LMFDB - Embedded newform 1080.2.d.i.109.7

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			109.7
Root			$0.847166 - 1.13239i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.i.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.847166 - 1.13239i) q^{2} +(-0.564618 + 1.91865i) q^{4} +(1.82935 + 1.28588i) q^{5} -1.09701i q^{7} +(2.65098 - 0.986045i) q^{8} +O(q^{10})$	\(q+(-0.847166 - 1.13239i) q^{2} +(-0.564618 + 1.91865i) q^{4} +(1.82935 + 1.28588i) q^{5} -1.09701i q^{7} +(2.65098 - 0.986045i) q^{8} +(-0.0936411 - 3.16089i) q^{10} +1.89459i q^{11} +4.10133 q^{13} +(-1.24224 + 0.929350i) q^{14} +(-3.36241 - 2.16661i) q^{16} +1.70100i q^{17} -5.95035i q^{19} +(-3.50003 + 2.78384i) q^{20} +(2.14542 - 1.60503i) q^{22} -0.424153i q^{23} +(1.69302 + 4.70465i) q^{25} +(-3.47451 - 4.64430i) q^{26} +(2.10477 + 0.619392i) q^{28} +7.44798i q^{29} +2.46635 q^{31} +(0.395078 + 5.64304i) q^{32} +(1.92620 - 1.44103i) q^{34} +(1.41062 - 2.00681i) q^{35} -4.00954 q^{37} +(-6.73812 + 5.04094i) q^{38} +(6.11751 + 1.60503i) q^{40} -8.17051 q^{41} +11.0436 q^{43} +(-3.63505 - 1.06972i) q^{44} +(-0.480307 + 0.359328i) q^{46} -2.28638i q^{47} +5.79657 q^{49} +(3.89323 - 5.90278i) q^{50} +(-2.31568 + 7.86900i) q^{52} +12.3020 q^{53} +(-2.43622 + 3.46586i) q^{55} +(-1.08170 - 2.90816i) q^{56} +(8.43402 - 6.30968i) q^{58} +12.4017i q^{59} -2.83171i q^{61} +(-2.08941 - 2.79287i) q^{62} +(6.05543 - 5.22798i) q^{64} +(7.50275 + 5.27382i) q^{65} +4.91266 q^{67} +(-3.26362 - 0.960415i) q^{68} +(-3.46753 + 0.102725i) q^{70} +1.69810 q^{71} +6.69321i q^{73} +(3.39675 + 4.54036i) q^{74} +(11.4166 + 3.35968i) q^{76} +2.07838 q^{77} -12.7388 q^{79} +(-3.36502 - 8.28714i) q^{80} +(6.92178 + 9.25221i) q^{82} -2.43343 q^{83} +(-2.18728 + 3.11172i) q^{85} +(-9.35574 - 12.5056i) q^{86} +(1.86815 + 5.02253i) q^{88} +12.0320 q^{89} -4.49919i q^{91} +(0.813800 + 0.239485i) q^{92} +(-2.58908 + 1.93695i) q^{94} +(7.65144 - 10.8853i) q^{95} +2.20448i q^{97} +(-4.91066 - 6.56398i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.847166	−	1.13239i	−0.599037	−	0.800721i
$2$	−0.847166	−	1.13239i	−0.599037	−	0.800721i
$3$		0			0
$3$		0			0
$4$	−0.564618	+	1.91865i	−0.282309	+	0.959323i
$5$	1.82935	+	1.28588i	0.818109	+	0.575064i
$5$	1.82935	+	1.28588i	0.818109	+	0.575064i
$6$		0			0
$7$		−	1.09701i		−	0.414631i	−0.978274	−	0.207315i	$-0.933527\pi$
$7$		−	1.09701i		−	0.414631i	0.978274	−	0.207315i	$-0.0664726\pi$
$8$	2.65098	−	0.986045i	0.937264	−	0.348619i
$9$		0			0
$10$	−0.0936411	−	3.16089i	−0.0296119	−	0.999561i
$11$			1.89459i			0.571240i	0.958343	+	0.285620i	$0.0921996\pi$
$11$			1.89459i			0.571240i	−0.958343	+	0.285620i	$0.907800\pi$
$12$		0			0
$13$	4.10133			1.13750			0.568752	−	0.822509i	$-0.307427\pi$
$13$	4.10133			1.13750			0.568752	+	0.822509i	$0.307427\pi$
$14$	−1.24224	+	0.929350i	−0.332004	+	0.248379i
$15$		0			0
$16$	−3.36241	−	2.16661i	−0.840603	−	0.541652i
$17$			1.70100i			0.412553i	0.978494	+	0.206276i	$0.0661346\pi$
$17$			1.70100i			0.412553i	−0.978494	+	0.206276i	$0.933865\pi$
$18$		0			0
$19$		−	5.95035i		−	1.36510i	−0.730837	−	0.682552i	$-0.760870\pi$
$19$		−	5.95035i		−	1.36510i	0.730837	−	0.682552i	$-0.239130\pi$
$20$	−3.50003	+	2.78384i	−0.782632	+	0.622485i
$21$		0			0
$22$	2.14542	−	1.60503i	0.457404	−	0.342194i
$23$		−	0.424153i		−	0.0884420i	−0.999022	−	0.0442210i	$-0.985919\pi$
$23$		−	0.424153i		−	0.0884420i	0.999022	−	0.0442210i	$-0.0140806\pi$
$24$		0			0
$25$	1.69302	+	4.70465i	0.338604	+	0.940929i
$26$	−3.47451	−	4.64430i	−0.681407	−	0.910823i
$27$		0			0
$28$	2.10477	+	0.619392i	0.397765	+	0.117054i
$29$			7.44798i			1.38306i	0.722350	+	0.691528i	$0.243062\pi$
$29$			7.44798i			1.38306i	−0.722350	+	0.691528i	$0.756938\pi$
$30$		0			0
$31$	2.46635			0.442970			0.221485	−	0.975164i	$-0.428910\pi$
$31$	2.46635			0.442970			0.221485	+	0.975164i	$0.428910\pi$
$32$	0.395078	+	5.64304i	0.0698405	+	0.997558i
$33$		0			0
$34$	1.92620	−	1.44103i	0.330340	−	0.247134i
$35$	1.41062	−	2.00681i	0.238439	−	0.339213i
$36$		0			0
$37$	−4.00954			−0.659164			−0.329582	−	0.944127i	$-0.606908\pi$
$37$	−4.00954			−0.659164			−0.329582	+	0.944127i	$0.606908\pi$
$38$	−6.73812	+	5.04094i	−1.09307	+	0.817748i
$39$		0			0
$40$	6.11751	+	1.60503i	0.967263	+	0.253778i
$41$	−8.17051			−1.27602			−0.638009	−	0.770029i	$-0.720242\pi$
$41$	−8.17051			−1.27602			−0.638009	+	0.770029i	$0.720242\pi$
$42$		0			0
$43$	11.0436			1.68413			0.842064	−	0.539377i	$-0.181340\pi$
$43$	11.0436			1.68413			0.842064	+	0.539377i	$0.181340\pi$
$44$	−3.63505	−	1.06972i	−0.548004	−	0.161266i
$45$		0			0
$46$	−0.480307	+	0.359328i	−0.0708174	+	0.0529801i
$47$		−	2.28638i		−	0.333503i	−0.985999	−	0.166752i	$-0.946672\pi$
$47$		−	2.28638i		−	0.333503i	0.985999	−	0.166752i	$-0.0533278\pi$
$48$		0			0
$49$	5.79657			0.828081
$50$	3.89323	−	5.90278i	0.550586	−	0.834779i
$51$		0			0
$52$	−2.31568	+	7.86900i	−0.321128	+	1.09123i
$53$	12.3020			1.68981			0.844907	−	0.534913i	$-0.179655\pi$
$53$	12.3020			1.68981			0.844907	+	0.534913i	$0.179655\pi$
$54$		0			0
$55$	−2.43622	+	3.46586i	−0.328499	+	0.467337i
$56$	−1.08170	−	2.90816i	−0.144548	−	0.388619i
$57$		0			0
$58$	8.43402	−	6.30968i	1.10744	−	0.828501i
$59$			12.4017i			1.61456i	0.590166	+	0.807282i	$0.299062\pi$
$59$			12.4017i			1.61456i	−0.590166	+	0.807282i	$0.700938\pi$
$60$		0			0
$61$		−	2.83171i		−	0.362564i	−0.983431	−	0.181282i	$-0.941975\pi$
$61$		−	2.83171i		−	0.362564i	0.983431	−	0.181282i	$-0.0580246\pi$
$62$	−2.08941	−	2.79287i	−0.265355	−	0.354695i
$63$		0			0
$64$	6.05543	−	5.22798i	0.756929	−	0.653497i
$65$	7.50275	+	5.27382i	0.930601	+	0.654137i
$66$		0			0
$67$	4.91266			0.600177			0.300089	−	0.953911i	$-0.402984\pi$
$67$	4.91266			0.600177			0.300089	+	0.953911i	$0.402984\pi$
$68$	−3.26362	−	0.960415i	−0.395772	−	0.116467i
$69$		0			0
$70$	−3.46753	+	0.102725i	−0.414449	+	0.0122780i
$71$	1.69810			0.201528			0.100764	−	0.994910i	$-0.467871\pi$
$71$	1.69810			0.201528			0.100764	+	0.994910i	$0.467871\pi$
$72$		0			0
$73$			6.69321i			0.783381i	0.920097	+	0.391691i	$0.128110\pi$
$73$			6.69321i			0.783381i	−0.920097	+	0.391691i	$0.871890\pi$
$74$	3.39675	+	4.54036i	0.394864	+	0.527807i
$75$		0			0
$76$	11.4166	+	3.35968i	1.30958	+	0.385381i
$77$	2.07838			0.236854
$78$		0			0
$79$	−12.7388			−1.43323			−0.716614	−	0.697470i	$-0.754309\pi$
$79$	−12.7388			−1.43323			−0.716614	+	0.697470i	$0.754309\pi$
$80$	−3.36502	−	8.28714i	−0.376221	−	0.926530i
$81$		0			0
$82$	6.92178	+	9.25221i	0.764383	+	1.02174i
$83$	−2.43343			−0.267104			−0.133552	−	0.991042i	$-0.542638\pi$
$83$	−2.43343			−0.267104			−0.133552	+	0.991042i	$0.542638\pi$
