LMFDB - Embedded newform 570.2.bh.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.b.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.21625 - 0.297081i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.959162 + 3.57964i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.21625 - 0.297081i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.959162 + 3.57964i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(2.18192 + 0.489109i) q^{10} +(0.301385 + 0.522015i) q^{11} +(0.965926 - 0.258819i) q^{12} +(2.53874 - 5.44435i) q^{13} +(-0.643525 - 3.64961i) q^{14} +(-2.13415 + 0.667379i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.594237 + 6.79216i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-0.257928 + 4.35126i) q^{19} +(-2.13099 - 0.677415i) q^{20} +(2.38212 + 2.83890i) q^{21} +(-0.254742 - 0.546296i) q^{22} +(-3.71259 + 2.59958i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(4.82349 + 1.31681i) q^{25} +(-3.00359 + 5.20237i) q^{26} +(0.258819 - 0.965926i) q^{27} +(0.322992 + 3.69181i) q^{28} +(5.26072 + 4.41427i) q^{29} +(2.18420 - 0.478835i) q^{30} +(1.89616 + 1.09475i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(0.493761 + 0.345735i) q^{33} +(1.18395 - 6.71452i) q^{34} +(-1.06229 - 8.21831i) q^{35} +(0.766044 - 0.642788i) q^{36} +(6.54922 + 6.54922i) q^{37} +(0.636184 - 4.31222i) q^{38} -6.00718i q^{39} +(2.06384 + 0.860565i) q^{40} +(3.84091 - 10.5528i) q^{41} +(-2.12563 - 3.03571i) q^{42} +(-5.03066 + 7.18452i) q^{43} +(0.206160 + 0.566419i) q^{44} +(-1.65215 + 1.50678i) q^{45} +(3.92503 - 2.26612i) q^{46} +(1.27160 - 0.111250i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(-5.83165 + 3.36690i) q^{49} +(-4.69036 - 1.73219i) q^{50} +(2.33193 + 6.40692i) q^{51} +(3.44558 - 4.92079i) q^{52} +(1.44827 + 2.06835i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-0.512863 - 1.24645i) q^{55} -3.70592i q^{56} +(1.60516 + 4.05259i) q^{57} +(-4.85597 - 4.85597i) q^{58} +(5.80010 - 4.86686i) q^{59} +(-2.21762 + 0.286648i) q^{60} +(1.63239 - 9.25773i) q^{61} +(-1.79353 - 1.25584i) q^{62} +(3.35870 + 1.56619i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-7.24390 + 11.3118i) q^{65} +(-0.461749 - 0.387454i) q^{66} +(0.585736 + 6.69499i) q^{67} +(-1.76466 + 6.58578i) q^{68} +(-2.26612 + 3.92503i) q^{69} +(0.341978 + 8.27962i) q^{70} +(-5.37368 + 0.947524i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(2.89794 + 6.21466i) q^{73} +(-5.95350 - 7.09510i) q^{74} +(4.92807 - 0.845058i) q^{75} +(-1.00960 + 4.24037i) q^{76} +(-1.57955 + 1.57955i) q^{77} +(-0.523560 + 5.98432i) q^{78} +(-10.8234 - 3.93939i) q^{79} +(-1.98098 - 1.03717i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.74603 + 10.1779i) q^{82} +(8.52857 - 2.28522i) q^{83} +(1.85296 + 3.20942i) q^{84} +(3.33480 - 14.8766i) q^{85} +(5.63769 - 6.71873i) q^{86} +(6.63338 + 1.77741i) q^{87} +(-0.156009 - 0.582232i) q^{88} +(-0.733198 + 0.266862i) q^{89} +(1.77719 - 1.35705i) q^{90} +(21.9239 + 3.86577i) q^{91} +(-4.10760 + 1.91541i) q^{92} +(2.18116 + 0.190827i) q^{93} -1.27645 q^{94} +(1.86431 - 9.56684i) q^{95} -1.00000 q^{96} +(-19.4079 - 1.69797i) q^{97} +(6.10290 - 2.84583i) q^{98} +(0.593613 + 0.104670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	0.906308	−	0.422618i	0.523257	−	0.243999i
$3$	0.906308	−	0.422618i	0.523257	−	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−2.21625	−	0.297081i	−0.991135	−	0.132859i
$5$	−2.21625	−	0.297081i	−0.991135	−	0.132859i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	0.959162	+	3.57964i	0.362529	+	1.35298i	0.870740	+	0.491744i	$0.163640\pi$
$7$	0.959162	+	3.57964i	0.362529	+	1.35298i	−0.508211	+	0.861233i	$0.669693\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	2.18192	+	0.489109i	0.689983	+	0.154670i
$11$	0.301385	+	0.522015i	0.0908711	+	0.157393i	0.907878	−	0.419235i	$-0.137702\pi$
$11$	0.301385	+	0.522015i	0.0908711	+	0.157393i	−0.817007	+	0.576628i	$0.804368\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	2.53874	−	5.44435i	0.704121	−	1.50999i	−0.149312	−	0.988790i	$-0.547706\pi$
$13$	2.53874	−	5.44435i	0.704121	−	1.50999i	0.853433	−	0.521202i	$-0.174516\pi$
$14$	−0.643525	−	3.64961i	−0.171989	−	0.975400i
$15$	−2.13415	+	0.667379i	−0.551036	+	0.172316i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.594237	+	6.79216i	−0.144124	+	1.64734i	0.488269	+	0.872693i	$0.337628\pi$
$17$	−0.594237	+	6.79216i	−0.144124	+	1.64734i	−0.632393	+	0.774648i	$0.717927\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−0.257928	+	4.35126i	−0.0591728	+	0.998248i
$19$	−0.257928	+	4.35126i	−0.0591728	+	0.998248i
$20$	−2.13099	−	0.677415i	−0.476503	−	0.151475i
$21$	2.38212	+	2.83890i	0.519820	+	0.619498i
$22$	−0.254742	−	0.546296i	−0.0543112	−	0.116471i
$23$	−3.71259	+	2.59958i	−0.774129	+	0.542051i	−0.892569	−	0.450910i	$-0.851099\pi$
$23$	−3.71259	+	2.59958i	−0.774129	+	0.542051i	0.118440	+	0.992961i	$0.462211\pi$
$24$	−0.984808	+	0.173648i	−0.201023	+	0.0354458i
$25$	4.82349	+	1.31681i	0.964697	+	0.263362i
$26$	−3.00359	+	5.20237i	−0.589053	+	1.02027i
$27$	0.258819	−	0.965926i	0.0498097	−	0.185893i
$28$	0.322992	+	3.69181i	0.0610397	+	0.697687i
$29$	5.26072	+	4.41427i	0.976891	+	0.819709i	0.983617	−	0.180269i	$-0.0576967\pi$
$29$	5.26072	+	4.41427i	0.976891	+	0.819709i	−0.00672665	+	0.999977i	$0.502141\pi$
$30$	2.18420	−	0.478835i	0.398778	−	0.0874230i
$31$	1.89616	+	1.09475i	0.340560	+	0.196622i	0.660520	−	0.750809i	$-0.270336\pi$
$31$	1.89616	+	1.09475i	0.340560	+	0.196622i	−0.319960	+	0.947431i	$0.603669\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	0.493761	+	0.345735i	0.0859528	+	0.0601848i
$34$	1.18395	−	6.71452i	0.203046	−	1.15153i
$35$	−1.06229	−	8.21831i	−0.179560	−	1.38915i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	6.54922	+	6.54922i	1.07669	+	1.07669i	0.996804	+	0.0798809i	$0.0254540\pi$
$37$	6.54922	+	6.54922i	1.07669	+	1.07669i	0.0798809	+	0.996804i	$0.474546\pi$
$38$	0.636184	−	4.31222i	0.103203	−	0.699535i
$39$		−	6.00718i		−	0.961919i
$40$	2.06384	+	0.860565i	0.326321	+	0.136067i
$41$	3.84091	−	10.5528i	0.599849	−	1.64807i	−0.151726	−	0.988423i	$-0.548483\pi$
$41$	3.84091	−	10.5528i	0.599849	−	1.64807i	0.751575	−	0.659648i	$-0.229295\pi$
$42$	−2.12563	−	3.03571i	−0.327991	−	0.468420i
$43$	−5.03066	+	7.18452i	−0.767168	+	1.09563i	0.225439	+	0.974257i	$0.427618\pi$
$43$	−5.03066	+	7.18452i	−0.767168	+	1.09563i	−0.992607	+	0.121372i	$0.961271\pi$
$44$	0.206160	+	0.566419i	0.0310798	+	0.0853909i
$45$	−1.65215	+	1.50678i	−0.246288	+	0.224618i
$46$	3.92503	−	2.26612i	0.578715	−	0.334121i
$47$	1.27160	−	0.111250i	0.185481	−	0.0162275i	0.00596349	−	0.999982i	$-0.498102\pi$
$47$	1.27160	−	0.111250i	0.185481	−	0.0162275i	0.179518	+	0.983755i	$0.442546\pi$
$48$	0.996195	−	0.0871557i	0.143788	−	0.0125798i
$49$	−5.83165	+	3.36690i	−0.833093	+	0.480986i
$50$	−4.69036	−	1.73219i	−0.663318	−	0.244969i
$51$	2.33193	+	6.40692i	0.326535	+	0.897149i
$52$	3.44558	−	4.92079i	0.477816	−	0.682391i
$53$	1.44827	+	2.06835i	0.198936	+	0.284110i	0.906208	−	0.422831i	$-0.138964\pi$
$53$	1.44827	+	2.06835i	0.198936	+	0.284110i	−0.707273	+	0.706941i	$0.750075\pi$
$54$	−0.342020	+	0.939693i	−0.0465430	+	0.127876i
$55$	−0.512863	−	1.24645i	−0.0691545	−	0.168071i
$56$		−	3.70592i		−	0.495224i
$57$	1.60516	+	4.05259i	0.212609	+	0.536778i
$58$	−4.85597	−	4.85597i	−0.637620	−	0.637620i
$59$	5.80010	−	4.86686i	0.755108	−	0.633611i	−0.181740	−	0.983347i	$-0.558173\pi$
$59$	5.80010	−	4.86686i	0.755108	−	0.633611i	0.936848	+	0.349736i	$0.113729\pi$
$60$	−2.21762	+	0.286648i	−0.286293	+	0.0370061i
$61$	1.63239	−	9.25773i	0.209006	−	1.18533i	−0.682004	−	0.731348i	$-0.738891\pi$
$61$	1.63239	−	9.25773i	0.209006	−	1.18533i	0.891010	−	0.453983i	$-0.149997\pi$
$62$	−1.79353	−	1.25584i	−0.227778	−	0.159492i
$63$	3.35870	+	1.56619i	0.423156	+	0.197321i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−7.24390	+	11.3118i	−0.898495	+	1.40306i
$66$	−0.461749	−	0.387454i	−0.0568374	−	0.0476922i
$67$	0.585736	+	6.69499i	0.0715590	+	0.817923i	0.944160	+	0.329489i	$0.106876\pi$
$67$	0.585736	+	6.69499i	0.0715590	+	0.817923i	−0.872601	+	0.488435i	$0.837568\pi$
$68$	−1.76466	+	6.58578i	−0.213996	+	0.798644i
$69$	−2.26612	+	3.92503i	−0.272809	+	0.472518i
$70$	0.341978	+	8.27962i	0.0408742	+	0.989604i
$71$	−5.37368	+	0.947524i	−0.637738	+	0.112450i	−0.483163	−	0.875531i	$-0.660512\pi$
$71$	−5.37368	+	0.947524i	−0.637738	+	0.112450i	−0.154575	+	0.987981i	$0.549401\pi$
$72$	−0.819152	+	0.573576i	−0.0965380	+	0.0675966i
$73$	2.89794	+	6.21466i	0.339178	+	0.727370i	0.999726	−	0.0234139i	$-0.00745354\pi$
$73$	2.89794	+	6.21466i	0.339178	+	0.727370i	−0.660547	+	0.750784i	$0.729676\pi$
$74$	−5.95350	−	7.09510i	−0.692080	−	0.824789i
$75$	4.92807	−	0.845058i	0.569045	−	0.0975789i
$76$	−1.00960	+	4.24037i	−0.115809	+	0.486403i
$77$	−1.57955	+	1.57955i	−0.180006	+	0.180006i
$78$	−0.523560	+	5.98432i	−0.0592815	+	0.677591i
$79$	−10.8234	−	3.93939i	−1.21773	−	0.443216i	−0.348349	−	0.937365i	$-0.613258\pi$
$79$	−10.8234	−	3.93939i	−1.21773	−	0.443216i	−0.869377	+	0.494149i	$0.835480\pi$
$80$	−1.98098	−	1.03717i	−0.221480	−	0.115959i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	−4.74603	+	10.1779i	−0.524111	+	1.12396i
