LMFDB - Embedded newform 504.2.ch.b.269.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 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("504.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.ch (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.17
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.202765 + 1.39960i) q^{2} +(-1.91777 + 0.567582i) q^{4} +(-3.18706 + 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(-1.18325 - 2.56903i) q^{8} +O(q^{10})$	\(q+(0.202765 + 1.39960i) q^{2} +(-1.91777 + 0.567582i) q^{4} +(-3.18706 + 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(-1.18325 - 2.56903i) q^{8} +(-3.22157 - 4.08752i) q^{10} +(-0.568599 + 0.984843i) q^{11} +3.62005 q^{13} +(3.22680 - 1.89414i) q^{14} +(3.35570 - 2.17699i) q^{16} +(2.84947 - 4.93542i) q^{17} +(-2.63386 - 4.56198i) q^{19} +(5.06768 - 5.33772i) q^{20} +(-1.49368 - 0.596121i) q^{22} +(-3.19122 + 1.84245i) q^{23} +(4.27158 - 7.39859i) q^{25} +(0.734022 + 5.06664i) q^{26} +(3.30533 + 4.13217i) q^{28} -1.82838 q^{29} +(-5.52097 - 3.18753i) q^{31} +(3.72733 + 4.25523i) q^{32} +(7.48540 + 2.98739i) q^{34} +(7.69030 + 5.97171i) q^{35} +(-8.63700 + 4.98657i) q^{37} +(5.85091 - 4.61137i) q^{38} +(8.49823 + 6.01043i) q^{40} -3.46900 q^{41} -7.00429i q^{43} +(0.531465 - 2.21143i) q^{44} +(-3.22577 - 4.09286i) q^{46} +(-3.98886 - 6.90891i) q^{47} +(-5.00648 + 4.89236i) q^{49} +(11.2212 + 4.47833i) q^{50} +(-6.94244 + 2.05468i) q^{52} +(-2.84057 + 4.92001i) q^{53} -4.18501i q^{55} +(-5.11319 + 5.46400i) q^{56} +(-0.370733 - 2.55901i) q^{58} +(0.813177 + 0.469488i) q^{59} +(-1.98482 - 3.43782i) q^{61} +(3.34181 - 8.37348i) q^{62} +(-5.19985 + 6.07960i) q^{64} +(-11.5373 + 6.66109i) q^{65} +(2.18293 + 1.26031i) q^{67} +(-2.66337 + 11.0823i) q^{68} +(-6.79869 + 11.9742i) q^{70} -14.0093i q^{71} +(6.72069 + 3.88019i) q^{73} +(-8.73050 - 11.0773i) q^{74} +(7.64045 + 7.25391i) q^{76} +(2.98069 + 0.409906i) q^{77} +(7.68289 + 13.3072i) q^{79} +(-6.68906 + 13.1129i) q^{80} +(-0.703394 - 4.85523i) q^{82} -2.89078i q^{83} +20.9727i q^{85} +(9.80322 - 1.42023i) q^{86} +(3.20289 + 0.295438i) q^{88} +(1.04281 + 1.80621i) q^{89} +(-3.61419 - 8.86968i) q^{91} +(5.07429 - 5.34469i) q^{92} +(8.86092 - 6.98371i) q^{94} +(16.7886 + 9.69289i) q^{95} -10.3900i q^{97} +(-7.86250 - 6.01507i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) $ 56 * q - 8 * q^4 - 20 * q^7	$ 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) $ 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.202765	+	1.39960i	0.143377	+	0.989668i
$2$	0.202765	+	1.39960i	0.143377	+	0.989668i
$3$		0			0
$3$		0			0
$4$	−1.91777	+	0.567582i	−0.958886	+	0.283791i
$5$	−3.18706	+	1.84005i	−1.42530	+	0.822896i	−0.996745	−	0.0806207i	$-0.974310\pi$
$5$	−3.18706	+	1.84005i	−1.42530	+	0.822896i	−0.428553	+	0.903517i	$0.640976\pi$
$6$		0			0
$7$	−0.998380	−	2.45015i	−0.377352	−	0.926070i
$7$	−0.998380	−	2.45015i	−0.377352	−	0.926070i
$8$	−1.18325	−	2.56903i	−0.418341	−	0.908290i
$9$		0			0
$10$	−3.22157	−	4.08752i	−1.01875	−	1.29259i
$11$	−0.568599	+	0.984843i	−0.171439	+	0.296941i	−0.938923	−	0.344127i	$-0.888175\pi$
$11$	−0.568599	+	0.984843i	−0.171439	+	0.296941i	0.767484	+	0.641068i	$0.221508\pi$
$12$		0			0
$13$	3.62005			1.00402			0.502011	−	0.864861i	$-0.332594\pi$
$13$	3.62005			1.00402			0.502011	+	0.864861i	$0.332594\pi$
$14$	3.22680	−	1.89414i	0.862398	−	0.506230i
$15$		0			0
$16$	3.35570	−	2.17699i	0.838925	−	0.544246i
$17$	2.84947	−	4.93542i	0.691097	−	1.19702i	−0.280381	−	0.959889i	$-0.590461\pi$
$17$	2.84947	−	4.93542i	0.691097	−	1.19702i	0.971479	−	0.237127i	$-0.0762057\pi$
$18$		0			0
$19$	−2.63386	−	4.56198i	−0.604250	−	1.04659i	−0.992170	−	0.124898i	$-0.960140\pi$
$19$	−2.63386	−	4.56198i	−0.604250	−	1.04659i	0.387920	−	0.921693i	$-0.373194\pi$
$20$	5.06768	−	5.33772i	1.13317	−	1.19355i
$21$		0			0
$22$	−1.49368	−	0.596121i	−0.318454	−	0.127093i
$23$	−3.19122	+	1.84245i	−0.665416	+	0.384178i	−0.794337	−	0.607477i	$-0.792182\pi$
$23$	−3.19122	+	1.84245i	−0.665416	+	0.384178i	0.128922	+	0.991655i	$0.458848\pi$
$24$		0			0
$25$	4.27158	−	7.39859i	0.854316	−	1.47972i
$26$	0.734022	+	5.06664i	0.143954	+	0.993649i
$27$		0			0
$28$	3.30533	+	4.13217i	0.624648	+	0.780906i
$29$	−1.82838			−0.339522			−0.169761	−	0.985485i	$-0.554300\pi$
$29$	−1.82838			−0.339522			−0.169761	+	0.985485i	$0.554300\pi$
$30$		0			0
$31$	−5.52097	−	3.18753i	−0.991595	−	0.572498i	−0.0858442	−	0.996309i	$-0.527359\pi$
$31$	−5.52097	−	3.18753i	−0.991595	−	0.572498i	−0.905751	+	0.423811i	$0.860692\pi$
$32$	3.72733	+	4.25523i	0.658906	+	0.752225i
$33$		0			0
$34$	7.48540	+	2.98739i	1.28374	+	0.512333i
$35$	7.69030	+	5.97171i	1.29990	+	1.00940i
$36$		0			0
$37$	−8.63700	+	4.98657i	−1.41991	+	0.819788i	−0.996291	−	0.0860510i	$-0.972575\pi$
$37$	−8.63700	+	4.98657i	−1.41991	+	0.819788i	−0.423623	+	0.905839i	$0.639242\pi$
$38$	5.85091	−	4.61137i	0.949142	−	0.748063i
$39$		0			0
$40$	8.49823	+	6.01043i	1.34369	+	0.950333i
$41$	−3.46900			−0.541767			−0.270884	−	0.962612i	$-0.587316\pi$
$41$	−3.46900			−0.541767			−0.270884	+	0.962612i	$0.587316\pi$
$42$		0			0
$43$		−	7.00429i		−	1.06814i	−0.845439	−	0.534072i	$-0.820661\pi$
$43$		−	7.00429i		−	1.06814i	0.845439	−	0.534072i	$-0.179339\pi$
$44$	0.531465	−	2.21143i	0.0801214	−	0.333386i
$45$		0			0
$46$	−3.22577	−	4.09286i	−0.475614	−	0.603459i
$47$	−3.98886	−	6.90891i	−0.581835	−	1.00777i	−0.995262	−	0.0972305i	$-0.969002\pi$
$47$	−3.98886	−	6.90891i	−0.581835	−	1.00777i	0.413427	−	0.910537i	$-0.364332\pi$
$48$		0			0
$49$	−5.00648	+	4.89236i	−0.715211	+	0.698909i
$50$	11.2212	+	4.47833i	1.58692	+	0.633332i
$51$		0			0
$52$	−6.94244	+	2.05468i	−0.962743	+	0.284933i
$53$	−2.84057	+	4.92001i	−0.390182	+	0.675815i	−0.992473	−	0.122461i	$-0.960921\pi$
$53$	−2.84057	+	4.92001i	−0.390182	+	0.675815i	0.602291	+	0.798276i	$0.294255\pi$
$54$		0			0
$55$		−	4.18501i		−	0.564306i
$56$	−5.11319	+	5.46400i	−0.683278	+	0.730158i
$57$		0			0
$58$	−0.370733	−	2.55901i	−0.0486796	−	0.336014i
$59$	0.813177	+	0.469488i	0.105867	+	0.0611221i	0.551998	−	0.833845i	$-0.313865\pi$
$59$	0.813177	+	0.469488i	0.105867	+	0.0611221i	−0.446132	+	0.894967i	$0.647199\pi$
$60$		0			0
$61$	−1.98482	−	3.43782i	−0.254131	−	0.440167i	0.710528	−	0.703669i	$-0.248456\pi$
$61$	−1.98482	−	3.43782i	−0.254131	−	0.440167i	−0.964659	+	0.263501i	$0.915123\pi$
$62$	3.34181	−	8.37348i	0.424411	−	1.06343i
$63$		0			0
$64$	−5.19985	+	6.07960i	−0.649982	+	0.759950i
$65$	−11.5373	+	6.66109i	−1.43103	+	0.826206i
$66$		0			0
$67$	2.18293	+	1.26031i	0.266687	+	0.153972i	0.627381	−	0.778712i	$-0.284127\pi$
$67$	2.18293	+	1.26031i	0.266687	+	0.153972i	−0.360694	+	0.932684i	$0.617460\pi$
$68$	−2.66337	+	11.0823i	−0.322981	+	1.34393i
$69$		0			0
$70$	−6.79869	+	11.9742i	−0.812599	+	1.43119i
$71$		−	14.0093i		−	1.66260i	−0.555821	−	0.831302i	$-0.687596\pi$
$71$		−	14.0093i		−	1.66260i	0.555821	−	0.831302i	$-0.312404\pi$
$72$		0			0
$73$	6.72069	+	3.88019i	0.786597	+	0.454142i	0.838763	−	0.544496i	$-0.183279\pi$
$73$	6.72069	+	3.88019i	0.786597	+	0.454142i	−0.0521661	+	0.998638i	$0.516613\pi$
$74$	−8.73050	−	11.0773i	−1.01490	−	1.28770i
$75$		0			0
$76$	7.64045	+	7.25391i	0.876420	+	0.832081i
$77$	2.98069	+	0.409906i	0.339681	+	0.0467132i
$78$		0			0
$79$	7.68289	+	13.3072i	0.864393	+	1.49717i	0.867649	+	0.497177i	$0.165630\pi$
$79$	7.68289	+	13.3072i	0.864393	+	1.49717i	−0.00325650	+	0.999995i	$0.501037\pi$