$84$		0			0
$85$	−2.18728	+	3.11172i	−0.237244	+	0.337513i
$86$	−9.35574	−	12.5056i	−1.00886	−	1.34852i
$87$		0			0
$88$	1.86815	+	5.02253i	0.199145	+	0.535403i
$89$	12.0320			1.27539			0.637695	−	0.770289i	$-0.279888\pi$
$89$	12.0320			1.27539			0.637695	+	0.770289i	$0.279888\pi$
$90$		0			0
$91$		−	4.49919i		−	0.471644i
$92$	0.813800	+	0.239485i	0.0848445	+	0.0249680i
$93$		0			0
$94$	−2.58908	+	1.93695i	−0.267043	+	0.199781i
$95$	7.65144	−	10.8853i	0.785021	−	1.11680i
$96$		0			0
$97$			2.20448i			0.223831i	0.993718	+	0.111916i	$0.0356987\pi$
$97$			2.20448i			0.223831i	−0.993718	+	0.111916i	$0.964301\pi$
$98$	−4.91066	−	6.56398i	−0.496051	−	0.663062i
$99$		0			0
$100$	−9.98246	+	0.591978i	−0.998246	+	0.0591978i
$101$			2.45373i			0.244156i	0.992521	+	0.122078i	$0.0389558\pi$
$101$			2.45373i			0.244156i	−0.992521	+	0.122078i	$0.961044\pi$
$102$		0			0
$103$		−	14.7324i		−	1.45163i	−0.687891	−	0.725814i	$-0.741463\pi$
$103$		−	14.7324i		−	1.45163i	0.687891	−	0.725814i	$-0.258537\pi$
$104$	10.8725	−	4.04409i	1.06614	−	0.396556i
$105$		0			0
$106$	−10.4219	−	13.9307i	−1.01226	−	1.35307i
$107$	11.1789			1.08070			0.540352	−	0.841439i	$-0.318291\pi$
$107$	11.1789			1.08070			0.540352	+	0.841439i	$0.318291\pi$
$108$		0			0
$109$			3.23427i			0.309787i	0.987931	+	0.154894i	$0.0495035\pi$
$109$			3.23427i			0.309787i	−0.987931	+	0.154894i	$0.950497\pi$
$110$	5.98859	−	0.177411i	0.570990	−	0.0169155i
$111$		0			0
$112$	−2.37679	+	3.68860i	−0.224585	+	0.348540i
$113$		−	14.2007i		−	1.33589i	−0.744210	−	0.667945i	$-0.767174\pi$
$113$		−	14.2007i		−	1.33589i	0.744210	−	0.667945i	$-0.232826\pi$
$114$		0			0
$115$	0.545411	−	0.775923i	0.0508598	−	0.0723552i
$116$	−14.2900	−	4.20527i	−1.32680	−	0.390449i
$117$		0			0
$118$	14.0436	−	10.5063i	1.29282	−	0.967183i
$119$	1.86601			0.171057
$120$		0			0
$121$	7.41053			0.673685
$122$	−3.20660	+	2.39893i	−0.290312	+	0.217189i
$123$		0			0
$124$	−1.39255	+	4.73206i	−0.125054	+	0.424951i
$125$	−2.95249	+	10.7834i	−0.264079	+	0.964501i
$126$		0			0
$127$		−	20.3182i		−	1.80294i	−0.432837	−	0.901472i	$-0.642487\pi$
$127$		−	20.3182i		−	1.80294i	0.432837	−	0.901472i	$-0.357513\pi$
$128$	−11.0501	−	2.42815i	−0.976698	−	0.214620i
$129$		0			0
$130$	−0.384053	−	12.9638i	−0.0336836	−	1.13700i
$131$		−	1.49044i		−	0.130221i	−0.997878	−	0.0651104i	$-0.979260\pi$
$131$		−	1.49044i		−	0.130221i	0.997878	−	0.0651104i	$-0.0207399\pi$
$132$		0			0
$133$	−6.52759			−0.566014
$134$	−4.16184	−	5.56305i	−0.359528	−	0.480575i
$135$		0			0
$136$	1.67726	+	4.50932i	0.143824	+	0.386671i
$137$		−	7.45176i		−	0.636647i	−0.947982	−	0.318324i	$-0.896880\pi$
$137$		−	7.45176i		−	0.636647i	0.947982	−	0.318324i	$-0.103120\pi$
$138$		0			0
$139$			2.71608i			0.230375i	0.993344	+	0.115187i	$0.0367468\pi$
$139$			2.71608i			0.230375i	−0.993344	+	0.115187i	$0.963253\pi$
$140$	3.05390	+	3.83957i	0.258102	+	0.324503i
$141$		0			0
$142$	−1.43857	−	1.92291i	−0.120722	−	0.161367i
$143$			7.77033i			0.649788i
$144$		0			0
$145$	−9.57722	+	13.6249i	−0.795344	+	1.13149i
$146$	7.57933	−	5.67027i	0.627270	−	0.469275i
$147$		0			0
$148$	2.26386	−	7.69289i	0.186088	−	0.632352i
$149$		−	6.06321i		−	0.496718i	−0.968668	−	0.248359i	$-0.920109\pi$
$149$		−	6.06321i		−	0.496718i	0.968668	−	0.248359i	$-0.0798912\pi$
$150$		0			0
$151$	−13.8664			−1.12843			−0.564215	−	0.825628i	$-0.690821\pi$
$151$	−13.8664			−1.12843			−0.564215	+	0.825628i	$0.690821\pi$
$152$	−5.86731	−	15.7743i	−0.475902	−	1.27946i
$153$		0			0
$154$	−1.76074	−	2.35354i	−0.141884	−	0.189654i
$155$	4.51181	+	3.17144i	0.362398	+	0.254736i
$156$		0			0
$157$	−11.6208			−0.927439			−0.463720	−	0.885982i	$-0.653486\pi$
$157$	−11.6208			−0.927439			−0.463720	+	0.885982i	$0.653486\pi$
$158$	10.7919	+	14.4253i	0.858557	+	1.14762i
$159$		0			0
$160$	−6.53355	+	10.8311i	−0.516522	+	0.856274i
$161$	−0.465300			−0.0366708
$162$		0			0
$163$	5.01908			0.393124			0.196562	−	0.980491i	$-0.437022\pi$
$163$	5.01908			0.393124			0.196562	+	0.980491i	$0.437022\pi$
$164$	4.61322	−	15.6763i	0.360232	−	1.22411i
$165$		0			0
$166$	2.06152	+	2.75559i	0.160005	+	0.213876i
$167$			3.74825i			0.290048i	0.989428	+	0.145024i	$0.0463260\pi$
$167$			3.74825i			0.290048i	−0.989428	+	0.145024i	$0.953674\pi$
$168$		0			0
$169$	3.82087			0.293913
$170$	5.37667	−	0.159283i	0.412372	−	0.0122165i
$171$		0			0
$172$	−6.23540	+	21.1887i	−0.475445	+	1.61562i
$173$	−10.6039			−0.806202			−0.403101	−	0.915155i	$-0.632068\pi$
$173$	−10.6039			−0.806202			−0.403101	+	0.915155i	$0.632068\pi$
$174$		0			0
$175$	5.16104	−	1.85726i	0.390138	−	0.140396i
$176$	4.10483	−	6.37039i	0.309413	−	0.480186i
$177$		0			0
$178$	−10.1931	−	13.6249i	−0.764006	−	1.02123i
$179$			15.7506i			1.17725i	0.808405	+	0.588627i	$0.200331\pi$
$179$			15.7506i			1.17725i	−0.808405	+	0.588627i	$0.799669\pi$
$180$		0			0
$181$			20.9558i			1.55764i	0.627250	+	0.778818i	$0.284180\pi$
$181$			20.9558i			1.55764i	−0.627250	+	0.778818i	$0.715820\pi$
$182$	−5.09485	+	3.81157i	−0.377655	+	0.282532i
$183$		0			0
$184$	−0.418234	−	1.12442i	−0.0308326	−	0.0828936i
$185$	−7.33484	−	5.15579i	−0.539268	−	0.379061i
$186$		0			0
$187$	−3.22269			−0.235667
$188$	4.38676	+	1.29093i	0.319938	+	0.0941510i
$189$		0			0
$190$	−18.8084	+	0.557197i	−1.36451	+	0.0404233i
$191$	−18.2070			−1.31741			−0.658707	−	0.752400i	$-0.728896\pi$
$191$	−18.2070			−1.31741			−0.658707	+	0.752400i	$0.728896\pi$
$192$		0			0
$193$			8.88723i			0.639717i	0.947465	+	0.319859i	$0.103635\pi$
$193$			8.88723i			0.639717i	−0.947465	+	0.319859i	$0.896365\pi$
$194$	2.49634	−	1.86756i	0.179227	−	0.134083i
$195$		0			0
$196$	−3.27285	+	11.1216i	−0.233775	+	0.794398i
$197$	−8.73792			−0.622551			−0.311276	−	0.950320i	$-0.600756\pi$
$197$	−8.73792			−0.622551			−0.311276	+	0.950320i	$0.600756\pi$
$198$		0			0
$199$	9.72289			0.689237			0.344619	−	0.938743i	$-0.388008\pi$
$199$	9.72289			0.689237			0.344619	+	0.938743i	$0.388008\pi$
$200$	9.12716	+	10.8025i	0.645388	+	0.763855i
$201$		0			0
$202$	2.77859	−	2.07872i	0.195501	−	0.146258i
$203$	8.17051			0.573457
$204$		0			0
$205$	−14.9467	−	10.5063i	−1.04392	−	0.733792i
$206$	−16.6828	+	12.4808i	−1.16235	+	0.869579i
$207$		0			0
$208$	−13.7903	−	8.88596i	−0.956189	−	0.616130i
$209$	11.2735			0.779802
$210$		0			0
$211$		−	14.0843i		−	0.969600i	−0.874625	−	0.484800i	$-0.838892\pi$
$211$		−	14.0843i		−	0.969600i	0.874625	−	0.484800i	$-0.161108\pi$
$212$	−6.94595	+	23.6033i	−0.477050	+	1.62108i
$213$		0			0
$214$	−9.47038	−	12.6589i	−0.647382	−	0.865343i
$215$	20.2025	+	14.2007i	1.37780	+	0.968481i
$216$		0			0
$217$		−	2.70561i		−	0.183669i
$218$	3.66246	−	2.73997i	0.248053	−	0.185574i
