LMFDB - Embedded newform 1134.2.e.r.919.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(865,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1134.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.e (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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1134.919
Dual form			1134.2.e.r.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +(-2.12132 + 3.67423i) q^{11} +(1.12132 - 1.94218i) q^{13} +(2.62132 + 0.358719i) q^{14} +1.00000 q^{16} +(1.12132 - 1.94218i) q^{19} +(2.12132 - 3.67423i) q^{22} +(-0.621320 - 1.07616i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-1.12132 + 1.94218i) q^{26} +(-2.62132 - 0.358719i) q^{28} +(2.12132 + 3.67423i) q^{29} +9.24264 q^{31} -1.00000 q^{32} +(2.00000 - 3.46410i) q^{37} +(-1.12132 + 1.94218i) q^{38} +(5.74264 - 9.94655i) q^{41} +(-5.24264 - 9.08052i) q^{43} +(-2.12132 + 3.67423i) q^{44} +(0.621320 + 1.07616i) q^{46} -4.75736 q^{47} +(6.74264 + 1.88064i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(1.12132 - 1.94218i) q^{52} +(-2.12132 - 3.67423i) q^{53} +(2.62132 + 0.358719i) q^{56} +(-2.12132 - 3.67423i) q^{58} -2.24264 q^{61} -9.24264 q^{62} +1.00000 q^{64} +0.242641 q^{67} -1.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(1.12132 - 1.94218i) q^{76} +(6.87868 - 8.87039i) q^{77} +0.757359 q^{79} +(-5.74264 + 9.94655i) q^{82} +(8.12132 + 14.0665i) q^{83} +(5.24264 + 9.08052i) q^{86} +(2.12132 - 3.67423i) q^{88} +(5.74264 - 9.94655i) q^{89} +(-3.63604 + 4.68885i) q^{91} +(-0.621320 - 1.07616i) q^{92} +4.75736 q^{94} +(-2.24264 - 3.88437i) q^{97} +(-6.74264 - 1.88064i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{19} + 6 q^{23} + 10 q^{25} + 4 q^{26} - 2 q^{28} + 20 q^{31} - 4 q^{32} + 8 q^{37} + 4 q^{38} + 6 q^{41} - 4 q^{43} - 6 q^{46} - 36 q^{47} + 10 q^{49} - 10 q^{50} - 4 q^{52} + 2 q^{56} + 8 q^{61} - 20 q^{62} + 4 q^{64} - 16 q^{67} + 12 q^{71} + 14 q^{73} - 8 q^{74} - 4 q^{76} + 36 q^{77} + 20 q^{79} - 6 q^{82} + 24 q^{83} + 4 q^{86} + 6 q^{89} - 40 q^{91} + 6 q^{92} + 36 q^{94} + 8 q^{97} - 10 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^19 + 6 * q^23 + 10 * q^25 + 4 * q^26 - 2 * q^28 + 20 * q^31 - 4 * q^32 + 8 * q^37 + 4 * q^38 + 6 * q^41 - 4 * q^43 - 6 * q^46 - 36 * q^47 + 10 * q^49 - 10 * q^50 - 4 * q^52 + 2 * q^56 + 8 * q^61 - 20 * q^62 + 4 * q^64 - 16 * q^67 + 12 * q^71 + 14 * q^73 - 8 * q^74 - 4 * q^76 + 36 * q^77 + 20 * q^79 - 6 * q^82 + 24 * q^83 + 4 * q^86 + 6 * q^89 - 40 * q^91 + 6 * q^92 + 36 * q^94 + 8 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	0.345918	+	0.938265i	$0.387568\pi$
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	−0.985520	+	0.169559i	$0.945766\pi$
$12$		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	$0.0660033\pi$
$14$	2.62132	+	0.358719i	0.700577	+	0.0958718i
$15$		0			0
$16$	1.00000			0.250000
$17$		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
$22$	2.12132	−	3.67423i	0.452267	−	0.783349i
$23$	−0.621320	−	1.07616i	−0.129554	−	0.224395i	0.793950	−	0.607983i	$-0.208021\pi$
$23$	−0.621320	−	1.07616i	−0.129554	−	0.224395i	−0.923504	+	0.383589i	$0.874688\pi$
$24$		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
$29$	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
$31$	9.24264			1.66003			0.830014	−	0.557743i	$-0.188333\pi$
$31$	9.24264			1.66003			0.830014	+	0.557743i	$0.188333\pi$
$32$	−1.00000			−0.176777
$33$		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
$41$	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
$47$	−4.75736			−0.693932			−0.346966	−	0.937878i	$-0.612788\pi$
$47$	−4.75736			−0.693932			−0.346966	+	0.937878i	$0.612788\pi$
$48$		0			0
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$	−2.50000	+	4.33013i	−0.353553	+	0.612372i
$51$		0			0
$52$	1.12132	−	1.94218i	0.155499	−	0.269332i
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	0.682752	−	0.730650i	$-0.260783\pi$
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	−0.974138	+	0.225955i	$0.927450\pi$
$54$		0			0
$55$		0			0
$56$	2.62132	+	0.358719i	0.350289	+	0.0479359i
$57$		0			0
$58$	−2.12132	−	3.67423i	−0.278543	−	0.482451i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	−2.24264			−0.287141			−0.143570	−	0.989640i	$-0.545858\pi$
$61$	−2.24264			−0.287141			−0.143570	+	0.989640i	$0.545858\pi$
$62$	−9.24264			−1.17382
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	0.242641			0.0296433			0.0148216	−	0.999890i	$-0.495282\pi$