$83$	8.52857	−	2.28522i	0.936132	−	0.250836i	0.241665	−	0.970360i	$-0.422307\pi$
$83$	8.52857	−	2.28522i	0.936132	−	0.250836i	0.694468	+	0.719524i	$0.255640\pi$
$84$	1.85296	+	3.20942i	0.202174	+	0.350176i
$85$	3.33480	−	14.8766i	0.361710	−	1.61359i
$86$	5.63769	−	6.71873i	0.607927	−	0.724500i
$87$	6.63338	+	1.77741i	0.711173	+	0.190558i
$88$	−0.156009	−	0.582232i	−0.0166306	−	0.0620661i
$89$	−0.733198	+	0.266862i	−0.0777188	+	0.0282873i	−0.380587	−	0.924745i	$-0.624278\pi$
$89$	−0.733198	+	0.266862i	−0.0777188	+	0.0282873i	0.302868	+	0.953032i	$0.402056\pi$
$90$	1.77719	−	1.35705i	0.187332	−	0.143046i
$91$	21.9239	+	3.86577i	2.29825	+	0.405243i
$92$	−4.10760	+	1.91541i	−0.428247	+	0.199695i
$93$	2.18116	+	0.190827i	0.226176	+	0.0197878i
$94$	−1.27645			−0.131656
$95$	1.86431	−	9.56684i	0.191274	−	0.981537i
$96$	−1.00000			−0.102062
$97$	−19.4079	−	1.69797i	−1.97058	−	0.172403i	−0.972426	−	0.233212i	$-0.925076\pi$
$97$	−19.4079	−	1.69797i	−1.97058	−	0.172403i	−0.998149	+	0.0608094i	$0.980632\pi$
$98$	6.10290	−	2.84583i	0.616486	−	0.287472i
$99$	0.593613	+	0.104670i	0.0596604	+	0.0105197i
$100$	4.52154	+	2.13439i	0.452154	+	0.213439i
$101$	−1.21036	+	0.440535i	−0.120435	+	0.0438349i	−0.401535	−	0.915844i	$-0.631523\pi$
$101$	−1.21036	+	0.440535i	−0.120435	+	0.0438349i	0.281099	+	0.959679i	$0.409301\pi$
$102$	−1.76466	−	6.58578i	−0.174727	−	0.652090i
$103$	4.39737	+	1.17827i	0.433286	+	0.116099i	0.468868	−	0.883268i	$-0.344662\pi$
$103$	4.39737	+	1.17827i	0.433286	+	0.116099i	−0.0355823	+	0.999367i	$0.511329\pi$
$104$	−3.86134	+	4.60177i	−0.378636	+	0.451240i
$105$	−4.43597	−	6.99937i	−0.432907	−	0.683069i
$106$	−1.26249	−	2.18670i	−0.122624	−	0.212391i
$107$	−2.12073	+	0.568249i	−0.205019	+	0.0549347i	−0.359867	−	0.933004i	$-0.617178\pi$
$107$	−2.12073	+	0.568249i	−0.205019	+	0.0549347i	0.154848	+	0.987938i	$0.450511\pi$
$108$	0.422618	−	0.906308i	0.0406665	−	0.0872095i
$109$	−1.39974	−	7.93832i	−0.134071	−	0.760353i	−0.975502	−	0.219989i	$-0.929398\pi$
$109$	−1.39974	−	7.93832i	−0.134071	−	0.760353i	0.841432	−	0.540364i	$-0.181713\pi$
$110$	0.402276	+	1.28640i	0.0383555	+	0.122654i
$111$	8.70343	+	3.16779i	0.826093	+	0.300673i
$112$	−0.322992	+	3.69181i	−0.0305199	+	0.348844i
$113$	−2.79902	+	2.79902i	−0.263310	+	0.263310i	−0.826397	−	0.563087i	$-0.809613\pi$
$113$	−2.79902	+	2.79902i	−0.263310	+	0.263310i	0.563087	+	0.826397i	$0.309613\pi$
$114$	−1.24585	−	4.17706i	−0.116684	−	0.391218i
$115$	9.00030	−	4.65838i	0.839282	−	0.434396i
$116$	4.41427	+	5.26072i	0.409854	+	0.488445i
$117$	−2.53874	−	5.44435i	−0.234707	−	0.503331i
$118$	−6.20220	+	4.34283i	−0.570959	+	0.399790i
$119$	−24.8835	+	4.38762i	−2.28106	+	0.402213i
$120$	2.23416	−	0.0922790i	0.203950	−	0.00842388i
$121$	5.31833	−	9.21162i	0.483485	−	0.837420i
$122$	−2.43304	+	9.08023i	−0.220277	+	0.822086i
$123$	−0.978764	−	11.1873i	−0.0882522	−	1.00873i
$124$	1.67725	+	1.40738i	0.150621	+	0.126386i
$125$	−10.2988	−	4.35134i	−0.921155	−	0.389196i
$126$	−3.20942	−	1.85296i	−0.285918	−	0.165075i
$127$	−18.5846	−	8.66613i	−1.64911	−	0.768995i	−0.999965	−	0.00833308i	$-0.997347\pi$
$127$	−18.5846	−	8.66613i	−1.64911	−	0.768995i	−0.649149	−	0.760661i	$-0.724875\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	−1.52301	+	8.63744i	−0.134094	+	0.760484i
$130$	8.20222	−	10.6374i	0.719382	−	0.932963i
$131$	−12.2709	+	10.2965i	−1.07211	+	0.899611i	−0.995242	−	0.0974297i	$-0.968938\pi$
$131$	−12.2709	+	10.2965i	−1.07211	+	0.899611i	−0.0768725	+	0.997041i	$0.524493\pi$
$132$	0.426223	+	0.426223i	0.0370980	+	0.0370980i
$133$	−15.8233	+	3.25027i	−1.37206	+	0.281834i
$134$		−	6.72056i		−	0.580568i
$135$	−0.860565	+	2.06384i	−0.0740656	+	0.177627i
$136$	2.33193	−	6.40692i	0.199961	−	0.549389i
$137$	5.24406	+	7.48930i	0.448031	+	0.639854i	0.978109	−	0.208095i	$-0.0667263\pi$
$137$	5.24406	+	7.48930i	0.448031	+	0.639854i	−0.530078	+	0.847949i	$0.677837\pi$
$138$	2.59958	−	3.71259i	0.221291	−	0.316037i
$139$	3.97741	+	10.9278i	0.337359	+	0.926887i	0.986141	+	0.165912i	$0.0530568\pi$
$139$	3.97741	+	10.9278i	0.337359	+	0.926887i	−0.648781	+	0.760975i	$0.724721\pi$
$140$	0.380939	−	8.27792i	0.0321953	−	0.699612i
$141$	1.10544	−	0.638227i	0.0930950	−	0.0537484i
$142$	5.43581	−	0.475572i	0.456163	−	0.0399091i
$143$	3.60717	−	0.315587i	0.301647	−	0.0263907i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−10.3476	−	11.3460i	−0.859325	−	0.942230i
$146$	−2.34527	−	6.44358i	−0.194096	−	0.533274i
$147$	−3.86235	+	5.51601i	−0.318562	+	0.454953i
$148$	5.31246	+	7.58698i	0.436682	+	0.623646i
$149$	5.08316	−	13.9659i	0.416429	−	1.14413i	−0.537282	−	0.843403i	$-0.680549\pi$
$149$	5.08316	−	13.9659i	0.416429	−	1.14413i	0.953711	−	0.300726i	$-0.0972289\pi$
$150$	−4.98297	+	0.412333i	−0.406858	+	0.0336668i
$151$		−	17.3864i		−	1.41488i	−0.706773	−	0.707441i	$-0.749850\pi$
$151$		−	17.3864i		−	1.41488i	0.706773	−	0.707441i	$-0.250150\pi$
$152$	1.37533	−	4.13624i	0.111554	−	0.335493i
$153$	4.82113	+	4.82113i	0.389765	+	0.389765i
$154$	1.71120	−	1.43587i	0.137893	−	0.115706i
$155$	−3.87712	−	2.98954i	−0.311418	−	0.240126i
$156$	1.04314	−	5.91592i	0.0835177	−	0.473653i
$157$	−2.27550	−	1.59332i	−0.181605	−	0.127161i	0.479239	−	0.877684i	$-0.340913\pi$
$157$	−2.27550	−	1.59332i	−0.181605	−	0.127161i	−0.660844	+	0.750523i	$0.729801\pi$
$158$	10.4389	+	4.86772i	0.830471	+	0.387255i
$159$	2.18670	+	1.26249i	0.173417	+	0.100122i
$160$	1.88305	+	1.20587i	0.148868	+	0.0953326i
$161$	−12.8666	−	10.7963i	−1.01403	−	0.850869i
$162$	0.0871557	+	0.996195i	0.00684760	+	0.0782684i
$163$	2.17622	−	8.12177i	0.170455	−	0.636146i	−0.826826	−	0.562457i	$-0.809856\pi$
$163$	2.17622	−	8.12177i	0.170455	−	0.636146i	0.997281	−	0.0736892i	$-0.0234773\pi$
$164$	5.61503	−	9.72551i	0.438460	−	0.759435i
$165$	−0.991584	−	0.912921i	−0.0771947	−	0.0710708i
$166$	−8.69529	+	1.53321i	−0.674885	+	0.119000i
$167$	4.37506	−	3.06345i	0.338552	−	0.237057i	−0.391920	−	0.919999i	$-0.628189\pi$
$167$	4.37506	−	3.06345i	0.338552	−	0.237057i	0.730472	+	0.682943i	$0.239300\pi$
$168$	−1.56619	−	3.35870i	−0.120834	−	0.259129i
$169$	−14.8395	−	17.6851i	−1.14150	−	1.36039i
$170$	−4.61869	+	14.5293i	−0.354237	+	1.11435i
$171$	3.16747	+	2.99452i	0.242222	+	0.228997i
$172$	−6.20181	+	6.20181i	−0.472884	+	0.472884i
$173$	0.854049	−	9.76183i	0.0649321	−	0.742178i	−0.892032	−	0.451972i	$-0.850721\pi$
$173$	0.854049	−	9.76183i	0.0649321	−	0.742178i	0.956964	−	0.290206i	$-0.0937238\pi$
$174$	−6.45323	−	2.34878i	−0.489218	−	0.178061i
$175$	−0.0872026	+	18.5294i	−0.00659190	+	1.40069i
$176$	0.104670	+	0.593613i	0.00788980	+	0.0447453i
$177$	3.19985	−	6.86210i	0.240515	−	0.515787i
$178$	0.753666	−	0.201944i	0.0564897	−	0.0151364i
$179$	8.96277	+	15.5240i	0.669909	+	1.16032i	0.977929	+	0.208937i	$0.0670003\pi$
$179$	8.96277	+	15.5240i	0.669909	+	1.16032i	−0.308020	+	0.951380i	$0.599666\pi$
$180$	−1.88870	+	1.19700i	−0.140776	+	0.0892189i
$181$	−2.92350	+	3.48409i	−0.217302	+	0.258971i	−0.863673	−	0.504053i	$-0.831842\pi$
$181$	−2.92350	+	3.48409i	−0.217302	+	0.258971i	0.646371	+	0.763024i	$0.276286\pi$
$182$	−21.5035	−	5.76186i	−1.59395	−	0.427097i
$183$	−2.43304	−	9.08023i	−0.179856	−	0.671230i
$184$	4.25891	−	1.55012i	0.313971	−	0.114276i
$185$	−12.5690	−	16.4603i	−0.924093	−	1.21019i
$186$	−2.15623	−	0.380201i	−0.158102	−	0.0278777i
$187$	−3.72470	+	1.73686i	−0.272377	+	0.127012i
$188$	1.27160	+	0.111250i	0.0927407	+	0.00811376i
$189$	3.70592			0.269566
$190$	−2.69102	+	9.36795i	−0.195227	+	0.679622i
$191$	2.66356			0.192728			0.0963641	−	0.995346i	$-0.469279\pi$
$191$	2.66356			0.192728			0.0963641	+	0.995346i	$0.469279\pi$
$192$	0.996195	+	0.0871557i	0.0718942	+	0.00628992i
$193$	−0.748801	+	0.349171i	−0.0538998	+	0.0251339i	−0.449381	−	0.893340i	$-0.648356\pi$
$193$	−0.748801	+	0.349171i	−0.0538998	+	0.0251339i	0.395481	+	0.918474i	$0.370578\pi$
$194$	19.1861	+	3.38302i	1.37748	+	0.242887i
$195$	−1.78462	+	13.3134i	−0.127799	+	0.953391i
$196$	−6.32771	+	2.30310i	−0.451979	+	0.164507i
$197$	−4.46528	−	16.6647i	−0.318138	−	1.18731i	−0.921032	−	0.389487i	$-0.872652\pi$
$197$	−4.46528	−	16.6647i	−0.318138	−	1.18731i	0.602894	−	0.797822i	$-0.294014\pi$
$198$	−0.582232	−	0.156009i	−0.0413774	−	0.0110870i
$199$	9.12382	−	10.8733i	0.646770	−	0.770791i	−0.338653	−	0.940911i	$-0.609971\pi$
$199$	9.12382	−	10.8733i	0.646770	−	0.770791i	0.985423	+	0.170121i	$0.0544157\pi$
$200$	−4.31831	−	2.52035i	−0.305351	−	0.178216i
$201$	3.36028	+	5.82018i	0.237016	+	0.410524i
$202$	1.24415	−	0.333369i	0.0875381	−	0.0234558i
$203$	−10.7556	+	23.0655i	−0.754895	+	1.61888i
$204$	1.18395	+	6.71452i	0.0828932	+	0.470111i
$205$	−11.6474	+	22.2465i	−0.813492	+	1.55377i
$206$	−4.27794	−	1.55704i	−0.298059	−	0.108484i
$207$	−0.395011	+	4.51499i	−0.0274551	+	0.313814i
$208$	4.24772	−	4.24772i	0.294526	−	0.294526i
$209$	−2.34916	+	1.17676i	−0.162495	+	0.0813985i
$210$	3.80906	+	7.35936i	0.262850	+	0.507844i
$211$	5.49835	+	6.55268i	0.378522	+	0.451105i	0.921347	−	0.388741i	$-0.127090\pi$
$211$	5.49835	+	6.55268i	0.378522	+	0.451105i	−0.542825	+	0.839846i	$0.682645\pi$
$212$	1.06711	+	2.28842i	0.0732891	+	0.157169i
$213$	−4.46977	+	3.12976i	−0.306263	+	0.214448i
$214$	2.16219	−	0.381252i	0.147804	−	0.0260619i
