LMFDB - Embedded newform 507.2.f.g.239.4

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			239.4
Character	$\chi$	$=$	507.239
Dual form			507.2.f.g.437.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42721 - 1.42721i) q^{2} +(-1.57050 + 0.730430i) q^{3} +2.07385i q^{4} +(1.72251 + 1.72251i) q^{5} +(3.28391 + 1.19895i) q^{6} +(2.20041 + 2.20041i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.93294 - 2.29428i) q^{9} +O(q^{10})$	\(q+(-1.42721 - 1.42721i) q^{2} +(-1.57050 + 0.730430i) q^{3} +2.07385i q^{4} +(1.72251 + 1.72251i) q^{5} +(3.28391 + 1.19895i) q^{6} +(2.20041 + 2.20041i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.93294 - 2.29428i) q^{9} -4.91676i q^{10} +(-1.95698 + 1.95698i) q^{11} +(-1.51480 - 3.25697i) q^{12} -6.28089i q^{14} +(-3.96338 - 1.44703i) q^{15} +3.84686 q^{16} -5.78844 q^{17} +(-6.03313 + 0.515706i) q^{18} +(-1.06036 + 1.06036i) q^{19} +(-3.57222 + 3.57222i) q^{20} +(-5.06299 - 1.84850i) q^{21} +5.58604 q^{22} -3.86536 q^{23} +(-0.0885372 + 0.242501i) q^{24} +0.934091i q^{25} +(-1.35988 + 5.01505i) q^{27} +(-4.56331 + 4.56331i) q^{28} -2.92300i q^{29} +(3.59135 + 7.72178i) q^{30} +(-3.56552 + 3.56552i) q^{31} +(-5.70105 - 5.70105i) q^{32} +(1.64400 - 4.50288i) q^{33} +(8.26131 + 8.26131i) q^{34} +7.58047i q^{35} +(4.75799 + 4.00863i) q^{36} +(2.83916 + 2.83916i) q^{37} +3.02672 q^{38} +0.363080 q^{40} +(4.79962 + 4.79962i) q^{41} +(4.58775 + 9.86414i) q^{42} -1.84251i q^{43} +(-4.05848 - 4.05848i) q^{44} +(7.28144 - 0.622410i) q^{45} +(5.51668 + 5.51668i) q^{46} +(0.115676 - 0.115676i) q^{47} +(-6.04149 + 2.80986i) q^{48} +2.68362i q^{49} +(1.33314 - 1.33314i) q^{50} +(9.09075 - 4.22805i) q^{51} +10.0745i q^{53} +(9.09835 - 5.21670i) q^{54} -6.74185 q^{55} +0.463814 q^{56} +(0.890781 - 2.43983i) q^{57} +(-4.17173 + 4.17173i) q^{58} +(-1.22007 + 1.22007i) q^{59} +(3.00092 - 8.21944i) q^{60} -5.39592 q^{61} +10.1775 q^{62} +(9.30163 - 0.795094i) q^{63} +8.57945i q^{64} +(-8.77288 + 4.08021i) q^{66} +(-9.65781 + 9.65781i) q^{67} -12.0043i q^{68} +(6.07055 - 2.82338i) q^{69} +(10.8189 - 10.8189i) q^{70} +(-0.239135 - 0.239135i) q^{71} +(-0.0380824 - 0.445518i) q^{72} +(-8.54904 - 8.54904i) q^{73} -8.10415i q^{74} +(-0.682288 - 1.46699i) q^{75} +(-2.19903 - 2.19903i) q^{76} -8.61233 q^{77} +10.4089 q^{79} +(6.62625 + 6.62625i) q^{80} +(-1.52746 - 8.86943i) q^{81} -13.7001i q^{82} +(2.83841 + 2.83841i) q^{83} +(3.83350 - 10.4999i) q^{84} +(-9.97066 - 9.97066i) q^{85} +(-2.62965 + 2.62965i) q^{86} +(2.13505 + 4.59057i) q^{87} +0.412503i q^{88} +(3.00755 - 3.00755i) q^{89} +(-11.2804 - 9.50383i) q^{90} -8.01616i q^{92} +(2.99529 - 8.20402i) q^{93} -0.330188 q^{94} -3.65298 q^{95} +(13.1177 + 4.78928i) q^{96} +(-6.99731 + 6.99731i) q^{97} +(3.83008 - 3.83008i) q^{98} +(0.707134 + 8.27261i) 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 $

$2$	−1.42721	−	1.42721i	−1.00919	−	1.00919i	−0.999957	−	0.00923105i	$-0.997062\pi$
$2$	−1.42721	−	1.42721i	−1.00919	−	1.00919i	−0.00923105	−	0.999957i	$-0.502938\pi$
$3$	−1.57050	+	0.730430i	−0.906729	+	0.421714i
$3$	−1.57050	+	0.730430i	−0.906729	+	0.421714i
$4$			2.07385i			1.03692i
$5$	1.72251	+	1.72251i	0.770331	+	0.770331i	0.978164	−	0.207834i	$-0.0666413\pi$
$5$	1.72251	+	1.72251i	0.770331	+	0.770331i	−0.207834	+	0.978164i	$0.566641\pi$
$6$	3.28391	+	1.19895i	1.34065	+	0.489471i
$7$	2.20041	+	2.20041i	0.831677	+	0.831677i	0.987746	−	0.156069i	$-0.0498822\pi$
$7$	2.20041	+	2.20041i	0.831677	+	0.831677i	−0.156069	+	0.987746i	$0.549882\pi$
$8$	0.105393	−	0.105393i	0.0372619	−	0.0372619i
$9$	1.93294	−	2.29428i	0.644314	−	0.764761i
$10$		−	4.91676i		−	1.55482i
$11$	−1.95698	+	1.95698i	−0.590052	+	0.590052i	−0.937646	−	0.347593i	$-0.886999\pi$
$11$	−1.95698	+	1.95698i	−0.590052	+	0.590052i	0.347593	+	0.937646i	$0.386999\pi$
$12$	−1.51480	−	3.25697i	−0.437285	−	0.940208i
$13$		0			0
$13$		0			0
$14$		−	6.28089i		−	1.67864i
$15$	−3.96338	−	1.44703i	−1.02334	−	0.373622i
$16$	3.84686			0.961714
$17$	−5.78844			−1.40390			−0.701952	−	0.712225i	$-0.747688\pi$
$17$	−5.78844			−1.40390			−0.701952	+	0.712225i	$0.747688\pi$
$18$	−6.03313	+	0.515706i	−1.42202	+	0.121553i
$19$	−1.06036	+	1.06036i	−0.243264	+	0.243264i	−0.818199	−	0.574935i	$-0.805027\pi$
$19$	−1.06036	+	1.06036i	−0.243264	+	0.243264i	0.574935	+	0.818199i	$0.305027\pi$
$20$	−3.57222	+	3.57222i	−0.798773	+	0.798773i
$21$	−5.06299	−	1.84850i	−1.10484	−	0.403376i
$22$	5.58604			1.19095
$23$	−3.86536			−0.805984			−0.402992	−	0.915204i	$-0.632030\pi$
$23$	−3.86536			−0.805984			−0.402992	+	0.915204i	$0.632030\pi$
$24$	−0.0885372	+	0.242501i	−0.0180726	+	0.0495003i
$25$			0.934091i			0.186818i
$26$		0			0
$27$	−1.35988	+	5.01505i	−0.261708	+	0.965147i
$28$	−4.56331	+	4.56331i	−0.862385	+	0.862385i
$29$		−	2.92300i		−	0.542788i	−0.962468	−	0.271394i	$-0.912515\pi$
$29$		−	2.92300i		−	0.542788i	0.962468	−	0.271394i	$-0.0874846\pi$
$30$	3.59135	+	7.72178i	0.655688	+	1.40980i
$31$	−3.56552	+	3.56552i	−0.640387	+	0.640387i	−0.950651	−	0.310264i	$-0.899583\pi$
$31$	−3.56552	+	3.56552i	−0.640387	+	0.640387i	0.310264	+	0.950651i	$0.399583\pi$
$32$	−5.70105	−	5.70105i	−1.00781	−	1.00781i
$33$	1.64400	−	4.50288i	0.286184	−	0.783851i
$34$	8.26131	+	8.26131i	1.41680	+	1.41680i
$35$			7.58047i			1.28133i
$36$	4.75799	+	4.00863i	0.792998	+	0.668104i
$37$	2.83916	+	2.83916i	0.466755	+	0.466755i	0.900862	−	0.434106i	$-0.142936\pi$
$37$	2.83916	+	2.83916i	0.466755	+	0.466755i	−0.434106	+	0.900862i	$0.642936\pi$
$38$	3.02672			0.490999
$39$		0			0
$40$	0.363080			0.0574080
$41$	4.79962	+	4.79962i	0.749574	+	0.749574i	0.974399	−	0.224825i	$-0.0721810\pi$
$41$	4.79962	+	4.79962i	0.749574	+	0.749574i	−0.224825	+	0.974399i	$0.572181\pi$
$42$	4.58775	+	9.86414i	0.707905	+	1.52207i
$43$		−	1.84251i		−	0.280981i	−0.990082	−	0.140490i	$-0.955132\pi$
$43$		−	1.84251i		−	0.280981i	0.990082	−	0.140490i	$-0.0448679\pi$
$44$	−4.05848	−	4.05848i	−0.611839	−	0.611839i
$45$	7.28144	−	0.622410i	1.08545	−	0.0927834i
$46$	5.51668	+	5.51668i	0.813390	+	0.813390i
$47$	0.115676	−	0.115676i	0.0168731	−	0.0168731i	−0.698620	−	0.715493i	$-0.746202\pi$
$47$	0.115676	−	0.115676i	0.0168731	−	0.0168731i	0.715493	+	0.698620i	$0.246202\pi$
$48$	−6.04149	+	2.80986i	−0.872014	+	0.405568i
$49$			2.68362i			0.383374i
$50$	1.33314	−	1.33314i	0.188535	−	0.188535i
$51$	9.09075	−	4.22805i	1.27296	−	0.592046i
$52$		0			0
$53$			10.0745i			1.38384i	0.721976	+	0.691918i	$0.243234\pi$
$53$			10.0745i			1.38384i	−0.721976	+	0.691918i	$0.756766\pi$
$54$	9.09835	−	5.21670i	1.23813	−	0.709902i
$55$	−6.74185			−0.909071
$56$	0.463814			0.0619797
$57$	0.890781	−	2.43983i	0.117987	−	0.323163i
$58$	−4.17173	+	4.17173i	−0.547775	+	0.547775i
$59$	−1.22007	+	1.22007i	−0.158839	+	0.158839i	−0.782052	−	0.623213i	$-0.785827\pi$
$59$	−1.22007	+	1.22007i	−0.158839	+	0.158839i	0.623213	+	0.782052i	$0.285827\pi$
$60$	3.00092	−	8.21944i	0.387417	−	1.06112i
$61$	−5.39592			−0.690876			−0.345438	−	0.938442i	$-0.612270\pi$
$61$	−5.39592			−0.690876			−0.345438	+	0.938442i	$0.612270\pi$
$62$	10.1775			1.29254
$63$	9.30163	−	0.795094i	1.17190	−	0.100172i
$64$			8.57945i			1.07243i
$65$		0			0
$66$	−8.77288	+	4.08021i	−1.07987	+	0.502240i
$67$	−9.65781	+	9.65781i	−1.17989	+	1.17989i	−0.200118	+	0.979772i	$0.564133\pi$
$67$	−9.65781	+	9.65781i	−1.17989	+	1.17989i	−0.979772	+	0.200118i	$0.935867\pi$
$68$		−	12.0043i		−	1.45574i
$69$	6.07055	−	2.82338i	0.730809	−	0.339895i
$70$	10.8189	−	10.8189i	1.29311	−	1.29311i
$71$	−0.239135	−	0.239135i	−0.0283801	−	0.0283801i	0.692774	−	0.721154i	$-0.256388\pi$
$71$	−0.239135	−	0.239135i	−0.0283801	−	0.0283801i	−0.721154	+	0.692774i	$0.756388\pi$
$72$	−0.0380824	−	0.445518i	−0.00448806	−	0.0525048i
$73$	−8.54904	−	8.54904i	−1.00059	−	1.00059i	−1.00000		0.000589733i	$-0.999812\pi$
$73$	−8.54904	−	8.54904i	−1.00059	−	1.00059i	−0.000589733	−	1.00000i	$-0.500188\pi$
$74$		−	8.10415i		−	0.942088i
$75$	−0.682288	−	1.46699i	−0.0787839	−	0.169393i
$76$	−2.19903	−	2.19903i	−0.252246	−	0.252246i
$77$	−8.61233			−0.981466
$78$		0			0
$79$	10.4089			1.17110			0.585549	−	0.810637i	$-0.300879\pi$
