LMFDB - Embedded newform 66.2.h.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [66,2,Mod(17,66)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(66, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("66.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.h (of order $10$, degree $4$, 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:	$0.527012653340$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.2
Root			$1.71634 + 0.232753i$ of defining polynomial
Character	$\chi$	$=$	66.29
Dual form			66.2.h.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(1.25174 - 1.19714i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.442723 - 0.609356i) q^{5} +(-1.71634 + 0.232753i) q^{6} +(-0.442723 + 0.143849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.133706 - 2.99702i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(1.25174 - 1.19714i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.442723 - 0.609356i) q^{5} +(-1.71634 + 0.232753i) q^{6} +(-0.442723 + 0.143849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.133706 - 2.99702i) q^{9} +0.753205i q^{10} +(2.46808 + 2.21553i) q^{11} +(1.52536 + 0.820539i) q^{12} +(-3.12151 + 4.29640i) q^{13} +(0.442723 + 0.143849i) q^{14} +(-1.28366 - 0.232753i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.99344 + 2.17486i) q^{17} +(-1.86977 + 2.34605i) q^{18} +(2.02884 + 0.659209i) q^{19} +(0.442723 - 0.609356i) q^{20} +(-0.381966 + 0.710064i) q^{21} +(-0.694463 - 3.24310i) q^{22} +6.24165i q^{23} +(-0.751740 - 1.56041i) q^{24} +(1.36977 - 4.21573i) q^{25} +(5.05072 - 1.64108i) q^{26} +(-3.42049 - 3.91155i) q^{27} +(-0.273618 - 0.376603i) q^{28} +(-3.09831 - 9.53561i) q^{29} +(0.901693 + 0.942817i) q^{30} +(2.96245 + 2.15235i) q^{31} +1.00000 q^{32} +(5.74170 - 0.181373i) q^{33} +3.70009 q^{34} +(0.283659 + 0.206090i) q^{35} +(2.89165 - 0.798968i) q^{36} +(-2.16527 - 6.66401i) q^{37} +(-1.25389 - 1.72583i) q^{38} +(1.23607 + 9.11486i) q^{39} +(-0.716341 + 0.232753i) q^{40} +(-0.0135213 + 0.0416142i) q^{41} +(0.726382 - 0.349940i) q^{42} -5.49863i q^{43} +(-1.34442 + 3.03192i) q^{44} +(-1.88545 + 1.24537i) q^{45} +(3.66875 - 5.04960i) q^{46} +(-3.03945 - 0.987579i) q^{47} +(-0.309017 + 1.70426i) q^{48} +(-5.48781 + 3.98713i) q^{49} +(-3.58611 + 2.60546i) q^{50} +(-1.14339 + 6.30593i) q^{51} +(-5.05072 - 1.64108i) q^{52} +(-3.00621 + 4.13769i) q^{53} +(0.468081 + 5.17503i) q^{54} +(0.257371 - 2.48481i) q^{55} +0.465507i q^{56} +(3.32874 - 1.60365i) q^{57} +(-3.09831 + 9.53561i) q^{58} +(11.0583 - 3.59304i) q^{59} +(-0.175311 - 1.29276i) q^{60} +(2.31813 + 3.19063i) q^{61} +(-1.13156 - 3.48257i) q^{62} +(0.371925 + 1.34608i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} +(-4.75174 - 3.22815i) q^{66} -6.70705 q^{67} +(-2.99344 - 2.17486i) q^{68} +(7.47214 + 7.81292i) q^{69} +(-0.108348 - 0.333461i) q^{70} +(-0.527864 - 0.726543i) q^{71} +(-2.80902 - 1.05329i) q^{72} +(7.32781 - 2.38095i) q^{73} +(-2.16527 + 6.66401i) q^{74} +(-3.33222 - 6.91681i) q^{75} +2.13325i q^{76} +(-1.41138 - 0.625834i) q^{77} +(4.35758 - 8.10062i) q^{78} +(-2.34058 + 3.22153i) q^{79} +(0.716341 + 0.232753i) q^{80} +(-8.96425 - 0.801439i) q^{81} +(0.0353991 - 0.0257190i) q^{82} +(8.76491 - 6.36808i) q^{83} +(-0.793345 - 0.143849i) q^{84} +(2.65053 + 0.861209i) q^{85} +(-3.23201 + 4.44848i) q^{86} +(-15.2937 - 8.22699i) q^{87} +(2.86977 - 1.66265i) q^{88} +6.48945i q^{89} +(2.25737 + 0.100708i) q^{90} +(0.763932 - 2.35114i) q^{91} +(-5.93616 + 1.92878i) q^{92} +(6.28488 - 0.852293i) q^{93} +(1.87849 + 2.58551i) q^{94} +(-0.496520 - 1.52813i) q^{95} +(1.25174 - 1.19714i) q^{96} +(2.13991 + 1.55474i) q^{97} +6.78330 q^{98} +(6.96999 - 7.10066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} - 3 q^{12} - 21 q^{15} - 2 q^{16} + 10 q^{17} + 2 q^{18} - 15 q^{19} - 12 q^{21} + 6 q^{22} + 2 q^{24} - 6 q^{25} + 10 q^{26} + 20 q^{27} + 5 q^{28} - 23 q^{29} + 9 q^{30} + 13 q^{31} + 8 q^{32} + 20 q^{33} + 10 q^{34} + 13 q^{35} + 7 q^{36} + 6 q^{37} - 10 q^{38} - 8 q^{39} + 5 q^{40} - 2 q^{41} + 13 q^{42} - 9 q^{44} - 8 q^{45} - 10 q^{46} - 10 q^{47} + 2 q^{48} - 18 q^{49} - q^{50} + 15 q^{51} - 10 q^{52} - 15 q^{53} - 15 q^{54} - 14 q^{55} + 15 q^{57} - 23 q^{58} + 25 q^{59} + 4 q^{60} - 10 q^{61} - 2 q^{62} - 6 q^{63} - 2 q^{64} + 32 q^{65} - 30 q^{66} - 2 q^{67} + 10 q^{68} + 24 q^{69} - 17 q^{70} - 40 q^{71} - 18 q^{72} + 5 q^{73} + 6 q^{74} + q^{75} + 12 q^{77} - 8 q^{78} + 10 q^{79} - 5 q^{80} - 26 q^{81} + 3 q^{82} + 21 q^{83} + 8 q^{84} + 30 q^{85} - 25 q^{86} - 42 q^{87} + 6 q^{88} + 2 q^{90} + 24 q^{91} - 10 q^{92} + 27 q^{93} + 40 q^{94} - 20 q^{95} + 2 q^{96} + 9 q^{97} + 22 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9 + q^11 - 3 * q^12 - 21 * q^15 - 2 * q^16 + 10 * q^17 + 2 * q^18 - 15 * q^19 - 12 * q^21 + 6 * q^22 + 2 * q^24 - 6 * q^25 + 10 * q^26 + 20 * q^27 + 5 * q^28 - 23 * q^29 + 9 * q^30 + 13 * q^31 + 8 * q^32 + 20 * q^33 + 10 * q^34 + 13 * q^35 + 7 * q^36 + 6 * q^37 - 10 * q^38 - 8 * q^39 + 5 * q^40 - 2 * q^41 + 13 * q^42 - 9 * q^44 - 8 * q^45 - 10 * q^46 - 10 * q^47 + 2 * q^48 - 18 * q^49 - q^50 + 15 * q^51 - 10 * q^52 - 15 * q^53 - 15 * q^54 - 14 * q^55 + 15 * q^57 - 23 * q^58 + 25 * q^59 + 4 * q^60 - 10 * q^61 - 2 * q^62 - 6 * q^63 - 2 * q^64 + 32 * q^65 - 30 * q^66 - 2 * q^67 + 10 * q^68 + 24 * q^69 - 17 * q^70 - 40 * q^71 - 18 * q^72 + 5 * q^73 + 6 * q^74 + q^75 + 12 * q^77 - 8 * q^78 + 10 * q^79 - 5 * q^80 - 26 * q^81 + 3 * q^82 + 21 * q^83 + 8 * q^84 + 30 * q^85 - 25 * q^86 - 42 * q^87 + 6 * q^88 + 2 * q^90 + 24 * q^91 - 10 * q^92 + 27 * q^93 + 40 * q^94 - 20 * q^95 + 2 * q^96 + 9 * q^97 + 22 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	1.25174	−	1.19714i	0.722692	−	0.691170i
$3$	1.25174	−	1.19714i	0.722692	−	0.691170i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.442723	−	0.609356i	−0.197992	−	0.272512i	0.698464	−	0.715645i	$-0.253867\pi$
$5$	−0.442723	−	0.609356i	−0.197992	−	0.272512i	−0.896456	+	0.443133i	$0.853867\pi$
$6$	−1.71634	+	0.232753i	−0.700693	+	0.0950211i
$7$	−0.442723	+	0.143849i	−0.167334	+	0.0543700i	−0.391486	−	0.920184i	$-0.628039\pi$
$7$	−0.442723	+	0.143849i	−0.167334	+	0.0543700i	0.224152	+	0.974554i	$0.428039\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.133706	−	2.99702i	0.0445687	−	0.999006i
$10$			0.753205i			0.238184i
$11$	2.46808	+	2.21553i	0.744154	+	0.668008i
$11$	2.46808	+	2.21553i	0.744154	+	0.668008i
$12$	1.52536	+	0.820539i	0.440333	+	0.236869i
$13$	−3.12151	+	4.29640i	−0.865752	+	1.19161i	0.114415	+	0.993433i	$0.463501\pi$
$13$	−3.12151	+	4.29640i	−0.865752	+	1.19161i	−0.980167	+	0.198173i	$0.936499\pi$
$14$	0.442723	+	0.143849i	0.118323	+	0.0384454i
$15$	−1.28366	−	0.232753i	−0.331439	−	0.0600966i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.99344	+	2.17486i	−0.726016	+	0.527481i	−0.888300	−	0.459263i	$-0.848114\pi$
$17$	−2.99344	+	2.17486i	−0.726016	+	0.527481i	0.162285	+	0.986744i	$0.448114\pi$
$18$	−1.86977	+	2.34605i	−0.440710	+	0.552969i
$19$	2.02884	+	0.659209i	0.465447	+	0.151233i	0.532346	−	0.846527i	$-0.321310\pi$
$19$	2.02884	+	0.659209i	0.465447	+	0.151233i	−0.0668988	+	0.997760i	$0.521310\pi$
$20$	0.442723	−	0.609356i	0.0989959	−	0.136256i
$21$	−0.381966	+	0.710064i	−0.0833518	+	0.154949i
$22$	−0.694463	−	3.24310i	−0.148060	−	0.691432i
$23$			6.24165i			1.30147i	0.759303	+	0.650737i	$0.225540\pi$
$23$			6.24165i			1.30147i	−0.759303	+	0.650737i	$0.774460\pi$
$24$	−0.751740	−	1.56041i	−0.153448	−	0.318518i
$25$	1.36977	−	4.21573i	0.273955	−	0.843146i
$26$	5.05072	−	1.64108i	0.990527	−	0.321842i
$27$	−3.42049	−	3.91155i	−0.658274	−	0.752779i
$28$	−0.273618	−	0.376603i	−0.0517089	−	0.0711712i
