LMFDB - Embedded newform 1134.2.f.h.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(379,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1134.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.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:	$9.05503558921$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.379
Dual form			1134.2.f.h.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{10} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +2.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(3.00000 + 5.19615i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} -1.00000 q^{26} +1.00000 q^{28} +(4.50000 - 7.79423i) q^{29} +(5.00000 + 8.66025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{35} -7.00000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} -6.00000 q^{44} -6.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(0.500000 - 0.866025i) q^{52} -6.00000 q^{53} +18.0000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(4.50000 + 7.79423i) q^{58} +(3.00000 + 5.19615i) q^{59} +(-5.50000 + 9.52628i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(1.50000 - 2.59808i) q^{70} +12.0000 q^{71} -7.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(3.00000 + 5.19615i) q^{77} +(-1.00000 + 1.73205i) q^{79} -3.00000 q^{80} +6.00000 q^{82} +(-3.00000 + 5.19615i) q^{83} +(4.50000 + 7.79423i) q^{85} +(2.00000 + 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{88} +3.00000 q^{89} -1.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 2 q^{8} - 6 q^{10} + 6 q^{11} + q^{13} - q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} - 4 q^{25} - 2 q^{26} + 2 q^{28} + 9 q^{29}+ \cdots + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 3 * q^5 - q^7 + 2 * q^8 - 6 * q^10 + 6 * q^11 + q^13 - q^14 - q^16 + 6 * q^17 + 4 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 - 4 * q^25 - 2 * q^26 + 2 * q^28 + 9 * q^29 + 10 * q^31 - q^32 - 3 * q^34 - 6 * q^35 - 14 * q^37 - 2 * q^38 + 3 * q^40 - 6 * q^41 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 6 * q^47 - q^49 - 4 * q^50 + q^52 - 12 * q^53 + 36 * q^55 - q^56 + 9 * q^58 + 6 * q^59 - 11 * q^61 - 20 * q^62 + 2 * q^64 - 3 * q^65 - 2 * q^67 - 3 * q^68 + 3 * q^70 + 24 * q^71 - 14 * q^73 + 7 * q^74 - 2 * q^76 + 6 * q^77 - 2 * q^79 - 6 * q^80 + 12 * q^82 - 6 * q^83 + 9 * q^85 + 4 * q^86 + 6 * q^88 + 6 * q^89 - 2 * q^91 + 6 * q^92 - 6 * q^94 + 6 * q^95 - 14 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.00000			−0.948683
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−1.00000			−0.196116
$27$		0			0
$28$	1.00000			0.188982
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	−0.0578882	−	0.998323i	$-0.518437\pi$
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	0.893517	−	0.449029i	$-0.148230\pi$
$30$		0			0
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.830014	+	0.557743i	$0.188333\pi$
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	−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	$0.695152\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$		0			0
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	−6.00000			−0.904534
$45$		0			0
$46$	−6.00000			−0.884652
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	18.0000			2.42712
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	0.262776	+	0.964857i	$0.415362\pi$
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	−0.966978	+	0.254858i	$0.917971\pi$
$62$	−10.0000			−1.27000
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.50000	+	2.59808i	−0.186052	+	0.322252i
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$		0			0
$70$	1.50000	−	2.59808i	0.179284	−	0.310530i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−7.00000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$	3.50000	−	6.06218i	0.406867	−	0.704714i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	3.00000	+	5.19615i	0.341882	+	0.592157i
$78$		0			0
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	−3.00000			−0.335410
$81$		0			0
$82$	6.00000			0.662589
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	−0.982372	−	0.186938i	$-0.940144\pi$
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	0.653079	+	0.757290i	$0.273477\pi$
$84$		0			0
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	4.00000			0.400000
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$		0			0
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$	0.500000	+	0.866025i	0.0490290	+	0.0849208i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$	−9.00000	+	15.5885i	−0.858116	+	1.48630i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	−9.00000	+	15.5885i	−0.839254	+	1.45363i
$116$	−9.00000			−0.835629
$117$		0			0
$118$	−6.00000			−0.552345
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	−5.50000	−	9.52628i	−0.497947	−	0.862469i
$123$		0			0
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	3.00000			0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−1.00000	+	1.73205i	−0.0867110	+	0.150188i
