LMFDB - Embedded newform 567.2.f.e.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(190,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("567.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.f (of order $3$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			190.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	567.190
Dual form			567.2.f.e.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(3.00000 + 5.19615i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-2.00000 - 3.46410i) q^{16} -3.00000 q^{17} +2.00000 q^{19} +(-3.00000 - 5.19615i) q^{20} +(-3.00000 + 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} -2.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} -3.00000 q^{35} -7.00000 q^{37} +(-1.50000 + 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +12.0000 q^{44} +(4.50000 + 7.79423i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-4.00000 - 6.92820i) q^{52} +6.00000 q^{53} +18.0000 q^{55} +(4.50000 - 7.79423i) q^{59} +(5.00000 + 8.66025i) q^{61} -8.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +2.00000 q^{73} +(2.00000 - 3.46410i) q^{76} +(3.00000 - 5.19615i) q^{77} +(0.500000 + 0.866025i) q^{79} -12.0000 q^{80} +(1.50000 + 2.59808i) q^{83} +(-4.50000 + 7.79423i) q^{85} -6.00000 q^{89} -4.00000 q^{91} +(6.00000 + 10.3923i) q^{92} +(3.00000 - 5.19615i) q^{95} +(5.00000 + 8.66025i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} + 3 q^{5} - q^{7}+O(q^{10}) $ 2 * q + 2 * q^4 + 3 * q^5 - q^7	$ 2 q + 2 q^{4} + 3 q^{5} - q^{7} + 6 q^{11} + 4 q^{13} - 4 q^{16} - 6 q^{17} + 4 q^{19} - 6 q^{20} - 6 q^{23} - 4 q^{25} - 4 q^{28} - 6 q^{29} + 4 q^{31} - 6 q^{35} - 14 q^{37} - 3 q^{41} + q^{43} + 24 q^{44} + 9 q^{47} - q^{49} - 8 q^{52} + 12 q^{53} + 36 q^{55} + 9 q^{59} + 10 q^{61} - 16 q^{64} - 12 q^{65} + 4 q^{67} - 6 q^{68} + 4 q^{73} + 4 q^{76} + 6 q^{77} + q^{79} - 24 q^{80} + 3 q^{83} - 9 q^{85} - 12 q^{89} - 8 q^{91} + 12 q^{92} + 6 q^{95} + 10 q^{97}+O(q^{100}) $ 2 * q + 2 * q^4 + 3 * q^5 - q^7 + 6 * q^11 + 4 * q^13 - 4 * q^16 - 6 * q^17 + 4 * q^19 - 6 * q^20 - 6 * q^23 - 4 * q^25 - 4 * q^28 - 6 * q^29 + 4 * q^31 - 6 * q^35 - 14 * q^37 - 3 * q^41 + q^43 + 24 * q^44 + 9 * q^47 - q^49 - 8 * q^52 + 12 * q^53 + 36 * q^55 + 9 * q^59 + 10 * q^61 - 16 * q^64 - 12 * q^65 + 4 * q^67 - 6 * q^68 + 4 * q^73 + 4 * q^76 + 6 * q^77 + q^79 - 24 * q^80 + 3 * q^83 - 9 * q^85 - 12 * q^89 - 8 * q^91 + 12 * q^92 + 6 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	−3.00000	−	5.19615i	−0.670820	−	1.16190i
$21$		0			0
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$	−2.00000			−0.377964
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.00000			−0.507093
$36$		0			0
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	12.0000			1.80907
$45$		0			0
$46$		0			0
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$	−4.00000	−	6.92820i	−0.554700	−	0.960769i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	18.0000			2.42712
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	3.00000	−	5.19615i	0.341882	−	0.592157i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−12.0000			−1.34164
$81$		0			0
$82$		0			0
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	0.936530	−	0.350588i	$-0.114018\pi$
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	−0.771883	+	0.635764i	$0.780685\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$	6.00000	+	10.3923i	0.625543	+	1.08347i
$93$		0			0
$94$		0			0
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$		0			0
$99$		0			0
$100$	−8.00000			−0.800000
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$		0			0
$109$	11.0000			1.05361			0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000			1.05361			0.526804	+	0.849987i	$0.323390\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000	+	3.46410i	−0.188982	+	0.327327i
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	0.432670	+	0.901553i	$0.357572\pi$
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	−0.997102	+	0.0760733i	$0.975762\pi$
