LMFDB - Embedded newform 189.2.ba.a.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22264 + 1.45709i) q^{2} +(-1.12031 + 1.32095i) q^{3} +(-0.280959 - 1.59339i) q^{4} +(-0.691544 + 0.580274i) q^{5} +(-0.555004 - 3.24744i) q^{6} +(-0.448602 + 2.60744i) q^{7} +(-0.629295 - 0.363324i) q^{8} +(-0.489815 - 2.95974i) q^{9} +O(q^{10})$	\(q+(-1.22264 + 1.45709i) q^{2} +(-1.12031 + 1.32095i) q^{3} +(-0.280959 - 1.59339i) q^{4} +(-0.691544 + 0.580274i) q^{5} +(-0.555004 - 3.24744i) q^{6} +(-0.448602 + 2.60744i) q^{7} +(-0.629295 - 0.363324i) q^{8} +(-0.489815 - 2.95974i) q^{9} -1.71711i q^{10} +(-2.24705 + 2.67793i) q^{11} +(2.41955 + 1.41396i) q^{12} +(1.35464 - 3.72184i) q^{13} +(-3.25080 - 3.84163i) q^{14} +(0.00822998 - 1.56358i) q^{15} +(4.33960 - 1.57949i) q^{16} -0.467865 q^{17} +(4.91149 + 2.90501i) q^{18} -3.62874i q^{19} +(1.11890 + 0.938869i) q^{20} +(-2.94173 - 3.51372i) q^{21} +(-1.15465 - 6.54832i) q^{22} +(-1.19589 + 3.28569i) q^{23} +(1.18494 - 0.424232i) q^{24} +(-0.726726 + 4.12147i) q^{25} +(3.76682 + 6.52432i) q^{26} +(4.45842 + 2.66881i) q^{27} +(4.28072 - 0.0177830i) q^{28} +(-1.79273 - 4.92550i) q^{29} +(2.26822 + 1.92370i) q^{30} +(-6.86071 + 1.20973i) q^{31} +(-2.50728 + 6.88869i) q^{32} +(-1.02002 - 5.96836i) q^{33} +(0.572032 - 0.681722i) q^{34} +(-1.20280 - 2.06347i) q^{35} +(-4.57842 + 1.61203i) q^{36} +(-4.92689 + 8.53362i) q^{37} +(5.28741 + 4.43666i) q^{38} +(3.39875 + 5.95902i) q^{39} +(0.646012 - 0.113909i) q^{40} +(-2.71326 - 0.987547i) q^{41} +(8.71650 + 0.00966928i) q^{42} +(-1.54504 + 8.76238i) q^{43} +(4.89833 + 2.82805i) q^{44} +(2.05619 + 1.76256i) q^{45} +(-3.32540 - 5.75976i) q^{46} +(-0.579339 + 3.28560i) q^{47} +(-2.77527 + 7.50190i) q^{48} +(-6.59751 - 2.33941i) q^{49} +(-5.11683 - 6.09800i) q^{50} +(0.524153 - 0.618026i) q^{51} +(-6.31096 - 1.11279i) q^{52} +(8.75304 + 5.05357i) q^{53} +(-9.33975 + 3.23332i) q^{54} -3.15581i q^{55} +(1.22965 - 1.47786i) q^{56} +(4.79338 + 4.06531i) q^{57} +(9.36878 + 3.40996i) q^{58} +(-3.04590 - 1.10862i) q^{59} +(-2.49371 + 0.426188i) q^{60} +(0.0601824 + 0.0106118i) q^{61} +(6.62553 - 11.4757i) q^{62} +(7.93709 + 0.0505822i) q^{63} +(-2.35384 - 4.07697i) q^{64} +(1.22290 + 3.35988i) q^{65} +(9.94356 + 5.81092i) q^{66} +(7.85348 - 6.58985i) q^{67} +(0.131451 + 0.745493i) q^{68} +(-3.00046 - 5.26070i) q^{69} +(4.47727 + 0.770299i) q^{70} +(-2.19935 + 1.26979i) q^{71} +(-0.767107 + 2.04051i) q^{72} +(-7.24870 + 4.18504i) q^{73} +(-6.41043 - 17.6125i) q^{74} +(-4.63009 - 5.57729i) q^{75} +(-5.78202 + 1.01953i) q^{76} +(-5.97452 - 7.06039i) q^{77} +(-12.8383 - 2.33348i) q^{78} +(7.23876 + 6.07404i) q^{79} +(-2.08449 + 3.61044i) q^{80} +(-8.52016 + 2.89945i) q^{81} +(4.75630 - 2.74605i) q^{82} +(10.6153 - 3.86367i) q^{83} +(-4.77224 + 5.67454i) q^{84} +(0.323549 - 0.271490i) q^{85} +(-10.8786 - 12.9646i) q^{86} +(8.51475 + 3.14997i) q^{87} +(2.38702 - 0.868803i) q^{88} -3.03736 q^{89} +(-5.08221 + 0.841067i) q^{90} +(9.09679 + 5.20177i) q^{91} +(5.57140 + 0.982388i) q^{92} +(6.08813 - 10.4179i) q^{93} +(-4.07909 - 4.86127i) q^{94} +(2.10566 + 2.50943i) q^{95} +(-6.29069 - 11.0295i) q^{96} +(-5.02929 - 0.886800i) q^{97} +(11.4751 - 6.75291i) q^{98} +(9.02664 + 5.33901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.22264	+	1.45709i	−0.864540	+	1.03032i	0.134682	+	0.990889i	$0.456999\pi$
$2$	−1.22264	+	1.45709i	−0.864540	+	1.03032i	−0.999222	+	0.0394303i	$0.987446\pi$
$3$	−1.12031	+	1.32095i	−0.646811	+	0.762651i
$3$	−1.12031	+	1.32095i	−0.646811	+	0.762651i
$4$	−0.280959	−	1.59339i	−0.140479	−	0.796697i
$5$	−0.691544	+	0.580274i	−0.309268	+	0.259506i	−0.784189	−	0.620522i	$-0.786921\pi$
$5$	−0.691544	+	0.580274i	−0.309268	+	0.259506i	0.474922	+	0.880028i	$0.342476\pi$
$6$	−0.555004	−	3.24744i	−0.226579	−	1.32576i
$7$	−0.448602	+	2.60744i	−0.169556	+	0.985521i
$7$	−0.448602	+	2.60744i	−0.169556	+	0.985521i
$8$	−0.629295	−	0.363324i	−0.222489	−	0.128454i
$9$	−0.489815	−	2.95974i	−0.163272	−	0.986581i
$10$		−	1.71711i		−	0.542998i
$11$	−2.24705	+	2.67793i	−0.677512	+	0.807427i	−0.989785	−	0.142565i	$-0.954465\pi$
$11$	−2.24705	+	2.67793i	−0.677512	+	0.807427i	0.312274	+	0.949992i	$0.398909\pi$
$12$	2.41955	+	1.41396i	0.698465	+	0.408176i
$13$	1.35464	−	3.72184i	0.375709	−	1.03225i	−0.597407	−	0.801938i	$-0.703802\pi$
$13$	1.35464	−	3.72184i	0.375709	−	1.03225i	0.973116	−	0.230315i	$-0.0739755\pi$
$14$	−3.25080	−	3.84163i	−0.868813	−	1.02672i
$15$	0.00822998	−	1.56358i	0.00212497	−	0.403715i
$16$	4.33960	−	1.57949i	1.08490	−	0.394871i
$17$	−0.467865			−0.113474			−0.0567369	−	0.998389i	$-0.518070\pi$
$17$	−0.467865			−0.113474			−0.0567369	+	0.998389i	$0.518070\pi$
$18$	4.91149	+	2.90501i	1.15765	+	0.684717i
$19$		−	3.62874i		−	0.832490i	−0.909252	−	0.416245i	$-0.863346\pi$
$19$		−	3.62874i		−	0.832490i	0.909252	−	0.416245i	$-0.136654\pi$
$20$	1.11890	+	0.938869i	0.250194	+	0.209938i
$21$	−2.94173	−	3.51372i	−0.641937	−	0.766757i
$22$	−1.15465	−	6.54832i	−0.246171	−	1.39611i
$23$	−1.19589	+	3.28569i	−0.249361	+	0.685114i	0.750349	+	0.661042i	$0.229885\pi$
$23$	−1.19589	+	3.28569i	−0.249361	+	0.685114i	−0.999710	+	0.0240721i	$0.992337\pi$
$24$	1.18494	−	0.424232i	0.241874	−	0.0865961i
$25$	−0.726726	+	4.12147i	−0.145345	+	0.824294i
$26$	3.76682	+	6.52432i	0.738734	+	1.27953i
$27$	4.45842	+	2.66881i	0.858023	+	0.513612i
$28$	4.28072	−	0.0177830i	0.808981	−	0.00336068i
$29$	−1.79273	−	4.92550i	−0.332902	−	0.914642i	−0.987353	−	0.158537i	$-0.949322\pi$
$29$	−1.79273	−	4.92550i	−0.332902	−	0.914642i	0.654451	−	0.756105i	$-0.272900\pi$
$30$	2.26822	+	1.92370i	0.414118	+	0.351217i
$31$	−6.86071	+	1.20973i	−1.23222	+	0.217274i	−0.751579	−	0.659644i	$-0.770707\pi$
$31$	−6.86071	+	1.20973i	−1.23222	+	0.217274i	−0.480641	+	0.876917i	$0.659596\pi$
$32$	−2.50728	+	6.88869i	−0.443229	+	1.21776i
$33$	−1.02002	−	5.96836i	−0.177563	−	1.03896i
$34$	0.572032	−	0.681722i	0.0981027	−	0.116914i
$35$	−1.20280	−	2.06347i	−0.203311	−	0.348790i
$36$	−4.57842	+	1.61203i	−0.763070	+	0.268672i
$37$	−4.92689	+	8.53362i	−0.809975	+	1.40292i	0.102905	+	0.994691i	$0.467186\pi$
$37$	−4.92689	+	8.53362i	−0.809975	+	1.40292i	−0.912881	+	0.408227i	$0.866147\pi$
$38$	5.28741	+	4.43666i	0.857731	+	0.719721i
$39$	3.39875	+	5.95902i	0.544235	+	0.954207i
$40$	0.646012	−	0.113909i	0.102144	−	0.0180107i
$41$	−2.71326	−	0.987547i	−0.423741	−	0.154229i	0.121343	−	0.992611i	$-0.461280\pi$
$41$	−2.71326	−	0.987547i	−0.423741	−	0.154229i	−0.545084	+	0.838382i	$0.683502\pi$
$42$	8.71650	+	0.00966928i	1.34499	+	0.00149200i
$43$	−1.54504	+	8.76238i	−0.235617	+	1.33625i	0.605693	+	0.795698i	$0.292896\pi$
$43$	−1.54504	+	8.76238i	−0.235617	+	1.33625i	−0.841310	+	0.540553i	$0.818215\pi$
$44$	4.89833	+	2.82805i	0.738452	+	0.426345i
$45$	2.05619	+	1.76256i	0.306519	+	0.262748i
$46$	−3.32540	−	5.75976i	−0.490303	−	0.849230i
$47$	−0.579339	+	3.28560i	−0.0845053	+	0.479253i	0.912957	+	0.408056i	$0.133793\pi$
$47$	−0.579339	+	3.28560i	−0.0845053	+	0.479253i	−0.997462	+	0.0711975i	$0.977318\pi$
$48$	−2.77527	+	7.50190i	−0.400576	+	1.08281i
$49$	−6.59751	−	2.33941i	−0.942502	−	0.334201i
$50$	−5.11683	−	6.09800i	−0.723629	−	0.862387i
$51$	0.524153	−	0.618026i	0.0733961	−	0.0865409i
$52$	−6.31096	−	1.11279i	−0.875173	−	0.154317i
$53$	8.75304	+	5.05357i	1.20232	+	0.694161i	0.961071	−	0.276302i	$-0.0891090\pi$
$53$	8.75304	+	5.05357i	1.20232	+	0.694161i	0.241251	+	0.970463i	$0.422442\pi$
$54$	−9.33975	+	3.23332i	−1.27098	+	0.439999i
$55$		−	3.15581i		−	0.425530i
$56$	1.22965	−	1.47786i	0.164319	−	0.197488i
$57$	4.79338	+	4.06531i	0.634899	+	0.538464i
$58$	9.36878	+	3.40996i	1.23018	+	0.447749i
$59$	−3.04590	−	1.10862i	−0.396543	−	0.144330i	0.136049	−	0.990702i	$-0.456560\pi$
$59$	−3.04590	−	1.10862i	−0.396543	−	0.144330i	−0.532592	+	0.846372i	$0.678782\pi$
$60$	−2.49371	+	0.426188i	−0.321937	+	0.0550206i
$61$	0.0601824	+	0.0106118i	0.00770557	+	0.00135870i	0.177500	−	0.984121i	$-0.443199\pi$
$61$	0.0601824	+	0.0106118i	0.00770557	+	0.00135870i	−0.169794	+	0.985480i	$0.554310\pi$
$62$	6.62553	−	11.4757i	0.841443	−	1.45742i
$63$	7.93709	+	0.0505822i	0.999980	+	0.00637276i
$64$	−2.35384	−	4.07697i	−0.294230	−	0.509621i
$65$	1.22290	+	3.35988i	0.151681	+	0.416741i
$66$	9.94356	+	5.81092i	1.22397	+	0.715274i
$67$	7.85348	−	6.58985i	0.959455	−	0.805078i	−0.0214094	−	0.999771i	$-0.506815\pi$
$67$	7.85348	−	6.58985i	0.959455	−	0.805078i	0.980864	+	0.194693i	$0.0623709\pi$
$68$	0.131451	+	0.745493i	0.0159407	+	0.0904043i
$69$	−3.00046	−	5.26070i	−0.361213	−	0.633314i
$70$	4.47727	+	0.770299i	0.535136	+	0.0920684i
$71$	−2.19935	+	1.26979i	−0.261014	+	0.150697i	−0.624797	−	0.780787i	$-0.714818\pi$
$71$	−2.19935	+	1.26979i	−0.261014	+	0.150697i	0.363783	+	0.931484i	$0.381485\pi$
$72$	−0.767107	+	2.04051i	−0.0904044	+	0.240477i
$73$	−7.24870	+	4.18504i	−0.848396	+	0.489822i	−0.860109	−	0.510110i	$-0.829605\pi$
$73$	−7.24870	+	4.18504i	−0.848396	+	0.489822i	0.0117134	+	0.999931i	$0.496271\pi$
$74$	−6.41043	−	17.6125i	−0.745197	−	2.04741i
$75$	−4.63009	−	5.57729i	−0.534637	−	0.644010i
$76$	−5.78202	+	1.01953i	−0.663243	+	0.116948i
$77$	−5.97452	−	7.06039i	−0.680860	−	0.804606i
$78$	−12.8383	−	2.33348i	−1.45365	−	0.264215i
