LMFDB - Embedded newform 504.2.bu.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(41,504)]

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, 0, 5, 3]))

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

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

chi := DirichletCharacter("504.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bu (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	504.41
Dual form			504.2.bu.a.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69695 - 0.346907i) q^{3} +(-1.79123 + 3.10250i) q^{5} +(1.83349 - 1.90743i) q^{7} +(2.75931 + 1.17737i) q^{9} +O(q^{10})$	\(q+(-1.69695 - 0.346907i) q^{3} +(-1.79123 + 3.10250i) q^{5} +(1.83349 - 1.90743i) q^{7} +(2.75931 + 1.17737i) q^{9} +(-0.200372 + 0.115685i) q^{11} +(-1.16716 - 0.673862i) q^{13} +(4.11592 - 4.64342i) q^{15} -7.94895 q^{17} +3.06168i q^{19} +(-3.77306 + 2.60078i) q^{21} +(-4.87566 - 2.81497i) q^{23} +(-3.91701 - 6.78446i) q^{25} +(-4.27399 - 2.95517i) q^{27} +(-2.33703 + 1.34928i) q^{29} +(-1.85401 - 1.07041i) q^{31} +(0.380154 - 0.126802i) q^{33} +(2.63361 + 9.10507i) q^{35} -7.27483 q^{37} +(1.74685 + 1.54841i) q^{39} +(0.813774 - 1.40950i) q^{41} +(-0.927618 - 1.60668i) q^{43} +(-8.59535 + 6.45183i) q^{45} +(0.0396273 + 0.0686364i) q^{47} +(-0.276612 - 6.99453i) q^{49} +(13.4890 + 2.75754i) q^{51} +11.6845i q^{53} -0.828872i q^{55} +(1.06212 - 5.19553i) q^{57} +(6.48614 - 11.2343i) q^{59} +(-0.729056 + 0.420921i) q^{61} +(7.30493 - 3.10451i) q^{63} +(4.18131 - 2.41408i) q^{65} +(-5.05736 + 8.75961i) q^{67} +(7.29725 + 6.46827i) q^{69} +7.47959i q^{71} +7.97751i q^{73} +(4.29342 + 12.8718i) q^{75} +(-0.146719 + 0.594303i) q^{77} +(-3.30854 - 5.73056i) q^{79} +(6.22760 + 6.49746i) q^{81} +(-6.41792 - 11.1162i) q^{83} +(14.2384 - 24.6616i) q^{85} +(4.43390 - 1.47894i) q^{87} +3.56067 q^{89} +(-3.42533 + 0.990766i) q^{91} +(2.77484 + 2.45961i) q^{93} +(-9.49885 - 5.48417i) q^{95} +(13.1326 - 7.58210i) q^{97} +(-0.689092 + 0.0832985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91} + 16 q^{93} - 108 q^{95} + 44 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.69695	−	0.346907i	−0.979737	−	0.200287i
$3$	−1.69695	−	0.346907i	−0.979737	−	0.200287i
$4$		0			0
$5$	−1.79123	+	3.10250i	−0.801063	+	1.38748i	0.117855	+	0.993031i	$0.462398\pi$
$5$	−1.79123	+	3.10250i	−0.801063	+	1.38748i	−0.918917	+	0.394450i	$0.870935\pi$
$6$		0			0
$7$	1.83349	−	1.90743i	0.692995	−	0.720942i
$7$	1.83349	−	1.90743i	0.692995	−	0.720942i
$8$		0			0
$9$	2.75931	+	1.17737i	0.919771	+	0.392457i
$10$		0			0
$11$	−0.200372	+	0.115685i	−0.0604144	+	0.0348803i	−0.529903	−	0.848058i	$-0.677772\pi$
$11$	−0.200372	+	0.115685i	−0.0604144	+	0.0348803i	0.469489	+	0.882939i	$0.344438\pi$
$12$		0			0
$13$	−1.16716	−	0.673862i	−0.323713	−	0.186896i	0.329334	−	0.944214i	$-0.393176\pi$
$13$	−1.16716	−	0.673862i	−0.323713	−	0.186896i	−0.653046	+	0.757318i	$0.726509\pi$
$14$		0			0
$15$	4.11592	−	4.64342i	1.06272	−	1.19892i
$16$		0			0
$17$	−7.94895			−1.92790			−0.963952	−	0.266075i	$-0.914273\pi$
$17$	−7.94895			−1.92790			−0.963952	+	0.266075i	$0.914273\pi$
$18$		0			0
$19$			3.06168i			0.702397i	0.936301	+	0.351198i	$0.114226\pi$
$19$			3.06168i			0.702397i	−0.936301	+	0.351198i	$0.885774\pi$
$20$		0			0
$21$	−3.77306	+	2.60078i	−0.823348	+	0.567537i
$22$		0			0
$23$	−4.87566	−	2.81497i	−1.01665	−	0.586961i	−0.103516	−	0.994628i	$-0.533009\pi$
$23$	−4.87566	−	2.81497i	−1.01665	−	0.586961i	−0.913131	+	0.407667i	$0.866342\pi$
$24$		0			0
$25$	−3.91701	−	6.78446i	−0.783402	−	1.35689i
$26$		0			0
$27$	−4.27399	−	2.95517i	−0.822530	−	0.568722i
$28$		0			0
$29$	−2.33703	+	1.34928i	−0.433975	+	0.250555i	−0.701038	−	0.713123i	$-0.747280\pi$
$29$	−2.33703	+	1.34928i	−0.433975	+	0.250555i	0.267064	+	0.963679i	$0.413947\pi$
$30$		0			0
$31$	−1.85401	−	1.07041i	−0.332990	−	0.192252i	0.324178	−	0.945996i	$-0.394912\pi$
$31$	−1.85401	−	1.07041i	−0.332990	−	0.192252i	−0.657168	+	0.753744i	$0.728246\pi$
$32$		0			0
$33$	0.380154	−	0.126802i	0.0661763	−	0.0220733i
$34$		0			0
$35$	2.63361	+	9.10507i	0.445162	+	1.53904i
$36$		0			0
$37$	−7.27483			−1.19597			−0.597987	−	0.801506i	$-0.704033\pi$
$37$	−7.27483			−1.19597			−0.597987	+	0.801506i	$0.704033\pi$
$38$		0			0
$39$	1.74685	+	1.54841i	0.279721	+	0.247944i
$40$		0			0
$41$	0.813774	−	1.40950i	0.127090	−	0.220127i	−0.795458	−	0.606009i	$-0.792770\pi$
$41$	0.813774	−	1.40950i	0.127090	−	0.220127i	0.922548	+	0.385882i	$0.126103\pi$
$42$		0			0
$43$	−0.927618	−	1.60668i	−0.141460	−	0.245017i	0.786586	−	0.617480i	$-0.211846\pi$
$43$	−0.927618	−	1.60668i	−0.141460	−	0.245017i	−0.928047	+	0.372464i	$0.878513\pi$
$44$		0			0
$45$	−8.59535	+	6.45183i	−1.28132	+	0.961782i
$46$		0			0
$47$	0.0396273	+	0.0686364i	0.00578023	+	0.0100117i	0.868901	−	0.494986i	$-0.164827\pi$
$47$	0.0396273	+	0.0686364i	0.00578023	+	0.0100117i	−0.863121	+	0.504997i	$0.831493\pi$
$48$		0			0
$49$	−0.276612	−	6.99453i	−0.0395160	−	0.999219i
$50$		0			0
$51$	13.4890	+	2.75754i	1.88884	+	0.386134i
$52$		0			0
$53$			11.6845i			1.60498i	0.596663	+	0.802492i	$0.296493\pi$
$53$			11.6845i			1.60498i	−0.596663	+	0.802492i	$0.703507\pi$
$54$		0			0
$55$		−	0.828872i		−	0.111765i
$56$		0			0
$57$	1.06212	−	5.19553i	0.140681	−	0.688164i
$58$		0			0
$59$	6.48614	−	11.2343i	0.844424	−	1.46258i	−0.0416970	−	0.999130i	$-0.513276\pi$
$59$	6.48614	−	11.2343i	0.844424	−	1.46258i	0.886121	−	0.463454i	$-0.153390\pi$
$60$		0			0
$61$	−0.729056	+	0.420921i	−0.0933461	+	0.0538934i	−0.545946	−	0.837820i	$-0.683830\pi$
$61$	−0.729056	+	0.420921i	−0.0933461	+	0.0538934i	0.452600	+	0.891713i	$0.350496\pi$
$62$		0			0
$63$	7.30493	−	3.10451i	0.920335	−	0.391131i
$64$		0			0
$65$	4.18131	−	2.41408i	0.518628	−	0.299430i
$66$		0			0
$67$	−5.05736	+	8.75961i	−0.617855	+	1.07016i	0.372021	+	0.928224i	$0.378665\pi$
$67$	−5.05736	+	8.75961i	−0.617855	+	1.07016i	−0.989876	+	0.141932i	$0.954668\pi$
$68$		0			0
$69$	7.29725	+	6.46827i	0.878486	+	0.778688i
$70$		0			0
$71$			7.47959i			0.887664i	0.896110	+	0.443832i	$0.146381\pi$
$71$			7.47959i			0.887664i	−0.896110	+	0.443832i	$0.853619\pi$
$72$		0			0
$73$			7.97751i			0.933697i	0.884337	+	0.466848i	$0.154611\pi$
$73$			7.97751i			0.933697i	−0.884337	+	0.466848i	$0.845389\pi$
$74$		0			0
$75$	4.29342	+	12.8718i	0.495761	+	1.48630i
$76$		0			0
$77$	−0.146719	+	0.594303i	−0.0167202	+	0.0677272i
$78$		0			0
$79$	−3.30854	−	5.73056i	−0.372240	−	0.644738i	0.617670	−	0.786437i	$-0.288077\pi$
$79$	−3.30854	−	5.73056i	−0.372240	−	0.644738i	−0.989910	+	0.141699i	$0.954743\pi$
$80$		0			0
$81$	6.22760	+	6.49746i	0.691956	+	0.721940i
$82$		0			0
