0.400264i	$-0.868918\pi$
$67$		−	6.55261i		−	0.800529i	0.916400	−	0.400264i	$-0.131082\pi$
$68$	−6.92653	+	5.15189i	−0.839965	+	0.624758i
$69$		0			0
$70$	2.16965	−	0.718415i	0.259322	−	0.0858670i
$71$	−3.13354			−0.371883			−0.185941	−	0.982561i	$-0.559533\pi$
$71$	−3.13354			−0.371883			−0.185941	+	0.982561i	$0.559533\pi$
$72$		0			0
$73$	−11.0660			−1.29518			−0.647588	−	0.761990i	$-0.724222\pi$
$73$	−11.0660			−1.29518			−0.647588	+	0.761990i	$0.724222\pi$
$74$	12.4364	−	4.11793i	1.44570	−	0.478700i
$75$		0			0
$76$	3.43687	+	4.62075i	0.394236	+	0.530036i
$77$		−	4.40094i		−	0.501534i
$78$		0			0
$79$	−1.53999			−0.173262			−0.0866312	−	0.996240i	$-0.527610\pi$
$79$	−1.53999			−0.173262			−0.0866312	+	0.996240i	$0.527610\pi$
$80$	−3.83095	−	1.15057i	−0.428313	−	0.128638i
$81$		0			0
$82$	3.01078	+	9.09271i	0.332485	+	1.00412i
$83$			8.44990i			0.927497i	0.885967	+	0.463749i	$0.153496\pi$
$83$			8.44990i			0.927497i	−0.885967	+	0.463749i	$0.846504\pi$
$84$		0			0
$85$		−	4.31621i		−	0.468159i
$86$	−10.1585	+	3.36368i	−1.09542	+	0.362715i
$87$		0			0
$88$	−4.42206	+	6.30652i	−0.471393	+	0.672277i
$89$	−7.56667			−0.802065			−0.401033	−	0.916064i	$-0.631349\pi$
$89$	−7.56667			−0.802065			−0.401033	+	0.916064i	$0.631349\pi$
$90$		0			0
$91$			9.90636i			1.03847i
$92$	11.9551	−	8.89212i	1.24641	−	0.927068i
$93$		0			0
$94$	−0.285832	−	0.863227i	−0.0294813	−	0.0890351i
$95$	−2.87938			−0.295418
$96$		0			0
$97$	−1.11061			−0.112765			−0.0563827	−	0.998409i	$-0.517957\pi$
$97$	−1.11061			−0.112765			−0.0563827	+	0.998409i	$0.517957\pi$
$98$	1.95075	+	5.89136i	0.197056	+	0.595118i
$99$		0			0
$100$	1.60477	−	1.19361i	0.160477	−	0.119361i
$101$			2.28114i			0.226982i	0.993539	+	0.113491i	$0.0362033\pi$
$101$			2.28114i			0.226982i	−0.993539	+	0.113491i	$0.963797\pi$
$102$		0			0
$103$	−11.7276			−1.15555			−0.577775	−	0.816196i	$-0.696079\pi$
$103$	−11.7276			−1.15555			−0.577775	+	0.816196i	$0.696079\pi$
$104$	9.95389	−	14.1957i	0.976060	−	1.39201i
$105$		0			0
$106$	−13.5139	+	4.47473i	−1.31259	+	0.434624i
$107$			0.0581529i			0.00562185i	0.999996	+	0.00281093i	$0.000894747\pi$
$107$			0.0581529i			0.00562185i	−0.999996	+	0.00281093i	$0.999105\pi$
$108$		0			0
$109$		−	11.2399i		−	1.07659i	−0.842758	−	0.538293i	$-0.819069\pi$
$109$		−	11.2399i		−	1.07659i	0.842758	−	0.538293i	$-0.180931\pi$
$110$	−1.21057	−	3.65598i	−0.115423	−	0.348584i
$111$		0			0
$112$	−1.85943	+	6.19116i	−0.175700	+	0.585009i
$113$	10.7519			1.01145			0.505727	−	0.862693i	$-0.331224\pi$
$113$	10.7519			1.01145			0.505727	+	0.862693i	$0.331224\pi$
$114$		0			0
$115$			7.44975i			0.694693i
$116$	−1.71030	−	2.29943i	−0.158797	−	0.213497i
$117$		0			0
$118$	19.4833	−	6.45133i	1.79359	−	0.593893i
$119$	−6.97538			−0.639432
$120$		0			0
$121$	3.58416			0.325832
$122$	−12.0951	+	4.00495i	−1.09504	+	0.362591i
$123$		0			0
$124$	14.7207	−	10.9491i	1.32196	−	0.983262i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	9.72755			0.863180			0.431590	−	0.902070i	$-0.357953\pi$
$127$	9.72755			0.863180			0.431590	+	0.902070i	$0.357953\pi$
$128$	8.88541	−	7.00353i	0.785367	−	0.619031i
$129$		0			0
$130$	2.72495	+	8.22949i	0.238994	+	0.721774i
$131$			0.244862i			0.0213937i	0.999943	+	0.0106969i	$0.00340498\pi$
$131$			0.244862i			0.0213937i	−0.999943	+	0.0106969i	$0.996595\pi$
$132$		0			0
$133$			4.65334i			0.403496i
$134$	−8.79707	+	2.91289i	−0.759951	+	0.251635i
$135$		0			0
$136$	9.99567	+	7.00885i	0.857122	+	0.601004i
$137$	9.14646			0.781435			0.390717	−	0.920511i	$-0.372227\pi$
$137$	9.14646			0.781435			0.390717	+	0.920511i	$0.372227\pi$
$138$		0			0
$139$		−	7.18356i		−	0.609302i	−0.952464	−	0.304651i	$-0.901460\pi$
$139$		−	7.18356i		−	0.609302i	0.952464	−	0.304651i	$-0.0985398\pi$
$140$	−1.92899	−	2.59345i	−0.163029	−	0.219187i
$141$		0			0
$142$	1.39298	+	4.20687i	0.116896	+	0.353033i
$143$	16.6928			1.39592
$144$		0			0
$145$	1.43287			0.118994
$146$	4.91927	+	14.8564i	0.407121	+	1.22953i
$147$		0			0
$148$	−11.0569	−	14.8656i	−0.908871	−	1.22194i
$149$		−	4.56713i		−	0.374154i	−0.982345	−	0.187077i	$-0.940099\pi$
$149$		−	4.56713i		−	0.374154i	0.982345	−	0.187077i	$-0.0599013\pi$
$150$		0			0
$151$	−5.57147			−0.453400			−0.226700	−	0.973965i	$-0.572794\pi$
$151$	−5.57147			−0.453400			−0.226700	+	0.973965i	$0.572794\pi$
$152$	4.67567	−	6.66820i	0.379247	−	0.540863i
$153$		0			0
$154$	−5.90839	+	1.95639i	−0.476112	+	0.157650i
$155$			9.17311i			0.736802i
$156$		0			0
$157$			8.76967i			0.699896i	0.936769	+	0.349948i	$0.113801\pi$
$157$			8.76967i			0.699896i	−0.936769	+	0.349948i	$0.886199\pi$
$158$	0.684586	+	2.06748i	0.0544627	+	0.164480i
$159$		0			0
$160$	0.158328	+	5.65464i	0.0125169	+	0.447038i
$161$	12.0395			0.948842
$162$		0			0
$163$			0.560015i			0.0438638i	0.999759	+	0.0219319i	$0.00698169\pi$
$163$			0.560015i			0.0438638i	−0.999759	+	0.0219319i	$0.993018\pi$
$164$	10.8688	−	8.08413i	0.848712	−	0.631265i
$165$		0			0
$166$	11.3442	−	3.75631i	0.880484	−	0.291546i
$167$	8.32657			0.644329			0.322165	−	0.946684i	$-0.395590\pi$
$167$	8.32657			0.644329			0.322165	+	0.946684i	$0.395590\pi$
$168$		0			0
$169$	−24.5749			−1.89038
$170$	−5.79464	+	1.91873i	−0.444429	+	0.147159i
$171$		0			0
$172$	9.03167	+	12.1428i	0.688659	+	0.925877i
$173$		−	12.4053i		−	0.943156i	−0.881824	−	0.471578i	$-0.843684\pi$
$173$		−	12.4053i		−	0.943156i	0.881824	−	0.471578i	$-0.156316\pi$
$174$		0			0
$175$	1.61609			0.122165
$176$	10.4325	+	3.13325i	0.786376	+	0.236177i
$177$		0			0
$178$	3.36368	+	10.1585i	0.252118	+	0.761410i
$179$		−	4.67859i		−	0.349694i	−0.984596	−	0.174847i	$-0.944057\pi$
$179$		−	4.67859i		−	0.349694i	0.984596	−	0.174847i	$-0.0559431\pi$
$180$		0			0
$181$			7.44975i			0.553736i	0.960908	+	0.276868i	$0.0892964\pi$
