LMFDB - Embedded newform 1134.2.h.s.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (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:	$4$
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			109.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1134.109
Dual form			1134.2.h.s.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} +4.24264 q^{11} +(1.12132 - 1.94218i) q^{13} +(-1.62132 - 2.09077i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.12132 + 1.94218i) q^{19} +(2.12132 - 3.67423i) q^{22} +1.24264 q^{23} -5.00000 q^{25} +(-1.12132 - 1.94218i) q^{26} +(-2.62132 + 0.358719i) q^{28} +(2.12132 + 3.67423i) q^{29} +(-4.62132 - 8.00436i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{37} +2.24264 q^{38} +(5.74264 - 9.94655i) q^{41} +(-5.24264 - 9.08052i) q^{43} +(-2.12132 - 3.67423i) q^{44} +(0.621320 - 1.07616i) q^{46} +(2.37868 - 4.11999i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-2.50000 + 4.33013i) q^{50} -2.24264 q^{52} +(-2.12132 + 3.67423i) q^{53} +(-1.00000 + 2.44949i) q^{56} +4.24264 q^{58} +(1.12132 - 1.94218i) q^{61} -9.24264 q^{62} +1.00000 q^{64} +(-0.121320 - 0.210133i) q^{67} -1.24264 q^{71} +(3.50000 - 6.06218i) q^{73} +4.00000 q^{74} +(1.12132 - 1.94218i) q^{76} +(4.24264 - 10.3923i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-5.74264 - 9.94655i) q^{82} +(8.12132 + 14.0665i) q^{83} -10.4853 q^{86} -4.24264 q^{88} +(5.74264 + 9.94655i) q^{89} +(-3.63604 - 4.68885i) q^{91} +(-0.621320 - 1.07616i) q^{92} +(-2.37868 - 4.11999i) q^{94} +(-2.24264 - 3.88437i) q^{97} +(-6.74264 + 1.88064i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{7} - 4 q^{8} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{19} - 12 q^{23} - 20 q^{25} + 4 q^{26} - 2 q^{28} - 10 q^{31} + 2 q^{32} + 8 q^{37} - 8 q^{38} + 6 q^{41} - 4 q^{43} - 6 q^{46} + 18 q^{47} - 20 q^{49} - 10 q^{50} + 8 q^{52} - 4 q^{56} - 4 q^{61} - 20 q^{62} + 4 q^{64} + 8 q^{67} + 12 q^{71} + 14 q^{73} + 16 q^{74} - 4 q^{76} - 10 q^{79} - 6 q^{82} + 24 q^{83} - 8 q^{86} + 6 q^{89} - 40 q^{91} + 6 q^{92} - 18 q^{94} + 8 q^{97} - 10 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 - 4 * q^8 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^19 - 12 * q^23 - 20 * q^25 + 4 * q^26 - 2 * q^28 - 10 * q^31 + 2 * q^32 + 8 * q^37 - 8 * q^38 + 6 * q^41 - 4 * q^43 - 6 * q^46 + 18 * q^47 - 20 * q^49 - 10 * q^50 + 8 * q^52 - 4 * q^56 - 4 * q^61 - 20 * q^62 + 4 * q^64 + 8 * q^67 + 12 * q^71 + 14 * q^73 + 16 * q^74 - 4 * q^76 - 10 * q^79 - 6 * q^82 + 24 * q^83 - 8 * q^86 + 6 * q^89 - 40 * q^91 + 6 * q^92 - 18 * q^94 + 8 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	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			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	4.24264			1.27920			0.639602	−	0.768706i	$-0.279099\pi$
$11$	4.24264			1.27920			0.639602	+	0.768706i	$0.279099\pi$
$12$		0			0
$13$	1.12132	−	1.94218i	0.310998	−	0.538665i	−0.667580	−	0.744538i	$-0.732670\pi$
$13$	1.12132	−	1.94218i	0.310998	−	0.538665i	0.978579	+	0.205873i	$0.0660033\pi$
$14$	−1.62132	−	2.09077i	−0.433316	−	0.558782i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	1.12132	+	1.94218i	0.257249	+	0.445568i	0.965504	−	0.260389i	$-0.0838508\pi$
$19$	1.12132	+	1.94218i	0.257249	+	0.445568i	−0.708255	+	0.705956i	$0.750517\pi$
$20$		0			0
$21$		0			0
$22$	2.12132	−	3.67423i	0.452267	−	0.783349i
$23$	1.24264			0.259108			0.129554	−	0.991572i	$-0.458645\pi$
$23$	1.24264			0.259108			0.129554	+	0.991572i	$0.458645\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$	−1.12132	−	1.94218i	−0.219909	−	0.380894i
$27$		0			0
$28$	−2.62132	+	0.358719i	−0.495383	+	0.0677916i
$29$	2.12132	+	3.67423i	0.393919	+	0.682288i	0.992963	−	0.118428i	$-0.0377856\pi$
$29$	2.12132	+	3.67423i	0.393919	+	0.682288i	−0.599043	+	0.800717i	$0.704452\pi$
$30$		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	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	2.24264			0.363804
$39$		0			0
$40$		0			0
$41$	5.74264	−	9.94655i	0.896850	−	1.55339i	0.0653514	−	0.997862i	$-0.479183\pi$
$41$	5.74264	−	9.94655i	0.896850	−	1.55339i	0.831498	−	0.555527i	$-0.187483\pi$
$42$		0			0
$43$	−5.24264	−	9.08052i	−0.799495	−	1.38477i	−0.919945	−	0.392047i	$-0.871767\pi$
$43$	−5.24264	−	9.08052i	−0.799495	−	1.38477i	0.120450	−	0.992719i	$-0.461566\pi$
$44$	−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	−0.638743	−	0.769420i	$-0.720545\pi$
$47$	2.37868	−	4.11999i	0.346966	−	0.600963i	0.985709	+	0.168457i	$0.0538786\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$	−2.50000	+	4.33013i	−0.353553	+	0.612372i
$51$		0			0
$52$	−2.24264			−0.310998
$53$	−2.12132	+	3.67423i	−0.291386	+	0.504695i	−0.974138	−	0.225955i	$-0.927450\pi$
$53$	−2.12132	+	3.67423i	−0.291386	+	0.504695i	0.682752	+	0.730650i	$0.260783\pi$
$54$		0			0
$55$		0			0
$56$	−1.00000	+	2.44949i	−0.133631	+	0.327327i
$57$		0			0
$58$	4.24264			0.557086
$59$		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	$-0.523493\pi$
$71$	−1.24264			−0.147474			−0.0737372	+	0.997278i	$0.523493\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	4.00000			0.464991
$75$		0			0
$76$	1.12132	−	1.94218i	0.128624	−	0.222784i
$77$	4.24264	−	10.3923i	0.483494	−	1.18431i
$78$		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
$83$	8.12132	+	14.0665i	0.891431	+	1.54400i	0.838161	+	0.545423i	$0.183631\pi$
