LMFDB - Embedded newform 168.2.u.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(17,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("168.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.u (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 $ x^16 - 6x^15 + 19x^14 - 42x^13 + 65x^12 - 48x^11 - 94x^10 + 444x^9 - 962x^8 + 1332x^7 - 846x^6 - 1296x^5 + 5265x^4 - 10206x^3 + 13851x^2 - 13122*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.1
Root			$1.22961 + 1.21986i$ of defining polynomial
Character	$\chi$	$=$	168.89
Dual form			168.2.u.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67480 + 0.441628i) q^{3} +(1.40397 - 2.43175i) q^{5} +(-2.08606 - 1.62738i) q^{7} +(2.60993 - 1.47928i) q^{9} +(4.74645 - 2.74036i) q^{11} +1.35669i q^{13} +(-1.27745 + 4.69274i) q^{15} +(-2.88753 - 5.00135i) q^{17} +(1.71973 + 0.992889i) q^{19} +(4.21243 + 1.80428i) q^{21} +(-2.09928 - 1.21202i) q^{23} +(-1.44228 - 2.49811i) q^{25} +(-3.71783 + 3.63012i) q^{27} +7.05668i q^{29} +(-3.07596 + 1.77591i) q^{31} +(-6.73914 + 6.68573i) q^{33} +(-6.88616 + 2.78798i) q^{35} +(-2.14377 + 3.71312i) q^{37} +(-0.599153 - 2.27219i) q^{39} +1.81976 q^{41} +11.2288 q^{43} +(0.0670332 - 8.42358i) q^{45} +(0.201213 - 0.348512i) q^{47} +(1.70327 + 6.78961i) q^{49} +(7.04478 + 7.10106i) q^{51} +(5.28097 - 3.04897i) q^{53} -15.3896i q^{55} +(-3.31870 - 0.903412i) q^{57} +(-1.28234 - 2.22108i) q^{59} +(-4.75817 - 2.74713i) q^{61} +(-7.85181 - 1.16149i) q^{63} +(3.29914 + 1.90476i) q^{65} +(3.45238 + 5.97970i) q^{67} +(4.05114 + 1.10279i) q^{69} +2.08251i q^{71} +(-0.295696 + 0.170720i) q^{73} +(3.51878 + 3.54689i) q^{75} +(-14.3610 - 2.00772i) q^{77} +(1.19139 - 2.06355i) q^{79} +(4.62347 - 7.72163i) q^{81} +11.8717 q^{83} -16.2161 q^{85} +(-3.11643 - 11.8186i) q^{87} +(0.576571 - 0.998650i) q^{89} +(2.20785 - 2.83014i) q^{91} +(4.36734 - 4.33272i) q^{93} +(4.82892 - 2.78798i) q^{95} +16.0187i q^{97} +(8.33413 - 14.1735i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67}+ \cdots + 20 q^{99}+O(q^{100}) $ 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	−1.67480	+	0.441628i	−0.966948	+	0.254974i
$3$	−1.67480	+	0.441628i	−0.966948	+	0.254974i
$4$		0			0
$5$	1.40397	−	2.43175i	0.627876	−	1.08751i	−0.360101	−	0.932913i	$-0.617258\pi$
$5$	1.40397	−	2.43175i	0.627876	−	1.08751i	0.987977	−	0.154600i	$-0.0494089\pi$
$6$		0			0
$7$	−2.08606	−	1.62738i	−0.788456	−	0.615092i
$7$	−2.08606	−	1.62738i	−0.788456	−	0.615092i
$8$		0			0
$9$	2.60993	−	1.47928i	0.869977	−	0.493093i
$10$		0			0
$11$	4.74645	−	2.74036i	1.43111	−	0.826250i	0.433902	−	0.900960i	$-0.357136\pi$
$11$	4.74645	−	2.74036i	1.43111	−	0.826250i	0.997205	+	0.0747101i	$0.0238032\pi$
$12$		0			0
$13$			1.35669i			0.376279i	0.982142	+	0.188139i	$0.0602457\pi$
$13$			1.35669i			0.376279i	−0.982142	+	0.188139i	$0.939754\pi$
$14$		0			0
$15$	−1.27745	+	4.69274i	−0.329836	+	1.21166i
$16$		0			0
$17$	−2.88753	−	5.00135i	−0.700329	−	1.21301i	−0.968351	−	0.249593i	$-0.919703\pi$
$17$	−2.88753	−	5.00135i	−0.700329	−	1.21301i	0.268022	−	0.963413i	$-0.413630\pi$
$18$		0			0
$19$	1.71973	+	0.992889i	0.394534	+	0.227784i	0.684123	−	0.729367i	$-0.260185\pi$
$19$	1.71973	+	0.992889i	0.394534	+	0.227784i	−0.289589	+	0.957151i	$0.593519\pi$
$20$		0			0
$21$	4.21243	+	1.80428i	0.919228	+	0.393726i
$22$		0			0
$23$	−2.09928	−	1.21202i	−0.437730	−	0.252723i	0.264904	−	0.964275i	$-0.414660\pi$
$23$	−2.09928	−	1.21202i	−0.437730	−	0.252723i	−0.702634	+	0.711551i	$0.747993\pi$
$24$		0			0
$25$	−1.44228	−	2.49811i	−0.288457	−	0.499622i
$26$		0			0
$27$	−3.71783	+	3.63012i	−0.715497	+	0.698616i
$28$		0			0
$29$			7.05668i			1.31039i	0.755458	+	0.655197i	$0.227414\pi$
$29$			7.05668i			1.31039i	−0.755458	+	0.655197i	$0.772586\pi$
$30$		0			0
$31$	−3.07596	+	1.77591i	−0.552459	+	0.318962i	−0.750113	−	0.661309i	$-0.770001\pi$
$31$	−3.07596	+	1.77591i	−0.552459	+	0.318962i	0.197654	+	0.980272i	$0.436668\pi$
$32$		0			0
$33$	−6.73914	+	6.68573i	−1.17313	+	1.16384i
$34$		0			0
$35$	−6.88616	+	2.78798i	−1.16397	+	0.471255i
$36$		0			0
$37$	−2.14377	+	3.71312i	−0.352434	+	0.610434i	−0.986675	−	0.162701i	$-0.947979\pi$
$37$	−2.14377	+	3.71312i	−0.352434	+	0.610434i	0.634241	+	0.773135i	$0.281313\pi$
$38$		0			0
$39$	−0.599153	−	2.27219i	−0.0959413	−	0.363842i
$40$		0			0
$41$	1.81976			0.284199			0.142100	−	0.989852i	$-0.454615\pi$
$41$	1.81976			0.284199			0.142100	+	0.989852i	$0.454615\pi$
$42$		0			0
$43$	11.2288			1.71238			0.856188	−	0.516665i	$-0.172827\pi$
$43$	11.2288			1.71238			0.856188	+	0.516665i	$0.172827\pi$
$44$		0			0
$45$	0.0670332	−	8.42358i	0.00999272	−	1.25571i
$46$		0			0
$47$	0.201213	−	0.348512i	0.0293500	−	0.0508356i	−0.850977	−	0.525202i	$-0.823990\pi$
$47$	0.201213	−	0.348512i	0.0293500	−	0.0508356i	0.880327	+	0.474367i	$0.157323\pi$
$48$		0			0
$49$	1.70327	+	6.78961i	0.243325	+	0.969945i
$50$		0			0
$51$	7.04478	+	7.10106i	0.986466	+	0.994348i
$52$		0			0
$53$	5.28097	−	3.04897i	0.725397	−	0.418808i	−0.0913389	−	0.995820i	$-0.529115\pi$
$53$	5.28097	−	3.04897i	0.725397	−	0.418808i	0.816736	+	0.577012i	$0.195781\pi$
$54$		0			0
$55$		−	15.3896i		−	2.07513i
$56$		0			0
$57$	−3.31870	−	0.903412i	−0.439573	−	0.119660i
$58$		0			0
$59$	−1.28234	−	2.22108i	−0.166947	−	0.289161i	0.770398	−	0.637563i	$-0.220058\pi$
$59$	−1.28234	−	2.22108i	−0.166947	−	0.289161i	−0.937345	+	0.348403i	$0.886724\pi$
$60$		0			0
$61$	−4.75817	−	2.74713i	−0.609222	−	0.351734i	0.163439	−	0.986553i	$-0.447741\pi$
$61$	−4.75817	−	2.74713i	−0.609222	−	0.351734i	−0.772661	+	0.634819i	$0.781075\pi$
$62$		0			0
$63$	−7.85181	−	1.16149i	−0.989235	−	0.146334i
$64$		0			0
$65$	3.29914	+	1.90476i	0.409208	+	0.236257i
$66$		0			0
$67$	3.45238	+	5.97970i	0.421775	+	0.730536i	0.996113	−	0.0880819i	$-0.0280737\pi$
$67$	3.45238	+	5.97970i	0.421775	+	0.730536i	−0.574338	+	0.818618i	$0.694740\pi$
$68$		0			0
$69$	4.05114	+	1.10279i	0.487700	+	0.132761i
$70$		0			0
$71$			2.08251i			0.247148i	0.992335	+	0.123574i	$0.0394357\pi$
$71$			2.08251i			0.247148i	−0.992335	+	0.123574i	$0.960564\pi$
$72$		0			0
$73$	−0.295696	+	0.170720i	−0.0346086	+	0.0199813i	−0.517204	−	0.855862i	$-0.673027\pi$
$73$	−0.295696	+	0.170720i	−0.0346086	+	0.0199813i	0.482596	+	0.875843i	$0.339694\pi$
$74$		0			0
$75$	3.51878	+	3.54689i	0.406313	+	0.409560i
$76$		0			0
$77$	−14.3610	−	2.00772i	−1.63658	−	0.228800i
$78$		0			0
$79$	1.19139	−	2.06355i	0.134042	−	0.232168i	−0.791189	−	0.611572i	$-0.790538\pi$
$79$	1.19139	−	2.06355i	0.134042	−	0.232168i	0.925231	+	0.379404i	$0.123871\pi$
$80$		0			0
