LMFDB - Embedded newform 504.2.ch.b.269.6

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			269.6
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11071 - 0.875401i) q^{2} +(0.467346 + 1.94463i) q^{4} +(3.18706 - 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(1.18325 - 2.56903i) q^{8} +O(q^{10})$	\(q+(-1.11071 - 0.875401i) q^{2} +(0.467346 + 1.94463i) q^{4} +(3.18706 - 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(1.18325 - 2.56903i) q^{8} +(-5.15068 - 0.746198i) q^{10} +(0.568599 - 0.984843i) q^{11} -3.62005 q^{13} +(-1.03596 + 3.59539i) q^{14} +(-3.56318 + 1.81763i) q^{16} +(2.84947 - 4.93542i) q^{17} +(2.63386 + 4.56198i) q^{19} +(5.06768 + 5.33772i) q^{20} +(-1.49368 + 0.596121i) q^{22} +(-3.19122 + 1.84245i) q^{23} +(4.27158 - 7.39859i) q^{25} +(4.02082 + 3.16900i) q^{26} +(4.29805 - 3.08655i) q^{28} +1.82838 q^{29} +(-5.52097 - 3.18753i) q^{31} +(5.54880 + 1.10035i) q^{32} +(-7.48540 + 2.98739i) q^{34} +(-7.69030 - 5.97171i) q^{35} +(8.63700 - 4.98657i) q^{37} +(1.06811 - 7.37272i) q^{38} +(-0.956070 - 10.3649i) q^{40} -3.46900 q^{41} +7.00429i q^{43} +(2.18089 + 0.645453i) q^{44} +(5.15740 + 0.747172i) q^{46} +(-3.98886 - 6.90891i) q^{47} +(-5.00648 + 4.89236i) q^{49} +(-11.2212 + 4.47833i) q^{50} +(-1.69182 - 7.03967i) q^{52} +(2.84057 - 4.92001i) q^{53} -4.18501i q^{55} +(-7.47585 - 0.334263i) q^{56} +(-2.03080 - 1.60057i) q^{58} +(-0.813177 - 0.469488i) q^{59} +(1.98482 + 3.43782i) q^{61} +(3.34181 + 8.37348i) q^{62} +(-5.19985 - 6.07960i) q^{64} +(-11.5373 + 6.66109i) q^{65} +(-2.18293 - 1.26031i) q^{67} +(10.9293 + 3.23461i) q^{68} +(3.31404 + 13.3649i) q^{70} -14.0093i q^{71} +(6.72069 + 3.88019i) q^{73} +(-13.9584 - 2.02221i) q^{74} +(-7.64045 + 7.25391i) q^{76} +(-2.98069 - 0.409906i) q^{77} +(7.68289 + 13.3072i) q^{79} +(-8.01153 + 12.3493i) q^{80} +(3.85305 + 3.03677i) q^{82} +2.89078i q^{83} -20.9727i q^{85} +(6.13156 - 7.77972i) q^{86} +(-1.85730 - 2.62606i) q^{88} +(1.04281 + 1.80621i) q^{89} +(3.61419 + 8.86968i) q^{91} +(-5.07429 - 5.34469i) q^{92} +(-1.61761 + 11.1656i) q^{94} +(16.7886 + 9.69289i) q^{95} -10.3900i q^{97} +(9.84351 - 1.05131i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.11071	−	0.875401i	−0.785389	−	0.619002i
$2$	−1.11071	−	0.875401i	−0.785389	−	0.619002i
$3$		0			0
$3$		0			0
$4$	0.467346	+	1.94463i	0.233673	+	0.972315i
$5$	3.18706	−	1.84005i	1.42530	−	0.822896i	0.428553	−	0.903517i	$-0.359024\pi$
$5$	3.18706	−	1.84005i	1.42530	−	0.822896i	0.996745	+	0.0806207i	$0.0256903\pi$
$6$		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
$10$	−5.15068	−	0.746198i	−1.62879	−	0.235968i
$11$	0.568599	−	0.984843i	0.171439	−	0.296941i	−0.767484	−	0.641068i	$-0.778492\pi$
$11$	0.568599	−	0.984843i	0.171439	−	0.296941i	0.938923	+	0.344127i	$0.111825\pi$
$12$		0			0
$13$	−3.62005			−1.00402			−0.502011	−	0.864861i	$-0.667406\pi$
$13$	−3.62005			−1.00402			−0.502011	+	0.864861i	$0.667406\pi$
$14$	−1.03596	+	3.59539i	−0.276871	+	0.960907i
$15$		0			0
$16$	−3.56318	+	1.81763i	−0.890794	+	0.454407i
$17$	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	$0.0398603\pi$
$19$	2.63386	+	4.56198i	0.604250	+	1.04659i	−0.387920	+	0.921693i	$0.626806\pi$
$20$	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
$26$	4.02082	+	3.16900i	0.788549	+	0.621492i
$27$		0			0
$28$	4.29805	−	3.08655i	0.812255	−	0.583303i
$29$	1.82838			0.339522			0.169761	−	0.985485i	$-0.445700\pi$
$29$	1.82838			0.339522			0.169761	+	0.985485i	$0.445700\pi$
$30$		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	$0.860692\pi$
$32$	5.54880	+	1.10035i	0.980899	+	0.194516i
$33$		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	0.423623	−	0.905839i	$-0.360758\pi$
$37$	8.63700	−	4.98657i	1.41991	−	0.819788i	0.996291	+	0.0860510i	$0.0274248\pi$
$38$	1.06811	−	7.37272i	0.173271	−	1.19601i
$39$		0			0
$40$	−0.956070	−	10.3649i	−0.151168	−	1.63883i
$41$	−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	$0.179339\pi$
$43$			7.00429i			1.06814i	−0.845439	+	0.534072i	$0.820661\pi$
$44$	2.18089	+	0.645453i	0.328781	+	0.0973057i
$45$		0			0
$46$	5.15740	+	0.747172i	0.760417	+	0.110164i
$47$	−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
$52$	−1.69182	−	7.03967i	−0.234613	−	0.976226i
$53$	2.84057	−	4.92001i	0.390182	−	0.675815i	−0.602291	−	0.798276i	$-0.705745\pi$
$53$	2.84057	−	4.92001i	0.390182	−	0.675815i	0.992473	+	0.122461i	$0.0390787\pi$
$54$		0			0
$55$		−	4.18501i		−	0.564306i
$56$	−7.47585	−	0.334263i	−0.999002	−	0.0446677i
$57$		0			0
$58$	−2.03080	−	1.60057i	−0.266657	−	0.210165i
$59$	−0.813177	−	0.469488i	−0.105867	−	0.0611221i	0.446132	−	0.894967i	$-0.352801\pi$
$59$	−0.813177	−	0.469488i	−0.105867	−	0.0611221i	−0.551998	+	0.833845i	$0.686135\pi$
$60$		0			0
$61$	1.98482	+	3.43782i	0.254131	+	0.440167i	0.964659	−	0.263501i	$-0.0848774\pi$
