LMFDB - Embedded newform 138.2.e.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	138.121
Dual form			138.2.e.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.27310 - 0.818172i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.369215 - 2.56794i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.27310 - 0.818172i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.369215 - 2.56794i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.215370 - 1.49793i) q^{10} +(-2.08004 - 4.55466i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.686393 + 4.77397i) q^{13} +(-2.18251 - 1.40261i) q^{14} +(-1.45204 + 0.426356i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.565599 - 0.652736i) q^{17} +(0.841254 - 0.540641i) q^{18} +(4.58506 + 5.29144i) q^{19} +(-1.45204 - 0.426356i) q^{20} +(-1.07773 + 2.35990i) q^{21} -5.00714 q^{22} +(4.66533 + 1.11118i) q^{23} +1.00000 q^{24} +(-1.12570 + 2.46493i) q^{25} +(4.62769 + 1.35881i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.18251 + 1.40261i) q^{28} +(-2.03899 + 2.35312i) q^{29} +(-0.215370 + 1.49793i) q^{30} +(1.12671 - 0.330833i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.712591 + 4.95618i) q^{33} +(-0.358791 - 0.785643i) q^{34} +(-1.63097 - 3.57133i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.506538 - 0.325532i) q^{37} +(6.71797 - 1.97257i) q^{38} +(0.686393 - 4.77397i) q^{39} +(-0.991025 + 1.14370i) q^{40} +(4.45305 - 2.86180i) q^{41} +(1.69894 + 1.96068i) q^{42} +(-1.40014 - 0.411119i) q^{43} +(-2.08004 + 4.55466i) q^{44} +1.51334 q^{45} +(2.94881 - 3.78213i) q^{46} -12.6797 q^{47} +(0.415415 - 0.909632i) q^{48} +(0.258432 + 0.0758824i) q^{49} +(1.77455 + 2.04794i) q^{50} +(-0.726585 + 0.466948i) q^{51} +(3.15843 - 3.64502i) q^{52} +(-0.602392 + 4.18973i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-6.37459 - 4.09670i) q^{55} +(0.369215 + 2.56794i) q^{56} +(-2.90856 - 6.36886i) q^{57} +(1.29345 + 2.83225i) q^{58} +(-0.566615 - 3.94090i) q^{59} +(1.27310 + 0.818172i) q^{60} +(6.96812 - 2.04602i) q^{61} +(0.167117 - 1.16233i) q^{62} +(1.69894 - 1.96068i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.77977 + 5.51615i) q^{65} +(4.80432 + 1.41067i) q^{66} +(-6.70359 + 14.6788i) q^{67} -0.863693 q^{68} +(-4.16330 - 2.38054i) q^{69} -3.92613 q^{70} +(2.44456 - 5.35285i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-9.41782 - 10.8687i) q^{73} +(-0.506538 + 0.325532i) q^{74} +(1.77455 - 2.04794i) q^{75} +(0.996429 - 6.93032i) q^{76} +(-12.4641 + 3.65979i) q^{77} +(-4.05742 - 2.60754i) q^{78} +(-1.47156 - 10.2349i) q^{79} +(0.628663 + 1.37658i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.753323 - 5.23948i) q^{82} +(2.22176 + 1.42784i) q^{83} +(2.48926 - 0.730913i) q^{84} +(0.186014 - 1.29376i) q^{85} +(-0.955607 + 1.10283i) q^{86} +(2.61935 - 1.68335i) q^{87} +(3.27898 + 3.78415i) q^{88} +(5.02538 + 1.47559i) q^{89} +(0.628663 - 1.37658i) q^{90} +12.5127 q^{91} +(-2.21537 - 4.25348i) q^{92} -1.17428 q^{93} +(-5.26732 + 11.5338i) q^{94} +(10.1666 + 2.98517i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(12.5782 - 8.08355i) q^{97} +(0.176382 - 0.203555i) q^{98} +(0.712591 - 4.95618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	1.27310	−	0.818172i	0.569348	−	0.365898i	−0.224072	−	0.974573i	$-0.571935\pi$
$5$	1.27310	−	0.818172i	0.569348	−	0.365898i	0.793420	+	0.608675i	$0.208299\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	0.369215	−	2.56794i	0.139550	−	0.970592i	−0.792915	−	0.609332i	$-0.791438\pi$
$7$	0.369215	−	2.56794i	0.139550	−	0.970592i	0.932465	−	0.361260i	$-0.117653\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.215370	−	1.49793i	−0.0681061	−	0.473688i
$11$	−2.08004	−	4.55466i	−0.627156	−	1.37328i	−0.910198	−	0.414173i	$-0.864071\pi$
$11$	−2.08004	−	4.55466i	−0.627156	−	1.37328i	0.283042	−	0.959108i	$-0.408656\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	0.686393	+	4.77397i	0.190371	+	1.32406i	0.831027	+	0.556232i	$0.187753\pi$
$13$	0.686393	+	4.77397i	0.190371	+	1.32406i	−0.640656	+	0.767828i	$0.721337\pi$
$14$	−2.18251	−	1.40261i	−0.583300	−	0.374864i
$15$	−1.45204	+	0.426356i	−0.374914	+	0.110085i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	0.565599	−	0.652736i	0.137178	−	0.158312i	−0.683004	−	0.730415i	$-0.739327\pi$
$17$	0.565599	−	0.652736i	0.137178	−	0.158312i	0.820182	+	0.572103i	$0.193872\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	4.58506	+	5.29144i	1.05189	+	1.21394i	0.976214	+	0.216807i	$0.0695644\pi$
$19$	4.58506	+	5.29144i	1.05189	+	1.21394i	0.0756708	+	0.997133i	$0.475890\pi$
$20$	−1.45204	−	0.426356i	−0.324685	−	0.0953362i
$21$	−1.07773	+	2.35990i	−0.235180	+	0.514973i
$22$	−5.00714			−1.06753
$23$	4.66533	+	1.11118i	0.972788	+	0.231696i
$23$	4.66533	+	1.11118i	0.972788	+	0.231696i
$24$	1.00000			0.204124
$25$	−1.12570	+	2.46493i	−0.225139	+	0.492986i
$26$	4.62769	+	1.35881i	0.907565	+	0.266485i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−2.18251	+	1.40261i	−0.412455	+	0.265069i
$29$	−2.03899	+	2.35312i	−0.378631	+	0.436963i	−0.912795	−	0.408417i	$-0.866081\pi$
$29$	−2.03899	+	2.35312i	−0.378631	+	0.436963i	0.534165	+	0.845381i	$0.320626\pi$
$30$	−0.215370	+	1.49793i	−0.0393211	+	0.273484i
$31$	1.12671	−	0.330833i	0.202364	−	0.0594193i	−0.178980	−	0.983853i	$-0.557280\pi$
$31$	1.12671	−	0.330833i	0.202364	−	0.0594193i	0.381343	+	0.924433i	$0.375462\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	0.712591	+	4.95618i	0.124046	+	0.862760i
$34$	−0.358791	−	0.785643i	−0.0615322	−	0.134737i
$35$	−1.63097	−	3.57133i	−0.275685	−	0.603665i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−0.506538	−	0.325532i	−0.0832743	−	0.0535171i	0.498341	−	0.866981i	$-0.333943\pi$
$37$	−0.506538	−	0.325532i	−0.0832743	−	0.0535171i	−0.581615	+	0.813464i	$0.697579\pi$
$38$	6.71797	−	1.97257i	1.08980	−	0.319994i
$39$	0.686393	−	4.77397i	0.109911	−	0.764446i
$40$	−0.991025	+	1.14370i	−0.156695	+	0.180835i
$41$	4.45305	−	2.86180i	0.695450	−	0.446939i	−0.144570	−	0.989495i	$-0.546180\pi$
$41$	4.45305	−	2.86180i	0.695450	−	0.446939i	0.840020	+	0.542556i	$0.182543\pi$
$42$	1.69894	+	1.96068i	0.262152	+	0.302539i
$43$	−1.40014	−	0.411119i	−0.213520	−	0.0626951i	0.173223	−	0.984883i	$-0.444582\pi$
$43$	−1.40014	−	0.411119i	−0.213520	−	0.0626951i	−0.386743	+	0.922188i	$0.626400\pi$
$44$	−2.08004	+	4.55466i	−0.313578	+	0.686640i
$45$	1.51334			0.225595
$46$	2.94881	−	3.78213i	0.434778	−	0.557645i
$47$	−12.6797			−1.84952			−0.924760	−	0.380552i	$-0.875734\pi$
$47$	−12.6797			−1.84952			−0.924760	+	0.380552i	$0.875734\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	0.258432	+	0.0758824i	0.0369188	+	0.0108403i
$50$	1.77455	+	2.04794i	0.250959	+	0.289622i
$51$	−0.726585	+	0.466948i	−0.101742	+	0.0653858i
$52$	3.15843	−	3.64502i	0.437996	−	0.505474i
$53$	−0.602392	+	4.18973i	−0.0827449	+	0.575504i	0.905700	+	0.423920i	$0.139346\pi$
$53$	−0.602392	+	4.18973i	−0.0827449	+	0.575504i	−0.988444	+	0.151583i	$0.951563\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	−6.37459	−	4.09670i	−0.859550	−	0.552399i
$56$	0.369215	+	2.56794i	0.0493384	+	0.343156i
$57$	−2.90856	−	6.36886i	−0.385249	−	0.843577i
$58$	1.29345	+	2.83225i	0.169838	+	0.371893i
$59$	−0.566615	−	3.94090i	−0.0737670	−	0.513061i	−0.992885	−	0.119078i	$-0.962006\pi$
$59$	−0.566615	−	3.94090i	−0.0737670	−	0.513061i	0.919118	−	0.393983i	$-0.128903\pi$
$60$	1.27310	+	0.818172i	0.164357	+	0.105626i
$61$	6.96812	−	2.04602i	0.892176	−	0.261966i	0.196655	−	0.980473i	$-0.436992\pi$
$61$	6.96812	−	2.04602i	0.892176	−	0.261966i	0.695520	+	0.718506i	$0.255174\pi$
$62$	0.167117	−	1.16233i	0.0212239	−	0.147616i
$63$	1.69894	−	1.96068i	0.214046	−	0.247022i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	4.77977	+	5.51615i	0.592858	+	0.684194i
$66$	4.80432	+	1.41067i	0.591371	+	0.173642i
$67$	−6.70359	+	14.6788i	−0.818973	+	1.79330i	−0.256360	+	0.966581i	$0.582523\pi$
$67$	−6.70359	+	14.6788i	−0.818973	+	1.79330i	−0.562614	+	0.826720i	$0.690204\pi$
$68$	−0.863693			−0.104738
$69$	−4.16330	−	2.38054i	−0.501202	−	0.286583i
$70$	−3.92613			−0.469262
$71$	2.44456	−	5.35285i	0.290116	−	0.635266i	−0.707315	−	0.706899i	$-0.750094\pi$
$71$	2.44456	−	5.35285i	0.290116	−	0.635266i	0.997431	+	0.0716327i	$0.0228209\pi$
$72$	−0.959493	−	0.281733i	−0.113077	−	0.0332025i
$73$	−9.41782	−	10.8687i	−1.10227	−	1.27209i	−0.959308	−	0.282362i	$-0.908882\pi$
$73$	−9.41782	−	10.8687i	−1.10227	−	1.27209i	−0.142964	−	0.989728i	$-0.545663\pi$
$74$	−0.506538	+	0.325532i	−0.0588838	+	0.0378423i
$75$	1.77455	−	2.04794i	0.204907	−	0.236476i
$76$	0.996429	−	6.93032i	0.114298	−	0.794962i
$77$	−12.4641	+	3.65979i	−1.42041	+	0.417071i
$78$	−4.05742	−	2.60754i	−0.459412	−	0.295246i
$79$	−1.47156	−	10.2349i	−0.165564	−	1.15152i	−0.887919	−	0.459999i	$-0.847850\pi$
$79$	−1.47156	−	10.2349i	−0.165564	−	1.15152i	0.722356	−	0.691522i	$-0.243059\pi$
$80$	0.628663	+	1.37658i	0.0702867	+	0.153906i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.753323	−	5.23948i	−0.0831906	−	0.578603i
$83$	2.22176	+	1.42784i	0.243870	+	0.156725i	0.656866	−	0.754007i	$-0.271882\pi$
$83$	2.22176	+	1.42784i	0.243870	+	0.156725i	−0.412997	+	0.910732i	$0.635518\pi$
$84$	2.48926	−	0.730913i	0.271601	−	0.0797492i
$85$	0.186014	−	1.29376i	0.0201760	−	0.140327i
$86$	−0.955607	+	1.10283i	−0.103046	+	0.118921i
$87$	2.61935	−	1.68335i	0.280823	−	0.180474i
