LMFDB - Embedded newform 1148.2.r.a.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	1148.81
Dual form			1148.2.r.a.737.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.67190 - 1.54262i) q^{3} +(-1.10096 - 1.90691i) q^{5} +(2.60761 + 0.447649i) q^{7} +(3.25937 + 5.64540i) q^{9} +O(q^{10})$	\(q+(-2.67190 - 1.54262i) q^{3} +(-1.10096 - 1.90691i) q^{5} +(2.60761 + 0.447649i) q^{7} +(3.25937 + 5.64540i) q^{9} +(-3.16097 - 1.82499i) q^{11} +0.353091i q^{13} +6.79344i q^{15} +(-3.88342 - 2.24210i) q^{17} +(-5.86226 + 3.38458i) q^{19} +(-6.27671 - 5.21863i) q^{21} +(3.07187 + 5.32063i) q^{23} +(0.0757913 - 0.131274i) q^{25} -10.8562i q^{27} +0.443384i q^{29} +(-2.14434 + 3.71411i) q^{31} +(5.63054 + 9.75239i) q^{33} +(-2.01723 - 5.46532i) q^{35} +(0.730118 + 1.26460i) q^{37} +(0.544686 - 0.943424i) q^{39} +(-0.647886 - 6.37026i) q^{41} -6.86200 q^{43} +(7.17685 - 12.4307i) q^{45} +(-5.36060 + 3.09494i) q^{47} +(6.59922 + 2.33458i) q^{49} +(6.91742 + 11.9813i) q^{51} +(9.66478 + 5.57996i) q^{53} +8.03693i q^{55} +20.8845 q^{57} +(5.14222 - 8.90659i) q^{59} +(5.88811 + 10.1985i) q^{61} +(5.97201 + 16.1800i) q^{63} +(0.673313 - 0.388737i) q^{65} +(9.36850 + 5.40891i) q^{67} -18.9550i q^{69} +12.5157i q^{71} +(-1.23009 + 2.13058i) q^{73} +(-0.405014 + 0.233835i) q^{75} +(-7.42562 - 6.17386i) q^{77} +(-1.47630 + 0.852345i) q^{79} +(-6.96891 + 12.0705i) q^{81} -1.57776 q^{83} +9.87380i q^{85} +(0.683975 - 1.18468i) q^{87} +(15.1590 - 8.75205i) q^{89} +(-0.158061 + 0.920722i) q^{91} +(11.4589 - 6.61582i) q^{93} +(12.9082 + 7.45254i) q^{95} +15.0452i q^{97} -23.7933i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.67190	−	1.54262i	−1.54262	−	0.890634i	−0.998672	−	0.0515172i	$-0.983594\pi$
$3$	−2.67190	−	1.54262i	−1.54262	−	0.890634i	−0.543951	−	0.839117i	$-0.683072\pi$
$4$		0			0
$5$	−1.10096	−	1.90691i	−0.492363	−	0.852797i	0.507599	−	0.861594i	$-0.330533\pi$
$5$	−1.10096	−	1.90691i	−0.492363	−	0.852797i	−0.999961	+	0.00879665i	$0.997200\pi$
$6$		0			0
$7$	2.60761	+	0.447649i	0.985583	+	0.169195i
$7$	2.60761	+	0.447649i	0.985583	+	0.169195i
$8$		0			0
$9$	3.25937	+	5.64540i	1.08646	+	1.88180i
$10$		0			0
$11$	−3.16097	−	1.82499i	−0.953070	−	0.550255i	−0.0590366	−	0.998256i	$-0.518803\pi$
$11$	−3.16097	−	1.82499i	−0.953070	−	0.550255i	−0.894033	+	0.448001i	$0.852136\pi$
$12$		0			0
$13$			0.353091i			0.0979297i	0.998801	+	0.0489649i	$0.0155922\pi$
$13$			0.353091i			0.0979297i	−0.998801	+	0.0489649i	$0.984408\pi$
$14$		0			0
$15$			6.79344i			1.75406i
$16$		0			0
$17$	−3.88342	−	2.24210i	−0.941869	−	0.543788i	−0.0513232	−	0.998682i	$-0.516344\pi$
$17$	−3.88342	−	2.24210i	−0.941869	−	0.543788i	−0.890546	+	0.454894i	$0.849677\pi$
$18$		0			0
$19$	−5.86226	+	3.38458i	−1.34490	+	0.776476i	−0.987521	−	0.157486i	$-0.949661\pi$
$19$	−5.86226	+	3.38458i	−1.34490	+	0.776476i	−0.357374	+	0.933961i	$0.616328\pi$
$20$		0			0
$21$	−6.27671	−	5.21863i	−1.36969	−	1.13880i
$22$		0			0
$23$	3.07187	+	5.32063i	0.640529	+	1.10943i	0.985315	+	0.170748i	$0.0546182\pi$
$23$	3.07187	+	5.32063i	0.640529	+	1.10943i	−0.344786	+	0.938681i	$0.612048\pi$
$24$		0			0
$25$	0.0757913	−	0.131274i	0.0151583	−	0.0262549i
$26$		0			0
$27$		−	10.8562i		−	2.08928i
$28$		0			0
$29$			0.443384i			0.0823344i	0.999152	+	0.0411672i	$0.0131076\pi$
$29$			0.443384i			0.0823344i	−0.999152	+	0.0411672i	$0.986892\pi$
$30$		0			0
$31$	−2.14434	+	3.71411i	−0.385135	+	0.667073i	−0.991788	−	0.127893i	$-0.959178\pi$
$31$	−2.14434	+	3.71411i	−0.385135	+	0.667073i	0.606653	+	0.794967i	$0.292512\pi$
$32$		0			0
$33$	5.63054	+	9.75239i	0.980152	+	1.69767i
$34$		0			0
$35$	−2.01723	−	5.46532i	−0.340975	−	0.923807i
$36$		0			0
$37$	0.730118	+	1.26460i	0.120031	+	0.207899i	0.919779	−	0.392436i	$-0.128367\pi$
$37$	0.730118	+	1.26460i	0.120031	+	0.207899i	−0.799749	+	0.600335i	$0.795034\pi$
$38$		0			0
$39$	0.544686	−	0.943424i	0.0872196	−	0.151069i
$40$		0			0
$41$	−0.647886	−	6.37026i	−0.101183	−	0.994868i
$41$	−0.647886	−	6.37026i	−0.101183	−	0.994868i
$42$		0			0
$43$	−6.86200			−1.04645			−0.523223	−	0.852196i	$-0.675270\pi$
$43$	−6.86200			−1.04645			−0.523223	+	0.852196i	$0.675270\pi$
$44$		0			0
$45$	7.17685	−	12.4307i	1.06986	−	1.85306i
$46$		0			0
$47$	−5.36060	+	3.09494i	−0.781924	+	0.451444i	−0.837112	−	0.547032i	$-0.815758\pi$
$47$	−5.36060	+	3.09494i	−0.781924	+	0.451444i	0.0551878	+	0.998476i	$0.482424\pi$
$48$		0			0
$49$	6.59922	+	2.33458i	0.942746	+	0.333512i
$50$		0			0
$51$	6.91742	+	11.9813i	0.968633	+	1.67772i
$52$		0			0
$53$	9.66478	+	5.57996i	1.32756	+	0.766467i	0.984922	−	0.173001i	$-0.0553463\pi$
$53$	9.66478	+	5.57996i	1.32756	+	0.766467i	0.342638	+	0.939468i	$0.388680\pi$
$54$		0			0
$55$			8.03693i			1.08370i
$56$		0			0
$57$	20.8845			2.76622
$58$		0			0
$59$	5.14222	−	8.90659i	0.669460	−	1.15954i	−0.308595	−	0.951194i	$-0.599859\pi$
$59$	5.14222	−	8.90659i	0.669460	−	1.15954i	0.978055	−	0.208346i	$-0.0668080\pi$
$60$		0			0
$61$	5.88811	+	10.1985i	0.753896	+	1.30579i	0.945921	+	0.324396i	$0.105161\pi$
$61$	5.88811	+	10.1985i	0.753896	+	1.30579i	−0.192026	+	0.981390i	$0.561506\pi$
$62$		0			0
$63$	5.97201	+	16.1800i	0.752402	+	2.03849i
$64$		0			0
$65$	0.673313	−	0.388737i	0.0835142	−	0.0482169i
$66$		0			0
$67$	9.36850	+	5.40891i	1.14454	+	0.660803i	0.947552	−	0.319602i	$-0.103549\pi$
$67$	9.36850	+	5.40891i	1.14454	+	0.660803i	0.196993	+	0.980405i	$0.436882\pi$
$68$		0			0
$69$		−	18.9550i		−	2.28191i
$70$		0			0
$71$			12.5157i			1.48534i	0.669660	+	0.742668i	$0.266440\pi$
$71$			12.5157i			1.48534i	−0.669660	+	0.742668i	$0.733560\pi$
$72$		0			0
$73$	−1.23009	+	2.13058i	−0.143971	+	0.249366i	−0.928989	−	0.370108i	$-0.879321\pi$
$73$	−1.23009	+	2.13058i	−0.143971	+	0.249366i	0.785017	+	0.619474i	$0.212654\pi$
$74$		0			0
$75$	−0.405014	+	0.233835i	−0.0467670	+	0.0270009i
$76$		0			0
$77$	−7.42562	−	6.17386i	−0.846228	−	0.703577i
$78$		0			0
$79$	−1.47630	+	0.852345i	−0.166097	+	0.0958963i	−0.580744	−	0.814086i	$-0.697238\pi$
$79$	−1.47630	+	0.852345i	−0.166097	+	0.0958963i	0.414647	+	0.909982i	$0.363905\pi$
$80$		0			0
$81$	−6.96891	+	12.0705i	−0.774324	+	1.34117i
$82$		0			0
$83$	−1.57776			−0.173182			−0.0865908	−	0.996244i	$-0.527597\pi$
$83$	−1.57776			−0.173182			−0.0865908	+	0.996244i	$0.527597\pi$
$84$		0			0