$61$	1.98482	+	3.43782i	0.254131	+	0.440167i	−0.710528	+	0.703669i	$0.751544\pi$
$62$	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	0.360694	−	0.932684i	$-0.382540\pi$
$67$	−2.18293	−	1.26031i	−0.266687	−	0.153972i	−0.627381	+	0.778712i	$0.715873\pi$
$68$	10.9293	+	3.23461i	1.32537	+	0.392254i
$69$		0			0
$70$	3.31404	+	13.3649i	0.396103	+	1.59741i
$71$		−	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	$0.516613\pi$
$74$	−13.9584	−	2.02221i	−1.62264	−	0.235077i
$75$		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	$0.501037\pi$
$80$	−8.01153	+	12.3493i	−0.895716	+	1.38070i
$81$		0			0
$82$	3.85305	+	3.03677i	0.425498	+	0.335355i
$83$			2.89078i			0.317304i	0.987335	+	0.158652i	$0.0507148\pi$
$83$			2.89078i			0.317304i	−0.987335	+	0.158652i	$0.949285\pi$
$84$		0			0
$85$		−	20.9727i		−	2.27480i
$86$	6.13156	−	7.77972i	0.661183	−	0.838909i
$87$		0			0
$88$	−1.85730	−	2.62606i	−0.197989	−	0.279939i
$89$	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
$94$	−1.61761	+	11.1656i	−0.166843	+	1.15165i
$95$	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	$-0.176860\pi$
$98$	9.84351	−	1.05131i	0.994345	−	0.106199i
$99$		0			0
$100$	16.3838	+	4.84894i	1.63838	+	0.484894i
$101$	17.0193	+	9.82609i	1.69348	+	0.977732i	0.951669	+	0.307126i	$0.0993674\pi$
$101$	17.0193	+	9.82609i	1.69348	+	0.977732i	0.741813	+	0.670606i	$0.233966\pi$
$102$		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	0.978784	−	0.204894i	$-0.0656850\pi$
$107$	3.22682	+	5.58902i	0.311949	+	0.540311i	−0.666836	+	0.745205i	$0.732352\pi$
$108$		0			0
$109$	−6.00494	−	3.46695i	−0.575169	−	0.332074i	0.184042	−	0.982918i	$-0.441082\pi$
$109$	−6.00494	−	3.46695i	−0.575169	−	0.332074i	−0.759211	+	0.650844i	$0.774415\pi$
$110$	−3.66356	+	4.64832i	−0.349307	+	0.443200i
$111$		0			0
$112$	8.01087	+	6.91563i	0.756956	+	0.653466i
$113$			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
$116$	0.854486	+	3.55553i	0.0793371	+	0.330122i
$117$		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
$122$	0.804907	−	5.55593i	0.0728729	−	0.503010i
$123$		0			0
$124$	3.61837	−	12.2259i	0.324939	−	1.09792i
$125$		−	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	$0.516395\pi$
$128$	0.453433	+	11.3046i	0.0400782	+	0.999197i
$129$		0			0
$130$	18.6457	+	2.70128i	1.63534	+	0.236918i
$131$	10.2555	−	5.92101i	0.896026	−	0.517321i	0.0201174	−	0.999798i	$-0.493596\pi$
$131$	10.2555	−	5.92101i	0.896026	−	0.517321i	0.875909	+	0.482477i	$0.160263\pi$
$132$		0			0
$133$	8.54795	−	11.0080i	0.741201	−	0.954511i
$134$	1.32132	+	3.31078i	0.114144	+	0.286008i
$135$		0			0
$136$	−9.30763	−	13.1602i	−0.798123	−	1.12848i
$137$	−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	$-0.395040\pi$
$139$	7.63508			0.647599			0.323799	+	0.946126i	$0.395040\pi$
$140$	8.01874	−	17.7457i	0.677708	−	1.49978i
$141$		0			0
$142$	−12.2638	+	15.5603i	−1.02916	+	1.30579i
$143$	−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	0.973100	−	0.230382i	$-0.0739975\pi$
$149$	3.50369	+	6.06857i	0.287034	+	0.497157i	−0.686067	+	0.727539i	$0.740664\pi$
$150$		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	$0.900532\pi$
$152$	14.8364	−	1.36853i	1.20339	−	0.111002i
$153$		0			0
$154$	2.95185	+	3.06459i	0.237867	+	0.246951i
$155$	−23.4609			−1.88442
$156$		0			0
$157$	−6.98079	+	12.0911i	−0.557128	+	0.964974i	0.440607	+	0.897700i	$0.354763\pi$
$157$	−6.98079	+	12.0911i	−0.557128	+	0.964974i	−0.997735	+	0.0672736i	$0.978570\pi$
$158$	3.11565	−	21.5060i	0.247868	−	1.71092i
$159$		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	−0.116379	−	0.993205i	$-0.537129\pi$
$163$	8.75280	−	5.05343i	0.685572	−	0.395815i	0.801951	+	0.597390i	$0.203795\pi$
$164$	−1.62122	−	6.74593i	−0.126596	−	0.526769i
$165$		0			0
$166$	2.53059	−	3.21081i	0.196412	−	0.249207i
$167$	−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
$170$	−18.3595	+	23.2945i	−1.40811	+	1.78661i
$171$		0			0
$172$	−13.6208	+	3.27342i	−1.03857	+	0.249596i
$173$	−3.22284	+	1.86071i	−0.245028	+	0.141467i	−0.617486	−	0.786582i	$-0.711849\pi$
$173$	−3.22284	+	1.86071i	−0.245028	+	0.141467i	0.372457	+	0.928049i	$0.378515\pi$
$174$		0			0
$175$	−22.3923	−	3.07941i	−1.69270	−	0.232781i
$176$	−0.235939	+	4.54267i	−0.0177846	+	0.342417i
$177$		0			0
$178$	0.422893	−	2.91905i	0.0316972	−	0.218792i
$179$	−13.1792	+	22.8270i	−0.985057	+	1.70617i	−0.343377	+	0.939198i	$0.611571\pi$
$179$	−13.1792	+	22.8270i	−0.985057	+	1.70617i	−0.641681	+	0.766972i	$0.721763\pi$
$180$		0			0
$181$	−4.91329			−0.365202			−0.182601	−	0.983187i	$-0.558452\pi$
$181$	−4.91329			−0.365202			−0.182601	+	0.983187i	$0.558452\pi$
$182$	3.75022	−	13.0155i	0.277984	−	0.964772i
$183$		0			0
$184$	0.957318	+	10.3784i	0.0705744	+	0.765108i
$185$	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	$0.934687\pi$
