LMFDB - Embedded newform 1134.2.e.s.865.1

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			865.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1134.865
Dual form			1134.2.e.s.919.1

$q$-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 $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		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	0.985520	+	0.169559i	$0.0542342\pi$
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	−0.345918	+	0.938265i	$0.612432\pi$
$12$		0			0
$13$	1.12132	+	1.94218i	0.310998	+	0.538665i	0.978579	−	0.205873i	$-0.0660033\pi$
$13$	1.12132	+	1.94218i	0.310998	+	0.538665i	−0.667580	+	0.744538i	$0.732670\pi$
$14$	−2.62132	+	0.358719i	−0.700577	+	0.0958718i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		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
$23$	0.621320	−	1.07616i	0.129554	−	0.224395i	−0.793950	−	0.607983i	$-0.791979\pi$
$23$	0.621320	−	1.07616i	0.129554	−	0.224395i	0.923504	+	0.383589i	$0.125312\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	1.12132	+	1.94218i	0.219909	+	0.380894i
$27$		0			0
$28$	−2.62132	+	0.358719i	−0.495383	+	0.0677916i
$29$	−2.12132	+	3.67423i	−0.393919	+	0.682288i	−0.992963	−	0.118428i	$-0.962214\pi$
$29$	−2.12132	+	3.67423i	−0.393919	+	0.682288i	0.599043	+	0.800717i	$0.295548\pi$
$30$		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	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	1.12132	+	1.94218i	0.181902	+	0.315064i
$39$		0			0
$40$		0			0
$41$	−5.74264	−	9.94655i	−0.896850	−	1.55339i	−0.831498	−	0.555527i	$-0.812517\pi$
$41$	−5.74264	−	9.94655i	−0.896850	−	1.55339i	−0.0653514	−	0.997862i	$-0.520817\pi$
$42$		0			0
$43$	−5.24264	+	9.08052i	−0.799495	+	1.38477i	0.120450	+	0.992719i	$0.461566\pi$
$43$	−5.24264	+	9.08052i	−0.799495	+	1.38477i	−0.919945	+	0.392047i	$0.871767\pi$
$44$	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	$-0.387212\pi$
$47$	4.75736			0.693932			0.346966	+	0.937878i	$0.387212\pi$
$48$		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	$-0.739217\pi$
$53$	2.12132	−	3.67423i	0.291386	−	0.504695i	0.974138	+	0.225955i	$0.0725503\pi$
$54$		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	$-0.476507\pi$
$71$	1.24264			0.147474			0.0737372	+	0.997278i	$0.476507\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	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	−0.0532699	+	0.998580i	$0.516964\pi$
$83$	−8.12132	+	14.0665i	−0.891431	+	1.54400i	−0.838161	+	0.545423i	$0.816369\pi$
$84$		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	−0.991452	−	0.130473i	$-0.958350\pi$
$89$	−5.74264	−	9.94655i	−0.608719	−	1.05433i	0.382733	−	0.923859i	$-0.374983\pi$
$90$		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	−0.957128	−	0.289666i	$-0.906456\pi$
$97$	−2.24264	+	3.88437i	−0.227706	+	0.394398i	0.729422	+	0.684064i	$0.239789\pi$
$98$	6.74264	−	1.88064i	0.681110	−	0.189973i
$99$		0			0
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	−8.12132	−	14.0665i	−0.808102	−	1.39967i	−0.914177	−	0.405315i	$-0.867162\pi$
$101$	−8.12132	−	14.0665i	−0.808102	−	1.39967i	0.106076	−	0.994358i	$-0.466171\pi$
$102$		0			0
