LMFDB - Embedded newform 504.2.bk.b.19.4

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			19.4
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.b.451.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02917 - 0.969953i) q^{2} +(0.118381 + 1.99649i) q^{4} +(1.09169 - 1.89086i) q^{5} +(-1.40064 + 2.24459i) q^{7} +(1.81467 - 2.16955i) q^{8} +O(q^{10})$	\(q+(-1.02917 - 0.969953i) q^{2} +(0.118381 + 1.99649i) q^{4} +(1.09169 - 1.89086i) q^{5} +(-1.40064 + 2.24459i) q^{7} +(1.81467 - 2.16955i) q^{8} +(-2.95757 + 0.887128i) q^{10} +(2.14393 + 3.71339i) q^{11} +2.03680 q^{13} +(3.61865 - 0.951512i) q^{14} +(-3.97197 + 0.472694i) q^{16} +(1.56503 - 0.903573i) q^{17} +(0.509293 + 0.294040i) q^{19} +(3.90432 + 1.95570i) q^{20} +(1.39535 - 5.90122i) q^{22} +(0.146540 + 0.0846050i) q^{23} +(0.116439 + 0.201678i) q^{25} +(-2.09621 - 1.97560i) q^{26} +(-4.64713 - 2.53065i) q^{28} -0.439341i q^{29} +(2.82167 + 4.88727i) q^{31} +(4.54632 + 3.36615i) q^{32} +(-2.48711 - 0.588080i) q^{34} +(2.71515 + 5.09881i) q^{35} +(7.72782 + 4.46166i) q^{37} +(-0.238943 - 0.796607i) q^{38} +(-2.12127 - 5.79976i) q^{40} -10.6450i q^{41} +8.59999 q^{43} +(-7.15996 + 4.71993i) q^{44} +(-0.0687518 - 0.229210i) q^{46} +(5.47872 - 9.48943i) q^{47} +(-3.07641 - 6.28774i) q^{49} +(0.0757829 - 0.320501i) q^{50} +(0.241118 + 4.06646i) q^{52} +(-4.53358 + 2.61746i) q^{53} +9.36199 q^{55} +(2.32807 + 7.11197i) q^{56} +(-0.426140 + 0.452157i) q^{58} +(-0.730458 + 0.421730i) q^{59} +(-4.22231 + 7.31325i) q^{61} +(1.83645 - 7.76671i) q^{62} +(-1.41394 - 7.87406i) q^{64} +(2.22355 - 3.85130i) q^{65} +(-6.87640 - 11.9103i) q^{67} +(1.98925 + 3.01762i) q^{68} +(2.15126 - 7.88110i) q^{70} +9.72611i q^{71} +(11.0785 - 6.39620i) q^{73} +(-3.62564 - 12.0874i) q^{74} +(-0.526759 + 1.05161i) q^{76} +(-11.3379 - 0.388881i) q^{77} +(-0.784867 - 0.453143i) q^{79} +(-3.44235 + 8.02647i) q^{80} +(-10.3252 + 10.9556i) q^{82} +11.4885i q^{83} -3.94568i q^{85} +(-8.85085 - 8.34159i) q^{86} +(11.9469 + 2.08722i) q^{88} +(-14.5327 - 8.39047i) q^{89} +(-2.85282 + 4.57179i) q^{91} +(-0.151566 + 0.302582i) q^{92} +(-14.8428 + 4.45213i) q^{94} +(1.11198 - 0.642000i) q^{95} +13.3483i q^{97} +(-2.93267 + 9.45513i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.02917	−	0.969953i	−0.727733	−	0.685861i
$2$	−1.02917	−	0.969953i	−0.727733	−	0.685861i
$3$		0			0
$3$		0			0
$4$	0.118381	+	1.99649i	0.0591905	+	0.998247i
$5$	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
$10$	−2.95757	+	0.887128i	−0.935267	+	0.280534i
$11$	2.14393	+	3.71339i	0.646418	+	1.11963i	0.983972	+	0.178323i	$0.0570672\pi$
$11$	2.14393	+	3.71339i	0.646418	+	1.11963i	−0.337554	+	0.941306i	$0.609599\pi$
$12$		0			0
$13$	2.03680			0.564906			0.282453	−	0.959281i	$-0.408852\pi$
$13$	2.03680			0.564906			0.282453	+	0.959281i	$0.408852\pi$
$14$	3.61865	−	0.951512i	0.967125	−	0.254302i
$15$		0			0
$16$	−3.97197	+	0.472694i	−0.992993	+	0.118173i
$17$	1.56503	−	0.903573i	0.379577	−	0.219149i	−0.298057	−	0.954548i	$-0.596339\pi$
$17$	1.56503	−	0.903573i	0.379577	−	0.219149i	0.677634	+	0.735399i	$0.263005\pi$
$18$		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
$26$	−2.09621	−	1.97560i	−0.411101	−	0.387447i
$27$		0			0
$28$	−4.64713	−	2.53065i	−0.878225	−	0.478249i
$29$		−	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	$0.00249993\pi$
$31$	2.82167	+	4.88727i	0.506786	+	0.877779i	−0.493183	+	0.869926i	$0.664167\pi$
$32$	4.54632	+	3.36615i	0.803684	+	0.595056i
$33$		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	0.975072	−	0.221890i	$-0.0712226\pi$
$37$	7.72782	+	4.46166i	1.27045	+	0.733492i	0.295373	+	0.955382i	$0.404556\pi$
$38$	−0.238943	−	0.796607i	−0.0387617	−	0.129227i
$39$		0			0
$40$	−2.12127	−	5.79976i	−0.335402	−	0.917023i
$41$		−	10.6450i		−	1.66248i	−0.555917	−	0.831238i	$-0.687633\pi$
$41$		−	10.6450i		−	1.66248i	0.555917	−	0.831238i	$-0.312367\pi$
$42$		0			0
$43$	8.59999			1.31149			0.655743	−	0.754984i	$-0.272356\pi$
$43$	8.59999			1.31149			0.655743	+	0.754984i	$0.272356\pi$
$44$	−7.15996	+	4.71993i	−1.07940	+	0.711556i
$45$		0			0
$46$	−0.0687518	−	0.229210i	−0.0101369	−	0.0337952i
$47$	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
$52$	0.241118	+	4.06646i	0.0334371	+	0.563916i
$53$	−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
$56$	2.32807	+	7.11197i	0.311101	+	0.950377i
$57$		0			0
$58$	−0.426140	+	0.452157i	−0.0559550	+	0.0593711i
$59$	−0.730458	+	0.421730i	−0.0950976	+	0.0549046i	−0.546795	−	0.837267i	$-0.684152\pi$
$59$	−0.730458	+	0.421730i	−0.0950976	+	0.0549046i	0.451697	+	0.892171i	$0.350819\pi$
$60$		0			0
$61$	−4.22231	+	7.31325i	−0.540611	+	0.936366i	0.458258	+	0.888819i	$0.348474\pi$
$61$	−4.22231	+	7.31325i	−0.540611	+	0.936366i	−0.998869	+	0.0475464i	$0.984860\pi$
$62$	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	$-0.484162\pi$
$68$	1.98925	+	3.01762i	0.241232	+	0.365940i
$69$		0			0
$70$	2.15126	−	7.88110i	0.257125	−	0.941972i
