LMFDB - Embedded newform 224.2.q.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(47,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("224.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.q (of order $6$, degree $2$, not 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.2
Root			$-0.0263223 + 0.217464i$ of defining polynomial
Character	$\chi$	$=$	224.47
Dual form			224.2.q.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18878 + 0.686340i) q^{3} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(-0.557875 + 0.966267i) q^{9} +O(q^{10})$	\(q+(-1.18878 + 0.686340i) q^{3} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(-0.557875 + 0.966267i) q^{9} +(1.63090 + 2.82480i) q^{11} +5.27279 q^{13} +0.947443i q^{15} +(-2.20393 + 1.27244i) q^{17} +(0.484848 + 0.279927i) q^{19} +(-2.98150 + 2.07374i) q^{21} +(2.50610 + 1.44690i) q^{23} +(2.26180 + 3.91756i) q^{25} -5.64961i q^{27} +0.444621i q^{29} +(-4.45228 - 7.71158i) q^{31} +(-3.87755 - 2.23871i) q^{33} +(0.776954 - 1.65261i) q^{35} +(-6.00295 - 3.46580i) q^{37} +(-6.26817 + 3.61893i) q^{39} -9.76765i q^{41} +(0.385053 + 0.666931i) q^{45} +(-2.20094 + 3.81214i) q^{47} +(6.90116 - 1.17220i) q^{49} +(1.74665 - 3.02529i) q^{51} +(-8.17440 + 4.71949i) q^{53} +2.25134 q^{55} -0.768501 q^{57} +(-8.59663 + 4.96327i) q^{59} +(5.23284 - 9.06355i) q^{61} +(-1.25597 + 2.67148i) q^{63} +(1.81968 - 3.15177i) q^{65} +(1.45058 + 2.51247i) q^{67} -3.97225 q^{69} -5.29150i q^{71} +(-5.28541 + 3.05153i) q^{73} +(-5.37755 - 3.10473i) q^{75} +(4.92768 + 7.08473i) q^{77} +(5.01803 + 2.89716i) q^{79} +(2.20393 + 3.81731i) q^{81} +1.83845i q^{83} +1.75651i q^{85} +(-0.305161 - 0.528555i) q^{87} +(1.50000 + 0.866025i) q^{89} +(13.9012 - 1.17220i) q^{91} +(10.5855 + 6.11156i) q^{93} +(0.334649 - 0.193210i) q^{95} +7.42325i q^{97} -3.63935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3}+O(q^{10}) $ 12 * q + 6 * q^3	$ 12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^11 - 6 * q^17 + 6 * q^19 - 6 * q^33 - 18 * q^35 - 12 * q^49 - 6 * q^51 - 36 * q^57 - 42 * q^59 - 12 * q^65 - 30 * q^67 + 18 * q^73 - 24 * q^75 + 6 * q^81 + 18 * q^89 + 72 * q^91 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	−1.18878	+	0.686340i	−0.686340	+	0.396259i	−0.802239	−	0.597002i	$-0.796358\pi$
$3$	−1.18878	+	0.686340i	−0.686340	+	0.396259i	0.115899	+	0.993261i	$0.463025\pi$
$4$		0			0
$5$	0.345107	−	0.597743i	0.154337	−	0.267319i	−0.778481	−	0.627669i	$-0.784009\pi$
$5$	0.345107	−	0.597743i	0.154337	−	0.267319i	0.932817	+	0.360350i	$0.117343\pi$
$6$		0			0
$7$	2.63639	−	0.222310i	0.996464	−	0.0840255i
$7$	2.63639	−	0.222310i	0.996464	−	0.0840255i
$8$		0			0
$9$	−0.557875	+	0.966267i	−0.185958	+	0.322089i
$10$		0			0
$11$	1.63090	+	2.82480i	0.491735	+	0.851710i	0.999955	−	0.00951723i	$-0.00302947\pi$
$11$	1.63090	+	2.82480i	0.491735	+	0.851710i	−0.508220	+	0.861228i	$0.669696\pi$
$12$		0			0
$13$	5.27279			1.46241			0.731204	−	0.682158i	$-0.238959\pi$
$13$	5.27279			1.46241			0.731204	+	0.682158i	$0.238959\pi$
$14$		0			0
$15$			0.947443i			0.244629i
$16$		0			0
$17$	−2.20393	+	1.27244i	−0.534531	+	0.308612i	−0.742860	−	0.669447i	$-0.766531\pi$
$17$	−2.20393	+	1.27244i	−0.534531	+	0.308612i	0.208329	+	0.978059i	$0.433198\pi$
$18$		0			0
$19$	0.484848	+	0.279927i	0.111232	+	0.0642197i	0.554584	−	0.832128i	$-0.312877\pi$
$19$	0.484848	+	0.279927i	0.111232	+	0.0642197i	−0.443352	+	0.896348i	$0.646211\pi$
$20$		0			0
$21$	−2.98150	+	2.07374i	−0.650617	+	0.452527i
$22$		0			0
$23$	2.50610	+	1.44690i	0.522558	+	0.301699i	0.737981	−	0.674822i	$-0.235780\pi$
$23$	2.50610	+	1.44690i	0.522558	+	0.301699i	−0.215423	+	0.976521i	$0.569113\pi$
$24$		0			0
$25$	2.26180	+	3.91756i	0.452360	+	0.783511i
$26$		0			0
$27$		−	5.64961i		−	1.08727i
$28$		0			0
$29$			0.444621i			0.0825640i	0.999148	+	0.0412820i	$0.0131442\pi$
$29$			0.444621i			0.0825640i	−0.999148	+	0.0412820i	$0.986856\pi$
$30$		0			0
$31$	−4.45228	−	7.71158i	−0.799653	−	1.38504i	−0.919842	−	0.392289i	$-0.871683\pi$
$31$	−4.45228	−	7.71158i	−0.799653	−	1.38504i	0.120189	−	0.992751i	$-0.461650\pi$
$32$		0			0
$33$	−3.87755	−	2.23871i	−0.674995	−	0.389709i
$34$		0			0
$35$	0.776954	−	1.65261i	0.131329	−	0.279342i
$36$		0			0
$37$	−6.00295	−	3.46580i	−0.986879	−	0.569775i	−0.0825390	−	0.996588i	$-0.526303\pi$
$37$	−6.00295	−	3.46580i	−0.986879	−	0.569775i	−0.904340	+	0.426813i	$0.859636\pi$
$38$		0			0
$39$	−6.26817	+	3.61893i	−1.00371	+	0.579492i
$40$		0			0
$41$		−	9.76765i		−	1.52545i	−0.646723	−	0.762725i	$-0.723861\pi$
$41$		−	9.76765i		−	1.52545i	0.646723	−	0.762725i	$-0.276139\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	0.385053	+	0.666931i	0.0574003	+	0.0994203i
$46$		0			0
$47$	−2.20094	+	3.81214i	−0.321040	+	0.556057i	−0.980703	−	0.195504i	$-0.937366\pi$
$47$	−2.20094	+	3.81214i	−0.321040	+	0.556057i	0.659663	+	0.751561i	$0.270699\pi$
$48$		0			0
$49$	6.90116	−	1.17220i	0.985879	−	0.167457i
$50$		0			0
$51$	1.74665	−	3.02529i	0.244580	−	0.423625i
$52$		0			0
$53$	−8.17440	+	4.71949i	−1.12284	+	0.648272i	−0.942124	−	0.335263i	$-0.891175\pi$
$53$	−8.17440	+	4.71949i	−1.12284	+	0.648272i	−0.180716	+	0.983535i	$0.557841\pi$
$54$		0			0
$55$	2.25134			0.303571
$56$		0			0
$57$	−0.768501			−0.101790
$58$		0			0
$59$	−8.59663	+	4.96327i	−1.11919	+	0.646162i	−0.941193	−	0.337869i	$-0.890294\pi$
$59$	−8.59663	+	4.96327i	−1.11919	+	0.646162i	−0.177993	+	0.984032i	$0.556960\pi$
$60$		0			0
$61$	5.23284	−	9.06355i	0.669997	−	1.16047i	−0.307907	−	0.951416i	$-0.599629\pi$
$61$	5.23284	−	9.06355i	0.669997	−	1.16047i	0.977904	−	0.209053i	$-0.0670380\pi$
$62$		0			0
$63$	−1.25597	+	2.67148i	−0.158237	+	0.336575i
$64$		0			0
$65$	1.81968	−	3.15177i	0.225703	−	0.390929i
$66$		0			0
$67$	1.45058	+	2.51247i	0.177216	+	0.306948i	0.940926	−	0.338612i	$-0.109957\pi$
$67$	1.45058	+	2.51247i	0.177216	+	0.306948i	−0.763710	+	0.645560i	$0.776624\pi$
$68$		0			0
$69$	−3.97225			−0.478203
$70$		0			0
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$		0			0
$73$	−5.28541	+	3.05153i	−0.618610	+	0.357155i	−0.776328	−	0.630330i	$-0.782920\pi$
$73$	−5.28541	+	3.05153i	−0.618610	+	0.357155i	0.157718	+	0.987484i	$0.449586\pi$
$74$		0			0
$75$	−5.37755	−	3.10473i	−0.620946	−	0.358503i
$76$		0			0
$77$	4.92768	+	7.08473i	0.561562	+	0.807380i
$78$		0			0
$79$	5.01803	+	2.89716i	0.564573	+	0.325956i	0.754979	−	0.655749i	$-0.227647\pi$
$79$	5.01803	+	2.89716i	0.564573	+	0.325956i	−0.190406	+	0.981705i	$0.560980\pi$
$80$		0			0
$81$	2.20393	+	3.81731i	0.244881	+	0.424146i
$82$		0			0
