LMFDB - Embedded newform 819.2.bm.h.550.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.1
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.h.478.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69813i q^{2} -5.27990 q^{4} +(0.933651 - 0.539043i) q^{5} +(2.30689 - 1.29548i) q^{7} +8.84961i q^{8} +O(q^{10})$	\(q-2.69813i q^{2} -5.27990 q^{4} +(0.933651 - 0.539043i) q^{5} +(2.30689 - 1.29548i) q^{7} +8.84961i q^{8} +(-1.45441 - 2.51911i) q^{10} +(-4.50041 + 2.59831i) q^{11} +(-1.40876 - 3.31894i) q^{13} +(-3.49539 - 6.22428i) q^{14} +13.3176 q^{16} -5.38051 q^{17} +(-5.71250 - 3.29811i) q^{19} +(-4.92959 + 2.84610i) q^{20} +(7.01059 + 12.1427i) q^{22} -2.00265 q^{23} +(-1.91886 + 3.32357i) q^{25} +(-8.95494 + 3.80102i) q^{26} +(-12.1801 + 6.84004i) q^{28} +(-2.56579 + 4.44409i) q^{29} +(4.21250 + 2.43209i) q^{31} -18.2333i q^{32} +14.5173i q^{34} +(1.45550 - 2.45304i) q^{35} -7.82597i q^{37} +(-8.89874 + 15.4131i) q^{38} +(4.77032 + 8.26244i) q^{40} +(-1.70119 - 0.982182i) q^{41} +(-3.82763 - 6.62964i) q^{43} +(23.7617 - 13.7188i) q^{44} +5.40340i q^{46} +(8.33272 - 4.81090i) q^{47} +(3.64344 - 5.97707i) q^{49} +(8.96742 + 5.17735i) q^{50} +(7.43812 + 17.5237i) q^{52} +(0.752985 - 1.30421i) q^{53} +(-2.80121 + 4.85183i) q^{55} +(11.4645 + 20.4150i) q^{56} +(11.9907 + 6.92285i) q^{58} -7.61536i q^{59} +(-2.74027 + 4.74628i) q^{61} +(6.56209 - 11.3659i) q^{62} -22.5608 q^{64} +(-3.10435 - 2.33935i) q^{65} +(4.83503 - 2.79151i) q^{67} +28.4086 q^{68} +(-6.61862 - 3.92713i) q^{70} +(-8.55573 + 4.93965i) q^{71} +(4.88610 + 2.82099i) q^{73} -21.1155 q^{74} +(30.1614 + 17.4137i) q^{76} +(-7.01586 + 11.8242i) q^{77} +(1.65033 + 2.85846i) q^{79} +(12.4340 - 7.17876i) q^{80} +(-2.65006 + 4.59003i) q^{82} -8.99871i q^{83} +(-5.02351 + 2.90033i) q^{85} +(-17.8876 + 10.3274i) q^{86} +(-22.9941 - 39.8269i) q^{88} +13.8382i q^{89} +(-7.54949 - 5.83140i) q^{91} +10.5738 q^{92} +(-12.9804 - 22.4828i) q^{94} -7.11130 q^{95} +(6.64083 - 3.83409i) q^{97} +(-16.1269 - 9.83047i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) $ 36 * q - 44 * q^4 + 8 * q^7	$ 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) $ 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	2.69813i		−	1.90787i	−0.300020	−	0.953933i	$-0.596993\pi$
$2$		−	2.69813i		−	1.90787i	0.300020	−	0.953933i	$-0.403007\pi$
$3$		0			0
$3$		0			0
$4$	−5.27990			−2.63995
$5$	0.933651	−	0.539043i	0.417541	−	0.241068i	−0.276484	−	0.961019i	$-0.589169\pi$
$5$	0.933651	−	0.539043i	0.417541	−	0.241068i	0.694025	+	0.719951i	$0.255836\pi$
$6$		0			0
$7$	2.30689	−	1.29548i	0.871921	−	0.489647i
$7$	2.30689	−	1.29548i	0.871921	−	0.489647i
$8$			8.84961i			3.12881i
$9$		0			0
$10$	−1.45441	−	2.51911i	−0.459925	−	0.796613i
$11$	−4.50041	+	2.59831i	−1.35693	+	0.783421i	−0.989208	−	0.146517i	$-0.953194\pi$
$11$	−4.50041	+	2.59831i	−1.35693	+	0.783421i	−0.367717	+	0.929938i	$0.619860\pi$
$12$		0			0
$13$	−1.40876	−	3.31894i	−0.390720	−	0.920510i
$13$	−1.40876	−	3.31894i	−0.390720	−	0.920510i
$14$	−3.49539	−	6.22428i	−0.934181	−	1.66351i
$15$		0			0
$16$	13.3176			3.32940
$17$	−5.38051			−1.30496			−0.652482	−	0.757804i	$-0.726272\pi$
$17$	−5.38051			−1.30496			−0.652482	+	0.757804i	$0.726272\pi$
$18$		0			0
$19$	−5.71250	−	3.29811i	−1.31054	−	0.756639i	−0.328352	−	0.944555i	$-0.606493\pi$
$19$	−5.71250	−	3.29811i	−1.31054	−	0.756639i	−0.982185	+	0.187916i	$0.939827\pi$
$20$	−4.92959	+	2.84610i	−1.10229	+	0.636407i
$21$		0			0
$22$	7.01059	+	12.1427i	1.49466	+	2.58883i
$23$	−2.00265			−0.417581			−0.208790	−	0.977960i	$-0.566953\pi$
$23$	−2.00265			−0.417581			−0.208790	+	0.977960i	$0.566953\pi$
$24$		0			0
$25$	−1.91886	+	3.32357i	−0.383773	+	0.664714i
$26$	−8.95494	+	3.80102i	−1.75621	+	0.745441i
$27$		0			0
$28$	−12.1801	+	6.84004i	−2.30183	+	1.29265i
$29$	−2.56579	+	4.44409i	−0.476456	+	0.825246i	−0.999636	−	0.0269760i	$-0.991412\pi$
$29$	−2.56579	+	4.44409i	−0.476456	+	0.825246i	0.523180	+	0.852222i	$0.324746\pi$
$30$		0			0
$31$	4.21250	+	2.43209i	0.756587	+	0.436816i	0.828069	−	0.560626i	$-0.189439\pi$
$31$	4.21250	+	2.43209i	0.756587	+	0.436816i	−0.0714819	+	0.997442i	$0.522773\pi$
$32$		−	18.2333i		−	3.22323i
$33$		0			0
$34$			14.5173i			2.48970i
$35$	1.45550	−	2.45304i	0.246025	−	0.414640i
$36$		0			0
$37$		−	7.82597i		−	1.28658i	−0.765622	−	0.643291i	$-0.777568\pi$
$37$		−	7.82597i		−	1.28658i	0.765622	−	0.643291i	$-0.222432\pi$
$38$	−8.89874	+	15.4131i	−1.44357	+	2.50033i
$39$		0			0
$40$	4.77032	+	8.26244i	0.754254	+	1.30641i
$41$	−1.70119	−	0.982182i	−0.265681	−	0.153391i	0.361242	−	0.932472i	$-0.382353\pi$
$41$	−1.70119	−	0.982182i	−0.265681	−	0.153391i	−0.626923	+	0.779081i	$0.715686\pi$
$42$		0			0
$43$	−3.82763	−	6.62964i	−0.583707	−	1.01101i	−0.995035	−	0.0995234i	$-0.968268\pi$
$43$	−3.82763	−	6.62964i	−0.583707	−	1.01101i	0.411328	−	0.911487i	$-0.365065\pi$
$44$	23.7617	−	13.7188i	3.58222	−	2.06819i
$45$		0			0
$46$			5.40340i			0.796688i
$47$	8.33272	−	4.81090i	1.21545	−	0.701741i	0.251510	−	0.967855i	$-0.419073\pi$
$47$	8.33272	−	4.81090i	1.21545	−	0.701741i	0.963942	+	0.266113i	$0.0857395\pi$
$48$		0			0
$49$	3.64344	−	5.97707i	0.520491	−	0.853867i
$50$	8.96742	+	5.17735i	1.26819	+	0.732187i
$51$		0			0
$52$	7.43812	+	17.5237i	1.03148	+	2.43010i
$53$	0.752985	−	1.30421i	0.103431	−	0.179147i	−0.809665	−	0.586892i	$-0.800351\pi$
$53$	0.752985	−	1.30421i	0.103431	−	0.179147i	0.913096	+	0.407745i	$0.133685\pi$
$54$		0			0
$55$	−2.80121	+	4.85183i	−0.377715	+	0.654221i
$56$	11.4645	+	20.4150i	1.53201	+	2.72807i
$57$		0			0
$58$	11.9907	+	6.92285i	1.57446	+	0.909014i
$59$		−	7.61536i		−	0.991435i	−0.868484	−	0.495718i	$-0.834905\pi$
$59$		−	7.61536i		−	0.991435i	0.868484	−	0.495718i	$-0.165095\pi$
$60$		0			0
$61$	−2.74027	+	4.74628i	−0.350855	+	0.607699i	−0.986400	−	0.164366i	$-0.947442\pi$
$61$	−2.74027	+	4.74628i	−0.350855	+	0.607699i	0.635544	+	0.772064i	$0.280776\pi$
$62$	6.56209	−	11.3659i	0.833386	−	1.44347i
$63$		0			0
$64$	−22.5608			−2.82010
$65$	−3.10435	−	2.33935i	−0.385047	−	0.290161i
$66$		0			0
$67$	4.83503	−	2.79151i	0.590693	−	0.341037i	−0.174678	−	0.984626i	$-0.555889\pi$
$67$	4.83503	−	2.79151i	0.590693	−	0.341037i	0.765372	+	0.643589i	$0.222555\pi$
$68$	28.4086			3.44504
$69$		0			0
$70$	−6.61862	−	3.92713i	−0.791077	−	0.469382i
$71$	−8.55573	+	4.93965i	−1.01538	+	0.586229i	−0.912762	−	0.408492i	$-0.866055\pi$
$71$	−8.55573	+	4.93965i	−1.01538	+	0.586229i	−0.102617	+	0.994721i	$0.532722\pi$
$72$		0			0
$73$	4.88610	+	2.82099i	0.571874	+	0.330172i	0.757898	−	0.652374i	$-0.226227\pi$
$73$	4.88610	+	2.82099i	0.571874	+	0.330172i	−0.186023	+	0.982545i	$0.559560\pi$
$74$	−21.1155			−2.45463
$75$		0			0
$76$	30.1614	+	17.4137i	3.45976	+	1.99749i
$77$	−7.01586	+	11.8242i	−0.799531	+	1.34750i
$78$		0			0
$79$	1.65033	+	2.85846i	0.185677	+	0.321602i	0.943804	−	0.330504i	$-0.107219\pi$
$79$	1.65033	+	2.85846i	0.185677	+	0.321602i	−0.758127	+	0.652106i	$0.773886\pi$
$80$	12.4340	−	7.17876i	1.39016	−	0.802609i
$81$		0			0
$82$	−2.65006	+	4.59003i	−0.292650	+	0.506884i
$83$		−	8.99871i		−	0.987737i	−0.869537	−	0.493868i	$-0.835582\pi$