$83$	−6.41792	−	11.1162i	−0.704458	−	1.22016i	−0.966887	−	0.255206i	$-0.917857\pi$
$83$	−6.41792	−	11.1162i	−0.704458	−	1.22016i	0.262429	−	0.964951i	$-0.415477\pi$
$84$		0			0
$85$	14.2384	−	24.6616i	1.54437	−	2.67493i
$86$		0			0
$87$	4.43390	−	1.47894i	0.475364	−	0.158559i
$88$		0			0
$89$	3.56067			0.377430			0.188715	−	0.982032i	$-0.439568\pi$
$89$	3.56067			0.377430			0.188715	+	0.982032i	$0.439568\pi$
$90$		0			0
$91$	−3.42533	+	0.990766i	−0.359072	+	0.103860i
$92$		0			0
$93$	2.77484	+	2.45961i	0.287737	+	0.255050i
$94$		0			0
$95$	−9.49885	−	5.48417i	−0.974562	−	0.562664i
$96$		0			0
$97$	13.1326	−	7.58210i	1.33341	−	0.769845i	0.347590	−	0.937647i	$-0.387000\pi$
$97$	13.1326	−	7.58210i	1.33341	−	0.769845i	0.985821	+	0.167801i	$0.0536667\pi$
$98$		0			0
$99$	−0.689092	+	0.0832985i	−0.0692564	+	0.00837182i
$100$		0			0
$101$	3.78084	+	6.54861i	0.376208	+	0.651611i	0.990507	−	0.137462i	$-0.0438945\pi$
$101$	3.78084	+	6.54861i	0.376208	+	0.651611i	−0.614299	+	0.789073i	$0.710561\pi$
$102$		0			0
$103$	−10.1520	−	5.86126i	−1.00031	−	0.577527i	−0.0919672	−	0.995762i	$-0.529315\pi$
$103$	−10.1520	−	5.86126i	−1.00031	−	0.577527i	−0.908339	+	0.418235i	$0.862649\pi$
$104$		0			0
$105$	−1.31051	−	16.3645i	−0.127893	−	1.59701i
$106$		0			0
$107$		−	12.1425i		−	1.17386i	−0.809636	−	0.586932i	$-0.800336\pi$
$107$		−	12.1425i		−	1.17386i	0.809636	−	0.586932i	$-0.199664\pi$
$108$		0			0
$109$	−13.8764			−1.32912			−0.664561	−	0.747234i	$-0.731381\pi$
$109$	−13.8764			−1.32912			−0.664561	+	0.747234i	$0.731381\pi$
$110$		0			0
$111$	12.3451	+	2.52369i	1.17174	+	0.239538i
$112$		0			0
$113$	15.6660	+	9.04479i	1.47374	+	0.850862i	0.999563	−	0.0295692i	$-0.00941355\pi$
$113$	15.6660	+	9.04479i	1.47374	+	0.850862i	0.474174	+	0.880431i	$0.342747\pi$
$114$		0			0
$115$	17.4669	−	10.0845i	1.62879	−	0.940385i
$116$		0			0
$117$	−2.42718	−	3.23358i	−0.224393	−	0.298944i
$118$		0			0
$119$	−14.5743	+	15.1621i	−1.33603	+	1.38991i
$120$		0			0
$121$	−5.47323	+	9.47992i	−0.497567	+	0.861811i
$122$		0			0
$123$	−1.86990	+	2.10955i	−0.168603	+	0.190212i
$124$		0			0
$125$	10.1528			0.908092
$126$		0			0
$127$	12.1457			1.07776			0.538878	−	0.842384i	$-0.318849\pi$
$127$	12.1457			1.07776			0.538878	+	0.842384i	$0.318849\pi$
$128$		0			0
$129$	1.01676	+	3.04826i	0.0895205	+	0.268385i
$130$		0			0
$131$	−8.27640	+	14.3352i	−0.723113	+	1.25247i	0.236633	+	0.971599i	$0.423956\pi$
$131$	−8.27640	+	14.3352i	−0.723113	+	1.25247i	−0.959746	+	0.280869i	$0.909377\pi$
$132$		0			0
$133$	5.83995	+	5.61356i	0.506388	+	0.486757i
$134$		0			0
$135$	16.8241	−	7.96668i	1.44799	−	0.685662i
$136$		0			0
$137$	−13.8250	+	7.98187i	−1.18115	+	0.681937i	−0.956280	−	0.292452i	$-0.905529\pi$
$137$	−13.8250	+	7.98187i	−1.18115	+	0.681937i	−0.224869	+	0.974389i	$0.572196\pi$
$138$		0			0
$139$	7.40140	+	4.27320i	0.627779	+	0.362448i	0.779891	−	0.625915i	$-0.215274\pi$
$139$	7.40140	+	4.27320i	0.627779	+	0.362448i	−0.152113	+	0.988363i	$0.548608\pi$
$140$		0			0
$141$	−0.0434353	−	0.130220i	−0.00365791	−	0.0109665i
$142$		0			0
$143$	0.311822			0.0260759
$144$		0			0
$145$		−	9.66750i		−	0.802842i
$146$		0			0
$147$	−1.95705	+	11.9654i	−0.161415	+	0.986887i
$148$		0			0
$149$	6.43319	+	3.71421i	0.527028	+	0.304280i	0.739805	−	0.672821i	$-0.234918\pi$
$149$	6.43319	+	3.71421i	0.527028	+	0.304280i	−0.212777	+	0.977101i	$0.568251\pi$
$150$		0			0
$151$	9.32926	+	16.1587i	0.759204	+	1.31498i	0.943257	+	0.332064i	$0.107745\pi$
$151$	9.32926	+	16.1587i	0.759204	+	1.31498i	−0.184053	+	0.982916i	$0.558922\pi$
$152$		0			0
$153$	−21.9336	−	9.35886i	−1.77323	−	0.756619i
$154$		0			0
$155$	6.64192	−	3.83471i	0.533492	−	0.308012i
$156$		0			0
$157$	19.9510	+	11.5187i	1.59226	+	0.919293i	0.992918	+	0.118801i	$0.0379050\pi$
$157$	19.9510	+	11.5187i	1.59226	+	0.919293i	0.599344	+	0.800492i	$0.295428\pi$
$158$		0			0
$159$	4.05341	−	19.8280i	0.321457	−	1.57246i
$160$		0			0
$161$	−14.3089	+	4.13879i	−1.12770	+	0.326182i
$162$		0			0
$163$	−9.75747			−0.764264			−0.382132	−	0.924108i	$-0.624810\pi$
$163$	−9.75747			−0.764264			−0.382132	+	0.924108i	$0.624810\pi$
$164$		0			0
$165$	−0.287541	+	1.40656i	−0.0223851	+	0.109500i
$166$		0			0
$167$	−8.15227	+	14.1202i	−0.630842	+	1.09265i	0.356538	+	0.934281i	$0.383957\pi$
$167$	−8.15227	+	14.1202i	−0.630842	+	1.09265i	−0.987380	+	0.158369i	$0.949376\pi$
$168$		0			0
$169$	−5.59182	−	9.68532i	−0.430140	−	0.745025i
$170$		0			0
$171$	−3.60472	+	8.44812i	−0.275660	+	0.646044i
$172$		0			0
$173$	−0.681518	−	1.18042i	−0.0518148	−	0.0897459i	0.838955	−	0.544201i	$-0.183167\pi$
$173$	−0.681518	−	1.18042i	−0.0518148	−	0.0897459i	−0.890769	+	0.454455i	$0.849834\pi$
$174$		0			0
$175$	−20.1227	−	4.96782i	−1.52114	−	0.375532i
$176$		0			0
$177$	−14.9040	+	16.8141i	−1.12025	+	1.26382i
$178$		0			0
$179$		−	15.5303i		−	1.16079i	−0.814336	−	0.580394i	$-0.802899\pi$
$179$		−	15.5303i		−	1.16079i	0.814336	−	0.580394i	$-0.197101\pi$
$180$		0			0
$181$			17.5414i			1.30384i	0.758287	+	0.651920i	$0.226036\pi$
$181$			17.5414i			1.30384i	−0.758287	+	0.651920i	$0.773964\pi$
$182$		0			0
$183$	1.38320	−	0.461369i	0.102249	−	0.0341054i
$184$		0			0
$185$	13.0309	−	22.5702i	0.958050	−	1.65939i
$186$		0			0
$187$	1.59275	−	0.919573i	0.116473	−	0.0672458i
$188$		0			0
$189$	−13.4731	+	2.73408i	−0.980025	+	0.198875i
$190$		0			0
$191$	−1.67352	+	0.966209i	−0.121092	+	0.0699124i	−0.559323	−	0.828950i	$-0.688939\pi$
$191$	−1.67352	+	0.966209i	−0.121092	+	0.0699124i	0.438231	+	0.898863i	$0.355605\pi$
$192$		0			0
$193$	1.95786	−	3.39111i	0.140930	−	0.244098i	−0.786917	−	0.617059i	$-0.788324\pi$
$193$	1.95786	−	3.39111i	0.140930	−	0.244098i	0.927847	+	0.372961i	$0.121657\pi$
$194$		0			0
$195$	−7.93296	+	2.64606i	−0.568091	+	0.189489i
$196$		0			0
$197$		−	12.5710i		−	0.895647i	−0.894122	−	0.447824i	$-0.852199\pi$
$197$		−	12.5710i		−	0.895647i	0.894122	−	0.447824i	$-0.147801\pi$
$198$		0			0
$199$			17.0255i			1.20691i	0.797398	+	0.603454i	$0.206209\pi$
$199$			17.0255i			1.20691i	−0.797398	+	0.603454i	$0.793791\pi$
$200$		0			0
$201$	11.6209	−	13.1102i	0.819674	−	0.924724i
$202$		0			0
$203$	−1.71125	+	6.93162i	−0.120106	+	0.486504i
$204$		0			0
$205$	2.91531	+	5.04947i	0.203614	+	0.352670i
$206$		0			0
$207$	−10.1392	−	13.5078i	−0.704725	−	0.938859i
$208$		0			0
$209$	−0.354189	−	0.613474i	−0.0244998	−	0.0424349i
$210$		0			0
$211$	1.81881	−	3.15027i	0.125212	−	0.216874i	−0.796604	−	0.604502i	$-0.793372\pi$
$211$	1.81881	−	3.15027i	0.125212	−	0.216874i	0.921816	+	0.387628i	$0.126706\pi$
$212$		0			0
$213$	2.59472	−	12.6925i	0.177787	−	0.869677i
$214$		0			0
$215$	6.64631			0.453274
$216$		0			0
$217$	−5.44106	+	1.57381i	−0.369363	+	0.106837i