$134$	2.00000			0.172774
$135$		0			0
$136$	3.00000			0.257248
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	−0.993724	−	0.111856i	$-0.964321\pi$
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	0.399992	−	0.916519i	$-0.369013\pi$
$140$	1.50000	+	2.59808i	0.126773	+	0.219578i
$141$		0			0
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	6.00000			0.501745
$144$		0			0
$145$	27.0000			2.24223
$146$	3.50000	−	6.06218i	0.289662	−	0.501709i
$147$		0			0
$148$	3.50000	+	6.06218i	0.287698	+	0.498308i
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	2.00000			0.162221
$153$		0			0
$154$	−6.00000			−0.483494
$155$	−15.0000	+	25.9808i	−1.20483	+	2.08683i
$156$		0			0
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.802749	−	0.596316i	$-0.796630\pi$
$157$	−11.5000	−	19.9186i	−0.917800	−	1.58968i	−0.115050	−	0.993360i	$-0.536703\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$		0			0
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	−6.00000			−0.472866
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	0.726293	−	0.687386i	$-0.241242\pi$
$167$	−3.00000	−	5.19615i	−0.232147	−	0.402090i	−0.958440	+	0.285295i	$0.907908\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−9.00000			−0.690268
$171$		0			0
$172$	−4.00000			−0.304997
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	−0.984828	−	0.173534i	$-0.944481\pi$
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	0.642699	+	0.766119i	$0.277815\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	3.00000	+	5.19615i	0.226134	+	0.391675i
$177$		0			0
$178$	−1.50000	+	2.59808i	−0.112430	+	0.194734i
$179$	6.00000			0.448461			0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000			0.448461			0.224231	+	0.974536i	$0.428013\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	0.500000	−	0.866025i	0.0370625	−	0.0641941i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−10.5000	−	18.1865i	−0.771975	−	1.33710i
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$	6.00000			0.437595
$189$		0			0
$190$	−6.00000			−0.435286
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$		0			0
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	9.00000	+	15.5885i	0.633238	+	1.09680i
$203$	4.50000	+	7.79423i	0.315838	+	0.547048i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$	−16.0000			−1.11477
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$		0			0
$211$	−1.00000	−	1.73205i	−0.0688428	−	0.119239i	0.829549	−	0.558433i	$-0.188597\pi$
$211$	−1.00000	−	1.73205i	−0.0688428	−	0.119239i	−0.898392	+	0.439194i	$0.855264\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$		0			0
$215$	12.0000			0.818393
$216$		0			0
$217$	−10.0000			−0.678844
$218$	−2.50000	+	4.33013i	−0.169321	+	0.293273i
$219$		0			0
$220$	−9.00000	−	15.5885i	−0.606780	−	1.05097i
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$		0			0
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.770097	−	0.637927i	$-0.220208\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−15.0000			−0.997785
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	−0.125435	−	0.992102i	$-0.540033\pi$
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	0.921903	−	0.387421i	$-0.126634\pi$
$228$		0			0
$229$	12.5000	+	21.6506i	0.826023	+	1.43071i	0.901135	+	0.433539i	$0.142735\pi$
$229$	12.5000	+	21.6506i	0.826023	+	1.43071i	−0.0751115	+	0.997175i	$0.523931\pi$
$230$	−9.00000	−	15.5885i	−0.593442	−	1.02787i
$231$		0			0
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	21.0000			1.37576			0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000			1.37576			0.687878	+	0.725826i	$0.258542\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$		0			0
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	−0.995223	−	0.0976302i	$-0.968874\pi$
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	0.413061	−	0.910703i	$-0.364460\pi$
$240$		0			0
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	−0.378963	−	0.925412i	$-0.623719\pi$
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	0.990912	−	0.134515i	$-0.0429475\pi$
$242$	25.0000			1.60706
$243$		0			0
$244$	11.0000			0.704203
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$		0			0
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$	5.00000	+	8.66025i	0.317500	+	0.549927i
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−6.00000			−0.378717			−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$		0			0
$253$	36.0000			2.26330
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	−0.888110	−	0.459631i	$-0.847982\pi$
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	0.0460033	−	0.998941i	$-0.485352\pi$
$258$		0			0
$259$	3.50000	−	6.06218i	0.217479	−	0.376685i
$260$	3.00000			0.186052
$261$		0			0
$262$		0			0
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$		0			0
$265$	−9.00000	−	15.5885i	−0.552866	−	0.957591i
$266$	−1.00000	−	1.73205i	−0.0613139	−	0.106199i
$267$		0			0
