LMFDB - Embedded newform 1080.2.d.i.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(109,1080)]

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, 1]))

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

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

chi := DirichletCharacter("1080.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.d (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} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 $ x^20 - 3x^18 + 8x^16 - 24x^14 + 56x^12 - 92x^10 + 224x^8 - 384x^6 + 512x^4 - 768*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.9
Root			$0.564088 - 1.29684i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.i.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.564088 - 1.29684i) q^{2} +(-1.36361 + 1.46307i) q^{4} +(-2.22935 - 0.173169i) q^{5} +3.43285i q^{7} +(2.66657 + 0.943090i) q^{8} +O(q^{10})$	\(q+(-0.564088 - 1.29684i) q^{2} +(-1.36361 + 1.46307i) q^{4} +(-2.22935 - 0.173169i) q^{5} +3.43285i q^{7} +(2.66657 + 0.943090i) q^{8} +(1.03298 + 2.98881i) q^{10} -4.54582i q^{11} +1.84104 q^{13} +(4.45187 - 1.93643i) q^{14} +(-0.281138 - 3.99011i) q^{16} +0.380882i q^{17} -1.23050i q^{19} +(3.29332 - 3.02556i) q^{20} +(-5.89523 + 2.56424i) q^{22} +5.35845i q^{23} +(4.94003 + 0.772107i) q^{25} +(-1.03851 - 2.38754i) q^{26} +(-5.02250 - 4.68107i) q^{28} -3.17705i q^{29} -6.89216 q^{31} +(-5.01596 + 2.61536i) q^{32} +(0.493945 - 0.214851i) q^{34} +(0.594462 - 7.65304i) q^{35} -6.60129 q^{37} +(-1.59576 + 0.694109i) q^{38} +(-5.78141 - 2.56424i) q^{40} -10.9064 q^{41} -7.34200 q^{43} +(6.65085 + 6.19873i) q^{44} +(6.94907 - 3.02264i) q^{46} -9.34062i q^{47} -4.78447 q^{49} +(-1.78531 - 6.84198i) q^{50} +(-2.51046 + 2.69357i) q^{52} -1.25351 q^{53} +(-0.787194 + 10.1342i) q^{55} +(-3.23749 + 9.15393i) q^{56} +(-4.12014 + 1.79214i) q^{58} -3.34812i q^{59} +7.74091i q^{61} +(3.88779 + 8.93806i) q^{62} +(6.22116 + 5.02962i) q^{64} +(-4.10433 - 0.318810i) q^{65} -13.3708 q^{67} +(-0.557256 - 0.519374i) q^{68} +(-10.2601 + 3.54606i) q^{70} -11.9198 q^{71} -13.1857i q^{73} +(3.72371 + 8.56084i) q^{74} +(1.80030 + 1.67792i) q^{76} +15.6051 q^{77} +13.9675 q^{79} +(-0.0642048 + 8.94404i) q^{80} +(6.15214 + 14.1438i) q^{82} +0.240083 q^{83} +(0.0659568 - 0.849120i) q^{85} +(4.14153 + 9.52142i) q^{86} +(4.28712 - 12.1217i) q^{88} +5.46154 q^{89} +6.32002i q^{91} +(-7.83978 - 7.30683i) q^{92} +(-12.1133 + 5.26893i) q^{94} +(-0.213084 + 2.74321i) q^{95} -15.7955i q^{97} +(2.69886 + 6.20471i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{4}+O(q^{10}) $ 20 * q + 6 * q^4	$ 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64} + 12 q^{70} - 24 q^{76} + 36 q^{79} + 32 q^{82} - 44 q^{85} - 30 q^{88} - 22 q^{94}+O(q^{100}) $ 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

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 $

$2$	−0.564088	−	1.29684i	−0.398870	−	0.917007i
$2$	−0.564088	−	1.29684i	−0.398870	−	0.917007i
$3$		0			0
$3$		0			0
$4$	−1.36361	+	1.46307i	−0.681805	+	0.731534i
$5$	−2.22935	−	0.173169i	−0.996997	−	0.0774433i
$5$	−2.22935	−	0.173169i	−0.996997	−	0.0774433i
$6$		0			0
$7$			3.43285i			1.29750i	0.761003	+	0.648748i	$0.224707\pi$
$7$			3.43285i			1.29750i	−0.761003	+	0.648748i	$0.775293\pi$
$8$	2.66657	+	0.943090i	0.942774	+	0.333433i
$9$		0			0
$10$	1.03298	+	2.98881i	0.326656	+	0.945143i
$11$		−	4.54582i		−	1.37062i	−0.728253	−	0.685309i	$-0.759667\pi$
$11$		−	4.54582i		−	1.37062i	0.728253	−	0.685309i	$-0.240333\pi$
$12$		0			0
$13$	1.84104			0.510613			0.255306	−	0.966860i	$-0.417824\pi$
$13$	1.84104			0.510613			0.255306	+	0.966860i	$0.417824\pi$
$14$	4.45187	−	1.93643i	1.18981	−	0.517533i
$15$		0			0
$16$	−0.281138	−	3.99011i	−0.0702846	−	0.997527i
$17$			0.380882i			0.0923774i	0.998933	+	0.0461887i	$0.0147076\pi$
$17$			0.380882i			0.0923774i	−0.998933	+	0.0461887i	$0.985292\pi$
$18$		0			0
$19$		−	1.23050i		−	0.282296i	−0.989989	−	0.141148i	$-0.954921\pi$
$19$		−	1.23050i		−	0.282296i	0.989989	−	0.141148i	$-0.0450793\pi$
$20$	3.29332	−	3.02556i	0.736410	−	0.676536i
$21$		0			0
$22$	−5.89523	+	2.56424i	−1.25687	+	0.546699i
$23$			5.35845i			1.11731i	0.829399	+	0.558657i	$0.188683\pi$
$23$			5.35845i			1.11731i	−0.829399	+	0.558657i	$0.811317\pi$
$24$		0			0
$25$	4.94003	+	0.772107i	0.988005	+	0.154421i
$26$	−1.03851	−	2.38754i	−0.203668	−	0.468235i
$27$		0			0
$28$	−5.02250	−	4.68107i	−0.949163	−	0.884639i
$29$		−	3.17705i		−	0.589964i	−0.955503	−	0.294982i	$-0.904686\pi$
$29$		−	3.17705i		−	0.589964i	0.955503	−	0.294982i	$-0.0953137\pi$
$30$		0			0
$31$	−6.89216			−1.23787			−0.618934	−	0.785443i	$-0.712435\pi$
$31$	−6.89216			−1.23787			−0.618934	+	0.785443i	$0.712435\pi$
$32$	−5.01596	+	2.61536i	−0.886705	+	0.462335i
$33$		0			0
$34$	0.493945	−	0.214851i	0.0847108	−	0.0368466i
$35$	0.594462	−	7.65304i	0.100482	−	1.29360i
$36$		0			0
$37$	−6.60129			−1.08524			−0.542622	−	0.839977i	$-0.682569\pi$
$37$	−6.60129			−1.08524			−0.542622	+	0.839977i	$0.682569\pi$
$38$	−1.59576	+	0.694109i	−0.258867	+	0.112599i
$39$		0			0
$40$	−5.78141	−	2.56424i	−0.914120	−	0.405443i
$41$	−10.9064			−1.70329			−0.851643	−	0.524122i	$-0.824393\pi$
$41$	−10.9064			−1.70329			−0.851643	+	0.524122i	$0.824393\pi$
$42$		0			0
$43$	−7.34200			−1.11964			−0.559822	−	0.828613i	$-0.689130\pi$
$43$	−7.34200			−1.11964			−0.559822	+	0.828613i	$0.689130\pi$
$44$	6.65085	+	6.19873i	1.00265	+	0.934494i
$45$		0			0
$46$	6.94907	−	3.02264i	1.02458	−	0.445663i
$47$		−	9.34062i		−	1.36247i	−0.732065	−	0.681235i	$-0.761443\pi$
$47$		−	9.34062i		−	1.36247i	0.732065	−	0.681235i	$-0.238557\pi$
$48$		0			0
$49$	−4.78447			−0.683496
$50$	−1.78531	−	6.84198i	−0.252480	−	0.967602i
$51$		0			0
$52$	−2.51046	+	2.69357i	−0.348138	+	0.373531i
$53$	−1.25351			−0.172183			−0.0860916	−	0.996287i	$-0.527438\pi$
$53$	−1.25351			−0.172183			−0.0860916	+	0.996287i	$0.527438\pi$
$54$		0			0
$55$	−0.787194	+	10.1342i	−0.106145	+	1.36650i
$56$	−3.23749	+	9.15393i	−0.432627	+	1.22325i
$57$		0			0
$58$	−4.12014	+	1.79214i	−0.541001	+	0.235319i
$59$		−	3.34812i		−	0.435889i	−0.975961	−	0.217944i	$-0.930065\pi$
$59$		−	3.34812i		−	0.435889i	0.975961	−	0.217944i	$-0.0699351\pi$
$60$		0			0
$61$			7.74091i			0.991122i	0.868573	+	0.495561i	$0.165038\pi$
$61$			7.74091i			0.991122i	−0.868573	+	0.495561i	$0.834962\pi$
$62$	3.88779	+	8.93806i	0.493749	+	1.13513i
$63$		0			0
$64$	6.22116	+	5.02962i	0.777645	+	0.628703i
$65$	−4.10433	−	0.318810i	−0.509079	−	0.0395435i
$66$		0			0
$67$	−13.3708			−1.63351			−0.816753	−	0.576988i	$-0.804228\pi$
$67$	−13.3708			−1.63351			−0.816753	+	0.576988i	$0.804228\pi$
$68$	−0.557256	−	0.519374i	−0.0675773	−	0.0629834i
$69$		0			0
$70$	−10.2601	+	3.54606i	−1.22632	+	0.423835i
$71$	−11.9198			−1.41462			−0.707309	−	0.706905i	$-0.750091\pi$