$83$			1.83845i			0.201796i	0.994897	+	0.100898i	$0.0321716\pi$
$83$			1.83845i			0.201796i	−0.994897	+	0.100898i	$0.967828\pi$
$84$		0			0
$85$			1.75651i			0.190520i
$86$		0			0
$87$	−0.305161	−	0.528555i	−0.0327167	−	0.0566670i
$88$		0			0
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	0.577389	−	0.816469i	$-0.304072\pi$
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	−0.418389	+	0.908268i	$0.637405\pi$
$90$		0			0
$91$	13.9012	−	1.17220i	1.45724	−	0.122880i
$92$		0			0
$93$	10.5855	+	6.11156i	1.09767	+	0.633739i
$94$		0			0
$95$	0.334649	−	0.193210i	0.0343343	−	0.0198229i
$96$		0			0
$97$			7.42325i			0.753717i	0.926271	+	0.376859i	$0.122996\pi$
$97$			7.42325i			0.753717i	−0.926271	+	0.376859i	$0.877004\pi$
$98$		0			0
$99$	−3.63935			−0.365769
$100$		0			0
$101$	−6.30811	−	10.9260i	−0.627681	−	1.08717i	−0.988016	−	0.154352i	$-0.950671\pi$
$101$	−6.30811	−	10.9260i	−0.627681	−	1.08717i	0.360335	−	0.932823i	$-0.382662\pi$
$102$		0			0
$103$	3.19631	−	5.53618i	0.314942	−	0.545496i	−0.664483	−	0.747303i	$-0.731348\pi$
$103$	3.19631	−	5.53618i	0.314942	−	0.545496i	0.979425	+	0.201808i	$0.0646816\pi$
$104$		0			0
$105$	0.210627	+	2.49783i	0.0205550	+	0.243764i
$106$		0			0
$107$	1.51515	−	2.62432i	0.146475	−	0.253703i	−0.783447	−	0.621458i	$-0.786540\pi$
$107$	1.51515	−	2.62432i	0.146475	−	0.253703i	0.929922	+	0.367756i	$0.119874\pi$
$108$		0			0
$109$	7.25892	−	4.19094i	0.695278	−	0.401419i	−0.110308	−	0.993897i	$-0.535184\pi$
$109$	7.25892	−	4.19094i	0.695278	−	0.401419i	0.805586	+	0.592478i	$0.201850\pi$
$110$		0			0
$111$	9.51488			0.903113
$112$		0			0
$113$	−12.6260			−1.18775			−0.593875	−	0.804557i	$-0.702403\pi$
$113$	−12.6260			−1.18775			−0.593875	+	0.804557i	$0.702403\pi$
$114$		0			0
$115$	1.72974	−	0.998669i	0.161300	−	0.0931263i
$116$		0			0
$117$	−2.94156	+	5.09492i	−0.271947	+	0.471026i
$118$		0			0
$119$	−5.52755	+	3.84461i	−0.506709	+	0.352434i
$120$		0			0
$121$	0.180323	−	0.312329i	0.0163930	−	0.0283935i
$122$		0			0
$123$	6.70393	+	11.6115i	0.604473	+	1.04698i
$124$		0			0
$125$	6.57333			0.587936
$126$		0			0
$127$		−	6.18074i		−	0.548452i	−0.961665	−	0.274226i	$-0.911578\pi$
$127$		−	6.18074i		−	0.548452i	0.961665	−	0.274226i	$-0.0884217\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.81122	+	1.04571i	0.158247	+	0.0913642i	0.577032	−	0.816721i	$-0.304211\pi$
$131$	1.81122	+	1.04571i	0.158247	+	0.0913642i	−0.418785	+	0.908085i	$0.637544\pi$
$132$		0			0
$133$	1.34048	+	0.630212i	0.116235	+	0.0546463i
$134$		0			0
$135$	−3.37701	−	1.94972i	−0.290647	−	0.167805i
$136$		0			0
$137$	2.43543	+	4.21828i	0.208073	+	0.360392i	0.951107	−	0.308861i	$-0.0999477\pi$
$137$	2.43543	+	4.21828i	0.208073	+	0.360392i	−0.743035	+	0.669253i	$0.766614\pi$
$138$		0			0
$139$		−	1.83845i		−	0.155935i	−0.996956	−	0.0779677i	$-0.975157\pi$
$139$		−	1.83845i		−	0.155935i	0.996956	−	0.0779677i	$-0.0248431\pi$
$140$		0			0
$141$		−	6.04237i		−	0.508859i
$142$		0			0
$143$	8.59940	+	14.8946i	0.719118	+	1.24555i
$144$		0			0
$145$	0.265769	+	0.153442i	0.0220709	+	0.0127426i
$146$		0			0
$147$	−7.39940	+	6.13002i	−0.610292	+	0.505595i
$148$		0			0
$149$	7.68854	+	4.43898i	0.629870	+	0.363655i	0.780702	−	0.624904i	$-0.214862\pi$
$149$	7.68854	+	4.43898i	0.629870	+	0.363655i	−0.150832	+	0.988559i	$0.548195\pi$
$150$		0			0
$151$	1.69142	−	0.976544i	0.137646	−	0.0794700i	−0.429596	−	0.903021i	$-0.641344\pi$
$151$	1.69142	−	0.976544i	0.137646	−	0.0794700i	0.567242	+	0.823551i	$0.308011\pi$
$152$		0			0
$153$		−	2.83944i		−	0.229555i
$154$		0			0
$155$	−6.14605			−0.493663
$156$		0			0
$157$	−0.650268	−	1.12630i	−0.0518970	−	0.0898883i	0.838910	−	0.544270i	$-0.183193\pi$
$157$	−0.650268	−	1.12630i	−0.0518970	−	0.0898883i	−0.890807	+	0.454382i	$0.849860\pi$
$158$		0			0
$159$	6.47835	−	11.2208i	0.513767	−	0.889870i
$160$		0			0
$161$	6.92873	+	3.25746i	0.546060	+	0.256724i
$162$		0			0
$163$	−4.30453	+	7.45566i	−0.337156	+	0.583972i	−0.983897	−	0.178738i	$-0.942798\pi$
$163$	−4.30453	+	7.45566i	−0.337156	+	0.583972i	0.646740	+	0.762710i	$0.276132\pi$
$164$		0			0
$165$	−2.67634	+	1.54519i	−0.208353	+	0.120293i
$166$		0			0
$167$	−5.27279			−0.408021			−0.204010	−	0.978969i	$-0.565398\pi$
$167$	−5.27279			−0.408021			−0.204010	+	0.978969i	$0.565398\pi$
$168$		0			0
$169$	14.8023			1.13864
$170$		0			0
$171$	−0.540969	+	0.312329i	−0.0413689	+	0.0238844i
$172$		0			0
$173$	−8.25429	+	14.2969i	−0.627562	+	1.08697i	0.360477	+	0.932768i	$0.382614\pi$
$173$	−8.25429	+	14.2969i	−0.627562	+	1.08697i	−0.988039	+	0.154202i	$0.950719\pi$
$174$		0			0
$175$	6.83392	+	9.82540i	0.516596	+	0.742731i
$176$		0			0
$177$	6.81298	−	11.8004i	0.512095	−	0.886974i
$178$		0			0
$179$	−11.1242	−	19.2677i	−0.831462	−	1.44013i	−0.896879	−	0.442276i	$-0.854171\pi$
$179$	−11.1242	−	19.2677i	−0.831462	−	1.44013i	0.0654170	−	0.997858i	$-0.479162\pi$
$180$		0			0
$181$	−10.0244			−0.745108			−0.372554	−	0.928011i	$-0.621518\pi$
$181$	−10.0244			−0.745108			−0.372554	+	0.928011i	$0.621518\pi$
$182$		0			0
$183$			14.3660i			1.06197i
$184$		0			0
$185$	−4.14332	+	2.39215i	−0.304623	+	0.175874i
$186$		0			0
$187$	−7.18878	−	4.15044i	−0.525695	−	0.303510i
$188$		0			0
$189$	−1.25597	−	14.8946i	−0.0913581	−	1.08342i
$190$		0			0
$191$	−21.6511	−	12.5003i	−1.56662	−	0.904487i	−0.996559	−	0.0828820i	$-0.973588\pi$
$191$	−21.6511	−	12.5003i	−1.56662	−	0.904487i	−0.570058	−	0.821605i	$-0.693079\pi$
$192$		0			0
$193$	−5.69723	−	9.86789i	−0.410095	−	0.710306i	0.584804	−	0.811174i	$-0.301171\pi$
$193$	−5.69723	−	9.86789i	−0.410095	−	0.710306i	−0.994900	+	0.100868i	$0.967838\pi$
$194$		0			0
$195$			4.99567i			0.357747i
$196$		0			0
$197$		−	10.1384i		−	0.722330i	−0.932502	−	0.361165i	$-0.882379\pi$
$197$		−	10.1384i		−	0.722330i	0.932502	−	0.361165i	$-0.117621\pi$
$198$		0			0
$199$	−5.40309	−	9.35842i	−0.383015	−	0.663401i	0.608477	−	0.793572i	$-0.291781\pi$
$199$	−5.40309	−	9.35842i	−0.383015	−	0.663401i	−0.991492	+	0.130171i	$0.958447\pi$
$200$		0			0
$201$	−3.44882	−	1.99118i	−0.243261	−	0.140447i
$202$		0			0
$203$	0.0988439	+	1.17220i	0.00693748	+	0.0822720i
$204$		0			0
$205$	−5.83854	−	3.37088i	−0.407781	−	0.235433i
$206$		0			0
$207$	−2.79618	+	1.61437i	−0.194348	+	0.112207i
$208$		0			0
$209$			1.82613i			0.126316i
$210$		0			0
$211$	15.8023			1.08788			0.543938	−	0.839125i	$-0.316933\pi$
$211$	15.8023			1.08788			0.543938	+	0.839125i	$0.316933\pi$
$212$		0			0
$213$	3.63177	+	6.29041i	0.248845	+	0.431012i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−13.4523	−	19.3410i	−0.913204	−	1.31295i
$218$		0			0