$194$	−9.09539	+	11.5402i	−0.653011	+	0.828540i
$195$		0			0
$196$	−11.8536	−	7.44932i	−0.846685	−	0.532094i
$197$	2.99827			0.213618			0.106809	−	0.994280i	$-0.465937\pi$
$197$	2.99827			0.213618			0.106809	+	0.994280i	$0.465937\pi$
$198$		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	$0.683313\pi$
$200$	−13.9529	−	19.7282i	−0.986618	−	1.39499i
$201$		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
$206$	−12.6191	−	1.82818i	−0.879215	−	0.127375i
$207$		0			0
$208$	12.8989	−	6.57992i	0.894377	−	0.456235i
$209$	5.99045			0.414368
$210$		0			0
$211$			17.8952i			1.23196i	0.787764	+	0.615978i	$0.211239\pi$
$211$			17.8952i			1.23196i	−0.787764	+	0.615978i	$0.788761\pi$
$212$	10.8951	+	3.22451i	0.748280	+	0.221460i
$213$		0			0
$214$	1.30858	−	9.03253i	0.0894524	−	0.617451i
$215$	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
$220$	8.13829	−	1.95585i	0.548684	−	0.131863i
$221$	−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	$0.986550\pi$
$224$	−2.84379	−	14.6940i	−0.190009	−	0.981782i
$225$		0			0
$226$	15.6761	−	19.8898i	1.04276	−	1.32305i
$227$	0.642193	+	0.370770i	0.0426238	+	0.0246089i	0.521160	−	0.853459i	$-0.325499\pi$
$227$	0.642193	+	0.370770i	0.0426238	+	0.0246089i	−0.478537	+	0.878068i	$0.658833\pi$
$228$		0			0
$229$	−4.62136	−	8.00442i	−0.305388	−	0.528947i	0.671960	−	0.740588i	$-0.265453\pi$
$229$	−4.62136	−	8.00442i	−0.305388	−	0.528947i	−0.977348	+	0.211640i	$0.932119\pi$
$230$	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
$236$	0.532946	−	1.80074i	0.0346918	−	0.117218i
$237$		0			0
$238$	14.7928	+	15.3578i	0.958876	+	0.995499i
$239$		−	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	$0.663322\pi$
$242$	1.96820	−	13.5856i	0.126521	−	0.873317i
$243$		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
$248$	−14.7215	+	10.4119i	−0.934819	+	0.661157i
$249$		0			0
$250$	−11.4145	+	14.4827i	−0.721917	+	0.915968i
$251$		−	0.972392i		−	0.0613768i	−0.999529	−	0.0306884i	$-0.990230\pi$
$251$		−	0.972392i		−	0.0613768i	0.999529	−	0.0306884i	$-0.00976996\pi$
$252$		0			0
$253$			4.19047i			0.263453i
$254$	1.28885	+	1.01580i	0.0808694	+	0.0637370i
$255$		0			0
$256$	9.39244	−	12.9531i	0.587028	−	0.809567i
$257$	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
$262$	−16.5741	−	2.40115i	−1.02395	−	0.148344i
$263$	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
$266$	−19.1307	+	4.74374i	−1.17298	+	0.290857i
$267$		0			0
$268$	1.43066	−	4.83399i	0.0873916	−	0.295283i
$269$	−16.9445	−	9.78291i	−1.03312	−	0.596475i	−0.115246	−	0.993337i	$-0.536766\pi$
$269$	−16.9445	−	9.78291i	−1.03312	−	0.596475i	−0.917878	+	0.396862i	$0.870099\pi$
$270$		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	0.690709	−	0.723132i	$-0.257298\pi$
$277$	6.82065	+	3.93790i	0.409813	+	0.236606i	−0.280896	+	0.959738i	$0.590632\pi$
$278$	−8.48034	−	6.68375i	−0.508617	−	0.400865i
$279$		0			0
$280$	−24.4410	+	12.6906i	−1.46063	+	0.758410i
$281$		−	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	$-0.604286\pi$
$283$	11.0872	−	19.2035i	0.659063	−	1.14153i	0.980859	−	0.194721i	$-0.0623803\pi$
$284$	27.2430	−	6.54721i	1.61657	−	0.388505i
$285$		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
$290$	−9.41741	−	1.36433i	−0.553009	−	0.0801164i
$291$		0			0
$292$	−4.40465	+	14.8826i	−0.257763	+	0.870941i
$293$		−	18.6531i		−	1.08973i	−0.838525	−	0.544863i	$-0.816582\pi$
$293$		−	18.6531i		−	1.08973i	0.838525	−	0.544863i	$-0.183418\pi$
$294$		0			0
$295$	−3.45553			−0.201189
$296$	−2.59097	−	28.0891i	−0.150597	−	1.63264i
$297$		0			0
$298$	1.42086	−	9.80755i	0.0823079	−	0.568136i
$299$	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
$304$	−17.6769	−	11.4678i	−1.01384	−	0.657721i
$305$	12.6515	+	7.30436i	0.724424	+	0.418246i
$306$		0			0
$307$	26.7926			1.52913			0.764566	−	0.644546i	$-0.222953\pi$
$307$	26.7926			1.52913			0.764566	+	0.644546i	$0.222953\pi$
$308$	−0.595897	−	5.98791i	−0.0339544	−	0.341193i
$309$		0			0
$310$	26.0582	+	20.5377i	1.48001	+	1.16646i
$311$	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	$-0.965698\pi$
$317$	−10.5090	−	18.2021i	−0.590243	−	1.02233i	0.403956	−	0.914778i	$-0.367635\pi$
$318$		0			0
$319$	1.03962	−	1.80067i	0.0582073	−	0.100818i
$320$	−27.7590	−	9.80806i	−1.55178	−	0.548287i
$321$		0			0
$322$	−3.31836	−	13.3824i	−0.184925	−	0.745770i
$323$	30.0204			1.67038
$324$		0			0
$325$	−15.4633	+	26.7833i	−0.857752	+	1.48567i
$326$	−14.1456	−	2.04932i	−0.783452	−	0.113501i
$327$		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	−0.784848	−	0.619688i	$-0.787259\pi$
$331$	−11.6548	+	6.72892i	−0.640607	+	0.369855i	0.144241	+	0.989543i	$0.453926\pi$
$332$	−5.62150	+	1.35099i	−0.308520	+	0.0741454i
$333$		0			0
$334$	5.79122	+	4.56433i	0.316881	+	0.249749i
$335$	−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	$0.728129\pi$