$83$	8.12132	+	14.0665i	0.891431	+	1.54400i	0.0532699	+	0.998580i	$0.483036\pi$
$84$		0			0
$85$		0			0
$86$	−10.4853			−1.13066
$87$		0			0
$88$	−4.24264			−0.452267
$89$	5.74264	+	9.94655i	0.608719	+	1.05433i	0.991452	+	0.130473i	$0.0416495\pi$
$89$	5.74264	+	9.94655i	0.608719	+	1.05433i	−0.382733	+	0.923859i	$0.625017\pi$
$90$		0			0
$91$	−3.63604	−	4.68885i	−0.381160	−	0.491525i
$92$	−0.621320	−	1.07616i	−0.0647771	−	0.112197i
$93$		0			0
$94$	−2.37868	−	4.11999i	−0.245342	−	0.424945i
$95$		0			0
$96$		0			0
$97$	−2.24264	−	3.88437i	−0.227706	−	0.394398i	0.729422	−	0.684064i	$-0.239789\pi$
$97$	−2.24264	−	3.88437i	−0.227706	−	0.394398i	−0.957128	+	0.289666i	$0.906456\pi$
$98$	−6.74264	+	1.88064i	−0.681110	+	0.189973i
$99$		0			0
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	−16.2426			−1.61620			−0.808102	−	0.589043i	$-0.799505\pi$
$101$	−16.2426			−1.61620			−0.808102	+	0.589043i	$0.799505\pi$
$102$		0			0
$103$	9.24264			0.910704			0.455352	−	0.890311i	$-0.349513\pi$
$103$	9.24264			0.910704			0.455352	+	0.890311i	$0.349513\pi$
$104$	−1.12132	+	1.94218i	−0.109955	+	0.190447i
$105$		0			0
$106$	2.12132	+	3.67423i	0.206041	+	0.356873i
$107$	7.24264	+	12.5446i	0.700173	+	1.21273i	0.968406	+	0.249380i	$0.0802269\pi$
$107$	7.24264	+	12.5446i	0.700173	+	1.21273i	−0.268233	+	0.963354i	$0.586440\pi$
$108$		0			0
$109$	−3.12132	+	5.40629i	−0.298968	+	0.517828i	−0.975900	−	0.218217i	$-0.929976\pi$
$109$	−3.12132	+	5.40629i	−0.298968	+	0.517828i	0.676932	+	0.736046i	$0.263309\pi$
$110$		0			0
$111$		0			0
$112$	1.62132	+	2.09077i	0.153200	+	0.197559i
$113$	−1.75736	+	3.04384i	−0.165318	+	0.286340i	−0.936768	−	0.349950i	$-0.886199\pi$
$113$	−1.75736	+	3.04384i	−0.165318	+	0.286340i	0.771450	+	0.636290i	$0.219532\pi$
$114$		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
$121$	7.00000			0.636364
$122$	−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
$131$	16.2426			1.41913			0.709563	−	0.704642i	$-0.248892\pi$
$131$	16.2426			1.41913			0.709563	+	0.704642i	$0.248892\pi$
$132$		0			0
$133$	5.87868	−	0.804479i	0.509746	−	0.0697572i
$134$	−0.242641			−0.0209610
$135$		0			0
$136$		0			0
$137$	−13.9706			−1.19359			−0.596793	−	0.802395i	$-0.703559\pi$
$137$	−13.9706			−1.19359			−0.596793	+	0.802395i	$0.703559\pi$
$138$		0			0
$139$	−10.3640	+	17.9509i	−0.879060	+	1.52258i	−0.0266854	+	0.999644i	$0.508495\pi$
$139$	−10.3640	+	17.9509i	−0.879060	+	1.52258i	−0.852374	+	0.522932i	$0.824838\pi$
$140$		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
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−7.75736			−0.635508			−0.317754	−	0.948173i	$-0.602929\pi$
$149$	−7.75736			−0.635508			−0.317754	+	0.948173i	$0.602929\pi$
$150$		0			0
$151$	−11.2426			−0.914913			−0.457457	−	0.889232i	$-0.651239\pi$
$151$	−11.2426			−0.914913			−0.457457	+	0.889232i	$0.651239\pi$
$152$	−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	0.924250	+	0.381788i	$0.124692\pi$
$163$	10.1213	+	17.5306i	0.792763	+	1.37311i	−0.131487	+	0.991318i	$0.541975\pi$
$164$	−11.4853			−0.896850
$165$		0			0
$166$	16.2426			1.26067
$167$	−9.10660	+	15.7731i	−0.704690	+	1.22056i	0.262113	+	0.965037i	$0.415581\pi$
$167$	−9.10660	+	15.7731i	−0.704690	+	1.22056i	−0.966803	+	0.255522i	$0.917753\pi$
$168$		0			0
$169$	3.98528	+	6.90271i	0.306560	+	0.530978i
$170$		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	$-0.495368\pi$
$173$	11.4853	−	19.8931i	0.873210	−	1.51244i	0.858658	−	0.512550i	$-0.171299\pi$
$174$		0			0
$175$	−5.00000	+	12.2474i	−0.377964	+	0.925820i
$176$	−2.12132	+	3.67423i	−0.159901	+	0.276956i
$177$		0			0
$178$	11.4853			0.860858
$179$	−3.87868	+	6.71807i	−0.289906	+	0.502132i	−0.973787	−	0.227461i	$-0.926957\pi$
$179$	−3.87868	+	6.71807i	−0.289906	+	0.502132i	0.683881	+	0.729594i	$0.260291\pi$
$180$		0			0
$181$	−11.7574			−0.873918			−0.436959	−	0.899482i	$-0.643944\pi$
$181$	−11.7574			−0.873918			−0.436959	+	0.899482i	$0.643944\pi$
$182$	−5.87868	+	0.804479i	−0.435757	+	0.0596319i
$183$		0			0
$184$	−1.24264			−0.0916087
$185$		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	−0.977702	−	0.209999i	$-0.932654\pi$
$191$	−4.24264	+	7.34847i	−0.306987	+	0.531717i	0.670715	+	0.741715i	$0.265987\pi$
$192$		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	$0.551952\pi$
$194$	−4.48528			−0.322024
$195$		0			0
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	16.9706			1.20910			0.604551	−	0.796566i	$-0.293352\pi$
$197$	16.9706			1.20910			0.604551	+	0.796566i	$0.293352\pi$
$198$		0			0
$199$	11.6213	−	20.1287i	0.823814	−	1.42689i	−0.0790091	−	0.996874i	$-0.525176\pi$
$199$	11.6213	−	20.1287i	0.823814	−	1.42689i	0.902823	−	0.430013i	$-0.141491\pi$
$200$	5.00000			0.353553
$201$		0			0
$202$	−8.12132	+	14.0665i	−0.571414	+	0.989718i
$203$	11.1213	−	1.52192i	0.780564	−	0.106818i
$204$		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
$209$	4.75736	+	8.23999i	0.329073	+	0.569972i
$210$		0			0
$211$	−5.24264	+	9.08052i	−0.360918	+	0.625129i	−0.988112	−	0.153734i	$-0.950870\pi$
$211$	−5.24264	+	9.08052i	−0.360918	+	0.625129i	0.627194	+	0.778863i	$0.284203\pi$
$212$	4.24264			0.291386
$213$		0			0
$214$	14.4853			0.990193
$215$		0			0
$216$		0			0
$217$	−24.2279	+	3.31552i	−1.64470	+	0.225072i
$218$	3.12132	+	5.40629i	0.211402	+	0.366160i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	6.86396	+	11.8887i	0.459645	+	0.796128i	0.998942	−	0.0459873i	$-0.0146434\pi$