$215$	13.2836	−	14.4282i	0.905931	−	0.983992i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−2.10008	+	7.83760i	−0.142563	+	0.532051i
$218$	0.702543	+	8.03011i	0.0475822	+	0.543867i
$219$	5.25285	+	4.40767i	0.354955	+	0.297843i
$220$	−0.288628	−	1.31657i	−0.0194593	−	0.0887632i
$221$	35.4703	+	20.4788i	2.38599	+	1.37755i
$222$	−8.39422	−	3.91429i	−0.563383	−	0.262710i
$223$	3.56297	+	2.49482i	0.238594	+	0.167065i	0.686758	−	0.726886i	$-0.259033\pi$
$223$	3.56297	+	2.49482i	0.238594	+	0.167065i	−0.448164	+	0.893951i	$0.647922\pi$
$224$	0.643525	−	3.64961i	0.0429974	−	0.243850i
$225$	4.10921	−	2.84858i	0.273947	−	0.189905i
$226$	3.03232	−	2.54442i	0.201707	−	0.169252i
$227$	−0.584551	−	0.584551i	−0.0387980	−	0.0387980i	0.687442	−	0.726240i	$-0.258734\pi$
$227$	−0.584551	−	0.584551i	−0.0387980	−	0.0387980i	−0.726240	+	0.687442i	$0.758734\pi$
$228$	0.877050	+	4.26975i	0.0580840	+	0.282771i
$229$		−	21.9764i		−	1.45224i	−0.687567	−	0.726121i	$-0.741321\pi$
$229$		−	21.9764i		−	1.45224i	0.687567	−	0.726121i	$-0.258679\pi$
$230$	−9.37206	+	3.85622i	−0.617975	+	0.254272i
$231$	−0.764011	+	2.09910i	−0.0502682	+	0.138111i
$232$	−3.93897	−	5.62543i	−0.258606	−	0.369327i
$233$	5.22792	−	7.46624i	0.342492	−	0.489130i	−0.610546	−	0.791981i	$-0.709050\pi$
$233$	5.22792	−	7.46624i	0.342492	−	0.489130i	0.953038	+	0.302852i	$0.0979387\pi$
$234$	2.05458	+	5.64490i	0.134312	+	0.369019i
$235$	−2.85122	−	0.131210i	−0.185993	−	0.00855917i
$236$	6.55710	−	3.78574i	0.426831	−	0.246431i
$237$	−11.4742	+	1.00386i	−0.745328	+	0.0652078i
$238$	25.1712	−	2.20219i	1.63160	−	0.142747i
$239$	16.5870	−	9.57649i	1.07292	−	0.619452i	0.143943	−	0.989586i	$-0.454022\pi$
$239$	16.5870	−	9.57649i	1.07292	−	0.619452i	0.928978	+	0.370134i	$0.120688\pi$
$240$	−2.23370	−	0.102792i	−0.144185	−	0.00663521i
$241$	4.82893	+	13.2674i	0.311059	+	0.854627i	0.992444	+	0.122702i	$0.0391559\pi$
$241$	4.82893	+	13.2674i	0.311059	+	0.854627i	−0.681385	+	0.731925i	$0.738622\pi$
$242$	−6.10094	+	8.71305i	−0.392183	+	0.560096i
$243$	−0.573576	−	0.819152i	−0.0367949	−	0.0525486i
$244$	3.21518	−	8.83363i	0.205831	−	0.565515i
$245$	13.9246	−	5.72941i	0.889611	−	0.366039i
$246$			11.2301i			0.716002i
$247$	23.0350	+	12.4510i	1.46568	+	0.792238i
$248$	−1.54821	−	1.54821i	−0.0983111	−	0.0983111i
$249$	6.76373	−	5.67545i	0.428634	−	0.359667i
$250$	9.88039	+	5.23238i	0.624891	+	0.330925i
$251$	−2.96951	+	16.8409i	−0.187434	+	1.06299i	0.735354	+	0.677683i	$0.237016\pi$
$251$	−2.96951	+	16.8409i	−0.187434	+	1.06299i	−0.922788	+	0.385308i	$0.874095\pi$
$252$	3.03571	+	2.12563i	0.191232	+	0.133902i
$253$	−2.47594	−	1.15455i	−0.155661	−	0.0725860i
$254$	17.7585	+	10.2529i	1.11427	+	0.643324i
$255$	−3.26475	−	14.8921i	−0.204447	−	0.932579i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.736542	−	8.41871i	−0.0459442	−	0.525145i	−0.983940	−	0.178499i	$-0.942876\pi$
$257$	−0.736542	−	8.41871i	−0.0459442	−	0.525145i	0.937996	−	0.346646i	$-0.112680\pi$
$258$	2.27002	−	8.47183i	0.141325	−	0.527433i
$259$	−17.1621	+	29.7256i	−1.06640	+	1.84706i
$260$	−9.09812	+	9.88207i	−0.564241	+	0.612860i
$261$	6.76305	−	1.19251i	0.418622	−	0.0738144i
$262$	13.1216	−	9.18786i	0.810657	−	0.567628i
$263$	0.217568	+	0.466577i	0.0134158	+	0.0287704i	0.912902	−	0.408180i	$-0.133836\pi$
$263$	0.217568	+	0.466577i	0.0134158	+	0.0287704i	−0.899486	+	0.436950i	$0.856059\pi$
$264$	−0.387454	−	0.461749i	−0.0238461	−	0.0284187i
$265$	−2.59526	−	5.01422i	−0.159426	−	0.308021i
$266$	16.0464	−	1.85881i	0.983868	−	0.113971i
$267$	−0.551722	+	0.551722i	−0.0337648	+	0.0337648i
$268$	−0.585736	+	6.69499i	−0.0357795	+	0.408962i
$269$	24.1594	+	8.79330i	1.47302	+	0.536137i	0.948920	−	0.315517i	$-0.102178\pi$
$269$	24.1594	+	8.79330i	1.47302	+	0.536137i	0.524104	+	0.851654i	$0.324400\pi$
$270$	1.03717	−	1.98098i	0.0631199	−	0.120559i
$271$	0.940645	+	5.33466i	0.0571401	+	0.324058i	0.999957	−	0.00925286i	$-0.00294532\pi$
$271$	0.940645	+	5.33466i	0.0571401	+	0.324058i	−0.942817	+	0.333311i	$0.891834\pi$
$272$	−2.88146	+	6.17930i	−0.174714	+	0.374675i
$273$	21.5035	−	5.76186i	1.30145	−	0.348723i
$274$	−4.57137	−	7.91785i	−0.276167	−	0.478335i
$275$	0.766334	+	2.91480i	0.0462117	+	0.175769i
$276$	−2.91327	+	3.47190i	−0.175358	+	0.208984i
$277$	11.5257	+	3.08829i	0.692510	+	0.185557i	0.587873	−	0.808953i	$-0.299965\pi$
$277$	11.5257	+	3.08829i	0.692510	+	0.185557i	0.104637	+	0.994511i	$0.466632\pi$
$278$	−3.00985	−	11.2329i	−0.180519	−	0.673705i
$279$	2.05745	−	0.748851i	0.123176	−	0.0448325i
$280$	−1.10096	+	8.21322i	−0.0657948	+	0.490834i
$281$	6.89743	+	1.21620i	0.411466	+	0.0725526i	0.375550	−	0.926802i	$-0.377454\pi$
$281$	6.89743	+	1.21620i	0.411466	+	0.0725526i	0.0359163	+	0.999355i	$0.488565\pi$
$282$	−1.15686	+	0.539453i	−0.0688900	+	0.0321239i
$283$	−3.30261	−	0.288941i	−0.196320	−	0.0171758i	−0.0114284	−	0.999935i	$-0.503638\pi$
$283$	−3.30261	−	0.288941i	−0.196320	−	0.0171758i	−0.184892	+	0.982759i	$0.559193\pi$
$284$	−5.45658			−0.323788
$285$	−2.35348	−	9.45839i	−0.139408	−	0.560267i
$286$	−3.62095			−0.214111
$287$	41.4593	+	3.62722i	2.44726	+	0.214108i
$288$	−0.906308	+	0.422618i	−0.0534047	+	0.0249030i
$289$	−29.0386	−	5.12029i	−1.70815	−	0.301193i
$290$	9.31940	+	12.2046i	0.547254	+	0.716681i
$291$	−18.3071	+	6.66325i	−1.07318	+	0.390607i
$292$	1.77475	+	6.62346i	0.103859	+	0.387609i
$293$	−1.39730	−	0.374405i	−0.0816311	−	0.0218730i	0.217772	−	0.976000i	$-0.430121\pi$
$293$	−1.39730	−	0.374405i	−0.0816311	−	0.0218730i	−0.299403	+	0.954127i	$0.596788\pi$
$294$	4.32841	−	5.15840i	0.252438	−	0.300844i
$295$	−14.3003	+	9.06305i	−0.832595	+	0.527671i
$296$	−4.63100	−	8.02112i	−0.269171	−	0.466218i
$297$	0.582232	−	0.156009i	0.0337845	−	0.00905254i
$298$	−6.28102	+	13.4697i	−0.363850	+	0.780279i
$299$	4.72774	+	26.8123i	0.273412	+	1.55060i
$300$	4.99994	+	0.0235307i	0.288672	+	0.00135854i
$301$	−30.5432	−	11.1168i	−1.76048	−	0.640763i
$302$	−1.51532	+	17.3202i	−0.0871969	+	0.996665i
$303$	−0.910781	+	0.910781i	−0.0523230	+	0.0523230i
$304$	−1.73059	+	4.00063i	−0.0992563	+	0.229452i
$305$	−6.36807	+	20.0325i	−0.364635	+	1.14706i
$306$	−4.38259	−	5.22297i	−0.250536	−	0.298577i
$307$	−3.62864	−	7.78163i	−0.207097	−	0.444121i	0.775134	−	0.631797i	$-0.217682\pi$
$307$	−3.62864	−	7.78163i	−0.207097	−	0.444121i	−0.982231	+	0.187676i	$0.939905\pi$
$308$	−1.82984	+	1.28127i	−0.104265	+	0.0730069i
$309$	4.48333	−	0.790532i	0.255048	−	0.0449718i
$310$	3.60181	+	3.31608i	0.204569	+	0.188340i
$311$	−12.1719	+	21.0824i	−0.690206	+	1.19547i	0.281564	+	0.959543i	$0.409147\pi$
$311$	−12.1719	+	21.0824i	−0.690206	+	1.19547i	−0.971770	+	0.235930i	$0.924186\pi$
$312$	−1.55477	+	5.80249i	−0.0880217	+	0.328501i
$313$	−0.444363	−	5.07909i	−0.0251169	−	0.287087i	−0.998357	−	0.0572973i	$-0.981752\pi$
$313$	−0.444363	−	5.07909i	−0.0251169	−	0.287087i	0.973240	−	0.229790i	$-0.0738038\pi$
$314$	2.12797	+	1.78558i	0.120089	+	0.100766i
$315$	−6.97842	−	4.46886i	−0.393189	−	0.251792i
$316$	−9.97489	−	5.75901i	−0.561131	−	0.323969i
$317$	−11.4133	−	5.32211i	−0.641035	−	0.298919i	0.0747902	−	0.997199i	$-0.476171\pi$
$317$	−11.4133	−	5.32211i	−0.641035	−	0.298919i	−0.715825	+	0.698280i	$0.753949\pi$
$318$	−2.06835	−	1.44827i	−0.115987	−	0.0812151i
$319$	−0.718809	+	4.07657i	−0.0402456	+	0.228244i
$320$	−1.77078	−	1.36540i	−0.0989898	−	0.0763283i
$321$	−1.68189	+	1.41127i	−0.0938737	+	0.0787694i
$322$	11.8766	+	11.8766i	0.661859	+	0.661859i
$323$	−29.4012	−	4.33757i	−1.63593	−	0.241349i
$324$		−	1.00000i		−	0.0555556i
$325$	19.4148	−	22.9177i	1.07694	−	1.27125i
$326$	−2.87580	+	7.90120i	−0.159276	+	0.437607i
$327$	−4.62347	−	6.60300i	−0.255679	−	0.365147i
$328$	−6.44130	+	9.19912i	−0.355661	+	0.507937i
$329$	1.61790	+	4.44515i	0.0891979	+	0.245069i
$330$	0.908244	+	0.995869i	0.0499972	+	0.0548208i
$331$	11.0363	−	6.37183i	0.606612	−	0.350227i	−0.165026	−	0.986289i	$-0.552771\pi$
$331$	11.0363	−	6.37183i	0.606612	−	0.350227i	0.771638	+	0.636062i	$0.219438\pi$
$332$	8.79583	−	0.769535i	0.482734	−	0.0422337i
$333$	9.22675	−	0.807236i	0.505623	−	0.0442363i
$334$	−4.62541	+	2.67048i	−0.253091	+	0.146122i
$335$	0.690822	−	15.0118i	0.0377436	−	0.820180i
$336$	1.26750	+	3.48242i	0.0691477	+	0.189982i
$337$	−6.24990	+	8.92578i	−0.340454	+	0.486218i	−0.952472	−	0.304625i	$-0.901469\pi$
$337$	−6.24990	+	8.92578i	−0.340454	+	0.486218i	0.612019	+	0.790843i	$0.290358\pi$
$338$	13.2417	+	18.9111i	0.720254	+	1.02863i
$339$	−1.35386	+	3.71969i	−0.0735315	+	0.202026i
$340$	5.86742	−	14.0715i	0.318206	−	0.763132i
$341$			1.31976i			0.0714692i
$342$	−2.89442	−	3.25919i	−0.156512	−	0.176237i
$343$	0.697545	+	0.697545i	0.0376639	+	0.0376639i
$344$	6.71873	−	5.63769i	0.362250	−	0.303964i
$345$	6.18833	−	8.02561i	0.333168	−	0.432085i
$346$	−1.70160	+	9.65024i	−0.0914785	+	0.518800i
$347$	5.87749	+	4.11546i	0.315520	+	0.220930i	0.720599	−	0.693352i	$-0.243867\pi$
$347$	5.87749	+	4.11546i	0.315520	+	0.220930i	−0.405079	+	0.914282i	$0.632756\pi$
$348$	6.22396	+	2.90228i	0.333639	+	0.155579i
$349$	14.4474	+	8.34122i	0.773353	+	0.446495i	0.834069	−	0.551660i	$-0.186005\pi$
$349$	14.4474	+	8.34122i	0.773353	+	0.446495i	−0.0607167	+	0.998155i	$0.519339\pi$
$350$	1.70181	−	18.4513i	0.0909657	−	0.986261i