$83$		−	8.99871i		−	0.987737i	0.869537	−	0.493868i	$-0.164418\pi$
$84$		0			0
$85$	−5.02351	+	2.90033i	−0.544877	+	0.314585i
$86$	−17.8876	+	10.3274i	−1.92887	+	1.11364i
$87$		0			0
$88$	−22.9941	−	39.8269i	−2.45118	−	4.24556i
$89$			13.8382i			1.46685i	0.679773	+	0.733423i	$0.262078\pi$
$89$			13.8382i			1.46685i	−0.679773	+	0.733423i	$0.737922\pi$
$90$		0			0
$91$	−7.54949	−	5.83140i	−0.791402	−	0.611296i
$92$	10.5738			1.10239
$93$		0			0
$94$	−12.9804	−	22.4828i	−1.33883	−	2.31892i
$95$	−7.11130			−0.729604
$96$		0			0
$97$	6.64083	−	3.83409i	0.674274	−	0.389293i	−0.123420	−	0.992355i	$-0.539386\pi$
$97$	6.64083	−	3.83409i	0.674274	−	0.389293i	0.797694	+	0.603062i	$0.206053\pi$
$98$	−16.1269	−	9.83047i	−1.62906	−	0.993028i
$99$		0			0
$100$	10.1314	−	17.5481i	1.01314	−	1.75481i
$101$	0.349323	+	0.605045i	0.0347589	+	0.0602042i	0.882882	−	0.469596i	$-0.155600\pi$
$101$	0.349323	+	0.605045i	0.0347589	+	0.0602042i	−0.848123	+	0.529800i	$0.822267\pi$
$102$		0			0
$103$	3.07305	+	5.32269i	0.302797	+	0.524460i	0.976768	−	0.214298i	$-0.0687463\pi$
$103$	3.07305	+	5.32269i	0.302797	+	0.524460i	−0.673971	+	0.738757i	$0.735413\pi$
$104$	29.3714	−	12.4670i	2.88010	−	1.22249i
$105$		0			0
$106$	−3.51893	−	2.03165i	−0.341788	−	0.197332i
$107$	4.66589			0.451069			0.225534	−	0.974235i	$-0.427587\pi$
$107$	4.66589			0.451069			0.225534	+	0.974235i	$0.427587\pi$
$108$		0			0
$109$	0.483341	+	0.279057i	0.0462957	+	0.0267288i	0.522969	−	0.852352i	$-0.324824\pi$
$109$	0.483341	+	0.279057i	0.0462957	+	0.0267288i	−0.476674	+	0.879080i	$0.658158\pi$
$110$	13.0909	+	7.55802i	1.24817	+	0.720629i
$111$		0			0
$112$	30.7221	−	17.2527i	2.90297	−	1.63023i
$113$	−8.84209	−	15.3149i	−0.831793	−	1.44071i	−0.896615	−	0.442812i	$-0.853981\pi$
$113$	−8.84209	−	15.3149i	−0.831793	−	1.44071i	0.0648213	−	0.997897i	$-0.479352\pi$
$114$		0			0
$115$	−1.86977	+	1.07951i	−0.174357	+	0.100665i
$116$	13.5472	−	23.4644i	1.25782	−	2.17861i
$117$		0			0
$118$	−20.5472			−1.89153
$119$	−12.4122	+	6.97036i	−1.13783	+	0.638972i
$120$		0			0
$121$	8.00247	−	13.8607i	0.727497	−	1.26006i
$122$	12.8061	+	7.39359i	1.15941	+	0.669384i
$123$		0			0
$124$	−22.2416	−	12.8412i	−1.99735	−	1.15317i
$125$			9.52784i			0.852196i
$126$		0			0
$127$	6.34559	−	10.9909i	0.563080	−	0.975283i	−0.434145	−	0.900843i	$-0.642950\pi$
$127$	6.34559	−	10.9909i	0.563080	−	0.975283i	0.997225	−	0.0744404i	$-0.0237171\pi$
$128$			24.4052i			2.15714i
$129$		0			0
$130$	−6.31187	+	8.37593i	−0.553588	+	0.734617i
$131$	−2.17460	−	3.76651i	−0.189995	−	0.329082i	0.755253	−	0.655433i	$-0.227514\pi$
$131$	−2.17460	−	3.76651i	−0.189995	−	0.329082i	−0.945248	+	0.326352i	$0.894181\pi$
$132$		0			0
$133$	−17.4507	−	0.207913i	−1.51317	−	0.0180284i
$134$	−7.53185	−	13.0456i	−0.650653	−	1.12696i
$135$		0			0
$136$		−	47.6154i		−	4.08298i
$137$			4.39580i			0.375559i	0.982211	+	0.187779i	$0.0601290\pi$
$137$			4.39580i			0.375559i	−0.982211	+	0.187779i	$0.939871\pi$
$138$		0			0
$139$	−4.61255	−	7.98917i	−0.391231	−	0.677633i	0.601381	−	0.798962i	$-0.294617\pi$
$139$	−4.61255	−	7.98917i	−0.391231	−	0.677633i	−0.992612	+	0.121330i	$0.961284\pi$
$140$	−7.68491	+	12.9518i	−0.649494	+	1.09463i
$141$		0			0
$142$	13.3278	+	23.0845i	1.11845	+	1.93721i
$143$	14.9637	+	11.2762i	1.25132	+	0.942964i
$144$		0			0
$145$			5.53230i			0.459432i
$146$	7.61139	−	13.1833i	0.629923	−	1.09106i
$147$		0			0
$148$			41.3204i			3.39652i
$149$	−3.42608	−	1.97805i	−0.280676	−	0.162048i	0.353054	−	0.935603i	$-0.385143\pi$
$149$	−3.42608	−	1.97805i	−0.280676	−	0.162048i	−0.633729	+	0.773555i	$0.718477\pi$
$150$		0			0
$151$	−3.29386	−	1.90171i	−0.268050	−	0.154759i	0.359951	−	0.932971i	$-0.382793\pi$
$151$	−3.29386	−	1.90171i	−0.268050	−	0.154759i	−0.628001	+	0.778212i	$0.716127\pi$
$152$	29.1870	−	50.5534i	2.36738	−	4.10042i
$153$		0			0
$154$	31.9033	+	18.9297i	2.57084	+	1.52540i
$155$	5.24400			0.421208
$156$		0			0
$157$	0.00467797	−	0.00810248i	0.000373342	−	0.000646648i	−0.865839	−	0.500323i	$-0.833214\pi$
$157$	0.00467797	−	0.00810248i	0.000373342	−	0.000646648i	0.866212	+	0.499677i	$0.166548\pi$
$158$	7.71250	−	4.45281i	0.613573	−	0.354247i
$159$		0			0
$160$	−9.82857	−	17.0236i	−0.777016	−	1.34583i
$161$	−4.61988	+	2.59440i	−0.364097	+	0.204467i
$162$		0			0
$163$	−6.15054	−	3.55102i	−0.481748	−	0.278137i	0.239397	−	0.970922i	$-0.423050\pi$
$163$	−6.15054	−	3.55102i	−0.481748	−	0.278137i	−0.721145	+	0.692785i	$0.756384\pi$
$164$	8.98212	+	5.18583i	0.701386	+	0.404945i
$165$		0			0
$166$	−24.2797			−1.88447
$167$	−8.39042	−	4.84421i	−0.649270	−	0.374856i	0.138906	−	0.990306i	$-0.455641\pi$
$167$	−8.39042	−	4.84421i	−0.649270	−	0.374856i	−0.788177	+	0.615449i	$0.788975\pi$
$168$		0			0
$169$	−9.03078	+	9.35120i	−0.694676	+	0.719323i
$170$	7.82546	+	13.5541i	0.600185	+	1.03955i
$171$		0			0
$172$	20.2095	+	35.0039i	1.54096	+	2.66902i
$173$	−0.0440638	+	0.0763208i	−0.00335011	+	0.00580256i	−0.867696	−	0.497096i	$-0.834400\pi$
$173$	−0.0440638	+	0.0763208i	−0.00335011	+	0.00580256i	0.864345	+	0.502898i	$0.167733\pi$
$174$		0			0
$175$	−0.120965	+	10.1530i	−0.00914412	+	0.767491i
$176$	−59.9346	+	34.6033i	−4.51774	+	2.60832i
$177$		0			0
$178$	37.3372			2.79854
$179$	−4.24422	−	7.35121i	−0.317228	−	0.549455i	0.662681	−	0.748902i	$-0.269419\pi$
$179$	−4.24422	−	7.35121i	−0.317228	−	0.549455i	−0.979909	+	0.199447i	$0.936085\pi$
$180$		0			0
$181$	−3.99506			−0.296950			−0.148475	−	0.988916i	$-0.547436\pi$
$181$	−3.99506			−0.296950			−0.148475	+	0.988916i	$0.547436\pi$
$182$	−15.7339	+	20.3695i	−1.16627	+	1.50989i
$183$		0			0
$184$		−	17.7226i		−	1.30653i
$185$	−4.21854	−	7.30673i	−0.310153	−	0.537201i
$186$		0			0
$187$	24.2145	−	13.9802i	1.77074	−	1.02234i
$188$	−43.9960	+	25.4011i	−3.20873	+	1.85256i
$189$		0			0
$190$			19.1872i			1.39199i
$191$	−3.18691	+	5.51989i	−0.230597	+	0.399406i	−0.957984	−	0.286822i	$-0.907401\pi$
$191$	−3.18691	+	5.51989i	−0.230597	+	0.399406i	0.727387	+	0.686227i	$0.240735\pi$
$192$		0			0
$193$	1.64699	−	0.950888i	0.118553	−	0.0684464i	−0.439551	−	0.898218i	$-0.644862\pi$
$193$	1.64699	−	0.950888i	0.118553	−	0.0684464i	0.558104	+	0.829771i	$0.311529\pi$
$194$	−10.3449	−	17.9178i	−0.742718	−	1.28643i
$195$		0			0
$196$	−19.2370	+	31.5584i	−1.37407	+	2.25417i
$197$	1.40221	+	0.809569i	0.0999037	+	0.0576794i	0.549119	−	0.835744i	$-0.314963\pi$
$197$	1.40221	+	0.809569i	0.0999037	+	0.0576794i	−0.449216	+	0.893423i	$0.648297\pi$
$198$		0			0
$199$	−24.7712			−1.75599			−0.877993	−	0.478674i	$-0.841118\pi$
$199$	−24.7712			−1.75599			−0.877993	+	0.478674i	$0.841118\pi$
$200$	−29.4123	−	16.9812i	−2.07976	−	1.20075i
$201$		0			0
$202$	1.63249	−	0.942518i	0.114862	−	0.0663154i
$203$	−0.161748	+	13.5759i	−0.0113525	+	0.952845i
$204$		0			0
$205$	−2.11776			−0.147910
$206$	14.3613	−	8.29150i	1.00060	−	0.577696i
$207$		0			0
$208$	−18.7613	−	44.2003i	−1.30086	−	3.06474i
$209$	34.2781			2.37107
$210$		0			0
$211$	4.32116	−	7.48447i	0.297481	−	0.515252i	−0.678078	−	0.734990i	$-0.737187\pi$
$211$	4.32116	−	7.48447i	0.297481	−	0.515252i	0.975559	+	0.219738i	$0.0705201\pi$
$212$	−3.97569	+	6.88610i	−0.273052	+	0.472939i
$213$		0			0
