LMFDB - Embedded newform 448.3.s.h.129.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,3,Mod(129,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("448.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.s (of order $6$, degree $2$, not 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:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 $ x^16 - 26x^14 - 16x^13 + 469x^12 + 144x^11 - 4526x^10 + 4440x^9 + 32608x^8 - 33728x^7 - 49760x^6 + 203528x^5 + 27401x^4 - 156928x^3 + 114964x^2 - 248608x + 208849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 7 $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.8
Root			$3.86852 - 1.41699i$ of defining polynomial
Character	$\chi$	$=$	448.129
Dual form			448.3.s.h.257.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.97091 + 2.86995i) q^{3} +(-5.45949 + 3.15204i) q^{5} +(5.64993 - 4.13259i) q^{7} +(11.9733 + 20.7383i) q^{9} +O(q^{10})$	\(q+(4.97091 + 2.86995i) q^{3} +(-5.45949 + 3.15204i) q^{5} +(5.64993 - 4.13259i) q^{7} +(11.9733 + 20.7383i) q^{9} +(-2.70557 + 4.68619i) q^{11} +15.9368i q^{13} -36.1848 q^{15} +(-17.7354 - 10.2395i) q^{17} +(11.7669 - 6.79363i) q^{19} +(39.9456 - 4.32768i) q^{21} +(2.35080 + 4.07170i) q^{23} +(7.37071 - 12.7664i) q^{25} +85.7918i q^{27} -1.76543 q^{29} +(11.9039 + 6.87274i) q^{31} +(-26.8983 + 15.5297i) q^{33} +(-17.8197 + 40.3706i) q^{35} +(5.23363 + 9.06491i) q^{37} +(-45.7380 + 79.2205i) q^{39} -11.2412i q^{41} +49.1704 q^{43} +(-130.736 - 75.4805i) q^{45} +(9.02382 - 5.20991i) q^{47} +(14.8434 - 46.6977i) q^{49} +(-58.7740 - 101.800i) q^{51} +(16.0506 - 27.8005i) q^{53} -34.1123i q^{55} +77.9897 q^{57} +(-57.2860 - 33.0741i) q^{59} +(27.6804 - 15.9813i) q^{61} +(153.351 + 67.6894i) q^{63} +(-50.2335 - 87.0070i) q^{65} +(-49.2688 + 85.3361i) q^{67} +26.9867i q^{69} -61.7537 q^{71} +(15.6253 + 9.02127i) q^{73} +(73.2782 - 42.3072i) q^{75} +(4.07980 + 37.6576i) q^{77} +(15.0018 + 25.9839i) q^{79} +(-138.459 + 239.818i) q^{81} -63.4583i q^{83} +129.102 q^{85} +(-8.77580 - 5.06671i) q^{87} +(119.129 - 68.7791i) q^{89} +(65.8604 + 90.0420i) q^{91} +(39.4489 + 68.3275i) q^{93} +(-42.8276 + 74.1796i) q^{95} -131.075i q^{97} -129.578 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{9}+O(q^{10}) $ 16 * q + 40 * q^9	$ 16 q + 40 q^{9} - 48 q^{17} + 136 q^{21} + 80 q^{25} + 16 q^{29} - 264 q^{33} - 72 q^{37} - 312 q^{45} + 128 q^{49} - 40 q^{53} + 368 q^{57} - 216 q^{61} - 168 q^{65} - 312 q^{73} - 64 q^{77} - 384 q^{81} + 1072 q^{85} + 24 q^{89} + 168 q^{93}+O(q^{100}) $ 16 * q + 40 * q^9 - 48 * q^17 + 136 * q^21 + 80 * q^25 + 16 * q^29 - 264 * q^33 - 72 * q^37 - 312 * q^45 + 128 * q^49 - 40 * q^53 + 368 * q^57 - 216 * q^61 - 168 * q^65 - 312 * q^73 - 64 * q^77 - 384 * q^81 + 1072 * q^85 + 24 * q^89 + 168 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.97091	+	2.86995i	1.65697	+	0.956651i	0.974102	+	0.226109i	$0.0726004\pi$
$3$	4.97091	+	2.86995i	1.65697	+	0.956651i	0.682867	+	0.730543i	$0.260733\pi$
$4$		0			0
$5$	−5.45949	+	3.15204i	−1.09190	+	0.630408i	−0.934081	−	0.357060i	$-0.883779\pi$
$5$	−5.45949	+	3.15204i	−1.09190	+	0.630408i	−0.157817	+	0.987468i	$0.550446\pi$
$6$		0			0
$7$	5.64993	−	4.13259i	0.807133	−	0.590370i
$7$	5.64993	−	4.13259i	0.807133	−	0.590370i
$8$		0			0
$9$	11.9733	+	20.7383i	1.33036	+	2.30426i
$10$		0			0
$11$	−2.70557	+	4.68619i	−0.245961	+	0.426017i	−0.962401	−	0.271631i	$-0.912437\pi$
$11$	−2.70557	+	4.68619i	−0.245961	+	0.426017i	0.716440	+	0.697648i	$0.245770\pi$
$12$		0			0
$13$			15.9368i			1.22591i	0.790118	+	0.612955i	$0.210019\pi$
$13$			15.9368i			1.22591i	−0.790118	+	0.612955i	$0.789981\pi$
$14$		0			0
$15$	−36.1848			−2.41232
$16$		0			0
$17$	−17.7354	−	10.2395i	−1.04326	−	0.602326i	−0.122505	−	0.992468i	$-0.539093\pi$
$17$	−17.7354	−	10.2395i	−1.04326	−	0.602326i	−0.920755	+	0.390142i	$0.872426\pi$
$18$		0			0
$19$	11.7669	−	6.79363i	0.619311	−	0.357560i	−0.157289	−	0.987553i	$-0.550276\pi$
$19$	11.7669	−	6.79363i	0.619311	−	0.357560i	0.776601	+	0.629993i	$0.216942\pi$
$20$		0			0
$21$	39.9456	−	4.32768i	1.90217	−	0.206080i
$22$		0			0
$23$	2.35080	+	4.07170i	0.102209	+	0.177030i	0.912594	−	0.408866i	$-0.134076\pi$
$23$	2.35080	+	4.07170i	0.102209	+	0.177030i	−0.810386	+	0.585897i	$0.800742\pi$
$24$		0			0
$25$	7.37071	−	12.7664i	0.294828	−	0.510658i
$26$		0			0
$27$			85.7918i			3.17748i
$28$		0			0
$29$	−1.76543			−0.0608770			−0.0304385	−	0.999537i	$-0.509690\pi$
$29$	−1.76543			−0.0608770			−0.0304385	+	0.999537i	$0.509690\pi$
$30$		0			0
$31$	11.9039	+	6.87274i	0.383998	+	0.221701i	0.679556	−	0.733623i	$-0.262172\pi$
$31$	11.9039	+	6.87274i	0.383998	+	0.221701i	−0.295558	+	0.955325i	$0.595506\pi$
$32$		0			0
$33$	−26.8983	+	15.5297i	−0.815099	+	0.470598i
$34$		0			0
$35$	−17.8197	+	40.3706i	−0.509133	+	1.15345i
$36$		0			0
$37$	5.23363	+	9.06491i	0.141449	+	0.244998i	0.928043	−	0.372474i	$-0.121490\pi$
$37$	5.23363	+	9.06491i	0.141449	+	0.244998i	−0.786593	+	0.617472i	$0.788157\pi$
$38$		0			0
$39$	−45.7380	+	79.2205i	−1.17277	+	2.03130i
$40$		0			0
$41$		−	11.2412i		−	0.274175i	−0.990559	−	0.137088i	$-0.956226\pi$
$41$		−	11.2412i		−	0.274175i	0.990559	−	0.137088i	$-0.0437742\pi$
$42$		0			0
$43$	49.1704			1.14350			0.571749	−	0.820428i	$-0.306265\pi$
$43$	49.1704			1.14350			0.571749	+	0.820428i	$0.306265\pi$
$44$		0			0
$45$	−130.736	−	75.4805i	−2.90525	−	1.67734i
$46$		0			0
$47$	9.02382	−	5.20991i	0.191996	−	0.110849i	−0.400921	−	0.916113i	$-0.631310\pi$
$47$	9.02382	−	5.20991i	0.191996	−	0.110849i	0.592917	+	0.805264i	$0.297976\pi$
$48$		0			0
$49$	14.8434	−	46.6977i	0.302927	−	0.953014i
$50$		0			0
$51$	−58.7740	−	101.800i	−1.15243	−	1.99607i
$52$		0			0
$53$	16.0506	−	27.8005i	0.302842	−	0.524538i	−0.673936	−	0.738789i	$-0.735398\pi$
$53$	16.0506	−	27.8005i	0.302842	−	0.524538i	0.976779	+	0.214251i	$0.0687311\pi$
$54$		0			0
$55$		−	34.1123i		−	0.620223i
$56$		0			0
$57$	77.9897			1.36824
$58$		0			0
$59$	−57.2860	−	33.0741i	−0.970950	−	0.560578i	−0.0714242	−	0.997446i	$-0.522754\pi$
$59$	−57.2860	−	33.0741i	−0.970950	−	0.560578i	−0.899526	+	0.436868i	$0.856088\pi$
$60$		0			0
$61$	27.6804	−	15.9813i	0.453778	−	0.261989i	−0.255647	−	0.966770i	$-0.582288\pi$
$61$	27.6804	−	15.9813i	0.453778	−	0.261989i	0.709424	+	0.704782i	$0.248955\pi$
$62$		0			0
$63$	153.351	+	67.6894i	2.43415	+	1.07444i
$64$		0			0
$65$	−50.2335	−	87.0070i	−0.772824	−	1.33857i
$66$		0			0
$67$	−49.2688	+	85.3361i	−0.735356	+	1.27367i	0.219211	+	0.975677i	$0.429652\pi$
$67$	−49.2688	+	85.3361i	−0.735356	+	1.27367i	−0.954567	+	0.297996i	$0.903682\pi$