$29$	−3.09831	−	9.53561i	−0.575341	−	1.77072i	−0.635015	−	0.772500i	$-0.719006\pi$
$29$	−3.09831	−	9.53561i	−0.575341	−	1.77072i	0.0596736	−	0.998218i	$-0.480994\pi$
$30$	0.901693	+	0.942817i	0.164626	+	0.172134i
$31$	2.96245	+	2.15235i	0.532072	+	0.386573i	0.821132	−	0.570738i	$-0.193343\pi$
$31$	2.96245	+	2.15235i	0.532072	+	0.386573i	−0.289060	+	0.957311i	$0.593343\pi$
$32$	1.00000			0.176777
$33$	5.74170	−	0.181373i	0.999501	−	0.0315729i
$34$	3.70009			0.634561
$35$	0.283659	+	0.206090i	0.0479471	+	0.0348356i
$36$	2.89165	−	0.798968i	0.481942	−	0.133161i
$37$	−2.16527	−	6.66401i	−0.355968	−	1.09556i	−0.955446	−	0.295166i	$-0.904625\pi$
$37$	−2.16527	−	6.66401i	−0.355968	−	1.09556i	0.599478	−	0.800391i	$-0.295375\pi$
$38$	−1.25389	−	1.72583i	−0.203408	−	0.279967i
$39$	1.23607	+	9.11486i	0.197929	+	1.45955i
$40$	−0.716341	+	0.232753i	−0.113263	+	0.0368015i
$41$	−0.0135213	+	0.0416142i	−0.00211167	+	0.00649904i	−0.952107	−	0.305766i	$-0.901088\pi$
$41$	−0.0135213	+	0.0416142i	−0.00211167	+	0.00649904i	0.949995	+	0.312265i	$0.101088\pi$
$42$	0.726382	−	0.349940i	0.112083	−	0.0539969i
$43$		−	5.49863i		−	0.838533i	−0.907863	−	0.419267i	$-0.862287\pi$
$43$		−	5.49863i		−	0.838533i	0.907863	−	0.419267i	$-0.137713\pi$
$44$	−1.34442	+	3.03192i	−0.202678	+	0.457079i
$45$	−1.88545	+	1.24537i	−0.281066	+	0.185649i
$46$	3.66875	−	5.04960i	0.540928	−	0.744523i
$47$	−3.03945	−	0.987579i	−0.443350	−	0.144053i	0.0788307	−	0.996888i	$-0.474881\pi$
$47$	−3.03945	−	0.987579i	−0.443350	−	0.144053i	−0.522181	+	0.852835i	$0.674881\pi$
$48$	−0.309017	+	1.70426i	−0.0446028	+	0.245989i
$49$	−5.48781	+	3.98713i	−0.783973	+	0.569589i
$50$	−3.58611	+	2.60546i	−0.507153	+	0.368468i
$51$	−1.14339	+	6.30593i	−0.160107	+	0.883007i
$52$	−5.05072	−	1.64108i	−0.700408	−	0.227576i
$53$	−3.00621	+	4.13769i	−0.412934	+	0.568355i	−0.963931	−	0.266152i	$-0.914248\pi$
$53$	−3.00621	+	4.13769i	−0.412934	+	0.568355i	0.550997	+	0.834507i	$0.314248\pi$
$54$	0.468081	+	5.17503i	0.0636977	+	0.704232i
$55$	0.257371	−	2.48481i	0.0347039	−	0.335051i
$56$			0.465507i			0.0622059i
$57$	3.32874	−	1.60365i	0.440903	−	0.212408i
$58$	−3.09831	+	9.53561i	−0.406828	+	1.25209i
$59$	11.0583	−	3.59304i	1.43966	−	0.467774i	0.517870	−	0.855459i	$-0.326725\pi$
$59$	11.0583	−	3.59304i	1.43966	−	0.467774i	0.921792	+	0.387685i	$0.126725\pi$
$60$	−0.175311	−	1.29276i	−0.0226326	−	0.166894i
$61$	2.31813	+	3.19063i	0.296806	+	0.408518i	0.931210	−	0.364483i	$-0.118754\pi$
$61$	2.31813	+	3.19063i	0.296806	+	0.408518i	−0.634404	+	0.773002i	$0.718754\pi$
$62$	−1.13156	−	3.48257i	−0.143708	−	0.442287i
$63$	0.371925	+	1.34608i	0.0468581	+	0.169590i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.00000			0.496139
$66$	−4.75174	−	3.22815i	−0.584899	−	0.397358i
$67$	−6.70705			−0.819397			−0.409699	−	0.912221i	$-0.634366\pi$
$67$	−6.70705			−0.819397			−0.409699	+	0.912221i	$0.634366\pi$
$68$	−2.99344	−	2.17486i	−0.363008	−	0.263741i
$69$	7.47214	+	7.81292i	0.899539	+	0.940565i
$70$	−0.108348	−	0.333461i	−0.0129501	−	0.0398563i
$71$	−0.527864	−	0.726543i	−0.0626459	−	0.0862247i	0.776544	−	0.630062i	$-0.216971\pi$
$71$	−0.527864	−	0.726543i	−0.0626459	−	0.0862247i	−0.839190	+	0.543838i	$0.816971\pi$
$72$	−2.80902	−	1.05329i	−0.331046	−	0.124132i
$73$	7.32781	−	2.38095i	0.857656	−	0.278669i	0.153007	−	0.988225i	$-0.451104\pi$
$73$	7.32781	−	2.38095i	0.857656	−	0.278669i	0.704649	+	0.709556i	$0.251104\pi$
$74$	−2.16527	+	6.66401i	−0.251707	+	0.774676i
$75$	−3.33222	−	6.91681i	−0.384772	−	0.798685i
$76$			2.13325i			0.244700i
$77$	−1.41138	−	0.625834i	−0.160842	−	0.0713205i
$78$	4.35758	−	8.10062i	0.493399	−	0.917215i
$79$	−2.34058	+	3.22153i	−0.263336	+	0.362451i	−0.920126	−	0.391623i	$-0.871914\pi$
$79$	−2.34058	+	3.22153i	−0.263336	+	0.362451i	0.656790	+	0.754074i	$0.271914\pi$
$80$	0.716341	+	0.232753i	0.0800893	+	0.0260226i
$81$	−8.96425	−	0.801439i	−0.996027	−	0.0890488i
$82$	0.0353991	−	0.0257190i	0.00390918	−	0.00284019i
$83$	8.76491	−	6.36808i	0.962073	−	0.698987i	0.00844204	−	0.999964i	$-0.497313\pi$
$83$	8.76491	−	6.36808i	0.962073	−	0.698987i	0.953631	+	0.300977i	$0.0973128\pi$
$84$	−0.793345	−	0.143849i	−0.0865610	−	0.0156953i
$85$	2.65053	+	0.861209i	0.287490	+	0.0934112i
$86$	−3.23201	+	4.44848i	−0.348517	+	0.479692i
$87$	−15.2937	−	8.22699i	−1.63966	−	0.882026i
$88$	2.86977	−	1.66265i	0.305919	−	0.177239i
$89$			6.48945i			0.687880i	0.938992	+	0.343940i	$0.111762\pi$
$89$			6.48945i			0.687880i	−0.938992	+	0.343940i	$0.888238\pi$
$90$	2.25737	+	0.100708i	0.237948	+	0.0106156i
$91$	0.763932	−	2.35114i	0.0800818	−	0.246467i
$92$	−5.93616	+	1.92878i	−0.618888	+	0.201089i
$93$	6.28488	−	0.852293i	0.651712	−	0.0883787i
$94$	1.87849	+	2.58551i	0.193751	+	0.266675i
$95$	−0.496520	−	1.52813i	−0.0509419	−	0.156783i
$96$	1.25174	−	1.19714i	0.127755	−	0.122183i
$97$	2.13991	+	1.55474i	0.217275	+	0.157860i	0.691099	−	0.722760i	$-0.257127\pi$
$97$	2.13991	+	1.55474i	0.217275	+	0.157860i	−0.473824	+	0.880620i	$0.657127\pi$
$98$	6.78330			0.685217
$99$	6.96999	−	7.10066i	0.700510	−	0.713643i
$100$	4.43268			0.443268
$101$	−1.36066	−	0.988580i	−0.135391	−	0.0983674i	0.518028	−	0.855363i	$-0.326666\pi$
$101$	−1.36066	−	0.988580i	−0.135391	−	0.0983674i	−0.653419	+	0.756996i	$0.726666\pi$
$102$	4.63156	−	4.42953i	0.458592	−	0.438589i
$103$	4.75389	+	14.6310i	0.468415	+	1.44163i	0.854637	+	0.519227i	$0.173780\pi$
$103$	4.75389	+	14.6310i	0.468415	+	1.44163i	−0.386222	+	0.922406i	$0.626220\pi$
$104$	3.12151	+	4.29640i	0.306090	+	0.421296i
$105$	0.601787	−	0.0816084i	0.0587284	−	0.00796417i
$106$	4.86414	−	1.58046i	0.472447	−	0.153507i
$107$	2.22018	−	6.83300i	0.214633	−	0.660571i	−0.784547	−	0.620069i	$-0.787104\pi$
$107$	2.22018	−	6.83300i	0.214633	−	0.660571i	0.999179	−	0.0405016i	$-0.0128956\pi$
$108$	2.66312	−	4.46182i	0.256259	−	0.429338i
$109$			0.522072i			0.0500054i	0.999687	+	0.0250027i	$0.00795944\pi$
$109$			0.522072i			0.0500054i	−0.999687	+	0.0250027i	$0.992041\pi$
$110$	−1.66875	+	1.85897i	−0.159109	+	0.177246i
$111$	−10.6881	−	5.74948i	−1.01447	−	0.545717i
$112$	0.273618	−	0.376603i	0.0258545	−	0.0355856i
$113$	−13.4302	−	4.36373i	−1.26340	−	0.410505i	−0.400698	−	0.916210i	$-0.631232\pi$
$113$	−13.4302	−	4.36373i	−1.26340	−	0.410505i	−0.862706	+	0.505705i	$0.831232\pi$
$114$	−3.63561	−	0.659209i	−0.340506	−	0.0617406i
$115$	3.80339	−	2.76332i	0.354668	−	0.257681i
$116$	8.11147	−	5.89333i	0.753131	−	0.547182i
$117$	12.4590	+	9.92969i	1.15184	+	0.918000i
$118$	−11.0583	−	3.59304i	−1.01799	−	0.330766i
$119$	1.01241	−	1.39347i	0.0928076	−	0.127739i
$120$	−0.618034	+	1.14891i	−0.0564185	+	0.104880i
$121$	1.18285	+	10.9362i	0.107531	+	0.994202i
$122$		−	3.94383i		−	0.357058i
$123$	0.0328929	+	0.0682770i	0.00296586	+	0.00615633i
$124$	−1.13156	+	3.48257i	−0.101617	+	0.312744i
$125$	−6.75702	+	2.19549i	−0.604366	+	0.196370i
$126$	0.490314	−	1.30762i	0.0436807	−	0.116492i
$127$	−8.15286	−	11.2214i	−0.723449	−	0.995742i	−0.999402	−	0.0345712i	$-0.988993\pi$
$127$	−8.15286	−	11.2214i	−0.723449	−	0.995742i	0.275953	−	0.961171i	$-0.411007\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−6.58263	−	6.88285i	−0.579569	−	0.606001i
$130$	−3.23607	−	2.35114i	−0.283822	−	0.206209i
$131$	1.26045			0.110126			0.0550631	−	0.998483i	$-0.482464\pi$
$131$	1.26045			0.110126			0.0550631	+	0.998483i	$0.482464\pi$
$132$	1.94678	+	5.40463i	0.169445	+	0.470413i
$133$	−0.993040			−0.0861075
$134$	5.42612	+	3.94231i	0.468745	+	0.340563i
$135$	−0.869199	+	3.81603i	−0.0748087	+	0.328432i
$136$	1.14339	+	3.51900i	0.0980450	+	0.301752i
$137$	9.65272	+	13.2858i	0.824688	+	1.13509i	0.988889	+	0.148658i	$0.0474955\pi$
