LMFDB - Embedded newform 1134.2.g.i.163.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(163,1134)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1134.163"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1134, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,-2,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.i.487.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(2.12132 + 3.67423i) q^{11} -2.24264 q^{13} +(1.00000 + 2.44949i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.12132 - 1.94218i) q^{19} -4.24264 q^{22} +(0.621320 - 1.07616i) q^{23} +(2.50000 + 4.33013i) q^{25} +(1.12132 - 1.94218i) q^{26} +(-2.62132 - 0.358719i) q^{28} +4.24264 q^{29} +(-4.62132 - 8.00436i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{37} +(1.12132 + 1.94218i) q^{38} +11.4853 q^{41} +10.4853 q^{43} +(2.12132 - 3.67423i) q^{44} +(0.621320 + 1.07616i) q^{46} +(-2.37868 + 4.11999i) q^{47} +(-1.74264 - 6.77962i) q^{49} -5.00000 q^{50} +(1.12132 + 1.94218i) q^{52} +(2.12132 + 3.67423i) q^{53} +(1.62132 - 2.09077i) q^{56} +(-2.12132 + 3.67423i) q^{58} +(1.12132 - 1.94218i) q^{61} +9.24264 q^{62} +1.00000 q^{64} +(-0.121320 - 0.210133i) q^{67} +1.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +(2.00000 + 3.46410i) q^{74} -2.24264 q^{76} +(11.1213 + 1.52192i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-5.74264 + 9.94655i) q^{82} +16.2426 q^{83} +(-5.24264 + 9.08052i) q^{86} +(2.12132 + 3.67423i) q^{88} +(-5.74264 + 9.94655i) q^{89} +(-3.63604 + 4.68885i) q^{91} -1.24264 q^{92} +(-2.37868 - 4.11999i) q^{94} +4.48528 q^{97} +(6.74264 + 1.88064i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 8 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{19} - 6 q^{23} + 10 q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} - 2 q^{32} + 8 q^{37} - 4 q^{38} + 12 q^{41} + 8 q^{43} - 6 q^{46}+ \cdots + 10 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 8 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^19 - 6 * q^23 + 10 * q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 - 2 * q^32 + 8 * q^37 - 4 * q^38 + 12 * q^41 + 8 * q^43 - 6 * q^46 - 18 * q^47 + 10 * q^49 - 20 * q^50 - 4 * q^52 - 2 * q^56 - 4 * q^61 + 20 * q^62 + 4 * q^64 + 8 * q^67 - 12 * q^71 + 14 * q^73 + 8 * q^74 + 8 * q^76 + 36 * q^77 - 10 * q^79 - 6 * q^82 + 48 * q^83 - 4 * q^86 - 6 * q^89 - 40 * q^91 + 12 * q^92 - 18 * q^94 - 16 * q^97 + 10 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	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
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	0.985520	+	0.169559i	$0.0542342\pi$
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	−0.345918	+	0.938265i	$0.612432\pi$
$12$		0			0
$13$	−2.24264			−0.621997			−0.310998	−	0.950410i	$-0.600663\pi$
$13$	−2.24264			−0.621997			−0.310998	+	0.950410i	$0.600663\pi$
$14$	1.00000	+	2.44949i	0.267261	+	0.654654i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	1.12132	−	1.94218i	0.257249	−	0.445568i	−0.708255	−	0.705956i	$-0.750517\pi$
$19$	1.12132	−	1.94218i	0.257249	−	0.445568i	0.965504	+	0.260389i	$0.0838508\pi$
$20$		0			0
$21$		0			0
$22$	−4.24264			−0.904534
$23$	0.621320	−	1.07616i	0.129554	−	0.224395i	−0.793950	−	0.607983i	$-0.791979\pi$
$23$	0.621320	−	1.07616i	0.129554	−	0.224395i	0.923504	+	0.383589i	$0.125312\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	1.12132	−	1.94218i	0.219909	−	0.380894i
$27$		0			0
$28$	−2.62132	−	0.358719i	−0.495383	−	0.0677916i
$29$	4.24264			0.787839			0.393919	−	0.919145i	$-0.371119\pi$
$29$	4.24264			0.787839			0.393919	+	0.919145i	$0.371119\pi$
$30$		0			0
$31$	−4.62132	−	8.00436i	−0.830014	−	1.43763i	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−4.62132	−	8.00436i	−0.830014	−	1.43763i	0.0680129	−	0.997684i	$-0.478334\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	1.12132	+	1.94218i	0.181902	+	0.315064i
$39$		0			0
$40$		0			0
$41$	11.4853			1.79370			0.896850	−	0.442335i	$-0.145850\pi$
$41$	11.4853			1.79370			0.896850	+	0.442335i	$0.145850\pi$
$42$		0			0
$43$	10.4853			1.59899			0.799495	−	0.600672i	$-0.205100\pi$
$43$	10.4853			1.59899			0.799495	+	0.600672i	$0.205100\pi$
$44$	2.12132	−	3.67423i	0.319801	−	0.553912i
$45$		0			0
$46$	0.621320	+	1.07616i	0.0916087	+	0.158671i
$47$	−2.37868	+	4.11999i	−0.346966	+	0.600963i	−0.985709	−	0.168457i	$-0.946121\pi$
$47$	−2.37868	+	4.11999i	−0.346966	+	0.600963i	0.638743	+	0.769420i	$0.279455\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	−5.00000			−0.707107
$51$		0			0
$52$	1.12132	+	1.94218i	0.155499	+	0.269332i
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	0.974138	−	0.225955i	$-0.0725503\pi$
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	−0.682752	+	0.730650i	$0.739217\pi$
$54$		0			0
$55$		0			0
$56$	1.62132	−	2.09077i	0.216658	−	0.279391i
$57$		0			0
$58$	−2.12132	+	3.67423i	−0.278543	+	0.482451i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	1.12132	−	1.94218i	0.143570	−	0.248671i	−0.785268	−	0.619156i	$-0.787475\pi$
$61$	1.12132	−	1.94218i	0.143570	−	0.248671i	0.928839	+	0.370484i	$0.120808\pi$
$62$	9.24264			1.17382
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−0.121320	−	0.210133i	−0.0148216	−	0.0256718i	0.858519	−	0.512781i	$-0.171385\pi$
$67$	−0.121320	−	0.210133i	−0.0148216	−	0.0256718i	−0.873341	+	0.487109i	$0.838051\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.24264			0.147474			0.0737372	−	0.997278i	$-0.476507\pi$
$71$	1.24264			0.147474			0.0737372	+	0.997278i	$0.476507\pi$
$72$		0			0
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$		0			0
$76$	−2.24264			−0.257249
$77$	11.1213	+	1.52192i	1.26739	+	0.173439i
$78$		0			0
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	−0.886541	−	0.462649i	$-0.846899\pi$
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	0.843937	+	0.536443i	$0.180232\pi$
$80$		0			0
$81$		0			0
$82$	−5.74264	+	9.94655i	−0.634169	+	1.09841i
$83$	16.2426			1.78286			0.891431	−	0.453157i	$-0.149702\pi$
$83$	16.2426			1.78286			0.891431	+	0.453157i	$0.149702\pi$
$84$		0			0
$85$		0			0
$86$	−5.24264	+	9.08052i	−0.565328	+	0.979178i
$87$		0			0
$88$	2.12132	+	3.67423i	0.226134	+	0.391675i
$89$	−5.74264	+	9.94655i	−0.608719	+	1.05433i	0.382733	+	0.923859i	$0.374983\pi$
