LMFDB - Embedded newform 1134.2.k.b.971.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (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:	$9.05503558921$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			971.6
Root			$-1.70672 - 0.295146i$ of defining polynomial
Character	$\chi$	$=$	1134.971
Dual form			1134.2.k.b.647.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 + 0.837727i) q^{5} +(-0.238876 - 2.63495i) q^{7} +1.00000i q^{8} +(-0.837727 + 0.483662i) q^{10} +(4.82689 - 2.78681i) q^{11} +4.35199i q^{13} +(1.11060 - 2.40137i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.97267 - 3.41677i) q^{17} +(3.86796 + 2.23317i) q^{19} -0.967324 q^{20} +5.57361 q^{22} +(2.29786 + 1.32667i) q^{23} +(2.03214 + 3.51977i) q^{25} +(-2.17600 + 3.76893i) q^{26} +(2.16249 - 1.52435i) q^{28} -5.32498i q^{29} +(5.34038 - 3.08327i) q^{31} +(-0.866025 + 0.500000i) q^{32} -3.94535i q^{34} +(2.32290 + 1.07431i) q^{35} +(0.243608 - 0.421942i) q^{37} +(2.23317 + 3.86796i) q^{38} +(-0.837727 - 0.483662i) q^{40} +0.163771 q^{41} +8.70089 q^{43} +(4.82689 + 2.78681i) q^{44} +(1.32667 + 2.29786i) q^{46} +(-4.74500 + 8.21859i) q^{47} +(-6.88588 + 1.25885i) q^{49} +4.06428i q^{50} +(-3.76893 + 2.17600i) q^{52} +(1.74520 - 1.00759i) q^{53} +5.39149i q^{55} +(2.63495 - 0.238876i) q^{56} +(2.66249 - 4.61157i) q^{58} +(0.836931 + 1.44961i) q^{59} +(4.47927 + 2.58611i) q^{61} +6.16655 q^{62} -1.00000 q^{64} +(-3.64578 - 2.10489i) q^{65} +(2.72126 + 4.71336i) q^{67} +(1.97267 - 3.41677i) q^{68} +(1.47454 + 2.09183i) q^{70} -3.64006i q^{71} +(-2.15468 + 1.24401i) q^{73} +(0.421942 - 0.243608i) q^{74} +4.46634i q^{76} +(-8.49611 - 12.0529i) q^{77} +(-2.30121 + 3.98581i) q^{79} +(-0.483662 - 0.837727i) q^{80} +(0.141830 + 0.0818856i) q^{82} -8.41959 q^{83} +3.81643 q^{85} +(7.53520 + 4.35045i) q^{86} +(2.78681 + 4.82689i) q^{88} +(2.05811 - 3.56475i) q^{89} +(11.4673 - 1.03959i) q^{91} +2.65334i q^{92} +(-8.21859 + 4.74500i) q^{94} +(-3.74157 + 2.16020i) q^{95} +11.8552i q^{97} +(-6.59277 - 2.35274i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{7} + 12 q^{11} - 8 q^{16} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 12 q^{41} + 4 q^{43} + 12 q^{44} + 6 q^{46} - 18 q^{47} - 2 q^{49}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^11 - 8 * q^16 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 12 * q^41 + 4 * q^43 + 12 * q^44 + 6 * q^46 - 18 * q^47 - 2 * q^49 + 6 * q^52 + 36 * q^53 + 6 * q^56 + 6 * q^58 + 30 * q^59 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^70 + 18 * q^74 - 24 * q^77 - 16 * q^79 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 + 66 * q^95 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.483662	+	0.837727i	−0.216300	+	0.374643i	−0.953674	−	0.300842i	$-0.902732\pi$
$5$	−0.483662	+	0.837727i	−0.216300	+	0.374643i	0.737374	+	0.675485i	$0.236066\pi$
$6$		0			0
$7$	−0.238876	−	2.63495i	−0.0902867	−	0.995916i
$7$	−0.238876	−	2.63495i	−0.0902867	−	0.995916i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.837727	+	0.483662i	−0.264913	+	0.152947i
$11$	4.82689	−	2.78681i	1.45536	−	0.840254i	0.456584	−	0.889680i	$-0.349073\pi$
$11$	4.82689	−	2.78681i	1.45536	−	0.840254i	0.998778	+	0.0494264i	$0.0157393\pi$
$12$		0			0
$13$			4.35199i			1.20702i	0.797354	+	0.603512i	$0.206233\pi$
$13$			4.35199i			1.20702i	−0.797354	+	0.603512i	$0.793767\pi$
$14$	1.11060	−	2.40137i	0.296820	−	0.641793i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.97267	−	3.41677i	−0.478443	−	0.828688i	0.521251	−	0.853403i	$-0.325465\pi$
$17$	−1.97267	−	3.41677i	−0.478443	−	0.828688i	−0.999695	+	0.0247150i	$0.992132\pi$
$18$		0			0
$19$	3.86796	+	2.23317i	0.887371	+	0.512324i	0.873082	−	0.487574i	$-0.162118\pi$
$19$	3.86796	+	2.23317i	0.887371	+	0.512324i	0.0142896	+	0.999898i	$0.495451\pi$
$20$	−0.967324			−0.216300
$21$		0			0
$22$	5.57361			1.18830
$23$	2.29786	+	1.32667i	0.479137	+	0.276630i	0.720057	−	0.693915i	$-0.244116\pi$
$23$	2.29786	+	1.32667i	0.479137	+	0.276630i	−0.240920	+	0.970545i	$0.577449\pi$
$24$		0			0
$25$	2.03214	+	3.51977i	0.406428	+	0.703955i
$26$	−2.17600	+	3.76893i	−0.426748	+	0.739149i
$27$		0			0
$28$	2.16249	−	1.52435i	0.408673	−	0.288074i
$29$		−	5.32498i		−	0.988825i	−0.869228	−	0.494412i	$-0.835383\pi$
$29$		−	5.32498i		−	0.988825i	0.869228	−	0.494412i	$-0.164617\pi$
$30$		0			0
$31$	5.34038	−	3.08327i	0.959161	−	0.553772i	0.0632466	−	0.997998i	$-0.479855\pi$
$31$	5.34038	−	3.08327i	0.959161	−	0.553772i	0.895915	+	0.444226i	$0.146521\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$		−	3.94535i		−	0.676621i
$35$	2.32290	+	1.07431i	0.392642	+	0.181592i
$36$		0			0
$37$	0.243608	−	0.421942i	0.0400490	−	0.0693669i	−0.845306	−	0.534282i	$-0.820582\pi$
$37$	0.243608	−	0.421942i	0.0400490	−	0.0693669i	0.885355	+	0.464915i	$0.153915\pi$
$38$	2.23317	+	3.86796i	0.362268	+	0.627466i
$39$		0			0
$40$	−0.837727	−	0.483662i	−0.132456	−	0.0764737i
$41$	0.163771			0.0255768			0.0127884	−	0.999918i	$-0.495929\pi$
$41$	0.163771			0.0255768			0.0127884	+	0.999918i	$0.495929\pi$
$42$		0			0
$43$	8.70089			1.32687			0.663437	−	0.748232i	$-0.269097\pi$
$43$	8.70089			1.32687			0.663437	+	0.748232i	$0.269097\pi$
$44$	4.82689	+	2.78681i	0.727681	+	0.420127i
$45$		0			0
$46$	1.32667	+	2.29786i	0.195607	+	0.338801i
$47$	−4.74500	+	8.21859i	−0.692130	+	1.19880i	0.279009	+	0.960289i	$0.409994\pi$
$47$	−4.74500	+	8.21859i	−0.692130	+	1.19880i	−0.971139	+	0.238516i	$0.923339\pi$
$48$		0			0
$49$	−6.88588	+	1.25885i	−0.983697	+	0.179836i
$50$			4.06428i			0.574777i
$51$		0			0
$52$	−3.76893	+	2.17600i	−0.522657	+	0.301756i
$53$	1.74520	−	1.00759i	0.239722	−	0.138403i	−0.375327	−	0.926892i	$-0.622470\pi$
$53$	1.74520	−	1.00759i	0.239722	−	0.138403i	0.615049	+	0.788489i	$0.289136\pi$
$54$		0			0
$55$			5.39149i			0.726988i
$56$	2.63495	−	0.238876i	0.352109	−	0.0319212i
$57$		0			0
$58$	2.66249	−	4.61157i	0.349602	−	0.605529i
$59$	0.836931	+	1.44961i	0.108959	+	0.188723i	0.915349	−	0.402662i	$-0.131915\pi$
$59$	0.836931	+	1.44961i	0.108959	+	0.188723i	−0.806390	+	0.591384i	$0.798582\pi$
$60$		0			0
$61$	4.47927	+	2.58611i	0.573512	+	0.331117i	0.758551	−	0.651614i	$-0.225908\pi$
$61$	4.47927	+	2.58611i	0.573512	+	0.331117i	−0.185039	+	0.982731i	$0.559241\pi$
$62$	6.16655			0.783152
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.64578	−	2.10489i	−0.452203	−	0.261080i
$66$		0			0
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	0.982993	−	0.183645i	$-0.0587898\pi$
$67$	2.72126	+	4.71336i	0.332455	+	0.575828i	−0.650538	+	0.759474i	$0.725456\pi$
$68$	1.97267	−	3.41677i	0.239222	−	0.414344i
$69$		0			0
$70$	1.47454	+	2.09183i	0.176241	+	0.250022i
$71$		−	3.64006i		−	0.431996i	−0.976394	−	0.215998i	$-0.930700\pi$
$71$		−	3.64006i		−	0.431996i	0.976394	−	0.215998i	$-0.0693005\pi$
$72$		0			0
$73$	−2.15468	+	1.24401i	−0.252186	+	0.145600i	−0.620765	−	0.783997i	$-0.713178\pi$
$73$	−2.15468	+	1.24401i	−0.252186	+	0.145600i	0.368579	+	0.929597i	$0.379845\pi$
$74$	0.421942	−	0.243608i	0.0490498	−	0.0283189i
$75$		0			0
$76$			4.46634i			0.512324i
$77$	−8.49611	−	12.0529i	−0.968222	−	1.37355i
$78$		0			0
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	−0.965949	−	0.258732i	$-0.916695\pi$
$79$	−2.30121	+	3.98581i	−0.258906	+	0.448438i	0.707043	+	0.707170i	$0.250029\pi$
$80$	−0.483662	−	0.837727i	−0.0540751	−	0.0936608i
$81$		0			0