$80$	−6.68906	+	13.1129i	−0.747860	+	1.46606i
$81$		0			0
$82$	−0.703394	−	4.85523i	−0.0776769	−	0.536170i
$83$		−	2.89078i		−	0.317304i	−0.987335	−	0.158652i	$-0.949285\pi$
$83$		−	2.89078i		−	0.317304i	0.987335	−	0.158652i	$-0.0507148\pi$
$84$		0			0
$85$			20.9727i			2.27480i
$86$	9.80322	−	1.42023i	1.05711	−	0.153147i
$87$		0			0
$88$	3.20289	+	0.295438i	0.341429	+	0.0314938i
$89$	1.04281	+	1.80621i	0.110538	+	0.191458i	0.915987	−	0.401207i	$-0.131409\pi$
$89$	1.04281	+	1.80621i	0.110538	+	0.191458i	−0.805449	+	0.592665i	$0.798076\pi$
$90$		0			0
$91$	−3.61419	−	8.86968i	−0.378870	−	0.929795i
$92$	5.07429	−	5.34469i	0.529032	−	0.557222i
$93$		0			0
$94$	8.86092	−	6.98371i	0.913934	−	0.720314i
$95$	16.7886	+	9.69289i	1.72247	+	0.994469i
$96$		0			0
$97$		−	10.3900i		−	1.05494i	−0.849573	−	0.527471i	$-0.823140\pi$
$97$		−	10.3900i		−	1.05494i	0.849573	−	0.527471i	$-0.176860\pi$
$98$	−7.86250	−	6.01507i	−0.794233	−	0.607614i
$99$		0			0
$100$	−3.99261	+	16.6133i	−0.399261	+	1.66133i
$101$	−17.0193	−	9.82609i	−1.69348	−	0.977732i	−0.951669	−	0.307126i	$-0.900633\pi$
$101$	−17.0193	−	9.82609i	−1.69348	−	0.977732i	−0.741813	−	0.670606i	$-0.766034\pi$
$102$		0			0
$103$	7.80827	−	4.50811i	0.769372	−	0.444197i	−0.0632787	−	0.997996i	$-0.520156\pi$
$103$	7.80827	−	4.50811i	0.769372	−	0.444197i	0.832650	+	0.553799i	$0.186822\pi$
$104$	−4.28342	−	9.30004i	−0.420024	−	0.911944i
$105$		0			0
$106$	−7.46202	−	2.97806i	−0.724776	−	0.289255i
$107$	−3.22682	−	5.58902i	−0.311949	−	0.540311i	0.666836	−	0.745205i	$-0.267648\pi$
$107$	−3.22682	−	5.58902i	−0.311949	−	0.540311i	−0.978784	+	0.204894i	$0.934315\pi$
$108$		0			0
$109$	6.00494	+	3.46695i	0.575169	+	0.332074i	0.759211	−	0.650844i	$-0.225585\pi$
$109$	6.00494	+	3.46695i	0.575169	+	0.332074i	−0.184042	+	0.982918i	$0.558918\pi$
$110$	5.85735	−	0.848575i	0.558476	−	0.0809084i
$111$		0			0
$112$	−8.68421	−	6.04851i	−0.820581	−	0.571531i
$113$			17.9073i			1.68458i	0.539028	+	0.842288i	$0.318792\pi$
$113$			17.9073i			1.68458i	−0.539028	+	0.842288i	$0.681208\pi$
$114$		0			0
$115$	6.78042	−	11.7440i	0.632277	−	1.09514i
$116$	3.50642	−	1.03776i	0.325563	−	0.0963532i
$117$		0			0
$118$	−0.492212	+	1.23332i	−0.0453118	+	0.113536i
$119$	−14.9374	−	2.05420i	−1.36931	−	0.188308i
$120$		0			0
$121$	4.85339	+	8.40632i	0.441217	+	0.764211i
$122$	4.40912	−	3.47503i	0.399183	−	0.314615i
$123$		0			0
$124$	12.3971	+	2.97936i	1.11330	+	0.267554i
$125$			13.0392i			1.16626i
$126$		0			0
$127$	−1.16038			−0.102967			−0.0514837	−	0.998674i	$-0.516395\pi$
$127$	−1.16038			−0.102967			−0.0514837	+	0.998674i	$0.516395\pi$
$128$	−9.56337	−	6.04499i	−0.845290	−	0.534307i
$129$		0			0
$130$	−11.6622	−	14.7970i	−1.02285	−	1.29779i
$131$	−10.2555	+	5.92101i	−0.896026	+	0.517321i	−0.875909	−	0.482477i	$-0.839737\pi$
$131$	−10.2555	+	5.92101i	−0.896026	+	0.517321i	−0.0201174	+	0.999798i	$0.506404\pi$
$132$		0			0
$133$	−8.54795	+	11.0080i	−0.741201	+	0.954511i
$134$	−1.32132	+	3.31078i	−0.114144	+	0.286008i
$135$		0			0
$136$	−16.0509	−	1.48055i	−1.37635	−	0.126956i
$137$	−3.36092	−	1.94043i	−0.287143	−	0.165782i	0.349510	−	0.936933i	$-0.386348\pi$
$137$	−3.36092	−	1.94043i	−0.287143	−	0.165782i	−0.636653	+	0.771151i	$0.719681\pi$
$138$		0			0
$139$	−7.63508			−0.647599			−0.323799	−	0.946126i	$-0.604960\pi$
$139$	−7.63508			−0.647599			−0.323799	+	0.946126i	$0.604960\pi$
$140$	−18.1377	−	7.08751i	−1.53291	−	0.599004i
$141$		0			0
$142$	19.6075	−	2.84061i	1.64543	−	0.238379i
$143$	−2.05836	+	3.56518i	−0.172129	+	0.298136i
$144$		0			0
$145$	5.82716	−	3.36432i	0.483920	−	0.279391i
$146$	−4.06800	+	10.1931i	−0.336670	+	0.843584i
$147$		0			0
$148$	13.7335	−	14.4653i	1.12889	−	1.18904i
$149$	−3.50369	−	6.06857i	−0.287034	−	0.497157i	0.686067	−	0.727539i	$-0.259336\pi$
$149$	−3.50369	−	6.06857i	−0.287034	−	0.497157i	−0.973100	+	0.230382i	$0.926002\pi$
$150$		0			0
$151$	−9.11816	+	15.7931i	−0.742025	+	1.28523i	0.209547	+	0.977799i	$0.432801\pi$
$151$	−9.11816	+	15.7931i	−0.742025	+	1.28523i	−0.951572	+	0.307427i	$0.900532\pi$
$152$	−8.60337	+	12.1644i	−0.697826	+	0.986666i
$153$		0			0
$154$	0.0306752	+	4.25490i	0.00247188	+	0.342869i
$155$	23.4609			1.88442
$156$		0			0
$157$	6.98079	−	12.0911i	0.557128	−	0.964974i	−0.440607	−	0.897700i	$-0.645237\pi$
$157$	6.98079	−	12.0911i	0.557128	−	0.964974i	0.997735	−	0.0672736i	$-0.0214300\pi$
$158$	−17.0669	+	13.4512i	−1.35777	+	1.07012i
$159$		0			0
$160$	−19.7091	−	6.70320i	−1.55814	−	0.529934i
$161$	7.70034	+	5.97951i	0.606872	+	0.471251i
$162$		0			0
$163$	−8.75280	+	5.05343i	−0.685572	+	0.395815i	−0.801951	−	0.597390i	$-0.796205\pi$
$163$	−8.75280	+	5.05343i	−0.685572	+	0.395815i	0.116379	+	0.993205i	$0.462871\pi$
$164$	6.65276	−	1.96894i	0.519493	−	0.153749i
$165$		0			0
$166$	4.04594	−	0.586150i	0.314026	−	0.0454941i
$167$	−5.21398			−0.403470			−0.201735	−	0.979440i	$-0.564658\pi$
$167$	−5.21398			−0.403470			−0.201735	+	0.979440i	$0.564658\pi$
$168$		0			0
$169$	0.104796			0.00806124
$170$	−29.3534	+	4.25253i	−2.25130	+	0.326154i
$171$		0			0
$172$	3.97551	+	13.4326i	0.303130	+	1.02423i
$173$	3.22284	−	1.86071i	0.245028	−	0.141467i	−0.372457	−	0.928049i	$-0.621485\pi$
$173$	3.22284	−	1.86071i	0.245028	−	0.141467i	0.617486	+	0.786582i	$0.288151\pi$
$174$		0			0
$175$	−22.3923	−	3.07941i	−1.69270	−	0.232781i
$176$	0.235939	+	4.54267i	0.0177846	+	0.342417i
$177$		0			0
$178$	−2.31652	+	1.82576i	−0.173631	+	0.136847i
$179$	13.1792	−	22.8270i	0.985057	−	1.70617i	0.343377	−	0.939198i	$-0.388429\pi$
$179$	13.1792	−	22.8270i	0.985057	−	1.70617i	0.641681	−	0.766972i	$-0.278237\pi$
$180$		0			0
$181$	4.91329			0.365202			0.182601	−	0.983187i	$-0.441548\pi$
$181$	4.91329			0.365202			0.182601	+	0.983187i	$0.441548\pi$
$182$	11.6812	−	6.85689i	0.865867	−	0.508267i
$183$		0			0
$184$	8.50932	+	6.01828i	0.627316	+	0.443673i
$185$	18.3511	−	31.7850i	1.34920	−	2.33688i
$186$		0			0
$187$	3.24041	+	5.61255i	0.236962	+	0.410431i
$188$	11.5711	+	10.9857i	0.843909	+	0.801215i
$189$		0			0
$190$	−10.1620	+	25.4627i	−0.737232	+	1.84726i
$191$	5.29844	−	3.05906i	0.383382	−	0.221345i	−0.295907	−	0.955217i	$-0.595622\pi$
$191$	5.29844	−	3.05906i	0.383382	−	0.221345i	0.679289	+	0.733871i	$0.262288\pi$
$192$		0			0
$193$	−9.25188	+	16.0247i	−0.665965	+	1.15349i	0.313058	+	0.949734i	$0.398647\pi$
$193$	−9.25188	+	16.0247i	−0.665965	+	1.15349i	−0.979023	+	0.203751i	$0.934687\pi$
$194$	14.5418	−	2.10673i	1.04404	−	0.151254i
$195$		0			0
$196$	6.82446	−	12.2240i	0.487462	−	0.873144i
$197$	−2.99827			−0.213618			−0.106809	−	0.994280i	$-0.534063\pi$
$197$	−2.99827			−0.213618			−0.106809	+	0.994280i	$0.534063\pi$
$198$		0			0
$199$	−1.27718	−	0.737381i	−0.0905370	−	0.0522715i	0.454048	−	0.890977i	$-0.349979\pi$
$199$	−1.27718	−	0.737381i	−0.0905370	−	0.0522715i	−0.544585	+	0.838706i	$0.683313\pi$
$200$	−24.0616	−	2.21946i	−1.70141	−	0.156940i
$201$		0			0
$202$	10.3017	−	25.8126i	0.724825	−	1.81617i
$203$	1.82542	+	4.47981i	0.128119	+	0.314421i
$204$		0			0
$205$	11.0559	−	6.38315i	0.772180	−	0.445818i
$206$	7.89280	+	10.0144i	0.549918	+	0.697735i
$207$		0			0
$208$	12.1478	−	7.88081i	0.842300	−	0.546436i
$209$	5.99045			0.414368
$210$		0			0
$211$		−	17.8952i		−	1.23196i	−0.787764	−	0.615978i	$-0.788761\pi$
$211$		−	17.8952i		−	1.23196i	0.787764	−	0.615978i	$-0.211239\pi$
$212$	2.65506	−	11.0477i	0.182350	−	0.758760i
$213$		0			0
