LMFDB - Embedded newform 168.2.p.a.139.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(139,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.139"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.20457921756784916168704.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 - 4x^12 - 4x^10 + 16x^8 - 16x^6 - 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.15
Root			$-0.474920 - 1.33209i$ of defining polynomial
Character	$\chi$	$=$	168.139
Dual form			168.2.p.a.139.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33209 + 0.474920i) q^{2} -1.00000i q^{3} +(1.54890 + 1.26527i) q^{4} +1.58069 q^{5} +(0.474920 - 1.33209i) q^{6} +(-2.37995 - 1.15578i) q^{7} +(1.46237 + 2.42105i) q^{8} -1.00000 q^{9} +(2.10562 + 0.750703i) q^{10} -2.26057 q^{11} +(1.26527 - 1.54890i) q^{12} +0.548664 q^{13} +(-2.62140 - 2.66988i) q^{14} -1.58069i q^{15} +(0.798200 + 3.91955i) q^{16} -0.433635i q^{17} +(-1.33209 - 0.474920i) q^{18} +6.02255i q^{19} +(2.44834 + 2.00000i) q^{20} +(-1.15578 + 2.37995i) q^{21} +(-3.01127 - 1.07359i) q^{22} -8.24028i q^{23} +(2.42105 - 1.46237i) q^{24} -2.50141 q^{25} +(0.730867 + 0.260571i) q^{26} +1.00000i q^{27} +(-2.22394 - 4.80147i) q^{28} +0.548664i q^{29} +(0.750703 - 2.10562i) q^{30} -7.50941 q^{31} +(-0.798200 + 5.60026i) q^{32} +2.26057i q^{33} +(0.205942 - 0.577639i) q^{34} +(-3.76198 - 1.82694i) q^{35} +(-1.54890 - 1.26527i) q^{36} +4.21124i q^{37} +(-2.86023 + 8.02255i) q^{38} -0.548664i q^{39} +(2.31156 + 3.82694i) q^{40} -7.09032i q^{41} +(-2.66988 + 2.62140i) q^{42} -1.82694 q^{43} +(-3.50141 - 2.86023i) q^{44} -1.58069 q^{45} +(3.91347 - 10.9768i) q^{46} +11.5839 q^{47} +(3.91955 - 0.798200i) q^{48} +(4.32834 + 5.50141i) q^{49} +(-3.33209 - 1.18797i) q^{50} -0.433635 q^{51} +(0.849827 + 0.694206i) q^{52} +3.71005i q^{53} +(-0.474920 + 1.33209i) q^{54} -3.57327 q^{55} +(-0.682172 - 7.45216i) q^{56} +6.02255 q^{57} +(-0.260571 + 0.730867i) q^{58} -11.5240i q^{59} +(2.00000 - 2.44834i) q^{60} +12.1325 q^{61} +(-10.0032 - 3.56636i) q^{62} +(2.37995 + 1.15578i) q^{63} +(-3.72294 + 7.08094i) q^{64} +0.867270 q^{65} +(-1.07359 + 3.01127i) q^{66} +9.35089 q^{67} +(0.548664 - 0.671659i) q^{68} -8.24028 q^{69} +(-4.14363 - 4.22027i) q^{70} -1.27953i q^{71} +(-1.46237 - 2.42105i) q^{72} -0.867270i q^{73} +(-2.00000 + 5.60973i) q^{74} +2.50141i q^{75} +(-7.62013 + 9.32834i) q^{76} +(5.38005 + 2.61272i) q^{77} +(0.260571 - 0.730867i) q^{78} +10.3696i q^{79} +(1.26171 + 6.19561i) q^{80} +1.00000 q^{81} +(3.36733 - 9.44491i) q^{82} +6.13554i q^{83} +(-4.80147 + 2.22394i) q^{84} -0.685444i q^{85} +(-2.43364 - 0.867648i) q^{86} +0.548664 q^{87} +(-3.30579 - 5.47295i) q^{88} +7.95759i q^{89} +(-2.10562 - 0.750703i) q^{90} +(-1.30579 - 0.634135i) q^{91} +(10.4261 - 12.7634i) q^{92} +7.50941i q^{93} +(15.4307 + 5.50141i) q^{94} +9.51981i q^{95} +(5.60026 + 0.798200i) q^{96} -19.1778i q^{97} +(3.15300 + 9.38396i) q^{98} +2.26057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 2 q^{4} - 10 q^{8} - 16 q^{9} - 8 q^{11} - 14 q^{14} + 18 q^{16} - 2 q^{18} + 8 q^{22} + 16 q^{25} - 10 q^{28} - 16 q^{30} - 18 q^{32} + 24 q^{35} - 2 q^{36} - 4 q^{42} - 8 q^{43} + 52 q^{46}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 + 2 * q^4 - 10 * q^8 - 16 * q^9 - 8 * q^11 - 14 * q^14 + 18 * q^16 - 2 * q^18 + 8 * q^22 + 16 * q^25 - 10 * q^28 - 16 * q^30 - 18 * q^32 + 24 * q^35 - 2 * q^36 - 4 * q^42 - 8 * q^43 + 52 * q^46 - 8 * q^49 - 34 * q^50 + 50 * q^56 - 16 * q^57 + 24 * q^58 + 32 * q^60 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 10 * q^72 - 32 * q^74 - 24 * q^78 + 16 * q^81 + 8 * q^84 - 32 * q^86 - 88 * q^88 - 56 * q^91 + 44 * q^92 + 66 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.33209	+	0.474920i	0.941927	+	0.335819i
$2$	1.33209	+	0.474920i	0.941927	+	0.335819i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.54890	+	1.26527i	0.774451	+	0.632633i
$5$	1.58069			0.706908			0.353454	−	0.935452i	$-0.385007\pi$
$5$	1.58069			0.706908			0.353454	+	0.935452i	$0.385007\pi$
$6$	0.474920	−	1.33209i	0.193885	−	0.543822i
$7$	−2.37995	−	1.15578i	−0.899537	−	0.436844i
$7$	−2.37995	−	1.15578i	−0.899537	−	0.436844i
$8$	1.46237	+	2.42105i	0.517026	+	0.855970i
$9$	−1.00000			−0.333333
$10$	2.10562	+	0.750703i	0.665855	+	0.237393i
$11$	−2.26057			−0.681588			−0.340794	−	0.940138i	$-0.610696\pi$
$11$	−2.26057			−0.681588			−0.340794	+	0.940138i	$0.610696\pi$
$12$	1.26527	−	1.54890i	0.365251	−	0.447130i
$13$	0.548664			0.152172			0.0760860	−	0.997101i	$-0.475758\pi$
$13$	0.548664			0.152172			0.0760860	+	0.997101i	$0.475758\pi$
$14$	−2.62140	−	2.66988i	−0.700598	−	0.713557i
$15$		−	1.58069i		−	0.408134i
$16$	0.798200	+	3.91955i	0.199550	+	0.979888i
$17$		−	0.433635i		−	0.105172i	−0.998616	−	0.0525860i	$-0.983254\pi$
$17$		−	0.433635i		−	0.105172i	0.998616	−	0.0525860i	$-0.0167464\pi$
$18$	−1.33209	−	0.474920i	−0.313976	−	0.111940i
$19$			6.02255i			1.38167i	0.723014	+	0.690834i	$0.242756\pi$
$19$			6.02255i			1.38167i	−0.723014	+	0.690834i	$0.757244\pi$
$20$	2.44834	+	2.00000i	0.547466	+	0.447214i
$21$	−1.15578	+	2.37995i	−0.252212	+	0.519348i
$22$	−3.01127	−	1.07359i	−0.642006	−	0.228890i
$23$		−	8.24028i		−	1.71822i	−0.511794	−	0.859108i	$-0.671019\pi$
$23$		−	8.24028i		−	1.71822i	0.511794	−	0.859108i	$-0.328981\pi$
$24$	2.42105	−	1.46237i	0.494194	−	0.298505i
$25$	−2.50141			−0.500281
$26$	0.730867	+	0.260571i	0.143335	+	0.0511022i
$27$			1.00000i			0.192450i
$28$	−2.22394	−	4.80147i	−0.420286	−	0.907392i
$29$			0.548664i			0.101884i	0.998702	+	0.0509422i	$0.0162224\pi$
$29$			0.548664i			0.101884i	−0.998702	+	0.0509422i	$0.983778\pi$
$30$	0.750703	−	2.10562i	0.137059	−	0.384432i
$31$	−7.50941			−1.34873			−0.674365	−	0.738398i	$-0.735582\pi$
$31$	−7.50941			−1.34873			−0.674365	+	0.738398i	$0.735582\pi$
$32$	−0.798200	+	5.60026i	−0.141103	+	0.989995i
$33$			2.26057i			0.393515i
$34$	0.205942	−	0.577639i	0.0353187	−	0.0990642i
$35$	−3.76198	−	1.82694i	−0.635890	−	0.308809i
$36$	−1.54890	−	1.26527i	−0.258150	−	0.210878i
$37$			4.21124i			0.692324i	0.938175	+	0.346162i	$0.112515\pi$
$37$			4.21124i			0.692324i	−0.938175	+	0.346162i	$0.887485\pi$
$38$	−2.86023	+	8.02255i	−0.463990	+	1.30143i
$39$		−	0.548664i		−	0.0878565i
$40$	2.31156	+	3.82694i	0.365490	+	0.605092i
$41$		−	7.09032i		−	1.10732i	−0.832742	−	0.553661i	$-0.813230\pi$
$41$		−	7.09032i		−	1.10732i	0.832742	−	0.553661i	$-0.186770\pi$
$42$	−2.66988	+	2.62140i	−0.411972	+	0.404490i
$43$	−1.82694			−0.278605			−0.139303	−	0.990250i	$-0.544486\pi$
$43$	−1.82694			−0.278605			−0.139303	+	0.990250i	$0.544486\pi$
$44$	−3.50141	−	2.86023i	−0.527857	−	0.431195i
$45$	−1.58069			−0.235636
$46$	3.91347	−	10.9768i	0.577009	−	1.61843i
$47$	11.5839			1.68968			0.844840	−	0.535018i	$-0.179695\pi$
$47$	11.5839			1.68968			0.844840	+	0.535018i	$0.179695\pi$
$48$	3.91955	−	0.798200i	0.565738	−	0.115210i
$49$	4.32834	+	5.50141i	0.618334	+	0.785915i
$50$	−3.33209	−	1.18797i	−0.471228	−	0.168004i
$51$	−0.433635			−0.0607210
$52$	0.849827	+	0.694206i	0.117850	+	0.0962691i
$53$			3.71005i			0.509615i	0.966992	+	0.254807i	$0.0820121\pi$
$53$			3.71005i			0.509615i	−0.966992	+	0.254807i	$0.917988\pi$
$54$	−0.474920	+	1.33209i	−0.0646284	+	0.181274i
$55$	−3.57327			−0.481820
$56$	−0.682172	−	7.45216i	−0.0911591	−	0.995836i
$57$	6.02255			0.797706
$58$	−0.260571	+	0.730867i	−0.0342147	+	0.0959676i
$59$		−	11.5240i		−	1.50029i	−0.661273	−	0.750145i	$-0.729983\pi$
$59$		−	11.5240i		−	1.50029i	0.661273	−	0.750145i	$-0.270017\pi$
$60$	2.00000	−	2.44834i	0.258199	−	0.316080i
$61$	12.1325			1.55341			0.776706	−	0.629864i	$-0.216889\pi$
$61$	12.1325			1.55341			0.776706	+	0.629864i	$0.216889\pi$
$62$	−10.0032	−	3.56636i	−1.27040	−	0.452929i
$63$	2.37995	+	1.15578i	0.299846	+	0.145615i
$64$	−3.72294	+	7.08094i	−0.465368	+	0.885117i
$65$	0.867270			0.107572
$66$	−1.07359	+	3.01127i	−0.132150	+	0.370662i
$67$	9.35089			1.14239			0.571196	−	0.820813i	$-0.306479\pi$
$67$	9.35089			1.14239			0.571196	+	0.820813i	$0.306479\pi$
$68$	0.548664	−	0.671659i	0.0665353	−	0.0814506i
$69$	−8.24028			−0.992013