$219$		0			0
$220$	−5.27423	−	6.63113i	−0.355589	−	0.447071i
$221$			6.97635i			0.469280i
$222$		0			0
$223$			6.23727i			0.417679i	0.977950	+	0.208839i	$0.0669686\pi$
$223$			6.23727i			0.417679i	−0.977950	+	0.208839i	$0.933031\pi$
$224$	6.19047	−	0.433404i	0.413618	−	0.0289580i
$225$		0			0
$226$	−16.0808	+	12.0304i	−1.06968	+	0.800248i
$227$	9.75082			0.647184			0.323592	−	0.946197i	$-0.395109\pi$
$227$	9.75082			0.647184			0.323592	+	0.946197i	$0.395109\pi$
$228$		0			0
$229$			26.7906i			1.77037i	0.465239	+	0.885185i	$0.345968\pi$
$229$			26.7906i			1.77037i	−0.465239	+	0.885185i	$0.654032\pi$
$230$	−1.34070	+	0.0397182i	−0.0884033	+	0.00261894i
$231$		0			0
$232$	7.34404	+	19.7445i	0.482160	+	1.29629i
$233$			27.7728i			1.81946i	0.415201	+	0.909730i	$0.363711\pi$
$233$			27.7728i			1.81946i	−0.415201	+	0.909730i	$0.636289\pi$
$234$		0			0
$235$	2.94002	−	4.18259i	0.191786	−	0.272842i
$236$	−23.7945	−	7.00222i	−1.54889	−	0.455806i
$237$		0			0
$238$	−1.58082	−	2.11306i	−0.102470	−	0.136969i
$239$	−6.89512			−0.446008			−0.223004	−	0.974817i	$-0.571586\pi$
$239$	−6.89512			−0.446008			−0.223004	+	0.974817i	$0.571586\pi$
$240$		0			0
$241$	10.7239			0.690784			0.345392	−	0.938458i	$-0.387746\pi$
$241$	10.7239			0.690784			0.345392	+	0.938458i	$0.387746\pi$
$242$	−6.27795	−	8.39162i	−0.403562	−	0.539434i
$243$		0			0
$244$	5.43306	+	1.59884i	0.347816	+	0.102355i
$245$	10.6039	+	7.45370i	0.677461	+	0.476199i
$246$		0			0
$247$		−	24.4043i		−	1.55281i
$248$	6.53826	−	2.43193i	0.415180	−	0.154428i
$249$		0			0
$250$	14.7123	−	5.79200i	0.930490	−	0.366318i
$251$		−	15.6506i		−	0.987859i	−0.869502	−	0.493930i	$-0.835560\pi$
$251$		−	15.6506i		−	0.987859i	0.869502	−	0.493930i	$-0.164440\pi$
$252$		0			0
$253$	0.803596			0.0505217
$254$	−23.0081	+	17.2129i	−1.44366	+	1.08003i
$255$		0			0
$256$	6.61163	+	14.5700i	0.413227	+	0.910628i
$257$		−	12.0836i		−	0.753755i	−0.926263	−	0.376878i	$-0.876998\pi$
$257$		−	12.0836i		−	0.753755i	0.926263	−	0.376878i	$-0.123002\pi$
$258$		0			0
$259$			4.39850i			0.273310i
$260$	−14.3548	+	11.4174i	−0.890246	+	0.708079i
$261$		0			0
$262$	−1.68777	+	1.26265i	−0.104270	+	0.0780070i
$263$		−	7.88836i		−	0.486417i	−0.969974	−	0.243208i	$-0.921800\pi$
$263$		−	7.88836i		−	0.486417i	0.969974	−	0.243208i	$-0.0781999\pi$
$264$		0			0
$265$	22.5047	+	15.8190i	1.38245	+	0.971751i
$266$	5.52996	+	7.39179i	0.339063	+	0.453219i
$267$		0			0
$268$	−2.77378	+	9.42566i	−0.169435	+	0.575764i
$269$		−	27.9544i		−	1.70441i	−0.523207	−	0.852206i	$-0.675265\pi$
$269$		−	27.9544i		−	1.70441i	0.523207	−	0.852206i	$-0.324735\pi$
$270$		0			0
$271$	−8.19311			−0.497696			−0.248848	−	0.968543i	$-0.580052\pi$
$271$	−8.19311			−0.497696			−0.248848	+	0.968543i	$0.580052\pi$
$272$	3.68539	−	5.71946i	0.223460	−	0.346793i
$273$		0			0
$274$	−8.43831	+	6.31288i	−0.509777	+	0.381375i
$275$	−8.91337	+	3.20758i	−0.537497	+	0.193424i
$276$		0			0
$277$	−28.7989			−1.73036			−0.865180	−	0.501461i	$-0.832796\pi$
$277$	−28.7989			−1.73036			−0.865180	+	0.501461i	$0.832796\pi$
$278$	3.07566	−	2.30097i	0.184466	−	0.138003i
$279$		0			0
$280$	1.76074	−	6.71096i	0.105224	−	0.401057i
$281$	−26.2790			−1.56767			−0.783836	−	0.620968i	$-0.786740\pi$
$281$	−26.2790			−1.56767			−0.783836	+	0.620968i	$0.786740\pi$
$282$		0			0
$283$	8.01908			0.476685			0.238342	−	0.971181i	$-0.423396\pi$
$283$	8.01908			0.476685			0.238342	+	0.971181i	$0.423396\pi$
$284$	−0.958779	+	3.25806i	−0.0568931	+	0.193330i
$285$		0			0
$286$	8.79905	−	6.58276i	0.520299	−	0.389247i
$287$			8.96313i			0.529077i
$288$		0			0
$289$	14.1066			0.829800
$290$	23.5423	−	0.697437i	1.38245	−	0.0409549i
$291$		0			0
$292$	−12.8419	−	3.77911i	−0.751516	−	0.221156i
$293$	−10.3414			−0.604154			−0.302077	−	0.953284i	$-0.597680\pi$
$293$	−10.3414			−0.604154			−0.302077	+	0.953284i	$0.597680\pi$
$294$		0			0
$295$	−15.9471	+	22.6870i	−0.928476	+	1.32089i
$296$	−10.6292	+	3.95358i	−0.617811	+	0.229797i
$297$		0			0
$298$	−6.86593	+	5.13655i	−0.397732	+	0.297552i
$299$		−	1.73959i		−	0.100603i
$300$		0			0
$301$		−	12.1149i		−	0.698291i
$302$	11.7471	+	15.7022i	0.675971	+	0.903558i
$303$		0			0
$304$	−12.8921	+	20.0075i	−0.739411	+	1.14751i
$305$	3.64124	−	5.18018i	0.208497	−	0.296616i
$306$		0			0
$307$	−15.5835			−0.889395			−0.444698	−	0.895681i	$-0.646689\pi$
$307$	−15.5835			−0.889395			−0.444698	+	0.895681i	$0.646689\pi$
$308$	−1.17349	+	3.98768i	−0.0668660	+	0.227219i
$309$		0			0
$310$	−0.230952	−	7.79587i	−0.0131172	−	0.442776i
$311$	−28.1450			−1.59596			−0.797978	−	0.602687i	$-0.794097\pi$
$311$	−28.1450			−1.59596			−0.797978	+	0.602687i	$0.794097\pi$
$312$		0			0
$313$			7.10412i			0.401548i	0.979638	+	0.200774i	$0.0643457\pi$
$313$			7.10412i			0.401548i	−0.979638	+	0.200774i	$0.935654\pi$
$314$	9.84474	+	13.1593i	0.555571	+	0.742621i
$315$		0			0
$316$	7.19257	−	24.4413i	0.404613	−	1.37493i
$317$	10.6039			0.595576			0.297788	−	0.954632i	$-0.403751\pi$
$317$	10.6039			0.595576			0.297788	+	0.954632i	$0.403751\pi$
$318$		0			0
$319$	−14.1109			−0.790057
$320$	17.8000	−	1.77722i	0.995053	−	0.0993495i
$321$		0			0
$322$	0.394187	+	0.526902i	0.0219672	+	0.0293631i
$323$	10.1215			0.563177
$324$		0			0
$325$	6.94362	+	19.2953i	0.385163	+	1.07031i
$326$	−4.25199	−	5.68356i	−0.235496	−	0.314783i
$327$		0			0
$328$	−21.6599	+	8.05648i	−1.19597	+	0.444845i
$329$	−2.50819			−0.138281
$330$		0			0
$331$			32.0939i			1.76404i	0.471214	+	0.882019i	$0.343816\pi$
$331$			32.0939i			1.76404i	−0.471214	+	0.882019i	$0.656184\pi$
$332$	1.37396	−	4.66889i	0.0754058	−	0.256239i
$333$		0			0
$334$	4.24449	−	3.17539i	0.232248	−	0.173750i
$335$	8.98696	+	6.31710i	0.491010	+	0.345140i
$336$		0			0
$337$		−	22.7507i		−	1.23931i	−0.784875	−	0.619654i	$-0.787273\pi$
$337$		−	22.7507i		−	1.23931i	0.784875	−	0.619654i	$-0.212727\pi$
$338$	−3.23692	−	4.32672i	−0.176065	−	0.235343i
$339$		0			0
$340$	−4.73531	−	5.95355i	−0.256808	−	0.322877i
$341$			4.67272i			0.253042i
$342$		0			0
$343$		−	14.0380i		−	0.757979i
$344$	29.2763	−	10.8895i	1.57847	−	0.587120i
$345$		0			0
$346$	8.98330	+	12.0078i	0.482945	+	0.645543i
$347$	−23.2109			−1.24603			−0.623013	−	0.782211i	$-0.714092\pi$
$347$	−23.2109			−1.24603			−0.623013	+	0.782211i	$0.714092\pi$
$348$		0			0
$349$		−	27.0786i		−	1.44948i	−0.689021	−	0.724742i	$-0.741959\pi$
$349$		−	27.0786i		−	1.44948i	0.689021	−	0.724742i	$-0.258041\pi$
$350$	−6.47540	−	4.27091i	−0.346125	−	0.228290i
$351$		0			0
$352$	−10.6912	+	0.748510i	−0.569845	+	0.0398957i
$353$		−	10.9128i		−	0.580832i	−0.956900	−	0.290416i	$-0.906206\pi$
$353$		−	10.9128i		−	0.580832i	0.956900	−	0.290416i	$-0.0937937\pi$