$85$			9.87380i			1.07096i
$86$		0			0
$87$	0.683975	−	1.18468i	0.0733298	−	0.127011i
$88$		0			0
$89$	15.1590	−	8.75205i	1.60685	−	0.927716i	0.616781	−	0.787135i	$-0.288436\pi$
$89$	15.1590	−	8.75205i	1.60685	−	0.927716i	0.990069	−	0.140581i	$-0.0448970\pi$
$90$		0			0
$91$	−0.158061	+	0.920722i	−0.0165693	+	0.0965178i
$92$		0			0
$93$	11.4589	−	6.61582i	1.18824	−	0.686029i
$94$		0			0
$95$	12.9082	+	7.45254i	1.32435	+	0.764615i
$96$		0			0
$97$			15.0452i			1.52761i	0.645450	+	0.763803i	$0.276670\pi$
$97$			15.0452i			1.52761i	−0.645450	+	0.763803i	$0.723330\pi$
$98$		0			0
$99$		−	23.7933i		−	2.39132i
$100$		0			0
$101$	2.65074	+	1.53041i	0.263759	+	0.152281i	0.626048	−	0.779785i	$-0.284671\pi$
$101$	2.65074	+	1.53041i	0.263759	+	0.152281i	−0.362289	+	0.932066i	$0.618005\pi$
$102$		0			0
$103$	3.80895	+	6.59730i	0.375307	+	0.650051i	0.990373	−	0.138425i	$-0.0442039\pi$
$103$	3.80895	+	6.59730i	0.375307	+	0.650051i	−0.615066	+	0.788476i	$0.710871\pi$
$104$		0			0
$105$	−3.04108	+	17.7146i	−0.296779	+	1.72877i
$106$		0			0
$107$	−6.76934	−	11.7248i	−0.654416	−	1.13348i	−0.982040	−	0.188674i	$-0.939581\pi$
$107$	−6.76934	−	11.7248i	−0.654416	−	1.13348i	0.327623	−	0.944808i	$-0.393752\pi$
$108$		0			0
$109$	−3.94788	−	2.27931i	−0.378139	−	0.218318i	0.298870	−	0.954294i	$-0.403390\pi$
$109$	−3.94788	−	2.27931i	−0.378139	−	0.218318i	−0.677008	+	0.735976i	$0.736724\pi$
$110$		0			0
$111$		−	4.50519i		−	0.427613i
$112$		0			0
$113$	0.643235			0.0605104			0.0302552	−	0.999542i	$-0.490368\pi$
$113$	0.643235			0.0605104			0.0302552	+	0.999542i	$0.490368\pi$
$114$		0			0
$115$	6.76399	−	11.7156i	0.630745	−	1.09248i
$116$		0			0
$117$	−1.99334	+	1.15085i	−0.184284	+	0.106397i
$118$		0			0
$119$	−9.12277	−	7.58492i	−0.836283	−	0.695308i
$120$		0			0
$121$	1.16118	+	2.01121i	0.105561	+	0.182838i
$122$		0			0
$123$	−8.09583	+	18.0202i	−0.729976	+	1.62482i
$124$		0			0
$125$	−11.3433			−1.01458
$126$		0			0
$127$	−11.6422			−1.03308			−0.516539	−	0.856264i	$-0.672780\pi$
$127$	−11.6422			−1.03308			−0.516539	+	0.856264i	$0.672780\pi$
$128$		0			0
$129$	18.3346	+	10.5855i	1.61427	+	0.932000i
$130$		0			0
$131$	−1.73254	−	3.00085i	−0.151373	−	0.262185i	0.780360	−	0.625331i	$-0.215036\pi$
$131$	−1.73254	−	3.00085i	−0.151373	−	0.262185i	−0.931732	+	0.363146i	$0.881703\pi$
$132$		0			0
$133$	−16.8016	+	6.20141i	−1.45688	+	0.537731i
$134$		0			0
$135$	−20.7018	+	11.9522i	−1.78173	+	1.02868i
$136$		0			0
$137$	−9.27868	−	5.35705i	−0.792731	−	0.457683i	0.0481921	−	0.998838i	$-0.484654\pi$
$137$	−9.27868	−	5.35705i	−0.792731	−	0.457683i	−0.840923	+	0.541155i	$0.817987\pi$
$138$		0			0
$139$	−11.7524			−0.996824			−0.498412	−	0.866940i	$-0.666083\pi$
$139$	−11.7524			−0.996824			−0.498412	+	0.866940i	$0.666083\pi$
$140$		0			0
$141$	19.0973			1.60829
$142$		0			0
$143$	0.644387	−	1.11611i	0.0538863	−	0.0933339i
$144$		0			0
$145$	0.845495	−	0.488147i	0.0702145	−	0.0405384i
$146$		0			0
$147$	−14.0311	−	16.4179i	−1.15726	−	1.35413i
$148$		0			0
$149$	−16.0374	+	9.25919i	−1.31383	+	0.758542i	−0.982729	−	0.185052i	$-0.940755\pi$
$149$	−16.0374	+	9.25919i	−1.31383	+	0.758542i	−0.331105	+	0.943594i	$0.607421\pi$
$150$		0			0
$151$	−6.70226	−	3.86955i	−0.545422	−	0.314900i	0.201851	−	0.979416i	$-0.435304\pi$
$151$	−6.70226	−	3.86955i	−0.545422	−	0.314900i	−0.747274	+	0.664517i	$0.768638\pi$
$152$		0			0
$153$		−	29.2313i		−	2.36321i
$154$		0			0
$155$	9.44330			0.758504
$156$		0			0
$157$	9.88381	+	5.70642i	0.788814	+	0.455422i	0.839545	−	0.543290i	$-0.182822\pi$
$157$	9.88381	+	5.70642i	0.788814	+	0.455422i	−0.0507309	+	0.998712i	$0.516155\pi$
$158$		0			0
$159$	−17.2156	−	29.8182i	−1.36528	−	2.36474i
$160$		0			0
$161$	5.62845	+	15.2492i	0.443584	+	1.20181i
$162$		0			0
$163$	6.26768	+	10.8559i	0.490923	+	0.850303i	0.999945	−	0.0104499i	$-0.00332635\pi$
$163$	6.26768	+	10.8559i	0.490923	+	0.850303i	−0.509023	+	0.860753i	$0.669993\pi$
$164$		0			0
$165$	12.3980	−	21.4739i	0.965180	−	1.67174i
$166$		0			0
$167$			9.92899i			0.768328i	0.923265	+	0.384164i	$0.125510\pi$
$167$			9.92899i			0.768328i	−0.923265	+	0.384164i	$0.874490\pi$
$168$		0			0
$169$	12.8753			0.990410
$170$		0			0
$171$	−38.2146	−	22.0632i	−2.92234	−	1.68722i
$172$		0			0
$173$	−0.419924	−	0.727330i	−0.0319263	−	0.0552979i	0.849621	−	0.527394i	$-0.176831\pi$
$173$	−0.419924	−	0.727330i	−0.0319263	−	0.0552979i	−0.881547	+	0.472096i	$0.843498\pi$
$174$		0			0
$175$	0.256399	−	0.308384i	0.0193819	−	0.0233117i
$176$		0			0
$177$	−27.4790	+	15.8650i	−2.06545	+	1.19249i
$178$		0			0
$179$	15.3809	+	8.88017i	1.14962	+	0.663735i	0.948795	−	0.315892i	$-0.102304\pi$
$179$	15.3809	+	8.88017i	1.14962	+	0.663735i	0.200827	+	0.979627i	$0.435637\pi$
$180$		0			0
$181$		−	11.6515i		−	0.866049i	−0.901382	−	0.433024i	$-0.857446\pi$
$181$		−	11.6515i		−	0.866049i	0.901382	−	0.433024i	$-0.142554\pi$
$182$		0			0
$183$		−	36.3326i		−	2.68578i
$184$		0			0
$185$	1.60765	−	2.78454i	0.118197	−	0.204723i
$186$		0			0
$187$	8.18361	+	14.1744i	0.598444	+	1.03654i
$188$		0			0
$189$	4.85977	−	28.3087i	0.353496	−	2.05916i
$190$		0			0
$191$	−7.32761	+	4.23060i	−0.530207	+	0.306115i	−0.741101	−	0.671394i	$-0.765696\pi$
$191$	−7.32761	+	4.23060i	−0.530207	+	0.306115i	0.210894	+	0.977509i	$0.432363\pi$
$192$		0			0
$193$	−10.2408	−	5.91251i	−0.737147	−	0.425592i	0.0838843	−	0.996476i	$-0.473267\pi$
$193$	−10.2408	−	5.91251i	−0.737147	−	0.425592i	−0.821031	+	0.570884i	$0.806601\pi$
$194$		0			0
$195$	−2.39870			−0.171775
$196$		0			0
$197$	−1.49928			−0.106819			−0.0534097	−	0.998573i	$-0.517009\pi$
$197$	−1.49928			−0.106819			−0.0534097	+	0.998573i	$0.517009\pi$
$198$		0			0
$199$	2.85211	+	1.64667i	0.202181	+	0.116729i	0.597672	−	0.801740i	$-0.296092\pi$
$199$	2.85211	+	1.64667i	0.202181	+	0.116729i	−0.395491	+	0.918470i	$0.629426\pi$
$200$		0			0
$201$	−16.6878	−	28.9041i	−1.17707	−	2.03874i
$202$		0			0
$203$	−0.198481	+	1.15617i	−0.0139306	+	0.0811473i
$204$		0			0
$205$	−11.4342	+	8.24884i	−0.798602	+	0.576124i
$206$		0			0
$207$	−20.0247	+	34.6839i	−1.39182	+	2.41070i
$208$		0			0
$209$	24.7073			1.70904
$210$		0			0
$211$			8.28479i			0.570348i	0.958476	+	0.285174i	$0.0920514\pi$
$211$			8.28479i			0.570348i	−0.958476	+	0.285174i	$0.907949\pi$
$212$		0			0