$79$	10.4089			1.17110			0.585549	+	0.810637i	$0.300879\pi$
$80$	6.62625	+	6.62625i	0.740838	+	0.740838i
$81$	−1.52746	−	8.86943i	−0.169718	−	0.985493i
$82$		−	13.7001i		−	1.51292i
$83$	2.83841	+	2.83841i	0.311556	+	0.311556i	0.845512	−	0.533956i	$-0.179295\pi$
$83$	2.83841	+	2.83841i	0.311556	+	0.311556i	−0.533956	+	0.845512i	$0.679295\pi$
$84$	3.83350	−	10.4999i	0.418269	−	1.14563i
$85$	−9.97066	−	9.97066i	−1.08147	−	1.08147i
$86$	−2.62965	+	2.62965i	−0.283562	+	0.283562i
$87$	2.13505	+	4.59057i	0.228901	+	0.492161i
$88$			0.412503i			0.0439730i
$89$	3.00755	−	3.00755i	0.318800	−	0.318800i	−0.529506	−	0.848306i	$-0.677623\pi$
$89$	3.00755	−	3.00755i	0.318800	−	0.318800i	0.848306	+	0.529506i	$0.177623\pi$
$90$	−11.2804	−	9.50383i	−1.18906	−	1.00179i
$91$		0			0
$92$		−	8.01616i		−	0.835743i
$93$	2.99529	−	8.20402i	0.310597	−	0.850717i
$94$	−0.330188			−0.0340563
$95$	−3.65298			−0.374788
$96$	13.1177	+	4.78928i	1.33882	+	0.488804i
$97$	−6.99731	+	6.99731i	−0.710470	+	0.710470i	−0.966633	−	0.256164i	$-0.917541\pi$
$97$	−6.99731	+	6.99731i	−0.710470	+	0.710470i	0.256164	+	0.966633i	$0.417541\pi$
$98$	3.83008	−	3.83008i	0.386897	−	0.386897i
$99$	0.707134	+	8.27261i	0.0710696	+	0.831428i
$100$	−1.93716			−0.193716
$101$	−9.23225			−0.918643			−0.459321	−	0.888270i	$-0.651907\pi$
$101$	−9.23225			−0.918643			−0.459321	+	0.888270i	$0.651907\pi$
$102$	−19.0087	−	6.94008i	−1.88214	−	0.687170i
$103$			17.2662i			1.70129i	0.525737	+	0.850647i	$0.323789\pi$
$103$			17.2662i			1.70129i	−0.525737	+	0.850647i	$0.676211\pi$
$104$		0			0
$105$	−5.53700	−	11.9051i	−0.540356	−	1.16182i
$106$	14.3784	−	14.3784i	1.39655	−	1.39655i
$107$			10.6323i			1.02786i	0.857832	+	0.513930i	$0.171811\pi$
$107$			10.6323i			1.02786i	−0.857832	+	0.513930i	$0.828189\pi$
$108$	−10.4004	−	2.82017i	−1.00078	−	0.271371i
$109$	0.625106	−	0.625106i	0.0598743	−	0.0598743i	−0.676536	−	0.736410i	$-0.736520\pi$
$109$	0.625106	−	0.625106i	0.0598743	−	0.0598743i	0.736410	+	0.676536i	$0.236520\pi$
$110$	9.62202	+	9.62202i	0.917424	+	0.917424i
$111$	−6.53271	−	2.38510i	−0.620058	−	0.226383i
$112$	8.46467	+	8.46467i	0.799836	+	0.799836i
$113$		−	6.79740i		−	0.639445i	−0.947511	−	0.319723i	$-0.896410\pi$
$113$		−	6.79740i		−	0.639445i	0.947511	−	0.319723i	$-0.103590\pi$
$114$	−4.75347	+	2.21081i	−0.445203	+	0.207061i
$115$	−6.65813	−	6.65813i	−0.620874	−	0.620874i
$116$	6.06185			0.562829
$117$		0			0
$118$	3.48258			0.320597
$119$	−12.7369	−	12.7369i	−1.16759	−	1.16759i
$120$	−0.570217	+	0.265204i	−0.0520535	+	0.0242097i
$121$			3.34044i			0.303676i
$122$	7.70110	+	7.70110i	0.697224	+	0.697224i
$123$	−11.0436	−	4.03202i	−0.995767	−	0.363555i
$124$	−7.39434	−	7.39434i	−0.664032	−	0.664032i
$125$	7.00357	−	7.00357i	0.626419	−	0.626419i
$126$	−14.4101	−	12.1406i	−1.28376	−	1.08157i
$127$			0.405664i			0.0359969i	0.999838	+	0.0179984i	$0.00572939\pi$
$127$			0.405664i			0.0359969i	−0.999838	+	0.0179984i	$0.994271\pi$
$128$	0.842566	−	0.842566i	0.0744730	−	0.0744730i
$129$	1.34583	+	2.89367i	0.118493	+	0.254773i
$130$		0			0
$131$		−	7.22040i		−	0.630850i	−0.948951	−	0.315425i	$-0.897853\pi$
$131$		−	7.22040i		−	0.630850i	0.948951	−	0.315425i	$-0.102147\pi$
$132$	9.33828	+	3.40941i	0.812793	+	0.296751i
$133$	−4.66648			−0.404635
$134$	27.5674			2.38146
$135$	−10.9809	+	6.29608i	−0.945084	+	0.541880i
$136$	−0.610059	+	0.610059i	−0.0523121	+	0.0523121i
$137$	13.9451	−	13.9451i	1.19141	−	1.19141i	0.214737	−	0.976672i	$-0.431110\pi$
$137$	13.9451	−	13.9451i	1.19141	−	1.19141i	0.976672	−	0.214737i	$-0.0688896\pi$
$138$	−12.6935	−	4.63440i	−1.08054	−	0.394506i
$139$	10.3585			0.878594			0.439297	−	0.898342i	$-0.355228\pi$
$139$	10.3585			0.878594			0.439297	+	0.898342i	$0.355228\pi$
$140$	−15.7207			−1.32864
$141$	−0.0971762	+	0.266163i	−0.00818371	+	0.0224150i
$142$			0.682592i			0.0572818i
$143$		0			0
$144$	7.43576	−	8.82577i	0.619646	−	0.735481i
$145$	5.03490	−	5.03490i	0.418126	−	0.418126i
$146$			24.4025i			2.01957i
$147$	−1.96020	−	4.21462i	−0.161674	−	0.347616i
$148$	−5.88798	+	5.88798i	−0.483989	+	0.483989i
$149$	3.44188	+	3.44188i	0.281969	+	0.281969i	0.833894	−	0.551925i	$-0.186106\pi$
$149$	3.44188	+	3.44188i	0.281969	+	0.281969i	−0.551925	+	0.833894i	$0.686106\pi$
$150$	−1.11993	+	3.06747i	−0.0914421	+	0.250458i
$151$	−3.11666	−	3.11666i	−0.253630	−	0.253630i	0.568827	−	0.822457i	$-0.307397\pi$
$151$	−3.11666	−	3.11666i	−0.253630	−	0.253630i	−0.822457	+	0.568827i	$0.807397\pi$
$152$			0.223509i			0.0181290i
$153$	−11.1887	+	13.2803i	−0.904555	+	1.07365i
$154$	12.2916	+	12.2916i	0.990485	+	0.990485i
$155$	−12.2833			−0.986619
$156$		0			0
$157$	−5.43153			−0.433483			−0.216741	−	0.976229i	$-0.569543\pi$
$157$	−5.43153			−0.433483			−0.216741	+	0.976229i	$0.569543\pi$
$158$	−14.8557	−	14.8557i	−1.18186	−	1.18186i
$159$	−7.35870	−	15.8220i	−0.583583	−	1.25476i
$160$		−	19.6402i		−	1.55270i
$161$	−8.50539	−	8.50539i	−0.670318	−	0.670318i
$162$	−10.4785	+	14.8385i	−0.823271	+	1.16583i
$163$	8.71350	+	8.71350i	0.682494	+	0.682494i	0.960562	−	0.278068i	$-0.0896939\pi$
$163$	8.71350	+	8.71350i	0.682494	+	0.682494i	−0.278068	+	0.960562i	$0.589694\pi$
$164$	−9.95367	+	9.95367i	−0.777251	+	0.777251i
$165$	10.5881	−	4.92445i	0.824281	−	0.383368i
$166$		−	8.10201i		−	0.628838i
$167$	−15.6494	+	15.6494i	−1.21099	+	1.21099i	−0.240283	+	0.970703i	$0.577240\pi$
$167$	−15.6494	+	15.6494i	−1.21099	+	1.21099i	−0.970703	+	0.240283i	$0.922760\pi$
$168$	−0.728420	+	0.338784i	−0.0561988	+	0.0261377i
$169$		0			0
$170$			28.4604i			2.18281i
$171$	0.383151	+	4.48240i	0.0293003	+	0.342778i
$172$	3.82109			0.291355
$173$	9.33141			0.709454			0.354727	−	0.934970i	$-0.384574\pi$
$173$	9.33141			0.709454			0.354727	+	0.934970i	$0.384574\pi$
$174$	3.50455	−	9.59886i	0.265679	−	0.727688i
$175$	−2.05538	+	2.05538i	−0.155372	+	0.155372i
$176$	−7.52823	+	7.52823i	−0.567462	+	0.567462i
$177$	1.02494	−	2.80729i	0.0770394	−	0.211009i
$178$	−8.58480			−0.643458
$179$	26.7156			1.99682			0.998409	−	0.0563954i	$-0.0179607\pi$
$179$	26.7156			1.99682			0.998409	+	0.0563954i	$0.0179607\pi$
$180$	1.29078	+	15.1006i	0.0962092	+	1.12553i
$181$		−	26.2746i		−	1.95297i	−0.215577	−	0.976487i	$-0.569163\pi$
$181$		−	26.2746i		−	1.95297i	0.215577	−	0.976487i	$-0.430837\pi$
$182$		0			0
$183$	8.47429	−	3.94134i	0.626438	−	0.291352i
$184$	−0.407380	+	0.407380i	−0.0300325	+	0.0300325i
$185$			9.78098i			0.719112i
$186$	−15.9837	+	7.43394i	−1.17199	+	0.545083i
$187$	11.3279	−	11.3279i	0.828377	−	0.828377i
$188$	0.239895	+	0.239895i	0.0174961	+	0.0174961i
$189$	−14.0275	+	8.04289i	−1.02035	+	0.585034i
$190$	5.21356	+	5.21356i	0.378232	+	0.378232i
$191$		−	7.70224i		−	0.557315i	−0.960391	−	0.278657i	$-0.910111\pi$
$191$		−	7.70224i		−	0.557315i	0.960391	−	0.278657i	$-0.0898894\pi$
$192$	−6.26669	−	13.4740i	−0.452260	−	0.972405i
$193$	−11.0184	−	11.0184i	−0.793124	−	0.793124i	0.188877	−	0.982001i	$-0.439515\pi$
$193$	−11.0184	−	11.0184i	−0.793124	−	0.793124i	−0.982001	+	0.188877i	$0.939515\pi$
$194$	19.9732			1.43400
$195$		0			0
$196$	−5.56541			−0.397529
$197$	18.5925	+	18.5925i	1.32466	+	1.32466i	0.909954	+	0.414709i	$0.136116\pi$
$197$	18.5925	+	18.5925i	1.32466	+	1.32466i	0.414709	+	0.909954i	$0.363884\pi$
$198$	10.7975	−	12.8160i	0.767345	−	0.910790i
$199$			13.7185i			0.972475i	0.873827	+	0.486238i	$0.161631\pi$
$199$			13.7185i			0.972475i	−0.873827	+	0.486238i	$0.838369\pi$
$200$	0.0984463	+	0.0984463i	0.00696120	+	0.00696120i
$201$	8.11324	−	22.2220i	0.572264	−	1.56742i
$202$	13.1763	+	13.1763i	0.927084	+	0.927084i
$203$	6.43180	−	6.43180i	0.451424	−	0.451424i
$204$	8.76833	+	18.8528i	0.613906	+	1.31996i
$205$			16.5348i			1.15484i
$206$	24.6425	−	24.6425i	1.71693	−	1.71693i
$207$	−7.47153	+	8.86823i	−0.519307	+	0.616385i
$208$		0			0
$209$		−	4.15023i		−	0.287078i
$210$	−9.08864	+	24.8935i	−0.627176	+	1.71782i
$211$	21.5434			1.48311			0.741555	−	0.670893i	$-0.234089\pi$
$211$	21.5434			1.48311			0.741555	+	0.670893i	$0.234089\pi$
$212$	−20.8929			−1.43493
$213$	0.550234	+	0.200890i	0.0377014	+	0.0137648i
$214$	15.1745	−	15.1745i	1.03730	−	1.03730i
$215$	3.17375	−	3.17375i	0.216448	−	0.216448i