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	−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
$271$	14.0000			0.850439			0.425220	−	0.905090i	$-0.360197\pi$
$271$	14.0000			0.850439			0.425220	+	0.905090i	$0.360197\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$		0			0
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$	12.0000	+	20.7846i	0.723627	+	1.25336i
$276$		0			0
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	14.0000			0.839664
$279$		0			0
$280$	−3.00000			−0.179284
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	0.361895	+	0.932219i	$0.382130\pi$
$281$	−10.5000	+	18.1865i	−0.626377	+	1.08492i	−0.988273	+	0.152699i	$0.951204\pi$
$282$		0			0
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	0.999608	−	0.0280052i	$-0.00891551\pi$
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	−0.524057	+	0.851683i	$0.675582\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	−3.00000	+	5.19615i	−0.177394	+	0.307255i
$287$	6.00000			0.354169
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−13.5000	+	23.3827i	−0.792747	+	1.37308i
$291$		0			0
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	−10.5000	−	18.1865i	−0.613417	−	1.06247i	−0.990660	−	0.136355i	$-0.956461\pi$
$293$	−10.5000	−	18.1865i	−0.613417	−	1.06247i	0.377244	−	0.926114i	$-0.376872\pi$
$294$		0			0
$295$	−9.00000	+	15.5885i	−0.524000	+	0.907595i
$296$	−7.00000			−0.406867
$297$		0			0
$298$	3.00000			0.173785
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$	2.00000	+	3.46410i	0.115278	+	0.199667i
$302$	−1.00000	−	1.73205i	−0.0575435	−	0.0996683i
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	−33.0000			−1.88957
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	3.00000	−	5.19615i	0.170941	−	0.296078i
$309$		0			0
$310$	−15.0000	−	25.9808i	−0.851943	−	1.47561i
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$		0			0
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	23.0000			1.29797
$315$		0			0
$316$	2.00000			0.112509
$317$	10.5000	−	18.1865i	0.589739	−	1.02146i	−0.404528	−	0.914526i	$-0.632564\pi$
$317$	10.5000	−	18.1865i	0.589739	−	1.02146i	0.994266	−	0.106932i	$-0.0341026\pi$
$318$		0			0
$319$	−27.0000	−	46.7654i	−1.51171	−	2.61836i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$		0			0
$322$	3.00000	−	5.19615i	0.167183	−	0.289570i
$323$	6.00000			0.333849
$324$		0			0
$325$	−4.00000			−0.221880
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	6.00000			0.329293
$333$		0			0
$334$	6.00000			0.328305
$335$	3.00000	−	5.19615i	0.163908	−	0.283896i
$336$		0			0
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	0.609936	−	0.792451i	$-0.291195\pi$
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	−0.991250	+	0.131995i	$0.957862\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$		0			0
$340$	4.50000	−	7.79423i	0.244047	−	0.422701i
$341$	60.0000			3.24918
$342$		0			0
$343$	1.00000			0.0539949
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$		0			0
$346$	−4.50000	−	7.79423i	−0.241921	−	0.419020i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−6.00000			−0.319801
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$	18.0000	+	31.1769i	0.955341	+	1.65470i
$356$	−1.50000	−	2.59808i	−0.0794998	−	0.137698i
$357$		0			0
$358$	−3.00000	+	5.19615i	−0.158555	+	0.274625i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$		0			0
$364$	0.500000	+	0.866025i	0.0262071	+	0.0453921i
$365$	−10.5000	−	18.1865i	−0.549595	−	0.951927i
$366$		0			0
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	21.0000			1.09174
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	0.996610	+	0.0822766i	$0.0262191\pi$
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	−0.427051	+	0.904227i	$0.640448\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	9.00000			0.463524
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$		0			0
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$383$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$	−9.00000	+	15.5885i	−0.458682	+	0.794461i
$386$	11.0000			0.559885
$387$		0			0
$388$	14.0000			0.710742
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$		0			0
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$		0			0
$394$	4.50000	−	7.79423i	0.226707	−	0.392668i
$395$	−6.00000			−0.301893
$396$		0			0
$397$	−13.0000			−0.652451			−0.326226	−	0.945292i	$-0.605777\pi$
$397$	−13.0000			−0.652451			−0.326226	+	0.945292i	$0.605777\pi$
$398$	5.00000	−	8.66025i	0.250627	−	0.434099i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$		0			0
$403$	−5.00000	+	8.66025i	−0.249068	+	0.431398i
$404$	−18.0000			−0.895533
$405$		0			0
$406$	−9.00000			−0.446663
$407$	−21.0000	+	36.3731i	−1.04093	+	1.80295i
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$	9.00000	+	15.5885i	0.444478	+	0.769859i
$411$		0			0
$412$	8.00000	−	13.8564i	0.394132	−	0.682656i
$413$	−6.00000			−0.295241
$414$		0			0
$415$	−18.0000			−0.883585