$219$	4.18878	−	7.25517i	0.283051	−	0.490259i
$220$		0			0
$221$	−11.6208	+	6.70930i	−0.781703	+	0.451316i
$222$		0			0
$223$	−14.8885			−0.997006			−0.498503	−	0.866888i	$-0.666117\pi$
$223$	−14.8885			−0.997006			−0.498503	+	0.866888i	$0.666117\pi$
$224$		0			0
$225$	−5.04721			−0.336481
$226$		0			0
$227$	24.3726	−	14.0715i	1.61767	−	0.933960i	0.630145	−	0.776477i	$-0.282995\pi$
$227$	24.3726	−	14.0715i	1.61767	−	0.933960i	0.987522	−	0.157483i	$-0.0503379\pi$
$228$		0			0
$229$	−3.36655	+	5.83104i	−0.222468	+	0.385326i	−0.955557	−	0.294807i	$-0.904745\pi$
$229$	−3.36655	+	5.83104i	−0.222468	+	0.385326i	0.733089	+	0.680133i	$0.238078\pi$
$230$		0			0
$231$	−10.7204	−	5.04009i	−0.705353	−	0.331614i
$232$		0			0
$233$	−8.58148	+	14.8636i	−0.562191	+	0.973744i	0.435114	+	0.900376i	$0.356708\pi$
$233$	−8.58148	+	14.8636i	−0.562191	+	0.973744i	−0.997305	+	0.0733685i	$0.976625\pi$
$234$		0			0
$235$	1.51912	+	2.63119i	0.0990964	+	0.171640i
$236$		0			0
$237$	−7.95375			−0.516652
$238$		0			0
$239$			11.9169i			0.770838i	0.922742	+	0.385419i	$0.125943\pi$
$239$			11.9169i			0.770838i	−0.922742	+	0.385419i	$0.874057\pi$
$240$		0			0
$241$	7.66296	−	4.42421i	0.493615	−	0.284988i	−0.232458	−	0.972606i	$-0.574677\pi$
$241$	7.66296	−	4.42421i	0.493615	−	0.284988i	0.726073	+	0.687618i	$0.241344\pi$
$242$		0			0
$243$	9.43816	+	5.44912i	0.605458	+	0.349561i
$244$		0			0
$245$	1.68097	−	4.52965i	0.107393	−	0.289389i
$246$		0			0
$247$	2.55650	+	1.47600i	0.162666	+	0.0939155i
$248$		0			0
$249$	−1.26180	−	2.18551i	−0.0799635	−	0.138501i
$250$		0			0
$251$		−	18.1333i		−	1.14457i	−0.820056	−	0.572283i	$-0.806058\pi$
$251$		−	18.1333i		−	1.14457i	0.820056	−	0.572283i	$-0.193942\pi$
$252$		0			0
$253$			9.43898i			0.593424i
$254$		0			0
$255$	−1.20556	−	2.08810i	−0.0754953	−	0.130762i
$256$		0			0
$257$	8.01964	+	4.63014i	0.500251	+	0.288820i	0.728817	−	0.684708i	$-0.240070\pi$
$257$	8.01964	+	4.63014i	0.500251	+	0.288820i	−0.228566	+	0.973528i	$0.573404\pi$
$258$		0			0
$259$	−16.5966	−	7.80271i	−1.03126	−	0.484837i
$260$		0			0
$261$	−0.429623	−	0.248043i	−0.0265930	−	0.0153535i
$262$		0			0
$263$	20.3951	−	11.7751i	1.25762	−	0.726085i	0.285006	−	0.958526i	$-0.408004\pi$
$263$	20.3951	−	11.7751i	1.25762	−	0.726085i	0.972611	+	0.232441i	$0.0746711\pi$
$264$		0			0
$265$			6.51492i			0.400208i
$266$		0			0
$267$	−2.37755			−0.145504
$268$		0			0
$269$	−0.810052	−	1.40305i	−0.0493897	−	0.0855455i	0.840274	−	0.542163i	$-0.182394\pi$
$269$	−0.810052	−	1.40305i	−0.0493897	−	0.0855455i	−0.889663	+	0.456617i	$0.849061\pi$
$270$		0			0
$271$	−4.22701	+	7.32140i	−0.256773	+	0.444743i	−0.965375	−	0.260864i	$-0.915992\pi$
$271$	−4.22701	+	7.32140i	−0.256773	+	0.444743i	0.708603	+	0.705608i	$0.249326\pi$
$272$		0			0
$273$	−15.7208	+	10.9344i	−0.951468	+	0.661780i
$274$		0			0
$275$	−7.37755	+	12.7783i	−0.444883	+	0.770560i
$276$		0			0
$277$	16.1282	−	9.31159i	0.969047	−	0.559479i	0.0701013	−	0.997540i	$-0.477668\pi$
$277$	16.1282	−	9.31159i	0.969047	−	0.559479i	0.898946	+	0.438060i	$0.144334\pi$
$278$		0			0
$279$	9.93526			0.594808
$280$		0			0
$281$	12.6260			0.753201			0.376601	−	0.926376i	$-0.377093\pi$
$281$	12.6260			0.753201			0.376601	+	0.926376i	$0.377093\pi$
$282$		0			0
$283$	−21.2096	+	12.2454i	−1.26078	+	0.727913i	−0.973226	−	0.229850i	$-0.926176\pi$
$283$	−21.2096	+	12.2454i	−1.26078	+	0.727913i	−0.287557	+	0.957764i	$0.592843\pi$
$284$		0			0
$285$	−0.265215	+	0.459366i	−0.0157100	+	0.0272105i
$286$		0			0
$287$	−2.17145	−	25.7514i	−0.128177	−	1.52006i
$288$		0			0
$289$	−5.26180	+	9.11371i	−0.309518	+	0.536101i
$290$		0			0
$291$	−5.09488	−	8.82459i	−0.298667	−	0.517306i
$292$		0			0
$293$	26.7727			1.56408			0.782038	−	0.623231i	$-0.214180\pi$
$293$	26.7727			1.56408			0.782038	+	0.623231i	$0.214180\pi$
$294$		0			0
$295$			6.85143i			0.398906i
$296$		0			0
$297$	15.9590	−	9.21395i	0.926037	−	0.534648i
$298$		0			0
$299$	13.2141	+	7.62918i	0.764193	+	0.441207i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	14.9979	+	8.65902i	0.861605	+	0.497448i
$304$		0			0
$305$	−3.61178	−	6.25579i	−0.206810	−	0.358206i
$306$		0			0
$307$			28.4069i			1.62127i	0.585553	+	0.810634i	$0.300878\pi$
$307$			28.4069i			1.62127i	−0.585553	+	0.810634i	$0.699122\pi$
$308$		0			0
$309$			8.77503i			0.499194i
$310$		0			0
$311$	12.2816	+	21.2723i	0.696424	+	1.20624i	0.969698	+	0.244306i	$0.0785600\pi$
$311$	12.2816	+	21.2723i	0.696424	+	1.20624i	−0.273274	+	0.961936i	$0.588107\pi$
$312$		0			0
$313$	8.12245	+	4.68950i	0.459108	+	0.265066i	0.711669	−	0.702515i	$-0.247940\pi$
$313$	8.12245	+	4.68950i	0.459108	+	0.265066i	−0.252561	+	0.967581i	$0.581273\pi$
$314$		0			0
$315$	1.16342	+	1.67269i	0.0655512	+	0.0942456i
$316$		0			0
$317$	−10.4847	−	6.05335i	−0.588880	−	0.339990i	0.175774	−	0.984430i	$-0.443757\pi$
$317$	−10.4847	−	6.05335i	−0.588880	−	0.339990i	−0.764655	+	0.644440i	$0.777090\pi$
$318$		0			0
$319$	−1.25597	+	0.725133i	−0.0703206	+	0.0405996i
$320$		0			0
$321$			4.15964i			0.232168i
$322$		0			0
$323$	−1.42476			−0.0792758
$324$		0			0
$325$	11.9260	+	20.6565i	0.661536	+	1.14581i
$326$		0			0
$327$	−5.75282	+	9.96417i	−0.318131	+	0.551020i
$328$		0			0
$329$	−4.95506	+	10.5396i	−0.273182	+	0.581066i
$330$		0			0
$331$	−4.62693	+	8.01409i	−0.254319	+	0.440494i	−0.964710	−	0.263313i	$-0.915185\pi$
$331$	−4.62693	+	8.01409i	−0.254319	+	0.440494i	0.710391	+	0.703807i	$0.248518\pi$
$332$		0			0
$333$	6.69779	−	3.86697i	0.367037	−	0.211909i
$334$		0			0
$335$	2.00242			0.109404
$336$		0			0
$337$	−0.823644			−0.0448667			−0.0224334	−	0.999748i	$-0.507141\pi$
$337$	−0.823644			−0.0448667			−0.0224334	+	0.999748i	$0.507141\pi$
$338$		0			0
$339$	15.0094	−	8.66570i	0.815200	−	0.470656i
$340$		0			0
$341$	14.5225	−	25.1536i	0.786435	−	1.36215i
$342$		0			0
$343$	17.9336	−	4.62457i	0.968322	−	0.249703i
$344$		0			0
$345$	−1.37085	+	2.37439i	−0.0738042	+	0.127833i
$346$		0			0
$347$	6.43367	+	11.1434i	0.345378	+	0.598212i	0.985422	−	0.170126i	$-0.0544175\pi$
$347$	6.43367	+	11.1434i	0.345378	+	0.598212i	−0.640045	+	0.768338i	$0.721084\pi$
$348$		0			0
$349$	−30.7068			−1.64370			−0.821850	−	0.569704i	$-0.807058\pi$
$349$	−30.7068			−1.64370			−0.821850	+	0.569704i	$0.807058\pi$
$350$		0			0
$351$		−	29.7892i		−	1.59003i
$352$		0			0
$353$	11.9893	−	6.92205i	0.638128	−	0.368423i	−0.145765	−	0.989319i	$-0.546564\pi$
$353$	11.9893	−	6.92205i	0.638128	−	0.368423i	0.783893	+	0.620896i	$0.213231\pi$
$354$		0			0
$355$	−3.16296	−	1.82613i	−0.167872	−	0.0969212i
$356$		0			0
$357$	3.93231	−	8.36415i	0.208120	−	0.442678i
$358$		0			0