$214$		−	12.5892i		−	0.860579i
$215$	−7.14733	−	4.12651i	−0.487444	−	0.281426i
$216$		0			0
$217$	12.8685	+	0.153319i	0.873570	+	0.0104080i
$218$	0.752932	−	1.30412i	0.0509950	−	0.0883259i
$219$		0			0
$220$	14.7901	−	25.6172i	0.997149	−	1.72711i
$221$	7.57985	+	17.8576i	0.509876	+	1.20123i
$222$		0			0
$223$	−0.199940	−	0.115435i	−0.0133890	−	0.00773013i	0.493291	−	0.869865i	$-0.335794\pi$
$223$	−0.199940	−	0.115435i	−0.0133890	−	0.00773013i	−0.506680	+	0.862134i	$0.669127\pi$
$224$	−23.6210	−	42.0622i	−1.57825	−	2.81040i
$225$		0			0
$226$	−41.3217	+	23.8571i	−2.74868	+	1.58695i
$227$		−	17.9577i		−	1.19189i	−0.803025	−	0.595946i	$-0.796777\pi$
$227$		−	17.9577i		−	1.19189i	0.803025	−	0.595946i	$-0.203223\pi$
$228$		0			0
$229$	6.60041	−	3.81075i	0.436167	−	0.251821i	−0.265803	−	0.964027i	$-0.585637\pi$
$229$	6.60041	−	3.81075i	0.436167	−	0.251821i	0.701971	+	0.712206i	$0.252304\pi$
$230$	2.91267	+	5.04489i	0.192056	+	0.332650i
$231$		0			0
$232$	−39.3284	−	22.7063i	−2.58204	−	1.49074i
$233$	−14.6265	−	25.3338i	−0.958212	−	1.65967i	−0.726841	−	0.686806i	$-0.759012\pi$
$233$	−14.6265	−	25.3338i	−0.958212	−	1.65967i	−0.231371	−	0.972866i	$-0.574321\pi$
$234$		0			0
$235$	5.18657	−	8.98339i	0.338334	−	0.586012i
$236$			40.2084i			2.61734i
$237$		0			0
$238$	18.8069	+	33.4898i	1.21907	+	2.17082i
$239$			5.13582i			0.332209i	0.986108	+	0.166104i	$0.0531189\pi$
$239$			5.13582i			0.332209i	−0.986108	+	0.166104i	$0.946881\pi$
$240$		0			0
$241$			23.1601i			1.49187i	0.666018	+	0.745936i	$0.267997\pi$
$241$			23.1601i			1.49187i	−0.666018	+	0.745936i	$0.732003\pi$
$242$	−37.3979	−	21.5917i	−2.40403	−	1.38797i
$243$		0			0
$244$	14.4683	−	25.0599i	0.926241	−	1.60430i
$245$	0.179800	−	7.54447i	0.0114870	−	0.481998i
$246$		0			0
$247$	−2.89871	+	23.6057i	−0.184440	+	1.50200i
$248$	−21.5230	+	37.2790i	−1.36671	+	2.36722i
$249$		0			0
$250$	25.7073			1.62588
$251$	9.83469	+	17.0342i	0.620760	+	1.07519i	0.989344	+	0.145594i	$0.0465093\pi$
$251$	9.83469	+	17.0342i	0.620760	+	1.07519i	−0.368584	+	0.929594i	$0.620157\pi$
$252$		0			0
$253$	9.01274	−	5.20351i	0.566626	−	0.327142i
$254$	−29.6548	−	17.1212i	−1.86071	−	1.07428i
$255$		0			0
$256$	20.7269			1.29543
$257$	22.1755			1.38327			0.691633	−	0.722249i	$-0.256891\pi$
$257$	22.1755			1.38327			0.691633	+	0.722249i	$0.256891\pi$
$258$		0			0
$259$	−10.1384	−	18.0536i	−0.629971	−	1.12180i
$260$	16.3906	+	12.3516i	1.01650	+	0.766011i
$261$		0			0
$262$	−10.1625	+	5.86735i	−0.627844	+	0.362486i
$263$	9.34338	+	16.1832i	0.576138	+	0.997900i	0.995917	+	0.0902735i	$0.0287741\pi$
$263$	9.34338	+	16.1832i	0.576138	+	0.997900i	−0.419779	+	0.907626i	$0.637893\pi$
$264$		0			0
$265$		−	1.62357i		−	0.0997350i
$266$	−0.560977	+	47.0843i	−0.0343957	+	2.88693i
$267$		0			0
$268$	−25.5285	+	14.7389i	−1.55940	+	0.900321i
$269$	5.64513			0.344189			0.172095	−	0.985080i	$-0.444946\pi$
$269$	5.64513			0.344189			0.172095	+	0.985080i	$0.444946\pi$
$270$		0			0
$271$		−	1.00407i		−	0.0609931i	−0.999535	−	0.0304966i	$-0.990291\pi$
$271$		−	1.00407i		−	0.0609931i	0.999535	−	0.0304966i	$-0.00970886\pi$
$272$	−71.6553			−4.34474
$273$		0			0
$274$	11.8604			0.716515
$275$		−	19.9432i		−	1.20262i
$276$		0			0
$277$	21.6611			1.30149			0.650746	−	0.759295i	$-0.274456\pi$
$277$	21.6611			1.30149			0.650746	+	0.759295i	$0.274456\pi$
$278$	−21.5558	+	12.4453i	−1.29283	+	0.746417i
$279$		0			0
$280$	21.7085	+	12.8806i	1.29733	+	0.769765i
$281$		−	2.58531i		−	0.154226i	−0.997022	−	0.0771132i	$-0.975430\pi$
$281$		−	2.58531i		−	0.154226i	0.997022	−	0.0771132i	$-0.0245703\pi$
$282$		0			0
$283$	−2.96888	−	5.14226i	−0.176482	−	0.305676i	0.764191	−	0.644990i	$-0.223138\pi$
$283$	−2.96888	−	5.14226i	−0.176482	−	0.305676i	−0.940673	+	0.339314i	$0.889805\pi$
$284$	45.1735	−	26.0809i	2.68055	−	1.54762i
$285$		0			0
$286$	30.4247	−	40.3739i	1.79905	−	2.38736i
$287$	−5.19685	−	0.0619168i	−0.306760	−	0.00365484i
$288$		0			0
$289$	11.9499			0.702932
$290$	14.9269			0.876536
$291$		0			0
$292$	−25.7981	−	14.8946i	−1.50972	−	0.871638i
$293$	26.8153	−	15.4818i	1.56656	−	0.904456i	0.569998	−	0.821646i	$-0.306944\pi$
$293$	26.8153	−	15.4818i	1.56656	−	0.904456i	0.996565	−	0.0828101i	$-0.0263895\pi$
$294$		0			0
$295$	−4.10501	−	7.11008i	−0.239003	−	0.413965i
$296$	69.2568			4.02547
$297$		0			0
$298$	−5.33703	+	9.24401i	−0.309166	+	0.535491i
$299$	2.82125	+	6.64667i	0.163157	+	0.384387i
$300$		0			0
$301$	−17.4185	−	10.3352i	−1.00399	−	0.595711i
$302$	−5.13106	+	8.88726i	−0.295259	+	0.511404i
$303$		0			0
$304$	−76.0767	−	43.9229i	−4.36330	−	2.51915i
$305$			5.90849i			0.338319i
$306$		0			0
$307$		−	12.1494i		−	0.693403i	−0.937975	−	0.346702i	$-0.887302\pi$
$307$		−	12.1494i		−	0.693403i	0.937975	−	0.346702i	$-0.112698\pi$
$308$	37.0431	−	62.4308i	2.11072	−	3.55732i
$309$		0			0
$310$		−	14.1490i		−	0.803609i
$311$	15.9039	−	27.5464i	0.901830	−	1.56202i	0.0767133	−	0.997053i	$-0.475557\pi$
$311$	15.9039	−	27.5464i	0.901830	−	1.56202i	0.825117	−	0.564962i	$-0.191109\pi$
$312$		0			0
$313$	5.79091	+	10.0302i	0.327322	+	0.566938i	0.981979	−	0.188988i	$-0.0605206\pi$
$313$	5.79091	+	10.0302i	0.327322	+	0.566938i	−0.654658	+	0.755925i	$0.727187\pi$
$314$	−0.0218615	−	0.0126218i	−0.00123372	−	0.000712287i
$315$		0			0
$316$	−8.71360	−	15.0924i	−0.490178	−	0.849014i
$317$	−8.86583	+	5.11869i	−0.497955	+	0.287494i	−0.727869	−	0.685717i	$-0.759489\pi$
$317$	−8.86583	+	5.11869i	−0.497955	+	0.287494i	0.229914	+	0.973211i	$0.426156\pi$
$318$		0			0
$319$		−	26.6670i		−	1.49306i
$320$	−21.0639	+	12.1612i	−1.17751	+	0.679834i
$321$		0			0
$322$	7.00002	+	12.4650i	0.390096	+	0.694649i
$323$	30.7361	+	17.7455i	1.71020	+	0.987387i
$324$		0			0
$325$	13.7340	+	1.68649i	0.761823	+	0.0935495i
$326$	−9.58111	+	16.5950i	−0.530649	+	0.919110i
$327$		0			0
$328$	8.69193	−	15.0549i	0.479931	−	0.831266i
$329$	12.9902	−	21.8931i	0.716172	−	1.20701i
$330$		0			0
$331$	−15.0349	−	8.68041i	−0.826393	−	0.477118i	0.0262228	−	0.999656i	$-0.491652\pi$
$331$	−15.0349	−	8.68041i	−0.826393	−	0.477118i	−0.852616	+	0.522538i	$0.824985\pi$
$332$			47.5123i			2.60758i
$333$		0			0
$334$	−13.0703	+	22.6384i	−0.715176	+	1.23872i
$335$	3.00949	−	5.21259i	0.164426	−	0.284794i
$336$		0			0
$337$	−32.4872			−1.76969			−0.884845	−	0.465886i	$-0.845736\pi$
$337$	−32.4872			−1.76969			−0.884845	+	0.465886i	$0.845736\pi$
$338$	25.2308	+	24.3662i	1.37237	+	1.32535i
$339$		0			0
$340$	26.5237	−	15.3134i	1.43845	−	0.830488i
$341$	−25.2773			−1.36884
$342$		0			0
$343$	0.661795	−	18.5084i	0.0357336	−	0.999361i
$344$	58.6697	−	33.8730i	3.16326	−	1.82631i
$345$		0			0
$346$	0.205923	+	0.118890i	0.0110705	+	0.00639156i
$347$	−26.6562			−1.43098			−0.715489	−	0.698624i	$-0.753796\pi$
$347$	−26.6562			−1.43098			−0.715489	+	0.698624i	$0.753796\pi$
$348$		0			0
$349$	−1.61030	−	0.929705i	−0.0861972	−	0.0497660i	0.456282	−	0.889835i	$-0.349181\pi$
$349$	−1.61030	−	0.929705i	−0.0861972	−	0.0497660i	−0.542479	+	0.840069i	$0.682514\pi$
$350$	27.3940	+	0.326380i	1.46427	+	0.0174458i
$351$		0			0
$352$	47.3760	+	82.0576i	2.52515	+	4.37368i
$353$	−25.8043	+	14.8981i	−1.37343	+	0.792948i	−0.991358	−	0.131186i	$-0.958122\pi$