$79$	7.23876	+	6.07404i	0.814424	+	0.683383i	0.951659	−	0.307156i	$-0.0993773\pi$
$79$	7.23876	+	6.07404i	0.814424	+	0.683383i	−0.137236	+	0.990538i	$0.543822\pi$
$80$	−2.08449	+	3.61044i	−0.233053	+	0.403659i
$81$	−8.52016	+	2.89945i	−0.946685	+	0.322162i
$82$	4.75630	−	2.74605i	0.525246	−	0.303251i
$83$	10.6153	−	3.86367i	1.16518	−	0.424092i	0.314237	−	0.949344i	$-0.398251\pi$
$83$	10.6153	−	3.86367i	1.16518	−	0.424092i	0.850947	+	0.525252i	$0.176029\pi$
$84$	−4.77224	+	5.67454i	−0.520694	+	0.619143i
$85$	0.323549	−	0.271490i	0.0350938	−	0.0294472i
$86$	−10.8786	−	12.9646i	−1.17306	−	1.39800i
$87$	8.51475	+	3.14997i	0.912877	+	0.337712i
$88$	2.38702	−	0.868803i	0.254457	−	0.0926147i
$89$	−3.03736			−0.321959			−0.160980	−	0.986958i	$-0.551465\pi$
$89$	−3.03736			−0.321959			−0.160980	+	0.986958i	$0.551465\pi$
$90$	−5.08221	+	0.841067i	−0.535712	+	0.0886562i
$91$	9.09679	+	5.20177i	0.953603	+	0.545294i
$92$	5.57140	+	0.982388i	0.580858	+	0.102421i
$93$	6.08813	−	10.4179i	0.631309	−	1.08029i
$94$	−4.07909	−	4.86127i	−0.420726	−	0.501401i
$95$	2.10566	+	2.50943i	0.216036	+	0.257462i
$96$	−6.29069	−	11.0295i	−0.642041	−	1.12569i
$97$	−5.02929	−	0.886800i	−0.510647	−	0.0900409i	−0.0876131	−	0.996155i	$-0.527924\pi$
$97$	−5.02929	−	0.886800i	−0.510647	−	0.0900409i	−0.423034	+	0.906114i	$0.639035\pi$
$98$	11.4751	−	6.75291i	1.15916	−	0.682147i
$99$	9.02664	+	5.33901i	0.907211	+	0.536590i
$100$	6.77131			0.677131
$101$	12.6062	−	4.58829i	1.25436	−	0.456552i	0.372491	−	0.928036i	$-0.378504\pi$
$101$	12.6062	−	4.58829i	1.25436	−	0.456552i	0.881874	+	0.471484i	$0.156282\pi$
$102$	0.259667	+	1.51936i	0.0257108	+	0.150440i
$103$	−9.69011	−	11.5482i	−0.954795	−	1.13788i	−0.990361	−	0.138513i	$-0.955768\pi$
$103$	−9.69011	−	11.5482i	−0.954795	−	1.13788i	0.0355656	−	0.999367i	$-0.488677\pi$
$104$	−2.20470	+	1.84996i	−0.216189	+	0.181404i
$105$	4.07325	+	0.722884i	0.397509	+	0.0705463i
$106$	−18.0654	+	6.57525i	−1.75466	+	0.638645i
$107$	−12.8332	+	7.40924i	−1.24063	+	0.716278i	−0.969222	−	0.246187i	$-0.920822\pi$
$107$	−12.8332	+	7.40924i	−1.24063	+	0.716278i	−0.271407	+	0.962465i	$0.587489\pi$
$108$	2.99983	−	7.85384i	0.288659	−	0.755736i
$109$	−1.48332	+	2.56918i	−0.142076	+	0.246083i	−0.928278	−	0.371886i	$-0.878711\pi$
$109$	−1.48332	+	2.56918i	−0.142076	+	0.246083i	0.786202	+	0.617969i	$0.212044\pi$
$110$	4.59831	+	3.85844i	0.438431	+	0.367888i
$111$	−5.75284	−	16.0685i	−0.546036	−	1.52515i
$112$	2.17166	+	12.0238i	0.205203	+	1.13614i
$113$	12.0005	−	2.11601i	1.12891	−	0.199058i	0.422162	−	0.906520i	$-0.361271\pi$
$113$	12.0005	−	2.11601i	1.12891	−	0.199058i	0.706751	+	0.707463i	$0.250160\pi$
$114$	−11.7841	+	2.01397i	−1.10369	+	0.188625i
$115$	−1.07959	−	2.96614i	−0.100672	−	0.276594i
$116$	−7.34458	+	4.24039i	−0.681927	+	0.393711i
$117$	−11.6792	−	2.18637i	−1.07974	−	0.202130i
$118$	5.33942	−	3.08271i	0.491533	−	0.283787i
$119$	0.209885	−	1.21993i	0.0192401	−	0.111831i
$120$	−0.573265	+	0.980963i	−0.0523317	+	0.0895493i
$121$	−0.211950	−	1.20203i	−0.0192682	−	0.109275i
$122$	−0.0890440	+	0.0747168i	−0.00806167	+	0.00676454i
$123$	4.34419	−	2.47773i	0.391703	−	0.223409i
$124$	3.85515	+	10.5919i	0.346203	+	0.951184i
$125$	−4.14588	−	7.18088i	−0.370819	−	0.642277i
$126$	−9.77795	+	11.5032i	−0.871089	+	1.02479i
$127$	−4.12812	+	7.15011i	−0.366311	+	0.634469i	−0.988986	−	0.148012i	$-0.952713\pi$
$127$	−4.12812	+	7.15011i	−0.366311	+	0.634469i	0.622675	+	0.782481i	$0.286046\pi$
$128$	−5.62043	−	0.991033i	−0.496780	−	0.0875958i
$129$	−9.84374	−	11.8575i	−0.866693	−	1.04400i
$130$	−6.39081	−	2.32607i	−0.560511	−	0.204009i
$131$	19.4938	+	7.09515i	1.70318	+	0.619906i	0.996181	−	0.0873113i	$-0.0278275\pi$
$131$	19.4938	+	7.09515i	1.70318	+	0.619906i	0.706996	+	0.707217i	$0.250050\pi$
$132$	−9.22336	+	3.30216i	−0.802791	+	0.287416i
$133$	9.46173	+	1.62786i	0.820436	+	0.141153i
$134$			19.5003i			1.68457i
$135$	−4.63183	+	0.741506i	−0.398644	+	0.0638187i
$136$	0.294425	+	0.169986i	0.0252467	+	0.0145762i
$137$	−12.0168	−	2.11888i	−1.02666	−	0.181028i	−0.365138	−	0.930953i	$-0.618978\pi$
$137$	−12.0168	−	2.11888i	−1.02666	−	0.181028i	−0.661522	+	0.749925i	$0.730089\pi$
$138$	11.3338	+	2.06003i	0.964799	+	0.175361i
$139$	11.5620	+	13.7791i	0.980677	+	1.16873i	0.985661	+	0.168738i	$0.0539691\pi$
$139$	11.5620	+	13.7791i	0.980677	+	1.16873i	−0.00498385	+	0.999988i	$0.501586\pi$
$140$	−2.94999	+	2.49629i	−0.249319	+	0.210975i
$141$	−3.69107	−	4.44616i	−0.310844	−	0.374434i
$142$	0.838815	−	4.75716i	0.0703918	−	0.399212i
$143$	6.92290	+	11.9908i	0.578922	+	1.00272i
$144$	−6.80047	−	12.0704i	−0.566706	−	1.00587i
$145$	4.09789	+	2.36592i	0.340311	+	0.196479i
$146$	2.76460	−	15.6788i	0.228800	−	1.29759i
$147$	10.4815	−	6.09412i	0.864499	−	0.502635i
$148$	14.9817	+	5.45288i	1.23149	+	0.448224i
$149$	11.0919	−	1.95580i	0.908685	−	0.160226i	0.300279	−	0.953852i	$-0.402920\pi$
$149$	11.0919	−	1.95580i	0.908685	−	0.160226i	0.608406	+	0.793626i	$0.291809\pi$
$150$	13.7876	+	0.0725716i	1.12575	+	0.00592544i
$151$	−4.66440	−	3.91390i	−0.379583	−	0.318508i	0.432955	−	0.901415i	$-0.357471\pi$
$151$	−4.66440	−	3.91390i	−0.379583	−	0.318508i	−0.812539	+	0.582907i	$0.801915\pi$
$152$	−1.31841	+	2.28355i	−0.106937	+	0.185220i
$153$	0.229167	+	1.38476i	0.0185271	+	0.111951i
$154$	17.5924	−	0.0730824i	1.41763	−	0.00588915i
$155$	4.04251	−	4.81767i	0.324702	−	0.386965i
$156$	8.54017	−	7.08979i	0.683761	−	0.567637i
$157$	−1.63498	+	4.49206i	−0.130485	+	0.358505i	−0.987680	−	0.156487i	$-0.949983\pi$
$157$	−1.63498	+	4.49206i	−0.130485	+	0.358505i	0.857195	+	0.514992i	$0.172205\pi$
$158$	−17.7009	+	3.12114i	−1.40820	+	0.248304i
$159$	−16.4816	+	5.90076i	−1.30708	+	0.467961i
$160$	−2.26344	−	6.21874i	−0.178940	−	0.491635i
$161$	−8.03077	−	4.59219i	−0.632913	−	0.361915i
$162$	6.19236	−	15.9597i	0.486518	−	1.25391i
$163$	3.98040	+	6.89426i	0.311769	+	0.540000i	0.978745	−	0.205079i	$-0.0657451\pi$
$163$	3.98040	+	6.89426i	0.311769	+	0.540000i	−0.666976	+	0.745079i	$0.732412\pi$
$164$	−0.811238	+	4.60076i	−0.0633471	+	0.359259i
$165$	4.16867	+	3.53549i	0.324531	+	0.275237i
$166$	−7.34907	+	20.1914i	−0.570398	+	1.56716i
$167$	3.90196	+	22.1291i	0.301943	+	1.71240i	0.637556	+	0.770404i	$0.279945\pi$
$167$	3.90196	+	22.1291i	0.301943	+	1.71240i	−0.335613	+	0.942000i	$0.608943\pi$
$168$	0.574596	+	3.27997i	0.0443310	+	0.253055i
$169$	−2.05848	−	1.72727i	−0.158344	−	0.132867i
$170$			0.803376i			0.0616161i
$171$	−10.7401	+	1.77741i	−0.821319	+	0.135922i
$172$	14.3960			1.09769
$173$	7.27776	−	2.64889i	0.553317	−	0.201391i	−0.0502024	−	0.998739i	$-0.515987\pi$
$173$	7.27776	−	2.64889i	0.553317	−	0.201391i	0.603520	+	0.797348i	$0.293764\pi$
$174$	−15.0003	+	8.55548i	−1.13717	+	0.648589i
$175$	−10.4205	−	3.74380i	−0.787715	−	0.283004i
$176$	−5.52155	+	15.1703i	−0.416203	+	1.14351i
$177$	4.87678	−	2.78149i	0.366561	−	0.209070i
$178$	3.71361	−	4.42571i	0.278347	−	0.331721i
$179$		−	1.87108i		−	0.139851i	−0.997552	−	0.0699256i	$-0.977724\pi$
$179$		−	1.87108i		−	0.139851i	0.997552	−	0.0699256i	$-0.0222762\pi$
$180$	2.23076	−	3.77153i	0.166271	−	0.281113i
$181$	18.1786	+	10.4954i	1.35121	+	0.780121i	0.988419	−	0.151751i	$-0.0484910\pi$
$181$	18.1786	+	10.4954i	1.35121	+	0.780121i	0.362790	+	0.931871i	$0.381824\pi$
$182$	−18.7016	+	6.89494i	−1.38625	+	0.511087i
$183$	−0.0814405	+	0.0676094i	−0.00602026	+	0.00499783i
$184$	1.94634	−	1.63317i	0.143486	−	0.120399i
$185$	−1.54468	−	8.76031i	−0.113567	−	0.644071i
$186$	7.73625	+	21.6084i	0.567249	+	1.58440i
$187$	1.05132	−	1.25291i	0.0768799	−	0.0916219i
$188$	5.39802			0.393691
$189$	−8.95881	+	10.4278i	−0.651658	+	0.758513i
$190$	−6.23095			−0.452041
$191$	−6.58893	+	7.85238i	−0.476758	+	0.568178i	−0.949798	−	0.312862i	$-0.898712\pi$
$191$	−6.58893	+	7.85238i	−0.476758	+	0.568178i	0.473040	+	0.881041i	$0.343157\pi$
$192$	8.02249	+	1.45816i	0.578973	+	0.105234i
$193$	−1.75083	−	9.92947i	−0.126028	−	0.714739i	−0.980692	−	0.195558i	$-0.937348\pi$
$193$	−1.75083	−	9.92947i	−0.126028	−	0.714739i	0.854664	−	0.519181i	$-0.173763\pi$
$194$	7.44119	−	6.24390i	0.534246	−	0.448286i
$195$	−5.80825	−	2.14872i	−0.415937	−	0.153873i
$196$	−1.87397	+	11.1697i	−0.133855	+	0.797837i
$197$	−23.0223	−	13.2919i	−1.64027	−	0.947010i	−0.980737	−	0.195334i	$-0.937421\pi$
$197$	−23.0223	−	13.2919i	−1.64027	−	0.947010i	−0.659533	−	0.751676i	$-0.729246\pi$
$198$	−18.8158	+	6.62492i	−1.33718	+	0.470813i
$199$		−	19.4827i		−	1.38109i	−0.723288	−	0.690546i	$-0.757370\pi$
$199$		−	19.4827i		−	1.38109i	0.723288	−	0.690546i	$-0.242630\pi$
$200$	1.95475	−	2.32958i	0.138222	−	0.164726i
$201$	−0.0934633	+	17.7567i	−0.00659239	+	1.25246i
$202$	−8.72737	+	23.9782i	−0.614055	+	1.68710i
$203$	13.6472	−	2.46486i	0.957844	−	0.173000i
$204$	−1.13202	−	0.661543i	−0.0792575	−	0.0463173i
$205$	2.44939	−	0.891504i	0.171073	−	0.0622654i
$206$	28.6744			1.99784
$207$	10.3106	+	1.93016i	0.716634	+	0.134155i
$208$		−	18.2909i		−	1.26825i
$209$	9.71752	+	8.15397i	0.672175	+	0.564022i
$210$	−6.03345	+	5.05127i	−0.416348	+	0.348571i
$211$	−0.926175	−	5.25260i	−0.0637605	−	0.361604i	−0.999949	−	0.0101053i	$-0.996783\pi$
$211$	−0.926175	−	5.25260i	−0.0637605	−	0.361604i	0.936188	−	0.351499i	$-0.114328\pi$