$88$	3.27898	+	3.78415i	0.349541	+	0.403391i
$89$	5.02538	+	1.47559i	0.532689	+	0.156412i	0.537005	−	0.843579i	$-0.319556\pi$
$89$	5.02538	+	1.47559i	0.532689	+	0.156412i	−0.00431578	+	0.999991i	$0.501374\pi$
$90$	0.628663	−	1.37658i	0.0662669	−	0.145104i
$91$	12.5127			1.31169
$92$	−2.21537	−	4.25348i	−0.230968	−	0.443456i
$93$	−1.17428			−0.121767
$94$	−5.26732	+	11.5338i	−0.543283	+	1.18962i
$95$	10.1666	+	2.98517i	1.04307	+	0.306272i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	12.5782	−	8.08355i	1.27713	−	0.820760i	0.286597	−	0.958051i	$-0.407476\pi$
$97$	12.5782	−	8.08355i	1.27713	−	0.820760i	0.990531	+	0.137291i	$0.0438397\pi$
$98$	0.176382	−	0.203555i	0.0178172	−	0.0205622i
$99$	0.712591	−	4.95618i	0.0716180	−	0.498114i
$100$	2.60004	−	0.763442i	0.260004	−	0.0763442i
$101$	−0.446103	−	0.286693i	−0.0443889	−	0.0285270i	0.518258	−	0.855224i	$-0.326581\pi$
$101$	−0.446103	−	0.286693i	−0.0443889	−	0.0285270i	−0.562647	+	0.826697i	$0.690217\pi$
$102$	0.122916	+	0.854902i	0.0121705	+	0.0846479i
$103$	0.382147	+	0.836786i	0.0376541	+	0.0824510i	0.927524	−	0.373763i	$-0.121933\pi$
$103$	0.382147	+	0.836786i	0.0376541	+	0.0824510i	−0.889870	+	0.456214i	$0.849205\pi$
$104$	−2.00357	−	4.38721i	−0.196466	−	0.430201i
$105$	0.558746	+	3.88617i	0.0545281	+	0.379251i
$106$	3.56087	+	2.28843i	0.345862	+	0.222272i
$107$	−12.9111	+	3.79104i	−1.24816	+	0.366493i	−0.838076	−	0.545554i	$-0.816319\pi$
$107$	−12.9111	+	3.79104i	−1.24816	+	0.366493i	−0.410086	+	0.912047i	$0.634501\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	3.25857	−	3.76059i	0.312114	−	0.360199i	−0.577920	−	0.816094i	$-0.696135\pi$
$109$	3.25857	−	3.76059i	0.312114	−	0.360199i	0.890034	+	0.455895i	$0.150681\pi$
$110$	−6.37459	+	4.09670i	−0.607794	+	0.390605i
$111$	0.394306	+	0.455054i	0.0374259	+	0.0431918i
$112$	2.48926	+	0.730913i	0.235213	+	0.0690648i
$113$	−5.65122	+	12.3744i	−0.531622	+	1.16409i	0.433227	+	0.901285i	$0.357375\pi$
$113$	−5.65122	+	12.3744i	−0.531622	+	1.16409i	−0.964849	+	0.262805i	$0.915352\pi$
$114$	−7.00158			−0.655758
$115$	6.84856	−	2.40240i	0.638632	−	0.224025i
$116$	3.11362			0.289093
$117$	−2.00357	+	4.38721i	−0.185230	+	0.405598i
$118$	−3.82014	−	1.12170i	−0.351673	−	0.103260i
$119$	−1.46736	−	1.69343i	−0.134513	−	0.155236i
$120$	1.27310	−	0.818172i	0.116218	−	0.0746885i
$121$	−9.21485	+	10.6345i	−0.837714	+	0.966773i
$122$	1.03353	−	7.18837i	0.0935715	−	0.650804i
$123$	−5.07894	+	1.49131i	−0.457952	+	0.134467i
$124$	−0.987866	−	0.634863i	−0.0887130	−	0.0570124i
$125$	1.66046	+	11.5488i	0.148516	+	1.03295i
$126$	−1.07773	−	2.35990i	−0.0960120	−	0.210237i
$127$	2.79580	+	6.12195i	0.248087	+	0.543235i	0.992176	−	0.124845i	$-0.0398435\pi$
$127$	2.79580	+	6.12195i	0.248087	+	0.543235i	−0.744089	+	0.668080i	$0.767116\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	1.22760	+	0.788932i	0.108084	+	0.0694615i
$130$	7.00326	−	2.05634i	0.614226	−	0.180353i
$131$	−2.70354	+	18.8035i	−0.236209	+	1.64287i	0.434155	+	0.900838i	$0.357047\pi$
$131$	−2.70354	+	18.8035i	−0.236209	+	1.64287i	−0.670364	+	0.742032i	$0.733862\pi$
$132$	3.27898	−	3.78415i	0.285399	−	0.329368i
$133$	15.2810	−	9.82050i	1.32503	−	0.851546i
$134$	10.5675	+	12.1956i	0.912896	+	1.05354i
$135$	−1.45204	−	0.426356i	−0.124971	−	0.0366949i
$136$	−0.358791	+	0.785643i	−0.0307661	+	0.0673683i
$137$	−2.62684			−0.224426			−0.112213	−	0.993684i	$-0.535794\pi$
$137$	−2.62684			−0.224426			−0.112213	+	0.993684i	$0.535794\pi$
$138$	−3.89491	+	2.79816i	−0.331557	+	0.238195i
$139$	−18.4268			−1.56294			−0.781471	−	0.623941i	$-0.785530\pi$
$139$	−18.4268			−1.56294			−0.781471	+	0.623941i	$0.785530\pi$
$140$	−1.63097	+	3.57133i	−0.137842	+	0.301833i
$141$	12.1660	+	3.57227i	1.02457	+	0.300840i
$142$	−3.85361	−	4.44731i	−0.323388	−	0.373210i
$143$	20.3161	−	13.0563i	1.69891	−	1.09183i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.670582	+	4.66400i	−0.0556888	+	0.387324i
$146$	−13.7989	+	4.05171i	−1.14200	+	0.335322i
$147$	−0.226585	−	0.145617i	−0.0186884	−	0.0120103i
$148$	0.0856910	+	0.595994i	0.00704376	+	0.0489904i
$149$	−1.64339	−	3.59852i	−0.134632	−	0.294802i	0.830294	−	0.557326i	$-0.188173\pi$
$149$	−1.64339	−	3.59852i	−0.134632	−	0.294802i	−0.964926	+	0.262524i	$0.915445\pi$
$150$	−1.12570	−	2.46493i	−0.0919127	−	0.201261i
$151$	2.31220	+	16.0817i	0.188164	+	1.30871i	0.836756	+	0.547575i	$0.184449\pi$
$151$	2.31220	+	16.0817i	0.188164	+	1.30871i	−0.648592	+	0.761136i	$0.724642\pi$
$152$	−5.89011	−	3.78534i	−0.477751	−	0.307032i
$153$	0.828708	−	0.243331i	0.0669970	−	0.0196721i
$154$	−1.84871	+	12.8581i	−0.148973	+	1.03613i
$155$	1.16374	−	1.34303i	0.0934738	−	0.107875i
$156$	−4.05742	+	2.60754i	−0.324853	+	0.208770i
$157$	−13.3213	−	15.3736i	−1.06316	−	1.22695i	−0.972948	−	0.231026i	$-0.925792\pi$
$157$	−13.3213	−	15.3736i	−1.06316	−	1.22695i	−0.0902098	−	0.995923i	$-0.528754\pi$
$158$	−9.92134	−	2.91317i	−0.789299	−	0.231759i
$159$	1.75837	−	3.85030i	0.139448	−	0.305349i
$160$	1.51334			0.119640
$161$	4.57594	−	11.5700i	0.360635	−	0.911847i
$162$	1.00000			0.0785674
$163$	−6.21157	+	13.6015i	−0.486528	+	1.06535i	0.494089	+	0.869412i	$0.335502\pi$
$163$	−6.21157	+	13.6015i	−0.486528	+	1.06535i	−0.980617	+	0.195936i	$0.937225\pi$
$164$	−5.07894	−	1.49131i	−0.396598	−	0.116452i
$165$	4.96220	+	5.72669i	0.386307	+	0.445822i
$166$	2.22176	−	1.42784i	0.172442	−	0.110822i
$167$	7.89124	−	9.10698i	0.610642	−	0.704719i	−0.363260	−	0.931688i	$-0.618336\pi$
$167$	7.89124	−	9.10698i	0.610642	−	0.704719i	0.973902	+	0.226969i	$0.0728816\pi$
$168$	0.369215	−	2.56794i	0.0284855	−	0.198121i
$169$	−9.84622	+	2.89111i	−0.757401	+	0.222393i
$170$	−1.09957	−	0.706649i	−0.0843330	−	0.0541975i
$171$	0.996429	+	6.93032i	0.0761988	+	0.529975i
$172$	0.606195	+	1.32738i	0.0462220	+	0.101212i
$173$	6.43950	+	14.1005i	0.489586	+	1.07204i	0.979715	+	0.200394i	$0.0642221\pi$
$173$	6.43950	+	14.1005i	0.489586	+	1.07204i	−0.490130	+	0.871650i	$0.663051\pi$
$174$	−0.443115	−	3.08193i	−0.0335924	−	0.233640i
$175$	5.91418	+	3.80081i	0.447070	+	0.287314i
$176$	4.80432	−	1.41067i	0.362139	−	0.106334i
$177$	−0.566615	+	3.94090i	−0.0425894	+	0.296216i
$178$	3.42986	−	3.95827i	0.257079	−	0.296685i
$179$	6.06984	−	3.90085i	0.453681	−	0.291563i	−0.293775	−	0.955875i	$-0.594911\pi$
$179$	6.06984	−	3.90085i	0.453681	−	0.291563i	0.747456	+	0.664311i	$0.231275\pi$
$180$	−0.991025	−	1.14370i	−0.0738666	−	0.0852467i
$181$	−3.20527	−	0.941152i	−0.238246	−	0.0699552i	0.160430	−	0.987047i	$-0.448712\pi$
$181$	−3.20527	−	0.941152i	−0.238246	−	0.0699552i	−0.398676	+	0.917092i	$0.630530\pi$
$182$	5.19797	−	11.3820i	0.385299	−	0.843687i
$183$	−7.26229			−0.536844
$184$	−4.78940	+	0.248210i	−0.353080	+	0.0182983i
$185$	−0.911214			−0.0669938
$186$	−0.487813	+	1.06816i	−0.0357682	+	0.0783214i
$187$	−4.14946	−	1.21839i	−0.303438	−	0.0890975i
$188$	8.30342	+	9.58265i	0.605589	+	0.698887i
$189$	−2.18251	+	1.40261i	−0.158754	+	0.102025i
$190$	6.93874	−	8.00774i	0.503389	−	0.580942i
$191$	2.42111	−	16.8392i	0.175185	−	1.21844i	−0.692534	−	0.721385i	$-0.743506\pi$
$191$	2.42111	−	16.8392i	0.175185	−	1.21844i	0.867719	−	0.497055i	$-0.165585\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	−19.1315	−	12.2951i	−1.37712	−	0.885020i	−0.377950	−	0.925826i	$-0.623371\pi$
$193$	−19.1315	−	12.2951i	−1.37712	−	0.885020i	−0.999167	+	0.0408061i	$0.987007\pi$
$194$	−2.12786	−	14.7996i	−0.152772	−	1.06255i
$195$	−3.03208	−	6.63933i	−0.217132	−	0.475452i
$196$	−0.111889	−	0.245002i	−0.00799205	−	0.0175002i
$197$	−1.43442	−	9.97664i	−0.102198	−	0.710806i	−0.974915	−	0.222578i	$-0.928553\pi$
$197$	−1.43442	−	9.97664i	−0.102198	−	0.710806i	0.872716	−	0.488228i	$-0.162356\pi$
$198$	−4.21228	−	2.70707i	−0.299353	−	0.192383i
$199$	9.05033	−	2.65742i	0.641561	−	0.188379i	0.0552593	−	0.998472i	$-0.482401\pi$
$199$	9.05033	−	2.65742i	0.641561	−	0.188379i	0.586302	+	0.810093i	$0.300583\pi$
$200$	0.385646	−	2.68223i	0.0272693	−	0.189662i
$201$	10.5675	−	12.1956i	0.745377	−	0.860211i
$202$	−0.446103	+	0.286693i	−0.0313877	+	0.0201716i
$203$	5.28985	+	6.10482i	0.371275	+	0.428474i
$204$	0.828708	+	0.243331i	0.0580211	+	0.0170365i
$205$	3.32774	−	7.28672i	0.232419	−	0.508927i
$206$	0.919917			0.0640937
$207$	3.32398	+	3.45705i	0.231032	+	0.240281i
$208$	−4.82306			−0.334419
$209$	14.5636	−	31.8898i	1.00738	−	2.20586i
$210$	3.76709	+	1.10612i	0.259954	+	0.0763294i
$211$	2.21294	+	2.55387i	0.152345	+	0.175816i	0.826792	−	0.562508i	$-0.190163\pi$
$211$	2.21294	+	2.55387i	0.152345	+	0.175816i	−0.674447	+	0.738323i	$0.735618\pi$
$212$	3.56087	−	2.28843i	0.244561	−	0.157170i
$213$	−3.85361	+	4.44731i	−0.264045	+	0.304724i
$214$	−1.91501	+	13.3192i	−0.130907	+	0.910481i
$215$	−2.11889	+	0.622162i	−0.144507	+	0.0424311i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−0.433561	−	3.01548i	−0.0294320	−	0.204704i
$218$	−2.06709	−	4.52630i	−0.140001	−	0.306560i
$219$	5.97425	+	13.0818i	0.403702	+	0.883985i
$220$	1.07839	+	7.50037i	0.0727050	+	0.505675i
$221$	3.50436	+	2.25212i	0.235729	+	0.151494i
$222$	0.577732	−	0.169638i	0.0387749	−	0.0113853i
$223$	2.46625	−	17.1532i	0.165152	−	1.14866i	−0.723582	−	0.690238i	$-0.757506\pi$
$223$	2.46625	−	17.1532i	0.165152	−	1.14866i	0.888735	−	0.458422i	$-0.151585\pi$
$224$	1.69894	−	1.96068i	0.113515	−	0.131003i
$225$	−2.27964	+	1.46503i	−0.151976	+	0.0976690i