$114$		0			0
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$	−12.0000			−1.11417
$117$		0			0
$118$		0			0
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		0			0
$123$		0			0
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	3.00000			0.268328
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	11.0000	−	19.0526i	0.933008	−	1.61602i	0.154859	−	0.987937i	$-0.450508\pi$
$139$	11.0000	−	19.0526i	0.933008	−	1.61602i	0.778148	−	0.628080i	$-0.216159\pi$
$140$	−3.00000	+	5.19615i	−0.253546	+	0.439155i
$141$		0			0
$142$		0			0
$143$	24.0000			2.00698
$144$		0			0
$145$	−18.0000			−1.49482
$146$		0			0
$147$		0			0
$148$	−7.00000	+	12.1244i	−0.575396	+	0.996616i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	0.935857	+	0.352381i	$0.114628\pi$
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	−0.162758	+	0.986666i	$0.552039\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.00000	−	10.3923i	−0.481932	−	0.834730i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.00000			0.472866
$162$		0			0
$163$	−7.00000			−0.548282			−0.274141	−	0.961689i	$-0.588394\pi$
$163$	−7.00000			−0.548282			−0.274141	+	0.961689i	$0.588394\pi$
$164$	3.00000	+	5.19615i	0.234261	+	0.405751i
$165$		0			0
$166$		0			0
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$	2.00000			0.152499
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	12.0000	−	20.7846i	0.904534	−	1.56670i
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.5000	+	18.1865i	−0.771975	+	1.33710i
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.658145	−	1.13994i
$188$	18.0000			1.31278
$189$		0			0
$190$		0			0
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		0			0
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	−0.531446	−	0.847092i	$-0.678351\pi$
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	0.999326	+	0.0366998i	$0.0116845\pi$
$194$		0			0
$195$		0			0
$196$	1.00000	+	1.73205i	0.0714286	+	0.123718i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$		0			0
$208$	−16.0000			−1.10940
$209$	6.00000	+	10.3923i	0.415029	+	0.718851i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		0			0
$214$		0			0
$215$	3.00000			0.204598
$216$		0			0
$217$	−4.00000			−0.271538
$218$		0			0
$219$		0			0
$220$	18.0000	−	31.1769i	1.21356	−	2.10195i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$		0			0
$235$	27.0000			1.76129
$236$	−9.00000	−	15.5885i	−0.585850	−	1.01472i
$237$		0			0
$238$		0			0
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$		0			0
$243$		0			0
$244$	20.0000			1.28037
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−27.0000			−1.70422			−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000			−1.70422			−0.852112	+	0.523359i	$0.824679\pi$
$252$		0			0
$253$	−36.0000			−2.26330
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$	3.50000	+	6.06218i	0.217479	+	0.376685i
$260$	−24.0000			−1.48842
$261$		0			0
$262$		0			0
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	9.00000	−	15.5885i	0.552866	−	0.957591i
$266$		0			0
$267$		0			0
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−3.00000			−0.182913			−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000			−0.182913			−0.0914566	+	0.995809i	$0.529152\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	6.00000	+	10.3923i	0.363803	+	0.630126i
$273$		0			0
$274$		0			0
$275$	12.0000	−	20.7846i	0.723627	−	1.25336i
$276$		0			0
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.0000	+	25.9808i	0.894825	+	1.54988i	0.834021	+	0.551733i	$0.186033\pi$
$281$	15.0000	+	25.9808i	0.894825	+	1.54988i	0.0608039	+	0.998150i	$0.480634\pi$
$282$		0			0
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$		0			0
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	16.5000	−	28.5788i	0.963940	−	1.66959i	0.251505	−	0.967856i	$-0.419075\pi$
$293$	16.5000	−	28.5788i	0.963940	−	1.66959i	0.712436	−	0.701737i	$-0.247592\pi$
$294$		0			0
$295$	−13.5000	−	23.3827i	−0.786000	−	1.36139i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.0000	+	20.7846i	0.693978	+	1.20201i