$137$	9.65272	+	13.2858i	0.824688	+	1.13509i	−0.164201	+	0.986427i	$0.552505\pi$
$138$	−1.45276	−	10.7128i	−0.123668	−	0.911934i
$139$	−14.5229	+	4.71876i	−1.23181	+	0.400240i	−0.851370	−	0.524565i	$-0.824228\pi$
$139$	−14.5229	+	4.71876i	−1.23181	+	0.400240i	−0.380442	+	0.924805i	$0.624228\pi$
$140$	−0.108348	+	0.333461i	−0.00915709	+	0.0281826i
$141$	−4.98688	+	2.40246i	−0.419971	+	0.202324i
$142$			0.898056i			0.0753632i
$143$	−17.2229	+	3.68804i	−1.44026	+	0.308409i
$144$	1.65343	+	2.50323i	0.137786	+	0.208602i
$145$	−4.43889	+	6.10960i	−0.368630	+	0.507375i
$146$	−7.32781	−	2.38095i	−0.606454	−	0.197049i
$147$	−2.09616	+	11.5605i	−0.172888	+	0.953496i
$148$	5.66875	−	4.11859i	0.465968	−	0.338546i
$149$	10.0751	−	7.32002i	0.825388	−	0.599679i	−0.0928628	−	0.995679i	$-0.529602\pi$
$149$	10.0751	−	7.32002i	0.825388	−	0.599679i	0.918251	+	0.396000i	$0.129602\pi$
$150$	−1.36977	+	7.55445i	−0.111842	+	0.616818i
$151$	10.0144	+	3.25387i	0.814959	+	0.264796i	0.686697	−	0.726944i	$-0.259060\pi$
$151$	10.0144	+	3.25387i	0.814959	+	0.264796i	0.128262	+	0.991740i	$0.459060\pi$
$152$	1.25389	−	1.72583i	0.101704	−	0.139984i
$153$	6.11786	+	9.26218i	0.494599	+	0.748803i
$154$	0.773973	+	1.33590i	0.0623685	+	0.107650i
$155$		−	2.75808i		−	0.221534i
$156$	−8.28678	+	3.99222i	−0.663474	+	0.319633i
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$	3.78714	−	1.23052i	0.301289	−	0.0978946i
$159$	1.19041	+	8.77816i	0.0944055	+	0.696153i
$160$	−0.442723	−	0.609356i	−0.0350003	−	0.0481738i
$161$	−0.897858	−	2.76332i	−0.0707611	−	0.217780i
$162$	6.78115	+	5.91743i	0.532778	+	0.464917i
$163$	2.75737	+	2.00335i	0.215974	+	0.156914i	0.690512	−	0.723320i	$-0.257385\pi$
$163$	2.75737	+	2.00335i	0.215974	+	0.156914i	−0.474539	+	0.880235i	$0.657385\pi$
$164$	−0.0437557			−0.00341675
$165$	−2.65250	−	3.41844i	−0.206497	−	0.266125i
$166$	−10.8340			−0.840883
$167$	4.43268	+	3.22053i	0.343011	+	0.249212i	0.745931	−	0.666023i	$-0.232005\pi$
$167$	4.43268	+	3.22053i	0.343011	+	0.249212i	−0.402920	+	0.915235i	$0.632005\pi$
$168$	0.557277	+	0.582693i	0.0429949	+	0.0449557i
$169$	−4.69794	−	14.4588i	−0.361380	−	1.11221i
$170$	−1.63812	−	2.25467i	−0.125638	−	0.172926i
$171$	2.24693	−	5.99233i	0.171827	−	0.458245i
$172$	5.22951	−	1.69917i	0.398746	−	0.129560i
$173$	−2.29682	+	7.06890i	−0.174624	+	0.537439i	−0.999616	−	0.0277062i	$-0.991180\pi$
$173$	−2.29682	+	7.06890i	−0.174624	+	0.537439i	0.824992	+	0.565145i	$0.191180\pi$
$174$	7.53719	+	15.6452i	0.571393	+	1.18606i
$175$			2.06344i			0.155982i
$176$	−3.29898	−	0.341701i	−0.248670	−	0.0257567i
$177$	9.54067	−	17.7358i	0.717121	−	1.33311i
$178$	3.81440	−	5.25007i	0.285901	−	0.393510i
$179$	−7.33072	−	2.38189i	−0.547924	−	0.178031i	0.0219566	−	0.999759i	$-0.493010\pi$
$179$	−7.33072	−	2.38189i	−0.547924	−	0.178031i	−0.569880	+	0.821728i	$0.693010\pi$
$180$	−1.76706	−	1.40832i	−0.131709	−	0.104970i
$181$	13.0376	−	9.47237i	0.969077	−	0.704075i	0.0138357	−	0.999904i	$-0.495596\pi$
$181$	13.0376	−	9.47237i	0.969077	−	0.704075i	0.955241	+	0.295829i	$0.0955958\pi$
$182$	−2.00000	+	1.45309i	−0.148250	+	0.107710i
$183$	6.72133	+	1.21871i	0.496855	+	0.0900898i
$184$	5.93616	+	1.92878i	0.437620	+	0.142191i
$185$	−3.10214	+	4.26973i	−0.228074	+	0.313917i
$186$	−5.58554	−	3.00464i	−0.409552	−	0.220311i
$187$	−12.2065	−	1.26432i	−0.892629	−	0.0924565i
$188$		−	3.19587i		−	0.233083i
$189$	2.07700	+	1.23970i	0.151080	+	0.0901748i
$190$	−0.496520	+	1.52813i	−0.0360213	+	0.110862i
$191$	5.54724	−	1.80241i	0.401384	−	0.130418i	−0.101367	−	0.994849i	$-0.532321\pi$
$191$	5.54724	−	1.80241i	0.401384	−	0.130418i	0.502750	+	0.864432i	$0.332321\pi$
$192$	−1.71634	+	0.232753i	−0.123866	+	0.0167975i
$193$	−8.46522	−	11.6514i	−0.609340	−	0.838684i	0.387183	−	0.922003i	$-0.373448\pi$
$193$	−8.46522	−	11.6514i	−0.609340	−	0.838684i	−0.996523	+	0.0833185i	$0.973448\pi$
$194$	−0.817374	−	2.51562i	−0.0586840	−	0.180611i
$195$	5.00696	−	4.78856i	0.358556	−	0.342916i
$196$	−5.48781	−	3.98713i	−0.391986	−	0.284795i
$197$	6.53863			0.465858			0.232929	−	0.972494i	$-0.425169\pi$
$197$	6.53863			0.465858			0.232929	+	0.972494i	$0.425169\pi$
$198$	−9.81250	+	1.64770i	−0.697344	+	0.117097i
$199$	8.53863			0.605288			0.302644	−	0.953104i	$-0.402131\pi$
$199$	8.53863			0.605288			0.302644	+	0.953104i	$0.402131\pi$
$200$	−3.58611	−	2.60546i	−0.253577	−	0.184234i
$201$	−8.39549	+	8.02929i	−0.592172	+	0.566342i
$202$	0.519727	+	1.59956i	0.0365679	+	0.112544i
$203$	2.74338	+	3.77594i	0.192548	+	0.265019i
$204$	−6.35062	+	0.861209i	−0.444632	+	0.0602967i
$205$	0.0313440	−	0.0101843i	0.00218916	−	0.000711302i
$206$	4.75389	−	14.6310i	0.331219	−	1.01939i
$207$	18.7063	+	0.834546i	1.30018	+	0.0580050i
$208$		−	5.31064i		−	0.368226i
$209$	3.54684	+	6.12193i	0.245340	+	0.423463i
$210$	−0.534824	−	0.287699i	−0.0369064	−	0.0198531i
$211$	15.5382	−	21.3865i	1.06969	−	1.47230i	0.199304	−	0.979938i	$-0.436132\pi$
$211$	15.5382	−	21.3865i	1.06969	−	1.47230i	0.870388	−	0.492366i	$-0.163868\pi$
$212$	−4.86414	−	1.58046i	−0.334071	−	0.108546i
$213$	−1.53052	−	0.277515i	−0.104870	−	0.0190150i
$214$	−5.81250	+	4.22303i	−0.397334	+	0.288680i
$215$	−3.35062	+	2.43437i	−0.228511	+	0.166023i
$216$	−4.77710	+	2.04434i	−0.325040	+	0.139100i
$217$	−1.62116	−	0.526746i	−0.110051	−	0.0357579i
$218$	0.306866	−	0.422365i	0.0207836	−	0.0286062i
$219$	6.32218	−	11.7528i	0.427214	−	0.794178i
$220$	2.44272	−	0.523073i	0.164688	−	0.0352656i
$221$		−	19.6499i		−	1.32179i
$222$	5.26741	+	10.9337i	0.353526	+	0.733825i
$223$	0.594827	−	1.83069i	0.0398326	−	0.122592i	−0.929163	−	0.369671i	$-0.879471\pi$
$223$	0.594827	−	1.83069i	0.0398326	−	0.122592i	0.968995	+	0.247079i	$0.0794706\pi$
$224$	−0.442723	+	0.143849i	−0.0295807	+	0.00961134i
$225$	−12.4515	−	4.66891i	−0.830099	−	0.311260i
$226$	8.30030	+	11.4244i	0.552128	+	0.759939i
$227$	5.02500	+	15.4654i	0.333521	+	1.02647i	0.967446	+	0.253078i	$0.0814429\pi$
$227$	5.02500	+	15.4654i	0.333521	+	1.02647i	−0.633925	+	0.773395i	$0.718557\pi$
$228$	2.55380	+	2.67027i	0.169129	+	0.176843i
$229$	1.28678	+	0.934903i	0.0850331	+	0.0617801i	0.629490	−	0.777009i	$-0.283264\pi$
$229$	1.28678	+	0.934903i	0.0850331	+	0.0617801i	−0.544456	+	0.838789i	$0.683264\pi$
$230$	−4.70124			−0.309991
$231$	−2.51589	+	0.906238i	−0.165534	+	0.0596261i
$232$	−10.0263			−0.658261
$233$	12.3616	+	8.98126i	0.809838	+	0.588382i	0.913784	−	0.406201i	$-0.133147\pi$
$233$	12.3616	+	8.98126i	0.809838	+	0.588382i	−0.103946	+	0.994583i	$0.533147\pi$
$234$	−4.24303	−	15.3565i	−0.277375	−	1.00389i
$235$	0.743849	+	2.28933i	0.0485234	+	0.149340i
$236$	6.83437	+	9.40671i	0.444880	+	0.612325i
$237$	0.926831	+	6.83453i	0.0602042	+	0.443950i
$238$	−1.63812	+	0.532256i	−0.106183	+	0.0345011i
$239$	−2.18965	+	6.73906i	−0.141637	+	0.435914i	−0.996563	−	0.0828359i	$-0.973602\pi$
$239$	−2.18965	+	6.73906i	−0.141637	+	0.435914i	0.854926	+	0.518750i	$0.173602\pi$
$240$	1.17531	−	0.566215i	0.0758660	−	0.0365490i
$241$			18.0415i			1.16216i	0.813847	+	0.581079i	$0.197369\pi$
$241$			18.0415i			1.16216i	−0.813847	+	0.581079i	$0.802631\pi$
$242$	5.47121	−	9.54285i	0.351702	−	0.613437i
$243$	−12.1803	+	9.72827i	−0.781369	+	0.624069i
$244$	−2.31813	+	3.19063i	−0.148403	+	0.204259i
$245$	4.85916	+	1.57884i	0.310440	+	0.100868i
$246$	0.0135213	−	0.0745712i	0.000862084	−	0.00475449i
$247$	−9.16527	+	6.65896i	−0.583172	+	0.423699i
$248$	2.96245	−	2.15235i	0.188116	−	0.136674i
$249$	3.34790	−	18.4640i	0.212164	−	1.17011i
$250$	6.75702	+	2.19549i	0.427351	+	0.138855i
$251$	−11.6231	+	15.9978i	−0.733641	+	1.00977i	0.265318	+	0.964161i	$0.414523\pi$
$251$	−11.6231	+	15.9978i	−0.733641	+	1.00977i	−0.998959	+	0.0456096i	$0.985477\pi$
