LMFDB - Embedded newform 507.2.f.g.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(239,507)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
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			239.2
Character	$\chi$	$=$	507.239
Dual form			507.2.f.g.437.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82526 - 1.82526i) q^{2} +(1.43862 + 0.964559i) q^{3} +4.66316i q^{4} +(0.624703 + 0.624703i) q^{5} +(-0.865285 - 4.38643i) q^{6} +(1.18894 + 1.18894i) q^{7} +(4.86096 - 4.86096i) q^{8} +(1.13925 + 2.77527i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 48 * q - 24 * q^9	$ 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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	−0.934382	−	0.356273i	$-0.884047\pi$
$2$	−1.82526	−	1.82526i	−1.29065	−	1.29065i	−0.356273	−	0.934382i	$-0.615953\pi$
$3$	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	$-0.186702\pi$
$5$	0.624703	+	0.624703i	0.279376	+	0.279376i	−0.553484	+	0.832860i	$0.686702\pi$
$6$	−0.865285	−	4.38643i	−0.353251	−	1.79075i
$7$	1.18894	+	1.18894i	0.449375	+	0.449375i	0.895147	−	0.445771i	$-0.147071\pi$
$7$	1.18894	+	1.18894i	0.449375	+	0.449375i	−0.445771	+	0.895147i	$0.647071\pi$
$8$	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	$-0.767199\pi$
$11$	−0.253306	+	0.253306i	−0.0763746	+	0.0763746i	0.667888	+	0.744262i	$0.267199\pi$
$12$	−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	$-0.997415\pi$
$19$	−4.32335	+	4.32335i	−0.991845	+	0.991845i	0.00812247	+	0.999967i	$0.497415\pi$
$20$	−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	$0.283374\pi$
$29$			8.37099i			1.55445i	−0.629221	+	0.777227i	$0.716626\pi$
$30$	2.19967	−	3.28076i	0.401603	−	0.598982i
$31$	−1.27341	+	1.27341i	−0.228712	+	0.228712i	−0.812154	−	0.583443i	$-0.801705\pi$
$31$	−1.27341	+	1.27341i	−0.228712	+	0.228712i	0.583443	+	0.812154i	$0.301705\pi$
$32$	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	$-0.158277\pi$
$37$	2.44464	+	2.44464i	0.401896	+	0.401896i	−0.477005	+	0.878901i	$0.658277\pi$
$38$	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	$-0.0681571\pi$
$41$	4.89630	+	4.89630i	0.764674	+	0.764674i	−0.212489	+	0.977163i	$0.568157\pi$
$42$	4.18641	−	6.24395i	0.645978	−	0.963462i
$43$			0.952948i			0.145323i	0.997357	+	0.0726616i	$0.0231493\pi$
$43$			0.952948i			0.145323i	−0.997357	+	0.0726616i	$0.976851\pi$
$44$	−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	$-0.935481\pi$
$47$	−5.33521	+	5.33521i	−0.778220	+	0.778220i	0.201308	+	0.979528i	$0.435481\pi$
$48$	−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	$-0.767985\pi$
$53$		−	9.69778i		−	1.33209i	0.745911	−	0.666046i	$-0.232015\pi$
$54$	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	$-0.515870\pi$
$59$	7.28881	−	7.28881i	0.948922	−	0.948922i	0.998757	+	0.0498356i	$0.0158697\pi$
$60$	−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	0.0919234	−	0.995766i	$-0.470698\pi$
$67$	8.90312	−	8.90312i	1.08769	−	1.08769i	0.995766	−	0.0919234i	$-0.0293015\pi$
$68$		−	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	$-0.311148\pi$
$71$	−2.27510	−	2.27510i	−0.270005	−	0.270005i	−0.829102	+	0.559097i	$0.811148\pi$
$72$	19.0283	+	7.95260i	2.24251	+	0.937223i
$73$	−0.246530	−	0.246530i	−0.0288542	−	0.0288542i	0.692532	−	0.721387i	$-0.256495\pi$