$354$		0			0
$355$	3.10642	+	2.18356i	0.164871	+	0.115891i
$356$	−6.79349	+	23.0852i	−0.360054	+	1.22351i
$357$		0			0
$358$	17.8358	−	13.3434i	0.942652	−	0.705219i
$359$	−4.15889			−0.219498			−0.109749	−	0.993959i	$-0.535005\pi$
$359$	−4.15889			−0.219498			−0.109749	+	0.993959i	$0.535005\pi$
$360$		0			0
$361$	−16.4067			−0.863508
$362$	23.7302	−	17.7531i	1.24723	−	0.933081i
$363$		0			0
$364$	8.63237	+	2.54033i	0.452459	+	0.133149i
$365$	−8.60668	+	12.2442i	−0.450494	+	0.640891i
$366$		0			0
$367$		−	29.0413i		−	1.51595i	−0.652286	−	0.757973i	$-0.726190\pi$
$367$		−	29.0413i		−	1.51595i	0.652286	−	0.757973i	$-0.273810\pi$
$368$	−0.918973	+	1.42618i	−0.0479048	+	0.0743447i
$369$		0			0
$370$	0.375457	+	12.6737i	0.0195191	+	0.658875i
$371$		−	13.4955i		−	0.700649i
$372$		0			0
$373$	−8.47589			−0.438865			−0.219432	−	0.975628i	$-0.570421\pi$
$373$	−8.47589			−0.438865			−0.219432	+	0.975628i	$0.570421\pi$
$374$	2.73016	+	3.64935i	0.141173	+	0.188703i
$375$		0			0
$376$	−2.25448	−	6.06117i	−0.116266	−	0.312581i
$377$			30.5466i			1.57323i
$378$		0			0
$379$		−	26.9629i		−	1.38499i	−0.721421	−	0.692497i	$-0.756511\pi$
$379$		−	26.9629i		−	1.38499i	0.721421	−	0.692497i	$-0.243489\pi$
$380$	16.5648	+	20.8264i	0.849757	+	1.06837i
$381$		0			0
$382$	15.4244	+	20.6175i	0.789180	+	1.05488i
$383$		−	28.1503i		−	1.43842i	−0.694795	−	0.719208i	$-0.744505\pi$
$383$		−	28.1503i		−	1.43842i	0.694795	−	0.719208i	$-0.255495\pi$
$384$		0			0
$385$	3.80208	+	2.67255i	0.193772	+	0.136206i
$386$	10.0638	−	7.52897i	0.512235	−	0.383214i
$387$		0			0
$388$	−4.22963	−	1.24469i	−0.214727	−	0.0631896i
$389$		−	28.4441i		−	1.44217i	−0.692844	−	0.721087i	$-0.743643\pi$
$389$		−	28.4441i		−	1.44217i	0.692844	−	0.721087i	$-0.256357\pi$
$390$		0			0
$391$	0.721484			0.0364870
$392$	15.3666	−	5.71568i	0.776131	−	0.288685i
$393$		0			0
$394$	7.40248	+	9.89475i	0.372931	+	0.498490i
$395$	−23.3037	−	16.3806i	−1.17254	−	0.824197i
$396$		0			0
$397$	18.9844			0.952800			0.476400	−	0.879229i	$-0.341941\pi$
$397$	18.9844			0.952800			0.476400	+	0.879229i	$0.341941\pi$
$398$	−8.23690	−	11.0101i	−0.412879	−	0.551887i
$399$		0			0
$400$	4.50048	−	19.4871i	0.225024	−	0.974353i
$401$	−5.95556			−0.297406			−0.148703	−	0.988882i	$-0.547510\pi$
$401$	−5.95556			−0.297406			−0.148703	+	0.988882i	$0.547510\pi$
$402$		0			0
$403$	10.1153			0.503880
$404$	−4.70785	−	1.38542i	−0.234224	−	0.0689274i
$405$		0			0
$406$	−6.92178	−	9.25221i	−0.343522	−	0.459179i
$407$		−	7.59643i		−	0.376541i
$408$		0			0
$409$	−30.3615			−1.50128			−0.750641	−	0.660711i	$-0.770255\pi$
$409$	−30.3615			−1.50128			−0.750641	+	0.660711i	$0.770255\pi$
$410$	0.765095	+	25.8261i	0.0377853	+	1.27546i
$411$		0			0
$412$	28.2663	+	8.31819i	1.39258	+	0.409808i
$413$	13.6048			0.669448
$414$		0			0
$415$	−4.45159	−	3.12910i	−0.218520	−	0.153602i
$416$	1.62034	+	23.1440i	0.0794438	+	1.13473i
$417$		0			0
$418$	−9.55050	−	12.7660i	−0.467130	−	0.624404i
$419$		−	2.72901i		−	0.133321i	−0.997776	−	0.0666604i	$-0.978766\pi$
$419$		−	2.72901i		−	0.133321i	0.997776	−	0.0666604i	$-0.0212344\pi$
$420$		0			0
$421$			9.28319i			0.452435i	0.974077	+	0.226218i	$0.0726360\pi$
$421$			9.28319i			0.452435i	−0.974077	+	0.226218i	$0.927364\pi$
$422$	−15.9489	+	11.9317i	−0.776379	+	0.580826i
$423$		0			0
$424$	32.6125	−	12.1304i	1.58380	−	0.589102i
$425$	−8.00260	+	2.87982i	−0.388183	+	0.139692i
$426$		0			0
$427$	−3.10642			−0.150330
$428$	−6.31181	+	21.4483i	−0.305093	+	1.03674i
$429$		0			0
$430$	−1.03413	−	34.9075i	−0.0498702	−	1.68339i
$431$	16.1731			0.779031			0.389515	−	0.921020i	$-0.372642\pi$
$431$	16.1731			0.779031			0.389515	+	0.921020i	$0.372642\pi$
$432$		0			0
$433$			25.0559i			1.20411i	0.798456	+	0.602054i	$0.205651\pi$
$433$			25.0559i			1.20411i	−0.798456	+	0.602054i	$0.794349\pi$
$434$	−3.06381	+	2.29210i	−0.147068	+	0.110024i
$435$		0			0
$436$	−6.20543	−	1.82613i	−0.297186	−	0.0874558i
$437$	−2.52386			−0.120733
$438$		0			0
$439$	−9.83550			−0.469423			−0.234711	−	0.972065i	$-0.575415\pi$
$439$	−9.83550			−0.469423			−0.234711	+	0.972065i	$0.575415\pi$
$440$	−3.04088	+	11.5902i	−0.144968	+	0.552539i
$441$		0			0
$442$	7.89996	−	5.91013i	0.375763	−	0.281116i
$443$	−34.2623			−1.62785			−0.813926	−	0.580968i	$-0.802674\pi$
$443$	−34.2623			−1.62785			−0.813926	+	0.580968i	$0.802674\pi$
$444$		0			0
$445$	22.0107	+	15.4717i	1.04341	+	0.733430i
$446$	7.06303	−	5.28401i	0.334444	−	0.250205i
$447$		0			0
$448$	−5.73514	−	6.64287i	−0.270960	−	0.313846i
$449$	39.1812			1.84907			0.924537	−	0.381091i	$-0.124452\pi$
$449$	39.1812			1.84907			0.924537	+	0.381091i	$0.124452\pi$
$450$		0			0
$451$		−	15.4798i		−	0.728913i
$452$	27.2462	+	8.01798i	1.28155	+	0.377134i
$453$		0			0
$454$	−8.26056	−	11.0417i	−0.387687	−	0.518214i
$455$	5.78543	−	8.23059i	0.271225	−	0.385856i
$456$		0			0
$457$		−	31.7386i		−	1.48467i	−0.670029	−	0.742335i	$-0.733718\pi$
$457$		−	31.7386i		−	1.48467i	0.670029	−	0.742335i	$-0.266282\pi$
$458$	30.3374	−	22.6961i	1.41757	−	1.06052i
$459$		0			0
$460$	1.18077	+	1.48455i	0.0550539	+	0.0692175i
$461$		−	25.3865i		−	1.18237i	−0.806537	−	0.591184i	$-0.798661\pi$
$461$		−	25.3865i		−	1.18237i	0.806537	−	0.591184i	$-0.201339\pi$
$462$		0			0
$463$			40.4827i			1.88139i	0.339252	+	0.940696i	$0.389826\pi$
$463$			40.4827i			1.88139i	−0.339252	+	0.940696i	$0.610174\pi$
$464$	16.1368	−	25.0432i	0.749134	−	1.16260i
$465$		0			0
$466$	31.4497	−	23.5282i	1.45688	−	1.08992i
$467$	−23.7161			−1.09745			−0.548724	−	0.836003i	$-0.684886\pi$
$467$	−23.7161			−1.09745			−0.548724	+	0.836003i	$0.684886\pi$
$468$		0			0
$469$		−	5.38924i		−	0.248852i
$470$	−7.22701	+	0.214099i	−0.333357	+	0.00987567i
$471$		0			0
$472$	12.2286	+	32.8767i	0.562868	+	1.51327i
$473$			20.9230i			0.962042i
$474$		0			0
$475$	27.9943	−	10.0741i	1.28447	−	0.462229i
$476$	−1.05358	+	3.58022i	−0.0482910	+	0.164099i
$477$		0			0
$478$	5.84132	+	7.80797i	0.267176	+	0.357128i
$479$	−16.8331			−0.769123			−0.384561	−	0.923099i	$-0.625647\pi$
$479$	−16.8331			−0.769123			−0.384561	+	0.923099i	$0.625647\pi$
$480$		0			0
$481$	−16.4444			−0.749801
$482$	−9.08489	−	12.1436i	−0.413806	−	0.553126i
$483$		0			0
$484$	−4.18412	+	14.2182i	−0.190187	+	0.646281i
$485$	−2.83470	+	4.03276i	−0.128717	+	0.183118i
$486$		0			0
$487$		−	12.5175i		−	0.567220i	−0.958940	−	0.283610i	$-0.908468\pi$
$487$		−	12.5175i		−	0.567220i	0.958940	−	0.283610i	$-0.0915322\pi$
$488$	−2.79219	−	7.50682i	−0.126397	−	0.339818i
$489$		0			0
$490$	−0.542797	−	18.3223i	−0.0245211	−	0.827718i
$491$		−	28.1884i		−	1.27213i	−0.771637	−	0.636063i	$-0.780562\pi$
$491$		−	28.1884i		−	1.27213i	0.771637	−	0.636063i	$-0.219438\pi$