$212$	5.59309	−	15.3669i	0.384135	−	1.05540i
$213$	0.786615	−	4.32779i	0.0538980	−	0.296535i
$214$	4.89448	−	27.7580i	0.334580	−	1.89750i
$215$	−4.01612	−	6.95612i	−0.273897	−	0.474403i
$216$	−1.83602	−	3.29932i	−0.124925	−	0.224490i
$217$	−0.0765688	−	18.4316i	−0.00519783	−	1.25122i
$218$	−1.92996	−	5.30253i	−0.130713	−	0.359132i
$219$	2.59256	−	14.2637i	0.175189	−	0.963851i
$220$	−5.02846	+	0.886653i	−0.339019	+	0.0597781i
$221$	−0.633788	+	1.74132i	−0.0426332	+	0.117134i
$222$	30.4469	+	11.2636i	2.04346	+	0.755963i
$223$	−5.44697	+	6.49144i	−0.364756	+	0.434699i	−0.916941	−	0.399022i	$-0.869350\pi$
$223$	−5.44697	+	6.49144i	−0.364756	+	0.434699i	0.552185	+	0.833721i	$0.313794\pi$
$224$	−16.8371	−	9.62787i	−1.12498	−	0.643289i
$225$	12.5545	+	0.132166i	0.836964	+	0.00881104i
$226$	−11.5891	+	20.0730i	−0.770898	+	1.33523i
$227$	−17.2296	−	14.4573i	−1.14357	−	0.959567i	−0.144017	−	0.989575i	$-0.546002\pi$
$227$	−17.2296	−	14.4573i	−1.14357	−	0.959567i	−0.999550	+	0.0300086i	$0.990447\pi$
$228$	5.13090	−	8.77994i	0.339802	−	0.581465i
$229$	0.780937	−	0.137700i	0.0516057	−	0.00909948i	−0.147786	−	0.989019i	$-0.547215\pi$
$229$	0.780937	−	0.137700i	0.0516057	−	0.00909948i	0.199391	+	0.979920i	$0.436103\pi$
$230$	5.64189	+	2.05348i	0.372015	+	0.135403i
$231$	16.0197	+	0.0177708i	1.05402	+	0.00116923i
$232$	−0.661391	+	3.75093i	−0.0434224	+	0.246261i
$233$	7.51477	+	4.33866i	0.492309	+	0.284235i	0.725532	−	0.688189i	$-0.241594\pi$
$233$	7.51477	+	4.33866i	0.492309	+	0.284235i	−0.233223	+	0.972423i	$0.574927\pi$
$234$	17.4653	−	14.3445i	1.14174	−	0.937731i
$235$	−1.50591	−	2.60831i	−0.0982346	−	0.170147i
$236$	−0.910694	+	5.16480i	−0.0592812	+	0.336200i
$237$	−16.1331	+	2.75723i	−1.04796	+	0.179101i
$238$	1.52093	+	1.79736i	0.0985876	+	0.116506i
$239$	14.4054	+	17.1677i	0.931810	+	1.11049i	0.993663	+	0.112403i	$0.0358546\pi$
$239$	14.4054	+	17.1677i	0.931810	+	1.11049i	−0.0618527	+	0.998085i	$0.519701\pi$
$240$	−2.43394	−	6.79831i	−0.157110	−	0.438829i
$241$	10.3548	+	1.82584i	0.667014	+	0.117613i	0.496895	−	0.867811i	$-0.334474\pi$
$241$	10.3548	+	1.82584i	0.667014	+	0.117613i	0.170119	+	0.985423i	$0.445585\pi$
$242$	2.01061	+	1.16082i	0.129247	+	0.0746206i
$243$	5.71518	−	14.5030i	0.366629	−	0.930367i
$244$		−	0.0988758i		−	0.00632987i
$245$	5.91996	−	2.21056i	0.378213	−	0.141228i
$246$	−1.70113	+	9.35927i	−0.108460	+	0.596725i
$247$	−13.5056	−	4.91563i	−0.859340	−	0.312774i
$248$	4.75694	+	1.73138i	0.302066	+	0.109943i
$249$	−6.78875	+	18.3508i	−0.430219	+	1.16294i
$250$	15.5321	+	2.73874i	0.982339	+	0.173213i
$251$	4.71175	−	8.16098i	0.297403	−	0.515117i	−0.678138	−	0.734934i	$-0.737213\pi$
$251$	4.71175	−	8.16098i	0.297403	−	0.515117i	0.975541	+	0.219818i	$0.0705463\pi$
$252$	−2.14940	−	12.6611i	−0.135399	−	0.797577i
$253$	−6.11162	−	10.5856i	−0.384234	−	0.665514i
$254$	−5.37114	−	14.7571i	−0.337015	−	0.925942i
$255$	−0.00385051	+	0.731544i	−0.000241129	+	0.0458111i
$256$	15.5284	−	13.0299i	0.970524	−	0.814367i
$257$	−2.04743	−	11.6115i	−0.127715	−	0.724308i	−0.979658	−	0.200673i	$-0.935687\pi$
$257$	−2.04743	−	11.6115i	−0.127715	−	0.724308i	0.851943	−	0.523634i	$-0.175424\pi$
$258$	29.3129	+	0.154290i	1.82494	+	0.00960565i
$259$	−20.0407	−	16.6748i	−1.24527	−	1.03612i
$260$	5.01003	−	2.89254i	0.310709	−	0.179388i
$261$	−13.7001	+	7.71862i	−0.848015	+	0.477770i
$262$	−34.1722	+	19.7293i	−2.11117	+	1.21888i
$263$	1.58821	+	4.36356i	0.0979331	+	0.269069i	0.978979	−	0.203962i	$-0.0653820\pi$
$263$	1.58821	+	4.36356i	0.0979331	+	0.269069i	−0.881046	+	0.473031i	$0.843160\pi$
$264$	−1.52655	+	4.12646i	−0.0939528	+	0.253966i
$265$	−8.98556	+	1.58440i	−0.551978	+	0.0973287i
$266$	−13.9403	+	11.7963i	−0.854733	+	0.723278i
$267$	3.40278	−	4.01220i	0.208247	−	0.245542i
$268$	−12.7067	−	10.6622i	−0.776187	−	0.651299i
$269$	−13.5452	+	23.4609i	−0.825864	+	1.43044i	0.0753937	+	0.997154i	$0.475979\pi$
$269$	−13.5452	+	23.4609i	−0.825864	+	1.43044i	−0.901257	+	0.433284i	$0.857355\pi$
$270$	4.58264	−	7.65559i	0.278890	−	0.465905i
$271$	−3.93162	+	2.26992i	−0.238829	+	0.137888i	−0.614638	−	0.788809i	$-0.710698\pi$
$271$	−3.93162	+	2.26992i	−0.238829	+	0.137888i	0.375810	+	0.926697i	$0.377365\pi$
$272$	−2.03035	+	0.738985i	−0.123108	+	0.0448076i
$273$	−17.0625	+	6.18881i	−1.03267	+	0.374564i
$274$	17.7796	−	14.9189i	1.07411	−	0.901282i
$275$	−9.40403	−	11.2073i	−0.567084	−	0.675825i
$276$	−7.53937	+	6.25896i	−0.453817	+	0.376745i
$277$	−7.49116	+	2.72656i	−0.450100	+	0.163823i	−0.557117	−	0.830434i	$-0.688092\pi$
$277$	−7.49116	+	2.72656i	−0.450100	+	0.163823i	0.107016	+	0.994257i	$0.465870\pi$
$278$	−34.2136			−2.05200
$279$	6.94096	+	19.7134i	0.415545	+	1.18021i
$280$	0.00720981	+	1.73554i	0.000430868	+	0.103718i
$281$	6.05459	+	1.06759i	0.361187	+	0.0636870i	0.351297	−	0.936264i	$-0.385741\pi$
$281$	6.05459	+	1.06759i	0.361187	+	0.0636870i	0.00988990	+	0.999951i	$0.496852\pi$
$282$	10.9913	+	0.0578534i	0.654524	+	0.00344512i
$283$	−7.37481	−	8.78895i	−0.438387	−	0.522449i	0.500936	−	0.865484i	$-0.332989\pi$
$283$	−7.37481	−	8.78895i	−0.438387	−	0.522449i	−0.939322	+	0.343036i	$0.888545\pi$
$284$	2.64121	+	3.14767i	0.156727	+	0.186780i
$285$	−5.67383	−	0.0298644i	−0.336088	−	0.00176902i
$286$	−25.9359	−	4.57321i	−1.53362	−	0.270419i
$287$	3.79215	−	6.63166i	0.223843	−	0.391455i
$288$	21.6169	+	4.04672i	1.27379	+	0.238455i
$289$	−16.7811			−0.987124
$290$	−8.45762	+	3.07832i	−0.496649	+	0.180765i
$291$	6.80578	−	5.64995i	0.398962	−	0.331206i
$292$	8.70500	+	10.3742i	0.509422	+	0.607105i
$293$	0.840836	−	0.705545i	0.0491222	−	0.0412184i	−0.617896	−	0.786260i	$-0.712015\pi$
$293$	0.840836	−	0.705545i	0.0491222	−	0.0412184i	0.667018	+	0.745041i	$0.267570\pi$
$294$	−3.93545	+	22.7234i	−0.229520	+	1.32526i
$295$	2.74968	−	1.00080i	0.160092	−	0.0582689i
$296$	6.20093	−	3.58011i	0.360422	−	0.208090i
$297$	−17.1652	+	5.94239i	−0.996025	+	0.344812i
$298$	−10.7117	+	18.5532i	−0.620511	+	1.07476i
$299$	10.6088	+	8.90185i	0.613523	+	0.514807i
$300$	−7.58596	+	8.94456i	−0.437976	+	0.516414i
$301$	−22.1543	−	7.95944i	−1.27695	−	0.458774i
$302$	11.4058	−	2.01115i	0.656331	−	0.115729i
$303$	−8.06196	+	21.7925i	−0.463147	+	1.25194i
$304$	−5.73154	−	15.7473i	−0.328726	−	0.903169i
$305$	−0.0477765	+	0.0275838i	−0.00273567	+	0.00157944i
$306$	−2.29791	−	1.35915i	−0.131363	−	0.0776975i
$307$	5.93612	−	3.42722i	0.338792	−	0.195602i	−0.320945	−	0.947098i	$-0.604001\pi$
$307$	5.93612	−	3.42722i	0.338792	−	0.195602i	0.659738	+	0.751496i	$0.270667\pi$
$308$	−9.57139	+	11.5035i	−0.545381	+	0.655470i
$309$	26.1105	+	0.137434i	1.48538	+	0.00781835i
$310$	2.07724	+	11.7806i	0.117979	+	0.669093i
$311$	−17.1024	+	14.3506i	−0.969788	+	0.813749i	−0.982517	−	0.186170i	$-0.940392\pi$
$311$	−17.1024	+	14.3506i	−0.969788	+	0.813749i	0.0127297	+	0.999919i	$0.495948\pi$
$312$	0.0262379	−	4.98483i	0.00148543	−	0.282211i
$313$	−0.345892	−	0.950332i	−0.0195510	−	0.0537159i	0.929533	−	0.368738i	$-0.120210\pi$
$313$	−0.345892	−	0.950332i	−0.0195510	−	0.0537159i	−0.949084	+	0.315022i	$0.897988\pi$
$314$	−4.54635	−	7.87450i	−0.256565	−	0.444384i
$315$	−5.51820	+	4.57071i	−0.310915	+	0.257530i
$316$	7.64455	−	13.2408i	0.430040	−	0.744850i
$317$	24.4774	+	4.31603i	1.37479	+	0.242412i	0.811743	−	0.584015i	$-0.198519\pi$
$317$	24.4774	+	4.31603i	1.37479	+	0.242412i	0.563044	+	0.826427i	$0.309630\pi$
$318$	11.5532	−	31.2298i	0.647872	−	1.75128i
$319$	17.2185	+	6.26703i	0.964052	+	0.350886i
$320$	3.99354	+	1.45353i	0.223246	+	0.0812547i
$321$	4.58989	−	25.2526i	0.256183	−	1.40946i
$322$	16.5100	−	6.08694i	0.920067	−	0.339212i
$323$			1.69776i			0.0944659i
$324$	7.01379	+	12.7614i	0.389655	+	0.708964i
$325$	14.3550	+	8.28786i	0.796272	+	0.459728i
$326$	−14.9122	−	2.62942i	−0.825910	−	0.145630i
$327$	−1.73198	−	4.83766i	−0.0957790	−	0.267523i
$328$	1.34864	+	1.60725i	0.0744664	+	0.0887457i
$329$	−8.30711	−	2.98452i	−0.457986	−	0.164542i
$330$	−10.2483	+	1.75149i	−0.564152	+	0.0964163i
$331$	4.60947	−	26.1416i	0.253360	−	1.43687i	−0.546889	−	0.837205i	$-0.684188\pi$
$331$	4.60947	−	26.1416i	0.253360	−	1.43687i	0.800248	−	0.599669i	$-0.204701\pi$
$332$	−9.13881	−	15.8289i	−0.501558	−	0.868723i
$333$	27.6706	+	10.4024i	1.51634	+	0.570049i
$334$	−37.0149	−	21.3706i	−2.02536	−	1.16934i
$335$	−1.60710	+	9.11434i	−0.0878054	+	0.497969i
$336$	−18.3158	−	10.6017i	−0.999208	−	0.578372i
$337$	23.2967	+	8.47930i	1.26905	+	0.461897i	0.886796	−	0.462161i	$-0.152926\pi$
$337$	23.2967	+	8.47930i	1.26905	+	0.461897i	0.382254	+	0.924057i	$0.375148\pi$
$338$	5.03357	−	0.887554i	0.273790	−	0.0482766i
$339$	−10.6491	+	18.2227i	−0.578381	+	0.989719i
$340$	−0.523494	−	0.439264i	−0.0283904	−	0.0238224i
$341$	12.1768	−	21.0908i	0.659411	−	1.14213i
$342$	10.5415	−	17.8225i	0.570020	−	0.963731i
$343$	9.05953	−	16.1532i	0.489169	−	0.872189i
$344$	4.15587	−	4.95278i	0.224070	−	0.267036i
$345$	5.12760	+	1.89692i	0.276061	+	0.102127i
$346$	−5.03844	+	13.8430i	−0.270868	+	0.744204i
$347$	18.4568	−	3.25443i	0.990813	−	0.174707i	0.345330	−	0.938481i	$-0.387767\pi$
$347$	18.4568	−	3.25443i	0.990813	−	0.174707i	0.645483	+	0.763774i	$0.276656\pi$
$348$	2.62685	−	14.4524i	0.140814	−	0.774728i
$349$	8.31455	+	22.8440i	0.445067	+	1.22281i	0.936119	+	0.351682i	$0.114390\pi$