$70$	−4.14363	−	4.22027i	−0.495258	−	0.504419i
$71$		−	1.27953i		−	0.151852i	−0.997113	−	0.0759262i	$-0.975809\pi$
$71$		−	1.27953i		−	0.151852i	0.997113	−	0.0759262i	$-0.0241913\pi$
$72$	−1.46237	−	2.42105i	−0.172342	−	0.285323i
$73$		−	0.867270i		−	0.101506i	−0.998711	−	0.0507531i	$-0.983838\pi$
$73$		−	0.867270i		−	0.101506i	0.998711	−	0.0507531i	$-0.0161622\pi$
$74$	−2.00000	+	5.60973i	−0.232495	+	0.652118i
$75$			2.50141i			0.288837i
$76$	−7.62013	+	9.32834i	−0.874089	+	1.07003i
$77$	5.38005	+	2.61272i	0.613114	+	0.297748i
$78$	0.260571	−	0.730867i	0.0295039	−	0.0827544i
$79$			10.3696i			1.16668i	0.812230	+	0.583338i	$0.198253\pi$
$79$			10.3696i			1.16668i	−0.812230	+	0.583338i	$0.801747\pi$
$80$	1.26171	+	6.19561i	0.141064	+	0.692690i
$81$	1.00000			0.111111
$82$	3.36733	−	9.44491i	0.371859	−	1.04302i
$83$			6.13554i			0.673463i	0.941601	+	0.336732i	$0.109321\pi$
$83$			6.13554i			0.673463i	−0.941601	+	0.336732i	$0.890679\pi$
$84$	−4.80147	+	2.22394i	−0.523883	+	0.242652i
$85$		−	0.685444i		−	0.0743469i
$86$	−2.43364	−	0.867648i	−0.262426	−	0.0935609i
$87$	0.548664			0.0588229
$88$	−3.30579	−	5.47295i	−0.352399	−	0.583418i
$89$			7.95759i			0.843503i	0.906712	+	0.421751i	$0.138584\pi$
$89$			7.95759i			0.843503i	−0.906712	+	0.421751i	$0.861416\pi$
$90$	−2.10562	−	0.750703i	−0.221952	−	0.0791310i
$91$	−1.30579	−	0.634135i	−0.136884	−	0.0664754i
$92$	10.4261	−	12.7634i	1.08700	−	1.33068i
$93$			7.50941i			0.778689i
$94$	15.4307	+	5.50141i	1.59156	+	0.567427i
$95$			9.51981i			0.976712i
$96$	5.60026	+	0.798200i	0.571574	+	0.0814660i
$97$		−	19.1778i		−	1.94721i	−0.228233	−	0.973607i	$-0.573295\pi$
$97$		−	19.1778i		−	1.94721i	0.228233	−	0.973607i	$-0.426705\pi$
$98$	3.15300	+	9.38396i	0.318501	+	0.947923i
$99$	2.26057			0.227196
$100$	−3.87443	−	3.16494i	−0.387443	−	0.316494i
$101$	−4.74208			−0.471855			−0.235927	−	0.971771i	$-0.575813\pi$
$101$	−4.74208			−0.471855			−0.235927	+	0.971771i	$0.575813\pi$
$102$	−0.577639	−	0.205942i	−0.0571948	−	0.0203913i
$103$	−2.01040			−0.198090			−0.0990452	−	0.995083i	$-0.531579\pi$
$103$	−2.01040			−0.198090			−0.0990452	+	0.995083i	$0.531579\pi$
$104$	0.802350	+	1.32834i	0.0786769	+	0.130255i
$105$	−1.82694	+	3.76198i	−0.178291	+	0.367131i
$106$	−1.76198	+	4.94211i	−0.171138	+	0.480020i
$107$	17.7845			1.71929			0.859647	−	0.510888i	$-0.170683\pi$
$107$	17.7845			1.71929			0.859647	+	0.510888i	$0.170683\pi$
$108$	−1.26527	+	1.54890i	−0.121750	+	0.149043i
$109$		−	12.0432i		−	1.15353i	−0.816909	−	0.576766i	$-0.804314\pi$
$109$		−	12.0432i		−	1.15353i	0.816909	−	0.576766i	$-0.195686\pi$
$110$	−4.75990	−	1.69702i	−0.453839	−	0.161804i
$111$	4.21124			0.399713
$112$	2.63046	−	10.2509i	0.248555	−	0.968618i
$113$	−2.86727			−0.269730			−0.134865	−	0.990864i	$-0.543060\pi$
$113$	−2.86727			−0.269730			−0.134865	+	0.990864i	$0.543060\pi$
$114$	8.02255	+	2.86023i	0.751380	+	0.267885i
$115$		−	13.0254i		−	1.21462i
$116$	−0.694206	+	0.849827i	−0.0644554	+	0.0789045i
$117$	−0.548664			−0.0507240
$118$	5.47295	−	15.3509i	0.503826	−	1.41316i
$119$	−0.501187	+	1.03203i	−0.0459437	+	0.0946061i
$120$	3.82694	−	2.31156i	0.349350	−	0.211016i
$121$	−5.88982			−0.535438
$122$	16.1616	+	5.76198i	1.46320	+	0.521665i
$123$	−7.09032			−0.639312
$124$	−11.6313	−	9.50141i	−1.04453	−	0.853251i
$125$	−11.8574			−1.06056
$126$	2.62140	+	2.66988i	0.233533	+	0.237852i
$127$			14.9928i			1.33039i	0.746669	+	0.665196i	$0.231652\pi$
$127$			14.9928i			1.33039i	−0.746669	+	0.665196i	$0.768348\pi$
$128$	−8.32215	+	7.66432i	−0.735581	+	0.677436i
$129$			1.82694i			0.160853i
$130$	1.15528	+	0.411883i	0.101325	+	0.0361246i
$131$			8.52114i			0.744496i	0.928133	+	0.372248i	$0.121413\pi$
$131$			8.52114i			0.744496i	−0.928133	+	0.372248i	$0.878587\pi$
$132$	−2.86023	+	3.50141i	−0.248951	+	0.304758i
$133$	6.96075	−	14.3334i	0.603573	−	1.24286i
$134$	12.4562	+	4.44092i	1.07605	+	0.383637i
$135$			1.58069i			0.136045i
$136$	1.04985	−	0.634135i	0.0900240	−	0.0543766i
$137$	5.00281			0.427419			0.213709	−	0.976897i	$-0.431445\pi$
$137$	5.00281			0.427419			0.213709	+	0.976897i	$0.431445\pi$
$138$	−10.9768	−	3.91347i	−0.934403	−	0.333137i
$139$			14.3106i			1.21381i	0.794776	+	0.606903i	$0.207588\pi$
$139$			14.3106i			1.21381i	−0.794776	+	0.606903i	$0.792412\pi$
$140$	−3.51537	−	7.58965i	−0.297103	−	0.641443i
$141$		−	11.5839i		−	0.975538i
$142$	0.607674	−	1.70444i	0.0509949	−	0.143034i
$143$	−1.24029			−0.103719
$144$	−0.798200	−	3.91955i	−0.0665167	−	0.326629i
$145$			0.867270i			0.0720229i
$146$	0.411883	−	1.15528i	0.0340877	−	0.0956115i
$147$	5.50141	−	4.32834i	0.453748	−	0.356996i
$148$	−5.32834	+	6.52280i	−0.437987	+	0.536171i
$149$		−	18.4553i		−	1.51192i	−0.654619	−	0.755959i	$-0.727171\pi$
$149$		−	18.4553i		−	1.51192i	0.654619	−	0.755959i	$-0.272829\pi$
$150$	−1.18797	+	3.33209i	−0.0969970	+	0.272064i
$151$		−	14.5334i		−	1.18271i	−0.806411	−	0.591356i	$-0.798593\pi$
$151$		−	14.5334i		−	1.18271i	0.806411	−	0.591356i	$-0.201407\pi$
$152$	−14.5809	+	8.80720i	−1.18267	+	0.714358i
$153$			0.433635i			0.0350573i
$154$	5.92585	+	6.03546i	0.477519	+	0.486352i
$155$	−11.8701			−0.953428
$156$	0.694206	−	0.849827i	0.0555810	−	0.0680406i
$157$	5.80975			0.463669			0.231834	−	0.972755i	$-0.425527\pi$
$157$	5.80975			0.463669			0.231834	+	0.972755i	$0.425527\pi$
$158$	−4.92474	+	13.8132i	−0.391791	+	1.09892i
$159$	3.71005			0.294226
$160$	−1.26171	+	8.85229i	−0.0997470	+	0.699835i
$161$	−9.52395	+	19.6115i	−0.750593	+	1.54560i
$162$	1.33209	+	0.474920i	0.104659	+	0.0373132i
$163$	−17.3509			−1.35903			−0.679513	−	0.733663i	$-0.737809\pi$
$163$	−17.3509			−1.35903			−0.679513	+	0.733663i	$0.737809\pi$
$164$	8.97114	−	10.9822i	0.700529	−	0.857567i
$165$			3.57327i			0.278179i
$166$	−2.91389	+	8.17306i	−0.226162	+	0.634353i
$167$	−0.823767			−0.0637450			−0.0318725	−	0.999492i	$-0.510147\pi$
$167$	−0.823767			−0.0637450			−0.0318725	+	0.999492i	$0.510147\pi$
$168$	−7.45216	+	0.682172i	−0.574946	+	0.0526307i
$169$	−12.6990			−0.976844
$170$	0.325531	−	0.913070i	0.0249671	−	0.0700293i
$171$		−	6.02255i		−	0.460556i
$172$	−2.82975	−	2.31156i	−0.215766	−	0.176255i
$173$	−19.5230			−1.48430			−0.742152	−	0.670231i	$-0.766195\pi$
$173$	−19.5230			−1.48430			−0.742152	+	0.670231i	$0.766195\pi$
$174$	0.730867	+	0.260571i	0.0554069	+	0.0197539i
$175$	5.95322	+	2.89108i	0.450021	+	0.218545i
$176$	−1.80439	−	8.86042i	−0.136011	−	0.667880i
$177$	−11.5240			−0.866193
$178$	−3.77921	+	10.6002i	−0.283264	+	0.794518i
$179$	−4.39611			−0.328581			−0.164290	−	0.986412i	$-0.552533\pi$
$179$	−4.39611			−0.328581			−0.164290	+	0.986412i	$0.552533\pi$
$180$	−2.44834	−	2.00000i	−0.182489	−	0.149071i
$181$	−8.14738			−0.605590			−0.302795	−	0.953056i	$-0.597920\pi$
$181$	−8.14738			−0.605590			−0.302795	+	0.953056i	$0.597920\pi$
$182$	−1.43827	−	1.46487i	−0.106611	−	0.108583i
$183$		−	12.1325i		−	0.896863i
$184$	19.9501	−	12.0503i	1.47074	−	0.888363i
$185$			6.65668i			0.489409i
$186$	−3.56636	+	10.0032i	−0.261499	+	0.733468i
$187$			0.980263i			0.0716839i
$188$	17.9423	+	14.6567i	1.30858	+	1.06895i
$189$	1.15578	−	2.37995i	0.0840707	−	0.173116i
$190$	−4.52114	+	12.6812i	−0.327998	+	0.919991i
$191$		−	0.420123i		−	0.0303990i	−0.999884	−	0.0151995i	$-0.995162\pi$
$191$		−	0.420123i		−	0.0303990i	0.999884	−	0.0151995i	$-0.00483834\pi$
$192$	7.08094	+	3.72294i	0.511023	+	0.268680i
$193$	−11.1553			−0.802974			−0.401487	−	0.915865i	$-0.631507\pi$
$193$	−11.1553			−0.802974			−0.401487	+	0.915865i	$0.631507\pi$
$194$	9.10792	−	25.5465i	0.653911	−	1.83413i
$195$		−	0.867270i		−	0.0621065i
$196$	−0.256564	+	13.9976i	−0.0183260	+	0.999832i
$197$			4.95035i			0.352698i	0.984328	+	0.176349i	$0.0564287\pi$
$197$			4.95035i			0.352698i	−0.984328	+	0.176349i	$0.943571\pi$
$198$	3.01127	+	1.07359i	0.214002	+	0.0762967i
$199$	−12.0851			−0.856687			−0.428343	−	0.903616i	$-0.640903\pi$
$199$	−12.0851			−0.856687			−0.428343	+	0.903616i	$0.640903\pi$
$200$	−3.65798	−	6.05602i	−0.258658	−	0.428225i
$201$		−	9.35089i		−	0.659561i
$202$	−6.31686	−	2.25211i	−0.444453	−	0.158458i
$203$	0.634135	−	1.30579i	0.0445076	−	0.0916488i