$89$	−5.74264	+	9.94655i	−0.608719	+	1.05433i	−0.991452	+	0.130473i	$0.958350\pi$
$90$		0			0
$91$	−3.63604	+	4.68885i	−0.381160	+	0.491525i
$92$	−1.24264			−0.129554
$93$		0			0
$94$	−2.37868	−	4.11999i	−0.245342	−	0.424945i
$95$		0			0
$96$		0			0
$97$	4.48528			0.455411			0.227706	−	0.973730i	$-0.426878\pi$
$97$	4.48528			0.455411			0.227706	+	0.973730i	$0.426878\pi$
$98$	6.74264	+	1.88064i	0.681110	+	0.189973i
$99$		0			0
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	−8.12132	−	14.0665i	−0.808102	−	1.39967i	−0.914177	−	0.405315i	$-0.867162\pi$
$101$	−8.12132	−	14.0665i	−0.808102	−	1.39967i	0.106076	−	0.994358i	$-0.466171\pi$
$102$		0			0
$103$	−4.62132	+	8.00436i	−0.455352	+	0.788693i	−0.998708	−	0.0508091i	$-0.983820\pi$
$103$	−4.62132	+	8.00436i	−0.455352	+	0.788693i	0.543356	+	0.839502i	$0.317153\pi$
$104$	−2.24264			−0.219909
$105$		0			0
$106$	−4.24264			−0.412082
$107$	−7.24264	+	12.5446i	−0.700173	+	1.21273i	0.268233	+	0.963354i	$0.413560\pi$
$107$	−7.24264	+	12.5446i	−0.700173	+	1.21273i	−0.968406	+	0.249380i	$0.919773\pi$
$108$		0			0
$109$	−3.12132	−	5.40629i	−0.298968	−	0.517828i	0.676932	−	0.736046i	$-0.263309\pi$
$109$	−3.12132	−	5.40629i	−0.298968	−	0.517828i	−0.975900	+	0.218217i	$0.929976\pi$
$110$		0			0
$111$		0			0
$112$	1.00000	+	2.44949i	0.0944911	+	0.231455i
$113$	−3.51472			−0.330637			−0.165318	−	0.986240i	$-0.552865\pi$
$113$	−3.51472			−0.330637			−0.165318	+	0.986240i	$0.552865\pi$
$114$		0			0
$115$		0			0
$116$	−2.12132	−	3.67423i	−0.196960	−	0.341144i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	1.12132	+	1.94218i	0.101520	+	0.175837i
$123$		0			0
$124$	−4.62132	+	8.00436i	−0.415007	+	0.718813i
$125$		0			0
$126$		0			0
$127$	15.2426			1.35257			0.676283	−	0.736642i	$-0.263590\pi$
$127$	15.2426			1.35257			0.676283	+	0.736642i	$0.263590\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	8.12132	−	14.0665i	0.709563	−	1.22900i	−0.255456	−	0.966821i	$-0.582226\pi$
$131$	8.12132	−	14.0665i	0.709563	−	1.22900i	0.965019	−	0.262179i	$-0.0844410\pi$
$132$		0			0
$133$	−2.24264	−	5.49333i	−0.194462	−	0.476332i
$134$	0.242641			0.0209610
$135$		0			0
$136$		0			0
$137$	−6.98528	−	12.0989i	−0.596793	−	1.03368i	−0.993291	−	0.115640i	$-0.963108\pi$
$137$	−6.98528	−	12.0989i	−0.596793	−	1.03368i	0.396498	−	0.918035i	$-0.370225\pi$
$138$		0			0
$139$	20.7279			1.75812			0.879060	−	0.476712i	$-0.158171\pi$
$139$	20.7279			1.75812			0.879060	+	0.476712i	$0.158171\pi$
$140$		0			0
$141$		0			0
$142$	−0.621320	+	1.07616i	−0.0521400	+	0.0903092i
$143$	−4.75736	−	8.23999i	−0.397830	−	0.689062i
$144$		0			0
$145$		0			0
$146$	−7.00000			−0.579324
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−3.87868	+	6.71807i	−0.317754	+	0.550366i	−0.980019	−	0.198904i	$-0.936262\pi$
$149$	−3.87868	+	6.71807i	−0.317754	+	0.550366i	0.662265	+	0.749270i	$0.269595\pi$
$150$		0			0
$151$	5.62132	+	9.73641i	0.457457	+	0.792338i	0.998826	−	0.0484470i	$-0.0154272\pi$
$151$	5.62132	+	9.73641i	0.457457	+	0.792338i	−0.541369	+	0.840785i	$0.682094\pi$
$152$	1.12132	−	1.94218i	0.0909511	−	0.157532i
$153$		0			0
$154$	−6.87868	+	8.87039i	−0.554300	+	0.714796i
$155$		0			0
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	−0.378680	−	0.655892i	−0.0301261	−	0.0521800i
$159$		0			0
$160$		0			0
$161$	−1.24264	−	3.04384i	−0.0979338	−	0.239888i
$162$		0			0
$163$	10.1213	−	17.5306i	0.792763	−	1.37311i	−0.131487	−	0.991318i	$-0.541975\pi$
$163$	10.1213	−	17.5306i	0.792763	−	1.37311i	0.924250	−	0.381788i	$-0.124692\pi$
$164$	−5.74264	−	9.94655i	−0.448425	−	0.776695i
$165$		0			0
$166$	−8.12132	+	14.0665i	−0.630337	+	1.09178i
$167$	−18.2132			−1.40938			−0.704690	−	0.709515i	$-0.748914\pi$
$167$	−18.2132			−1.40938			−0.704690	+	0.709515i	$0.748914\pi$
$168$		0			0
$169$	−7.97056			−0.613120
$170$		0			0
$171$		0			0
$172$	−5.24264	−	9.08052i	−0.399748	−	0.692383i
$173$	−11.4853	+	19.8931i	−0.873210	+	1.51244i	−0.0145521	+	0.999894i	$0.504632\pi$
$173$	−11.4853	+	19.8931i	−0.873210	+	1.51244i	−0.858658	+	0.512550i	$0.828701\pi$
$174$		0			0
$175$	13.1066	+	1.79360i	0.990766	+	0.135583i
$176$	−4.24264			−0.319801
$177$		0			0
$178$	−5.74264	−	9.94655i	−0.430429	−	0.745525i
$179$	3.87868	+	6.71807i	0.289906	+	0.502132i	0.973787	−	0.227461i	$-0.0730426\pi$
$179$	3.87868	+	6.71807i	0.289906	+	0.502132i	−0.683881	+	0.729594i	$0.739709\pi$
$180$		0			0
$181$	−11.7574			−0.873918			−0.436959	−	0.899482i	$-0.643944\pi$
$181$	−11.7574			−0.873918			−0.436959	+	0.899482i	$0.643944\pi$
$182$	−2.24264	−	5.49333i	−0.166236	−	0.407192i
$183$		0			0
$184$	0.621320	−	1.07616i	0.0458043	−	0.0793355i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	4.75736			0.346966
$189$		0			0
$190$		0			0
$191$	4.24264	−	7.34847i	0.306987	−	0.531717i	−0.670715	−	0.741715i	$-0.734013\pi$
$191$	4.24264	−	7.34847i	0.306987	−	0.531717i	0.977702	+	0.209999i	$0.0673460\pi$
$192$		0			0
$193$	10.7426	+	18.6068i	0.773272	+	1.33935i	0.935760	+	0.352636i	$0.114715\pi$
$193$	10.7426	+	18.6068i	0.773272	+	1.33935i	−0.162488	+	0.986710i	$0.551952\pi$
$194$	−2.24264	+	3.88437i	−0.161012	+	0.278881i
$195$		0			0
$196$	−5.00000	+	4.89898i	−0.357143	+	0.349927i
$197$	−16.9706			−1.20910			−0.604551	−	0.796566i	$-0.706648\pi$
$197$	−16.9706			−1.20910			−0.604551	+	0.796566i	$0.706648\pi$
$198$		0			0
$199$	11.6213	+	20.1287i	0.823814	+	1.42689i	0.902823	+	0.430013i	$0.141491\pi$
$199$	11.6213	+	20.1287i	0.823814	+	1.42689i	−0.0790091	+	0.996874i	$0.525176\pi$
$200$	2.50000	+	4.33013i	0.176777	+	0.306186i
$201$		0			0
$202$	16.2426			1.14283
$203$	6.87868	−	8.87039i	0.482789	−	0.622579i
$204$		0			0
$205$		0			0
$206$	−4.62132	−	8.00436i	−0.321983	−	0.557690i
$207$		0			0
$208$	1.12132	−	1.94218i	0.0777496	−	0.134666i
$209$	9.51472			0.658147
$210$		0			0
$211$	10.4853			0.721837			0.360918	−	0.932597i	$-0.382463\pi$
$211$	10.4853			0.721837			0.360918	+	0.932597i	$0.382463\pi$
$212$	2.12132	−	3.67423i	0.145693	−	0.252347i
$213$		0			0
$214$	−7.24264	−	12.5446i	−0.495097	−	0.857533i
$215$		0			0
$216$		0			0
$217$	−24.2279	−	3.31552i	−1.64470	−	0.225072i
$218$	6.24264			0.422805
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−13.7279			−0.919290			−0.459645	−	0.888103i	$-0.652023\pi$
$223$	−13.7279			−0.919290			−0.459645	+	0.888103i	$0.652023\pi$