$252$	−1.16527	+	0.769684i	−0.0734051	+	0.0484855i
$253$	−13.8286	+	15.4049i	−0.869395	+	0.968498i
$254$			13.8705i			0.870311i
$255$	4.34876	−	2.09505i	0.272330	−	0.131197i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−8.38236	+	2.72360i	−0.522878	+	0.169893i	−0.558551	−	0.829470i	$-0.688642\pi$
$257$	−8.38236	+	2.72360i	−0.522878	+	0.169893i	0.0356733	+	0.999364i	$0.488642\pi$
$258$	1.27982	+	9.43752i	0.0796783	+	0.587554i
$259$	1.91723	+	2.63884i	0.119131	+	0.163970i
$260$	1.23607	+	3.80423i	0.0766577	+	0.235928i
$261$	−28.9927	+	8.01072i	−1.79460	+	0.495851i
$262$	−1.01973	−	0.740875i	−0.0629990	−	0.0457714i
$263$	−8.61373			−0.531145			−0.265573	−	0.964091i	$-0.585561\pi$
$263$	−8.61373			−0.531145			−0.265573	+	0.964091i	$0.585561\pi$
$264$	1.60179	−	5.51673i	0.0985832	−	0.339531i
$265$	3.85224			0.236641
$266$	0.803386	+	0.583694i	0.0492588	+	0.0357886i
$267$	7.76878	+	8.12310i	0.475442	+	0.497126i
$268$	−2.07259	−	6.37879i	−0.126604	−	0.389646i
$269$	−15.9242	−	21.9178i	−0.970915	−	1.33635i	−0.941583	−	0.336780i	$-0.890662\pi$
$269$	−15.9242	−	21.9178i	−0.970915	−	1.33635i	−0.0293316	−	0.999570i	$-0.509338\pi$
$270$	2.94620	−	2.57633i	0.179300	−	0.156791i
$271$	−13.3557	+	4.33954i	−0.811302	+	0.263608i	−0.685149	−	0.728403i	$-0.740263\pi$
$271$	−13.3557	+	4.33954i	−0.811302	+	0.263608i	−0.126153	+	0.992011i	$0.540263\pi$
$272$	1.14339	−	3.51900i	0.0693283	−	0.213371i
$273$	−1.85840	−	3.85755i	−0.112476	−	0.233470i
$274$		−	16.4222i		−	0.992101i
$275$	12.7208	−	7.36999i	0.767093	−	0.444427i
$276$	−5.12151	+	9.52075i	−0.308279	+	0.573082i
$277$	−7.93186	+	10.9173i	−0.476579	+	0.655955i	−0.977843	−	0.209339i	$-0.932869\pi$
$277$	−7.93186	+	10.9173i	−0.476579	+	0.655955i	0.501264	+	0.865295i	$0.332869\pi$
$278$	14.5229	+	4.71876i	0.871023	+	0.283012i
$279$	6.84672	−	8.59074i	0.409902	−	0.514314i
$280$	0.283659	−	0.206090i	0.0169519	−	0.0123163i
$281$	−5.28969	+	3.84318i	−0.315556	+	0.229265i	−0.734277	−	0.678850i	$-0.762479\pi$
$281$	−5.28969	+	3.84318i	−0.315556	+	0.229265i	0.418721	+	0.908115i	$0.362479\pi$
$282$	5.44660	+	0.987579i	0.324340	+	0.0588094i
$283$	12.4353	+	4.04049i	0.739204	+	0.240182i	0.654329	−	0.756210i	$-0.272951\pi$
$283$	12.4353	+	4.04049i	0.739204	+	0.240182i	0.0848748	+	0.996392i	$0.472951\pi$
$284$	0.527864	−	0.726543i	0.0313230	−	0.0431124i
$285$	−2.45090	−	1.31842i	−0.145179	−	0.0780964i
$286$	16.1014	+	7.13971i	0.952098	+	0.422180i
$287$		−	0.0203686i		−	0.00120232i
$288$	0.133706	−	2.99702i	0.00787870	−	0.176601i
$289$	−1.02263	+	3.14734i	−0.0601548	+	0.185138i
$290$	7.18227	−	2.33366i	0.421757	−	0.137037i
$291$	4.53985	−	0.615650i	0.266131	−	0.0360901i
$292$	4.52884	+	6.23341i	0.265030	+	0.364783i
$293$	−1.85869	−	5.72046i	−0.108586	−	0.334193i	0.881969	−	0.471307i	$-0.156217\pi$
$293$	−1.85869	−	5.72046i	−0.108586	−	0.334193i	−0.990555	+	0.137114i	$0.956217\pi$
$294$	8.49093	−	8.12057i	0.495201	−	0.473601i
$295$	−7.08518	−	5.14769i	−0.412515	−	0.299710i
$296$	−7.00696			−0.407271
$297$	0.224122	−	17.2322i	0.0130049	−	0.999915i
$298$	−12.4536			−0.721415
$299$	−26.8166	−	19.4834i	−1.55084	−	1.12675i
$300$	5.54856	−	5.30655i	0.320347	−	0.306374i
$301$	0.790975	+	2.43437i	0.0455910	+	0.140315i
$302$	−6.18923	−	8.51875i	−0.356150	−	0.490199i
$303$	−2.88667	+	0.391461i	−0.165835	+	0.0224889i
$304$	−2.02884	+	0.659209i	−0.116362	+	0.0378083i
$305$	0.917940	−	2.82513i	0.0525611	−	0.161766i
$306$	0.494725	−	11.0893i	0.0282815	−	0.633930i
$307$			25.3112i			1.44458i	0.691588	+	0.722292i	$0.256911\pi$
$307$			25.3112i			1.44458i	−0.691588	+	0.722292i	$0.743089\pi$
$308$	0.159064	−	1.53569i	0.00906350	−	0.0875043i
$309$	23.4660	+	12.6231i	1.33493	+	0.718103i
$310$	−1.62116	+	2.23133i	−0.0920756	+	0.126731i
$311$	18.0333	+	5.85937i	1.02257	+	0.332254i	0.771850	−	0.635804i	$-0.219331\pi$
$311$	18.0333	+	5.85937i	1.02257	+	0.332254i	0.250724	+	0.968059i	$0.419331\pi$
$312$	9.05072	+	1.64108i	0.512396	+	0.0929077i
$313$	5.98526	−	4.34854i	0.338307	−	0.245794i	−0.405640	−	0.914033i	$-0.632951\pi$
$313$	5.98526	−	4.34854i	0.338307	−	0.245794i	0.743947	+	0.668239i	$0.232951\pi$
$314$	−7.85410	+	5.70634i	−0.443233	+	0.322027i
$315$	0.655584	−	0.822576i	0.0369380	−	0.0463469i
$316$	−3.78714	−	1.23052i	−0.213043	−	0.0692219i
$317$	18.9852	−	26.1309i	1.06632	−	1.46766i	0.192567	−	0.981284i	$-0.438319\pi$
$317$	18.9852	−	26.1309i	1.06632	−	1.46766i	0.873750	−	0.486376i	$-0.161681\pi$
$318$	4.19661	−	7.80139i	0.235334	−	0.437480i
$319$	13.4796	−	30.3990i	0.754711	−	1.70202i
$320$			0.753205i			0.0421055i
$321$	−5.40098	−	11.2110i	−0.301453	−	0.625737i
$322$	−0.897858	+	2.76332i	−0.0500357	+	0.153994i
$323$	−7.50689	+	2.43914i	−0.417695	+	0.135717i
$324$	−2.00789	−	8.77316i	−0.111549	−	0.487398i
$325$	13.8367	+	19.0446i	0.767521	+	1.05640i
$326$	−1.05322	−	3.24148i	−0.0583326	−	0.179529i
$327$	0.624994	+	0.653498i	0.0345622	+	0.0361385i
$328$	0.0353991	+	0.0257190i	0.00195459	+	0.00142009i
$329$	1.48770			0.0820195
$330$	0.136611	+	4.32468i	0.00752018	+	0.238066i
$331$	26.8604			1.47638			0.738189	−	0.674594i	$-0.235681\pi$
$331$	26.8604			1.47638			0.738189	+	0.674594i	$0.235681\pi$
$332$	8.76491	+	6.36808i	0.481037	+	0.349494i
$333$	−20.2617	+	5.59834i	−1.11033	+	0.306787i
$334$	−1.69313	−	5.21093i	−0.0926442	−	0.285129i
$335$	2.96937	+	4.08698i	0.162234	+	0.223296i
$336$	−0.108348	−	0.798968i	−0.00591088	−	0.0435873i
$337$	11.1334	−	3.61747i	0.606476	−	0.197056i	0.0103494	−	0.999946i	$-0.496706\pi$
$337$	11.1334	−	3.61747i	0.606476	−	0.197056i	0.596127	+	0.802890i	$0.296706\pi$
$338$	−4.69794	+	14.4588i	−0.255534	+	0.786454i
$339$	−22.0351	+	10.6156i	−1.19678	+	0.576558i
$340$			2.78693i			0.151143i
$341$	2.54298	+	11.8756i	0.137710	+	0.643098i
$342$	−5.34001	+	3.52718i	−0.288754	+	0.190728i
$343$	3.77136	−	5.19083i	0.203634	−	0.280278i
$344$	−5.22951	−	1.69917i	−0.281956	−	0.0916131i
$345$	1.45276	−	8.01215i	0.0782142	−	0.431360i
$346$	6.01317	−	4.36882i	0.323270	−	0.234869i
$347$	−22.7373	+	16.5196i	−1.22060	+	0.886821i	−0.996150	−	0.0876641i	$-0.972060\pi$
$347$	−22.7373	+	16.5196i	−1.22060	+	0.886821i	−0.224454	+	0.974485i	$0.572060\pi$
$348$	3.09831	−	17.0875i	0.166087	−	0.915986i
$349$	−29.3933	−	9.55047i	−1.57339	−	0.511225i	−0.613045	−	0.790048i	$-0.710056\pi$
$349$	−29.3933	−	9.55047i	−1.57339	−	0.511225i	−0.960343	+	0.278823i	$0.910056\pi$
$350$	1.21286	−	1.66936i	0.0648301	−	0.0892310i
$351$	27.4827	−	2.48581i	1.46692	−	0.132683i
$352$	2.46808	+	2.21553i	0.131549	+	0.118088i
$353$			3.74631i			0.199396i	0.995018	+	0.0996979i	$0.0317876\pi$
$353$			3.74631i			0.199396i	−0.995018	+	0.0996979i	$0.968212\pi$
$354$	−18.1434	+	8.74073i	−0.964313	+	0.464565i
$355$	−0.209025	+	0.643314i	−0.0110939	+	0.0341436i
$356$	−6.17183	+	2.00535i	−0.327106	+	0.106283i
$357$	−0.400898	−	2.95626i	−0.0212178	−	0.156462i
$358$	4.53063	+	6.23588i	0.239451	+	0.329577i
$359$	−4.38391	−	13.4923i	−0.231374	−	0.712096i	−0.997582	−	0.0695032i	$-0.977859\pi$
$359$	−4.38391	−	13.4923i	−0.231374	−	0.712096i	0.766208	−	0.642593i	$-0.222141\pi$
$360$	0.601787	+	2.17801i	0.0317170	+	0.114791i
$361$	−11.6897	−	8.49306i	−0.615247	−	0.447003i
$362$	−16.1154			−0.847004
$363$	14.5728	+	12.2733i	0.764874	+	0.644180i
$364$	2.47214			0.129575
$365$	−4.69504	−	3.41114i	−0.245750	−	0.178547i
$366$	−4.72133	−	4.93666i	−0.246788	−	0.258043i
$367$	7.57740	+	23.3208i	0.395537	+	1.21734i	0.928542	+	0.371226i	$0.121063\pi$
$367$	7.57740	+	23.3208i	0.395537	+	1.21734i	−0.533005	+	0.846112i	$0.678937\pi$
$368$	−3.66875	−	5.04960i	−0.191247	−	0.263229i
$369$	0.122911	+	0.0460876i	0.00639847	+	0.00239922i
$370$	5.01937	−	1.63089i	0.260945	−	0.0847861i
$371$	0.735713	−	2.26429i	0.0381963	−	0.117556i