$73$	−0.246530	−	0.246530i	−0.0288542	−	0.0288542i	−0.721387	+	0.692532i	$0.756495\pi$
$74$		−	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	$-0.0216560\pi$
$83$	8.47001	+	8.47001i	0.929705	+	0.929705i	−0.0679819	+	0.997687i	$0.521656\pi$
$84$	−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	$-0.631717\pi$
$89$	4.84440	−	4.84440i	0.513505	−	0.513505i	0.915599	+	0.402093i	$0.131717\pi$
$90$	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	$-0.836557\pi$
$97$	−3.74098	+	3.74098i	−0.379839	+	0.379839i	0.491205	+	0.871044i	$0.336557\pi$
$98$	−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	$-0.991298\pi$
$103$		−	0.554855i		−	0.0546714i	0.999626	−	0.0273357i	$-0.00870232\pi$
$104$		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	$-0.948703\pi$
$107$		−	3.31960i		−	0.320918i	0.987042	−	0.160459i	$-0.0512975\pi$
$108$	−23.7421	−	4.84016i	−2.28459	−	0.465744i
$109$	1.95379	−	1.95379i	0.187139	−	0.187139i	−0.607319	−	0.794458i	$-0.707755\pi$
$109$	1.95379	−	1.95379i	0.187139	−	0.187139i	0.794458	+	0.607319i	$0.207755\pi$
$110$	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	$-0.913008\pi$
$113$		−	5.73825i		−	0.539809i	0.962887	−	0.269905i	$-0.0869922\pi$
$114$	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	$0.206611\pi$
$127$			13.6238i			1.20892i	−0.796636	+	0.604459i	$0.793389\pi$
$128$	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	$-0.910395\pi$
$131$		−	6.35913i		−	0.555599i	0.960639	−	0.277800i	$-0.0896052\pi$
$132$	−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	$-0.722186\pi$
$137$	1.44455	−	1.44455i	0.123416	−	0.123416i	0.766117	+	0.642701i	$0.222186\pi$
$138$	−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	$-0.392975\pi$
$149$	−7.49573	−	7.49573i	−0.614074	−	0.614074i	−0.944005	+	0.329931i	$0.892975\pi$
$150$	−18.5085	+	3.65106i	−1.51121	+	0.298108i
$151$	−6.62875	−	6.62875i	−0.539440	−	0.539440i	0.383925	−	0.923364i	$-0.374572\pi$
$151$	−6.62875	−	6.62875i	−0.539440	−	0.539440i	−0.923364	+	0.383925i	$0.874572\pi$
$152$			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	0.988620	+	0.150434i	$0.0480671\pi$
$163$	14.5425	+	14.5425i	1.13905	+	1.13905i	0.150434	+	0.988620i	$0.451933\pi$
$164$	−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	$-0.623209\pi$
$167$	7.08868	−	7.08868i	0.548538	−	0.548538i	0.926018	+	0.377480i	$0.123209\pi$
$168$	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	$-0.731490\pi$
$181$		−	20.0999i		−	1.49402i	0.664815	−	0.747008i	$-0.268510\pi$
$182$		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	$-0.789999\pi$
$191$		−	16.9411i		−	1.22582i	0.790154	−	0.612909i	$-0.210001\pi$
$192$	3.63428	−	5.42045i	0.262281	−	0.391187i
$193$	−11.8306	−	11.8306i	−0.851587	−	0.851587i	0.138742	−	0.990329i	$-0.455694\pi$
$193$	−11.8306	−	11.8306i	−0.851587	−	0.851587i	−0.990329	+	0.138742i	$0.955694\pi$
$194$	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	$-0.424453\pi$
$197$	−10.3422	−	10.3422i	−0.736851	−	0.736851i	−0.971967	+	0.235116i	$0.924453\pi$
$198$	1.05347	+	2.56628i	0.0748665	+	0.182378i
$199$		−	0.334295i		−	0.0236976i	−0.999930	−	0.0118488i	$-0.996228\pi$
$199$		−	0.334295i		−	0.0236976i	0.999930	−	0.0118488i	$-0.00377167\pi$