$492$		0			0
$493$	−12.6690			−0.570583
$494$	−27.6352	+	20.6745i	−1.24337	+	0.930191i
$495$		0			0
$496$	−8.29289	−	5.34361i	−0.372362	−	0.239935i
$497$		−	1.86283i		−	0.0835595i
$498$		0			0
$499$			16.8003i			0.752086i	0.926602	+	0.376043i	$0.122716\pi$
$499$			16.8003i			0.752086i	−0.926602	+	0.376043i	$0.877284\pi$
$500$	−19.0226	−	11.7533i	−0.850717	−	0.525625i
$501$		0			0
$502$	−17.7226	+	13.2587i	−0.791000	+	0.591764i
$503$			30.4521i			1.35779i	0.734234	+	0.678897i	$0.237542\pi$
$503$			30.4521i			1.35779i	−0.734234	+	0.678897i	$0.762458\pi$
$504$		0			0
$505$	−3.15521	+	4.48873i	−0.140405	+	0.199746i
$506$	−0.680780	−	0.909985i	−0.0302643	−	0.0404538i
$507$		0			0
$508$	38.9834	+	11.4720i	1.72961	+	0.508988i
$509$		−	21.7030i		−	0.961968i	−0.876729	−	0.480984i	$-0.840279\pi$
$509$		−	21.7030i		−	0.961968i	0.876729	−	0.480984i	$-0.159721\pi$
$510$		0			0
$511$	7.34252			0.324814
$512$	10.8978	−	19.8302i	0.481621	−	0.876380i
$513$		0			0
$514$	−13.6834	+	10.2368i	−0.603548	+	0.451527i
$515$	18.9441	−	26.9507i	0.834778	−	1.18759i
$516$		0			0
$517$	4.33176			0.190511
$518$	4.98082	−	3.72626i	0.218845	−	0.163723i
$519$		0			0
$520$	25.0899	+	6.58276i	1.10026	+	0.288673i
$521$	−25.8137			−1.13092			−0.565459	−	0.824777i	$-0.691301\pi$
$521$	−25.8137			−1.13092			−0.565459	+	0.824777i	$0.691301\pi$
$522$		0			0
$523$	−35.2453			−1.54117			−0.770584	−	0.637339i	$-0.780035\pi$
$523$	−35.2453			−1.54117			−0.770584	+	0.637339i	$0.780035\pi$
$524$	2.85964	+	0.841532i	0.124924	+	0.0367625i
$525$		0			0
$526$	−8.93270	+	6.68275i	−0.389484	+	0.291382i
$527$			4.19526i			0.182748i
$528$		0			0
$529$	22.8201			0.992178
$530$	−1.15198	−	38.8854i	−0.0500386	−	1.68907i
$531$		0			0
$532$	3.68560	−	12.5241i	0.159791	−	0.542991i
$533$	−33.5099			−1.45148
$534$		0			0
$535$	20.4501	+	14.3747i	0.884133	+	0.621473i
$536$	13.0234	−	4.84410i	0.562525	−	0.209233i
$537$		0			0
$538$	−31.6553	+	23.6820i	−1.36476	+	1.02101i
$539$			10.9821i			0.473033i
$540$		0			0
$541$			3.29103i			0.141492i	0.997494	+	0.0707462i	$0.0225380\pi$
$541$			3.29103i			0.141492i	−0.997494	+	0.0707462i	$0.977462\pi$
$542$	6.94093	+	9.27781i	0.298138	+	0.398516i
$543$		0			0
$544$	−9.59881	+	0.672026i	−0.411545	+	0.0288129i
$545$	−4.15889	+	5.91661i	−0.178147	+	0.253440i
$546$		0			0
$547$	32.4815			1.38881			0.694404	−	0.719585i	$-0.255668\pi$
$547$	32.4815			1.38881			0.694404	+	0.719585i	$0.255668\pi$
$548$	14.2973	+	4.20740i	0.610750	+	0.179731i
$549$		0			0
$550$	11.1833	+	7.37607i	0.476859	+	0.314517i
$551$	44.3181			1.88801
$552$		0			0
$553$			13.9746i			0.594260i
$554$	24.3975	+	32.6117i	1.03655	+	1.38554i
$555$		0			0
$556$	−5.21119	−	1.53355i	−0.221004	−	0.0650368i
$557$	−19.5774			−0.829523			−0.414761	−	0.909930i	$-0.636135\pi$
$557$	−19.5774			−0.829523			−0.414761	+	0.909930i	$0.636135\pi$
$558$		0			0
$559$	45.2933			1.91570
$560$	−9.09107	+	3.69146i	−0.384168	+	0.155993i
$561$		0			0
$562$	22.2627	+	29.7581i	0.939093	+	1.25527i
$563$	−7.22281			−0.304405			−0.152203	−	0.988349i	$-0.548637\pi$
$563$	−7.22281			−0.304405			−0.152203	+	0.988349i	$0.548637\pi$
$564$		0			0
$565$	18.2604	−	25.9780i	0.768222	−	1.09290i
$566$	−6.79349	−	9.08073i	−0.285552	−	0.381692i
$567$		0			0
$568$	4.50164	−	1.67440i	0.188885	−	0.0702564i
$569$	−13.6522			−0.572329			−0.286165	−	0.958180i	$-0.592380\pi$
$569$	−13.6522			−0.572329			−0.286165	+	0.958180i	$0.592380\pi$
$570$		0			0
$571$		−	42.9453i		−	1.79721i	−0.438762	−	0.898603i	$-0.644583\pi$
$571$		−	42.9453i		−	1.79721i	0.438762	−	0.898603i	$-0.355417\pi$
$572$	−14.9085	−	4.38727i	−0.623356	−	0.183441i
$573$		0			0
$574$	10.1498	−	7.59326i	0.423643	−	0.316937i
$575$	1.99549	−	0.718100i	0.0832177	−	0.0299468i
$576$		0			0
$577$		−	3.16155i		−	0.131617i	−0.997832	−	0.0658086i	$-0.979037\pi$
$577$		−	3.16155i		−	0.131617i	0.997832	−	0.0658086i	$-0.0209627\pi$
$578$	−11.9506	−	15.9742i	−0.497081	−	0.664439i
$579$		0			0
$580$	−20.7340	−	26.0682i	−0.860931	−	1.08242i
$581$			2.66950i			0.110749i
$582$		0			0
$583$			23.3073i			0.965290i
$584$	6.59981	+	17.7436i	0.273102	+	0.734236i
$585$		0			0
$586$	8.76092	+	11.7106i	0.361910	+	0.483759i
$587$	−15.2097			−0.627773			−0.313886	−	0.949461i	$-0.601631\pi$
$587$	−15.2097			−0.627773			−0.313886	+	0.949461i	$0.601631\pi$
$588$		0			0
$589$		−	14.6757i		−	0.604700i
$590$	39.2004	−	1.16131i	1.61386	−	0.0478103i
$591$		0			0
$592$	13.4817	+	8.68709i	0.554095	+	0.357037i
$593$		−	20.6555i		−	0.848219i	−0.905611	−	0.424110i	$-0.860587\pi$
$593$		−	20.6555i		−	0.848219i	0.905611	−	0.424110i	$-0.139413\pi$
$594$		0			0
$595$	3.41358	+	2.39947i	0.139943	+	0.0983687i
$596$	11.6332	+	3.42340i	0.476513	+	0.140228i
$597$		0			0
$598$	−1.96990	+	1.47372i	−0.0805550	+	0.0602650i
$599$	−33.1741			−1.35546			−0.677728	−	0.735313i	$-0.737035\pi$
$599$	−33.1741			−1.35546			−0.677728	+	0.735313i	$0.737035\pi$
$600$		0			0
$601$	48.2851			1.96959			0.984796	−	0.173716i	$-0.0555774\pi$
$601$	48.2851			1.96959			0.984796	+	0.173716i	$0.0555774\pi$
$602$	−13.7188	+	10.2633i	−0.559137	+	0.418302i
$603$		0			0
$604$	7.82921	−	26.6047i	0.318566	−	1.08253i
$605$	13.5564	+	9.52906i	0.551147	+	0.387411i
$606$		0			0
$607$		−	0.630607i		−	0.0255955i	−0.999918	−	0.0127978i	$-0.995926\pi$
$607$		−	0.630607i		−	0.0255955i	0.999918	−	0.0127978i	$-0.00407377\pi$
$608$	33.5781	−	2.35085i	1.36177	−	0.0953395i
$609$		0			0
$610$	−8.95073	+	0.265165i	−0.362405	+	0.0107362i
$611$		−	9.37720i		−	0.379361i
$612$		0			0
$613$	22.1293			0.893794			0.446897	−	0.894585i	$-0.352529\pi$
$613$	22.1293			0.893794			0.446897	+	0.894585i	$0.352529\pi$
$614$	13.2018	+	17.6466i	0.532781	+	0.712158i
$615$		0			0
$616$	5.50976	−	2.04938i	0.221995	−	0.0825718i
$617$		−	20.2904i		−	0.816860i	−0.912790	−	0.408430i	$-0.866076\pi$
$617$		−	20.2904i		−	0.816860i	0.912790	−	0.408430i	$-0.133924\pi$
$618$		0			0
$619$			20.6122i			0.828473i	0.910169	+	0.414236i	$0.135951\pi$
$619$			20.6122i			0.828473i	−0.910169	+	0.414236i	$0.864049\pi$
$620$	−8.63232	+	6.86593i	−0.346682	+	0.275742i
$621$		0			0
$622$	23.8435	+	31.8711i	0.956036	+	1.27792i
$623$		−	13.1992i		−	0.528816i
$624$		0			0
$625$	−19.2674	+	15.9301i	−0.770695	+	0.637204i
$626$	8.04464	−	6.01837i	0.321528	−	0.240542i
$627$		0			0
$628$	6.56131	−	22.2962i	0.261825	−	0.889714i
$629$		−	6.82022i		−	0.271940i
$630$		0			0
$631$	24.4121			0.971829			0.485915	−	0.874006i	$-0.338487\pi$
$631$	24.4121			0.971829			0.485915	+	0.874006i	$0.338487\pi$
$632$	−33.7704	+	12.5610i	−1.34331	+	0.499651i
$633$		0			0
$634$	−8.98330	−	12.0078i	−0.356772	−	0.476891i
$635$	26.1267	−	37.1689i	1.03681	−	1.47500i