$349$	8.31455	+	22.8440i	0.445067	+	1.22281i	−0.491052	+	0.871130i	$0.663387\pi$
$350$	18.1956	−	10.6063i	0.972596	−	0.566929i
$351$	15.9724	−	12.9782i	0.852545	−	0.692727i
$352$	−12.8135	−	22.1936i	−0.682960	−	1.18292i
$353$	−3.97293	+	22.5316i	−0.211458	+	1.19924i	0.675490	+	0.737369i	$0.263932\pi$
$353$	−3.97293	+	22.5316i	−0.211458	+	1.19924i	−0.886948	+	0.461869i	$0.847179\pi$
$354$	−1.90969	+	10.5067i	−0.101499	+	0.558424i
$355$	0.784116	−	2.15434i	0.0416166	−	0.114341i
$356$	0.853371	+	4.83971i	0.0452286	+	0.256504i
$357$	1.37633	+	1.64395i	0.0728431	+	0.0870069i
$358$	2.72634	+	2.28767i	0.144091	+	0.120907i
$359$			8.35250i			0.440828i	0.975406	+	0.220414i	$0.0707409\pi$
$359$			8.35250i			0.440828i	−0.975406	+	0.220414i	$0.929259\pi$
$360$	−0.653569	−	1.85624i	−0.0344461	−	0.0978322i
$361$	5.83224			0.306960
$362$	−37.5189	+	13.6557i	−1.97195	+	0.717730i
$363$	1.82527	+	1.06667i	0.0958018	+	0.0559856i
$364$	5.73265	−	15.9563i	0.300473	−	0.836336i
$365$	2.58432	−	7.10037i	0.135270	−	0.371650i
$366$	0.00105970	−	0.201329i	5.53915e−5	−	0.0105236i
$367$	−6.27438	+	7.47752i	−0.327520	+	0.390323i	−0.904527	−	0.426416i	$-0.859776\pi$
$367$	−6.27438	+	7.47752i	−0.327520	+	0.390323i	0.577007	+	0.816739i	$0.304220\pi$
$368$			16.1475i			0.841745i
$369$	−1.59389	+	8.51428i	−0.0829746	+	0.443236i
$370$	14.6532	+	8.46001i	0.761782	+	0.439815i
$371$	−17.1035	+	20.5560i	−0.887970	+	1.06721i
$372$	−18.3104	−	6.77379i	−0.949349	−	0.351204i
$373$	8.11869	−	6.81239i	0.420370	−	0.352732i	−0.407934	−	0.913012i	$-0.633751\pi$
$373$	8.11869	−	6.81239i	0.420370	−	0.352732i	0.828304	+	0.560279i	$0.189306\pi$
$374$	0.540218	+	3.06373i	0.0279340	+	0.158422i
$375$	14.1303	+	2.56830i	0.729683	+	0.132627i
$376$	1.55831	−	1.85712i	0.0803637	−	0.0957738i
$377$	−20.7604			−1.06922
$378$	−4.24085	−	25.8033i	−0.218126	−	1.32718i
$379$	−6.26462			−0.321792			−0.160896	−	0.986971i	$-0.551438\pi$
$379$	−6.26462			−0.321792			−0.160896	+	0.986971i	$0.551438\pi$
$380$	3.40691	−	4.06020i	0.174771	−	0.208284i
$381$	−4.82016	−	13.4634i	−0.246944	−	0.689749i
$382$	−3.38572	−	19.2013i	−0.173228	−	0.982427i
$383$	6.40797	−	5.37692i	0.327432	−	0.274748i	−0.464221	−	0.885720i	$-0.653666\pi$
$383$	6.40797	−	5.37692i	0.327432	−	0.274748i	0.791652	+	0.610972i	$0.209221\pi$
$384$	7.60572	−	6.31404i	0.388128	−	0.322212i
$385$	8.22860	+	1.41570i	0.419368	+	0.0721510i
$386$	16.6088	+	9.58909i	0.845365	+	0.488072i
$387$	26.6912	+	0.280988i	1.35679	+	0.0142834i
$388$			8.26281i			0.419480i
$389$	−12.4908	+	14.8860i	−0.633309	+	0.754748i	−0.983297	−	0.182006i	$-0.941741\pi$
$389$	−12.4908	+	14.8860i	−0.633309	+	0.754748i	0.349989	+	0.936754i	$0.386185\pi$
$390$	10.2323	−	5.83603i	0.518133	−	0.295519i
$391$	0.559516	−	1.53726i	0.0282960	−	0.0777425i
$392$	3.30182	+	3.86921i	0.166767	+	0.195425i
$393$	−31.2114	+	17.8015i	−1.57441	+	0.897967i
$394$	47.5156	−	17.2943i	2.39380	−	0.871273i
$395$	−8.53052			−0.429217
$396$	5.97104	−	15.8830i	0.300056	−	0.798153i
$397$			28.3683i			1.42376i	0.702299	+	0.711882i	$0.252157\pi$
$397$			28.3683i			1.42376i	−0.702299	+	0.711882i	$0.747843\pi$
$398$	28.3881	+	23.8204i	1.42297	+	1.19401i
$399$	−12.7504	+	10.6748i	−0.638318	+	0.534407i
$400$	3.35610	+	19.0334i	0.167805	+	0.951669i
$401$	6.67751	−	18.3463i	0.333459	−	0.916171i	−0.653746	−	0.756714i	$-0.726803\pi$
$401$	6.67751	−	18.3463i	0.333459	−	0.916171i	0.987205	−	0.159457i	$-0.0509743\pi$
$402$	−25.7589	−	21.8463i	−1.28474	−	1.08960i
$403$	−4.79137	+	27.1732i	−0.238675	+	1.35359i
$404$	−10.8528	−	18.7976i	−0.539946	−	0.935213i
$405$	4.20959	−	6.94913i	0.209176	−	0.345305i
$406$	−13.0941	+	22.8988i	−0.649850	+	1.13645i
$407$	−11.7815	−	32.3694i	−0.583986	−	1.60449i
$408$	−0.554390	+	0.198483i	−0.0274464	+	0.00982639i
$409$	34.4362	−	6.07202i	1.70276	−	0.300242i	0.764102	−	0.645096i	$-0.223183\pi$
$409$	34.4362	−	6.07202i	1.70276	−	0.300242i	0.938657	+	0.344854i	$0.112071\pi$
$410$	−1.69573	+	4.65897i	−0.0837460	+	0.230090i
$411$	16.2614	−	13.4997i	0.802116	−	0.665893i
$412$	−15.6784	+	18.6847i	−0.772418	+	0.920531i
$413$	4.25706	−	7.44469i	0.209476	−	0.366329i
$414$	−15.4186	+	12.6635i	−0.757782	+	0.622379i
$415$	−5.09898	+	8.83169i	−0.250299	+	0.433531i
$416$	22.2422	+	18.6634i	1.09051	+	0.915048i
$417$	−31.1545	−	0.163983i	−1.52564	−	0.00803028i
$418$	−23.7622	+	4.18991i	−1.16225	+	0.204935i
$419$	−38.1160	−	13.8731i	−1.86209	−	0.677745i	−0.977340	−	0.211674i	$-0.932108\pi$
$419$	−38.1160	−	13.8731i	−1.86209	−	0.677745i	−0.884748	−	0.466070i	$-0.845669\pi$
$420$	0.00742504	−	6.69340i	0.000362305	−	0.326605i
$421$	2.74861	−	15.5881i	0.133959	−	0.759718i	−0.841620	−	0.540070i	$-0.818398\pi$
$421$	2.74861	−	15.5881i	0.133959	−	0.759718i	0.975579	−	0.219649i	$-0.0704911\pi$
$422$	8.78590	+	5.07254i	0.427691	+	0.246927i
$423$	10.0083	+	0.105361i	0.486620	+	0.00512283i
$424$	−3.67216	−	6.36037i	−0.178336	−	0.308887i
$425$	0.340010	−	1.92829i	0.0164929	−	0.0935358i
$426$	5.34423	+	6.43752i	0.258929	+	0.311899i
$427$	−0.0546675	+	0.152162i	−0.00264555	+	0.00736362i
$428$	15.4114	+	18.3666i	0.744939	+	0.887784i
$429$	−23.5950	−	4.28861i	−1.13918	−	0.207056i
$430$	15.0460	+	2.65301i	0.725582	+	0.127940i
$431$	6.88208	+	3.97337i	0.331498	+	0.191391i	0.656506	−	0.754321i	$-0.272034\pi$
$431$	6.88208	+	3.97337i	0.331498	+	0.191391i	−0.325008	+	0.945711i	$0.605367\pi$
$432$	23.5631	+	4.53955i	1.13368	+	0.218409i
$433$		−	16.4757i		−	0.791770i	−0.918300	−	0.395885i	$-0.870438\pi$
$433$		−	16.4757i		−	0.791770i	0.918300	−	0.395885i	$-0.129562\pi$
$434$	26.9501	+	22.4237i	1.29365	+	1.07637i
$435$	−7.71616	+	2.76255i	−0.369962	+	0.132454i
$436$	4.51047	+	1.64168i	0.216012	+	0.0786221i
$437$	11.9229	+	4.33959i	0.570350	+	0.207591i
$438$	17.6137	+	21.2170i	0.841617	+	1.01379i
$439$	6.00878	+	1.05951i	0.286783	+	0.0505677i	0.315189	−	0.949029i	$-0.397932\pi$
$439$	6.00878	+	1.05951i	0.286783	+	0.0505677i	−0.0284059	+	0.999596i	$0.509043\pi$
$440$	−1.14658	+	1.98594i	−0.0546612	+	0.0946759i
$441$	−3.69249	+	20.6728i	−0.175833	+	0.984420i
$442$	−1.76236	−	3.05250i	−0.0838270	−	0.145193i
$443$	6.80864	+	18.7066i	0.323488	+	0.888776i	0.989718	+	0.143030i	$0.0456846\pi$
$443$	6.80864	+	18.7066i	0.323488	+	0.888776i	−0.666230	+	0.745746i	$0.732093\pi$
$444$	−23.9871	+	13.6811i	−1.13838	+	0.649277i
$445$	2.10046	−	1.76250i	0.0995716	−	0.0835505i
$446$	−2.79892	−	15.8735i	−0.132533	−	0.751630i
$447$	−9.84285	+	16.8430i	−0.465551	+	0.796645i
$448$	11.6864	−	4.30856i	0.552130	−	0.203560i
$449$	−0.412263	+	0.238020i	−0.0194559	+	0.0112329i	−0.509696	−	0.860354i	$-0.670242\pi$
$449$	−0.412263	+	0.238020i	−0.0194559	+	0.0112329i	0.490241	+	0.871587i	$0.336909\pi$
$450$	−15.5422	+	18.1314i	−0.732667	+	0.854722i
$451$	8.74143	−	5.04687i	0.411618	−	0.237648i
$452$	−6.74329	−	18.5270i	−0.317178	−	0.871438i
$453$	10.3956	−	1.77666i	0.488429	−	0.0834749i
$454$	42.1313	−	7.42888i	1.97732	−	0.348655i
$455$	−9.30928	+	1.68138i	−0.436426	+	0.0788244i
$456$	−1.53943	−	4.29983i	−0.0720904	−	0.201358i
$457$	8.85251	+	7.42814i	0.414103	+	0.347474i	0.825914	−	0.563795i	$-0.190659\pi$
$457$	8.85251	+	7.42814i	0.414103	+	0.347474i	−0.411812	+	0.911269i	$0.635104\pi$
$458$	−0.754166	+	1.30625i	−0.0352399	+	0.0610373i
$459$	−2.08594	−	1.24864i	−0.0973631	−	0.0582815i
$460$	−4.42292	+	2.55357i	−0.206220	+	0.119061i
$461$	−19.0273	+	6.92536i	−0.886189	+	0.322546i	−0.744705	−	0.667394i	$-0.767410\pi$
$461$	−19.0273	+	6.92536i	−0.886189	+	0.322546i	−0.141484	+	0.989941i	$0.545187\pi$
$462$	−19.6123	+	23.3205i	−0.912448	+	1.08497i
$463$	−4.74389	+	3.98059i	−0.220467	+	0.184994i	−0.746331	−	0.665575i	$-0.768186\pi$
$463$	−4.74389	+	3.98059i	−0.220467	+	0.184994i	0.525864	+	0.850569i	$0.323742\pi$
$464$	−15.5595	−	18.5431i	−0.722332	−	0.860841i
$465$	1.83504	+	10.7372i	0.0850981	+	0.497927i
$466$	−15.5097	+	5.64507i	−0.718474	+	0.261503i
$467$	3.80696			0.176165			0.0880826	−	0.996113i	$-0.471926\pi$
$467$	3.80696			0.176165			0.0880826	+	0.996113i	$0.471926\pi$
$468$	−0.202377	+	19.2239i	−0.00935489	+	0.888624i
$469$	13.6596	+	23.4337i	0.630740	+	1.08207i
$470$	5.64173	+	0.994790i	0.260234	+	0.0458862i
$471$	−4.10211	−	7.19222i	−0.189015	−	0.331400i
$472$	1.51399	+	1.80430i	0.0696868	+	0.0830495i
$473$	−19.9933	−	23.8271i	−0.919292	−	1.09557i
$474$	15.7076	−	26.8786i	0.721472	−	1.23457i
$475$	14.9557	+	2.63710i	0.686217	+	0.120998i
$476$	−2.00280	+	0.00832006i	−0.0917982	+	0.000381349i
$477$	10.6699	−	28.3821i	0.488541	−	1.29952i
$478$	−42.6277			−1.94974
$479$	−28.2447	+	10.2802i	−1.29053	+	0.469716i	−0.893902	−	0.448262i	$-0.852043\pi$
$479$	−28.2447	+	10.2802i	−1.29053	+	0.469716i	−0.396632	+	0.917978i	$0.629821\pi$
$480$	10.7504	+	3.97703i	0.490686	+	0.181526i
$481$	25.0866	+	29.8971i	1.14385	+	1.36319i
$482$	−15.3207	+	12.8556i	−0.697839	+	0.585556i
$483$	15.0630	−	5.46357i	0.685390	−	0.248601i
$484$	−1.85576	+	0.675440i	−0.0843526	+	0.0307018i
$485$	3.99256	−	2.30511i	0.181293	−	0.104670i
$486$	14.1445	+	26.0595i	0.641609	+	1.18209i
$487$	−18.9944	+	32.8993i	−0.860720	+	1.49081i	0.0105150	+	0.999945i	$0.496653\pi$
$487$	−18.9944	+	32.8993i	−0.860720	+	1.49081i	−0.871235	+	0.490866i	$0.836680\pi$