$67$	0.242641			0.0296433			0.0148216	+	0.999890i	$0.495282\pi$
$68$		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	0.994850	−	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
$76$	1.12132	−	1.94218i	0.128624	−	0.222784i
$77$	6.87868	−	8.87039i	0.783898	−	1.01087i
$78$		0			0
$79$	0.757359			0.0852096			0.0426048	−	0.999092i	$-0.486434\pi$
$79$	0.757359			0.0852096			0.0426048	+	0.999092i	$0.486434\pi$
$80$		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
$86$	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	$-0.625017\pi$
$89$	5.74264	−	9.94655i	0.608719	−	1.05433i	0.991452	−	0.130473i	$-0.0416495\pi$
$90$		0			0
$91$	−3.63604	+	4.68885i	−0.381160	+	0.491525i
$92$	−0.621320	−	1.07616i	−0.0647771	−	0.112197i
$93$		0			0
$94$	4.75736			0.490684
$95$		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
$101$	8.12132	−	14.0665i	0.808102	−	1.39967i	−0.106076	−	0.994358i	$-0.533829\pi$
$101$	8.12132	−	14.0665i	0.808102	−	1.39967i	0.914177	−	0.405315i	$-0.132838\pi$
$102$		0			0
$103$	−4.62132	−	8.00436i	−0.455352	−	0.788693i	0.543356	−	0.839502i	$-0.317153\pi$
$103$	−4.62132	−	8.00436i	−0.455352	−	0.788693i	−0.998708	+	0.0508091i	$0.983820\pi$
$104$	−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	−0.268233	−	0.963354i	$-0.586440\pi$
$107$	7.24264	−	12.5446i	0.700173	−	1.21273i	0.968406	−	0.249380i	$-0.0802269\pi$
$108$		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
$112$	−2.62132	−	0.358719i	−0.247691	−	0.0338958i
$113$	−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
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	2.24264			0.203039
$123$		0			0
$124$	9.24264			0.830014
$125$		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	$0.263590\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$		0			0
$131$	−8.12132	−	14.0665i	−0.709563	−	1.22900i	−0.965019	−	0.262179i	$-0.915559\pi$
$131$	−8.12132	−	14.0665i	−0.709563	−	1.22900i	0.255456	−	0.966821i	$-0.417774\pi$
$132$		0			0
$133$	−3.63604	+	4.68885i	−0.315285	+	0.406575i
$134$	−0.242641			−0.0209610
$135$		0			0
$136$		0			0
$137$	6.98528	−	12.0989i	0.596793	−	1.03368i	−0.396498	−	0.918035i	$-0.629775\pi$
$137$	6.98528	−	12.0989i	0.596793	−	1.03368i	0.993291	−	0.115640i	$-0.0368919\pi$
$138$		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
$142$	1.24264			0.104280
$143$	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
$149$	3.87868	+	6.71807i	0.317754	+	0.550366i	0.980019	−	0.198904i	$-0.0637381\pi$
$149$	3.87868	+	6.71807i	0.317754	+	0.550366i	−0.662265	+	0.749270i	$0.730405\pi$
$150$		0			0
$151$	5.62132	−	9.73641i	0.457457	−	0.792338i	−0.541369	−	0.840785i	$-0.682094\pi$
$151$	5.62132	−	9.73641i	0.457457	−	0.792338i	0.998826	+	0.0484470i	$0.0154272\pi$
$152$	−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
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−0.757359			−0.0602523
$159$		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
$167$	−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
$173$	−22.9706			−1.74642			−0.873210	−	0.487345i	$-0.837966\pi$
$173$	−22.9706			−1.74642			−0.873210	+	0.487345i	$0.837966\pi$
$174$		0			0
$175$	−8.10660	+	10.4539i	−0.612801	+	0.790237i
$176$	−2.12132	+	3.67423i	−0.159901	+	0.276956i
$177$		0			0
$178$	−5.74264	+	9.94655i	−0.430429	+	0.745525i
$179$	−3.87868	−	6.71807i	−0.289906	−	0.502132i	0.683881	−	0.729594i	$-0.260291\pi$
$179$	−3.87868	−	6.71807i	−0.289906	−	0.502132i	−0.973787	+	0.227461i	$0.926957\pi$
$180$		0			0
$181$	−11.7574			−0.873918			−0.436959	−	0.899482i	$-0.643944\pi$
$181$	−11.7574			−0.873918			−0.436959	+	0.899482i	$0.643944\pi$
$182$	3.63604	−	4.68885i	0.269521	−	0.347560i
$183$		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
$191$	8.48528			0.613973			0.306987	−	0.951714i	$-0.400679\pi$
$191$	8.48528			0.613973			0.306987	+	0.951714i	$0.400679\pi$
$192$		0			0
$193$	−21.4853			−1.54654			−0.773272	−	0.634074i	$-0.781381\pi$
$193$	−21.4853			−1.54654			−0.773272	+	0.634074i	$0.781381\pi$
$194$	2.24264	+	3.88437i	0.161012	+	0.278881i
$195$		0			0
$196$	6.74264	+	1.88064i	0.481617	+	0.134331i
$197$	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	0.902823	+	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
$202$	−8.12132	+	14.0665i	−0.571414	+	0.989718i
$203$	−4.24264	−	10.3923i	−0.297775	−	0.729397i
$204$		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	$0.284203\pi$