$218$		0			0
$219$	2.76745	−	13.5375i	0.187007	−	0.914778i
$220$		0			0
$221$	9.27772	+	5.35649i	0.624087	+	0.360317i
$222$		0			0
$223$	−10.2325	+	5.90773i	−0.685218	+	0.395611i	−0.801818	−	0.597568i	$-0.796134\pi$
$223$	−10.2325	+	5.90773i	−0.685218	+	0.395611i	0.116600	+	0.993179i	$0.462800\pi$
$224$		0			0
$225$	−2.82043	−	23.3322i	−0.188029	−	1.55548i
$226$		0			0
$227$	−8.97271	−	15.5412i	−0.595539	−	1.03150i	−0.993471	−	0.114089i	$-0.963605\pi$
$227$	−8.97271	−	15.5412i	−0.595539	−	1.03150i	0.397931	−	0.917415i	$-0.369728\pi$
$228$		0			0
$229$	−16.0434	−	9.26264i	−1.06017	−	0.612092i	−0.134694	−	0.990887i	$-0.543005\pi$
$229$	−16.0434	−	9.26264i	−1.06017	−	0.612092i	−0.925481	+	0.378795i	$0.876339\pi$
$230$		0			0
$231$	0.455144	−	0.957608i	0.0299463	−	0.0630060i
$232$		0			0
$233$		−	9.83034i		−	0.644007i	−0.946738	−	0.322004i	$-0.895644\pi$
$233$		−	9.83034i		−	0.644007i	0.946738	−	0.322004i	$-0.104356\pi$
$234$		0			0
$235$	−0.283926			−0.0185213
$236$		0			0
$237$	3.62647	+	10.8723i	0.235565	+	0.706229i
$238$		0			0
$239$	−9.28151	−	5.35868i	−0.600371	−	0.346624i	0.168817	−	0.985647i	$-0.446005\pi$
$239$	−9.28151	−	5.35868i	−0.600371	−	0.346624i	−0.769188	+	0.639023i	$0.779339\pi$
$240$		0			0
$241$	8.99246	−	5.19180i	0.579256	−	0.334433i	−0.181582	−	0.983376i	$-0.558122\pi$
$241$	8.99246	−	5.19180i	0.579256	−	0.334433i	0.760837	+	0.648942i	$0.224788\pi$
$242$		0			0
$243$	−8.31395	−	13.1863i	−0.533340	−	0.845901i
$244$		0			0
$245$	22.1960	+	11.6706i	1.41805	+	0.745609i
$246$		0			0
$247$	2.06315	−	3.57347i	0.131275	−	0.227375i
$248$		0			0
$249$	7.03465	+	21.0900i	0.445803	+	1.33653i
$250$		0			0
$251$	17.1797			1.08437			0.542187	−	0.840258i	$-0.317596\pi$
$251$	17.1797			1.08437			0.542187	+	0.840258i	$0.317596\pi$
$252$		0			0
$253$	1.30259			0.0818934
$254$		0			0
$255$	−32.7172	+	36.9103i	−2.04883	+	2.31141i
$256$		0			0
$257$	−0.751617	+	1.30184i	−0.0468846	+	0.0812065i	−0.888515	−	0.458847i	$-0.848263\pi$
$257$	−0.751617	+	1.30184i	−0.0468846	+	0.0812065i	0.841631	+	0.540053i	$0.181596\pi$
$258$		0			0
$259$	−13.3383	+	13.8763i	−0.828804	+	0.862229i
$260$		0			0
$261$	−8.03718	+	0.971547i	−0.497489	+	0.0601373i
$262$		0			0
$263$	7.80797	−	4.50793i	0.481460	−	0.277971i	−0.239565	−	0.970880i	$-0.577005\pi$
$263$	7.80797	−	4.50793i	0.481460	−	0.277971i	0.721025	+	0.692909i	$0.243671\pi$
$264$		0			0
$265$	−36.2510	−	20.9296i	−2.22688	−	1.28569i
$266$		0			0
$267$	−6.04229	−	1.23522i	−0.369782	−	0.0755942i
$268$		0			0
$269$	−21.6914			−1.32255			−0.661273	−	0.750145i	$-0.729984\pi$
$269$	−21.6914			−1.32255			−0.661273	+	0.750145i	$0.729984\pi$
$270$		0			0
$271$			13.5501i			0.823111i	0.911385	+	0.411556i	$0.135014\pi$
$271$			13.5501i			0.823111i	−0.911385	+	0.411556i	$0.864986\pi$
$272$		0			0
$273$	6.15633	−	0.493015i	0.372598	−	0.0298386i
$274$		0			0
$275$	1.56972	+	0.906277i	0.0946576	+	0.0546506i
$276$		0			0
$277$	−0.996101	−	1.72530i	−0.0598499	−	0.103663i	0.834548	−	0.550935i	$-0.185729\pi$
$277$	−0.996101	−	1.72530i	−0.0598499	−	0.103663i	−0.894398	+	0.447272i	$0.852396\pi$
$278$		0			0
$279$	−3.85552	−	5.13646i	−0.230824	−	0.307512i
$280$		0			0
$281$	22.9759	−	13.2652i	1.37063	−	0.791333i	0.379621	−	0.925142i	$-0.376054\pi$
$281$	22.9759	−	13.2652i	1.37063	−	0.791333i	0.991007	+	0.133809i	$0.0427209\pi$
$282$		0			0
$283$	−10.3080	−	5.95134i	−0.612748	−	0.353770i	0.161292	−	0.986907i	$-0.448434\pi$
$283$	−10.3080	−	5.95134i	−0.612748	−	0.353770i	−0.774040	+	0.633136i	$0.781767\pi$
$284$		0			0
$285$	14.2166	+	12.6016i	0.842121	+	0.746454i
$286$		0			0
$287$	−1.19648	−	4.13652i	−0.0706258	−	0.244171i
$288$		0			0
$289$	46.1859			2.71682
$290$		0			0
$291$	−24.9157	+	8.31070i	−1.46058	+	0.487182i
$292$		0			0
$293$	−3.36418	+	5.82693i	−0.196537	+	0.340413i	−0.947403	−	0.320042i	$-0.896303\pi$
$293$	−3.36418	+	5.82693i	−0.196537	+	0.340413i	0.750866	+	0.660455i	$0.229636\pi$
$294$		0			0
$295$	23.2363	+	40.2465i	1.35287	+	2.34324i
$296$		0			0
$297$	1.19826	+	0.0976968i	0.0695298	+	0.00566894i
$298$		0			0
$299$	3.79379	+	6.57105i	0.219401	+	0.380013i
$300$		0			0
$301$	−4.76542	−	1.17647i	−0.274674	−	0.0678105i
$302$		0			0
$303$	−4.14416	−	12.4243i	−0.238076	−	0.713757i
$304$		0			0
$305$		−	3.01586i		−	0.172688i
$306$		0			0
$307$			14.2812i			0.815069i	0.913190	+	0.407535i	$0.133611\pi$
$307$			14.2812i			0.815069i	−0.913190	+	0.407535i	$0.866389\pi$
$308$		0			0
$309$	15.1942	+	13.4681i	0.864366	+	0.766173i
$310$		0			0
$311$	4.99609	−	8.65348i	0.283302	−	0.490694i	−0.688894	−	0.724862i	$-0.741903\pi$
$311$	4.99609	−	8.65348i	0.283302	−	0.490694i	0.972196	+	0.234168i	$0.0752367\pi$
$312$		0			0
$313$	−2.05595	+	1.18701i	−0.116209	+	0.0670935i	−0.556978	−	0.830527i	$-0.688039\pi$
$313$	−2.05595	+	1.18701i	−0.116209	+	0.0670935i	0.440769	+	0.897621i	$0.354706\pi$
$314$		0			0
$315$	−3.45307	+	28.2245i	−0.194559	+	1.59027i
$316$		0			0
$317$	1.48046	−	0.854744i	0.0831509	−	0.0480072i	−0.457848	−	0.889030i	$-0.651380\pi$
$317$	1.48046	−	0.854744i	0.0831509	−	0.0480072i	0.540999	+	0.841023i	$0.318046\pi$
$318$		0			0
$319$	0.312183	−	0.540716i	0.0174789	−	0.0302743i
$320$		0			0
$321$	−4.21233	+	20.6054i	−0.235109	+	1.15008i
$322$		0			0
$323$		−	24.3371i		−	1.35415i
$324$		0			0
$325$			10.5581i			0.585658i
$326$		0			0
$327$	23.5477	+	4.81383i	1.30219	+	0.266205i
$328$		0			0
$329$	0.203576	+	0.0502580i	0.0112235	+	0.00277081i
$330$		0			0
$331$	−10.5054	−	18.1959i	−0.577430	−	1.00014i	−0.995773	−	0.0918494i	$-0.970722\pi$
$331$	−10.5054	−	18.1959i	−0.577430	−	1.00014i	0.418343	−	0.908289i	$-0.362611\pi$
$332$		0			0
$333$	−20.0735	−	8.56516i	−1.10002	−	0.469368i
$334$		0			0
$335$	−18.1178	−	31.3810i	−0.989881	−	1.71452i
$336$		0			0
$337$	−8.04527	+	13.9348i	−0.438254	+	0.759077i	−0.997555	−	0.0698870i	$-0.977736\pi$
$337$	−8.04527	+	13.9348i	−0.438254	+	0.759077i	0.559301	+	0.828964i	$0.311069\pi$
$338$		0			0
$339$	−23.4469	−	20.7832i	−1.27346	−	1.12879i
$340$		0			0
$341$	0.495322			0.0268232
$342$		0			0
$343$	−13.8488	−	12.2968i	−0.747764	−	0.663965i
$344$		0			0
$345$	−33.1389	+	11.0536i	−1.78414	+	0.595105i
$346$		0			0
$347$	11.2415	+	6.49029i	0.603476	+	0.348417i	0.770408	−	0.637551i	$-0.220053\pi$
$347$	11.2415	+	6.49029i	0.603476	+	0.348417i	−0.166932	+	0.985968i	$0.553386\pi$
$348$		0			0
$349$	12.2260	−	7.05868i	0.654442	−	0.377842i	−0.135714	−	0.990748i	$-0.543333\pi$
$349$	12.2260	−	7.05868i	0.654442	−	0.377842i	0.790156	+	0.612906i	$0.209999\pi$
$350$		0			0
$351$	2.99707	+	6.32924i	0.159972	+	0.337830i
$352$		0			0
$353$	−10.3917	−	17.9990i	−0.553096	−	0.957991i	−0.998049	−	0.0624367i	$-0.980113\pi$