$82$	0.141830	+	0.0818856i	0.0156625	+	0.00904275i
$83$	−8.41959			−0.924170			−0.462085	−	0.886836i	$-0.652898\pi$
$83$	−8.41959			−0.924170			−0.462085	+	0.886836i	$0.652898\pi$
$84$		0			0
$85$	3.81643			0.413950
$86$	7.53520	+	4.35045i	0.812541	+	0.469121i
$87$		0			0
$88$	2.78681	+	4.82689i	0.297075	+	0.514548i
$89$	2.05811	−	3.56475i	0.218159	−	0.377863i	−0.736086	−	0.676888i	$-0.763328\pi$
$89$	2.05811	−	3.56475i	0.218159	−	0.377863i	0.954245	+	0.299025i	$0.0966615\pi$
$90$		0			0
$91$	11.4673	−	1.03959i	1.20210	−	0.108978i
$92$			2.65334i			0.276630i
$93$		0			0
$94$	−8.21859	+	4.74500i	−0.847683	+	0.489410i
$95$	−3.74157	+	2.16020i	−0.383877	+	0.221632i
$96$		0			0
$97$			11.8552i			1.20372i	0.798603	+	0.601859i	$0.205573\pi$
$97$			11.8552i			1.20372i	−0.798603	+	0.601859i	$0.794427\pi$
$98$	−6.59277	−	2.35274i	−0.665970	−	0.237663i
$99$		0			0
$100$	−2.03214	+	3.51977i	−0.203214	+	0.351977i
$101$	−2.65813	−	4.60402i	−0.264494	−	0.458117i	0.702937	−	0.711252i	$-0.251872\pi$
$101$	−2.65813	−	4.60402i	−0.264494	−	0.458117i	−0.967431	+	0.253135i	$0.918538\pi$
$102$		0			0
$103$	−7.74616	−	4.47225i	−0.763252	−	0.440664i	0.0672102	−	0.997739i	$-0.478590\pi$
$103$	−7.74616	−	4.47225i	−0.763252	−	0.440664i	−0.830462	+	0.557075i	$0.811924\pi$
$104$	−4.35199			−0.426748
$105$		0			0
$106$	2.01518			0.195732
$107$	−16.5898	−	9.57813i	−1.60380	−	0.925953i	−0.990718	−	0.135931i	$-0.956597\pi$
$107$	−16.5898	−	9.57813i	−1.60380	−	0.925953i	−0.613079	−	0.790022i	$-0.710069\pi$
$108$		0			0
$109$	−9.62168	−	16.6652i	−0.921590	−	1.59624i	−0.796955	−	0.604038i	$-0.793557\pi$
$109$	−9.62168	−	16.6652i	−0.921590	−	1.59624i	−0.124635	−	0.992203i	$-0.539776\pi$
$110$	−2.69574	+	4.66917i	−0.257029	+	0.445188i
$111$		0			0
$112$	2.40137	+	1.11060i	0.226908	+	0.104942i
$113$			8.44316i			0.794266i	0.917761	+	0.397133i	$0.129995\pi$
$113$			8.44316i			0.794266i	−0.917761	+	0.397133i	$0.870005\pi$
$114$		0			0
$115$	−2.22278	+	1.28332i	−0.207275	+	0.119670i
$116$	4.61157	−	2.66249i	0.428174	−	0.247206i
$117$		0			0
$118$			1.67386i			0.154091i
$119$	−8.53178	+	6.01407i	−0.782107	+	0.551309i
$120$		0			0
$121$	10.0326	−	17.3769i	0.912053	−	1.57972i
$122$	2.58611	+	4.47927i	0.234135	+	0.405534i
$123$		0			0
$124$	5.34038	+	3.08327i	0.479581	+	0.276886i
$125$	−8.76810			−0.784243
$126$		0			0
$127$	3.31883			0.294498			0.147249	−	0.989099i	$-0.452958\pi$
$127$	3.31883			0.294498			0.147249	+	0.989099i	$0.452958\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.10489	−	3.64578i	−0.184611	−	0.319756i
$131$	9.37335	−	16.2351i	0.818954	−	1.41847i	−0.0875000	−	0.996165i	$-0.527888\pi$
$131$	9.37335	−	16.2351i	0.818954	−	1.41847i	0.906454	−	0.422305i	$-0.138779\pi$
$132$		0			0
$133$	4.96031	−	10.7253i	0.430114	−	0.930003i
$134$			5.44252i			0.470162i
$135$		0			0
$136$	3.41677	−	1.97267i	0.292986	−	0.169155i
$137$	14.6656	−	8.46717i	1.25296	−	0.723399i	0.281267	−	0.959630i	$-0.409245\pi$
$137$	14.6656	−	8.46717i	1.25296	−	0.723399i	0.971697	+	0.236230i	$0.0759120\pi$
$138$		0			0
$139$			12.1281i			1.02869i	0.857582	+	0.514347i	$0.171966\pi$
$139$			12.1281i			1.02869i	−0.857582	+	0.514347i	$0.828034\pi$
$140$	0.231071	+	2.54885i	0.0195290	+	0.215417i
$141$		0			0
$142$	1.82003	−	3.15239i	0.152734	−	0.264543i
$143$	12.1282	+	21.0066i	1.01421	+	1.75666i
$144$		0			0
$145$	4.46088	+	2.57549i	0.370456	+	0.213883i
$146$	−2.48801			−0.205909
$147$		0			0
$148$	0.487217			0.0400490
$149$	−7.56951	−	4.37026i	−0.620118	−	0.358025i	0.156797	−	0.987631i	$-0.449883\pi$
$149$	−7.56951	−	4.37026i	−0.620118	−	0.358025i	−0.776915	+	0.629606i	$0.783217\pi$
$150$		0			0
$151$	−11.0471	−	19.1341i	−0.898997	−	1.55711i	−0.828778	−	0.559578i	$-0.810963\pi$
$151$	−11.0471	−	19.1341i	−0.898997	−	1.55711i	−0.0702195	−	0.997532i	$-0.522370\pi$
$152$	−2.23317	+	3.86796i	−0.181134	+	0.313733i
$153$		0			0
$154$	−1.33140	−	14.6862i	−0.107288	−	1.18345i
$155$			5.96505i			0.479124i
$156$		0			0
$157$	−1.23372	+	0.712287i	−0.0984614	+	0.0568467i	−0.548422	−	0.836202i	$-0.684771\pi$
$157$	−1.23372	+	0.712287i	−0.0984614	+	0.0568467i	0.449961	+	0.893048i	$0.351438\pi$
$158$	−3.98581	+	2.30121i	−0.317094	+	0.183074i
$159$		0			0
$160$		−	0.967324i		−	0.0764737i
$161$	2.94680	−	6.37165i	0.232241	−	0.502157i
$162$		0			0
$163$	−3.72148	+	6.44579i	−0.291489	+	0.504873i	−0.974162	−	0.225851i	$-0.927484\pi$
$163$	−3.72148	+	6.44579i	−0.291489	+	0.504873i	0.682673	+	0.730724i	$0.260817\pi$
$164$	0.0818856	+	0.141830i	0.00639419	+	0.0110751i
$165$		0			0
$166$	−7.29158	−	4.20979i	−0.565936	−	0.326743i
$167$	−6.49710			−0.502761			−0.251380	−	0.967888i	$-0.580884\pi$
$167$	−6.49710			−0.502761			−0.251380	+	0.967888i	$0.580884\pi$
$168$		0			0
$169$	−5.93982			−0.456909
$170$	3.30512	+	1.90821i	0.253491	+	0.146353i
$171$		0			0
$172$	4.35045	+	7.53520i	0.331718	+	0.574553i
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	−0.549057	−	0.835785i	$-0.685013\pi$
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	0.998339	+	0.0576053i	$0.0183465\pi$
$174$		0			0
$175$	8.78898	−	6.19537i	0.664384	−	0.468326i
$176$			5.57361i			0.420127i
$177$		0			0
$178$	3.56475	−	2.05811i	0.267189	−	0.154262i
$179$	2.10764	−	1.21685i	0.157533	−	0.0909515i	−0.419161	−	0.907912i	$-0.637676\pi$
$179$	2.10764	−	1.21685i	0.157533	−	0.0909515i	0.576694	+	0.816960i	$0.304343\pi$
$180$		0			0
$181$			11.5342i			0.857327i	0.903464	+	0.428663i	$0.141015\pi$
$181$			11.5342i			0.857327i	−0.903464	+	0.428663i	$0.858985\pi$
$182$	10.4507	+	4.83332i	0.774660	+	0.358270i
$183$		0			0
$184$	−1.32667	+	2.29786i	−0.0978035	+	0.169401i
$185$	0.235648	+	0.408155i	0.0173252	+	0.0300081i
$186$		0			0
$187$	−19.0438	−	10.9949i	−1.39262	−	0.804028i
$188$	−9.49001			−0.692130
$189$		0			0
$190$	−4.32040			−0.313435
$191$	−19.1122	−	11.0345i	−1.38291	−	0.798425i	−0.390409	−	0.920641i	$-0.627666\pi$
$191$	−19.1122	−	11.0345i	−1.38291	−	0.798425i	−0.992503	+	0.122216i	$0.961000\pi$
$192$		0			0
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	0.961932	+	0.273289i	$0.0881116\pi$
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	−0.244291	+	0.969702i	$0.578555\pi$
$194$	−5.92762	+	10.2669i	−0.425578	+	0.737123i
$195$		0			0
$196$	−4.53314	−	5.33392i	−0.323795	−	0.380994i
$197$			4.62560i			0.329560i	0.986330	+	0.164780i	$0.0526914\pi$
$197$			4.62560i			0.329560i	−0.986330	+	0.164780i	$0.947309\pi$
$198$		0			0
$199$	−18.1024	+	10.4514i	−1.28324	+	0.740882i	−0.977440	−	0.211212i	$-0.932259\pi$
$199$	−18.1024	+	10.4514i	−1.28324	+	0.740882i	−0.305805	+	0.952094i	$0.598925\pi$
$200$	−3.51977	+	2.03214i	−0.248886	+	0.143694i
$201$		0			0
$202$		−	5.31626i		−	0.374051i
$203$	−14.0310	+	1.27201i	−0.984786	+	0.0892777i
$204$		0			0
$205$	−0.0792099	+	0.137196i	−0.00553226	+	0.00958215i
$206$	−4.47225	−	7.74616i	−0.311596	−	0.539701i
$207$		0			0
$208$	−3.76893	−	2.17600i	−0.261329	−	0.150878i
$209$	24.8936			1.72193
$210$		0			0
$211$	6.68620			0.460297			0.230148	−	0.973156i	$-0.426079\pi$
$211$	6.68620			0.460297			0.230148	+	0.973156i	$0.426079\pi$
$212$	1.74520	+	1.00759i	0.119861	+	0.0692017i
$213$		0			0
$214$	−9.57813	−	16.5898i	−0.654747	−	1.13406i
$215$	−4.20829	+	7.28898i	−0.287003	+	0.497104i
$216$		0			0
$217$	−9.39995	−	13.3351i	−0.638110	−	0.905246i
$218$		−	19.2434i		−	1.30333i
$219$		0			0
$220$	−4.66917	+	2.69574i	−0.314795	+	0.181747i