$81$	4.62347	−	7.72163i	0.513719	−	0.857958i
$82$		0			0
$83$	11.8717			1.30309			0.651543	−	0.758611i	$-0.274122\pi$
$83$	11.8717			1.30309			0.651543	+	0.758611i	$0.274122\pi$
$84$		0			0
$85$	−16.2161			−1.75888
$86$		0			0
$87$	−3.11643	−	11.8186i	−0.334116	−	1.26708i
$88$		0			0
$89$	0.576571	−	0.998650i	0.0611164	−	0.105857i	−0.833848	−	0.551994i	$-0.813867\pi$
$89$	0.576571	−	0.998650i	0.0611164	−	0.105857i	0.894965	+	0.446137i	$0.147201\pi$
$90$		0			0
$91$	2.20785	−	2.83014i	0.231446	−	0.296679i
$92$		0			0
$93$	4.36734	−	4.33272i	0.452872	−	0.449283i
$94$		0			0
$95$	4.82892	−	2.78798i	0.495437	−	0.286041i
$96$		0			0
$97$			16.0187i			1.62645i	0.581950	+	0.813225i	$0.302290\pi$
$97$			16.0187i			1.62645i	−0.581950	+	0.813225i	$0.697710\pi$
$98$		0			0
$99$	8.33413	−	14.1735i	0.837612	−	1.42449i
$100$		0			0
$101$	7.33982	+	12.7129i	0.730339	+	1.26498i	0.956738	+	0.290950i	$0.0939712\pi$
$101$	7.33982	+	12.7129i	0.730339	+	1.26498i	−0.226399	+	0.974035i	$0.572695\pi$
$102$		0			0
$103$	4.06960	+	2.34958i	0.400989	+	0.231511i	0.686911	−	0.726742i	$-0.258966\pi$
$103$	4.06960	+	2.34958i	0.400989	+	0.231511i	−0.285922	+	0.958253i	$0.592300\pi$
$104$		0			0
$105$	10.3017	−	7.71043i	1.00534	−	0.752461i
$106$		0			0
$107$	−7.14150	−	4.12315i	−0.690395	−	0.398600i	0.113365	−	0.993553i	$-0.463837\pi$
$107$	−7.14150	−	4.12315i	−0.690395	−	0.398600i	−0.803760	+	0.594954i	$0.797170\pi$
$108$		0			0
$109$	−4.41113	−	7.64030i	−0.422509	−	0.731808i	0.573675	−	0.819083i	$-0.305517\pi$
$109$	−4.41113	−	7.64030i	−0.422509	−	0.731808i	−0.996184	+	0.0872755i	$0.972184\pi$
$110$		0			0
$111$	1.95058	−	7.16550i	0.185141	−	0.680119i
$112$		0			0
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		0			0
$115$	−5.89467	+	3.40329i	−0.549680	+	0.317358i
$116$		0			0
$117$	2.00693	+	3.54087i	0.185540	+	0.327354i
$118$		0			0
$119$	−2.11554	+	15.1322i	−0.193931	+	1.38717i
$120$		0			0
$121$	9.51916	−	16.4877i	0.865378	−	1.49888i
$122$		0			0
$123$	−3.04775	+	0.803658i	−0.274806	+	0.0724634i
$124$		0			0
$125$	5.94002			0.531291
$126$		0			0
$127$	−6.93769			−0.615620			−0.307810	−	0.951448i	$-0.599596\pi$
$127$	−6.93769			−0.615620			−0.307810	+	0.951448i	$0.599596\pi$
$128$		0			0
$129$	−18.8060	+	4.95895i	−1.65578	+	0.436611i
$130$		0			0
$131$	−0.118734	+	0.205654i	−0.0103739	+	0.0179680i	−0.871166	−	0.490989i	$-0.836635\pi$
$131$	−0.118734	+	0.205654i	−0.0103739	+	0.0179680i	0.860792	+	0.508957i	$0.169969\pi$
$132$		0			0
$133$	−1.97166	−	4.86988i	−0.170964	−	0.422273i
$134$		0			0
$135$	3.60782	+	14.1374i	0.310511	+	1.21676i
$136$		0			0
$137$	−9.58873	+	5.53606i	−0.819221	+	0.472977i	−0.850148	−	0.526544i	$-0.823487\pi$
$137$	−9.58873	+	5.53606i	−0.819221	+	0.472977i	0.0309270	+	0.999522i	$0.490154\pi$
$138$		0			0
$139$		−	1.02466i		−	0.0869108i	−0.999055	−	0.0434554i	$-0.986163\pi$
$139$		−	1.02466i		−	0.0869108i	0.999055	−	0.0434554i	$-0.0138366\pi$
$140$		0			0
$141$	−0.183080	+	0.672550i	−0.0154181	+	0.0566389i
$142$		0			0
$143$	3.71783	+	6.43947i	0.310900	+	0.538495i
$144$		0			0
$145$	17.1601	+	9.90740i	1.42507	+	0.822765i
$146$		0			0
$147$	−5.85113	−	10.6191i	−0.482593	−	0.875845i
$148$		0			0
$149$	−19.0549	−	11.0013i	−1.56104	−	0.901266i	−0.997152	−	0.0754127i	$-0.975973\pi$
$149$	−19.0549	−	11.0013i	−1.56104	−	0.901266i	−0.563886	−	0.825853i	$-0.690694\pi$
$150$		0			0
$151$	3.63368	+	6.29371i	0.295704	+	0.512175i	0.975149	−	0.221552i	$-0.0711123\pi$
$151$	3.63368	+	6.29371i	0.295704	+	0.512175i	−0.679444	+	0.733727i	$0.737779\pi$
$152$		0			0
$153$	−14.9346	−	8.78171i	−1.20739	−	0.709959i
$154$		0			0
$155$			9.97331i			0.801075i
$156$		0			0
$157$	19.6994	−	11.3735i	1.57219	−	0.907702i	0.576285	−	0.817249i	$-0.304502\pi$
$157$	19.6994	−	11.3735i	1.57219	−	0.907702i	0.995901	−	0.0904525i	$-0.0288313\pi$
$158$		0			0
$159$	−7.49807	+	7.43864i	−0.594636	+	0.589923i
$160$		0			0
$161$	2.40680	+	5.94467i	0.189683	+	0.468505i
$162$		0			0
$163$	−9.06678	+	15.7041i	−0.710165	+	1.23004i	0.254630	+	0.967039i	$0.418046\pi$
$163$	−9.06678	+	15.7041i	−0.710165	+	1.23004i	−0.964795	+	0.263003i	$0.915287\pi$
$164$		0			0
$165$	6.79646	+	25.7745i	0.529104	+	2.00654i
$166$		0			0
$167$	−24.0942			−1.86447			−0.932233	−	0.361858i	$-0.882143\pi$
$167$	−24.0942			−1.86447			−0.932233	+	0.361858i	$0.882143\pi$
$168$		0			0
$169$	11.1594			0.858414
$170$		0			0
$171$	5.95715	+	0.0474059i	0.455554	+	0.00362522i
$172$		0			0
$173$	5.18802	−	8.98592i	0.394438	−	0.683187i	−0.598591	−	0.801055i	$-0.704273\pi$
$173$	5.18802	−	8.98592i	0.394438	−	0.683187i	0.993029	+	0.117868i	$0.0376059\pi$
$174$		0			0
$175$	−1.05668	+	7.55835i	−0.0798778	+	0.571357i
$176$		0			0
$177$	3.12856	+	3.15356i	0.235157	+	0.237036i
$178$		0			0
$179$	−11.5922	+	6.69274i	−0.866439	+	0.500239i	−0.866163	−	0.499761i	$-0.833421\pi$
$179$	−11.5922	+	6.69274i	−0.866439	+	0.500239i	−0.000276030		1.00000i	$0.500088\pi$
$180$		0			0
$181$			18.4339i			1.37018i	0.728457	+	0.685092i	$0.240238\pi$
$181$			18.4339i			1.37018i	−0.728457	+	0.685092i	$0.759762\pi$
$182$		0			0
$183$	9.18221	+	2.49957i	0.678769	+	0.184773i
$184$		0			0
$185$	6.01960	+	10.4263i	0.442570	+	0.766554i
$186$		0			0
$187$	−27.4110	−	15.8258i	−2.00449	−	1.15729i
$188$		0			0
$189$	13.6632	−	1.52231i	0.993850	−	0.110732i
$190$		0			0
$191$	3.59492	+	2.07553i	0.260119	+	0.150180i	0.624389	−	0.781114i	$-0.285348\pi$
$191$	3.59492	+	2.07553i	0.260119	+	0.150180i	−0.364270	+	0.931293i	$0.618681\pi$
$192$		0			0
$193$	−9.75462	−	16.8955i	−0.702153	−	1.21616i	−0.967709	−	0.252069i	$-0.918889\pi$
$193$	−9.75462	−	16.8955i	−0.702153	−	1.21616i	0.265556	−	0.964095i	$-0.414444\pi$
$194$		0			0
$195$	−6.36661	−	1.73311i	−0.455922	−	0.124110i
$196$		0			0
$197$		−	3.80952i		−	0.271417i	−0.990749	−	0.135709i	$-0.956669\pi$
$197$		−	3.80952i		−	0.271417i	0.990749	−	0.135709i	$-0.0433311\pi$
$198$		0			0
$199$	−5.30327	+	3.06185i	−0.375939	+	0.217049i	−0.676050	−	0.736856i	$-0.736310\pi$
$199$	−5.30327	+	3.06185i	−0.375939	+	0.217049i	0.300111	+	0.953904i	$0.402976\pi$
$200$		0			0
$201$	−8.42286	−	8.49015i	−0.594103	−	0.598849i
$202$		0			0
$203$	11.4839	−	14.7206i	0.806012	−	1.03319i
$204$		0			0
$205$	2.55490	−	4.42522i	0.178442	−	0.309071i
$206$		0			0
$207$	−7.27189	−	0.0578683i	−0.505431	−	0.00402212i
$208$		0			0
$209$	10.8835			0.752827
$210$		0			0
$211$	2.93058			0.201750			0.100875	−	0.994899i	$-0.467836\pi$
$211$	2.93058			0.201750			0.100875	+	0.994899i	$0.467836\pi$
$212$		0			0
$213$	−0.919693	−	3.48779i	−0.0630163	−	0.238979i
$214$		0			0