$200$	−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	$-0.666441\pi$
$223$	5.48040	−	5.48040i	0.366995	−	0.366995i	0.866380	+	0.499385i	$0.166441\pi$
$224$			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	$-0.0362230\pi$
$227$	13.2582	+	13.2582i	0.879980	+	0.879980i	−0.113552	+	0.993532i	$0.536223\pi$
$228$	−9.55729	−	48.4492i	−0.632947	−	3.20863i
$229$	−8.11488	−	8.11488i	−0.536246	−	0.536246i	0.386178	−	0.922424i	$-0.373795\pi$
$229$	−8.11488	−	8.11488i	−0.536246	−	0.536246i	−0.922424	+	0.386178i	$0.873795\pi$
$230$		−	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	$-0.269258\pi$
$239$	−1.32193	−	1.32193i	−0.0855084	−	0.0855084i	−0.748567	+	0.663059i	$0.769258\pi$
$240$	−2.49319	−	12.6388i	−0.160934	−	0.815832i
$241$	−16.4480	−	16.4480i	−1.05951	−	1.05951i	−0.998113	−	0.0613973i	$-0.980444\pi$
$241$	−16.4480	−	16.4480i	−1.05951	−	1.05951i	−0.0613973	−	0.998113i	$-0.519556\pi$
$242$	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	$-0.714470\pi$
$263$		−	25.3466i		−	1.56294i	0.623943	−	0.781470i	$-0.285530\pi$
$264$	−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	$-0.757189\pi$
$269$		−	22.6651i		−	1.38192i	0.722895	−	0.690958i	$-0.242811\pi$
$270$	11.6110	+	2.36705i	0.706621	+	0.144054i
$271$	15.0720	+	15.0720i	0.915557	+	0.915557i	0.996702	−	0.0811452i	$-0.0258578\pi$
$271$	15.0720	+	15.0720i	0.915557	+	0.915557i	−0.0811452	+	0.996702i	$0.525858\pi$
$272$	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	$-0.896013\pi$
$277$		−	10.6818i		−	0.641809i	0.947112	−	0.320905i	$-0.103987\pi$
$278$	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	$-0.613737\pi$
$281$	9.84122	−	9.84122i	0.587078	−	0.587078i	0.936839	+	0.349761i	$0.113737\pi$
$282$	28.0190	+	18.7860i	1.66851	+	1.11869i
$283$			16.2964i			0.968722i	0.874868	+	0.484361i	$0.160948\pi$
$283$			16.2964i			0.968722i	−0.874868	+	0.484361i	$0.839052\pi$
$284$	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	$-0.909548\pi$
$293$	−11.6319	+	11.6319i	−0.679542	+	0.679542i	0.280355	+	0.959897i	$0.409548\pi$
$294$	−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	$-0.323976\pi$
$307$	−5.70702	−	5.70702i	−0.325717	−	0.325717i	−0.850955	+	0.525238i	$0.823976\pi$
$308$		−	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	$-0.316950\pi$
$317$	−5.25697	−	5.25697i	−0.295261	−	0.295261i	−0.839154	+	0.543893i	$0.816950\pi$
$318$	−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	$-0.585466\pi$
$331$	12.7151	−	12.7151i	0.698884	−	0.698884i	0.964170	+	0.265286i	$0.0854663\pi$
$332$	−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	$0.147251\pi$
$337$			16.3852i			0.892558i	−0.894894	+	0.446279i	$0.852749\pi$
$338$		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	$0.223612\pi$
$347$			24.0720i			1.29225i	−0.763231	+	0.646126i	$0.776388\pi$
$348$	−56.1569	−	37.6518i	−3.01032	−	2.01835i
$349$	−12.2384	−	12.2384i	−0.655108	−	0.655108i	0.299111	−	0.954218i	$-0.403310\pi$
$349$	−12.2384	−	12.2384i	−0.655108	−	0.655108i	−0.954218	+	0.299111i	$0.903310\pi$
$350$	−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	$-0.0592612\pi$
$353$	14.9859	+	14.9859i	0.797619	+	0.797619i	−0.185101	+	0.982720i	$0.559261\pi$
$354$	−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	$-0.503310\pi$
