LMFDB - Embedded newform 504.2.p.g.307.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(307,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.p (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
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} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 - 4x^12 - 4x^10 + 16x^8 - 16x^6 - 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			307.16
Root			$0.310478 + 1.37971i$ of defining polynomial
Character	$\chi$	$=$	504.307
Dual form			504.2.p.g.307.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37971 + 0.310478i) q^{2} +(1.80721 + 0.856739i) q^{4} +2.33443 q^{5} +(-0.490487 + 2.59989i) q^{7} +(2.22743 + 1.74315i) q^{8} +O(q^{10})$	\(q+(1.37971 + 0.310478i) q^{2} +(1.80721 + 0.856739i) q^{4} +2.33443 q^{5} +(-0.490487 + 2.59989i) q^{7} +(2.22743 + 1.74315i) q^{8} +(3.22084 + 0.724789i) q^{10} +0.304570 q^{11} -5.46072 q^{13} +(-1.48394 + 3.43481i) q^{14} +(2.53200 + 3.09661i) q^{16} -6.37384i q^{17} +0.840438i q^{19} +(4.21880 + 2.00000i) q^{20} +(0.420219 + 0.0945622i) q^{22} +0.111550i q^{23} +0.449578 q^{25} +(-7.53421 - 1.69543i) q^{26} +(-3.11384 + 4.27832i) q^{28} -5.46072i q^{29} +7.64576 q^{31} +(2.53200 + 5.05856i) q^{32} +(1.97893 - 8.79406i) q^{34} +(-1.14501 + 6.06927i) q^{35} -6.44169i q^{37} +(-0.260937 + 1.15956i) q^{38} +(5.19978 + 4.06927i) q^{40} +8.66385i q^{41} +6.06927 q^{43} +(0.550422 + 0.260937i) q^{44} +(-0.0346336 + 0.153906i) q^{46} -8.21451 q^{47} +(-6.51885 - 2.55042i) q^{49} +(0.620289 + 0.139584i) q^{50} +(-9.86864 - 4.67841i) q^{52} -10.1296i q^{53} +0.710999 q^{55} +(-5.62452 + 4.93607i) q^{56} +(1.69543 - 7.53421i) q^{58} -1.70998i q^{59} +2.75380 q^{61} +(10.5489 + 2.37384i) q^{62} +(1.92286 + 7.76548i) q^{64} -12.7477 q^{65} -8.35928 q^{67} +(5.46072 - 11.5188i) q^{68} +(-3.46415 + 8.01834i) q^{70} -2.07350i q^{71} +12.7477i q^{73} +(2.00000 - 8.88767i) q^{74} +(-0.720036 + 1.51885i) q^{76} +(-0.149388 + 0.791849i) q^{77} +7.90670i q^{79} +(5.91078 + 7.22883i) q^{80} +(-2.68993 + 11.9536i) q^{82} -11.6468i q^{83} -14.8793i q^{85} +(8.37384 + 1.88437i) q^{86} +(0.678408 + 0.530912i) q^{88} +4.08382i q^{89} +(2.67841 - 14.1973i) q^{91} +(-0.0955689 + 0.201593i) q^{92} +(-11.3337 - 2.55042i) q^{94} +1.96195i q^{95} -6.42855i q^{97} +(-8.20228 - 5.54280i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8	$ 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64} - 40 q^{67} - 24 q^{70} + 32 q^{74} + 32 q^{86} - 88 q^{88} - 56 q^{91} - 44 q^{92} - 66 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.37971	+	0.310478i	0.975603	+	0.219541i
$2$	1.37971	+	0.310478i	0.975603	+	0.219541i
$3$		0			0
$3$		0			0
$4$	1.80721	+	0.856739i	0.903604	+	0.428370i
$5$	2.33443			1.04399			0.521995	−	0.852948i	$-0.325188\pi$
$5$	2.33443			1.04399			0.521995	+	0.852948i	$0.325188\pi$
$6$		0			0
$7$	−0.490487	+	2.59989i	−0.185387	+	0.982666i
$7$	−0.490487	+	2.59989i	−0.185387	+	0.982666i
$8$	2.22743	+	1.74315i	0.787514	+	0.616297i
$9$		0			0
$10$	3.22084	+	0.724789i	1.01852	+	0.229198i
$11$	0.304570			0.0918314			0.0459157	−	0.998945i	$-0.485379\pi$
$11$	0.304570			0.0918314			0.0459157	+	0.998945i	$0.485379\pi$
$12$		0			0
$13$	−5.46072			−1.51453			−0.757265	−	0.653108i	$-0.773465\pi$
$13$	−5.46072			−1.51453			−0.757265	+	0.653108i	$0.773465\pi$
$14$	−1.48394	+	3.43481i	−0.396599	+	0.917992i
$15$		0			0
$16$	2.53200	+	3.09661i	0.632999	+	0.774152i
$17$		−	6.37384i		−	1.54588i	−0.634477	−	0.772941i	$-0.718785\pi$
$17$		−	6.37384i		−	1.54588i	0.634477	−	0.772941i	$-0.281215\pi$
$18$		0			0
$19$			0.840438i			0.192810i	0.995342	+	0.0964049i	$0.0307344\pi$
$19$			0.840438i			0.192810i	−0.995342	+	0.0964049i	$0.969266\pi$
$20$	4.21880	+	2.00000i	0.943353	+	0.447214i
$21$		0			0
$22$	0.420219	+	0.0945622i	0.0895910	+	0.0201607i
$23$			0.111550i			0.0232597i	0.999932	+	0.0116298i	$0.00370198\pi$
$23$			0.111550i			0.0232597i	−0.999932	+	0.0116298i	$0.996298\pi$
$24$		0			0
$25$	0.449578			0.0899157
$26$	−7.53421	−	1.69543i	−1.47758	−	0.332501i
$27$		0			0
$28$	−3.11384	+	4.27832i	−0.588460	+	0.808526i
$29$		−	5.46072i		−	1.01403i	−0.861937	−	0.507015i	$-0.830749\pi$
$29$		−	5.46072i		−	1.01403i	0.861937	−	0.507015i	$-0.169251\pi$
$30$		0			0
$31$	7.64576			1.37322			0.686610	−	0.727026i	$-0.259098\pi$
$31$	7.64576			1.37322			0.686610	+	0.727026i	$0.259098\pi$
$32$	2.53200	+	5.05856i	0.447598	+	0.894235i
$33$		0			0
$34$	1.97893	−	8.79406i	0.339384	−	1.50817i
$35$	−1.14501	+	6.06927i	−0.193542	+	1.02589i
$36$		0			0
$37$		−	6.44169i		−	1.05901i	−0.848308	−	0.529504i	$-0.822378\pi$
$37$		−	6.44169i		−	1.05901i	0.848308	−	0.529504i	$-0.177622\pi$
$38$	−0.260937	+	1.15956i	−0.0423296	+	0.188106i
$39$		0			0
$40$	5.19978	+	4.06927i	0.822157	+	0.643408i
$41$			8.66385i			1.35307i	0.736412	+	0.676533i	$0.236519\pi$
$41$			8.66385i			1.35307i	−0.736412	+	0.676533i	$0.763481\pi$
$42$		0			0
$43$	6.06927			0.925555			0.462777	−	0.886475i	$-0.346853\pi$
$43$	6.06927			0.925555			0.462777	+	0.886475i	$0.346853\pi$
$44$	0.550422	+	0.260937i	0.0829792	+	0.0393378i
$45$		0			0
$46$	−0.0346336	+	0.153906i	−0.00510645	+	0.0226922i
$47$	−8.21451			−1.19821			−0.599105	−	0.800671i	$-0.704477\pi$
$47$	−8.21451			−1.19821			−0.599105	+	0.800671i	$0.704477\pi$
$48$		0			0
$49$	−6.51885	−	2.55042i	−0.931264	−	0.364346i
$50$	0.620289	+	0.139584i	0.0877220	+	0.0197402i
$51$		0			0
$52$	−9.86864	−	4.67841i	−1.36853	−	0.648778i
$53$		−	10.1296i		−	1.39141i	−0.718330	−	0.695703i	$-0.755093\pi$
$53$		−	10.1296i		−	1.39141i	0.718330	−	0.695703i	$-0.244907\pi$
$54$		0			0
$55$	0.710999			0.0958711
$56$	−5.62452	+	4.93607i	−0.751608	+	0.659610i
$57$		0			0
$58$	1.69543	−	7.53421i	0.222621	−	0.989290i
$59$		−	1.70998i		−	0.222621i	−0.993786	−	0.111310i	$-0.964495\pi$
$59$		−	1.70998i		−	0.222621i	0.993786	−	0.111310i	$-0.0355048\pi$
$60$		0			0
$61$	2.75380			0.352587			0.176294	−	0.984338i	$-0.443589\pi$
$61$	2.75380			0.352587			0.176294	+	0.984338i	$0.443589\pi$
$62$	10.5489	+	2.37384i	1.33972	+	0.301478i
$63$		0			0
$64$	1.92286	+	7.76548i	0.240357	+	0.970685i
$65$	−12.7477			−1.58115
$66$		0			0
$67$	−8.35928			−1.02125			−0.510625	−	0.859804i	$-0.670586\pi$
$67$	−8.35928			−1.02125			−0.510625	+	0.859804i	$0.670586\pi$
$68$	5.46072	−	11.5188i	0.662209	−	1.39687i
$69$		0			0
$70$	−3.46415	+	8.01834i	−0.414045	+	0.958375i
$71$		−	2.07350i		−	0.246079i	−0.992402	−	0.123039i	$-0.960736\pi$
$71$		−	2.07350i		−	0.246079i	0.992402	−	0.123039i	$-0.0392641\pi$
$72$		0			0
$73$			12.7477i			1.49200i	0.665945	+	0.746001i	$0.268029\pi$
$73$			12.7477i			1.49200i	−0.665945	+	0.746001i	$0.731971\pi$
$74$	2.00000	−	8.88767i	0.232495	−	1.03317i
$75$		0			0
$76$	−0.720036	+	1.51885i	−0.0825938	+	0.174224i
