LMFDB - Embedded newform 132.2.i.b.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [132,2,Mod(25,132)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(132, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("132.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.i (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	132.25
Dual form			132.2.i.b.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{3} +(-2.30902 - 1.67760i) q^{5} +(1.30902 - 4.02874i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.19098 + 2.48990i) q^{11} +(1.42705 - 1.03681i) q^{13} +(-0.881966 + 2.71441i) q^{15} +(-3.73607 - 2.71441i) q^{17} +(1.88197 + 5.79210i) q^{19} -4.23607 q^{21} +4.23607 q^{23} +(0.972136 + 2.99193i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-1.38197 + 4.25325i) q^{29} +(6.97214 - 5.06555i) q^{31} +(1.69098 - 2.85317i) q^{33} +(-9.78115 + 7.10642i) q^{35} +(-2.54508 + 7.83297i) q^{37} +(-1.42705 - 1.03681i) q^{39} +(0.163119 + 0.502029i) q^{41} +0.527864 q^{43} +2.85410 q^{45} +(0.427051 + 1.31433i) q^{47} +(-8.85410 - 6.43288i) q^{49} +(-1.42705 + 4.39201i) q^{51} +(10.9721 - 7.97172i) q^{53} +(-0.881966 - 9.42481i) q^{55} +(4.92705 - 3.57971i) q^{57} +(2.73607 - 8.42075i) q^{59} +(0.309017 + 0.224514i) q^{61} +(1.30902 + 4.02874i) q^{63} -5.03444 q^{65} -6.85410 q^{67} +(-1.30902 - 4.02874i) q^{69} +(2.92705 + 2.12663i) q^{71} +(-0.381966 + 1.17557i) q^{73} +(2.54508 - 1.84911i) q^{75} +(12.8992 - 5.56758i) q^{77} +(-7.89919 + 5.73910i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-5.28115 - 3.83698i) q^{83} +(4.07295 + 12.5352i) q^{85} +4.47214 q^{87} +1.00000 q^{89} +(-2.30902 - 7.10642i) q^{91} +(-6.97214 - 5.06555i) q^{93} +(5.37132 - 16.5312i) q^{95} +(-4.92705 + 3.57971i) q^{97} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 7 q^{5} + 3 q^{7} - q^{9} + 11 q^{11} - q^{13} - 8 q^{15} - 6 q^{17} + 12 q^{19} - 8 q^{21} + 8 q^{23} - 14 q^{25} + q^{27} - 10 q^{29} + 10 q^{31} + 9 q^{33} - 19 q^{35} + q^{37} + q^{39}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + q^3 - 7 * q^5 + 3 * q^7 - q^9 + 11 * q^11 - q^13 - 8 * q^15 - 6 * q^17 + 12 * q^19 - 8 * q^21 + 8 * q^23 - 14 * q^25 + q^27 - 10 * q^29 + 10 * q^31 + 9 * q^33 - 19 * q^35 + q^37 + q^39 - 15 * q^41 + 20 * q^43 - 2 * q^45 - 5 * q^47 - 22 * q^49 + q^51 + 26 * q^53 - 8 * q^55 + 13 * q^57 + 2 * q^59 - q^61 + 3 * q^63 + 38 * q^65 - 14 * q^67 - 3 * q^69 + 5 * q^71 - 6 * q^73 - q^75 + 27 * q^77 - 7 * q^79 - q^81 - q^83 + 23 * q^85 + 4 * q^89 - 7 * q^91 - 10 * q^93 - 21 * q^95 - 13 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	−2.30902	−	1.67760i	−1.03262	−	0.750245i	−0.0637916	−	0.997963i	$-0.520319\pi$
$5$	−2.30902	−	1.67760i	−1.03262	−	0.750245i	−0.968832	+	0.247718i	$0.920319\pi$
$6$		0			0
$7$	1.30902	−	4.02874i	0.494762	−	1.52272i	−0.322566	−	0.946547i	$-0.604545\pi$
$7$	1.30902	−	4.02874i	0.494762	−	1.52272i	0.817327	−	0.576173i	$-0.195455\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$12$		0			0
$13$	1.42705	−	1.03681i	0.395793	−	0.287560i	−0.372032	−	0.928220i	$-0.621339\pi$
$13$	1.42705	−	1.03681i	0.395793	−	0.287560i	0.767825	+	0.640660i	$0.221339\pi$
$14$		0			0
$15$	−0.881966	+	2.71441i	−0.227723	+	0.700858i
$16$		0			0
$17$	−3.73607	−	2.71441i	−0.906130	−	0.658342i	0.0339034	−	0.999425i	$-0.489206\pi$
$17$	−3.73607	−	2.71441i	−0.906130	−	0.658342i	−0.940033	+	0.341083i	$0.889206\pi$
$18$		0			0
$19$	1.88197	+	5.79210i	0.431753	+	1.32880i	0.896378	+	0.443291i	$0.146189\pi$
$19$	1.88197	+	5.79210i	0.431753	+	1.32880i	−0.464625	+	0.885507i	$0.653811\pi$
$20$		0			0
$21$	−4.23607			−0.924386
$22$		0			0
$23$	4.23607			0.883281			0.441641	−	0.897192i	$-0.354397\pi$
$23$	4.23607			0.883281			0.441641	+	0.897192i	$0.354397\pi$
$24$		0			0
$25$	0.972136	+	2.99193i	0.194427	+	0.598385i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−1.38197	+	4.25325i	−0.256625	+	0.789809i	0.736881	+	0.676023i	$0.236298\pi$
$29$	−1.38197	+	4.25325i	−0.256625	+	0.789809i	−0.993505	+	0.113787i	$0.963702\pi$
$30$		0			0
$31$	6.97214	−	5.06555i	1.25223	−	0.909800i	0.253883	−	0.967235i	$-0.418292\pi$
$31$	6.97214	−	5.06555i	1.25223	−	0.909800i	0.998349	+	0.0574346i	$0.0182921\pi$
$32$		0			0
$33$	1.69098	−	2.85317i	0.294362	−	0.496673i
$34$		0			0
$35$	−9.78115	+	7.10642i	−1.65332	+	1.20120i
$36$		0			0
$37$	−2.54508	+	7.83297i	−0.418409	+	1.28773i	0.490756	+	0.871297i	$0.336721\pi$
$37$	−2.54508	+	7.83297i	−0.418409	+	1.28773i	−0.909166	+	0.416435i	$0.863279\pi$
$38$		0			0
$39$	−1.42705	−	1.03681i	−0.228511	−	0.166023i
$40$		0			0
$41$	0.163119	+	0.502029i	0.0254749	+	0.0784037i	0.962986	−	0.269553i	$-0.0868758\pi$
$41$	0.163119	+	0.502029i	0.0254749	+	0.0784037i	−0.937511	+	0.347956i	$0.886876\pi$
$42$		0			0
$43$	0.527864			0.0804985			0.0402493	−	0.999190i	$-0.487185\pi$
$43$	0.527864			0.0804985			0.0402493	+	0.999190i	$0.487185\pi$
$44$		0			0
$45$	2.85410			0.425464
$46$		0			0
$47$	0.427051	+	1.31433i	0.0622918	+	0.191714i	0.977359	−	0.211586i	$-0.0678629\pi$
$47$	0.427051	+	1.31433i	0.0622918	+	0.191714i	−0.915068	+	0.403301i	$0.867863\pi$
$48$		0			0
$49$	−8.85410	−	6.43288i	−1.26487	−	0.918983i
$50$		0			0
$51$	−1.42705	+	4.39201i	−0.199827	+	0.615005i
$52$		0			0
$53$	10.9721	−	7.97172i	1.50714	−	1.09500i	0.539712	−	0.841850i	$-0.318533\pi$
$53$	10.9721	−	7.97172i	1.50714	−	1.09500i	0.967427	−	0.253151i	$-0.0814668\pi$
$54$		0			0
$55$	−0.881966	−	9.42481i	−0.118924	−	1.27084i
$56$		0			0
$57$	4.92705	−	3.57971i	0.652604	−	0.474144i
$58$		0			0
$59$	2.73607	−	8.42075i	0.356206	−	1.09629i	−0.599101	−	0.800673i	$-0.704475\pi$
$59$	2.73607	−	8.42075i	0.356206	−	1.09629i	0.955307	−	0.295615i	$-0.0955246\pi$
$60$		0			0
$61$	0.309017	+	0.224514i	0.0395656	+	0.0287461i	0.607392	−	0.794402i	$-0.292216\pi$
$61$	0.309017	+	0.224514i	0.0395656	+	0.0287461i	−0.567827	+	0.823148i	$0.692216\pi$
$62$		0			0
$63$	1.30902	+	4.02874i	0.164921	+	0.507574i
$64$		0			0
$65$	−5.03444			−0.624446
$66$		0			0
$67$	−6.85410			−0.837362			−0.418681	−	0.908133i	$-0.637507\pi$
$67$	−6.85410			−0.837362			−0.418681	+	0.908133i	$0.637507\pi$
$68$		0			0
$69$	−1.30902	−	4.02874i	−0.157587	−	0.485003i
$70$		0			0
$71$	2.92705	+	2.12663i	0.347377	+	0.252384i	0.747768	−	0.663960i	$-0.231126\pi$
$71$	2.92705	+	2.12663i	0.347377	+	0.252384i	−0.400391	+	0.916344i	$0.631126\pi$
$72$		0			0
$73$	−0.381966	+	1.17557i	−0.0447057	+	0.137590i	−0.970918	−	0.239412i	$-0.923045\pi$
$73$	−0.381966	+	1.17557i	−0.0447057	+	0.137590i	0.926212	+	0.377003i	$0.123045\pi$
$74$		0			0
$75$	2.54508	−	1.84911i	0.293881	−	0.213517i
$76$		0			0
$77$	12.8992	−	5.56758i	1.47000	−	0.634485i
$78$		0			0