$71$			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	$0.0640508\pi$
$74$	−3.62564	−	12.0874i	−0.421472	−	1.40513i
$75$		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	0.455198	−	0.890390i	$-0.349569\pi$
$79$	−0.784867	−	0.453143i	−0.0883044	−	0.0509826i	−0.543502	+	0.839408i	$0.682902\pi$
$80$	−3.44235	+	8.02647i	−0.384867	+	0.897386i
$81$		0			0
$82$	−10.3252	+	10.9556i	−1.14023	+	1.20984i
$83$			11.4885i			1.26103i	0.776178	+	0.630513i	$0.217156\pi$
$83$			11.4885i			1.26103i	−0.776178	+	0.630513i	$0.782844\pi$
$84$		0			0
$85$		−	3.94568i		−	0.427969i
$86$	−8.85085	−	8.34159i	−0.954412	−	0.899497i
$87$		0			0
$88$	11.9469	+	2.08722i	1.27355	+	0.222498i
$89$	−14.5327	−	8.39047i	−1.54046	−	0.889388i	−0.998809	−	0.0487874i	$-0.984464\pi$
$89$	−14.5327	−	8.39047i	−1.54046	−	0.889388i	−0.541656	−	0.840600i	$-0.682202\pi$
$90$		0			0
$91$	−2.85282	+	4.57179i	−0.299057	+	0.479254i
$92$	−0.151566	+	0.302582i	−0.0158018	+	0.0315464i
$93$		0			0
$94$	−14.8428	+	4.45213i	−1.53092	+	0.459202i
$95$	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	$0.762996\pi$
$98$	−2.93267	+	9.45513i	−0.296244	+	0.955112i
$99$		0			0
$100$	−0.388865	+	0.256344i	−0.0388865	+	0.0256344i
$101$	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	−0.798234	−	0.602347i	$-0.794232\pi$
$103$	1.24356	−	2.15390i	0.122531	−	0.212230i	0.920765	+	0.390117i	$0.127566\pi$
$104$	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	$0.447580\pi$
$107$	−7.98914	+	13.8376i	−0.772340	+	1.33773i	−0.936278	+	0.351261i	$0.885753\pi$
$108$		0			0
$109$	−6.56763	+	3.79182i	−0.629065	+	0.363191i	−0.780390	−	0.625293i	$-0.784979\pi$
$109$	−6.56763	+	3.79182i	−0.629065	+	0.363191i	0.151325	+	0.988484i	$0.451646\pi$
$110$	−9.63508	−	9.08069i	−0.918669	−	0.865810i
$111$		0			0
$112$	4.50230	−	9.57754i	0.425427	−	0.904993i
$113$	0.526715			0.0495492			0.0247746	−	0.999693i	$-0.492113\pi$
$113$	0.526715			0.0495492			0.0247746	+	0.999693i	$0.492113\pi$
$114$		0			0
$115$	0.319952	−	0.184724i	0.0298357	−	0.0172256i
$116$	0.877142	−	0.0520096i	0.0814405	−	0.00482897i
$117$		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
$122$	11.4390	−	3.43114i	1.03564	−	0.310640i
$123$		0			0
$124$	−9.42337	+	6.21200i	−0.846243	+	0.557854i
$125$	11.4253			1.02191
$126$		0			0
$127$		−	7.96196i		−	0.706510i	−0.935527	−	0.353255i	$-0.885075\pi$
$127$		−	7.96196i		−	0.706510i	0.935527	−	0.353255i	$-0.114925\pi$
$128$	−6.18229	+	9.47519i	−0.546442	+	0.837497i
$129$		0			0
$130$	−6.02398	+	1.80690i	−0.528338	+	0.158476i
$131$	−5.91716	−	3.41628i	−0.516985	−	0.298481i	0.218715	−	0.975789i	$-0.429813\pi$
$131$	−5.91716	−	3.41628i	−0.516985	−	0.298481i	−0.735700	+	0.677307i	$0.763147\pi$
$132$		0			0
$133$	−1.37334	+	0.731311i	−0.119083	+	0.0634127i
$134$	−4.47543	+	18.9275i	−0.386618	+	1.63509i
$135$		0			0
$136$	0.879672	−	5.03512i	0.0754313	−	0.431758i
$137$	−7.91720	−	13.7130i	−0.676412	−	1.17158i	−0.976054	−	0.217528i	$-0.930201\pi$
$137$	−7.91720	−	13.7130i	−0.676412	−	1.17158i	0.299642	−	0.954052i	$-0.403133\pi$
$138$		0			0
$139$			15.2651i			1.29477i	0.762165	+	0.647383i	$0.224137\pi$
$139$			15.2651i			1.29477i	−0.762165	+	0.647383i	$0.775863\pi$
$140$	−9.85831	+	6.02437i	−0.833180	+	0.509153i
$141$		0			0
$142$	9.43387	−	10.0098i	0.791673	−	0.840005i
$143$	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	−0.940694	−	0.339257i	$-0.889824\pi$
$151$	−13.7288	+	7.92633i	−1.11724	+	0.645036i	−0.176541	+	0.984293i	$0.556491\pi$
$152$	1.56214	−	0.571352i	0.126706	−	0.0463428i
$153$		0			0
$154$	11.2915	+	11.3975i	0.909892	+	0.918436i
$155$	12.3215			0.989687
$156$		0			0
$157$	−7.01102	−	12.1434i	−0.559540	−	0.969152i	−0.997535	−	0.0701745i	$-0.977644\pi$
$157$	−7.01102	−	12.1434i	−0.559540	−	0.969152i	0.437994	−	0.898978i	$-0.355689\pi$
$158$	0.368234	+	1.22765i	0.0292951	+	0.0976662i
$159$		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	$0.160860\pi$
$164$	21.2528	−	1.26017i	1.65956	−	0.0984028i
$165$		0			0
$166$	11.1433	−	11.8236i	0.864888	−	0.917691i
$167$	−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
$170$	−3.82712	+	4.06077i	−0.293527	+	0.311447i
$171$		0			0
$172$	1.01808	+	17.1698i	0.0776275	+	1.30919i
$173$	−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
$178$	6.81827	+	22.7313i	0.511051	+	1.70378i
$179$	0.914196	+	1.58343i	0.0683302	+	0.118351i	0.898166	−	0.439656i	$-0.144900\pi$
$179$	0.914196	+	1.58343i	0.0683302	+	0.118351i	−0.829836	+	0.558007i	$0.811566\pi$
$180$		0			0
$181$	14.7458			1.09604			0.548022	−	0.836464i	$-0.315381\pi$
$181$	14.7458			1.09604			0.548022	+	0.836464i	$0.315381\pi$
$182$	7.37046	−	1.93804i	0.546335	−	0.143657i
$183$		0			0
$184$	0.449478	−	0.164397i	0.0331359	−	0.0121195i
$185$	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	$0.947146\pi$
$194$	12.9472	−	13.7377i	0.929556	−	0.986306i
$195$		0			0
$196$	12.1892	−	6.88638i	0.870661	−	0.491884i