$372$	2.75271	+	5.71390i	0.142722	+	0.296252i
$373$		−	22.5726i		−	1.16877i	−0.811478	−	0.584383i	$-0.801337\pi$
$373$		−	22.5726i		−	1.16877i	0.811478	−	0.584383i	$-0.198663\pi$
$374$	9.13213	+	8.19767i	0.472211	+	0.423892i
$375$	−5.82972	+	10.8373i	−0.301045	+	0.559635i
$376$	−1.87849	+	2.58551i	−0.0968755	+	0.133338i
$377$	50.6402	+	16.4540i	2.60810	+	0.847423i
$378$	−0.951655	−	2.22377i	−0.0489478	−	0.114378i
$379$	−13.3799	+	9.72104i	−0.687277	+	0.499336i	−0.875764	−	0.482740i	$-0.839642\pi$
$379$	−13.3799	+	9.72104i	−0.687277	+	0.499336i	0.188487	+	0.982076i	$0.439642\pi$
$380$	1.29991	−	0.944437i	0.0666838	−	0.0484486i
$381$	−23.6389	−	4.28621i	−1.21106	−	0.219589i
$382$	−5.54724	−	1.80241i	−0.283821	−	0.0922191i
$383$	10.6764	−	14.6948i	0.545540	−	0.750871i	−0.443859	−	0.896097i	$-0.646391\pi$
$383$	10.6764	−	14.6948i	0.545540	−	0.750871i	0.989399	+	0.145226i	$0.0463909\pi$
$384$	1.52536	+	0.820539i	0.0778406	+	0.0418729i
$385$	0.243494	+	1.13710i	0.0124096	+	0.0579522i
$386$			14.4019i			0.733037i
$387$	−16.4795	−	0.735200i	−0.837700	−	0.0373723i
$388$	−0.817374	+	2.51562i	−0.0414959	+	0.127711i
$389$	21.3383	−	6.93323i	1.08189	−	0.351529i	0.286785	−	0.957995i	$-0.407413\pi$
$389$	21.3383	−	6.93323i	1.08189	−	0.351529i	0.795109	+	0.606466i	$0.207413\pi$
$390$	−6.86536	+	0.931013i	−0.347641	+	0.0471437i
$391$	−13.5747	−	18.6840i	−0.686503	−	0.944890i
$392$	2.09616	+	6.45131i	0.105872	+	0.325840i
$393$	1.57776	−	1.50894i	0.0795874	−	0.0761159i
$394$	−5.28987	−	3.84331i	−0.266500	−	0.193623i
$395$	2.99929			0.150911
$396$	8.90697	+	4.43463i	0.447592	+	0.222848i
$397$	4.87397			0.244617			0.122309	−	0.992492i	$-0.460970\pi$
$397$	4.87397			0.244617			0.122309	+	0.992492i	$0.460970\pi$
$398$	−6.90790	−	5.01888i	−0.346262	−	0.251574i
$399$	−1.24303	+	1.18881i	−0.0622292	+	0.0595149i
$400$	1.36977	+	4.21573i	0.0684887	+	0.210787i
$401$	−3.03039	−	4.17097i	−0.151330	−	0.208288i	0.726621	−	0.687039i	$-0.241090\pi$
$401$	−3.03039	−	4.17097i	−0.151330	−	0.208288i	−0.877951	+	0.478751i	$0.841090\pi$
$402$	11.5116	−	1.56109i	0.574146	−	0.0778600i
$403$	−18.4947	+	6.00928i	−0.921285	+	0.299344i
$404$	0.519727	−	1.59956i	0.0258574	−	0.0795809i
$405$	3.48032	+	5.81723i	0.172938	+	0.289061i
$406$		−	4.66732i		−	0.231635i
$407$	9.42027	−	21.2445i	0.466945	−	1.05305i
$408$	5.64397	+	3.03607i	0.279418	+	0.150308i
$409$	0.622624	−	0.856968i	0.0307868	−	0.0423743i	−0.793346	−	0.608771i	$-0.791663\pi$
$409$	0.622624	−	0.856968i	0.0307868	−	0.0423743i	0.824133	+	0.566396i	$0.191663\pi$
$410$	−0.0313440	−	0.0101843i	−0.00154797	−	0.000502966i
$411$	27.9877	+	5.07474i	1.38053	+	0.250318i
$412$	−12.4458	+	9.04244i	−0.613163	+	0.445489i
$413$	−4.37888	+	3.18145i	−0.215471	+	0.156549i
$414$	−14.6432	−	11.6705i	−0.719675	−	0.573573i
$415$	−7.76085	−	2.52165i	−0.380965	−	0.123783i
$416$	−3.12151	+	4.29640i	−0.153045	+	0.210648i
$417$	−12.5298	+	23.2926i	−0.613588	+	1.14064i
$418$	0.728932	−	7.03753i	0.0356532	−	0.344217i
$419$			12.6535i			0.618162i	0.951036	+	0.309081i	$0.100021\pi$
$419$			12.6535i			0.618162i	−0.951036	+	0.309081i	$0.899979\pi$
$420$	0.263577	+	0.547115i	0.0128612	+	0.0266965i
$421$	3.14089	−	9.66665i	0.153077	−	0.471124i	−0.844884	−	0.534950i	$-0.820330\pi$
$421$	3.14089	−	9.66665i	0.153077	−	0.471124i	0.997961	+	0.0638264i	$0.0203304\pi$
$422$	−25.1413	+	8.16890i	−1.22386	+	0.397656i
$423$	−3.36618	+	8.97726i	−0.163670	+	0.436489i
$424$	3.00621	+	4.13769i	0.145994	+	0.200944i
$425$	5.06829	+	15.5986i	0.245848	+	0.756643i
$426$	1.07510	+	1.12413i	0.0520888	+	0.0544644i
$427$	−1.48526	−	1.07910i	−0.0718767	−	0.0522215i
$428$	7.18464			0.347283
$429$	−17.1435	+	25.2348i	−0.827698	+	1.21835i
$430$	4.14160			0.199726
$431$	0.753821	+	0.547683i	0.0363103	+	0.0263810i	0.605792	−	0.795623i	$-0.292856\pi$
$431$	0.753821	+	0.547683i	0.0363103	+	0.0263810i	−0.569482	+	0.822004i	$0.692856\pi$
$432$	5.06639	+	1.15400i	0.243757	+	0.0555218i
$433$	−8.26684	−	25.4427i	−0.397279	−	1.22270i	−0.927173	−	0.374634i	$-0.877768\pi$
$433$	−8.26684	−	25.4427i	−0.397279	−	1.22270i	0.529894	−	0.848064i	$-0.322232\pi$
$434$	1.00193	+	1.37904i	0.0480942	+	0.0661960i
$435$	1.75773	+	12.9616i	0.0842765	+	0.621462i
$436$	−0.496520	+	0.161329i	−0.0237790	+	0.00772626i
$437$	−4.11455	+	12.6633i	−0.196826	+	0.605768i
$438$	−12.0229	+	5.79210i	−0.574474	+	0.276757i
$439$		−	13.8139i		−	0.659302i	−0.944103	−	0.329651i	$-0.893069\pi$
$439$		−	13.8139i		−	0.659302i	0.944103	−	0.329651i	$-0.106931\pi$
$440$	−2.28366	−	1.01262i	−0.108869	−	0.0482748i
$441$	11.2157	+	16.9802i	0.534083	+	0.808579i
$442$	−11.5499	+	15.8971i	−0.549372	+	0.756146i
$443$	−12.9396	−	4.20434i	−0.614781	−	0.199754i	−0.0149592	−	0.999888i	$-0.504762\pi$
$443$	−12.9396	−	4.20434i	−0.614781	−	0.199754i	−0.599822	+	0.800134i	$0.704762\pi$
$444$	2.16527	−	11.9417i	0.102759	−	0.566728i
$445$	3.95438	−	2.87303i	0.187456	−	0.136195i
$446$	−1.55728	+	1.13143i	−0.0737392	+	0.0535747i
$447$	3.84836	−	21.2241i	0.182021	−	1.00387i
$448$	0.442723	+	0.143849i	0.0209167	+	0.00679625i
$449$	−4.22449	+	5.81452i	−0.199366	+	0.274404i	−0.896981	−	0.442069i	$-0.854245\pi$
$449$	−4.22449	+	5.81452i	−0.199366	+	0.274404i	0.697615	+	0.716473i	$0.254245\pi$
$450$	7.32914	+	11.0960i	0.345499	+	0.523071i
$451$	−0.125569	+	0.0727504i	−0.00591282	+	0.00342568i
$452$		−	14.1213i		−	0.664211i
$453$	16.4308	−	7.91563i	0.771984	−	0.371909i
$454$	5.02500	−	15.4654i	0.235835	−	0.725826i
$455$	−1.77089	+	0.575398i	−0.0830207	+	0.0269751i
$456$	−0.496520	−	3.66138i	−0.0232517	−	0.171460i
$457$	4.83211	+	6.65083i	0.226037	+	0.311113i	0.906939	−	0.421261i	$-0.138412\pi$
$457$	4.83211	+	6.65083i	0.226037	+	0.311113i	−0.680903	+	0.732374i	$0.738412\pi$
$458$	−0.491508	−	1.51270i	−0.0229666	−	0.0706841i
$459$	18.7461	+	4.26991i	0.874993	+	0.199302i
$460$	3.80339	+	2.76332i	0.177334	+	0.128841i
$461$	−19.2609			−0.897069			−0.448535	−	0.893765i	$-0.648054\pi$
$461$	−19.2609			−0.897069			−0.448535	+	0.893765i	$0.648054\pi$
$462$	2.56807	+	0.745642i	0.119478	+	0.0346904i
$463$	−1.41876			−0.0659355			−0.0329677	−	0.999456i	$-0.510496\pi$
$463$	−1.41876			−0.0659355			−0.0329677	+	0.999456i	$0.510496\pi$
$464$	8.11147	+	5.89333i	0.376566	+	0.273591i
$465$	−3.30181	−	3.45240i	−0.153118	−	0.160101i
$466$	−4.72173	−	14.5320i	−0.218730	−	0.673181i
$467$	−16.7534	−	23.0591i	−0.775256	−	1.06705i	−0.995790	−	0.0916690i	$-0.970780\pi$
$467$	−16.7534	−	23.0591i	−0.775256	−	1.06705i	0.220533	−	0.975379i	$-0.429220\pi$
$468$	−5.59365	+	14.9177i	−0.258567	+	0.689569i
$469$	2.96937	−	0.964806i	0.137113	−	0.0445506i
$470$	0.743849	−	2.28933i	0.0343112	−	0.105599i
$471$	−7.29805	−	15.1488i	−0.336276	−	0.698020i
$472$		−	11.6273i		−	0.535191i
$473$	12.1824	−	13.5711i	0.560147	−	0.623998i
$474$	3.26741	−	6.07403i	0.150077	−	0.278989i
$475$	5.55810	−	7.65007i	0.255023	−	0.351009i
$476$	1.63812	+	0.532256i	0.0750829	+	0.0243959i
$477$	11.9988	+	9.56289i	0.549386	+	0.437855i
$478$	5.73259	−	4.16497i	0.262202	−	0.190501i
$479$	−15.2361	+	11.0697i	−0.696154	+	0.505785i	−0.878677	−	0.477416i	$-0.841573\pi$
$479$	−15.2361	+	11.0697i	−0.696154	+	0.505785i	0.182524	+	0.983201i	$0.441573\pi$
$480$	−1.28366	−	0.232753i	−0.0585908	−	0.0106237i
$481$	35.3902	+	11.4990i	1.61365	+	0.524307i
$482$	10.6046	−	14.5959i	0.483024	−	0.664826i
$483$	−4.43197	−	2.38410i	−0.201662	−	0.108480i
$484$	−10.0354	+	4.50443i	−0.456156	+	0.204747i
$485$		−	1.99229i		−	0.0904650i
$486$	15.5722	−	0.710915i	0.706371	−	0.0322478i
$487$	−2.28987	+	7.04748i	−0.103764	+	0.319352i	−0.989438	−	0.144955i	$-0.953696\pi$
$487$	−2.28987	+	7.04748i	−0.103764	+	0.319352i	0.885675	+	0.464306i	$0.153696\pi$