$300$		0			0
$301$	0.500000	−	0.866025i	0.0288195	−	0.0499169i
$302$		0			0
$303$		0			0
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$	30.0000			1.71780
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−6.00000	−	10.3923i	−0.341882	−	0.592157i
$309$		0			0
$310$		0			0
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	−0.709771	−	0.704433i	$-0.751201\pi$
$311$	4.50000	−	7.79423i	0.255172	−	0.441970i	0.964942	+	0.262463i	$0.0845347\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$		0			0
$315$		0			0
$316$	2.00000			0.112509
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$	−12.0000	+	20.7846i	−0.670820	+	1.16190i
$321$		0			0
$322$		0			0
$323$	−6.00000			−0.333849
$324$		0			0
$325$	−16.0000			−0.887520
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.50000	−	7.79423i	0.248093	−	0.429710i
$330$		0			0
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	0.879440	−	0.476011i	$-0.157918\pi$
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	6.00000			0.329293
$333$		0			0
$334$		0			0
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$		0			0
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	−0.632882	−	0.774248i	$-0.718128\pi$
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	0.986960	+	0.160968i	$0.0514616\pi$
$338$		0			0
$339$		0			0
$340$	9.00000	+	15.5885i	0.488094	+	0.845403i
$341$	24.0000			1.29967
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	0.738883	−	0.673833i	$-0.235353\pi$
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	−0.952998	+	0.302975i	$0.902020\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000	+	10.3923i	−0.317999	+	0.550791i
$357$		0			0
$358$		0			0
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$		0			0
$364$	−4.00000	+	6.92820i	−0.209657	+	0.363137i
$365$	3.00000	−	5.19615i	0.157027	−	0.271979i
$366$		0			0
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	0.966507	−	0.256639i	$-0.0826151\pi$
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	−0.705509	+	0.708700i	$0.749282\pi$
$368$	24.0000			1.25109
$369$		0			0
$370$		0			0
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$		0			0
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$		0			0
$382$		0			0
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$	−9.00000	−	15.5885i	−0.458682	−	0.794461i
$386$		0			0
$387$		0			0
$388$	20.0000			1.01535
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.00000			0.150946
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$		0			0
$399$		0			0
$400$	−8.00000	+	13.8564i	−0.400000	+	0.692820i
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	12.0000			0.597022
$405$		0			0
$406$		0			0
$407$	−21.0000	−	36.3731i	−1.04093	−	1.80295i
$408$		0			0
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$		0			0
$411$		0			0
$412$	14.0000	+	24.2487i	0.689730	+	1.19465i
$413$	−9.00000			−0.442861
$414$		0			0
$415$	9.00000			0.441793
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	5.00000	−	8.66025i	0.241967	−	0.419099i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$		0			0
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$		0			0
$436$	11.0000	−	19.0526i	0.526804	−	0.912452i
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.00000	+	15.5885i	0.427603	+	0.740630i	0.996660	−	0.0816684i	$-0.0260248\pi$
$443$	9.00000	+	15.5885i	0.427603	+	0.740630i	−0.569057	+	0.822298i	$0.692691\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$		0			0
$447$		0			0
$448$	4.00000	+	6.92820i	0.188982	+	0.327327i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−18.0000			−0.847587
$452$	12.0000	+	20.7846i	0.564433	+	0.977626i
$453$		0			0
$454$		0			0
$455$	−6.00000	+	10.3923i	−0.281284	+	0.487199i
$456$		0			0
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	−0.991551	−	0.129718i	$-0.958593\pi$
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	0.383437	−	0.923567i	$-0.374740\pi$
$458$		0			0
$459$		0			0
$460$	36.0000			1.67851