$213$	19.3070	−	33.4406i	1.32289	−	2.29131i
$214$		0			0
$215$	7.55477	+	13.0852i	0.515231	+	0.892406i
$216$		0			0
$217$	−7.25421	+	8.72502i	−0.492448	+	0.592293i
$218$		0			0
$219$	6.57337	−	3.79514i	0.444187	−	0.256451i
$220$		0			0
$221$	0.791663	−	1.37120i	0.0532530	−	0.0922370i
$222$		0			0
$223$	−18.8726			−1.26380			−0.631900	−	0.775050i	$-0.717725\pi$
$223$	−18.8726			−1.26380			−0.631900	+	0.775050i	$0.717725\pi$
$224$		0			0
$225$	0.988129			0.0658753
$226$		0			0
$227$	−1.20151	−	0.693691i	−0.0797469	−	0.0460419i	0.459596	−	0.888128i	$-0.347994\pi$
$227$	−1.20151	−	0.693691i	−0.0797469	−	0.0460419i	−0.539343	+	0.842086i	$0.681327\pi$
$228$		0			0
$229$	16.0766	−	9.28180i	1.06237	−	0.613359i	0.136282	−	0.990670i	$-0.456485\pi$
$229$	16.0766	−	9.28180i	1.06237	−	0.613359i	0.926086	+	0.377311i	$0.123151\pi$
$230$		0			0
$231$	10.3166	+	27.9509i	0.678782	+	1.83903i
$232$		0			0
$233$	5.33949	−	3.08276i	0.349802	−	0.201958i	−0.314796	−	0.949159i	$-0.601936\pi$
$233$	5.33949	−	3.08276i	0.349802	−	0.201958i	0.664598	+	0.747201i	$0.268603\pi$
$234$		0			0
$235$	11.8036	+	6.81479i	0.769980	+	0.444548i
$236$		0			0
$237$	5.25939			0.341634
$238$		0			0
$239$			2.10642i			0.136253i	0.997677	+	0.0681265i	$0.0217022\pi$
$239$			2.10642i			0.136253i	−0.997677	+	0.0681265i	$0.978298\pi$
$240$		0			0
$241$	7.58032	−	13.1295i	0.488291	−	0.845746i	−0.511618	−	0.859213i	$-0.670954\pi$
$241$	7.58032	−	13.1295i	0.488291	−	0.845746i	0.999909	+	0.0134675i	$0.00428696\pi$
$242$		0			0
$243$	9.03526	−	5.21651i	0.579612	−	0.334639i
$244$		0			0
$245$	−2.81361	−	15.1544i	−0.179755	−	0.968180i
$246$		0			0
$247$	−1.19506	−	2.06991i	−0.0760400	−	0.131705i
$248$		0			0
$249$	4.21562	+	2.43389i	0.267154	+	0.154242i
$250$		0			0
$251$	−18.6633			−1.17802			−0.589008	−	0.808127i	$-0.700481\pi$
$251$	−18.6633			−1.17802			−0.589008	+	0.808127i	$0.700481\pi$
$252$		0			0
$253$		−	22.4245i		−	1.40982i
$254$		0			0
$255$	15.2316	−	26.3818i	0.953837	−	1.65209i
$256$		0			0
$257$	0.499938	−	0.288639i	0.0311853	−	0.0180048i	−0.484326	−	0.874887i	$-0.660935\pi$
$257$	0.499938	−	0.288639i	0.0311853	−	0.0180048i	0.515512	+	0.856883i	$0.327602\pi$
$258$		0			0
$259$	1.33776	+	3.62442i	0.0831245	+	0.225210i
$260$		0			0
$261$	−2.50308	+	1.44516i	−0.154937	+	0.0894529i
$262$		0			0
$263$	13.0450	+	7.53154i	0.804389	+	0.464414i	0.845004	−	0.534760i	$-0.179598\pi$
$263$	13.0450	+	7.53154i	0.804389	+	0.464414i	−0.0406143	+	0.999175i	$0.512931\pi$
$264$		0			0
$265$		−	24.5732i		−	1.50952i
$266$		0			0
$267$	−54.0045			−3.30502
$268$		0			0
$269$	−13.6509	+	23.6441i	−0.832311	+	1.44160i	0.0638904	+	0.997957i	$0.479649\pi$
$269$	−13.6509	+	23.6441i	−0.832311	+	1.44160i	−0.896201	+	0.443648i	$0.853684\pi$
$270$		0			0
$271$	15.6601	+	27.1240i	0.951281	+	1.64767i	0.742658	+	0.669670i	$0.233565\pi$
$271$	15.6601	+	27.1240i	0.951281	+	1.64767i	0.208622	+	0.977996i	$0.433102\pi$
$272$		0			0
$273$	1.84265	−	2.21625i	0.111522	−	0.134134i
$274$		0			0
$275$	−0.479149	+	0.276637i	−0.0288938	+	0.0166818i
$276$		0			0
$277$	−14.6452	+	25.3663i	−0.879946	+	1.52411i	−0.0285468	+	0.999592i	$0.509088\pi$
$277$	−14.6452	+	25.3663i	−0.879946	+	1.52411i	−0.851399	+	0.524518i	$0.824245\pi$
$278$		0			0
$279$	−27.9568			−1.67373
$280$		0			0
$281$			10.1121i			0.603240i	0.953428	+	0.301620i	$0.0975274\pi$
$281$			10.1121i			0.603240i	−0.953428	+	0.301620i	$0.902473\pi$
$282$		0			0
$283$	−8.19895	+	14.2010i	−0.487377	+	0.844161i	−0.999895	−	0.0145153i	$-0.995379\pi$
$283$	−8.19895	+	14.2010i	−0.487377	+	0.844161i	0.512518	+	0.858677i	$0.328713\pi$
$284$		0			0
$285$	−22.9929	−	39.8249i	−1.36198	−	2.35903i
$286$		0			0
$287$	1.16221	−	16.9012i	0.0686030	−	0.997644i
$288$		0			0
$289$	1.55399	+	2.69159i	0.0914112	+	0.158329i
$290$		0			0
$291$	23.2090	−	40.1992i	1.36054	−	2.35652i
$292$		0			0
$293$			26.6413i			1.55640i	0.628016	+	0.778200i	$0.283867\pi$
$293$			26.6413i			1.55640i	−0.628016	+	0.778200i	$0.716133\pi$
$294$		0			0
$295$	−22.6454			−1.31847
$296$		0			0
$297$	−19.8125	+	34.3162i	−1.14964	+	1.99123i
$298$		0			0
$299$	−1.87867	+	1.08465i	−0.108646	+	0.0627268i
$300$		0			0
$301$	−17.8934	−	3.07177i	−1.03136	−	0.177054i
$302$		0			0
$303$	−4.72168	−	8.17819i	−0.271254	−	0.469825i
$304$		0			0
$305$	12.9651	−	22.4562i	0.742380	−	1.28584i
$306$		0			0
$307$	−19.2979			−1.10139			−0.550696	−	0.834706i	$-0.685638\pi$
$307$	−19.2979			−1.10139			−0.550696	+	0.834706i	$0.685638\pi$
$308$		0			0
$309$		−	23.5031i		−	1.33705i
$310$		0			0
$311$	−2.36240	−	1.36393i	−0.133960	−	0.0773416i	0.431523	−	0.902102i	$-0.357977\pi$
$311$	−2.36240	−	1.36393i	−0.133960	−	0.0773416i	−0.565482	+	0.824761i	$0.691310\pi$
$312$		0			0
$313$	−10.7098	+	6.18329i	−0.605353	+	0.349500i	−0.771144	−	0.636660i	$-0.780315\pi$
$313$	−10.7098	+	6.18329i	−0.605353	+	0.349500i	0.165792	+	0.986161i	$0.446982\pi$
$314$		0			0
$315$	24.2790	−	29.2016i	1.36797	−	1.64532i
$316$		0			0
$317$	−27.9405	+	16.1315i	−1.56930	+	0.906034i	−0.573047	+	0.819523i	$0.694239\pi$
$317$	−27.9405	+	16.1315i	−1.56930	+	0.906034i	−0.996251	+	0.0865117i	$0.972428\pi$
$318$		0			0
$319$	0.809172	−	1.40153i	0.0453049	−	0.0784704i
$320$		0			0
$321$			41.7701i			2.33138i
$322$		0			0
$323$	30.3542			1.68895
$324$		0			0
$325$	0.0463518	+	0.0267612i	0.00257113	+	0.00148445i
$326$		0			0
$327$	7.03224	+	12.1802i	0.388884	+	0.673566i
$328$		0			0
$329$	−15.3638	+	5.67073i	−0.847033	+	0.312637i
$330$		0			0
$331$	20.9546	−	12.0982i	1.15177	−	0.664975i	0.202453	−	0.979292i	$-0.435109\pi$
$331$	20.9546	−	12.0982i	1.15177	−	0.664975i	0.949318	+	0.314317i	$0.101775\pi$
$332$		0			0
$333$	−4.75945	+	8.24361i	−0.260816	+	0.451747i
$334$		0			0
$335$		−	23.8199i		−	1.30142i
$336$		0			0
$337$	−5.11428			−0.278593			−0.139296	−	0.990251i	$-0.544484\pi$
$337$	−5.11428			−0.278593			−0.139296	+	0.990251i	$0.544484\pi$
$338$		0			0
$339$	−1.71866	−	0.992269i	−0.0933448	−	0.0538927i
$340$		0			0
$341$	13.5564	−	7.82680i	0.734121	−	0.423845i
$342$		0			0
$343$	16.1631	+	9.04181i	0.872725	+	0.488212i
$344$		0			0
$345$	−36.1454	+	20.8686i	−1.94600	+	1.12353i
$346$		0			0
$347$	−28.2404	−	16.3046i	−1.51603	−	0.875278i	−0.999823	−	0.0188119i	$-0.994012\pi$
$347$	−28.2404	−	16.3046i	−1.51603	−	0.875278i	−0.516203	−	0.856466i	$-0.672655\pi$
