LMFDB - Embedded newform 504.2.bk.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.b.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35459 - 0.406311i) q^{2} +(1.66982 + 1.10077i) q^{4} +(1.09169 - 1.89086i) q^{5} +(1.40064 - 2.24459i) q^{7} +(-1.81467 - 2.16955i) q^{8} +O(q^{10})$	\(q+(-1.35459 - 0.406311i) q^{2} +(1.66982 + 1.10077i) q^{4} +(1.09169 - 1.89086i) q^{5} +(1.40064 - 2.24459i) q^{7} +(-1.81467 - 2.16955i) q^{8} +(-2.24706 + 2.11777i) q^{10} +(-2.14393 - 3.71339i) q^{11} -2.03680 q^{13} +(-2.80930 + 2.47141i) q^{14} +(1.57662 + 3.67618i) q^{16} +(-1.56503 + 0.903573i) q^{17} +(0.509293 + 0.294040i) q^{19} +(3.90432 - 1.95570i) q^{20} +(1.39535 + 5.90122i) q^{22} +(0.146540 + 0.0846050i) q^{23} +(0.116439 + 0.201678i) q^{25} +(2.75903 + 0.827573i) q^{26} +(4.80960 - 2.20630i) q^{28} -0.439341i q^{29} +(-2.82167 - 4.88727i) q^{31} +(-0.642005 - 5.62031i) q^{32} +(2.48711 - 0.588080i) q^{34} +(-2.71515 - 5.09881i) q^{35} +(-7.72782 - 4.46166i) q^{37} +(-0.570411 - 0.605235i) q^{38} +(-6.08337 + 1.06281i) q^{40} +10.6450i q^{41} +8.59999 q^{43} +(0.507600 - 8.56067i) q^{44} +(-0.164126 - 0.174146i) q^{46} +(5.47872 - 9.48943i) q^{47} +(-3.07641 - 6.28774i) q^{49} +(-0.0757829 - 0.320501i) q^{50} +(-3.40109 - 2.24204i) q^{52} +(-4.53358 + 2.61746i) q^{53} -9.36199 q^{55} +(-7.41147 + 1.03443i) q^{56} +(-0.178509 + 0.595127i) q^{58} +(0.730458 - 0.421730i) q^{59} +(4.22231 - 7.31325i) q^{61} +(1.83645 + 7.76671i) q^{62} +(-1.41394 + 7.87406i) q^{64} +(-2.22355 + 3.85130i) q^{65} +(-6.87640 - 11.9103i) q^{67} +(-3.60796 - 0.213932i) q^{68} +(1.60621 + 8.00998i) q^{70} +9.72611i q^{71} +(11.0785 - 6.39620i) q^{73} +(8.65520 + 9.18361i) q^{74} +(0.526759 + 1.05161i) q^{76} +(-11.3379 - 0.388881i) q^{77} +(0.784867 + 0.453143i) q^{79} +(8.67230 + 1.03207i) q^{80} +(4.32519 - 14.4197i) q^{82} -11.4885i q^{83} +3.94568i q^{85} +(-11.6495 - 3.49427i) q^{86} +(-4.16588 + 11.3900i) q^{88} +(14.5327 + 8.39047i) q^{89} +(-2.85282 + 4.57179i) q^{91} +(0.151566 + 0.302582i) q^{92} +(-11.2771 + 10.6282i) q^{94} +(1.11198 - 0.642000i) q^{95} +13.3483i q^{97} +(1.61249 + 9.76729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4}+O(q^{10}) $ 32 * q + 2 * q^4	$ 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) $ 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.35459	−	0.406311i	−0.957839	−	0.287305i
$2$	−1.35459	−	0.406311i	−0.957839	−	0.287305i
$3$		0			0
$3$		0			0
$4$	1.66982	+	1.10077i	0.834912	+	0.550384i
$5$	1.09169	−	1.89086i	0.488217	−	0.845617i	−0.511691	−	0.859170i	$-0.670981\pi$
$5$	1.09169	−	1.89086i	0.488217	−	0.845617i	0.999908	+	0.0135525i	$0.00431402\pi$
$6$		0			0
$7$	1.40064	−	2.24459i	0.529393	−	0.848377i
$7$	1.40064	−	2.24459i	0.529393	−	0.848377i
$8$	−1.81467	−	2.16955i	−0.641583	−	0.767053i
$9$		0			0
$10$	−2.24706	+	2.11777i	−0.710584	+	0.669698i
$11$	−2.14393	−	3.71339i	−0.646418	−	1.11963i	−0.983972	−	0.178323i	$-0.942933\pi$
$11$	−2.14393	−	3.71339i	−0.646418	−	1.11963i	0.337554	−	0.941306i	$-0.390401\pi$
$12$		0			0
$13$	−2.03680			−0.564906			−0.282453	−	0.959281i	$-0.591148\pi$
$13$	−2.03680			−0.564906			−0.282453	+	0.959281i	$0.591148\pi$
$14$	−2.80930	+	2.47141i	−0.750816	+	0.660512i
$15$		0			0
$16$	1.57662	+	3.67618i	0.394155	+	0.919044i
$17$	−1.56503	+	0.903573i	−0.379577	+	0.219149i	−0.677634	−	0.735399i	$-0.736995\pi$
$17$	−1.56503	+	0.903573i	−0.379577	+	0.219149i	0.298057	+	0.954548i	$0.403661\pi$
$18$		0			0
$19$	0.509293	+	0.294040i	0.116840	+	0.0674575i	0.557281	−	0.830324i	$-0.311845\pi$
$19$	0.509293	+	0.294040i	0.116840	+	0.0674575i	−0.440441	+	0.897781i	$0.645178\pi$
$20$	3.90432	−	1.95570i	0.873032	−	0.437309i
$21$		0			0
$22$	1.39535	+	5.90122i	0.297490	+	1.25814i
$23$	0.146540	+	0.0846050i	0.0305557	+	0.0176414i	0.515200	−	0.857070i	$-0.327718\pi$
$23$	0.146540	+	0.0846050i	0.0305557	+	0.0176414i	−0.484644	+	0.874711i	$0.661051\pi$
$24$		0			0
$25$	0.116439	+	0.201678i	0.0232878	+	0.0403356i
$26$	2.75903	+	0.827573i	0.541089	+	0.162300i
$27$		0			0
$28$	4.80960	−	2.20630i	0.908929	−	0.416951i
$29$		−	0.439341i		−	0.0815836i	−0.999168	−	0.0407918i	$-0.987012\pi$
$29$		−	0.439341i		−	0.0815836i	0.999168	−	0.0407918i	$-0.0129880\pi$
$30$		0			0
$31$	−2.82167	−	4.88727i	−0.506786	−	0.877779i	−0.999969	−	0.00785368i	$-0.997500\pi$
$31$	−2.82167	−	4.88727i	−0.506786	−	0.877779i	0.493183	−	0.869926i	$-0.335833\pi$
$32$	−0.642005	−	5.62031i	−0.113492	−	0.993539i
$33$		0			0
$34$	2.48711	−	0.588080i	0.426536	−	0.100855i
$35$	−2.71515	−	5.09881i	−0.458944	−	0.861856i
$36$		0			0
$37$	−7.72782	−	4.46166i	−1.27045	−	0.733492i	−0.295373	−	0.955382i	$-0.595444\pi$
$37$	−7.72782	−	4.46166i	−1.27045	−	0.733492i	−0.975072	+	0.221890i	$0.928777\pi$
$38$	−0.570411	−	0.605235i	−0.0925328	−	0.0981820i
$39$		0			0
$40$	−6.08337	+	1.06281i	−0.961866	+	0.168045i
$41$			10.6450i			1.66248i	0.555917	+	0.831238i	$0.312367\pi$
$41$			10.6450i			1.66248i	−0.555917	+	0.831238i	$0.687633\pi$
$42$		0			0
$43$	8.59999			1.31149			0.655743	−	0.754984i	$-0.272356\pi$
$43$	8.59999			1.31149			0.655743	+	0.754984i	$0.272356\pi$
$44$	0.507600	−	8.56067i	0.0765237	−	1.29057i
$45$		0			0
$46$	−0.164126	−	0.174146i	−0.0241990	−	0.0256764i
$47$	5.47872	−	9.48943i	0.799154	−	1.38418i	−0.121014	−	0.992651i	$-0.538614\pi$
$47$	5.47872	−	9.48943i	0.799154	−	1.38418i	0.920168	−	0.391525i	$-0.128052\pi$
$48$		0			0
$49$	−3.07641	−	6.28774i	−0.439487	−	0.898249i
$50$	−0.0757829	−	0.320501i	−0.0107173	−	0.0453257i
$51$		0			0
$52$	−3.40109	−	2.24204i	−0.471647	−	0.310915i
$53$	−4.53358	+	2.61746i	−0.622735	+	0.359536i	−0.777933	−	0.628347i	$-0.783732\pi$
$53$	−4.53358	+	2.61746i	−0.622735	+	0.359536i	0.155198	+	0.987883i	$0.450398\pi$
$54$		0			0
$55$	−9.36199			−1.26237
$56$	−7.41147	+	1.03443i	−0.990400	+	0.138232i
$57$		0			0
$58$	−0.178509	+	0.595127i	−0.0234394	+	0.0781440i
$59$	0.730458	−	0.421730i	0.0950976	−	0.0549046i	−0.451697	−	0.892171i	$-0.649181\pi$
$59$	0.730458	−	0.421730i	0.0950976	−	0.0549046i	0.546795	+	0.837267i	$0.315848\pi$
$60$		0			0
$61$	4.22231	−	7.31325i	0.540611	−	0.936366i	−0.458258	−	0.888819i	$-0.651526\pi$
$61$	4.22231	−	7.31325i	0.540611	−	0.936366i	0.998869	−	0.0475464i	$-0.0151402\pi$
$62$	1.83645	+	7.76671i	0.233229	+	0.986373i
$63$		0			0
$64$	−1.41394	+	7.87406i	−0.176742	+	0.984257i
$65$	−2.22355	+	3.85130i	−0.275797	+	0.477694i
$66$		0			0
$67$	−6.87640	−	11.9103i	−0.840086	−	1.45507i	−0.889821	−	0.456310i	$-0.849171\pi$
$67$	−6.87640	−	11.9103i	−0.840086	−	1.45507i	0.0497346	−	0.998762i	$-0.484162\pi$
$68$	−3.60796	−	0.213932i	−0.437529	−	0.0259430i
$69$		0			0
$70$	1.60621	+	8.00998i	0.191979	+	0.957376i
$71$			9.72611i			1.15428i	0.816646	+	0.577139i	$0.195831\pi$
$71$			9.72611i			1.15428i	−0.816646	+	0.577139i	$0.804169\pi$
$72$		0			0
$73$	11.0785	−	6.39620i	1.29665	−	0.748619i	0.316822	−	0.948485i	$-0.397384\pi$
$73$	11.0785	−	6.39620i	1.29665	−	0.748619i	0.979823	+	0.199866i	$0.0640508\pi$
$74$	8.65520	+	9.18361i	1.00615	+	1.06757i
$75$		0			0
$76$	0.526759	+	1.05161i	0.0604234	+	0.120628i
$77$	−11.3379	−	0.388881i	−1.29208	−	0.0443171i
$78$		0			0
$79$	0.784867	+	0.453143i	0.0883044	+	0.0509826i	0.543502	−	0.839408i	$-0.317098\pi$
$79$	0.784867	+	0.453143i	0.0883044	+	0.0509826i	−0.455198	+	0.890390i	$0.650431\pi$
$80$	8.67230	+	1.03207i	0.969593	+	0.115389i
$81$		0			0
$82$	4.32519	−	14.4197i	0.477637	−	1.59238i
