LMFDB - Embedded newform 507.2.f.g.437.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(239,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.239"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.23
Character	$\chi$	$=$	507.437
Dual form			507.2.f.g.239.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.82526 - 1.82526i) q^{2} +(1.43862 - 0.964559i) q^{3} -4.66316i q^{4} +(-0.624703 + 0.624703i) q^{5} +(0.865285 - 4.38643i) q^{6} +(-1.18894 + 1.18894i) q^{7} +(-4.86096 - 4.86096i) q^{8} +(1.13925 - 2.77527i) q^{9} +2.28049i q^{10} +(0.253306 + 0.253306i) q^{11} +(-4.49789 - 6.70851i) q^{12} +4.34024i q^{14} +(-0.296147 + 1.50127i) q^{15} -8.41874 q^{16} -2.62761 q^{17} +(-2.98615 - 7.14502i) q^{18} +(4.32335 + 4.32335i) q^{19} +(2.91309 + 2.91309i) q^{20} +(-0.563628 + 2.85722i) q^{21} +0.924699 q^{22} +5.41774 q^{23} +(-11.6818 - 2.30439i) q^{24} +4.21949i q^{25} +(-1.03796 - 5.09143i) q^{27} +(5.54420 + 5.54420i) q^{28} -8.37099i q^{29} +(2.19967 + 3.28076i) q^{30} +(1.27341 + 1.27341i) q^{31} +(-5.64448 + 5.64448i) q^{32} +(0.608739 + 0.120082i) q^{33} +(-4.79608 + 4.79608i) q^{34} -1.48546i q^{35} +(-12.9415 - 5.31252i) q^{36} +(-2.44464 + 2.44464i) q^{37} +15.7825 q^{38} +6.07331 q^{40} +(-4.89630 + 4.89630i) q^{41} +(4.18641 + 6.24395i) q^{42} -0.952948i q^{43} +(1.18121 - 1.18121i) q^{44} +(1.02202 + 2.44541i) q^{45} +(9.88879 - 9.88879i) q^{46} +(5.33521 + 5.33521i) q^{47} +(-12.1114 + 8.12037i) q^{48} +4.17286i q^{49} +(7.70168 + 7.70168i) q^{50} +(-3.78013 + 2.53449i) q^{51} +9.69778i q^{53} +(-11.1877 - 7.39865i) q^{54} -0.316482 q^{55} +11.5587 q^{56} +(10.3898 + 2.04953i) q^{57} +(-15.2792 - 15.2792i) q^{58} +(-7.28881 - 7.28881i) q^{59} +(7.00067 + 1.38098i) q^{60} +4.87861 q^{61} +4.64863 q^{62} +(1.94512 + 4.65411i) q^{63} +3.76781i q^{64} +(1.33029 - 0.891926i) q^{66} +(-8.90312 - 8.90312i) q^{67} +12.2530i q^{68} +(7.79406 - 5.22573i) q^{69} +(-2.71136 - 2.71136i) q^{70} +(2.27510 - 2.27510i) q^{71} +(-19.0283 + 7.95260i) q^{72} +(0.246530 - 0.246530i) q^{73} +8.92421i q^{74} +(4.06995 + 6.07025i) q^{75} +(20.1605 - 20.1605i) q^{76} -0.602329 q^{77} -3.68180 q^{79} +(5.25921 - 5.25921i) q^{80} +(-6.40421 - 6.32346i) q^{81} +17.8741i q^{82} +(-8.47001 + 8.47001i) q^{83} +(13.3237 + 2.62829i) q^{84} +(1.64148 - 1.64148i) q^{85} +(-1.73938 - 1.73938i) q^{86} +(-8.07431 - 12.0427i) q^{87} -2.46262i q^{88} +(-4.84440 - 4.84440i) q^{89} +(6.32897 + 2.59806i) q^{90} -25.2638i q^{92} +(3.06024 + 0.603676i) q^{93} +19.4763 q^{94} -5.40162 q^{95} +(-2.67583 + 13.5647i) q^{96} +(3.74098 + 3.74098i) q^{97} +(7.61657 + 7.61657i) q^{98} +(0.991570 - 0.414412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) $ 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.82526	−	1.82526i	1.29065	−	1.29065i	0.356273	−	0.934382i	$-0.384047\pi$
$2$	1.82526	−	1.82526i	1.29065	−	1.29065i	0.934382	−	0.356273i	$-0.115953\pi$
$3$	1.43862	−	0.964559i	0.830587	−	0.556888i
$3$	1.43862	−	0.964559i	0.830587	−	0.556888i
$4$		−	4.66316i		−	2.33158i
$5$	−0.624703	+	0.624703i	−0.279376	+	0.279376i	−0.832860	−	0.553484i	$-0.813298\pi$
$5$	−0.624703	+	0.624703i	−0.279376	+	0.279376i	0.553484	+	0.832860i	$0.313298\pi$
$6$	0.865285	−	4.38643i	0.353251	−	1.79075i
$7$	−1.18894	+	1.18894i	−0.449375	+	0.449375i	−0.895147	−	0.445771i	$-0.852929\pi$
$7$	−1.18894	+	1.18894i	−0.449375	+	0.449375i	0.445771	+	0.895147i	$0.352929\pi$
$8$	−4.86096	−	4.86096i	−1.71861	−	1.71861i
$9$	1.13925	−	2.77527i	0.379751	−	0.925089i
$10$			2.28049i			0.721155i
$11$	0.253306	+	0.253306i	0.0763746	+	0.0763746i	0.744262	−	0.667888i	$-0.232801\pi$
$11$	0.253306	+	0.253306i	0.0763746	+	0.0763746i	−0.667888	+	0.744262i	$0.732801\pi$
$12$	−4.49789	−	6.70851i	−1.29843	−	1.93658i
$13$		0			0
$13$		0			0
$14$			4.34024i			1.15998i
$15$	−0.296147	+	1.50127i	−0.0764648	+	0.387627i
$16$	−8.41874			−2.10469
$17$	−2.62761			−0.637289			−0.318645	−	0.947874i	$-0.603228\pi$
$17$	−2.62761			−0.637289			−0.318645	+	0.947874i	$0.603228\pi$
$18$	−2.98615	−	7.14502i	−0.703843	−	1.68410i
$19$	4.32335	+	4.32335i	0.991845	+	0.991845i	0.999967	−	0.00812247i	$-0.00258549\pi$
$19$	4.32335	+	4.32335i	0.991845	+	0.991845i	−0.00812247	+	0.999967i	$0.502585\pi$
$20$	2.91309	+	2.91309i	0.651386	+	0.651386i
$21$	−0.563628	+	2.85722i	−0.122994	+	0.623498i
$22$	0.924699			0.197146
$23$	5.41774			1.12968			0.564838	−	0.825202i	$-0.308939\pi$
$23$	5.41774			1.12968			0.564838	+	0.825202i	$0.308939\pi$
$24$	−11.6818	−	2.30439i	−2.38453	−	0.470382i
$25$			4.21949i			0.843899i
$26$		0			0
$27$	−1.03796	−	5.09143i	−0.199755	−	0.979846i
$28$	5.54420	+	5.54420i	1.04775	+	1.04775i
$29$		−	8.37099i		−	1.55445i	−0.629221	−	0.777227i	$-0.716626\pi$
$29$		−	8.37099i		−	1.55445i	0.629221	−	0.777227i	$-0.283374\pi$
$30$	2.19967	+	3.28076i	0.401603	+	0.598982i
$31$	1.27341	+	1.27341i	0.228712	+	0.228712i	0.812154	−	0.583443i	$-0.198295\pi$
$31$	1.27341	+	1.27341i	0.228712	+	0.228712i	−0.583443	+	0.812154i	$0.698295\pi$
$32$	−5.64448	+	5.64448i	−0.997812	+	0.997812i
$33$	0.608739	+	0.120082i	0.105968	+	0.0209036i
$34$	−4.79608	+	4.79608i	−0.822521	+	0.822521i
$35$		−	1.48546i		−	0.251089i
$36$	−12.9415	−	5.31252i	−2.15692	−	0.885419i
$37$	−2.44464	+	2.44464i	−0.401896	+	0.401896i	−0.878901	−	0.477005i	$-0.841723\pi$
$37$	−2.44464	+	2.44464i	−0.401896	+	0.401896i	0.477005	+	0.878901i	$0.341723\pi$
$38$	15.7825			2.56026
$39$		0			0
$40$	6.07331			0.960275
$41$	−4.89630	+	4.89630i	−0.764674	+	0.764674i	−0.977163	−	0.212489i	$-0.931843\pi$
$41$	−4.89630	+	4.89630i	−0.764674	+	0.764674i	0.212489	+	0.977163i	$0.431843\pi$
$42$	4.18641	+	6.24395i	0.645978	+	0.963462i
$43$		−	0.952948i		−	0.145323i	−0.997357	−	0.0726616i	$-0.976851\pi$
$43$		−	0.952948i		−	0.145323i	0.997357	−	0.0726616i	$-0.0231493\pi$
$44$	1.18121	−	1.18121i	0.178073	−	0.178073i
$45$	1.02202	+	2.44541i	0.152354	+	0.364540i
$46$	9.88879	−	9.88879i	1.45802	−	1.45802i
$47$	5.33521	+	5.33521i	0.778220	+	0.778220i	0.979528	−	0.201308i	$-0.0645191\pi$
$47$	5.33521	+	5.33521i	0.778220	+	0.778220i	−0.201308	+	0.979528i	$0.564519\pi$
$48$	−12.1114	+	8.12037i	−1.74813	+	1.17207i
$49$			4.17286i			0.596123i
$50$	7.70168	+	7.70168i	1.08918	+	1.08918i
$51$	−3.78013	+	2.53449i	−0.529325	+	0.354899i
$52$		0			0
$53$			9.69778i			1.33209i	0.745911	+	0.666046i	$0.232015\pi$
$53$			9.69778i			1.33209i	−0.745911	+	0.666046i	$0.767985\pi$
$54$	−11.1877	−	7.39865i	−1.52246	−	1.00683i
$55$	−0.316482			−0.0426744
$56$	11.5587			1.54460
$57$	10.3898	+	2.04953i	1.37616	+	0.271467i
$58$	−15.2792	−	15.2792i	−2.00626	−	2.00626i
$59$	−7.28881	−	7.28881i	−0.948922	−	0.948922i	0.0498356	−	0.998757i	$-0.484130\pi$
$59$	−7.28881	−	7.28881i	−0.948922	−	0.948922i	−0.998757	+	0.0498356i	$0.984130\pi$
$60$	7.00067	+	1.38098i	0.903783	+	0.178284i
$61$	4.87861			0.624643			0.312321	−	0.949977i	$-0.398893\pi$
$61$	4.87861			0.624643			0.312321	+	0.949977i	$0.398893\pi$
$62$	4.64863			0.590376
$63$	1.94512	+	4.65411i	0.245061	+	0.586363i
$64$			3.76781i			0.470977i
$65$		0			0
$66$	1.33029	−	0.891926i	0.163747	−	0.109789i
$67$	−8.90312	−	8.90312i	−1.08769	−	1.08769i	−0.995766	−	0.0919234i	$-0.970698\pi$
$67$	−8.90312	−	8.90312i	−1.08769	−	1.08769i	−0.0919234	−	0.995766i	$-0.529302\pi$
$68$			12.2530i			1.48589i
$69$	7.79406	−	5.22573i	0.938295	−	0.629103i
$70$	−2.71136	−	2.71136i	−0.324069	−	0.324069i
$71$	2.27510	−	2.27510i	0.270005	−	0.270005i	−0.559097	−	0.829102i	$-0.688852\pi$
$71$	2.27510	−	2.27510i	0.270005	−	0.270005i	0.829102	+	0.559097i	$0.188852\pi$
$72$	−19.0283	+	7.95260i	−2.24251	+	0.937223i
$73$	0.246530	−	0.246530i	0.0288542	−	0.0288542i	−0.692532	−	0.721387i	$-0.743505\pi$
$73$	0.246530	−	0.246530i	0.0288542	−	0.0288542i	0.721387	+	0.692532i	$0.243505\pi$
$74$			8.92421i			1.03742i
$75$	4.06995	+	6.07025i	0.469957	+	0.700932i
$76$	20.1605	−	20.1605i	2.31256	−	2.31256i
$77$	−0.602329			−0.0686417
$78$		0			0
$79$	−3.68180			−0.414235			−0.207118	−	0.978316i	$-0.566408\pi$
$79$	−3.68180			−0.414235			−0.207118	+	0.978316i	$0.566408\pi$