$77$	−0.149388	+	0.791849i	−0.0170243	+	0.0902395i
$78$		0			0
$79$			7.90670i			0.889573i	0.895637	+	0.444787i	$0.146720\pi$
$79$			7.90670i			0.889573i	−0.895637	+	0.444787i	$0.853280\pi$
$80$	5.91078	+	7.22883i	0.660845	+	0.808208i
$81$		0			0
$82$	−2.68993	+	11.9536i	−0.297053	+	1.32006i
$83$		−	11.6468i		−	1.27841i	−0.769038	−	0.639203i	$-0.779264\pi$
$83$		−	11.6468i		−	1.27841i	0.769038	−	0.639203i	$-0.220736\pi$
$84$		0			0
$85$		−	14.8793i		−	1.61389i
$86$	8.37384	+	1.88437i	0.902974	+	0.203197i
$87$		0			0
$88$	0.678408	+	0.530912i	0.0723185	+	0.0565954i
$89$			4.08382i			0.432884i	0.976295	+	0.216442i	$0.0694452\pi$
$89$			4.08382i			0.432884i	−0.976295	+	0.216442i	$0.930555\pi$
$90$		0			0
$91$	2.67841	−	14.1973i	0.280773	−	1.48828i
$92$	−0.0955689	+	0.201593i	−0.00996374	+	0.0210175i
$93$		0			0
$94$	−11.3337	−	2.55042i	−1.16898	−	0.263056i
$95$			1.96195i			0.201291i
$96$		0			0
$97$		−	6.42855i		−	0.652720i	−0.945245	−	0.326360i	$-0.894178\pi$
$97$		−	6.42855i		−	0.652720i	0.945245	−	0.326360i	$-0.105822\pi$
$98$	−8.20228	−	5.54280i	−0.828555	−	0.559907i
$99$		0			0
$100$	0.812482	+	0.385171i	0.0812482	+	0.0385171i
$101$	−7.00330			−0.696854			−0.348427	−	0.937336i	$-0.613284\pi$
$101$	−7.00330			−0.696854			−0.348427	+	0.937336i	$0.613284\pi$
$102$		0			0
$103$	−9.60771			−0.946676			−0.473338	−	0.880881i	$-0.656951\pi$
$103$	−9.60771			−0.946676			−0.473338	+	0.880881i	$0.656951\pi$
$104$	−12.1633	−	9.51885i	−1.19271	−	0.933400i
$105$		0			0
$106$	3.14501	−	13.9759i	0.305470	−	1.35746i
$107$	−6.01455			−0.581449			−0.290724	−	0.956807i	$-0.593896\pi$
$107$	−6.01455			−0.581449			−0.290724	+	0.956807i	$0.593896\pi$
$108$		0			0
$109$		−	9.85961i		−	0.944379i	−0.881497	−	0.472190i	$-0.843464\pi$
$109$		−	9.85961i		−	0.944379i	0.881497	−	0.472190i	$-0.156536\pi$
$110$	0.980973	+	0.220749i	0.0935321	+	0.0210476i
$111$		0			0
$112$	−9.29275	+	5.06406i	−0.878083	+	0.478509i
$113$	14.7477			1.38734			0.693672	−	0.720291i	$-0.255992\pi$
$113$	14.7477			1.38734			0.693672	+	0.720291i	$0.255992\pi$
$114$		0			0
$115$			0.260405i			0.0242829i
$116$	4.67841	−	9.86864i	0.434379	−	0.916281i
$117$		0			0
$118$	0.530912	−	2.35928i	0.0488744	−	0.217190i
$119$	16.5713	+	3.12628i	1.51909	+	0.286586i
$120$		0			0
$121$	−10.9072			−0.991567
$122$	3.79944	+	0.854992i	0.343985	+	0.0774073i
$123$		0			0
$124$	13.8175	+	6.55042i	1.24085	+	0.588245i
$125$	−10.6227			−0.950119
$126$		0			0
$127$		−	2.49286i		−	0.221205i	−0.993865	−	0.110603i	$-0.964722\pi$
$127$		−	2.49286i		−	0.221205i	0.993865	−	0.110603i	$-0.0352781\pi$
$128$	0.241980	+	11.3111i	0.0213882	+	0.999771i
$129$		0			0
$130$	−17.5881	−	3.95787i	−1.54258	−	0.347128i
$131$			4.60914i			0.402702i	0.979519	+	0.201351i	$0.0645333\pi$
$131$			4.60914i			0.402702i	−0.979519	+	0.201351i	$0.935467\pi$
$132$		0			0
$133$	−2.18505	−	0.412224i	−0.189467	−	0.0357443i
$134$	−11.5334	−	2.59537i	−0.996334	−	0.224206i
$135$		0			0
$136$	11.1106	−	14.1973i	0.952722	−	1.21740i
$137$	0.899157			0.0768202			0.0384101	−	0.999262i	$-0.487771\pi$
$137$	0.899157			0.0768202			0.0384101	+	0.999262i	$0.487771\pi$
$138$		0			0
$139$			23.1762i			1.96578i	0.184189	+	0.982891i	$0.441034\pi$
$139$			23.1762i			1.96578i	−0.184189	+	0.982891i	$0.558966\pi$
$140$	−7.26905	+	9.98745i	−0.614346	+	0.844094i
$141$		0			0
$142$	0.643774	−	2.86083i	0.0540243	−	0.240075i
$143$	−1.66317			−0.139081
$144$		0			0
$145$		−	12.7477i		−	1.05864i
$146$	−3.95787	+	17.5881i	−0.327555	+	1.45560i
$147$		0			0
$148$	5.51885	−	11.6415i	0.453646	−	0.956923i
$149$			6.58394i			0.539377i	0.962948	+	0.269689i	$0.0869208\pi$
$149$			6.58394i			0.539377i	−0.962948	+	0.269689i	$0.913079\pi$
$150$		0			0
$151$			20.5670i			1.67372i	0.547419	+	0.836858i	$0.315610\pi$
$151$			20.5670i			1.67372i	−0.547419	+	0.836858i	$0.684390\pi$
$152$	−1.46501	+	1.87201i	−0.118828	+	0.151840i
$153$		0			0
$154$	−0.451963	+	1.04614i	−0.0364202	+	0.0843005i
$155$	17.8485			1.43363
$156$		0			0
$157$	12.0915			0.965009			0.482505	−	0.875893i	$-0.339727\pi$
$157$	12.0915			0.965009			0.482505	+	0.875893i	$0.339727\pi$
$158$	−2.45485	+	10.9090i	−0.195298	+	0.867870i
$159$		0			0
$160$	5.91078	+	11.8089i	0.467288	+	0.933573i
$161$	−0.290017	−	0.0547136i	−0.0228565	−	0.00431203i
$162$		0			0
$163$	0.359284			0.0281413			0.0140706	−	0.999901i	$-0.495521\pi$
$163$	0.359284			0.0281413			0.0140706	+	0.999901i	$0.495521\pi$
$164$	−7.42266	+	15.6574i	−0.579612	+	1.22264i
$165$		0			0
$166$	3.61608	−	16.0693i	0.280662	−	1.24722i
$167$	7.91574			0.612538			0.306269	−	0.951945i	$-0.400919\pi$
$167$	7.91574			0.612538			0.306269	+	0.951945i	$0.400919\pi$
$168$		0			0
$169$	16.8194			1.29380
$170$	4.61969	−	20.5291i	0.354314	−	1.57451i
$171$		0			0
$172$	10.9684	+	5.19978i	0.836335	+	0.396479i
$173$	12.5109			0.951185			0.475593	−	0.879666i	$-0.342234\pi$
$173$	12.5109			0.951185			0.475593	+	0.879666i	$0.342234\pi$
$174$		0			0
$175$	−0.220512	+	1.16885i	−0.0166692	+	0.0883571i
$176$	0.771171	+	0.943135i	0.0581292	+	0.0710915i
$177$		0			0
$178$	−1.26793	+	5.63449i	−0.0950357	+	0.422323i
$179$	−15.3423			−1.14673			−0.573367	−	0.819298i	$-0.694363\pi$
$179$	−15.3423			−1.14673			−0.573367	+	0.819298i	$0.694363\pi$
$180$		0			0
$181$	0.493074			0.0366499			0.0183249	−	0.999832i	$-0.494167\pi$
$181$	0.493074			0.0366499			0.0183249	+	0.999832i	$0.494167\pi$
$182$	8.10336	−	18.7565i	0.600661	−	1.39033i
$183$		0			0
$184$	−0.194448	+	0.248468i	−0.0143349	+	0.0183173i
$185$		−	15.0377i		−	1.10559i
$186$		0			0
$187$		−	1.94128i		−	0.141961i
$188$	−14.8453	−	7.03769i	−1.08271	−	0.513276i
$189$		0			0
$190$	−0.609140	+	2.70692i	−0.0441917	+	0.196381i
$191$			21.8108i			1.57817i	0.614282	+	0.789087i	$0.289446\pi$
$191$			21.8108i			1.57817i	−0.614282	+	0.789087i	$0.710554\pi$
$192$		0			0
$193$	7.58811			0.546204			0.273102	−	0.961985i	$-0.411950\pi$
$193$	7.58811			0.546204			0.273102	+	0.961985i	$0.411950\pi$
$194$	1.99592	−	8.86955i	0.143299	−	0.636796i
$195$		0			0
$196$	−9.59586	−	10.1941i	−0.685419	−	0.728149i
$197$		−	11.7928i		−	0.840199i	−0.907478	−	0.420099i	$-0.861995\pi$
$197$		−	11.7928i		−	0.840199i	0.907478	−	0.420099i	$-0.138005\pi$
$198$		0			0
$199$	−24.7858			−1.75702			−0.878509	−	0.477726i	$-0.841461\pi$
$199$	−24.7858			−1.75702			−0.878509	+	0.477726i	$0.841461\pi$
$200$	1.00140	+	0.783683i	0.0708099	+	0.0554147i
$201$		0			0
$202$	−9.66253	−	2.17437i	−0.679853	−	0.152988i
$203$	14.1973	+	2.67841i	0.996452	+	0.187987i
$204$		0			0
$205$			20.2252i			1.41259i
$206$	−13.2559	−	2.98298i	−0.923580	−	0.207834i
$207$		0			0
$208$	−13.8265	−	16.9097i	−0.958696	−	1.17248i
$209$			0.255972i			0.0177060i
$210$		0			0
$211$	14.0693			0.968568			0.484284	−	0.874911i	$-0.339080\pi$