$351$	−4.60177	−	3.86134i	−0.245624	−	0.206103i
$352$	−0.0525349	−	0.600477i	−0.00280012	−	0.0320055i
$353$	−3.47356	+	12.9635i	−0.184879	+	0.689979i	0.809777	+	0.586738i	$0.199588\pi$
$353$	−3.47356	+	12.9635i	−0.184879	+	0.689979i	−0.994656	+	0.103241i	$0.967079\pi$
$354$	−3.78574	+	6.55710i	−0.201210	+	0.348506i
$355$	12.1909	−	0.503528i	0.647025	−	0.0267245i
$356$	−0.768399	+	0.135489i	−0.0407251	+	0.00718093i
$357$	−20.6978	+	14.4927i	−1.09544	+	0.767037i
$358$	−7.57566	−	16.2461i	−0.400386	−	0.858631i
$359$	−21.1330	−	25.1853i	−1.11536	−	1.32923i	−0.938613	−	0.344973i	$-0.887888\pi$
$359$	−21.1330	−	25.1853i	−1.11536	−	1.32923i	−0.176744	−	0.984257i	$-0.556556\pi$
$360$	1.98584	−	1.02783i	0.104663	−	0.0541715i
$361$	−18.8669	−	2.24463i	−0.992997	−	0.118138i
$362$	3.21603	−	3.21603i	0.169031	−	0.169031i
$363$	0.927047	−	10.5962i	0.0486573	−	0.556156i
$364$	20.9195	+	7.61409i	1.09648	+	0.399087i
$365$	−4.57629	−	14.6341i	−0.239534	−	0.765985i
$366$	1.63239	+	9.25773i	0.0853263	+	0.483910i
$367$	7.13301	−	15.2968i	0.372340	−	0.798486i	−0.627463	−	0.778646i	$-0.715907\pi$
$367$	7.13301	−	15.2968i	0.372340	−	0.798486i	0.999803	−	0.0198397i	$-0.00631559\pi$
$368$	−4.37781	+	1.17303i	−0.228209	+	0.0611484i
$369$	−5.61503	−	9.72551i	−0.292307	−	0.506290i
$370$	11.0866	+	17.4932i	0.576364	+	0.909426i
$371$	−6.01481	+	7.16818i	−0.312274	+	0.372153i
$372$	2.11489	+	0.566683i	0.109652	+	0.0293811i
$373$	−6.04546	−	22.5620i	−0.313022	−	1.16821i	−0.925817	−	0.377972i	$-0.876621\pi$
$373$	−6.04546	−	22.5620i	−0.313022	−	1.16821i	0.612795	−	0.790242i	$-0.290045\pi$
$374$	3.86191	−	1.40562i	0.199694	−	0.0726828i
$375$	−11.1729	+	0.408819i	−0.576964	+	0.0211113i
$376$	−1.25706	−	0.221654i	−0.0648280	−	0.0114309i
$377$	37.3885	−	17.4345i	1.92560	−	0.897923i
$378$	−3.69181	−	0.322992i	−0.189886	−	0.0166129i
$379$	−2.75005			−0.141261			−0.0706303	−	0.997503i	$-0.522501\pi$
$379$	−2.75005			−0.141261			−0.0706303	+	0.997503i	$0.522501\pi$
$380$	3.49725	−	9.09776i	0.179405	−	0.466705i
$381$	−20.5058			−1.05054
$382$	−2.65342	−	0.232144i	−0.135761	−	0.0118775i
$383$	32.9762	−	15.3771i	1.68501	−	0.785731i	0.686737	−	0.726906i	$-0.259042\pi$
$383$	32.9762	−	15.3771i	1.68501	−	0.785731i	0.998268	−	0.0588254i	$-0.0187355\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	3.96992	−	3.03141i	0.202326	−	0.154495i
$386$	0.776383	−	0.282580i	0.0395169	−	0.0143830i
$387$	2.27002	+	8.47183i	0.115392	+	0.430647i
$388$	−18.8182	−	5.04233i	−0.955350	−	0.255985i
$389$	−18.8441	+	22.4575i	−0.955433	+	1.13864i	0.0348242	+	0.999393i	$0.488913\pi$
$389$	−18.8441	+	22.4575i	−0.955433	+	1.13864i	−0.990258	+	0.139248i	$0.955532\pi$
$390$	2.93817	−	13.1072i	0.148780	−	0.663708i
$391$	−15.4506	−	26.7613i	−0.781372	−	1.35338i
$392$	6.50436	−	1.74284i	0.328520	−	0.0880266i
$393$	−6.76973	+	14.5177i	−0.341488	+	0.732323i
$394$	2.99587	+	16.9904i	0.150930	+	0.855966i
$395$	22.8170	+	11.9461i	1.14805	+	0.601073i
$396$	0.566419	+	0.206160i	0.0284636	+	0.0103599i
$397$	0.380607	−	4.35036i	0.0191021	−	0.218338i	−0.980644	−	0.195800i	$-0.937270\pi$
$397$	0.380607	−	4.35036i	0.0191021	−	0.218338i	0.999746	−	0.0225383i	$-0.00717478\pi$
$398$	−10.0368	+	10.0368i	−0.503098	+	0.503098i
$399$	−12.9672	+	9.63298i	−0.649172	+	0.482252i
$400$	4.08222	+	2.88713i	0.204111	+	0.144356i
$401$	−0.188816	−	0.225022i	−0.00942901	−	0.0112371i	0.761309	−	0.648389i	$-0.224557\pi$
$401$	−0.188816	−	0.225022i	−0.00942901	−	0.0112371i	−0.770738	+	0.637152i	$0.780112\pi$
$402$	−2.84023	−	6.09090i	−0.141658	−	0.303786i
$403$	10.7740	−	7.54407i	0.536693	−	0.375797i
$404$	−1.26847	+	0.223666i	−0.0631088	+	0.0111278i
$405$	0.0922790	+	2.23416i	0.00458538	+	0.111016i
$406$	12.7250	−	22.0403i	0.631529	−	1.09384i
$407$	−1.44495	+	5.39263i	−0.0716236	+	0.267303i
$408$	−0.594237	−	6.79216i	−0.0294191	−	0.336262i
$409$	−3.96859	−	3.33004i	−0.196234	−	0.164660i	0.539376	−	0.842065i	$-0.318660\pi$
$409$	−3.96859	−	3.33004i	−0.196234	−	0.164660i	−0.735610	+	0.677405i	$0.763105\pi$
$410$	13.5420	−	21.1467i	0.668793	−	1.04436i
$411$	7.91785	+	4.57137i	0.390559	+	0.225489i
$412$	4.12596	+	1.92397i	0.203271	+	0.0947871i
$413$	22.9848	+	16.0941i	1.13101	+	0.791941i
$414$	0.787015	−	4.46338i	0.0386797	−	0.219363i
$415$	−19.5803	+	2.53094i	−0.961159	+	0.124239i
$416$	−4.60177	+	3.86134i	−0.225620	+	0.189318i
$417$	8.22306	+	8.22306i	0.402685	+	0.402685i
$418$	2.44278	−	0.967544i	0.119480	−	0.0473241i
$419$		−	17.5487i		−	0.857311i	−0.903468	−	0.428655i	$-0.858987\pi$
$419$		−	17.5487i		−	0.857311i	0.903468	−	0.428655i	$-0.141013\pi$
$420$	−3.15315	−	7.66333i	−0.153858	−	0.373932i
$421$	10.7808	−	29.6199i	0.525423	−	1.44359i	−0.338983	−	0.940793i	$-0.610083\pi$
$421$	10.7808	−	29.6199i	0.525423	−	1.44359i	0.864406	−	0.502795i	$-0.167695\pi$
$422$	−4.90632	−	7.00695i	−0.238836	−	0.341093i
$423$	0.732144	−	1.04561i	0.0355981	−	0.0508393i
$424$	−0.863597	−	2.37271i	−0.0419400	−	0.115229i
$425$	−11.8103	+	31.9794i	−0.572883	+	1.55123i
$426$	4.72553	−	2.72829i	0.228953	−	0.132186i
$427$	34.7051	−	3.03630i	1.67950	−	0.146937i
$428$	−2.18719	+	0.191354i	−0.105722	+	0.00924946i
$429$	3.13584	−	1.81048i	0.151400	−	0.0874106i
$430$	−14.4905	+	13.2155i	−0.698794	+	0.637308i
$431$	2.87149	+	7.88936i	0.138315	+	0.380017i	0.989439	−	0.144947i	$-0.0463010\pi$
$431$	2.87149	+	7.88936i	0.138315	+	0.380017i	−0.851124	+	0.524964i	$0.824079\pi$
$432$	0.573576	−	0.819152i	0.0275962	−	0.0394115i
$433$	18.1695	+	25.9487i	0.873170	+	1.24702i	0.967855	+	0.251509i	$0.0809267\pi$
$433$	18.1695	+	25.9487i	0.873170	+	1.24702i	−0.0946852	+	0.995507i	$0.530184\pi$
$434$	2.77518	−	7.62474i	0.133213	−	0.365999i
$435$	−14.1732	−	5.90983i	−0.679551	−	0.283354i
$436$		−	8.06078i		−	0.386041i
$437$	−10.3539	−	16.8250i	−0.495294	−	0.804847i
$438$	−4.84871	−	4.84871i	−0.231680	−	0.231680i
$439$	−23.0519	+	19.3429i	−1.10021	+	0.923185i	−0.997439	−	0.0715199i	$-0.977215\pi$
$439$	−23.0519	+	19.3429i	−1.10021	+	0.923185i	−0.102770	+	0.994705i	$0.532771\pi$
$440$	0.172783	+	1.33672i	0.00823711	+	0.0637254i
$441$	−1.16931	+	6.63151i	−0.0556816	+	0.315786i
$442$	−33.5505	−	23.4923i	−1.59583	−	1.11742i
$443$	29.8150	+	13.9030i	1.41655	+	0.660550i	0.971952	−	0.235178i	$-0.0755672\pi$
$443$	29.8150	+	13.9030i	1.41655	+	0.660550i	0.444602	+	0.895728i	$0.353345\pi$
$444$	8.02112	+	4.63100i	0.380666	+	0.219777i
$445$	1.70423	−	0.373613i	0.0807880	−	0.0177109i
$446$	−3.33197	−	2.79586i	−0.157774	−	0.132388i
$447$	−1.29532	−	14.8056i	−0.0612667	−	0.700282i
$448$	−0.959162	+	3.57964i	−0.0453161	+	0.169122i
$449$	5.54477	−	9.60382i	0.261674	−	0.453232i	−0.705013	−	0.709194i	$-0.749059\pi$
$449$	5.54477	−	9.60382i	0.261674	−	0.453232i	0.966687	+	0.255962i	$0.0823922\pi$
$450$	−4.34184	+	2.47959i	−0.204677	+	0.116889i
$451$	6.66631	−	1.17545i	0.313904	−	0.0553498i
$452$	−3.24254	+	2.27045i	−0.152516	+	0.106793i
$453$	−7.34779	−	15.7574i	−0.345229	−	0.740347i
$454$	0.531379	+	0.633273i	0.0249389	+	0.0297210i
$455$	−47.4403	−	15.0807i	−2.22403	−	0.706993i
$456$	−0.501579	−	4.32994i	−0.0234886	−	0.202768i
$457$	−16.0364	+	16.0364i	−0.750152	+	0.750152i	−0.974507	−	0.224355i	$-0.927972\pi$
$457$	−16.0364	+	16.0364i	−0.750152	+	0.750152i	0.224355	+	0.974507i	$0.427972\pi$
$458$	−1.91537	+	21.8928i	−0.0894994	+	1.02298i
$459$	6.40692	+	2.33193i	0.299050	+	0.108845i
$460$	9.67249	−	3.02472i	0.450982	−	0.141028i
$461$	1.63710	+	9.28443i	0.0762472	+	0.432419i	0.998904	+	0.0467980i	$0.0149017\pi$
$461$	1.63710	+	9.28443i	0.0762472	+	0.432419i	−0.922657	+	0.385621i	$0.873987\pi$
$462$	0.944052	−	2.02453i	0.0439213	−	0.0941895i
$463$	−7.31248	+	1.95937i	−0.339840	+	0.0910598i	−0.424703	−	0.905333i	$-0.639621\pi$
$463$	−7.31248	+	1.95937i	−0.339840	+	0.0910598i	0.0848629	+	0.996393i	$0.472955\pi$
$464$	3.43369	+	5.94732i	0.159405	+	0.276098i
$465$	−4.77730	−	1.07090i	−0.221542	−	0.0496619i
$466$	−5.85875	+	6.98218i	−0.271401	+	0.323443i
$467$	6.28702	+	1.68460i	0.290928	+	0.0779540i	0.401332	−	0.915933i	$-0.368548\pi$
$467$	6.28702	+	1.68460i	0.290928	+	0.0779540i	−0.110403	+	0.993887i	$0.535214\pi$
$468$	−1.55477	−	5.80249i	−0.0718694	−	0.268220i
$469$	−23.4038	+	8.51830i	−1.08069	+	0.393339i
$470$	2.82894	+	0.379211i	0.130489	+	0.0174917i
$471$	−2.73567	−	0.482372i	−0.126053	−	0.0222266i
$472$	−6.86210	+	3.19985i	−0.315854	+	0.147285i
$473$	−5.26659	−	0.460767i	−0.242158	−	0.0211861i
$474$	11.5180			0.529040
$475$	−6.97390	+	20.6486i	−0.319984	+	0.947423i
$476$	−25.2673			−1.15813
$477$	2.51538	+	0.220067i	0.115171	+	0.0100762i
$478$	−17.3585	+	8.09440i	−0.793959	+	0.370229i
$479$	18.3248	+	3.23116i	0.837282	+	0.147635i	0.575818	−	0.817578i	$-0.304684\pi$
$479$	18.3248	+	3.23116i	0.837282	+	0.147635i	0.261464	+	0.965213i	$0.415795\pi$
$480$	2.21625	+	0.297081i	0.101157	+	0.0135598i
$481$	52.2831	−	19.0295i	2.38390	−	0.867670i
$482$	−3.65423	−	13.6378i	−0.166446	−	0.621183i
$483$	−16.2238	−	4.34715i	−0.738207	−	0.197802i
$484$	6.83712	−	8.14816i	0.310778	−	0.370371i
$485$	42.5083	+	9.52885i	1.93020	+	0.432683i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	38.0053	−	10.1835i	1.72218	−	0.461458i	0.743825	−	0.668375i	$-0.233010\pi$
$487$	38.0053	−	10.1835i	1.72218	−	0.461458i	0.978359	+	0.206917i	$0.0663430\pi$