$353$	−25.8043	+	14.8981i	−1.37343	+	0.792948i	−0.382069	+	0.924134i	$0.624788\pi$
$354$		0			0
$355$	−5.32538	+	9.22382i	−0.282642	+	0.489550i
$356$		−	73.0643i		−	3.87240i
$357$		0			0
$358$	−19.8345	+	11.4515i	−1.04829	+	0.605229i
$359$	−1.05029	+	0.606386i	−0.0554323	+	0.0320039i	−0.527460	−	0.849580i	$-0.676856\pi$
$359$	−1.05029	+	0.606386i	−0.0554323	+	0.0320039i	0.472028	+	0.881584i	$0.343522\pi$
$360$		0			0
$361$	12.2551	+	21.2264i	0.645005	+	1.11718i
$362$			10.7792i			0.566541i
$363$		0			0
$364$	39.8606	+	30.7892i	2.08926	+	1.61379i
$365$	6.08254			0.318375
$366$		0			0
$367$	−16.7039	−	28.9321i	−0.871938	−	1.51024i	−0.859989	−	0.510312i	$-0.829530\pi$
$367$	−16.7039	−	28.9321i	−0.871938	−	1.51024i	−0.0119488	−	0.999929i	$-0.503804\pi$
$368$	−26.6704			−1.39029
$369$		0			0
$370$	−19.7145	+	11.3822i	−1.02491	+	0.591731i
$371$	0.0474682	−	3.98414i	0.00246443	−	0.206846i
$372$		0			0
$373$	−12.6803	+	21.9629i	−0.656560	+	1.13720i	0.324940	+	0.945735i	$0.394656\pi$
$373$	−12.6803	+	21.9629i	−0.656560	+	1.13720i	−0.981500	+	0.191461i	$0.938678\pi$
$374$	−37.7205	−	65.3339i	−1.95048	−	3.37833i
$375$		0			0
$376$	42.5746	+	73.7413i	2.19562	+	3.80292i
$377$	18.3643	+	2.25507i	0.945808	+	0.116142i
$378$		0			0
$379$	21.3881	+	12.3484i	1.09863	+	0.634296i	0.935862	−	0.352368i	$-0.114623\pi$
$379$	21.3881	+	12.3484i	1.09863	+	0.634296i	0.162771	+	0.986664i	$0.447957\pi$
$380$	37.5470			1.92612
$381$		0			0
$382$	14.8934	+	8.59870i	0.762012	+	0.439948i
$383$	13.2157	+	7.63008i	0.675290	+	0.389879i	0.798078	−	0.602554i	$-0.205850\pi$
$383$	13.2157	+	7.63008i	0.675290	+	0.389879i	−0.122788	+	0.992433i	$0.539184\pi$
$384$		0			0
$385$	−0.176588	+	14.8215i	−0.00899977	+	0.755376i
$386$	−2.56562	−	4.44378i	−0.130587	−	0.226183i
$387$		0			0
$388$	−35.0630	+	20.2436i	−1.78005	+	1.02771i
$389$	10.0091	−	17.3363i	0.507484	−	0.878988i	−0.492479	−	0.870324i	$-0.663909\pi$
$389$	10.0091	−	17.3363i	0.507484	−	0.878988i	0.999962	−	0.00866314i	$-0.00275760\pi$
$390$		0			0
$391$	10.7753			0.544928
$392$	52.8947	+	32.2430i	2.67159	+	1.62852i
$393$		0			0
$394$	2.18432	−	3.78336i	0.110045	−	0.190603i
$395$	3.08167	+	1.77920i	0.155056	+	0.0895214i
$396$		0			0
$397$	9.53965	+	5.50772i	0.478782	+	0.276425i	0.719909	−	0.694069i	$-0.244184\pi$
$397$	9.53965	+	5.50772i	0.478782	+	0.276425i	−0.241127	+	0.970494i	$0.577517\pi$
$398$			66.8360i			3.35019i
$399$		0			0
$400$	−25.5546	+	44.2619i	−1.27773	+	2.21310i
$401$		−	16.6533i		−	0.831627i	−0.909450	−	0.415813i	$-0.863497\pi$
$401$		−	16.6533i		−	0.831627i	0.909450	−	0.415813i	$-0.136503\pi$
$402$		0			0
$403$	2.13756	−	17.4073i	0.106479	−	0.867118i
$404$	−1.84439	−	3.19458i	−0.0917619	−	0.158936i
$405$		0			0
$406$	36.6297	+	0.436417i	1.81790	+	0.0216590i
$407$	20.3343	+	35.2201i	1.00794	+	1.74580i
$408$		0			0
$409$			36.1340i			1.78671i	0.449349	+	0.893357i	$0.351656\pi$
$409$			36.1340i			1.78671i	−0.449349	+	0.893357i	$0.648344\pi$
$410$			5.71398i			0.282193i
$411$		0			0
$412$	−16.2254	−	28.1033i	−0.799370	−	1.38455i
$413$	−9.86558	−	17.5678i	−0.485453	−	0.864453i
$414$		0			0
$415$	−4.85070	−	8.40165i	−0.238111	−	0.412421i
$416$	−60.5155	+	25.6864i	−2.96702	+	1.25938i
$417$		0			0
$418$		−	92.4868i		−	4.52368i
$419$	8.16396	−	14.1404i	0.398835	−	0.690803i	−0.594747	−	0.803913i	$-0.702748\pi$
$419$	8.16396	−	14.1404i	0.398835	−	0.690803i	0.993583	+	0.113110i	$0.0360812\pi$
$420$		0			0
$421$			16.3622i			0.797446i	0.917071	+	0.398723i	$0.130547\pi$
$421$			16.3622i			0.797446i	−0.917071	+	0.398723i	$0.869453\pi$
$422$	−20.1941	−	11.6591i	−0.983032	−	0.567554i
$423$		0			0
$424$	11.5417	+	6.66363i	0.560516	+	0.323614i
$425$	10.3245	−	17.8825i	0.500810	−	0.867428i
$426$		0			0
$427$	−0.172746	+	14.4991i	−0.00835979	+	0.701660i
$428$	−24.6355			−1.19080
$429$		0			0
$430$	−11.1339	+	19.2844i	−0.536923	+	0.929977i
$431$	−9.88953	+	5.70972i	−0.476362	+	0.275028i	−0.718899	−	0.695114i	$-0.755354\pi$
$431$	−9.88953	+	5.70972i	−0.476362	+	0.275028i	0.242537	+	0.970142i	$0.422020\pi$
$432$		0			0
$433$	11.8186	+	20.4705i	0.567967	+	0.983748i	0.996767	+	0.0803485i	$0.0256033\pi$
$433$	11.8186	+	20.4705i	0.567967	+	0.983748i	−0.428800	+	0.903400i	$0.641063\pi$
$434$	0.413674	−	34.7208i	0.0198570	−	1.66665i
$435$		0			0
$436$	−2.55199	−	1.47339i	−0.122218	−	0.0705628i
$437$	11.4401	+	6.60496i	0.547255	+	0.315958i
$438$		0			0
$439$	−10.7981			−0.515366			−0.257683	−	0.966229i	$-0.582959\pi$
$439$	−10.7981			−0.515366			−0.257683	+	0.966229i	$0.582959\pi$
$440$	−42.9368	−	24.7896i	−2.04693	−	1.18180i
$441$		0			0
$442$	48.1821	−	20.4514i	2.29179	−	0.972775i
$443$	−12.1900	−	21.1138i	−0.579167	−	1.00315i	−0.995575	−	0.0939686i	$-0.970045\pi$
$443$	−12.1900	−	21.1138i	−0.579167	−	1.00315i	0.416408	−	0.909178i	$-0.363289\pi$
$444$		0			0
$445$	7.45939	+	12.9200i	0.353609	+	0.612468i
$446$	−0.311460	+	0.539464i	−0.0147481	+	0.0255444i
$447$		0			0
$448$	−52.0451	+	29.2271i	−2.45890	+	1.38085i
$449$	5.53097	−	3.19331i	0.261022	−	0.150701i	−0.363778	−	0.931486i	$-0.618513\pi$
$449$	5.53097	−	3.19331i	0.261022	−	0.150701i	0.624801	+	0.780784i	$0.285180\pi$
$450$		0			0
$451$	10.2081			0.480679
$452$	46.6854	+	80.8614i	2.19589	+	3.80340i
$453$		0			0
$454$	−48.4521			−2.27397
$455$	−10.1920	−	1.37498i	−0.477807	−	0.0644602i
$456$		0			0
$457$			7.61827i			0.356367i	0.983997	+	0.178184i	$0.0570221\pi$
$457$			7.61827i			0.356367i	−0.983997	+	0.178184i	$0.942978\pi$
$458$	−10.2819	−	17.8088i	−0.480441	−	0.832149i
$459$		0			0
$460$	9.87222	−	5.69973i	0.460295	−	0.265751i
$461$	−5.20150	+	3.00309i	−0.242258	+	0.139868i	−0.616214	−	0.787579i	$-0.711334\pi$
$461$	−5.20150	+	3.00309i	−0.242258	+	0.139868i	0.373956	+	0.927446i	$0.378001\pi$
$462$		0			0
$463$		−	32.0867i		−	1.49120i	−0.666396	−	0.745598i	$-0.732164\pi$
$463$		−	32.0867i		−	1.49120i	0.666396	−	0.745598i	$-0.267836\pi$
$464$	−34.1702	+	59.1845i	−1.58631	+	2.74757i
$465$		0			0
$466$	−68.3538	+	39.4641i	−3.16643	+	1.82814i
$467$	16.3916	+	28.3910i	0.758510	+	1.31378i	0.943610	+	0.331059i	$0.107406\pi$
$467$	16.3916	+	28.3910i	0.758510	+	1.31378i	−0.185100	+	0.982720i	$0.559261\pi$
$468$		0			0
$469$	7.53751	−	12.7034i	0.348050	−	0.586589i
$470$	−24.2384	−	13.9940i	−1.11803	−	0.645496i
$471$		0			0
$472$	67.3929			3.10201
$473$	34.4518	+	19.8907i	1.58409	+	0.914577i
$474$		0			0
$475$	21.9230	−	12.6573i	1.00590	−	0.580755i
$476$	65.5353	−	36.8029i	3.00381	−	1.68686i
$477$		0			0
$478$	13.8571			0.633810
$479$	−10.2323	+	5.90760i	−0.467524	+	0.269925i	−0.715203	−	0.698917i	$-0.753666\pi$
$479$	−10.2323	+	5.90760i	−0.467524	+	0.269925i	0.247679	+	0.968842i	$0.420332\pi$
$480$		0			0
$481$	−25.9740	+	11.0249i	−1.18431	+	0.502693i
$482$	62.4889			2.84629
$483$		0			0
$484$	−42.2523	+	73.1831i	−1.92056	+	3.32650i
$485$	4.13348	−	7.15940i	0.187692	−	0.325091i
$486$		0			0
$487$			17.4039i			0.788644i	0.918972	+	0.394322i	$0.129021\pi$
$487$			17.4039i			0.788644i	−0.918972	+	0.394322i	$0.870979\pi$
$488$	−42.0027	−	24.2503i	−1.90137	−	1.09776i
$489$		0			0
$490$	−20.3559	−	0.485122i	−0.919588	−	0.0219156i