$204$	−0.671659	−	0.548664i	−0.0470255	−	0.0384142i
$205$		−	11.2076i		−	0.782775i
$206$	−2.67802	−	0.954777i	−0.186587	−	0.0665225i
$207$			8.24028i			0.572739i
$208$	0.437944	+	2.15052i	0.0303659	+	0.149111i
$209$		−	13.6144i		−	0.941728i
$210$	−4.22027	+	4.14363i	−0.291226	+	0.285937i
$211$	6.17306			0.424971			0.212486	−	0.977164i	$-0.431844\pi$
$211$	6.17306			0.424971			0.212486	+	0.977164i	$0.431844\pi$
$212$	−4.69421	+	5.74651i	−0.322399	+	0.394672i
$213$	−1.27953			−0.0876720
$214$	23.6905	+	8.44622i	1.61945	+	0.577372i
$215$	−2.88783			−0.196948
$216$	−2.42105	+	1.46237i	−0.164731	+	0.0995017i
$217$	17.8720	+	8.67923i	1.21323	+	0.589185i
$218$	5.71956	−	16.0426i	0.387378	−	1.08654i
$219$	−0.867270			−0.0586047
$220$	−5.53465	−	4.52114i	−0.373146	−	0.304815i
$221$		−	0.237920i		−	0.0160042i
$222$	5.60973	+	2.00000i	0.376500	+	0.134231i
$223$	18.4078			1.23268			0.616340	−	0.787480i	$-0.288615\pi$
$223$	18.4078			1.23268			0.616340	+	0.787480i	$0.288615\pi$
$224$	8.37235	−	12.4058i	0.559401	−	0.828897i
$225$	2.50141			0.166760
$226$	−3.81945	−	1.36172i	−0.254066	−	0.0905804i
$227$		−	10.6567i		−	0.707309i	−0.935376	−	0.353654i	$-0.884939\pi$
$227$		−	10.6567i		−	0.707309i	0.935376	−	0.353654i	$-0.115061\pi$
$228$	9.32834	+	7.62013i	0.617785	+	0.504655i
$229$	−8.97114			−0.592830			−0.296415	−	0.955059i	$-0.595791\pi$
$229$	−8.97114			−0.592830			−0.296415	+	0.955059i	$0.595791\pi$
$230$	6.18600	−	17.3509i	0.407893	−	1.14408i
$231$	2.61272	−	5.38005i	0.171905	−	0.353981i
$232$	−1.32834	+	0.802350i	−0.0872099	+	0.0526769i
$233$	14.9124			0.976942			0.488471	−	0.872580i	$-0.337555\pi$
$233$	14.9124			0.976942			0.488471	+	0.872580i	$0.337555\pi$
$234$	−0.730867	−	0.260571i	−0.0477783	−	0.0170341i
$235$	18.3106			1.19445
$236$	14.5809	−	17.8495i	0.949134	−	1.16190i
$237$	10.3696			0.673580
$238$	−1.15776	+	1.13673i	−0.0750461	+	0.0736832i
$239$			13.1370i			0.849759i	0.905250	+	0.424880i	$0.139684\pi$
$239$			13.1370i			0.849759i	−0.905250	+	0.424880i	$0.860316\pi$
$240$	6.19561	−	1.26171i	0.399925	−	0.0814431i
$241$			10.1355i			0.652888i	0.945217	+	0.326444i	$0.105850\pi$
$241$			10.1355i			0.652888i	−0.945217	+	0.326444i	$0.894150\pi$
$242$	−7.84574	−	2.79719i	−0.504343	−	0.179810i
$243$		−	1.00000i		−	0.0641500i
$244$	18.7921	+	15.3509i	1.20304	+	0.982740i
$245$	6.84179	+	8.69604i	0.437106	+	0.555570i
$246$	−9.44491	−	3.36733i	−0.602185	−	0.214693i
$247$			3.30435i			0.210251i
$248$	−10.9815	−	18.1806i	−0.697329	−	1.15447i
$249$	6.13554			0.388824
$250$	−15.7951	−	5.63132i	−0.998970	−	0.356156i
$251$			22.7018i			1.43292i	0.697626	+	0.716462i	$0.254240\pi$
$251$			22.7018i			1.43292i	−0.697626	+	0.716462i	$0.745760\pi$
$252$	2.22394	+	4.80147i	0.140095	+	0.302464i
$253$			18.6277i			1.17112i
$254$	−7.12035	+	19.9716i	−0.446771	+	1.25313i
$255$	−0.685444			−0.0429242
$256$	−14.7258	+	6.25717i	−0.920360	+	0.391073i
$257$		−	16.1326i		−	1.00632i	−0.864192	−	0.503162i	$-0.832170\pi$
$257$		−	16.1326i		−	1.00632i	0.864192	−	0.503162i	$-0.167830\pi$
$258$	−0.867648	+	2.43364i	−0.0540174	+	0.151511i
$259$	4.86727	−	10.0225i	0.302437	−	0.622771i
$260$	1.34332	+	1.09733i	0.0833090	+	0.0680534i
$261$		−	0.548664i		−	0.0339614i
$262$	−4.04686	+	11.3509i	−0.250016	+	0.701260i
$263$		−	15.0581i		−	0.928519i	−0.885699	−	0.464260i	$-0.846320\pi$
$263$		−	15.0581i		−	0.928519i	0.885699	−	0.464260i	$-0.153680\pi$
$264$	−5.47295	+	3.30579i	−0.336837	+	0.203458i
$265$			5.86446i			0.360251i
$266$	16.0795	−	15.7875i	0.985898	−	0.967993i
$267$	7.95759			0.486996
$268$	14.4836	+	11.8314i	0.884728	+	0.722716i
$269$	−8.76288			−0.534282			−0.267141	−	0.963657i	$-0.586079\pi$
$269$	−8.76288			−0.534282			−0.267141	+	0.963657i	$0.586079\pi$
$270$	−0.750703	+	2.10562i	−0.0456863	+	0.128144i
$271$	−4.31238			−0.261958			−0.130979	−	0.991385i	$-0.541812\pi$
$271$	−4.31238			−0.261958			−0.130979	+	0.991385i	$0.541812\pi$
$272$	1.69965	−	0.346128i	0.103057	−	0.0209871i
$273$	−0.634135	+	1.30579i	−0.0383796	+	0.0790302i
$274$	6.66417	+	2.37593i	0.402597	+	0.143535i
$275$	5.65460			0.340985
$276$	−12.7634	−	10.4261i	−0.768266	−	0.627580i
$277$			25.5528i			1.53532i	0.640857	+	0.767661i	$0.278579\pi$
$277$			25.5528i			1.53532i	−0.640857	+	0.767661i	$0.721421\pi$
$278$	−6.79636	+	19.0629i	−0.407619	+	1.14332i
$279$	7.50941			0.449577
$280$	−1.07831	−	11.7796i	−0.0644411	−	0.703965i
$281$	2.17501			0.129751			0.0648753	−	0.997893i	$-0.479335\pi$
$281$	2.17501			0.129751			0.0648753	+	0.997893i	$0.479335\pi$
$282$	5.50141	−	15.4307i	0.327604	−	0.918885i
$283$		−	12.2880i		−	0.730446i	−0.930920	−	0.365223i	$-0.880993\pi$
$283$		−	12.2880i		−	0.730446i	0.930920	−	0.365223i	$-0.119007\pi$
$284$	1.61895	−	1.98187i	0.0960669	−	0.117602i
$285$	9.51981			0.563905
$286$	−1.65218	−	0.589040i	−0.0976953	−	0.0348307i
$287$	−8.19485	+	16.8746i	−0.483727	+	0.996077i
$288$	0.798200	−	5.60026i	0.0470344	−	0.329998i
$289$	16.8120			0.988939
$290$	−0.411883	+	1.15528i	−0.0241866	+	0.0678402i
$291$	−19.1778			−1.12422
$292$	1.09733	−	1.34332i	0.0642163	−	0.0786117i
$293$	24.8790			1.45345			0.726724	−	0.686929i	$-0.241042\pi$
$293$	24.8790			1.45345			0.726724	+	0.686929i	$0.241042\pi$
$294$	9.38396	−	3.15300i	0.547283	−	0.183886i
$295$		−	18.2158i		−	1.06057i
$296$	−10.1956	+	6.15839i	−0.592608	+	0.357949i
$297$		−	2.26057i		−	0.131172i
$298$	8.76479	−	24.5840i	0.507730	−	1.42412i
$299$		−	4.52114i		−	0.261464i
$300$	−3.16494	+	3.87443i	−0.182728	+	0.223691i
$301$	4.34802	+	2.11154i	0.250616	+	0.121707i
$302$	6.90219	−	19.3597i	0.397177	−	1.11403i
$303$			4.74208i			0.272426i
$304$	−23.6057	+	4.80720i	−1.35388	+	0.275712i
$305$	19.1778			1.09812
$306$	−0.205942	+	0.577639i	−0.0117729	+	0.0330214i
$307$			17.0254i			0.971689i	0.874045	+	0.485844i	$0.161488\pi$
$307$			17.0254i			0.971689i	−0.874045	+	0.485844i	$0.838512\pi$
$308$	5.02738	+	10.8541i	0.286462	+	0.618467i
$309$			2.01040i			0.114368i
$310$	−15.8120	−	5.63733i	−0.898059	−	0.320179i
$311$	−23.2983			−1.32113			−0.660564	−	0.750770i	$-0.729683\pi$
$311$	−23.2983			−1.32113			−0.660564	+	0.750770i	$0.729683\pi$
$312$	1.32834	−	0.802350i	0.0752025	−	0.0454241i
$313$		−	15.0479i		−	0.850558i	−0.905062	−	0.425279i	$-0.860176\pi$
$313$		−	15.0479i		−	0.850558i	0.905062	−	0.425279i	$-0.139824\pi$
$314$	7.73909	+	2.75917i	0.436742	+	0.155709i
$315$	3.76198	+	1.82694i	0.211963	+	0.102936i
$316$	−13.1204	+	16.0616i	−0.738078	+	0.903533i
$317$			22.4761i			1.26238i	0.775627	+	0.631192i	$0.217434\pi$
$317$			22.4761i			1.26238i	−0.775627	+	0.631192i	$0.782566\pi$
$318$	4.94211	+	1.76198i	0.277140	+	0.0988067i
$319$		−	1.24029i		−	0.0694431i
$320$	−5.88483	+	11.1928i	−0.328972	+	0.625697i
$321$		−	17.7845i		−	0.992635i
$322$	−22.0006	+	21.6010i	−1.22604	+	1.20378i
$323$	2.61159			0.145313
$324$	1.54890	+	1.26527i	0.0860502	+	0.0702926i
$325$	−1.37243			−0.0761288
$326$	−23.1129	−	8.24028i	−1.28010	−	0.456387i
$327$	−12.0432			−0.665992
$328$	17.1660	−	10.3687i	0.947834	−	0.572514i
$329$	−27.5690	−	13.3884i	−1.51993	−	0.738127i
$330$	−1.69702	+	4.75990i	−0.0934177	+	0.262024i
$331$	−23.5315			−1.29341			−0.646705	−	0.762740i	$-0.723853\pi$
$331$	−23.5315			−1.29341			−0.646705	+	0.762740i	$0.723853\pi$
$332$	−7.76310	+	9.50336i	−0.426055	+	0.521564i
$333$		−	4.21124i		−	0.230775i
$334$	−1.09733	−	0.391223i	−0.0600431	−	0.0214068i
$335$	14.7809			0.807567
$336$	−10.2509	−	2.63046i	−0.559232	−	0.143504i
$337$	8.77682			0.478104			0.239052	−	0.971007i	$-0.423163\pi$
$337$	8.77682			0.478104			0.239052	+	0.971007i	$0.423163\pi$
$338$	−16.9161	−	6.03099i	−0.920115	−	0.328042i
$339$			2.86727i			0.155729i
$340$	0.867270	−	1.06169i	0.0470343	−	0.0575781i
$341$	16.9756			0.919278
$342$	2.86023	−	8.02255i	0.154663	−	0.433810i
$343$	−3.94283	−	18.0957i	−0.212893	−	0.977076i
$344$	−2.67166	−	4.42310i	−0.144046	−	0.238478i
$345$	−13.0254			−0.701262
$346$	−26.0063	−	9.27185i	−1.39811	−	0.498457i
$347$	−4.00489			−0.214994			−0.107497	−	0.994205i	$-0.534284\pi$
$347$	−4.00489			−0.214994			−0.107497	+	0.994205i	$0.534284\pi$