$79$	−7.89919	+	5.73910i	−0.888728	+	0.645699i	−0.935546	−	0.353205i	$-0.885092\pi$
$79$	−7.89919	+	5.73910i	−0.888728	+	0.645699i	0.0468181	+	0.998903i	$0.485092\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−5.28115	−	3.83698i	−0.579682	−	0.421164i	0.258928	−	0.965897i	$-0.416631\pi$
$83$	−5.28115	−	3.83698i	−0.579682	−	0.421164i	−0.838609	+	0.544733i	$0.816631\pi$
$84$		0			0
$85$	4.07295	+	12.5352i	0.441773	+	1.35964i
$86$		0			0
$87$	4.47214			0.479463
$88$		0			0
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	−2.30902	−	7.10642i	−0.242051	−	0.744956i
$92$		0			0
$93$	−6.97214	−	5.06555i	−0.722977	−	0.525273i
$94$		0			0
$95$	5.37132	−	16.5312i	0.551086	−	1.69607i
$96$		0			0
$97$	−4.92705	+	3.57971i	−0.500266	+	0.363465i	−0.809119	−	0.587645i	$-0.800055\pi$
$97$	−4.92705	+	3.57971i	−0.500266	+	0.363465i	0.308852	+	0.951110i	$0.400055\pi$
$98$		0			0
$99$	−3.23607	−	0.726543i	−0.325237	−	0.0730203i
$100$		0			0
$101$	−9.66312	+	7.02067i	−0.961516	+	0.698582i	−0.953502	−	0.301385i	$-0.902551\pi$
$101$	−9.66312	+	7.02067i	−0.961516	+	0.698582i	−0.00801387	+	0.999968i	$0.502551\pi$
$102$		0			0
$103$	1.09017	−	3.35520i	0.107418	−	0.330597i	−0.882873	−	0.469613i	$-0.844394\pi$
$103$	1.09017	−	3.35520i	0.107418	−	0.330597i	0.990290	+	0.139015i	$0.0443936\pi$
$104$		0			0
$105$	9.78115	+	7.10642i	0.954543	+	0.693516i
$106$		0			0
$107$	4.78115	+	14.7149i	0.462212	+	1.42254i	0.862456	+	0.506132i	$0.168925\pi$
$107$	4.78115	+	14.7149i	0.462212	+	1.42254i	−0.400244	+	0.916408i	$0.631075\pi$
$108$		0			0
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$	8.23607			0.781733
$112$		0			0
$113$	2.39919	+	7.38394i	0.225697	+	0.694622i	0.998220	+	0.0596365i	$0.0189941\pi$
$113$	2.39919	+	7.38394i	0.225697	+	0.694622i	−0.772524	+	0.634986i	$0.781006\pi$
$114$		0			0
$115$	−9.78115	−	7.10642i	−0.912097	−	0.662677i
$116$		0			0
$117$	−0.545085	+	1.67760i	−0.0503931	+	0.155094i
$118$		0			0
$119$	−15.8262	+	11.4984i	−1.45079	+	1.05406i
$120$		0			0
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$		0			0
$123$	0.427051	−	0.310271i	0.0385059	−	0.0279762i
$124$		0			0
$125$	−1.63525	+	5.03280i	−0.146262	+	0.450147i
$126$		0			0
$127$	−1.85410	−	1.34708i	−0.164525	−	0.119534i	0.502476	−	0.864591i	$-0.332422\pi$
$127$	−1.85410	−	1.34708i	−0.164525	−	0.119534i	−0.667001	+	0.745057i	$0.732422\pi$
$128$		0			0
$129$	−0.163119	−	0.502029i	−0.0143618	−	0.0442011i
$130$		0			0
$131$	11.5623			1.01020			0.505102	−	0.863060i	$-0.331455\pi$
$131$	11.5623			1.01020			0.505102	+	0.863060i	$0.331455\pi$
$132$		0			0
$133$	25.7984			2.23700
$134$		0			0
$135$	−0.881966	−	2.71441i	−0.0759075	−	0.233619i
$136$		0			0
$137$	16.9894	+	12.3435i	1.45150	+	1.05458i	0.985478	+	0.169802i	$0.0543127\pi$
$137$	16.9894	+	12.3435i	1.45150	+	1.05458i	0.466020	+	0.884774i	$0.345687\pi$
$138$		0			0
$139$	−6.42705	+	19.7804i	−0.545135	+	1.67775i	0.175533	+	0.984474i	$0.443835\pi$
$139$	−6.42705	+	19.7804i	−0.545135	+	1.67775i	−0.720668	+	0.693280i	$0.756165\pi$
$140$		0			0
$141$	1.11803	−	0.812299i	0.0941554	−	0.0684079i
$142$		0			0
$143$	5.70820	+	1.28157i	0.477344	+	0.107170i
$144$		0			0
$145$	10.3262	−	7.50245i	0.857547	−	0.623045i
$146$		0			0
$147$	−3.38197	+	10.4086i	−0.278940	+	0.858489i
$148$		0			0
$149$	−15.2812	−	11.1024i	−1.25188	−	0.909545i	−0.253551	−	0.967322i	$-0.581599\pi$
$149$	−15.2812	−	11.1024i	−1.25188	−	0.909545i	−0.998329	+	0.0577773i	$0.981599\pi$
$150$		0			0
$151$	−1.38197	−	4.25325i	−0.112463	−	0.346125i	0.878947	−	0.476920i	$-0.158247\pi$
$151$	−1.38197	−	4.25325i	−0.112463	−	0.346125i	−0.991409	+	0.130795i	$0.958247\pi$
$152$		0			0
$153$	4.61803			0.373346
$154$		0			0
$155$	−24.5967			−1.97566
$156$		0			0
$157$	−3.94427	−	12.1392i	−0.314787	−	0.968815i	−0.975842	−	0.218478i	$-0.929891\pi$
$157$	−3.94427	−	12.1392i	−0.314787	−	0.968815i	0.661055	−	0.750338i	$-0.270109\pi$
$158$		0			0
$159$	−10.9721	−	7.97172i	−0.870147	−	0.632199i
$160$		0			0
$161$	5.54508	−	17.0660i	0.437014	−	1.34499i
$162$		0			0
$163$	−1.50000	+	1.08981i	−0.117489	+	0.0853608i	−0.644978	−	0.764201i	$-0.723134\pi$
$163$	−1.50000	+	1.08981i	−0.117489	+	0.0853608i	0.527489	+	0.849562i	$0.323134\pi$
$164$		0			0
$165$	−8.69098	+	3.75123i	−0.676592	+	0.292033i
$166$		0			0
$167$	−1.30902	+	0.951057i	−0.101295	+	0.0735950i	−0.637280	−	0.770633i	$-0.719940\pi$
$167$	−1.30902	+	0.951057i	−0.101295	+	0.0735950i	0.535985	+	0.844228i	$0.319940\pi$
$168$		0			0
$169$	−3.05573	+	9.40456i	−0.235056	+	0.723428i
$170$		0			0
$171$	−4.92705	−	3.57971i	−0.376781	−	0.273747i
$172$		0			0
$173$	−4.50000	−	13.8496i	−0.342129	−	1.05296i	−0.963103	−	0.269133i	$-0.913263\pi$
$173$	−4.50000	−	13.8496i	−0.342129	−	1.05296i	0.620974	−	0.783831i	$-0.286737\pi$
$174$		0			0
$175$	13.3262			1.00737
$176$		0			0
$177$	−8.85410			−0.665515
$178$		0			0
$179$	−0.0172209	−	0.0530006i	−0.00128715	−	0.00396145i	0.950411	−	0.310997i	$-0.100663\pi$
$179$	−0.0172209	−	0.0530006i	−0.00128715	−	0.00396145i	−0.951698	+	0.307036i	$0.900663\pi$
$180$		0			0
$181$	9.66312	+	7.02067i	0.718254	+	0.521842i	0.885826	−	0.464018i	$-0.153593\pi$
$181$	9.66312	+	7.02067i	0.718254	+	0.521842i	−0.167572	+	0.985860i	$0.553593\pi$
$182$		0			0
$183$	0.118034	−	0.363271i	0.00872532	−	0.0268538i
$184$		0			0
$185$	19.0172	−	13.8168i	1.39817	−	1.01583i
$186$		0			0
$187$	−1.42705	−	15.2497i	−0.104356	−	1.11517i
$188$		0			0
$189$	3.42705	−	2.48990i	0.249281	−	0.181113i
$190$		0			0
$191$	2.98278	−	9.18005i	0.215826	−	0.664245i	−0.783268	−	0.621685i	$-0.786449\pi$
$191$	2.98278	−	9.18005i	0.215826	−	0.664245i	0.999094	−	0.0425604i	$-0.0135515\pi$
$192$		0			0
$193$	0.263932	+	0.191758i	0.0189982	+	0.0138030i	0.597244	−	0.802060i	$-0.296262\pi$
$193$	0.263932	+	0.191758i	0.0189982	+	0.0138030i	−0.578246	+	0.815863i	$0.696262\pi$
$194$		0			0
$195$	1.55573	+	4.78804i	0.111408	+	0.342879i
$196$		0			0
$197$	−17.0902			−1.21762			−0.608812	−	0.793314i	$-0.708354\pi$
$197$	−17.0902			−1.21762			−0.608812	+	0.793314i	$0.708354\pi$
$198$		0			0
$199$	16.4164			1.16373			0.581864	−	0.813286i	$-0.302324\pi$
$199$	16.4164			1.16373			0.581864	+	0.813286i	$0.302324\pi$
$200$		0			0
$201$	2.11803	+	6.51864i	0.149395	+	0.459789i
$202$		0			0
$203$	15.3262	+	11.1352i	1.07569	+	0.781535i
$204$		0			0
$205$	0.465558	−	1.43284i	0.0325160	−	0.100074i
$206$		0			0
$207$	−3.42705	+	2.48990i	−0.238197	+	0.173060i
$208$		0			0
$209$	−10.2984	+	17.3763i	−0.712353	+	1.20194i
$210$		0			0
$211$	19.2082	−	13.9556i	1.32235	−	0.960742i	0.322447	−	0.946587i	$-0.395494\pi$
$211$	19.2082	−	13.9556i	1.32235	−	0.960742i	0.999900	−	0.0141542i	$-0.00450557\pi$
$212$		0			0
$213$	1.11803	−	3.44095i	0.0766064	−	0.235770i
$214$		0			0