$181$			7.44975i			0.553736i	−0.960908	+	0.276868i	$0.910704\pi$
$182$	13.2996	−	4.40376i	0.985831	−	0.326429i
$183$		0			0
$184$	−17.2525	−	12.0972i	−1.27187	−	0.891819i
$185$	9.26338			0.681057
$186$		0			0
$187$			11.7539i			0.859532i
$188$	−1.03184	+	0.767476i	−0.0752549	+	0.0559739i
$189$		0			0
$190$	1.28000	+	3.86566i	0.0928608	+	0.280444i
$191$	−23.6546			−1.71158			−0.855792	−	0.517320i	$-0.826930\pi$
$191$	−23.6546			−1.71158			−0.855792	+	0.517320i	$0.826930\pi$
$192$		0			0
$193$	6.50897			0.468526			0.234263	−	0.972173i	$-0.424732\pi$
$193$	6.50897			0.468526			0.234263	+	0.972173i	$0.424732\pi$
$194$	0.493710	+	1.49103i	0.0354463	+	0.107049i
$195$		0			0
$196$	7.04214	−	5.23788i	0.503010	−	0.374134i
$197$		−	24.1910i		−	1.72354i	−0.507302	−	0.861768i	$-0.669357\pi$
$197$		−	24.1910i		−	1.72354i	0.507302	−	0.861768i	$-0.330643\pi$
$198$		0			0
$199$	−10.6239			−0.753110			−0.376555	−	0.926394i	$-0.622891\pi$
$199$	−10.6239			−0.753110			−0.376555	+	0.926394i	$0.622891\pi$
$200$	−2.31584	−	1.62384i	−0.163755	−	0.114823i
$201$		0			0
$202$	3.06250	−	1.01406i	0.215477	−	0.0713487i
$203$		−	2.31565i		−	0.162527i
$204$		0			0
$205$			6.77282i			0.473034i
$206$	5.21335	+	15.7446i	0.363232	+	1.09698i
$207$		0			0
$208$	−23.4831	−	7.05283i	−1.62826	−	0.489026i
$209$	7.84115			0.542384
$210$		0			0
$211$		−	22.7720i		−	1.56769i	−0.620956	−	0.783846i	$-0.713255\pi$
$211$		−	22.7720i		−	1.56769i	0.620956	−	0.783846i	$-0.286745\pi$
$212$	12.0149	+	16.1536i	0.825187	+	1.10943i
$213$		0			0
$214$	0.0780720	−	0.0258512i	0.00533689	−	0.00176715i
$215$	−7.56667			−0.516042
$216$		0			0
$217$	14.8246			1.00636
$218$	−15.0899	+	4.99657i	−1.02202	+	0.338411i
$219$		0			0
$220$	−4.37012	+	3.25045i	−0.294633	+	0.219146i
$221$		−	26.4577i		−	1.77974i
$222$		0			0
$223$	23.6637			1.58464			0.792319	−	0.610107i	$-0.208874\pi$
$223$	23.6637			1.58464			0.792319	+	0.610107i	$0.208874\pi$
$224$	9.13840	−	0.255872i	0.610585	−	0.0170962i
$225$		0			0
$226$	−4.77964	−	14.4348i	−0.317937	−	0.960185i
$227$			9.52600i			0.632263i	0.948715	+	0.316132i	$0.102384\pi$
$227$			9.52600i			0.632263i	−0.948715	+	0.316132i	$0.897616\pi$
$228$		0			0
$229$		−	6.60421i		−	0.436418i	−0.975902	−	0.218209i	$-0.929979\pi$
$229$		−	6.60421i		−	0.436418i	0.975902	−	0.218209i	$-0.0700215\pi$
$230$	10.0015	−	3.31171i	0.659480	−	0.218367i
$231$		0			0
$232$	−2.32676	+	3.31831i	−0.152759	+	0.217858i
$233$	25.3649			1.66171			0.830855	−	0.556489i	$-0.187852\pi$
$233$	25.3649			1.66171			0.830855	+	0.556489i	$0.187852\pi$
$234$		0			0
$235$		−	0.642985i		−	0.0419437i
$236$	−17.3222	−	23.2891i	−1.12758	−	1.51599i
$237$		0			0
$238$	3.10083	+	9.36466i	0.200997	+	0.607021i
$239$	−7.34645			−0.475203			−0.237601	−	0.971363i	$-0.576361\pi$
$239$	−7.34645			−0.475203			−0.237601	+	0.971363i	$0.576361\pi$
$240$		0			0
$241$	7.92390			0.510423			0.255212	−	0.966885i	$-0.417855\pi$
$241$	7.92390			0.510423			0.255212	+	0.966885i	$0.417855\pi$
$242$	−1.59330	−	4.81183i	−0.102421	−	0.309316i
$243$		0			0
$244$	10.7535	+	14.4577i	0.688424	+	0.925561i
$245$			4.38826i			0.280355i
$246$		0			0
$247$	−17.6501			−1.12305
$248$	−21.2435	−	14.8957i	−1.34896	−	0.945877i
$249$		0			0
$250$	1.34253	−	0.444539i	0.0849090	−	0.0281151i
$251$		−	2.86575i		−	0.180884i	−0.995902	−	0.0904422i	$-0.971172\pi$
$251$		−	2.86575i		−	0.180884i	0.995902	−	0.0904422i	$-0.0288280\pi$
$252$		0			0
$253$		−	20.2872i		−	1.27545i
$254$	−4.32428	−	13.0595i	−0.271329	−	0.819427i
$255$		0			0
$256$	−13.3524	−	8.81558i	−0.834522	−	0.550974i
$257$	−8.46381			−0.527958			−0.263979	−	0.964528i	$-0.585035\pi$
$257$	−8.46381			−0.527958			−0.263979	+	0.964528i	$0.585035\pi$
$258$		0			0
$259$		−	14.9704i		−	0.930218i
$260$	9.83698	−	7.31666i	0.610064	−	0.453760i
$261$		0			0
$262$	0.328735	−	0.108851i	0.0203093	−	0.00672483i
$263$	16.4590			1.01490			0.507452	−	0.861680i	$-0.330588\pi$
$263$	16.4590			1.01490			0.507452	+	0.861680i	$0.330588\pi$
$264$		0			0
$265$	−10.0660			−0.618349
$266$	6.24724	−	2.06859i	0.383043	−	0.126833i
$267$		0			0
$268$	7.82128	+	10.5154i	0.477761	+	0.642332i
$269$			12.4644i			0.759965i	0.924994	+	0.379983i	$0.124070\pi$
$269$			12.4644i			0.759965i	−0.924994	+	0.379983i	$0.875930\pi$
$270$		0			0
$271$	−2.33495			−0.141838			−0.0709190	−	0.997482i	$-0.522593\pi$
$271$	−2.33495			−0.141838			−0.0709190	+	0.997482i	$0.522593\pi$
$272$	4.96612	−	16.5352i	0.301115	−	1.00259i
$273$		0			0
$274$	−4.06596	−	12.2794i	−0.245634	−	0.741825i
$275$		−	2.72320i		−	0.164215i
$276$		0			0
$277$		−	20.3984i		−	1.22562i	−0.790230	−	0.612810i	$-0.790039\pi$
$277$		−	20.3984i		−	1.22562i	0.790230	−	0.612810i	$-0.209961\pi$
$278$	−9.64414	+	3.19337i	−0.578417	+	0.191526i
$279$		0			0
$280$	−2.62427	+	3.74261i	−0.156830	+	0.223664i
$281$	−11.1939			−0.667773			−0.333886	−	0.942613i	$-0.608360\pi$
$281$	−11.1939			−0.667773			−0.333886	+	0.942613i	$0.608360\pi$
$282$		0			0
$283$		−	0.780227i		−	0.0463797i	−0.999731	−	0.0231898i	$-0.992618\pi$
$283$		−	0.780227i		−	0.0463797i	0.999731	−	0.0231898i	$-0.00738222\pi$
$284$	5.02861	−	3.74023i	0.298393	−	0.221942i
$285$		0			0
$286$	−7.42060	−	22.4106i	−0.438789	−	1.32517i
$287$	10.9455			0.646091
$288$		0			0
$289$	1.62969			0.0958641
$290$	−0.636968	−	1.92368i	−0.0374041	−	0.112962i
$291$		0			0
$292$	17.7584	−	13.2085i	1.03923	−	0.772970i
$293$		−	22.1910i		−	1.29641i	−0.761465	−	0.648206i	$-0.775520\pi$
$293$		−	22.1910i		−	1.29641i	0.761465	−	0.648206i	$-0.224480\pi$
$294$		0			0
$295$	14.5124			0.844945
$296$	−15.0423	+	21.4525i	−0.874314	+	1.24690i
$297$		0			0
$298$	−6.13150	+	2.03027i	−0.355188	+	0.117610i
$299$			45.6658i			2.64092i
$300$		0			0
$301$			12.2284i			0.704834i
$302$	2.47674	+	7.47986i	0.142520	+	0.430418i
$303$		0			0
$304$	−11.0308	−	3.31294i	−0.632658	−	0.190010i