$359$	3.76207	+	2.17203i	0.198554	+	0.114635i	0.595981	−	0.802999i	$-0.296763\pi$
$359$	3.76207	+	2.17203i	0.198554	+	0.114635i	−0.397427	+	0.917634i	$0.630097\pi$
$360$		0			0
$361$	−9.34328	−	16.1830i	−0.491752	−	0.851739i
$362$		0			0
$363$			0.495052i			0.0259835i
$364$		0			0
$365$			4.21242i			0.220488i
$366$		0			0
$367$	2.07648	+	3.59656i	0.108391	+	0.187739i	0.915119	−	0.403185i	$-0.132097\pi$
$367$	2.07648	+	3.59656i	0.108391	+	0.187739i	−0.806727	+	0.590924i	$0.798763\pi$
$368$		0			0
$369$	9.43816	+	5.44912i	0.491331	+	0.283670i
$370$		0			0
$371$	−20.5018	+	14.2597i	−1.06440	+	0.740327i
$372$		0			0
$373$	−1.52118	−	0.878255i	−0.0787638	−	0.0454743i	0.460101	−	0.887867i	$-0.347813\pi$
$373$	−1.52118	−	0.878255i	−0.0787638	−	0.0454743i	−0.538865	+	0.842392i	$0.681147\pi$
$374$		0			0
$375$	−7.81421	+	4.51154i	−0.403524	+	0.232975i
$376$		0			0
$377$			2.34439i			0.120742i
$378$		0			0
$379$	14.9787			0.769403			0.384701	−	0.923041i	$-0.374304\pi$
$379$	14.9787			0.769403			0.384701	+	0.923041i	$0.374304\pi$
$380$		0			0
$381$	4.24209	+	7.34752i	0.217329	+	0.376425i
$382$		0			0
$383$	−8.26475	+	14.3150i	−0.422309	+	0.731461i	−0.996165	−	0.0874957i	$-0.972114\pi$
$383$	−8.26475	+	14.3150i	−0.422309	+	0.731461i	0.573856	+	0.818956i	$0.305447\pi$
$384$		0			0
$385$	5.93543	−	0.500497i	0.302497	−	0.0255077i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	21.8776	−	12.6310i	1.10924	−	0.640418i	0.170605	−	0.985340i	$-0.445428\pi$
$389$	21.8776	−	12.6310i	1.10924	−	0.640418i	0.938631	+	0.344922i	$0.112095\pi$
$390$		0			0
$391$	−7.36435			−0.372431
$392$		0			0
$393$	−2.87085			−0.144815
$394$		0			0
$395$	3.46352	−	1.99966i	0.174268	−	0.100614i
$396$		0			0
$397$	4.05677	−	7.02653i	0.203603	−	0.352651i	−0.746083	−	0.665852i	$-0.768068\pi$
$397$	4.05677	−	7.02653i	0.203603	−	0.352651i	0.949687	+	0.313201i	$0.101401\pi$
$398$		0			0
$399$	−2.02607	+	0.170846i	−0.101431	+	0.00855299i
$400$		0			0
$401$	0.564574	−	0.977870i	0.0281935	−	0.0488325i	−0.851584	−	0.524217i	$-0.824358\pi$
$401$	0.564574	−	0.977870i	0.0281935	−	0.0488325i	0.879778	+	0.475385i	$0.157691\pi$
$402$		0			0
$403$	−23.4759	−	40.6615i	−1.16942	−	2.02549i
$404$		0			0
$405$	3.04236			0.151176
$406$		0			0
$407$		−	22.6095i		−	1.12071i
$408$		0			0
$409$	−10.8567	+	6.26811i	−0.536828	+	0.309938i	−0.743793	−	0.668411i	$-0.766975\pi$
$409$	−10.8567	+	6.26811i	−0.536828	+	0.309938i	0.206964	+	0.978349i	$0.433642\pi$
$410$		0			0
$411$	−5.79035	−	3.34306i	−0.285617	−	0.164901i
$412$		0			0
$413$	−21.5607	+	14.9963i	−1.06093	+	0.737917i
$414$		0			0
$415$	1.09892	+	0.634462i	0.0539439	+	0.0311445i
$416$		0			0
$417$	1.26180	+	2.18551i	0.0617907	+	0.107025i
$418$		0			0
$419$			27.3950i			1.33834i	0.743111	+	0.669168i	$0.233349\pi$
$419$			27.3950i			1.33834i	−0.743111	+	0.669168i	$0.766651\pi$
$420$		0			0
$421$			30.7814i			1.50019i	0.661329	+	0.750096i	$0.269993\pi$
$421$			30.7814i			1.50019i	−0.661329	+	0.750096i	$0.730007\pi$
$422$		0			0
$423$	−2.45570	−	4.25339i	−0.119400	−	0.206807i
$424$		0			0
$425$	−9.96970	−	5.75601i	−0.483601	−	0.279207i
$426$		0			0
$427$	11.7809	−	25.0584i	0.570119	−	1.21266i
$428$		0			0
$429$	−20.4455	−	11.8042i	−0.987119	−	0.569913i
$430$		0			0
$431$	13.0280	−	7.52173i	0.627538	−	0.362309i	−0.152260	−	0.988340i	$-0.548655\pi$
$431$	13.0280	−	7.52173i	0.627538	−	0.362309i	0.779798	+	0.626031i	$0.215322\pi$
$432$		0			0
$433$			16.8008i			0.807396i	0.914892	+	0.403698i	$0.132275\pi$
$433$			16.8008i			0.807396i	−0.914892	+	0.403698i	$0.867725\pi$
$434$		0			0
$435$	−0.421253			−0.0201975
$436$		0			0
$437$	0.810052	+	1.40305i	0.0387500	+	0.0671170i
$438$		0			0
$439$	−5.91260	+	10.2409i	−0.282193	+	0.488773i	−0.971925	−	0.235293i	$-0.924395\pi$
$439$	−5.91260	+	10.2409i	−0.282193	+	0.488773i	0.689732	+	0.724065i	$0.257729\pi$
$440$		0			0
$441$	−2.71733	+	7.32230i	−0.129396	+	0.348681i
$442$		0			0
$443$	9.12420	−	15.8036i	0.433504	−	0.750851i	−0.563668	−	0.826001i	$-0.690610\pi$
$443$	9.12420	−	15.8036i	0.433504	−	0.750851i	0.997172	+	0.0751504i	$0.0239437\pi$
$444$		0			0
$445$	1.03532	−	0.597743i	0.0490789	−	0.0283357i
$446$		0			0
$447$	−12.1866			−0.576406
$448$		0			0
$449$	−3.17636			−0.149902			−0.0749508	−	0.997187i	$-0.523880\pi$
$449$	−3.17636			−0.149902			−0.0749508	+	0.997187i	$0.523880\pi$
$450$		0			0
$451$	27.5917	−	15.9301i	1.29924	−	0.750118i
$452$		0			0
$453$	−1.34048	+	2.32178i	−0.0629814	+	0.109087i
$454$		0			0
$455$	4.09671	−	8.71385i	0.192057	−	0.408512i
$456$		0			0
$457$	−0.714593	+	1.23771i	−0.0334273	+	0.0578977i	−0.882255	−	0.470772i	$-0.843976\pi$
$457$	−0.714593	+	1.23771i	−0.0334273	+	0.0578977i	0.848828	+	0.528669i	$0.177309\pi$
$458$		0			0
$459$	7.18878	+	12.4513i	0.335543	+	0.581178i
$460$		0			0
$461$	−11.4755			−0.534466			−0.267233	−	0.963632i	$-0.586109\pi$
$461$	−11.4755			−0.534466			−0.267233	+	0.963632i	$0.586109\pi$
$462$		0			0
$463$			35.6282i			1.65578i	0.560887	+	0.827892i	$0.310460\pi$
$463$			35.6282i			1.65578i	−0.560887	+	0.827892i	$0.689540\pi$
$464$		0			0
$465$	7.30628	−	4.21828i	0.338821	−	0.195618i
$466$		0			0
$467$	21.4541	+	12.3865i	0.992777	+	0.573180i	0.906103	−	0.423057i	$-0.139043\pi$
$467$	21.4541	+	12.3865i	0.992777	+	0.573180i	0.0866736	+	0.996237i	$0.472376\pi$
$468$		0			0
$469$	4.38285	+	6.30140i	0.202381	+	0.290971i
$470$		0			0
$471$	1.54605	+	0.892610i	0.0712380	+	0.0411293i
$472$		0			0
$473$		0			0
$474$		0			0
$475$			2.53256i			0.116202i
$476$		0			0
$477$		−	10.5315i		−	0.482206i
$478$		0			0
$479$	−11.9318	−	20.6666i	−0.545180	−	0.944279i	−0.998596	−	0.0529800i	$-0.983128\pi$
$479$	−11.9318	−	20.6666i	−0.545180	−	0.944279i	0.453416	−	0.891299i	$-0.350205\pi$
$480$		0			0
$481$	−31.6523	−	18.2745i	−1.44322	−	0.833244i
$482$		0			0
$483$	−10.4724	+	0.883073i	−0.476512	+	0.0401812i
$484$		0			0
$485$	4.43720	+	2.56182i	0.201483	+	0.116326i
$486$		0			0
$487$	−15.3829	+	8.88133i	−0.697066	+	0.402451i	−0.806254	−	0.591570i	$-0.798508\pi$
$487$	−15.3829	+	8.88133i	−0.697066	+	0.402451i	0.109188	+	0.994021i	$0.465175\pi$
$488$		0			0
$489$		−	11.8175i		−	0.534405i
$490$		0			0
$491$	−24.6260			−1.11135			−0.555677	−	0.831398i	$-0.687541\pi$
$491$	−24.6260			−1.11135			−0.555677	+	0.831398i	$0.687541\pi$
$492$		0			0
$493$	−0.565753	−	0.979912i	−0.0254802	−	0.0441330i
$494$		0			0
$495$	−1.25597	+	2.17540i	−0.0564515	+	0.0977769i
$496$		0			0
$497$	−1.17636	−	13.9505i	−0.0527668	−	0.625765i
$498$		0			0
$499$	7.20568	−	12.4806i	0.322571	−	0.558709i	−0.658447	−	0.752627i	$-0.728786\pi$