$221$	14.8697	−	8.58505i	1.00025	−	0.577493i
$222$		0			0
$223$			8.18246i			0.547938i	0.961738	+	0.273969i	$0.0883366\pi$
$223$			8.18246i			0.547938i	−0.961738	+	0.273969i	$0.911663\pi$
$224$	1.52435	+	2.16249i	0.101850	+	0.144488i
$225$		0			0
$226$	−4.22158	+	7.31199i	−0.280815	+	0.486386i
$227$	5.34688	+	9.26106i	0.354885	+	0.614678i	0.987098	−	0.160116i	$-0.0511868\pi$
$227$	5.34688	+	9.26106i	0.354885	+	0.614678i	−0.632214	+	0.774794i	$0.717853\pi$
$228$		0			0
$229$	−25.2942	−	14.6036i	−1.67149	−	0.965034i	−0.966806	−	0.255510i	$-0.917757\pi$
$229$	−25.2942	−	14.6036i	−1.67149	−	0.965034i	−0.704682	−	0.709524i	$-0.748910\pi$
$230$	−2.56664			−0.169239
$231$		0			0
$232$	5.32498			0.349602
$233$	−5.57664	−	3.21967i	−0.365338	−	0.210928i	0.306082	−	0.952005i	$-0.400982\pi$
$233$	−5.57664	−	3.21967i	−0.365338	−	0.210928i	−0.671420	+	0.741077i	$0.734315\pi$
$234$		0			0
$235$	−4.58996	−	7.95004i	−0.299416	−	0.518603i
$236$	−0.836931	+	1.44961i	−0.0544796	+	0.0943614i
$237$		0			0
$238$	−10.3958	+	0.942449i	−0.673858	+	0.0610899i
$239$		−	4.63557i		−	0.299850i	−0.988697	−	0.149925i	$-0.952097\pi$
$239$		−	4.63557i		−	0.299850i	0.988697	−	0.149925i	$-0.0479032\pi$
$240$		0			0
$241$	−9.08846	+	5.24722i	−0.585439	+	0.338003i	−0.763292	−	0.646054i	$-0.776418\pi$
$241$	−9.08846	+	5.24722i	−0.585439	+	0.338003i	0.177853	+	0.984057i	$0.443085\pi$
$242$	17.3769	−	10.0326i	1.11703	−	0.644919i
$243$		0			0
$244$			5.17221i			0.331117i
$245$	2.27586	−	6.37734i	0.145400	−	0.407434i
$246$		0			0
$247$	−9.71873	+	16.8333i	−0.618388	+	1.07108i
$248$	3.08327	+	5.34038i	0.195788	+	0.339115i
$249$		0			0
$250$	−7.59340	−	4.38405i	−0.480249	−	0.277272i
$251$	−7.85271			−0.495659			−0.247829	−	0.968804i	$-0.579717\pi$
$251$	−7.85271			−0.495659			−0.247829	+	0.968804i	$0.579717\pi$
$252$		0			0
$253$	14.7887			0.929758
$254$	2.87419	+	1.65941i	0.180343	+	0.104121i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.71568	−	2.97164i	0.107021	−	0.185366i	−0.807541	−	0.589811i	$-0.799202\pi$
$257$	1.71568	−	2.97164i	0.107021	−	0.185366i	0.914562	+	0.404445i	$0.132535\pi$
$258$		0			0
$259$	−1.16999	−	0.541103i	−0.0726995	−	0.0336225i
$260$		−	4.20979i		−	0.261080i
$261$		0			0
$262$	16.2351	−	9.37335i	1.00301	−	0.579088i
$263$	−3.17080	+	1.83066i	−0.195520	+	0.112883i	−0.594564	−	0.804048i	$-0.702675\pi$
$263$	−3.17080	+	1.83066i	−0.195520	+	0.112883i	0.399044	+	0.916932i	$0.369342\pi$
$264$		0			0
$265$			1.94934i			0.119747i
$266$	9.65842	−	6.80824i	0.592196	−	0.417440i
$267$		0			0
$268$	−2.72126	+	4.71336i	−0.166227	+	0.287914i
$269$	6.34303	+	10.9865i	0.386741	+	0.669856i	0.992009	−	0.126166i	$-0.0402673\pi$
$269$	6.34303	+	10.9865i	0.386741	+	0.669856i	−0.605268	+	0.796022i	$0.706934\pi$
$270$		0			0
$271$	−17.2136	−	9.93828i	−1.04565	−	0.603708i	−0.124223	−	0.992254i	$-0.539644\pi$
$271$	−17.2136	−	9.93828i	−1.04565	−	0.603708i	−0.921429	+	0.388547i	$0.872977\pi$
$272$	3.94535			0.239222
$273$		0			0
$274$	16.9343			1.02304
$275$	19.6179	+	11.3264i	1.18300	+	0.683006i
$276$		0			0
$277$	3.73302	+	6.46579i	0.224296	+	0.388491i	0.956108	−	0.293015i	$-0.0946585\pi$
$277$	3.73302	+	6.46579i	0.224296	+	0.388491i	−0.731812	+	0.681506i	$0.761325\pi$
$278$	−6.06406	+	10.5033i	−0.363698	+	0.629944i
$279$		0			0
$280$	−1.07431	+	2.32290i	−0.0642023	+	0.138820i
$281$			22.2564i			1.32771i	0.747862	+	0.663854i	$0.231080\pi$
$281$			22.2564i			1.32771i	−0.747862	+	0.663854i	$0.768920\pi$
$282$		0			0
$283$	−14.0125	+	8.09012i	−0.832957	+	0.480908i	−0.854864	−	0.518852i	$-0.826359\pi$
$283$	−14.0125	+	8.09012i	−0.832957	+	0.480908i	0.0219073	+	0.999760i	$0.493026\pi$
$284$	3.15239	−	1.82003i	0.187060	−	0.107999i
$285$		0			0
$286$			24.2563i			1.43431i
$287$	−0.0391210	−	0.431528i	−0.00230924	−	0.0254723i
$288$		0			0
$289$	0.717124	−	1.24210i	0.0421838	−	0.0730644i
$290$	2.57549	+	4.46088i	0.151238	+	0.261952i
$291$		0			0
$292$	−2.15468	−	1.24401i	−0.126093	−	0.0727999i
$293$	−8.86813			−0.518082			−0.259041	−	0.965866i	$-0.583406\pi$
$293$	−8.86813			−0.518082			−0.259041	+	0.965866i	$0.583406\pi$
$294$		0			0
$295$	−1.61917			−0.0942715
$296$	0.421942	+	0.243608i	0.0245249	+	0.0141595i
$297$		0			0
$298$	−4.37026	−	7.56951i	−0.253162	−	0.438490i
$299$	−5.77366	+	10.0003i	−0.333899	+	0.578331i
$300$		0			0
$301$	−2.07844	−	22.9264i	−0.119799	−	1.32145i
$302$		−	22.0941i		−	1.27137i
$303$		0			0
$304$	−3.86796	+	2.23317i	−0.221843	+	0.128081i
$305$	−4.33290	+	2.50160i	−0.248101	+	0.143241i
$306$		0			0
$307$		−	27.1427i		−	1.54912i	−0.632501	−	0.774559i	$-0.717972\pi$
$307$		−	27.1427i		−	1.54912i	0.632501	−	0.774559i	$-0.282028\pi$
$308$	6.19005	−	13.3843i	0.352711	−	0.762641i
$309$		0			0
$310$	−2.98252	+	5.16588i	−0.169396	+	0.293402i
$311$	8.44774	+	14.6319i	0.479028	+	0.829700i	0.999711	−	0.0240499i	$-0.00765605\pi$
$311$	8.44774	+	14.6319i	0.479028	+	0.829700i	−0.520683	+	0.853750i	$0.674323\pi$
$312$		0			0
$313$	−3.70433	−	2.13870i	−0.209381	−	0.120886i	0.391643	−	0.920117i	$-0.371907\pi$
$313$	−3.70433	−	2.13870i	−0.209381	−	0.120886i	−0.601024	+	0.799231i	$0.705240\pi$
$314$	−1.42457			−0.0803934
$315$		0			0
$316$	−4.60242			−0.258906
$317$	5.74123	+	3.31470i	0.322460	+	0.186172i	0.652488	−	0.757799i	$-0.273725\pi$
$317$	5.74123	+	3.31470i	0.322460	+	0.186172i	−0.330029	+	0.943971i	$0.607058\pi$
$318$		0			0
$319$	−14.8397	−	25.7031i	−0.830864	−	1.43910i
$320$	0.483662	−	0.837727i	0.0270375	−	0.0468304i
$321$		0			0
$322$	5.73783	−	4.04461i	0.319757	−	0.225397i
$323$		−	17.6212i		−	0.980472i
$324$		0			0
$325$	−15.3180	+	8.84386i	−0.849691	+	0.490569i
$326$	−6.44579	+	3.72148i	−0.356999	+	0.206114i
$327$		0			0
$328$			0.163771i			0.00904275i
$329$	22.7890	+	10.5396i	1.25640	+	0.581067i
$330$		0			0
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	−0.855425	−	0.517927i	$-0.826704\pi$
$331$	0.378896	−	0.656267i	0.0208260	−	0.0360717i	0.876251	+	0.481856i	$0.160037\pi$
$332$	−4.20979	−	7.29158i	−0.231042	−	0.400177i
$333$		0			0
$334$	−5.62665	−	3.24855i	−0.307877	−	0.177753i
$335$	−5.26468			−0.287640
$336$		0			0
$337$	−2.02176			−0.110132			−0.0550660	−	0.998483i	$-0.517537\pi$
$337$	−2.02176			−0.110132			−0.0550660	+	0.998483i	$0.517537\pi$
$338$	−5.14404	−	2.96991i	−0.279799	−	0.161542i
$339$		0			0
$340$	1.90821	+	3.30512i	0.103487	+	0.179245i
$341$	17.1850	−	29.7652i	0.930618	−	1.61188i
$342$		0			0
$343$	4.96188	+	17.8432i	0.267916	+	0.963442i
$344$			8.70089i			0.469121i
$345$		0			0
$346$	10.2354	−	5.90938i	0.550256	−	0.317690i
$347$	−18.1572	+	10.4831i	−0.974730	+	0.562761i	−0.900675	−	0.434494i	$-0.856927\pi$
$347$	−18.1572	+	10.4831i	−0.974730	+	0.562761i	−0.0740550	+	0.997254i	$0.523594\pi$
$348$		0			0
$349$		−	6.19389i		−	0.331551i	−0.986164	−	0.165776i	$-0.946987\pi$
$349$		−	6.19389i		−	0.331551i	0.986164	−	0.165776i	$-0.0530127\pi$
$350$	10.7092	−	0.970861i	0.572429	−	0.0518947i
$351$		0			0
$352$	−2.78681	+	4.82689i	−0.148537	+	0.257274i
$353$	−9.41889	−	16.3140i	−0.501317	−	0.868306i	−0.999999	−	0.00152110i	$-0.999516\pi$
$353$	−9.41889	−	16.3140i	−0.501317	−	0.868306i	0.498682	−	0.866785i	$-0.333818\pi$
$354$		0			0
$355$	3.04938	+	1.76056i	0.161844	+	0.0934409i
$356$	4.11622			0.218159
$357$		0			0
$358$	2.43370			0.128625
$359$	24.0735	+	13.8988i	1.27055	+	0.733553i	0.975092	−	0.221803i	$-0.0711942\pi$
$359$	24.0735	+	13.8988i	1.27055	+	0.733553i	0.295459	+	0.955355i	$0.404527\pi$