$338$	−0.116398	−	0.0917387i	−0.00633122	−	0.00498993i
$339$		0			0
$340$	40.7841	−	9.80149i	2.21183	−	0.531560i
$341$	−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
$346$	5.20850	+	0.754575i	0.280011	+	0.0405662i
$347$	2.10821	−	3.65153i	0.113175	−	0.196025i	−0.803874	−	0.594800i	$-0.797231\pi$
$347$	2.10821	−	3.65153i	0.113175	−	0.196025i	0.917049	+	0.398775i	$0.130565\pi$
$348$		0			0
$349$	−9.32452			−0.499130			−0.249565	−	0.968358i	$-0.580288\pi$
$349$	−9.32452			−0.499130			−0.249565	+	0.968358i	$0.580288\pi$
$350$	22.1756	+	23.0226i	1.18534	+	1.23061i
$351$		0			0
$352$	4.23872	−	4.83904i	0.225924	−	0.257922i
$353$	−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
$362$	5.45723	+	4.30110i	0.286825	+	0.226061i
$363$		0			0
$364$	−15.5592	+	11.1735i	−0.815522	+	0.585649i
$365$	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	$0.497068\pi$
$368$	8.02199	−	12.3654i	0.418175	−	0.644593i
$369$		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	−0.503377	−	0.864067i	$-0.667909\pi$
$373$	−0.130569	+	0.0753842i	−0.00676062	+	0.00390325i	0.496616	+	0.867970i	$0.334576\pi$
$374$	−1.31409	+	9.07057i	−0.0679498	+	0.469028i
$375$		0			0
$376$	−22.4690	+	2.07257i	−1.15875	+	0.106884i
$377$	−6.61884			−0.340888
$378$		0			0
$379$			32.9127i			1.69061i	0.534283	+	0.845306i	$0.320582\pi$
$379$			32.9127i			1.69061i	−0.534283	+	0.845306i	$0.679418\pi$
$380$	−11.0030	+	37.1775i	−0.564443	+	1.90717i
$381$		0			0
$382$	−8.56292	−	1.24054i	−0.438117	−	0.0634716i
$383$	−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
$388$	20.2047	−	4.85571i	1.02574	−	0.246511i
$389$	−12.6509	+	21.9121i	−0.641428	+	1.11099i	0.343686	+	0.939085i	$0.388324\pi$
$389$	−12.6509	+	21.9121i	−0.641428	+	1.11099i	−0.985114	+	0.171902i	$0.945009\pi$
$390$		0			0
$391$			21.0000i			1.06202i
$392$	6.64474	+	18.6507i	0.335610	+	0.942001i
$393$		0			0
$394$	−3.33021	−	2.62469i	−0.167773	−	0.132230i
$395$	48.9717	+	28.2738i	2.46403	+	1.42261i
$396$		0			0
$397$	17.7452	+	30.7356i	0.890606	+	1.54257i	0.839151	+	0.543899i	$0.183053\pi$
$397$	17.7452	+	30.7356i	0.890606	+	1.54257i	0.0514552	+	0.998675i	$0.483614\pi$
$398$	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
$404$	−11.1542	+	37.6884i	−0.554943	+	1.87507i
$405$		0			0
$406$	−1.89412	+	6.57373i	−0.0940037	+	0.326249i
$407$		−	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	$0.715042\pi$
$410$	17.8677	+	2.58856i	0.882424	+	0.127840i
$411$		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
$416$	−20.0870	−	3.98333i	−0.984845	−	0.195299i
$417$		0			0
$418$	−6.65364	−	5.24405i	−0.325440	−	0.256495i
$419$			11.9546i			0.584022i	0.956415	+	0.292011i	$0.0943244\pi$
$419$			11.9546i			0.584022i	−0.956415	+	0.292011i	$0.905676\pi$
$420$		0			0
$421$			12.1616i			0.592720i	0.955076	+	0.296360i	$0.0957728\pi$
$421$			12.1616i			0.592720i	−0.955076	+	0.296360i	$0.904227\pi$
$422$	15.6655	−	19.8763i	0.762583	−	0.967565i
$423$		0			0
$424$	−9.27857	−	13.1191i	−0.450607	−	0.637120i
$425$	−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
$430$	5.22658	−	36.0768i	0.252048	−	1.73978i
$431$	−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	$0.994227\pi$
$434$	17.1799	−	16.5479i	0.824661	−	0.794323i
$435$		0			0
$436$	3.93556	−	13.2977i	0.188479	−	0.636842i
$437$	−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	0.771994	−	0.635630i	$-0.219260\pi$
$443$	−3.46180	−	5.99600i	−0.164475	−	0.284879i	−0.936469	+	0.350751i	$0.885926\pi$
$444$		0			0
$445$	6.64703	+	3.83766i	0.315099	+	0.181923i
$446$	1.10440	−	1.40127i	0.0522950	−	0.0663519i
$447$		0			0
$448$	−9.70450	+	18.8102i	−0.458495	+	0.888697i
$449$		−	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
$452$	−34.8231	+	8.36890i	−1.63794	+	0.393640i
$453$		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	$0.861893\pi$
$458$	−1.87410	+	12.9361i	−0.0875711	+	0.604465i
$459$		0			0
$460$	−26.0066	−	7.69688i	−1.21256	−	0.358869i
$461$		−	15.4863i		−	0.721267i	−0.932708	−	0.360634i	$-0.882561\pi$
$461$		−	15.4863i		−	0.721267i	0.932708	−	0.360634i	$-0.117439\pi$
$462$		0			0
$463$	−6.51872			−0.302950			−0.151475	−	0.988461i	$-0.548402\pi$
$463$	−6.51872			−0.302950			−0.151475	+	0.988461i	$0.548402\pi$
$464$	−6.51484	+	3.32332i	−0.302444	+	0.154281i
$465$		0			0
$466$	−0.684241	−	0.0991285i	−0.0316969	−	0.00459204i
$467$	19.1086	−	11.0323i	0.884240	−	0.510516i	0.0121856	−	0.999926i	$-0.496121\pi$
$467$	19.1086	−	11.0323i	0.884240	−	0.510516i	0.872054	+	0.489410i	$0.162788\pi$
$468$		0			0
$469$	−0.908568	+	6.60677i	−0.0419538	+	0.305072i
$470$	15.3899	+	38.5621i	0.709885	+	1.77873i
$471$		0			0
$472$	−2.16832	+	1.53356i	−0.0998050	+	0.0705877i
$473$	6.89812	+	3.98263i	0.317176	+	0.183122i
$474$		0			0
$475$	45.0030			2.06488
$476$	−2.98627	−	30.0077i	−0.136875	−	1.37540i