$68$		0			0
$69$			26.9867i			0.391112i
$70$		0			0
$71$	−61.7537			−0.869770			−0.434885	−	0.900486i	$-0.643211\pi$
$71$	−61.7537			−0.869770			−0.434885	+	0.900486i	$0.643211\pi$
$72$		0			0
$73$	15.6253	+	9.02127i	0.214045	+	0.123579i	0.603190	−	0.797598i	$-0.293896\pi$
$73$	15.6253	+	9.02127i	0.214045	+	0.123579i	−0.389145	+	0.921177i	$0.627229\pi$
$74$		0			0
$75$	73.2782	−	42.3072i	0.977043	−	0.564096i
$76$		0			0
$77$	4.07980	+	37.6576i	0.0529844	+	0.489060i
$78$		0			0
$79$	15.0018	+	25.9839i	0.189896	+	0.328910i	0.945215	−	0.326447i	$-0.105851\pi$
$79$	15.0018	+	25.9839i	0.189896	+	0.328910i	−0.755319	+	0.655357i	$0.772518\pi$
$80$		0			0
$81$	−138.459	+	239.818i	−1.70937	+	2.96072i
$82$		0			0
$83$		−	63.4583i		−	0.764558i	−0.924047	−	0.382279i	$-0.875139\pi$
$83$		−	63.4583i		−	0.764558i	0.924047	−	0.382279i	$-0.124861\pi$
$84$		0			0
$85$	129.102			1.51884
$86$		0			0
$87$	−8.77580	−	5.06671i	−0.100871	−	0.0582381i
$88$		0			0
$89$	119.129	−	68.7791i	1.33853	−	0.772799i	0.351938	−	0.936023i	$-0.385523\pi$
$89$	119.129	−	68.7791i	1.33853	−	0.772799i	0.986589	+	0.163224i	$0.0521894\pi$
$90$		0			0
$91$	65.8604	+	90.0420i	0.723741	+	0.989472i
$92$		0			0
$93$	39.4489	+	68.3275i	0.424182	+	0.734705i
$94$		0			0
$95$	−42.8276	+	74.1796i	−0.450817	+	0.780838i
$96$		0			0
$97$		−	131.075i		−	1.35129i	−0.737228	−	0.675644i	$-0.763866\pi$
$97$		−	131.075i		−	1.35129i	0.737228	−	0.675644i	$-0.236134\pi$
$98$		0			0
$99$	−129.578			−1.30887
$100$		0			0
$101$	99.2877	+	57.3238i	0.983046	+	0.567562i	0.903188	−	0.429244i	$-0.141220\pi$
$101$	99.2877	+	57.3238i	0.983046	+	0.567562i	0.0798578	+	0.996806i	$0.474553\pi$
$102$		0			0
$103$	173.736	−	100.307i	1.68676	−	0.973851i	0.729786	−	0.683675i	$-0.239620\pi$
$103$	173.736	−	100.307i	1.68676	−	0.973851i	0.956973	−	0.290176i	$-0.0937137\pi$
$104$		0			0
$105$	−204.442	+	149.537i	−1.94706	+	1.42416i
$106$		0			0
$107$	−49.7054	−	86.0923i	−0.464537	−	0.804601i	0.534644	−	0.845078i	$-0.320446\pi$
$107$	−49.7054	−	86.0923i	−0.464537	−	0.804601i	−0.999181	+	0.0404762i	$0.987113\pi$
$108$		0			0
$109$	−7.59446	+	13.1540i	−0.0696740	+	0.120679i	−0.898758	−	0.438445i	$-0.855529\pi$
$109$	−7.59446	+	13.1540i	−0.0696740	+	0.120679i	0.829084	+	0.559124i	$0.188863\pi$
$110$		0			0
$111$			60.0811i			0.541271i
$112$		0			0
$113$	114.050			1.00929			0.504645	−	0.863327i	$-0.331623\pi$
$113$	114.050			1.00929			0.504645	+	0.863327i	$0.331623\pi$
$114$		0			0
$115$	−25.6683	−	14.8196i	−0.223203	−	0.128866i
$116$		0			0
$117$	−330.503	+	190.816i	−2.82481	+	1.63091i
$118$		0			0
$119$	−142.520	+	15.4405i	−1.19764	+	0.129752i
$120$		0			0
$121$	45.8598	+	79.4315i	0.379006	+	0.656458i
$122$		0			0
$123$	32.2617	−	55.8789i	0.262290	−	0.454300i
$124$		0			0
$125$		−	64.6709i		−	0.517367i
$126$		0			0
$127$	27.7466			0.218477			0.109239	−	0.994016i	$-0.465159\pi$
$127$	27.7466			0.218477			0.109239	+	0.994016i	$0.465159\pi$
$128$		0			0
$129$	244.422	+	141.117i	1.89474	+	1.09393i
$130$		0			0
$131$	158.266	−	91.3750i	1.20814	−	0.697519i	0.245786	−	0.969324i	$-0.420954\pi$
$131$	158.266	−	91.3750i	1.20814	−	0.697519i	0.962352	+	0.271805i	$0.0876206\pi$
$132$		0			0
$133$	38.4069	−	87.0114i	0.288774	−	0.654221i
$134$		0			0
$135$	−270.419	−	468.380i	−2.00311	−	3.46948i
$136$		0			0
$137$	−50.5536	+	87.5614i	−0.369004	+	0.639134i	−0.989410	−	0.145147i	$-0.953635\pi$
$137$	−50.5536	+	87.5614i	−0.369004	+	0.639134i	0.620406	+	0.784281i	$0.286968\pi$
$138$		0			0
$139$			88.5595i			0.637119i	0.947903	+	0.318559i	$0.103199\pi$
$139$			88.5595i			0.637119i	−0.947903	+	0.318559i	$0.896801\pi$
$140$		0			0
$141$	59.8088			0.424176
$142$		0			0
$143$	−74.6830	−	43.1182i	−0.522258	−	0.301526i
$144$		0			0
$145$	9.63837	−	5.56472i	0.0664715	−	0.0383773i
$146$		0			0
$147$	207.805	−	189.530i	1.41364	−	1.28932i
$148$		0			0
$149$	−63.5182	−	110.017i	−0.426296	−	0.738367i	0.570244	−	0.821475i	$-0.306849\pi$
$149$	−63.5182	−	110.017i	−0.426296	−	0.738367i	−0.996541	+	0.0831082i	$0.973515\pi$
$150$		0			0
$151$	145.693	−	252.347i	0.964852	−	1.67117i	0.254841	−	0.966983i	$-0.417977\pi$
$151$	145.693	−	252.347i	0.964852	−	1.67117i	0.710011	−	0.704190i	$-0.248690\pi$
$152$		0			0
$153$		−	490.403i		−	3.20525i
$154$		0			0
$155$	−86.6526			−0.559049
$156$		0			0
$157$	−186.624	−	107.747i	−1.18869	−	0.686289i	−0.230679	−	0.973030i	$-0.574095\pi$
$157$	−186.624	−	107.747i	−1.18869	−	0.686289i	−0.958008	+	0.286741i	$0.907428\pi$
$158$		0			0
$159$	159.572	−	92.1292i	1.00360	−	0.579429i
$160$		0			0
$161$	30.1085	+	13.2899i	0.187009	+	0.0825462i
$162$		0			0
$163$	87.0084	+	150.703i	0.533794	+	0.924558i	0.999221	+	0.0394714i	$0.0125674\pi$
$163$	87.0084	+	150.703i	0.533794	+	0.924558i	−0.465427	+	0.885086i	$0.654099\pi$
$164$		0			0
$165$	97.9006	−	169.569i	0.593337	−	1.02769i
$166$		0			0
$167$			241.170i			1.44413i	0.691823	+	0.722067i	$0.256808\pi$
$167$			241.170i			1.44413i	−0.691823	+	0.722067i	$0.743192\pi$
$168$		0			0
$169$	−84.9827			−0.502856
$170$		0			0
$171$	281.777	+	162.684i	1.64782	+	0.951369i
$172$		0			0
$173$	187.037	−	107.986i	1.08114	−	0.624197i	0.149937	−	0.988696i	$-0.452093\pi$
$173$	187.037	−	107.986i	1.08114	−	0.624197i	0.931204	+	0.364499i	$0.118760\pi$
$174$		0			0
$175$	−11.1145	−	102.590i	−0.0635114	−	0.586227i
$176$		0			0
$177$	−189.842	−	328.817i	−1.07256	−	1.85772i
$178$		0			0
$179$	−89.0372	+	154.217i	−0.497414	+	0.861547i	−0.999996	−	0.00298291i	$-0.999051\pi$
$179$	−89.0372	+	154.217i	−0.497414	+	0.861547i	0.502581	+	0.864530i	$0.332384\pi$
$180$		0			0
$181$		−	172.429i		−	0.952648i	−0.879270	−	0.476324i	$-0.841969\pi$
$181$		−	172.429i		−	0.952648i	0.879270	−	0.476324i	$-0.158031\pi$
$182$		0			0
$183$	183.462			1.00253
$184$		0			0
$185$	−57.1459	−	32.9932i	−0.308897	−	0.178342i
$186$		0			0
$187$	95.9688	−	55.4076i	0.513202	−	0.296297i
$188$		0			0
$189$	354.543	+	484.718i	1.87589	+	2.56464i
$190$		0			0
$191$	69.6230	+	120.591i	0.364518	+	0.631364i	0.988699	−	0.149916i	$-0.0479004\pi$
$191$	69.6230	+	120.591i	0.364518	+	0.631364i	−0.624181	+	0.781280i	$0.714567\pi$
$192$		0			0
$193$	21.6165	−	37.4409i	0.112003	−	0.193994i	−0.804575	−	0.593851i	$-0.797607\pi$
$193$	21.6165	−	37.4409i	0.112003	−	0.193994i	0.916578	+	0.399857i	$0.130940\pi$
$194$		0			0
$195$		−	576.672i		−	2.95729i
$196$		0			0
$197$	−205.910			−1.04523			−0.522614	−	0.852570i	$-0.675043\pi$
$197$	−205.910			−1.04523			−0.522614	+	0.852570i	$0.675043\pi$
$198$		0			0