$360$		0			0
$361$	0.474089	+	0.821146i	0.0249520	+	0.0432182i
$362$	−5.76708	+	9.98887i	−0.303111	+	0.525003i
$363$		0			0
$364$	6.63394	+	9.41114i	0.347713	+	0.493278i
$365$		−	2.40671i		−	0.125973i
$366$		0			0
$367$	18.8390	−	10.8767i	0.983388	−	0.567759i	0.0800968	−	0.996787i	$-0.474477\pi$
$367$	18.8390	−	10.8767i	0.983388	−	0.567759i	0.903291	+	0.429028i	$0.141144\pi$
$368$	−2.29786	+	1.32667i	−0.119784	+	0.0691575i
$369$		0			0
$370$			0.471297i			0.0245016i
$371$	−3.07184	−	4.35782i	−0.159482	−	0.226247i
$372$		0			0
$373$	−5.86560	+	10.1595i	−0.303709	+	0.526040i	−0.976973	−	0.213362i	$-0.931558\pi$
$373$	−5.86560	+	10.1595i	−0.303709	+	0.526040i	0.673264	+	0.739402i	$0.264892\pi$
$374$	−10.9949	−	19.0438i	−0.568533	−	0.984729i
$375$		0			0
$376$	−8.21859	−	4.74500i	−0.423841	−	0.244705i
$377$	23.1743			1.19354
$378$		0			0
$379$	34.8881			1.79208			0.896041	−	0.443971i	$-0.146431\pi$
$379$	34.8881			1.79208			0.896041	+	0.443971i	$0.146431\pi$
$380$	−3.74157	−	2.16020i	−0.191939	−	0.110816i
$381$		0			0
$382$	−11.0345	−	19.1122i	−0.564572	−	0.977867i
$383$	−5.92412	+	10.2609i	−0.302708	+	0.524306i	−0.976748	−	0.214389i	$-0.931224\pi$
$383$	−5.92412	+	10.2609i	−0.302708	+	0.524306i	0.674040	+	0.738695i	$0.264557\pi$
$384$		0			0
$385$	14.2063	−	1.28790i	0.724019	−	0.0656374i
$386$			19.9396i			1.01490i
$387$		0			0
$388$	−10.2669	+	5.92762i	−0.521225	+	0.300929i
$389$	−5.50224	+	3.17672i	−0.278975	+	0.161066i	−0.632959	−	0.774185i	$-0.718160\pi$
$389$	−5.50224	+	3.17672i	−0.278975	+	0.161066i	0.353984	+	0.935251i	$0.384827\pi$
$390$		0			0
$391$		−	10.4684i		−	0.529407i
$392$	−1.25885	−	6.88588i	−0.0635816	−	0.347789i
$393$		0			0
$394$	−2.31280	+	4.00588i	−0.116517	+	0.201814i
$395$	−2.22601	−	3.85557i	−0.112003	−	0.193995i
$396$		0			0
$397$	−7.42647	−	4.28768i	−0.372724	−	0.215192i	0.301924	−	0.953332i	$-0.402371\pi$
$397$	−7.42647	−	4.28768i	−0.372724	−	0.215192i	−0.674648	+	0.738140i	$0.735704\pi$
$398$	−20.9028			−1.04777
$399$		0			0
$400$	−4.06428			−0.203214
$401$	−20.0216	−	11.5595i	−0.999833	−	0.577254i	−0.0916343	−	0.995793i	$-0.529209\pi$
$401$	−20.0216	−	11.5595i	−0.999833	−	0.577254i	−0.908199	+	0.418539i	$0.862542\pi$
$402$		0			0
$403$	13.4184	+	23.2413i	0.668417	+	1.15773i
$404$	2.65813	−	4.60402i	0.132247	−	0.229058i
$405$		0			0
$406$	−12.7872	−	5.91393i	−0.634620	−	0.293503i
$407$		−	2.71556i		−	0.134605i
$408$		0			0
$409$	1.35091	−	0.779947i	0.0667981	−	0.0385659i	−0.466229	−	0.884664i	$-0.654388\pi$
$409$	1.35091	−	0.779947i	0.0667981	−	0.0385659i	0.533027	+	0.846098i	$0.321054\pi$
$410$	−0.137196	+	0.0792099i	−0.00677561	+	0.00391190i
$411$		0			0
$412$		−	8.94450i		−	0.440664i
$413$	3.61971	−	2.55154i	0.178114	−	0.125553i
$414$		0			0
$415$	4.07224	−	7.05332i	0.199898	−	0.346234i
$416$	−2.17600	−	3.76893i	−0.106687	−	0.184787i
$417$		0			0
$418$	21.5585	+	12.4468i	1.05446	+	0.608794i
$419$	6.81644			0.333005			0.166502	−	0.986041i	$-0.446753\pi$
$419$	6.81644			0.333005			0.166502	+	0.986041i	$0.446753\pi$
$420$		0			0
$421$	13.5145			0.658659			0.329329	−	0.944215i	$-0.393177\pi$
$421$	13.5145			0.658659			0.329329	+	0.944215i	$0.393177\pi$
$422$	5.79042	+	3.34310i	0.281873	+	0.162740i
$423$		0			0
$424$	1.00759	+	1.74520i	0.0489330	+	0.0847544i
$425$	8.01750	−	13.8867i	0.388906	−	0.673605i
$426$		0			0
$427$	5.74426	−	12.4204i	0.277984	−	0.601065i
$428$		−	19.1563i		−	0.925953i
$429$		0			0
$430$	−7.28898	+	4.20829i	−0.351506	+	0.202942i
$431$	−12.2628	+	7.07990i	−0.590676	+	0.341027i	−0.765365	−	0.643597i	$-0.777441\pi$
$431$	−12.2628	+	7.07990i	−0.590676	+	0.341027i	0.174689	+	0.984624i	$0.444108\pi$
$432$		0			0
$433$			23.4830i			1.12852i	0.825597	+	0.564260i	$0.190839\pi$
$433$			23.4830i			1.12852i	−0.825597	+	0.564260i	$0.809161\pi$
$434$	−1.47304	−	16.2485i	−0.0707082	−	0.779954i
$435$		0			0
$436$	9.62168	−	16.6652i	0.460795	−	0.798121i
$437$	5.92536	+	10.2630i	0.283449	+	0.490947i
$438$		0			0
$439$	−3.66398	−	2.11540i	−0.174872	−	0.100963i	0.410009	−	0.912081i	$-0.365526\pi$
$439$	−3.66398	−	2.11540i	−0.174872	−	0.100963i	−0.584881	+	0.811119i	$0.698859\pi$
$440$	−5.39149			−0.257029
$441$		0			0
$442$	17.1701			0.816699
$443$	25.8161	+	14.9049i	1.22656	+	0.708154i	0.966308	−	0.257388i	$-0.0828618\pi$
$443$	25.8161	+	14.9049i	1.22656	+	0.708154i	0.260250	+	0.965541i	$0.416195\pi$
$444$		0			0
$445$	1.99086	+	3.44827i	0.0943757	+	0.163464i
$446$	−4.09123	+	7.08622i	−0.193725	+	0.335542i
$447$		0			0
$448$	0.238876	+	2.63495i	0.0112858	+	0.124489i
$449$		−	8.41716i		−	0.397230i	−0.980078	−	0.198615i	$-0.936356\pi$
$449$		−	8.41716i		−	0.397230i	0.980078	−	0.198615i	$-0.0636444\pi$
$450$		0			0
$451$	0.790505	−	0.456399i	0.0372234	−	0.0214910i
$452$	−7.31199	+	4.22158i	−0.343927	+	0.198566i
$453$		0			0
$454$			10.6938i			0.501883i
$455$	−4.67539	+	10.1092i	−0.219186	+	0.473929i
$456$		0			0
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	−0.817048	−	0.576570i	$-0.804391\pi$
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	0.907848	+	0.419299i	$0.137724\pi$
$458$	−14.6036	−	25.2942i	−0.682382	−	1.18192i
$459$		0			0
$460$	−2.22278	−	1.28332i	−0.103638	−	0.0598352i
$461$	−34.0846			−1.58748			−0.793739	−	0.608259i	$-0.791868\pi$
$461$	−34.0846			−1.58748			−0.793739	+	0.608259i	$0.791868\pi$
$462$		0			0
$463$	12.2192			0.567877			0.283938	−	0.958843i	$-0.408359\pi$
$463$	12.2192			0.567877			0.283938	+	0.958843i	$0.408359\pi$
$464$	4.61157	+	2.66249i	0.214087	+	0.123603i
$465$		0			0
$466$	−3.21967	−	5.57664i	−0.149148	−	0.258333i
$467$	−15.4057	+	26.6835i	−0.712893	+	1.23477i	0.250874	+	0.968020i	$0.419282\pi$
$467$	−15.4057	+	26.6835i	−0.712893	+	1.23477i	−0.963767	+	0.266747i	$0.914051\pi$
$468$		0			0
$469$	11.7694	−	8.29628i	0.543460	−	0.383087i
$470$		−	9.17991i		−	0.423438i
$471$		0			0
$472$	−1.44961	+	0.836931i	−0.0667236	+	0.0385229i
$473$	41.9983	−	24.2477i	1.93108	−	1.11491i
$474$		0			0
$475$			18.1525i			0.832892i
$476$	−9.47423	−	4.38170i	−0.434250	−	0.200835i
$477$		0			0
$478$	2.31778	−	4.01452i	0.106013	−	0.183620i
$479$	20.8747	+	36.1560i	0.953788	+	1.65201i	0.737118	+	0.675764i	$0.236186\pi$
$479$	20.8747	+	36.1560i	0.953788	+	1.65201i	0.216670	+	0.976245i	$0.430481\pi$
$480$		0			0
$481$	1.83629	+	1.06018i	0.0837276	+	0.0483401i
$482$	−10.4944			−0.478009
$483$		0			0
$484$	20.0652			0.912053
$485$	−9.93146	−	5.73393i	−0.450964	−	0.260364i
$486$		0			0
$487$	10.5832	+	18.3306i	0.479568	+	0.830637i	0.999725	−	0.0234338i	$-0.00745988\pi$
$487$	10.5832	+	18.3306i	0.479568	+	0.830637i	−0.520157	+	0.854071i	$0.674127\pi$
$488$	−2.58611	+	4.47927i	−0.117068	+	0.202767i
$489$		0			0
$490$	5.15963	−	4.38501i	0.233088	−	0.198095i
$491$			37.3463i			1.68541i	0.538373	+	0.842707i	$0.319039\pi$
$491$			37.3463i			1.68541i	−0.538373	+	0.842707i	$0.680961\pi$
$492$		0			0
$493$	−18.1942	+	10.5044i	−0.819427	+	0.473097i
$494$	−16.8333	+	9.71873i	−0.757368	+	0.437266i
$495$		0			0
$496$			6.16655i			0.276886i
$497$	−9.59137	+	0.869525i	−0.430232	+	0.0390035i
$498$		0			0
$499$	−13.7099	+	23.7462i	−0.613738	+	1.06303i	0.376867	+	0.926267i	$0.377001\pi$
$499$	−13.7099	+	23.7462i	−0.613738	+	1.06303i	−0.990605	+	0.136758i	$0.956332\pi$
$500$	−4.38405	−	7.59340i	−0.196061	−	0.339587i
$501$		0			0
$502$	−6.80065	−	3.92635i	−0.303528	−	0.175242i
$503$	11.2791			0.502909			0.251454	−	0.967869i	$-0.419091\pi$