$212$	−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
$218$	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
$227$	4.75736	−	8.23999i	0.315757	−	0.546907i	−0.663841	−	0.747874i	$-0.731075\pi$
$227$	4.75736	−	8.23999i	0.315757	−	0.546907i	0.979598	+	0.200966i	$0.0644082\pi$
$228$		0			0
$229$	4.48528	+	7.76874i	0.296396	+	0.513372i	0.975309	−	0.220846i	$-0.0708819\pi$
$229$	4.48528	+	7.76874i	0.296396	+	0.513372i	−0.678913	+	0.734219i	$0.737549\pi$
$230$		0			0
$231$		0			0
$232$	−2.12132	−	3.67423i	−0.139272	−	0.241225i
$233$	1.75736	−	3.04384i	0.115128	−	0.199408i	−0.802703	−	0.596379i	$-0.796605\pi$
$233$	1.75736	−	3.04384i	0.115128	−	0.199408i	0.917831	+	0.396971i	$0.129939\pi$
$234$		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
$241$	−12.7426	+	22.0709i	−0.820826	+	1.42171i	0.0842426	+	0.996445i	$0.473153\pi$
$241$	−12.7426	+	22.0709i	−0.820826	+	1.42171i	−0.905068	+	0.425266i	$0.860180\pi$
$242$	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
$248$	−9.24264			−0.586908
$249$		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
$254$	−15.2426			−0.956408
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.74264	−	9.94655i	−0.358216	−	0.620448i	0.629447	−	0.777044i	$-0.283282\pi$
$257$	−5.74264	−	9.94655i	−0.358216	−	0.620448i	−0.987663	+	0.156595i	$0.949948\pi$
$258$		0			0
$259$	−6.48528	+	8.36308i	−0.402976	+	0.519657i
$260$		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	$-0.943164\pi$
$263$	−5.48528	+	9.50079i	−0.338237	+	0.585844i	0.645864	+	0.763452i	$0.276497\pi$
$264$		0			0
$265$		0			0
$266$	3.63604	−	4.68885i	0.222940	−	0.287492i
$267$		0			0
$268$	0.242641			0.0148216
$269$	11.4853	+	19.8931i	0.700270	+	1.21290i	0.968372	+	0.249513i	$0.0802704\pi$
$269$	11.4853	+	19.8931i	0.700270	+	1.21290i	−0.268102	+	0.963391i	$0.586396\pi$
$270$		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
$274$	−6.98528	+	12.0989i	−0.421996	+	0.730919i
$275$	10.6066	+	18.3712i	0.639602	+	1.10782i
$276$		0			0
$277$	−11.6066	+	20.1032i	−0.697373	+	1.20789i	0.272001	+	0.962297i	$0.412315\pi$
$277$	−11.6066	+	20.1032i	−0.697373	+	1.20789i	−0.969374	+	0.245589i	$0.921019\pi$
$278$	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
$283$	−8.97056			−0.533245			−0.266622	−	0.963801i	$-0.585908\pi$
$283$	−8.97056			−0.533245			−0.266622	+	0.963801i	$0.585908\pi$
$284$	−1.24264			−0.0737372
$285$		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
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	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
$299$	−2.78680			−0.161165
$300$		0			0
$301$	10.4853	+	25.6836i	0.604362	+	1.48038i
$302$	−5.62132	+	9.73641i	−0.323471	+	0.560268i
$303$		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	$0.794649\pi$
$308$	6.87868	−	8.87039i	0.391949	−	0.505437i
$309$		0			0
$310$		0			0
$311$	−22.9706			−1.30254			−0.651271	−	0.758846i	$-0.725764\pi$
$311$	−22.9706			−1.30254			−0.651271	+	0.758846i	$0.725764\pi$
$312$		0			0
$313$	15.9706			0.902710			0.451355	−	0.892345i	$-0.350941\pi$
$313$	15.9706			0.902710			0.451355	+	0.892345i	$0.350941\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	0.757359			0.0426048
$317$	−16.9706			−0.953162			−0.476581	−	0.879131i	$-0.658124\pi$
$317$	−16.9706			−0.953162			−0.476581	+	0.879131i	$0.658124\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$		0			0
$321$		0			0
$322$	−1.24264	−	3.04384i	−0.0692497	−	0.169626i
$323$		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
$328$	−5.74264	+	9.94655i	−0.317084	+	0.549206i
$329$	12.4706	+	1.70656i	0.687524	+	0.0940856i
$330$		0			0
$331$	−1.51472			−0.0832565			−0.0416282	−	0.999133i	$-0.513255\pi$
$331$	−1.51472			−0.0832565			−0.0416282	+	0.999133i	$0.513255\pi$
$332$	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	$0.0562199\pi$
$338$	−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
$344$	5.24264	+	9.08052i	0.282664	+	0.489589i
$345$		0			0
$346$	22.9706			1.23491
$347$	−18.7279			−1.00537			−0.502684	−	0.864470i	$-0.667654\pi$
$347$	−18.7279			−1.00537			−0.502684	+	0.864470i	$0.667654\pi$
$348$		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
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$		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	−0.492165	−	0.870502i	$-0.663794\pi$
$359$	9.62132	−	16.6646i	0.507794	−	0.879525i	0.999959	−	0.00902308i	$-0.00287218\pi$
$360$		0			0
$361$	6.98528	+	12.0989i	0.367646	+	0.636782i
$362$	11.7574			0.617953