$348$		0			0
$349$	29.5204			1.58019			0.790094	−	0.612986i	$-0.210032\pi$
$349$	29.5204			1.58019			0.790094	+	0.612986i	$0.210032\pi$
$350$		0			0
$351$	3.83322			0.204602
$352$		0			0
$353$	−7.04235	+	12.1977i	−0.374827	+	0.649219i	−0.990301	−	0.138938i	$-0.955631\pi$
$353$	−7.04235	+	12.1977i	−0.374827	+	0.649219i	0.615474	+	0.788157i	$0.288964\pi$
$354$		0			0
$355$	23.8663	−	13.7792i	1.26669	−	0.731324i
$356$		0			0
$357$	12.6745	+	34.3391i	0.670805	+	1.81742i
$358$		0			0
$359$	10.9820	+	19.0214i	0.579610	+	1.00391i	0.995524	+	0.0945096i	$0.0301283\pi$
$359$	10.9820	+	19.0214i	0.579610	+	1.00391i	−0.415914	+	0.909404i	$0.636538\pi$
$360$		0			0
$361$	13.4107	−	23.2281i	0.705829	−	1.22253i
$362$		0			0
$363$		−	7.16502i		−	0.376066i
$364$		0			0
$365$	5.41711			0.283544
$366$		0			0
$367$	6.32376	−	10.9531i	0.330097	−	0.571745i	−0.652433	−	0.757846i	$-0.726252\pi$
$367$	6.32376	−	10.9531i	0.330097	−	0.571745i	0.982531	+	0.186101i	$0.0595851\pi$
$368$		0			0
$369$	33.8510	−	24.4206i	1.76221	−	1.27129i
$370$		0			0
$371$	22.7041	+	18.8768i	1.17874	+	0.980033i
$372$		0			0
$373$	0.728596	+	1.26197i	0.0377253	+	0.0653421i	0.884272	−	0.466973i	$-0.154655\pi$
$373$	0.728596	+	1.26197i	0.0377253	+	0.0653421i	−0.846546	+	0.532315i	$0.821322\pi$
$374$		0			0
$375$	30.3083	+	17.4985i	1.56511	+	0.903618i
$376$		0			0
$377$	−0.156555			−0.00806299
$378$		0			0
$379$	−15.4850			−0.795410			−0.397705	−	0.917513i	$-0.630193\pi$
$379$	−15.4850			−0.795410			−0.397705	+	0.917513i	$0.630193\pi$
$380$		0			0
$381$	31.1068	+	17.9595i	1.59365	+	0.920095i
$382$		0			0
$383$	14.5637	−	8.40835i	0.744170	−	0.429647i	−0.0794136	−	0.996842i	$-0.525305\pi$
$383$	14.5637	−	8.40835i	0.744170	−	0.429647i	0.823583	+	0.567195i	$0.191971\pi$
$384$		0			0
$385$	−3.59773	+	20.9572i	−0.183357	+	1.06808i
$386$		0			0
$387$	−22.3658	−	38.7388i	−1.13692	−	1.96920i
$388$		0			0
$389$	16.4452	−	28.4839i	0.833803	−	1.44419i	−0.0611984	−	0.998126i	$-0.519492\pi$
$389$	16.4452	−	28.4839i	0.833803	−	1.44419i	0.895001	−	0.446063i	$-0.147174\pi$
$390$		0			0
$391$		−	27.5497i		−	1.39325i
$392$		0			0
$393$			10.6906i			0.539271i
$394$		0			0
$395$	3.25069	+	1.87679i	0.163560	+	0.0944315i
$396$		0			0
$397$	−18.1591	+	10.4842i	−0.911380	+	0.526185i	−0.880875	−	0.473349i	$-0.843045\pi$
$397$	−18.1591	+	10.4842i	−0.911380	+	0.526185i	−0.0305048	+	0.999535i	$0.509711\pi$
$398$		0			0
$399$	54.4586	+	9.34893i	2.72634	+	0.468032i
$400$		0			0
$401$	−18.1720	−	31.4748i	−0.907466	−	1.57178i	−0.817572	−	0.575826i	$-0.804680\pi$
$401$	−18.1720	−	31.4748i	−0.907466	−	1.57178i	−0.0898942	−	0.995951i	$-0.528653\pi$
$402$		0			0
$403$	−1.31142	−	0.757147i	−0.0653263	−	0.0377162i
$404$		0			0
$405$	30.6899			1.52499
$406$		0			0
$407$		−	5.32983i		−	0.264190i
$408$		0			0
$409$	−13.8339	+	23.9611i	−0.684043	+	1.18480i	0.289693	+	0.957120i	$0.406447\pi$
$409$	−13.8339	+	23.9611i	−0.684043	+	1.18480i	−0.973736	+	0.227678i	$0.926887\pi$
$410$		0			0
$411$	16.5278	+	28.6270i	0.815257	+	1.41207i
$412$		0			0
$413$	17.3959	−	20.9230i	0.855997	−	1.02955i
$414$		0			0
$415$	1.73704	+	3.00865i	0.0852682	+	0.147689i
$416$		0			0
$417$	31.4012	+	18.1295i	1.53772	+	0.887806i
$418$		0			0
$419$	5.83932			0.285270			0.142635	−	0.989775i	$-0.454443\pi$
$419$	5.83932			0.285270			0.142635	+	0.989775i	$0.454443\pi$
$420$		0			0
$421$			18.3691i			0.895254i	0.894220	+	0.447627i	$0.147731\pi$
$421$			18.3691i			0.895254i	−0.894220	+	0.447627i	$0.852269\pi$
$422$		0			0
$423$	−34.9444	−	20.1752i	−1.69905	−	0.980950i
$424$		0			0
$425$	−0.588660	+	0.339863i	−0.0285542	+	0.0164858i
$426$		0			0
$427$	10.7885	+	29.2295i	0.522093	+	1.41452i
$428$		0			0
$429$	−3.44348	+	1.98809i	−0.166253	+	0.0959860i
$430$		0			0
$431$	−4.62032	+	8.00263i	−0.222553	+	0.385473i	−0.955583	−	0.294724i	$-0.904772\pi$
$431$	−4.62032	+	8.00263i	−0.222553	+	0.385473i	0.733029	+	0.680197i	$0.238106\pi$
$432$		0			0
$433$	−33.1993			−1.59545			−0.797727	−	0.603019i	$-0.793964\pi$
$433$	−33.1993			−1.59545			−0.797727	+	0.603019i	$0.793964\pi$
$434$		0			0
$435$	−3.01211			−0.144419
$436$		0			0
$437$	−36.0162	−	20.7940i	−1.72289	−	0.994710i
$438$		0			0
$439$	−6.49173	+	3.74800i	−0.309833	+	0.178882i	−0.646852	−	0.762616i	$-0.723915\pi$
$439$	−6.49173	+	3.74800i	−0.309833	+	0.178882i	0.337019	+	0.941498i	$0.390581\pi$
$440$		0			0
$441$	8.32966	+	44.8645i	0.396651	+	2.13641i
$442$		0			0
$443$	−15.5961	−	27.0133i	−0.740995	−	1.28344i	−0.952043	−	0.305966i	$-0.901021\pi$
$443$	−15.5961	−	27.0133i	−0.740995	−	1.28344i	0.211047	−	0.977476i	$-0.432313\pi$
$444$		0			0
$445$	−33.3788	−	19.2712i	−1.58231	−	0.913545i
$446$		0			0
$447$	57.1337			2.70233
$448$		0			0
$449$	−15.7738			−0.744409			−0.372205	−	0.928151i	$-0.621398\pi$
$449$	−15.7738			−0.744409			−0.372205	+	0.928151i	$0.621398\pi$
$450$		0			0
$451$	−9.57771	+	21.3186i	−0.450997	+	1.00385i
$452$		0			0
$453$	11.9385	+	20.6781i	0.560921	+	0.971543i
$454$		0			0
$455$	1.92975	−	0.712266i	0.0904682	−	0.0333916i
$456$		0			0
$457$	−25.1813	+	14.5384i	−1.17793	+	0.680078i	−0.955535	−	0.294878i	$-0.904721\pi$
$457$	−25.1813	+	14.5384i	−1.17793	+	0.680078i	−0.222395	+	0.974957i	$0.571388\pi$
$458$		0			0
$459$	−24.3407	+	42.1593i	−1.13612	+	1.96783i
$460$		0			0
$461$	5.50886			0.256573			0.128286	−	0.991737i	$-0.459052\pi$
$461$	5.50886			0.256573			0.128286	+	0.991737i	$0.459052\pi$
$462$		0			0
$463$			3.43337i			0.159562i	0.996812	+	0.0797810i	$0.0254221\pi$
$463$			3.43337i			0.159562i	−0.996812	+	0.0797810i	$0.974578\pi$
$464$		0			0
$465$	−25.2316	−	14.5675i	−1.17009	−	0.675550i
$466$		0			0
$467$	−2.28786	−	3.96269i	−0.105870	−	0.183372i	0.808224	−	0.588876i	$-0.200429\pi$
$467$	−2.28786	−	3.96269i	−0.105870	−	0.183372i	−0.914093	+	0.405504i	$0.867096\pi$
$468$		0			0
$469$	22.0081	+	18.2981i	1.01624	+	0.844928i
$470$		0			0
$471$	−17.6057	−	30.4940i	−0.811229	−	1.40509i
$472$		0			0
$473$	21.6906	+	12.5231i	0.997336	+	0.575812i
$474$		0			0
$475$			1.02609i			0.0470801i
$476$		0			0
$477$			72.7487i			3.33094i
$478$		0			0
$479$	5.67862	+	3.27856i	0.259463	+	0.149801i	0.624090	−	0.781353i	$-0.285470\pi$
$479$	5.67862	+	3.27856i	0.259463	+	0.149801i	−0.364627	+	0.931154i	$0.618803\pi$
$480$		0			0