$488$	3.75081	−	1.21871i	0.169791	−	0.0551685i
$489$	5.84980	−	0.793292i	0.264537	−	0.0358739i
$490$	−3.00312	−	4.13345i	−0.135667	−	0.186730i
$491$	7.88699	+	24.2737i	0.355935	+	1.09546i	0.955465	+	0.295103i	$0.0953541\pi$
$491$	7.88699	+	24.2737i	0.355935	+	1.09546i	−0.599530	+	0.800352i	$0.704646\pi$
$492$	−0.0547708	+	0.0523818i	−0.00246926	+	0.00236155i
$493$	30.0132	+	21.8059i	1.35173	+	0.982087i
$494$	11.3289			0.509711
$495$	−7.41260	−	1.10358i	−0.333172	−	0.0496022i
$496$	−3.66179			−0.164419
$497$	0.338210	+	0.245724i	0.0151708	+	0.0110222i
$498$	−13.5614	+	12.9699i	−0.607700	+	0.581193i
$499$	−1.19816	−	3.68757i	−0.0536371	−	0.165078i	0.920650	−	0.390390i	$-0.127660\pi$
$499$	−1.19816	−	3.68757i	−0.0536371	−	0.165078i	−0.974287	+	0.225312i	$0.927660\pi$
$500$	−4.17607	−	5.74786i	−0.186759	−	0.257052i
$501$	9.40400	−	1.27528i	0.420140	−	0.0569752i
$502$	18.8065	−	6.11061i	0.839376	−	0.272730i
$503$	12.9923	−	39.9863i	0.579299	−	1.78290i	−0.0417495	−	0.999128i	$-0.513293\pi$
$503$	12.9923	−	39.9863i	0.579299	−	1.78290i	0.621049	−	0.783772i	$-0.286707\pi$
$504$	1.39513	+	0.0622410i	0.0621441	+	0.00277244i
$505$			1.26680i			0.0563716i
$506$	20.2423	−	4.33459i	0.899881	−	0.192696i
$507$	−23.1898	−	12.4745i	−1.02990	−	0.554014i
$508$	8.15286	−	11.2214i	0.361725	−	0.497871i
$509$	−23.4505	−	7.61952i	−1.03942	−	0.337729i	−0.260915	−	0.965362i	$-0.584024\pi$
$509$	−23.4505	−	7.61952i	−1.03942	−	0.337729i	−0.778510	+	0.627632i	$0.784024\pi$
$510$	−4.74966	−	0.861209i	−0.210318	−	0.0381350i
$511$	−2.90169	+	2.10820i	−0.128363	+	0.0932614i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.36109	−	10.1907i	−0.192547	−	0.449932i
$514$	8.38236	+	2.72360i	0.369730	+	0.120133i
$515$	6.81081	−	9.37428i	0.300120	−	0.413080i
$516$	4.51184	−	8.38738i	0.198623	−	0.369234i
$517$	−5.31361	−	9.17143i	−0.233692	−	0.403359i
$518$		−	3.26179i		−	0.143315i
$519$	5.58744	+	11.5980i	0.245262	+	0.509098i
$520$	1.23607	−	3.80423i	0.0542052	−	0.166826i
$521$	−21.3814	+	6.94724i	−0.936736	+	0.304364i	−0.737315	−	0.675550i	$-0.763906\pi$
$521$	−21.3814	+	6.94724i	−0.936736	+	0.304364i	−0.199422	+	0.979914i	$0.563906\pi$
$522$	28.1641	+	10.5607i	1.23271	+	0.462227i
$523$	−8.36299	−	11.5107i	−0.365688	−	0.503327i	0.586034	−	0.810286i	$-0.300688\pi$
$523$	−8.36299	−	11.5107i	−0.365688	−	0.503327i	−0.951723	+	0.306960i	$0.900688\pi$
$524$	0.389501	+	1.19876i	0.0170154	+	0.0523681i
$525$	2.47023	+	2.58289i	0.107810	+	0.112727i
$526$	6.96866	+	5.06302i	0.303848	+	0.220758i
$527$	−13.5490			−0.590202
$528$	−4.53852	+	3.52162i	−0.197514	+	0.153259i
$529$	−15.9582			−0.693834
$530$	−3.11653	−	2.26429i	−0.135373	−	0.0983545i
$531$	−9.28987	−	33.6222i	−0.403146	−	1.45908i
$532$	−0.306866	−	0.944437i	−0.0133043	−	0.0409465i
$533$	−0.136584	−	0.187992i	−0.00591612	−	0.00814284i
$534$	−1.51044	−	11.1381i	−0.0653631	−	0.481993i
$535$	−5.14665	+	1.67225i	−0.222509	+	0.0722976i
$536$	−2.07259	+	6.37879i	−0.0895224	+	0.275522i
$537$	−12.0276	+	5.79439i	−0.519030	+	0.250046i
$538$			27.0918i			1.16801i
$539$	−22.3780	−	2.31786i	−0.963887	−	0.0998372i
$540$	−3.89786	+	0.352561i	−0.167737	+	0.0151718i
$541$	−15.3344	+	21.1060i	−0.659277	+	0.907418i	−0.999457	−	0.0329429i	$-0.989512\pi$
$541$	−15.3344	+	21.1060i	−0.659277	+	0.907418i	0.340180	+	0.940360i	$0.389512\pi$
$542$	13.3557	+	4.33954i	0.573677	+	0.186399i
$543$	4.97992	−	27.4648i	0.213709	−	1.17863i
$544$	−2.99344	+	2.17486i	−0.128343	+	0.0932464i
$545$	0.318128	−	0.231133i	0.0136271	−	0.00990066i
$546$	−0.763932	+	4.21317i	−0.0326933	+	0.180307i
$547$	−11.2861	−	3.66709i	−0.482560	−	0.156793i	0.0576269	−	0.998338i	$-0.481647\pi$
$547$	−11.2861	−	3.66709i	−0.482560	−	0.156793i	−0.540187	+	0.841545i	$0.681647\pi$
$548$	−9.65272	+	13.2858i	−0.412344	+	0.567543i
$549$	9.87232	−	6.52087i	0.421340	−	0.278304i
$550$	−14.6233	−	1.51465i	−0.623540	−	0.0645849i
$551$		−	21.3886i		−	0.911186i
$552$	9.73955	−	4.69210i	0.414543	−	0.199709i
$553$	0.572813	−	1.76294i	0.0243585	−	0.0749677i
$554$	12.8340	−	4.17003i	0.545265	−	0.177167i
$555$	1.22840	+	9.05830i	0.0521426	+	0.384503i
$556$	−8.97562	−	12.3539i	−0.380651	−	0.523921i
$557$	14.5167	+	44.6777i	0.615091	+	1.89306i	0.400246	+	0.916408i	$0.368925\pi$
$557$	14.5167	+	44.6777i	0.615091	+	1.89306i	0.214845	+	0.976648i	$0.431075\pi$
$558$	−10.5886	+	2.92565i	−0.448252	+	0.123853i
$559$	23.6243	+	17.1640i	0.999201	+	0.725962i
$560$	−0.350622			−0.0148165
$561$	−16.7930	+	13.0303i	−0.708999	+	0.550141i
$562$	6.53841			0.275806
$563$	11.5057	+	8.35936i	0.484906	+	0.352305i	0.803222	−	0.595680i	$-0.203117\pi$
$563$	11.5057	+	8.35936i	0.484906	+	0.352305i	−0.318316	+	0.947985i	$0.603117\pi$
$564$	−3.82591	−	4.00040i	−0.161100	−	0.168447i
$565$	3.28678	+	10.1157i	0.138276	+	0.425570i
$566$	−7.68546	−	10.5781i	−0.323044	−	0.444632i
$567$	4.08396	−	0.934686i	0.171510	−	0.0392531i
$568$	−0.854102	+	0.277515i	−0.0358373	+	0.0116443i
$569$	−10.6399	+	32.7463i	−0.446048	+	1.37280i	0.435282	+	0.900294i	$0.356649\pi$
$569$	−10.6399	+	32.7463i	−0.446048	+	1.37280i	−0.881330	+	0.472501i	$0.843351\pi$
$570$	1.20788	+	2.50723i	0.0505923	+	0.105016i
$571$			22.2374i			0.930605i	0.885152	+	0.465302i	$0.154054\pi$
$571$			22.2374i			0.930605i	−0.885152	+	0.465302i	$0.845946\pi$
$572$	−8.82972	−	15.2403i	−0.369189	−	0.637230i
$573$	4.78596	−	8.89697i	0.199936	−	0.371676i
$574$	−0.0119724	+	0.0164785i	−0.000499716	+	0.000687800i
$575$	26.3131	+	8.54965i	1.09733	+	0.356545i
$576$	−1.86977	+	2.34605i	−0.0779072	+	0.0977520i
$577$	−23.8588	+	17.3345i	−0.993257	+	0.721643i	−0.960632	−	0.277824i	$-0.910387\pi$
$577$	−23.8588	+	17.3345i	−0.993257	+	0.721643i	−0.0326249	+	0.999468i	$0.510387\pi$
$578$	2.67729	−	1.94516i	0.111360	−	0.0809081i
$579$	−24.5446	−	4.45043i	−1.02004	−	0.184954i
$580$	−7.18227	−	2.33366i	−0.298228	−	0.0969000i
$581$	−2.96438	+	4.08012i	−0.122983	+	0.169272i
$582$	−4.03469	−	2.17039i	−0.167243	−	0.0899654i
$583$	−16.5867	+	3.55181i	−0.686952	+	0.147101i
$584$		−	7.70492i		−	0.318832i
$585$	0.534824	−	11.9881i	0.0221123	−	0.495646i
$586$	−1.85869	+	5.72046i	−0.0767818	+	0.236310i
$587$	−30.9775	+	10.0652i	−1.27858	+	0.415436i	−0.868080	−	0.496425i	$-0.834646\pi$
$587$	−30.9775	+	10.0652i	−1.27858	+	0.415436i	−0.410500	+	0.911861i	$0.634646\pi$
$588$	−11.6425	+	1.57884i	−0.480127	+	0.0651101i
$589$	4.59148	+	6.31964i	0.189189	+	0.260396i
$590$	2.70630	+	8.32913i	0.111417	+	0.342905i
$591$	8.18467	−	7.82767i	0.336672	−	0.321987i
$592$	5.66875	+	4.11859i	0.232984	+	0.169273i
$593$	18.3913			0.755241			0.377620	−	0.925961i	$-0.376742\pi$
$593$	18.3913			0.755241			0.377620	+	0.925961i	$0.376742\pi$
$594$	−10.3102	+	13.8094i	−0.423031	+	0.566608i
$595$	−1.29733			−0.0531855
$596$	10.0751	+	7.32002i	0.412694	+	0.299840i
$597$	10.6881	−	10.2219i	0.437437	−	0.418357i
$598$	10.2430	+	31.5248i	0.418869	+	1.28914i
$599$	25.6545	+	35.3104i	1.04821	+	1.44274i	0.890348	+	0.455282i	$0.150461\pi$
$599$	25.6545	+	35.3104i	1.04821	+	1.44274i	0.157866	+	0.987461i	$0.449539\pi$
$600$	−7.60799	+	1.03172i	−0.310595	+	0.0421198i
$601$	18.1367	−	5.89297i	0.739811	−	0.240379i	0.0852199	−	0.996362i	$-0.472841\pi$
$601$	18.1367	−	5.89297i	0.739811	−	0.240379i	0.654591	+	0.755983i	$0.272841\pi$
$602$	0.790975	−	2.43437i	0.0322377	−	0.0992175i
$603$	−0.896773	+	20.1012i	−0.0365194	+	0.818583i
$604$			10.5297i			0.428449i
$605$	6.14038	−	5.56249i	0.249642	−	0.226147i
$606$	2.56546	+	1.38004i	0.104215	+	0.0560603i
$607$	5.38312	−	7.40922i	0.218494	−	0.300731i	−0.685674	−	0.727909i	$-0.740492\pi$
$607$	5.38312	−	7.40922i	0.218494	−	0.300731i	0.904168	+	0.427178i	$0.140492\pi$
$608$	2.02884	+	0.659209i	0.0822802	+	0.0267345i