$83$		−	11.4885i		−	1.26103i	−0.776178	−	0.630513i	$-0.782844\pi$
$83$		−	11.4885i		−	1.26103i	0.776178	−	0.630513i	$-0.217156\pi$
$84$		0			0
$85$			3.94568i			0.427969i
$86$	−11.6495	−	3.49427i	−1.25619	−	0.376796i
$87$		0			0
$88$	−4.16588	+	11.3900i	−0.444084	+	1.21417i
$89$	14.5327	+	8.39047i	1.54046	+	0.889388i	0.998809	+	0.0487874i	$0.0155357\pi$
$89$	14.5327	+	8.39047i	1.54046	+	0.889388i	0.541656	+	0.840600i	$0.317798\pi$
$90$		0			0
$91$	−2.85282	+	4.57179i	−0.299057	+	0.479254i
$92$	0.151566	+	0.302582i	0.0158018	+	0.0315464i
$93$		0			0
$94$	−11.2771	+	10.6282i	−1.16314	+	1.09622i
$95$	1.11198	−	0.642000i	0.114086	−	0.0658678i
$96$		0			0
$97$			13.3483i			1.35531i	0.735378	+	0.677657i	$0.237004\pi$
$97$			13.3483i			1.35531i	−0.735378	+	0.677657i	$0.762996\pi$
$98$	1.61249	+	9.76729i	0.162887	+	0.986645i
$99$		0			0
$100$	−0.0275683	+	0.464939i	−0.00275683	+	0.0464939i
$101$	5.33218	+	9.23561i	0.530572	+	0.918978i	0.999364	+	0.0356691i	$0.0113562\pi$
$101$	5.33218	+	9.23561i	0.530572	+	0.918978i	−0.468791	+	0.883309i	$0.655310\pi$
$102$		0			0
$103$	−1.24356	+	2.15390i	−0.122531	+	0.212230i	−0.920765	−	0.390117i	$-0.872434\pi$
$103$	−1.24356	+	2.15390i	−0.122531	+	0.212230i	0.798234	+	0.602347i	$0.205768\pi$
$104$	3.69612	+	4.41895i	0.362434	+	0.433313i
$105$		0			0
$106$	7.20464	−	1.70355i	0.699776	−	0.165463i
$107$	7.98914	−	13.8376i	0.772340	−	1.33773i	−0.163938	−	0.986471i	$-0.552420\pi$
$107$	7.98914	−	13.8376i	0.772340	−	1.33773i	0.936278	−	0.351261i	$-0.114247\pi$
$108$		0			0
$109$	6.56763	−	3.79182i	0.629065	−	0.363191i	−0.151325	−	0.988484i	$-0.548354\pi$
$109$	6.56763	−	3.79182i	0.629065	−	0.363191i	0.780390	+	0.625293i	$0.215021\pi$
$110$	12.6817	+	3.80388i	1.20915	+	0.362685i
$111$		0			0
$112$	10.4598	+	1.61013i	0.988359	+	0.152143i
$113$	−0.526715			−0.0495492			−0.0247746	−	0.999693i	$-0.507887\pi$
$113$	−0.526715			−0.0495492			−0.0247746	+	0.999693i	$0.507887\pi$
$114$		0			0
$115$	0.319952	−	0.184724i	0.0298357	−	0.0172256i
$116$	0.483612	−	0.733622i	0.0449023	−	0.0681151i
$117$		0			0
$118$	−1.16082	+	0.274478i	−0.106863	+	0.0252678i
$119$	−0.163896	+	4.77845i	−0.0150244	+	0.438040i
$120$		0			0
$121$	−3.69285	+	6.39620i	−0.335713	+	0.581473i
$122$	−8.69094	+	8.19088i	−0.786841	+	0.741567i
$123$		0			0
$124$	0.668063	−	11.2669i	0.0599938	−	1.01180i
$125$	11.4253			1.02191
$126$		0			0
$127$			7.96196i			0.706510i	0.935527	+	0.353255i	$0.114925\pi$
$127$			7.96196i			0.706510i	−0.935527	+	0.353255i	$0.885075\pi$
$128$	5.11461	−	10.0916i	0.452072	−	0.891981i
$129$		0			0
$130$	4.57681	−	4.31347i	0.401413	−	0.378317i
$131$	5.91716	+	3.41628i	0.516985	+	0.298481i	0.735700	−	0.677307i	$-0.236853\pi$
$131$	5.91716	+	3.41628i	0.516985	+	0.298481i	−0.218715	+	0.975789i	$0.570187\pi$
$132$		0			0
$133$	1.37334	−	0.731311i	0.119083	−	0.0634127i
$134$	4.47543	+	18.9275i	0.386618	+	1.63509i
$135$		0			0
$136$	4.80038	+	1.75574i	0.411629	+	0.150553i
$137$	7.91720	+	13.7130i	0.676412	+	1.17158i	0.976054	+	0.217528i	$0.0697993\pi$
$137$	7.91720	+	13.7130i	0.676412	+	1.17158i	−0.299642	+	0.954052i	$0.596867\pi$
$138$		0			0
$139$			15.2651i			1.29477i	0.762165	+	0.647383i	$0.224137\pi$
$139$			15.2651i			1.29477i	−0.762165	+	0.647383i	$0.775863\pi$
$140$	1.07879	−	11.5029i	0.0911741	−	0.972169i
$141$		0			0
$142$	3.95182	−	13.1749i	0.331629	−	1.10561i
$143$	4.36675	+	7.56343i	0.365166	+	0.632486i
$144$		0			0
$145$	−0.830731	−	0.479623i	−0.0689885	−	0.0398305i
$146$	−17.6057	+	4.16289i	−1.45706	+	0.344524i
$147$		0			0
$148$	−7.99284	−	15.9567i	−0.657008	−	1.31163i
$149$	−7.51556	−	4.33911i	−0.615699	−	0.355474i	0.159494	−	0.987199i	$-0.449014\pi$
$149$	−7.51556	−	4.33911i	−0.615699	−	0.355474i	−0.775192	+	0.631725i	$0.782347\pi$
$150$		0			0
$151$	13.7288	−	7.92633i	1.11724	−	0.645036i	0.176541	−	0.984293i	$-0.443509\pi$
$151$	13.7288	−	7.92633i	1.11724	−	0.645036i	0.940694	+	0.339257i	$0.110176\pi$
$152$	−0.286262	−	1.63852i	−0.0232189	−	0.132902i
$153$		0			0
$154$	15.2002	+	5.13349i	1.22487	+	0.413669i
$155$	−12.3215			−0.989687
$156$		0			0
$157$	7.01102	+	12.1434i	0.559540	+	0.969152i	0.997535	+	0.0701745i	$0.0223556\pi$
$157$	7.01102	+	12.1434i	0.559540	+	0.969152i	−0.437994	+	0.898978i	$0.644311\pi$
$158$	−0.879055	−	0.932722i	−0.0699339	−	0.0742034i
$159$		0			0
$160$	−11.3281	−	4.92167i	−0.895562	−	0.389093i
$161$	0.395154	−	0.210422i	0.0311425	−	0.0165836i
$162$		0			0
$163$	0.232878	−	0.403356i	0.0182404	−	0.0315933i	−0.856761	−	0.515713i	$-0.827527\pi$
$163$	0.232878	−	0.403356i	0.0182404	−	0.0315933i	0.875002	+	0.484120i	$0.160860\pi$
$164$	−11.7177	+	17.7753i	−0.915000	+	1.38802i
$165$		0			0
$166$	−4.66790	+	15.5622i	−0.362299	+	1.20786i
$167$	−8.11262			−0.627774			−0.313887	−	0.949460i	$-0.601631\pi$
$167$	−8.11262			−0.627774			−0.313887	+	0.949460i	$0.601631\pi$
$168$		0			0
$169$	−8.85145			−0.680881
$170$	1.60317	−	5.34477i	0.122958	−	0.409925i
$171$		0			0
$172$	14.3605	+	9.46659i	1.09498	+	0.721821i
$173$	−2.73068	+	4.72968i	−0.207610	+	0.359591i	−0.950961	−	0.309310i	$-0.899902\pi$
$173$	−2.73068	+	4.72968i	−0.207610	+	0.359591i	0.743351	+	0.668901i	$0.233235\pi$
$174$		0			0
$175$	0.615774	+	0.0211205i	0.0465482	+	0.00159656i
$176$	10.2709	−	13.7361i	0.774199	−	1.03539i
$177$		0			0
$178$	−16.2767	−	17.2704i	−1.21999	−	1.29447i
$179$	−0.914196	−	1.58343i	−0.0683302	−	0.118351i	0.829836	−	0.558007i	$-0.188434\pi$
$179$	−0.914196	−	1.58343i	−0.0683302	−	0.118351i	−0.898166	+	0.439656i	$0.855100\pi$
$180$		0			0
$181$	−14.7458			−1.09604			−0.548022	−	0.836464i	$-0.684619\pi$
$181$	−14.7458			−1.09604			−0.548022	+	0.836464i	$0.684619\pi$
$182$	5.72197	−	5.03376i	0.424141	−	0.373127i
$183$		0			0
$184$	−0.0823671	−	0.471457i	−0.00607218	−	0.0347563i
$185$	−16.8727	+	9.74147i	−1.24051	+	0.716207i
$186$		0			0
$187$	6.71064	+	3.87439i	0.490731	+	0.283324i
$188$	19.5942	−	9.81487i	1.42905	−	0.715823i
$189$		0			0
$190$	−1.76712	+	0.417838i	−0.128201	+	0.0303132i
$191$	−15.1777	−	8.76282i	−1.09822	−	0.634056i	−0.162465	−	0.986714i	$-0.551944\pi$
$191$	−15.1777	−	8.76282i	−1.09822	−	0.634056i	−0.935752	+	0.352659i	$0.885278\pi$
$192$		0			0
$193$	−4.86212	−	8.42143i	−0.349983	−	0.606188i	0.636263	−	0.771472i	$-0.280479\pi$
$193$	−4.86212	−	8.42143i	−0.349983	−	0.606188i	−0.986246	+	0.165284i	$0.947146\pi$
$194$	5.42355	−	18.0814i	0.389388	−	1.29817i
$195$		0			0
$196$	1.78428	−	13.8858i	0.127449	−	0.991845i
$197$		−	16.6844i		−	1.18871i	−0.804202	−	0.594356i	$-0.797407\pi$
$197$		−	16.6844i		−	1.18871i	0.804202	−	0.594356i	$-0.202593\pi$
$198$		0			0
$199$	10.4281	+	18.0620i	0.739227	+	1.28038i	0.952844	+	0.303461i	$0.0981422\pi$
$199$	10.4281	+	18.0620i	0.739227	+	1.28038i	−0.213617	+	0.976917i	$0.568525\pi$
$200$	0.226253	−	0.618600i	0.0159985	−	0.0437416i
$201$		0			0
$202$	−3.47039	−	14.6770i	−0.244176	−	1.03267i
$203$	−0.986143	−	0.615359i	−0.0692136	−	0.0431897i
$204$		0			0
$205$	20.1283	+	11.6211i	1.40582	+	0.811649i
$206$	2.55966	−	2.41238i	0.178340	−	0.168079i
$207$		0			0
$208$	−3.21126	−	7.48763i	−0.222661	−	0.519174i
$209$		−	2.52160i		−	0.174423i
$210$		0			0
$211$	1.15282			0.0793633			0.0396816	−	0.999212i	$-0.487366\pi$
$211$	1.15282			0.0793633			0.0396816	+	0.999212i	$0.487366\pi$
$212$	−10.4515	−	0.619716i	−0.717811	−	0.0425622i
$213$		0			0
$214$	−16.4444	+	15.4982i	−1.12411	+	1.05943i
$215$	9.38850	−	16.2614i	0.640290	−	1.10901i
$216$		0			0
$217$	−14.9221	−	0.511814i	−1.01298	−	0.0347442i