$353$	−10.3917	−	17.9990i	−0.553096	−	0.957991i	0.444953	−	0.895554i	$-0.353220\pi$
$354$		0			0
$355$	−23.2054	−	13.3977i	−1.23162	−	0.711074i
$356$		0			0
$357$	29.9918	−	20.6735i	1.58734	−	1.09416i
$358$		0			0
$359$			11.2290i			0.592644i	0.955088	+	0.296322i	$0.0957601\pi$
$359$			11.2290i			0.592644i	−0.955088	+	0.296322i	$0.904240\pi$
$360$		0			0
$361$	9.62614			0.506639
$362$		0			0
$363$	12.5765	−	14.1883i	0.660094	−	0.744692i
$364$		0			0
$365$	−24.7502	−	14.2896i	−1.29549	−	0.747950i
$366$		0			0
$367$	−5.16800	+	2.98375i	−0.269768	+	0.155750i	−0.628782	−	0.777582i	$-0.716446\pi$
$367$	−5.16800	+	2.98375i	−0.269768	+	0.155750i	0.359014	+	0.933332i	$0.383113\pi$
$368$		0			0
$369$	3.90496	−	2.93113i	0.203284	−	0.152589i
$370$		0			0
$371$	22.2873	+	21.4234i	1.15710	+	1.11225i
$372$		0			0
$373$	−11.5890	+	20.0727i	−0.600055	+	1.03933i	0.392757	+	0.919642i	$0.371521\pi$
$373$	−11.5890	+	20.0727i	−0.600055	+	1.03933i	−0.992812	+	0.119684i	$0.961812\pi$
$374$		0			0
$375$	−17.2288	−	3.52207i	−0.889692	−	0.181879i
$376$		0			0
$377$	3.63692			0.187311
$378$		0			0
$379$	−33.7053			−1.73132			−0.865662	−	0.500629i	$-0.833102\pi$
$379$	−33.7053			−1.73132			−0.865662	+	0.500629i	$0.833102\pi$
$380$		0			0
$381$	−20.6107	−	4.21342i	−1.05592	−	0.215860i
$382$		0			0
$383$	1.09459	−	1.89589i	0.0559310	−	0.0968754i	−0.836704	−	0.547655i	$-0.815521\pi$
$383$	1.09459	−	1.89589i	0.0559310	−	0.0968754i	0.892635	+	0.450780i	$0.148854\pi$
$384$		0			0
$385$	−1.58102	−	1.51973i	−0.0805762	−	0.0774527i
$386$		0			0
$387$	−0.667929	−	5.52548i	−0.0339527	−	0.280876i
$388$		0			0
$389$	−8.71424	+	5.03117i	−0.441829	+	0.255090i	−0.704373	−	0.709830i	$-0.748772\pi$
$389$	−8.71424	+	5.03117i	−0.441829	+	0.255090i	0.262544	+	0.964920i	$0.415439\pi$
$390$		0			0
$391$	38.7564	+	22.3760i	1.96000	+	1.13160i
$392$		0			0
$393$	19.0176	−	21.4550i	0.959313	−	1.08226i
$394$		0			0
$395$	23.7054			1.19275
$396$		0			0
$397$		−	14.7293i		−	0.739243i	−0.929182	−	0.369621i	$-0.879487\pi$
$397$		−	14.7293i		−	0.739243i	0.929182	−	0.369621i	$-0.120513\pi$
$398$		0			0
$399$	−7.96274	−	11.5519i	−0.398636	−	0.578317i
$400$		0			0
$401$	−9.40832	−	5.43190i	−0.469829	−	0.271256i	0.246339	−	0.969184i	$-0.420772\pi$
$401$	−9.40832	−	5.43190i	−0.469829	−	0.271256i	−0.716168	+	0.697928i	$0.754106\pi$
$402$		0			0
$403$	1.44262	+	2.49869i	0.0718621	+	0.124469i
$404$		0			0
$405$	−31.3134	+	7.68270i	−1.55598	+	0.381756i
$406$		0			0
$407$	1.45767	−	0.841587i	0.0722541	−	0.0417159i
$408$		0			0
$409$	19.4688	+	11.2403i	0.962672	+	0.555799i	0.896994	−	0.442042i	$-0.145746\pi$
$409$	19.4688	+	11.2403i	0.962672	+	0.555799i	0.0656773	+	0.997841i	$0.479079\pi$
$410$		0			0
$411$	26.2294	−	8.74889i	1.29380	−	0.431551i
$412$		0			0
$413$	−9.53645	−	32.9699i	−0.469258	−	1.62234i
$414$		0			0
$415$	45.9839			2.25726
$416$		0			0
$417$	−11.0774	−	9.81902i	−0.542465	−	0.480840i
$418$		0			0
$419$	−14.2135	+	24.6184i	−0.694373	+	1.20269i	0.276018	+	0.961152i	$0.410985\pi$
$419$	−14.2135	+	24.6184i	−0.694373	+	1.20269i	−0.970392	+	0.241537i	$0.922348\pi$
$420$		0			0
$421$	10.7934	+	18.6947i	0.526037	+	0.911123i	0.999540	+	0.0303305i	$0.00965599\pi$
$421$	10.7934	+	18.6947i	0.526037	+	0.911123i	−0.473503	+	0.880792i	$0.657011\pi$
$422$		0			0
$423$	0.0285335	+	0.236045i	0.00138735	+	0.0114769i
$424$		0			0
$425$	31.1361	+	53.9294i	1.51033	+	2.61596i
$426$		0			0
$427$	−0.533840	+	2.16238i	−0.0258343	+	0.104645i
$428$		0			0
$429$	−0.529148	−	0.108173i	−0.0255475	−	0.00522265i
$430$		0			0
$431$			19.1530i			0.922567i	0.887253	+	0.461284i	$0.152611\pi$
$431$			19.1530i			0.922567i	−0.887253	+	0.461284i	$0.847389\pi$
$432$		0			0
$433$		−	3.46577i		−	0.166554i	−0.996526	−	0.0832772i	$-0.973461\pi$
$433$		−	3.46577i		−	0.166554i	0.996526	−	0.0832772i	$-0.0265387\pi$
$434$		0			0
$435$	−3.35372	+	16.4053i	−0.160799	+	0.786574i
$436$		0			0
$437$	8.61851	−	14.9277i	0.412279	−	0.714089i
$438$		0			0
$439$	21.9087	−	12.6490i	1.04565	−	0.603704i	0.124218	−	0.992255i	$-0.460358\pi$
$439$	21.9087	−	12.6490i	1.04565	−	0.603704i	0.921427	+	0.388551i	$0.127024\pi$
$440$		0			0
$441$	7.47189	−	19.6258i	0.355804	−	0.934560i
$442$		0			0
$443$	16.6599	−	9.61858i	0.791534	−	0.456992i	−0.0489683	−	0.998800i	$-0.515593\pi$
$443$	16.6599	−	9.61858i	0.791534	−	0.456992i	0.840502	+	0.541808i	$0.182260\pi$
$444$		0			0
$445$	−6.37798	+	11.0470i	−0.302345	+	0.523677i
$446$		0			0
$447$	−9.62836	−	8.53456i	−0.455406	−	0.403671i
$448$		0			0
$449$		−	3.44859i		−	0.162749i	−0.996684	−	0.0813744i	$-0.974069\pi$
$449$		−	3.44859i		−	0.162749i	0.996684	−	0.0813744i	$-0.0259309\pi$
$450$		0			0
$451$			0.376565i			0.0177318i
$452$		0			0
$453$	−10.2258	−	30.6570i	−0.480448	−	1.44039i
$454$		0			0
$455$	3.06170	−	12.4018i	0.143535	−	0.581405i
$456$		0			0
$457$	3.88750	+	6.73335i	0.181850	+	0.314973i	0.942510	−	0.334177i	$-0.108458\pi$
$457$	3.88750	+	6.73335i	0.181850	+	0.314973i	−0.760661	+	0.649150i	$0.775125\pi$
$458$		0			0
$459$	33.9738	+	23.4905i	1.58576	+	1.09644i
$460$		0			0
$461$	−1.88500	−	3.26492i	−0.0877933	−	0.152062i	0.818785	−	0.574101i	$-0.194648\pi$
$461$	−1.88500	−	3.26492i	−0.0877933	−	0.152062i	−0.906578	+	0.422038i	$0.861315\pi$
$462$		0			0
$463$	−1.71692	+	2.97379i	−0.0797919	+	0.138204i	−0.903160	−	0.429304i	$-0.858759\pi$
$463$	−1.71692	+	2.97379i	−0.0797919	+	0.138204i	0.823368	+	0.567508i	$0.192092\pi$
$464$		0			0
$465$	−12.6013	+	4.20321i	−0.584373	+	0.194919i
$466$		0			0
$467$	7.92981			0.366948			0.183474	−	0.983025i	$-0.441266\pi$
$467$	7.92981			0.366948			0.183474	+	0.983025i	$0.441266\pi$
$468$		0			0
$469$	7.43574	+	25.7073i	0.343351	+	1.18705i
$470$		0			0
$471$	−29.8600	−	26.4678i	−1.37588	−	1.21957i
$472$		0			0
$473$	0.371737	+	0.214623i	0.0170925	+	0.00986835i
$474$		0			0
$475$	20.7718	−	11.9926i	0.953077	−	0.550259i
$476$		0			0
$477$	−13.7569	+	32.2411i	−0.629886	+	1.47622i
$478$		0			0
$479$	−4.22428	−	7.31666i	−0.193012	−	0.334307i	0.753235	−	0.657752i	$-0.228492\pi$
$479$	−4.22428	−	7.31666i	−0.193012	−	0.334307i	−0.946247	+	0.323445i	$0.895159\pi$
$480$		0			0
$481$	8.49091	+	4.90223i	0.387152	+	0.223522i
$482$		0			0
$483$	25.7173	−	2.05951i	1.17018	−	0.0937107i
$484$		0			0
$485$			54.3251i			2.46678i
$486$		0			0
$487$	13.5361			0.613377			0.306689	−	0.951810i	$-0.400779\pi$
$487$	13.5361			0.613377			0.306689	+	0.951810i	$0.400779\pi$
$488$		0			0
$489$	16.5580	+	3.38493i	0.748778	+	0.153072i
$490$		0			0
$491$	6.60993	+	3.81624i	0.298302	+	0.172225i	0.641680	−	0.766973i	$-0.278238\pi$
$491$	6.60993	+	3.81624i	0.298302	+	0.172225i	−0.343378	+	0.939197i	$0.611571\pi$
$492$		0			0
$493$	18.5769	−	10.7254i	0.836662	−	0.483047i