$223$	6.86396	+	11.8887i	0.459645	+	0.796128i	−0.539297	+	0.842116i	$0.681310\pi$
$224$	2.62132	−	0.358719i	0.175144	−	0.0239680i
$225$		0			0
$226$	1.75736	+	3.04384i	0.116898	+	0.202473i
$227$	−9.51472			−0.631514			−0.315757	−	0.948840i	$-0.602258\pi$
$227$	−9.51472			−0.631514			−0.315757	+	0.948840i	$0.602258\pi$
$228$		0			0
$229$	−8.97056			−0.592791			−0.296396	−	0.955065i	$-0.595785\pi$
$229$	−8.97056			−0.592791			−0.296396	+	0.955065i	$0.595785\pi$
$230$		0			0
$231$		0			0
$232$	−2.12132	−	3.67423i	−0.139272	−	0.241225i
$233$	1.75736	+	3.04384i	0.115128	+	0.199408i	0.917831	−	0.396971i	$-0.129939\pi$
$233$	1.75736	+	3.04384i	0.115128	+	0.199408i	−0.802703	+	0.596379i	$0.796605\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.8640	+	18.8169i	−0.702731	+	1.21717i	0.264773	+	0.964311i	$0.414703\pi$
$239$	−10.8640	+	18.8169i	−0.702731	+	1.21717i	−0.967504	+	0.252855i	$0.918630\pi$
$240$		0			0
$241$	25.4853			1.64165			0.820826	−	0.571179i	$-0.193514\pi$
$241$	25.4853			1.64165			0.820826	+	0.571179i	$0.193514\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$		0			0
$244$	−2.24264			−0.143570
$245$		0			0
$246$		0			0
$247$	5.02944			0.320015
$248$	4.62132	+	8.00436i	0.293454	+	0.508277i
$249$		0			0
$250$		0			0
$251$	6.72792			0.424663			0.212331	−	0.977198i	$-0.431894\pi$
$251$	6.72792			0.424663			0.212331	+	0.977198i	$0.431894\pi$
$252$		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
$257$	11.4853			0.716432			0.358216	−	0.933639i	$-0.383385\pi$
$257$	11.4853			0.716432			0.358216	+	0.933639i	$0.383385\pi$
$258$		0			0
$259$	10.4853	−	1.43488i	0.651524	−	0.0891590i
$260$		0			0
$261$		0			0
$262$	8.12132	−	14.0665i	0.501737	−	0.869034i
$263$	10.9706			0.676474			0.338237	−	0.941061i	$-0.390169\pi$
$263$	10.9706			0.676474			0.338237	+	0.941061i	$0.390169\pi$
$264$		0			0
$265$		0			0
$266$	2.24264	−	5.49333i	0.137505	−	0.336817i
$267$		0			0
$268$	−0.121320	+	0.210133i	−0.00741082	+	0.0128359i
$269$	11.4853	−	19.8931i	0.700270	−	1.21290i	−0.268102	−	0.963391i	$-0.586396\pi$
$269$	11.4853	−	19.8931i	0.700270	−	1.21290i	0.968372	−	0.249513i	$-0.0802704\pi$
$270$		0			0
$271$	−2.24264	−	3.88437i	−0.136231	−	0.235959i	0.789836	−	0.613318i	$-0.210166\pi$
$271$	−2.24264	−	3.88437i	−0.136231	−	0.235959i	−0.926067	+	0.377359i	$0.876832\pi$
$272$		0			0
$273$		0			0
$274$	−6.98528	+	12.0989i	−0.421996	+	0.730919i
$275$	−21.2132			−1.27920
$276$		0			0
$277$	23.2132			1.39475			0.697373	−	0.716708i	$-0.254352\pi$
$277$	23.2132			1.39475			0.697373	+	0.716708i	$0.254352\pi$
$278$	10.3640	+	17.9509i	0.621589	+	1.07662i
$279$		0			0
$280$		0			0
$281$	−14.2279	−	24.6435i	−0.848767	−	1.47011i	−0.882309	−	0.470670i	$-0.844012\pi$
$281$	−14.2279	−	24.6435i	−0.848767	−	1.47011i	0.0335428	−	0.999437i	$-0.489321\pi$
$282$		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
$286$	−4.75736	−	8.23999i	−0.281309	−	0.487241i
$287$	−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
$292$	−7.00000			−0.409644
$293$	11.4853	−	19.8931i	0.670977	−	1.16217i	−0.306650	−	0.951822i	$-0.599208\pi$
$293$	11.4853	−	19.8931i	0.670977	−	1.16217i	0.977627	−	0.210344i	$-0.0674585\pi$
$294$		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
$301$	−27.4853	+	3.76127i	−1.58423	+	0.216796i
$302$	−5.62132	+	9.73641i	−0.323471	+	0.560268i
$303$		0			0
$304$	−2.24264			−0.128624
$305$		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	$0.794649\pi$
$308$	−11.1213	+	1.52192i	−0.633696	+	0.0867193i
$309$		0			0
$310$		0			0
$311$	11.4853	+	19.8931i	0.651271	+	1.12803i	0.982815	+	0.184594i	$0.0590970\pi$
$311$	11.4853	+	19.8931i	0.651271	+	1.12803i	−0.331544	+	0.943440i	$0.607570\pi$
$312$		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	−0.523059	−	0.852296i	$-0.675209\pi$
$317$	8.48528	−	14.6969i	0.476581	−	0.825462i	0.999640	+	0.0268342i	$0.00854260\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$		0			0
$322$	−2.01472	−	2.59808i	−0.112276	−	0.144785i
$323$		0			0
$324$		0			0
$325$	−5.60660	+	9.71092i	−0.310998	+	0.538665i
$326$	20.2426			1.12114
$327$		0			0
$328$	−5.74264	+	9.94655i	−0.317084	+	0.549206i
$329$	−7.71320	−	9.94655i	−0.425243	−	0.548371i
$330$		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
$337$	6.24264	−	10.8126i	0.340058	−	0.588998i	−0.644385	−	0.764701i	$-0.722887\pi$
$337$	6.24264	−	10.8126i	0.340058	−	0.588998i	0.984443	+	0.175703i	$0.0562199\pi$
$338$	7.97056			0.433541
$339$		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
$344$	5.24264	+	9.08052i	0.282664	+	0.489589i
$345$		0			0
$346$	−11.4853	−	19.8931i	−0.617453	−	1.06946i
$347$	9.36396	+	16.2189i	0.502684	+	0.870674i	0.999995	+	0.00310172i	$0.000987311\pi$
$347$	9.36396	+	16.2189i	0.502684	+	0.870674i	−0.497311	+	0.867572i	$0.665679\pi$
$348$		0			0
$349$	4.48528	+	7.76874i	0.240092	+	0.415851i	0.960740	−	0.277450i	$-0.0894892\pi$
$349$	4.48528	+	7.76874i	0.240092	+	0.415851i	−0.720649	+	0.693301i	$0.756156\pi$
$350$	8.10660	+	10.4539i	0.433316	+	0.558782i
$351$		0			0
$352$	2.12132	+	3.67423i	0.113067	+	0.195837i
$353$	−21.0000			−1.11772			−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$		0			0
$355$		0			0
$356$	5.74264	−	9.94655i	0.304359	−	0.527166i
$357$		0			0
$358$	3.87868	+	6.71807i	0.204995	+	0.355061i
$359$	9.62132	+	16.6646i	0.507794	+	0.879525i	0.999959	+	0.00902308i	$0.00287218\pi$