$224$	−2.62132	−	0.358719i	−0.175144	−	0.0239680i
$225$		0			0
$226$	1.75736	−	3.04384i	0.116898	−	0.202473i
$227$	−4.75736	−	8.23999i	−0.315757	−	0.546907i	0.663841	−	0.747874i	$-0.268925\pi$
$227$	−4.75736	−	8.23999i	−0.315757	−	0.546907i	−0.979598	+	0.200966i	$0.935592\pi$
$228$		0			0
$229$	4.48528	−	7.76874i	0.296396	−	0.513372i	−0.678913	−	0.734219i	$-0.737549\pi$
$229$	4.48528	−	7.76874i	0.296396	−	0.513372i	0.975309	+	0.220846i	$0.0708819\pi$
$230$		0			0
$231$		0			0
$232$	4.24264			0.278543
$233$	−1.75736	+	3.04384i	−0.115128	+	0.199408i	−0.917831	−	0.396971i	$-0.870061\pi$
$233$	−1.75736	+	3.04384i	−0.115128	+	0.199408i	0.802703	+	0.596379i	$0.203395\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−21.7279			−1.40546			−0.702731	−	0.711455i	$-0.748036\pi$
$239$	−21.7279			−1.40546			−0.702731	+	0.711455i	$0.748036\pi$
$240$		0			0
$241$	−12.7426	−	22.0709i	−0.820826	−	1.42171i	−0.905068	−	0.425266i	$-0.860180\pi$
$241$	−12.7426	−	22.0709i	−0.820826	−	1.42171i	0.0842426	−	0.996445i	$-0.473153\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	−2.24264			−0.143570
$245$		0			0
$246$		0			0
$247$	−2.51472	+	4.35562i	−0.160008	+	0.277141i
$248$	−4.62132	−	8.00436i	−0.293454	−	0.508277i
$249$		0			0
$250$		0			0
$251$	−6.72792			−0.424663			−0.212331	−	0.977198i	$-0.568106\pi$
$251$	−6.72792			−0.424663			−0.212331	+	0.977198i	$0.568106\pi$
$252$		0			0
$253$	5.27208			0.331453
$254$	−7.62132	+	13.2005i	−0.478204	+	0.828274i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.74264	−	9.94655i	0.358216	−	0.620448i	−0.629447	−	0.777044i	$-0.716718\pi$
$257$	5.74264	−	9.94655i	0.358216	−	0.620448i	0.987663	+	0.156595i	$0.0500518\pi$
$258$		0			0
$259$	−4.00000	−	9.79796i	−0.248548	−	0.608816i
$260$		0			0
$261$		0			0
$262$	8.12132	+	14.0665i	0.501737	+	0.869034i
$263$	5.48528	+	9.50079i	0.338237	+	0.585844i	0.984101	−	0.177609i	$-0.0568361\pi$
$263$	5.48528	+	9.50079i	0.338237	+	0.585844i	−0.645864	+	0.763452i	$0.723503\pi$
$264$		0			0
$265$		0			0
$266$	5.87868	+	0.804479i	0.360445	+	0.0493258i
$267$		0			0
$268$	−0.121320	+	0.210133i	−0.00741082	+	0.0128359i
$269$	−11.4853	−	19.8931i	−0.700270	−	1.21290i	−0.968372	−	0.249513i	$-0.919730\pi$
$269$	−11.4853	−	19.8931i	−0.700270	−	1.21290i	0.268102	−	0.963391i	$-0.413604\pi$
$270$		0			0
$271$	−2.24264	+	3.88437i	−0.136231	+	0.235959i	−0.926067	−	0.377359i	$-0.876832\pi$
$271$	−2.24264	+	3.88437i	−0.136231	+	0.235959i	0.789836	+	0.613318i	$0.210166\pi$
$272$		0			0
$273$		0			0
$274$	13.9706			0.843993
$275$	−10.6066	+	18.3712i	−0.639602	+	1.10782i
$276$		0			0
$277$	−11.6066	−	20.1032i	−0.697373	−	1.20789i	−0.969374	−	0.245589i	$-0.921019\pi$
$277$	−11.6066	−	20.1032i	−0.697373	−	1.20789i	0.272001	−	0.962297i	$-0.412315\pi$
$278$	−10.3640	+	17.9509i	−0.621589	+	1.07662i
$279$		0			0
$280$		0			0
$281$	−28.4558			−1.69753			−0.848767	−	0.528768i	$-0.822654\pi$
$281$	−28.4558			−1.69753			−0.848767	+	0.528768i	$0.822654\pi$
$282$		0			0
$283$	4.48528	+	7.76874i	0.266622	+	0.461803i	0.967987	−	0.250999i	$-0.0807590\pi$
$283$	4.48528	+	7.76874i	0.266622	+	0.461803i	−0.701365	+	0.712802i	$0.747426\pi$
$284$	−0.621320	−	1.07616i	−0.0368686	−	0.0638583i
$285$		0			0
$286$	9.51472			0.562617
$287$	18.6213	−	24.0131i	1.09918	−	1.41745i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$	3.50000	−	6.06218i	0.204822	−	0.354762i
$293$	22.9706			1.34195			0.670977	−	0.741478i	$-0.265875\pi$
$293$	22.9706			1.34195			0.670977	+	0.741478i	$0.265875\pi$
$294$		0			0
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$		0			0
$298$	−3.87868	−	6.71807i	−0.224686	−	0.389167i
$299$	−1.39340	+	2.41344i	−0.0805823	+	0.139573i
$300$		0			0
$301$	17.0000	−	21.9223i	0.979864	−	1.26358i
$302$	−11.2426			−0.646941
$303$		0			0
$304$	1.12132	+	1.94218i	0.0643121	+	0.111392i
$305$		0			0
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−4.24264	−	10.3923i	−0.241747	−	0.592157i
$309$		0			0
$310$		0			0
$311$	−11.4853	−	19.8931i	−0.651271	−	1.12803i	−0.982815	−	0.184594i	$-0.940903\pi$
$311$	−11.4853	−	19.8931i	−0.651271	−	1.12803i	0.331544	−	0.943440i	$-0.392430\pi$
$312$		0			0
$313$	−7.98528	+	13.8309i	−0.451355	+	0.781769i	−0.998470	−	0.0552876i	$-0.982392\pi$
$313$	−7.98528	+	13.8309i	−0.451355	+	0.781769i	0.547116	+	0.837057i	$0.315726\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	0.757359			0.0426048
$317$	−8.48528	+	14.6969i	−0.476581	+	0.825462i	−0.999640	−	0.0268342i	$-0.991457\pi$
$317$	−8.48528	+	14.6969i	−0.476581	+	0.825462i	0.523059	+	0.852296i	$0.324791\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$		0			0
$322$	3.25736	+	0.445759i	0.181526	+	0.0248412i
$323$		0			0
$324$		0			0
$325$	−5.60660	−	9.71092i	−0.310998	−	0.538665i
$326$	10.1213	+	17.5306i	0.560568	+	0.970932i
$327$		0			0
$328$	11.4853			0.634169
$329$	4.75736	+	11.6531i	0.262282	+	0.642456i
$330$		0			0
$331$	0.757359	−	1.31178i	0.0416282	−	0.0721022i	−0.844461	−	0.535618i	$-0.820079\pi$
$331$	0.757359	−	1.31178i	0.0416282	−	0.0721022i	0.886089	+	0.463515i	$0.153412\pi$
$332$	−8.12132	−	14.0665i	−0.445715	−	0.772002i
$333$		0			0
$334$	9.10660	−	15.7731i	0.498291	−	0.863065i
$335$		0			0
$336$		0			0
$337$	−12.4853			−0.680117			−0.340058	−	0.940404i	$-0.610447\pi$
$337$	−12.4853			−0.680117			−0.340058	+	0.940404i	$0.610447\pi$
$338$	3.98528	−	6.90271i	0.216771	−	0.375458i
$339$		0			0
$340$		0			0
$341$	19.6066	−	33.9596i	1.06176	−	1.83902i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	10.4853			0.565328
$345$		0			0
$346$	−11.4853	−	19.8931i	−0.617453	−	1.06946i
$347$	−9.36396	−	16.2189i	−0.502684	−	0.870674i	−0.999995	−	0.00310172i	$-0.999013\pi$
$347$	−9.36396	−	16.2189i	−0.502684	−	0.870674i	0.497311	−	0.867572i	$-0.334321\pi$
$348$		0			0
$349$	−8.97056			−0.480183			−0.240092	−	0.970750i	$-0.577177\pi$
$349$	−8.97056			−0.480183			−0.240092	+	0.970750i	$0.577177\pi$
$350$	−8.10660	+	10.4539i	−0.433316	+	0.558782i
$351$		0			0
$352$	2.12132	−	3.67423i	0.113067	−	0.195837i
$353$	−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
$356$	11.4853			0.608719
$357$		0			0
$358$	−7.75736			−0.409989
$359$	−9.62132	+	16.6646i	−0.507794	+	0.879525i	0.492165	+	0.870502i	$0.336206\pi$
$359$	−9.62132	+	16.6646i	−0.507794	+	0.879525i	−0.999959	+	0.00902308i	$0.997128\pi$