$216$	0.385228	+	0.671870i	0.0262115	+	0.0457150i
$217$	−15.6912			−1.06519
$218$	−1.78431			−0.120849
$219$	19.6708	+	7.18179i	1.32923	+	0.485301i
$220$		−	13.9816i		−	0.942636i
$221$		0			0
$222$	5.91951	+	12.7276i	0.397292	+	0.854218i
$223$	−10.4949	+	10.4949i	−0.702792	+	0.702792i	−0.965009	−	0.262217i	$-0.915547\pi$
$223$	−10.4949	+	10.4949i	−0.702792	+	0.702792i	0.262217	+	0.965009i	$0.415547\pi$
$224$		−	25.0893i		−	1.67635i
$225$	2.14307	+	1.80554i	0.142871	+	0.120370i
$226$	−9.70130	+	9.70130i	−0.645321	+	0.645321i
$227$	1.61344	+	1.61344i	0.107088	+	0.107088i	0.758621	−	0.651533i	$-0.225874\pi$
$227$	1.61344	+	1.61344i	0.107088	+	0.107088i	−0.651533	+	0.758621i	$0.725874\pi$
$228$	5.05982	+	1.84734i	0.335095	+	0.122343i
$229$	1.83952	+	1.83952i	0.121559	+	0.121559i	0.765269	−	0.643711i	$-0.222606\pi$
$229$	1.83952	+	1.83952i	0.121559	+	0.121559i	−0.643711	+	0.765269i	$0.722606\pi$
$230$			19.0051i			1.25316i
$231$	13.5257	−	6.29071i	0.889924	−	0.413898i
$232$	−0.308063	−	0.308063i	−0.0202253	−	0.0202253i
$233$	16.4441			1.07729			0.538645	−	0.842533i	$-0.318936\pi$
$233$	16.4441			1.07729			0.538645	+	0.842533i	$0.318936\pi$
$234$		0			0
$235$	0.398508			0.0259958
$236$	−2.53023	−	2.53023i	−0.164704	−	0.164704i
$237$	−16.3473	+	7.60301i	−1.06187	+	0.493868i
$238$			36.3566i			2.35665i
$239$	−7.33986	−	7.33986i	−0.474776	−	0.474776i	0.428680	−	0.903456i	$-0.358979\pi$
$239$	−7.33986	−	7.33986i	−0.474776	−	0.474776i	−0.903456	+	0.428680i	$0.858979\pi$
$240$	−15.2466	−	5.56652i	−0.984161	−	0.359317i
$241$	−4.16468	−	4.16468i	−0.268271	−	0.268271i	0.560132	−	0.828403i	$-0.310750\pi$
$241$	−4.16468	−	4.16468i	−0.268271	−	0.268271i	−0.828403	+	0.560132i	$0.810750\pi$
$242$	4.76750	−	4.76750i	0.306466	−	0.306466i
$243$	8.87738	+	12.8137i	0.569484	+	0.822002i
$244$		−	11.1903i		−	0.716385i
$245$	−4.62256	+	4.62256i	−0.295325	+	0.295325i
$246$	10.0070	+	21.5160i	0.638021	+	1.37181i
$247$		0			0
$248$			0.751559i			0.0477241i
$249$	−6.53099	−	2.38447i	−0.413885	−	0.151109i
$250$	−19.9911			−1.26435
$251$	−0.222154			−0.0140222			−0.00701111	−	0.999975i	$-0.502232\pi$
$251$	−0.222154			−0.0140222			−0.00701111	+	0.999975i	$0.502232\pi$
$252$	1.64890	+	19.2901i	0.103871	+	1.21517i
$253$	7.56445	−	7.56445i	0.475573	−	0.475573i
$254$	0.578967	−	0.578967i	0.0363276	−	0.0363276i
$255$	22.9418	+	8.37605i	1.43667	+	0.524529i
$256$	14.7539			0.922117
$257$	25.2863			1.57732			0.788658	−	0.614832i	$-0.210776\pi$
$257$	25.2863			1.57732			0.788658	+	0.614832i	$0.210776\pi$
$258$	2.20909	−	6.05064i	0.137532	−	0.376696i
$259$			12.4946i			0.776379i
$260$		0			0
$261$	−6.70619	−	5.65000i	−0.415103	−	0.349726i
$262$	−10.3050	+	10.3050i	−0.636646	+	0.636646i
$263$		−	4.89126i		−	0.301608i	−0.988564	−	0.150804i	$-0.951814\pi$
$263$		−	4.89126i		−	0.301608i	0.988564	−	0.150804i	$-0.0481863\pi$
$264$	−0.301305	−	0.647836i	−0.0185440	−	0.0398715i
$265$	−17.3534	+	17.3534i	−1.06601	+	1.06601i
$266$	6.66003	+	6.66003i	0.408353	+	0.408353i
$267$	−2.52655	+	6.92016i	−0.154622	+	0.423507i
$268$	−20.0288	−	20.0288i	−1.22345	−	1.22345i
$269$			21.1450i			1.28923i	0.764506	+	0.644616i	$0.222983\pi$
$269$			21.1450i			1.28923i	−0.764506	+	0.644616i	$0.777017\pi$
$270$	24.6578	+	6.68619i	1.50063	+	0.406908i
$271$	−1.34577	−	1.34577i	−0.0817494	−	0.0817494i	0.665050	−	0.746799i	$-0.268410\pi$
$271$	−1.34577	−	1.34577i	−0.0817494	−	0.0817494i	−0.746799	+	0.665050i	$0.768410\pi$
$272$	−22.2673			−1.35015
$273$		0			0
$274$	−39.8051			−2.40471
$275$	−1.82800	−	1.82800i	−0.110233	−	0.110233i
$276$	5.85525	+	12.5894i	0.352445	+	0.757792i
$277$			3.95003i			0.237334i	0.992934	+	0.118667i	$0.0378621\pi$
$277$			3.95003i			0.237334i	−0.992934	+	0.118667i	$0.962138\pi$
$278$	−14.7837	−	14.7837i	−0.886667	−	0.886667i
$279$	1.28836	+	15.0723i	0.0771322	+	0.902353i
$280$	0.798925	+	0.798925i	0.0477449	+	0.0477449i
$281$	3.08435	−	3.08435i	0.183997	−	0.183997i	−0.609098	−	0.793095i	$-0.708468\pi$
$281$	3.08435	−	3.08435i	0.183997	−	0.183997i	0.793095	+	0.609098i	$0.208468\pi$
$282$	0.518561	−	0.241180i	0.0308799	−	0.0143620i
$283$		−	18.4359i		−	1.09590i	−0.836510	−	0.547951i	$-0.815408\pi$
$283$		−	18.4359i		−	1.09590i	0.836510	−	0.547951i	$-0.184592\pi$
$284$	0.495930	−	0.495930i	0.0294280	−	0.0294280i
$285$	5.73701	−	2.66825i	0.339831	−	0.158053i
$286$		0			0
$287$			21.1223i			1.24681i
$288$	−24.0996	+	2.06001i	−1.42008	+	0.121387i
$289$	16.5060			0.970944
$290$	−14.3717			−0.843936
$291$	5.87824	−	16.1003i	0.344588	−	0.943818i
$292$	17.7294	−	17.7294i	1.03753	−	1.03753i
$293$	−11.0702	+	11.0702i	−0.646728	+	0.646728i	−0.952201	−	0.305473i	$-0.901186\pi$
$293$	−11.0702	+	11.0702i	−0.646728	+	0.646728i	0.305473	+	0.952201i	$0.401186\pi$
$294$	−3.21754	+	8.81275i	−0.187651	+	0.513970i
$295$	−4.20316			−0.244717
$296$	0.598453			0.0347844
$297$	−7.15312	−	12.4756i	−0.415066	−	0.723909i
$298$		−	9.82454i		−	0.569121i
$299$		0			0
$300$	3.04231	−	1.41496i	0.175648	−	0.0816928i
$301$	4.05429	−	4.05429i	0.233685	−	0.233685i
$302$			8.89625i			0.511922i
$303$	14.4992	−	6.74351i	0.832960	−	0.387405i
$304$	−4.07907	+	4.07907i	−0.233951	+	0.233951i
$305$	−9.29453	−	9.29453i	−0.532203	−	0.532203i
$306$	34.9224	−	2.98513i	1.99638	−	0.170649i
$307$	4.22784	+	4.22784i	0.241295	+	0.241295i	0.817386	−	0.576090i	$-0.195422\pi$
$307$	4.22784	+	4.22784i	0.241295	+	0.241295i	−0.576090	+	0.817386i	$0.695422\pi$
$308$		−	17.8606i		−	1.01770i
$309$	−12.6118	−	27.1166i	−0.717460	−	1.54261i
$310$	17.5308	+	17.5308i	0.995684	+	0.995684i
$311$	−20.8485			−1.18221			−0.591106	−	0.806594i	$-0.701308\pi$
$311$	−20.8485			−1.18221			−0.591106	+	0.806594i	$0.701308\pi$
$312$		0			0
$313$	6.93682			0.392092			0.196046	−	0.980595i	$-0.437190\pi$
$313$	6.93682			0.392092			0.196046	+	0.980595i	$0.437190\pi$
$314$	7.75192	+	7.75192i	0.437466	+	0.437466i
$315$	17.3917	+	14.6526i	0.979913	+	0.825581i
$316$			21.5865i			1.21434i
$317$	7.43185	+	7.43185i	0.417414	+	0.417414i	0.884311	−	0.466897i	$-0.154628\pi$
$317$	7.43185	+	7.43185i	0.417414	+	0.417414i	−0.466897	+	0.884311i	$0.654628\pi$
$318$	−12.0788	+	33.0836i	−0.677348	+	1.85524i
$319$	5.72026	+	5.72026i	0.320273	+	0.320273i
$320$	−14.7782	+	14.7782i	−0.826127	+	0.826127i
$321$	−7.76613	−	16.6980i	−0.433463	−	0.931990i
$322$			24.2779i			1.35296i
$323$	6.13786	−	6.13786i	0.341520	−	0.341520i
$324$	18.3938	−	3.16772i	1.02188	−	0.175984i
$325$		0			0
$326$		−	24.8719i		−	1.37753i
$327$	−0.525133	+	1.43832i	−0.0290399	+	0.0795395i
$328$	1.01169			0.0558611
$329$	0.509071			0.0280660
$330$	−22.1396	−	8.08317i	−1.21875	−	0.444964i
$331$	−15.3800	+	15.3800i	−0.845360	+	0.845360i	−0.989550	−	0.144190i	$-0.953942\pi$
$331$	−15.3800	+	15.3800i	−0.845360	+	0.845360i	0.144190	+	0.989550i	$0.453942\pi$
$332$	−5.88643	+	5.88643i	−0.323060	+	0.323060i
$333$	12.0018	−	1.02590i	0.657693	−	0.0562189i
$334$	44.6699			2.44423
$335$	−33.2714			−1.81781
$336$	−19.4766	−	7.11091i	−1.06254	−	0.387932i
$337$		−	33.1734i		−	1.80707i	−0.428512	−	0.903536i	$-0.640962\pi$
$337$		−	33.1734i		−	1.80707i	0.428512	−	0.903536i	$-0.359038\pi$
$338$		0			0
$339$	4.96502	+	10.6753i	0.269663	+	0.579804i
$340$	20.6776	−	20.6776i	1.12140	−	1.12140i
$341$		−	13.9553i		−	0.755724i
$342$	5.85048	−	6.94416i	0.316358	−	0.375497i
$343$	9.49781	−	9.49781i	0.512834	−	0.512834i
$344$	−0.194187	−	0.194187i	−0.0104699	−	0.0104699i
$345$	15.3199	+	5.59330i	0.824796	+	0.301133i
$346$	−13.3179	−	13.3179i	−0.715973	−	0.715973i
$347$		−	33.6849i		−	1.80830i	−0.427216	−	0.904150i	$-0.640505\pi$
$347$		−	33.6849i		−	1.80830i	0.427216	−	0.904150i	$-0.359495\pi$
$348$	−9.52014	+	4.42776i	−0.510333	+	0.237353i
$349$	14.2744	+	14.2744i	0.764089	+	0.764089i	0.977059	−	0.212970i	$-0.0683137\pi$
$349$	14.2744	+	14.2744i	0.764089	+	0.764089i	−0.212970	+	0.977059i	$0.568314\pi$
$350$	5.86692			0.313600
$351$		0			0
$352$	22.3137			1.18932
$353$	−12.7414	−	12.7414i	−0.678157	−	0.678157i	0.281426	−	0.959583i	$-0.409193\pi$
$353$	−12.7414	−	12.7414i	−0.678157	−	0.678157i	−0.959583	+	0.281426i	$0.909193\pi$
$354$	−5.46939	+	2.54378i	−0.290695	+	0.135200i
$355$		−	0.823827i		−	0.0437242i