$491$	18.3338	−	31.7551i	0.827394	−	1.43309i	−0.0726824	−	0.997355i	$-0.523156\pi$
$491$	18.3338	−	31.7551i	0.827394	−	1.43309i	0.900076	−	0.435733i	$-0.143511\pi$
$492$		0			0
$493$	13.8053	−	23.9114i	0.621758	−	1.07692i
$494$	63.6913	+	7.82109i	2.86561	+	0.351887i
$495$		0			0
$496$	56.1003	+	32.3895i	2.51898	+	1.45433i
$497$	−13.3378	+	22.4790i	−0.598284	+	1.00832i
$498$		0			0
$499$	−8.94809	+	5.16618i	−0.400572	+	0.231270i	−0.686731	−	0.726912i	$-0.740955\pi$
$499$	−8.94809	+	5.16618i	−0.400572	+	0.231270i	0.286159	+	0.958182i	$0.407621\pi$
$500$		−	50.3061i		−	2.24976i
$501$		0			0
$502$	45.9605	−	26.5353i	2.05132	−	1.18433i
$503$	15.8015	+	27.3691i	0.704555	+	1.22033i	0.966852	+	0.255338i	$0.0821869\pi$
$503$	15.8015	+	27.3691i	0.704555	+	1.22033i	−0.262296	+	0.964987i	$0.584480\pi$
$504$		0			0
$505$	0.652291	+	0.376600i	0.0290266	+	0.0167585i
$506$	−14.0397	−	24.3175i	−0.624142	−	1.08105i
$507$		0			0
$508$	−33.5041	+	58.0308i	−1.48650	+	2.57470i
$509$			32.9106i			1.45874i	0.684121	+	0.729369i	$0.260186\pi$
$509$			32.9106i			1.45874i	−0.684121	+	0.729369i	$0.739814\pi$
$510$		0			0
$511$	14.9262	+	0.177835i	0.660297	+	0.00786697i
$512$		−	7.11337i		−	0.314369i
$513$		0			0
$514$		−	59.8322i		−	2.63909i
$515$	5.73832	+	3.31302i	0.252860	+	0.145989i
$516$		0			0
$517$	−25.0004	+	43.3020i	−1.09952	+	1.90442i
$518$	−48.7110	+	27.3548i	−2.14024	+	1.20190i
$519$		0			0
$520$	20.7023	−	27.4722i	0.907858	−	1.20474i
$521$	11.6136	−	20.1154i	0.508803	−	0.881273i	−0.491145	−	0.871078i	$-0.663421\pi$
$521$	11.6136	−	20.1154i	0.508803	−	0.881273i	0.999948	−	0.0101950i	$-0.00324524\pi$
$522$		0			0
$523$	3.86711			0.169097			0.0845485	−	0.996419i	$-0.473055\pi$
$523$	3.86711			0.169097			0.0845485	+	0.996419i	$0.473055\pi$
$524$	11.4817	+	19.8868i	0.501579	+	0.868760i
$525$		0			0
$526$	43.6644	−	25.2097i	1.90386	−	1.09919i
$527$	−22.6654	−	13.0859i	−0.987319	−	0.570029i
$528$		0			0
$529$	−18.9894			−0.825626
$530$	−4.38060			−0.190281
$531$		0			0
$532$	92.1382	+	1.09776i	3.99470	+	0.0475940i
$533$	−0.863239	+	7.02981i	−0.0373910	+	0.304495i
$534$		0			0
$535$	4.35631	−	2.51512i	0.188340	−	0.108738i
$536$	24.7038	+	42.7882i	1.06704	+	1.84817i
$537$		0			0
$538$		−	15.2313i		−	0.656667i
$539$	−0.866675	+	36.3661i	−0.0373303	+	1.56640i
$540$		0			0
$541$	6.44139	−	3.71894i	0.276937	−	0.159890i	−0.355099	−	0.934829i	$-0.615553\pi$
$541$	6.44139	−	3.71894i	0.276937	−	0.159890i	0.632036	+	0.774939i	$0.282220\pi$
$542$	−2.70912			−0.116367
$543$		0			0
$544$			98.1047i			4.20620i
$545$	0.601696			0.0257738
$546$		0			0
$547$	3.95036			0.168905			0.0844526	−	0.996427i	$-0.473086\pi$
$547$	3.95036			0.168905			0.0844526	+	0.996427i	$0.473086\pi$
$548$		−	23.2094i		−	0.991457i
$549$		0			0
$550$	−53.8095			−2.29444
$551$	29.3142	−	16.9246i	1.24883	−	0.721011i
$552$		0			0
$553$	7.51022	+	4.45616i	0.319367	+	0.189495i
$554$		−	58.4446i		−	2.48307i
$555$		0			0
$556$	24.3538	+	42.1821i	1.03283	+	1.78892i
$557$	−25.9401	+	14.9765i	−1.09912	+	0.634576i	−0.935989	−	0.352029i	$-0.885492\pi$
$557$	−25.9401	+	14.9765i	−1.09912	+	0.634576i	−0.163129	+	0.986605i	$0.552159\pi$
$558$		0			0
$559$	−16.6112	+	22.0433i	−0.702579	+	0.932330i
$560$	19.3838	−	32.6686i	0.819114	−	1.38050i
$561$		0			0
$562$	−6.97549			−0.294243
$563$	14.1080			0.594583			0.297292	−	0.954787i	$-0.403917\pi$
$563$	14.1080			0.594583			0.297292	+	0.954787i	$0.403917\pi$
$564$		0			0
$565$	−16.5108	−	9.53254i	−0.694616	−	0.401037i
$566$	−13.8745	+	8.01044i	−0.583188	+	0.336704i
$567$		0			0
$568$	−43.7140	−	75.7149i	−1.83420	−	3.17693i
$569$	−20.8138			−0.872559			−0.436280	−	0.899811i	$-0.643704\pi$
$569$	−20.8138			−0.872559			−0.436280	+	0.899811i	$0.643704\pi$
$570$		0			0
$571$	7.58732	−	13.1416i	0.317519	−	0.549960i	−0.662450	−	0.749106i	$-0.730483\pi$
$571$	7.58732	−	13.1416i	0.317519	−	0.549960i	0.979970	+	0.199146i	$0.0638168\pi$
$572$	−79.0067	−	59.5373i	−3.30344	−	2.48938i
$573$		0			0
$574$	−0.167060	+	14.0218i	−0.00697294	+	0.585258i
$575$	3.84281	−	6.65594i	0.160256	−	0.277572i
$576$		0			0
$577$	−19.8542	−	11.4629i	−0.826543	−	0.477205i	0.0261247	−	0.999659i	$-0.491683\pi$
$577$	−19.8542	−	11.4629i	−0.826543	−	0.477205i	−0.852667	+	0.522454i	$0.825017\pi$
$578$		−	32.2423i		−	1.34110i
$579$		0			0
$580$		−	29.2100i		−	1.21288i
$581$	−11.6577	−	20.7590i	−0.483642	−	0.861228i
$582$		0			0
$583$			7.82597i			0.324119i
$584$	−24.9646	+	43.2400i	−1.03304	+	1.78929i
$585$		0			0
$586$	−41.7719	−	72.3510i	−1.72558	−	2.98879i
$587$	−37.6909	−	21.7609i	−1.55567	−	0.898168i	−0.997663	−	0.0683329i	$-0.978232\pi$
$587$	−37.6909	−	21.7609i	−1.55567	−	0.898168i	−0.558009	−	0.829835i	$-0.688435\pi$
$588$		0			0
$589$	−16.0426	−	27.7866i	−0.661024	−	1.14493i
$590$	−19.1839	+	11.0758i	−0.789790	+	0.455985i
$591$		0			0
$592$		−	104.223i		−	4.28354i
$593$	−27.8786	+	16.0957i	−1.14484	+	0.660971i	−0.947623	−	0.319390i	$-0.896522\pi$
$593$	−27.8786	+	16.0957i	−1.14484	+	0.660971i	−0.197212	+	0.980361i	$0.563189\pi$
$594$		0			0
$595$	−7.83134	+	13.1986i	−0.321054	+	0.541090i
$596$	18.0894	+	10.4439i	0.740970	+	0.427799i
$597$		0			0
$598$	17.9336	−	7.61210i	0.733359	−	0.311282i
$599$	−2.80821	+	4.86395i	−0.114740	+	0.198736i	−0.917676	−	0.397330i	$-0.869937\pi$
$599$	−2.80821	+	4.86395i	−0.114740	+	0.198736i	0.802936	+	0.596066i	$0.203270\pi$
$600$		0			0
$601$	−15.7466	+	27.2739i	−0.642317	+	1.11253i	0.342598	+	0.939482i	$0.388693\pi$
$601$	−15.7466	+	27.2739i	−0.642317	+	1.11253i	−0.984914	+	0.173043i	$0.944640\pi$
$602$	−27.8857	+	46.9974i	−1.13654	+	1.91547i
$603$		0			0
$604$	17.3913	+	10.0408i	0.707640	+	0.408556i
$605$		−	17.2547i		−	0.701504i
$606$		0			0
$607$	1.90642	−	3.30201i	0.0773790	−	0.134024i	−0.824739	−	0.565513i	$-0.808678\pi$
$607$	1.90642	−	3.30201i	0.0773790	−	0.134024i	0.902118	+	0.431489i	$0.142012\pi$
$608$	−60.1356	+	104.158i	−2.43882	+	4.22416i
$609$		0			0
$610$	15.9419			0.645467
$611$	−27.7059	−	20.8784i	−1.12086	−	0.844651i
$612$		0			0
$613$	−6.36981	+	3.67761i	−0.257274	+	0.148537i	−0.623091	−	0.782150i	$-0.714123\pi$
$613$	−6.36981	+	3.67761i	−0.257274	+	0.148537i	0.365816	+	0.930687i	$0.380790\pi$
$614$	−32.7807			−1.32292
$615$		0			0
$616$	−104.640	−	62.0876i	−4.21606	−	2.50158i
$617$	−0.0786516	+	0.0454095i	−0.00316640	+	0.00182812i	−0.501582	−	0.865110i	$-0.667249\pi$
$617$	−0.0786516	+	0.0454095i	−0.00316640	+	0.00182812i	0.498416	+	0.866938i	$0.333915\pi$
$618$		0			0
$619$	−24.8251	−	14.3328i	−0.997807	−	0.576084i	−0.0902080	−	0.995923i	$-0.528753\pi$
$619$	−24.8251	−	14.3328i	−0.997807	−	0.576084i	−0.907599	+	0.419839i	$0.862087\pi$
$620$	−27.6878			−1.11197
$621$		0			0
$622$	−74.3239	−	42.9109i	−2.98012	−	1.72057i
$623$	17.9272	+	31.9231i	0.718237	+	1.27897i
$624$		0			0
$625$	−4.45840	−	7.72218i	−0.178336	−	0.308887i
$626$	27.0627	−	15.6246i	1.08164	−	0.624486i
$627$		0			0
$628$	−0.0246992	+	0.0427803i	−0.000985606	+	0.00170712i
$629$			42.1077i			1.67894i
$630$		0			0
$631$	15.6971	−	9.06270i	0.624890	−	0.360780i	−0.153881	−	0.988089i	$-0.549177\pi$
$631$	15.6971	−	9.06270i	0.624890	−	0.360780i	0.778770	+	0.627309i	$0.215844\pi$