$348$	0.849827	+	0.694206i	0.0455555	+	0.0372134i
$349$	3.43649			0.183951			0.0919756	−	0.995761i	$-0.470682\pi$
$349$	3.43649			0.183951			0.0919756	+	0.995761i	$0.470682\pi$
$350$	6.55717	+	6.67846i	0.350496	+	0.356979i
$351$			0.548664i			0.0292855i
$352$	1.80439	−	12.6598i	0.0961742	−	0.674769i
$353$			23.0903i			1.22897i	0.788927	+	0.614487i	$0.210637\pi$
$353$			23.0903i			1.22897i	−0.788927	+	0.614487i	$0.789363\pi$
$354$	−15.3509	−	5.47295i	−0.815891	−	0.290884i
$355$		−	2.02255i		−	0.107346i
$356$	−10.0685	+	12.3255i	−0.533628	+	0.653252i
$357$	1.03203	+	0.501187i	0.0546208	+	0.0265256i
$358$	−5.85600	−	2.08780i	−0.309499	−	0.110344i
$359$		−	21.8882i		−	1.15522i	−0.816315	−	0.577608i	$-0.803986\pi$
$359$		−	21.8882i		−	1.15522i	0.816315	−	0.577608i	$-0.196014\pi$
$360$	−2.31156	−	3.82694i	−0.121830	−	0.201697i
$361$	−17.2711			−0.909004
$362$	−10.8530	−	3.86935i	−0.570421	−	0.203368i
$363$			5.88982i			0.309135i
$364$	−1.22020	−	2.63439i	−0.0639557	−	0.138080i
$365$		−	1.37089i		−	0.0717556i
$366$	5.76198	−	16.1616i	0.301183	−	0.844779i
$367$	27.9276			1.45781			0.728905	−	0.684614i	$-0.240029\pi$
$367$	27.9276			1.45781			0.728905	+	0.684614i	$0.240029\pi$
$368$	32.2982	−	6.57739i	1.68366	−	0.342870i
$369$			7.09032i			0.369107i
$370$	−3.16139	+	8.86727i	−0.164353	+	0.460987i
$371$	4.28801	−	8.82975i	0.222622	−	0.458418i
$372$	−9.50141	+	11.6313i	−0.492625	+	0.603057i
$373$			15.2403i			0.789111i	0.918872	+	0.394555i	$0.129101\pi$
$373$			15.2403i			0.789111i	−0.918872	+	0.394555i	$0.870899\pi$
$374$	−0.465546	+	1.30579i	−0.0240728	+	0.0675210i
$375$			11.8574i			0.612315i
$376$	16.9399	+	28.0451i	0.873609	+	1.44632i
$377$			0.301032i			0.0155039i
$378$	2.66988	−	2.62140i	0.137324	−	0.134830i
$379$	11.4864			0.590018			0.295009	−	0.955494i	$-0.404677\pi$
$379$	11.4864			0.590018			0.295009	+	0.955494i	$0.404677\pi$
$380$	−12.0451	+	14.7453i	−0.617900	+	0.756416i
$381$	14.9928			0.768102
$382$	0.199525	−	0.559640i	0.0102086	−	0.0286337i
$383$	−22.4746			−1.14840			−0.574198	−	0.818716i	$-0.694686\pi$
$383$	−22.4746			−1.14840			−0.574198	+	0.818716i	$0.694686\pi$
$384$	7.66432	+	8.32215i	0.391118	+	0.424688i
$385$	8.50422	+	4.12992i	0.433415	+	0.210480i
$386$	−14.8598	−	5.29786i	−0.756343	−	0.269654i
$387$	1.82694			0.0928684
$388$	24.2651	−	29.7046i	1.23187	−	1.50802i
$389$		−	20.5907i		−	1.04399i	−0.852949	−	0.521994i	$-0.825188\pi$
$389$		−	20.5907i		−	1.04399i	0.852949	−	0.521994i	$-0.174812\pi$
$390$	0.411883	−	1.15528i	0.0208565	−	0.0584998i
$391$	−3.57327			−0.180708
$392$	−6.98952	+	18.5242i	−0.353024	+	0.935614i
$393$	8.52114			0.429835
$394$	−2.35102	+	6.59428i	−0.118442	+	0.332215i
$395$			16.3912i			0.824732i
$396$	3.50141	+	2.86023i	0.175952	+	0.143732i
$397$	−26.8778			−1.34896			−0.674479	−	0.738294i	$-0.735632\pi$
$397$	−26.8778			−1.34896			−0.674479	+	0.738294i	$0.735632\pi$
$398$	−16.0983	−	5.73943i	−0.806936	−	0.287692i
$399$	−14.3334	−	6.96075i	−0.717566	−	0.348473i
$400$	−1.99662	−	9.80438i	−0.0998311	−	0.490219i
$401$	9.00281			0.449579			0.224789	−	0.974407i	$-0.427831\pi$
$401$	9.00281			0.449579			0.224789	+	0.974407i	$0.427831\pi$
$402$	4.44092	−	12.4562i	0.221493	−	0.621258i
$403$	−4.12014			−0.205239
$404$	−7.34503	−	6.00000i	−0.365429	−	0.298511i
$405$	1.58069			0.0785453
$406$	1.46487	−	1.43827i	0.0727002	−	0.0713799i
$407$		−	9.51981i		−	0.471879i
$408$	−0.634135	−	1.04985i	−0.0313944	−	0.0519754i
$409$			4.91237i			0.242901i	0.992597	+	0.121450i	$0.0387545\pi$
$409$			4.91237i			0.242901i	−0.992597	+	0.121450i	$0.961245\pi$
$410$	5.32272	−	14.9295i	0.262870	−	0.737316i
$411$		−	5.00281i		−	0.246770i
$412$	−3.11391	−	2.54369i	−0.153411	−	0.125319i
$413$	−13.3192	+	27.4265i	−0.655393	+	1.34957i
$414$	−3.91347	+	10.9768i	−0.192336	+	0.539478i
$415$			9.69841i			0.476076i
$416$	−0.437944	+	3.07266i	−0.0214720	+	0.150650i
$417$	14.3106			0.700791
$418$	6.46574	−	18.1355i	0.316250	−	0.887038i
$419$			4.17501i			0.203963i	0.994786	+	0.101981i	$0.0325182\pi$
$419$			4.17501i			0.203963i	−0.994786	+	0.101981i	$0.967482\pi$
$420$	−7.58965	+	3.51537i	−0.370337	+	0.171533i
$421$		−	3.11391i		−	0.151763i	−0.997117	−	0.0758814i	$-0.975823\pi$
$421$		−	3.11391i		−	0.151763i	0.997117	−	0.0758814i	$-0.0241770\pi$
$422$	8.22305	+	2.93171i	0.400292	+	0.142713i
$423$	−11.5839			−0.563227
$424$	−8.98221	+	5.42547i	−0.436215	+	0.263484i
$425$			1.08470i			0.0526155i
$426$	−1.70444	−	0.607674i	−0.0825806	−	0.0294419i
$427$	−28.8748	−	14.0225i	−1.39735	−	0.678599i
$428$	27.5465	+	22.5022i	1.33151	+	1.08768i
$429$			1.24029i			0.0598820i
$430$	−3.84683	−	1.37149i	−0.185511	−	0.0661389i
$431$		−	0.641564i		−	0.0309030i	−0.999881	−	0.0154515i	$-0.995081\pi$
$431$		−	0.641564i		−	0.0309030i	0.999881	−	0.0154515i	$-0.00491857\pi$
$432$	−3.91955	+	0.798200i	−0.188579	+	0.0384034i
$433$		−	6.95772i		−	0.334366i	−0.985926	−	0.167183i	$-0.946533\pi$
$433$		−	6.95772i		−	0.334366i	0.985926	−	0.167183i	$-0.0534671\pi$
$434$	19.6851	+	20.0493i	0.944917	+	0.962395i
$435$	0.867270			0.0415824
$436$	15.2379	−	18.6538i	0.729763	−	0.893355i
$437$	49.6275			2.37400
$438$	−1.15528	−	0.411883i	−0.0552013	−	0.0196806i
$439$	17.4055			0.830717			0.415359	−	0.909658i	$-0.363656\pi$
$439$	17.4055			0.830717			0.415359	+	0.909658i	$0.363656\pi$
$440$	−5.22545	−	8.65106i	−0.249114	−	0.412423i
$441$	−4.32834	−	5.50141i	−0.206111	−	0.261972i
$442$	0.112993	−	0.316930i	0.00537452	−	0.0150748i
$443$	18.0856			0.859271			0.429635	−	0.903002i	$-0.358642\pi$
$443$	18.0856			0.859271			0.429635	+	0.903002i	$0.358642\pi$
$444$	6.52280	+	5.32834i	0.309558	+	0.252872i
$445$			12.5785i			0.596279i
$446$	24.5208	+	8.74224i	1.16109	+	0.413957i
$447$	−18.4553			−0.872906
$448$	17.0444	−	12.5494i	0.805274	−	0.592903i
$449$	−21.2229			−1.00157			−0.500786	−	0.865571i	$-0.666956\pi$
$449$	−21.2229			−1.00157			−0.500786	+	0.865571i	$0.666956\pi$
$450$	3.33209	+	1.18797i	0.157076	+	0.0560013i
$451$			16.0282i			0.754737i
$452$	−4.44112	−	3.62786i	−0.208893	−	0.170640i
$453$	−14.5334			−0.682839
$454$	5.06107	−	14.1956i	0.237528	−	0.666233i
$455$	−2.06406	−	1.00237i	−0.0967647	−	0.0469920i
$456$	8.80720	+	14.5809i	0.412435	+	0.682812i
$457$	27.7046			1.29597			0.647983	−	0.761655i	$-0.275613\pi$
$457$	27.7046			1.29597			0.647983	+	0.761655i	$0.275613\pi$
$458$	−11.9503	−	4.26057i	−0.558402	−	0.199083i
$459$	0.433635			0.0202403
$460$	16.4806	−	20.1750i	0.768410	−	0.940665i
$461$	−23.5438			−1.09654			−0.548272	−	0.836300i	$-0.684714\pi$
$461$	−23.5438			−1.09654			−0.548272	+	0.836300i	$0.684714\pi$
$462$	6.03546	−	5.92585i	0.280795	−	0.275696i
$463$		−	26.8145i		−	1.24618i	−0.782151	−	0.623089i	$-0.785878\pi$
$463$		−	26.8145i		−	1.24618i	0.782151	−	0.623089i	$-0.214122\pi$
$464$	−2.15052	+	0.437944i	−0.0998352	+	0.0203310i
$465$			11.8701i			0.550462i
$466$	19.8645	+	7.08217i	0.920207	+	0.328075i
$467$		−	17.3884i		−	0.804640i	−0.915499	−	0.402320i	$-0.868204\pi$
$467$		−	17.3884i		−	0.804640i	0.915499	−	0.402320i	$-0.131796\pi$
$468$	−0.849827	−	0.694206i	−0.0392833	−	0.0320897i
$469$	−22.2547	−	10.8076i	−1.02762	−	0.499048i
$470$	24.3912	+	8.69604i	1.12508	+	0.401118i
$471$		−	5.80975i		−	0.267699i
$472$	27.9000	−	16.8523i	1.28420	−	0.775690i
$473$	4.12992			0.189894
$474$	13.8132	+	4.92474i	0.634463	+	0.226201i
$475$		−	15.0648i		−	0.691222i
$476$	−2.08208	+	0.964380i	−0.0954322	+	0.0442023i
$477$		−	3.71005i		−	0.169872i
$478$	−6.23900	+	17.4996i	−0.285365	+	0.800411i
$479$	25.6003			1.16971			0.584854	−	0.811139i	$-0.301152\pi$
$479$	25.6003			1.16971			0.584854	+	0.811139i	$0.301152\pi$
$480$	8.85229	+	1.26171i	0.404050	+	0.0575889i
$481$			2.31056i			0.105352i
$482$	−4.81357	+	13.5014i	−0.219252	+	0.614972i
$483$	19.6115	+	9.52395i	0.892352	+	0.433355i
$484$	−9.12276	−	7.45219i	−0.414671	−	0.338736i
$485$		−	30.3143i		−	1.37650i
$486$	0.474920	−	1.33209i	0.0215428	−	0.0604246i
$487$			0.940673i			0.0426260i	0.999773	+	0.0213130i	$0.00678464\pi$
$487$			0.940673i			0.0426260i	−0.999773	+	0.0213130i	$0.993215\pi$
$488$	17.7423	+	29.3734i	0.803155	+	1.32967i
$489$			17.3509i			0.784634i