$197$		−	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	$-0.901858\pi$
$199$	−10.4281	−	18.0620i	−0.739227	−	1.28038i	0.213617	−	0.976917i	$-0.431475\pi$
$200$	0.648850	+	0.113359i	0.0458806	+	0.00801568i
$201$		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
$206$	−3.36901	+	1.01054i	−0.234730	+	0.0704076i
$207$		0			0
$208$	−8.09011	+	0.962782i	−0.560948	+	0.0667569i
$209$			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	$0.487366\pi$
$212$	−5.76244	−	8.74140i	−0.395766	−	0.600362i
$213$		0			0
$214$	21.6440	−	6.49215i	1.47955	−	0.443794i
$215$	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
$220$	1.10828	+	18.6912i	0.0747203	+	1.26016i
$221$	3.18766	−	1.84040i	0.214425	−	0.123798i
$222$		0			0
$223$	−10.0719			−0.674462			−0.337231	−	0.941422i	$-0.609490\pi$
$223$	−10.0719			−0.674462			−0.337231	+	0.941422i	$0.609490\pi$
$224$	−13.9234	+	5.48989i	−0.930296	+	0.366809i
$225$		0			0
$226$	−0.542079	−	0.510889i	−0.0360586	−	0.0339838i
$227$	8.10094	−	4.67708i	0.537678	−	0.310429i	−0.206459	−	0.978455i	$-0.566194\pi$
$227$	8.10094	−	4.67708i	0.537678	−	0.310429i	0.744137	+	0.668027i	$0.232861\pi$
$228$		0			0
$229$	13.3304	−	23.0889i	0.880896	−	1.52576i	0.0305504	−	0.999533i	$-0.490274\pi$
$229$	13.3304	−	23.0889i	0.880896	−	1.52576i	0.850346	−	0.526224i	$-0.176393\pi$
$230$	−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	$0.363250\pi$
$233$	−8.83907	+	15.3097i	−0.579066	+	1.00297i	−0.995587	+	0.0938461i	$0.970084\pi$
$234$		0			0
$235$	−11.9621	−	20.7190i	−0.780322	−	1.35156i
$236$	−0.928454	−	1.40843i	−0.0604372	−	0.0916810i
$237$		0			0
$238$	4.80355	−	4.75887i	0.311368	−	0.308471i
$239$			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	$0.0955340\pi$
$242$	10.0046	−	3.00089i	0.643119	−	0.192904i
$243$		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
$248$	15.7236	+	2.74703i	0.998449	+	0.174436i
$249$		0			0
$250$	−11.7586	−	11.0820i	−0.743679	−	0.700890i
$251$		−	8.90673i		−	0.562188i	−0.959680	−	0.281094i	$-0.909303\pi$
$251$		−	8.90673i		−	0.562188i	0.959680	−	0.281094i	$-0.0906972\pi$
$252$		0			0
$253$			0.725548i			0.0456148i
$254$	−7.72273	+	8.19421i	−0.484567	+	0.514151i
$255$		0			0
$256$	15.5531	−	3.75505i	0.972070	−	0.234691i
$257$	21.9783	+	12.6892i	1.37097	+	0.791530i	0.991050	−	0.133490i	$-0.0426183\pi$
$257$	21.9783	+	12.6892i	1.37097	+	0.791530i	0.379920	+	0.925019i	$0.375952\pi$
$258$		0			0
$259$	−20.8385	+	11.0966i	−1.29484	+	0.689511i
$260$	7.95231	+	3.98338i	0.493181	+	0.247038i
$261$		0			0
$262$	2.77614	+	9.25530i	0.171510	+	0.571794i
$263$	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
$266$	2.12273	+	0.579430i	0.130153	+	0.0355272i
$267$		0			0
$268$	22.9648	−	15.1386i	1.40280	−	0.924740i
$269$	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	−0.851757	−	0.523936i	$-0.824463\pi$
$271$	0.458689	−	0.794472i	0.0278633	−	0.0482607i	0.879621	+	0.475676i	$0.157796\pi$
$272$	−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	−0.277544	−	0.960713i	$-0.589521\pi$
$277$	6.91838	−	3.99433i	0.415685	−	0.239996i	0.693230	+	0.720717i	$0.256187\pi$
$278$	14.8064	−	15.7103i	0.888029	−	0.942244i
$279$		0			0
$280$	15.9892	+	3.36200i	0.955540	+	0.200918i
$281$	−8.33678			−0.497331			−0.248665	−	0.968589i	$-0.579992\pi$
$281$	−8.33678			−0.497331			−0.248665	+	0.968589i	$0.579992\pi$
$282$		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	$0.242088\pi$
$284$	−19.4181	+	1.15139i	−1.15225	+	0.0683222i
$285$		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
$290$	0.389752	+	1.29938i	0.0228870	+	0.0763025i
$291$		0			0
$292$	14.0815	+	21.3611i	0.824055	+	1.25006i
$293$	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
$296$	23.7033	−	8.66948i	1.37772	−	0.503903i
$297$		0			0
$298$	3.52605	+	11.7554i	0.204259	+	0.680973i
$299$	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
$304$	−2.16189	−	0.927180i	−0.123993	−	0.0531774i
$305$	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	$0.976500\pi$
$308$	−0.565798	−	22.6821i	−0.0322393	−	1.29243i
$309$		0			0
$310$	−12.6809	−	11.9513i	−0.720228	−	0.678787i
$311$	−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
$320$	−16.4323	−	5.92246i	−0.918593	−	0.331075i
$321$		0			0
$322$	0.610780	+	0.166721i	0.0340375	+	0.00929101i
$323$	1.06275			0.0591329
$324$		0			0
$325$	0.237163	+	0.410778i	0.0131554	+	0.0227858i
$326$	−0.630907	+	0.189241i	−0.0349427	+	0.0104811i
$327$		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	$0.261099\pi$
$332$	−22.9367	+	1.36002i	−1.25882	+	0.0746408i
$333$		0			0
$334$	8.34927	+	7.86887i	0.456852	+	0.430565i
$335$	−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	$0.446077\pi$
$338$	9.10965	+	8.58549i	0.495499	+	0.466989i
$339$		0			0
$340$	7.87752	−	0.467093i	0.427218	−	0.0253317i
$341$	−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
$346$	7.39791	−	2.21901i	0.397714	−	0.119295i
$347$	−13.9217	−	24.1130i	−0.747353	−	1.29445i	−0.949087	−	0.315014i	$-0.897991\pi$