$215$	−1.21885	−	0.885544i	−0.0831247	−	0.0603936i
$216$		0			0
$217$	−11.2812	−	34.7198i	−0.765815	−	2.35693i
$218$		0			0
$219$	1.23607			0.0835257
$220$		0			0
$221$	−8.14590			−0.547952
$222$		0			0
$223$	0.454915	+	1.40008i	0.0304634	+	0.0937566i	0.965132	−	0.261763i	$-0.0843039\pi$
$223$	0.454915	+	1.40008i	0.0304634	+	0.0937566i	−0.934669	+	0.355520i	$0.884304\pi$
$224$		0			0
$225$	−2.54508	−	1.84911i	−0.169672	−	0.123274i
$226$		0			0
$227$	−0.218847	+	0.673542i	−0.0145254	+	0.0447046i	−0.958057	−	0.286579i	$-0.907482\pi$
$227$	−0.218847	+	0.673542i	−0.0145254	+	0.0447046i	0.943531	+	0.331284i	$0.107482\pi$
$228$		0			0
$229$	5.61803	−	4.08174i	0.371250	−	0.269729i	−0.386479	−	0.922298i	$-0.626309\pi$
$229$	5.61803	−	4.08174i	0.371250	−	0.269729i	0.757729	+	0.652569i	$0.226309\pi$
$230$		0			0
$231$	−9.28115	−	10.5474i	−0.610655	−	0.693967i
$232$		0			0
$233$	−20.8713	+	15.1639i	−1.36733	+	0.993420i	−0.369385	+	0.929276i	$0.620432\pi$
$233$	−20.8713	+	15.1639i	−1.36733	+	0.993420i	−0.997941	+	0.0641440i	$0.979568\pi$
$234$		0			0
$235$	1.21885	−	3.75123i	0.0795088	−	0.244703i
$236$		0			0
$237$	7.89919	+	5.73910i	0.513107	+	0.372794i
$238$		0			0
$239$	−6.33688	−	19.5029i	−0.409899	−	1.26154i	−0.916735	−	0.399496i	$-0.869185\pi$
$239$	−6.33688	−	19.5029i	−0.409899	−	1.26154i	0.506836	−	0.862042i	$-0.330815\pi$
$240$		0			0
$241$	−10.2918			−0.662953			−0.331476	−	0.943463i	$-0.607547\pi$
$241$	−10.2918			−0.662953			−0.331476	+	0.943463i	$0.607547\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	9.65248	+	29.7073i	0.616674	+	1.89793i
$246$		0			0
$247$	8.69098	+	6.31437i	0.552994	+	0.401774i
$248$		0			0
$249$	−2.01722	+	6.20837i	−0.127836	+	0.393439i
$250$		0			0
$251$	−10.4443	+	7.58821i	−0.659237	+	0.478963i	−0.866405	−	0.499342i	$-0.833575\pi$
$251$	−10.4443	+	7.58821i	−0.659237	+	0.478963i	0.207168	+	0.978305i	$0.433575\pi$
$252$		0			0
$253$	9.28115	+	10.5474i	0.583501	+	0.663108i
$254$		0			0
$255$	10.6631	−	7.74721i	0.667750	−	0.485149i
$256$		0			0
$257$	6.73607	−	20.7315i	0.420184	−	1.29319i	−0.487346	−	0.873209i	$-0.662035\pi$
$257$	6.73607	−	20.7315i	0.420184	−	1.29319i	0.907531	−	0.419986i	$-0.137965\pi$
$258$		0			0
$259$	28.2254	+	20.5070i	1.75384	+	1.27424i
$260$		0			0
$261$	−1.38197	−	4.25325i	−0.0855415	−	0.263270i
$262$		0			0
$263$	17.1459			1.05726			0.528631	−	0.848852i	$-0.322706\pi$
$263$	17.1459			1.05726			0.528631	+	0.848852i	$0.322706\pi$
$264$		0			0
$265$	−38.7082			−2.37783
$266$		0			0
$267$	−0.309017	−	0.951057i	−0.0189115	−	0.0582037i
$268$		0			0
$269$	−15.7984	−	11.4782i	−0.963244	−	0.699838i	−0.00934200	−	0.999956i	$-0.502974\pi$
$269$	−15.7984	−	11.4782i	−0.963244	−	0.699838i	−0.953902	+	0.300119i	$0.902974\pi$
$270$		0			0
$271$	−6.97214	+	21.4580i	−0.423527	+	1.30348i	0.480870	+	0.876792i	$0.340321\pi$
$271$	−6.97214	+	21.4580i	−0.423527	+	1.30348i	−0.904398	+	0.426691i	$0.859679\pi$
$272$		0			0
$273$	−6.04508	+	4.39201i	−0.365865	+	0.265817i
$274$		0			0
$275$	−5.31966	+	8.97578i	−0.320788	+	0.541260i
$276$		0			0
$277$	14.2082	−	10.3229i	0.853688	−	0.620241i	−0.0724723	−	0.997370i	$-0.523089\pi$
$277$	14.2082	−	10.3229i	0.853688	−	0.620241i	0.926160	+	0.377130i	$0.123089\pi$
$278$		0			0
$279$	−2.66312	+	8.19624i	−0.159437	+	0.490696i
$280$		0			0
$281$	18.7082	+	13.5923i	1.11604	+	0.810849i	0.983604	−	0.180343i	$-0.0577207\pi$
$281$	18.7082	+	13.5923i	1.11604	+	0.810849i	0.132434	+	0.991192i	$0.457721\pi$
$282$		0			0
$283$	5.79837	+	17.8456i	0.344678	+	1.06081i	0.961756	+	0.273907i	$0.0883160\pi$
$283$	5.79837	+	17.8456i	0.344678	+	1.06081i	−0.617079	+	0.786901i	$0.711684\pi$
$284$		0			0
$285$	−17.3820			−1.02962
$286$		0			0
$287$	2.23607			0.131991
$288$		0			0
$289$	1.33688	+	4.11450i	0.0786401	+	0.242029i
$290$		0			0
$291$	4.92705	+	3.57971i	0.288829	+	0.209846i
$292$		0			0
$293$	−1.54508	+	4.75528i	−0.0902648	+	0.277807i	−0.985991	−	0.166800i	$-0.946657\pi$
$293$	−1.54508	+	4.75528i	−0.0902648	+	0.277807i	0.895726	+	0.444607i	$0.146657\pi$
$294$		0			0
$295$	−20.4443	+	14.8536i	−1.19031	+	0.864812i
$296$		0			0
$297$	0.309017	+	3.30220i	0.0179310	+	0.191613i
$298$		0			0
$299$	6.04508	−	4.39201i	0.349596	−	0.253997i
$300$		0			0
$301$	0.690983	−	2.12663i	0.0398276	−	0.122577i
$302$		0			0
$303$	9.66312	+	7.02067i	0.555132	+	0.403327i
$304$		0			0
$305$	−0.336881	−	1.03681i	−0.0192898	−	0.0593678i
$306$		0			0
$307$	−16.3262			−0.931788			−0.465894	−	0.884841i	$-0.654267\pi$
$307$	−16.3262			−0.931788			−0.465894	+	0.884841i	$0.654267\pi$
$308$		0			0
$309$	−3.52786			−0.200693
$310$		0			0
$311$	−2.10739	−	6.48588i	−0.119499	−	0.367781i	0.873360	−	0.487076i	$-0.161936\pi$
$311$	−2.10739	−	6.48588i	−0.119499	−	0.367781i	−0.992859	+	0.119295i	$0.961936\pi$
$312$		0			0
$313$	0.809017	+	0.587785i	0.0457283	+	0.0332236i	0.610415	−	0.792082i	$-0.291003\pi$
$313$	0.809017	+	0.587785i	0.0457283	+	0.0332236i	−0.564686	+	0.825306i	$0.691003\pi$
$314$		0			0
$315$	3.73607	−	11.4984i	0.210504	−	0.647863i
$316$		0			0
$317$	−14.1353	+	10.2699i	−0.793915	+	0.576813i	−0.909123	−	0.416528i	$-0.863247\pi$
$317$	−14.1353	+	10.2699i	−0.793915	+	0.576813i	0.115208	+	0.993341i	$0.463247\pi$
$318$		0			0
$319$	−13.6180	+	5.87785i	−0.762464	+	0.329097i
$320$		0			0
$321$	12.5172	−	9.09429i	0.698643	−	0.507594i
$322$		0			0
$323$	8.69098	−	26.7481i	0.483579	−	1.48830i
$324$		0			0
$325$	4.48936	+	3.26171i	0.249025	+	0.180927i
$326$		0			0
$327$	2.47214	+	7.60845i	0.136709	+	0.420748i
$328$		0			0
$329$	5.85410			0.322747
$330$		0			0
$331$	−5.94427			−0.326727			−0.163363	−	0.986566i	$-0.552234\pi$
$331$	−5.94427			−0.326727			−0.163363	+	0.986566i	$0.552234\pi$
$332$		0			0
$333$	−2.54508	−	7.83297i	−0.139470	−	0.429244i
$334$		0			0
$335$	15.8262	+	11.4984i	0.864680	+	0.628227i
$336$		0			0
$337$	9.76393	−	30.0503i	0.531875	−	1.63694i	−0.218430	−	0.975853i	$-0.570094\pi$
$337$	9.76393	−	30.0503i	0.531875	−	1.63694i	0.750306	−	0.661091i	$-0.229906\pi$
$338$		0			0
$339$	6.28115	−	4.56352i	0.341145	−	0.247857i
$340$		0			0
$341$	27.8885	+	6.26137i	1.51025	+	0.339072i
$342$		0			0
$343$	−13.5172	+	9.82084i	−0.729861	+	0.530275i
$344$		0			0
$345$	−3.73607	+	11.4984i	−0.201143	+	0.619055i
$346$		0			0
$347$	6.47214	+	4.70228i	0.347442	+	0.252432i	0.747795	−	0.663929i	$-0.231112\pi$
$347$	6.47214	+	4.70228i	0.347442	+	0.252432i	−0.400353	+	0.916361i	$0.631112\pi$
$348$		0			0
$349$	−7.34346	−	22.6008i	−0.393086	−	1.20980i	−0.930442	−	0.366440i	$-0.880577\pi$
$349$	−7.34346	−	22.6008i	−0.393086	−	1.20980i	0.537356	−	0.843356i	$-0.319423\pi$
$350$		0			0
$351$	1.76393			0.0941517
$352$		0			0