$488$	−3.97284	+	8.51979i	−0.179842	+	0.385673i
$489$	−1.46008	−	8.28054i	−0.0660272	−	0.374459i
$490$	−14.3710	+	4.49400i	−0.649214	+	0.203018i
$491$	−29.0709	−	10.5809i	−1.31195	−	0.477511i	−0.411081	−	0.911599i	$-0.634849\pi$
$491$	−29.0709	−	10.5809i	−1.31195	−	0.477511i	−0.900871	+	0.434088i	$0.857071\pi$
$492$	0.978764	−	11.1873i	0.0441261	−	0.504363i
$493$	−33.1085	+	33.1085i	−1.49113	+	1.49113i
$494$	−21.8622	−	14.4112i	−0.983625	−	0.648393i
$495$	−1.28450	−	0.408326i	−0.0577339	−	0.0183529i
$496$	1.40738	+	1.67725i	0.0631932	+	0.0753107i
$497$	−8.54602	−	18.3270i	−0.383341	−	0.822078i
$498$	−7.23264	+	5.06435i	−0.324102	+	0.226939i
$499$	25.1652	−	4.43730i	1.12655	−	0.198641i	0.420834	−	0.907137i	$-0.361737\pi$
$499$	25.1652	−	4.43730i	1.12655	−	0.198641i	0.705714	+	0.708497i	$0.250626\pi$
$500$	−9.38676	−	6.07361i	−0.419789	−	0.271620i
$501$	2.67048	−	4.62541i	0.119308	−	0.206648i
$502$	4.42600	−	16.5181i	0.197542	−	0.737237i
$503$	−2.23511	−	25.5475i	−0.0996588	−	1.13911i	−0.867150	−	0.498046i	$-0.834051\pi$
$503$	−2.23511	−	25.5475i	−0.0996588	−	1.13911i	0.767492	−	0.641059i	$-0.221505\pi$
$504$	−2.83890	−	2.38212i	−0.126454	−	0.106108i
$505$	2.81333	−	0.616759i	0.125192	−	0.0274454i
$506$	2.36590	+	1.36595i	0.105177	+	0.0607239i
$507$	−20.9232	−	9.75666i	−0.929233	−	0.433308i
$508$	−16.7974	−	11.7616i	−0.745263	−	0.521839i
$509$	−0.500052	+	2.83594i	−0.0221644	+	0.125701i	−0.993882	−	0.110444i	$-0.964773\pi$
$509$	−0.500052	+	2.83594i	−0.0221644	+	0.125701i	0.971718	+	0.236145i	$0.0758839\pi$
$510$	1.95440	+	15.1200i	0.0865421	+	0.669523i
$511$	−19.4666	+	16.3344i	−0.861153	+	0.722593i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.13624	+	1.37533i	0.182619	+	0.0607223i
$514$			8.45087i			0.372752i
$515$	−9.39561	−	3.91772i	−0.414020	−	0.172635i
$516$	−2.99975	+	8.24175i	−0.132057	+	0.362823i
$517$	0.441315	+	0.630263i	0.0194090	+	0.0277189i
$518$	19.6875	−	28.1167i	0.865021	−	1.23538i
$519$	−3.35149	−	9.20816i	−0.147114	−	0.404193i
$520$	9.92478	−	9.05151i	0.435230	−	0.396935i
$521$	21.5579	−	12.4465i	0.944468	−	0.545289i	0.0531102	−	0.998589i	$-0.483087\pi$
$521$	21.5579	−	12.4465i	0.944468	−	0.545289i	0.891358	+	0.453300i	$0.149753\pi$
$522$	−6.84125	+	0.598532i	−0.299433	+	0.0261970i
$523$	20.1639	−	1.76411i	0.881704	−	0.0771391i	0.362695	−	0.931908i	$-0.381857\pi$
$523$	20.1639	−	1.76411i	0.881704	−	0.0771391i	0.519009	+	0.854769i	$0.326301\pi$
$524$	−13.8725	+	8.00927i	−0.606021	+	0.349887i
$525$	7.75182	+	16.8302i	0.338317	+	0.734529i
$526$	−0.176076	−	0.483764i	−0.00767726	−	0.0210931i
$527$	−8.56246	+	12.2285i	−0.372987	+	0.532680i
$528$	0.345735	+	0.493761i	0.0150462	+	0.0214882i
$529$	−0.840967	+	2.31054i	−0.0365638	+	0.100458i
$530$	2.14837	+	5.22133i	0.0933191	+	0.226800i
$531$		−	7.57149i		−	0.328575i
$532$	−16.1474	+	0.453199i	−0.700077	+	0.0196487i
$533$	−47.7021	−	47.7021i	−2.06621	−	2.06621i
$534$	0.597708	−	0.501537i	0.0258654	−	0.0217036i
$535$	4.86888	−	0.629349i	0.210500	−	0.0272091i
$536$	1.16701	−	6.61846i	0.0504073	−	0.285874i
$537$	14.6837	+	10.2817i	0.633650	+	0.443687i
$538$	−23.3011	−	10.8655i	−1.00458	−	0.468444i
$539$	−3.51515	−	2.02947i	−0.151408	−	0.0874156i
$540$	−1.20587	+	1.88305i	−0.0518925	+	0.0810335i
$541$	−4.56194	−	3.82792i	−0.196133	−	0.164575i	0.539432	−	0.842029i	$-0.318639\pi$
$541$	−4.56194	−	3.82792i	−0.196133	−	0.164575i	−0.735565	+	0.677454i	$0.763083\pi$
$542$	−0.472119	−	5.39635i	−0.0202793	−	0.231793i
$543$	−1.17715	+	4.39318i	−0.0505163	+	0.188530i
$544$	3.40905	−	5.90465i	0.146162	−	0.253160i
$545$	0.743841	+	18.0091i	0.0318626	+	0.771425i
$546$	−21.9239	+	3.86577i	−0.938256	+	0.165440i
$547$	−20.7319	+	14.5167i	−0.886434	+	0.620688i	−0.925583	−	0.378546i	$-0.876424\pi$
$547$	−20.7319	+	14.5167i	−0.886434	+	0.620688i	0.0391486	+	0.999233i	$0.487535\pi$
$548$	3.86389	+	8.28614i	0.165057	+	0.353966i
$549$	−6.04256	−	7.20124i	−0.257890	−	0.307341i
$550$	−0.509376	−	2.97050i	−0.0217199	−	0.126662i
$551$	−20.5645	+	21.7522i	−0.876078	+	0.926675i
$552$	3.20478	−	3.20478i	0.136404	−	0.136404i
$553$	3.72022	−	42.5224i	0.158200	−	1.80823i
$554$	−11.2126	−	4.08107i	−0.476379	−	0.173388i
$555$	−18.3478	−	9.60622i	−0.778823	−	0.407762i
$556$	2.01938	+	11.4525i	0.0856409	+	0.485694i
$557$	3.13382	−	6.72049i	0.132784	−	0.284756i	−0.828662	−	0.559749i	$-0.810898\pi$
$557$	3.13382	−	6.72049i	0.132784	−	0.284756i	0.961446	+	0.274993i	$0.0886754\pi$
$558$	−2.11489	+	0.566683i	−0.0895303	+	0.0239896i
$559$	26.3435	+	45.6283i	1.11421	+	1.92987i
$560$	1.81260	−	8.08601i	0.0765962	−	0.341696i
$561$	−2.64170	+	3.14826i	−0.111533	+	0.132919i
$562$	−6.76518	−	1.81272i	−0.285372	−	0.0764652i
$563$	−2.76690	−	10.3262i	−0.116611	−	0.435198i	0.882792	−	0.469765i	$-0.155661\pi$
$563$	−2.76690	−	10.3262i	−0.116611	−	0.435198i	−0.999402	+	0.0345673i	$0.988995\pi$
$564$	1.19947	−	0.436573i	0.0505070	−	0.0183830i
$565$	7.03486	−	5.37178i	0.295959	−	0.225993i
$566$	3.26486	+	0.575683i	0.137232	+	0.0241978i
$567$	3.35870	−	1.56619i	0.141052	−	0.0657737i
$568$	5.43581	+	0.475572i	0.228082	+	0.0199546i
$569$	3.99572			0.167509			0.0837545	−	0.996486i	$-0.473309\pi$
$569$	3.99572			0.167509			0.0837545	+	0.996486i	$0.473309\pi$
$570$	1.52017	+	9.62752i	0.0636730	+	0.403252i
$571$	12.4719			0.521934			0.260967	−	0.965348i	$-0.415959\pi$
$571$	12.4719			0.521934			0.260967	+	0.965348i	$0.415959\pi$
$572$	3.60717	+	0.315587i	0.150824	+	0.0131954i
$573$	2.41400	−	1.12567i	0.100846	−	0.0470255i
$574$	−40.9854	−	7.22683i	−1.71070	−	0.301642i
$575$	−21.3308	+	7.65028i	−0.889555	+	0.319039i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	−2.47846	−	9.24976i	−0.103180	−	0.385072i	0.894952	−	0.446161i	$-0.147209\pi$
$577$	−2.47846	−	9.24976i	−0.103180	−	0.385072i	−0.998132	+	0.0610891i	$0.980543\pi$
$578$	28.4818	+	7.63169i	1.18469	+	0.317436i
$579$	−0.531078	+	0.632914i	−0.0220708	+	0.0263030i
$580$	−8.22024	−	12.9704i	−0.341327	−	0.538568i
$581$	16.3606	+	28.3373i	0.678750	+	1.17563i
$582$	18.8182	−	5.04233i	0.780040	−	0.209011i
$583$	−0.643220	+	1.37939i	−0.0266395	+	0.0571285i
$584$	−1.19073	−	6.75294i	−0.0492726	−	0.279439i
$585$	4.00906	+	12.8202i	0.165754	+	0.530052i
$586$	1.35935	+	0.494763i	0.0561543	+	0.0204385i
$587$	1.86555	−	21.3234i	0.0769996	−	0.880109i	−0.855232	−	0.518246i	$-0.826585\pi$
$587$	1.86555	−	21.3234i	0.0769996	−	0.880109i	0.932231	−	0.361863i	$-0.117859\pi$
$588$	−4.76152	+	4.76152i	−0.196362	+	0.196362i
$589$	−5.25260	+	7.96831i	−0.216430	+	0.328328i
$590$	15.0358	−	7.78221i	0.619013	−	0.320389i
$591$	−11.0897	−	13.2162i	−0.456170	−	0.543642i
$592$	3.91429	+	8.39422i	0.160876	+	0.345000i
$593$	19.8419	−	13.8934i	0.814808	−	0.570534i	−0.0902031	−	0.995923i	$-0.528752\pi$
$593$	19.8419	−	13.8934i	0.814808	−	0.570534i	0.905011	+	0.425389i	$0.139863\pi$
$594$	−0.593613	+	0.104670i	−0.0243563	+	0.00429466i
$595$	56.4513	−	2.33164i	2.31428	−	0.0955881i
$596$	7.43108	−	12.8710i	0.304389	−	0.527217i
$597$	3.67371	−	13.7105i	0.150355	−	0.561133i
$598$	−2.37290	−	27.1224i	−0.0970351	−	1.10912i
$599$	−4.87382	−	4.08962i	−0.199139	−	0.167097i	0.537765	−	0.843095i	$-0.319269\pi$
$599$	−4.87382	−	4.08962i	−0.199139	−	0.167097i	−0.736904	+	0.675997i	$0.763713\pi$
$600$	−4.97887	−	0.459215i	−0.203261	−	0.0187474i
$601$	13.0607	+	7.54058i	0.532755	+	0.307586i	0.742138	−	0.670247i	$-0.233812\pi$
$601$	13.0607	+	7.54058i	0.532755	+	0.307586i	−0.209382	+	0.977834i	$0.567145\pi$
$602$	29.4581	+	13.7365i	1.20062	+	0.559859i
$603$	5.50516	+	3.85476i	0.224188	+	0.156978i
$604$	3.01911	−	17.1222i	0.122846	−	0.696693i
$605$	−14.5233	+	18.8352i	−0.590457	+	0.765761i
$606$	0.986695	−	0.827936i	0.0400818	−	0.0336326i
$607$	−4.08047	−	4.08047i	−0.165621	−	0.165621i	0.619430	−	0.785051i	$-0.287364\pi$
$607$	−4.08047	−	4.08047i	−0.165621	−	0.165621i	−0.785051	+	0.619430i	$0.787364\pi$
$608$	2.07268	−	3.83458i	0.0840585	−	0.155513i
$609$			25.4499i			1.03128i
$610$	8.08978	−	19.4012i	0.327546	−	0.785532i
$611$	2.62257	−	7.20546i	0.106098	−	0.291502i
$612$	3.91070	+	5.58507i	0.158081	+	0.225763i
$613$	−2.70789	+	3.86727i	−0.109371	+	0.156198i	−0.870106	−	0.492865i	$-0.835950\pi$
$613$	−2.70789	+	3.86727i	−0.109371	+	0.156198i	0.760735	+	0.649062i	$0.224839\pi$
$614$	2.93661	+	8.06828i	0.118512	+	0.325609i
$615$	−1.15436	+	25.0846i	−0.0465484	+	1.01151i
$616$	1.93454	−	1.11691i	0.0779450	−	0.0450015i
$617$	−46.2209	+	4.04380i	−1.86078	+	0.162797i	−0.961542	−	0.274657i	$-0.911436\pi$
$617$	−46.2209	+	4.04380i	−1.86078	+	0.162797i	−0.899241	+	0.437454i	$0.855880\pi$
$618$	−4.53517	+	0.396776i	−0.182431	+	0.0159607i
$619$	−15.1973	+	8.77417i	−0.610832	+	0.352664i	−0.773291	−	0.634051i	$-0.781391\pi$
$619$	−15.1973	+	8.77417i	−0.610832	+	0.352664i	0.162459	+	0.986715i	$0.448057\pi$
$620$	−3.29909	−	3.61738i	−0.132495	−	0.145277i
$621$	1.55012	+	4.25891i	0.0622040	+	0.170904i
$622$	13.9631	−	19.9413i	0.559867	−	0.799574i
$623$	−1.65853	−	2.36862i	−0.0664474	−	0.0948967i
$624$	2.05458	−	5.64490i	0.0822489	−	0.225977i
$625$	21.5320	+	12.7032i	0.861281	+	0.508129i
$626$			5.09849i			0.203777i
$627$	−1.63174	+	2.05931i	−0.0651654	+	0.0822408i
$628$	−1.96425	−	1.96425i	−0.0783822	−	0.0783822i