$636$		0			0
$637$	23.7736			0.941945
$638$	11.9542	+	15.9790i	0.473273	+	0.632615i
$639$		0			0
$640$	−17.0921	−	18.6510i	−0.675625	−	0.737246i
$641$	6.81719			0.269263			0.134631	−	0.990896i	$-0.457015\pi$
$641$	6.81719			0.269263			0.134631	+	0.990896i	$0.457015\pi$
$642$		0			0
$643$	−15.9317			−0.628286			−0.314143	−	0.949376i	$-0.601717\pi$
$643$	−15.9317			−0.628286			−0.314143	+	0.949376i	$0.601717\pi$
$644$	0.262717	−	0.892747i	0.0103525	−	0.0351792i
$645$		0			0
$646$	−8.57463	−	11.4615i	−0.337364	−	0.450948i
$647$		−	32.9746i		−	1.29636i	−0.761485	−	0.648182i	$-0.775530\pi$
$647$		−	32.9746i		−	1.29636i	0.761485	−	0.648182i	$-0.224470\pi$
$648$		0			0
$649$	−23.4961			−0.922304
$650$	15.9674	−	24.2092i	0.626293	−	0.949563i
$651$		0			0
$652$	−2.83386	+	9.62984i	−0.110983	+	0.377133i
$653$	9.46910			0.370555			0.185277	−	0.982686i	$-0.440682\pi$
$653$	9.46910			0.370555			0.185277	+	0.982686i	$0.440682\pi$
$654$		0			0
$655$	1.91653	−	2.72654i	0.0748852	−	0.106535i
$656$	27.4726	+	17.7023i	1.07263	+	0.691158i
$657$		0			0
$658$	2.12485	+	2.84025i	0.0828353	+	0.110724i
$659$			41.5026i			1.61671i	0.588695	+	0.808356i	$0.299642\pi$
$659$			41.5026i			1.61671i	−0.588695	+	0.808356i	$0.700358\pi$
$660$		0			0
$661$		−	39.7673i		−	1.54677i	−0.633937	−	0.773385i	$-0.718562\pi$
$661$		−	39.7673i		−	1.54677i	0.633937	−	0.773385i	$-0.281438\pi$
$662$	36.3428	−	27.1888i	1.41250	−	1.05672i
$663$		0			0
$664$	−6.45098	+	2.39947i	−0.250347	+	0.0931175i
$665$	−11.9412	−	8.39371i	−0.463061	−	0.325494i
$666$		0			0
$667$	3.15908			0.122320
$668$	−7.19157	−	2.11633i	−0.278250	−	0.0818833i
$669$		0			0
$670$	−0.460027	−	15.5284i	−0.0177724	−	0.599914i
$671$	5.36493			0.207111
$672$		0			0
$673$		−	16.8069i		−	0.647860i	−0.946081	−	0.323930i	$-0.894996\pi$
$673$		−	16.8069i		−	0.647860i	0.946081	−	0.323930i	$-0.105004\pi$
$674$	−25.7627	+	19.2736i	−0.992341	+	0.742392i
$675$		0			0
$676$	−2.15733	+	7.33091i	−0.0829744	+	0.281958i
$677$	8.73792			0.335826			0.167913	−	0.985802i	$-0.446297\pi$
$677$	8.73792			0.335826			0.167913	+	0.985802i	$0.446297\pi$
$678$		0			0
$679$	2.41834			0.0928074
$680$	−2.73016	+	10.4059i	−0.104697	+	0.399047i
$681$		0			0
$682$	5.29135	−	3.95858i	0.202616	−	0.151582i
$683$	37.2358			1.42479			0.712395	−	0.701779i	$-0.247611\pi$
$683$	37.2358			1.42479			0.712395	+	0.701779i	$0.247611\pi$
$684$		0			0
$685$	9.58208	−	13.6319i	0.366112	−	0.520847i
$686$	−15.8965	+	11.8925i	−0.606930	+	0.454057i
$687$		0			0
$688$	−37.1330	−	23.9271i	−1.41568	−	0.912211i
$689$	50.4547			1.92217
$690$		0			0
$691$			46.4665i			1.76767i	0.467798	+	0.883835i	$0.345047\pi$
$691$			46.4665i			1.76767i	−0.467798	+	0.883835i	$0.654953\pi$
$692$	5.98718	−	20.3452i	0.227598	−	0.773409i
$693$		0			0
$694$	19.6635	+	26.2838i	0.746416	+	0.997720i
$695$	−3.49255	+	4.96864i	−0.132480	+	0.188471i
$696$		0			0
$697$		−	13.8980i		−	0.526425i
$698$	−30.6635	+	22.9401i	−1.16063	+	0.868294i
$699$		0			0
$700$	0.649406	+	10.9509i	0.0245452	+	0.413904i
$701$		−	12.8977i		−	0.487141i	−0.969883	−	0.243571i	$-0.921681\pi$
$701$		−	12.8977i		−	0.487141i	0.969883	−	0.243571i	$-0.0783187\pi$
$702$		0			0
$703$			23.8582i			0.899827i
$704$	9.90487	+	11.4726i	0.373304	+	0.432388i
$705$		0			0
$706$	−12.3576	+	9.24500i	−0.465085	+	0.347940i
$707$	2.69177			0.101234
$708$		0			0
$709$		−	18.8715i		−	0.708733i	−0.935107	−	0.354367i	$-0.884696\pi$
$709$		−	18.8715i		−	0.708733i	0.935107	−	0.354367i	$-0.115304\pi$
$710$	−0.159012	−	5.36751i	−0.00596761	−	0.201439i
$711$		0			0
$712$	31.8967	−	11.8641i	1.19538	−	0.444626i
$713$		−	1.04611i		−	0.0391772i
$714$		0			0
$715$	−9.99172	+	14.2146i	−0.373669	+	0.531597i
$716$	−30.2198	−	8.89307i	−1.12937	−	0.332350i
$717$		0			0
$718$	3.52327	+	4.70949i	0.131487	+	0.175757i
$719$	−18.6339			−0.694927			−0.347463	−	0.937694i	$-0.612957\pi$
$719$	−18.6339			−0.694927			−0.347463	+	0.937694i	$0.612957\pi$
$720$		0			0
$721$	−16.1616			−0.601889
$722$	13.8992	+	18.5787i	0.517273	+	0.691429i
$723$		0			0
$724$	−40.2069	−	11.8321i	−1.49428	−	0.439735i
$725$	−35.0401	+	12.6096i	−1.30136	+	0.468308i
$726$		0			0
$727$			24.8278i			0.920812i	0.887708	+	0.460406i	$0.152296\pi$
$727$			24.8278i			0.920812i	−0.887708	+	0.460406i	$0.847704\pi$
$728$	−4.43641	−	11.9273i	−0.164424	−	0.442055i
$729$		0			0
$730$	21.1565	−	0.626760i	0.783038	−	0.0231974i
$731$			18.7851i			0.694792i
$732$		0			0
$733$	0.393641			0.0145395			0.00726973	−	0.999974i	$-0.497686\pi$
$733$	0.393641			0.0145395			0.00726973	+	0.999974i	$0.497686\pi$
$734$	−32.8861	+	24.6028i	−1.21385	+	0.908107i
$735$		0			0
$736$	2.39351	−	0.167573i	0.0882261	−	0.00617684i
$737$			9.30748i			0.342845i
$738$		0			0
$739$		−	12.8787i		−	0.473750i	−0.971540	−	0.236875i	$-0.923877\pi$
$739$		−	12.8787i		−	0.473750i	0.971540	−	0.236875i	$-0.0761233\pi$
$740$	14.0335	−	11.1619i	0.515883	−	0.410320i
$741$		0			0
$742$	−15.2821	+	11.4329i	−0.561025	+	0.419715i
$743$			17.7082i			0.649650i	0.945774	+	0.324825i	$0.105305\pi$
$743$			17.7082i			0.649650i	−0.945774	+	0.324825i	$0.894695\pi$
$744$		0			0
$745$	7.79657	−	11.0917i	0.285644	−	0.406369i
$746$	7.18049	+	9.59802i	0.262896	+	0.351409i
$747$		0			0
$748$	1.81959	−	6.18321i	0.0665309	−	0.226081i
$749$		−	12.2634i		−	0.448093i
$750$		0			0
$751$	−25.8147			−0.941993			−0.470996	−	0.882135i	$-0.656106\pi$
$751$	−25.8147			−0.941993			−0.470996	+	0.882135i	$0.656106\pi$
$752$	−4.95369	+	7.68777i	−0.180643	+	0.280344i
$753$		0			0
$754$	34.5907	−	25.8780i	1.25972	−	0.942423i
$755$	−25.3664	−	17.8305i	−0.923178	−	0.648919i
$756$		0			0
$757$	−9.20871			−0.334696			−0.167348	−	0.985898i	$-0.553520\pi$
$757$	−9.20871			−0.334696			−0.167348	+	0.985898i	$0.553520\pi$
$758$	−30.5326	+	22.8421i	−1.10899	+	0.829663i
$759$		0			0
$760$	9.55050	−	36.4013i	0.346433	−	1.32041i
$761$	−6.94667			−0.251816			−0.125908	−	0.992042i	$-0.540184\pi$
$761$	−6.94667			−0.251816			−0.125908	+	0.992042i	$0.540184\pi$
$762$		0			0
$763$	3.54803			0.128447
$764$	10.2800	−	34.9329i	0.371918	−	1.26383i
$765$		0			0
$766$	−31.8772	+	23.8480i	−1.15177	+	0.861664i
$767$			50.8634i			1.83657i
$768$		0			0
$769$	0.468151			0.0168820			0.00844098	−	0.999964i	$-0.497313\pi$
$769$	0.468151			0.0168820			0.00844098	+	0.999964i	$0.497313\pi$
$770$	−0.194622	−	6.56954i	−0.00701369	−	0.236750i
$771$		0			0
$772$	−17.0515	−	5.01789i	−0.613696	−	0.180598i
$773$	14.0083			0.503843			0.251921	−	0.967748i	$-0.418938\pi$
$773$	14.0083			0.503843			0.251921	+	0.967748i	$0.418938\pi$
$774$		0			0
$775$	4.17558	+	11.6033i	0.149991	+	0.416803i
$776$	2.17372	+	5.84405i	0.0780320	+	0.209789i
$777$		0			0