$215$	15.7649	−	27.3057i	1.07516	−	1.86223i
$216$		0			0
$217$	9.30671	+	1.30111i	0.631780	+	0.0883252i
$218$		0			0
$219$	0.419838	−	0.416510i	0.0283700	−	0.0281451i
$220$		0			0
$221$	6.78530	−	3.91749i	0.456428	−	0.263519i
$222$		0			0
$223$			4.61145i			0.308806i	0.988008	+	0.154403i	$0.0493454\pi$
$223$			4.61145i			0.308806i	−0.988008	+	0.154403i	$0.950655\pi$
$224$		0			0
$225$	−7.45966	−	4.38635i	−0.497311	−	0.292424i
$226$		0			0
$227$	8.62344	+	14.9362i	0.572358	+	0.991353i	0.996323	+	0.0856745i	$0.0273045\pi$
$227$	8.62344	+	14.9362i	0.572358	+	0.991353i	−0.423965	+	0.905678i	$0.639362\pi$
$228$		0			0
$229$	−11.5705	−	6.68024i	−0.764601	−	0.441443i	0.0663443	−	0.997797i	$-0.478866\pi$
$229$	−11.5705	−	6.68024i	−0.764601	−	0.441443i	−0.830945	+	0.556354i	$0.812200\pi$
$230$		0			0
$231$	24.9385	−	2.97967i	1.64083	−	0.196048i
$232$		0			0
$233$	−15.5908	−	9.00135i	−1.02139	−	0.589698i	−0.106882	−	0.994272i	$-0.534087\pi$
$233$	−15.5908	−	9.00135i	−1.02139	−	0.589698i	−0.914505	+	0.404574i	$0.867420\pi$
$234$		0			0
$235$	−0.564996	−	0.978602i	−0.0368563	−	0.0638370i
$236$		0			0
$237$	−1.08403	+	3.98220i	−0.0704151	+	0.258671i
$238$		0			0
$239$		−	23.6499i		−	1.52979i	−0.644158	−	0.764893i	$-0.722792\pi$
$239$		−	23.6499i		−	1.52979i	0.644158	−	0.764893i	$-0.277208\pi$
$240$		0			0
$241$	3.53574	−	2.04136i	0.227757	−	0.131496i	−0.381780	−	0.924253i	$-0.624689\pi$
$241$	3.53574	−	2.04136i	0.227757	−	0.131496i	0.609537	+	0.792758i	$0.291355\pi$
$242$		0			0
$243$	−4.33332	+	14.9741i	−0.277983	+	0.960586i
$244$		0			0
$245$	18.9020	+	5.39050i	1.20761	+	0.344386i
$246$		0			0
$247$	−1.34705	+	2.33315i	−0.0857105	+	0.148455i
$248$		0			0
$249$	−19.8827	+	5.24286i	−1.26002	+	0.332253i
$250$		0			0
$251$	5.78085			0.364884			0.182442	−	0.983217i	$-0.441600\pi$
$251$	5.78085			0.364884			0.182442	+	0.983217i	$0.441600\pi$
$252$		0			0
$253$	−13.2855			−0.835251
$254$		0			0
$255$	27.1587	−	7.16146i	1.70075	−	0.448468i
$256$		0			0
$257$	10.4824	−	18.1560i	0.653871	−	1.13254i	−0.328304	−	0.944572i	$-0.606477\pi$
$257$	10.4824	−	18.1560i	0.653871	−	1.13254i	0.982175	−	0.187966i	$-0.0601896\pi$
$258$		0			0
$259$	10.5147	−	4.25706i	0.653351	−	0.264521i
$260$		0			0
$261$	10.4388	+	18.4175i	0.646145	+	1.14001i
$262$		0			0
$263$	4.32937	−	2.49957i	0.266961	−	0.154130i	−0.360545	−	0.932742i	$-0.617409\pi$
$263$	4.32937	−	2.49957i	0.266961	−	0.154130i	0.627506	+	0.778612i	$0.284076\pi$
$264$		0			0
$265$		−	17.1227i		−	1.05184i
$266$		0			0
$267$	−0.524611	+	1.92717i	−0.0321057	+	0.117941i
$268$		0			0
$269$	−7.67602	−	13.2953i	−0.468015	−	0.810626i	0.531317	−	0.847173i	$-0.321697\pi$
$269$	−7.67602	−	13.2953i	−0.468015	−	0.810626i	−0.999332	+	0.0365470i	$0.988364\pi$
$270$		0			0
$271$	14.4761	+	8.35779i	0.879362	+	0.507700i	0.870448	−	0.492260i	$-0.163829\pi$
$271$	14.4761	+	8.35779i	0.879362	+	0.507700i	0.00891391	+	0.999960i	$0.497163\pi$
$272$		0			0
$273$	−2.44785	+	5.71498i	−0.148151	+	0.345886i
$274$		0			0
$275$	−13.6914	−	7.90476i	−0.825625	−	0.476675i
$276$		0			0
$277$	11.2571	+	19.4979i	0.676376	+	1.17152i	0.976065	+	0.217481i	$0.0697839\pi$
$277$	11.2571	+	19.4979i	0.676376	+	1.17152i	−0.299689	+	0.954037i	$0.596883\pi$
$278$		0			0
$279$	−5.40098	+	9.18520i	−0.323348	+	0.549903i
$280$		0			0
$281$		−	18.1134i		−	1.08055i	−0.841488	−	0.540276i	$-0.818320\pi$
$281$		−	18.1134i		−	1.08055i	0.841488	−	0.540276i	$-0.181680\pi$
$282$		0			0
$283$	−5.00728	+	2.89095i	−0.297652	+	0.171849i	−0.641388	−	0.767217i	$-0.721641\pi$
$283$	−5.00728	+	2.89095i	−0.297652	+	0.171849i	0.343736	+	0.939066i	$0.388308\pi$
$284$		0			0
$285$	−6.85625	+	6.80190i	−0.406129	+	0.402910i
$286$		0			0
$287$	−3.79613	−	2.96145i	−0.224079	−	0.174809i
$288$		0			0
$289$	−8.17567	+	14.1607i	−0.480921	+	0.832980i
$290$		0			0
$291$	−7.07428	−	26.8281i	−0.414702	−	1.57269i
$292$		0			0
$293$	−9.38786			−0.548445			−0.274222	−	0.961666i	$-0.588420\pi$
$293$	−9.38786			−0.548445			−0.274222	+	0.961666i	$0.588420\pi$
$294$		0			0
$295$	−7.20151			−0.419288
$296$		0			0
$297$	−7.69864	+	27.4183i	−0.446720	+	1.59097i
$298$		0			0
$299$	1.64434	−	2.84808i	0.0950945	−	0.164709i
$300$		0			0
$301$	−23.4239	−	18.2735i	−1.35013	−	1.05327i
$302$		0			0
$303$	−17.9071	−	18.0502i	−1.02874	−	1.03696i
$304$		0			0
$305$	−13.3607	+	7.71380i	−0.765031	+	0.441691i
$306$		0			0
$307$		−	19.7599i		−	1.12776i	−0.825857	−	0.563880i	$-0.809308\pi$
$307$		−	19.7599i		−	1.12776i	0.825857	−	0.563880i	$-0.190692\pi$
$308$		0			0
$309$	−7.85341	−	2.13784i	−0.446765	−	0.121618i
$310$		0			0
$311$	10.1911	+	17.6515i	0.577884	+	1.00092i	0.995722	+	0.0924025i	$0.0294546\pi$
$311$	10.1911	+	17.6515i	0.577884	+	1.00092i	−0.417838	+	0.908522i	$0.637212\pi$
$312$		0			0
$313$	6.19972	+	3.57941i	0.350429	+	0.202320i	0.664874	−	0.746955i	$-0.268485\pi$
$313$	6.19972	+	3.57941i	0.350429	+	0.202320i	−0.314445	+	0.949276i	$0.601818\pi$
$314$		0			0
$315$	−13.8482	+	17.4630i	−0.780257	+	0.983927i
$316$		0			0
$317$	9.81412	+	5.66618i	0.551216	+	0.318245i	0.749612	−	0.661877i	$-0.230240\pi$
$317$	9.81412	+	5.66618i	0.551216	+	0.318245i	−0.198396	+	0.980122i	$0.563573\pi$
$318$		0			0
$319$	19.3379	+	33.4942i	1.08271	+	1.87531i
$320$		0			0
$321$	13.7815	+	3.75158i	0.769208	+	0.209393i
$322$		0			0
$323$		−	11.4680i		−	0.638096i
$324$		0			0
$325$	3.38917	−	1.95674i	0.187997	−	0.108540i
$326$		0			0
$327$	10.7619	+	10.8479i	0.595136	+	0.599891i
$328$		0			0
$329$	−0.986903	+	0.399565i	−0.0544097	+	0.0220287i
$330$		0			0
$331$	9.41383	−	16.3052i	0.517431	−	0.896216i	−0.482364	−	0.875971i	$-0.660222\pi$
$331$	9.41383	−	16.3052i	0.517431	−	0.896216i	0.999795	−	0.0202456i	$-0.00644480\pi$
$332$		0			0
$333$	−0.102355	+	12.8622i	−0.00560903	+	0.704846i
$334$		0			0
$335$	19.3882			1.05929
$336$		0			0
$337$	28.9739			1.57831			0.789156	−	0.614193i	$-0.210518\pi$
$337$	28.9739			1.57831			0.789156	+	0.614193i	$0.210518\pi$
$338$		0			0
$339$	−1.76651	−	6.69921i	−0.0959437	−	0.363851i
$340$		0			0
$341$	−9.73325	+	16.8585i	−0.527085	+	0.912939i
$342$		0			0
$343$	7.49615	−	16.9354i	0.404754	−	0.914426i
$344$		0			0
$345$	8.36942	−	8.30308i	0.450594	−	0.447023i
$346$		0			0
$347$	−15.6525	+	9.03697i	−0.840270	+	0.485130i	−0.857356	−	0.514724i	$-0.827894\pi$
$347$	−15.6525	+	9.03697i	−0.840270	+	0.485130i	0.0170860	+	0.999854i	$0.494561\pi$
$348$		0			0
$349$		−	12.8624i		−	0.688510i	−0.938876	−	0.344255i	$-0.888132\pi$
$349$		−	12.8624i		−	0.688510i	0.938876	−	0.344255i	$-0.111868\pi$
$350$		0			0
$351$	−4.92495	−	5.04395i	−0.262875	−	0.269226i
$352$		0			0