$609$	7.95434	+	1.44228i	0.322326	+	0.0584442i
$610$	−2.40320	+	1.74603i	−0.0973027	+	0.0706945i
$611$	13.7307	−	9.97596i	0.555486	−	0.403584i
$612$	−6.91834	+	8.68060i	−0.279657	+	0.350892i
$613$	0.951725	+	0.309234i	0.0384398	+	0.0124898i	0.328174	−	0.944617i	$-0.393567\pi$
$613$	0.951725	+	0.309234i	0.0384398	+	0.0124898i	−0.289734	+	0.957107i	$0.593567\pi$
$614$	14.8775	−	20.4772i	0.600408	−	0.826391i
$615$	0.0270425	−	0.0502713i	0.00109046	−	0.00202713i
$616$	−1.03134	+	1.14891i	−0.0415540	+	0.0462908i
$617$		−	13.2827i		−	0.534741i	−0.963594	−	0.267371i	$-0.913845\pi$
$617$		−	13.2827i		−	0.534741i	0.963594	−	0.267371i	$-0.0861548\pi$
$618$	−11.5647	−	24.0053i	−0.465201	−	0.965633i
$619$	−9.43018	+	29.0231i	−0.379031	+	1.16654i	0.561688	+	0.827349i	$0.310152\pi$
$619$	−9.43018	+	29.0231i	−0.379031	+	1.16654i	−0.940719	+	0.339188i	$0.889848\pi$
$620$	2.62309	−	0.852293i	0.105346	−	0.0342289i
$621$	24.4145	−	21.3495i	0.979722	−	0.856726i
$622$	−11.1452	−	15.3400i	−0.446881	−	0.615079i
$623$	−0.933503	−	2.87303i	−0.0374000	−	0.115105i
$624$	−6.35758	−	6.64754i	−0.254507	−	0.266114i
$625$	−13.6013	−	9.88189i	−0.544050	−	0.395276i
$626$	−7.39819			−0.295691
$627$	11.7685	+	3.41701i	0.469990	+	0.136462i
$628$	9.70820			0.387400
$629$	20.9749	+	15.2392i	0.836324	+	0.607625i
$630$	−1.01388	+	0.280136i	−0.0403938	+	0.0111609i
$631$	−1.04258	−	3.20873i	−0.0415044	−	0.127737i	0.928157	−	0.372188i	$-0.121392\pi$
$631$	−1.04258	−	3.20873i	−0.0415044	−	0.127737i	−0.969662	+	0.244451i	$0.921392\pi$
$632$	2.34058	+	3.22153i	0.0931033	+	0.128146i
$633$	−6.15286	−	45.3717i	−0.244554	−	1.80336i
$634$	−30.7188	+	9.98113i	−1.22000	+	0.396401i
$635$	−3.22840	+	9.93598i	−0.128115	+	0.394298i
$636$	−7.98067	+	3.84475i	−0.316454	+	0.152454i
$637$		−	36.0237i		−	1.42731i
$638$	−28.7733	+	16.6703i	−1.13915	+	0.659982i
$639$	−2.24804	+	1.48488i	−0.0889311	+	0.0587408i
$640$	0.442723	−	0.609356i	0.0175002	−	0.0240869i
$641$	−30.6472	−	9.95788i	−1.21049	−	0.393313i	−0.366881	−	0.930268i	$-0.619574\pi$
$641$	−30.6472	−	9.95788i	−1.21049	−	0.393313i	−0.843611	+	0.536955i	$0.819574\pi$
$642$	−2.22018	+	12.2445i	−0.0876234	+	0.483252i
$643$	11.5382	−	8.38297i	0.455021	−	0.330592i	−0.336554	−	0.941664i	$-0.609261\pi$
$643$	11.5382	−	8.38297i	0.455021	−	0.330592i	0.791575	+	0.611072i	$0.209261\pi$
$644$	2.35062	−	1.70783i	0.0926275	−	0.0672978i
$645$	−1.27982	+	7.05837i	−0.0503930	+	0.277923i
$646$	7.50689	+	2.43914i	0.295355	+	0.0959665i
$647$	3.42235	−	4.71046i	0.134547	−	0.185187i	−0.736427	−	0.676516i	$-0.763489\pi$
$647$	3.42235	−	4.71046i	0.134547	−	0.185187i	0.870974	+	0.491329i	$0.163489\pi$
$648$	−3.53232	+	8.27785i	−0.138763	+	0.325184i
$649$	35.2532	+	15.6320i	1.38381	+	0.613609i
$650$		−	23.5404i		−	0.923329i
$651$	−2.65986	+	1.28141i	−0.104248	+	0.0502223i
$652$	−1.05322	+	3.24148i	−0.0412474	+	0.126946i
$653$	−9.88161	+	3.21073i	−0.386697	+	0.125646i	−0.495912	−	0.868373i	$-0.665166\pi$
$653$	−9.88161	+	3.21073i	−0.386697	+	0.125646i	0.109215	+	0.994018i	$0.465166\pi$
$654$	−0.121514	−	0.896054i	−0.00475157	−	0.0350385i
$655$	−0.558031	−	0.768064i	−0.0218041	−	0.0300107i
$656$	−0.0135213	−	0.0416142i	−0.000527917	−	0.00162476i
$657$	−6.15598	−	22.2799i	−0.240168	−	0.869223i
$658$	−1.20357	−	0.874447i	−0.0469202	−	0.0340895i
$659$	7.49200			0.291847			0.145923	−	0.989296i	$-0.453385\pi$
$659$	7.49200			0.291847			0.145923	+	0.989296i	$0.453385\pi$
$660$	2.43146	−	3.57904i	0.0946445	−	0.139314i
$661$	−36.2014			−1.40807			−0.704036	−	0.710164i	$-0.748621\pi$
$661$	−36.2014			−1.40807			−0.704036	+	0.710164i	$0.748621\pi$
$662$	−21.7305	−	15.7881i	−0.844579	−	0.613623i
$663$	−23.5236	−	24.5965i	−0.913583	−	0.955249i
$664$	−3.34790	−	10.3038i	−0.129924	−	0.399864i
$665$	0.439642	+	0.605115i	0.0170486	+	0.0234653i
$666$	19.6827	+	7.38037i	0.762688	+	0.285984i
$667$	59.5179	−	19.3385i	2.30454	−	0.748792i
$668$	−1.69313	+	5.21093i	−0.0655093	+	0.201617i
$669$	−1.44702	−	3.00364i	−0.0559452	−	0.116127i
$670$		−	5.05179i		−	0.195168i
$671$	−1.34761	+	13.0106i	−0.0520239	+	0.502269i
$672$	−0.381966	+	0.710064i	−0.0147347	+	0.0273913i
$673$	−16.8310	+	23.1659i	−0.648787	+	0.892978i	−0.999046	−	0.0436747i	$-0.986093\pi$
$673$	−16.8310	+	23.1659i	−0.648787	+	0.892978i	0.350259	+	0.936653i	$0.386093\pi$
$674$	−11.1334	−	3.61747i	−0.428843	−	0.139340i
$675$	−21.1754	+	9.06192i	−0.815040	+	0.348793i
$676$	12.2994	−	8.93602i	0.473053	−	0.343693i
$677$	22.8611	−	16.6096i	0.878624	−	0.638357i	−0.0542633	−	0.998527i	$-0.517281\pi$
$677$	22.8611	−	16.6096i	0.878624	−	0.638357i	0.932887	+	0.360169i	$0.117281\pi$
$678$	24.0664	+	4.36373i	0.924266	+	0.167588i
$679$	−1.17104	−	0.380493i	−0.0449402	−	0.0146020i
$680$	1.63812	−	2.25467i	0.0628189	−	0.0864628i
$681$	24.8042	+	13.3430i	0.950500	+	0.511304i
$682$	4.92297	−	11.1023i	0.188510	−	0.425127i
$683$		−	2.83054i		−	0.108307i	−0.998533	−	0.0541537i	$-0.982754\pi$
$683$		−	2.83054i		−	0.108307i	0.998533	−	0.0541537i	$-0.0172461\pi$
$684$	6.39338	+	0.285228i	0.244457	+	0.0109060i
$685$	3.82232	−	11.7639i	0.146043	−	0.449475i
$686$	−6.10219	+	1.98272i	−0.232983	+	0.0757006i
$687$	2.72993	−	0.370206i	0.104153	−	0.0141242i
$688$	3.23201	+	4.44848i	0.123219	+	0.169597i
$689$	−8.39323	−	25.8317i	−0.319757	−	0.984109i
$690$	−5.88474	+	5.62805i	−0.224028	+	0.214256i
$691$	−17.1738	−	12.4775i	−0.653321	−	0.474666i	0.211080	−	0.977469i	$-0.432302\pi$
$691$	−17.1738	−	12.4775i	−0.653321	−	0.474666i	−0.864401	+	0.502803i	$0.832302\pi$
$692$	−7.43268			−0.282548
$693$	−2.06435	+	4.14625i	−0.0784181	+	0.157503i
$694$	28.1049			1.06685
$695$	9.30501	+	6.76048i	0.352959	+	0.256440i
$696$	−12.5504	+	12.0029i	−0.475720	+	0.454970i
$697$	−0.0500300	−	0.153976i	−0.00189502	−	0.00583227i
$698$	18.1661	+	25.0034i	0.687596	+	0.946394i
$699$	26.2254	−	3.55643i	0.991935	−	0.134516i
$700$	−1.96245	+	0.637639i	−0.0741736	+	0.0241005i
$701$	15.3112	−	47.1229i	0.578295	−	1.77981i	−0.0463805	−	0.998924i	$-0.514769\pi$
$701$	15.3112	−	47.1229i	0.578295	−	1.77981i	0.624675	−	0.780885i	$-0.285231\pi$
$702$	−23.6951	−	14.1429i	−0.894313	−	0.533788i
$703$		−	14.9476i		−	0.563758i
$704$	−0.694463	−	3.24310i	−0.0261736	−	0.122229i
$705$	3.67176	+	1.97516i	0.138287	+	0.0743887i
$706$	2.20202	−	3.03083i	0.0828743	−	0.114067i
$707$	0.744604	+	0.241936i	0.0280037	+	0.00909895i
$708$	19.8160	+	3.59304i	0.744732	+	0.135035i
$709$	39.4440	−	28.6578i	1.48135	−	1.07626i	0.504234	−	0.863567i	$-0.331775\pi$
$709$	39.4440	−	28.6578i	1.48135	−	1.07626i	0.977118	−	0.212698i	$-0.0682249\pi$
$710$	0.547236	−	0.397590i	0.0205374	−	0.0149213i
$711$	9.34205	+	7.44550i	0.350354	+	0.279228i
$712$	6.17183	+	2.00535i	0.231299	+	0.0751536i
$713$	−13.4342	+	18.4906i	−0.503114	+	0.692478i
$714$	−1.41331	+	2.62730i	−0.0528918	+	0.0983244i
$715$	9.87232	+	8.86212i	0.369204	+	0.331425i
$716$		−	7.70797i		−	0.288060i
$717$	5.32673	+	11.0569i	0.198930	+	0.412927i
$718$	−4.38391	+	13.4923i	−0.163606	+	0.503528i
$719$	−10.7662	+	3.49816i	−0.401513	+	0.130459i	−0.502810	−	0.864397i	$-0.667701\pi$
$719$	−10.7662	+	3.49816i	−0.401513	+	0.130459i	0.101298	+	0.994856i	$0.467701\pi$
$720$	0.793345	−	2.11577i	0.0295662	−	0.0788500i
$721$	−4.20931	−	5.79362i	−0.156763	−	0.215766i
$722$	4.46507	+	13.7421i	0.166173	+	0.511427i
$723$	21.5983	+	22.5833i	0.803249	+	0.839883i
$724$	13.0376	+	9.47237i	0.484538	+	0.352038i
$725$	−44.4435			−1.65059
$726$	−4.57561	−	18.4950i	−0.169817	−	0.686413i
$727$	−11.9575			−0.443480			−0.221740	−	0.975106i	$-0.571174\pi$
$727$	−11.9575			−0.443480			−0.221740	+	0.975106i	$0.571174\pi$
$728$	−2.00000	−	1.45309i	−0.0741249	−	0.0538549i
$729$	−3.60050	+	26.7589i	−0.133352	+	0.991069i