$199$	−260.927	−	150.646i	−1.31119	−	0.757016i	−0.328896	−	0.944366i	$-0.606677\pi$
$199$	−260.927	−	150.646i	−1.31119	−	0.757016i	−0.982293	+	0.187350i	$0.940010\pi$
$200$		0			0
$201$	−489.822	+	282.799i	−2.43692	+	1.40696i
$202$		0			0
$203$	−9.97457	+	7.29581i	−0.0491358	+	0.0359400i
$204$		0			0
$205$	35.4327	+	61.3712i	0.172842	+	0.299372i
$206$		0			0
$207$	−56.2935	+	97.5032i	−0.271949	+	0.471030i
$208$		0			0
$209$			73.5226i			0.351783i
$210$		0			0
$211$	−310.102			−1.46968			−0.734839	−	0.678241i	$-0.762742\pi$
$211$	−310.102			−1.46968			−0.734839	+	0.678241i	$0.762742\pi$
$212$		0			0
$213$	−306.972	−	177.230i	−1.44118	−	0.832067i
$214$		0			0
$215$	−268.446	+	154.987i	−1.24858	+	0.720871i
$216$		0			0
$217$	95.6586	−	10.3636i	0.440823	−	0.0477585i
$218$		0			0
$219$	51.7812	+	89.6877i	0.236444	+	0.409533i
$220$		0			0
$221$	163.186	−	282.646i	0.738398	−	1.27894i
$222$		0			0
$223$		−	266.090i		−	1.19323i	−0.802528	−	0.596614i	$-0.796512\pi$
$223$		−	266.090i		−	1.19323i	0.802528	−	0.596614i	$-0.203488\pi$
$224$		0			0
$225$	353.006			1.56892
$226$		0			0
$227$	−264.188	−	152.529i	−1.16382	−	0.671933i	−0.211605	−	0.977355i	$-0.567869\pi$
$227$	−264.188	−	152.529i	−1.16382	−	0.671933i	−0.952217	+	0.305422i	$0.901202\pi$
$228$		0			0
$229$	−171.968	+	99.2857i	−0.750952	+	0.433562i	−0.826038	−	0.563615i	$-0.809410\pi$
$229$	−171.968	+	99.2857i	−0.750952	+	0.433562i	0.0750860	+	0.997177i	$0.476077\pi$
$230$		0			0
$231$	−87.7954	+	198.901i	−0.380066	+	0.861045i
$232$		0			0
$233$	123.928	+	214.650i	0.531881	+	0.921246i	0.999307	+	0.0372134i	$0.0118481\pi$
$233$	123.928	+	214.650i	0.531881	+	0.921246i	−0.467426	+	0.884032i	$0.654819\pi$
$234$		0			0
$235$	−32.8437	+	56.8869i	−0.139760	+	0.242072i
$236$		0			0
$237$			172.218i			0.726658i
$238$		0			0
$239$	120.884			0.505790			0.252895	−	0.967494i	$-0.418617\pi$
$239$	120.884			0.505790			0.252895	+	0.967494i	$0.418617\pi$
$240$		0			0
$241$	125.956	+	72.7209i	0.522640	+	0.301746i	0.738014	−	0.674785i	$-0.235764\pi$
$241$	125.956	+	72.7209i	0.522640	+	0.301746i	−0.215374	+	0.976532i	$0.569097\pi$
$242$		0			0
$243$	−707.854	+	408.680i	−2.91298	+	1.68181i
$244$		0			0
$245$	66.1555	+	301.733i	0.270023	+	1.23156i
$246$		0			0
$247$	108.269	+	187.527i	0.438336	+	0.759220i
$248$		0			0
$249$	182.123	−	315.446i	0.731416	−	1.26685i
$250$		0			0
$251$			212.061i			0.844865i	0.906394	+	0.422432i	$0.138824\pi$
$251$			212.061i			0.844865i	−0.906394	+	0.422432i	$0.861176\pi$
$252$		0			0
$253$	−25.4410			−0.100557
$254$		0			0
$255$	641.753	+	370.516i	2.51668	+	1.45300i
$256$		0			0
$257$	8.71846	−	5.03361i	0.0339240	−	0.0195860i	−0.482942	−	0.875652i	$-0.660432\pi$
$257$	8.71846	−	5.03361i	0.0339240	−	0.0195860i	0.516866	+	0.856066i	$0.327099\pi$
$258$		0			0
$259$	67.0312	+	29.5877i	0.258808	+	0.114238i
$260$		0			0
$261$	−21.1380	−	36.6121i	−0.0809886	−	0.140276i
$262$		0			0
$263$	0.0417642	−	0.0723377i	0.000158799	−	0.000275048i	−0.865946	−	0.500138i	$-0.833283\pi$
$263$	0.0417642	−	0.0723377i	0.000158799	−	0.000275048i	0.866105	+	0.499862i	$0.166616\pi$
$264$		0			0
$265$			202.369i			0.763657i
$266$		0			0
$267$	789.572			2.95720
$268$		0			0
$269$	1.10371	+	0.637226i	0.00410301	+	0.00236887i	0.502050	−	0.864839i	$-0.332579\pi$
$269$	1.10371	+	0.637226i	0.00410301	+	0.00236887i	−0.497947	+	0.867207i	$0.665913\pi$
$270$		0			0
$271$	−309.749	+	178.834i	−1.14298	+	0.659903i	−0.947168	−	0.320738i	$-0.896069\pi$
$271$	−309.749	+	178.834i	−1.14298	+	0.659903i	−0.195817	+	0.980641i	$0.562736\pi$
$272$		0			0
$273$	68.9695	+	636.607i	0.252636	+	2.33189i
$274$		0			0
$275$	39.8840	+	69.0810i	0.145033	+	0.251204i
$276$		0			0
$277$	−84.6074	+	146.544i	−0.305442	+	0.529041i	−0.977360	−	0.211585i	$-0.932137\pi$
$277$	−84.6074	+	146.544i	−0.305442	+	0.529041i	0.671918	+	0.740626i	$0.265471\pi$
$278$		0			0
$279$			329.157i			1.17977i
$280$		0			0
$281$	246.835			0.878418			0.439209	−	0.898385i	$-0.355259\pi$
$281$	246.835			0.878418			0.439209	+	0.898385i	$0.355259\pi$
$282$		0			0
$283$	−198.888	−	114.828i	−0.702783	−	0.405752i	0.105600	−	0.994409i	$-0.466324\pi$
$283$	−198.888	−	114.828i	−0.702783	−	0.405752i	−0.808383	+	0.588657i	$0.799657\pi$
$284$		0			0
$285$	−425.784	+	245.827i	−1.49398	+	0.862549i
$286$		0			0
$287$	−46.4552	−	63.5119i	−0.161865	−	0.221296i
$288$		0			0
$289$	65.1965	+	112.924i	0.225593	+	0.390739i
$290$		0			0
$291$	376.179	−	651.561i	1.29271	−	2.23904i
$292$		0			0
$293$			228.171i			0.778740i	0.921081	+	0.389370i	$0.127307\pi$
$293$			228.171i			0.778740i	−0.921081	+	0.389370i	$0.872693\pi$
$294$		0			0
$295$	417.004			1.41357
$296$		0			0
$297$	−402.036	−	232.116i	−1.35366	−	0.781535i
$298$		0			0
$299$	−64.8900	+	37.4643i	−0.217023	+	0.125299i
$300$		0			0
$301$	277.810	−	203.201i	0.922955	−	0.675087i
$302$		0			0
$303$	329.033	+	569.902i	1.08592	+	1.88087i
$304$		0			0
$305$	−100.747	+	174.500i	−0.330319	+	0.572130i
$306$		0			0
$307$			333.745i			1.08712i	0.839371	+	0.543559i	$0.182924\pi$
$307$			333.745i			1.08712i	−0.839371	+	0.543559i	$0.817076\pi$
$308$		0			0
$309$	1151.50			3.72654
$310$		0			0
$311$	−215.654	−	124.508i	−0.693421	−	0.400347i	0.111471	−	0.993768i	$-0.464444\pi$
$311$	−215.654	−	124.508i	−0.693421	−	0.400347i	−0.804892	+	0.593421i	$0.797777\pi$
$312$		0			0
$313$	−34.5147	+	19.9271i	−0.110271	+	0.0636648i	−0.554121	−	0.832436i	$-0.686946\pi$
$313$	−34.5147	+	19.9271i	−0.110271	+	0.0636648i	0.443850	+	0.896101i	$0.353612\pi$
$314$		0			0
$315$	−1050.58	+	113.819i	−3.33517	+	0.361330i
$316$		0			0
$317$	−221.206	−	383.140i	−0.697811	−	1.20864i	−0.969224	−	0.246181i	$-0.920824\pi$
$317$	−221.206	−	383.140i	−0.697811	−	1.20864i	0.271413	−	0.962463i	$-0.412509\pi$
$318$		0			0
$319$	4.77650	−	8.27315i	0.0149734	−	0.0259346i
$320$		0			0
$321$		−	570.609i		−	1.77760i
$322$		0			0
$323$	−278.255			−0.861470
$324$		0			0
$325$	203.457	+	117.466i	0.626021	+	0.361433i
$326$		0			0
$327$	−75.5027	+	43.5915i	−0.230895	+	0.133307i
$328$		0			0
$329$	29.4535	−	66.7274i	0.0895245	−	0.202819i
$330$		0			0
$331$	−71.9641	−	124.646i	−0.217414	−	0.376573i	0.736602	−	0.676326i	$-0.236429\pi$
$331$	−71.9641	−	124.646i	−0.217414	−	0.376573i	−0.954017	+	0.299753i	$0.903096\pi$
$332$		0			0
$333$	−125.327	+	217.073i	−0.376359	+	0.651872i
$334$		0			0
$335$		−	621.189i		−	1.85430i
$336$		0			0
$337$	−428.372			−1.27113			−0.635567	−	0.772046i	$-0.719234\pi$
$337$	−428.372			−1.27113			−0.635567	+	0.772046i	$0.719234\pi$
$338$		0			0
$339$	566.930	+	327.317i	1.67236	+	0.965538i
$340$		0			0