$353$	13.6386	+	23.6227i	0.725909	+	1.25731i	0.958599	+	0.284760i	$0.0919140\pi$
$353$	13.6386	+	23.6227i	0.725909	+	1.25731i	−0.232690	+	0.972551i	$0.574753\pi$
$354$		0			0
$355$	5.06415	+	2.92379i	0.268777	+	0.155178i
$356$		0			0
$357$	−3.13969	−	26.2778i	−0.166170	−	1.39077i
$358$		0			0
$359$	−0.773273	−	0.446450i	−0.0408118	−	0.0235627i	0.479455	−	0.877566i	$-0.340834\pi$
$359$	−0.773273	−	0.446450i	−0.0408118	−	0.0235627i	−0.520267	+	0.854004i	$0.674168\pi$
$360$		0			0
$361$	−7.52834	−	13.0395i	−0.396229	−	0.686288i
$362$		0			0
$363$	−8.66131	+	31.8175i	−0.454601	+	1.66999i
$364$		0			0
$365$			0.958746i			0.0501831i
$366$		0			0
$367$	−9.57418	+	5.52765i	−0.499768	+	0.288541i	−0.728618	−	0.684921i	$-0.759837\pi$
$367$	−9.57418	+	5.52765i	−0.499768	+	0.288541i	0.228850	+	0.973462i	$0.426504\pi$
$368$		0			0
$369$	4.74946	−	2.69194i	0.247247	−	0.140137i
$370$		0			0
$371$	−15.9782	−	2.23382i	−0.829549	−	0.115974i
$372$		0			0
$373$	−11.5503	+	20.0057i	−0.598053	+	1.03586i	0.395055	+	0.918657i	$0.370725\pi$
$373$	−11.5503	+	20.0057i	−0.598053	+	1.03586i	−0.993108	+	0.117201i	$0.962608\pi$
$374$		0			0
$375$	−9.94836	+	2.62328i	−0.513731	+	0.135465i
$376$		0			0
$377$	−9.57375			−0.493073
$378$		0			0
$379$	−23.3938			−1.20166			−0.600830	−	0.799377i	$-0.705163\pi$
$379$	−23.3938			−1.20166			−0.600830	+	0.799377i	$0.705163\pi$
$380$		0			0
$381$	11.6193	−	3.06387i	0.595273	−	0.156967i
$382$		0			0
$383$	−11.5139	+	19.9426i	−0.588331	+	1.01902i	0.406120	+	0.913820i	$0.366881\pi$
$383$	−11.5139	+	19.9426i	−0.588331	+	1.01902i	−0.994451	+	0.105200i	$0.966452\pi$
$384$		0			0
$385$	−25.0447	+	32.1036i	−1.27640	+	1.63615i
$386$		0			0
$387$	29.3064	−	16.6105i	1.48973	−	0.844360i
$388$		0			0
$389$	−5.45545	+	3.14970i	−0.276602	+	0.159696i	−0.631884	−	0.775063i	$-0.717718\pi$
$389$	−5.45545	+	3.14970i	−0.276602	+	0.159696i	0.355282	+	0.934759i	$0.384385\pi$
$390$		0			0
$391$			13.9990i			0.707958i
$392$		0			0
$393$	0.108034	−	0.396866i	0.00544960	−	0.0200192i
$394$		0			0
$395$	−3.34537	−	5.79435i	−0.168324	−	0.291545i
$396$		0			0
$397$	6.27940	+	3.62541i	0.315154	+	0.181954i	0.649230	−	0.760592i	$-0.275091\pi$
$397$	6.27940	+	3.62541i	0.315154	+	0.181954i	−0.334077	+	0.942546i	$0.608424\pi$
$398$		0			0
$399$	5.45281	+	7.28536i	0.272982	+	0.364724i
$400$		0			0
$401$	−11.8188	−	6.82360i	−0.590204	−	0.340755i	0.174974	−	0.984573i	$-0.444016\pi$
$401$	−11.8188	−	6.82360i	−0.590204	−	0.340755i	−0.765178	+	0.643819i	$0.777349\pi$
$402$		0			0
$403$	−2.40936	−	4.17314i	−0.120019	−	0.207879i
$404$		0			0
$405$	−12.2859	−	22.0841i	−0.610489	−	1.09737i
$406$		0			0
$407$			23.4989i			1.16479i
$408$		0			0
$409$	−11.9303	+	6.88797i	−0.589916	+	0.340588i	−0.765064	−	0.643954i	$-0.777293\pi$
$409$	−11.9303	+	6.88797i	−0.589916	+	0.340588i	0.175148	+	0.984542i	$0.443959\pi$
$410$		0			0
$411$	13.6144	−	13.5065i	0.671547	−	0.666224i
$412$		0			0
$413$	−0.939504	+	6.72017i	−0.0462300	+	0.330678i
$414$		0			0
$415$	16.6675	−	28.8690i	0.818177	−	1.41712i
$416$		0			0
$417$	0.452519	+	1.71611i	0.0221600	+	0.0840382i
$418$		0			0
$419$	6.94914			0.339488			0.169744	−	0.985488i	$-0.445706\pi$
$419$	6.94914			0.339488			0.169744	+	0.985488i	$0.445706\pi$
$420$		0			0
$421$	−0.349861			−0.0170512			−0.00852560	−	0.999964i	$-0.502714\pi$
$421$	−0.349861			−0.0170512			−0.00852560	+	0.999964i	$0.502714\pi$
$422$		0			0
$423$	0.00960700	−	1.20724i	0.000467108	−	0.0586981i
$424$		0			0
$425$	−8.32928	+	14.4267i	−0.404029	+	0.699800i
$426$		0			0
$427$	5.45520	+	13.4740i	0.263995	+	0.652054i
$428$		0			0
$429$	−9.07048	−	9.14295i	−0.437927	−	0.441426i
$430$		0			0
$431$	−17.4513	+	10.0755i	−0.840601	+	0.485321i	−0.857468	−	0.514537i	$-0.827964\pi$
$431$	−17.4513	+	10.0755i	−0.840601	+	0.485321i	0.0168676	+	0.999858i	$0.494631\pi$
$432$		0			0
$433$			1.42453i			0.0684585i	0.999414	+	0.0342292i	$0.0108976\pi$
$433$			1.42453i			0.0684585i	−0.999414	+	0.0342292i	$0.989102\pi$
$434$		0			0
$435$	−33.1152	−	9.01456i	−1.58775	−	0.432215i
$436$		0			0
$437$	−2.40680	−	4.16870i	−0.115133	−	0.199416i
$438$		0			0
$439$	1.76541	+	1.01926i	0.0842583	+	0.0486465i	0.541537	−	0.840677i	$-0.317843\pi$
$439$	1.76541	+	1.01926i	0.0842583	+	0.0486465i	−0.457279	+	0.889323i	$0.651176\pi$
$440$		0			0
$441$	14.4892	+	15.2008i	0.689960	+	0.723848i
$442$		0			0
$443$	11.1751	+	6.45195i	0.530945	+	0.306541i	0.741401	−	0.671062i	$-0.234162\pi$
$443$	11.1751	+	6.45195i	0.530945	+	0.306541i	−0.210456	+	0.977603i	$0.567495\pi$
$444$		0			0
$445$	−1.61898	−	2.80416i	−0.0767471	−	0.132930i
$446$		0			0
$447$	36.7717	+	10.0099i	1.73924	+	0.473453i
$448$		0			0
$449$		−	2.49432i		−	0.117714i	−0.998266	−	0.0588572i	$-0.981254\pi$
$449$		−	2.49432i		−	0.117714i	0.998266	−	0.0588572i	$-0.0187457\pi$
$450$		0			0
$451$	8.63741	−	4.98681i	0.406720	−	0.234820i
$452$		0			0
$453$	−8.86517	−	8.93600i	−0.416522	−	0.419850i
$454$		0			0
$455$	−3.78243	−	9.34240i	−0.177323	−	0.437978i
$456$		0			0
$457$	−7.30952	+	12.6605i	−0.341925	+	0.592232i	−0.984790	−	0.173748i	$-0.944412\pi$
$457$	−7.30952	+	12.6605i	−0.341925	+	0.592232i	0.642865	+	0.765979i	$0.277746\pi$
$458$		0			0
$459$	28.8908	+	8.11209i	1.34851	+	0.378640i
$460$		0			0
$461$	−2.83467			−0.132024			−0.0660120	−	0.997819i	$-0.521028\pi$
$461$	−2.83467			−0.132024			−0.0660120	+	0.997819i	$0.521028\pi$
$462$		0			0
$463$	14.1594			0.658042			0.329021	−	0.944323i	$-0.393281\pi$
$463$	14.1594			0.658042			0.329021	+	0.944323i	$0.393281\pi$
$464$		0			0
$465$	−4.40449	−	16.7033i	−0.204253	−	0.774598i
$466$		0			0
$467$	4.98809	−	8.63963i	0.230821	−	0.399794i	−0.727229	−	0.686395i	$-0.759192\pi$
$467$	4.98809	−	8.63963i	0.230821	−	0.399794i	0.958050	+	0.286601i	$0.0925254\pi$
$468$		0			0
$469$	2.52937	−	18.0923i	0.116796	−	0.835426i
$470$		0			0
$471$	−27.9698	+	27.7481i	−1.28878	+	1.27857i
$472$		0			0
$473$	53.2969	−	30.7710i	2.45059	−	1.41485i
$474$		0			0
$475$		−	5.72811i		−	0.262824i
$476$		0			0
$477$	9.27269	−	15.7696i	0.424567	−	0.722041i
$478$		0			0
$479$	−21.7575	−	37.6850i	−0.994124	−	1.72187i	−0.590805	−	0.806815i	$-0.701190\pi$
$479$	−21.7575	−	37.6850i	−0.994124	−	1.72187i	−0.403320	−	0.915059i	$-0.632144\pi$
$480$		0			0
$481$	−5.03757	−	2.90844i	−0.229693	−	0.132614i
$482$		0			0
$483$	−6.65625	−	8.89323i	−0.302870	−	0.404656i
$484$		0			0
$485$	38.9535	+	22.4898i	1.76879	+	1.02121i
$486$		0			0
$487$	−18.5796	−	32.1808i	−0.841921	−	1.45825i	−0.888269	−	0.459324i	$-0.848092\pi$
$487$	−18.5796	−	32.1808i	−0.841921	−	1.45825i	0.0463476	−	0.998925i	$-0.485242\pi$