$71$	−11.9198			−1.41462			−0.707309	+	0.706905i	$0.750091\pi$
$72$		0			0
$73$		−	13.1857i		−	1.54327i	−0.636065	−	0.771636i	$-0.719439\pi$
$73$		−	13.1857i		−	1.54327i	0.636065	−	0.771636i	$-0.280561\pi$
$74$	3.72371	+	8.56084i	0.432872	+	0.995178i
$75$		0			0
$76$	1.80030	+	1.67792i	0.206509	+	0.192471i
$77$	15.6051			1.77837
$78$		0			0
$79$	13.9675			1.57147			0.785734	−	0.618565i	$-0.212286\pi$
$79$	13.9675			1.57147			0.785734	+	0.618565i	$0.212286\pi$
$80$	−0.0642048	+	8.94404i	−0.00717832	+	0.999974i
$81$		0			0
$82$	6.15214	+	14.1438i	0.679390	+	1.56193i
$83$	0.240083			0.0263525			0.0131763	−	0.999913i	$-0.495806\pi$
$83$	0.240083			0.0263525			0.0131763	+	0.999913i	$0.495806\pi$
$84$		0			0
$85$	0.0659568	−	0.849120i	0.00715402	−	0.0921000i
$86$	4.14153	+	9.52142i	0.446593	+	1.02672i
$87$		0			0
$88$	4.28712	−	12.1217i	0.457009	−	1.29218i
$89$	5.46154			0.578923			0.289461	−	0.957190i	$-0.406524\pi$
$89$	5.46154			0.578923			0.289461	+	0.957190i	$0.406524\pi$
$90$		0			0
$91$			6.32002i			0.662518i
$92$	−7.83978	−	7.30683i	−0.817353	−	0.761790i
$93$		0			0
$94$	−12.1133	+	5.26893i	−1.24939	+	0.543449i
$95$	−0.213084	+	2.74321i	−0.0218619	+	0.281448i
$96$		0			0
$97$		−	15.7955i		−	1.60379i	−0.597462	−	0.801897i	$-0.703824\pi$
$97$		−	15.7955i		−	1.60379i	0.597462	−	0.801897i	$-0.296176\pi$
$98$	2.69886	+	6.20471i	0.272626	+	0.626771i
$99$		0			0
$100$	−7.86591	+	6.17474i	−0.786591	+	0.617474i
$101$		−	1.17066i		−	0.116485i	−0.998302	−	0.0582426i	$-0.981450\pi$
$101$		−	1.17066i		−	0.116485i	0.998302	−	0.0582426i	$-0.0185497\pi$
$102$		0			0
$103$			5.27991i			0.520245i	0.965576	+	0.260123i	$0.0837630\pi$
$103$			5.27991i			0.520245i	−0.965576	+	0.260123i	$0.916237\pi$
$104$	4.90926	+	1.73627i	0.481392	+	0.170255i
$105$		0			0
$106$	0.707091	+	1.62561i	0.0686788	+	0.157893i
$107$	−14.3622			−1.38845			−0.694224	−	0.719759i	$-0.744252\pi$
$107$	−14.3622			−1.38845			−0.694224	+	0.719759i	$0.744252\pi$
$108$		0			0
$109$		−	13.4994i		−	1.29301i	−0.762909	−	0.646506i	$-0.776230\pi$
$109$		−	13.4994i		−	1.29301i	0.762909	−	0.646506i	$-0.223770\pi$
$110$	13.5866	−	4.69574i	1.29543	−	0.447721i
$111$		0			0
$112$	13.6974	−	0.965106i	1.29429	−	0.0911939i
$113$		−	1.27140i		−	0.119603i	−0.998210	−	0.0598017i	$-0.980953\pi$
$113$		−	1.27140i		−	0.119603i	0.998210	−	0.0598017i	$-0.0190469\pi$
$114$		0			0
$115$	0.927914	−	11.9459i	0.0865285	−	1.11396i
$116$	4.64825	+	4.33226i	0.431579	+	0.402240i
$117$		0			0
$118$	−4.34200	+	1.88864i	−0.399713	+	0.173863i
$119$	−1.30751			−0.119859
$120$		0			0
$121$	−9.66452			−0.878593
$122$	10.0388	−	4.36655i	0.908866	−	0.395329i
$123$		0			0
$124$	9.39822	−	10.0837i	0.843985	−	0.905543i
$125$	−10.8794	−	2.57676i	−0.973079	−	0.230472i
$126$		0			0
$127$			6.10295i			0.541549i	0.962643	+	0.270774i	$0.0872798\pi$
$127$			6.10295i			0.541549i	−0.962643	+	0.270774i	$0.912720\pi$
$128$	3.01336	−	10.9050i	0.266346	−	0.963878i
$129$		0			0
$130$	1.90175	+	5.50251i	0.166795	+	0.482602i
$131$			2.60170i			0.227311i	0.993520	+	0.113656i	$0.0362561\pi$
$131$			2.60170i			0.227311i	−0.993520	+	0.113656i	$0.963744\pi$
$132$		0			0
$133$	4.22412			0.366278
$134$	7.54232	+	17.3399i	0.651557	+	1.49794i
$135$		0			0
$136$	−0.359206	+	1.01565i	−0.0308016	+	0.0870911i
$137$			7.58216i			0.647787i	0.946093	+	0.323894i	$0.104992\pi$
$137$			7.58216i			0.647787i	−0.946093	+	0.323894i	$0.895008\pi$
$138$		0			0
$139$			14.7299i			1.24938i	0.780874	+	0.624688i	$0.214774\pi$
$139$			14.7299i			1.24938i	−0.780874	+	0.624688i	$0.785226\pi$
$140$	10.3863	+	11.3055i	0.877803	+	0.955488i
$141$		0			0
$142$	6.72381	+	15.4581i	0.564249	+	1.29721i
$143$		−	8.36904i		−	0.699855i
$144$		0			0
$145$	−0.550166	+	7.08277i	−0.0456888	+	0.588192i
$146$	−17.0998	+	7.43791i	−1.41519	+	0.615565i
$147$		0			0
$148$	9.00158	−	9.65814i	0.739925	−	0.793894i
$149$		−	16.0795i		−	1.31729i	−0.752455	−	0.658644i	$-0.771131\pi$
$149$		−	16.0795i		−	1.31729i	0.752455	−	0.658644i	$-0.228869\pi$
$150$		0			0
$151$	9.54189			0.776508			0.388254	−	0.921552i	$-0.373078\pi$
$151$	9.54189			0.776508			0.388254	+	0.921552i	$0.373078\pi$
$152$	1.16047	−	3.28121i	0.0941266	−	0.266141i
$153$		0			0
$154$	−8.80267	−	20.2374i	−0.709340	−	1.63078i
$155$	15.3651	+	1.19351i	1.23415	+	0.0958647i
$156$		0			0
$157$	15.7918			1.26033			0.630163	−	0.776463i	$-0.282988\pi$
$157$	15.7918			1.26033			0.630163	+	0.776463i	$0.282988\pi$
$158$	−7.87890	−	18.1137i	−0.626812	−	1.44105i
$159$		0			0
$160$	11.6352	−	4.96196i	0.919847	−	0.392278i
$161$	−18.3948			−1.44971
$162$		0			0
$163$	10.2026			0.799127			0.399564	−	0.916705i	$-0.369162\pi$
$163$	10.2026			0.799127			0.399564	+	0.916705i	$0.369162\pi$
$164$	14.8720	−	15.9567i	1.16131	−	1.24601i
$165$		0			0
$166$	−0.135428	−	0.311350i	−0.0105112	−	0.0241655i
$167$			21.5787i			1.66981i	0.550394	+	0.834905i	$0.314478\pi$
$167$			21.5787i			1.66981i	−0.550394	+	0.834905i	$0.685522\pi$
$168$		0			0
$169$	−9.61057			−0.739275
$170$	−1.13838	+	0.393443i	−0.0873099	+	0.0301757i
$171$		0			0
$172$	10.0116	−	10.7418i	0.763379	−	0.819058i
$173$	−10.6663			−0.810941			−0.405471	−	0.914108i	$-0.632892\pi$
$173$	−10.6663			−0.810941			−0.405471	+	0.914108i	$0.632892\pi$
$174$		0			0
$175$	−2.65053	+	16.9584i	−0.200361	+	1.28193i
$176$	−18.1383	+	1.27801i	−1.36723	+	0.0963333i
$177$		0			0
$178$	−3.08079	−	7.08277i	−0.230915	−	0.530876i
$179$			13.1543i			0.983202i	0.870821	+	0.491601i	$0.163588\pi$
$179$			13.1543i			0.983202i	−0.870821	+	0.491601i	$0.836412\pi$
$180$		0			0
$181$		−	6.97815i		−	0.518682i	−0.965786	−	0.259341i	$-0.916495\pi$
$181$		−	6.97815i		−	0.518682i	0.965786	−	0.259341i	$-0.0835054\pi$
$182$	8.19608	−	3.56504i	0.607534	−	0.264259i
$183$		0			0
$184$	−5.05350	+	14.2887i	−0.372549	+	1.05337i
$185$	14.7166	+	1.14314i	1.08199	+	0.0840450i
$186$		0			0
$187$	1.73142			0.126614
$188$	13.6660	+	12.7370i	0.996693	+	0.928938i
$189$		0			0
$190$	3.67772	−	1.27108i	0.266810	−	0.0922137i
$191$	−20.5052			−1.48370			−0.741852	−	0.670564i	$-0.766052\pi$
$191$	−20.5052			−1.48370			−0.741852	+	0.670564i	$0.766052\pi$
$192$		0			0
$193$		−	20.0514i		−	1.44333i	−0.692241	−	0.721666i	$-0.743376\pi$
$193$		−	20.0514i		−	1.44333i	0.692241	−	0.721666i	$-0.256624\pi$
$194$	−20.4843	+	8.91007i	−1.47069	+	0.639706i
$195$		0			0
$196$	6.52415	−	7.00001i	0.466011	−	0.500000i
$197$	−11.9738			−0.853097			−0.426548	−	0.904465i	$-0.640271\pi$
$197$	−11.9738			−0.853097			−0.426548	+	0.904465i	$0.640271\pi$
$198$		0			0
$199$	−4.84840			−0.343694			−0.171847	−	0.985124i	$-0.554973\pi$
$199$	−4.84840			−0.343694			−0.171847	+	0.985124i	$0.554973\pi$
$200$	12.4447	+	6.71776i	0.879976	+	0.475018i
$201$		0			0
$202$	−1.51817	+	0.660356i	−0.106818	+	0.0464625i
$203$	10.9064			0.765476
