LMFDB - Embedded newform 680.2.l.a.101.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(101,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	680.101
Dual form			680.2.l.a.101.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27109 - 0.619947i) q^{2} +3.03317 q^{3} +(1.23133 + 1.57602i) q^{4} +1.00000 q^{5} +(-3.85542 - 1.88040i) q^{6} -1.14609i q^{7} +(-0.588085 - 2.76661i) q^{8} +6.20011 q^{9} +(-1.27109 - 0.619947i) q^{10} +1.02326 q^{11} +(3.73483 + 4.78032i) q^{12} -5.48640i q^{13} +(-0.710516 + 1.45678i) q^{14} +3.03317 q^{15} +(-0.967647 + 3.88119i) q^{16} +(-3.36364 + 2.38451i) q^{17} +(-7.88088 - 3.84374i) q^{18} -0.131183i q^{19} +(1.23133 + 1.57602i) q^{20} -3.47629i q^{21} +(-1.30066 - 0.634370i) q^{22} -2.38954i q^{23} +(-1.78376 - 8.39161i) q^{24} +1.00000 q^{25} +(-3.40127 + 6.97369i) q^{26} +9.70646 q^{27} +(1.80626 - 1.41122i) q^{28} +3.08229 q^{29} +(-3.85542 - 1.88040i) q^{30} +0.752428i q^{31} +(3.63610 - 4.33345i) q^{32} +3.10373 q^{33} +(5.75376 - 0.945646i) q^{34} -1.14609i q^{35} +(7.63438 + 9.77146i) q^{36} -7.71836 q^{37} +(-0.0813267 + 0.166745i) q^{38} -16.6412i q^{39} +(-0.588085 - 2.76661i) q^{40} +6.10135i q^{41} +(-2.15511 + 4.41867i) q^{42} +9.64227i q^{43} +(1.25998 + 1.61268i) q^{44} +6.20011 q^{45} +(-1.48139 + 3.03732i) q^{46} -3.00424 q^{47} +(-2.93503 + 11.7723i) q^{48} +5.68647 q^{49} +(-1.27109 - 0.619947i) q^{50} +(-10.2025 + 7.23263i) q^{51} +(8.64664 - 6.75557i) q^{52} +13.4640i q^{53} +(-12.3378 - 6.01749i) q^{54} +1.02326 q^{55} +(-3.17079 + 0.673999i) q^{56} -0.397901i q^{57} +(-3.91786 - 1.91086i) q^{58} +10.0052i q^{59} +(3.73483 + 4.78032i) q^{60} +3.72365 q^{61} +(0.466465 - 0.956402i) q^{62} -7.10589i q^{63} +(-7.30831 + 3.25401i) q^{64} -5.48640i q^{65} +(-3.94512 - 1.92415i) q^{66} -3.72428i q^{67} +(-7.89979 - 2.36503i) q^{68} -7.24788i q^{69} +(-0.710516 + 1.45678i) q^{70} +6.62521i q^{71} +(-3.64619 - 17.1533i) q^{72} -14.9275i q^{73} +(9.81072 + 4.78498i) q^{74} +3.03317 q^{75} +(0.206747 - 0.161530i) q^{76} -1.17275i q^{77} +(-10.3166 + 21.1524i) q^{78} -13.7272i q^{79} +(-0.967647 + 3.88119i) q^{80} +10.8410 q^{81} +(3.78251 - 7.75535i) q^{82} -3.85242i q^{83} +(5.47868 - 4.28046i) q^{84} +(-3.36364 + 2.38451i) q^{85} +(5.97770 - 12.2562i) q^{86} +9.34909 q^{87} +(-0.601766 - 2.83098i) q^{88} -3.64410 q^{89} +(-7.88088 - 3.84374i) q^{90} -6.28791 q^{91} +(3.76595 - 2.94232i) q^{92} +2.28224i q^{93} +(3.81866 + 1.86247i) q^{94} -0.131183i q^{95} +(11.0289 - 13.1441i) q^{96} -3.73153i q^{97} +(-7.22801 - 3.52531i) q^{98} +6.34435 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) $ 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−1.27109	−	0.619947i	−0.898795	−	0.438369i
$2$	−1.27109	−	0.619947i	−0.898795	−	0.438369i
$3$	3.03317			1.75120			0.875600	−	0.483037i	$-0.160466\pi$
$3$	3.03317			1.75120			0.875600	+	0.483037i	$0.160466\pi$
$4$	1.23133	+	1.57602i	0.615666	+	0.788008i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−3.85542	−	1.88040i	−1.57397	−	0.767671i
$7$		−	1.14609i		−	0.433182i	−0.976262	−	0.216591i	$-0.930506\pi$
$7$		−	1.14609i		−	0.433182i	0.976262	−	0.216591i	$-0.0694938\pi$
$8$	−0.588085	−	2.76661i	−0.207919	−	0.978146i
$9$	6.20011			2.06670
$10$	−1.27109	−	0.619947i	−0.401953	−	0.196044i
$11$	1.02326			0.308526			0.154263	−	0.988030i	$-0.450700\pi$
$11$	1.02326			0.308526			0.154263	+	0.988030i	$0.450700\pi$
$12$	3.73483	+	4.78032i	1.07815	+	1.37996i
$13$		−	5.48640i		−	1.52165i	−0.648956	−	0.760826i	$-0.724794\pi$
$13$		−	5.48640i		−	1.52165i	0.648956	−	0.760826i	$-0.275206\pi$
$14$	−0.710516	+	1.45678i	−0.189893	+	0.389342i
$15$	3.03317			0.783161
$16$	−0.967647	+	3.88119i	−0.241912	+	0.970298i
$17$	−3.36364	+	2.38451i	−0.815803	+	0.578329i
$17$	−3.36364	+	2.38451i	−0.815803	+	0.578329i
$18$	−7.88088	−	3.84374i	−1.85754	−	0.905978i
$19$		−	0.131183i		−	0.0300955i	−0.999887	−	0.0150477i	$-0.995210\pi$
$19$		−	0.131183i		−	0.0300955i	0.999887	−	0.0150477i	$-0.00479003\pi$
$20$	1.23133	+	1.57602i	0.275334	+	0.352408i
$21$		−	3.47629i		−	0.758588i
$22$	−1.30066	−	0.634370i	−0.277302	−	0.135248i
$23$		−	2.38954i		−	0.498254i	−0.968471	−	0.249127i	$-0.919856\pi$
$23$		−	2.38954i		−	0.498254i	0.968471	−	0.249127i	$-0.0801436\pi$
$24$	−1.78376	−	8.39161i	−0.364109	−	1.71293i
$25$	1.00000			0.200000
$26$	−3.40127	+	6.97369i	−0.667045	+	1.36765i
$27$	9.70646			1.86801
$28$	1.80626	−	1.41122i	0.341351	−	0.266695i
$29$	3.08229			0.572366			0.286183	−	0.958175i	$-0.407613\pi$
$29$	3.08229			0.572366			0.286183	+	0.958175i	$0.407613\pi$
$30$	−3.85542	−	1.88040i	−0.703901	−	0.343313i
$31$			0.752428i			0.135140i	0.997715	+	0.0675700i	$0.0215246\pi$
$31$			0.752428i			0.135140i	−0.997715	+	0.0675700i	$0.978475\pi$
$32$	3.63610	−	4.33345i	0.642778	−	0.766053i
$33$	3.10373			0.540291
$34$	5.75376	−	0.945646i	0.986762	−	0.162177i
$35$		−	1.14609i		−	0.193725i
$36$	7.63438	+	9.77146i	1.27240	+	1.62858i
$37$	−7.71836			−1.26889			−0.634445	−	0.772968i	$-0.718771\pi$
$37$	−7.71836			−1.26889			−0.634445	+	0.772968i	$0.718771\pi$
$38$	−0.0813267	+	0.166745i	−0.0131929	+	0.0270497i
$39$		−	16.6412i		−	2.66472i
$40$	−0.588085	−	2.76661i	−0.0929844	−	0.437440i
$41$			6.10135i			0.952871i	0.879210	+	0.476435i	$0.158071\pi$
$41$			6.10135i			0.952871i	−0.879210	+	0.476435i	$0.841929\pi$
$42$	−2.15511	+	4.41867i	−0.332541	+	0.681815i
$43$			9.64227i			1.47043i	0.677833	+	0.735216i	$0.262919\pi$
$43$			9.64227i			1.47043i	−0.677833	+	0.735216i	$0.737081\pi$
$44$	1.25998	+	1.61268i	0.189949	+	0.243121i
$45$	6.20011			0.924257
$46$	−1.48139	+	3.03732i	−0.218419	+	0.447828i
$47$	−3.00424			−0.438214			−0.219107	−	0.975701i	$-0.570314\pi$
$47$	−3.00424			−0.438214			−0.219107	+	0.975701i	$0.570314\pi$
$48$	−2.93503	+	11.7723i	−0.423636	+	1.69919i
$49$	5.68647			0.812353
$50$	−1.27109	−	0.619947i	−0.179759	−	0.0876738i
$51$	−10.2025	+	7.23263i	−1.42864	+	1.01277i
$52$	8.64664	−	6.75557i	1.19907	−	0.936829i
$53$			13.4640i			1.84942i	0.380677	+	0.924708i	$0.375691\pi$
$53$			13.4640i			1.84942i	−0.380677	+	0.924708i	$0.624309\pi$
$54$	−12.3378	−	6.01749i	−1.67896	−	0.818877i
$55$	1.02326			0.137977
$56$	−3.17079	+	0.673999i	−0.423715	+	0.0900669i
$57$		−	0.397901i		−	0.0527032i
$58$	−3.91786	−	1.91086i	−0.514440	−	0.250908i
$59$			10.0052i			1.30257i	0.758835	+	0.651283i	$0.225769\pi$
$59$			10.0052i			1.30257i	−0.758835	+	0.651283i	$0.774231\pi$
$60$	3.73483	+	4.78032i	0.482165	+	0.617136i
$61$	3.72365			0.476765			0.238383	−	0.971171i	$-0.423383\pi$
$61$	3.72365			0.476765			0.238383	+	0.971171i	$0.423383\pi$
$62$	0.466465	−	0.956402i	0.0592411	−	0.121463i
$63$		−	7.10589i		−	0.895258i
$64$	−7.30831	+	3.25401i	−0.913539	+	0.406751i
$65$		−	5.48640i		−	0.680504i
$66$	−3.94512	−	1.92415i	−0.485611	−	0.236846i
$67$		−	3.72428i		−	0.454993i	−0.973779	−	0.227497i	$-0.926946\pi$
$67$		−	3.72428i		−	0.454993i	0.973779	−	0.227497i	$-0.0730541\pi$
$68$	−7.89979	−	2.36503i	−0.957990	−	0.286802i
$69$		−	7.24788i		−	0.872542i
$70$	−0.710516	+	1.45678i	−0.0849229	+	0.174119i
$71$			6.62521i			0.786268i	0.919481	+	0.393134i	$0.128609\pi$
$71$			6.62521i			0.786268i	−0.919481	+	0.393134i	$0.871391\pi$
$72$	−3.64619	−	17.1533i	−0.429707	−	2.02154i
$73$		−	14.9275i		−	1.74713i	−0.486708	−	0.873565i	$-0.661802\pi$
$73$		−	14.9275i		−	1.74713i	0.486708	−	0.873565i	$-0.338198\pi$
$74$	9.81072	+	4.78498i	1.14047	+	0.556242i
$75$	3.03317			0.350240
$76$	0.206747	−	0.161530i	0.0237155	−	0.0185288i
$77$		−	1.17275i		−	0.133648i
$78$	−10.3166	+	21.1524i	−1.16813	+	2.39504i
$79$		−	13.7272i		−	1.54443i	−0.635358	−	0.772217i	$-0.719148\pi$
$79$		−	13.7272i		−	1.54443i	0.635358	−	0.772217i	$-0.280852\pi$