$226$	8.90859	+	10.2811i	0.592591	+	0.683886i
$227$	−11.4377	−	3.35842i	−0.759148	−	0.222906i	−0.120824	−	0.992674i	$-0.538554\pi$
$227$	−11.4377	−	3.35842i	−0.759148	−	0.222906i	−0.638324	+	0.769768i	$0.720372\pi$
$228$	−2.90856	+	6.36886i	−0.192624	+	0.421788i
$229$	16.9000			1.11678			0.558390	−	0.829578i	$-0.311419\pi$
$229$	16.9000			1.11678			0.558390	+	0.829578i	$0.311419\pi$
$230$	0.659693	−	7.22767i	0.0434989	−	0.476578i
$231$	12.9903			0.854698
$232$	1.29345	−	2.83225i	0.0849188	−	0.185946i
$233$	−27.3383	−	8.02724i	−1.79099	−	0.525882i	−0.794324	−	0.607494i	$-0.792175\pi$
$233$	−27.3383	−	8.02724i	−1.79099	−	0.525882i	−0.996664	+	0.0816122i	$0.973993\pi$
$234$	3.15843	+	3.64502i	0.206473	+	0.238283i
$235$	−16.1425	+	10.3741i	−1.05302	+	0.676735i
$236$	−2.60728	+	3.00896i	−0.169719	+	0.195866i
$237$	−1.47156	+	10.2349i	−0.0955883	+	0.664831i
$238$	−2.14996	+	0.631285i	−0.139361	+	0.0409201i
$239$	−18.5912	−	11.9478i	−1.20256	−	0.772841i	−0.223165	−	0.974781i	$-0.571639\pi$
$239$	−18.5912	−	11.9478i	−1.20256	−	0.772841i	−0.979398	+	0.201940i	$0.935275\pi$
$240$	−0.215370	−	1.49793i	−0.0139021	−	0.0966912i
$241$	−0.663894	−	1.45372i	−0.0427651	−	0.0936426i	0.887044	−	0.461686i	$-0.152755\pi$
$241$	−0.663894	−	1.45372i	−0.0427651	−	0.0936426i	−0.929809	+	0.368043i	$0.880028\pi$
$242$	5.84550	+	12.7999i	0.375763	+	0.822806i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	−6.10943	−	3.92629i	−0.391116	−	0.251355i
$245$	0.391095	−	0.114836i	0.0249861	−	0.00733659i
$246$	−0.753323	+	5.23948i	−0.0480301	+	0.334057i
$247$	−22.1140	+	25.5209i	−1.40708	+	1.62386i
$248$	−0.987866	+	0.634863i	−0.0627296	+	0.0403139i
$249$	−1.72949	−	1.99594i	−0.109602	−	0.126488i
$250$	11.1949	+	3.28713i	0.708029	+	0.207896i
$251$	−7.30661	+	15.9992i	−0.461189	+	1.00986i	0.526026	+	0.850469i	$0.323682\pi$
$251$	−7.30661	+	15.9992i	−0.461189	+	1.00986i	−0.987215	+	0.159395i	$0.949046\pi$
$252$	−2.59435			−0.163429
$253$	−4.64306	−	23.5603i	−0.291907	−	1.48122i
$254$	6.73013			0.422286
$255$	−0.542972	+	1.18894i	−0.0340022	+	0.0744545i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	13.5533	+	15.6413i	0.845430	+	0.975678i	0.999924	−	0.0123156i	$-0.00392026\pi$
$257$	13.5533	+	15.6413i	0.845430	+	0.975678i	−0.154494	+	0.987994i	$0.549375\pi$
$258$	1.22760	−	0.788932i	0.0764271	−	0.0491167i
$259$	−1.02297	+	1.18057i	−0.0635642	+	0.0733570i
$260$	1.03874	−	7.22462i	0.0644201	−	0.448052i
$261$	−2.98750	+	0.877209i	−0.184922	+	0.0542979i
$262$	15.9812	+	10.2705i	0.987321	+	0.634513i
$263$	3.91717	+	27.2445i	0.241543	+	1.67997i	0.644387	+	0.764699i	$0.277113\pi$
$263$	3.91717	+	27.2445i	0.241543	+	1.67997i	−0.402844	+	0.915269i	$0.631978\pi$
$264$	−2.08004	−	4.55466i	−0.128018	−	0.280320i
$265$	2.66101	+	5.82680i	0.163465	+	0.357938i
$266$	−2.58509	−	17.9797i	−0.158502	−	1.10240i
$267$	−4.40610	−	2.83163i	−0.269649	−	0.173293i
$268$	15.4834	−	4.54634i	0.945800	−	0.277712i
$269$	1.88933	−	13.1406i	0.115194	−	0.801195i	−0.847537	−	0.530736i	$-0.821915\pi$
$269$	1.88933	−	13.1406i	0.115194	−	0.801195i	0.962731	−	0.270459i	$-0.0871755\pi$
$270$	−0.991025	+	1.14370i	−0.0603119	+	0.0696036i
$271$	20.2562	−	13.0179i	1.23048	−	0.790779i	0.246511	−	0.969140i	$-0.420716\pi$
$271$	20.2562	−	13.0179i	1.23048	−	0.790779i	0.983965	+	0.178361i	$0.0570795\pi$
$272$	0.565599	+	0.652736i	0.0342945	+	0.0395779i
$273$	−12.0059	−	3.52524i	−0.726627	−	0.213357i
$274$	−1.09123	+	2.38946i	−0.0659235	+	0.144352i
$275$	13.5684			0.818206
$276$	0.927287	+	4.70533i	0.0558161	+	0.283228i
$277$	−18.3404			−1.10197			−0.550983	−	0.834516i	$-0.685747\pi$
$277$	−18.3404			−1.10197			−0.550983	+	0.834516i	$0.685747\pi$
$278$	−7.65478	+	16.7616i	−0.459103	+	1.00530i
$279$	1.12671	+	0.330833i	0.0674545	+	0.0198064i
$280$	2.57107	+	2.96717i	0.153651	+	0.177322i
$281$	−0.0168026	+	0.0107984i	−0.00100236	+	0.000644178i	−0.541142	−	0.840931i	$-0.682008\pi$
$281$	−0.0168026	+	0.0107984i	−0.00100236	+	0.000644178i	0.540140	+	0.841575i	$0.318371\pi$
$282$	8.30342	−	9.58265i	0.494461	−	0.570639i
$283$	−2.49815	+	17.3750i	−0.148500	+	1.03284i	0.770178	+	0.637829i	$0.220167\pi$
$283$	−2.49815	+	17.3750i	−0.148500	+	1.03284i	−0.918678	+	0.395008i	$0.870742\pi$
$284$	−5.64626	+	1.65789i	−0.335044	+	0.0983778i
$285$	−8.91372	−	5.72850i	−0.528003	−	0.339327i
$286$	−3.43687	−	23.9039i	−0.203226	−	1.41347i
$287$	−5.70482	−	12.4918i	−0.336745	−	0.737368i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	2.31319	+	16.0886i	0.136070	+	0.946388i
$290$	3.96395	+	2.54748i	0.232771	+	0.149593i
$291$	−14.3461	+	4.21241i	−0.840985	+	0.246936i
$292$	−2.04669	+	14.2350i	−0.119773	+	0.833042i
$293$	1.90332	−	2.19655i	0.111193	−	0.128324i	−0.697424	−	0.716658i	$-0.745671\pi$
$293$	1.90332	−	2.19655i	0.111193	−	0.128324i	0.808618	+	0.588335i	$0.200216\pi$
$294$	−0.226585	+	0.145617i	−0.0132147	+	0.00849258i
$295$	−3.94569	−	4.55357i	−0.229727	−	0.265119i
$296$	0.577732	+	0.169638i	0.0335800	+	0.00985998i
$297$	−2.08004	+	4.55466i	−0.120696	+	0.264288i
$298$	−3.95602			−0.229166
$299$	−2.10247	+	23.0348i	−0.121589	+	1.33214i
$300$	−2.70981			−0.156451
$301$	−1.57268	+	3.44370i	−0.0906480	+	0.198491i
$302$	15.5890	+	4.57733i	0.897044	+	0.263396i
$303$	0.347262	+	0.400761i	0.0199497	+	0.0230231i
$304$	−5.89011	+	3.78534i	−0.337821	+	0.217104i
$305$	7.19711	−	8.30591i	0.412105	−	0.475595i
$306$	0.122916	−	0.854902i	0.00702666	−	0.0488715i
$307$	12.1970	−	3.58138i	0.696122	−	0.204400i	0.0855190	−	0.996337i	$-0.472745\pi$
$307$	12.1970	−	3.58138i	0.696122	−	0.204400i	0.610603	+	0.791937i	$0.290927\pi$
$308$	10.9281	+	7.02308i	0.622688	+	0.400177i
$309$	−0.130918	−	0.910554i	−0.00744766	−	0.0517996i
$310$	−0.738226	−	1.61649i	−0.0419284	−	0.0918104i
$311$	−8.84860	−	19.3757i	−0.501758	−	1.09870i	−0.975894	−	0.218245i	$-0.929967\pi$
$311$	−8.84860	−	19.3757i	−0.501758	−	1.09870i	0.474136	−	0.880452i	$-0.342760\pi$
$312$	0.686393	+	4.77397i	0.0388593	+	0.270273i
$313$	1.59110	+	1.02253i	0.0899340	+	0.0577971i	0.584835	−	0.811152i	$-0.301159\pi$
$313$	1.59110	+	1.02253i	0.0899340	+	0.0577971i	−0.494901	+	0.868949i	$0.664796\pi$
$314$	−19.5182	+	5.73107i	−1.10148	+	0.323423i
$315$	0.558746	−	3.88617i	0.0314818	−	0.218961i
$316$	−6.77138	+	7.81459i	−0.380920	+	0.439605i
$317$	−18.3490	+	11.7922i	−1.03058	+	0.662314i	−0.942640	−	0.333811i	$-0.891665\pi$
$317$	−18.3490	+	11.7922i	−1.03058	+	0.662314i	−0.0879413	+	0.996126i	$0.528029\pi$
$318$	−2.77190	−	3.19895i	−0.155441	−	0.179388i
$319$	14.9588	+	4.39231i	0.837534	+	0.245922i
$320$	0.628663	−	1.37658i	0.0351433	−	0.0769532i
$321$	13.4562			0.751049
$322$	−8.62356	−	8.96879i	−0.480572	−	0.499811i
$323$	6.04722			0.336476
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−12.5402	−	3.68213i	−0.695603	−	0.204248i
$326$	9.79193	+	11.3005i	0.542325	+	0.625876i
$327$	−4.18605	+	2.69021i	−0.231489	+	0.148769i
$328$	−3.46641	+	4.00045i	−0.191400	+	0.220888i
$329$	−4.68152	+	32.5607i	−0.258100	+	1.79513i
$330$	7.27055	−	2.13483i	0.400231	−	0.117518i
$331$	14.6532	+	9.41704i	0.805413	+	0.517608i	0.877378	−	0.479800i	$-0.159291\pi$
$331$	14.6532	+	9.41704i	0.805413	+	0.517608i	−0.0719651	+	0.997407i	$0.522927\pi$
$332$	−0.375855	−	2.61413i	−0.0206277	−	0.143469i
$333$	−0.250131	−	0.547710i	−0.0137071	−	0.0300143i
$334$	−5.00586	−	10.9613i	−0.273908	−	0.599776i
$335$	3.47545	+	24.1723i	0.189884	+	1.32067i
$336$	−2.18251	−	1.40261i	−0.119066	−	0.0765188i
$337$	17.2210	−	5.05653i	0.938086	−	0.275447i	0.223268	−	0.974757i	$-0.428328\pi$
$337$	17.2210	−	5.05653i	0.938086	−	0.275447i	0.714818	+	0.699310i	$0.246509\pi$
$338$	−1.46042	+	10.1574i	−0.0794364	+	0.552492i
$339$	8.90859	−	10.2811i	0.483848	−	0.558391i
$340$	−1.09957	+	0.706649i	−0.0596325	+	0.0383234i
$341$	−3.85044	−	4.44364i	−0.208513	−	0.240637i
$342$	6.71797	+	1.97257i	0.363266	+	0.106665i
$343$	7.83441	−	17.1550i	0.423018	−	0.926281i
$344$	1.45925			0.0786776
$345$	−7.24798	+	0.375626i	−0.390218	+	0.0202230i
$346$	15.5014			0.833358
$347$	−2.00445	+	4.38914i	−0.107605	+	0.235621i	−0.955773	−	0.294105i	$-0.904978\pi$
$347$	−2.00445	+	4.38914i	−0.107605	+	0.235621i	0.848168	+	0.529727i	$0.177706\pi$
$348$	−2.98750	−	0.877209i	−0.160147	−	0.0470233i
$349$	−6.78166	−	7.82645i	−0.363014	−	0.418940i	0.544633	−	0.838674i	$-0.316669\pi$
$349$	−6.78166	−	7.82645i	−0.363014	−	0.418940i	−0.907647	+	0.419734i	$0.862123\pi$
$350$	5.91418	−	3.80081i	0.316126	−	0.203162i
$351$	3.15843	−	3.64502i	0.168585	−	0.194557i
$352$	0.712591	−	4.95618i	0.0379812	−	0.264165i
$353$	28.1818	−	8.27493i	1.49997	−	0.440430i	0.574261	−	0.818673i	$-0.305290\pi$
$353$	28.1818	−	8.27493i	1.49997	−	0.440430i	0.925707	+	0.378242i	$0.123471\pi$
$354$	3.34938	+	2.15252i	0.178018	+	0.114405i
$355$	−1.26737	−	8.81478i	−0.0672652	−	0.467840i
$356$	−2.17575	−	4.76423i	−0.115315	−	0.252504i
$357$	0.930830	+	2.03823i	0.0492648	+	0.107875i
$358$	−1.02684	−	7.14180i	−0.0542699	−	0.377456i
$359$	−8.41063	−	5.40518i	−0.443896	−	0.285275i	0.299537	−	0.954085i	$-0.403168\pi$
$359$	−8.41063	−	5.40518i	−0.443896	−	0.285275i	−0.743434	+	0.668810i	$0.766804\pi$
$360$	−1.45204	+	0.426356i	−0.0765290	+	0.0224710i
$361$	−4.27260	+	29.7166i	−0.224874	+	1.56403i
$362$	−2.18762	+	2.52465i	−0.114979	+	0.132692i
$363$	11.8377	−	7.60761i	0.621317	−	0.399296i
$364$	−8.19408	−	9.45647i	−0.429487	−	0.495654i
$365$	−20.8823	−	6.13160i	−1.09303	−	0.320943i