$363$		0			0
$364$	−3.63604	+	4.68885i	−0.190580	+	0.245762i
$365$		0			0
$366$		0			0
$367$	6.86396	−	11.8887i	0.358296	−	0.620587i	−0.629380	−	0.777097i	$-0.716691\pi$
$367$	6.86396	−	11.8887i	0.358296	−	0.620587i	0.987676	+	0.156511i	$0.0500246\pi$
$368$	−0.621320	−	1.07616i	−0.0323886	−	0.0560986i
$369$		0			0
$370$		0			0
$371$	4.24264	+	10.3923i	0.220267	+	0.539542i
$372$		0			0
$373$	−17.6066	−	30.4955i	−0.911635	−	1.57900i	−0.811754	−	0.583999i	$-0.801487\pi$
$373$	−17.6066	−	30.4955i	−0.911635	−	1.57900i	−0.0998811	−	0.994999i	$-0.531846\pi$
$374$		0			0
$375$		0			0
$376$	4.75736			0.245342
$377$	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
$382$	−8.48528			−0.434145
$383$	9.10660	+	15.7731i	0.465326	+	0.805968i	0.999216	−	0.0395860i	$-0.0126039\pi$
$383$	9.10660	+	15.7731i	0.465326	+	0.805968i	−0.533891	+	0.845554i	$0.679271\pi$
$384$		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	$-0.819148\pi$
$389$	0.878680	−	1.52192i	0.0445508	−	0.0771643i	0.887441	+	0.460921i	$0.152481\pi$
$390$		0			0
$391$		0			0
$392$	−6.74264	−	1.88064i	−0.340555	−	0.0949865i
$393$		0			0
$394$	−16.9706			−0.854965
$395$		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	$0.0713329\pi$
$398$	−11.6213	−	20.1287i	−0.582524	−	1.00896i
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	6.25736	+	10.8381i	0.312478	+	0.541227i	0.978898	−	0.204349i	$-0.0655077\pi$
$401$	6.25736	+	10.8381i	0.312478	+	0.541227i	−0.666420	+	0.745576i	$0.732174\pi$
$402$		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
$407$	8.48528	+	14.6969i	0.420600	+	0.728500i
$408$		0			0
$409$	35.0000			1.73064			0.865319	−	0.501221i	$-0.167116\pi$
$409$	35.0000			1.73064			0.865319	+	0.501221i	$0.167116\pi$
$410$		0			0
$411$		0			0
$412$	−4.62132	−	8.00436i	−0.227676	−	0.394347i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−1.12132	+	1.94218i	−0.0549773	+	0.0952234i
$417$		0			0
$418$	−4.75736	−	8.23999i	−0.232690	−	0.403031i
$419$	−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
$427$	5.87868	+	0.804479i	0.284489	+	0.0389315i
$428$	7.24264	−	12.5446i	0.350086	−	0.606367i
$429$		0			0
$430$		0			0
$431$	−14.3787	−	24.9046i	−0.692597	−	1.19961i	−0.970984	−	0.239144i	$-0.923133\pi$
$431$	−14.3787	−	24.9046i	−0.692597	−	1.19961i	0.278388	−	0.960469i	$-0.410200\pi$
$432$		0			0
$433$	−29.9706			−1.44029			−0.720147	−	0.693822i	$-0.755926\pi$
$433$	−29.9706			−1.44029			−0.720147	+	0.693822i	$0.755926\pi$
$434$	24.2279	+	3.31552i	1.16298	+	0.159150i
$435$		0			0
$436$	−3.12132	−	5.40629i	−0.149484	−	0.258914i
$437$	−2.78680			−0.133311
$438$		0			0
$439$	−13.7279			−0.655198			−0.327599	−	0.944817i	$-0.606239\pi$
$439$	−13.7279			−0.655198			−0.327599	+	0.944817i	$0.606239\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−26.4853			−1.25835			−0.629177	−	0.777262i	$-0.716608\pi$
$443$	−26.4853			−1.25835			−0.629177	+	0.777262i	$0.716608\pi$
$444$		0			0
$445$		0			0
$446$	−6.86396	−	11.8887i	−0.325018	−	0.562948i
$447$		0			0
$448$	−2.62132	−	0.358719i	−0.123846	−	0.0169479i
$449$	−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
$452$	−1.75736	+	3.04384i	−0.0826592	+	0.143170i
$453$		0			0
$454$	−4.75736	+	8.23999i	−0.223274	+	0.386722i
$455$		0			0
$456$		0			0
$457$	28.4853			1.33249			0.666243	−	0.745735i	$-0.267902\pi$
$457$	28.4853			1.33249			0.666243	+	0.745735i	$0.267902\pi$
$458$	−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	$0.0354452\pi$
$464$	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
$473$	44.4853			2.04544
$474$		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
$479$	−2.37868	+	4.11999i	−0.108685	+	0.188247i	−0.915238	−	0.402914i	$-0.867997\pi$
$479$	−2.37868	+	4.11999i	−0.108685	+	0.188247i	0.806553	+	0.591162i	$0.201331\pi$
$480$		0			0
$481$	−4.48528	−	7.76874i	−0.204511	−	0.354224i
$482$	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	0.964821	−	0.262907i	$-0.0846813\pi$
$487$	5.62132	+	9.73641i	0.254726	+	0.441199i	−0.710095	+	0.704106i	$0.751348\pi$
$488$	2.24264			0.101520
$489$		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
$497$	3.25736	+	0.445759i	0.146113	+	0.0199950i
$498$		0			0
$499$	−7.36396	−	12.7548i	−0.329656	−	0.570981i	0.652787	−	0.757541i	$-0.273599\pi$
$499$	−7.36396	−	12.7548i	−0.329656	−	0.570981i	−0.982444	+	0.186560i	$0.940266\pi$
$500$		0			0
$501$		0			0
$502$	−6.72792			−0.300282
$503$	−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