$305$	−9.00922			−0.515866
$306$		0			0
$307$			30.2781i			1.72806i	0.503438	+	0.864032i	$0.332068\pi$
$307$			30.2781i			1.72806i	−0.503438	+	0.864032i	$0.667932\pi$
$308$	5.25302	+	7.06250i	0.299319	+	0.402423i
$309$		0			0
$310$	12.3152	−	4.07781i	0.699455	−	0.231604i
$311$	33.4117			1.89460			0.947301	−	0.320346i	$-0.103799\pi$
$311$	33.4117			1.89460			0.947301	+	0.320346i	$0.103799\pi$
$312$		0			0
$313$	−31.6947			−1.79149			−0.895745	−	0.444568i	$-0.853357\pi$
$313$	−31.6947			−1.79149			−0.895745	+	0.444568i	$0.853357\pi$
$314$	11.7735	−	3.89846i	0.664419	−	0.220003i
$315$		0			0
$316$	2.47133	−	1.83815i	0.139023	−	0.103404i
$317$			2.49452i			0.140106i	0.997543	+	0.0700531i	$0.0223169\pi$
$317$			2.49452i			0.140106i	−0.997543	+	0.0700531i	$0.977683\pi$
$318$		0			0
$319$	−3.90201			−0.218471
$320$	7.52113	−	2.72627i	0.420444	−	0.152403i
$321$		0			0
$322$	−5.35201	−	16.1633i	−0.298256	−	0.900747i
$323$		−	12.4280i		−	0.691514i
$324$		0			0
$325$			6.12984i			0.340022i
$326$	0.751836	−	0.248948i	0.0416404	−	0.0137880i
$327$		0			0
$328$	−15.6848	−	10.9980i	−0.866048	−	0.607263i
$329$	−1.03912			−0.0572886
$330$		0			0
$331$		−	20.7292i		−	1.13938i	−0.821860	−	0.569690i	$-0.807063\pi$
$331$		−	20.7292i		−	1.13938i	0.821860	−	0.569690i	$-0.192937\pi$
$332$	−10.0859	−	13.5602i	−0.553537	−	0.744210i
$333$		0			0
$334$	−3.70148	−	11.1787i	−0.202536	−	0.611669i
$335$	−6.55261			−0.358007
$336$		0			0
$337$	33.5285			1.82641			0.913207	−	0.407495i	$-0.133598\pi$
$337$	33.5285			1.82641			0.913207	+	0.407495i	$0.133598\pi$
$338$	10.9245	+	32.9925i	0.594215	+	1.79456i
$339$		0			0
$340$	5.15189	+	6.92653i	0.279400	+	0.375644i
$341$		−	24.9803i		−	1.35276i
$342$		0			0
$343$	18.4044			0.993746
$344$	12.2871	−	17.5232i	0.662475	−	0.944789i
$345$		0			0
$346$	−16.6545	+	5.51463i	−0.895349	+	0.296469i
$347$			7.14163i			0.383383i	0.981455	+	0.191691i	$0.0613972\pi$
$347$			7.14163i			0.383383i	−0.981455	+	0.191691i	$0.938603\pi$
$348$		0			0
$349$		−	11.6490i		−	0.623559i	−0.950154	−	0.311780i	$-0.899075\pi$
$349$		−	11.6490i		−	0.623559i	0.950154	−	0.311780i	$-0.100925\pi$
$350$	−0.718415	−	2.16965i	−0.0384009	−	0.115973i
$351$		0			0
$352$	−0.431159	−	15.3987i	−0.0229809	−	0.820755i
$353$	−32.9179			−1.75205			−0.876023	−	0.482270i	$-0.839812\pi$
$353$	−32.9179			−1.75205			−0.876023	+	0.482270i	$0.839812\pi$
$354$		0			0
$355$			3.13354i			0.166311i
$356$	12.1428	−	9.03167i	0.643565	−	0.478678i
$357$		0			0
$358$	−6.28114	+	2.07981i	−0.331969	+	0.109922i
$359$	−12.3823			−0.653513			−0.326757	−	0.945108i	$-0.605956\pi$
$359$	−12.3823			−0.653513			−0.326757	+	0.945108i	$0.605956\pi$
$360$		0			0
$361$	10.7092			0.563640
$362$	10.0015	−	3.31171i	0.525668	−	0.174059i
$363$		0			0
$364$	−11.8244	−	15.8974i	−0.619765	−	0.833252i
$365$			11.0660i			0.579221i
$366$		0			0
$367$	6.11146			0.319016			0.159508	−	0.987197i	$-0.449009\pi$
$367$	6.11146			0.319016			0.159508	+	0.987197i	$0.449009\pi$
$368$	−8.57149	+	28.5396i	−0.446820	+	1.48773i
$369$		0			0
$370$	−4.11793	−	12.4364i	−0.214081	−	0.646535i
$371$			16.2675i			0.844569i
$372$		0			0
$373$			11.6287i			0.602112i	0.953606	+	0.301056i	$0.0973392\pi$
$373$			11.6287i			0.602112i	−0.953606	+	0.301056i	$0.902661\pi$
$374$	15.7800	−	5.22508i	0.815964	−	0.270183i
$375$		0			0
$376$	1.48905	+	1.04411i	0.0767921	+	0.0538457i
$377$	8.78328			0.452362
$378$		0			0
$379$		−	4.31621i		−	0.221709i	−0.993837	−	0.110854i	$-0.964641\pi$
$379$		−	4.31621i		−	0.221709i	0.993837	−	0.110854i	$-0.0353587\pi$
$380$	4.62075	−	3.43687i	0.237039	−	0.176308i
$381$		0			0
$382$	10.5154	+	31.7570i	0.538014	+	1.62483i
$383$	−9.51753			−0.486323			−0.243162	−	0.969986i	$-0.578185\pi$
$383$	−9.51753			−0.486323			−0.243162	+	0.969986i	$0.578185\pi$
$384$		0			0
$385$	−4.40094			−0.224293
$386$	−2.89349	−	8.73849i	−0.147275	−	0.444777i
$387$		0			0
$388$	1.78227	−	1.32564i	0.0904813	−	0.0672991i
$389$		−	8.50022i		−	0.430978i	−0.976506	−	0.215489i	$-0.930865\pi$
$389$		−	8.50022i		−	0.430978i	0.976506	−	0.215489i	$-0.0691346\pi$
$390$		0			0
$391$	−32.1547			−1.62613
$392$	−10.1625	−	7.12584i	−0.513285	−	0.359909i
$393$		0			0
$394$	−32.4771	+	10.7538i	−1.63617	+	0.541771i
$395$			1.53999i			0.0774853i
$396$		0			0
$397$			30.8638i			1.54901i	0.632569	+	0.774504i	$0.282001\pi$
$397$			30.8638i			1.54901i	−0.632569	+	0.774504i	$0.717999\pi$
$398$	4.72275	+	14.2629i	0.236730	+	0.714936i
$399$		0			0
$400$	−1.15057	+	3.83095i	−0.0575287	+	0.191548i
$401$	38.6250			1.92884			0.964420	−	0.264373i	$-0.0851651\pi$
$401$	38.6250			1.92884			0.964420	+	0.264373i	$0.0851651\pi$
$402$		0			0
$403$			56.2297i			2.80100i
$404$	−2.72280	−	3.66071i	−0.135464	−	0.182127i
$405$		0			0
$406$	−3.10883	+	1.02940i	−0.154289	+	0.0510881i
$407$	−25.2261			−1.25041
$408$		0			0
$409$	36.2149			1.79071			0.895357	−	0.445349i	$-0.146921\pi$
$409$	36.2149			1.79071			0.895357	+	0.445349i	$0.146921\pi$
$410$	9.09271	−	3.01078i	0.449057	−	0.148692i
$411$		0			0
$412$	18.8200	−	13.9982i	0.927196	−	0.689640i
$413$		−	23.4533i		−	1.15406i
$414$		0			0
$415$	8.44990			0.414789
$416$	0.970524	+	34.6620i	0.0475839	+	1.69944i
$417$		0			0
$418$	−3.48570	−	10.5270i	−0.170491	−	0.514891i
$419$			2.26754i			0.110777i	0.998465	+	0.0553883i	$0.0176397\pi$
$419$			2.26754i			0.110777i	−0.998465	+	0.0553883i	$0.982360\pi$
$420$		0			0
$421$			9.85477i			0.480292i	0.970737	+	0.240146i	$0.0771953\pi$
$421$			9.85477i			0.480292i	−0.970737	+	0.240146i	$0.922805\pi$
$422$	−30.5721	+	10.1231i	−1.48823	+	0.492783i
$423$		0			0
$424$	16.3456	−	23.3113i	0.793812	−	1.13210i
$425$	−4.31621			−0.209367
$426$		0			0
$427$			14.5597i			0.704593i
$428$	−0.0694121	−	0.0933221i	−0.00335516	−	0.00451089i
$429$		0			0