$629$	−48.3752	+	40.5916i	−1.92884	+	1.61849i
$630$	6.56238	+	5.06007i	0.261451	+	0.201598i
$631$	−2.86727	+	16.2611i	−0.114144	+	0.647345i	0.873026	+	0.487674i	$0.162154\pi$
$631$	−2.86727	+	16.2611i	−0.114144	+	0.647345i	−0.987170	+	0.159671i	$0.948957\pi$
$632$	9.43500	+	6.60646i	0.375304	+	0.262791i
$633$	7.75248	+	3.61504i	0.308133	+	0.143685i
$634$	10.9060	+	6.29659i	0.433133	+	0.250070i
$635$	38.6134	+	24.7274i	1.53233	+	0.981277i
$636$	1.93425	+	1.62303i	0.0766981	+	0.0643573i
$637$	3.52556	+	40.2973i	0.139688	+	1.59664i
$638$	1.07137	−	3.99841i	0.0424159	−	0.158298i
$639$	−2.72829	+	4.72553i	−0.107929	+	0.186939i
$640$	1.64504	+	1.51454i	0.0650260	+	0.0598675i
$641$	4.21917	−	0.743954i	0.166647	−	0.0293844i	−0.0897019	−	0.995969i	$-0.528591\pi$
$641$	4.21917	−	0.743954i	0.166647	−	0.0293844i	0.256349	+	0.966584i	$0.417480\pi$
$642$	1.79849	−	1.25931i	0.0709805	−	0.0497011i
$643$	9.54549	+	20.4704i	0.376437	+	0.807273i	0.999681	+	0.0252452i	$0.00803665\pi$
$643$	9.54549	+	20.4704i	0.376437	+	0.807273i	−0.623244	+	0.782028i	$0.714186\pi$
$644$	−10.7963	−	12.8666i	−0.425435	−	0.507013i
$645$	5.94139	−	18.6902i	0.233942	−	0.735927i
$646$	28.9113	+	6.88355i	1.13750	+	0.270830i
$647$	21.0476	−	21.0476i	0.827466	−	0.827466i	−0.159700	−	0.987166i	$-0.551053\pi$
$647$	21.0476	−	21.0476i	0.827466	−	0.827466i	0.987166	+	0.159700i	$0.0510527\pi$
$648$	−0.0871557	+	0.996195i	−0.00342380	+	0.0391342i
$649$	4.28864	+	1.56094i	0.168344	+	0.0612721i
$650$	−21.3383	+	21.1384i	−0.836957	+	0.829116i
$651$	1.40899	+	7.99081i	0.0552229	+	0.313184i
$652$	3.55349	−	7.62049i	0.139166	−	0.298441i
$653$	−43.4143	+	11.6328i	−1.69893	+	0.455228i	−0.972671	−	0.232188i	$-0.925411\pi$
$653$	−43.4143	+	11.6328i	−1.69893	+	0.455228i	−0.726263	+	0.687417i	$0.758745\pi$
$654$	4.03039	+	6.98084i	0.157601	+	0.272972i
$655$	30.2543	−	19.1742i	1.18213	−	0.749196i
$656$	7.21854	−	8.60272i	0.281837	−	0.335880i
$657$	6.62346	+	1.77475i	0.258406	+	0.0692397i
$658$	−1.22433	−	4.56925i	−0.0477292	−	0.178128i
$659$	−8.44558	+	3.07394i	−0.328993	+	0.119744i	−0.501236	−	0.865311i	$-0.667121\pi$
$659$	−8.44558	+	3.07394i	−0.328993	+	0.119744i	0.172242	+	0.985055i	$0.444899\pi$
$660$	−0.817993	−	1.07124i	−0.0318403	−	0.0416979i
$661$	−26.5607	−	4.68338i	−1.03309	−	0.182162i	−0.368702	−	0.929547i	$-0.620198\pi$
$661$	−26.5607	−	4.68338i	−1.03309	−	0.182162i	−0.664391	+	0.747385i	$0.731309\pi$
$662$	−11.5497	+	5.38570i	−0.448891	+	0.209321i
$663$	40.8017	+	3.56969i	1.58461	+	0.138635i
$664$	−8.82943			−0.342648
$665$	36.0340	−	2.50258i	1.39734	−	0.0970460i
$666$	−9.26200			−0.358895
$667$	−31.0062	−	2.71269i	−1.20056	−	0.105036i
$668$	4.84055	−	2.25719i	0.187287	−	0.0873332i
$669$	4.28350	+	0.755297i	0.165610	+	0.0292015i
$670$	−1.99655	+	14.8944i	−0.0771336	+	0.575422i
$671$	5.32465	−	1.93802i	0.205556	−	0.0748162i
$672$	−0.959162	−	3.57964i	−0.0370005	−	0.138088i
$673$	−44.5165	−	11.9282i	−1.71599	−	0.459797i	−0.739107	−	0.673588i	$-0.764752\pi$
$673$	−44.5165	−	11.9282i	−1.71599	−	0.459797i	−0.976880	+	0.213791i	$0.931419\pi$
$674$	7.00405	−	8.34710i	0.269786	−	0.321518i
$675$	2.52035	−	4.31831i	0.0970083	−	0.166212i
$676$	−11.5431	−	19.9933i	−0.443966	−	0.768971i
$677$	3.83921	−	1.02871i	0.147553	−	0.0395367i	−0.184286	−	0.982873i	$-0.558997\pi$
$677$	3.83921	−	1.02871i	0.147553	−	0.0395367i	0.331840	+	0.943336i	$0.392331\pi$
$678$	1.67290	−	3.58754i	0.0642473	−	0.137779i
$679$	−12.5372	−	71.1020i	−0.481133	−	2.72864i
$680$	−7.07150	+	13.5065i	−0.271180	+	0.517952i
$681$	−0.776825	−	0.282741i	−0.0297680	−	0.0108347i
$682$	0.115025	−	1.31474i	0.00440453	−	0.0503440i
$683$	10.7197	−	10.7197i	0.410177	−	0.410177i	−0.471623	−	0.881800i	$-0.656332\pi$
$683$	10.7197	−	10.7197i	0.410177	−	0.410177i	0.881800	+	0.471623i	$0.156332\pi$
$684$	2.59935	+	3.49905i	0.0993887	+	0.133790i
$685$	−9.39720	−	18.1560i	−0.359049	−	0.693707i
$686$	−0.634096	−	0.755686i	−0.0242099	−	0.0288522i
$687$	−9.28763	−	19.9174i	−0.354345	−	0.759896i
$688$	−7.18452	+	5.03066i	−0.273907	+	0.191792i
$689$	14.9376	−	2.63391i	0.569078	−	0.100344i
$690$	−6.86426	+	7.45573i	−0.261318	+	0.283835i
$691$	5.99874	−	10.3901i	0.228203	−	0.395259i	−0.729073	−	0.684436i	$-0.760048\pi$
$691$	5.99874	−	10.3901i	0.228203	−	0.395259i	0.957276	+	0.289177i	$0.0933817\pi$
$692$	2.53620	−	9.46522i	0.0964118	−	0.359814i
$693$	0.194690	+	2.22532i	0.00739566	+	0.0845328i
$694$	−5.49644	−	4.61206i	−0.208642	−	0.175071i
$695$	−5.56845	−	25.4004i	−0.211224	−	0.963491i
$696$	−5.94732	−	3.43369i	−0.225433	−	0.130154i
$697$	69.3939	+	32.3589i	2.62848	+	1.22568i
$698$	−13.6655	−	9.56866i	−0.517245	−	0.362179i
$699$	1.58273	−	8.97612i	0.0598644	−	0.339508i
$700$	−3.30347	+	18.2327i	−0.124859	+	0.689132i
$701$	−7.65525	+	6.42352i	−0.289135	+	0.242613i	−0.775805	−	0.630973i	$-0.782656\pi$
$701$	−7.65525	+	6.42352i	−0.289135	+	0.242613i	0.486670	+	0.873586i	$0.338211\pi$
$702$	4.24772	+	4.24772i	0.160320	+	0.160320i
$703$	−30.1866	+	26.8081i	−1.13851	+	1.01109i
$704$			0.602771i			0.0227178i
$705$	−2.63954	+	1.08606i	−0.0994106	+	0.0409035i
$706$	4.59019	−	12.6114i	0.172754	−	0.474638i
$707$	−2.73789	−	3.91011i	−0.102969	−	0.147055i
$708$	4.34283	−	6.20220i	0.163213	−	0.233093i
$709$	11.4424	+	31.4376i	0.429727	+	1.18066i	0.945979	+	0.324228i	$0.105104\pi$
$709$	11.4424	+	31.4376i	0.429727	+	1.18066i	−0.516252	+	0.856437i	$0.672673\pi$
$710$	−12.1884	−	0.560894i	−0.457422	−	0.0210500i
$711$	−9.97489	+	5.75901i	−0.374088	+	0.215980i
$712$	0.777284	−	0.0680035i	0.0291299	−	0.00254854i
$713$	−9.88554	+	0.864873i	−0.370216	+	0.0323897i
$714$	21.8821	−	12.6337i	0.818919	−	0.472803i
$715$	−8.08814	−	0.372206i	−0.302479	−	0.0139197i
$716$	6.13090	+	16.8445i	0.229122	+	0.629509i
$717$	10.9857	−	15.6892i	0.410268	−	0.585924i
$718$	18.8575	+	26.9313i	0.703757	+	1.00507i
$719$	3.58006	−	9.83614i	0.133514	−	0.366826i	−0.854862	−	0.518855i	$-0.826358\pi$
$719$	3.58006	−	9.83614i	0.133514	−	0.366826i	0.988376	+	0.152029i	$0.0485807\pi$
$720$	−2.06787	+	0.850843i	−0.0770648	+	0.0317090i
$721$			16.8712i			0.628315i
$722$	18.5995	+	3.88045i	0.692202	+	0.144415i
$723$	9.98354	+	9.98354i	0.371292	+	0.371292i
$724$	−3.48409	+	2.92350i	−0.129485	+	0.108651i
$725$	19.5622	+	28.2195i	0.726524	+	1.04805i
$726$	−1.84704	+	10.4751i	−0.0685500	+	0.388766i
$727$	−14.6308	−	10.2446i	−0.542626	−	0.379951i	0.269889	−	0.962892i	$-0.413013\pi$
$727$	−14.6308	−	10.2446i	−0.542626	−	0.379951i	−0.812515	+	0.582941i	$0.801902\pi$
$728$	−20.1763	−	9.40837i	−0.747784	−	0.348697i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	3.28343	+	14.9773i	0.121525	+	0.554334i
$731$	−45.8090	−	38.4383i	−1.69431	−	1.42169i
$732$	−0.819312	−	9.36478i	−0.0302826	−	0.346132i
$733$	−1.73194	+	6.46368i	−0.0639705	+	0.238741i	−0.990507	−	0.137464i	$-0.956105\pi$
$733$	−1.73194	+	6.46368i	−0.0639705	+	0.238741i	0.926536	+	0.376206i	$0.122771\pi$
$734$	−8.43907	+	14.6169i	−0.311492	+	0.539520i
$735$	10.1986	−	11.0774i	0.376182	−	0.408596i
$736$	4.46338	−	0.787015i	0.164522	−	0.0290098i
$737$	−3.31835	+	2.32354i	−0.122233	+	0.0855885i
$738$	4.74603	+	10.1779i	0.174704	+	0.374653i
$739$	0.143125	+	0.170570i	0.00526495	+	0.00627452i	0.768670	−	0.639645i	$-0.220919\pi$
$739$	0.143125	+	0.170570i	0.00526495	+	0.00627452i	−0.763406	+	0.645919i	$0.776474\pi$
$740$	−9.51977	−	18.3928i	−0.349954	−	0.676135i
$741$	26.1388	+	1.54942i	0.960233	+	0.0569194i
$742$	6.61667	−	6.61667i	0.242906	−	0.242906i
$743$	−2.72585	+	31.1566i	−0.100002	+	1.14302i	0.765951	+	0.642899i	$0.222268\pi$
$743$	−2.72585	+	31.1566i	−0.100002	+	1.14302i	−0.865953	+	0.500126i	$0.833287\pi$
$744$	−2.05745	−	0.748851i	−0.0754298	−	0.0274542i
$745$	−15.4145	+	29.4417i	−0.564745	+	1.07866i
$746$	4.05605	+	23.0030i	0.148503	+	0.842200i
$747$	3.73148	−	8.00218i	0.136528	−	0.292784i
$748$	−3.96972	+	1.06368i	−0.145147	+	0.0388921i
$749$	−4.06825	−	7.04642i	−0.148651	−	0.257471i
$750$	11.1660	+	0.566516i	0.407724	+	0.0206862i
$751$	−8.04065	+	9.58247i	−0.293407	+	0.349669i	−0.892530	−	0.450988i	$-0.851072\pi$
$751$	−8.04065	+	9.58247i	−0.293407	+	0.349669i	0.599123	+	0.800657i	$0.295516\pi$
$752$	1.23296	+	0.330371i	0.0449614	+	0.0120474i
$753$	4.42600	+	16.5181i	0.161292	+	0.601951i
$754$	−38.7657	+	14.1096i	−1.41176	+	0.513840i
$755$	−5.16516	+	38.5324i	−0.187979	+	1.40234i
$756$	3.64961	+	0.643525i	0.132735	+	0.0234048i
$757$	19.4563	−	9.07263i	0.707152	−	0.329750i	−0.0355544	−	0.999368i	$-0.511320\pi$
$757$	19.4563	−	9.07263i	0.707152	−	0.329750i	0.742706	+	0.669617i	$0.233542\pi$
$758$	2.73959	+	0.239683i	0.0995063	+	0.00870567i
$759$	−2.73190			−0.0991617
$760$	−4.27686	+	8.75833i	−0.155138	+	0.317698i
$761$	−11.7100			−0.424487			−0.212244	−	0.977217i	$-0.568077\pi$
$761$	−11.7100			−0.424487			−0.212244	+	0.977217i	$0.568077\pi$
$762$	20.4278	+	1.78720i	0.740020	+	0.0647434i
$763$	27.0737	−	12.6247i	0.980135	−	0.457045i
$764$	2.62309	+	0.462522i	0.0949002	+	0.0167335i
$765$	−9.25254	−	12.1171i	−0.334526	−	0.438094i
$766$	−34.1909	+	12.4445i	−1.23537	+	0.449637i
$767$	−11.7719	−	43.9335i	−0.425060	−	1.58635i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	11.2611	−	13.4205i	0.406087	−	0.483955i	−0.523779	−	0.851854i	$-0.675478\pi$