$632$	−25.2963	+	14.6048i	−1.00623	+	0.580948i
$633$		0			0
$634$	13.8109	+	23.9212i	0.548501	+	0.950031i
$635$		−	13.6822i		−	0.542961i
$636$		0			0
$637$	−24.9703	−	3.67211i	−0.989359	−	0.145494i
$638$	−71.9509			−2.84856
$639$		0			0
$640$	13.1555	+	22.7859i	0.520016	+	0.900693i
$641$	16.9367			0.668961			0.334480	−	0.942403i	$-0.391439\pi$
$641$	16.9367			0.668961			0.334480	+	0.942403i	$0.391439\pi$
$642$		0			0
$643$	32.6129	−	18.8291i	1.28613	−	0.742547i	0.308167	−	0.951332i	$-0.400284\pi$
$643$	32.6129	−	18.8291i	1.28613	−	0.742547i	0.977961	+	0.208785i	$0.0669510\pi$
$644$	24.3925	−	13.6982i	0.961200	−	0.539784i
$645$		0			0
$646$	47.8797	−	82.9301i	1.88380	−	3.26284i
$647$	−14.7007	−	25.4624i	−0.577944	−	1.00103i	−0.995715	−	0.0924764i	$-0.970522\pi$
$647$	−14.7007	−	25.4624i	−0.577944	−	1.00103i	0.417771	−	0.908553i	$-0.362812\pi$
$648$		0			0
$649$	19.7871	+	34.2722i	0.776711	+	1.34530i
$650$	4.55036	−	37.0560i	0.178480	−	1.45346i
$651$		0			0
$652$	32.4743	+	18.7490i	1.27179	+	0.734269i
$653$	23.0686			0.902746			0.451373	−	0.892335i	$-0.350934\pi$
$653$	23.0686			0.902746			0.451373	+	0.892335i	$0.350934\pi$
$654$		0			0
$655$	−4.06063	−	2.34440i	−0.158662	−	0.0916035i
$656$	−22.6557	−	13.0803i	−0.884558	−	0.510700i
$657$		0			0
$658$	−59.0704	−	35.0492i	−2.30280	−	1.36636i
$659$	−19.5305	−	33.8278i	−0.760800	−	1.31774i	−0.942439	−	0.334378i	$-0.891474\pi$
$659$	−19.5305	−	33.8278i	−0.760800	−	1.31774i	0.181639	−	0.983365i	$-0.441860\pi$
$660$		0			0
$661$	39.7497	−	22.9495i	1.54608	−	0.892631i	0.547647	−	0.836709i	$-0.315524\pi$
$661$	39.7497	−	22.9495i	1.54608	−	0.892631i	0.998435	−	0.0559215i	$-0.0178097\pi$
$662$	−23.4209	+	40.5661i	−0.910278	+	1.57665i
$663$		0			0
$664$	79.6351			3.09044
$665$	−16.4050	+	9.21259i	−0.636157	+	0.357249i
$666$		0			0
$667$	5.13838	−	8.89994i	0.198959	−	0.344607i
$668$	44.3006	+	25.5770i	1.71404	+	0.989603i
$669$		0			0
$670$	−14.0642	−	8.11999i	−0.543349	−	0.313703i
$671$		−	28.4803i		−	1.09947i
$672$		0			0
$673$	2.71947	−	4.71026i	0.104828	−	0.181567i	−0.808840	−	0.588029i	$-0.799904\pi$
$673$	2.71947	−	4.71026i	0.104828	−	0.181567i	0.913668	+	0.406462i	$0.133237\pi$
$674$			87.6547i			3.37633i
$675$		0			0
$676$	47.6817	−	49.3734i	1.83391	−	1.89898i
$677$	−9.40664	−	16.2928i	−0.361527	−	0.626182i	0.626686	−	0.779272i	$-0.284411\pi$
$677$	−9.40664	−	16.2928i	−0.361527	−	0.626182i	−0.988212	+	0.153090i	$0.951078\pi$
$678$		0			0
$679$	10.3526	−	17.4479i	0.397298	−	0.669589i
$680$	−25.6668	−	44.4561i	−0.984275	−	1.70481i
$681$		0			0
$682$			68.2015i			2.61157i
$683$			21.5146i			0.823234i	0.911357	+	0.411617i	$0.135036\pi$
$683$			21.5146i			0.823234i	−0.911357	+	0.411617i	$0.864964\pi$
$684$		0			0
$685$	2.36953	+	4.10414i	0.0905350	+	0.156811i
$686$	−49.9382	−	1.78561i	−1.90665	−	0.0681749i
$687$		0			0
$688$	−50.9747	−	88.2908i	−1.94339	−	3.36606i
$689$	−5.38937	−	0.661798i	−0.205319	−	0.0252125i
$690$		0			0
$691$			50.7955i			1.93235i	0.257886	+	0.966175i	$0.416974\pi$
$691$			50.7955i			1.93235i	−0.257886	+	0.966175i	$0.583026\pi$
$692$	0.232653	−	0.402967i	0.00884413	−	0.0153185i
$693$		0			0
$694$			71.9218i			2.73012i
$695$	−8.61302	−	4.97273i	−0.326710	−	0.188626i
$696$		0			0
$697$	9.15326	+	5.28464i	0.346705	+	0.200170i
$698$	−2.50847	+	4.34479i	−0.0949468	+	0.164453i
$699$		0			0
$700$	0.638685	−	53.6066i	0.0241400	−	2.02614i
$701$	0.267194			0.0100918			0.00504589	−	0.999987i	$-0.498394\pi$
$701$	0.267194			0.0100918			0.00504589	+	0.999987i	$0.498394\pi$
$702$		0			0
$703$	−25.8109	+	44.7059i	−0.973478	+	1.68611i
$704$	101.533	−	58.6200i	3.82666	−	2.20932i
$705$		0			0
$706$	40.1971	+	69.6235i	1.51284	+	2.62031i
$707$	1.58967	+	0.943227i	0.0597859	+	0.0354737i
$708$		0			0
$709$	35.7130	+	20.6189i	1.34123	+	0.774359i	0.986988	−	0.160796i	$-0.0514060\pi$
$709$	35.7130	+	20.6189i	1.34123	+	0.774359i	0.354241	+	0.935154i	$0.384739\pi$
$710$	24.8871	+	14.3686i	0.933995	+	0.539242i
$711$		0			0
$712$	−122.463			−4.58948
$713$	−8.43615	−	4.87061i	−0.315936	−	0.182406i
$714$		0			0
$715$	20.0492	+	2.46198i	0.749798	+	0.0920728i
$716$	22.4091	+	38.8137i	0.837467	+	1.45054i
$717$		0			0
$718$	1.63611	+	2.83382i	0.0610591	+	0.105757i
$719$	−3.96487	+	6.86735i	−0.147865	+	0.256109i	−0.930438	−	0.366449i	$-0.880573\pi$
$719$	−3.96487	+	6.86735i	−0.147865	+	0.256109i	0.782573	+	0.622558i	$0.213907\pi$
$720$		0			0
$721$	13.9846	+	8.29773i	0.520815	+	0.309024i
$722$	57.2717	−	33.0658i	2.13143	−	1.23058i
$723$		0			0
$724$	21.0935			0.783934
$725$	−9.84682	−	17.0552i	−0.365702	−	0.633414i
$726$		0			0
$727$	40.6445			1.50742			0.753711	−	0.657206i	$-0.228262\pi$
$727$	40.6445			1.50742			0.753711	+	0.657206i	$0.228262\pi$
$728$	51.6056	−	66.8100i	1.91263	−	2.47614i
$729$		0			0
$730$		−	16.4115i		−	0.607416i
$731$	20.5946	+	35.6708i	0.761717	+	1.31933i
$732$		0			0
$733$	7.63512	−	4.40814i	0.282010	−	0.162818i	−0.352323	−	0.935878i	$-0.614608\pi$
$733$	7.63512	−	4.40814i	0.282010	−	0.162818i	0.634333	+	0.773060i	$0.281275\pi$
$734$	−78.0624	+	45.0694i	−2.88134	+	1.66354i
$735$		0			0
$736$			36.5150i			1.34596i
$737$	−14.5064	+	25.1259i	−0.534351	+	0.925523i
$738$		0			0
$739$	−0.797353	+	0.460352i	−0.0293311	+	0.0169343i	−0.514594	−	0.857434i	$-0.672057\pi$
$739$	−0.797353	+	0.460352i	−0.0293311	+	0.0169343i	0.485263	+	0.874368i	$0.338724\pi$
$740$	22.2735	+	38.5788i	0.818790	+	1.41819i
$741$		0			0
$742$	−10.7497	−	0.128075i	−0.394635	−	0.00470180i
$743$	−42.6584	−	24.6289i	−1.56499	−	0.903545i	−0.996739	−	0.0806874i	$-0.974288\pi$
$743$	−42.6584	−	24.6289i	−1.56499	−	0.903545i	−0.568247	−	0.822858i	$-0.692378\pi$
$744$		0			0
$745$	−4.26502			−0.156258
$746$	59.2587	+	34.2130i	2.16962	+	1.25263i
$747$		0			0
$748$	−127.850	+	73.8144i	−4.67467	+	2.69892i
$749$	10.7637	−	6.04459i	0.393296	−	0.220865i
$750$		0			0
$751$	18.6011			0.678765			0.339383	−	0.940648i	$-0.389782\pi$
$751$	18.6011			0.678765			0.339383	+	0.940648i	$0.389782\pi$
$752$	110.972	−	64.0695i	4.04672	−	2.33637i
$753$		0			0
$754$	6.08448	−	49.5492i	0.221584	−	1.80447i
$755$	−4.10042			−0.149229
$756$		0			0
$757$	−14.7035	+	25.4672i	−0.534407	+	0.925621i	0.464784	+	0.885424i	$0.346132\pi$
$757$	−14.7035	+	25.4672i	−0.534407	+	0.925621i	−0.999192	+	0.0401970i	$0.987201\pi$
$758$	33.3176	−	57.7079i	1.21015	−	2.09604i
$759$		0			0
$760$		−	62.9323i		−	2.28279i
$761$	6.05910	+	3.49822i	0.219642	+	0.126811i	0.605785	−	0.795629i	$-0.292859\pi$
$761$	6.05910	+	3.49822i	0.219642	+	0.126811i	−0.386142	+	0.922439i	$0.626193\pi$
$762$		0			0
$763$	1.47653	+	0.0175918i	0.0534538	+	0.000636865i
$764$	16.8266	−	29.1445i	0.608765	−	1.05441i
$765$		0			0
$766$	20.5870	−	35.6576i	0.743837	−	1.28836i
$767$	−25.2749	+	10.7282i	−0.912625	+	0.387374i
$768$		0			0
$769$	7.49138	+	4.32515i	0.270146	+	0.155969i	0.628954	−	0.777443i	$-0.283483\pi$
$769$	7.49138	+	4.32515i	0.270146	+	0.155969i	−0.358808	+	0.933411i	$0.616817\pi$
$770$	39.9905	+	0.476458i	1.44116	+	0.0171704i
$771$		0			0
$772$	−8.69593	+	5.02060i	−0.312973	+	0.180695i
$773$			11.7589i			0.422938i	0.977385	+	0.211469i	$0.0678248\pi$