$80$	−0.967647	+	3.88119i	−0.108186	+	0.433931i
$81$	10.8410			1.20456
$82$	3.78251	−	7.75535i	0.417709	−	0.856436i
$83$		−	3.85242i		−	0.422858i	−0.977393	−	0.211429i	$-0.932188\pi$
$83$		−	3.85242i		−	0.422858i	0.977393	−	0.211429i	$-0.0678117\pi$
$84$	5.47868	−	4.28046i	0.597773	−	0.467037i
$85$	−3.36364	+	2.38451i	−0.364838	+	0.258637i
$86$	5.97770	−	12.2562i	0.644592	−	1.32162i
$87$	9.34909			1.00233
$88$	−0.601766	−	2.83098i	−0.0641485	−	0.301783i
$89$	−3.64410			−0.386274			−0.193137	−	0.981172i	$-0.561866\pi$
$89$	−3.64410			−0.386274			−0.193137	+	0.981172i	$0.561866\pi$
$90$	−7.88088	−	3.84374i	−0.830718	−	0.405166i
$91$	−6.28791			−0.659152
$92$	3.76595	−	2.94232i	0.392628	−	0.306758i
$93$			2.28224i			0.236657i
$94$	3.81866	+	1.86247i	0.393864	+	0.192099i
$95$		−	0.131183i		−	0.0134591i
$96$	11.0289	−	13.1441i	1.12563	−	1.34151i
$97$		−	3.73153i		−	0.378880i	−0.981892	−	0.189440i	$-0.939333\pi$
$97$		−	3.73153i		−	0.378880i	0.981892	−	0.189440i	$-0.0606672\pi$
$98$	−7.22801	−	3.52531i	−0.730139	−	0.356110i
$99$	6.34435			0.637631
$100$	1.23133	+	1.57602i	0.123133	+	0.157602i
$101$			12.0231i			1.19635i	0.801366	+	0.598174i	$0.204107\pi$
$101$			12.0231i			1.19635i	−0.801366	+	0.598174i	$0.795893\pi$
$102$	17.4521	−	2.86830i	1.72802	−	0.284004i
$103$	−3.61534			−0.356230			−0.178115	−	0.984010i	$-0.557000\pi$
$103$	−3.61534			−0.356230			−0.178115	+	0.984010i	$0.557000\pi$
$104$	−15.1787	+	3.22647i	−1.48840	+	0.316381i
$105$		−	3.47629i		−	0.339251i
$106$	8.34694	−	17.1139i	0.810726	−	1.66225i
$107$	13.7464			1.32892			0.664459	−	0.747324i	$-0.268662\pi$
$107$	13.7464			1.32892			0.664459	+	0.747324i	$0.268662\pi$
$108$	11.9519	+	15.2975i	1.15007	+	1.47200i
$109$	−16.8047			−1.60960			−0.804798	−	0.593549i	$-0.797726\pi$
$109$	−16.8047			−1.60960			−0.804798	+	0.593549i	$0.797726\pi$
$110$	−1.30066	−	0.634370i	−0.124013	−	0.0604848i
$111$	−23.4111			−2.22208
$112$	4.44820	+	1.10901i	0.420316	+	0.104792i
$113$		−	2.53084i		−	0.238081i	−0.992889	−	0.119041i	$-0.962018\pi$
$113$		−	2.53084i		−	0.238081i	0.992889	−	0.119041i	$-0.0379818\pi$
$114$	−0.246677	+	0.505767i	−0.0231035	+	0.0473694i
$115$		−	2.38954i		−	0.222826i
$116$	3.79532	+	4.85773i	0.352386	+	0.451029i
$117$		−	34.0162i		−	3.14480i
$118$	6.20269	−	12.7175i	0.571004	−	1.17074i
$119$	2.73287	+	3.85504i	0.250522	+	0.353391i
$120$	−1.78376	−	8.39161i	−0.162834	−	0.766045i
$121$	−9.95293			−0.904812
$122$	−4.73309	−	2.30847i	−0.428514	−	0.208999i
$123$			18.5064i			1.66867i
$124$	−1.18584	+	0.926488i	−0.106491	+	0.0832010i
$125$	1.00000			0.0894427
$126$	−4.40528	+	9.03221i	−0.392453	+	0.804654i
$127$	9.53470			0.846068			0.423034	−	0.906114i	$-0.360965\pi$
$127$	9.53470			0.846068			0.423034	+	0.906114i	$0.360965\pi$
$128$	11.3068	+	0.394634i	0.999391	+	0.0348811i
$129$			29.2466i			2.57502i
$130$	−3.40127	+	6.97369i	−0.298312	+	0.611633i
$131$	−18.4141			−1.60884			−0.804422	−	0.594059i	$-0.797525\pi$
$131$	−18.4141			−1.60884			−0.804422	+	0.594059i	$0.797525\pi$
$132$	3.82172	+	4.89153i	0.332638	+	0.425753i
$133$	−0.150348			−0.0130368
$134$	−2.30886	+	4.73389i	−0.199455	+	0.408946i
$135$	9.70646			0.835399
$136$	8.57514	+	7.90361i	0.735312	+	0.677729i
$137$	−13.1861			−1.12656			−0.563282	−	0.826264i	$-0.690462\pi$
$137$	−13.1861			−1.12656			−0.563282	+	0.826264i	$0.690462\pi$
$138$	−4.49330	+	9.21270i	−0.382495	+	0.784237i
$139$	16.9269			1.43572			0.717862	−	0.696185i	$-0.245121\pi$
$139$	16.9269			1.43572			0.717862	+	0.696185i	$0.245121\pi$
$140$	1.80626	−	1.41122i	0.152657	−	0.119270i
$141$	−9.11237			−0.767400
$142$	4.10728	−	8.42123i	0.344675	−	0.706694i
$143$		−	5.61403i		−	0.469469i
$144$	−5.99951	+	24.0638i	−0.499959	+	2.00532i
$145$	3.08229			0.255970
$146$	−9.25425	+	18.9742i	−0.765887	+	1.57031i
$147$	17.2480			1.42259
$148$	−9.50386	−	12.1643i	−0.781212	−	0.999895i
$149$		−	11.7779i		−	0.964881i	−0.875929	−	0.482441i	$-0.839750\pi$
$149$		−	11.7779i		−	0.964881i	0.875929	−	0.482441i	$-0.160250\pi$
$150$	−3.85542	−	1.88040i	−0.314794	−	0.153534i
$151$	2.90058			0.236046			0.118023	−	0.993011i	$-0.462344\pi$
$151$	2.90058			0.236046			0.118023	+	0.993011i	$0.462344\pi$
$152$	−0.362933	+	0.0771469i	−0.0294378	+	0.00625744i
$153$	−20.8549	+	14.7842i	−1.68602	+	1.19523i
$154$	−0.727046	+	1.49068i	−0.0585870	+	0.120122i
$155$			0.752428i			0.0604364i
$156$	26.2267	−	20.4908i	2.09982	−	1.64058i
$157$			9.13785i			0.729280i	0.931149	+	0.364640i	$0.118808\pi$
$157$			9.13785i			0.729280i	−0.931149	+	0.364640i	$0.881192\pi$
$158$	−8.51016	+	17.4485i	−0.677032	+	1.38813i
$159$			40.8384i			3.23870i
$160$	3.63610	−	4.33345i	0.287459	−	0.342589i
$161$	−2.73863			−0.215835
$162$	−13.7799	−	6.72084i	−1.08265	−	0.528039i
$163$	22.3320			1.74917			0.874587	−	0.484868i	$-0.161132\pi$
$163$	22.3320			1.74917			0.874587	+	0.484868i	$0.161132\pi$
$164$	−9.61582	+	7.51278i	−0.750869	+	0.586650i
$165$	3.10373			0.241625
$166$	−2.38830	+	4.89677i	−0.185368	+	0.380063i
$167$		−	0.350738i		−	0.0271409i	−0.999908	−	0.0135704i	$-0.995680\pi$
$167$		−	0.350738i		−	0.0271409i	0.999908	−	0.0135704i	$-0.00431974\pi$
$168$	−9.61755	+	2.04435i	−0.742010	+	0.157725i
$169$	−17.1005			−1.31543
$170$	5.75376	−	0.945646i	0.441293	−	0.0725277i
$171$		−	0.813350i		−	0.0621984i
$172$	−15.1964	+	11.8728i	−1.15871	+	0.905295i
$173$	−21.6007			−1.64227			−0.821137	−	0.570731i	$-0.806660\pi$
$173$	−21.6007			−1.64227			−0.821137	+	0.570731i	$0.806660\pi$
$174$	−11.8835	−	5.79594i	−0.900888	−	0.439389i
$175$		−	1.14609i		−	0.0866364i
$176$	−0.990158	+	3.97149i	−0.0746360	+	0.299362i
$177$			30.3474i			2.28105i
$178$	4.63197	+	2.25915i	0.347181	+	0.169330i
$179$			20.4689i			1.52991i	0.644082	+	0.764957i	$0.277240\pi$
$179$			20.4689i			1.52991i	−0.644082	+	0.764957i	$0.722760\pi$
$180$	7.63438	+	9.77146i	0.569033	+	0.728322i
$181$	−10.2177			−0.759472			−0.379736	−	0.925095i	$-0.623985\pi$
$181$	−10.2177			−0.759472			−0.379736	+	0.925095i	$0.623985\pi$
$182$	7.99249	+	3.89817i	0.592443	+	0.288952i
$183$	11.2945			0.834911
$184$	−6.61094	+	1.40525i	−0.487365	+	0.103597i
$185$	−7.71836			−0.567465
$186$	1.41487	−	2.90093i	0.103743	−	0.212706i
$187$	−3.44190	+	2.43999i	−0.251696	+	0.178430i
$188$	−3.69922	−	4.73473i	−0.269793	−	0.345316i
$189$		−	11.1245i		−	0.809188i
$190$	−0.0813267	+	0.166745i	−0.00590006	+	0.0120970i
$191$	−10.7086			−0.774847			−0.387424	−	0.921902i	$-0.626635\pi$
$191$	−10.7086			−0.774847			−0.387424	+	0.921902i	$0.626635\pi$
$192$	−22.1673	+	9.86995i	−1.59979	+	0.712303i
$193$		−	5.68548i		−	0.409250i	−0.978840	−	0.204625i	$-0.934403\pi$
$193$		−	5.68548i		−	0.409250i	0.978840	−	0.204625i	$-0.0655974\pi$
$194$	−2.31335	+	4.74311i	−0.166089	+	0.340535i
$195$		−	16.6412i		−	1.19170i
$196$	7.00193	+	8.96197i	0.500138	+	0.640141i
$197$	−18.1950			−1.29634			−0.648170	−	0.761496i	$-0.724465\pi$
$197$	−18.1950			−1.29634			−0.648170	+	0.761496i	$0.724465\pi$
$198$	−8.06423	−	3.93316i	−0.573100	−	0.279518i
$199$			6.43510i			0.456172i	0.973641	+	0.228086i	$0.0732468\pi$
$199$			6.43510i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$200$	−0.588085	−	2.76661i	−0.0415839	−	0.195629i
$201$		−	11.2964i		−	0.796785i
$202$	7.45371	−	15.2825i	0.524441	−	1.07527i
$203$		−	3.53258i		−	0.247939i
$204$	−23.9614	−	7.17352i	−1.67763	−	0.502247i
$205$			6.10135i			0.426137i
$206$	4.59542	+	2.24132i	0.320178	+	0.156160i
$207$		−	14.8154i		−	1.02974i
$208$	21.2938	+	5.30889i	1.47646	+	0.368105i
$209$		−	0.134235i		−	0.00928524i
$210$	−2.15511	+	4.41867i	−0.148717	+	0.304917i
$211$	0.0864097			0.00594869			0.00297434	−	0.999996i	$-0.499053\pi$
$211$	0.0864097			0.00594869			0.00297434	+	0.999996i	$0.499053\pi$