$204$		0			0
$205$	24.3141	+	1.88864i	1.69817	+	0.131908i
$206$	6.84723	−	2.97834i	0.477069	−	0.207510i
$207$		0			0
$208$	−0.517587	−	7.34595i	−0.0358882	−	0.509350i
$209$	−5.59363			−0.386919
$210$		0			0
$211$		−	4.52513i		−	0.311523i	−0.987795	−	0.155761i	$-0.950217\pi$
$211$		−	4.52513i		−	0.311523i	0.987795	−	0.155761i	$-0.0497831\pi$
$212$	1.70930	−	1.83397i	0.117395	−	0.125958i
$213$		0			0
$214$	8.10155	+	18.6256i	0.553811	+	1.27322i
$215$	16.3679	+	1.27140i	1.11628	+	0.0867089i
$216$		0			0
$217$		−	23.6598i		−	1.60613i
$218$	−17.5067	+	7.61487i	−1.18570	+	0.515744i
$219$		0			0
$220$	−13.7537	−	14.9709i	−0.927272	−	1.00934i
$221$			0.701219i			0.0471691i
$222$		0			0
$223$			17.9428i			1.20154i	0.799422	+	0.600770i	$0.205139\pi$
$223$			17.9428i			1.20154i	−0.799422	+	0.600770i	$0.794861\pi$
$224$	−8.97816	−	17.2191i	−0.599878	−	1.15050i
$225$		0			0
$226$	−1.64881	+	0.717183i	−0.109677	+	0.0477063i
$227$	−9.15749			−0.607804			−0.303902	−	0.952703i	$-0.598290\pi$
$227$	−9.15749			−0.607804			−0.303902	+	0.952703i	$0.598290\pi$
$228$		0			0
$229$			16.7232i			1.10510i	0.833480	+	0.552550i	$0.186345\pi$
$229$			16.7232i			1.10510i	−0.833480	+	0.552550i	$0.813655\pi$
$230$	−16.0154	+	5.53516i	−1.05602	+	0.364978i
$231$		0			0
$232$	2.99625	−	8.47183i	0.196713	−	0.556203i
$233$		−	19.9108i		−	1.30440i	−0.758047	−	0.652200i	$-0.773846\pi$
$233$		−	19.9108i		−	1.30440i	0.758047	−	0.652200i	$-0.226154\pi$
$234$		0			0
$235$	−1.61750	+	20.8235i	−0.105514	+	1.35838i
$236$	4.89854	+	4.56553i	0.318867	+	0.297191i
$237$		0			0
$238$	0.737551	+	1.69564i	0.0478084	+	0.109912i
$239$	−12.6568			−0.818698			−0.409349	−	0.912378i	$-0.634244\pi$
$239$	−12.6568			−0.818698			−0.409349	+	0.912378i	$0.634244\pi$
$240$		0			0
$241$	10.1784			0.655645			0.327823	−	0.944739i	$-0.393685\pi$
$241$	10.1784			0.655645			0.327823	+	0.944739i	$0.393685\pi$
$242$	5.45164	+	12.5334i	0.350445	+	0.805676i
$243$		0			0
$244$	−11.3255	−	10.5556i	−0.725040	−	0.675752i
$245$	10.6663	+	0.828520i	0.681443	+	0.0529322i
$246$		0			0
$247$		−	2.26540i		−	0.144144i
$248$	−18.3784	−	6.49993i	−1.16703	−	0.412746i
$249$		0			0
$250$	2.79526	+	15.5623i	0.176788	+	0.984249i
$251$		−	0.505026i		−	0.0318769i	−0.999873	−	0.0159385i	$-0.994926\pi$
$251$		−	0.505026i		−	0.0318769i	0.999873	−	0.0159385i	$-0.00507359\pi$
$252$		0			0
$253$	24.3586			1.53141
$254$	7.91457	−	3.44260i	0.496604	−	0.216008i
$255$		0			0
$256$	−15.8419	+	2.24354i	−0.990120	+	0.140221i
$257$			10.1698i			0.634376i	0.948363	+	0.317188i	$0.102739\pi$
$257$			10.1698i			0.634376i	−0.948363	+	0.317188i	$0.897261\pi$
$258$		0			0
$259$		−	22.6612i		−	1.40810i
$260$	6.06314	−	5.57018i	0.376020	−	0.345448i
$261$		0			0
$262$	3.37400	−	1.46759i	0.208446	−	0.0906678i
$263$			7.54472i			0.465227i	0.972569	+	0.232614i	$0.0747278\pi$
$263$			7.54472i			0.465227i	−0.972569	+	0.232614i	$0.925272\pi$
$264$		0			0
$265$	2.79452	+	0.217069i	0.171666	+	0.0133344i
$266$	−2.38277	−	5.47802i	−0.146097	−	0.335879i
$267$		0			0
$268$	18.2326	−	19.5624i	1.11373	−	1.19497i
$269$		−	26.7466i		−	1.63077i	−0.578919	−	0.815385i	$-0.696525\pi$
$269$		−	26.7466i		−	1.63077i	0.578919	−	0.815385i	$-0.303475\pi$
$270$		0			0
$271$	−1.08079			−0.0656534			−0.0328267	−	0.999461i	$-0.510451\pi$
$271$	−1.08079			−0.0656534			−0.0328267	+	0.999461i	$0.510451\pi$
$272$	1.51976	−	0.107080i	0.0921490	−	0.00649271i
$273$		0			0
$274$	9.83288	−	4.27700i	0.594026	−	0.258383i
$275$	3.50986	−	22.4565i	0.211653	−	1.35418i
$276$		0			0
$277$	−20.4348			−1.22781			−0.613905	−	0.789380i	$-0.710402\pi$
$277$	−20.4348			−1.22781			−0.613905	+	0.789380i	$0.710402\pi$
$278$	19.1024	−	8.30898i	1.14569	−	0.498339i
$279$		0			0
$280$	8.80267	−	19.8467i	0.526060	−	1.18607i
$281$	13.8023			0.823375			0.411688	−	0.911325i	$-0.364940\pi$
$281$	13.8023			0.823375			0.411688	+	0.911325i	$0.364940\pi$
$282$		0			0
$283$	13.2026			0.784812			0.392406	−	0.919792i	$-0.371643\pi$
$283$	13.2026			0.784812			0.392406	+	0.919792i	$0.371643\pi$
$284$	16.2539	−	17.4395i	0.964493	−	1.03484i
$285$		0			0
$286$	−10.8533	+	4.72088i	−0.641772	+	0.279151i
$287$		−	37.4399i		−	2.21001i
$288$		0			0
$289$	16.8549			0.991466
$290$	9.49559	−	3.28183i	0.557600	−	0.192716i
$291$		0			0
$292$	19.2916	+	17.9802i	1.12896	+	1.05221i
$293$	8.71459			0.509112			0.254556	−	0.967058i	$-0.418071\pi$
$293$	8.71459			0.509112			0.254556	+	0.967058i	$0.418071\pi$
$294$		0			0
$295$	−0.579790	+	7.46415i	−0.0337567	+	0.434580i
$296$	−17.6028	−	6.22561i	−1.02314	−	0.361856i
$297$		0			0
$298$	−20.8527	+	9.07027i	−1.20796	+	0.525427i
$299$			9.86511i			0.570514i
$300$		0			0
$301$		−	25.2040i		−	1.45273i
$302$	−5.38247	−	12.3743i	−0.309726	−	0.712064i
$303$		0			0
$304$	−4.90982	+	0.345940i	−0.281598	+	0.0198410i
$305$	1.34048	−	17.2572i	0.0767558	−	0.988145i
$306$		0			0
$307$	−25.5908			−1.46054			−0.730272	−	0.683156i	$-0.760607\pi$
$307$	−25.5908			−1.46054			−0.730272	+	0.683156i	$0.760607\pi$
$308$	−21.2793	+	22.8314i	−1.21250	+	1.30094i
$309$		0			0
$310$	−7.11945	−	20.5993i	−0.404358	−	1.16996i
$311$	15.1098			0.856798			0.428399	−	0.903590i	$-0.359078\pi$
$311$	15.1098			0.856798			0.428399	+	0.903590i	$0.359078\pi$
$312$		0			0
$313$			0.998527i			0.0564401i	0.999602	+	0.0282200i	$0.00898391\pi$
$313$			0.998527i			0.0564401i	−0.999602	+	0.0282200i	$0.991016\pi$
$314$	−8.90798	−	20.4795i	−0.502706	−	1.15573i
$315$		0			0
$316$	−19.0462	+	20.4354i	−1.07143	+	1.14958i
$317$	10.6663			0.599077			0.299539	−	0.954084i	$-0.403167\pi$
$317$	10.6663			0.599077			0.299539	+	0.954084i	$0.403167\pi$
$318$		0			0
$319$	−14.4423			−0.808615
$320$	−12.9982	−	12.2901i	−0.726621	−	0.687038i
$321$		0			0
$322$	10.3763	+	23.8551i	0.578246	+	1.32939i
$323$	0.468675			0.0260778
$324$		0			0
$325$	9.09478	+	1.42148i	0.504488	+	0.0788495i
$326$	−5.75515	−	13.2311i	−0.318748	−	0.732806i
$327$		0			0
$328$	−29.0825	−	10.2857i	−1.60581	−	0.567931i
$329$	32.0650			1.76780
$330$		0			0
$331$		−	30.6944i		−	1.68712i	−0.537038	−	0.843558i	$-0.680457\pi$
$331$		−	30.6944i		−	1.68712i	0.537038	−	0.843558i	$-0.319543\pi$
$332$	−0.327379	+	0.351258i	−0.0179673	+	0.0192778i
$333$		0			0
$334$	27.9842	−	12.1723i	1.53123	−	0.666038i
$335$	29.8083	+	2.31541i	1.62860	+	0.126504i
$336$		0			0
$337$		−	20.4856i		−	1.11592i	−0.829868	−	0.557960i	$-0.811584\pi$
$337$		−	20.4856i		−	1.11592i	0.829868	−	0.557960i	$-0.188416\pi$
$338$	5.42121	+	12.4634i	0.294875	+	0.677920i
$339$		0			0
$340$	1.15238	+	1.25437i	0.0624967	+	0.0680276i
$341$			31.3306i			1.69664i
$342$		0			0
$343$			7.60559i			0.410663i
$344$	−19.5779	−	6.92416i	−1.05557	−	0.373326i
$345$		0			0
$346$	6.01671	+	13.8325i	0.323461	+	0.743639i
$347$	8.90067			0.477813			0.238907	−	0.971043i	$-0.423211\pi$