$359$	18.7493	−	18.7493i	0.989548	−	0.989548i	0.999946	+	0.0103977i	$0.00330975\pi$
$360$	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	$-0.602268\pi$
$379$	12.3240	−	12.3240i	0.633044	−	0.633044i	0.948830	+	0.315787i	$0.102268\pi$
$380$		−	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	$-0.437072\pi$
$383$	−15.3454	−	15.3454i	−0.784113	−	0.784113i	−0.980522	+	0.196409i	$0.937072\pi$
$384$	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	−0.990305	−	0.138908i	$-0.955641\pi$
$397$	−22.4994	−	22.4994i	−1.12921	−	1.12921i	−0.138908	−	0.990305i	$-0.544359\pi$
$398$	−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	−0.434165	+	0.900834i	$0.642956\pi$
$401$	−26.7333	+	26.7333i	−1.33500	+	1.33500i	−0.900834	+	0.434165i	$0.857044\pi$
$402$	−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	$-0.773901\pi$
$409$	−2.14554	+	2.14554i	−0.106090	+	0.106090i	0.652069	+	0.758159i	$0.273901\pi$
$410$	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	$0.361967\pi$
$419$			37.1497i			1.81488i	−0.420178	+	0.907442i	$0.638033\pi$
$420$	−9.96525	−	6.68145i	−0.486254	−	0.326021i
$421$	18.7201	−	18.7201i	0.912361	−	0.912361i	−0.0840970	−	0.996458i	$-0.526801\pi$
$421$	18.7201	−	18.7201i	0.912361	−	0.912361i	0.996458	+	0.0840970i	$0.0268006\pi$
$422$	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	$-0.305960\pi$
$431$	−5.13505	−	5.13505i	−0.247347	−	0.247347i	−0.819881	+	0.572534i	$0.805960\pi$
$432$	8.73829	−	42.8634i	0.420421	−	2.06227i
$433$		−	6.80226i		−	0.326896i	−0.986552	−	0.163448i	$-0.947738\pi$
$433$		−	6.80226i		−	0.326896i	0.986552	−	0.163448i	$-0.0522615\pi$
$434$	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	$0.126453\pi$
$439$			16.2128i			0.773794i	−0.922123	+	0.386897i	$0.873547\pi$
$440$	−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	$0.0462799\pi$
$443$			6.09878i			0.289762i	−0.989449	+	0.144881i	$0.953720\pi$
$444$	−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	$-0.968036\pi$
$449$	−18.9586	+	18.9586i	−0.894714	+	0.894714i	0.100249	+	0.994962i	$0.468036\pi$
$450$	−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	$-0.897903\pi$
$457$	−13.5475	+	13.5475i	−0.633726	+	0.633726i	0.315275	+	0.949000i	$0.397903\pi$
$458$			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	$-0.216789\pi$
$461$	3.16238	+	3.16238i	0.147287	+	0.147287i	−0.629618	+	0.776905i	$0.716789\pi$
$462$	0.521186	+	2.64207i	0.0242478	+	0.122920i
$463$	25.0898	+	25.0898i	1.16602	+	1.16602i	0.983134	+	0.182885i	$0.0585437\pi$
$463$	25.0898	+	25.0898i	1.16602	+	1.16602i	0.182885	+	0.983134i	$0.441456\pi$
$464$		−	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	$-0.793141\pi$
$479$	−4.18209	+	4.18209i	−0.191084	+	0.191084i	0.605080	+	0.796165i	$0.293141\pi$
$480$	−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	$-0.818289\pi$
$487$	−6.64419	+	6.64419i	−0.301077	+	0.301077i	0.540358	+	0.841435i	$0.318289\pi$
$488$	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	$-0.679168\pi$
$499$	6.97195	−	6.97195i	0.312107	−	0.312107i	0.845725	+	0.533618i	$0.179168\pi$
$500$	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	$0.0947499\pi$
$503$			13.1556i			0.586579i	−0.956024	+	0.293289i	$0.905250\pi$
$504$	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	$-0.104595\pi$