$211$	14.0693			0.968568			0.484284	+	0.874911i	$0.339080\pi$
$212$	8.67841	−	18.3063i	0.596035	−	1.25728i
$213$		0			0
$214$	−8.29835	−	1.86738i	−0.567263	−	0.127652i
$215$	14.1683			0.966270
$216$		0			0
$217$	−3.75014	+	19.8781i	−0.254576	+	1.34942i
$218$	3.06119	−	13.6034i	0.207330	−	0.921339i
$219$		0			0
$220$	1.28492	+	0.609140i	0.0866294	+	0.0410682i
$221$			34.8057i			2.34129i
$222$		0			0
$223$	15.4480			1.03448			0.517239	−	0.855841i	$-0.326960\pi$
$223$	15.4480			1.03448			0.517239	+	0.855841i	$0.326960\pi$
$224$	−14.3936	+	4.10176i	−0.961713	+	0.274060i
$225$		0			0
$226$	20.3475	+	4.57882i	1.35350	+	0.304579i
$227$			11.0377i			0.732597i	0.930497	+	0.366299i	$0.119375\pi$
$227$			11.0377i			0.732597i	−0.930497	+	0.366299i	$0.880625\pi$
$228$		0			0
$229$	−7.42266			−0.490503			−0.245252	−	0.969459i	$-0.578871\pi$
$229$	−7.42266			−0.490503			−0.245252	+	0.969459i	$0.578871\pi$
$230$	−0.0808499	+	0.359284i	−0.00533109	+	0.0236905i
$231$		0			0
$232$	9.51885	−	12.1633i	0.624943	−	0.798562i
$233$	−13.0668			−0.856034			−0.428017	−	0.903771i	$-0.640788\pi$
$233$	−13.0668			−0.856034			−0.428017	+	0.903771i	$0.640788\pi$
$234$		0			0
$235$	−19.1762			−1.25092
$236$	1.46501	−	3.09029i	0.0953640	−	0.201161i
$237$		0			0
$238$	21.8929	+	9.45838i	1.41911	+	0.613095i
$239$		−	8.54916i		−	0.552999i	−0.961014	−	0.276500i	$-0.910826\pi$
$239$		−	8.54916i		−	0.552999i	0.961014	−	0.276500i	$-0.0891744\pi$
$240$		0			0
$241$			7.64683i			0.492576i	0.969197	+	0.246288i	$0.0792109\pi$
$241$			7.64683i			0.492576i	−0.969197	+	0.246288i	$0.920789\pi$
$242$	−15.0488	−	3.38645i	−0.967376	−	0.217689i
$243$		0			0
$244$	4.97668	+	2.35928i	0.318599	+	0.151038i
$245$	−15.2178	−	5.95379i	−0.972230	−	0.380374i
$246$		0			0
$247$		−	4.58939i		−	0.292016i
$248$	17.0304	+	13.3277i	1.08143	+	0.846310i
$249$		0			0
$250$	−14.6562	−	3.29810i	−0.926939	−	0.208590i
$251$		−	12.7186i		−	0.802789i	−0.915905	−	0.401394i	$-0.868526\pi$
$251$		−	12.7186i		−	0.802789i	0.915905	−	0.401394i	$-0.131474\pi$
$252$		0			0
$253$			0.0339747i			0.00213597i
$254$	0.773977	−	3.43942i	0.0485636	−	0.215809i
$255$		0			0
$256$	−3.17799	+	15.6812i	−0.198624	+	0.980076i
$257$			7.44557i			0.464442i	0.972663	+	0.232221i	$0.0745993\pi$
$257$			7.44557i			0.464442i	−0.972663	+	0.232221i	$0.925401\pi$
$258$		0			0
$259$	16.7477	+	3.15956i	1.04065	+	0.196326i
$260$	−23.0377	−	10.9214i	−1.42874	−	0.677318i
$261$		0			0
$262$	−1.43103	+	6.35928i	−0.0884096	+	0.392878i
$263$			11.5549i			0.712503i	0.934390	+	0.356251i	$0.115945\pi$
$263$			11.5549i			0.712503i	−0.934390	+	0.356251i	$0.884055\pi$
$264$		0			0
$265$		−	23.6468i		−	1.45261i
$266$	−2.88675	−	1.24716i	−0.176998	−	0.0764681i
$267$		0			0
$268$	−15.1070	−	7.16172i	−0.922804	−	0.437472i
$269$	12.2121			0.744586			0.372293	−	0.928115i	$-0.378572\pi$
$269$	12.2121			0.744586			0.372293	+	0.928115i	$0.378572\pi$
$270$		0			0
$271$	18.9454			1.15085			0.575427	−	0.817853i	$-0.304836\pi$
$271$	18.9454			1.15085			0.575427	+	0.817853i	$0.304836\pi$
$272$	19.7373	−	16.1385i	1.19675	−	0.978542i
$273$		0			0
$274$	1.24058	+	0.279168i	0.0749460	+	0.0168652i
$275$	0.136928			0.00825708
$276$		0			0
$277$			18.1876i			1.09278i	0.837529	+	0.546392i	$0.183999\pi$
$277$			18.1876i			1.09278i	−0.837529	+	0.546392i	$0.816001\pi$
$278$	−7.19570	+	31.9765i	−0.431569	+	1.91782i
$279$		0			0
$280$	−13.1301	+	11.5229i	−0.784671	+	0.688626i
$281$	17.5294			1.04572			0.522858	−	0.852420i	$-0.324866\pi$
$281$	17.5294			1.04572			0.522858	+	0.852420i	$0.324866\pi$
$282$		0			0
$283$		−	18.3358i		−	1.08995i	−0.838452	−	0.544975i	$-0.816539\pi$
$283$		−	18.3358i		−	1.08995i	0.838452	−	0.544975i	$-0.183461\pi$
$284$	1.77644	−	3.74724i	0.105413	−	0.222358i
$285$		0			0
$286$	−2.29470	−	0.516377i	−0.135688	−	0.0305340i
$287$	−22.5251	−	4.24950i	−1.32961	−	0.250840i
$288$		0			0
$289$	−23.6258			−1.38975
$290$	3.95787	−	17.5881i	0.232414	−	1.03281i
$291$		0			0
$292$	−10.9214	+	23.0377i	−0.639128	+	1.34818i
$293$	14.0008			0.817938			0.408969	−	0.912548i	$-0.365888\pi$
$293$	14.0008			0.817938			0.408969	+	0.912548i	$0.365888\pi$
$294$		0			0
$295$		−	3.99184i		−	0.232414i
$296$	11.2288	−	14.3484i	0.652662	−	0.833983i
$297$		0			0
$298$	−2.04417	+	9.08393i	−0.118415	+	0.526218i
$299$		−	0.609140i		−	0.0352275i
$300$		0			0
$301$	−2.97689	+	15.7794i	−0.171585	+	0.909511i
$302$	−6.38559	+	28.3765i	−0.367449	+	1.63288i
$303$		0			0
$304$	−2.60251	+	2.12799i	−0.149264	+	0.122048i
$305$	6.42855			0.368098
$306$		0			0
$307$		−	4.26041i		−	0.243154i	−0.992582	−	0.121577i	$-0.961205\pi$
$307$		−	4.26041i		−	0.243154i	0.992582	−	0.121577i	$-0.0387952\pi$
$308$	−0.948382	+	1.30305i	−0.0540391	+	0.0742481i
$309$		0			0
$310$	24.6258	+	5.54157i	1.39865	+	0.314740i
$311$	−11.6664			−0.661541			−0.330771	−	0.943711i	$-0.607309\pi$
$311$	−11.6664			−0.661541			−0.330771	+	0.943711i	$0.607309\pi$
$312$		0			0
$313$		−	4.58003i		−	0.258879i	−0.991587	−	0.129439i	$-0.958682\pi$
$313$		−	4.58003i		−	0.258879i	0.991587	−	0.129439i	$-0.0413178\pi$
$314$	16.6828	+	3.75415i	0.941466	+	0.211859i
$315$		0			0
$316$	−6.77398	+	14.2890i	−0.381066	+	0.803821i
$317$			12.6315i			0.709454i	0.934970	+	0.354727i	$0.115426\pi$
$317$			12.6315i			0.709454i	−0.934970	+	0.354727i	$0.884574\pi$
$318$		0			0
$319$		−	1.66317i		−	0.0931197i
$320$	4.48878	+	18.1280i	0.250930	+	1.01339i
$321$		0			0
$322$	−0.383152	−	0.165533i	−0.0213522	−	0.00922477i
$323$	5.35682			0.298061
$324$		0			0
$325$	−2.45502			−0.136180
$326$	0.495708	+	0.111550i	0.0274547	+	0.00617816i
$327$		0			0
$328$	−15.1024	+	19.2981i	−0.833890	+	1.06556i
$329$	4.02911	−	21.3568i	0.222132	−	1.17744i
$330$		0			0
$331$	25.6870			1.41188			0.705942	−	0.708269i	$-0.250524\pi$
$331$	25.6870			1.41188			0.705942	+	0.708269i	$0.250524\pi$
$332$	9.97830	−	21.0482i	0.547630	−	1.15517i
$333$		0			0
$334$	10.9214	+	2.45766i	0.597594	+	0.134477i
$335$	−19.5142			−1.06617
$336$		0			0
$337$	24.7136			1.34624			0.673119	−	0.739535i	$-0.264954\pi$
$337$	24.7136			1.34624			0.673119	+	0.739535i	$0.264954\pi$
$338$	23.2059	+	5.22205i	1.26224	+	0.284042i
$339$		0			0
$340$	12.7477	−	26.8900i	0.691340	−	1.45831i
$341$	2.32867			0.126105
$342$		0			0
$343$	9.82822	−	15.6973i	0.530674	−	0.847576i
$344$	13.5188	+	10.5796i	0.728887	+	0.570416i
$345$		0			0
$346$	17.2614	+	3.88435i	0.927980	+	0.208824i
$347$	−17.7999			−0.955550			−0.477775	−	0.878482i	$-0.658557\pi$
$347$	−17.7999			−0.955550			−0.477775	+	0.878482i	$0.658557\pi$
$348$		0			0
$349$	8.70758			0.466106			0.233053	−	0.972464i	$-0.425128\pi$
$349$	8.70758			0.466106			0.233053	+	0.972464i	$0.425128\pi$
$350$	−0.667146	+	1.54422i	−0.0356605	+	0.0825419i
$351$		0			0