$773$			11.7589i			0.422938i	−0.977385	+	0.211469i	$0.932175\pi$
$774$		0			0
$775$	−16.1664	+	9.33369i	−0.580715	+	0.335276i
$776$	33.9302	+	58.7688i	1.21802	+	2.10968i
$777$		0			0
$778$	−46.7757	−	27.0060i	−1.67699	−	0.968211i
$779$	6.47870	+	11.2214i	0.232123	+	0.402049i
$780$		0			0
$781$	25.6695	−	44.4610i	0.918529	−	1.59094i
$782$		−	29.0730i		−	1.03965i
$783$		0			0
$784$	48.5218	−	79.6001i	1.73292	−	2.84286i
$785$		−	0.0100865i		−	0.000360003i
$786$		0			0
$787$			11.5328i			0.411101i	0.978647	+	0.205550i	$0.0658984\pi$
$787$			11.5328i			0.411101i	−0.978647	+	0.205550i	$0.934102\pi$
$788$	−7.40356	−	4.27445i	−0.263741	−	0.152271i
$789$		0			0
$790$	4.80052	−	8.31474i	0.170795	−	0.295825i
$791$	−40.2379	−	23.8750i	−1.43070	−	0.848898i
$792$		0			0
$793$	19.6130	+	2.40842i	0.696479	+	0.0855254i
$794$	14.8605	−	25.7392i	0.527381	−	0.913451i
$795$		0			0
$796$	130.790			4.63572
$797$	9.37256	+	16.2337i	0.331993	+	0.575029i	0.982903	−	0.184126i	$-0.0589456\pi$
$797$	9.37256	+	16.2337i	0.331993	+	0.575029i	−0.650909	+	0.759155i	$0.725612\pi$
$798$		0			0
$799$	−44.8342	+	25.8851i	−1.58612	+	0.915748i
$800$	60.5998	+	34.9873i	2.14253	+	1.23699i
$801$		0			0
$802$	−44.9328			−1.58663
$803$	−29.3193			−1.03465
$804$		0			0
$805$	−2.91486	+	4.91258i	−0.102735	+	0.173146i
$806$	−46.9671	−	5.76741i	−1.65435	−	0.203148i
$807$		0			0
$808$	−5.35441	+	3.09137i	−0.188368	+	0.108754i
$809$	12.6747	+	21.9532i	0.445619	+	0.771834i	0.998095	−	0.0616942i	$-0.0196504\pi$
$809$	12.6747	+	21.9532i	0.445619	+	0.771834i	−0.552476	+	0.833529i	$0.686317\pi$
$810$		0			0
$811$			0.934401i			0.0328112i	0.999865	+	0.0164056i	$0.00522231\pi$
$811$			0.934401i			0.0328112i	−0.999865	+	0.0164056i	$0.994778\pi$
$812$	0.854013	−	71.6797i	0.0299700	−	2.51546i
$813$		0			0
$814$	95.0284	−	54.8647i	3.33074	−	1.92301i
$815$	−7.65661			−0.268199
$816$		0			0
$817$			50.4958i			1.76662i
$818$	97.4943			3.40881
$819$		0			0
$820$	11.1815			0.390477
$821$		−	26.2019i		−	0.914453i	−0.889350	−	0.457227i	$-0.848843\pi$
$821$		−	26.2019i		−	0.914453i	0.889350	−	0.457227i	$-0.151157\pi$
$822$		0			0
$823$	14.8912			0.519076			0.259538	−	0.965733i	$-0.416430\pi$
$823$	14.8912			0.519076			0.259538	+	0.965733i	$0.416430\pi$
$824$	−47.1037	+	27.1953i	−1.64093	+	0.947394i
$825$		0			0
$826$	−47.4001	+	26.6186i	−1.64926	+	0.926180i
$827$			6.95539i			0.241863i	0.992661	+	0.120931i	$0.0385881\pi$
$827$			6.95539i			0.241863i	−0.992661	+	0.120931i	$0.961412\pi$
$828$		0			0
$829$	16.2583	+	28.1602i	0.564674	+	0.978044i	0.997080	+	0.0763648i	$0.0243314\pi$
$829$	16.2583	+	28.1602i	0.564674	+	0.978044i	−0.432406	+	0.901679i	$0.642335\pi$
$830$	−22.6687	+	13.0878i	−0.786844	+	0.454284i
$831$		0			0
$832$	31.7827	+	74.8780i	1.10187	+	2.59593i
$833$	−19.6035	+	32.1597i	−0.679223	+	1.11427i
$834$		0			0
$835$	−10.4450			−0.361463
$836$	−180.985			−6.25951
$837$		0			0
$838$	−38.1526	−	22.0274i	−1.31796	−	0.760924i
$839$	28.4832	−	16.4448i	0.983348	−	0.567736i	0.0800686	−	0.996789i	$-0.474486\pi$
$839$	28.4832	−	16.4448i	0.983348	−	0.567736i	0.903279	+	0.429053i	$0.141153\pi$
$840$		0			0
$841$	1.33339	+	2.30951i	0.0459791	+	0.0796381i
$842$	44.1474			1.52142
$843$		0			0
$844$	−22.8153	+	39.5173i	−0.785336	+	1.36024i
$845$	−3.39089	+	13.5987i	−0.116650	+	0.467811i
$846$		0			0
$847$	0.504476	−	42.3421i	0.0173340	−	1.45489i
$848$	10.0279	−	17.3689i	0.344361	−	0.596451i
$849$		0			0
$850$	−48.2493	−	27.8567i	−1.65494	−	0.955478i
$851$			15.6727i			0.537252i
$852$		0			0
$853$			56.1628i			1.92298i	0.274843	+	0.961489i	$0.411374\pi$
$853$			56.1628i			1.92298i	−0.274843	+	0.961489i	$0.588626\pi$
$854$	39.1204	+	0.466092i	1.33867	+	0.0159494i
$855$		0			0
$856$			41.2913i			1.41131i
$857$	3.67309	−	6.36198i	0.125470	−	0.217321i	−0.796446	−	0.604709i	$-0.793289\pi$
$857$	3.67309	−	6.36198i	0.125470	−	0.217321i	0.921917	+	0.387388i	$0.126623\pi$
$858$		0			0
$859$	−5.19425	−	8.99670i	−0.177226	−	0.306964i	0.763704	−	0.645567i	$-0.223379\pi$
$859$	−5.19425	−	8.99670i	−0.177226	−	0.306964i	−0.940929	+	0.338603i	$0.890046\pi$
$860$	37.7372	+	21.7876i	1.28683	+	0.742951i
$861$		0			0
$862$	15.4056	+	26.6832i	0.524716	+	0.908835i
$863$	−0.210030	+	0.121261i	−0.00714949	+	0.00412776i	−0.503570	−	0.863954i	$-0.667981\pi$
$863$	−0.210030	+	0.121261i	−0.00714949	+	0.00412776i	0.496421	+	0.868082i	$0.334647\pi$
$864$		0			0
$865$			0.0950093i			0.00323041i
$866$	55.2320	−	31.8882i	1.87686	−	1.08361i
$867$		0			0
$868$	−67.9444	−	0.809509i	−2.30618	−	0.0274765i
$869$	−14.8544	−	8.57617i	−0.503899	−	0.290926i
$870$		0			0
$871$	−16.0763	−	12.1146i	−0.544724	−	0.410489i
$872$	−2.46955	+	4.27738i	−0.0836294	+	0.144850i
$873$		0			0
$874$	17.8210	−	30.8669i	0.602805	−	1.04409i
$875$	12.3432	+	21.9796i	0.417275	+	0.743047i
$876$		0			0
$877$	−40.4518	−	23.3548i	−1.36596	−	0.788637i	−0.375550	−	0.926802i	$-0.622546\pi$
$877$	−40.4518	−	23.3548i	−1.36596	−	0.788637i	−0.990409	+	0.138165i	$0.955879\pi$
$878$			29.1347i			0.983250i
$879$		0			0
$880$	−37.3053	+	64.6147i	−1.25756	+	2.17816i
$881$	12.2401	−	21.2005i	0.412380	−	0.714264i	−0.582769	−	0.812638i	$-0.698031\pi$
$881$	12.2401	−	21.2005i	0.412380	−	0.714264i	0.995150	+	0.0983741i	$0.0313642\pi$
$882$		0			0
$883$	−38.6912			−1.30206			−0.651032	−	0.759050i	$-0.725664\pi$
$883$	−38.6912			−1.30206			−0.651032	+	0.759050i	$0.725664\pi$
$884$	−40.0209	−	94.2864i	−1.34605	−	3.17120i
$885$		0			0
$886$	−56.9677	+	32.8903i	−1.91387	+	1.10497i
$887$	11.2478			0.377665			0.188832	−	0.982009i	$-0.439530\pi$
$887$	11.2478			0.377665			0.188832	+	0.982009i	$0.439530\pi$
$888$		0			0
$889$	0.400026	−	33.5753i	0.0134165	−	1.12608i
$890$	34.8599	−	20.1264i	1.16851	−	0.674638i
$891$		0			0
$892$	1.05566	+	0.609488i	0.0353463	+	0.0204072i
$893$	−63.4675			−2.12386
$894$		0			0
$895$	−7.92524	−	4.57564i	−0.264912	−	0.152947i
$896$	31.6166	+	56.3000i	1.05624	+	1.88085i
$897$		0			0
$898$	−8.61595	−	14.9233i	−0.287518	−	0.497996i
$899$	−21.6168	+	12.4805i	−0.720961	+	0.416247i
$900$		0			0
$901$	−4.05144	+	7.01731i	−0.134973	+	0.233780i
$902$		−	27.5427i		−	0.917072i
$903$		0			0
$904$	135.531	−	78.2490i	4.50770	−	2.60252i
$905$	−3.72999	+	2.15351i	−0.123989	+	0.0715850i
$906$		0			0
$907$	−10.0842	−	17.4664i	−0.334842	−	0.579963i	0.648613	−	0.761119i	$-0.275350\pi$
$907$	−10.0842	−	17.4664i	−0.334842	−	0.579963i	−0.983454	+	0.181156i	$0.942016\pi$
$908$			94.8147i			3.14654i
$909$		0			0
$910$	−3.70988	+	27.4992i	−0.122981	+	0.911591i
$911$	59.7999			1.98126			0.990629	−	0.136578i	$-0.0436105\pi$
$911$	59.7999			1.98126			0.990629	+	0.136578i	$0.0436105\pi$
$912$		0			0
$913$	23.3815	+	40.4979i	0.773814	+	1.34028i
$914$	20.5551			0.679901
$915$		0			0
$916$	−34.8495	+	20.1204i	−1.15146	+	0.664796i
$917$	−9.89601	−	5.87176i	−0.326795	−	0.193902i
$918$		0			0
$919$	−8.88019	+	15.3809i	−0.292931	+	0.507371i	−0.974501	−	0.224382i	$-0.927964\pi$
$919$	−8.88019	+	15.3809i	−0.292931	+	0.507371i	0.681571	+	0.731752i	$0.261297\pi$
$920$	−9.55327	−	16.5468i	−0.314962	−	0.545530i
$921$		0			0
$922$	8.10271	+	14.0343i	0.266849	+	0.462196i
$923$	28.4474	+	21.4372i	0.936358	+	0.705614i
$924$		0			0