$509$	14.0732	+	14.0732i	0.623784	+	0.623784i	−0.322713	+	0.946497i	$0.604595\pi$
$510$	−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	$0.0918865\pi$
$521$			12.9958i			0.569355i	−0.958623	+	0.284678i	$0.908113\pi$
$522$	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	$-0.343132\pi$
$541$	−9.48746	−	9.48746i	−0.407898	−	0.407898i	−0.881005	+	0.473107i	$0.843132\pi$
$542$		−	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	$-0.904781\pi$
$557$	−15.5976	+	15.5976i	−0.660892	+	0.660892i	0.294699	+	0.955590i	$0.404781\pi$
$558$	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	$-0.968582\pi$
$571$		−	4.70947i		−	0.197085i	0.995133	−	0.0985425i	$-0.0314181\pi$
$572$		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	−0.0462290	+	0.998931i	$0.514720\pi$
$577$	−25.1056	+	25.1056i	−1.04516	+	1.04516i	−0.998931	+	0.0462290i	$0.985280\pi$
$578$	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	$-0.366796\pi$
$587$	−12.2920	−	12.2920i	−0.507347	−	0.507347i	−0.913711	+	0.406364i	$0.866796\pi$
$588$	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	$-0.785048\pi$
$593$	−3.78428	+	3.78428i	−0.155402	+	0.155402i	0.625124	+	0.780526i	$0.285048\pi$
$594$	−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	$-0.958559\pi$
$599$		−	6.35465i		−	0.259644i	0.991537	−	0.129822i	$-0.0414406\pi$
$600$	−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	0.0481897	−	0.998838i	$-0.484655\pi$
$613$	25.9232	−	25.9232i	1.04703	−	1.04703i	0.998838	−	0.0481897i	$-0.0153452\pi$
$614$			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	$-0.460731\pi$
$617$	−21.5941	−	21.5941i	−0.869345	−	0.869345i	−0.992400	+	0.123055i	$0.960731\pi$
$618$	−2.43383	+	0.480107i	−0.0979030	+	0.0193127i
$619$	11.8576	+	11.8576i	0.476599	+	0.476599i	0.904042	−	0.427443i	$-0.140586\pi$
$619$	11.8576	+	11.8576i	0.476599	+	0.476599i	−0.427443	+	0.904042i	$0.640586\pi$
$620$		−	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	$-0.0634236\pi$
$631$	19.6506	+	19.6506i	0.782280	+	0.782280i	−0.197935	+	0.980215i	$0.563424\pi$
$632$	−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	$-0.764144\pi$
$643$	−1.59295	+	1.59295i	−0.0628196	+	0.0628196i	0.674999	+	0.737819i	$0.264144\pi$
$644$	−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	$0.0805152\pi$
$653$			12.7901i			0.500515i	−0.968179	+	0.250257i	$0.919485\pi$
$654$	−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	$0.199894\pi$
$659$			30.1642i			1.17503i	−0.809213	+	0.587515i	$0.800106\pi$
$660$	1.42350	−	2.12312i	0.0554097	−	0.0826424i
$661$	17.7053	+	17.7053i	0.688656	+	0.688656i	0.961935	−	0.273279i	$-0.0881083\pi$
$661$	17.7053	+	17.7053i	0.688656	+	0.688656i	−0.273279	+	0.961935i	$0.588108\pi$
$662$	−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	$-0.702340\pi$
$673$		−	41.7501i		−	1.60935i	0.593716	−	0.804674i	$-0.297660\pi$
$674$	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	$0.150183\pi$
$677$			23.6516i			0.909004i	−0.890746	+	0.454502i	$0.849817\pi$
$678$	−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	$-0.799992\pi$
$683$	−5.78078	+	5.78078i	−0.221195	+	0.221195i	0.587806	+	0.809002i	$0.299992\pi$
$684$	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	$-0.657974\pi$