$352$	0.771171	+	1.54069i	0.0411035	+	0.0821188i
$353$			7.33615i			0.390464i	0.980757	+	0.195232i	$0.0625459\pi$
$353$			7.33615i			0.390464i	−0.980757	+	0.195232i	$0.937454\pi$
$354$		0			0
$355$		−	4.84044i		−	0.256904i
$356$	−3.49877	+	7.38031i	−0.185434	+	0.391156i
$357$		0			0
$358$	−21.1679	−	4.76343i	−1.11876	−	0.251755i
$359$		−	14.3555i		−	0.757656i	−0.925467	−	0.378828i	$-0.876327\pi$
$359$		−	14.3555i		−	0.757656i	0.925467	−	0.378828i	$-0.123673\pi$
$360$		0			0
$361$	18.2937			0.962824
$362$	0.680299	+	0.153088i	0.0357557	+	0.00804614i
$363$		0			0
$364$	17.0038	−	23.3627i	0.891240	−	1.22454i
$365$			29.7586i			1.55764i
$366$		0			0
$367$	17.4100			0.908794			0.454397	−	0.890799i	$-0.349855\pi$
$367$	17.4100			0.908794			0.454397	+	0.890799i	$0.349855\pi$
$368$	−0.345426	+	0.282443i	−0.0180065	+	0.0147234i
$369$		0			0
$370$	4.66887	−	20.7477i	0.242723	−	1.07862i
$371$	26.3358	+	4.96842i	1.36729	+	0.257948i
$372$		0			0
$373$		−	1.44007i		−	0.0745641i	−0.999305	−	0.0372821i	$-0.988130\pi$
$373$		−	1.44007i		−	0.0745641i	0.999305	−	0.0372821i	$-0.0118700\pi$
$374$	0.602724	−	2.67841i	0.0311661	−	0.138497i
$375$		0			0
$376$	−18.2972	−	14.3191i	−0.943607	−	0.738452i
$377$			29.8194i			1.53578i
$378$		0			0
$379$	−24.0061			−1.23311			−0.616556	−	0.787311i	$-0.711472\pi$
$379$	−24.0061			−1.23311			−0.616556	+	0.787311i	$0.711472\pi$
$380$	−1.68088	+	3.54564i	−0.0862271	+	0.181888i
$381$		0			0
$382$	−6.77176	+	30.0926i	−0.346473	+	1.53967i
$383$	−19.5821			−1.00060			−0.500300	−	0.865852i	$-0.666777\pi$
$383$	−19.5821			−1.00060			−0.500300	+	0.865852i	$0.666777\pi$
$384$		0			0
$385$	−0.348735	+	1.84852i	−0.0177732	+	0.0942092i
$386$	10.4694	+	2.35594i	0.532879	+	0.119914i
$387$		0			0
$388$	5.50759	−	11.6177i	0.279606	−	0.589801i
$389$		−	31.6057i		−	1.60247i	−0.598347	−	0.801237i	$-0.704176\pi$
$389$		−	31.6057i		−	1.60247i	0.598347	−	0.801237i	$-0.295824\pi$
$390$		0			0
$391$	0.710999			0.0359568
$392$	−10.0745	−	17.0442i	−0.508838	−	0.860862i
$393$		0			0
$394$	3.66139	−	16.2706i	0.184458	−	0.819701i
$395$			18.4577i			0.928706i
$396$		0			0
$397$	−6.29944			−0.316160			−0.158080	−	0.987426i	$-0.550530\pi$
$397$	−6.29944			−0.316160			−0.158080	+	0.987426i	$0.550530\pi$
$398$	−34.1972	−	7.69543i	−1.71415	−	0.385737i
$399$		0			0
$400$	1.13833	+	1.39217i	0.0569166	+	0.0696085i
$401$	−3.10084			−0.154849			−0.0774244	−	0.996998i	$-0.524670\pi$
$401$	−3.10084			−0.154849			−0.0774244	+	0.996998i	$0.524670\pi$
$402$		0			0
$403$	−41.7513			−2.07978
$404$	−12.6564	−	6.00000i	−0.629680	−	0.298511i
$405$		0			0
$406$	18.7565	+	8.10336i	0.930871	+	0.402163i
$407$		−	1.96195i		−	0.0972501i
$408$		0			0
$409$		−	3.06680i		−	0.151643i	−0.997121	−	0.0758217i	$-0.975842\pi$
$409$		−	3.06680i		−	0.151643i	0.997121	−	0.0758217i	$-0.0241580\pi$
$410$	−6.27947	+	27.9049i	−0.310121	+	1.37813i
$411$		0			0
$412$	−17.3631	−	8.23130i	−0.855419	−	0.405527i
$413$	4.44577	+	0.838724i	0.218762	+	0.0412709i
$414$		0			0
$415$		−	27.1888i		−	1.33464i
$416$	−13.8265	−	27.6233i	−0.677901	−	1.35435i
$417$		0			0
$418$	−0.0794737	+	0.353168i	−0.00388719	+	0.0172740i
$419$		−	15.5294i		−	0.758661i	−0.925261	−	0.379330i	$-0.876154\pi$
$419$		−	15.5294i		−	0.758661i	0.925261	−	0.379330i	$-0.123846\pi$
$420$		0			0
$421$			17.3631i			0.846227i	0.906077	+	0.423113i	$0.139063\pi$
$421$			17.3631i			0.846227i	−0.906077	+	0.423113i	$0.860937\pi$
$422$	19.4115	+	4.36819i	0.944938	+	0.212640i
$423$		0			0
$424$	17.6574	−	22.5629i	0.857518	−	1.09575i
$425$		−	2.86554i		−	0.138999i
$426$		0			0
$427$	−1.35070	+	7.15956i	−0.0653649	+	0.346475i
$428$	−10.8695	−	5.15290i	−0.525399	−	0.249075i
$429$		0			0
$430$	19.5482	+	4.39894i	0.942696	+	0.212136i
$431$			5.07919i			0.244656i	0.992490	+	0.122328i	$0.0390360\pi$
$431$			5.07919i			0.244656i	−0.992490	+	0.122328i	$0.960964\pi$
$432$		0			0
$433$			14.7817i			0.710364i	0.934797	+	0.355182i	$0.115581\pi$
$433$			14.7817i			0.710364i	−0.934797	+	0.355182i	$0.884419\pi$
$434$	−11.3458	+	26.2617i	−0.544617	+	1.26060i
$435$		0			0
$436$	8.44711	−	17.8184i	0.404543	−	0.853344i
$437$	−0.0937505			−0.00448469
$438$		0			0
$439$	−17.6945			−0.844512			−0.422256	−	0.906477i	$-0.638762\pi$
$439$	−17.6945			−0.844512			−0.422256	+	0.906477i	$0.638762\pi$
$440$	1.58370	+	1.23938i	0.0754998	+	0.0590850i
$441$		0			0
$442$	−10.8064	+	48.0218i	−0.514008	+	2.28417i
$443$	−35.8340			−1.70252			−0.851262	−	0.524742i	$-0.824162\pi$
$443$	−35.8340			−1.70252			−0.851262	+	0.524742i	$0.824162\pi$
$444$		0			0
$445$			9.53341i			0.451927i
$446$	21.3138	+	4.79627i	1.00924	+	0.227110i
$447$		0			0
$448$	−21.1325	+	1.19035i	−0.998417	+	0.0562388i
$449$	−18.1094			−0.854637			−0.427318	−	0.904101i	$-0.640542\pi$
$449$	−18.1094			−0.854637			−0.427318	+	0.904101i	$0.640542\pi$
$450$		0			0
$451$			2.63875i			0.124254i
$452$	26.6521	+	12.6349i	1.25361	+	0.594296i
$453$		0			0
$454$	−3.42696	+	15.2288i	−0.160835	+	0.714724i
$455$	6.25256	−	33.1425i	0.293125	−	1.55375i
$456$		0			0
$457$	−13.6177			−0.637010			−0.318505	−	0.947921i	$-0.603181\pi$
$457$	−13.6177			−0.637010			−0.318505	+	0.947921i	$0.603181\pi$
$458$	−10.2411	−	2.30457i	−0.478537	−	0.107685i
$459$		0			0
$460$	−0.223099	+	0.470606i	−0.0104021	+	0.0219421i
$461$	31.7263			1.47764			0.738821	−	0.673902i	$-0.235383\pi$
$461$	31.7263			1.47764			0.738821	+	0.673902i	$0.235383\pi$
$462$		0			0
$463$		−	24.0983i		−	1.11994i	−0.828511	−	0.559972i	$-0.810812\pi$
$463$		−	24.0983i		−	1.11994i	0.828511	−	0.559972i	$-0.189188\pi$
$464$	16.9097	−	13.8265i	0.785013	−	0.641880i
$465$		0			0
$466$	−18.0284	−	4.05695i	−0.835150	−	0.187935i
$467$		−	25.3568i		−	1.17337i	−0.809814	−	0.586687i	$-0.800432\pi$
$467$		−	25.3568i		−	1.17337i	0.809814	−	0.586687i	$-0.199568\pi$
$468$		0			0
$469$	4.10012	−	21.7332i	0.189326	−	1.00355i
$470$	−26.4577	−	5.95379i	−1.22040	−	0.274628i
$471$		0			0
$472$	2.98076	−	3.80886i	0.137200	−	0.175317i
$473$	1.84852			0.0849950
$474$		0			0
$475$			0.377843i			0.0173366i
$476$	27.2693	+	19.8471i	1.24989	+	0.909690i
$477$		0			0
$478$	2.65432	−	11.7954i	0.121406	−	0.539508i
$479$	40.2196			1.83768			0.918839	−	0.394632i	$-0.129128\pi$
$479$	40.2196			1.83768			0.918839	+	0.394632i	$0.129128\pi$
$480$		0			0
$481$			35.1762i			1.60390i
$482$	−2.37417	+	10.5504i	−0.108140	+	0.480559i
$483$		0			0
$484$	−19.7116	−	9.34466i	−0.895984	−	0.424757i
$485$		−	15.0070i		−	0.681434i
$486$		0			0
$487$		−	34.9584i		−	1.58412i	−0.610446	−	0.792058i	$-0.709010\pi$
$487$		−	34.9584i		−	1.58412i	0.610446	−	0.792058i	$-0.290990\pi$
$488$	6.13388	+	4.80028i	0.277668	+	0.217298i
$489$		0			0
$490$	−19.1477	−	12.9393i	−0.865003	−	0.584538i
$491$	−11.4808			−0.518121			−0.259061	−	0.965861i	$-0.583413\pi$