$778$	−32.2099	+	24.0969i	−1.15478	+	0.863916i
$779$			48.6174i			1.74190i
$780$		0			0
$781$			3.21720i			0.115121i
$782$	−0.611217	−	0.817002i	−0.0218571	−	0.0292159i
$783$		0			0
$784$	−19.4905	−	12.5589i	−0.696088	−	0.448532i
$785$	−21.2584	−	14.9429i	−0.758746	−	0.533337i
$786$		0			0
$787$	−30.3214			−1.08084			−0.540421	−	0.841395i	$-0.681735\pi$
$787$	−30.3214			−1.08084			−0.540421	+	0.841395i	$0.681735\pi$
$788$	4.93359	−	16.7650i	0.175752	−	0.597228i
$789$		0			0
$790$	1.19288	+	40.2660i	0.0424406	+	1.43260i
$791$	−15.5783			−0.553901
$792$		0			0
$793$		−	11.6138i		−	0.412417i
$794$	−16.0829	−	21.4978i	−0.570763	−	0.762927i
$795$		0			0
$796$	−5.48972	+	18.6548i	−0.194578	+	0.661202i
$797$	12.7941			0.453190			0.226595	−	0.973989i	$-0.427241\pi$
$797$	12.7941			0.453190			0.226595	+	0.973989i	$0.427241\pi$
$798$		0			0
$799$	3.88914			0.137588
$800$	−25.8796	+	11.4125i	−0.914983	+	0.403492i
$801$		0			0
$802$	5.04535	+	6.74402i	0.178157	+	0.238140i
$803$	−12.6809			−0.447499
$804$		0			0
$805$	−0.851195	−	0.598321i	−0.0300007	−	0.0210880i
$806$	−8.56935	−	11.4545i	−0.301843	−	0.403467i
$807$		0			0
$808$	2.41949	+	6.50481i	0.0851174	+	0.228838i
$809$	−36.8282			−1.29481			−0.647405	−	0.762146i	$-0.724146\pi$
$809$	−36.8282			−1.29481			−0.647405	+	0.762146i	$0.724146\pi$
$810$		0			0
$811$			20.4801i			0.719153i	0.933116	+	0.359576i	$0.117079\pi$
$811$			20.4801i			0.719153i	−0.933116	+	0.359576i	$0.882921\pi$
$812$	−4.61322	+	15.6763i	−0.161892	+	0.550131i
$813$		0			0
$814$	−8.60213	+	6.43544i	−0.301504	+	0.225562i
$815$	9.18163	+	6.45394i	0.321619	+	0.226072i
$816$		0			0
$817$		−	65.7131i		−	2.29901i
$818$	25.7213	+	34.3811i	0.899323	+	1.20211i
$819$		0			0
$820$	28.5971	−	22.7454i	0.998652	−	0.794303i
$821$			37.8925i			1.32246i	0.750184	+	0.661229i	$0.229965\pi$
$821$			37.8925i			1.32246i	−0.750184	+	0.661229i	$0.770035\pi$
$822$		0			0
$823$		−	1.89215i		−	0.0659562i	−0.999456	−	0.0329781i	$-0.989501\pi$
$823$		−	1.89215i		−	0.0659562i	0.999456	−	0.0329781i	$-0.0104992\pi$
$824$	−14.5268	−	39.0554i	−0.506066	−	1.36056i
$825$		0			0
$826$	−11.5255	−	15.4059i	−0.401024	−	0.536041i
$827$	45.9585			1.59813			0.799067	−	0.601242i	$-0.205327\pi$
$827$	45.9585			1.59813			0.799067	+	0.601242i	$0.205327\pi$
$828$		0			0
$829$			44.1972i			1.53503i	0.641029	+	0.767517i	$0.278508\pi$
$829$			44.1972i			1.53503i	−0.641029	+	0.767517i	$0.721492\pi$
$830$	0.227869	+	7.69180i	0.00790945	+	0.266986i
$831$		0			0
$832$	24.8353	−	21.4416i	0.861009	−	0.743355i
$833$			9.85996i			0.341627i
$834$		0			0
$835$	−4.81981	+	6.85685i	−0.166796	+	0.237291i
$836$	−6.36521	+	21.6298i	−0.220145	+	0.748083i
$837$		0			0
$838$	−3.09030	+	2.31192i	−0.106753	+	0.0798640i
$839$	−29.2610			−1.01020			−0.505102	−	0.863060i	$-0.668545\pi$
$839$	−29.2610			−1.01020			−0.505102	+	0.863060i	$0.668545\pi$
$840$		0			0
$841$	−26.4724			−0.912841
$842$	10.5122	−	7.86441i	0.362274	−	0.271025i
$843$		0			0
$844$	27.0227	+	7.95223i	0.930160	+	0.273727i
$845$	6.98970	+	4.91319i	0.240453	+	0.169019i
$846$		0			0
$847$		−	8.12942i		−	0.279330i
$848$	−41.3645	−	26.6537i	−1.42046	−	0.915291i
$849$		0			0
$850$	10.0406	+	6.62238i	0.344390	+	0.227146i
$851$			1.70066i			0.0582978i
$852$		0			0
$853$	10.0803			0.345143			0.172572	−	0.984997i	$-0.444792\pi$
$853$	10.0803			0.345143			0.172572	+	0.984997i	$0.444792\pi$
$854$	2.63165	+	3.51768i	0.0900532	+	0.120372i
$855$		0			0
$856$	29.6351	−	11.0229i	1.01291	−	0.376754i
$857$			43.9269i			1.50052i	0.661145	+	0.750258i	$0.270071\pi$
$857$			43.9269i			1.50052i	−0.661145	+	0.750258i	$0.729929\pi$
$858$		0			0
$859$			9.28531i			0.316811i	0.987374	+	0.158405i	$0.0506353\pi$
$859$			9.28531i			0.316811i	−0.987374	+	0.158405i	$0.949365\pi$
$860$	−38.6529	+	30.7435i	−1.31805	+	1.04835i
$861$		0			0
$862$	−13.7013	−	18.3143i	−0.466668	−	0.623787i
$863$			33.4004i			1.13696i	0.822696	+	0.568481i	$0.192469\pi$
$863$			33.4004i			1.13696i	−0.822696	+	0.568481i	$0.807531\pi$
$864$		0			0
$865$	−19.3983	−	13.6354i	−0.659561	−	0.463618i
$866$	28.3730	−	21.2265i	0.964155	−	0.721305i
$867$		0			0
$868$	5.19111	+	1.52764i	0.176198	+	0.0518514i
$869$		−	24.1348i		−	0.818718i
$870$		0			0
$871$	20.1484			0.682703
$872$	3.18914	+	8.57401i	0.107998	+	0.290353i
$873$		0			0
$874$	2.13813	+	2.85800i	0.0723233	+	0.0966731i
$875$	11.8295	+	3.23892i	0.399912	+	0.109495i
$876$		0			0
$877$	5.85859			0.197830			0.0989152	−	0.995096i	$-0.468463\pi$
$877$	5.85859			0.197830			0.0989152	+	0.995096i	$0.468463\pi$
$878$	8.33231	+	11.1376i	0.281202	+	0.375877i
$879$		0			0
$880$	15.7007	−	6.37533i	0.529271	−	0.214912i
$881$	33.5615			1.13071			0.565357	−	0.824846i	$-0.308738\pi$
$881$	33.5615			1.13071			0.565357	+	0.824846i	$0.308738\pi$
$882$		0			0
$883$	0.194722			0.00655291			0.00327645	−	0.999995i	$-0.498957\pi$
$883$	0.194722			0.00655291			0.00327645	+	0.999995i	$0.498957\pi$
$884$	−13.3852	−	3.93897i	−0.450191	−	0.132482i
$885$		0			0
$886$	29.0259	+	38.7984i	0.975144	+	1.30346i
$887$		−	7.68201i		−	0.257937i	−0.991649	−	0.128968i	$-0.958833\pi$
$887$		−	7.68201i		−	0.257937i	0.991649	−	0.128968i	$-0.0411665\pi$
$888$		0			0
$889$	−22.2892			−0.747556
$890$	−1.12669	−	38.0319i	−0.0377667	−	1.27483i
$891$		0			0
$892$	−11.9671	−	3.52168i	−0.400689	−	0.117915i
$893$	−13.6048			−0.455267
$894$		0			0
$895$	−20.2534	+	28.8133i	−0.676996	+	0.963122i
$896$	−2.66370	+	12.1220i	−0.0889881	+	0.404969i
$897$		0			0
$898$	−33.1930	−	44.3684i	−1.10766	−	1.48059i
$899$			18.3693i			0.612652i
$900$		0			0
$901$			20.9257i			0.697138i
$902$	−17.5291	+	13.1139i	−0.583656	+	0.436646i
$903$		0			0
$904$	−14.0025	−	37.6459i	−0.465718	−	1.25208i
$905$	−26.9467	+	38.3355i	−0.895739	+	1.27432i
$906$		0			0
$907$	−34.7134			−1.15264			−0.576320	−	0.817224i	$-0.695512\pi$
$907$	−34.7134			−1.15264			−0.576320	+	0.817224i	$0.695512\pi$
$908$	−5.50549	+	18.7084i	−0.182706	+	0.620859i
$909$		0			0
$910$	−14.2215	+	0.421309i	−0.471437	+	0.0139663i
$911$	18.8670			0.625091			0.312546	−	0.949903i	$-0.398818\pi$
$911$	18.8670			0.625091			0.312546	+	0.949903i	$0.398818\pi$
$912$		0			0
$913$		−	4.61035i		−	0.152580i
$914$	−35.9405	+	26.8879i	−1.18881	+	0.889372i
$915$		0			0
$916$	−51.4016	−	15.1264i	−1.69836	−	0.499792i
$917$	−1.63503			−0.0539935
$918$		0			0
$919$	−26.4932			−0.873931			−0.436965	−	0.899478i	$-0.643947\pi$
$919$	−26.4932			−0.873931			−0.436965	+	0.899478i	$0.643947\pi$
$920$	0.680780	−	2.59476i	0.0224446	−	0.0855467i
$921$		0			0
$922$	−28.7474	+	21.5066i	−0.946747	+	0.708282i
$923$	6.96447			0.229238
$924$		0			0
$925$	−6.78823	−	18.8635i	−0.223196	−	0.620227i