$506$	−5.27208			−0.234372
$507$		0			0
$508$	15.2426			0.676283
$509$	8.12132	+	14.0665i	0.359971	+	0.623488i	0.987956	−	0.154738i	$-0.0494532\pi$
$509$	8.12132	+	14.0665i	0.359971	+	0.623488i	−0.627984	+	0.778226i	$0.716120\pi$
$510$		0			0
$511$	−7.00000	−	17.1464i	−0.309662	−	0.758513i
$512$	−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
$518$	6.48528	−	8.36308i	0.284947	−	0.367453i
$519$		0			0
$520$		0			0
$521$	−17.2279	−	29.8396i	−0.754769	−	1.30730i	−0.945489	−	0.325654i	$-0.894416\pi$
$521$	−17.2279	−	29.8396i	−0.754769	−	1.30730i	0.190720	−	0.981644i	$-0.438918\pi$
$522$		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	$0.0839139\pi$
$524$	−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
$529$	10.7279	−	18.5813i	0.466431	−	0.807883i
$530$		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
$536$	−0.242641			−0.0104805
$537$		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	−0.994643	−	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
$547$	−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
$551$	9.51472			0.405341
$552$		0			0
$553$	−1.98528	−	0.271680i	−0.0844228	−	0.0115530i
$554$	11.6066	−	20.1032i	0.493117	−	0.854104i
$555$		0			0
$556$	−10.3640	+	17.9509i	−0.439530	+	0.761288i
$557$	−3.51472	−	6.08767i	−0.148923	−	0.257943i	0.781906	−	0.623396i	$-0.214247\pi$
$557$	−3.51472	−	6.08767i	−0.148923	−	0.257943i	−0.930830	+	0.365453i	$0.880914\pi$
$558$		0			0
$559$	−23.5147			−0.994567
$560$		0			0
$561$		0			0
$562$	14.2279	+	24.6435i	0.600169	+	1.03952i
$563$	6.72792			0.283548			0.141774	−	0.989899i	$-0.454719\pi$
$563$	6.72792			0.283548			0.141774	+	0.989899i	$0.454719\pi$
$564$		0			0
$565$		0			0
$566$	8.97056			0.377061
$567$		0			0
$568$	1.24264			0.0521400
$569$	42.9411			1.80019			0.900093	−	0.435698i	$-0.143499\pi$
$569$	42.9411			1.80019			0.900093	+	0.435698i	$0.143499\pi$
$570$		0			0
$571$	12.9706			0.542801			0.271401	−	0.962466i	$-0.412513\pi$
$571$	12.9706			0.542801			0.271401	+	0.962466i	$0.412513\pi$
$572$	4.75736	+	8.23999i	0.198915	+	0.344531i
$573$		0			0
$574$	18.6213	−	24.0131i	0.777239	−	1.00229i
$575$	−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
$581$	−16.2426	−	39.7862i	−0.673858	−	1.65061i
$582$		0			0
$583$	18.0000			0.745484
$584$	−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
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	5.74264	−	9.94655i	0.235822	−	0.408456i	−0.723689	−	0.690126i	$-0.757555\pi$
$593$	5.74264	−	9.94655i	0.235822	−	0.408456i	0.959511	+	0.281670i	$0.0908884\pi$
$594$		0			0
$595$		0			0
$596$	3.87868	+	6.71807i	0.158877	+	0.275183i
$597$		0			0
$598$	2.78680			0.113961
$599$	10.9706			0.448245			0.224123	−	0.974561i	$-0.428048\pi$
$599$	10.9706			0.448245			0.224123	+	0.974561i	$0.428048\pi$
$600$		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
$607$	2.51472	+	4.35562i	0.102069	+	0.176789i	0.912537	−	0.408994i	$-0.134120\pi$
$607$	2.51472	+	4.35562i	0.102069	+	0.176789i	−0.810468	+	0.585783i	$0.800787\pi$
$608$	−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	−0.992106	−	0.125403i	$-0.959978\pi$
$613$	−14.9706	−	25.9298i	−0.604655	−	1.04729i	0.387451	−	0.921891i	$-0.373356\pi$
$614$	28.0000			1.12999
$615$		0			0
$616$	−6.87868	+	8.87039i	−0.277150	+	0.357398i
$617$	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
$619$	9.24264	−	16.0087i	0.371493	−	0.643445i	−0.618302	−	0.785940i	$-0.712179\pi$
$619$	9.24264	−	16.0087i	0.371493	−	0.643445i	0.989795	+	0.142495i	$0.0455126\pi$
$620$		0			0
$621$		0			0
$622$	22.9706			0.921036
$623$	−18.6213	+	24.0131i	−0.746047	+	0.962064i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−15.9706			−0.638312
$627$		0			0
$628$	14.0000			0.558661
$629$		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	$0.547792\pi$
$632$	−0.757359			−0.0301261
$633$		0			0
$634$	16.9706			0.673987
$635$		0			0
$636$		0			0
$637$	11.2132	−	10.9867i	0.444283	−	0.435307i
$638$	18.0000			0.712627
$639$		0			0
$640$		0			0
$641$	23.2279	−	40.2319i	0.917448	−	1.58907i	0.114170	−	0.993461i	$-0.463579\pi$
$641$	23.2279	−	40.2319i	0.917448	−	1.58907i	0.803278	−	0.595605i	$-0.203088\pi$
$642$		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	$0.0288916\pi$
$644$	1.24264	+	3.04384i	0.0489669	+	0.119944i
$645$		0			0
$646$		0			0
$647$	13.8640	+	24.0131i	0.545049	+	0.944052i	0.998604	+	0.0528236i	$0.0168221\pi$
$647$	13.8640	+	24.0131i	0.545049	+	0.944052i	−0.453555	+	0.891228i	$0.649845\pi$