$503$	11.2791			0.502909			0.251454	+	0.967869i	$0.419091\pi$
$504$		0			0
$505$	5.14255			0.228840
$506$	12.8074	+	7.39435i	0.569358	+	0.328719i
$507$		0			0
$508$	1.65941	+	2.87419i	0.0736246	+	0.127522i
$509$	−9.31667	+	16.1370i	−0.412954	+	0.715258i	−0.995211	−	0.0977470i	$-0.968836\pi$
$509$	−9.31667	+	16.1370i	−0.412954	+	0.715258i	0.582257	+	0.813005i	$0.302170\pi$
$510$		0			0
$511$	3.79259	+	5.38031i	0.167774	+	0.238011i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	2.97164	−	1.71568i	0.131074	−	0.0756753i
$515$	7.49305	−	4.32611i	0.330183	−	0.190631i
$516$		0			0
$517$			52.8936i			2.32626i
$518$	−0.742687	−	1.05360i	−0.0326318	−	0.0462926i
$519$		0			0
$520$	2.10489	−	3.64578i	0.0923056	−	0.159878i
$521$	7.64255	+	13.2373i	0.334826	+	0.579936i	0.983451	−	0.181172i	$-0.0579891\pi$
$521$	7.64255	+	13.2373i	0.334826	+	0.579936i	−0.648625	+	0.761108i	$0.724656\pi$
$522$		0			0
$523$	−31.5991	−	18.2437i	−1.38173	−	0.797743i	−0.389368	−	0.921082i	$-0.627306\pi$
$523$	−31.5991	−	18.2437i	−1.38173	−	0.797743i	−0.992365	+	0.123339i	$0.960640\pi$
$524$	18.7467			0.818954
$525$		0			0
$526$	−3.66132			−0.159641
$527$	−21.0697	−	12.1646i	−0.917809	−	0.529897i
$528$		0			0
$529$	−7.97989	−	13.8216i	−0.346952	−	0.600938i
$530$	−0.974668	+	1.68817i	−0.0423369	+	0.0733296i
$531$		0			0
$532$	11.7686	−	1.06690i	0.510232	−	0.0462561i
$533$			0.712731i			0.0308718i
$534$		0			0
$535$	16.0477	−	9.26516i	0.693803	−	0.400568i
$536$	−4.71336	+	2.72126i	−0.203586	+	0.117540i
$537$		0			0
$538$			12.6861i			0.546935i
$539$	−29.7292	+	25.2659i	−1.28053	+	1.08828i
$540$		0			0
$541$	2.63647	−	4.56649i	0.113351	−	0.196329i	−0.803769	−	0.594942i	$-0.797175\pi$
$541$	2.63647	−	4.56649i	0.113351	−	0.196329i	0.917119	+	0.398613i	$0.130508\pi$
$542$	−9.93828	−	17.2136i	−0.426886	−	0.739388i
$543$		0			0
$544$	3.41677	+	1.97267i	0.146493	+	0.0845776i
$545$	18.6146			0.797361
$546$		0			0
$547$	18.5966			0.795134			0.397567	−	0.917573i	$-0.369855\pi$
$547$	18.5966			0.795134			0.397567	+	0.917573i	$0.369855\pi$
$548$	14.6656	+	8.46717i	0.626482	+	0.361700i
$549$		0			0
$550$	11.3264	+	19.6179i	0.482958	+	0.836508i
$551$	11.8916	−	20.5968i	0.506599	−	0.877455i
$552$		0			0
$553$	11.0521	+	5.11144i	0.469983	+	0.217361i
$554$			7.46605i			0.317202i
$555$		0			0
$556$	−10.5033	+	6.06406i	−0.445438	+	0.257174i
$557$	−23.8694	+	13.7810i	−1.01138	+	0.583920i	−0.911595	−	0.411089i	$-0.865149\pi$
$557$	−23.8694	+	13.7810i	−1.01138	+	0.583920i	−0.0997845	+	0.995009i	$0.531815\pi$
$558$		0			0
$559$			37.8662i			1.60157i
$560$	−2.09183	+	1.47454i	−0.0883960	+	0.0623105i
$561$		0			0
$562$	−11.1282	+	19.2746i	−0.469416	+	0.813052i
$563$	−9.42577	−	16.3259i	−0.397249	−	0.688055i	0.596137	−	0.802883i	$-0.296702\pi$
$563$	−9.42577	−	16.3259i	−0.397249	−	0.688055i	−0.993385	+	0.114828i	$0.963368\pi$
$564$		0			0
$565$	−7.07306	−	4.08364i	−0.297566	−	0.171800i
$566$	−16.1802			−0.680106
$567$		0			0
$568$	3.64006			0.152734
$569$	−3.87103	−	2.23494i	−0.162282	−	0.0936936i	0.416659	−	0.909063i	$-0.363201\pi$
$569$	−3.87103	−	2.23494i	−0.162282	−	0.0936936i	−0.578942	+	0.815369i	$0.696534\pi$
$570$		0			0
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	0.602697	−	0.797970i	$-0.294093\pi$
$571$	−9.31245	−	16.1296i	−0.389714	−	0.675004i	−0.992411	+	0.122966i	$0.960759\pi$
$572$	−12.1282	+	21.0066i	−0.507104	+	0.878329i
$573$		0			0
$574$	0.181884	−	0.393275i	0.00759170	−	0.0164150i
$575$			10.7839i			0.449721i
$576$		0			0
$577$	31.9418	−	18.4416i	1.32976	−	0.767735i	0.344495	−	0.938788i	$-0.388050\pi$
$577$	31.9418	−	18.4416i	1.32976	−	0.767735i	0.985262	+	0.171053i	$0.0547170\pi$
$578$	1.24210	−	0.717124i	0.0516644	−	0.0298284i
$579$		0			0
$580$			5.15098i			0.213883i
$581$	2.01124	+	22.1852i	0.0834403	+	0.920395i
$582$		0			0
$583$	5.61593	−	9.72707i	0.232588	−	0.402854i
$584$	−1.24401	−	2.15468i	−0.0514773	−	0.0891614i
$585$		0			0
$586$	−7.68002	−	4.43406i	−0.317259	−	0.183170i
$587$	26.4589			1.09208			0.546039	−	0.837760i	$-0.316135\pi$
$587$	26.4589			1.09208			0.546039	+	0.837760i	$0.316135\pi$
$588$		0			0
$589$	27.5419			1.13484
$590$	−1.40224	−	0.809584i	−0.0577293	−	0.0333300i
$591$		0			0
$592$	0.243608	+	0.421942i	0.0100122	+	0.0173417i
$593$	17.3351	−	30.0254i	0.711869	−	1.23299i	−0.252285	−	0.967653i	$-0.581182\pi$
$593$	17.3351	−	30.0254i	0.711869	−	1.23299i	0.964155	−	0.265341i	$-0.0854845\pi$
$594$		0			0
$595$	−0.911654	−	10.0561i	−0.0373742	−	0.412259i
$596$		−	8.74051i		−	0.358025i
$597$		0			0
$598$	−10.0003	+	5.77366i	−0.408942	+	0.236103i
$599$	−21.2079	+	12.2444i	−0.866530	+	0.500291i	−0.866193	−	0.499709i	$-0.833440\pi$
$599$	−21.2079	+	12.2444i	−0.866530	+	0.500291i	−0.000336253		1.00000i	$0.500107\pi$
$600$		0			0
$601$		−	22.3795i		−	0.912880i	−0.889754	−	0.456440i	$-0.849124\pi$
$601$		−	22.3795i		−	0.912880i	0.889754	−	0.456440i	$-0.150876\pi$
$602$	9.66321	−	20.8940i	0.393843	−	0.851578i
$603$		0			0
$604$	11.0471	−	19.1341i	0.449499	−	0.778555i
$605$	9.70476	+	16.8091i	0.394554	+	0.683388i
$606$		0			0
$607$	28.2180	+	16.2917i	1.14533	+	0.661259i	0.947746	−	0.319026i	$-0.103356\pi$
$607$	28.2180	+	16.2917i	1.14533	+	0.661259i	0.197589	+	0.980285i	$0.436689\pi$
$608$	−4.46634			−0.181134
$609$		0			0
$610$	−5.00321			−0.202574
$611$	−35.7672	−	20.6502i	−1.44699	−	0.835418i
$612$		0			0
$613$	5.86931	+	10.1659i	0.237059	+	0.410598i	0.959869	−	0.280449i	$-0.0904832\pi$
$613$	5.86931	+	10.1659i	0.237059	+	0.410598i	−0.722810	+	0.691047i	$0.757150\pi$
$614$	13.5714	−	23.5063i	0.547696	−	0.948637i
$615$		0			0
$616$	12.0529	−	8.49611i	0.485625	−	0.342318i
$617$		−	44.1035i		−	1.77554i	−0.460288	−	0.887770i	$-0.652254\pi$
$617$		−	44.1035i		−	1.77554i	0.460288	−	0.887770i	$-0.347746\pi$
$618$		0			0
$619$	4.28374	−	2.47322i	0.172178	−	0.0994070i	−0.411434	−	0.911439i	$-0.634972\pi$
$619$	4.28374	−	2.47322i	0.172178	−	0.0994070i	0.583612	+	0.812032i	$0.301639\pi$
$620$	−5.16588	+	2.98252i	−0.207467	+	0.119781i
$621$		0			0
$622$			16.8955i			0.677447i
$623$	−9.88455	−	4.57147i	−0.396016	−	0.183152i
$624$		0			0
$625$	−5.91991	+	10.2536i	−0.236797	+	0.410144i
$626$	−2.13870	−	3.70433i	−0.0854795	−	0.148055i
$627$		0			0
$628$	−1.23372	−	0.712287i	−0.0492307	−	0.0284233i
$629$	−1.92224			−0.0766447
$630$		0			0
$631$	−9.08478			−0.361659			−0.180830	−	0.983514i	$-0.557878\pi$
$631$	−9.08478			−0.361659			−0.180830	+	0.983514i	$0.557878\pi$
$632$	−3.98581	−	2.30121i	−0.158547	−	0.0915371i
$633$		0			0
$634$	3.31470	+	5.74123i	0.131644	+	0.228013i
$635$	−1.60519	+	2.78027i	−0.0637001	+	0.110332i
$636$		0			0
$637$	−5.47851	−	29.9673i	−0.217066	−	1.18735i
$638$		−	29.6794i		−	1.17502i
$639$		0			0
$640$	0.837727	−	0.483662i	0.0331141	−	0.0191184i
$641$	−12.1954	+	7.04105i	−0.481691	+	0.278105i	−0.721121	−	0.692809i	$-0.756373\pi$
$641$	−12.1954	+	7.04105i	−0.481691	+	0.278105i	0.239430	+	0.970914i	$0.423040\pi$
$642$		0			0
$643$		−	8.46577i		−	0.333857i	−0.985969	−	0.166929i	$-0.946615\pi$
$643$		−	8.46577i		−	0.333857i	0.985969	−	0.166929i	$-0.0533850\pi$
$644$	6.99141	−	0.633821i	0.275500	−	0.0249760i
$645$		0			0
$646$	8.81062	−	15.2604i	0.346649	−	0.600414i
$647$	12.1662	+	21.0725i	0.478304	+	0.828446i	0.999691	−	0.0248742i	$-0.00791854\pi$
$647$	12.1662	+	21.0725i	0.478304	+	0.828446i	−0.521387	+	0.853320i	$0.674585\pi$
$648$		0			0