$730$	1.79334	+	5.51935i	0.0663747	+	0.204280i
$731$	11.9588	+	16.4598i	0.442310	+	0.608788i
$732$	0.917940	+	6.76896i	0.0339280	+	0.250188i
$733$	−11.0725	+	3.59768i	−0.408973	+	0.132883i	−0.506276	−	0.862371i	$-0.668978\pi$
$733$	−11.0725	+	3.59768i	−0.408973	+	0.132883i	0.0973031	+	0.995255i	$0.468978\pi$
$734$	7.57740	−	23.3208i	0.279687	−	0.860788i
$735$	7.97249	−	3.84081i	0.294070	−	0.141670i
$736$			6.24165i			0.230070i
$737$	−16.5536	−	14.8597i	−0.609758	−	0.547364i
$738$	−0.0723472	−	0.109531i	−0.00266314	−	0.00403188i
$739$	−1.50401	+	2.07010i	−0.0553260	+	0.0761497i	−0.835784	−	0.549059i	$-0.814986\pi$
$739$	−1.50401	+	2.07010i	−0.0553260	+	0.0761497i	0.780458	+	0.625209i	$0.214986\pi$
$740$	−5.01937	−	1.63089i	−0.184516	−	0.0599528i
$741$	−3.50082	+	19.3074i	−0.128606	+	0.709275i
$742$	−1.92612	+	1.39941i	−0.0707101	+	0.0513739i
$743$	31.0438	−	22.5547i	1.13889	−	0.827451i	0.151924	−	0.988392i	$-0.451453\pi$
$743$	31.0438	−	22.5547i	1.13889	−	0.827451i	0.986964	+	0.160942i	$0.0514530\pi$
$744$	1.13156	−	6.24065i	0.0414848	−	0.228793i
$745$	−8.92099	−	2.89861i	−0.326840	−	0.106197i
$746$	−13.2679	+	18.2616i	−0.485771	+	0.668606i
$747$	−17.9133	−	27.1200i	−0.655414	−	0.992270i
$748$	−2.56958	−	11.9998i	−0.0939531	−	0.438756i
$749$			3.34450i			0.122205i
$750$	11.0863	−	5.34092i	0.404816	−	0.195023i
$751$	−7.01507	+	21.5902i	−0.255984	+	0.787836i	0.737651	+	0.675182i	$0.235935\pi$
$751$	−7.01507	+	21.5902i	−0.255984	+	0.787836i	−0.993634	+	0.112654i	$0.964065\pi$
$752$	3.03945	−	0.987579i	0.110837	−	0.0360133i
$753$	4.60254	+	33.9395i	0.167726	+	1.23682i
$754$	−31.2973	−	43.0771i	−1.13978	−	1.56877i
$755$	−2.45083	−	7.54289i	−0.0891950	−	0.274514i
$756$	−0.537194	+	2.35844i	−0.0195376	+	0.0857755i
$757$	−20.8185	−	15.1255i	−0.756660	−	0.549745i	0.141224	−	0.989978i	$-0.454896\pi$
$757$	−20.8185	−	15.1255i	−0.756660	−	0.549745i	−0.897884	+	0.440232i	$0.854896\pi$
$758$	16.5384			0.600702
$759$	1.13206	+	35.8377i	0.0410913	+	1.30083i
$760$	−1.60677			−0.0582838
$761$	−29.3704	−	21.3388i	−1.06468	−	0.773532i	−0.0897281	−	0.995966i	$-0.528600\pi$
$761$	−29.3704	−	21.3388i	−1.06468	−	0.773532i	−0.974948	+	0.222434i	$0.928600\pi$
$762$	16.6049	+	17.3622i	0.601532	+	0.628967i
$763$	−0.0750998	−	0.231133i	−0.00271879	−	0.00836759i
$764$	3.42838	+	4.71876i	0.124034	+	0.170719i
$765$	2.93545	−	7.82853i	0.106131	−	0.283041i

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.25174 - 1.19714i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.442723 - 0.609356i) q^{5} +(-1.71634 + 0.232753i) q^{6} +(-0.442723 + 0.143849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.133706 - 2.99702i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.25174 - 1.19714i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.442723 - 0.609356i) q^{5} +(-1.71634 + 0.232753i) q^{6} +(-0.442723 + 0.143849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.133706 - 2.99702i) q^{9} +0.753205i q^{10} +(2.46808 + 2.21553i) q^{11} +(1.52536 + 0.820539i) q^{12} +(-3.12151 + 4.29640i) q^{13} +(0.442723 + 0.143849i) q^{14} +(-1.28366 - 0.232753i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.99344 + 2.17486i) q^{17} +(-1.86977 + 2.34605i) q^{18} +(2.02884 + 0.659209i) q^{19} +(0.442723 - 0.609356i) q^{20} +(-0.381966 + 0.710064i) q^{21} +(-0.694463 - 3.24310i) q^{22} +6.24165i q^{23} +(-0.751740 - 1.56041i) q^{24} +(1.36977 - 4.21573i) q^{25} +(5.05072 - 1.64108i) q^{26} +(-3.42049 - 3.91155i) q^{27} +(-0.273618 - 0.376603i) q^{28} +(-3.09831 - 9.53561i) q^{29} +(0.901693 + 0.942817i) q^{30} +(2.96245 + 2.15235i) q^{31} +1.00000 q^{32} +(5.74170 - 0.181373i) q^{33} +3.70009 q^{34} +(0.283659 + 0.206090i) q^{35} +(2.89165 - 0.798968i) q^{36} +(-2.16527 - 6.66401i) q^{37} +(-1.25389 - 1.72583i) q^{38} +(1.23607 + 9.11486i) q^{39} +(-0.716341 + 0.232753i) q^{40} +(-0.0135213 + 0.0416142i) q^{41} +(0.726382 - 0.349940i) q^{42} -5.49863i q^{43} +(-1.34442 + 3.03192i) q^{44} +(-1.88545 + 1.24537i) q^{45} +(3.66875 - 5.04960i) q^{46} +(-3.03945 - 0.987579i) q^{47} +(-0.309017 + 1.70426i) q^{48} +(-5.48781 + 3.98713i) q^{49} +(-3.58611 + 2.60546i) q^{50} +(-1.14339 + 6.30593i) q^{51} +(-5.05072 - 1.64108i) q^{52} +(-3.00621 + 4.13769i) q^{53} +(0.468081 + 5.17503i) q^{54} +(0.257371 - 2.48481i) q^{55} +0.465507i q^{56} +(3.32874 - 1.60365i) q^{57} +(-3.09831 + 9.53561i) q^{58} +(11.0583 - 3.59304i) q^{59} +(-0.175311 - 1.29276i) q^{60} +(2.31813 + 3.19063i) q^{61} +(-1.13156 - 3.48257i) q^{62} +(0.371925 + 1.34608i) q^{63} +(-0.809017 - 0.587785i) q^{64} +4.00000 q^{65} +(-4.75174 - 3.22815i) q^{66} -6.70705 q^{67} +(-2.99344 - 2.17486i) q^{68} +(7.47214 + 7.81292i) q^{69} +(-0.108348 - 0.333461i) q^{70} +(-0.527864 - 0.726543i) q^{71} +(-2.80902 - 1.05329i) q^{72} +(7.32781 - 2.38095i) q^{73} +(-2.16527 + 6.66401i) q^{74} +(-3.33222 - 6.91681i) q^{75} +2.13325i q^{76} +(-1.41138 - 0.625834i) q^{77} +(4.35758 - 8.10062i) q^{78} +(-2.34058 + 3.22153i) q^{79} +(0.716341 + 0.232753i) q^{80} +(-8.96425 - 0.801439i) q^{81} +(0.0353991 - 0.0257190i) q^{82} +(8.76491 - 6.36808i) q^{83} +(-0.793345 - 0.143849i) q^{84} +(2.65053 + 0.861209i) q^{85} +(-3.23201 + 4.44848i) q^{86} +(-15.2937 - 8.22699i) q^{87} +(2.86977 - 1.66265i) q^{88} +6.48945i q^{89} +(2.25737 + 0.100708i) q^{90} +(0.763932 - 2.35114i) q^{91} +(-5.93616 + 1.92878i) q^{92} +(6.28488 - 0.852293i) q^{93} +(1.87849 + 2.58551i) q^{94} +(-0.496520 - 1.52813i) q^{95} +(1.25174 - 1.19714i) q^{96} +(2.13991 + 1.55474i) q^{97} +6.78330 q^{98} +(6.96999 - 7.10066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 3 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} - 3 q^{12} - 21 q^{15} - 2 q^{16} + 10 q^{17} + 2 q^{18} - 15 q^{19} - 12 q^{21} + 6 q^{22} + 2 q^{24} - 6 q^{25} + 10 q^{26} + 20 q^{27} + 5 q^{28} - 23 q^{29} + 9 q^{30} + 13 q^{31} + 8 q^{32} + 20 q^{33} + 10 q^{34} + 13 q^{35} + 7 q^{36} + 6 q^{37} - 10 q^{38} - 8 q^{39} + 5 q^{40} - 2 q^{41} + 13 q^{42} - 9 q^{44} - 8 q^{45} - 10 q^{46} - 10 q^{47} + 2 q^{48} - 18 q^{49} - q^{50} + 15 q^{51} - 10 q^{52} - 15 q^{53} - 15 q^{54} - 14 q^{55} + 15 q^{57} - 23 q^{58} + 25 q^{59} + 4 q^{60} - 10 q^{61} - 2 q^{62} - 6 q^{63} - 2 q^{64} + 32 q^{65} - 30 q^{66} - 2 q^{67} + 10 q^{68} + 24 q^{69} - 17 q^{70} - 40 q^{71} - 18 q^{72} + 5 q^{73} + 6 q^{74} + q^{75} + 12 q^{77} - 8 q^{78} + 10 q^{79} - 5 q^{80} - 26 q^{81} + 3 q^{82} + 21 q^{83} + 8 q^{84} + 30 q^{85} - 25 q^{86} - 42 q^{87} + 6 q^{88} + 2 q^{90} + 24 q^{91} - 10 q^{92} + 27 q^{93} + 40 q^{94} - 20 q^{95} + 2 q^{96} + 9 q^{97} + 22 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 3 * q^6 - 2 * q^8 + 2 * q^9 + q^11 - 3 * q^12 - 21 * q^15 - 2 * q^16 + 10 * q^17 + 2 * q^18 - 15 * q^19 - 12 * q^21 + 6 * q^22 + 2 * q^24 - 6 * q^25 + 10 * q^26 + 20 * q^27 + 5 * q^28 - 23 * q^29 + 9 * q^30 + 13 * q^31 + 8 * q^32 + 20 * q^33 + 10 * q^34 + 13 * q^35 + 7 * q^36 + 6 * q^37 - 10 * q^38 - 8 * q^39 + 5 * q^40 - 2 * q^41 + 13 * q^42 - 9 * q^44 - 8 * q^45 - 10 * q^46 - 10 * q^47 + 2 * q^48 - 18 * q^49 - q^50 + 15 * q^51 - 10 * q^52 - 15 * q^53 - 15 * q^54 - 14 * q^55 + 15 * q^57 - 23 * q^58 + 25 * q^59 + 4 * q^60 - 10 * q^61 - 2 * q^62 - 6 * q^63 - 2 * q^64 + 32 * q^65 - 30 * q^66 - 2 * q^67 + 10 * q^68 + 24 * q^69 - 17 * q^70 - 40 * q^71 - 18 * q^72 + 5 * q^73 + 6 * q^74 + q^75 + 12 * q^77 - 8 * q^78 + 10 * q^79 - 5 * q^80 - 26 * q^81 + 3 * q^82 + 21 * q^83 + 8 * q^84 + 30 * q^85 - 25 * q^86 - 42 * q^87 + 6 * q^88 + 2 * q^90 + 24 * q^91 - 10 * q^92 + 27 * q^93 + 40 * q^94 - 20 * q^95 + 2 * q^96 + 9 * q^97 + 22 * q^98 + 12 * q^99

Introduction

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