$347$	−13.9217	−	24.1130i	−0.747353	−	1.29445i	0.201734	−	0.979440i	$-0.435342\pi$
$348$		0			0
$349$	−29.5982			−1.58435			−0.792177	−	0.610291i	$-0.791052\pi$
$349$	−29.5982			−1.58435			−0.792177	+	0.610291i	$0.791052\pi$
$350$	0.613251	+	0.619009i	0.0327796	+	0.0330874i
$351$		0			0
$352$	−2.75282	+	24.0991i	−0.146726	+	1.28448i
$353$	−18.0733	+	10.4346i	−0.961944	+	0.555379i	−0.896771	−	0.442495i	$-0.854093\pi$
$353$	−18.0733	+	10.4346i	−0.961944	+	0.555379i	−0.0651732	+	0.997874i	$0.520760\pi$
$354$		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
$362$	−15.1759	−	14.3027i	−0.797627	−	0.751733i
$363$		0			0
$364$	−9.46526	−	5.15443i	−0.496115	−	0.270166i
$365$		−	27.9306i		−	1.46195i
$366$		0			0
$367$	−11.2129	−	19.4214i	−0.585311	−	1.01379i	−0.994837	−	0.101490i	$-0.967639\pi$
$367$	−11.2129	−	19.4214i	−0.585311	−	1.01379i	0.409526	−	0.912299i	$-0.365694\pi$
$368$	−0.622046	−	0.266780i	−0.0324264	−	0.0139069i
$369$		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	0.840456	−	0.541880i	$-0.182287\pi$
$373$	15.2845	+	8.82452i	0.791403	+	0.456916i	−0.0490535	+	0.998796i	$0.515620\pi$
$374$	−3.14841	−	10.4964i	−0.162800	−	0.542757i
$375$		0			0
$376$	−10.6458	−	29.1066i	−0.549013	−	1.50106i
$377$		−	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	$0.534250\pi$
$380$	1.41339	+	2.14405i	0.0725051	+	0.109988i
$381$		0			0
$382$	7.12086	+	23.7401i	0.364335	+	1.21465i
$383$	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
$388$	−26.6498	+	1.58018i	−1.35294	+	0.0802217i
$389$	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
$392$	−19.2243	−	4.73575i	−0.970972	−	0.239191i
$393$		0			0
$394$	−16.1831	+	17.1711i	−0.815291	+	0.865065i
$395$	−1.71366	+	0.989381i	−0.0862235	+	0.0497811i
$396$		0			0
$397$	−0.0602558	+	0.104366i	−0.00302415	+	0.00523798i	−0.867534	−	0.497379i	$-0.834296\pi$
$397$	−0.0602558	+	0.104366i	−0.00302415	+	0.00523798i	0.864509	+	0.502617i	$0.167629\pi$
$398$	−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	−0.774289	−	0.632832i	$-0.781893\pi$
$401$	3.22209	−	5.58083i	0.160904	−	0.278693i	0.935193	+	0.354138i	$0.115226\pi$
$402$		0			0
$403$	5.74716	+	9.95438i	0.286287	+	0.495863i
$404$	−17.8076	+	11.7390i	−0.885962	+	0.584037i
$405$		0			0
$406$	−0.418038	−	1.58982i	−0.0207469	−	0.0789015i
$407$			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	$0.307511\pi$
$410$	9.44351	+	31.4835i	0.466382	+	1.55486i
$411$		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
$416$	9.25995	+	6.85616i	0.454006	+	0.336151i
$417$		0			0
$418$	2.44584	−	2.59516i	0.119630	−	0.126933i
$419$		−	28.8123i		−	1.40757i	−0.710412	−	0.703786i	$-0.751491\pi$
$419$		−	28.8123i		−	1.40757i	0.710412	−	0.703786i	$-0.248509\pi$
$420$		0			0
$421$			15.2534i			0.743407i	0.928351	+	0.371704i	$0.121226\pi$
$421$			15.2534i			0.743407i	−0.928351	+	0.371704i	$0.878774\pi$
$422$	−1.18645	−	1.11818i	−0.0577553	−	0.0544321i
$423$		0			0
$424$	−2.54823	+	14.5857i	−0.123753	+	0.708343i
$425$	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
$430$	−25.4351	+	7.62929i	−1.22659	+	0.367917i
$431$	−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	$-0.133933\pi$
$434$	14.8609	+	15.0005i	0.713347	+	0.720045i
$435$		0			0
$436$	−8.34783	−	12.6633i	−0.399789	−	0.606464i
$437$	0.0497546	+	0.0861774i	0.00238008	+	0.00412243i
$438$		0			0
$439$	0.772860	−	1.33863i	0.0368866	−	0.0638895i	−0.846993	−	0.531604i	$-0.821589\pi$
$439$	0.772860	−	1.33863i	0.0368866	−	0.0638895i	0.883879	+	0.467715i	$0.154923\pi$
$440$	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	$-0.625699\pi$
$443$	12.7763	−	22.1292i	0.607019	−	1.05139i	0.991729	−	0.128350i	$-0.0409681\pi$
$444$		0			0
$445$	−31.7304	+	18.3195i	−1.50416	+	0.868429i
$446$	10.3657	+	9.76924i	0.490828	+	0.462587i
$447$		0			0
$448$	19.6545	+	7.85502i	0.928587	+	0.371115i
$449$	−15.9139			−0.751025			−0.375513	−	0.926817i	$-0.622533\pi$
$449$	−15.9139			−0.751025			−0.375513	+	0.926817i	$0.622533\pi$
$450$		0			0
$451$	39.5292	−	22.8222i	1.86136	−	1.07465i
$452$	0.0623531	+	1.05158i	0.00293284	+	0.0494623i
$453$		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	$0.0589016\pi$
$458$	−36.1144	+	10.8325i	−1.68751	+	0.506172i
$459$		0			0
$460$	0.406677	+	0.616914i	0.0189614	+	0.0287638i
$461$	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	$0.0609164\pi$
$463$			8.18559i			0.380417i	−0.981744	+	0.190208i	$0.939084\pi$
$464$	0.207674	+	1.74505i	0.00964101	+	0.0810119i
$465$		0			0
$466$	23.9466	−	7.18281i	1.10931	−	0.332737i
$467$	−20.2861	−	11.7122i	−0.938731	−	0.541977i	−0.0491686	−	0.998790i	$-0.515657\pi$
$467$	−20.2861	−	11.7122i	−0.938731	−	0.541977i	−0.889562	+	0.456814i	$0.848991\pi$
$468$		0			0
$469$	36.3651	+	1.24729i	1.67919	+	0.0575945i
$470$	−7.78540	+	32.9260i	−0.359114	+	1.51876i
$471$		0			0
$472$	−0.410575	+	2.35007i	−0.0188982	+	0.108171i
$473$	18.4377	+	31.9351i	0.847769	+	1.46838i
$474$		0			0