$356$	6.23719	+	6.23719i	0.330570	+	0.330570i
$357$	29.3068	+	10.6999i	1.55108	+	0.566300i
$358$	−38.1287	−	38.1287i	−2.01516	−	2.01516i
$359$	−17.0308	+	17.0308i	−0.898849	+	0.898849i	−0.995334	−	0.0964857i	$-0.969240\pi$
$359$	−17.0308	+	17.0308i	−0.898849	+	0.898849i	0.0964857	+	0.995334i	$0.469240\pi$
$360$	0.701813	−	0.833007i	0.0369888	−	0.0439033i
$361$			16.7513i			0.881645i
$362$	−37.4993	+	37.4993i	−1.97092	+	1.97092i
$363$	−2.43996	−	5.24616i	−0.128064	−	0.275352i
$364$		0			0
$365$		−	29.4516i		−	1.54157i
$366$	−17.7197	−	6.46946i	−0.926223	−	0.338164i
$367$	−18.8412			−0.983502			−0.491751	−	0.870736i	$-0.663643\pi$
$367$	−18.8412			−0.983502			−0.491751	+	0.870736i	$0.663643\pi$
$368$	−14.8695			−0.775126
$369$	20.2891	−	1.73429i	1.05621	−	0.0902834i
$370$	13.9595	−	13.9595i	0.725719	−	0.725719i
$371$	−22.1680	+	22.1680i	−1.15090	+	1.15090i
$372$	17.0139	+	6.21177i	0.882128	+	0.322065i
$373$	−17.9702			−0.930463			−0.465231	−	0.885189i	$-0.654029\pi$
$373$	−17.9702			−0.930463			−0.465231	+	0.885189i	$0.654029\pi$
$374$	−32.3345			−1.67198
$375$	−5.88349	+	16.1147i	−0.303822	+	0.832162i
$376$		−	0.0243828i		−	0.00125745i
$377$		0			0
$378$	31.4990	+	8.54123i	1.62013	+	0.439313i
$379$	11.4372	−	11.4372i	0.587491	−	0.587491i	−0.349460	−	0.936951i	$-0.613635\pi$
$379$	11.4372	−	11.4372i	0.587491	−	0.587491i	0.936951	+	0.349460i	$0.113635\pi$
$380$		−	7.57572i		−	0.388626i
$381$	−0.296309	−	0.637095i	−0.0151804	−	0.0326394i
$382$	−10.9927	+	10.9927i	−0.562436	+	0.562436i
$383$	−11.9464	−	11.9464i	−0.610431	−	0.610431i	0.332627	−	0.943058i	$-0.392065\pi$
$383$	−11.9464	−	11.9464i	−0.610431	−	0.610431i	−0.943058	+	0.332627i	$0.892065\pi$
$384$	−0.707814	+	1.93869i	−0.0361205	+	0.0989331i
$385$	−14.8348	−	14.8348i	−0.756054	−	0.756054i
$386$			31.4512i			1.60082i
$387$	−4.22725	−	3.56147i	−0.214883	−	0.181040i
$388$	−14.5113	−	14.5113i	−0.736702	−	0.736702i
$389$	29.3747			1.48936			0.744678	−	0.667424i	$-0.232603\pi$
$389$	29.3747			1.48936			0.744678	+	0.667424i	$0.232603\pi$
$390$		0			0
$391$	22.3744			1.13152
$392$	0.282833	+	0.282833i	0.0142852	+	0.0142852i
$393$	5.27400	+	11.3396i	0.266038	+	0.572009i
$394$		−	53.0708i		−	2.67367i
$395$	17.9295	+	17.9295i	0.902132	+	0.902132i
$396$	−17.1561	+	1.46649i	−0.862127	+	0.0736937i
$397$	11.4923	+	11.4923i	0.576781	+	0.576781i	0.934015	−	0.357234i	$-0.116280\pi$
$397$	11.4923	+	11.4923i	0.576781	+	0.576781i	−0.357234	+	0.934015i	$0.616280\pi$
$398$	19.5791	−	19.5791i	0.981411	−	0.981411i
$399$	7.32871	−	3.40854i	0.366894	−	0.170640i
$400$			3.59331i			0.179666i
$401$	−1.46255	+	1.46255i	−0.0730363	+	0.0730363i	−0.742681	−	0.669645i	$-0.766446\pi$
$401$	−1.46255	+	1.46255i	−0.0730363	+	0.0730363i	0.669645	+	0.742681i	$0.266446\pi$
$402$	−43.2946	+	20.1361i	−2.15934	+	1.00430i
$403$		0			0
$404$		−	19.1463i		−	0.952562i
$405$	12.6466	−	17.9088i	0.628416	−	0.889894i
$406$	−18.3590			−0.911144
$407$	−11.1124			−0.550820
$408$	0.512492	−	1.40370i	0.0253721	−	0.0694936i
$409$	5.77245	−	5.77245i	0.285430	−	0.285430i	−0.549840	−	0.835270i	$-0.685311\pi$
$409$	5.77245	−	5.77245i	0.285430	−	0.285430i	0.835270	+	0.549840i	$0.185311\pi$
$410$	23.5986	−	23.5986i	1.16545	−	1.16545i
$411$	−11.7149	+	32.0867i	−0.577851	+	1.58272i
$412$	−35.8075			−1.76411
$413$	−5.36930			−0.264206
$414$	23.3202	−	1.99339i	1.14613	−	0.0979697i
$415$			9.77840i			0.480003i
$416$		0			0
$417$	−16.2680	+	7.56614i	−0.796647	+	0.370516i
$418$	−5.92324	+	5.92324i	−0.289715	+	0.289715i
$419$		−	4.77351i		−	0.233201i	−0.993179	−	0.116601i	$-0.962800\pi$
$419$		−	4.77351i		−	0.233201i	0.993179	−	0.116601i	$-0.0371998\pi$
$420$	24.6894	−	11.4829i	1.20472	−	0.560307i
$421$	−6.32386	+	6.32386i	−0.308206	+	0.308206i	−0.844213	−	0.536007i	$-0.819932\pi$
$421$	−6.32386	+	6.32386i	−0.308206	+	0.308206i	0.536007	+	0.844213i	$0.319932\pi$
$422$	−30.7469	−	30.7469i	−1.49674	−	1.49674i
$423$	−0.0417983	−	0.488990i	−0.00203230	−	0.0237755i
$424$	1.06177	+	1.06177i	0.0515643	+	0.0515643i
$425$		−	5.40693i		−	0.262275i
$426$	−0.498586	−	1.07201i	−0.0241566	−	0.0519391i
$427$	−11.8732	−	11.8732i	−0.574586	−	0.574586i
$428$	−22.0497			−1.06581
$429$		0			0
$430$	−9.05920			−0.436874
$431$	12.8098	+	12.8098i	0.617026	+	0.617026i	0.944767	−	0.327742i	$-0.106288\pi$
$431$	12.8098	+	12.8098i	0.617026	+	0.617026i	−0.327742	+	0.944767i	$0.606288\pi$
$432$	−5.23124	+	19.2922i	−0.251688	+	0.928196i
$433$			25.5038i			1.22563i	0.790225	+	0.612816i	$0.209964\pi$
$433$			25.5038i			1.22563i	−0.790225	+	0.612816i	$0.790036\pi$
$434$	22.3947	+	22.3947i	1.07498	+	1.07498i
$435$	−4.22967	+	11.5850i	−0.202797	+	0.555456i
$436$	1.29637	+	1.29637i	0.0620850	+	0.0620850i
$437$	4.09869	−	4.09869i	0.196067	−	0.196067i
$438$	−17.8243	−	38.3242i	−0.851680	−	1.83120i
$439$		−	10.0865i		−	0.481405i	−0.970599	−	0.240702i	$-0.922622\pi$
$439$		−	10.0865i		−	0.481405i	0.970599	−	0.240702i	$-0.0773778\pi$
$440$	−0.710541	+	0.710541i	−0.0338737	+	0.0338737i
$441$	6.15698	+	5.18728i	0.293189	+	0.247013i
$442$		0			0
$443$		−	19.3012i		−	0.917028i	−0.888687	−	0.458514i	$-0.848382\pi$
$443$		−	19.3012i		−	0.917028i	0.888687	−	0.458514i	$-0.151618\pi$
$444$	4.94632	−	13.5478i	0.234742	−	0.642952i
$445$	10.3611			0.491162
$446$	29.9569			1.41850
$447$	−7.91952	−	2.89142i	−0.374580	−	0.136759i
$448$	−18.8783	+	18.8783i	−0.891917	+	0.891917i
$449$	1.34937	−	1.34937i	0.0636809	−	0.0636809i	−0.674549	−	0.738230i	$-0.735662\pi$
$449$	1.34937	−	1.34937i	0.0636809	−	0.0636809i	0.738230	+	0.674549i	$0.235662\pi$
$450$	−0.481716	−	5.63549i	−0.0227083	−	0.265660i
$451$	−18.7855			−0.884577
$452$	14.0968			0.663055
$453$	7.17122	+	2.61822i	0.336934	+	0.123014i
$454$		−	4.60544i		−	0.216144i
$455$		0			0
$456$	−0.163258	−	0.351021i	−0.00764525	−	0.0164381i
$457$	26.8350	−	26.8350i	1.25529	−	1.25529i	0.301972	−	0.953317i	$-0.402355\pi$
$457$	26.8350	−	26.8350i	1.25529	−	1.25529i	0.953317	−	0.301972i	$-0.0976450\pi$
$458$		−	5.25074i		−	0.245351i
$459$	7.87156	−	29.0293i	0.367413	−	1.35497i
$460$	13.8079	−	13.8079i	0.643798	−	0.643798i
$461$	10.2883	+	10.2883i	0.479176	+	0.479176i	0.904868	−	0.425692i	$-0.139969\pi$
$461$	10.2883	+	10.2883i	0.479176	+	0.479176i	−0.425692	+	0.904868i	$0.639969\pi$
$462$	−28.2821	−	10.3258i	−1.31580	−	0.480400i
$463$	0.201603	+	0.201603i	0.00936928	+	0.00936928i	0.711776	−	0.702407i	$-0.247891\pi$
$463$	0.201603	+	0.201603i	0.00936928	+	0.00936928i	−0.702407	+	0.711776i	$0.747891\pi$
$464$		−	11.2444i		−	0.522007i
$465$	19.2909	−	8.97210i	0.894596	−	0.416071i
$466$	−23.4692	−	23.4692i	−1.08719	−	1.08719i
$467$	13.1442			0.608242			0.304121	−	0.952633i	$-0.401637\pi$
$467$	13.1442			0.608242			0.304121	+	0.952633i	$0.401637\pi$
$468$		0			0
$469$	−42.5023			−1.96258
$470$	−0.568753	−	0.568753i	−0.0262346	−	0.0262346i
$471$	8.53021	−	3.96735i	0.393051	−	0.182806i
$472$			0.257172i			0.0118373i
$473$	3.60577	+	3.60577i	0.165793	+	0.165793i
$474$	34.1820	+	12.4799i	1.57003	+	0.573219i
$475$	−0.990477	−	0.990477i	−0.0454462	−	0.0454462i
$476$	26.4145	−	26.4145i	1.21070	−	1.21070i
$477$	23.1137	+	19.4734i	1.05830	+	0.891625i
$478$			20.9510i			0.958277i
$479$	21.6809	−	21.6809i	0.990624	−	0.990624i	−0.00933239	−	0.999956i	$-0.502971\pi$
$479$	21.6809	−	21.6809i	0.990624	−	0.990624i	0.999956	+	0.00933239i	$0.00297064\pi$
$480$	14.3458	+	30.8450i	0.654794	+	1.40788i
$481$		0			0
$482$			11.8877i			0.541471i
$483$	19.5703	+	7.14512i	0.890480	+	0.325114i
$484$	−6.92755			−0.314889
$485$	−24.1059			−1.09459
$486$	5.61801	−	30.9578i	0.254838	−	1.40427i
$487$	0.733074	−	0.733074i	0.0332188	−	0.0332188i	−0.690302	−	0.723521i	$-0.742522\pi$
$487$	0.733074	−	0.733074i	0.0332188	−	0.0332188i	0.723521	+	0.690302i	$0.242522\pi$
$488$	−0.568690	+	0.568690i	−0.0257434	+	0.0257434i
$489$	−20.0492	−	7.31995i	−0.906654	−	0.331020i
$490$	13.1947			0.596077
$491$	−5.85975			−0.264447			−0.132223	−	0.991220i	$-0.542212\pi$
$491$	−5.85975			−0.264447			−0.132223	+	0.991220i	$0.542212\pi$
$492$	8.36178	−	22.9027i	0.376978	−	1.03253i
$493$			16.9196i			0.762021i
$494$		0			0
$495$	−13.0316	+	15.4677i	−0.585727	+	0.695222i