$341$	−64.4139	+	37.1894i	−0.188897	+	0.109060i
$342$		0			0
$343$	−109.118	−	325.180i	−0.318129	−	0.948047i
$344$		0			0
$345$	−85.0632	−	147.334i	−0.246560	−	0.427054i
$346$		0			0
$347$	−122.803	+	212.700i	−0.353898	+	0.612969i	−0.986929	−	0.161158i	$-0.948477\pi$
$347$	−122.803	+	212.700i	−0.353898	+	0.612969i	0.633031	+	0.774126i	$0.281811\pi$
$348$		0			0
$349$		−	675.578i		−	1.93575i	−0.251428	−	0.967876i	$-0.580900\pi$
$349$		−	675.578i		−	1.93575i	0.251428	−	0.967876i	$-0.419100\pi$
$350$		0			0
$351$	−1367.25			−3.89530
$352$		0			0
$353$	−492.343	−	284.254i	−1.39474	−	0.805252i	−0.400903	−	0.916121i	$-0.631304\pi$
$353$	−492.343	−	284.254i	−1.39474	−	0.805252i	−0.993835	+	0.110868i	$0.964637\pi$
$354$		0			0
$355$	337.144	−	194.650i	0.949701	−	0.548310i
$356$		0			0
$357$	−752.765	−	332.272i	−2.10859	−	0.930733i
$358$		0			0
$359$	336.956	+	583.625i	0.938596	+	1.62570i	0.768092	+	0.640339i	$0.221206\pi$
$359$	336.956	+	583.625i	0.938596	+	1.62570i	0.170504	+	0.985357i	$0.445460\pi$
$360$		0			0
$361$	−88.1931	+	152.755i	−0.244302	+	0.423144i
$362$		0			0
$363$			526.462i			1.45031i
$364$		0			0
$365$	−113.742			−0.311621
$366$		0			0
$367$	37.3366	+	21.5563i	0.101735	+	0.0587366i	0.550004	−	0.835162i	$-0.314626\pi$
$367$	37.3366	+	21.5563i	0.101735	+	0.0587366i	−0.448269	+	0.893899i	$0.647959\pi$
$368$		0			0
$369$	233.123	−	134.594i	0.631771	−	0.364753i
$370$		0			0
$371$	−24.2032	−	223.402i	−0.0652377	−	0.602161i
$372$		0			0
$373$	316.582	+	548.337i	0.848746	+	1.47007i	0.882328	+	0.470636i	$0.155975\pi$
$373$	316.582	+	548.337i	0.848746	+	1.47007i	−0.0335811	+	0.999436i	$0.510691\pi$
$374$		0			0
$375$	185.603	−	321.473i	0.494940	−	0.857261i
$376$		0			0
$377$		−	28.1354i		−	0.0746297i
$378$		0			0
$379$	611.641			1.61383			0.806914	−	0.590669i	$-0.201136\pi$
$379$	611.641			1.61383			0.806914	+	0.590669i	$0.201136\pi$
$380$		0			0
$381$	137.926	+	79.6316i	0.362010	+	0.209007i
$382$		0			0
$383$	−555.198	+	320.544i	−1.44960	+	0.836929i	−0.998457	−	0.0555219i	$-0.982318\pi$
$383$	−555.198	+	320.544i	−1.44960	+	0.836929i	−0.451145	+	0.892450i	$0.648984\pi$
$384$		0			0
$385$	−140.972	−	192.732i	−0.366161	−	0.500602i
$386$		0			0
$387$	588.731	+	1019.71i	1.52127	+	2.63492i
$388$		0			0
$389$	−177.180	+	306.884i	−0.455475	+	0.788905i	−0.998715	−	0.0506717i	$-0.983864\pi$
$389$	−177.180	+	306.884i	−0.455475	+	0.788905i	0.543241	+	0.839577i	$0.317197\pi$
$390$		0			0
$391$		−	96.2843i		−	0.246251i
$392$		0			0
$393$	1048.97			2.66913
$394$		0			0
$395$	−163.805	−	94.5726i	−0.414695	−	0.239424i
$396$		0			0
$397$	−271.796	+	156.922i	−0.684625	+	0.395268i	−0.801595	−	0.597867i	$-0.796015\pi$
$397$	−271.796	+	156.922i	−0.684625	+	0.395268i	0.116970	+	0.993135i	$0.462682\pi$
$398$		0			0
$399$	440.636	−	322.299i	1.10435	−	0.807768i
$400$		0			0
$401$	−161.060	−	278.963i	−0.401645	−	0.695669i	0.592280	−	0.805732i	$-0.298228\pi$
$401$	−161.060	−	278.963i	−0.401645	−	0.695669i	−0.993925	+	0.110063i	$0.964895\pi$
$402$		0			0
$403$	−109.530	+	189.711i	−0.271786	+	0.470747i
$404$		0			0
$405$		−	1745.72i		−	4.31041i
$406$		0			0
$407$	−56.6398			−0.139164
$408$		0			0
$409$	413.847	+	238.935i	1.01185	+	0.584192i	0.911733	−	0.410784i	$-0.134745\pi$
$409$	413.847	+	238.935i	1.01185	+	0.584192i	0.100117	+	0.994976i	$0.468078\pi$
$410$		0			0
$411$	−502.594	+	290.173i	−1.22286	+	0.706017i
$412$		0			0
$413$	−460.344	+	49.8733i	−1.11463	+	0.120759i
$414$		0			0
$415$	200.023	+	346.450i	0.481984	+	0.834820i
$416$		0			0
$417$	−254.162	+	440.221i	−0.609500	+	1.05569i
$418$		0			0
$419$			194.885i			0.465119i	0.972582	+	0.232560i	$0.0747101\pi$
$419$			194.885i			0.465119i	−0.972582	+	0.232560i	$0.925290\pi$
$420$		0			0
$421$	−290.331			−0.689621			−0.344811	−	0.938672i	$-0.612057\pi$
$421$	−290.331			−0.689621			−0.344811	+	0.938672i	$0.612057\pi$
$422$		0			0
$423$	216.089	+	124.759i	0.510850	+	0.294939i
$424$		0			0
$425$	−261.445	+	150.945i	−0.615165	+	0.355166i
$426$		0			0
$427$	90.3483	−	204.685i	0.211589	−	0.479356i
$428$		0			0
$429$	−247.495	−	428.673i	−0.576911	−	0.999239i
$430$		0			0
$431$	−191.169	+	331.115i	−0.443549	+	0.768249i	−0.997950	−	0.0640009i	$-0.979614\pi$
$431$	−191.169	+	331.115i	−0.443549	+	0.768249i	0.554401	+	0.832249i	$0.312947\pi$
$432$		0			0
$433$		−	295.254i		−	0.681879i	−0.940085	−	0.340940i	$-0.889255\pi$
$433$		−	295.254i		−	0.681879i	0.940085	−	0.340940i	$-0.110745\pi$
$434$		0			0
$435$	63.8819			0.146855
$436$		0			0
$437$	55.3233	+	31.9409i	0.126598	+	0.0730913i
$438$		0			0
$439$	−42.5045	+	24.5400i	−0.0968212	+	0.0558997i	−0.547629	−	0.836721i	$-0.684469\pi$
$439$	−42.5045	+	24.5400i	−0.0968212	+	0.0558997i	0.450808	+	0.892621i	$0.351136\pi$
$440$		0			0
$441$	1146.16	−	251.297i	2.59899	−	0.569835i
$442$		0			0
$443$	−316.862	−	548.821i	−0.715264	−	1.23887i	−0.962858	−	0.270010i	$-0.912973\pi$
$443$	−316.862	−	548.821i	−0.715264	−	1.23887i	0.247594	−	0.968864i	$-0.420360\pi$
$444$		0			0
$445$	−433.589	+	750.998i	−0.974357	+	1.68764i
$446$		0			0
$447$		−	729.177i		−	1.63127i
$448$		0			0
$449$	−27.3296			−0.0608677			−0.0304339	−	0.999537i	$-0.509689\pi$
$449$	−27.3296			−0.0608677			−0.0304339	+	0.999537i	$0.509689\pi$
$450$		0			0
$451$	52.6783	+	30.4138i	0.116803	+	0.0674364i
$452$		0			0
$453$	1448.45	−	836.263i	3.19746	−	1.84605i
$454$		0			0
$455$	−643.380	−	283.989i	−1.41402	−	0.624152i
$456$		0			0
$457$	−169.555	−	293.677i	−0.371017	−	0.642620i	0.618705	−	0.785623i	$-0.287658\pi$
$457$	−169.555	−	293.677i	−0.371017	−	0.642620i	−0.989722	+	0.143003i	$0.954324\pi$
$458$		0			0
$459$	878.469	−	1521.55i	1.91388	−	3.31493i
$460$		0			0
$461$			580.237i			1.25865i	0.777143	+	0.629324i	$0.216668\pi$
$461$			580.237i			1.25865i	−0.777143	+	0.629324i	$0.783332\pi$
$462$		0			0
$463$	433.685			0.936684			0.468342	−	0.883547i	$-0.344852\pi$
$463$	433.685			0.936684			0.468342	+	0.883547i	$0.344852\pi$
$464$		0			0
$465$	−430.742	−	248.689i	−0.926327	−	0.534815i
$466$		0			0
$467$	−86.6558	+	50.0308i	−0.185558	+	0.107132i	−0.589902	−	0.807475i	$-0.700833\pi$
$467$	−86.6558	+	50.0308i	−0.185558	+	0.107132i	0.404343	+	0.914607i	$0.367500\pi$
$468$		0			0
$469$	74.2938	+	685.751i	0.158409	+	1.46216i
$470$		0			0
$471$	−618.460	−	1071.20i	−1.31308	−	2.27432i
$472$		0			0
$473$	−133.034	+	230.422i	−0.281256	+	0.487150i
$474$		0			0
$475$		−	200.296i		−	0.421675i
$476$		0			0
$477$	768.715			1.61156
$478$		0			0
$479$	−418.996	−	241.907i	−0.874730	−	0.505026i	−0.00581309	−	0.999983i	$-0.501850\pi$