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$		0			0
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	−0.918253	−	0.395995i	$-0.870400\pi$
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	0.802068	+	0.597233i	$0.203733\pi$
$464$	−12.0000	+	20.7846i	−0.557086	+	0.964901i
$465$		0			0
$466$		0			0
$467$	−24.0000			−1.11059			−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000			−1.11059			−0.555294	+	0.831654i	$0.687394\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$		0			0
$475$	−4.00000	−	6.92820i	−0.183533	−	0.317888i
$476$	6.00000			0.275010
$477$		0			0
$478$		0			0
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	0.519973	−	0.854183i	$-0.325942\pi$
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	−0.999730	+	0.0232187i	$0.992609\pi$
$480$		0			0
$481$	−14.0000	+	24.2487i	−0.638345	+	1.10565i
$482$		0			0
$483$		0			0
$484$	25.0000	+	43.3013i	1.13636	+	1.96824i
$485$	30.0000			1.36223
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	−0.457263	−	0.889332i	$-0.651170\pi$
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	0.998815	−	0.0486647i	$-0.0154966\pi$
$492$		0			0
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$		0			0
$495$		0			0
$496$	−16.0000			−0.718421
$497$		0			0
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	3.00000	−	5.19615i	0.134164	−	0.232379i
$501$		0			0
$502$		0			0
$503$	27.0000			1.20387			0.601935	−	0.798545i	$-0.294397\pi$
$503$	27.0000			1.20387			0.601935	+	0.798545i	$0.294397\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$		0			0
$508$	−7.00000	+	12.1244i	−0.310575	+	0.537931i
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	−0.00339621	−	0.999994i	$-0.501081\pi$
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	0.867719	−	0.497056i	$-0.165586\pi$
$510$		0			0
$511$	−1.00000	−	1.73205i	−0.0442374	−	0.0766214i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	21.0000	+	36.3731i	0.925371	+	1.60279i
$516$		0			0
$517$	−27.0000	+	46.7654i	−1.18746	+	2.05674i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−39.0000			−1.70862			−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000			−1.70862			−0.854311	+	0.519763i	$0.826020\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−12.0000	−	20.7846i	−0.524222	−	0.907980i
$525$		0			0
$526$		0			0
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$	−4.00000			−0.173422
$533$	6.00000	+	10.3923i	0.259889	+	0.450141i
$534$		0			0
$535$	−9.00000	+	15.5885i	−0.389104	+	0.673948i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.00000			−0.258438
$540$		0			0
$541$	−43.0000			−1.84871			−0.924357	−	0.381528i	$-0.875398\pi$
$541$	−43.0000			−1.84871			−0.924357	+	0.381528i	$0.875398\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.5000	−	28.5788i	0.706782	−	1.22418i
$546$		0			0
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	0.876517	−	0.481371i	$-0.159861\pi$
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	−0.855138	+	0.518400i	$0.826528\pi$
$548$	−24.0000			−1.02523
$549$		0			0
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$	0.500000	−	0.866025i	0.0212622	−	0.0368271i
$554$		0			0
$555$		0			0
$556$	−22.0000	−	38.1051i	−0.933008	−	1.61602i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	6.00000	+	10.3923i	0.253546	+	0.439155i
$561$		0			0
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	18.0000	+	31.1769i	0.757266	+	1.31162i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	−11.5000	+	19.9186i	−0.481260	+	0.833567i	−0.999769	−	0.0215055i	$-0.993154\pi$
$571$	−11.5000	+	19.9186i	−0.481260	+	0.833567i	0.518509	+	0.855072i	$0.326487\pi$
$572$	24.0000	−	41.5692i	1.00349	−	1.73810i
$573$		0			0
$574$		0			0
$575$	24.0000			1.00087
$576$		0			0
$577$	−16.0000			−0.666089			−0.333044	−	0.942911i	$-0.608076\pi$
$577$	−16.0000			−0.666089			−0.333044	+	0.942911i	$0.608076\pi$
$578$		0			0
$579$		0			0
$580$	−18.0000	+	31.1769i	−0.747409	+	1.29455i
$581$	1.50000	−	2.59808i	0.0622305	−	0.107786i
$582$		0			0
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$		0			0