$648$		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
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	0.999396	−	0.0347583i	$-0.0110661\pi$
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	−0.529799	+	0.848123i	$0.677733\pi$
$654$		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
$661$	34.1838			1.32959			0.664797	−	0.747024i	$-0.268518\pi$
$661$	34.1838			1.32959			0.664797	+	0.747024i	$0.268518\pi$
$662$	1.51472			0.0588712
$663$		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
$668$	−9.10660	+	15.7731i	−0.352345	+	0.610279i
$669$		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
$677$	−25.7574			−0.989936			−0.494968	−	0.868911i	$-0.664820\pi$
$677$	−25.7574			−0.989936			−0.494968	+	0.868911i	$0.664820\pi$
$678$		0			0
$679$	4.48528	+	10.9867i	0.172129	+	0.421629i
$680$		0			0
$681$		0			0
$682$	19.6066	−	33.9596i	0.750776	−	1.30038i
$683$	−8.84924	−	15.3273i	−0.338607	−	0.586484i	0.645564	−	0.763706i	$-0.276622\pi$
$683$	−8.84924	−	15.3273i	−0.338607	−	0.586484i	−0.984171	+	0.177222i	$0.943289\pi$
$684$		0			0
$685$		0			0
$686$	17.0000	+	7.34847i	0.649063	+	0.280566i
$687$		0			0
$688$	−5.24264	−	9.08052i	−0.199874	−	0.346192i
$689$	−9.51472			−0.362482
$690$		0			0
$691$	−2.24264			−0.0853141			−0.0426570	−	0.999090i	$-0.513582\pi$
$691$	−2.24264			−0.0853141			−0.0426570	+	0.999090i	$0.513582\pi$
$692$	−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
$700$	−8.10660	+	10.4539i	−0.306401	+	0.395118i
$701$	−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
$704$	−2.12132	+	3.67423i	−0.0799503	+	0.138478i
$705$		0			0
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	−26.3345	+	33.9596i	−0.990412	+	1.27718i
$708$		0			0
$709$	−33.6985			−1.26557			−0.632787	−	0.774326i	$-0.718089\pi$
$709$	−33.6985			−1.26557			−0.632787	+	0.774326i	$0.718089\pi$
$710$		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
$716$	−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	$0.339632\pi$
$719$	−13.8640	+	24.0131i	−0.517039	+	0.895537i	−0.999804	+	0.0197874i	$0.993701\pi$
$720$		0			0
$721$	9.24264	+	22.6398i	0.344214	+	0.843148i
$722$	−6.98528	−	12.0989i	−0.259965	−	0.450273i
$723$		0			0
$724$	−11.7574			−0.436959
$725$	21.2132			0.787839
$726$		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
$733$	2.51472	+	4.35562i	0.0928833	+	0.160879i	0.908723	−	0.417399i	$-0.137058\pi$
$733$	2.51472	+	4.35562i	0.0928833	+	0.160879i	−0.815840	+	0.578278i	$0.803725\pi$
$734$	−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	0.919484	−	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
$742$	−4.24264	−	10.3923i	−0.155752	−	0.381514i
$743$	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
$749$	−23.4853	+	30.2854i	−0.858134	+	1.10660i
$750$		0			0
$751$	4.37868	+	7.58410i	0.159780	+	0.276748i	0.934789	−	0.355203i	$-0.115588\pi$
$751$	4.37868	+	7.58410i	0.159780	+	0.276748i	−0.775009	+	0.631950i	$0.782255\pi$
$752$	−4.75736			−0.173483
$753$		0			0
$754$	−9.51472			−0.346506
$755$		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	$0.624453\pi$
$758$	−26.7279			−0.970802
$759$		0			0
$760$		0			0
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	0.991152	−	0.132734i	$-0.0423756\pi$
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	−0.610527	+	0.791995i	$0.709042\pi$
$762$		0			0
$763$	6.24264	+	15.2913i	0.225999	+	0.553582i
$764$	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
$772$	−21.4853			−0.773272
$773$	−1.39340	−	2.41344i	−0.0501171	−	0.0868053i	0.839879	−	0.542774i	$-0.182626\pi$
$773$	−1.39340	−	2.41344i	−0.0501171	−	0.0868053i	−0.889996	+	0.455969i	$0.849293\pi$
$774$		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
$779$	−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
$787$	11.2132			0.399708			0.199854	−	0.979826i	$-0.435953\pi$
$787$	11.2132			0.399708			0.199854	+	0.979826i	$0.435953\pi$
$788$	16.9706			0.604551
$789$		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		−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
$803$	−29.6985			−1.04804
$804$		0			0
$805$		0			0
$806$	−10.3640	+	17.9509i	−0.365055	+	0.632294i
$807$		0			0
$808$	−8.12132	+	14.0665i	−0.285707	+	0.494859i
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	0.776012	−	0.630718i	$-0.217239\pi$
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	−0.934224	+	0.356687i	$0.883906\pi$
$810$		0			0