$218$	−10.4371	+	2.46786i	−0.706889	+	0.167145i
$219$		0			0
$220$	−15.6329	−	10.3054i	−1.05397	−	0.694788i
$221$	3.18766	−	1.84040i	0.214425	−	0.123798i
$222$		0			0
$223$	10.0719			0.674462			0.337231	−	0.941422i	$-0.390510\pi$
$223$	10.0719			0.674462			0.337231	+	0.941422i	$0.390510\pi$
$224$	−13.5145	−	6.43099i	−0.902977	−	0.429689i
$225$		0			0
$226$	0.713483	+	0.214010i	0.0474602	+	0.0142357i
$227$	−8.10094	+	4.67708i	−0.537678	+	0.310429i	−0.744137	−	0.668027i	$-0.767139\pi$
$227$	−8.10094	+	4.67708i	−0.537678	+	0.310429i	0.206459	+	0.978455i	$0.433806\pi$
$228$		0			0
$229$	−13.3304	+	23.0889i	−0.880896	+	1.52576i	−0.0305504	+	0.999533i	$0.509726\pi$
$229$	−13.3304	+	23.0889i	−0.880896	+	1.52576i	−0.850346	+	0.526224i	$0.823607\pi$
$230$	−0.508459	+	0.120226i	−0.0335268	+	0.00792746i
$231$		0			0
$232$	−0.953175	+	0.797260i	−0.0625790	+	0.0523427i
$233$	8.83907	−	15.3097i	0.579066	−	1.00297i	−0.416520	−	0.909126i	$-0.636750\pi$
$233$	8.83907	−	15.3097i	0.579066	−	1.00297i	0.995587	−	0.0938461i	$-0.0299162\pi$
$234$		0			0
$235$	−11.9621	−	20.7190i	−0.780322	−	1.35156i
$236$	1.68396	+	0.0998497i	0.109617	+	0.00649966i
$237$		0			0
$238$	2.16355	−	6.40624i	0.140242	−	0.415255i
$239$			13.5781i			0.878295i	0.898415	+	0.439147i	$0.144719\pi$
$239$			13.5781i			0.878295i	−0.898415	+	0.439147i	$0.855281\pi$
$240$		0			0
$241$	18.2706	−	10.5485i	1.17691	−	0.679491i	0.221614	−	0.975134i	$-0.428867\pi$
$241$	18.2706	−	10.5485i	1.17691	−	0.679491i	0.955298	+	0.295643i	$0.0955340\pi$
$242$	7.60114	−	7.16378i	0.488619	−	0.460505i
$243$		0			0
$244$	15.1007	−	7.56406i	0.966723	−	0.484239i
$245$	−15.2477	−	1.04720i	−0.974140	−	0.0669029i
$246$		0			0
$247$	−1.03733	−	0.598901i	−0.0660035	−	0.0381071i
$248$	−5.48280	+	14.9905i	−0.348158	+	0.951900i
$249$		0			0
$250$	−15.4766	−	4.64223i	−0.978828	−	0.293601i
$251$			8.90673i			0.562188i	0.959680	+	0.281094i	$0.0906972\pi$
$251$			8.90673i			0.562188i	−0.959680	+	0.281094i	$0.909303\pi$
$252$		0			0
$253$		−	0.725548i		−	0.0456148i
$254$	3.23503	−	10.7852i	0.202984	−	0.676723i
$255$		0			0
$256$	−11.0285	+	11.5919i	−0.689283	+	0.724492i
$257$	−21.9783	−	12.6892i	−1.37097	−	0.791530i	−0.379920	−	0.925019i	$-0.624048\pi$
$257$	−21.9783	−	12.6892i	−1.37097	−	0.791530i	−0.991050	+	0.133490i	$0.957382\pi$
$258$		0			0
$259$	−20.8385	+	11.0966i	−1.29484	+	0.689511i
$260$	−7.95231	+	3.98338i	−0.493181	+	0.247038i
$261$		0			0
$262$	−6.62726	−	7.03186i	−0.409433	−	0.434429i
$263$	22.6353	−	13.0685i	1.39575	−	0.805837i	0.401807	−	0.915724i	$-0.368382\pi$
$263$	22.6353	−	13.0685i	1.39575	−	0.805837i	0.993944	+	0.109887i	$0.0350489\pi$
$264$		0			0
$265$			11.4298i			0.702127i
$266$	−2.15745	+	0.432624i	−0.132282	+	0.0265259i
$267$		0			0
$268$	1.62807	−	27.4574i	0.0994503	−	1.67723i
$269$	6.00575	+	10.4023i	0.366177	+	0.634237i	0.988964	−	0.148154i	$-0.0473332\pi$
$269$	6.00575	+	10.4023i	0.366177	+	0.634237i	−0.622788	+	0.782391i	$0.714000\pi$
$270$		0			0
$271$	−0.458689	+	0.794472i	−0.0278633	+	0.0482607i	−0.879621	−	0.475676i	$-0.842204\pi$
$271$	−0.458689	+	0.794472i	−0.0278633	+	0.0482607i	0.851757	+	0.523936i	$0.175537\pi$
$272$	−5.78916	−	4.32875i	−0.351019	−	0.262469i
$273$		0			0
$274$	−5.15282	−	21.7923i	−0.311293	−	1.31652i
$275$	0.499273	−	0.864766i	0.0301073	−	0.0521473i
$276$		0			0
$277$	−6.91838	+	3.99433i	−0.415685	+	0.239996i	−0.693230	−	0.720717i	$-0.743813\pi$
$277$	−6.91838	+	3.99433i	−0.415685	+	0.239996i	0.277544	+	0.960713i	$0.410479\pi$
$278$	6.20236	−	20.6779i	0.371993	−	1.24018i
$279$		0			0
$280$	−6.13504	+	15.1433i	−0.366639	+	0.904986i
$281$	8.33678			0.497331			0.248665	−	0.968589i	$-0.420008\pi$
$281$	8.33678			0.497331			0.248665	+	0.968589i	$0.420008\pi$
$282$		0			0
$283$	8.23852	−	4.75651i	0.489729	−	0.282745i	−0.234733	−	0.972060i	$-0.575422\pi$
$283$	8.23852	−	4.75651i	0.489729	−	0.282745i	0.724462	+	0.689315i	$0.242088\pi$
$284$	−10.7062	+	16.2409i	−0.635295	+	0.963719i
$285$		0			0
$286$	−2.84205	−	12.0196i	−0.168054	−	0.710734i
$287$	23.8938	+	14.9099i	1.41041	+	0.880102i
$288$		0			0
$289$	−6.86711	+	11.8942i	−0.403948	+	0.699658i
$290$	0.930424	+	0.987227i	0.0546364	+	0.0579720i
$291$		0			0
$292$	25.5399	+	1.51438i	1.49461	+	0.0886222i
$293$	31.0816			1.81580			0.907902	−	0.419182i	$-0.137683\pi$
$293$	31.0816			1.81580			0.907902	+	0.419182i	$0.137683\pi$
$294$		0			0
$295$		−	1.84159i		−	0.107221i
$296$	4.34364	+	24.8624i	0.252469	+	1.44510i
$297$		0			0
$298$	8.41747	+	8.93136i	0.487611	+	0.517380i
$299$	−0.298473	−	0.172323i	−0.0172611	−	0.00996572i
$300$		0			0
$301$	12.0455	−	19.3035i	0.694291	−	1.11263i
$302$	−21.8175	+	5.15876i	−1.25545	+	0.296854i
$303$		0			0
$304$	−0.277982	+	2.33584i	−0.0159434	+	0.133970i
$305$	−9.21887	−	15.9676i	−0.527871	−	0.914300i
$306$		0			0
$307$			2.58482i			0.147523i	0.997276	+	0.0737617i	$0.0235004\pi$
$307$			2.58482i			0.147523i	−0.997276	+	0.0737617i	$0.976500\pi$
$308$	−18.5043	−	13.1298i	−1.05438	−	0.748139i
$309$		0			0
$310$	16.6906	+	5.00636i	0.947961	+	0.284342i
$311$	−12.9363	−	22.4064i	−0.733553	−	1.27055i	−0.955355	−	0.295459i	$-0.904527\pi$
$311$	−12.9363	−	22.4064i	−0.733553	−	1.27055i	0.221802	−	0.975092i	$-0.428806\pi$
$312$		0			0
$313$	11.2106	+	6.47247i	0.633663	+	0.365845i	0.782169	−	0.623066i	$-0.214113\pi$
$313$	11.2106	+	6.47247i	0.633663	+	0.365845i	−0.148506	+	0.988911i	$0.547447\pi$
$314$	−4.56304	−	19.2980i	−0.257507	−	1.08905i
$315$		0			0
$316$	0.811784	+	1.62062i	0.0456664	+	0.0911673i
$317$	−6.16964	−	3.56204i	−0.346522	−	0.200064i	0.316631	−	0.948549i	$-0.397448\pi$
$317$	−6.16964	−	3.56204i	−0.346522	−	0.200064i	−0.663152	+	0.748485i	$0.730782\pi$
$318$		0			0
$319$	−1.63145	+	0.941915i	−0.0913434	+	0.0527371i
$320$	13.3451	+	11.2696i	0.746016	+	0.629987i
$321$		0			0
$322$	−0.620768	+	0.124480i	−0.0345941	+	0.00693701i
$323$	−1.06275			−0.0591329
$324$		0			0
$325$	−0.237163	−	0.410778i	−0.0131554	−	0.0227858i
$326$	−0.479341	+	0.451761i	−0.0265483	+	0.0250207i
$327$		0			0
$328$	23.0950	−	19.3172i	1.27521	−	1.06662i
$329$	−13.6262	−	25.5888i	−0.751236	−	1.41076i
$330$		0			0
$331$	−5.31858	+	9.21205i	−0.292336	+	0.506340i	−0.974362	−	0.224988i	$-0.927766\pi$
$331$	−5.31858	+	9.21205i	−0.292336	+	0.506340i	0.682026	+	0.731328i	$0.261099\pi$
$332$	12.6462	−	19.1838i	0.694049	−	1.05285i
$333$		0			0
$334$	10.9893	+	3.29624i	0.601306	+	0.180362i
$335$	−30.0275			−1.64058
$336$		0			0
$337$	6.18999			0.337190			0.168595	−	0.985685i	$-0.446077\pi$
$337$	6.18999			0.337190			0.168595	+	0.985685i	$0.446077\pi$
$338$	11.9901	+	3.59644i	0.652174	+	0.195620i
$339$		0			0
$340$	−4.34327	+	6.58858i	−0.235547	+	0.357316i
$341$	−12.0989	+	20.9559i	−0.655192	+	1.13483i
$342$		0			0
$343$	−18.4224	−	1.90158i	−0.994715	−	0.102676i
$344$	−15.6062	−	18.6581i	−0.841427	−	1.00598i
$345$		0			0
$346$	5.62068	−	5.29727i	0.302169	−	0.284783i
$347$	13.9217	+	24.1130i	0.747353	+	1.29445i	0.949087	+	0.315014i	$0.102009\pi$
$347$	13.9217	+	24.1130i	0.747353	+	1.29445i	−0.201734	+	0.979440i	$0.564658\pi$
$348$		0			0
$349$	29.5982			1.58435			0.792177	−	0.610291i	$-0.208948\pi$
$349$	29.5982			1.58435			0.792177	+	0.610291i	$0.208948\pi$
$350$	−0.825540	−	0.278805i	−0.0441270	−	0.0149028i
$351$		0			0
$352$	−19.4940	+	14.4335i	−1.03903	+	0.769310i
$353$	18.0733	−	10.4346i	0.961944	−	0.555379i	0.0651732	−	0.997874i	$-0.479240\pi$