$212$	−21.2194	+	16.5786i	−1.45735	+	1.13862i
$213$			20.0954i			1.37691i
$214$	−17.4729	−	8.52207i	−1.19443	−	0.582556i
$215$			9.64227i			0.657597i
$216$	−5.70822	−	26.8540i	−0.388395	−	1.82719i
$217$	0.862351			0.0585402
$218$	21.3602	+	10.4180i	1.44670	+	0.705596i
$219$		−	45.2776i		−	3.05957i
$220$	1.25998	+	1.61268i	0.0849477	+	0.108727i
$221$	13.0824	+	18.4543i	0.880016	+	1.24137i
$222$	29.7576	+	14.5136i	1.99720	+	0.974091i
$223$	24.4718			1.63876			0.819378	−	0.573254i	$-0.194319\pi$
$223$	24.4718			1.63876			0.819378	+	0.573254i	$0.194319\pi$
$224$	−4.96653	−	4.16730i	−0.331840	−	0.278440i
$225$	6.20011			0.413340
$226$	−1.56898	+	3.21692i	−0.104367	+	0.213986i
$227$	−1.45822			−0.0967854			−0.0483927	−	0.998828i	$-0.515410\pi$
$227$	−1.45822			−0.0967854			−0.0483927	+	0.998828i	$0.515410\pi$
$228$	0.627097	−	0.489948i	0.0415305	−	0.0324476i
$229$			15.5745i			1.02919i	0.857434	+	0.514595i	$0.172058\pi$
$229$			15.5745i			1.02919i	−0.857434	+	0.514595i	$0.827942\pi$
$230$	−1.48139	+	3.03732i	−0.0976799	+	0.200275i
$231$		−	3.55716i		−	0.234044i
$232$	−1.81265	−	8.52750i	−0.119006	−	0.559858i
$233$		−	27.4971i		−	1.80140i	−0.434445	−	0.900698i	$-0.643055\pi$
$233$		−	27.4971i		−	1.80140i	0.434445	−	0.900698i	$-0.356945\pi$
$234$	−21.0883	+	43.2376i	−1.37858	+	2.82653i
$235$	−3.00424			−0.195975
$236$	−15.7683	+	12.3197i	−1.02643	+	0.801945i
$237$		−	41.6370i		−	2.70461i
$238$	−1.08380	−	6.59434i	−0.0702521	−	0.427447i
$239$	24.6460			1.59422			0.797109	−	0.603836i	$-0.206362\pi$
$239$	24.6460			1.59422			0.797109	+	0.603836i	$0.206362\pi$
$240$	−2.93503	+	11.7723i	−0.189456	+	0.759899i
$241$			4.94166i			0.318320i	0.987253	+	0.159160i	$0.0508786\pi$
$241$			4.94166i			0.318320i	−0.987253	+	0.159160i	$0.949121\pi$
$242$	12.6511	+	6.17029i	0.813241	+	0.396641i
$243$	3.76319			0.241409
$244$	4.58505	+	5.86853i	0.293528	+	0.375694i
$245$	5.68647			0.363295
$246$	11.4730	−	23.5233i	0.731492	−	1.49979i
$247$	−0.719723			−0.0457949
$248$	2.08168	−	0.442491i	0.132187	−	0.0280982i
$249$		−	11.6850i		−	0.740509i
$250$	−1.27109	−	0.619947i	−0.0803907	−	0.0392089i
$251$		−	14.0131i		−	0.884498i	−0.896892	−	0.442249i	$-0.854181\pi$
$251$		−	14.0131i		−	0.884498i	0.896892	−	0.442249i	$-0.145819\pi$
$252$	11.1990	−	8.74970i	0.705470	−	0.551180i
$253$		−	2.44513i		−	0.153724i
$254$	−12.1194	−	5.91101i	−0.760441	−	0.370890i
$255$	−10.2025	+	7.23263i	−0.638905	+	0.452925i
$256$	−14.1273	−	7.51125i	−0.882957	−	0.469453i
$257$	4.66350			0.290901			0.145451	−	0.989366i	$-0.453537\pi$
$257$	4.66350			0.290901			0.145451	+	0.989366i	$0.453537\pi$
$258$	18.1314	−	37.1750i	1.12881	−	2.31442i
$259$			8.84595i			0.549661i
$260$	8.64664	−	6.75557i	0.536242	−	0.418963i
$261$	19.1105			1.18291
$262$	23.4059	+	11.4157i	1.44602	+	0.705267i
$263$	14.1307			0.871339			0.435669	−	0.900107i	$-0.356512\pi$
$263$	14.1307			0.871339			0.435669	+	0.900107i	$0.356512\pi$
$264$	−1.82526	−	8.58683i	−0.112337	−	0.528483i
$265$			13.4640i			0.827084i
$266$	0.191106	+	0.0932078i	0.0117174	+	0.00571494i
$267$	−11.0532			−0.676443
$268$	5.86952	−	4.58582i	0.358538	−	0.280124i
$269$	8.14611			0.496677			0.248339	−	0.968673i	$-0.420115\pi$
$269$	8.14611			0.496677			0.248339	+	0.968673i	$0.420115\pi$
$270$	−12.3378	−	6.01749i	−0.750853	−	0.366213i
$271$	−15.1993			−0.923289			−0.461644	−	0.887065i	$-0.652740\pi$
$271$	−15.1993			−0.923289			−0.461644	+	0.887065i	$0.652740\pi$
$272$	−5.99994	−	15.3623i	−0.363800	−	0.931477i
$273$	−19.0723			−1.15431
$274$	16.7607	+	8.17469i	1.01255	+	0.493851i
$275$	1.02326			0.0617052
$276$	11.4228	−	8.92454i	0.687570	−	0.537194i
$277$	−8.47445			−0.509180			−0.254590	−	0.967049i	$-0.581941\pi$
$277$	−8.47445			−0.509180			−0.254590	+	0.967049i	$0.581941\pi$
$278$	−21.5156	−	10.4938i	−1.29042	−	0.629377i
$279$			4.66513i			0.279294i
$280$	−3.17079	+	0.673999i	−0.189491	+	0.0402792i
$281$	−18.0326			−1.07574			−0.537868	−	0.843029i	$-0.680770\pi$
$281$	−18.0326			−1.07574			−0.537868	+	0.843029i	$0.680770\pi$
$282$	11.5826	+	5.64919i	0.689735	+	0.336404i
$283$	−19.9346			−1.18499			−0.592493	−	0.805576i	$-0.701856\pi$
$283$	−19.9346			−1.18499			−0.592493	+	0.805576i	$0.701856\pi$
$284$	−10.4414	+	8.15783i	−0.619585	+	0.484078i
$285$		−	0.397901i		−	0.0235696i
$286$	−3.48040	+	7.13593i	−0.205801	+	0.421957i
$287$	6.99271			0.412766
$288$	22.5442	−	26.8678i	1.32843	−	1.58320i
$289$	5.62819	−	16.0413i	0.331070	−	0.943606i
$290$	−3.91786	−	1.91086i	−0.230065	−	0.112209i
$291$		−	11.3184i		−	0.663494i
$292$	23.5259	−	18.3807i	1.37675	−	1.07565i
$293$			7.57931i			0.442788i	0.975184	+	0.221394i	$0.0710607\pi$
$293$			7.57931i			0.442788i	−0.975184	+	0.221394i	$0.928939\pi$
$294$	−21.9238	−	10.6929i	−1.27862	−	0.623621i
$295$			10.0052i			0.582525i
$296$	4.53905	+	21.3537i	0.263827	+	1.24116i
$297$	9.93227			0.576329
$298$	−7.30166	+	14.9707i	−0.422974	+	0.867230i
$299$	−13.1100			−0.758169
$300$	3.73483	+	4.78032i	0.215631	+	0.275992i
$301$	11.0509			0.636965
$302$	−3.68689	−	1.79821i	−0.212157	−	0.103475i
$303$			36.4682i			2.09504i
$304$	0.509147	+	0.126939i	0.0292016	+	0.00728045i
$305$	3.72365			0.213216
$306$	35.6739	−	5.86311i	2.03934	−	0.335171i
$307$			19.8260i			1.13153i	0.824567	+	0.565765i	$0.191419\pi$
$307$			19.8260i			1.13153i	−0.824567	+	0.565765i	$0.808581\pi$
$308$	1.84828	−	1.44405i	0.105315	−	0.0822824i
$309$	−10.9659			−0.623830
$310$	0.466465	−	0.956402i	0.0264934	−	0.0543200i
$311$			16.7810i			0.951565i	0.879563	+	0.475782i	$0.157835\pi$
$311$			16.7810i			0.951565i	−0.879563	+	0.475782i	$0.842165\pi$
$312$	−46.0397	+	9.78641i	−2.60648	+	0.554047i
$313$		−	10.1370i		−	0.572979i	−0.958083	−	0.286490i	$-0.907512\pi$
$313$		−	10.1370i		−	0.572979i	0.958083	−	0.286490i	$-0.0924884\pi$
$314$	5.66498	−	11.6150i	0.319694	−	0.655473i
$315$		−	7.10589i		−	0.400372i
$316$	21.6343	−	16.9028i	1.21703	−	0.950855i
$317$	16.3655			0.919177			0.459589	−	0.888132i	$-0.347997\pi$
$317$	16.3655			0.919177			0.459589	+	0.888132i	$0.347997\pi$
$318$	25.3177	−	51.9093i	1.41974	−	2.91093i
$319$	3.15400			0.176590
$320$	−7.30831	+	3.25401i	−0.408547	+	0.181905i
$321$	41.6953			2.32720
$322$	3.48105	+	1.69781i	0.193991	+	0.0946151i
$323$	0.312808	+	0.441254i	0.0174051	+	0.0245520i
$324$	13.3489	+	17.0856i	0.741603	+	0.949199i
$325$		−	5.48640i		−	0.304330i
$326$	−28.3859	−	13.8446i	−1.57215	−	0.766784i
$327$	−50.9714			−2.81872
$328$	16.8801	−	3.58811i	0.932047	−	0.198120i
$329$			3.44314i			0.189826i
$330$	−3.94512	−	1.92415i	−0.217172	−	0.105921i
$331$		−	25.3181i		−	1.39161i	−0.718232	−	0.695804i	$-0.755048\pi$
$331$		−	25.3181i		−	1.39161i	0.718232	−	0.695804i	$-0.244952\pi$
$332$	6.07147	−	4.74360i	0.333215	−	0.260339i
$333$	−47.8547			−2.62242
$334$	−0.217439	+	0.445818i	−0.0118977	+	0.0243941i
$335$		−	3.72428i		−	0.203479i
$336$	13.4921	+	3.36382i	0.736057	+	0.183511i
$337$			13.6016i			0.740928i	0.928847	+	0.370464i	$0.120801\pi$
$337$			13.6016i			0.740928i	−0.928847	+	0.370464i	$0.879199\pi$
$338$	21.7363	+	10.6014i	1.18230	+	0.576642i
$339$		−	7.67645i		−	0.416928i
$340$	−7.89979	−	2.36503i	−0.428426	−	0.128262i
$341$			0.769932i			0.0416942i
$342$	−0.504234	+	1.03384i	−0.0272658	+	0.0559036i
$343$		−	14.5399i		−	0.785079i
$344$	26.6764	−	5.67047i	1.43830	−	0.305731i
$345$		−	7.24788i		−	0.390213i
$346$	27.4565	+	13.3913i	1.47607	+	0.719922i
$347$	2.58624			0.138837			0.0694183	−	0.997588i	$-0.477886\pi$
$347$	2.58624			0.138837			0.0694183	+	0.997588i	$0.477886\pi$
$348$	11.5118	+	14.7343i	0.617099	+	0.789842i
$349$		−	14.5552i		−	0.779123i	−0.921000	−	0.389561i	$-0.872627\pi$
$349$		−	14.5552i		−	0.779123i	0.921000	−	0.389561i	$-0.127373\pi$