$360$		0			0
$361$	6.98528	+	12.0989i	0.367646	+	0.636782i
$362$	5.87868	−	10.1822i	0.308977	−	0.535163i
$363$		0			0
$364$	5.87868	+	0.804479i	0.308127	+	0.0421662i
$365$		0			0
$366$		0			0
$367$	6.86396	+	11.8887i	0.358296	+	0.620587i	0.987676	−	0.156511i	$-0.0500246\pi$
$367$	6.86396	+	11.8887i	0.358296	+	0.620587i	−0.629380	+	0.777097i	$0.716691\pi$
$368$	0.621320	+	1.07616i	0.0323886	+	0.0560986i
$369$		0			0
$370$		0			0
$371$	11.1213	+	1.52192i	0.577390	+	0.0790140i
$372$		0			0
$373$	−17.6066	+	30.4955i	−0.911635	+	1.57900i	−0.0998811	+	0.994999i	$0.531846\pi$
$373$	−17.6066	+	30.4955i	−0.911635	+	1.57900i	−0.811754	+	0.583999i	$0.801487\pi$
$374$		0			0
$375$		0			0
$376$	−2.37868	+	4.11999i	−0.122671	+	0.212472i
$377$	−9.51472			−0.490033
$378$		0			0
$379$	26.7279			1.37292			0.686461	−	0.727167i	$-0.259163\pi$
$379$	26.7279			1.37292			0.686461	+	0.727167i	$0.259163\pi$
$380$		0			0
$381$		0			0
$382$	4.24264	+	7.34847i	0.217072	+	0.375980i
$383$	−9.10660	+	15.7731i	−0.465326	+	0.805968i	−0.999216	−	0.0395860i	$-0.987396\pi$
$383$	−9.10660	+	15.7731i	−0.465326	+	0.805968i	0.533891	+	0.845554i	$0.320729\pi$
$384$		0			0
$385$		0			0
$386$	−21.4853			−1.09357
$387$		0			0
$388$	−2.24264	−	3.88437i	−0.113853	−	0.197199i
$389$	−0.878680	−	1.52192i	−0.0445508	−	0.0771643i	0.842890	−	0.538086i	$-0.180852\pi$
$389$	−0.878680	−	1.52192i	−0.0445508	−	0.0771643i	−0.887441	+	0.460921i	$0.847519\pi$
$390$		0			0
$391$		0			0
$392$	−1.74264	−	6.77962i	−0.0880166	−	0.342422i
$393$		0			0
$394$	8.48528	−	14.6969i	0.427482	−	0.740421i
$395$		0			0
$396$		0			0
$397$	5.87868	−	10.1822i	0.295042	−	0.511029i	−0.679952	−	0.733256i	$-0.738000\pi$
$397$	5.87868	−	10.1822i	0.295042	−	0.511029i	0.974995	+	0.222228i	$0.0713329\pi$
$398$	−23.2426			−1.16505
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−6.25736	+	10.8381i	−0.312478	+	0.541227i	−0.978898	−	0.204349i	$-0.934492\pi$
$401$	−6.25736	+	10.8381i	−0.312478	+	0.541227i	0.666420	+	0.745576i	$0.267826\pi$
$402$		0			0
$403$	10.3640	+	17.9509i	0.516266	+	0.894198i
$404$	−8.12132	+	14.0665i	−0.404051	+	0.699836i
$405$		0			0
$406$	4.24264	+	10.3923i	0.210559	+	0.515761i
$407$	16.9706			0.841200
$408$		0			0
$409$	−17.5000	−	30.3109i	−0.865319	−	1.49878i	−0.866730	−	0.498778i	$-0.833782\pi$
$409$	−17.5000	−	30.3109i	−0.865319	−	1.49878i	0.00141047	−	0.999999i	$-0.499551\pi$
$410$		0			0
$411$		0			0
$412$	9.24264			0.455352
$413$		0			0
$414$		0			0
$415$		0			0
$416$	1.12132	+	1.94218i	0.0549773	+	0.0952234i
$417$		0			0
$418$	−4.75736	+	8.23999i	−0.232690	+	0.403031i
$419$	−16.2426			−0.793505			−0.396752	−	0.917926i	$-0.629863\pi$
$419$	−16.2426			−0.793505			−0.396752	+	0.917926i	$0.629863\pi$
$420$		0			0
$421$	−5.75736			−0.280597			−0.140298	−	0.990109i	$-0.544806\pi$
$421$	−5.75736			−0.280597			−0.140298	+	0.990109i	$0.544806\pi$
$422$	−5.24264	+	9.08052i	−0.255208	+	0.442033i
$423$		0			0
$424$	2.12132	+	3.67423i	0.103020	+	0.178437i
$425$		0			0
$426$		0			0
$427$	−2.24264	−	5.49333i	−0.108529	−	0.265841i
$428$	14.4853			0.700173
$429$		0			0
$430$		0			0
$431$	14.3787	+	24.9046i	0.692597	+	1.19961i	0.970984	+	0.239144i	$0.0768667\pi$
$431$	14.3787	+	24.9046i	0.692597	+	1.19961i	−0.278388	+	0.960469i	$0.589800\pi$
$432$		0			0
$433$	−29.9706			−1.44029			−0.720147	−	0.693822i	$-0.755926\pi$
$433$	−29.9706			−1.44029			−0.720147	+	0.693822i	$0.755926\pi$
$434$	14.9853	−	19.3242i	0.719317	−	0.927593i
$435$		0			0
$436$	−3.12132	+	5.40629i	−0.149484	+	0.258914i
$437$	−1.39340	−	2.41344i	−0.0666553	−	0.115450i
$438$		0			0
$439$	6.86396	−	11.8887i	0.327599	−	0.567418i	−0.654436	−	0.756117i	$-0.727094\pi$
$439$	6.86396	−	11.8887i	0.327599	−	0.567418i	0.982035	+	0.188699i	$0.0604272\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.2426	+	22.9369i	−0.629177	+	1.08977i	0.358540	+	0.933514i	$0.383275\pi$
$443$	−13.2426	+	22.9369i	−0.629177	+	1.08977i	−0.987717	+	0.156252i	$0.950059\pi$
$444$		0			0
$445$		0			0
$446$	6.86396	−	11.8887i	0.325018	−	0.562948i
$447$		0			0
$448$	1.62132	−	2.09077i	0.0766002	−	0.0987796i
$449$	28.9706			1.36721			0.683603	−	0.729854i	$-0.260412\pi$
$449$	28.9706			1.36721			0.683603	+	0.729854i	$0.260412\pi$
$450$		0			0
$451$	24.3640	+	42.1996i	1.14725	+	1.98710i
$452$	1.75736	+	3.04384i	0.0826592	+	0.143170i
$453$		0			0
$454$	9.51472			0.446548
$455$		0			0
$456$		0			0
$457$	−14.2426	+	24.6690i	−0.666243	+	1.15397i	0.312704	+	0.949851i	$0.398765\pi$
$457$	−14.2426	+	24.6690i	−0.666243	+	1.15397i	−0.978947	+	0.204116i	$0.934568\pi$
$458$	4.48528	+	7.76874i	0.209583	+	0.363009i
$459$		0			0
$460$		0			0
$461$	25.7574			1.19964			0.599820	−	0.800135i	$-0.295239\pi$
$461$	25.7574			1.19964			0.599820	+	0.800135i	$0.295239\pi$
$462$		0			0
$463$	−17.2426			−0.801333			−0.400667	−	0.916224i	$-0.631221\pi$
$463$	−17.2426			−0.801333			−0.400667	+	0.916224i	$0.631221\pi$
$464$	−2.12132	+	3.67423i	−0.0984798	+	0.170572i
$465$		0			0
$466$	−1.75736	−	3.04384i	−0.0814081	−	0.141003i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$	−0.636039	−	0.0870399i	−0.0293696	−	0.00401913i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	22.2426	+	38.5254i	1.02272	+	1.77140i
$474$		0			0
$475$	11.2132			0.514497
$476$		0			0
$477$		0			0
$478$	10.8640	−	18.8169i	0.496906	−	0.860666i
$479$	2.37868	+	4.11999i	0.108685	+	0.188247i	0.915238	−	0.402914i	$-0.132003\pi$
$479$	2.37868	+	4.11999i	0.108685	+	0.188247i	−0.806553	+	0.591162i	$0.798669\pi$
$480$		0			0
$481$	−4.48528	+	7.76874i	−0.204511	+	0.354224i
$482$	25.4853			1.16082
$483$		0			0
$484$	7.00000			0.318182
$485$		0			0
$486$		0			0
$487$	5.62132	+	9.73641i	0.254726	+	0.441199i	0.964821	−	0.262907i	$-0.0846813\pi$
$487$	5.62132	+	9.73641i	0.254726	+	0.441199i	−0.710095	+	0.704106i	$0.751348\pi$
$488$	1.12132	−	1.94218i	0.0507598	−	0.0879185i
$489$		0			0
$490$		0			0
$491$	−18.7279			−0.845179			−0.422590	−	0.906321i	$-0.638879\pi$
$491$	−18.7279			−0.845179			−0.422590	+	0.906321i	$0.638879\pi$
$492$		0			0
$493$		0			0
$494$	−2.51472	−	4.35562i	−0.113143	−	0.195969i
$495$		0			0
$496$	9.24264			0.415007
$497$	2.01472	−	2.59808i	0.0903725	−	0.116540i
$498$		0			0
$499$	−7.36396	+	12.7548i	−0.329656	+	0.570981i	−0.982444	−	0.186560i	$-0.940266\pi$