$430$	3.36368	+	10.1585i	0.162211	+	0.489885i
$431$	14.9961			0.722336			0.361168	−	0.932501i	$-0.382378\pi$
$431$	14.9961			0.722336			0.361168	+	0.932501i	$0.382378\pi$
$432$		0			0
$433$	−30.4572			−1.46368			−0.731840	−	0.681476i	$-0.761338\pi$
$433$	−30.4572			−1.46368			−0.731840	+	0.681476i	$0.761338\pi$
$434$	−6.59010	−	19.9024i	−0.316335	−	0.955346i
$435$		0			0
$436$	13.4161	+	18.0374i	0.642514	+	0.863837i
$437$			21.4507i			1.02613i
$438$		0			0
$439$	27.3598			1.30581			0.652905	−	0.757440i	$-0.273550\pi$
$439$	27.3598			1.30581			0.652905	+	0.757440i	$0.273550\pi$
$440$	6.30652	+	4.42206i	0.300651	+	0.210813i
$441$		0			0
$442$	−35.5202	+	11.7615i	−1.68952	+	0.559436i
$443$		−	36.7961i		−	1.74824i	−0.485713	−	0.874118i	$-0.661440\pi$
$443$		−	36.7961i		−	1.74824i	0.485713	−	0.874118i	$-0.338560\pi$
$444$		0			0
$445$			7.56667i			0.358694i
$446$	−10.5194	−	31.7692i	−0.498110	−	1.50431i
$447$		0			0
$448$	−4.40589	−	12.1548i	−0.208159	−	0.574261i
$449$	−2.65345			−0.125224			−0.0626119	−	0.998038i	$-0.519943\pi$
$449$	−2.65345			−0.125224			−0.0626119	+	0.998038i	$0.519943\pi$
$450$		0			0
$451$		−	18.4438i		−	0.868484i
$452$	−17.2543	+	12.8336i	−0.811576	+	0.603643i
$453$		0			0
$454$	12.7889	−	4.23468i	0.600215	−	0.198743i
$455$	9.90636			0.464417
$456$		0			0
$457$	−4.79146			−0.224135			−0.112068	−	0.993701i	$-0.535747\pi$
$457$	−4.79146			−0.224135			−0.112068	+	0.993701i	$0.535747\pi$
$458$	−8.86634	+	2.93583i	−0.414297	+	0.137182i
$459$		0			0
$460$	−8.89212	−	11.9551i	−0.414597	−	0.557411i
$461$			25.8236i			1.20273i	0.798976	+	0.601363i	$0.205376\pi$
$461$			25.8236i			1.20273i	−0.798976	+	0.601363i	$0.794624\pi$
$462$		0			0
$463$	23.6693			1.10001			0.550004	−	0.835162i	$-0.314626\pi$
$463$	23.6693			1.10001			0.550004	+	0.835162i	$0.314626\pi$
$464$	5.48927	+	1.64863i	0.254833	+	0.0765356i
$465$		0			0
$466$	−11.2757	−	34.0531i	−0.522336	−	1.57748i
$467$			21.3751i			0.989123i	0.869143	+	0.494561i	$0.164671\pi$
$467$			21.3751i			0.989123i	−0.869143	+	0.494561i	$0.835329\pi$
$468$		0			0
$469$			10.5896i			0.488982i
$470$	−0.863227	+	0.285832i	−0.0398177	+	0.0131845i
$471$		0			0
$472$	−23.5659	+	33.6085i	−1.08471	+	1.54695i
$473$	20.6056			0.947446
$474$		0			0
$475$			2.87938i			0.132115i
$476$	11.1939	−	8.32591i	0.513071	−	0.381618i
$477$		0			0
$478$	3.26579	+	9.86283i	0.149374	+	0.451115i
$479$	−22.2314			−1.01578			−0.507888	−	0.861423i	$-0.669574\pi$
$479$	−22.2314			−1.01578			−0.507888	+	0.861423i	$0.669574\pi$
$480$		0			0
$481$	56.7830			2.58908
$482$	−3.52248	−	10.6381i	−0.160445	−	0.484551i
$483$		0			0
$484$	−5.75175	+	4.27810i	−0.261443	+	0.194459i
$485$			1.11061i			0.0504302i
$486$		0			0
$487$	22.0602			0.999645			0.499822	−	0.866128i	$-0.333399\pi$
$487$	22.0602			0.999645			0.499822	+	0.866128i	$0.333399\pi$
$488$	14.6296	−	20.8639i	0.662249	−	0.944467i
$489$		0			0
$490$	5.89136	−	1.95075i	0.266145	−	0.0881260i
$491$		−	6.68202i		−	0.301555i	−0.988568	−	0.150778i	$-0.951822\pi$
$491$		−	6.68202i		−	0.301555i	0.988568	−	0.150778i	$-0.0481777\pi$
$492$		0			0
$493$			6.18459i			0.278540i
$494$	7.84618	+	23.6958i	0.353016	+	1.06613i
$495$		0			0
$496$	−10.5543	+	35.1417i	−0.473904	+	1.57791i
$497$	5.06408			0.227155
$498$		0			0
$499$			28.3982i			1.27128i	0.771987	+	0.635639i	$0.219263\pi$
$499$			28.3982i			1.27128i	−0.771987	+	0.635639i	$0.780737\pi$
$500$	−1.19361	−	1.60477i	−0.0533800	−	0.0717675i
$501$		0			0
$502$	−3.84735	+	1.27394i	−0.171716	+	0.0568586i
$503$	−5.08441			−0.226702			−0.113351	−	0.993555i	$-0.536159\pi$
$503$	−5.08441			−0.226702			−0.113351	+	0.993555i	$0.536159\pi$
$504$		0			0
$505$	2.28114			0.101509
$506$	−27.2362	+	9.01845i	−1.21079	+	0.400919i
$507$		0			0
$508$	−15.6105	+	11.6109i	−0.692603	+	0.515152i
$509$			39.8906i			1.76812i	0.467376	+	0.884059i	$0.345200\pi$
$509$			39.8906i			1.76812i	−0.467376	+	0.884059i	$0.654800\pi$
$510$		0			0
$511$	17.8836			0.791125
$512$	−5.89953	+	21.8448i	−0.260725	+	0.965413i
$513$		0			0
$514$	3.76249	+	11.3629i	0.165956	+	0.501196i
$515$			11.7276i			0.516778i
$516$		0			0
$517$			1.75098i			0.0770081i
$518$	−20.0983	+	6.65495i	−0.883067	+	0.292402i
$519$		0			0
$520$	−14.1957	−	9.95389i	−0.622525	−	0.436507i
$521$	−3.35533			−0.147000			−0.0734999	−	0.997295i	$-0.523417\pi$
$521$	−3.35533			−0.147000			−0.0734999	+	0.997295i	$0.523417\pi$
$522$		0			0
$523$		−	26.8194i		−	1.17273i	−0.810047	−	0.586365i	$-0.800559\pi$
$523$		−	26.8194i		−	1.17273i	0.810047	−	0.586365i	$-0.199441\pi$
$524$	−0.292271	−	0.392948i	−0.0127679	−	0.0171660i
$525$		0			0
$526$	−7.31666	−	22.0967i	−0.319021	−	0.963460i
$527$	−39.5931			−1.72470
$528$		0			0
$529$	32.4988			1.41299
$530$	4.47473	+	13.5139i	0.194370	+	0.587006i
$531$		0			0
$532$	−5.55429	−	7.46754i	−0.240809	−	0.323759i
$533$			41.5163i			1.79827i
$534$		0			0
$535$	0.0581529			0.00251417
$536$	10.6404	−	15.1748i	0.459596	−	0.655453i
$537$		0			0
$538$	16.7338	−	5.54089i	0.721444	−	0.238885i
$539$		−	11.9501i		−	0.514728i
$540$		0			0
$541$			22.2177i			0.955215i	0.878573	+	0.477608i	$0.158496\pi$
$541$			22.2177i			0.955215i	−0.878573	+	0.477608i	$0.841504\pi$
$542$	1.03798	+	3.13474i	0.0445849	+	0.134648i
$543$		0			0
$544$	−24.4066	+	0.683377i	−1.04643	+	0.0292995i
$545$	−11.2399			−0.481464
$546$		0			0
$547$		−	25.2996i		−	1.08173i	−0.841109	−	0.540866i	$-0.818097\pi$
$547$		−	25.2996i		−	1.08173i	0.841109	−	0.540866i	$-0.181903\pi$
$548$	−14.6780	+	10.9173i	−0.627012	+	0.466366i
$549$		0			0
$550$	−3.65598	+	1.21057i	−0.155892	+	0.0516189i
$551$	4.12579			0.175765
$552$		0			0
$553$	2.48876			0.105833
$554$	−27.3854	+	9.06788i	−1.16350	+	0.385257i
$555$		0			0
$556$	8.57440	+	11.5280i	0.363635	+	0.488895i
$557$		−	2.15957i		−	0.0915040i	−0.998953	−	0.0457520i	$-0.985432\pi$