$103$	−4.62132	+	8.00436i	−0.455352	+	0.788693i	−0.998708	−	0.0508091i	$-0.983820\pi$
$103$	−4.62132	+	8.00436i	−0.455352	+	0.788693i	0.543356	+	0.839502i	$0.317153\pi$
$104$	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	$-0.919773\pi$
$107$	−7.24264	−	12.5446i	−0.700173	−	1.21273i	0.268233	−	0.963354i	$-0.413560\pi$
$108$		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
$112$	−2.62132	+	0.358719i	−0.247691	+	0.0338958i
$113$	1.75736	+	3.04384i	0.165318	+	0.286340i	0.936768	−	0.349950i	$-0.113801\pi$
$113$	1.75736	+	3.04384i	0.165318	+	0.286340i	−0.771450	+	0.636290i	$0.780468\pi$
$114$		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	−0.255456	−	0.966821i	$-0.582226\pi$
$131$	8.12132	−	14.0665i	0.709563	−	1.22900i	0.965019	−	0.262179i	$-0.0844410\pi$
$132$		0			0
$133$	−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	−0.993291	−	0.115640i	$-0.963108\pi$
$137$	−6.98528	−	12.0989i	−0.596793	−	1.03368i	0.396498	−	0.918035i	$-0.370225\pi$
$138$		0			0
$139$	−10.3640	−	17.9509i	−0.879060	−	1.52258i	−0.852374	−	0.522932i	$-0.824838\pi$
$139$	−10.3640	−	17.9509i	−0.879060	−	1.52258i	−0.0266854	−	0.999644i	$-0.508495\pi$
$140$		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	$-0.936262\pi$
$149$	−3.87868	+	6.71807i	−0.317754	+	0.550366i	0.662265	+	0.749270i	$0.269595\pi$
$150$		0			0
$151$	5.62132	+	9.73641i	0.457457	+	0.792338i	0.998826	−	0.0484470i	$-0.0154272\pi$
$151$	5.62132	+	9.73641i	0.457457	+	0.792338i	−0.541369	+	0.840785i	$0.682094\pi$
$152$	1.12132	+	1.94218i	0.0909511	+	0.157532i
$153$		0			0
$154$	−6.87868	−	8.87039i	−0.554300	−	0.714796i
$155$		0			0
$156$		0			0
$157$	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	0.924250	+	0.381788i	$0.124692\pi$
$163$	10.1213	+	17.5306i	0.792763	+	1.37311i	−0.131487	+	0.991318i	$0.541975\pi$
$164$	−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	0.966803	+	0.255522i	$0.0822472\pi$
$167$	9.10660	+	15.7731i	0.704690	+	1.22056i	−0.262113	+	0.965037i	$0.584419\pi$
$168$		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	$-0.162034\pi$
$173$	22.9706			1.74642			0.873210	+	0.487345i	$0.162034\pi$
$174$		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	$-0.739709\pi$
$179$	3.87868	−	6.71807i	0.289906	−	0.502132i	0.973787	+	0.227461i	$0.0730426\pi$
$180$		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	$-0.599321\pi$
$191$	−8.48528			−0.613973			−0.306987	+	0.951714i	$0.599321\pi$
$192$		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	$-0.706648\pi$
$197$	−16.9706			−1.20910			−0.604551	+	0.796566i	$0.706648\pi$
$198$		0			0
$199$	11.6213	−	20.1287i	0.823814	−	1.42689i	−0.0790091	−	0.996874i	$-0.525176\pi$
$199$	11.6213	−	20.1287i	0.823814	−	1.42689i	0.902823	−	0.430013i	$-0.141491\pi$
$200$	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	0.627194	−	0.778863i	$-0.284203\pi$
$211$	−5.24264	−	9.08052i	−0.360918	−	0.625129i	−0.988112	+	0.153734i	$0.950870\pi$
$212$	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	−0.539297	−	0.842116i	$-0.681310\pi$
$223$	6.86396	−	11.8887i	0.459645	−	0.796128i	0.998942	+	0.0459873i	$0.0146434\pi$
$224$	−2.62132	+	0.358719i	−0.175144	+	0.0239680i
$225$		0			0
$226$	1.75736	+	3.04384i	0.116898	+	0.202473i