$359$	9.62132	+	16.6646i	0.507794	+	0.879525i	−0.492165	+	0.870502i	$0.663794\pi$
$360$		0			0
$361$	6.98528	−	12.0989i	0.367646	−	0.636782i
$362$	−5.87868	+	10.1822i	−0.308977	+	0.535163i
$363$		0			0
$364$	−2.24264	+	5.49333i	−0.117546	+	0.287928i
$365$		0			0
$366$		0			0
$367$	−13.7279			−0.716592			−0.358296	−	0.933608i	$-0.616642\pi$
$367$	−13.7279			−0.716592			−0.358296	+	0.933608i	$0.616642\pi$
$368$	−0.621320	+	1.07616i	−0.0323886	+	0.0560986i
$369$		0			0
$370$		0			0
$371$	6.87868	+	8.87039i	0.357123	+	0.460528i
$372$		0			0
$373$	35.2132			1.82327			0.911635	−	0.411000i	$-0.134820\pi$
$373$	35.2132			1.82327			0.911635	+	0.411000i	$0.134820\pi$
$374$		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
$383$	−18.2132			−0.930651			−0.465326	−	0.885140i	$-0.654063\pi$
$383$	−18.2132			−0.930651			−0.465326	+	0.885140i	$0.654063\pi$
$384$		0			0
$385$		0			0
$386$	21.4853			1.09357
$387$		0			0
$388$	−2.24264	+	3.88437i	−0.113853	+	0.197199i
$389$	−1.75736			−0.0891017			−0.0445508	−	0.999007i	$-0.514186\pi$
$389$	−1.75736			−0.0891017			−0.0445508	+	0.999007i	$0.514186\pi$
$390$		0			0
$391$		0			0
$392$	5.00000	+	4.89898i	0.252538	+	0.247436i
$393$		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	0.974995	−	0.222228i	$-0.0713329\pi$
$397$	5.87868	+	10.1822i	0.295042	+	0.511029i	−0.679952	+	0.733256i	$0.738000\pi$
$398$	−11.6213	−	20.1287i	−0.582524	−	1.00896i
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	−12.5147			−0.624955			−0.312478	−	0.949925i	$-0.601159\pi$
$401$	−12.5147			−0.624955			−0.312478	+	0.949925i	$0.601159\pi$
$402$		0			0
$403$	−20.7279			−1.03253
$404$	8.12132	+	14.0665i	0.404051	+	0.699836i
$405$		0			0
$406$	4.24264	−	10.3923i	0.210559	−	0.515761i
$407$	8.48528	+	14.6969i	0.420600	+	0.728500i
$408$		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
$412$	−4.62132	−	8.00436i	−0.227676	−	0.394347i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	2.24264			0.109955
$417$		0			0
$418$	9.51472			0.465380
$419$	−8.12132	+	14.0665i	−0.396752	+	0.687195i	−0.993323	−	0.115365i	$-0.963196\pi$
$419$	−8.12132	+	14.0665i	−0.396752	+	0.687195i	0.596571	+	0.802561i	$0.296530\pi$
$420$		0			0
$421$	2.87868	+	4.98602i	0.140298	+	0.243004i	0.927609	−	0.373553i	$-0.121861\pi$
$421$	2.87868	+	4.98602i	0.140298	+	0.243004i	−0.787311	+	0.616557i	$0.788527\pi$
$422$	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
$427$	−3.63604	−	4.68885i	−0.175960	−	0.226909i
$428$	7.24264	−	12.5446i	0.350086	−	0.606367i
$429$		0			0
$430$		0			0
$431$	−14.3787	+	24.9046i	−0.692597	+	1.19961i	0.278388	+	0.960469i	$0.410200\pi$
$431$	−14.3787	+	24.9046i	−0.692597	+	1.19961i	−0.970984	+	0.239144i	$0.923133\pi$
$432$		0			0
$433$	−29.9706			−1.44029			−0.720147	−	0.693822i	$-0.755926\pi$
$433$	−29.9706			−1.44029			−0.720147	+	0.693822i	$0.755926\pi$
$434$	−9.24264	+	22.6398i	−0.443661	+	1.08674i
$435$		0			0
$436$	6.24264			0.298968
$437$	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	$-0.616725\pi$
$443$	13.2426	−	22.9369i	0.629177	−	1.08977i	0.987717	−	0.156252i	$-0.0499412\pi$
$444$		0			0
$445$		0			0
$446$	13.7279			0.650036
$447$		0			0
$448$	1.00000	−	2.44949i	0.0472456	−	0.115728i
$449$	−28.9706			−1.36721			−0.683603	−	0.729854i	$-0.739588\pi$
$449$	−28.9706			−1.36721			−0.683603	+	0.729854i	$0.739588\pi$
$450$		0			0
$451$	24.3640	−	42.1996i	1.14725	−	1.98710i
$452$	3.51472			0.165318
$453$		0			0
$454$	−4.75736	+	8.23999i	−0.223274	+	0.386722i
$455$		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
$461$	12.8787	+	22.3065i	0.599820	+	1.03892i	0.992847	+	0.119392i	$0.0380944\pi$
$461$	12.8787	+	22.3065i	0.599820	+	1.03892i	−0.393027	+	0.919527i	$0.628572\pi$
$462$		0			0
$463$	8.62132	−	14.9326i	0.400667	−	0.693975i	−0.593140	−	0.805100i	$-0.702112\pi$
$463$	8.62132	−	14.9326i	0.400667	−	0.693975i	0.993807	+	0.111124i	$0.0354452\pi$
$464$	−4.24264			−0.196960
$465$		0			0
$466$	3.51472			0.162816
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$		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
$475$	−5.60660	−	9.71092i	−0.257249	−	0.445568i
$476$		0			0
$477$		0			0
$478$	10.8640	+	18.8169i	0.496906	+	0.860666i
$479$	4.75736			0.217369			0.108685	−	0.994076i	$-0.465336\pi$
$479$	4.75736			0.217369			0.108685	+	0.994076i	$0.465336\pi$
$480$		0			0
$481$	8.97056			0.409022
$482$	12.7426	−	22.0709i	0.580411	−	1.00530i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$		0			0
$486$		0			0
$487$	5.62132	−	9.73641i	0.254726	−	0.441199i	−0.710095	−	0.704106i	$-0.751348\pi$
$487$	5.62132	−	9.73641i	0.254726	−	0.441199i	0.964821	+	0.262907i	$0.0846813\pi$
$488$	−1.12132	+	1.94218i	−0.0507598	+	0.0879185i
$489$		0			0
$490$		0			0
$491$	−9.36396	+	16.2189i	−0.422590	+	0.731947i	−0.996192	−	0.0871872i	$-0.972212\pi$
$491$	−9.36396	+	16.2189i	−0.422590	+	0.731947i	0.573602	+	0.819134i	$0.305546\pi$
$492$		0			0
$493$		0			0
$494$	2.51472	−	4.35562i	0.113143	−	0.195969i
$495$		0			0
$496$	9.24264			0.415007
$497$	−1.24264	+	3.04384i	−0.0557401	+	0.136535i
$498$		0			0
$499$	14.7279			0.659312			0.329656	−	0.944101i	$-0.393067\pi$
$499$	14.7279			0.659312			0.329656	+	0.944101i	$0.393067\pi$
$500$		0			0
$501$		0			0
$502$	3.36396	−	5.82655i	0.150141	−	0.260052i
$503$	−18.2132			−0.812087			−0.406043	−	0.913854i	$-0.633092\pi$
$503$	−18.2132			−0.812087			−0.406043	+	0.913854i	$0.633092\pi$