$80$	5.25921	−	5.25921i	0.587998	−	0.587998i
$81$	−6.40421	−	6.32346i	−0.711579	−	0.702607i
$82$			17.8741i			1.97386i
$83$	−8.47001	+	8.47001i	−0.929705	+	0.929705i	−0.997687	−	0.0679819i	$-0.978344\pi$
$83$	−8.47001	+	8.47001i	−0.929705	+	0.929705i	0.0679819	+	0.997687i	$0.478344\pi$
$84$	13.3237	+	2.62829i	1.45373	+	0.286770i
$85$	1.64148	−	1.64148i	0.178043	−	0.178043i
$86$	−1.73938	−	1.73938i	−0.187562	−	0.187562i
$87$	−8.07431	−	12.0427i	−0.865657	−	1.29111i
$88$		−	2.46262i		−	0.262516i
$89$	−4.84440	−	4.84440i	−0.513505	−	0.513505i	0.402093	−	0.915599i	$-0.368283\pi$
$89$	−4.84440	−	4.84440i	−0.513505	−	0.513505i	−0.915599	+	0.402093i	$0.868283\pi$
$90$	6.32897	+	2.59806i	0.667132	+	0.273859i
$91$		0			0
$92$		−	25.2638i		−	2.63393i
$93$	3.06024	+	0.603676i	0.317332	+	0.0625982i
$94$	19.4763			2.00883
$95$	−5.40162			−0.554194
$96$	−2.67583	+	13.5647i	−0.273100	+	1.38444i
$97$	3.74098	+	3.74098i	0.379839	+	0.379839i	0.871044	−	0.491205i	$-0.163443\pi$
$97$	3.74098	+	3.74098i	0.379839	+	0.379839i	−0.491205	+	0.871044i	$0.663443\pi$
$98$	7.61657	+	7.61657i	0.769390	+	0.769390i
$99$	0.991570	−	0.414412i	0.0996566	−	0.0416499i
$100$	19.6762			1.96762
$101$	−8.48208			−0.843999			−0.421999	−	0.906596i	$-0.638672\pi$
$101$	−8.48208			−0.843999			−0.421999	+	0.906596i	$0.638672\pi$
$102$	−2.27363	+	11.5258i	−0.225123	+	1.14123i
$103$			0.554855i			0.0546714i	0.999626	+	0.0273357i	$0.00870232\pi$
$103$			0.554855i			0.0546714i	−0.999626	+	0.0273357i	$0.991298\pi$
$104$		0			0
$105$	−1.43282	−	2.13702i	−0.139829	−	0.208551i
$106$	17.7010	+	17.7010i	1.71927	+	1.71927i
$107$			3.31960i			0.320918i	0.987042	+	0.160459i	$0.0512975\pi$
$107$			3.31960i			0.320918i	−0.987042	+	0.160459i	$0.948703\pi$
$108$	−23.7421	+	4.84016i	−2.28459	+	0.465744i
$109$	−1.95379	−	1.95379i	−0.187139	−	0.187139i	0.607319	−	0.794458i	$-0.292245\pi$
$109$	−1.95379	−	1.95379i	−0.187139	−	0.187139i	−0.794458	+	0.607319i	$0.792245\pi$
$110$	−0.577662	+	0.577662i	−0.0550779	+	0.0550779i
$111$	−1.15891	+	5.87491i	−0.109999	+	0.557621i
$112$	10.0093	−	10.0093i	0.945794	−	0.945794i
$113$			5.73825i			0.539809i	0.962887	+	0.269905i	$0.0869922\pi$
$113$			5.73825i			0.539809i	−0.962887	+	0.269905i	$0.913008\pi$
$114$	22.7050	−	15.2231i	2.12652	−	1.42578i
$115$	−3.38448	+	3.38448i	−0.315604	+	0.315604i
$116$	−39.0352			−3.62433
$117$		0			0
$118$	−26.6080			−2.44946
$119$	3.12406	−	3.12406i	0.286382	−	0.286382i
$120$	8.73719	−	5.85807i	0.797593	−	0.534766i
$121$		−	10.8717i		−	0.988334i
$122$	8.90475	−	8.90475i	0.806198	−	0.806198i
$123$	−2.32114	+	11.7667i	−0.209291	+	1.06097i
$124$	5.93813	−	5.93813i	0.533260	−	0.533260i
$125$	−5.75944	−	5.75944i	−0.515140	−	0.515140i
$126$	12.0453	+	4.94463i	1.07308	+	0.440502i
$127$		−	13.6238i		−	1.20892i	−0.796636	−	0.604459i	$-0.793389\pi$
$127$		−	13.6238i		−	1.20892i	0.796636	−	0.604459i	$-0.206611\pi$
$128$	−4.41171	−	4.41171i	−0.389944	−	0.389944i
$129$	−0.919175	−	1.37093i	−0.0809288	−	0.120704i
$130$		0			0
$131$			6.35913i			0.555599i	0.960639	+	0.277800i	$0.0896052\pi$
$131$			6.35913i			0.555599i	−0.960639	+	0.277800i	$0.910395\pi$
$132$	0.559963	−	2.83865i	0.0487385	−	0.247073i
$133$	−10.2804			−0.891421
$134$	−32.5011			−2.80766
$135$	3.82904	+	2.53222i	0.329552	+	0.217938i
$136$	12.7727	+	12.7727i	1.09525	+	1.09525i
$137$	−1.44455	−	1.44455i	−0.123416	−	0.123416i	0.642701	−	0.766117i	$-0.277814\pi$
$137$	−1.44455	−	1.44455i	−0.123416	−	0.123416i	−0.766117	+	0.642701i	$0.777814\pi$
$138$	4.68789	−	23.7645i	0.399059	−	2.02297i
$139$	−5.11351			−0.433722			−0.216861	−	0.976202i	$-0.569582\pi$
$139$	−5.11351			−0.433722			−0.216861	+	0.976202i	$0.569582\pi$
$140$	−6.92695			−0.585434
$141$	12.8215	+	2.52921i	1.07976	+	0.212998i
$142$		−	8.30531i		−	0.696966i
$143$		0			0
$144$	−9.59107	+	23.3642i	−0.799256	+	1.94702i
$145$	5.22938	+	5.22938i	0.434276	+	0.434276i
$146$		−	0.899965i		−	0.0744816i
$147$	4.02497	+	6.00316i	0.331974	+	0.495133i
$148$	11.3997	+	11.3997i	0.937053	+	0.937053i
$149$	7.49573	−	7.49573i	0.614074	−	0.614074i	−0.329931	−	0.944005i	$-0.607025\pi$
$149$	7.49573	−	7.49573i	0.614074	−	0.614074i	0.944005	+	0.329931i	$0.107025\pi$
$150$	18.5085	+	3.65106i	1.51121	+	0.298108i
$151$	6.62875	−	6.62875i	0.539440	−	0.539440i	−0.383925	−	0.923364i	$-0.625428\pi$
$151$	6.62875	−	6.62875i	0.539440	−	0.539440i	0.923364	+	0.383925i	$0.125428\pi$
$152$		−	42.0313i		−	3.40919i
$153$	−2.99351	+	7.29232i	−0.242011	+	0.589549i
$154$	−1.09941	+	1.09941i	−0.0885928	+	0.0885928i
$155$	−1.59101			−0.127793
$156$		0			0
$157$	21.9960			1.75547			0.877735	−	0.479147i	$-0.159054\pi$
$157$	21.9960			1.75547			0.877735	+	0.479147i	$0.159054\pi$
$158$	−6.72026	+	6.72026i	−0.534635	+	0.534635i
$159$	9.35407	+	13.9514i	0.741826	+	1.10642i
$160$		−	7.05224i		−	0.557529i
$161$	−6.44134	+	6.44134i	−0.507649	+	0.507649i
$162$	−23.2313	+	0.147387i	−1.82522	+	0.0115798i
$163$	−14.5425	+	14.5425i	−1.13905	+	1.13905i	−0.150434	+	0.988620i	$0.548067\pi$
$163$	−14.5425	+	14.5425i	−1.13905	+	1.13905i	−0.988620	+	0.150434i	$0.951933\pi$
$164$	22.8322	+	22.8322i	1.78290	+	1.78290i
$165$	−0.455297	+	0.305265i	−0.0354448	+	0.0237649i
$166$			30.9200i			2.39986i
$167$	−7.08868	−	7.08868i	−0.548538	−	0.548538i	0.377480	−	0.926018i	$-0.376791\pi$
$167$	−7.08868	−	7.08868i	−0.548538	−	0.548538i	−0.926018	+	0.377480i	$0.876791\pi$
$168$	16.6286	−	11.1491i	1.28293	−	0.860171i
$169$		0			0
$170$		−	5.99225i		−	0.459584i
$171$	16.9238	−	7.07306i	1.29420	−	0.540890i
$172$	−4.44375			−0.338833
$173$	11.7644			0.894430			0.447215	−	0.894426i	$-0.352416\pi$
$173$	11.7644			0.894430			0.447215	+	0.894426i	$0.352416\pi$
$174$	−36.7187	−	7.24329i	−2.78364	−	0.549112i
$175$	−5.01671	−	5.01671i	−0.379227	−	0.379227i
$176$	−2.13252	−	2.13252i	−0.160744	−	0.160744i
$177$	−17.5163	−	3.45534i	−1.31661	−	0.259719i
$178$	−17.6846			−1.32552
$179$	−11.8119			−0.882861			−0.441431	−	0.897295i	$-0.645529\pi$
$179$	−11.8119			−0.882861			−0.441431	+	0.897295i	$0.645529\pi$
$180$	11.4033	−	4.76585i	0.849955	−	0.355226i
$181$			20.0999i			1.49402i	0.664815	+	0.747008i	$0.268510\pi$
$181$			20.0999i			1.49402i	−0.664815	+	0.747008i	$0.731490\pi$
$182$		0			0
$183$	7.01847	−	4.70571i	0.518820	−	0.347856i
$184$	−26.3354	−	26.3354i	−1.94147	−	1.94147i
$185$		−	3.05435i		−	0.224560i
$186$	6.68761	−	4.48387i	0.490359	−	0.328774i
$187$	−0.665589	−	0.665589i	−0.0486727	−	0.0486727i
$188$	24.8789	−	24.8789i	1.81448	−	1.81448i
$189$	7.28745	+	4.81932i	0.530084	+	0.350554i
$190$	−9.85936	+	9.85936i	−0.715274	+	0.715274i
$191$			16.9411i			1.22582i	0.790154	+	0.612909i	$0.210001\pi$
$191$			16.9411i			1.22582i	−0.790154	+	0.612909i	$0.789999\pi$
$192$	3.63428	+	5.42045i	0.262281	+	0.391187i
$193$	11.8306	−	11.8306i	0.851587	−	0.851587i	−0.138742	−	0.990329i	$-0.544306\pi$
$193$	11.8306	−	11.8306i	0.851587	−	0.851587i	0.990329	+	0.138742i	$0.0443059\pi$
$194$	13.6565			0.980482
$195$		0			0
$196$	19.4587			1.38991
$197$	10.3422	−	10.3422i	0.736851	−	0.736851i	−0.235116	−	0.971967i	$-0.575547\pi$
$197$	10.3422	−	10.3422i	0.736851	−	0.736851i	0.971967	+	0.235116i	$0.0755471\pi$
$198$	1.05347	−	2.56628i	0.0748665	−	0.182378i
$199$			0.334295i			0.0236976i	0.999930	+	0.0118488i	$0.00377167\pi$
$199$			0.334295i			0.0236976i	−0.999930	+	0.0118488i	$0.996228\pi$
$200$	20.5108	−	20.5108i	1.45033	−	1.45033i
$201$	−21.3958	−	4.22062i	−1.50914	−	0.297700i
$202$	−15.4820	+	15.4820i	−1.08931	+	1.08931i
$203$	9.95256	+	9.95256i	0.698533	+	0.698533i
$204$	11.8187	+	17.6274i	0.827475	+	1.23416i
$205$		−	6.11747i		−	0.427262i
$206$	1.01275	+	1.01275i	0.0705620	+	0.0705620i
$207$	6.17217	−	15.0357i	0.428996	−	1.04505i
$208$		0			0
$209$			2.19026i			0.151503i
$210$	−6.51588	−	1.28535i	−0.449638	−	0.0886975i
$211$	−2.68910			−0.185125			−0.0925626	−	0.995707i	$-0.529506\pi$
$211$	−2.68910			−0.185125			−0.0925626	+	0.995707i	$0.529506\pi$
$212$	45.2223			3.10588
$213$	1.07854	−	5.46748i	0.0739001	−	0.374625i
$214$	6.05914	+	6.05914i	0.414195	+	0.414195i
$215$	0.595309	+	0.595309i	0.0405998	+	0.0405998i