$227$	−4.75736	−	8.23999i	−0.315757	−	0.546907i	0.663841	−	0.747874i	$-0.268925\pi$
$227$	−4.75736	−	8.23999i	−0.315757	−	0.546907i	−0.979598	+	0.200966i	$0.935592\pi$
$228$		0			0
$229$	4.48528	−	7.76874i	0.296396	−	0.513372i	−0.678913	−	0.734219i	$-0.737549\pi$
$229$	4.48528	−	7.76874i	0.296396	−	0.513372i	0.975309	+	0.220846i	$0.0708819\pi$
$230$		0			0
$231$		0			0
$232$	−2.12132	+	3.67423i	−0.139272	+	0.241225i
$233$	−1.75736	−	3.04384i	−0.115128	−	0.199408i	0.802703	−	0.596379i	$-0.203395\pi$
$233$	−1.75736	−	3.04384i	−0.115128	−	0.199408i	−0.917831	+	0.396971i	$0.870061\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.8640	+	18.8169i	0.702731	+	1.21717i	0.967504	+	0.252855i	$0.0813697\pi$
$239$	10.8640	+	18.8169i	0.702731	+	1.21717i	−0.264773	+	0.964311i	$0.585297\pi$
$240$		0			0
$241$	−12.7426	−	22.0709i	−0.820826	−	1.42171i	−0.905068	−	0.425266i	$-0.860180\pi$
$241$	−12.7426	−	22.0709i	−0.820826	−	1.42171i	0.0842426	−	0.996445i	$-0.473153\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−2.24264			−0.143570
$245$		0			0
$246$		0			0
$247$	−2.51472	+	4.35562i	−0.160008	+	0.277141i
$248$	9.24264			0.586908
$249$		0			0
$250$		0			0
$251$	−6.72792			−0.424663			−0.212331	−	0.977198i	$-0.568106\pi$
$251$	−6.72792			−0.424663			−0.212331	+	0.977198i	$0.568106\pi$
$252$		0			0
$253$	5.27208			0.331453
$254$	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	$-0.716718\pi$
$257$	5.74264	−	9.94655i	0.358216	−	0.620448i	0.987663	+	0.156595i	$0.0500518\pi$
$258$		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	$-0.0568361\pi$
$263$	5.48528	+	9.50079i	0.338237	+	0.585844i	−0.645864	+	0.763452i	$0.723503\pi$
$264$		0			0
$265$		0			0
$266$	−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	0.268102	+	0.963391i	$0.413604\pi$
$269$	−11.4853	+	19.8931i	−0.700270	+	1.21290i	−0.968372	+	0.249513i	$0.919730\pi$
$270$		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
$275$	−10.6066	+	18.3712i	−0.639602	+	1.10782i
$276$		0			0
$277$	−11.6066	−	20.1032i	−0.697373	−	1.20789i	−0.969374	−	0.245589i	$-0.921019\pi$
$277$	−11.6066	−	20.1032i	−0.697373	−	1.20789i	0.272001	−	0.962297i	$-0.412315\pi$
$278$	−10.3640	−	17.9509i	−0.621589	−	1.07662i
$279$		0			0
$280$		0			0
$281$	14.2279	−	24.6435i	0.848767	−	1.47011i	−0.0335428	−	0.999437i	$-0.510679\pi$
$281$	14.2279	−	24.6435i	0.848767	−	1.47011i	0.882309	−	0.470670i	$-0.155988\pi$
$282$		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	−0.977627	−	0.210344i	$-0.932541\pi$
$293$	−11.4853	−	19.8931i	−0.670977	−	1.16217i	0.306650	−	0.951822i	$-0.400792\pi$
$294$		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	$-0.274236\pi$
$311$	22.9706			1.30254			0.651271	+	0.758846i	$0.274236\pi$
$312$		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	$-0.341876\pi$
$317$	16.9706			0.953162			0.476581	+	0.879131i	$0.341876\pi$
$318$		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	0.984443	−	0.175703i	$-0.0562199\pi$
$337$	6.24264	+	10.8126i	0.340058	+	0.588998i	−0.644385	+	0.764701i	$0.722887\pi$
$338$	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	$-0.332346\pi$
$347$	18.7279			1.00537			0.502684	+	0.864470i	$0.332346\pi$