$475$			0.136951i			0.00628373i
$476$	−9.55955	+	0.238460i	−0.438161	+	0.0109298i
$477$		0			0
$478$	13.1701	−	13.9742i	0.602388	−	0.639164i
$479$	−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	−0.388897	−	0.921281i	$-0.627144\pi$
$487$	4.73377	−	2.73304i	0.214508	−	0.123846i	0.603404	+	0.797435i	$0.293810\pi$
$488$	8.20440	+	22.4317i	0.371396	+	1.01543i
$489$		0			0
$490$	14.6767	+	15.8673i	0.663028	+	0.716812i
$491$	−25.7761			−1.16326			−0.581630	−	0.813453i	$-0.697585\pi$
$491$	−25.7761			−1.16326			−0.581630	+	0.813453i	$0.697585\pi$
$492$		0			0
$493$	−0.396977	−	0.687584i	−0.0178789	−	0.0309672i
$494$	−0.486679	−	1.62253i	−0.0218967	−	0.0730010i
$495$		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	$0.182143\pi$
$500$	1.35254	+	22.8106i	0.0604875	+	1.02012i
$501$		0			0
$502$	−8.63911	+	9.16654i	−0.385582	+	0.409123i
$503$	−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
$506$	0.703748	−	0.746712i	0.0312854	−	0.0331954i
$507$		0			0
$508$	15.8960	−	0.942545i	0.705271	−	0.0418187i
$509$	−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
$514$	−10.3115	−	34.3773i	−0.454821	−	1.51632i
$515$	−2.71515	−	4.70277i	−0.119644	−	0.207229i
$516$		0			0
$517$	46.9839			2.06635
$518$	32.2096	+	8.79206i	1.41521	+	0.386301i
$519$		0			0
$520$	−4.32059	−	11.8129i	−0.189470	−	0.518032i
$521$	−7.24334	+	4.18194i	−0.317336	+	0.183214i	−0.650205	−	0.759759i	$-0.725317\pi$
$521$	−7.24334	+	4.18194i	−0.317336	+	0.183214i	0.332868	+	0.942973i	$0.391984\pi$
$522$		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
$530$	11.0864	−	11.7632i	0.481561	−	0.510961i
$531$		0			0
$532$	−1.62263	−	2.65529i	−0.0703501	−	0.115121i
$533$		−	21.6818i		−	0.939143i
$534$		0			0
$535$	17.4433	+	30.2127i	0.754139	+	1.30621i
$536$	−38.3184	−	6.69451i	−1.65510	−	0.289159i
$537$		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	0.716639	−	0.697444i	$-0.245679\pi$
$541$	10.9541	+	6.32437i	0.470955	+	0.271906i	−0.245685	+	0.969350i	$0.579013\pi$
$542$	−1.24267	+	0.372740i	−0.0533772	+	0.0160106i
$543$		0			0
$544$	10.1567	+	1.16020i	0.435466	+	0.0497431i
$545$			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	$0.649366\pi$
$548$	26.4406	−	17.4300i	1.12949	−	0.744572i
$549$		0			0
$550$	1.35262	−	0.405720i	0.0576759	−	0.0172999i
$551$	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
$556$	−30.4766	+	1.80709i	−1.29250	+	0.0766378i
$557$	−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
$560$	−13.1947	−	18.9689i	−0.557576	−	0.801582i
$561$		0			0
$562$	8.57996	+	8.08629i	0.361924	+	0.341099i
$563$	−23.7961	+	13.7387i	−1.00289	+	0.579016i	−0.909101	−	0.416576i	$-0.863230\pi$
$563$	−23.7961	+	13.7387i	−1.00289	+	0.579016i	−0.0937850	+	0.995592i	$0.529897\pi$
$564$		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	$0.377417\pi$
$569$	−14.6645	+	25.3997i	−0.614768	+	1.06481i	−0.990425	+	0.138051i	$0.955916\pi$
$570$		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	$0.846991\pi$
$572$	−14.5834	+	9.61355i	−0.609762	+	0.401963i
$573$		0			0
$574$	−10.1289	−	38.5207i	−0.422772	−	1.60782i
$575$			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	$0.355610\pi$
$578$	18.6042	−	5.58036i	0.773834	−	0.232112i
$579$		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
$584$	6.22701	−	35.6425i	0.257675	−	1.47490i
$585$		0			0
$586$	−31.9882	−	30.1477i	−1.32142	−	1.24539i
$587$			30.9449i			1.27723i	0.769526	+	0.638615i	$0.220492\pi$
$587$			30.9449i			1.27723i	−0.769526	+	0.638615i	$0.779508\pi$
$588$		0			0
$589$			3.31873i			0.136746i
$590$	1.78626	−	1.89531i	0.0735390	−	0.0780286i
$591$		0			0
$592$	−32.8037	−	14.0687i	−1.34822	−	0.578219i
$593$	19.2127	+	11.0925i	0.788971	+	0.455513i	0.839600	−	0.543205i	$-0.182789\pi$
$593$	19.2127	+	11.0925i	0.788971	+	0.455513i	−0.0506289	+	0.998718i	$0.516123\pi$
$594$		0			0
$595$	8.85645	+	5.52648i	0.363079	+	0.226563i
$596$	7.77330	−	15.5184i	0.318407	−	0.635660i
$597$		0			0
$598$	−0.140034	−	0.466855i	−0.00572640	−	0.0190911i
$599$	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	$0.888358\pi$
$602$	31.1203	−	8.18300i	1.26837	−	0.333514i
$603$		0			0
$604$	−17.4501	−	26.4712i	−0.710035	−	1.07710i
$605$	8.06287	+	13.9653i	0.327802	+	0.567770i
$606$		0			0
$607$	7.65975	−	13.2671i	0.310900	−	0.538494i	−0.667658	−	0.744468i	$-0.732703\pi$
$607$	7.65975	−	13.2671i	0.310900	−	0.538494i	0.978557	+	0.205975i	$0.0660364\pi$
$608$	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	0.260609	−	0.965444i	$-0.416077\pi$
$613$	30.3794	−	17.5396i	1.22701	−	0.708416i	0.966404	+	0.257028i	$0.0827432\pi$
$614$	2.50715	−	2.66022i	0.101181	−	0.107358i
$615$		0			0
$616$	−21.4183	+	23.8926i	−0.862968	+	0.962659i
$617$	34.0392			1.37037			0.685184	−	0.728370i	$-0.259722\pi$
$617$	34.0392			1.37037			0.685184	+	0.728370i	$0.259722\pi$
$618$		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	$0.223082\pi$
$620$	1.45863	+	24.5998i	0.0585801	+	0.987952i