$499$	−7.36396	+	12.7548i	−0.329656	+	0.570981i	0.652787	+	0.757541i	$0.273599\pi$
$500$		0			0
$501$		0			0
$502$	3.36396	−	5.82655i	0.150141	−	0.260052i
$503$	18.2132			0.812087			0.406043	−	0.913854i	$-0.366908\pi$
$503$	18.2132			0.812087			0.406043	+	0.913854i	$0.366908\pi$
$504$		0			0
$505$		0			0
$506$	−2.63604	+	4.56575i	−0.117186	+	0.202972i
$507$		0			0
$508$	−7.62132	−	13.2005i	−0.338141	−	0.585678i
$509$	−8.12132	+	14.0665i	−0.359971	+	0.623488i	−0.987956	−	0.154738i	$-0.950547\pi$
$509$	−8.12132	+	14.0665i	−0.359971	+	0.623488i	0.627984	+	0.778226i	$0.283880\pi$
$510$		0			0
$511$	18.3492	+	2.51104i	0.811723	+	0.111082i
$512$	1.00000			0.0441942
$513$		0			0
$514$	5.74264	+	9.94655i	0.253297	+	0.438723i
$515$		0			0
$516$		0			0
$517$	−20.1838			−0.887681
$518$	10.4853	+	1.43488i	0.460697	+	0.0630449i
$519$		0			0
$520$		0			0
$521$	17.2279	+	29.8396i	0.754769	+	1.30730i	0.945489	+	0.325654i	$0.105584\pi$
$521$	17.2279	+	29.8396i	0.754769	+	1.30730i	−0.190720	+	0.981644i	$0.561082\pi$
$522$		0			0
$523$	5.87868	−	10.1822i	0.257057	−	0.445235i	−0.708395	−	0.705816i	$-0.750581\pi$
$523$	5.87868	−	10.1822i	0.257057	−	0.445235i	0.965452	+	0.260581i	$0.0839139\pi$
$524$	−16.2426			−0.709563
$525$		0			0
$526$	−10.9706			−0.478339
$527$		0			0
$528$		0			0
$529$	10.7279	+	18.5813i	0.466431	+	0.807883i
$530$		0			0
$531$		0			0
$532$	−3.63604	+	4.68885i	−0.157642	+	0.203287i
$533$	−25.7574			−1.11568
$534$		0			0
$535$		0			0
$536$	−0.121320	−	0.210133i	−0.00524024	−	0.00907636i
$537$		0			0
$538$	22.9706			0.990331
$539$	21.2132	−	20.7846i	0.913717	−	0.895257i
$540$		0			0
$541$	−9.48528	+	16.4290i	−0.407804	+	0.706337i	−0.994643	−	0.103366i	$-0.967039\pi$
$541$	−9.48528	+	16.4290i	−0.407804	+	0.706337i	0.586839	+	0.809703i	$0.300372\pi$
$542$	−2.24264	−	3.88437i	−0.0963297	−	0.166848i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	10.4853			0.448318			0.224159	−	0.974553i	$-0.428036\pi$
$547$	10.4853			0.448318			0.224159	+	0.974553i	$0.428036\pi$
$548$	−6.98528	+	12.0989i	−0.298396	+	0.516838i
$549$		0			0
$550$	−10.6066	−	18.3712i	−0.452267	−	0.783349i
$551$	4.75736	−	8.23999i	0.202670	−	0.351035i
$552$		0			0
$553$	0.757359	+	1.85514i	0.0322062	+	0.0788887i
$554$	23.2132			0.986235
$555$		0			0
$556$	−10.3640	−	17.9509i	−0.439530	−	0.761288i
$557$	3.51472	+	6.08767i	0.148923	+	0.257943i	0.930830	−	0.365453i	$-0.119086\pi$
$557$	3.51472	+	6.08767i	0.148923	+	0.257943i	−0.781906	+	0.623396i	$0.785753\pi$
$558$		0			0
$559$	−23.5147			−0.994567
$560$		0			0
$561$		0			0
$562$	14.2279	−	24.6435i	0.600169	−	1.03952i
$563$	3.36396	+	5.82655i	0.141774	+	0.245560i	0.928165	−	0.372170i	$-0.121386\pi$
$563$	3.36396	+	5.82655i	0.141774	+	0.245560i	−0.786391	+	0.617729i	$0.788053\pi$
$564$		0			0
$565$		0			0
$566$	−8.97056			−0.377061
$567$		0			0
$568$	1.24264			0.0521400
$569$	21.4706	−	37.1881i	0.900093	−	1.55901i	0.0727207	−	0.997352i	$-0.476832\pi$
$569$	21.4706	−	37.1881i	0.900093	−	1.55901i	0.827372	−	0.561654i	$-0.189835\pi$
$570$		0			0
$571$	−6.48528	−	11.2328i	−0.271401	−	0.470080i	0.697820	−	0.716273i	$-0.254153\pi$
$571$	−6.48528	−	11.2328i	−0.271401	−	0.470080i	−0.969221	+	0.246193i	$0.920820\pi$
$572$	−4.75736	+	8.23999i	−0.198915	+	0.344531i
$573$		0			0
$574$	11.4853	+	28.1331i	0.479386	+	1.17425i
$575$	6.21320			0.259108
$576$		0			0
$577$	15.9706	+	27.6618i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648435\pi$
$577$	15.9706	+	27.6618i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$		0			0
$580$		0			0
$581$	26.3345	−	33.9596i	1.09254	−	1.40888i
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$	3.50000	+	6.06218i	0.144831	+	0.250855i
$585$		0			0
$586$	−11.4853	+	19.8931i	−0.474453	+	0.821776i
$587$	39.2132			1.61850			0.809251	−	0.587463i	$-0.199873\pi$
$587$	39.2132			1.61850			0.809251	+	0.587463i	$0.199873\pi$
$588$		0			0
$589$	−20.7279			−0.854079
$590$		0			0
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	−5.74264	+	9.94655i	−0.235822	+	0.408456i	−0.959511	−	0.281670i	$-0.909112\pi$
$593$	−5.74264	+	9.94655i	−0.235822	+	0.408456i	0.723689	+	0.690126i	$0.242445\pi$
$594$		0			0
$595$		0			0
$596$	7.75736			0.317754
$597$		0			0
$598$	−1.39340	−	2.41344i	−0.0569803	−	0.0986928i
$599$	5.48528	+	9.50079i	0.224123	+	0.388192i	0.956056	−	0.293185i	$-0.0947151\pi$
$599$	5.48528	+	9.50079i	0.224123	+	0.388192i	−0.731933	+	0.681376i	$0.761382\pi$
$600$		0			0
$601$	15.9706			0.651453			0.325726	−	0.945464i	$-0.394391\pi$
$601$	15.9706			0.651453			0.325726	+	0.945464i	$0.394391\pi$
$602$	10.4853	+	25.6836i	0.427348	+	1.04678i
$603$		0			0
$604$	5.62132	−	9.73641i	0.228728	−	0.396169i
$605$		0			0
$606$		0			0
$607$	2.51472	−	4.35562i	0.102069	−	0.176789i	−0.810468	−	0.585783i	$-0.800787\pi$
$607$	2.51472	−	4.35562i	0.102069	−	0.176789i	0.912537	+	0.408994i	$0.134120\pi$
$608$	−2.24264			−0.0909511
$609$		0			0
$610$		0			0
$611$	5.33452	−	9.23967i	0.215812	−	0.373797i
$612$		0			0
$613$	−14.9706	−	25.9298i	−0.604655	−	1.04729i	−0.992106	−	0.125403i	$-0.959978\pi$
$613$	−14.9706	−	25.9298i	−0.604655	−	1.04729i	0.387451	−	0.921891i	$-0.373356\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		0			0
$616$	11.1213	+	1.52192i	0.448091	+	0.0613198i
$617$	22.4558			0.904038			0.452019	−	0.892008i	$-0.350704\pi$
$617$	22.4558			0.904038			0.452019	+	0.892008i	$0.350704\pi$
$618$		0			0
$619$	9.24264	+	16.0087i	0.371493	+	0.643445i	0.989795	−	0.142495i	$-0.0455126\pi$
$619$	9.24264	+	16.0087i	0.371493	+	0.643445i	−0.618302	+	0.785940i	$0.712179\pi$
$620$		0			0
$621$		0			0
$622$	22.9706			0.921036
$623$	11.4853	+	28.1331i	0.460148	+	1.12713i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−7.98528	−	13.8309i	−0.319156	−	0.552794i
$627$		0			0
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$		0			0
$630$		0			0
$631$	−7.51472			−0.299156			−0.149578	−	0.988750i	$-0.547792\pi$
$631$	−7.51472			−0.299156			−0.149578	+	0.988750i	$0.547792\pi$
$632$	−0.378680	+	0.655892i	−0.0150631	+	0.0260900i
$633$		0			0
$634$	−8.48528	−	14.6969i	−0.336994	−	0.583690i
$635$		0			0
$636$		0			0
$637$	3.90812	+	15.2042i	0.154845	+	0.602414i
$638$	−18.0000			−0.712627
$639$		0			0
$640$		0			0