$216$	−19.7038	+	29.7947i	−1.34067	+	2.02727i
$217$	−3.02801			−0.205555
$218$	−7.13234			−0.483063
$219$	0.116870	−	0.592457i	0.00789737	−	0.0400345i
$220$			1.47580i			0.0994987i
$221$		0			0
$222$	8.60793	+	12.8386i	0.577726	+	0.861667i
$223$	−5.48040	−	5.48040i	−0.366995	−	0.366995i	0.499385	−	0.866380i	$-0.333559\pi$
$223$	−5.48040	−	5.48040i	−0.366995	−	0.366995i	−0.866380	+	0.499385i	$0.833559\pi$
$224$		−	13.4218i		−	0.896784i
$225$	11.7102	+	4.80707i	0.780681	+	0.320471i
$226$	10.4738	+	10.4738i	0.696708	+	0.696708i
$227$	−13.2582	+	13.2582i	−0.879980	+	0.879980i	−0.993532	−	0.113552i	$-0.963777\pi$
$227$	−13.2582	+	13.2582i	−0.879980	+	0.879980i	0.113552	+	0.993532i	$0.463777\pi$
$228$	9.55729	−	48.4492i	0.632947	−	3.20863i
$229$	8.11488	−	8.11488i	0.536246	−	0.536246i	−0.386178	−	0.922424i	$-0.626205\pi$
$229$	8.11488	−	8.11488i	0.536246	−	0.536246i	0.922424	+	0.386178i	$0.126205\pi$
$230$			12.3551i			0.814672i
$231$	−0.866522	+	0.580981i	−0.0570129	+	0.0382258i
$232$	−40.6911	+	40.6911i	−2.67150	+	2.67150i
$233$	−11.2799			−0.738973			−0.369486	−	0.929236i	$-0.620466\pi$
$233$	−11.2799			−0.738973			−0.369486	+	0.929236i	$0.620466\pi$
$234$		0			0
$235$	−6.66584			−0.434832
$236$	−33.9889	+	33.9889i	−2.21249	+	2.21249i
$237$	−5.29672	+	3.55132i	−0.344059	+	0.230683i
$238$		−	11.4045i		−	0.739241i
$239$	1.32193	−	1.32193i	0.0855084	−	0.0855084i	−0.663059	−	0.748567i	$-0.730742\pi$
$239$	1.32193	−	1.32193i	0.0855084	−	0.0855084i	0.748567	+	0.663059i	$0.230742\pi$
$240$	2.49319	−	12.6388i	0.160934	−	0.815832i
$241$	16.4480	−	16.4480i	1.05951	−	1.05951i	0.0613973	−	0.998113i	$-0.480444\pi$
$241$	16.4480	−	16.4480i	1.05951	−	1.05951i	0.998113	−	0.0613973i	$-0.0195557\pi$
$242$	−19.8436	−	19.8436i	−1.27560	−	1.27560i
$243$	−15.3126	−	2.91982i	−0.982302	−	0.187306i
$244$		−	22.7498i		−	1.45640i
$245$	−2.60680	−	2.60680i	−0.166542	−	0.166542i
$246$	17.2406	+	25.7140i	1.09922	+	1.63946i
$247$		0			0
$248$		−	12.3800i		−	0.786133i
$249$	−4.01530	+	20.3550i	−0.254459	+	1.28994i
$250$	−21.0250			−1.32974
$251$	−10.7936			−0.681288			−0.340644	−	0.940192i	$-0.610645\pi$
$251$	−10.7936			−0.681288			−0.340644	+	0.940192i	$0.610645\pi$
$252$	21.7029	−	9.07038i	1.36715	−	0.571380i
$253$	1.37234	+	1.37234i	0.0862785	+	0.0862785i
$254$	−24.8670	−	24.8670i	−1.56030	−	1.56030i
$255$	0.778159	−	3.94476i	0.0487302	−	0.247030i
$256$	−23.6407			−1.47754
$257$	−4.25601			−0.265483			−0.132741	−	0.991151i	$-0.542378\pi$
$257$	−4.25601			−0.265483			−0.132741	+	0.991151i	$0.542378\pi$
$258$	−4.18004	−	0.824572i	−0.260238	−	0.0513356i
$259$		−	5.81304i		−	0.361205i
$260$		0			0
$261$	−23.2317	−	9.53667i	−1.43801	−	0.590305i
$262$	11.6071	+	11.6071i	0.717087	+	0.717087i
$263$			25.3466i			1.56294i	0.623943	+	0.781470i	$0.285530\pi$
$263$			25.3466i			1.56294i	−0.623943	+	0.781470i	$0.714470\pi$
$264$	−2.37534	−	3.54277i	−0.146192	−	0.218043i
$265$	−6.05823	−	6.05823i	−0.372154	−	0.372154i
$266$	−18.7644	+	18.7644i	−1.15052	+	1.15052i
$267$	−11.6420	−	2.29654i	−0.712476	−	0.140546i
$268$	−41.5167	+	41.5167i	−2.53604	+	2.53604i
$269$			22.6651i			1.38192i	0.722895	+	0.690958i	$0.242811\pi$
$269$			22.6651i			1.38192i	−0.722895	+	0.690958i	$0.757189\pi$
$270$	11.6110	−	2.36705i	0.706621	−	0.144054i
$271$	−15.0720	+	15.0720i	−0.915557	+	0.915557i	−0.996702	−	0.0811452i	$-0.974142\pi$
$271$	−15.0720	+	15.0720i	−0.915557	+	0.915557i	0.0811452	+	0.996702i	$0.474142\pi$
$272$	22.1212			1.34129
$273$		0			0
$274$	−5.27335			−0.318575
$275$	−1.06882	+	1.06882i	−0.0644524	+	0.0644524i
$276$	−24.3684	−	36.3450i	−1.46681	−	2.18771i
$277$			10.6818i			0.641809i	0.947112	+	0.320905i	$0.103987\pi$
$277$			10.6818i			0.641809i	−0.947112	+	0.320905i	$0.896013\pi$
$278$	−9.33349	+	9.33349i	−0.559786	+	0.559786i
$279$	4.98480	−	2.08332i	0.298432	−	0.124725i
$280$	−7.22078	+	7.22078i	−0.431524	+	0.431524i
$281$	−9.84122	−	9.84122i	−0.587078	−	0.587078i	0.349761	−	0.936839i	$-0.386263\pi$
$281$	−9.84122	−	9.84122i	−0.587078	−	0.587078i	−0.936839	+	0.349761i	$0.886263\pi$
$282$	28.0190	−	18.7860i	1.66851	−	1.11869i
$283$		−	16.2964i		−	0.968722i	−0.874868	−	0.484361i	$-0.839052\pi$
$283$		−	16.2964i		−	0.968722i	0.874868	−	0.484361i	$-0.160948\pi$
$284$	−10.6092	−	10.6092i	−0.629538	−	0.629538i
$285$	−7.77087	+	5.21018i	−0.460307	+	0.308624i
$286$		0			0
$287$		−	11.6428i		−	0.687251i
$288$	9.23444	+	22.0954i	0.544145	+	1.30198i
$289$	−10.0957			−0.593862
$290$	19.0900			1.12100
$291$	8.99024	+	1.77345i	0.527017	+	0.103962i
$292$	−1.14961	−	1.14961i	−0.0672759	−	0.0672759i
$293$	11.6319	+	11.6319i	0.679542	+	0.679542i	0.959897	−	0.280355i	$-0.0904520\pi$
$293$	11.6319	+	11.6319i	0.679542	+	0.679542i	−0.280355	+	0.959897i	$0.590452\pi$
$294$	18.3040	+	3.61072i	1.06751	+	0.210581i
$295$	9.10668			0.530211
$296$	23.7666			1.38141
$297$	1.02677	−	1.55261i	0.0595791	−	0.0900915i
$298$		−	27.3633i		−	1.58512i
$299$		0			0
$300$	28.3065	−	18.9788i	1.63428	−	1.09574i
$301$	1.13299	+	1.13299i	0.0653047	+	0.0653047i
$302$		−	24.1984i		−	1.39246i
$303$	−12.2025	+	8.18147i	−0.701015	+	0.470013i
$304$	−36.3972	−	36.3972i	−2.08752	−	2.08752i
$305$	−3.04768	+	3.04768i	−0.174510	+	0.174510i
$306$	7.84645	+	18.7743i	0.448552	+	1.07326i
$307$	5.70702	−	5.70702i	0.325717	−	0.325717i	−0.525238	−	0.850955i	$-0.676024\pi$
$307$	5.70702	−	5.70702i	0.325717	−	0.325717i	0.850955	+	0.525238i	$0.176024\pi$
$308$			2.80875i			0.160044i
$309$	0.535190	+	0.798225i	0.0304459	+	0.0454094i
$310$	−2.90401	+	2.90401i	−0.164937	+	0.164937i
$311$	25.3416			1.43699			0.718496	−	0.695531i	$-0.244831\pi$
$311$	25.3416			1.43699			0.718496	+	0.695531i	$0.244831\pi$
$312$		0			0
$313$	−3.49487			−0.197542			−0.0987709	−	0.995110i	$-0.531491\pi$
$313$	−3.49487			−0.197542			−0.0987709	+	0.995110i	$0.531491\pi$
$314$	40.1484	−	40.1484i	2.26571	−	2.26571i
$315$	−4.12255	−	1.69232i	−0.232280	−	0.0953513i
$316$			17.1688i			0.965823i
$317$	5.25697	−	5.25697i	0.295261	−	0.295261i	−0.543893	−	0.839154i	$-0.683050\pi$
$317$	5.25697	−	5.25697i	0.295261	−	0.295261i	0.839154	+	0.543893i	$0.183050\pi$
$318$	42.5386	+	8.39134i	2.38545	+	0.470563i
$319$	2.12042	−	2.12042i	0.118721	−	0.118721i
$320$	−2.35376	−	2.35376i	−0.131579	−	0.131579i
$321$	3.20195	+	4.77565i	0.178716	+	0.266551i
$322$			23.5143i			1.31040i
$323$	−11.3601	−	11.3601i	−0.632092	−	0.632092i
$324$	−29.4873	+	29.8638i	−1.63818	+	1.65910i
$325$		0			0
$326$			53.0876i			2.94025i
$327$	−4.69530	−	0.926214i	−0.259651	−	0.0512197i
$328$	47.6015			2.62835
$329$	−12.6864			−0.699426
$330$	−0.273847	+	1.38822i	−0.0150748	+	0.0764192i
$331$	−12.7151	−	12.7151i	−0.698884	−	0.698884i	0.265286	−	0.964170i	$-0.414534\pi$
$331$	−12.7151	−	12.7151i	−0.698884	−	0.698884i	−0.964170	+	0.265286i	$0.914534\pi$
$332$	39.4970	+	39.4970i	2.16768	+	2.16768i
$333$	3.99946	+	9.56959i	0.219169	+	0.524410i
$334$	−25.8774			−1.41595
$335$	11.1236			0.607748
$336$	4.74504	−	24.0542i	0.258863	−	1.31227i
$337$		−	16.3852i		−	0.892558i	−0.894894	−	0.446279i	$-0.852749\pi$
$337$		−	16.3852i		−	0.892558i	0.894894	−	0.446279i	$-0.147251\pi$
$338$		0			0
$339$	5.53488	+	8.25516i	0.300614	+	0.448359i
$340$	−7.65447	−	7.65447i	−0.415122	−	0.415122i
$341$			0.645126i			0.0349355i
$342$	17.9802	−	43.8006i	0.972260	−	2.36847i
$343$	−13.2838	−	13.2838i	−0.717259	−	0.717259i
$344$	−4.63225	+	4.63225i	−0.249754	+	0.249754i
$345$	−1.60445	+	8.13350i	−0.0863805	+	0.437893i
$346$	21.4731	−	21.4731i	1.15440	−	1.15440i
$347$		−	24.0720i		−	1.29225i	−0.763231	−	0.646126i	$-0.776388\pi$
$347$		−	24.0720i		−	1.29225i	0.763231	−	0.646126i	$-0.223612\pi$
$348$	−56.1569	+	37.6518i	−3.01032	+	2.01835i
$349$	12.2384	−	12.2384i	0.655108	−	0.655108i	−0.299111	−	0.954218i	$-0.596690\pi$
$349$	12.2384	−	12.2384i	0.655108	−	0.655108i	0.954218	+	0.299111i	$0.0966899\pi$
$350$	−18.3136			−0.978903
$351$		0			0
$352$	−2.85956			−0.152415
$353$	−14.9859	+	14.9859i	−0.797619	+	0.797619i	−0.982720	−	0.185101i	$-0.940739\pi$
$353$	−14.9859	+	14.9859i	−0.797619	+	0.797619i	0.185101	+	0.982720i	$0.440739\pi$