$479$	−418.996	−	241.907i	−0.874730	−	0.505026i	−0.868917	+	0.494957i	$0.835184\pi$
$480$		0			0
$481$	−144.466	+	83.4075i	−0.300345	+	0.173404i
$482$		0			0
$483$	111.525	+	152.473i	0.230901	+	0.315679i
$484$		0			0
$485$	413.154	+	715.603i	0.851863	+	1.47547i
$486$		0			0
$487$	114.763	−	198.776i	0.235654	−	0.408164i	−0.723809	−	0.690001i	$-0.757610\pi$
$487$	114.763	−	198.776i	0.235654	−	0.408164i	0.959462	+	0.281836i	$0.0909436\pi$
$488$		0			0
$489$			998.840i			2.04262i
$490$		0			0
$491$	221.445			0.451008			0.225504	−	0.974242i	$-0.427597\pi$
$491$	221.445			0.451008			0.225504	+	0.974242i	$0.427597\pi$
$492$		0			0
$493$	31.3107	+	18.0772i	0.0635105	+	0.0366678i
$494$		0			0
$495$	707.431	−	408.436i	1.42915	−	0.825122i
$496$		0			0
$497$	−348.904	+	255.203i	−0.702020	+	0.513486i
$498$		0			0
$499$	−256.703	−	444.622i	−0.514435	−	0.891027i	−0.999860	−	0.0167486i	$-0.994668\pi$
$499$	−256.703	−	444.622i	−0.514435	−	0.891027i	0.485425	−	0.874278i	$-0.338665\pi$
$500$		0			0
$501$	−692.148	+	1198.83i	−1.38153	+	2.39288i
$502$		0			0
$503$			360.553i			0.716806i	0.933567	+	0.358403i	$0.116679\pi$
$503$			360.553i			0.716806i	−0.933567	+	0.358403i	$0.883321\pi$
$504$		0			0
$505$	−722.747			−1.43118
$506$		0			0
$507$	−422.441	−	243.896i	−0.833217	−	0.481058i
$508$		0			0
$509$	−163.560	+	94.4312i	−0.321335	+	0.185523i	−0.651988	−	0.758230i	$-0.726065\pi$
$509$	−163.560	+	94.4312i	−0.321335	+	0.185523i	0.330652	+	0.943753i	$0.392731\pi$
$510$		0			0
$511$	125.563	−	13.6034i	0.245720	−	0.0266212i
$512$		0			0
$513$	582.838	+	1009.51i	1.13614	+	1.96785i
$514$		0			0
$515$	−632.341	+	1095.25i	−1.22785	+	2.12669i
$516$		0			0
$517$			56.3831i			0.109058i
$518$		0			0
$519$	1239.66			2.38856
$520$		0			0
$521$	−409.657	−	236.516i	−0.786291	−	0.453965i	0.0523644	−	0.998628i	$-0.483324\pi$
$521$	−409.657	−	236.516i	−0.786291	−	0.453965i	−0.838655	+	0.544663i	$0.816658\pi$
$522$		0			0
$523$	362.994	−	209.575i	0.694061	−	0.400716i	−0.111071	−	0.993812i	$-0.535428\pi$
$523$	362.994	−	209.575i	0.694061	−	0.400716i	0.805131	+	0.593096i	$0.202095\pi$
$524$		0			0
$525$	239.178	−	541.862i	0.455578	−	1.03212i
$526$		0			0
$527$	−140.747	−	243.782i	−0.267073	−	0.462584i
$528$		0			0
$529$	253.448	−	438.984i	0.479107	−	0.829837i
$530$		0			0
$531$		−	1584.02i		−	2.98309i
$532$		0			0
$533$	179.149			0.336114
$534$		0			0
$535$	542.733	+	313.347i	1.01445	+	0.585695i
$536$		0			0
$537$	−885.191	+	511.065i	−1.64840	+	0.951705i
$538$		0			0
$539$	178.674	+	195.903i	0.331492	+	0.363456i
$540$		0			0
$541$	−309.243	−	535.625i	−0.571614	−	0.990065i	−0.996400	−	0.0847712i	$-0.972984\pi$
$541$	−309.243	−	535.625i	−0.571614	−	0.990065i	0.424786	−	0.905294i	$-0.360349\pi$
$542$		0			0
$543$	494.864	−	857.129i	0.911352	−	1.57851i
$544$		0			0
$545$		−	95.7522i		−	0.175692i
$546$		0			0
$547$	255.031			0.466236			0.233118	−	0.972448i	$-0.425107\pi$
$547$	255.031			0.466236			0.233118	+	0.972448i	$0.425107\pi$
$548$		0			0
$549$	662.851	+	382.697i	1.20738	+	0.697081i
$550$		0			0
$551$	−20.7737	+	11.9937i	−0.0377018	+	0.0217672i
$552$		0			0
$553$	192.140	+	84.8108i	0.347450	+	0.153365i
$554$		0			0
$555$	−189.378	−	328.013i	−0.341222	−	0.591014i
$556$		0			0
$557$	244.130	−	422.845i	0.438294	−	0.759148i	−0.559264	−	0.828990i	$-0.688916\pi$
$557$	244.130	−	422.845i	0.438294	−	0.759148i	0.997558	+	0.0698419i	$0.0222495\pi$
$558$		0			0
$559$			783.621i			1.40183i
$560$		0			0
$561$	636.069			1.13381
$562$		0			0
$563$	42.5152	+	24.5462i	0.0755155	+	0.0435989i	0.537282	−	0.843402i	$-0.319451\pi$
$563$	42.5152	+	24.5462i	0.0755155	+	0.0435989i	−0.461767	+	0.887001i	$0.652784\pi$
$564$		0			0
$565$	−622.654	+	359.489i	−1.10204	+	0.636264i
$566$		0			0
$567$	208.786	+	1927.15i	0.368230	+	3.39886i
$568$		0			0
$569$	304.056	+	526.641i	0.534370	+	0.925556i	0.999194	+	0.0401523i	$0.0127843\pi$
$569$	304.056	+	526.641i	0.534370	+	0.925556i	−0.464824	+	0.885403i	$0.653882\pi$
$570$		0			0
$571$	−150.396	+	260.494i	−0.263391	+	0.456207i	−0.967141	−	0.254241i	$-0.918174\pi$
$571$	−150.396	+	260.494i	−0.263391	+	0.456207i	0.703750	+	0.710448i	$0.251508\pi$
$572$		0			0
$573$			799.259i			1.39487i
$574$		0			0
$575$	69.3082			0.120536
$576$		0			0
$577$	−150.719	−	87.0176i	−0.261211	−	0.150810i	0.363676	−	0.931526i	$-0.381522\pi$
$577$	−150.719	−	87.0176i	−0.261211	−	0.150810i	−0.624887	+	0.780715i	$0.714855\pi$
$578$		0			0
$579$	214.907	−	124.077i	0.371170	−	0.214295i
$580$		0			0
$581$	−262.247	−	358.535i	−0.451372	−	0.617100i
$582$		0			0
$583$	86.8523	+	150.433i	0.148975	+	0.258032i
$584$		0			0
$585$	1202.92	−	2083.52i	2.05627	−	3.56157i
$586$		0			0
$587$		−	477.592i		−	0.813614i	−0.913514	−	0.406807i	$-0.866642\pi$
$587$		−	477.592i		−	0.813614i	0.913514	−	0.406807i	$-0.133358\pi$
$588$		0			0
$589$	186.764			0.317086
$590$		0			0
$591$	−1023.56	−	590.952i	−1.73191	−	0.999918i
$592$		0			0
$593$	382.387	−	220.771i	0.644834	−	0.372295i	−0.141640	−	0.989918i	$-0.545238\pi$
$593$	382.387	−	220.771i	0.644834	−	0.372295i	0.786474	+	0.617623i	$0.211904\pi$
$594$		0			0
$595$	729.416	−	533.525i	1.22591	−	0.896680i
$596$		0			0
$597$	−864.695	−	1497.70i	−1.44840	−	2.50870i
$598$		0			0
$599$	−146.046	+	252.959i	−0.243816	+	0.422302i	−0.961798	−	0.273759i	$-0.911733\pi$
$599$	−146.046	+	252.959i	−0.243816	+	0.422302i	0.717982	+	0.696062i	$0.245066\pi$
$600$		0			0
$601$			614.010i			1.02165i	0.859685	+	0.510824i	$0.170660\pi$
$601$			614.010i			1.02165i	−0.859685	+	0.510824i	$0.829340\pi$
$602$		0			0
$603$	−2359.64			−3.91316
$604$		0			0
$605$	−500.742	−	289.104i	−0.827673	−	0.477857i
$606$		0			0
$607$	−281.659	+	162.616i	−0.464019	+	0.267901i	−0.713732	−	0.700418i	$-0.752997\pi$
$607$	−281.659	+	162.616i	−0.464019	+	0.267901i	0.249714	+	0.968320i	$0.419663\pi$
$608$		0			0
$609$	−70.5213	+	7.64023i	−0.115799	+	0.0125455i
$610$		0			0
$611$	83.0294	+	143.811i	0.135891	+	0.235370i
$612$		0			0
$613$	278.468	−	482.321i	0.454271	−	0.786820i	−0.544375	−	0.838842i	$-0.683233\pi$
$613$	278.468	−	482.321i	0.454271	−	0.786820i	0.998646	+	0.0520217i	$0.0165665\pi$
$614$		0			0
$615$			406.761i			0.661399i
$616$		0			0
$617$	277.944			0.450476			0.225238	−	0.974304i	$-0.427684\pi$
$617$	277.944			0.450476			0.225238	+	0.974304i	$0.427684\pi$
$618$		0			0
$619$	−111.665	−	64.4696i	−0.180395	−	0.104151i	0.407083	−	0.913391i	$-0.366546\pi$
$619$	−111.665	−	64.4696i	−0.180395	−	0.104151i	−0.587478	+	0.809240i	$0.699879\pi$
$620$		0			0
$621$	−349.319	+	201.679i	−0.562510	+	0.324765i
$622$		0			0