$504$		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
$509$	−16.2426			−0.719942			−0.359971	−	0.932963i	$-0.617213\pi$
$509$	−16.2426			−0.719942			−0.359971	+	0.932963i	$0.617213\pi$
$510$		0			0
$511$	−11.3492	−	14.6354i	−0.502061	−	0.647432i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	5.74264	−	9.94655i	0.253297	−	0.438723i
$515$		0			0
$516$		0			0
$517$	10.0919	−	17.4797i	0.443841	−	0.768754i
$518$	4.00000	−	9.79796i	0.175750	−	0.430498i
$519$		0			0
$520$		0			0
$521$	−17.2279	+	29.8396i	−0.754769	+	1.30730i	0.190720	+	0.981644i	$0.438918\pi$
$521$	−17.2279	+	29.8396i	−0.754769	+	1.30730i	−0.945489	+	0.325654i	$0.894416\pi$
$522$		0			0
$523$	5.87868	+	10.1822i	0.257057	+	0.445235i	0.965452	−	0.260581i	$-0.0839139\pi$
$523$	5.87868	+	10.1822i	0.257057	+	0.445235i	−0.708395	+	0.705816i	$0.750581\pi$
$524$	−8.12132	−	14.0665i	−0.354782	−	0.614500i
$525$		0			0
$526$	5.48528	−	9.50079i	0.239170	−	0.414254i
$527$		0			0
$528$		0			0
$529$	−21.4558			−0.932863
$530$		0			0
$531$		0			0
$532$	−3.63604	−	4.68885i	−0.157642	−	0.203287i
$533$	−12.8787	−	22.3065i	−0.557838	−	0.966203i
$534$		0			0
$535$		0			0
$536$	0.121320	+	0.210133i	0.00524024	+	0.00907636i
$537$		0			0
$538$	−11.4853	−	19.8931i	−0.495166	−	0.857652i
$539$	−21.2132	−	20.7846i	−0.913717	−	0.895257i
$540$		0			0
$541$	−9.48528	−	16.4290i	−0.407804	−	0.706337i	0.586839	−	0.809703i	$-0.300372\pi$
$541$	−9.48528	−	16.4290i	−0.407804	−	0.706337i	−0.994643	+	0.103366i	$0.967039\pi$
$542$	−4.48528			−0.192659
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−5.24264	−	9.08052i	−0.224159	−	0.388255i	0.731908	−	0.681404i	$-0.238630\pi$
$547$	−5.24264	−	9.08052i	−0.224159	−	0.388255i	−0.956067	+	0.293149i	$0.905297\pi$
$548$	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
$553$	1.22792	+	1.58346i	0.0522166	+	0.0673358i
$554$	11.6066	−	20.1032i	0.493117	−	0.854104i
$555$		0			0
$556$	20.7279			0.879060
$557$	−3.51472	+	6.08767i	−0.148923	+	0.257943i	−0.930830	−	0.365453i	$-0.880914\pi$
$557$	−3.51472	+	6.08767i	−0.148923	+	0.257943i	0.781906	+	0.623396i	$0.214247\pi$
$558$		0			0
$559$	−23.5147			−0.994567
$560$		0			0
$561$		0			0
$562$	−28.4558			−1.20034
$563$	−3.36396	−	5.82655i	−0.141774	−	0.245560i	0.786391	−	0.617729i	$-0.211947\pi$
$563$	−3.36396	−	5.82655i	−0.141774	−	0.245560i	−0.928165	+	0.372170i	$0.878614\pi$
$564$		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	$0.523168\pi$
$569$	−21.4706	+	37.1881i	−0.900093	+	1.55901i	−0.827372	+	0.561654i	$0.810165\pi$
$570$		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	$0.920820\pi$
$572$	−9.51472			−0.397830
$573$		0			0
$574$	−30.1066	+	4.11999i	−1.25663	+	0.171965i
$575$	−6.21320			−0.259108
$576$		0			0
$577$	15.9706	−	27.6618i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$577$	15.9706	−	27.6618i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648435\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$		0			0
$581$	42.5772	−	5.82655i	1.76640	−	0.241726i
$582$		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
$587$	19.6066	+	33.9596i	0.809251	+	1.40166i	0.913383	+	0.407100i	$0.133460\pi$
$587$	19.6066	+	33.9596i	0.809251	+	1.40166i	−0.104132	+	0.994563i	$0.533207\pi$
$588$		0			0
$589$	10.3640	−	17.9509i	0.427040	−	0.739654i
$590$		0			0
$591$		0			0
$592$	−4.00000			−0.164399
$593$	5.74264	+	9.94655i	0.235822	+	0.408456i	0.959511	−	0.281670i	$-0.0908884\pi$
$593$	5.74264	+	9.94655i	0.235822	+	0.408456i	−0.723689	+	0.690126i	$0.757555\pi$
$594$		0			0
$595$		0			0
$596$	3.87868	+	6.71807i	0.158877	+	0.275183i
$597$		0			0
$598$	−1.39340	−	2.41344i	−0.0569803	−	0.0986928i
$599$	−5.48528	−	9.50079i	−0.224123	−	0.388192i	0.731933	−	0.681376i	$-0.238618\pi$
$599$	−5.48528	−	9.50079i	−0.224123	−	0.388192i	−0.956056	+	0.293185i	$0.905285\pi$
$600$		0			0
$601$	−7.98528	−	13.8309i	−0.325726	−	0.564175i	0.655933	−	0.754819i	$-0.272276\pi$
$601$	−7.98528	−	13.8309i	−0.325726	−	0.564175i	−0.981659	+	0.190645i	$0.938942\pi$
$602$	−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
$607$	−5.02944			−0.204139			−0.102069	−	0.994777i	$-0.532546\pi$
$607$	−5.02944			−0.204139			−0.102069	+	0.994777i	$0.532546\pi$
$608$	−1.12132	+	1.94218i	−0.0454755	+	0.0787660i
$609$		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	0.387451	+	0.921891i	$0.373356\pi$
$613$	−14.9706	+	25.9298i	−0.604655	+	1.04729i	−0.992106	+	0.125403i	$0.959978\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$		0			0
$616$	−4.24264	+	10.3923i	−0.170941	+	0.418718i
$617$	11.2279	−	19.4473i	0.452019	−	0.782920i	−0.546492	−	0.837464i	$-0.684037\pi$
$617$	11.2279	−	19.4473i	0.452019	−	0.782920i	0.998511	+	0.0545441i	$0.0173705\pi$
$618$		0			0
$619$	−18.4853			−0.742986			−0.371493	−	0.928436i	$-0.621154\pi$
$619$	−18.4853			−0.742986			−0.371493	+	0.928436i	$0.621154\pi$
$620$		0			0
$621$		0			0
$622$	22.9706			0.921036
$623$	30.1066	−	4.11999i	1.20620	−	0.165064i
$624$		0			0
$625$	25.0000			1.00000
$626$	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
$637$	−15.1213	+	4.21759i	−0.599129	+	0.167107i
$638$	18.0000			0.712627
$639$		0			0
$640$		0			0
$641$	−46.4558			−1.83490			−0.917448	−	0.397856i	$-0.869754\pi$
$641$	−46.4558			−1.83490			−0.917448	+	0.397856i	$0.869754\pi$
$642$		0			0
$643$	10.6360	−	18.4222i	0.419444	−	0.726499i	−0.576439	−	0.817140i	$-0.695558\pi$