$621$		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
$626$	−5.25966	−	17.5351i	−0.210218	−	0.700842i
$627$		0			0
$628$	23.4143	−	15.4350i	0.934334	−	0.615924i
$629$	16.1257			0.642975
$630$		0			0
$631$			31.5662i			1.25663i	0.777959	+	0.628315i	$0.216255\pi$
$631$			31.5662i			1.25663i	−0.777959	+	0.628315i	$0.783745\pi$
$632$	−2.40739	+	0.880506i	−0.0957610	+	0.0350246i
$633$		0			0
$634$	2.89459	+	9.65021i	0.114959	+	0.383259i
$635$	−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
$640$	11.1671	+	22.0338i	0.441419	+	0.870961i
$641$	−8.82372	−	15.2831i	−0.348516	−	0.603647i	0.637470	−	0.770475i	$-0.279981\pi$
$641$	−8.82372	−	15.2831i	−0.348516	−	0.603647i	−0.985986	+	0.166828i	$0.946648\pi$
$642$		0			0
$643$			9.96415i			0.392948i	0.980509	+	0.196474i	$0.0629491\pi$
$643$			9.96415i			0.392948i	−0.980509	+	0.196474i	$0.937051\pi$
$644$	−0.466885	−	0.764013i	−0.0183978	−	0.0301063i
$645$		0			0
$646$	−1.09375	−	1.03082i	−0.0430329	−	0.0405569i
$647$	−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
$656$	5.03184	+	42.2818i	0.196460	+	1.65083i
$657$		0			0
$658$	10.7963	−	39.5520i	0.420883	−	1.54190i
$659$	43.9413			1.71171			0.855855	−	0.517216i	$-0.173032\pi$
$659$	43.9413			1.71171			0.855855	+	0.517216i	$0.173032\pi$
$660$		0			0
$661$	4.46365	+	7.73127i	0.173616	+	0.300712i	0.939681	−	0.342051i	$-0.111122\pi$
$661$	4.46365	+	7.73127i	0.173616	+	0.300712i	−0.766065	+	0.642763i	$0.777788\pi$
$662$	14.4090	−	4.32199i	0.560021	−	0.167979i
$663$		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
$668$	−0.960380	−	16.1968i	−0.0371582	−	0.626673i
$669$		0			0
$670$	30.9034	+	29.1253i	1.19390	+	1.12521i
$671$	−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	$0.585512\pi$
$674$	−6.37055	−	6.00400i	−0.245384	−	0.231265i
$675$		0			0
$676$	−1.04784	−	17.6719i	−0.0403017	−	0.679687i
$677$	−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
$682$	32.7781	−	9.83181i	1.25514	−	0.376480i
$683$	7.87269	+	13.6359i	0.301240	+	0.521763i	0.976417	−	0.215892i	$-0.0692661\pi$
$683$	7.87269	+	13.6359i	0.301240	+	0.521763i	−0.675177	+	0.737656i	$0.735933\pi$
$684$		0			0
$685$	−34.5724			−1.32094
$686$	−17.1153	−	19.8259i	−0.653466	−	0.756956i
$687$		0			0
$688$	−34.1589	+	4.06516i	−1.30230	+	0.154983i
$689$	−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
$698$	30.4616	+	28.7089i	1.15299	+	1.08665i
$699$		0			0
$700$	−0.0307291	−	1.23189i	−0.00116145	−	0.0465611i
$701$		−	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
$704$	26.2081	−	22.1319i	0.987754	−	0.834128i
$705$		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	0.745265	−	0.666769i	$-0.232323\pi$
$709$	14.3908	+	8.30854i	0.540459	+	0.312034i	−0.204806	+	0.978803i	$0.565656\pi$
$710$	−8.62830	−	28.7657i	−0.323814	−	1.07956i
$711$		0			0
$712$	−44.5757	+	16.3036i	−1.67054	+	0.611003i
$713$			0.954908i			0.0357616i
$714$		0			0
$715$	19.0685			0.713121
$716$	−3.05309	+	2.01264i	−0.114099	+	0.0752157i
$717$		0			0
$718$	5.20148	+	17.3411i	0.194118	+	0.647164i
$719$	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
$724$	1.74562	+	29.4398i	0.0648754	+	1.09412i
$725$	0.0886054	−	0.0511564i	0.00329072	−	0.00189990i
$726$		0			0
$727$	17.4768			0.648179			0.324089	−	0.946026i	$-0.394942\pi$
$727$	17.4768			0.648179			0.324089	+	0.946026i	$0.394942\pi$
$728$	4.74180	+	14.4856i	0.175743	+	0.536874i
$729$		0			0
$730$	−27.0914	+	28.7453i	−1.00270	+	1.06391i
$731$	13.4593	−	7.77072i	0.497810	−	0.287410i
$732$		0			0
$733$	−18.8796	+	32.7004i	−0.697334	+	1.20782i	0.272053	+	0.962282i	$0.412297\pi$
$733$	−18.8796	+	32.7004i	−0.697334	+	1.20782i	−0.969387	+	0.245536i	$0.921036\pi$
$734$	−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	$0.773431\pi$
$740$	21.4462	+	32.5331i	0.788377	+	1.19594i
$741$		0			0
$742$	−13.9149	+	13.7854i	−0.510831	+	0.506079i
$743$			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
$746$	−7.17099	−	23.9072i	−0.262549	−	0.875305i
$747$		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	0.0525142	−	0.998620i	$-0.483277\pi$
$751$	−21.5415	−	12.4370i	−0.786059	−	0.453831i	−0.838573	+	0.544789i	$0.816610\pi$
$752$	−17.2757	+	40.2815i	−0.629982	+	1.46892i
$753$		0			0
$754$	−0.867962	+	0.920952i	−0.0316093	+	0.0335391i
$755$			34.6123i			1.25967i
$756$		0			0
$757$		−	40.1442i		−	1.45907i	−0.683945	−	0.729533i	$-0.739737\pi$
$757$		−	40.1442i		−	1.45907i	0.683945	−	0.729533i	$-0.260263\pi$
$758$	4.30336	+	4.05575i	0.156305	+	0.147312i
$759$		0			0
$760$	0.625018	−	3.57751i	0.0226718	−	0.129770i
$761$	18.0272	+	10.4080i	0.653487	+	0.377291i	0.789791	−	0.613376i	$-0.210189\pi$
$761$	18.0272	+	10.4080i	0.653487	+	0.377291i	−0.136304	+	0.990667i	$0.543522\pi$
$762$		0			0
$763$	0.687787	−	20.0526i	0.0248996	−	0.725954i
$764$	15.6982	−	31.3394i	0.567940	−	1.13382i
$765$		0			0
$766$	−7.57973	+	2.27355i	−0.273867	+	0.0821466i
$767$	−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	$0.890549\pi$