$477$		0			0
$478$	−1.19107	+	1.51123i	−0.0544783	+	0.0691220i
$479$	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	$0.150300\pi$
$488$	11.1804	−	1.03129i	0.506113	−	0.0466844i
$489$		0			0
$490$	29.4374	−	21.4632i	1.32985	−	0.969607i
$491$	−15.1155			−0.682153			−0.341077	−	0.940036i	$-0.610792\pi$
$491$	−15.1155			−0.682153			−0.341077	+	0.940036i	$0.610792\pi$
$492$		0			0
$493$	5.20991	−	9.02383i	0.234643	−	0.406413i
$494$	−3.86663	+	26.6896i	−0.173968	+	1.20082i
$495$		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	$-0.257676\pi$
$499$	37.1204	−	21.4315i	1.66174	−	0.959404i	0.971886	−	0.235452i	$-0.0756571\pi$
$500$	25.3564	−	6.09381i	1.13397	−	0.272523i
$501$		0			0
$502$	−0.851233	+	1.08004i	−0.0379924	+	0.0482047i
$503$	−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
$506$	3.66834	−	4.65439i	0.163078	−	0.206913i
$507$		0			0
$508$	−0.542300	−	2.25652i	−0.0240607	−	0.100117i
$509$	−9.81718	+	5.66795i	−0.435139	+	0.251227i	−0.701533	−	0.712637i	$-0.747501\pi$
$509$	−9.81718	+	5.66795i	−0.435139	+	0.251227i	0.266395	+	0.963864i	$0.414168\pi$
$510$		0			0
$511$	2.79725	−	20.3406i	0.123743	−	0.899815i
$512$	−21.7714	+	6.16493i	−0.962169	+	0.272454i
$513$		0			0
$514$	2.87143	−	19.8202i	0.126653	−	0.874233i
$515$	16.5903	−	28.7352i	0.731056	−	1.26623i
$516$		0			0
$517$	−9.07225			−0.398997
$518$	8.98111	+	36.2192i	0.394607	+	1.59138i
$519$		0			0
$520$	3.46103	+	37.5215i	0.151776	+	1.64543i
$521$	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	0.588408	−	0.808564i	$-0.299755\pi$
$523$	−9.28564	−	16.0832i	−0.406033	−	0.703269i	−0.994441	+	0.105295i	$0.966421\pi$
$524$	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
$530$	−18.3022	+	23.2218i	−0.794995	+	1.00869i
$531$		0			0
$532$	25.4013	+	11.4781i	1.10128	+	0.497638i
$533$	12.5580			0.543947
$534$		0			0
$535$	20.5682	+	11.8750i	0.889239	+	0.513402i
$536$	−5.82073	+	4.11675i	−0.251417	+	0.177816i
$537$		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	−0.517004	−	0.855983i	$-0.672953\pi$
$541$	−0.795518	+	0.459292i	−0.0342020	+	0.0197465i	0.482802	+	0.875730i	$0.339619\pi$
$542$	−28.1618	−	4.07990i	−1.20965	−	0.175247i
$543$		0			0
$544$	21.2418	−	24.2503i	0.910736	−	1.03972i
$545$	−25.5175			−1.09305
$546$		0			0
$547$		−	28.4217i		−	1.21523i	−0.794233	−	0.607613i	$-0.792127\pi$
$547$		−	28.4217i		−	1.21523i	0.794233	−	0.607613i	$-0.207873\pi$
$548$	2.20270	−	7.44260i	0.0940949	−	0.317932i
$549$		0			0
$550$	−1.96992	+	13.5975i	−0.0839977	+	0.579800i
$551$	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
$556$	3.56822	+	14.8474i	0.151326	+	0.629670i
$557$	−12.7308	+	22.0504i	−0.539420	+	0.934304i	0.459515	+	0.888170i	$0.348023\pi$
$557$	−12.7308	+	22.0504i	−0.539420	+	0.934304i	−0.998935	+	0.0461335i	$0.985310\pi$
$558$		0			0
$559$		−	25.3559i		−	1.07244i
$560$	38.2563	+	7.30014i	1.61662	+	0.308487i
$561$		0			0
$562$	−17.1886	+	21.8089i	−0.725057	+	0.919952i
$563$	−15.6292	−	9.02355i	−0.658694	−	0.380297i	0.133085	−	0.991105i	$-0.457512\pi$
$563$	−15.6292	−	9.02355i	−0.658694	−	0.380297i	−0.791779	+	0.610807i	$0.790845\pi$
$564$		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	$-0.962848\pi$
$571$	−38.0094	−	21.9447i	−1.59064	−	0.918359i	−0.597447	−	0.801908i	$-0.703818\pi$
$572$	−7.89493	−	2.33658i	−0.330104	−	0.0976972i
$573$		0			0
$574$	3.59373	−	12.4724i	0.150000	−	0.520588i
$575$			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	$0.878685\pi$
$578$	−3.13837	+	21.6628i	−0.130539	+	0.901055i
$579$		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
$584$	17.9206	−	12.6744i	0.741558	−	0.524472i
$585$		0			0
$586$	−16.3290	+	20.7182i	−0.674543	+	0.855859i
$587$		−	39.8767i		−	1.64589i	−0.568122	−	0.822944i	$-0.692330\pi$
$587$		−	39.8767i		−	1.64589i	0.568122	−	0.822944i	$-0.307670\pi$
$588$		0			0
$589$		−	33.5821i		−	1.38373i
$590$	3.83808	+	3.02497i	0.158011	+	0.124536i
$591$		0			0
$592$	−21.7114	+	33.4669i	−0.892333	+	1.37548i
$593$	−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
$598$	−18.6701	−	2.70480i	−0.763476	−	0.110608i
$599$	−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	$0.835158\pi$
$602$	−25.1831	−	7.25613i	−1.02639	−	0.295738i
$603$		0			0
$604$	−34.9731	−	10.3506i	−1.42304	−	0.421160i
$605$	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	0.519489	−	0.854477i	$-0.326122\pi$
$613$	0.971418	+	0.560849i	0.0392352	+	0.0226525i	−0.480254	+	0.877129i	$0.659456\pi$
$614$	−29.7587	−	23.4542i	−1.20096	−	0.946536i
$615$		0			0
$616$	−4.57996	+	7.17247i	−0.184532	+	0.288987i
$617$		−	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	$-0.600829\pi$
$619$	16.5995	−	28.7513i	0.667192	−	1.15561i	0.978686	−	0.205362i	$-0.0658373\pi$
$620$	−10.9643	−	45.6228i	−0.440339	−	1.83225i
$621$		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