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	−8.50000	+	14.7224i	−0.414265	+	0.717527i	−0.995351	−	0.0963145i	$-0.969295\pi$
$421$	−8.50000	+	14.7224i	−0.414265	+	0.717527i	0.581086	+	0.813842i	$0.302628\pi$
$422$	2.00000			0.0973585
$423$		0			0
$424$	−6.00000			−0.291386
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	−5.50000	−	9.52628i	−0.266164	−	0.461009i
$428$		0			0
$429$		0			0
$430$	−6.00000	+	10.3923i	−0.289346	+	0.501161i
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$		0			0
$433$	17.0000			0.816968			0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000			0.816968			0.408484	+	0.912766i	$0.366058\pi$
$434$	5.00000	−	8.66025i	0.240008	−	0.415705i
$435$		0			0
$436$	−2.50000	−	4.33013i	−0.119728	−	0.207375i
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$	18.0000			0.858116
$441$		0			0
$442$	−3.00000			−0.142695
$443$	15.0000	−	25.9808i	0.712672	−	1.23438i	−0.251179	−	0.967941i	$-0.580818\pi$
$443$	15.0000	−	25.9808i	0.712672	−	1.23438i	0.963851	−	0.266443i	$-0.0858483\pi$
$444$		0			0
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$	14.0000	+	24.2487i	0.662919	+	1.14821i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−36.0000			−1.69517
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$		0			0
$454$	12.0000	+	20.7846i	0.563188	+	0.975470i
$455$	−1.50000	−	2.59808i	−0.0703211	−	0.121800i
$456$		0			0
$457$	−11.5000	+	19.9186i	−0.537947	+	0.931752i	0.461067	+	0.887365i	$0.347467\pi$
$457$	−11.5000	+	19.9186i	−0.537947	+	0.931752i	−0.999014	+	0.0443868i	$0.985867\pi$
$458$	−25.0000			−1.16817
$459$		0			0
$460$	18.0000			0.839254
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	−0.927392	−	0.374091i	$-0.877955\pi$
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	0.787668	+	0.616100i	$0.211288\pi$
$462$		0			0
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	0.999916	+	0.0129968i	$0.00413714\pi$
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	−0.488702	+	0.872451i	$0.662530\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−10.5000	+	18.1865i	−0.486403	+	0.842475i
$467$	−30.0000			−1.38823			−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000			−1.38823			−0.694117	+	0.719862i	$0.744205\pi$
$468$		0			0
$469$	2.00000			0.0923514
$470$	9.00000	−	15.5885i	0.415139	−	0.719042i
$471$		0			0
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−12.0000	−	20.7846i	−0.551761	−	0.955677i
$474$		0			0
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$	3.00000			0.137505
$477$		0			0
$478$	18.0000			0.823301
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	−3.50000	−	6.06218i	−0.159586	−	0.276412i
$482$	9.50000	+	16.4545i	0.432713	+	0.749481i
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	−42.0000			−1.90712
$486$		0			0
$487$	−34.0000			−1.54069			−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000			−1.54069			−0.770344	+	0.637629i	$0.779915\pi$
$488$	−5.50000	+	9.52628i	−0.248973	+	0.431234i
$489$		0			0
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$		0			0
$493$	13.5000	−	23.3827i	0.608009	−	1.05310i
$494$	−2.00000			−0.0899843
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	0.665725	−	0.746197i	$-0.268122\pi$
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	−0.979088	+	0.203436i	$0.934789\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$		0			0
$502$	3.00000	−	5.19615i	0.133897	−	0.231916i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	54.0000			2.40297
$506$	−18.0000	+	31.1769i	−0.800198	+	1.38598i
$507$		0			0
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	3.50000	−	6.06218i	0.154831	−	0.268175i
$512$	1.00000			0.0441942
$513$		0			0
$514$	27.0000			1.19092
$515$	−24.0000	+	41.5692i	−1.05757	+	1.83176i
$516$		0			0
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$	3.50000	+	6.06218i	0.153781	+	0.266357i
$519$		0			0
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	44.0000			1.92399			0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000			1.92399			0.961993	+	0.273075i	$0.0880406\pi$
$524$		0			0
$525$		0			0
$526$	−3.00000	−	5.19615i	−0.130806	−	0.226563i
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	18.0000			0.781870
$531$		0			0
$532$	2.00000			0.0867110
$533$	3.00000	−	5.19615i	0.129944	−	0.225070i
$534$		0			0
$535$		0			0
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	1.50000	−	2.59808i	0.0646696	−	0.112011i
$539$	−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	$0.875398\pi$
$542$	−7.00000	+	12.1244i	−0.300676	+	0.520786i
$543$		0			0
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	7.50000	+	12.9904i	0.321265	+	0.556447i
$546$		0			0
$547$	−1.00000	+	1.73205i	−0.0427569	+	0.0740571i	−0.886612	−	0.462514i	$-0.846947\pi$
$547$	−1.00000	+	1.73205i	−0.0427569	+	0.0740571i	0.843855	+	0.536571i	$0.180281\pi$
$548$	−3.00000			−0.128154
$549$		0			0
$550$	−24.0000			−1.02336
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$		0			0
$553$	−1.00000	−	1.73205i	−0.0425243	−	0.0736543i