$499$	7.20568	−	12.4806i	0.322571	−	0.558709i	0.981018	+	0.193918i	$0.0621197\pi$
$500$		0			0
$501$	6.26817	−	3.61893i	0.280041	−	0.161682i
$502$		0			0
$503$	−27.2938			−1.21697			−0.608486	−	0.793565i	$-0.708223\pi$
$503$	−27.2938			−1.21697			−0.608486	+	0.793565i	$0.708223\pi$
$504$		0			0
$505$	−8.70789			−0.387496
$506$		0			0
$507$	−17.5966	+	10.1594i	−0.781494	+	0.451196i
$508$		0			0
$509$	−9.43037	+	16.3339i	−0.417994	+	0.723986i	−0.995738	−	0.0922319i	$-0.970600\pi$
$509$	−9.43037	+	16.3339i	−0.417994	+	0.723986i	0.577744	+	0.816218i	$0.303933\pi$
$510$		0			0
$511$	−13.2560	+	9.22004i	−0.586412	+	0.407871i
$512$		0			0
$513$	1.58148	−	2.73920i	0.0698240	−	0.120939i
$514$		0			0
$515$	−2.20614	−	3.82115i	−0.0972142	−	0.168380i
$516$		0			0
$517$	−14.3580			−0.631466
$518$		0			0
$519$		−	22.6610i		−	0.994708i
$520$		0			0
$521$	23.7236	−	13.6968i	1.03935	−	0.600068i	0.119700	−	0.992810i	$-0.461807\pi$
$521$	23.7236	−	13.6968i	1.03935	−	0.600068i	0.919649	+	0.392742i	$0.128474\pi$
$522$		0			0
$523$	−25.7805	−	14.8844i	−1.12730	−	0.650847i	−0.184046	−	0.982918i	$-0.558920\pi$
$523$	−25.7805	−	14.8844i	−1.12730	−	0.650847i	−0.943255	+	0.332070i	$0.892253\pi$
$524$		0			0
$525$	−14.8676	−	6.98981i	−0.648874	−	0.305060i
$526$		0			0
$527$	19.6250	+	11.3305i	0.854879	+	0.493564i
$528$		0			0
$529$	−7.31298	−	12.6664i	−0.317956	−	0.550715i
$530$		0			0
$531$		−	11.0755i		−	0.480637i
$532$		0			0
$533$		−	51.5028i		−	2.23083i
$534$		0			0
$535$	−1.04578	−	1.81134i	−0.0452130	−	0.0783112i
$536$		0			0
$537$	26.4484	+	15.2700i	1.14133	+	0.658948i
$538$		0			0
$539$	14.5663	+	17.5827i	0.627416	+	0.757339i
$540$		0			0
$541$	−8.21897	−	4.74522i	−0.353361	−	0.204013i	0.312804	−	0.949818i	$-0.398732\pi$
$541$	−8.21897	−	4.74522i	−0.353361	−	0.204013i	−0.666165	+	0.745805i	$0.732065\pi$
$542$		0			0
$543$	11.9168	−	6.88014i	0.511397	−	0.295255i
$544$		0			0
$545$		−	5.78529i		−	0.247815i
$546$		0			0
$547$	−10.2732			−0.439252			−0.219626	−	0.975584i	$-0.570484\pi$
$547$	−10.2732			−0.439252			−0.219626	+	0.975584i	$0.570484\pi$
$548$		0			0
$549$	5.83854	+	10.1127i	0.249183	+	0.431597i
$550$		0			0
$551$	−0.124462	+	0.215574i	−0.00530224	+	0.00918375i
$552$		0			0
$553$	13.8736	+	6.52250i	0.589965	+	0.277365i
$554$		0			0
$555$	3.28365	−	5.68745i	0.139383	−	0.241419i
$556$		0			0
$557$	−31.8011	+	18.3604i	−1.34746	+	0.777955i	−0.987889	−	0.155163i	$-0.950410\pi$
$557$	−31.8011	+	18.3604i	−1.34746	+	0.777955i	−0.359569	+	0.933119i	$0.617076\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	11.3945			0.481074
$562$		0			0
$563$	−5.48439	+	3.16641i	−0.231139	+	0.133448i	−0.611098	−	0.791555i	$-0.709272\pi$
$563$	−5.48439	+	3.16641i	−0.231139	+	0.133448i	0.379958	+	0.925004i	$0.375938\pi$
$564$		0			0
$565$	−4.35731	+	7.54708i	−0.183313	+	0.317508i
$566$		0			0
$567$	6.65905	+	9.57399i	0.279654	+	0.402070i
$568$		0			0
$569$	19.7484	−	34.2052i	0.827896	−	1.43396i	−0.0717894	−	0.997420i	$-0.522871\pi$
$569$	19.7484	−	34.2052i	0.827896	−	1.43396i	0.899686	−	0.436538i	$-0.143796\pi$
$570$		0			0
$571$	6.22305	+	10.7786i	0.260426	+	0.451072i	0.966355	−	0.257211i	$-0.0828035\pi$
$571$	6.22305	+	10.7786i	0.260426	+	0.451072i	−0.705929	+	0.708283i	$0.749470\pi$
$572$		0			0
$573$	34.3177			1.43364
$574$		0			0
$575$			13.0904i			0.545907i
$576$		0			0
$577$	−10.8259	+	6.25035i	−0.450689	+	0.260205i	−0.708121	−	0.706091i	$-0.750457\pi$
$577$	−10.8259	+	6.25035i	−0.450689	+	0.260205i	0.257432	+	0.966296i	$0.417124\pi$
$578$		0			0
$579$	13.5455	+	7.82047i	0.562930	+	0.325008i
$580$		0			0
$581$	0.408707	+	4.84688i	0.0169560	+	0.201083i
$582$		0			0
$583$	−26.6633	−	15.3940i	−1.10428	−	0.637556i
$584$		0			0
$585$	2.03030	+	3.51659i	0.0839427	+	0.145393i
$586$		0			0
$587$		−	32.0838i		−	1.32424i	−0.749397	−	0.662121i	$-0.769657\pi$
$587$		−	32.0838i		−	1.32424i	0.749397	−	0.662121i	$-0.230343\pi$
$588$		0			0
$589$		−	4.98526i		−	0.205414i
$590$		0			0
$591$	6.95838	+	12.0523i	0.286229	+	0.495764i
$592$		0			0
$593$	17.2760	+	9.97429i	0.709439	+	0.409595i	0.810853	−	0.585249i	$-0.199003\pi$
$593$	17.2760	+	9.97429i	0.709439	+	0.409595i	−0.101414	+	0.994844i	$0.532337\pi$
$594$		0			0
$595$	0.390490	+	4.63085i	0.0160085	+	0.189846i
$596$		0			0
$597$	12.8461	+	7.41671i	0.525756	+	0.303546i
$598$		0			0
$599$	9.05851	−	5.22993i	0.370121	−	0.213689i	−0.303391	−	0.952866i	$-0.598119\pi$
$599$	9.05851	−	5.22993i	0.370121	−	0.213689i	0.673511	+	0.739177i	$0.264785\pi$
$600$		0			0
$601$			30.6355i			1.24965i	0.780766	+	0.624823i	$0.214829\pi$
$601$			30.6355i			1.24965i	−0.780766	+	0.624823i	$0.785171\pi$
$602$		0			0
$603$	−3.23696			−0.131819
$604$		0			0
$605$	−0.124462	−	0.215574i	−0.00506008	−	0.00876432i
$606$		0			0
$607$	18.7095	−	32.4058i	0.759396	−	1.31531i	−0.183763	−	0.982971i	$-0.558828\pi$
$607$	18.7095	−	32.4058i	0.759396	−	1.31531i	0.943159	−	0.332342i	$-0.107839\pi$
$608$		0			0
$609$	−0.922028	−	1.32564i	−0.0373625	−	0.0537176i
$610$		0			0
$611$	−11.6051	+	20.1006i	−0.469491	+	0.813183i
$612$		0			0
$613$	−23.6077	+	13.6299i	−0.953507	+	0.550507i	−0.894169	−	0.447731i	$-0.852232\pi$
$613$	−23.6077	+	13.6299i	−0.953507	+	0.550507i	−0.0593382	+	0.998238i	$0.518899\pi$
$614$		0			0
$615$	9.25429			0.373169
$616$		0			0
$617$	−26.7810			−1.07816			−0.539081	−	0.842254i	$-0.681228\pi$
$617$	−26.7810			−1.07816			−0.539081	+	0.842254i	$0.681228\pi$
$618$		0			0
$619$	−31.4426	+	18.1534i	−1.26379	+	0.729648i	−0.973805	−	0.227385i	$-0.926983\pi$
$619$	−31.4426	+	18.1534i	−1.26379	+	0.729648i	−0.289982	+	0.957032i	$0.593649\pi$
$620$		0			0
$621$	8.17440	−	14.1585i	0.328027	−	0.568160i
$622$		0			0
$623$	4.14712	+	1.94972i	0.166151	+	0.0781139i
$624$		0			0
$625$	−9.04051	+	15.6586i	−0.361620	+	0.626345i
$626$		0			0
$627$	−1.25335	−	2.17086i	−0.0500540	−	0.0866960i
$628$		0			0
$629$	17.6401			0.703356
$630$		0			0
$631$			25.5683i			1.01786i	0.860809	+	0.508928i	$0.169958\pi$
$631$			25.5683i			1.01786i	−0.860809	+	0.508928i	$0.830042\pi$
$632$		0			0
$633$	−18.7854	+	10.8458i	−0.746653	+	0.431080i
$634$		0			0
$635$	−3.69450	−	2.13302i	−0.146612	−	0.0846463i
$636$		0			0
$637$	36.3883	−	6.18074i	1.44176	−	0.244890i
$638$		0			0
$639$	5.11301	+	2.95200i	0.202267	+	0.116779i
$640$		0			0
$641$	8.66296	+	15.0047i	0.342166	+	0.592649i	0.984835	−	0.173495i	$-0.0555061\pi$
$641$	8.66296	+	15.0047i	0.342166	+	0.592649i	−0.642668	+	0.766144i	$0.722173\pi$
$642$		0			0
$643$			19.0294i			0.750444i	0.926935	+	0.375222i	$0.122434\pi$