$490$	4.98392	+	14.8332i	0.225151	+	0.670094i
$491$	−24.0500			−1.08536			−0.542680	−	0.839939i	$-0.682590\pi$
$491$	−24.0500			−1.08536			−0.542680	+	0.839939i	$0.682590\pi$
$492$	−10.9822	−	8.97114i	−0.495116	−	0.404450i
$493$	0.237920			0.0107154
$494$	−1.56930	+	4.40168i	−0.0706063	+	0.198041i
$495$	3.57327			0.160607
$496$	−5.99401	−	29.4335i	−0.269139	−	1.32160i
$497$	−1.47886	+	3.04522i	−0.0663358	+	0.136597i
$498$	8.17306	+	2.91389i	0.366244	+	0.130574i
$499$	−26.8354			−1.20132			−0.600658	−	0.799506i	$-0.705095\pi$
$499$	−26.8354			−1.20132			−0.600658	+	0.799506i	$0.705095\pi$
$500$	−18.3660	−	15.0028i	−0.821353	−	0.670946i
$501$			0.823767i			0.0368032i
$502$	−10.7815	+	30.2407i	−0.481203	+	1.34971i
$503$	−1.13297			−0.0505166			−0.0252583	−	0.999681i	$-0.508041\pi$
$503$	−1.13297			−0.0505166			−0.0252583	+	0.999681i	$0.508041\pi$
$504$	0.682172	+	7.45216i	0.0303864	+	0.331945i
$505$	−7.49578			−0.333558
$506$	−8.84667	+	24.8137i	−0.393283	+	1.10310i
$507$			12.6990i			0.563981i
$508$	−18.9698	+	23.2223i	−0.841650	+	1.03032i
$509$	11.7937			0.522745			0.261373	−	0.965238i	$-0.415825\pi$
$509$	11.7937			0.522745			0.261373	+	0.965238i	$0.415825\pi$
$510$	−0.913070	−	0.325531i	−0.0404314	−	0.0144148i
$511$	−1.00237	+	2.06406i	−0.0443424	+	0.0913087i
$512$	−22.5876	+	1.34154i	−0.998241	+	0.0592883i
$513$	−6.02255			−0.265902
$514$	7.66169	−	21.4900i	0.337943	−	0.947883i
$515$	−3.17783			−0.140032
$516$	−2.31156	+	2.82975i	−0.101761	+	0.124573i
$517$	−26.1862			−1.15167
$518$	11.2435	−	11.0393i	0.494012	−	0.485040i
$519$			19.5230i			0.856964i
$520$	1.26827	+	2.09970i	0.0556173	+	0.0920780i
$521$		−	14.6991i		−	0.643979i	−0.946743	−	0.321990i	$-0.895648\pi$
$521$		−	14.6991i		−	0.643979i	0.946743	−	0.321990i	$-0.104352\pi$
$522$	0.260571	−	0.730867i	0.0114049	−	0.0319892i
$523$		−	7.69507i		−	0.336482i	−0.985746	−	0.168241i	$-0.946191\pi$
$523$		−	7.69507i		−	0.336482i	0.985746	−	0.168241i	$-0.0538086\pi$
$524$	−10.7815	+	13.1984i	−0.470993	+	0.576576i
$525$	2.89108	−	5.95322i	0.126177	−	0.259820i
$526$	7.15136	−	20.0586i	0.311814	−	0.874597i
$527$			3.25634i			0.141849i
$528$	−8.86042	+	1.80439i	−0.385600	+	0.0785259i
$529$	−44.9022			−1.95227
$530$	−2.78515	+	7.81196i	−0.120979	+	0.339330i
$531$			11.5240i			0.500097i
$532$	28.9171	−	13.3938i	1.25371	−	0.580695i
$533$		−	3.89020i		−	0.168503i
$534$	10.6002	+	3.77921i	0.458715	+	0.163543i
$535$	28.1119			1.21538
$536$	13.6745	+	22.6389i	0.590647	+	0.977854i
$537$			4.39611i			0.189706i
$538$	−11.6729	−	4.16166i	−0.503255	−	0.179422i
$539$	−9.78452	−	12.4363i	−0.421449	−	0.535670i
$540$	−2.00000	+	2.44834i	−0.0860663	+	0.105360i
$541$			11.6313i			0.500071i	0.968237	+	0.250035i	$0.0804422\pi$
$541$			11.6313i			0.500071i	−0.968237	+	0.250035i	$0.919558\pi$
$542$	−5.74446	−	2.04803i	−0.246746	−	0.0879706i
$543$			8.14738i			0.349637i
$544$	2.42847	+	0.346128i	0.104120	+	0.0148401i
$545$		−	19.0367i		−	0.815441i
$546$	−1.46487	+	1.43827i	−0.0626906	+	0.0615521i
$547$	21.0048			0.898099			0.449049	−	0.893507i	$-0.351763\pi$
$547$	21.0048			0.898099			0.449049	+	0.893507i	$0.351763\pi$
$548$	7.74887	+	6.32989i	0.331015	+	0.270399i
$549$	−12.1325			−0.517804
$550$	7.53242	+	2.68548i	0.321183	+	0.114509i
$551$	−3.30435			−0.140770
$552$	−12.0503	−	19.9501i	−0.512897	−	0.849133i
$553$	11.9850	−	24.6792i	0.509655	−	1.04947i
$554$	−12.1355	+	34.0386i	−0.515590	+	1.44616i
$555$	6.65668			0.282560
$556$	−18.1067	+	22.1657i	−0.767894	+	0.940033i
$557$		−	34.7501i		−	1.47241i	−0.676760	−	0.736204i	$-0.736617\pi$
$557$		−	34.7501i		−	1.47241i	0.676760	−	0.736204i	$-0.263383\pi$
$558$	10.0032	+	3.56636i	0.423468	+	0.150976i
$559$	−1.00237			−0.0423959
$560$	4.15796	−	16.2035i	0.175706	−	0.684724i
$561$	0.980263			0.0413867
$562$	2.89731	+	1.03296i	0.122215	+	0.0435727i
$563$			16.9124i			0.712771i	0.934339	+	0.356386i	$0.115991\pi$
$563$			16.9124i			0.712771i	−0.934339	+	0.356386i	$0.884009\pi$
$564$	14.6567	−	17.9423i	0.617158	−	0.755507i
$565$	−4.53228			−0.190674
$566$	5.83581	−	16.3687i	0.245298	−	0.688027i
$567$	−2.37995	−	1.15578i	−0.0999486	−	0.0485382i
$568$	3.09781	−	1.87115i	0.129981	−	0.0785117i
$569$	−20.4856			−0.858800			−0.429400	−	0.903114i	$-0.641275\pi$
$569$	−20.4856			−0.858800			−0.429400	+	0.903114i	$0.641275\pi$
$570$	12.6812	+	4.52114i	0.531157	+	0.189370i
$571$	46.0132			1.92559			0.962796	−	0.270229i	$-0.0870994\pi$
$571$	46.0132			1.92559			0.962796	+	0.270229i	$0.0870994\pi$
$572$	−1.92109	−	1.56930i	−0.0803250	−	0.0656158i
$573$	−0.420123			−0.0175509
$574$	−18.9303	+	18.5865i	−0.790137	+	0.775787i
$575$			20.6123i			0.859591i
$576$	3.72294	−	7.08094i	0.155123	−	0.295039i
$577$			35.8191i			1.49117i	0.666411	+	0.745585i	$0.267830\pi$
$577$			35.8191i			1.49117i	−0.666411	+	0.745585i	$0.732170\pi$
$578$	22.3950	+	7.98433i	0.931508	+	0.332104i
$579$			11.1553i			0.463598i
$580$	−1.09733	+	1.34332i	−0.0455641	+	0.0557782i
$581$	7.09134	−	14.6023i	0.294198	−	0.605805i
$582$	−25.5465	−	9.10792i	−1.05894	−	0.377536i
$583$		−	8.38684i		−	0.347347i
$584$	2.09970	−	1.26827i	0.0868863	−	0.0524814i
$585$	−0.867270			−0.0358572
$586$	33.1410	+	11.8155i	1.36904	+	0.488095i
$587$		−	30.4007i		−	1.25477i	−0.778708	−	0.627387i	$-0.784125\pi$
$587$		−	30.4007i		−	1.25477i	0.778708	−	0.627387i	$-0.215875\pi$
$588$	13.9976	+	0.256564i	0.577253	+	0.0105805i
$589$		−	45.2258i		−	1.86350i
$590$	8.65106	−	24.2651i	0.356159	−	0.998977i
$591$	4.95035			0.203630
$592$	−16.5062	+	3.36141i	−0.678399	+	0.138153i
$593$		−	23.3065i		−	0.957084i	−0.878065	−	0.478542i	$-0.841165\pi$
$593$		−	23.3065i		−	0.957084i	0.878065	−	0.478542i	$-0.158835\pi$
$594$	1.07359	−	3.01127i	0.0440499	−	0.123554i
$595$	−0.792224	+	1.63132i	−0.0324780	+	0.0668778i
$596$	23.3509	−	28.5855i	0.956490	−	1.17091i
$597$			12.0851i			0.494608i
$598$	2.14718	−	6.02255i	0.0878047	−	0.246280i
$599$			19.9547i			0.815329i	0.913132	+	0.407664i	$0.133657\pi$
$599$			19.9547i			0.815329i	−0.913132	+	0.407664i	$0.866343\pi$
$600$	−6.05602	+	3.65798i	−0.247236	+	0.149337i
$601$			27.0028i			1.10147i	0.834681	+	0.550734i	$0.185652\pi$
$601$			27.0028i			1.10147i	−0.834681	+	0.550734i	$0.814348\pi$
$602$	4.78912	+	4.87771i	0.195190	+	0.198801i
$603$	−9.35089			−0.380798
$604$	18.3886	−	22.5108i	0.748222	−	0.915952i
$605$	−9.31000			−0.378505
$606$	−2.25211	+	6.31686i	−0.0914856	+	0.256605i
$607$	1.63416			0.0663283			0.0331642	−	0.999450i	$-0.489442\pi$
$607$	1.63416			0.0663283			0.0331642	+	0.999450i	$0.489442\pi$
$608$	−33.7278	−	4.80720i	−1.36784	−	0.194958i
$609$	−1.30579	−	0.634135i	−0.0529134	−	0.0256965i
$610$	25.5465	+	9.10792i	1.03435	+	0.368769i
$611$	6.35565			0.257122
$612$	−0.548664	+	0.671659i	−0.0221784	+	0.0271502i
$613$			16.3500i			0.660369i	0.943916	+	0.330184i	$0.107111\pi$
$613$			16.3500i			0.660369i	−0.943916	+	0.330184i	$0.892889\pi$
$614$	−8.08568	+	22.6792i	−0.326311	+	0.915259i
$615$	−11.2076			−0.451935
$616$	1.54210	+	16.8461i	0.0621329	+	0.678750i
$617$	0.220365			0.00887154			0.00443577	−	0.999990i	$-0.498588\pi$
$617$	0.220365			0.00887154			0.00443577	+	0.999990i	$0.498588\pi$
$618$	−0.954777	+	2.67802i	−0.0384068	+	0.107726i
$619$			16.9972i			0.683175i	0.939850	+	0.341587i	$0.110965\pi$
$619$			16.9972i			0.683175i	−0.939850	+	0.341587i	$0.889035\pi$
$620$	−18.3856	−	15.0188i	−0.738384	−	0.603170i
$621$	8.24028			0.330671
$622$	−31.0354	−	11.0648i	−1.24440	−	0.443659i
$623$	9.19723	−	18.9387i	0.368479	−	0.758762i
$624$	2.15052	−	0.437944i	0.0860895	−	0.0175318i
$625$	−6.23595			−0.249438
$626$	7.14654	−	20.0451i	0.285633	−	0.801163i
$627$	−13.6144			−0.543707
$628$	8.99875	+	7.35089i	0.359089	+	0.293332i
$629$	1.82614			0.0728130
$630$	4.14363	+	4.22027i	0.165086	+	0.168140i
$631$			13.8402i			0.550971i	0.961305	+	0.275485i	$0.0888386\pi$
$631$			13.8402i			0.550971i	−0.961305	+	0.275485i	$0.911161\pi$
$632$	−25.1054	+	15.1643i	−0.998638	+	0.603202i
$633$		−	6.17306i		−	0.245357i
$634$	−10.6743	+	29.9401i	−0.423932	+	1.18907i
$635$			23.6990i			0.940465i
$636$	5.74651	+	4.69421i	0.227864	+	0.186137i