$554$	−7.00000	−	12.1244i	−0.297402	−	0.515115i
$555$		0			0
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	−9.00000			−0.381342			−0.190671	−	0.981654i	$-0.561066\pi$
$557$	−9.00000			−0.381342			−0.190671	+	0.981654i	$0.561066\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	1.50000	−	2.59808i	0.0633866	−	0.109789i
$561$		0			0
$562$	−10.5000	−	18.1865i	−0.442916	−	0.767153i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$		0			0
$565$	−22.5000	+	38.9711i	−0.946582	+	1.63953i
$566$	−16.0000			−0.672530
$567$		0			0
$568$	12.0000			0.503509
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	−0.832870	−	0.553469i	$-0.813304\pi$
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	0.895753	+	0.444552i	$0.146637\pi$
$570$		0			0
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	0.998978	−	0.0452101i	$-0.0143957\pi$
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	−0.538642	+	0.842535i	$0.681062\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$		0			0
$574$	−3.00000	+	5.19615i	−0.125218	+	0.216883i
$575$	−24.0000			−1.00087
$576$		0			0
$577$	17.0000			0.707719			0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000			0.707719			0.353860	+	0.935299i	$0.384869\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	−13.5000	−	23.3827i	−0.560557	−	0.970913i
$581$	−3.00000	−	5.19615i	−0.124461	−	0.215573i
$582$		0			0
$583$	−18.0000	+	31.1769i	−0.745484	+	1.29122i
$584$	−7.00000			−0.289662
$585$		0			0
$586$	21.0000			0.867502
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	−0.989792	−	0.142520i	$-0.954479\pi$
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	0.618322	+	0.785925i	$0.287813\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$	−9.00000	−	15.5885i	−0.370524	−	0.641767i
$591$		0			0
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	3.00000			0.123195			0.0615976	−	0.998101i	$-0.480380\pi$
$593$	3.00000			0.123195			0.0615976	+	0.998101i	$0.480380\pi$
$594$		0			0
$595$	−9.00000			−0.368964
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$		0			0
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	3.50000	−	6.06218i	0.142768	−	0.247281i	−0.785770	−	0.618519i	$-0.787733\pi$
$601$	3.50000	−	6.06218i	0.142768	−	0.247281i	0.928538	+	0.371237i	$0.121066\pi$
$602$	−4.00000			−0.163028
$603$		0			0
$604$	2.00000			0.0813788
$605$	37.5000	−	64.9519i	1.52459	−	2.64067i
$606$		0			0
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$		0			0
$610$	16.5000	−	28.5788i	0.668065	−	1.15712i
$611$	−6.00000			−0.242734
$612$		0			0
$613$	14.0000			0.565455			0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000			0.565455			0.282727	+	0.959200i	$0.408761\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$		0			0
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	0.976575	−	0.215177i	$-0.0690329\pi$
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	−0.674636	+	0.738150i	$0.735700\pi$
$618$		0			0
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$	30.0000			1.20483
$621$		0			0
$622$	−30.0000			−1.20289
$623$	−1.50000	+	2.59808i	−0.0600962	+	0.104090i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	9.50000	+	16.4545i	0.379696	+	0.657653i
$627$		0			0
$628$	−11.5000	+	19.9186i	−0.458900	+	0.794838i
$629$	−21.0000			−0.837325
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−1.00000	+	1.73205i	−0.0397779	+	0.0688973i
$633$		0			0
$634$	10.5000	+	18.1865i	0.417008	+	0.722280i
$635$	−6.00000	−	10.3923i	−0.238103	−	0.412406i
$636$		0			0
$637$	0.500000	−	0.866025i	0.0198107	−	0.0343132i
$638$	54.0000			2.13788
$639$		0			0
$640$	−3.00000			−0.118585
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	11.0000	+	19.0526i	0.433798	+	0.751360i	0.997197	−	0.0748254i	$-0.0238399\pi$
$643$	11.0000	+	19.0526i	0.433798	+	0.751360i	−0.563399	+	0.826185i	$0.690507\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	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
$649$	36.0000			1.41312
$650$	2.00000	−	3.46410i	0.0784465	−	0.135873i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$		0			0
$656$	6.00000			0.234261
$657$		0			0
$658$	6.00000			0.233904
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	0.964301	−	0.264807i	$-0.0853084\pi$
$661$	6.50000	+	11.2583i	0.252821	+	0.437898i	−0.711481	+	0.702706i	$0.751975\pi$
$662$	14.0000	+	24.2487i	0.544125	+	0.942453i
$663$		0			0
$664$	−3.00000	+	5.19615i	−0.116423	+	0.201650i
$665$	−6.00000			−0.232670
$666$		0			0
$667$	54.0000			2.09089
$668$	−3.00000	+	5.19615i	−0.116073	+	0.201045i
$669$		0			0
$670$	3.00000	+	5.19615i	0.115900	+	0.200745i
$671$	33.0000	+	57.1577i	1.27395	+	2.20655i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	14.0000			0.539260
$675$		0			0
$676$	−12.0000			−0.461538
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$		0			0
$679$	−7.00000	−	12.1244i	−0.268635	−	0.465290i
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$		0			0