$643$			19.0294i			0.750444i	−0.926935	+	0.375222i	$0.877566\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.28545	+	2.22647i	0.0505364	+	0.0875317i	0.890187	−	0.455595i	$-0.150574\pi$
$647$	1.28545	+	2.22647i	0.0505364	+	0.0875317i	−0.839651	+	0.543127i	$0.817240\pi$
$648$		0			0
$649$	−28.0405	−	16.1892i	−1.10069	−	0.635482i
$650$		0			0
$651$	29.2663	+	13.7592i	1.14704	+	0.539266i
$652$		0			0
$653$	37.8296	+	21.8410i	1.48039	+	0.854702i	0.999753	−	0.0222184i	$-0.00707291\pi$
$653$	37.8296	+	21.8410i	1.48039	+	0.854702i	0.480635	+	0.876921i	$0.340406\pi$
$654$		0			0
$655$	1.25013	−	0.721764i	0.0488467	−	0.0282017i
$656$		0			0
$657$		−	6.80949i		−	0.265663i
$658$		0			0
$659$	25.4496			0.991376			0.495688	−	0.868501i	$-0.334916\pi$
$659$	25.4496			0.991376			0.495688	+	0.868501i	$0.334916\pi$
$660$		0			0
$661$	−11.9660	−	20.7256i	−0.465422	−	0.806134i	0.533799	−	0.845612i	$-0.320764\pi$
$661$	−11.9660	−	20.7256i	−0.465422	−	0.806134i	−0.999220	+	0.0394776i	$0.987431\pi$
$662$		0			0
$663$	9.20972	−	15.9517i	0.357676	−	0.619513i
$664$		0			0
$665$	0.839315	−	0.583773i	0.0325472	−	0.0226378i
$666$		0			0
$667$	−0.643321	+	1.11426i	−0.0249095	+	0.0431445i
$668$		0			0
$669$	17.6991	−	10.2186i	0.684285	−	0.395072i
$670$		0			0
$671$	34.1370			1.31784
$672$		0			0
$673$	42.7810			1.64909			0.824543	−	0.565800i	$-0.191432\pi$
$673$	42.7810			1.64909			0.824543	+	0.565800i	$0.191432\pi$
$674$		0			0
$675$	22.1327	−	12.7783i	0.851886	−	0.491837i
$676$		0			0
$677$	0.685590	−	1.18748i	0.0263494	−	0.0456385i	−0.852550	−	0.522646i	$-0.824945\pi$
$677$	0.685590	−	1.18748i	0.0263494	−	0.0456385i	0.878899	+	0.477007i	$0.158278\pi$
$678$		0			0
$679$	1.65027	+	19.5706i	0.0633314	+	0.751052i
$680$		0			0
$681$	−19.3157	+	33.4558i	−0.740180	+	1.28203i
$682$		0			0
$683$	22.9399	+	39.7331i	0.877771	+	1.52034i	0.853781	+	0.520632i	$0.174304\pi$
$683$	22.9399	+	39.7331i	0.877771	+	1.52034i	0.0239904	+	0.999712i	$0.492363\pi$
$684$		0			0
$685$	3.36193			0.128453
$686$		0			0
$687$		−	9.24241i		−	0.352620i
$688$		0			0
$689$	−43.1019	+	24.8849i	−1.64205	+	0.948039i
$690$		0			0
$691$	−8.57530	−	4.95095i	−0.326220	−	0.188343i	0.327942	−	0.944698i	$-0.393645\pi$
$691$	−8.57530	−	4.95095i	−0.326220	−	0.188343i	−0.654162	+	0.756355i	$0.726978\pi$
$692$		0			0
$693$	−9.59477	+	0.809066i	−0.364475	+	0.0307339i
$694$		0			0
$695$	−1.09892	−	0.634462i	−0.0416844	−	0.0240665i
$696$		0			0
$697$	12.4287	+	21.5272i	0.470772	+	0.815400i
$698$		0			0
$699$		−	23.5593i		−	0.891093i
$700$		0			0
$701$			22.9445i			0.866602i	0.901249	+	0.433301i	$0.142651\pi$
$701$			22.9445i			0.866602i	−0.901249	+	0.433301i	$0.857349\pi$
$702$		0			0
$703$	−1.94035	−	3.36078i	−0.0731816	−	0.126754i
$704$		0			0
$705$	−3.61178	−	2.08526i	−0.136028	−	0.0785356i
$706$		0			0
$707$	−19.0596	−	27.4028i	−0.716811	−	1.03059i
$708$		0			0
$709$	17.4404	+	10.0692i	0.654986	+	0.378157i	0.790364	−	0.612637i	$-0.209891\pi$
$709$	17.4404	+	10.0692i	0.654986	+	0.378157i	−0.135378	+	0.990794i	$0.543225\pi$
$710$		0			0
$711$	−5.59887	+	3.23251i	−0.209974	+	0.121228i
$712$		0			0
$713$		−	25.7680i		−	0.965018i
$714$		0			0
$715$	11.8709			0.443945
$716$		0			0
$717$	−8.17902	−	14.1665i	−0.305451	−	0.529057i
$718$		0			0
$719$	3.19631	−	5.53618i	0.119202	−	0.206465i	−0.800249	−	0.599667i	$-0.795300\pi$
$719$	3.19631	−	5.53618i	0.119202	−	0.206465i	0.919452	+	0.393203i	$0.128633\pi$
$720$		0			0
$721$	7.19599	−	15.3061i	0.267993	−	0.570030i
$722$		0			0
$723$	−6.07303	+	10.5188i	−0.225858	+	0.391198i
$724$		0			0
$725$	−1.74183	+	1.00564i	−0.0646898	+	0.0373487i
$726$		0			0
$727$	27.2938			1.01227			0.506136	−	0.862454i	$-0.331073\pi$
$727$	27.2938			1.01227			0.506136	+	0.862454i	$0.331073\pi$
$728$		0			0
$729$	−28.1834			−1.04383
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−5.90214	+	10.2228i	−0.218001	+	0.377588i	−0.954197	−	0.299180i	$-0.903287\pi$
$733$	−5.90214	+	10.2228i	−0.218001	+	0.377588i	0.736196	+	0.676768i	$0.236620\pi$
$734$		0			0
$735$	1.11059	+	6.53845i	0.0409647	+	0.241174i
$736$		0			0
$737$	−4.73150	+	8.19520i	−0.174287	+	0.301874i
$738$		0			0
$739$	5.17141	+	8.95715i	0.190233	+	0.329494i	0.945328	−	0.326122i	$-0.105742\pi$
$739$	5.17141	+	8.95715i	0.190233	+	0.329494i	−0.755094	+	0.655616i	$0.772409\pi$
$740$		0			0
$741$	−4.05215			−0.148859
$742$		0			0
$743$			7.06999i			0.259373i	0.991555	+	0.129686i	$0.0413970\pi$
$743$			7.06999i			0.259373i	−0.991555	+	0.129686i	$0.958603\pi$
$744$		0			0
$745$	5.30674	−	3.06385i	0.194424	−	0.112251i
$746$		0			0
$747$	−1.77643	−	1.02563i	−0.0649963	−	0.0375257i
$748$		0			0
$749$	3.41112	−	7.25558i	0.124640	−	0.265113i
$750$		0			0
$751$	−24.1630	−	13.9505i	−0.881721	−	0.509062i	−0.0104954	−	0.999945i	$-0.503341\pi$
$751$	−24.1630	−	13.9505i	−0.881721	−	0.509062i	−0.871225	+	0.490883i	$0.836674\pi$
$752$		0			0
$753$	12.4456	+	21.5565i	0.453544	+	0.785561i
$754$		0			0
$755$		−	1.34805i		−	0.0490605i
$756$		0			0
$757$			18.9429i			0.688492i	0.938880	+	0.344246i	$0.111865\pi$
$757$			18.9429i			0.688492i	−0.938880	+	0.344246i	$0.888135\pi$
$758$		0			0
$759$	−6.47835	−	11.2208i	−0.235149	−	0.407291i
$760$		0			0
$761$	10.8780	+	6.28042i	0.394328	+	0.227665i	0.684034	−	0.729451i	$-0.260224\pi$
$761$	10.8780	+	6.28042i	0.394328	+	0.227665i	−0.289706	+	0.957116i	$0.593558\pi$
$762$		0			0
$763$	18.2057	−	12.6627i	0.659090	−	0.458420i
$764$		0			0
$765$	−1.69726	−	0.979912i	−0.0613645	−	0.0354288i
$766$		0			0
$767$	−45.3282	+	26.1703i	−1.63671	+	0.944953i
$768$		0			0
$769$		−	32.9798i		−	1.18928i	−0.803991	−	0.594642i	$-0.797294\pi$
$769$		−	32.9798i		−	1.18928i	0.803991	−	0.594642i	$-0.202706\pi$
$770$		0			0
$771$	−12.7114			−0.457790
$772$		0			0
$773$	−19.3656	−	33.5422i	−0.696533	−	1.20643i	−0.969661	−	0.244453i	$-0.921392\pi$
$773$	−19.3656	−	33.5422i	−0.696533	−	1.20643i	0.273128	−	0.961978i	$-0.411942\pi$
$774$		0			0
$775$	20.1404	−	34.8841i	0.723463	−	1.25307i
$776$		0			0
$777$	25.0850	−	2.11526i	0.899919	−	0.0758844i
$778$		0			0
$779$	2.73423	−	4.73583i	0.0979640	−	0.169679i
$780$		0			0
$781$	14.9475	−	8.62992i	0.534862	−	0.308803i
$782$		0			0
$783$	2.51193			0.0897692
$784$		0			0
$785$	−0.897649			−0.0320384
$786$		0			0
$787$	−25.8406	+	14.9191i	−0.921118	+	0.531808i	−0.883992	−	0.467503i	$-0.845154\pi$
$787$	−25.8406	+	14.9191i	−0.921118	+	0.531808i	−0.0371266	+	0.999311i	$0.511820\pi$
$788$		0			0
$789$	−16.1635	+	27.9960i	−0.575435	+	0.996683i
$790$		0			0
$791$	−33.2870	+	2.80688i	−1.18355	+	0.0998012i
$792$		0			0
$793$	27.5917	−	47.7902i	0.979809	−	1.69708i
$794$		0			0
$795$	−4.47145	−	7.74478i	−0.158586	−	0.274679i