$925$	26.0102	+	15.0170i	0.855209	+	0.493755i
$926$	−86.5741			−2.84500
$927$		0			0
$928$	81.0306	+	46.7830i	2.65996	+	1.53573i
$929$	8.49059	+	4.90205i	0.278567	+	0.160831i	0.632775	−	0.774336i	$-0.281916\pi$
$929$	8.49059	+	4.90205i	0.278567	+	0.160831i	−0.354207	+	0.935167i	$0.615249\pi$
$930$		0			0
$931$	−40.5262	+	22.1275i	−1.32819	+	0.725200i
$932$	77.2264	+	133.760i	2.52963	+	4.38145i
$933$		0			0
$934$	76.6026	−	44.2265i	2.50651	−	1.44714i
$935$	15.0719	−	26.1053i	0.492904	−	0.853736i
$936$		0			0
$937$	44.5759			1.45623			0.728116	−	0.685454i	$-0.240396\pi$
$937$	44.5759			1.45623			0.728116	+	0.685454i	$0.240396\pi$
$938$	−34.2754	−	20.3372i	−1.11913	−	0.664033i
$939$		0			0
$940$	−27.3846	+	47.4315i	−0.893186	+	1.54704i
$941$	6.05732	+	3.49720i	0.197463	+	0.114005i	0.595472	−	0.803376i	$-0.296965\pi$
$941$	6.05732	+	3.49720i	0.197463	+	0.114005i	−0.398009	+	0.917382i	$0.630299\pi$
$942$		0			0
$943$	3.40688	+	1.96696i	0.110943	+	0.0640532i
$944$		−	101.418i		−	3.30088i
$945$		0			0
$946$	53.6678	−	92.9554i	1.74489	−	3.02224i
$947$		−	9.59979i		−	0.311951i	−0.987761	−	0.155976i	$-0.950148\pi$
$947$		−	9.59979i		−	0.311951i	0.987761	−	0.155976i	$-0.0498521\pi$
$948$		0			0
$949$	2.47936	−	20.1908i	0.0804835	−	0.655420i
$950$	−34.1509	−	59.1512i	−1.10800	−	1.91912i
$951$		0			0
$952$	−61.6850	−	109.843i	−1.99922	−	3.56004i
$953$	−20.6489	−	35.7650i	−0.668884	−	1.15854i	−0.978217	−	0.207587i	$-0.933439\pi$
$953$	−20.6489	−	35.7650i	−0.668884	−	1.15854i	0.309333	−	0.950954i	$-0.399894\pi$
$954$		0			0
$955$			6.87154i			0.222358i
$956$		−	27.1167i		−	0.877016i
$957$		0			0
$958$	15.9395	+	27.6080i	0.514981	+	0.891973i
$959$	5.69469	+	10.1406i	0.183891	+	0.327457i
$960$		0			0
$961$	−3.66990	−	6.35646i	−0.118384	−	0.205047i
$962$	29.7467	+	70.0812i	0.959072	+	2.25951i
$963$		0			0
$964$		−	122.283i		−	3.93847i
$965$	1.02514	−	1.77559i	0.0330004	−	0.0571584i
$966$		0			0
$967$			22.9913i			0.739352i	0.929161	+	0.369676i	$0.120531\pi$
$967$			22.9913i			0.739352i	−0.929161	+	0.369676i	$0.879469\pi$
$968$	122.662	+	70.8187i	3.94249	+	2.27620i
$969$		0			0
$970$	−19.3170	−	11.1527i	−0.620231	−	0.358090i
$971$	−14.1541	+	24.5155i	−0.454225	+	0.786741i	−0.998643	−	0.0520728i	$-0.983417\pi$
$971$	−14.1541	+	24.5155i	−0.454225	+	0.786741i	0.544418	+	0.838814i	$0.316751\pi$
$972$		0			0
$973$	−20.9905	−	12.4546i	−0.672924	−	0.399277i
$974$	46.9579			1.50463
$975$		0			0
$976$	−36.4937	+	63.2090i	−1.16814	+	2.02327i
$977$	−47.5077	+	27.4286i	−1.51991	+	0.877519i	−0.520182	+	0.854055i	$0.674136\pi$
$977$	−47.5077	+	27.4286i	−1.51991	+	0.877519i	−0.999725	+	0.0234636i	$0.992531\pi$
$978$		0			0
$979$	−35.9560	−	62.2776i	−1.14916	−	1.99040i
$980$	−0.949324	+	39.8341i	−0.0303251	+	1.27245i
$981$		0			0
$982$	−85.6794	−	49.4670i	−2.73414	−	1.57856i
$983$	−9.62359	−	5.55618i	−0.306945	−	0.177215i	0.338614	−	0.940925i	$-0.390042\pi$
$983$	−9.62359	−	5.55618i	−0.306945	−	0.177215i	−0.645559	+	0.763711i	$0.723375\pi$
$984$		0			0
$985$	1.74557			0.0556185
$986$	−64.5162	−	37.2484i	−2.05461	−	1.18623i
$987$		0			0
$988$	15.3049	−	124.636i	0.486914	−	3.96520i
$989$	7.66538	+	13.2768i	0.243745	+	0.422179i
$990$		0			0
$991$	−10.7826	−	18.6760i	−0.342520	−	0.593262i	0.642380	−	0.766386i	$-0.277947\pi$
$991$	−10.7826	−	18.6760i	−0.342520	−	0.593262i	−0.984900	+	0.173124i	$0.944614\pi$
$992$	44.3451	−	76.8080i	1.40796	−	2.43866i
$993$		0			0
$994$	60.6514	+	35.9872i	1.92374	+	1.14145i
$995$	−23.1277	+	13.3528i	−0.733197	+	0.423311i
$996$		0			0
$997$	−17.2827			−0.547348			−0.273674	−	0.961823i	$-0.588239\pi$
$997$	−17.2827			−0.547348			−0.273674	+	0.961823i	$0.588239\pi$
$998$	13.9390	+	24.1431i	0.441232	+	0.764237i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.h.550.1	yes	36
3.2	odd	2	inner	819.2.bm.h.550.18	yes	36
7.2	even	3		819.2.do.h.667.1	yes	36
13.10	even	6		819.2.do.h.361.1	yes	36
21.2	odd	6		819.2.do.h.667.18	yes	36
39.23	odd	6		819.2.do.h.361.18	yes	36
91.23	even	6	inner	819.2.bm.h.478.18	yes	36
273.23	odd	6	inner	819.2.bm.h.478.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bm.h.478.1	✓	36	273.23	odd	6	inner
819.2.bm.h.478.18	yes	36	91.23	even	6	inner
819.2.bm.h.550.1	yes	36	1.1	even	1	trivial
819.2.bm.h.550.18	yes	36	3.2	odd	2	inner
819.2.do.h.361.1	yes	36	13.10	even	6
819.2.do.h.361.18	yes	36	39.23	odd	6
819.2.do.h.667.1	yes	36	7.2	even	3
819.2.do.h.667.18	yes	36	21.2	odd	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.69813i q^{2} -5.27990 q^{4} +(0.933651 - 0.539043i) q^{5} +(2.30689 - 1.29548i) q^{7} +8.84961i q^{8} +O(q^{10})\)	\(q-2.69813i q^{2} -5.27990 q^{4} +(0.933651 - 0.539043i) q^{5} +(2.30689 - 1.29548i) q^{7} +8.84961i q^{8} +(-1.45441 - 2.51911i) q^{10} +(-4.50041 + 2.59831i) q^{11} +(-1.40876 - 3.31894i) q^{13} +(-3.49539 - 6.22428i) q^{14} +13.3176 q^{16} -5.38051 q^{17} +(-5.71250 - 3.29811i) q^{19} +(-4.92959 + 2.84610i) q^{20} +(7.01059 + 12.1427i) q^{22} -2.00265 q^{23} +(-1.91886 + 3.32357i) q^{25} +(-8.95494 + 3.80102i) q^{26} +(-12.1801 + 6.84004i) q^{28} +(-2.56579 + 4.44409i) q^{29} +(4.21250 + 2.43209i) q^{31} -18.2333i q^{32} +14.5173i q^{34} +(1.45550 - 2.45304i) q^{35} -7.82597i q^{37} +(-8.89874 + 15.4131i) q^{38} +(4.77032 + 8.26244i) q^{40} +(-1.70119 - 0.982182i) q^{41} +(-3.82763 - 6.62964i) q^{43} +(23.7617 - 13.7188i) q^{44} +5.40340i q^{46} +(8.33272 - 4.81090i) q^{47} +(3.64344 - 5.97707i) q^{49} +(8.96742 + 5.17735i) q^{50} +(7.43812 + 17.5237i) q^{52} +(0.752985 - 1.30421i) q^{53} +(-2.80121 + 4.85183i) q^{55} +(11.4645 + 20.4150i) q^{56} +(11.9907 + 6.92285i) q^{58} -7.61536i q^{59} +(-2.74027 + 4.74628i) q^{61} +(6.56209 - 11.3659i) q^{62} -22.5608 q^{64} +(-3.10435 - 2.33935i) q^{65} +(4.83503 - 2.79151i) q^{67} +28.4086 q^{68} +(-6.61862 - 3.92713i) q^{70} +(-8.55573 + 4.93965i) q^{71} +(4.88610 + 2.82099i) q^{73} -21.1155 q^{74} +(30.1614 + 17.4137i) q^{76} +(-7.01586 + 11.8242i) q^{77} +(1.65033 + 2.85846i) q^{79} +(12.4340 - 7.17876i) q^{80} +(-2.65006 + 4.59003i) q^{82} -8.99871i q^{83} +(-5.02351 + 2.90033i) q^{85} +(-17.8876 + 10.3274i) q^{86} +(-22.9941 - 39.8269i) q^{88} +13.8382i q^{89} +(-7.54949 - 5.83140i) q^{91} +10.5738 q^{92} +(-12.9804 - 22.4828i) q^{94} -7.11130 q^{95} +(6.64083 - 3.83409i) q^{97} +(-16.1269 - 9.83047i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 44 q^{4} + 8 q^{7}+O(q^{10}) \) 36 * q - 44 * q^4 + 8 * q^7	\( 36 q - 44 q^{4} + 8 q^{7} + 8 q^{10} + 52 q^{16} - 36 q^{19} + 2 q^{22} + 22 q^{25} + 16 q^{28} - 18 q^{31} - 34 q^{40} + 4 q^{43} + 12 q^{49} + 74 q^{52} - 22 q^{55} + 84 q^{58} - 54 q^{61} - 100 q^{64} + 36 q^{67} - 72 q^{70} - 30 q^{73} + 42 q^{76} + 40 q^{79} + 18 q^{82} + 12 q^{88} + 32 q^{91} - 56 q^{94} - 36 q^{97}+O(q^{100}) \) 36 * q - 44 * q^4 + 8 * q^7 + 8 * q^10 + 52 * q^16 - 36 * q^19 + 2 * q^22 + 22 * q^25 + 16 * q^28 - 18 * q^31 - 34 * q^40 + 4 * q^43 + 12 * q^49 + 74 * q^52 - 22 * q^55 + 84 * q^58 - 54 * q^61 - 100 * q^64 + 36 * q^67 - 72 * q^70 - 30 * q^73 + 42 * q^76 + 40 * q^79 + 18 * q^82 + 12 * q^88 + 32 * q^91 - 56 * q^94 - 36 * q^97

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