$682$	−30.0000	+	51.9615i	−1.14876	+	1.98971i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	9.00000			0.343872
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−3.00000	−	5.19615i	−0.114291	−	0.197958i
$690$		0			0
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	−0.825473	−	0.564441i	$-0.809092\pi$
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	0.901557	+	0.432660i	$0.142425\pi$
$692$	9.00000			0.342129
$693$		0			0
$694$	−12.0000			−0.455514
$695$	21.0000	−	36.3731i	0.796575	−	1.37971i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$		0			0
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	3.00000	−	5.19615i	0.113067	−	0.195837i
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	9.00000	+	15.5885i	0.338480	+	0.586264i
$708$		0			0
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$	−36.0000			−1.35106
$711$		0			0
$712$	3.00000			0.112430
$713$	−30.0000	+	51.9615i	−1.12351	+	1.94597i
$714$		0			0
$715$	9.00000	+	15.5885i	0.336581	+	0.582975i
$716$	−3.00000	−	5.19615i	−0.112115	−	0.194189i
$717$		0			0
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$	−16.0000			−0.595871
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$		0			0
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	−1.00000			−0.0370625
$729$		0			0
$730$	21.0000			0.777245
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$		0			0
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	0.519575	−	0.854425i	$-0.326090\pi$
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	−0.999741	+	0.0227529i	$0.992757\pi$
$734$	5.00000	+	8.66025i	0.184553	+	0.319656i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	−12.0000			−0.442026
$738$		0			0
$739$	50.0000			1.83928			0.919640	−	0.392763i	$-0.128481\pi$
$739$	50.0000			1.83928			0.919640	+	0.392763i	$0.128481\pi$
$740$	−10.5000	+	18.1865i	−0.385988	+	0.668550i
$741$		0			0
$742$	3.00000	+	5.19615i	0.110133	+	0.190757i
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	0.557470	−	0.830197i	$-0.311772\pi$
$743$	−12.0000	−	20.7846i	−0.440237	−	0.762513i	−0.997707	+	0.0676840i	$0.978439\pi$
$744$		0			0
$745$	4.50000	−	7.79423i	0.164867	−	0.285558i
$746$	−22.0000			−0.805477
$747$		0			0
$748$	−18.0000			−0.658145
$749$		0			0
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$		0			0
$754$	−4.50000	+	7.79423i	−0.163880	+	0.283849i
$755$	−6.00000			−0.218362
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−1.00000	+	1.73205i	−0.0363216	+	0.0629109i
$759$		0			0
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	0.993098	+	0.117289i	$0.0374205\pi$
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	−0.394973	+	0.918693i	$0.629246\pi$
$762$		0			0
$763$	−2.50000	+	4.33013i	−0.0905061	+	0.156761i
$764$	6.00000			0.217072
$765$		0			0
$766$		0			0
$767$	−3.00000	+	5.19615i	−0.108324	+	0.187622i
$768$		0			0
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$	−9.00000	−	15.5885i	−0.324337	−	0.561769i
$771$		0			0
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	9.00000			0.323708			0.161854	−	0.986815i	$-0.448253\pi$
$773$	9.00000			0.323708			0.161854	+	0.986815i	$0.448253\pi$
$774$		0			0
$775$	−40.0000			−1.43684
$776$	−7.00000	+	12.1244i	−0.251285	+	0.435239i
$777$		0			0
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$	36.0000	−	62.3538i	1.28818	−	2.23120i
$782$	−18.0000			−0.643679
$783$		0			0
$784$	1.00000			0.0357143
$785$	34.5000	−	59.7558i	1.23136	−	2.13277i
$786$		0			0
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	0.785885	−	0.618373i	$-0.212208\pi$
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	−0.928469	+	0.371409i	$0.878875\pi$
$788$	4.50000	+	7.79423i	0.160306	+	0.277658i
$789$		0			0
$790$	3.00000	−	5.19615i	0.106735	−	0.184871i
$791$	−15.0000			−0.533339
$792$		0			0
$793$	−11.0000			−0.390621
$794$	6.50000	−	11.2583i	0.230676	−	0.399543i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−4.50000	−	7.79423i	−0.159398	−	0.276086i	0.775254	−	0.631650i	$-0.217622\pi$
$797$	−4.50000	−	7.79423i	−0.159398	−	0.276086i	−0.934652	+	0.355564i	$0.884289\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$	4.00000			0.141421
$801$		0			0
$802$	21.0000			0.741536
$803$	−21.0000	+	36.3731i	−0.741074	+	1.28358i
$804$		0			0
$805$	−9.00000	−	15.5885i	−0.317208	−	0.549421i
$806$	−5.00000	−	8.66025i	−0.176117	−	0.305044i
$807$		0			0
$808$	9.00000	−	15.5885i	0.316619	−	0.548400i
$809$	−15.0000			−0.527372			−0.263686	−	0.964609i	$-0.584938\pi$
$809$	−15.0000			−0.527372			−0.263686	+	0.964609i	$0.584938\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	4.50000	−	7.79423i	0.157919	−	0.273524i
$813$		0			0
$814$	−21.0000	−	36.3731i	−0.736050	−	1.27488i
$815$	−24.0000	−	41.5692i	−0.840683	−	1.45611i
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$	5.00000			0.174821
$819$		0			0
$820$	−18.0000			−0.628587
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	−0.143591	−	0.989637i	$-0.545865\pi$