$637$	2.37480	+	3.01842i	0.0940932	+	0.119594i
$638$	0.589040	−	1.65218i	0.0233203	−	0.0654103i
$639$			1.27953i			0.0506175i
$640$	−13.1548	+	12.1149i	−0.519988	+	0.478885i
$641$	13.0479			0.515361			0.257681	−	0.966230i	$-0.417042\pi$
$641$	13.0479			0.515361			0.257681	+	0.966230i	$0.417042\pi$
$642$	8.44622	−	23.6905i	0.333346	−	0.934990i
$643$		−	12.2880i		−	0.484592i	−0.970202	−	0.242296i	$-0.922100\pi$
$643$		−	12.2880i		−	0.484592i	0.970202	−	0.242296i	$-0.0779005\pi$
$644$	−39.5654	+	18.3259i	−1.55910	+	0.722142i
$645$			2.88783i			0.113708i
$646$	3.47886	+	1.24029i	0.136874	+	0.0487987i
$647$	31.8638			1.25269			0.626347	−	0.779544i	$-0.284549\pi$
$647$	31.8638			1.25269			0.626347	+	0.779544i	$0.284549\pi$
$648$	1.46237	+	2.42105i	0.0574474	+	0.0951077i
$649$			26.0507i			1.02258i
$650$	−1.82820	−	0.651794i	−0.0717077	−	0.0255655i
$651$	8.67923	−	17.8720i	0.340166	−	0.700460i
$652$	−26.8748	−	21.9535i	−1.05250	−	0.859766i
$653$		−	14.6007i		−	0.571371i	−0.958323	−	0.285686i	$-0.907779\pi$
$653$		−	14.6007i		−	0.571371i	0.958323	−	0.285686i	$-0.0922213\pi$
$654$	−16.0426	−	5.71956i	−0.627316	−	0.223653i
$655$			13.4693i			0.526290i
$656$	27.7909	−	5.65949i	1.08505	−	0.220966i
$657$			0.867270i			0.0338354i
$658$	−30.3659	−	30.9276i	−1.18379	−	1.20568i
$659$	7.25776			0.282722			0.141361	−	0.989958i	$-0.454852\pi$
$659$	7.25776			0.282722			0.141361	+	0.989958i	$0.454852\pi$
$660$	−4.52114	+	5.53465i	−0.175985	+	0.215436i
$661$	−15.6031			−0.606891			−0.303446	−	0.952849i	$-0.598137\pi$
$661$	−15.6031			−0.606891			−0.303446	+	0.952849i	$0.598137\pi$
$662$	−31.3460	−	11.1756i	−1.21830	−	0.434351i
$663$	−0.237920			−0.00924004
$664$	−14.8544	+	8.97244i	−0.576464	+	0.348198i
$665$	11.0028	−	22.6567i	0.426671	−	0.878588i
$666$	2.00000	−	5.60973i	0.0774984	−	0.217373i
$667$	4.52114			0.175059
$668$	−1.27593	−	1.04228i	−0.0493674	−	0.0403272i
$669$		−	18.4078i		−	0.711688i
$670$	19.6894	+	7.01974i	0.760669	+	0.271196i
$671$	−27.4265			−1.05879
$672$	−12.4058	−	8.37235i	−0.478564	−	0.322970i
$673$	9.19475			0.354432			0.177216	−	0.984172i	$-0.443291\pi$
$673$	9.19475			0.354432			0.177216	+	0.984172i	$0.443291\pi$
$674$	11.6915	+	4.16829i	0.450339	+	0.160556i
$675$		−	2.50141i		−	0.0962791i
$676$	−19.6695	−	16.0676i	−0.756518	−	0.617984i
$677$	14.1669			0.544480			0.272240	−	0.962229i	$-0.412236\pi$
$677$	14.1669			0.544480			0.272240	+	0.962229i	$0.412236\pi$
$678$	−1.36172	+	3.81945i	−0.0522966	+	0.146685i
$679$	−22.1654	+	45.6423i	−0.850629	+	1.75159i
$680$	1.65949	−	1.00237i	0.0636387	−	0.0384393i
$681$	−10.6567			−0.408365
$682$	22.6129	+	8.06202i	0.865892	+	0.308711i
$683$	−35.9201			−1.37444			−0.687222	−	0.726448i	$-0.741170\pi$
$683$	−35.9201			−1.37444			−0.687222	+	0.726448i	$0.741170\pi$
$684$	7.62013	−	9.32834i	0.291363	−	0.356678i
$685$	7.90791			0.302146
$686$	3.34182	−	25.9775i	0.127591	−	0.991827i
$687$			8.97114i			0.342270i
$688$	−1.45826	−	7.16077i	−0.0555957	−	0.273002i
$689$			2.03557i			0.0775491i
$690$	−17.3509	−	6.18600i	−0.660537	−	0.235497i
$691$		−	24.0451i		−	0.914719i	−0.889282	−	0.457359i	$-0.848795\pi$
$691$		−	24.0451i		−	0.914719i	0.889282	−	0.457359i	$-0.151205\pi$
$692$	−30.2392	−	24.7018i	−1.14952	−	0.939021i
$693$	−5.38005	−	2.61272i	−0.204371	−	0.0992492i
$694$	−5.33485	−	1.90200i	−0.202508	−	0.0721989i
$695$			22.6206i			0.858049i
$696$	0.802350	+	1.32834i	0.0304130	+	0.0503507i
$697$	−3.07461			−0.116459
$698$	4.57770	+	1.63206i	0.173269	+	0.0617743i
$699$		−	14.9124i		−	0.564037i
$700$	5.56298	+	12.0104i	0.210261	+	0.453951i
$701$			39.3211i			1.48514i	0.669771	+	0.742568i	$0.266392\pi$
$701$			39.3211i			1.48514i	−0.669771	+	0.742568i	$0.733608\pi$
$702$	−0.260571	+	0.730867i	−0.00983463	+	0.0275848i
$703$	−25.3624			−0.956561
$704$	8.41598	−	16.0070i	0.317189	−	0.603285i
$705$		−	18.3106i		−	0.689615i
$706$	−10.9660	+	30.7583i	−0.412712	+	1.15760i
$707$	11.2859	+	5.48081i	0.424451	+	0.206127i
$708$	−17.8495	−	14.5809i	−0.670825	−	0.547983i
$709$		−	37.8578i		−	1.42178i	−0.703304	−	0.710890i	$-0.748293\pi$
$709$		−	37.8578i		−	1.42178i	0.703304	−	0.710890i	$-0.251707\pi$
$710$	0.960547	−	2.69421i	0.0360487	−	0.101112i
$711$		−	10.3696i		−	0.388892i
$712$	−19.2657	+	11.6369i	−0.722013	+	0.436113i
$713$			61.8796i			2.31741i
$714$	1.13673	+	1.15776i	0.0425410	+	0.0433279i
$715$	−1.96053			−0.0733195
$716$	−6.80915	−	5.56225i	−0.254470	−	0.207871i
$717$	13.1370			0.490609
$718$	10.3951	−	29.1570i	0.387943	−	1.08813i
$719$	25.6003			0.954731			0.477365	−	0.878705i	$-0.341592\pi$
$719$	25.6003			0.954731			0.477365	+	0.878705i	$0.341592\pi$
$720$	−1.26171	−	6.19561i	−0.0470212	−	0.230897i
$721$	4.78465	+	2.32358i	0.178190	+	0.0865346i
$722$	−23.0066	−	8.20237i	−0.856215	−	0.305261i
$723$	10.1355			0.376945
$724$	−12.6195	−	10.3086i	−0.469000	−	0.383116i
$725$		−	1.37243i		−	0.0509708i
$726$	−2.79719	+	7.84574i	−0.103813	+	0.291183i
$727$	−2.11772			−0.0785420			−0.0392710	−	0.999229i	$-0.512504\pi$
$727$	−2.11772			−0.0785420			−0.0392710	+	0.999229i	$0.512504\pi$
$728$	−0.374283	−	4.08873i	−0.0138719	−	0.151538i
$729$	−1.00000			−0.0370370
$730$	0.651062	−	1.82614i	0.0240969	−	0.0675885i
$731$			0.792224i			0.0293014i
$732$	15.3509	−	18.7921i	0.567385	−	0.694577i
$733$	20.4120			0.753936			0.376968	−	0.926226i	$-0.376967\pi$
$733$	20.4120			0.753936			0.376968	+	0.926226i	$0.376967\pi$
$734$	37.2020	+	13.2634i	1.37315	+	0.489560i
$735$	8.69604	−	6.84179i	0.320758	−	0.252363i
$736$	46.1477	+	6.57739i	1.70103	+	0.242446i
$737$	−21.1384			−0.778641
$738$	−3.36733	+	9.44491i	−0.123953	+	0.347672i
$739$	18.3932			0.676604			0.338302	−	0.941038i	$-0.390147\pi$
$739$	18.3932			0.676604			0.338302	+	0.941038i	$0.390147\pi$
$740$	−8.42248	+	10.3106i	−0.309617	+	0.379024i
$741$	3.30435			0.121389
$742$	9.90541	−	9.72552i	0.363639	−	0.357035i
$743$			33.3812i			1.22464i	0.790611	+	0.612319i	$0.209763\pi$
$743$			33.3812i			1.22464i	−0.790611	+	0.612319i	$0.790237\pi$
$744$	−18.1806	+	10.9815i	−0.666534	+	0.402603i
$745$		−	29.1722i		−	1.06879i
$746$	−7.23790	+	20.3013i	−0.264998	+	0.743284i
$747$		−	6.13554i		−	0.224488i
$748$	−1.24029	+	1.51833i	−0.0453496	+	0.0555157i
$749$	−42.3263	−	20.5550i	−1.54657	−	0.751064i
$750$	−5.63132	+	15.7951i	−0.205627	+	0.576756i
$751$			9.83899i			0.359030i	0.983755	+	0.179515i	$0.0574528\pi$
$751$			9.83899i			0.359030i	−0.983755	+	0.179515i	$0.942547\pi$
$752$	9.24625	+	45.4036i	0.337176	+	1.65570i
$753$	22.7018			0.827299
$754$	−0.142966	+	0.401000i	−0.00520652	+	0.0146036i
$755$		−	22.9729i		−	0.836068i
$756$	4.80147	−	2.22394i	0.174628	−	0.0808840i
$757$			23.9363i			0.869980i	0.900435	+	0.434990i	$0.143248\pi$
$757$			23.9363i			0.869980i	−0.900435	+	0.434990i	$0.856752\pi$
$758$	15.3009	+	5.45513i	0.555754	+	0.198139i
$759$	18.6277			0.676144
$760$	−23.0479	+	13.9215i	−0.836035	+	0.504986i
$761$			14.6991i			0.532842i	0.963857	+	0.266421i	$0.0858411\pi$
$761$			14.6991i			0.532842i	−0.963857	+	0.266421i	$0.914159\pi$
$762$	19.9716	+	7.12035i	0.723496	+	0.257943i
$763$	−13.9193	+	28.6623i	−0.503914	+	1.03765i
$764$	0.531568	−	0.650730i	0.0192315	−	0.0235426i
$765$			0.685444i			0.0247823i
$766$	−29.9380	−	10.6736i	−1.08171	−	0.385653i
$767$		−	6.32278i		−	0.228302i
$768$	6.25717	+	14.7258i	0.225786	+	0.531370i
$769$		−	22.7317i		−	0.819727i	−0.912147	−	0.409864i	$-0.865576\pi$
$769$		−	22.7317i		−	0.819727i	0.912147	−	0.409864i	$-0.134424\pi$
$770$	9.36696	+	9.54022i	0.337562	+	0.343806i
$771$	−16.1326			−0.581002
$772$	−17.2784	−	14.1144i	−0.621865	−	0.507988i
$773$	8.21267			0.295389			0.147695	−	0.989033i	$-0.452815\pi$
$773$	8.21267			0.295389			0.147695	+	0.989033i	$0.452815\pi$
$774$	2.43364	+	0.867648i	0.0874752	+	0.0311870i
$775$	18.7841			0.674744
$776$	46.4304	−	28.0451i	1.66676	−	1.00676i
$777$	−10.0225	−	4.86727i	−0.359557	−	0.174612i
$778$	9.77890	−	27.4285i	0.350591	−	0.983360i
$779$	42.7018			1.52995
$780$	1.09733	−	1.34332i	0.0392906	−	0.0480985i
$781$			2.89247i			0.103501i
$782$	−4.75990	−	1.69702i	−0.170214	−	0.0606852i
$783$	−0.548664			−0.0196076
$784$	−18.1082	+	21.3564i	−0.646720	+	0.762728i