$643$	10.6360	−	18.4222i	0.419444	−	0.726499i	0.995884	+	0.0906410i	$0.0288916\pi$
$644$	−3.25736	+	0.445759i	−0.128358	+	0.0175654i
$645$		0			0
$646$		0			0
$647$	13.8640	−	24.0131i	0.545049	−	0.944052i	−0.453555	−	0.891228i	$-0.649845\pi$
$647$	13.8640	−	24.0131i	0.545049	−	0.944052i	0.998604	−	0.0528236i	$-0.0168221\pi$
$648$		0			0
$649$		0			0
$650$	5.60660	+	9.71092i	0.219909	+	0.380894i
$651$		0			0
$652$	10.1213	−	17.5306i	0.396381	−	0.686553i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		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
$659$	1.60660	+	2.78272i	0.0625843	+	0.108399i	0.895620	−	0.444820i	$-0.146732\pi$
$659$	1.60660	+	2.78272i	0.0625843	+	0.108399i	−0.833036	+	0.553219i	$0.813399\pi$
$660$		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
$664$	−8.12132	−	14.0665i	−0.315168	−	0.545888i
$665$		0			0
$666$		0			0
$667$	2.63604	+	4.56575i	0.102068	+	0.176787i
$668$	18.2132			0.704690
$669$		0			0
$670$		0			0
$671$	4.75736	−	8.23999i	0.183656	−	0.318101i
$672$		0			0
$673$	5.25736	+	9.10601i	0.202656	+	0.351011i	0.949383	−	0.314119i	$-0.101709\pi$
$673$	5.25736	+	9.10601i	0.202656	+	0.351011i	−0.746727	+	0.665130i	$0.768376\pi$
$674$	−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	−0.505015	−	0.863110i	$-0.668513\pi$
$677$	12.8787	−	22.3065i	0.494968	−	0.857309i	0.999983	+	0.00580089i	$0.00184649\pi$
$678$		0			0
$679$	−11.7574	+	1.60896i	−0.451206	+	0.0617461i
$680$		0			0
$681$		0			0
$682$	−39.2132			−1.50155
$683$	−8.84924	+	15.3273i	−0.338607	+	0.586484i	−0.984171	−	0.177222i	$-0.943289\pi$
$683$	−8.84924	+	15.3273i	−0.338607	+	0.586484i	0.645564	+	0.763706i	$0.276622\pi$
$684$		0			0
$685$		0			0
$686$	−2.13604	+	18.3967i	−0.0815543	+	0.702388i
$687$		0			0
$688$	10.4853			0.399748
$689$	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
$698$	8.97056			0.339541
$699$		0			0
$700$	13.1066	−	1.79360i	0.495383	−	0.0677916i
$701$	−22.2426			−0.840093			−0.420046	−	0.907503i	$-0.637986\pi$
$701$	−22.2426			−0.840093			−0.420046	+	0.907503i	$0.637986\pi$
$702$		0			0
$703$	−4.48528	+	7.76874i	−0.169166	+	0.293003i
$704$	4.24264			0.159901
$705$		0			0
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	−16.2426	+	39.7862i	−0.610867	+	1.49631i
$708$		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
$713$	−5.74264	−	9.94655i	−0.215064	−	0.372501i
$714$		0			0
$715$		0			0
$716$	7.75736			0.289906
$717$		0			0
$718$	19.2426			0.718129
$719$	−13.8640	−	24.0131i	−0.517039	−	0.895537i	−0.999804	−	0.0197874i	$-0.993701\pi$
$719$	−13.8640	−	24.0131i	−0.517039	−	0.895537i	0.482766	−	0.875750i	$-0.339632\pi$
$720$		0			0
$721$	9.24264	−	22.6398i	0.344214	−	0.843148i
$722$	−6.98528	−	12.0989i	−0.259965	−	0.450273i
$723$		0			0
$724$	5.87868	+	10.1822i	0.218479	+	0.378417i
$725$	−10.6066	−	18.3712i	−0.393919	−	0.682288i
$726$		0			0
$727$	0.136039	+	0.235626i	0.00504541	+	0.00873890i	0.868537	−	0.495624i	$-0.165061\pi$
$727$	0.136039	+	0.235626i	0.00504541	+	0.00873890i	−0.863492	+	0.504363i	$0.831727\pi$
$728$	3.63604	+	4.68885i	0.134761	+	0.173780i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−5.02944			−0.185767			−0.0928833	−	0.995677i	$-0.529608\pi$
$733$	−5.02944			−0.185767			−0.0928833	+	0.995677i	$0.529608\pi$
$734$	−6.86396	+	11.8887i	−0.253353	+	0.438821i
$735$		0			0
$736$	0.621320	+	1.07616i	0.0229022	+	0.0396677i
$737$	−0.514719	−	0.891519i	−0.0189599	−	0.0328395i
$738$		0			0
$739$	3.24264	−	5.61642i	0.119282	−	0.206603i	−0.800201	−	0.599732i	$-0.795274\pi$
$739$	3.24264	−	5.61642i	0.119282	−	0.206603i	0.919484	+	0.393129i	$0.128607\pi$
$740$		0			0
$741$		0			0
$742$	11.1213	−	1.52192i	0.408277	−	0.0558714i
$743$	21.6213	−	37.4492i	0.793209	−	1.37388i	−0.130761	−	0.991414i	$-0.541742\pi$
$743$	21.6213	−	37.4492i	0.793209	−	1.37388i	0.923970	−	0.382465i	$-0.124925\pi$
$744$		0			0
$745$		0			0
$746$	17.6066	−	30.4955i	0.644623	−	1.11652i
$747$		0			0
$748$		0			0
$749$	37.9706	−	5.19615i	1.38741	−	0.189863i
$750$		0			0
$751$	−8.75736			−0.319561			−0.159780	−	0.987153i	$-0.551079\pi$
$751$	−8.75736			−0.319561			−0.159780	+	0.987153i	$0.551079\pi$
$752$	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
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$		0			0
$763$	10.1213	+	13.0519i	0.366416	+	0.472512i
$764$	8.48528			0.306987
$765$		0			0
$766$	−9.10660	+	15.7731i	−0.329035	+	0.569905i
$767$		0			0
$768$		0			0
$769$	−2.24264	+	3.88437i	−0.0808717	+	0.140074i	−0.903625	−	0.428325i	$-0.859104\pi$
$769$	−2.24264	+	3.88437i	−0.0808717	+	0.140074i	0.822753	+	0.568399i	$0.192437\pi$
$770$		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	$-0.849293\pi$
$773$	−1.39340	+	2.41344i	−0.0501171	+	0.0868053i	0.839879	+	0.542774i	$0.182626\pi$
$774$		0			0
$775$	23.1066	+	40.0218i	0.830014	+	1.43763i
$776$	2.24264	+	3.88437i	0.0805061	+	0.139441i
$777$		0			0
$778$	−0.878680	+	1.52192i	−0.0315022	+	0.0545634i
$779$	25.7574			0.922853
$780$		0			0
$781$	−5.27208			−0.188650
$782$		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
$794$	11.7574			0.417253
$795$		0			0
$796$	−23.2426			−0.823814
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		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
$806$	−10.3640	+	17.9509i	−0.365055	+	0.632294i
$807$		0			0
$808$	16.2426			0.571414
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	27.4558			0.964105			0.482053	−	0.876142i	$-0.339891\pi$