$354$	−38.2787	+	25.6649i	−2.03449	+	1.36408i
$355$			2.84253i			0.150866i
$356$	−22.5902	+	22.5902i	−1.19728	+	1.19728i
$357$	1.48099	−	7.50768i	0.0783826	−	0.397348i
$358$	−21.5598	+	21.5598i	−1.13947	+	1.13947i
$359$	−18.7493	−	18.7493i	−0.989548	−	0.989548i	0.0103977	−	0.999946i	$-0.496690\pi$
$359$	−18.7493	−	18.7493i	−0.989548	−	0.989548i	−0.999946	+	0.0103977i	$0.996690\pi$
$360$	6.91904	−	16.8551i	0.364665	−	0.888340i
$361$			18.3827i			0.967511i
$362$	36.6876	+	36.6876i	1.92826	+	1.92826i
$363$	−10.4864	−	15.6402i	−0.550392	−	0.820898i
$364$		0			0
$365$			0.308016i			0.0161223i
$366$	4.22139	−	21.3997i	0.220656	−	1.11858i
$367$	20.3307			1.06125			0.530626	−	0.847606i	$-0.321957\pi$
$367$	20.3307			1.06125			0.530626	+	0.847606i	$0.321957\pi$
$368$	−45.6105			−2.37761
$369$	8.01042	+	19.1667i	0.417006	+	0.997777i
$370$	−5.57498	−	5.57498i	−0.289829	−	0.289829i
$371$	−11.5300	−	11.5300i	−0.598609	−	0.598609i
$372$	2.81504	−	14.2704i	0.145953	−	0.739885i
$373$	32.0111			1.65747			0.828735	−	0.559641i	$-0.189061\pi$
$373$	32.0111			1.65747			0.828735	+	0.559641i	$0.189061\pi$
$374$	−2.42975			−0.125639
$375$	−13.8410	−	2.73033i	−0.714745	−	0.140993i
$376$		−	51.8685i		−	2.67492i
$377$		0			0
$378$	22.0980	−	4.50498i	1.13660	−	0.231711i
$379$	−12.3240	−	12.3240i	−0.633044	−	0.633044i	0.315787	−	0.948830i	$-0.397732\pi$
$379$	−12.3240	−	12.3240i	−0.633044	−	0.633044i	−0.948830	+	0.315787i	$0.897732\pi$
$380$			25.1886i			1.29215i
$381$	−13.1410	−	19.5995i	−0.673232	−	1.00411i
$382$	30.9220	+	30.9220i	1.58211	+	1.58211i
$383$	15.3454	−	15.3454i	0.784113	−	0.784113i	−0.196409	−	0.980522i	$-0.562928\pi$
$383$	15.3454	−	15.3454i	0.784113	−	0.784113i	0.980522	+	0.196409i	$0.0629280\pi$
$384$	−10.6021	−	2.09142i	−0.541037	−	0.106727i
$385$	0.376276	−	0.376276i	0.0191768	−	0.0191768i
$386$		−	43.1880i		−	2.19821i
$387$	−2.64469	−	1.08565i	−0.134437	−	0.0551866i
$388$	17.4448	−	17.4448i	0.885625	−	0.885625i
$389$	−3.24468			−0.164512			−0.0822559	−	0.996611i	$-0.526212\pi$
$389$	−3.24468			−0.164512			−0.0822559	+	0.996611i	$0.526212\pi$
$390$		0			0
$391$	−14.2357			−0.719931
$392$	20.2841	−	20.2841i	1.02450	−	1.02450i
$393$	6.13375	+	9.14836i	0.309407	+	0.461474i
$394$		−	37.7544i		−	1.90204i
$395$	2.30003	−	2.30003i	0.115727	−	0.115727i
$396$	−1.93247	−	4.62385i	−0.0971102	−	0.232357i
$397$	22.4994	−	22.4994i	1.12921	−	1.12921i	0.138908	−	0.990305i	$-0.455641\pi$
$397$	22.4994	−	22.4994i	1.12921	−	1.12921i	0.990305	−	0.138908i	$-0.0443593\pi$
$398$	0.610176	+	0.610176i	0.0305854	+	0.0305854i
$399$	−14.7895	+	9.91602i	−0.740403	+	0.496422i
$400$		−	35.5228i		−	1.77614i
$401$	26.7333	+	26.7333i	1.33500	+	1.33500i	0.900834	+	0.434165i	$0.142956\pi$
$401$	26.7333	+	26.7333i	1.33500	+	1.33500i	0.434165	+	0.900834i	$0.357044\pi$
$402$	−46.7567	+	31.3492i	−2.33201	+	1.56355i
$403$		0			0
$404$			39.5533i			1.96785i
$405$	7.95101	−	0.0504438i	0.395089	−	0.00250657i
$406$	36.3321			1.80313
$407$	−1.23848			−0.0613893
$408$	30.6951	+	6.05505i	1.51964	+	0.299770i
$409$	2.14554	+	2.14554i	0.106090	+	0.106090i	0.758159	−	0.652069i	$-0.226099\pi$
$409$	2.14554	+	2.14554i	0.106090	+	0.106090i	−0.652069	+	0.758159i	$0.726099\pi$
$410$	−11.1660	−	11.1660i	−0.551448	−	0.551448i
$411$	−3.47151	−	0.684803i	−0.171237	−	0.0337789i
$412$	2.58738			0.127471
$413$	17.3318			0.852844
$414$	−16.1782	−	38.7098i	−0.795115	−	1.90249i
$415$		−	10.5825i		−	0.519474i
$416$		0			0
$417$	−7.35640	+	4.93228i	−0.360244	+	0.241535i
$418$	3.99780	+	3.99780i	0.195539	+	0.195539i
$419$		−	37.1497i		−	1.81488i	−0.420178	−	0.907442i	$-0.638033\pi$
$419$		−	37.1497i		−	1.81488i	0.420178	−	0.907442i	$-0.361967\pi$
$420$	−9.96525	+	6.68145i	−0.486254	+	0.326021i
$421$	−18.7201	−	18.7201i	−0.912361	−	0.912361i	0.0840970	−	0.996458i	$-0.473199\pi$
$421$	−18.7201	−	18.7201i	−0.912361	−	0.912361i	−0.996458	+	0.0840970i	$0.973199\pi$
$422$	−4.90831	+	4.90831i	−0.238933	+	0.238933i
$423$	20.8848	−	8.72848i	1.01545	−	0.424393i
$424$	47.1405	−	47.1405i	2.28935	−	2.28935i
$425$		−	11.0872i		−	0.537808i
$426$	−8.01096	−	11.9482i	−0.388132	−	0.578892i
$427$	−5.80036	+	5.80036i	−0.280699	+	0.280699i
$428$	15.4798			0.748246
$429$		0			0
$430$	2.17319			0.104801
$431$	5.13505	−	5.13505i	0.247347	−	0.247347i	−0.572534	−	0.819881i	$-0.694040\pi$
$431$	5.13505	−	5.13505i	0.247347	−	0.247347i	0.819881	+	0.572534i	$0.194040\pi$
$432$	8.73829	+	42.8634i	0.420421	+	2.06227i
$433$			6.80226i			0.326896i	0.986552	+	0.163448i	$0.0522615\pi$
$433$			6.80226i			0.326896i	−0.986552	+	0.163448i	$0.947738\pi$
$434$	−5.52692	+	5.52692i	−0.265301	+	0.265301i
$435$	12.5671	+	2.47904i	0.602548	+	0.118861i
$436$	−9.11082	+	9.11082i	−0.436329	+	0.436329i
$437$	23.4228	+	23.4228i	1.12046	+	1.12046i
$438$	−0.868069	−	1.29471i	−0.0414780	−	0.0618635i
$439$		−	16.2128i		−	0.773794i	−0.922123	−	0.386897i	$-0.873547\pi$
$439$		−	16.2128i		−	0.773794i	0.922123	−	0.386897i	$-0.126453\pi$
$440$	1.53841	+	1.53841i	0.0733406	+	0.0733406i
$441$	11.5808	+	4.75395i	0.551467	+	0.226378i
$442$		0			0
$443$		−	6.09878i		−	0.289762i	−0.989449	−	0.144881i	$-0.953720\pi$
$443$		−	6.09878i		−	0.289762i	0.989449	−	0.144881i	$-0.0462799\pi$
$444$	27.3956	+	5.40417i	1.30014	+	0.256471i
$445$	6.05262			0.286922
$446$	−20.0063			−0.947327
$447$	3.55343	−	18.0136i	0.168072	−	0.852013i
$448$	−4.47969	−	4.47969i	−0.211645	−	0.211645i
$449$	18.9586	+	18.9586i	0.894714	+	0.894714i	0.994962	−	0.100249i	$-0.0319638\pi$
$449$	18.9586	+	18.9586i	0.894714	+	0.894714i	−0.100249	+	0.994962i	$0.531964\pi$
$450$	30.1484	−	12.6001i	1.42121	−	0.593972i
$451$	−2.48052			−0.116803
$452$	26.7584			1.25861
$453$	3.14243	−	15.9301i	0.147644	−	0.748460i
$454$			48.3995i			2.27150i
$455$		0			0
$456$	−40.5417	−	60.4670i	−1.89854	−	2.83163i
$457$	13.5475	+	13.5475i	0.633726	+	0.633726i	0.949000	−	0.315275i	$-0.102097\pi$
$457$	13.5475	+	13.5475i	0.633726	+	0.633726i	−0.315275	+	0.949000i	$0.602097\pi$
$458$		−	29.6236i		−	1.38422i
$459$	2.72735	+	13.3783i	0.127302	+	0.624445i
$460$	15.7823	+	15.7823i	0.735856	+	0.735856i
$461$	−3.16238	+	3.16238i	−0.147287	+	0.147287i	−0.776905	−	0.629618i	$-0.783211\pi$
$461$	−3.16238	+	3.16238i	−0.147287	+	0.147287i	0.629618	+	0.776905i	$0.283211\pi$
$462$	−0.521186	+	2.64207i	−0.0242478	+	0.122920i
$463$	−25.0898	+	25.0898i	−1.16602	+	1.16602i	−0.182885	+	0.983134i	$0.558544\pi$
$463$	−25.0898	+	25.0898i	−1.16602	+	1.16602i	−0.983134	+	0.182885i	$0.941456\pi$
$464$			70.4732i			3.27163i
$465$	−2.28886	+	1.53462i	−0.106143	+	0.0711664i
$466$	−20.5888	+	20.5888i	−0.953759	+	0.953759i
$467$	10.0568			0.465374			0.232687	−	0.972552i	$-0.425248\pi$
$467$	10.0568			0.465374			0.232687	+	0.972552i	$0.425248\pi$
$468$		0			0
$469$	21.1705			0.977562
$470$	−12.1669	+	12.1669i	−0.561217	+	0.561217i
$471$	31.6438	−	21.2164i	1.45807	−	0.977601i
$472$			70.8613i			3.26165i
$473$	0.241387	−	0.241387i	0.0110990	−	0.0110990i
$474$	−3.18581	+	16.1500i	−0.146329	+	0.741793i
$475$	−18.2423	+	18.2423i	−0.837016	+	0.837016i
$476$	−14.5680	−	14.5680i	−0.667723	−	0.667723i
$477$	26.9139	+	11.0482i	1.23230	+	0.505863i
$478$		−	4.82573i		−	0.220724i
$479$	4.18209	+	4.18209i	0.191084	+	0.191084i	0.796165	−	0.605080i	$-0.206859\pi$
$479$	4.18209	+	4.18209i	0.191084	+	0.191084i	−0.605080	+	0.796165i	$0.706859\pi$
$480$	−6.80230	−	10.1455i	−0.310481	−	0.463076i
$481$		0			0
$482$		−	60.0439i		−	2.73493i
$483$	−3.05359	+	15.4797i	−0.138943	+	0.704350i
$484$	−50.6963			−2.30438
$485$	−4.67400			−0.212235
$486$	−33.2789	+	22.6200i	−1.50956	+	1.02606i
$487$	6.64419	+	6.64419i	0.301077	+	0.301077i	0.841435	−	0.540358i	$-0.181711\pi$
$487$	6.64419	+	6.64419i	0.301077	+	0.301077i	−0.540358	+	0.841435i	$0.681711\pi$
$488$	−23.7148	−	23.7148i	−1.07352	−	1.07352i
$489$	−6.89401	+	34.9481i	−0.311758	+	1.58041i
$490$	−9.51618			−0.429897
$491$	24.3543			1.09910			0.549548	−	0.835462i	$-0.314800\pi$
$491$	24.3543			1.09910			0.549548	+	0.835462i	$0.314800\pi$
$492$	54.8699	+	10.8239i	2.47373	+	0.487978i
$493$			21.9957i			0.990637i