$347$	8.90067			0.477813			0.238907	+	0.971043i	$0.423211\pi$
$348$		0			0
$349$			25.0176i			1.33916i	0.742739	+	0.669581i	$0.233526\pi$
$349$			25.0176i			1.33916i	−0.742739	+	0.669581i	$0.766474\pi$
$350$	23.4875	−	6.12869i	1.25546	−	0.327592i
$351$		0			0
$352$	11.8890	+	22.8017i	0.633685	+	1.21533i
$353$			28.0893i			1.49504i	0.664238	+	0.747521i	$0.268756\pi$
$353$			28.0893i			1.49504i	−0.664238	+	0.747521i	$0.731244\pi$
$354$		0			0
$355$	26.5734	+	2.06413i	1.41037	+	0.109553i
$356$	−7.44741	+	7.99061i	−0.394712	+	0.423502i
$357$		0			0
$358$	17.0591	−	7.42021i	0.901603	−	0.392170i
$359$	−2.33768			−0.123378			−0.0616889	−	0.998095i	$-0.519649\pi$
$359$	−2.33768			−0.123378			−0.0616889	+	0.998095i	$0.519649\pi$
$360$		0			0
$361$	17.4859			0.920309
$362$	−9.04958	+	3.93629i	−0.475635	+	0.206887i
$363$		0			0
$364$	−9.24661	−	8.61803i	−0.484654	−	0.451708i
$365$	−2.28335	+	29.3956i	−0.119516	+	1.53864i
$366$		0			0
$367$		−	13.0584i		−	0.681641i	−0.940128	−	0.340821i	$-0.889295\pi$
$367$		−	13.0584i		−	0.681641i	0.940128	−	0.340821i	$-0.110705\pi$
$368$	21.3808	−	1.50646i	1.11455	−	0.0785299i
$369$		0			0
$370$	−6.81899	−	19.7300i	−0.354502	−	1.02571i
$371$		−	4.30312i		−	0.223407i
$372$		0			0
$373$	−1.70913			−0.0884952			−0.0442476	−	0.999021i	$-0.514089\pi$
$373$	−1.70913			−0.0884952			−0.0442476	+	0.999021i	$0.514089\pi$
$374$	−0.976675	−	2.24539i	−0.0505026	−	0.116106i
$375$		0			0
$376$	8.80904	−	24.9074i	0.454292	−	1.28450i
$377$		−	5.84908i		−	0.301243i
$378$		0			0
$379$			2.54678i			0.130819i	0.997859	+	0.0654095i	$0.0208354\pi$
$379$			2.54678i			0.130819i	−0.997859	+	0.0654095i	$0.979165\pi$
$380$	−3.72295	−	4.05243i	−0.190983	−	0.207885i
$381$		0			0
$382$	11.5667	+	26.5920i	0.591806	+	1.36057i
$383$		−	1.39555i		−	0.0713091i	−0.999364	−	0.0356545i	$-0.988648\pi$
$383$		−	1.39555i		−	0.0713091i	0.999364	−	0.0356545i	$-0.0113516\pi$
$384$		0			0
$385$	−34.7894	−	2.70232i	−1.77303	−	0.137723i
$386$	−26.0036	+	11.3108i	−1.32355	+	0.575703i
$387$		0			0
$388$	23.1100	+	21.5389i	1.17323	+	1.09347i
$389$		−	11.0433i		−	0.559920i	−0.960012	−	0.279960i	$-0.909679\pi$
$389$		−	11.0433i		−	0.559920i	0.960012	−	0.279960i	$-0.0903212\pi$
$390$		0			0
$391$	−2.04094			−0.103215
$392$	−12.7581	−	4.51218i	−0.644382	−	0.227900i
$393$		0			0
$394$	6.75427	+	15.5281i	0.340275	+	0.782296i
$395$	−31.1385	−	2.41873i	−1.56675	−	0.121700i
$396$		0			0
$397$	−3.71757			−0.186579			−0.0932897	−	0.995639i	$-0.529738\pi$
$397$	−3.71757			−0.186579			−0.0932897	+	0.995639i	$0.529738\pi$
$398$	2.73492	+	6.28762i	0.137089	+	0.315170i
$399$		0			0
$400$	1.69196	−	19.9283i	0.0845981	−	0.996415i
$401$	−35.6317			−1.77936			−0.889682	−	0.456581i	$-0.849074\pi$
$401$	−35.6317			−1.77936			−0.889682	+	0.456581i	$0.849074\pi$
$402$		0			0
$403$	−12.6887			−0.632071
$404$	1.71276	+	1.59633i	0.0852129	+	0.0794202i
$405$		0			0
$406$	−6.15214	−	14.1438i	−0.305326	−	0.701947i
$407$			30.0083i			1.48746i
$408$		0			0
$409$	15.3487			0.758942			0.379471	−	0.925204i	$-0.376106\pi$
$409$	15.3487			0.758942			0.379471	+	0.925204i	$0.376106\pi$
$410$	−11.2660	−	32.5970i	−0.556389	−	1.60985i
$411$		0			0
$412$	−7.72487	−	7.19974i	−0.380577	−	0.354706i
$413$	11.4936			0.565564
$414$		0			0
$415$	−0.535230	−	0.0415748i	−0.0262734	−	0.00204083i
$416$	−9.23458	+	4.81499i	−0.452763	+	0.236074i
$417$		0			0
$418$	3.15530	+	7.25407i	0.154331	+	0.354808i
$419$			36.6779i			1.79183i	0.444225	+	0.895915i	$0.353479\pi$
$419$			36.6779i			1.79183i	−0.444225	+	0.895915i	$0.646521\pi$
$420$		0			0
$421$			32.9449i			1.60564i	0.596224	+	0.802818i	$0.296667\pi$
$421$			32.9449i			1.60564i	−0.596224	+	0.802818i	$0.703333\pi$
$422$	−5.86839	+	2.55257i	−0.285669	+	0.124257i
$423$		0			0
$424$	−3.34258	−	1.18217i	−0.162330	−	0.0574115i
$425$	−0.294082	+	1.88157i	−0.0142651	+	0.0912694i
$426$		0			0
$427$	−26.5734			−1.28598
$428$	19.5845	−	21.0129i	0.946650	−	1.01570i
$429$		0			0
$430$	−7.58412	−	21.9438i	−0.365739	−	1.05822i
$431$	11.2004			0.539506			0.269753	−	0.962930i	$-0.413058\pi$
$431$	11.2004			0.539506			0.269753	+	0.962930i	$0.413058\pi$
$432$		0			0
$433$			21.0312i			1.01070i	0.862915	+	0.505349i	$0.168636\pi$
$433$			21.0312i			1.01070i	−0.862915	+	0.505349i	$0.831364\pi$
$434$	−30.6830	+	13.3462i	−1.47283	+	0.640638i
$435$		0			0
$436$	19.7506	+	18.4080i	0.945882	+	0.881581i
$437$	6.59356			0.315413
$438$		0			0
$439$	−24.7231			−1.17997			−0.589984	−	0.807415i	$-0.700866\pi$
$439$	−24.7231			−1.17997			−0.589984	+	0.807415i	$0.700866\pi$
$440$	−11.6566	+	26.2813i	−0.555707	+	1.25291i
$441$		0			0
$442$	0.909371	−	0.395549i	0.0432544	−	0.0188144i
$443$	−23.5616			−1.11944			−0.559722	−	0.828681i	$-0.689092\pi$
$443$	−23.5616			−1.11944			−0.559722	+	0.828681i	$0.689092\pi$
$444$		0			0
$445$	−12.1757	−	0.945768i	−0.577184	−	0.0448337i
$446$	23.2690	−	10.1213i	1.10182	−	0.479259i
$447$		0			0
$448$	−17.2660	+	21.3563i	−0.815740	+	1.00899i
$449$	3.28586			0.155069			0.0775347	−	0.996990i	$-0.475295\pi$
$449$	3.28586			0.155069			0.0775347	+	0.996990i	$0.475295\pi$
$450$		0			0
$451$			49.5784i			2.33455i
$452$	1.86015	+	1.73370i	0.0874940	+	0.0815462i
$453$		0			0
$454$	5.16563	+	11.8758i	0.242435	+	0.557361i
$455$	1.09443	−	14.0895i	0.0513076	−	0.660528i
$456$		0			0
$457$		−	16.7754i		−	0.784718i	−0.919812	−	0.392359i	$-0.871659\pi$
$457$		−	16.7754i		−	0.784718i	0.919812	−	0.392359i	$-0.128341\pi$
$458$	21.6874	−	9.43335i	1.01338	−	0.440791i
$459$		0			0
$460$	16.2123	+	17.6471i	0.755903	+	0.822800i
$461$			41.9007i			1.95151i	0.218862	+	0.975756i	$0.429765\pi$
$461$			41.9007i			1.95151i	−0.218862	+	0.975756i	$0.570235\pi$
$462$		0			0
$463$			18.0770i			0.840110i	0.907499	+	0.420055i	$0.137989\pi$
$463$			18.0770i			0.840110i	−0.907499	+	0.420055i	$0.862011\pi$
$464$	−12.6768	+	0.893191i	−0.588505	+	0.0414654i
$465$		0			0
$466$	−25.8212	+	11.2314i	−1.19614	+	0.520286i
$467$	10.7324			0.496637			0.248318	−	0.968678i	$-0.420122\pi$
$467$	10.7324			0.496637			0.248318	+	0.968678i	$0.420122\pi$
$468$		0			0
$469$		−	45.9000i		−	2.11947i
$470$	27.9173	−	9.64866i	1.28773	−	0.445059i
$471$		0			0
$472$	3.15758	−	8.92800i	0.145339	−	0.410945i
$473$			33.3754i			1.53460i
$474$		0			0
$475$	0.950077	−	6.07869i	0.0435925	−	0.278910i
$476$	1.78293	−	1.91298i	0.0817207	−	0.0876812i
$477$		0			0
$478$	7.13953	+	16.4139i	0.326555	+	0.750752i
$479$	22.9582			1.04899			0.524494	−	0.851414i	$-0.324255\pi$
$479$	22.9582			1.04899			0.524494	+	0.851414i	$0.324255\pi$
$480$		0			0
$481$	−12.1532			−0.554140
$482$	−5.74149	−	13.1997i	−0.261518	−	0.601232i
$483$		0			0
$484$	13.1786	−	14.1399i	0.599029	−	0.642721i
$485$	−2.73529	+	35.2138i	−0.124203	+	1.59898i
$486$		0			0
$487$		−	19.4455i		−	0.881158i	−0.897714	−	0.440579i	$-0.854773\pi$