$811$	27.4558			0.964105			0.482053	+	0.876142i	$0.339891\pi$
$812$	−6.87868	−	8.87039i	−0.241394	−	0.311290i
$813$		0			0
$814$	16.9706			0.594818
$815$		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	$-0.553084\pi$
$821$	22.0919	−	38.2643i	0.771012	−	1.33543i	0.937009	−	0.349306i	$-0.113583\pi$
$822$		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	$0.727668\pi$
$824$	−9.24264			−0.321983
$825$		0			0
$826$		0			0
$827$	16.9706			0.590124			0.295062	−	0.955478i	$-0.404660\pi$
$827$	16.9706			0.590124			0.295062	+	0.955478i	$0.404660\pi$
$828$		0			0
$829$	−8.97056	+	15.5375i	−0.311561	+	0.539639i	−0.978700	−	0.205294i	$-0.934185\pi$
$829$	−8.97056	+	15.5375i	−0.311561	+	0.539639i	0.667140	+	0.744932i	$0.267518\pi$
$830$		0			0
$831$		0			0
$832$	1.12132	−	1.94218i	0.0388748	−	0.0673331i
$833$		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
$839$	16.2426	+	28.1331i	0.560758	+	0.971262i	0.997430	+	0.0716411i	$0.0228236\pi$
$839$	16.2426	+	28.1331i	0.560758	+	0.971262i	−0.436672	+	0.899621i	$0.643843\pi$
$840$		0			0
$841$	5.50000	−	9.52628i	0.189655	−	0.328492i
$842$	5.75736			0.198412
$843$		0			0
$844$	10.4853			0.360918
$845$		0			0
$846$		0			0
$847$	7.00000	−	17.1464i	0.240523	−	0.589158i
$848$	−2.12132	−	3.67423i	−0.0728464	−	0.126174i
$849$		0			0
$850$		0			0
$851$	2.48528	+	4.30463i	0.0851943	+	0.147561i
$852$		0			0
$853$	24.0919	+	41.7284i	0.824890	+	1.42875i	0.902003	+	0.431730i	$0.142097\pi$
$853$	24.0919	+	41.7284i	0.824890	+	1.42875i	−0.0771127	+	0.997022i	$0.524570\pi$
$854$	−5.87868	+	0.804479i	−0.201164	+	0.0275287i
$855$		0			0
$856$	−7.24264	−	12.5446i	−0.247548	−	0.428766i
$857$	−11.4853			−0.392330			−0.196165	−	0.980571i	$-0.562849\pi$
$857$	−11.4853			−0.392330			−0.196165	+	0.980571i	$0.562849\pi$
$858$		0			0
$859$	−15.6985			−0.535625			−0.267813	−	0.963471i	$-0.586301\pi$
$859$	−15.6985			−0.535625			−0.267813	+	0.963471i	$0.586301\pi$
$860$		0			0
$861$		0			0
$862$	14.3787	+	24.9046i	0.489740	+	0.848254i
$863$	21.1066	+	36.5577i	0.718477	+	1.24444i	0.961603	+	0.274444i	$0.0884938\pi$
$863$	21.1066	+	36.5577i	0.718477	+	1.24444i	−0.243126	+	0.969995i	$0.578173\pi$
$864$		0			0
$865$		0			0
$866$	−14.9853	+	25.9553i	−0.509221	+	0.881996i
$867$		0			0
$868$	14.9853	+	19.3242i	0.508634	+	0.655907i
$869$	−1.60660	+	2.78272i	−0.0545002	+	0.0943972i
$870$		0			0
$871$	−0.544156			−0.0184380
$872$	3.12132	−	5.40629i	0.105701	−	0.183080i
$873$		0			0
$874$	2.78680			0.0942648
$875$		0			0
$876$		0			0
$877$	−33.6985			−1.13792			−0.568958	−	0.822366i	$-0.692653\pi$
$877$	−33.6985			−1.13792			−0.568958	+	0.822366i	$0.692653\pi$
$878$	−6.86396	−	11.8887i	−0.231647	−	0.401225i
$879$		0			0
$880$		0			0
$881$	53.4853			1.80196			0.900982	−	0.433856i	$-0.142847\pi$
$881$	53.4853			1.80196			0.900982	+	0.433856i	$0.142847\pi$
$882$		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
$887$	−14.2721			−0.479209			−0.239605	−	0.970871i	$-0.577018\pi$
$887$	−14.2721			−0.479209			−0.239605	+	0.970871i	$0.577018\pi$
$888$		0			0
$889$	15.2426	−	37.3367i	0.511222	−	1.25223i
$890$		0			0
$891$		0			0
$892$	6.86396	−	11.8887i	0.229822	−	0.398064i
$893$	10.6690			0.357026
$894$		0			0
$895$		0			0
$896$	−1.62132	−	2.09077i	−0.0541645	−	0.0698477i
$897$		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
$902$	−24.3640	−	42.1996i	−0.811231	−	1.40509i
$903$		0			0
$904$	1.75736	−	3.04384i	0.0584489	−	0.101236i
$905$		0			0
$906$		0			0
$907$	29.9411			0.994179			0.497089	−	0.867699i	$-0.334402\pi$
$907$	29.9411			0.994179			0.497089	+	0.867699i	$0.334402\pi$
$908$	4.75736	+	8.23999i	0.157879	+	0.273454i
$909$		0			0
$910$		0			0
$911$	−19.8640	−	34.4054i	−0.658122	−	1.13990i	−0.981101	−	0.193495i	$-0.938018\pi$
$911$	−19.8640	−	34.4054i	−0.658122	−	1.13990i	0.322979	−	0.946406i	$-0.395316\pi$
$912$		0			0
$913$	34.4558	+	59.6793i	1.14032	+	1.97510i
$914$	14.2426	+	24.6690i	0.471105	+	0.815977i
$915$		0			0
$916$	4.48528	+	7.76874i	0.148198	+	0.256686i
$917$	16.2426	−	39.7862i	0.536379	−	1.31386i
$918$		0			0
$919$	8.72792	+	15.1172i	0.287908	+	0.498671i	0.973310	−	0.229494i	$-0.0737071\pi$
$919$	8.72792	+	15.1172i	0.287908	+	0.498671i	−0.685403	+	0.728164i	$0.740374\pi$
$920$		0			0
$921$		0			0
$922$	25.7574			0.848273
$923$	−1.39340	+	2.41344i	−0.0458643	+	0.0794392i
$924$		0			0
$925$	−10.0000	−	17.3205i	−0.328798	−	0.569495i
$926$	−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	$0.423128\pi$
$929$	−21.9853	+	38.0796i	−0.721314	+	1.24935i	−0.960473	+	0.278372i	$0.910205\pi$
$930$		0			0
$931$	3.90812	−	15.2042i	0.128083	−	0.498299i
$932$	1.75736	−	3.04384i	0.0575642	−	0.0997042i
$933$		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	$0.608443\pi$
$938$	−0.242641	+	0.594346i	−0.00792250	+	0.0194061i
$939$		0			0
$940$		0			0
$941$	26.3345	+	45.6127i	0.858481	+	1.48693i	0.873378	+	0.487044i	$0.161925\pi$
$941$	26.3345	+	45.6127i	0.858481	+	1.48693i	−0.0148967	+	0.999889i	$0.504742\pi$
$942$		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	$0.381691\pi$
$947$	−19.2426	+	33.3292i	−0.625302	+	1.08305i	−0.988482	+	0.151336i	$0.951643\pi$
$948$		0			0
$949$	−7.84924	−	13.5953i	−0.254797	−	0.441322i
$950$	−11.2132			−0.363804
$951$		0			0
$952$		0			0
$953$	23.4853			0.760763			0.380381	−	0.924830i	$-0.375793\pi$
$953$	23.4853			0.760763			0.380381	+	0.924830i	$0.375793\pi$