$494$		0			0
$495$	0.975889	−	2.28712i	0.0438630	−	0.102798i
$496$		0			0
$497$	14.2668	+	13.7138i	0.639954	+	0.615146i
$498$		0			0
$499$	12.8845	−	22.3165i	0.576788	−	0.999025i	−0.419057	−	0.907960i	$-0.637639\pi$
$499$	12.8845	−	22.3165i	0.576788	−	0.999025i	0.995845	−	0.0910656i	$-0.0290273\pi$
$500$		0			0
$501$	18.7324	−	21.1332i	0.836903	−	0.944161i
$502$		0			0
$503$	−2.94027			−0.131100			−0.0655500	−	0.997849i	$-0.520880\pi$
$503$	−2.94027			−0.131100			−0.0655500	+	0.997849i	$0.520880\pi$
$504$		0			0
$505$	−27.0894			−1.20546
$506$		0			0
$507$	6.12917	+	18.3754i	0.272206	+	0.816080i
$508$		0			0
$509$	−4.91221	+	8.50821i	−0.217730	+	0.377120i	−0.954114	−	0.299445i	$-0.903199\pi$
$509$	−4.91221	+	8.50821i	−0.217730	+	0.377120i	0.736384	+	0.676564i	$0.236532\pi$
$510$		0			0
$511$	15.2166	+	14.6267i	0.673142	+	0.647047i
$512$		0			0
$513$	9.04776	−	13.0856i	0.399468	−	0.577742i
$514$		0			0
$515$	36.3691	−	20.9977i	1.60262	−	0.925270i
$516$		0			0
$517$	−0.0158804	−	0.00916854i	−0.000698418	−	0.000403232i
$518$		0			0
$519$	0.747008	+	2.23955i	0.0327900	+	0.0983052i
$520$		0			0
$521$	−6.59400			−0.288889			−0.144444	−	0.989513i	$-0.546139\pi$
$521$	−6.59400			−0.288889			−0.144444	+	0.989513i	$0.546139\pi$
$522$		0			0
$523$		−	3.05847i		−	0.133737i	−0.997762	−	0.0668687i	$-0.978699\pi$
$523$		−	3.05847i		−	0.133737i	0.997762	−	0.0668687i	$-0.0213009\pi$
$524$		0			0
$525$	32.4240	+	15.4109i	1.41510	+	0.672586i
$526$		0			0
$527$	14.7374	+	8.50867i	0.641973	+	0.370643i
$528$		0			0
$529$	4.34807	+	7.53108i	0.189046	+	0.327438i
$530$		0			0
$531$	31.1242	−	23.3624i	1.35068	−	1.01384i
$532$		0			0
$533$	−1.89961	+	1.09674i	−0.0822814	+	0.0475052i
$534$		0			0
$535$	37.6723	+	21.7501i	1.62871	+	0.940339i
$536$		0			0
$537$	−5.38756	+	26.3542i	−0.232490	+	1.13727i
$538$		0			0
$539$	0.864586	+	1.36951i	0.0372404	+	0.0589889i
$540$		0			0
$541$	−28.2396			−1.21411			−0.607057	−	0.794659i	$-0.707650\pi$
$541$	−28.2396			−1.21411			−0.607057	+	0.794659i	$0.707650\pi$
$542$		0			0
$543$	6.08522	−	29.7669i	0.261142	−	1.27742i
$544$		0			0
$545$	24.8559	−	43.0517i	1.06471	−	1.84413i
$546$		0			0
$547$	−15.2952	−	26.4921i	−0.653976	−	1.13272i	−0.982150	−	0.188102i	$-0.939766\pi$
$547$	−15.2952	−	26.4921i	−0.653976	−	1.13272i	0.328174	−	0.944617i	$-0.393567\pi$
$548$		0			0
$549$	−2.50727	+	0.303083i	−0.107008	+	0.0129353i
$550$		0			0
$551$	−4.13106	−	7.15521i	−0.175989	−	0.304822i
$552$		0			0
$553$	−16.9968	−	4.19611i	−0.722779	−	0.178437i
$554$		0			0
$555$	−29.9426	+	33.7801i	−1.27099	+	1.43388i
$556$		0			0
$557$		−	19.7931i		−	0.838660i	−0.907834	−	0.419330i	$-0.862265\pi$
$557$		−	19.7931i		−	0.838660i	0.907834	−	0.419330i	$-0.137735\pi$
$558$		0			0
$559$			2.50034i			0.105753i
$560$		0			0
$561$	−3.02183	+	1.00794i	−0.127582	+	0.0425552i
$562$		0			0
$563$	3.05934	−	5.29894i	0.128936	−	0.223324i	−0.794329	−	0.607488i	$-0.792177\pi$
$563$	3.05934	−	5.29894i	0.128936	−	0.223324i	0.923265	+	0.384165i	$0.125510\pi$
$564$		0			0
$565$	−56.1229	+	32.4026i	−2.36111	+	1.36319i
$566$		0			0
$567$	23.8117	+	0.0343016i	0.999999	+	0.00144053i
$568$		0			0
$569$	−24.3621	+	14.0655i	−1.02131	+	0.589655i	−0.914484	−	0.404623i	$-0.867403\pi$
$569$	−24.3621	+	14.0655i	−1.02131	+	0.589655i	−0.106828	+	0.994277i	$0.534070\pi$
$570$		0			0
$571$	9.64625	−	16.7078i	0.403683	−	0.699199i	−0.590484	−	0.807049i	$-0.701063\pi$
$571$	9.64625	−	16.7078i	0.403683	−	0.699199i	0.994167	+	0.107850i	$0.0343965\pi$
$572$		0			0
$573$	3.17508	−	1.05906i	0.132641	−	0.0442427i
$574$		0			0
$575$			44.1050i			1.83931i
$576$		0			0
$577$			19.8248i			0.825317i	0.910886	+	0.412659i	$0.135400\pi$
$577$			19.8248i			0.825317i	−0.910886	+	0.412659i	$0.864600\pi$
$578$		0			0
$579$	−4.49880	+	5.07537i	−0.186964	+	0.210925i
$580$		0			0
$581$	−32.9705	−	8.13964i	−1.36785	−	0.337689i
$582$		0			0
$583$	−1.35171	−	2.34124i	−0.0559823	−	0.0969641i
$584$		0			0
$585$	14.3798	−	1.73825i	0.594532	−	0.0718680i
$586$		0			0
$587$	−2.51705	−	4.35967i	−0.103890	−	0.179943i	0.809394	−	0.587266i	$-0.199796\pi$
$587$	−2.51705	−	4.35967i	−0.103890	−	0.179943i	−0.913284	+	0.407323i	$0.866462\pi$
$588$		0			0
$589$	3.27726	−	5.67638i	0.135037	−	0.233891i
$590$		0			0
$591$	−4.36097	+	21.3324i	−0.179386	+	0.877499i
$592$		0			0
$593$	−28.7225			−1.17949			−0.589747	−	0.807588i	$-0.700772\pi$
$593$	−28.7225			−1.17949			−0.589747	+	0.807588i	$0.700772\pi$
$594$		0			0
$595$	−20.9345	−	72.3758i	−0.858229	−	2.96712i
$596$		0			0
$597$	5.90627	−	28.8915i	0.241727	−	1.18245i
$598$		0			0
$599$	−41.0308	−	23.6892i	−1.67647	−	0.967913i	−0.963880	−	0.266335i	$-0.914187\pi$
$599$	−41.0308	−	23.6892i	−1.67647	−	0.967913i	−0.712593	−	0.701577i	$-0.752480\pi$
$600$		0			0
$601$	−19.9885	+	11.5404i	−0.815347	+	0.470741i	−0.848809	−	0.528699i	$-0.822680\pi$
$601$	−19.9885	+	11.5404i	−0.815347	+	0.470741i	0.0334621	+	0.999440i	$0.489347\pi$
$602$		0			0
$603$	−24.2681	+	18.2161i	−0.988275	+	0.741817i
$604$		0			0
$605$	−19.6076	−	33.9614i	−0.797164	−	1.38073i
$606$		0			0
$607$	−26.3852	−	15.2335i	−1.07094	−	0.618309i	−0.142504	−	0.989794i	$-0.545515\pi$
$607$	−26.3852	−	15.2335i	−1.07094	−	0.618309i	−0.928439	+	0.371485i	$0.878849\pi$
$608$		0			0
$609$	5.30854	−	11.1690i	0.215113	−	0.452591i
$610$		0			0
$611$		−	0.106813i		−	0.00432120i
$612$		0			0
$613$	27.6918			1.11846			0.559231	−	0.829012i	$-0.311096\pi$
$613$	27.6918			1.11846			0.559231	+	0.829012i	$0.311096\pi$
$614$		0			0
$615$	−3.19546	−	9.58006i	−0.128853	−	0.386305i
$616$		0			0
$617$	−6.04021	−	3.48732i	−0.243170	−	0.140394i	0.373463	−	0.927645i	$-0.378170\pi$
$617$	−6.04021	−	3.48732i	−0.243170	−	0.140394i	−0.616633	+	0.787251i	$0.711504\pi$
$618$		0			0
$619$	13.9319	−	8.04361i	0.559972	−	0.323300i	−0.193162	−	0.981167i	$-0.561874\pi$
$619$	13.9319	−	8.04361i	0.559972	−	0.323300i	0.753134	+	0.657867i	$0.228541\pi$
$620$		0			0
$621$	12.5198	+	26.4395i	0.502404	+	1.06098i
$622$		0			0
$623$	6.52846	−	6.79174i	0.261557	−	0.272105i
$624$		0			0
$625$	1.39910	−	2.42331i	0.0559639	−	0.0969323i
$626$		0			0
$627$	0.388225	+	1.16391i	0.0155042	+	0.0464820i
$628$		0			0
$629$	57.8273			2.30572
$630$		0			0
$631$	−21.9346			−0.873201			−0.436601	−	0.899655i	$-0.643818\pi$
$631$	−21.9346			−0.873201			−0.436601	+	0.899655i	$0.643818\pi$
$632$		0			0
$633$	−4.17929	+	4.71492i	−0.166112	+	0.187401i
$634$		0			0
$635$	−21.7557	+	37.6820i	−0.863349	+	1.49536i
$636$		0			0
$637$	−4.39050	+	8.35015i	−0.173958	+	0.330845i
$638$		0			0
$639$	−8.80624	+	20.6385i	−0.348369	+	0.816447i
$640$		0			0
$641$	−5.46275	+	3.15392i	−0.215766	+	0.124572i	−0.603988	−	0.796993i	$-0.706423\pi$