$641$	−23.2279	−	40.2319i	−0.917448	−	1.58907i	−0.803278	−	0.595605i	$-0.796912\pi$
$641$	−23.2279	−	40.2319i	−0.917448	−	1.58907i	−0.114170	−	0.993461i	$-0.536421\pi$
$642$		0			0
$643$	−21.2721			−0.838889			−0.419444	−	0.907781i	$-0.637775\pi$
$643$	−21.2721			−0.838889			−0.419444	+	0.907781i	$0.637775\pi$
$644$	−2.01472	+	2.59808i	−0.0793910	+	0.102379i
$645$		0			0
$646$		0			0
$647$	−13.8640	−	24.0131i	−0.545049	−	0.944052i	−0.998604	−	0.0528236i	$-0.983178\pi$
$647$	−13.8640	−	24.0131i	−0.545049	−	0.944052i	0.453555	−	0.891228i	$-0.350155\pi$
$648$		0			0
$649$		0			0
$650$	11.2132			0.439818
$651$		0			0
$652$	−20.2426			−0.792763
$653$	−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
$655$		0			0
$656$	−5.74264	+	9.94655i	−0.224212	+	0.388347i
$657$		0			0
$658$	−12.4706	−	1.70656i	−0.486153	−	0.0665285i
$659$	3.21320			0.125169			0.0625843	−	0.998040i	$-0.480066\pi$
$659$	3.21320			0.125169			0.0625843	+	0.998040i	$0.480066\pi$
$660$		0			0
$661$	−17.0919	−	29.6040i	−0.664797	−	1.15146i	−0.979340	−	0.202219i	$-0.935185\pi$
$661$	−17.0919	−	29.6040i	−0.664797	−	1.15146i	0.314543	−	0.949243i	$-0.398149\pi$
$662$	0.757359	+	1.31178i	0.0294356	+	0.0509840i
$663$		0			0
$664$	16.2426			0.630337
$665$		0			0
$666$		0			0
$667$	2.63604	−	4.56575i	0.102068	−	0.176787i
$668$	9.10660	+	15.7731i	0.352345	+	0.610279i
$669$		0			0
$670$		0			0
$671$	9.51472			0.367312
$672$		0			0
$673$	−10.5147			−0.405313			−0.202656	−	0.979250i	$-0.564957\pi$
$673$	−10.5147			−0.405313			−0.202656	+	0.979250i	$0.564957\pi$
$674$	6.24264	−	10.8126i	0.240458	−	0.416485i
$675$		0			0
$676$	3.98528	+	6.90271i	0.153280	+	0.265489i
$677$	−12.8787	+	22.3065i	−0.494968	+	0.857309i	−0.999983	−	0.00580089i	$-0.998154\pi$
$677$	−12.8787	+	22.3065i	−0.494968	+	0.857309i	0.505015	+	0.863110i	$0.331487\pi$
$678$		0			0
$679$	7.27208	−	9.37769i	0.279077	−	0.359883i
$680$		0			0
$681$		0			0
$682$	19.6066	+	33.9596i	0.750776	+	1.30038i
$683$	8.84924	+	15.3273i	0.338607	+	0.586484i	0.984171	−	0.177222i	$-0.0567110\pi$
$683$	8.84924	+	15.3273i	0.338607	+	0.586484i	−0.645564	+	0.763706i	$0.723378\pi$
$684$		0			0
$685$		0			0
$686$	14.8640	−	11.0482i	0.567509	−	0.421822i
$687$		0			0
$688$	−5.24264	+	9.08052i	−0.199874	+	0.346192i
$689$	−4.75736	−	8.23999i	−0.181241	−	0.313919i
$690$		0			0
$691$	1.12132	−	1.94218i	0.0426570	−	0.0738842i	−0.843909	−	0.536487i	$-0.819751\pi$
$691$	1.12132	−	1.94218i	0.0426570	−	0.0738842i	0.886566	+	0.462603i	$0.153084\pi$
$692$	22.9706			0.873210
$693$		0			0
$694$	18.7279			0.710902
$695$		0			0
$696$		0			0
$697$		0			0
$698$	4.48528	−	7.76874i	0.169770	−	0.294051i
$699$		0			0
$700$	−5.00000	−	12.2474i	−0.188982	−	0.462910i
$701$	22.2426			0.840093			0.420046	−	0.907503i	$-0.362014\pi$
$701$	22.2426			0.840093			0.420046	+	0.907503i	$0.362014\pi$
$702$		0			0
$703$	−4.48528	−	7.76874i	−0.169166	−	0.293003i
$704$	2.12132	+	3.67423i	0.0799503	+	0.138478i
$705$		0			0
$706$	21.0000			0.790345
$707$	−42.5772	−	5.82655i	−1.60128	−	0.219130i
$708$		0			0
$709$	16.8492	−	29.1837i	0.632787	−	1.09602i	−0.354193	−	0.935172i	$-0.615244\pi$
$709$	16.8492	−	29.1837i	0.632787	−	1.09602i	0.986979	−	0.160846i	$-0.0514223\pi$
$710$		0			0
$711$		0			0
$712$	−5.74264	+	9.94655i	−0.215215	+	0.372763i
$713$	−11.4853			−0.430127
$714$		0			0
$715$		0			0
$716$	3.87868	−	6.71807i	0.144953	−	0.251066i
$717$		0			0
$718$	−9.62132	−	16.6646i	−0.359064	−	0.621918i
$719$	13.8640	−	24.0131i	0.517039	−	0.895537i	−0.482766	−	0.875750i	$-0.660368\pi$
$719$	13.8640	−	24.0131i	0.517039	−	0.895537i	0.999804	−	0.0197874i	$-0.00629894\pi$
$720$		0			0
$721$	9.24264	+	22.6398i	0.344214	+	0.843148i
$722$	−13.9706			−0.519931
$723$		0			0
$724$	5.87868	+	10.1822i	0.218479	+	0.378417i
$725$	10.6066	+	18.3712i	0.393919	+	0.682288i
$726$		0			0
$727$	−0.272078			−0.0100908			−0.00504541	−	0.999987i	$-0.501606\pi$
$727$	−0.272078			−0.0100908			−0.00504541	+	0.999987i	$0.501606\pi$
$728$	−3.63604	+	4.68885i	−0.134761	+	0.173780i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	2.51472	−	4.35562i	0.0928833	−	0.160879i	−0.815840	−	0.578278i	$-0.803725\pi$
$733$	2.51472	−	4.35562i	0.0928833	−	0.160879i	0.908723	+	0.417399i	$0.137058\pi$
$734$	−13.7279			−0.506707
$735$		0			0
$736$	−1.24264			−0.0458043
$737$	0.514719	−	0.891519i	0.0189599	−	0.0328395i
$738$		0			0
$739$	3.24264	+	5.61642i	0.119282	+	0.206603i	0.919484	−	0.393129i	$-0.128607\pi$
$739$	3.24264	+	5.61642i	0.119282	+	0.206603i	−0.800201	+	0.599732i	$0.795274\pi$
$740$		0			0
$741$		0			0
$742$	−6.87868	+	8.87039i	−0.252524	+	0.325642i
$743$	43.2426			1.58642			0.793209	−	0.608949i	$-0.208409\pi$
$743$	43.2426			1.58642			0.793209	+	0.608949i	$0.208409\pi$
$744$		0			0
$745$		0			0
$746$	−17.6066	−	30.4955i	−0.644623	−	1.11652i
$747$		0			0
$748$		0			0
$749$	14.4853	+	35.4815i	0.529281	+	1.29647i
$750$		0			0
$751$	4.37868	−	7.58410i	0.159780	−	0.276748i	−0.775009	−	0.631950i	$-0.782255\pi$
$751$	4.37868	−	7.58410i	0.159780	−	0.276748i	0.934789	+	0.355203i	$0.115588\pi$
$752$	−2.37868	−	4.11999i	−0.0867415	−	0.150241i
$753$		0			0
$754$	4.75736	−	8.23999i	0.173253	−	0.300083i
$755$		0			0
$756$		0			0
$757$	−20.9706			−0.762188			−0.381094	−	0.924536i	$-0.624453\pi$
$757$	−20.9706			−0.762188			−0.381094	+	0.924536i	$0.624453\pi$
$758$	−13.3640	+	23.1471i	−0.485401	+	0.840739i
$759$		0			0
$760$		0			0
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	−0.991152	−	0.132734i	$-0.957624\pi$
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	0.610527	+	0.791995i	$0.290958\pi$
$762$		0			0
$763$	−16.3640	−	2.23936i	−0.592415	−	0.0810702i
$764$	−8.48528			−0.306987
$765$		0			0
$766$	−9.10660	−	15.7731i	−0.329035	−	0.569905i
$767$		0			0
$768$		0			0
$769$	4.48528			0.161743			0.0808717	−	0.996725i	$-0.474230\pi$
$769$	4.48528			0.161743			0.0808717	+	0.996725i	$0.474230\pi$
$770$		0			0
$771$		0			0
$772$	10.7426	−	18.6068i	0.386636	−	0.669673i
$773$	1.39340	+	2.41344i	0.0501171	+	0.0868053i	0.889996	−	0.455969i	$-0.150707\pi$
$773$	1.39340	+	2.41344i	0.0501171	+	0.0868053i	−0.839879	+	0.542774i	$0.817374\pi$
$774$		0			0
$775$	23.1066	−	40.0218i	0.830014	−	1.43763i
$776$	4.48528			0.161012
$777$		0			0
$778$	1.75736			0.0630044
$779$	12.8787	−	22.3065i	0.461427	−	0.799214i
$780$		0			0