$649$	8.07955	+	4.66473i	0.317150	+	0.183107i
$650$	−17.6877			−0.693770
$651$		0			0
$652$	−7.44296			−0.291489
$653$	−36.0653	−	20.8223i	−1.41134	−	0.814840i	−0.415829	−	0.909443i	$-0.636509\pi$
$653$	−36.0653	−	20.8223i	−1.41134	−	0.814840i	−0.995515	+	0.0946029i	$0.969842\pi$
$654$		0			0
$655$	9.06707	+	15.7046i	0.354280	+	0.613631i
$656$	−0.0818856	+	0.141830i	−0.00319709	+	0.00553753i
$657$		0			0
$658$	14.4661	+	20.5221i	0.563946	+	0.800033i
$659$			10.5062i			0.409265i	0.978839	+	0.204632i	$0.0655999\pi$
$659$			10.5062i			0.409265i	−0.978839	+	0.204632i	$0.934400\pi$
$660$		0			0
$661$	16.8988	−	9.75655i	0.657289	−	0.379486i	−0.133954	−	0.990987i	$-0.542768\pi$
$661$	16.8988	−	9.75655i	0.657289	−	0.379486i	0.791243	+	0.611502i	$0.209434\pi$
$662$	0.656267	−	0.378896i	0.0255065	−	0.0147262i
$663$		0			0
$664$		−	8.41959i		−	0.326743i
$665$	6.58578	+	9.34282i	0.255386	+	0.362299i
$666$		0			0
$667$	7.06450	−	12.2361i	0.273539	−	0.473783i
$668$	−3.24855	−	5.62665i	−0.125690	−	0.217702i
$669$		0			0
$670$	−4.55935	−	2.63234i	−0.176143	−	0.101696i
$671$	28.8279			1.11289
$672$		0			0
$673$	6.20554			0.239206			0.119603	−	0.992822i	$-0.461838\pi$
$673$	6.20554			0.239206			0.119603	+	0.992822i	$0.461838\pi$
$674$	−1.75089	−	1.01088i	−0.0674419	−	0.0389376i
$675$		0			0
$676$	−2.96991	−	5.14404i	−0.114227	−	0.197848i
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	−0.523942	−	0.851754i	$-0.675539\pi$
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	0.999612	+	0.0278703i	$0.00887255\pi$
$678$		0			0
$679$	31.2379	−	2.83194i	1.19880	−	0.108680i
$680$			3.81643i			0.146353i
$681$		0			0
$682$	29.7652	−	17.1850i	1.13977	−	0.658046i
$683$	18.3119	−	10.5724i	0.700687	−	0.404542i	−0.106916	−	0.994268i	$-0.534098\pi$
$683$	18.3119	−	10.5724i	0.700687	−	0.404542i	0.807603	+	0.589726i	$0.200764\pi$
$684$		0			0
$685$			16.3810i			0.625886i
$686$	−4.62449	+	17.9336i	−0.176564	+	0.684708i
$687$		0			0
$688$	−4.35045	+	7.53520i	−0.165859	+	0.287277i
$689$	4.38503	+	7.59509i	0.167056	+	0.289350i
$690$		0			0
$691$	−5.58127	−	3.22235i	−0.212322	−	0.122584i	0.390068	−	0.920786i	$-0.372451\pi$
$691$	−5.58127	−	3.22235i	−0.212322	−	0.122584i	−0.602390	+	0.798202i	$0.705785\pi$
$692$	11.8188			0.449282
$693$		0			0
$694$	−20.9661			−0.795864
$695$	−10.1601	−	5.86591i	−0.385393	−	0.222507i
$696$		0			0
$697$	−0.323067	−	0.559568i	−0.0122370	−	0.0211952i
$698$	3.09694	−	5.36406i	0.117221	−	0.203033i
$699$		0			0
$700$	9.75984	+	4.51379i	0.368887	+	0.170605i
$701$			24.5717i			0.928061i	0.885819	+	0.464031i	$0.153597\pi$
$701$			24.5717i			0.928061i	−0.885819	+	0.464031i	$0.846403\pi$
$702$		0			0
$703$	1.88454	−	1.08804i	0.0710767	−	0.0410361i
$704$	−4.82689	+	2.78681i	−0.181920	+	0.105032i
$705$		0			0
$706$		−	18.8378i		−	0.708969i
$707$	−11.4964	+	8.10382i	−0.432366	+	0.304776i
$708$		0			0
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	0.0655765	+	0.997848i	$0.479111\pi$
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	−0.896950	+	0.442133i	$0.854222\pi$
$710$	1.76056	+	3.04938i	0.0660727	+	0.114441i
$711$		0			0
$712$	3.56475	+	2.05811i	0.133595	+	0.0771309i
$713$	16.3620			0.612760
$714$		0			0
$715$	−23.4637			−0.877493
$716$	2.10764	+	1.21685i	0.0787663	+	0.0454757i
$717$		0			0
$718$	13.8988	+	24.0735i	0.518700	+	0.898415i
$719$	−2.22433	+	3.85266i	−0.0829537	+	0.143680i	−0.904517	−	0.426437i	$-0.859769\pi$
$719$	−2.22433	+	3.85266i	−0.0829537	+	0.143680i	0.821564	+	0.570117i	$0.193102\pi$
$720$		0			0
$721$	−9.93376	+	21.4790i	−0.369952	+	0.799921i
$722$			0.948177i			0.0352875i
$723$		0			0
$724$	−9.98887	+	5.76708i	−0.371233	+	0.214332i
$725$	18.7427	−	10.8211i	0.696088	−	0.401886i
$726$		0			0
$727$			35.1341i			1.30305i	0.758627	+	0.651525i	$0.225871\pi$
$727$			35.1341i			1.30305i	−0.758627	+	0.651525i	$0.774129\pi$
$728$	1.03959	+	11.4673i	0.0385297	+	0.425005i
$729$		0			0
$730$	1.20336	−	2.08428i	0.0445382	−	0.0771425i
$731$	−17.1640	−	29.7289i	−0.634834	−	1.09956i
$732$		0			0
$733$	5.03789	+	2.90863i	0.186079	+	0.107433i	0.590145	−	0.807297i	$-0.299070\pi$
$733$	5.03789	+	2.90863i	0.186079	+	0.107433i	−0.404067	+	0.914729i	$0.632404\pi$
$734$	21.7534			0.802933
$735$		0			0
$736$	−2.65334			−0.0978035
$737$	26.2704	+	15.1672i	0.967684	+	0.558693i
$738$		0			0
$739$	−5.51675	−	9.55529i	−0.202937	−	0.351497i	0.746537	−	0.665344i	$-0.231715\pi$
$739$	−5.51675	−	9.55529i	−0.202937	−	0.351497i	−0.949473	+	0.313847i	$0.898382\pi$
$740$	−0.235648	+	0.408155i	−0.00866261	+	0.0150041i
$741$		0			0
$742$	−0.481379	−	5.30990i	−0.0176720	−	0.194932i
$743$		−	0.627229i		−	0.0230108i	−0.999934	−	0.0115054i	$-0.996338\pi$
$743$		−	0.627229i		−	0.0230108i	0.999934	−	0.0115054i	$-0.00366236\pi$
$744$		0			0
$745$	7.32216	−	4.22745i	0.268263	−	0.154882i
$746$	−10.1595	+	5.86560i	−0.371966	+	0.214755i
$747$		0			0
$748$		−	21.9898i		−	0.804028i
$749$	−21.2749	+	46.0012i	−0.777369	+	1.68085i
$750$		0			0
$751$	−2.23529	+	3.87163i	−0.0815668	+	0.141278i	−0.903923	−	0.427695i	$-0.859326\pi$
$751$	−2.23529	+	3.87163i	−0.0815668	+	0.141278i	0.822356	+	0.568973i	$0.192659\pi$
$752$	−4.74500	−	8.21859i	−0.173033	−	0.299701i
$753$		0			0
$754$	20.0695	+	11.5871i	0.730889	+	0.421979i
$755$	21.3722			0.777813
$756$		0			0
$757$	5.75624			0.209214			0.104607	−	0.994514i	$-0.466642\pi$
$757$	5.75624			0.209214			0.104607	+	0.994514i	$0.466642\pi$
$758$	30.2140	+	17.4441i	1.09742	+	0.633597i
$759$		0			0
$760$	−2.16020	−	3.74157i	−0.0783586	−	0.135721i
$761$	10.4970	−	18.1813i	0.380516	−	0.659073i	−0.610620	−	0.791924i	$-0.709080\pi$
$761$	10.4970	−	18.1813i	0.380516	−	0.659073i	0.991136	+	0.132851i	$0.0424131\pi$
$762$		0			0
$763$	−41.6136	+	29.3335i	−1.50651	+	1.06195i
$764$		−	22.0689i		−	0.798425i
$765$		0			0
$766$	−10.2609	+	5.92412i	−0.370740	+	0.214047i
$767$	−6.30868	+	3.64232i	−0.227793	+	0.131516i
$768$		0			0
$769$		−	39.4595i		−	1.42295i	−0.702713	−	0.711473i	$-0.748028\pi$
$769$		−	39.4595i		−	1.42295i	0.702713	−	0.711473i	$-0.251972\pi$
$770$	12.9470	+	5.98779i	0.466576	+	0.215785i
$771$		0			0
$772$	−9.96979	+	17.2682i	−0.358821	+	0.621496i
$773$	−17.3164	−	29.9929i	−0.622829	−	1.07877i	−0.988956	−	0.148206i	$-0.952650\pi$
$773$	−17.3164	−	29.9929i	−0.622829	−	1.07877i	0.366128	−	0.930565i	$-0.380683\pi$
$774$		0			0
$775$	21.7048	+	12.5313i	0.779661	+	0.450137i
$776$	−11.8552			−0.425578
$777$		0			0
$778$	−6.35344			−0.227782
$779$	0.633461	+	0.365729i	0.0226961	+	0.0131036i
$780$		0			0
$781$	−10.1442	−	17.5702i	−0.362986	−	0.628711i
$782$	5.23418	−	9.06586i	0.187174	−	0.324195i
$783$		0			0
$784$	2.35274	−	6.59277i	0.0840264	−	0.235456i
$785$		−	1.37802i		−	0.0491838i
$786$		0			0
$787$	−30.5793	+	17.6550i	−1.09003	+	0.629332i	−0.933586	−	0.358355i	$-0.883338\pi$
$787$	−30.5793	+	17.6550i	−1.09003	+	0.629332i	−0.156449	+	0.987686i	$0.550005\pi$
$788$	−4.00588	+	2.31280i	−0.142704	+	0.0823900i
$789$		0			0
$790$		−	4.45203i		−	0.158396i
$791$	22.2473	−	2.01687i	0.791022	−	0.0717116i
$792$		0			0
$793$	−11.2547	+	19.4937i	−0.399667	+	0.692243i
$794$	−4.28768	−	7.42647i	−0.152164	−	0.263556i
$795$		0			0
$796$	−18.1024	−	10.4514i	−0.641622	−	0.370441i
$797$	19.2198			0.680802			0.340401	−	0.940280i	$-0.389437\pi$
$797$	19.2198			0.680802			0.340401	+	0.940280i	$0.389437\pi$
$798$		0			0
$799$	37.4414			1.32458
$800$	−3.51977	−	2.03214i	−0.124443	−	0.0718471i