$348$		0			0
$349$	4.48528	−	7.76874i	0.240092	−	0.415851i	−0.720649	−	0.693301i	$-0.756156\pi$
$349$	4.48528	−	7.76874i	0.240092	−	0.415851i	0.960740	+	0.277450i	$0.0894892\pi$
$350$	−8.10660	−	10.4539i	−0.433316	−	0.558782i
$351$		0			0
$352$	2.12132	+	3.67423i	0.113067	+	0.195837i
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$		0			0
$355$		0			0
$356$	−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	$-0.997128\pi$
$359$	−9.62132	−	16.6646i	−0.507794	−	0.879525i	0.492165	−	0.870502i	$-0.336206\pi$
$360$		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	0.987676	−	0.156511i	$-0.0500246\pi$
$367$	6.86396	+	11.8887i	0.358296	+	0.620587i	−0.629380	+	0.777097i	$0.716691\pi$
$368$	0.621320	−	1.07616i	0.0323886	−	0.0560986i
$369$		0			0
$370$		0			0
$371$	−4.24264	+	10.3923i	−0.220267	+	0.539542i
$372$		0			0
$373$	−17.6066	+	30.4955i	−0.911635	+	1.57900i	−0.0998811	+	0.994999i	$0.531846\pi$
$373$	−17.6066	+	30.4955i	−0.911635	+	1.57900i	−0.811754	+	0.583999i	$0.801487\pi$
$374$		0			0
$375$		0			0
$376$	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	$-0.987396\pi$
$383$	−9.10660	+	15.7731i	−0.465326	+	0.805968i	0.533891	+	0.845554i	$0.320729\pi$
$384$		0			0
$385$		0			0
$386$	−21.4853			−1.09357
$387$		0			0
$388$	−2.24264	+	3.88437i	−0.113853	+	0.197199i
$389$	−0.878680	−	1.52192i	−0.0445508	−	0.0771643i	0.842890	−	0.538086i	$-0.180852\pi$
$389$	−0.878680	−	1.52192i	−0.0445508	−	0.0771643i	−0.887441	+	0.460921i	$0.847519\pi$
$390$		0			0
$391$		0			0
$392$	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	0.974995	−	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
$401$	−6.25736	+	10.8381i	−0.312478	+	0.541227i	−0.978898	−	0.204349i	$-0.934492\pi$
$401$	−6.25736	+	10.8381i	−0.312478	+	0.541227i	0.666420	+	0.745576i	$0.267826\pi$
$402$		0			0
$403$	10.3640	+	17.9509i	0.516266	+	0.894198i
$404$	−8.12132	−	14.0665i	−0.404051	−	0.699836i
$405$		0			0
$406$	4.24264	−	10.3923i	0.210559	−	0.515761i
$407$	−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	$-0.0368038\pi$
$419$	8.12132	+	14.0665i	0.396752	+	0.687195i	−0.596571	+	0.802561i	$0.703470\pi$
$420$		0			0
$421$	2.87868	−	4.98602i	0.140298	−	0.243004i	−0.787311	−	0.616557i	$-0.788527\pi$
$421$	2.87868	−	4.98602i	0.140298	−	0.243004i	0.927609	+	0.373553i	$0.121861\pi$
$422$	−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	−0.278388	−	0.960469i	$-0.589800\pi$
$431$	14.3787	−	24.9046i	0.692597	−	1.19961i	0.970984	−	0.239144i	$-0.0768667\pi$
$432$		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	$-0.283392\pi$
$443$	26.4853			1.25835			0.629177	+	0.777262i	$0.283392\pi$
$444$		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	$-0.260412\pi$
$449$	28.9706			1.36721			0.683603	+	0.729854i	$0.260412\pi$
$450$		0			0
$451$	24.3640	−	42.1996i	1.14725	−	1.98710i
$452$	1.75736	+	3.04384i	0.0826592	+	0.143170i
$453$		0			0
$454$	−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	0.393027	+	0.919527i	$0.371428\pi$
$461$	−12.8787	+	22.3065i	−0.599820	+	1.03892i	−0.992847	+	0.119392i	$0.961906\pi$
$462$		0			0
$463$	8.62132	+	14.9326i	0.400667	+	0.693975i	0.993807	−	0.111124i	$-0.0354452\pi$