$781$	2.63604	+	4.56575i	0.0943249	+	0.163376i
$782$		0			0
$783$		0			0
$784$	6.74264	+	1.88064i	0.240809	+	0.0671656i
$785$		0			0
$786$		0			0
$787$	−5.60660	−	9.71092i	−0.199854	−	0.346157i	0.748627	−	0.662991i	$-0.230713\pi$
$787$	−5.60660	−	9.71092i	−0.199854	−	0.346157i	−0.948481	+	0.316834i	$0.897380\pi$
$788$	8.48528	+	14.6969i	0.302276	+	0.523557i
$789$		0			0
$790$		0			0
$791$	−5.69848	+	7.34847i	−0.202615	+	0.261281i
$792$		0			0
$793$	−2.51472	+	4.35562i	−0.0893003	+	0.154673i
$794$	5.87868	+	10.1822i	0.208627	+	0.361352i
$795$		0			0
$796$	11.6213	−	20.1287i	0.411907	−	0.713443i
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$		0			0
$802$	−6.25736	−	10.8381i	−0.220955	−	0.382705i
$803$	−14.8492	+	25.7196i	−0.524018	+	0.907626i
$804$		0			0
$805$		0			0
$806$	−20.7279			−0.730110
$807$		0			0
$808$	−8.12132	−	14.0665i	−0.285707	−	0.494859i
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$		0			0
$811$	27.4558			0.964105			0.482053	−	0.876142i	$-0.339891\pi$
$811$	27.4558			0.964105			0.482053	+	0.876142i	$0.339891\pi$
$812$	−11.1213	−	1.52192i	−0.390282	−	0.0534088i
$813$		0			0
$814$	−8.48528	+	14.6969i	−0.297409	+	0.515127i
$815$		0			0
$816$		0			0
$817$	11.7574	−	20.3643i	0.411338	−	0.712458i
$818$	35.0000			1.22375
$819$		0			0
$820$		0			0
$821$	−22.0919	+	38.2643i	−0.771012	+	1.33543i	0.165997	+	0.986126i	$0.446916\pi$
$821$	−22.0919	+	38.2643i	−0.771012	+	1.33543i	−0.937009	+	0.349306i	$0.886417\pi$
$822$		0			0
$823$	9.34924	+	16.1934i	0.325894	+	0.564465i	0.981693	−	0.190471i	$-0.0610014\pi$
$823$	9.34924	+	16.1934i	0.325894	+	0.564465i	−0.655799	+	0.754936i	$0.727668\pi$
$824$	−4.62132	+	8.00436i	−0.160991	+	0.278845i
$825$		0			0
$826$		0			0
$827$	−16.9706			−0.590124			−0.295062	−	0.955478i	$-0.595340\pi$
$827$	−16.9706			−0.590124			−0.295062	+	0.955478i	$0.595340\pi$
$828$		0			0
$829$	−8.97056	−	15.5375i	−0.311561	−	0.539639i	0.667140	−	0.744932i	$-0.267518\pi$
$829$	−8.97056	−	15.5375i	−0.311561	−	0.539639i	−0.978700	+	0.205294i	$0.934185\pi$
$830$		0			0
$831$		0			0
$832$	−2.24264			−0.0777496
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−4.75736	−	8.23999i	−0.164537	−	0.284986i
$837$		0			0
$838$	8.12132	−	14.0665i	0.280546	−	0.485921i
$839$	32.4853			1.12152			0.560758	−	0.827980i	$-0.310510\pi$
$839$	32.4853			1.12152			0.560758	+	0.827980i	$0.310510\pi$
$840$		0			0
$841$	−11.0000			−0.379310
$842$	2.87868	−	4.98602i	0.0992059	−	0.171830i
$843$		0			0
$844$	−5.24264	−	9.08052i	−0.180459	−	0.312564i
$845$		0			0
$846$		0			0
$847$	7.00000	+	17.1464i	0.240523	+	0.589158i
$848$	−4.24264			−0.145693
$849$		0			0
$850$		0			0
$851$	−2.48528	−	4.30463i	−0.0851943	−	0.147561i
$852$		0			0
$853$	−48.1838			−1.64978			−0.824890	−	0.565293i	$-0.808763\pi$
$853$	−48.1838			−1.64978			−0.824890	+	0.565293i	$0.808763\pi$
$854$	5.87868	+	0.804479i	0.201164	+	0.0275287i
$855$		0			0
$856$	−7.24264	+	12.5446i	−0.247548	+	0.428766i
$857$	−5.74264	−	9.94655i	−0.196165	−	0.339768i	0.751117	−	0.660169i	$-0.229515\pi$
$857$	−5.74264	−	9.94655i	−0.196165	−	0.339768i	−0.947282	+	0.320402i	$0.896182\pi$
$858$		0			0
$859$	7.84924	−	13.5953i	0.267813	−	0.463865i	−0.700484	−	0.713668i	$-0.747032\pi$
$859$	7.84924	−	13.5953i	0.267813	−	0.463865i	0.968297	+	0.249803i	$0.0803658\pi$
$860$		0			0
$861$		0			0
$862$	−28.7574			−0.979480
$863$	−21.1066	+	36.5577i	−0.718477	+	1.24444i	0.243126	+	0.969995i	$0.421827\pi$
$863$	−21.1066	+	36.5577i	−0.718477	+	1.24444i	−0.961603	+	0.274444i	$0.911506\pi$
$864$		0			0
$865$		0			0
$866$	14.9853	−	25.9553i	0.509221	−	0.881996i
$867$		0			0
$868$	9.24264	+	22.6398i	0.313716	+	0.768443i
$869$	−3.21320			−0.109000
$870$		0			0
$871$	0.272078	+	0.471253i	0.00921901	+	0.0159678i
$872$	−3.12132	−	5.40629i	−0.105701	−	0.183080i
$873$		0			0
$874$	2.78680			0.0942648
$875$		0			0
$876$		0			0
$877$	16.8492	−	29.1837i	0.568958	−	0.985465i	−0.427711	−	0.903916i	$-0.640680\pi$
$877$	16.8492	−	29.1837i	0.568958	−	0.985465i	0.996669	−	0.0815494i	$-0.0259868\pi$
$878$	6.86396	+	11.8887i	0.231647	+	0.401225i
$879$		0			0
$880$		0			0
$881$	−53.4853			−1.80196			−0.900982	−	0.433856i	$-0.857153\pi$
$881$	−53.4853			−1.80196			−0.900982	+	0.433856i	$0.857153\pi$
$882$		0			0
$883$	−9.69848			−0.326380			−0.163190	−	0.986595i	$-0.552178\pi$
$883$	−9.69848			−0.326380			−0.163190	+	0.986595i	$0.552178\pi$
$884$		0			0
$885$		0			0
$886$	−13.2426	−	22.9369i	−0.444895	−	0.770581i
$887$	−7.13604	+	12.3600i	−0.239605	+	0.415008i	−0.960601	−	0.277931i	$-0.910351\pi$
$887$	−7.13604	+	12.3600i	−0.239605	+	0.415008i	0.720996	+	0.692939i	$0.243685\pi$
$888$		0			0
$889$	24.7132	−	31.8689i	0.828854	−	1.06885i
$890$		0			0
$891$		0			0
$892$	6.86396	+	11.8887i	0.229822	+	0.398064i
$893$	5.33452	+	9.23967i	0.178513	+	0.309194i
$894$		0			0
$895$		0			0
$896$	1.00000	+	2.44949i	0.0334077	+	0.0818317i
$897$		0			0
$898$	−14.4853	+	25.0892i	−0.483380	+	0.837239i
$899$	−19.6066	−	33.9596i	−0.653917	−	1.13262i
$900$		0			0
$901$		0			0
$902$	−48.7279			−1.62246
$903$		0			0
$904$	−3.51472			−0.116898
$905$		0			0
$906$		0			0
$907$	−14.9706	−	25.9298i	−0.497089	−	0.860984i	0.502905	−	0.864342i	$-0.332265\pi$
$907$	−14.9706	−	25.9298i	−0.497089	−	0.860984i	−0.999994	+	0.00335764i	$0.998931\pi$
$908$	−4.75736	+	8.23999i	−0.157879	+	0.273454i
$909$		0			0
$910$		0			0
$911$	−39.7279			−1.31624			−0.658122	−	0.752911i	$-0.728649\pi$
$911$	−39.7279			−1.31624			−0.658122	+	0.752911i	$0.728649\pi$
$912$		0			0
$913$	34.4558	+	59.6793i	1.14032	+	1.97510i
$914$	−14.2426	−	24.6690i	−0.471105	−	0.815977i
$915$		0			0
$916$	−8.97056			−0.296396
$917$	−16.2426	−	39.7862i	−0.536379	−	1.31386i
$918$		0			0
$919$	8.72792	−	15.1172i	0.287908	−	0.498671i	−0.685403	−	0.728164i	$-0.740374\pi$
$919$	8.72792	−	15.1172i	0.287908	−	0.498671i	0.973310	+	0.229494i	$0.0737071\pi$
$920$		0			0
$921$		0			0
$922$	−12.8787	+	22.3065i	−0.424137	+	0.734626i
$923$	−2.78680			−0.0917285
$924$		0			0
$925$	20.0000			0.657596
$926$	8.62132	−	14.9326i	0.283314	−	0.490715i
$927$		0			0
$928$	−2.12132	−	3.67423i	−0.0696358	−	0.120613i
$929$	21.9853	−	38.0796i	0.721314	−	1.24935i	−0.239160	−	0.970980i	$-0.576872\pi$
$929$	21.9853	−	38.0796i	0.721314	−	1.24935i	0.960473	−	0.278372i	$-0.0897947\pi$