$488$		0			0
$489$	8.24970	−	30.3055i	0.373064	−	1.37046i
$490$		0			0
$491$			22.1831i			1.00111i	0.865704	+	0.500556i	$0.166871\pi$
$491$			22.1831i			1.00111i	−0.865704	+	0.500556i	$0.833129\pi$
$492$		0			0
$493$	35.2929	−	20.3764i	1.58951	−	0.917707i
$494$		0			0
$495$	−22.7655	−	40.1657i	−1.02323	−	1.80532i
$496$		0			0
$497$	3.38903	−	4.34423i	0.152019	−	0.194865i
$498$		0			0
$499$	−8.33695	+	14.4400i	−0.373213	+	0.646424i	−0.990058	−	0.140661i	$-0.955077\pi$
$499$	−8.33695	+	14.4400i	−0.373213	+	0.646424i	0.616845	+	0.787085i	$0.288411\pi$
$500$		0			0
$501$	40.3531	−	10.6407i	1.80284	−	0.475390i
$502$		0			0
$503$	8.55884			0.381620			0.190810	−	0.981627i	$-0.438889\pi$
$503$	8.55884			0.381620			0.190810	+	0.981627i	$0.438889\pi$
$504$		0			0
$505$	41.2196			1.83425
$506$		0			0
$507$	−18.6898	+	4.92829i	−0.830042	+	0.218873i
$508$		0			0
$509$	−14.1072	+	24.4345i	−0.625292	+	1.08304i	0.363192	+	0.931714i	$0.381687\pi$
$509$	−14.1072	+	24.4345i	−0.625292	+	1.08304i	−0.988484	+	0.151324i	$0.951646\pi$
$510$		0			0
$511$	0.894665	+	0.125077i	0.0395777	+	0.00553310i
$512$		0			0
$513$	−9.99798	+	2.55144i	−0.441422	+	0.112649i
$514$		0			0
$515$	11.4272	−	6.59750i	0.503543	−	0.290721i
$516$		0			0
$517$		−	2.20559i		−	0.0970017i
$518$		0			0
$519$	−4.72049	+	17.3408i	−0.207206	+	0.761177i
$520$		0			0
$521$	−9.00041	−	15.5892i	−0.394315	−	0.682974i	0.598698	−	0.800975i	$-0.295685\pi$
$521$	−9.00041	−	15.5892i	−0.394315	−	0.682974i	−0.993014	+	0.118001i	$0.962352\pi$
$522$		0			0
$523$	−11.9049	−	6.87332i	−0.520567	−	0.300549i	0.216600	−	0.976260i	$-0.430503\pi$
$523$	−11.9049	−	6.87332i	−0.520567	−	0.300549i	−0.737167	+	0.675711i	$0.763837\pi$
$524$		0			0
$525$	−1.56824	−	13.1254i	−0.0684434	−	0.572839i
$526$		0			0
$527$	17.7639	+	10.2560i	0.773806	+	0.446757i
$528$		0			0
$529$	−8.56202	−	14.8299i	−0.372262	−	0.644776i
$530$		0			0
$531$	−6.63243	−	3.89993i	−0.287823	−	0.169243i
$532$		0			0
$533$			2.46886i			0.106938i
$534$		0			0
$535$	−20.0530	+	11.5776i	−0.866965	+	0.500542i
$536$		0			0
$537$	16.4589	−	16.3284i	0.710254	−	0.704624i
$538$		0			0
$539$	26.6905	+	27.5589i	1.14964	+	1.18705i
$540$		0			0
$541$	−19.6272	+	33.9953i	−0.843839	+	1.46157i	0.0427866	+	0.999084i	$0.486376\pi$
$541$	−19.6272	+	33.9953i	−0.843839	+	1.46157i	−0.886626	+	0.462488i	$0.846957\pi$
$542$		0			0
$543$	−8.14094	−	30.8732i	−0.349361	−	1.32490i
$544$		0			0
$545$	−24.7724			−1.06113
$546$		0			0
$547$	−12.4980			−0.534375			−0.267188	−	0.963645i	$-0.586094\pi$
$547$	−12.4980			−0.534375			−0.267188	+	0.963645i	$0.586094\pi$
$548$		0			0
$549$	−16.4823	−	0.131163i	−0.703446	−	0.00559789i
$550$		0			0
$551$	−7.00651	+	12.1356i	−0.298487	+	0.516995i
$552$		0			0
$553$	−5.84350	+	2.36584i	−0.248491	+	0.100606i
$554$		0			0
$555$	−14.6862	−	14.8035i	−0.623393	−	0.628374i
$556$		0			0
$557$	−15.4816	+	8.93830i	−0.655976	+	0.378728i	−0.790742	−	0.612150i	$-0.790305\pi$
$557$	−15.4816	+	8.93830i	−0.655976	+	0.378728i	0.134766	+	0.990877i	$0.456972\pi$
$558$		0			0
$559$			15.2340i			0.644331i
$560$		0			0
$561$	52.8971	+	14.3996i	2.23332	+	0.607950i
$562$		0			0
$563$	1.36644	+	2.36674i	0.0575885	+	0.0997462i	0.893382	−	0.449297i	$-0.148326\pi$
$563$	1.36644	+	2.36674i	0.0575885	+	0.0997462i	−0.835794	+	0.549043i	$0.814992\pi$
$564$		0			0
$565$	9.72702	+	5.61589i	0.409219	+	0.236262i
$566$		0			0
$567$	−22.2108	+	8.58361i	−0.932768	+	0.360478i
$568$		0			0
$569$	1.72971	+	0.998650i	0.0725133	+	0.0418656i	0.535818	−	0.844333i	$-0.320003\pi$
$569$	1.72971	+	0.998650i	0.0725133	+	0.0418656i	−0.463305	+	0.886199i	$0.653337\pi$
$570$		0			0
$571$	1.00728	+	1.74466i	0.0421534	+	0.0730118i	0.886332	−	0.463050i	$-0.153245\pi$
$571$	1.00728	+	1.74466i	0.0421534	+	0.0730118i	−0.844179	+	0.536061i	$0.819912\pi$
$572$		0			0
$573$	−6.93739	−	1.88848i	−0.289814	−	0.0788926i
$574$		0			0
$575$			6.99231i			0.291599i
$576$		0			0
$577$	−22.0199	+	12.7132i	−0.916701	+	0.529258i	−0.882581	−	0.470160i	$-0.844196\pi$
$577$	−22.0199	+	12.7132i	−0.916701	+	0.529258i	−0.0341199	+	0.999418i	$0.510863\pi$
$578$		0			0
$579$	23.7986	+	23.9887i	0.989036	+	0.996938i
$580$		0			0
$581$	−24.7650	−	19.3197i	−1.02743	−	0.801518i
$582$		0			0
$583$	16.7106	−	28.9435i	0.692080	−	1.19872i
$584$		0			0
$585$	11.4282	+	0.0909435i	0.472498	+	0.00376005i
$586$		0			0
$587$	−34.4645			−1.42250			−0.711251	−	0.702939i	$-0.751871\pi$
$587$	−34.4645			−1.42250			−0.711251	+	0.702939i	$0.751871\pi$
$588$		0			0
$589$	−7.05312			−0.290619
$590$		0			0
$591$	1.68239	+	6.38020i	0.0692043	+	0.262446i
$592$		0			0
$593$	3.62199	−	6.27347i	0.148737	−	0.257620i	−0.782024	−	0.623249i	$-0.785812\pi$
$593$	3.62199	−	6.27347i	0.148737	−	0.257620i	0.930761	+	0.365628i	$0.119146\pi$
$594$		0			0
$595$	33.8277	+	26.3897i	1.38680	+	1.08187i
$596$		0			0
$597$	7.52974	−	7.47006i	0.308172	−	0.305729i
$598$		0			0
$599$	32.5464	−	18.7907i	1.32981	−	0.767766i	0.344540	−	0.938772i	$-0.388035\pi$
$599$	32.5464	−	18.7907i	1.32981	−	0.767766i	0.985270	+	0.171005i	$0.0547015\pi$
$600$		0			0
$601$		−	3.78103i		−	0.154232i	−0.997022	−	0.0771158i	$-0.975429\pi$
$601$		−	3.78103i		−	0.154232i	0.997022	−	0.0771158i	$-0.0245711\pi$
$602$		0			0
$603$	17.8561	+	10.4996i	0.727157	+	0.427575i
$604$		0			0
$605$	−26.7293	−	46.2965i	−1.08670	−	1.88222i
$606$		0			0
$607$	−24.0353	−	13.8768i	−0.975565	−	0.563242i	−0.0746364	−	0.997211i	$-0.523780\pi$
$607$	−24.0353	−	13.8768i	−0.975565	−	0.563242i	−0.900928	+	0.433968i	$0.857113\pi$
$608$		0			0
$609$	−12.7322	+	29.7258i	−0.515936	+	1.20455i
$610$		0			0
$611$	0.472823	+	0.272985i	0.0191284	+	0.0110438i
$612$		0			0
$613$	15.3570	+	26.5991i	0.620264	+	1.07433i	0.989436	+	0.144968i	$0.0463080\pi$
$613$	15.3570	+	26.5991i	0.620264	+	1.07433i	−0.369172	+	0.929361i	$0.620359\pi$
$614$		0			0
$615$	−2.32466	+	8.53968i	−0.0937392	+	0.344353i
$616$		0			0
$617$			44.3075i			1.78375i	0.452279	+	0.891877i	$0.350611\pi$
$617$			44.3075i			1.78375i	−0.452279	+	0.891877i	$0.649389\pi$
$618$		0			0
$619$	27.4026	−	15.8209i	1.10140	−	0.635895i	0.164813	−	0.986325i	$-0.447298\pi$
$619$	27.4026	−	15.8209i	1.10140	−	0.635895i	0.936589	+	0.350430i	$0.113965\pi$
$620$		0			0
$621$	12.2045	−	3.11455i	0.489751	−	0.124982i
$622$		0			0
$623$	−2.82794	+	1.14494i	−0.113299	+	0.0458711i
$624$		0			0
$625$	15.5511	−	26.9352i	0.622042	−	1.07741i
$626$		0			0
$627$	−18.2277	+	4.80645i	−0.727945	+	0.191951i
$628$		0			0
$629$	24.7608			0.987279
$630$		0			0
$631$	−20.7528			−0.826157			−0.413079	−	0.910695i	$-0.635547\pi$