$353$	18.0733	−	10.4346i	0.961944	−	0.555379i	0.896771	+	0.442495i	$0.145907\pi$
$354$		0			0
$355$	18.3907	+	10.6179i	0.976076	+	0.563538i
$356$	15.0311	+	30.0077i	0.796648	+	1.59041i
$357$		0			0
$358$	0.594994	+	2.51635i	0.0314464	+	0.132993i
$359$	−11.0866	−	6.40087i	−0.585130	−	0.337825i	0.178039	−	0.984023i	$-0.443025\pi$
$359$	−11.0866	−	6.40087i	−0.585130	−	0.337825i	−0.763170	+	0.646198i	$0.776358\pi$
$360$		0			0
$361$	−9.32708	−	16.1550i	−0.490899	−	0.850262i
$362$	19.9744	+	5.99136i	1.04983	+	0.314899i
$363$		0			0
$364$	−9.79619	+	4.49378i	−0.513460	+	0.235538i
$365$		−	27.9306i		−	1.46195i
$366$		0			0
$367$	11.2129	+	19.4214i	0.585311	+	1.01379i	0.994837	+	0.101490i	$0.0323609\pi$
$367$	11.2129	+	19.4214i	0.585311	+	1.01379i	−0.409526	+	0.912299i	$0.634306\pi$
$368$	−0.0799845	+	0.672098i	−0.00416948	+	0.0350355i
$369$		0			0
$370$	26.8137	−	6.34012i	1.39398	−	0.329607i
$371$	−0.474774	+	13.8422i	−0.0246490	+	0.718650i
$372$		0			0
$373$	−15.2845	−	8.82452i	−0.791403	−	0.456916i	0.0490535	−	0.998796i	$-0.484380\pi$
$373$	−15.2845	−	8.82452i	−0.791403	−	0.456916i	−0.840456	+	0.541880i	$0.817713\pi$
$374$	−7.51596	−	7.97481i	−0.388641	−	0.412368i
$375$		0			0
$376$	−30.5299	+	5.33380i	−1.57446	+	0.275070i
$377$			0.894849i			0.0460871i
$378$		0			0
$379$	−4.18139			−0.214784			−0.107392	−	0.994217i	$-0.534250\pi$
$379$	−4.18139			−0.214784			−0.107392	+	0.994217i	$0.534250\pi$
$380$	2.56350	+	0.152001i	0.131505	+	0.00779749i
$381$		0			0
$382$	16.9991	+	18.0369i	0.869748	+	0.922846i
$383$	2.79779	−	4.84592i	0.142961	−	0.247615i	−0.785650	−	0.618672i	$-0.787671\pi$
$383$	2.79779	−	4.84592i	0.142961	−	0.247615i	0.928610	+	0.371057i	$0.121004\pi$
$384$		0			0
$385$	−13.1128	+	21.0139i	−0.668290	+	1.07097i
$386$	3.16445	+	13.3831i	0.161066	+	0.681182i
$387$		0			0
$388$	−14.6934	+	22.2893i	−0.745943	+	1.13157i
$389$	3.09906	−	1.78924i	0.157128	−	0.0907181i	−0.419374	−	0.907813i	$-0.637750\pi$
$389$	3.09906	−	1.78924i	0.157128	−	0.0907181i	0.576502	+	0.817095i	$0.304417\pi$
$390$		0			0
$391$	−0.305787			−0.0154643
$392$	−8.05893	+	18.0846i	−0.407037	+	0.913411i
$393$		0			0
$394$	−6.77904	+	22.6005i	−0.341523	+	1.13860i
$395$	1.71366	−	0.989381i	0.0862235	−	0.0497811i
$396$		0			0
$397$	0.0602558	−	0.104366i	0.00302415	−	0.00523798i	−0.864509	−	0.502617i	$-0.832371\pi$
$397$	0.0602558	−	0.104366i	0.00302415	−	0.00523798i	0.867534	+	0.497379i	$0.165704\pi$
$398$	−6.78700	−	28.7036i	−0.340201	−	1.43878i
$399$		0			0
$400$	−0.557824	+	0.746019i	−0.0278912	+	0.0373010i
$401$	−3.22209	+	5.58083i	−0.160904	+	0.278693i	−0.935193	−	0.354138i	$-0.884774\pi$
$401$	−3.22209	+	5.58083i	−0.160904	+	0.278693i	0.774289	+	0.632832i	$0.218107\pi$
$402$		0			0
$403$	5.74716	+	9.95438i	0.286287	+	0.495863i
$404$	−1.26246	+	21.2913i	−0.0628097	+	1.05928i
$405$		0			0
$406$	1.08579	+	1.23424i	0.0538869	+	0.0612543i
$407$			38.2619i			1.89657i
$408$		0			0
$409$	2.83854	−	1.63883i	0.140357	−	0.0810349i	−0.428177	−	0.903695i	$-0.640844\pi$
$409$	2.83854	−	1.63883i	0.140357	−	0.0810349i	0.568534	+	0.822660i	$0.307511\pi$
$410$	−22.5438	−	23.9201i	−1.11336	−	1.18133i
$411$		0			0
$412$	−4.44746	+	2.22777i	−0.219111	+	0.109754i
$413$	0.0764964	−	2.23028i	0.00376414	−	0.109745i
$414$		0			0
$415$	−21.7231	−	12.5418i	−1.06635	−	0.615655i
$416$	1.30764	+	11.4474i	0.0641121	+	0.561256i
$417$		0			0
$418$	−1.02455	+	3.41574i	−0.0501126	+	0.167069i
$419$			28.8123i			1.40757i	0.710412	+	0.703786i	$0.248509\pi$
$419$			28.8123i			1.40757i	−0.710412	+	0.703786i	$0.751491\pi$
$420$		0			0
$421$		−	15.2534i		−	0.743407i	−0.928351	−	0.371704i	$-0.878774\pi$
$421$		−	15.2534i		−	0.743407i	0.928351	−	0.371704i	$-0.121226\pi$
$422$	−1.56159	−	0.468402i	−0.0760172	−	0.0228015i
$423$		0			0
$424$	13.9057	+	5.08601i	0.675320	+	0.246999i
$425$	−0.364462	−	0.210422i	−0.0176790	−	0.0102070i
$426$		0			0
$427$	−10.5013	−	19.7206i	−0.508196	−	0.954347i
$428$	28.5724	−	14.3122i	1.38110	−	0.691805i
$429$		0			0
$430$	−19.3247	+	18.2128i	−0.931920	+	0.878299i
$431$	−20.0014	+	11.5478i	−0.963433	+	0.556238i	−0.897228	−	0.441568i	$-0.854422\pi$
$431$	−20.0014	+	11.5478i	−0.963433	+	0.556238i	−0.0662048	+	0.997806i	$0.521089\pi$
$432$		0			0
$433$		−	16.9988i		−	0.816912i	−0.912778	−	0.408456i	$-0.866067\pi$
$433$		−	16.9988i		−	0.816912i	0.912778	−	0.408456i	$-0.133933\pi$
$434$	20.0053	+	6.75629i	0.960286	+	0.324312i
$435$		0			0
$436$	15.1407	+	0.897759i	0.725108	+	0.0429949i
$437$	0.0497546	+	0.0861774i	0.00238008	+	0.00412243i
$438$		0			0
$439$	−0.772860	+	1.33863i	−0.0368866	+	0.0638895i	−0.883879	−	0.467715i	$-0.845077\pi$
$439$	−0.772860	+	1.33863i	−0.0368866	+	0.0638895i	0.846993	+	0.531604i	$0.178411\pi$
$440$	16.9889	+	20.3114i	0.809916	+	0.968306i
$441$		0			0
$442$	−5.06574	+	1.19780i	−0.240953	+	0.0569736i
$443$	−12.7763	+	22.1292i	−0.607019	+	1.05139i	0.384710	+	0.923038i	$0.374301\pi$
$443$	−12.7763	+	22.1292i	−0.607019	+	1.05139i	−0.991729	+	0.128350i	$0.959032\pi$
$444$		0			0
$445$	31.7304	−	18.3195i	1.50416	−	0.868429i
$446$	−13.6432	−	4.09231i	−0.646026	−	0.193776i
$447$		0			0
$448$	15.6936	+	14.2024i	0.741455	+	0.671002i
$449$	15.9139			0.751025			0.375513	−	0.926817i	$-0.377467\pi$
$449$	15.9139			0.751025			0.375513	+	0.926817i	$0.377467\pi$
$450$		0			0
$451$	39.5292	−	22.8222i	1.86136	−	1.07465i
$452$	−0.879521	−	0.579791i	−0.0413692	−	0.0272711i
$453$		0			0
$454$	12.8738	−	3.04402i	0.604197	−	0.142863i
$455$	5.53021	+	10.3852i	0.259260	+	0.486868i
$456$		0			0
$457$	7.09999	−	12.2975i	0.332123	−	0.575255i	−0.650805	−	0.759245i	$-0.725568\pi$
$457$	7.09999	−	12.2975i	0.332123	−	0.575255i	0.982928	+	0.183991i	$0.0589016\pi$
$458$	27.4385	−	25.8597i	1.28211	−	1.20834i
$459$		0			0
$460$	0.737602	+	0.0437357i	0.0343909	+	0.00203919i
$461$	21.5871			1.00541			0.502706	−	0.864458i	$-0.332338\pi$
$461$	21.5871			1.00541			0.502706	+	0.864458i	$0.332338\pi$
$462$		0			0
$463$		−	8.18559i		−	0.380417i	−0.981744	−	0.190208i	$-0.939084\pi$
$463$		−	8.18559i		−	0.380417i	0.981744	−	0.190208i	$-0.0609164\pi$
$464$	1.61509	−	0.692674i	0.0749789	−	0.0321566i
$465$		0			0
$466$	−18.1938	+	17.1470i	−0.842812	+	0.794318i
$467$	20.2861	+	11.7122i	0.938731	+	0.541977i	0.889562	−	0.456814i	$-0.151009\pi$
$467$	20.2861	+	11.7122i	0.938731	+	0.541977i	0.0491686	+	0.998790i	$0.484343\pi$
$468$		0			0
$469$	−36.3651	−	1.24729i	−1.67919	−	0.0575945i
$470$	7.78540	+	32.9260i	0.359114	+	1.51876i
$471$		0			0
$472$	−2.24051	−	0.819467i	−0.103128	−	0.0377190i
$473$	−18.4377	−	31.9351i	−0.847769	−	1.46838i
$474$		0			0
$475$			0.136951i			0.00628373i
$476$	−5.53364	+	7.79876i	−0.253634	+	0.357455i
$477$		0			0
$478$	5.51693	−	18.3928i	0.252338	−	0.841265i
$479$	−0.948080	−	1.64212i	−0.0433189	−	0.0750305i	0.843553	−	0.537046i	$-0.180460\pi$
$479$	−0.948080	−	1.64212i	−0.0433189	−	0.0750305i	−0.886872	+	0.462015i	$0.847126\pi$
$480$		0			0
$481$	15.7400	+	9.08750i	0.717683	+	0.414354i
$482$	−29.0351	+	6.86540i	−1.32251	+	0.312710i
$483$		0			0
$484$	−13.2071	+	6.61556i	−0.600324	+	0.300707i
$485$	25.2397	+	14.5722i	1.14608	+	0.661687i
$486$		0			0
$487$	−4.73377	+	2.73304i	−0.214508	+	0.123846i	−0.603404	−	0.797435i	$-0.706190\pi$
$487$	−4.73377	+	2.73304i	−0.214508	+	0.123846i	0.388897	+	0.921281i	$0.372856\pi$
$488$	−23.5286	+	4.11062i	−1.06509	+	0.186079i
$489$		0			0
$490$	20.2289	+	7.61382i	0.913848	+	0.343957i
$491$	25.7761			1.16326			0.581630	−	0.813453i	$-0.302415\pi$