$350$	−0.710516	+	1.45678i	−0.0379787	+	0.0778684i
$351$		−	53.2535i		−	2.84246i
$352$	3.72069	−	4.43427i	0.198313	−	0.236347i
$353$	12.1646			0.647456			0.323728	−	0.946150i	$-0.395064\pi$
$353$	12.1646			0.647456			0.323728	+	0.946150i	$0.395064\pi$
$354$	18.8138	−	38.5743i	0.999943	−	2.05020i
$355$			6.62521i			0.351630i
$356$	−4.48709	−	5.74316i	−0.237816	−	0.304387i
$357$	8.28925	+	11.6930i	0.438714	+	0.618859i
$358$	12.6896	−	26.0177i	0.670666	−	1.37508i
$359$	2.79598			0.147566			0.0737830	−	0.997274i	$-0.476493\pi$
$359$	2.79598			0.147566			0.0737830	+	0.997274i	$0.476493\pi$
$360$	−3.64619	−	17.1533i	−0.192171	−	0.904059i
$361$	18.9828			0.999094
$362$	12.9875	+	6.33440i	0.682610	+	0.332929i
$363$	−30.1889			−1.58451
$364$	−7.74250	−	9.90984i	−0.405817	−	0.519417i
$365$		−	14.9275i		−	0.781340i
$366$	−14.3563	−	7.00197i	−0.750414	−	0.365999i
$367$			8.02582i			0.418944i	0.977815	+	0.209472i	$0.0671746\pi$
$367$			8.02582i			0.418944i	−0.977815	+	0.209472i	$0.932825\pi$
$368$	9.27427	+	2.31223i	0.483455	+	0.120533i
$369$			37.8290i			1.96930i
$370$	9.81072	+	4.78498i	0.510035	+	0.248759i
$371$	15.4309			0.801134
$372$	−3.59684	+	2.81019i	−0.186488	+	0.145702i
$373$			7.11793i			0.368553i	0.982874	+	0.184276i	$0.0589941\pi$
$373$			7.11793i			0.368553i	−0.982874	+	0.184276i	$0.941006\pi$
$374$	5.88762	−	0.967646i	0.304441	−	0.0500358i
$375$	3.03317			0.156632
$376$	1.76675	+	8.31158i	0.0911131	+	0.428637i
$377$		−	16.9106i		−	0.870943i
$378$	−6.89660	+	14.1402i	−0.354723	+	0.727294i
$379$	6.32540			0.324914			0.162457	−	0.986716i	$-0.448058\pi$
$379$	6.32540			0.324914			0.162457	+	0.986716i	$0.448058\pi$
$380$	0.206747	−	0.161530i	0.0106059	−	0.00828631i
$381$	28.9203			1.48163
$382$	13.6116	+	6.63877i	0.696429	+	0.339669i
$383$	2.87869			0.147094			0.0735472	−	0.997292i	$-0.476568\pi$
$383$	2.87869			0.147094			0.0735472	+	0.997292i	$0.476568\pi$
$384$	34.2955	+	1.19699i	1.75013	+	0.0610837i
$385$		−	1.17275i		−	0.0597691i
$386$	−3.52469	+	7.22674i	−0.179402	+	0.367832i
$387$			59.7831i			3.03895i
$388$	5.88095	−	4.59475i	0.298560	−	0.233263i
$389$		−	0.0104623i		−	0.000530459i	−1.00000		0.000265230i	$-0.999916\pi$
$389$		−	0.0104623i		−	0.000530459i	1.00000		0.000265230i	$-8.44253e-5\pi$
$390$	−10.3166	+	21.1524i	−0.522403	+	1.07109i
$391$	5.69789	+	8.03757i	0.288155	+	0.406477i
$392$	−3.34413	−	15.7323i	−0.168904	−	0.794600i
$393$	−55.8529			−2.81741
$394$	23.1274	+	11.2799i	1.16514	+	0.568275i
$395$		−	13.7272i		−	0.690692i
$396$	7.81199	+	9.99879i	0.392567	+	0.502458i
$397$	−10.7463			−0.539343			−0.269672	−	0.962952i	$-0.586915\pi$
$397$	−10.7463			−0.539343			−0.269672	+	0.962952i	$0.586915\pi$
$398$	3.98942	−	8.17959i	0.199972	−	0.410006i
$399$	−0.456031			−0.0228301
$400$	−0.967647	+	3.88119i	−0.0483823	+	0.194060i
$401$		−	17.1586i		−	0.856858i	−0.903575	−	0.428429i	$-0.859067\pi$
$401$		−	17.1586i		−	0.856858i	0.903575	−	0.428429i	$-0.140933\pi$
$402$	−7.00315	+	14.3587i	−0.349285	+	0.716146i
$403$	4.12811			0.205636
$404$	−18.9487	+	14.8045i	−0.942731	+	0.736550i
$405$	10.8410			0.538694
$406$	−2.19001	+	4.49023i	−0.108689	+	0.222846i
$407$	−7.89792			−0.391486
$408$	26.0098	+	23.9730i	1.28768	+	1.18684i
$409$	−24.4746			−1.21019			−0.605096	−	0.796153i	$-0.706865\pi$
$409$	−24.4746			−1.21019			−0.605096	+	0.796153i	$0.706865\pi$
$410$	3.78251	−	7.75535i	0.186805	−	0.383010i
$411$	−39.9957			−1.97284
$412$	−4.45168	−	5.69783i	−0.219319	−	0.280712i
$413$	11.4669			0.564248
$414$	−9.18477	+	18.8317i	−0.451407	+	0.925528i
$415$		−	3.85242i		−	0.189108i
$416$	−23.7750	−	19.9491i	−1.16567	−	0.978084i
$417$	51.3422			2.51424
$418$	−0.0832187	+	0.170625i	−0.00407036	+	0.00834553i
$419$	31.5503			1.54133			0.770667	−	0.637238i	$-0.219923\pi$
$419$	31.5503			1.54133			0.770667	+	0.637238i	$0.219923\pi$
$420$	5.47868	−	4.28046i	0.267332	−	0.208865i
$421$		−	34.3300i		−	1.67314i	−0.547858	−	0.836571i	$-0.684557\pi$
$421$		−	34.3300i		−	1.67314i	0.547858	−	0.836571i	$-0.315443\pi$
$422$	−0.109834	−	0.0535694i	−0.00534665	−	0.00260772i
$423$	−18.6266			−0.905657
$424$	37.2496	−	7.91795i	1.80900	−	0.384530i
$425$	−3.36364	+	2.38451i	−0.163161	+	0.115666i
$426$	12.4581	−	25.5430i	0.603596	−	1.23756i
$427$		−	4.26765i		−	0.206526i
$428$	16.9264	+	21.6646i	0.818170	+	1.04720i
$429$		−	17.0283i		−	0.822134i
$430$	5.97770	−	12.2562i	0.288270	−	0.591045i
$431$		−	23.6707i		−	1.14018i	−0.821584	−	0.570088i	$-0.806909\pi$
$431$		−	23.6707i		−	1.14018i	0.821584	−	0.570088i	$-0.193091\pi$
$432$	−9.39242	+	37.6726i	−0.451893	+	1.81253i
$433$	−35.0893			−1.68628			−0.843142	−	0.537691i	$-0.819297\pi$
$433$	−35.0893			−1.68628			−0.843142	+	0.537691i	$0.819297\pi$
$434$	−1.09612	−	0.534612i	−0.0526156	−	0.0256622i
$435$	9.34909			0.448255
$436$	−20.6921	−	26.4844i	−0.990973	−	1.26837i
$437$	−0.313468			−0.0149952
$438$	−28.0697	+	57.5518i	−1.34122	+	2.74993i
$439$		−	23.9757i		−	1.14430i	−0.820150	−	0.572149i	$-0.806110\pi$
$439$		−	23.9757i		−	1.14430i	0.820150	−	0.572149i	$-0.193890\pi$
$440$	−0.601766	−	2.83098i	−0.0286881	−	0.134962i
$441$	35.2567			1.67889
$442$	−5.18819	−	31.5674i	−0.246777	−	1.50151i
$443$			2.98605i			0.141872i	0.997481	+	0.0709358i	$0.0225985\pi$
$443$			2.98605i			0.141872i	−0.997481	+	0.0709358i	$0.977401\pi$
$444$	−28.8268	−	36.8962i	−1.36806	−	1.75102i
$445$	−3.64410			−0.172747
$446$	−31.1059	−	15.1712i	−1.47291	−	0.718379i
$447$		−	35.7243i		−	1.68970i
$448$	3.72939	+	8.37600i	0.176197	+	0.395729i
$449$		−	23.9517i		−	1.13035i	−0.824970	−	0.565176i	$-0.808808\pi$
$449$		−	23.9517i		−	1.13035i	0.824970	−	0.565176i	$-0.191192\pi$
$450$	−7.88088	−	3.84374i	−0.371508	−	0.181196i
$451$			6.24329i			0.293985i
$452$	3.98864	−	3.11630i	0.187610	−	0.146578i
$453$	8.79794			0.413363
$454$	1.85353	+	0.904019i	0.0869903	+	0.0424277i
$455$	−6.28791			−0.294782
$456$	−1.10084	+	0.233999i	−0.0515515	+	0.0109580i
$457$	−18.6341			−0.871666			−0.435833	−	0.900027i	$-0.643546\pi$
$457$	−18.6341			−0.871666			−0.435833	+	0.900027i	$0.643546\pi$
$458$	9.65534	−	19.7965i	0.451165	−	0.925031i
$459$	−32.6491	+	23.1452i	−1.52393	+	1.08032i
$460$	3.76595	−	2.94232i	0.175589	−	0.137186i
$461$			13.9508i			0.649753i	0.945756	+	0.324877i	$0.105323\pi$
$461$			13.9508i			0.649753i	−0.945756	+	0.324877i	$0.894677\pi$
$462$	−2.20525	+	4.52147i	−0.102598	+	0.210358i
$463$	−20.8212			−0.967644			−0.483822	−	0.875166i	$-0.660752\pi$
$463$	−20.8212			−0.967644			−0.483822	+	0.875166i	$0.660752\pi$
$464$	−2.98257	+	11.9630i	−0.138462	+	0.555366i
$465$			2.28224i			0.105836i
$466$	−17.0468	+	34.9513i	−0.789676	+	1.61909i
$467$		−	16.4551i		−	0.761453i	−0.924688	−	0.380726i	$-0.875674\pi$
$467$		−	16.4551i		−	0.761453i	0.924688	−	0.380726i	$-0.124326\pi$
$468$	53.6101	−	41.8853i	2.47813	−	1.93615i
$469$	−4.26837			−0.197095
$470$	3.81866	+	1.86247i	0.176141	+	0.0859094i
$471$			27.7166i			1.27712i
$472$	27.6805	−	5.88391i	1.27410	−	0.270829i
$473$			9.86659i			0.453666i
$474$	−25.8127	+	52.9243i	−1.18562	+	2.43089i
$475$		−	0.131183i		−	0.00601910i
$476$	−2.71054	+	9.05388i	−0.124237	+	0.414984i
$477$			83.4780i			3.82219i
$478$	−31.3272	−	15.2792i	−1.43287	−	0.698855i
$479$		−	4.95366i		−	0.226338i	−0.993576	−	0.113169i	$-0.963900\pi$
$479$		−	4.95366i		−	0.226338i	0.993576	−	0.113169i	$-0.0361002\pi$
$480$	11.0289	−	13.1441i	0.503398	−	0.599942i
$481$			42.3460i			1.93081i
$482$	3.06357	−	6.28128i	0.139542	−	0.286105i
$483$	−8.30674			−0.377970
$484$	−12.2554	−	15.6860i	−0.557062	−	0.712998i
$485$		−	3.73153i		−	0.169440i
$486$	−4.78335	−	2.33298i	−0.216977	−	0.105826i
$487$		−	38.6316i		−	1.75057i	−0.483611	−	0.875283i	$-0.660675\pi$