$785$	9.18345			0.327771
$786$	11.3509	+	4.04686i	0.404873	+	0.144347i
$787$			25.3134i			0.902324i	0.892442	+	0.451162i	$0.148990\pi$
$787$			25.3134i			0.902324i	−0.892442	+	0.451162i	$0.851010\pi$
$788$	−6.26351	+	7.66761i	−0.223128	+	0.273147i
$789$	−15.0581			−0.536081
$790$	−7.78451	+	21.8345i	−0.276961	+	0.776837i
$791$	6.82396	+	3.31394i	0.242632	+	0.117830i
$792$	3.30579	+	5.47295i	0.117466	+	0.194473i
$793$	6.65668			0.236386
$794$	−35.8035	−	12.7648i	−1.27062	−	0.453005i
$795$	5.86446			0.207991
$796$	−18.7186	−	15.2908i	−0.663462	−	0.541969i
$797$	10.2767			0.364021			0.182010	−	0.983297i	$-0.441740\pi$
$797$	10.2767			0.364021			0.182010	+	0.983297i	$0.441740\pi$
$798$	−15.7875	−	16.0795i	−0.558871	−	0.569208i
$799$		−	5.02317i		−	0.177707i
$800$	1.99662	−	14.0085i	0.0705913	−	0.495276i
$801$		−	7.95759i		−	0.281168i
$802$	11.9925	+	4.27561i	0.423470	+	0.150977i
$803$			1.96053i			0.0691854i
$804$	11.8314	−	14.4836i	0.417260	−	0.510798i
$805$	−15.0545	+	30.9997i	−0.530600	+	1.09260i
$806$	−5.48838	−	1.95674i	−0.193320	−	0.0689231i
$807$			8.76288i			0.308468i
$808$	−6.93468	−	11.4808i	−0.243961	−	0.403893i
$809$	28.4968			1.00189			0.500947	−	0.865478i	$-0.332985\pi$
$809$	28.4968			1.00189			0.500947	+	0.865478i	$0.332985\pi$
$810$	2.10562	+	0.750703i	0.0739839	+	0.0263770i
$811$		−	13.2683i		−	0.465912i	−0.972487	−	0.232956i	$-0.925160\pi$
$811$		−	13.2683i		−	0.465912i	0.972487	−	0.232956i	$-0.0748398\pi$
$812$	2.63439	−	1.22020i	0.0924490	−	0.0428205i
$813$			4.31238i			0.151242i
$814$	4.52114	−	12.6812i	0.158466	−	0.444476i
$815$	−27.4265			−0.960707
$816$	−0.346128	−	1.69965i	−0.0121169	−	0.0594998i
$817$		−	11.0028i		−	0.384940i
$818$	−2.33298	+	6.54369i	−0.0815707	+	0.228795i
$819$	1.30579	+	0.634135i	0.0456281	+	0.0221585i
$820$	14.1806	−	17.3595i	0.495209	−	0.606221i
$821$			50.5926i			1.76570i	0.469659	+	0.882848i	$0.344377\pi$
$821$			50.5926i			1.76570i	−0.469659	+	0.882848i	$0.655623\pi$
$822$	2.37593	−	6.66417i	0.0828702	−	0.232440i
$823$		−	19.5730i		−	0.682274i	−0.940014	−	0.341137i	$-0.889188\pi$
$823$		−	19.5730i		−	0.682274i	0.940014	−	0.341137i	$-0.110812\pi$
$824$	−2.93995	−	4.86727i	−0.102418	−	0.169559i
$825$		−	5.65460i		−	0.196868i
$826$	−30.7676	+	30.2088i	−1.07054	+	1.05110i
$827$	−4.64617			−0.161563			−0.0807816	−	0.996732i	$-0.525742\pi$
$827$	−4.64617			−0.161563			−0.0807816	+	0.996732i	$0.525742\pi$
$828$	−10.4261	+	12.7634i	−0.362334	+	0.443558i
$829$	22.2382			0.772364			0.386182	−	0.922423i	$-0.373794\pi$
$829$	22.2382			0.772364			0.386182	+	0.922423i	$0.373794\pi$
$830$	−4.60597	+	12.9191i	−0.159875	+	0.448429i
$831$	25.5528			0.886418
$832$	−2.04264	+	3.88506i	−0.0708159	+	0.134690i
$833$	2.38560	−	1.87692i	0.0826562	−	0.0650314i
$834$	19.0629	+	6.79636i	0.660094	+	0.235339i
$835$	−1.30212			−0.0450619
$836$	17.2258	−	21.0874i	0.595768	−	0.729322i
$837$		−	7.50941i		−	0.259563i
$838$	−1.98280	+	5.56148i	−0.0684946	+	0.192118i
$839$	36.5297			1.26115			0.630573	−	0.776130i	$-0.282820\pi$
$839$	36.5297			1.26115			0.630573	+	0.776130i	$0.282820\pi$
$840$	−11.7796	+	1.07831i	−0.406434	+	0.0372051i
$841$	28.6990			0.989620
$842$	1.47886	−	4.14800i	0.0509648	−	0.142949i
$843$		−	2.17501i		−	0.0749115i
$844$	9.56148	+	7.81057i	0.329120	+	0.268851i
$845$	−20.0732			−0.690539
$846$	−15.4307	−	5.50141i	−0.530518	−	0.189142i
$847$	14.0175	+	6.80734i	0.481646	+	0.233903i
$848$	−14.5417	+	2.96136i	−0.499365	+	0.101694i
$849$	−12.2880			−0.421723
$850$	−0.515144	+	1.44491i	−0.0176693	+	0.0495600i
$851$	34.7018			1.18956
$852$	−1.98187	−	1.61895i	−0.0678977	−	0.0554643i
$853$	42.1702			1.44388			0.721940	−	0.691956i	$-0.243251\pi$
$853$	42.1702			1.44388			0.721940	+	0.691956i	$0.243251\pi$
$854$	−31.8042	−	32.3925i	−1.08832	−	1.10845i
$855$		−	9.51981i		−	0.325571i
$856$	26.0076	+	43.0572i	0.888921	+	1.47166i
$857$		−	37.5720i		−	1.28343i	−0.766941	−	0.641717i	$-0.778222\pi$
$857$		−	37.5720i		−	1.28343i	0.766941	−	0.641717i	$-0.221778\pi$
$858$	−0.589040	+	1.65218i	−0.0201095	+	0.0564044i
$859$			12.7543i			0.435170i	0.976041	+	0.217585i	$0.0698180\pi$
$859$			12.7543i			0.435170i	−0.976041	+	0.217585i	$0.930182\pi$
$860$	−4.47296	−	3.65387i	−0.152527	−	0.124596i
$861$	16.8746	+	8.19485i	0.575085	+	0.279280i
$862$	0.304691	−	0.854618i	0.0103778	−	0.0291084i
$863$		−	51.1449i		−	1.74099i	−0.492175	−	0.870496i	$-0.663798\pi$
$863$		−	51.1449i		−	1.74099i	0.492175	−	0.870496i	$-0.336202\pi$
$864$	−5.60026	−	0.798200i	−0.190525	−	0.0271553i
$865$	−30.8599			−1.04927
$866$	3.30435	−	9.26827i	0.112287	−	0.314949i
$867$		−	16.8120i		−	0.570964i
$868$	16.7005	+	36.0562i	0.566852	+	1.22383i
$869$		−	23.4413i		−	0.795192i
$870$	1.15528	+	0.411883i	0.0391676	+	0.0139642i
$871$	5.13050			0.173840
$872$	29.1572	−	17.6117i	0.987388	−	0.596406i
$873$			19.1778i			0.649071i
$874$	66.1080	+	23.5690i	2.23614	+	0.797235i
$875$	28.2201	+	13.7046i	0.954014	+	0.463300i
$876$	−1.34332	−	1.09733i	−0.0453865	−	0.0370753i
$877$		−	13.8694i		−	0.468335i	−0.972196	−	0.234168i	$-0.924764\pi$
$877$		−	13.8694i		−	0.468335i	0.972196	−	0.234168i	$-0.0752365\pi$
$878$	23.1856	+	8.26619i	0.782475	+	0.278970i
$879$		−	24.8790i		−	0.839149i
$880$	−2.85219	−	14.0056i	−0.0961472	−	0.472129i
$881$			5.92202i			0.199518i	0.995012	+	0.0997589i	$0.0318071\pi$
$881$			5.92202i			0.199518i	−0.995012	+	0.0997589i	$0.968193\pi$
$882$	−3.15300	−	9.38396i	−0.106167	−	0.315974i
$883$	−3.17025			−0.106688			−0.0533438	−	0.998576i	$-0.516988\pi$
$883$	−3.17025			−0.106688			−0.0533438	+	0.998576i	$0.516988\pi$
$884$	0.301032	−	0.368515i	0.0101248	−	0.0123945i
$885$	−18.2158			−0.612319
$886$	24.0915	+	8.58918i	0.809370	+	0.288559i
$887$	−49.9010			−1.67551			−0.837756	−	0.546045i	$-0.816133\pi$
$887$	−49.9010			−1.67551			−0.837756	+	0.546045i	$0.816133\pi$
$888$	6.15839	+	10.1956i	0.206662	+	0.342142i
$889$	17.3283	−	35.6820i	0.581174	−	1.19674i
$890$	−5.97378	+	16.7557i	−0.200242	+	0.561651i
$891$	−2.26057			−0.0757320
$892$	28.5119	+	23.2908i	0.954651	+	0.779834i
$893$			69.7644i			2.33458i
$894$	−24.5840	−	8.76479i	−0.822214	−	0.293138i
$895$	−6.94891			−0.232276
$896$	28.6646	−	8.62212i	0.957617	−	0.288045i
$897$	−4.52114			−0.150957
$898$	−28.2707	−	10.0792i	−0.943407	−	0.336347i
$899$		−	4.12014i		−	0.137414i
$900$	3.87443	+	3.16494i	0.129148	+	0.105498i
$901$	1.60881			0.0535972
$902$	−7.61209	+	21.3509i	−0.253455	+	0.710907i
$903$	2.11154	−	4.34802i	0.0702676	−	0.144693i
$904$	−4.19301	−	6.94180i	−0.139458	−	0.230881i
$905$	−12.8785			−0.428096
$906$	−19.3597	−	6.90219i	−0.643184	−	0.229310i
$907$	−2.60938			−0.0866431			−0.0433216	−	0.999061i	$-0.513794\pi$
$907$	−2.60938			−0.0866431			−0.0433216	+	0.999061i	$0.513794\pi$
$908$	13.4835	−	16.5062i	0.447467	−	0.547776i
$909$	4.74208			0.157285
$910$	−2.27346	−	2.31551i	−0.0753644	−	0.0767584i
$911$		−	42.9082i		−	1.42161i	−0.703388	−	0.710807i	$-0.748330\pi$
$911$		−	42.9082i		−	1.42161i	0.703388	−	0.710807i	$-0.251670\pi$
$912$	4.80720	+	23.6057i	0.159182	+	0.781662i
$913$		−	13.8698i		−	0.459024i
$914$	36.9049	+	13.1575i	1.22070	+	0.435210i
$915$		−	19.1778i		−	0.633999i
$916$	−13.8954	−	11.3509i	−0.459118	−	0.375044i
$917$	9.84857	−	20.2799i	0.325229	−	0.669702i
$918$	0.577639	+	0.205942i	0.0190649	+	0.00679709i
$919$			24.4217i			0.805598i	0.915288	+	0.402799i	$0.131963\pi$
$919$			24.4217i			0.805598i	−0.915288	+	0.402799i	$0.868037\pi$
$920$	31.5350	−	19.0479i	1.03968	−	0.627991i
$921$	17.0254			0.561005
$922$	−31.3623	−	11.1814i	−1.03286	−	0.368240i
$923$		−	0.702033i		−	0.0231077i
$924$	10.8541	−	5.02738i	0.357072	−	0.165389i
$925$		−	10.5340i		−	0.346356i
$926$	12.7348	−	35.7193i	0.418490	−	1.17381i
$927$	2.01040			0.0660301
$928$	−3.07266	−	0.437944i	−0.100865	−	0.0143762i
$929$			32.9150i			1.07991i	0.841695	+	0.539954i	$0.181558\pi$
$929$			32.9150i			1.07991i	−0.841695	+	0.539954i	$0.818442\pi$
$930$	−5.63733	+	15.8120i	−0.184855	+	0.518495i
$931$	−33.1325	+	26.0676i	−1.08587	+	0.854332i
$932$	23.0978	+	18.8681i	0.756594	+	0.618046i
$933$			23.2983i			0.762753i