$491$	25.7761			1.16326			0.581630	+	0.813453i	$0.302415\pi$
$492$		0			0
$493$	0.396977	+	0.687584i	0.0178789	+	0.0309672i
$494$	1.16181	+	1.23274i	0.0522724	+	0.0554636i
$495$		0			0
$496$	13.5178	−	18.0783i	0.606965	−	0.811740i
$497$	21.8312	+	13.6228i	0.979262	+	0.611066i
$498$		0			0
$499$	−1.08570	+	1.88049i	−0.0486027	+	0.0841823i	−0.889303	−	0.457318i	$-0.848810\pi$
$499$	−1.08570	+	1.88049i	−0.0486027	+	0.0841823i	0.840701	+	0.541500i	$0.182143\pi$
$500$	19.0783	+	12.5766i	0.853207	+	0.562444i
$501$		0			0
$502$	3.61890	−	12.0650i	0.161519	−	0.538485i
$503$	−21.5871			−0.962521			−0.481261	−	0.876578i	$-0.659821\pi$
$503$	−21.5871			−0.962521			−0.481261	+	0.876578i	$0.659821\pi$
$504$		0			0
$505$	23.2843			1.03614
$506$	−0.294798	+	0.982820i	−0.0131054	+	0.0436917i
$507$		0			0
$508$	−8.76427	+	13.2951i	−0.388852	+	0.589874i
$509$	−11.5516	+	20.0079i	−0.512015	+	0.886836i	0.487888	+	0.872906i	$0.337767\pi$
$509$	−11.5516	+	20.0079i	−0.512015	+	0.886836i	−0.999903	+	0.0139295i	$0.995566\pi$
$510$		0			0
$511$	1.16019	−	33.8256i	0.0513237	−	1.49636i
$512$	19.6490	−	11.2212i	0.868373	−	0.495912i
$513$		0			0
$514$	24.6158	+	26.1187i	1.08576	+	1.15204i
$515$	2.71515	+	4.70277i	0.119644	+	0.207229i
$516$		0			0
$517$	−46.9839			−2.06635
$518$	32.7363	−	6.56448i	1.43835	−	0.288426i
$519$		0			0
$520$	12.3906	−	2.16473i	0.543364	−	0.0949297i
$521$	7.24334	−	4.18194i	0.317336	−	0.183214i	−0.332868	−	0.942973i	$-0.608016\pi$
$521$	7.24334	−	4.18194i	0.317336	−	0.183214i	0.650205	+	0.759759i	$0.274683\pi$
$522$		0			0
$523$	−16.8628	−	9.73575i	−0.737359	−	0.425715i	0.0837491	−	0.996487i	$-0.473311\pi$
$523$	−16.8628	−	9.73575i	−0.737359	−	0.425715i	−0.821108	+	0.570772i	$0.806644\pi$
$524$	6.12009	+	12.2180i	0.267357	+	0.533746i
$525$		0			0
$526$	−35.9714	+	8.50548i	−1.56843	+	0.370856i
$527$	8.83201	+	5.09916i	0.384728	+	0.222123i
$528$		0			0
$529$	−11.4857	−	19.8938i	−0.499378	−	0.864947i
$530$	4.64405	−	15.4827i	0.201725	−	0.672525i
$531$		0			0
$532$	3.09823	+	0.290566i	0.134325	+	0.0125976i
$533$		−	21.6818i		−	0.939143i
$534$		0			0
$535$	−17.4433	−	30.2127i	−0.754139	−	1.30621i
$536$	−13.3616	+	36.5320i	−0.577133	+	1.57794i
$537$		0			0
$538$	−3.90877	−	16.5310i	−0.168519	−	0.712701i
$539$	−16.7532	+	24.9044i	−0.721614	+	1.07271i
$540$		0			0
$541$	−10.9541	−	6.32437i	−0.470955	−	0.271906i	0.245685	−	0.969350i	$-0.420987\pi$
$541$	−10.9541	−	6.32437i	−0.470955	−	0.271906i	−0.716639	+	0.697444i	$0.754321\pi$
$542$	0.944137	−	0.889813i	0.0405542	−	0.0382207i
$543$		0			0
$544$	6.08312	+	8.21587i	0.260812	+	0.352253i
$545$		−	16.5579i		−	0.709264i
$546$		0			0
$547$	−21.1528			−0.904429			−0.452215	−	0.891909i	$-0.649366\pi$
$547$	−21.1528			−0.904429			−0.452215	+	0.891909i	$0.649366\pi$
$548$	−1.87449	+	31.6133i	−0.0800743	+	1.35045i
$549$		0			0
$550$	−1.02767	+	0.968543i	−0.0438201	+	0.0412988i
$551$	0.129184	−	0.223753i	0.00550342	−	0.00953221i
$552$		0			0
$553$	2.11644	−	1.12702i	0.0900001	−	0.0479256i
$554$	10.9945	−	2.59966i	0.467112	−	0.110449i
$555$		0			0
$556$	−16.8033	+	25.4900i	−0.712618	+	1.08102i
$557$	−31.0289	+	17.9145i	−1.31474	+	0.759063i	−0.982876	−	0.184266i	$-0.941009\pi$
$557$	−31.0289	+	17.9145i	−1.31474	+	0.759063i	−0.331859	+	0.943329i	$0.607676\pi$
$558$		0			0
$559$	−17.5164			−0.740867
$560$	14.4634	−	18.0202i	0.611188	−	0.761494i
$561$		0			0
$562$	−11.2929	−	3.38732i	−0.476363	−	0.142886i
$563$	23.7961	−	13.7387i	1.00289	−	0.579016i	0.0937850	−	0.995592i	$-0.470103\pi$
$563$	23.7961	−	13.7387i	1.00289	−	0.579016i	0.909101	+	0.416576i	$0.136770\pi$
$564$		0			0
$565$	−0.575008	+	0.995943i	−0.0241908	+	0.0418996i
$566$	−13.0924	+	3.09572i	−0.550316	+	0.130123i
$567$		0			0
$568$	21.1013	−	17.6497i	0.885392	−	0.740565i
$569$	14.6645	−	25.3997i	0.614768	−	1.06481i	−0.375657	−	0.926759i	$-0.622583\pi$
$569$	14.6645	−	25.3997i	0.614768	−	1.06481i	0.990425	−	0.138051i	$-0.0440838\pi$
$570$		0			0
$571$	−1.02495	−	1.77527i	−0.0428929	−	0.0742927i	0.843782	−	0.536686i	$-0.180324\pi$
$571$	−1.02495	−	1.77527i	−0.0428929	−	0.0742927i	−0.886675	+	0.462393i	$0.846991\pi$
$572$	−1.03388	+	17.4364i	−0.0432287	+	0.729051i
$573$		0			0
$574$	−26.3082	−	29.9051i	−1.09808	−	1.24821i
$575$			0.0394053i			0.00164331i
$576$		0			0
$577$	−2.90927	+	1.67967i	−0.121115	+	0.0699256i	−0.559333	−	0.828943i	$-0.688943\pi$
$577$	−2.90927	+	1.67967i	−0.121115	+	0.0699256i	0.438219	+	0.898868i	$0.355610\pi$
$578$	14.1348	−	13.3216i	0.587932	−	0.554104i
$579$		0			0
$580$	−0.859221	−	1.71533i	−0.0356772	−	0.0712251i
$581$	−25.7870	−	16.0913i	−1.06983	−	0.667578i
$582$		0			0
$583$	19.4393	+	11.2233i	0.805094	+	0.464821i
$584$	−33.9808	−	12.4285i	−1.40614	−	0.514295i
$585$		0			0
$586$	−42.1027	−	12.6288i	−1.73925	−	0.521690i
$587$		−	30.9449i		−	1.27723i	−0.769526	−	0.638615i	$-0.779508\pi$
$587$		−	30.9449i		−	1.27723i	0.769526	−	0.638615i	$-0.220492\pi$
$588$		0			0
$589$		−	3.31873i		−	0.136746i
$590$	−0.748257	+	2.49460i	−0.0308053	+	0.102701i
$591$		0			0
$592$	4.21799	−	35.4432i	0.173359	−	1.45670i
$593$	−19.2127	−	11.0925i	−0.788971	−	0.455513i	0.0506289	−	0.998718i	$-0.483877\pi$
$593$	−19.2127	−	11.0925i	−0.788971	−	0.455513i	−0.839600	+	0.543205i	$0.817211\pi$
$594$		0			0
$595$	8.85645	+	5.52648i	0.363079	+	0.226563i
$596$	−7.77330	−	15.5184i	−0.318407	−	0.635660i
$597$		0			0
$598$	0.334291	+	0.354700i	0.0136702	+	0.0145048i
$599$	11.8417	−	6.83682i	0.483840	−	0.279345i	−0.238175	−	0.971222i	$-0.576549\pi$
$599$	11.8417	−	6.83682i	0.483840	−	0.279345i	0.722015	+	0.691877i	$0.243216\pi$
$600$		0			0
$601$			16.8463i			0.687175i	0.939121	+	0.343587i	$0.111642\pi$
$601$			16.8463i			0.687175i	−0.939121	+	0.343587i	$0.888358\pi$
$602$	−24.1599	+	21.2541i	−0.984684	+	0.866252i
$603$		0			0
$604$	31.6497	+	1.87665i	1.28781	+	0.0763600i
$605$	8.06287	+	13.9653i	0.327802	+	0.567770i
$606$		0			0
$607$	−7.65975	+	13.2671i	−0.310900	+	0.538494i	−0.978557	−	0.205975i	$-0.933964\pi$
$607$	−7.65975	+	13.2671i	−0.310900	+	0.538494i	0.667658	+	0.744468i	$0.267297\pi$
$608$	1.32563	−	3.05116i	0.0537613	−	0.123741i
$609$		0			0
$610$	6.00000	+	25.3752i	0.242933	+	1.02741i
$611$	−11.1591	+	19.3281i	−0.451447	+	0.781929i
$612$		0			0
$613$	−30.3794	+	17.5396i	−1.22701	+	0.708416i	−0.966404	−	0.257028i	$-0.917257\pi$
$613$	−30.3794	+	17.5396i	−1.22701	+	0.708416i	−0.260609	+	0.965444i	$0.583923\pi$
$614$	1.05024	−	3.50137i	0.0423842	−	0.141304i
$615$		0			0
$616$	19.7309	+	25.3039i	0.794981	+	1.01953i
$617$	−34.0392			−1.37037			−0.685184	−	0.728370i	$-0.740278\pi$
$617$	−34.0392			−1.37037			−0.685184	+	0.728370i	$0.740278\pi$
$618$		0			0
$619$	14.6292	−	8.44618i	0.587998	−	0.339481i	−0.176308	−	0.984335i	$-0.556415\pi$
$619$	14.6292	−	8.44618i	0.587998	−	0.339481i	0.764305	+	0.644855i	$0.223082\pi$
$620$	−20.5747	−	13.5631i	−0.826301	−	0.544708i
$621$		0			0
$622$	8.41948	+	35.6077i	0.337590	+	1.42774i
$623$	39.1883	−	20.8680i	1.57005	−	0.836060i
$624$		0			0
$625$	11.8907	−	20.5953i	0.475628	−	0.823811i
$626$	−12.5560	−	13.3225i	−0.501838	−	0.532476i
$627$		0			0
$628$	−1.65994	+	27.9949i	−0.0662389	+	1.11712i
$629$	16.1257			0.642975
$630$		0			0
$631$		−	31.5662i		−	1.25663i	−0.777959	−	0.628315i	$-0.783745\pi$
$631$		−	31.5662i		−	1.25663i	0.777959	−	0.628315i	$-0.216255\pi$
$632$	−0.441157	−	2.52512i	−0.0175483	−	0.100444i
$633$		0			0
$634$	6.91003	+	7.33190i	0.274432	+	0.291187i