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	0.928846	−	0.370465i	$-0.120802\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	8.00000	+	13.8564i	0.278693	+	0.482711i
$825$		0			0
$826$	3.00000	−	5.19615i	0.104383	−	0.180797i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$	9.00000	−	15.5885i	0.312395	−	0.541083i
$831$		0			0
$832$	0.500000	+	0.866025i	0.0173344	+	0.0300240i
$833$	−1.50000	−	2.59808i	−0.0519719	−	0.0900180i
$834$		0			0
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$	−12.0000			−0.415029
$837$		0			0
$838$	12.0000			0.414533
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	0.0705865	+	0.997506i	$0.477513\pi$
$839$	−24.0000	+	41.5692i	−0.828572	+	1.43513i	−0.899158	+	0.437623i	$0.855820\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	−8.50000	−	14.7224i	−0.292929	−	0.507369i
$843$		0			0
$844$	−1.00000	+	1.73205i	−0.0344214	+	0.0596196i
$845$	36.0000			1.23844
$846$		0			0
$847$	25.0000			0.859010
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$	−21.0000	−	36.3731i	−0.719871	−	1.24685i
$852$		0			0
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$	11.0000			0.376412
$855$		0			0
$856$		0			0
$857$	4.50000	−	7.79423i	0.153717	−	0.266246i	−0.778874	−	0.627180i	$-0.784209\pi$
$857$	4.50000	−	7.79423i	0.153717	−	0.266246i	0.932591	+	0.360935i	$0.117542\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	−6.00000	−	10.3923i	−0.204598	−	0.354375i
$861$		0			0
$862$	18.0000	−	31.1769i	0.613082	−	1.06189i
$863$	−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
$865$	−27.0000			−0.918028
$866$	−8.50000	+	14.7224i	−0.288842	+	0.500289i
$867$		0			0
$868$	5.00000	+	8.66025i	0.169711	+	0.293948i
$869$	6.00000	+	10.3923i	0.203536	+	0.352535i
$870$		0			0
$871$	1.00000	−	1.73205i	0.0338837	−	0.0586883i
$872$	5.00000			0.169321
$873$		0			0
$874$	−12.0000			−0.405906
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	−20.5000	−	35.5070i	−0.692236	−	1.19899i	−0.971104	−	0.238658i	$-0.923292\pi$
$877$	−20.5000	−	35.5070i	−0.692236	−	1.19899i	0.278868	−	0.960329i	$-0.410041\pi$
$878$	14.0000	+	24.2487i	0.472477	+	0.818354i
$879$		0			0
$880$	−9.00000	+	15.5885i	−0.303390	+	0.525487i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	1.50000	−	2.59808i	0.0504505	−	0.0873828i
$885$		0			0
$886$	15.0000	+	25.9808i	0.503935	+	0.872841i
$887$	−21.0000	−	36.3731i	−0.705111	−	1.22129i	−0.966651	−	0.256096i	$-0.917564\pi$
$887$	−21.0000	−	36.3731i	−0.705111	−	1.22129i	0.261540	−	0.965193i	$-0.415770\pi$
$888$		0			0
$889$	2.00000	−	3.46410i	0.0670778	−	0.116182i
$890$	−9.00000			−0.301681
$891$		0			0
$892$	−28.0000			−0.937509
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$	9.00000	+	15.5885i	0.300837	+	0.521065i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	90.0000			3.00167
$900$		0			0
$901$	−18.0000			−0.599667
$902$	18.0000	−	31.1769i	0.599334	−	1.03808i
$903$		0			0
$904$	7.50000	+	12.9904i	0.249446	+	0.432054i
$905$	3.00000	+	5.19615i	0.0997234	+	0.172726i
$906$		0			0
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	−0.982913	−	0.184073i	$-0.941072\pi$
$907$	−10.0000	+	17.3205i	−0.332045	+	0.575118i	0.650868	+	0.759191i	$0.274405\pi$
$908$	−24.0000			−0.796468
$909$		0			0
$910$	3.00000			0.0994490
$911$	18.0000	−	31.1769i	0.596367	−	1.03294i	−0.396986	−	0.917825i	$-0.629944\pi$
$911$	18.0000	−	31.1769i	0.596367	−	1.03294i	0.993352	−	0.115113i	$-0.0367229\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−11.5000	−	19.9186i	−0.380386	−	0.658848i
$915$		0			0
$916$	12.5000	−	21.6506i	0.413012	−	0.715357i
$917$		0			0
$918$		0			0
$919$	2.00000			0.0659739			0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000			0.0659739			0.0329870	+	0.999456i	$0.489498\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$		0			0
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	6.00000	+	10.3923i	0.197492	+	0.342067i
$924$		0			0
$925$	14.0000	−	24.2487i	0.460317	−	0.797293i
$926$	−22.0000			−0.722965
$927$		0			0
$928$	−9.00000			−0.295439
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	−0.640768	−	0.767735i	$-0.721384\pi$
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	0.985262	+	0.171054i	$0.0547172\pi$
$930$		0			0
$931$	−1.00000	−	1.73205i	−0.0327737	−	0.0567657i
$932$	−10.5000	−	18.1865i	−0.343939	−	0.595720i
$933$		0			0
$934$	15.0000	−	25.9808i	0.490815	−	0.850117i
$935$	54.0000			1.76599
$936$		0			0
$937$	−7.00000			−0.228680			−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000			−0.228680			−0.114340	+	0.993442i	$0.536475\pi$
$938$	−1.00000	+	1.73205i	−0.0326512	+	0.0565535i
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	0.889439	−	0.457054i	$-0.151096\pi$
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	−0.840540	+	0.541749i	$0.817762\pi$
$942$		0			0
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	24.0000			0.780307
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	0.409964	+	0.912102i	$0.365541\pi$
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	−0.994885	+	0.101012i	$0.967792\pi$