$589$	4.00000	−	6.92820i	0.164817	−	0.285472i
$590$		0			0
$591$		0			0
$592$	14.0000	+	24.2487i	0.575396	+	0.996616i
$593$	−15.0000			−0.615976			−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000			−0.615976			−0.307988	+	0.951390i	$0.599656\pi$
$594$		0			0
$595$	9.00000			0.368964
$596$	6.00000	+	10.3923i	0.245770	+	0.425685i
$597$		0			0
$598$		0			0
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	−0.621480	−	0.783430i	$-0.713468\pi$
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	0.989210	+	0.146503i	$0.0468017\pi$
$600$		0			0
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	0.772838	−	0.634603i	$-0.218836\pi$
$601$	−4.00000	−	6.92820i	−0.163163	−	0.282607i	−0.936002	+	0.351996i	$0.885503\pi$
$602$		0			0
$603$		0			0
$604$	38.0000			1.54620
$605$	37.5000	+	64.9519i	1.52459	+	2.64067i
$606$		0			0
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	−0.0998457	−	0.995003i	$-0.531835\pi$
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	0.911621	−	0.411033i	$-0.134832\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	36.0000			1.45640
$612$		0			0
$613$	−34.0000			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	0.388351	+	0.921512i	$0.373045\pi$
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	−0.992228	+	0.124434i	$0.960288\pi$
$618$		0			0
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$	−24.0000			−0.963863
$621$		0			0
$622$		0			0
$623$	3.00000	+	5.19615i	0.120192	+	0.208179i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$	14.0000	+	24.2487i	0.558661	+	0.967629i
$629$	21.0000			0.837325
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.5000	+	18.1865i	−0.416680	+	0.721711i
$636$		0			0
$637$	2.00000	+	3.46410i	0.0792429	+	0.137253i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$		0			0
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	−0.970400	−	0.241502i	$-0.922360\pi$
$643$	−7.00000	+	12.1244i	−0.276053	+	0.478138i	0.694347	+	0.719640i	$0.255693\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$		0			0
$646$		0			0
$647$	24.0000			0.943537			0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000			0.943537			0.471769	+	0.881722i	$0.343616\pi$
$648$		0			0
$649$	54.0000			2.11969
$650$		0			0
$651$		0			0
$652$	−7.00000	+	12.1244i	−0.274141	+	0.474826i
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	−0.999396	−	0.0347583i	$-0.988934\pi$
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	0.529799	+	0.848123i	$0.322267\pi$
$654$		0			0
$655$	−18.0000	−	31.1769i	−0.703318	−	1.21818i
$656$	12.0000			0.468521
$657$		0			0
$658$		0			0
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	0.531855	−	0.846836i	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.00000			−0.232670
$666$		0			0
$667$	36.0000			1.39393
$668$	3.00000	+	5.19615i	0.116073	+	0.201045i
$669$		0			0
$670$		0			0
$671$	−30.0000	+	51.9615i	−1.15814	+	2.00595i
$672$		0			0
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	−0.999999	−	0.00128586i	$-0.999591\pi$
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	0.498886	−	0.866668i	$-0.333743\pi$
$674$		0			0
$675$		0			0
$676$	−6.00000			−0.230769
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	0.639618	−	0.768693i	$-0.279092\pi$
$677$	−9.00000	−	15.5885i	−0.345898	−	0.599113i	−0.985517	+	0.169580i	$0.945759\pi$
$678$		0			0
$679$	5.00000	−	8.66025i	0.191882	−	0.332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	−36.0000			−1.37549
$686$		0			0
$687$		0			0
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	−36.0000			−1.36851
$693$		0			0
$694$		0			0
$695$	−33.0000	−	57.1577i	−1.25176	−	2.16811i
$696$		0			0
$697$	4.50000	−	7.79423i	0.170450	−	0.295227i
$698$		0			0
$699$		0			0
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−24.0000	−	41.5692i	−0.904534	−	1.56670i
$705$		0			0
$706$		0			0
$707$	3.00000	−	5.19615i	0.112827	−	0.195421i
$708$		0			0
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$		0			0
$715$	36.0000	−	62.3538i	1.34632	−	2.33190i