$930$		0			0
$931$	−15.1213	−	4.21759i	−0.495581	−	0.138226i
$932$	3.51472			0.115128
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−20.4558			−0.668263			−0.334132	−	0.942526i	$-0.608443\pi$
$937$	−20.4558			−0.668263			−0.334132	+	0.942526i	$0.608443\pi$
$938$	0.393398	−	0.507306i	0.0128449	−	0.0165641i
$939$		0			0
$940$		0			0
$941$	−26.3345	−	45.6127i	−0.858481	−	1.48693i	−0.873378	−	0.487044i	$-0.838075\pi$
$941$	−26.3345	−	45.6127i	−0.858481	−	1.48693i	0.0148967	−	0.999889i	$-0.495258\pi$
$942$		0			0
$943$	7.13604	−	12.3600i	0.232381	−	0.402496i
$944$		0			0
$945$		0			0
$946$	−44.4853			−1.44634
$947$	19.2426	−	33.3292i	0.625302	−	1.08305i	−0.363181	−	0.931719i	$-0.618309\pi$
$947$	19.2426	−	33.3292i	0.625302	−	1.08305i	0.988482	−	0.151336i	$-0.0483575\pi$
$948$		0			0
$949$	−7.84924	−	13.5953i	−0.254797	−	0.441322i
$950$	−5.60660	+	9.71092i	−0.181902	+	0.315064i
$951$		0			0
$952$		0			0
$953$	−23.4853			−0.760763			−0.380381	−	0.924830i	$-0.624207\pi$
$953$	−23.4853			−0.760763			−0.380381	+	0.924830i	$0.624207\pi$
$954$		0			0
$955$		0			0
$956$	10.8640	+	18.8169i	0.351366	+	0.608583i
$957$		0			0
$958$	−4.75736			−0.153703
$959$	−36.6213	−	5.01151i	−1.18256	−	0.161830i
$960$		0			0
$961$	−27.2132	+	47.1347i	−0.877845	+	1.52047i
$962$	−4.48528	−	7.76874i	−0.144611	−	0.250474i
$963$		0			0
$964$	−12.7426	+	22.0709i	−0.410413	+	0.710856i
$965$		0			0
$966$		0			0
$967$	52.6985			1.69467			0.847335	−	0.531060i	$-0.178206\pi$
$967$	52.6985			1.69467			0.847335	+	0.531060i	$0.178206\pi$
$968$	−3.50000	+	6.06218i	−0.112494	+	0.194846i
$969$		0			0
$970$		0			0
$971$	4.75736	−	8.23999i	0.152671	−	0.264434i	−0.779538	−	0.626355i	$-0.784546\pi$
$971$	4.75736	−	8.23999i	0.152671	−	0.264434i	0.932209	+	0.361922i	$0.117879\pi$
$972$		0			0
$973$	33.6066	−	43.3373i	1.07738	−	1.38933i
$974$	−11.2426			−0.360237
$975$		0			0
$976$	1.12132	+	1.94218i	0.0358926	+	0.0621678i
$977$	−9.98528	−	17.2950i	−0.319457	−	0.553317i	0.660917	−	0.750459i	$-0.270167\pi$
$977$	−9.98528	−	17.2950i	−0.319457	−	0.553317i	−0.980375	+	0.197142i	$0.936834\pi$
$978$		0			0
$979$	−48.7279			−1.55735
$980$		0			0
$981$		0			0
$982$	9.36396	−	16.2189i	0.298816	−	0.517565i
$983$	16.2426	+	28.1331i	0.518060	+	0.897306i	0.999780	+	0.0209807i	$0.00667886\pi$
$983$	16.2426	+	28.1331i	0.518060	+	0.897306i	−0.481720	+	0.876325i	$0.659988\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	5.02944			0.160008
$989$	6.51472	−	11.2838i	0.207156	−	0.358805i
$990$		0			0
$991$	−3.89340	−	6.74356i	−0.123678	−	0.214216i	0.797537	−	0.603269i	$-0.206136\pi$
$991$	−3.89340	−	6.74356i	−0.123678	−	0.214216i	−0.921215	+	0.389053i	$0.872802\pi$
$992$	−4.62132	+	8.00436i	−0.146727	+	0.254139i
$993$		0			0
$994$	1.24264	+	3.04384i	0.0394142	+	0.0965446i
$995$		0			0
$996$		0			0
$997$	−7.00000	−	12.1244i	−0.221692	−	0.383982i	0.733630	−	0.679549i	$-0.237825\pi$
$997$	−7.00000	−	12.1244i	−0.221692	−	0.383982i	−0.955322	+	0.295567i	$0.904491\pi$
$998$	−7.36396	−	12.7548i	−0.233102	−	0.403745i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.g.i.163.2	✓	4
3.2	odd	2		1134.2.g.j.163.2	yes	4
7.2	even	3		7938.2.a.bq.1.1		2
7.4	even	3	inner	1134.2.g.i.487.2	yes	4
7.5	odd	6		7938.2.a.bp.1.1		2
9.2	odd	6		1134.2.e.r.919.1		4
9.4	even	3		1134.2.h.r.541.2		4
9.5	odd	6		1134.2.h.s.541.2		4
9.7	even	3		1134.2.e.s.919.1		4
21.2	odd	6		7938.2.a.bk.1.2		2
21.5	even	6		7938.2.a.bj.1.2		2
21.11	odd	6		1134.2.g.j.487.2	yes	4
63.4	even	3		1134.2.e.s.865.1		4
63.11	odd	6		1134.2.h.s.109.1		4
63.25	even	3		1134.2.h.r.109.1		4
63.32	odd	6		1134.2.e.r.865.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.r.865.1		4	63.32	odd	6
1134.2.e.r.919.1		4	9.2	odd	6
1134.2.e.s.865.1		4	63.4	even	3
1134.2.e.s.919.1		4	9.7	even	3
1134.2.g.i.163.2	✓	4	1.1	even	1	trivial
1134.2.g.i.487.2	yes	4	7.4	even	3	inner
1134.2.g.j.163.2	yes	4	3.2	odd	2
1134.2.g.j.487.2	yes	4	21.11	odd	6
1134.2.h.r.109.1		4	63.25	even	3
1134.2.h.r.541.2		4	9.4	even	3
1134.2.h.s.109.1		4	63.11	odd	6
1134.2.h.s.541.2		4	9.5	odd	6
7938.2.a.bj.1.2		2	21.5	even	6
7938.2.a.bk.1.2		2	21.2	odd	6
7938.2.a.bp.1.1		2	7.5	odd	6
7938.2.a.bq.1.1		2	7.2	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(2.12132 + 3.67423i) q^{11} -2.24264 q^{13} +(1.00000 + 2.44949i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.12132 - 1.94218i) q^{19} -4.24264 q^{22} +(0.621320 - 1.07616i) q^{23} +(2.50000 + 4.33013i) q^{25} +(1.12132 - 1.94218i) q^{26} +(-2.62132 - 0.358719i) q^{28} +4.24264 q^{29} +(-4.62132 - 8.00436i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{37} +(1.12132 + 1.94218i) q^{38} +11.4853 q^{41} +10.4853 q^{43} +(2.12132 - 3.67423i) q^{44} +(0.621320 + 1.07616i) q^{46} +(-2.37868 + 4.11999i) q^{47} +(-1.74264 - 6.77962i) q^{49} -5.00000 q^{50} +(1.12132 + 1.94218i) q^{52} +(2.12132 + 3.67423i) q^{53} +(1.62132 - 2.09077i) q^{56} +(-2.12132 + 3.67423i) q^{58} +(1.12132 - 1.94218i) q^{61} +9.24264 q^{62} +1.00000 q^{64} +(-0.121320 - 0.210133i) q^{67} +1.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +(2.00000 + 3.46410i) q^{74} -2.24264 q^{76} +(11.1213 + 1.52192i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-5.74264 + 9.94655i) q^{82} +16.2426 q^{83} +(-5.24264 + 9.08052i) q^{86} +(2.12132 + 3.67423i) q^{88} +(-5.74264 + 9.94655i) q^{89} +(-3.63604 + 4.68885i) q^{91} -1.24264 q^{92} +(-2.37868 - 4.11999i) q^{94} +4.48528 q^{97} +(6.74264 + 1.88064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 8 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{19} - 6 q^{23} + 10 q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} - 2 q^{32} + 8 q^{37} - 4 q^{38} + 12 q^{41} + 8 q^{43} - 6 q^{46}+ \cdots + 10 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 8 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^19 - 6 * q^23 + 10 * q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 - 2 * q^32 + 8 * q^37 - 4 * q^38 + 12 * q^41 + 8 * q^43 - 6 * q^46 - 18 * q^47 + 10 * q^49 - 20 * q^50 - 4 * q^52 - 2 * q^56 - 4 * q^61 + 20 * q^62 + 4 * q^64 + 8 * q^67 - 12 * q^71 + 14 * q^73 + 8 * q^74 + 8 * q^76 + 36 * q^77 - 10 * q^79 - 6 * q^82 + 48 * q^83 - 4 * q^86 - 6 * q^89 - 40 * q^91 + 12 * q^92 - 18 * q^94 - 16 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more