$481$	−0.446519	+	0.257798i	−0.0203595	+	0.0117546i
$482$		0			0
$483$	8.48516	−	49.4271i	0.386088	−	2.24901i
$484$		0			0
$485$	28.6898	−	16.5641i	1.30274	−	0.752136i
$486$		0			0
$487$	16.6579	−	28.8523i	0.754842	−	1.30742i	−0.190611	−	0.981666i	$-0.561047\pi$
$487$	16.6579	−	28.8523i	0.754842	−	1.30742i	0.945453	−	0.325759i	$-0.105620\pi$
$488$		0			0
$489$		−	38.6747i		−	1.74893i
$490$		0			0
$491$	13.7108			0.618760			0.309380	−	0.950939i	$-0.399879\pi$
$491$	13.7108			0.618760			0.309380	+	0.950939i	$0.399879\pi$
$492$		0			0
$493$	0.994110	−	1.72185i	0.0447725	−	0.0775482i
$494$		0			0
$495$	−45.3717	+	26.1954i	−2.03931	+	1.17739i
$496$		0			0
$497$	−5.60262	+	32.6359i	−0.251312	+	1.46392i
$498$		0			0
$499$	27.6743	−	15.9778i	1.23887	−	0.715264i	0.270009	−	0.962858i	$-0.412973\pi$
$499$	27.6743	−	15.9778i	1.23887	−	0.715264i	0.968864	+	0.247594i	$0.0796399\pi$
$500$		0			0
$501$	15.3167	−	26.5293i	0.684299	−	1.18524i
$502$		0			0
$503$		−	7.02693i		−	0.313315i	−0.987653	−	0.156658i	$-0.949928\pi$
$503$		−	7.02693i		−	0.313315i	0.987653	−	0.156658i	$-0.0500719\pi$
$504$		0			0
$505$		−	6.73964i		−	0.299910i
$506$		0			0
$507$	−34.4016	−	19.8618i	−1.52783	−	0.882093i
$508$		0			0
$509$	−30.6836	+	17.7152i	−1.36003	+	0.785213i	−0.989627	−	0.143659i	$-0.954113\pi$
$509$	−30.6836	+	17.7152i	−1.36003	+	0.785213i	−0.370402	+	0.928872i	$0.620780\pi$
$510$		0			0
$511$	−4.16135	+	5.00507i	−0.184087	+	0.221411i
$512$		0			0
$513$	36.7437	+	63.6419i	1.62227	+	2.80986i
$514$		0			0
$515$	8.38698	−	14.5267i	0.369574	−	0.640122i
$516$		0			0
$517$	22.5930			0.993637
$518$		0			0
$519$			2.59114i			0.113738i
$520$		0			0
$521$	−27.3229	−	15.7749i	−1.19704	−	0.691109i	−0.237143	−	0.971475i	$-0.576211\pi$
$521$	−27.3229	−	15.7749i	−1.19704	−	0.691109i	−0.959893	+	0.280365i	$0.909544\pi$
$522$		0			0
$523$	−5.13477	−	8.89368i	−0.224528	−	0.388893i	0.731650	−	0.681681i	$-0.238751\pi$
$523$	−5.13477	−	8.89368i	−0.224528	−	0.388893i	−0.956178	+	0.292787i	$0.905417\pi$
$524$		0			0
$525$	−1.16079	+	0.428445i	−0.0506612	+	0.0186989i
$526$		0			0
$527$	16.6548	−	9.61564i	0.725493	−	0.418864i
$528$		0			0
$529$	−7.37277	+	12.7700i	−0.320555	+	0.555218i
$530$		0			0
$531$	67.0417			2.90936
$532$		0			0
$533$	2.24928	−	0.228763i	0.0974272	−	0.00990881i
$534$		0			0
$535$	−14.9055	+	25.8171i	−0.644420	+	1.11617i
$536$		0			0
$537$	−27.3975	−	47.4539i	−1.18229	−	2.04779i
$538$		0			0
$539$	−16.5994	−	19.4231i	−0.714986	−	0.836611i
$540$		0			0
$541$	−2.45504	−	4.25226i	−0.105551	−	0.182819i	0.808412	−	0.588616i	$-0.200327\pi$
$541$	−2.45504	−	4.25226i	−0.105551	−	0.182819i	−0.913963	+	0.405798i	$0.866994\pi$
$542$		0			0
$543$	−17.9739	+	31.1316i	−0.771332	+	1.33599i
$544$		0			0
$545$			10.0377i			0.429967i
$546$		0			0
$547$			16.8764i			0.721584i	0.932646	+	0.360792i	$0.117493\pi$
$547$			16.8764i			0.721584i	−0.932646	+	0.360792i	$0.882507\pi$
$548$		0			0
$549$	−38.3831	+	66.4815i	−1.63815	+	2.83736i
$550$		0			0
$551$	−1.50067	−	2.59923i	−0.0639306	−	0.110731i
$552$		0			0
$553$	−4.23117	+	1.56171i	−0.179928	+	0.0664108i
$554$		0			0
$555$	−8.59099	+	4.96001i	−0.364667	+	0.210541i
$556$		0			0
$557$	6.00870	+	3.46912i	0.254597	+	0.146991i	0.621867	−	0.783123i	$-0.286374\pi$
$557$	6.00870	+	3.46912i	0.254597	+	0.146991i	−0.367271	+	0.930114i	$0.619708\pi$
$558$		0			0
$559$		−	2.42291i		−	0.102478i
$560$		0			0
$561$		−	50.4969i		−	2.13198i
$562$		0			0
$563$	3.54394	+	2.04610i	0.149359	+	0.0862326i	0.572817	−	0.819683i	$-0.305850\pi$
$563$	3.54394	+	2.04610i	0.149359	+	0.0862326i	−0.423458	+	0.905916i	$0.639184\pi$
$564$		0			0
$565$	−0.708173	−	1.22659i	−0.0297931	−	0.0516031i
$566$		0			0
$567$	−23.5755	+	28.3555i	−0.990079	+	1.19082i
$568$		0			0
$569$	−10.3866	−	17.9902i	−0.435431	−	0.754188i	0.561900	−	0.827205i	$-0.310071\pi$
$569$	−10.3866	−	17.9902i	−0.435431	−	0.754188i	−0.997331	+	0.0730169i	$0.976737\pi$
$570$		0			0
$571$	−24.8882	−	14.3692i	−1.04154	−	0.601333i	−0.121270	−	0.992620i	$-0.538697\pi$
$571$	−24.8882	−	14.3692i	−1.04154	−	0.601333i	−0.920269	+	0.391287i	$0.872030\pi$
$572$		0			0
$573$	26.1049			1.09055
$574$		0			0
$575$	0.931285			0.0388372
$576$		0			0
$577$	−8.33918	−	4.81463i	−0.347165	−	0.200436i	0.316271	−	0.948669i	$-0.397569\pi$
$577$	−8.33918	−	4.81463i	−0.347165	−	0.200436i	−0.663436	+	0.748233i	$0.730902\pi$
$578$		0			0
$579$	18.2416	+	31.5953i	0.758093	+	1.31306i
$580$		0			0
$581$	−4.11418	−	0.706283i	−0.170685	−	0.0293015i
$582$		0			0
$583$	−20.3667	−	35.2762i	−0.843505	−	1.46099i
$584$		0			0
$585$	4.38916	+	2.53408i	0.181469	+	0.104771i
$586$		0			0
$587$			12.3233i			0.508637i	0.967120	+	0.254319i	$0.0818512\pi$
$587$			12.3233i			0.508637i	−0.967120	+	0.254319i	$0.918149\pi$
$588$		0			0
$589$		−	29.0308i		−	1.19619i
$590$		0			0
$591$	4.00593	+	2.31283i	0.164782	+	0.0951370i
$592$		0			0
$593$	−0.787934	+	0.454914i	−0.0323566	+	0.0186811i	−0.516091	−	0.856534i	$-0.672613\pi$
$593$	−0.787934	+	0.454914i	−0.0323566	+	0.0186811i	0.483734	+	0.875215i	$0.339280\pi$
$594$		0			0
$595$	−4.42000	+	25.7470i	−0.181202	+	1.05552i
$596$		0			0
$597$	−5.08037	−	8.79947i	−0.207926	−	0.360138i
$598$		0			0
$599$	−7.72441	+	13.3791i	−0.315611	+	0.546654i	−0.979567	−	0.201117i	$-0.935543\pi$
$599$	−7.72441	+	13.3791i	−0.315611	+	0.546654i	0.663956	+	0.747771i	$0.268876\pi$
$600$		0			0
$601$		−	37.8156i		−	1.54253i	−0.636514	−	0.771265i	$-0.719624\pi$
$601$		−	37.8156i		−	1.54253i	0.636514	−	0.771265i	$-0.280376\pi$
$602$		0			0
$603$			70.5186i			2.87174i
$604$		0			0
$605$	2.55681	−	4.42852i	0.103949	−	0.180045i
$606$		0			0
$607$	−0.581403	−	1.00702i	−0.0235984	−	0.0408737i	0.853985	−	0.520298i	$-0.174179\pi$
$607$	−0.581403	−	1.00702i	−0.0235984	−	0.0408737i	−0.877583	+	0.479424i	$0.840846\pi$
$608$		0			0
$609$	2.31386	−	2.78300i	0.0937623	−	0.112773i
$610$		0			0
$611$	−1.09280	−	1.89278i	−0.0442098	−	0.0765736i
$612$		0			0
$613$	−6.63135	+	11.4858i	−0.267838	+	0.463908i	−0.968303	−	0.249778i	$-0.919642\pi$
$613$	−6.63135	+	11.4858i	−0.267838	+	0.463908i	0.700465	+	0.713686i	$0.252976\pi$
$614$		0			0
$615$	43.2760	−	4.40138i	1.74506	−	0.177481i
$616$		0			0
$617$	19.9252			0.802158			0.401079	−	0.916044i	$-0.368635\pi$
$617$	19.9252			0.802158			0.401079	+	0.916044i	$0.368635\pi$