$796$		0			0
$797$	−0.929890			−0.0329384			−0.0164692	−	0.999864i	$-0.505243\pi$
$797$	−0.929890			−0.0329384			−0.0164692	+	0.999864i	$0.505243\pi$
$798$		0			0
$799$		−	11.2022i		−	0.396306i
$800$		0			0
$801$	−1.67362	+	0.966267i	−0.0591346	+	0.0341414i
$802$		0			0
$803$	−17.2400	−	9.95349i	−0.608385	−	0.351251i
$804$		0			0
$805$	4.33828	−	3.01743i	0.152904	−	0.106350i
$806$		0			0
$807$	1.92594	+	1.11194i	0.0677963	+	0.0391422i
$808$		0			0
$809$	8.69326	+	15.0572i	0.305639	+	0.529382i	0.977403	−	0.211383i	$-0.0677967\pi$
$809$	8.69326	+	15.0572i	0.305639	+	0.529382i	−0.671765	+	0.740765i	$0.734463\pi$
$810$		0			0
$811$		−	19.0294i		−	0.668211i	−0.942536	−	0.334105i	$-0.891566\pi$
$811$		−	19.0294i		−	0.668211i	0.942536	−	0.334105i	$-0.108434\pi$
$812$		0			0
$813$		−	11.6047i		−	0.406993i
$814$		0			0
$815$	2.97104	+	5.14600i	0.104071	+	0.180256i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−6.62245	+	14.0862i	−0.231407	+	0.492211i
$820$		0			0
$821$	−38.6560	−	22.3180i	−1.34910	−	0.778905i	−0.360981	−	0.932573i	$-0.617558\pi$
$821$	−38.6560	−	22.3180i	−1.34910	−	0.778905i	−0.988122	+	0.153668i	$0.950891\pi$
$822$		0			0
$823$	−0.764272	+	0.441253i	−0.0266408	+	0.0153811i	−0.513261	−	0.858232i	$-0.671563\pi$
$823$	−0.764272	+	0.441253i	−0.0266408	+	0.0153811i	0.486620	+	0.873614i	$0.338229\pi$
$824$		0			0
$825$		−	20.2540i		−	0.705155i
$826$		0			0
$827$	−18.3527			−0.638186			−0.319093	−	0.947723i	$-0.603378\pi$
$827$	−18.3527			−0.638186			−0.319093	+	0.947723i	$0.603378\pi$
$828$		0			0
$829$	−18.2550	−	31.6186i	−0.634024	−	1.09816i	−0.986721	−	0.162424i	$-0.948069\pi$
$829$	−18.2550	−	31.6186i	−0.634024	−	1.09816i	0.352698	−	0.935737i	$-0.385264\pi$
$830$		0			0
$831$	−12.7818	+	22.1388i	−0.443397	+	0.767986i
$832$		0			0
$833$	−13.7181	+	11.3647i	−0.475304	+	0.393765i
$834$		0			0
$835$	−1.81968	+	3.15177i	−0.0629725	+	0.109072i
$836$		0			0
$837$	−43.5674	+	25.1536i	−1.50591	+	0.869437i
$838$		0			0
$839$	31.6367			1.09222			0.546111	−	0.837713i	$-0.316108\pi$
$839$	31.6367			1.09222			0.546111	+	0.837713i	$0.316108\pi$
$840$		0			0
$841$	28.8023			0.993183
$842$		0			0
$843$	−15.0094	+	8.66570i	−0.516952	+	0.298463i
$844$		0			0
$845$	5.10838	−	8.84798i	0.175734	−	0.304380i
$846$		0			0
$847$	0.405969	−	0.863509i	0.0139493	−	0.0296705i
$848$		0			0
$849$	16.8090	−	29.1141i	0.576884	−	0.999192i
$850$		0			0
$851$	−10.0293	−	17.3713i	−0.343801	−	0.595481i
$852$		0			0
$853$	−26.3639			−0.902684			−0.451342	−	0.892351i	$-0.649055\pi$
$853$	−26.3639			−0.902684			−0.451342	+	0.892351i	$0.649055\pi$
$854$		0			0
$855$			0.431147i			0.0147449i
$856$		0			0
$857$	−22.5909	+	13.0429i	−0.771691	+	0.445536i	−0.833477	−	0.552553i	$-0.813653\pi$
$857$	−22.5909	+	13.0429i	−0.771691	+	0.445536i	0.0617866	+	0.998089i	$0.480320\pi$
$858$		0			0
$859$	−6.13760	−	3.54355i	−0.209412	−	0.120904i	0.391626	−	0.920124i	$-0.371913\pi$
$859$	−6.13760	−	3.54355i	−0.209412	−	0.120904i	−0.601038	+	0.799220i	$0.705246\pi$
$860$		0			0
$861$	20.2556	+	29.1223i	0.690308	+	0.992484i
$862$		0			0
$863$	−13.4014	−	7.73731i	−0.456189	−	0.263381i	0.254251	−	0.967138i	$-0.418171\pi$
$863$	−13.4014	−	7.73731i	−0.456189	−	0.263381i	−0.710441	+	0.703757i	$0.751504\pi$
$864$		0			0
$865$	5.69723	+	9.86789i	0.193712	+	0.335518i
$866$		0			0
$867$		−	14.4455i		−	0.490596i
$868$		0			0
$869$			18.8999i			0.641137i
$870$		0			0
$871$	7.64859	+	13.2478i	0.259163	+	0.448883i
$872$		0			0
$873$	−7.17285	−	4.14125i	−0.242764	−	0.140160i
$874$		0			0
$875$	17.3299	−	1.46132i	0.585857	−	0.0494016i
$876$		0			0
$877$	40.0954	+	23.1491i	1.35392	+	0.781689i	0.988797	−	0.149268i	$-0.0476918\pi$
$877$	40.0954	+	23.1491i	1.35392	+	0.781689i	0.365128	+	0.930957i	$0.381025\pi$
$878$		0			0
$879$	−31.8267	+	18.3751i	−1.07349	+	0.619778i
$880$		0			0
$881$		−	37.7381i		−	1.27143i	−0.771925	−	0.635714i	$-0.780706\pi$
$881$		−	37.7381i		−	1.27143i	0.771925	−	0.635714i	$-0.219294\pi$
$882$		0			0
$883$	37.0542			1.24697			0.623487	−	0.781834i	$-0.285715\pi$
$883$	37.0542			1.24697			0.623487	+	0.781834i	$0.285715\pi$
$884$		0			0
$885$	−4.70241	−	8.14482i	−0.158070	−	0.273785i
$886$		0			0
$887$	−21.7519	+	37.6754i	−0.730357	+	1.26502i	0.226374	+	0.974040i	$0.427313\pi$
$887$	−21.7519	+	37.6754i	−0.730357	+	1.26502i	−0.956731	+	0.290975i	$0.906020\pi$
$888$		0			0
$889$	−1.37404	−	16.2949i	−0.0460840	−	0.546513i
$890$		0			0
$891$	−7.18878	+	12.4513i	−0.240833	+	0.417135i
$892$		0			0
$893$	−2.13424	+	1.23221i	−0.0714197	+	0.0412342i
$894$		0			0
$895$	−15.3562			−0.513300
$896$		0			0
$897$	−20.9449			−0.699328
$898$		0			0
$899$	3.42873	−	1.97958i	0.114354	−	0.0660226i
$900$		0			0
$901$	12.0105	−	20.8028i	0.400129	−	0.693043i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.45949	+	5.99201i	−0.114997	+	0.199181i
$906$		0			0
$907$	26.6304	+	46.1253i	0.884249	+	1.53156i	0.846572	+	0.532275i	$0.178663\pi$
$907$	26.6304	+	46.1253i	0.884249	+	1.53156i	0.0376777	+	0.999290i	$0.488004\pi$
$908$		0			0
$909$	14.0765			0.466889
$910$		0			0
$911$		−	46.2112i		−	1.53105i	−0.643408	−	0.765523i	$-0.722480\pi$
$911$		−	46.2112i		−	1.53105i	0.643408	−	0.765523i	$-0.277520\pi$
$912$		0			0
$913$	−5.19326	+	2.99833i	−0.171872	+	0.0992303i
$914$		0			0
$915$	8.58720	+	4.95782i	0.283884	+	0.163901i
$916$		0			0
$917$	5.00757	+	2.35425i	0.165365	+	0.0777443i
$918$		0			0
$919$	12.7256	+	7.34713i	0.419779	+	0.242359i	0.694983	−	0.719026i	$-0.255412\pi$
$919$	12.7256	+	7.34713i	0.419779	+	0.242359i	−0.275204	+	0.961386i	$0.588745\pi$
$920$		0			0
$921$	−19.4968	−	33.7695i	−0.642442	−	1.11274i
$922$		0			0
$923$		−	27.9010i		−	0.918372i
$924$		0			0
$925$		−	31.3559i		−	1.03097i
$926$		0			0
$927$	3.56628	+	6.17699i	0.117132	+	0.202879i
$928$		0			0
$929$	10.5507	+	6.09146i	0.346158	+	0.199854i	0.662992	−	0.748627i	$-0.269286\pi$
$929$	10.5507	+	6.09146i	0.346158	+	0.199854i	−0.316834	+	0.948481i	$0.602620\pi$
$930$		0			0
$931$	3.67414	+	1.36348i	0.120415	+	0.0446864i
$932$		0			0
$933$	−29.2001	−	16.8587i	−0.955967	−	0.551928i
$934$		0			0
$935$	−4.96179	+	2.86469i	−0.162268	+	0.0936855i
$936$		0			0
$937$			30.7049i			1.00309i	0.865133	+	0.501543i	$0.167234\pi$
$937$			30.7049i			1.00309i	−0.865133	+	0.501543i	$0.832766\pi$
$938$		0			0
$939$	−12.8744			−0.420139
$940$		0			0
$941$	20.8705	+	36.1488i	0.680359	+	1.17842i	0.974871	+	0.222769i	$0.0715096\pi$
$941$	20.8705	+	36.1488i	0.680359	+	1.17842i	−0.294512	+	0.955648i	$0.595157\pi$
$942$		0			0
$943$	14.1328	−	24.4787i	0.460227	−	0.797136i
$944$		0			0