$366$	−3.01686	+	6.60601i	−0.157694	+	0.345302i
$367$	16.7049			0.871991			0.435995	−	0.899949i	$-0.356396\pi$
$367$	16.7049			0.871991			0.435995	+	0.899949i	$0.356396\pi$
$368$	−1.76381	+	4.45971i	−0.0919450	+	0.232478i
$369$	5.29335			0.275561
$370$	−0.378532	+	0.828870i	−0.0196790	+	0.0430909i
$371$	10.5366	+	3.09382i	0.547032	+	0.160623i
$372$	0.768989	+	0.887461i	0.0398702	+	0.0460127i
$373$	27.9494	−	17.9620i	1.44717	−	0.930037i	0.447811	−	0.894128i	$-0.352204\pi$
$373$	27.9494	−	17.9620i	1.44717	−	0.930037i	0.999355	−	0.0359089i	$-0.0114326\pi$
$374$	−2.83203	+	3.26834i	−0.146441	+	0.169002i
$375$	1.66046	−	11.5488i	0.0857460	−	0.596377i
$376$	12.1660	−	3.57227i	0.627416	−	0.184226i
$377$	−12.6333	−	8.11890i	−0.650646	−	0.418145i
$378$	0.369215	+	2.56794i	0.0189904	+	0.132081i
$379$	3.51150	+	7.68911i	0.180374	+	0.394963i	0.978123	−	0.208026i	$-0.0667037\pi$
$379$	3.51150	+	7.68911i	0.180374	+	0.394963i	−0.797750	+	0.602989i	$0.793976\pi$
$380$	−4.40164	−	9.63824i	−0.225799	−	0.494431i
$381$	−0.957798	−	6.66163i	−0.0490695	−	0.341286i
$382$	−14.3117	−	9.19757i	−0.732250	−	0.470588i
$383$	4.22491	−	1.24055i	0.215883	−	0.0633889i	−0.172003	−	0.985096i	$-0.555024\pi$
$383$	4.22491	−	1.24055i	0.215883	−	0.0633889i	0.387886	+	0.921708i	$0.373206\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−12.8737	+	14.8570i	−0.656104	+	0.757185i
$386$	−19.1315	+	12.2951i	−0.973769	+	0.625803i
$387$	−0.955607	−	1.10283i	−0.0485762	−	0.0560600i
$388$	−14.3461	−	4.21241i	−0.728315	−	0.213852i
$389$	8.42800	−	18.4548i	0.427317	−	0.935693i	−0.566438	−	0.824105i	$-0.691679\pi$
$389$	8.42800	−	18.4548i	0.427317	−	0.935693i	0.993754	−	0.111589i	$-0.0355939\pi$
$390$	−7.29891			−0.369595
$391$	3.36401	−	2.41675i	0.170125	−	0.122220i
$392$	−0.269342			−0.0136038
$393$	7.89159	−	17.2802i	0.398078	−	0.871669i
$394$	−9.67095	−	2.83965i	−0.487216	−	0.143059i
$395$	−10.2474	−	11.8261i	−0.515602	−	0.595036i
$396$	−4.21228	+	2.70707i	−0.211675	+	0.136035i
$397$	9.40180	−	10.8503i	0.471863	−	0.544559i	−0.469066	−	0.883163i	$-0.655409\pi$
$397$	9.40180	−	10.8503i	0.471863	−	0.544559i	0.940929	+	0.338604i	$0.109955\pi$
$398$	1.34237	−	9.33640i	0.0672870	−	0.467992i
$399$	−17.4288	+	5.11755i	−0.872530	+	0.256198i
$400$	−2.27964	−	1.46503i	−0.113982	−	0.0732517i
$401$	1.64117	+	11.4146i	0.0819562	+	0.570018i	0.988879	+	0.148721i	$0.0475157\pi$
$401$	1.64117	+	11.4146i	0.0819562	+	0.570018i	−0.906923	+	0.421296i	$0.861575\pi$
$402$	−6.70359	−	14.6788i	−0.334344	−	0.732112i
$403$	2.35275	+	5.15181i	0.117199	+	0.256630i
$404$	0.0754672	+	0.524886i	0.00375463	+	0.0261140i
$405$	1.27310	+	0.818172i	0.0632609	+	0.0406553i
$406$	7.75062	−	2.27579i	0.384657	−	0.112945i
$407$	−0.429067	+	2.98423i	−0.0212681	+	0.147923i
$408$	0.565599	−	0.652736i	0.0280013	−	0.0323152i
$409$	−19.9128	+	12.7972i	−0.984624	+	0.632779i	−0.930707	−	0.365766i	$-0.880807\pi$
$409$	−19.9128	+	12.7972i	−0.984624	+	0.632779i	−0.0539169	+	0.998545i	$0.517171\pi$
$410$	−5.24585	−	6.05403i	−0.259074	−	0.298987i
$411$	2.52043	+	0.740066i	0.124324	+	0.0365048i
$412$	0.382147	−	0.836786i	0.0188270	−	0.0412255i
$413$	−10.3292			−0.508267
$414$	4.52547	−	1.58749i	0.222415	−	0.0780207i
$415$	3.99674			0.196192
$416$	−2.00357	+	4.38721i	−0.0982331	+	0.215101i
$417$	17.6804	+	5.19143i	0.865813	+	0.254226i
$418$	−22.9581	−	26.4950i	−1.12292	−	1.29591i
$419$	−1.87628	+	1.20581i	−0.0916621	+	0.0589076i	−0.585669	−	0.810550i	$-0.699168\pi$
$419$	−1.87628	+	1.20581i	−0.0916621	+	0.0589076i	0.494007	+	0.869458i	$0.335532\pi$
$420$	2.57107	−	2.96717i	0.125455	−	0.144783i
$421$	2.56625	−	17.8486i	0.125071	−	0.869889i	−0.826604	−	0.562784i	$-0.809730\pi$
$421$	2.56625	−	17.8486i	0.125071	−	0.869889i	0.951675	−	0.307106i	$-0.0993605\pi$
$422$	3.24237	−	0.952047i	0.157836	−	0.0463449i
$423$	−10.6668	−	6.85514i	−0.518638	−	0.333309i
$424$	−0.602392	−	4.18973i	−0.0292547	−	0.203471i
$425$	0.972256	+	2.12894i	0.0471614	+	0.103269i
$426$	2.44456	+	5.35285i	0.118439	+	0.259346i
$427$	−2.68134	−	18.6492i	−0.129759	−	0.902496i
$428$	11.3200	+	7.27495i	0.547175	+	0.351648i
$429$	−23.1715	+	6.80377i	−1.11873	+	0.328489i
$430$	−0.314280	+	2.18586i	−0.0151559	+	0.105412i
$431$	−14.6477	+	16.9043i	−0.705553	+	0.814252i	−0.989492	−	0.144591i	$-0.953813\pi$
$431$	−14.6477	+	16.9043i	−0.705553	+	0.814252i	0.283938	+	0.958842i	$0.408359\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	−11.4632	−	13.2292i	−0.550887	−	0.635757i	0.410203	−	0.911994i	$-0.365458\pi$
$433$	−11.4632	−	13.2292i	−0.550887	−	0.635757i	−0.961089	+	0.276237i	$0.910912\pi$
$434$	−2.92309	−	0.858296i	−0.140313	−	0.0411995i
$435$	1.95742	−	4.28615i	0.0938510	−	0.205505i
$436$	−4.97597			−0.238306
$437$	15.5111	+	29.7811i	0.741996	+	1.42462i
$438$	14.3814			0.687170
$439$	−6.27863	+	13.7483i	−0.299662	+	0.656169i	−0.998236	−	0.0593689i	$-0.981091\pi$
$439$	−6.27863	+	13.7483i	−0.299662	+	0.656169i	0.698574	+	0.715538i	$0.253818\pi$
$440$	7.27055	+	2.13483i	0.346610	+	0.101774i
$441$	0.176382	+	0.203555i	0.00839912	+	0.00969311i
$442$	3.50436	−	2.25212i	0.166686	−	0.107122i
$443$	7.74333	−	8.93627i	0.367897	−	0.424575i	−0.541373	−	0.840782i	$-0.682095\pi$
$443$	7.74333	−	8.93627i	0.367897	−	0.424575i	0.909270	+	0.416207i	$0.136641\pi$
$444$	0.0856910	−	0.595994i	0.00406671	−	0.0282846i
$445$	7.60510	−	2.23306i	0.360516	−	0.105857i
$446$	−14.5785	−	9.36906i	−0.690314	−	0.443638i
$447$	0.563000	+	3.91575i	0.0266290	+	0.185209i
$448$	−1.07773	−	2.35990i	−0.0509181	−	0.111495i
$449$	−1.94712	−	4.26359i	−0.0918900	−	0.201211i	0.858106	−	0.513472i	$-0.171641\pi$
$449$	−1.94712	−	4.26359i	−0.0918900	−	0.201211i	−0.949996	+	0.312261i	$0.898914\pi$
$450$	0.385646	+	2.68223i	0.0181795	+	0.126441i
$451$	−22.2971	−	14.3295i	−1.04993	−	0.674748i
$452$	13.0527	−	3.83263i	0.613949	−	0.180272i
$453$	2.31220	−	16.0817i	0.108637	−	0.755585i
$454$	−7.80632	+	9.00898i	−0.366369	+	0.422812i
$455$	15.9299	−	10.2375i	0.746807	−	0.479943i
$456$	4.58506	+	5.29144i	0.214715	+	0.247795i
$457$	27.6933	+	8.13149i	1.29544	+	0.380375i	0.855570	−	0.517687i	$-0.173207\pi$
$457$	27.6933	+	8.13149i	1.29544	+	0.380375i	0.439869	+	0.898062i	$0.355025\pi$
$458$	7.02050	−	15.3727i	0.328046	−	0.718321i
$459$	−0.863693			−0.0403138
$460$	−6.30047	−	3.60256i	−0.293761	−	0.167970i
$461$	−1.23414			−0.0574794			−0.0287397	−	0.999587i	$-0.509149\pi$
$461$	−1.23414			−0.0574794			−0.0287397	+	0.999587i	$0.509149\pi$
$462$	5.39636	−	11.8164i	0.251061	−	0.549748i
$463$	−0.523678	−	0.153766i	−0.0243374	−	0.00714610i	0.269541	−	0.962989i	$-0.413128\pi$
$463$	−0.523678	−	0.153766i	−0.0243374	−	0.00714610i	−0.293879	+	0.955843i	$0.594946\pi$
$464$	−2.03899	−	2.35312i	−0.0946577	−	0.109241i
$465$	−1.49497	+	0.960762i	−0.0693278	+	0.0445543i
$466$	−18.6586	+	21.5331i	−0.864341	+	0.997502i
$467$	−2.26688	+	15.7665i	−0.104899	+	0.729586i	0.867699	+	0.497090i	$0.165598\pi$
$467$	−2.26688	+	15.7665i	−0.104899	+	0.729586i	−0.972597	+	0.232496i	$0.925311\pi$
$468$	4.62769	−	1.35881i	0.213915	−	0.0628111i
$469$	35.2193	+	22.6341i	1.62628	+	1.04514i
$470$	2.73082	+	18.9933i	0.125964	+	0.876095i
$471$	8.45046	+	18.5039i	0.389377	+	0.852616i
$472$	1.65394	+	3.62163i	0.0761288	+	0.166699i
$473$	1.03985	+	7.23231i	0.0478123	+	0.332542i
$474$	8.69872	+	5.59033i	0.399546	+	0.256772i
$475$	−18.2044	+	5.34530i	−0.835276	+	0.245259i
$476$	−0.318888	+	2.21792i	−0.0146162	+	0.101658i
$477$	−2.77190	+	3.19895i	−0.126917	+	0.146470i
$478$	−18.5912	+	11.9478i	−0.850341	+	0.546481i
$479$	0.167294	+	0.193068i	0.00764388	+	0.00882150i	0.759559	−	0.650439i	$-0.225415\pi$
$479$	0.167294	+	0.193068i	0.00764388	+	0.00882150i	−0.751915	+	0.659260i	$0.770870\pi$
$480$	−1.45204	−	0.426356i	−0.0662761	−	0.0194604i
$481$	1.20640	−	2.64164i	0.0550069	−	0.120448i
$482$	−1.59815			−0.0727935
$483$	−7.65024	+	9.81218i	−0.348098	+	0.446470i
$484$	14.0715			0.639612
$485$	9.39964	−	20.5823i	0.426815	−	0.934596i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	−16.7486	−	19.3289i	−0.758952	−	0.875877i	0.236452	−	0.971643i	$-0.424015\pi$
$487$	−16.7486	−	19.3289i	−0.758952	−	0.875877i	−0.995404	+	0.0957661i	$0.969470\pi$
$488$	−6.10943	+	3.92629i	−0.276561	+	0.177735i
$489$	9.79193	−	11.3005i	0.442807	−	0.511026i
$490$	0.0580083	−	0.403457i	0.00262055	−	0.0182263i
$491$	7.22173	−	2.12049i	0.325912	−	0.0956964i	−0.114684	−	0.993402i	$-0.536585\pi$
$491$	7.22173	−	2.12049i	0.325912	−	0.0956964i	0.440596	+	0.897706i	$0.354767\pi$
$492$	4.45305	+	2.86180i	0.200759	+	0.129020i
$493$	0.382715	+	2.66184i	0.0172366	+	0.119883i
$494$	14.0282	+	30.7174i	0.631157	+	1.38204i
$495$	−3.14780	−	6.89273i	−0.141483	−	0.309805i
$496$	0.167117	+	1.16233i	0.00750379	+	0.0521900i
$497$	−12.8432	−	8.25385i	−0.576098	−	0.370236i
$498$	−2.53403	+	0.744058i	−0.113553	+	0.0333420i
$499$	5.71269	−	39.7326i	0.255735	−	1.77868i	−0.306671	−	0.951815i	$-0.599215\pi$
$499$	5.71269	−	39.7326i	0.255735	−	1.77868i	0.562406	−	0.826861i	$-0.309876\pi$
$500$	7.64062	−	8.81774i	0.341699	−	0.394341i
$501$	−10.1373	+	6.51486i	−0.452902	+	0.291062i
$502$	11.5181	+	13.2927i	0.514080	+	0.593280i
$503$	23.1700	+	6.80333i	1.03310	+	0.303346i	0.753971	−	0.656908i	$-0.228136\pi$
$503$	23.1700	+	6.80333i	1.03310	+	0.303346i	0.279129	+	0.960254i	$0.409954\pi$
$504$	−1.07773	+	2.35990i	−0.0480060	+	0.105119i
$505$	−0.802497			−0.0357107