$488$	−0.0340170	−	0.0285436i	−0.00153988	−	0.00129211i
$489$	−13.5663	−	2.46579i	−0.613487	−	0.111507i
$490$	−4.01702	+	11.3287i	−0.181471	+	0.511777i
$491$	−31.0131	+	5.46844i	−1.39960	+	0.246787i	−0.821979	−	0.569517i	$-0.807130\pi$
$491$	−31.0131	+	5.46844i	−1.39960	+	0.246787i	−0.577622	+	0.816305i	$0.696019\pi$
$492$	−5.16853	−	6.22588i	−0.233016	−	0.280684i
$493$	0.838757	+	2.30447i	0.0377757	+	0.103788i
$494$	23.6751	−	13.6688i	1.06519	−	0.614989i
$495$	−9.34040	+	1.54576i	−0.419820	+	0.0694770i
$496$	−27.8620	+	16.0861i	−1.25104	+	0.722288i
$497$	−2.32428	−	6.30430i	−0.104258	−	0.282787i
$498$	−18.4386	−	32.3284i	−0.826253	−	1.44867i
$499$	−3.26628	−	18.5240i	−0.146219	−	0.829247i	−0.966381	−	0.257116i	$-0.917228\pi$
$499$	−3.26628	−	18.5240i	−0.146219	−	0.829247i	0.820162	−	0.572131i	$-0.193883\pi$
$500$	−10.2772	+	8.62356i	−0.459608	+	0.385657i
$501$	−33.6029	−	19.6372i	−1.50127	−	0.877324i
$502$	6.13051	+	16.8434i	0.273618	+	0.751759i
$503$	−3.04934	−	5.28161i	−0.135963	−	0.235495i	0.790002	−	0.613105i	$-0.210080\pi$
$503$	−3.04934	−	5.28161i	−0.135963	−	0.235495i	−0.925965	+	0.377609i	$0.876746\pi$
$504$	−4.97640	−	2.91557i	−0.221666	−	0.129870i
$505$	−6.05528	+	10.4881i	−0.269456	+	0.466712i
$506$	22.8966	+	4.03729i	1.01788	+	0.179479i
$507$	4.58776	−	0.784070i	0.203750	−	0.0348218i
$508$	12.5528	+	4.56884i	0.556939	+	0.202709i
$509$	40.6536	+	14.7967i	1.80194	+	0.655852i	0.998141	+	0.0609481i	$0.0194124\pi$
$509$	40.6536	+	14.7967i	1.80194	+	0.655852i	0.803797	+	0.594904i	$0.202810\pi$
$510$	−1.06122	−	0.900029i	−0.0469915	−	0.0398539i
$511$	−7.66046	−	20.7780i	−0.338879	−	0.919164i
$512$			27.1429i			1.19956i
$513$	9.68441	−	16.1784i	0.427577	−	0.714295i
$514$	19.4223	+	11.2135i	0.856683	+	0.494606i
$515$	13.4023	+	2.36318i	0.590574	+	0.104134i
$516$	−16.1280	+	19.0164i	−0.709996	+	0.837152i
$517$	−7.49680	−	8.93434i	−0.329709	−	0.392932i
$518$	48.7993	−	8.81382i	2.14412	−	0.387257i
$519$	−4.65429	+	12.5811i	−0.204301	+	0.552250i
$520$	0.451161	−	2.55866i	0.0197847	−	0.112205i
$521$	−10.0216	−	17.3579i	−0.439053	−	0.760462i	0.558564	−	0.829461i	$-0.311353\pi$
$521$	−10.0216	−	17.3579i	−0.439053	−	0.760462i	−0.997617	+	0.0689999i	$0.978019\pi$
$522$	5.50363	−	29.3994i	0.240887	−	1.28678i
$523$	−23.1000	−	13.3368i	−1.01009	−	0.583177i	−0.0988740	−	0.995100i	$-0.531524\pi$
$523$	−23.1000	−	13.3368i	−1.01009	−	0.583177i	−0.911219	+	0.411923i	$0.864857\pi$
$524$	5.82843	−	33.0547i	0.254616	−	1.44400i
$525$	16.6195	−	9.57072i	0.725336	−	0.417701i
$526$	−8.29992	−	3.02093i	−0.361894	−	0.131719i
$527$	3.20988	−	0.565989i	0.139825	−	0.0246549i
$528$	−13.8534	−	24.2892i	−0.602892	−	1.05705i
$529$	8.25343	+	6.92545i	0.358845	+	0.301106i
$530$	8.67754	−	15.0299i	0.376928	−	0.652859i
$531$	−1.78930	+	9.55811i	−0.0776489	+	0.414787i
$532$	−0.0645301	−	15.5336i	−0.00279773	−	0.673469i
$533$	−7.35099	+	8.76057i	−0.318407	+	0.379462i
$534$	1.68575	+	9.86365i	0.0729493	+	0.426842i
$535$	4.57531	−	12.5706i	0.197808	−	0.543473i
$536$	−7.33641	+	1.29361i	−0.316884	+	0.0558753i
$537$	2.47160	+	2.09619i	0.106658	+	0.0904573i
$538$	−17.6238	−	48.4209i	−0.759815	−	2.08757i
$539$	21.0897	−	12.4109i	0.908399	−	0.534576i
$540$	2.48286	+	7.17200i	0.106845	+	0.308634i
$541$	−5.16825	−	8.95167i	−0.222200	−	0.384862i	0.733275	−	0.679932i	$-0.237991\pi$
$541$	−5.16825	−	8.95167i	−0.222200	−	0.384862i	−0.955476	+	0.295069i	$0.904657\pi$
$542$	1.49949	−	8.50404i	0.0644086	−	0.365280i
$543$	−34.2297	+	12.2549i	−1.46894	+	0.525909i
$544$	1.17307	−	3.22298i	0.0502948	−	0.138184i
$545$	−0.465050	−	2.63743i	−0.0199206	−	0.112975i
$546$	11.8437	−	32.4283i	0.506864	−	1.38780i
$547$	2.39360	+	2.00847i	0.102343	+	0.0858758i	0.692523	−	0.721396i	$-0.256499\pi$
$547$	2.39360	+	2.00847i	0.102343	+	0.0858758i	−0.590181	+	0.807271i	$0.700943\pi$
$548$			19.7428i			0.843369i
$549$	0.00192990	−	0.183322i	8.23663e−5	−	0.00782400i
$550$	27.8278			1.18658
$551$	−17.8733	+	6.50537i	−0.761430	+	0.277138i
$552$	−0.0231632	+	4.40067i	−0.000985889	+	0.187305i
$553$	−19.0850	+	16.1498i	−0.811578	+	0.686760i
$554$	5.18618	−	14.2489i	0.220340	−	0.605379i
$555$	13.3024	+	7.77381i	0.564657	+	0.329980i
$556$	18.7071	−	22.2942i	0.793356	−	0.945485i
$557$		−	14.1576i		−	0.599878i	−0.953958	−	0.299939i	$-0.903034\pi$
$557$		−	14.1576i		−	0.599878i	0.953958	−	0.299939i	$-0.0969663\pi$
$558$	−37.2106	−	13.9889i	−1.57525	−	0.592196i
$559$	30.5192	+	17.6203i	1.29083	+	0.745259i
$560$	−8.47891	−	7.05483i	−0.358299	−	0.298121i
$561$	0.477232	+	2.79238i	0.0201487	+	0.117894i
$562$	−8.95819	+	7.51681i	−0.377878	+	0.317078i
$563$	−3.90078	−	22.1224i	−0.164398	−	0.932348i	−0.949683	−	0.313213i	$-0.898595\pi$
$563$	−3.90078	−	22.1224i	−0.164398	−	0.932348i	0.785285	−	0.619135i	$-0.212517\pi$
$564$	−6.04745	+	7.13051i	−0.254644	+	0.300249i
$565$	−7.07101	+	8.42690i	−0.297479	+	0.354522i
$566$	21.8231			0.917292
$567$	−3.73800	−	23.5165i	−0.156981	−	0.987602i
$568$	1.84539			0.0774306
$569$	12.0098	−	14.3127i	0.503478	−	0.600021i	−0.453114	−	0.891453i	$-0.649687\pi$
$569$	12.0098	−	14.3127i	0.503478	−	0.600021i	0.956592	+	0.291431i	$0.0941314\pi$
$570$	6.98059	−	8.23077i	0.292385	−	0.344749i
$571$	−6.32831	−	35.8896i	−0.264832	−	1.50193i	−0.769514	−	0.638630i	$-0.779502\pi$
$571$	−6.32831	−	35.8896i	−0.264832	−	1.50193i	0.504683	−	0.863305i	$-0.331610\pi$
$572$	17.1610	−	14.3998i	0.717539	−	0.602087i
$573$	−2.99096	−	17.5007i	−0.124949	−	0.731104i
$574$	5.02649	+	13.6337i	0.209802	+	0.569059i
$575$	−12.6728	−	7.31663i	−0.528492	−	0.305125i
$576$	−10.9138	+	8.96371i	−0.454743	+	0.373488i
$577$		−	28.9410i		−	1.20483i	−0.798183	−	0.602416i	$-0.794205\pi$
$577$		−	28.9410i		−	1.20483i	0.798183	−	0.602416i	$-0.205795\pi$
$578$	20.5173	−	24.4516i	0.853408	−	1.01705i
$579$	15.0778	+	8.81131i	0.626612	+	0.366186i
$580$	2.61850	−	7.19428i	0.108728	−	0.298726i
$581$	5.31223	+	29.4121i	0.220388	+	1.22022i
$582$	−0.0885567	+	16.8245i	−0.00367079	+	0.697399i
$583$	−33.2016	+	12.0844i	−1.37507	+	0.500485i
$584$	6.08210			0.251679
$585$	9.34538	−	5.26517i	0.386384	−	0.217688i
$586$			2.08781i			0.0862465i
$587$	−24.4251	−	20.4951i	−1.00813	−	0.845924i	−0.0200431	−	0.999799i	$-0.506380\pi$
$587$	−24.4251	−	20.4951i	−1.00813	−	0.845924i	−0.988090	+	0.153875i	$0.950825\pi$
$588$	−12.6552	−	14.9890i	−0.521892	−	0.618134i
$589$	4.38979	+	24.8957i	0.180878	+	1.02581i
$590$	−1.90362	+	5.23016i	−0.0783708	+	0.215322i
$591$	43.3500	−	15.5202i	1.78318	−	0.638416i
$592$	−7.90199	+	44.8144i	−0.324770	+	1.84186i
$593$	−2.99491	−	5.18734i	−0.122986	−	0.213018i	0.797958	−	0.602713i	$-0.205914\pi$
$593$	−2.99491	−	5.18734i	−0.122986	−	0.213018i	−0.920944	+	0.389695i	$0.872580\pi$
$594$	12.3283	−	32.2767i	0.505837	−	1.32433i
$595$	0.562749	+	0.965426i	0.0230705	+	0.0395786i
$596$	−6.23273	−	17.1243i	−0.255303	−	0.701438i
$597$	25.7357	+	21.8267i	1.05329	+	0.893306i
$598$	−25.9416	+	4.57421i	−1.06083	+	0.187053i
$599$	2.80083	−	7.69521i	0.114439	−	0.314418i	−0.869230	−	0.494409i	$-0.835385\pi$
$599$	2.80083	−	7.69521i	0.114439	−	0.314418i	0.983668	+	0.179991i	$0.0576068\pi$
$600$	0.887335	+	5.19199i	0.0362253	+	0.211962i
$601$	11.1245	−	13.2576i	0.453777	−	0.540791i	−0.489847	−	0.871808i	$-0.662948\pi$
$601$	11.1245	−	13.2576i	0.453777	−	0.540791i	0.943625	+	0.331018i	$0.107392\pi$
$602$	38.6845	−	22.5493i	1.57666	−	0.919040i
$603$	−23.3510	−	20.0165i	−0.950927	−	0.815134i
$604$	−4.92588	+	8.53187i	−0.200431	+	0.347157i
$605$	0.844079	+	0.708266i	0.0343167	+	0.0287951i
$606$	−21.8967	−	38.3915i	−0.889493	−	1.55955i
$607$	−19.3178	+	3.40626i	−0.784087	+	0.138256i	−0.551339	−	0.834281i	$-0.685883\pi$
$607$	−19.3178	+	3.40626i	−0.784087	+	0.138256i	−0.232748	+	0.972537i	$0.574772\pi$
$608$	24.9973	+	9.09826i	1.01377	+	0.368983i
$609$	−12.0331	+	20.7886i	−0.487605	+	0.842398i
$610$	0.0182216	−	0.103340i	0.000737771	−	0.00418411i
$611$	11.4437	+	6.60701i	0.462961	+	0.267291i
$612$	2.14208	−	0.754214i	0.0865885	−	0.0304873i
$613$	−13.9117	−	24.0958i	−0.561889	−	0.973220i	−0.997332	−	0.0730039i	$-0.976741\pi$
$613$	−13.9117	−	24.0958i	−0.561889	−	0.973220i	0.435443	−	0.900216i	$-0.356592\pi$
$614$	−2.26399	+	12.8397i	−0.0913674	+	0.518170i
$615$	−1.56644	+	4.23428i	−0.0631649	+	0.170743i
$616$	1.19453	+	6.61376i	0.0481291	+	0.266476i
$617$	−18.1901	−	21.6782i	−0.732308	−	0.872730i	0.263457	−	0.964671i	$-0.415137\pi$
$617$	−18.1901	−	21.6782i	−0.732308	−	0.872730i	−0.995764	+	0.0919408i	$0.970693\pi$
$618$	−32.1242	+	37.8774i	−1.29222	+	1.52365i
$619$	−28.6553	−	5.05271i	−1.15176	−	0.203086i	−0.435014	−	0.900424i	$-0.643256\pi$
$619$	−28.6553	−	5.05271i	−1.15176	−	0.203086i	−0.716742	+	0.697338i	$0.754368\pi$
$620$	−8.81223	−	5.08774i	−0.353908	−	0.204329i
$621$	−14.1007	+	11.4574i	−0.565840	+	0.459768i
$622$		−	42.4655i		−	1.70271i
$623$	1.36256	−	7.91973i	0.0545900	−	0.317297i
$624$	24.1614	+	20.4915i	0.967230	+	0.820317i
$625$	−12.6294	−	4.59671i	−0.505175	−	0.183869i
$626$	1.80762	+	0.657921i	0.0722472	+	0.0262958i
$627$	−21.6576	+	3.70139i	−0.864922	+	0.147819i
$628$	7.61699	+	1.34308i	0.303951	+	0.0535947i
$629$	2.30512	−	3.99258i	0.0919110	−	0.159194i
$630$	0.0868553	−	13.6289i	0.00346040	−	0.542987i