$641$	−5.46275	+	3.15392i	−0.215766	+	0.124572i	0.388222	+	0.921566i	$0.373089\pi$
$642$		0			0
$643$	−5.64446	−	3.25883i	−0.222596	−	0.128516i	0.384556	−	0.923102i	$-0.374355\pi$
$643$	−5.64446	−	3.25883i	−0.222596	−	0.128516i	−0.607152	+	0.794586i	$0.707688\pi$
$644$		0			0
$645$	−11.2785	−	2.30565i	−0.444090	−	0.0907848i
$646$		0			0
$647$	14.6209			0.574806			0.287403	−	0.957810i	$-0.407208\pi$
$647$	14.6209			0.574806			0.287403	+	0.957810i	$0.407208\pi$
$648$		0			0
$649$			3.00139i			0.117815i
$650$		0			0
$651$	9.77919	−	0.783143i	0.383277	−	0.0306938i
$652$		0			0
$653$	15.7716	+	9.10576i	0.617192	+	0.356336i	0.775775	−	0.631010i	$-0.217359\pi$
$653$	15.7716	+	9.10576i	0.617192	+	0.356336i	−0.158583	+	0.987346i	$0.550693\pi$
$654$		0			0
$655$	−29.6499	−	51.3551i	−1.15852	−	2.00661i
$656$		0			0
$657$	−9.39248	+	22.0124i	−0.366435	+	0.858787i
$658$		0			0
$659$	−17.6278	+	10.1774i	−0.686682	+	0.396456i	−0.802368	−	0.596830i	$-0.796427\pi$
$659$	−17.6278	+	10.1774i	−0.686682	+	0.396456i	0.115686	+	0.993286i	$0.463093\pi$
$660$		0			0
$661$	26.6406	+	15.3810i	1.03620	+	0.598250i	0.918754	−	0.394829i	$-0.129196\pi$
$661$	26.6406	+	15.3810i	1.03620	+	0.598250i	0.117445	+	0.993079i	$0.462530\pi$
$662$		0			0
$663$	−13.8857	−	12.3082i	−0.539275	−	0.478012i
$664$		0			0
$665$	−27.8768	+	8.06327i	−1.08101	+	0.312680i
$666$		0			0
$667$	15.1927			0.588265
$668$		0			0
$669$	19.4135	−	6.47543i	0.750569	−	0.250355i
$670$		0			0
$671$	0.0973882	−	0.168681i	0.00375963	−	0.00651187i
$672$		0			0
$673$	−2.27563	−	3.94151i	−0.0877191	−	0.151934i	0.818828	−	0.574040i	$-0.194624\pi$
$673$	−2.27563	−	3.94151i	−0.0877191	−	0.151934i	−0.906547	+	0.422106i	$0.861291\pi$
$674$		0			0
$675$	−3.30795	+	40.5722i	−0.127323	+	1.56162i
$676$		0			0
$677$	−10.2205	−	17.7025i	−0.392807	−	0.680361i	0.600012	−	0.799991i	$-0.295163\pi$
$677$	−10.2205	−	17.7025i	−0.392807	−	0.680361i	−0.992819	+	0.119630i	$0.961829\pi$
$678$		0			0
$679$	9.61613	−	38.9512i	0.369033	−	1.49481i
$680$		0			0
$681$	9.83494	+	29.4854i	0.376876	+	1.12988i
$682$		0			0
$683$			44.3113i			1.69553i	0.530376	+	0.847763i	$0.322051\pi$
$683$			44.3113i			1.69553i	−0.530376	+	0.847763i	$0.677949\pi$
$684$		0			0
$685$		−	57.1895i		−	2.18510i
$686$		0			0
$687$	24.0116	+	21.2838i	0.916099	+	0.812028i
$688$		0			0
$689$	7.87371	−	13.6377i	0.299964	−	0.519553i
$690$		0			0
$691$	−11.6403	+	6.72051i	−0.442817	+	0.255660i	−0.704792	−	0.709414i	$-0.748960\pi$
$691$	−11.6403	+	6.72051i	−0.442817	+	0.255660i	0.261975	+	0.965075i	$0.415626\pi$
$692$		0			0
$693$	−1.10456	+	1.46713i	−0.0419587	+	0.0557315i
$694$		0			0
$695$	−26.5152	+	15.3086i	−1.00578	+	0.580687i
$696$		0			0
$697$	−6.46865	+	11.2040i	−0.245018	+	0.424383i
$698$		0			0
$699$	−3.41021	+	16.6817i	−0.128986	+	0.630958i
$700$		0			0
$701$		−	25.5980i		−	0.966823i	−0.875393	−	0.483411i	$-0.839398\pi$
$701$		−	25.5980i		−	0.966823i	0.875393	−	0.483411i	$-0.160602\pi$
$702$		0			0
$703$		−	22.2732i		−	0.840048i
$704$		0			0
$705$	0.481810	+	0.0984959i	0.0181460	+	0.00370957i
$706$		0			0
$707$	19.4232	+	4.79512i	0.730485	+	0.180339i
$708$		0			0
$709$	−20.0523	−	34.7316i	−0.753080	−	1.30437i	−0.946323	−	0.323222i	$-0.895234\pi$
$709$	−20.0523	−	34.7316i	−0.753080	−	1.30437i	0.193243	−	0.981151i	$-0.438099\pi$
$710$		0			0
$711$	−2.38230	−	19.7078i	−0.0893434	−	0.739099i
$712$		0			0
$713$	6.02636	+	10.4380i	0.225689	+	0.390904i
$714$		0			0
$715$	−0.558545	+	0.967429i	−0.0208884	+	0.0361798i
$716$		0			0
$717$	13.8913	+	12.3133i	0.518782	+	0.459847i
$718$		0			0
$719$	−32.5961			−1.21563			−0.607815	−	0.794079i	$-0.707954\pi$
$719$	−32.5961			−1.21563			−0.607815	+	0.794079i	$0.707954\pi$
$720$		0			0
$721$	−29.7936	+	8.61770i	−1.10957	+	0.320940i
$722$		0			0
$723$	−17.0609	+	5.69071i	−0.634501	+	0.211640i
$724$		0			0
$725$	18.3083	+	10.5703i	0.679954	+	0.392571i
$726$		0			0
$727$	−29.2124	+	16.8658i	−1.08343	+	0.625517i	−0.931819	−	0.362924i	$-0.881778\pi$
$727$	−29.2124	+	16.8658i	−1.08343	+	0.625517i	−0.151608	+	0.988441i	$0.548445\pi$
$728$		0			0
$729$	9.53398	+	25.2607i	0.353110	+	0.935582i
$730$		0			0
$731$	7.37359	+	12.7714i	0.272722	+	0.472369i
$732$		0			0
$733$	−16.0129	−	9.24503i	−0.591448	−	0.341473i	0.174222	−	0.984706i	$-0.444259\pi$
$733$	−16.0129	−	9.24503i	−0.591448	−	0.341473i	−0.765670	+	0.643234i	$0.777592\pi$
$734$		0			0
$735$	−33.6170	−	27.5045i	−1.23998	−	1.01452i
$736$		0			0
$737$		−	2.34024i		−	0.0862038i
$738$		0			0
$739$	4.77060			0.175489			0.0877446	−	0.996143i	$-0.472034\pi$
$739$	4.77060			0.175489			0.0877446	+	0.996143i	$0.472034\pi$
$740$		0			0
$741$	−4.74073	+	5.34830i	−0.174155	+	0.196475i
$742$		0			0
$743$	34.5888	+	19.9698i	1.26894	+	0.732622i	0.974787	−	0.223136i	$-0.0716296\pi$
$743$	34.5888	+	19.9698i	1.26894	+	0.732622i	0.294152	+	0.955759i	$0.404963\pi$
$744$		0			0
$745$	−23.0467	+	13.3060i	−0.844365	+	0.487494i
$746$		0			0
$747$	−4.62121	−	38.2292i	−0.169081	−	1.39873i
$748$		0			0
$749$	−23.1611	−	22.2633i	−0.846289	−	0.813482i
$750$		0			0
$751$	−14.3918	+	24.9273i	−0.525164	+	0.909611i	0.474406	+	0.880306i	$0.342663\pi$
$751$	−14.3918	+	24.9273i	−0.525164	+	0.909611i	−0.999571	+	0.0293052i	$0.990671\pi$
$752$		0			0
$753$	−29.1532	−	5.95976i	−1.06240	−	0.217186i
$754$		0			0
$755$	−66.8434			−2.43268
$756$		0			0
$757$	−3.83374			−0.139340			−0.0696699	−	0.997570i	$-0.522195\pi$
$757$	−3.83374			−0.139340			−0.0696699	+	0.997570i	$0.522195\pi$
$758$		0			0
$759$	−2.21044	−	0.451879i	−0.0802341	−	0.0164022i
$760$		0			0
$761$	−1.51888	+	2.63077i	−0.0550592	+	0.0953654i	−0.892241	−	0.451559i	$-0.850868\pi$
$761$	−1.51888	+	2.63077i	−0.0550592	+	0.0953654i	0.837182	+	0.546924i	$0.184201\pi$
$762$		0			0
$763$	−25.4423	+	26.4684i	−0.921074	+	0.958220i
$764$		0			0
$765$	68.3241	−	51.2853i	2.47026	−	1.85422i
$766$		0			0
$767$	−15.1408	+	8.74152i	−0.546701	+	0.315638i
$768$		0			0
$769$	26.0647	+	15.0484i	0.939916	+	0.542661i	0.889934	−	0.456089i	$-0.150750\pi$
$769$	26.0647	+	15.0484i	0.939916	+	0.542661i	0.0499822	+	0.998750i	$0.484084\pi$
$770$		0			0
$771$	1.72708	−	1.94842i	0.0621992	−	0.0701707i
$772$		0			0
$773$	−36.9887			−1.33039			−0.665196	−	0.746669i	$-0.731652\pi$
$773$	−36.9887			−1.33039			−0.665196	+	0.746669i	$0.731652\pi$
$774$		0			0
$775$			16.7713i			0.602443i
$776$		0			0
$777$	27.4483	−	18.9202i	0.984703	−	0.678759i
$778$		0			0
$779$	4.31543	+	2.49151i	0.154616	+	0.0892677i
$780$		0			0
$781$	−0.865274	−	1.49870i	−0.0309619	−	0.0536277i
$782$		0			0
$783$	13.9758	+	1.13948i	0.499453	+	0.0407217i
$784$		0			0
$785$	−71.4736	+	41.2653i	−2.55100	+	1.47282i
$786$		0			0