$801$		0			0
$802$	−11.5595	−	20.0216i	−0.408180	−	0.706989i
$803$	−6.93361	+	12.0094i	−0.244682	+	0.423801i
$804$		0			0
$805$	3.91245	+	5.55034i	0.137896	+	0.195624i
$806$			26.8367i			0.945284i
$807$		0			0
$808$	4.60402	−	2.65813i	0.161969	−	0.0935127i
$809$	34.0157	−	19.6390i	1.19593	−	0.690469i	0.236283	−	0.971684i	$-0.424071\pi$
$809$	34.0157	−	19.6390i	1.19593	−	0.690469i	0.959645	+	0.281215i	$0.0907374\pi$
$810$		0			0
$811$		−	9.68436i		−	0.340064i	−0.985439	−	0.170032i	$-0.945613\pi$
$811$		−	9.68436i		−	0.340064i	0.985439	−	0.170032i	$-0.0543871\pi$
$812$	−8.11712	−	11.5152i	−0.284855	−	0.404105i
$813$		0			0
$814$	1.35778	−	2.35174i	0.0475901	−	0.0824285i
$815$	−3.59987	−	6.23517i	−0.126098	−	0.218408i
$816$		0			0
$817$	33.6547	+	19.4306i	1.17743	+	0.679790i
$818$	1.55989			0.0545404
$819$		0			0
$820$	−0.158420			−0.00553226
$821$	−10.9919	−	6.34620i	−0.383621	−	0.221484i	0.295771	−	0.955259i	$-0.404423\pi$
$821$	−10.9919	−	6.34620i	−0.383621	−	0.221484i	−0.679393	+	0.733775i	$0.737757\pi$
$822$		0			0
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	0.672572	−	0.740032i	$-0.265190\pi$
$823$	−8.73837	−	15.1353i	−0.304600	−	0.527583i	−0.977172	+	0.212448i	$0.931856\pi$
$824$	4.47225	−	7.74616i	0.155798	−	0.269850i
$825$		0			0
$826$	4.41054	−	0.399846i	0.153462	−	0.0139124i
$827$			46.9482i			1.63255i	0.577665	+	0.816274i	$0.303964\pi$
$827$			46.9482i			1.63255i	−0.577665	+	0.816274i	$0.696036\pi$
$828$		0			0
$829$	−1.99797	+	1.15353i	−0.0693924	+	0.0400637i	−0.534295	−	0.845298i	$-0.679423\pi$
$829$	−1.99797	+	1.15353i	−0.0693924	+	0.0400637i	0.464902	+	0.885362i	$0.346089\pi$
$830$	7.05332	−	4.07224i	0.244824	−	0.141349i
$831$		0			0
$832$		−	4.35199i		−	0.150878i
$833$	17.8848	+	21.0441i	0.619671	+	0.729137i
$834$		0			0
$835$	3.14240	−	5.44280i	0.108747	−	0.188356i
$836$	12.4468	+	21.5585i	0.430482	+	0.745617i
$837$		0			0
$838$	5.90321	+	3.40822i	0.203923	+	0.117735i
$839$	17.0333			0.588054			0.294027	−	0.955797i	$-0.405004\pi$
$839$	17.0333			0.588054			0.294027	+	0.955797i	$0.405004\pi$
$840$		0			0
$841$	0.644552			0.0222259
$842$	11.7039	+	6.75727i	0.403344	+	0.232871i
$843$		0			0
$844$	3.34310	+	5.79042i	0.115074	+	0.199314i
$845$	2.87287	−	4.97595i	0.0988296	−	0.171178i
$846$		0			0
$847$	−48.1838	−	22.2844i	−1.65562	−	0.765700i
$848$			2.01518i			0.0692017i
$849$		0			0
$850$	13.8867	−	8.01750i	0.476311	−	0.274998i
$851$	1.11956	−	0.646377i	0.0383779	−	0.0221575i
$852$		0			0
$853$			3.31581i			0.113531i	0.998388	+	0.0567656i	$0.0180788\pi$
$853$			3.31581i			0.113531i	−0.998388	+	0.0567656i	$0.981921\pi$
$854$	11.1849	−	7.88424i	0.382738	−	0.269793i
$855$		0			0
$856$	9.57813	−	16.5898i	0.327374	−	0.567028i
$857$	4.74512	+	8.21879i	0.162090	+	0.280748i	0.935618	−	0.353014i	$-0.114843\pi$
$857$	4.74512	+	8.21879i	0.162090	+	0.280748i	−0.773528	+	0.633762i	$0.781510\pi$
$858$		0			0
$859$	25.5104	+	14.7284i	0.870404	+	0.502528i	0.867482	−	0.497468i	$-0.165737\pi$
$859$	25.5104	+	14.7284i	0.870404	+	0.502528i	0.00292142	+	0.999996i	$0.499070\pi$
$860$	−8.41658			−0.287003
$861$		0			0
$862$	−14.1598			−0.482285
$863$	−13.4610	−	7.77172i	−0.458218	−	0.264553i	0.253076	−	0.967446i	$-0.418558\pi$
$863$	−13.4610	−	7.77172i	−0.458218	−	0.264553i	−0.711295	+	0.702894i	$0.751891\pi$
$864$		0			0
$865$	5.71629	+	9.90090i	0.194360	+	0.336641i
$866$	−11.7415	+	20.3369i	−0.398992	+	0.691075i
$867$		0			0
$868$	6.84856	−	14.8081i	0.232455	−	0.502621i
$869$			25.6521i			0.870187i
$870$		0			0
$871$	−20.5125	+	11.8429i	−0.695039	+	0.401281i
$872$	16.6652	−	9.62168i	0.564356	−	0.325831i
$873$		0			0
$874$			11.8507i			0.400857i
$875$	2.09449	+	23.1035i	0.0708067	+	0.781040i
$876$		0			0
$877$	22.7249	−	39.3606i	0.767364	−	1.32911i	−0.171624	−	0.985163i	$-0.554901\pi$
$877$	22.7249	−	39.3606i	0.767364	−	1.32911i	0.938988	−	0.343950i	$-0.111765\pi$
$878$	−2.11540	−	3.66398i	−0.0713913	−	0.123653i
$879$		0			0
$880$	−4.66917	−	2.69574i	−0.157398	−	0.0908735i
$881$	−15.6912			−0.528651			−0.264326	−	0.964433i	$-0.585149\pi$
$881$	−15.6912			−0.528651			−0.264326	+	0.964433i	$0.585149\pi$
$882$		0			0
$883$	−10.5344			−0.354510			−0.177255	−	0.984165i	$-0.556722\pi$
$883$	−10.5344			−0.354510			−0.177255	+	0.984165i	$0.556722\pi$
$884$	14.8697	+	8.58505i	0.500124	+	0.288747i
$885$		0			0
$886$	14.9049	+	25.8161i	0.500740	+	0.867307i
$887$	−0.0302741	+	0.0524362i	−0.00101650	+	0.00176064i	−0.866533	−	0.499119i	$-0.833657\pi$
$887$	−0.0302741	+	0.0524362i	−0.00101650	+	0.00176064i	0.865517	+	0.500880i	$0.166990\pi$
$888$		0			0
$889$	−0.792789	−	8.74493i	−0.0265893	−	0.293296i
$890$			3.98172i			0.133467i
$891$		0			0
$892$	−7.08622	+	4.09123i	−0.237264	+	0.136985i
$893$	−36.7070	+	21.1928i	−1.22835	+	0.709190i
$894$		0			0
$895$			2.35417i			0.0786913i
$896$	−1.11060	+	2.40137i	−0.0371025	+	0.0802241i
$897$		0			0
$898$	4.20858	−	7.28948i	0.140442	−	0.243253i
$899$	−16.4184	−	28.4375i	−0.547583	−	0.948442i
$900$		0			0
$901$	−6.88542	−	3.97530i	−0.229386	−	0.132436i
$902$	0.912797			0.0303928
$903$		0			0
$904$	−8.44316			−0.280815
$905$	−9.66247	−	5.57863i	−0.321192	−	0.185440i
$906$		0			0
$907$	−12.0490	−	20.8695i	−0.400081	−	0.692961i	0.593654	−	0.804720i	$-0.297685\pi$
$907$	−12.0490	−	20.8695i	−0.400081	−	0.692961i	−0.993735	+	0.111760i	$0.964351\pi$
$908$	−5.34688	+	9.26106i	−0.177442	+	0.307339i
$909$		0			0
$910$	−9.10363	+	6.41717i	−0.301782	+	0.212727i
$911$		−	25.4604i		−	0.843541i	−0.906703	−	0.421771i	$-0.861409\pi$
$911$		−	25.4604i		−	0.843541i	0.906703	−	0.421771i	$-0.138591\pi$
$912$		0			0
$913$	−40.6404	+	23.4638i	−1.34500	+	0.776537i
$914$	3.36207	−	1.94109i	0.111208	−	0.0642057i
$915$		0			0
$916$		−	29.2072i		−	0.965034i
$917$	−45.0177	−	20.8201i	−1.48662	−	0.687540i
$918$		0			0
$919$	11.4534	−	19.8378i	0.377812	−	0.654389i	−0.612932	−	0.790136i	$-0.710010\pi$
$919$	11.4534	−	19.8378i	0.377812	−	0.654389i	0.990744	+	0.135747i	$0.0433433\pi$
$920$	−1.28332	−	2.22278i	−0.0423098	−	0.0732828i
$921$		0			0
$922$	−29.5181	−	17.0423i	−0.972128	−	0.561258i
$923$	15.8415			0.521430
$924$		0			0
$925$	1.98019			0.0651082
$926$	10.5822	+	6.10962i	0.347752	+	0.200775i
$927$		0			0
$928$	2.66249	+	4.61157i	0.0874006	+	0.151382i
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	−0.527097	−	0.849805i	$-0.676720\pi$
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	0.999501	+	0.0315768i	$0.0100529\pi$
$930$		0			0
$931$	−29.4455	−	10.5081i	−0.965039	−	0.344390i
$932$		−	6.43935i		−	0.210928i
$933$		0			0
$934$	−26.6835	+	15.4057i	−0.873112	+	0.504091i
$935$	18.4215	−	10.6356i	0.602447	−	0.347823i
$936$		0			0
$937$		−	53.6825i		−	1.75373i	−0.480736	−	0.876865i	$-0.659631\pi$
$937$		−	53.6825i		−	1.75373i	0.480736	−	0.876865i	$-0.340369\pi$
$938$	14.3407	−	1.30009i	0.468242	−	0.0424494i
$939$		0			0
$940$	4.58996	−	7.95004i	0.149708	−	0.259302i
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	−0.948693	−	0.316200i	$-0.897593\pi$
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	0.200509	−	0.979692i	$-0.435740\pi$
$942$		0			0
$943$	0.376324	+	0.217271i	0.0122548	+	0.00707530i
$944$	−1.67386			−0.0544796
$945$		0			0
$946$	48.4954			1.57672
$947$	25.0440	+	14.4591i	0.813820	+	0.469859i	0.848281	−	0.529547i	$-0.177638\pi$
$947$	25.0440	+	14.4591i	0.813820	+	0.469859i	−0.0344607	+	0.999406i	$0.510971\pi$
$948$		0			0