$353$	−1.52786			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$353$	−1.52786			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$354$		0			0
$355$	−3.19098	−	9.82084i	−0.169360	−	0.521236i
$356$		0			0
$357$	15.8262	+	11.4984i	0.837613	+	0.608562i
$358$		0			0
$359$	−5.79837	+	17.8456i	−0.306026	+	0.941853i	0.673266	+	0.739401i	$0.264891\pi$
$359$	−5.79837	+	17.8456i	−0.306026	+	0.941853i	−0.979292	+	0.202452i	$0.935109\pi$
$360$		0			0
$361$	−14.6353	+	10.6331i	−0.770277	+	0.559639i
$362$		0			0
$363$	10.8090	−	2.04087i	0.567326	−	0.107118i
$364$		0			0
$365$	2.85410	−	2.07363i	0.149391	−	0.108539i
$366$		0			0
$367$	−2.35410	+	7.24518i	−0.122883	+	0.378195i	−0.993509	−	0.113750i	$-0.963714\pi$
$367$	−2.35410	+	7.24518i	−0.122883	+	0.378195i	0.870626	+	0.491945i	$0.163714\pi$
$368$		0			0
$369$	−0.427051	−	0.310271i	−0.0222314	−	0.0161520i
$370$		0			0
$371$	−17.7533	−	54.6390i	−0.921705	−	2.83672i
$372$		0			0
$373$	3.94427			0.204227			0.102113	−	0.994773i	$-0.467440\pi$
$373$	3.94427			0.204227			0.102113	+	0.994773i	$0.467440\pi$
$374$		0			0
$375$	5.29180			0.273267
$376$		0			0
$377$	2.43769	+	7.50245i	0.125548	+	0.386396i
$378$		0			0
$379$	−0.572949	−	0.416272i	−0.0294304	−	0.0213824i	0.572973	−	0.819574i	$-0.305790\pi$
$379$	−0.572949	−	0.416272i	−0.0294304	−	0.0213824i	−0.602403	+	0.798192i	$0.705790\pi$
$380$		0			0
$381$	−0.708204	+	2.17963i	−0.0362824	+	0.111666i
$382$		0			0
$383$	−4.66312	+	3.38795i	−0.238274	+	0.173116i	−0.700514	−	0.713639i	$-0.747046\pi$
$383$	−4.66312	+	3.38795i	−0.238274	+	0.173116i	0.462240	+	0.886755i	$0.347046\pi$
$384$		0			0
$385$	−39.1246	−	8.78402i	−1.99397	−	0.447675i
$386$		0			0
$387$	−0.427051	+	0.310271i	−0.0217082	+	0.0157719i
$388$		0			0
$389$	1.51722	−	4.66953i	0.0769262	−	0.236754i	−0.905198	−	0.424991i	$-0.860277\pi$
$389$	1.51722	−	4.66953i	0.0769262	−	0.236754i	0.982124	+	0.188237i	$0.0602772\pi$
$390$		0			0
$391$	−15.8262	−	11.4984i	−0.800367	−	0.581501i
$392$		0			0
$393$	−3.57295	−	10.9964i	−0.180231	−	0.554695i
$394$		0			0
$395$	27.8673			1.40215
$396$		0			0
$397$	4.81966			0.241892			0.120946	−	0.992659i	$-0.461407\pi$
$397$	4.81966			0.241892			0.120946	+	0.992659i	$0.461407\pi$
$398$		0			0
$399$	−7.97214	−	24.5357i	−0.399106	−	1.22832i
$400$		0			0
$401$	−3.11803	−	2.26538i	−0.155707	−	0.113128i	0.507204	−	0.861826i	$-0.330679\pi$
$401$	−3.11803	−	2.26538i	−0.155707	−	0.113128i	−0.662911	+	0.748698i	$0.730679\pi$
$402$		0			0
$403$	4.69756	−	14.4576i	0.234002	−	0.720185i
$404$		0			0
$405$	−2.30902	+	1.67760i	−0.114736	+	0.0833606i
$406$		0			0
$407$	−25.0795	+	10.8249i	−1.24315	+	0.536570i
$408$		0			0
$409$	20.9443	−	15.2169i	1.03563	−	0.752427i	0.0662003	−	0.997806i	$-0.478912\pi$
$409$	20.9443	−	15.2169i	1.03563	−	0.752427i	0.969427	+	0.245379i	$0.0789124\pi$
$410$		0			0
$411$	6.48936	−	19.9722i	0.320096	−	0.985155i
$412$		0			0
$413$	−30.3435	−	22.0458i	−1.49310	−	1.08480i
$414$		0			0
$415$	5.75735	+	17.7193i	0.282617	+	0.869807i
$416$		0			0
$417$	20.7984			1.01850
$418$		0			0
$419$	11.1459			0.544513			0.272256	−	0.962225i	$-0.412230\pi$
$419$	11.1459			0.544513			0.272256	+	0.962225i	$0.412230\pi$
$420$		0			0
$421$	7.50000	+	23.0826i	0.365528	+	1.12498i	0.949650	+	0.313313i	$0.101439\pi$
$421$	7.50000	+	23.0826i	0.365528	+	1.12498i	−0.584122	+	0.811666i	$0.698561\pi$
$422$		0			0
$423$	−1.11803	−	0.812299i	−0.0543607	−	0.0394953i
$424$		0			0
$425$	4.48936	−	13.8168i	0.217766	−	0.670214i
$426$		0			0
$427$	1.30902	−	0.951057i	0.0633478	−	0.0460249i
$428$		0			0
$429$	−0.545085	−	5.82485i	−0.0263170	−	0.281227i
$430$		0			0
$431$	1.88197	−	1.36733i	0.0906511	−	0.0658619i	−0.541536	−	0.840677i	$-0.682157\pi$
$431$	1.88197	−	1.36733i	0.0906511	−	0.0658619i	0.632188	+	0.774815i	$0.282157\pi$
$432$		0			0
$433$	0.909830	−	2.80017i	0.0437236	−	0.134568i	−0.926812	−	0.375526i	$-0.877462\pi$
$433$	0.909830	−	2.80017i	0.0437236	−	0.134568i	0.970535	+	0.240959i	$0.0774619\pi$
$434$		0			0
$435$	−10.3262	−	7.50245i	−0.495105	−	0.359715i
$436$		0			0
$437$	7.97214	+	24.5357i	0.381359	+	1.17370i
$438$		0			0
$439$	25.3607			1.21040			0.605200	−	0.796074i	$-0.293093\pi$
$439$	25.3607			1.21040			0.605200	+	0.796074i	$0.293093\pi$
$440$		0			0
$441$	10.9443			0.521156
$442$		0			0
$443$	−6.85410	−	21.0948i	−0.325648	−	1.00224i	−0.971147	−	0.238481i	$-0.923351\pi$
$443$	−6.85410	−	21.0948i	−0.325648	−	1.00224i	0.645499	−	0.763761i	$-0.276649\pi$
$444$		0			0
$445$	−2.30902	−	1.67760i	−0.109458	−	0.0795258i
$446$		0			0
$447$	−5.83688	+	17.9641i	−0.276075	+	0.849671i
$448$		0			0
$449$	13.3262	−	9.68208i	0.628904	−	0.456926i	−0.227116	−	0.973868i	$-0.572930\pi$
$449$	13.3262	−	9.68208i	0.628904	−	0.456926i	0.856020	+	0.516942i	$0.172930\pi$
$450$		0			0
$451$	−0.892609	+	1.50609i	−0.0420313	+	0.0709188i
$452$		0			0
$453$	−3.61803	+	2.62866i	−0.169990	+	0.123505i
$454$		0			0
$455$	−6.59017	+	20.2825i	−0.308952	+	0.950856i
$456$		0			0
$457$	−6.35410	−	4.61653i	−0.297232	−	0.215952i	0.429166	−	0.903225i	$-0.358807\pi$
$457$	−6.35410	−	4.61653i	−0.297232	−	0.215952i	−0.726399	+	0.687274i	$0.758807\pi$
$458$		0			0
$459$	−1.42705	−	4.39201i	−0.0666090	−	0.205002i
$460$		0			0
$461$	−0.562306			−0.0261892			−0.0130946	−	0.999914i	$-0.504168\pi$
$461$	−0.562306			−0.0261892			−0.0130946	+	0.999914i	$0.504168\pi$
$462$		0			0
$463$	−30.2148			−1.40420			−0.702100	−	0.712078i	$-0.747754\pi$
$463$	−30.2148			−1.40420			−0.702100	+	0.712078i	$0.747754\pi$
$464$		0			0
$465$	7.60081	+	23.3929i	0.352479	+	1.08482i
$466$		0			0
$467$	27.3713	+	19.8864i	1.26659	+	0.920234i	0.999061	−	0.0433147i	$-0.0137918\pi$
$467$	27.3713	+	19.8864i	1.26659	+	0.920234i	0.267532	+	0.963549i	$0.413792\pi$
$468$		0			0
$469$	−8.97214	+	27.6134i	−0.414295	+	1.27507i
$470$		0			0
$471$	−10.3262	+	7.50245i	−0.475808	+	0.345695i
$472$		0			0
$473$	1.15654	+	1.31433i	0.0531778	+	0.0604329i
$474$		0			0
$475$	−15.5000	+	11.2614i	−0.711189	+	0.516709i
$476$		0			0
$477$	−4.19098	+	12.8985i	−0.191892	+	0.590583i
$478$		0			0
$479$	1.88197	+	1.36733i	0.0859892	+	0.0624748i	0.629949	−	0.776636i	$-0.283076\pi$
$479$	1.88197	+	1.36733i	0.0859892	+	0.0624748i	−0.543960	+	0.839111i	$0.683076\pi$
$480$		0			0
$481$	4.48936	+	13.8168i	0.204697	+	0.629993i
$482$		0			0
$483$	−17.9443			−0.816493
$484$		0			0
$485$	17.3820			0.789274
$486$		0			0
$487$	−5.51064	−	16.9600i	−0.249711	−	0.768532i	−0.994826	−	0.101595i	$-0.967605\pi$
$487$	−5.51064	−	16.9600i	−0.249711	−	0.768532i	0.745115	−	0.666936i	$-0.232395\pi$
$488$		0			0
$489$	1.50000	+	1.08981i	0.0678323	+	0.0492831i
$490$		0			0
$491$	−3.66312	+	11.2739i	−0.165314	+	0.508785i	−0.999059	−	0.0433647i	$-0.986192\pi$
$491$	−3.66312	+	11.2739i	−0.165314	+	0.508785i	0.833745	+	0.552150i	$0.186192\pi$