$787$	15.7679	+	9.10359i	0.562064	+	0.324508i	0.753974	−	0.656905i	$-0.228135\pi$
$787$	15.7679	+	9.10359i	0.562064	+	0.324508i	−0.191910	+	0.981413i	$0.561468\pi$
$788$		0			0
$789$	−14.8136	+	4.94112i	−0.527378	+	0.175909i
$790$		0			0
$791$	45.9759	−	13.2984i	1.63471	−	0.472836i
$792$		0			0
$793$	1.13457			0.0402897
$794$		0			0
$795$	54.2558	+	48.0922i	1.92425	+	1.70566i
$796$		0			0
$797$	−3.25236	+	5.63325i	−0.115204	+	0.199540i	−0.917861	−	0.396901i	$-0.870086\pi$
$797$	−3.25236	+	5.63325i	−0.115204	+	0.199540i	0.802657	+	0.596441i	$0.203419\pi$
$798$		0			0
$799$	−0.314995	−	0.545588i	−0.0111437	−	0.0193015i
$800$		0			0
$801$	9.82499	+	4.19222i	0.347149	+	0.148125i
$802$		0			0
$803$	−0.922876	−	1.59847i	−0.0325676	−	0.0564087i
$804$		0			0
$805$	12.7898	−	51.8068i	0.450783	−	1.82595i
$806$		0			0
$807$	36.8093	+	7.52488i	1.29575	+	0.264888i
$808$		0			0
$809$		−	53.4736i		−	1.88003i	−0.341129	−	0.940016i	$-0.610809\pi$
$809$		−	53.4736i		−	1.88003i	0.341129	−	0.940016i	$-0.389191\pi$
$810$		0			0
$811$			26.2305i			0.921078i	0.887640	+	0.460539i	$0.152344\pi$
$811$			26.2305i			0.921078i	−0.887640	+	0.460539i	$0.847656\pi$
$812$		0			0
$813$	4.70063	−	22.9939i	0.164858	−	0.806433i
$814$		0			0
$815$	17.4779	−	30.2726i	0.612224	−	1.06040i
$816$		0			0
$817$	4.91914	−	2.84006i	0.172099	−	0.0993613i
$818$		0			0
$819$	−10.6181	−	1.29905i	−0.371025	−	0.0453924i
$820$		0			0
$821$	−10.7877	+	6.22830i	−0.376495	+	0.217369i	−0.676292	−	0.736634i	$-0.736414\pi$
$821$	−10.7877	+	6.22830i	−0.376495	+	0.217369i	0.299797	+	0.954003i	$0.403081\pi$
$822$		0			0
$823$	11.8574	−	20.5376i	0.413323	−	0.715897i	−0.581928	−	0.813241i	$-0.697701\pi$
$823$	11.8574	−	20.5376i	0.413323	−	0.715897i	0.995251	+	0.0973438i	$0.0310346\pi$
$824$		0			0
$825$	−2.34935	−	2.08246i	−0.0817938	−	0.0725019i
$826$		0			0
$827$			13.9408i			0.484770i	0.970180	+	0.242385i	$0.0779298\pi$
$827$			13.9408i			0.484770i	−0.970180	+	0.242385i	$0.922070\pi$
$828$		0			0
$829$			13.9568i			0.484739i	0.970184	+	0.242369i	$0.0779246\pi$
$829$			13.9568i			0.484739i	−0.970184	+	0.242369i	$0.922075\pi$
$830$		0			0
$831$	1.09182	+	3.27331i	0.0378749	+	0.113550i
$832$		0			0
$833$	2.19878	+	55.5992i	0.0761831	+	1.92640i
$834$		0			0
$835$	−29.2052	−	50.5849i	−1.01069	−	1.75056i
$836$		0			0
$837$	4.76077	+	10.0538i	0.164556	+	0.347512i
$838$		0			0
$839$	−3.81179	−	6.60221i	−0.131597	−	0.227933i	0.792695	−	0.609618i	$-0.208677\pi$
$839$	−3.81179	−	6.60221i	−0.131597	−	0.227933i	−0.924293	+	0.381685i	$0.875344\pi$
$840$		0			0
$841$	−10.8589	+	18.8081i	−0.374444	+	0.648556i
$842$		0			0
$843$	−43.5909	+	14.5399i	−1.50135	+	0.500780i
$844$		0			0
$845$	40.0650			1.37828
$846$		0			0
$847$	8.04719	+	27.8212i	0.276505	+	0.955948i
$848$		0			0
$849$	15.4277	+	13.6751i	0.529477	+	0.469327i
$850$		0			0
$851$	35.4696	+	20.4784i	1.21588	+	0.701990i
$852$		0			0
$853$	26.8767	−	15.5173i	0.920242	−	0.531302i	0.0365294	−	0.999333i	$-0.488370\pi$
$853$	26.8767	−	15.5173i	0.920242	−	0.531302i	0.883712	+	0.468031i	$0.155036\pi$
$854$		0			0
$855$	−19.7534	−	26.3162i	−0.675552	−	0.899995i
$856$		0			0
$857$	11.1297	+	19.2772i	0.380184	+	0.658497i	0.991088	−	0.133207i	$-0.0425275\pi$
$857$	11.1297	+	19.2772i	0.380184	+	0.658497i	−0.610905	+	0.791704i	$0.709194\pi$
$858$		0			0
$859$	27.9713	+	16.1492i	0.954369	+	0.551005i	0.894435	−	0.447197i	$-0.147578\pi$
$859$	27.9713	+	16.1492i	0.954369	+	0.551005i	0.0599334	+	0.998202i	$0.480911\pi$
$860$		0			0
$861$	0.595379	+	7.43456i	0.0202905	+	0.253369i
$862$		0			0
$863$		−	33.0060i		−	1.12354i	−0.827295	−	0.561768i	$-0.810121\pi$
$863$		−	33.0060i		−	1.12354i	0.827295	−	0.561768i	$-0.189879\pi$
$864$		0			0
$865$	4.88302			0.166028
$866$		0			0
$867$	−78.3754	−	16.0222i	−2.66177	−	0.544142i
$868$		0			0
$869$	1.32588	+	0.765495i	0.0449773	+	0.0259676i
$870$		0			0
$871$	11.8055	−	6.81592i	0.400015	−	0.230949i
$872$		0			0
$873$	45.1638	−	5.45947i	1.52856	−	0.184775i
$874$		0			0
$875$	18.6150	−	19.3658i	0.629303	−	0.654682i
$876$		0			0
$877$	−16.7520	+	29.0153i	−0.565675	+	0.979778i	0.431311	+	0.902203i	$0.358051\pi$
$877$	−16.7520	+	29.0153i	−0.565675	+	0.979778i	−0.996987	+	0.0775752i	$0.975282\pi$
$878$		0			0
$879$	7.73026	−	8.72098i	0.260735	−	0.294151i
$880$		0			0
$881$	−18.6150			−0.627156			−0.313578	−	0.949562i	$-0.601528\pi$
$881$	−18.6150			−0.627156			−0.313578	+	0.949562i	$0.601528\pi$
$882$		0			0
$883$	−31.6752			−1.06595			−0.532977	−	0.846130i	$-0.678927\pi$
$883$	−31.6752			−1.06595			−0.532977	+	0.846130i	$0.678927\pi$
$884$		0			0
$885$	−25.4692	−	76.3574i	−0.856139	−	2.56673i
$886$		0			0
$887$	−21.8400	+	37.8280i	−0.733315	+	1.27014i	0.222144	+	0.975014i	$0.428695\pi$
$887$	−21.8400	+	37.8280i	−0.733315	+	1.27014i	−0.955459	+	0.295125i	$0.904639\pi$
$888$		0			0
$889$	22.2690	−	23.1671i	0.746879	−	0.776999i
$890$		0			0
$891$	−1.99949	−	0.581470i	−0.0669856	−	0.0194800i
$892$		0			0
$893$	−0.210143	+	0.121326i	−0.00703215	+	0.00406001i
$894$		0			0
$895$	48.1827	+	27.8183i	1.61057	+	0.929863i
$896$		0			0
$897$	−4.15836	−	12.4669i	−0.138844	−	0.416256i
$898$		0			0
$899$	5.77716			0.192679
$900$		0			0
$901$		−	92.8792i		−	3.09426i
$902$		0			0
$903$	7.67858	+	3.64957i	0.255527	+	0.121450i
$904$		0			0
$905$	−54.4222	−	31.4207i	−1.80905	−	1.04446i
$906$		0			0
$907$	−24.0218	−	41.6070i	−0.797631	−	1.38154i	−0.921155	−	0.389196i	$-0.872753\pi$
$907$	−24.0218	−	41.6070i	−0.797631	−	1.38154i	0.123524	−	0.992342i	$-0.460580\pi$
$908$		0			0
$909$	2.72239	+	22.5211i	0.0902959	+	0.746978i
$910$		0			0
$911$	−36.8038	+	21.2487i	−1.21937	+	0.704001i	−0.964782	−	0.263050i	$-0.915272\pi$
$911$	−36.8038	+	21.2487i	−1.21937	+	0.704001i	−0.254584	+	0.967051i	$0.581938\pi$
$912$		0			0
$913$	2.57194	+	1.48491i	0.0851188	+	0.0491434i
$914$		0			0
$915$	−1.04622	+	5.11779i	−0.0345871	+	0.169189i
$916$		0			0
$917$	12.1686	+	42.0701i	0.401844	+	1.38928i
$918$		0			0
$919$	11.3790			0.375358			0.187679	−	0.982230i	$-0.439904\pi$
$919$	11.3790			0.375358			0.187679	+	0.982230i	$0.439904\pi$
$920$		0			0
$921$	4.95423	−	24.2345i	0.163247	−	0.798554i
$922$		0			0
$923$	5.04021	−	8.72989i	0.165900	−	0.287348i
$924$		0			0
$925$	28.4956	+	49.3558i	0.936929	+	1.62281i
$926$		0			0
$927$	−21.1117	−	28.1257i	−0.693398	−	0.923769i
$928$		0			0
$929$	0.0349888	+	0.0606024i	0.00114795	+	0.00198830i	0.866599	−	0.499006i	$-0.166301\pi$
$929$	0.0349888	+	0.0606024i	0.00114795	+	0.00198830i	−0.865451	+	0.500994i	$0.832968\pi$
$930$		0			0
$931$	21.4150	−	0.846896i	0.701848	−	0.0277559i
$932$		0			0
$933$	−11.4801	+	12.9514i	−0.375841	+	0.424009i
$934$		0			0
$935$			6.58867i			0.215472i
$936$		0			0