$496$	−13.7161	+	13.7161i	−0.615869	+	0.615869i
$497$		−	1.05239i		−	0.0472062i
$498$	5.91795	+	12.7242i	0.265190	+	0.570185i
$499$	14.2320	−	14.2320i	0.637111	−	0.637111i	−0.312731	−	0.949842i	$-0.601244\pi$
$499$	14.2320	−	14.2320i	0.637111	−	0.637111i	0.949842	+	0.312731i	$0.101244\pi$
$500$	14.5243	+	14.5243i	0.649548	+	0.649548i
$501$	13.1466	−	36.0082i	0.587346	−	1.60873i
$502$	0.317060	+	0.317060i	0.0141511	+	0.0141511i
$503$			30.1910i			1.34615i	0.739574	+	0.673075i	$0.235027\pi$
$503$			30.1910i			1.34615i	−0.739574	+	0.673075i	$0.764973\pi$
$504$	0.896526	−	1.06412i	0.0399344	−	0.0473997i
$505$	−15.9027	−	15.9027i	−0.707659	−	0.707659i
$506$	−21.5921			−0.959885
$507$		0			0
$508$	−0.841284			−0.0373260
$509$	2.82402	+	2.82402i	0.125173	+	0.125173i	0.766918	−	0.641745i	$-0.221789\pi$
$509$	2.82402	+	2.82402i	0.125173	+	0.125173i	−0.641745	+	0.766918i	$0.721789\pi$
$510$	−20.7883	−	44.6971i	−0.920523	−	1.97922i
$511$		−	37.6228i		−	1.66434i
$512$	−22.7420	−	22.7420i	−1.00506	−	1.00506i
$513$	−3.87582	−	6.75975i	−0.171122	−	0.298450i
$514$	−36.0888	−	36.0888i	−1.59181	−	1.59181i
$515$	−29.7413	+	29.7413i	−1.31056	+	1.31056i
$516$	−6.00102	+	2.79104i	−0.264180	+	0.122869i
$517$			0.452753i			0.0199121i
$518$	17.8325	−	17.8325i	0.783513	−	0.783513i
$519$	−14.6550	+	6.81594i	−0.643282	+	0.299187i
$520$		0			0
$521$			30.7954i			1.34917i	0.738197	+	0.674585i	$0.235678\pi$
$521$			30.7954i			1.34917i	−0.738197	+	0.674585i	$0.764322\pi$
$522$	1.50741	+	17.6348i	0.0659775	+	0.771856i
$523$	13.5482			0.592421			0.296211	−	0.955123i	$-0.404277\pi$
$523$	13.5482			0.592421			0.296211	+	0.955123i	$0.404277\pi$
$524$	14.9740			0.654142
$525$	1.72667	−	4.72930i	0.0753579	−	0.206403i
$526$	−6.98085	+	6.98085i	−0.304380	+	0.304380i
$527$	20.6388	−	20.6388i	0.899041	−	0.899041i
$528$	6.32424	−	17.3219i	0.275227	−	0.753841i
$529$	−8.05897			−0.350390
$530$	49.5338			2.15161
$531$	0.440858	+	5.15750i	0.0191316	+	0.223816i
$532$		−	9.67755i		−	0.419575i
$533$		0			0
$534$	13.4824	−	6.27059i	0.583442	−	0.271355i
$535$	−18.3142	+	18.3142i	−0.791792	+	0.791792i
$536$			2.03572i			0.0879299i
$537$	−41.9568	+	19.5139i	−1.81057	+	0.842086i
$538$	30.1783	−	30.1783i	1.30108	−	1.30108i
$539$	−5.25179	−	5.25179i	−0.226211	−	0.226211i
$540$	−13.0571	−	22.7727i	−0.561888	−	0.979979i
$541$	17.8219	+	17.8219i	0.766224	+	0.766224i	0.977439	−	0.211216i	$-0.0677422\pi$
$541$	17.8219	+	17.8219i	0.766224	+	0.766224i	−0.211216	+	0.977439i	$0.567742\pi$
$542$			3.84137i			0.165001i
$543$	19.1917	+	41.2642i	0.823597	+	1.77082i
$544$	33.0002	+	33.0002i	1.41487	+	1.41487i
$545$	2.15350			0.0922459
$546$		0			0
$547$	−27.9877			−1.19667			−0.598333	−	0.801248i	$-0.704170\pi$
$547$	−27.9877			−1.19667			−0.598333	+	0.801248i	$0.704170\pi$
$548$	28.9200	+	28.9200i	1.23540	+	1.23540i
$549$	−10.4300	+	12.3798i	−0.445142	+	0.528355i
$550$			5.21787i			0.222491i
$551$	3.09945	+	3.09945i	0.132041	+	0.132041i
$552$	0.342228	−	0.937354i	0.0145662	−	0.0398964i
$553$	22.9040	+	22.9040i	0.973975	+	0.973975i
$554$	5.63751	−	5.63751i	0.239515	−	0.239515i
$555$	−7.14432	−	15.3610i	−0.303260	−	0.652039i
$556$			21.4819i			0.911034i
$557$	13.8024	−	13.8024i	0.584828	−	0.584828i	−0.351398	−	0.936226i	$-0.614294\pi$
$557$	13.8024	−	13.8024i	0.584828	−	0.584828i	0.936226	+	0.351398i	$0.114294\pi$
$558$	19.6725	−	23.3500i	0.832803	−	0.988485i
$559$		0			0
$560$			29.1610i			1.23228i
$561$	−9.51621	+	26.0647i	−0.401775	+	1.10045i
$562$	−8.80403			−0.371375
$563$	33.9551			1.43104			0.715519	−	0.698593i	$-0.246190\pi$
$563$	33.9551			1.43104			0.715519	+	0.698593i	$0.246190\pi$
$564$	−0.551981	−	0.201528i	−0.0232426	−	0.00848588i
$565$	11.7086	−	11.7086i	0.492584	−	0.492584i
$566$	−26.3119	+	26.3119i	−1.10597	+	1.10597i
$567$	16.1554	−	22.8774i	0.678461	−	0.960762i
$568$	−0.0504062			−0.00211500
$569$	−8.16147			−0.342147			−0.171073	−	0.985258i	$-0.554723\pi$
$569$	−8.16147			−0.342147			−0.171073	+	0.985258i	$0.554723\pi$
$570$	−11.9960	−	4.37976i	−0.502459	−	0.183448i
$571$			19.3616i			0.810257i	0.914260	+	0.405128i	$0.132773\pi$
$571$			19.3616i			0.810257i	−0.914260	+	0.405128i	$0.867227\pi$
$572$		0			0
$573$	5.62595	+	12.0964i	0.235028	+	0.505333i
$574$	30.1459	−	30.1459i	1.25826	−	1.25826i
$575$		−	3.61060i		−	0.150572i
$576$	19.6837	+	16.5836i	0.820154	+	0.690983i
$577$	−10.9086	+	10.9086i	−0.454132	+	0.454132i	−0.896723	−	0.442592i	$-0.854059\pi$
$577$	−10.9086	+	10.9086i	−0.454132	+	0.454132i	0.442592	+	0.896723i	$0.354059\pi$
$578$	−23.5576	−	23.5576i	−0.979865	−	0.979865i
$579$	25.3526	+	9.25625i	1.05362	+	0.384677i
$580$	10.4416	+	10.4416i	0.433564	+	0.433564i
$581$			12.4913i			0.518228i
$582$	−31.3680	+	14.5891i	−1.30025	+	0.604736i
$583$	−19.7156	−	19.7156i	−0.816536	−	0.816536i
$584$	−1.80201			−0.0745677
$585$		0			0
$586$	31.5990			1.30534
$587$	1.09507	+	1.09507i	0.0451983	+	0.0451983i	0.729345	−	0.684146i	$-0.239825\pi$
$587$	1.09507	+	1.09507i	0.0451983	+	0.0451983i	−0.684146	+	0.729345i	$0.739825\pi$
$588$	8.74048	−	4.06514i	0.360451	−	0.167644i
$589$		−	7.56151i		−	0.311567i
$590$	5.99878	+	5.99878i	0.246966	+	0.246966i
$591$	−42.7801	−	15.6190i	−1.75974	−	0.642481i
$592$	10.9218	+	10.9218i	0.448885	+	0.448885i
$593$	−3.02210	+	3.02210i	−0.124103	+	0.124103i	−0.766430	−	0.642327i	$-0.777969\pi$
$593$	−3.02210	+	3.02210i	−0.124103	+	0.124103i	0.642327	+	0.766430i	$0.277969\pi$
$594$	−7.59632	+	28.0143i	−0.311681	+	1.14944i
$595$		−	43.8791i		−	1.79887i
$596$	−7.13792	+	7.13792i	−0.292380	+	0.292380i
$597$	−10.0204	−	21.5448i	−0.410107	−	0.881772i
$598$		0			0
$599$			16.9927i			0.694302i	0.937809	+	0.347151i	$0.112851\pi$
$599$			16.9927i			0.694302i	−0.937809	+	0.347151i	$0.887149\pi$
$600$	−0.226518	−	0.0827018i	−0.00924756	−	0.00337629i
$601$	32.5639			1.32831			0.664154	−	0.747596i	$-0.268792\pi$
$601$	32.5639			1.32831			0.664154	+	0.747596i	$0.268792\pi$
$602$	−11.5726			−0.471665
$603$	3.48974	+	40.8258i	0.142113	+	1.66255i
$604$	6.46348	−	6.46348i	0.262995	−	0.262995i
$605$	−5.75394	+	5.75394i	−0.233931	+	0.233931i
$606$	−30.3178	−	11.0690i	−1.23158	−	0.449649i
$607$	−13.0252			−0.528675			−0.264338	−	0.964430i	$-0.585153\pi$
$607$	−13.0252			−0.528675			−0.264338	+	0.964430i	$0.585153\pi$
$608$	12.0904			0.490330
$609$	−5.40317	+	14.7991i	−0.218947	+	0.599691i
$610$			26.5304i			1.07419i
$611$		0			0
$612$	−27.5413	−	23.2037i	−1.11329	−	0.937954i
$613$	3.73521	−	3.73521i	0.150864	−	0.150864i	−0.627640	−	0.778504i	$-0.715979\pi$
$613$	3.73521	−	3.73521i	0.150864	−	0.150864i	0.778504	+	0.627640i	$0.215979\pi$
$614$		−	12.0680i		−	0.487025i
$615$	−12.0775	−	25.9679i	−0.487012	−	1.04713i
$616$	−0.907676	+	0.907676i	−0.0365713	+	0.0365713i
$617$	19.0985	+	19.0985i	0.768879	+	0.768879i	0.977909	−	0.209031i	$-0.0670308\pi$
$617$	19.0985	+	19.0985i	0.768879	+	0.768879i	−0.209031	+	0.977909i	$0.567031\pi$
$618$	−20.7015	+	56.7007i	−0.832734	+	2.28084i
$619$	21.7905	+	21.7905i	0.875835	+	0.875835i	0.993101	−	0.117266i	$-0.0374129\pi$
$619$	21.7905	+	21.7905i	0.875835	+	0.875835i	−0.117266	+	0.993101i	$0.537413\pi$
$620$		−	25.4737i		−	1.02305i
$621$	5.25641	−	19.3850i	0.210933	−	0.777893i
$622$	29.7552	+	29.7552i	1.19307	+	1.19307i
$623$	13.2357			0.530277
$624$		0			0
$625$	28.7979			1.15192
$626$	−9.90028	−	9.90028i	−0.395695	−	0.395695i
$627$	3.03145	+	6.51794i	0.121065	+	0.260301i
$628$		−	11.2641i		−	0.449488i
$629$	−16.4343	−	16.4343i	−0.655279	−	0.655279i
$630$	−3.90929	−	45.7339i	−0.155750	−	1.82208i
$631$	−2.57093	−	2.57093i	−0.102347	−	0.102347i	0.654079	−	0.756426i	$-0.273056\pi$
$631$	−2.57093	−	2.57093i	−0.102347	−	0.102347i	−0.756426	+	0.654079i	$0.773056\pi$
$632$	1.09703	−	1.09703i	0.0436373	−	0.0436373i
$633$	−33.8339	+	15.7360i	−1.34478	+	0.625448i
$634$		−	21.2136i		−	0.842499i
$635$	−0.698761	+	0.698761i	−0.0277295	+	0.0277295i
$636$	32.8123	−	15.2608i	1.30109	−	0.605130i
$637$		0			0
$638$		−	16.3280i		−	0.646432i
$639$	−1.01088	+	0.0864089i	−0.0399898	+	0.00341828i
$640$	2.90266			0.114738
$641$	−4.88359			−0.192890			−0.0964452	−	0.995338i	$-0.530747\pi$
$641$	−4.88359			−0.192890			−0.0964452	+	0.995338i	$0.530747\pi$