$506$	−23.3600	−	5.56381i	−1.03848	−	0.247342i
$507$	10.2619			0.455747
$508$	2.79580	−	6.12195i	0.124044	−	0.271617i
$509$	−0.614059	−	0.180304i	−0.0272177	−	0.00799183i	0.268095	−	0.963392i	$-0.413606\pi$
$509$	−0.614059	−	0.180304i	−0.0272177	−	0.00799183i	−0.295313	+	0.955401i	$0.595424\pi$
$510$	0.855942	+	0.987809i	0.0379017	+	0.0437409i
$511$	−31.3875	+	20.1715i	−1.38850	+	0.892336i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	0.996429	−	6.93032i	0.0439934	−	0.305981i
$514$	19.8581	−	5.83086i	0.875902	−	0.257188i
$515$	1.17115	+	0.752650i	0.0516069	+	0.0331657i
$516$	−0.207673	−	1.44440i	−0.00914231	−	0.0635861i
$517$	26.3742	+	57.7515i	1.15994	+	2.53991i
$518$	0.648927	+	1.42095i	0.0285122	+	0.0624330i
$519$	−2.20607	−	15.3436i	−0.0968358	−	0.673508i
$520$	−6.14024	−	3.94609i	−0.269267	−	0.173048i
$521$	−21.8174	+	6.40617i	−0.955838	+	0.280659i	−0.722216	−	0.691668i	$-0.756876\pi$
$521$	−21.8174	+	6.40617i	−0.955838	+	0.280659i	−0.233622	+	0.972327i	$0.575058\pi$
$522$	−0.443115	+	3.08193i	−0.0193946	+	0.134892i
$523$	−0.550626	+	0.635456i	−0.0240772	+	0.0277866i	−0.767660	−	0.640857i	$-0.778579\pi$
$523$	−0.550626	+	0.635456i	−0.0240772	+	0.0277866i	0.743583	+	0.668643i	$0.233125\pi$
$524$	15.9812	−	10.2705i	0.698141	−	0.448668i
$525$	−4.60380	−	5.31307i	−0.200926	−	0.231881i
$526$	26.4097	+	7.75459i	1.15152	+	0.338116i
$527$	0.421321	−	0.922564i	0.0183530	−	0.0401875i
$528$	−5.00714			−0.217908
$529$	20.5306	+	10.3680i	0.892634	+	0.450782i
$530$	6.40567			0.278245
$531$	1.65394	−	3.62163i	0.0717750	−	0.157165i
$532$	−17.4288	−	5.11755i	−0.755633	−	0.221874i
$533$	16.7187	+	19.2944i	0.724167	+	0.835733i
$534$	−4.40610	+	2.83163i	−0.190670	+	0.122536i
$535$	−13.3354	+	15.3899i	−0.576539	+	0.665362i
$536$	2.29655	−	15.9728i	0.0991957	−	0.689921i
$537$	−6.92297	+	2.03277i	−0.298748	+	0.0877204i
$538$	−11.1682	−	7.17739i	−0.481497	−	0.309439i
$539$	−0.191931	−	1.33491i	−0.00826704	−	0.0574985i
$540$	0.628663	+	1.37658i	0.0270533	+	0.0592386i
$541$	9.49585	+	20.7930i	0.408259	+	0.893962i	0.996366	+	0.0851787i	$0.0271461\pi$
$541$	9.49585	+	20.7930i	0.408259	+	0.893962i	−0.588107	+	0.808783i	$0.700127\pi$
$542$	−3.42674	−	23.8335i	−0.147191	−	1.02374i
$543$	2.81028	+	1.80606i	0.120601	+	0.0775053i
$544$	0.828708	−	0.243331i	0.0355305	−	0.0104327i
$545$	1.07168	−	7.45367i	0.0459055	−	0.319280i
$546$	−8.19408	+	9.45647i	−0.350674	+	0.404700i
$547$	8.80067	−	5.65585i	0.376289	−	0.241827i	−0.338802	−	0.940858i	$-0.610022\pi$
$547$	8.80067	−	5.65585i	0.376289	−	0.241827i	0.715091	+	0.699031i	$0.246385\pi$
$548$	1.72021	+	1.98523i	0.0734839	+	0.0848050i
$549$	6.96812	+	2.04602i	0.297392	+	0.0873221i
$550$	5.63652	−	12.3423i	0.240342	−	0.526276i
$551$	−21.8003			−0.928723
$552$	4.66533	+	1.11118i	0.198570	+	0.0472948i
$553$	−26.8261			−1.14076
$554$	−7.61887	+	16.6830i	−0.323695	+	0.708793i
$555$	0.874304	+	0.256719i	0.0371121	+	0.0108971i
$556$	12.0670	+	13.9261i	0.511755	+	0.590597i
$557$	−22.1144	+	14.2120i	−0.937015	+	0.602183i	−0.917547	−	0.397627i	$-0.869834\pi$
$557$	−22.1144	+	14.2120i	−0.937015	+	0.602183i	−0.0194682	+	0.999810i	$0.506197\pi$
$558$	0.768989	−	0.887461i	0.0325539	−	0.0375692i
$559$	1.00162	−	6.96642i	0.0423640	−	0.294648i
$560$	3.76709	−	1.10612i	0.159189	−	0.0467420i
$561$	3.63811	+	2.33807i	0.153601	+	0.0987136i
$562$	0.00284250	+	0.0197700i	0.000119904	+	0.000833948i
$563$	−11.5774	−	25.3509i	−0.487928	−	1.06841i	−0.980207	−	0.197976i	$-0.936563\pi$
$563$	−11.5774	−	25.3509i	−0.487928	−	1.06841i	0.492279	−	0.870437i	$-0.336164\pi$
$564$	−5.26732	−	11.5338i	−0.221794	−	0.485662i
$565$	2.92985	+	20.3776i	0.123260	+	0.857291i
$566$	14.7671	+	9.49024i	0.620708	+	0.398905i
$567$	2.48926	−	0.730913i	0.104539	−	0.0306955i
$568$	−0.837470	+	5.82473i	−0.0351395	+	0.244400i
$569$	21.0907	−	24.3399i	0.884166	−	1.02038i	−0.115467	−	0.993311i	$-0.536837\pi$
$569$	21.0907	−	24.3399i	0.884166	−	1.02038i	0.999634	−	0.0270710i	$-0.00861801\pi$
$570$	−8.91372	+	5.72850i	−0.373354	+	0.239940i
$571$	−10.8030	−	12.4673i	−0.452091	−	0.521740i	0.483253	−	0.875481i	$-0.339455\pi$
$571$	−10.8030	−	12.4673i	−0.452091	−	0.521740i	−0.935344	+	0.353740i	$0.884910\pi$
$572$	−23.1715	−	6.80377i	−0.968849	−	0.284480i
$573$	−7.06718	+	15.4750i	−0.295236	+	0.646476i
$574$	−13.7328			−0.573197
$575$	−7.99071	+	10.2489i	−0.333236	+	0.427407i
$576$	1.00000			0.0416667
$577$	−2.73102	+	5.98010i	−0.113694	+	0.248955i	−0.957922	−	0.287030i	$-0.907332\pi$
$577$	−2.73102	+	5.98010i	−0.113694	+	0.248955i	0.844228	+	0.535984i	$0.180059\pi$
$578$	15.5956	+	4.57929i	0.648693	+	0.190473i
$579$	14.8926	+	17.1870i	0.618917	+	0.714268i
$580$	3.96395	−	2.54748i	0.164594	−	0.105778i
$581$	4.48691	−	5.17817i	0.186148	−	0.214827i
$582$	−2.12786	+	14.7996i	−0.0882027	+	0.613463i
$583$	20.3358	−	5.97112i	0.842222	−	0.247299i
$584$	12.0984	+	7.77517i	0.500636	+	0.321739i
$585$	1.03874	+	7.22462i	0.0429468	+	0.298701i
$586$	−1.20738	−	2.64380i	−0.0498765	−	0.109214i
$587$	−6.40693	−	14.0292i	−0.264442	−	0.579048i	0.730105	−	0.683335i	$-0.239471\pi$
$587$	−6.40693	−	14.0292i	−0.264442	−	0.579048i	−0.994547	+	0.104287i	$0.966744\pi$
$588$	0.0383314	+	0.266601i	0.00158076	+	0.0109944i
$589$	6.91663	+	4.44505i	0.284995	+	0.183155i
$590$	−5.78117	+	1.69750i	−0.238007	+	0.0698851i
$591$	−1.43442	+	9.97664i	−0.0590043	+	0.410384i
$592$	0.394306	−	0.455054i	0.0162059	−	0.0187026i
$593$	−12.0884	+	7.76876i	−0.496412	+	0.319025i	−0.764780	−	0.644292i	$-0.777152\pi$
$593$	−12.0884	+	7.76876i	−0.496412	+	0.319025i	0.268368	+	0.963317i	$0.413516\pi$
$594$	3.27898	+	3.78415i	0.134538	+	0.155265i
$595$	−3.25361	−	0.955347i	−0.133385	−	0.0391654i
$596$	−1.64339	+	3.59852i	−0.0673158	+	0.147401i
$597$	−9.43241			−0.386043
$598$	20.0798	+	11.4815i	0.821125	+	0.469513i
$599$	7.73316			0.315968			0.157984	−	0.987442i	$-0.449500\pi$
$599$	7.73316			0.315968			0.157984	+	0.987442i	$0.449500\pi$
$600$	−1.12570	+	2.46493i	−0.0459564	+	0.100630i
$601$	−30.7273	−	9.02234i	−1.25339	−	0.368029i	−0.413361	−	0.910567i	$-0.635645\pi$
$601$	−30.7273	−	9.02234i	−1.25339	−	0.368029i	−0.840031	+	0.542538i	$0.817463\pi$
$602$	2.47918	+	2.86113i	0.101044	+	0.116611i
$603$	−13.5754	+	8.72436i	−0.552832	+	0.355284i
$604$	10.6396	−	12.2787i	0.432918	−	0.499614i
$605$	−3.03058	+	21.0781i	−0.123210	+	0.856948i
$606$	0.508803	−	0.149398i	0.0206687	−	0.00606888i
$607$	−0.772604	−	0.496522i	−0.0313590	−	0.0201532i	0.524867	−	0.851184i	$-0.324115\pi$
$607$	−0.772604	−	0.496522i	−0.0313590	−	0.0201532i	−0.556226	+	0.831031i	$0.687751\pi$
$608$	0.996429	+	6.93032i	0.0404105	+	0.281061i
$609$	−3.35565	−	7.34785i	−0.135978	−	0.297750i
$610$	−4.56553	−	9.99712i	−0.184853	−	0.404772i
$611$	−8.70323	−	60.5323i	−0.352095	−	2.44887i
$612$	−0.726585	−	0.466948i	−0.0293705	−	0.0188752i
$613$	−18.9616	+	5.56762i	−0.765850	+	0.224874i	−0.641249	−	0.767333i	$-0.721583\pi$
$613$	−18.9616	+	5.56762i	−0.765850	+	0.224874i	−0.124601	+	0.992207i	$0.539765\pi$
$614$	1.80910	−	12.5826i	0.0730094	−	0.507792i
$615$	−5.24585	+	6.05403i	−0.211533	+	0.244122i
$616$	10.9281	−	7.02308i	0.440307	−	0.282968i
$617$	−4.51857	−	5.21471i	−0.181911	−	0.209936i	0.657469	−	0.753482i	$-0.271627\pi$
$617$	−4.51857	−	5.21471i	−0.181911	−	0.209936i	−0.839380	+	0.543545i	$0.817082\pi$
$618$	−0.882654	−	0.259171i	−0.0355055	−	0.0104254i
$619$	9.44337	−	20.6781i	0.379561	−	0.831123i	−0.619379	−	0.785092i	$-0.712616\pi$
$619$	9.44337	−	20.6781i	0.379561	−	0.831123i	0.998940	−	0.0460306i	$-0.0146572\pi$
$620$	−1.77708			−0.0713693
$621$	−2.21537	−	4.25348i	−0.0888997	−	0.170686i
$622$	−21.3006			−0.854077
$623$	5.64466	−	12.3601i	0.226149	−	0.495197i
$624$	4.62769	+	1.35881i	0.185256	+	0.0543960i
$625$	2.69008	+	3.10452i	0.107603	+	0.124181i
$626$	1.59110	−	1.02253i	0.0635929	−	0.0408687i
$627$	−22.9581	+	26.4950i	−0.916856	+	1.05811i
$628$	−2.89500	+	20.1352i	−0.115523	+	0.803481i
$629$	−0.498984	+	0.146515i	−0.0198958	+	0.00584193i
$630$	−3.30287	−	2.12262i	−0.131589	−	0.0845674i
$631$	−4.79472	−	33.3480i	−0.190875	−	1.32756i	−0.829700	−	0.558210i	$-0.811488\pi$
$631$	−4.79472	−	33.3480i	−0.190875	−	1.32756i	0.638825	−	0.769352i	$-0.279421\pi$
$632$	4.29547	+	9.40577i	0.170865	+	0.374141i
$633$	−1.40379	−	3.07388i	−0.0557958	−	0.122176i
$634$	3.10410	+	21.5895i	0.123279	+	0.857427i
$635$	8.56814	+	5.50641i	0.340016	+	0.218515i
$636$	−4.06135	+	1.19252i	−0.161043	+	0.0472865i
$637$	−0.184875	+	1.28583i	−0.00732499	+	0.0509465i
$638$	10.2095	−	11.7824i	0.404198	−	0.466470i
$639$	4.95046	−	3.18147i	0.195837	−	0.125857i
$640$	−0.991025	−	1.14370i	−0.0391737	−	0.0452089i
$641$	4.06760	+	1.19436i	0.160661	+	0.0471742i	0.361074	−	0.932537i	$-0.382410\pi$
$641$	4.06760	+	1.19436i	0.160661	+	0.0471742i	−0.200413	+	0.979711i	$0.564228\pi$
$642$	5.58989	−	12.2401i	0.220615	−	0.483080i
$643$	40.0914			1.58105			0.790525	−	0.612430i	$-0.209808\pi$
$643$	40.0914			1.58105			0.790525	+	0.612430i	$0.209808\pi$
$644$	−11.7407	+	4.11850i	−0.462647	+	0.162292i
$645$	2.20834			0.0869533
$646$	2.51211	−	5.50074i	0.0988375	−	0.216424i
$647$	5.46621	+	1.60502i	0.214899	+	0.0631000i	0.387410	−	0.921908i	$-0.373370\pi$
$647$	5.46621	+	1.60502i	0.214899	+	0.0631000i	−0.172511	+	0.985008i	$0.555188\pi$
$648$	−0.654861	−	0.755750i	−0.0257254	−	0.0296886i
$649$	−16.7708	+	10.7780i	−0.658313	+	0.423072i
$650$	−8.55875	+	9.87733i	−0.335702	+	0.387421i