$487$		−	38.6316i		−	1.75057i	0.483611	−	0.875283i	$-0.339325\pi$
$488$	−2.18982	−	10.3019i	−0.0991287	−	0.466346i
$489$	67.7366			3.06315
$490$	−7.22801	−	3.52531i	−0.326528	−	0.159257i
$491$			34.3423i			1.54985i	0.632054	+	0.774924i	$0.282212\pi$
$491$			34.3423i			1.54985i	−0.632054	+	0.774924i	$0.717788\pi$
$492$	−29.1664	+	22.7875i	−1.31492	+	1.02734i
$493$	−10.3677	+	7.34975i	−0.466938	+	0.331016i
$494$	0.914832	+	0.446190i	0.0411602	+	0.0200750i
$495$	6.34435			0.285157
$496$	−2.92032	−	0.728084i	−0.131126	−	0.0326919i
$497$	7.59310			0.340597
$498$	−7.24410	+	14.8527i	−0.324616	+	0.665566i
$499$	12.3584			0.553240			0.276620	−	0.960979i	$-0.410786\pi$
$499$	12.3584			0.553240			0.276620	+	0.960979i	$0.410786\pi$
$500$	1.23133	+	1.57602i	0.0550668	+	0.0704815i
$501$		−	1.06385i		−	0.0475291i
$502$	−8.68737	+	17.8119i	−0.387736	+	0.794983i
$503$			41.3000i			1.84147i	0.390183	+	0.920737i	$0.372412\pi$
$503$			41.3000i			1.84147i	−0.390183	+	0.920737i	$0.627588\pi$
$504$	−19.6593	+	4.17887i	−0.875693	+	0.186142i
$505$			12.0231i			0.535023i
$506$	−1.51585	+	3.10798i	−0.0673879	+	0.138167i
$507$	−51.8688			−2.30357
$508$	11.7404	+	15.0268i	0.520895	+	0.666708i
$509$			27.2031i			1.20576i	0.797833	+	0.602878i	$0.205980\pi$
$509$			27.2031i			1.20576i	−0.797833	+	0.602878i	$0.794020\pi$
$510$	17.4521	−	2.86830i	0.772793	−	0.127011i
$511$	−17.1083			−0.756825
$512$	13.3005	+	18.3056i	0.587804	+	0.809003i
$513$		−	1.27332i		−	0.0562186i
$514$	−5.92773	−	2.89113i	−0.261461	−	0.127522i
$515$	−3.61534			−0.159311
$516$	−46.0931	+	36.0123i	−2.02914	+	1.58535i
$517$	−3.07413			−0.135200
$518$	5.48402	−	11.2440i	0.240954	−	0.494032i
$519$	−65.5187			−2.87595
$520$	−15.1787	+	3.22647i	−0.665632	+	0.141490i
$521$		−	28.1207i		−	1.23199i	−0.787750	−	0.615995i	$-0.788754\pi$
$521$		−	28.1207i		−	1.23199i	0.787750	−	0.615995i	$-0.211246\pi$
$522$	−24.2911	−	11.8475i	−1.06319	−	0.518551i
$523$		−	39.9777i		−	1.74810i	−0.485834	−	0.874051i	$-0.661484\pi$
$523$		−	39.9777i		−	1.74810i	0.485834	−	0.874051i	$-0.338516\pi$
$524$	−22.6738	−	29.0208i	−0.990510	−	1.26778i
$525$		−	3.47629i		−	0.151718i
$526$	−17.9614	−	8.76031i	−0.783155	−	0.381968i
$527$	−1.79417	−	2.53090i	−0.0781554	−	0.110248i
$528$	−3.00332	+	12.0462i	−0.130703	+	0.524243i
$529$	17.2901			0.751743
$530$	8.34694	−	17.1139i	0.362568	−	0.743379i
$531$			62.0333i			2.69202i
$532$	−0.185128	−	0.236951i	−0.00802632	−	0.0102731i
$533$	33.4744			1.44994
$534$	14.0496	+	6.85238i	0.607983	+	0.296531i
$535$	13.7464			0.594311
$536$	−10.3037	+	2.19019i	−0.445050	+	0.0946020i
$537$			62.0855i			2.67919i
$538$	−10.3544	−	5.05016i	−0.446411	−	0.217728i
$539$	5.81877			0.250632
$540$	11.9519	+	15.2975i	0.514326	+	0.658301i
$541$	26.3948			1.13480			0.567401	−	0.823442i	$-0.307949\pi$
$541$	26.3948			1.13480			0.567401	+	0.823442i	$0.307949\pi$
$542$	19.3196	+	9.42273i	0.829848	+	0.404741i
$543$	−30.9919			−1.32999
$544$	−1.89737	+	23.2465i	−0.0813492	+	0.996686i
$545$	−16.8047			−0.719833
$546$	24.2426	+	11.8238i	1.03749	+	0.506012i
$547$	−3.38133			−0.144575			−0.0722877	−	0.997384i	$-0.523030\pi$
$547$	−3.38133			−0.144575			−0.0722877	+	0.997384i	$0.523030\pi$
$548$	−16.2365	−	20.7815i	−0.693587	−	0.887742i
$549$	23.0871			0.985331
$550$	−1.30066	−	0.634370i	−0.0554603	−	0.0270496i
$551$		−	0.404344i		−	0.0172256i
$552$	−20.0521	+	4.26237i	−0.853474	+	0.181419i
$553$	−15.7327			−0.669021
$554$	10.7718	+	5.25371i	0.457649	+	0.223209i
$555$	−23.4111			−0.993745
$556$	20.8427	+	26.6771i	0.883926	+	1.13136i
$557$		−	6.09342i		−	0.258187i	−0.991632	−	0.129093i	$-0.958793\pi$
$557$		−	6.09342i		−	0.258187i	0.991632	−	0.129093i	$-0.0412067\pi$
$558$	2.89213	−	5.92979i	0.122434	−	0.251028i
$559$	52.9013			2.23749
$560$	4.44820	+	1.10901i	0.187971	+	0.0468643i
$561$	−10.4399	+	7.40089i	−0.440771	+	0.312466i
$562$	22.9211	+	11.1793i	0.966867	+	0.471569i
$563$		−	41.4270i		−	1.74594i	−0.487774	−	0.872970i	$-0.662191\pi$
$563$		−	41.4270i		−	1.74594i	0.487774	−	0.872970i	$-0.337809\pi$
$564$	−11.2203	−	14.3612i	−0.472462	−	0.604717i
$565$		−	2.53084i		−	0.106473i
$566$	25.3386	+	12.3584i	1.06506	+	0.519461i
$567$		−	12.4248i		−	0.521792i
$568$	18.3294	−	3.89619i	0.769085	−	0.163480i
$569$	−1.99334			−0.0835653			−0.0417827	−	0.999127i	$-0.513304\pi$
$569$	−1.99334			−0.0835653			−0.0417827	+	0.999127i	$0.513304\pi$
$570$	−0.246677	+	0.505767i	−0.0103322	+	0.0211842i
$571$	−12.1058			−0.506614			−0.253307	−	0.967386i	$-0.581518\pi$
$571$	−12.1058			−0.506614			−0.253307	+	0.967386i	$0.581518\pi$
$572$	8.84780	−	6.91273i	0.369945	−	0.289036i
$573$	−32.4810			−1.35691
$574$	−8.88835	−	4.33511i	−0.370992	−	0.180944i
$575$		−	2.38954i		−	0.0996508i
$576$	−45.3123	+	20.1752i	−1.88801	+	0.840633i
$577$	19.1678			0.797967			0.398984	−	0.916958i	$-0.369363\pi$
$577$	19.1678			0.797967			0.398984	+	0.916958i	$0.369363\pi$
$578$	−17.0987	+	16.9007i	−0.711212	+	0.702978i
$579$		−	17.2450i		−	0.716678i
$580$	3.79532	+	4.85773i	0.157592	+	0.201706i
$581$	−4.41523			−0.183174
$582$	−7.01679	+	14.3866i	−0.290855	+	0.596346i
$583$			13.7772i			0.570593i
$584$	−41.2986	+	8.77863i	−1.70895	+	0.363262i
$585$		−	34.0162i		−	1.40640i
$586$	4.69877	−	9.63397i	0.194104	−	0.397976i
$587$		−	16.6238i		−	0.686137i	−0.939310	−	0.343068i	$-0.888534\pi$
$587$		−	16.6238i		−	0.686137i	0.939310	−	0.343068i	$-0.111466\pi$
$588$	21.2380	+	27.1832i	0.875842	+	1.12101i
$589$	0.0987059			0.00406710
$590$	6.20269	−	12.7175i	0.255361	−	0.523571i
$591$	−55.1885			−2.27015
$592$	7.46865	−	29.9565i	0.306959	−	1.23120i
$593$	24.6362			1.01169			0.505844	−	0.862625i	$-0.331181\pi$
$593$	24.6362			1.01169			0.505844	+	0.862625i	$0.331181\pi$
$594$	−12.6248	−	6.15748i	−0.518002	−	0.252645i
$595$	2.73287	+	3.85504i	0.112037	+	0.158041i
$596$	18.5621	−	14.5025i	0.760333	−	0.594044i
$597$			19.5188i			0.798849i
$598$	16.6639	+	8.12749i	0.681439	+	0.332358i
$599$	0.908614			0.0371249			0.0185625	−	0.999828i	$-0.494091\pi$
$599$	0.908614			0.0371249			0.0185625	+	0.999828i	$0.494091\pi$
$600$	−1.78376	−	8.39161i	−0.0728217	−	0.342586i
$601$		−	25.0001i		−	1.01977i	−0.860241	−	0.509887i	$-0.829687\pi$
$601$		−	25.0001i		−	1.01977i	0.860241	−	0.509887i	$-0.170313\pi$
$602$	−14.0467	−	6.85099i	−0.572501	−	0.279225i
$603$		−	23.0909i		−	0.940336i
$604$	3.57157	+	4.57136i	0.145325	+	0.186006i
$605$	−9.95293			−0.404644
$606$	22.6084	−	46.3543i	0.918402	−	1.88302i
$607$			36.9035i			1.49787i	0.662645	+	0.748933i	$0.269434\pi$
$607$			36.9035i			1.49787i	−0.662645	+	0.748933i	$0.730566\pi$
$608$	−0.568476	−	0.476995i	−0.0230547	−	0.0193447i
$609$		−	10.7149i		−	0.434190i
$610$	−4.73309	−	2.30847i	−0.191637	−	0.0934672i
$611$			16.4825i			0.666809i
$612$	−48.9795	−	14.6634i	−1.97988	−	0.592734i
$613$		−	6.42995i		−	0.259703i	−0.991533	−	0.129852i	$-0.958550\pi$
$613$		−	6.42995i		−	0.259703i	0.991533	−	0.129852i	$-0.0414501\pi$
$614$	12.2911	−	25.2006i	0.496027	−	1.01701i
$615$			18.5064i			0.746251i
$616$	−3.24456	+	0.689679i	−0.130727	+	0.0277880i
$617$		−	14.0811i		−	0.566883i	−0.958989	−	0.283442i	$-0.908524\pi$
$617$		−	14.0811i		−	0.566883i	0.958989	−	0.283442i	$-0.0914762\pi$
$618$	13.9387	+	6.79830i	0.560696	+	0.273468i
$619$	−0.313074			−0.0125835			−0.00629176	−	0.999980i	$-0.502003\pi$
$619$	−0.313074			−0.0125835			−0.00629176	+	0.999980i	$0.502003\pi$
$620$	−1.18584	+	0.926488i	−0.0476244	+	0.0372086i
$621$		−	23.1940i		−	0.930743i
$622$	10.4033	−	21.3302i	0.417136	−	0.855262i
$623$			4.17647i			0.167327i
$624$	64.5875	+	16.1028i	2.58557	+	0.644626i
$625$	1.00000			0.0400000
$626$	−6.28443	+	12.8851i	−0.251176	+	0.514991i
$627$		−	0.407158i		−	0.0162603i
$628$	−14.4014	+	11.2517i	−0.574678	+	0.448993i