$487$		−	19.4455i		−	0.881158i	0.897714	−	0.440579i	$-0.145227\pi$
$488$	−7.30037	+	20.6417i	−0.330472	+	0.934404i
$489$		0			0
$490$	−4.94225	−	14.2998i	−0.223268	−	0.646001i
$491$			13.8438i			0.624761i	0.949957	+	0.312380i	$0.101126\pi$
$491$			13.8438i			0.624761i	−0.949957	+	0.312380i	$0.898874\pi$
$492$		0			0
$493$	1.21008			0.0544994
$494$	−2.93787	+	1.27788i	−0.132181	+	0.0574947i
$495$		0			0
$496$	1.93765	+	27.5005i	0.0870031	+	1.23481i
$497$		−	40.9188i		−	1.83546i
$498$		0			0
$499$			19.2551i			0.861975i	0.902358	+	0.430987i	$0.141835\pi$
$499$			19.2551i			0.861975i	−0.902358	+	0.430987i	$0.858165\pi$
$500$	18.6052	−	12.4035i	0.832048	−	0.554704i
$501$		0			0
$502$	−0.654940	+	0.284879i	−0.0292314	+	0.0127148i
$503$		−	16.4180i		−	0.732043i	−0.930606	−	0.366021i	$-0.880720\pi$
$503$		−	16.4180i		−	0.732043i	0.930606	−	0.366021i	$-0.119280\pi$
$504$		0			0
$505$	−0.202722	+	2.60982i	−0.00902100	+	0.116135i
$506$	−13.7404	−	31.5893i	−0.610834	−	1.40431i
$507$		0			0
$508$	−8.92903	−	8.32204i	−0.396162	−	0.369231i
$509$			16.1542i			0.716022i	0.933717	+	0.358011i	$0.116545\pi$
$509$			16.1542i			0.716022i	−0.933717	+	0.358011i	$0.883455\pi$
$510$		0			0
$511$	45.2646			2.00239
$512$	11.8458	+	19.2789i	0.523514	+	0.852017i
$513$		0			0
$514$	13.1887	−	5.73667i	0.581727	−	0.253034i
$515$	0.914315	−	11.7708i	0.0402895	−	0.518683i
$516$		0			0
$517$	−42.4608			−1.86742
$518$	−29.3881	+	12.7829i	−1.29124	+	0.561650i
$519$		0			0
$520$	−10.6438	−	4.72088i	−0.466761	−	0.207024i
$521$	32.1970			1.41058			0.705289	−	0.708920i	$-0.250817\pi$
$521$	32.1970			1.41058			0.705289	+	0.708920i	$0.250817\pi$
$522$		0			0
$523$	−17.9562			−0.785168			−0.392584	−	0.919716i	$-0.628419\pi$
$523$	−17.9562			−0.785168			−0.392584	+	0.919716i	$0.628419\pi$
$524$	−3.80646	−	3.54770i	−0.166286	−	0.154982i
$525$		0			0
$526$	9.78432	−	4.25588i	0.426617	−	0.185565i
$527$		−	2.62510i		−	0.114351i
$528$		0			0
$529$	−5.71296			−0.248390
$530$	−1.29485	−	3.74650i	−0.0562447	−	0.162738i
$531$		0			0
$532$	−5.76005	+	6.18017i	−0.249730	+	0.267945i
$533$	−20.0790			−0.869719
$534$		0			0
$535$	32.0184	+	2.48708i	1.38428	+	0.107526i
$536$	−35.6542	−	12.6099i	−1.54003	−	0.544664i
$537$		0			0
$538$	−34.6862	+	15.0874i	−1.49543	+	0.650466i
$539$			21.7494i			0.936811i
$540$		0			0
$541$		−	10.2986i		−	0.442769i	−0.975187	−	0.221385i	$-0.928942\pi$
$541$		−	10.2986i		−	0.442769i	0.975187	−	0.221385i	$-0.0710577\pi$
$542$	0.609662	+	1.40162i	0.0261872	+	0.0602047i
$543$		0			0
$544$	−0.996145	−	1.91049i	−0.0427094	−	0.0819116i
$545$	−2.33768	+	30.0950i	−0.100135	+	1.28913i
$546$		0			0
$547$	−4.11366			−0.175887			−0.0879436	−	0.996125i	$-0.528030\pi$
$547$	−4.11366			−0.175887			−0.0879436	+	0.996125i	$0.528030\pi$
$548$	−11.0932	−	10.3391i	−0.473879	−	0.441665i
$549$		0			0
$550$	−31.1024	+	8.11569i	−1.32621	+	0.346054i
$551$	−3.90936			−0.166544
$552$		0			0
$553$			47.9484i			2.03897i
$554$	11.5270	+	26.5008i	0.489737	+	1.12591i
$555$		0			0
$556$	−21.5509	−	20.0859i	−0.913962	−	0.851831i
$557$	−38.9282			−1.64944			−0.824720	−	0.565541i	$-0.808667\pi$
$557$	−38.9282			−1.64944			−0.824720	+	0.565541i	$0.808667\pi$
$558$		0			0
$559$	−13.5169			−0.571704
$560$	−30.7036	−	0.220406i	−1.29746	−	0.00931384i
$561$		0			0
$562$	−7.78570	−	17.8994i	−0.328420	−	0.755041i
$563$	17.6860			0.745376			0.372688	−	0.927957i	$-0.378436\pi$
$563$	17.6860			0.745376			0.372688	+	0.927957i	$0.378436\pi$
$564$		0			0
$565$	−0.220167	+	2.83440i	−0.00926249	+	0.119244i
$566$	−7.44741	−	17.1217i	−0.313038	−	0.719678i
$567$		0			0
$568$	−31.7849	−	11.2414i	−1.33366	−	0.471680i
$569$	34.8288			1.46010			0.730050	−	0.683394i	$-0.239497\pi$
$569$	34.8288			1.46010			0.730050	+	0.683394i	$0.239497\pi$
$570$		0			0
$571$		−	38.1648i		−	1.59715i	−0.601897	−	0.798574i	$-0.705588\pi$
$571$		−	38.1648i		−	1.59715i	0.601897	−	0.798574i	$-0.294412\pi$
$572$	12.2445	+	11.4121i	0.511968	+	0.477164i
$573$		0			0
$574$	−48.5537	+	21.1194i	−2.02659	+	0.881506i
$575$	−4.13730	+	26.4709i	−0.172537	+	1.10391i
$576$		0			0
$577$			7.46877i			0.310929i	0.987841	+	0.155464i	$0.0496874\pi$
$577$			7.46877i			0.310929i	−0.987841	+	0.155464i	$0.950313\pi$
$578$	−9.50766	−	21.8582i	−0.395467	−	0.909182i
$579$		0			0
$580$	−9.61237	−	10.4631i	−0.399132	−	0.434455i
$581$			0.824169i			0.0341923i
$582$		0			0
$583$			5.69825i			0.235997i
$584$	12.4353	−	35.1606i	0.514577	−	1.45496i
$585$		0			0
$586$	−4.91580	−	11.3015i	−0.203070	−	0.466859i
$587$	42.8633			1.76916			0.884579	−	0.466390i	$-0.154446\pi$
$587$	42.8633			1.76916			0.884579	+	0.466390i	$0.154446\pi$
$588$		0			0
$589$			8.48079i			0.349445i
$590$	10.0069	−	3.45854i	0.411977	−	0.142386i
$591$		0			0
$592$	1.85587	+	26.3398i	0.0762760	+	1.08256i
$593$		−	29.3122i		−	1.20371i	−0.798606	−	0.601854i	$-0.794429\pi$
$593$		−	29.3122i		−	1.20371i	0.798606	−	0.601854i	$-0.205571\pi$
$594$		0			0
$595$	2.91490	+	0.226420i	0.119499	+	0.00928231i
$596$	23.5255	+	21.9262i	0.963641	+	0.898133i
$597$		0			0
$598$	12.7935	−	5.56479i	0.523166	−	0.227561i
$599$	1.14551			0.0468045			0.0234022	−	0.999726i	$-0.492550\pi$
$599$	1.14551			0.0468045			0.0234022	+	0.999726i	$0.492550\pi$
$600$		0			0
$601$	−24.9257			−1.01674			−0.508369	−	0.861139i	$-0.669752\pi$
$601$	−24.9257			−1.01674			−0.508369	+	0.861139i	$0.669752\pi$
$602$	−32.6856	+	14.2173i	−1.33217	+	0.579452i
$603$		0			0
$604$	−13.0114	+	13.9604i	−0.529427	+	0.568042i
$605$	21.5456	+	1.67359i	0.875954	+	0.0680411i
$606$		0			0
$607$		−	36.6255i		−	1.48658i	−0.668967	−	0.743292i	$-0.733263\pi$
$607$		−	36.6255i		−	1.48658i	0.668967	−	0.743292i	$-0.266737\pi$
$608$	3.21820	+	6.17213i	0.130515	+	0.250313i
$609$		0			0
$610$	−23.1361	+	7.99619i	−0.936752	+	0.323756i
$611$		−	17.1964i		−	0.695694i
$612$		0			0
$613$	−21.2185			−0.857008			−0.428504	−	0.903540i	$-0.640959\pi$
$613$	−21.2185			−0.857008			−0.428504	+	0.903540i	$0.640959\pi$
$614$	14.4355	+	33.1873i	0.582568	+	1.33933i
$615$		0			0
$616$	41.6122	+	14.7170i	1.67660	+	0.592967i
$617$		−	24.8607i		−	1.00085i	−0.865779	−	0.500427i	$-0.833176\pi$
$617$		−	24.8607i		−	1.00085i	0.865779	−	0.500427i	$-0.166824\pi$
$618$		0			0
$619$		−	26.8914i		−	1.08085i	−0.841391	−	0.540427i	$-0.818263\pi$
$619$		−	26.8914i		−	1.08085i	0.841391	−	0.540427i	$-0.181737\pi$
$620$	−22.6981	+	20.8527i	−0.911578	+	0.837463i
$621$		0			0
$622$	−8.52325	−	19.5950i	−0.341751	−	0.785690i
$623$			18.7487i			0.751150i
$624$		0			0
$625$	23.8077	+	7.62846i	0.952308	+	0.305138i
$626$	1.29493	−	0.563257i	0.0517560	−	0.0225123i
$627$		0			0
$628$	−21.5339	+	23.1045i	−0.859296	+	0.921971i
$629$		−	2.51431i		−	0.100252i
$630$		0			0
$631$	−18.5902			−0.740064			−0.370032	−	0.929019i	$-0.620653\pi$
$631$	−18.5902			−0.740064			−0.370032	+	0.929019i	$0.620653\pi$