$623$	388.834	−	880.908i	0.624132	−	1.41398i
$624$		0			0
$625$	388.113	+	672.231i	0.620981	+	1.07557i
$626$		0			0
$627$	−211.006	+	365.474i	−0.336533	+	0.582893i
$628$		0			0
$629$		−	214.360i		−	0.340795i
$630$		0			0
$631$	279.339			0.442692			0.221346	−	0.975195i	$-0.428955\pi$
$631$	279.339			0.442692			0.221346	+	0.975195i	$0.428955\pi$
$632$		0			0
$633$	−1541.49	−	889.979i	−2.43521	−	1.40597i
$634$		0			0
$635$	−151.483	+	87.4585i	−0.238555	+	0.137730i
$636$		0			0
$637$	744.213	+	236.557i	1.16831	+	0.371361i
$638$		0			0
$639$	−739.394	−	1280.67i	−1.15711	−	2.00417i
$640$		0			0
$641$	441.133	−	764.064i	0.688194	−	1.19199i	−0.284227	−	0.958757i	$-0.591737\pi$
$641$	441.133	−	764.064i	0.688194	−	1.19199i	0.972421	−	0.233231i	$-0.0749297\pi$
$642$		0			0
$643$		−	575.210i		−	0.894572i	−0.894391	−	0.447286i	$-0.852391\pi$
$643$		−	575.210i		−	0.894572i	0.894391	−	0.447286i	$-0.147609\pi$
$644$		0			0
$645$	−1779.22			−2.75849
$646$		0			0
$647$	406.207	+	234.524i	0.627832	+	0.362479i	0.779912	−	0.625889i	$-0.215264\pi$
$647$	406.207	+	234.524i	0.627832	+	0.362479i	−0.152080	+	0.988368i	$0.548597\pi$
$648$		0			0
$649$	309.983	−	178.969i	0.477632	−	0.275761i
$650$		0			0
$651$	505.253	+	223.019i	0.776119	+	0.342580i
$652$		0			0
$653$	412.463	+	714.407i	0.631644	+	1.09404i	0.987216	+	0.159390i	$0.0509527\pi$
$653$	412.463	+	714.407i	0.631644	+	1.09404i	−0.355572	+	0.934649i	$0.615714\pi$
$654$		0			0
$655$	−576.035	+	997.722i	−0.879443	+	1.52324i
$656$		0			0
$657$			432.056i			0.657620i
$658$		0			0
$659$	−888.926			−1.34890			−0.674451	−	0.738320i	$-0.735619\pi$
$659$	−888.926			−1.34890			−0.674451	+	0.738320i	$0.735619\pi$
$660$		0			0
$661$	131.019	+	75.6439i	0.198214	+	0.114439i	0.595822	−	0.803117i	$-0.296826\pi$
$661$	131.019	+	75.6439i	0.198214	+	0.114439i	−0.397608	+	0.917555i	$0.630160\pi$
$662$		0			0
$663$	1622.36	−	936.672i	2.44700	−	1.41278i
$664$		0			0
$665$	64.5809	+	596.098i	0.0971141	+	0.896388i
$666$		0			0
$667$	−4.15017	−	7.18831i	−0.00622215	−	0.0107771i
$668$		0			0
$669$	763.666	−	1322.71i	1.14150	−	1.97714i
$670$		0			0
$671$			172.954i			0.257756i
$672$		0			0
$673$	−904.158			−1.34347			−0.671737	−	0.740790i	$-0.734452\pi$
$673$	−904.158			−1.34347			−0.671737	+	0.740790i	$0.734452\pi$
$674$		0			0
$675$	1095.26	+	632.347i	1.62260	+	0.936810i
$676$		0			0
$677$	762.576	−	440.273i	1.12640	−	0.650330i	0.183376	−	0.983043i	$-0.441297\pi$
$677$	762.576	−	440.273i	1.12640	−	0.650330i	0.943028	+	0.332713i	$0.107964\pi$
$678$		0			0
$679$	−541.679	−	740.564i	−0.797760	−	1.09067i
$680$		0			0
$681$	−875.501	−	1516.41i	−1.28561	−	2.22674i
$682$		0			0
$683$	−272.776	+	472.461i	−0.399379	+	0.691744i	−0.993649	−	0.112521i	$-0.964107\pi$
$683$	−272.776	+	472.461i	−0.399379	+	0.691744i	0.594271	+	0.804265i	$0.297441\pi$
$684$		0			0
$685$		−	637.388i		−	0.930493i
$686$		0			0
$687$	−1139.78			−1.65907
$688$		0			0
$689$	443.052	+	255.796i	0.643037	+	0.371257i
$690$		0			0
$691$	815.732	−	470.963i	1.18051	−	0.681568i	0.224377	−	0.974502i	$-0.427965\pi$
$691$	815.732	−	470.963i	1.18051	−	0.681568i	0.956132	+	0.292935i	$0.0946318\pi$
$692$		0			0
$693$	−732.107	+	535.493i	−1.05643	+	0.772718i
$694$		0			0
$695$	−279.143	−	483.490i	−0.401645	−	0.695669i
$696$		0			0
$697$	−115.105	+	199.367i	−0.165143	+	0.286036i
$698$		0			0
$699$			1422.67i			2.03530i
$700$		0			0
$701$	304.580			0.434494			0.217247	−	0.976117i	$-0.430292\pi$
$701$	304.580			0.434494			0.217247	+	0.976117i	$0.430292\pi$
$702$		0			0
$703$	123.167	+	71.1107i	0.175203	+	0.101153i
$704$		0			0
$705$	−326.526	+	188.520i	−0.463157	+	0.267404i
$706$		0			0
$707$	797.864	−	86.4400i	1.12852	−	0.122263i
$708$		0			0
$709$	−321.938	−	557.614i	−0.454074	−	0.786479i	0.544561	−	0.838722i	$-0.316696\pi$
$709$	−321.938	−	557.614i	−0.454074	−	0.786479i	−0.998634	+	0.0522425i	$0.983363\pi$
$710$		0			0
$711$	−359.242	+	622.225i	−0.505262	+	0.875140i
$712$		0			0
$713$			64.6257i			0.0906391i
$714$		0			0
$715$	543.641			0.760338
$716$		0			0
$717$	600.902	+	346.931i	0.838079	+	0.483865i
$718$		0			0
$719$	628.047	−	362.603i	0.873500	−	0.504316i	0.00499056	−	0.999988i	$-0.498411\pi$
$719$	628.047	−	362.603i	0.873500	−	0.504316i	0.868510	+	0.495672i	$0.165078\pi$
$720$		0			0
$721$	567.071	−	1284.71i	0.786506	−	1.78184i
$722$		0			0
$723$	417.411	+	722.977i	0.577332	+	0.999968i
$724$		0			0
$725$	−13.0125	+	22.5383i	−0.0179483	+	0.0310873i
$726$		0			0
$727$			1090.68i			1.50025i	0.661295	+	0.750126i	$0.270007\pi$
$727$			1090.68i			1.50025i	−0.661295	+	0.750126i	$0.729993\pi$
$728$		0			0
$729$	−2199.30			−3.01688
$730$		0			0
$731$	−872.058	−	503.483i	−1.19297	−	0.688759i
$732$		0			0
$733$	204.559	−	118.102i	0.279071	−	0.161122i	−0.353932	−	0.935271i	$-0.615155\pi$
$733$	204.559	−	118.102i	0.279071	−	0.161122i	0.633003	+	0.774149i	$0.281822\pi$
$734$		0			0
$735$	−537.106	+	1689.75i	−0.730757	+	2.29898i
$736$		0			0
$737$	−266.601	−	461.766i	−0.361738	−	0.626548i
$738$		0			0
$739$	−0.140534	+	0.243412i	−0.000190168	+	0.000329381i	−0.866120	−	0.499835i	$-0.833394\pi$
$739$	−0.140534	+	0.243412i	−0.000190168	+	0.000329381i	0.865930	+	0.500165i	$0.166727\pi$
$740$		0			0
$741$			1242.91i			1.67734i
$742$		0			0
$743$	−172.285			−0.231878			−0.115939	−	0.993256i	$-0.536988\pi$
$743$	−172.285			−0.231878			−0.115939	+	0.993256i	$0.536988\pi$
$744$		0			0
$745$	693.554	+	400.424i	0.930945	+	0.537481i
$746$		0			0
$747$	1316.02	−	759.804i	1.76174	−	1.01714i
$748$		0			0
$749$	−636.617	−	281.003i	−0.849955	−	0.375172i
$750$		0			0
$751$	25.4735	+	44.1215i	0.0339195	+	0.0587503i	0.882487	−	0.470337i	$-0.155868\pi$
$751$	25.4735	+	44.1215i	0.0339195	+	0.0587503i	−0.848567	+	0.529087i	$0.822534\pi$
$752$		0			0
$753$	−608.606	+	1054.14i	−0.808241	+	1.39991i
$754$		0			0
$755$			1836.92i			2.43300i
$756$		0			0
$757$	472.598			0.624304			0.312152	−	0.950032i	$-0.398950\pi$
$757$	472.598			0.624304			0.312152	+	0.950032i	$0.398950\pi$
$758$		0			0
$759$	−126.465	−	73.0145i	−0.166620	−	0.0961982i
$760$		0			0
$761$	−370.248	+	213.763i	−0.486528	+	0.280897i	−0.723133	−	0.690709i	$-0.757299\pi$
$761$	−370.248	+	213.763i	−0.486528	+	0.280897i	0.236605	+	0.971606i	$0.423965\pi$
$762$		0			0
$763$	11.4519	+	105.704i	0.0150090	+	0.138537i
$764$		0			0
$765$	1545.77	+	2677.35i	2.02062	+	3.49981i
$766$		0			0
$767$	527.097	−	912.958i	0.687219	−	1.19030i
$768$		0			0
$769$			199.651i			0.259625i	0.991539	+	0.129812i	$0.0414375\pi$
$769$			199.651i			0.259625i	−0.991539	+	0.129812i	$0.958563\pi$