$642$	−12.7476	+	34.9154i	−0.503108	+	1.37800i
$643$	2.00667	−	2.00667i	0.0791355	−	0.0791355i	−0.666431	−	0.745567i	$-0.732179\pi$
$643$	2.00667	−	2.00667i	0.0791355	−	0.0791355i	0.745567	+	0.666431i	$0.232179\pi$
$644$	17.6389	−	17.6389i	0.695068	−	0.695068i
$645$	−2.66617	+	7.30258i	−0.104980	+	0.287539i
$646$	−17.5200			−0.689315
$647$	−15.6612			−0.615706			−0.307853	−	0.951434i	$-0.599611\pi$
$647$	−15.6612			−0.615706			−0.307853	+	0.951434i	$0.599611\pi$
$648$	−1.09576	−	0.773789i	−0.0430453	−	0.0303973i
$649$		−	4.77530i		−	0.187447i
$650$		0			0
$651$	24.6431	−	11.4614i	0.965839	−	0.449206i
$652$	−18.0704	+	18.0704i	−0.707693	+	0.707693i
$653$			30.5498i			1.19551i	0.801680	+	0.597753i	$0.203940\pi$
$653$			30.5498i			1.19551i	−0.801680	+	0.597753i	$0.796060\pi$
$654$	2.80226	−	1.30332i	0.109577	−	0.0509637i
$655$	12.4372	−	12.4372i	0.485963	−	0.485963i
$656$	18.4634	+	18.4634i	0.720876	+	0.720876i
$657$	−36.1387	+	3.08910i	−1.40991	+	0.120517i
$658$	−0.726550	−	0.726550i	−0.0283239	−	0.0283239i
$659$			4.83845i			0.188479i	0.995550	+	0.0942397i	$0.0300420\pi$
$659$			4.83845i			0.188479i	−0.995550	+	0.0942397i	$0.969958\pi$
$660$	10.2125	+	21.9580i	0.397523	+	0.854715i
$661$	34.7980	+	34.7980i	1.35349	+	1.35349i	0.881728	+	0.471758i	$0.156380\pi$
$661$	34.7980	+	34.7980i	1.35349	+	1.35349i	0.471758	+	0.881728i	$0.343620\pi$
$662$	43.9009			1.70626
$663$		0			0
$664$	0.598295			0.0232184
$665$	−8.03806	−	8.03806i	−0.311703	−	0.311703i
$666$	−18.5932	−	15.6649i	−0.720472	−	0.607001i
$667$			11.2985i			0.437478i
$668$	−32.4544	−	32.4544i	−1.25570	−	1.25570i
$669$	8.81648	−	24.1481i	0.340865	−	0.933620i
$670$	47.4852	+	47.4852i	1.83451	+	1.83451i
$671$	10.5597	−	10.5597i	0.407653	−	0.407653i
$672$	18.3260	+	39.4028i	0.706940	+	1.51999i
$673$			5.63801i			0.217329i	0.994078	+	0.108665i	$0.0346575\pi$
$673$			5.63801i			0.217329i	−0.994078	+	0.108665i	$0.965343\pi$
$674$	−47.3454	+	47.3454i	−1.82368	+	1.82368i
$675$	−4.68451	−	1.27025i	−0.180307	−	0.0488918i
$676$		0			0
$677$		−	20.0063i		−	0.768905i	−0.923145	−	0.384452i	$-0.874390\pi$
$677$		−	20.0063i		−	0.768905i	0.923145	−	0.384452i	$-0.125610\pi$
$678$	8.14977	−	22.3220i	0.312990	−	0.857272i
$679$	−30.7939			−1.18176
$680$	−2.10167			−0.0805952
$681$	−3.71242	−	1.35540i	−0.142260	−	0.0519392i
$682$	−19.9172	+	19.9172i	−0.762668	+	0.762668i
$683$	10.1258	−	10.1258i	0.387453	−	0.387453i	−0.486325	−	0.873778i	$-0.661663\pi$
$683$	10.1258	−	10.1258i	0.387453	−	0.387453i	0.873778	+	0.486325i	$0.161663\pi$
$684$	−9.29581	+	0.794596i	−0.355434	+	0.0303821i
$685$	48.0411			1.83556
$686$	−27.1107			−1.03509
$687$	−4.23260	−	1.54532i	−0.161484	−	0.0589577i
$688$		−	7.08788i		−	0.270223i
$689$		0			0
$690$	−13.8819	−	29.8475i	−0.528474	−	1.13627i
$691$	−7.48019	+	7.48019i	−0.284560	+	0.284560i	−0.834924	−	0.550365i	$-0.814489\pi$
$691$	−7.48019	+	7.48019i	−0.284560	+	0.284560i	0.550365	+	0.834924i	$0.314489\pi$
$692$			19.3519i			0.735649i
$693$	−16.6472	+	19.7591i	−0.632373	+	0.750587i
$694$	−48.0753	+	48.0753i	−1.82492	+	1.82492i
$695$	17.8426	+	17.8426i	0.676808	+	0.676808i
$696$	0.708831	+	0.258794i	0.0268682	+	0.00980957i
$697$	−27.7823	−	27.7823i	−1.05233	−	1.05233i
$698$		−	40.7449i		−	1.54222i
$699$	−25.8255	+	12.0113i	−0.976811	+	0.454309i
$700$	−4.26255	−	4.26255i	−0.161109	−	0.161109i
$701$	−34.6355			−1.30816			−0.654082	−	0.756423i	$-0.726945\pi$
$701$	−34.6355			−1.30816			−0.654082	+	0.756423i	$0.726945\pi$
$702$		0			0
$703$	−6.02109			−0.227090
$704$	−16.7898	−	16.7898i	−0.632791	−	0.632791i
$705$	−0.625856	+	0.291082i	−0.0235711	+	0.0109628i
$706$			36.3693i			1.36878i
$707$	−20.3147	−	20.3147i	−0.764014	−	0.764014i
$708$	5.82188	+	2.12557i	0.218800	+	0.0798839i
$709$	−24.8773	−	24.8773i	−0.934286	−	0.934286i	0.0636839	−	0.997970i	$-0.479715\pi$
$709$	−24.8773	−	24.8773i	−0.934286	−	0.934286i	−0.997970	+	0.0636839i	$0.979715\pi$
$710$	−1.17577	+	1.17577i	−0.0441259	+	0.0441259i
$711$	20.1199	−	23.8811i	0.754555	−	0.895609i
$712$		−	0.633947i		−	0.0237582i
$713$	13.7820	−	13.7820i	0.516141	−	0.516141i
$714$	−26.5559	−	57.0980i	−0.993831	−	2.13684i
$715$		0			0
$716$			55.4040i			2.07054i
$717$	16.8885	+	6.16600i	0.630713	+	0.230273i
$718$	48.6128			1.81422
$719$	19.2610			0.718315			0.359157	−	0.933277i	$-0.383064\pi$
$719$	19.2610			0.718315			0.359157	+	0.933277i	$0.383064\pi$
$720$	28.0107	−	2.39432i	1.04390	−	0.0892311i
$721$	−37.9928	+	37.9928i	−1.41493	+	1.41493i
$722$	23.9075	−	23.9075i	0.889746	−	0.889746i
$723$	9.58264	+	3.49862i	0.356382	+	0.130115i
$724$	54.4894			2.02508
$725$	2.73035			0.101403
$726$	−4.00503	+	10.9697i	−0.148641	+	0.407123i
$727$		−	9.68612i		−	0.359238i	−0.983736	−	0.179619i	$-0.942513\pi$
$727$		−	9.68612i		−	0.359238i	0.983736	−	0.179619i	$-0.0574865\pi$
$728$		0			0
$729$	−23.3015	−	13.6397i	−0.863018	−	0.505174i
$730$	−42.0336	+	42.0336i	−1.55573	+	1.55573i
$731$			10.6653i			0.394470i
$732$	8.17373	+	17.5744i	0.302110	+	0.649567i
$733$	−14.7153	+	14.7153i	−0.543522	+	0.543522i	−0.924559	−	0.381038i	$-0.875567\pi$
$733$	−14.7153	+	14.7153i	−0.543522	+	0.543522i	0.381038	+	0.924559i	$0.375567\pi$
$734$	26.8903	+	26.8903i	0.992539	+	0.992539i
$735$	3.88328	−	10.6362i	0.143237	−	0.392322i
$736$	22.0366	+	22.0366i	0.812281	+	0.812281i
$737$		−	37.8004i		−	1.39239i
$738$	−31.4319	−	26.4815i	−1.15702	−	0.974799i
$739$	−14.9685	−	14.9685i	−0.550626	−	0.550626i	0.375995	−	0.926622i	$-0.377301\pi$
$739$	−14.9685	−	14.9685i	−0.550626	−	0.550626i	−0.926622	+	0.375995i	$0.877301\pi$
$740$	−20.2842			−0.745663
$741$		0			0
$742$	63.2766			2.32296
$743$	−29.3231	−	29.3231i	−1.07576	−	1.07576i	−0.996884	−	0.0788775i	$-0.974866\pi$
$743$	−29.3231	−	29.3231i	−1.07576	−	1.07576i	−0.0788775	−	0.996884i	$-0.525134\pi$
$744$	−0.548962	−	1.18032i	−0.0201259	−	0.0432728i
$745$			11.8573i			0.434419i
$746$	25.6472	+	25.6472i	0.939012	+	0.939012i
$747$	11.9986	−	1.02563i	0.439006	−	0.0375258i
$748$	23.4923	+	23.4923i	0.858962	+	0.858962i
$749$	−23.3954	+	23.3954i	−0.854848	+	0.854848i
$750$	31.3961	−	14.6021i	1.14642	−	0.533194i
$751$		−	5.55426i		−	0.202678i	−0.994852	−	0.101339i	$-0.967687\pi$
$751$		−	5.55426i		−	0.202678i	0.994852	−	0.101339i	$-0.0323127\pi$
$752$	0.444990	−	0.444990i	0.0162271	−	0.0162271i
$753$	0.348893	−	0.162268i	0.0127144	−	0.00591337i
$754$		0			0
$755$		−	10.7370i		−	0.390758i
$756$	−16.6797	−	29.0908i	−0.606635	−	1.05802i
$757$	11.9803			0.435431			0.217716	−	0.976012i	$-0.430139\pi$
$757$	11.9803			0.435431			0.217716	+	0.976012i	$0.430139\pi$
$758$	−32.6466			−1.18578
$759$	−6.35467	+	17.4053i	−0.230660	+	0.631771i
$760$	−0.384997	+	0.384997i	−0.0139653	+	0.0139653i
$761$	−29.3479	+	29.3479i	−1.06386	+	1.06386i	−0.0660429	+	0.997817i	$0.521037\pi$
$761$	−29.3479	+	29.3479i	−1.06386	+	1.06386i	−0.997817	+	0.0660429i	$0.978963\pi$
$762$	−0.486373	+	1.33216i	−0.0176194	+	0.0482592i
$763$	2.75098			0.0995921
$764$	15.9733			0.577892
$765$	−42.1482	+	3.60278i	−1.52387	+	0.130259i
$766$			34.0999i			1.23208i
$767$		0			0
$768$	−23.1710	+	10.7767i	−0.836110	+	0.388870i
$769$	−21.1622	+	21.1622i	−0.763129	+	0.763129i	−0.976887	−	0.213757i	$-0.931430\pi$
$769$	−21.1622	+	21.1622i	−0.763129	+	0.763129i	0.213757	+	0.976887i	$0.431430\pi$
$770$			42.3448i			1.52600i
$771$	−39.7121	+	18.4699i	−1.43020	+	0.665176i
$772$	22.8505	−	22.8505i	0.822408	−	0.822408i
$773$	13.5115	+	13.5115i	0.485976	+	0.485976i	0.907034	−	0.421058i	$-0.138341\pi$
$773$	13.5115	+	13.5115i	0.485976	+	0.485976i	−0.421058	+	0.907034i	$0.638341\pi$
$774$	0.950194	+	11.1161i	0.0341540	+	0.399561i
$775$	−3.33052	−	3.33052i	−0.119636	−	0.119636i
$776$			1.47493i			0.0529469i
$777$	−9.12647	−	19.6228i	−0.327410	−	0.703966i
$778$	−41.9238	−	41.9238i	−1.50304	−	1.50304i
$779$	−10.1787			−0.364690
$780$		0			0
$781$	0.935968			0.0334916
$782$	−31.9330	−	31.9330i	−1.14192	−	1.14192i
$783$	14.6590	+	3.97492i	0.523870	+	0.142052i
$784$			10.3235i			0.368696i
$785$	−9.35586	−	9.35586i	−0.333925	−	0.333925i
$786$	8.65694	−	23.7111i	0.308783	−	0.845748i
$787$	−12.4018	−	12.4018i	−0.442075	−	0.442075i	0.450634	−	0.892709i	$-0.351198\pi$