$716$	−12.0000	+	20.7846i	−0.448461	+	0.776757i
$717$		0			0
$718$		0			0
$719$	−33.0000			−1.23069			−0.615346	−	0.788257i	$-0.710984\pi$
$719$	−33.0000			−1.23069			−0.615346	+	0.788257i	$0.710984\pi$
$720$		0			0
$721$	14.0000			0.521387
$722$		0			0
$723$		0			0
$724$	20.0000	−	34.6410i	0.743294	−	1.28742i
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$		0			0
$727$	5.00000	+	8.66025i	0.185440	+	0.321191i	0.943725	−	0.330732i	$-0.107296\pi$
$727$	5.00000	+	8.66025i	0.185440	+	0.321191i	−0.758285	+	0.651923i	$0.773962\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.0000			0.884051
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	21.0000	+	36.3731i	0.771975	+	1.33710i
$741$		0			0
$742$		0			0
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$		0			0
$747$		0			0
$748$	−36.0000			−1.31629
$749$	3.00000	+	5.19615i	0.109618	+	0.189863i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	18.0000	−	31.1769i	0.656392	−	1.13691i
$753$		0			0
$754$		0			0
$755$	57.0000			2.07444
$756$		0			0
$757$	47.0000			1.70824			0.854122	−	0.520073i	$-0.174095\pi$
$757$	47.0000			1.70824			0.854122	+	0.520073i	$0.174095\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−25.5000	+	44.1673i	−0.924374	+	1.60106i	−0.131810	+	0.991275i	$0.542079\pi$
$761$	−25.5000	+	44.1673i	−0.924374	+	1.60106i	−0.792564	+	0.609788i	$0.791255\pi$
$762$		0			0
$763$	−5.50000	−	9.52628i	−0.199113	−	0.344874i
$764$	36.0000			1.30243
$765$		0			0
$766$		0			0
$767$	−18.0000	−	31.1769i	−0.649942	−	1.12573i
$768$		0			0
$769$	20.0000	−	34.6410i	0.721218	−	1.24919i	−0.239293	−	0.970947i	$-0.576916\pi$
$769$	20.0000	−	34.6410i	0.721218	−	1.24919i	0.960512	−	0.278240i	$-0.0897509\pi$
$770$		0			0
$771$		0			0
$772$	−13.0000	−	22.5167i	−0.467880	−	0.810392i
$773$	−21.0000			−0.755318			−0.377659	−	0.925945i	$-0.623271\pi$
$773$	−21.0000			−0.755318			−0.377659	+	0.925945i	$0.623271\pi$
$774$		0			0
$775$	−16.0000			−0.574737
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	4.00000			0.142857
$785$	21.0000	+	36.3731i	0.749522	+	1.29821i
$786$		0			0
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	−0.963394	−	0.268091i	$-0.913607\pi$
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	0.713871	+	0.700278i	$0.246941\pi$
$788$	18.0000	−	31.1769i	0.641223	−	1.11063i
$789$		0			0
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$	40.0000			1.42044
$794$		0			0
$795$		0			0
$796$	20.0000	−	34.6410i	0.708881	−	1.22782i
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	−0.807989	−	0.589197i	$-0.799444\pi$
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	0.914255	+	0.405140i	$0.132777\pi$
$798$		0			0
$799$	−13.5000	−	23.3827i	−0.477596	−	0.827220i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$		0			0
$805$	9.00000	−	15.5885i	0.317208	−	0.549421i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.00000			0.210949			0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000			0.210949			0.105474	+	0.994422i	$0.466364\pi$
$810$		0			0
$811$	−52.0000			−1.82597			−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000			−1.82597			−0.912983	+	0.407997i	$0.866228\pi$
$812$	6.00000	+	10.3923i	0.210559	+	0.364698i
$813$		0			0
$814$		0			0
$815$	−10.5000	+	18.1865i	−0.367799	+	0.637046i
$816$		0			0
$817$	1.00000	+	1.73205i	0.0349856	+	0.0605968i
$818$		0			0
$819$		0			0
$820$	18.0000			0.628587
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	−0.987912	−	0.155017i	$-0.950457\pi$
$821$	−18.0000	−	31.1769i	−0.628204	−	1.08808i	0.359708	−	0.933065i	$-0.382876\pi$
$822$		0			0
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	0.819159	+	0.573567i	$0.194441\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$		0			0
$831$		0			0
$832$	−16.0000	+	27.7128i	−0.554700	+	0.960769i
$833$	1.50000	−	2.59808i	0.0519719	−	0.0900180i
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	24.0000			0.830057
$837$		0			0
$838$		0			0
$839$	10.5000	+	18.1865i	0.362500	+	0.627869i	0.988372	−	0.152057i	$-0.0485899\pi$