$631$	−20.7528			−0.826157			−0.413079	+	0.910695i	$0.635547\pi$
$632$		0			0
$633$	−4.90815	+	1.29423i	−0.195082	+	0.0514409i
$634$		0			0
$635$	−9.74033	+	16.8707i	−0.386533	+	0.669495i
$636$		0			0
$637$	−9.21142	+	2.31082i	−0.364970	+	0.0915580i
$638$		0			0
$639$	3.08061	+	5.43520i	0.121867	+	0.215013i
$640$		0			0
$641$	−33.0033	+	19.0545i	−1.30355	+	0.752606i	−0.981012	−	0.193949i	$-0.937870\pi$
$641$	−33.0033	+	19.0545i	−1.30355	+	0.752606i	−0.322541	+	0.946556i	$0.604537\pi$
$642$		0			0
$643$			29.5791i			1.16648i	0.812298	+	0.583242i	$0.198216\pi$
$643$			29.5791i			1.16648i	−0.812298	+	0.583242i	$0.801784\pi$
$644$		0			0
$645$	−14.3442	+	52.6939i	−0.564804	+	2.07482i
$646$		0			0
$647$	−10.5935	−	18.3485i	−0.416474	−	0.721354i	0.579108	−	0.815251i	$-0.303401\pi$
$647$	−10.5935	−	18.3485i	−0.416474	−	0.721354i	−0.995582	+	0.0938966i	$0.970068\pi$
$648$		0			0
$649$	−12.1731	−	7.02817i	−0.477838	−	0.275880i
$650$		0			0
$651$	−16.1615	+	1.93099i	−0.633419	+	0.0756816i
$652$		0			0
$653$	23.0548	+	13.3107i	0.902204	+	0.520888i	0.877915	−	0.478817i	$-0.158934\pi$
$653$	23.0548	+	13.3107i	0.902204	+	0.520888i	0.0242893	+	0.999705i	$0.492268\pi$
$654$		0			0
$655$	0.333399	+	0.577465i	0.0130270	+	0.0225634i
$656$		0			0
$657$	−0.519203	+	0.882984i	−0.0202560	+	0.0344485i
$658$		0			0
$659$			16.3864i			0.638322i	0.947701	+	0.319161i	$0.103401\pi$
$659$			16.3864i			0.638322i	−0.947701	+	0.319161i	$0.896599\pi$
$660$		0			0
$661$	−16.0227	+	9.25072i	−0.623211	+	0.359811i	−0.778118	−	0.628118i	$-0.783826\pi$
$661$	−16.0227	+	9.25072i	−0.623211	+	0.359811i	0.154907	+	0.987929i	$0.450492\pi$
$662$		0			0
$663$	−9.63396	+	9.55760i	−0.374152	+	0.371186i
$664$		0			0
$665$	−14.6105	−	2.04260i	−0.566572	−	0.0792088i
$666$		0			0
$667$	8.55284	−	14.8139i	0.331167	−	0.573598i
$668$		0			0
$669$	−2.03654	−	7.72327i	−0.0787373	−	0.298599i
$670$		0			0
$671$	−30.1125			−1.16248
$672$		0			0
$673$	−45.4357			−1.75142			−0.875708	−	0.482841i	$-0.839605\pi$
$673$	−45.4357			−1.75142			−0.875708	+	0.482841i	$0.839605\pi$
$674$		0			0
$675$	14.4306	+	4.05189i	0.555434	+	0.155957i
$676$		0			0
$677$	15.8566	−	27.4644i	0.609419	−	1.05554i	−0.381917	−	0.924196i	$-0.624736\pi$
$677$	15.8566	−	27.4644i	0.609419	−	1.05554i	0.991336	−	0.131348i	$-0.0419305\pi$
$678$		0			0
$679$	26.0684	−	33.4159i	1.00042	−	1.28238i
$680$		0			0
$681$	−21.0388	−	21.2069i	−0.806209	−	0.812650i
$682$		0			0
$683$	31.0917	−	17.9508i	1.18969	−	0.686868i	0.231454	−	0.972846i	$-0.425652\pi$
$683$	31.0917	−	17.9508i	1.18969	−	0.686868i	0.958236	+	0.285978i	$0.0923183\pi$
$684$		0			0
$685$			31.0899i			1.18788i
$686$		0			0
$687$	22.3285	+	6.07823i	0.851886	+	0.231899i
$688$		0			0
$689$	4.13651	+	7.16465i	0.157589	+	0.272952i
$690$		0			0
$691$	22.2415	+	12.8411i	0.846106	+	0.488499i	0.859335	−	0.511413i	$-0.170878\pi$
$691$	22.2415	+	12.8411i	0.846106	+	0.488499i	−0.0132293	+	0.999912i	$0.504211\pi$
$692$		0			0
$693$	−40.4511	+	16.0039i	−1.53661	+	0.607937i
$694$		0			0
$695$	−2.49173	−	1.43860i	−0.0945167	−	0.0545692i
$696$		0			0
$697$	−5.25462	−	9.10127i	−0.199033	−	0.344735i
$698$		0			0
$699$	30.0868	+	8.19016i	1.13799	+	0.309780i
$700$		0			0
$701$		−	1.29881i		−	0.0490553i	−0.999699	−	0.0245276i	$-0.992192\pi$
$701$		−	1.29881i		−	0.0490553i	0.999699	−	0.0245276i	$-0.00780818\pi$
$702$		0			0
$703$	−7.37344	+	4.25706i	−0.278095	+	0.160558i
$704$		0			0
$705$	1.37844	+	1.38945i	0.0519149	+	0.0523296i
$706$		0			0
$707$	5.37749	−	38.4646i	0.202241	−	1.44661i
$708$		0			0
$709$	13.8609	−	24.0077i	0.520556	−	0.901629i	−0.479158	−	0.877728i	$-0.659058\pi$
$709$	13.8609	−	24.0077i	0.520556	−	0.901629i	0.999714	−	0.0239010i	$-0.00760863\pi$
$710$		0			0
$711$	0.0568835	−	7.14813i	0.00213330	−	0.268076i
$712$		0			0
$713$	8.60973			0.322437
$714$		0			0
$715$	20.8789			0.780828
$716$		0			0
$717$	10.4444	+	39.6089i	0.390055	+	1.47922i
$718$		0			0
$719$	−20.9122	+	36.2210i	−0.779893	+	1.35081i	0.152109	+	0.988364i	$0.451393\pi$
$719$	−20.9122	+	36.2210i	−0.779893	+	1.35081i	−0.932003	+	0.362451i	$0.881940\pi$
$720$		0			0
$721$	−4.66575	−	11.5241i	−0.173762	−	0.429181i
$722$		0			0
$723$	−5.02015	+	4.98036i	−0.186701	+	0.185221i
$724$		0			0
$725$	17.6284	−	10.1777i	0.654701	−	0.377992i
$726$		0			0
$727$		−	2.19295i		−	0.0813319i	−0.999173	−	0.0406660i	$-0.987052\pi$
$727$		−	2.19295i		−	0.0813319i	0.999173	−	0.0406660i	$-0.0129479\pi$
$728$		0			0
$729$	0.644508	−	26.9923i	0.0238707	−	0.999715i
$730$		0			0
$731$	−32.4235	−	56.1592i	−1.19923	−	2.07712i
$732$		0			0
$733$	18.0850	+	10.4414i	0.667986	+	0.385662i	0.795313	−	0.606199i	$-0.207307\pi$
$733$	18.0850	+	10.4414i	0.667986	+	0.385662i	−0.127327	+	0.991861i	$0.540640\pi$
$734$		0			0
$735$	−34.0378	−	0.680374i	−1.25550	−	0.0250960i
$736$		0			0
$737$	32.7731	+	18.9215i	1.20721	+	0.696984i
$738$		0			0
$739$	6.65032	+	11.5187i	0.244636	+	0.423722i	0.962029	−	0.272947i	$-0.0879982\pi$
$739$	6.65032	+	11.5187i	0.244636	+	0.423722i	−0.717393	+	0.696668i	$0.754665\pi$
$740$		0			0
$741$	1.22565	−	4.50246i	0.0450255	−	0.165402i
$742$		0			0
$743$		−	24.8226i		−	0.910653i	−0.890324	−	0.455327i	$-0.849522\pi$
$743$		−	24.8226i		−	0.910653i	0.890324	−	0.455327i	$-0.150478\pi$
$744$		0			0
$745$	−53.5051	+	30.8912i	−1.96028	+	1.13177i
$746$		0			0
$747$	30.9843	−	17.5615i	1.13366	−	0.642543i
$748$		0			0
$749$	8.18765	+	20.2230i	0.299170	+	0.738934i
$750$		0			0
$751$	5.98635	−	10.3687i	0.218445	−	0.378358i	−0.735888	−	0.677104i	$-0.763235\pi$
$751$	5.98635	−	10.3687i	0.218445	−	0.378358i	0.954333	+	0.298746i	$0.0965682\pi$
$752$		0			0
$753$	−9.68179	+	2.55298i	−0.352824	+	0.0930359i
$754$		0			0
$755$	20.4063			0.742663
$756$		0			0
$757$	29.8095			1.08345			0.541723	−	0.840557i	$-0.317772\pi$
$757$	29.8095			1.08345			0.541723	+	0.840557i	$0.317772\pi$
$758$		0			0
$759$	22.2506	−	5.86723i	0.807644	−	0.212967i
$760$		0			0
$761$	−16.7439	+	29.0013i	−0.606967	+	1.05130i	0.384770	+	0.923012i	$0.374281\pi$
$761$	−16.7439	+	29.0013i	−0.606967	+	1.05130i	−0.991737	+	0.128286i	$0.959053\pi$
$762$		0			0
$763$	−3.23180	+	23.1167i	−0.116999	+	0.836880i
$764$		0			0
$765$	−42.3228	+	23.9881i	−1.53018	+	0.867291i
$766$		0			0
$767$	3.01333	−	1.73975i	0.108805	−	0.0628186i
$768$		0			0
$769$		−	19.6491i		−	0.708566i	−0.935138	−	0.354283i	$-0.884725\pi$
$769$		−	19.6491i		−	0.708566i	0.935138	−	0.354283i	$-0.115275\pi$
$770$		0			0
$771$	−9.53770	+	35.0370i	−0.343492	+	1.26183i
$772$		0			0
$773$	−6.51659	−	11.2871i	−0.234385	−	0.405968i	0.724708	−	0.689056i	$-0.241974\pi$