$769$	11.2611	−	13.4205i	0.406087	−	0.483955i	0.929866	+	0.367899i	$0.119923\pi$
$770$	−4.21902	+	2.67387i	−0.152043	+	0.0963597i
$771$	−4.22543	−	7.31867i	−0.152175	−	0.263575i
$772$	−0.798058	+	0.213839i	−0.0287227	+	0.00769623i
$773$	16.9236	−	36.2928i	0.608700	−	1.30536i	−0.324459	−	0.945900i	$-0.605182\pi$
$773$	16.9236	−	36.2928i	0.608700	−	1.30536i	0.933160	−	0.359463i	$-0.117040\pi$
$774$	−1.52301	−	8.63744i	−0.0547436	−	0.310466i
$775$	7.70451	+	7.77737i	0.276754	+	0.279371i
$776$	18.3071	+	6.66325i	0.657188	+	0.239197i
$777$	−2.99155	+	34.1936i	−0.107321	+	1.22669i
$778$	20.7297	−	20.7297i	0.743195	−	0.743195i
$779$	44.9273	+	19.4346i	1.60969	+	0.696319i
$780$	−4.06935	+	12.8012i	−0.145706	+	0.458358i
$781$	−2.11417	−	2.51957i	−0.0756510	−	0.0901573i
$782$	13.0594	+	28.0061i	0.467005	+	1.00149i
$783$	5.62543	−	3.93897i	0.201036	−	0.140767i
$784$	−6.63151	+	1.16931i	−0.236840	+	0.0417612i
$785$	4.56972	+	4.20720i	0.163100	+	0.150161i
$786$	8.00927	−	13.8725i	0.285681	−	0.494814i
$787$	3.76871	−	14.0650i	0.134340	−	0.501364i	−0.865660	−	0.500633i	$-0.833101\pi$
$787$	3.76871	−	14.0650i	0.134340	−	0.501364i	1.00000		0.000731056i	$-0.000232702\pi$
$788$	−1.50366	−	17.1869i	−0.0535656	−	0.612257i
$789$	0.394368	+	0.330914i	0.0140399	+	0.0117809i
$790$	−21.6890	−	13.8893i	−0.771659	−	0.494158i
$791$	−12.7042	−	7.33478i	−0.451710	−	0.260795i
$792$	−0.546296	−	0.254742i	−0.0194118	−	0.00905186i
$793$	−46.2582	−	32.3903i	−1.64268	−	1.15021i
$794$	−0.758318	+	4.30063i	−0.0269117	+	0.152624i
$795$	−4.47121	−	3.44762i	−0.158577	−	0.122275i
$796$	10.8733	−	9.12382i	0.385395	−	0.323385i
$797$	11.8715	+	11.8715i	0.420511	+	0.420511i	0.885380	−	0.464868i	$-0.153898\pi$
$797$	11.8715	+	11.8715i	0.420511	+	0.420511i	−0.464868	+	0.885380i	$0.653898\pi$
$798$	13.7574	−	8.46616i	0.487007	−	0.299699i
$799$			8.70300i			0.307890i
$800$	−3.81505	−	3.23193i	−0.134883	−	0.114266i
$801$	−0.266862	+	0.733198i	−0.00942911	+	0.0259063i
$802$	0.168485	+	0.240622i	0.00594942	+	0.00849665i
$803$	−2.37075	+	3.38578i	−0.0836618	+	0.119481i
$804$	2.29857	+	6.31526i	0.0810643	+	0.222722i
$805$	25.3080	+	27.7497i	0.891992	+	0.978048i
$806$	−11.3906	+	6.57634i	−0.401215	+	0.231642i
$807$	25.6121	−	2.24076i	0.901587	−	0.0788787i
$808$	1.28314	−	0.112260i	0.0451406	−	0.00394929i
$809$	−5.57331	+	3.21775i	−0.195947	+	0.113130i	−0.594764	−	0.803901i	$-0.702754\pi$
$809$	−5.57331	+	3.21775i	−0.195947	+	0.113130i	0.398816	+	0.917031i	$0.369421\pi$
$810$	0.102792	−	2.23370i	0.00361175	−	0.0784844i
$811$	−6.67861	−	18.3493i	−0.234518	−	0.644332i	−1.00000		0.000874883i	$-0.999722\pi$
$811$	−6.67861	−	18.3493i	−0.234518	−	0.644332i	0.765482	−	0.643458i	$-0.222501\pi$
$812$	−14.5975	+	20.8474i	−0.512271	+	0.731599i
$813$	3.10704	+	4.43731i	0.108969	+	0.155623i
$814$	1.90945	−	5.24617i	0.0669262	−	0.183878i
$815$	−7.23587	+	17.3533i	−0.253461	+	0.607861i
$816$			6.81811i			0.238681i
$817$	−29.9642	−	23.7428i	−1.04831	−	0.830655i
$818$	3.66326	+	3.66326i	0.128083	+	0.128083i
$819$	17.0538	−	14.3098i	0.595907	−	0.500025i
$820$	−15.3335	+	19.8860i	−0.535471	+	0.694449i
$821$	4.29366	−	24.3505i	0.149850	−	0.849840i	−0.813495	−	0.581572i	$-0.802438\pi$
$821$	4.29366	−	24.3505i	0.149850	−	0.849840i	0.963344	−	0.268267i	$-0.0864511\pi$
$822$	−7.48930	−	5.24406i	−0.261219	−	0.182908i
$823$	−5.67597	−	2.64675i	−0.197852	−	0.0922598i	0.321167	−	0.947022i	$-0.395925\pi$
$823$	−5.67597	−	2.64675i	−0.197852	−	0.0922598i	−0.519019	+	0.854763i	$0.673703\pi$
$824$	−3.94258	−	2.27625i	−0.137346	−	0.0792968i
$825$	1.92638	+	2.31784i	0.0670680	+	0.0806968i
$826$	−21.4947	−	18.0362i	−0.747895	−	0.627558i
$827$	0.170735	+	1.95151i	0.00593705	+	0.0678608i	0.998585	−	0.0531748i	$-0.0169340\pi$
$827$	0.170735	+	1.95151i	0.00593705	+	0.0678608i	−0.992648	+	0.121036i	$0.961378\pi$
$828$	−1.17303	+	4.37781i	−0.0407656	+	0.152139i
$829$	7.24228	−	12.5440i	0.251535	−	0.435671i	−0.712414	−	0.701760i	$-0.752398\pi$
$829$	7.24228	−	12.5440i	0.251535	−	0.435671i	0.963949	+	0.266089i	$0.0857314\pi$
$830$	19.7264	−	0.814771i	0.684713	−	0.0282811i
$831$	11.7510	−	2.07201i	0.407636	−	0.0718773i
$832$	4.92079	−	3.44558i	0.170598	−	0.119454i
$833$	−19.4032	−	41.6102i	−0.672280	−	1.44171i
$834$	−7.47508	−	8.90845i	−0.258841	−	0.308475i
$835$	−10.6063	+	5.48960i	−0.367046	+	0.189976i
$836$	−2.51781	+	0.750959i	−0.0870804	+	0.0259725i
$837$	1.54821	−	1.54821i	0.0535138	−	0.0535138i
$838$	−1.52947	+	17.4819i	−0.0528347	+	0.603903i
$839$	50.8306	+	18.5008i	1.75487	+	0.638719i	0.999856	−	0.0169935i	$-0.00540946\pi$
$839$	50.8306	+	18.5008i	1.75487	+	0.638719i	0.755011	+	0.655713i	$0.227632\pi$
$840$	2.47325	+	7.90899i	0.0853352	+	0.272886i
$841$	3.15361	+	17.8850i	0.108745	+	0.616724i
$842$	−13.3213	+	28.5676i	−0.459082	+	0.984505i
$843$	6.76518	−	1.81272i	0.233005	−	0.0624336i
$844$	4.27696	+	7.40791i	0.147219	+	0.254991i
$845$	27.6342	+	43.6030i	0.950644	+	1.49999i
$846$	−0.820489	+	0.977821i	−0.0282090	+	0.0336182i
$847$	38.0754	+	10.2023i	1.30829	+	0.350555i
$848$	0.653515	+	2.43895i	0.0224418	+	0.0837539i
$849$	−3.11530	+	1.13387i	−0.106917	+	0.0389145i
$850$	14.5525	−	30.8284i	0.499147	−	1.05740i
$851$	−41.3398	−	7.28933i	−1.41711	−	0.249875i
$852$	−4.94534	+	2.30605i	−0.169424	+	0.0790039i
$853$	−23.2732	−	2.03614i	−0.796858	−	0.0697160i	−0.318547	−	0.947907i	$-0.603195\pi$
$853$	−23.2732	−	2.03614i	−0.796858	−	0.0697160i	−0.478310	+	0.878191i	$0.658751\pi$
$854$	−34.8376			−1.19212
$855$	−6.13027	−	7.57759i	−0.209651	−	0.259148i
$856$	2.19555			0.0750422
$857$	−20.5206	−	1.79532i	−0.700969	−	0.0613268i	−0.268901	−	0.963168i	$-0.586660\pi$
$857$	−20.5206	−	1.79532i	−0.700969	−	0.0613268i	−0.432068	+	0.901841i	$0.642216\pi$
$858$	−3.28170	+	1.53028i	−0.112035	+	0.0522429i
$859$	42.7853	+	7.54421i	1.45982	+	0.257405i	0.846482	−	0.532418i	$-0.178716\pi$
$859$	42.7853	+	7.54421i	1.45982	+	0.257405i	0.613335	+	0.789823i	$0.289828\pi$
$860$	15.5872	−	11.9023i	0.531518	−	0.405865i
$861$	39.1078	−	14.2341i	1.33279	−	0.485096i
$862$	−2.17296	−	8.10961i	−0.0740114	−	0.276214i
$863$	−40.5779	−	10.8728i	−1.38129	−	0.370115i	−0.509700	−	0.860352i	$-0.670244\pi$
$863$	−40.5779	−	10.8728i	−1.38129	−	0.370115i	−0.871589	+	0.490237i	$0.836910\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	−4.79284	+	21.3809i	−0.162961	+	0.726972i
$866$	−15.8388	−	27.4336i	−0.538223	−	0.932230i
$867$	−28.4818	+	7.63169i	−0.967294	+	0.259186i
$868$	−3.42916	+	7.35385i	−0.116393	+	0.249606i
$869$	−1.20559	−	6.83725i	−0.0408969	−	0.231938i
$870$	13.6042	+	7.12261i	0.461224	+	0.241479i
$871$	37.9369	+	13.8079i	1.28544	+	0.467863i
$872$	−0.702543	+	8.03011i	−0.0237911	+	0.271934i
$873$	−13.7759	+	13.7759i	−0.466243	+	0.466243i
$874$	8.84810	+	17.6633i	0.299291	+	0.597471i
$875$	5.69799	−	41.0397i	0.192627	−	1.38740i
$876$	4.40767	+	5.25285i	0.148921	+	0.177477i
$877$	11.3529	+	24.3464i	0.383361	+	0.822120i	0.999408	+	0.0344107i	$0.0109554\pi$
$877$	11.3529	+	24.3464i	0.383361	+	0.822120i	−0.616047	+	0.787710i	$0.711267\pi$
$878$	24.6501	−	17.2602i	0.831900	−	0.582502i
$879$	−1.42461	+	0.251198i	−0.0480510	+	0.00847269i
$880$	−0.0556231	−	1.34669i	−0.00187505	−	0.0453969i
$881$	11.3485	−	19.6562i	0.382341	−	0.662234i	−0.609056	−	0.793128i	$-0.708451\pi$
$881$	11.3485	−	19.6562i	0.382341	−	0.662234i	0.991396	+	0.130894i	$0.0417847\pi$
$882$	1.74284	−	6.50436i	0.0586844	−	0.219013i
$883$	0.144119	+	1.64729i	0.00484998	+	0.0554356i	0.998234	−	0.0594042i	$-0.0189201\pi$
$883$	0.144119	+	1.64729i	0.00484998	+	0.0554356i	−0.993384	+	0.114840i	$0.963365\pi$
$884$	31.3753	+	26.3270i	1.05527	+	0.885474i
$885$	−9.13025	+	14.2575i	−0.306910	+	0.479260i
$886$	−28.4898	−	16.4486i	−0.957135	−	0.552602i
$887$	−8.68205	−	4.04851i	−0.291515	−	0.135936i	0.271360	−	0.962478i	$-0.412527\pi$
$887$	−8.68205	−	4.04851i	−0.291515	−	0.135936i	−0.562874	+	0.826543i	$0.690304\pi$
$888$	−7.58698	−	5.31246i	−0.254603	−	0.178275i
$889$	13.1960	−	74.8383i	0.442580	−	2.51000i
$890$	−1.73030	+	0.223658i	−0.0579999	+	0.00749703i
$891$	0.461749	−	0.387454i	0.0154692	−	0.0129802i
$892$	3.07562	+	3.07562i	0.102979	+	0.102979i
$893$	0.156098	+	5.56174i	0.00522363	+	0.186117i
$894$			14.8622i			0.497065i
$895$	−15.2518	−	37.0676i	−0.509812	−	1.23903i
$896$	1.26750	−	3.48242i	0.0423441	−	0.116340i
$897$	15.6162	+	22.3022i	0.521409	+	0.744649i
$898$	−6.36069	+	9.08401i	−0.212259	+	0.303137i
$899$	5.14264	+	14.1293i	0.171517	+	0.471238i
$900$	4.54143	−	2.09174i	0.151381	−	0.0697247i
$901$	−14.9092	+	8.60782i	−0.496697	+	0.286768i
$902$	−6.74339	+	0.589970i	−0.224530	+	0.0196439i
$903$	−32.3797	+	2.83286i	−1.07753	+	0.0942716i
$904$	3.42809	−	1.97921i	0.114017	−	0.0658275i
$905$	7.51425	−	6.85308i	0.249782	−	0.227804i
$906$	5.94648	+	16.3378i	0.197559	+	0.542788i
$907$	12.7823	−	18.2550i	0.424429	−	0.606148i	−0.548808	−	0.835948i	$-0.684918\pi$
$907$	12.7823	−	18.2550i	0.424429	−	0.606148i	0.973238	+	0.229800i	$0.0738072\pi$
$908$	−0.474164	−	0.677176i	−0.0157357	−	0.0224729i
$909$	−0.440535	+	1.21036i	−0.0146116	+	0.0401451i
$910$	45.9454	+	19.1580i	1.52307	+	0.635081i
$911$			26.6196i			0.881947i	0.897520	+	0.440973i	$0.145367\pi$
$911$			26.6196i			0.881947i	−0.897520	+	0.440973i	$0.854633\pi$
$912$	0.122291	+	4.35718i	0.00404945	+	0.144281i