$214$	7.16811	−	5.64953i	0.490002	−	0.386194i
$215$	12.8882	+	22.3231i	0.878971	+	1.52242i
$216$		0			0
$217$	−2.29791	+	16.7096i	−0.155992	+	1.13432i
$218$	−3.63476	+	9.10750i	−0.246177	+	0.616838i
$219$		0			0
$220$	2.37533	+	8.02589i	0.160145	+	0.541105i
$221$	10.3152	−	17.8665i	0.693877	−	1.20183i
$222$		0			0
$223$			1.26160i			0.0844828i	0.999107	+	0.0422414i	$0.0134499\pi$
$223$			1.26160i			0.0844828i	−0.999107	+	0.0422414i	$0.986550\pi$
$224$	6.70466	−	13.3809i	0.447974	−	0.894047i
$225$		0			0
$226$	−25.0631	+	3.63098i	−1.66717	+	0.241529i
$227$	−0.642193	−	0.370770i	−0.0426238	−	0.0246089i	0.478537	−	0.878068i	$-0.341167\pi$
$227$	−0.642193	−	0.370770i	−0.0426238	−	0.0246089i	−0.521160	+	0.853459i	$0.674501\pi$
$228$		0			0
$229$	4.62136	+	8.00442i	0.305388	+	0.528947i	0.977348	−	0.211640i	$-0.0678806\pi$
$229$	4.62136	+	8.00442i	0.305388	+	0.528947i	−0.671960	+	0.740588i	$0.734547\pi$
$230$	17.8118	+	7.10860i	1.17448	+	0.468727i
$231$		0			0
$232$	2.16343	+	4.69717i	0.142036	+	0.308384i
$233$	0.423385	−	0.244441i	0.0277369	−	0.0160139i	−0.486067	−	0.873921i	$-0.661569\pi$
$233$	0.423385	−	0.244441i	0.0277369	−	0.0160139i	0.513804	+	0.857907i	$0.328236\pi$
$234$		0			0
$235$	25.4255	+	14.6794i	1.65858	+	0.957579i
$236$	−1.82596	−	0.438826i	−0.118860	−	0.0285652i
$237$		0			0
$238$	−0.153725	−	21.3229i	−0.00996452	−	1.38216i
$239$		−	1.36060i		−	0.0880098i	−0.999031	−	0.0440049i	$-0.985988\pi$
$239$		−	1.36060i		−	0.0880098i	0.999031	−	0.0440049i	$-0.0140117\pi$
$240$		0			0
$241$	0.282523	+	0.163115i	0.0181989	+	0.0105071i	0.509072	−	0.860724i	$-0.329989\pi$
$241$	0.282523	+	0.163115i	0.0181989	+	0.0105071i	−0.490873	+	0.871231i	$0.663322\pi$
$242$	−10.7814	+	8.49733i	−0.693055	+	0.546229i
$243$		0			0
$244$	5.75768	+	5.46640i	0.368598	+	0.349950i
$245$	6.95375	−	24.8044i	0.444259	−	1.58470i
$246$		0			0
$247$	−9.53473	−	16.5146i	−0.606680	−	1.05080i
$248$	−1.65621	+	17.9552i	−0.105169	+	1.14015i
$249$		0			0
$250$	−18.2497	+	2.64390i	−1.15421	+	0.167215i
$251$			0.972392i			0.0613768i	0.999529	+	0.0306884i	$0.00976996\pi$
$251$			0.972392i			0.0613768i	−0.999529	+	0.0306884i	$0.990230\pi$
$252$		0			0
$253$		−	4.19047i		−	0.263453i
$254$	−0.235286	−	1.62407i	−0.0147631	−	0.101903i
$255$		0			0
$256$	6.52147	−	14.6106i	0.407592	−	0.913164i
$257$	7.08066	+	12.2641i	0.441680	+	0.765012i	0.997814	−	0.0660806i	$-0.0210494\pi$
$257$	7.08066	+	12.2641i	0.441680	+	0.765012i	−0.556135	+	0.831092i	$0.687716\pi$
$258$		0			0
$259$	20.8409	+	16.1835i	1.29499	+	1.00559i
$260$	18.3453	−	19.3228i	1.13773	−	1.19835i
$261$		0			0
$262$	−10.3665	−	13.1530i	−0.640445	−	0.812597i
$263$	15.9754	+	9.22341i	0.985086	+	0.568740i	0.903802	−	0.427951i	$-0.140764\pi$
$263$	15.9754	+	9.22341i	0.985086	+	0.568740i	0.0812844	+	0.996691i	$0.474098\pi$
$264$		0			0
$265$		−	20.9072i		−	1.28432i
$266$	−17.1400	−	9.73170i	−1.05092	−	0.596689i
$267$		0			0
$268$	−4.90169	−	1.17800i	−0.299418	−	0.0719581i
$269$	16.9445	+	9.78291i	1.03312	+	0.596475i	0.917878	−	0.396862i	$-0.129901\pi$
$269$	16.9445	+	9.78291i	1.03312	+	0.596475i	0.115246	+	0.993337i	$0.463234\pi$
$270$		0			0
$271$	17.4255	−	10.0606i	1.05853	−	0.611141i	0.133502	−	0.991049i	$-0.457378\pi$
$271$	17.4255	−	10.0606i	1.05853	−	0.611141i	0.925024	+	0.379908i	$0.124044\pi$
$272$	−1.18238	−	22.7651i	−0.0716924	−	1.38033i
$273$		0			0
$274$	2.03435	−	5.09741i	0.122900	−	0.307946i
$275$	4.85763	+	8.41367i	0.292926	+	0.507363i
$276$		0			0
$277$	−6.82065	−	3.93790i	−0.409813	−	0.236606i	0.280896	−	0.959738i	$-0.409368\pi$
$277$	−6.82065	−	3.93790i	−0.409813	−	0.236606i	−0.690709	+	0.723132i	$0.742702\pi$
$278$	−1.54813	−	10.6861i	−0.0928506	−	0.640908i
$279$		0			0
$280$	6.24200	−	26.8226i	0.373031	−	1.60296i
$281$		−	19.6351i		−	1.17133i	−0.810552	−	0.585666i	$-0.800833\pi$
$281$		−	19.6351i		−	1.17133i	0.810552	−	0.585666i	$-0.199167\pi$
$282$		0			0
$283$	−11.0872	+	19.2035i	−0.659063	+	1.14153i	0.321796	+	0.946809i	$0.395714\pi$
$283$	−11.0872	+	19.2035i	−0.659063	+	1.14153i	−0.980859	+	0.194721i	$0.937620\pi$
$284$	7.95145	+	26.8667i	0.471832	+	1.59425i
$285$		0			0
$286$	−5.40720	−	2.15799i	−0.319735	−	0.127605i
$287$	3.46338	+	8.49958i	0.204437	+	0.501715i
$288$		0			0
$289$	−7.73892	−	13.4042i	−0.455231	−	0.788483i
$290$	5.89025	+	7.47355i	0.345887	+	0.438862i
$291$		0			0
$292$	−15.0911	−	3.62678i	−0.883138	−	0.212241i
$293$			18.6531i			1.08973i	0.838525	+	0.544863i	$0.183418\pi$
$293$			18.6531i			1.08973i	−0.838525	+	0.544863i	$0.816582\pi$
$294$		0			0
$295$	−3.45553			−0.201189
$296$	23.0304	+	16.2884i	1.33861	+	0.946743i
$297$		0			0
$298$	7.78316	−	6.13427i	0.450866	−	0.355349i
$299$	−11.5524	+	6.66978i	−0.668092	+	0.385723i
$300$		0			0
$301$	−17.1616	+	6.99294i	−0.989176	+	0.403066i
$302$	−23.9529	−	9.55950i	−1.37834	−	0.550087i
$303$		0			0
$304$	−18.7698	−	9.57477i	−1.07652	−	0.549151i
$305$	12.6515	+	7.30436i	0.724424	+	0.418246i
$306$		0			0
$307$	−26.7926			−1.52913			−0.764566	−	0.644546i	$-0.777047\pi$
$307$	−26.7926			−1.52913			−0.764566	+	0.644546i	$0.777047\pi$
$308$	−5.94894	+	0.905679i	−0.338972	+	0.0516059i
$309$		0			0
$310$	4.75706	+	32.8359i	0.270183	+	1.86495i
$311$	12.8790	−	22.3071i	0.730302	−	1.26492i	−0.226452	−	0.974022i	$-0.572713\pi$
$311$	12.8790	−	22.3071i	0.730302	−	1.26492i	0.956754	−	0.290898i	$-0.0939540\pi$
$312$		0			0
$313$	11.2421	−	6.49065i	0.635443	−	0.366873i	−0.147414	−	0.989075i	$-0.547095\pi$
$313$	11.2421	−	6.49065i	0.635443	−	0.366873i	0.782857	+	0.622202i	$0.213762\pi$
$314$	18.3382	+	7.31868i	1.03488	+	0.413017i
$315$		0			0
$316$	−22.2869	−	21.1594i	−1.25374	−	1.19031i
$317$	10.5090	+	18.2021i	0.590243	+	1.02233i	0.994199	+	0.107553i	$0.0343015\pi$
$317$	10.5090	+	18.2021i	0.590243	+	1.02233i	−0.403956	+	0.914778i	$0.632365\pi$
$318$		0			0
$319$	1.03962	−	1.80067i	0.0582073	−	0.100818i
$320$	5.38549	−	28.9441i	0.301058	−	1.61802i
$321$		0			0
$322$	−6.80757	+	11.9898i	−0.379371	+	0.668168i
$323$	−30.0204			−1.67038
$324$		0			0
$325$	15.4633	−	26.7833i	0.857752	−	1.48567i
$326$	−8.84756	−	11.2258i	−0.490021	−	0.621738i
$327$		0			0
$328$	4.10469	+	8.91198i	0.226644	+	0.492082i
$329$	−12.9455	+	16.6710i	−0.713707	+	0.919103i
$330$		0			0
$331$	11.6548	−	6.72892i	0.640607	−	0.369855i	−0.144241	−	0.989543i	$-0.546074\pi$
$331$	11.6548	−	6.72892i	0.640607	−	0.369855i	0.784848	+	0.619688i	$0.212741\pi$
$332$	1.64075	+	5.54386i	0.0900481	+	0.304259i
$333$		0			0
$334$	−1.05722	−	7.29750i	−0.0578483	−	0.399302i
$335$	−9.27617			−0.506811
$336$		0			0
$337$	−24.1178			−1.31378			−0.656891	−	0.753985i	$-0.728129\pi$
$337$	−24.1178			−1.31378			−0.656891	+	0.753985i	$0.728129\pi$
$338$	0.0212490	+	0.146673i	0.00115580	+	0.00797796i
$339$		0			0
$340$	−11.9037	−	40.2208i	−0.645569	−	2.18128i
$341$	6.27843	−	3.62486i	0.339996	−	0.196297i
$342$		0			0
$343$	16.9854	+	7.38218i	0.917125	+	0.398600i
$344$	−17.9942	+	8.28780i	−0.970184	+	0.446848i
$345$		0			0
$346$	3.25773	+	4.13341i	0.175137	+	0.222213i
$347$	−2.10821	+	3.65153i	−0.113175	+	0.196025i	−0.917049	−	0.398775i	$-0.869435\pi$
$347$	−2.10821	+	3.65153i	−0.113175	+	0.196025i	0.803874	+	0.594800i	$0.202769\pi$
$348$		0			0
$349$	9.32452			0.499130			0.249565	−	0.968358i	$-0.419712\pi$
$349$	9.32452			0.499130			0.249565	+	0.968358i	$0.419712\pi$
$350$	−0.230446	−	31.9647i	−0.0123179	−	1.70859i
$351$		0			0
$352$	−6.31009	+	1.25132i	−0.336329	+	0.0666955i