$954$		0			0
$955$		0			0
$956$	21.7279			0.702731
$957$		0			0
$958$	2.37868	−	4.11999i	0.0768517	−	0.133111i
$959$	−13.9706	+	34.2208i	−0.451133	+	1.10505i
$960$		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
$967$	−26.3492	+	45.6382i	−0.847335	+	1.46763i	0.0362438	+	0.999343i	$0.488461\pi$
$967$	−26.3492	+	45.6382i	−0.847335	+	1.46763i	−0.883578	+	0.468283i	$0.844873\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$		0			0
$971$	−4.75736	−	8.23999i	−0.152671	−	0.264434i	0.779538	−	0.626355i	$-0.215454\pi$
$971$	−4.75736	−	8.23999i	−0.152671	−	0.264434i	−0.932209	+	0.361922i	$0.882121\pi$
$972$		0			0
$973$	33.6066	+	43.3373i	1.07738	+	1.38933i
$974$	−5.62132	−	9.73641i	−0.180119	−	0.311975i
$975$		0			0
$976$	1.12132	+	1.94218i	0.0358926	+	0.0621678i
$977$	9.98528	+	17.2950i	0.319457	+	0.553317i	0.980375	−	0.197142i	$-0.0631660\pi$
$977$	9.98528	+	17.2950i	0.319457	+	0.553317i	−0.660917	+	0.750459i	$0.729833\pi$
$978$		0			0
$979$	24.3640	+	42.1996i	0.778676	+	1.34871i
$980$		0			0
$981$		0			0
$982$	9.36396	+	16.2189i	0.298816	+	0.517565i
$983$	32.4853			1.03612			0.518060	−	0.855344i	$-0.326654\pi$
$983$	32.4853			1.03612			0.518060	+	0.855344i	$0.326654\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−2.51472	−	4.35562i	−0.0800039	−	0.138571i
$989$	−6.51472	−	11.2838i	−0.207156	−	0.358805i
$990$		0			0
$991$	−3.89340	+	6.74356i	−0.123678	+	0.214216i	−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−3.89340	+	6.74356i	−0.123678	+	0.214216i	0.797537	+	0.603269i	$0.206136\pi$
$992$	4.62132	−	8.00436i	0.146727	−	0.254139i
$993$		0			0
$994$	2.01472	+	2.59808i	0.0639030	+	0.0824060i
$995$		0			0
$996$		0			0
$997$	14.0000			0.443384			0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000			0.443384			0.221692	+	0.975117i	$0.428842\pi$
$998$	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.h.s.109.1		4
3.2	odd	2		1134.2.h.r.109.1		4
7.2	even	3		1134.2.e.r.919.1		4
9.2	odd	6		1134.2.e.s.865.1		4
9.4	even	3		1134.2.g.j.487.2	yes	4
9.5	odd	6		1134.2.g.i.487.2	yes	4
9.7	even	3		1134.2.e.r.865.1		4
21.2	odd	6		1134.2.e.s.919.1		4
63.2	odd	6		1134.2.h.r.541.2		4
63.4	even	3		7938.2.a.bk.1.2		2
63.16	even	3	inner	1134.2.h.s.541.2		4
63.23	odd	6		1134.2.g.i.163.2	✓	4
63.31	odd	6		7938.2.a.bj.1.2		2
63.32	odd	6		7938.2.a.bq.1.1		2
63.58	even	3		1134.2.g.j.163.2	yes	4
63.59	even	6		7938.2.a.bp.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.r.865.1		4	9.7	even	3
1134.2.e.r.919.1		4	7.2	even	3
1134.2.e.s.865.1		4	9.2	odd	6
1134.2.e.s.919.1		4	21.2	odd	6
1134.2.g.i.163.2	✓	4	63.23	odd	6
1134.2.g.i.487.2	yes	4	9.5	odd	6
1134.2.g.j.163.2	yes	4	63.58	even	3
1134.2.g.j.487.2	yes	4	9.4	even	3
1134.2.h.r.109.1		4	3.2	odd	2
1134.2.h.r.541.2		4	63.2	odd	6
1134.2.h.s.109.1		4	1.1	even	1	trivial
1134.2.h.s.541.2		4	63.16	even	3	inner
7938.2.a.bj.1.2		2	63.31	odd	6
7938.2.a.bk.1.2		2	63.4	even	3
7938.2.a.bp.1.1		2	63.59	even	6
7938.2.a.bq.1.1		2	63.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} +4.24264 q^{11} +(1.12132 - 1.94218i) q^{13} +(-1.62132 - 2.09077i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.12132 + 1.94218i) q^{19} +(2.12132 - 3.67423i) q^{22} +1.24264 q^{23} -5.00000 q^{25} +(-1.12132 - 1.94218i) q^{26} +(-2.62132 + 0.358719i) q^{28} +(2.12132 + 3.67423i) q^{29} +(-4.62132 - 8.00436i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{37} +2.24264 q^{38} +(5.74264 - 9.94655i) q^{41} +(-5.24264 - 9.08052i) q^{43} +(-2.12132 - 3.67423i) q^{44} +(0.621320 - 1.07616i) q^{46} +(2.37868 - 4.11999i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-2.50000 + 4.33013i) q^{50} -2.24264 q^{52} +(-2.12132 + 3.67423i) q^{53} +(-1.00000 + 2.44949i) q^{56} +4.24264 q^{58} +(1.12132 - 1.94218i) q^{61} -9.24264 q^{62} +1.00000 q^{64} +(-0.121320 - 0.210133i) q^{67} -1.24264 q^{71} +(3.50000 - 6.06218i) q^{73} +4.00000 q^{74} +(1.12132 - 1.94218i) q^{76} +(4.24264 - 10.3923i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-5.74264 - 9.94655i) q^{82} +(8.12132 + 14.0665i) q^{83} -10.4853 q^{86} -4.24264 q^{88} +(5.74264 + 9.94655i) q^{89} +(-3.63604 - 4.68885i) q^{91} +(-0.621320 - 1.07616i) q^{92} +(-2.37868 - 4.11999i) q^{94} +(-2.24264 - 3.88437i) q^{97} +(-6.74264 + 1.88064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{7} - 4 q^{8} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 4 q^{19} - 12 q^{23} - 20 q^{25} + 4 q^{26} - 2 q^{28} - 10 q^{31} + 2 q^{32} + 8 q^{37} - 8 q^{38} + 6 q^{41} - 4 q^{43} - 6 q^{46} + 18 q^{47} - 20 q^{49} - 10 q^{50} + 8 q^{52} - 4 q^{56} - 4 q^{61} - 20 q^{62} + 4 q^{64} + 8 q^{67} + 12 q^{71} + 14 q^{73} + 16 q^{74} - 4 q^{76} - 10 q^{79} - 6 q^{82} + 24 q^{83} - 8 q^{86} + 6 q^{89} - 40 q^{91} + 6 q^{92} - 18 q^{94} + 8 q^{97} - 10 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 - 4 * q^8 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 4 * q^19 - 12 * q^23 - 20 * q^25 + 4 * q^26 - 2 * q^28 - 10 * q^31 + 2 * q^32 + 8 * q^37 - 8 * q^38 + 6 * q^41 - 4 * q^43 - 6 * q^46 + 18 * q^47 - 20 * q^49 - 10 * q^50 + 8 * q^52 - 4 * q^56 - 4 * q^61 - 20 * q^62 + 4 * q^64 + 8 * q^67 + 12 * q^71 + 14 * q^73 + 16 * q^74 - 4 * q^76 - 10 * q^79 - 6 * q^82 + 24 * q^83 - 8 * q^86 + 6 * q^89 - 40 * q^91 + 6 * q^92 - 18 * q^94 + 8 * q^97 - 10 * q^98

Introduction

L-functions

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