$770$		0			0
$771$	57.7849			0.0749480
$772$		0			0
$773$	36.7213	+	21.2011i	0.0475049	+	0.0274270i	0.523564	−	0.851986i	$-0.324602\pi$
$773$	36.7213	+	21.2011i	0.0475049	+	0.0274270i	−0.476059	+	0.879413i	$0.657935\pi$
$774$		0			0
$775$	175.481	−	101.314i	0.226427	−	0.130728i
$776$		0			0
$777$	248.291	+	339.454i	0.319550	+	0.436878i
$778$		0			0
$779$	−76.3685	−	132.274i	−0.0980340	−	0.169800i
$780$		0			0
$781$	167.079	−	289.389i	0.213929	−	0.370537i
$782$		0			0
$783$		−	151.460i		−	0.193435i
$784$		0			0
$785$	1358.50			1.73057
$786$		0			0
$787$	−524.104	−	302.591i	−0.665951	−	0.384487i	0.128589	−	0.991698i	$-0.458955\pi$
$787$	−524.104	−	302.591i	−0.665951	−	0.384487i	−0.794541	+	0.607211i	$0.792288\pi$
$788$		0			0
$789$	0.415212	−	0.239723i	0.000526251	−	0.000303831i
$790$		0			0
$791$	644.373	−	471.321i	0.814631	−	0.595854i
$792$		0			0
$793$	254.691	+	441.139i	0.321175	+	0.556291i
$794$		0			0
$795$	−580.790	+	1005.96i	−0.730553	+	1.26536i
$796$		0			0
$797$		−	349.434i		−	0.438437i	−0.975676	−	0.219219i	$-0.929649\pi$
$797$		−	349.434i		−	0.438437i	0.975676	−	0.219219i	$-0.0703508\pi$
$798$		0			0
$799$	−213.388			−0.267069
$800$		0			0
$801$	2852.73	+	1647.02i	3.56146	+	2.05621i
$802$		0			0
$803$	−84.5507	+	48.8153i	−0.105293	+	0.0607912i
$804$		0			0
$805$	−206.268	+	22.3469i	−0.256233	+	0.0277601i
$806$		0			0
$807$	3.65762	+	6.33519i	0.00453237	+	0.00785029i
$808$		0			0
$809$	29.7935	−	51.6039i	0.0368276	−	0.0637873i	−0.847024	−	0.531554i	$-0.821608\pi$
$809$	29.7935	−	51.6039i	0.0368276	−	0.0637873i	0.883852	+	0.467767i	$0.154941\pi$
$810$		0			0
$811$		−	157.670i		−	0.194414i	−0.995264	−	0.0972069i	$-0.969009\pi$
$811$		−	157.670i		−	0.194414i	0.995264	−	0.0972069i	$-0.0309909\pi$
$812$		0			0
$813$	−2052.98			−2.52519
$814$		0			0
$815$	−950.043	−	548.508i	−1.16570	−	0.673015i
$816$		0			0
$817$	578.584	−	334.046i	0.708182	−	0.408869i
$818$		0			0
$819$	−1078.75	+	2443.93i	−1.31716	+	2.98404i
$820$		0			0
$821$	−169.068	−	292.835i	−0.205930	−	0.356681i	0.744499	−	0.667624i	$-0.232688\pi$
$821$	−169.068	−	292.835i	−0.205930	−	0.356681i	−0.950429	+	0.310943i	$0.899355\pi$
$822$		0			0
$823$	−557.669	+	965.911i	−0.677605	+	1.17365i	0.298095	+	0.954536i	$0.403649\pi$
$823$	−557.669	+	965.911i	−0.677605	+	1.17365i	−0.975700	+	0.219111i	$0.929684\pi$
$824$		0			0
$825$			457.861i			0.554982i
$826$		0			0
$827$	1368.45			1.65472			0.827359	−	0.561673i	$-0.189842\pi$
$827$	1368.45			1.65472			0.827359	+	0.561673i	$0.189842\pi$
$828$		0			0
$829$	−293.704	−	169.570i	−0.354288	−	0.204548i	0.312284	−	0.949989i	$-0.398906\pi$
$829$	−293.704	−	169.570i	−0.354288	−	0.204548i	−0.666572	+	0.745441i	$0.732239\pi$
$830$		0			0
$831$	−841.151	+	485.639i	−1.01222	+	0.584403i
$832$		0			0
$833$	−741.417	+	676.213i	−0.890056	+	0.811780i
$834$		0			0
$835$	−760.178	−	1316.67i	−0.910393	−	1.57685i
$836$		0			0
$837$	−589.625	+	1021.26i	−0.704451	+	1.22014i
$838$		0			0
$839$			402.959i			0.480284i	0.970738	+	0.240142i	$0.0771941\pi$
$839$			402.959i			0.480284i	−0.970738	+	0.240142i	$0.922806\pi$
$840$		0			0
$841$	−837.883			−0.996294
$842$		0			0
$843$	1227.00	+	708.406i	1.45551	+	0.840340i
$844$		0			0
$845$	463.962	−	267.869i	0.549068	−	0.317004i
$846$		0			0
$847$	587.362	+	259.262i	0.693462	+	0.306095i
$848$		0			0
$849$	−659.101	−	1141.60i	−0.776326	−	1.34464i
$850$		0			0
$851$	−24.6064	+	42.6195i	−0.0289147	+	0.0500817i
$852$		0			0
$853$		−	1179.46i		−	1.38272i	−0.722512	−	0.691359i	$-0.757012\pi$
$853$		−	1179.46i		−	1.38272i	0.722512	−	0.691359i	$-0.242988\pi$
$854$		0			0
$855$	−2051.15			−2.39900
$856$		0			0
$857$	579.907	+	334.810i	0.676671	+	0.390676i	0.798600	−	0.601863i	$-0.205575\pi$
$857$	579.907	+	334.810i	0.676671	+	0.390676i	−0.121929	+	0.992539i	$0.538908\pi$
$858$		0			0
$859$	−753.231	+	434.878i	−0.876869	+	0.506261i	−0.869625	−	0.493713i	$-0.835639\pi$
$859$	−753.231	+	434.878i	−0.876869	+	0.506261i	−0.00724440	+	0.999974i	$0.502306\pi$
$860$		0			0
$861$	−48.6483	−	449.036i	−0.0565021	−	0.521529i
$862$		0			0
$863$	45.9704	+	79.6231i	0.0532681	+	0.0922631i	0.891430	−	0.453159i	$-0.149703\pi$
$863$	45.9704	+	79.6231i	0.0532681	+	0.0922631i	−0.838162	+	0.545422i	$0.816370\pi$
$864$		0			0
$865$	−680.753	+	1179.10i	−0.786998	+	1.36312i
$866$		0			0
$867$			748.444i			0.863257i
$868$		0			0
$869$	−162.354			−0.186828
$870$		0			0
$871$	−1359.99	−	785.189i	−1.56141	−	0.901480i
$872$		0			0
$873$	2718.27	−	1569.40i	3.11372	−	1.79771i
$874$		0			0
$875$	−267.258	−	365.386i	−0.305438	−	0.417584i
$876$		0			0
$877$	−218.160	−	377.864i	−0.248757	−	0.430860i	0.714424	−	0.699713i	$-0.246689\pi$
$877$	−218.160	−	377.864i	−0.248757	−	0.430860i	−0.963181	+	0.268853i	$0.913355\pi$
$878$		0			0
$879$	−654.840	+	1134.22i	−0.744983	+	1.29035i
$880$		0			0
$881$		−	884.017i		−	1.00342i	−0.865035	−	0.501712i	$-0.832704\pi$
$881$		−	884.017i		−	1.00342i	0.865035	−	0.501712i	$-0.167296\pi$
$882$		0			0
$883$	62.8499			0.0711776			0.0355888	−	0.999367i	$-0.488669\pi$
$883$	62.8499			0.0711776			0.0355888	+	0.999367i	$0.488669\pi$
$884$		0			0
$885$	2072.89	+	1196.78i	2.34224	+	1.35230i
$886$		0			0
$887$	−901.243	+	520.333i	−1.01606	+	0.586621i	−0.912959	−	0.408050i	$-0.866209\pi$
$887$	−901.243	+	520.333i	−1.01606	+	0.586621i	−0.103098	+	0.994671i	$0.532875\pi$
$888$		0			0
$889$	156.767	−	114.665i	0.176340	−	0.128983i
$890$		0			0
$891$	−749.222	−	1297.69i	−0.840878	−	1.45644i
$892$		0			0
$893$	70.7884	−	122.609i	0.0792703	−	0.137300i
$894$		0			0
$895$		−	1122.60i		−	1.25430i
$896$		0			0
$897$	−430.083			−0.479468
$898$		0			0
$899$	−21.0156	−	12.1334i	−0.0233766	−	0.0134965i
$900$		0			0
$901$	−569.329	+	328.702i	−0.631886	+	0.364820i
$902$		0			0
$903$	1964.14	−	212.794i	2.17513	−	0.235652i
$904$		0			0
$905$	543.504	+	941.376i	0.600557	+	1.04019i
$906$		0			0
$907$	−599.568	+	1038.48i	−0.661045	+	1.14496i	0.319297	+	0.947655i	$0.396553\pi$
$907$	−599.568	+	1038.48i	−0.661045	+	1.14496i	−0.980341	+	0.197308i	$0.936780\pi$
$908$		0			0
$909$			2745.41i			3.02026i
$910$		0			0
$911$	1588.16			1.74331			0.871657	−	0.490116i	$-0.163046\pi$
$911$	1588.16			1.74331			0.871657	+	0.490116i	$0.163046\pi$
$912$		0			0
$913$	297.378	+	171.691i	0.325715	+	0.188052i
$914$		0			0
$915$	−1001.61	+	578.281i	−1.09466	+	0.632001i
$916$		0			0
$917$	516.577	−	1170.31i	0.563334	−	1.27624i
$918$		0			0
$919$	573.073	+	992.592i	0.623584	+	1.08008i	0.988813	+	0.149161i	$0.0476572\pi$
$919$	573.073	+	992.592i	0.623584	+	1.08008i	−0.365229	+	0.930918i	$0.619009\pi$