$651$	−0.433561	+	3.01548i	−0.0169926	+	0.118186i
$652$	14.3470	−	4.21266i	0.561872	−	0.164981i
$653$	27.1715	+	17.4620i	1.06330	+	0.683343i	0.950642	−	0.310291i	$-0.100426\pi$
$653$	27.1715	+	17.4620i	1.06330	+	0.683343i	0.112660	+	0.993634i	$0.464063\pi$
$654$	0.708154	+	4.92532i	0.0276910	+	0.192595i
$655$	11.9426	+	26.1507i	0.466637	+	1.02179i
$656$	2.19894	+	4.81500i	0.0858541	+	0.187994i
$657$	−2.04669	−	14.2350i	−0.0798489	−	0.555361i
$658$	27.6735	+	17.7847i	1.07882	+	0.693318i
$659$	−8.86774	+	2.60380i	−0.345438	+	0.101430i	−0.449849	−	0.893104i	$-0.648522\pi$
$659$	−8.86774	+	2.60380i	−0.345438	+	0.101430i	0.104411	+	0.994534i	$0.466704\pi$
$660$	1.07839	−	7.50037i	0.0419763	−	0.291951i
$661$	21.2094	−	24.4770i	0.824952	−	0.952045i	−0.174516	−	0.984654i	$-0.555836\pi$
$661$	21.2094	−	24.4770i	0.824952	−	0.952045i	0.999468	+	0.0326090i	$0.0103816\pi$
$662$	14.6532	−	9.41704i	0.569513	−	0.366004i
$663$	−2.72792	−	3.14818i	−0.105943	−	0.122265i
$664$	−2.53403	−	0.744058i	−0.0983394	−	0.0288750i
$665$	11.4194	−	25.0050i	0.442825	−	0.969651i
$666$	−0.602123			−0.0233318
$667$	−12.1273	+	8.71240i	−0.469570	+	0.337345i
$668$	−12.0503			−0.466238
$669$	−7.19895	+	15.7635i	−0.278328	+	0.609452i
$670$	23.4316	+	6.88015i	0.905243	+	0.265803i
$671$	−23.8129	−	27.4816i	−0.919287	−	1.06091i
$672$	−2.18251	+	1.40261i	−0.0841920	+	0.0541069i
$673$	−25.3577	+	29.2644i	−0.977468	+	1.12806i	0.0142851	+	0.999898i	$0.495453\pi$
$673$	−25.3577	+	29.2644i	−0.977468	+	1.12806i	−0.991753	+	0.128161i	$0.959093\pi$
$674$	2.55426	−	17.7653i	0.0983866	−	0.684294i
$675$	2.60004	−	0.763442i	0.100076	−	0.0293849i
$676$	8.63285	+	5.54800i	0.332033	+	0.213385i
$677$	−4.16456	−	28.9652i	−0.160057	−	1.11322i	−0.898522	−	0.438929i	$-0.855358\pi$
$677$	−4.16456	−	28.9652i	−0.160057	−	1.11322i	0.738465	−	0.674292i	$-0.235551\pi$
$678$	−5.65122	−	12.3744i	−0.217034	−	0.475238i
$679$	−16.1140	−	35.2848i	−0.618400	−	1.35411i
$680$	0.186014	+	1.29376i	0.00713331	+	0.0496132i
$681$	10.0282	+	6.44475i	0.384283	+	0.246964i
$682$	−5.64161	+	1.65653i	−0.216028	+	0.0634317i
$683$	4.68194	−	32.5636i	0.179150	−	1.24601i	−0.679587	−	0.733595i	$-0.737841\pi$
$683$	4.68194	−	32.5636i	0.179150	−	1.24601i	0.858736	−	0.512418i	$-0.171250\pi$
$684$	4.58506	−	5.29144i	0.175314	−	0.202323i
$685$	−3.34423	+	2.14921i	−0.127776	+	0.0821170i
$686$	−12.3502	−	14.2529i	−0.471532	−	0.544176i
$687$	−16.2154	−	4.76127i	−0.618656	−	0.181654i
$688$	0.606195	−	1.32738i	0.0231110	−	0.0506060i
$689$	−20.4151			−0.777754
$690$	−2.66924	+	6.74904i	−0.101616	+	0.256931i
$691$	−12.3215			−0.468730			−0.234365	−	0.972149i	$-0.575301\pi$
$691$	−12.3215			−0.468730			−0.234365	+	0.972149i	$0.575301\pi$
$692$	6.43950	−	14.1005i	0.244793	−	0.536022i
$693$	−12.4641	−	3.65979i	−0.473471	−	0.139024i
$694$	3.15982	+	3.64663i	0.119945	+	0.138424i
$695$	−23.4592	+	15.0763i	−0.889858	+	0.571877i
$696$	−2.03899	+	2.35312i	−0.0772877	+	0.0891947i
$697$	0.650640	−	4.52530i	0.0246447	−	0.171408i
$698$	−9.93639	+	2.91759i	−0.376098	+	0.110432i
$699$	23.9693	+	15.4042i	0.906603	+	0.582639i
$700$	−1.00050	−	6.95864i	−0.0378154	−	0.263012i
$701$	−11.3429	−	24.8375i	−0.428415	−	0.938098i	−0.993581	−	0.113121i	$-0.963915\pi$
$701$	−11.3429	−	24.8375i	−0.428415	−	0.938098i	0.565166	−	0.824977i	$-0.308812\pi$
$702$	−2.00357	−	4.38721i	−0.0756199	−	0.165585i
$703$	−0.599972	−	4.17290i	−0.0226284	−	0.157384i
$704$	−4.21228	−	2.70707i	−0.158756	−	0.102026i
$705$	18.4113	−	5.40606i	0.693411	−	0.203604i
$706$	4.18001	−	29.0726i	0.157317	−	1.09416i
$707$	−0.900919	+	1.03972i	−0.0338825	+	0.0391025i
$708$	3.34938	−	2.15252i	0.125878	−	0.0808966i
$709$	−7.28814	−	8.41096i	−0.273712	−	0.315880i	0.602206	−	0.798341i	$-0.294289\pi$
$709$	−7.28814	−	8.41096i	−0.273712	−	0.315880i	−0.875918	+	0.482461i	$0.839743\pi$
$710$	−8.54469	−	2.50895i	−0.320677	−	0.0941592i
$711$	4.29547	−	9.40577i	0.161093	−	0.352744i
$712$	−5.23754			−0.196285
$713$	5.62410	−	0.291468i	0.210624	−	0.0109156i
$714$	2.24072			0.0838570
$715$	15.1820	−	33.2440i	0.567776	−	1.24326i
$716$	−6.92297	−	2.03277i	−0.258724	−	0.0759681i
$717$	14.4720	+	16.7016i	0.540467	+	0.623732i
$718$	−8.41063	+	5.40518i	−0.313882	+	0.201720i
$719$	−16.8352	+	19.4289i	−0.627848	+	0.724575i	−0.977177	−	0.212425i	$-0.931864\pi$
$719$	−16.8352	+	19.4289i	−0.627848	+	0.724575i	0.349330	+	0.937000i	$0.386409\pi$
$720$	−0.215370	+	1.49793i	−0.00802638	+	0.0558247i
$721$	2.28991	−	0.672380i	0.0852809	−	0.0250407i
$722$	25.2562	+	16.2312i	0.939940	+	0.604063i
$723$	0.227440	+	1.58188i	0.00845858	+	0.0588307i
$724$	1.38773	+	3.03870i	0.0515745	+	0.112933i
$725$	−3.50499	−	7.67486i	−0.130172	−	0.285037i
$726$	−2.00258	−	13.9282i	−0.0743227	−	0.516926i
$727$	0.0404181	+	0.0259751i	0.00149903	+	0.000963365i	0.541390	−	0.840772i	$-0.317898\pi$
$727$	0.0404181	+	0.0259751i	0.00149903	+	0.000963365i	−0.539891	+	0.841735i	$0.681535\pi$
$728$	−12.0059	+	3.52524i	−0.444967	+	0.130654i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−14.2523	+	16.4481i	−0.527502	+	0.608770i
$731$	−1.06027	+	0.681395i	−0.0392155	+	0.0252023i
$732$	4.75579	+	5.48847i	0.175779	+	0.202860i
$733$	−29.3610	−	8.62117i	−1.08447	−	0.318430i	−0.309806	−	0.950800i	$-0.600264\pi$
$733$	−29.3610	−	8.62117i	−1.08447	−	0.318430i	−0.774667	+	0.632370i	$0.782082\pi$
$734$	6.93948	−	15.1953i	0.256141	−	0.560870i
$735$	−0.407605			−0.0150348
$736$	3.32398	+	3.45705i	0.122523	+	0.127428i
$737$	80.8007			2.97633
$738$	2.19894	−	4.81500i	0.0809441	−	0.177243i
$739$	11.5414	+	3.38886i	0.424557	+	0.124661i	0.487030	−	0.873385i	$-0.338080\pi$
$739$	11.5414	+	3.38886i	0.424557	+	0.124661i	−0.0624723	+	0.998047i	$0.519899\pi$
$740$	0.596719	+	0.688650i	0.0219358	+	0.0253153i
$741$	28.4083	−	18.2569i	1.04361	−	0.670685i
$742$	7.19129	−	8.29919i	0.264001	−	0.304673i
$743$	1.44897	−	10.0778i	0.0531576	−	0.369719i	−0.945827	−	0.324670i	$-0.894747\pi$
$743$	1.44897	−	10.0778i	0.0531576	−	0.369719i	0.998985	−	0.0450487i	$-0.0143443\pi$
$744$	1.12671	−	0.330833i	0.0413073	−	0.0121289i
$745$	−5.03641	−	3.23670i	−0.184520	−	0.118584i
$746$	−4.72820	−	32.8854i	−0.173112	−	1.20402i
$747$	1.09711	+	2.40235i	0.0401413	+	0.0878972i
$748$	1.79652	+	3.93383i	0.0656872	+	0.143835i
$749$	4.96821	+	34.5547i	0.181534	+	1.26260i
$750$	−9.81536	−	6.30795i	−0.358406	−	0.230334i
$751$	8.70241	−	2.55526i	0.317555	−	0.0932427i	−0.119071	−	0.992886i	$-0.537992\pi$
$751$	8.70241	−	2.55526i	0.317555	−	0.0932427i	0.436626	+	0.899643i	$0.356173\pi$
$752$	1.80450	−	12.5506i	0.0658035	−	0.457673i
$753$	11.5181	−	13.2927i	0.419745	−	0.484411i
$754$	−12.6333	+	8.11890i	−0.460076	+	0.295673i
$755$	16.1013	+	18.5819i	0.585985	+	0.676263i
$756$	2.48926	+	0.730913i	0.0905336	+	0.0265831i
$757$	7.27301	−	15.9257i	0.264342	−	0.578829i	−0.730192	−	0.683242i	$-0.760569\pi$
$757$	7.27301	−	15.9257i	0.264342	−	0.578829i	0.994534	+	0.104414i	$0.0332966\pi$
$758$	8.45299			0.307026
$759$	−2.18271	+	23.9140i	−0.0792274	+	0.868023i
$760$	−10.5958			−0.384348
$761$	−10.3746	+	22.7172i	−0.376080	+	0.823499i	0.623066	+	0.782169i	$0.285887\pi$
$761$	−10.3746	+	22.7172i	−0.376080	+	0.823499i	−0.999146	+	0.0413301i	$0.986840\pi$
$762$	−6.45752	−	1.89610i	−0.233931	−	0.0686884i
$763$	−8.45386	−	9.75628i	−0.306050	−	0.353201i
$764$	−14.3117	+	9.19757i	−0.517779	+	0.332756i
$765$	0.855942	−	0.987809i	0.0309466	−	0.0357143i
$766$	0.626651	−	4.35846i	0.0226418	−	0.157477i
$767$	18.4248	−	5.41000i	0.665280	−	0.195344i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	1.21150	+	8.42615i	0.0436877	+	0.303855i	0.999936	+	0.0112988i	$0.00359661\pi$
$769$	1.21150	+	8.42615i	0.0436877	+	0.303855i	−0.956248	+	0.292556i	$0.905494\pi$
$770$	8.16651	+	17.8822i	0.294301	+	0.644428i
$771$	−8.59760	−	18.8261i	−0.309635	−	0.678006i
$772$	3.23648	+	22.5102i	0.116483	+	0.810160i
$773$	41.2916	+	26.5365i	1.48515	+	0.954451i	0.996641	+	0.0818945i	$0.0260971\pi$
$773$	41.2916	+	26.5365i	1.48515	+	0.954451i	0.488513	+	0.872556i	$0.337539\pi$
$774$	−1.40014	+	0.411119i	−0.0503271	+	0.0147774i
$775$	−0.452856	+	3.14969i	−0.0162671	+	0.113140i
$776$	−9.79134	+	11.2998i	−0.351489	+	0.405639i
$777$	1.31414	−	0.844544i	0.0471444	−	0.0302979i
$778$	−13.2859	−	15.3328i	−0.476323	−	0.549706i
$779$	35.5606	+	10.4415i	1.27409	+	0.374107i
$780$	−3.03208	+	6.63933i	−0.108566	+	0.237726i
$781$	−29.4652			−1.05435
$782$	−0.800892	−	4.06396i	−0.0286398	−	0.145327i
$783$	3.11362			0.111272
$784$	−0.111889	+	0.245002i	−0.00399603	+	0.00875008i
$785$	−29.5376	−	8.67304i	−1.05424	−	0.309554i
$786$	−12.4403	−	14.3569i	−0.443731	−	0.512093i
$787$	3.64692	−	2.34373i	0.129999	−	0.0835451i	−0.474025	−	0.880511i	$-0.657199\pi$
$787$	3.64692	−	2.34373i	0.129999	−	0.0835451i	0.604024	+	0.796966i	$0.293563\pi$
$788$	−6.60049	+	7.61738i	−0.235133	+	0.271358i
$789$	3.91717	−	27.2445i	0.139455	−	0.969930i
$790$	−15.0143	+	4.40861i	−0.534186	+	0.156851i
$791$	29.6904	+	19.0808i	1.05567	+	0.678437i
$792$	0.712591	+	4.95618i	0.0253208	+	0.176110i
$793$	14.5505	+	31.8612i	0.516704	+	1.13142i
$794$	−5.96409	−	13.0595i	−0.211658	−	0.463466i
$795$	−0.911622	−	6.34047i	−0.0323319	−	0.224873i
$796$	−7.93505	−	5.09955i	−0.281250	−	0.180749i
$797$	4.30154	−	1.26305i	0.152369	−	0.0447394i	−0.204659	−	0.978833i	$-0.565608\pi$
$797$	4.30154	−	1.26305i	0.152369	−	0.0447394i	0.357027	+	0.934094i	$0.383790\pi$