$494$		0			0
$495$	−0.360552	+	0.878321i	−0.0162056	+	0.0394776i
$496$	−10.7205	−	10.7205i	−0.481366	−	0.481366i
$497$			5.40990i			0.242667i
$498$	29.8241	+	44.4821i	1.33645	+	1.99329i
$499$	−6.97195	−	6.97195i	−0.312107	−	0.312107i	0.533618	−	0.845725i	$-0.320832\pi$
$499$	−6.97195	−	6.97195i	−0.312107	−	0.312107i	−0.845725	+	0.533618i	$0.820832\pi$
$500$	−26.8572	+	26.8572i	−1.20109	+	1.20109i
$501$	−17.0354	−	3.36046i	−0.761084	−	0.150134i
$502$	−19.7012	+	19.7012i	−0.879307	+	0.879307i
$503$		−	13.1556i		−	0.586579i	−0.956024	−	0.293289i	$-0.905250\pi$
$503$		−	13.1556i		−	0.586579i	0.956024	−	0.293289i	$-0.0947499\pi$
$504$	13.1683	−	32.0786i	0.586564	−	1.42889i
$505$	5.29878	−	5.29878i	0.235793	−	0.235793i
$506$	5.00977			0.222712
$507$		0			0
$508$	−63.5300			−2.81869
$509$	−14.0732	+	14.0732i	−0.623784	+	0.623784i	−0.946497	−	0.322713i	$-0.895405\pi$
$509$	−14.0732	+	14.0732i	−0.623784	+	0.623784i	0.322713	+	0.946497i	$0.395405\pi$
$510$	−5.77987	−	8.62056i	−0.255937	−	0.381725i
$511$			0.586218i			0.0259327i
$512$	−34.3270	+	34.3270i	−1.51705	+	1.51705i
$513$	17.5246	−	26.4995i	0.773729	−	1.16998i
$514$	−7.76834	+	7.76834i	−0.342647	+	0.342647i
$515$	−0.346619	−	0.346619i	−0.0152739	−	0.0152739i
$516$	−6.39287	+	4.28626i	−0.281430	+	0.188692i
$517$			2.70288i			0.118872i
$518$	−10.6103	−	10.6103i	−0.466191	−	0.466191i
$519$	16.9245	−	11.3474i	0.742902	−	0.498098i
$520$		0			0
$521$		−	12.9958i		−	0.569355i	−0.958623	−	0.284678i	$-0.908113\pi$
$521$		−	12.9958i		−	0.569355i	0.958623	−	0.284678i	$-0.0918865\pi$
$522$	−59.8109	+	24.9970i	−2.61785	+	1.09409i
$523$	6.11952			0.267588			0.133794	−	0.991009i	$-0.457284\pi$
$523$	6.11952			0.267588			0.133794	+	0.991009i	$0.457284\pi$
$524$	29.6536			1.29542
$525$	−12.0560	−	2.37822i	−0.526169	−	0.103794i
$526$	46.2642	+	46.2642i	2.01722	+	2.01722i
$527$	−3.34604	−	3.34604i	−0.145756	−	0.145756i
$528$	−5.12482	−	1.01094i	−0.223029	−	0.0439956i
$529$	6.35187			0.276168
$530$	−22.1157			−0.960645
$531$	−28.5322	+	11.9246i	−1.23819	+	0.517483i
$532$			47.9390i			2.07842i
$533$		0			0
$534$	−25.4414	+	17.0578i	−1.10096	+	0.738164i
$535$	−2.07377	−	2.07377i	−0.0896567	−	0.0896567i
$536$			86.5555i			3.73863i
$537$	−16.9928	+	11.3932i	−0.733293	+	0.491655i
$538$	41.3698	+	41.3698i	1.78358	+	1.78358i
$539$	−1.05701	+	1.05701i	−0.0455287	+	0.0455287i
$540$	11.8081	−	17.8554i	0.508141	−	0.768376i
$541$	9.48746	−	9.48746i	0.407898	−	0.407898i	−0.473107	−	0.881005i	$-0.656868\pi$
$541$	9.48746	−	9.48746i	0.407898	−	0.407898i	0.881005	+	0.473107i	$0.156868\pi$
$542$			55.0206i			2.36334i
$543$	19.3876	+	28.9161i	0.832000	+	1.24091i
$544$	14.8315	−	14.8315i	0.635895	−	0.635895i
$545$	2.44107			0.104564
$546$		0			0
$547$	8.20259			0.350717			0.175359	−	0.984505i	$-0.443892\pi$
$547$	8.20259			0.350717			0.175359	+	0.984505i	$0.443892\pi$
$548$	−6.73616	+	6.73616i	−0.287754	+	0.287754i
$549$	5.55797	−	13.5395i	0.237209	−	0.577850i
$550$			3.90176i			0.166372i
$551$	36.1907	−	36.1907i	1.54178	−	1.54178i
$552$	−63.2887	−	12.4846i	−2.69375	−	0.531379i
$553$	4.37743	−	4.37743i	0.186147	−	0.186147i
$554$	19.4971	+	19.4971i	0.828354	+	0.828354i
$555$	−2.94610	−	4.39404i	−0.125055	−	0.186517i
$556$			23.8451i			1.01126i
$557$	15.5976	+	15.5976i	0.660892	+	0.660892i	0.955590	−	0.294699i	$-0.0952193\pi$
$557$	15.5976	+	15.5976i	0.660892	+	0.660892i	−0.294699	+	0.955590i	$0.595219\pi$
$558$	5.29596	−	12.9012i	0.224196	−	0.546150i
$559$		0			0
$560$			12.5057i			0.528463i
$561$	−1.59953	−	0.315530i	−0.0675322	−	0.0133217i
$562$	−35.9256			−1.51543
$563$	39.4461			1.66245			0.831227	−	0.555934i	$-0.187639\pi$
$563$	39.4461			1.66245			0.831227	+	0.555934i	$0.187639\pi$
$564$	11.7941	−	59.7885i	0.496622	−	2.51755i
$565$	−3.58470	−	3.58470i	−0.150810	−	0.150810i
$566$	−29.7453	−	29.7453i	−1.25029	−	1.25029i
$567$	15.1324	−	0.0960047i	0.635500	−	0.00403182i
$568$	−22.1184			−0.928067
$569$	−15.3498			−0.643496			−0.321748	−	0.946825i	$-0.604270\pi$
$569$	−15.3498			−0.643496			−0.321748	+	0.946825i	$0.604270\pi$
$570$	−4.67394	+	23.6938i	−0.195770	+	0.992425i
$571$			4.70947i			0.197085i	0.995133	+	0.0985425i	$0.0314181\pi$
$571$			4.70947i			0.197085i	−0.995133	+	0.0985425i	$0.968582\pi$
$572$		0			0
$573$	16.3407	+	24.3718i	0.682643	+	1.01815i
$574$	−21.2511	−	21.2511i	−0.887004	−	0.887004i
$575$			22.8601i			0.953332i
$576$	10.4567	+	4.29249i	0.435695	+	0.178854i
$577$	25.1056	+	25.1056i	1.04516	+	1.04516i	0.998931	+	0.0462290i	$0.0147204\pi$
$577$	25.1056	+	25.1056i	1.04516	+	1.04516i	0.0462290	+	0.998931i	$0.485280\pi$
$578$	−18.4272	+	18.4272i	−0.766471	+	0.766471i
$579$	5.60843	−	28.4311i	0.233078	−	1.18156i
$580$	24.3854	−	24.3854i	1.01255	−	1.01255i
$581$		−	20.1406i		−	0.835573i
$582$	19.6466	−	13.1725i	0.814376	−	0.546019i
$583$	−2.45650	+	2.45650i	−0.101738	+	0.101738i
$584$	−2.39675			−0.0991783
$585$		0			0
$586$	42.4625			1.75411
$587$	12.2920	−	12.2920i	0.507347	−	0.507347i	−0.406364	−	0.913711i	$-0.633204\pi$
$587$	12.2920	−	12.2920i	0.507347	−	0.507347i	0.913711	+	0.406364i	$0.133204\pi$
$588$	27.9937	−	18.7691i	1.15444	−	0.774024i
$589$			11.0108i			0.453693i
$590$	16.6221	−	16.6221i	0.684320	−	0.684320i
$591$	4.90283	−	24.8541i	0.201675	−	1.02236i
$592$	20.5808	−	20.5808i	0.845865	−	0.845865i
$593$	3.78428	+	3.78428i	0.155402	+	0.155402i	0.780526	−	0.625124i	$-0.214952\pi$
$593$	3.78428	+	3.78428i	0.155402	+	0.155402i	−0.625124	+	0.780526i	$0.714952\pi$
$594$	−0.959797	−	4.70804i	−0.0393809	−	0.193173i
$595$			3.90322i			0.160016i
$596$	−34.9538	−	34.9538i	−1.43176	−	1.43176i
$597$	0.322448	+	0.480924i	0.0131969	+	0.0196829i
$598$		0			0
$599$			6.35465i			0.259644i	0.991537	+	0.129822i	$0.0414406\pi$
$599$			6.35465i			0.259644i	−0.991537	+	0.129822i	$0.958559\pi$
$600$	9.72337	−	49.2911i	0.396955	−	2.01230i
$601$	24.9523			1.01782			0.508912	−	0.860819i	$-0.330048\pi$
$601$	24.9523			1.01782			0.508912	+	0.860819i	$0.330048\pi$
$602$	4.13602			0.168572
$603$	−34.8514	+	14.5656i	−1.41926	+	0.593158i
$604$	−30.9109	−	30.9109i	−1.25775	−	1.25775i
$605$	6.79156	+	6.79156i	0.276116	+	0.276116i
$606$	−7.33942	+	37.2061i	−0.298143	+	1.51139i
$607$	4.23514			0.171899			0.0859494	−	0.996300i	$-0.472608\pi$
$607$	4.23514			0.171899			0.0859494	+	0.996300i	$0.472608\pi$
$608$	−48.8061			−1.97935
$609$	23.9178	+	4.71812i	0.969198	+	0.191188i
$610$			11.1256i			0.450464i
$611$		0			0
$612$	34.0053	+	13.9592i	1.37458	+	0.564268i
$613$	−25.9232	−	25.9232i	−1.04703	−	1.04703i	−0.998838	−	0.0481897i	$-0.984655\pi$
$613$	−25.9232	−	25.9232i	−1.04703	−	1.04703i	−0.0481897	−	0.998838i	$-0.515345\pi$
$614$		−	20.8336i		−	0.840776i
$615$	−5.90066	−	8.80071i	−0.237937	−	0.354879i
$616$	2.92790	+	2.92790i	0.117968	+	0.117968i
$617$	21.5941	−	21.5941i	0.869345	−	0.869345i	−0.123055	−	0.992400i	$-0.539269\pi$
$617$	21.5941	−	21.5941i	0.869345	−	0.869345i	0.992400	+	0.123055i	$0.0392692\pi$
$618$	2.43383	+	0.480107i	0.0979030	+	0.0193127i
$619$	−11.8576	+	11.8576i	−0.476599	+	0.476599i	−0.904042	−	0.427443i	$-0.859414\pi$
$619$	−11.8576	+	11.8576i	−0.476599	+	0.476599i	0.427443	+	0.904042i	$0.359414\pi$
$620$			7.41914i			0.297960i
$621$	−5.62338	−	27.5840i	−0.225658	−	1.10691i
$622$	46.2551	−	46.2551i	1.85466	−	1.85466i
$623$	11.5194			0.461513
$624$		0			0
$625$	−13.9016			−0.556063
$626$	−6.37905	+	6.37905i	−0.254958	+	0.254958i
$627$	2.11263	+	3.15095i	0.0843705	+	0.125837i
$628$		−	102.571i		−	4.09302i
$629$	6.42356	−	6.42356i	0.256124	−	0.256124i
$630$	−10.6137	+	4.43582i	−0.422858	+	0.176727i
$631$	−19.6506	+	19.6506i	−0.782280	+	0.782280i	−0.980215	−	0.197935i	$-0.936576\pi$
$631$	−19.6506	+	19.6506i	−0.782280	+	0.782280i	0.197935	+	0.980215i	$0.436576\pi$
$632$	17.8971	+	17.8971i	0.711909	+	0.711909i
$633$	−3.86859	+	2.59379i	−0.153763	+	0.103094i
$634$		−	19.1907i		−	0.762160i
$635$	8.51083	+	8.51083i	0.337742	+	0.337742i
$636$	65.0577	−	43.6195i	2.57970	−	1.72963i
$637$		0			0
$638$		−	7.74064i		−	0.306455i
$639$	−3.72210	−	8.90593i	−0.147244	−	0.352313i
$640$	5.51201			0.217881