$618$		0			0
$619$	20.3345	−	35.2203i	0.817311	−	1.41562i	−0.0903459	−	0.995910i	$-0.528797\pi$
$619$	20.3345	−	35.2203i	0.817311	−	1.41562i	0.907657	−	0.419713i	$-0.137869\pi$
$620$		0			0
$621$	57.7619	−	33.3488i	2.31790	−	1.33824i
$622$		0			0
$623$	43.4465	−	16.0360i	1.74065	−	0.642469i
$624$		0			0
$625$	12.1096	+	20.9744i	0.484382	+	0.838975i
$626$		0			0
$627$	−66.0154	−	38.1140i	−2.63640	−	1.52213i
$628$		0			0
$629$		−	6.54797i		−	0.261085i
$630$		0			0
$631$	17.4244			0.693655			0.346828	−	0.937929i	$-0.387259\pi$
$631$	17.4244			0.693655			0.346828	+	0.937929i	$0.387259\pi$
$632$		0			0
$633$	12.7803	−	22.1361i	0.507972	−	0.879833i
$634$		0			0
$635$	12.8176	+	22.2007i	0.508649	+	0.881006i
$636$		0			0
$637$	−0.824320	+	2.33012i	−0.0326608	+	0.0923229i
$638$		0			0
$639$	−70.6559	+	40.7932i	−2.79511	+	1.61375i
$640$		0			0
$641$	1.01731	+	0.587342i	0.0401812	+	0.0231986i	0.519956	−	0.854193i	$-0.325948\pi$
$641$	1.01731	+	0.587342i	0.0401812	+	0.0231986i	−0.479775	+	0.877392i	$0.659282\pi$
$642$		0			0
$643$			38.7130i			1.52669i	0.645989	+	0.763347i	$0.276445\pi$
$643$			38.7130i			1.52669i	−0.645989	+	0.763347i	$0.723555\pi$
$644$		0			0
$645$		−	46.6166i		−	1.83553i
$646$		0			0
$647$	12.2559	−	21.2278i	0.481828	−	0.834551i	−0.517954	−	0.855408i	$-0.673306\pi$
$647$	12.2559	−	21.2278i	0.481828	−	0.834551i	0.999782	+	0.0208572i	$0.00663952\pi$
$648$		0			0
$649$	−32.5089	+	18.7690i	−1.27608	+	0.736748i
$650$		0			0
$651$	32.8420	−	12.1219i	1.28718	−	0.475094i
$652$		0			0
$653$	3.37942	−	1.95111i	0.132247	−	0.0763527i	−0.432417	−	0.901674i	$-0.642339\pi$
$653$	3.37942	−	1.95111i	0.132247	−	0.0763527i	0.564664	+	0.825321i	$0.309006\pi$
$654$		0			0
$655$	−3.81490	+	6.60761i	−0.149061	+	0.258181i
$656$		0			0
$657$	−16.0373			−0.625675
$658$		0			0
$659$		−	0.994257i		−	0.0387308i	−0.999812	−	0.0193654i	$-0.993835\pi$
$659$		−	0.994257i		−	0.0387308i	0.999812	−	0.0193654i	$-0.00616458\pi$
$660$		0			0
$661$	−22.9645	+	39.7757i	−0.893217	+	1.54710i	−0.0572208	+	0.998362i	$0.518224\pi$
$661$	−22.9645	+	39.7757i	−0.893217	+	1.54710i	−0.835996	+	0.548735i	$0.815109\pi$
$662$		0			0
$663$	−4.23049	+	2.44248i	−0.164299	+	0.0948579i
$664$		0			0
$665$	30.3233	+	25.2116i	1.17589	+	0.977665i
$666$		0			0
$667$	−2.35909	+	1.36202i	−0.0913442	+	0.0527376i
$668$		0			0
$669$	50.4256	+	29.1132i	1.94957	+	1.12558i
$670$		0			0
$671$		−	42.9830i		−	1.65934i
$672$		0			0
$673$		−	42.9532i		−	1.65573i	−0.560930	−	0.827863i	$-0.689556\pi$
$673$		−	42.9532i		−	1.65573i	0.560930	−	0.827863i	$-0.310444\pi$
$674$		0			0
$675$	−1.42514	−	0.822806i	−0.0548538	−	0.0316698i
$676$		0			0
$677$	18.4167	+	31.8987i	0.707813	+	1.22597i	0.965667	+	0.259784i	$0.0836515\pi$
$677$	18.4167	+	31.8987i	0.707813	+	1.22597i	−0.257854	+	0.966184i	$0.583015\pi$
$678$		0			0
$679$	−6.73496	+	39.2319i	−0.258464	+	1.50558i
$680$		0			0
$681$	2.14021	+	3.70695i	0.0820130	+	0.142051i
$682$		0			0
$683$	30.4639	+	17.5883i	1.16567	+	0.672999i	0.952656	−	0.304051i	$-0.0983392\pi$
$683$	30.4639	+	17.5883i	1.16567	+	0.672999i	0.213012	+	0.977049i	$0.431673\pi$
$684$		0			0
$685$			23.5915i			0.901385i
$686$		0			0
$687$	−57.2733			−2.18511
$688$		0			0
$689$	−1.97023	+	3.41254i	−0.0750599	+	0.130008i
$690$		0			0
$691$	−3.36680	+	1.94382i	−0.128079	+	0.0739466i	−0.562671	−	0.826681i	$-0.690226\pi$
$691$	−3.36680	+	1.94382i	−0.128079	+	0.0739466i	0.434591	+	0.900628i	$0.356893\pi$
$692$		0			0
$693$	10.6510	−	62.0435i	0.404600	−	2.35684i
$694$		0			0
$695$	12.9389	+	22.4108i	0.490799	+	0.850089i
$696$		0			0
$697$	−11.7667	+	26.1911i	−0.445696	+	0.992057i
$698$		0			0
$699$	−19.0221			−0.719483
$700$		0			0
$701$	−3.09568			−0.116922			−0.0584611	−	0.998290i	$-0.518619\pi$
$701$	−3.09568			−0.116922			−0.0584611	+	0.998290i	$0.518619\pi$
$702$		0			0
$703$	−8.56028	−	4.94228i	−0.322857	−	0.186402i
$704$		0			0
$705$	−21.0253	−	36.4169i	−0.791860	−	1.37154i
$706$		0			0
$707$	6.22701	+	5.17730i	0.234191	+	0.194712i
$708$		0			0
$709$	22.1444	−	12.7851i	0.831650	−	0.480153i	−0.0227676	−	0.999741i	$-0.507248\pi$
$709$	22.1444	−	12.7851i	0.831650	−	0.480153i	0.854417	+	0.519588i	$0.173914\pi$
$710$		0			0
$711$	−9.62366	−	5.55622i	−0.360915	−	0.208375i
$712$		0			0
$713$	−26.3485			−0.986761
$714$		0			0
$715$	−2.83777			−0.106126
$716$		0			0
$717$	3.24942	−	5.62815i	0.121352	−	0.210187i
$718$		0			0
$719$	12.2466	−	7.07060i	0.456723	−	0.263689i	−0.253943	−	0.967219i	$-0.581727\pi$
$719$	12.2466	−	7.07060i	0.456723	−	0.263689i	0.710665	+	0.703530i	$0.248394\pi$
$720$		0			0
$721$	6.97897	+	18.9082i	0.259911	+	0.704179i
$722$		0			0
$723$	−40.5078	+	23.3872i	−1.50650	+	0.869778i
$724$		0			0
$725$	0.0582050	+	0.0336047i	0.00216168	+	0.00124805i
$726$		0			0
$727$		−	45.4858i		−	1.68697i	−0.537149	−	0.843487i	$-0.680499\pi$
$727$		−	45.4858i		−	1.68697i	0.537149	−	0.843487i	$-0.319501\pi$
$728$		0			0
$729$	9.62503			0.356483
$730$		0			0
$731$	26.6481	+	15.3853i	0.985615	+	0.569045i
$732$		0			0
$733$	6.14908	+	10.6505i	0.227121	+	0.393386i	0.956954	−	0.290240i	$-0.0937352\pi$
$733$	6.14908	+	10.6505i	0.227121	+	0.393386i	−0.729832	+	0.683626i	$0.760402\pi$
$734$		0			0
$735$	−15.8599	+	44.8314i	−0.585000	+	1.65363i
$736$		0			0
$737$	−19.7424	−	34.1948i	−0.727221	−	1.25958i
$738$		0			0
$739$	4.97466	−	8.61637i	0.182996	−	0.316958i	−0.759903	−	0.650036i	$-0.774754\pi$
$739$	4.97466	−	8.61637i	0.182996	−	0.316958i	0.942899	+	0.333078i	$0.108087\pi$
$740$		0			0
$741$			7.37413i			0.270895i
$742$		0			0
$743$	−34.5550			−1.26770			−0.633849	−	0.773456i	$-0.718526\pi$
$743$	−34.5550			−1.26770			−0.633849	+	0.773456i	$0.718526\pi$
$744$		0			0
$745$	35.3129	+	20.3879i	1.29376	+	0.746955i
$746$		0			0
$747$	−5.14251	−	8.90709i	−0.188155	−	0.325893i
$748$		0			0
$749$	−12.4032	−	33.6040i	−0.453201	−	1.22786i
$750$		0			0
$751$	−26.0938	+	15.0653i	−0.952176	+	0.549739i	−0.893756	−	0.448553i	$-0.851940\pi$
$751$	−26.0938	+	15.0653i	−0.952176	+	0.549739i	−0.0584200	+	0.998292i	$0.518606\pi$
$752$		0			0
$753$	49.8664	+	28.7904i	1.81723	+	1.04918i
$754$		0			0
$755$			17.0408i			0.620179i
$756$		0			0
$757$			25.4331i			0.924380i	0.886781	+	0.462190i	$0.152936\pi$
$757$			25.4331i			0.924380i	−0.886781	+	0.462190i	$0.847064\pi$