$949$	−5.41390	−	9.37715i	−0.175743	−	0.304395i
$950$	−9.07623	+	15.7205i	−0.294472	+	0.510040i
$951$		0			0
$952$	−6.01407	−	8.53178i	−0.194917	−	0.276516i
$953$			12.8715i			0.416949i	0.978028	+	0.208475i	$0.0668498\pi$
$953$			12.8715i			0.416949i	−0.978028	+	0.208475i	$0.933150\pi$
$954$		0			0
$955$	18.4877	−	10.6739i	0.598249	−	0.345399i
$956$	4.01452	−	2.31778i	0.129839	−	0.0749624i
$957$		0			0
$958$			41.7493i			1.34886i
$959$	−25.8138	−	36.6204i	−0.833571	−	1.18253i
$960$		0			0
$961$	3.51314	−	6.08494i	0.113327	−	0.196288i
$962$	1.06018	+	1.83629i	0.0341816	+	0.0592043i
$963$		0			0
$964$	−9.08846	−	5.24722i	−0.292719	−	0.169002i
$965$	−19.2880			−0.620904
$966$		0			0
$967$	−6.23449			−0.200488			−0.100244	−	0.994963i	$-0.531962\pi$
$967$	−6.23449			−0.200488			−0.100244	+	0.994963i	$0.531962\pi$
$968$	17.3769	+	10.0326i	0.558516	+	0.322459i
$969$		0			0
$970$	−5.73393	−	9.93146i	−0.184105	−	0.318880i
$971$	19.6863	−	34.0977i	0.631764	−	1.09425i	−0.355426	−	0.934704i	$-0.615664\pi$
$971$	19.6863	−	34.0977i	0.631764	−	1.09425i	0.987191	−	0.159544i	$-0.0510023\pi$
$972$		0			0
$973$	31.9570	−	2.89712i	1.02449	−	0.0928774i
$974$			21.1663i			0.678212i
$975$		0			0
$976$	−4.47927	+	2.58611i	−0.143378	+	0.0827793i
$977$	−23.2474	+	13.4219i	−0.743751	+	0.429405i	−0.823431	−	0.567416i	$-0.807943\pi$
$977$	−23.2474	+	13.4219i	−0.743751	+	0.429405i	0.0796807	+	0.996820i	$0.474610\pi$
$978$		0			0
$979$		−	22.9422i		−	0.733236i
$980$	6.66087	−	1.21772i	0.212774	−	0.0388986i
$981$		0			0
$982$	−18.6731	+	32.3428i	−0.595884	+	1.03210i
$983$	−5.98457	−	10.3656i	−0.190878	−	0.330611i	0.754663	−	0.656112i	$-0.227800\pi$
$983$	−5.98457	−	10.3656i	−0.190878	−	0.330611i	−0.945541	+	0.325502i	$0.894467\pi$
$984$		0			0
$985$	−3.87499	−	2.23723i	−0.123467	−	0.0712839i
$986$	−21.0089			−0.669060
$987$		0			0
$988$	−19.4375			−0.618388
$989$	19.9935	+	11.5432i	0.635755	+	0.367053i
$990$		0			0
$991$	−5.40420	−	9.36036i	−0.171670	−	0.297342i	0.767334	−	0.641248i	$-0.221583\pi$
$991$	−5.40420	−	9.36036i	−0.171670	−	0.297342i	−0.939004	+	0.343906i	$0.888250\pi$
$992$	−3.08327	+	5.34038i	−0.0978940	+	0.169557i
$993$		0			0
$994$	−8.74113	−	4.04266i	−0.277252	−	0.128225i
$995$		−	20.2198i		−	0.641012i
$996$		0			0
$997$	11.6653	−	6.73498i	0.369445	−	0.213299i	−0.303771	−	0.952745i	$-0.598246\pi$
$997$	11.6653	−	6.73498i	0.369445	−	0.213299i	0.673216	+	0.739446i	$0.264912\pi$
$998$	−23.7462	+	13.7099i	−0.751672	+	0.433978i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.b.971.6		16
3.2	odd	2		1134.2.k.a.971.3		16
7.3	odd	6		1134.2.k.a.647.3		16
9.2	odd	6		126.2.l.a.5.7	✓	16
9.4	even	3		126.2.t.a.47.1	yes	16
9.5	odd	6		378.2.t.a.89.6		16
9.7	even	3		378.2.l.a.341.2		16
21.17	even	6	inner	1134.2.k.b.647.6		16
36.7	odd	6		3024.2.ca.c.2609.4		16
36.11	even	6		1008.2.ca.c.257.5		16
36.23	even	6		3024.2.df.c.1601.4		16
36.31	odd	6		1008.2.df.c.929.7		16
63.2	odd	6		882.2.m.b.293.6		16
63.4	even	3		882.2.l.b.227.2		16
63.5	even	6		2646.2.m.b.1763.2		16
63.11	odd	6		882.2.t.a.815.4		16
63.13	odd	6		882.2.t.a.803.4		16
63.16	even	3		2646.2.m.b.881.2		16
63.20	even	6		882.2.l.b.509.6		16
63.23	odd	6		2646.2.m.a.1763.3		16
63.25	even	3		2646.2.t.b.2285.7		16
63.31	odd	6		126.2.l.a.101.3	yes	16
63.32	odd	6		2646.2.l.a.521.7		16
63.34	odd	6		2646.2.l.a.1097.3		16
63.38	even	6		126.2.t.a.59.1	yes	16
63.40	odd	6		882.2.m.b.587.6		16
63.41	even	6		2646.2.t.b.1979.7		16
63.47	even	6		882.2.m.a.293.7		16
63.52	odd	6		378.2.t.a.17.6		16
63.58	even	3		882.2.m.a.587.7		16
63.59	even	6		378.2.l.a.143.6		16
63.61	odd	6		2646.2.m.a.881.3		16
252.31	even	6		1008.2.ca.c.353.5		16
252.59	odd	6		3024.2.ca.c.2033.4		16
252.115	even	6		3024.2.df.c.17.4		16
252.227	odd	6		1008.2.df.c.689.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	9.2	odd	6
126.2.l.a.101.3	yes	16	63.31	odd	6
126.2.t.a.47.1	yes	16	9.4	even	3
126.2.t.a.59.1	yes	16	63.38	even	6
378.2.l.a.143.6		16	63.59	even	6
378.2.l.a.341.2		16	9.7	even	3
378.2.t.a.17.6		16	63.52	odd	6
378.2.t.a.89.6		16	9.5	odd	6
882.2.l.b.227.2		16	63.4	even	3
882.2.l.b.509.6		16	63.20	even	6
882.2.m.a.293.7		16	63.47	even	6
882.2.m.a.587.7		16	63.58	even	3
882.2.m.b.293.6		16	63.2	odd	6
882.2.m.b.587.6		16	63.40	odd	6
882.2.t.a.803.4		16	63.13	odd	6
882.2.t.a.815.4		16	63.11	odd	6
1008.2.ca.c.257.5		16	36.11	even	6
1008.2.ca.c.353.5		16	252.31	even	6
1008.2.df.c.689.7		16	252.227	odd	6
1008.2.df.c.929.7		16	36.31	odd	6
1134.2.k.a.647.3		16	7.3	odd	6
1134.2.k.a.971.3		16	3.2	odd	2
1134.2.k.b.647.6		16	21.17	even	6	inner
1134.2.k.b.971.6		16	1.1	even	1	trivial
2646.2.l.a.521.7		16	63.32	odd	6
2646.2.l.a.1097.3		16	63.34	odd	6
2646.2.m.a.881.3		16	63.61	odd	6
2646.2.m.a.1763.3		16	63.23	odd	6
2646.2.m.b.881.2		16	63.16	even	3
2646.2.m.b.1763.2		16	63.5	even	6
2646.2.t.b.1979.7		16	63.41	even	6
2646.2.t.b.2285.7		16	63.25	even	3
3024.2.ca.c.2033.4		16	252.59	odd	6
3024.2.ca.c.2609.4		16	36.7	odd	6
3024.2.df.c.17.4		16	252.115	even	6
3024.2.df.c.1601.4		16	36.23	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.483662 + 0.837727i) q^{5} +(-0.238876 - 2.63495i) q^{7} +1.00000i q^{8} +(-0.837727 + 0.483662i) q^{10} +(4.82689 - 2.78681i) q^{11} +4.35199i q^{13} +(1.11060 - 2.40137i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.97267 - 3.41677i) q^{17} +(3.86796 + 2.23317i) q^{19} -0.967324 q^{20} +5.57361 q^{22} +(2.29786 + 1.32667i) q^{23} +(2.03214 + 3.51977i) q^{25} +(-2.17600 + 3.76893i) q^{26} +(2.16249 - 1.52435i) q^{28} -5.32498i q^{29} +(5.34038 - 3.08327i) q^{31} +(-0.866025 + 0.500000i) q^{32} -3.94535i q^{34} +(2.32290 + 1.07431i) q^{35} +(0.243608 - 0.421942i) q^{37} +(2.23317 + 3.86796i) q^{38} +(-0.837727 - 0.483662i) q^{40} +0.163771 q^{41} +8.70089 q^{43} +(4.82689 + 2.78681i) q^{44} +(1.32667 + 2.29786i) q^{46} +(-4.74500 + 8.21859i) q^{47} +(-6.88588 + 1.25885i) q^{49} +4.06428i q^{50} +(-3.76893 + 2.17600i) q^{52} +(1.74520 - 1.00759i) q^{53} +5.39149i q^{55} +(2.63495 - 0.238876i) q^{56} +(2.66249 - 4.61157i) q^{58} +(0.836931 + 1.44961i) q^{59} +(4.47927 + 2.58611i) q^{61} +6.16655 q^{62} -1.00000 q^{64} +(-3.64578 - 2.10489i) q^{65} +(2.72126 + 4.71336i) q^{67} +(1.97267 - 3.41677i) q^{68} +(1.47454 + 2.09183i) q^{70} -3.64006i q^{71} +(-2.15468 + 1.24401i) q^{73} +(0.421942 - 0.243608i) q^{74} +4.46634i q^{76} +(-8.49611 - 12.0529i) q^{77} +(-2.30121 + 3.98581i) q^{79} +(-0.483662 - 0.837727i) q^{80} +(0.141830 + 0.0818856i) q^{82} -8.41959 q^{83} +3.81643 q^{85} +(7.53520 + 4.35045i) q^{86} +(2.78681 + 4.82689i) q^{88} +(2.05811 - 3.56475i) q^{89} +(11.4673 - 1.03959i) q^{91} +2.65334i q^{92} +(-8.21859 + 4.74500i) q^{94} +(-3.74157 + 2.16020i) q^{95} +11.8552i q^{97} +(-6.59277 - 2.35274i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7} + 12 q^{11} - 8 q^{16} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 12 q^{41} + 4 q^{43} + 12 q^{44} + 6 q^{46} - 18 q^{47} - 2 q^{49}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^11 - 8 * q^16 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 12 * q^41 + 4 * q^43 + 12 * q^44 + 6 * q^46 - 18 * q^47 - 2 * q^49 + 6 * q^52 + 36 * q^53 + 6 * q^56 + 6 * q^58 + 30 * q^59 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^70 + 18 * q^74 - 24 * q^77 - 16 * q^79 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 + 66 * q^95 + 24 * q^98

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