$632$	37.2453	+	13.1726i	1.48154	+	0.523978i
$633$		0			0
$634$	−6.01671	−	13.8325i	−0.238954	−	0.549358i
$635$	1.05684	−	13.6056i	0.0419393	−	0.539923i
$636$		0			0
$637$	−8.80840			−0.349001
$638$	8.14674	+	18.7294i	0.322533	+	0.741506i
$639$		0			0
$640$	−8.60624	+	23.7893i	−0.340192	+	0.940356i
$641$	−15.7138			−0.620657			−0.310329	−	0.950629i	$-0.600439\pi$
$641$	−15.7138			−0.620657			−0.310329	+	0.950629i	$0.600439\pi$
$642$		0			0
$643$	−2.83175			−0.111673			−0.0558367	−	0.998440i	$-0.517783\pi$
$643$	−2.83175			−0.111673			−0.0558367	+	0.998440i	$0.517783\pi$
$644$	25.0833	−	26.9128i	0.988419	−	1.06051i
$645$		0			0
$646$	−0.264374	−	0.607798i	−0.0104016	−	0.0239135i
$647$			5.42874i			0.213426i	0.994290	+	0.106713i	$0.0340326\pi$
$647$			5.42874i			0.213426i	−0.994290	+	0.106713i	$0.965967\pi$
$648$		0			0
$649$	−15.2200			−0.597437
$650$	−3.28682	−	12.5964i	−0.128920	−	0.494070i
$651$		0			0
$652$	−13.9123	+	14.9271i	−0.544849	+	0.584589i
$653$	8.53141			0.333860			0.166930	−	0.985969i	$-0.446615\pi$
$653$	8.53141			0.333860			0.166930	+	0.985969i	$0.446615\pi$
$654$		0			0
$655$	0.450532	−	5.80010i	0.0176037	−	0.226629i
$656$	3.06619	+	43.5175i	0.119715	+	1.69907i
$657$		0			0
$658$	−18.0875	−	41.5832i	−0.705122	−	1.62108i
$659$			44.1441i			1.71961i	0.510624	+	0.859804i	$0.329415\pi$
$659$			44.1441i			1.71961i	−0.510624	+	0.859804i	$0.670585\pi$
$660$		0			0
$661$		−	33.6110i		−	1.30732i	−0.756790	−	0.653658i	$-0.773233\pi$
$661$		−	33.6110i		−	1.30732i	0.756790	−	0.653658i	$-0.226767\pi$
$662$	−39.8059	+	17.3143i	−1.54710	+	0.672941i
$663$		0			0
$664$	0.640197	+	0.226420i	0.0248445	+	0.00878679i
$665$	−9.41705	−	0.731484i	−0.365177	−	0.0283657i
$666$		0			0
$667$	17.0241			0.659175
$668$	−31.5711	−	29.4249i	−1.22152	−	1.13848i
$669$		0			0
$670$	−13.8118	−	39.9628i	−0.533595	−	1.54390i
$671$	35.1888			1.35845
$672$		0			0
$673$			39.4998i			1.52260i	0.648397	+	0.761302i	$0.275440\pi$
$673$			39.4998i			1.52260i	−0.648397	+	0.761302i	$0.724560\pi$
$674$	−26.5666	+	11.5557i	−1.02331	+	0.445107i
$675$		0			0
$676$	13.1051	−	14.0609i	0.504041	−	0.540805i
$677$	11.9738			0.460190			0.230095	−	0.973168i	$-0.426096\pi$
$677$	11.9738			0.460190			0.230095	+	0.973168i	$0.426096\pi$
$678$		0			0
$679$	54.2237			2.08092
$680$	0.976675	−	2.20203i	0.0374538	−	0.0844441i
$681$		0			0
$682$	40.6308	−	17.6732i	1.55584	−	0.676741i
$683$	9.89137			0.378483			0.189241	−	0.981931i	$-0.439397\pi$
$683$	9.89137			0.378483			0.189241	+	0.981931i	$0.439397\pi$
$684$		0			0
$685$	1.31299	−	16.9033i	0.0501668	−	0.645842i
$686$	9.86326	−	4.29022i	0.376581	−	0.163801i
$687$		0			0
$688$	2.06412	+	29.2954i	0.0786937	+	1.11687i
$689$	−2.30777			−0.0879189
$690$		0			0
$691$			41.3777i			1.57408i	0.616901	+	0.787041i	$0.288388\pi$
$691$			41.3777i			1.57408i	−0.616901	+	0.787041i	$0.711612\pi$
$692$	14.5446	−	15.6055i	0.552904	−	0.593231i
$693$		0			0
$694$	−5.02076	−	11.5428i	−0.190586	−	0.438158i
$695$	2.55076	−	32.8382i	0.0967559	−	1.24562i
$696$		0			0
$697$		−	4.15403i		−	0.157345i
$698$	32.4440	−	14.1121i	1.22802	−	0.534152i
$699$		0			0
$700$	−21.1970	−	27.0025i	−0.801170	−	1.02060i
$701$		−	23.7759i		−	0.898002i	−0.893531	−	0.449001i	$-0.851780\pi$
$701$		−	23.7759i		−	0.898002i	0.893531	−	0.449001i	$-0.148220\pi$
$702$		0			0
$703$			8.12287i			0.306360i
$704$	22.8638	−	28.2803i	0.861712	−	1.06585i
$705$		0			0
$706$	36.4274	−	15.8448i	1.37096	−	0.596328i
$707$	4.01871			0.151139
$708$		0			0
$709$			43.5357i			1.63502i	0.575916	+	0.817509i	$0.304645\pi$
$709$			43.5357i			1.63502i	−0.575916	+	0.817509i	$0.695355\pi$
$710$	−12.3129	−	35.6259i	−0.462094	−	1.33702i
$711$		0			0
$712$	14.5636	+	5.15073i	0.545793	+	0.193032i
$713$		−	36.9313i		−	1.38309i
$714$		0			0
$715$	−1.44925	+	18.6575i	−0.0541991	+	0.697753i
$716$	−19.2457	−	17.9374i	−0.719246	−	0.670352i
$717$		0			0
$718$	1.31866	+	3.03160i	0.0492118	+	0.113138i
$719$	−25.4579			−0.949419			−0.474710	−	0.880142i	$-0.657447\pi$
$719$	−25.4579			−0.949419			−0.474710	+	0.880142i	$0.657447\pi$
$720$		0			0
$721$	−18.1252			−0.675016
$722$	−9.86357	−	22.6765i	−0.367084	−	0.843930i
$723$		0			0
$724$	10.2095	+	9.51548i	0.379434	+	0.353640i
$725$	2.45303	−	15.6947i	0.0911031	−	0.582887i
$726$		0			0
$727$		−	21.3528i		−	0.791931i	−0.918265	−	0.395966i	$-0.870410\pi$
$727$		−	21.3528i		−	0.791931i	0.918265	−	0.395966i	$-0.129590\pi$
$728$	−5.96034	+	16.8527i	−0.220905	+	0.624604i
$729$		0			0
$730$	39.4095	−	13.6206i	1.45861	−	0.504120i
$731$		−	2.79643i		−	0.103430i
$732$		0			0
$733$	1.07066			0.0395458			0.0197729	−	0.999804i	$-0.493706\pi$
$733$	1.07066			0.0395458			0.0197729	+	0.999804i	$0.493706\pi$
$734$	−16.9347	+	7.36607i	−0.625070	+	0.271886i
$735$		0			0
$736$	−14.0143	−	26.8778i	−0.516574	−	0.990728i
$737$			60.7814i			2.23891i
$738$		0			0
$739$			7.07190i			0.260144i	0.991505	+	0.130072i	$0.0415209\pi$
$739$			7.07190i			0.260144i	−0.991505	+	0.130072i	$0.958479\pi$
$740$	−21.7402	+	19.9726i	−0.799185	+	0.734207i
$741$		0			0
$742$	−5.58048	+	2.42734i	−0.204866	+	0.0891104i
$743$		−	36.3668i		−	1.33417i	−0.744983	−	0.667083i	$-0.767542\pi$
$743$		−	36.3668i		−	1.33417i	0.744983	−	0.667083i	$-0.232458\pi$
$744$		0			0
$745$	−2.78447	+	35.8470i	−0.102015	+	1.31333i
$746$	0.964097	+	2.21647i	0.0352981	+	0.0811507i
$747$		0			0
$748$	−2.36098	+	2.53319i	−0.0863261	+	0.0926226i
$749$		−	49.3034i		−	1.80151i
$750$		0			0
$751$	−39.0768			−1.42593			−0.712965	−	0.701199i	$-0.752648\pi$
$751$	−39.0768			−1.42593			−0.712965	+	0.701199i	$0.752648\pi$
$752$	−37.2701	+	2.62600i	−1.35910	+	0.0957605i
$753$		0			0
$754$	−7.58535	+	3.29940i	−0.276242	+	0.120157i
$755$	−21.2722	−	1.65236i	−0.774176	−	0.0601354i
$756$		0			0
$757$	−24.7984			−0.901312			−0.450656	−	0.892698i	$-0.648810\pi$
$757$	−24.7984			−0.901312			−0.450656	+	0.892698i	$0.648810\pi$
$758$	3.30277	−	1.43661i	0.119962	−	0.0521799i
$759$		0			0
$760$	−3.15530	+	7.11401i	−0.114455	+	0.258052i
$761$	18.5436			0.672204			0.336102	−	0.941826i	$-0.390891\pi$
$761$	18.5436			0.672204			0.336102	+	0.941826i	$0.390891\pi$
$762$		0			0
$763$	46.3416			1.67768
$764$	27.9611	−	30.0005i	1.01160	−	1.08538i
$765$		0			0
$766$	−1.80981	+	0.787211i	−0.0653910	+	0.0284431i
$767$		−	6.16403i		−	0.222570i
$768$		0			0
$769$	33.2796			1.20009			0.600046	−	0.799966i	$-0.295149\pi$
$769$	33.2796			1.20009			0.600046	+	0.799966i	$0.295149\pi$
$770$	16.1198	+	46.6407i	0.580916	+	1.68081i
$771$		0			0
$772$	29.3366	+	27.3423i	1.05585	+	0.984071i
$773$	38.3940			1.38094			0.690468	−	0.723363i	$-0.257404\pi$
$773$	38.3940			1.38094			0.690468	+	0.723363i	$0.257404\pi$
$774$		0			0
$775$	−34.0475	−	5.32149i	−1.22302	−	0.191154i
$776$	14.8966	−	42.1199i	0.534757	−	1.51202i