$492$		0			0
$493$	16.7082	−	12.1392i	0.752500	−	0.546723i
$494$		0			0
$495$	6.25329	+	7.10642i	0.281064	+	0.319410i
$496$		0			0
$497$	12.3992	−	9.00854i	0.556180	−	0.404088i
$498$		0			0
$499$	−5.64590	+	17.3763i	−0.252745	+	0.777869i	0.741520	+	0.670930i	$0.234105\pi$
$499$	−5.64590	+	17.3763i	−0.252745	+	0.777869i	−0.994266	+	0.106939i	$0.965895\pi$
$500$		0			0
$501$	1.30902	+	0.951057i	0.0584826	+	0.0424901i
$502$		0			0
$503$	3.94427	+	12.1392i	0.175866	+	0.541261i	0.999672	−	0.0256113i	$-0.00815323\pi$
$503$	3.94427	+	12.1392i	0.175866	+	0.541261i	−0.823806	+	0.566872i	$0.808153\pi$
$504$		0			0
$505$	34.0902			1.51699
$506$		0			0
$507$	9.88854			0.439166
$508$		0			0
$509$	−9.19098	−	28.2869i	−0.407383	−	1.25380i	−0.918889	−	0.394517i	$-0.870912\pi$
$509$	−9.19098	−	28.2869i	−0.407383	−	1.25380i	0.511506	−	0.859280i	$-0.329088\pi$
$510$		0			0
$511$	4.23607	+	3.07768i	0.187393	+	0.136149i
$512$		0			0
$513$	−1.88197	+	5.79210i	−0.0830908	+	0.255727i
$514$		0			0
$515$	−8.14590	+	5.91834i	−0.358951	+	0.260793i
$516$		0			0
$517$	−2.33688	+	3.94298i	−0.102776	+	0.173412i
$518$		0			0
$519$	−11.7812	+	8.55951i	−0.517135	+	0.375721i
$520$		0			0
$521$	−12.0000	+	36.9322i	−0.525730	+	1.61803i	0.237139	+	0.971476i	$0.423790\pi$
$521$	−12.0000	+	36.9322i	−0.525730	+	1.61803i	−0.762869	+	0.646553i	$0.776210\pi$
$522$		0			0
$523$	−2.26393	−	1.64484i	−0.0989948	−	0.0719240i	0.537187	−	0.843463i	$-0.319487\pi$
$523$	−2.26393	−	1.64484i	−0.0989948	−	0.0719240i	−0.636182	+	0.771539i	$0.719487\pi$
$524$		0			0
$525$	−4.11803	−	12.6740i	−0.179726	−	0.553139i
$526$		0			0
$527$	−39.7984			−1.73364
$528$		0			0
$529$	−5.05573			−0.219814
$530$		0			0
$531$	2.73607	+	8.42075i	0.118735	+	0.365429i
$532$		0			0
$533$	0.753289	+	0.547296i	0.0326286	+	0.0237060i
$534$		0			0
$535$	13.6459	−	41.9978i	0.589964	−	1.81572i
$536$		0			0
$537$	−0.0450850	+	0.0327561i	−0.00194556	+	0.00141353i
$538$		0			0
$539$	−3.38197	−	36.1401i	−0.145672	−	1.55667i
$540$		0			0
$541$	−7.54508	+	5.48183i	−0.324389	+	0.235682i	−0.738046	−	0.674751i	$-0.764251\pi$
$541$	−7.54508	+	5.48183i	−0.324389	+	0.235682i	0.413657	+	0.910433i	$0.364251\pi$
$542$		0			0
$543$	3.69098	−	11.3597i	0.158395	−	0.487490i
$544$		0			0
$545$	18.4721	+	13.4208i	0.791259	+	0.574884i
$546$		0			0
$547$	−0.718847	−	2.21238i	−0.0307357	−	0.0945947i	0.934512	−	0.355932i	$-0.115837\pi$
$547$	−0.718847	−	2.21238i	−0.0307357	−	0.0945947i	−0.965248	+	0.261337i	$0.915837\pi$
$548$		0			0
$549$	−0.381966			−0.0163019
$550$		0			0
$551$	−27.2361			−1.16030
$552$		0			0
$553$	12.7812	+	39.3363i	0.543510	+	1.67275i
$554$		0			0
$555$	−19.0172	−	13.8168i	−0.807236	−	0.586491i
$556$		0			0
$557$	−1.88197	+	5.79210i	−0.0797415	+	0.245419i	−0.982978	−	0.183725i	$-0.941185\pi$
$557$	−1.88197	+	5.79210i	−0.0797415	+	0.245419i	0.903236	+	0.429144i	$0.141185\pi$
$558$		0			0
$559$	0.753289	−	0.547296i	0.0318607	−	0.0231482i
$560$		0			0
$561$	−14.0623	+	6.06961i	−0.593711	+	0.256259i
$562$		0			0
$563$	−22.0795	+	16.0417i	−0.930541	+	0.676078i	−0.946125	−	0.323801i	$-0.895039\pi$
$563$	−22.0795	+	16.0417i	−0.930541	+	0.676078i	0.0155841	+	0.999879i	$0.495039\pi$
$564$		0			0
$565$	6.84752	−	21.0745i	0.288078	−	0.886611i
$566$		0			0
$567$	−3.42705	−	2.48990i	−0.143923	−	0.104566i
$568$		0			0
$569$	13.9443	+	42.9161i	0.584574	+	1.79913i	0.600973	+	0.799269i	$0.294780\pi$
$569$	13.9443	+	42.9161i	0.584574	+	1.79913i	−0.0163990	+	0.999866i	$0.505220\pi$
$570$		0			0
$571$	8.67376			0.362986			0.181493	−	0.983392i	$-0.441907\pi$
$571$	8.67376			0.362986			0.181493	+	0.983392i	$0.441907\pi$
$572$		0			0
$573$	−9.65248			−0.403238
$574$		0			0
$575$	4.11803	+	12.6740i	0.171734	+	0.528543i
$576$		0			0
$577$	−20.0344	−	14.5559i	−0.834045	−	0.605969i	0.0866560	−	0.996238i	$-0.472382\pi$
$577$	−20.0344	−	14.5559i	−0.834045	−	0.605969i	−0.920701	+	0.390269i	$0.872382\pi$
$578$		0			0
$579$	0.100813	−	0.310271i	0.00418965	−	0.0128944i
$580$		0			0
$581$	−22.3713	+	16.2537i	−0.928119	+	0.674318i
$582$		0			0
$583$	43.8885	+	9.85359i	1.81768	+	0.408094i
$584$		0			0
$585$	4.07295	−	2.95917i	0.168396	−	0.122347i
$586$		0			0
$587$	9.34346	−	28.7562i	0.385646	−	1.18690i	−0.550365	−	0.834924i	$-0.685511\pi$
$587$	9.34346	−	28.7562i	0.385646	−	1.18690i	0.936011	−	0.351972i	$-0.114489\pi$
$588$		0			0
$589$	42.4615	+	30.8501i	1.74960	+	1.27116i
$590$		0			0
$591$	5.28115	+	16.2537i	0.217238	+	0.668589i
$592$		0			0
$593$	−36.4508			−1.49686			−0.748428	−	0.663215i	$-0.769191\pi$
$593$	−36.4508			−1.49686			−0.748428	+	0.663215i	$0.769191\pi$
$594$		0			0
$595$	55.8328			2.28892
$596$		0			0
$597$	−5.07295	−	15.6129i	−0.207622	−	0.638995i
$598$		0			0
$599$	−7.56231	−	5.49434i	−0.308987	−	0.224493i	0.422474	−	0.906375i	$-0.361162\pi$
$599$	−7.56231	−	5.49434i	−0.308987	−	0.224493i	−0.731462	+	0.681882i	$0.761162\pi$
$600$		0			0
$601$	0.635255	−	1.95511i	0.0259126	−	0.0797507i	−0.937264	−	0.348621i	$-0.886650\pi$
$601$	0.635255	−	1.95511i	0.0259126	−	0.0797507i	0.963177	+	0.268870i	$0.0866502\pi$
$602$		0			0
$603$	5.54508	−	4.02874i	0.225813	−	0.164063i
$604$		0			0
$605$	21.5344	−	22.8456i	0.875500	−	0.928806i
$606$		0			0
$607$	−19.6803	+	14.2986i	−0.798800	+	0.580362i	−0.910562	−	0.413373i	$-0.864351\pi$
$607$	−19.6803	+	14.2986i	−0.798800	+	0.580362i	0.111762	+	0.993735i	$0.464351\pi$
$608$		0			0
$609$	5.85410	−	18.0171i	0.237220	−	0.730089i
$610$		0			0
$611$	1.97214	+	1.43284i	0.0797841	+	0.0579665i
$612$		0			0
$613$	−7.14590	−	21.9928i	−0.288620	−	0.888281i	−0.985290	−	0.170890i	$-0.945336\pi$
$613$	−7.14590	−	21.9928i	−0.288620	−	0.888281i	0.696670	−	0.717392i	$-0.254664\pi$
$614$		0			0
$615$	−1.50658			−0.0607511
$616$		0			0
$617$	−7.00000			−0.281809			−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000			−0.281809			−0.140905	+	0.990023i	$0.545001\pi$
$618$		0			0
$619$	0.454915	+	1.40008i	0.0182846	+	0.0562741i	0.959782	−	0.280745i	$-0.0905814\pi$
$619$	0.454915	+	1.40008i	0.0182846	+	0.0562741i	−0.941498	+	0.337019i	$0.890581\pi$
$620$		0			0
$621$	3.42705	+	2.48990i	0.137523	+	0.0999162i
$622$		0			0
$623$	1.30902	−	4.02874i	0.0524447	−	0.161408i
$624$		0			0
$625$	24.9443	−	18.1231i	0.997771	−	0.724923i
$626$		0			0
$627$	19.7082	+	4.42477i	0.787070	+	0.176708i
$628$		0			0
$629$	30.7705	−	22.3561i	1.22690	−	0.891395i
$630$		0			0
$631$	12.7533	−	39.2506i	0.507700	−	1.56254i	−0.288482	−	0.957485i	$-0.593151\pi$
$631$	12.7533	−	39.2506i	0.507700	−	1.56254i	0.796183	−	0.605056i	$-0.206849\pi$
$632$		0			0
$633$	−19.2082	−	13.9556i	−0.763458	−	0.554684i
$634$		0			0
$635$	2.02129	+	6.22088i	0.0802123	+	0.246868i
$636$		0			0