$557$		−	2.15957i		−	0.0915040i	0.998953	−	0.0457520i	$-0.0145684\pi$
$558$		0			0
$559$	−46.3824			−1.96177
$560$	6.19116	+	1.85943i	0.261624	+	0.0785752i
$561$		0			0
$562$	4.97613	+	15.0282i	0.209905	+	0.633925i
$563$		−	13.6021i		−	0.573260i	−0.958041	−	0.286630i	$-0.907465\pi$
$563$		−	13.6021i		−	0.573260i	0.958041	−	0.286630i	$-0.0925351\pi$
$564$		0			0
$565$		−	10.7519i		−	0.452336i
$566$	−1.04748	+	0.346841i	−0.0440288	+	0.0145788i
$567$		0			0
$568$	−7.25679	−	5.08838i	−0.304488	−	0.213504i
$569$	−40.7184			−1.70701			−0.853503	−	0.521088i	$-0.825526\pi$
$569$	−40.7184			−1.70701			−0.853503	+	0.521088i	$0.825526\pi$
$570$		0			0
$571$			29.5098i			1.23495i	0.786592	+	0.617474i	$0.211844\pi$
$571$			29.5098i			1.23495i	−0.786592	+	0.617474i	$0.788156\pi$
$572$	−26.7881	+	19.9248i	−1.12007	+	0.833096i
$573$		0			0
$574$	−4.86569	−	14.6946i	−0.203090	−	0.613342i
$575$	7.44975			0.310676
$576$		0			0
$577$	40.3375			1.67927			0.839636	−	0.543150i	$-0.182768\pi$
$577$	40.3375			1.67927			0.839636	+	0.543150i	$0.182768\pi$
$578$	−0.724461	−	2.18791i	−0.0301336	−	0.0910049i
$579$		0			0
$580$	−2.29943	+	1.71030i	−0.0954788	+	0.0710162i
$581$		−	13.6558i		−	0.566538i
$582$		0			0
$583$	27.4118			1.13528
$584$	−25.6271	−	17.9694i	−1.06046	−	0.743581i
$585$		0			0
$586$	−29.7921	+	9.86476i	−1.23070	+	0.407510i
$587$		−	38.2714i		−	1.57963i	−0.613344	−	0.789816i	$-0.710176\pi$
$587$		−	38.2714i		−	1.57963i	0.613344	−	0.789816i	$-0.289824\pi$
$588$		0			0
$589$			26.4129i			1.08832i
$590$	−6.45133	−	19.4833i	−0.265597	−	0.802116i
$591$		0			0
$592$	35.4875	+	10.6582i	1.45853	+	0.438049i
$593$	−19.8779			−0.816289			−0.408144	−	0.912917i	$-0.633824\pi$
$593$	−19.8779			−0.816289			−0.408144	+	0.912917i	$0.633824\pi$
$594$		0			0
$595$			6.97538i			0.285963i
$596$	5.45138	+	7.32919i	0.223297	+	0.300215i
$597$		0			0
$598$	61.3076	−	20.3002i	2.50706	−	0.830138i
$599$	−19.0445			−0.778138			−0.389069	−	0.921209i	$-0.627203\pi$
$599$	−19.0445			−0.778138			−0.389069	+	0.921209i	$0.627203\pi$
$600$		0			0
$601$	−31.2811			−1.27598			−0.637991	−	0.770044i	$-0.720234\pi$
$601$	−31.2811			−1.27598			−0.637991	+	0.770044i	$0.720234\pi$
$602$	16.4170	−	5.43600i	0.669107	−	0.221555i
$603$		0			0
$604$	8.94093	−	6.65018i	0.363801	−	0.270592i
$605$		−	3.58416i		−	0.145717i
$606$		0			0
$607$	−39.7239			−1.61234			−0.806172	−	0.591681i	$-0.798464\pi$
$607$	−39.7239			−1.61234			−0.806172	+	0.591681i	$0.798464\pi$
$608$	0.455887	+	16.2819i	0.0184886	+	0.660317i
$609$		0			0
$610$	4.00495	+	12.0951i	0.162156	+	0.489718i
$611$		−	3.94140i		−	0.159452i
$612$		0			0
$613$		−	43.6464i		−	1.76286i	−0.472314	−	0.881430i	$-0.656581\pi$
$613$		−	43.6464i		−	1.76286i	0.472314	−	0.881430i	$-0.343419\pi$
$614$	40.6493	−	13.4598i	1.64047	−	0.543193i
$615$		0			0
$616$	7.14644	−	10.1919i	0.287938	−	0.410643i
$617$	−46.5967			−1.87591			−0.937956	−	0.346754i	$-0.887284\pi$
$617$	−46.5967			−1.87591			−0.937956	+	0.346754i	$0.887284\pi$
$618$		0			0
$619$			35.2592i			1.41719i	0.705617	+	0.708594i	$0.250670\pi$
$619$			35.2592i			1.41719i	−0.705617	+	0.708594i	$0.749330\pi$
$620$	−10.9491	−	14.7207i	−0.439728	−	0.591199i
$621$		0			0
$622$	−14.8528	−	44.8561i	−0.595542	−	1.79857i
$623$	12.2284			0.489921
$624$		0			0
$625$	1.00000			0.0400000
$626$	14.0895	+	42.5511i	0.563131	+	1.70068i
$627$		0			0
$628$	−10.4676	−	14.0733i	−0.417702	−	0.561586i
$629$			39.9827i			1.59421i
$630$		0			0
$631$	−14.4669			−0.575917			−0.287958	−	0.957643i	$-0.592977\pi$
$631$	−14.4669			−0.575917			−0.287958	+	0.957643i	$0.592977\pi$
$632$	−3.56638	−	2.50070i	−0.141863	−	0.0994726i
$633$		0			0
$634$	3.34897	−	1.10891i	0.133005	−	0.0440405i
$635$		−	9.72755i		−	0.386026i
$636$		0			0
$637$			26.8993i			1.06579i
$638$	1.73460	+	5.23856i	0.0686733	+	0.207397i
$639$		0			0
$640$	−7.00353	−	8.88541i	−0.276839	−	0.351227i
$641$	−1.12003			−0.0442385			−0.0221193	−	0.999755i	$-0.507041\pi$
$641$	−1.12003			−0.0442385			−0.0221193	+	0.999755i	$0.507041\pi$
$642$		0			0
$643$		−	18.4725i		−	0.728484i	−0.931304	−	0.364242i	$-0.881328\pi$
$643$		−	18.4725i		−	0.728484i	0.931304	−	0.364242i	$-0.118672\pi$
$644$	−19.3206	+	14.3705i	−0.761337	+	0.566276i
$645$		0			0
$646$	−16.6850	+	5.52474i	−0.656462	+	0.217368i
$647$	−11.7200			−0.460760			−0.230380	−	0.973101i	$-0.573997\pi$
$647$	−11.7200			−0.460760			−0.230380	+	0.973101i	$0.573997\pi$
$648$		0			0
$649$	−39.5202			−1.55131
$650$	8.22949	−	2.72495i	0.322787	−	0.106881i
$651$		0			0
$652$	−0.668441	−	0.898695i	−0.0261782	−	0.0351956i
$653$			2.45994i			0.0962651i	0.998841	+	0.0481325i	$0.0153270\pi$
$653$			2.45994i			0.0962651i	−0.998841	+	0.0481325i	$0.984673\pi$
$654$		0			0
$655$	0.244862			0.00956757
$656$	−7.79263	+	25.9463i	−0.304251	+	1.01303i
$657$		0			0
$658$	0.461930	+	1.39505i	0.0180079	+	0.0543848i
$659$			24.5071i			0.954663i	0.878723	+	0.477331i	$0.158396\pi$
$659$			24.5071i			0.954663i	−0.878723	+	0.477331i	$0.841604\pi$
$660$		0			0
$661$			9.10947i			0.354317i	0.984182	+	0.177159i	$0.0566906\pi$
$661$			9.10947i			0.354317i	−0.984182	+	0.177159i	$0.943309\pi$
$662$	−27.8296	+	9.21494i	−1.08163	+	0.358149i
$663$		0			0
$664$	−13.7213	+	19.5687i	−0.532490	+	0.759411i
$665$	4.65334			0.180449
$666$		0			0
$667$		−	10.6746i		−	0.413320i
$668$	−13.3622	+	9.93870i	−0.517000	+	0.384540i
$669$		0			0
$670$	2.91289	+	8.79707i	0.112535	+	0.339861i
$671$	24.5340			0.947123
$672$		0			0
$673$	−7.76995			−0.299510			−0.149755	−	0.988723i	$-0.547848\pi$
$673$	−7.76995			−0.299510			−0.149755	+	0.988723i	$0.547848\pi$
$674$	−14.9047	−	45.0130i	−0.574109	−	1.73384i
$675$		0			0
$676$	39.4371	−	29.3329i	1.51681	−	1.12819i
$677$			0.277261i			0.0106560i	0.999986	+	0.00532800i	$0.00169596\pi$