$691$	10.5985	−	10.5985i	0.403187	−	0.403187i	0.879355	+	0.476167i	$0.157974\pi$
$692$			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	$-0.493160\pi$
$709$	−26.0488	−	26.0488i	−0.978284	−	0.978284i	−0.999769	+	0.0214855i	$0.993160\pi$
$710$	−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	$0.161671\pi$
$727$			26.2267i			0.972694i	−0.873766	+	0.486347i	$0.838329\pi$
$728$		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	$-0.669812\pi$
$733$	9.54380	−	9.54380i	0.352508	−	0.352508i	0.861042	+	0.508534i	$0.169812\pi$
$734$	−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	$-0.321155\pi$
$739$	−8.52260	−	8.52260i	−0.313509	−	0.313509i	−0.846267	+	0.532758i	$0.821155\pi$
$740$	−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	$-0.116315\pi$
$743$	15.7181	+	15.7181i	0.576641	+	0.576641i	−0.357336	+	0.933976i	$0.616315\pi$
$744$	−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	$0.239887\pi$
$751$			37.5050i			1.36858i	−0.729212	+	0.684288i	$0.760113\pi$
$752$	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	0.386350	−	0.922352i	$-0.373736\pi$
$761$	36.1022	−	36.1022i	1.30870	−	1.30870i	0.922352	−	0.386350i	$-0.126264\pi$
$762$	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	−0.171005	+	0.985270i	$0.554701\pi$
$769$	−32.0645	+	32.0645i	−1.15627	+	1.15627i	−0.985270	+	0.171005i	$0.945299\pi$
$770$			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	0.999248	+	0.0387789i	$0.0123468\pi$
$773$	28.8601	+	28.8601i	1.03803	+	1.03803i	0.0387789	+	0.999248i	$0.487653\pi$
$774$	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	$-0.295813\pi$
$787$	−5.69039	−	5.69039i	−0.202841	−	0.202841i	−0.801216	+	0.598375i	$0.795813\pi$
$788$	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	$-0.750268\pi$
$809$		−	40.1905i		−	1.41302i	0.707702	−	0.706511i	$-0.249732\pi$
$810$	14.4206	+	14.6047i	0.506688	+	0.513158i
$811$	−24.5095	+	24.5095i	−0.860644	+	0.860644i	−0.991413	−	0.130769i	$-0.958255\pi$
$811$	−24.5095	+	24.5095i	−0.860644	+	0.860644i	0.130769	+	0.991413i	$0.458255\pi$
$812$	−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	$-0.473630\pi$
$821$	−26.1838	−	26.1838i	−0.913821	−	0.913821i	−0.996570	+	0.0827498i	$0.973630\pi$
$822$	−7.58635	−	5.08646i	−0.264604	−	0.177411i
$823$		−	38.2880i		−	1.33464i	−0.744773	−	0.667318i	$-0.767442\pi$
$823$		−	38.2880i		−	1.33464i	0.744773	−	0.667318i	$-0.232558\pi$
$824$	−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	$-0.663754\pi$
$827$	10.8851	−	10.8851i	0.378512	−	0.378512i	0.870565	+	0.492053i	$0.163754\pi$
$828$	−70.1137	+	28.7818i	−2.43662	+	1.00024i
$829$			5.39042i			0.187217i	0.995609	+	0.0936085i	$0.0298402\pi$
$829$			5.39042i			0.187217i	−0.995609	+	0.0936085i	$0.970160\pi$
$830$	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	−0.413620	+	0.910450i	$0.635736\pi$
$839$	−38.3523	+	38.3523i	−1.32407	+	1.32407i	−0.910450	+	0.413620i	$0.864264\pi$
$840$	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	$-0.475513\pi$
$853$	−26.8752	−	26.8752i	−0.920190	−	0.920190i	−0.997042	+	0.0768525i	$0.975513\pi$
$854$		−	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	$-0.150062\pi$
$863$	12.8305	+	12.8305i	0.436756	+	0.436756i	−0.454163	+	0.890919i	$0.650062\pi$