$773$	−6.51659	−	11.2871i	−0.234385	−	0.405968i	−0.959094	+	0.283088i	$0.908641\pi$
$774$		0			0
$775$	8.87282	+	5.12273i	0.318721	+	0.184014i
$776$		0			0
$777$	−15.7300	+	11.7733i	−0.564311	+	0.422365i
$778$		0			0
$779$	3.12951	+	1.80682i	0.112126	+	0.0647362i
$780$		0			0
$781$	5.70682	+	9.88451i	0.204206	+	0.353695i
$782$		0			0
$783$	−25.6166	−	26.2355i	−0.915462	−	0.937582i
$784$		0			0
$785$		−	63.8722i		−	2.27970i
$786$		0			0
$787$	21.1053	−	12.1852i	0.752324	−	0.434354i	−0.0742091	−	0.997243i	$-0.523643\pi$
$787$	21.1053	−	12.1852i	0.752324	−	0.434354i	0.826533	+	0.562888i	$0.190310\pi$
$788$		0			0
$789$	−6.14697	+	6.09825i	−0.218838	+	0.217103i
$790$		0			0
$791$	6.50952	−	8.34423i	0.231452	−	0.296687i
$792$		0			0
$793$	3.72702	−	6.45538i	0.132350	−	0.229237i
$794$		0			0
$795$	7.56185	+	28.6771i	0.268191	+	1.01707i
$796$		0			0
$797$	3.14465			0.111389			0.0556947	−	0.998448i	$-0.482263\pi$
$797$	3.14465			0.111389			0.0556947	+	0.998448i	$0.482263\pi$
$798$		0			0
$799$	−2.32404			−0.0822186
$800$		0			0
$801$	0.0275286	−	3.45932i	0.000972675	−	0.122229i
$802$		0			0
$803$	−0.935670	+	1.62063i	−0.0330191	+	0.0571907i
$804$		0			0
$805$	17.8350	+	2.49340i	0.628603	+	0.0878810i
$806$		0			0
$807$	18.7274	+	18.8770i	0.659235	+	0.664502i
$808$		0			0
$809$	5.76799	−	3.33015i	0.202792	−	0.117082i	−0.395165	−	0.918610i	$-0.629313\pi$
$809$	5.76799	−	3.33015i	0.202792	−	0.117082i	0.597957	+	0.801528i	$0.295979\pi$
$810$		0			0
$811$		−	48.8504i		−	1.71537i	−0.514176	−	0.857685i	$-0.671902\pi$
$811$		−	48.8504i		−	1.71537i	0.514176	−	0.857685i	$-0.328098\pi$
$812$		0			0
$813$	−27.9357	−	7.60460i	−0.979747	−	0.266705i
$814$		0			0
$815$	25.4590	+	44.0964i	0.891791	+	1.54463i
$816$		0			0
$817$	19.3106	+	11.1490i	0.675591	+	0.390053i
$818$		0			0
$819$	1.57578	−	10.6525i	0.0550623	−	0.372228i
$820$		0			0
$821$	−35.0636	−	20.2440i	−1.22373	−	0.706520i	−0.258017	−	0.966140i	$-0.583069\pi$
$821$	−35.0636	−	20.2440i	−1.22373	−	0.706520i	−0.965711	+	0.259621i	$0.916402\pi$
$822$		0			0
$823$	−17.2956	−	29.9568i	−0.602886	−	1.04423i	−0.992382	−	0.123201i	$-0.960684\pi$
$823$	−17.2956	−	29.9568i	−0.602886	−	1.04423i	0.389496	−	0.921028i	$-0.372649\pi$
$824$		0			0
$825$	26.4214	+	7.19240i	0.919876	+	0.250407i
$826$		0			0
$827$		−	29.3071i		−	1.01911i	−0.860438	−	0.509555i	$-0.829810\pi$
$827$		−	29.3071i		−	1.01911i	0.860438	−	0.509555i	$-0.170190\pi$
$828$		0			0
$829$	12.7957	−	7.38763i	0.444414	−	0.256583i	−0.261054	−	0.965324i	$-0.584070\pi$
$829$	12.7957	−	7.38763i	0.444414	−	0.256583i	0.705468	+	0.708741i	$0.250737\pi$
$830$		0			0
$831$	−27.4643	−	27.6837i	−0.952727	−	0.960339i
$832$		0			0
$833$	29.0390	−	28.1239i	1.00614	−	0.974435i
$834$		0			0
$835$	−33.8277	+	58.5912i	−1.17065	+	2.02763i
$836$		0			0
$837$	4.98915	−	17.7686i	0.172450	−	0.614173i
$838$		0			0
$839$	32.0373			1.10605			0.553026	−	0.833164i	$-0.313473\pi$
$839$	32.0373			1.10605			0.553026	+	0.833164i	$0.313473\pi$
$840$		0			0
$841$	−20.7968			−0.717131
$842$		0			0
$843$	7.99936	+	30.3363i	0.275513	+	1.04484i
$844$		0			0
$845$	15.6675	−	27.1369i	0.538978	−	0.933537i
$846$		0			0
$847$	−46.6892	+	18.9029i	−1.60426	+	0.649513i
$848$		0			0
$849$	7.10948	−	7.05313i	0.243997	−	0.242063i
$850$		0			0
$851$	9.00076	−	5.19659i	0.308542	−	0.178137i
$852$		0			0
$853$		−	33.1110i		−	1.13370i	−0.823821	−	0.566850i	$-0.808162\pi$
$853$		−	33.1110i		−	1.13370i	0.823821	−	0.566850i	$-0.191838\pi$
$854$		0			0
$855$	8.47896	−	14.4198i	0.289974	−	0.493145i
$856$		0			0
$857$	−9.00041	−	15.5892i	−0.307448	−	0.532516i	0.670355	−	0.742040i	$-0.266142\pi$
$857$	−9.00041	−	15.5892i	−0.307448	−	0.532516i	−0.977803	+	0.209524i	$0.932808\pi$
$858$		0			0
$859$	−23.1107	−	13.3430i	−0.788528	−	0.455257i	0.0509160	−	0.998703i	$-0.483786\pi$
$859$	−23.1107	−	13.3430i	−0.788528	−	0.455257i	−0.839444	+	0.543446i	$0.817119\pi$
$860$		0			0
$861$	7.66563	+	3.28336i	0.261244	+	0.111897i
$862$		0			0
$863$	8.69289	+	5.01884i	0.295909	+	0.170843i	0.640604	−	0.767872i	$-0.278684\pi$
$863$	8.69289	+	5.01884i	0.295909	+	0.170843i	−0.344694	+	0.938715i	$0.612017\pi$
$864$		0			0
$865$	−14.5677	−	25.2320i	−0.495317	−	0.857913i
$866$		0			0
$867$	7.43889	−	27.3269i	0.252638	−	0.928071i
$868$		0			0
$869$		−	13.0594i		−	0.443009i
$870$		0			0
$871$	−8.11262	+	4.68382i	−0.274885	+	0.158705i
$872$		0			0
$873$	23.6961	+	41.8076i	0.801990	+	1.41497i
$874$		0			0
$875$	−12.3912	−	9.66666i	−0.418900	−	0.326793i
$876$		0			0
$877$	7.38102	−	12.7843i	0.249239	−	0.431695i	−0.714076	−	0.700069i	$-0.753153\pi$
$877$	7.38102	−	12.7843i	0.249239	−	0.431695i	0.963315	+	0.268373i	$0.0864861\pi$
$878$		0			0
$879$	15.7228	−	4.14594i	0.530318	−	0.139839i
$880$		0			0
$881$	4.42345			0.149030			0.0745148	−	0.997220i	$-0.476259\pi$
$881$	4.42345			0.149030			0.0745148	+	0.997220i	$0.476259\pi$
$882$		0			0
$883$	−10.5403			−0.354711			−0.177355	−	0.984147i	$-0.556754\pi$
$883$	−10.5403			−0.354711			−0.177355	+	0.984147i	$0.556754\pi$
$884$		0			0
$885$	12.0611	−	3.18038i	0.405430	−	0.106907i
$886$		0			0
$887$	4.92026	−	8.52213i	0.165206	−	0.286145i	−0.771522	−	0.636202i	$-0.780504\pi$
$887$	4.92026	−	8.52213i	0.165206	−	0.286145i	0.936728	+	0.350057i	$0.113838\pi$
$888$		0			0
$889$	14.4724	+	11.2902i	0.485389	+	0.378663i
$890$		0			0
$891$	0.785012	−	49.3203i	0.0262989	−	1.65229i
$892$		0			0
$893$	0.692067	−	0.399565i	0.0231591	−	0.0133709i
$894$		0			0
$895$			37.5857i			1.25635i
$896$		0			0
$897$	−1.49615	+	5.49615i	−0.0499551	+	0.183511i
$898$		0			0
$899$	−12.5320	−	21.7061i	−0.417966	−	0.723939i
$900$		0			0
$901$	−30.4979	−	17.6080i	−1.01603	−	0.586607i
$902$		0			0
$903$	47.3005	+	20.2599i	1.57406	+	0.674207i
$904$		0			0
$905$	44.8268	+	25.8808i	1.49009	+	0.860306i
$906$		0			0
$907$	4.10609	+	7.11195i	0.136340	+	0.236148i	0.926109	−	0.377257i	$-0.123133\pi$
$907$	4.10609	+	7.11195i	0.136340	+	0.236148i	−0.789768	+	0.613405i	$0.789799\pi$
$908$		0			0
$909$	37.9624	+	22.3222i	1.25913	+	0.740382i
$910$		0			0
$911$		−	44.6131i		−	1.47810i	−0.673652	−	0.739049i	$-0.735275\pi$
$911$		−	44.6131i		−	1.47810i	0.673652	−	0.739049i	$-0.264725\pi$
$912$		0			0
$913$	56.3483	−	32.5327i	1.86486	−	1.07668i
$914$		0			0
$915$	18.9699	−	18.8196i	0.627126	−	0.622155i
$916$		0			0
$917$	0.582363	−	0.235780i	0.0192313	−	0.00778614i
$918$		0			0
$919$	−15.3222	+	26.5388i	−0.505431	+	0.875433i	0.494549	+	0.869150i	$0.335333\pi$
$919$	−15.3222	+	26.5388i	−0.505431	+	0.875433i	−0.999980	+	0.00628290i	$0.998000\pi$
$920$		0			0
$921$	8.72654	+	33.0940i	0.287549	+	1.09048i