$463$	8.62132	+	14.9326i	0.400667	+	0.693975i	−0.593140	+	0.805100i	$0.702112\pi$
$464$	−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	$-0.166667\pi$
$467$		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
$473$	−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	$-0.132003\pi$
$479$	2.37868	+	4.11999i	0.108685	+	0.188247i	−0.806553	+	0.591162i	$0.798669\pi$
$480$		0			0
$481$	−4.48528	+	7.76874i	−0.204511	+	0.354224i
$482$	−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	$0.0846813\pi$
$488$	−2.24264			−0.101520
$489$		0			0
$490$		0			0
$491$	9.36396	+	16.2189i	0.422590	+	0.731947i	0.996192	−	0.0871872i	$-0.0277878\pi$
$491$	9.36396	+	16.2189i	0.422590	+	0.731947i	−0.573602	+	0.819134i	$0.694454\pi$
$492$		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	−0.982444	−	0.186560i	$-0.940266\pi$
$499$	−7.36396	+	12.7548i	−0.329656	+	0.570981i	0.652787	+	0.757541i	$0.273599\pi$
$500$		0			0
$501$		0			0
$502$	−6.72792			−0.300282
$503$	18.2132			0.812087			0.406043	−	0.913854i	$-0.366908\pi$
$503$	18.2132			0.812087			0.406043	+	0.913854i	$0.366908\pi$
$504$		0			0
$505$		0			0
$506$	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	$-0.950547\pi$
$509$	−8.12132	+	14.0665i	−0.359971	+	0.623488i	0.627984	+	0.778226i	$0.283880\pi$
$510$		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	−0.190720	−	0.981644i	$-0.561082\pi$
$521$	17.2279	−	29.8396i	0.754769	−	1.30730i	0.945489	−	0.325654i	$-0.105584\pi$
$522$		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
$529$	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	0.586839	−	0.809703i	$-0.300372\pi$
$541$	−9.48528	−	16.4290i	−0.407804	−	0.706337i	−0.994643	+	0.103366i	$0.967039\pi$
$542$	−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	−0.956067	−	0.293149i	$-0.905297\pi$
$547$	−5.24264	+	9.08052i	−0.224159	+	0.388255i	0.731908	+	0.681404i	$0.238630\pi$
$548$	−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	$-0.785753\pi$
$557$	3.51472	−	6.08767i	0.148923	−	0.257943i	0.930830	+	0.365453i	$0.119086\pi$
$558$		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	$-0.545281\pi$
$563$	−6.72792			−0.283548			−0.141774	+	0.989899i	$0.545281\pi$
$564$		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	$-0.856501\pi$
$569$	−42.9411			−1.80019			−0.900093	+	0.435698i	$0.856501\pi$
$570$		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	−0.314459	−	0.949271i	$-0.601823\pi$
$577$	15.9706	−	27.6618i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648435\pi$
$578$	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	0.104132	+	0.994563i	$0.466793\pi$
$587$	−19.6066	+	33.9596i	−0.809251	+	1.40166i	−0.913383	+	0.407100i	$0.866540\pi$
$588$		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	$-0.242445\pi$
$593$	−5.74264	−	9.94655i	−0.235822	−	0.408456i	−0.959511	+	0.281670i	$0.909112\pi$
$594$		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	$-0.571952\pi$
$599$	−10.9706			−0.448245			−0.224123	+	0.974561i	$0.571952\pi$
$600$		0			0
$601$	−7.98528	+	13.8309i	−0.325726	+	0.564175i	−0.981659	−	0.190645i	$-0.938942\pi$
$601$	−7.98528	+	13.8309i	−0.325726	+	0.564175i	0.655933	+	0.754819i	$0.272276\pi$