$839$	10.5000	+	18.1865i	0.362500	+	0.627869i	−0.625871	+	0.779926i	$0.715257\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$		0			0
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−9.00000			−0.309609
$846$		0			0
$847$	25.0000			0.859010
$848$	−12.0000	−	20.7846i	−0.412082	−	0.713746i
$849$		0			0
$850$		0			0
$851$	21.0000	−	36.3731i	0.719871	−	1.24685i
$852$		0			0
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	−0.946232	−	0.323489i	$-0.895144\pi$
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	0.192966	−	0.981205i	$-0.438189\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$		0			0
$859$	11.0000	−	19.0526i	0.375315	−	0.650065i	−0.615059	−	0.788481i	$-0.710868\pi$
$859$	11.0000	−	19.0526i	0.375315	−	0.650065i	0.990374	+	0.138416i	$0.0442012\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$		0			0
$862$		0			0
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$		0			0
$865$	−54.0000			−1.83606
$866$		0			0
$867$		0			0
$868$	−4.00000	+	6.92820i	−0.135769	+	0.235159i
$869$	−3.00000	+	5.19615i	−0.101768	+	0.176267i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.50000	−	2.59808i	−0.0507093	−	0.0878310i
$876$		0			0
$877$	15.5000	−	26.8468i	0.523398	−	0.906552i	−0.476231	−	0.879320i	$-0.657998\pi$
$877$	15.5000	−	26.8468i	0.523398	−	0.906552i	0.999629	−	0.0272316i	$-0.00866915\pi$
$878$		0			0
$879$		0			0
$880$	−36.0000	−	62.3538i	−1.21356	−	2.10195i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$		0			0
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	−0.634141	−	0.773217i	$-0.718646\pi$
$887$	10.5000	−	18.1865i	0.352555	−	0.610644i	0.986696	+	0.162573i	$0.0519794\pi$
$888$		0			0
$889$	3.50000	+	6.06218i	0.117386	+	0.203319i
$890$		0			0
$891$		0			0
$892$	−16.0000			−0.535720
$893$	9.00000	+	15.5885i	0.301174	+	0.521648i
$894$		0			0
$895$	−18.0000	+	31.1769i	−0.601674	+	1.04213i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−24.0000			−0.800445
$900$		0			0
$901$	−18.0000			−0.599667
$902$		0			0
$903$		0			0
$904$		0			0
$905$	30.0000	−	51.9615i	0.997234	−	1.72726i
$906$		0			0
$907$	27.5000	+	47.6314i	0.913123	+	1.58157i	0.809627	+	0.586945i	$0.199669\pi$
$907$	27.5000	+	47.6314i	0.913123	+	1.58157i	0.103495	+	0.994630i	$0.466997\pi$
$908$	−24.0000			−0.796468
$909$		0			0
$910$		0			0
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	0.999994	−	0.00349271i	$-0.00111177\pi$
$911$	15.0000	+	25.9808i	0.496972	+	0.860781i	−0.503022	+	0.864274i	$0.667778\pi$
$912$		0			0
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$		0			0
$915$		0			0
$916$	−4.00000	−	6.92820i	−0.132164	−	0.228914i
$917$	−12.0000			−0.396275
$918$		0			0
$919$	29.0000			0.956622			0.478311	−	0.878191i	$-0.341249\pi$
$919$	29.0000			0.956622			0.478311	+	0.878191i	$0.341249\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	−1.00000	+	1.73205i	−0.0327737	+	0.0567657i
$932$	−24.0000	+	41.5692i	−0.786146	+	1.36165i
$933$		0			0
$934$		0			0
$935$	−54.0000			−1.76599
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$		0			0
$940$	27.0000	−	46.7654i	0.880643	−	1.52532i
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	−0.557608	−	0.830104i	$-0.688281\pi$
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	0.997695	+	0.0678506i	$0.0216141\pi$
$942$		0			0
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$	−36.0000			−1.17170
$945$		0			0
$946$		0			0
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	0.994885	+	0.101012i	$0.0322080\pi$
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	−0.409964	+	0.912102i	$0.634459\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$		0			0
$955$	54.0000			1.74740
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$		0			0
$959$	−6.00000	+	10.3923i	−0.193750	+	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$		0			0
$964$	−16.0000			−0.515325
$965$	−19.5000	−	33.7750i	−0.627727	−	1.08726i
$966$		0			0
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	−0.341567	−	0.939857i	$-0.610958\pi$