$922$		0			0
$923$	−2.82532			−0.0929966
$924$		0			0
$925$	12.3677			0.406648
$926$		0			0
$927$	14.0970	+	0.112182i	0.463008	+	0.00368453i
$928$		0			0
$929$	−10.7198	+	18.5673i	−0.351706	+	0.609173i	−0.986548	−	0.163469i	$-0.947732\pi$
$929$	−10.7198	+	18.5673i	−0.351706	+	0.609173i	0.634842	+	0.772642i	$0.281065\pi$
$930$		0			0
$931$	−3.81216	+	13.3675i	−0.124938	+	0.438102i
$932$		0			0
$933$	−24.8635	−	25.0621i	−0.813993	−	0.820496i
$934$		0			0
$935$	−76.9687	+	44.4379i	−2.51714	+	1.45327i
$936$		0			0
$937$			25.1409i			0.821319i	0.911789	+	0.410659i	$0.134701\pi$
$937$			25.1409i			0.821319i	−0.911789	+	0.410659i	$0.865299\pi$
$938$		0			0
$939$	−11.9641	−	3.25684i	−0.390433	−	0.106283i
$940$		0			0
$941$	26.0598	+	45.1369i	0.849525	+	1.47142i	0.881633	+	0.471936i	$0.156445\pi$
$941$	26.0598	+	45.1369i	0.849525	+	1.47142i	−0.0321082	+	0.999484i	$0.510222\pi$
$942$		0			0
$943$	−3.82019	−	2.20559i	−0.124403	−	0.0718238i
$944$		0			0
$945$	15.4809	−	35.3628i	0.503592	−	1.15035i
$946$		0			0
$947$	35.8943	+	20.7236i	1.16641	+	0.673427i	0.952832	−	0.303500i	$-0.0981551\pi$
$947$	35.8943	+	20.7236i	1.16641	+	0.673427i	0.213578	+	0.976926i	$0.431488\pi$
$948$		0			0
$949$	−0.231615	−	0.401169i	−0.00751853	−	0.0130225i
$950$		0			0
$951$	−18.9391	−	5.15556i	−0.614141	−	0.167180i
$952$		0			0
$953$			29.7579i			0.963952i	0.876184	+	0.481976i	$0.160081\pi$
$953$			29.7579i			0.963952i	−0.876184	+	0.481976i	$0.839919\pi$
$954$		0			0
$955$	10.0943	−	5.82797i	0.326645	−	0.188589i
$956$		0			0
$957$	−47.1791	−	47.5560i	−1.52508	−	1.53727i
$958$		0			0
$959$	29.0119	+	4.05597i	0.936844	+	0.130974i
$960$		0			0
$961$	−9.19231	+	15.9215i	−0.296526	+	0.513598i
$962$		0			0
$963$	−24.7381	−	0.196861i	−0.797174	−	0.00634376i
$964$		0			0
$965$	−54.7809			−1.76346
$966$		0			0
$967$	−16.6814			−0.536436			−0.268218	−	0.963358i	$-0.586435\pi$
$967$	−16.6814			−0.536436			−0.268218	+	0.963358i	$0.586435\pi$
$968$		0			0
$969$	5.06458	+	19.2066i	0.162698	+	0.617006i
$970$		0			0
$971$	−25.6466	+	44.4211i	−0.823037	+	1.42554i	0.0803734	+	0.996765i	$0.474389\pi$
$971$	−25.6466	+	44.4211i	−0.823037	+	1.42554i	−0.903410	+	0.428777i	$0.858945\pi$
$972$		0			0
$973$	−1.66752	+	2.13751i	−0.0534581	+	0.0685253i
$974$		0			0
$975$	−4.81204	+	4.77390i	−0.154109	+	0.152887i
$976$		0			0
$977$	−16.6912	+	9.63669i	−0.534000	+	0.308305i	−0.742644	−	0.669687i	$-0.766428\pi$
$977$	−16.6912	+	9.63669i	−0.534000	+	0.308305i	0.208644	+	0.977992i	$0.433095\pi$
$978$		0			0
$979$		−	6.32005i		−	0.201990i
$980$		0			0
$981$	−22.8149	−	13.4154i	−0.728422	−	0.428319i
$982$		0			0
$983$	−1.85925	−	3.22031i	−0.0593008	−	0.102712i	0.834851	−	0.550476i	$-0.185554\pi$
$983$	−1.85925	−	3.22031i	−0.0593008	−	0.102712i	−0.894152	+	0.447764i	$0.852220\pi$
$984$		0			0
$985$	−9.26382	−	5.34847i	−0.295170	−	0.170416i
$986$		0			0
$987$	1.47641	−	1.10504i	0.0469946	−	0.0351737i
$988$		0			0
$989$	−23.5724	−	13.6095i	−0.749558	−	0.432758i
$990$		0			0
$991$	25.4914	+	44.1525i	0.809762	+	1.40255i	0.913029	+	0.407896i	$0.133737\pi$
$991$	25.4914	+	44.1525i	0.809762	+	1.40255i	−0.103266	+	0.994654i	$0.532929\pi$
$992$		0			0
$993$	−8.56547	+	31.4654i	−0.271817	+	0.998526i
$994$		0			0
$995$			17.1950i			0.545118i
$996$		0			0
$997$	45.6801	−	26.3734i	1.44670	−	0.835254i	0.448419	−	0.893823i	$-0.351987\pi$
$997$	45.6801	−	26.3734i	1.44670	−	0.835254i	0.998283	+	0.0585692i	$0.0186538\pi$
$998$		0			0
$999$	−5.50889	−	21.5869i	−0.174294	−	0.682980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.u.a.89.1	yes	16
3.2	odd	2	inner	168.2.u.a.89.3	yes	16
4.3	odd	2		336.2.bc.f.257.8		16
7.2	even	3		1176.2.k.a.881.9		16
7.3	odd	6	inner	168.2.u.a.17.3	yes	16
7.4	even	3		1176.2.u.b.521.6		16
7.5	odd	6		1176.2.k.a.881.8		16
7.6	odd	2		1176.2.u.b.1097.8		16
12.11	even	2		336.2.bc.f.257.6		16
21.2	odd	6		1176.2.k.a.881.7		16
21.5	even	6		1176.2.k.a.881.10		16
21.11	odd	6		1176.2.u.b.521.8		16
21.17	even	6	inner	168.2.u.a.17.1	✓	16
21.20	even	2		1176.2.u.b.1097.6		16
28.3	even	6		336.2.bc.f.17.6		16
28.19	even	6		2352.2.k.i.881.9		16
28.23	odd	6		2352.2.k.i.881.8		16
84.23	even	6		2352.2.k.i.881.10		16
84.47	odd	6		2352.2.k.i.881.7		16
84.59	odd	6		336.2.bc.f.17.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.1	✓	16	21.17	even	6	inner
168.2.u.a.17.3	yes	16	7.3	odd	6	inner
168.2.u.a.89.1	yes	16	1.1	even	1	trivial
168.2.u.a.89.3	yes	16	3.2	odd	2	inner
336.2.bc.f.17.6		16	28.3	even	6
336.2.bc.f.17.8		16	84.59	odd	6
336.2.bc.f.257.6		16	12.11	even	2
336.2.bc.f.257.8		16	4.3	odd	2
1176.2.k.a.881.7		16	21.2	odd	6
1176.2.k.a.881.8		16	7.5	odd	6
1176.2.k.a.881.9		16	7.2	even	3
1176.2.k.a.881.10		16	21.5	even	6
1176.2.u.b.521.6		16	7.4	even	3
1176.2.u.b.521.8		16	21.11	odd	6
1176.2.u.b.1097.6		16	21.20	even	2
1176.2.u.b.1097.8		16	7.6	odd	2
2352.2.k.i.881.7		16	84.47	odd	6
2352.2.k.i.881.8		16	28.23	odd	6
2352.2.k.i.881.9		16	28.19	even	6
2352.2.k.i.881.10		16	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67480 + 0.441628i) q^{3} +(1.40397 - 2.43175i) q^{5} +(-2.08606 - 1.62738i) q^{7} +(2.60993 - 1.47928i) q^{9} +(4.74645 - 2.74036i) q^{11} +1.35669i q^{13} +(-1.27745 + 4.69274i) q^{15} +(-2.88753 - 5.00135i) q^{17} +(1.71973 + 0.992889i) q^{19} +(4.21243 + 1.80428i) q^{21} +(-2.09928 - 1.21202i) q^{23} +(-1.44228 - 2.49811i) q^{25} +(-3.71783 + 3.63012i) q^{27} +7.05668i q^{29} +(-3.07596 + 1.77591i) q^{31} +(-6.73914 + 6.68573i) q^{33} +(-6.88616 + 2.78798i) q^{35} +(-2.14377 + 3.71312i) q^{37} +(-0.599153 - 2.27219i) q^{39} +1.81976 q^{41} +11.2288 q^{43} +(0.0670332 - 8.42358i) q^{45} +(0.201213 - 0.348512i) q^{47} +(1.70327 + 6.78961i) q^{49} +(7.04478 + 7.10106i) q^{51} +(5.28097 - 3.04897i) q^{53} -15.3896i q^{55} +(-3.31870 - 0.903412i) q^{57} +(-1.28234 - 2.22108i) q^{59} +(-4.75817 - 2.74713i) q^{61} +(-7.85181 - 1.16149i) q^{63} +(3.29914 + 1.90476i) q^{65} +(3.45238 + 5.97970i) q^{67} +(4.05114 + 1.10279i) q^{69} +2.08251i q^{71} +(-0.295696 + 0.170720i) q^{73} +(3.51878 + 3.54689i) q^{75} +(-14.3610 - 2.00772i) q^{77} +(1.19139 - 2.06355i) q^{79} +(4.62347 - 7.72163i) q^{81} +11.8717 q^{83} -16.2161 q^{85} +(-3.11643 - 11.8186i) q^{87} +(0.576571 - 0.998650i) q^{89} +(2.20785 - 2.83014i) q^{91} +(4.36734 - 4.33272i) q^{93} +(4.82892 - 2.78798i) q^{95} +16.0187i q^{97} +(8.33413 - 14.1735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67}+ \cdots + 20 q^{99}+O(q^{100}) \) 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Introduction

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