$353$	−10.5650	+	18.2992i	−0.562320	+	0.973967i	0.434974	+	0.900443i	$0.356758\pi$
$353$	−10.5650	+	18.2992i	−0.562320	+	0.973967i	−0.997293	+	0.0735234i	$0.976576\pi$
$354$		0			0
$355$	25.7779	+	44.6487i	1.36815	+	2.36970i
$356$	−3.02505	−	2.87201i	−0.160327	−	0.152216i
$357$		0			0
$358$	34.6210	+	13.8171i	1.82978	+	0.730255i
$359$	−9.51917	+	5.49590i	−0.502403	+	0.290062i	−0.729705	−	0.683762i	$-0.760343\pi$
$359$	−9.51917	+	5.49590i	−0.502403	+	0.290062i	0.227303	+	0.973824i	$0.427009\pi$
$360$		0			0
$361$	−4.37446	+	7.57680i	−0.230235	+	0.398779i
$362$	0.996245	+	6.87665i	0.0523615	+	0.361428i
$363$		0			0
$364$	11.9655	+	14.9587i	0.627161	+	0.784048i
$365$	−28.5590			−1.49485
$366$		0			0
$367$	16.8547	+	9.73104i	0.879806	+	0.507956i	0.870594	−	0.492002i	$-0.163735\pi$
$367$	16.8547	+	9.73104i	0.879806	+	0.507956i	0.00921137	+	0.999958i	$0.497068\pi$
$368$	−6.69780	+	13.1300i	−0.349147	+	0.684447i
$369$		0			0
$370$	48.2074	+	19.2393i	2.50618	+	1.00021i
$371$	14.8907	+	2.04778i	0.773088	+	0.106316i
$372$		0			0
$373$	0.130569	−	0.0753842i	0.00676062	−	0.00390325i	−0.496616	−	0.867970i	$-0.665424\pi$
$373$	0.130569	−	0.0753842i	0.00676062	−	0.00390325i	0.503377	+	0.864067i	$0.332091\pi$
$374$	−7.19830	+	5.67332i	−0.372215	+	0.293360i
$375$		0			0
$376$	−13.0294	+	18.4225i	−0.671940	+	0.950066i
$377$	−6.61884			−0.340888
$378$		0			0
$379$		−	32.9127i		−	1.69061i	−0.534283	−	0.845306i	$-0.679418\pi$
$379$		−	32.9127i		−	1.69061i	0.534283	−	0.845306i	$-0.320582\pi$
$380$	−37.6982	−	9.05986i	−1.93387	−	0.464761i
$381$		0			0
$382$	5.35580	+	6.79544i	0.274027	+	0.347685i
$383$	−8.38834	−	14.5290i	−0.428624	−	0.742398i	0.568127	−	0.822941i	$-0.307668\pi$
$383$	−8.38834	−	14.5290i	−0.428624	−	0.742398i	−0.996751	+	0.0805423i	$0.974335\pi$
$384$		0			0
$385$	−10.2539	+	4.17823i	−0.522587	+	0.212942i
$386$	−24.3042	−	9.69969i	−1.23705	−	0.493701i
$387$		0			0
$388$	5.89716	+	19.9256i	0.299383	+	1.01157i
$389$	12.6509	−	21.9121i	0.641428	−	1.11099i	−0.343686	−	0.939085i	$-0.611676\pi$
$389$	12.6509	−	21.9121i	0.641428	−	1.11099i	0.985114	−	0.171902i	$-0.0549912\pi$
$390$		0			0
$391$			21.0000i			1.06202i
$392$	18.4925	+	7.07292i	0.934014	+	0.357237i
$393$		0			0
$394$	−0.607946	−	4.19639i	−0.0306279	−	0.211411i
$395$	−48.9717	−	28.2738i	−2.46403	−	1.42261i
$396$		0			0
$397$	−17.7452	−	30.7356i	−0.890606	−	1.54257i	−0.839151	−	0.543899i	$-0.816947\pi$
$397$	−17.7452	−	30.7356i	−0.890606	−	1.54257i	−0.0514552	−	0.998675i	$-0.516386\pi$
$398$	0.773072	−	1.93706i	0.0387506	−	0.0970961i
$399$		0			0
$400$	−1.77248	−	34.1266i	−0.0886242	−	1.70633i
$401$	2.98000	−	1.72050i	0.148814	−	0.0859179i	−0.423744	−	0.905782i	$-0.639284\pi$
$401$	2.98000	−	1.72050i	0.148814	−	0.0859179i	0.572558	+	0.819864i	$0.305951\pi$
$402$		0			0
$403$	−19.9862	−	11.5390i	−0.995584	−	0.574800i
$404$	38.2162	+	9.18436i	1.90133	+	0.456939i
$405$		0			0
$406$	−5.89982	+	3.46321i	−0.292803	+	0.171876i
$407$		−	11.3414i		−	0.562175i
$408$		0			0
$409$	−5.30301	−	3.06169i	−0.262217	−	0.151391i	0.363129	−	0.931739i	$-0.381709\pi$
$409$	−5.30301	−	3.06169i	−0.262217	−	0.151391i	−0.625345	+	0.780348i	$0.715042\pi$
$410$	11.1756	+	14.1796i	0.551925	+	0.700282i
$411$		0			0
$412$	−12.4158	+	13.0774i	−0.611681	+	0.644275i
$413$	0.338457	−	2.46113i	0.0166544	−	0.121104i
$414$		0			0
$415$	5.31918	+	9.21309i	0.261108	+	0.452253i
$416$	13.4932	+	15.4042i	0.661556	+	0.755251i
$417$		0			0
$418$	1.21466	+	8.38425i	0.0594108	+	0.410087i
$419$		−	11.9546i		−	0.584022i	−0.956415	−	0.292011i	$-0.905676\pi$
$419$		−	11.9546i		−	0.584022i	0.956415	−	0.292011i	$-0.0943244\pi$
$420$		0			0
$421$		−	12.1616i		−	0.592720i	−0.955076	−	0.296360i	$-0.904227\pi$
$421$		−	12.1616i		−	0.592720i	0.955076	−	0.296360i	$-0.0957728\pi$
$422$	25.0461	−	3.62853i	1.21923	−	0.176634i
$423$		0			0
$424$	16.0008	+	1.47593i	0.777065	+	0.0716773i
$425$	−24.3434	−	42.1641i	−1.18083	−	2.04526i
$426$		0			0
$427$	−6.44156	+	8.29536i	−0.311729	+	0.401441i
$428$	9.36053	+	8.88698i	0.452459	+	0.429568i
$429$		0			0
$430$	−28.6302	+	22.5648i	−1.38067	+	1.08817i
$431$	−19.6396	−	11.3389i	−0.946006	−	0.546177i	−0.0541683	−	0.998532i	$-0.517251\pi$
$431$	−19.6396	−	11.3389i	−0.946006	−	0.546177i	−0.891838	+	0.452355i	$0.850584\pi$
$432$		0			0
$433$			0.754762i			0.0362716i	0.999836	+	0.0181358i	$0.00577312\pi$
$433$			0.754762i			0.0362716i	−0.999836	+	0.0181358i	$0.994227\pi$
$434$	−23.8527	+	0.171963i	−1.14497	+	0.00825450i
$435$		0			0
$436$	−13.4839	−	3.24053i	−0.645761	−	0.155193i
$437$	16.8105	+	9.70554i	0.804154	+	0.464279i
$438$		0			0
$439$	16.2969	−	9.40902i	0.777809	−	0.449068i	−0.0578444	−	0.998326i	$-0.518423\pi$
$439$	16.2969	−	9.40902i	0.777809	−	0.449068i	0.835653	+	0.549258i	$0.185089\pi$
$440$	−10.7514	+	4.95190i	−0.512554	+	0.236072i
$441$		0			0
$442$	27.0976	+	10.8145i	1.28890	+	0.514394i
$443$	3.46180	+	5.99600i	0.164475	+	0.284879i	0.936469	−	0.350751i	$-0.114074\pi$
$443$	3.46180	+	5.99600i	0.164475	+	0.284879i	−0.771994	+	0.635630i	$0.780740\pi$
$444$		0			0
$445$	−6.64703	−	3.83766i	−0.315099	−	0.181923i
$446$	−1.76573	+	0.255808i	−0.0836100	+	0.0121129i
$447$		0			0
$448$	20.0874	+	6.67068i	0.949039	+	0.315160i
$449$		−	0.270365i		−	0.0127593i	−0.999980	−	0.00637965i	$-0.997969\pi$
$449$		−	0.270365i		−	0.0127593i	0.999980	−	0.00637965i	$-0.00203072\pi$
$450$		0			0
$451$	1.97247	−	3.41642i	0.0928801	−	0.160873i
$452$	−10.1639	−	34.3421i	−0.478067	−	1.61532i
$453$		0			0
$454$	0.388716	−	0.973993i	0.0182433	−	0.0457118i
$455$	27.8393	+	21.6179i	1.30513	+	1.01346i
$456$		0			0
$457$	−1.91551	−	3.31776i	−0.0896037	−	0.155198i	0.817740	−	0.575588i	$-0.195227\pi$
$457$	−1.91551	−	3.31776i	−0.0896037	−	0.155198i	−0.907344	+	0.420390i	$0.861893\pi$
$458$	−10.2660	+	8.09108i	−0.479697	+	0.378071i
$459$		0			0
$460$	−6.33760	+	26.3708i	−0.295492	+	1.22955i
$461$			15.4863i			0.721267i	0.932708	+	0.360634i	$0.117439\pi$
$461$			15.4863i			0.721267i	−0.932708	+	0.360634i	$0.882561\pi$
$462$		0			0
$463$	−6.51872			−0.302950			−0.151475	−	0.988461i	$-0.548402\pi$
$463$	−6.51872			−0.302950			−0.151475	+	0.988461i	$0.548402\pi$
$464$	−6.13550	+	3.98036i	−0.284833	+	0.184784i
$465$		0			0
$466$	0.427968	+	0.543006i	0.0198253	+	0.0251543i
$467$	−19.1086	+	11.0323i	−0.884240	+	0.510516i	−0.872054	−	0.489410i	$-0.837212\pi$
$467$	−19.1086	+	11.0323i	−0.884240	+	0.510516i	−0.0121856	+	0.999926i	$0.503879\pi$
$468$		0			0
$469$	0.908568	−	6.60677i	0.0419538	−	0.305072i
$470$	−15.3899	+	38.5621i	−0.709885	+	1.77873i
$471$		0			0
$472$	0.243941	−	2.64460i	0.0112283	−	0.121727i
$473$	6.89812	+	3.98263i	0.317176	+	0.183122i
$474$		0			0
$475$	−45.0030			−2.06488
$476$	29.8124	−	4.53870i	1.36645	−	0.208031i
$477$		0			0
$478$	1.90430	−	0.275882i	0.0871005	−	0.0126186i
$479$	5.97672	−	10.3520i	0.273083	−	0.472994i	−0.696567	−	0.717492i	$-0.745290\pi$
$479$	5.97672	−	10.3520i	0.273083	−	0.472994i	0.969650	+	0.244498i	$0.0786233\pi$
$480$		0			0
$481$	−31.2664	+	18.0517i	−1.42563	+	0.823085i
$482$	−0.171010	+	0.428494i	−0.00778928	+	0.0195174i
$483$		0			0
$484$	−14.0790	−	13.3667i	−0.639953	−	0.607578i
$485$	19.1181	+	33.1135i	0.868107	+	1.50361i
$486$		0			0
$487$	1.13421	−	1.96451i	0.0513959	−	0.0890203i	−0.839183	−	0.543849i	$-0.816966\pi$
$487$	1.13421	−	1.96451i	0.0513959	−	0.0890203i	0.890579	+	0.454829i	$0.150300\pi$
$488$	−6.48332	+	9.16686i	−0.293486	+	0.414964i