$787$	−12.4018	−	12.4018i	−0.442075	−	0.442075i	−0.892709	+	0.450634i	$0.851198\pi$
$788$	−38.5580	+	38.5580i	−1.37357	+	1.37357i
$789$	3.57273	+	7.68173i	0.127192	+	0.273477i
$790$		−	51.1783i		−	1.82084i
$791$	14.9571	−	14.9571i	0.531812	−	0.531812i
$792$	0.946398	+	0.797345i	0.0336288	+	0.0283324i
$793$		0			0
$794$		−	32.8038i		−	1.16416i
$795$	14.5781	−	39.9290i	0.517031	−	1.41613i
$796$	−28.4500			−1.00838
$797$	32.1908			1.14026			0.570128	−	0.821556i	$-0.306894\pi$
$797$	32.1908			1.14026			0.570128	+	0.821556i	$0.306894\pi$
$798$	−15.3243	−	5.59490i	−0.542474	−	0.198057i
$799$	−0.669586	+	0.669586i	−0.0236882	+	0.0236882i
$800$	5.32530	−	5.32530i	0.188278	−	0.188278i
$801$	−1.08674	−	12.7136i	−0.0383982	−	0.449213i
$802$	4.17473			0.147415
$803$	33.4607			1.18080
$804$	46.0849	+	16.8256i	1.62529	+	0.593393i
$805$		−	29.3013i		−	1.03273i
$806$		0			0
$807$	−15.4449	−	33.2082i	−0.543688	−	1.16898i
$808$	−0.973010	+	0.973010i	−0.0342304	+	0.0342304i
$809$		−	12.2082i		−	0.429216i	−0.976700	−	0.214608i	$-0.931153\pi$
$809$		−	12.2082i		−	0.429216i	0.976700	−	0.214608i	$-0.0688474\pi$
$810$	−43.6089	+	7.51016i	−1.53226	+	0.263880i
$811$	−6.35825	+	6.35825i	−0.223268	+	0.223268i	−0.809873	−	0.586605i	$-0.800464\pi$
$811$	−6.35825	+	6.35825i	−0.223268	+	0.223268i	0.586605	+	0.809873i	$0.300464\pi$
$812$	13.3386	+	13.3386i	0.468092	+	0.468092i
$813$	3.09651	+	1.13054i	0.108599	+	0.0396497i
$814$	15.8597	+	15.8597i	0.555881	+	0.555881i
$815$			30.0182i			1.05149i
$816$	34.9708	−	16.2647i	1.22422	−	0.569379i
$817$	1.95374	+	1.95374i	0.0683526	+	0.0683526i
$818$	−16.4770			−0.576104
$819$		0			0
$820$	−34.2906			−1.19748
$821$	−15.3861	−	15.3861i	−0.536978	−	0.536978i	0.385662	−	0.922640i	$-0.373973\pi$
$821$	−15.3861	−	15.3861i	−0.536978	−	0.536978i	−0.922640	+	0.385662i	$0.873973\pi$
$822$	62.5139	−	29.0748i	2.18042	−	1.01410i
$823$			19.5683i			0.682107i	0.940044	+	0.341054i	$0.110784\pi$
$823$			19.5683i			0.682107i	−0.940044	+	0.341054i	$0.889216\pi$
$824$	1.81973	+	1.81973i	0.0633934	+	0.0633934i
$825$	4.20610	+	1.53565i	0.146438	+	0.0534644i
$826$	7.66311	+	7.66311i	0.266634	+	0.266634i
$827$	11.8247	−	11.8247i	0.411186	−	0.411186i	−0.470966	−	0.882152i	$-0.656094\pi$
$827$	11.8247	−	11.8247i	0.411186	−	0.411186i	0.882152	+	0.470966i	$0.156094\pi$
$828$	−18.3913	−	15.4948i	−0.639143	−	0.538481i
$829$			19.6511i			0.682512i	0.939970	+	0.341256i	$0.110852\pi$
$829$			19.6511i			0.682512i	−0.939970	+	0.341256i	$0.889148\pi$
$830$	13.9558	−	13.9558i	0.484413	−	0.484413i
$831$	−2.88522	−	6.20352i	−0.100087	−	0.215198i
$832$		0			0
$833$		−	15.5340i		−	0.538220i
$834$	34.0163	+	12.4193i	1.17789	+	0.430047i
$835$	−53.9125			−1.86572
$836$	8.60694			0.297677
$837$	−13.0326	−	22.7299i	−0.450473	−	0.785662i
$838$	−6.81279	+	6.81279i	−0.235344	+	0.235344i
$839$	−2.66649	+	2.66649i	−0.0920575	+	0.0920575i	−0.751636	−	0.659578i	$-0.770735\pi$
$839$	−2.66649	+	2.66649i	−0.0920575	+	0.0920575i	0.659578	+	0.751636i	$0.270735\pi$
$840$	−1.83827	−	0.671153i	−0.0634264	−	0.0231570i
$841$	20.4561			0.705382
$842$	18.0509			0.622076
$843$	−2.59107	+	7.09688i	−0.0892413	+	0.244430i
$844$			44.6777i			1.53787i
$845$		0			0
$846$	−0.638235	+	0.757545i	−0.0219430	+	0.0260449i
$847$	−7.35034	+	7.35034i	−0.252561	+	0.252561i
$848$			38.7551i			1.33085i
$849$	13.4662	+	28.9536i	0.462157	+	0.993686i
$850$	−7.71681	+	7.71681i	−0.264685	+	0.264685i
$851$	−10.9744	−	10.9744i	−0.376197	−	0.376197i
$852$	−0.416616	+	1.14110i	−0.0142730	+	0.0390934i
$853$	4.56091	+	4.56091i	0.156162	+	0.156162i	0.780864	−	0.624701i	$-0.214779\pi$
$853$	4.56091	+	4.56091i	0.156162	+	0.156162i	−0.624701	+	0.780864i	$0.714779\pi$
$854$			33.8912i			1.15973i
$855$	−7.06101	+	8.38097i	−0.241481	+	0.286623i
$856$	1.12056	+	1.12056i	0.0383000	+	0.0383000i
$857$	31.9796			1.09240			0.546201	−	0.837654i	$-0.316073\pi$
$857$	31.9796			1.09240			0.546201	+	0.837654i	$0.316073\pi$
$858$		0			0
$859$	18.1029			0.617664			0.308832	−	0.951117i	$-0.400062\pi$
$859$	18.1029			0.617664			0.308832	+	0.951117i	$0.400062\pi$
$860$	6.58187	+	6.58187i	0.224440	+	0.224440i
$861$	−15.4283	−	33.1725i	−0.525796	−	1.13052i
$862$		−	36.5645i		−	1.24539i
$863$	33.7030	+	33.7030i	1.14726	+	1.14726i	0.987089	+	0.160173i	$0.0512051\pi$
$863$	33.7030	+	33.7030i	1.14726	+	1.14726i	0.160173	+	0.987089i	$0.448795\pi$
$864$	36.3438	−	20.8383i	1.23644	−	0.708935i
$865$	16.0735	+	16.0735i	0.546514	+	0.546514i
$866$	36.3992	−	36.3992i	1.23689	−	1.23689i
$867$	−25.9228	+	12.0565i	−0.880383	+	0.409461i
$868$		−	32.5412i		−	1.10452i
$869$	−20.3701	+	20.3701i	−0.691009	+	0.691009i
$870$	22.5708	−	10.4975i	0.765221	−	0.355900i
$871$		0			0
$872$		−	0.131763i		−	0.00446206i
$873$	2.52840	+	29.5792i	0.0855734	+	1.00111i
$874$	−11.6994			−0.395737
$875$	30.8215			1.04196
$876$	−14.8939	+	40.7941i	−0.503219	+	1.37830i
$877$	23.4194	−	23.4194i	0.790818	−	0.790818i	−0.190809	−	0.981627i	$-0.561111\pi$
$877$	23.4194	−	23.4194i	0.790818	−	0.790818i	0.981627	+	0.190809i	$0.0611111\pi$
$878$	−14.3956	+	14.3956i	−0.485828	+	0.485828i
$879$	9.29975	−	25.4718i	0.313673	−	0.859141i
$880$	−25.9349			−0.874266
$881$	−51.6657			−1.74066			−0.870331	−	0.492467i	$-0.836095\pi$
$881$	−51.6657			−1.74066			−0.870331	+	0.492467i	$0.836095\pi$
$882$	−1.38396	−	16.1906i	−0.0466003	−	0.545166i
$883$			29.2334i			0.983782i	0.870657	+	0.491891i	$0.163694\pi$
$883$			29.2334i			0.983782i	−0.870657	+	0.491891i	$0.836306\pi$
$884$		0			0
$885$	6.60106	−	3.07011i	0.221892	−	0.103201i
$886$	−27.5468	+	27.5468i	−0.925454	+	0.925454i
$887$		−	47.9281i		−	1.60927i	−0.593771	−	0.804634i	$-0.702362\pi$
$887$		−	47.9281i		−	1.60927i	0.593771	−	0.804634i	$-0.297638\pi$
$888$	−0.939871	+	0.437128i	−0.0315400	+	0.0146691i
$889$	−0.892628	+	0.892628i	−0.0299378	+	0.0299378i
$890$	−14.7874	−	14.7874i	−0.495675	−	0.495675i
$891$	20.3465	+	14.3681i	0.681635	+	0.481350i
$892$	−21.7649	−	21.7649i	−0.728741	−	0.728741i
$893$			0.245318i			0.00820926i
$894$	7.17614	+	15.4294i	0.240006	+	0.516038i
$895$	46.0179	+	46.0179i	1.53821	+	1.53821i
$896$	3.70798			0.123875
$897$		0			0
$898$	−3.85168			−0.128532
$899$	10.4220	+	10.4220i	0.347594	+	0.347594i
$900$	−3.74442	+	4.44439i	−0.124814	+	0.148146i
$901$		−	58.3155i		−	1.94277i
$902$	26.8109	+	26.8109i	0.892704	+	0.892704i
$903$	−3.40589	+	9.32863i	−0.113341	+	0.310437i
$904$	−0.716395	−	0.716395i	−0.0238269	−	0.0238269i
$905$	45.2583	−	45.2583i	1.50444	−	1.50444i
$906$	−6.49809	−	13.9716i	−0.215885	−	0.464174i
$907$			23.3627i			0.775746i	0.921713	+	0.387873i	$0.126790\pi$
$907$			23.3627i			0.775746i	−0.921713	+	0.387873i	$0.873210\pi$
$908$	−3.34603	+	3.34603i	−0.111042	+	0.111042i
$909$	−17.8454	+	21.1814i	−0.591895	+	0.702542i
$910$		0			0
$911$			27.4965i			0.910999i	0.890236	+	0.455500i	$0.150539\pi$
$911$			27.4965i			0.910999i	−0.890236	+	0.455500i	$0.849461\pi$
$912$	3.42671	−	9.38566i	0.113470	−	0.310790i
$913$	−11.1094			−0.367669
$914$	−76.5983			−2.53365
$915$	21.3861	+	7.80806i	0.707002	+	0.258126i
$916$	−3.81487	+	3.81487i	−0.126047	+	0.126047i
$917$	15.8879	−	15.8879i	0.524663	−	0.524663i
$918$	−52.6652	+	30.1965i	−1.73821	+	0.996634i
$919$	22.7820			0.751508			0.375754	−	0.926720i	$-0.377384\pi$
$919$	22.7820			0.751508			0.375754	+	0.926720i	$0.377384\pi$
$920$	−1.40344			−0.0462699
$921$	−9.72796	−	3.55168i	−0.320547	−	0.117032i
$922$		−	29.3672i		−	0.967157i
$923$		0			0
$924$	13.0460	+	28.0502i	0.429180	+	0.922782i
$925$	−2.65204	+	2.65204i	−0.0871984	+	0.0871984i
$926$		−	0.575459i		−	0.0189107i
$927$	39.6136	+	33.3747i	1.30108	+	1.09617i
$928$	−16.6642	+	16.6642i	−0.547028	+	0.547028i
$929$	−32.7341	−	32.7341i	−1.07397	−	1.07397i	−0.997036	−	0.0769338i	$-0.975487\pi$
$929$	−32.7341	−	32.7341i	−1.07397	−	1.07397i	−0.0769338	−	0.997036i	$-0.524513\pi$
$930$	−40.3372	−	14.7271i	−1.32271	−	0.482922i
$931$	−2.84561	−	2.84561i	−0.0932613	−	0.0932613i
$932$			34.1026i			1.11707i
$933$	32.7426	−	15.2284i	1.07195	−	0.498555i
$934$	−18.7595	−	18.7595i	−0.613831	−	0.613831i
$935$	39.0248			1.27625
$936$		0			0