$491$	−11.4808			−0.518121			−0.259061	+	0.965861i	$0.583413\pi$
$492$		0			0
$493$	−34.8057			−1.56757
$494$	1.42490	−	6.33204i	0.0641094	−	0.284892i
$495$		0			0
$496$	19.3590	+	23.6759i	0.869247	+	1.06308i
$497$	5.39086	+	1.01702i	0.241813	+	0.0456197i
$498$		0			0
$499$	−1.23326			−0.0552084			−0.0276042	−	0.999619i	$-0.508788\pi$
$499$	−1.23326			−0.0552084			−0.0276042	+	0.999619i	$0.508788\pi$
$500$	−19.1973	−	9.10084i	−0.858531	−	0.407002i
$501$		0			0
$502$	3.94883	−	17.5480i	0.176245	−	0.783203i
$503$	5.04712			0.225040			0.112520	−	0.993649i	$-0.464108\pi$
$503$	5.04712			0.225040			0.112520	+	0.993649i	$0.464108\pi$
$504$		0			0
$505$	−16.3487			−0.727509
$506$	−0.0105484	+	0.0468753i	−0.000468933	+	0.00208386i
$507$		0			0
$508$	2.13573	−	4.50511i	0.0947576	−	0.199882i
$509$	−35.6387			−1.57966			−0.789828	−	0.613328i	$-0.789830\pi$
$509$	−35.6387			−1.57966			−0.789828	+	0.613328i	$0.789830\pi$
$510$		0			0
$511$	−33.1425	−	6.25256i	−1.46614	−	0.276597i
$512$	−9.25337	+	20.6489i	−0.408945	+	0.912559i
$513$		0			0
$514$	−2.31168	+	10.2727i	−0.101964	+	0.453111i
$515$	−22.4286			−0.988320
$516$		0			0
$517$	−2.50190			−0.110033
$518$	22.1260	+	9.55906i	0.972160	+	0.420001i
$519$		0			0
$520$	−28.3945	−	22.2211i	−1.24518	−	0.974460i
$521$			3.12151i			0.136756i	0.997659	+	0.0683780i	$0.0217824\pi$
$521$			3.12151i			0.136756i	−0.997659	+	0.0683780i	$0.978218\pi$
$522$		0			0
$523$			33.3779i			1.45951i	0.683706	+	0.729757i	$0.260367\pi$
$523$			33.3779i			1.45951i	−0.683706	+	0.729757i	$0.739633\pi$
$524$	−3.94883	+	8.32967i	−0.172505	+	0.363883i
$525$		0			0
$526$	−3.58752	+	15.9424i	−0.156423	+	0.695120i
$527$		−	48.7328i		−	2.12284i
$528$		0			0
$529$	22.9876			0.999459
$530$	7.34181	−	32.6258i	0.318908	−	1.41717i
$531$		0			0
$532$	−3.59566	−	2.61699i	−0.155892	−	0.113461i
$533$		−	47.3108i		−	2.04926i
$534$		0			0
$535$	−14.0406			−0.607027
$536$	−18.6197	−	14.5715i	−0.804248	−	0.629392i
$537$		0			0
$538$	16.8492	+	3.79159i	0.726420	+	0.163467i
$539$	−1.98545	−	0.776782i	−0.0855192	−	0.0334584i
$540$		0			0
$541$			13.8175i			0.594060i	0.954868	+	0.297030i	$0.0959961\pi$
$541$			13.8175i			0.594060i	−0.954868	+	0.297030i	$0.904004\pi$
$542$	26.1392	+	5.88213i	1.12278	+	0.252659i
$543$		0			0
$544$	32.2424	−	16.1385i	1.38238	−	0.691934i
$545$		−	23.0166i		−	0.985923i
$546$		0			0
$547$	−12.4978			−0.534368			−0.267184	−	0.963646i	$-0.586093\pi$
$547$	−12.4978			−0.534368			−0.267184	+	0.963646i	$0.586093\pi$
$548$	1.62496	+	0.770343i	0.0694150	+	0.0329074i
$549$		0			0
$550$	0.188921	+	0.0425131i	0.00805564	+	0.00181277i
$551$	4.58939			0.195515
$552$		0			0
$553$	−20.5565	−	3.87813i	−0.874153	−	0.164915i
$554$	−5.64683	+	25.0936i	−0.239911	+	1.06612i
$555$		0			0
$556$	−19.8560	+	41.8842i	−0.842081	+	1.77629i
$557$			7.57008i			0.320755i	0.987056	+	0.160377i	$0.0512711\pi$
$557$			7.57008i			0.320755i	−0.987056	+	0.160377i	$0.948729\pi$
$558$		0			0
$559$	−33.1425			−1.40178
$560$	−21.6933	+	11.8217i	−0.916710	+	0.499559i
$561$		0			0
$562$	24.1855	+	5.44248i	1.02020	+	0.229577i
$563$			15.0668i			0.634990i	0.948260	+	0.317495i	$0.102842\pi$
$563$			15.0668i			0.634990i	−0.948260	+	0.317495i	$0.897158\pi$
$564$		0			0
$565$	34.4275			1.44837
$566$	5.69285	−	25.2981i	0.239288	−	1.06336i
$567$		0			0
$568$	3.61441	−	4.61856i	0.151657	−	0.193790i
$569$	−36.7056			−1.53878			−0.769390	−	0.638780i	$-0.779440\pi$
$569$	−36.7056			−1.53878			−0.769390	+	0.638780i	$0.779440\pi$
$570$		0			0
$571$	−5.19529			−0.217416			−0.108708	−	0.994074i	$-0.534671\pi$
$571$	−5.19529			−0.217416			−0.108708	+	0.994074i	$0.534671\pi$
$572$	−3.00570	−	1.42490i	−0.125674	−	0.0595782i
$573$		0			0
$574$	−29.7587	−	12.8566i	−1.24210	−	0.536625i
$575$			0.0501503i			0.00209141i
$576$		0			0
$577$		−	43.9319i		−	1.82891i	−0.404688	−	0.914455i	$-0.632620\pi$
$577$		−	43.9319i		−	1.82891i	0.404688	−	0.914455i	$-0.367380\pi$
$578$	−32.5968	−	7.33528i	−1.35585	−	0.305108i
$579$		0			0
$580$	10.9214	−	23.0377i	0.453488	−	0.956588i
$581$	30.2805	+	5.71262i	1.25625	+	0.236999i
$582$		0			0
$583$		−	3.08517i		−	0.127775i
$584$	−22.2211	+	28.3945i	−0.919516	+	1.17497i
$585$		0			0
$586$	19.3171	+	4.34695i	0.797983	+	0.179571i
$587$			34.5380i			1.42553i	0.701400	+	0.712767i	$0.252559\pi$
$587$			34.5380i			1.42553i	−0.701400	+	0.712767i	$0.747441\pi$
$588$		0			0
$589$			6.42579i			0.264770i
$590$	1.23938	−	5.50759i	0.0510244	−	0.226744i
$591$		0			0
$592$	19.9474	−	16.3103i	0.819833	−	0.670351i
$593$		−	29.3232i		−	1.20416i	−0.798436	−	0.602080i	$-0.794339\pi$
$593$		−	29.3232i		−	1.20416i	0.798436	−	0.602080i	$-0.205661\pi$
$594$		0			0
$595$	38.6845	+	7.29810i	1.58591	+	0.299193i
$596$	−5.64072	+	11.8985i	−0.231053	+	0.487383i
$597$		0			0
$598$	0.189124	−	0.840438i	0.00773387	−	0.0343681i
$599$		−	19.9925i		−	0.816870i	−0.912787	−	0.408435i	$-0.866075\pi$
$599$		−	19.9925i		−	0.816870i	0.912787	−	0.408435i	$-0.133925\pi$
$600$		0			0
$601$		−	21.1008i		−	0.860721i	−0.902657	−	0.430361i	$-0.858386\pi$
$601$		−	21.1008i		−	0.860721i	0.902657	−	0.430361i	$-0.141614\pi$
$602$	−9.00641	+	20.8468i	−0.367074	+	0.849652i
$603$		0			0
$604$	−17.6205	+	37.1688i	−0.716969	+	1.51238i
$605$	−25.4622			−1.03519
$606$		0			0
$607$	21.6184			0.877463			0.438732	−	0.898618i	$-0.355428\pi$
$607$	21.6184			0.877463			0.438732	+	0.898618i	$0.355428\pi$
$608$	−4.25140	+	2.12799i	−0.172417	+	0.0863012i
$609$		0			0
$610$	8.86955	+	1.99592i	0.359117	+	0.0808125i
$611$	44.8571			1.81472
$612$		0			0
$613$		−	27.8723i		−	1.12575i	−0.826541	−	0.562876i	$-0.809695\pi$
$613$		−	27.8723i		−	1.12575i	0.826541	−	0.562876i	$-0.190305\pi$
$614$	1.32276	−	5.87813i	0.0533823	−	0.237222i
$615$		0			0
$616$	−1.71306	+	1.50338i	−0.0690212	+	0.0605729i
$617$	9.81447			0.395116			0.197558	−	0.980291i	$-0.436699\pi$
$617$	9.81447			0.395116			0.197558	+	0.980291i	$0.436699\pi$
$618$		0			0
$619$		−	22.8992i		−	0.920395i	−0.887817	−	0.460197i	$-0.847779\pi$
$619$		−	22.8992i		−	0.920395i	0.887817	−	0.460197i	$-0.152221\pi$
$620$	32.2560	+	15.2915i	1.29543	+	0.614122i
$621$		0			0
$622$	−16.0963	−	3.62216i	−0.645402	−	0.145235i
$623$	−10.6175	−	2.00306i	−0.425380	−	0.0802509i
$624$		0			0
$625$	−27.0458			−1.08183
$626$	1.42200	−	6.31912i	0.0568345	−	0.252563i
$627$		0			0
$628$	21.8519	+	10.3593i	0.871986	+	0.413380i
$629$	−41.0583			−1.63710
$630$		0			0
$631$			15.4442i			0.614823i	0.951577	+	0.307412i	$0.0994628\pi$
$631$			15.4442i			0.614823i	−0.951577	+	0.307412i	$0.900537\pi$
$632$	−13.7826	+	17.6116i	−0.548241	+	0.700551i
$633$		0			0
$634$	−3.92179	+	17.4278i	−0.155754	+	0.692146i
$635$		−	5.81941i		−	0.230936i
$636$		0			0
$637$	35.5976	+	13.9271i	1.41043	+	0.551813i