$489$		0			0
$490$	36.1263	+	4.70300i	1.63202	+	0.212460i
$491$	15.1155			0.682153			0.341077	−	0.940036i	$-0.389208\pi$
$491$	15.1155			0.682153			0.341077	+	0.940036i	$0.389208\pi$
$492$		0			0
$493$	−5.20991	+	9.02383i	−0.234643	+	0.406413i
$494$	21.1806	−	16.6934i	0.952960	−	0.751073i
$495$		0			0
$496$	−25.4659	+	1.32266i	−1.14345	+	0.0593892i
$497$	−34.3250	+	13.9867i	−1.53969	+	0.627387i
$498$		0			0
$499$	−37.1204	+	21.4315i	−1.66174	+	0.959404i	−0.689851	+	0.723952i	$0.742324\pi$
$499$	−37.1204	+	21.4315i	−1.66174	+	0.959404i	−0.971886	+	0.235452i	$0.924343\pi$
$500$	−7.40080	−	25.0062i	−0.330974	−	1.11831i
$501$		0			0
$502$	−1.36096	+	0.197167i	−0.0607427	+	0.00880001i
$503$	−40.5210			−1.80674			−0.903372	−	0.428858i	$-0.858916\pi$
$503$	−40.5210			−1.80674			−0.903372	+	0.428858i	$0.858916\pi$
$504$		0			0
$505$	72.3220			3.21829
$506$	5.86499	−	0.849682i	0.260731	−	0.0377730i
$507$		0			0
$508$	2.22535	−	0.658612i	0.0987339	−	0.0292212i
$509$	9.81718	−	5.66795i	0.435139	−	0.251227i	−0.266395	−	0.963864i	$-0.585832\pi$
$509$	9.81718	−	5.66795i	0.435139	−	0.251227i	0.701533	+	0.712637i	$0.252499\pi$
$510$		0			0
$511$	2.79725	−	20.3406i	0.123743	−	0.899815i
$512$	21.7714	+	6.16493i	0.962169	+	0.272454i
$513$		0			0
$514$	−15.7291	+	12.3968i	−0.693781	+	0.546801i
$515$	−16.5903	+	28.7352i	−0.731056	+	1.26623i
$516$		0			0
$517$	9.07225			0.398997
$518$	−18.4246	+	32.4504i	−0.809530	+	1.42579i
$519$		0			0
$520$	30.7641	+	21.7581i	1.34909	+	0.954155i
$521$	4.86146	−	8.42029i	0.212984	−	0.368900i	−0.739663	−	0.672978i	$-0.765015\pi$
$521$	4.86146	−	8.42029i	0.212984	−	0.368900i	0.952647	+	0.304078i	$0.0983483\pi$
$522$		0			0
$523$	9.28564	+	16.0832i	0.406033	+	0.703269i	0.994441	−	0.105295i	$-0.0335786\pi$
$523$	9.28564	+	16.0832i	0.406033	+	0.703269i	−0.588408	+	0.808564i	$0.700245\pi$
$524$	16.3070	−	17.1760i	0.712376	−	0.750336i
$525$		0			0
$526$	−9.66984	+	24.2294i	−0.421625	+	1.05645i
$527$	−31.4636	+	18.1655i	−1.37058	+	0.791303i
$528$		0			0
$529$	−4.71073	+	8.15923i	−0.204815	+	0.354749i
$530$	29.2617	−	4.23925i	1.27105	−	0.184141i
$531$		0			0
$532$	10.1451	−	25.9624i	0.439846	−	1.12561i
$533$	−12.5580			−0.543947
$534$		0			0
$535$	20.5682	+	11.8750i	0.889239	+	0.513402i
$536$	0.654845	−	7.09927i	0.0282850	−	0.306642i
$537$		0			0
$538$	−10.2564	+	25.6992i	−0.442186	+	1.10797i
$539$	−1.97153	−	7.71238i	−0.0849198	−	0.332196i
$540$		0			0
$541$	0.795518	−	0.459292i	0.0342020	−	0.0197465i	−0.482802	−	0.875730i	$-0.660381\pi$
$541$	0.795518	−	0.459292i	0.0342020	−	0.0197465i	0.517004	+	0.855983i	$0.327047\pi$
$542$	17.6142	+	22.3489i	0.756595	+	0.959967i
$543$		0			0
$544$	31.6223	−	6.27083i	1.35579	−	0.268860i
$545$	−25.5175			−1.09305
$546$		0			0
$547$			28.4217i			1.21523i	0.794233	+	0.607613i	$0.207873\pi$
$547$			28.4217i			1.21523i	−0.794233	+	0.607613i	$0.792127\pi$
$548$	7.54684	+	1.81370i	0.322385	+	0.0774775i
$549$		0			0
$550$	−10.7908	+	8.50475i	−0.460122	+	0.362644i
$551$	4.81570	+	8.34105i	0.205156	+	0.355340i
$552$		0			0
$553$	24.9341	−	32.1098i	1.06031	−	1.36545i
$554$	4.12851	−	10.3447i	0.175403	−	0.439503i
$555$		0			0
$556$	14.6423	−	4.33353i	0.620973	−	0.183783i
$557$	12.7308	−	22.0504i	0.539420	−	0.934304i	−0.459515	−	0.888170i	$-0.651977\pi$
$557$	12.7308	−	22.0504i	0.539420	−	0.934304i	0.998935	−	0.0461335i	$-0.0146900\pi$
$558$		0			0
$559$		−	25.3559i		−	1.07244i
$560$	38.8067	+	3.29761i	1.63988	+	0.139349i
$561$		0			0
$562$	27.4814	−	3.98132i	1.15923	−	0.167942i
$563$	15.6292	+	9.02355i	0.658694	+	0.380297i	0.791779	−	0.610807i	$-0.209155\pi$
$563$	15.6292	+	9.02355i	0.658694	+	0.380297i	−0.133085	+	0.991105i	$0.542488\pi$
$564$		0			0
$565$	−32.9503	−	57.0716i	−1.38623	−	2.40102i
$566$	−29.1254	−	11.6238i	−1.22423	−	0.488585i
$567$		0			0
$568$	−35.9905	+	16.5765i	−1.51013	+	0.695535i
$569$	26.9348	−	15.5508i	1.12917	−	0.651925i	0.185442	−	0.982655i	$-0.440628\pi$
$569$	26.9348	−	15.5508i	1.12917	−	0.651925i	0.943725	+	0.330730i	$0.107295\pi$
$570$		0			0
$571$	38.0094	+	21.9447i	1.59064	+	0.918359i	0.993197	+	0.116450i	$0.0371516\pi$
$571$	38.0094	+	21.9447i	1.59064	+	0.918359i	0.597447	+	0.801908i	$0.296182\pi$
$572$	1.92393	−	8.00550i	0.0804436	−	0.334727i
$573$		0			0
$574$	−11.1938	+	6.57078i	−0.467219	+	0.274259i
$575$			31.4807i			1.31284i
$576$		0			0
$577$	−25.7081	−	14.8426i	−1.07024	−	0.617906i	−0.141996	−	0.989867i	$-0.545352\pi$
$577$	−25.7081	−	14.8426i	−1.07024	−	0.617906i	−0.928248	+	0.371962i	$0.878685\pi$
$578$	17.1914	−	13.5493i	0.715067	−	0.563578i
$579$		0			0
$580$	−9.26565	+	9.75938i	−0.384735	+	0.405236i
$581$	−7.08284	+	2.88610i	−0.293846	+	0.119735i
$582$		0			0
$583$	−3.23029	−	5.59503i	−0.133785	−	0.231722i
$584$	2.01610	−	21.8569i	0.0834269	−	0.904444i
$585$		0			0
$586$	−26.1069	+	3.78221i	−1.07847	+	0.156242i
$587$			39.8767i			1.64589i	0.568122	+	0.822944i	$0.307670\pi$
$587$			39.8767i			1.64589i	−0.568122	+	0.822944i	$0.692330\pi$
$588$		0			0
$589$			33.5821i			1.38373i
$590$	−0.700662	−	4.83636i	−0.0288458	−	0.199110i
$591$		0			0
$592$	−18.1275	+	35.5361i	−0.745035	+	1.46052i
$593$	−2.90705	−	5.03515i	−0.119378	−	0.206769i	0.800143	−	0.599809i	$-0.204757\pi$
$593$	−2.90705	−	5.03515i	−0.119378	−	0.206769i	−0.919521	+	0.393040i	$0.871423\pi$
$594$		0			0
$595$	51.3862	−	20.9387i	2.10663	−	0.858402i
$596$	10.1637	+	9.64951i	0.416321	+	0.395259i
$597$		0			0
$598$	−11.6775	−	14.8164i	−0.477527	−	0.605886i
$599$	−7.85117	−	4.53288i	−0.320790	−	0.185208i	0.330955	−	0.943647i	$-0.392629\pi$
$599$	−7.85117	−	4.53288i	−0.320790	−	0.185208i	−0.651745	+	0.758438i	$0.725963\pi$
$600$		0			0
$601$			24.2715i			0.990056i	0.868877	+	0.495028i	$0.164842\pi$
$601$			24.2715i			0.990056i	−0.868877	+	0.495028i	$0.835158\pi$
$602$	−13.2671	−	22.6014i	−0.540727	−	0.921165i
$603$		0			0
$604$	8.52267	−	35.4629i	0.346782	−	1.44296i
$605$	−30.9361	−	17.8610i	−1.25773	−	0.726152i
$606$		0			0
$607$	−21.9254	+	12.6586i	−0.889923	+	0.513797i	−0.873917	−	0.486074i	$-0.838428\pi$
$607$	−21.9254	+	12.6586i	−0.889923	+	0.513797i	−0.0160059	+	0.999872i	$0.505095\pi$
$608$	9.59500	−	28.2117i	0.389129	−	1.14414i
$609$		0			0
$610$	−7.65790	+	19.1882i	−0.310059	+	0.776906i
$611$	−14.4399	−	25.0106i	−0.584175	−	1.01182i
$612$		0			0
$613$	−0.971418	−	0.560849i	−0.0392352	−	0.0226525i	0.480254	−	0.877129i	$-0.340544\pi$
$613$	−0.971418	−	0.560849i	−0.0392352	−	0.0226525i	−0.519489	+	0.854477i	$0.673878\pi$
$614$	−5.43260	−	37.4989i	−0.219242	−	1.51333i
$615$		0			0
$616$	−2.47383	−	8.14251i	−0.0996735	−	0.328071i
$617$		−	24.9684i		−	1.00519i	−0.864522	−	0.502596i	$-0.832378\pi$
$617$		−	24.9684i		−	1.00519i	0.864522	−	0.502596i	$-0.167622\pi$
$618$		0			0
$619$	−16.5995	+	28.7513i	−0.667192	+	1.15561i	0.311494	+	0.950248i	$0.399171\pi$
$619$	−16.5995	+	28.7513i	−0.667192	+	1.15561i	−0.978686	+	0.205362i	$0.934163\pi$
$620$	−44.9926	+	13.3160i	−1.80695	+	0.534782i
$621$		0			0
$622$	33.8325	+	13.5024i	1.35656	+	0.541396i
$623$	3.38435	−	4.35833i	0.135591	−	0.174613i
$624$		0			0
$625$	−2.63487	−	4.56373i	−0.105395	−	0.182549i
$626$	11.3638	+	14.4184i	0.454191	+	0.576277i
$627$		0			0
$628$	−6.52489	+	27.1501i	−0.260371	+	1.08341i
$629$			56.8363i			2.26621i
$630$		0			0
$631$	−15.5394			−0.618613			−0.309307	−	0.950962i	$-0.600097\pi$
$631$	−15.5394			−0.618613			−0.309307	+	0.950962i	$0.600097\pi$