$798$	−2.58509	+	17.9797i	−0.0915111	+	0.636474i
$799$	−7.17160	+	8.27647i	−0.253713	+	0.292801i
$800$	−2.27964	+	1.46503i	−0.0805974	+	0.0517968i
$801$	3.42986	+	3.95827i	0.121188	+	0.139858i
$802$	11.0648	+	3.24893i	0.390713	+	0.114724i
$803$	−29.9139	+	65.5024i	−1.05564	+	2.31153i
$804$	−16.1371			−0.569111
$805$	−3.64065	−	18.4737i	−0.128316	−	0.651113i
$806$	5.66362			0.199492
$807$	−5.51493	+	12.0760i	−0.194135	+	0.425096i
$808$	0.508803	+	0.149398i	0.0178996	+	0.00525580i
$809$	−18.4045	−	21.2399i	−0.647068	−	0.746756i	0.333540	−	0.942736i	$-0.391757\pi$
$809$	−18.4045	−	21.2399i	−0.647068	−	0.746756i	−0.980608	+	0.195980i	$0.937211\pi$
$810$	1.27310	−	0.818172i	0.0447322	−	0.0287476i
$811$	−28.6382	+	33.0503i	−1.00562	+	1.16055i	−0.0186242	+	0.999827i	$0.505929\pi$
$811$	−28.6382	+	33.0503i	−1.00562	+	1.16055i	−0.986999	+	0.160725i	$0.948617\pi$
$812$	1.14959	−	7.99561i	0.0403429	−	0.280591i
$813$	−23.1032	+	6.78372i	−0.810266	+	0.237915i
$814$	2.53631	+	1.62999i	0.0888975	+	0.0571310i
$815$	3.22037	+	22.3981i	0.112805	+	0.784573i
$816$	−0.358791	−	0.785643i	−0.0125602	−	0.0275030i
$817$	−4.24433	−	9.29378i	−0.148490	−	0.325148i
$818$	3.36864	+	23.4294i	0.117782	+	0.819191i
$819$	10.5264	+	6.76488i	0.367821	+	0.236384i
$820$	−7.68614	+	2.25685i	−0.268412	+	0.0788128i
$821$	0.929349	−	6.46377i	0.0324345	−	0.225587i	−0.967157	−	0.254181i	$-0.918194\pi$
$821$	0.929349	−	6.46377i	0.0324345	−	0.225587i	0.999591	+	0.0285943i	$0.00910310\pi$
$822$	1.72021	−	1.98523i	0.0599994	−	0.0692430i
$823$	−0.768728	+	0.494031i	−0.0267962	+	0.0172208i	−0.553970	−	0.832536i	$-0.686888\pi$
$823$	−0.768728	+	0.494031i	−0.0267962	+	0.0172208i	0.527174	+	0.849757i	$0.323252\pi$
$824$	−0.602418	−	0.695227i	−0.0209862	−	0.0242194i
$825$	−13.0188	−	3.82266i	−0.453256	−	0.133088i
$826$	−4.29091	+	9.39577i	−0.149300	+	0.326921i
$827$	−19.0247			−0.661554			−0.330777	−	0.943709i	$-0.607311\pi$
$827$	−19.0247			−0.661554			−0.330777	+	0.943709i	$0.607311\pi$
$828$	0.435919	−	4.77598i	0.0151492	−	0.165977i
$829$	14.2601			0.495272			0.247636	−	0.968853i	$-0.420346\pi$
$829$	14.2601			0.495272			0.247636	+	0.968853i	$0.420346\pi$
$830$	1.66030	−	3.63556i	0.0576300	−	0.126192i
$831$	17.5975	+	5.16708i	0.610449	+	0.179244i
$832$	3.15843	+	3.64502i	0.109499	+	0.126368i
$833$	0.195700	−	0.125769i	0.00678060	−	0.00435763i
$834$	12.0670	−	13.9261i	0.417846	−	0.482220i
$835$	2.59527	−	18.0505i	0.0898129	−	0.624663i
$836$	−33.6378	+	9.87696i	−1.16339	+	0.341602i
$837$	−0.987866	−	0.634863i	−0.0341457	−	0.0219441i
$838$	0.317409	+	2.20763i	0.0109647	+	0.0762614i
$839$	23.0443	+	50.4601i	0.795579	+	1.74208i	0.659942	+	0.751316i	$0.270581\pi$
$839$	23.0443	+	50.4601i	0.795579	+	1.74208i	0.135637	+	0.990759i	$0.456692\pi$
$840$	−1.63097	−	3.57133i	−0.0562739	−	0.123223i
$841$	2.74744	+	19.1089i	0.0947393	+	0.658926i
$842$	−15.1696	−	9.74893i	−0.522780	−	0.335970i
$843$	0.0191643	−	0.00562713i	0.000660052	−	0.000193809i
$844$	0.480919	−	3.34486i	0.0165539	−	0.115135i
$845$	−10.1698	+	11.7366i	−0.349852	+	0.403750i
$846$	−10.6668	+	6.85514i	−0.366733	+	0.235685i
$847$	23.9066	+	27.5896i	0.821439	+	0.947991i
$848$	−4.06135	−	1.19252i	−0.139467	−	0.0409513i
$849$	7.29206	−	15.9674i	0.250263	−	0.548000i
$850$	2.34045			0.0802766
$851$	−2.00144	−	2.08157i	−0.0686085	−	0.0713552i
$852$	5.88463			0.201604
$853$	−3.08258	+	6.74992i	−0.105546	+	0.231113i	−0.955035	−	0.296493i	$-0.904183\pi$
$853$	−3.08258	+	6.74992i	−0.105546	+	0.231113i	0.849489	+	0.527606i	$0.176910\pi$
$854$	−18.0777	−	5.30810i	−0.618607	−	0.181640i
$855$	6.93874	+	8.00774i	0.237300	+	0.273859i
$856$	11.3200	−	7.27495i	0.386911	−	0.248653i
$857$	16.9617	−	19.5749i	0.579402	−	0.668666i	−0.388074	−	0.921628i	$-0.626859\pi$
$857$	16.9617	−	19.5749i	0.579402	−	0.668666i	0.967476	+	0.252962i	$0.0814049\pi$
$858$	−3.43687	+	23.9039i	−0.117333	+	0.816067i
$859$	39.5100	−	11.6012i	1.34807	−	0.395828i	0.473525	−	0.880780i	$-0.342981\pi$
$859$	39.5100	−	11.6012i	1.34807	−	0.395828i	0.874540	+	0.484953i	$0.161163\pi$
$860$	1.85777	+	1.19392i	0.0633496	+	0.0407123i
$861$	1.95438	+	13.5930i	0.0666052	+	0.463250i
$862$	9.29184	+	20.3463i	0.316481	+	0.692997i
$863$	20.8680	+	45.6946i	0.710356	+	1.55546i	0.826945	+	0.562282i	$0.190076\pi$
$863$	20.8680	+	45.6946i	0.710356	+	1.55546i	−0.116590	+	0.993180i	$0.537196\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	19.7348	+	12.6828i	0.671003	+	0.431227i
$866$	−16.7957	+	4.93167i	−0.570742	+	0.167585i
$867$	2.31319	−	16.0886i	0.0785601	−	0.546397i
$868$	−1.99503	+	2.30239i	−0.0677157	+	0.0781480i
$869$	−43.5557	+	27.9916i	−1.47753	+	0.949549i
$870$	−3.08568	−	3.56106i	−0.104614	−	0.120731i
$871$	−74.6774	−	21.9273i	−2.53035	−	0.742977i
$872$	−2.06709	+	4.52630i	−0.0700006	+	0.153280i
$873$	14.9518			0.506041
$874$	33.5334	−	1.73786i	1.13428	−	0.0587841i
$875$	30.2697			1.02330
$876$	5.97425	−	13.0818i	0.201851	−	0.441993i
$877$	−17.7533	−	5.21283i	−0.599485	−	0.176025i	−0.0321104	−	0.999484i	$-0.510223\pi$
$877$	−17.7533	−	5.21283i	−0.599485	−	0.176025i	−0.567375	+	0.823460i	$0.692041\pi$
$878$	9.89763	+	11.4225i	0.334029	+	0.385490i
$879$	−2.44506	+	1.57135i	−0.0824699	+	0.0530002i
$880$	4.96220	−	5.72669i	0.167276	−	0.193047i
$881$	−1.94626	+	13.5365i	−0.0655710	+	0.456056i	0.930412	+	0.366515i	$0.119449\pi$
$881$	−1.94626	+	13.5365i	−0.0655710	+	0.456056i	−0.995983	+	0.0895413i	$0.971460\pi$
$882$	0.258432	−	0.0758824i	0.00870185	−	0.00255509i
$883$	−1.03867	−	0.667510i	−0.0349539	−	0.0224635i	0.523047	−	0.852304i	$-0.324795\pi$
$883$	−1.03867	−	0.667510i	−0.0349539	−	0.0224635i	−0.558001	+	0.829840i	$0.688432\pi$
$884$	−0.592833	−	4.12324i	−0.0199391	−	0.138680i
$885$	2.50297	+	5.48074i	0.0841365	+	0.184233i
$886$	−4.91203	−	10.7558i	−0.165023	−	0.361349i
$887$	1.85055	+	12.8709i	0.0621355	+	0.432162i	0.997016	+	0.0771985i	$0.0245975\pi$
$887$	1.85055	+	12.8709i	0.0621355	+	0.432162i	−0.934880	+	0.354963i	$0.884493\pi$
$888$	−0.506538	−	0.325532i	−0.0169983	−	0.0109241i
$889$	16.7531	−	4.91914i	0.561880	−	0.164983i
$890$	1.12801	−	7.84548i	0.0378110	−	0.262981i
$891$	3.27898	−	3.78415i	0.109850	−	0.126774i
$892$	−14.5785	+	9.36906i	−0.488126	+	0.313699i
$893$	−58.1370	−	67.0937i	−1.94548	−	2.24521i
$894$	3.79577	+	1.11454i	0.126950	+	0.0372758i
$895$	4.53595	−	9.93235i	0.151620	−	0.332002i
$896$	−2.59435			−0.0866712
$897$	8.50696	−	21.5094i	0.284039	−	0.718179i
$898$	−4.68716			−0.156412
$899$	−1.51887	+	3.32585i	−0.0506570	+	0.110923i
$900$	2.60004	+	0.763442i	0.0866681	+	0.0254481i
$901$	2.39407	+	2.76291i	0.0797582	+	0.0920458i
$902$	−22.2971	+	14.3295i	−0.742411	+	0.477119i
$903$	2.47918	−	2.86113i	0.0825020	−	0.0952123i
$904$	1.93602	−	13.4653i	0.0643911	−	0.447850i
$905$	−4.85065	+	1.42428i	−0.161241	+	0.0473447i
$906$	−13.6679	−	8.78384i	−0.454086	−	0.291823i
$907$	1.11653	+	7.76562i	0.0370737	+	0.257853i	0.999926	−	0.0121759i	$-0.00387581\pi$
$907$	1.11653	+	7.76562i	0.0370737	+	0.257853i	−0.962852	+	0.270029i	$0.912967\pi$
$908$	4.95199	+	10.8433i	0.164338	+	0.359849i
$909$	−0.220288	−	0.482363i	−0.00730648	−	0.0159990i
$910$	−2.69487	−	18.7432i	−0.0893339	−	0.621331i
$911$	−36.4641	−	23.4341i	−1.20811	−	0.776406i	−0.227769	−	0.973715i	$-0.573143\pi$
$911$	−36.4641	−	23.4341i	−1.20811	−	0.776406i	−0.980341	+	0.197309i	$0.936780\pi$
$912$	6.71797	−	1.97257i	0.222454	−	0.0653184i
$913$	1.88196	−	13.0893i	0.0622837	−	0.433193i
$914$	18.9009	−	21.8128i	0.625186	−	0.721503i
$915$	−9.24562	+	5.94180i	−0.305651	+	0.196430i
$916$	−11.0671	−	12.7721i	−0.365668	−	0.422003i
$917$	47.2882	+	13.8851i	1.56159	+	0.458525i
$918$	−0.358791	+	0.785643i	−0.0118419	+	0.0259301i
$919$	−39.3327			−1.29747			−0.648733	−	0.761016i	$-0.724701\pi$
$919$	−39.3327			−1.29747			−0.648733	+	0.761016i	$0.724701\pi$
$920$	−5.89431	+	4.23455i	−0.194330	+	0.139609i
$921$	−12.7120			−0.418874
$922$	−0.512678	+	1.12261i	−0.0168842	+	0.0369712i
$923$	27.2322	+	7.99611i	0.896360	+	0.263195i
$924$	−8.50683	−	9.81740i	−0.279854	−	0.322969i
$925$	1.37262	−	0.882130i	0.0451315	−	0.0290043i
$926$	−0.357414	+	0.412478i	−0.0117454	+	0.0135549i
$927$	−0.130918	+	0.910554i	−0.00429991	+	0.0299065i
$928$	−2.98750	+	0.877209i	−0.0980694	+	0.0287958i
$929$	24.8982	+	16.0011i	0.816885	+	0.524980i	0.881085	−	0.472957i	$-0.156813\pi$
$929$	24.8982	+	16.0011i	0.816885	+	0.524980i	−0.0642007	+	0.997937i	$0.520450\pi$
$930$	0.252905	+	1.75899i	0.00829308	+	0.0576796i
$931$	0.783398	+	1.71540i	0.0256748	+	0.0562201i
$932$	11.8362	+	25.9176i	0.387707	+	0.848959i
$933$	3.03139	+	21.0838i	0.0992434	+	0.690253i
$934$	13.4000	+	8.61166i	0.438462	+	0.281782i
$935$	−6.27953	+	1.84384i	−0.205362	+	0.0602999i
$936$	0.686393	−	4.77397i	0.0224355	−	0.156042i
$937$	16.4869	−	19.0269i	0.538604	−	0.621582i	−0.419586	−	0.907716i	$-0.637825\pi$
$937$	16.4869	−	19.0269i	0.538604	−	0.621582i	0.958190	+	0.286134i	$0.0923702\pi$
$938$	35.2193	−	22.6341i	1.14995	−	0.739028i
$939$	−1.23856	−	1.42938i	−0.0404190	−	0.0466460i
$940$	18.4113	+	5.40606i	0.600512	+	0.176326i
$941$	7.01577	−	15.3624i	0.228707	−	0.500800i	−0.760135	−	0.649765i	$-0.774867\pi$
$941$	7.01577	−	15.3624i	0.228707	−	0.500800i	0.988842	+	0.148966i	$0.0475944\pi$
$942$	20.3422			0.662785
$943$	23.9549	−	8.40313i	0.780079	−	0.273644i
$944$	3.98142			0.129584
$945$	−1.63097	+	3.57133i	−0.0530555	+	0.116175i