$602$	10.4853	−	25.6836i	0.427348	−	1.04678i
$603$		0			0
$604$	5.62132	+	9.73641i	0.228728	+	0.396169i
$605$		0			0
$606$		0			0
$607$	2.51472	−	4.35562i	0.102069	−	0.176789i	−0.810468	−	0.585783i	$-0.800787\pi$
$607$	2.51472	−	4.35562i	0.102069	−	0.176789i	0.912537	+	0.408994i	$0.134120\pi$
$608$	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	$0.959978\pi$
$614$	−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	$-0.315963\pi$
$617$	−11.2279	−	19.4473i	−0.452019	−	0.782920i	−0.998511	+	0.0545441i	$0.982629\pi$
$618$		0			0
$619$	9.24264	+	16.0087i	0.371493	+	0.643445i	0.989795	−	0.142495i	$-0.0455126\pi$
$619$	9.24264	+	16.0087i	0.371493	+	0.643445i	−0.618302	+	0.785940i	$0.712179\pi$
$620$		0			0
$621$		0			0
$622$	22.9706			0.921036
$623$	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	−0.803278	−	0.595605i	$-0.796912\pi$
$641$	−23.2279	−	40.2319i	−0.917448	−	1.58907i	−0.114170	−	0.993461i	$-0.536421\pi$
$642$		0			0
$643$	10.6360	+	18.4222i	0.419444	+	0.726499i	0.995884	−	0.0906410i	$-0.0288916\pi$
$643$	10.6360	+	18.4222i	0.419444	+	0.726499i	−0.576439	+	0.817140i	$0.695558\pi$
$644$	−1.24264	+	3.04384i	−0.0489669	+	0.119944i
$645$		0			0
$646$		0			0
$647$	−13.8640	+	24.0131i	−0.545049	+	0.944052i	0.453555	+	0.891228i	$0.350155\pi$
$647$	−13.8640	+	24.0131i	−0.545049	+	0.944052i	−0.998604	+	0.0528236i	$0.983178\pi$
$648$		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	$-0.988934\pi$
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	0.529799	+	0.848123i	$0.322267\pi$
$654$		0			0
$655$		0			0
$656$	−5.74264	−	9.94655i	−0.224212	−	0.388347i
$657$		0			0
$658$	−12.4706	+	1.70656i	−0.486153	+	0.0665285i
$659$	−1.60660	+	2.78272i	−0.0625843	+	0.108399i	−0.895620	−	0.444820i	$-0.853268\pi$
$659$	−1.60660	+	2.78272i	−0.0625843	+	0.108399i	0.833036	+	0.553219i	$0.186601\pi$
$660$		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	−0.746727	−	0.665130i	$-0.768376\pi$
$673$	5.25736	−	9.10601i	0.202656	−	0.351011i	0.949383	+	0.314119i	$0.101709\pi$
$674$	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	$-0.335180\pi$
$677$	25.7574			0.989936			0.494968	+	0.868911i	$0.335180\pi$
$678$		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	$-0.723378\pi$
$683$	8.84924	−	15.3273i	0.338607	−	0.586484i	0.984171	+	0.177222i	$0.0567110\pi$
$684$		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	$-0.362014\pi$
$701$	22.2426			0.840093			0.420046	+	0.907503i	$0.362014\pi$
$702$		0			0
$703$	−4.48528	+	7.76874i	−0.169166	+	0.293003i
$704$	2.12132	+	3.67423i	0.0799503	+	0.138478i
$705$		0			0
$706$	−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	0.999804	+	0.0197874i	$0.00629894\pi$
$719$	13.8640	+	24.0131i	0.517039	+	0.895537i	−0.482766	+	0.875750i	$0.660368\pi$
$720$		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	−0.863492	−	0.504363i	$-0.831727\pi$
$727$	0.136039	−	0.235626i	0.00504541	−	0.00873890i	0.868537	+	0.495624i	$0.165061\pi$
$728$	−3.63604	−	4.68885i	−0.134761	−	0.173780i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	2.51472	−	4.35562i	0.0928833	−	0.160879i	−0.815840	−	0.578278i	$-0.803725\pi$