$626$	−18.1687	−	2.63216i	−0.726166	−	0.105202i
$627$		0			0
$628$	−26.7751	−	7.92434i	−1.06844	−	0.316216i
$629$		−	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	$0.600097\pi$
$632$	43.2773	−	3.99194i	1.72148	−	0.158791i
$633$		0			0
$634$	−4.26172	+	29.4168i	−0.169254	+	1.16829i
$635$	−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
$640$	22.2462	+	35.1942i	0.879358	+	1.39117i
$641$	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	$-0.480030\pi$
$643$	3.17969			0.125395			0.0626974	+	0.998033i	$0.480030\pi$
$644$	−8.02921	+	17.7688i	−0.316395	+	0.700189i
$645$		0			0
$646$	−33.3439	−	26.2799i	−1.31190	−	1.03397i
$647$	−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	$0.169528\pi$
$653$	22.2442	+	38.5282i	0.870485	+	1.50772i	0.00898848	+	0.999960i	$0.497139\pi$
$654$		0			0
$655$	21.7899	−	37.7413i	0.851403	−	1.47467i
$656$	12.3607	−	6.30537i	0.482603	−	0.246183i
$657$		0			0
$658$	28.9725	−	7.18417i	1.12946	−	0.280068i
$659$	−24.7165			−0.962818			−0.481409	−	0.876496i	$-0.659875\pi$
$659$	−24.7165			−0.962818			−0.481409	+	0.876496i	$0.659875\pi$
$660$		0			0
$661$	−9.39973	+	16.2808i	−0.365607	+	0.633250i	−0.988873	−	0.148760i	$-0.952472\pi$
$661$	−9.39973	+	16.2808i	−0.365607	+	0.633250i	0.623266	+	0.782010i	$0.285805\pi$
$662$	18.8356	+	2.72878i	0.732067	+	0.106057i
$663$		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
$668$	−2.43673	−	10.1393i	−0.0942801	−	0.392300i
$669$		0			0
$670$	10.3031	+	8.12037i	0.398044	+	0.313717i
$671$	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	$0.355770\pi$
$674$	26.7879	+	21.1128i	1.03183	+	0.813234i
$675$		0			0
$676$	0.0489761	+	0.203790i	0.00188369	+	0.00783807i
$677$	−31.0283	+	17.9142i	−1.19251	+	0.688498i	−0.958876	−	0.283825i	$-0.908396\pi$
$677$	−31.0283	+	17.9142i	−1.19251	+	0.688498i	−0.233638	+	0.972324i	$0.575063\pi$
$678$		0			0
$679$	−25.4570	+	10.3731i	−0.976950	+	0.398084i
$680$	−53.8794	−	24.8158i	−2.06618	−	0.951644i
$681$		0			0
$682$	10.1467	+	1.46999i	0.388538	+	0.0562889i
$683$	5.91001	−	10.2364i	0.226140	−	0.391686i	−0.730521	−	0.682891i	$-0.760723\pi$
$683$	5.91001	−	10.2364i	0.226140	−	0.391686i	0.956661	+	0.291204i	$0.0940559\pi$
$684$		0			0
$685$	−14.2820			−0.545686
$686$	−12.4034	−	23.0685i	−0.473566	−	0.880759i
$687$		0			0
$688$	−12.7312	−	24.9575i	−0.485373	−	0.951496i
$689$	−10.2830	+	17.8107i	−0.391752	+	0.678534i
$690$		0			0
$691$	16.8555	+	29.1945i	0.641213	+	1.11061i	0.985162	+	0.171625i	$0.0549016\pi$
$691$	16.8555	+	29.1945i	0.641213	+	1.11061i	−0.343950	+	0.938988i	$0.611765\pi$
$692$	−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
$698$	10.3568	+	8.16269i	0.392011	+	0.308962i
$699$		0			0
$700$	−4.47665	−	44.9839i	−0.169202	−	1.70023i
$701$	7.35428			0.277767			0.138884	−	0.990309i	$-0.455649\pi$
$701$	7.35428			0.277767			0.138884	+	0.990309i	$0.455649\pi$
$702$		0			0
$703$	45.4973	+	26.2679i	1.71596	+	0.990713i
$704$	−8.94408	+	1.66418i	−0.337093	+	0.0627213i
$705$		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	−0.962523	−	0.271202i	$-0.912579\pi$
$709$	−32.1899	+	18.5848i	−1.20892	+	0.697968i	−0.246394	+	0.969170i	$0.579246\pi$
$710$	−10.4537	+	72.1577i	−0.392322	+	2.70803i
$711$		0			0
$712$	5.87411	−	0.541834i	0.220142	−	0.0203061i
$713$	23.4915			0.879764
$714$		0			0
$715$			15.1500i			0.566576i
$716$	−50.5493	−	14.9605i	−1.88912	−	0.559101i
$717$		0			0
$718$	15.3841	+	2.22876i	0.574131	+	0.0831764i
$719$	−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
$724$	−2.29620	−	9.55453i	−0.0853377	−	0.355091i
$725$	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	$-0.147739\pi$
$728$	27.0630	+	1.21005i	1.00302	+	0.0448474i
$729$		0			0
$730$	−31.7207	−	25.0006i	−1.17404	−	0.925313i
$731$	34.5691	+	19.9585i	1.27858	+	0.738191i
$732$		0			0
$733$	0.741275	+	1.28393i	0.0273796	+	0.0474229i	0.879391	−	0.476101i	$-0.157950\pi$
$733$	0.741275	+	1.28393i	0.0273796	+	0.0474229i	−0.852011	+	0.523524i	$0.824617\pi$
$734$	−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	0.824854	−	0.565346i	$-0.191257\pi$
$739$	20.3252	+	11.7348i	0.747676	+	0.431671i	−0.0771774	+	0.997017i	$0.524591\pi$
$740$	70.3865	+	20.8315i	2.58746	+	0.765781i
$741$		0			0
$742$	14.7466	+	15.3098i	0.541366	+	0.562042i
$743$			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
$746$	0.211016	+	0.0305706i	0.00772584	+	0.00111927i
$747$		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	$-0.367210\pi$
$752$	26.7708	+	17.3674i	0.976232	+	0.633323i
$753$		0			0
$754$	7.35160	+	5.79414i	0.267729	+	0.211010i
$755$			67.1115i			2.44244i
$756$		0			0
$757$		−	7.01154i		−	0.254839i	−0.991849	−	0.127419i	$-0.959331\pi$
$757$		−	7.01154i		−	0.254839i	0.991849	−	0.127419i	$-0.0406694\pi$
$758$	28.8118	−	36.5564i	1.04649	−	1.32779i
$759$		0			0