$677$			0.277261i			0.0106560i	−0.999986	+	0.00532800i	$0.998304\pi$
$678$		0			0
$679$	1.79484			0.0688798
$680$	7.00885	−	9.99567i	0.268777	−	0.383317i
$681$		0			0
$682$	−33.5367	+	11.1047i	−1.28419	+	0.425221i
$683$			7.71316i			0.295136i	0.989052	+	0.147568i	$0.0471445\pi$
$683$			7.71316i			0.295136i	−0.989052	+	0.147568i	$0.952855\pi$
$684$		0			0
$685$		−	9.14646i		−	0.349468i
$686$	−8.18149	−	24.7085i	−0.312371	−	0.943375i
$687$		0			0
$688$	−28.9875	−	8.70601i	−1.10514	−	0.331913i
$689$	−61.7029			−2.35069
$690$		0			0
$691$			21.6279i			0.822765i	0.911463	+	0.411383i	$0.134954\pi$
$691$			21.6279i			0.822765i	−0.911463	+	0.411383i	$0.865046\pi$
$692$	14.8071	+	19.9076i	0.562882	+	0.756775i
$693$		0			0
$694$	9.58784	−	3.17473i	0.363950	−	0.120511i
$695$	−7.18356			−0.272488
$696$		0			0
$697$	−29.2329			−1.10728
$698$	−15.6392	+	5.17846i	−0.591952	+	0.196008i
$699$		0			0
$700$	−2.59345	+	1.92899i	−0.0980232	+	0.0729088i
$701$		−	9.60072i		−	0.362614i	−0.983427	−	0.181307i	$-0.941967\pi$
$701$		−	9.60072i		−	0.362614i	0.983427	−	0.181307i	$-0.0580328\pi$
$702$		0			0
$703$	26.6728			1.00598
$704$	−20.4816	+	7.42418i	−0.771929	+	0.279809i
$705$		0			0
$706$	14.6333	+	44.1933i	0.550732	+	1.66324i
$707$		−	3.68653i		−	0.138646i
$708$		0			0
$709$		−	0.547981i		−	0.0205798i	−0.999947	−	0.0102899i	$-0.996725\pi$
$709$		−	0.547981i		−	0.0205798i	0.999947	−	0.0102899i	$-0.00327544\pi$
$710$	4.20687	−	1.39298i	0.157881	−	0.0522776i
$711$		0			0
$712$	−17.5232	−	12.2871i	−0.656710	−	0.460478i
$713$	68.3374			2.55926
$714$		0			0
$715$		−	16.6928i		−	0.624275i
$716$	5.58442	+	7.50806i	0.208700	+	0.280589i
$717$		0			0
$718$	5.50442	+	16.6236i	0.205423	+	0.620388i
$719$	19.8806			0.741422			0.370711	−	0.928748i	$-0.379114\pi$
$719$	19.8806			0.741422			0.370711	+	0.928748i	$0.379114\pi$
$720$		0			0
$721$	18.9528			0.705838
$722$	−4.76064	−	14.3774i	−0.177173	−	0.535070i
$723$		0			0
$724$	−8.89212	−	11.9551i	−0.330473	−	0.444309i
$725$		−	1.43287i		−	0.0532156i
$726$		0			0
$727$	13.1343			0.487122			0.243561	−	0.969886i	$-0.421684\pi$
$727$	13.1343			0.487122			0.243561	+	0.969886i	$0.421684\pi$
$728$	−16.0864	+	22.9416i	−0.596201	+	0.850272i
$729$		0			0
$730$	14.8564	−	4.91927i	0.549861	−	0.182070i
$731$		−	32.6593i		−	1.20795i
$732$		0			0
$733$			3.74989i			0.138505i	0.997599	+	0.0692526i	$0.0220615\pi$
$733$			3.74989i			0.138505i	−0.997599	+	0.0692526i	$0.977939\pi$
$734$	−2.71678	−	8.20482i	−0.100278	−	0.302845i
$735$		0			0
$736$	42.1257	−	1.17950i	1.55277	−	0.0434771i
$737$	17.8441			0.657296
$738$		0			0
$739$		−	29.9149i		−	1.10044i	−0.835020	−	0.550219i	$-0.814544\pi$
$739$		−	29.9149i		−	1.10044i	0.835020	−	0.550219i	$-0.185456\pi$
$740$	−14.8656	+	11.0569i	−0.546470	+	0.406459i
$741$		0			0
$742$	21.8396	−	7.23156i	0.801759	−	0.265479i
$743$	35.4221			1.29951			0.649756	−	0.760143i	$-0.274871\pi$
$743$	35.4221			1.29951			0.649756	+	0.760143i	$0.274871\pi$
$744$		0			0
$745$	−4.56713			−0.167327
$746$	15.6119	−	5.16942i	0.571592	−	0.189266i
$747$		0			0
$748$	−14.0296	−	18.8624i	−0.512975	−	0.689676i
$749$		−	0.0939803i		−	0.00343397i
$750$		0			0
$751$	−13.7262			−0.500878			−0.250439	−	0.968132i	$-0.580575\pi$
$751$	−13.7262			−0.500878			−0.250439	+	0.968132i	$0.580575\pi$
$752$	0.739802	−	2.46325i	0.0269778	−	0.0898253i
$753$		0			0
$754$	−3.90451	−	11.7918i	−0.142194	−	0.429433i
$755$			5.57147i			0.202767i
$756$		0			0
$757$		−	25.9572i		−	0.943429i	−0.881751	−	0.471715i	$-0.843635\pi$
$757$		−	25.9572i		−	0.943429i	0.881751	−	0.471715i	$-0.156365\pi$
$758$	−5.79464	+	1.91873i	−0.210471	+	0.0696912i
$759$		0			0
$760$	−6.66820	−	4.67567i	−0.241881	−	0.169604i
$761$	11.1939			0.405779			0.202890	−	0.979202i	$-0.434967\pi$
$761$	11.1939			0.405779			0.202890	+	0.979202i	$0.434967\pi$
$762$		0			0
$763$			18.1647i			0.657605i
$764$	37.9601	−	28.2344i	1.37335	−	1.02149i
$765$		0			0
$766$	4.23091	+	12.7776i	0.152869	+	0.461672i
$767$	88.9587			3.21211
$768$		0			0
$769$	40.2990			1.45322			0.726610	−	0.687050i	$-0.241095\pi$
$769$	40.2990			1.45322			0.726610	+	0.687050i	$0.241095\pi$
$770$	1.95639	+	5.90839i	0.0705034	+	0.212924i
$771$		0			0
$772$	−10.4454	+	7.76920i	−0.375938	+	0.279620i
$773$		−	2.65541i		−	0.0955085i	−0.998859	−	0.0477542i	$-0.984794\pi$
$773$		−	2.65541i		−	0.0955085i	0.998859	−	0.0477542i	$-0.0152064\pi$
$774$		0			0
$775$	9.17311			0.329508
$776$	−2.57200	−	1.80346i	−0.0923294	−	0.0647403i
$777$		0			0
$778$	−11.4118	+	3.77868i	−0.409133	+	0.135472i
$779$			19.5016i			0.698716i
$780$		0			0
$781$		−	8.53327i		−	0.305344i
$782$	14.2940	+	43.1686i	0.511153	+	1.54371i
$783$		0			0
$784$	−5.04901	+	16.8112i	−0.180322	+	0.600400i
$785$	8.76967			0.313003
$786$		0			0
$787$		−	41.3819i		−	1.47510i	−0.675290	−	0.737552i	$-0.735982\pi$
$787$		−	41.3819i		−	1.47510i	0.675290	−	0.737552i	$-0.264018\pi$
$788$	28.8747	+	38.8210i	1.02862	+	1.38294i
$789$		0			0
$790$	2.06748	−	0.684586i	0.0735577	−	0.0243565i
$791$	−17.3760			−0.617821
$792$		0			0
$793$	−55.2250			−1.96110
$794$	41.4355	−	13.7202i	1.47049	−	0.486910i
$795$		0			0
$796$	17.0490	−	12.6809i	0.604284	−	0.449461i
$797$			21.3322i			0.755626i	0.925882	+	0.377813i	$0.123324\pi$
$797$			21.3322i			0.755626i	−0.925882	+	0.377813i	$0.876676\pi$
$798$		0			0
$799$	2.77526			0.0981817
$800$	5.65464	−	0.158328i	0.199922	−	0.00559774i
$801$		0			0
$802$	−17.1703	−	51.8552i	−0.606305	−	1.83107i
$803$		−	30.1350i		−	1.06344i
$804$		0			0
$805$		−	12.0395i		−	0.424335i
$806$	75.4900	−	24.9963i	2.65902	−	0.880456i
$807$		0			0
$808$	−3.70421	+	5.28277i	−0.130314	+	0.185847i
$809$	−16.8625			−0.592854			−0.296427	−	0.955055i	$-0.595795\pi$
$809$	−16.8625			−0.592854			−0.296427	+	0.955055i	$0.595795\pi$
$810$		0			0