$631$	3.11061	+	5.38773i	0.123831	+	0.214482i	0.921275	−	0.388911i	$-0.127149\pi$
$631$	3.11061	+	5.38773i	0.123831	+	0.214482i	−0.797444	+	0.603393i	$0.793815\pi$
$632$	−2.34847	−	6.45238i	−0.0934172	−	0.256662i
$633$	7.97602	+	4.66110i	0.317018	+	0.185262i
$634$	−36.2160	+	30.3888i	−1.43832	+	1.20689i
$635$	−1.29425	−	7.34005i	−0.0513607	−	0.291281i
$636$	14.0329	+	24.6039i	0.556440	+	0.975606i
$637$	−17.6442	+	21.3858i	−0.699087	+	0.847338i
$638$	−30.1838	+	17.4266i	−1.19499	+	0.689926i
$639$	4.83554	+	5.88754i	0.191291	+	0.232907i
$640$	4.46184	−	2.57605i	0.176370	−	0.101827i
$641$	−2.18684	−	6.00829i	−0.0863749	−	0.237313i	0.888984	−	0.457939i	$-0.151412\pi$
$641$	−2.18684	−	6.00829i	−0.0863749	−	0.237313i	−0.975359	+	0.220626i	$0.929190\pi$
$642$	31.1835	+	37.5629i	1.23072	+	1.48249i
$643$	−2.20568	+	0.388920i	−0.0869834	+	0.0153375i	−0.216970	−	0.976178i	$-0.569618\pi$
$643$	−2.20568	+	0.388920i	−0.0869834	+	0.0153375i	0.129987	+	0.991516i	$0.458506\pi$
$644$	−5.06086	+	14.0864i	−0.199426	+	0.555082i
$645$	13.6880	+	2.48792i	0.538964	+	0.0979616i
$646$	−2.47379	−	2.07576i	−0.0973300	−	0.0816696i
$647$	13.4891	−	23.3638i	0.530311	−	0.918525i	−0.469064	−	0.883164i	$-0.655409\pi$
$647$	13.4891	−	23.3638i	0.530311	−	0.918525i	0.999375	−	0.0353609i	$-0.0112581\pi$
$648$	6.41514	+	1.27097i	0.252010	+	0.0499282i
$649$	9.81311	−	5.66560i	0.385198	−	0.222394i
$650$	−29.6272	+	10.7834i	−1.16208	+	0.422961i
$651$	24.4330	+	20.5479i	0.957604	+	0.805337i
$652$	9.86695	−	8.27936i	0.386420	−	0.324245i
$653$	−14.6649	−	17.4769i	−0.573880	−	0.683924i	0.398542	−	0.917150i	$-0.369516\pi$
$653$	−14.6649	−	17.4769i	−0.573880	−	0.683924i	−0.972423	+	0.233226i	$0.925072\pi$
$654$	9.16652	+	3.39109i	0.358439	+	0.132602i
$655$	−17.5979	+	6.40512i	−0.687607	+	0.250269i
$656$	−13.3343			−0.520617
$657$	15.9372	+	19.4044i	0.621768	+	0.757037i
$658$	14.5054	−	8.45521i	0.565478	−	0.329618i
$659$	21.2918	+	3.75431i	0.829409	+	0.146247i	0.572206	−	0.820110i	$-0.306088\pi$
$659$	21.2918	+	3.75431i	0.829409	+	0.146247i	0.257203	+	0.966357i	$0.417199\pi$
$660$	4.46220	−	7.63566i	0.173691	−	0.297218i
$661$	18.7716	+	22.3711i	0.730130	+	0.870135i	0.995573	−	0.0939915i	$-0.0299627\pi$
$661$	18.7716	+	22.3711i	0.730130	+	0.870135i	−0.265443	+	0.964127i	$0.585518\pi$
$662$	32.4550	+	38.6784i	1.26140	+	1.50328i
$663$	−1.59015	−	2.78802i	−0.0617565	−	0.108278i
$664$	−8.08394	−	1.42542i	−0.313718	−	0.0553169i
$665$	−7.48780	+	4.36466i	−0.290365	+	0.169254i
$666$	−48.9886	+	27.6001i	−1.89827	+	1.06948i
$667$	18.3276			0.709646
$668$	34.1642	−	12.4347i	1.32185	−	0.481114i
$669$	−2.47258	−	14.4676i	−0.0955955	−	0.559349i
$670$	−11.3155	−	13.4853i	−0.437156	−	0.520982i
$671$	−0.163651	+	0.137319i	−0.00631766	+	0.00530115i
$672$	31.5807	−	11.4548i	1.21825	−	0.441877i
$673$	22.4647	−	8.17648i	0.865950	−	0.315180i	0.129424	−	0.991589i	$-0.458687\pi$
$673$	22.4647	−	8.17648i	0.865950	−	0.315180i	0.736526	+	0.676409i	$0.236465\pi$
$674$	−40.8387	+	23.5782i	−1.57305	+	0.908199i
$675$	−14.2395	+	16.4357i	−0.548077	+	0.632612i
$676$	−2.17387	+	3.76525i	−0.0836104	+	0.144817i
$677$	23.7257	+	19.9082i	0.911852	+	0.765135i	0.972470	−	0.233026i	$-0.0748628\pi$
$677$	23.7257	+	19.9082i	0.911852	+	0.765135i	−0.0606183	+	0.998161i	$0.519307\pi$
$678$	−13.5320	−	37.7966i	−0.519692	−	1.45157i
$679$	4.56843	−	12.7158i	0.175320	−	0.487987i
$680$	−0.302246	+	0.0532942i	−0.0115906	+	0.00204374i
$681$	38.3998	−	6.56272i	1.47149	−	0.251484i
$682$	15.8434	+	43.5293i	0.606674	+	1.66682i
$683$	−3.31809	+	1.91570i	−0.126963	+	0.0733022i	−0.562136	−	0.827044i	$-0.690020\pi$
$683$	−3.31809	+	1.91570i	−0.126963	+	0.0733022i	0.435173	+	0.900347i	$0.356687\pi$
$684$	5.84965	+	16.6139i	0.223667	+	0.635249i
$685$	9.53964	−	5.50771i	0.364491	−	0.210439i
$686$	12.4601	+	32.9502i	0.475727	+	1.25804i
$687$	−0.692995	+	1.18584i	−0.0264394	+	0.0452428i
$688$	7.13518	+	40.4656i	0.272026	+	1.54274i
$689$	30.6658	−	25.7316i	1.16827	−	0.980298i
$690$	−9.03321	+	5.15212i	−0.343888	+	0.196138i
$691$	2.82846	+	7.77112i	0.107600	+	0.295627i	0.981794	−	0.189949i	$-0.0608321\pi$
$691$	2.82846	+	7.77112i	0.107600	+	0.295627i	−0.874194	+	0.485576i	$0.838610\pi$
$692$	−6.26547	−	10.8521i	−0.238177	−	0.412535i
$693$	−17.9705	+	21.1413i	−0.682644	+	0.803093i
$694$	−17.8241	+	30.8723i	−0.676594	+	1.17190i
$695$	−15.9913	−	2.81969i	−0.606583	−	0.106957i
$696$	−4.21383	−	5.07587i	−0.159725	−	0.192400i
$697$	1.26944	+	0.462038i	0.0480835	+	0.0175010i
$698$	−43.4516	−	15.8151i	−1.64467	−	0.598609i
$699$	−14.1500	+	5.06600i	−0.535203	+	0.191614i
$700$	−3.03762	+	17.6558i	−0.114811	+	0.667326i
$701$		−	19.8898i		−	0.751226i	−0.926777	−	0.375613i	$-0.877432\pi$
$701$		−	19.8898i		−	0.751226i	0.926777	−	0.375613i	$-0.122568\pi$
$702$	−0.618108	+	39.1411i	−0.0233290	+	1.47728i
$703$	30.9663	+	17.8784i	1.16792	+	0.674296i
$704$	16.2070	+	2.85774i	0.610826	+	0.107705i
$705$	5.13252	+	0.932884i	0.193302	+	0.0351344i
$706$	−27.9732	−	33.3371i	−1.05278	−	1.25466i
$707$	6.30852	+	34.9283i	0.237256	+	1.31361i
$708$	−5.80219	−	6.98916i	−0.218060	−	0.262669i
$709$	2.42708	−	13.7647i	0.0911511	−	0.516943i	−0.904708	−	0.426032i	$-0.859911\pi$
$709$	2.42708	−	13.7647i	0.0911511	−	0.516943i	0.995859	−	0.0909111i	$-0.0289779\pi$
$710$	2.18038	+	3.77652i	0.0818281	+	0.141730i
$711$	14.4319	−	24.4000i	0.541240	−	0.915072i
$712$	1.91139	+	1.10354i	0.0716325	+	0.0413571i
$713$	4.22989	−	23.9889i	0.158410	−	0.898390i
$714$	−4.07814	−	0.00452391i	−0.152621	−	0.000169303i
$715$	−11.7454	−	4.27499i	−0.439254	−	0.159876i
$716$	−2.98137	+	0.525696i	−0.111419	+	0.0196462i
$717$	−38.8162	−	0.204311i	−1.44962	−	0.00763014i
$718$	−12.1704	−	10.2121i	−0.454194	−	0.381114i
$719$	−15.7165	+	27.2219i	−0.586128	+	1.01520i	0.408606	+	0.912711i	$0.366015\pi$
$719$	−15.7165	+	27.2219i	−0.586128	+	1.01520i	−0.994734	+	0.102493i	$0.967318\pi$
$720$	11.7070	+	4.40110i	0.436294	+	0.164019i
$721$	34.4583	−	20.0859i	1.28330	−	0.748036i
$722$	−7.13076	+	8.49811i	−0.265380	+	0.316267i
$723$	−14.0125	+	11.6327i	−0.521129	+	0.432625i
$724$	11.6159	−	31.9146i	0.431703	−	1.18610i
$725$	21.6031	−	3.80921i	0.802319	−	0.141471i
$726$	−3.78589	+	1.35543i	−0.140508	+	0.0503046i
$727$	9.57818	+	26.3158i	0.355235	+	0.976000i	0.980661	+	0.195716i	$0.0627031\pi$
$727$	9.57818	+	26.3158i	0.355235	+	0.976000i	−0.625426	+	0.780284i	$0.715075\pi$
$728$	−3.83464	−	6.57853i	−0.142121	−	0.243817i
$729$	12.7549	+	23.7973i	0.472405	+	0.881381i
$730$	7.18617	+	12.4468i	0.265972	+	0.460677i
$731$	0.722872	−	4.09961i	0.0267364	−	0.151630i
$732$	0.130610	+	0.110771i	0.00482748	+	0.00409423i
$733$	−8.51889	+	23.4055i	−0.314653	+	0.864501i	0.677049	+	0.735938i	$0.263259\pi$
$733$	−8.51889	+	23.4055i	−0.314653	+	0.864501i	−0.991701	+	0.128563i	$0.958964\pi$
$734$	−3.22409	−	18.2847i	−0.119003	−	0.674900i
$735$	−3.71215	+	10.2965i	−0.136925	+	0.379792i
$736$	−19.6357	−	16.4763i	−0.723780	−	0.607324i
$737$			35.8388i			1.32014i
$738$	−10.4573	−	12.7324i	−0.384939	−	0.468685i
$739$	46.5319			1.71170			0.855851	−	0.517222i	$-0.173034\pi$
$739$	46.5319			1.71170			0.855851	+	0.517222i	$0.173034\pi$
$740$	−13.5246	+	4.92257i	−0.497176	+	0.180957i
$741$	21.6237	−	12.3332i	0.794368	−	0.453071i
$742$	−9.04044	−	50.0541i	−0.331885	−	1.83754i
$743$	−11.9890	+	32.9395i	−0.439834	+	1.20843i	0.499767	+	0.866160i	$0.333419\pi$
$743$	−11.9890	+	32.9395i	−0.439834	+	1.20843i	−0.939600	+	0.342273i	$0.888803\pi$
$744$	−7.61631	+	4.34399i	−0.279227	+	0.159258i
$745$	−6.53564	+	7.78887i	−0.239447	+	0.285362i
$746$			20.1588i			0.738067i
$747$	−16.6350	−	29.5262i	−0.608643	−	1.08031i
$748$	−2.29176	−	1.32315i	−0.0837949	−	0.0483790i
$749$	−13.5622	−	36.7856i	−0.495551	−	1.34411i
$750$	−21.0185	+	17.4489i	−0.767488	+	0.637145i
$751$	3.14628	−	2.64004i	0.114809	−	0.0963364i	−0.583576	−	0.812059i	$-0.698347\pi$
$751$	3.14628	−	2.64004i	0.114809	−	0.0963364i	0.698385	+	0.715722i	$0.253902\pi$
$752$	2.67545	+	15.1732i	0.0975636	+	0.553311i
$753$	5.50163	+	15.3668i	0.200491	+	0.559997i
$754$	25.3826	−	30.2498i	0.924381	−	1.10163i
$755$	5.49677			0.200048
$756$	19.1327	+	11.3451i	0.695850	+	0.412619i
$757$	−15.6872			−0.570161			−0.285081	−	0.958504i	$-0.592020\pi$
$757$	−15.6872			−0.570161			−0.285081	+	0.958504i	$0.592020\pi$
$758$	7.65941	−	9.12813i	0.278202	−	0.331549i
$759$	20.8300	+	3.78605i	0.756081	+	0.137425i
$760$	−0.413348	−	2.34421i	−0.0149937	−	0.0850335i
$761$	−21.5384	+	18.0728i	−0.780766	+	0.655140i	−0.943441	−	0.331539i	$-0.892432\pi$
$761$	−21.5384	+	18.0728i	−0.780766	+	0.655140i	0.162676	+	0.986680i	$0.447988\pi$
$762$	25.5107	+	9.43749i	0.924155	+	0.341884i
$763$	−6.03357	−	5.02020i	−0.218430	−	0.181744i
$764$	14.3632	+	8.29258i	0.519641	+	0.300015i
$765$	−0.962019	−	0.824642i	−0.0347819	−	0.0298150i
$766$			15.9111i			0.574890i
$767$	−8.25220	+	9.83459i	−0.297970	+	0.355107i
$768$	−0.184801	+	35.1097i	−0.00666845	+	1.26691i
$769$	−9.49574	+	26.0893i	−0.342425	+	0.940806i	0.642263	+	0.766484i	$0.277996\pi$
$769$	−9.49574	+	26.0893i	−0.342425	+	0.940806i	−0.984689	+	0.174322i	$0.944227\pi$
$770$	−12.1235	+	10.2589i	−0.436899	+	0.369706i
$771$	17.6320	+	10.3040i	0.635001	+	0.371088i
$772$	−15.3297	+	5.57954i	−0.551726	+	0.200812i