$948$		0			0
$949$	−3.50000	−	6.06218i	−0.113615	−	0.196787i
$950$	−4.00000	−	6.92820i	−0.129777	−	0.224781i
$951$		0			0
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	−3.00000			−0.0971795			−0.0485898	−	0.998819i	$-0.515473\pi$
$953$	−3.00000			−0.0971795			−0.0485898	+	0.998819i	$0.515473\pi$
$954$		0			0
$955$	−18.0000			−0.582466
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$		0			0
$958$	3.00000	+	5.19615i	0.0969256	+	0.167880i
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	7.00000			0.225689
$963$		0			0
$964$	−19.0000			−0.611949
$965$	16.5000	−	28.5788i	0.531154	−	0.919985i
$966$		0			0
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	0.849499	−	0.527591i	$-0.176905\pi$
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	−0.881656	+	0.471892i	$0.843571\pi$
$968$	−12.5000	−	21.6506i	−0.401765	−	0.695878i
$969$		0			0
$970$	21.0000	−	36.3731i	0.674269	−	1.16787i
$971$	6.00000			0.192549			0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000			0.192549			0.0962746	+	0.995355i	$0.469307\pi$
$972$		0			0
$973$	14.0000			0.448819
$974$	17.0000	−	29.4449i	0.544715	−	0.943474i
$975$		0			0
$976$	−5.50000	−	9.52628i	−0.176051	−	0.304929i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$	−3.00000			−0.0958315
$981$		0			0
$982$	−12.0000			−0.382935
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	−13.5000	−	23.3827i	−0.430146	−	0.745034i
$986$	13.5000	+	23.3827i	0.429928	+	0.744656i
$987$		0			0
$988$	1.00000	−	1.73205i	0.0318142	−	0.0551039i
$989$	24.0000			0.763156
$990$		0			0
$991$	−10.0000			−0.317660			−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000			−0.317660			−0.158830	+	0.987306i	$0.550772\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$		0			0
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$	−15.0000	−	25.9808i	−0.475532	−	0.823646i
$996$		0			0
$997$	18.5000	−	32.0429i	0.585901	−	1.01481i	−0.408862	−	0.912596i	$-0.634074\pi$
$997$	18.5000	−	32.0429i	0.585901	−	1.01481i	0.994762	−	0.102214i	$-0.0325925\pi$
$998$	14.0000			0.443162
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.h.379.1		2
3.2	odd	2		1134.2.f.i.379.1		2
9.2	odd	6		1134.2.a.d.1.1	✓	1
9.4	even	3	inner	1134.2.f.h.757.1		2
9.5	odd	6		1134.2.f.i.757.1		2
9.7	even	3		1134.2.a.e.1.1	yes	1
36.7	odd	6		9072.2.a.b.1.1		1
36.11	even	6		9072.2.a.v.1.1		1
63.20	even	6		7938.2.a.d.1.1		1
63.34	odd	6		7938.2.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.a.d.1.1	✓	1	9.2	odd	6
1134.2.a.e.1.1	yes	1	9.7	even	3
1134.2.f.h.379.1		2	1.1	even	1	trivial
1134.2.f.h.757.1		2	9.4	even	3	inner
1134.2.f.i.379.1		2	3.2	odd	2
1134.2.f.i.757.1		2	9.5	odd	6
7938.2.a.d.1.1		1	63.20	even	6
7938.2.a.bc.1.1		1	63.34	odd	6
9072.2.a.b.1.1		1	36.7	odd	6
9072.2.a.v.1.1		1	36.11	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{10} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} +2.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(3.00000 + 5.19615i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} -1.00000 q^{26} +1.00000 q^{28} +(4.50000 - 7.79423i) q^{29} +(5.00000 + 8.66025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{35} -7.00000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} -6.00000 q^{44} -6.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(0.500000 - 0.866025i) q^{52} -6.00000 q^{53} +18.0000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(4.50000 + 7.79423i) q^{58} +(3.00000 + 5.19615i) q^{59} +(-5.50000 + 9.52628i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(1.50000 - 2.59808i) q^{70} +12.0000 q^{71} -7.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(3.00000 + 5.19615i) q^{77} +(-1.00000 + 1.73205i) q^{79} -3.00000 q^{80} +6.00000 q^{82} +(-3.00000 + 5.19615i) q^{83} +(4.50000 + 7.79423i) q^{85} +(2.00000 + 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{88} +3.00000 q^{89} -1.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 2 q^{8} - 6 q^{10} + 6 q^{11} + q^{13} - q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} - 4 q^{25} - 2 q^{26} + 2 q^{28} + 9 q^{29}+ \cdots + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 3 * q^5 - q^7 + 2 * q^8 - 6 * q^10 + 6 * q^11 + q^13 - q^14 - q^16 + 6 * q^17 + 4 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 - 4 * q^25 - 2 * q^26 + 2 * q^28 + 9 * q^29 + 10 * q^31 - q^32 - 3 * q^34 - 6 * q^35 - 14 * q^37 - 2 * q^38 + 3 * q^40 - 6 * q^41 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 6 * q^47 - q^49 - 4 * q^50 + q^52 - 12 * q^53 + 36 * q^55 - q^56 + 9 * q^58 + 6 * q^59 - 11 * q^61 - 20 * q^62 + 2 * q^64 - 3 * q^65 - 2 * q^67 - 3 * q^68 + 3 * q^70 + 24 * q^71 - 14 * q^73 + 7 * q^74 - 2 * q^76 + 6 * q^77 - 2 * q^79 - 6 * q^80 + 12 * q^82 - 6 * q^83 + 9 * q^85 + 4 * q^86 + 6 * q^88 + 6 * q^89 - 2 * q^91 + 6 * q^92 - 6 * q^94 + 6 * q^95 - 14 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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