$638$	0.516377	−	2.29470i	0.0204436	−	0.0908479i
$639$		0			0
$640$	0.564886	+	26.4051i	0.0223291	+	1.04375i
$641$	6.58003			0.259896			0.129948	−	0.991521i	$-0.458519\pi$
$641$	6.58003			0.259896			0.129948	+	0.991521i	$0.458519\pi$
$642$		0			0
$643$		−	18.3358i		−	0.723093i	−0.932354	−	0.361546i	$-0.882249\pi$
$643$		−	18.3358i		−	0.723093i	0.932354	−	0.361546i	$-0.117751\pi$
$644$	−0.477245	−	0.347347i	−0.0188061	−	0.0136874i
$645$		0			0
$646$	7.39086	+	1.66317i	0.290789	+	0.0654366i
$647$	−10.4752			−0.411824			−0.205912	−	0.978571i	$-0.566016\pi$
$647$	−10.4752			−0.411824			−0.205912	+	0.978571i	$0.566016\pi$
$648$		0			0
$649$		−	0.520810i		−	0.0204436i
$650$	−3.38722	−	0.762229i	−0.132858	−	0.0298971i
$651$		0			0
$652$	0.649300	+	0.307812i	0.0254286	+	0.0120549i
$653$			37.9262i			1.48417i	0.670307	+	0.742084i	$0.266162\pi$
$653$			37.9262i			1.48417i	−0.670307	+	0.742084i	$0.733838\pi$
$654$		0			0
$655$			10.7597i			0.420417i
$656$	−26.8286	+	21.9368i	−1.04748	+	0.856490i
$657$		0			0
$658$	12.1898	−	28.2153i	0.475209	−	1.09995i
$659$	−11.2037			−0.436435			−0.218218	−	0.975900i	$-0.570024\pi$
$659$	−11.2037			−0.436435			−0.218218	+	0.975900i	$0.570024\pi$
$660$		0			0
$661$	4.78369			0.186064			0.0930320	−	0.995663i	$-0.470344\pi$
$661$	4.78369			0.186064			0.0930320	+	0.995663i	$0.470344\pi$
$662$	35.4406	+	7.97524i	1.37744	+	0.309966i
$663$		0			0
$664$	20.3022	−	25.9425i	0.787877	−	1.00676i
$665$	−5.10084	−	0.962308i	−0.197802	−	0.0373167i
$666$		0			0
$667$	0.609140			0.0235860
$668$	14.3054	+	6.78172i	0.553492	+	0.262393i
$669$		0			0
$670$	−26.9240	−	6.05872i	−1.04016	−	0.234069i
$671$	0.838724			0.0323786
$672$		0			0
$673$	−11.4707			−0.442162			−0.221081	−	0.975255i	$-0.570959\pi$
$673$	−11.4707			−0.442162			−0.221081	+	0.975255i	$0.570959\pi$
$674$	34.0977	+	7.67303i	1.31339	+	0.295554i
$675$		0			0
$676$	30.3962	+	14.4098i	1.16908	+	0.554225i
$677$	−39.0226			−1.49976			−0.749881	−	0.661573i	$-0.769889\pi$
$677$	−39.0226			−1.49976			−0.749881	+	0.661573i	$0.769889\pi$
$678$		0			0
$679$	16.7135	+	3.15312i	0.641406	+	0.121006i
$680$	25.9368	−	33.1425i	0.994633	−	1.27096i
$681$		0			0
$682$	3.21289	+	0.723000i	0.123028	+	0.0276851i
$683$	6.36772			0.243654			0.121827	−	0.992551i	$-0.461125\pi$
$683$	6.36772			0.243654			0.121827	+	0.992551i	$0.461125\pi$
$684$		0			0
$685$	2.09902			0.0801995
$686$	18.4338	−	18.6063i	0.703805	−	0.710393i
$687$		0			0
$688$	15.3674	+	18.7942i	0.585875	+	0.716520i
$689$			55.3148i			2.10732i
$690$		0			0
$691$			10.3191i			0.392558i	0.980548	+	0.196279i	$0.0628858\pi$
$691$			10.3191i			0.392558i	−0.980548	+	0.196279i	$0.937114\pi$
$692$	22.6098	+	10.7186i	0.859495	+	0.407459i
$693$		0			0
$694$	−24.5588	−	5.52648i	−0.932238	−	0.209782i
$695$			54.1034i			2.05226i
$696$		0			0
$697$	55.2220			2.09168
$698$	12.0140	+	2.70351i	0.454735	+	0.102329i
$699$		0			0
$700$	−1.39991	+	1.92344i	−0.0529118	+	0.0726992i
$701$			38.3982i			1.45028i	0.688601	+	0.725141i	$0.258225\pi$
$701$			38.3982i			1.45028i	−0.688601	+	0.725141i	$0.741775\pi$
$702$		0			0
$703$	5.41384			0.204187
$704$	0.585645	+	2.36513i	0.0220723	+	0.0891393i
$705$		0			0
$706$	−2.27771	+	10.1218i	−0.0857227	+	0.380938i
$707$	3.43502	−	18.2078i	0.129187	−	0.684775i
$708$		0			0
$709$		−	8.88381i		−	0.333638i	−0.985988	−	0.166819i	$-0.946650\pi$
$709$		−	8.88381i		−	0.333638i	0.985988	−	0.166819i	$-0.0533496\pi$
$710$	1.50285	−	6.67841i	0.0564009	−	0.250636i
$711$		0			0
$712$	−7.11871	+	9.09641i	−0.266785	+	0.340902i
$713$			0.852881i			0.0319407i
$714$		0			0
$715$	−3.88256			−0.145200
$716$	−27.7266	−	13.1443i	−1.03619	−	0.491226i
$717$		0			0
$718$	4.45707	−	19.8065i	0.166336	−	0.739171i
$719$	40.2196			1.49994			0.749968	−	0.661474i	$-0.230069\pi$
$719$	40.2196			1.49994			0.749968	+	0.661474i	$0.230069\pi$
$720$		0			0
$721$	4.71245	−	24.9790i	0.175501	−	0.930266i
$722$	25.2400	+	5.67977i	0.939335	+	0.211379i
$723$		0			0
$724$	0.891086	+	0.422435i	0.0331170	+	0.0156997i
$725$		−	2.45502i		−	0.0911772i
$726$		0			0
$727$	−2.89742			−0.107459			−0.0537297	−	0.998556i	$-0.517111\pi$
$727$	−2.89742			−0.107459			−0.0537297	+	0.998556i	$0.517111\pi$
$728$	30.7139	−	26.9545i	1.13833	−	0.998999i
$729$		0			0
$730$	−9.23938	+	41.0583i	−0.341965	+	1.51963i
$731$		−	38.6845i		−	1.43080i
$732$		0			0
$733$	6.37891			0.235611			0.117805	−	0.993037i	$-0.462414\pi$
$733$	6.37891			0.235611			0.117805	+	0.993037i	$0.462414\pi$
$734$	24.0208	+	5.40541i	0.886623	+	0.199517i
$735$		0			0
$736$	−0.564280	+	0.282443i	−0.0207996	+	0.0104110i
$737$	−2.54599			−0.0937827
$738$		0			0
$739$	−7.14100			−0.262686			−0.131343	−	0.991337i	$-0.541929\pi$
$739$	−7.14100			−0.262686			−0.131343	+	0.991337i	$0.541929\pi$
$740$	12.8834	−	27.1762i	0.473602	−	0.999018i
$741$		0			0
$742$	34.7932	+	15.0317i	1.27730	+	0.551830i
$743$		−	22.2570i		−	0.816530i	−0.912864	−	0.408265i	$-0.866134\pi$
$743$		−	22.2570i		−	0.816530i	0.912864	−	0.408265i	$-0.133866\pi$
$744$		0			0
$745$			15.3698i			0.563105i
$746$	0.447110	−	1.98688i	0.0163699	−	0.0727450i
$747$		0			0
$748$	1.66317	−	3.50830i	0.0608116	−	0.128276i
$749$	2.95006	−	15.6372i	0.107793	−	0.571370i
$750$		0			0
$751$			21.7697i			0.794387i	0.917735	+	0.397193i	$0.130016\pi$
$751$			21.7697i			0.794387i	−0.917735	+	0.397193i	$0.869984\pi$
$752$	−20.7991	−	25.4371i	−0.758466	−	0.927597i
$753$		0			0
$754$	−9.25826	+	41.1422i	−0.337166	+	1.49831i
$755$			48.0122i			1.74734i
$756$		0			0
$757$			4.51372i			0.164054i	0.996630	+	0.0820269i	$0.0261393\pi$
$757$			4.51372i			0.164054i	−0.996630	+	0.0820269i	$0.973861\pi$
$758$	−33.1215	−	7.45336i	−1.20303	−	0.270718i
$759$		0			0
$760$	−3.41997	+	4.37009i	−0.124055	+	0.158520i
$761$		−	3.12151i		−	0.113155i	−0.998398	−	0.0565774i	$-0.981981\pi$
$761$		−	3.12151i		−	0.113155i	0.998398	−	0.0565774i	$-0.0180188\pi$
$762$		0			0
$763$	25.6339	+	4.83601i	0.928009	+	0.175075i
$764$	−18.6862	+	39.4166i	−0.676041	+	1.42604i
$765$		0			0
$766$	−27.0177	−	6.07982i	−0.976189	−	0.219673i
$767$			9.33773i			0.337166i
$768$		0			0
$769$			52.3945i			1.88939i	0.327944	+	0.944697i	$0.393644\pi$
$769$			52.3945i			1.88939i	−0.327944	+	0.944697i	$0.606356\pi$
$770$	−1.05508	+	2.44215i	−0.0380224	+	0.0880089i
$771$		0			0
$772$	13.7133	+	6.50103i	0.493552	+	0.233977i
$773$	14.5408			0.522996			0.261498	−	0.965204i	$-0.415784\pi$
$773$	14.5408			0.522996			0.261498	+	0.965204i	$0.415784\pi$
$774$		0			0
$775$	3.43737			0.123474
$776$	11.2059	−	14.3191i	0.402269	−	0.514027i
$777$		0			0
$778$	9.81287	−	43.6068i	0.351808	−	1.56338i
$779$	−7.28143			−0.260884
$780$		0			0
$781$		−	0.631525i		−	0.0225977i
$782$	0.980973	+	0.220749i	0.0350795	+	0.00789398i
$783$		0			0