$946$	7.01071	+	2.05853i	0.227938	+	0.0669286i
$947$	10.1205	+	11.6796i	0.328871	+	0.379537i	0.895972	−	0.444111i	$-0.146480\pi$
$947$	10.1205	+	11.6796i	0.328871	+	0.379537i	−0.567101	+	0.823648i	$0.691935\pi$
$948$	8.69872	−	5.59033i	0.282521	−	0.181565i
$949$	45.4227	−	52.4206i	1.47448	−	1.70164i
$950$	−2.70013	+	18.7798i	−0.0876039	+	0.609299i
$951$	20.9280	−	6.14500i	0.678635	−	0.199265i
$952$	1.88502	+	1.21143i	0.0610937	+	0.0392626i
$953$	−0.147874	−	1.02848i	−0.00479010	−	0.0333159i	0.987286	−	0.158953i	$-0.0508117\pi$
$953$	−0.147874	−	1.02848i	−0.00479010	−	0.0333159i	−0.992076	+	0.125637i	$0.959903\pi$
$954$	1.75837	+	3.85030i	0.0569295	+	0.124658i
$955$	−10.6950	−	23.4188i	−0.346083	−	0.757816i
$956$	3.14507	+	21.8744i	0.101719	+	0.707470i
$957$	−13.1154	−	8.42878i	−0.423962	−	0.272464i
$958$	0.245117	−	0.0719730i	0.00791939	−	0.00232534i
$959$	−0.969868	+	6.74558i	−0.0313187	+	0.217826i
$960$	−0.991025	+	1.14370i	−0.0319852	+	0.0369129i
$961$	−24.9188	+	16.0144i	−0.803833	+	0.516592i
$962$	−1.90176	−	2.19475i	−0.0613153	−	0.0707616i
$963$	−12.9111	−	3.79104i	−0.416054	−	0.122164i
$964$	−0.663894	+	1.45372i	−0.0213826	+	0.0468213i
$965$	−34.4158			−1.10789
$966$	5.74745	+	11.0350i	0.184921	+	0.355046i
$967$	23.1795			0.745404			0.372702	−	0.927951i	$-0.378431\pi$
$967$	23.1795			0.745404			0.372702	+	0.927951i	$0.378431\pi$
$968$	5.84550	−	12.7999i	0.187881	−	0.411403i
$969$	−5.80226	−	1.70370i	−0.186396	−	0.0547307i
$970$	−14.8176	−	17.1004i	−0.475764	−	0.549061i
$971$	5.20032	−	3.34204i	0.166886	−	0.107251i	−0.454532	−	0.890731i	$-0.650193\pi$
$971$	5.20032	−	3.34204i	0.166886	−	0.107251i	0.621418	+	0.783479i	$0.286557\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−6.80345	+	47.3190i	−0.218109	+	1.51698i
$974$	−24.5398	+	7.20554i	−0.786307	+	0.230881i
$975$	10.9948	+	7.06595i	0.352116	+	0.226291i
$976$	1.03353	+	7.18837i	0.0330825	+	0.230094i
$977$	−12.6508	−	27.7014i	−0.404735	−	0.886247i	−0.996768	−	0.0803331i	$-0.974402\pi$
$977$	−12.6508	−	27.7014i	−0.404735	−	0.886247i	0.592033	−	0.805914i	$-0.298326\pi$
$978$	−6.21157	−	13.6015i	−0.198624	−	0.434926i
$979$	−3.73222	−	25.9582i	−0.119282	−	0.829626i
$980$	−0.342900	−	0.220368i	−0.0109535	−	0.00703940i
$981$	4.77441	−	1.40189i	0.152435	−	0.0447590i
$982$	1.07115	−	7.45000i	0.0341817	−	0.237739i
$983$	−0.963632	+	1.11209i	−0.0307351	+	0.0354702i	−0.770909	−	0.636945i	$-0.780198\pi$
$983$	−0.963632	+	1.11209i	−0.0307351	+	0.0354702i	0.740174	+	0.672415i	$0.234743\pi$
$984$	4.45305	−	2.86180i	0.141958	−	0.0912310i
$985$	−9.98877	−	11.5277i	−0.318269	−	0.367302i
$986$	2.58028	+	0.757639i	0.0821729	+	0.0241281i
$987$	13.6653	−	29.9228i	0.434971	−	0.952453i
$988$	33.7690			1.07434
$989$	−6.07530	−	3.47381i	−0.193183	−	0.110461i
$990$	−7.57749			−0.240829
$991$	−13.1105	+	28.7080i	−0.416470	+	0.911941i	0.578862	+	0.815426i	$0.303497\pi$
$991$	−13.1105	+	28.7080i	−0.416470	+	0.911941i	−0.995331	+	0.0965155i	$0.969230\pi$
$992$	1.12671	+	0.330833i	0.0357732	+	0.0105039i
$993$	−11.4066	−	13.1639i	−0.361976	−	0.417743i
$994$	−12.8432	+	8.25385i	−0.407363	+	0.261796i
$995$	9.34776	−	10.7879i	0.296344	−	0.341999i
$996$	−0.375855	+	2.61413i	−0.0119094	+	0.0828318i
$997$	−14.7556	+	4.33262i	−0.467313	+	0.137216i	−0.506908	−	0.862000i	$-0.669212\pi$
$997$	−14.7556	+	4.33262i	−0.467313	+	0.137216i	0.0395945	+	0.999216i	$0.487393\pi$
$998$	−33.7689	−	21.7020i	−1.06894	−	0.686964i
$999$	0.0856910	+	0.595994i	0.00271114	+	0.0188564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.a.121.1	yes	10
3.2	odd	2		414.2.i.d.397.1		10
23.2	even	11		3174.2.a.bc.1.5		5
23.4	even	11	inner	138.2.e.a.73.1	✓	10
23.21	odd	22		3174.2.a.bd.1.1		5
69.2	odd	22		9522.2.a.bt.1.1		5
69.44	even	22		9522.2.a.bq.1.5		5
69.50	odd	22		414.2.i.d.73.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.a.73.1	✓	10	23.4	even	11	inner
138.2.e.a.121.1	yes	10	1.1	even	1	trivial
414.2.i.d.73.1		10	69.50	odd	22
414.2.i.d.397.1		10	3.2	odd	2
3174.2.a.bc.1.5		5	23.2	even	11
3174.2.a.bd.1.1		5	23.21	odd	22
9522.2.a.bq.1.5		5	69.44	even	22
9522.2.a.bt.1.1		5	69.2	odd	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.27310 - 0.818172i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.369215 - 2.56794i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(1.27310 - 0.818172i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.369215 - 2.56794i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.215370 - 1.49793i) q^{10} +(-2.08004 - 4.55466i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.686393 + 4.77397i) q^{13} +(-2.18251 - 1.40261i) q^{14} +(-1.45204 + 0.426356i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.565599 - 0.652736i) q^{17} +(0.841254 - 0.540641i) q^{18} +(4.58506 + 5.29144i) q^{19} +(-1.45204 - 0.426356i) q^{20} +(-1.07773 + 2.35990i) q^{21} -5.00714 q^{22} +(4.66533 + 1.11118i) q^{23} +1.00000 q^{24} +(-1.12570 + 2.46493i) q^{25} +(4.62769 + 1.35881i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.18251 + 1.40261i) q^{28} +(-2.03899 + 2.35312i) q^{29} +(-0.215370 + 1.49793i) q^{30} +(1.12671 - 0.330833i) q^{31} +(0.841254 + 0.540641i) q^{32} +(0.712591 + 4.95618i) q^{33} +(-0.358791 - 0.785643i) q^{34} +(-1.63097 - 3.57133i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.506538 - 0.325532i) q^{37} +(6.71797 - 1.97257i) q^{38} +(0.686393 - 4.77397i) q^{39} +(-0.991025 + 1.14370i) q^{40} +(4.45305 - 2.86180i) q^{41} +(1.69894 + 1.96068i) q^{42} +(-1.40014 - 0.411119i) q^{43} +(-2.08004 + 4.55466i) q^{44} +1.51334 q^{45} +(2.94881 - 3.78213i) q^{46} -12.6797 q^{47} +(0.415415 - 0.909632i) q^{48} +(0.258432 + 0.0758824i) q^{49} +(1.77455 + 2.04794i) q^{50} +(-0.726585 + 0.466948i) q^{51} +(3.15843 - 3.64502i) q^{52} +(-0.602392 + 4.18973i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(-6.37459 - 4.09670i) q^{55} +(0.369215 + 2.56794i) q^{56} +(-2.90856 - 6.36886i) q^{57} +(1.29345 + 2.83225i) q^{58} +(-0.566615 - 3.94090i) q^{59} +(1.27310 + 0.818172i) q^{60} +(6.96812 - 2.04602i) q^{61} +(0.167117 - 1.16233i) q^{62} +(1.69894 - 1.96068i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.77977 + 5.51615i) q^{65} +(4.80432 + 1.41067i) q^{66} +(-6.70359 + 14.6788i) q^{67} -0.863693 q^{68} +(-4.16330 - 2.38054i) q^{69} -3.92613 q^{70} +(2.44456 - 5.35285i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-9.41782 - 10.8687i) q^{73} +(-0.506538 + 0.325532i) q^{74} +(1.77455 - 2.04794i) q^{75} +(0.996429 - 6.93032i) q^{76} +(-12.4641 + 3.65979i) q^{77} +(-4.05742 - 2.60754i) q^{78} +(-1.47156 - 10.2349i) q^{79} +(0.628663 + 1.37658i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.753323 - 5.23948i) q^{82} +(2.22176 + 1.42784i) q^{83} +(2.48926 - 0.730913i) q^{84} +(0.186014 - 1.29376i) q^{85} +(-0.955607 + 1.10283i) q^{86} +(2.61935 - 1.68335i) q^{87} +(3.27898 + 3.78415i) q^{88} +(5.02538 + 1.47559i) q^{89} +(0.628663 - 1.37658i) q^{90} +12.5127 q^{91} +(-2.21537 - 4.25348i) q^{92} -1.17428 q^{93} +(-5.26732 + 11.5338i) q^{94} +(10.1666 + 2.98517i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(12.5782 - 8.08355i) q^{97} +(0.176382 - 0.203555i) q^{98} +(0.712591 - 4.95618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} + 8 q^{5} - q^{6} + 8 q^{7} - q^{8} - q^{9} - 3 q^{10} + 7 q^{11} - q^{12} + 3 q^{13} - 3 q^{14} - 3 q^{15} - q^{16} + 4 q^{17} - q^{18} - 3 q^{20} - 3 q^{21} - 26 q^{22} - 12 q^{23} + 10 q^{24} - 15 q^{25} + 3 q^{26} - q^{27} - 3 q^{28} - 25 q^{29} - 3 q^{30} + 6 q^{31} - q^{32} - 4 q^{33} - 7 q^{34} + 2 q^{35} - q^{36} + 9 q^{37} + 11 q^{38} + 3 q^{39} - 3 q^{40} + 24 q^{41} + 8 q^{42} - 30 q^{43} + 7 q^{44} - 14 q^{45} + 21 q^{46} - 48 q^{47} - q^{48} + 9 q^{49} + 7 q^{50} + 15 q^{51} + 14 q^{52} + 15 q^{53} - q^{54} - 23 q^{55} + 8 q^{56} - 11 q^{57} - 3 q^{58} + 5 q^{59} + 8 q^{60} + 12 q^{61} + 28 q^{62} + 8 q^{63} - q^{64} - 13 q^{65} + 18 q^{66} + 18 q^{67} - 18 q^{68} - q^{69} + 2 q^{70} + 28 q^{71} - q^{72} + 19 q^{73} + 9 q^{74} + 7 q^{75} + 22 q^{76} - 12 q^{77} - 8 q^{78} - 52 q^{79} + 8 q^{80} - q^{81} - 20 q^{82} + 7 q^{83} - 3 q^{84} + 23 q^{85} + 14 q^{86} + 30 q^{87} - 4 q^{88} + 3 q^{89} + 8 q^{90} + 42 q^{91} - 23 q^{92} - 16 q^{93} + 29 q^{94} + 22 q^{95} - q^{96} + 51 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 + 8 * q^5 - q^6 + 8 * q^7 - q^8 - q^9 - 3 * q^10 + 7 * q^11 - q^12 + 3 * q^13 - 3 * q^14 - 3 * q^15 - q^16 + 4 * q^17 - q^18 - 3 * q^20 - 3 * q^21 - 26 * q^22 - 12 * q^23 + 10 * q^24 - 15 * q^25 + 3 * q^26 - q^27 - 3 * q^28 - 25 * q^29 - 3 * q^30 + 6 * q^31 - q^32 - 4 * q^33 - 7 * q^34 + 2 * q^35 - q^36 + 9 * q^37 + 11 * q^38 + 3 * q^39 - 3 * q^40 + 24 * q^41 + 8 * q^42 - 30 * q^43 + 7 * q^44 - 14 * q^45 + 21 * q^46 - 48 * q^47 - q^48 + 9 * q^49 + 7 * q^50 + 15 * q^51 + 14 * q^52 + 15 * q^53 - q^54 - 23 * q^55 + 8 * q^56 - 11 * q^57 - 3 * q^58 + 5 * q^59 + 8 * q^60 + 12 * q^61 + 28 * q^62 + 8 * q^63 - q^64 - 13 * q^65 + 18 * q^66 + 18 * q^67 - 18 * q^68 - q^69 + 2 * q^70 + 28 * q^71 - q^72 + 19 * q^73 + 9 * q^74 + 7 * q^75 + 22 * q^76 - 12 * q^77 - 8 * q^78 - 52 * q^79 + 8 * q^80 - q^81 - 20 * q^82 + 7 * q^83 - 3 * q^84 + 23 * q^85 + 14 * q^86 + 30 * q^87 - 4 * q^88 + 3 * q^89 + 8 * q^90 + 42 * q^91 - 23 * q^92 - 16 * q^93 + 29 * q^94 + 22 * q^95 - q^96 + 51 * q^97 - 2 * q^98 - 4 * q^99

Introduction

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