$913$	3.76331	+	3.76331i	0.124547	+	0.124547i
$914$	17.3731	−	14.5777i	0.574650	−	0.482189i
$915$	2.69465	+	20.8468i	0.0890823	+	0.689175i
$916$	3.81616	−	21.6425i	0.126090	−	0.715090i
$917$	−48.6276	−	34.0494i	−1.60583	−	1.12441i
$918$	−6.17930	−	2.88146i	−0.203947	−	0.0951022i
$919$	−25.0880	−	14.4845i	−0.827576	−	0.477801i	0.0254461	−	0.999676i	$-0.491899\pi$
$919$	−25.0880	−	14.4845i	−0.827576	−	0.477801i	−0.853022	+	0.521875i	$0.825233\pi$
$920$	−9.89930	+	2.17020i	−0.326370	+	0.0715492i
$921$	−6.57732	−	5.51903i	−0.216730	−	0.181858i
$922$	−0.821675	−	9.39179i	−0.0270604	−	0.309302i
$923$	−8.48374	+	31.6617i	−0.279246	+	1.04216i
$924$	−1.11691	+	1.93454i	−0.0367436	+	0.0636418i
$925$	22.9660	+	40.2141i	0.755117	+	1.32223i
$926$	7.45543	−	1.31459i	0.245001	−	0.0432002i
$927$	3.72918	−	2.61120i	0.122482	−	0.0857632i
$928$	−2.90228	−	6.22396i	−0.0952720	−	0.204311i
$929$	22.1850	+	26.4390i	0.727865	+	0.867436i	0.995370	−	0.0961210i	$-0.0306436\pi$
$929$	22.1850	+	26.4390i	0.727865	+	0.867436i	−0.267505	+	0.963557i	$0.586199\pi$
$930$	4.66578	+	1.48320i	0.152997	+	0.0486359i
$931$	−13.1461	−	26.2435i	−0.430847	−	0.860094i
$932$	6.44499	−	6.44499i	0.211113	−	0.211113i
$933$	−2.12171	+	24.2512i	−0.0694615	+	0.793949i
$934$	−6.11627	−	2.22614i	−0.200130	−	0.0728415i
$935$	8.77084	−	2.74276i	0.286837	−	0.0896979i
$936$	1.04314	+	5.91592i	0.0340960	+	0.193368i
$937$	−9.99114	+	21.4261i	−0.326396	+	0.699959i	−0.999205	−	0.0398571i	$-0.987310\pi$
$937$	−9.99114	+	21.4261i	−0.326396	+	0.699959i	0.672809	+	0.739816i	$0.265088\pi$
$938$	24.0572	−	6.44611i	0.785495	−	0.210473i
$939$	−2.54924	−	4.41542i	−0.0831915	−	0.144092i
$940$	−2.78512	−	0.624326i	−0.0908406	−	0.0203633i
$941$	−13.6514	+	16.2691i	−0.445023	+	0.530358i	−0.941194	−	0.337867i	$-0.890295\pi$
$941$	−13.6514	+	16.2691i	−0.445023	+	0.530358i	0.496171	+	0.868225i	$0.334739\pi$
$942$	2.68322	+	0.718966i	0.0874240	+	0.0234252i
$943$	13.1732	+	49.1630i	0.428978	+	1.60097i
$944$	7.11487	−	2.58960i	0.231569	−	0.0842843i
$945$	−8.21322	−	1.10096i	−0.267176	−	0.0358142i
$946$	5.20640	+	0.918028i	0.169275	+	0.0298477i
$947$	4.52056	−	2.10797i	0.146899	−	0.0684999i	−0.347779	−	0.937577i	$-0.613064\pi$
$947$	4.52056	−	2.10797i	0.146899	−	0.0684999i	0.494677	+	0.869077i	$0.335286\pi$
$948$	−11.4742	−	1.00386i	−0.372664	−	0.0326039i
$949$	41.1919			1.33715
$950$	8.74700	−	19.9622i	0.283790	−	0.647660i
$951$	−12.5932			−0.408362
$952$	25.1712	+	2.20219i	0.815802	+	0.0713735i
$953$	19.8814	−	9.27083i	0.644020	−	0.300312i	−0.0730335	−	0.997329i	$-0.523268\pi$
$953$	19.8814	−	9.27083i	0.644020	−	0.300312i	0.717054	+	0.697018i	$0.245490\pi$
$954$	−2.48663	−	0.438459i	−0.0805075	−	0.0141956i
$955$	−5.90310	−	0.791293i	−0.191020	−	0.0256056i
$956$	17.9979	−	6.55070i	0.582094	−	0.211865i
$957$	1.07137	+	3.99841i	0.0346325	+	0.129250i
$958$	−17.9735	−	4.81597i	−0.580696	−	0.155597i
$959$	−21.7791	+	25.9553i	−0.703283	+	0.838141i
$960$	−2.18192	−	0.489109i	−0.0704211	−	0.0157859i
$961$	−13.1031	−	22.6952i	−0.422679	−	0.732102i
$962$	−53.7427	+	14.4003i	−1.73273	+	0.464284i
$963$	−0.927877	+	1.98984i	−0.0299004	+	0.0641217i
$964$	2.45171	+	13.9044i	0.0789644	+	0.447829i
$965$	1.76326	−	0.551395i	0.0567613	−	0.0177500i
$966$	15.7832	+	5.74460i	0.507815	+	0.184830i
$967$	−3.28935	+	37.5975i	−0.105778	+	1.20905i	0.738913	+	0.673800i	$0.235339\pi$
$967$	−3.28935	+	37.5975i	−0.105778	+	1.20905i	−0.844692	+	0.535253i	$0.820216\pi$
$968$	−7.52126	+	7.52126i	−0.241742	+	0.241742i
$969$	−28.4797	+	8.49431i	−0.914899	+	0.272876i
$970$	−41.5160	−	13.1974i	−1.33300	−	0.423744i
$971$	−31.7759	−	37.8691i	−1.01974	−	1.21528i	−0.976345	−	0.216218i	$-0.930628\pi$
$971$	−31.7759	−	37.8691i	−1.01974	−	1.21528i	−0.0433927	−	0.999058i	$-0.513817\pi$
$972$	−0.422618	−	0.906308i	−0.0135555	−	0.0290698i
$973$	−35.3027	+	24.7192i	−1.13175	+	0.792463i
$974$	−38.7482	+	6.83235i	−1.24157	+	0.218923i
$975$	7.91031	−	28.9756i	0.253333	−	0.927960i
$976$	4.70027	−	8.14111i	0.150452	−	0.260591i
$977$	−4.75978	+	17.7637i	−0.152279	+	0.568312i	0.847044	+	0.531523i	$0.178380\pi$
$977$	−4.75978	+	17.7637i	−0.152279	+	0.568312i	−0.999323	+	0.0367899i	$0.988287\pi$
$978$	0.732830	+	8.37628i	0.0234333	+	0.267844i
$979$	−0.360281	−	0.302312i	−0.0115146	−	0.00966193i
$980$	14.7080	−	3.22439i	0.469829	−	0.102999i
$981$	−6.98084	−	4.03039i	−0.222881	−	0.128680i
$982$	28.0381	+	13.0744i	0.894731	+	0.417220i
$983$	−30.9147	−	21.6467i	−0.986025	−	0.690422i	−0.0349524	−	0.999389i	$-0.511128\pi$
$983$	−30.9147	−	21.6467i	−0.986025	−	0.690422i	−0.951073	+	0.308967i	$0.900017\pi$
$984$	−1.95008	+	11.0594i	−0.0621662	+	0.352562i
$985$	4.94541	+	38.2595i	0.157574	+	1.21905i
$986$	35.8681	−	30.0969i	1.14227	−	0.958482i
$987$	3.34492	+	3.34492i	0.106470	+	0.106470i
$988$	20.5230	+	16.2618i	0.652922	+	0.517357i
$989$		−	39.7508i		−	1.26400i
$990$	1.24402	+	0.518723i	0.0395376	+	0.0164861i
$991$	−2.31913	+	6.37174i	−0.0736694	+	0.202405i	−0.971062	−	0.238828i	$-0.923237\pi$
$991$	−2.31913	+	6.37174i	−0.0736694	+	0.202405i	0.897392	+	0.441233i	$0.145459\pi$
$992$	−1.25584	−	1.79353i	−0.0398730	−	0.0569446i
$993$	7.30946	−	10.4390i	0.231959	−	0.331271i
$994$	6.91620	+	19.0021i	0.219368	+	0.602710i
$995$	−23.4509	+	21.3875i	−0.743443	+	0.678029i
$996$	7.64651	−	4.41471i	0.242289	−	0.139886i
$997$	−16.7557	+	1.46593i	−0.530659	+	0.0464266i	−0.349337	−	0.936997i	$-0.613593\pi$
$997$	−16.7557	+	1.46593i	−0.530659	+	0.0464266i	−0.181322	+	0.983424i	$0.558038\pi$
$998$	−25.4562	+	2.22713i	−0.805801	+	0.0704984i
$999$	8.02112	−	4.63100i	0.253777	−	0.146518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.13.1	✓	120
5.2	odd	4	inner	570.2.bh.b.127.9	yes	120
19.3	odd	18	inner	570.2.bh.b.193.9	yes	120
95.22	even	36	inner	570.2.bh.b.307.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.13.1	✓	120	1.1	even	1	trivial
570.2.bh.b.127.9	yes	120	5.2	odd	4	inner
570.2.bh.b.193.9	yes	120	19.3	odd	18	inner
570.2.bh.b.307.1	yes	120	95.22	even	36	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.21625 - 0.297081i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.959162 + 3.57964i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.21625 - 0.297081i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.959162 + 3.57964i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(2.18192 + 0.489109i) q^{10} +(0.301385 + 0.522015i) q^{11} +(0.965926 - 0.258819i) q^{12} +(2.53874 - 5.44435i) q^{13} +(-0.643525 - 3.64961i) q^{14} +(-2.13415 + 0.667379i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.594237 + 6.79216i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-0.257928 + 4.35126i) q^{19} +(-2.13099 - 0.677415i) q^{20} +(2.38212 + 2.83890i) q^{21} +(-0.254742 - 0.546296i) q^{22} +(-3.71259 + 2.59958i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(4.82349 + 1.31681i) q^{25} +(-3.00359 + 5.20237i) q^{26} +(0.258819 - 0.965926i) q^{27} +(0.322992 + 3.69181i) q^{28} +(5.26072 + 4.41427i) q^{29} +(2.18420 - 0.478835i) q^{30} +(1.89616 + 1.09475i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(0.493761 + 0.345735i) q^{33} +(1.18395 - 6.71452i) q^{34} +(-1.06229 - 8.21831i) q^{35} +(0.766044 - 0.642788i) q^{36} +(6.54922 + 6.54922i) q^{37} +(0.636184 - 4.31222i) q^{38} -6.00718i q^{39} +(2.06384 + 0.860565i) q^{40} +(3.84091 - 10.5528i) q^{41} +(-2.12563 - 3.03571i) q^{42} +(-5.03066 + 7.18452i) q^{43} +(0.206160 + 0.566419i) q^{44} +(-1.65215 + 1.50678i) q^{45} +(3.92503 - 2.26612i) q^{46} +(1.27160 - 0.111250i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(-5.83165 + 3.36690i) q^{49} +(-4.69036 - 1.73219i) q^{50} +(2.33193 + 6.40692i) q^{51} +(3.44558 - 4.92079i) q^{52} +(1.44827 + 2.06835i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(-0.512863 - 1.24645i) q^{55} -3.70592i q^{56} +(1.60516 + 4.05259i) q^{57} +(-4.85597 - 4.85597i) q^{58} +(5.80010 - 4.86686i) q^{59} +(-2.21762 + 0.286648i) q^{60} +(1.63239 - 9.25773i) q^{61} +(-1.79353 - 1.25584i) q^{62} +(3.35870 + 1.56619i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-7.24390 + 11.3118i) q^{65} +(-0.461749 - 0.387454i) q^{66} +(0.585736 + 6.69499i) q^{67} +(-1.76466 + 6.58578i) q^{68} +(-2.26612 + 3.92503i) q^{69} +(0.341978 + 8.27962i) q^{70} +(-5.37368 + 0.947524i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(2.89794 + 6.21466i) q^{73} +(-5.95350 - 7.09510i) q^{74} +(4.92807 - 0.845058i) q^{75} +(-1.00960 + 4.24037i) q^{76} +(-1.57955 + 1.57955i) q^{77} +(-0.523560 + 5.98432i) q^{78} +(-10.8234 - 3.93939i) q^{79} +(-1.98098 - 1.03717i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.74603 + 10.1779i) q^{82} +(8.52857 - 2.28522i) q^{83} +(1.85296 + 3.20942i) q^{84} +(3.33480 - 14.8766i) q^{85} +(5.63769 - 6.71873i) q^{86} +(6.63338 + 1.77741i) q^{87} +(-0.156009 - 0.582232i) q^{88} +(-0.733198 + 0.266862i) q^{89} +(1.77719 - 1.35705i) q^{90} +(21.9239 + 3.86577i) q^{91} +(-4.10760 + 1.91541i) q^{92} +(2.18116 + 0.190827i) q^{93} -1.27645 q^{94} +(1.86431 - 9.56684i) q^{95} -1.00000 q^{96} +(-19.4079 - 1.69797i) q^{97} +(6.10290 - 2.84583i) q^{98} +(0.593613 + 0.104670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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