$637$	−19.3050			−0.764890
$638$		0			0
$639$	−3.61803			−0.143127
$640$		0			0
$641$	−6.79180	−	20.9030i	−0.268260	−	0.825619i	−0.990924	−	0.134420i	$-0.957083\pi$
$641$	−6.79180	−	20.9030i	−0.268260	−	0.825619i	0.722665	−	0.691199i	$-0.242917\pi$
$642$		0			0
$643$	−23.5902	−	17.1393i	−0.930305	−	0.675907i	0.0157621	−	0.999876i	$-0.494983\pi$
$643$	−23.5902	−	17.1393i	−0.930305	−	0.675907i	−0.946068	+	0.323969i	$0.894983\pi$
$644$		0			0
$645$	−0.465558	+	1.43284i	−0.0183313	+	0.0564180i
$646$		0			0
$647$	19.9721	−	14.5106i	0.785186	−	0.570471i	−0.121345	−	0.992610i	$-0.538721\pi$
$647$	19.9721	−	14.5106i	0.785186	−	0.570471i	0.906531	+	0.422140i	$0.138721\pi$
$648$		0			0
$649$	26.9615	−	11.6372i	1.05833	−	0.456800i
$650$		0			0
$651$	−29.5344	+	21.4580i	−1.15755	+	0.841006i
$652$		0			0
$653$	−8.60739	+	26.4908i	−0.336833	+	1.03667i	0.628979	+	0.777423i	$0.283473\pi$
$653$	−8.60739	+	26.4908i	−0.336833	+	1.03667i	−0.965812	+	0.259244i	$0.916527\pi$
$654$		0			0
$655$	−26.6976	−	19.3969i	−1.04316	−	0.757900i
$656$		0			0
$657$	−0.381966	−	1.17557i	−0.0149019	−	0.0458634i
$658$		0			0
$659$	−3.70820			−0.144451			−0.0722256	−	0.997388i	$-0.523010\pi$
$659$	−3.70820			−0.144451			−0.0722256	+	0.997388i	$0.523010\pi$
$660$		0			0
$661$	2.32624			0.0904802			0.0452401	−	0.998976i	$-0.485595\pi$
$661$	2.32624			0.0904802			0.0452401	+	0.998976i	$0.485595\pi$
$662$		0			0
$663$	2.51722	+	7.74721i	0.0977608	+	0.300877i
$664$		0			0
$665$	−59.5689	−	43.2793i	−2.30998	−	1.67830i
$666$		0			0
$667$	−5.85410	+	18.0171i	−0.226672	+	0.697624i
$668$		0			0
$669$	1.19098	−	0.865300i	0.0460461	−	0.0334544i
$670$		0			0
$671$	0.118034	+	1.26133i	0.00455665	+	0.0486930i
$672$		0			0
$673$	−21.4615	+	15.5927i	−0.827280	+	0.601054i	−0.918788	−	0.394750i	$-0.870831\pi$
$673$	−21.4615	+	15.5927i	−0.827280	+	0.601054i	0.0915087	+	0.995804i	$0.470831\pi$
$674$		0			0
$675$	−0.972136	+	2.99193i	−0.0374175	+	0.115159i
$676$		0			0
$677$	5.23607	+	3.80423i	0.201238	+	0.146208i	0.683841	−	0.729631i	$-0.260308\pi$
$677$	5.23607	+	3.80423i	0.201238	+	0.146208i	−0.482602	+	0.875840i	$0.660308\pi$
$678$		0			0
$679$	7.97214	+	24.5357i	0.305942	+	0.941594i
$680$		0			0
$681$	0.708204			0.0271384
$682$		0			0
$683$	−6.34752			−0.242881			−0.121441	−	0.992599i	$-0.538751\pi$
$683$	−6.34752			−0.242881			−0.121441	+	0.992599i	$0.538751\pi$
$684$		0			0
$685$	−18.5213	−	57.0027i	−0.707662	−	2.17796i
$686$		0			0
$687$	−5.61803	−	4.08174i	−0.214341	−	0.155728i
$688$		0			0
$689$	7.39261	−	22.7521i	0.281636	−	0.866786i
$690$		0			0
$691$	27.9443	−	20.3027i	1.06305	−	0.772351i	0.0883999	−	0.996085i	$-0.471825\pi$
$691$	27.9443	−	20.3027i	1.06305	−	0.772351i	0.974650	+	0.223734i	$0.0718246\pi$
$692$		0			0
$693$	−7.16312	+	12.0862i	−0.272104	+	0.459118i
$694$		0			0
$695$	48.0238	−	34.8913i	1.82165	−	1.32350i
$696$		0			0
$697$	0.753289	−	2.31838i	0.0285329	−	0.0878151i
$698$		0			0
$699$	20.8713	+	15.1639i	0.789426	+	0.573552i
$700$		0			0
$701$	2.93769	+	9.04129i	0.110955	+	0.341485i	0.991082	−	0.133254i	$-0.0425426\pi$
$701$	2.93769	+	9.04129i	0.110955	+	0.341485i	−0.880127	+	0.474739i	$0.842543\pi$
$702$		0			0
$703$	−50.1591			−1.89178
$704$		0			0
$705$	−3.94427			−0.148550
$706$		0			0
$707$	15.6353	+	48.1204i	0.588024	+	1.80975i
$708$		0			0
$709$	20.8262	+	15.1311i	0.782146	+	0.568262i	0.905622	−	0.424085i	$-0.139404\pi$
$709$	20.8262	+	15.1311i	0.782146	+	0.568262i	−0.123476	+	0.992348i	$0.539404\pi$
$710$		0			0
$711$	3.01722	−	9.28605i	0.113155	−	0.348254i
$712$		0			0
$713$	29.5344	−	21.4580i	1.10607	−	0.803609i
$714$		0			0
$715$	−11.0304	−	12.5352i	−0.412513	−	0.468792i
$716$		0			0
$717$	−16.5902	+	12.0535i	−0.619571	+	0.450145i
$718$		0			0
$719$	−12.0729	+	37.1567i	−0.450245	+	1.38571i	0.426383	+	0.904543i	$0.359788\pi$
$719$	−12.0729	+	37.1567i	−0.450245	+	1.38571i	−0.876628	+	0.481169i	$0.840212\pi$
$720$		0			0
$721$	−12.0902	−	8.78402i	−0.450261	−	0.327134i
$722$		0			0
$723$	3.18034	+	9.78808i	0.118278	+	0.364023i
$724$		0			0
$725$	−14.0689			−0.522505
$726$		0			0
$727$	−2.14590			−0.0795870			−0.0397935	−	0.999208i	$-0.512670\pi$
$727$	−2.14590			−0.0795870			−0.0397935	+	0.999208i	$0.512670\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−1.97214	−	1.43284i	−0.0729421	−	0.0529955i
$732$		0			0
$733$	−6.96556	+	21.4378i	−0.257279	+	0.791823i	0.736093	+	0.676880i	$0.236668\pi$
$733$	−6.96556	+	21.4378i	−0.257279	+	0.791823i	−0.993372	+	0.114943i	$0.963332\pi$
$734$		0			0
$735$	25.2705	−	18.3601i	0.932117	−	0.677222i
$736$		0			0
$737$	−15.0172	−	17.0660i	−0.553166	−	0.628635i
$738$		0			0
$739$	28.4615	−	20.6785i	1.04697	−	0.760670i	0.0753384	−	0.997158i	$-0.475996\pi$
$739$	28.4615	−	20.6785i	1.04697	−	0.760670i	0.971634	+	0.236488i	$0.0759963\pi$
$740$		0			0
$741$	3.31966	−	10.2169i	0.121951	−	0.375326i
$742$		0			0
$743$	−2.04508	−	1.48584i	−0.0750269	−	0.0545102i	0.549640	−	0.835402i	$-0.314765\pi$
$743$	−2.04508	−	1.48584i	−0.0750269	−	0.0545102i	−0.624666	+	0.780892i	$0.714765\pi$
$744$		0			0
$745$	16.6591	+	51.2713i	0.610341	+	1.87843i
$746$		0			0
$747$	6.52786			0.238842
$748$		0			0
$749$	65.5410			2.39482
$750$		0			0
$751$	11.3197	+	34.8383i	0.413060	+	1.27127i	0.913974	+	0.405772i	$0.132997\pi$
$751$	11.3197	+	34.8383i	0.413060	+	1.27127i	−0.500914	+	0.865497i	$0.667003\pi$
$752$		0			0
$753$	10.4443	+	7.58821i	0.380610	+	0.276530i
$754$		0			0
$755$	−3.94427	+	12.1392i	−0.143547	+	0.441791i
$756$		0			0
$757$	−13.2812	+	9.64932i	−0.482712	+	0.350711i	−0.802375	−	0.596821i	$-0.796430\pi$
$757$	−13.2812	+	9.64932i	−0.482712	+	0.350711i	0.319663	+	0.947531i	$0.396430\pi$
$758$		0			0
$759$	7.16312	−	12.0862i	0.260005	−	0.438702i
$760$		0			0
$761$	−41.4615	+	30.1235i	−1.50298	+	1.09198i	−0.533801	+	0.845610i	$0.679237\pi$
$761$	−41.4615	+	30.1235i	−1.50298	+	1.09198i	−0.969176	+	0.246368i	$0.920763\pi$
$762$		0			0
$763$	−10.4721	+	32.2299i	−0.379117	+	1.16680i
$764$		0			0
$765$	−10.6631	−	7.74721i	−0.385526	−	0.280101i
$766$		0			0
$767$	−4.82624	−	14.8536i	−0.174265	−	0.536334i
$768$		0			0
$769$	−13.4377			−0.484576			−0.242288	−	0.970204i	$-0.577898\pi$
$769$	−13.4377			−0.484576			−0.242288	+	0.970204i	$0.577898\pi$
$770$		0			0
$771$	−21.7984			−0.785049
$772$		0			0
$773$	−4.74671	−	14.6089i	−0.170727	−	0.525445i	0.828685	−	0.559715i	$-0.189089\pi$
$773$	−4.74671	−	14.6089i	−0.170727	−	0.525445i	−0.999413	+	0.0342702i	$0.989089\pi$
$774$		0			0
$775$	21.9336	+	15.9357i	0.787879	+	0.572428i
$776$		0			0
$777$	10.7812	−	33.1810i	0.386772	−	1.19036i
$778$		0			0
$779$	−2.60081	+	1.88960i	−0.0931838	+	0.0677020i
$780$		0			0
$781$	1.11803	+	11.9475i	0.0400064	+	0.427514i