$641$	8.57527			0.338703			0.169351	−	0.985556i	$-0.445833\pi$
$641$	8.57527			0.338703			0.169351	+	0.985556i	$0.445833\pi$
$642$	14.5612	+	2.87240i	0.574685	+	0.113365i
$643$	1.59295	+	1.59295i	0.0628196	+	0.0628196i	0.737819	−	0.674999i	$-0.235856\pi$
$643$	1.59295	+	1.59295i	0.0628196	+	0.0628196i	−0.674999	+	0.737819i	$0.735856\pi$
$644$	30.0370	+	30.0370i	1.18362	+	1.18362i
$645$	1.43063	+	0.282213i	0.0563312	+	0.0111121i
$646$	−41.4703			−1.63163
$647$	−24.4338			−0.960592			−0.480296	−	0.877106i	$-0.659471\pi$
$647$	−24.4338			−0.960592			−0.480296	+	0.877106i	$0.659471\pi$
$648$	0.392515	+	61.8687i	0.0154195	+	2.43043i
$649$		−	3.69259i		−	0.144947i
$650$		0			0
$651$	−4.35616	+	2.92070i	−0.170731	+	0.114471i
$652$	67.8139	+	67.8139i	2.65580	+	2.65580i
$653$		−	12.7901i		−	0.500515i	−0.968179	−	0.250257i	$-0.919485\pi$
$653$		−	12.7901i		−	0.500515i	0.968179	−	0.250257i	$-0.0805152\pi$
$654$	−10.2607	+	6.87956i	−0.401226	+	0.269012i
$655$	−3.97256	−	3.97256i	−0.155221	−	0.155221i
$656$	41.2207	−	41.2207i	1.60940	−	1.60940i
$657$	−0.403327	−	0.965048i	−0.0157353	−	0.0376501i
$658$	−23.1561	+	23.1561i	−0.902718	+	0.902718i
$659$		−	30.1642i		−	1.17503i	−0.809213	−	0.587515i	$-0.800106\pi$
$659$		−	30.1642i		−	1.17503i	0.809213	−	0.587515i	$-0.199894\pi$
$660$	1.42350	+	2.12312i	0.0554097	+	0.0826424i
$661$	−17.7053	+	17.7053i	−0.688656	+	0.688656i	−0.961935	−	0.273279i	$-0.911892\pi$
$661$	−17.7053	+	17.7053i	−0.688656	+	0.688656i	0.273279	+	0.961935i	$0.411892\pi$
$662$	−46.4167			−1.80404
$663$		0			0
$664$	82.3448			3.19560
$665$	6.42218	−	6.42218i	0.249041	−	0.249041i
$666$	24.7671	+	10.1669i	0.959705	+	0.393961i
$667$		−	45.3518i		−	1.75603i
$668$	−33.0556	+	33.0556i	−1.27896	+	1.27896i
$669$	−13.1704	−	2.59804i	−0.509196	−	0.100446i
$670$	20.3035	−	20.3035i	0.784393	−	0.784393i
$671$	1.23578	+	1.23578i	0.0477068	+	0.0477068i
$672$	−12.9462	−	19.3089i	−0.499409	−	0.744858i
$673$			41.7501i			1.60935i	0.593716	+	0.804674i	$0.297660\pi$
$673$			41.7501i			1.60935i	−0.593716	+	0.804674i	$0.702340\pi$
$674$	−29.9073	−	29.9073i	−1.15198	−	1.15198i
$675$	21.4832	−	4.37965i	0.826891	−	0.168573i
$676$		0			0
$677$		−	23.6516i		−	0.909004i	−0.890746	−	0.454502i	$-0.849817\pi$
$677$		−	23.6516i		−	0.909004i	0.890746	−	0.454502i	$-0.150183\pi$
$678$	25.1704	+	4.96522i	0.966665	+	0.190688i
$679$	−8.89557			−0.341381
$680$	−15.9583			−0.611973
$681$	−6.28521	+	31.8619i	−0.240850	+	1.22095i
$682$	1.17752	+	1.17752i	0.0450897	+	0.0450897i
$683$	5.78078	+	5.78078i	0.221195	+	0.221195i	0.809002	−	0.587806i	$-0.200008\pi$
$683$	5.78078	+	5.78078i	0.221195	+	0.221195i	−0.587806	+	0.809002i	$0.700008\pi$
$684$	−32.9828	−	78.9186i	−1.26113	−	3.01753i
$685$	1.80483			0.0689588
$686$	−48.4929			−1.85147
$687$	3.84695	−	19.5015i	0.146770	−	0.744029i
$688$			8.02262i			0.305860i
$689$		0			0
$690$	11.9172	+	17.7743i	0.453681	+	0.676656i
$691$	−10.5985	−	10.5985i	−0.403187	−	0.403187i	0.476167	−	0.879355i	$-0.342026\pi$
$691$	−10.5985	−	10.5985i	−0.403187	−	0.403187i	−0.879355	+	0.476167i	$0.842026\pi$
$692$		−	54.8592i		−	2.08544i
$693$	−0.686204	+	1.67162i	−0.0260667	+	0.0634997i
$694$	−43.9377	−	43.9377i	−1.66785	−	1.66785i
$695$	3.19442	−	3.19442i	0.121171	−	0.121171i
$696$	−19.2900	+	97.7879i	−0.731187	+	3.70664i
$697$	12.8656	−	12.8656i	0.487319	−	0.487319i
$698$		−	44.6767i		−	1.69104i
$699$	−16.2275	+	10.8802i	−0.613781	+	0.411525i
$700$	−23.3937	+	23.3937i	−0.884199	+	0.884199i
$701$	−38.5186			−1.45483			−0.727414	−	0.686199i	$-0.759278\pi$
$701$	−38.5186			−1.45483			−0.727414	+	0.686199i	$0.759278\pi$
$702$		0			0
$703$	−21.1381			−0.797237
$704$	−0.954409	+	0.954409i	−0.0359706	+	0.0359706i
$705$	−9.58961	+	6.42960i	−0.361166	+	0.242153i
$706$			54.7063i			2.05890i
$707$	10.0847	−	10.0847i	0.379272	−	0.379272i
$708$	−16.1128	+	81.6813i	−0.605556	+	3.06977i
$709$	26.0488	−	26.0488i	0.978284	−	0.978284i	−0.0214855	−	0.999769i	$-0.506840\pi$
$709$	26.0488	−	26.0488i	0.978284	−	0.978284i	0.999769	+	0.0214855i	$0.00683958\pi$
$710$	5.18835	+	5.18835i	0.194715	+	0.194715i
$711$	−4.19450	+	10.2180i	−0.157306	+	0.383204i
$712$			47.0969i			1.76503i
$713$	6.89902	+	6.89902i	0.258370	+	0.258370i
$714$	−11.0003	−	16.4067i	−0.411675	−	0.614004i
$715$		0			0
$716$			55.0807i			2.05846i
$717$	0.626674	−	3.17683i	0.0234036	−	0.118641i
$718$	−68.4446			−2.55433
$719$	4.77635			0.178128			0.0890640	−	0.996026i	$-0.471612\pi$
$719$	4.77635			0.178128			0.0890640	+	0.996026i	$0.471612\pi$
$720$	−8.60414	−	20.5873i	−0.320657	−	0.767243i
$721$	−0.659686	−	0.659686i	−0.0245680	−	0.0245680i
$722$	33.5533	+	33.5533i	1.24872	+	1.24872i
$723$	7.79737	−	39.5276i	0.289987	−	1.47005i
$724$	93.7292			3.48342
$725$	35.3213			1.31180
$726$	−47.6878	−	9.40709i	−1.76986	−	0.349130i
$727$		−	26.2267i		−	0.972694i	−0.873766	−	0.486347i	$-0.838329\pi$
$727$		−	26.2267i		−	0.972694i	0.873766	−	0.486347i	$-0.161671\pi$
$728$		0			0
$729$	−24.8453	+	10.5694i	−0.920196	+	0.391458i
$730$	0.562211	+	0.562211i	0.0208084	+	0.0208084i
$731$			2.50398i			0.0926130i
$732$	−21.9435	−	32.7282i	−0.811054	−	1.20967i
$733$	−9.54380	−	9.54380i	−0.352508	−	0.352508i	0.508534	−	0.861042i	$-0.330188\pi$
$733$	−9.54380	−	9.54380i	−0.352508	−	0.352508i	−0.861042	+	0.508534i	$0.830188\pi$
$734$	37.1088	−	37.1088i	1.36971	−	1.36971i
$735$	−6.26460	−	1.23578i	−0.231073	−	0.0455825i
$736$	−30.5803	+	30.5803i	−1.12720	+	1.12720i
$737$		−	4.51042i		−	0.166144i
$738$	49.6053	+	20.3631i	1.82600	+	0.749575i
$739$	8.52260	−	8.52260i	0.313509	−	0.313509i	−0.532758	−	0.846267i	$-0.678845\pi$
$739$	8.52260	−	8.52260i	0.313509	−	0.313509i	0.846267	+	0.532758i	$0.178845\pi$
$740$	−14.2429			−0.523580
$741$		0			0
$742$	−42.0906			−1.54520
$743$	−15.7181	+	15.7181i	−0.576641	+	0.576641i	−0.933976	−	0.357336i	$-0.883685\pi$
$743$	−15.7181	+	15.7181i	−0.576641	+	0.576641i	0.357336	+	0.933976i	$0.383685\pi$
$744$	−11.9413	−	17.8102i	−0.437788	−	0.652952i
$745$			9.36521i			0.343115i
$746$	58.4286	−	58.4286i	2.13922	−	2.13922i
$747$	13.8571	+	33.1560i	0.507003	+	1.21312i
$748$	−3.10375	+	3.10375i	−0.113484	+	0.113484i
$749$	−3.94679	−	3.94679i	−0.144213	−	0.144213i
$750$	−30.2469	+	20.2798i	−1.10446	+	0.740515i
$751$		−	37.5050i		−	1.36858i	−0.729212	−	0.684288i	$-0.760113\pi$
$751$		−	37.5050i		−	1.36858i	0.729212	−	0.684288i	$-0.239887\pi$
$752$	−44.9158	−	44.9158i	−1.63791	−	1.63791i
$753$	−15.5279	+	10.4111i	−0.565869	+	0.379401i
$754$		0			0
$755$			8.28200i			0.301413i
$756$	22.4732	−	33.9825i	0.817344	−	1.23593i
$757$	−21.3917			−0.777494			−0.388747	−	0.921345i	$-0.627092\pi$
$757$	−21.3917			−0.777494			−0.388747	+	0.921345i	$0.627092\pi$
$758$	−44.9892			−1.63408
$759$	3.29799	+	0.650574i	0.119709	+	0.0236144i
$760$	26.2571	+	26.2571i	0.952444	+	0.952444i
$761$	−36.1022	−	36.1022i	−1.30870	−	1.30870i	−0.922352	−	0.386350i	$-0.873736\pi$
$761$	−36.1022	−	36.1022i	−1.30870	−	1.30870i	−0.386350	−	0.922352i	$-0.626264\pi$
$762$	−59.7599	−	11.7885i	−2.16487	−	0.427051i
$763$	4.64585			0.168191
$764$	78.9992			2.85809
$765$	−2.68548	−	6.42559i	−0.0970936	−	0.232318i
$766$		−	56.0187i		−	2.02404i
$767$		0			0
$768$	−34.0099	+	22.8028i	−1.22723	+	0.822826i
$769$	32.0645	+	32.0645i	1.15627	+	1.15627i	0.985270	+	0.171005i	$0.0547013\pi$
$769$	32.0645	+	32.0645i	1.15627	+	1.15627i	0.171005	+	0.985270i	$0.445299\pi$
$770$		−	1.37361i		−	0.0495013i
$771$	−6.12278	+	4.10517i	−0.220507	+	0.147844i
$772$	−55.1681	−	55.1681i	−1.98554	−	1.98554i
$773$	−28.8601	+	28.8601i	−1.03803	+	1.03803i	−0.0387789	+	0.999248i	$0.512347\pi$
$773$	−28.8601	+	28.8601i	−1.03803	+	1.03803i	−0.999248	+	0.0387789i	$0.987653\pi$
$774$	−6.80884	+	2.84565i	−0.244739	+	0.102285i
$775$	−5.37316	+	5.37316i	−0.193010	+	0.193010i
$776$		−	36.3695i		−	1.30559i
$777$	−5.60702	−	8.36275i	−0.201151	−	0.300012i
$778$	−5.92239	+	5.92239i	−0.212328	+	0.212328i
$779$	−42.3369			−1.51688
$780$		0			0
$781$	1.15259			0.0412430
$782$	−25.9839	+	25.9839i	−0.929182	+	0.929182i
$783$	−42.6203	+	8.68872i	−1.52312	+	0.310510i
$784$		−	35.1303i		−	1.25465i