$770$	33.8778	−	8.90805i	1.22087	−	0.321024i
$771$		0			0
$772$	16.2378	−	10.7041i	0.584410	−	0.385250i
$773$	−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
$782$	−0.314707	−	0.296600i	−0.0112539	−	0.0106064i
$783$		0			0
$784$	15.1916	+	23.5205i	0.542557	+	0.840019i
$785$	−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	$0.379552\pi$
$788$	33.3102	−	1.97511i	1.18663	−	0.0703605i
$789$		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
$794$	0.163244	−	0.0489651i	0.00579330	−	0.00173771i
$795$		0			0
$796$	34.8261	−	22.9578i	1.23438	−	0.813717i
$797$	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
$800$	−0.149509	+	1.30884i	−0.00528593	+	0.0462746i
$801$		0			0
$802$	−8.72922	+	2.61834i	−0.308240	+	0.0924568i
$803$	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
$808$	29.7133	+	5.19114i	1.04531	+	0.182624i
$809$	−0.395154	−	0.684427i	−0.0138929	−	0.0240632i	0.858995	−	0.511983i	$-0.171089\pi$
$809$	−0.395154	−	0.684427i	−0.0138929	−	0.0240632i	−0.872888	+	0.487920i	$0.837756\pi$
$810$		0			0
$811$			34.7227i			1.21928i	0.792679	+	0.609639i	$0.208686\pi$
$811$			34.7227i			1.21928i	−0.792679	+	0.609639i	$0.791314\pi$
$812$	−1.11182	+	2.04167i	−0.0390172	+	0.0716487i
$813$		0			0
$814$	37.1122	−	39.3780i	1.30078	−	1.38020i
$815$	−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	−0.0855784	−	0.996331i	$-0.527274\pi$
$823$	21.0708	−	12.1652i	0.734481	−	0.424053i	0.820059	+	0.572279i	$0.193940\pi$
$824$	−2.41636	−	6.60658i	−0.0841780	−	0.230151i
$825$		0			0
$826$	−2.24199	+	2.22113i	−0.0780088	+	0.0772831i
$827$	8.66472			0.301302			0.150651	−	0.988587i	$-0.451863\pi$
$827$	8.66472			0.301302			0.150651	+	0.988587i	$0.451863\pi$
$828$		0			0
$829$	−14.7388	−	25.5284i	−0.511901	−	0.886638i	−0.999905	−	0.0137970i	$-0.995608\pi$
$829$	−14.7388	−	25.5284i	−0.511901	−	0.886638i	0.488004	−	0.872841i	$-0.337725\pi$
$830$	−10.1918	−	33.9781i	−0.353761	−	1.17940i
$831$		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
$836$	−5.03436	+	0.298510i	−0.174117	+	0.0103242i
$837$		0			0
$838$	−27.9466	+	29.6527i	−0.965398	+	1.02434i
$839$	−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
$842$	14.7951	−	15.6984i	0.509874	−	0.541002i
$843$		0			0
$844$	0.136472	+	2.30159i	0.00469755	+	0.0792241i
$845$	−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
$850$	−0.170993	−	0.570071i	−0.00586503	−	0.0195533i
$851$	0.754957	+	1.30762i	0.0258796	+	0.0448248i
$852$		0			0
$853$	15.1498			0.518721			0.259360	−	0.965781i	$-0.416488\pi$
$853$	15.1498			0.518721			0.259360	+	0.965781i	$0.416488\pi$
$854$	−8.32040	+	30.4817i	−0.284718	+	1.04306i
$855$		0			0
$856$	15.5238	+	42.4436i	0.530591	+	1.45069i
$857$	29.8035	−	17.2071i	1.01807	−	0.587782i	0.104524	−	0.994522i	$-0.466668\pi$
$857$	29.8035	−	17.2071i	1.01807	−	0.587782i	0.913544	+	0.406741i	$0.133335\pi$
$858$		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
$866$	−16.4881	+	17.4947i	−0.560288	+	0.594494i
$867$		0			0
$868$	−0.744658	−	29.8524i	−0.0252753	−	1.01326i
$869$		−	3.88602i		−	0.131824i
$870$		0			0
$871$	−14.0058	−	24.2588i	−0.474570	−	0.821979i
$872$	−3.69152	+	21.1297i	−0.125011	+	0.715543i
$873$		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	−0.233982	−	0.972241i	$-0.575176\pi$
$877$	−35.3285	−	20.3969i	−1.19296	−	0.688755i	−0.958976	+	0.283486i	$0.908509\pi$
$878$	−2.09382	+	0.628042i	−0.0706629	+	0.0211954i
$879$		0			0
$880$	−37.1856	+	4.42535i	−1.25353	+	0.149179i
$881$		−	33.9401i		−	1.14347i	−0.820438	−	0.571736i	$-0.806270\pi$
$881$		−	33.9401i		−	1.14347i	0.820438	−	0.571736i	$-0.193730\pi$
$882$		0			0
$883$	−35.7900			−1.20443			−0.602214	−	0.798334i	$-0.705715\pi$
$883$	−35.7900			−1.20443			−0.602214	+	0.798334i	$0.705715\pi$
$884$	4.05170	+	6.14628i	0.136273	+	0.206722i
$885$		0			0
$886$	−34.6132	+	10.3823i	−1.16285	+	0.348799i
$887$	−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
$892$	−1.19232	−	20.1084i	−0.0399217	−	0.673280i
$893$	5.58055	−	3.22193i	0.186746	−	0.107818i
$894$		0			0
$895$	3.99206			0.133440
$896$	−12.6088	−	27.1481i	−0.421231	−	0.906954i
$897$		0			0
$898$	16.3781	+	15.4358i	0.546546	+	0.515099i
$899$	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	$0.707624\pi$
$908$	10.2968	+	15.6198i	0.341710	+	0.518361i
$909$		0			0
$910$	4.38168	−	16.0522i	0.145251	−	0.532126i
$911$		−	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
$914$	−19.2351	+	5.76960i	−0.636242	+	0.190841i
$915$		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	0.803989	−	0.594644i	$-0.202707\pi$
$919$	20.9479	+	12.0943i	0.691008	+	0.398953i	−0.112982	+	0.993597i	$0.536040\pi$
$920$	0.179838	−	1.02937i	0.00592909	−	0.0339373i
$921$		0			0
$922$	−22.2168	−	20.9385i	−0.731671	−	0.689572i
$923$			19.8101i			0.652058i
$924$		0			0
$925$			2.07804i			0.0683256i
$926$	7.93964	−	8.42436i	0.260913	−	0.276842i
$927$		0			0
$928$	1.47889	−	1.99739i	0.0485468	−	0.0655674i