$937$		−	21.7954i		−	0.712026i	−0.934481	−	0.356013i	$-0.884136\pi$
$937$		−	21.7954i		−	0.712026i	0.934481	−	0.356013i	$-0.115864\pi$
$938$		0			0
$939$	3.90064	−	1.30107i	0.127293	−	0.0424588i
$940$		0			0
$941$	−14.4480	+	25.0247i	−0.470993	+	0.815784i	−0.999450	−	0.0331768i	$-0.989438\pi$
$941$	−14.4480	+	25.0247i	−0.470993	+	0.815784i	0.528457	+	0.848960i	$0.322771\pi$
$942$		0			0
$943$	−7.93538	+	4.58149i	−0.258411	+	0.149194i
$944$		0			0
$945$	15.6510	−	46.6977i	0.509126	−	1.51908i
$946$		0			0
$947$	9.77197	−	5.64185i	0.317546	−	0.183335i	−0.332752	−	0.943014i	$-0.607977\pi$
$947$	9.77197	−	5.64185i	0.317546	−	0.183335i	0.650298	+	0.759679i	$0.274644\pi$
$948$		0			0
$949$	5.37574	−	9.31105i	0.174504	−	0.302249i
$950$		0			0
$951$	−2.80879	+	0.936881i	−0.0910813	+	0.0303804i
$952$		0			0
$953$			40.5950i			1.31500i	0.753454	+	0.657501i	$0.228386\pi$
$953$			40.5950i			1.31500i	−0.753454	+	0.657501i	$0.771614\pi$
$954$		0			0
$955$		−	6.92281i		−	0.224017i
$956$		0			0
$957$	−0.717338	+	0.809273i	−0.0231883	+	0.0261601i
$958$		0			0
$959$	−10.1231	+	41.0050i	−0.326893	+	1.32412i
$960$		0			0
$961$	−13.2084	−	22.8777i	−0.426078	−	0.737989i
$962$		0			0
$963$	14.2963	−	33.5051i	0.460691	−	1.07969i
$964$		0			0
$965$	7.01395	+	12.1485i	0.225787	+	0.391075i
$966$		0			0
$967$	5.88584	−	10.1946i	0.189276	−	0.327835i	−0.755733	−	0.654880i	$-0.772719\pi$
$967$	5.88584	−	10.1946i	0.189276	−	0.327835i	0.945009	+	0.327044i	$0.106053\pi$
$968$		0			0
$969$	−8.44271	+	41.2990i	−0.271219	+	1.32672i
$970$		0			0
$971$	35.5390			1.14050			0.570250	−	0.821471i	$-0.306846\pi$
$971$	35.5390			1.14050			0.570250	+	0.821471i	$0.306846\pi$
$972$		0			0
$973$	21.7213	−	6.28281i	0.696352	−	0.201417i
$974$		0			0
$975$	3.66267	−	17.9166i	0.117299	−	0.573791i
$976$		0			0
$977$	8.68968	+	5.01699i	0.278007	+	0.160508i	0.632521	−	0.774543i	$-0.282020\pi$
$977$	8.68968	+	5.01699i	0.278007	+	0.160508i	−0.354514	+	0.935051i	$0.615354\pi$
$978$		0			0
$979$	−0.713458	+	0.411915i	−0.0228022	+	0.0131649i
$980$		0			0
$981$	−38.2894	−	16.3377i	−1.22249	−	0.521622i
$982$		0			0
$983$	−16.6532	−	28.8443i	−0.531156	−	0.919989i	−0.999339	−	0.0363574i	$-0.988425\pi$
$983$	−16.6532	−	28.8443i	−0.531156	−	0.919989i	0.468183	−	0.883632i	$-0.344909\pi$
$984$		0			0
$985$	39.0016	+	22.5176i	1.24269	+	0.717469i
$986$		0			0
$987$	−0.328024	−	0.155907i	−0.0104411	−	0.00496258i
$988$		0			0
$989$			10.4449i			0.332127i
$990$		0			0
$991$	−0.563501			−0.0179002			−0.00895010	−	0.999960i	$-0.502849\pi$
$991$	−0.563501			−0.0179002			−0.00895010	+	0.999960i	$0.502849\pi$
$992$		0			0
$993$	11.5149	+	34.5221i	0.365416	+	1.09552i
$994$		0			0
$995$	−52.8217	−	30.4966i	−1.67456	−	0.966808i
$996$		0			0
$997$	17.1879	−	9.92344i	0.544346	−	0.314278i	−0.202492	−	0.979284i	$-0.564904\pi$
$997$	17.1879	−	9.92344i	0.544346	−	0.314278i	0.746839	+	0.665005i	$0.231571\pi$
$998$		0			0
$999$	31.0925	+	21.4983i	0.983725	+	0.680177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bu.a.41.2	✓	48
3.2	odd	2		1512.2.bu.a.881.22		48
4.3	odd	2		1008.2.cc.d.545.23		48
7.6	odd	2	inner	504.2.bu.a.41.23	yes	48
9.2	odd	6	inner	504.2.bu.a.209.23	yes	48
9.4	even	3		4536.2.k.a.3401.44		48
9.5	odd	6		4536.2.k.a.3401.5		48
9.7	even	3		1512.2.bu.a.1385.3		48
12.11	even	2		3024.2.cc.d.881.22		48
21.20	even	2		1512.2.bu.a.881.3		48
28.27	even	2		1008.2.cc.d.545.2		48
36.7	odd	6		3024.2.cc.d.2897.3		48
36.11	even	6		1008.2.cc.d.209.2		48
63.13	odd	6		4536.2.k.a.3401.6		48
63.20	even	6	inner	504.2.bu.a.209.2	yes	48
63.34	odd	6		1512.2.bu.a.1385.22		48
63.41	even	6		4536.2.k.a.3401.43		48
84.83	odd	2		3024.2.cc.d.881.3		48
252.83	odd	6		1008.2.cc.d.209.23		48
252.223	even	6		3024.2.cc.d.2897.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.2	✓	48	1.1	even	1	trivial
504.2.bu.a.41.23	yes	48	7.6	odd	2	inner
504.2.bu.a.209.2	yes	48	63.20	even	6	inner
504.2.bu.a.209.23	yes	48	9.2	odd	6	inner
1008.2.cc.d.209.2		48	36.11	even	6
1008.2.cc.d.209.23		48	252.83	odd	6
1008.2.cc.d.545.2		48	28.27	even	2
1008.2.cc.d.545.23		48	4.3	odd	2
1512.2.bu.a.881.3		48	21.20	even	2
1512.2.bu.a.881.22		48	3.2	odd	2
1512.2.bu.a.1385.3		48	9.7	even	3
1512.2.bu.a.1385.22		48	63.34	odd	6
3024.2.cc.d.881.3		48	84.83	odd	2
3024.2.cc.d.881.22		48	12.11	even	2
3024.2.cc.d.2897.3		48	36.7	odd	6
3024.2.cc.d.2897.22		48	252.223	even	6
4536.2.k.a.3401.5		48	9.5	odd	6
4536.2.k.a.3401.6		48	63.13	odd	6
4536.2.k.a.3401.43		48	63.41	even	6
4536.2.k.a.3401.44		48	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69695 - 0.346907i) q^{3} +(-1.79123 + 3.10250i) q^{5} +(1.83349 - 1.90743i) q^{7} +(2.75931 + 1.17737i) q^{9} +O(q^{10})\)	\(q+(-1.69695 - 0.346907i) q^{3} +(-1.79123 + 3.10250i) q^{5} +(1.83349 - 1.90743i) q^{7} +(2.75931 + 1.17737i) q^{9} +(-0.200372 + 0.115685i) q^{11} +(-1.16716 - 0.673862i) q^{13} +(4.11592 - 4.64342i) q^{15} -7.94895 q^{17} +3.06168i q^{19} +(-3.77306 + 2.60078i) q^{21} +(-4.87566 - 2.81497i) q^{23} +(-3.91701 - 6.78446i) q^{25} +(-4.27399 - 2.95517i) q^{27} +(-2.33703 + 1.34928i) q^{29} +(-1.85401 - 1.07041i) q^{31} +(0.380154 - 0.126802i) q^{33} +(2.63361 + 9.10507i) q^{35} -7.27483 q^{37} +(1.74685 + 1.54841i) q^{39} +(0.813774 - 1.40950i) q^{41} +(-0.927618 - 1.60668i) q^{43} +(-8.59535 + 6.45183i) q^{45} +(0.0396273 + 0.0686364i) q^{47} +(-0.276612 - 6.99453i) q^{49} +(13.4890 + 2.75754i) q^{51} +11.6845i q^{53} -0.828872i q^{55} +(1.06212 - 5.19553i) q^{57} +(6.48614 - 11.2343i) q^{59} +(-0.729056 + 0.420921i) q^{61} +(7.30493 - 3.10451i) q^{63} +(4.18131 - 2.41408i) q^{65} +(-5.05736 + 8.75961i) q^{67} +(7.29725 + 6.46827i) q^{69} +7.47959i q^{71} +7.97751i q^{73} +(4.29342 + 12.8718i) q^{75} +(-0.146719 + 0.594303i) q^{77} +(-3.30854 - 5.73056i) q^{79} +(6.22760 + 6.49746i) q^{81} +(-6.41792 - 11.1162i) q^{83} +(14.2384 - 24.6616i) q^{85} +(4.43390 - 1.47894i) q^{87} +3.56067 q^{89} +(-3.42533 + 0.990766i) q^{91} +(2.77484 + 2.45961i) q^{93} +(-9.49885 - 5.48417i) q^{95} +(13.1326 - 7.58210i) q^{97} +(-0.689092 + 0.0832985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} - 4 q^{21} + 12 q^{23} - 24 q^{25} - 36 q^{29} + 32 q^{39} + 12 q^{43} + 6 q^{49} + 24 q^{51} + 28 q^{57} - 14 q^{63} + 36 q^{65} - 60 q^{77} - 12 q^{79} - 36 q^{81} - 12 q^{91} + 16 q^{93} - 108 q^{95} + 44 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 - 4 * q^21 + 12 * q^23 - 24 * q^25 - 36 * q^29 + 32 * q^39 + 12 * q^43 + 6 * q^49 + 24 * q^51 + 28 * q^57 - 14 * q^63 + 36 * q^65 - 60 * q^77 - 12 * q^79 - 36 * q^81 - 12 * q^91 + 16 * q^93 - 108 * q^95 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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