$733$	2.51472	−	4.35562i	0.0928833	−	0.160879i	0.908723	+	0.417399i	$0.137058\pi$
$734$	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
$742$	−4.24264	+	10.3923i	−0.155752	+	0.381514i
$743$	−21.6213	−	37.4492i	−0.793209	−	1.37388i	−0.923970	−	0.382465i	$-0.875075\pi$
$743$	−21.6213	−	37.4492i	−0.793209	−	1.37388i	0.130761	−	0.991414i	$-0.458258\pi$
$744$		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	−0.775009	−	0.631950i	$-0.782255\pi$
$751$	4.37868	−	7.58410i	0.159780	−	0.276748i	0.934789	+	0.355203i	$0.115588\pi$
$752$	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	$-0.957624\pi$
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	0.610527	+	0.791995i	$0.290958\pi$
$762$		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	0.822753	−	0.568399i	$-0.192437\pi$
$769$	−2.24264	−	3.88437i	−0.0808717	−	0.140074i	−0.903625	+	0.428325i	$0.859104\pi$
$770$		0			0
$771$		0			0
$772$	−21.4853			−0.773272
$773$	1.39340	−	2.41344i	0.0501171	−	0.0868053i	−0.839879	−	0.542774i	$-0.817374\pi$
$773$	1.39340	−	2.41344i	0.0501171	−	0.0868053i	0.889996	+	0.455969i	$0.150707\pi$
$774$		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	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		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	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$		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	$-0.219751\pi$
$821$	44.1838			1.54202			0.771012	+	0.636821i	$0.219751\pi$
$822$		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	$-0.595340\pi$
$827$	−16.9706			−0.590124			−0.295062	+	0.955478i	$0.595340\pi$
$828$		0			0
$829$	−8.97056	+	15.5375i	−0.311561	+	0.539639i	−0.978700	−	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	0.436672	+	0.899621i	$0.356157\pi$
$839$	−16.2426	+	28.1331i	−0.560758	+	0.971262i	−0.997430	+	0.0716411i	$0.977176\pi$
$840$		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	−0.0771127	−	0.997022i	$-0.524570\pi$
$853$	24.0919	−	41.7284i	0.824890	−	1.42875i	0.902003	−	0.431730i	$-0.142097\pi$
$854$	5.87868	−	0.804479i	0.201164	−	0.0275287i
$855$		0			0
$856$	−7.24264	−	12.5446i	−0.247548	−	0.428766i
$857$	−5.74264	−	9.94655i	−0.196165	−	0.339768i	0.751117	−	0.660169i	$-0.229515\pi$
$857$	−5.74264	−	9.94655i	−0.196165	−	0.339768i	−0.947282	+	0.320402i	$0.896182\pi$
$858$		0			0
$859$	7.84924	−	13.5953i	0.267813	−	0.463865i	−0.700484	−	0.713668i	$-0.747032\pi$
$859$	7.84924	−	13.5953i	0.267813	−	0.463865i	0.968297	+	0.249803i	$0.0803658\pi$
$860$		0			0
$861$		0			0
$862$	14.3787	−	24.9046i	0.489740	−	0.848254i
$863$	−21.1066	−	36.5577i	−0.718477	−	1.24444i	−0.961603	−	0.274444i	$-0.911506\pi$
$863$	−21.1066	−	36.5577i	−0.718477	−	1.24444i	0.243126	−	0.969995i	$-0.421827\pi$
$864$		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	−0.427711	−	0.903916i	$-0.640680\pi$
$877$	16.8492	−	29.1837i	0.568958	−	0.985465i	0.996669	−	0.0815494i	$-0.0259868\pi$
$878$	−13.7279			−0.463295
$879$		0			0
$880$		0			0
$881$	−53.4853			−1.80196			−0.900982	−	0.433856i	$-0.857153\pi$
$881$	−53.4853			−1.80196			−0.900982	+	0.433856i	$0.857153\pi$
$882$		0			0
$883$	−9.69848			−0.326380			−0.163190	−	0.986595i	$-0.552178\pi$