$758$		0			0
$759$	−34.5926	+	59.9161i	−1.25563	+	2.17482i
$760$		0			0
$761$	11.7092	+	20.2809i	0.424457	+	0.735181i	0.996370	−	0.0851335i	$-0.0271317\pi$
$761$	11.7092	+	20.2809i	0.424457	+	0.735181i	−0.571913	+	0.820315i	$0.693798\pi$
$762$		0			0
$763$	−9.27419	−	7.71081i	−0.335748	−	0.279150i
$764$		0			0
$765$	−55.7415	+	32.1824i	−2.01534	+	1.16356i
$766$		0			0
$767$	3.14483	+	1.81567i	0.113553	+	0.0655601i
$768$		0			0
$769$	−28.7089			−1.03527			−0.517634	−	0.855602i	$-0.673187\pi$
$769$	−28.7089			−1.03527			−0.517634	+	0.855602i	$0.673187\pi$
$770$		0			0
$771$	−1.78105			−0.0641428
$772$		0			0
$773$	−3.81317	−	2.20153i	−0.137150	−	0.0791837i	0.429855	−	0.902898i	$-0.358565\pi$
$773$	−3.81317	−	2.20153i	−0.137150	−	0.0791837i	−0.567005	+	0.823714i	$0.691898\pi$
$774$		0			0
$775$	0.325045	+	0.562994i	0.0116760	+	0.0202234i
$776$		0			0
$777$	2.01674	−	11.7477i	0.0723502	−	0.421448i
$778$		0			0
$779$	25.3587	+	35.1513i	0.908571	+	1.25943i
$780$		0			0
$781$	22.8410	−	39.5617i	0.817314	−	1.41563i
$782$		0			0
$783$	4.81347			0.172019
$784$		0			0
$785$		−	25.1301i		−	0.896931i
$786$		0			0
$787$	−17.1731	+	29.7448i	−0.612157	+	1.06029i	0.378720	+	0.925511i	$0.376364\pi$
$787$	−17.1731	+	29.7448i	−0.612157	+	1.06029i	−0.990876	+	0.134775i	$0.956969\pi$
$788$		0			0
$789$	−23.2366	−	40.2471i	−0.827247	−	1.43283i
$790$		0			0
$791$	1.67730	+	0.287943i	0.0596380	+	0.0102381i
$792$		0			0
$793$	−3.60100	+	2.07904i	−0.127875	+	0.0738288i
$794$		0			0
$795$	−37.9072	+	65.6571i	−1.34443	+	2.32862i
$796$		0			0
$797$	−32.9362			−1.16666			−0.583330	−	0.812235i	$-0.698251\pi$
$797$	−32.9362			−1.16666			−0.583330	+	0.812235i	$0.698251\pi$
$798$		0			0
$799$	27.7566			0.981960
$800$		0			0
$801$	98.8177	+	57.0524i	3.49155	+	2.01585i
$802$		0			0
$803$	7.77658	−	4.48981i	0.274429	−	0.158442i
$804$		0			0
$805$	22.8823	−	27.5217i	0.806494	−	0.970012i
$806$		0			0
$807$	72.9478	−	42.1164i	2.56788	−	1.48257i
$808$		0			0
$809$	−32.4905	−	18.7584i	−1.14230	−	0.659510i	−0.195304	−	0.980743i	$-0.562569\pi$
$809$	−32.4905	−	18.7584i	−1.14230	−	0.659510i	−0.947000	+	0.321233i	$0.895903\pi$
$810$		0			0
$811$	−10.3349			−0.362908			−0.181454	−	0.983399i	$-0.558080\pi$
$811$	−10.3349			−0.362908			−0.181454	+	0.983399i	$0.558080\pi$
$812$		0			0
$813$		−	96.6303i		−	3.38897i
$814$		0			0
$815$	13.8009	−	23.9038i	0.483424	−	0.837315i
$816$		0			0
$817$	40.2269	−	23.2250i	1.40736	−	0.812540i
$818$		0			0
$819$	−5.71302	+	2.10866i	−0.199629	+	0.0736825i
$820$		0			0
$821$	−13.9409	−	24.1464i	−0.486541	−	0.842714i	0.513339	−	0.858186i	$-0.328408\pi$
$821$	−13.9409	−	24.1464i	−0.486541	−	0.842714i	−0.999880	+	0.0154718i	$0.995075\pi$
$822$		0			0
$823$	29.9752	+	17.3062i	1.04487	+	0.603255i	0.921208	−	0.389070i	$-0.127203\pi$
$823$	29.9752	+	17.3062i	1.04487	+	0.603255i	0.123660	+	0.992325i	$0.460537\pi$
$824$		0			0
$825$	1.70699			0.0594296
$826$		0			0
$827$			14.1260i			0.491211i	0.969370	+	0.245605i	$0.0789867\pi$
$827$			14.1260i			0.491211i	−0.969370	+	0.245605i	$0.921013\pi$
$828$		0			0
$829$	−12.1560	+	21.0548i	−0.422195	+	0.731263i	−0.996154	−	0.0876213i	$-0.972073\pi$
$829$	−12.1560	+	21.0548i	−0.422195	+	0.731263i	0.573959	+	0.818884i	$0.305407\pi$
$830$		0			0
$831$	78.2612	−	45.1841i	2.71485	−	1.56742i
$832$		0			0
$833$	−20.3932	−	23.8623i	−0.706583	−	0.826779i
$834$		0			0
$835$	18.9337	−	10.9314i	0.655228	−	0.378296i
$836$		0			0
$837$	40.3211	+	23.2794i	1.39370	+	0.804654i
$838$		0			0
$839$			30.5112i			1.05336i	0.850063	+	0.526682i	$0.176564\pi$
$839$			30.5112i			1.05336i	−0.850063	+	0.526682i	$0.823436\pi$
$840$		0			0
$841$	28.8034			0.993221
$842$		0			0
$843$	15.5992	−	27.0187i	0.537266	−	0.930572i
$844$		0			0
$845$	−14.1752	−	24.5521i	−0.487641	−	0.844618i
$846$		0			0
$847$	2.12757	+	5.76425i	0.0731042	+	0.198062i
$848$		0			0
$849$	43.8136	−	25.2958i	1.50368	−	0.868149i
$850$		0			0
$851$	−4.48565	+	7.76938i	−0.153766	+	0.266331i
$852$		0			0
$853$	48.8989			1.67427			0.837133	−	0.547000i	$-0.184230\pi$
$853$	48.8989			1.67427			0.837133	+	0.547000i	$0.184230\pi$
$854$		0			0
$855$			97.1625i			3.32289i
$856$		0			0
$857$	−0.408558	+	0.707642i	−0.0139561	+	0.0241726i	−0.872919	−	0.487865i	$-0.837776\pi$
$857$	−0.408558	+	0.707642i	−0.0139561	+	0.0241726i	0.858963	+	0.512038i	$0.171109\pi$
$858$		0			0
$859$	1.01695	+	1.76140i	0.0346978	+	0.0600983i	0.882853	−	0.469650i	$-0.155620\pi$
$859$	1.01695	+	1.76140i	0.0346978	+	0.0600983i	−0.848155	+	0.529748i	$0.822286\pi$
$860$		0			0
$861$	−29.1774	+	43.3654i	−0.994364	+	1.47789i
$862$		0			0
$863$	2.18418	+	3.78310i	0.0743502	+	0.128778i	0.900804	−	0.434227i	$-0.142978\pi$
$863$	2.18418	+	3.78310i	0.0743502	+	0.128778i	−0.826453	+	0.563005i	$0.809645\pi$
$864$		0			0
$865$	−0.924636	+	1.60152i	−0.0314386	+	0.0544532i
$866$		0			0
$867$		−	9.58889i		−	0.325656i
$868$		0			0
$869$	6.22208			0.211070
$870$		0			0
$871$	−1.90984	+	3.30793i	−0.0647123	+	0.112085i
$872$		0			0
$873$	−84.9360	+	49.0378i	−2.87465	+	1.65968i
$874$		0			0
$875$	−29.5789	−	5.07783i	−0.999951	−	0.171662i
$876$		0			0
$877$	24.9397	+	43.1969i	0.842155	+	1.45866i	0.888069	+	0.459711i	$0.152047\pi$
$877$	24.9397	+	43.1969i	0.842155	+	1.45866i	−0.0459133	+	0.998945i	$0.514620\pi$
$878$		0			0
$879$	41.0975	−	71.1829i	1.38618	−	2.40094i
$880$		0			0
$881$	−29.4572			−0.992437			−0.496219	−	0.868198i	$-0.665279\pi$
$881$	−29.4572			−0.992437			−0.496219	+	0.868198i	$0.665279\pi$
$882$		0			0
$883$		−	28.0341i		−	0.943423i	−0.881753	−	0.471711i	$-0.843636\pi$
$883$		−	28.0341i		−	0.943423i	0.881753	−	0.471711i	$-0.156364\pi$
$884$		0			0
$885$	60.5064	+	34.9334i	2.03390	+	1.17427i
$886$		0			0
$887$	−11.0159	+	6.36005i	−0.369878	+	0.213549i	−0.673405	−	0.739273i	$-0.735169\pi$
$887$	−11.0159	+	6.36005i	−0.369878	+	0.213549i	0.303527	+	0.952823i	$0.401836\pi$
$888$		0			0
$889$	−30.3583	−	5.21162i	−1.01818	−	0.174792i
$890$		0			0
$891$	44.0571	−	25.4364i	1.47597	−	0.852151i
$892$		0			0
$893$	20.9502	−	36.2867i	0.701070	−	1.21429i
$894$		0			0
$895$		−	39.1067i		−	1.30719i
$896$		0			0
$897$	6.69282			0.223467
$898$		0			0
$899$	−1.64678	−	0.950767i	−0.0549231	−	0.0317099i
$900$		0			0
$901$	−25.0216	−	43.3387i	−0.833591	−	1.44382i
$902$		0			0