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	0.984724	−	0.174123i	$-0.0557089\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21.0000			0.673922			0.336961	−	0.941519i	$-0.390601\pi$
$971$	21.0000			0.673922			0.336961	+	0.941519i	$0.390601\pi$
$972$		0			0
$973$	−22.0000			−0.705288
$974$		0			0
$975$		0			0
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	−18.0000	+	31.1769i	−0.575871	+	0.997438i	0.420075	+	0.907489i	$0.362004\pi$
$977$	−18.0000	+	31.1769i	−0.575871	+	0.997438i	−0.995946	+	0.0899487i	$0.971330\pi$
$978$		0			0
$979$	−18.0000	−	31.1769i	−0.575282	−	0.996419i
$980$	6.00000			0.191663
$981$		0			0
$982$		0			0
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$		0			0
$987$		0			0
$988$	−8.00000	−	13.8564i	−0.254514	−	0.440831i
$989$	−6.00000			−0.190789
$990$		0			0
$991$	47.0000			1.49300			0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000			1.49300			0.746502	+	0.665383i	$0.231732\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	30.0000	−	51.9615i	0.951064	−	1.64729i
$996$		0			0
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.e.190.1		2
3.2	odd	2		567.2.f.d.190.1		2
9.2	odd	6		567.2.f.d.379.1		2
9.4	even	3		189.2.a.b.1.1	✓	1
9.5	odd	6		189.2.a.c.1.1	yes	1
9.7	even	3	inner	567.2.f.e.379.1		2
36.23	even	6		3024.2.a.y.1.1		1
36.31	odd	6		3024.2.a.f.1.1		1
45.4	even	6		4725.2.a.i.1.1		1
45.14	odd	6		4725.2.a.k.1.1		1
63.13	odd	6		1323.2.a.l.1.1		1
63.41	even	6		1323.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.a.b.1.1	✓	1	9.4	even	3
189.2.a.c.1.1	yes	1	9.5	odd	6
567.2.f.d.190.1		2	3.2	odd	2
567.2.f.d.379.1		2	9.2	odd	6
567.2.f.e.190.1		2	1.1	even	1	trivial
567.2.f.e.379.1		2	9.7	even	3	inner
1323.2.a.h.1.1		1	63.41	even	6
1323.2.a.l.1.1		1	63.13	odd	6
3024.2.a.f.1.1		1	36.31	odd	6
3024.2.a.y.1.1		1	36.23	even	6
4725.2.a.i.1.1		1	45.4	even	6
4725.2.a.k.1.1		1	45.14	odd	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(3.00000 + 5.19615i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-2.00000 - 3.46410i) q^{16} -3.00000 q^{17} +2.00000 q^{19} +(-3.00000 - 5.19615i) q^{20} +(-3.00000 + 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} -2.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} -3.00000 q^{35} -7.00000 q^{37} +(-1.50000 + 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +12.0000 q^{44} +(4.50000 + 7.79423i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-4.00000 - 6.92820i) q^{52} +6.00000 q^{53} +18.0000 q^{55} +(4.50000 - 7.79423i) q^{59} +(5.00000 + 8.66025i) q^{61} -8.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +2.00000 q^{73} +(2.00000 - 3.46410i) q^{76} +(3.00000 - 5.19615i) q^{77} +(0.500000 + 0.866025i) q^{79} -12.0000 q^{80} +(1.50000 + 2.59808i) q^{83} +(-4.50000 + 7.79423i) q^{85} -6.00000 q^{89} -4.00000 q^{91} +(6.00000 + 10.3923i) q^{92} +(3.00000 - 5.19615i) q^{95} +(5.00000 + 8.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} + 3 q^{5} - q^{7}+O(q^{10}) \) 2 * q + 2 * q^4 + 3 * q^5 - q^7	\( 2 q + 2 q^{4} + 3 q^{5} - q^{7} + 6 q^{11} + 4 q^{13} - 4 q^{16} - 6 q^{17} + 4 q^{19} - 6 q^{20} - 6 q^{23} - 4 q^{25} - 4 q^{28} - 6 q^{29} + 4 q^{31} - 6 q^{35} - 14 q^{37} - 3 q^{41} + q^{43} + 24 q^{44} + 9 q^{47} - q^{49} - 8 q^{52} + 12 q^{53} + 36 q^{55} + 9 q^{59} + 10 q^{61} - 16 q^{64} - 12 q^{65} + 4 q^{67} - 6 q^{68} + 4 q^{73} + 4 q^{76} + 6 q^{77} + q^{79} - 24 q^{80} + 3 q^{83} - 9 q^{85} - 12 q^{89} - 8 q^{91} + 12 q^{92} + 6 q^{95} + 10 q^{97}+O(q^{100}) \) 2 * q + 2 * q^4 + 3 * q^5 - q^7 + 6 * q^11 + 4 * q^13 - 4 * q^16 - 6 * q^17 + 4 * q^19 - 6 * q^20 - 6 * q^23 - 4 * q^25 - 4 * q^28 - 6 * q^29 + 4 * q^31 - 6 * q^35 - 14 * q^37 - 3 * q^41 + q^43 + 24 * q^44 + 9 * q^47 - q^49 - 8 * q^52 + 12 * q^53 + 36 * q^55 + 9 * q^59 + 10 * q^61 - 16 * q^64 - 12 * q^65 + 4 * q^67 - 6 * q^68 + 4 * q^73 + 4 * q^76 + 6 * q^77 + q^79 - 24 * q^80 + 3 * q^83 - 9 * q^85 - 12 * q^89 - 8 * q^91 + 12 * q^92 + 6 * q^95 + 10 * q^97

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