$635$	15.0549	+	8.69197i	0.597437	+	0.344930i
$636$		0			0
$637$	6.26603	+	12.8069i	0.248269	+	0.507427i
$638$	2.59265	−	0.613035i	0.102644	−	0.0242703i
$639$		0			0
$640$	−13.4982	−	20.6879i	−0.533565	−	0.817761i
$641$	8.82372	+	15.2831i	0.348516	+	0.603647i	0.985986	−	0.166828i	$-0.0533524\pi$
$641$	8.82372	+	15.2831i	0.348516	+	0.603647i	−0.637470	+	0.770475i	$0.720019\pi$
$642$		0			0
$643$			9.96415i			0.392948i	0.980509	+	0.196474i	$0.0629491\pi$
$643$			9.96415i			0.392948i	−0.980509	+	0.196474i	$0.937051\pi$
$644$	0.891464	+	0.0836053i	0.0351286	+	0.00329451i
$645$		0			0
$646$	1.43959	+	0.431806i	0.0566398	+	0.0169892i
$647$	−18.1393	−	31.4183i	−0.713131	−	1.23518i	−0.963676	−	0.267075i	$-0.913943\pi$
$647$	−18.1393	−	31.4183i	−0.713131	−	1.23518i	0.250544	−	0.968105i	$-0.419390\pi$
$648$		0			0
$649$	−3.13210	−	1.80832i	−0.122946	−	0.0709827i
$650$	0.154355	+	0.652796i	0.00605428	+	0.0256048i
$651$		0			0
$652$	0.832866	−	0.417189i	0.0326175	−	0.0163384i
$653$	28.8049	+	16.6305i	1.12722	+	0.650803i	0.943235	−	0.332125i	$-0.107766\pi$
$653$	28.8049	+	16.6305i	1.12722	+	0.650803i	0.183988	+	0.982928i	$0.441099\pi$
$654$		0			0
$655$	12.9194	−	7.45901i	0.504802	−	0.291448i
$656$	−39.1330	+	16.7832i	−1.52789	+	0.655274i
$657$		0			0
$658$	8.06090	+	40.1988i	0.314246	+	1.56711i
$659$	−43.9413			−1.71171			−0.855855	−	0.517216i	$-0.826968\pi$
$659$	−43.9413			−1.71171			−0.855855	+	0.517216i	$0.826968\pi$
$660$		0			0
$661$	−4.46365	−	7.73127i	−0.173616	−	0.300712i	0.766065	−	0.642763i	$-0.222212\pi$
$661$	−4.46365	−	7.73127i	−0.173616	−	0.300712i	−0.939681	+	0.342051i	$0.888878\pi$
$662$	10.9474	−	10.3175i	0.425484	−	0.401003i
$663$		0			0
$664$	−24.9249	+	20.8479i	−0.967275	+	0.809054i
$665$	0.116450	−	3.39515i	0.00451575	−	0.131658i
$666$		0			0
$667$	0.0371705	−	0.0643811i	0.00143925	−	0.00249285i
$668$	−13.5466	−	8.93011i	−0.524136	−	0.345516i
$669$		0			0
$670$	40.6750	+	12.2005i	1.57141	+	0.471346i
$671$	−36.2093			−1.39784
$672$		0			0
$673$	−13.7714			−0.530848			−0.265424	−	0.964132i	$-0.585512\pi$
$673$	−13.7714			−0.530848			−0.265424	+	0.964132i	$0.585512\pi$
$674$	−8.38489	−	2.51506i	−0.322974	−	0.0968764i
$675$		0			0
$676$	−14.7804	−	9.74339i	−0.568475	−	0.374746i
$677$	−12.3034	+	21.3101i	−0.472857	+	0.819012i	−0.999517	−	0.0310637i	$-0.990111\pi$
$677$	−12.3034	+	21.3101i	−0.472857	+	0.819012i	0.526661	+	0.850076i	$0.323444\pi$
$678$		0			0
$679$	29.9615	+	18.6962i	1.14982	+	0.717493i
$680$	8.56036	−	7.16011i	0.328275	−	0.274578i
$681$		0			0
$682$	24.9036	−	23.4707i	0.953609	−	0.898740i
$683$	−7.87269	−	13.6359i	−0.301240	−	0.521763i	0.675177	−	0.737656i	$-0.264067\pi$
$683$	−7.87269	−	13.6359i	−0.301240	−	0.521763i	−0.976417	+	0.215892i	$0.930734\pi$
$684$		0			0
$685$	34.5724			1.32094
$686$	24.1821	+	10.0611i	0.923278	+	0.384133i
$687$		0			0
$688$	13.5589	+	31.6151i	0.516929	+	1.20531i
$689$	9.23398	−	5.33124i	0.351787	−	0.203104i
$690$		0			0
$691$	12.8292	+	7.40697i	0.488047	+	0.281774i	0.723764	−	0.690047i	$-0.242410\pi$
$691$	12.8292	+	7.40697i	0.488047	+	0.281774i	−0.235717	+	0.971822i	$0.575744\pi$
$692$	−9.76604	+	4.89189i	−0.371249	+	0.185962i
$693$		0			0
$694$	−9.06075	−	38.3197i	−0.343941	−	1.45460i
$695$	28.8641	+	16.6647i	1.09488	+	0.632127i
$696$		0			0
$697$	−9.61857	−	16.6599i	−0.364329	−	0.631037i
$698$	−40.0934	−	12.0261i	−1.51756	−	0.455193i
$699$		0			0
$700$	1.00499	+	0.713092i	0.0379849	+	0.0269523i
$701$		−	44.0371i		−	1.66326i	−0.555333	−	0.831628i	$-0.687409\pi$
$701$		−	44.0371i		−	1.66326i	0.555333	−	0.831628i	$-0.312591\pi$
$702$		0			0
$703$	−2.62381	−	4.54458i	−0.0989590	−	0.171402i
$704$	32.2708	−	11.6309i	1.21625	−	0.438356i
$705$		0			0
$706$	−28.7216	+	6.79125i	−1.08095	+	0.255592i
$707$	28.1987	+	0.967189i	1.06052	+	0.0363749i
$708$		0			0
$709$	−14.3908	−	8.30854i	−0.540459	−	0.312034i	0.204806	−	0.978803i	$-0.434344\pi$
$709$	−14.3908	−	8.30854i	−0.540459	−	0.312034i	−0.745265	+	0.666769i	$0.767677\pi$
$710$	−20.5977	−	21.8552i	−0.773017	−	0.820210i
$711$		0			0
$712$	−8.16852	−	46.7555i	−0.306128	−	1.75224i
$713$		−	0.954908i		−	0.0357616i
$714$		0			0
$715$	19.0685			0.713121
$716$	0.216447	−	3.65037i	0.00808900	−	0.136421i
$717$		0			0
$718$	12.4171	+	13.1752i	0.463402	+	0.491693i
$719$	23.7299	−	41.1014i	0.884976	−	1.53282i	0.0392347	−	0.999230i	$-0.487508\pi$
$719$	23.7299	−	41.1014i	0.884976	−	1.53282i	0.845741	−	0.533593i	$-0.179159\pi$
$720$		0			0
$721$	3.09286	+	5.80812i	0.115184	+	0.216306i
$722$	6.07042	+	25.6730i	0.225918	+	0.955452i
$723$		0			0
$724$	−24.6228	−	16.2317i	−0.915100	−	0.603245i
$725$	0.0886054	−	0.0511564i	0.00329072	−	0.00189990i
$726$		0			0
$727$	−17.4768			−0.648179			−0.324089	−	0.946026i	$-0.605058\pi$
$727$	−17.4768			−0.648179			−0.324089	+	0.946026i	$0.605058\pi$
$728$	15.0957	−	2.10693i	0.559483	−	0.0780881i
$729$		0			0
$730$	−11.3485	+	37.8345i	−0.420027	+	1.40032i
$731$	−13.4593	+	7.77072i	−0.497810	+	0.287410i
$732$		0			0
$733$	18.8796	−	32.7004i	0.697334	−	1.20782i	−0.272053	−	0.962282i	$-0.587703\pi$
$733$	18.8796	−	32.7004i	0.697334	−	1.20782i	0.969387	−	0.245536i	$-0.0789640\pi$
$734$	−7.29782	−	30.8639i	−0.269367	−	1.13921i
$735$		0			0
$736$	0.381427	−	0.877918i	0.0140596	−	0.0323605i
$737$	−29.4850	+	51.0695i	−1.08609	+	1.88117i
$738$		0			0
$739$	5.08570	+	8.80869i	0.187081	+	0.324033i	0.944276	−	0.329156i	$-0.106764\pi$
$739$	5.08570	+	8.80869i	0.187081	+	0.324033i	−0.757195	+	0.653189i	$0.773431\pi$
$740$	−38.8975	−	2.30641i	−1.42990	−	0.0847853i
$741$		0			0
$742$	6.26734	−	18.5575i	0.230081	−	0.681269i
$743$			45.6235i			1.67376i	0.547385	+	0.836881i	$0.315624\pi$
$743$			45.6235i			1.67376i	−0.547385	+	0.836881i	$0.684376\pi$
$744$		0			0
$745$	−16.4093	+	9.47390i	−0.601189	+	0.347097i
$746$	17.1188	+	18.1639i	0.626762	+	0.665026i
$747$		0			0
$748$	6.94078	+	13.8564i	0.253780	+	0.506640i
$749$	−19.8699	−	37.3139i	−0.726030	−	1.36342i
$750$		0			0
$751$	21.5415	+	12.4370i	0.786059	+	0.453831i	0.838573	−	0.544789i	$-0.183390\pi$
$751$	21.5415	+	12.4370i	0.786059	+	0.453831i	−0.0525142	+	0.998620i	$0.516723\pi$
$752$	43.5227	+	5.17952i	1.58711	+	0.188878i
$753$		0			0
$754$	0.363587	−	1.21215i	0.0132410	−	0.0441440i
$755$		−	34.6123i		−	1.25967i
$756$		0			0
$757$			40.1442i			1.45907i	0.683945	+	0.729533i	$0.260263\pi$
$757$			40.1442i			1.45907i	−0.683945	+	0.729533i	$0.739737\pi$
$758$	5.66407	+	1.69894i	0.205728	+	0.0617084i
$759$		0			0
$760$	−3.41073	−	1.24747i	−0.123720	−	0.0452507i
$761$	−18.0272	−	10.4080i	−0.653487	−	0.377291i	0.136304	−	0.990667i	$-0.456478\pi$
$761$	−18.0272	−	10.4080i	−0.653487	−	0.377291i	−0.789791	+	0.613376i	$0.789811\pi$
$762$		0			0
$763$	0.687787	−	20.0526i	0.0248996	−	0.725954i
$764$	−15.6982	−	31.3394i	−0.567940	−	1.13382i
$765$		0			0
$766$	−5.75881	+	5.42746i	−0.208074	+	0.196102i
$767$	−1.48780	+	0.858980i	−0.0537212	+	0.0310160i
$768$		0			0
$769$			18.6970i			0.674230i	0.941463	+	0.337115i	$0.109451\pi$
$769$			18.6970i			0.674230i	−0.941463	+	0.337115i	$0.890549\pi$
$770$	26.3006	−	23.1373i	0.947808	−	0.833810i
$771$		0			0
$772$	1.15116	−	19.4144i	0.0414313	−	0.698738i
$773$	−7.98344	−	13.8277i	−0.287144	−	0.497349i	0.685983	−	0.727618i	$-0.259373\pi$
$773$	−7.98344	−	13.8277i	−0.287144	−	0.497349i	−0.973127	+	0.230269i	$0.926039\pi$
$774$		0			0
$775$	0.657103	−	1.13814i	0.0236038	−	0.0408830i
$776$	28.9598	−	24.2228i	1.03960	−	0.869546i