$760$	44.7664	−	31.6613i	1.62385	−	1.14848i
$761$	−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
$766$	−3.40173	+	23.4807i	−0.122909	+	0.848391i
$767$	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	$-0.261978\pi$
$770$	15.0467	+	4.33548i	0.542246	+	0.156240i
$771$		0			0
$772$	−35.4860	−	10.5024i	−1.27717	−	0.377990i
$773$	−35.3357	−	20.4011i	−1.27094	−	0.733777i	−0.295774	−	0.955258i	$-0.595577\pi$
$773$	−35.3357	−	20.4011i	−1.27094	−	0.733777i	−0.975165	+	0.221481i	$0.928911\pi$
$774$		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
$782$	18.3835	−	23.3249i	0.657391	−	0.834097i
$783$		0			0
$784$	8.94645	−	26.5323i	0.319516	−	0.947581i
$785$			51.3801i			1.83383i
$786$		0			0
$787$	−15.9930	+	27.7007i	−0.570089	+	0.987423i	0.426467	+	0.904503i	$0.359758\pi$
$787$	−15.9930	+	27.7007i	−0.570089	+	0.987423i	−0.996556	+	0.0829199i	$0.973575\pi$
$788$	1.40123	+	5.83053i	0.0499168	+	0.207704i
$789$		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
$794$	7.19622	−	49.6724i	0.255384	−	1.76281i
$795$		0			0
$796$	0.837048	−	2.82826i	0.0296684	−	0.100245i
$797$			27.1417i			0.961410i	0.876883	+	0.480705i	$0.159619\pi$
$797$			27.1417i			0.961410i	−0.876883	+	0.480705i	$0.840381\pi$
$798$		0			0
$799$	−45.4645			−1.60842
$800$	31.8432	−	36.3531i	1.12583	−	1.28528i
$801$		0			0
$802$	−4.81604	−	0.697717i	−0.170060	−	0.0246373i
$803$	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
$808$	45.3816	−	32.0964i	1.59652	−	1.12915i
$809$	−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	$-0.431939\pi$
$811$	12.0857			0.424388			0.212194	+	0.977228i	$0.431939\pi$
$812$	7.85847	−	5.64339i	0.275778	−	0.198044i
$813$		0			0
$814$	−9.92831	+	12.5970i	−0.347987	+	0.441526i
$815$	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	$0.0122734\pi$
$821$	15.2725	+	26.4527i	0.533012	+	0.923204i	−0.466245	+	0.884656i	$0.654393\pi$
$822$		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	$0.0482180\pi$
$824$	−2.34236	−	25.3939i	−0.0816000	−	0.884639i
$825$		0			0
$826$	2.53041	−	2.43732i	0.0880441	−	0.0848051i
$827$	−50.1969			−1.74552			−0.872759	−	0.488151i	$-0.837672\pi$
$827$	−50.1969			−1.74552			−0.872759	+	0.488151i	$0.837672\pi$
$828$		0			0
$829$	9.59915	−	16.6262i	0.333392	−	0.577453i	−0.649782	−	0.760120i	$-0.725140\pi$
$829$	9.59915	−	16.6262i	0.333392	−	0.577453i	0.983175	+	0.182668i	$0.0584733\pi$
$830$	2.15709	−	14.8895i	0.0748738	−	0.516821i
$831$		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
$836$	2.79961	+	11.6492i	0.0968266	+	0.402896i
$837$		0			0
$838$	10.4651	−	13.2781i	0.361511	−	0.458685i
$839$	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
$842$	10.6463	−	13.5080i	0.366895	−	0.465516i
$843$		0			0
$844$	−34.7995	+	8.36324i	−1.19785	+	0.287875i
$845$	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
$850$	−9.87202	+	68.1423i	−0.338607	+	2.33726i
$851$	−18.3751	+	31.8265i	−0.629889	+	1.09100i
$852$		0			0
$853$	−52.3052			−1.79090			−0.895449	−	0.445165i	$-0.853145\pi$
$853$	−52.3052			−1.79090			−0.895449	+	0.445165i	$0.853145\pi$
$854$	−14.4165	+	3.57478i	−0.493321	+	0.122327i
$855$		0			0
$856$	18.1765	−	1.67662i	0.621260	−	0.0573057i
$857$	−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	$0.137733\pi$
$859$	23.9471	+	41.4775i	0.817063	+	1.41520i	−0.0907734	+	0.995872i	$0.528934\pi$
$860$	−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
$866$	0.660720	−	0.838321i	0.0224522	−	0.0284873i
$867$		0			0
$868$	−33.5679	+	3.34056i	−1.13937	+	0.113386i
$869$	17.4739			0.592763
$870$		0			0
$871$	7.90232	+	4.56241i	0.267760	+	0.154591i
$872$	−16.0120	+	11.3246i	−0.542236	+	0.383500i
$873$		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	−0.103715	−	0.994607i	$-0.533073\pi$
$877$	20.9012	−	12.0673i	0.705783	−	0.407484i	0.809498	+	0.587123i	$0.199740\pi$
$878$	−26.3378	−	3.81565i	−0.888857	−	0.128772i
$879$		0			0
$880$	7.60679	+	14.9119i	0.256425	+	0.502681i
$881$	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	$0.0547932\pi$
$883$			10.1798i			0.342578i	−0.985221	+	0.171289i	$0.945207\pi$
$884$	−39.5645	−	11.7095i	−1.33070	−	0.393832i
$885$		0			0
$886$	−1.40386	+	9.69027i	−0.0471638	+	0.325551i
$887$	−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
$892$	−2.45334	+	0.589602i	−0.0821440	+	0.0197414i
$893$	21.0122	−	36.3942i	0.703147	−	1.21789i
$894$		0			0
$895$			97.0014i			3.24240i
$896$	27.2453	−	12.3973i	0.910202	−	0.414164i
$897$		0			0
$898$	−0.236677	+	0.300296i	−0.00789803	+	0.0100210i
$899$	−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	−0.139248	−	0.990258i	$-0.544468\pi$
$907$	−32.1180	−	18.5433i	−1.06646	−	0.615721i	−0.927212	+	0.374537i	$0.877802\pi$
$908$	−0.420885	+	1.42211i	−0.0139676	+	0.0471942i
$909$		0			0
$910$	−11.9970	−	48.3818i	−0.397697	−	1.60384i
$911$		−	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