$937$	37.0828			1.21144			0.605722	−	0.795677i	$-0.292885\pi$
$937$	37.0828			1.21144			0.605722	+	0.795677i	$0.292885\pi$
$938$	60.6597	+	60.6597i	1.98061	+	1.98061i
$939$	−10.8943	+	5.06686i	−0.355521	+	0.165351i
$940$			0.826443i			0.0269556i
$941$	−28.3019	−	28.3019i	−0.922617	−	0.922617i	0.0745966	−	0.997214i	$-0.476233\pi$
$941$	−28.3019	−	28.3019i	−0.922617	−	0.922617i	−0.997214	+	0.0745966i	$0.976233\pi$
$942$	−17.8366	−	6.51215i	−0.581149	−	0.212177i
$943$	−18.5523	−	18.5523i	−0.604145	−	0.604145i
$944$	−4.69342	+	4.69342i	−0.152758	+	0.152758i
$945$	−38.0164	−	10.3085i	−1.23667	−	0.335335i
$946$		−	10.2924i		−	0.334633i
$947$	6.18668	−	6.18668i	0.201040	−	0.201040i	−0.599405	−	0.800446i	$-0.704596\pi$
$947$	6.18668	−	6.18668i	0.201040	−	0.201040i	0.800446	+	0.599405i	$0.204596\pi$
$948$	−15.7675	−	33.9017i	−0.512103	−	1.10108i
$949$		0			0
$950$			2.82723i			0.0917276i
$951$	−17.1002	−	6.24327i	−0.554511	−	0.202452i
$952$	−2.68476			−0.0870136
$953$	−14.1539			−0.458490			−0.229245	−	0.973369i	$-0.573626\pi$
$953$	−14.1539			−0.458490			−0.229245	+	0.973369i	$0.573626\pi$
$954$	−5.19546	−	60.7806i	−0.168209	−	1.96784i
$955$	13.2672	−	13.2672i	0.429317	−	0.429317i
$956$	15.2217	−	15.2217i	0.492306	−	0.492306i
$957$	−13.1619	−	4.80542i	−0.425465	−	0.155337i
$958$	−61.8862			−1.99945
$959$	61.3699			1.98174
$960$	12.4147	−	34.0036i	0.400684	−	1.09746i
$961$			5.57410i			0.179810i
$962$		0			0
$963$	24.3934	+	20.5516i	0.786067	+	0.662265i
$964$	8.63690	−	8.63690i	0.278176	−	0.278176i
$965$		−	37.9587i		−	1.22193i
$966$	−17.7333	−	38.1285i	−0.570560	−	1.22676i
$967$	38.9465	−	38.9465i	1.25244	−	1.25244i	0.297811	−	0.954625i	$-0.403744\pi$
$967$	38.9465	−	38.9465i	1.25244	−	1.25244i	0.954625	−	0.297811i	$-0.0962564\pi$
$968$	0.352057	+	0.352057i	0.0113155	+	0.0113155i
$969$	−5.15623	+	14.1228i	−0.165642	+	0.453689i
$970$	34.4041	+	34.4041i	1.10465	+	1.10465i
$971$		−	15.5368i		−	0.498599i	−0.968426	−	0.249300i	$-0.919800\pi$
$971$		−	15.5368i		−	0.498599i	0.968426	−	0.249300i	$-0.0802004\pi$
$972$	−26.5737	+	18.4103i	−0.852353	+	0.590511i
$973$	22.7929	+	22.7929i	0.730707	+	0.730707i
$974$	−2.09250			−0.0670480
$975$		0			0
$976$	−20.7573			−0.664426
$977$	0.704289	+	0.704289i	0.0225322	+	0.0225322i	0.718283	−	0.695751i	$-0.244928\pi$
$977$	0.704289	+	0.704289i	0.0225322	+	0.0225322i	−0.695751	+	0.718283i	$0.744928\pi$
$978$	18.1672	+	39.0614i	0.580924	+	1.24905i
$979$			11.7714i			0.376217i
$980$	−9.58648	−	9.58648i	−0.306229	−	0.306229i
$981$	−0.225875	−	2.64246i	−0.00721163	−	0.0843673i
$982$	8.36308	+	8.36308i	0.266877	+	0.266877i
$983$	15.8405	−	15.8405i	0.505234	−	0.505234i	−0.407826	−	0.913060i	$-0.633713\pi$
$983$	15.8405	−	15.8405i	0.505234	−	0.505234i	0.913060	+	0.407826i	$0.133713\pi$
$984$	−1.58886	+	0.738968i	−0.0506509	+	0.0235574i
$985$			64.0517i			2.04086i
$986$	24.1478	−	24.1478i	0.769023	−	0.769023i
$987$	−0.799496	+	0.371841i	−0.0254482	+	0.0118358i
$988$		0			0
$989$			7.12198i			0.226466i
$990$	40.6745	−	3.47681i	1.29272	−	0.110500i
$991$	27.3446			0.868630			0.434315	−	0.900761i	$-0.356991\pi$
$991$	27.3446			0.868630			0.434315	+	0.900761i	$0.356991\pi$
$992$	40.6544			1.29078
$993$	12.9203	−	35.3883i	0.410012	−	1.12301i
$994$	−1.50198	+	1.50198i	−0.0476400	+	0.0476400i
$995$	−23.6302	+	23.6302i	−0.749128	+	0.749128i
$996$	4.94501	−	13.5443i	0.156689	−	0.429166i
$997$	37.2896			1.18097			0.590486	−	0.807048i	$-0.298936\pi$
$997$	37.2896			1.18097			0.590486	+	0.807048i	$0.298936\pi$
$998$	−40.6240			−1.28593
$999$	−18.0994	+	10.3776i	−0.572641	+	0.328334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.f.g.239.4	yes	48
3.2	odd	2	inner	507.2.f.g.239.21	yes	48
13.2	odd	12		507.2.k.k.488.3		96
13.3	even	3		507.2.k.k.188.21		96
13.4	even	6		507.2.k.k.80.22		96
13.5	odd	4	inner	507.2.f.g.437.4	yes	48
13.6	odd	12		507.2.k.k.89.22		96
13.7	odd	12		507.2.k.k.89.4		96
13.8	odd	4	inner	507.2.f.g.437.22	yes	48
13.9	even	3		507.2.k.k.80.4		96
13.10	even	6		507.2.k.k.188.3		96
13.11	odd	12		507.2.k.k.488.21		96
13.12	even	2	inner	507.2.f.g.239.22	yes	48
39.2	even	12		507.2.k.k.488.22		96
39.5	even	4	inner	507.2.f.g.437.21	yes	48
39.8	even	4	inner	507.2.f.g.437.3	yes	48
39.11	even	12		507.2.k.k.488.4		96
39.17	odd	6		507.2.k.k.80.3		96
39.20	even	12		507.2.k.k.89.21		96
39.23	odd	6		507.2.k.k.188.22		96
39.29	odd	6		507.2.k.k.188.4		96
39.32	even	12		507.2.k.k.89.3		96
39.35	odd	6		507.2.k.k.80.21		96
39.38	odd	2	inner	507.2.f.g.239.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.3	✓	48	39.38	odd	2	inner
507.2.f.g.239.4	yes	48	1.1	even	1	trivial
507.2.f.g.239.21	yes	48	3.2	odd	2	inner
507.2.f.g.239.22	yes	48	13.12	even	2	inner
507.2.f.g.437.3	yes	48	39.8	even	4	inner
507.2.f.g.437.4	yes	48	13.5	odd	4	inner
507.2.f.g.437.21	yes	48	39.5	even	4	inner
507.2.f.g.437.22	yes	48	13.8	odd	4	inner
507.2.k.k.80.3		96	39.17	odd	6
507.2.k.k.80.4		96	13.9	even	3
507.2.k.k.80.21		96	39.35	odd	6
507.2.k.k.80.22		96	13.4	even	6
507.2.k.k.89.3		96	39.32	even	12
507.2.k.k.89.4		96	13.7	odd	12
507.2.k.k.89.21		96	39.20	even	12
507.2.k.k.89.22		96	13.6	odd	12
507.2.k.k.188.3		96	13.10	even	6
507.2.k.k.188.4		96	39.29	odd	6
507.2.k.k.188.21		96	13.3	even	3
507.2.k.k.188.22		96	39.23	odd	6
507.2.k.k.488.3		96	13.2	odd	12
507.2.k.k.488.4		96	39.11	even	12
507.2.k.k.488.21		96	13.11	odd	12
507.2.k.k.488.22		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)

\(f(q)\)	\(=\)	\(q+(-1.42721 - 1.42721i) q^{2} +(-1.57050 + 0.730430i) q^{3} +2.07385i q^{4} +(1.72251 + 1.72251i) q^{5} +(3.28391 + 1.19895i) q^{6} +(2.20041 + 2.20041i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.93294 - 2.29428i) q^{9} +O(q^{10})\)	\(q+(-1.42721 - 1.42721i) q^{2} +(-1.57050 + 0.730430i) q^{3} +2.07385i q^{4} +(1.72251 + 1.72251i) q^{5} +(3.28391 + 1.19895i) q^{6} +(2.20041 + 2.20041i) q^{7} +(0.105393 - 0.105393i) q^{8} +(1.93294 - 2.29428i) q^{9} -4.91676i q^{10} +(-1.95698 + 1.95698i) q^{11} +(-1.51480 - 3.25697i) q^{12} -6.28089i q^{14} +(-3.96338 - 1.44703i) q^{15} +3.84686 q^{16} -5.78844 q^{17} +(-6.03313 + 0.515706i) q^{18} +(-1.06036 + 1.06036i) q^{19} +(-3.57222 + 3.57222i) q^{20} +(-5.06299 - 1.84850i) q^{21} +5.58604 q^{22} -3.86536 q^{23} +(-0.0885372 + 0.242501i) q^{24} +0.934091i q^{25} +(-1.35988 + 5.01505i) q^{27} +(-4.56331 + 4.56331i) q^{28} -2.92300i q^{29} +(3.59135 + 7.72178i) q^{30} +(-3.56552 + 3.56552i) q^{31} +(-5.70105 - 5.70105i) q^{32} +(1.64400 - 4.50288i) q^{33} +(8.26131 + 8.26131i) q^{34} +7.58047i q^{35} +(4.75799 + 4.00863i) q^{36} +(2.83916 + 2.83916i) q^{37} +3.02672 q^{38} +0.363080 q^{40} +(4.79962 + 4.79962i) q^{41} +(4.58775 + 9.86414i) q^{42} -1.84251i q^{43} +(-4.05848 - 4.05848i) q^{44} +(7.28144 - 0.622410i) q^{45} +(5.51668 + 5.51668i) q^{46} +(0.115676 - 0.115676i) q^{47} +(-6.04149 + 2.80986i) q^{48} +2.68362i q^{49} +(1.33314 - 1.33314i) q^{50} +(9.09075 - 4.22805i) q^{51} +10.0745i q^{53} +(9.09835 - 5.21670i) q^{54} -6.74185 q^{55} +0.463814 q^{56} +(0.890781 - 2.43983i) q^{57} +(-4.17173 + 4.17173i) q^{58} +(-1.22007 + 1.22007i) q^{59} +(3.00092 - 8.21944i) q^{60} -5.39592 q^{61} +10.1775 q^{62} +(9.30163 - 0.795094i) q^{63} +8.57945i q^{64} +(-8.77288 + 4.08021i) q^{66} +(-9.65781 + 9.65781i) q^{67} -12.0043i q^{68} +(6.07055 - 2.82338i) q^{69} +(10.8189 - 10.8189i) q^{70} +(-0.239135 - 0.239135i) q^{71} +(-0.0380824 - 0.445518i) q^{72} +(-8.54904 - 8.54904i) q^{73} -8.10415i q^{74} +(-0.682288 - 1.46699i) q^{75} +(-2.19903 - 2.19903i) q^{76} -8.61233 q^{77} +10.4089 q^{79} +(6.62625 + 6.62625i) q^{80} +(-1.52746 - 8.86943i) q^{81} -13.7001i q^{82} +(2.83841 + 2.83841i) q^{83} +(3.83350 - 10.4999i) q^{84} +(-9.97066 - 9.97066i) q^{85} +(-2.62965 + 2.62965i) q^{86} +(2.13505 + 4.59057i) q^{87} +0.412503i q^{88} +(3.00755 - 3.00755i) q^{89} +(-11.2804 - 9.50383i) q^{90} -8.01616i q^{92} +(2.99529 - 8.20402i) q^{93} -0.330188 q^{94} -3.65298 q^{95} +(13.1177 + 4.78928i) q^{96} +(-6.99731 + 6.99731i) q^{97} +(3.83008 - 3.83008i) q^{98} +(0.707134 + 8.27261i) 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

Modular forms

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