$784$	−8.60803	−	26.6440i	−0.307430	−	0.951571i
$785$	28.2269			1.00746
$786$		0			0
$787$			18.0754i			0.644318i	0.946686	+	0.322159i	$0.104409\pi$
$787$			18.0754i			0.644318i	−0.946686	+	0.322159i	$0.895591\pi$
$788$	10.1033	−	21.3119i	0.359916	−	0.759207i
$789$		0			0
$790$	−5.73069	+	25.4662i	−0.203889	+	0.906048i
$791$	−7.23354	+	38.3423i	−0.257195	+	1.36330i
$792$		0			0
$793$	−15.0377			−0.534004
$794$	−8.69141	−	1.95583i	−0.308447	−	0.0694100i
$795$		0			0
$796$	−44.7930	−	21.2349i	−1.58765	−	0.752653i
$797$	8.28822			0.293584			0.146792	−	0.989167i	$-0.453105\pi$
$797$	8.28822			0.293584			0.146792	+	0.989167i	$0.453105\pi$
$798$		0			0
$799$			52.3580i			1.85229i
$800$	1.13833	+	2.27422i	0.0402461	+	0.0804058i
$801$		0			0
$802$	−4.27827	−	0.962742i	−0.151071	−	0.0339956i
$803$			3.88256i			0.137013i
$804$		0			0
$805$	−0.677024	−	0.127725i	−0.0238620	−	0.00450172i
$806$	−57.6048	−	12.9629i	−2.02904	−	0.456597i
$807$		0			0
$808$	−15.5993	−	12.2078i	−0.548783	−	0.429469i
$809$	52.3022			1.83885			0.919425	−	0.393266i	$-0.128655\pi$
$809$	52.3022			1.83885			0.919425	+	0.393266i	$0.128655\pi$
$810$		0			0
$811$		−	16.3945i		−	0.575689i	−0.957677	−	0.287845i	$-0.907061\pi$
$811$		−	16.3945i		−	0.575689i	0.957677	−	0.287845i	$-0.0929386\pi$
$812$	23.3627	+	17.0038i	0.819869	+	0.596716i
$813$		0			0
$814$	0.609140	−	2.70692i	0.0213504	−	0.0948775i
$815$	0.838724			0.0293792
$816$		0			0
$817$			5.10084i			0.178456i
$818$	0.952172	−	4.23130i	0.0332919	−	0.147944i
$819$		0			0
$820$	−17.3277	+	36.5511i	−0.605110	+	1.27642i
$821$		−	14.9459i		−	0.521614i	−0.965391	−	0.260807i	$-0.916011\pi$
$821$		−	14.9459i		−	0.521614i	0.965391	−	0.260807i	$-0.0839887\pi$
$822$		0			0
$823$			21.3876i			0.745526i	0.927927	+	0.372763i	$0.121590\pi$
$823$			21.3876i			0.745526i	−0.927927	+	0.372763i	$0.878410\pi$
$824$	−21.4005	−	16.7477i	−0.745520	−	0.583433i
$825$		0			0
$826$	5.87347	+	2.53751i	0.204364	+	0.0882912i
$827$	16.5605			0.575866			0.287933	−	0.957650i	$-0.407032\pi$
$827$	16.5605			0.575866			0.287933	+	0.957650i	$0.407032\pi$
$828$		0			0
$829$	47.4372			1.64756			0.823781	−	0.566908i	$-0.191861\pi$
$829$	47.4372			1.64756			0.823781	+	0.566908i	$0.191861\pi$
$830$	8.44150	−	37.5126i	0.293009	−	1.30208i
$831$		0			0
$832$	−10.5002	−	42.4051i	−0.364028	−	1.47013i
$833$	−16.2560	+	41.5501i	−0.563236	+	1.43962i
$834$		0			0
$835$	18.4788			0.639484
$836$	−0.219302	+	0.462595i	−0.00758470	+	0.0159992i
$837$		0			0
$838$	4.82153	−	21.4261i	0.166557	−	0.740152i
$839$	−12.3796			−0.427390			−0.213695	−	0.976900i	$-0.568550\pi$
$839$	−12.3796			−0.427390			−0.213695	+	0.976900i	$0.568550\pi$
$840$		0			0
$841$	−0.819411			−0.0282555
$842$	−5.39086	+	23.9561i	−0.185781	+	0.825582i
$843$		0			0
$844$	25.4261	+	12.0537i	0.875202	+	0.414905i
$845$	39.2638			1.35072
$846$		0			0
$847$	5.34985	−	28.3576i	0.183823	−	0.974379i
$848$	31.3674	−	25.6481i	1.07716	−	0.880758i
$849$		0			0
$850$	0.889686	−	3.95362i	0.0305160	−	0.135608i
$851$	0.718568			0.0246322
$852$		0			0
$853$	−27.8292			−0.952855			−0.476428	−	0.879214i	$-0.658069\pi$
$853$	−27.8292			−0.952855			−0.476428	+	0.879214i	$0.658069\pi$
$854$	−4.08646	+	9.45877i	−0.139836	+	0.323672i
$855$		0			0
$856$	−13.3970	−	10.4843i	−0.457899	−	0.358345i
$857$		−	19.8278i		−	0.677306i	−0.940911	−	0.338653i	$-0.890029\pi$
$857$		−	19.8278i		−	0.677306i	0.940911	−	0.338653i	$-0.109971\pi$
$858$		0			0
$859$		−	35.5541i		−	1.21309i	−0.795049	−	0.606545i	$-0.792555\pi$
$859$		−	35.5541i		−	1.21309i	0.795049	−	0.606545i	$-0.207445\pi$
$860$	25.6051	+	12.1385i	0.873125	+	0.413921i
$861$		0			0
$862$	−1.57698	+	7.00782i	−0.0537120	+	0.238687i
$863$			32.6385i			1.11103i	0.831508	+	0.555513i	$0.187478\pi$
$863$			32.6385i			1.11103i	−0.831508	+	0.555513i	$0.812522\pi$
$864$		0			0
$865$	29.2058			0.993028
$866$	−4.58939	+	20.3945i	−0.155954	+	0.693034i
$867$		0			0
$868$	−23.8077	+	32.7110i	−0.808084	+	1.11028i
$869$			2.40814i			0.0816907i
$870$		0			0
$871$	45.6477			1.54671
$872$	17.1868	−	21.9615i	0.582018	−	0.743712i
$873$		0			0
$874$	−0.129349	−	0.0291074i	−0.00437528	−	0.000984574i
$875$	5.21027	−	27.6177i	0.176139	−	0.933649i
$876$		0			0
$877$			31.1987i			1.05350i	0.850019	+	0.526752i	$0.176590\pi$
$877$			31.1987i			1.05350i	−0.850019	+	0.526752i	$0.823410\pi$
$878$	−24.4133	−	5.49374i	−0.823909	−	0.185405i
$879$		0			0
$880$	1.80025	+	2.20169i	0.0606863	+	0.0742188i
$881$		−	51.2309i		−	1.72601i	−0.505192	−	0.863007i	$-0.668578\pi$
$881$		−	51.2309i		−	1.72601i	0.505192	−	0.863007i	$-0.331422\pi$
$882$		0			0
$883$	−16.9684			−0.571033			−0.285516	−	0.958374i	$-0.592165\pi$
$883$	−16.9684			−0.571033			−0.285516	+	0.958374i	$0.592165\pi$
$884$	−29.8194	+	62.9011i	−1.00294	+	2.11559i
$885$		0			0
$886$	−49.4405	−	11.1256i	−1.66099	−	0.373773i
$887$	−18.7434			−0.629342			−0.314671	−	0.949201i	$-0.601894\pi$
$887$	−18.7434			−0.629342			−0.314671	+	0.949201i	$0.601894\pi$
$888$		0			0
$889$	6.48115	+	1.22271i	0.217371	+	0.0410085i
$890$	−2.95991	+	13.1534i	−0.0992164	+	0.440901i
$891$		0			0
$892$	27.9178	+	13.2349i	0.934758	+	0.443139i
$893$		−	6.90379i		−	0.231026i
$894$		0			0
$895$	−35.8155			−1.19718
$896$	−29.5263	−	4.91883i	−0.986406	−	0.164327i
$897$		0			0
$898$	−24.9858	−	5.62257i	−0.833786	−	0.187628i
$899$		−	41.7513i		−	1.39248i
$900$		0			0
$901$	−64.5643			−2.15095
$902$	−0.819273	+	3.64072i	−0.0272788	+	0.121223i
$903$		0			0
$904$	32.8494	+	25.7074i	1.09255	+	0.855016i
$905$	1.15105			0.0382621
$906$		0			0
$907$	1.15395			0.0383163			0.0191581	−	0.999816i	$-0.493901\pi$
$907$	1.15395			0.0383163			0.0191581	+	0.999816i	$0.493901\pi$
$908$	−9.45642	+	19.9474i	−0.313822	+	0.661978i
$909$		0			0
$910$	18.9168	−	43.7859i	0.627084	−	1.45149i
$911$			44.7588i			1.48292i	0.670994	+	0.741462i	$0.265867\pi$
$911$			44.7588i			1.48292i	−0.670994	+	0.741462i	$0.734133\pi$
$912$		0			0
$913$		−	3.54728i		−	0.117398i
$914$	−18.7885	−	4.22800i	−0.621469	−	0.139850i
$915$		0			0
$916$	−13.4143	−	6.35928i	−0.443221	−	0.210117i
$917$	−11.9833	−	2.26072i	−0.395722	−	0.0746556i
$918$		0			0
$919$			40.3722i			1.33176i	0.746060	+	0.665878i	$0.231943\pi$
$919$			40.3722i			1.33176i	−0.746060	+	0.665878i	$0.768057\pi$
$920$	−0.453925	+	0.580033i	−0.0149655	+	0.0191231i
$921$		0			0
$922$	43.7731	+	9.85031i	1.44159	+	0.324403i
$923$			11.3228i			0.372694i
$924$		0			0
$925$		−	2.89604i		−	0.0952214i
$926$	7.48200	−	33.2488i	0.245874	−	1.09262i
$927$		0			0
$928$	27.6233	−	13.8265i	0.906780	−	0.453877i
$929$			13.4697i			0.441928i	0.975282	+	0.220964i	$0.0709203\pi$
$929$			13.4697i			0.441928i	−0.975282	+	0.220964i	$0.929080\pi$
$930$		0			0
$931$	2.14347	−	5.47869i	0.0702494	−	0.179557i