$773$	−13.0962			−0.471036			−0.235518	−	0.971870i	$-0.575679\pi$
$773$	−13.0962			−0.471036			−0.235518	+	0.971870i	$0.575679\pi$
$774$	−33.0433	+	38.5480i	−1.18772	+	1.38558i
$775$		−	29.1553i		−	1.04729i
$776$	2.84272	+	2.38532i	0.102048	+	0.0856280i
$777$	44.4783	−	7.79186i	1.59565	−	0.279531i
$778$	−6.41839	−	36.4005i	−0.230110	−	1.30502i
$779$	−3.58355	+	9.84573i	−0.128394	+	0.352760i
$780$	−1.79188	+	9.85853i	−0.0641596	+	0.352992i
$781$	1.54163	−	8.74300i	0.0551637	−	0.312849i
$782$	1.55584	+	2.69479i	0.0556366	+	0.0963654i
$783$	5.15244	−	26.7444i	0.184133	−	0.955766i
$784$	−32.3256	+	0.268580i	−1.15449	+	0.00959214i
$785$	−1.47597	−	4.05519i	−0.0526796	−	0.144736i
$786$	12.2220	−	67.2427i	0.435944	−	2.39847i
$787$	46.4006	−	8.18167i	1.65400	−	0.291645i	0.732717	−	0.680533i	$-0.238252\pi$
$787$	46.4006	−	8.18167i	1.65400	−	0.291645i	0.921285	+	0.388888i	$0.127141\pi$
$788$	−14.7110	+	40.4181i	−0.524057	+	1.43983i
$789$	−7.54333	−	2.79060i	−0.268550	−	0.0993479i
$790$	10.4298	−	12.4297i	0.371076	−	0.442231i
$791$	0.133931	+	32.2399i	0.00476205	+	1.14632i
$792$	−3.74063	−	6.63940i	−0.132918	−	0.235921i
$793$	0.121021	−	0.209614i	0.00429757	−	0.00744362i
$794$	−41.3352	−	34.6844i	−1.46693	−	1.23090i
$795$	7.97370	−	13.6445i	0.282798	−	0.483920i
$796$	−31.0437	+	5.47383i	−1.10031	+	0.194015i
$797$	35.7462	+	13.0105i	1.26619	+	0.460857i	0.885843	−	0.463985i	$-0.153581\pi$
$797$	35.7462	+	13.0105i	1.26619	+	0.460857i	0.380352	+	0.924842i	$0.375803\pi$
$798$	0.0350873	−	31.6299i	0.00124208	−	1.11969i
$799$	0.271052	−	1.53721i	0.00958914	−	0.0543827i
$800$	−26.5694	−	15.3399i	−0.939371	−	0.542346i
$801$	1.48774	+	8.98980i	0.0525668	+	0.317639i
$802$	18.5680	+	32.1608i	0.655660	+	1.13564i
$803$	5.08096	−	28.8155i	0.179303	−	1.01688i
$804$	28.3197	−	4.83998i	0.998760	−	0.170693i
$805$	8.21835	−	1.48435i	0.289659	−	0.0523163i
$806$	−33.7357	−	40.2047i	−1.18829	−	1.41615i
$807$	−15.8159	−	44.1760i	−0.556747	−	1.55507i
$808$	−9.60006	−	1.69275i	−0.337729	−	0.0595507i
$809$	7.26934	+	4.19695i	0.255576	+	0.147557i	0.622315	−	0.782767i	$-0.286192\pi$
$809$	7.26934	+	4.19695i	0.255576	+	0.147557i	−0.366739	+	0.930324i	$0.619526\pi$
$810$	4.97868	+	14.6301i	0.174933	+	0.514048i
$811$		−	36.2880i		−	1.27425i	−0.770762	−	0.637123i	$-0.780124\pi$
$811$		−	36.2880i		−	1.27425i	0.770762	−	0.637123i	$-0.219876\pi$
$812$	−7.76179	−	21.0528i	−0.272385	−	0.738809i
$813$	1.40618	−	7.73648i	0.0493168	−	0.271330i
$814$	61.5697	+	22.4095i	2.15802	+	0.785454i
$815$	−6.75318	−	2.45796i	−0.236554	−	0.0860985i
$816$	1.29845	−	3.50988i	0.0454549	−	0.122870i
$817$	31.7964	+	5.60657i	1.11242	+	0.196149i
$818$	−33.2557	+	57.6006i	−1.16276	+	2.01396i
$819$	10.9402	−	29.4721i	0.382280	−	1.02984i
$820$	−2.10869	−	3.65237i	−0.0736388	−	0.127546i
$821$	17.4948	+	48.0666i	0.610573	+	1.67754i	0.728950	+	0.684567i	$0.240009\pi$
$821$	17.4948	+	48.0666i	0.610573	+	1.67754i	−0.118377	+	0.992969i	$0.537769\pi$
$822$	−0.211593	+	40.1997i	−0.00738016	+	1.40213i
$823$	3.25771	−	2.73354i	0.113556	−	0.0952852i	−0.584241	−	0.811580i	$-0.698608\pi$
$823$	3.25771	−	2.73354i	0.113556	−	0.0952852i	0.697798	+	0.716295i	$0.254163\pi$
$824$	1.90220	+	10.7879i	0.0662661	+	0.375814i
$825$	25.3397	+	0.133377i	0.882214	+	0.00464357i
$826$	5.64273	+	15.3051i	0.196336	+	0.532534i
$827$	15.9647	−	9.21722i	0.555147	−	0.320514i	−0.196048	−	0.980594i	$-0.562811\pi$
$827$	15.9647	−	9.21722i	0.555147	−	0.320514i	0.751195	+	0.660080i	$0.229478\pi$
$828$	0.178661	−	16.9711i	0.00620891	−	0.589786i
$829$	2.14109	−	1.23616i	0.0743630	−	0.0429335i	−0.462357	−	0.886694i	$-0.652996\pi$
$829$	2.14109	−	1.23616i	0.0743630	−	0.0429335i	0.536720	+	0.843760i	$0.319663\pi$
$830$	−6.63434	−	18.2277i	−0.230281	−	0.632693i
$831$	4.79077	−	12.9500i	0.166190	−	0.449232i
$832$	−18.3624	+	3.23779i	−0.636602	+	0.112250i
$833$	3.08674	+	1.09453i	0.106949	+	0.0379231i
$834$	38.3298	−	45.1944i	1.32725	−	1.56496i
$835$	−15.5393	−	13.0391i	−0.537761	−	0.451235i
$836$	10.2623	−	17.7748i	0.354928	−	0.614754i
$837$	−33.8164	−	12.9164i	−1.16887	−	0.446457i
$838$	66.8167	−	38.5766i	2.30814	−	1.33261i
$839$	−11.0811	+	4.03321i	−0.382563	+	0.139242i	−0.526141	−	0.850397i	$-0.676362\pi$
$839$	−11.0811	+	4.03321i	−0.382563	+	0.139242i	0.143578	+	0.989639i	$0.454139\pi$
$840$	−2.30064	−	1.93482i	−0.0793796	−	0.0667576i
$841$	1.16867	−	0.980630i	0.0402989	−	0.0338148i
$842$	19.3527	+	23.0637i	0.666940	+	0.794828i
$843$	−8.19325	+	6.80178i	−0.282190	+	0.234266i
$844$	−8.10925	+	2.95152i	−0.279132	+	0.101596i
$845$	2.42581			0.0834505
$846$	−12.3901	+	14.4542i	−0.425981	+	0.496945i
$847$	3.22930	−	0.0134152i	0.110960	−	0.000460952i
$848$	45.9667	+	8.10517i	1.57850	+	0.278333i
$849$	19.8718	+	0.104596i	0.681999	+	0.00358973i
$850$	2.39398	+	2.85304i	0.0821130	+	0.0978584i
$851$	−22.1468	−	26.3935i	−0.759182	−	0.904758i
$852$	−7.11688	−	0.0374600i	−0.243820	−	0.00128336i
$853$	−14.3072	−	2.52275i	−0.489869	−	0.0863772i	−0.0767431	−	0.997051i	$-0.524452\pi$
$853$	−14.3072	−	2.52275i	−0.489869	−	0.0863772i	−0.413126	+	0.910674i	$0.635563\pi$
$854$	−0.154874	−	0.265695i	−0.00529969	−	0.00909191i
$855$	6.39589	−	7.46138i	0.218735	−	0.255174i
$856$	10.7678			0.368036
$857$	15.5951	−	5.67614i	0.532717	−	0.193893i	−0.0616339	−	0.998099i	$-0.519631\pi$
$857$	15.5951	−	5.67614i	0.532717	−	0.193893i	0.594351	+	0.804206i	$0.297409\pi$
$858$	35.0972	−	29.1367i	1.19820	−	0.994709i
$859$	−14.0869	−	16.7881i	−0.480639	−	0.572803i	0.470172	−	0.882575i	$-0.344192\pi$
$859$	−14.0869	−	16.7881i	−0.480639	−	0.572803i	−0.950811	+	0.309772i	$0.899747\pi$
$860$	−9.95548	+	8.35364i	−0.339479	+	0.284857i
$861$	4.51171	+	12.4387i	0.153759	+	0.423911i
$862$	−14.2039	+	5.16980i	−0.483787	+	0.176084i
$863$	−6.94716	+	4.01095i	−0.236484	+	0.136534i	−0.613560	−	0.789648i	$-0.710263\pi$
$863$	−6.94716	+	4.01095i	−0.236484	+	0.136534i	0.377076	+	0.926182i	$0.376930\pi$
$864$	−29.5631	+	24.0212i	−1.00576	+	0.817218i
$865$	−3.49580	+	6.05491i	−0.118861	+	0.205873i
$866$	24.0066	+	20.1439i	0.815776	+	0.684517i
$867$	18.8000	−	22.1670i	0.638482	−	0.752830i
$868$	−29.3473	+	5.30052i	−0.996112	+	0.179911i
$869$	−32.5317	+	5.73622i	−1.10356	+	0.194588i
$870$	5.40884	−	14.6208i	0.183377	−	0.495690i
$871$	−13.8877	−	38.1563i	−0.470568	−	1.29288i
$872$	1.86689	−	1.07785i	0.0632209	−	0.0365006i
$873$	−0.161277	+	15.3198i	−0.00545841	+	0.518496i
$874$	−20.9007	+	12.0670i	−0.706976	+	0.408173i
$875$	20.5836	−	7.58879i	0.695852	−	0.256548i
$876$	−23.4561	−	0.123462i	−0.792508	−	0.00417140i
$877$	6.25755	+	35.4883i	0.211302	+	1.19836i	0.887209	+	0.461368i	$0.152641\pi$
$877$	6.25755	+	35.4883i	0.211302	+	1.19836i	−0.675906	+	0.736988i	$0.736248\pi$
$878$	−8.89041	+	7.45994i	−0.300037	+	0.251761i
$879$	−0.0100067	+	1.90113i	−0.000337517	+	0.0641235i
$880$	−4.98456	−	13.6950i	−0.168030	−	0.461657i
$881$	21.1819	+	36.6881i	0.713636	+	1.23605i	0.963483	+	0.267769i	$0.0862865\pi$
$881$	21.1819	+	36.6881i	0.713636	+	1.23605i	−0.249847	+	0.968285i	$0.580380\pi$
$882$	−25.6076	−	30.6558i	−0.862252	−	1.03223i
$883$	−3.68137	+	6.37633i	−0.123888	+	0.214580i	−0.921298	−	0.388858i	$-0.872870\pi$
$883$	−3.68137	+	6.37633i	−0.123888	+	0.214580i	0.797410	+	0.603438i	$0.206203\pi$
$884$	2.95268	+	0.520636i	0.0993092	+	0.0175109i
$885$	−1.75848	+	4.75339i	−0.0591107	+	0.159784i
$886$	−35.5817	−	12.9507i	−1.19539	−	0.435087i
$887$	0.457707	+	0.166592i	0.0153683	+	0.00559360i	0.349693	−	0.936864i	$-0.386286\pi$
$887$	0.457707	+	0.166592i	0.0153683	+	0.00559360i	−0.334325	+	0.942458i	$0.608508\pi$
$888$	−2.21782	+	12.2019i	−0.0744250	+	0.409471i
$889$	−16.7916	−	13.9714i	−0.563173	−	0.468585i
$890$			5.21548i			0.174823i
$891$	11.3807	−	29.3317i	0.381268	−	0.982647i
$892$	11.8738	+	6.85534i	0.397564	+	0.229534i
$893$	11.9226	+	2.10227i	0.398974	+	0.0703498i
$894$	−12.5074	−	34.9349i	−0.418311	−	1.16840i
$895$	1.08574	+	1.29393i	0.0362923	+	0.0432515i
$896$	5.10540	−	14.2104i	0.170559	−	0.474735i
$897$	−23.6440	+	4.04088i	−0.789452	+	0.134921i
$898$	0.157234	−	0.891718i	0.00524696	−	0.0297570i
$899$	18.2579	+	31.6237i	0.608936	+	1.05471i
$900$	−3.31669	−	20.0413i	−0.110556	−	0.668045i
$901$	−4.09524	−	2.36439i	−0.136432	−	0.0787691i
$902$	−3.33392	+	18.9076i	−0.111007	+	0.629554i
$903$	35.3337	−	20.3477i	1.17583	−	0.677129i
$904$	−8.32066	−	3.02847i	−0.276741	−	0.100726i
$905$	−18.6616	+	3.29054i	−0.620331	+	0.109381i
$906$	−10.1214	+	17.3196i	−0.336261	+	0.575405i
$907$	−1.78620	−	1.49880i	−0.0593098	−	0.0497668i	0.612651	−	0.790354i	$-0.290103\pi$
$907$	−1.78620	−	1.49880i	−0.0593098	−	0.0497668i	−0.671961	+	0.740587i	$0.734548\pi$
$908$	−18.1954	+	31.5154i	−0.603837	+	1.04588i
$909$	−19.7549	−	35.0637i	−0.655227	−	1.16299i
$910$	8.93202	−	15.6202i	0.296093	−	0.517805i
$911$	−17.0700	+	20.3432i	−0.565553	+	0.674000i	−0.970712	−	0.240246i	$-0.922772\pi$
$911$	−17.0700	+	20.3432i	−0.565553	+	0.674000i	0.405159	+	0.914246i	$0.367216\pi$
$912$	27.2225	+	10.0707i	0.901426	+	0.333476i
$913$	−13.5066	+	37.1090i	−0.447002	+	1.22813i
$914$	−21.6469	+	3.81694i	−0.716017	+	0.126253i
$915$	0.0170877	−	0.0940127i	0.000564901	−	0.00310796i
$916$	−0.438822	−	1.20565i	−0.0144991	−	0.0398359i
$917$	−27.2451	+	47.6460i	−0.899713	+	1.57341i