$785$	−13.7409	+	13.7409i	−0.490435	+	0.490435i
$786$	27.8939	+	5.50246i	0.994941	+	0.196266i
$787$	5.69039	−	5.69039i	0.202841	−	0.202841i	−0.598375	−	0.801216i	$-0.704187\pi$
$787$	5.69039	−	5.69039i	0.202841	−	0.202841i	0.801216	+	0.598375i	$0.204187\pi$
$788$	−48.2273	−	48.2273i	−1.71803	−	1.71803i
$789$	24.4483	+	36.4642i	0.870383	+	1.29816i
$790$		−	8.39632i		−	0.298728i
$791$	−6.82241	−	6.82241i	−0.242577	−	0.242577i
$792$	−6.83443	−	2.80555i	−0.242851	−	0.0996908i
$793$		0			0
$794$		−	82.1347i		−	2.91485i
$795$	−14.5590	−	2.87197i	−0.516355	−	0.101858i
$796$	1.55887			0.0552528
$797$	−15.3922			−0.545220			−0.272610	−	0.962125i	$-0.587887\pi$
$797$	−15.3922			−0.545220			−0.272610	+	0.962125i	$0.587887\pi$
$798$	−8.89545	+	45.0941i	−0.314895	+	1.59631i
$799$	−14.0189	−	14.0189i	−0.495952	−	0.495952i
$800$	−23.8168	−	23.8168i	−0.842052	−	0.842052i
$801$	−18.9635	+	7.92550i	−0.670042	+	0.280034i
$802$	97.5906			3.44604
$803$	0.124895			0.00440745
$804$	−19.6814	+	99.7720i	−0.694111	+	3.51869i
$805$		−	8.04785i		−	0.283649i
$806$		0			0
$807$	21.8618	+	32.6065i	0.769573	+	1.14780i
$808$	41.2311	+	41.2311i	1.45050	+	1.45050i
$809$			40.1905i			1.41302i	0.707702	+	0.706511i	$0.249732\pi$
$809$			40.1905i			1.41302i	−0.707702	+	0.706511i	$0.750268\pi$
$810$	14.4206	−	14.6047i	0.506688	−	0.513158i
$811$	24.5095	+	24.5095i	0.860644	+	0.860644i	0.991413	−	0.130769i	$-0.0417446\pi$
$811$	24.5095	+	24.5095i	0.860644	+	0.860644i	−0.130769	+	0.991413i	$0.541745\pi$
$812$	46.4104	−	46.4104i	1.62869	−	1.62869i
$813$	−7.14503	+	36.2206i	−0.250587	+	1.27031i
$814$	−2.26056	+	2.26056i	−0.0792324	+	0.0792324i
$815$		−	18.1694i		−	0.636448i
$816$	31.8240	−	21.3372i	1.11406	−	0.746951i
$817$	4.11993	−	4.11993i	0.144138	−	0.144138i
$818$	7.83235			0.273852
$819$		0			0
$820$	−28.5267			−0.996197
$821$	26.1838	−	26.1838i	0.913821	−	0.913821i	−0.0827498	−	0.996570i	$-0.526370\pi$
$821$	26.1838	−	26.1838i	0.913821	−	0.913821i	0.996570	+	0.0827498i	$0.0263702\pi$
$822$	−7.58635	+	5.08646i	−0.264604	+	0.177411i
$823$			38.2880i			1.33464i	0.744773	+	0.667318i	$0.232558\pi$
$823$			38.2880i			1.33464i	−0.744773	+	0.667318i	$0.767442\pi$
$824$	2.69713	−	2.69713i	0.0939589	−	0.0939589i
$825$	−0.506687	+	2.56857i	−0.0176406	+	0.0894261i
$826$	31.6352	−	31.6352i	1.10073	−	1.10073i
$827$	−10.8851	−	10.8851i	−0.378512	−	0.378512i	0.492053	−	0.870565i	$-0.336246\pi$
$827$	−10.8851	−	10.8851i	−0.378512	−	0.378512i	−0.870565	+	0.492053i	$0.836246\pi$
$828$	−70.1137	−	28.7818i	−2.43662	−	1.00024i
$829$		−	5.39042i		−	0.187217i	−0.995609	−	0.0936085i	$-0.970160\pi$
$829$		−	5.39042i		−	0.187217i	0.995609	−	0.0936085i	$-0.0298402\pi$
$830$	−19.3158	−	19.3158i	−0.670461	−	0.670461i
$831$	10.3033	+	15.3671i	0.357416	+	0.533079i
$832$		0			0
$833$		−	10.9647i		−	0.379903i
$834$	−4.42464	+	22.4301i	−0.153213	+	0.776689i
$835$	8.85663			0.306496
$836$	10.2135			0.353242
$837$	5.16175	−	7.80524i	0.178416	−	0.269789i
$838$	−67.8080	−	67.8080i	−2.34239	−	2.34239i
$839$	38.3523	+	38.3523i	1.32407	+	1.32407i	0.910450	+	0.413620i	$0.135736\pi$
$839$	38.3523	+	38.3523i	1.32407	+	1.32407i	0.413620	+	0.910450i	$0.364264\pi$
$840$	−3.42309	+	17.3528i	−0.118108	+	0.598729i
$841$	−41.0734			−1.41632
$842$	−68.3381			−2.35509
$843$	−23.6502	−	4.66534i	−0.814556	−	0.160683i
$844$			12.5397i			0.431634i
$845$		0			0
$846$	22.1884	−	54.0520i	0.762854	−	1.85834i
$847$	12.9257	+	12.9257i	0.444133	+	0.444133i
$848$		−	81.6431i		−	2.80363i
$849$	−15.7189	−	23.4444i	−0.539470	−	0.804609i
$850$	−20.2370	−	20.2370i	−0.694124	−	0.694124i
$851$	−13.2444	+	13.2444i	−0.454013	+	0.454013i
$852$	−25.4957	−	5.02939i	−0.873469	−	0.172304i
$853$	26.8752	−	26.8752i	0.920190	−	0.920190i	−0.0768525	−	0.997042i	$-0.524487\pi$
$853$	26.8752	−	26.8752i	0.920190	−	0.920190i	0.997042	+	0.0768525i	$0.0244871\pi$
$854$			21.1743i			0.724571i
$855$	−6.15381	+	14.9909i	−0.210456	+	0.512679i
$856$	16.1365	−	16.1365i	0.551533	−	0.551533i
$857$	26.9236			0.919691			0.459846	−	0.887999i	$-0.347905\pi$
$857$	26.9236			0.919691			0.459846	+	0.887999i	$0.347905\pi$
$858$		0			0
$859$	2.86268			0.0976735			0.0488368	−	0.998807i	$-0.484449\pi$
$859$	2.86268			0.0976735			0.0488368	+	0.998807i	$0.484449\pi$
$860$	2.77602	−	2.77602i	0.0946616	−	0.0946616i
$861$	−11.2301	−	16.7495i	−0.382722	−	0.570822i
$862$		−	18.7456i		−	0.638479i
$863$	−12.8305	+	12.8305i	−0.436756	+	0.436756i	−0.890919	−	0.454163i	$-0.849938\pi$
$863$	−12.8305	+	12.8305i	−0.436756	+	0.436756i	0.454163	+	0.890919i	$0.349938\pi$
$864$	34.5972	+	22.8797i	1.17702	+	0.778384i
$865$	−7.34925	+	7.34925i	−0.249882	+	0.249882i
$866$	12.4159	+	12.4159i	0.421909	+	0.421909i
$867$	−14.5238	+	9.73786i	−0.493254	+	0.330715i
$868$			14.1201i			0.479268i
$869$	−0.932622	−	0.932622i	−0.0316370	−	0.0316370i
$870$	27.4632	−	18.4134i	0.931090	−	0.624273i
$871$		0			0
$872$			18.9946i			0.643237i
$873$	14.6441	−	6.12030i	0.495629	−	0.207141i
$874$	85.5054			2.89226
$875$	13.6952			0.462983
$876$	−2.76272	−	0.544985i	−0.0933437	−	0.0184134i
$877$	18.1856	+	18.1856i	0.614085	+	0.614085i	0.944008	−	0.329923i	$-0.107023\pi$
$877$	18.1856	+	18.1856i	0.614085	+	0.614085i	−0.329923	+	0.944008i	$0.607023\pi$
$878$	−29.5926	−	29.5926i	−0.998700	−	0.998700i
$879$	27.9535	+	5.51422i	0.942848	+	0.185990i
$880$	2.66438			0.0898161
$881$	−50.4146			−1.69851			−0.849255	−	0.527983i	$-0.822948\pi$
$881$	−50.4146			−1.69851			−0.849255	+	0.527983i	$0.822948\pi$
$882$	29.8152	−	12.4608i	1.00393	−	0.419577i
$883$			22.1092i			0.744035i	0.928226	+	0.372018i	$0.121334\pi$
$883$			22.1092i			0.744035i	−0.928226	+	0.372018i	$0.878666\pi$
$884$		0			0
$885$	13.1010	−	8.78392i	0.440387	−	0.295268i
$886$	−11.1319	−	11.1319i	−0.373983	−	0.373983i
$887$		−	21.3351i		−	0.716362i	−0.933652	−	0.358181i	$-0.883397\pi$
$887$		−	21.3351i		−	0.716362i	0.933652	−	0.358181i	$-0.116603\pi$
$888$	34.1911	−	22.9243i	1.14738	−	0.769289i
$889$	16.1978	+	16.1978i	0.543258	+	0.543258i
$890$	11.0476	−	11.0476i	0.370317	−	0.370317i
$891$	−0.0204541	−	3.22399i	−0.000685237	−	0.108008i
$892$	−25.5560	+	25.5560i	−0.855677	+	0.855677i
$893$			46.1320i			1.54375i
$894$	−26.3935	−	39.3654i	−0.882732	−	1.31658i
$895$	7.37891	−	7.37891i	0.246650	−	0.246650i
$896$	10.4905			0.350462
$897$		0			0
$898$	69.2090			2.30953
$899$	10.6597	−	10.6597i	0.355522	−	0.355522i
$900$	22.4161	−	54.6066i	0.747204	−	1.82022i
$901$		−	25.4820i		−	0.848928i
$902$	−4.52760	+	4.52760i	−0.150753	+	0.150753i
$903$	2.72279	+	0.537108i	0.0906087	+	0.0178738i
$904$	27.8934	−	27.8934i	0.927722	−	0.927722i
$905$	−12.5565	−	12.5565i	−0.417391	−	0.417391i
$906$	−23.3408	−	34.8123i	−0.775446	−	1.15656i
$907$		−	11.3836i		−	0.377985i	−0.981979	−	0.188992i	$-0.939478\pi$
$907$		−	11.3836i		−	0.377985i	0.981979	−	0.188992i	$-0.0605222\pi$
$908$	61.8252	+	61.8252i	2.05174	+	2.05174i
$909$	−9.66324	+	23.5400i	−0.320509	+	0.780774i
$910$		0			0
$911$		−	21.7806i		−	0.721625i	−0.932638	−	0.360812i	$-0.882499\pi$
$911$		−	21.7806i		−	0.721625i	0.932638	−	0.360812i	$-0.117501\pi$
$912$	−87.4689	−	17.2545i	−2.89638	−	0.571353i
$913$	−4.29101			−0.142012
$914$	49.4555			1.63584
$915$	−1.44479	+	7.32413i	−0.0477632	+	0.242128i
$916$	−37.8410	−	37.8410i	−1.25030	−	1.25030i
$917$	−7.56059	−	7.56059i	−0.249673	−	0.249673i
$918$	29.3970	+	19.4408i	0.970246	+	0.641641i
$919$	−22.4613			−0.740931			−0.370465	−	0.928846i	$-0.620802\pi$
$919$	−22.4613			−0.740931			−0.370465	+	0.928846i	$0.620802\pi$
$920$	32.9036			1.08480
$921$	2.70548	−	13.7150i	0.0891485	−	0.451924i
$922$			11.5443i			0.380192i
$923$		0			0
$924$	2.70921	+	4.04073i	0.0891264	+	0.132930i
$925$	−10.3151	−	10.3151i	−0.339160	−	0.339160i
$926$			91.5907i			3.00986i
$927$	1.53987	+	0.632120i	0.0505759	+	0.0207615i
$928$	47.2498	+	47.2498i	1.55105	+	1.55105i
$929$	−19.2087	+	19.2087i	−0.630218	+	0.630218i	−0.948123	−	0.317905i	$-0.897021\pi$
$929$	−19.2087	+	19.2087i	−0.630218	+	0.630218i	0.317905	+	0.948123i	$0.397021\pi$
$930$	−1.37668	+	6.97885i	−0.0451430	+	0.228846i