$811$			16.4073i			0.576137i	0.957610	+	0.288069i	$0.0930131\pi$
$811$			16.4073i			0.576137i	−0.957610	+	0.288069i	$0.906987\pi$
$812$	2.76399	+	3.71609i	0.0969971	+	0.130409i
$813$		0			0
$814$	11.2140	+	33.8667i	0.393050	+	1.18703i
$815$	0.560015			0.0196165
$816$		0			0
$817$	−21.7873			−0.762242
$818$	−16.0990	−	48.6196i	−0.562887	−	1.69995i
$819$		0			0
$820$	−8.08413	−	10.8688i	−0.282310	−	0.379556i
$821$			22.7949i			0.795547i	0.917484	+	0.397774i	$0.130217\pi$
$821$			22.7949i			0.795547i	−0.917484	+	0.397774i	$0.869783\pi$
$822$		0			0
$823$	28.9803			1.01019			0.505094	−	0.863064i	$-0.331458\pi$
$823$	28.9803			1.01019			0.505094	+	0.863064i	$0.331458\pi$
$824$	−27.1592	−	19.0437i	−0.946135	−	0.663419i
$825$		0			0
$826$	−31.4868	+	10.4259i	−1.09557	+	0.362764i
$827$		−	30.5167i		−	1.06117i	−0.847631	−	0.530586i	$-0.821972\pi$
$827$		−	30.5167i		−	1.06117i	0.847631	−	0.530586i	$-0.178028\pi$
$828$		0			0
$829$		−	24.8169i		−	0.861927i	−0.902369	−	0.430964i	$-0.858174\pi$
$829$		−	24.8169i		−	0.861927i	0.902369	−	0.430964i	$-0.141826\pi$
$830$	−3.75631	−	11.3442i	−0.130384	−	0.393764i
$831$		0			0
$832$	46.1033	−	16.7116i	1.59835	−	0.579370i
$833$	−18.9406			−0.656255
$834$		0			0
$835$		−	8.32657i		−	0.288153i
$836$	−12.5832	+	9.35930i	−0.435201	+	0.323698i
$837$		0			0
$838$	3.04424	−	1.00801i	0.105161	−	0.0348211i
$839$	−3.71920			−0.128401			−0.0642006	−	0.997937i	$-0.520450\pi$
$839$	−3.71920			−0.128401			−0.0642006	+	0.997937i	$0.520450\pi$
$840$		0			0
$841$	26.9469			0.929202
$842$	13.2303	−	4.38083i	0.455947	−	0.150973i
$843$		0			0
$844$	27.1810	+	36.5439i	0.935609	+	1.25789i
$845$			24.5749i			0.845402i
$846$		0			0
$847$	−5.79232			−0.199026
$848$	−38.5623	−	11.5817i	−1.32424	−	0.397716i
$849$		0			0
$850$	1.91873	+	5.79464i	0.0658117	+	0.198755i
$851$		−	69.0099i		−	2.36563i
$852$		0			0
$853$		−	33.0213i		−	1.13063i	−0.824875	−	0.565315i	$-0.808755\pi$
$853$		−	33.0213i		−	1.13063i	0.824875	−	0.565315i	$-0.191245\pi$
$854$	19.5468	−	6.47236i	0.668879	−	0.221479i
$855$		0			0
$856$	−0.0944312	+	0.134673i	−0.00322759	+	0.00460303i
$857$	−20.8149			−0.711022			−0.355511	−	0.934672i	$-0.615693\pi$
$857$	−20.8149			−0.711022			−0.355511	+	0.934672i	$0.615693\pi$
$858$		0			0
$859$		−	39.2623i		−	1.33961i	−0.742536	−	0.669806i	$-0.766377\pi$
$859$		−	39.2623i		−	1.33961i	0.742536	−	0.669806i	$-0.233623\pi$
$860$	12.1428	−	9.03167i	0.414065	−	0.307978i
$861$		0			0
$862$	−6.66635	−	20.1327i	−0.227057	−	0.685722i
$863$	−22.5831			−0.768737			−0.384369	−	0.923180i	$-0.625581\pi$
$863$	−22.5831			−0.768737			−0.384369	+	0.923180i	$0.625581\pi$
$864$		0			0
$865$	−12.4053			−0.421792
$866$	13.5394	+	40.8897i	0.460088	+	1.38949i
$867$		0			0
$868$	−23.7900	+	17.6948i	−0.807486	+	0.600600i
$869$		−	4.19371i		−	0.142262i
$870$		0			0
$871$	−40.1664			−1.36099
$872$	18.2518	−	26.0298i	0.618085	−	0.881482i
$873$		0			0
$874$	28.7982	−	9.53567i	0.974113	−	0.322549i
$875$		−	1.61609i		−	0.0546338i
$876$		0			0
$877$		−	24.2595i		−	0.819184i	−0.912269	−	0.409592i	$-0.865671\pi$
$877$		−	24.2595i		−	0.819184i	0.912269	−	0.409592i	$-0.134329\pi$
$878$	−12.1625	−	36.7313i	−0.410464	−	1.23962i
$879$		0			0
$880$	3.13325	−	10.4325i	0.105622	−	0.351678i
$881$	4.13299			0.139244			0.0696220	−	0.997573i	$-0.477821\pi$
$881$	4.13299			0.139244			0.0696220	+	0.997573i	$0.477821\pi$
$882$		0			0
$883$			11.0003i			0.370191i	0.982721	+	0.185095i	$0.0592594\pi$
$883$			11.0003i			0.370191i	−0.982721	+	0.185095i	$0.940741\pi$
$884$	31.5802	+	42.4585i	1.06216	+	1.42803i
$885$		0			0
$886$	−49.3999	+	16.3573i	−1.65962	+	0.549535i
$887$	−6.23472			−0.209341			−0.104671	−	0.994507i	$-0.533379\pi$
$887$	−6.23472			−0.209341			−0.104671	+	0.994507i	$0.533379\pi$
$888$		0			0
$889$	−15.7206			−0.527252
$890$	10.1585	−	3.36368i	0.340513	−	0.112751i
$891$		0			0
$892$	−37.9748	+	28.2453i	−1.27149	+	0.945722i
$893$		−	1.85140i		−	0.0619548i
$894$		0			0
$895$	−4.67859			−0.156388
$896$	−14.3596	+	11.3183i	−0.479721	+	0.378119i
$897$		0			0
$898$	1.17956	+	3.56233i	0.0393624	+	0.118876i
$899$		−	13.1439i		−	0.438374i
$900$		0			0
$901$		−	43.4470i		−	1.44743i
$902$	−24.7613	+	8.19898i	−0.824462	+	0.272996i
$903$		0			0
$904$	24.8997	+	17.4594i	0.828153	+	0.580691i
$905$	7.44975			0.247638
$906$		0			0
$907$		−	11.7675i		−	0.390735i	−0.980730	−	0.195367i	$-0.937410\pi$
$907$		−	11.7675i		−	0.390735i	0.980730	−	0.195367i	$-0.0625900\pi$
$908$	−11.3704	−	15.2870i	−0.377339	−	0.507318i
$909$		0			0
$910$	−4.40376	−	13.2996i	−0.145983	−	0.440877i
$911$	−1.89087			−0.0626473			−0.0313237	−	0.999509i	$-0.509972\pi$
$911$	−1.89087			−0.0626473			−0.0313237	+	0.999509i	$0.509972\pi$
$912$		0			0
$913$	−23.0108			−0.761547
$914$	2.12999	+	6.43268i	0.0704539	+	0.212774i
$915$		0			0
$916$	7.88287	+	10.5982i	0.260457	+	0.350175i
$917$		−	0.395719i		−	0.0130678i
$918$		0			0
$919$	31.7512			1.04738			0.523688	−	0.851910i	$-0.324556\pi$
$919$	31.7512			1.04738			0.523688	+	0.851910i	$0.324556\pi$
$920$	−12.0972	+	17.2525i	−0.398834	+	0.568797i
$921$		0			0
$922$	34.6690	−	11.4796i	1.14176	−	0.378061i
$923$			19.2081i			0.632242i
$924$		0			0
$925$		−	9.26338i		−	0.304578i
$926$	−10.5219	−	31.7768i	−0.345772	−	1.04425i
$927$		0			0
$928$	−0.226864	−	8.10238i	−0.00744717	−	0.265974i
$929$	49.7288			1.63155			0.815774	−	0.578371i	$-0.196311\pi$
$929$	49.7288			1.63155			0.815774	+	0.578371i	$0.196311\pi$
$930$		0			0
$931$			12.6355i			0.414111i
$932$	−40.7048	+	30.2759i	−1.33333	+	0.991719i
$933$		0			0
$934$	28.6967	−	9.50208i	0.938986	−	0.310917i
$935$	11.7539			0.384395
$936$		0			0
$937$	−20.0962			−0.656514			−0.328257	−	0.944588i	$-0.606461\pi$
$937$	−20.0962			−0.656514			−0.328257	+	0.944588i	$0.606461\pi$
$938$	14.2168	−	4.70749i	0.464197	−	0.153705i
$939$		0			0