$918$	4.36974	−	1.51275i	0.144223	−	0.0499283i
$919$	−4.06315	−	7.03758i	−0.134031	−	0.232148i	0.791196	−	0.611563i	$-0.209459\pi$
$919$	−4.06315	−	7.03758i	−0.134031	−	0.232148i	−0.925227	+	0.379414i	$0.876125\pi$
$920$	−0.398291	+	2.25882i	−0.0131313	+	0.0744711i
$921$	−2.12311	+	11.6809i	−0.0699587	+	0.384898i
$922$	13.1727	−	36.1917i	0.433820	−	1.19191i
$923$	1.74665	+	9.90573i	0.0574916	+	0.326051i
$924$	−4.47256	−	25.5307i	−0.147137	−	0.839900i
$925$	−31.5905	−	26.5076i	−1.03869	−	0.871565i
$926$		−	11.7791i		−	0.387086i
$927$	−29.4334	+	34.3367i	−0.966720	+	1.12777i
$928$	38.4251			1.26137
$929$	19.2006	−	6.98845i	0.629952	−	0.229284i	−0.00725854	−	0.999974i	$-0.502310\pi$
$929$	19.2006	−	6.98845i	0.629952	−	0.229284i	0.637210	+	0.770690i	$0.280088\pi$
$930$	−17.8887	−	10.4540i	−0.586594	−	0.342800i
$931$	−8.48910	+	23.9407i	−0.278219	+	0.784623i
$932$	4.80185	−	13.1930i	0.157290	−	0.432150i
$933$	0.203534	−	38.6685i	0.00666339	−	1.26595i
$934$	−4.65456	+	5.54709i	−0.152302	+	0.181506i
$935$			1.47649i			0.0482865i
$936$	6.55532	+	5.61921i	0.214267	+	0.183670i
$937$	−29.2827	−	16.9064i	−0.956625	−	0.552308i	−0.0614921	−	0.998108i	$-0.519586\pi$
$937$	−29.2827	−	16.9064i	−0.956625	−	0.552308i	−0.895133	+	0.445800i	$0.852919\pi$
$938$	−50.8459	−	8.74786i	−1.66018	−	0.285628i
$939$	1.64285	+	0.607759i	0.0536123	+	0.0198335i
$940$	−3.73297	+	3.13233i	−0.121756	+	0.102165i
$941$	−7.81855	−	44.3412i	−0.254878	−	1.44548i	−0.796387	−	0.604788i	$-0.793258\pi$
$941$	−7.81855	−	44.3412i	−0.254878	−	1.44548i	0.541509	−	0.840695i	$-0.317853\pi$
$942$	15.4951	+	2.81638i	0.504859	+	0.0917627i
$943$	6.48955	−	7.73394i	0.211329	−	0.251852i
$944$	−14.9691			−0.487201
$945$	0.144411	−	12.4099i	0.00469770	−	0.403693i
$946$	59.1629			1.92355
$947$	0.805471	−	0.959923i	0.0261743	−	0.0311933i	−0.752799	−	0.658251i	$-0.771297\pi$
$947$	0.805471	−	0.959923i	0.0261743	−	0.0311933i	0.778973	+	0.627058i	$0.215741\pi$
$948$	8.92610	+	24.9318i	0.289906	+	0.809747i
$949$	5.75667	+	32.6477i	0.186870	+	1.05979i
$950$	−22.1281	+	18.5676i	−0.717929	+	0.602414i
$951$	−33.1235	+	27.4981i	−1.07410	+	0.891688i
$952$	−0.575309	+	0.691440i	−0.0186459	+	0.0224097i
$953$	41.3947	+	23.8992i	1.34091	+	0.774172i	0.986940	−	0.161086i	$-0.0514997\pi$
$953$	41.3947	+	23.8992i	1.34091	+	0.774172i	0.353965	+	0.935259i	$0.384833\pi$
$954$	28.3098	+	50.2482i	0.916562	+	1.62684i
$955$		−	9.25365i		−	0.299441i
$956$	23.3076	−	27.7770i	0.753823	−	0.898371i
$957$	−27.5685	+	15.7238i	−0.891163	+	0.508278i
$958$	19.5540	−	53.7242i	0.631762	−	1.73575i
$959$	10.9156	−	30.3825i	0.352483	−	0.981101i
$960$	−6.39403	+	3.64686i	−0.206367	+	0.117702i
$961$	16.4754	−	5.99657i	0.531465	−	0.193438i
$962$	−74.2348			−2.39342
$963$	28.2153	+	34.3537i	0.909226	+	1.10703i
$964$		−	17.0123i		−	0.547930i
$965$	6.97259	+	5.85070i	0.224456	+	0.188341i
$966$	−10.4558	+	28.6282i	−0.336409	+	0.921096i
$967$	−3.01993	−	17.1269i	−0.0971143	−	0.550763i	−0.994079	−	0.108660i	$-0.965344\pi$
$967$	−3.01993	−	17.1269i	−0.0971143	−	0.550763i	0.896965	−	0.442102i	$-0.145767\pi$
$968$	−0.303346	+	0.833438i	−0.00974992	+	0.0267877i
$969$	−2.24265	−	1.90202i	−0.0720444	−	0.0611015i
$970$	−1.52273	+	8.63586i	−0.0488921	+	0.277281i
$971$	−13.6117	−	23.5762i	−0.436821	−	0.756596i	0.560622	−	0.828072i	$-0.310562\pi$
$971$	−13.6117	−	23.5762i	−0.436821	−	0.756596i	−0.997442	+	0.0714765i	$0.977229\pi$
$972$	−24.7147	−	5.03181i	−0.792725	−	0.161395i
$973$	−41.1149	+	23.9660i	−1.31808	+	0.768314i
$974$	−24.7139	−	67.9008i	−0.791884	−	2.17568i
$975$	−27.0299	+	9.67726i	−0.865649	+	0.309920i
$976$	0.277929	−	0.0490063i	0.00889628	−	0.00156865i
$977$	−7.73653	+	21.2560i	−0.247514	+	0.680038i	0.752262	+	0.658864i	$0.228963\pi$
$977$	−7.73653	+	21.2560i	−0.247514	+	0.680038i	−0.999776	+	0.0211742i	$0.993260\pi$
$978$	20.1796	−	16.7525i	0.645272	−	0.535685i
$979$	6.82510	−	8.13384i	0.218131	−	0.259959i
$980$	−5.18556	−	8.81176i	−0.165647	−	0.281482i
$981$	8.33067	+	3.13182i	0.265978	+	0.0999912i
$982$	29.9500	−	51.8749i	0.955742	−	1.65539i
$983$	−16.9151	−	14.1935i	−0.539509	−	0.452702i	0.331861	−	0.943328i	$-0.392324\pi$
$983$	−16.9151	−	14.1935i	−0.539509	−	0.452702i	−0.871370	+	0.490626i	$0.836768\pi$
$984$	−3.63400	−	0.0191277i	−0.115848	−	0.000609769i
$985$	23.6339	−	4.16729i	0.753037	−	0.132781i
$986$	−4.38332	−	1.59540i	−0.139593	−	0.0508078i
$987$	13.2489	−	7.62969i	0.421718	−	0.242856i
$988$	−4.03804	+	22.9008i	−0.128467	+	0.728573i
$989$	−26.9428	−	15.5554i	−0.856730	−	0.494633i
$990$	9.16767	−	15.4997i	0.291368	−	0.492614i
$991$	−5.44079	−	9.42373i	−0.172832	−	0.299355i	0.766577	−	0.642153i	$-0.221959\pi$
$991$	−5.44079	−	9.42373i	−0.172832	−	0.299355i	−0.939409	+	0.342798i	$0.888625\pi$
$992$	8.86827	−	50.2944i	0.281568	−	1.59685i
$993$	29.3677	+	35.3756i	0.931957	+	1.12261i
$994$	12.0277	+	4.32123i	0.381496	+	0.137061i
$995$	11.3053	+	13.4731i	0.358402	+	0.427127i
$996$	31.1475	+	5.66134i	0.986945	+	0.179386i
$997$	5.88948	+	1.03847i	0.186522	+	0.0328888i	0.266129	−	0.963938i	$-0.414255\pi$
$997$	5.88948	+	1.03847i	0.186522	+	0.0328888i	−0.0796069	+	0.996826i	$0.525367\pi$
$998$	30.9846	+	17.8890i	0.980801	+	0.566266i
$999$	−44.7407	+	24.8975i	−1.41553	+	0.787722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.4	✓	132
3.2	odd	2		567.2.ba.a.143.19		132
7.5	odd	6		189.2.bd.a.47.19	yes	132
21.5	even	6		567.2.bd.a.467.4		132
27.4	even	9		567.2.bd.a.17.4		132
27.23	odd	18		189.2.bd.a.185.19	yes	132
189.131	even	18	inner	189.2.ba.a.131.4	yes	132
189.166	odd	18		567.2.ba.a.341.19		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.4	✓	132	1.1	even	1	trivial
189.2.ba.a.131.4	yes	132	189.131	even	18	inner
189.2.bd.a.47.19	yes	132	7.5	odd	6
189.2.bd.a.185.19	yes	132	27.23	odd	18
567.2.ba.a.143.19		132	3.2	odd	2
567.2.ba.a.341.19		132	189.166	odd	18
567.2.bd.a.17.4		132	27.4	even	9
567.2.bd.a.467.4		132	21.5	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22264 + 1.45709i) q^{2} +(-1.12031 + 1.32095i) q^{3} +(-0.280959 - 1.59339i) q^{4} +(-0.691544 + 0.580274i) q^{5} +(-0.555004 - 3.24744i) q^{6} +(-0.448602 + 2.60744i) q^{7} +(-0.629295 - 0.363324i) q^{8} +(-0.489815 - 2.95974i) q^{9} +O(q^{10})\)	\(q+(-1.22264 + 1.45709i) q^{2} +(-1.12031 + 1.32095i) q^{3} +(-0.280959 - 1.59339i) q^{4} +(-0.691544 + 0.580274i) q^{5} +(-0.555004 - 3.24744i) q^{6} +(-0.448602 + 2.60744i) q^{7} +(-0.629295 - 0.363324i) q^{8} +(-0.489815 - 2.95974i) q^{9} -1.71711i q^{10} +(-2.24705 + 2.67793i) q^{11} +(2.41955 + 1.41396i) q^{12} +(1.35464 - 3.72184i) q^{13} +(-3.25080 - 3.84163i) q^{14} +(0.00822998 - 1.56358i) q^{15} +(4.33960 - 1.57949i) q^{16} -0.467865 q^{17} +(4.91149 + 2.90501i) q^{18} -3.62874i q^{19} +(1.11890 + 0.938869i) q^{20} +(-2.94173 - 3.51372i) q^{21} +(-1.15465 - 6.54832i) q^{22} +(-1.19589 + 3.28569i) q^{23} +(1.18494 - 0.424232i) q^{24} +(-0.726726 + 4.12147i) q^{25} +(3.76682 + 6.52432i) q^{26} +(4.45842 + 2.66881i) q^{27} +(4.28072 - 0.0177830i) q^{28} +(-1.79273 - 4.92550i) q^{29} +(2.26822 + 1.92370i) q^{30} +(-6.86071 + 1.20973i) q^{31} +(-2.50728 + 6.88869i) q^{32} +(-1.02002 - 5.96836i) q^{33} +(0.572032 - 0.681722i) q^{34} +(-1.20280 - 2.06347i) q^{35} +(-4.57842 + 1.61203i) q^{36} +(-4.92689 + 8.53362i) q^{37} +(5.28741 + 4.43666i) q^{38} +(3.39875 + 5.95902i) q^{39} +(0.646012 - 0.113909i) q^{40} +(-2.71326 - 0.987547i) q^{41} +(8.71650 + 0.00966928i) q^{42} +(-1.54504 + 8.76238i) q^{43} +(4.89833 + 2.82805i) q^{44} +(2.05619 + 1.76256i) q^{45} +(-3.32540 - 5.75976i) q^{46} +(-0.579339 + 3.28560i) q^{47} +(-2.77527 + 7.50190i) q^{48} +(-6.59751 - 2.33941i) q^{49} +(-5.11683 - 6.09800i) q^{50} +(0.524153 - 0.618026i) q^{51} +(-6.31096 - 1.11279i) q^{52} +(8.75304 + 5.05357i) q^{53} +(-9.33975 + 3.23332i) q^{54} -3.15581i q^{55} +(1.22965 - 1.47786i) q^{56} +(4.79338 + 4.06531i) q^{57} +(9.36878 + 3.40996i) q^{58} +(-3.04590 - 1.10862i) q^{59} +(-2.49371 + 0.426188i) q^{60} +(0.0601824 + 0.0106118i) q^{61} +(6.62553 - 11.4757i) q^{62} +(7.93709 + 0.0505822i) q^{63} +(-2.35384 - 4.07697i) q^{64} +(1.22290 + 3.35988i) q^{65} +(9.94356 + 5.81092i) q^{66} +(7.85348 - 6.58985i) q^{67} +(0.131451 + 0.745493i) q^{68} +(-3.00046 - 5.26070i) q^{69} +(4.47727 + 0.770299i) q^{70} +(-2.19935 + 1.26979i) q^{71} +(-0.767107 + 2.04051i) q^{72} +(-7.24870 + 4.18504i) q^{73} +(-6.41043 - 17.6125i) q^{74} +(-4.63009 - 5.57729i) q^{75} +(-5.78202 + 1.01953i) q^{76} +(-5.97452 - 7.06039i) q^{77} +(-12.8383 - 2.33348i) q^{78} +(7.23876 + 6.07404i) q^{79} +(-2.08449 + 3.61044i) q^{80} +(-8.52016 + 2.89945i) q^{81} +(4.75630 - 2.74605i) q^{82} +(10.6153 - 3.86367i) q^{83} +(-4.77224 + 5.67454i) q^{84} +(0.323549 - 0.271490i) q^{85} +(-10.8786 - 12.9646i) q^{86} +(8.51475 + 3.14997i) q^{87} +(2.38702 - 0.868803i) q^{88} -3.03736 q^{89} +(-5.08221 + 0.841067i) q^{90} +(9.09679 + 5.20177i) q^{91} +(5.57140 + 0.982388i) q^{92} +(6.08813 - 10.4179i) q^{93} +(-4.07909 - 4.86127i) q^{94} +(2.10566 + 2.50943i) q^{95} +(-6.29069 - 11.0295i) q^{96} +(-5.02929 - 0.886800i) q^{97} +(11.4751 - 6.75291i) q^{98} +(9.02664 + 5.33901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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