$782$		0			0
$783$	−3.61803	+	2.62866i	−0.129298	+	0.0939405i
$784$		0			0
$785$	−11.2574	+	34.6466i	−0.401792	+	1.23659i
$786$		0			0
$787$	−39.8328	−	28.9402i	−1.41989	−	1.03161i	−0.991790	−	0.127875i	$-0.959184\pi$
$787$	−39.8328	−	28.9402i	−1.41989	−	1.03161i	−0.428096	−	0.903733i	$-0.640816\pi$
$788$		0			0
$789$	−5.29837	−	16.3067i	−0.188627	−	0.580535i
$790$		0			0
$791$	32.8885			1.16938
$792$		0			0
$793$	0.673762			0.0239260
$794$		0			0
$795$	11.9615	+	36.8137i	0.424230	+	1.30565i
$796$		0			0
$797$	−21.8541	−	15.8779i	−0.774112	−	0.562425i	0.129094	−	0.991632i	$-0.458793\pi$
$797$	−21.8541	−	15.8779i	−0.774112	−	0.562425i	−0.903206	+	0.429207i	$0.858793\pi$
$798$		0			0
$799$	1.97214	−	6.06961i	0.0697692	−	0.214727i
$800$		0			0
$801$	−0.809017	+	0.587785i	−0.0285852	+	0.0207684i
$802$		0			0
$803$	−3.76393	+	1.62460i	−0.132826	+	0.0573308i
$804$		0			0
$805$	−41.4336	+	30.1033i	−1.46034	+	1.06100i
$806$		0			0
$807$	−6.03444	+	18.5721i	−0.212422	+	0.653769i
$808$		0			0
$809$	−1.39919	−	1.01657i	−0.0491928	−	0.0357407i	0.562917	−	0.826513i	$-0.309679\pi$
$809$	−1.39919	−	1.01657i	−0.0491928	−	0.0357407i	−0.612110	+	0.790773i	$0.709679\pi$
$810$		0			0
$811$	−8.28115	−	25.4868i	−0.290791	−	0.894961i	−0.984603	−	0.174806i	$-0.944070\pi$
$811$	−8.28115	−	25.4868i	−0.290791	−	0.894961i	0.693812	−	0.720156i	$-0.255930\pi$
$812$		0			0
$813$	22.5623			0.791295
$814$		0			0
$815$	5.29180			0.185364
$816$		0			0
$817$	0.993422	+	3.05744i	0.0347554	+	0.106966i
$818$		0			0
$819$	6.04508	+	4.39201i	0.211232	+	0.153469i
$820$		0			0
$821$	−5.36475	+	16.5110i	−0.187231	+	0.576237i	−0.999980	−	0.00637687i	$-0.997970\pi$
$821$	−5.36475	+	16.5110i	−0.187231	+	0.576237i	0.812749	+	0.582614i	$0.197970\pi$
$822$		0			0
$823$	−0.663119	+	0.481784i	−0.0231149	+	0.0167939i	−0.599283	−	0.800537i	$-0.704547\pi$
$823$	−0.663119	+	0.481784i	−0.0231149	+	0.0167939i	0.576168	+	0.817331i	$0.304547\pi$
$824$		0			0
$825$	10.1803	+	2.28563i	0.354434	+	0.0795754i
$826$		0			0
$827$	0.708204	−	0.514540i	0.0246267	−	0.0178923i	−0.575404	−	0.817869i	$-0.695155\pi$
$827$	0.708204	−	0.514540i	0.0246267	−	0.0178923i	0.600030	+	0.799977i	$0.295155\pi$
$828$		0			0
$829$	−11.6631	+	35.8954i	−0.405077	+	1.24670i	0.515754	+	0.856737i	$0.327512\pi$
$829$	−11.6631	+	35.8954i	−0.405077	+	1.24670i	−0.920831	+	0.389962i	$0.872488\pi$
$830$		0			0
$831$	−14.2082	−	10.3229i	−0.492877	−	0.358096i
$832$		0			0
$833$	15.6180	+	48.0674i	0.541133	+	1.66544i
$834$		0			0
$835$	4.61803			0.159814
$836$		0			0
$837$	8.61803			0.297883
$838$		0			0
$839$	−4.89261	−	15.0579i	−0.168912	−	0.519857i	0.830392	−	0.557180i	$-0.188117\pi$
$839$	−4.89261	−	15.0579i	−0.168912	−	0.519857i	−0.999303	+	0.0373237i	$0.988117\pi$
$840$		0			0
$841$	7.28115	+	5.29007i	0.251074	+	0.182416i
$842$		0			0
$843$	7.14590	−	21.9928i	0.246118	−	0.757473i
$844$		0			0
$845$	22.8328	−	16.5890i	0.785473	−	0.570679i
$846$		0			0
$847$	42.1246	+	19.9192i	1.44742	+	0.684431i
$848$		0			0
$849$	15.1803	−	11.0292i	0.520988	−	0.378520i
$850$		0			0
$851$	−10.7812	+	33.1810i	−0.369573	+	1.13743i
$852$		0			0
$853$	−44.7877	−	32.5402i	−1.53350	−	1.11415i	−0.954251	−	0.299006i	$-0.903345\pi$
$853$	−44.7877	−	32.5402i	−1.53350	−	1.11415i	−0.579251	−	0.815149i	$-0.696655\pi$
$854$		0			0
$855$	5.37132	+	16.5312i	0.183695	+	0.565356i
$856$		0			0
$857$	48.1935			1.64626			0.823129	−	0.567854i	$-0.192226\pi$
$857$	48.1935			1.64626			0.823129	+	0.567854i	$0.192226\pi$
$858$		0			0
$859$	31.1803			1.06386			0.531930	−	0.846788i	$-0.321467\pi$
$859$	31.1803			1.06386			0.531930	+	0.846788i	$0.321467\pi$
$860$		0			0
$861$	−0.690983	−	2.12663i	−0.0235486	−	0.0724753i
$862$		0			0
$863$	−24.5623	−	17.8456i	−0.836111	−	0.607470i	0.0851709	−	0.996366i	$-0.472856\pi$
$863$	−24.5623	−	17.8456i	−0.836111	−	0.607470i	−0.921281	+	0.388896i	$0.872856\pi$
$864$		0			0
$865$	−12.8435	+	39.5281i	−0.436691	+	1.34400i
$866$		0			0
$867$	3.50000	−	2.54290i	0.118866	−	0.0863614i
$868$		0			0
$869$	−31.5967	−	7.09391i	−1.07185	−	0.240644i
$870$		0			0
$871$	−9.78115	+	7.10642i	−0.331422	+	0.240792i
$872$		0			0
$873$	1.88197	−	5.79210i	0.0636949	−	0.196033i
$874$		0			0
$875$	18.1353	+	13.1760i	0.613084	+	0.445431i
$876$		0			0
$877$	−10.7812	−	33.1810i	−0.364054	−	1.12044i	−0.950572	−	0.310506i	$-0.899502\pi$
$877$	−10.7812	−	33.1810i	−0.364054	−	1.12044i	0.586518	−	0.809936i	$-0.300498\pi$
$878$		0			0
$879$	5.00000			0.168646
$880$		0			0
$881$	20.4377			0.688563			0.344282	−	0.938866i	$-0.388122\pi$
$881$	20.4377			0.688563			0.344282	+	0.938866i	$0.388122\pi$
$882$		0			0
$883$	−0.909830	−	2.80017i	−0.0306182	−	0.0942332i	0.934580	−	0.355754i	$-0.115776\pi$
$883$	−0.909830	−	2.80017i	−0.0306182	−	0.0942332i	−0.965198	+	0.261521i	$0.915776\pi$
$884$		0			0
$885$	20.4443	+	14.8536i	0.687227	+	0.499299i
$886$		0			0
$887$	−14.4336	+	44.4221i	−0.484634	+	1.49155i	0.347877	+	0.937540i	$0.386903\pi$
$887$	−14.4336	+	44.4221i	−0.484634	+	1.49155i	−0.832511	+	0.554009i	$0.813097\pi$
$888$		0			0
$889$	−7.85410	+	5.70634i	−0.263418	+	0.191384i
$890$		0			0
$891$	3.04508	−	1.31433i	0.102014	−	0.0440316i
$892$		0			0
$893$	−6.80902	+	4.94704i	−0.227855	+	0.165546i
$894$		0			0
$895$	−0.0491503	+	0.151269i	−0.00164291	+	0.00505637i
$896$		0			0
$897$	−6.04508	−	4.39201i	−0.201840	−	0.146645i
$898$		0			0
$899$	11.9098	+	36.6547i	0.397215	+	1.22250i
$900$		0			0
$901$	−62.6312			−2.08655
$902$		0			0
$903$	−2.23607			−0.0744117
$904$		0			0
$905$	−10.5344	−	32.4217i	−0.350177	−	1.07773i
$906$		0			0
$907$	−32.2533	−	23.4334i	−1.07095	−	0.778093i	−0.0948696	−	0.995490i	$-0.530243\pi$
$907$	−32.2533	−	23.4334i	−1.07095	−	0.778093i	−0.976083	+	0.217397i	$0.930243\pi$
$908$		0			0
$909$	3.69098	−	11.3597i	0.122422	−	0.376777i
$910$		0			0
$911$	33.6074	−	24.4172i	1.11346	−	0.808978i	0.130257	−	0.991480i	$-0.458420\pi$
$911$	33.6074	−	24.4172i	1.11346	−	0.808978i	0.983205	+	0.182502i	$0.0584197\pi$
$912$		0			0
$913$	−2.01722	−	21.5563i	−0.0667603	−	0.713409i
$914$		0			0
$915$	−0.881966	+	0.640786i	−0.0291569	+	0.0211837i
$916$		0			0
$917$	15.1353	−	46.5815i	0.499810	−	1.53826i
$918$		0			0
$919$	−30.6074	−	22.2376i	−1.00964	−	0.733550i	−0.0455101	−	0.998964i	$-0.514491\pi$
$919$	−30.6074	−	22.2376i	−1.00964	−	0.733550i	−0.964135	+	0.265414i	$0.914491\pi$
$920$		0			0
$921$	5.04508	+	15.5272i	0.166241	+	0.511638i
$922$		0			0
$923$	6.38197			0.210065
$924$		0			0
$925$	−25.9098			−0.851910
$926$		0			0
$927$	1.09017	+	3.35520i	0.0358059	+	0.110199i
$928$		0			0
$929$	−37.5517	−	27.2829i	−1.23203	−	0.895122i	−0.234989	−	0.971998i	$-0.575506\pi$
$929$	−37.5517	−	27.2829i	−1.23203	−	0.895122i	−0.997041	+	0.0768757i	$0.975506\pi$