$629$	25.9618	−	18.4045i	1.03517	−	0.733837i
$630$	−4.40528	+	9.03221i	−0.175510	+	0.359852i
$631$	47.2286			1.88014			0.940070	−	0.340982i	$-0.110759\pi$
$631$	47.2286			1.88014			0.940070	+	0.340982i	$0.110759\pi$
$632$	−37.9780	+	8.07278i	−1.51068	+	0.321118i
$633$	0.262095			0.0104173
$634$	−20.8020	−	10.1457i	−0.826152	−	0.402939i
$635$	9.53470			0.378373
$636$	−64.3620	+	50.2856i	−2.55212	+	1.99396i
$637$		−	31.1982i		−	1.23612i
$638$	−4.00901	−	1.95531i	−0.158718	−	0.0774115i
$639$			41.0770i			1.62498i
$640$	11.3068	+	0.394634i	0.446941	+	0.0155993i
$641$			33.8478i			1.33691i	0.743754	+	0.668453i	$0.233043\pi$
$641$			33.8478i			1.33691i	−0.743754	+	0.668453i	$0.766957\pi$
$642$	−52.9984	−	25.8489i	−2.09168	−	1.02017i
$643$	12.8818			0.508008			0.254004	−	0.967203i	$-0.418252\pi$
$643$	12.8818			0.508008			0.254004	+	0.967203i	$0.418252\pi$
$644$	−3.37217	−	4.31613i	−0.132882	−	0.170079i
$645$			29.2466i			1.15158i
$646$	−0.124053	−	0.754797i	−0.00488080	−	0.0296971i
$647$	−12.8495			−0.505166			−0.252583	−	0.967575i	$-0.581280\pi$
$647$	−12.8495			−0.505166			−0.252583	+	0.967575i	$0.581280\pi$
$648$	−6.37543	−	29.9929i	−0.250450	−	1.17823i
$649$			10.2380i			0.401875i
$650$	−3.40127	+	6.97369i	−0.133409	+	0.273531i
$651$	2.61565			0.102516
$652$	27.4980	+	35.1955i	1.07691	+	1.37836i
$653$	35.7866			1.40044			0.700219	−	0.713928i	$-0.253086\pi$
$653$	35.7866			1.40044			0.700219	+	0.713928i	$0.253086\pi$
$654$	64.7891	+	31.5996i	2.53346	+	1.23564i
$655$	−18.4141			−0.719497
$656$	−23.6805	−	5.90395i	−0.924569	−	0.230511i
$657$		−	92.5520i		−	3.61080i
$658$	2.13456	−	4.37653i	0.0832139	−	0.170615i
$659$		−	31.8870i		−	1.24214i	−0.783754	−	0.621071i	$-0.786698\pi$
$659$		−	31.8870i		−	1.24214i	0.783754	−	0.621071i	$-0.213302\pi$
$660$	3.82172	+	4.89153i	0.148760	+	0.190403i
$661$		−	4.27000i		−	0.166084i	−0.996546	−	0.0830420i	$-0.973536\pi$
$661$		−	4.27000i		−	0.166084i	0.996546	−	0.0830420i	$-0.0264636\pi$
$662$	−15.6959	+	32.1815i	−0.610037	+	1.25077i
$663$	39.6811	+	55.9749i	1.54108	+	2.17389i
$664$	−10.6582	+	2.26555i	−0.413617	+	0.0879204i
$665$	−0.150348			−0.00583024
$666$	60.8275	+	29.6674i	2.35702	+	1.14959i
$667$		−	7.36525i		−	0.285184i
$668$	0.552768	−	0.431874i	0.0213872	−	0.0167097i
$669$	74.2272			2.86979
$670$	−2.30886	+	4.73389i	−0.0891989	+	0.182886i
$671$	3.81028			0.147094
$672$	−15.0643	−	12.6401i	−0.581119	−	0.487603i
$673$			48.6589i			1.87566i	0.347089	+	0.937832i	$0.387170\pi$
$673$			48.6589i			1.87566i	−0.347089	+	0.937832i	$0.612830\pi$
$674$	8.43229	−	17.2889i	0.324800	−	0.665942i
$675$	9.70646			0.373602
$676$	−21.0564	−	26.9507i	−0.809862	−	1.03657i
$677$	13.6262			0.523698			0.261849	−	0.965109i	$-0.415668\pi$
$677$	13.6262			0.523698			0.261849	+	0.965109i	$0.415668\pi$
$678$	−4.75899	+	9.75745i	−0.182768	+	0.374733i
$679$	−4.27668			−0.164124
$680$	8.57514	+	7.90361i	0.328841	+	0.303090i
$681$	−4.42302			−0.169491
$682$	0.477317	−	0.978652i	0.0182774	−	0.0374745i
$683$	−4.24075			−0.162268			−0.0811339	−	0.996703i	$-0.525854\pi$
$683$	−4.24075			−0.162268			−0.0811339	+	0.996703i	$0.525854\pi$
$684$	1.28185	−	1.00150i	0.0490128	−	0.0382934i
$685$	−13.1861			−0.503815
$686$	−9.01394	+	18.4814i	−0.344154	+	0.705625i
$687$			47.2400i			1.80232i
$688$	−37.4235	−	9.33031i	−1.42676	−	0.355715i
$689$	73.8686			2.81417
$690$	−4.49330	+	9.21270i	−0.171057	+	0.350721i
$691$	37.5781			1.42954			0.714769	−	0.699361i	$-0.246532\pi$
$691$	37.5781			1.42954			0.714769	+	0.699361i	$0.246532\pi$
$692$	−26.5977	−	34.0431i	−1.01109	−	1.29412i
$693$		−	7.27120i		−	0.276210i
$694$	−3.28734	−	1.60333i	−0.124786	−	0.0608616i
$695$	16.9269			0.642075
$696$	−5.49806	−	25.8653i	−0.208403	−	0.980423i
$697$	−14.5487	−	20.5228i	−0.551073	−	0.777355i
$698$	−9.02346	+	18.5010i	−0.341543	+	0.700272i
$699$		−	83.4034i		−	3.15461i
$700$	1.80626	−	1.41122i	0.0682701	−	0.0533390i
$701$			24.2590i			0.916249i	0.888888	+	0.458124i	$0.151479\pi$
$701$			24.2590i			0.916249i	−0.888888	+	0.458124i	$0.848521\pi$
$702$	−33.0143	+	67.6899i	−1.24605	+	2.55479i
$703$			1.01252i			0.0381879i
$704$	−7.47834	+	3.32971i	−0.281850	+	0.125493i
$705$	−9.11237			−0.343192
$706$	−15.4623	−	7.54141i	−0.581931	−	0.283825i
$707$	13.7796			0.518236
$708$	−47.8280	+	37.3678i	−1.79749	+	1.40437i
$709$	−21.6792			−0.814181			−0.407090	−	0.913388i	$-0.633457\pi$
$709$	−21.6792			−0.814181			−0.407090	+	0.913388i	$0.633457\pi$
$710$	4.10728	−	8.42123i	0.154144	−	0.316043i
$711$		−	85.1103i		−	3.19189i
$712$	2.14304	+	10.0818i	0.0803138	+	0.377832i
$713$	1.79796			0.0673340
$714$	−3.28734	−	20.0017i	−0.123026	−	0.748546i
$715$		−	5.61403i		−	0.209953i
$716$	−32.2592	+	25.2039i	−1.20558	+	0.941915i
$717$	74.7555			2.79179
$718$	−3.55393	−	1.73336i	−0.132632	−	0.0646883i
$719$		−	23.9297i		−	0.892427i	−0.894926	−	0.446214i	$-0.852772\pi$
$719$		−	23.9297i		−	0.892427i	0.894926	−	0.446214i	$-0.147228\pi$
$720$	−5.99951	+	24.0638i	−0.223589	+	0.896805i
$721$			4.14351i			0.154312i
$722$	−24.1288	−	11.7683i	−0.897981	−	0.437972i
$723$			14.9889i			0.557442i
$724$	−12.5813	−	16.1032i	−0.467581	−	0.598470i
$725$	3.08229			0.114473
$726$	38.3728	+	18.7155i	1.42415	+	0.694598i
$727$	−5.88741			−0.218352			−0.109176	−	0.994022i	$-0.534821\pi$
$727$	−5.88741			−0.218352			−0.109176	+	0.994022i	$0.534821\pi$
$728$	3.69783	+	17.3962i	0.137051	+	0.644747i
$729$	−21.1086			−0.781800
$730$	−9.25425	+	18.9742i	−0.342515	+	0.702265i
$731$	−22.9921	−	32.4332i	−0.850394	−	1.19958i
$732$	13.9072	+	17.8002i	0.514026	+	0.657916i
$733$			17.0070i			0.628167i	0.949395	+	0.314084i	$0.101697\pi$
$733$			17.0070i			0.628167i	−0.949395	+	0.314084i	$0.898303\pi$
$734$	4.97558	−	10.2015i	0.183652	−	0.376545i
$735$	17.2480			0.636203
$736$	−10.3550	−	8.68861i	−0.381689	−	0.320266i
$737$		−	3.81093i		−	0.140377i
$738$	23.4520	−	48.0840i	0.863280	−	1.77000i
$739$			26.7139i			0.982687i	0.870966	+	0.491344i	$0.163494\pi$
$739$			26.7139i			0.982687i	−0.870966	+	0.491344i	$0.836506\pi$
$740$	−9.50386	−	12.1643i	−0.349369	−	0.447167i
$741$	−2.18304			−0.0801960
$742$	−19.6141	−	9.56636i	−0.720055	−	0.351192i
$743$		−	49.2505i		−	1.80683i	−0.428771	−	0.903413i	$-0.641053\pi$
$743$		−	49.2505i		−	1.80683i	0.428771	−	0.903413i	$-0.358947\pi$
$744$	6.31408	−	1.34215i	0.231485	−	0.0492056i
$745$		−	11.7779i		−	0.431508i
$746$	4.41274	−	9.04752i	0.161562	−	0.331253i
$747$		−	23.8854i		−	0.873921i
$748$	−8.08357	−	2.42005i	−0.295565	−	0.0884857i
$749$		−	15.7547i		−	0.575664i
$750$	−3.85542	−	1.88040i	−0.140780	−	0.0686626i
$751$			9.44928i			0.344809i	0.985026	+	0.172405i	$0.0551537\pi$
$751$			9.44928i			0.344809i	−0.985026	+	0.172405i	$0.944846\pi$
$752$	2.90704	−	11.6600i	0.106009	−	0.425198i
$753$		−	42.5040i		−	1.54893i
$754$	−10.4837	+	21.4949i	−0.381794	+	0.782799i
$755$	2.90058			0.105563
$756$	17.5324	−	13.6979i	0.637646	−	0.498189i
$757$			1.63895i			0.0595685i	0.999556	+	0.0297843i	$0.00948203\pi$
$757$			1.63895i			0.0595685i	−0.999556	+	0.0297843i	$0.990518\pi$
$758$	−8.04015	−	3.92142i	−0.292031	−	0.142432i
$759$		−	7.41650i		−	0.269202i
$760$	−0.362933	+	0.0771469i	−0.0131650	+	0.00279841i
$761$	28.2428			1.02380			0.511901	−	0.859044i	$-0.328941\pi$
$761$	28.2428			1.02380			0.511901	+	0.859044i	$0.328941\pi$
$762$	−36.7603	−	17.9291i	−1.33169	−	0.649502i
$763$			19.2597i			0.697248i
$764$	−13.1858	−	16.8769i	−0.477047	−	0.610585i
$765$	−20.8549	+	14.7842i	−0.754012	+	0.534525i
$766$	−3.65908	−	1.78464i	−0.132208	−	0.0644816i
$767$	54.8925			1.98205
$768$	−42.8505	−	22.7829i	−1.54624	−	0.822106i
$769$	5.94202			0.214275			0.107137	−	0.994244i	$-0.465832\pi$