$777$		0			0
$778$	−14.3215	+	6.22942i	−0.513450	+	0.223335i
$779$			13.4202i			0.480830i
$780$		0			0
$781$			54.1852i			1.93890i
$782$	1.15127	+	2.64678i	0.0411692	+	0.0946485i
$783$		0			0
$784$	1.34510	+	19.0906i	0.0480392	+	0.681805i
$785$	−35.2056	−	2.73465i	−1.25654	−	0.0976038i
$786$		0			0
$787$	14.5217			0.517641			0.258821	−	0.965925i	$-0.416666\pi$
$787$	14.5217			0.517641			0.258821	+	0.965925i	$0.416666\pi$
$788$	16.3276	−	17.5185i	0.581645	−	0.624069i
$789$		0			0
$790$	14.4281	+	41.7462i	0.513330	+	1.48526i
$791$	4.36454			0.155185
$792$		0			0
$793$			14.2513i			0.506079i
$794$	2.09704	+	4.82111i	0.0744210	+	0.171095i
$795$		0			0
$796$	6.61132	−	7.09354i	0.234332	−	0.251424i
$797$	−46.0244			−1.63027			−0.815135	−	0.579272i	$-0.803337\pi$
$797$	−46.0244			−1.63027			−0.815135	+	0.579272i	$0.803337\pi$
$798$		0			0
$799$	3.55767			0.125861
$800$	−26.7983	+	9.04711i	−0.947464	+	0.319863i
$801$		0			0
$802$	20.0994	+	46.2088i	0.709735	+	1.63169i
$803$	−59.9400			−2.11524
$804$		0			0
$805$	41.0084	+	3.18539i	1.44536	+	0.112270i
$806$	7.15757	+	16.4553i	0.252115	+	0.579614i
$807$		0			0
$808$	1.10404	−	3.12165i	0.0388400	−	0.109819i
$809$	32.1311			1.12967			0.564835	−	0.825204i	$-0.308940\pi$
$809$	32.1311			1.12967			0.564835	+	0.825204i	$0.308940\pi$
$810$		0			0
$811$		−	16.4431i		−	0.577394i	−0.957420	−	0.288697i	$-0.906778\pi$
$811$		−	16.4431i		−	0.577394i	0.957420	−	0.288697i	$-0.0932221\pi$
$812$	−14.8720	+	15.9567i	−0.521905	+	0.559972i
$813$		0			0
$814$	38.9161	−	16.9273i	1.36401	−	0.593302i
$815$	−22.7451	−	1.76676i	−0.796727	−	0.0618871i
$816$		0			0
$817$			9.03431i			0.316071i
$818$	−8.65799	−	19.9048i	−0.302720	−	0.695956i
$819$		0			0
$820$	−35.9181	+	32.9978i	−1.25432	+	1.15233i
$821$		−	10.7849i		−	0.376394i	−0.982131	−	0.188197i	$-0.939736\pi$
$821$		−	10.7849i		−	0.376394i	0.982131	−	0.188197i	$-0.0602644\pi$
$822$		0			0
$823$		−	15.2340i		−	0.531025i	−0.964107	−	0.265513i	$-0.914459\pi$
$823$		−	15.2340i		−	0.531025i	0.964107	−	0.265513i	$-0.0855412\pi$
$824$	−4.97943	+	14.0792i	−0.173467	+	0.490474i
$825$		0			0
$826$	−6.48341	−	14.9054i	−0.225587	−	0.518626i
$827$	7.79857			0.271183			0.135591	−	0.990765i	$-0.456707\pi$
$827$	7.79857			0.271183			0.135591	+	0.990765i	$0.456707\pi$
$828$		0			0
$829$		−	15.8397i		−	0.550137i	−0.961425	−	0.275068i	$-0.911299\pi$
$829$		−	15.8397i		−	0.550137i	0.961425	−	0.275068i	$-0.0887005\pi$
$830$	0.248001	+	0.717561i	0.00860822	+	0.0249069i
$831$		0			0
$832$	11.4534	+	9.25974i	0.397075	+	0.321024i
$833$		−	1.82232i		−	0.0631396i
$834$		0			0
$835$	3.73675	−	48.1065i	0.129316	−	1.66480i
$836$	7.62753	−	8.18386i	0.263804	−	0.283045i
$837$		0			0
$838$	47.5655	−	20.6895i	1.64312	−	0.714708i
$839$	−35.4996			−1.22558			−0.612792	−	0.790244i	$-0.709954\pi$
$839$	−35.4996			−1.22558			−0.612792	+	0.790244i	$0.709954\pi$
$840$		0			0
$841$	18.9063			0.651942
$842$	42.7244	−	18.5838i	1.47238	−	0.640441i
$843$		0			0
$844$	6.62057	+	6.17051i	0.227889	+	0.212398i
$845$	21.4254	+	1.66425i	0.737055	+	0.0572519i
$846$		0			0
$847$		−	33.1769i		−	1.13997i
$848$	0.352410	+	5.00165i	0.0121018	+	0.171757i
$849$		0			0
$850$	2.60599	−	0.679991i	0.0893846	−	0.0233235i
$851$		−	35.3727i		−	1.21256i
$852$		0			0
$853$	13.8706			0.474921			0.237460	−	0.971397i	$-0.423685\pi$
$853$	13.8706			0.474921			0.237460	+	0.971397i	$0.423685\pi$
$854$	14.9897	+	34.4616i	0.512938	+	1.17925i
$855$		0			0
$856$	−38.2978	−	13.5449i	−1.30899	−	0.462954i
$857$			18.2093i			0.622017i	0.950407	+	0.311009i	$0.100667\pi$
$857$			18.2093i			0.622017i	−0.950407	+	0.311009i	$0.899333\pi$
$858$		0			0
$859$			4.07229i			0.138945i	0.997584	+	0.0694723i	$0.0221316\pi$
$859$			4.07229i			0.138945i	−0.997584	+	0.0694723i	$0.977868\pi$
$860$	−24.1796	+	22.2137i	−0.824516	+	0.757479i
$861$		0			0
$862$	−6.31803	−	14.5252i	−0.215193	−	0.494731i
$863$			45.5027i			1.54893i	0.632616	+	0.774465i	$0.281981\pi$
$863$			45.5027i			1.54893i	−0.632616	+	0.774465i	$0.718019\pi$
$864$		0			0
$865$	23.7789	+	1.84706i	0.808506	+	0.0628020i
$866$	27.2742	−	11.8635i	0.926817	−	0.403137i
$867$		0			0
$868$	34.6159	+	32.2627i	1.17494	+	1.09507i
$869$		−	63.4938i		−	2.15388i
$870$		0			0
$871$	−24.6162			−0.834088
$872$	12.7312	−	35.9972i	0.431132	−	1.21902i
$873$		0			0
$874$	−3.71935	−	8.55082i	−0.125809	−	0.289236i
$875$	8.84562	−	37.3472i	0.299037	−	1.26257i
$876$		0			0
$877$	8.98596			0.303434			0.151717	−	0.988424i	$-0.451520\pi$
$877$	8.98596			0.303434			0.151717	+	0.988424i	$0.451520\pi$
$878$	13.9460	+	32.0620i	0.470654	+	1.08204i
$879$		0			0
$880$	40.6580	+	0.291864i	1.37058	+	0.00983873i
$881$	−11.1213			−0.374687			−0.187343	−	0.982294i	$-0.559988\pi$
$881$	−11.1213			−0.374687			−0.187343	+	0.982294i	$0.559988\pi$
$882$		0			0
$883$	36.3281			1.22254			0.611270	−	0.791422i	$-0.290659\pi$
$883$	36.3281			1.22254			0.611270	+	0.791422i	$0.290659\pi$
$884$	−1.02593	−	0.956189i	−0.0345058	−	0.0321601i
$885$		0			0
$886$	13.2908	+	30.5557i	0.446513	+	1.02654i
$887$			31.1655i			1.04644i	0.852199	+	0.523218i	$0.175269\pi$
$887$			31.1655i			1.04644i	−0.852199	+	0.523218i	$0.824731\pi$
$888$		0			0
$889$	−20.9505			−0.702658
$890$	5.64166	+	16.3235i	0.189109	+	0.547165i
$891$		0			0
$892$	−26.2516	−	24.4670i	−0.878968	−	0.819216i
$893$	−11.4936			−0.384619
$894$		0			0
$895$	2.27792	−	29.3257i	0.0761424	−	0.980249i
$896$	37.4354	+	10.3444i	1.25063	+	0.345582i
$897$		0			0
$898$	−1.85352	−	4.26125i	−0.0618526	−	0.142200i
$899$			21.8968i			0.730298i
$900$		0			0
$901$		−	0.477440i		−	0.0159058i
$902$	64.2954	−	27.9666i	2.14080	−	0.931185i
$903$		0			0
$904$	1.19905	−	3.39028i	0.0398797	−	0.112759i
$905$	−1.20840	+	15.5568i	−0.0401685	+	0.517124i
$906$		0			0
$907$	−50.2357			−1.66805			−0.834025	−	0.551727i	$-0.813969\pi$
$907$	−50.2357			−1.66805			−0.834025	+	0.551727i	$0.813969\pi$
$908$	12.4872	−	13.3980i	0.414404	−	0.444630i
$909$		0			0
$910$	−18.8893	+	6.52844i	−0.626174	+	0.216416i
$911$	−13.6535			−0.452359			−0.226180	−	0.974086i	$-0.572624\pi$
$911$	−13.6535			−0.452359			−0.226180	+	0.974086i	$0.572624\pi$
$912$		0			0
$913$		−	1.09138i		−	0.0361192i
$914$	−21.7550	+	9.46278i	−0.719592	+	0.313001i
$915$		0			0
$916$	−24.4672	−	22.8039i	−0.808418	−	0.753462i
$917$	−8.93124			−0.294935
$918$		0			0
$919$	4.21744			0.139121			0.0695603	−	0.997578i	$-0.477840\pi$
$919$	4.21744			0.139121			0.0695603	+	0.997578i	$0.477840\pi$
$920$	13.7404	−	30.9794i	0.453007	−	1.02136i
$921$		0			0
$922$	54.3387	−	23.6357i	1.78955	−	0.778400i
$923$	−21.9448			−0.722322
$924$		0			0
$925$	−32.6105	−	5.09690i	−1.07223	−	0.167585i
$926$	23.4431	−	10.1970i	0.770387	−	0.335095i
$927$		0			0
$928$	8.30915	+	15.9360i	0.272761	+	0.523124i
$929$	−28.7624			−0.943662			−0.471831	−	0.881689i	$-0.656407\pi$