$811$	27.4558			0.964105			0.482053	−	0.876142i	$-0.339891\pi$
$811$	27.4558			0.964105			0.482053	+	0.876142i	$0.339891\pi$
$812$	−4.24264	−	10.3923i	−0.148888	−	0.364698i
$813$		0			0
$814$	−8.48528	−	14.6969i	−0.297409	−	0.515127i
$815$		0			0
$816$		0			0
$817$	−23.5147			−0.822676
$818$	−35.0000			−1.22375
$819$		0			0
$820$		0			0
$821$	−44.1838			−1.54202			−0.771012	−	0.636821i	$-0.780249\pi$
$821$	−44.1838			−1.54202			−0.771012	+	0.636821i	$0.780249\pi$
$822$		0			0
$823$	−18.6985			−0.651788			−0.325894	−	0.945406i	$-0.605665\pi$
$823$	−18.6985			−0.651788			−0.325894	+	0.945406i	$0.605665\pi$
$824$	4.62132	+	8.00436i	0.160991	+	0.278845i
$825$		0			0
$826$		0			0
$827$	16.9706			0.590124			0.295062	−	0.955478i	$-0.404660\pi$
$827$	16.9706			0.590124			0.295062	+	0.955478i	$0.404660\pi$
$828$		0			0
$829$	−8.97056	−	15.5375i	−0.311561	−	0.539639i	0.667140	−	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
$832$	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
$842$	−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
$848$	−2.12132	−	3.67423i	−0.0728464	−	0.126174i
$849$		0			0
$850$		0			0
$851$	−4.97056			−0.170389
$852$		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
$857$	5.74264	−	9.94655i	0.196165	−	0.339768i	−0.751117	−	0.660169i	$-0.770485\pi$
$857$	5.74264	−	9.94655i	0.196165	−	0.339768i	0.947282	+	0.320402i	$0.103818\pi$
$858$		0			0
$859$	7.84924	+	13.5953i	0.267813	+	0.463865i	0.968297	−	0.249803i	$-0.0803658\pi$
$859$	7.84924	+	13.5953i	0.267813	+	0.463865i	−0.700484	+	0.713668i	$0.747032\pi$
$860$		0			0
$861$		0			0
$862$	14.3787	+	24.9046i	0.489740	+	0.848254i
$863$	21.1066	−	36.5577i	0.718477	−	1.24444i	−0.243126	−	0.969995i	$-0.578173\pi$
$863$	21.1066	−	36.5577i	0.718477	−	1.24444i	0.961603	−	0.274444i	$-0.0884938\pi$
$864$		0			0
$865$		0			0
$866$	29.9706			1.01844
$867$		0			0
$868$	−24.2279	−	3.31552i	−0.822349	−	0.112536i
$869$	−1.60660	+	2.78272i	−0.0545002	+	0.0943972i
$870$		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	0.996669	+	0.0815494i	$0.0259868\pi$
$877$	16.8492	+	29.1837i	0.568958	+	0.985465i	−0.427711	+	0.903916i	$0.640680\pi$
$878$	13.7279			0.463295
$879$		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
$886$	26.4853			0.889790
$887$	7.13604	+	12.3600i	0.239605	+	0.415008i	0.960601	−	0.277931i	$-0.0896488\pi$
$887$	7.13604	+	12.3600i	0.239605	+	0.415008i	−0.720996	+	0.692939i	$0.756315\pi$
$888$		0			0
$889$	−39.9558	−	5.46783i	−1.34008	−	0.183385i
$890$		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
$896$	2.62132	+	0.358719i	0.0875722	+	0.0119840i
$897$		0			0
$898$	28.9706			0.966760
$899$	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
$907$	−14.9706	+	25.9298i	−0.497089	+	0.860984i	−0.999994	−	0.00335764i	$-0.998931\pi$
$907$	−14.9706	+	25.9298i	−0.497089	+	0.860984i	0.502905	+	0.864342i	$0.332265\pi$
$908$	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
$913$	−68.9117			−2.28064
$914$	−28.4853			−0.942209
$915$		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	−0.685403	−	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
$923$	−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
$929$	43.9706			1.44263			0.721314	−	0.692609i	$-0.243539\pi$
$929$	43.9706			1.44263			0.721314	+	0.692609i	$0.243539\pi$
$930$		0			0
$931$	11.2132	−	10.9867i	0.367498	−	0.360073i
$932$	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	$0.608443\pi$
$938$	0.636039	+	0.0870399i	0.0207674	+	0.00284195i
$939$		0			0
$940$		0			0
$941$	−52.6690			−1.71696			−0.858481	−	0.512845i	$-0.828591\pi$
$941$	−52.6690			−1.71696			−0.858481	+	0.512845i	$0.828591\pi$
$942$		0			0
$943$	−14.2721			−0.464763
$944$		0			0
$945$		0			0
$946$	−44.4853			−1.44634
$947$	38.4853			1.25060			0.625302	−	0.780383i	$-0.284976\pi$
$947$	38.4853			1.25060			0.625302	+	0.780383i	$0.284976\pi$
$948$		0			0
$949$	15.6985			0.509594
$950$	5.60660	+	9.71092i	0.181902	+	0.315064i
$951$		0			0
$952$		0			0
$953$	23.4853			0.760763			0.380381	−	0.924830i	$-0.375793\pi$
$953$	23.4853			0.760763			0.380381	+	0.924830i	$0.375793\pi$
$954$		0			0
$955$		0			0
$956$	−10.8640	+	18.8169i	−0.351366	+	0.608583i
$957$		0			0
$958$	2.37868	−	4.11999i	0.0768517	−	0.133111i
$959$	−22.6508	+	29.2092i	−0.731431	+	0.943215i
$960$		0			0
$961$	54.4264			1.75569
$962$	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	$0.844873\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$		0			0