$929$	−21.2034	−	12.2418i	−0.695660	−	0.401639i	0.110069	−	0.993924i	$-0.464893\pi$
$929$	−21.2034	−	12.2418i	−0.695660	−	0.401639i	−0.805729	+	0.592285i	$0.798226\pi$
$930$		0			0
$931$	0.282057	−	4.10689i	0.00924404	−	0.134598i
$932$	−31.6121	−	15.8348i	−1.03549	−	0.518685i
$933$		0			0
$934$	9.51759	+	31.7305i	0.311425	+	1.03825i
$935$	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	$-0.158852\pi$
$938$	−36.2161	−	36.5561i	−1.18250	−	1.19360i
$939$		0			0
$940$	39.9492	−	26.3350i	1.30300	−	0.858953i
$941$	−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	$0.397697\pi$
$947$	−20.4254	+	35.3778i	−0.663736	+	1.14962i	−0.979626	+	0.200828i	$0.935637\pi$
$948$		0			0
$949$	22.5648	−	13.0278i	0.732483	−	0.422899i
$950$	0.132836	−	0.140946i	0.00430977	−	0.00457288i
$951$		0			0
$952$	10.0697	+	9.02690i	0.326361	+	0.292564i
$953$	−35.0318			−1.13479			−0.567395	−	0.823446i	$-0.692049\pi$
$953$	−35.0318			−1.13479			−0.567395	+	0.823446i	$0.692049\pi$
$954$		0			0
$955$	−33.1385	+	19.1325i	−1.07234	+	0.619114i
$956$	−27.1086	+	1.60739i	−0.876755	+	0.0519867i
$957$		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
$962$	−7.38469	−	24.6196i	−0.238092	−	0.793769i
$963$		0			0
$964$	23.2230	+	35.2284i	0.747962	+	1.13463i
$965$	−21.2316			−0.683471
$966$		0			0
$967$		−	56.3266i		−	1.81134i	−0.423981	−	0.905671i	$-0.639368\pi$
$967$		−	56.3266i		−	1.81134i	0.423981	−	0.905671i	$-0.360632\pi$
$968$	7.17560	+	19.6188i	0.230633	+	0.630573i
$969$		0			0
$970$	−11.8416	−	39.4786i	−0.380212	−	1.26758i
$971$	28.8496	+	16.6563i	0.925828	+	0.534527i	0.885490	−	0.464659i	$-0.153823\pi$
$971$	28.8496	+	16.6563i	0.925828	+	0.534527i	0.0403380	+	0.999186i	$0.487157\pi$
$972$		0			0
$973$	−34.2639	−	21.3809i	−1.09845	−	0.685439i
$974$	−7.52277	−	1.77877i	−0.241045	−	0.0569955i
$975$		0			0
$976$	13.3140	−	31.0439i	0.426169	−	0.993690i
$977$	−9.57425	−	16.5831i	−0.306308	−	0.530540i	0.671244	−	0.741236i	$-0.265760\pi$
$977$	−9.57425	−	16.5831i	−0.306308	−	0.530540i	−0.977552	+	0.210696i	$0.932427\pi$
$978$		0			0
$979$		−	71.9542i		−	2.29967i
$980$	0.285683	−	30.5659i	0.00912579	−	0.976392i
$981$		0			0
$982$	26.5280	+	25.0016i	0.846543	+	0.797834i
$983$	−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	−0.622458	−	0.782653i	$-0.713866\pi$
$991$	−8.05545	+	4.65082i	−0.255890	+	0.147738i	0.366568	+	0.930391i	$0.380533\pi$
$992$	−3.62305	+	31.7172i	−0.115032	+	1.00702i
$993$		0			0
$994$	9.25452	+	35.1954i	0.293535	+	1.11633i
$995$	−45.5368			−1.44361
$996$		0			0
$997$	5.43145	+	9.40755i	0.172016	+	0.297940i	0.939125	−	0.343577i	$-0.111639\pi$
$997$	5.43145	+	9.40755i	0.172016	+	0.297940i	−0.767109	+	0.641517i	$0.778305\pi$
$998$	2.94136	−	0.882264i	0.0931071	−	0.0279276i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.02917 - 0.969953i) q^{2} +(0.118381 + 1.99649i) q^{4} +(1.09169 - 1.89086i) q^{5} +(-1.40064 + 2.24459i) q^{7} +(1.81467 - 2.16955i) q^{8} +O(q^{10})\)	\(q+(-1.02917 - 0.969953i) q^{2} +(0.118381 + 1.99649i) q^{4} +(1.09169 - 1.89086i) q^{5} +(-1.40064 + 2.24459i) q^{7} +(1.81467 - 2.16955i) q^{8} +(-2.95757 + 0.887128i) q^{10} +(2.14393 + 3.71339i) q^{11} +2.03680 q^{13} +(3.61865 - 0.951512i) q^{14} +(-3.97197 + 0.472694i) q^{16} +(1.56503 - 0.903573i) q^{17} +(0.509293 + 0.294040i) q^{19} +(3.90432 + 1.95570i) q^{20} +(1.39535 - 5.90122i) q^{22} +(0.146540 + 0.0846050i) q^{23} +(0.116439 + 0.201678i) q^{25} +(-2.09621 - 1.97560i) q^{26} +(-4.64713 - 2.53065i) q^{28} -0.439341i q^{29} +(2.82167 + 4.88727i) q^{31} +(4.54632 + 3.36615i) q^{32} +(-2.48711 - 0.588080i) q^{34} +(2.71515 + 5.09881i) q^{35} +(7.72782 + 4.46166i) q^{37} +(-0.238943 - 0.796607i) q^{38} +(-2.12127 - 5.79976i) q^{40} -10.6450i q^{41} +8.59999 q^{43} +(-7.15996 + 4.71993i) q^{44} +(-0.0687518 - 0.229210i) q^{46} +(5.47872 - 9.48943i) q^{47} +(-3.07641 - 6.28774i) q^{49} +(0.0757829 - 0.320501i) q^{50} +(0.241118 + 4.06646i) q^{52} +(-4.53358 + 2.61746i) q^{53} +9.36199 q^{55} +(2.32807 + 7.11197i) q^{56} +(-0.426140 + 0.452157i) q^{58} +(-0.730458 + 0.421730i) q^{59} +(-4.22231 + 7.31325i) q^{61} +(1.83645 - 7.76671i) q^{62} +(-1.41394 - 7.87406i) q^{64} +(2.22355 - 3.85130i) q^{65} +(-6.87640 - 11.9103i) q^{67} +(1.98925 + 3.01762i) q^{68} +(2.15126 - 7.88110i) q^{70} +9.72611i q^{71} +(11.0785 - 6.39620i) q^{73} +(-3.62564 - 12.0874i) q^{74} +(-0.526759 + 1.05161i) q^{76} +(-11.3379 - 0.388881i) q^{77} +(-0.784867 - 0.453143i) q^{79} +(-3.44235 + 8.02647i) q^{80} +(-10.3252 + 10.9556i) q^{82} +11.4885i q^{83} -3.94568i q^{85} +(-8.85085 - 8.34159i) q^{86} +(11.9469 + 2.08722i) q^{88} +(-14.5327 - 8.39047i) q^{89} +(-2.85282 + 4.57179i) q^{91} +(-0.151566 + 0.302582i) q^{92} +(-14.8428 + 4.45213i) q^{94} +(1.11198 - 0.642000i) q^{95} +13.3483i q^{97} +(-2.93267 + 9.45513i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 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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