$883$	−9.69848			−0.326380			−0.163190	+	0.986595i	$0.552178\pi$
$884$		0			0
$885$		0			0
$886$	26.4853			0.889790
$887$	−7.13604	+	12.3600i	−0.239605	+	0.415008i	−0.960601	−	0.277931i	$-0.910351\pi$
$887$	−7.13604	+	12.3600i	−0.239605	+	0.415008i	0.720996	+	0.692939i	$0.243685\pi$
$888$		0			0
$889$	−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	0.502905	−	0.864342i	$-0.332265\pi$
$907$	−14.9706	−	25.9298i	−0.497089	−	0.860984i	−0.999994	+	0.00335764i	$0.998931\pi$
$908$	−4.75736	−	8.23999i	−0.157879	−	0.273454i
$909$		0			0
$910$		0			0
$911$	19.8640	−	34.4054i	0.658122	−	1.13990i	−0.322979	−	0.946406i	$-0.604684\pi$
$911$	19.8640	−	34.4054i	0.658122	−	1.13990i	0.981101	−	0.193495i	$-0.0619824\pi$
$912$		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	0.973310	−	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
$922$	−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	$-0.756461\pi$
$929$	−43.9706			−1.44263			−0.721314	+	0.692609i	$0.756461\pi$
$930$		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	$-0.171409\pi$
$941$	52.6690			1.71696			0.858481	+	0.512845i	$0.171409\pi$
$942$		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	$-0.715024\pi$
$947$	−38.4853			−1.25060			−0.625302	+	0.780383i	$0.715024\pi$
$948$		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	$-0.624207\pi$
$953$	−23.4853			−0.760763			−0.380381	+	0.924830i	$0.624207\pi$
$954$		0			0
$955$		0			0
$956$	10.8640	+	18.8169i	0.351366	+	0.608583i
$957$		0			0
$958$	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	−0.883578	−	0.468283i	$-0.844873\pi$
$967$	−26.3492	−	45.6382i	−0.847335	−	1.46763i	0.0362438	−	0.999343i	$-0.488461\pi$
$968$	−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	$-0.117879\pi$
$971$	4.75736	+	8.23999i	0.152671	+	0.264434i	−0.779538	+	0.626355i	$0.784546\pi$
$972$		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	$-0.396499\pi$
$977$	19.9706			0.638915			0.319457	+	0.947601i	$0.396499\pi$
$978$		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	0.999780	+	0.0209807i	$0.00667886\pi$
$983$	16.2426	+	28.1331i	0.518060	+	0.897306i	−0.481720	+	0.876325i	$0.659988\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−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	$0.206136\pi$
$992$	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	0.733630	−	0.679549i	$-0.237825\pi$
$997$	−7.00000	−	12.1244i	−0.221692	−	0.383982i	−0.955322	+	0.295567i	$0.904491\pi$
$998$	−7.36396	+	12.7548i	−0.233102	+	0.403745i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.r.865.1		4	3.2	odd	2
1134.2.e.r.919.1		4	63.23	odd	6
1134.2.e.s.865.1		4	1.1	even	1	trivial
1134.2.e.s.919.1		4	63.58	even	3	inner
1134.2.g.i.163.2	✓	4	63.16	even	3
1134.2.g.i.487.2	yes	4	9.7	even	3
1134.2.g.j.163.2	yes	4	63.2	odd	6
1134.2.g.j.487.2	yes	4	9.2	odd	6
1134.2.h.r.109.1		4	9.4	even	3
1134.2.h.r.541.2		4	7.2	even	3
1134.2.h.s.109.1		4	9.5	odd	6
1134.2.h.s.541.2		4	21.2	odd	6
7938.2.a.bj.1.2		2	63.38	even	6
7938.2.a.bk.1.2		2	63.11	odd	6
7938.2.a.bp.1.1		2	63.52	odd	6
7938.2.a.bq.1.1		2	63.25	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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