$769$	5.94202			0.214275			0.107137	+	0.994244i	$0.465832\pi$
$770$	−0.727046	+	1.49068i	−0.0262009	+	0.0537202i
$771$	14.1452			0.509427
$772$	8.96040	−	7.00071i	0.322492	−	0.251961i
$773$			20.5173i			0.737957i	0.929438	+	0.368978i	$0.120292\pi$
$773$			20.5173i			0.737957i	−0.929438	+	0.368978i	$0.879708\pi$
$774$	37.0624	−	75.9896i	1.33218	−	2.73139i
$775$			0.752428i			0.0270280i
$776$	−10.3237	+	2.19446i	−0.370600	+	0.0787765i
$777$			26.8312i			0.962566i
$778$	−0.00648607	+	0.0132985i	−0.000232537	+	0.000476774i
$779$	0.800395			0.0286771
$780$	26.2267	−	20.4908i	0.939067	−	0.733688i
$781$			6.77935i			0.242584i
$782$	−2.25966	−	13.7489i	−0.0808053	−	0.491658i
$783$	29.9181			1.06919
$784$	−5.50250	+	22.0703i	−0.196518	+	0.788225i
$785$			9.13785i			0.326144i
$786$	70.9940	+	34.6258i	2.53227	+	1.23506i
$787$	30.1991			1.07648			0.538241	−	0.842791i	$-0.319089\pi$
$787$	30.1991			1.07648			0.538241	+	0.842791i	$0.319089\pi$
$788$	−22.4041	−	28.6756i	−0.798112	−	1.02153i
$789$	42.8609			1.52589
$790$	−8.51016	+	17.4485i	−0.302778	+	0.620791i
$791$	−2.90057			−0.103132
$792$	−3.73102	−	17.5524i	−0.132576	−	0.623696i
$793$		−	20.4294i		−	0.725471i
$794$	13.6595	+	6.66216i	0.484759	+	0.236431i
$795$			40.8384i			1.44839i
$796$	−10.1418	+	7.92375i	−0.359467	+	0.280850i
$797$			24.2150i			0.857738i	0.903367	+	0.428869i	$0.141088\pi$
$797$			24.2150i			0.857738i	−0.903367	+	0.428869i	$0.858912\pi$
$798$	0.579655	+	0.282715i	0.0205196	+	0.0100080i
$799$	10.1052	−	7.16365i	0.357496	−	0.253432i
$800$	3.63610	−	4.33345i	0.128556	−	0.153211i
$801$	−22.5938			−0.798313
$802$	−10.6374	+	21.8101i	−0.375620	+	0.770140i
$803$		−	15.2748i		−	0.539035i
$804$	17.8032	−	13.9096i	0.627872	−	0.490553i
$805$	−2.73863			−0.0965242
$806$	−5.24720	−	2.55921i	−0.184825	−	0.0901444i
$807$	24.7085			0.869781
$808$	33.2634	−	7.07063i	1.17020	−	0.248744i
$809$		−	42.8270i		−	1.50572i	−0.658183	−	0.752858i	$-0.728675\pi$
$809$		−	42.8270i		−	1.50572i	0.658183	−	0.752858i	$-0.271325\pi$
$810$	−13.7799	−	6.72084i	−0.484175	−	0.236146i
$811$	35.3651			1.24184			0.620919	−	0.783875i	$-0.286760\pi$
$811$	35.3651			1.24184			0.620919	+	0.783875i	$0.286760\pi$
$812$	5.56740	−	4.34978i	0.195378	−	0.152647i
$813$	−46.1019			−1.61686
$814$	10.0390	+	4.89630i	0.351865	+	0.171615i
$815$	22.3320			0.782255
$816$	−18.1988	−	46.5965i	−0.637086	−	1.63120i
$817$	1.26490			0.0442534
$818$	31.1094	+	15.1730i	1.08771	+	0.530510i
$819$	−38.9857			−1.36227
$820$	−9.61582	+	7.51278i	−0.335799	+	0.262358i
$821$	−40.2892			−1.40610			−0.703051	−	0.711139i	$-0.748179\pi$
$821$	−40.2892			−1.40610			−0.703051	+	0.711139i	$0.748179\pi$
$822$	50.8380	+	24.7952i	1.77318	+	0.864832i
$823$			15.8735i			0.553315i	0.960969	+	0.276658i	$0.0892268\pi$
$823$			15.8735i			0.553315i	−0.960969	+	0.276658i	$0.910773\pi$
$824$	2.12613	+	10.0023i	0.0740672	+	0.348445i
$825$	3.10373			0.108058
$826$	−14.5754	−	7.10885i	−0.507143	−	0.247349i
$827$	−50.7719			−1.76551			−0.882756	−	0.469833i	$-0.844314\pi$
$827$	−50.7719			−1.76551			−0.882756	+	0.469833i	$0.844314\pi$
$828$	23.3493	−	18.2427i	0.811445	−	0.633977i
$829$		−	17.3126i		−	0.601290i	−0.953736	−	0.300645i	$-0.902798\pi$
$829$		−	17.3126i		−	0.601290i	0.953736	−	0.300645i	$-0.0972019\pi$
$830$	−2.38830	+	4.89677i	−0.0828990	+	0.169969i
$831$	−25.7044			−0.891677
$832$	17.8528	+	40.0963i	0.618934	+	1.39009i
$833$	−19.1273	+	13.5595i	−0.662721	+	0.469808i
$834$	−65.2605	−	31.8295i	−2.25979	−	1.10216i
$835$		−	0.350738i		−	0.0121378i
$836$	0.211557	−	0.165288i	0.00731684	−	0.00571660i
$837$			7.30341i			0.252443i
$838$	−40.1033	−	19.5595i	−1.38534	−	0.675673i
$839$		−	37.2470i		−	1.28591i	−0.765904	−	0.642955i	$-0.777708\pi$
$839$		−	37.2470i		−	1.28591i	0.765904	−	0.642955i	$-0.222292\pi$
$840$	−9.61755	+	2.04435i	−0.331837	+	0.0705369i
$841$	−19.4995			−0.672397
$842$	−21.2828	+	43.6365i	−0.733453	+	1.50381i
$843$	−54.6960			−1.88383
$844$	0.106399	+	0.136183i	0.00366240	+	0.00468761i
$845$	−17.1005			−0.588276
$846$	23.6761	+	11.5475i	0.814000	+	0.397012i
$847$			11.4070i			0.391948i
$848$	−52.2562	−	13.0284i	−1.79449	−	0.447395i
$849$	−60.4648			−2.07515
$850$	5.75376	−	0.945646i	0.197352	−	0.0324354i
$851$			18.4433i			0.632230i
$852$	−31.6706	+	24.7441i	−1.08502	+	0.847718i
$853$	23.8943			0.818125			0.409062	−	0.912506i	$-0.365856\pi$
$853$	23.8943			0.818125			0.409062	+	0.912506i	$0.365856\pi$
$854$	−2.64572	+	5.42456i	−0.0905345	+	0.185625i
$855$		−	0.813350i		−	0.0278160i
$856$	−8.08408	−	38.0311i	−0.276308	−	1.29988i
$857$		−	22.7277i		−	0.776363i	−0.921583	−	0.388181i	$-0.873103\pi$
$857$		−	22.7277i		−	0.776363i	0.921583	−	0.388181i	$-0.126897\pi$
$858$	−10.5566	+	21.6445i	−0.360398	+	0.738930i
$859$			48.5724i			1.65727i	0.559790	+	0.828635i	$0.310882\pi$
$859$			48.5724i			1.65727i	−0.559790	+	0.828635i	$0.689118\pi$
$860$	−15.1964	+	11.8728i	−0.518192	+	0.404860i
$861$	21.2100			0.722836
$862$	−14.6746	+	30.0875i	−0.499818	+	1.02478i
$863$	32.4151			1.10342			0.551711	−	0.834035i	$-0.313975\pi$
$863$	32.4151			1.10342			0.551711	+	0.834035i	$0.313975\pi$
$864$	35.2936	−	42.0624i	1.20071	−	1.43099i
$865$	−21.6007			−0.734447
$866$	44.6016	+	21.7535i	1.51562	+	0.739214i
$867$	17.0713	−	48.6560i	0.579770	−	1.65244i
$868$	1.06184	+	1.35908i	0.0360412	+	0.0461301i
$869$		−	14.0466i		−	0.476498i
$870$	−11.8835	−	5.79594i	−0.402889	−	0.196501i
$871$	−20.4329			−0.692342
$872$	9.88257	+	46.4920i	0.334666	+	1.57442i
$873$		−	23.1359i		−	0.783032i
$874$	0.398445	+	0.194333i	0.0134776	+	0.00657343i
$875$		−	1.14609i		−	0.0387450i
$876$	71.3581	−	55.7517i	2.41097	−	1.88367i
$877$	−48.4637			−1.63650			−0.818252	−	0.574860i	$-0.805056\pi$
$877$	−48.4637			−1.63650			−0.818252	+	0.574860i	$0.805056\pi$
$878$	−14.8637	+	30.4752i	−0.501624	+	1.02849i
$879$			22.9893i			0.775410i
$880$	−0.990158	+	3.97149i	−0.0333782	+	0.133879i
$881$		−	19.3636i		−	0.652377i	−0.945305	−	0.326188i	$-0.894236\pi$
$881$		−	19.3636i		−	0.652377i	0.945305	−	0.326188i	$-0.105764\pi$
$882$	−44.8144	−	21.8573i	−1.50898	−	0.735974i
$883$			48.0780i			1.61795i	0.587841	+	0.808977i	$0.299978\pi$
$883$			48.0780i			1.61795i	−0.587841	+	0.808977i	$0.700022\pi$
$884$	−12.9755	+	43.3414i	−0.436412	+	1.45773i
$885$			30.3474i			1.02012i
$886$	1.85119	−	3.79553i	0.0621921	−	0.127513i
$887$			57.0934i			1.91701i	0.285078	+	0.958504i	$0.407981\pi$
$887$			57.0934i			1.91701i	−0.285078	+	0.958504i	$0.592019\pi$
$888$	13.7677	+	64.7694i	0.462014	+	2.17352i
$889$		−	10.9276i		−	0.366501i
$890$	4.63197	+	2.25915i	0.155264	+	0.0757268i
$891$	11.0932			0.371636
$892$	30.1329	+	38.5680i	1.00893	+	1.29135i
$893$			0.394106i			0.0131883i
$894$	−22.1472	+	45.4087i	−0.740712	+	1.51869i
$895$			20.4689i			0.684198i
$896$	0.452287	−	12.9587i	0.0151098	−	0.432918i
$897$	−39.7647			−1.32771
$898$	−14.8488	+	30.4448i	−0.495511	+	1.01595i
$899$			2.31920i			0.0773496i
$900$	7.63438	+	9.77146i	0.254479	+	0.325715i
$901$	−32.1050	−	45.2879i	−1.06957	−	1.50876i
$902$	3.87051	−	7.93578i	0.128874	−	0.264233i
$903$	33.5193			1.11545
$904$	−7.00185	+	1.48835i	−0.232878	+	0.0495017i
$905$	−10.2177			−0.339646
$906$	−11.1830	−	5.45426i	−0.371529	−	0.181206i
$907$	2.35855			0.0783144			0.0391572	−	0.999233i	$-0.487533\pi$
$907$	2.35855			0.0783144			0.0391572	+	0.999233i	$0.487533\pi$
$908$	−1.79555	−	2.29818i	−0.0595874	−	0.0762676i
$909$			74.5448i			2.47249i
$910$	7.99249	+	3.89817i	0.264949	+	0.129223i
$911$		−	36.5217i		−	1.21002i	−0.796218	−	0.605009i	$-0.793169\pi$
$911$		−	36.5217i		−	1.21002i	0.796218	−	0.605009i	$-0.206831\pi$
$912$	1.54433	+	0.385027i	0.0511379	+	0.0127495i
$913$		−	3.94204i		−	0.130463i
$914$	23.6856	+	11.5522i	0.783450	+	0.382111i