$777$		0			0
$778$	−4.92493	+	1.16451i	−0.176567	+	0.0417496i
$779$	−3.13007	+	5.42144i	−0.112146	+	0.194243i
$780$		0			0
$781$	36.1169	−	20.8521i	1.29236	−	0.746146i
$782$	0.414216	+	0.124245i	0.0148123	+	0.00444298i
$783$		0			0
$784$	18.2645	−	21.2228i	0.652304	−	0.757957i
$785$	30.6154			1.09271
$786$		0			0
$787$	−7.03059	+	4.05912i	−0.250614	+	0.144692i	−0.620045	−	0.784566i	$-0.712886\pi$
$787$	−7.03059	+	4.05912i	−0.250614	+	0.144692i	0.369432	+	0.929258i	$0.379552\pi$
$788$	18.3656	−	27.8600i	0.654248	−	0.992470i
$789$		0			0
$790$	−2.72330	+	0.643927i	−0.0968906	+	0.0229099i
$791$	−0.737739	+	1.18226i	−0.0262310	+	0.0420364i
$792$		0			0
$793$	−8.59999	+	14.8956i	−0.305395	+	0.528959i
$794$	−0.124027	+	0.116891i	−0.00440155	+	0.00414829i
$795$		0			0
$796$	−2.46897	+	41.6392i	−0.0875104	+	1.47586i
$797$	16.4777			0.583672			0.291836	−	0.956468i	$-0.405734\pi$
$797$	16.4777			0.583672			0.291836	+	0.956468i	$0.405734\pi$
$798$		0			0
$799$			19.8017i			0.700534i
$800$	1.05874	−	0.783900i	0.0374320	−	0.0277151i
$801$		0			0
$802$	6.63216	−	6.25056i	0.234190	−	0.220715i
$803$	−47.5032	−	27.4260i	−1.67635	−	0.967842i
$804$		0			0
$805$	0.0335066	−	0.976895i	0.00118095	−	0.0344310i
$806$	−3.74048	−	15.8192i	−0.131753	−	0.557209i
$807$		0			0
$808$	10.3610	−	28.3281i	0.364499	−	0.996578i
$809$	0.395154	+	0.684427i	0.0138929	+	0.0240632i	0.872888	−	0.487920i	$-0.162244\pi$
$809$	0.395154	+	0.684427i	0.0138929	+	0.0240632i	−0.858995	+	0.511983i	$0.828911\pi$
$810$		0			0
$811$			34.7227i			1.21928i	0.792679	+	0.609639i	$0.208686\pi$
$811$			34.7227i			1.21928i	−0.792679	+	0.609639i	$0.791314\pi$
$812$	−0.969317	−	2.11306i	−0.0340163	−	0.0741537i
$813$		0			0
$814$	15.5462	−	51.8291i	0.544894	−	1.81661i
$815$	−0.508459	−	0.880677i	−0.0178105	−	0.0308488i
$816$		0			0
$817$	4.37991	+	2.52874i	0.153234	+	0.0884695i
$818$	−4.51093	+	1.06661i	−0.157721	+	0.0372933i
$819$		0			0
$820$	20.8185	+	41.5616i	0.727015	+	1.45140i
$821$	11.9605	+	6.90542i	0.417425	+	0.241001i	0.693975	−	0.719999i	$-0.255858\pi$
$821$	11.9605	+	6.90542i	0.417425	+	0.241001i	−0.276550	+	0.961000i	$0.589191\pi$
$822$		0			0
$823$	−21.0708	+	12.1652i	−0.734481	+	0.424053i	−0.820059	−	0.572279i	$-0.806060\pi$
$823$	−21.0708	+	12.1652i	−0.734481	+	0.424053i	0.0855784	+	0.996331i	$0.472726\pi$
$824$	6.92965	−	1.21066i	0.241406	−	0.0421754i
$825$		0			0
$826$	−1.00981	+	2.99003i	−0.0351356	+	0.104036i
$827$	−8.66472			−0.301302			−0.150651	−	0.988587i	$-0.548137\pi$
$827$	−8.66472			−0.301302			−0.150651	+	0.988587i	$0.548137\pi$
$828$		0			0
$829$	14.7388	+	25.5284i	0.511901	+	0.886638i	0.999905	+	0.0137970i	$0.00439186\pi$
$829$	14.7388	+	25.5284i	0.511901	+	0.886638i	−0.488004	+	0.872841i	$0.662275\pi$
$830$	24.3300	+	25.8154i	0.844507	+	0.896065i
$831$		0			0
$832$	2.87990	−	16.0379i	0.0998427	−	0.556013i
$833$	10.4961	+	7.06078i	0.363669	+	0.244641i
$834$		0			0
$835$	−8.85645	+	15.3398i	−0.306490	+	0.530856i
$836$	2.77570	−	4.21063i	0.0959996	−	0.145628i
$837$		0			0
$838$	11.7067	−	39.0288i	0.404402	−	1.34823i
$839$	−31.9931			−1.10452			−0.552262	−	0.833670i	$-0.686235\pi$
$839$	−31.9931			−1.10452			−0.552262	+	0.833670i	$0.686235\pi$
$840$		0			0
$841$	28.8070			0.993344
$842$	−6.19763	+	20.6621i	−0.213585	+	0.712065i
$843$		0			0
$844$	1.92500	+	1.26898i	0.0662613	+	0.0436803i
$845$	−9.66301	+	16.7368i	−0.332418	+	0.575765i
$846$		0			0
$847$	9.18452	+	17.2477i	0.315584	+	0.592639i
$848$	−16.7700	−	12.5395i	−0.575884	−	0.430608i
$849$		0			0
$850$	0.408199	+	0.433120i	0.0140011	+	0.0148559i
$851$	−0.754957	−	1.30762i	−0.0258796	−	0.0448248i
$852$		0			0
$853$	−15.1498			−0.518721			−0.259360	−	0.965781i	$-0.583512\pi$
$853$	−15.1498			−0.518721			−0.259360	+	0.965781i	$0.583512\pi$
$854$	6.21232	+	30.9801i	0.212581	+	1.06012i
$855$		0			0
$856$	−44.5191	+	7.77782i	−1.52163	+	0.265840i
$857$	−29.8035	+	17.2071i	−1.01807	+	0.587782i	−0.913544	−	0.406741i	$-0.866665\pi$
$857$	−29.8035	+	17.2071i	−1.01807	+	0.587782i	−0.104524	+	0.994522i	$0.533332\pi$
$858$		0			0
$859$	−41.4956	−	23.9575i	−1.41581	−	0.817420i	−0.419885	−	0.907577i	$-0.637930\pi$
$859$	−41.4956	−	23.9575i	−1.41581	−	0.817420i	−0.995928	+	0.0901577i	$0.971263\pi$
$860$	33.5771	−	16.8190i	1.14497	−	0.573524i
$861$		0			0
$862$	31.7856	−	7.51576i	1.08262	−	0.255988i
$863$	−9.53504	−	5.50506i	−0.324576	−	0.187394i	0.328854	−	0.944381i	$-0.393338\pi$
$863$	−9.53504	−	5.50506i	−0.324576	−	0.187394i	−0.653431	+	0.756986i	$0.726671\pi$
$864$		0			0
$865$	5.96210	+	10.3267i	0.202718	+	0.351117i
$866$	−6.90680	+	23.0264i	−0.234703	+	0.782470i
$867$		0			0
$868$	−24.3538	−	17.2804i	−0.826623	−	0.586534i
$869$		−	3.88602i		−	0.131824i
$870$		0			0
$871$	14.0058	+	24.2588i	0.474570	+	0.821979i
$872$	−20.1447	−	7.36792i	−0.682184	−	0.249509i
$873$		0			0
$874$	−0.0323822	−	0.136951i	−0.00109534	−	0.00463243i
$875$	16.0028	−	25.6452i	0.540993	−	0.866967i
$876$		0			0
$877$	35.3285	+	20.3969i	1.19296	+	0.688755i	0.958976	−	0.283486i	$-0.0914909\pi$
$877$	35.3285	+	20.3969i	1.19296	+	0.688755i	0.233982	+	0.972241i	$0.424824\pi$
$878$	1.59081	−	1.49928i	0.0536872	−	0.0505981i
$879$		0			0
$880$	−14.7603	−	34.4163i	−0.497570	−	1.16017i
$881$			33.9401i			1.14347i	0.820438	+	0.571736i	$0.193730\pi$
$881$			33.9401i			1.14347i	−0.820438	+	0.571736i	$0.806270\pi$
$882$		0			0
$883$	−35.7900			−1.20443			−0.602214	−	0.798334i	$-0.705715\pi$
$883$	−35.7900			−1.20443			−0.602214	+	0.798334i	$0.705715\pi$
$884$	7.34868	+	0.435736i	0.247163	+	0.0146554i
$885$		0			0
$886$	26.2979	−	24.7848i	0.883495	−	0.832661i
$887$	−7.60416	+	13.1708i	−0.255323	+	0.442232i	−0.964983	−	0.262312i	$-0.915515\pi$
$887$	−7.60416	+	13.1708i	−0.255323	+	0.442232i	0.709660	+	0.704544i	$0.248848\pi$
$888$		0			0
$889$	17.8714	+	11.1519i	0.599387	+	0.374021i
$890$	−50.4250	+	11.9231i	−1.69025	+	0.399662i
$891$		0			0
$892$	16.8182	+	11.0868i	0.563116	+	0.371213i
$893$	5.58055	−	3.22193i	0.186746	−	0.107818i
$894$		0			0
$895$	−3.99206			−0.133440
$896$	−15.4878	−	25.6150i	−0.517413	−	0.855736i
$897$		0			0
$898$	−21.5569	−	6.46600i	−0.719362	−	0.215773i
$899$	−2.14718	+	1.23967i	−0.0716124	+	0.0413454i
$900$		0			0
$901$	4.73014	−	8.19284i	0.157584	−	0.272943i
$902$	−62.8187	+	14.8536i	−2.09163	+	0.494570i
$903$		0			0
$904$	0.955815	+	1.14274i	0.0317899	+	0.0380069i
$905$	−16.0978	+	27.8821i	−0.535107	+	0.926833i
$906$		0			0
$907$	11.5870	+	20.0694i	0.384742	+	0.666392i	0.991733	−	0.128316i	$-0.0409573\pi$
$907$	11.5870	+	20.0694i	0.384742	+	0.666392i	−0.606992	+	0.794708i	$0.707624\pi$
$908$	−18.6755	−	1.10735i	−0.619768	−	0.0367488i
$909$		0			0
$910$	−3.27152	−	16.3147i	−0.108450	−	0.540828i
$911$		−	3.30496i		−	0.109498i	−0.998500	−	0.0547492i	$-0.982564\pi$
$911$		−	3.30496i		−	0.109498i	0.998500	−	0.0547492i	$-0.0174359\pi$
$912$		0			0
$913$	−42.6613	+	24.6305i	−1.41188	+	0.815151i
$914$	−14.6142	+	13.7733i	−0.483394	+	0.455581i
$915$		0			0
$916$	−47.6749	+	23.8807i	−1.57522	+	0.789042i
$917$	15.9560	−	8.49665i	0.526913	−	0.280584i
$918$		0			0
$919$	−20.9479	−	12.0943i	−0.691008	−	0.398953i	0.112982	−	0.993597i	$-0.463960\pi$
$919$	−20.9479	−	12.0943i	−0.691008	−	0.398953i	−0.803989	+	0.594644i	$0.797293\pi$
$920$	−0.981378	−	0.358939i	−0.0323551	−	0.0118339i
$921$		0			0
$922$	−29.2417	−	8.77107i	−0.963023	−	0.288860i
$923$		−	19.8101i		−	0.652058i
$924$		0			0
$925$		−	2.07804i		−	0.0683256i