$632$	25.0958	−	35.4832i	0.998256	−	1.41145i
$633$		0			0
$634$	−23.3448	+	18.3992i	−0.927142	+	0.730724i
$635$	3.69821	−	2.13516i	0.146759	−	0.0847314i
$636$		0			0
$637$	−18.1237	+	17.7106i	−0.718088	+	0.701720i
$638$	2.73102	+	1.08994i	0.108122	+	0.0431510i
$639$		0			0
$640$	41.6022	+	1.66868i	1.64447	+	0.0659604i
$641$	33.1136	+	19.1182i	1.30791	+	0.755122i	0.981747	−	0.190191i	$-0.0609108\pi$
$641$	33.1136	+	19.1182i	1.30791	+	0.755122i	0.326163	+	0.945314i	$0.394244\pi$
$642$		0			0
$643$	−3.17969			−0.125395			−0.0626974	−	0.998033i	$-0.519970\pi$
$643$	−3.17969			−0.125395			−0.0626974	+	0.998033i	$0.519970\pi$
$644$	−18.1614	−	7.09676i	−0.715658	−	0.279651i
$645$		0			0
$646$	−6.08710	−	42.0166i	−0.239494	−	1.65312i
$647$	−9.13828	+	15.8280i	−0.359263	+	0.622262i	−0.987838	−	0.155487i	$-0.950305\pi$
$647$	−9.13828	+	15.8280i	−0.359263	+	0.622262i	0.628575	+	0.777749i	$0.283639\pi$
$648$		0			0
$649$	−0.924744	+	0.533901i	−0.0362994	+	0.0209574i
$650$	40.6214	+	16.2118i	1.59330	+	0.635879i
$651$		0			0
$652$	13.9176	−	14.6593i	0.545057	−	0.574101i
$653$	−22.2442	−	38.5282i	−0.870485	−	1.50772i	−0.861496	−	0.507764i	$-0.830472\pi$
$653$	−22.2442	−	38.5282i	−0.870485	−	1.50772i	−0.00898848	−	0.999960i	$-0.502861\pi$
$654$		0			0
$655$	21.7899	−	37.7413i	0.851403	−	1.47467i
$656$	−11.6409	+	7.55197i	−0.454502	+	0.294855i
$657$		0			0
$658$	−25.9577	−	14.7382i	−1.01194	−	0.574555i
$659$	24.7165			0.962818			0.481409	−	0.876496i	$-0.340125\pi$
$659$	24.7165			0.962818			0.481409	+	0.876496i	$0.340125\pi$
$660$		0			0
$661$	9.39973	−	16.2808i	0.365607	−	0.633250i	−0.623266	−	0.782010i	$-0.714195\pi$
$661$	9.39973	−	16.2808i	0.365607	−	0.633250i	0.988873	+	0.148760i	$0.0475281\pi$
$662$	11.7810	+	14.9477i	0.457882	+	0.580960i
$663$		0			0
$664$	−7.42651	+	3.42051i	−0.288204	+	0.132741i
$665$	6.98766	−	50.8117i	0.270970	−	1.97039i
$666$		0			0
$667$	5.83477	−	3.36871i	0.225923	−	0.130437i
$668$	9.99924	−	2.95936i	0.386882	−	0.114501i
$669$		0			0
$670$	−1.88089	−	12.9829i	−0.0726650	−	0.501575i
$671$	4.51428			0.174272
$672$		0			0
$673$	22.7132			0.875531			0.437766	−	0.899089i	$-0.355770\pi$
$673$	22.7132			0.875531			0.437766	+	0.899089i	$0.355770\pi$
$674$	−4.89027	−	33.7554i	−0.188366	−	1.30021i
$675$		0			0
$676$	−0.200975	+	0.0594804i	−0.00772982	+	0.00228771i
$677$	31.0283	−	17.9142i	1.19251	−	0.688498i	0.233638	−	0.972324i	$-0.424937\pi$
$677$	31.0283	−	17.9142i	1.19251	−	0.688498i	0.958876	+	0.283825i	$0.0916036\pi$
$678$		0			0
$679$	−25.4570	+	10.3731i	−0.976950	+	0.398084i
$680$	53.8794	−	24.8158i	2.06618	−	0.951644i
$681$		0			0
$682$	6.34641	+	8.05231i	0.243016	+	0.308339i
$683$	−5.91001	+	10.2364i	−0.226140	+	0.391686i	−0.956661	−	0.291204i	$-0.905944\pi$
$683$	−5.91001	+	10.2364i	−0.226140	+	0.391686i	0.730521	+	0.682891i	$0.239277\pi$
$684$		0			0
$685$	14.2820			0.545686
$686$	−6.88807	+	25.2696i	−0.262988	+	0.964799i
$687$		0			0
$688$	−15.2482	−	23.5043i	−0.581333	−	0.896093i
$689$	−10.2830	+	17.8107i	−0.391752	+	0.678534i
$690$		0			0
$691$	−16.8555	−	29.1945i	−0.641213	−	1.11061i	−0.985162	−	0.171625i	$-0.945098\pi$
$691$	−16.8555	−	29.1945i	−0.641213	−	1.11061i	0.343950	−	0.938988i	$-0.388235\pi$
$692$	−5.12457	+	5.39764i	−0.194807	+	0.205188i
$693$		0			0
$694$	−5.53817	−	2.21026i	−0.210226	−	0.0839002i
$695$	24.3335	−	14.0489i	0.923021	−	0.532906i
$696$		0			0
$697$	−9.88481	+	17.1210i	−0.374414	+	0.648504i
$698$	1.89069	+	13.0506i	0.0715637	+	0.493973i
$699$		0			0
$700$	44.6912	−	6.80388i	1.68917	−	0.257162i
$701$	−7.35428			−0.277767			−0.138884	−	0.990309i	$-0.544351\pi$
$701$	−7.35428			−0.277767			−0.138884	+	0.990309i	$0.544351\pi$
$702$		0			0
$703$	45.4973	+	26.2679i	1.71596	+	0.990713i
$704$	−3.03082	−	8.57789i	−0.114228	−	0.323292i
$705$		0			0
$706$	−27.7538	−	11.0764i	−1.04453	−	0.416866i
$707$	−7.08368	+	51.5100i	−0.266409	+	1.93723i
$708$		0			0
$709$	32.1899	−	18.5848i	1.20892	−	0.697968i	0.246394	−	0.969170i	$-0.420754\pi$
$709$	32.1899	−	18.5848i	1.20892	−	0.697968i	0.962523	+	0.271202i	$0.0874210\pi$
$710$	−57.2635	+	45.1320i	−2.14906	+	1.69378i
$711$		0			0
$712$	3.40630	−	4.81621i	0.127656	−	0.180495i
$713$	23.4915			0.879764
$714$		0			0
$715$		−	15.1500i		−	0.566576i
$716$	−12.3185	+	51.2572i	−0.460362	+	1.91557i
$717$		0			0
$718$	−9.62223	−	12.2087i	−0.359098	−	0.455624i
$719$	−9.83186	−	17.0293i	−0.366667	−	0.635085i	0.622376	−	0.782719i	$-0.286168\pi$
$719$	−9.83186	−	17.0293i	−0.366667	−	0.635085i	−0.989042	+	0.147634i	$0.952834\pi$
$720$		0			0
$721$	−18.8412	−	14.6306i	−0.701682	−	0.544873i
$722$	−11.4915	−	4.58620i	−0.427669	−	0.170681i
$723$		0			0
$724$	−9.42256	+	2.78869i	−0.350187	+	0.103641i
$725$	−7.81007	+	13.5274i	−0.290059	+	0.502397i
$726$		0			0
$727$		−	24.1400i		−	0.895302i	−0.894208	−	0.447651i	$-0.852261\pi$
$727$		−	24.1400i		−	0.895302i	0.894208	−	0.447651i	$-0.147739\pi$
$728$	−18.5100	+	19.7800i	−0.686027	+	0.733095i
$729$		0			0
$730$	−5.79078	−	39.9712i	−0.214326	−	1.47940i
$731$	−34.5691	−	19.9585i	−1.27858	−	0.738191i
$732$		0			0
$733$	−0.741275	−	1.28393i	−0.0273796	−	0.0474229i	0.852011	−	0.523524i	$-0.175383\pi$
$733$	−0.741275	−	1.28393i	−0.0273796	−	0.0474229i	−0.879391	+	0.476101i	$0.842050\pi$
$734$	−10.2020	+	25.5629i	−0.376564	+	0.943545i
$735$		0			0
$736$	−19.7348	−	6.71194i	−0.727435	−	0.247406i
$737$	−2.48242	+	1.43323i	−0.0914412	+	0.0527936i
$738$		0			0
$739$	−20.3252	−	11.7348i	−0.747676	−	0.431671i	0.0771774	−	0.997017i	$-0.475409\pi$
$739$	−20.3252	−	11.7348i	−0.747676	−	0.431671i	−0.824854	+	0.565346i	$0.808743\pi$
$740$	−17.1526	+	71.3722i	−0.630543	+	2.62370i
$741$		0			0
$742$	0.153245	+	21.2563i	0.00562580	+	0.780344i
$743$			5.90858i			0.216765i	0.994109	+	0.108382i	$0.0345671\pi$
$743$			5.90858i			0.216765i	−0.994109	+	0.108382i	$0.965433\pi$
$744$		0			0
$745$	22.3330	+	12.8939i	0.818217	+	0.472398i
$746$	0.131983	+	0.167460i	0.00483223	+	0.00613114i
$747$		0			0
$748$	−9.39995	−	8.92440i	−0.343696	−	0.326308i
$749$	−10.4723	+	13.4862i	−0.382651	+	0.492774i
$750$		0			0
$751$	−16.1457	−	27.9652i	−0.589166	−	1.02047i	−0.994342	−	0.106227i	$-0.966123\pi$
$751$	−16.1457	−	27.9652i	−0.589166	−	1.02047i	0.405175	−	0.914239i	$-0.367210\pi$
$752$	−28.4260	−	14.5005i	−1.03659	−	0.528780i
$753$		0			0
$754$	−1.34207	−	9.26374i	−0.0488754	−	0.337366i
$755$		−	67.1115i		−	2.44244i
$756$		0			0
$757$			7.01154i			0.254839i	0.991849	+	0.127419i	$0.0406694\pi$
$757$			7.01154i			0.254839i	−0.991849	+	0.127419i	$0.959331\pi$
$758$	46.0647	−	6.67356i	1.67314	−	0.242395i
$759$		0			0
$760$	5.03631	−	54.5995i	0.182686	−	1.98053i
$761$	−17.4606	−	30.2426i	−0.632945	−	1.09629i	−0.986946	−	0.161049i	$-0.948512\pi$
$761$	−17.4606	−	30.2426i	−0.632945	−	1.09629i	0.354001	−	0.935245i	$-0.384821\pi$
$762$		0			0
$763$	2.49935	−	18.1743i	0.0904824	−	0.657955i
$764$	−8.42494	+	8.87387i	−0.304803	+	0.321045i
$765$		0			0
$766$	18.6340	−	14.6863i	0.673273	−	0.530638i
$767$	2.94375	+	1.69957i	0.106292	+	0.0613680i
$768$		0			0
$769$		−	40.6649i		−	1.46642i	−0.680005	−	0.733208i	$-0.738022\pi$
$769$		−	40.6649i		−	1.46642i	0.680005	−	0.733208i	$-0.261978\pi$
$770$	−7.92699	−	13.5042i	−0.285669	−	0.486657i
$771$		0			0
$772$	8.64766	−	35.9830i	0.311236	−	1.29506i
$773$	35.3357	+	20.4011i	1.27094	+	0.733777i	0.975165	−	0.221481i	$-0.0710892\pi$
$773$	35.3357	+	20.4011i	1.27094	+	0.733777i	0.295774	+	0.955258i	$0.404423\pi$