$926$	45.8423	−	34.2956i	1.50647	−	1.12702i
$927$		0			0
$928$	−42.0293	+	2.94253i	−1.37968	+	0.0965933i
$929$	57.5829			1.88923			0.944617	−	0.328176i	$-0.106434\pi$
$929$	57.5829			1.88923			0.944617	+	0.328176i	$0.106434\pi$
$930$		0			0
$931$		−	34.4916i		−	1.13042i
$932$	−53.2863	−	15.6811i	−1.74545	−	0.513650i
$933$		0			0
$934$	20.0914	+	26.8558i	0.657412	+	0.878750i
$935$	−5.89543	−	4.14400i	−0.192801	−	0.135523i
$936$		0			0
$937$		−	27.1596i		−	0.887267i	−0.896208	−	0.443633i	$-0.853689\pi$
$937$		−	27.1596i		−	0.887267i	0.896208	−	0.443633i	$-0.146311\pi$
$938$	−6.10272	+	4.56558i	−0.199261	+	0.149071i
$939$		0			0
$940$	6.36492	+	8.00242i	0.207601	+	0.261010i
$941$			47.4407i			1.54652i	0.634088	+	0.773261i	$0.281375\pi$
$941$			47.4407i			1.54652i	−0.634088	+	0.773261i	$0.718625\pi$
$942$		0			0
$943$			3.46555i			0.112854i
$944$	26.8696	−	41.6996i	0.874531	−	1.35721i
$945$		0			0
$946$	23.6930	−	17.7253i	0.770327	−	0.576299i
$947$	24.5863			0.798947			0.399473	−	0.916745i	$-0.369193\pi$
$947$	24.5863			0.798947			0.399473	+	0.916745i	$0.369193\pi$
$948$		0			0
$949$			27.4511i			0.891099i
$950$	−35.1236	−	23.1661i	−1.13956	−	0.751606i
$951$		0			0
$952$	4.94677	−	1.83997i	0.160326	−	0.0596338i
$953$		−	50.0020i		−	1.61973i	−0.586620	−	0.809863i	$-0.699542\pi$
$953$		−	50.0020i		−	1.61973i	0.586620	−	0.809863i	$-0.300458\pi$
$954$		0			0
$955$	−33.3070	−	23.4121i	−1.07779	−	0.757597i
$956$	3.89311	−	13.2293i	0.125912	−	0.427866i
$957$		0			0
$958$	14.2604	+	19.0616i	0.460733	+	0.615853i
$959$	−8.17466			−0.263973
$960$		0			0
$961$	−24.9171			−0.803778
$962$	13.9312	+	18.6215i	0.449159	+	0.600382i
$963$		0			0
$964$	−6.05489	+	20.5753i	−0.195015	+	0.662686i
$965$	−11.4279	+	16.2578i	−0.367878	+	0.523358i
$966$		0			0
$967$		−	6.52916i		−	0.209964i	−0.994474	−	0.104982i	$-0.966522\pi$
$967$		−	6.52916i		−	0.209964i	0.994474	−	0.104982i	$-0.0334784\pi$
$968$	19.6452	−	7.30711i	0.631421	−	0.234860i
$969$		0			0
$970$	6.96813	−	0.206430i	0.223733	−	0.00662807i
$971$			22.2092i			0.712726i	0.934348	+	0.356363i	$0.115983\pi$
$971$			22.2092i			0.712726i	−0.934348	+	0.356363i	$0.884017\pi$
$972$		0			0
$973$	2.97956			0.0955204
$974$	−14.1747	+	10.6044i	−0.454185	+	0.339786i
$975$		0			0
$976$	−6.13520	+	9.52138i	−0.196383	+	0.304772i
$977$		−	48.6812i		−	1.55745i	−0.627366	−	0.778725i	$-0.715867\pi$
$977$		−	48.6812i		−	1.55745i	0.627366	−	0.778725i	$-0.284133\pi$
$978$		0			0
$979$			22.7957i			0.728554i
$980$	−20.2882	+	16.1367i	−0.648083	+	0.515468i
$981$		0			0
$982$	−31.9203	+	23.8803i	−1.01862	+	0.762051i
$983$			1.13847i			0.0363115i	0.999835	+	0.0181558i	$0.00577948\pi$
$983$			1.13847i			0.0363115i	−0.999835	+	0.0181558i	$0.994221\pi$
$984$		0			0
$985$	−15.9847	−	11.2359i	−0.509315	−	0.358007i
$986$	10.7328	+	14.3463i	0.341801	+	0.456878i
$987$		0			0
$988$	46.8233	+	13.7791i	1.48965	+	0.438372i
$989$		−	4.68416i		−	0.148948i
$990$		0			0
$991$	43.1309			1.37010			0.685049	−	0.728497i	$-0.259781\pi$
$991$	43.1309			1.37010			0.685049	+	0.728497i	$0.259781\pi$
$992$	0.974400	+	13.9177i	0.0309372	+	0.441888i
$993$		0			0
$994$	−2.10946	+	1.57813i	−0.0669079	+	0.0500552i
$995$	17.7865	+	12.5025i	0.563871	+	0.396355i
$996$		0			0
$997$	−27.7853			−0.879969			−0.439984	−	0.898005i	$-0.645016\pi$
$997$	−27.7853			−0.879969			−0.439984	+	0.898005i	$0.645016\pi$
$998$	19.0245	−	14.2327i	0.602211	−	0.450527i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.i.109.7	✓	20
3.2	odd	2	inner	1080.2.d.i.109.14	yes	20
4.3	odd	2		4320.2.d.i.3889.16		20
5.4	even	2		1080.2.d.j.109.14	yes	20
8.3	odd	2		4320.2.d.j.3889.5		20
8.5	even	2		1080.2.d.j.109.13	yes	20
12.11	even	2		4320.2.d.i.3889.5		20
15.14	odd	2		1080.2.d.j.109.7	yes	20
20.19	odd	2		4320.2.d.j.3889.6		20
24.5	odd	2		1080.2.d.j.109.8	yes	20
24.11	even	2		4320.2.d.j.3889.16		20
40.19	odd	2		4320.2.d.i.3889.15		20
40.29	even	2	inner	1080.2.d.i.109.8	yes	20
60.59	even	2		4320.2.d.j.3889.15		20
120.29	odd	2	inner	1080.2.d.i.109.13	yes	20
120.59	even	2		4320.2.d.i.3889.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.i.109.7	✓	20	1.1	even	1	trivial
1080.2.d.i.109.8	yes	20	40.29	even	2	inner
1080.2.d.i.109.13	yes	20	120.29	odd	2	inner
1080.2.d.i.109.14	yes	20	3.2	odd	2	inner
1080.2.d.j.109.7	yes	20	15.14	odd	2
1080.2.d.j.109.8	yes	20	24.5	odd	2
1080.2.d.j.109.13	yes	20	8.5	even	2
1080.2.d.j.109.14	yes	20	5.4	even	2
4320.2.d.i.3889.5		20	12.11	even	2
4320.2.d.i.3889.6		20	120.59	even	2
4320.2.d.i.3889.15		20	40.19	odd	2
4320.2.d.i.3889.16		20	4.3	odd	2
4320.2.d.j.3889.5		20	8.3	odd	2
4320.2.d.j.3889.6		20	20.19	odd	2
4320.2.d.j.3889.15		20	60.59	even	2
4320.2.d.j.3889.16		20	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.847166 - 1.13239i) q^{2} +(-0.564618 + 1.91865i) q^{4} +(1.82935 + 1.28588i) q^{5} -1.09701i q^{7} +(2.65098 - 0.986045i) q^{8} +O(q^{10})\)	\(q+(-0.847166 - 1.13239i) q^{2} +(-0.564618 + 1.91865i) q^{4} +(1.82935 + 1.28588i) q^{5} -1.09701i q^{7} +(2.65098 - 0.986045i) q^{8} +(-0.0936411 - 3.16089i) q^{10} +1.89459i q^{11} +4.10133 q^{13} +(-1.24224 + 0.929350i) q^{14} +(-3.36241 - 2.16661i) q^{16} +1.70100i q^{17} -5.95035i q^{19} +(-3.50003 + 2.78384i) q^{20} +(2.14542 - 1.60503i) q^{22} -0.424153i q^{23} +(1.69302 + 4.70465i) q^{25} +(-3.47451 - 4.64430i) q^{26} +(2.10477 + 0.619392i) q^{28} +7.44798i q^{29} +2.46635 q^{31} +(0.395078 + 5.64304i) q^{32} +(1.92620 - 1.44103i) q^{34} +(1.41062 - 2.00681i) q^{35} -4.00954 q^{37} +(-6.73812 + 5.04094i) q^{38} +(6.11751 + 1.60503i) q^{40} -8.17051 q^{41} +11.0436 q^{43} +(-3.63505 - 1.06972i) q^{44} +(-0.480307 + 0.359328i) q^{46} -2.28638i q^{47} +5.79657 q^{49} +(3.89323 - 5.90278i) q^{50} +(-2.31568 + 7.86900i) q^{52} +12.3020 q^{53} +(-2.43622 + 3.46586i) q^{55} +(-1.08170 - 2.90816i) q^{56} +(8.43402 - 6.30968i) q^{58} +12.4017i q^{59} -2.83171i q^{61} +(-2.08941 - 2.79287i) q^{62} +(6.05543 - 5.22798i) q^{64} +(7.50275 + 5.27382i) q^{65} +4.91266 q^{67} +(-3.26362 - 0.960415i) q^{68} +(-3.46753 + 0.102725i) q^{70} +1.69810 q^{71} +6.69321i q^{73} +(3.39675 + 4.54036i) q^{74} +(11.4166 + 3.35968i) q^{76} +2.07838 q^{77} -12.7388 q^{79} +(-3.36502 - 8.28714i) q^{80} +(6.92178 + 9.25221i) q^{82} -2.43343 q^{83} +(-2.18728 + 3.11172i) q^{85} +(-9.35574 - 12.5056i) q^{86} +(1.86815 + 5.02253i) q^{88} +12.0320 q^{89} -4.49919i q^{91} +(0.813800 + 0.239485i) q^{92} +(-2.58908 + 1.93695i) q^{94} +(7.65144 - 10.8853i) q^{95} +2.20448i q^{97} +(-4.91066 - 6.56398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4}+O(q^{10}) \) 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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