$929$	−28.7624			−0.943662			−0.471831	+	0.881689i	$0.656407\pi$
$930$		0			0
$931$			5.88728i			0.192948i
$932$	29.1308	+	27.1505i	0.954213	+	0.889346i
$933$		0			0
$934$	−6.05403	−	13.9183i	−0.198094	−	0.455420i
$935$	−3.85995	−	0.299828i	−0.126234	−	0.00980542i
$936$		0			0
$937$			11.1055i			0.362801i	0.983409	+	0.181401i	$0.0580631\pi$
$937$			11.1055i			0.362801i	−0.983409	+	0.181401i	$0.941937\pi$
$938$	−59.5252	+	25.8917i	−1.94357	+	0.845393i
$939$		0			0
$940$	−28.2606	−	30.7617i	−0.921759	−	1.00334i
$941$		−	10.4300i		−	0.340007i	−0.985443	−	0.170004i	$-0.945622\pi$
$941$		−	10.4300i		−	0.340007i	0.985443	−	0.170004i	$-0.0543780\pi$
$942$		0			0
$943$		−	58.4411i		−	1.90310i
$944$	−13.3594	+	0.941286i	−0.434811	+	0.0306362i
$945$		0			0
$946$	43.2827	−	18.8267i	1.40724	−	0.612108i
$947$	0.894188			0.0290572			0.0145286	−	0.999894i	$-0.495375\pi$
$947$	0.894188			0.0290572			0.0145286	+	0.999894i	$0.495375\pi$
$948$		0			0
$949$		−	24.2754i		−	0.788014i
$950$	−8.41904	+	2.19682i	−0.273150	+	0.0712741i
$951$		0			0
$952$	−3.48657	−	1.23310i	−0.113000	−	0.0399650i
$953$			27.0628i			0.876650i	0.898817	+	0.438325i	$0.144428\pi$
$953$			27.0628i			0.876650i	−0.898817	+	0.438325i	$0.855572\pi$
$954$		0			0
$955$	45.7133	+	3.55085i	1.47925	+	0.114903i
$956$	17.2589	−	18.5177i	0.558192	−	0.598906i
$957$		0			0
$958$	−12.9505	−	29.7732i	−0.418410	−	0.961930i
$959$	−26.0284			−0.840502
$960$		0			0
$961$	16.5019			0.532319
$962$	6.85549	+	15.7608i	0.221030	+	0.508150i
$963$		0			0
$964$	−13.8793	+	14.8916i	−0.447022	+	0.479627i
$965$	−3.47227	+	44.7017i	−0.111776	+	1.43900i
$966$		0			0
$967$		−	26.0270i		−	0.836972i	−0.908223	−	0.418486i	$-0.862561\pi$
$967$		−	26.0270i		−	0.836972i	0.908223	−	0.418486i	$-0.137439\pi$
$968$	−25.7711	−	9.11451i	−0.828314	−	0.292951i
$969$		0			0
$970$	47.2098	−	16.3164i	1.51581	−	0.523890i
$971$		−	16.3396i		−	0.524362i	−0.965019	−	0.262181i	$-0.915558\pi$
$971$		−	16.3396i		−	0.524362i	0.965019	−	0.262181i	$-0.0844418\pi$
$972$		0			0
$973$	−50.5657			−1.62106
$974$	−25.2177	+	10.9689i	−0.808028	+	0.351468i
$975$		0			0
$976$	30.8871	−	2.17627i	0.988671	−	0.0696606i
$977$		−	49.7196i		−	1.59067i	−0.606170	−	0.795335i	$-0.707295\pi$
$977$		−	49.7196i		−	1.59067i	0.606170	−	0.795335i	$-0.292705\pi$
$978$		0			0
$979$		−	24.8272i		−	0.793481i
$980$	−15.7568	+	14.4757i	−0.503333	+	0.462409i
$981$		0			0
$982$	17.9532	−	7.80910i	0.572910	−	0.249199i
$983$		−	27.4242i		−	0.874697i	−0.899292	−	0.437348i	$-0.855918\pi$
$983$		−	27.4242i		−	0.874697i	0.899292	−	0.437348i	$-0.144082\pi$
$984$		0			0
$985$	26.6938	+	2.07348i	0.850535	+	0.0660666i
$986$	−0.682593	−	1.56929i	−0.0217382	−	0.0499763i
$987$		0			0
$988$	3.31443	+	3.08912i	0.105446	+	0.0982779i
$989$		−	39.3417i		−	1.25099i
$990$		0			0
$991$	−13.1016			−0.416187			−0.208093	−	0.978109i	$-0.566726\pi$
$991$	−13.1016			−0.416187			−0.208093	+	0.978109i	$0.566726\pi$
$992$	34.5708	−	18.0255i	1.09762	−	0.572311i
$993$		0			0
$994$	−53.0654	+	23.0818i	−1.68313	+	0.732111i
$995$	10.8088	+	0.839590i	0.342662	+	0.0266168i
$996$		0			0
$997$	14.5149			0.459692			0.229846	−	0.973227i	$-0.426178\pi$
$997$	14.5149			0.459692			0.229846	+	0.973227i	$0.426178\pi$
$998$	24.9708	−	10.8615i	0.790437	−	0.343816i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.i.109.9	✓	20
3.2	odd	2	inner	1080.2.d.i.109.12	yes	20
4.3	odd	2		4320.2.d.i.3889.1		20
5.4	even	2		1080.2.d.j.109.12	yes	20
8.3	odd	2		4320.2.d.j.3889.20		20
8.5	even	2		1080.2.d.j.109.11	yes	20
12.11	even	2		4320.2.d.i.3889.20		20
15.14	odd	2		1080.2.d.j.109.9	yes	20
20.19	odd	2		4320.2.d.j.3889.19		20
24.5	odd	2		1080.2.d.j.109.10	yes	20
24.11	even	2		4320.2.d.j.3889.1		20
40.19	odd	2		4320.2.d.i.3889.2		20
40.29	even	2	inner	1080.2.d.i.109.10	yes	20
60.59	even	2		4320.2.d.j.3889.2		20
120.29	odd	2	inner	1080.2.d.i.109.11	yes	20
120.59	even	2		4320.2.d.i.3889.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.i.109.9	✓	20	1.1	even	1	trivial
1080.2.d.i.109.10	yes	20	40.29	even	2	inner
1080.2.d.i.109.11	yes	20	120.29	odd	2	inner
1080.2.d.i.109.12	yes	20	3.2	odd	2	inner
1080.2.d.j.109.9	yes	20	15.14	odd	2
1080.2.d.j.109.10	yes	20	24.5	odd	2
1080.2.d.j.109.11	yes	20	8.5	even	2
1080.2.d.j.109.12	yes	20	5.4	even	2
4320.2.d.i.3889.1		20	4.3	odd	2
4320.2.d.i.3889.2		20	40.19	odd	2
4320.2.d.i.3889.19		20	120.59	even	2
4320.2.d.i.3889.20		20	12.11	even	2
4320.2.d.j.3889.1		20	24.11	even	2
4320.2.d.j.3889.2		20	60.59	even	2
4320.2.d.j.3889.19		20	20.19	odd	2
4320.2.d.j.3889.20		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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.564088 - 1.29684i) q^{2} +(-1.36361 + 1.46307i) q^{4} +(-2.22935 - 0.173169i) q^{5} +3.43285i q^{7} +(2.66657 + 0.943090i) q^{8} +O(q^{10})\)	\(q+(-0.564088 - 1.29684i) q^{2} +(-1.36361 + 1.46307i) q^{4} +(-2.22935 - 0.173169i) q^{5} +3.43285i q^{7} +(2.66657 + 0.943090i) q^{8} +(1.03298 + 2.98881i) q^{10} -4.54582i q^{11} +1.84104 q^{13} +(4.45187 - 1.93643i) q^{14} +(-0.281138 - 3.99011i) q^{16} +0.380882i q^{17} -1.23050i q^{19} +(3.29332 - 3.02556i) q^{20} +(-5.89523 + 2.56424i) q^{22} +5.35845i q^{23} +(4.94003 + 0.772107i) q^{25} +(-1.03851 - 2.38754i) q^{26} +(-5.02250 - 4.68107i) q^{28} -3.17705i q^{29} -6.89216 q^{31} +(-5.01596 + 2.61536i) q^{32} +(0.493945 - 0.214851i) q^{34} +(0.594462 - 7.65304i) q^{35} -6.60129 q^{37} +(-1.59576 + 0.694109i) q^{38} +(-5.78141 - 2.56424i) q^{40} -10.9064 q^{41} -7.34200 q^{43} +(6.65085 + 6.19873i) q^{44} +(6.94907 - 3.02264i) q^{46} -9.34062i q^{47} -4.78447 q^{49} +(-1.78531 - 6.84198i) q^{50} +(-2.51046 + 2.69357i) q^{52} -1.25351 q^{53} +(-0.787194 + 10.1342i) q^{55} +(-3.23749 + 9.15393i) q^{56} +(-4.12014 + 1.79214i) q^{58} -3.34812i q^{59} +7.74091i q^{61} +(3.88779 + 8.93806i) q^{62} +(6.22116 + 5.02962i) q^{64} +(-4.10433 - 0.318810i) q^{65} -13.3708 q^{67} +(-0.557256 - 0.519374i) q^{68} +(-10.2601 + 3.54606i) q^{70} -11.9198 q^{71} -13.1857i q^{73} +(3.72371 + 8.56084i) q^{74} +(1.80030 + 1.67792i) q^{76} +15.6051 q^{77} +13.9675 q^{79} +(-0.0642048 + 8.94404i) q^{80} +(6.15214 + 14.1438i) q^{82} +0.240083 q^{83} +(0.0659568 - 0.849120i) q^{85} +(4.14153 + 9.52142i) q^{86} +(4.28712 - 12.1217i) q^{88} +5.46154 q^{89} +6.32002i q^{91} +(-7.83978 - 7.30683i) q^{92} +(-12.1133 + 5.26893i) q^{94} +(-0.213084 + 2.74321i) q^{95} -15.7955i q^{97} +(2.69886 + 6.20471i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4}+O(q^{10}) \) 20 * q + 6 * q^4	\( 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64} + 12 q^{70} - 24 q^{76} + 36 q^{79} + 32 q^{82} - 44 q^{85} - 30 q^{88} - 22 q^{94}+O(q^{100}) \) 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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