$774$		0			0
$775$	−47.1665	+	27.2316i	−1.69427	+	0.978187i
$776$	−26.6922	+	12.2939i	−0.958193	+	0.441325i
$777$		0			0
$778$	33.2334	+	13.2633i	1.19147	+	0.475511i
$779$	9.13688	+	15.8255i	0.327363	+	0.567009i
$780$		0			0
$781$	13.7970	+	7.96570i	0.493696	+	0.285035i
$782$	−29.3917	+	4.25808i	−1.05104	+	0.152269i
$783$		0			0
$784$	−6.14963	+	27.3163i	−0.219630	+	0.975583i
$785$			51.3801i			1.83383i
$786$		0			0
$787$	15.9930	−	27.7007i	0.570089	−	0.987423i	−0.426467	−	0.904503i	$-0.640242\pi$
$787$	15.9930	−	27.7007i	0.570089	−	0.987423i	0.996556	−	0.0829199i	$-0.0264246\pi$
$788$	5.75000	−	1.70177i	0.204835	−	0.0606229i
$789$		0			0
$790$	29.6423	−	74.2738i	1.05463	−	2.64254i
$791$	43.8755	−	17.8783i	1.56003	−	0.635678i
$792$		0			0
$793$	−7.18517	−	12.4451i	−0.255153	−	0.441938i
$794$	39.4195	−	31.0683i	1.39894	−	1.10257i
$795$		0			0
$796$	2.86787	+	0.689224i	0.101649	+	0.0244289i
$797$		−	27.1417i		−	0.961410i	−0.876883	−	0.480705i	$-0.840381\pi$
$797$		−	27.1417i		−	0.961410i	0.876883	−	0.480705i	$-0.159619\pi$
$798$		0			0
$799$	−45.4645			−1.60842
$800$	47.4043	−	9.40047i	1.67600	−	0.332357i
$801$		0			0
$802$	3.01226	+	3.82196i	0.106367	+	0.134958i
$803$	−7.64276	+	4.41255i	−0.269707	+	0.155715i
$804$		0			0
$805$	−35.5441	−	4.88804i	−1.25276	−	0.172281i
$806$	12.0976	−	30.3124i	0.426118	−	1.06771i
$807$		0			0
$808$	−5.10552	+	55.3498i	−0.179612	+	1.94720i
$809$	−10.8693	−	6.27540i	−0.382144	−	0.220631i	0.296606	−	0.955000i	$-0.404145\pi$
$809$	−10.8693	−	6.27540i	−0.382144	−	0.220631i	−0.678751	+	0.734369i	$0.737478\pi$
$810$		0			0
$811$	−12.0857			−0.424388			−0.212194	−	0.977228i	$-0.568061\pi$
$811$	−12.0857			−0.424388			−0.212194	+	0.977228i	$0.568061\pi$
$812$	−6.04340	−	7.55518i	−0.212082	−	0.265135i
$813$		0			0
$814$	15.8735	−	2.29965i	0.556366	−	0.0806028i
$815$	18.5971	−	32.2112i	0.651430	−	1.12831i
$816$		0			0
$817$	−31.9534	+	18.4483i	−1.11791	+	0.645425i
$818$	3.20989	−	8.04291i	0.112231	−	0.281214i
$819$		0			0
$820$	−17.5798	+	18.5166i	−0.613913	+	0.646627i
$821$	−15.2725	−	26.4527i	−0.533012	−	0.923204i	−0.999257	−	0.0385483i	$-0.987727\pi$
$821$	−15.2725	−	26.4527i	−0.533012	−	0.923204i	0.466245	−	0.884656i	$-0.345607\pi$
$822$		0			0
$823$	10.4306	−	18.0664i	0.363589	−	0.629754i	−0.624960	−	0.780657i	$-0.714885\pi$
$823$	10.4306	−	18.0664i	0.363589	−	0.629754i	0.988549	+	0.150903i	$0.0482180\pi$
$824$	−20.8206	−	14.7255i	−0.725319	−	0.512987i
$825$		0			0
$826$	3.51323	−	0.0253283i	0.122241	−	0.000881283i
$827$	50.1969			1.74552			0.872759	−	0.488151i	$-0.162328\pi$
$827$	50.1969			1.74552			0.872759	+	0.488151i	$0.162328\pi$
$828$		0			0
$829$	−9.59915	+	16.6262i	−0.333392	+	0.577453i	−0.983175	−	0.182668i	$-0.941527\pi$
$829$	−9.59915	+	16.6262i	−0.333392	+	0.577453i	0.649782	+	0.760120i	$0.274860\pi$
$830$	−11.8161	+	9.31284i	−0.410144	+	0.323253i
$831$		0			0
$832$	−18.8238	+	22.0085i	−0.652596	+	0.763007i
$833$	9.88008	+	38.6497i	0.342325	+	1.33913i
$834$		0			0
$835$	16.6173	−	9.59400i	0.575065	−	0.332014i
$836$	−11.4883	+	3.40007i	−0.397332	+	0.117594i
$837$		0			0
$838$	16.7317	−	2.42399i	0.577988	−	0.0837352i
$839$	9.77418			0.337442			0.168721	−	0.985664i	$-0.446036\pi$
$839$	9.77418			0.337442			0.168721	+	0.985664i	$0.446036\pi$
$840$		0			0
$841$	−25.6570			−0.884725
$842$	17.0214	−	2.46595i	0.586596	−	0.0849823i
$843$		0			0
$844$	10.1570	+	34.3189i	0.349618	+	1.18131i
$845$	−0.333992	+	0.192830i	−0.0114897	+	0.00663357i
$846$		0			0
$847$	15.7512	−	20.2842i	0.541218	−	0.696975i
$848$	1.17869	+	22.6940i	0.0404764	+	0.779314i
$849$		0			0
$850$	54.0769	−	42.6206i	1.85482	−	1.46187i
$851$	18.3751	−	31.8265i	0.629889	−	1.09100i
$852$		0			0
$853$	52.3052			1.79090			0.895449	−	0.445165i	$-0.146855\pi$
$853$	52.3052			1.79090			0.895449	+	0.445165i	$0.146855\pi$
$854$	−12.9163	−	7.33360i	−0.441988	−	0.250951i
$855$		0			0
$856$	−10.5402	+	14.9030i	−0.360258	+	0.509374i
$857$	−19.5757	+	33.9062i	−0.668695	+	1.15821i	0.309575	+	0.950875i	$0.399813\pi$
$857$	−19.5757	+	33.9062i	−0.668695	+	1.15821i	−0.978269	+	0.207338i	$0.933520\pi$
$858$		0			0
$859$	−23.9471	−	41.4775i	−0.817063	−	1.41520i	−0.907837	−	0.419324i	$-0.862267\pi$
$859$	−23.9471	−	41.4775i	−0.817063	−	1.41520i	0.0907734	−	0.995872i	$-0.471066\pi$
$860$	−37.3869	−	35.4955i	−1.27488	−	1.21039i
$861$		0			0
$862$	11.8878	−	29.7868i	0.404899	−	1.01454i
$863$	19.8433	−	11.4565i	0.675473	−	0.389985i	−0.122674	−	0.992447i	$-0.539147\pi$
$863$	19.8433	−	11.4565i	0.675473	−	0.389985i	0.798147	+	0.602462i	$0.205814\pi$
$864$		0			0
$865$	−6.84760	+	11.8604i	−0.232825	+	0.403265i
$866$	−1.05637	+	0.153040i	−0.0358968	+	0.00520050i
$867$		0			0
$868$	−5.07718	−	33.3494i	−0.172331	−	1.13195i
$869$	−17.4739			−0.592763
$870$		0			0
$871$	7.90232	+	4.56241i	0.267760	+	0.154591i
$872$	1.80139	−	19.5291i	0.0610027	−	0.661340i
$873$		0			0
$874$	−10.1753	+	25.4959i	−0.344185	+	0.862413i
$875$	31.9480	−	13.0181i	1.08004	−	0.440091i
$876$		0			0
$877$	−20.9012	+	12.0673i	−0.705783	+	0.407484i	−0.809498	−	0.587123i	$-0.800260\pi$
$877$	−20.9012	+	12.0673i	−0.705783	+	0.407484i	0.103715	+	0.994607i	$0.466927\pi$
$878$	16.4733	+	20.9014i	0.555948	+	0.705387i
$879$		0			0
$880$	−9.11070	−	14.0436i	−0.307122	−	0.473411i
$881$	49.8730			1.68026			0.840131	−	0.542383i	$-0.182478\pi$
$881$	49.8730			1.68026			0.840131	+	0.542383i	$0.182478\pi$
$882$		0			0
$883$		−	10.1798i		−	0.342578i	−0.985221	−	0.171289i	$-0.945207\pi$
$883$		−	10.1798i		−	0.342578i	0.985221	−	0.171289i	$-0.0547932\pi$
$884$	−9.64156	+	40.1186i	−0.324281	+	1.34933i
$885$		0			0
$886$	−7.69009	+	6.06092i	−0.258354	+	0.203621i
$887$	−10.2756	−	17.7979i	−0.345022	−	0.597596i	0.640336	−	0.768095i	$-0.278795\pi$
$887$	−10.2756	−	17.7979i	−0.345022	−	0.597596i	−0.985358	+	0.170499i	$0.945462\pi$
$888$		0			0
$889$	1.15850	+	2.84311i	0.0388549	+	0.0953549i
$890$	4.02341	−	10.0813i	0.134865	−	0.337927i
$891$		0			0
$892$	−0.716060	−	2.41946i	−0.0239755	−	0.0810094i
$893$	−21.0122	+	36.3942i	−0.703147	+	1.21789i
$894$		0			0
$895$			97.0014i			3.24240i
$896$	−5.26327	+	29.4669i	−0.175833	+	0.984420i
$897$		0			0
$898$	0.378403	−	0.0548206i	0.0126275	−	0.00182939i
$899$	10.0944	+	5.82802i	0.336668	+	0.194375i
$900$		0			0
$901$	16.1882	+	28.0388i	0.539307	+	0.934108i
$902$	5.18158	+	2.06795i	0.172528	+	0.0688550i
$903$		0			0
$904$	46.0044	−	21.1887i	1.53008	−	0.704727i
$905$	−15.6589	+	9.04070i	−0.520521	+	0.300523i
$906$		0			0
$907$	32.1180	+	18.5433i	1.06646	+	0.615721i	0.927212	−	0.374537i	$-0.122198\pi$
$907$	32.1180	+	18.5433i	1.06646	+	0.615721i	0.139248	+	0.990258i	$0.455532\pi$
$908$	1.44202	+	0.346556i	0.0478552	+	0.0115009i
$909$		0			0
$910$	−24.6116	+	43.3473i	−0.815868	+	1.43695i
$911$		−	9.53166i		−	0.315798i	−0.987455	−	0.157899i	$-0.949528\pi$
$911$		−	9.53166i		−	0.315798i	0.987455	−	0.157899i	$-0.0504720\pi$
$912$		0			0
$913$	2.84696	+	1.64369i	0.0942207	+	0.0543984i
$914$	4.25514	−	3.35368i	0.140748	−	0.110930i
$915$		0			0
$916$	−13.4059	−	12.7277i	−0.442943	−	0.420534i
$917$	24.7462	+	19.2161i	0.817193	+	0.634571i
$918$		0			0
$919$	13.0199	+	22.5511i	0.429487	+	0.743894i	0.996828	−	0.0795896i	$-0.0253610\pi$
$919$	13.0199	+	22.5511i	0.429487	+	0.743894i	−0.567340	+	0.823483i	$0.692028\pi$
$920$	−38.1937	−	3.52303i	−1.25921	−	0.116151i
$921$		0			0
$922$	−21.6746	+	3.14008i	−0.713815	+	0.103413i
$923$		−	50.7146i		−	1.66929i