$914$	−0.776798	+	5.36190i	−0.0256942	+	0.177356i
$915$		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	$0.692028\pi$
$920$	22.1479	+	31.3152i	0.730194	+	1.03243i
$921$		0			0
$922$	−13.5567	+	17.2007i	−0.446466	+	0.566476i
$923$			50.7146i			1.66929i
$924$		0			0
$925$		−	85.2022i		−	2.80143i
$926$	7.24039	+	5.70649i	0.237934	+	0.187527i
$927$		0			0
$928$	10.1453	+	2.01186i	0.333037	+	0.0660426i
$929$	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
$934$	−30.8818	−	4.47396i	−1.01048	−	0.146392i
$935$	−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	$-0.100311\pi$
$938$	6.79273	−	6.54284i	0.221791	−	0.213631i
$939$		0			0
$940$	16.6635	−	56.3036i	0.543505	−	1.83642i
$941$	−3.97034	−	2.29228i	−0.129429	−	0.0747261i	0.433887	−	0.900967i	$-0.357142\pi$
$941$	−3.97034	−	2.29228i	−0.129429	−	0.0747261i	−0.563317	+	0.826241i	$0.690475\pi$
$942$		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	0.717225	−	0.696842i	$-0.245412\pi$
$947$	−7.53547	−	13.0518i	−0.244870	−	0.424127i	−0.962095	+	0.272714i	$0.912079\pi$
$948$		0			0
$949$	−24.3293	−	14.0465i	−0.789761	−	0.455969i
$950$	−49.9852	−	39.3957i	−1.62173	−	1.27816i
$951$		0			0
$952$	−22.9519	+	35.9440i	−0.743875	+	1.16495i
$953$			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
$956$	2.64586	−	0.635870i	0.0855733	−	0.0205655i
$957$		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
$962$	50.5303	+	7.32051i	1.62916	+	0.236023i
$963$		0			0
$964$	−0.185162	+	0.625634i	−0.00596367	+	0.0201503i
$965$			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	$0.200689\pi$
$968$	27.3389	−	2.52177i	0.878704	−	0.0810526i
$969$		0			0
$970$	−7.75297	+	53.5154i	−0.248933	+	1.71828i
$971$	−19.2190	+	11.0961i	−0.616767	+	0.356091i	−0.775609	−	0.631213i	$-0.782557\pi$
$971$	−19.2190	+	11.0961i	−0.616767	+	0.356091i	0.158842	+	0.987304i	$0.449224\pi$
$972$		0			0
$973$	−7.62271	−	18.7071i	−0.244373	−	0.599722i
$974$	−2.97951	+	1.18911i	−0.0954695	+	0.0381014i
$975$		0			0
$976$	−13.3210	−	8.64187i	−0.426393	−	0.276619i
$977$	−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
$980$	−51.4853	−	1.93023i	−1.64464	−	0.0616588i
$981$		0			0
$982$	16.7889	+	13.2321i	0.535756	+	0.422254i
$983$	−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	$0.802645\pi$
$992$	−27.1274	−	23.7620i	−0.861294	−	0.754444i
$993$		0			0
$994$	50.3690	+	14.5131i	1.59761	+	0.460326i
$995$	−5.42727			−0.172056
$996$		0			0
$997$	10.3607	−	17.9452i	0.328125	−	0.568330i	−0.654015	−	0.756482i	$-0.726917\pi$
$997$	10.3607	−	17.9452i	0.328125	−	0.568330i	0.982140	+	0.188152i	$0.0602499\pi$
$998$	−59.9910	−	8.69112i	−1.89898	−	0.275113i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.11071 - 0.875401i) q^{2} +(0.467346 + 1.94463i) q^{4} +(3.18706 - 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(1.18325 - 2.56903i) q^{8} +O(q^{10})\)	\(q+(-1.11071 - 0.875401i) q^{2} +(0.467346 + 1.94463i) q^{4} +(3.18706 - 1.84005i) q^{5} +(-0.998380 - 2.45015i) q^{7} +(1.18325 - 2.56903i) q^{8} +(-5.15068 - 0.746198i) q^{10} +(0.568599 - 0.984843i) q^{11} -3.62005 q^{13} +(-1.03596 + 3.59539i) q^{14} +(-3.56318 + 1.81763i) q^{16} +(2.84947 - 4.93542i) q^{17} +(2.63386 + 4.56198i) q^{19} +(5.06768 + 5.33772i) q^{20} +(-1.49368 + 0.596121i) q^{22} +(-3.19122 + 1.84245i) q^{23} +(4.27158 - 7.39859i) q^{25} +(4.02082 + 3.16900i) q^{26} +(4.29805 - 3.08655i) q^{28} +1.82838 q^{29} +(-5.52097 - 3.18753i) q^{31} +(5.54880 + 1.10035i) q^{32} +(-7.48540 + 2.98739i) q^{34} +(-7.69030 - 5.97171i) q^{35} +(8.63700 - 4.98657i) q^{37} +(1.06811 - 7.37272i) q^{38} +(-0.956070 - 10.3649i) q^{40} -3.46900 q^{41} +7.00429i q^{43} +(2.18089 + 0.645453i) q^{44} +(5.15740 + 0.747172i) q^{46} +(-3.98886 - 6.90891i) q^{47} +(-5.00648 + 4.89236i) q^{49} +(-11.2212 + 4.47833i) q^{50} +(-1.69182 - 7.03967i) q^{52} +(2.84057 - 4.92001i) q^{53} -4.18501i q^{55} +(-7.47585 - 0.334263i) q^{56} +(-2.03080 - 1.60057i) q^{58} +(-0.813177 - 0.469488i) q^{59} +(1.98482 + 3.43782i) q^{61} +(3.34181 + 8.37348i) q^{62} +(-5.19985 - 6.07960i) q^{64} +(-11.5373 + 6.66109i) q^{65} +(-2.18293 - 1.26031i) q^{67} +(10.9293 + 3.23461i) q^{68} +(3.31404 + 13.3649i) q^{70} -14.0093i q^{71} +(6.72069 + 3.88019i) q^{73} +(-13.9584 - 2.02221i) q^{74} +(-7.64045 + 7.25391i) q^{76} +(-2.98069 - 0.409906i) q^{77} +(7.68289 + 13.3072i) q^{79} +(-8.01153 + 12.3493i) q^{80} +(3.85305 + 3.03677i) q^{82} +2.89078i q^{83} -20.9727i q^{85} +(6.13156 - 7.77972i) q^{86} +(-1.85730 - 2.62606i) q^{88} +(1.04281 + 1.80621i) q^{89} +(3.61419 + 8.86968i) q^{91} +(-5.07429 - 5.34469i) q^{92} +(-1.61761 + 11.1656i) q^{94} +(16.7886 + 9.69289i) q^{95} -10.3900i q^{97} +(9.84351 - 1.05131i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 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