$940$	0.767476	+	1.03184i	0.0250323	+	0.0336550i
$941$			16.9339i			0.552028i	0.961154	+	0.276014i	$0.0890137\pi$
$941$			16.9339i			0.552028i	−0.961154	+	0.276014i	$0.910986\pi$
$942$		0			0
$943$	50.4558			1.64307
$944$	55.5963	+	16.6976i	1.80951	+	0.543460i
$945$		0			0
$946$	−9.15999	−	27.6636i	−0.297817	−	0.899421i
$947$		−	5.77817i		−	0.187765i	−0.995583	−	0.0938827i	$-0.970072\pi$
$947$		−	5.77817i		−	0.187765i	0.995583	−	0.0938827i	$-0.0299279\pi$
$948$		0			0
$949$			67.8327i			2.20194i
$950$	3.86566	−	1.28000i	0.125418	−	0.0415286i
$951$		0			0
$952$	−16.1539	−	11.3269i	−0.523551	−	0.367108i
$953$	6.10419			0.197734			0.0988670	−	0.995101i	$-0.468478\pi$
$953$	6.10419			0.197734			0.0988670	+	0.995101i	$0.468478\pi$
$954$		0			0
$955$			23.6546i			0.765444i
$956$	11.7894	−	8.76883i	0.381295	−	0.283604i
$957$		0			0
$958$	9.88271	+	29.8462i	0.319296	+	0.964288i
$959$	−14.7815			−0.477319
$960$		0			0
$961$	53.1459			1.71438
$962$	−25.2423	−	76.2328i	−0.813843	−	2.45784i
$963$		0			0
$964$	−12.7160	+	9.45807i	−0.409556	+	0.304624i
$965$		−	6.50897i		−	0.209531i
$966$		0			0
$967$	−57.3680			−1.84483			−0.922415	−	0.386200i	$-0.873787\pi$
$967$	−57.3680			−1.84483			−0.922415	+	0.386200i	$0.873787\pi$
$968$	8.30035	+	5.82011i	0.266783	+	0.187065i
$969$		0			0
$970$	1.49103	−	0.493710i	0.0478740	−	0.0158521i
$971$			9.69127i			0.311008i	0.987835	+	0.155504i	$0.0497001\pi$
$971$			9.69127i			0.311008i	−0.987835	+	0.155504i	$0.950300\pi$
$972$		0			0
$973$			11.6093i			0.372176i
$974$	−9.80663	−	29.6165i	−0.314225	−	0.948974i
$975$		0			0
$976$	−34.5139	−	10.3658i	−1.10476	−	0.331800i
$977$	27.3930			0.876380			0.438190	−	0.898882i	$-0.355620\pi$
$977$	27.3930			0.876380			0.438190	+	0.898882i	$0.355620\pi$
$978$		0			0
$979$		−	20.6056i		−	0.658557i
$980$	−5.23788	−	7.04214i	−0.167318	−	0.224953i
$981$		0			0
$982$	−8.97080	+	2.97042i	−0.286270	+	0.0947898i
$983$	−10.0926			−0.321905			−0.160952	−	0.986962i	$-0.551457\pi$
$983$	−10.0926			−0.321905			−0.160952	+	0.986962i	$0.551457\pi$
$984$		0			0
$985$	−24.1910			−0.770789
$986$	8.30299	−	2.74929i	0.264421	−	0.0875553i
$987$		0			0
$988$	28.3244	−	21.0675i	0.901120	−	0.670245i
$989$			56.3698i			1.79245i
$990$		0			0
$991$	−43.5897			−1.38467			−0.692337	−	0.721575i	$-0.743419\pi$
$991$	−43.5897			−1.38467			−0.692337	+	0.721575i	$0.743419\pi$
$992$	51.8706	−	1.45236i	1.64689	−	0.0461125i
$993$		0			0
$994$	−2.25118	−	6.79867i	−0.0714031	−	0.215641i
$995$			10.6239i			0.336801i
$996$		0			0
$997$			33.5876i			1.06373i	0.846830	+	0.531864i	$0.178508\pi$
$997$			33.5876i			1.06373i	−0.846830	+	0.531864i	$0.821492\pi$
$998$	38.1254	−	12.6241i	1.20684	−	0.399609i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.k.d.541.9	✓	20
3.2	odd	2	inner	1080.2.k.d.541.12	yes	20
4.3	odd	2		4320.2.k.d.2161.7		20
8.3	odd	2		4320.2.k.d.2161.18		20
8.5	even	2	inner	1080.2.k.d.541.10	yes	20
12.11	even	2		4320.2.k.d.2161.17		20
24.5	odd	2	inner	1080.2.k.d.541.11	yes	20
24.11	even	2		4320.2.k.d.2161.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.k.d.541.9	✓	20	1.1	even	1	trivial
1080.2.k.d.541.10	yes	20	8.5	even	2	inner
1080.2.k.d.541.11	yes	20	24.5	odd	2	inner
1080.2.k.d.541.12	yes	20	3.2	odd	2	inner
4320.2.k.d.2161.7		20	4.3	odd	2
4320.2.k.d.2161.8		20	24.11	even	2
4320.2.k.d.2161.17		20	12.11	even	2
4320.2.k.d.2161.18		20	8.3	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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.444539 - 1.34253i) q^{2} +(-1.60477 + 1.19361i) q^{4} -1.00000i q^{5} -1.61609 q^{7} +(2.31584 + 1.62384i) q^{8} +O(q^{10})\)	\(q+(-0.444539 - 1.34253i) q^{2} +(-1.60477 + 1.19361i) q^{4} -1.00000i q^{5} -1.61609 q^{7} +(2.31584 + 1.62384i) q^{8} +(-1.34253 + 0.444539i) q^{10} +2.72320i q^{11} -6.12984i q^{13} +(0.718415 + 2.16965i) q^{14} +(1.15057 - 3.83095i) q^{16} +4.31621 q^{17} -2.87938i q^{19} +(1.19361 + 1.60477i) q^{20} +(3.65598 - 1.21057i) q^{22} -7.44975 q^{23} -1.00000 q^{25} +(-8.22949 + 2.72495i) q^{26} +(2.59345 - 1.92899i) q^{28} +1.43287i q^{29} -9.17311 q^{31} +(-5.65464 + 0.158328i) q^{32} +(-1.91873 - 5.79464i) q^{34} +1.61609i q^{35} +9.26338i q^{37} +(-3.86566 + 1.28000i) q^{38} +(1.62384 - 2.31584i) q^{40} -6.77282 q^{41} -7.56667i q^{43} +(-3.25045 - 4.37012i) q^{44} +(3.31171 + 10.0015i) q^{46} +0.642985 q^{47} -4.38826 q^{49} +(0.444539 + 1.34253i) q^{50} +(7.31666 + 9.83698i) q^{52} -10.0660i q^{53} +2.72320 q^{55} +(-3.74261 - 2.62427i) q^{56} +(1.92368 - 0.636968i) q^{58} +14.5124i q^{59} -9.00922i q^{61} +(4.07781 + 12.3152i) q^{62} +(2.72627 + 7.52113i) q^{64} -6.12984 q^{65} -6.55261i q^{67} +(-6.92653 + 5.15189i) q^{68} +(2.16965 - 0.718415i) q^{70} -3.13354 q^{71} -11.0660 q^{73} +(12.4364 - 4.11793i) q^{74} +(3.43687 + 4.62075i) q^{76} -4.40094i q^{77} -1.53999 q^{79} +(-3.83095 - 1.15057i) q^{80} +(3.01078 + 9.09271i) q^{82} +8.44990i q^{83} -4.31621i q^{85} +(-10.1585 + 3.36368i) q^{86} +(-4.42206 + 6.30652i) q^{88} -7.56667 q^{89} +9.90636i q^{91} +(11.9551 - 8.89212i) q^{92} +(-0.285832 - 0.863227i) q^{94} -2.87938 q^{95} -1.11061 q^{97} +(1.95075 + 5.89136i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4}+O(q^{10}) \) 20 * q + 2 * q^4	\( 20 q + 2 q^{4} - 2 q^{10} - 18 q^{16} + 16 q^{22} - 20 q^{25} + 16 q^{28} + 20 q^{31} - 6 q^{34} - 4 q^{40} + 54 q^{46} + 36 q^{49} + 56 q^{52} - 72 q^{58} - 28 q^{64} - 40 q^{73} + 58 q^{76} - 4 q^{79} - 92 q^{82} - 116 q^{88} + 72 q^{94} + 40 q^{97}+O(q^{100}) \) 20 * q + 2 * q^4 - 2 * q^10 - 18 * q^16 + 16 * q^22 - 20 * q^25 + 16 * q^28 + 20 * q^31 - 6 * q^34 - 4 * q^40 + 54 * q^46 + 36 * q^49 + 56 * q^52 - 72 * q^58 - 28 * q^64 - 40 * q^73 + 58 * q^76 - 4 * q^79 - 92 * q^82 - 116 * q^88 + 72 * q^94 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more