$920$		0			0
$921$	−957.834	+	1659.02i	−1.03999	+	1.80132i
$922$		0			0
$923$		−	984.158i		−	1.06626i
$924$		0			0
$925$	154.302			0.166813
$926$		0			0
$927$	4160.38	+	2402.00i	4.48801	+	2.59115i
$928$		0			0
$929$	−296.299	+	171.068i	−0.318944	+	0.184142i	−0.650922	−	0.759145i	$-0.725617\pi$
$929$	−296.299	+	171.068i	−0.318944	+	0.184142i	0.331978	+	0.943287i	$0.392284\pi$
$930$		0			0
$931$	−142.586	−	650.328i	−0.153153	−	0.698527i
$932$		0			0
$933$	−714.664	−	1237.83i	−0.765985	−	1.32672i
$934$		0			0
$935$	−349.294	+	604.995i	−0.373576	+	0.647053i
$936$		0			0
$937$		−	77.2601i		−	0.0824548i	−0.999150	−	0.0412274i	$-0.986873\pi$
$937$		−	77.2601i		−	0.0824548i	0.999150	−	0.0412274i	$-0.0131268\pi$
$938$		0			0
$939$	−228.759			−0.243620
$940$		0			0
$941$	−415.988	−	240.171i	−0.442070	−	0.255229i	0.262405	−	0.964958i	$-0.415484\pi$
$941$	−415.988	−	240.171i	−0.442070	−	0.255229i	−0.704475	+	0.709728i	$0.748818\pi$
$942$		0			0
$943$	45.7707	−	26.4257i	0.0485374	−	0.0280231i
$944$		0			0
$945$	−3463.47	−	1528.78i	−3.66505	−	1.61776i
$946$		0			0
$947$	195.244	+	338.173i	0.206171	+	0.357099i	0.950505	−	0.310708i	$-0.100566\pi$
$947$	195.244	+	338.173i	0.206171	+	0.357099i	−0.744334	+	0.667808i	$0.767233\pi$
$948$		0			0
$949$	−143.770	+	249.018i	−0.151497	+	0.262400i
$950$		0			0
$951$		−	2539.40i		−	2.67025i
$952$		0			0
$953$	−1234.80			−1.29570			−0.647851	−	0.761767i	$-0.724332\pi$
$953$	−1234.80			−1.29570			−0.647851	+	0.761767i	$0.724332\pi$
$954$		0			0
$955$	−760.212	−	438.909i	−0.796034	−	0.459590i
$956$		0			0
$957$	47.4871	−	27.4167i	0.0496208	−	0.0286486i
$958$		0			0
$959$	76.2311	+	703.633i	0.0794902	+	0.733715i
$960$		0			0
$961$	−386.031	−	668.625i	−0.401697	−	0.695760i
$962$		0			0
$963$	1190.27	−	2061.61i	1.23601	−	2.14083i
$964$		0			0
$965$			272.545i			0.282430i
$966$		0			0
$967$	−719.055			−0.743593			−0.371797	−	0.928314i	$-0.621258\pi$
$967$	−719.055			−0.743593			−0.371797	+	0.928314i	$0.621258\pi$
$968$		0			0
$969$	−1383.18	−	798.578i	−1.42743	−	0.824126i
$970$		0			0
$971$	837.747	−	483.674i	0.862767	−	0.498119i	−0.00217068	−	0.999998i	$-0.500691\pi$
$971$	837.747	−	483.674i	0.862767	−	0.498119i	0.864938	+	0.501879i	$0.167358\pi$
$972$		0			0
$973$	365.980	+	500.355i	0.376136	+	0.514239i
$974$		0			0
$975$	674.243	+	1167.82i	0.691531	+	1.19777i
$976$		0			0
$977$	668.456	−	1157.80i	0.684192	−	1.18506i	−0.289498	−	0.957179i	$-0.593488\pi$
$977$	668.456	−	1157.80i	0.684192	−	1.18506i	0.973690	−	0.227877i	$-0.0731783\pi$
$978$		0			0
$979$			744.347i			0.760313i
$980$		0			0
$981$	−363.722			−0.370767
$982$		0			0
$983$	465.567	+	268.795i	0.473619	+	0.273444i	0.717753	−	0.696297i	$-0.245170\pi$
$983$	465.567	+	268.795i	0.473619	+	0.273444i	−0.244134	+	0.969741i	$0.578504\pi$
$984$		0			0
$985$	1124.16	−	649.036i	1.14128	−	0.658920i
$986$		0			0
$987$	337.915	−	247.165i	0.342366	−	0.250421i
$988$		0			0
$989$	115.590	+	200.207i	0.116875	+	0.202434i
$990$		0			0
$991$	−185.587	+	321.446i	−0.187273	+	0.324366i	−0.944340	−	0.328971i	$-0.893298\pi$
$991$	−185.587	+	321.446i	−0.187273	+	0.324366i	0.757067	+	0.653337i	$0.226631\pi$
$992$		0			0
$993$		−	826.135i		−	0.831959i
$994$		0			0
$995$	1899.37			1.90891
$996$		0			0
$997$	702.022	+	405.313i	0.704134	+	0.406532i	0.808885	−	0.587966i	$-0.200071\pi$
$997$	702.022	+	405.313i	0.704134	+	0.406532i	−0.104751	+	0.994498i	$0.533405\pi$
$998$		0			0
$999$	−777.696	+	449.003i	−0.778474	+	0.449452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.s.h.129.8		16
4.3	odd	2	inner	448.3.s.h.129.1		16
7.5	odd	6	inner	448.3.s.h.257.8		16
8.3	odd	2		224.3.s.b.129.8	yes	16
8.5	even	2		224.3.s.b.129.1	yes	16
28.19	even	6	inner	448.3.s.h.257.1		16
56.3	even	6		1568.3.c.g.97.15		16
56.5	odd	6		224.3.s.b.33.1	✓	16
56.11	odd	6		1568.3.c.g.97.2		16
56.19	even	6		224.3.s.b.33.8	yes	16
56.45	odd	6		1568.3.c.g.97.1		16
56.53	even	6		1568.3.c.g.97.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.b.33.1	✓	16	56.5	odd	6
224.3.s.b.33.8	yes	16	56.19	even	6
224.3.s.b.129.1	yes	16	8.5	even	2
224.3.s.b.129.8	yes	16	8.3	odd	2
448.3.s.h.129.1		16	4.3	odd	2	inner
448.3.s.h.129.8		16	1.1	even	1	trivial
448.3.s.h.257.1		16	28.19	even	6	inner
448.3.s.h.257.8		16	7.5	odd	6	inner
1568.3.c.g.97.1		16	56.45	odd	6
1568.3.c.g.97.2		16	56.11	odd	6
1568.3.c.g.97.15		16	56.3	even	6
1568.3.c.g.97.16		16	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.97091 + 2.86995i) q^{3} +(-5.45949 + 3.15204i) q^{5} +(5.64993 - 4.13259i) q^{7} +(11.9733 + 20.7383i) q^{9} +O(q^{10})\)	\(q+(4.97091 + 2.86995i) q^{3} +(-5.45949 + 3.15204i) q^{5} +(5.64993 - 4.13259i) q^{7} +(11.9733 + 20.7383i) q^{9} +(-2.70557 + 4.68619i) q^{11} +15.9368i q^{13} -36.1848 q^{15} +(-17.7354 - 10.2395i) q^{17} +(11.7669 - 6.79363i) q^{19} +(39.9456 - 4.32768i) q^{21} +(2.35080 + 4.07170i) q^{23} +(7.37071 - 12.7664i) q^{25} +85.7918i q^{27} -1.76543 q^{29} +(11.9039 + 6.87274i) q^{31} +(-26.8983 + 15.5297i) q^{33} +(-17.8197 + 40.3706i) q^{35} +(5.23363 + 9.06491i) q^{37} +(-45.7380 + 79.2205i) q^{39} -11.2412i q^{41} +49.1704 q^{43} +(-130.736 - 75.4805i) q^{45} +(9.02382 - 5.20991i) q^{47} +(14.8434 - 46.6977i) q^{49} +(-58.7740 - 101.800i) q^{51} +(16.0506 - 27.8005i) q^{53} -34.1123i q^{55} +77.9897 q^{57} +(-57.2860 - 33.0741i) q^{59} +(27.6804 - 15.9813i) q^{61} +(153.351 + 67.6894i) q^{63} +(-50.2335 - 87.0070i) q^{65} +(-49.2688 + 85.3361i) q^{67} +26.9867i q^{69} -61.7537 q^{71} +(15.6253 + 9.02127i) q^{73} +(73.2782 - 42.3072i) q^{75} +(4.07980 + 37.6576i) q^{77} +(15.0018 + 25.9839i) q^{79} +(-138.459 + 239.818i) q^{81} -63.4583i q^{83} +129.102 q^{85} +(-8.77580 - 5.06671i) q^{87} +(119.129 - 68.7791i) q^{89} +(65.8604 + 90.0420i) q^{91} +(39.4489 + 68.3275i) q^{93} +(-42.8276 + 74.1796i) q^{95} -131.075i q^{97} -129.578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{9}+O(q^{10}) \) 16 * q + 40 * q^9	\( 16 q + 40 q^{9} - 48 q^{17} + 136 q^{21} + 80 q^{25} + 16 q^{29} - 264 q^{33} - 72 q^{37} - 312 q^{45} + 128 q^{49} - 40 q^{53} + 368 q^{57} - 216 q^{61} - 168 q^{65} - 312 q^{73} - 64 q^{77} - 384 q^{81} + 1072 q^{85} + 24 q^{89} + 168 q^{93}+O(q^{100}) \) 16 * q + 40 * q^9 - 48 * q^17 + 136 * q^21 + 80 * q^25 + 16 * q^29 - 264 * q^33 - 72 * q^37 - 312 * q^45 + 128 * q^49 - 40 * q^53 + 368 * q^57 - 216 * q^61 - 168 * q^65 - 312 * q^73 - 64 * q^77 - 384 * q^81 + 1072 * q^85 + 24 * q^89 + 168 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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