$932$	−23.6144	−	11.1948i	−0.773516	−	0.366699i
$933$		0			0
$934$	7.87272	−	34.9851i	0.257603	−	1.14475i
$935$		−	4.53179i		−	0.148205i
$936$		0			0
$937$		−	11.6055i		−	0.379135i	−0.981868	−	0.189567i	$-0.939291\pi$
$937$		−	11.6055i		−	0.379135i	0.981868	−	0.189567i	$-0.0607086\pi$
$938$	12.4047	−	28.7126i	0.405026	−	0.937498i
$939$		0			0
$940$	−34.6554	−	16.4290i	−1.13034	−	0.535856i
$941$	29.2387			0.953154			0.476577	−	0.879133i	$-0.341877\pi$
$941$	29.2387			0.953154			0.476577	+	0.879133i	$0.341877\pi$
$942$		0			0
$943$	−0.966449			−0.0314719
$944$	5.29515	−	4.32967i	0.172343	−	0.140919i
$945$		0			0
$946$	2.55042	+	0.573923i	0.0829214	+	0.0186599i
$947$	24.0096			0.780208			0.390104	−	0.920771i	$-0.372439\pi$
$947$	24.0096			0.780208			0.390104	+	0.920771i	$0.372439\pi$
$948$		0			0
$949$		−	69.6114i		−	2.25968i
$950$	−0.117312	+	0.521314i	−0.00380610	+	0.0169137i
$951$		0			0
$952$	31.4617	+	35.8498i	1.01968	+	1.16190i
$953$	−38.6716			−1.25270			−0.626348	−	0.779544i	$-0.715451\pi$
$953$	−38.6716			−1.25270			−0.626348	+	0.779544i	$0.715451\pi$
$954$		0			0
$955$			50.9158i			1.64760i
$956$	7.32440	−	15.4501i	0.236888	−	0.499692i
$957$		0			0
$958$	55.4914	+	12.4873i	1.79284	+	0.403445i
$959$	−0.441024	+	2.33771i	−0.0142414	+	0.0754885i
$960$		0			0
$961$	27.4577			0.885731
$962$	−10.9214	+	48.5330i	−0.352121	+	1.56477i
$963$		0			0
$964$	−6.55134	+	13.8194i	−0.211004	+	0.445093i
$965$	17.7139			0.570232
$966$		0			0
$967$		−	12.2768i		−	0.394795i	−0.980324	−	0.197397i	$-0.936751\pi$
$967$		−	12.2768i		−	0.394795i	0.980324	−	0.197397i	$-0.0632489\pi$
$968$	−24.2951	−	19.0130i	−0.780873	−	0.611099i
$969$		0			0
$970$	4.65934	−	20.7054i	0.149603	−	0.664809i
$971$			20.5330i			0.658937i	0.944167	+	0.329468i	$0.106869\pi$
$971$			20.5330i			0.658937i	−0.944167	+	0.329468i	$0.893131\pi$
$972$		0			0
$973$	−60.2556	−	11.3676i	−1.93171	−	0.364429i
$974$	10.8538	−	48.2325i	0.347778	−	1.54547i
$975$		0			0
$976$	6.97260	+	8.52743i	0.223187	+	0.272956i
$977$	10.7477			0.343849			0.171924	−	0.985110i	$-0.445002\pi$
$977$	10.7477			0.343849			0.171924	+	0.985110i	$0.445002\pi$
$978$		0			0
$979$			1.24381i			0.0397523i
$980$	−22.4009	−	23.7974i	−0.715570	−	0.760181i
$981$		0			0
$982$	−15.8402	−	3.56453i	−0.505481	−	0.113749i
$983$	−26.5912			−0.848128			−0.424064	−	0.905632i	$-0.639397\pi$
$983$	−26.5912			−0.848128			−0.424064	+	0.905632i	$0.639397\pi$
$984$		0			0
$985$		−	27.5294i		−	0.877159i
$986$	−48.0218	−	10.8064i	−1.52933	−	0.344146i
$987$		0			0
$988$	3.93191	−	8.29398i	0.125091	−	0.263867i
$989$			0.677024i			0.0215281i
$990$		0			0
$991$			30.5203i			0.969510i	0.874650	+	0.484755i	$0.161091\pi$
$991$			30.5203i			0.969510i	−0.874650	+	0.484755i	$0.838909\pi$
$992$	19.3590	+	38.6765i	0.614650	+	1.22798i
$993$		0			0
$994$	7.12207	+	3.07694i	0.225898	+	0.0975946i
$995$	−57.8607			−1.83431
$996$		0			0
$997$	−23.6105			−0.747752			−0.373876	−	0.927479i	$-0.621971\pi$
$997$	−23.6105			−0.747752			−0.373876	+	0.927479i	$0.621971\pi$
$998$	−1.70155	−	0.382900i	−0.0538615	−	0.0121205i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.p.g.307.16		16
3.2	odd	2		168.2.p.a.139.2	yes	16
4.3	odd	2		2016.2.p.g.559.13		16
7.6	odd	2	inner	504.2.p.g.307.15		16
8.3	odd	2	inner	504.2.p.g.307.13		16
8.5	even	2		2016.2.p.g.559.4		16
12.11	even	2		672.2.p.a.559.2		16
21.20	even	2		168.2.p.a.139.1	✓	16
24.5	odd	2		672.2.p.a.559.7		16
24.11	even	2		168.2.p.a.139.4	yes	16
28.27	even	2		2016.2.p.g.559.3		16
56.13	odd	2		2016.2.p.g.559.14		16
56.27	even	2	inner	504.2.p.g.307.14		16
84.83	odd	2		672.2.p.a.559.15		16
168.83	odd	2		168.2.p.a.139.3	yes	16
168.125	even	2		672.2.p.a.559.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.p.a.139.1	✓	16	21.20	even	2
168.2.p.a.139.2	yes	16	3.2	odd	2
168.2.p.a.139.3	yes	16	168.83	odd	2
168.2.p.a.139.4	yes	16	24.11	even	2
504.2.p.g.307.13		16	8.3	odd	2	inner
504.2.p.g.307.14		16	56.27	even	2	inner
504.2.p.g.307.15		16	7.6	odd	2	inner
504.2.p.g.307.16		16	1.1	even	1	trivial
672.2.p.a.559.2		16	12.11	even	2
672.2.p.a.559.7		16	24.5	odd	2
672.2.p.a.559.10		16	168.125	even	2
672.2.p.a.559.15		16	84.83	odd	2
2016.2.p.g.559.3		16	28.27	even	2
2016.2.p.g.559.4		16	8.5	even	2
2016.2.p.g.559.13		16	4.3	odd	2
2016.2.p.g.559.14		16	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37971 + 0.310478i) q^{2} +(1.80721 + 0.856739i) q^{4} +2.33443 q^{5} +(-0.490487 + 2.59989i) q^{7} +(2.22743 + 1.74315i) q^{8} +O(q^{10})\)	\(q+(1.37971 + 0.310478i) q^{2} +(1.80721 + 0.856739i) q^{4} +2.33443 q^{5} +(-0.490487 + 2.59989i) q^{7} +(2.22743 + 1.74315i) q^{8} +(3.22084 + 0.724789i) q^{10} +0.304570 q^{11} -5.46072 q^{13} +(-1.48394 + 3.43481i) q^{14} +(2.53200 + 3.09661i) q^{16} -6.37384i q^{17} +0.840438i q^{19} +(4.21880 + 2.00000i) q^{20} +(0.420219 + 0.0945622i) q^{22} +0.111550i q^{23} +0.449578 q^{25} +(-7.53421 - 1.69543i) q^{26} +(-3.11384 + 4.27832i) q^{28} -5.46072i q^{29} +7.64576 q^{31} +(2.53200 + 5.05856i) q^{32} +(1.97893 - 8.79406i) q^{34} +(-1.14501 + 6.06927i) q^{35} -6.44169i q^{37} +(-0.260937 + 1.15956i) q^{38} +(5.19978 + 4.06927i) q^{40} +8.66385i q^{41} +6.06927 q^{43} +(0.550422 + 0.260937i) q^{44} +(-0.0346336 + 0.153906i) q^{46} -8.21451 q^{47} +(-6.51885 - 2.55042i) q^{49} +(0.620289 + 0.139584i) q^{50} +(-9.86864 - 4.67841i) q^{52} -10.1296i q^{53} +0.710999 q^{55} +(-5.62452 + 4.93607i) q^{56} +(1.69543 - 7.53421i) q^{58} -1.70998i q^{59} +2.75380 q^{61} +(10.5489 + 2.37384i) q^{62} +(1.92286 + 7.76548i) q^{64} -12.7477 q^{65} -8.35928 q^{67} +(5.46072 - 11.5188i) q^{68} +(-3.46415 + 8.01834i) q^{70} -2.07350i q^{71} +12.7477i q^{73} +(2.00000 - 8.88767i) q^{74} +(-0.720036 + 1.51885i) q^{76} +(-0.149388 + 0.791849i) q^{77} +7.90670i q^{79} +(5.91078 + 7.22883i) q^{80} +(-2.68993 + 11.9536i) q^{82} -11.6468i q^{83} -14.8793i q^{85} +(8.37384 + 1.88437i) q^{86} +(0.678408 + 0.530912i) q^{88} +4.08382i q^{89} +(2.67841 - 14.1973i) q^{91} +(-0.0955689 + 0.201593i) q^{92} +(-11.3337 - 2.55042i) q^{94} +1.96195i q^{95} -6.42855i q^{97} +(-8.20228 - 5.54280i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8	\( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64} - 40 q^{67} - 24 q^{70} + 32 q^{74} + 32 q^{86} - 88 q^{88} - 56 q^{91} - 44 q^{92} - 66 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 2 * q^4 + 10 * q^8 + 8 * q^11 + 14 * q^14 + 18 * q^16 + 8 * q^22 + 16 * q^25 - 10 * q^28 + 18 * q^32 - 24 * q^35 - 8 * q^43 + 52 * q^46 - 8 * q^49 + 34 * q^50 - 50 * q^56 + 24 * q^58 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 32 * q^74 + 32 * q^86 - 88 * q^88 - 56 * q^91 - 44 * q^92 - 66 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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