$926$	−3.32589	+	11.0881i	−0.109296	+	0.364378i
$927$		0			0
$928$	−2.46923	+	0.282059i	−0.0810565	+	0.00925905i
$929$	21.2034	+	12.2418i	0.695660	+	0.401639i	0.805729	−	0.592285i	$-0.201774\pi$
$929$	21.2034	+	12.2418i	0.695660	+	0.401639i	−0.110069	+	0.993924i	$0.535107\pi$
$930$		0			0
$931$	0.282057	−	4.10689i	0.00924404	−	0.134598i
$932$	31.6121	−	15.8348i	1.03549	−	0.518685i
$933$		0			0
$934$	−22.7206	−	24.1077i	−0.743441	−	0.788828i
$935$	14.6518	−	8.45924i	0.479166	−	0.276647i
$936$		0			0
$937$		−	29.2997i		−	0.957180i	−0.878038	−	0.478590i	$-0.841148\pi$
$937$		−	29.2997i		−	0.957180i	0.878038	−	0.478590i	$-0.158852\pi$
$938$	48.7530	+	16.4651i	1.59184	+	0.537604i
$939$		0			0
$940$	2.83217	−	47.7645i	0.0923753	−	1.55791i
$941$	−0.623806	−	1.08046i	−0.0203355	−	0.0352221i	0.855679	−	0.517508i	$-0.173140\pi$
$941$	−0.623806	−	1.08046i	−0.0203355	−	0.0352221i	−0.876014	+	0.482286i	$0.839807\pi$
$942$		0			0
$943$	−0.900624	+	1.55993i	−0.0293284	+	0.0507982i
$944$	2.70201	+	2.02038i	0.0879429	+	0.0657579i
$945$		0			0
$946$	12.0000	+	50.7504i	0.390154	+	1.65004i
$947$	20.4254	−	35.3778i	0.663736	−	1.14962i	−0.315891	−	0.948796i	$-0.602303\pi$
$947$	20.4254	−	35.3778i	0.663736	−	1.14962i	0.979626	−	0.200828i	$-0.0643633\pi$
$948$		0			0
$949$	−22.5648	+	13.0278i	−0.732483	+	0.422899i
$950$	0.0556446	−	0.185512i	0.00180535	−	0.00601881i
$951$		0			0
$952$	10.6645	−	8.31573i	0.345639	−	0.269515i
$953$	35.0318			1.13479			0.567395	−	0.823446i	$-0.307951\pi$
$953$	35.0318			1.13479			0.567395	+	0.823446i	$0.307951\pi$
$954$		0			0
$955$	−33.1385	+	19.1325i	−1.07234	+	0.619114i
$956$	−14.9463	+	22.6730i	−0.483399	+	0.733299i
$957$		0			0
$958$	0.617047	+	2.60962i	0.0199359	+	0.0843129i
$959$	41.8692	+	1.43608i	1.35203	+	0.0463733i
$960$		0			0
$961$	−0.423591	+	0.733681i	−0.0136642	+	0.0236671i
$962$	−17.6289	−	18.7052i	−0.568378	−	0.603078i
$963$		0			0
$964$	42.1202	+	2.49749i	1.35660	+	0.0804388i
$965$	−21.2316			−0.683471
$966$		0			0
$967$			56.3266i			1.81134i	0.423981	+	0.905671i	$0.360632\pi$
$967$			56.3266i			1.81134i	−0.423981	+	0.905671i	$0.639368\pi$
$968$	20.5782	−	3.59517i	0.661409	−	0.115553i
$969$		0			0
$970$	−28.2686	−	29.9944i	−0.907651	−	0.963064i
$971$	−28.8496	−	16.6563i	−0.925828	−	0.534527i	−0.0403380	−	0.999186i	$-0.512843\pi$
$971$	−28.8496	−	16.6563i	−0.925828	−	0.534527i	−0.885490	+	0.464659i	$0.846177\pi$
$972$		0			0
$973$	34.2639	+	21.3809i	1.09845	+	0.685439i
$974$	7.52277	−	1.77877i	0.241045	−	0.0569955i
$975$		0			0
$976$	33.5418	+	3.99172i	1.07365	+	0.127772i
$977$	9.57425	+	16.5831i	0.306308	+	0.530540i	0.977552	−	0.210696i	$-0.0675731\pi$
$977$	9.57425	+	16.5831i	0.306308	+	0.530540i	−0.671244	+	0.741236i	$0.734240\pi$
$978$		0			0
$979$		−	71.9542i		−	2.29967i
$980$	−24.3082	−	18.5328i	−0.776499	−	0.592009i
$981$		0			0
$982$	−34.9161	−	10.4731i	−1.11422	−	0.334210i
$983$	−11.5610	−	20.0242i	−0.368738	−	0.638672i	0.620631	−	0.784103i	$-0.286877\pi$
$983$	−11.5610	−	20.0242i	−0.368738	−	0.638672i	−0.989368	+	0.145431i	$0.953543\pi$
$984$		0			0
$985$	−31.5478	−	18.2141i	−1.00520	−	0.580350i
$986$	−0.258368	−	1.09269i	−0.00822811	−	0.0347983i
$987$		0			0
$988$	−1.07290	−	2.14191i	−0.0341335	−	0.0681434i
$989$	1.26024	+	0.727602i	0.0400734	+	0.0231364i
$990$		0			0
$991$	8.05545	−	4.65082i	0.255890	−	0.147738i	−0.366568	−	0.930391i	$-0.619467\pi$
$991$	8.05545	−	4.65082i	0.255890	−	0.147738i	0.622458	+	0.782653i	$0.286134\pi$
$992$	−25.6564	+	18.9963i	−0.814592	+	0.603132i
$993$		0			0
$994$	−24.0372	−	27.3235i	−0.762413	−	0.866649i
$995$	45.5368			1.44361
$996$		0			0
$997$	−5.43145	−	9.40755i	−0.172016	−	0.297940i	0.767109	−	0.641517i	$-0.221695\pi$
$997$	−5.43145	−	9.40755i	−0.172016	−	0.297940i	−0.939125	+	0.343577i	$0.888361\pi$
$998$	2.23474	−	2.10616i	0.0707395	−	0.0666693i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.b.19.2	✓	32
3.2	odd	2	inner	504.2.bk.b.19.15	yes	32
4.3	odd	2		2016.2.bs.b.271.13		32
7.3	odd	6	inner	504.2.bk.b.451.13	yes	32
8.3	odd	2	inner	504.2.bk.b.19.13	yes	32
8.5	even	2		2016.2.bs.b.271.3		32
12.11	even	2		2016.2.bs.b.271.4		32
21.17	even	6	inner	504.2.bk.b.451.4	yes	32
24.5	odd	2		2016.2.bs.b.271.14		32
24.11	even	2	inner	504.2.bk.b.19.4	yes	32
28.3	even	6		2016.2.bs.b.1711.3		32
56.3	even	6	inner	504.2.bk.b.451.2	yes	32
56.45	odd	6		2016.2.bs.b.1711.13		32
84.59	odd	6		2016.2.bs.b.1711.14		32
168.59	odd	6	inner	504.2.bk.b.451.15	yes	32
168.101	even	6		2016.2.bs.b.1711.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bk.b.19.2	✓	32	1.1	even	1	trivial
504.2.bk.b.19.4	yes	32	24.11	even	2	inner
504.2.bk.b.19.13	yes	32	8.3	odd	2	inner
504.2.bk.b.19.15	yes	32	3.2	odd	2	inner
504.2.bk.b.451.2	yes	32	56.3	even	6	inner
504.2.bk.b.451.4	yes	32	21.17	even	6	inner
504.2.bk.b.451.13	yes	32	7.3	odd	6	inner
504.2.bk.b.451.15	yes	32	168.59	odd	6	inner
2016.2.bs.b.271.3		32	8.5	even	2
2016.2.bs.b.271.4		32	12.11	even	2
2016.2.bs.b.271.13		32	4.3	odd	2
2016.2.bs.b.271.14		32	24.5	odd	2
2016.2.bs.b.1711.3		32	28.3	even	6
2016.2.bs.b.1711.4		32	168.101	even	6
2016.2.bs.b.1711.13		32	56.45	odd	6
2016.2.bs.b.1711.14		32	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35459 - 0.406311i) q^{2} +(1.66982 + 1.10077i) q^{4} +(1.09169 - 1.89086i) q^{5} +(1.40064 - 2.24459i) q^{7} +(-1.81467 - 2.16955i) q^{8} +O(q^{10})\)	\(q+(-1.35459 - 0.406311i) q^{2} +(1.66982 + 1.10077i) q^{4} +(1.09169 - 1.89086i) q^{5} +(1.40064 - 2.24459i) q^{7} +(-1.81467 - 2.16955i) q^{8} +(-2.24706 + 2.11777i) q^{10} +(-2.14393 - 3.71339i) q^{11} -2.03680 q^{13} +(-2.80930 + 2.47141i) q^{14} +(1.57662 + 3.67618i) q^{16} +(-1.56503 + 0.903573i) q^{17} +(0.509293 + 0.294040i) q^{19} +(3.90432 - 1.95570i) q^{20} +(1.39535 + 5.90122i) q^{22} +(0.146540 + 0.0846050i) q^{23} +(0.116439 + 0.201678i) q^{25} +(2.75903 + 0.827573i) q^{26} +(4.80960 - 2.20630i) q^{28} -0.439341i q^{29} +(-2.82167 - 4.88727i) q^{31} +(-0.642005 - 5.62031i) q^{32} +(2.48711 - 0.588080i) q^{34} +(-2.71515 - 5.09881i) q^{35} +(-7.72782 - 4.46166i) q^{37} +(-0.570411 - 0.605235i) q^{38} +(-6.08337 + 1.06281i) q^{40} +10.6450i q^{41} +8.59999 q^{43} +(0.507600 - 8.56067i) q^{44} +(-0.164126 - 0.174146i) q^{46} +(5.47872 - 9.48943i) q^{47} +(-3.07641 - 6.28774i) q^{49} +(-0.0757829 - 0.320501i) q^{50} +(-3.40109 - 2.24204i) q^{52} +(-4.53358 + 2.61746i) q^{53} -9.36199 q^{55} +(-7.41147 + 1.03443i) q^{56} +(-0.178509 + 0.595127i) q^{58} +(0.730458 - 0.421730i) q^{59} +(4.22231 - 7.31325i) q^{61} +(1.83645 + 7.76671i) q^{62} +(-1.41394 + 7.87406i) q^{64} +(-2.22355 + 3.85130i) q^{65} +(-6.87640 - 11.9103i) q^{67} +(-3.60796 - 0.213932i) q^{68} +(1.60621 + 8.00998i) q^{70} +9.72611i q^{71} +(11.0785 - 6.39620i) q^{73} +(8.65520 + 9.18361i) q^{74} +(0.526759 + 1.05161i) q^{76} +(-11.3379 - 0.388881i) q^{77} +(0.784867 + 0.453143i) q^{79} +(8.67230 + 1.03207i) q^{80} +(4.32519 - 14.4197i) q^{82} -11.4885i q^{83} +3.94568i q^{85} +(-11.6495 - 3.49427i) q^{86} +(-4.16588 + 11.3900i) q^{88} +(14.5327 + 8.39047i) q^{89} +(-2.85282 + 4.57179i) q^{91} +(0.151566 + 0.302582i) q^{92} +(-11.2771 + 10.6282i) q^{94} +(1.11198 - 0.642000i) q^{95} +13.3483i q^{97} +(1.61249 + 9.76729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 32 * q + 2 * q^4	\( 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) \) 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

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