$864$	−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	$-0.892977\pi$
$877$	−18.1856	+	18.1856i	−0.614085	+	0.614085i	0.329923	+	0.944008i	$0.392977\pi$
$878$	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	$-0.878666\pi$
$883$		−	22.1092i		−	0.744035i	0.928226	−	0.372018i	$-0.121334\pi$
$884$		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	$0.116603\pi$
$887$			21.3351i			0.716362i	−0.933652	+	0.358181i	$0.883397\pi$
$888$	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	$0.0605222\pi$
$907$			11.3836i			0.377985i	−0.981979	+	0.188992i	$0.939478\pi$
$908$	−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	$0.117501\pi$
$911$			21.7806i			0.721625i	−0.932638	+	0.360812i	$0.882499\pi$
$912$	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	$-0.102979\pi$
$929$	19.2087	+	19.2087i	0.630218	+	0.630218i	−0.317905	+	0.948123i	$0.602979\pi$
$930$	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	$-0.386999\pi$
$941$	−18.1003	−	18.1003i	−0.590052	−	0.590052i	−0.937645	+	0.347593i	$0.886999\pi$
$942$	−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	$-0.598875\pi$
$947$	19.8947	−	19.8947i	0.646491	−	0.646491i	0.952143	+	0.305652i	$0.0988746\pi$
$948$	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	$-0.704371\pi$
$967$	6.28251	−	6.28251i	0.202032	−	0.202032i	0.800870	+	0.598838i	$0.204371\pi$
$968$	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	$-0.681382\pi$
$971$		−	52.4745i		−	1.68399i	0.539488	−	0.841993i	$-0.318618\pi$
$972$	−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	$-0.150758\pi$
$977$	13.5597	+	13.5597i	0.433812	+	0.433812i	−0.456111	+	0.889923i	$0.650758\pi$
$978$	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	$-0.665903\pi$
$983$	11.5787	−	11.5787i	0.369303	−	0.369303i	0.867223	+	0.497920i	$0.165903\pi$
$984$	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.239.2	yes	48
3.2	odd	2	inner	507.2.f.g.239.23	yes	48
13.2	odd	12		507.2.k.k.488.1		96
13.3	even	3		507.2.k.k.188.23		96
13.4	even	6		507.2.k.k.80.24		96
13.5	odd	4	inner	507.2.f.g.437.2	yes	48
13.6	odd	12		507.2.k.k.89.24		96
13.7	odd	12		507.2.k.k.89.2		96
13.8	odd	4	inner	507.2.f.g.437.24	yes	48
13.9	even	3		507.2.k.k.80.2		96
13.10	even	6		507.2.k.k.188.1		96
13.11	odd	12		507.2.k.k.488.23		96
13.12	even	2	inner	507.2.f.g.239.24	yes	48
39.2	even	12		507.2.k.k.488.24		96
39.5	even	4	inner	507.2.f.g.437.23	yes	48
39.8	even	4	inner	507.2.f.g.437.1	yes	48
39.11	even	12		507.2.k.k.488.2		96
39.17	odd	6		507.2.k.k.80.1		96
39.20	even	12		507.2.k.k.89.23		96
39.23	odd	6		507.2.k.k.188.24		96
39.29	odd	6		507.2.k.k.188.2		96
39.32	even	12		507.2.k.k.89.1		96
39.35	odd	6		507.2.k.k.80.23		96
39.38	odd	2	inner	507.2.f.g.239.1	✓	48

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

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

\(f(q)\)	\(=\)	\(q+(-1.82526 - 1.82526i) q^{2} +(1.43862 + 0.964559i) q^{3} +4.66316i q^{4} +(0.624703 + 0.624703i) q^{5} +(-0.865285 - 4.38643i) q^{6} +(1.18894 + 1.18894i) q^{7} +(4.86096 - 4.86096i) q^{8} +(1.13925 + 2.77527i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^9	\( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) 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

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