$930$		0			0
$931$	20.5967	−	63.3903i	0.675031	−	2.07753i
$932$		0			0
$933$	−5.51722	+	4.00850i	−0.180626	+	0.131232i
$934$		0			0
$935$	−22.2877	+	37.6057i	−0.728887	+	1.22984i
$936$		0			0
$937$	−19.6074	+	14.2456i	−0.640546	+	0.465384i	−0.860038	−	0.510231i	$-0.829560\pi$
$937$	−19.6074	+	14.2456i	−0.640546	+	0.465384i	0.219492	+	0.975614i	$0.429560\pi$
$938$		0			0
$939$	0.309017	−	0.951057i	0.0100844	−	0.0310366i
$940$		0			0
$941$	−14.2082	−	10.3229i	−0.463174	−	0.336516i	0.331601	−	0.943420i	$-0.392411\pi$
$941$	−14.2082	−	10.3229i	−0.463174	−	0.336516i	−0.794775	+	0.606904i	$0.792411\pi$
$942$		0			0
$943$	0.690983	+	2.12663i	0.0225015	+	0.0692525i
$944$		0			0
$945$	−12.0902			−0.393293
$946$		0			0
$947$	21.7984			0.708352			0.354176	−	0.935179i	$-0.384761\pi$
$947$	21.7984			0.708352			0.354176	+	0.935179i	$0.384761\pi$
$948$		0			0
$949$	0.673762	+	2.07363i	0.0218712	+	0.0673128i
$950$		0			0
$951$	14.1353	+	10.2699i	0.458367	+	0.333023i
$952$		0			0
$953$	12.1246	−	37.3157i	0.392755	−	1.20877i	−0.537942	−	0.842982i	$-0.680798\pi$
$953$	12.1246	−	37.3157i	0.392755	−	1.20877i	0.930696	−	0.365793i	$-0.119202\pi$
$954$		0			0
$955$	−22.2877	+	16.1930i	−0.721214	+	0.523993i
$956$		0			0
$957$	9.79837	+	11.1352i	0.316736	+	0.359949i
$958$		0			0
$959$	71.9681	−	52.2879i	2.32397	−	1.68846i
$960$		0			0
$961$	13.3713	−	41.1527i	0.431333	−	1.32751i
$962$		0			0
$963$	−12.5172	−	9.09429i	−0.403362	−	0.293060i
$964$		0			0
$965$	−0.287731	−	0.885544i	−0.00926238	−	0.0285067i
$966$		0			0
$967$	48.2705			1.55227			0.776137	−	0.630564i	$-0.217176\pi$
$967$	48.2705			1.55227			0.776137	+	0.630564i	$0.217176\pi$
$968$		0			0
$969$	−28.1246			−0.903493
$970$		0			0
$971$	−13.0902	−	40.2874i	−0.420084	−	1.29288i	−0.907624	−	0.419784i	$-0.862106\pi$
$971$	−13.0902	−	40.2874i	−0.420084	−	1.29288i	0.487541	−	0.873100i	$-0.337894\pi$
$972$		0			0
$973$	71.2771	+	51.7858i	2.28504	+	1.66018i
$974$		0			0
$975$	1.71478	−	5.27756i	0.0549170	−	0.169017i
$976$		0			0
$977$	−2.33688	+	1.69784i	−0.0747634	+	0.0543188i	−0.624539	−	0.780993i	$-0.714713\pi$
$977$	−2.33688	+	1.69784i	−0.0747634	+	0.0543188i	0.549776	+	0.835312i	$0.314713\pi$
$978$		0			0
$979$	2.19098	+	2.48990i	0.0700241	+	0.0795775i
$980$		0			0
$981$	6.47214	−	4.70228i	0.206639	−	0.150132i
$982$		0			0
$983$	5.20163	−	16.0090i	0.165906	−	0.510606i	−0.833196	−	0.552978i	$-0.813491\pi$
$983$	5.20163	−	16.0090i	0.165906	−	0.510606i	0.999102	+	0.0423716i	$0.0134913\pi$
$984$		0			0
$985$	39.4615	+	28.6705i	1.25735	+	0.913517i
$986$		0			0
$987$	−1.80902	−	5.56758i	−0.0575816	−	0.177218i
$988$		0			0
$989$	2.23607			0.0711028
$990$		0			0
$991$	9.72949			0.309067			0.154534	−	0.987988i	$-0.450612\pi$
$991$	9.72949			0.309067			0.154534	+	0.987988i	$0.450612\pi$
$992$		0			0
$993$	1.83688	+	5.65334i	0.0582917	+	0.179403i
$994$		0			0
$995$	−37.9058	−	27.5402i	−1.20169	−	0.873081i
$996$		0			0
$997$	−1.31966	+	4.06150i	−0.0417941	+	0.128629i	−0.969776	−	0.243995i	$-0.921542\pi$
$997$	−1.31966	+	4.06150i	−0.0417941	+	0.128629i	0.927982	+	0.372624i	$0.121542\pi$
$998$		0			0
$999$	−6.66312	+	4.84104i	−0.210812	+	0.153164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.i.b.25.1	✓	4
3.2	odd	2		396.2.j.c.289.1		4
4.3	odd	2		528.2.y.a.289.1		4
11.2	odd	10		1452.2.a.i.1.2		2
11.3	even	5		1452.2.i.o.1237.1		4
11.4	even	5	inner	132.2.i.b.37.1	yes	4
11.5	even	5		1452.2.i.o.493.1		4
11.6	odd	10		1452.2.i.p.493.1		4
11.7	odd	10		1452.2.i.j.565.1		4
11.8	odd	10		1452.2.i.p.1237.1		4
11.9	even	5		1452.2.a.j.1.2		2
11.10	odd	2		1452.2.i.j.1213.1		4
33.2	even	10		4356.2.a.s.1.1		2
33.20	odd	10		4356.2.a.v.1.1		2
33.26	odd	10		396.2.j.c.37.1		4
44.15	odd	10		528.2.y.a.433.1		4
44.31	odd	10		5808.2.a.cc.1.2		2
44.35	even	10		5808.2.a.cf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.b.25.1	✓	4	1.1	even	1	trivial
132.2.i.b.37.1	yes	4	11.4	even	5	inner
396.2.j.c.37.1		4	33.26	odd	10
396.2.j.c.289.1		4	3.2	odd	2
528.2.y.a.289.1		4	4.3	odd	2
528.2.y.a.433.1		4	44.15	odd	10
1452.2.a.i.1.2		2	11.2	odd	10
1452.2.a.j.1.2		2	11.9	even	5
1452.2.i.j.565.1		4	11.7	odd	10
1452.2.i.j.1213.1		4	11.10	odd	2
1452.2.i.o.493.1		4	11.5	even	5
1452.2.i.o.1237.1		4	11.3	even	5
1452.2.i.p.493.1		4	11.6	odd	10
1452.2.i.p.1237.1		4	11.8	odd	10
4356.2.a.s.1.1		2	33.2	even	10
4356.2.a.v.1.1		2	33.20	odd	10
5808.2.a.cc.1.2		2	44.31	odd	10
5808.2.a.cf.1.2		2	44.35	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-2.30902 - 1.67760i) q^{5} +(1.30902 - 4.02874i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.19098 + 2.48990i) q^{11} +(1.42705 - 1.03681i) q^{13} +(-0.881966 + 2.71441i) q^{15} +(-3.73607 - 2.71441i) q^{17} +(1.88197 + 5.79210i) q^{19} -4.23607 q^{21} +4.23607 q^{23} +(0.972136 + 2.99193i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-1.38197 + 4.25325i) q^{29} +(6.97214 - 5.06555i) q^{31} +(1.69098 - 2.85317i) q^{33} +(-9.78115 + 7.10642i) q^{35} +(-2.54508 + 7.83297i) q^{37} +(-1.42705 - 1.03681i) q^{39} +(0.163119 + 0.502029i) q^{41} +0.527864 q^{43} +2.85410 q^{45} +(0.427051 + 1.31433i) q^{47} +(-8.85410 - 6.43288i) q^{49} +(-1.42705 + 4.39201i) q^{51} +(10.9721 - 7.97172i) q^{53} +(-0.881966 - 9.42481i) q^{55} +(4.92705 - 3.57971i) q^{57} +(2.73607 - 8.42075i) q^{59} +(0.309017 + 0.224514i) q^{61} +(1.30902 + 4.02874i) q^{63} -5.03444 q^{65} -6.85410 q^{67} +(-1.30902 - 4.02874i) q^{69} +(2.92705 + 2.12663i) q^{71} +(-0.381966 + 1.17557i) q^{73} +(2.54508 - 1.84911i) q^{75} +(12.8992 - 5.56758i) q^{77} +(-7.89919 + 5.73910i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-5.28115 - 3.83698i) q^{83} +(4.07295 + 12.5352i) q^{85} +4.47214 q^{87} +1.00000 q^{89} +(-2.30902 - 7.10642i) q^{91} +(-6.97214 - 5.06555i) q^{93} +(5.37132 - 16.5312i) q^{95} +(-4.92705 + 3.57971i) q^{97} +(-3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 7 q^{5} + 3 q^{7} - q^{9} + 11 q^{11} - q^{13} - 8 q^{15} - 6 q^{17} + 12 q^{19} - 8 q^{21} + 8 q^{23} - 14 q^{25} + q^{27} - 10 q^{29} + 10 q^{31} + 9 q^{33} - 19 q^{35} + q^{37} + q^{39}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + q^3 - 7 * q^5 + 3 * q^7 - q^9 + 11 * q^11 - q^13 - 8 * q^15 - 6 * q^17 + 12 * q^19 - 8 * q^21 + 8 * q^23 - 14 * q^25 + q^27 - 10 * q^29 + 10 * q^31 + 9 * q^33 - 19 * q^35 + q^37 + q^39 - 15 * q^41 + 20 * q^43 - 2 * q^45 - 5 * q^47 - 22 * q^49 + q^51 + 26 * q^53 - 8 * q^55 + 13 * q^57 + 2 * q^59 - q^61 + 3 * q^63 + 38 * q^65 - 14 * q^67 - 3 * q^69 + 5 * q^71 - 6 * q^73 - q^75 + 27 * q^77 - 7 * q^79 - q^81 - q^83 + 23 * q^85 + 4 * q^89 - 7 * q^91 - 10 * q^93 - 21 * q^95 - 13 * q^97 - 4 * q^99

Introduction

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