$931$	−18.0408	+	18.0408i	−0.591262	+	0.591262i
$932$			52.6001i			1.72297i
$933$	36.4570	−	24.4435i	1.19355	−	0.800245i
$934$	18.3563	−	18.3563i	0.600637	−	0.600637i
$935$	0.831591			0.0271959
$936$		0			0
$937$	31.2647			1.02137			0.510687	−	0.859767i	$-0.329391\pi$
$937$	31.2647			1.02137			0.510687	+	0.859767i	$0.329391\pi$
$938$	38.6417	−	38.6417i	1.26170	−	1.26170i
$939$	−5.02779	+	3.37101i	−0.164076	+	0.110009i
$940$			31.0839i			1.01384i
$941$	18.1003	−	18.1003i	0.590052	−	0.590052i	−0.347593	−	0.937645i	$-0.613001\pi$
$941$	18.1003	−	18.1003i	0.590052	−	0.590052i	0.937645	+	0.347593i	$0.113001\pi$
$942$	19.0328	−	96.4838i	0.620122	−	3.14361i
$943$	−26.5269	+	26.5269i	−0.863834	+	0.863834i
$944$	61.3626	+	61.3626i	1.99718	+	1.99718i
$945$	−7.56313	+	1.54185i	−0.246029	+	0.0501563i
$946$		−	0.881190i		−	0.0286500i
$947$	−19.8947	−	19.8947i	−0.646491	−	0.646491i	0.305652	−	0.952143i	$-0.401125\pi$
$947$	−19.8947	−	19.8947i	−0.646491	−	0.646491i	−0.952143	+	0.305652i	$0.901125\pi$
$948$	16.5604	+	24.6994i	0.537855	+	0.802200i
$949$		0			0
$950$			66.5941i			2.16060i
$951$	2.49213	−	12.6334i	0.0808127	−	0.409668i
$952$	−30.3719			−0.984359
$953$	53.0607			1.71881			0.859403	−	0.511299i	$-0.170836\pi$
$953$	53.0607			1.71881			0.859403	+	0.511299i	$0.170836\pi$
$954$	69.2908	−	28.9590i	2.24337	−	0.937584i
$955$	−10.5832	−	10.5832i	−0.342463	−	0.342463i
$956$	−6.16436	−	6.16436i	−0.199370	−	0.199370i
$957$	1.00521	−	5.09575i	0.0324937	−	0.164722i
$958$	15.2668			0.493248
$959$	3.43495			0.110920
$960$	−5.65651	−	1.11583i	−0.182563	−	0.0360132i
$961$		−	27.7568i		−	0.895382i
$962$		0			0
$963$	9.21278	+	3.78187i	0.296878	+	0.121869i
$964$	−76.6998	−	76.6998i	−2.47033	−	2.47033i
$965$			14.7812i			0.475825i
$966$	22.6809	+	33.8281i	0.729746	+	1.08840i
$967$	−6.28251	−	6.28251i	−0.202032	−	0.202032i	0.598838	−	0.800870i	$-0.295629\pi$
$967$	−6.28251	−	6.28251i	−0.202032	−	0.202032i	−0.800870	+	0.598838i	$0.795629\pi$
$968$	−52.8468	+	52.8468i	−1.69856	+	1.69856i
$969$	−27.3003	−	5.38537i	−0.877012	−	0.173003i
$970$	−8.53128	+	8.53128i	−0.273923	+	0.273923i
$971$			52.4745i			1.68399i	0.539488	+	0.841993i	$0.318618\pi$
$971$			52.4745i			1.68399i	−0.539488	+	0.841993i	$0.681382\pi$
$972$	−13.6156	+	71.4049i	−0.436720	+	2.29031i
$973$	6.07964	−	6.07964i	0.194904	−	0.194904i
$974$	24.2548			0.777173
$975$		0			0
$976$	−41.0718			−1.31468
$977$	−13.5597	+	13.5597i	−0.433812	+	0.433812i	−0.889923	−	0.456111i	$-0.849242\pi$
$977$	−13.5597	+	13.5597i	−0.433812	+	0.433812i	0.456111	+	0.889923i	$0.349242\pi$
$978$	51.2061	+	76.3729i	1.63739	+	2.44214i
$979$		−	2.45423i		−	0.0784375i
$980$	−12.1559	+	12.1559i	−0.388307	+	0.388307i
$981$	−7.64813	+	3.19642i	−0.244186	+	0.102054i
$982$	44.4530	−	44.4530i	1.41855	−	1.41855i
$983$	−11.5787	−	11.5787i	−0.369303	−	0.369303i	0.497920	−	0.867223i	$-0.334097\pi$
$983$	−11.5787	−	11.5787i	−0.369303	−	0.369303i	−0.867223	+	0.497920i	$0.834097\pi$
$984$	68.4804	−	45.9144i	2.18308	−	1.46370i
$985$			12.9216i			0.411716i
$986$	40.1479	+	40.1479i	1.27857	+	1.27857i
$987$	−18.2510	+	12.2368i	−0.580935	+	0.389502i
$988$		0			0
$989$		−	5.16282i		−	0.164168i
$990$	0.945063	+	2.26127i	0.0300361	+	0.0718678i
$991$	−35.3765			−1.12377			−0.561886	−	0.827215i	$-0.689924\pi$
$991$	−35.3765			−1.12377			−0.561886	+	0.827215i	$0.689924\pi$
$992$	−14.3755			−0.456423
$993$	−30.5566	−	6.02772i	−0.969685	−	0.191284i
$994$	9.87448	+	9.87448i	0.313200	+	0.313200i
$995$	−0.208835	−	0.208835i	−0.00662052	−	0.00662052i
$996$	94.9184	+	18.7240i	3.00760	+	0.593292i
$997$	−54.5615			−1.72798			−0.863990	−	0.503510i	$-0.832042\pi$
$997$	−54.5615			−1.72798			−0.863990	+	0.503510i	$0.832042\pi$
$998$	−25.4513			−0.805646
$999$	14.9841	+	9.90928i	0.474077	+	0.313516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.f.g.437.23	yes	48
3.2	odd	2	inner	507.2.f.g.437.2	yes	48
13.2	odd	12		507.2.k.k.188.24		96
13.3	even	3		507.2.k.k.488.24		96
13.4	even	6		507.2.k.k.89.23		96
13.5	odd	4	inner	507.2.f.g.239.1	✓	48
13.6	odd	12		507.2.k.k.80.1		96
13.7	odd	12		507.2.k.k.80.23		96
13.8	odd	4	inner	507.2.f.g.239.23	yes	48
13.9	even	3		507.2.k.k.89.1		96
13.10	even	6		507.2.k.k.488.2		96
13.11	odd	12		507.2.k.k.188.2		96
13.12	even	2	inner	507.2.f.g.437.1	yes	48
39.2	even	12		507.2.k.k.188.1		96
39.5	even	4	inner	507.2.f.g.239.24	yes	48
39.8	even	4	inner	507.2.f.g.239.2	yes	48
39.11	even	12		507.2.k.k.188.23		96
39.17	odd	6		507.2.k.k.89.2		96
39.20	even	12		507.2.k.k.80.2		96
39.23	odd	6		507.2.k.k.488.23		96
39.29	odd	6		507.2.k.k.488.1		96
39.32	even	12		507.2.k.k.80.24		96
39.35	odd	6		507.2.k.k.89.24		96
39.38	odd	2	inner	507.2.f.g.437.24	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.1	✓	48	13.5	odd	4	inner
507.2.f.g.239.2	yes	48	39.8	even	4	inner
507.2.f.g.239.23	yes	48	13.8	odd	4	inner
507.2.f.g.239.24	yes	48	39.5	even	4	inner
507.2.f.g.437.1	yes	48	13.12	even	2	inner
507.2.f.g.437.2	yes	48	3.2	odd	2	inner
507.2.f.g.437.23	yes	48	1.1	even	1	trivial
507.2.f.g.437.24	yes	48	39.38	odd	2	inner
507.2.k.k.80.1		96	13.6	odd	12
507.2.k.k.80.2		96	39.20	even	12
507.2.k.k.80.23		96	13.7	odd	12
507.2.k.k.80.24		96	39.32	even	12
507.2.k.k.89.1		96	13.9	even	3
507.2.k.k.89.2		96	39.17	odd	6
507.2.k.k.89.23		96	13.4	even	6
507.2.k.k.89.24		96	39.35	odd	6
507.2.k.k.188.1		96	39.2	even	12
507.2.k.k.188.2		96	13.11	odd	12
507.2.k.k.188.23		96	39.11	even	12
507.2.k.k.188.24		96	13.2	odd	12
507.2.k.k.488.1		96	39.29	odd	6
507.2.k.k.488.2		96	13.10	even	6
507.2.k.k.488.23		96	39.23	odd	6
507.2.k.k.488.24		96	13.3	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82526 - 1.82526i) q^{2} +(1.43862 - 0.964559i) q^{3} -4.66316i q^{4} +(-0.624703 + 0.624703i) q^{5} +(0.865285 - 4.38643i) q^{6} +(-1.18894 + 1.18894i) q^{7} +(-4.86096 - 4.86096i) q^{8} +(1.13925 - 2.77527i) q^{9} +2.28049i q^{10} +(0.253306 + 0.253306i) q^{11} +(-4.49789 - 6.70851i) q^{12} +4.34024i q^{14} +(-0.296147 + 1.50127i) q^{15} -8.41874 q^{16} -2.62761 q^{17} +(-2.98615 - 7.14502i) q^{18} +(4.32335 + 4.32335i) q^{19} +(2.91309 + 2.91309i) q^{20} +(-0.563628 + 2.85722i) q^{21} +0.924699 q^{22} +5.41774 q^{23} +(-11.6818 - 2.30439i) q^{24} +4.21949i q^{25} +(-1.03796 - 5.09143i) q^{27} +(5.54420 + 5.54420i) q^{28} -8.37099i q^{29} +(2.19967 + 3.28076i) q^{30} +(1.27341 + 1.27341i) q^{31} +(-5.64448 + 5.64448i) q^{32} +(0.608739 + 0.120082i) q^{33} +(-4.79608 + 4.79608i) q^{34} -1.48546i q^{35} +(-12.9415 - 5.31252i) q^{36} +(-2.44464 + 2.44464i) q^{37} +15.7825 q^{38} +6.07331 q^{40} +(-4.89630 + 4.89630i) q^{41} +(4.18641 + 6.24395i) q^{42} -0.952948i q^{43} +(1.18121 - 1.18121i) q^{44} +(1.02202 + 2.44541i) q^{45} +(9.88879 - 9.88879i) q^{46} +(5.33521 + 5.33521i) q^{47} +(-12.1114 + 8.12037i) q^{48} +4.17286i q^{49} +(7.70168 + 7.70168i) q^{50} +(-3.78013 + 2.53449i) q^{51} +9.69778i q^{53} +(-11.1877 - 7.39865i) q^{54} -0.316482 q^{55} +11.5587 q^{56} +(10.3898 + 2.04953i) q^{57} +(-15.2792 - 15.2792i) q^{58} +(-7.28881 - 7.28881i) q^{59} +(7.00067 + 1.38098i) q^{60} +4.87861 q^{61} +4.64863 q^{62} +(1.94512 + 4.65411i) q^{63} +3.76781i q^{64} +(1.33029 - 0.891926i) q^{66} +(-8.90312 - 8.90312i) q^{67} +12.2530i q^{68} +(7.79406 - 5.22573i) q^{69} +(-2.71136 - 2.71136i) q^{70} +(2.27510 - 2.27510i) q^{71} +(-19.0283 + 7.95260i) q^{72} +(0.246530 - 0.246530i) q^{73} +8.92421i q^{74} +(4.06995 + 6.07025i) q^{75} +(20.1605 - 20.1605i) q^{76} -0.602329 q^{77} -3.68180 q^{79} +(5.25921 - 5.25921i) q^{80} +(-6.40421 - 6.32346i) q^{81} +17.8741i q^{82} +(-8.47001 + 8.47001i) q^{83} +(13.3237 + 2.62829i) q^{84} +(1.64148 - 1.64148i) q^{85} +(-1.73938 - 1.73938i) q^{86} +(-8.07431 - 12.0427i) q^{87} -2.46262i q^{88} +(-4.84440 - 4.84440i) q^{89} +(6.32897 + 2.59806i) q^{90} -25.2638i q^{92} +(3.06024 + 0.603676i) q^{93} +19.4763 q^{94} -5.40162 q^{95} +(-2.67583 + 13.5647i) q^{96} +(3.74098 + 3.74098i) q^{97} +(7.61657 + 7.61657i) q^{98} +(0.991570 - 0.414412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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