$934$	8.25810	−	23.1628i	0.270213	−	0.757912i
$935$			1.54950i			0.0506739i
$936$	−0.802350	−	1.32834i	−0.0262256	−	0.0434182i
$937$			41.2683i			1.34818i	0.738651	+	0.674088i	$0.235463\pi$
$937$			41.2683i			1.34818i	−0.738651	+	0.674088i	$0.764537\pi$
$938$	−24.5124	−	24.9658i	−0.800358	−	0.815162i
$939$	−15.0479			−0.491070
$940$	28.3613	+	23.1677i	0.925043	+	0.755648i
$941$	−53.4508			−1.74245			−0.871223	−	0.490887i	$-0.836673\pi$
$941$	−53.4508			−1.74245			−0.871223	+	0.490887i	$0.836673\pi$
$942$	2.75917	−	7.73909i	0.0898985	−	0.252153i
$943$	−58.4262			−1.90262
$944$	45.1687	−	9.19842i	1.47012	−	0.299383i
$945$	1.82694	−	3.76198i	0.0594302	−	0.122377i
$946$	5.50141	+	1.96138i	0.178866	+	0.0637699i
$947$	−55.2631			−1.79581			−0.897905	−	0.440189i	$-0.854911\pi$
$947$	−55.2631			−1.79581			−0.897905	+	0.440189i	$0.854911\pi$
$948$	16.0616	+	13.1204i	0.521655	+	0.426129i
$949$		−	0.475840i		−	0.0154464i
$950$	7.15458	−	20.0676i	0.232125	−	0.651080i
$951$	22.4761			0.728838
$952$	−3.23152	+	0.295814i	−0.104734	+	0.00958738i
$953$	−22.5760			−0.731309			−0.365654	−	0.930751i	$-0.619155\pi$
$953$	−22.5760			−0.731309			−0.365654	+	0.930751i	$0.619155\pi$
$954$	1.76198	−	4.94211i	0.0570461	−	0.160007i
$955$		−	0.664086i		−	0.0214893i
$956$	−16.6218	+	20.3479i	−0.537586	+	0.658097i
$957$	−1.24029			−0.0400930
$958$	34.1018	+	12.1581i	1.10178	+	0.392810i
$959$	−11.9064	−	5.78215i	−0.384479	−	0.186715i
$960$	11.1928	+	5.88483i	0.361246	+	0.189932i
$961$	25.3912			0.819072
$962$	−1.09733	+	3.07786i	−0.0353793	+	0.0992341i
$963$	−17.7845			−0.573098
$964$	−12.8242	+	15.6990i	−0.413038	+	0.505630i
$965$	−17.6331			−0.567629
$966$	21.6010	+	22.0006i	0.695002	+	0.707857i
$967$		−	24.2911i		−	0.781150i	−0.920571	−	0.390575i	$-0.872276\pi$
$967$		−	24.2911i		−	0.781150i	0.920571	−	0.390575i	$-0.127724\pi$
$968$	−8.61310	−	14.2595i	−0.276835	−	0.458319i
$969$		−	2.61159i		−	0.0838963i
$970$	14.3968	−	40.3812i	0.462255	−	1.29656i
$971$		−	24.9221i		−	0.799790i	−0.916561	−	0.399895i	$-0.869047\pi$
$971$		−	24.9221i		−	0.799790i	0.916561	−	0.399895i	$-0.130953\pi$
$972$	1.26527	−	1.54890i	0.0405834	−	0.0496811i
$973$	16.5399	−	34.0584i	0.530244	−	1.09186i
$974$	−0.446744	+	1.25306i	−0.0143146	+	0.0401505i
$975$			1.37243i			0.0439530i
$976$	9.68419	+	47.5541i	0.309983	+	1.52217i
$977$	1.13273			0.0362392			0.0181196	−	0.999836i	$-0.494232\pi$
$977$	1.13273			0.0362392			0.0181196	+	0.999836i	$0.494232\pi$
$978$	−8.24028	+	23.1129i	−0.263495	+	0.739068i
$979$		−	17.9887i		−	0.574921i
$980$	−0.405550	+	22.1260i	−0.0129548	+	0.706789i
$981$			12.0432i			0.384511i
$982$	−32.0366	−	11.4218i	−1.02233	−	0.364485i
$983$	−11.8218			−0.377056			−0.188528	−	0.982068i	$-0.560372\pi$
$983$	−11.8218			−0.377056			−0.188528	+	0.982068i	$0.560372\pi$
$984$	−10.3687	−	17.1660i	−0.330541	−	0.547232i
$985$			7.82499i			0.249325i
$986$	0.316930	+	0.112993i	0.0100931	+	0.00359842i
$987$	−13.3884	+	27.5690i	−0.426158	+	0.877532i
$988$	−4.18089	+	5.11812i	−0.133012	+	0.162829i
$989$			15.0545i			0.478704i
$990$	4.75990	+	1.69702i	0.151280	+	0.0539347i
$991$		−	52.1176i		−	1.65557i	−0.561045	−	0.827785i	$-0.689600\pi$
$991$		−	52.1176i		−	1.65557i	0.561045	−	0.827785i	$-0.310400\pi$
$992$	5.99401	−	42.0546i	0.190310	−	1.33524i
$993$			23.5315i			0.746750i
$994$	−3.41620	+	3.35416i	−0.108355	+	0.106387i
$995$	−19.1028			−0.605599
$996$	9.50336	+	7.76310i	0.301125	+	0.245983i
$997$	−26.2326			−0.830796			−0.415398	−	0.909640i	$-0.636358\pi$
$997$	−26.2326			−0.830796			−0.415398	+	0.909640i	$0.636358\pi$
$998$	−35.7470	−	12.7446i	−1.13155	−	0.403425i
$999$	−4.21124			−0.133238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.p.a.139.15	yes	16
3.2	odd	2		504.2.p.g.307.1		16
4.3	odd	2		672.2.p.a.559.14		16
7.6	odd	2	inner	168.2.p.a.139.16	yes	16
8.3	odd	2	inner	168.2.p.a.139.13	✓	16
8.5	even	2		672.2.p.a.559.11		16
12.11	even	2		2016.2.p.g.559.6		16
21.20	even	2		504.2.p.g.307.2		16
24.5	odd	2		2016.2.p.g.559.11		16
24.11	even	2		504.2.p.g.307.4		16
28.27	even	2		672.2.p.a.559.3		16
56.13	odd	2		672.2.p.a.559.6		16
56.27	even	2	inner	168.2.p.a.139.14	yes	16
84.83	odd	2		2016.2.p.g.559.12		16
168.83	odd	2		504.2.p.g.307.3		16
168.125	even	2		2016.2.p.g.559.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.p.a.139.13	✓	16	8.3	odd	2	inner
168.2.p.a.139.14	yes	16	56.27	even	2	inner
168.2.p.a.139.15	yes	16	1.1	even	1	trivial
168.2.p.a.139.16	yes	16	7.6	odd	2	inner
504.2.p.g.307.1		16	3.2	odd	2
504.2.p.g.307.2		16	21.20	even	2
504.2.p.g.307.3		16	168.83	odd	2
504.2.p.g.307.4		16	24.11	even	2
672.2.p.a.559.3		16	28.27	even	2
672.2.p.a.559.6		16	56.13	odd	2
672.2.p.a.559.11		16	8.5	even	2
672.2.p.a.559.14		16	4.3	odd	2
2016.2.p.g.559.5		16	168.125	even	2
2016.2.p.g.559.6		16	12.11	even	2
2016.2.p.g.559.11		16	24.5	odd	2
2016.2.p.g.559.12		16	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33209 + 0.474920i) q^{2} -1.00000i q^{3} +(1.54890 + 1.26527i) q^{4} +1.58069 q^{5} +(0.474920 - 1.33209i) q^{6} +(-2.37995 - 1.15578i) q^{7} +(1.46237 + 2.42105i) q^{8} -1.00000 q^{9} +(2.10562 + 0.750703i) q^{10} -2.26057 q^{11} +(1.26527 - 1.54890i) q^{12} +0.548664 q^{13} +(-2.62140 - 2.66988i) q^{14} -1.58069i q^{15} +(0.798200 + 3.91955i) q^{16} -0.433635i q^{17} +(-1.33209 - 0.474920i) q^{18} +6.02255i q^{19} +(2.44834 + 2.00000i) q^{20} +(-1.15578 + 2.37995i) q^{21} +(-3.01127 - 1.07359i) q^{22} -8.24028i q^{23} +(2.42105 - 1.46237i) q^{24} -2.50141 q^{25} +(0.730867 + 0.260571i) q^{26} +1.00000i q^{27} +(-2.22394 - 4.80147i) q^{28} +0.548664i q^{29} +(0.750703 - 2.10562i) q^{30} -7.50941 q^{31} +(-0.798200 + 5.60026i) q^{32} +2.26057i q^{33} +(0.205942 - 0.577639i) q^{34} +(-3.76198 - 1.82694i) q^{35} +(-1.54890 - 1.26527i) q^{36} +4.21124i q^{37} +(-2.86023 + 8.02255i) q^{38} -0.548664i q^{39} +(2.31156 + 3.82694i) q^{40} -7.09032i q^{41} +(-2.66988 + 2.62140i) q^{42} -1.82694 q^{43} +(-3.50141 - 2.86023i) q^{44} -1.58069 q^{45} +(3.91347 - 10.9768i) q^{46} +11.5839 q^{47} +(3.91955 - 0.798200i) q^{48} +(4.32834 + 5.50141i) q^{49} +(-3.33209 - 1.18797i) q^{50} -0.433635 q^{51} +(0.849827 + 0.694206i) q^{52} +3.71005i q^{53} +(-0.474920 + 1.33209i) q^{54} -3.57327 q^{55} +(-0.682172 - 7.45216i) q^{56} +6.02255 q^{57} +(-0.260571 + 0.730867i) q^{58} -11.5240i q^{59} +(2.00000 - 2.44834i) q^{60} +12.1325 q^{61} +(-10.0032 - 3.56636i) q^{62} +(2.37995 + 1.15578i) q^{63} +(-3.72294 + 7.08094i) q^{64} +0.867270 q^{65} +(-1.07359 + 3.01127i) q^{66} +9.35089 q^{67} +(0.548664 - 0.671659i) q^{68} -8.24028 q^{69} +(-4.14363 - 4.22027i) q^{70} -1.27953i q^{71} +(-1.46237 - 2.42105i) q^{72} -0.867270i q^{73} +(-2.00000 + 5.60973i) q^{74} +2.50141i q^{75} +(-7.62013 + 9.32834i) q^{76} +(5.38005 + 2.61272i) q^{77} +(0.260571 - 0.730867i) q^{78} +10.3696i q^{79} +(1.26171 + 6.19561i) q^{80} +1.00000 q^{81} +(3.36733 - 9.44491i) q^{82} +6.13554i q^{83} +(-4.80147 + 2.22394i) q^{84} -0.685444i q^{85} +(-2.43364 - 0.867648i) q^{86} +0.548664 q^{87} +(-3.30579 - 5.47295i) q^{88} +7.95759i q^{89} +(-2.10562 - 0.750703i) q^{90} +(-1.30579 - 0.634135i) q^{91} +(10.4261 - 12.7634i) q^{92} +7.50941i q^{93} +(15.4307 + 5.50141i) q^{94} +9.51981i q^{95} +(5.60026 + 0.798200i) q^{96} -19.1778i q^{97} +(3.15300 + 9.38396i) q^{98} +2.26057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 2 q^{4} - 10 q^{8} - 16 q^{9} - 8 q^{11} - 14 q^{14} + 18 q^{16} - 2 q^{18} + 8 q^{22} + 16 q^{25} - 10 q^{28} - 16 q^{30} - 18 q^{32} + 24 q^{35} - 2 q^{36} - 4 q^{42} - 8 q^{43} + 52 q^{46}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 2 * q^4 - 10 * q^8 - 16 * q^9 - 8 * q^11 - 14 * q^14 + 18 * q^16 - 2 * q^18 + 8 * q^22 + 16 * q^25 - 10 * q^28 - 16 * q^30 - 18 * q^32 + 24 * q^35 - 2 * q^36 - 4 * q^42 - 8 * q^43 + 52 * q^46 - 8 * q^49 - 34 * q^50 + 50 * q^56 - 16 * q^57 + 24 * q^58 + 32 * q^60 + 2 * q^64 - 40 * q^67 - 24 * q^70 + 10 * q^72 - 32 * q^74 - 24 * q^78 + 16 * q^81 + 8 * q^84 - 32 * q^86 - 88 * q^88 - 56 * q^91 + 44 * q^92 + 66 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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