$945$	−9.33658	−	4.38948i	−0.303719	−	0.142790i
$946$		0			0
$947$	24.1540	−	41.8360i	0.784901	−	1.35949i	−0.144157	−	0.989555i	$-0.546047\pi$
$947$	24.1540	−	41.8360i	0.784901	−	1.35949i	0.929058	−	0.369934i	$-0.120620\pi$
$948$		0			0
$949$	−27.8688	+	16.0901i	−0.904661	+	0.522306i
$950$		0			0
$951$	16.6186			0.538896
$952$		0			0
$953$	−26.2732			−0.851074			−0.425537	−	0.904941i	$-0.639915\pi$
$953$	−26.2732			−0.851074			−0.425537	+	0.904941i	$0.639915\pi$
$954$		0			0
$955$	−14.9439	+	8.62785i	−0.483573	+	0.279191i
$956$		0			0
$957$	0.995375	−	1.72404i	0.0321759	−	0.0557303i
$958$		0			0
$959$	7.35851	+	10.5796i	0.237619	+	0.341634i
$960$		0			0
$961$	−24.1456	+	41.8214i	−0.778890	+	1.34908i
$962$		0			0
$963$	1.69053	+	2.92808i	0.0544766	+	0.0943562i
$964$		0			0
$965$	−7.86462			−0.253171
$966$		0			0
$967$			3.51302i			0.112971i	0.998403	+	0.0564855i	$0.0179895\pi$
$967$			3.51302i			0.112971i	−0.998403	+	0.0564855i	$0.982011\pi$
$968$		0			0
$969$	1.69372	−	0.977870i	0.0544102	−	0.0314137i
$970$		0			0
$971$	−37.4934	−	21.6468i	−1.20322	−	0.694679i	−0.241950	−	0.970289i	$-0.577787\pi$
$971$	−37.4934	−	21.6468i	−1.20322	−	0.694679i	−0.961270	+	0.275610i	$0.911120\pi$
$972$		0			0
$973$	−0.408707	−	4.84688i	−0.0131025	−	0.155384i
$974$		0			0
$975$	−28.3547	−	16.3706i	−0.908077	−	0.524279i
$976$		0			0
$977$	11.4106	+	19.7637i	0.365057	+	0.632297i	0.988785	−	0.149344i	$-0.0477162\pi$
$977$	11.4106	+	19.7637i	0.365057	+	0.632297i	−0.623728	+	0.781641i	$0.714383\pi$
$978$		0			0
$979$			5.64961i			0.180562i
$980$		0			0
$981$			9.35207i			0.298589i
$982$		0			0
$983$	−26.9239	−	46.6335i	−0.858738	−	1.48738i	−0.873133	−	0.487481i	$-0.837916\pi$
$983$	−26.9239	−	46.6335i	−0.858738	−	1.48738i	0.0143953	−	0.999896i	$-0.495418\pi$
$984$		0			0
$985$	−6.06015	−	3.49883i	−0.193092	−	0.111482i
$986$		0			0
$987$	−1.34328	−	15.9301i	−0.0427571	−	0.507060i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	33.3611	−	19.2610i	1.05975	−	0.611846i	0.134386	−	0.990929i	$-0.457094\pi$
$991$	33.3611	−	19.2610i	1.05975	−	0.611846i	0.925363	+	0.379083i	$0.123760\pi$
$992$		0			0
$993$		−	12.7026i		−	0.403105i
$994$		0			0
$995$	−7.45857			−0.236453
$996$		0			0
$997$	−10.0643	−	17.4320i	−0.318741	−	0.552075i	0.661485	−	0.749959i	$-0.269927\pi$
$997$	−10.0643	−	17.4320i	−0.318741	−	0.552075i	−0.980226	+	0.197883i	$0.936593\pi$
$998$		0			0
$999$	−19.5804	+	33.9143i	−0.619498	+	1.07300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.q.a.47.2		12
3.2	odd	2		2016.2.bs.a.271.3		12
4.3	odd	2		56.2.m.a.19.4	yes	12
7.2	even	3		1568.2.e.e.783.3		12
7.3	odd	6	inner	224.2.q.a.143.1		12
7.4	even	3		1568.2.q.g.815.6		12
7.5	odd	6		1568.2.e.e.783.10		12
7.6	odd	2		1568.2.q.g.1391.5		12
8.3	odd	2	inner	224.2.q.a.47.1		12
8.5	even	2		56.2.m.a.19.2	yes	12
12.11	even	2		504.2.bk.a.19.3		12
21.17	even	6		2016.2.bs.a.1711.4		12
24.5	odd	2		504.2.bk.a.19.5		12
24.11	even	2		2016.2.bs.a.271.4		12
28.3	even	6		56.2.m.a.3.1	✓	12
28.11	odd	6		392.2.m.g.227.1		12
28.19	even	6		392.2.e.e.195.9		12
28.23	odd	6		392.2.e.e.195.10		12
28.27	even	2		392.2.m.g.19.4		12
56.3	even	6	inner	224.2.q.a.143.2		12
56.5	odd	6		392.2.e.e.195.11		12
56.11	odd	6		1568.2.q.g.815.5		12
56.13	odd	2		392.2.m.g.19.2		12
56.19	even	6		1568.2.e.e.783.9		12
56.27	even	2		1568.2.q.g.1391.6		12
56.37	even	6		392.2.e.e.195.12		12
56.45	odd	6		56.2.m.a.3.3	yes	12
56.51	odd	6		1568.2.e.e.783.4		12
56.53	even	6		392.2.m.g.227.3		12
84.59	odd	6		504.2.bk.a.451.6		12
168.59	odd	6		2016.2.bs.a.1711.3		12
168.101	even	6		504.2.bk.a.451.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.1	✓	12	28.3	even	6
56.2.m.a.3.3	yes	12	56.45	odd	6
56.2.m.a.19.2	yes	12	8.5	even	2
56.2.m.a.19.4	yes	12	4.3	odd	2
224.2.q.a.47.1		12	8.3	odd	2	inner
224.2.q.a.47.2		12	1.1	even	1	trivial
224.2.q.a.143.1		12	7.3	odd	6	inner
224.2.q.a.143.2		12	56.3	even	6	inner
392.2.e.e.195.9		12	28.19	even	6
392.2.e.e.195.10		12	28.23	odd	6
392.2.e.e.195.11		12	56.5	odd	6
392.2.e.e.195.12		12	56.37	even	6
392.2.m.g.19.2		12	56.13	odd	2
392.2.m.g.19.4		12	28.27	even	2
392.2.m.g.227.1		12	28.11	odd	6
392.2.m.g.227.3		12	56.53	even	6
504.2.bk.a.19.3		12	12.11	even	2
504.2.bk.a.19.5		12	24.5	odd	2
504.2.bk.a.451.4		12	168.101	even	6
504.2.bk.a.451.6		12	84.59	odd	6
1568.2.e.e.783.3		12	7.2	even	3
1568.2.e.e.783.4		12	56.51	odd	6
1568.2.e.e.783.9		12	56.19	even	6
1568.2.e.e.783.10		12	7.5	odd	6
1568.2.q.g.815.5		12	56.11	odd	6
1568.2.q.g.815.6		12	7.4	even	3
1568.2.q.g.1391.5		12	7.6	odd	2
1568.2.q.g.1391.6		12	56.27	even	2
2016.2.bs.a.271.3		12	3.2	odd	2
2016.2.bs.a.271.4		12	24.11	even	2
2016.2.bs.a.1711.3		12	168.59	odd	6
2016.2.bs.a.1711.4		12	21.17	even	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.18878 + 0.686340i) q^{3} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(-0.557875 + 0.966267i) q^{9} +O(q^{10})\)	\(q+(-1.18878 + 0.686340i) q^{3} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(-0.557875 + 0.966267i) q^{9} +(1.63090 + 2.82480i) q^{11} +5.27279 q^{13} +0.947443i q^{15} +(-2.20393 + 1.27244i) q^{17} +(0.484848 + 0.279927i) q^{19} +(-2.98150 + 2.07374i) q^{21} +(2.50610 + 1.44690i) q^{23} +(2.26180 + 3.91756i) q^{25} -5.64961i q^{27} +0.444621i q^{29} +(-4.45228 - 7.71158i) q^{31} +(-3.87755 - 2.23871i) q^{33} +(0.776954 - 1.65261i) q^{35} +(-6.00295 - 3.46580i) q^{37} +(-6.26817 + 3.61893i) q^{39} -9.76765i q^{41} +(0.385053 + 0.666931i) q^{45} +(-2.20094 + 3.81214i) q^{47} +(6.90116 - 1.17220i) q^{49} +(1.74665 - 3.02529i) q^{51} +(-8.17440 + 4.71949i) q^{53} +2.25134 q^{55} -0.768501 q^{57} +(-8.59663 + 4.96327i) q^{59} +(5.23284 - 9.06355i) q^{61} +(-1.25597 + 2.67148i) q^{63} +(1.81968 - 3.15177i) q^{65} +(1.45058 + 2.51247i) q^{67} -3.97225 q^{69} -5.29150i q^{71} +(-5.28541 + 3.05153i) q^{73} +(-5.37755 - 3.10473i) q^{75} +(4.92768 + 7.08473i) q^{77} +(5.01803 + 2.89716i) q^{79} +(2.20393 + 3.81731i) q^{81} +1.83845i q^{83} +1.75651i q^{85} +(-0.305161 - 0.528555i) q^{87} +(1.50000 + 0.866025i) q^{89} +(13.9012 - 1.17220i) q^{91} +(10.5855 + 6.11156i) q^{93} +(0.334649 - 0.193210i) q^{95} +7.42325i q^{97} -3.63935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3}+O(q^{10}) \) 12 * q + 6 * q^3	\( 12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^11 - 6 * q^17 + 6 * q^19 - 6 * q^33 - 18 * q^35 - 12 * q^49 - 6 * q^51 - 36 * q^57 - 42 * q^59 - 12 * q^65 - 30 * q^67 + 18 * q^73 - 24 * q^75 + 6 * q^81 + 18 * q^89 + 72 * q^91 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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