$903$	43.0708	+	35.8102i	1.43331	+	1.19169i
$904$		0			0
$905$	−22.2184	+	12.8278i	−0.738564	+	0.426410i
$906$		0			0
$907$	3.01389	−	5.22021i	0.100075	−	0.173334i	−0.811641	−	0.584157i	$-0.801425\pi$
$907$	3.01389	−	5.22021i	0.100075	−	0.173334i	0.911715	+	0.410823i	$0.134759\pi$
$908$		0			0
$909$			19.9527i			0.661788i
$910$		0			0
$911$	22.7915			0.755117			0.377558	−	0.925986i	$-0.376764\pi$
$911$	22.7915			0.755117			0.377558	+	0.925986i	$0.376764\pi$
$912$		0			0
$913$	4.98726	+	2.87940i	0.165054	+	0.0952941i
$914$		0			0
$915$	−69.2830	+	40.0006i	−2.29043	+	1.32238i
$916$		0			0
$917$	−3.17446	−	8.60061i	−0.104830	−	0.284017i
$918$		0			0
$919$	4.60146	−	2.65666i	0.151788	−	0.0876350i	−0.422182	−	0.906511i	$-0.638736\pi$
$919$	4.60146	−	2.65666i	0.151788	−	0.0876350i	0.573970	+	0.818876i	$0.305402\pi$
$920$		0			0
$921$	51.5622	+	29.7695i	1.69903	+	0.980937i
$922$		0			0
$923$	−4.41916			−0.145459
$924$		0			0
$925$	0.221346			0.00727782
$926$		0			0
$927$	−24.8296	+	43.0061i	−0.815511	+	1.41251i
$928$		0			0
$929$	37.1428	−	21.4444i	1.21862	−	0.703568i	0.253994	−	0.967206i	$-0.418256\pi$
$929$	37.1428	−	21.4444i	1.21862	−	0.703568i	0.964622	+	0.263637i	$0.0849222\pi$
$930$		0			0
$931$	−46.5879	+	8.64963i	−1.52686	+	0.283480i
$932$		0			0
$933$	4.20807	+	7.28860i	0.137766	+	0.238618i
$934$		0			0
$935$	18.0196	−	31.2108i	0.589303	−	1.02070i
$936$		0			0
$937$			46.1036i			1.50614i	0.657941	+	0.753070i	$0.271428\pi$
$937$			46.1036i			1.50614i	−0.657941	+	0.753070i	$0.728572\pi$
$938$		0			0
$939$	38.1540			1.24511
$940$		0			0
$941$	21.6317	−	37.4673i	0.705175	−	1.22140i	−0.261454	−	0.965216i	$-0.584202\pi$
$941$	21.6317	−	37.4673i	0.705175	−	1.22140i	0.966628	−	0.256182i	$-0.0824648\pi$
$942$		0			0
$943$	31.9036	−	23.0158i	1.03892	−	0.749497i
$944$		0			0
$945$	−59.3326	+	21.8995i	−1.93009	+	0.712391i
$946$		0			0
$947$	−14.0965	−	24.4158i	−0.458073	−	0.793406i	0.540786	−	0.841160i	$-0.318127\pi$
$947$	−14.0965	−	24.4158i	−0.458073	−	0.793406i	−0.998859	+	0.0477542i	$0.984794\pi$
$948$		0			0
$949$	−0.752288	−	0.434334i	−0.0244203	−	0.0140991i
$950$		0			0
$951$	99.5392			3.22778
$952$		0			0
$953$	−44.9250			−1.45526			−0.727631	−	0.685968i	$-0.759379\pi$
$953$	−44.9250			−1.45526			−0.727631	+	0.685968i	$0.759379\pi$
$954$		0			0
$955$	16.1348	+	9.31541i	0.522109	+	0.301439i
$956$		0			0
$957$	−4.32406	+	2.49649i	−0.139777	+	0.0807002i
$958$		0			0
$959$	−21.7971	−	18.1227i	−0.703864	−	0.585211i
$960$		0			0
$961$	6.30360	+	10.9182i	0.203342	+	0.352199i
$962$		0			0
$963$	44.1276	−	76.4312i	1.42199	−	2.46296i
$964$		0			0
$965$			26.0377i			0.838182i
$966$		0			0
$967$			17.4158i			0.560056i	0.959992	+	0.280028i	$0.0903437\pi$
$967$			17.4158i			0.560056i	−0.959992	+	0.280028i	$0.909656\pi$
$968$		0			0
$969$	−81.1035	−	46.8251i	−2.60542	−	1.50424i
$970$		0			0
$971$	−0.489865	+	0.282823i	−0.0157205	+	0.00907624i	−0.507840	−	0.861452i	$-0.669556\pi$
$971$	−0.489865	+	0.282823i	−0.0157205	+	0.00907624i	0.492119	+	0.870528i	$0.336222\pi$
$972$		0			0
$973$	−30.6456	−	5.26094i	−0.982453	−	0.168658i
$974$		0			0
$975$	−0.0825650	−	0.143007i	−0.00264420	−	0.00457988i
$976$		0			0
$977$	−10.9454	−	6.31935i	−0.350176	−	0.202174i	0.314587	−	0.949229i	$-0.398134\pi$
$977$	−10.9454	−	6.31935i	−0.350176	−	0.202174i	−0.664763	+	0.747055i	$0.731467\pi$
$978$		0			0
$979$	−63.8896			−2.04192
$980$		0			0
$981$		−	29.7165i		−	0.948775i
$982$		0			0
$983$	10.0513	−	17.4094i	0.320588	−	0.555274i	−0.660022	−	0.751247i	$-0.729453\pi$
$983$	10.0513	−	17.4094i	0.320588	−	0.555274i	0.980609	+	0.195972i	$0.0627862\pi$
$984$		0			0
$985$	1.65064	+	2.85900i	0.0525939	+	0.0910953i
$986$		0			0
$987$	49.7983	+	8.54890i	1.58510	+	0.272115i
$988$		0			0
$989$	−21.0792	−	36.5102i	−0.670279	−	1.16096i
$990$		0			0
$991$	−21.5973	−	12.4692i	−0.686060	−	0.396097i	0.116074	−	0.993241i	$-0.462969\pi$
$991$	−21.5973	−	12.4692i	−0.686060	−	0.396097i	−0.802134	+	0.597144i	$0.796302\pi$
$992$		0			0
$993$	−74.6517			−2.36900
$994$		0			0
$995$		−	7.25163i		−	0.229892i
$996$		0			0
$997$	−17.4557	−	10.0781i	−0.552828	−	0.319175i	0.197434	−	0.980316i	$-0.436739\pi$
$997$	−17.4557	−	10.0781i	−0.552828	−	0.319175i	−0.750262	+	0.661141i	$0.770072\pi$
$998$		0			0
$999$	13.7288	−	7.92631i	0.434359	−	0.250777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.81.3	✓	56
7.2	even	3	inner	1148.2.r.a.737.26	yes	56
41.40	even	2	inner	1148.2.r.a.81.26	yes	56
287.163	even	6	inner	1148.2.r.a.737.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.3	✓	56	1.1	even	1	trivial
1148.2.r.a.81.26	yes	56	41.40	even	2	inner
1148.2.r.a.737.3	yes	56	287.163	even	6	inner
1148.2.r.a.737.26	yes	56	7.2	even	3	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.67190 - 1.54262i) q^{3} +(-1.10096 - 1.90691i) q^{5} +(2.60761 + 0.447649i) q^{7} +(3.25937 + 5.64540i) q^{9} +O(q^{10})\)	\(q+(-2.67190 - 1.54262i) q^{3} +(-1.10096 - 1.90691i) q^{5} +(2.60761 + 0.447649i) q^{7} +(3.25937 + 5.64540i) q^{9} +(-3.16097 - 1.82499i) q^{11} +0.353091i q^{13} +6.79344i q^{15} +(-3.88342 - 2.24210i) q^{17} +(-5.86226 + 3.38458i) q^{19} +(-6.27671 - 5.21863i) q^{21} +(3.07187 + 5.32063i) q^{23} +(0.0757913 - 0.131274i) q^{25} -10.8562i q^{27} +0.443384i q^{29} +(-2.14434 + 3.71411i) q^{31} +(5.63054 + 9.75239i) q^{33} +(-2.01723 - 5.46532i) q^{35} +(0.730118 + 1.26460i) q^{37} +(0.544686 - 0.943424i) q^{39} +(-0.647886 - 6.37026i) q^{41} -6.86200 q^{43} +(7.17685 - 12.4307i) q^{45} +(-5.36060 + 3.09494i) q^{47} +(6.59922 + 2.33458i) q^{49} +(6.91742 + 11.9813i) q^{51} +(9.66478 + 5.57996i) q^{53} +8.03693i q^{55} +20.8845 q^{57} +(5.14222 - 8.90659i) q^{59} +(5.88811 + 10.1985i) q^{61} +(5.97201 + 16.1800i) q^{63} +(0.673313 - 0.388737i) q^{65} +(9.36850 + 5.40891i) q^{67} -18.9550i q^{69} +12.5157i q^{71} +(-1.23009 + 2.13058i) q^{73} +(-0.405014 + 0.233835i) q^{75} +(-7.42562 - 6.17386i) q^{77} +(-1.47630 + 0.852345i) q^{79} +(-6.96891 + 12.0705i) q^{81} -1.57776 q^{83} +9.87380i q^{85} +(0.683975 - 1.18468i) q^{87} +(15.1590 - 8.75205i) q^{89} +(-0.158061 + 0.920722i) q^{91} +(11.4589 - 6.61582i) q^{93} +(12.9082 + 7.45254i) q^{95} +15.0452i q^{97} -23.7933i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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