$970$		0			0
$971$	−4.75736	+	8.23999i	−0.152671	+	0.264434i	−0.932209	−	0.361922i	$-0.882121\pi$
$971$	−4.75736	+	8.23999i	−0.152671	+	0.264434i	0.779538	+	0.626355i	$0.215454\pi$
$972$		0			0
$973$	33.6066	−	43.3373i	1.07738	−	1.38933i
$974$	−5.62132	−	9.73641i	−0.180119	−	0.311975i
$975$		0			0
$976$	−2.24264			−0.0717852
$977$	−19.9706			−0.638915			−0.319457	−	0.947601i	$-0.603501\pi$
$977$	−19.9706			−0.638915			−0.319457	+	0.947601i	$0.603501\pi$
$978$		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
$983$	−16.2426	+	28.1331i	−0.518060	+	0.897306i	0.481720	+	0.876325i	$0.340012\pi$
$983$	−16.2426	+	28.1331i	−0.518060	+	0.897306i	−0.999780	+	0.0209807i	$0.993321\pi$
$984$		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	0.797537	−	0.603269i	$-0.206136\pi$
$991$	−3.89340	−	6.74356i	−0.123678	−	0.214216i	−0.921215	+	0.389053i	$0.872802\pi$
$992$	−9.24264			−0.293454
$993$		0			0
$994$	−3.25736	−	0.445759i	−0.103317	−	0.0141386i
$995$		0			0
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	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.e.r.919.1		4
3.2	odd	2		1134.2.e.s.919.1		4
7.4	even	3		1134.2.h.s.109.1		4
9.2	odd	6		1134.2.h.r.541.2		4
9.4	even	3		1134.2.g.j.163.2	yes	4
9.5	odd	6		1134.2.g.i.163.2	✓	4
9.7	even	3		1134.2.h.s.541.2		4
21.11	odd	6		1134.2.h.r.109.1		4
63.4	even	3		1134.2.g.j.487.2	yes	4
63.5	even	6		7938.2.a.bp.1.1		2
63.11	odd	6		1134.2.e.s.865.1		4
63.23	odd	6		7938.2.a.bq.1.1		2
63.25	even	3	inner	1134.2.e.r.865.1		4
63.32	odd	6		1134.2.g.i.487.2	yes	4
63.40	odd	6		7938.2.a.bj.1.2		2
63.58	even	3		7938.2.a.bk.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.r.865.1		4	63.25	even	3	inner
1134.2.e.r.919.1		4	1.1	even	1	trivial
1134.2.e.s.865.1		4	63.11	odd	6
1134.2.e.s.919.1		4	3.2	odd	2
1134.2.g.i.163.2	✓	4	9.5	odd	6
1134.2.g.i.487.2	yes	4	63.32	odd	6
1134.2.g.j.163.2	yes	4	9.4	even	3
1134.2.g.j.487.2	yes	4	63.4	even	3
1134.2.h.r.109.1		4	21.11	odd	6
1134.2.h.r.541.2		4	9.2	odd	6
1134.2.h.s.109.1		4	7.4	even	3
1134.2.h.s.541.2		4	9.7	even	3
7938.2.a.bj.1.2		2	63.40	odd	6
7938.2.a.bk.1.2		2	63.58	even	3
7938.2.a.bp.1.1		2	63.5	even	6
7938.2.a.bq.1.1		2	63.23	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +(-2.12132 + 3.67423i) q^{11} +(1.12132 - 1.94218i) q^{13} +(2.62132 + 0.358719i) q^{14} +1.00000 q^{16} +(1.12132 - 1.94218i) q^{19} +(2.12132 - 3.67423i) q^{22} +(-0.621320 - 1.07616i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-1.12132 + 1.94218i) q^{26} +(-2.62132 - 0.358719i) q^{28} +(2.12132 + 3.67423i) q^{29} +9.24264 q^{31} -1.00000 q^{32} +(2.00000 - 3.46410i) q^{37} +(-1.12132 + 1.94218i) q^{38} +(5.74264 - 9.94655i) q^{41} +(-5.24264 - 9.08052i) q^{43} +(-2.12132 + 3.67423i) q^{44} +(0.621320 + 1.07616i) q^{46} -4.75736 q^{47} +(6.74264 + 1.88064i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(1.12132 - 1.94218i) q^{52} +(-2.12132 - 3.67423i) q^{53} +(2.62132 + 0.358719i) q^{56} +(-2.12132 - 3.67423i) q^{58} -2.24264 q^{61} -9.24264 q^{62} +1.00000 q^{64} +0.242641 q^{67} -1.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(1.12132 - 1.94218i) q^{76} +(6.87868 - 8.87039i) q^{77} +0.757359 q^{79} +(-5.74264 + 9.94655i) q^{82} +(8.12132 + 14.0665i) q^{83} +(5.24264 + 9.08052i) q^{86} +(2.12132 - 3.67423i) q^{88} +(5.74264 - 9.94655i) q^{89} +(-3.63604 + 4.68885i) q^{91} +(-0.621320 - 1.07616i) q^{92} +4.75736 q^{94} +(-2.24264 - 3.88437i) q^{97} +(-6.74264 - 1.88064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{19} + 6 q^{23} + 10 q^{25} + 4 q^{26} - 2 q^{28} + 20 q^{31} - 4 q^{32} + 8 q^{37} + 4 q^{38} + 6 q^{41} - 4 q^{43} - 6 q^{46} - 36 q^{47} + 10 q^{49} - 10 q^{50} - 4 q^{52} + 2 q^{56} + 8 q^{61} - 20 q^{62} + 4 q^{64} - 16 q^{67} + 12 q^{71} + 14 q^{73} - 8 q^{74} - 4 q^{76} + 36 q^{77} + 20 q^{79} - 6 q^{82} + 24 q^{83} + 4 q^{86} + 6 q^{89} - 40 q^{91} + 6 q^{92} + 36 q^{94} + 8 q^{97} - 10 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^19 + 6 * q^23 + 10 * q^25 + 4 * q^26 - 2 * q^28 + 20 * q^31 - 4 * q^32 + 8 * q^37 + 4 * q^38 + 6 * q^41 - 4 * q^43 - 6 * q^46 - 36 * q^47 + 10 * q^49 - 10 * q^50 - 4 * q^52 + 2 * q^56 + 8 * q^61 - 20 * q^62 + 4 * q^64 - 16 * q^67 + 12 * q^71 + 14 * q^73 - 8 * q^74 - 4 * q^76 + 36 * q^77 + 20 * q^79 - 6 * q^82 + 24 * q^83 + 4 * q^86 + 6 * q^89 - 40 * q^91 + 6 * q^92 + 36 * q^94 + 8 * q^97 - 10 * q^98

Introduction

L-functions

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