$915$	11.2945			0.373384
$916$	−24.5456	+	19.1773i	−0.811009	+	0.633637i
$917$			21.1042i			0.696922i
$918$	55.8486	−	9.17887i	1.84328	−	0.302948i
$919$	28.1923			0.929978			0.464989	−	0.885317i	$-0.346058\pi$
$919$	28.1923			0.929978			0.464989	+	0.885317i	$0.346058\pi$
$920$	−6.61094	+	1.40525i	−0.217956	+	0.0463298i
$921$			60.1356i			1.98153i
$922$	8.64875	−	17.7327i	0.284832	−	0.583995i
$923$	36.3485			1.19643
$924$	5.60614	−	4.38004i	0.184428	−	0.144093i
$925$	−7.71836			−0.253778
$926$	26.4656	+	12.9081i	0.869714	+	0.424185i
$927$	−22.4155			−0.736222
$928$	11.2075	−	13.3569i	0.367904	−	0.438463i
$929$			13.5645i			0.445038i	0.974928	+	0.222519i	$0.0714280\pi$
$929$			13.5645i			0.445038i	−0.974928	+	0.222519i	$0.928572\pi$
$930$	1.41487	−	2.90093i	0.0463953	−	0.0951252i
$931$		−	0.745970i		−	0.0244482i
$932$	43.3359	−	33.8581i	1.41951	−	1.10906i
$933$			50.8997i			1.66638i
$934$	−10.2013	+	20.9159i	−0.333797	+	0.684390i
$935$	−3.44190	+	2.43999i	−0.112562	+	0.0797961i
$936$	−94.1098	+	20.0044i	−3.07608	+	0.653865i
$937$	−36.5498			−1.19403			−0.597015	−	0.802230i	$-0.703647\pi$
$937$	−36.5498			−1.19403			−0.597015	+	0.802230i	$0.703647\pi$
$938$	5.42547	+	2.64616i	0.177148	+	0.0864003i
$939$		−	30.7473i		−	1.00340i
$940$	−3.69922	−	4.73473i	−0.120655	−	0.154430i
$941$	−12.6597			−0.412695			−0.206347	−	0.978479i	$-0.566158\pi$
$941$	−12.6597			−0.412695			−0.206347	+	0.978479i	$0.566158\pi$
$942$	17.1828	−	35.2303i	0.559847	−	1.14787i
$943$	14.5794			0.474772
$944$	−38.8321	−	9.68150i	−1.26388	−	0.315106i
$945$		−	11.1245i		−	0.361880i
$946$	6.11677	−	12.5413i	0.198873	−	0.407753i
$947$	−15.4599			−0.502378			−0.251189	−	0.967938i	$-0.580822\pi$
$947$	−15.4599			−0.502378			−0.251189	+	0.967938i	$0.580822\pi$
$948$	65.6205	−	51.2689i	2.13126	−	1.66514i
$949$	−81.8981			−2.65852
$950$	−0.0813267	+	0.166745i	−0.00263859	+	0.00540994i
$951$	49.6393			1.60966
$952$	9.05826	−	9.82789i	0.293580	−	0.318524i
$953$	36.0503			1.16778			0.583891	−	0.811832i	$-0.301529\pi$
$953$	36.0503			1.16778			0.583891	+	0.811832i	$0.301529\pi$
$954$	51.7519	−	106.108i	1.67553	−	3.43537i
$955$	−10.7086			−0.346522
$956$	30.3474	+	38.8425i	0.981505	+	1.25626i
$957$	9.56660			0.309244
$958$	−3.07101	+	6.29654i	−0.0992197	+	0.203432i
$959$			15.1125i			0.488007i
$960$	−22.1673	+	9.86995i	−0.715448	+	0.318551i
$961$	30.4339			0.981737
$962$	26.2523	−	53.8255i	0.846407	−	1.73540i
$963$	85.2294			2.74648
$964$	−7.78813	+	6.08482i	−0.250839	+	0.195979i
$965$		−	5.68548i		−	0.183022i
$966$	10.5586	+	5.14974i	0.339717	+	0.165690i
$967$	−41.1709			−1.32397			−0.661984	−	0.749518i	$-0.730285\pi$
$967$	−41.1709			−1.32397			−0.661984	+	0.749518i	$0.730285\pi$
$968$	5.85317	+	27.5359i	0.188128	+	0.885038i
$969$	0.948799	+	1.33840i	0.0304798	+	0.0429955i
$970$	−2.31335	+	4.74311i	−0.0742773	+	0.152292i
$971$			28.5053i			0.914777i	0.889267	+	0.457389i	$0.151215\pi$
$971$			28.5053i			0.914777i	−0.889267	+	0.457389i	$0.848785\pi$
$972$	4.63373	+	5.93084i	0.148627	+	0.190232i
$973$		−	19.3998i		−	0.621930i
$974$	−23.9496	+	49.1042i	−0.767393	+	1.57340i
$975$		−	16.6412i		−	0.532944i
$976$	−3.60318	+	14.4522i	−0.115335	+	0.462604i
$977$	−15.7285			−0.503198			−0.251599	−	0.967832i	$-0.580956\pi$
$977$	−15.7285			−0.503198			−0.251599	+	0.967832i	$0.580956\pi$
$978$	−86.0992	−	41.9931i	−2.75315	−	1.34279i
$979$	−3.72888			−0.119175
$980$	7.00193	+	8.96197i	0.223669	+	0.286280i
$981$	−104.191			−3.32655
$982$	21.2904	−	43.6522i	0.679405	−	1.39300i
$983$		−	24.3987i		−	0.778196i	−0.921196	−	0.389098i	$-0.872787\pi$
$983$		−	24.3987i		−	0.778196i	0.921196	−	0.389098i	$-0.127213\pi$
$984$	51.2001	−	10.8833i	1.63220	−	0.346948i
$985$	−18.1950			−0.579741
$986$	17.7347	−	2.91475i	0.564789	−	0.0928246i
$987$			10.4436i			0.332424i
$988$	−0.886217	−	1.13429i	−0.0281943	−	0.0360867i
$989$	23.0406			0.732649
$990$	−8.06423	−	3.93316i	−0.256298	−	0.125004i
$991$			6.73788i			0.214036i	0.994257	+	0.107018i	$0.0341302\pi$
$991$			6.73788i			0.214036i	−0.994257	+	0.107018i	$0.965870\pi$
$992$	3.26061	+	2.73590i	0.103524	+	0.0868649i
$993$		−	76.7940i		−	2.43698i
$994$	−9.65150	−	4.70732i	−0.306127	−	0.149307i
$995$			6.43510i			0.204007i
$996$	18.4158	−	14.3881i	0.583527	−	0.455906i
$997$	49.0657			1.55393			0.776964	−	0.629545i	$-0.216759\pi$
$997$	49.0657			1.55393			0.776964	+	0.629545i	$0.216759\pi$
$998$	−15.7087	−	7.66158i	−0.497249	−	0.242523i
$999$	−74.9180			−2.37030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.a.101.5	✓	36
4.3	odd	2		2720.2.l.b.2481.2		36
8.3	odd	2		2720.2.l.a.2481.36		36
8.5	even	2		680.2.l.b.101.6	yes	36
17.16	even	2		680.2.l.b.101.5	yes	36
68.67	odd	2		2720.2.l.a.2481.35		36
136.67	odd	2		2720.2.l.b.2481.1		36
136.101	even	2	inner	680.2.l.a.101.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.5	✓	36	1.1	even	1	trivial
680.2.l.a.101.6	yes	36	136.101	even	2	inner
680.2.l.b.101.5	yes	36	17.16	even	2
680.2.l.b.101.6	yes	36	8.5	even	2
2720.2.l.a.2481.35		36	68.67	odd	2
2720.2.l.a.2481.36		36	8.3	odd	2
2720.2.l.b.2481.1		36	136.67	odd	2
2720.2.l.b.2481.2		36	4.3	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27109 - 0.619947i) q^{2} +3.03317 q^{3} +(1.23133 + 1.57602i) q^{4} +1.00000 q^{5} +(-3.85542 - 1.88040i) q^{6} -1.14609i q^{7} +(-0.588085 - 2.76661i) q^{8} +6.20011 q^{9} +(-1.27109 - 0.619947i) q^{10} +1.02326 q^{11} +(3.73483 + 4.78032i) q^{12} -5.48640i q^{13} +(-0.710516 + 1.45678i) q^{14} +3.03317 q^{15} +(-0.967647 + 3.88119i) q^{16} +(-3.36364 + 2.38451i) q^{17} +(-7.88088 - 3.84374i) q^{18} -0.131183i q^{19} +(1.23133 + 1.57602i) q^{20} -3.47629i q^{21} +(-1.30066 - 0.634370i) q^{22} -2.38954i q^{23} +(-1.78376 - 8.39161i) q^{24} +1.00000 q^{25} +(-3.40127 + 6.97369i) q^{26} +9.70646 q^{27} +(1.80626 - 1.41122i) q^{28} +3.08229 q^{29} +(-3.85542 - 1.88040i) q^{30} +0.752428i q^{31} +(3.63610 - 4.33345i) q^{32} +3.10373 q^{33} +(5.75376 - 0.945646i) q^{34} -1.14609i q^{35} +(7.63438 + 9.77146i) q^{36} -7.71836 q^{37} +(-0.0813267 + 0.166745i) q^{38} -16.6412i q^{39} +(-0.588085 - 2.76661i) q^{40} +6.10135i q^{41} +(-2.15511 + 4.41867i) q^{42} +9.64227i q^{43} +(1.25998 + 1.61268i) q^{44} +6.20011 q^{45} +(-1.48139 + 3.03732i) q^{46} -3.00424 q^{47} +(-2.93503 + 11.7723i) q^{48} +5.68647 q^{49} +(-1.27109 - 0.619947i) q^{50} +(-10.2025 + 7.23263i) q^{51} +(8.64664 - 6.75557i) q^{52} +13.4640i q^{53} +(-12.3378 - 6.01749i) q^{54} +1.02326 q^{55} +(-3.17079 + 0.673999i) q^{56} -0.397901i q^{57} +(-3.91786 - 1.91086i) q^{58} +10.0052i q^{59} +(3.73483 + 4.78032i) q^{60} +3.72365 q^{61} +(0.466465 - 0.956402i) q^{62} -7.10589i q^{63} +(-7.30831 + 3.25401i) q^{64} -5.48640i q^{65} +(-3.94512 - 1.92415i) q^{66} -3.72428i q^{67} +(-7.89979 - 2.36503i) q^{68} -7.24788i q^{69} +(-0.710516 + 1.45678i) q^{70} +6.62521i q^{71} +(-3.64619 - 17.1533i) q^{72} -14.9275i q^{73} +(9.81072 + 4.78498i) q^{74} +3.03317 q^{75} +(0.206747 - 0.161530i) q^{76} -1.17275i q^{77} +(-10.3166 + 21.1524i) q^{78} -13.7272i q^{79} +(-0.967647 + 3.88119i) q^{80} +10.8410 q^{81} +(3.78251 - 7.75535i) q^{82} -3.85242i q^{83} +(5.47868 - 4.28046i) q^{84} +(-3.36364 + 2.38451i) q^{85} +(5.97770 - 12.2562i) q^{86} +9.34909 q^{87} +(-0.601766 - 2.83098i) q^{88} -3.64410 q^{89} +(-7.88088 - 3.84374i) q^{90} -6.28791 q^{91} +(3.76595 - 2.94232i) q^{92} +2.28224i q^{93} +(3.81866 + 1.86247i) q^{94} -0.131183i q^{95} +(11.0289 - 13.1441i) q^{96} -3.73153i q^{97} +(-7.22801 - 3.52531i) q^{98} +6.34435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) \) 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Introduction

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