$924$		0			0
$925$			85.2022i			2.80143i
$926$	−1.32177	−	9.12361i	−0.0434361	−	0.299820i
$927$		0			0
$928$	−6.81499	−	7.78018i	−0.223713	−	0.255397i
$929$	16.7273	+	28.9725i	0.548804	+	0.950556i	0.998357	+	0.0573025i	$0.0182499\pi$
$929$	16.7273	+	28.9725i	0.548804	+	0.950556i	−0.449553	+	0.893254i	$0.648417\pi$
$930$		0			0
$931$	35.5052	+	9.95365i	1.16364	+	0.326218i
$932$	−0.673215	+	0.709088i	−0.0220519	+	0.0232270i
$933$		0			0
$934$	−19.3155	−	24.5074i	−0.632021	−	0.801908i
$935$	−20.6548	−	11.9250i	−0.675483	−	0.389991i
$936$		0			0
$937$		−	18.9751i		−	0.619890i	−0.950754	−	0.309945i	$-0.899689\pi$
$937$		−	18.9751i		−	0.619890i	0.950754	−	0.309945i	$-0.100311\pi$
$938$	9.43108	−	0.0679923i	0.307936	−	0.00222003i
$939$		0			0
$940$	−57.0921	−	13.7207i	−1.86214	−	0.447521i
$941$	3.97034	+	2.29228i	0.129429	+	0.0747261i	0.563317	−	0.826241i	$-0.309525\pi$
$941$	3.97034	+	2.29228i	0.129429	+	0.0747261i	−0.433887	+	0.900967i	$0.642858\pi$
$942$		0			0
$943$	11.0704	−	6.39148i	0.360501	−	0.208135i
$944$	3.75085	−	0.194813i	0.122080	−	0.00634063i
$945$		0			0
$946$	−4.17540	+	10.4622i	−0.135754	+	0.340154i
$947$	7.53547	+	13.0518i	0.244870	+	0.424127i	0.962095	−	0.272714i	$-0.0879214\pi$
$947$	7.53547	+	13.0518i	0.244870	+	0.424127i	−0.717225	+	0.696842i	$0.754588\pi$
$948$		0			0
$949$	24.3293	+	14.0465i	0.789761	+	0.455969i
$950$	−9.12505	−	62.9863i	−0.296056	−	2.04355i
$951$		0			0
$952$	12.3973	+	40.8052i	0.401799	+	1.32250i
$953$			1.61355i			0.0522679i	0.999658	+	0.0261339i	$0.00831964\pi$
$953$			1.61355i			0.0522679i	−0.999658	+	0.0261339i	$0.991680\pi$
$954$		0			0
$955$	−11.2576	+	19.4988i	−0.364289	+	0.630966i
$956$	0.772251	+	2.60932i	0.0249764	+	0.0843914i
$957$		0			0
$958$	15.7005	+	6.26600i	0.507261	+	0.202445i
$959$	−1.39887	+	10.1720i	−0.0451718	+	0.328473i
$960$		0			0
$961$	4.82071	+	8.34972i	0.155507	+	0.269346i
$962$	−31.6049	−	40.1003i	−1.01898	−	1.29288i
$963$		0			0
$964$	−0.634396	−	0.152462i	−0.0204325	−	0.00491047i
$965$		−	68.0957i		−	2.19208i
$966$		0			0
$967$	50.2361			1.61548			0.807742	−	0.589536i	$-0.200689\pi$
$967$	50.2361			1.61548			0.807742	+	0.589536i	$0.200689\pi$
$968$	15.8533	−	22.4153i	0.509546	−	0.720454i
$969$		0			0
$970$	−42.4692	+	33.4720i	−1.36360	+	1.07472i
$971$	19.2190	−	11.0961i	0.616767	−	0.356091i	−0.158842	−	0.987304i	$-0.550776\pi$
$971$	19.2190	−	11.0961i	0.616767	−	0.356091i	0.775609	+	0.631213i	$0.217443\pi$
$972$		0			0
$973$	7.62271	+	18.7071i	0.244373	+	0.599722i
$974$	2.97951	+	1.18911i	0.0954695	+	0.0381014i
$975$		0			0
$976$	−14.1446	−	7.21535i	−0.452756	−	0.230958i
$977$	−1.72372	−	0.995188i	−0.0551466	−	0.0318389i	0.472173	−	0.881506i	$-0.343470\pi$
$977$	−1.72372	−	0.995188i	−0.0551466	−	0.0318389i	−0.527320	+	0.849667i	$0.676803\pi$
$978$		0			0
$979$	−2.37177			−0.0758022
$980$	0.742838	+	51.5161i	0.0237291	+	1.64562i
$981$		0			0
$982$	3.06490	+	21.1557i	0.0978049	+	0.675105i
$983$	−28.8788	+	50.0195i	−0.921089	+	1.59537i	−0.123356	+	0.992362i	$0.539366\pi$
$983$	−28.8788	+	50.0195i	−0.921089	+	1.59537i	−0.797733	+	0.603011i	$0.793968\pi$
$984$		0			0
$985$	9.55568	−	5.51698i	0.304469	−	0.175785i
$986$	−13.6862	−	5.46208i	−0.435856	−	0.173948i
$987$		0			0
$988$	27.6588	+	26.2596i	0.879945	+	0.835428i
$989$	12.9051	+	22.3522i	0.410357	+	0.710760i
$990$		0			0
$991$	−28.6512	+	49.6252i	−0.910134	+	1.57640i	−0.0962601	+	0.995356i	$0.530688\pi$
$991$	−28.6512	+	49.6252i	−0.910134	+	1.57640i	−0.813874	+	0.581042i	$0.802645\pi$
$992$	−7.01481	−	35.3740i	−0.222720	−	1.12312i
$993$		0			0
$994$	−26.5357	−	45.2053i	−0.841660	−	1.43383i
$995$	5.42727			0.172056
$996$		0			0
$997$	−10.3607	+	17.9452i	−0.328125	+	0.568330i	−0.982140	−	0.188152i	$-0.939750\pi$
$997$	−10.3607	+	17.9452i	−0.328125	+	0.568330i	0.654015	+	0.756482i	$0.273083\pi$
$998$	−37.5223	−	47.6082i	−1.18775	−	1.50701i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.269.17	yes	56
3.2	odd	2	inner	504.2.ch.b.269.12	yes	56
4.3	odd	2		2016.2.cp.b.17.2		56
7.5	odd	6	inner	504.2.ch.b.341.23	yes	56
8.3	odd	2		2016.2.cp.b.17.27		56
8.5	even	2	inner	504.2.ch.b.269.6	✓	56
12.11	even	2		2016.2.cp.b.17.28		56
21.5	even	6	inner	504.2.ch.b.341.6	yes	56
24.5	odd	2	inner	504.2.ch.b.269.23	yes	56
24.11	even	2		2016.2.cp.b.17.1		56
28.19	even	6		2016.2.cp.b.593.1		56
56.5	odd	6	inner	504.2.ch.b.341.12	yes	56
56.19	even	6		2016.2.cp.b.593.28		56
84.47	odd	6		2016.2.cp.b.593.27		56
168.5	even	6	inner	504.2.ch.b.341.17	yes	56
168.131	odd	6		2016.2.cp.b.593.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.6	✓	56	8.5	even	2	inner
504.2.ch.b.269.12	yes	56	3.2	odd	2	inner
504.2.ch.b.269.17	yes	56	1.1	even	1	trivial
504.2.ch.b.269.23	yes	56	24.5	odd	2	inner
504.2.ch.b.341.6	yes	56	21.5	even	6	inner
504.2.ch.b.341.12	yes	56	56.5	odd	6	inner
504.2.ch.b.341.17	yes	56	168.5	even	6	inner
504.2.ch.b.341.23	yes	56	7.5	odd	6	inner
2016.2.cp.b.17.1		56	24.11	even	2
2016.2.cp.b.17.2		56	4.3	odd	2
2016.2.cp.b.17.27		56	8.3	odd	2
2016.2.cp.b.17.28		56	12.11	even	2
2016.2.cp.b.593.1		56	28.19	even	6
2016.2.cp.b.593.2		56	168.131	odd	6
2016.2.cp.b.593.27		56	84.47	odd	6
2016.2.cp.b.593.28		56	56.19	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.ch (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.202765 + 1.39960i) q^{2} +(-1.91777 + 0.567582i) q^{4} +(-3.18706 + 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(-1.18325 - 2.56903i) q^{8} +O(q^{10})\)	\(q+(0.202765 + 1.39960i) q^{2} +(-1.91777 + 0.567582i) q^{4} +(-3.18706 + 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(-1.18325 - 2.56903i) q^{8} +(-3.22157 - 4.08752i) q^{10} +(-0.568599 + 0.984843i) q^{11} +3.62005 q^{13} +(3.22680 - 1.89414i) q^{14} +(3.35570 - 2.17699i) q^{16} +(2.84947 - 4.93542i) q^{17} +(-2.63386 - 4.56198i) q^{19} +(5.06768 - 5.33772i) q^{20} +(-1.49368 - 0.596121i) q^{22} +(-3.19122 + 1.84245i) q^{23} +(4.27158 - 7.39859i) q^{25} +(0.734022 + 5.06664i) q^{26} +(3.30533 + 4.13217i) q^{28} -1.82838 q^{29} +(-5.52097 - 3.18753i) q^{31} +(3.72733 + 4.25523i) q^{32} +(7.48540 + 2.98739i) q^{34} +(7.69030 + 5.97171i) q^{35} +(-8.63700 + 4.98657i) q^{37} +(5.85091 - 4.61137i) q^{38} +(8.49823 + 6.01043i) q^{40} -3.46900 q^{41} -7.00429i q^{43} +(0.531465 - 2.21143i) q^{44} +(-3.22577 - 4.09286i) q^{46} +(-3.98886 - 6.90891i) q^{47} +(-5.00648 + 4.89236i) q^{49} +(11.2212 + 4.47833i) q^{50} +(-6.94244 + 2.05468i) q^{52} +(-2.84057 + 4.92001i) q^{53} -4.18501i q^{55} +(-5.11319 + 5.46400i) q^{56} +(-0.370733 - 2.55901i) q^{58} +(0.813177 + 0.469488i) q^{59} +(-1.98482 - 3.43782i) q^{61} +(3.34181 - 8.37348i) q^{62} +(-5.19985 + 6.07960i) q^{64} +(-11.5373 + 6.66109i) q^{65} +(2.18293 + 1.26031i) q^{67} +(-2.66337 + 11.0823i) q^{68} +(-6.79869 + 11.9742i) q^{70} -14.0093i q^{71} +(6.72069 + 3.88019i) q^{73} +(-8.73050 - 11.0773i) q^{74} +(7.64045 + 7.25391i) q^{76} +(2.98069 + 0.409906i) q^{77} +(7.68289 + 13.3072i) q^{79} +(-6.68906 + 13.1129i) q^{80} +(-0.703394 - 4.85523i) q^{82} -2.89078i q^{83} +20.9727i q^{85} +(9.80322 - 1.42023i) q^{86} +(3.20289 + 0.295438i) q^{88} +(1.04281 + 1.80621i) q^{89} +(-3.61419 - 8.86968i) q^{91} +(5.07429 - 5.34469i) q^{92} +(8.86092 - 6.98371i) q^{94} +(16.7886 + 9.69289i) q^{95} -10.3900i q^{97} +(-7.86250 - 6.01507i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 56 * q - 8 * q^4 - 20 * q^7	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more